Finite Group Databasebeta

← #14916799

Subgroups — #14916799

Order 2816.

2190 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623088C211yesmaximal, characteristic
2#13071765C214yesmaximal, complemented
3#13071717C212yesmaximal, complemented
4#13071689C212yesmaximal, complemented
5#13071571C211yesmaximal, characteristic, complemented
6#13071565C211yesmaximal, characteristic, complemented
7#13071560C212yesmaximal, complemented
8#13071541C212yesmaximal, complemented
9#13071528C211yesmaximal, characteristic, complemented
10#13071392C214yesmaximal, complemented
11#13071303C212yesmaximal
12#13071296C212yesmaximal, complemented
13#13071240C212yesmaximal, complemented
14#13071223C212yesmaximal, complemented
15#13071021C211yesmaximal, characteristic, complemented
16#13071020C211yesmaximal, characteristic, complemented
17D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
18C2×C4×D4×C11C2212yes—
19C2×C4×D4×C11C2211yescharacteristic
20C22×C11×C4⋊C4C2212yes—
21C2×#66991C2211yescharacteristic
22C2×#66989C2211yescharacteristic
23C2×C4×C22⋊D11C2212yes—
24C2×#66979C2212yes—
25C2×#66979C2212yes—
26#10623088C4116yescomplemented
27C2×#66950C2211yescharacteristic
28C2×#66945C2212yes—
29C2×#66943C2211yescharacteristic
30C2×#66940C2212yes—
31C2×#66936C2212yes—
32C2×#66932C2212yes—
33C2×#66925C2212yes—
34C2×C42×D11C2211yescharacteristic
35C2×C4×Dic22C2211yescharacteristic
36C11×#389C2212yes—
37C11×#385C2214yes—
38C11×#384C2211yescharacteristic
39C11×#380C2212yes—
40C4×C11×C4⋊C4C2211yescharacteristic
41#10622834C2212yes—
42#10622826C2214yes—
43#10622825C2212yes—
44#10622823C2214yes—
45#10622823C2214yes—
46C4×C22⋊Dic11C2214yes—
47#10622603C2214yes—
48#10622600C2212yes—
49#10622600C2211yescharacteristic
50#10622600C2211yescharacteristic
51#10622600C2212yes—
52#10622591C2214yes—
53#10622590C2212yes—
54#10622590C2212yes—
55#10622589C2211yescharacteristic
56#10622589C2211yescharacteristic
57#10622589C2212yes—
58C4⋊C4×Dic11C2212yes—
59C4⋊C4×Dic11C2212yes—
60C4⋊C4×Dic11C2212yes—
61C4⋊C4×Dic11C2212yes—
62C4⋊C4×Dic11C2212yes—
63#10622586C2214yes—
64#10622586C2214yes—
65#10622586C2212yes—
66#10622585C2214yes—
67#10622570C2214yes—
68#10622564C2214yes—
69#10622558C2214yes—
70#10622558C2214yes—
71#10622557C2214yes—
72#10622548C2211yescharacteristic
73C4×C4⋊Dic11C2212yes—
74C4×C4⋊Dic11C2211yescharacteristic
75C4×Dic11⋊C4C2212yes—
76#10622542C2212yes—
77#10622282C2214yes—
78#10622280C2212yes—
79#10622268C2214yes—
80#10622267C2214yes—
81#10622266C2214yes—
82#10622263C2212yes—
83#10622262C2214yes—
84C22×D4×C11C2311yescharacteristic
85C23×C4×C11C2312yes—
86C23×C4×C11C2314yes—
87C22×C22⋊D11C2312yes—
88C22×C4×D11C2311yescharacteristic
89C22×C4×D11C2311yescharacteristic
90C22×C4×D11C2311yescharacteristic
91C22×Dic22C2311yescharacteristic
92C4×D4×C11—44no—
93C4×D4×C11C2×C418yes—
94C2×C11×C4⋊C4—44no—
95C2×C11×C4⋊C4C2312yes—
96C2×C11×C4⋊C4C2312yes—
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2312yes—
100C2×C11×C4⋊C4C2314yes—
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C22⋊C4C2314yes—
103C2×C11×C22⋊C4C2312yes—
104C2×C42×C11C2312yes—
105C2×C42×C11C2311yescharacteristic
106C2×C22⋊Dic11C2314yes—
107C2×C22⋊Dic11C2314yes—
108C2×C22⋊Dic11C2312yes—
109C2×C22⋊Dic11C2312yes—
110C2×C22⋊Dic11C2312yes—
111#66991C2×C418yes—
112#66989C2×C418yes—
113C4×C22⋊D11C2×C4116yescomplemented
114C2×(C2×D11)⋊C4C2312yes—
115C2×(C2×D11)⋊C4C2312yes—
116C2×(C2×D11)⋊C4C2314yes—
117C2×(C2×D11)⋊C4C2312yes—
118#66979—44no—
119#66979C2×C4116yescomplemented
120C2×C4⋊Dic11C2312yes—
121C2×C4⋊Dic11C2312yes—
122C2×C4⋊Dic11C2311yescharacteristic
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2312yes—
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4⋊Dic11C2312yes—
127C2×C4⋊Dic11C2312yes—
128C2×Dic11⋊C4C2312yes—
129C2×Dic11⋊C4C2312yes—
130C2×Dic11⋊C4C2314yes—
131C2×Dic11⋊C4C2314yes—
132C2×Dic11⋊C4C2312yes—
133C2×Dic11⋊C4C2312yes—
134C2×Dic11⋊C4C2312yes—
135C2×Dic11⋊C4C2312yes—
136C2×C4×Dic11C2312yes—
137C2×C4×Dic11C2314yes—
138C2×C4×Dic11C2314yes—
139C2×C4×Dic11C2314yes—
140C2×C4×Dic11C2314yes—
141C2×C4×Dic11C2312yes—
142C2×C4×Dic11C2311yescharacteristic
143C2×C4×Dic11C2311yescharacteristic
144C2×C4×Dic11C2311yescharacteristic
145#66950C2×C418yescomplemented
146#66945—44no—
147#66943C2×C418yescomplemented
148#66940—44no—
149#66936C2×C4116yescomplemented
150#66932C2×C4116yescomplemented
151#66925—44no—
152C42×D11C2×C418yescomplemented
153C4×Dic22C2×C418yescomplemented
154C11×#95C2314yes—
155C11×#95C2312yes—
156C11⋊#95C2312yes—
157C11⋊#95C2312yes—
158C11⋊#95C2312yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166#34383—111nomaximal, Sylow
167C24×C11C2412yes—
168C23×D11C2411yescharacteristic
169C2×D4×C11—22no—
170C2×D4×C11—22no—
171C2×D4×C11C22×C414yes—
172C22×C4×C11—24no—
173C22×C4×C11—24no—
174C22×C4×C11—44no—
175C22×C4×C11—44no—
176C22×C4×C11—44no—
177C22×C4×C11C22×C418yes—
178C22×C4×C11C2412yes—
179C22×C4×C11C2412yes—
180C22×C4×C11C2414yes—
181C22×C4×C11C2412yes—
182C22×C4×C11C2411yescharacteristic
183C22×C4×C11C2411yescharacteristic
184C22×C4×C11C2411yescharacteristic
185C2×C22⋊D11—42no—
186C2×C22⋊D11—42no—
187C2×C22⋊D11C22×C418yes—
188C22×Dic11C2412yes—
189C22×Dic11C2414yes—
190C22×Dic11C2412yes—
191C22×Dic11C2411yescharacteristic
192C22×Dic11C2412yes—
193C22×Dic11C2412yes—
194C22×Dic11C2411yescharacteristic
195C22×Dic11C2411yescharacteristic
196C2×C4×D11—22no—
197C2×C4×D11—22no—
198C2×C4×D11—22no—
199C2×C4×D11—22no—
200C2×C4×D11—41no—
201C2×C4×D11—41no—
202C2×C4×D11C22×C414yes—
203C2×C4×D11C22×C414yes—
204C2×C4×D11C22×C414yes—
205C2×Dic22—22no—
206C2×Dic22—22no—
207C2×Dic22C22×C414yes—
208C11×C4⋊C4—24no—
209C11×C4⋊C4—24no—
210C11×C4⋊C4—22no—
211C11×C4⋊C4—22no—
212C11×C4⋊C4—44no—
213C11×C4⋊C4—42no—
214C11×C4⋊C4C22×C414yes—
215C11×C22⋊C4—44no—
216C11×C22⋊C4C22×C418yes—
217C42×C11—24no—
218C42×C11C22×C414yes—
219C22⋊Dic11—44no—
220C22⋊Dic11—44no—
221C22⋊Dic11C22×C418yes—
222C22⋊Dic11C22×C418yes—
223C22⋊Dic11C22×C418yes—
224(C2×D11)⋊C4—42no—
225(C2×D11)⋊C4—42no—
226(C2×D11)⋊C4—44no—
227(C2×D11)⋊C4C22×C418yes—
228C4⋊Dic11—24no—
229C4⋊Dic11—22no—
230C4⋊Dic11—24no—
231C4⋊Dic11—22no—
232C4⋊Dic11—42no—
233C4⋊Dic11C22×C414yes—
234C4⋊Dic11C22×C418yes—
235C4⋊Dic11C22×C418yes—
236Dic11⋊C4—42no—
237Dic11⋊C4—42no—
238Dic11⋊C4—44no—
239Dic11⋊C4—42no—
240Dic11⋊C4—44no—
241Dic11⋊C4—42no—
242Dic11⋊C4C22×C418yes—
243Dic11⋊C4C22×C418yes—
244C4×Dic11—24no—
245C4×Dic11—44no—
246C4×Dic11—44no—
247C4×Dic11—44no—
248C4×Dic11—44no—
249C4×Dic11C22×C418yes—
250C4×Dic11C22×C414yes—
251C4×Dic11C22×C414yes—
252C4×Dic11C22×C414yes—
253C2×#529—111no—
254#2376—114no—
255#2370—112no—
256#2367—112no—
257#2355—111no—
258#2354—112no—
259#2354—111no—
260#2352—112no—
261Q8×C4⋊C4—111no—
262D4×C4⋊C4D1111yescharacteristic, complemented
263#2334—114no—
264#2324—112no—
265#2323—112no—
266#2317—112no—
267#2314—112no—
268#2285—111no—
269#2285—111no—
270C23×C11—22no—
271C23×C11—22no—
272C23×C11—22no—
273C23×C11—22no—
274C23×C11—22no—
275C23×C11—22no—
276C23×C11C23×C414yes—
277C23×C11C2511yescharacteristic
278C22×D11—21no—
279C22×D11—21no—
280C22×D11—21no—
281C22×D11—21no—
282C22×D11—21no—
283C22×D11—21no—
284C22×D11C23×C412yes—
285D4×C11—28no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—216no—
291C2×C4×C11—24no—
292C2×C4×C11—24no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—24no—
299C2×C4×C11—22no—
300C2×C4×C11—88no—
301C2×C4×C11C23×C412yes—
302C2×C4×C11C23×C414yes—
303C2×C4×C11C23×C412yes—
304C2×C4×C11C23×C412yes—
305C2×C4×C11H(5,𝔽2)12yes—
306C2×C4×C11H(5,𝔽2)12yes—
307C2×C4×C112−1+412yes—
308C2×C4×C112−1+412yes—
309C22⋊D11—48no—
310C2×Dic11—21no—
311C2×Dic11—22no—
312C2×Dic11—21no—
313C2×Dic11—22no—
314C2×Dic11—21no—
315C2×Dic11—21no—
316C2×Dic11—22no—
317C2×Dic11—21no—
318C2×Dic11—21no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—24no—
323C2×Dic11—22no—
324C2×Dic11—24no—
325C2×Dic11—22no—
326C2×Dic11—24no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11C23×C412yes—
330C2×Dic11C23×C412yes—
331C2×Dic11C23×C412yes—
332C2×Dic11C23×C414yes—
333C2×Dic11C23×C414yes—
334C4×D11—28no—
335C4×D11—28no—
336C4×D11—44no—
337Dic22—28no—
338#529—1116no—
339C2×#126—112no—
340C2×#125—111no—
341C2×#124—111no—
342C2×#123—112no—
343C2×C22⋊Q8—111no—
344C2×#121—111no—
345C2×C4×Q8—112no—
346C2×C4×Q8—111no—
347C2×C4×D4—112no—
348C2×C4×D4C2×D1112yes—
349C2×C4×D4C2×D1111yescharacteristic
350C2×#117—112no—
351C2×#117—112no—
352C2×#117—112no—
353C2×#117—112no—
354C22×C4⋊C4C2×D1112yes—
355C22×C42—111no—
356#391—112no—
357#390—112no—
358#390—114no—
359#389—114no—
360#389—114no—
361#389—112no—
362#389—114no—
363#389C2×D1112yes—
364#388—114no—
365#388—114no—
366#388—114no—
367#388—114no—
368#388—114no—
369#388—114no—
370#387—114no—
371#387—114no—
372#387—114no—
373#387—114no—
374#386—114no—
375#385—114no—
376#385—114no—
377#385C2×D1114yes—
378#384—111no—
379#384—111no—
380#384—112no—
381#384—111no—
382#384C2×D1111yescharacteristic
383#382—112no—
384#382—112no—
385#382—112no—
386#380—112no—
387#380—112no—
388#380—111no—
389#380—111no—
390#380—112no—
391#380—112no—
392#380C2×D1112yes—
393C4×C4⋊C4—112no—
394C4×C4⋊C4—112no—
395C4×C4⋊C4—112no—
396C4×C4⋊C4—112no—
397C4×C4⋊C4—112no—
398C4×C4⋊C4—112no—
399C4×C4⋊C4—111no—
400C4×C4⋊C4—112no—
401C4×C4⋊C4—114no—
402C4×C4⋊C4C2×D1111yescharacteristic
403C4×C22⋊C4—114no—
404C22×C11—24no—
405C22×C11—24no—
406C22×C11—24no—
407C22×C11—42no—
408C22×C11—42no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11C24×C411yescharacteristic
412C22×C11C2×H(5,𝔽2)11yescharacteristic
413C22×C11C2×H(5,𝔽2)11yescharacteristic
414C22×C11C2×2−1+411yescharacteristic
415C22×C11C2×2−1+411yescharacteristic
416C22×C11#58511yescharacteristic
417C22×C11#58511yescharacteristic
418C2×D11—22no—
419C2×D11—22no—
420C2×D11—22no—
421C2×D11—41no—
422C2×D11—41no—
423C2×D11—41no—
424C2×D11—41no—
425C4×C11—24no—
426C4×C11—22no—
427C4×C11—44no—
428C4×C11—42no—
429C4×C11—42no—
430C4×C11#52014yes—
431C4×C11#52014yes—
432Dic11—24no—
433Dic11—22no—
434Dic11—22no—
435Dic11—22no—
436Dic11—24no—
437Dic11—42no—
438Dic11—42no—
439Dic11—44no—
440C22×Q8—111no—
441C22×D4—112no—
442C22×D4C22×D1111yescharacteristic
443C23×C4—111no—
444C23×C4—111no—
445C23×C4—111no—
446C23×C4C22×D1112yes—
447C23×C4C22×D1114yes—
448#126—1116no—
449#125—118no—
450#124—118no—
451#123—1116no—
452C22⋊Q8—118no—
453#121—118no—
454C4×Q8—118no—
455C4×Q8—444no—
456C4×D4—44no—
457C4×D4—1116no—
458C4×D4C4×D1118yes—
459#117—1116no—
460#117—444no—
461#117—444no—
462#117—444no—
463C2×C4⋊C4—44no—
464C2×C4⋊C4—112no—
465C2×C4⋊C4—112no—
466C2×C4⋊C4—112no—
467C2×C4⋊C4—111no—
468C2×C4⋊C4—112no—
469C2×C4⋊C4—112no—
470C2×C4⋊C4—111no—
471C2×C4⋊C4—111no—
472C2×C4⋊C4—112no—
473C2×C4⋊C4—112no—
474C2×C4⋊C4—112no—
475C2×C4⋊C4—114no—
476C2×C4⋊C4—112no—
477C2×C4⋊C4—112no—
478C2×C4⋊C4—112no—
479C2×C4⋊C4—114no—
480C2×C4⋊C4C22×D1111yescharacteristic
481C2×C4⋊C4C22×D1112yes—
482C2×C4⋊C4C22×D1112yes—
483C2×C4⋊C4C22×D1111yescharacteristic
484C2×C4⋊C4C22×D1114yes—
485C2×C4⋊C4C22×D1112yes—
486C2×C4⋊C4C22×D1111yescharacteristic
487C2×C22⋊C4—112no—
488C2×C22⋊C4—112no—
489C2×C22⋊C4—112no—
490C2×C22⋊C4—112no—
491C2×C22⋊C4—114no—
492C2×C22⋊C4—114no—
493C2×C22⋊C4—112no—
494C2×C22⋊C4—114no—
495C2×C22⋊C4—112no—
496C2×C22⋊C4C22×D1114yes—
497C2×C22⋊C4C22×D1112yes—
498C2×C42—111no—
499C2×C42—112no—
500C2×C42—111no—
501C2×C42—111no—
502C2×C42—118no—
503C2×C42—112no—
504C2×C42—114no—
505C2×C42—114no—
506C2×C42—114no—
507C2×C42—114no—
508C2×C42C22×D1112yes—
509C2×C42C22×D1111yescharacteristic
510#95—112no—
511#95—114no—
512#95—112no—
513#95—114no—
514#95—114no—
515#95—112no—
516#95—114no—
517#95—114no—
518#95—114no—
519#95—114no—
520#95C22×D1114yes—
521#95C22×D1112yes—
522C2×C11—44no—
523C2×C11C2×#52011yescharacteristic
524C2×C11C2×#52011yescharacteristic
525C2×C11#342811yescharacteristic
526C2×C11#354611yescharacteristic
527C2×C11#354711yescharacteristic
528C2×C11#355411yescharacteristic
529C2×C11#355511yescharacteristic
530D11—42no—
531C24—111no—
532C24C23×D1112yes—
533C2×Q8—114no—
534C2×Q8—222no—
535C2×Q8—222no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—118no—
539C2×D4—442no—
540C2×D4—442no—
541C2×D4C2×C4×D1114yes—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—111no—
548C22×C4—112no—
549C22×C4—112no—
550C22×C4—111no—
551C22×C4—111no—
552C22×C4—114no—
553C22×C4—114no—
554C22×C4—114no—
555C22×C4—112no—
556C22×C4—114no—
557C22×C4—112no—
558C22×C4—222no—
559C22×C4—222no—
560C22×C4—222no—
561C22×C4—222no—
562C22×C4—441no—
563C22×C4—441no—
564C22×C4C2×C4×D1118yes—
565C22×C4C23×D1112yes—
566C22×C4C23×D1112yes—
567C22×C4C23×D1114yes—
568C22×C4C23×D1112yes—
569C22×C4C23×D1111yescharacteristic
570C22×C4C23×D1111yescharacteristic
571C22×C4C23×D1111yescharacteristic
572C4⋊C4—22no—
573C4⋊C4—24no—
574C4⋊C4—24no—
575C4⋊C4—22no—
576C4⋊C4—44no—
577C4⋊C4—42no—
578C4⋊C4—118no—
579C4⋊C4—118no—
580C4⋊C4—118no—
581C4⋊C4—114no—
582C4⋊C4—118no—
583C4⋊C4—224no—
584C4⋊C4—222no—
585C4⋊C4—224no—
586C4⋊C4—222no—
587C4⋊C4—442no—
588C4⋊C4—442no—
589C4⋊C4—444no—
590C4⋊C4—444no—
591C4⋊C4—442no—
592C4⋊C4—442no—
593C4⋊C4—442no—
594C4⋊C4C2×C4×D1114yes—
595C22⋊C4—44no—
596C22⋊C4—118no—
597C22⋊C4—118no—
598C22⋊C4—118no—
599C22⋊C4—118no—
600C22⋊C4—442no—
601C22⋊C4—442no—
602C22⋊C4—444no—
603C22⋊C4—444no—
604C22⋊C4—444no—
605C22⋊C4C2×C4×D1118yes—
606C42—24no—
607C42—114no—
608C42—114no—
609C42—114no—
610C42—118no—
611C42—224no—
612C42—444no—
613C42—444no—
614C42—444no—
615C42—444no—
616C42C2×C4×D1114yes—
617C11#3438311yescharacteristic, complemented, Sylow
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—112no—
625C23—221no—
626C23—221no—
627C23—221no—
628C23—221no—
629C23—221no—
630C23—221no—
631C23C22×C4×D1114yes—
632C23C24×D1111yescharacteristic
633Q8—228no—
634D4—28no—
635D4—448no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—216no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—24no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—88no—
651C2×C4—112no—
652C2×C4—112no—
653C2×C4—112no—
654C2×C4—114no—
655C2×C4—114no—
656C2×C4—221no—
657C2×C4—222no—
658C2×C4—221no—
659C2×C4—221no—
660C2×C4—222no—
661C2×C4—221no—
662C2×C4—221no—
663C2×C4—222no—
664C2×C4—222no—
665C2×C4—221no—
666C2×C4—228no—
667C2×C4—228no—
668C2×C4—222no—
669C2×C4—222no—
670C2×C4—222no—
671C2×C4—224no—
672C2×C4—224no—
673C2×C4—222no—
674C2×C4—222no—
675C2×C4—224no—
676C2×C4—222no—
677C2×C4—444no—
678C2×C4C22×C4×D1112yes—
679C2×C4C22×C4×D1114yes—
680C2×C4C22×C4×D1112yes—
681C2×C4C22×C4×D1112yes—
682C2×C4#6703712yes—
683C2×C4#6703712yes—
684C2×C4#6704012yes—
685C2×C4#6704312yes—
686C22—24no—
687C22—24no—
688C22—24no—
689C22—42no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—222no—
694C22—222no—
695C22—222no—
696C22—441no—
697C22—441no—
698C22—441no—
699C22—441no—
700C22C23×C4×D1111yescharacteristic
701C22C2×#6703711yescharacteristic
702C22C2×#6703711yescharacteristic
703C22C2×#6704011yescharacteristic
704C22C2×#6704311yescharacteristic
705C22#1062345511yescharacteristic
706C22#1062345711yescharacteristic
707C4—24no—
708C4—22no—
709C4—42no—
710C4—44no—
711C4—42no—
712C4—222no—
713C4—222no—
714C4—224no—
715C4—222no—
716C4—224no—
717C4—442no—
718C4—442no—
719C4—444no—
720C4#1062303514yes—
721C4#1062307714yes—
722C2—44no—
723C2—442no—
724C2C2×#1062307711yescharacteristic
725C2C2×#1062303511yescharacteristic
726C2#1308181611yescharacteristic
727C2#1308298411yescharacteristic
728C2#1308299311yescharacteristic
729C2#1308308811yescharacteristic
730C2#1308310711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingD4×C11×C4⋊C4C2
socle, cosocleC23×C11C25
prime radicalC2×#66991C22
hypercenterD4×C4⋊C4D11
hypocenterC11#34383
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13071765C2semidirect
3. #13071717C2semidirect
4. #13071689C2semidirect
5. #13071571C2semidirect
6. #13071565C2semidirect
7. #13071560C2semidirect
8. #13071541C2semidirect
9. #13071528C2semidirect
10. #13071392C2semidirect
12. #13071296C2semidirect
13. #13071240C2semidirect
14. #13071223C2semidirect
15. #13071021C2semidirect
16. #13071020C2semidirect
17. D4×C11×C4⋊C4C2semidirect
26. #10623088C4semidirect
113. C4×C22⋊D11C2×C4semidirect
119. #66979C2×C4semidirect
145. #66950C2×C4semidirect
147. #66943C2×C4semidirect
149. #66936C2×C4semidirect
150. #66932C2×C4semidirect
152. C42×D11C2×C4semidirect
153. C4×Dic22C2×C4semidirect
262. D4×C4⋊C4D11semidirect
617. C11#34383semidirect

Maximal subgroups

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

subgroupindex
C2×#106230882
#130717652
#130717172
#130716892
#130715712
#130715652
#130715602
#130715412
#130715282
#130713922
#130713032
#130712962
#130712402
#130712232
#130710212
#130710202
D4×C11×C4⋊C42
#3438311