Finite Group Databasebeta

← #14914620

Subgroups — #14914620

Order 2816.

2286 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623131C211yesmaximal, characteristic
2#13071738C212yesmaximal, complemented
3#13071734C212yesmaximal, complemented
4#13071658C211yesmaximal, characteristic
5#13071643C211yesmaximal, characteristic, complemented
6#13071641C211yesmaximal, characteristic, complemented
7#13071569C211yesmaximal, characteristic, complemented
8#13071564C212yesmaximal, complemented
9#13071564C211yesmaximal, characteristic, complemented
10#13071543C212yesmaximal, complemented
11#13071530C211yesmaximal, characteristic, complemented
12D4×Dic11⋊C4C211yesmaximal, characteristic, complemented
13#13071407C212yesmaximal, complemented
14#13071403C212yesmaximal, complemented
15#13071220C212yesmaximal, complemented
16#13071175C211yesmaximal, characteristic, complemented
17C4×#66943C211yesmaximal, characteristic, complemented
18#13071163C211yesmaximal, characteristic, complemented
19C4×#66989C211yesmaximal, characteristic, complemented
20#13071019C211yesmaximal, characteristic, complemented
21#13070971C212yesmaximal, complemented
22C4×#66930C211yesmaximal, characteristic, complemented
23C11×#2363C211yesmaximal, characteristic
24C2×C11×#121C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C2×C11×#117C2211yescharacteristic
27C2×#66989C2211yescharacteristic
28C2×#66988C2212yes—
29C2×D4×Dic11C2211yescharacteristic
30C2×D4×Dic11C2211yescharacteristic
31C2×D4×Dic11C2212yes—
32C2×#66979C2211yescharacteristic
33C2×#66977C2211yescharacteristic
34C22×Dic11⋊C4C2212yes—
35C22×C4×Dic11C2211yescharacteristic
36#10623131C4116yescomplemented
37C2×#66943C2211yescharacteristic
38C2×#66940C2211yescharacteristic
39C2×#66940C2211yescharacteristic
40C2×#66932C2212yes—
41C2×#66930C2211yescharacteristic
42C2×#66930C2211yescharacteristic
43C2×#66930C2212yes—
44C2×#66930C2212yes—
45C2×C4×Dic22C2211yescharacteristic
46C11×#390C2212yes—
47C11×#390C2211yescharacteristic
48C11×#389C2211yescharacteristic
49C11×#388C2212yes—
50C11×#386C2212yes—
51C4×C11×C4⋊C4C2211yescharacteristic
52C4×C11×C22⋊C4C2211yescharacteristic
53C4×C11×C22⋊C4C2212yes—
54#10622834C2212yes—
55#10622834C2211yescharacteristic
56#10622833C2212yes—
57#10622823C2212yes—
58C4×C22⋊Dic11C2211yescharacteristic
59C4×C22⋊Dic11C2212yes—
60C4×C22⋊Dic11C2212yes—
61#10622598C2211yescharacteristic
62#10622591C2212yes—
63#10622590C2211yescharacteristic
64#10622590C2211yescharacteristic
65#10622589C2212yes—
66#10622589C2211yescharacteristic
67#10622589C2211yescharacteristic
68C4⋊C4×Dic11C2211yescharacteristic
69C4⋊C4×Dic11C2211yescharacteristic
70C4⋊C4×Dic11C2212yes—
71#10622587C2211yescharacteristic
72#10622586C2211yescharacteristic
73#10622585C2212yes—
74#10622564C2212yes—
75#10622559C2212yes—
76#10622558C2212yes—
77#10622558C2212yes—
78#10622558C2212yes—
79#10622558C2212yes—
80#10622558C2212yes—
81#10622557C2212yes—
82#10622557C2212yes—
83#10622557C2212yes—
84#10622557C2212yes—
85#10622557C2212yes—
86#10622555C2212yes—
87#10622555C2212yes—
88#10622555C2212yes—
89#10622555C2212yes—
90C22⋊C4×Dic11C2212yes—
91C22⋊C4×Dic11C2211yescharacteristic
92C22⋊C4×Dic11C2212yes—
93C22⋊C4×Dic11C2211yescharacteristic
94C22⋊C4×Dic11C2212yes—
95C4×C4⋊Dic11C2211yescharacteristic
96C4×C4⋊Dic11C2212yes—
97#10622546C2212yes—
98#10622546C2212yes—
99C4×Dic11⋊C4C2212yes—
100C4×Dic11⋊C4C2212yes—
101C4×Dic11⋊C4C2211yescharacteristic
102C4×Dic11⋊C4C2211yescharacteristic
103C4×Dic11⋊C4C2212yes—
104C4×Dic11⋊C4C2212yes—
105C4×Dic11⋊C4C2212yes—
106C42×Dic11C2211yescharacteristic
107C42×Dic11C2211yescharacteristic
108#10622542C2211yescharacteristic
109#10622541C2211yescharacteristic
110#10622268C2212yes—
111#10622267C2212yes—
112#10622266C2212yes—
113#10622265C2212yes—
114#10622265C2212yes—
115#10622263C2212yes—
116#10622262C2212yes—
117#10622262C2212yes—
118#10622262C2211yescharacteristic
119#10622262C2211yescharacteristic
120#10622262C2212yes—
121#10622261C2211yescharacteristic
122#10622261C2211yescharacteristic
123#10622260C2212yes—
124C22×D4×C11C2311yescharacteristic
125C22×D4×C11C2312yes—
126C23×C4×C11C2311yescharacteristic
127C23×C4×C11C2312yes—
128C23×Dic11C2311yescharacteristic
129C23×Dic11C2312yes—
130C23×Dic11C2312yes—
131C23×Dic11C2311yescharacteristic
132C22×Dic22C2311yescharacteristic
133C11×#121C2×C418yes—
134C4×D4×C11—42no—
135C11×#117—42no—
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2312yes—
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C22⋊C4C2311yescharacteristic
141C2×C11×C22⋊C4C2312yes—
142C2×C11×C22⋊C4C2311yescharacteristic
143C2×C11×C22⋊C4C2312yes—
144C2×C11×C22⋊C4C2312yes—
145C2×C11×C22⋊C4C2312yes—
146C2×C11×C22⋊C4C2312yes—
147C2×C42×C11C2311yescharacteristic
148C2×C42×C11C2311yescharacteristic
149C2×C42×C11C2312yes—
150C2×C42×C11C2312yes—
151C2×C22⋊Dic11C2311yescharacteristic
152C2×C22⋊Dic11C2311yescharacteristic
153C2×C22⋊Dic11C2312yes—
154C2×C22⋊Dic11C2312yes—
155C2×C22⋊Dic11C2312yes—
156C2×C22⋊Dic11C2312yes—
157C2×C22⋊Dic11C2312yes—
158C2×C22⋊Dic11C2312yes—
159C2×C22⋊Dic11C2312yes—
160C2×C22⋊Dic11C2312yes—
161#66989C2×C418yes—
162#66988C2×C4116yescomplemented
163D4×Dic11—42no—
164D4×Dic11C2×C418yes—
165D4×Dic11C2×C4116yescomplemented
166#66979—42no—
167C2×C4⋊Dic11C2311yescharacteristic
168C2×C4⋊Dic11C2311yescharacteristic
169C2×C4⋊Dic11C2312yes—
170C2×C4⋊Dic11C2312yes—
171C2×C4⋊Dic11C2311yescharacteristic
172#66977C2×C418yescomplemented
173C2×Dic11⋊C4—28no—
174C2×Dic11⋊C4C2311yescharacteristic
175C2×Dic11⋊C4C2311yescharacteristic
176C2×Dic11⋊C4C2312yes—
177C2×Dic11⋊C4C2312yes—
178C2×Dic11⋊C4C2312yes—
179C2×Dic11⋊C4C2312yes—
180C2×Dic11⋊C4C2312yes—
181C2×Dic11⋊C4C2312yes—
182C2×Dic11⋊C4C2312yes—
183C2×Dic11⋊C4C2312yes—
184C2×Dic11⋊C4C2312yes—
185C2×Dic11⋊C4C2312yes—
186C2×Dic11⋊C4C2312yes—
187C2×Dic11⋊C4C2311yescharacteristic
188C2×Dic11⋊C4C2311yescharacteristic
189C2×C4×Dic11C2×C418yescomplemented
190C2×C4×Dic11C2311yescharacteristic
191C2×C4×Dic11C2311yescharacteristic
192C2×C4×Dic11C2311yescharacteristic
193C2×C4×Dic11C2311yescharacteristic
194C2×C4×Dic11C2312yes—
195C2×C4×Dic11C2312yes—
196C2×C4×Dic11C2311yescharacteristic
197C2×C4×Dic11C2311yescharacteristic
198C2×C4×Dic11C2312yes—
199C2×C4×Dic11C2312yes—
200C2×C4×Dic11C2311yescharacteristic
201C2×C4×Dic11C2312yes—
202C2×C4×Dic11C2312yes—
203C2×C4×Dic11C2311yescharacteristic
204C2×C4×Dic11C2311yescharacteristic
205C2×C4×Dic11C2311yescharacteristic
206C2×C4×Dic11C2311yescharacteristic
207C2×C4×Dic11C2312yes—
208C2×C4×Dic11C2311yescharacteristic
209C2×C4×Dic11C2311yescharacteristic
210C2×C4×Dic11C2311yescharacteristic
211#66943C2×C418yescomplemented
212#66940—42no—
213#66940C2×C418yescomplemented
214#66932C2×C4116yescomplemented
215#66930—24no—
216#66930—28no—
217#66930—24no—
218#66930C2×C4116yescomplemented
219C4×Dic22—42no—
220C11×#95C2312yes—
221C11×#95C2311yescharacteristic
222C11×#95C2311yescharacteristic
223C11×#95C2312yes—
224C11⋊#95C2311yescharacteristic
225C11⋊#95C2311yescharacteristic
226C11⋊#95C2311yescharacteristic
227C11⋊#95C2311yescharacteristic
228C11⋊#95C2311yescharacteristic
229C11⋊#95C2311yescharacteristic
230C11⋊#95C2312yes—
231C11⋊#95C2312yes—
232C11⋊#95C2312yes—
233C11⋊#95C2312yes—
234C11⋊#95C2312yes—
235C11⋊#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244#34242—111nomaximal, Sylow
245C24×C11C2411yescharacteristic
246C24×C11C2412yes—
247C2×D4×C11—22no—
248C2×D4×C11—22no—
249C2×D4×C11—42no—
250C2×D4×C11—42no—
251C2×D4×C11C22×C414yes—
252C2×D4×C11C22×C418yes—
253C22×C4×C11—22no—
254C22×C4×C11—22no—
255C22×C4×C11—24no—
256C22×C4×C11—42no—
257C22×C4×C11—42no—
258C22×C4×C11C22×C414yes—
259C22×C4×C11C2411yescharacteristic
260C22×C4×C11C2412yes—
261C22×C4×C11C2412yes—
262C22×C4×C11C2411yescharacteristic
263C22×C4×C11C2411yescharacteristic
264C22×C4×C11C2412yes—
265C22×C4×C11C2411yescharacteristic
266C22×C4×C11C2411yescharacteristic
267C22×C4×C11C2411yescharacteristic
268C22×Dic11—22no—
269C22×Dic11—22no—
270C22×Dic11—24no—
271C22×Dic11—24no—
272C22×Dic11—24no—
273C22×Dic11—41no—
274C22×Dic11—41no—
275C22×Dic11—42no—
276C22×Dic11—42no—
277C22×Dic11C22×C418yes—
278C22×Dic11C22×C414yes—
279C22×Dic11C22×C414yes—
280C22×Dic11C2411yescharacteristic
281C22×Dic11C2412yes—
282C22×Dic11C2411yescharacteristic
283C22×Dic11C2412yes—
284C22×Dic11C2411yescharacteristic
285C22×Dic11C2411yescharacteristic
286C22×Dic11C2412yes—
287C22×Dic11C2411yescharacteristic
288C22×Dic11C2412yes—
289C22×Dic11C2411yescharacteristic
290C22×Dic11C2411yescharacteristic
291C22×Dic11C2411yescharacteristic
292C2×Dic22—22no—
293C2×Dic22—22no—
294C2×Dic22C22×C414yes—
295C11×C4⋊C4—22no—
296C11×C4⋊C4—22no—
297C11×C4⋊C4—42no—
298C11×C4⋊C4C22×C414yes—
299C11×C22⋊C4—22no—
300C11×C22⋊C4—24no—
301C11×C22⋊C4—22no—
302C11×C22⋊C4—42no—
303C11×C22⋊C4—42no—
304C11×C22⋊C4—42no—
305C11×C22⋊C4C22×C418yes—
306C42×C11—22no—
307C42×C11—22no—
308C42×C11—42no—
309C42×C11—42no—
310C22⋊Dic11—22no—
311C22⋊Dic11—24no—
312C22⋊Dic11—22no—
313C22⋊Dic11—42no—
314C22⋊Dic11—42no—
315C22⋊Dic11—42no—
316C22⋊Dic11C22×C418yes—
317C22⋊Dic11C22×C418yes—
318C22⋊Dic11C22×C418yes—
319C22⋊Dic11C22×C418yes—
320C4⋊Dic11—22no—
321C4⋊Dic11—22no—
322C4⋊Dic11—42no—
323C4⋊Dic11C22×C418yes—
324C4⋊Dic11C22×C414yes—
325Dic11⋊C4—22no—
326Dic11⋊C4—22no—
327Dic11⋊C4—24no—
328Dic11⋊C4—24no—
329Dic11⋊C4—24no—
330Dic11⋊C4—24no—
331Dic11⋊C4—42no—
332Dic11⋊C4—42no—
333Dic11⋊C4—42no—
334Dic11⋊C4—42no—
335Dic11⋊C4C22×C418yes—
336Dic11⋊C4C22×C418yes—
337Dic11⋊C4C22×C418yes—
338Dic11⋊C4#4114yes—
339Dic11⋊C4#4114yes—
340C4×Dic11—22no—
341C4×Dic11—24no—
342C4×Dic11—22no—
343C4×Dic11—22no—
344C4×Dic11—24no—
345C4×Dic11—22no—
346C4×Dic11—22no—
347C4×Dic11—22no—
348C4×Dic11—42no—
349C4×Dic11—42no—
350C4×Dic11—41no—
351C4×Dic11—42no—
352C4×Dic11—41no—
353C4×Dic11—41no—
354C4×Dic11—41no—
355C4×Dic11—42no—
356C4×Dic11C22×C414yes—
357C4×Dic11C22×C418yes—
358C4×Dic11C22×C414yes—
359C4×Dic11C22×C414yes—
360C4×Dic11C22×C414yes—
361C2×#529—111no—
362#2373—112no—
363#2373—112no—
364#2363—111no—
365#2363D1111yescharacteristic
366#2362—111no—
367#2362—111no—
368#2355—111no—
369#2354—112no—
370#2354—111no—
371#2352—112no—
372Q8×C4⋊C4—111no—
373D4×C4⋊C4—111no—
374#2335—112no—
375#2335—112no—
376#2314—112no—
377C4×#125—111no—
378C4×#125—111no—
379C4×#124—111no—
380C4×#124—111no—
381#2285—111no—
382#2274—112no—
383C4×#117—111no—
384C23×C11—21no—
385C23×C11—21no—
386C23×C11—22no—
387C23×C11—22no—
388C23×C11—21no—
389C23×C11—22no—
390C23×C11—21no—
391C23×C11—22no—
392C23×C11—22no—
393C23×C11—22no—
394C23×C11—21no—
395C23×C11—21no—
396C23×C11C23×C414yes—
397C23×C11C23×C412yes—
398C23×C11C2511yescharacteristic
399D4×C11—28no—
400D4×C11—48no—
401C2×C4×C11—21no—
402C2×C4×C11—21no—
403C2×C4×C11—21no—
404C2×C4×C11—21no—
405C2×C4×C11—21no—
406C2×C4×C11—22no—
407C2×C4×C11—21no—
408C2×C4×C11—22no—
409C2×C4×C11—28no—
410C2×C4×C11—22no—
411C2×C4×C11—21no—
412C2×C4×C11—21no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—21no—
416C2×C4×C11—22no—
417C2×C4×C11—21no—
418C2×C4×C11—21no—
419C2×C4×C11—21no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—84no—
423C2×C4×C11C23×C412yes—
424C2×C4×C11C23×C414yes—
425C2×C4×C11C23×C412yes—
426C2×C4×C11C2×#4112yes—
427C2×C4×C11C2×#4112yes—
428C2×C4×C11H(5,𝔽2)12yes—
429C2×C4×C112−1+412yes—
430C2×Dic11—21no—
431C2×Dic11—21no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—21no—
435C2×Dic11—22no—
436C2×Dic11—21no—
437C2×Dic11—22no—
438C2×Dic11—21no—
439C2×Dic11—21no—
440C2×Dic11—21no—
441C2×Dic11—21no—
442C2×Dic11—21no—
443C2×Dic11—21no—
444C2×Dic11—28no—
445C2×Dic11—216no—
446C2×Dic11—21no—
447C2×Dic11—22no—
448C2×Dic11—21no—
449C2×Dic11—22no—
450C2×Dic11—21no—
451C2×Dic11—22no—
452C2×Dic11—22no—
453C2×Dic11—21no—
454C2×Dic11—22no—
455C2×Dic11—21no—
456C2×Dic11—21no—
457C2×Dic11—22no—
458C2×Dic11—44no—
459C2×Dic11—84no—
460C2×Dic11C23×C412yes—
461C2×Dic11C23×C412yes—
462C2×Dic11C23×C412yes—
463C2×Dic11C23×C414yes—
464C2×Dic11C23×C414yes—
465C2×Dic11C23×C412yes—
466C2×Dic11C2×#4112yes—
467C2×Dic11C2×#4112yes—
468C2×Dic11C2×#4112yes—
469C2×Dic11C2×#4112yes—
470Dic22—28no—
471#529—1116no—
472C2×#126—112no—
473C2×#125—111no—
474C2×#124—111no—
475C2×#123—112no—
476C2×C22⋊Q8—111no—
477C2×#121C2×D1111yescharacteristic
478C2×C4×Q8—111no—
479C2×C4×Q8—111no—
480C2×C4×Q8—111no—
481C2×C4×D4—111no—
482C2×C4×D4—112no—
483C2×C4×D4—111no—
484C2×C4×D4C2×D1111yescharacteristic
485C2×#117—111no—
486C2×#117—112no—
487C2×#117—111no—
488C2×#117—111no—
489C2×#117—112no—
490C2×#117C2×D1111yescharacteristic
491C22×C4⋊C4—112no—
492C22×C42—111no—
493#391—111no—
494#391—111no—
495#390—112no—
496#390—111no—
497#390C2×D1112yes—
498#390C2×D1111yescharacteristic
499#389—111no—
500#389—111no—
501#389—112no—
502#389—111no—
503#389—112no—
504#389C2×D1111yescharacteristic
505#388—112no—
506#388—112no—
507#388—112no—
508#388—112no—
509#388—112no—
510#388—112no—
511#388—112no—
512#388—112no—
513#388—112no—
514#388—112no—
515#388—112no—
516#388C2×D1112yes—
517#387—112no—
518#387—112no—
519#387—112no—
520#387—112no—
521#387—112no—
522#387—112no—
523#387—112no—
524#387—112no—
525#386—112no—
526#386C2×D1112yes—
527#385—112no—
528#385—112no—
529#384—112no—
530#384—111no—
531#384—111no—
532#382—111no—
533#382—111no—
534#382—112no—
535#380—112no—
536#380—112no—
537#380—112no—
538#380—112no—
539C4×C4⋊C4—111no—
540C4×C4⋊C4—112no—
541C4×C4⋊C4—111no—
542C4×C4⋊C4—112no—
543C4×C4⋊C4—111no—
544C4×C4⋊C4—112no—
545C4×C4⋊C4—112no—
546C4×C4⋊C4—111no—
547C4×C4⋊C4—111no—
548C4×C4⋊C4—112no—
549C4×C4⋊C4—112no—
550C4×C4⋊C4—112no—
551C4×C4⋊C4—112no—
552C4×C4⋊C4—111no—
553C4×C4⋊C4—112no—
554C4×C4⋊C4—112no—
555C4×C4⋊C4—111no—
556C4×C4⋊C4C2×D1111yescharacteristic
557C4×C22⋊C4—112no—
558C4×C22⋊C4—112no—
559C4×C22⋊C4—111no—
560C4×C22⋊C4—111no—
561C4×C22⋊C4—111no—
562C4×C22⋊C4—112no—
563C4×C22⋊C4—112no—
564C4×C22⋊C4—112no—
565C4×C22⋊C4C2×D1111yescharacteristic
566C4×C22⋊C4C2×D1112yes—
567#376—111no—
568#376—111no—
569C43—111no—
570C43—111no—
571C22×C11—22no—
572C22×C11—24no—
573C22×C11—22no—
574C22×C11—24no—
575C22×C11—22no—
576C22×C11—24no—
577C22×C11—42no—
578C22×C11—41no—
579C22×C11—41no—
580C22×C11—42no—
581C22×C11—41no—
582C22×C11—42no—
583C22×C11—41no—
584C22×C11—42no—
585C22×C11C24×C411yescharacteristic
586C22×C11C22×#4111yescharacteristic
587C22×C11C22×#4111yescharacteristic
588C22×C11C2×H(5,𝔽2)11yescharacteristic
589C22×C11C2×2−1+411yescharacteristic
590C22×C11#58511yescharacteristic
591C22×C11#58511yescharacteristic
592C4×C11—22no—
593C4×C11—24no—
594C4×C11—22no—
595C4×C11—22no—
596C4×C11—42no—
597C4×C11—42no—
598C4×C11—41no—
599C4×C11—41no—
600C4×C11#52014yes—
601Dic11—22no—
602Dic11—24no—
603Dic11—24no—
604Dic11—22no—
605Dic11—22no—
606Dic11—22no—
607Dic11—22no—
608Dic11—42no—
609Dic11—41no—
610Dic11—42no—
611Dic11—41no—
612Dic11C4×#4114yes—
613C22×Q8—111no—
614C22×D4C22×D1111yescharacteristic
615C22×D4C22×D1112yes—
616C23×C4—112no—
617C23×C4—111no—
618C23×C4—111no—
619C23×C4—112no—
620C23×C4C22×D1111yescharacteristic
621C23×C4C22×D1112yes—
622#126—1116no—
623#125—118no—
624#124—118no—
625#123—1116no—
626C22⋊Q8—118no—
627#121C4×D1118yes—
628C4×Q8—118no—
629C4×Q8—442no—
630C4×Q8—442no—
631C4×D4—42no—
632C4×D4—118no—
633C4×D4—1116no—
634C4×D4—442no—
635#117—42no—
636#117—1116no—
637#117—224no—
638#117—224no—
639#117—228no—
640#117—442no—
641C2×C4⋊C4—111no—
642C2×C4⋊C4—111no—
643C2×C4⋊C4—112no—
644C2×C4⋊C4—112no—
645C2×C4⋊C4—111no—
646C2×C4⋊C4—112no—
647C2×C4⋊C4—112no—
648C2×C4⋊C4—112no—
649C2×C4⋊C4—112no—
650C2×C4⋊C4—112no—
651C2×C4⋊C4—111no—
652C2×C4⋊C4—111no—
653C2×C4⋊C4—111no—
654C2×C4⋊C4—111no—
655C2×C4⋊C4—112no—
656C2×C4⋊C4—112no—
657C2×C4⋊C4—112no—
658C2×C4⋊C4—112no—
659C2×C4⋊C4—112no—
660C2×C4⋊C4—112no—
661C2×C4⋊C4—228no—
662C2×C4⋊C4C22×D1111yescharacteristic
663C2×C4⋊C4C22×D1111yescharacteristic
664C2×C4⋊C4C22×D1112yes—
665C2×C4⋊C4C22×D1111yescharacteristic
666C2×C22⋊C4—112no—
667C2×C22⋊C4—112no—
668C2×C22⋊C4—112no—
669C2×C22⋊C4—112no—
670C2×C22⋊C4—111no—
671C2×C22⋊C4—111no—
672C2×C22⋊C4—112no—
673C2×C22⋊C4—112no—
674C2×C22⋊C4—112no—
675C2×C22⋊C4—112no—
676C2×C22⋊C4C22×D1111yescharacteristic
677C2×C22⋊C4C22×D1111yescharacteristic
678C2×C22⋊C4C22×D1112yes—
679C2×C22⋊C4C22×D1112yes—
680C2×C22⋊C4C22×D1112yes—
681C2×C22⋊C4C22×D1112yes—
682C2×C22⋊C4C22×D1112yes—
683C2×C42—118no—
684C2×C42—111no—
685C2×C42—112no—
686C2×C42—111no—
687C2×C42—111no—
688C2×C42—111no—
689C2×C42—111no—
690C2×C42—111no—
691C2×C42—111no—
692C2×C42—111no—
693C2×C42—112no—
694C2×C42—112no—
695C2×C42—111no—
696C2×C42—111no—
697C2×C42—112no—
698C2×C42—112no—
699C2×C42—112no—
700C2×C42—111no—
701C2×C42—111no—
702C2×C42—111no—
703C2×C42—111no—
704C2×C42—112no—
705C2×C42C22×D1111yescharacteristic
706C2×C42C22×D1111yescharacteristic
707C2×C42C22×D1112yes—
708C2×C42C22×D1112yes—
709#95—111no—
710#95—111no—
711#95—111no—
712#95—111no—
713#95—111no—
714#95—111no—
715#95—112no—
716#95—112no—
717#95—112no—
718#95—112no—
719#95—112no—
720#95—112no—
721#95—112no—
722#95—112no—
723#95—112no—
724#95—112no—
725#95—112no—
726#95—112no—
727#95—112no—
728#95—112no—
729#95C22×D1111yescharacteristic
730#95C22×D1111yescharacteristic
731#95C22×D1112yes—
732#95C22×D1112yes—
733C2×C11—42no—
734C2×C11—44no—
735C2×C11C2×C4×#4111yescharacteristic
736C2×C11C2×#52011yescharacteristic
737C2×C11#342811yescharacteristic
738C2×C11#351411yescharacteristic
739C2×C11#351511yescharacteristic
740C2×C11#351711yescharacteristic
741C2×C11#351811yescharacteristic
742C24C23×D1111yescharacteristic
743C24C23×D1112yes—
744C2×Q8—114no—
745C2×Q8—222no—
746C2×Q8—222no—
747C2×D4—22no—
748C2×D4—22no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4C2×C4×D1114yes—
752C2×D4C2×C4×D1118yes—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—24no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—111no—
759C22×C4—114no—
760C22×C4—118no—
761C22×C4—111no—
762C22×C4—111no—
763C22×C4—111no—
764C22×C4—111no—
765C22×C4—112no—
766C22×C4—111no—
767C22×C4—112no—
768C22×C4—114no—
769C22×C4—111no—
770C22×C4—112no—
771C22×C4—111no—
772C22×C4—112no—
773C22×C4—224no—
774C22×C4—224no—
775C22×C4—222no—
776C22×C4—222no—
777C22×C4—224no—
778C22×C4—441no—
779C22×C4—441no—
780C22×C4—442no—
781C22×C4—442no—
782C22×C4C2×C4×D1114yes—
783C22×C4C23×D1111yescharacteristic
784C22×C4C23×D1112yes—
785C22×C4C23×D1111yescharacteristic
786C22×C4C23×D1112yes—
787C22×C4C23×D1111yescharacteristic
788C22×C4C23×D1112yes—
789C22×C4C23×D1111yescharacteristic
790C22×C4C23×D1111yescharacteristic
791C22×C4C23×D1111yescharacteristic
792C4⋊C4—22no—
793C4⋊C4—22no—
794C4⋊C4—42no—
795C4⋊C4—118no—
796C4⋊C4—118no—
797C4⋊C4—114no—
798C4⋊C4—118no—
799C4⋊C4—118no—
800C4⋊C4—114no—
801C4⋊C4—114no—
802C4⋊C4—224no—
803C4⋊C4—224no—
804C4⋊C4—222no—
805C4⋊C4—222no—
806C4⋊C4—224no—
807C4⋊C4—222no—
808C4⋊C4—222no—
809C4⋊C4—224no—
810C4⋊C4—442no—
811C4⋊C4—442no—
812C4⋊C4—442no—
813C4⋊C4—442no—
814C4⋊C4—442no—
815C4⋊C4C2×C4×D1114yes—
816C22⋊C4—22no—
817C22⋊C4—24no—
818C22⋊C4—22no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—42no—
822C22⋊C4—118no—
823C22⋊C4—118no—
824C22⋊C4—118no—
825C22⋊C4—118no—
826C22⋊C4—222no—
827C22⋊C4—224no—
828C22⋊C4—222no—
829C22⋊C4—442no—
830C22⋊C4—442no—
831C22⋊C4—442no—
832C22⋊C4C2×C4×D1118yes—
833C42—22no—
834C42—22no—
835C42—42no—
836C42—42no—
837C42—114no—
838C42—114no—
839C42—114no—
840C42—114no—
841C42—118no—
842C42—222no—
843C42—224no—
844C42—222no—
845C42—222no—
846C42—222no—
847C42—224no—
848C42—222no—
849C42—222no—
850C42—442no—
851C42—442no—
852C42—442no—
853C42—441no—
854C42—442no—
855C42—441no—
856C42—441no—
857C42—441no—
858C11#3424211yescharacteristic, complemented, Sylow
859C23—21no—
860C23—22no—
861C23—21no—
862C23—21no—
863C23—22no—
864C23—22no—
865C23—21no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—21no—
870C23—21no—
871C23C22×C4×D1114yes—
872C23C22×C4×D1112yes—
873C23C24×D1111yescharacteristic
874Q8—228no—
875D4—28no—
876D4—48no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—22no—
883C2×C4—21no—
884C2×C4—22no—
885C2×C4—28no—
886C2×C4—21no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—21no—
890C2×C4—21no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—21no—
894C2×C4—22no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—22no—
898C2×C4—84no—
899C2×C4—112no—
900C2×C4—112no—
901C2×C4—112no—
902C2×C4—112no—
903C2×C4—112no—
904C2×C4—112no—
905C2×C4—114no—
906C2×C4—114no—
907C2×C4—112no—
908C2×C4—112no—
909C2×C4—228no—
910C2×C4—2216no—
911C2×C4—221no—
912C2×C4—222no—
913C2×C4—221no—
914C2×C4—221no—
915C2×C4—222no—
916C2×C4—222no—
917C2×C4—221no—
918C2×C4—222no—
919C2×C4—221no—
920C2×C4—221no—
921C2×C4—221no—
922C2×C4—221no—
923C2×C4—221no—
924C2×C4—221no—
925C2×C4—221no—
926C2×C4—222no—
927C2×C4—222no—
928C2×C4—221no—
929C2×C4—221no—
930C2×C4—222no—
931C2×C4—222no—
932C2×C4—221no—
933C2×C4—221no—
934C2×C4—221no—
935C2×C4—222no—
936C2×C4—222no—
937C2×C4—444no—
938C2×C4—884no—
939C2×C4C22×C4×D1112yes—
940C2×C4C22×C4×D1114yes—
941C2×C4C22×C4×D1112yes—
942C2×C4#6703712yes—
943C2×C4#41×D1112yes—
944C2×C4#41×D1112yes—
945C2×C4#6704312yes—
946C22—22no—
947C22—24no—
948C22—22no—
949C22—24no—
950C22—22no—
951C22—24no—
952C22—41no—
953C22—42no—
954C22—42no—
955C22—41no—
956C22—41no—
957C22—42no—
958C22—41no—
959C22—42no—
960C22C23×C4×D1111yescharacteristic
961C22C2×#6703711yescharacteristic
962C22C2×#41×D1111yescharacteristic
963C22C2×#41×D1111yescharacteristic
964C22C2×#6704311yescharacteristic
965C22#1062345511yescharacteristic
966C22#1062345511yescharacteristic
967C4—22no—
968C4—22no—
969C4—24no—
970C4—22no—
971C4—41no—
972C4—42no—
973C4—41no—
974C4—42no—
975C4—114no—
976C4—222no—
977C4—224no—
978C4—222no—
979C4—224no—
980C4—222no—
981C4—222no—
982C4—222no—
983C4—441no—
984C4—442no—
985C4—441no—
986C4—442no—
987C4#1062307714yes—
988C2—42no—
989C2—44no—
990C2C4×#41×D1111yescharacteristic
991C2C2×#1062307711yescharacteristic
992C2#1308181411yescharacteristic
993C2#1308257411yescharacteristic
994C2#1308258711yescharacteristic
995C2#1308261911yescharacteristic
996C2#1308263211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2363C2
socle, cosocleC23×C11C25
prime radicalC2×C11×#121C22
hypercenter#2363D11
hypocenterC11#34242
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2363

Complements

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

NH ≅ G/Ntype
2. #13071738C2semidirect
3. #13071734C2semidirect
5. #13071643C2semidirect
6. #13071641C2semidirect
7. #13071569C2semidirect
8. #13071564C2semidirect
9. #13071564C2semidirect
10. #13071543C2semidirect
11. #13071530C2semidirect
12. D4×Dic11⋊C4C2semidirect
13. #13071407C2semidirect
14. #13071403C2semidirect
15. #13071220C2semidirect
16. #13071175C2semidirect
17. C4×#66943C2semidirect
18. #13071163C2semidirect
19. C4×#66989C2semidirect
20. #13071019C2semidirect
21. #13070971C2semidirect
22. C4×#66930C2semidirect
36. #10623131C4semidirect
162. #66988C2×C4semidirect
165. D4×Dic11C2×C4semidirect
172. #66977C2×C4semidirect
189. C2×C4×Dic11C2×C4semidirect
211. #66943C2×C4semidirect
213. #66940C2×C4semidirect
214. #66932C2×C4semidirect
218. #66930C2×C4semidirect
858. C11#34242semidirect

Maximal subgroups

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

subgroupindex
C2×#106231312
#130717382
#130717342
#130716582
#130716432
#130716412
#130715692
#130715642
#130715432
#130715302
D4×Dic11⋊C42
#130714072
#130714032
#130712202
#130711752
C4×#669432
#130711632
C4×#669892
#130710192
#130709712
C4×#669302
C11×#23632
#3424211