Finite Group Databasebeta

← C61×#34450 #29537883

Subgroups — C61×#34450 #29537883

Order 15616.

2290 conjugacy classes of subgroups.

The subgroup lattice has 1564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#540C211yesmaximal, characteristic
2C61×#2382C211yesmaximal, characteristic, complemented
3C61×#2377C211yesmaximal, characteristic, complemented
4C61×#2377C211yesmaximal, characteristic, complemented
5C61×#2376C211yesmaximal, characteristic, complemented
6C61×#2374C211yesmaximal, characteristic, complemented
7C61×#2371C211yesmaximal, characteristic, complemented
8C61×#2364C211yesmaximal, characteristic, complemented
9C61×#2364C211yesmaximal, characteristic, complemented
10C61×#2363C211yesmaximal, characteristic, complemented
11C61×#2361C211yesmaximal, characteristic, complemented
12C61×#2359C211yesmaximal, characteristic, complemented
13C61×#2359C211yesmaximal, characteristic, complemented
14C61×#2353C211yesmaximal, characteristic, complemented
15C61×#2352C211yesmaximal, characteristic, complemented
16C61×#2346C211yesmaximal, characteristic, complemented
17C61×#2343C211yesmaximal, characteristic, complemented
18C61×#2335C211yesmaximal, characteristic, complemented
19C61×#2335C211yesmaximal, characteristic, complemented
20C61×#2333C211yesmaximal, characteristic, complemented
21C61×#2333C211yesmaximal, characteristic, complemented
22C61×#2328C211yesmaximal, characteristic, complemented
23C61×#2328C211yesmaximal, characteristic, complemented
24C61×#2325C211yesmaximal, characteristic, complemented
25C61×#2325C211yesmaximal, characteristic, complemented
26C61×#2324C211yesmaximal, characteristic, complemented
27C61×#2322C211yesmaximal, characteristic, complemented
28C61×#2318C211yesmaximal, characteristic, complemented
29C4×#123×C61C211yesmaximal, characteristic, complemented
30C4×#121×C61C211yesmaximal, characteristic, complemented
31C61×#2290C211yesmaximal, characteristic, complemented
32C61×#540C4116yescomplemented
33C2×#127×C61C2211yescharacteristic
34C2×#125×C61C2211yescharacteristic
35C2×#123×C61C2211yescharacteristic
36C2×#123×C61C2211yescharacteristic
37C2×#123×C61C2211yescharacteristic
38C2×#123×C61C2211yescharacteristic
39C2×#121×C61C2211yescharacteristic
40C2×#121×C61C2211yescharacteristic
41C2×#121×C61C2211yescharacteristic
42C2×#121×C61C2211yescharacteristic
43C2×#121×C61C2211yescharacteristic
44C2×#121×C61C2211yescharacteristic
45C2×C4×D4×C61C2211yescharacteristic
46C2×C4×D4×C61C2211yescharacteristic
47C2×C4×D4×C61C2211yescharacteristic
48C2×C4×D4×C61C2211yescharacteristic
49C2×C4×D4×C61C2211yescharacteristic
50C2×C4×D4×C61C2211yescharacteristic
51C2×C4×D4×C61C2211yescharacteristic
52C2×C4×D4×C61C2211yescharacteristic
53C2×C4×D4×C61C2211yescharacteristic
54C2×C4×D4×C61C2211yescharacteristic
55C2×#117×C61C2211yescharacteristic
56C2×#117×C61C2211yescharacteristic
57C2×#117×C61C2211yescharacteristic
58C22×C4⋊C4×C61C2211yescharacteristic
59C22×C42×C61C2211yescharacteristic
60C61×#390C2211yescharacteristic
61C61×#390C2211yescharacteristic
62C61×#390C2211yescharacteristic
63C61×#390C2211yescharacteristic
64C61×#390C2211yescharacteristic
65C61×#390C2211yescharacteristic
66C61×#390C2211yescharacteristic
67C61×#390C2211yescharacteristic
68C61×#389C2211yescharacteristic
69C61×#389C2211yescharacteristic
70C61×#389C2211yescharacteristic
71C61×#389C2211yescharacteristic
72C61×#389C2211yescharacteristic
73C61×#389C2211yescharacteristic
74C61×#388C2211yescharacteristic
75C61×#388C2211yescharacteristic
76C61×#388C2211yescharacteristic
77C61×#388C2211yescharacteristic
78C61×#388C2211yescharacteristic
79C61×#388C2211yescharacteristic
80C61×#388C2211yescharacteristic
81C61×#388C2211yescharacteristic
82C61×#388C2211yescharacteristic
83C61×#388C2211yescharacteristic
84C61×#388C2211yescharacteristic
85C61×#388C2211yescharacteristic
86C61×#388C2211yescharacteristic
87C61×#388C2211yescharacteristic
88C61×#388C2211yescharacteristic
89C61×#388C2211yescharacteristic
90C61×#388C2211yescharacteristic
91C61×#388C2211yescharacteristic
92C61×#388C2211yescharacteristic
93C61×#388C2211yescharacteristic
94C61×#387C2211yescharacteristic
95C61×#387C2211yescharacteristic
96C61×#387C2211yescharacteristic
97C61×#387C2211yescharacteristic
98C61×#387C2211yescharacteristic
99C61×#387C2211yescharacteristic
100C61×#387C2211yescharacteristic
101C61×#387C2211yescharacteristic
102C61×#387C2211yescharacteristic
103C61×#387C2211yescharacteristic
104C61×#387C2211yescharacteristic
105C61×#387C2211yescharacteristic
106C61×#387C2211yescharacteristic
107C61×#387C2211yescharacteristic
108C61×#387C2211yescharacteristic
109C61×#387C2211yescharacteristic
110C61×#387C2211yescharacteristic
111C61×#387C2211yescharacteristic
112C61×#387C2211yescharacteristic
113C61×#387C2211yescharacteristic
114C61×#386C2211yescharacteristic
115C61×#386C2211yescharacteristic
116C61×#386C2211yescharacteristic
117C61×#386C2211yescharacteristic
118C61×#386C2211yescharacteristic
119C61×#386C2211yescharacteristic
120C61×#386C2211yescharacteristic
121C61×#386C2211yescharacteristic
122C61×#386C2211yescharacteristic
123C61×#386C2211yescharacteristic
124C61×#386C2211yescharacteristic
125C61×#386C2211yescharacteristic
126C61×#386C2211yescharacteristic
127C61×#386C2211yescharacteristic
128C61×#386C2211yescharacteristic
129C61×#386C2211yescharacteristic
130C61×#386C2211yescharacteristic
131C61×#386C2211yescharacteristic
132C61×#386C2211yescharacteristic
133C61×#386C2211yescharacteristic
134C61×#386C2211yescharacteristic
135C61×#386C2211yescharacteristic
136C61×#386C2211yescharacteristic
137C61×#386C2211yescharacteristic
138C61×#385C2211yescharacteristic
139C61×#385C2211yescharacteristic
140C61×#385C2211yescharacteristic
141C61×#385C2211yescharacteristic
142C61×#385C2211yescharacteristic
143C61×#385C2211yescharacteristic
144C61×#385C2211yescharacteristic
145C61×#385C2211yescharacteristic
146C61×#385C2211yescharacteristic
147C61×#385C2211yescharacteristic
148C61×#383C2211yescharacteristic
149C61×#382C2211yescharacteristic
150C61×#382C2211yescharacteristic
151C61×#382C2211yescharacteristic
152C61×#381C2211yescharacteristic
153C61×#381C2211yescharacteristic
154C61×#381C2211yescharacteristic
155C61×#380C2211yescharacteristic
156C61×#380C2211yescharacteristic
157C61×#380C2211yescharacteristic
158C61×#380C2211yescharacteristic
159C61×#380C2211yescharacteristic
160C4×C4⋊C4×C61C2211yescharacteristic
161C4×C4⋊C4×C61C2211yescharacteristic
162C4×C4⋊C4×C61C2211yescharacteristic
163C4×C4⋊C4×C61C2211yescharacteristic
164C4×C4⋊C4×C61C2211yescharacteristic
165C4×C4⋊C4×C61C2211yescharacteristic
166C4×C4⋊C4×C61C2211yescharacteristic
167C4×C22⋊C4×C61C2211yescharacteristic
168C4×C22⋊C4×C61C2211yescharacteristic
169C4×C22⋊C4×C61C2211yescharacteristic
170C4×C22⋊C4×C61C2211yescharacteristic
171C4×C22⋊C4×C61C2211yescharacteristic
172C4×C22⋊C4×C61C2211yescharacteristic
173C4×C22⋊C4×C61C2211yescharacteristic
174C4×C22⋊C4×C61C2211yescharacteristic
175C4×C22⋊C4×C61C2211yescharacteristic
176C4×C22⋊C4×C61C2211yescharacteristic
177C4×C22⋊C4×C61C2211yescharacteristic
178C4×C22⋊C4×C61C2211yescharacteristic
179C4×C22⋊C4×C61C2211yescharacteristic
180C4×C22⋊C4×C61C2211yescharacteristic
181C4×C22⋊C4×C61C2211yescharacteristic
182C61×#376C2211yescharacteristic
183C61×#376C2211yescharacteristic
184C61×#376C2211yescharacteristic
185C2×#95×C61C2211yescharacteristic
186C2×#95×C61C2211yescharacteristic
187C2×#95×C61C2211yescharacteristic
188C22×D4×C61C2311yescharacteristic
189C22×D4×C61C2311yescharacteristic
190C22×D4×C61C2311yescharacteristic
191C22×D4×C61C2311yescharacteristic
192C22×D4×C61C2311yescharacteristic
193C22×D4×C61C2311yescharacteristic
194C22×D4×C61C2311yescharacteristic
195C22×D4×C61C2311yescharacteristic
196C22×D4×C61C2311yescharacteristic
197C22×D4×C61C2311yescharacteristic
198C23×C4×C61C2311yescharacteristic
199C23×C4×C61C2311yescharacteristic
200C23×C4×C61C2311yescharacteristic
201C23×C4×C61C2311yescharacteristic
202C23×C4×C61C2311yescharacteristic
203C23×C4×C61C2311yescharacteristic
204C23×C4×C61C2311yescharacteristic
205C23×C4×C61C2311yescharacteristic
206C23×C4×C61C2311yescharacteristic
207C23×C4×C61C2311yescharacteristic
208C23×C4×C61C2311yescharacteristic
209C23×C4×C61C2311yescharacteristic
210C23×C4×C61C2311yescharacteristic
211C23×C4×C61C2311yescharacteristic
212C23×C4×C61C2311yescharacteristic
213#127×C61C2×C418yescomplemented
214#125×C61C2×C418yescomplemented
215#123×C61C2×C418yescomplemented
216#123×C61C2×C418yescomplemented
217#123×C61C2×C418yescomplemented
218#123×C61C2×C418yescomplemented
219#121×C61C2×C418yescomplemented
220#121×C61C2×C418yescomplemented
221#121×C61C2×C418yescomplemented
222#121×C61C2×C418yescomplemented
223#121×C61C2×C418yescomplemented
224#121×C61C2×C418yescomplemented
225C4×D4×C61—42no—
226C4×D4×C61—42no—
227C4×D4×C61—42no—
228C4×D4×C61—42no—
229C4×D4×C61—42no—
230C4×D4×C61—42no—
231C4×D4×C61—42no—
232C4×D4×C61—42no—
233C4×D4×C61C2×C418yescomplemented
234C4×D4×C61C2×C418yescomplemented
235#117×C61—42no—
236#117×C61—42no—
237#117×C61C2×C418yescomplemented
238C2×C4⋊C4×C61—42no—
239C2×C4⋊C4×C61C2311yescharacteristic
240C2×C4⋊C4×C61C2311yescharacteristic
241C2×C4⋊C4×C61C2311yescharacteristic
242C2×C4⋊C4×C61C2311yescharacteristic
243C2×C4⋊C4×C61C2311yescharacteristic
244C2×C4⋊C4×C61C2311yescharacteristic
245C2×C4⋊C4×C61C2311yescharacteristic
246C2×C4⋊C4×C61C2311yescharacteristic
247C2×C4⋊C4×C61C2311yescharacteristic
248C2×C4⋊C4×C61C2311yescharacteristic
249C2×C4⋊C4×C61C2311yescharacteristic
250C2×C4⋊C4×C61C2311yescharacteristic
251C2×C4⋊C4×C61C2311yescharacteristic
252C2×C4⋊C4×C61C2311yescharacteristic
253C2×C4⋊C4×C61C2311yescharacteristic
254C2×C4⋊C4×C61C2311yescharacteristic
255C2×C4⋊C4×C61C2311yescharacteristic
256C2×C4⋊C4×C61C2311yescharacteristic
257C2×C4⋊C4×C61C2311yescharacteristic
258C2×C4⋊C4×C61C2311yescharacteristic
259C2×C4⋊C4×C61C2311yescharacteristic
260C2×C4⋊C4×C61C2311yescharacteristic
261C2×C4⋊C4×C61C2311yescharacteristic
262C2×C4⋊C4×C61C2311yescharacteristic
263C2×C4⋊C4×C61C2311yescharacteristic
264C2×C4⋊C4×C61C2311yescharacteristic
265C2×C22⋊C4×C61C2311yescharacteristic
266C2×C22⋊C4×C61C2311yescharacteristic
267C2×C22⋊C4×C61C2311yescharacteristic
268C2×C22⋊C4×C61C2311yescharacteristic
269C2×C22⋊C4×C61C2311yescharacteristic
270C2×C22⋊C4×C61C2311yescharacteristic
271C2×C22⋊C4×C61C2311yescharacteristic
272C2×C22⋊C4×C61C2311yescharacteristic
273C2×C22⋊C4×C61C2311yescharacteristic
274C2×C22⋊C4×C61C2311yescharacteristic
275C2×C22⋊C4×C61C2311yescharacteristic
276C2×C22⋊C4×C61C2311yescharacteristic
277C2×C22⋊C4×C61C2311yescharacteristic
278C2×C22⋊C4×C61C2311yescharacteristic
279C2×C22⋊C4×C61C2311yescharacteristic
280C2×C22⋊C4×C61C2311yescharacteristic
281C2×C22⋊C4×C61C2311yescharacteristic
282C2×C22⋊C4×C61C2311yescharacteristic
283C2×C22⋊C4×C61C2311yescharacteristic
284C2×C22⋊C4×C61C2311yescharacteristic
285C2×C22⋊C4×C61C2311yescharacteristic
286C2×C22⋊C4×C61C2311yescharacteristic
287C2×C22⋊C4×C61C2311yescharacteristic
288C2×C22⋊C4×C61C2311yescharacteristic
289C2×C22⋊C4×C61C2311yescharacteristic
290C2×C22⋊C4×C61C2311yescharacteristic
291C2×C22⋊C4×C61C2311yescharacteristic
292C2×C22⋊C4×C61C2311yescharacteristic
293C2×C22⋊C4×C61C2311yescharacteristic
294C2×C22⋊C4×C61C2311yescharacteristic
295C2×C22⋊C4×C61C2311yescharacteristic
296C2×C22⋊C4×C61C2311yescharacteristic
297C2×C22⋊C4×C61C2311yescharacteristic
298C2×C22⋊C4×C61C2311yescharacteristic
299C2×C22⋊C4×C61C2311yescharacteristic
300C2×C22⋊C4×C61C2311yescharacteristic
301C2×C22⋊C4×C61C2311yescharacteristic
302C2×C22⋊C4×C61C2311yescharacteristic
303C2×C22⋊C4×C61C2311yescharacteristic
304C2×C22⋊C4×C61C2311yescharacteristic
305C2×C42×C61—42no—
306C2×C42×C61C2311yescharacteristic
307C2×C42×C61C2311yescharacteristic
308C2×C42×C61C2311yescharacteristic
309C2×C42×C61C2311yescharacteristic
310C2×C42×C61C2311yescharacteristic
311C2×C42×C61C2311yescharacteristic
312C2×C42×C61C2311yescharacteristic
313C2×C42×C61C2311yescharacteristic
314C2×C42×C61C2311yescharacteristic
315C2×C42×C61C2311yescharacteristic
316C2×C42×C61C2311yescharacteristic
317C2×C42×C61C2311yescharacteristic
318C2×C42×C61C2311yescharacteristic
319C2×C42×C61C2311yescharacteristic
320C2×C42×C61C2311yescharacteristic
321C2×C42×C61C2311yescharacteristic
322C2×C42×C61C2311yescharacteristic
323C2×C42×C61C2311yescharacteristic
324C2×C42×C61C2311yescharacteristic
325C2×C42×C61C2311yescharacteristic
326#95×C61C2311yescharacteristic
327#95×C61C2311yescharacteristic
328#95×C61C2311yescharacteristic
329#95×C61C2311yescharacteristic
330#95×C61C2311yescharacteristic
331#95×C61C2311yescharacteristic
332#95×C61C2311yescharacteristic
333#95×C61C2311yescharacteristic
334#95×C61C2311yescharacteristic
335#95×C61C2311yescharacteristic
336#95×C61C2311yescharacteristic
337#95×C61C2311yescharacteristic
338#95×C61C2311yescharacteristic
339#95×C61C2311yescharacteristic
340#95×C61C2311yescharacteristic
341#95×C61C2311yescharacteristic
342#95×C61C2311yescharacteristic
343#95×C61C2311yescharacteristic
344#95×C61C2311yescharacteristic
345#95×C61C2311yescharacteristic
346#95×C61C2311yescharacteristic
347#95×C61C2311yescharacteristic
348#95×C61C2311yescharacteristic
349#95×C61C2311yescharacteristic
350#95×C61C2311yescharacteristic
351#95×C61C2311yescharacteristic
352#95×C61C2311yescharacteristic
353#95×C61C2311yescharacteristic
354#95×C61C2311yescharacteristic
355#95×C61C2311yescharacteristic
356#95×C61C2311yescharacteristic
357#95×C61C2311yescharacteristic
358#95×C61C2311yescharacteristic
359#95×C61C2311yescharacteristic
360#95×C61C2311yescharacteristic
361#95×C61C2311yescharacteristic
362#95×C61C2311yescharacteristic
363#95×C61C2311yescharacteristic
364#95×C61C2311yescharacteristic
365#95×C61C2311yescharacteristic
366#95×C61C2311yescharacteristic
367#95×C61C2311yescharacteristic
368#95×C61C2311yescharacteristic
369#95×C61C2311yescharacteristic
370C24×C61C2411yescharacteristic
371C24×C61C2411yescharacteristic
372C24×C61C2411yescharacteristic
373C24×C61C2411yescharacteristic
374C24×C61C2411yescharacteristic
375C2×D4×C61—41no—
376C2×D4×C61—41no—
377C2×D4×C61—41no—
378C2×D4×C61—41no—
379C2×D4×C61—41no—
380C2×D4×C61—41no—
381C2×D4×C61—41no—
382C2×D4×C61—41no—
383C2×D4×C61—41no—
384C2×D4×C61—41no—
385C2×D4×C61—41no—
386C2×D4×C61—41no—
387C2×D4×C61—41no—
388C2×D4×C61—41no—
389C2×D4×C61—41no—
390C2×D4×C61—41no—
391C2×D4×C61—41no—
392C2×D4×C61—41no—
393C2×D4×C61—41no—
394C2×D4×C61—41no—
395C2×D4×C61C22×C414yes—
396C2×D4×C61C22×C414yes—
397C2×D4×C61C22×C414yes—
398C2×D4×C61C22×C414yes—
399C2×D4×C61C22×C414yes—
400C2×D4×C61C22×C414yes—
401C2×D4×C61C22×C414yes—
402C2×D4×C61C22×C414yes—
403C2×D4×C61C22×C414yes—
404C2×D4×C61C22×C414yes—
405C22×C4×C61—22no—
406C22×C4×C61—22no—
407C22×C4×C61—22no—
408C22×C4×C61—22no—
409C22×C4×C61—22no—
410C22×C4×C61—41no—
411C22×C4×C61—41no—
412C22×C4×C61—41no—
413C22×C4×C61—41no—
414C22×C4×C61—41no—
415C22×C4×C61—41no—
416C22×C4×C61—41no—
417C22×C4×C61—41no—
418C22×C4×C61—41no—
419C22×C4×C61—41no—
420C22×C4×C61—41no—
421C22×C4×C61—41no—
422C22×C4×C61—41no—
423C22×C4×C61—41no—
424C22×C4×C61—41no—
425C22×C4×C61—41no—
426C22×C4×C61—41no—
427C22×C4×C61—41no—
428C22×C4×C61—41no—
429C22×C4×C61—41no—
430C22×C4×C61—41no—
431C22×C4×C61—41no—
432C22×C4×C61—41no—
433C22×C4×C61—41no—
434C22×C4×C61—41no—
435C22×C4×C61—41no—
436C22×C4×C61—41no—
437C22×C4×C61—41no—
438C22×C4×C61—41no—
439C22×C4×C61—41no—
440C22×C4×C61—41no—
441C22×C4×C61—41no—
442C22×C4×C61—41no—
443C22×C4×C61—41no—
444C22×C4×C61—41no—
445C22×C4×C61C22×C414yes—
446C22×C4×C61C22×C414yes—
447C22×C4×C61C22×C414yes—
448C22×C4×C61C22×C414yes—
449C22×C4×C61C22×C414yes—
450C22×C4×C61C2411yescharacteristic
451C22×C4×C61C2411yescharacteristic
452C22×C4×C61C2411yescharacteristic
453C22×C4×C61C2411yescharacteristic
454C22×C4×C61C2411yescharacteristic
455C22×C4×C61C2411yescharacteristic
456C22×C4×C61C2411yescharacteristic
457C22×C4×C61C2411yescharacteristic
458C22×C4×C61C2411yescharacteristic
459C22×C4×C61C2411yescharacteristic
460C22×C4×C61C2411yescharacteristic
461C22×C4×C61C2411yescharacteristic
462C22×C4×C61C2411yescharacteristic
463C22×C4×C61C2411yescharacteristic
464C22×C4×C61C2411yescharacteristic
465C22×C4×C61C2411yescharacteristic
466C22×C4×C61C2411yescharacteristic
467C22×C4×C61C2411yescharacteristic
468C22×C4×C61C2411yescharacteristic
469C22×C4×C61C2411yescharacteristic
470C22×C4×C61C2411yescharacteristic
471C22×C4×C61C2411yescharacteristic
472C22×C4×C61C2411yescharacteristic
473C22×C4×C61C2411yescharacteristic
474C22×C4×C61C2411yescharacteristic
475C22×C4×C61C2411yescharacteristic
476C4⋊C4×C61—22no—
477C4⋊C4×C61—22no—
478C4⋊C4×C61—22no—
479C4⋊C4×C61—41no—
480C4⋊C4×C61—41no—
481C4⋊C4×C61—41no—
482C4⋊C4×C61—41no—
483C4⋊C4×C61—41no—
484C4⋊C4×C61—41no—
485C4⋊C4×C61—41no—
486C4⋊C4×C61—41no—
487C4⋊C4×C61—41no—
488C4⋊C4×C61—41no—
489C4⋊C4×C61—41no—
490C4⋊C4×C61—41no—
491C4⋊C4×C61—41no—
492C4⋊C4×C61—41no—
493C4⋊C4×C61—41no—
494C4⋊C4×C61C22×C414yes—
495C4⋊C4×C61C22×C414yes—
496C4⋊C4×C61C22×C414yes—
497C4⋊C4×C61C22×C414yes—
498C4⋊C4×C61C22×C414yes—
499C4⋊C4×C61C22×C414yes—
500C4⋊C4×C61C22×C414yes—
501C4⋊C4×C61C22×C414yes—
502C22⋊C4×C61—22no—
503C22⋊C4×C61—22no—
504C22⋊C4×C61—22no—
505C22⋊C4×C61—22no—
506C22⋊C4×C61—22no—
507C22⋊C4×C61—41no—
508C22⋊C4×C61—41no—
509C22⋊C4×C61—41no—
510C22⋊C4×C61—41no—
511C22⋊C4×C61—41no—
512C22⋊C4×C61—41no—
513C22⋊C4×C61—41no—
514C22⋊C4×C61—41no—
515C22⋊C4×C61—41no—
516C22⋊C4×C61—41no—
517C22⋊C4×C61—41no—
518C22⋊C4×C61—41no—
519C22⋊C4×C61—41no—
520C22⋊C4×C61—41no—
521C22⋊C4×C61—41no—
522C22⋊C4×C61—41no—
523C22⋊C4×C61—41no—
524C22⋊C4×C61—41no—
525C22⋊C4×C61—41no—
526C22⋊C4×C61—41no—
527C22⋊C4×C61—41no—
528C22⋊C4×C61—41no—
529C22⋊C4×C61—41no—
530C22⋊C4×C61—41no—
531C22⋊C4×C61—41no—
532C22⋊C4×C61C22×C414yes—
533C22⋊C4×C61C22×C414yes—
534C22⋊C4×C61C22×C414yes—
535C22⋊C4×C61C22×C414yes—
536C22⋊C4×C61C22×C414yes—
537C22⋊C4×C61C22×C414yes—
538C22⋊C4×C61C22×C414yes—
539C22⋊C4×C61C22×C414yes—
540C22⋊C4×C61C22×C414yes—
541C22⋊C4×C61C22×C414yes—
542C42×C61—22no—
543C42×C61—22no—
544C42×C61—22no—
545C42×C61—22no—
546C42×C61—22no—
547C42×C61—41no—
548C42×C61—41no—
549C42×C61—41no—
550C42×C61—41no—
551C42×C61—41no—
552C42×C61—41no—
553C42×C61—41no—
554C42×C61—41no—
555C42×C61—41no—
556C42×C61—41no—
557C42×C61—41no—
558C42×C61—41no—
559C42×C61—41no—
560C42×C61C22×C414yes—
561C42×C61C22×C414yes—
562C23×C61—21no—
563C23×C61—21no—
564C23×C61—21no—
565C23×C61—21no—
566C23×C61—21no—
567C23×C61—21no—
568C23×C61—21no—
569C23×C61—21no—
570C23×C61—21no—
571C23×C61—21no—
572C23×C61—21no—
573C23×C61—21no—
574C23×C61—21no—
575C23×C61—21no—
576C23×C61—21no—
577C23×C61—21no—
578C23×C61—21no—
579C23×C61—21no—
580C23×C61—21no—
581C23×C61—21no—
582C23×C61—21no—
583C23×C61—21no—
584C23×C61—21no—
585C23×C61—21no—
586C23×C61—21no—
587C23×C61—21no—
588C23×C61—21no—
589C23×C61—21no—
590C23×C61—21no—
591C23×C61—21no—
592C23×C61C23×C412yes—
593C23×C61C23×C412yes—
594C23×C61C23×C412yes—
595C23×C61C23×C412yes—
596C23×C61C23×C412yes—
597C23×C61C2511yescharacteristic
598D4×C61—44no—
599D4×C61—44no—
600D4×C61—44no—
601D4×C61—44no—
602D4×C61—44no—
603D4×C61—44no—
604D4×C61—44no—
605D4×C61—44no—
606D4×C61—44no—
607D4×C61—44no—
608C2×C4×C61—21no—
609C2×C4×C61—21no—
610C2×C4×C61—21no—
611C2×C4×C61—21no—
612C2×C4×C61—21no—
613C2×C4×C61—21no—
614C2×C4×C61—21no—
615C2×C4×C61—21no—
616C2×C4×C61—21no—
617C2×C4×C61—21no—
618C2×C4×C61—21no—
619C2×C4×C61—21no—
620C2×C4×C61—21no—
621C2×C4×C61—21no—
622C2×C4×C61—21no—
623C2×C4×C61—21no—
624C2×C4×C61—21no—
625C2×C4×C61—21no—
626C2×C4×C61—21no—
627C2×C4×C61—21no—
628C2×C4×C61—21no—
629C2×C4×C61—21no—
630C2×C4×C61—21no—
631C2×C4×C61—21no—
632C2×C4×C61—21no—
633C2×C4×C61—21no—
634C2×C4×C61—21no—
635C2×C4×C61—21no—
636C2×C4×C61—21no—
637C2×C4×C61—21no—
638C2×C4×C61—21no—
639C2×C4×C61—21no—
640C2×C4×C61—21no—
641C2×C4×C61—21no—
642C2×C4×C61—21no—
643C2×C4×C61—21no—
644C2×C4×C61—21no—
645C2×C4×C61—21no—
646C2×C4×C61—21no—
647C2×C4×C61—21no—
648C2×C4×C61—21no—
649C2×C4×C61—21no—
650C2×C4×C61—21no—
651C2×C4×C61—21no—
652C2×C4×C61—21no—
653C2×C4×C61—21no—
654C2×C4×C61—21no—
655C2×C4×C61—21no—
656C2×C4×C61—21no—
657C2×C4×C61—21no—
658C2×C4×C61—21no—
659C2×C4×C61—21no—
660C2×C4×C61—21no—
661C2×C4×C61—21no—
662C2×C4×C61—21no—
663C2×C4×C61—21no—
664C2×C4×C61—21no—
665C2×C4×C61—21no—
666C2×C4×C61—21no—
667C2×C4×C61—21no—
668C2×C4×C61—21no—
669C2×C4×C61—21no—
670C2×C4×C61—21no—
671C2×C4×C61—21no—
672C2×C4×C61—21no—
673C2×C4×C61—21no—
674C2×C4×C61—44no—
675C2×C4×C61—44no—
676C2×C4×C61—44no—
677C2×C4×C61—44no—
678C2×C4×C61—44no—
679C2×C4×C61—44no—
680C2×C4×C61—44no—
681C2×C4×C61—82no—
682C2×C4×C61—82no—
683C2×C4×C61—82no—
684C2×C4×C61—82no—
685C2×C4×C61—82no—
686C2×C4×C61—82no—
687C2×C4×C61—82no—
688C2×C4×C61—82no—
689C2×C4×C61C23×C412yes—
690C2×C4×C61C23×C412yes—
691C2×C4×C61C23×C412yes—
692C2×C4×C61C23×C412yes—
693C2×C4×C61C23×C412yes—
694C2×C4×C61C23×C412yes—
695C2×C4×C61C23×C412yes—
696C2×C4×C61C23×C412yes—
697C2×C4×C61C23×C412yes—
698C2×C4×C61C23×C412yes—
699C2×C4×C61H(5,𝔽2)12yes—
700C2×C4×C61H(5,𝔽2)12yes—
701#34450C6111yesmaximal, characteristic, direct product factor, Sylow
702C22×C61—22no—
703C22×C61—22no—
704C22×C61—22no—
705C22×C61—22no—
706C22×C61—22no—
707C22×C61—22no—
708C22×C61—22no—
709C22×C61—22no—
710C22×C61—22no—
711C22×C61—22no—
712C22×C61—22no—
713C22×C61—22no—
714C22×C61—22no—
715C22×C61—22no—
716C22×C61—22no—
717C22×C61—41no—
718C22×C61—41no—
719C22×C61—41no—
720C22×C61—41no—
721C22×C61—41no—
722C22×C61—41no—
723C22×C61—41no—
724C22×C61—41no—
725C22×C61—41no—
726C22×C61—41no—
727C22×C61—41no—
728C22×C61—41no—
729C22×C61—41no—
730C22×C61—41no—
731C22×C61—41no—
732C22×C61—41no—
733C22×C61—41no—
734C22×C61—41no—
735C22×C61—41no—
736C22×C61—41no—
737C22×C61C24×C411yescharacteristic
738C22×C61C2×H(5,𝔽2)11yescharacteristic
739C22×C61C2×H(5,𝔽2)11yescharacteristic
740C22×C61#58511yescharacteristic
741C22×C61#58511yescharacteristic
742C22×C61#58511yescharacteristic
743C22×C61#58511yescharacteristic
744C4×C61—22no—
745C4×C61—22no—
746C4×C61—22no—
747C4×C61—22no—
748C4×C61—22no—
749C4×C61—22no—
750C4×C61—22no—
751C4×C61—22no—
752C4×C61—22no—
753C4×C61—22no—
754C4×C61—22no—
755C4×C61—22no—
756C4×C61—41no—
757C4×C61—41no—
758C4×C61—41no—
759C4×C61—41no—
760C4×C61—41no—
761C4×C61—41no—
762C4×C61—41no—
763C4×C61—41no—
764C4×C61—41no—
765C4×C61—41no—
766C4×C61—41no—
767C4×C61—41no—
768C4×C61—41no—
769C4×C61—41no—
770C2×#540C2×C6111yescharacteristic
771#2382C2×C6111yescharacteristic, complemented
772#2377C2×C6111yescharacteristic, complemented
773#2377C2×C6111yescharacteristic, complemented
774#2376C2×C6111yescharacteristic, complemented
775#2374C2×C6111yescharacteristic, complemented
776#2371C2×C6111yescharacteristic, complemented
777#2364C2×C6111yescharacteristic, complemented
778#2364C2×C6111yescharacteristic, complemented
779#2363C2×C6111yescharacteristic, complemented
780#2361C2×C6111yescharacteristic, complemented
781#2359C2×C6111yescharacteristic, complemented
782#2359C2×C6111yescharacteristic, complemented
783#2353C2×C6111yescharacteristic, complemented
784#2352C2×C6111yescharacteristic, complemented
785#2346C2×C6111yescharacteristic, complemented
786#2343C2×C6111yescharacteristic, complemented
787#2335C2×C6111yescharacteristic, complemented
788#2335C2×C6111yescharacteristic, complemented
789#2333C2×C6111yescharacteristic, complemented
790#2333C2×C6111yescharacteristic, complemented
791#2328C2×C6111yescharacteristic, complemented
792#2328C2×C6111yescharacteristic, complemented
793#2325C2×C6111yescharacteristic, complemented
794#2325C2×C6111yescharacteristic, complemented
795#2324C2×C6111yescharacteristic, complemented
796#2322C2×C6111yescharacteristic, complemented
797#2318C2×C6111yescharacteristic, complemented
798C4×#123C2×C6111yescharacteristic, complemented
799C4×#121C2×C6111yescharacteristic, complemented
800#2290C2×C6111yescharacteristic, complemented
801C2×C61—42no—
802C2×C61—42no—
803C2×C61—42no—
804C2×C61—42no—
805C2×C61—42no—
806C2×C61#342811yescharacteristic
807C2×C61C4×H(5,𝔽2)11yescharacteristic
808C2×C61C4×H(5,𝔽2)11yescharacteristic
809C2×C61#353311yescharacteristic
810C2×C61#354211yescharacteristic
811C2×C61#355111yescharacteristic
812C2×C61#356711yescharacteristic
813#540C4×C61116yescomplemented
814C2×#127C22×C6111yescharacteristic
815C2×#125C22×C6111yescharacteristic
816C2×#123C22×C6111yescharacteristic
817C2×#123C22×C6111yescharacteristic
818C2×#123C22×C6111yescharacteristic
819C2×#123C22×C6111yescharacteristic
820C2×#121C22×C6111yescharacteristic
821C2×#121C22×C6111yescharacteristic
822C2×#121C22×C6111yescharacteristic
823C2×#121C22×C6111yescharacteristic
824C2×#121C22×C6111yescharacteristic
825C2×#121C22×C6111yescharacteristic
826C2×C4×D4C22×C6111yescharacteristic
827C2×C4×D4C22×C6111yescharacteristic
828C2×C4×D4C22×C6111yescharacteristic
829C2×C4×D4C22×C6111yescharacteristic
830C2×C4×D4C22×C6111yescharacteristic
831C2×C4×D4C22×C6111yescharacteristic
832C2×C4×D4C22×C6111yescharacteristic
833C2×C4×D4C22×C6111yescharacteristic
834C2×C4×D4C22×C6111yescharacteristic
835C2×C4×D4C22×C6111yescharacteristic
836C2×#117C22×C6111yescharacteristic
837C2×#117C22×C6111yescharacteristic
838C2×#117C22×C6111yescharacteristic
839C22×C4⋊C4C22×C6111yescharacteristic
840C22×C42C22×C6111yescharacteristic
841#390C22×C6111yescharacteristic
842#390C22×C6111yescharacteristic
843#390C22×C6111yescharacteristic
844#390C22×C6111yescharacteristic
845#390C22×C6111yescharacteristic
846#390C22×C6111yescharacteristic
847#390C22×C6111yescharacteristic
848#390C22×C6111yescharacteristic
849#389C22×C6111yescharacteristic
850#389C22×C6111yescharacteristic
851#389C22×C6111yescharacteristic
852#389C22×C6111yescharacteristic
853#389C22×C6111yescharacteristic
854#389C22×C6111yescharacteristic
855#388C22×C6111yescharacteristic
856#388C22×C6111yescharacteristic
857#388C22×C6111yescharacteristic
858#388C22×C6111yescharacteristic
859#388C22×C6111yescharacteristic
860#388C22×C6111yescharacteristic
861#388C22×C6111yescharacteristic
862#388C22×C6111yescharacteristic
863#388C22×C6111yescharacteristic
864#388C22×C6111yescharacteristic
865#388C22×C6111yescharacteristic
866#388C22×C6111yescharacteristic
867#388C22×C6111yescharacteristic
868#388C22×C6111yescharacteristic
869#388C22×C6111yescharacteristic
870#388C22×C6111yescharacteristic
871#388C22×C6111yescharacteristic
872#388C22×C6111yescharacteristic
873#388C22×C6111yescharacteristic
874#388C22×C6111yescharacteristic
875#387C22×C6111yescharacteristic
876#387C22×C6111yescharacteristic
877#387C22×C6111yescharacteristic
878#387C22×C6111yescharacteristic
879#387C22×C6111yescharacteristic
880#387C22×C6111yescharacteristic
881#387C22×C6111yescharacteristic
882#387C22×C6111yescharacteristic
883#387C22×C6111yescharacteristic
884#387C22×C6111yescharacteristic
885#387C22×C6111yescharacteristic
886#387C22×C6111yescharacteristic
887#387C22×C6111yescharacteristic
888#387C22×C6111yescharacteristic
889#387C22×C6111yescharacteristic
890#387C22×C6111yescharacteristic
891#387C22×C6111yescharacteristic
892#387C22×C6111yescharacteristic
893#387C22×C6111yescharacteristic
894#387C22×C6111yescharacteristic
895#386C22×C6111yescharacteristic
896#386C22×C6111yescharacteristic
897#386C22×C6111yescharacteristic
898#386C22×C6111yescharacteristic
899#386C22×C6111yescharacteristic
900#386C22×C6111yescharacteristic
901#386C22×C6111yescharacteristic
902#386C22×C6111yescharacteristic
903#386C22×C6111yescharacteristic
904#386C22×C6111yescharacteristic
905#386C22×C6111yescharacteristic
906#386C22×C6111yescharacteristic
907#386C22×C6111yescharacteristic
908#386C22×C6111yescharacteristic
909#386C22×C6111yescharacteristic
910#386C22×C6111yescharacteristic
911#386C22×C6111yescharacteristic
912#386C22×C6111yescharacteristic
913#386C22×C6111yescharacteristic
914#386C22×C6111yescharacteristic
915#386C22×C6111yescharacteristic
916#386C22×C6111yescharacteristic
917#386C22×C6111yescharacteristic
918#386C22×C6111yescharacteristic
919#385C22×C6111yescharacteristic
920#385C22×C6111yescharacteristic
921#385C22×C6111yescharacteristic
922#385C22×C6111yescharacteristic
923#385C22×C6111yescharacteristic
924#385C22×C6111yescharacteristic
925#385C22×C6111yescharacteristic
926#385C22×C6111yescharacteristic
927#385C22×C6111yescharacteristic
928#385C22×C6111yescharacteristic
929#383C22×C6111yescharacteristic
930#382C22×C6111yescharacteristic
931#382C22×C6111yescharacteristic
932#382C22×C6111yescharacteristic
933#381C22×C6111yescharacteristic
934#381C22×C6111yescharacteristic
935#381C22×C6111yescharacteristic
936#380C22×C6111yescharacteristic
937#380C22×C6111yescharacteristic
938#380C22×C6111yescharacteristic
939#380C22×C6111yescharacteristic
940#380C22×C6111yescharacteristic
941C4×C4⋊C4C22×C6111yescharacteristic
942C4×C4⋊C4C22×C6111yescharacteristic
943C4×C4⋊C4C22×C6111yescharacteristic
944C4×C4⋊C4C22×C6111yescharacteristic
945C4×C4⋊C4C22×C6111yescharacteristic
946C4×C4⋊C4C22×C6111yescharacteristic
947C4×C4⋊C4C22×C6111yescharacteristic
948C4×C22⋊C4C22×C6111yescharacteristic
949C4×C22⋊C4C22×C6111yescharacteristic
950C4×C22⋊C4C22×C6111yescharacteristic
951C4×C22⋊C4C22×C6111yescharacteristic
952C4×C22⋊C4C22×C6111yescharacteristic
953C4×C22⋊C4C22×C6111yescharacteristic
954C4×C22⋊C4C22×C6111yescharacteristic
955C4×C22⋊C4C22×C6111yescharacteristic
956C4×C22⋊C4C22×C6111yescharacteristic
957C4×C22⋊C4C22×C6111yescharacteristic
958C4×C22⋊C4C22×C6111yescharacteristic
959C4×C22⋊C4C22×C6111yescharacteristic
960C4×C22⋊C4C22×C6111yescharacteristic
961C4×C22⋊C4C22×C6111yescharacteristic
962C4×C22⋊C4C22×C6111yescharacteristic
963#376C22×C6111yescharacteristic
964#376C22×C6111yescharacteristic
965#376C22×C6111yescharacteristic
966C2×#95C22×C6111yescharacteristic
967C2×#95C22×C6111yescharacteristic
968C2×#95C22×C6111yescharacteristic
969C61#3445011yescharacteristic, direct product factor, Sylow
970C22×D4C23×C6111yescharacteristic
971C22×D4C23×C6111yescharacteristic
972C22×D4C23×C6111yescharacteristic
973C22×D4C23×C6111yescharacteristic
974C22×D4C23×C6111yescharacteristic
975C22×D4C23×C6111yescharacteristic
976C22×D4C23×C6111yescharacteristic
977C22×D4C23×C6111yescharacteristic
978C22×D4C23×C6111yescharacteristic
979C22×D4C23×C6111yescharacteristic
980C23×C4C23×C6111yescharacteristic
981C23×C4C23×C6111yescharacteristic
982C23×C4C23×C6111yescharacteristic
983C23×C4C23×C6111yescharacteristic
984C23×C4C23×C6111yescharacteristic
985C23×C4C23×C6111yescharacteristic
986C23×C4C23×C6111yescharacteristic
987C23×C4C23×C6111yescharacteristic
988C23×C4C23×C6111yescharacteristic
989C23×C4C23×C6111yescharacteristic
990C23×C4C23×C6111yescharacteristic
991C23×C4C23×C6111yescharacteristic
992C23×C4C23×C6111yescharacteristic
993C23×C4C23×C6111yescharacteristic
994C23×C4C23×C6111yescharacteristic
995#127C2×C4×C6118yescomplemented
996#125C2×C4×C6118yescomplemented
997#123C2×C4×C6118yescomplemented
998#123C2×C4×C6118yescomplemented
999#123C2×C4×C6118yescomplemented
1000#123C2×C4×C6118yescomplemented
1001#121C2×C4×C6118yescomplemented
1002#121C2×C4×C6118yescomplemented
1003#121C2×C4×C6118yescomplemented
1004#121C2×C4×C6118yescomplemented
1005#121C2×C4×C6118yescomplemented
1006#121C2×C4×C6118yescomplemented
1007C4×D4—42no—
1008C4×D4—42no—
1009C4×D4—42no—
1010C4×D4—42no—
1011C4×D4—42no—
1012C4×D4—42no—
1013C4×D4—42no—
1014C4×D4—42no—
1015C4×D4C2×C4×C6118yescomplemented
1016C4×D4C2×C4×C6118yescomplemented
1017#117—42no—
1018#117—42no—
1019#117C2×C4×C6118yescomplemented
1020C2×C4⋊C4—42no—
1021C2×C4⋊C4C23×C6111yescharacteristic
1022C2×C4⋊C4C23×C6111yescharacteristic
1023C2×C4⋊C4C23×C6111yescharacteristic
1024C2×C4⋊C4C23×C6111yescharacteristic
1025C2×C4⋊C4C23×C6111yescharacteristic
1026C2×C4⋊C4C23×C6111yescharacteristic
1027C2×C4⋊C4C23×C6111yescharacteristic
1028C2×C4⋊C4C23×C6111yescharacteristic
1029C2×C4⋊C4C23×C6111yescharacteristic
1030C2×C4⋊C4C23×C6111yescharacteristic
1031C2×C4⋊C4C23×C6111yescharacteristic
1032C2×C4⋊C4C23×C6111yescharacteristic
1033C2×C4⋊C4C23×C6111yescharacteristic
1034C2×C4⋊C4C23×C6111yescharacteristic
1035C2×C4⋊C4C23×C6111yescharacteristic
1036C2×C4⋊C4C23×C6111yescharacteristic
1037C2×C4⋊C4C23×C6111yescharacteristic
1038C2×C4⋊C4C23×C6111yescharacteristic
1039C2×C4⋊C4C23×C6111yescharacteristic
1040C2×C4⋊C4C23×C6111yescharacteristic
1041C2×C4⋊C4C23×C6111yescharacteristic
1042C2×C4⋊C4C23×C6111yescharacteristic
1043C2×C4⋊C4C23×C6111yescharacteristic
1044C2×C4⋊C4C23×C6111yescharacteristic
1045C2×C4⋊C4C23×C6111yescharacteristic
1046C2×C4⋊C4C23×C6111yescharacteristic
1047C2×C22⋊C4C23×C6111yescharacteristic
1048C2×C22⋊C4C23×C6111yescharacteristic
1049C2×C22⋊C4C23×C6111yescharacteristic
1050C2×C22⋊C4C23×C6111yescharacteristic
1051C2×C22⋊C4C23×C6111yescharacteristic
1052C2×C22⋊C4C23×C6111yescharacteristic
1053C2×C22⋊C4C23×C6111yescharacteristic
1054C2×C22⋊C4C23×C6111yescharacteristic
1055C2×C22⋊C4C23×C6111yescharacteristic
1056C2×C22⋊C4C23×C6111yescharacteristic
1057C2×C22⋊C4C23×C6111yescharacteristic
1058C2×C22⋊C4C23×C6111yescharacteristic
1059C2×C22⋊C4C23×C6111yescharacteristic
1060C2×C22⋊C4C23×C6111yescharacteristic
1061C2×C22⋊C4C23×C6111yescharacteristic
1062C2×C22⋊C4C23×C6111yescharacteristic
1063C2×C22⋊C4C23×C6111yescharacteristic
1064C2×C22⋊C4C23×C6111yescharacteristic
1065C2×C22⋊C4C23×C6111yescharacteristic
1066C2×C22⋊C4C23×C6111yescharacteristic
1067C2×C22⋊C4C23×C6111yescharacteristic
1068C2×C22⋊C4C23×C6111yescharacteristic
1069C2×C22⋊C4C23×C6111yescharacteristic
1070C2×C22⋊C4C23×C6111yescharacteristic
1071C2×C22⋊C4C23×C6111yescharacteristic
1072C2×C22⋊C4C23×C6111yescharacteristic
1073C2×C22⋊C4C23×C6111yescharacteristic
1074C2×C22⋊C4C23×C6111yescharacteristic
1075C2×C22⋊C4C23×C6111yescharacteristic
1076C2×C22⋊C4C23×C6111yescharacteristic
1077C2×C22⋊C4C23×C6111yescharacteristic
1078C2×C22⋊C4C23×C6111yescharacteristic
1079C2×C22⋊C4C23×C6111yescharacteristic
1080C2×C22⋊C4C23×C6111yescharacteristic
1081C2×C22⋊C4C23×C6111yescharacteristic
1082C2×C22⋊C4C23×C6111yescharacteristic
1083C2×C22⋊C4C23×C6111yescharacteristic
1084C2×C22⋊C4C23×C6111yescharacteristic
1085C2×C22⋊C4C23×C6111yescharacteristic
1086C2×C22⋊C4C23×C6111yescharacteristic
1087C2×C42—42no—
1088C2×C42C23×C6111yescharacteristic
1089C2×C42C23×C6111yescharacteristic
1090C2×C42C23×C6111yescharacteristic
1091C2×C42C23×C6111yescharacteristic
1092C2×C42C23×C6111yescharacteristic
1093C2×C42C23×C6111yescharacteristic
1094C2×C42C23×C6111yescharacteristic
1095C2×C42C23×C6111yescharacteristic
1096C2×C42C23×C6111yescharacteristic
1097C2×C42C23×C6111yescharacteristic
1098C2×C42C23×C6111yescharacteristic
1099C2×C42C23×C6111yescharacteristic
1100C2×C42C23×C6111yescharacteristic
1101C2×C42C23×C6111yescharacteristic
1102C2×C42C23×C6111yescharacteristic
1103C2×C42C23×C6111yescharacteristic
1104C2×C42C23×C6111yescharacteristic
1105C2×C42C23×C6111yescharacteristic
1106C2×C42C23×C6111yescharacteristic
1107C2×C42C23×C6111yescharacteristic
1108#95C23×C6111yescharacteristic
1109#95C23×C6111yescharacteristic
1110#95C23×C6111yescharacteristic
1111#95C23×C6111yescharacteristic
1112#95C23×C6111yescharacteristic
1113#95C23×C6111yescharacteristic
1114#95C23×C6111yescharacteristic
1115#95C23×C6111yescharacteristic
1116#95C23×C6111yescharacteristic
1117#95C23×C6111yescharacteristic
1118#95C23×C6111yescharacteristic
1119#95C23×C6111yescharacteristic
1120#95C23×C6111yescharacteristic
1121#95C23×C6111yescharacteristic
1122#95C23×C6111yescharacteristic
1123#95C23×C6111yescharacteristic
1124#95C23×C6111yescharacteristic
1125#95C23×C6111yescharacteristic
1126#95C23×C6111yescharacteristic
1127#95C23×C6111yescharacteristic
1128#95C23×C6111yescharacteristic
1129#95C23×C6111yescharacteristic
1130#95C23×C6111yescharacteristic
1131#95C23×C6111yescharacteristic
1132#95C23×C6111yescharacteristic
1133#95C23×C6111yescharacteristic
1134#95C23×C6111yescharacteristic
1135#95C23×C6111yescharacteristic
1136#95C23×C6111yescharacteristic
1137#95C23×C6111yescharacteristic
1138#95C23×C6111yescharacteristic
1139#95C23×C6111yescharacteristic
1140#95C23×C6111yescharacteristic
1141#95C23×C6111yescharacteristic
1142#95C23×C6111yescharacteristic
1143#95C23×C6111yescharacteristic
1144#95C23×C6111yescharacteristic
1145#95C23×C6111yescharacteristic
1146#95C23×C6111yescharacteristic
1147#95C23×C6111yescharacteristic
1148#95C23×C6111yescharacteristic
1149#95C23×C6111yescharacteristic
1150#95C23×C6111yescharacteristic
1151#95C23×C6111yescharacteristic
1152C24C24×C6111yescharacteristic
1153C24C24×C6111yescharacteristic
1154C24C24×C6111yescharacteristic
1155C24C24×C6111yescharacteristic
1156C24C24×C6111yescharacteristic
1157C2×D4—41no—
1158C2×D4—41no—
1159C2×D4—41no—
1160C2×D4—41no—
1161C2×D4—41no—
1162C2×D4—41no—
1163C2×D4—41no—
1164C2×D4—41no—
1165C2×D4—41no—
1166C2×D4—41no—
1167C2×D4—41no—
1168C2×D4—41no—
1169C2×D4—41no—
1170C2×D4—41no—
1171C2×D4—41no—
1172C2×D4—41no—
1173C2×D4—41no—
1174C2×D4—41no—
1175C2×D4—41no—
1176C2×D4—41no—
1177C2×D4C22×C4×C6114yes—
1178C2×D4C22×C4×C6114yes—
1179C2×D4C22×C4×C6114yes—
1180C2×D4C22×C4×C6114yes—
1181C2×D4C22×C4×C6114yes—
1182C2×D4C22×C4×C6114yes—
1183C2×D4C22×C4×C6114yes—
1184C2×D4C22×C4×C6114yes—
1185C2×D4C22×C4×C6114yes—
1186C2×D4C22×C4×C6114yes—
1187C22×C4—22no—
1188C22×C4—22no—
1189C22×C4—22no—
1190C22×C4—22no—
1191C22×C4—22no—
1192C22×C4—41no—
1193C22×C4—41no—
1194C22×C4—41no—
1195C22×C4—41no—
1196C22×C4—41no—
1197C22×C4—41no—
1198C22×C4—41no—
1199C22×C4—41no—
1200C22×C4—41no—
1201C22×C4—41no—
1202C22×C4—41no—
1203C22×C4—41no—
1204C22×C4—41no—
1205C22×C4—41no—
1206C22×C4—41no—
1207C22×C4—41no—
1208C22×C4—41no—
1209C22×C4—41no—
1210C22×C4—41no—
1211C22×C4—41no—
1212C22×C4—41no—
1213C22×C4—41no—
1214C22×C4—41no—
1215C22×C4—41no—
1216C22×C4—41no—
1217C22×C4—41no—
1218C22×C4—41no—
1219C22×C4—41no—
1220C22×C4—41no—
1221C22×C4—41no—
1222C22×C4—41no—
1223C22×C4—41no—
1224C22×C4—41no—
1225C22×C4—41no—
1226C22×C4—41no—
1227C22×C4C22×C4×C6114yes—
1228C22×C4C22×C4×C6114yes—
1229C22×C4C22×C4×C6114yes—
1230C22×C4C22×C4×C6114yes—
1231C22×C4C22×C4×C6114yes—
1232C22×C4C24×C6111yescharacteristic
1233C22×C4C24×C6111yescharacteristic
1234C22×C4C24×C6111yescharacteristic
1235C22×C4C24×C6111yescharacteristic
1236C22×C4C24×C6111yescharacteristic
1237C22×C4C24×C6111yescharacteristic
1238C22×C4C24×C6111yescharacteristic
1239C22×C4C24×C6111yescharacteristic
1240C22×C4C24×C6111yescharacteristic
1241C22×C4C24×C6111yescharacteristic
1242C22×C4C24×C6111yescharacteristic
1243C22×C4C24×C6111yescharacteristic
1244C22×C4C24×C6111yescharacteristic
1245C22×C4C24×C6111yescharacteristic
1246C22×C4C24×C6111yescharacteristic
1247C22×C4C24×C6111yescharacteristic
1248C22×C4C24×C6111yescharacteristic
1249C22×C4C24×C6111yescharacteristic
1250C22×C4C24×C6111yescharacteristic
1251C22×C4C24×C6111yescharacteristic
1252C22×C4C24×C6111yescharacteristic
1253C22×C4C24×C6111yescharacteristic
1254C22×C4C24×C6111yescharacteristic
1255C22×C4C24×C6111yescharacteristic
1256C22×C4C24×C6111yescharacteristic
1257C22×C4C24×C6111yescharacteristic
1258C4⋊C4—22no—
1259C4⋊C4—22no—
1260C4⋊C4—22no—
1261C4⋊C4—41no—
1262C4⋊C4—41no—
1263C4⋊C4—41no—
1264C4⋊C4—41no—
1265C4⋊C4—41no—
1266C4⋊C4—41no—
1267C4⋊C4—41no—
1268C4⋊C4—41no—
1269C4⋊C4—41no—
1270C4⋊C4—41no—
1271C4⋊C4—41no—
1272C4⋊C4—41no—
1273C4⋊C4—41no—
1274C4⋊C4—41no—
1275C4⋊C4—41no—
1276C4⋊C4C22×C4×C6114yes—
1277C4⋊C4C22×C4×C6114yes—
1278C4⋊C4C22×C4×C6114yes—
1279C4⋊C4C22×C4×C6114yes—
1280C4⋊C4C22×C4×C6114yes—
1281C4⋊C4C22×C4×C6114yes—
1282C4⋊C4C22×C4×C6114yes—
1283C4⋊C4C22×C4×C6114yes—
1284C22⋊C4—22no—
1285C22⋊C4—22no—
1286C22⋊C4—22no—
1287C22⋊C4—22no—
1288C22⋊C4—22no—
1289C22⋊C4—41no—
1290C22⋊C4—41no—
1291C22⋊C4—41no—
1292C22⋊C4—41no—
1293C22⋊C4—41no—
1294C22⋊C4—41no—
1295C22⋊C4—41no—
1296C22⋊C4—41no—
1297C22⋊C4—41no—
1298C22⋊C4—41no—
1299C22⋊C4—41no—
1300C22⋊C4—41no—
1301C22⋊C4—41no—
1302C22⋊C4—41no—
1303C22⋊C4—41no—
1304C22⋊C4—41no—
1305C22⋊C4—41no—
1306C22⋊C4—41no—
1307C22⋊C4—41no—
1308C22⋊C4—41no—
1309C22⋊C4—41no—
1310C22⋊C4—41no—
1311C22⋊C4—41no—
1312C22⋊C4—41no—
1313C22⋊C4—41no—
1314C22⋊C4C22×C4×C6114yes—
1315C22⋊C4C22×C4×C6114yes—
1316C22⋊C4C22×C4×C6114yes—
1317C22⋊C4C22×C4×C6114yes—
1318C22⋊C4C22×C4×C6114yes—
1319C22⋊C4C22×C4×C6114yes—
1320C22⋊C4C22×C4×C6114yes—
1321C22⋊C4C22×C4×C6114yes—
1322C22⋊C4C22×C4×C6114yes—
1323C22⋊C4C22×C4×C6114yes—
1324C42—22no—
1325C42—22no—
1326C42—22no—
1327C42—22no—
1328C42—22no—
1329C42—41no—
1330C42—41no—
1331C42—41no—
1332C42—41no—
1333C42—41no—
1334C42—41no—
1335C42—41no—
1336C42—41no—
1337C42—41no—
1338C42—41no—
1339C42—41no—
1340C42—41no—
1341C42—41no—
1342C42C22×C4×C6114yes—
1343C42C22×C4×C6114yes—
1344C23—21no—
1345C23—21no—
1346C23—21no—
1347C23—21no—
1348C23—21no—
1349C23—21no—
1350C23—21no—
1351C23—21no—
1352C23—21no—
1353C23—21no—
1354C23—21no—
1355C23—21no—
1356C23—21no—
1357C23—21no—
1358C23—21no—
1359C23—21no—
1360C23—21no—
1361C23—21no—
1362C23—21no—
1363C23—21no—
1364C23—21no—
1365C23—21no—
1366C23—21no—
1367C23—21no—
1368C23—21no—
1369C23—21no—
1370C23—21no—
1371C23—21no—
1372C23—21no—
1373C23—21no—
1374C23C23×C4×C6112yes—
1375C23C23×C4×C6112yes—
1376C23C23×C4×C6112yes—
1377C23C23×C4×C6112yes—
1378C23C23×C4×C6112yes—
1379C23C25×C6111yescharacteristic
1380D4—44no—
1381D4—44no—
1382D4—44no—
1383D4—44no—
1384D4—44no—
1385D4—44no—
1386D4—44no—
1387D4—44no—
1388D4—44no—
1389D4—44no—
1390C2×C4—21no—
1391C2×C4—21no—
1392C2×C4—21no—
1393C2×C4—21no—
1394C2×C4—21no—
1395C2×C4—21no—
1396C2×C4—21no—
1397C2×C4—21no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—21no—
1418C2×C4—21no—
1419C2×C4—21no—
1420C2×C4—21no—
1421C2×C4—21no—
1422C2×C4—21no—
1423C2×C4—21no—
1424C2×C4—21no—
1425C2×C4—21no—
1426C2×C4—21no—
1427C2×C4—21no—
1428C2×C4—21no—
1429C2×C4—21no—
1430C2×C4—21no—
1431C2×C4—21no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—21no—
1442C2×C4—21no—
1443C2×C4—21no—
1444C2×C4—21no—
1445C2×C4—21no—
1446C2×C4—21no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—44no—
1457C2×C4—44no—
1458C2×C4—44no—
1459C2×C4—44no—
1460C2×C4—44no—
1461C2×C4—44no—
1462C2×C4—44no—
1463C2×C4—82no—
1464C2×C4—82no—
1465C2×C4—82no—
1466C2×C4—82no—
1467C2×C4—82no—
1468C2×C4—82no—
1469C2×C4—82no—
1470C2×C4—82no—
1471C2×C4C23×C4×C6112yes—
1472C2×C4C23×C4×C6112yes—
1473C2×C4C23×C4×C6112yes—
1474C2×C4C23×C4×C6112yes—
1475C2×C4C23×C4×C6112yes—
1476C2×C4C23×C4×C6112yes—
1477C2×C4C23×C4×C6112yes—
1478C2×C4C23×C4×C6112yes—
1479C2×C4C23×C4×C6112yes—
1480C2×C4C23×C4×C6112yes—
1481C2×C4H(5,𝔽2)×C6112yes—
1482C2×C4H(5,𝔽2)×C6112yes—
1483C22—22no—
1484C22—22no—
1485C22—22no—
1486C22—22no—
1487C22—22no—
1488C22—22no—
1489C22—22no—
1490C22—22no—
1491C22—22no—
1492C22—22no—
1493C22—22no—
1494C22—22no—
1495C22—22no—
1496C22—22no—
1497C22—22no—
1498C22—41no—
1499C22—41no—
1500C22—41no—
1501C22—41no—
1502C22—41no—
1503C22—41no—
1504C22—41no—
1505C22—41no—
1506C22—41no—
1507C22—41no—
1508C22—41no—
1509C22—41no—
1510C22—41no—
1511C22—41no—
1512C22—41no—
1513C22—41no—
1514C22—41no—
1515C22—41no—
1516C22—41no—
1517C22—41no—
1518C22C24×C4×C6111yescharacteristic
1519C22C2×H(5,𝔽2)×C6111yescharacteristic
1520C22C2×H(5,𝔽2)×C6111yescharacteristic
1521C22C61×#58511yescharacteristic
1522C22C61×#58511yescharacteristic
1523C22C61×#58511yescharacteristic
1524C22C61×#58511yescharacteristic
1525C4—22no—
1526C4—22no—
1527C4—22no—
1528C4—22no—
1529C4—22no—
1530C4—22no—
1531C4—22no—
1532C4—22no—
1533C4—22no—
1534C4—22no—
1535C4—22no—
1536C4—22no—
1537C4—41no—
1538C4—41no—
1539C4—41no—
1540C4—41no—
1541C4—41no—
1542C4—41no—
1543C4—41no—
1544C4—41no—
1545C4—41no—
1546C4—41no—
1547C4—41no—
1548C4—41no—
1549C4—41no—
1550C4—41no—
1551C2—42no—
1552C2—42no—
1553C2—42no—
1554C2—42no—
1555C2—42no—
1556C2C61×#342811yescharacteristic
1557C2C4×H(5,𝔽2)×C6111yescharacteristic
1558C2C4×H(5,𝔽2)×C6111yescharacteristic
1559C2C61×#353311yescharacteristic
1560C2C61×#354211yescharacteristic
1561C2C61×#355111yescharacteristic
1562C2C61×#356711yescharacteristic
subgroupG/H
center, socleC23×C61C25
commutatorC22C24×C4×C61
Frattini, cosocleC23C25×C61
prime radicalC2×C61×#540C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C61 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C61×#2382C2semidirect
3. C61×#2377C2semidirect
4. C61×#2377C2semidirect
5. C61×#2376C2semidirect
6. C61×#2374C2semidirect
7. C61×#2371C2semidirect
8. C61×#2364C2semidirect
9. C61×#2364C2semidirect
10. C61×#2363C2semidirect
11. C61×#2361C2semidirect
12. C61×#2359C2semidirect
13. C61×#2359C2semidirect
14. C61×#2353C2semidirect
15. C61×#2352C2semidirect
16. C61×#2346C2semidirect
17. C61×#2343C2semidirect
18. C61×#2335C2semidirect
19. C61×#2335C2semidirect
20. C61×#2333C2semidirect
21. C61×#2333C2semidirect
22. C61×#2328C2semidirect
23. C61×#2328C2semidirect
24. C61×#2325C2semidirect
25. C61×#2325C2semidirect
26. C61×#2324C2semidirect
27. C61×#2322C2semidirect
28. C61×#2318C2semidirect
29. C4×#123×C61C2semidirect
30. C4×#121×C61C2semidirect
31. C61×#2290C2semidirect
32. C61×#540C4semidirect
213. #127×C61C2×C4semidirect
214. #125×C61C2×C4semidirect
215. #123×C61C2×C4semidirect
216. #123×C61C2×C4semidirect
217. #123×C61C2×C4semidirect
218. #123×C61C2×C4semidirect
219. #121×C61C2×C4semidirect
220. #121×C61C2×C4semidirect
221. #121×C61C2×C4semidirect
222. #121×C61C2×C4semidirect
223. #121×C61C2×C4semidirect
224. #121×C61C2×C4semidirect
233. C4×D4×C61C2×C4semidirect
234. C4×D4×C61C2×C4semidirect
237. #117×C61C2×C4semidirect
701. #34450C61direct (N × H)
771. #2382C2×C61semidirect
772. #2377C2×C61semidirect
773. #2377C2×C61semidirect
774. #2376C2×C61semidirect
775. #2374C2×C61semidirect
776. #2371C2×C61semidirect
777. #2364C2×C61semidirect
778. #2364C2×C61semidirect
779. #2363C2×C61semidirect
780. #2361C2×C61semidirect
781. #2359C2×C61semidirect
782. #2359C2×C61semidirect
783. #2353C2×C61semidirect
784. #2352C2×C61semidirect
785. #2346C2×C61semidirect
786. #2343C2×C61semidirect
787. #2335C2×C61semidirect
788. #2335C2×C61semidirect
789. #2333C2×C61semidirect
790. #2333C2×C61semidirect
791. #2328C2×C61semidirect
792. #2328C2×C61semidirect
793. #2325C2×C61semidirect
794. #2325C2×C61semidirect
795. #2324C2×C61semidirect
796. #2322C2×C61semidirect
797. #2318C2×C61semidirect
798. C4×#123C2×C61semidirect
799. C4×#121C2×C61semidirect
800. #2290C2×C61semidirect
813. #540C4×C61semidirect
969. C61#34450direct (N × H)
995. #127C2×C4×C61semidirect
996. #125C2×C4×C61semidirect
997. #123C2×C4×C61semidirect
998. #123C2×C4×C61semidirect
999. #123C2×C4×C61semidirect
1000. #123C2×C4×C61semidirect
1001. #121C2×C4×C61semidirect
1002. #121C2×C4×C61semidirect
1003. #121C2×C4×C61semidirect
1004. #121C2×C4×C61semidirect
1005. #121C2×C4×C61semidirect
1006. #121C2×C4×C61semidirect
1015. C4×D4C2×C4×C61semidirect
1016. C4×D4C2×C4×C61semidirect
1019. #117C2×C4×C61semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C61×#5402
C61×#23822
C61×#23772
C61×#23762
C61×#23742
C61×#23712
C61×#23642
C61×#23632
C61×#23612
C61×#23592
C61×#23532
C61×#23522
C61×#23462
C61×#23432
C61×#23352
C61×#23332
C61×#23282
C61×#23252
C61×#23242
C61×#23222
C61×#23182
C4×#123×C612
C4×#121×C612
C61×#22902
#3445061