Finite Group Databasebeta

← C61×#22334 #29525767

Subgroups — C61×#22334 #29525767

Order 15616.

806 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#2392C211yesmaximal, characteristic
2C61×#1955C211yesmaximal, characteristic, complemented
3C61×#1954C211yesmaximal, characteristic, complemented
4C61×#1924C211yesmaximal, characteristic, complemented
5C61×#1924C211yesmaximal, characteristic, complemented
6C61×#1917C211yesmaximal, characteristic, complemented
7C61×#1916C211yesmaximal, characteristic, complemented
8C61×#1870C211yesmaximal, characteristic, complemented
9C61×#1870C211yesmaximal, characteristic, complemented
10C61×#1869C211yesmaximal, characteristic, complemented
11C61×#1869C211yesmaximal, characteristic, complemented
12C61×#1818C211yesmaximal, characteristic, complemented
13C61×#1753C211yesmaximal, characteristic, complemented
14C8×C22⋊C4×C61C211yesmaximal, characteristic, complemented
15C61×#1750C211yesmaximal, characteristic, complemented
16C22×M16×C61C2211yescharacteristic
17C23×C8×C61C2211yescharacteristic
18C2×C4×D4×C61C2211yescharacteristic
19C2×C4×D4×C61C2211yescharacteristic
20C2×C4×D4×C61C2211yescharacteristic
21C2×#117×C61C2211yescharacteristic
22C2×C4⋊C8×C61C2211yescharacteristic
23C2×C4⋊C8×C61C2211yescharacteristic
24C2×C22⋊C8×C61C2211yescharacteristic
25C2×C22⋊C8×C61C2211yescharacteristic
26C2×C22⋊C8×C61C2211yescharacteristic
27C2×C22⋊C8×C61C2211yescharacteristic
28C2×C22⋊C8×C61C2211yescharacteristic
29C2×C22⋊C8×C61C2211yescharacteristic
30C2×C22⋊C8×C61C2211yescharacteristic
31C2×C22⋊C8×C61C2211yescharacteristic
32C2×C22⋊C8×C61C2211yescharacteristic
33C2×C22⋊C8×C61C2211yescharacteristic
34C2×#97×C61C2211yescharacteristic
35C2×#97×C61C2211yescharacteristic
36C2×C4×C8×C61C2211yescharacteristic
37C2×C4×C8×C61C2211yescharacteristic
38C61×#398C411yescharacteristic
39C61×#397C411yescharacteristic
40C61×#396C411yescharacteristic
41C61×#396C411yescharacteristic
42C61×#394C411yescharacteristic
43C61×#394C411yescharacteristic
44C61×#394C411yescharacteristic
45C61×#392C411yescharacteristic
46C4×C4⋊C4×C61C2211yescharacteristic
47C4×C22⋊C4×C61C2211yescharacteristic
48C4×C22⋊C4×C61C2211yescharacteristic
49C61×#336C2211yescharacteristic
50C61×#336C2211yescharacteristic
51C61×#336C2211yescharacteristic
52C61×#336C2211yescharacteristic
53C61×#336C2211yescharacteristic
54C61×#336C2211yescharacteristic
55C61×#336C2211yescharacteristic
56C61×#336C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C22×D4×C61C2×C411yescharacteristic
60C22×D4×C61C2×C411yescharacteristic
61C22×D4×C61C2×C411yescharacteristic
62C23×C4×C61C2311yescharacteristic
63C23×C4×C61C2311yescharacteristic
64C23×C4×C61C2311yescharacteristic
65C2×M16×C61—22no—
66C2×M16×C61—41no—
67C2×M16×C61—41no—
68C22×C8×C61—22no—
69C22×C8×C61—41no—
70C22×C8×C61—41no—
71C22×C8×C61C2311yescharacteristic
72C22×C8×C61C2311yescharacteristic
73C22×C8×C61C2311yescharacteristic
74C22×C8×C61C2311yescharacteristic
75C22×C8×C61C2311yescharacteristic
76C22×C8×C61C2311yescharacteristic
77C22×C8×C61C2311yescharacteristic
78C22×C8×C61C2311yescharacteristic
79C4×D4×C61—41no—
80C4×D4×C61—41no—
81C4×D4×C61—41no—
82C4×D4×C61—41no—
83C4×D4×C61—41no—
84C4×D4×C61—41no—
85#117×C61—41no—
86#117×C61—41no—
87C2×C4⋊C4×C61C2×C411yescharacteristic
88C2×C4⋊C4×C61C2×C411yescharacteristic
89C2×C4⋊C4×C61C2×C411yescharacteristic
90C2×C4⋊C4×C61C2×C411yescharacteristic
91C2×C4⋊C4×C61C2×C411yescharacteristic
92C2×C4⋊C4×C61C2×C411yescharacteristic
93C2×C4⋊C4×C61C2×C411yescharacteristic
94C2×C22⋊C4×C61C2×C411yescharacteristic
95C2×C22⋊C4×C61C2×C411yescharacteristic
96C2×C22⋊C4×C61C2×C411yescharacteristic
97C2×C22⋊C4×C61C2×C411yescharacteristic
98C2×C22⋊C4×C61C2×C411yescharacteristic
99C2×C22⋊C4×C61C2×C411yescharacteristic
100C2×C22⋊C4×C61C2×C411yescharacteristic
101C2×C22⋊C4×C61C2×C411yescharacteristic
102C2×C22⋊C4×C61C2×C411yescharacteristic
103C2×C22⋊C4×C61C2×C411yescharacteristic
104C2×C22⋊C4×C61C2×C411yescharacteristic
105C2×C22⋊C4×C61C2×C411yescharacteristic
106C2×C42×C61C2311yescharacteristic
107C2×C42×C61C2311yescharacteristic
108C2×C42×C61C2311yescharacteristic
109C2×C42×C61C2311yescharacteristic
110C4⋊C8×C61—41no—
111C4⋊C8×C61—41no—
112C22⋊C8×C61—22no—
113C22⋊C8×C61—22no—
114C22⋊C8×C61—22no—
115C22⋊C8×C61—22no—
116C22⋊C8×C61—41no—
117C22⋊C8×C61—41no—
118C22⋊C8×C61—41no—
119C22⋊C8×C61—41no—
120C22⋊C8×C61—41no—
121C22⋊C8×C61—41no—
122#97×C61—41no—
123#97×C61—41no—
124C4×C8×C61—41no—
125C4×C8×C61—41no—
126#95×C61C2×C411yescharacteristic
127#95×C61C2×C411yescharacteristic
128#95×C61C2×C411yescharacteristic
129#95×C61C2×C411yescharacteristic
130#95×C61C2×C411yescharacteristic
131#95×C61C2×C411yescharacteristic
132C24×C61C22×C411yescharacteristic
133C24×C61C22×C411yescharacteristic
134C24×C61C22×C411yescharacteristic
135C2×D4×C61—22no—
136C2×D4×C61—22no—
137C2×D4×C61—22no—
138C2×D4×C61—41no—
139C2×D4×C61—41no—
140C2×D4×C61—41no—
141C2×D4×C61—41no—
142C2×D4×C61—41no—
143C2×D4×C61—41no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61C22×C411yescharacteristic
163C22×C4×C61C22×C411yescharacteristic
164C22×C4×C61C22×C411yescharacteristic
165C22×C4×C61C22×C411yescharacteristic
166C22×C4×C61C22×C411yescharacteristic
167C22×C4×C61C22×C411yescharacteristic
168C22×C4×C61C22×C411yescharacteristic
169C22×C4×C61C22×C411yescharacteristic
170C22×C4×C61C22×C411yescharacteristic
171C22×C4×C61C22×C411yescharacteristic
172C22×C4×C61C22×C411yescharacteristic
173C22×C4×C61C2411yescharacteristic
174M16×C61—44no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C2×C8×C61—21no—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61—21no—
184C2×C8×C61—21no—
185C2×C8×C61—21no—
186C2×C8×C61—21no—
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—44no—
198C2×C8×C61#4112yes—
199C2×C8×C61#4112yes—
200C4⋊C4×C61—22no—
201C4⋊C4×C61—41no—
202C4⋊C4×C61—41no—
203C4⋊C4×C61—41no—
204C4⋊C4×C61—41no—
205C4⋊C4×C61—41no—
206C4⋊C4×C61—41no—
207C22⋊C4×C61—22no—
208C22⋊C4×C61—22no—
209C22⋊C4×C61—41no—
210C22⋊C4×C61—41no—
211C22⋊C4×C61—41no—
212C22⋊C4×C61—41no—
213C22⋊C4×C61—41no—
214C22⋊C4×C61—41no—
215C22⋊C4×C61—41no—
216C22⋊C4×C61—41no—
217C22⋊C4×C61—41no—
218C22⋊C4×C61—41no—
219C42×C61—21no—
220C42×C61—21no—
221C42×C61—21no—
222C42×C61—21no—
223C42×C61—21no—
224C42×C61—21no—
225C42×C61—21no—
226C42×C61—21no—
227C23×C61—21no—
228C23×C61—21no—
229C23×C61—21no—
230C23×C61—21no—
231C23×C61—21no—
232C23×C61—21no—
233C23×C61—21no—
234C23×C61—21no—
235C23×C61—21no—
236C23×C61—21no—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61#13112yes—
248C23×C61C23×C411yescharacteristic
249D4×C61—44no—
250D4×C61—44no—
251D4×C61—44no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61#13112yes—
297C2×C4×C61C2×#4111yescharacteristic
298C2×C4×C61C2×#4111yescharacteristic
299C2×C4×C61H(5,𝔽2)11yescharacteristic
300C2×C4×C61H(5,𝔽2)11yescharacteristic
301C2×C4×C61H(5,𝔽2)11yescharacteristic
302C2×C4×C61H(5,𝔽2)11yescharacteristic
303C8×C61—22no—
304C8×C61—22no—
305C8×C61—41no—
306C8×C61—41no—
307C8×C61—41no—
308C8×C61—41no—
309C8×C61—41no—
310C8×C61—41no—
311#22334C6111yesmaximal, characteristic, direct product factor, Sylow
312C22×C61—22no—
313C22×C61—22no—
314C22×C61—22no—
315C22×C61—41no—
316C22×C61—41no—
317C22×C61—41no—
318C22×C61—41no—
319C22×C61—41no—
320C22×C61—41no—
321C22×C61—41no—
322C22×C61—41no—
323C22×C61—41no—
324C22×C61—41no—
325C22×C61—41no—
326C22×C61—41no—
327C22×C61—41no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61C4×#4111yescharacteristic
334C22×C61#51811yescharacteristic
335C22×C61#51811yescharacteristic
336C22×C61C2×#13111yescharacteristic
337C22×C61C2×#13111yescharacteristic
338C22×C61#56811yescharacteristic
339C22×C61#56811yescharacteristic
340C4×C61—22no—
341C4×C61—41no—
342C4×C61—41no—
343C4×C61—41no—
344C4×C61—41no—
345C4×C61—41no—
346C4×C61—41no—
347C4×C61—41no—
348C4×C61—41no—
349C4×C61—41no—
350C4×C61—41no—
351C4×C61#53811yescharacteristic
352C4×C61#53811yescharacteristic
353C4×C61#54011yescharacteristic
354C4×C61#54011yescharacteristic
355#2392C2×C6111yescharacteristic
356#1955C2×C6111yescharacteristic, complemented
357#1954C2×C6111yescharacteristic, complemented
358#1924C2×C6111yescharacteristic, complemented
359#1924C2×C6111yescharacteristic, complemented
360#1917C2×C6111yescharacteristic, complemented
361#1916C2×C6111yescharacteristic, complemented
362#1870C2×C6111yescharacteristic, complemented
363#1870C2×C6111yescharacteristic, complemented
364#1869C2×C6111yescharacteristic, complemented
365#1869C2×C6111yescharacteristic, complemented
366#1818C2×C6111yescharacteristic, complemented
367#1753C2×C6111yescharacteristic, complemented
368C8×C22⋊C4C2×C6111yescharacteristic, complemented
369#1750C2×C6111yescharacteristic, complemented
370C2×C61—42no—
371C2×C61—81no—
372C2×C61—81no—
373C2×C61#233311yescharacteristic
374C2×C61#296611yescharacteristic
375C2×C61#296711yescharacteristic
376C2×C61#297611yescharacteristic
377C2×C61#297611yescharacteristic
378C2×C61#297611yescharacteristic
379C2×C61#298111yescharacteristic
380C22×M16C22×C6111yescharacteristic
381C23×C8C22×C6111yescharacteristic
382C2×C4×D4C22×C6111yescharacteristic
383C2×C4×D4C22×C6111yescharacteristic
384C2×C4×D4C22×C6111yescharacteristic
385C2×#117C22×C6111yescharacteristic
386C2×C4⋊C8C22×C6111yescharacteristic
387C2×C4⋊C8C22×C6111yescharacteristic
388C2×C22⋊C8C22×C6111yescharacteristic
389C2×C22⋊C8C22×C6111yescharacteristic
390C2×C22⋊C8C22×C6111yescharacteristic
391C2×C22⋊C8C22×C6111yescharacteristic
392C2×C22⋊C8C22×C6111yescharacteristic
393C2×C22⋊C8C22×C6111yescharacteristic
394C2×C22⋊C8C22×C6111yescharacteristic
395C2×C22⋊C8C22×C6111yescharacteristic
396C2×C22⋊C8C22×C6111yescharacteristic
397C2×C22⋊C8C22×C6111yescharacteristic
398C2×#97C22×C6111yescharacteristic
399C2×#97C22×C6111yescharacteristic
400C2×C4×C8C22×C6111yescharacteristic
401C2×C4×C8C22×C6111yescharacteristic
402#398C4×C6111yescharacteristic
403#397C4×C6111yescharacteristic
404#396C4×C6111yescharacteristic
405#396C4×C6111yescharacteristic
406#394C4×C6111yescharacteristic
407#394C4×C6111yescharacteristic
408#394C4×C6111yescharacteristic
409#392C4×C6111yescharacteristic
410C4×C4⋊C4C22×C6111yescharacteristic
411C4×C22⋊C4C22×C6111yescharacteristic
412C4×C22⋊C4C22×C6111yescharacteristic
413#336C22×C6111yescharacteristic
414#336C22×C6111yescharacteristic
415#336C22×C6111yescharacteristic
416#336C22×C6111yescharacteristic
417#336C22×C6111yescharacteristic
418#336C22×C6111yescharacteristic
419#336C22×C6111yescharacteristic
420#336C22×C6111yescharacteristic
421#336C22×C6111yescharacteristic
422#336C22×C6111yescharacteristic
423C61#2233411yescharacteristic, direct product factor, Sylow
424C22×D4C2×C4×C6111yescharacteristic
425C22×D4C2×C4×C6111yescharacteristic
426C22×D4C2×C4×C6111yescharacteristic
427C23×C4C23×C6111yescharacteristic
428C23×C4C23×C6111yescharacteristic
429C23×C4C23×C6111yescharacteristic
430C2×M16—22no—
431C2×M16—41no—
432C2×M16—41no—
433C22×C8—22no—
434C22×C8—41no—
435C22×C8—41no—
436C22×C8C23×C6111yescharacteristic
437C22×C8C23×C6111yescharacteristic
438C22×C8C23×C6111yescharacteristic
439C22×C8C23×C6111yescharacteristic
440C22×C8C23×C6111yescharacteristic
441C22×C8C23×C6111yescharacteristic
442C22×C8C23×C6111yescharacteristic
443C22×C8C23×C6111yescharacteristic
444C4×D4—41no—
445C4×D4—41no—
446C4×D4—41no—
447C4×D4—41no—
448C4×D4—41no—
449C4×D4—41no—
450#117—41no—
451#117—41no—
452C2×C4⋊C4C2×C4×C6111yescharacteristic
453C2×C4⋊C4C2×C4×C6111yescharacteristic
454C2×C4⋊C4C2×C4×C6111yescharacteristic
455C2×C4⋊C4C2×C4×C6111yescharacteristic
456C2×C4⋊C4C2×C4×C6111yescharacteristic
457C2×C4⋊C4C2×C4×C6111yescharacteristic
458C2×C4⋊C4C2×C4×C6111yescharacteristic
459C2×C22⋊C4C2×C4×C6111yescharacteristic
460C2×C22⋊C4C2×C4×C6111yescharacteristic
461C2×C22⋊C4C2×C4×C6111yescharacteristic
462C2×C22⋊C4C2×C4×C6111yescharacteristic
463C2×C22⋊C4C2×C4×C6111yescharacteristic
464C2×C22⋊C4C2×C4×C6111yescharacteristic
465C2×C22⋊C4C2×C4×C6111yescharacteristic
466C2×C22⋊C4C2×C4×C6111yescharacteristic
467C2×C22⋊C4C2×C4×C6111yescharacteristic
468C2×C22⋊C4C2×C4×C6111yescharacteristic
469C2×C22⋊C4C2×C4×C6111yescharacteristic
470C2×C22⋊C4C2×C4×C6111yescharacteristic
471C2×C42C23×C6111yescharacteristic
472C2×C42C23×C6111yescharacteristic
473C2×C42C23×C6111yescharacteristic
474C2×C42C23×C6111yescharacteristic
475C4⋊C8—41no—
476C4⋊C8—41no—
477C22⋊C8—22no—
478C22⋊C8—22no—
479C22⋊C8—22no—
480C22⋊C8—22no—
481C22⋊C8—41no—
482C22⋊C8—41no—
483C22⋊C8—41no—
484C22⋊C8—41no—
485C22⋊C8—41no—
486C22⋊C8—41no—
487#97—41no—
488#97—41no—
489C4×C8—41no—
490C4×C8—41no—
491#95C2×C4×C6111yescharacteristic
492#95C2×C4×C6111yescharacteristic
493#95C2×C4×C6111yescharacteristic
494#95C2×C4×C6111yescharacteristic
495#95C2×C4×C6111yescharacteristic
496#95C2×C4×C6111yescharacteristic
497C24C22×C4×C6111yescharacteristic
498C24C22×C4×C6111yescharacteristic
499C24C22×C4×C6111yescharacteristic
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—41no—
504C2×D4—41no—
505C2×D4—41no—
506C2×D4—41no—
507C2×D4—41no—
508C2×D4—41no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4C22×C4×C6111yescharacteristic
528C22×C4C22×C4×C6111yescharacteristic
529C22×C4C22×C4×C6111yescharacteristic
530C22×C4C22×C4×C6111yescharacteristic
531C22×C4C22×C4×C6111yescharacteristic
532C22×C4C22×C4×C6111yescharacteristic
533C22×C4C22×C4×C6111yescharacteristic
534C22×C4C22×C4×C6111yescharacteristic
535C22×C4C22×C4×C6111yescharacteristic
536C22×C4C22×C4×C6111yescharacteristic
537C22×C4C22×C4×C6111yescharacteristic
538C22×C4C24×C6111yescharacteristic
539M16—44no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—44no—
563C2×C8#41×C6112yes—
564C2×C8#41×C6112yes—
565C4⋊C4—22no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C4⋊C4—41no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—41no—
575C22⋊C4—41no—
576C22⋊C4—41no—
577C22⋊C4—41no—
578C22⋊C4—41no—
579C22⋊C4—41no—
580C22⋊C4—41no—
581C22⋊C4—41no—
582C22⋊C4—41no—
583C22⋊C4—41no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23#131×C6112yes—
613C23C23×C4×C6111yescharacteristic
614D4—44no—
615D4—44no—
616D4—44no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4#131×C6112yes—
662C2×C4C2×#41×C6111yescharacteristic
663C2×C4C2×#41×C6111yescharacteristic
664C2×C4H(5,𝔽2)×C6111yescharacteristic
665C2×C4H(5,𝔽2)×C6111yescharacteristic
666C2×C4H(5,𝔽2)×C6111yescharacteristic
667C2×C4H(5,𝔽2)×C6111yescharacteristic
668C8—22no—
669C8—22no—
670C8—41no—
671C8—41no—
672C8—41no—
673C8—41no—
674C8—41no—
675C8—41no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22C4×#41×C6111yescharacteristic
698C22C61×#51811yescharacteristic
699C22C61×#51811yescharacteristic
700C22C2×#131×C6111yescharacteristic
701C22C2×#131×C6111yescharacteristic
702C22C61×#56811yescharacteristic
703C22C61×#56811yescharacteristic
704C4—22no—
705C4—41no—
706C4—41no—
707C4—41no—
708C4—41no—
709C4—41no—
710C4—41no—
711C4—41no—
712C4—41no—
713C4—41no—
714C4—41no—
715C4C61×#53811yescharacteristic
716C4C61×#53811yescharacteristic
717C4C61×#54011yescharacteristic
718C4C61×#54011yescharacteristic
719C2—42no—
720C2—81no—
721C2—81no—
722C2C61×#233311yescharacteristic
723C2C61×#296611yescharacteristic
724C2C61×#296711yescharacteristic
725C2C61×#297611yescharacteristic
726C2C61×#297611yescharacteristic
727C2C61×#297611yescharacteristic
728C2C61×#298111yescharacteristic
subgroupG/H
centerC22×C4×C61C24
commutatorC23C23×C4×C61
Frattini, cosocleC22×C4C24×C61
socleC23×C61C23×C4
prime radicalC61×#392C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#1955C2semidirect
3. C61×#1954C2semidirect
4. C61×#1924C2semidirect
5. C61×#1924C2semidirect
6. C61×#1917C2semidirect
7. C61×#1916C2semidirect
8. C61×#1870C2semidirect
9. C61×#1870C2semidirect
10. C61×#1869C2semidirect
11. C61×#1869C2semidirect
12. C61×#1818C2semidirect
13. C61×#1753C2semidirect
14. C8×C22⋊C4×C61C2semidirect
15. C61×#1750C2semidirect
311. #22334C61direct (N × H)
356. #1955C2×C61semidirect
357. #1954C2×C61semidirect
358. #1924C2×C61semidirect
359. #1924C2×C61semidirect
360. #1917C2×C61semidirect
361. #1916C2×C61semidirect
362. #1870C2×C61semidirect
363. #1870C2×C61semidirect
364. #1869C2×C61semidirect
365. #1869C2×C61semidirect
366. #1818C2×C61semidirect
367. #1753C2×C61semidirect
368. C8×C22⋊C4C2×C61semidirect
369. #1750C2×C61semidirect
423. C61#22334direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#23922
C61×#19552
C61×#19542
C61×#19242
C61×#19172
C61×#19162
C61×#18702
C61×#18692
C61×#18182
C61×#17532
C8×C22⋊C4×C612
C61×#17502
#2233461