Finite Group Databasebeta

← C47×#34506 #26074204

Subgroups — C47×#34506 #26074204

Order 12032.

2132 conjugacy classes of subgroups.

The subgroup lattice has 1480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#553C211yesmaximal, characteristic
2C47×#2382C211yesmaximal, characteristic, complemented
3C47×#2377C211yesmaximal, characteristic, complemented
4C47×#2377C211yesmaximal, characteristic, complemented
5C47×#2376C211yesmaximal, characteristic, complemented
6C47×#2373C211yesmaximal, characteristic, complemented
7C47×#2373C211yesmaximal, characteristic, complemented
8C47×#2364C211yesmaximal, characteristic, complemented
9C47×#2363C211yesmaximal, characteristic, complemented
10C47×#2359C211yesmaximal, characteristic, complemented
11C47×#2357C211yesmaximal, characteristic, complemented
12C47×#2353C211yesmaximal, characteristic, complemented
13C47×#2352C211yesmaximal, characteristic, complemented
14C47×#2352C211yesmaximal, characteristic, complemented
15C47×#2344C211yesmaximal, characteristic, complemented
16C47×#2343C211yesmaximal, characteristic, complemented
17C47×#2336C211yesmaximal, characteristic, complemented
18C47×#2335C211yesmaximal, characteristic, complemented
19C47×#2334C211yesmaximal, characteristic, complemented
20C47×#2333C211yesmaximal, characteristic, complemented
21C47×#2333C211yesmaximal, characteristic, complemented
22C47×#2333C211yesmaximal, characteristic, complemented
23C47×#2324C211yesmaximal, characteristic, complemented
24C47×#2322C211yesmaximal, characteristic, complemented
25C47×#2319C211yesmaximal, characteristic, complemented
26C47×#2318C211yesmaximal, characteristic, complemented
27C47×#2318C211yesmaximal, characteristic, complemented
28C47×#2313C211yesmaximal, characteristic, complemented
29C4×#126×C47C211yesmaximal, characteristic, complemented
30C47×#2298C211yesmaximal, characteristic, complemented
31C47×#2293C211yesmaximal, characteristic, complemented
32C47×#553C4116yescomplemented
33C2×#126×C47C2211yescharacteristic
34C2×#126×C47C2211yescharacteristic
35C2×#125×C47C2211yescharacteristic
36C2×#123×C47C2211yescharacteristic
37C2×#123×C47C2211yescharacteristic
38C2×#121×C47C2211yescharacteristic
39C2×#121×C47C2211yescharacteristic
40C2×#121×C47C2211yescharacteristic
41C2×#121×C47C2211yescharacteristic
42C2×C4×D4×C47C2211yescharacteristic
43C2×C4×D4×C47C2211yescharacteristic
44C2×C4×D4×C47C2211yescharacteristic
45C2×C4×D4×C47C2211yescharacteristic
46C2×C4×D4×C47C2211yescharacteristic
47C2×C4×D4×C47C2211yescharacteristic
48C2×#117×C47C2211yescharacteristic
49C2×#117×C47C2211yescharacteristic
50C2×#117×C47C2211yescharacteristic
51C2×#117×C47C2211yescharacteristic
52C22×C4⋊C4×C47C2211yescharacteristic
53C22×C4⋊C4×C47C2211yescharacteristic
54C47×#390C2211yescharacteristic
55C47×#390C2211yescharacteristic
56C47×#390C2211yescharacteristic
57C47×#390C2211yescharacteristic
58C47×#390C2211yescharacteristic
59C47×#390C2211yescharacteristic
60C47×#390C2211yescharacteristic
61C47×#390C2211yescharacteristic
62C47×#389C2211yescharacteristic
63C47×#389C2211yescharacteristic
64C47×#389C2211yescharacteristic
65C47×#389C2211yescharacteristic
66C47×#389C2211yescharacteristic
67C47×#389C2211yescharacteristic
68C47×#389C2211yescharacteristic
69C47×#389C2211yescharacteristic
70C47×#388C2211yescharacteristic
71C47×#388C2211yescharacteristic
72C47×#388C2211yescharacteristic
73C47×#388C2211yescharacteristic
74C47×#388C2211yescharacteristic
75C47×#388C2211yescharacteristic
76C47×#388C2211yescharacteristic
77C47×#388C2211yescharacteristic
78C47×#388C2211yescharacteristic
79C47×#388C2211yescharacteristic
80C47×#388C2211yescharacteristic
81C47×#388C2211yescharacteristic
82C47×#388C2211yescharacteristic
83C47×#388C2211yescharacteristic
84C47×#388C2211yescharacteristic
85C47×#388C2211yescharacteristic
86C47×#388C2211yescharacteristic
87C47×#388C2211yescharacteristic
88C47×#388C2211yescharacteristic
89C47×#388C2211yescharacteristic
90C47×#388C2211yescharacteristic
91C47×#388C2211yescharacteristic
92C47×#387C2211yescharacteristic
93C47×#387C2211yescharacteristic
94C47×#387C2211yescharacteristic
95C47×#387C2211yescharacteristic
96C47×#387C2211yescharacteristic
97C47×#387C2211yescharacteristic
98C47×#387C2211yescharacteristic
99C47×#387C2211yescharacteristic
100C47×#387C2211yescharacteristic
101C47×#387C2211yescharacteristic
102C47×#387C2211yescharacteristic
103C47×#387C2211yescharacteristic
104C47×#387C2211yescharacteristic
105C47×#387C2211yescharacteristic
106C47×#387C2211yescharacteristic
107C47×#387C2211yescharacteristic
108C47×#387C2211yescharacteristic
109C47×#387C2211yescharacteristic
110C47×#387C2211yescharacteristic
111C47×#387C2211yescharacteristic
112C47×#387C2211yescharacteristic
113C47×#387C2211yescharacteristic
114C47×#387C2211yescharacteristic
115C47×#387C2211yescharacteristic
116C47×#387C2211yescharacteristic
117C47×#387C2211yescharacteristic
118C47×#386C2211yescharacteristic
119C47×#386C2211yescharacteristic
120C47×#386C2211yescharacteristic
121C47×#386C2211yescharacteristic
122C47×#386C2211yescharacteristic
123C47×#386C2211yescharacteristic
124C47×#386C2211yescharacteristic
125C47×#386C2211yescharacteristic
126C47×#386C2211yescharacteristic
127C47×#386C2211yescharacteristic
128C47×#386C2211yescharacteristic
129C47×#386C2211yescharacteristic
130C47×#386C2211yescharacteristic
131C47×#386C2211yescharacteristic
132C47×#385C2211yescharacteristic
133C47×#385C2211yescharacteristic
134C47×#385C2211yescharacteristic
135C47×#385C2211yescharacteristic
136C47×#385C2211yescharacteristic
137C47×#385C2211yescharacteristic
138C47×#385C2211yescharacteristic
139C47×#385C2211yescharacteristic
140C47×#383C2211yescharacteristic
141C47×#383C2211yescharacteristic
142C47×#382C2211yescharacteristic
143C47×#382C2211yescharacteristic
144C47×#382C2211yescharacteristic
145C47×#381C2211yescharacteristic
146C47×#381C2211yescharacteristic
147C47×#381C2211yescharacteristic
148C47×#381C2211yescharacteristic
149C47×#381C2211yescharacteristic
150C47×#381C2211yescharacteristic
151C47×#380C2211yescharacteristic
152C47×#380C2211yescharacteristic
153C47×#380C2211yescharacteristic
154C47×#380C2211yescharacteristic
155C47×#380C2211yescharacteristic
156C47×#380C2211yescharacteristic
157C4×C4⋊C4×C47C2211yescharacteristic
158C4×C4⋊C4×C47C2211yescharacteristic
159C4×C4⋊C4×C47C2211yescharacteristic
160C4×C4⋊C4×C47C2211yescharacteristic
161C4×C4⋊C4×C47C2211yescharacteristic
162C4×C4⋊C4×C47C2211yescharacteristic
163C4×C4⋊C4×C47C2211yescharacteristic
164C4×C4⋊C4×C47C2211yescharacteristic
165C4×C4⋊C4×C47C2211yescharacteristic
166C4×C4⋊C4×C47C2211yescharacteristic
167C4×C22⋊C4×C47C2211yescharacteristic
168C4×C22⋊C4×C47C2211yescharacteristic
169C4×C22⋊C4×C47C2211yescharacteristic
170C4×C22⋊C4×C47C2211yescharacteristic
171C4×C22⋊C4×C47C2211yescharacteristic
172C4×C22⋊C4×C47C2211yescharacteristic
173C4×C22⋊C4×C47C2211yescharacteristic
174C4×C22⋊C4×C47C2211yescharacteristic
175C4×C22⋊C4×C47C2211yescharacteristic
176C4×C22⋊C4×C47C2211yescharacteristic
177C4×C22⋊C4×C47C2211yescharacteristic
178C4×C22⋊C4×C47C2211yescharacteristic
179C4×C22⋊C4×C47C2211yescharacteristic
180C4×C22⋊C4×C47C2211yescharacteristic
181C4×C22⋊C4×C47C2211yescharacteristic
182C4×C22⋊C4×C47C2211yescharacteristic
183C47×#376C2211yescharacteristic
184C47×#376C2211yescharacteristic
185C2×#95×C47C2211yescharacteristic
186C2×#95×C47C2211yescharacteristic
187C43×C47C2211yescharacteristic
188C22×D4×C47C2311yescharacteristic
189C22×D4×C47C2311yescharacteristic
190C22×D4×C47C2311yescharacteristic
191C22×D4×C47C2311yescharacteristic
192C22×D4×C47C2311yescharacteristic
193C22×D4×C47C2311yescharacteristic
194C23×C4×C47C2311yescharacteristic
195C23×C4×C47C2311yescharacteristic
196C23×C4×C47C2311yescharacteristic
197C23×C4×C47C2311yescharacteristic
198C23×C4×C47C2311yescharacteristic
199C23×C4×C47C2311yescharacteristic
200C23×C4×C47C2311yescharacteristic
201C23×C4×C47C2311yescharacteristic
202C23×C4×C47C2311yescharacteristic
203C23×C4×C47C2311yescharacteristic
204C23×C4×C47C2311yescharacteristic
205C23×C4×C47C2311yescharacteristic
206#126×C47C2×C418yescomplemented
207#126×C47C2×C418yescomplemented
208#125×C47C2×C418yescomplemented
209#123×C47C2×C418yescomplemented
210#123×C47C2×C418yescomplemented
211#121×C47C2×C418yes—
212#121×C47C2×C418yescomplemented
213#121×C47C2×C418yescomplemented
214#121×C47C2×C418yescomplemented
215C4×D4×C47—42no—
216C4×D4×C47—42no—
217C4×D4×C47C2×C418yescomplemented
218C4×D4×C47C2×C418yescomplemented
219C4×D4×C47C2×C418yescomplemented
220C4×D4×C47C2×C418yescomplemented
221#117×C47—42no—
222#117×C47—42no—
223#117×C47—42no—
224#117×C47C2×C418yescomplemented
225C2×C4⋊C4×C47—42no—
226C2×C4⋊C4×C47C2×C418yescomplemented
227C2×C4⋊C4×C47C2311yescharacteristic
228C2×C4⋊C4×C47C2311yescharacteristic
229C2×C4⋊C4×C47C2311yescharacteristic
230C2×C4⋊C4×C47C2311yescharacteristic
231C2×C4⋊C4×C47C2311yescharacteristic
232C2×C4⋊C4×C47C2311yescharacteristic
233C2×C4⋊C4×C47C2311yescharacteristic
234C2×C4⋊C4×C47C2311yescharacteristic
235C2×C4⋊C4×C47C2311yescharacteristic
236C2×C4⋊C4×C47C2311yescharacteristic
237C2×C4⋊C4×C47C2311yescharacteristic
238C2×C4⋊C4×C47C2311yescharacteristic
239C2×C4⋊C4×C47C2311yescharacteristic
240C2×C4⋊C4×C47C2311yescharacteristic
241C2×C4⋊C4×C47C2311yescharacteristic
242C2×C4⋊C4×C47C2311yescharacteristic
243C2×C4⋊C4×C47C2311yescharacteristic
244C2×C4⋊C4×C47C2311yescharacteristic
245C2×C4⋊C4×C47C2311yescharacteristic
246C2×C4⋊C4×C47C2311yescharacteristic
247C2×C4⋊C4×C47C2311yescharacteristic
248C2×C4⋊C4×C47C2311yescharacteristic
249C2×C4⋊C4×C47C2311yescharacteristic
250C2×C4⋊C4×C47C2311yescharacteristic
251C2×C4⋊C4×C47C2311yescharacteristic
252C2×C4⋊C4×C47C2311yescharacteristic
253C2×C4⋊C4×C47C2311yescharacteristic
254C2×C4⋊C4×C47C2311yescharacteristic
255C2×C4⋊C4×C47C2311yescharacteristic
256C2×C4⋊C4×C47C2311yescharacteristic
257C2×C22⋊C4×C47C2311yescharacteristic
258C2×C22⋊C4×C47C2311yescharacteristic
259C2×C22⋊C4×C47C2311yescharacteristic
260C2×C22⋊C4×C47C2311yescharacteristic
261C2×C22⋊C4×C47C2311yescharacteristic
262C2×C22⋊C4×C47C2311yescharacteristic
263C2×C22⋊C4×C47C2311yescharacteristic
264C2×C22⋊C4×C47C2311yescharacteristic
265C2×C22⋊C4×C47C2311yescharacteristic
266C2×C22⋊C4×C47C2311yescharacteristic
267C2×C22⋊C4×C47C2311yescharacteristic
268C2×C22⋊C4×C47C2311yescharacteristic
269C2×C22⋊C4×C47C2311yescharacteristic
270C2×C22⋊C4×C47C2311yescharacteristic
271C2×C22⋊C4×C47C2311yescharacteristic
272C2×C22⋊C4×C47C2311yescharacteristic
273C2×C22⋊C4×C47C2311yescharacteristic
274C2×C22⋊C4×C47C2311yescharacteristic
275C2×C22⋊C4×C47C2311yescharacteristic
276C2×C22⋊C4×C47C2311yescharacteristic
277C2×C22⋊C4×C47C2311yescharacteristic
278C2×C22⋊C4×C47C2311yescharacteristic
279C2×C22⋊C4×C47C2311yescharacteristic
280C2×C22⋊C4×C47C2311yescharacteristic
281C2×C22⋊C4×C47C2311yescharacteristic
282C2×C22⋊C4×C47C2311yescharacteristic
283C2×C22⋊C4×C47C2311yescharacteristic
284C2×C22⋊C4×C47C2311yescharacteristic
285C2×C22⋊C4×C47C2311yescharacteristic
286C2×C22⋊C4×C47C2311yescharacteristic
287C2×C22⋊C4×C47C2311yescharacteristic
288C2×C22⋊C4×C47C2311yescharacteristic
289C2×C22⋊C4×C47C2311yescharacteristic
290C2×C22⋊C4×C47C2311yescharacteristic
291C2×C22⋊C4×C47C2311yescharacteristic
292C2×C22⋊C4×C47C2311yescharacteristic
293C2×C42×C47C2311yescharacteristic
294C2×C42×C47C2311yescharacteristic
295C2×C42×C47C2311yescharacteristic
296C2×C42×C47C2311yescharacteristic
297C2×C42×C47C2311yescharacteristic
298C2×C42×C47C2311yescharacteristic
299C2×C42×C47C2311yescharacteristic
300C2×C42×C47C2311yescharacteristic
301C2×C42×C47C2311yescharacteristic
302C2×C42×C47C2311yescharacteristic
303C2×C42×C47C2311yescharacteristic
304C2×C42×C47C2311yescharacteristic
305C2×C42×C47C2311yescharacteristic
306C2×C42×C47C2311yescharacteristic
307C2×C42×C47C2311yescharacteristic
308C2×C42×C47C2311yescharacteristic
309C2×C42×C47C2311yescharacteristic
310C2×C42×C47C2311yescharacteristic
311C2×C42×C47C2311yescharacteristic
312C2×C42×C47C2311yescharacteristic
313C2×C42×C47C2311yescharacteristic
314C2×C42×C47C2311yescharacteristic
315C2×C42×C47C2311yescharacteristic
316#95×C47C2311yescharacteristic
317#95×C47C2311yescharacteristic
318#95×C47C2311yescharacteristic
319#95×C47C2311yescharacteristic
320#95×C47C2311yescharacteristic
321#95×C47C2311yescharacteristic
322#95×C47C2311yescharacteristic
323#95×C47C2311yescharacteristic
324#95×C47C2311yescharacteristic
325#95×C47C2311yescharacteristic
326#95×C47C2311yescharacteristic
327#95×C47C2311yescharacteristic
328#95×C47C2311yescharacteristic
329#95×C47C2311yescharacteristic
330#95×C47C2311yescharacteristic
331#95×C47C2311yescharacteristic
332#95×C47C2311yescharacteristic
333#95×C47C2311yescharacteristic
334#95×C47C2311yescharacteristic
335#95×C47C2311yescharacteristic
336#95×C47C2311yescharacteristic
337#95×C47C2311yescharacteristic
338#95×C47C2311yescharacteristic
339#95×C47C2311yescharacteristic
340#95×C47C2311yescharacteristic
341#95×C47C2311yescharacteristic
342#95×C47C2311yescharacteristic
343#95×C47C2311yescharacteristic
344#95×C47C2311yescharacteristic
345#95×C47C2311yescharacteristic
346#95×C47C2311yescharacteristic
347#95×C47C2311yescharacteristic
348#95×C47C2311yescharacteristic
349#95×C47C2311yescharacteristic
350#95×C47C2311yescharacteristic
351#95×C47C2311yescharacteristic
352#95×C47C2311yescharacteristic
353#95×C47C2311yescharacteristic
354#95×C47C2311yescharacteristic
355#95×C47C2311yescharacteristic
356#95×C47C2311yescharacteristic
357#95×C47C2311yescharacteristic
358#95×C47C2311yescharacteristic
359#95×C47C2311yescharacteristic
360#95×C47C2311yescharacteristic
361#95×C47C2311yescharacteristic
362#95×C47C2311yescharacteristic
363#95×C47C2311yescharacteristic
364C24×C47C2411yescharacteristic
365C24×C47C2411yescharacteristic
366C24×C47C2411yescharacteristic
367C24×C47C2411yescharacteristic
368C2×D4×C47—41no—
369C2×D4×C47—41no—
370C2×D4×C47—41no—
371C2×D4×C47—41no—
372C2×D4×C47—41no—
373C2×D4×C47—41no—
374C2×D4×C47—41no—
375C2×D4×C47—41no—
376C2×D4×C47—41no—
377C2×D4×C47—41no—
378C2×D4×C47—41no—
379C2×D4×C47—41no—
380C2×D4×C47C22×C414yes—
381C2×D4×C47C22×C414yes—
382C2×D4×C47C22×C414yes—
383C2×D4×C47C22×C414yes—
384C2×D4×C47C22×C414yes—
385C2×D4×C47C22×C414yes—
386C22×C4×C47—22no—
387C22×C4×C47—41no—
388C22×C4×C47—41no—
389C22×C4×C47—41no—
390C22×C4×C47—41no—
391C22×C4×C47—41no—
392C22×C4×C47—41no—
393C22×C4×C47—41no—
394C22×C4×C47—41no—
395C22×C4×C47—41no—
396C22×C4×C47—41no—
397C22×C4×C47—41no—
398C22×C4×C47—41no—
399C22×C4×C47—41no—
400C22×C4×C47—41no—
401C22×C4×C47—41no—
402C22×C4×C47—41no—
403C22×C4×C47—41no—
404C22×C4×C47—41no—
405C22×C4×C47—41no—
406C22×C4×C47—41no—
407C22×C4×C47—41no—
408C22×C4×C47—41no—
409C22×C4×C47—41no—
410C22×C4×C47—41no—
411C22×C4×C47—41no—
412C22×C4×C47—41no—
413C22×C4×C47—41no—
414C22×C4×C47—41no—
415C22×C4×C47—41no—
416C22×C4×C47C22×C414yes—
417C22×C4×C47C22×C414yes—
418C22×C4×C47C22×C414yes—
419C22×C4×C47C22×C414yes—
420C22×C4×C47C22×C414yes—
421C22×C4×C47C22×C414yes—
422C22×C4×C47C2411yescharacteristic
423C22×C4×C47C2411yescharacteristic
424C22×C4×C47C2411yescharacteristic
425C22×C4×C47C2411yescharacteristic
426C22×C4×C47C2411yescharacteristic
427C22×C4×C47C2411yescharacteristic
428C22×C4×C47C2411yescharacteristic
429C22×C4×C47C2411yescharacteristic
430C22×C4×C47C2411yescharacteristic
431C22×C4×C47C2411yescharacteristic
432C22×C4×C47C2411yescharacteristic
433C22×C4×C47C2411yescharacteristic
434C22×C4×C47C2411yescharacteristic
435C22×C4×C47C2411yescharacteristic
436C22×C4×C47C2411yescharacteristic
437C22×C4×C47C2411yescharacteristic
438C22×C4×C47C2411yescharacteristic
439C22×C4×C47C2411yescharacteristic
440C22×C4×C47C2411yescharacteristic
441C22×C4×C47C2411yescharacteristic
442C22×C4×C47C2411yescharacteristic
443C22×C4×C47C2411yescharacteristic
444C22×C4×C47C2411yescharacteristic
445C22×C4×C47C2411yescharacteristic
446C22×C4×C47C2411yescharacteristic
447C22×C4×C47C2411yescharacteristic
448C22×C4×C47C2411yescharacteristic
449C4⋊C4×C47—22no—
450C4⋊C4×C47—22no—
451C4⋊C4×C47—22no—
452C4⋊C4×C47—41no—
453C4⋊C4×C47—41no—
454C4⋊C4×C47—41no—
455C4⋊C4×C47—41no—
456C4⋊C4×C47—41no—
457C4⋊C4×C47—41no—
458C4⋊C4×C47—41no—
459C4⋊C4×C47—41no—
460C4⋊C4×C47—41no—
461C4⋊C4×C47—41no—
462C4⋊C4×C47—41no—
463C4⋊C4×C47—41no—
464C4⋊C4×C47—41no—
465C4⋊C4×C47—41no—
466C4⋊C4×C47—41no—
467C4⋊C4×C47—41no—
468C4⋊C4×C47—41no—
469C4⋊C4×C47C22×C414yes—
470C4⋊C4×C47C22×C414yes—
471C4⋊C4×C47C22×C414yes—
472C4⋊C4×C47C22×C414yes—
473C4⋊C4×C47C22×C414yes—
474C4⋊C4×C47C22×C414yes—
475C4⋊C4×C47C22×C414yes—
476C4⋊C4×C47C22×C414yes—
477C4⋊C4×C47C22×C414yes—
478C4⋊C4×C47C22×C414yes—
479C22⋊C4×C47—22no—
480C22⋊C4×C47—22no—
481C22⋊C4×C47—22no—
482C22⋊C4×C47—41no—
483C22⋊C4×C47—41no—
484C22⋊C4×C47—41no—
485C22⋊C4×C47—41no—
486C22⋊C4×C47—41no—
487C22⋊C4×C47—41no—
488C22⋊C4×C47—41no—
489C22⋊C4×C47—41no—
490C22⋊C4×C47—41no—
491C22⋊C4×C47—41no—
492C22⋊C4×C47—41no—
493C22⋊C4×C47—41no—
494C22⋊C4×C47—41no—
495C22⋊C4×C47—41no—
496C22⋊C4×C47—41no—
497C22⋊C4×C47—41no—
498C22⋊C4×C47—41no—
499C22⋊C4×C47—41no—
500C22⋊C4×C47—41no—
501C22⋊C4×C47—41no—
502C22⋊C4×C47—41no—
503C22⋊C4×C47—41no—
504C22⋊C4×C47—41no—
505C22⋊C4×C47C22×C414yes—
506C22⋊C4×C47C22×C414yes—
507C22⋊C4×C47C22×C414yes—
508C22⋊C4×C47C22×C414yes—
509C22⋊C4×C47C22×C414yes—
510C22⋊C4×C47C22×C414yes—
511C22⋊C4×C47C22×C414yes—
512C22⋊C4×C47C22×C414yes—
513C22⋊C4×C47C22×C414yes—
514C22⋊C4×C47C22×C414yes—
515C42×C47—22no—
516C42×C47—22no—
517C42×C47—41no—
518C42×C47—41no—
519C42×C47—41no—
520C42×C47—41no—
521C42×C47—41no—
522C42×C47—41no—
523C42×C47—41no—
524C42×C47—41no—
525C42×C47—41no—
526C42×C47—41no—
527C42×C47—41no—
528C42×C47—41no—
529C42×C47—41no—
530C42×C47—41no—
531C42×C47—41no—
532C42×C47—41no—
533C42×C47—41no—
534C42×C47—41no—
535C42×C47C22×C414yes—
536C42×C47C22×C414yes—
537C42×C47C22×C414yes—
538C23×C47—21no—
539C23×C47—21no—
540C23×C47—21no—
541C23×C47—21no—
542C23×C47—21no—
543C23×C47—21no—
544C23×C47—21no—
545C23×C47—21no—
546C23×C47—21no—
547C23×C47—21no—
548C23×C47—21no—
549C23×C47—21no—
550C23×C47—21no—
551C23×C47—21no—
552C23×C47—21no—
553C23×C47—21no—
554C23×C47—21no—
555C23×C47—21no—
556C23×C47—21no—
557C23×C47—21no—
558C23×C47—21no—
559C23×C47—21no—
560C23×C47—21no—
561C23×C47—21no—
562C23×C47C23×C412yes—
563C23×C47C23×C412yes—
564C23×C47C23×C412yes—
565C23×C47C23×C412yes—
566C23×C47C2511yescharacteristic
567D4×C47—44no—
568D4×C47—44no—
569D4×C47—44no—
570D4×C47—44no—
571D4×C47—44no—
572D4×C47—44no—
573C2×C4×C47—21no—
574C2×C4×C47—21no—
575C2×C4×C47—21no—
576C2×C4×C47—21no—
577C2×C4×C47—21no—
578C2×C4×C47—21no—
579C2×C4×C47—21no—
580C2×C4×C47—21no—
581C2×C4×C47—21no—
582C2×C4×C47—21no—
583C2×C4×C47—21no—
584C2×C4×C47—21no—
585C2×C4×C47—21no—
586C2×C4×C47—21no—
587C2×C4×C47—21no—
588C2×C4×C47—21no—
589C2×C4×C47—21no—
590C2×C4×C47—21no—
591C2×C4×C47—21no—
592C2×C4×C47—21no—
593C2×C4×C47—21no—
594C2×C4×C47—21no—
595C2×C4×C47—21no—
596C2×C4×C47—21no—
597C2×C4×C47—21no—
598C2×C4×C47—21no—
599C2×C4×C47—21no—
600C2×C4×C47—21no—
601C2×C4×C47—21no—
602C2×C4×C47—21no—
603C2×C4×C47—21no—
604C2×C4×C47—21no—
605C2×C4×C47—21no—
606C2×C4×C47—21no—
607C2×C4×C47—21no—
608C2×C4×C47—21no—
609C2×C4×C47—21no—
610C2×C4×C47—21no—
611C2×C4×C47—21no—
612C2×C4×C47—21no—
613C2×C4×C47—21no—
614C2×C4×C47—21no—
615C2×C4×C47—21no—
616C2×C4×C47—21no—
617C2×C4×C47—21no—
618C2×C4×C47—21no—
619C2×C4×C47—21no—
620C2×C4×C47—21no—
621C2×C4×C47—21no—
622C2×C4×C47—21no—
623C2×C4×C47—21no—
624C2×C4×C47—21no—
625C2×C4×C47—21no—
626C2×C4×C47—21no—
627C2×C4×C47—21no—
628C2×C4×C47—21no—
629C2×C4×C47—21no—
630C2×C4×C47—21no—
631C2×C4×C47—21no—
632C2×C4×C47—21no—
633C2×C4×C47—21no—
634C2×C4×C47—21no—
635C2×C4×C47—21no—
636C2×C4×C47—21no—
637C2×C4×C47—21no—
638C2×C4×C47—21no—
639C2×C4×C47—21no—
640C2×C4×C47—21no—
641C2×C4×C47—21no—
642C2×C4×C47—44no—
643C2×C4×C47—44no—
644C2×C4×C47—44no—
645C2×C4×C47—44no—
646C2×C4×C47—44no—
647C2×C4×C47—44no—
648C2×C4×C47—82no—
649C2×C4×C47—82no—
650C2×C4×C47—82no—
651C2×C4×C47—82no—
652C2×C4×C47—82no—
653C2×C4×C47—82no—
654C2×C4×C47C23×C412yes—
655C2×C4×C47C23×C412yes—
656C2×C4×C47C23×C412yes—
657C2×C4×C47C23×C412yes—
658C2×C4×C47C23×C412yes—
659C2×C4×C47C23×C412yes—
660C2×C4×C47C23×C412yes—
661C2×C4×C47C23×C412yes—
662C2×C4×C47C23×C412yes—
663C2×C4×C47C23×C412yes—
664C2×C4×C47C23×C412yes—
665C2×C4×C47H(5,𝔽2)12yes—
666#34506C4711yesmaximal, characteristic, direct product factor, Sylow
667C22×C47—22no—
668C22×C47—22no—
669C22×C47—22no—
670C22×C47—22no—
671C22×C47—22no—
672C22×C47—22no—
673C22×C47—22no—
674C22×C47—22no—
675C22×C47—22no—
676C22×C47—22no—
677C22×C47—22no—
678C22×C47—22no—
679C22×C47—41no—
680C22×C47—41no—
681C22×C47—41no—
682C22×C47—41no—
683C22×C47—41no—
684C22×C47—41no—
685C22×C47—41no—
686C22×C47—41no—
687C22×C47—41no—
688C22×C47—41no—
689C22×C47—41no—
690C22×C47—41no—
691C22×C47—41no—
692C22×C47—41no—
693C22×C47—41no—
694C22×C47—41no—
695C22×C47C24×C411yescharacteristic
696C22×C47C2×H(5,𝔽2)11yescharacteristic
697C22×C47#58511yescharacteristic
698C22×C47#58511yescharacteristic
699C22×C47#58511yescharacteristic
700C22×C47#58511yescharacteristic
701C22×C47#58511yescharacteristic
702C4×C47—22no—
703C4×C47—22no—
704C4×C47—22no—
705C4×C47—22no—
706C4×C47—22no—
707C4×C47—22no—
708C4×C47—22no—
709C4×C47—22no—
710C4×C47—22no—
711C4×C47—22no—
712C4×C47—22no—
713C4×C47—22no—
714C4×C47—41no—
715C4×C47—41no—
716C4×C47—41no—
717C4×C47—41no—
718C4×C47—41no—
719C4×C47—41no—
720C4×C47—41no—
721C4×C47—41no—
722C4×C47—41no—
723C4×C47—41no—
724C4×C47—41no—
725C4×C47—41no—
726C4×C47—41no—
727C4×C47—41no—
728C4×C47—41no—
729C2×#553C2×C4711yescharacteristic
730#2382C2×C4711yescharacteristic, complemented
731#2377C2×C4711yescharacteristic, complemented
732#2377C2×C4711yescharacteristic, complemented
733#2376C2×C4711yescharacteristic, complemented
734#2373C2×C4711yescharacteristic, complemented
735#2373C2×C4711yescharacteristic, complemented
736#2364C2×C4711yescharacteristic, complemented
737#2363C2×C4711yescharacteristic, complemented
738#2359C2×C4711yescharacteristic, complemented
739#2357C2×C4711yescharacteristic, complemented
740#2353C2×C4711yescharacteristic, complemented
741#2352C2×C4711yescharacteristic, complemented
742#2352C2×C4711yescharacteristic, complemented
743#2344C2×C4711yescharacteristic, complemented
744#2343C2×C4711yescharacteristic, complemented
745#2336C2×C4711yescharacteristic, complemented
746#2335C2×C4711yescharacteristic, complemented
747#2334C2×C4711yescharacteristic, complemented
748#2333C2×C4711yescharacteristic, complemented
749#2333C2×C4711yescharacteristic, complemented
750#2333C2×C4711yescharacteristic, complemented
751#2324C2×C4711yescharacteristic, complemented
752#2322C2×C4711yescharacteristic, complemented
753#2319C2×C4711yescharacteristic, complemented
754#2318C2×C4711yescharacteristic, complemented
755#2318C2×C4711yescharacteristic, complemented
756#2313C2×C4711yescharacteristic, complemented
757C4×#126C2×C4711yescharacteristic, complemented
758#2298C2×C4711yescharacteristic, complemented
759#2293C2×C4711yescharacteristic, complemented
760C2×C47—42no—
761C2×C47—42no—
762C2×C47—42no—
763C2×C47—42no—
764C2×C47#342811yescharacteristic
765C2×C47#342811yescharacteristic
766C2×C47C4×H(5,𝔽2)11yescharacteristic
767C2×C47#356011yescharacteristic
768C2×C47#356211yescharacteristic
769C2×C47#356611yescharacteristic
770C2×C47#356711yescharacteristic
771#553C4×C47116yescomplemented
772C2×#126C22×C4711yescharacteristic
773C2×#126C22×C4711yescharacteristic
774C2×#125C22×C4711yescharacteristic
775C2×#123C22×C4711yescharacteristic
776C2×#123C22×C4711yescharacteristic
777C2×#121C22×C4711yescharacteristic
778C2×#121C22×C4711yescharacteristic
779C2×#121C22×C4711yescharacteristic
780C2×#121C22×C4711yescharacteristic
781C2×C4×D4C22×C4711yescharacteristic
782C2×C4×D4C22×C4711yescharacteristic
783C2×C4×D4C22×C4711yescharacteristic
784C2×C4×D4C22×C4711yescharacteristic
785C2×C4×D4C22×C4711yescharacteristic
786C2×C4×D4C22×C4711yescharacteristic
787C2×#117C22×C4711yescharacteristic
788C2×#117C22×C4711yescharacteristic
789C2×#117C22×C4711yescharacteristic
790C2×#117C22×C4711yescharacteristic
791C22×C4⋊C4C22×C4711yescharacteristic
792C22×C4⋊C4C22×C4711yescharacteristic
793#390C22×C4711yescharacteristic
794#390C22×C4711yescharacteristic
795#390C22×C4711yescharacteristic
796#390C22×C4711yescharacteristic
797#390C22×C4711yescharacteristic
798#390C22×C4711yescharacteristic
799#390C22×C4711yescharacteristic
800#390C22×C4711yescharacteristic
801#389C22×C4711yescharacteristic
802#389C22×C4711yescharacteristic
803#389C22×C4711yescharacteristic
804#389C22×C4711yescharacteristic
805#389C22×C4711yescharacteristic
806#389C22×C4711yescharacteristic
807#389C22×C4711yescharacteristic
808#389C22×C4711yescharacteristic
809#388C22×C4711yescharacteristic
810#388C22×C4711yescharacteristic
811#388C22×C4711yescharacteristic
812#388C22×C4711yescharacteristic
813#388C22×C4711yescharacteristic
814#388C22×C4711yescharacteristic
815#388C22×C4711yescharacteristic
816#388C22×C4711yescharacteristic
817#388C22×C4711yescharacteristic
818#388C22×C4711yescharacteristic
819#388C22×C4711yescharacteristic
820#388C22×C4711yescharacteristic
821#388C22×C4711yescharacteristic
822#388C22×C4711yescharacteristic
823#388C22×C4711yescharacteristic
824#388C22×C4711yescharacteristic
825#388C22×C4711yescharacteristic
826#388C22×C4711yescharacteristic
827#388C22×C4711yescharacteristic
828#388C22×C4711yescharacteristic
829#388C22×C4711yescharacteristic
830#388C22×C4711yescharacteristic
831#387C22×C4711yescharacteristic
832#387C22×C4711yescharacteristic
833#387C22×C4711yescharacteristic
834#387C22×C4711yescharacteristic
835#387C22×C4711yescharacteristic
836#387C22×C4711yescharacteristic
837#387C22×C4711yescharacteristic
838#387C22×C4711yescharacteristic
839#387C22×C4711yescharacteristic
840#387C22×C4711yescharacteristic
841#387C22×C4711yescharacteristic
842#387C22×C4711yescharacteristic
843#387C22×C4711yescharacteristic
844#387C22×C4711yescharacteristic
845#387C22×C4711yescharacteristic
846#387C22×C4711yescharacteristic
847#387C22×C4711yescharacteristic
848#387C22×C4711yescharacteristic
849#387C22×C4711yescharacteristic
850#387C22×C4711yescharacteristic
851#387C22×C4711yescharacteristic
852#387C22×C4711yescharacteristic
853#387C22×C4711yescharacteristic
854#387C22×C4711yescharacteristic
855#387C22×C4711yescharacteristic
856#387C22×C4711yescharacteristic
857#386C22×C4711yescharacteristic
858#386C22×C4711yescharacteristic
859#386C22×C4711yescharacteristic
860#386C22×C4711yescharacteristic
861#386C22×C4711yescharacteristic
862#386C22×C4711yescharacteristic
863#386C22×C4711yescharacteristic
864#386C22×C4711yescharacteristic
865#386C22×C4711yescharacteristic
866#386C22×C4711yescharacteristic
867#386C22×C4711yescharacteristic
868#386C22×C4711yescharacteristic
869#386C22×C4711yescharacteristic
870#386C22×C4711yescharacteristic
871#385C22×C4711yescharacteristic
872#385C22×C4711yescharacteristic
873#385C22×C4711yescharacteristic
874#385C22×C4711yescharacteristic
875#385C22×C4711yescharacteristic
876#385C22×C4711yescharacteristic
877#385C22×C4711yescharacteristic
878#385C22×C4711yescharacteristic
879#383C22×C4711yescharacteristic
880#383C22×C4711yescharacteristic
881#382C22×C4711yescharacteristic
882#382C22×C4711yescharacteristic
883#382C22×C4711yescharacteristic
884#381C22×C4711yescharacteristic
885#381C22×C4711yescharacteristic
886#381C22×C4711yescharacteristic
887#381C22×C4711yescharacteristic
888#381C22×C4711yescharacteristic
889#381C22×C4711yescharacteristic
890#380C22×C4711yescharacteristic
891#380C22×C4711yescharacteristic
892#380C22×C4711yescharacteristic
893#380C22×C4711yescharacteristic
894#380C22×C4711yescharacteristic
895#380C22×C4711yescharacteristic
896C4×C4⋊C4C22×C4711yescharacteristic
897C4×C4⋊C4C22×C4711yescharacteristic
898C4×C4⋊C4C22×C4711yescharacteristic
899C4×C4⋊C4C22×C4711yescharacteristic
900C4×C4⋊C4C22×C4711yescharacteristic
901C4×C4⋊C4C22×C4711yescharacteristic
902C4×C4⋊C4C22×C4711yescharacteristic
903C4×C4⋊C4C22×C4711yescharacteristic
904C4×C4⋊C4C22×C4711yescharacteristic
905C4×C4⋊C4C22×C4711yescharacteristic
906C4×C22⋊C4C22×C4711yescharacteristic
907C4×C22⋊C4C22×C4711yescharacteristic
908C4×C22⋊C4C22×C4711yescharacteristic
909C4×C22⋊C4C22×C4711yescharacteristic
910C4×C22⋊C4C22×C4711yescharacteristic
911C4×C22⋊C4C22×C4711yescharacteristic
912C4×C22⋊C4C22×C4711yescharacteristic
913C4×C22⋊C4C22×C4711yescharacteristic
914C4×C22⋊C4C22×C4711yescharacteristic
915C4×C22⋊C4C22×C4711yescharacteristic
916C4×C22⋊C4C22×C4711yescharacteristic
917C4×C22⋊C4C22×C4711yescharacteristic
918C4×C22⋊C4C22×C4711yescharacteristic
919C4×C22⋊C4C22×C4711yescharacteristic
920C4×C22⋊C4C22×C4711yescharacteristic
921C4×C22⋊C4C22×C4711yescharacteristic
922#376C22×C4711yescharacteristic
923#376C22×C4711yescharacteristic
924C2×#95C22×C4711yescharacteristic
925C2×#95C22×C4711yescharacteristic
926C43C22×C4711yescharacteristic
927C47#3450611yescharacteristic, direct product factor, Sylow
928C22×D4C23×C4711yescharacteristic
929C22×D4C23×C4711yescharacteristic
930C22×D4C23×C4711yescharacteristic
931C22×D4C23×C4711yescharacteristic
932C22×D4C23×C4711yescharacteristic
933C22×D4C23×C4711yescharacteristic
934C23×C4C23×C4711yescharacteristic
935C23×C4C23×C4711yescharacteristic
936C23×C4C23×C4711yescharacteristic
937C23×C4C23×C4711yescharacteristic
938C23×C4C23×C4711yescharacteristic
939C23×C4C23×C4711yescharacteristic
940C23×C4C23×C4711yescharacteristic
941C23×C4C23×C4711yescharacteristic
942C23×C4C23×C4711yescharacteristic
943C23×C4C23×C4711yescharacteristic
944C23×C4C23×C4711yescharacteristic
945C23×C4C23×C4711yescharacteristic
946#126C2×C4×C4718yescomplemented
947#126C2×C4×C4718yescomplemented
948#125C2×C4×C4718yescomplemented
949#123C2×C4×C4718yescomplemented
950#123C2×C4×C4718yescomplemented
951#121C2×C4×C4718yes—
952#121C2×C4×C4718yescomplemented
953#121C2×C4×C4718yescomplemented
954#121C2×C4×C4718yescomplemented
955C4×D4—42no—
956C4×D4—42no—
957C4×D4C2×C4×C4718yescomplemented
958C4×D4C2×C4×C4718yescomplemented
959C4×D4C2×C4×C4718yescomplemented
960C4×D4C2×C4×C4718yescomplemented
961#117—42no—
962#117—42no—
963#117—42no—
964#117C2×C4×C4718yescomplemented
965C2×C4⋊C4—42no—
966C2×C4⋊C4C2×C4×C4718yescomplemented
967C2×C4⋊C4C23×C4711yescharacteristic
968C2×C4⋊C4C23×C4711yescharacteristic
969C2×C4⋊C4C23×C4711yescharacteristic
970C2×C4⋊C4C23×C4711yescharacteristic
971C2×C4⋊C4C23×C4711yescharacteristic
972C2×C4⋊C4C23×C4711yescharacteristic
973C2×C4⋊C4C23×C4711yescharacteristic
974C2×C4⋊C4C23×C4711yescharacteristic
975C2×C4⋊C4C23×C4711yescharacteristic
976C2×C4⋊C4C23×C4711yescharacteristic
977C2×C4⋊C4C23×C4711yescharacteristic
978C2×C4⋊C4C23×C4711yescharacteristic
979C2×C4⋊C4C23×C4711yescharacteristic
980C2×C4⋊C4C23×C4711yescharacteristic
981C2×C4⋊C4C23×C4711yescharacteristic
982C2×C4⋊C4C23×C4711yescharacteristic
983C2×C4⋊C4C23×C4711yescharacteristic
984C2×C4⋊C4C23×C4711yescharacteristic
985C2×C4⋊C4C23×C4711yescharacteristic
986C2×C4⋊C4C23×C4711yescharacteristic
987C2×C4⋊C4C23×C4711yescharacteristic
988C2×C4⋊C4C23×C4711yescharacteristic
989C2×C4⋊C4C23×C4711yescharacteristic
990C2×C4⋊C4C23×C4711yescharacteristic
991C2×C4⋊C4C23×C4711yescharacteristic
992C2×C4⋊C4C23×C4711yescharacteristic
993C2×C4⋊C4C23×C4711yescharacteristic
994C2×C4⋊C4C23×C4711yescharacteristic
995C2×C4⋊C4C23×C4711yescharacteristic
996C2×C4⋊C4C23×C4711yescharacteristic
997C2×C22⋊C4C23×C4711yescharacteristic
998C2×C22⋊C4C23×C4711yescharacteristic
999C2×C22⋊C4C23×C4711yescharacteristic
1000C2×C22⋊C4C23×C4711yescharacteristic
1001C2×C22⋊C4C23×C4711yescharacteristic
1002C2×C22⋊C4C23×C4711yescharacteristic
1003C2×C22⋊C4C23×C4711yescharacteristic
1004C2×C22⋊C4C23×C4711yescharacteristic
1005C2×C22⋊C4C23×C4711yescharacteristic
1006C2×C22⋊C4C23×C4711yescharacteristic
1007C2×C22⋊C4C23×C4711yescharacteristic
1008C2×C22⋊C4C23×C4711yescharacteristic
1009C2×C22⋊C4C23×C4711yescharacteristic
1010C2×C22⋊C4C23×C4711yescharacteristic
1011C2×C22⋊C4C23×C4711yescharacteristic
1012C2×C22⋊C4C23×C4711yescharacteristic
1013C2×C22⋊C4C23×C4711yescharacteristic
1014C2×C22⋊C4C23×C4711yescharacteristic
1015C2×C22⋊C4C23×C4711yescharacteristic
1016C2×C22⋊C4C23×C4711yescharacteristic
1017C2×C22⋊C4C23×C4711yescharacteristic
1018C2×C22⋊C4C23×C4711yescharacteristic
1019C2×C22⋊C4C23×C4711yescharacteristic
1020C2×C22⋊C4C23×C4711yescharacteristic
1021C2×C22⋊C4C23×C4711yescharacteristic
1022C2×C22⋊C4C23×C4711yescharacteristic
1023C2×C22⋊C4C23×C4711yescharacteristic
1024C2×C22⋊C4C23×C4711yescharacteristic
1025C2×C22⋊C4C23×C4711yescharacteristic
1026C2×C22⋊C4C23×C4711yescharacteristic
1027C2×C22⋊C4C23×C4711yescharacteristic
1028C2×C22⋊C4C23×C4711yescharacteristic
1029C2×C22⋊C4C23×C4711yescharacteristic
1030C2×C22⋊C4C23×C4711yescharacteristic
1031C2×C22⋊C4C23×C4711yescharacteristic
1032C2×C22⋊C4C23×C4711yescharacteristic
1033C2×C42C23×C4711yescharacteristic
1034C2×C42C23×C4711yescharacteristic
1035C2×C42C23×C4711yescharacteristic
1036C2×C42C23×C4711yescharacteristic
1037C2×C42C23×C4711yescharacteristic
1038C2×C42C23×C4711yescharacteristic
1039C2×C42C23×C4711yescharacteristic
1040C2×C42C23×C4711yescharacteristic
1041C2×C42C23×C4711yescharacteristic
1042C2×C42C23×C4711yescharacteristic
1043C2×C42C23×C4711yescharacteristic
1044C2×C42C23×C4711yescharacteristic
1045C2×C42C23×C4711yescharacteristic
1046C2×C42C23×C4711yescharacteristic
1047C2×C42C23×C4711yescharacteristic
1048C2×C42C23×C4711yescharacteristic
1049C2×C42C23×C4711yescharacteristic
1050C2×C42C23×C4711yescharacteristic
1051C2×C42C23×C4711yescharacteristic
1052C2×C42C23×C4711yescharacteristic
1053C2×C42C23×C4711yescharacteristic
1054C2×C42C23×C4711yescharacteristic
1055C2×C42C23×C4711yescharacteristic
1056#95C23×C4711yescharacteristic
1057#95C23×C4711yescharacteristic
1058#95C23×C4711yescharacteristic
1059#95C23×C4711yescharacteristic
1060#95C23×C4711yescharacteristic
1061#95C23×C4711yescharacteristic
1062#95C23×C4711yescharacteristic
1063#95C23×C4711yescharacteristic
1064#95C23×C4711yescharacteristic
1065#95C23×C4711yescharacteristic
1066#95C23×C4711yescharacteristic
1067#95C23×C4711yescharacteristic
1068#95C23×C4711yescharacteristic
1069#95C23×C4711yescharacteristic
1070#95C23×C4711yescharacteristic
1071#95C23×C4711yescharacteristic
1072#95C23×C4711yescharacteristic
1073#95C23×C4711yescharacteristic
1074#95C23×C4711yescharacteristic
1075#95C23×C4711yescharacteristic
1076#95C23×C4711yescharacteristic
1077#95C23×C4711yescharacteristic
1078#95C23×C4711yescharacteristic
1079#95C23×C4711yescharacteristic
1080#95C23×C4711yescharacteristic
1081#95C23×C4711yescharacteristic
1082#95C23×C4711yescharacteristic
1083#95C23×C4711yescharacteristic
1084#95C23×C4711yescharacteristic
1085#95C23×C4711yescharacteristic
1086#95C23×C4711yescharacteristic
1087#95C23×C4711yescharacteristic
1088#95C23×C4711yescharacteristic
1089#95C23×C4711yescharacteristic
1090#95C23×C4711yescharacteristic
1091#95C23×C4711yescharacteristic
1092#95C23×C4711yescharacteristic
1093#95C23×C4711yescharacteristic
1094#95C23×C4711yescharacteristic
1095#95C23×C4711yescharacteristic
1096#95C23×C4711yescharacteristic
1097#95C23×C4711yescharacteristic
1098#95C23×C4711yescharacteristic
1099#95C23×C4711yescharacteristic
1100#95C23×C4711yescharacteristic
1101#95C23×C4711yescharacteristic
1102#95C23×C4711yescharacteristic
1103#95C23×C4711yescharacteristic
1104C24C24×C4711yescharacteristic
1105C24C24×C4711yescharacteristic
1106C24C24×C4711yescharacteristic
1107C24C24×C4711yescharacteristic
1108C2×D4—41no—
1109C2×D4—41no—
1110C2×D4—41no—
1111C2×D4—41no—
1112C2×D4—41no—
1113C2×D4—41no—
1114C2×D4—41no—
1115C2×D4—41no—
1116C2×D4—41no—
1117C2×D4—41no—
1118C2×D4—41no—
1119C2×D4—41no—
1120C2×D4C22×C4×C4714yes—
1121C2×D4C22×C4×C4714yes—
1122C2×D4C22×C4×C4714yes—
1123C2×D4C22×C4×C4714yes—
1124C2×D4C22×C4×C4714yes—
1125C2×D4C22×C4×C4714yes—
1126C22×C4—22no—
1127C22×C4—41no—
1128C22×C4—41no—
1129C22×C4—41no—
1130C22×C4—41no—
1131C22×C4—41no—
1132C22×C4—41no—
1133C22×C4—41no—
1134C22×C4—41no—
1135C22×C4—41no—
1136C22×C4—41no—
1137C22×C4—41no—
1138C22×C4—41no—
1139C22×C4—41no—
1140C22×C4—41no—
1141C22×C4—41no—
1142C22×C4—41no—
1143C22×C4—41no—
1144C22×C4—41no—
1145C22×C4—41no—
1146C22×C4—41no—
1147C22×C4—41no—
1148C22×C4—41no—
1149C22×C4—41no—
1150C22×C4—41no—
1151C22×C4—41no—
1152C22×C4—41no—
1153C22×C4—41no—
1154C22×C4—41no—
1155C22×C4—41no—
1156C22×C4C22×C4×C4714yes—
1157C22×C4C22×C4×C4714yes—
1158C22×C4C22×C4×C4714yes—
1159C22×C4C22×C4×C4714yes—
1160C22×C4C22×C4×C4714yes—
1161C22×C4C22×C4×C4714yes—
1162C22×C4C24×C4711yescharacteristic
1163C22×C4C24×C4711yescharacteristic
1164C22×C4C24×C4711yescharacteristic
1165C22×C4C24×C4711yescharacteristic
1166C22×C4C24×C4711yescharacteristic
1167C22×C4C24×C4711yescharacteristic
1168C22×C4C24×C4711yescharacteristic
1169C22×C4C24×C4711yescharacteristic
1170C22×C4C24×C4711yescharacteristic
1171C22×C4C24×C4711yescharacteristic
1172C22×C4C24×C4711yescharacteristic
1173C22×C4C24×C4711yescharacteristic
1174C22×C4C24×C4711yescharacteristic
1175C22×C4C24×C4711yescharacteristic
1176C22×C4C24×C4711yescharacteristic
1177C22×C4C24×C4711yescharacteristic
1178C22×C4C24×C4711yescharacteristic
1179C22×C4C24×C4711yescharacteristic
1180C22×C4C24×C4711yescharacteristic
1181C22×C4C24×C4711yescharacteristic
1182C22×C4C24×C4711yescharacteristic
1183C22×C4C24×C4711yescharacteristic
1184C22×C4C24×C4711yescharacteristic
1185C22×C4C24×C4711yescharacteristic
1186C22×C4C24×C4711yescharacteristic
1187C22×C4C24×C4711yescharacteristic
1188C22×C4C24×C4711yescharacteristic
1189C4⋊C4—22no—
1190C4⋊C4—22no—
1191C4⋊C4—22no—
1192C4⋊C4—41no—
1193C4⋊C4—41no—
1194C4⋊C4—41no—
1195C4⋊C4—41no—
1196C4⋊C4—41no—
1197C4⋊C4—41no—
1198C4⋊C4—41no—
1199C4⋊C4—41no—
1200C4⋊C4—41no—
1201C4⋊C4—41no—
1202C4⋊C4—41no—
1203C4⋊C4—41no—
1204C4⋊C4—41no—
1205C4⋊C4—41no—
1206C4⋊C4—41no—
1207C4⋊C4—41no—
1208C4⋊C4—41no—
1209C4⋊C4C22×C4×C4714yes—
1210C4⋊C4C22×C4×C4714yes—
1211C4⋊C4C22×C4×C4714yes—
1212C4⋊C4C22×C4×C4714yes—
1213C4⋊C4C22×C4×C4714yes—
1214C4⋊C4C22×C4×C4714yes—
1215C4⋊C4C22×C4×C4714yes—
1216C4⋊C4C22×C4×C4714yes—
1217C4⋊C4C22×C4×C4714yes—
1218C4⋊C4C22×C4×C4714yes—
1219C22⋊C4—22no—
1220C22⋊C4—22no—
1221C22⋊C4—22no—
1222C22⋊C4—41no—
1223C22⋊C4—41no—
1224C22⋊C4—41no—
1225C22⋊C4—41no—
1226C22⋊C4—41no—
1227C22⋊C4—41no—
1228C22⋊C4—41no—
1229C22⋊C4—41no—
1230C22⋊C4—41no—
1231C22⋊C4—41no—
1232C22⋊C4—41no—
1233C22⋊C4—41no—
1234C22⋊C4—41no—
1235C22⋊C4—41no—
1236C22⋊C4—41no—
1237C22⋊C4—41no—
1238C22⋊C4—41no—
1239C22⋊C4—41no—
1240C22⋊C4—41no—
1241C22⋊C4—41no—
1242C22⋊C4—41no—
1243C22⋊C4—41no—
1244C22⋊C4—41no—
1245C22⋊C4C22×C4×C4714yes—
1246C22⋊C4C22×C4×C4714yes—
1247C22⋊C4C22×C4×C4714yes—
1248C22⋊C4C22×C4×C4714yes—
1249C22⋊C4C22×C4×C4714yes—
1250C22⋊C4C22×C4×C4714yes—
1251C22⋊C4C22×C4×C4714yes—
1252C22⋊C4C22×C4×C4714yes—
1253C22⋊C4C22×C4×C4714yes—
1254C22⋊C4C22×C4×C4714yes—
1255C42—22no—
1256C42—22no—
1257C42—41no—
1258C42—41no—
1259C42—41no—
1260C42—41no—
1261C42—41no—
1262C42—41no—
1263C42—41no—
1264C42—41no—
1265C42—41no—
1266C42—41no—
1267C42—41no—
1268C42—41no—
1269C42—41no—
1270C42—41no—
1271C42—41no—
1272C42—41no—
1273C42—41no—
1274C42—41no—
1275C42C22×C4×C4714yes—
1276C42C22×C4×C4714yes—
1277C42C22×C4×C4714yes—
1278C23—21no—
1279C23—21no—
1280C23—21no—
1281C23—21no—
1282C23—21no—
1283C23—21no—
1284C23—21no—
1285C23—21no—
1286C23—21no—
1287C23—21no—
1288C23—21no—
1289C23—21no—
1290C23—21no—
1291C23—21no—
1292C23—21no—
1293C23—21no—
1294C23—21no—
1295C23—21no—
1296C23—21no—
1297C23—21no—
1298C23—21no—
1299C23—21no—
1300C23—21no—
1301C23—21no—
1302C23C23×C4×C4712yes—
1303C23C23×C4×C4712yes—
1304C23C23×C4×C4712yes—
1305C23C23×C4×C4712yes—
1306C23C25×C4711yescharacteristic
1307D4—44no—
1308D4—44no—
1309D4—44no—
1310D4—44no—
1311D4—44no—
1312D4—44no—
1313C2×C4—21no—
1314C2×C4—21no—
1315C2×C4—21no—
1316C2×C4—21no—
1317C2×C4—21no—
1318C2×C4—21no—
1319C2×C4—21no—
1320C2×C4—21no—
1321C2×C4—21no—
1322C2×C4—21no—
1323C2×C4—21no—
1324C2×C4—21no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—21no—
1328C2×C4—21no—
1329C2×C4—21no—
1330C2×C4—21no—
1331C2×C4—21no—
1332C2×C4—21no—
1333C2×C4—21no—
1334C2×C4—21no—
1335C2×C4—21no—
1336C2×C4—21no—
1337C2×C4—21no—
1338C2×C4—21no—
1339C2×C4—21no—
1340C2×C4—21no—
1341C2×C4—21no—
1342C2×C4—21no—
1343C2×C4—21no—
1344C2×C4—21no—
1345C2×C4—21no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—21no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—21no—
1354C2×C4—21no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—21no—
1360C2×C4—21no—
1361C2×C4—21no—
1362C2×C4—21no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—21no—
1381C2×C4—21no—
1382C2×C4—44no—
1383C2×C4—44no—
1384C2×C4—44no—
1385C2×C4—44no—
1386C2×C4—44no—
1387C2×C4—44no—
1388C2×C4—82no—
1389C2×C4—82no—
1390C2×C4—82no—
1391C2×C4—82no—
1392C2×C4—82no—
1393C2×C4—82no—
1394C2×C4C23×C4×C4712yes—
1395C2×C4C23×C4×C4712yes—
1396C2×C4C23×C4×C4712yes—
1397C2×C4C23×C4×C4712yes—
1398C2×C4C23×C4×C4712yes—
1399C2×C4C23×C4×C4712yes—
1400C2×C4C23×C4×C4712yes—
1401C2×C4C23×C4×C4712yes—
1402C2×C4C23×C4×C4712yes—
1403C2×C4C23×C4×C4712yes—
1404C2×C4C23×C4×C4712yes—
1405C2×C4H(5,𝔽2)×C4712yes—
1406C22—22no—
1407C22—22no—
1408C22—22no—
1409C22—22no—
1410C22—22no—
1411C22—22no—
1412C22—22no—
1413C22—22no—
1414C22—22no—
1415C22—22no—
1416C22—22no—
1417C22—22no—
1418C22—41no—
1419C22—41no—
1420C22—41no—
1421C22—41no—
1422C22—41no—
1423C22—41no—
1424C22—41no—
1425C22—41no—
1426C22—41no—
1427C22—41no—
1428C22—41no—
1429C22—41no—
1430C22—41no—
1431C22—41no—
1432C22—41no—
1433C22—41no—
1434C22C24×C4×C4711yescharacteristic
1435C22C2×H(5,𝔽2)×C4711yescharacteristic
1436C22C47×#58511yescharacteristic
1437C22C47×#58511yescharacteristic
1438C22C47×#58511yescharacteristic
1439C22C47×#58511yescharacteristic
1440C22C47×#58511yescharacteristic
1441C4—22no—
1442C4—22no—
1443C4—22no—
1444C4—22no—
1445C4—22no—
1446C4—22no—
1447C4—22no—
1448C4—22no—
1449C4—22no—
1450C4—22no—
1451C4—22no—
1452C4—22no—
1453C4—41no—
1454C4—41no—
1455C4—41no—
1456C4—41no—
1457C4—41no—
1458C4—41no—
1459C4—41no—
1460C4—41no—
1461C4—41no—
1462C4—41no—
1463C4—41no—
1464C4—41no—
1465C4—41no—
1466C4—41no—
1467C4—41no—
1468C2—42no—
1469C2—42no—
1470C2—42no—
1471C2—42no—
1472C2C47×#342811yescharacteristic
1473C2C47×#342811yescharacteristic
1474C2C4×H(5,𝔽2)×C4711yescharacteristic
1475C2C47×#356011yescharacteristic
1476C2C47×#356211yescharacteristic
1477C2C47×#356611yescharacteristic
1478C2C47×#356711yescharacteristic
subgroupG/H
center, socleC23×C47C25
commutatorC22C24×C4×C47
Frattini, cosocleC23C25×C47
prime radicalC2×C47×#553C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2382C2semidirect
3. C47×#2377C2semidirect
4. C47×#2377C2semidirect
5. C47×#2376C2semidirect
6. C47×#2373C2semidirect
7. C47×#2373C2semidirect
8. C47×#2364C2semidirect
9. C47×#2363C2semidirect
10. C47×#2359C2semidirect
11. C47×#2357C2semidirect
12. C47×#2353C2semidirect
13. C47×#2352C2semidirect
14. C47×#2352C2semidirect
15. C47×#2344C2semidirect
16. C47×#2343C2semidirect
17. C47×#2336C2semidirect
18. C47×#2335C2semidirect
19. C47×#2334C2semidirect
20. C47×#2333C2semidirect
21. C47×#2333C2semidirect
22. C47×#2333C2semidirect
23. C47×#2324C2semidirect
24. C47×#2322C2semidirect
25. C47×#2319C2semidirect
26. C47×#2318C2semidirect
27. C47×#2318C2semidirect
28. C47×#2313C2semidirect
29. C4×#126×C47C2semidirect
30. C47×#2298C2semidirect
31. C47×#2293C2semidirect
32. C47×#553C4semidirect
206. #126×C47C2×C4semidirect
207. #126×C47C2×C4semidirect
208. #125×C47C2×C4semidirect
209. #123×C47C2×C4semidirect
210. #123×C47C2×C4semidirect
212. #121×C47C2×C4semidirect
213. #121×C47C2×C4semidirect
214. #121×C47C2×C4semidirect
217. C4×D4×C47C2×C4semidirect
218. C4×D4×C47C2×C4semidirect
219. C4×D4×C47C2×C4semidirect
220. C4×D4×C47C2×C4semidirect
224. #117×C47C2×C4semidirect
226. C2×C4⋊C4×C47C2×C4semidirect
666. #34506C47direct (N × H)
730. #2382C2×C47semidirect
731. #2377C2×C47semidirect
732. #2377C2×C47semidirect
733. #2376C2×C47semidirect
734. #2373C2×C47semidirect
735. #2373C2×C47semidirect
736. #2364C2×C47semidirect
737. #2363C2×C47semidirect
738. #2359C2×C47semidirect
739. #2357C2×C47semidirect
740. #2353C2×C47semidirect
741. #2352C2×C47semidirect
742. #2352C2×C47semidirect
743. #2344C2×C47semidirect
744. #2343C2×C47semidirect
745. #2336C2×C47semidirect
746. #2335C2×C47semidirect
747. #2334C2×C47semidirect
748. #2333C2×C47semidirect
749. #2333C2×C47semidirect
750. #2333C2×C47semidirect
751. #2324C2×C47semidirect
752. #2322C2×C47semidirect
753. #2319C2×C47semidirect
754. #2318C2×C47semidirect
755. #2318C2×C47semidirect
756. #2313C2×C47semidirect
757. C4×#126C2×C47semidirect
758. #2298C2×C47semidirect
759. #2293C2×C47semidirect
771. #553C4×C47semidirect
927. C47#34506direct (N × H)
946. #126C2×C4×C47semidirect
947. #126C2×C4×C47semidirect
948. #125C2×C4×C47semidirect
949. #123C2×C4×C47semidirect
950. #123C2×C4×C47semidirect
952. #121C2×C4×C47semidirect
953. #121C2×C4×C47semidirect
954. #121C2×C4×C47semidirect
957. C4×D4C2×C4×C47semidirect
958. C4×D4C2×C4×C47semidirect
959. C4×D4C2×C4×C47semidirect
960. C4×D4C2×C4×C47semidirect
964. #117C2×C4×C47semidirect
966. C2×C4⋊C4C2×C4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5532
C47×#23822
C47×#23772
C47×#23762
C47×#23732
C47×#23642
C47×#23632
C47×#23592
C47×#23572
C47×#23532
C47×#23522
C47×#23442
C47×#23432
C47×#23362
C47×#23352
C47×#23342
C47×#23332
C47×#23242
C47×#23222
C47×#23192
C47×#23182
C47×#23132
C4×#126×C472
C47×#22982
C47×#22932
#3450647