Finite Group Databasebeta

← #14926697

Subgroups — #14926697

Order 2816.

2642 conjugacy classes of subgroups.

The subgroup lattice has 1208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623209C212yesmaximal, complemented
2#13076963C211yesmaximal, characteristic, complemented
3#13076960C211yesmaximal, characteristic, complemented
4#13076899C211yesmaximal, characteristic, complemented
5#13076895C211yesmaximal, characteristic, complemented
6#13074545C212yesmaximal, complemented
7#13074355C212yesmaximal, complemented
8#13073751C212yesmaximal, complemented
9#13073738C212yesmaximal, complemented
10#13073716C212yesmaximal, complemented
11#13073713C212yesmaximal, complemented
12#13073034C211yesmaximal, characteristic, complemented
13#13073032C211yesmaximal, characteristic, complemented
14#13072982C211yesmaximal, characteristic, complemented
15#13072206C211yesmaximal, characteristic, complemented
16#13072205C211yesmaximal, characteristic, complemented
17#13072130C211yesmaximal, characteristic, complemented
18#13072128C211yesmaximal, characteristic, complemented
19#13071320C212yesmaximal, complemented
20#13071132C211yesmaximal, characteristic, complemented
21C4×#66948C211yesmaximal, characteristic, complemented
22C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
23C11×#2491C211yesmaximal, characteristic, complemented
24C23×C4×D11C2211yescharacteristic
25C2×C11×C4⋊Q8C2211yescharacteristic, complemented
26C2×C11×#124C2212yes—
27C2×C11×#121C2211yescharacteristic
28C2×#67000C2212yes—
29C2×#66999C2212yes—
30C2×#66993C2211yescharacteristic, complemented
31C2×#66992C2212yes—
32C2×#66991C2211yescharacteristic
33C2×#66991C2211yescharacteristic
34C2×#66990C2212yes—
35C2×D4×Dic11C2211yescharacteristic, complemented
36C2×#66983C2211yescharacteristic
37#10623209—216no—
38C2×#66948C2211yescharacteristic
39C2×#66948C2211yescharacteristic
40C2×#66939C2212yes—
41C2×#66937C2212yes—
42C2×#66937C2212yes—
43C2×#66937C2212yes—
44C2×#66936C2212yes—
45C2×#66935C2212yes—
46C2×(C22⋊D11)⋊C4C2212yes—
47C2×C22⋊C4×D11C2211yescharacteristic
48C2×C22⋊C4×D11C2211yescharacteristic
49C2×#66932C2212yes—
50C2×#66929C2212yes—
51C2×C4×D44C2212yes—
52C2×C4×D44C2211yescharacteristic, complemented
53C2×C42×D11C2211yescharacteristic
54C2×C42×D11C2211yescharacteristic
55C11×#394C2212yes—
56C11×#393C2212yescomplemented
57C11×#390C2211yescharacteristic, complemented
58C11×#390C2211yescharacteristic, complemented
59C11×#388C2212yescomplemented
60C11×#380C2211yescharacteristic
61C4×C11×C4⋊C4C2211yescharacteristic, complemented
62C4×C11×C22⋊C4C2211yescharacteristic
63#10622844C2212yescomplemented
64#10622843C2212yescomplemented
65#10622836C2212yes—
66#10622833C2212yes—
67#10622825C2211yescharacteristic
68C4×C22⋊Dic11C2211yescharacteristic
69#10622604C2212yes—
70#10622603C2212yescomplemented
71#10622601C2211yescharacteristic, complemented
72#10622600C2211yescharacteristic
73#10622600C2211yescharacteristic
74#10622600C2211yescharacteristic
75#10622600C2211yescharacteristic
76#10622600C2212yes—
77#10622598C2211yescharacteristic, complemented
78#10622589C2211yescharacteristic, complemented
79C4⋊C4×Dic11C2211yescharacteristic, complemented
80#10622586C2212yescomplemented
81#10622586C2211yescharacteristic, complemented
82#10622586C2211yescharacteristic, complemented
83#10622574C2212yes—
84#10622574C2212yes—
85#10622573C2212yes—
86#10622572C2212yescomplemented
87#10622572C2212yescomplemented
88#10622571C2212yes—
89#10622571C2212yescomplemented
90#10622570C2212yescomplemented
91#10622570C2212yescomplemented
92#10622569C2212yes—
93#10622569C2212yes—
94#10622569C2212yes—
95#10622569C2212yescomplemented
96#10622566C2212yescomplemented
97#10622565C2212yes—
98#10622563C2212yescomplemented
99#10622558C2212yescomplemented
100C22⋊C4×Dic11C2211yescharacteristic
101C22⋊C4×Dic11C2211yescharacteristic
102C22⋊C4×Dic11C2212yescomplemented
103#10622552C2211yescharacteristic, complemented
104C4×(C2×D11)⋊C4C2211yescharacteristic
105C4×(C2×D11)⋊C4C2211yescharacteristic
106C4×(C2×D11)⋊C4C2212yescomplemented
107#10622548C2211yescharacteristic, complemented
108#10622546C2212yescomplemented
109#10622541C2211yescharacteristic, complemented
110#10622288C2212yes—
111#10622287C2212yescomplemented
112#10622283C2212yescomplemented
113#10622281C2212yescomplemented
114#10622279C2211yescharacteristic
115#10622279C2211yescharacteristic
116#10622278C2212yes—
117#10622278C2212yes—
118#10622278C2212yes—
119D11×#95C2211yescharacteristic
120D11×#95C2211yescharacteristic
121#10622271C2212yescomplemented
122#10622271C2212yescomplemented
123#10622268C2212yescomplemented
124C24×D11C2311yescharacteristic
125C22×Q8×C11C2312yes—
126C22×D4×C11C2311yescharacteristic
127C22×D4×C11C2312yes—
128C23×C4×C11C2311yescharacteristic
129C22×C22⋊D11C2312yes—
130C22×C22⋊D11C2312yes—
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yes—
133C22×C22⋊D11C2312yes—
134C23×Dic11C2312yes—
135C23×Dic11C2311yescharacteristic
136C22×D44C2312yes—
137C22×D44C2311yescharacteristic
138C22×D44C2312yes—
139C22×C4×D11—24no—
140C22×C4×D11—42no—
141C22×C4×D11—42no—
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2312yes—
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C22×C4×D11C2311yescharacteristic
151C11×C4⋊Q8—42no—
152C11×#124—28no—
153C11×#121—42no—
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C4⋊C4C2312yes—
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2311yescharacteristic
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2311yescharacteristic
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2311yescharacteristic
168C2×C42×C11C2312yes—
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2311yescharacteristic
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2311yescharacteristic
175#67000—28no—
176#66999—28no—
177#66993—42no—
178#66992—28no—
179#66991—24no—
180#66991—42no—
181#66990—28no—
182D4×Dic11—42no—
183#66983—42no—
184C2×(C2×D11)⋊C4C2312yes—
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2311yescharacteristic
189C2×(C2×D11)⋊C4C2311yescharacteristic
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2311yescharacteristic
199C2×(C2×D11)⋊C4C2311yescharacteristic
200C2×C4⋊Dic11C2312yes—
201C2×C4⋊Dic11C2311yescharacteristic
202C2×C4⋊Dic11C2312yes—
203C2×C4⋊Dic11C2311yescharacteristic
204C2×C4⋊Dic11C2311yescharacteristic
205C2×C4⋊Dic11C2312yes—
206C2×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2312yes—
208C2×Dic11⋊C4C2312yes—
209C2×Dic11⋊C4C2312yes—
210C2×Dic11⋊C4C2312yes—
211C2×C4×Dic11C2311yescharacteristic
212C2×C4×Dic11C2311yescharacteristic
213C2×C4×Dic11C2312yes—
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2311yescharacteristic
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2311yescharacteristic
218#66948—24no—
219#66948—42no—
220#66939—28no—
221#66937—28no—
222#66937—28no—
223#66937—28no—
224#66936—28no—
225#66935—28no—
226(C22⋊D11)⋊C4—28no—
227C22⋊C4×D11—24no—
228C22⋊C4×D11D418yescomplemented
229#66932—28no—
230#66929—28no—
231C4×D44—28no—
232C4×D44—42no—
233C42×D11—42no—
234C42×D11—42no—
235C11×#95C2312yes—
236C11×#95C2312yes—
237C11×#95C2311yescharacteristic
238C11×#95C2311yescharacteristic
239C11⋊#95C2311yescharacteristic
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2311yescharacteristic
243C11⋊#95C2311yescharacteristic
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2311yescharacteristic
250C11⋊#95C2311yescharacteristic
251C11⋊#95C2311yescharacteristic
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255#35005—111nomaximal, Sylow
256C24×C11C2412yes—
257C24×C11C2411yescharacteristic
258C23×D11—22no—
259C23×D11—22no—
260C23×D11—41no—
261C23×D11—41no—
262C23×D11—41no—
263C23×D11—41no—
264C23×D11C2×D414yes—
265C23×D11C2412yes—
266C23×D11C2411yescharacteristic
267C23×D11C2411yescharacteristic
268C2×Q8×C11—24no—
269C2×Q8×C11—42no—
270C2×Q8×C11—42no—
271C2×D4×C11—24no—
272C2×D4×C11—22no—
273C2×D4×C11—22no—
274C2×D4×C11—22no—
275C2×D4×C11—42no—
276C2×D4×C11—42no—
277C22×C4×C11—22no—
278C22×C4×C11—22no—
279C22×C4×C11—22no—
280C22×C4×C11C2411yescharacteristic
281C22×C4×C11C2411yescharacteristic
282C22×C4×C11C2412yes—
283C22×C4×C11C2412yes—
284C22×C4×C11C2412yes—
285C22×C4×C11C2411yescharacteristic
286C22×C4×C11C2411yescharacteristic
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2411yescharacteristic
289C2×C22⋊D11—24no—
290C2×C22⋊D11—24no—
291C2×C22⋊D11—24no—
292C2×C22⋊D11—24no—
293C2×C22⋊D11—24no—
294C2×C22⋊D11—24no—
295C2×C22⋊D11—24no—
296C2×C22⋊D11—42no—
297C2×C22⋊D11—42no—
298C2×C22⋊D11—42no—
299C2×C22⋊D11—42no—
300C2×C22⋊D11—42no—
301C2×C22⋊D11—42no—
302C2×C22⋊D11—42no—
303C2×C22⋊D11—42no—
304C22×Dic11—22no—
305C22×Dic11—24no—
306C22×Dic11—41no—
307C22×Dic11—41no—
308C22×Dic11—42no—
309C22×Dic11—42no—
310C22×Dic11C2411yescharacteristic
311C22×Dic11C2411yescharacteristic
312C22×Dic11C2412yes—
313C22×Dic11C2412yes—
314C22×Dic11C2412yes—
315C22×Dic11C2411yescharacteristic
316C22×Dic11C2411yescharacteristic
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2411yescharacteristic
319C2×D44—24no—
320C2×D44—24no—
321C2×D44—24no—
322C2×D44—24no—
323C2×D44—22no—
324C2×D44—22no—
325C2×D44—22no—
326C2×D44—42no—
327C2×D44—42no—
328C2×C4×D11—22no—
329C2×C4×D11—22no—
330C2×C4×D11—22no—
331C2×C4×D11—24no—
332C2×C4×D11—22no—
333C2×C4×D11—22no—
334C2×C4×D11—22no—
335C2×C4×D11—22no—
336C2×C4×D11—22no—
337C2×C4×D11—41no—
338C2×C4×D11—41no—
339C2×C4×D11—41no—
340C2×C4×D11—41no—
341C2×C4×D11—41no—
342C2×C4×D11—41no—
343C2×C4×D11—41no—
344C2×C4×D11—41no—
345C2×C4×D11—41no—
346C2×C4×D11—41no—
347C2×C4×D11—41no—
348C2×C4×D11—41no—
349C2×C4×D11—42no—
350C2×C4×D11—42no—
351C2×C4×D11—416no—
352C2×C4×D11C2×D414yes—
353C2×C4×D11C2×D414yes—
354C2×C4×D11#4114yes—
355C2×C4×D11#4114yes—
356C11×C4⋊C4—22no—
357C11×C4⋊C4—22no—
358C11×C4⋊C4—22no—
359C11×C4⋊C4—42no—
360C11×C22⋊C4—24no—
361C11×C22⋊C4—24no—
362C11×C22⋊C4—24no—
363C11×C22⋊C4—22no—
364C11×C22⋊C4—24no—
365C11×C22⋊C4—42no—
366C11×C22⋊C4—42no—
367C11×C22⋊C4C2×D414yes—
368C42×C11—24no—
369C42×C11—22no—
370C42×C11—22no—
371C22⋊Dic11—22no—
372C22⋊Dic11—24no—
373C22⋊Dic11—24no—
374C22⋊Dic11—42no—
375C22⋊Dic11—42no—
376C22⋊Dic11C2×D414yes—
377(C2×D11)⋊C4—24no—
378(C2×D11)⋊C4—22no—
379(C2×D11)⋊C4—24no—
380(C2×D11)⋊C4—24no—
381(C2×D11)⋊C4—24no—
382(C2×D11)⋊C4—24no—
383(C2×D11)⋊C4—24no—
384(C2×D11)⋊C4—24no—
385(C2×D11)⋊C4—22no—
386(C2×D11)⋊C4—24no—
387(C2×D11)⋊C4—42no—
388(C2×D11)⋊C4—42no—
389(C2×D11)⋊C4—42no—
390(C2×D11)⋊C4—42no—
391(C2×D11)⋊C4C2×D414yes—
392(C2×D11)⋊C4C2×D414yes—
393C4⋊Dic11—24no—
394C4⋊Dic11—24no—
395C4⋊Dic11—22no—
396C4⋊Dic11—22no—
397C4⋊Dic11—22no—
398C4⋊Dic11—42no—
399Dic11⋊C4—24no—
400Dic11⋊C4—24no—
401Dic11⋊C4—24no—
402Dic11⋊C4—24no—
403Dic11⋊C4—24no—
404C4×Dic11—24no—
405C4×Dic11—22no—
406C4×Dic11—22no—
407C4×Dic11—41no—
408C4×Dic11—41no—
409C4×Dic11—41no—
410C4×Dic11—41no—
411C2×#538—112no—
412#2857—111no—
413#2856—111no—
414#2847—111no—
415#2847—111no—
416#2639—112no—
417#2617—112no—
418#2559—112no—
419#2559—112no—
420#2557—112no—
421#2557—112no—
422#2496—111no—
423#2496—111no—
424#2491—111no—
425#2491D1111yescharacteristic, complemented
426#2428—111no—
427#2428—111no—
428#2422—111no—
429#2422—111no—
430#2325—112no—
431C4×#121—111no—
432C4×#121—111no—
433C2×C4×C22⋊C4—111no—
434C23×C11—21no—
435C23×C11—21no—
436C23×C11—21no—
437C23×C11—21no—
438C23×C11—21no—
439C23×C11—21no—
440C23×C11—22no—
441C23×C11—22no—
442C23×C11—22no—
443C23×C11—22no—
444C23×C11—22no—
445C23×C11—22no—
446C23×C11—22no—
447C23×C11C22×D412yes—
448C23×C11C2511yescharacteristic
449C22×D11—21no—
450C22×D11—21no—
451C22×D11—21no—
452C22×D11—21no—
453C22×D11—21no—
454C22×D11—21no—
455C22×D11—21no—
456C22×D11—21no—
457C22×D11—21no—
458C22×D11—21no—
459C22×D11—28no—
460C22×D11—22no—
461C22×D11—22no—
462C22×D11—22no—
463C22×D11—22no—
464C22×D11—22no—
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—44no—
468C22×D11—44no—
469C22×D11—44no—
470C22×D11—44no—
471C22×D11—44no—
472C22×D11—44no—
473C22×D11C22×D412yes—
474C22×D11C22×D412yes—
475C22×D11C2×#4112yes—
476C22×D11C2×#4112yes—
477Q8×C11—84no—
478D4×C11—44no—
479D4×C11—84no—
480C2×C4×C11—21no—
481C2×C4×C11—21no—
482C2×C4×C11—21no—
483C2×C4×C11—21no—
484C2×C4×C11—21no—
485C2×C4×C11—21no—
486C2×C4×C11—22no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—22no—
490C2×C4×C11—21no—
491C2×C4×C11—22no—
492C2×C4×C11—21no—
493C2×C4×C11—21no—
494C2×C4×C11—21no—
495C2×C4×C11—22no—
496C2×C4×C11—21no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—21no—
500C2×C4×C11—22no—
501C2×C4×C11—44no—
502C2×C4×C11C22×D412yes—
503C2×C4×C11C22×D412yes—
504C2×C4×C11C2×#4112yes—
505C2×C4×C11C2×#4112yes—
506C2×C4×C11H(5,𝔽2)12yes—
507C2×C4×C11H(5,𝔽2)12yes—
508C22⋊D11—48no—
509C22⋊D11—84no—
510C22⋊D11—84no—
511C22⋊D11—84no—
512C22⋊D11—84no—
513C2×Dic11—21no—
514C2×Dic11—21no—
515C2×Dic11—21no—
516C2×Dic11—21no—
517C2×Dic11—21no—
518C2×Dic11—21no—
519C2×Dic11—21no—
520C2×Dic11—21no—
521C2×Dic11—22no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—22no—
526C2×Dic11—21no—
527C2×Dic11—21no—
528C2×Dic11—21no—
529C2×Dic11—22no—
530C2×Dic11—22no—
531C2×Dic11—21no—
532C2×Dic11—21no—
533C2×Dic11—22no—
534C2×Dic11—22no—
535C2×Dic11—21no—
536C2×Dic11—44no—
537C2×Dic11—84no—
538C2×Dic11C22×D412yes—
539C2×Dic11C22×D412yes—
540C2×Dic11C2×#4112yes—
541C2×Dic11C2×#4112yes—
542D44—48no—
543D44—44no—
544D44—84no—
545C4×D11—28no—
546C4×D11—44no—
547C4×D11—44no—
548C4×D11—44no—
549C4×D11—44no—
550C4×D11—44no—
551C4×D11—44no—
552C4×D11—44no—
553C4×D11—84no—
554C24×C4—111no—
555#538—2216no—
556C2×C4⋊Q8C2×D1111yescharacteristic, complemented
557C2×#127—111no—
558C2×#126—112no—
559C2×#126—112no—
560C2×#124—112no—
561C2×#124C2×D1112yes—
562C2×#123—112no—
563C2×#123—112no—
564C2×C22⋊Q8—112no—
565C2×#121—111no—
566C2×#121—112no—
567C2×#121—111no—
568C2×#121—111no—
569C2×#121—111no—
570C2×#121—111no—
571C2×#121—112no—
572C2×#121—112no—
573C2×#121—112no—
574C2×#121C2×D1111yescharacteristic
575C2×#120—112no—
576C2×#120—112no—
577C2×C4×D4—111no—
578C2×C4×D4—112no—
579C2×C4×D4—112no—
580C2×C4×D4—111no—
581C22×C22⋊C4—111no—
582C22×C22⋊C4—111no—
583C22×C42—111no—
584C22×C42—111no—
585#400—112no—
586#400—112no—
587#397—112no—
588#397—112no—
589#397—112no—
590#397—112no—
591#394—112no—
592#394—112no—
593#394—112no—
594#394—112no—
595#394—112no—
596#394C2×D1112yes—
597#393—112no—
598#393C2×D1112yescomplemented
599#392—112no—
600#392—112no—
601#391—112no—
602#390—111no—
603#390—112no—
604#390—112no—
605#390—111no—
606#390C2×D1111yescharacteristic, complemented
607#390C2×D1111yescharacteristic, complemented
608#389—111no—
609#389—111no—
610#389—112no—
611#389—111no—
612#389—111no—
613#388—112no—
614#388—112no—
615#388—112no—
616#388C2×D1112yescomplemented
617#387—112no—
618#387—112no—
619#386—112no—
620#386—112no—
621#386—112no—
622#386—112no—
623#386—112no—
624#386—112no—
625#386—112no—
626#386—112no—
627#386—112no—
628#386—112no—
629#385—112no—
630#385—112no—
631#384—111no—
632#384—111no—
633#380—111no—
634#380—112no—
635#380—111no—
636#380—111no—
637#380—111no—
638#380—111no—
639#380C2×D1111yescharacteristic
640C4×C4⋊C4—111no—
641C4×C4⋊C4C2×D1111yescharacteristic, complemented
642C4×C22⋊C4—111no—
643C4×C22⋊C4—111no—
644C4×C22⋊C4—111no—
645C4×C22⋊C4—112no—
646C4×C22⋊C4—111no—
647C4×C22⋊C4—111no—
648C4×C22⋊C4—112no—
649C4×C22⋊C4—111no—
650C4×C22⋊C4—111no—
651C4×C22⋊C4C2×D1111yescharacteristic
652C2×#95—111no—
653C2×#95—111no—
654C22×C11—22no—
655C22×C11—22no—
656C22×C11—22no—
657C22×C11—41no—
658C22×C11—41no—
659C22×C11—41no—
660C22×C11—41no—
661C22×C11—42no—
662C22×C11—42no—
663C22×C11—42no—
664C22×C11—42no—
665C22×C11—42no—
666C22×C11—42no—
667C22×C11—42no—
668C22×C11C23×D411yescharacteristic
669C22×C11C22×#4111yescharacteristic
670C22×C11C22×#4111yescharacteristic
671C22×C11C2×H(5,𝔽2)11yescharacteristic
672C22×C11C2×H(5,𝔽2)11yescharacteristic
673C22×C11#58511yescharacteristic
674C22×C11#58511yescharacteristic
675C2×D11—22no—
676C2×D11—22no—
677C2×D11—22no—
678C2×D11—22no—
679C2×D11—22no—
680C2×D11—22no—
681C2×D11—22no—
682C2×D11—22no—
683C2×D11—22no—
684C2×D11—416no—
685C2×D11—41no—
686C2×D11—41no—
687C2×D11—41no—
688C2×D11—41no—
689C2×D11—42no—
690C2×D11—42no—
691C2×D11—42no—
692C2×D11—42no—
693C2×D11—42no—
694C2×D11—42no—
695C2×D11—42no—
696C2×D11#53214yes—
697C4×C11—22no—
698C4×C11—22no—
699C4×C11—22no—
700C4×C11—42no—
701C4×C11—41no—
702C4×C11—42no—
703C4×C11—42no—
704C4×C11—41no—
705C4×C11#53814yescomplemented
706Dic11—22no—
707Dic11—22no—
708Dic11—22no—
709Dic11—22no—
710Dic11—42no—
711Dic11—41no—
712Dic11—42no—
713Dic11—42no—
714Dic11—41no—
715C25—111no—
716C22×Q8C22×D1112yes—
717C22×D4—112no—
718C22×D4—112no—
719C22×D4—112no—
720C22×D4—112no—
721C22×D4—112no—
722C22×D4—112no—
723C22×D4—111no—
724C22×D4—112no—
725C22×D4C22×D1111yescharacteristic
726C22×D4C22×D1112yes—
727C23×C4—111no—
728C23×C4—111no—
729C23×C4—111no—
730C23×C4—111no—
731C23×C4—112no—
732C23×C4—111no—
733C23×C4—111no—
734C23×C4—111no—
735C23×C4—112no—
736C23×C4—111no—
737C23×C4—111no—
738C23×C4—224no—
739C23×C4—442no—
740C23×C4—442no—
741C23×C4C22×D1111yescharacteristic
742C4⋊Q8—42no—
743#127—442no—
744#126—228no—
745#126—228no—
746#124—28no—
747#124—228no—
748#123—228no—
749#123—228no—
750C22⋊Q8—228no—
751#121—42no—
752#121—228no—
753#121—228no—
754#121—228no—
755#121—228no—
756#121—224no—
757#121—224no—
758#121—442no—
759#121—442no—
760#121—442no—
761#120—228no—
762#120—228no—
763C4×D4—228no—
764C4×D4—228no—
765C4×D4—442no—
766C4×D4—442no—
767C2×C4⋊C4—111no—
768C2×C4⋊C4—111no—
769C2×C4⋊C4—112no—
770C2×C4⋊C4—112no—
771C2×C4⋊C4—112no—
772C2×C4⋊C4—112no—
773C2×C4⋊C4—112no—
774C2×C4⋊C4—111no—
775C2×C4⋊C4—112no—
776C2×C4⋊C4—112no—
777C2×C4⋊C4—112no—
778C2×C4⋊C4C22×D1111yescharacteristic
779C2×C4⋊C4C22×D1111yescharacteristic
780C2×C4⋊C4C22×D1111yescharacteristic
781C2×C4⋊C4C22×D1112yes—
782C2×C22⋊C4—111no—
783C2×C22⋊C4—111no—
784C2×C22⋊C4—111no—
785C2×C22⋊C4—118no—
786C2×C22⋊C4—111no—
787C2×C22⋊C4—112no—
788C2×C22⋊C4—112no—
789C2×C22⋊C4—111no—
790C2×C22⋊C4—111no—
791C2×C22⋊C4—112no—
792C2×C22⋊C4—112no—
793C2×C22⋊C4—112no—
794C2×C22⋊C4—112no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—112no—
797C2×C22⋊C4—112no—
798C2×C22⋊C4—112no—
799C2×C22⋊C4—112no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—112no—
802C2×C22⋊C4—112no—
803C2×C22⋊C4—112no—
804C2×C22⋊C4—112no—
805C2×C22⋊C4—224no—
806C2×C22⋊C4C22×D1111yescharacteristic
807C2×C22⋊C4C22×D1112yes—
808C2×C22⋊C4C22×D1112yes—
809C2×C22⋊C4C22×D1112yes—
810C2×C22⋊C4C22×D1112yes—
811C2×C22⋊C4C22×D1112yes—
812C2×C22⋊C4C22×D1112yes—
813C2×C22⋊C4C22×D1111yescharacteristic
814C2×C42—112no—
815C2×C42—111no—
816C2×C42—111no—
817C2×C42—111no—
818C2×C42—111no—
819C2×C42—111no—
820C2×C42—111no—
821C2×C42—442no—
822C2×C42—442no—
823C2×C42C22×D1112yes—
824C2×C42C22×D1111yescharacteristic
825C2×C42C22×D1111yescharacteristic
826#95—111no—
827#95—111no—
828#95—111no—
829#95—111no—
830#95—111no—
831#95—111no—
832#95—112no—
833#95—112no—
834#95—112no—
835#95—112no—
836#95—112no—
837#95—112no—
838#95—112no—
839#95—112no—
840#95—112no—
841#95—112no—
842#95C22×D1111yescharacteristic
843#95C22×D1111yescharacteristic
844#95C22×D1112yes—
845#95C22×D1112yes—
846C2×C11—42no—
847C2×C11—82no—
848C2×C11C2×#53211yescharacteristic
849C2×C11C2×#53811yescharacteristic
850C2×C11#345511yescharacteristic
851C2×C11#349611yescharacteristic
852C2×C11#349611yescharacteristic
853C2×C11#350511yescharacteristic
854C2×C11#350611yescharacteristic
855D11—24no—
856D11—42no—
857D11—82no—
858C24—111no—
859C24—111no—
860C24—114no—
861C24—112no—
862C24—222no—
863C24—222no—
864C24—441no—
865C24—441no—
866C24—441no—
867C24—441no—
868C24C23×D1112yes—
869C24C23×D1111yescharacteristic
870C2×Q8—24no—
871C2×Q8—42no—
872C2×Q8—42no—
873C2×D4—24no—
874C2×D4—22no—
875C2×D4—22no—
876C2×D4—22no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—224no—
880C2×D4—224no—
881C2×D4—224no—
882C2×D4—224no—
883C2×D4—224no—
884C2×D4—224no—
885C2×D4—224no—
886C2×D4—224no—
887C2×D4—224no—
888C2×D4—224no—
889C2×D4—224no—
890C2×D4—222no—
891C2×D4—222no—
892C2×D4—222no—
893C2×D4—442no—
894C2×D4—442no—
895C2×D4—442no—
896C2×D4—442no—
897C2×D4—442no—
898C2×D4—442no—
899C2×D4—442no—
900C2×D4—442no—
901C2×D4—442no—
902C2×D4—442no—
903C22×C4—22no—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—111no—
907C22×C4—111no—
908C22×C4—111no—
909C22×C4—111no—
910C22×C4—114no—
911C22×C4—114no—
912C22×C4—114no—
913C22×C4—114no—
914C22×C4—111no—
915C22×C4—111no—
916C22×C4—112no—
917C22×C4—112no—
918C22×C4—112no—
919C22×C4—222no—
920C22×C4—222no—
921C22×C4—222no—
922C22×C4—222no—
923C22×C4—224no—
924C22×C4—222no—
925C22×C4—222no—
926C22×C4—222no—
927C22×C4—222no—
928C22×C4—222no—
929C22×C4—224no—
930C22×C4—441no—
931C22×C4—441no—
932C22×C4—441no—
933C22×C4—441no—
934C22×C4—441no—
935C22×C4—441no—
936C22×C4—441no—
937C22×C4—441no—
938C22×C4—441no—
939C22×C4—441no—
940C22×C4—441no—
941C22×C4—441no—
942C22×C4—442no—
943C22×C4—442no—
944C22×C4—4416no—
945C22×C4—441no—
946C22×C4—441no—
947C22×C4—442no—
948C22×C4—442no—
949C22×C4C23×D1111yescharacteristic
950C22×C4C23×D1111yescharacteristic
951C22×C4C23×D1112yes—
952C22×C4C23×D1112yes—
953C22×C4C23×D1112yes—
954C22×C4C23×D1111yescharacteristic
955C22×C4C23×D1111yescharacteristic
956C22×C4C23×D1111yescharacteristic
957C22×C4C23×D1111yescharacteristic
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—42no—
962C4⋊C4—224no—
963C4⋊C4—224no—
964C4⋊C4—224no—
965C4⋊C4—224no—
966C4⋊C4—224no—
967C4⋊C4—224no—
968C4⋊C4—224no—
969C4⋊C4—222no—
970C4⋊C4—222no—
971C4⋊C4—222no—
972C4⋊C4—442no—
973C22⋊C4—24no—
974C22⋊C4—24no—
975C22⋊C4—24no—
976C22⋊C4—22no—
977C22⋊C4—24no—
978C22⋊C4—42no—
979C22⋊C4—42no—
980C22⋊C4—114no—
981C22⋊C4—114no—
982C22⋊C4—114no—
983C22⋊C4—222no—
984C22⋊C4—224no—
985C22⋊C4—224no—
986C22⋊C4—224no—
987C22⋊C4—224no—
988C22⋊C4—224no—
989C22⋊C4—224no—
990C22⋊C4—222no—
991C22⋊C4—224no—
992C22⋊C4—224no—
993C22⋊C4—224no—
994C22⋊C4—222no—
995C22⋊C4—224no—
996C22⋊C4—442no—
997C22⋊C4—442no—
998C22⋊C4—442no—
999C22⋊C4—442no—
1000C22⋊C4—442no—
1001C22⋊C4—442no—
1002C22⋊C4D4×D1114yes—
1003C42—24no—
1004C42—22no—
1005C42—22no—
1006C42—224no—
1007C42—222no—
1008C42—222no—
1009C42—441no—
1010C42—441no—
1011C42—441no—
1012C42—441no—
1013C11#3500511yescharacteristic, complemented, Sylow
1014C23—21no—
1015C23—21no—
1016C23—21no—
1017C23—21no—
1018C23—21no—
1019C23—21no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—112no—
1028C23—112no—
1029C23—112no—
1030C23—112no—
1031C23—228no—
1032C23—221no—
1033C23—221no—
1034C23—221no—
1035C23—221no—
1036C23—221no—
1037C23—221no—
1038C23—221no—
1039C23—221no—
1040C23—221no—
1041C23—221no—
1042C23—222no—
1043C23—222no—
1044C23—222no—
1045C23—222no—
1046C23—222no—
1047C23—222no—
1048C23—222no—
1049C23—444no—
1050C23—444no—
1051C23—444no—
1052C23—444no—
1053C23—444no—
1054C23—444no—
1055C23C2×D4×D1112yes—
1056C23C24×D1111yescharacteristic
1057Q8—84no—
1058D4—44no—
1059D4—84no—
1060D4—448no—
1061D4—448no—
1062D4—444no—
1063D4—884no—
1064D4—884no—
1065D4—884no—
1066D4—884no—
1067D4—884no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—21no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—21no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—44no—
1090C2×C4—112no—
1091C2×C4—112no—
1092C2×C4—112no—
1093C2×C4—112no—
1094C2×C4—221no—
1095C2×C4—221no—
1096C2×C4—221no—
1097C2×C4—221no—
1098C2×C4—221no—
1099C2×C4—221no—
1100C2×C4—221no—
1101C2×C4—221no—
1102C2×C4—228no—
1103C2×C4—222no—
1104C2×C4—222no—
1105C2×C4—222no—
1106C2×C4—221no—
1107C2×C4—221no—
1108C2×C4—222no—
1109C2×C4—222no—
1110C2×C4—221no—
1111C2×C4—221no—
1112C2×C4—222no—
1113C2×C4—222no—
1114C2×C4—221no—
1115C2×C4—221no—
1116C2×C4—222no—
1117C2×C4—222no—
1118C2×C4—444no—
1119C2×C4—444no—
1120C2×C4—444no—
1121C2×C4—444no—
1122C2×C4—444no—
1123C2×C4—444no—
1124C2×C4—444no—
1125C2×C4—444no—
1126C2×C4—884no—
1127C2×C4—884no—
1128C2×C4C2×D4×D1112yes—
1129C2×C4C2×D4×D1112yes—
1130C2×C4#6703712yes—
1131C2×C4#41×D1112yes—
1132C2×C4#41×D1112yes—
1133C2×C4#6704212yes—
1134C22—22no—
1135C22—22no—
1136C22—22no—
1137C22—41no—
1138C22—41no—
1139C22—41no—
1140C22—41no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—42no—
1147C22—42no—
1148C22—114no—
1149C22—222no—
1150C22—222no—
1151C22—222no—
1152C22—222no—
1153C22—222no—
1154C22—222no—
1155C22—222no—
1156C22—222no—
1157C22—222no—
1158C22—4416no—
1159C22—441no—
1160C22—441no—
1161C22—441no—
1162C22—441no—
1163C22—442no—
1164C22—442no—
1165C22—442no—
1166C22—442no—
1167C22—442no—
1168C22—442no—
1169C22—442no—
1170C22C22×D4×D1111yescharacteristic
1171C22C2×#6703711yescharacteristic
1172C22C2×#41×D1111yescharacteristic
1173C22C2×#41×D1111yescharacteristic
1174C22C2×#6704211yescharacteristic
1175C22#1062345511yescharacteristic
1176C22#1062345711yescharacteristic
1177C4—22no—
1178C4—22no—
1179C4—22no—
1180C4—42no—
1181C4—42no—
1182C4—42no—
1183C4—41no—
1184C4—41no—
1185C4—222no—
1186C4—222no—
1187C4—222no—
1188C4—222no—
1189C4—442no—
1190C4—442no—
1191C4—442no—
1192C4—441no—
1193C4—441no—
1194C4#1062320914yescomplemented
1195C2—42no—
1196C2—82no—
1197C2—224no—
1198C2—442no—
1199C2—882no—
1200C2D11×#53211yescharacteristic
1201C2C2×#1062320911yescharacteristic
1202C2#1308200311yescharacteristic
1203C2#1308237211yescharacteristic
1204C2#1308237411yescharacteristic
1205C2#1308245211yescharacteristic
1206C2#1308245811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2491C2
hypercenter#2491D11
hypocenterC11#35005
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2491

Complements

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

NH ≅ G/Ntype
1. C2×#10623209C2semidirect
2. #13076963C2semidirect
3. #13076960C2semidirect
4. #13076899C2semidirect
5. #13076895C2semidirect
6. #13074545C2semidirect
7. #13074355C2semidirect
8. #13073751C2semidirect
9. #13073738C2semidirect
10. #13073716C2semidirect
11. #13073713C2semidirect
12. #13073034C2semidirect
13. #13073032C2semidirect
14. #13072982C2semidirect
15. #13072206C2semidirect
16. #13072205C2semidirect
17. #13072130C2semidirect
18. #13072128C2semidirect
19. #13071320C2semidirect
20. #13071132C2semidirect
21. C4×#66948C2semidirect
22. C4×C22⋊C4×D11C2semidirect
23. C11×#2491C2semidirect
25. C2×C11×C4⋊Q8C22semidirect
30. C2×#66993C22semidirect
35. C2×D4×Dic11C22semidirect
52. C2×C4×D44C22semidirect
56. C11×#393C22semidirect
57. C11×#390C22semidirect
58. C11×#390C22semidirect
59. C11×#388C22semidirect
61. C4×C11×C4⋊C4C22semidirect
63. #10622844C22semidirect
64. #10622843C22semidirect
70. #10622603C22semidirect
71. #10622601C22semidirect
77. #10622598C22semidirect
78. #10622589C22semidirect
79. C4⋊C4×Dic11C22semidirect
80. #10622586C22semidirect
81. #10622586C22semidirect
82. #10622586C22semidirect
86. #10622572C22semidirect
87. #10622572C22semidirect
89. #10622571C22semidirect
90. #10622570C22semidirect
91. #10622570C22semidirect
95. #10622569C22semidirect
96. #10622566C22semidirect
98. #10622563C22semidirect
99. #10622558C22semidirect
102. C22⋊C4×Dic11C22semidirect
103. #10622552C22semidirect
106. C4×(C2×D11)⋊C4C22semidirect
107. #10622548C22semidirect
108. #10622546C22semidirect
109. #10622541C22semidirect
111. #10622287C22semidirect
112. #10622283C22semidirect
113. #10622281C22semidirect
121. #10622271C22semidirect
122. #10622271C22semidirect
123. #10622268C22semidirect
228. C22⋊C4×D11D4semidirect
425. #2491D11semidirect
556. C2×C4⋊Q8C2×D11semidirect
598. #393C2×D11semidirect
606. #390C2×D11semidirect
607. #390C2×D11semidirect
616. #388C2×D11semidirect
641. C4×C4⋊C4C2×D11semidirect
705. C4×C11#538semidirect
1013. C11#35005semidirect
1194. C4#10623209semidirect

Maximal subgroups

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

subgroupindex
C2×#106232092
#130769632
#130769602
#130768992
#130768952
#130745452
#130743552
#130737512
#130737382
#130737162
#130737132
#130730342
#130730322
#130729822
#130722062
#130722052
#130721302
#130721282
#130713202
#130711322
C4×#669482
C4×C22⋊C4×D112
C11×#24912
#3500511