Finite Group Databasebeta

← #14926686

Subgroups — #14926686

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×#10623188C212yesmaximal, complemented
2#13076969C211yesmaximal, characteristic, complemented
3#13076960C211yesmaximal, characteristic, complemented
4#13076899C211yesmaximal, characteristic, complemented
5#13076895C211yesmaximal, characteristic, complemented
6#13074543C212yesmaximal, complemented
7#13074355C212yesmaximal, complemented
8#13073749C212yesmaximal, complemented
9#13073740C212yesmaximal, complemented
10#13073718C212yesmaximal, complemented
11#13073711C212yesmaximal, complemented
12#13073040C211yesmaximal, characteristic, complemented
13#13073039C211yesmaximal, characteristic, complemented
14#13072979C211yesmaximal, characteristic, complemented
15#13072977C211yesmaximal, characteristic, complemented
16#13072200C211yesmaximal, characteristic, complemented
17#13072198C211yesmaximal, characteristic, complemented
18#13072133C211yesmaximal, characteristic, complemented
19#13071313C212yesmaximal, complemented
20#13071124C211yesmaximal, characteristic, complemented
21C4×#66991C211yesmaximal, characteristic, complemented
22C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
23C11×#2422C211yesmaximal, characteristic, complemented
24C23×C4×D11C2211yescharacteristic
25C2×C11×#123C2212yes—
26C2×C11×#121C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic, complemented
28C2×#66993C2211yescharacteristic, complemented
29C2×#66991C2211yescharacteristic
30C2×#66991C2212yes—
31C2×#66991C2211yescharacteristic
32C2×#66990C2212yes—
33C2×#66983C2212yes—
34C2×#66983C2211yescharacteristic
35C2×C4×C22⋊D11C2212yes—
36#10623188—216no—
37C2×#66951C2212yes—
38C2×#66950C2212yes—
39C2×#66948C2211yescharacteristic
40C2×#66948C2211yescharacteristic
41C2×#66947C2212yes—
42C2×#66946C2212yes—
43C2×#66946C2211yescharacteristic, complemented
44C2×#66938C2212yes—
45C2×#66938C2212yes—
46C2×#66937C2212yes—
47C2×#66937C2212yes—
48C2×#66935C2212yes—
49C2×C22⋊C4×D11C2211yescharacteristic
50C2×C22⋊C4×D11C2211yescharacteristic
51C2×#66932C2212yes—
52C2×C42×D11C2211yescharacteristic
53C2×C42×D11C2211yescharacteristic
54C2×#66922C2211yescharacteristic, complemented
55C11×#397C2212yescomplemented
56C11×#394C2212yes—
57C11×#390C2211yescharacteristic, complemented
58C11×#389C2211yescharacteristic, complemented
59C11×#385C2212yescomplemented
60C11×#384C2211yescharacteristic, complemented
61C11×#380C2211yescharacteristic
62C4×C11×C22⋊C4C2211yescharacteristic
63#10622836C2212yes—
64#10622834C2211yescharacteristic, complemented
65#10622833C2212yes—
66#10622826C2212yescomplemented
67#10622825C2211yescharacteristic
68C4×C22⋊Dic11C2211yescharacteristic
69C4×C22⋊Dic11C2212yescomplemented
70#10622606C2212yescomplemented
71#10622604C2212yes—
72#10622603C2212yescomplemented
73#10622602C2212yescomplemented
74#10622600C2211yescharacteristic
75#10622600C2211yescharacteristic
76#10622600C2211yescharacteristic
77#10622600C2211yescharacteristic
78#10622600C2212yes—
79#10622598C2211yescharacteristic, complemented
80#10622598C2211yescharacteristic, complemented
81#10622598C2212yescomplemented
82#10622591C2212yescomplemented
83#10622589C2211yescharacteristic, complemented
84C4⋊C4×Dic11C2211yescharacteristic, complemented
85#10622587C2212yescomplemented
86#10622586C2211yescharacteristic, complemented
87#10622574C2212yes—
88#10622574C2212yes—
89#10622574C2212yescomplemented
90#10622574C2212yescomplemented
91#10622573C2212yes—
92#10622571C2212yes—
93#10622570C2212yescomplemented
94#10622570C2212yescomplemented
95#10622569C2212yes—
96#10622569C2212yes—
97#10622569C2212yes—
98#10622569C2212yescomplemented
99#10622565C2212yes—
100#10622564C2212yescomplemented
101#10622560C2212yescomplemented
102#10622557C2212yescomplemented
103C22⋊C4×Dic11C2211yescharacteristic
104C22⋊C4×Dic11C2211yescharacteristic
105#10622552C2211yescharacteristic, complemented
106#10622552C2211yescharacteristic, complemented
107C4×(C2×D11)⋊C4C2211yescharacteristic
108C4×(C2×D11)⋊C4C2211yescharacteristic
109C4×C4⋊Dic11C2211yescharacteristic, complemented
110#10622288C2212yes—
111#10622286C2212yescomplemented
112#10622283C2212yescomplemented
113#10622279C2211yescharacteristic
114#10622279C2211yescharacteristic
115#10622279C2212yescomplemented
116#10622278C2212yes—
117#10622278C2212yes—
118#10622278C2212yes—
119D11×#95C2211yescharacteristic
120D11×#95C2211yescharacteristic
121#10622273C2212yescomplemented
122#10622273C2212yescomplemented
123#10622265C2212yescomplemented
124C24×D11C2311yescharacteristic
125C22×D4×C11C2311yescharacteristic
126C22×D4×C11C2312yes—
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2312yes—
129C22×C22⋊D11C2312yes—
130C22×C22⋊D11C2312yes—
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yes—
133C22×C22⋊D11C2312yes—
134C23×Dic11C2311yescharacteristic
135C22×D44C2312yes—
136C22×D44C2311yescharacteristic
137C22×D44C2312yes—
138C22×C4×D11—24no—
139C22×C4×D11—42no—
140C22×C4×D11—42no—
141C22×C4×D11C2311yescharacteristic
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2312yes—
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C22×Dic22C2312yes—
151C11×#123—28no—
152C11×#121—42no—
153C4×D4×C11—42no—
154C2×C11×C4⋊C4C2312yes—
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C4⋊C4C2312yes—
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2311yescharacteristic
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2312yes—
166C2×C11×C22⋊C4C2311yescharacteristic
167C2×C42×C11C2311yescharacteristic
168C2×C42×C11C2311yescharacteristic
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2311yescharacteristic
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2311yescharacteristic
176#66993—42no—
177#66991—24no—
178#66991—28no—
179#66991—42no—
180#66990—28no—
181#66983—28no—
182#66983—42no—
183C4×C22⋊D11—28no—
184C2×(C2×D11)⋊C4C2311yescharacteristic
185C2×(C2×D11)⋊C4C2311yescharacteristic
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
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⋊Dic11C2311yescharacteristic
201C2×C4⋊Dic11C2311yescharacteristic
202C2×C4⋊Dic11C2312yes—
203C2×C4⋊Dic11C2312yes—
204C2×C4⋊Dic11C2311yescharacteristic
205C2×C4⋊Dic11C2312yes—
206C2×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2312yes—
208C2×Dic11⋊C4C2312yes—
209C2×C4×Dic11C2311yescharacteristic
210C2×C4×Dic11C2311yescharacteristic
211C2×C4×Dic11C2312yes—
212C2×C4×Dic11C2312yes—
213C2×C4×Dic11C2311yescharacteristic
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2311yescharacteristic
216C2×C4×Dic11C2311yescharacteristic
217#66951—28no—
218#66950—28no—
219#66948—24no—
220#66948—42no—
221#66947—28no—
222#66946—28no—
223#66946—42no—
224#66938—28no—
225#66938—28no—
226#66937—28no—
227#66937—28no—
228#66935—28no—
229C22⋊C4×D11—24no—
230C22⋊C4×D11D418yescomplemented
231#66932—28no—
232C42×D11—42no—
233C42×D11—42no—
234#66922—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×D4×C11—24no—
269C2×D4×C11—22no—
270C2×D4×C11—22no—
271C2×D4×C11—22no—
272C2×D4×C11—42no—
273C2×D4×C11—42no—
274C22×C4×C11—22no—
275C22×C4×C11—22no—
276C22×C4×C11—22no—
277C22×C4×C11—24no—
278C22×C4×C11—42no—
279C22×C4×C11—42no—
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—41no—
306C22×Dic11—41no—
307C22×Dic11C2411yescharacteristic
308C22×Dic11C2411yescharacteristic
309C22×Dic11C2412yes—
310C22×Dic11C2412yes—
311C22×Dic11C2412yes—
312C22×Dic11C2411yescharacteristic
313C22×Dic11C2411yescharacteristic
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2411yescharacteristic
316C2×D44—24no—
317C2×D44—24no—
318C2×D44—24no—
319C2×D44—24no—
320C2×D44—22no—
321C2×D44—22no—
322C2×D44—22no—
323C2×D44—42no—
324C2×D44—42no—
325C2×C4×D11—22no—
326C2×C4×D11—24no—
327C2×C4×D11—22no—
328C2×C4×D11—22no—
329C2×C4×D11—22no—
330C2×C4×D11—22no—
331C2×C4×D11—22no—
332C2×C4×D11—22no—
333C2×C4×D11—22no—
334C2×C4×D11—41no—
335C2×C4×D11—41no—
336C2×C4×D11—41no—
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—42no—
347C2×C4×D11—42no—
348C2×C4×D11—416no—
349C2×C4×D11C2×D414yes—
350C2×C4×D11C2×D414yes—
351C2×C4×D11#4114yes—
352C2×C4×D11#4114yes—
353C2×Dic22—24no—
354C2×Dic22—42no—
355C2×Dic22—42no—
356C11×C4⋊C4—24no—
357C11×C4⋊C4—24no—
358C11×C4⋊C4—22no—
359C11×C4⋊C4—22no—
360C11×C4⋊C4—22no—
361C11×C4⋊C4—42no—
362C11×C22⋊C4—24no—
363C11×C22⋊C4—24no—
364C11×C22⋊C4—22no—
365C11×C22⋊C4—24no—
366C11×C22⋊C4—42no—
367C11×C22⋊C4—42no—
368C11×C22⋊C4C2×D414yes—
369C42×C11—22no—
370C42×C11—22no—
371C22⋊Dic11—24no—
372C22⋊Dic11—22no—
373C22⋊Dic11—24no—
374C22⋊Dic11—24no—
375C22⋊Dic11—42no—
376C22⋊Dic11—42no—
377C22⋊Dic11C2×D414yes—
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—24no—
386(C2×D11)⋊C4—22no—
387(C2×D11)⋊C4—24no—
388(C2×D11)⋊C4—42no—
389(C2×D11)⋊C4—42no—
390(C2×D11)⋊C4—42no—
391(C2×D11)⋊C4—42no—
392(C2×D11)⋊C4C2×D414yes—
393(C2×D11)⋊C4C2×D414yes—
394C4⋊Dic11—24no—
395C4⋊Dic11—24no—
396C4⋊Dic11—22no—
397C4⋊Dic11—22no—
398C4⋊Dic11—22no—
399C4⋊Dic11—42no—
400Dic11⋊C4—24no—
401Dic11⋊C4—24no—
402Dic11⋊C4—24no—
403C4×Dic11—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#2491—111no—
426#2428—111no—
427#2428—111no—
428#2422—111no—
429#2422D1111yescharacteristic, complemented
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—
477D4×C11—44no—
478D4×C11—84no—
479C2×C4×C11—21no—
480C2×C4×C11—21no—
481C2×C4×C11—21no—
482C2×C4×C11—21no—
483C2×C4×C11—21no—
484C2×C4×C11—21no—
485C2×C4×C11—22no—
486C2×C4×C11—22no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—21no—
490C2×C4×C11—22no—
491C2×C4×C11—21no—
492C2×C4×C11—21no—
493C2×C4×C11—21no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—21no—
497C2×C4×C11—21no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—44no—
501C2×C4×C11—84no—
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—21no—
535C2×Dic11—22no—
536C2×Dic11—44no—
537C2×Dic11C22×D412yes—
538C2×Dic11C22×D412yes—
539C2×Dic11C2×#4112yes—
540C2×Dic11C2×#4112yes—
541D44—48no—
542D44—44no—
543D44—84no—
544C4×D11—28no—
545C4×D11—44no—
546C4×D11—44no—
547C4×D11—44no—
548C4×D11—44no—
549C4×D11—44no—
550C4×D11—44no—
551C4×D11—44no—
552C4×D11—84no—
553Dic22—84no—
554C24×C4—111no—
555#538—2216no—
556C2×C4⋊Q8—111no—
557C2×#127—111no—
558C2×#126—112no—
559C2×#126—112no—
560C2×#124—112no—
561C2×#124—112no—
562C2×#123—112no—
563C2×#123C2×D1112yes—
564C2×C22⋊Q8—112no—
565C2×#121—111no—
566C2×#121—112no—
567C2×#121—112no—
568C2×#121—111no—
569C2×#121—111no—
570C2×#121—111no—
571C2×#121—111no—
572C2×#121—112no—
573C2×#121—112no—
574C2×#121C2×D1111yescharacteristic
575C2×#120—112no—
576C2×#120—112no—
577C2×C4×D4—112no—
578C2×C4×D4—112no—
579C2×C4×D4—111no—
580C2×C4×D4C2×D1111yescharacteristic, complemented
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#397C2×D1112yescomplemented
591#394—112no—
592#394—112no—
593#394—112no—
594#394—112no—
595#394—112no—
596#394C2×D1112yes—
597#393—112no—
598#393—112no—
599#392—112no—
600#392—112no—
601#391—112no—
602#390—111no—
603#390—112no—
604#390—112no—
605#390—111no—
606#390—111no—
607#390C2×D1111yescharacteristic, complemented
608#389—111no—
609#389—111no—
610#389—112no—
611#389—111no—
612#389C2×D1111yescharacteristic, complemented
613#388—112no—
614#388—112no—
615#388—112no—
616#388—112no—
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#385C2×D1112yescomplemented
631#384—111no—
632#384C2×D1111yescharacteristic, complemented
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⋊C4—111no—
642C4×C22⋊C4—111no—
643C4×C22⋊C4—112no—
644C4×C22⋊C4—111no—
645C4×C22⋊C4—111no—
646C4×C22⋊C4—111no—
647C4×C22⋊C4—111no—
648C4×C22⋊C4—111no—
649C4×C22⋊C4—111no—
650C4×C22⋊C4—112no—
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×Q8—112no—
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—111no—
732C23×C4—111no—
733C23×C4—111no—
734C23×C4—112no—
735C23×C4—111no—
736C23×C4—111no—
737C23×C4—224no—
738C23×C4—442no—
739C23×C4—442no—
740C23×C4C22×D1111yescharacteristic
741C23×C4C22×D1112yes—
742C4⋊Q8—442no—
743#127—442no—
744#126—228no—
745#126—228no—
746#124—228no—
747#124—228no—
748#123—28no—
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—42no—
764C4×D4—228no—
765C4×D4—228no—
766C4×D4—442no—
767C2×C4⋊C4—112no—
768C2×C4⋊C4—112no—
769C2×C4⋊C4—112no—
770C2×C4⋊C4—112no—
771C2×C4⋊C4—111no—
772C2×C4⋊C4—111no—
773C2×C4⋊C4—111no—
774C2×C4⋊C4—112no—
775C2×C4⋊C4—112no—
776C2×C4⋊C4C22×D1111yescharacteristic
777C2×C4⋊C4C22×D1112yes—
778C2×C4⋊C4C22×D1111yescharacteristic
779C2×C4⋊C4C22×D1111yescharacteristic
780C2×C4⋊C4C22×D1112yes—
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—112no—
790C2×C22⋊C4—111no—
791C2×C22⋊C4—111no—
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—112no—
806C2×C22⋊C4—224no—
807C2×C22⋊C4C22×D1111yescharacteristic
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—112no—
816C2×C42—111no—
817C2×C42—111no—
818C2×C42—111no—
819C2×C42—111no—
820C2×C42—111no—
821C2×C42—111no—
822C2×C42—442no—
823C2×C42—442no—
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—224no—
871C2×Q8—442no—
872C2×Q8—442no—
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—24no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—111no—
910C22×C4—111no—
911C22×C4—111no—
912C22×C4—111no—
913C22×C4—114no—
914C22×C4—114no—
915C22×C4—114no—
916C22×C4—114no—
917C22×C4—111no—
918C22×C4—111no—
919C22×C4—112no—
920C22×C4—112no—
921C22×C4—112no—
922C22×C4—222no—
923C22×C4—224no—
924C22×C4—222no—
925C22×C4—222no—
926C22×C4—222no—
927C22×C4—222no—
928C22×C4—222no—
929C22×C4—222no—
930C22×C4—222no—
931C22×C4—222no—
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—441no—
943C22×C4—441no—
944C22×C4—442no—
945C22×C4—442no—
946C22×C4—4416no—
947C22×C4—441no—
948C22×C4—441no—
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—24no—
959C4⋊C4—24no—
960C4⋊C4—22no—
961C4⋊C4—22no—
962C4⋊C4—22no—
963C4⋊C4—42no—
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—22no—
976C22⋊C4—24no—
977C22⋊C4—42no—
978C22⋊C4—42no—
979C22⋊C4—114no—
980C22⋊C4—114no—
981C22⋊C4—114no—
982C22⋊C4—222no—
983C22⋊C4—224no—
984C22⋊C4—224no—
985C22⋊C4—224no—
986C22⋊C4—224no—
987C22⋊C4—224no—
988C22⋊C4—222no—
989C22⋊C4—224no—
990C22⋊C4—224no—
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—22no—
1004C42—22no—
1005C42—224no—
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—884no—
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—21no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—21no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—21no—
1089C2×C4—44no—
1090C2×C4—84no—
1091C2×C4—112no—
1092C2×C4—112no—
1093C2×C4—112no—
1094C2×C4—112no—
1095C2×C4—221no—
1096C2×C4—221no—
1097C2×C4—221no—
1098C2×C4—221no—
1099C2×C4—221no—
1100C2×C4—221no—
1101C2×C4—221no—
1102C2×C4—221no—
1103C2×C4—228no—
1104C2×C4—222no—
1105C2×C4—222no—
1106C2×C4—222no—
1107C2×C4—221no—
1108C2×C4—221no—
1109C2×C4—221no—
1110C2×C4—222no—
1111C2×C4—222no—
1112C2×C4—221no—
1113C2×C4—221no—
1114C2×C4—222no—
1115C2×C4—222no—
1116C2×C4—221no—
1117C2×C4—222no—
1118C2×C4—222no—
1119C2×C4—444no—
1120C2×C4—444no—
1121C2×C4—444no—
1122C2×C4—444no—
1123C2×C4—444no—
1124C2×C4—444no—
1125C2×C4—444no—
1126C2×C4—444no—
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#1062318814yescomplemented
1195C2—42no—
1196C2—82no—
1197C2—224no—
1198C2—442no—
1199C2—882no—
1200C2D11×#53211yescharacteristic
1201C2C2×#1062318811yescharacteristic
1202C2#1308200311yescharacteristic
1203C2#1308237211yescharacteristic
1204C2#1308237411yescharacteristic
1205C2#1308244511yescharacteristic
1206C2#1308246611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2422C2
hypercenter#2422D11
hypocenterC11#35005
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2422

Complements

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

NH ≅ G/Ntype
1. C2×#10623188C2semidirect
2. #13076969C2semidirect
3. #13076960C2semidirect
4. #13076899C2semidirect
5. #13076895C2semidirect
6. #13074543C2semidirect
7. #13074355C2semidirect
8. #13073749C2semidirect
9. #13073740C2semidirect
10. #13073718C2semidirect
11. #13073711C2semidirect
12. #13073040C2semidirect
13. #13073039C2semidirect
14. #13072979C2semidirect
15. #13072977C2semidirect
16. #13072200C2semidirect
17. #13072198C2semidirect
18. #13072133C2semidirect
19. #13071313C2semidirect
20. #13071124C2semidirect
21. C4×#66991C2semidirect
22. C4×C22⋊C4×D11C2semidirect
23. C11×#2422C2semidirect
27. C2×C4×D4×C11C22semidirect
28. C2×#66993C22semidirect
43. C2×#66946C22semidirect
54. C2×#66922C22semidirect
55. C11×#397C22semidirect
57. C11×#390C22semidirect
58. C11×#389C22semidirect
59. C11×#385C22semidirect
60. C11×#384C22semidirect
64. #10622834C22semidirect
66. #10622826C22semidirect
69. C4×C22⋊Dic11C22semidirect
70. #10622606C22semidirect
72. #10622603C22semidirect
73. #10622602C22semidirect
79. #10622598C22semidirect
80. #10622598C22semidirect
81. #10622598C22semidirect
82. #10622591C22semidirect
83. #10622589C22semidirect
84. C4⋊C4×Dic11C22semidirect
85. #10622587C22semidirect
86. #10622586C22semidirect
89. #10622574C22semidirect
90. #10622574C22semidirect
93. #10622570C22semidirect
94. #10622570C22semidirect
98. #10622569C22semidirect
100. #10622564C22semidirect
101. #10622560C22semidirect
102. #10622557C22semidirect
105. #10622552C22semidirect
106. #10622552C22semidirect
109. C4×C4⋊Dic11C22semidirect
111. #10622286C22semidirect
112. #10622283C22semidirect
115. #10622279C22semidirect
121. #10622273C22semidirect
122. #10622273C22semidirect
123. #10622265C22semidirect
230. C22⋊C4×D11D4semidirect
429. #2422D11semidirect
580. C2×C4×D4C2×D11semidirect
590. #397C2×D11semidirect
607. #390C2×D11semidirect
612. #389C2×D11semidirect
630. #385C2×D11semidirect
632. #384C2×D11semidirect
705. C4×C11#538semidirect
1013. C11#35005semidirect
1194. C4#10623188semidirect

Maximal subgroups

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

subgroupindex
C2×#106231882
#130769692
#130769602
#130768992
#130768952
#130745432
#130743552
#130737492
#130737402
#130737182
#130737112
#130730402
#130730392
#130729792
#130729772
#130722002
#130721982
#130721332
#130713132
#130711242
C4×#669912
C4×C22⋊C4×D112
C11×#24222
#3500511