Finite Group Databasebeta

← #26424497

Subgroups — #26424497

Order 12032.

1494 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251740C211yesmaximal, characteristic, complemented
2#20251274C211yesmaximal, characteristic, complemented
3#20251264C211yesmaximal, characteristic, complemented
4#20251201C211yesmaximal, characteristic, complemented
5#20251173C211yesmaximal, characteristic, complemented
6#20251119C211yesmaximal, characteristic, complemented
7#20251045C211yesmaximal, characteristic
8#20251021C211yesmaximal, characteristic
9#20250890C211yesmaximal, characteristic, complemented
10#20250756C211yesmaximal, characteristic, complemented
11#20250696C211yesmaximal, characteristic, complemented
12#20250583C211yesmaximal, characteristic, complemented
13#20250499C211yesmaximal, characteristic
14#20250215C211yesmaximal, characteristic, complemented
15#20250170C211yesmaximal, characteristic, complemented
16#20250012C211yesmaximal, characteristic
17#20249850C211yesmaximal, characteristic, complemented
18#20249308C211yesmaximal, characteristic
19#20249308C211yesmaximal, characteristic
20#20248861C211yesmaximal, characteristic, complemented
21#20248846C211yesmaximal, characteristic, complemented
22#20248831C211yesmaximal, characteristic, complemented
23#20248816C211yesmaximal, characteristic, complemented
24#20248272C211yesmaximal, characteristic, complemented
25#20248197C211yesmaximal, characteristic, complemented
26#20247611C211yesmaximal, characteristic, complemented
27#20247566C211yesmaximal, characteristic, complemented
28#20246141C211yesmaximal, characteristic, complemented
29#20246141C211yesmaximal, characteristic, complemented
30#20245831C211yesmaximal, characteristic
31C47×#2855C211yesmaximal, characteristic, complemented
32C2×#13094024C2211yescharacteristic
33C2×#13094019C2211yescharacteristic
34C2×#13094015C2211yescharacteristic
35C2×#13094003C2211yescharacteristic
36C2×#13094003C2211yescharacteristic
37C2×C4×C22⋊D47C2211yescharacteristic
38C2×#13093981C2211yescharacteristic
39C47⋊#401C2211yescharacteristic
40#15689065C2211yescharacteristic
41#15689065C2211yescharacteristic
42#15689065C2211yescharacteristic
43#15689065C2211yescharacteristic
44#15689065C2211yescharacteristic
45#15689062C2211yescharacteristic
46#15689062C2211yescharacteristic
47#15689062C2211yescharacteristic
48#15689062C2211yescharacteristic
49#15689062C2211yescharacteristic
50#15689061C2211yescharacteristic
51#15689061C2211yescharacteristic
52#15689058C2211yescharacteristic
53#15689056C2211yescharacteristic
54#15689056C2211yescharacteristic
55#15689056C2211yescharacteristic
56#15689056C2211yescharacteristic
57#15689056C2211yescharacteristic
58#15689056C2211yescharacteristic
59#15689055C2211yescharacteristic
60#15689055C2211yescharacteristic
61#15689055C2211yescharacteristic
62#15689055C2211yescharacteristic
63#15689055C2211yescharacteristic
64#15689055C2211yescharacteristic
65#15689052C2211yescharacteristic
66#15689050C2211yescharacteristic
67#15689050C2211yescharacteristic
68#15689050C2211yescharacteristic
69#15689049C2211yescharacteristic
70#15689048C2211yescharacteristic
71#15689048C2211yescharacteristic
72#15689048C2211yescharacteristic
73#15689048C2211yescharacteristic
74#15689045C2211yescharacteristic
75#15689045C2211yescharacteristic
76#15689045C2211yescharacteristic
77#15689044C2211yescharacteristic
78#15689044C2211yescharacteristic
79#15689042C2211yescharacteristic
80#15689039C2211yescharacteristic
81#15689039C2211yescharacteristic
82#15689039C2211yescharacteristic
83#15689039C2211yescharacteristic
84#15689036C2211yescharacteristic
85#15689036C2211yescharacteristic
86#15689034C2211yescharacteristic
87#15689030C2211yescharacteristic
88#15689030C2211yescharacteristic
89#15689029C2211yescharacteristic
90#15689029C2211yescharacteristic
91#15689027C2211yescharacteristic
92#15689027C2211yescharacteristic
93#15689027C2211yescharacteristic
94#15689027C2211yescharacteristic
95#15689022C2211yescharacteristic
96#15689022C2211yescharacteristic
97#15689022C2211yescharacteristic
98#15689021C2211yescharacteristic
99#15689021C2211yescharacteristic
100#15689021C2211yescharacteristic
101#15689021C2211yescharacteristic
102#15689019C2211yescharacteristic
103#15689017C2211yescharacteristic
104#15689017C2211yescharacteristic
105#15689017C2211yescharacteristic
106#15689017C2211yescharacteristic
107#15689015C2211yescharacteristic
108#15689015C2211yescharacteristic
109#15689015C2211yescharacteristic
110#15689014C2211yescharacteristic
111#15689014C2211yescharacteristic
112#15689013C2211yescharacteristic
113#15689013C2211yescharacteristic
114#15689013C2211yescharacteristic
115#15689012C2211yescharacteristic
116#15689011C2211yescharacteristic
117#15689011C2211yescharacteristic
118#15689011C2211yescharacteristic
119#15689011C2211yescharacteristic
120#15689010C2211yescharacteristic
121#15689010C2211yescharacteristic
122#15689010C2211yescharacteristic
123#15689010C2211yescharacteristic
124#15689009C2211yescharacteristic
125#15689009C2211yescharacteristic
126#15689009C2211yescharacteristic
127#15689009C2211yescharacteristic
128#15689009C2211yescharacteristic
129#15689008C2211yescharacteristic
130#15689008C2211yescharacteristic
131#15689008C2211yescharacteristic
132#15689008C2211yescharacteristic
133#15689007C2211yescharacteristic
134#15689007C2211yescharacteristic
135#15689006C2211yescharacteristic
136#15689006C2211yescharacteristic
137#15689006C2211yescharacteristic
138#15689006C2211yescharacteristic
139#15689006C2211yescharacteristic
140#15689006C2211yescharacteristic
141#15689006C2211yescharacteristic
142#15689005C2211yescharacteristic
143#15689005C2211yescharacteristic
144#15689005C2211yescharacteristic
145#15689005C2211yescharacteristic
146#15689004C2211yescharacteristic
147#15689004C2211yescharacteristic
148#15689004C2211yescharacteristic
149#15689002C2211yescharacteristic
150#15689002C2211yescharacteristic
151#15688997C2211yescharacteristic
152#15688997C2211yescharacteristic
153#15688997C2211yescharacteristic
154#15688997C2211yescharacteristic
155#15688996C2211yescharacteristic
156#15688996C2211yescharacteristic
157#15688993C2211yescharacteristic
158#15688990C2211yescharacteristic
159#15688988C2211yescharacteristic
160#15688983C2211yescharacteristic
161#15688983C2211yescharacteristic
162#15688983C2211yescharacteristic
163#15688983C2211yescharacteristic
164C4×Dic47⋊C4C2211yescharacteristic
165#15688974C2211yescharacteristic
166#15688974C2211yescharacteristic
167#15688974C2211yescharacteristic
168#15688974C2211yescharacteristic
169C4×(C2×D47)⋊C4C2211yescharacteristic
170C4×C22⋊Dic47C2211yescharacteristic
171#15688969C2211yescharacteristic
172C2×C22⋊Q8×C47C2211yescharacteristic
173C22×C42×C47C2211yescharacteristic
174C47×#391C2211yescharacteristic
175C47×#391C2211yescharacteristic
176C47×#389C2211yescharacteristic
177C47×#389C2211yescharacteristic
178C47×#387C2211yescharacteristic
179C47×#387C2211yescharacteristic
180C47×#387C2211yescharacteristic
181C47×#387C2211yescharacteristic
182C47×#385C2211yescharacteristic
183C47×#385C2211yescharacteristic
184C47×#381C2211yescharacteristic
185C47×#381C2211yescharacteristic
186C47×#380C2211yescharacteristic
187C22×Dic94C2311yescharacteristic
188C22×Dic94C2311yescharacteristic
189C22×C22⋊D47C2311yescharacteristic
190C22×C4×D47C2311yescharacteristic
191#13094024—42no—
192#13094019—42no—
193#13094015—42no—
194#13094003—24no—
195#13094003—24no—
196C4×C22⋊D47—24no—
197#13093981—42no—
198C2×C4⋊Dic47C2311yescharacteristic
199C2×C4⋊Dic47C2311yescharacteristic
200C2×C4⋊Dic47C2311yescharacteristic
201C2×C4⋊Dic47C2311yescharacteristic
202C2×C4⋊Dic47C2311yescharacteristic
203C2×C4⋊Dic47C2311yescharacteristic
204C2×C4⋊Dic47C2311yescharacteristic
205C2×C4⋊Dic47C2311yescharacteristic
206C2×C4⋊Dic47C2311yescharacteristic
207C2×C4⋊Dic47C2311yescharacteristic
208C2×C4⋊Dic47C2311yescharacteristic
209C2×C4⋊Dic47C2311yescharacteristic
210C2×C4⋊Dic47C2311yescharacteristic
211C2×C4⋊Dic47C2311yescharacteristic
212C2×C4⋊Dic47C2311yescharacteristic
213C2×C4⋊Dic47C2311yescharacteristic
214C2×C4⋊Dic47C2311yescharacteristic
215C2×C4⋊Dic47C2311yescharacteristic
216C2×Dic47⋊C4C2311yescharacteristic
217C2×Dic47⋊C4C2311yescharacteristic
218C2×Dic47⋊C4C2311yescharacteristic
219C2×Dic47⋊C4C2311yescharacteristic
220C2×Dic47⋊C4C2311yescharacteristic
221C2×Dic47⋊C4C2311yescharacteristic
222C2×Dic47⋊C4C2311yescharacteristic
223C2×Dic47⋊C4C2311yescharacteristic
224C2×Dic47⋊C4C2311yescharacteristic
225C2×Dic47⋊C4C2311yescharacteristic
226C2×Dic47⋊C4C2311yescharacteristic
227C2×Dic47⋊C4C2311yescharacteristic
228C2×Dic47⋊C4C2311yescharacteristic
229C2×Dic47⋊C4C2311yescharacteristic
230C2×Dic47⋊C4C2311yescharacteristic
231C2×Dic47⋊C4C2311yescharacteristic
232C2×Dic47⋊C4C2311yescharacteristic
233C2×C22⋊Dic47C2311yescharacteristic
234C2×C22⋊Dic47C2311yescharacteristic
235C2×C22⋊Dic47C2311yescharacteristic
236C2×C22⋊Dic47C2311yescharacteristic
237C2×C22⋊Dic47C2311yescharacteristic
238C2×C22⋊Dic47C2311yescharacteristic
239C2×C22⋊Dic47C2311yescharacteristic
240C2×(C2×D47)⋊C4C2311yescharacteristic
241C2×(C2×D47)⋊C4C2311yescharacteristic
242C2×(C2×D47)⋊C4C2311yescharacteristic
243C2×(C2×D47)⋊C4C2311yescharacteristic
244C2×(C2×D47)⋊C4C2311yescharacteristic
245C2×(C2×D47)⋊C4C2311yescharacteristic
246C2×(C2×D47)⋊C4C2311yescharacteristic
247C2×(C2×D47)⋊C4C2311yescharacteristic
248C2×(C2×D47)⋊C4C2311yescharacteristic
249C2×(C2×D47)⋊C4C2311yescharacteristic
250C2×(C2×D47)⋊C4C2311yescharacteristic
251C2×(C2×D47)⋊C4C2311yescharacteristic
252C2×(C2×D47)⋊C4C2311yescharacteristic
253C2×C4×Dic47C2311yescharacteristic
254C2×C4×Dic47C2311yescharacteristic
255C2×C4×Dic47C2311yescharacteristic
256C2×C4×Dic47C2311yescharacteristic
257C2×C4×Dic47C2311yescharacteristic
258C2×C4×Dic47C2311yescharacteristic
259C2×C4×Dic47C2311yescharacteristic
260C2×C4×Dic47C2311yescharacteristic
261C2×C4×Dic47C2311yescharacteristic
262C2×C4×Dic47C2311yescharacteristic
263C2×C4×Dic47C2311yescharacteristic
264C47⋊#95C2311yescharacteristic
265C47⋊#95C2311yescharacteristic
266C47⋊#95C2311yescharacteristic
267C47⋊#95C2311yescharacteristic
268C47⋊#95C2311yescharacteristic
269C47⋊#95C2311yescharacteristic
270C47⋊#95C2311yescharacteristic
271C47⋊#95C2311yescharacteristic
272C47⋊#95C2311yescharacteristic
273C47⋊#95C2311yescharacteristic
274C47⋊#95C2311yescharacteristic
275C47⋊#95C2311yescharacteristic
276C47⋊#95C2311yescharacteristic
277C47⋊#95C2311yescharacteristic
278C47⋊#95C2311yescharacteristic
279C47⋊#95C2311yescharacteristic
280C47⋊#95C2311yescharacteristic
281C47⋊#95C2311yescharacteristic
282C47⋊#95C2311yescharacteristic
283C47⋊#95C2311yescharacteristic
284C47⋊#95C2311yescharacteristic
285C47⋊#95C2311yescharacteristic
286C47⋊#95C2311yescharacteristic
287C47⋊#95C2311yescharacteristic
288C47⋊#95C2311yescharacteristic
289C47⋊#95C2311yescharacteristic
290C47⋊#95C2311yescharacteristic
291C47⋊#95C2311yescharacteristic
292C47⋊#95C2311yescharacteristic
293C47⋊#95C2311yescharacteristic
294C47⋊#95C2311yescharacteristic
295C47⋊#95C2311yescharacteristic
296C47⋊#95C2311yescharacteristic
297C47⋊#95C2311yescharacteristic
298C47⋊#95C2311yescharacteristic
299C47⋊#95C2311yescharacteristic
300C47⋊#95C2311yescharacteristic
301C47⋊#95C2311yescharacteristic
302C47⋊#95C2311yescharacteristic
303C47⋊#95C2311yescharacteristic
304C47⋊#95C2311yescharacteristic
305C47⋊#95C2311yescharacteristic
306C47⋊#95C2311yescharacteristic
307C47⋊#95C2311yescharacteristic
308C47⋊#95C2311yescharacteristic
309C47⋊#95C2311yescharacteristic
310C47⋊#95C2311yescharacteristic
311C47⋊#95C2311yescharacteristic
312C47⋊#95C2311yescharacteristic
313C47⋊#95C2311yescharacteristic
314C22×Q8×C47C2311yescharacteristic
315C23×C4×C47C2311yescharacteristic
316C23×C4×C47C2311yescharacteristic
317C23×C4×C47C2311yescharacteristic
318C22⋊Q8×C47—42no—
319C2×C4⋊C4×C47C2311yescharacteristic
320C2×C4⋊C4×C47C2311yescharacteristic
321C2×C4⋊C4×C47C2311yescharacteristic
322C2×C4⋊C4×C47C2311yescharacteristic
323C2×C4⋊C4×C47C2311yescharacteristic
324C2×C4⋊C4×C47C2311yescharacteristic
325C2×C4⋊C4×C47C2311yescharacteristic
326C2×C4⋊C4×C47C2311yescharacteristic
327C2×C4⋊C4×C47C2311yescharacteristic
328C2×C22⋊C4×C47C2311yescharacteristic
329C2×C22⋊C4×C47C2311yescharacteristic
330C2×C22⋊C4×C47C2311yescharacteristic
331C2×C22⋊C4×C47C2311yescharacteristic
332C2×C42×C47—42no—
333C2×C42×C47C2311yescharacteristic
334C2×C42×C47C2311yescharacteristic
335C2×C42×C47C2311yescharacteristic
336C2×C42×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
351C24×C47C2411yescharacteristic
352C23×D47C2411yescharacteristic
353C2×Q8×C47—22no—
354C2×Q8×C47—41no—
355C2×Q8×C47—41no—
356C22×C4×C47—22no—
357C22×C4×C47—22no—
358C22×C4×C47—22no—
359C22×C4×C47—41no—
360C22×C4×C47—41no—
361C22×C4×C47—41no—
362C22×C4×C47—41no—
363C22×C4×C47—41no—
364C22×C4×C47#4114yes—
365C22×C4×C47C2411yescharacteristic
366C22×C4×C47C2411yescharacteristic
367C22×C4×C47C2411yescharacteristic
368C22×C4×C47C2411yescharacteristic
369C22×C4×C47C2411yescharacteristic
370C22×C4×C47C2411yescharacteristic
371C22×C4×C47C2411yescharacteristic
372C22×C4×C47C2411yescharacteristic
373C22×C4×C47C2411yescharacteristic
374C22×C4×C47C2411yescharacteristic
375C22×C4×C47C2411yescharacteristic
376C22×C4×C47C2411yescharacteristic
377C22×C4×C47C2411yescharacteristic
378C22×C4×C47C2411yescharacteristic
379C2×C22⋊D47—22no—
380C2×C22⋊D47—41no—
381C2×C22⋊D47—41no—
382C22×Dic47C2411yescharacteristic
383C22×Dic47C2411yescharacteristic
384C22×Dic47C2411yescharacteristic
385C22×Dic47C2411yescharacteristic
386C22×Dic47C2411yescharacteristic
387C22×Dic47C2411yescharacteristic
388C22×Dic47C2411yescharacteristic
389C22×Dic47C2411yescharacteristic
390C22×Dic47C2411yescharacteristic
391C22×Dic47C2411yescharacteristic
392C22×Dic47C2411yescharacteristic
393C22×Dic47C2411yescharacteristic
394C22×Dic47C2411yescharacteristic
395C22×Dic47C2411yescharacteristic
396C22×Dic47C2411yescharacteristic
397C2×C4×D47—22no—
398C2×C4×D47—41no—
399C2×C4×D47—41no—
400C2×Dic94—22no—
401C2×Dic94—22no—
402C2×Dic94—41no—
403C2×Dic94—41no—
404C2×Dic94—41no—
405C2×Dic94—41no—
406C4⋊C4×C47—22no—
407C4⋊C4×C47—22no—
408C4⋊C4×C47—22no—
409C4⋊C4×C47—22no—
410C4⋊C4×C47—22no—
411C4⋊C4×C47—41no—
412C4⋊C4×C47—41no—
413C4⋊C4×C47—41no—
414C4⋊C4×C47—41no—
415C22⋊C4×C47—41no—
416C22⋊C4×C47—41no—
417C22⋊C4×C47—41no—
418C22⋊C4×C47—41no—
419C42×C47—22no—
420C42×C47—22no—
421C42×C47—41no—
422C42×C47—41no—
423C22⋊Dic47—22no—
424C22⋊Dic47—22no—
425C22⋊Dic47—22no—
426C22⋊Dic47—22no—
427C22⋊Dic47—22no—
428C22⋊Dic47—41no—
429C22⋊Dic47—41no—
430(C2×D47)⋊C4—22no—
431(C2×D47)⋊C4—22no—
432(C2×D47)⋊C4—22no—
433(C2×D47)⋊C4—22no—
434(C2×D47)⋊C4—41no—
435(C2×D47)⋊C4—41no—
436(C2×D47)⋊C4—41no—
437(C2×D47)⋊C4—41no—
438(C2×D47)⋊C4—41no—
439(C2×D47)⋊C4—41no—
440(C2×D47)⋊C4—41no—
441(C2×D47)⋊C4—41no—
442(C2×D47)⋊C4—41no—
443C4⋊Dic47—22no—
444C4⋊Dic47—22no—
445C4⋊Dic47—22no—
446C4⋊Dic47—22no—
447C4⋊Dic47—41no—
448C4⋊Dic47—41no—
449C4⋊Dic47—41no—
450C4⋊Dic47—41no—
451C4⋊Dic47—41no—
452C4⋊Dic47—41no—
453C4⋊Dic47—41no—
454C4⋊Dic47—41no—
455C4⋊Dic47—41no—
456C4⋊Dic47—41no—
457C4⋊Dic47—41no—
458C4⋊Dic47—41no—
459C4⋊Dic47—41no—
460C4⋊Dic47—41no—
461Dic47⋊C4—22no—
462Dic47⋊C4—22no—
463Dic47⋊C4—22no—
464Dic47⋊C4—22no—
465Dic47⋊C4—22no—
466Dic47⋊C4—22no—
467Dic47⋊C4—22no—
468Dic47⋊C4—22no—
469Dic47⋊C4—41no—
470Dic47⋊C4—41no—
471Dic47⋊C4—41no—
472Dic47⋊C4—41no—
473Dic47⋊C4—41no—
474Dic47⋊C4—41no—
475Dic47⋊C4—41no—
476Dic47⋊C4—41no—
477Dic47⋊C4—41no—
478C4×Dic47—22no—
479C4×Dic47—41no—
480C4×Dic47—41no—
481C4×Dic47—41no—
482C4×Dic47—41no—
483C4×Dic47—41no—
484C4×Dic47—41no—
485C4×Dic47—41no—
486C4×Dic47—41no—
487C4×Dic47—41no—
488C4×Dic47—41no—
489C23×C47—21no—
490C23×C47—21no—
491C23×C47—21no—
492C23×C47—21no—
493C23×C47—21no—
494C23×C47—21no—
495C23×C47C2×#4112yes—
496C23×C47C2511yescharacteristic
497C22×D47—21no—
498C22×D47—21no—
499C22×D47—21no—
500C22×D47—21no—
501C22×D47—21no—
502C22×D47—21no—
503C22×D47—21no—
504Q8×C47—82no—
505C2×C4×C47—21no—
506C2×C4×C47—21no—
507C2×C4×C47—21no—
508C2×C4×C47—21no—
509C2×C4×C47—21no—
510C2×C4×C47—21no—
511C2×C4×C47—21no—
512C2×C4×C47—21no—
513C2×C4×C47—21no—
514C2×C4×C47—21no—
515C2×C4×C47—21no—
516C2×C4×C47—21no—
517C2×C4×C47—21no—
518C2×C4×C47—21no—
519C2×C4×C47—21no—
520C2×C4×C47—21no—
521C2×C4×C47—21no—
522C2×C4×C47—21no—
523C2×C4×C47—21no—
524C2×C4×C47—21no—
525C2×C4×C47—21no—
526C2×C4×C47—21no—
527C2×C4×C47—21no—
528C2×C4×C47—21no—
529C2×C4×C47—21no—
530C2×C4×C47—21no—
531C2×C4×C47—21no—
532C2×C4×C47—21no—
533C2×C4×C47—21no—
534C2×C4×C47—21no—
535C2×C4×C47—21no—
536C2×C4×C47—21no—
537C2×C4×C47—21no—
538C2×C4×C47—21no—
539C2×C4×C47—21no—
540C2×C4×C47—21no—
541C2×C4×C47—21no—
542C2×C4×C47—44no—
543C2×C4×C47—44no—
544C2×C4×C47—44no—
545C2×C4×C47C2×#4112yes—
546C2×C4×C47C2×#4112yes—
547C2×C4×C47H(5,𝔽2)12yes—
548C2×C4×C472−1+412yes—
549C2×C4×C472−1+412yes—
550C22⋊D47—44no—
551C2×Dic47—21no—
552C2×Dic47—21no—
553C2×Dic47—21no—
554C2×Dic47—21no—
555C2×Dic47—21no—
556C2×Dic47—21no—
557C2×Dic47—21no—
558C2×Dic47—21no—
559C2×Dic47—21no—
560C2×Dic47—21no—
561C2×Dic47—21no—
562C2×Dic47—21no—
563C2×Dic47—21no—
564C2×Dic47—21no—
565C2×Dic47—21no—
566C2×Dic47—21no—
567C2×Dic47—21no—
568C2×Dic47—21no—
569C2×Dic47—21no—
570C2×Dic47—21no—
571C2×Dic47—21no—
572C2×Dic47—21no—
573C2×Dic47—21no—
574C2×Dic47—21no—
575C2×Dic47—21no—
576C2×Dic47—21no—
577C2×Dic47—21no—
578C2×Dic47—21no—
579C2×Dic47—21no—
580C2×Dic47—21no—
581C2×Dic47—21no—
582C2×Dic47—21no—
583C2×Dic47—21no—
584C2×Dic47—21no—
585C2×Dic47—21no—
586C2×Dic47—21no—
587C2×Dic47—21no—
588C2×Dic47—21no—
589C2×Dic47—21no—
590C2×Dic47—21no—
591C2×Dic47—21no—
592C2×Dic47—21no—
593C2×Dic47—21no—
594C2×Dic47—21no—
595C2×Dic47—21no—
596C4×D47—44no—
597Dic94—82no—
598Dic94—82no—
599#36772—471nomaximal, Sylow
600C22×C47—22no—
601C22×C47—22no—
602C22×C47—22no—
603C22×C47—41no—
604C22×C47—41no—
605C22×C47—41no—
606C22×C47—41no—
607C22×C47C22×#4111yescharacteristic
608C22×C47C2×H(5,𝔽2)11yescharacteristic
609C22×C47C2×2−1+411yescharacteristic
610C22×C47C2×2−1+411yescharacteristic
611C22×C47#58511yescharacteristic
612C22×C47#58511yescharacteristic
613C22×C47#58511yescharacteristic
614C2×D47—41no—
615C2×D47—41no—
616C2×D47—41no—
617C2×D47—41no—
618C2×D47—41no—
619C2×D47—41no—
620C2×D47—41no—
621C4×C47—22no—
622C4×C47—22no—
623C4×C47—22no—
624C4×C47—22no—
625C4×C47—22no—
626C4×C47—41no—
627C4×C47—41no—
628C4×C47—41no—
629C4×C47—41no—
630C4×C47—41no—
631C4×C47—41no—
632C4×C47—41no—
633C4×C47—41no—
634C4×C47—41no—
635Dic47—41no—
636Dic47—41no—
637Dic47—41no—
638Dic47—41no—
639Dic47—41no—
640Dic47—41no—
641Dic47—41no—
642Dic47—41no—
643Dic47—41no—
644Dic47—41no—
645Dic47—41no—
646Dic47—41no—
647Dic47—41no—
648Dic47—41no—
649Dic47—41no—
650#2857—471no—
651#2855D4711yescharacteristic, complemented
652#2799—471no—
653#2798—471no—
654#2793—471no—
655#2791—471no—
656#2787—471no—
657#2781—471no—
658#2779—471no—
659#2770—471no—
660#2759—471no—
661#2755—471no—
662#2747—471no—
663#2741—471no—
664#2716—471no—
665#2713—471no—
666#2702—471no—
667#2690—471no—
668#2638—471no—
669#2638—471no—
670#2590—471no—
671#2589—471no—
672#2588—471no—
673#2587—471no—
674#2533—471no—
675#2528—471no—
676#2478—471no—
677#2475—471no—
678#2332—471no—
679#2332—471no—
680#2290—471no—
681C2×C47—42no—
682C2×C47#345511yescharacteristic
683C2×C47#350511yescharacteristic
684C2×C47#350911yescharacteristic
685C2×C47#353511yescharacteristic
686C2×C47#354111yescharacteristic
687C2×C47#355711yescharacteristic
688C2×C47#356511yescharacteristic
689D47—81no—
690C2×C4⋊Q8—471no—
691C2×#126—471no—
692C2×#125—471no—
693C2×C22⋊Q8—471no—
694C2×C22⋊Q8—471no—
695C2×C22⋊Q8C2×D4711yescharacteristic
696C2×C4×D4—471no—
697C2×#117—471no—
698C22×C42C2×D4711yescharacteristic
699#401—471no—
700#400—471no—
701#400—471no—
702#400—471no—
703#400—471no—
704#400—471no—
705#400—471no—
706#400—471no—
707#400—471no—
708#400—471no—
709#400—471no—
710#400—471no—
711#400—471no—
712#399—471no—
713#398—471no—
714#398—471no—
715#398—471no—
716#398—471no—
717#398—471no—
718#398—471no—
719#398—471no—
720#398—471no—
721#398—471no—
722#398—471no—
723#398—471no—
724#398—471no—
725#397—471no—
726#397—471no—
727#397—471no—
728#397—471no—
729#397—471no—
730#397—471no—
731#397—471no—
732#397—471no—
733#397—471no—
734#396—471no—
735#396—471no—
736#396—471no—
737#395—471no—
738#395—471no—
739#395—471no—
740#394—471no—
741#394—471no—
742#394—471no—
743#394—471no—
744#393—471no—
745#393—471no—
746#393—471no—
747#391—471no—
748#391—471no—
749#391—471no—
750#391—471no—
751#391—471no—
752#391—471no—
753#391—471no—
754#391—471no—
755#391C2×D4711yescharacteristic
756#391C2×D4711yescharacteristic
757#389—471no—
758#389—471no—
759#389—471no—
760#389—471no—
761#389—471no—
762#389—471no—
763#389—471no—
764#389—471no—
765#389C2×D4711yescharacteristic
766#389C2×D4711yescharacteristic
767#388—471no—
768#388—471no—
769#388—471no—
770#388—471no—
771#388—471no—
772#388—471no—
773#388—471no—
774#388—471no—
775#388—471no—
776#388—471no—
777#388—471no—
778#388—471no—
779#388—471no—
780#388—471no—
781#388—471no—
782#388—471no—
783#388—471no—
784#387—471no—
785#387—471no—
786#387—471no—
787#387—471no—
788#387—471no—
789#387—471no—
790#387—471no—
791#387—471no—
792#387—471no—
793#387—471no—
794#387—471no—
795#387—471no—
796#387—471no—
797#387—471no—
798#387—471no—
799#387—471no—
800#387—471no—
801#387—471no—
802#387—471no—
803#387—471no—
804#387—471no—
805#387—471no—
806#387—471no—
807#387—471no—
808#387—471no—
809#387—471no—
810#387—471no—
811#387—471no—
812#387—471no—
813#387C2×D4711yescharacteristic
814#387C2×D4711yescharacteristic
815#387C2×D4711yescharacteristic
816#387C2×D4711yescharacteristic
817#386—471no—
818#386—471no—
819#385—471no—
820#385—471no—
821#385—471no—
822#385—471no—
823#385—471no—
824#385—471no—
825#385C2×D4711yescharacteristic
826#385C2×D4711yescharacteristic
827#384—471no—
828#383—471no—
829#382—471no—
830#381C2×D4711yescharacteristic
831#381C2×D4711yescharacteristic
832#380—471no—
833#380—471no—
834#380—471no—
835#380—471no—
836#380C2×D4711yescharacteristic
837C4×C4⋊C4—471no—
838C4×C4⋊C4—471no—
839C4×C4⋊C4—471no—
840C4×C4⋊C4—471no—
841C4×C4⋊C4—471no—
842C4×C22⋊C4—471no—
843C4×C22⋊C4—471no—
844#376—471no—
845C47#3677211yescharacteristic, complemented, Sylow
846C22×Q8—471no—
847C22×Q8—471no—
848C22×Q8C22×D4711yescharacteristic
849C22×D4—471no—
850C23×C4—471no—
851C23×C4C22×D4711yescharacteristic
852C23×C4C22×D4711yescharacteristic
853C23×C4C22×D4711yescharacteristic
854C4⋊Q8—1882no—
855#126—1882no—
856#125—1882no—
857C22⋊Q8—42no—
858C22⋊Q8—944no—
859C22⋊Q8—944no—
860C4×D4—944no—
861#117—1882no—
862C2×C4⋊C4—471no—
863C2×C4⋊C4—471no—
864C2×C4⋊C4—471no—
865C2×C4⋊C4—471no—
866C2×C4⋊C4—471no—
867C2×C4⋊C4—471no—
868C2×C4⋊C4—471no—
869C2×C4⋊C4—471no—
870C2×C4⋊C4—471no—
871C2×C4⋊C4—471no—
872C2×C4⋊C4—471no—
873C2×C4⋊C4—471no—
874C2×C4⋊C4—471no—
875C2×C4⋊C4—471no—
876C2×C4⋊C4—471no—
877C2×C4⋊C4—471no—
878C2×C4⋊C4—471no—
879C2×C4⋊C4—471no—
880C2×C4⋊C4—471no—
881C2×C4⋊C4—471no—
882C2×C4⋊C4—471no—
883C2×C4⋊C4—471no—
884C2×C4⋊C4—471no—
885C2×C4⋊C4—471no—
886C2×C4⋊C4—471no—
887C2×C4⋊C4—471no—
888C2×C4⋊C4—471no—
889C2×C4⋊C4—471no—
890C2×C4⋊C4—471no—
891C2×C4⋊C4—471no—
892C2×C4⋊C4—471no—
893C2×C4⋊C4—471no—
894C2×C4⋊C4—471no—
895C2×C4⋊C4—471no—
896C2×C4⋊C4—471no—
897C2×C4⋊C4C22×D4711yescharacteristic
898C2×C4⋊C4C22×D4711yescharacteristic
899C2×C4⋊C4C22×D4711yescharacteristic
900C2×C4⋊C4C22×D4711yescharacteristic
901C2×C4⋊C4C22×D4711yescharacteristic
902C2×C4⋊C4C22×D4711yescharacteristic
903C2×C4⋊C4C22×D4711yescharacteristic
904C2×C4⋊C4C22×D4711yescharacteristic
905C2×C4⋊C4C22×D4711yescharacteristic
906C2×C22⋊C4—471no—
907C2×C22⋊C4—471no—
908C2×C22⋊C4—471no—
909C2×C22⋊C4—471no—
910C2×C22⋊C4—471no—
911C2×C22⋊C4—471no—
912C2×C22⋊C4—471no—
913C2×C22⋊C4—471no—
914C2×C22⋊C4—471no—
915C2×C22⋊C4—471no—
916C2×C22⋊C4—471no—
917C2×C22⋊C4—471no—
918C2×C22⋊C4—471no—
919C2×C22⋊C4—471no—
920C2×C22⋊C4—471no—
921C2×C22⋊C4—471no—
922C2×C22⋊C4—471no—
923C2×C22⋊C4—471no—
924C2×C22⋊C4—471no—
925C2×C22⋊C4—471no—
926C2×C22⋊C4C22×D4711yescharacteristic
927C2×C22⋊C4C22×D4711yescharacteristic
928C2×C22⋊C4C22×D4711yescharacteristic
929C2×C22⋊C4C22×D4711yescharacteristic
930C2×C42—42no—
931C2×C42—471no—
932C2×C42—471no—
933C2×C42—471no—
934C2×C42—471no—
935C2×C42—471no—
936C2×C42—471no—
937C2×C42—471no—
938C2×C42—471no—
939C2×C42—471no—
940C2×C42—471no—
941C2×C42—471no—
942C2×C42C22×D4711yescharacteristic
943C2×C42C22×D4711yescharacteristic
944C2×C42C22×D4711yescharacteristic
945C2×C42C22×D4711yescharacteristic
946#95—471no—
947#95—471no—
948#95—471no—
949#95—471no—
950#95—471no—
951#95—471no—
952#95—471no—
953#95—471no—
954#95—471no—
955#95—471no—
956#95—471no—
957#95—471no—
958#95—471no—
959#95—471no—
960#95—471no—
961#95—471no—
962#95—471no—
963#95—471no—
964#95—471no—
965#95—471no—
966#95—471no—
967#95—471no—
968#95—471no—
969#95—471no—
970#95—471no—
971#95—471no—
972#95—471no—
973#95—471no—
974#95—471no—
975#95—471no—
976#95—471no—
977#95—471no—
978#95—471no—
979#95—471no—
980#95—471no—
981#95—471no—
982#95—471no—
983#95—471no—
984#95—471no—
985#95—471no—
986#95—471no—
987#95—471no—
988#95—471no—
989#95—471no—
990#95—471no—
991#95—471no—
992#95—471no—
993#95—471no—
994#95—471no—
995#95—471no—
996#95C22×D4711yescharacteristic
997#95C22×D4711yescharacteristic
998#95C22×D4711yescharacteristic
999#95C22×D4711yescharacteristic
1000#95C22×D4711yescharacteristic
1001#95C22×D4711yescharacteristic
1002#95C22×D4711yescharacteristic
1003#95C22×D4711yescharacteristic
1004#95C22×D4711yescharacteristic
1005#95C22×D4711yescharacteristic
1006#95C22×D4711yescharacteristic
1007#95C22×D4711yescharacteristic
1008#95C22×D4711yescharacteristic
1009#95C22×D4711yescharacteristic
1010C24—471no—
1011C24C23×D4711yescharacteristic
1012C2×Q8—22no—
1013C2×Q8—41no—
1014C2×Q8—41no—
1015C2×Q8—942no—
1016C2×Q8—942no—
1017C2×Q8—1881no—
1018C2×Q8—1881no—
1019C2×Q8—1881no—
1020C2×Q8—1881no—
1021C2×D4—942no—
1022C2×D4—1881no—
1023C2×D4—1881no—
1024C22×C4—22no—
1025C22×C4—22no—
1026C22×C4—22no—
1027C22×C4—41no—
1028C22×C4—41no—
1029C22×C4—41no—
1030C22×C4—41no—
1031C22×C4—41no—
1032C22×C4—471no—
1033C22×C4—471no—
1034C22×C4—471no—
1035C22×C4—471no—
1036C22×C4—471no—
1037C22×C4—471no—
1038C22×C4—471no—
1039C22×C4—471no—
1040C22×C4—471no—
1041C22×C4—471no—
1042C22×C4—471no—
1043C22×C4—471no—
1044C22×C4—471no—
1045C22×C4—471no—
1046C22×C4—471no—
1047C22×C4—942no—
1048C22×C4—1881no—
1049C22×C4—1881no—
1050C22×C4#1062535414yes—
1051C22×C4C23×D4711yescharacteristic
1052C22×C4C23×D4711yescharacteristic
1053C22×C4C23×D4711yescharacteristic
1054C22×C4C23×D4711yescharacteristic
1055C22×C4C23×D4711yescharacteristic
1056C22×C4C23×D4711yescharacteristic
1057C22×C4C23×D4711yescharacteristic
1058C22×C4C23×D4711yescharacteristic
1059C22×C4C23×D4711yescharacteristic
1060C22×C4C23×D4711yescharacteristic
1061C22×C4C23×D4711yescharacteristic
1062C22×C4C23×D4711yescharacteristic
1063C22×C4C23×D4711yescharacteristic
1064C22×C4C23×D4711yescharacteristic
1065C4⋊C4—22no—
1066C4⋊C4—22no—
1067C4⋊C4—22no—
1068C4⋊C4—22no—
1069C4⋊C4—22no—
1070C4⋊C4—41no—
1071C4⋊C4—41no—
1072C4⋊C4—41no—
1073C4⋊C4—41no—
1074C4⋊C4—942no—
1075C4⋊C4—942no—
1076C4⋊C4—942no—
1077C4⋊C4—942no—
1078C4⋊C4—942no—
1079C4⋊C4—942no—
1080C4⋊C4—942no—
1081C4⋊C4—942no—
1082C4⋊C4—942no—
1083C4⋊C4—942no—
1084C4⋊C4—942no—
1085C4⋊C4—942no—
1086C4⋊C4—1881no—
1087C4⋊C4—1881no—
1088C4⋊C4—1881no—
1089C4⋊C4—1881no—
1090C4⋊C4—1881no—
1091C4⋊C4—1881no—
1092C4⋊C4—1881no—
1093C4⋊C4—1881no—
1094C4⋊C4—1881no—
1095C4⋊C4—1881no—
1096C4⋊C4—1881no—
1097C4⋊C4—1881no—
1098C4⋊C4—1881no—
1099C4⋊C4—1881no—
1100C4⋊C4—1881no—
1101C4⋊C4—1881no—
1102C4⋊C4—1881no—
1103C4⋊C4—1881no—
1104C4⋊C4—1881no—
1105C4⋊C4—1881no—
1106C4⋊C4—1881no—
1107C4⋊C4—1881no—
1108C4⋊C4—1881no—
1109C22⋊C4—41no—
1110C22⋊C4—41no—
1111C22⋊C4—41no—
1112C22⋊C4—41no—
1113C22⋊C4—942no—
1114C22⋊C4—942no—
1115C22⋊C4—942no—
1116C22⋊C4—942no—
1117C22⋊C4—942no—
1118C22⋊C4—942no—
1119C22⋊C4—942no—
1120C22⋊C4—942no—
1121C22⋊C4—942no—
1122C22⋊C4—1881no—
1123C22⋊C4—1881no—
1124C22⋊C4—1881no—
1125C22⋊C4—1881no—
1126C22⋊C4—1881no—
1127C22⋊C4—1881no—
1128C22⋊C4—1881no—
1129C22⋊C4—1881no—
1130C22⋊C4—1881no—
1131C22⋊C4—1881no—
1132C22⋊C4—1881no—
1133C42—22no—
1134C42—22no—
1135C42—41no—
1136C42—41no—
1137C42—942no—
1138C42—1881no—
1139C42—1881no—
1140C42—1881no—
1141C42—1881no—
1142C42—1881no—
1143C42—1881no—
1144C42—1881no—
1145C42—1881no—
1146C42—1881no—
1147C42—1881no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—941no—
1155C23—941no—
1156C23—941no—
1157C23—941no—
1158C23—941no—
1159C23—941no—
1160C23—941no—
1161C23C2×#1062535412yes—
1162C23C24×D4711yescharacteristic
1163Q8—82no—
1164Q8—3762no—
1165Q8—3762no—
1166D4—1884no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—44no—
1205C2×C4—44no—
1206C2×C4—44no—
1207C2×C4—941no—
1208C2×C4—941no—
1209C2×C4—941no—
1210C2×C4—941no—
1211C2×C4—941no—
1212C2×C4—941no—
1213C2×C4—941no—
1214C2×C4—941no—
1215C2×C4—941no—
1216C2×C4—941no—
1217C2×C4—941no—
1218C2×C4—941no—
1219C2×C4—941no—
1220C2×C4—941no—
1221C2×C4—941no—
1222C2×C4—941no—
1223C2×C4—941no—
1224C2×C4—941no—
1225C2×C4—941no—
1226C2×C4—941no—
1227C2×C4—941no—
1228C2×C4—941no—
1229C2×C4—941no—
1230C2×C4—941no—
1231C2×C4—941no—
1232C2×C4—941no—
1233C2×C4—941no—
1234C2×C4—941no—
1235C2×C4—941no—
1236C2×C4—941no—
1237C2×C4—941no—
1238C2×C4—941no—
1239C2×C4—941no—
1240C2×C4—941no—
1241C2×C4—941no—
1242C2×C4—941no—
1243C2×C4—941no—
1244C2×C4—941no—
1245C2×C4—941no—
1246C2×C4—941no—
1247C2×C4—941no—
1248C2×C4—941no—
1249C2×C4—941no—
1250C2×C4—941no—
1251C2×C4—941no—
1252C2×C4—1884no—
1253C2×C4C2×#1062535412yes—
1254C2×C4C2×#1062535412yes—
1255C2×C4#1309406912yes—
1256C2×C4#1309407112yes—
1257C2×C4#1309407112yes—
1258C22—22no—
1259C22—22no—
1260C22—22no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—1881no—
1266C22—1881no—
1267C22—1881no—
1268C22—1881no—
1269C22—1881no—
1270C22—1881no—
1271C22—1881no—
1272C22C22×#1062535411yescharacteristic
1273C22C2×#1309406911yescharacteristic
1274C22C2×#1309407111yescharacteristic
1275C22C2×#1309407111yescharacteristic
1276C22#1568995911yescharacteristic
1277C22#1568995911yescharacteristic
1278C22#1568995911yescharacteristic
1279C4—22no—
1280C4—22no—
1281C4—22no—
1282C4—22no—
1283C4—22no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—1881no—
1294C4—1881no—
1295C4—1881no—
1296C4—1881no—
1297C4—1881no—
1298C4—1881no—
1299C4—1881no—
1300C4—1881no—
1301C4—1881no—
1302C4—1881no—
1303C4—1881no—
1304C4—1881no—
1305C4—1881no—
1306C4—1881no—
1307C4—1881no—
1308C2—42no—
1309C2—3761no—
1310C2#2025678011yescharacteristic
1311C2#2025722911yescharacteristic
1312C2#2025727511yescharacteristic
1313C2#2025760111yescharacteristic
1314C2#2025768111yescharacteristic
1315C2#2025789011yescharacteristic
1316C2#2025803311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2855C2
prime radicalC22×C22⋊D47C23
hypercenter#2855D47
hypocenterC47#36772
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2855

Complements

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

NH ≅ G/Ntype
1. #20251740C2semidirect
2. #20251274C2semidirect
3. #20251264C2semidirect
4. #20251201C2semidirect
5. #20251173C2semidirect
6. #20251119C2semidirect
9. #20250890C2semidirect
10. #20250756C2semidirect
11. #20250696C2semidirect
12. #20250583C2semidirect
14. #20250215C2semidirect
15. #20250170C2semidirect
17. #20249850C2semidirect
20. #20248861C2semidirect
21. #20248846C2semidirect
22. #20248831C2semidirect
23. #20248816C2semidirect
24. #20248272C2semidirect
25. #20248197C2semidirect
26. #20247611C2semidirect
27. #20247566C2semidirect
28. #20246141C2semidirect
29. #20246141C2semidirect
31. C47×#2855C2semidirect
651. #2855D47semidirect
845. C47#36772semidirect

Maximal subgroups

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

subgroupindex
#202517402
#202512742
#202512642
#202512012
#202511732
#202511192
#202510452
#202510212
#202508902
#202507562
#202506962
#202505832
#202504992
#202502152
#202501702
#202500122
#202498502
#202493082
#202488612
#202488462
#202488312
#202488162
#202482722
#202481972
#202476112
#202475662
#202461412
#202458312
C47×#28552
#3677247