Finite Group Databasebeta

← #14960564

Subgroups — #14960564

Order 2816.

3038 conjugacy classes of subgroups.

The subgroup lattice has 1272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623091C211yesmaximal, characteristic, complemented
2C22×#66948C211yesmaximal, characteristic, complemented
3#13076902C211yesmaximal, characteristic, complemented
4#13076897C211yesmaximal, characteristic, complemented
5#13075104C212yesmaximal, complemented
6#13075100C212yesmaximal, complemented
7#13074923C212yesmaximal, complemented
8#13074915C212yesmaximal, complemented
9#13074909C212yesmaximal, complemented
10#13074907C212yesmaximal, complemented
11#13074859C212yesmaximal, complemented
12#13074856C212yesmaximal, complemented
13#13074427C211yesmaximal, characteristic, complemented
14#13074356C211yesmaximal, characteristic, complemented
15#13073963C211yesmaximal, characteristic, complemented
16#13071993C211yesmaximal, characteristic, complemented
17#13071993C211yesmaximal, characteristic, complemented
18#13071988C211yesmaximal, characteristic, complemented
19#13071988C211yesmaximal, characteristic, complemented
20#13071973C211yesmaximal, characteristic, complemented
21#13071972C211yesmaximal, characteristic, complemented
22#13071229C211yesmaximal, characteristic, complemented
23C11×#2579C211yesmaximal, characteristic, complemented
24C23×D44C2211yescharacteristic
25C23×D44C2211yescharacteristic
26C23×D44C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C22×C11×C4⋊C4C2211yescharacteristic
30C2×#66992C2211yescharacteristic
31C2×#66990C2211yescharacteristic
32C2×#66990C2211yescharacteristic
33C2×#66990C2211yescharacteristic
34C2×#66983C2211yescharacteristic, complemented
35C2×#66983C2212yescomplemented
36C2×#66982C2211yescharacteristic, complemented
37C2×C4×C22⋊D11C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40#10623091—28no—
41C2×#66951C2211yescharacteristic, complemented
42C2×#66949C2212yescomplemented
43C2×#66948—28no—
44C2×#66948C2212yes—
45C2×#66948C2212yes—
46C2×#66948C2212yes—
47C2×#66948C2212yes—
48C2×#66948C2212yescomplemented
49C2×#66948C2212yescomplemented
50C2×#66948C2212yescomplemented
51C2×#66947C2211yescharacteristic, complemented
52C2×#66938C2211yescharacteristic, complemented
53C2×#66937C2211yescharacteristic, complemented
54C2×#66937C2212yescomplemented
55C2×#66937C2212yescomplemented
56C2×#66937C2212yescomplemented
57C2×#66935C2211yescharacteristic
58C2×#66935C2211yescharacteristic
59C2×#66935C2211yescharacteristic
60C2×C22⋊C4×D11C2211yescharacteristic
61C2×C22⋊C4×D11C2211yescharacteristic
62C2×#66931C2211yescharacteristic
63C2×#66929C2211yescharacteristic, complemented
64C2×#66928C2211yescharacteristic, complemented
65C11×#398C2212yescomplemented
66C11×#396C2212yescomplemented
67C11×#387C2212yescomplemented
68C11×#386C2211yescharacteristic
69C11×#386C2211yescharacteristic
70C11×#385C2211yescharacteristic
71C11×#385C2211yescharacteristic
72C11×#385C2212yescomplemented
73C11×#380C2211yescharacteristic
74#10622826C2211yescharacteristic
75#10622826C2211yescharacteristic
76#10622825C2211yescharacteristic
77#10622823C2211yescharacteristic
78#10622823C2211yescharacteristic
79#10622607C2212yescomplemented
80#10622607C2212yescomplemented
81#10622605C2212yescomplemented
82#10622604C2212yescomplemented
83#10622604C2212yescomplemented
84#10622604C2212yescomplemented
85#10622602C2212yescomplemented
86#10622602C2212yescomplemented
87#10622602C2212yescomplemented
88#10622602C2212yescomplemented
89#10622601C2212yescomplemented
90#10622597C2212yescomplemented
91#10622591C2212yescomplemented
92#10622573C2212yescomplemented
93#10622573C2212yescomplemented
94#10622573C2212yescomplemented
95#10622573C2212yescomplemented
96#10622572C2212yescomplemented
97#10622569C2212yescomplemented
98#10622568C2211yescharacteristic
99#10622568C2211yescharacteristic
100#10622568C2211yescharacteristic
101#10622568C2211yescharacteristic
102#10622555C2211yescharacteristic
103#10622555C2211yescharacteristic
104#10622552C2212yescomplemented
105#10622289C2212yescomplemented
106#10622288C2212yescomplemented
107#10622286C2212yescomplemented
108#10622285C2212yescomplemented
109#10622285C2212yescomplemented
110#10622285C2212yescomplemented
111#10622285C2212yescomplemented
112#10622284C2212yescomplemented
113#10622284C2212yescomplemented
114#10622284C2212yescomplemented
115#10622281C2212yescomplemented
116#10622281C2212yescomplemented
117#10622281C2212yescomplemented
118#10622280C2212yescomplemented
119#10622280C2212yescomplemented
120#10622278C2212yescomplemented
121#10622278C2212yescomplemented
122#10622278C2212yescomplemented
123#10622278C2212yescomplemented
124#10622278C2212yescomplemented
125C24×D11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C24×D11C2311yescharacteristic
128C22×D4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C23×C4×C11C2311yescharacteristic
132C23×C4×C11C2311yescharacteristic
133C22×C22⋊D11C2311yescharacteristic
134C22×C22⋊D11C2311yescharacteristic
135C22×C22⋊D11C2311yescharacteristic
136C22×C22⋊D11C2311yescharacteristic
137C22×C22⋊D11C2312yes—
138C22×C22⋊D11C2312yes—
139C23×Dic11C2311yescharacteristic
140C22×D44—24no—
141C22×D44—24no—
142C22×D44—24no—
143C22×D44—44no—
144C22×D44—44no—
145C22×D44—44no—
146C22×D44C2312yes—
147C22×D44C2312yes—
148C22×D44C2312yes—
149C22×D44C2312yes—
150C22×D44C2312yes—
151C22×D44C2312yes—
152C22×D44C2311yescharacteristic
153C22×D44C2312yes—
154C22×D44C2311yescharacteristic
155C22×D44C2312yes—
156C22×C4×D11—24no—
157C22×C4×D11—44no—
158C22×C4×D11C2312yes—
159C22×C4×D11C2312yes—
160C22×C4×D11C2311yescharacteristic
161C22×C4×D11C2312yes—
162C22×C4×D11C2312yes—
163C22×Dic22C2311yescharacteristic
164C4×D4×C11—24no—
165C2×C11×C4⋊C4—24no—
166C2×C11×C4⋊C4C2311yescharacteristic
167C2×C11×C4⋊C4C2312yes—
168C2×C11×C4⋊C4C2312yes—
169C2×C11×C4⋊C4C2312yes—
170C2×C11×C4⋊C4C2312yes—
171C2×C11×C4⋊C4C2312yes—
172C2×C11×C22⋊C4C2311yescharacteristic
173C2×C11×C22⋊C4C2311yescharacteristic
174C2×C11×C22⋊C4C2311yescharacteristic
175C2×C11×C22⋊C4C2312yes—
176C2×C11×C22⋊C4C2311yescharacteristic
177C2×C11×C22⋊C4C2312yes—
178C2×C42×C11C2311yescharacteristic
179C2×C22⋊Dic11C2311yescharacteristic
180C2×C22⋊Dic11C2311yescharacteristic
181C2×C22⋊Dic11C2311yescharacteristic
182C2×C22⋊Dic11C2311yescharacteristic
183#66992—24no—
184#66990—24no—
185#66990—42no—
186#66990—42no—
187#66983—24no—
188#66983—44no—
189#66982—24no—
190C4×C22⋊D11—24no—
191C2×(C2×D11)⋊C4—24no—
192C2×(C2×D11)⋊C4D418yescomplemented
193C2×(C2×D11)⋊C4C2311yescharacteristic
194C2×(C2×D11)⋊C4C2311yescharacteristic
195C2×(C2×D11)⋊C4C2311yescharacteristic
196C2×(C2×D11)⋊C4C2311yescharacteristic
197C2×(C2×D11)⋊C4C2311yescharacteristic
198C2×(C2×D11)⋊C4C2311yescharacteristic
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2312yes—
205C2×(C2×D11)⋊C4C2312yes—
206C2×(C2×D11)⋊C4C2312yes—
207C2×(C2×D11)⋊C4C2312yes—
208C2×(C2×D11)⋊C4C2312yes—
209C2×(C2×D11)⋊C4C2312yes—
210C2×(C2×D11)⋊C4C2312yes—
211C2×(C2×D11)⋊C4C2312yes—
212C2×(C2×D11)⋊C4C2312yes—
213C2×(C2×D11)⋊C4C2312yes—
214C2×(C2×D11)⋊C4C2312yes—
215C2×(C2×D11)⋊C4C2312yes—
216C2×(C2×D11)⋊C4C2312yes—
217C2×(C2×D11)⋊C4C2311yescharacteristic
218C2×(C2×D11)⋊C4C2311yescharacteristic
219C2×(C2×D11)⋊C4C2311yescharacteristic
220C2×(C2×D11)⋊C4C2311yescharacteristic
221C2×C4⋊Dic11C2311yescharacteristic
222C2×C4⋊Dic11C2312yes—
223C2×Dic11⋊C4C2311yescharacteristic
224C2×Dic11⋊C4C2311yescharacteristic
225C2×Dic11⋊C4C2311yescharacteristic
226C2×Dic11⋊C4C2311yescharacteristic
227C2×Dic11⋊C4C2312yes—
228C2×Dic11⋊C4C2312yes—
229C2×Dic11⋊C4C2312yes—
230C2×Dic11⋊C4C2312yes—
231C2×C4×Dic11C2311yescharacteristic
232#66951—24no—
233#66949—44no—
234#66948—28no—
235#66948—28no—
236#66948—28no—
237#66948—28no—
238#66948—44no—
239#66948—44no—
240#66948—44no—
241#66947—24no—
242#66938—24no—
243#66937—24no—
244#66937—44no—
245#66937—44no—
246#66937—44no—
247#66935—24no—
248#66935—42no—
249#66935—42no—
250C22⋊C4×D11—42no—
251C22⋊C4×D11—42no—
252#66931—24no—
253#66929—24no—
254#66928—24no—
255C11×#95C2312yes—
256C11×#95C2312yes—
257C11×#95C2312yes—
258C11×#95C2312yes—
259C11×#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262C11⋊#95C2312yes—
263C11⋊#95C2312yes—
264C11⋊#95C2312yes—
265C11⋊#95C2312yes—
266C11⋊#95C2312yes—
267#36706—111nomaximal, Sylow
268C24×C11C2411yescharacteristic
269C24×C11C2411yescharacteristic
270C23×D11—22no—
271C23×D11—22no—
272C23×D11—22no—
273C23×D11—24no—
274C23×D11—22no—
275C23×D11—22no—
276C23×D11—22no—
277C23×D11—22no—
278C23×D11—22no—
279C23×D11—42no—
280C23×D11—42no—
281C23×D11—42no—
282C23×D11—42no—
283C23×D11—42no—
284C23×D11C2×D414yes—
285C23×D11C2412yes—
286C23×D11C2411yescharacteristic
287C23×D11C2411yescharacteristic
288C23×D11C2411yescharacteristic
289C23×D11C2412yes—
290C2×D4×C11—22no—
291C2×D4×C11—22no—
292C2×D4×C11—22no—
293C22×C4×C11—22no—
294C22×C4×C11—24no—
295C22×C4×C11—22no—
296C22×C4×C11—22no—
297C22×C4×C11—42no—
298C22×C4×C11—42no—
299C22×C4×C11—42no—
300C22×C4×C11C2×D414yes—
301C22×C4×C11C2412yes—
302C22×C4×C11C2412yes—
303C22×C4×C11C2412yes—
304C22×C4×C11C2411yescharacteristic
305C22×C4×C11C2411yescharacteristic
306C22×C4×C11C2411yescharacteristic
307C22×C4×C11C2411yescharacteristic
308C22×C4×C11C2411yescharacteristic
309C22×C4×C11C2412yes—
310C2×C22⋊D11—22no—
311C2×C22⋊D11—22no—
312C2×C22⋊D11—22no—
313C2×C22⋊D11—22no—
314C2×C22⋊D11—22no—
315C2×C22⋊D11—22no—
316C2×C22⋊D11—24no—
317C2×C22⋊D11—42no—
318C2×C22⋊D11—42no—
319C2×C22⋊D11—42no—
320C2×C22⋊D11—42no—
321C2×C22⋊D11—42no—
322C2×C22⋊D11—42no—
323C2×C22⋊D11—42no—
324C2×C22⋊D11—42no—
325C22×Dic11—42no—
326C22×Dic11C2×D414yes—
327C22×Dic11C2411yescharacteristic
328C22×Dic11C2412yes—
329C22×Dic11C2412yes—
330C22×Dic11C2411yescharacteristic
331C22×Dic11C2411yescharacteristic
332C22×Dic11C2411yescharacteristic
333C22×Dic11C2411yescharacteristic
334C2×D44—24no—
335C2×D44—24no—
336C2×D44—24no—
337C2×D44—24no—
338C2×D44—22no—
339C2×D44—22no—
340C2×D44—24no—
341C2×D44—24no—
342C2×D44—24no—
343C2×D44—24no—
344C2×D44—24no—
345C2×D44—24no—
346C2×D44—24no—
347C2×D44—24no—
348C2×D44—24no—
349C2×D44—42no—
350C2×D44—42no—
351C2×D44—42no—
352C2×D44—42no—
353C2×D44—42no—
354C2×D44—42no—
355C2×D44—42no—
356C2×D44—42no—
357C2×D44—42no—
358C2×D44—42no—
359C2×D44—42no—
360C2×D44—42no—
361C2×D44—42no—
362C2×D44—416no—
363C2×D44—416no—
364C2×D44—416no—
365C2×C4×D11—24no—
366C2×C4×D11—24no—
367C2×C4×D11—22no—
368C2×C4×D11—24no—
369C2×C4×D11—24no—
370C2×C4×D11—42no—
371C2×C4×D11—42no—
372C2×C4×D11—42no—
373C2×C4×D11—42no—
374C2×C4×D11—42no—
375C2×C4×D11—42no—
376C2×C4×D11—42no—
377C2×C4×D11—42no—
378C2×C4×D11—42no—
379C2×C4×D11—416no—
380C2×Dic22—22no—
381C2×Dic22—42no—
382C11×C4⋊C4—22no—
383C11×C4⋊C4—24no—
384C11×C4⋊C4—24no—
385C11×C4⋊C4—24no—
386C11×C4⋊C4—42no—
387C11×C4⋊C4—42no—
388C11×C22⋊C4—22no—
389C11×C22⋊C4—22no—
390C11×C22⋊C4—22no—
391C11×C22⋊C4—22no—
392C11×C22⋊C4—24no—
393C11×C22⋊C4—42no—
394C42×C11—22no—
395C22⋊Dic11—22no—
396C22⋊Dic11—22no—
397C22⋊Dic11—22no—
398C22⋊Dic11—22no—
399(C2×D11)⋊C4—22no—
400(C2×D11)⋊C4—24no—
401(C2×D11)⋊C4—24no—
402(C2×D11)⋊C4—22no—
403(C2×D11)⋊C4—22no—
404(C2×D11)⋊C4—22no—
405(C2×D11)⋊C4—22no—
406(C2×D11)⋊C4—24no—
407(C2×D11)⋊C4—24no—
408(C2×D11)⋊C4—22no—
409(C2×D11)⋊C4—24no—
410(C2×D11)⋊C4—42no—
411(C2×D11)⋊C4—42no—
412(C2×D11)⋊C4—42no—
413(C2×D11)⋊C4—42no—
414(C2×D11)⋊C4—42no—
415(C2×D11)⋊C4—42no—
416(C2×D11)⋊C4—42no—
417(C2×D11)⋊C4—42no—
418(C2×D11)⋊C4—42no—
419(C2×D11)⋊C4—42no—
420(C2×D11)⋊C4—42no—
421(C2×D11)⋊C4—42no—
422(C2×D11)⋊C4—42no—
423(C2×D11)⋊C4C2×D414yes—
424(C2×D11)⋊C4C2×D414yes—
425(C2×D11)⋊C4C2×D414yes—
426(C2×D11)⋊C4C2×D414yes—
427C4⋊Dic11—22no—
428C4⋊Dic11—42no—
429Dic11⋊C4—22no—
430Dic11⋊C4—22no—
431Dic11⋊C4—22no—
432Dic11⋊C4—22no—
433Dic11⋊C4—24no—
434Dic11⋊C4—42no—
435Dic11⋊C4—42no—
436Dic11⋊C4—42no—
437C4×Dic11—22no—
438C2×#538—111no—
439C22×#121—111no—
440#2848—111no—
441#2847—111no—
442#2691—112no—
443#2691—112no—
444#2676—112no—
445#2676—112no—
446#2675—112no—
447#2675—112no—
448#2671—112no—
449#2671—112no—
450#2626—111no—
451#2617—111no—
452#2579—111no—
453#2579D1111yescharacteristic, complemented
454#2410—111no—
455#2410—111no—
456#2410—111no—
457#2410—111no—
458#2408—111no—
459#2408—111no—
460#2315—111no—
461C23×C11—22no—
462C23×C11—22no—
463C23×C11—21no—
464C23×C11—22no—
465C23×C11—22no—
466C23×C11—21no—
467C23×C11—21no—
468C23×C11C22×D412yes—
469C23×C11H(5,𝔽2)12yes—
470C23×C112−1+412yes—
471C23×C11C2511yescharacteristic
472C22×D11—28no—
473C22×D11—22no—
474C22×D11—22no—
475C22×D11—21no—
476C22×D11—21no—
477C22×D11—22no—
478C22×D11—22no—
479C22×D11—22no—
480C22×D11—22no—
481C22×D11—22no—
482C22×D11—22no—
483C22×D11—22no—
484C22×D11—21no—
485C22×D11—21no—
486C22×D11—22no—
487C22×D11—28no—
488C22×D11—21no—
489C22×D11—22no—
490C22×D11—22no—
491C22×D11—22no—
492C22×D11—22no—
493C22×D11—22no—
494C22×D11—22no—
495C22×D11—22no—
496C22×D11—22no—
497C22×D11—21no—
498C22×D11—21no—
499C22×D11—22no—
500C22×D11—44no—
501C22×D11—44no—
502C22×D11—48no—
503C22×D11—48no—
504C22×D11—44no—
505C22×D11—44no—
506C22×D11—44no—
507C22×D11—44no—
508C22×D11—44no—
509C22×D11—84no—
510C22×D11—84no—
511C22×D11—84no—
512C22×D11—84no—
513C22×D11C22×D412yes—
514C22×D11C22×D412yes—
515C22×D11H(5,𝔽2)14yes—
516D4×C11—44no—
517C2×C4×C11—28no—
518C2×C4×C11—22no—
519C2×C4×C11—22no—
520C2×C4×C11—22no—
521C2×C4×C11—22no—
522C2×C4×C11—21no—
523C2×C4×C11—21no—
524C2×C4×C11—21no—
525C2×C4×C11—22no—
526C2×C4×C11—22no—
527C2×C4×C11—22no—
528C2×C4×C11—22no—
529C2×C4×C11—22no—
530C2×C4×C11—22no—
531C2×C4×C11—21no—
532C2×C4×C11—22no—
533C2×C4×C11—22no—
534C2×C4×C11—22no—
535C2×C4×C11—22no—
536C2×C4×C11—22no—
537C2×C4×C11—21no—
538C2×C4×C11—44no—
539C2×C4×C11—44no—
540C2×C4×C11—82no—
541C2×C4×C11C22×D412yes—
542C2×C4×C11C22×D412yes—
543C2×C4×C11H(5,𝔽2)14yes—
544C22⋊D11—44no—
545C22⋊D11—82no—
546C22⋊D11—82no—
547C22⋊D11—82no—
548C22⋊D11—84no—
549C22⋊D11—84no—
550C2×Dic11—22no—
551C2×Dic11—22no—
552C2×Dic11—21no—
553C2×Dic11—21no—
554C2×Dic11—21no—
555C2×Dic11—22no—
556C2×Dic11—22no—
557C2×Dic11—22no—
558C2×Dic11—22no—
559C2×Dic11—22no—
560C2×Dic11—22no—
561C2×Dic11—21no—
562C2×Dic11—22no—
563C2×Dic11—22no—
564C2×Dic11—21no—
565C2×Dic11—44no—
566C2×Dic11C22×D412yes—
567C2×Dic11C22×D412yes—
568D44—48no—
569D44—48no—
570D44—48no—
571D44—48no—
572D44—48no—
573D44—48no—
574D44—82no—
575D44—82no—
576D44—84no—
577D44—84no—
578C4×D11—48no—
579C4×D11—48no—
580C4×D11—82no—
581C4×D11—84no—
582C4×D11—84no—
583Dic22—82no—
584C23×D4—111no—
585C23×D4—111no—
586C23×D4—111no—
587C24×C4—111no—
588#538—228no—
589C2×#126—111no—
590C2×#126—111no—
591C2×#124—111no—
592C2×#124—111no—
593C2×#123—111no—
594C2×#123—111no—
595C2×C22⋊Q8—112no—
596C2×C22⋊Q8—111no—
597C2×#121—111no—
598C2×#121—111no—
599C2×#121—112no—
600C2×#121—112no—
601C2×#121—112no—
602C2×#121—112no—
603C2×#121—112no—
604C2×#121—112no—
605C2×#121—112no—
606C2×#121—112no—
607C2×#121—111no—
608C2×#121—112no—
609C2×#121—112no—
610C2×#121—112no—
611C2×#121—228no—
612C2×#120—111no—
613C2×#120—111no—
614C2×#120—111no—
615C2×#120—111no—
616C2×#120—111no—
617C2×#120—111no—
618C2×C4×D4—111no—
619C2×C4×D4C2×D1111yescharacteristic
620C22×C4⋊C4C2×D1111yescharacteristic
621C22×C22⋊C4—111no—
622C22×C22⋊C4—111no—
623C22×C22⋊C4—111no—
624C22×C22⋊C4—111no—
625#399—112no—
626#398—112no—
627#398C2×D1112yescomplemented
628#397—112no—
629#396—112no—
630#396—112no—
631#396—112no—
632#396C2×D1112yescomplemented
633#394—112no—
634#394—112no—
635#394—112no—
636#394—112no—
637#394—112no—
638#394—112no—
639#394—112no—
640#394—112no—
641#393—112no—
642#392—112no—
643#392—112no—
644#392—112no—
645#392—112no—
646#392—112no—
647#392—112no—
648#392—112no—
649#390—112no—
650#390—112no—
651#387—112no—
652#387C2×D1112yescomplemented
653#386—111no—
654#386—111no—
655#386—112no—
656#386—112no—
657#386—112no—
658#386—112no—
659#386—112no—
660#386—112no—
661#386C2×D1111yescharacteristic
662#386C2×D1111yescharacteristic
663#385—111no—
664#385—111no—
665#385—112no—
666#385—112no—
667#385—112no—
668#385—112no—
669#385—112no—
670#385—112no—
671#385—112no—
672#385C2×D1111yescharacteristic
673#385C2×D1111yescharacteristic
674#385C2×D1112yescomplemented
675#380—111no—
676#380—111no—
677#380—111no—
678#380—112no—
679#380—112no—
680#380C2×D1111yescharacteristic
681#379—111no—
682#379—111no—
683#379—111no—
684#379—111no—
685C22×C11—22no—
686C22×C11—22no—
687C22×C11—24no—
688C22×C11—24no—
689C22×C11—41no—
690C22×C11—41no—
691C22×C11—41no—
692C22×C11—42no—
693C22×C11—42no—
694C22×C11#53714yes—
695C22×C11C23×D411yescharacteristic
696C22×C11C2×H(5,𝔽2)11yescharacteristic
697C22×C11C2×H(5,𝔽2)12yes—
698C22×C11C2×H(5,𝔽2)12yes—
699C22×C11C2×2−1+411yescharacteristic
700C2×D11—22no—
701C2×D11—22no—
702C2×D11—24no—
703C2×D11—22no—
704C2×D11—22no—
705C2×D11—22no—
706C2×D11—22no—
707C2×D11—24no—
708C2×D11—24no—
709C2×D11—416no—
710C2×D11—42no—
711C2×D11—42no—
712C2×D11—42no—
713C2×D11—42no—
714C2×D11—42no—
715C2×D11—42no—
716C2×D11—42no—
717C2×D11—42no—
718C2×D11—42no—
719C2×D11—41no—
720C2×D11—42no—
721C2×D11—42no—
722C2×D11—41no—
723C2×D11—41no—
724C2×D11—42no—
725C2×D11—42no—
726C2×D11—42no—
727C2×D11—42no—
728C2×D11—42no—
729C2×D11—42no—
730C2×D11—88no—
731C2×D11—88no—
732C4×C11—24no—
733C4×C11—22no—
734C4×C11—22no—
735C4×C11—41no—
736C4×C11—42no—
737C4×C11—41no—
738C4×C11—41no—
739C4×C11—42no—
740C4×C11—42no—
741Dic11—22no—
742Dic11—22no—
743Dic11—41no—
744Dic11—41no—
745Dic11—41no—
746Dic11—42no—
747Dic11—42no—
748C25—111no—
749C25—111no—
750C25—111no—
751C22×Q8—111no—
752C22×D4—111no—
753C22×D4—111no—
754C22×D4—111no—
755C22×D4—112no—
756C22×D4—111no—
757C22×D4—112no—
758C22×D4—112no—
759C22×D4—112no—
760C22×D4—112no—
761C22×D4—112no—
762C22×D4—112no—
763C22×D4—112no—
764C22×D4—111no—
765C22×D4—111no—
766C22×D4—112no—
767C22×D4—112no—
768C22×D4—224no—
769C22×D4—224no—
770C22×D4—224no—
771C22×D4—444no—
772C22×D4—444no—
773C22×D4—444no—
774C22×D4C22×D1111yescharacteristic
775C23×C4—111no—
776C23×C4—112no—
777C23×C4—112no—
778C23×C4—111no—
779C23×C4—112no—
780C23×C4—112no—
781C23×C4—224no—
782C23×C4—444no—
783C23×C4C22×D1111yescharacteristic
784C23×C4C22×D1111yescharacteristic
785C23×C4C22×D1111yescharacteristic
786C23×C4C22×D1111yescharacteristic
787#126—224no—
788#126—224no—
789#124—224no—
790#124—224no—
791#123—224no—
792#123—224no—
793C22⋊Q8—224no—
794C22⋊Q8—444no—
795#121—224no—
796#121—228no—
797#121—228no—
798#121—228no—
799#121—228no—
800#121—224no—
801#121—224no—
802#121—444no—
803#121—444no—
804#121—444no—
805#121—444no—
806#121—444no—
807#121—444no—
808#121—444no—
809#120—224no—
810#120—224no—
811#120—442no—
812#120—442no—
813#120—442no—
814#120—442no—
815C4×D4—24no—
816C4×D4—224no—
817C2×C4⋊C4—24no—
818C2×C4⋊C4—111no—
819C2×C4⋊C4—111no—
820C2×C4⋊C4—111no—
821C2×C4⋊C4—112no—
822C2×C4⋊C4—111no—
823C2×C4⋊C4—111no—
824C2×C4⋊C4—112no—
825C2×C4⋊C4—112no—
826C2×C4⋊C4—112no—
827C2×C4⋊C4—112no—
828C2×C4⋊C4C22×D1112yes—
829C2×C4⋊C4C22×D1112yes—
830C2×C4⋊C4C22×D1111yescharacteristic
831C2×C4⋊C4C22×D1112yes—
832C2×C4⋊C4C22×D1112yes—
833C2×C4⋊C4C22×D1112yes—
834C2×C22⋊C4—118no—
835C2×C22⋊C4—111no—
836C2×C22⋊C4—111no—
837C2×C22⋊C4—111no—
838C2×C22⋊C4—111no—
839C2×C22⋊C4—111no—
840C2×C22⋊C4—111no—
841C2×C22⋊C4—111no—
842C2×C22⋊C4—111no—
843C2×C22⋊C4—112no—
844C2×C22⋊C4—112no—
845C2×C22⋊C4—111no—
846C2×C22⋊C4—111no—
847C2×C22⋊C4—111no—
848C2×C22⋊C4—111no—
849C2×C22⋊C4—111no—
850C2×C22⋊C4—112no—
851C2×C22⋊C4—112no—
852C2×C22⋊C4—112no—
853C2×C22⋊C4—111no—
854C2×C22⋊C4—112no—
855C2×C22⋊C4—112no—
856C2×C22⋊C4—112no—
857C2×C22⋊C4—112no—
858C2×C22⋊C4—112no—
859C2×C22⋊C4—112no—
860C2×C22⋊C4—112no—
861C2×C22⋊C4—112no—
862C2×C22⋊C4—112no—
863C2×C22⋊C4—112no—
864C2×C22⋊C4—112no—
865C2×C22⋊C4—112no—
866C2×C22⋊C4—112no—
867C2×C22⋊C4—224no—
868C2×C22⋊C4—442no—
869C2×C22⋊C4—442no—
870C2×C22⋊C4C22×D1111yescharacteristic
871C2×C22⋊C4C22×D1111yescharacteristic
872C2×C22⋊C4C22×D1111yescharacteristic
873C2×C22⋊C4C22×D1111yescharacteristic
874C2×C22⋊C4C22×D1112yes—
875C2×C22⋊C4C22×D1112yes—
876C2×C42—111no—
877C2×C42C22×D1111yescharacteristic
878#95—112no—
879#95—112no—
880#95—112no—
881#95—112no—
882#95—112no—
883#95—112no—
884#95—112no—
885#95C22×D1112yes—
886#95C22×D1112yes—
887#95C22×D1112yes—
888#95C22×D1112yes—
889#95C22×D1112yes—
890C2×C11—24no—
891C2×C11—81no—
892C2×C11C2×#53711yescharacteristic
893C2×C11#348411yescharacteristic
894C2×C11#348411yescharacteristic
895C2×C11#353612yes—
896C2×C11#353712yes—
897D11—44no—
898D11—42no—
899D11—42no—
900D11—81no—
901D11—82no—
902C24—111no—
903C24—111no—
904C24—112no—
905C24—114no—
906C24—112no—
907C24—111no—
908C24—224no—
909C24—222no—
910C24—222no—
911C24—222no—
912C24—222no—
913C24—222no—
914C24—222no—
915C24—222no—
916C24—222no—
917C24—442no—
918C24—442no—
919C24—442no—
920C24—442no—
921C24—442no—
922C24C23×D1111yescharacteristic
923C24C23×D1111yescharacteristic
924C2×Q8—222no—
925C2×Q8—442no—
926C2×D4—22no—
927C2×D4—22no—
928C2×D4—22no—
929C2×D4—224no—
930C2×D4—224no—
931C2×D4—224no—
932C2×D4—224no—
933C2×D4—224no—
934C2×D4—224no—
935C2×D4—224no—
936C2×D4—224no—
937C2×D4—222no—
938C2×D4—222no—
939C2×D4—224no—
940C2×D4—222no—
941C2×D4—222no—
942C2×D4—222no—
943C2×D4—222no—
944C2×D4—222no—
945C2×D4—222no—
946C2×D4—224no—
947C2×D4—224no—
948C2×D4—224no—
949C2×D4—224no—
950C2×D4—224no—
951C2×D4—442no—
952C2×D4—442no—
953C2×D4—442no—
954C2×D4—442no—
955C2×D4—442no—
956C2×D4—442no—
957C2×D4—4416no—
958C2×D4—442no—
959C2×D4—442no—
960C2×D4—442no—
961C2×D4—442no—
962C2×D4—442no—
963C2×D4—442no—
964C2×D4—442no—
965C2×D4—4416no—
966C2×D4—4416no—
967C2×D4—442no—
968C2×D4—442no—
969C2×D4—442no—
970C2×D4—442no—
971C2×D4—442no—
972C2×D4—442no—
973C2×D4—442no—
974C2×D4—442no—
975C22×C4—22no—
976C22×C4—24no—
977C22×C4—22no—
978C22×C4—22no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—42no—
982C22×C4—111no—
983C22×C4—111no—
984C22×C4—114no—
985C22×C4—111no—
986C22×C4—112no—
987C22×C4—112no—
988C22×C4—111no—
989C22×C4—111no—
990C22×C4—224no—
991C22×C4—224no—
992C22×C4—224no—
993C22×C4—224no—
994C22×C4—222no—
995C22×C4—442no—
996C22×C4—442no—
997C22×C4—442no—
998C22×C4—442no—
999C22×C4—442no—
1000C22×C4—442no—
1001C22×C4—442no—
1002C22×C4—442no—
1003C22×C4—442no—
1004C22×C4—4416no—
1005C22×C4—442no—
1006C22×C4D4×D1114yes—
1007C22×C4C23×D1112yes—
1008C22×C4C23×D1112yes—
1009C22×C4C23×D1112yes—
1010C22×C4C23×D1111yescharacteristic
1011C22×C4C23×D1111yescharacteristic
1012C22×C4C23×D1111yescharacteristic
1013C22×C4C23×D1111yescharacteristic
1014C22×C4C23×D1111yescharacteristic
1015C22×C4C23×D1112yes—
1016C4⋊C4—24no—
1017C4⋊C4—24no—
1018C4⋊C4—22no—
1019C4⋊C4—24no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—222no—
1023C4⋊C4—222no—
1024C4⋊C4—222no—
1025C4⋊C4—222no—
1026C4⋊C4—222no—
1027C4⋊C4—224no—
1028C4⋊C4—442no—
1029C4⋊C4—442no—
1030C4⋊C4—442no—
1031C4⋊C4—442no—
1032C22⋊C4—22no—
1033C22⋊C4—22no—
1034C22⋊C4—22no—
1035C22⋊C4—22no—
1036C22⋊C4—24no—
1037C22⋊C4—42no—
1038C22⋊C4—114no—
1039C22⋊C4—114no—
1040C22⋊C4—114no—
1041C22⋊C4—114no—
1042C22⋊C4—224no—
1043C22⋊C4—224no—
1044C22⋊C4—222no—
1045C22⋊C4—222no—
1046C22⋊C4—222no—
1047C22⋊C4—222no—
1048C22⋊C4—222no—
1049C22⋊C4—224no—
1050C22⋊C4—224no—
1051C22⋊C4—222no—
1052C22⋊C4—222no—
1053C22⋊C4—222no—
1054C22⋊C4—222no—
1055C22⋊C4—222no—
1056C22⋊C4—224no—
1057C22⋊C4—442no—
1058C22⋊C4—442no—
1059C22⋊C4—442no—
1060C22⋊C4—442no—
1061C22⋊C4—442no—
1062C22⋊C4—442no—
1063C22⋊C4—442no—
1064C22⋊C4—442no—
1065C22⋊C4—442no—
1066C22⋊C4—442no—
1067C22⋊C4—442no—
1068C22⋊C4—442no—
1069C22⋊C4—442no—
1070C42—22no—
1071C42—222no—
1072C11#3670611yescharacteristic, complemented, Sylow
1073C23—22no—
1074C23—22no—
1075C23—21no—
1076C23—21no—
1077C23—22no—
1078C23—21no—
1079C23—22no—
1080C23—112no—
1081C23—112no—
1082C23—114no—
1083C23—228no—
1084C23—222no—
1085C23—221no—
1086C23—221no—
1087C23—222no—
1088C23—222no—
1089C23—221no—
1090C23—221no—
1091C23—222no—
1092C23—222no—
1093C23—222no—
1094C23—222no—
1095C23—222no—
1096C23—222no—
1097C23—222no—
1098C23—228no—
1099C23—221no—
1100C23—222no—
1101C23—221no—
1102C23—222no—
1103C23—222no—
1104C23—222no—
1105C23—222no—
1106C23—222no—
1107C23—221no—
1108C23—222no—
1109C23—222no—
1110C23—222no—
1111C23—444no—
1112C23—444no—
1113C23—448no—
1114C23—448no—
1115C23—444no—
1116C23—444no—
1117C23—444no—
1118C23—444no—
1119C23—444no—
1120C23—884no—
1121C23—884no—
1122C23—884no—
1123C23—884no—
1124C23C2×D4×D1112yes—
1125C23#6704012yes—
1126C23#6704212yes—
1127C23C24×D1111yescharacteristic
1128Q8—882no—
1129D4—44no—
1130D4—448no—
1131D4—448no—
1132D4—448no—
1133D4—448no—
1134D4—448no—
1135D4—448no—
1136D4—444no—
1137D4—882no—
1138D4—882no—
1139D4—884no—
1140D4—884no—
1141D4—882no—
1142D4—882no—
1143D4—882no—
1144D4—884no—
1145D4—884no—
1146C2×C4—28no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—22no—
1155C2×C4—21no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—21no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—44no—
1168C2×C4—44no—
1169C2×C4—82no—
1170C2×C4—112no—
1171C2×C4—112no—
1172C2×C4—222no—
1173C2×C4—222no—
1174C2×C4—221no—
1175C2×C4—221no—
1176C2×C4—221no—
1177C2×C4—221no—
1178C2×C4—222no—
1179C2×C4—222no—
1180C2×C4—222no—
1181C2×C4—221no—
1182C2×C4—222no—
1183C2×C4—222no—
1184C2×C4—222no—
1185C2×C4—222no—
1186C2×C4—222no—
1187C2×C4—448no—
1188C2×C4—448no—
1189C2×C4—444no—
1190C2×C4—882no—
1191C2×C4—884no—
1192C2×C4—884no—
1193C2×C4C2×D4×D1112yes—
1194C2×C4C2×D4×D1112yes—
1195C2×C4#6704214yes—
1196C22—22no—
1197C22—22no—
1198C22—24no—
1199C22—24no—
1200C22—41no—
1201C22—41no—
1202C22—41no—
1203C22—42no—
1204C22—42no—
1205C22—222no—
1206C22—222no—
1207C22—224no—
1208C22—222no—
1209C22—222no—
1210C22—222no—
1211C22—222no—
1212C22—224no—
1213C22—224no—
1214C22—4416no—
1215C22—442no—
1216C22—442no—
1217C22—442no—
1218C22—442no—
1219C22—442no—
1220C22—442no—
1221C22—442no—
1222C22—442no—
1223C22—441no—
1224C22—442no—
1225C22—441no—
1226C22—442no—
1227C22—442no—
1228C22—441no—
1229C22—442no—
1230C22—442no—
1231C22—442no—
1232C22—442no—
1233C22—442no—
1234C22—442no—
1235C22—888no—
1236C22—888no—
1237C22#1062316014yes—
1238C22C22×D4×D1111yescharacteristic
1239C22C2×#6704011yescharacteristic
1240C22C2×#6704211yescharacteristic
1241C22C2×#6704212yes—
1242C22D11×H(5,𝔽2)12yes—
1243C4—22no—
1244C4—22no—
1245C4—24no—
1246C4—41no—
1247C4—42no—
1248C4—41no—
1249C4—41no—
1250C4—42no—
1251C4—42no—
1252C4—222no—
1253C4—222no—
1254C4—441no—
1255C4—441no—
1256C4—441no—
1257C4—442no—
1258C4—442no—
1259C2—24no—
1260C2—81no—
1261C2—444no—
1262C2—442no—
1263C2—442no—
1264C2—882no—
1265C2—881no—
1266C2C2×#1062316011yescharacteristic
1267C2#1308224811yescharacteristic
1268C2#1308224911yescharacteristic
1269C2#1308284412yes—
1270C2#1308285212yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2579C2
hypercenter#2579D11
hypocenterC11#36706
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2579

Complements

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

NH ≅ G/Ntype
1. C2×#10623091C2semidirect
2. C22×#66948C2semidirect
3. #13076902C2semidirect
4. #13076897C2semidirect
5. #13075104C2semidirect
6. #13075100C2semidirect
7. #13074923C2semidirect
8. #13074915C2semidirect
9. #13074909C2semidirect
10. #13074907C2semidirect
11. #13074859C2semidirect
12. #13074856C2semidirect
13. #13074427C2semidirect
14. #13074356C2semidirect
15. #13073963C2semidirect
16. #13071993C2semidirect
17. #13071993C2semidirect
18. #13071988C2semidirect
19. #13071988C2semidirect
20. #13071973C2semidirect
21. #13071972C2semidirect
22. #13071229C2semidirect
23. C11×#2579C2semidirect
34. C2×#66983C22semidirect
35. C2×#66983C22semidirect
36. C2×#66982C22semidirect
41. C2×#66951C22semidirect
42. C2×#66949C22semidirect
48. C2×#66948C22semidirect
49. C2×#66948C22semidirect
50. C2×#66948C22semidirect
51. C2×#66947C22semidirect
52. C2×#66938C22semidirect
53. C2×#66937C22semidirect
54. C2×#66937C22semidirect
55. C2×#66937C22semidirect
56. C2×#66937C22semidirect
63. C2×#66929C22semidirect
64. C2×#66928C22semidirect
65. C11×#398C22semidirect
66. C11×#396C22semidirect
67. C11×#387C22semidirect
72. C11×#385C22semidirect
79. #10622607C22semidirect
80. #10622607C22semidirect
81. #10622605C22semidirect
82. #10622604C22semidirect
83. #10622604C22semidirect
84. #10622604C22semidirect
85. #10622602C22semidirect
86. #10622602C22semidirect
87. #10622602C22semidirect
88. #10622602C22semidirect
89. #10622601C22semidirect
90. #10622597C22semidirect
91. #10622591C22semidirect
92. #10622573C22semidirect
93. #10622573C22semidirect
94. #10622573C22semidirect
95. #10622573C22semidirect
96. #10622572C22semidirect
97. #10622569C22semidirect
104. #10622552C22semidirect
105. #10622289C22semidirect
106. #10622288C22semidirect
107. #10622286C22semidirect
108. #10622285C22semidirect
109. #10622285C22semidirect
110. #10622285C22semidirect
111. #10622285C22semidirect
112. #10622284C22semidirect
113. #10622284C22semidirect
114. #10622284C22semidirect
115. #10622281C22semidirect
116. #10622281C22semidirect
117. #10622281C22semidirect
118. #10622280C22semidirect
119. #10622280C22semidirect
120. #10622278C22semidirect
121. #10622278C22semidirect
122. #10622278C22semidirect
123. #10622278C22semidirect
124. #10622278C22semidirect
192. C2×(C2×D11)⋊C4D4semidirect
453. #2579D11semidirect
627. #398C2×D11semidirect
632. #396C2×D11semidirect
652. #387C2×D11semidirect
674. #385C2×D11semidirect
1072. C11#36706semidirect

Maximal subgroups

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

subgroupindex
C2×#106230912
C22×#669482
#130769022
#130768972
#130751042
#130751002
#130749232
#130749152
#130749092
#130749072
#130748592
#130748562
#130744272
#130743562
#130739632
#130719932
#130719882
#130719732
#130719722
#130712292
C11×#25792
#3670611