Finite Group Databasebeta

← #14914768

Subgroups — #14914768

Order 2816.

2426 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071556C214yesmaximal, complemented
2#13071545C214yesmaximal, complemented
3#13071509C212yesmaximal, complemented
4#13071501C212yesmaximal, complemented
5#13071493C212yesmaximal, complemented
6#13071485C212yesmaximal, complemented
7#13071267C212yesmaximal, complemented
8#13071259C212yesmaximal, complemented
9#13071234C211yesmaximal, characteristic, complemented
10#13071208C211yesmaximal, characteristic
11#13071107C211yesmaximal, characteristic
12#13071094C212yesmaximal, complemented
13#13071081C212yesmaximal, complemented
14C2×#10622598C211yesmaximal, characteristic, complemented
15#13070972C211yesmaximal, characteristic, complemented
16#117×Dic11C211yesmaximal, characteristic, complemented
17C2×C11×#520C211yesmaximal, characteristic
18C22×C11×#41C2211yescharacteristic
19C11×#520C4116yescomplemented
20C2×C4×Q8×C11C2212yes—
21C2×C4×D4×C11C2214yes—
22C2×C4×D4×C11C2212yes—
23C2×C11×#117C2211yescharacteristic
24C2×C11×#117C2212yes—
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C4⋊C4C2212yes—
27C2×#66979C2211yescharacteristic
28C2×#66979C2211yescharacteristic
29C2×#66979C2214yes—
30C22×C4⋊Dic11C2211yescharacteristic
31C22×C4⋊Dic11C2212yes—
32C22×C4×Dic11C2211yescharacteristic
33#10622843C2211yescharacteristic
34#10622843C2211yescharacteristic
35#10622843C2212yes—
36#10622834C2211yescharacteristic
37#10622834C2211yescharacteristic
38#10622834C2212yes—
39#10622833C2212yes—
40#10622833C2212yes—
41#10622833C2214yes—
42#10622825C2212yes—
43#10622825C2212yes—
44#10622825C2214yes—
45#10622825C2214yes—
46#10622824C2214yes—
47C4×C22⋊Dic11C2212yes—
48C4×C22⋊Dic11C2212yes—
49C4×C22⋊Dic11C2214yes—
50C2×C11⋊#95C2212yes—
51#10622598C2212yes—
52#10622598C2212yes—
53#10622598C2212yes—
54#10622598C2212yes—
55#10622598C2212yes—
56#10622598C2212yes—
57#10622598C2212yes—
58#10622598C2212yes—
59#10622594C2214yes—
60#10622594C2214yes—
61#10622594C2214yes—
62#10622594C2214yes—
63C4⋊C4×Dic11C2211yescharacteristic
64C4⋊C4×Dic11C2211yescharacteristic
65C4⋊C4×Dic11C2211yescharacteristic
66C4⋊C4×Dic11C2211yescharacteristic
67C4⋊C4×Dic11C2212yes—
68C4⋊C4×Dic11C2212yes—
69#10622564C2214yes—
70#10622564C2214yes—
71#10622564C2214yes—
72#10622564C2214yes—
73C22⋊C4×Dic11C2212yes—
74C22⋊C4×Dic11C2212yes—
75C22⋊C4×Dic11C2214yes—
76#10622550C2214yes—
77#10622549C2214yes—
78C4×C4⋊Dic11C2212yes—
79C4×C4⋊Dic11C2212yes—
80C4×C4⋊Dic11C2214yes—
81#10622545C2212yes—
82#10622545C2214yes—
83C42×Dic11C2212yes—
84C2×C11×#41—24no—
85C2×C11×#41—24no—
86C2×C11×#41C2×C418yes—
87C22×Q8×C11C2311yescharacteristic
88C22×D4×C11C2312yes—
89C22×D4×C11C2311yescharacteristic
90C23×C4×C11C2312yes—
91C23×C4×C11C2312yes—
92C23×C4×C11C2314yes—
93C23×C4×C11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2312yes—
97C4×Q8×C11C2×C4116yescomplemented
98C4×D4×C11C2×C4132yes—
99C4×D4×C11C2×C4116yescomplemented
100C11×#117C2×C418yes—
101C11×#117C2×C4116yescomplemented
102C2×C11×C4⋊C4C2×C418yes—
103C2×C11×C4⋊C4C2×C4116yescomplemented
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C4⋊C4C2314yes—
107C2×C11×C4⋊C4C2312yes—
108C2×C11×C4⋊C4C2312yes—
109C2×C11×C22⋊C4C2312yes—
110C2×C11×C22⋊C4C2314yes—
111C2×C42×C11C2312yes—
112C2×C42×C11C2314yes—
113C2×C22⋊Dic11C2312yes—
114C2×C22⋊Dic11C2312yes—
115C2×C22⋊Dic11C2312yes—
116C2×C22⋊Dic11C2312yes—
117C2×C22⋊Dic11C2314yes—
118C2×C22⋊Dic11C2312yes—
119C2×C22⋊Dic11C2312yes—
120C2×C22⋊Dic11C2314yes—
121#66979—24no—
122#66979—24no—
123#66979—48no—
124C2×C4⋊Dic11—24no—
125C2×C4⋊Dic11—44no—
126C2×C4⋊Dic11C2312yes—
127C2×C4⋊Dic11C2311yescharacteristic
128C2×C4⋊Dic11C2311yescharacteristic
129C2×C4⋊Dic11C2314yes—
130C2×C4⋊Dic11C2312yes—
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4⋊Dic11C2311yescharacteristic
133C2×C4⋊Dic11C2314yes—
134C2×C4⋊Dic11C2314yes—
135C2×C4⋊Dic11C2314yes—
136C2×C4×Dic11—24no—
137C2×C4×Dic11C2311yescharacteristic
138C2×C4×Dic11C2312yes—
139C2×C4×Dic11C2312yes—
140C2×C4×Dic11C2312yes—
141C2×C4×Dic11C2311yescharacteristic
142C2×C4×Dic11C2311yescharacteristic
143C2×C4×Dic11C2311yescharacteristic
144C2×C4×Dic11C2312yes—
145C2×C4×Dic11C2312yes—
146C2×C4×Dic11C2312yes—
147C2×C4×Dic11C2314yes—
148C2×C4×Dic11C2314yes—
149C11⋊#95C2312yes—
150C11⋊#95C2312yes—
151C11⋊#95C2314yes—
152C11⋊#95C2312yes—
153C11⋊#95C2312yes—
154C11⋊#95C2312yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2312yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2312yes—
162C11⋊#95C2312yes—
163C11⋊#95C2314yes—
164C11⋊#95C2314yes—
165#34253—111nomaximal, Sylow
166C24×C11C2412yes—
167C24×C11C2411yescharacteristic
168C11×#41—232no—
169C2×Q8×C11—22no—
170C2×Q8×C11—22no—
171C2×Q8×C11C22×C414yes—
172C2×D4×C11—24no—
173C2×D4×C11—24no—
174C2×D4×C11—22no—
175C2×D4×C11—22no—
176C2×D4×C11C22×C418yes—
177C2×D4×C11C22×C414yes—
178C22×C4×C11—24no—
179C22×C4×C11—24no—
180C22×C4×C11—42no—
181C22×C4×C11—44no—
182C22×C4×C11—44no—
183C22×C4×C11—42no—
184C22×C4×C11C22×C418yes—
185C22×C4×C11C22×C418yes—
186C22×C4×C11C22×C4116yes—
187C22×C4×C11C22×C414yes—
188C22×C4×C11#4114yes—
189C22×C4×C11#4114yes—
190C22×C4×C11C2412yes—
191C22×C4×C11C2412yes—
192C22×C4×C11C2412yes—
193C22×C4×C11C2414yes—
194C22×C4×C11C2411yescharacteristic
195C22×C4×C11C2411yescharacteristic
196C22×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—22no—
200C22×Dic11—24no—
201C22×Dic11—41no—
202C22×Dic11—41no—
203C22×Dic11—42no—
204C22×Dic11—42no—
205C22×Dic11C2411yescharacteristic
206C22×Dic11C2412yes—
207C22×Dic11C2412yes—
208C22×Dic11C2412yes—
209C22×Dic11C2412yes—
210C22×Dic11C2411yescharacteristic
211C22×Dic11C2414yes—
212C22×Dic11C2411yescharacteristic
213C22×Dic11C2411yescharacteristic
214C11×C4⋊C4C22×C418yes—
215C11×C4⋊C4C22×C418yes—
216C11×C4⋊C4C22×C414yes—
217C11×C4⋊C4C22×C4116yes—
218C11×C4⋊C4C22×C414yes—
219C11×C22⋊C4C22×C418yes—
220C11×C22⋊C4C22×C4116yes—
221C42×C11C22×C418yes—
222C42×C11C22×C4116yes—
223C22⋊Dic11—24no—
224C22⋊Dic11—24no—
225C22⋊Dic11—24no—
226C22⋊Dic11—24no—
227C22⋊Dic11—44no—
228C22⋊Dic11—42no—
229C22⋊Dic11—44no—
230C22⋊Dic11—42no—
231C4⋊Dic11—28no—
232C4⋊Dic11—24no—
233C4⋊Dic11—24no—
234C4⋊Dic11—22no—
235C4⋊Dic11—22no—
236C4⋊Dic11—22no—
237C4⋊Dic11—22no—
238C4⋊Dic11—44no—
239C4⋊Dic11—44no—
240C4⋊Dic11—44no—
241C4×Dic11—24no—
242C4×Dic11—24no—
243C4×Dic11—22no—
244C4×Dic11—22no—
245C4×Dic11—22no—
246C4×Dic11—22no—
247C4×Dic11—24no—
248C4×Dic11—24no—
249C4×Dic11—42no—
250C4×Dic11—44no—
251C4×Dic11—42no—
252C4×Dic11—44no—
253C2×#520D1111yescharacteristic
254#2353—114no—
255#2352—114no—
256#2347—112no—
257#2346—112no—
258#2345—112no—
259#2344—112no—
260#2320—112no—
261#2319—112no—
262#2316—111no—
263#2311—111no—
264#2297—111no—
265#2295—112no—
266#2293—112no—
267C2×#389—111no—
268#2274—111no—
269C4×#117—111no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—22no—
275C23×C11—22no—
276C23×C11—22no—
277C23×C11—22no—
278C23×C11—22no—
279C23×C11—22no—
280C23×C11C23×C414yes—
281C23×C11C23×C412yes—
282C23×C11C2×#4112yes—
283C23×C11C2×#4112yes—
284C23×C11C2511yescharacteristic
285Q8×C11—28no—
286D4×C11—216no—
287D4×C11—28no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—24no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—24no—
296C2×C4×C11—216no—
297C2×C4×C11—48no—
298C2×C4×C11—416no—
299C2×C4×C11#117116yescomplemented
300C2×C4×C11C23×C414yes—
301C2×C4×C11C23×C414yes—
302C2×C4×C11C23×C414yes—
303C2×C4×C11C23×C418yes—
304C2×C4×C11C23×C412yes—
305C2×C4×C11C23×C412yes—
306C2×C4×C11C2×#4112yes—
307C2×C4×C11C2×#4112yes—
308C2×C4×C11C2×#4112yes—
309C2×C4×C11C2×#4112yes—
310C2×Dic11—21no—
311C2×Dic11—21no—
312C2×Dic11—21no—
313C2×Dic11—21no—
314C2×Dic11—21no—
315C2×Dic11—21no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—24no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—24no—
324C2×Dic11—21no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—21no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—24no—
332C2×Dic11—22no—
333C2×Dic11—21no—
334C2×Dic11—21no—
335C2×Dic11—44no—
336C2×Dic11—44no—
337C2×Dic11—84no—
338C2×Dic11H(5,𝔽2)12yes—
339C2×Dic112−1+412yes—
340C22×#41C2×D1111yescharacteristic
341#520Dic11116yescomplemented
342C2×C4×Q8C2×D1112yes—
343C2×C4×D4C2×D1114yes—
344C2×C4×D4C2×D1112yes—
345C2×#117—111no—
346C2×#117—111no—
347C2×#117—114no—
348C2×#117C2×D1111yescharacteristic
349C2×#117C2×D1112yes—
350C22×C4⋊C4—111no—
351C22×C4⋊C4—112no—
352C22×C4⋊C4C2×D1111yescharacteristic
353C22×C4⋊C4C2×D1112yes—
354C22×C42—111no—
355#391—112no—
356#391—111no—
357#391—111no—
358#390—112no—
359#390—111no—
360#390—111no—
361#389—112no—
362#389—112no—
363#389—112no—
364#389—112no—
365#389—112no—
366#389—112no—
367#389—112no—
368#389—112no—
369#388—114no—
370#388—114no—
371#388—114no—
372#388—114no—
373#387—114no—
374#387—114no—
375#387—114no—
376#387—114no—
377#386—114no—
378#386—112no—
379#386—112no—
380#383—114no—
381#382—114no—
382#381—114no—
383#380—112no—
384#380—112no—
385#380—114no—
386#380—114no—
387C4×C4⋊C4—111no—
388C4×C4⋊C4—112no—
389C4×C4⋊C4—111no—
390C4×C4⋊C4—111no—
391C4×C4⋊C4—112no—
392C4×C4⋊C4—111no—
393C4×C4⋊C4—112no—
394C4×C4⋊C4—112no—
395C4×C4⋊C4—114no—
396C4×C22⋊C4—112no—
397C4×C22⋊C4—112no—
398C4×C22⋊C4—114no—
399C4×C22⋊C4—112no—
400C4×C22⋊C4—114no—
401C4×C22⋊C4—112no—
402#376—112no—
403#376—114no—
404C2×#95—112no—
405C43—112no—
406C22×C11—22no—
407C22×C11—22no—
408C22×C11—22no—
409C22×C11—22no—
410C22×C11—22no—
411C22×C11—22no—
412C22×C11—24no—
413C22×C11—24no—
414C22×C11—24no—
415C22×C11—42no—
416C22×C11—42no—
417C22×C11—42no—
418C22×C11—42no—
419C22×C11C2×#11714yes—
420C22×C11C24×C411yescharacteristic
421C22×C11C22×#4111yescharacteristic
422C22×C11C22×#4111yescharacteristic
423C22×C11C2×H(5,𝔽2)11yescharacteristic
424C22×C11C2×2−1+411yescharacteristic
425C22×C11#58511yescharacteristic
426C22×C11#58511yescharacteristic
427C4×C11—24no—
428C4×C11—24no—
429C4×C11—28no—
430C4×C11—24no—
431C4×C11C2×#11714yes—
432C4×C11C2×#11714yes—
433Dic11—22no—
434Dic11—22no—
435Dic11—41no—
436Dic11—44no—
437Dic11—41no—
438Dic11—42no—
439Dic11—42no—
440Dic11—42no—
441Dic11—42no—
442C2×#41—24no—
443C2×#41—24no—
444C2×#41C2×Dic1118yes—
445C22×Q8C22×D1111yescharacteristic
446C22×D4C22×D1112yes—
447C22×D4C22×D1111yescharacteristic
448C23×C4—111no—
449C23×C4—111no—
450C23×C4—112no—
451C23×C4C22×D1112yes—
452C23×C4C22×D1112yes—
453C23×C4C22×D1114yes—
454C23×C4C22×D1111yescharacteristic
455C4×Q8C2×Dic11116yescomplemented
456C4×D4C2×Dic11132yes—
457C4×D4C2×Dic11116yescomplemented
458#117—224no—
459#117—224no—
460#117—448no—
461#117C2×Dic1118yes—
462#117C2×Dic11116yescomplemented
463C2×C4⋊C4—114no—
464C2×C4⋊C4—112no—
465C2×C4⋊C4—112no—
466C2×C4⋊C4—111no—
467C2×C4⋊C4—111no—
468C2×C4⋊C4—111no—
469C2×C4⋊C4—111no—
470C2×C4⋊C4—114no—
471C2×C4⋊C4—114no—
472C2×C4⋊C4—114no—
473C2×C4⋊C4—224no—
474C2×C4⋊C4—444no—
475C2×C4⋊C4C2×Dic1118yes—
476C2×C4⋊C4C2×Dic11116yescomplemented
477C2×C4⋊C4C22×D1111yescharacteristic
478C2×C4⋊C4C22×D1112yes—
479C2×C4⋊C4C22×D1114yes—
480C2×C4⋊C4C22×D1112yes—
481C2×C4⋊C4C22×D1111yescharacteristic
482C2×C22⋊C4—112no—
483C2×C22⋊C4—112no—
484C2×C22⋊C4—112no—
485C2×C22⋊C4—112no—
486C2×C22⋊C4—114no—
487C2×C22⋊C4—112no—
488C2×C22⋊C4—114no—
489C2×C22⋊C4—112no—
490C2×C22⋊C4C22×D1112yes—
491C2×C22⋊C4C22×D1114yes—
492C2×C42—112no—
493C2×C42—112no—
494C2×C42—112no—
495C2×C42—111no—
496C2×C42—112no—
497C2×C42—111no—
498C2×C42—111no—
499C2×C42—111no—
500C2×C42—114no—
501C2×C42—112no—
502C2×C42—112no—
503C2×C42—114no—
504C2×C42—224no—
505C2×C42C22×D1112yes—
506C2×C42C22×D1114yes—
507#95—114no—
508#95—114no—
509#95—112no—
510#95—112no—
511#95—112no—
512#95—112no—
513#95—112no—
514#95—114no—
515#95—114no—
516#95—114no—
517#95—114no—
518#95—112no—
519#95—114no—
520#95—112no—
521#95—112no—
522#95—114no—
523C2×C11—24no—
524C2×C11—44no—
525C2×C11C22×#11711yescharacteristic
526C2×C11C4×H(5,𝔽2)11yescharacteristic
527C2×C11C4×2−1+411yescharacteristic
528C2×C11#349411yescharacteristic
529C2×C11#349511yescharacteristic
530C2×C11#351111yescharacteristic
531C2×C11#351211yescharacteristic
532C24C23×D1112yes—
533C24C23×D1111yescharacteristic
534#41—232no—
535C2×Q8—22no—
536C2×Q8—22no—
537C2×Q8C22×Dic1114yes—
538C2×D4—24no—
539C2×D4—24no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4C22×Dic1118yes—
543C2×D4C22×Dic1114yes—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—42no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—42no—
550C22×C4—111no—
551C22×C4—111no—
552C22×C4—111no—
553C22×C4—112no—
554C22×C4—112no—
555C22×C4—112no—
556C22×C4—112no—
557C22×C4—111no—
558C22×C4—114no—
559C22×C4—222no—
560C22×C4—222no—
561C22×C4—222no—
562C22×C4—222no—
563C22×C4—224no—
564C22×C4—441no—
565C22×C4—441no—
566C22×C4—442no—
567C22×C4—442no—
568C22×C4#433914yes—
569C22×C4#433914yes—
570C22×C4C22×Dic1118yes—
571C22×C4C22×Dic1118yes—
572C22×C4C22×Dic11116yes—
573C22×C4C22×Dic1114yes—
574C22×C4C23×D1112yes—
575C22×C4C23×D1112yes—
576C22×C4C23×D1112yes—
577C22×C4C23×D1114yes—
578C22×C4C23×D1111yescharacteristic
579C22×C4C23×D1111yescharacteristic
580C4⋊C4—228no—
581C4⋊C4—224no—
582C4⋊C4—224no—
583C4⋊C4—222no—
584C4⋊C4—222no—
585C4⋊C4—222no—
586C4⋊C4—222no—
587C4⋊C4—444no—
588C4⋊C4—444no—
589C4⋊C4—444no—
590C4⋊C4C22×Dic1118yes—
591C4⋊C4C22×Dic1118yes—
592C4⋊C4C22×Dic1114yes—
593C4⋊C4C22×Dic11116yes—
594C4⋊C4C22×Dic1114yes—
595C22⋊C4—224no—
596C22⋊C4—224no—
597C22⋊C4—224no—
598C22⋊C4—224no—
599C22⋊C4—444no—
600C22⋊C4—442no—
601C22⋊C4—442no—
602C22⋊C4—444no—
603C22⋊C4C22×Dic1118yes—
604C22⋊C4C22×Dic11116yes—
605C42—224no—
606C42—224no—
607C42—222no—
608C42—222no—
609C42—222no—
610C42—222no—
611C42—224no—
612C42—224no—
613C42—444no—
614C42—442no—
615C42—442no—
616C42—444no—
617C42C22×Dic1118yes—
618C42C22×Dic11116yes—
619C11#3425311yescharacteristic, complemented, Sylow
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23C2×#433912yes—
631C23C2×#433912yes—
632C23C23×Dic1114yes—
633C23C23×Dic1112yes—
634C23C24×D1111yescharacteristic
635Q8—28no—
636D4—216no—
637D4—28no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—22no—
643C2×C4—24no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—216no—
647C2×C4—48no—
648C2×C4—416no—
649C2×C4—112no—
650C2×C4—112no—
651C2×C4—221no—
652C2×C4—221no—
653C2×C4—221no—
654C2×C4—221no—
655C2×C4—221no—
656C2×C4—221no—
657C2×C4—222no—
658C2×C4—222no—
659C2×C4—222no—
660C2×C4—222no—
661C2×C4—224no—
662C2×C4—222no—
663C2×C4—222no—
664C2×C4—224no—
665C2×C4—221no—
666C2×C4—222no—
667C2×C4—221no—
668C2×C4—222no—
669C2×C4—222no—
670C2×C4—222no—
671C2×C4—221no—
672C2×C4—222no—
673C2×C4—222no—
674C2×C4—224no—
675C2×C4—221no—
676C2×C4—444no—
677C2×C4—444no—
678C2×C4—884no—
679C2×C4#66979116yescomplemented
680C2×C4C2×#433912yes—
681C2×C4C2×#433912yes—
682C2×C4C2×#433912yes—
683C2×C4C2×#433912yes—
684C2×C4C23×Dic1114yes—
685C2×C4C23×Dic1114yes—
686C2×C4C23×Dic1114yes—
687C2×C4C23×Dic1118yes—
688C2×C4C23×Dic1112yes—
689C2×C4C23×Dic1112yes—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—24no—
697C22—24no—
698C22—24no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22C2×#6697914yes—
704C22C22×#433911yescharacteristic
705C22C22×#433911yescharacteristic
706C22D11×H(5,𝔽2)11yescharacteristic
707C22#1062345511yescharacteristic
708C22D11×2−1+411yescharacteristic
709C22#1062345711yescharacteristic
710C22C24×Dic1111yescharacteristic
711C4—24no—
712C4—24no—
713C4—28no—
714C4—24no—
715C4—222no—
716C4—222no—
717C4—441no—
718C4—442no—
719C4—442no—
720C4—442no—
721C4—442no—
722C4—441no—
723C4—444no—
724C4C2×#6697914yes—
725C4C2×#6697914yes—
726C2—24no—
727C2—44no—
728C2C22×#6697911yescharacteristic
729C2H(5,𝔽2)×Dic1111yescharacteristic
730C22−1+4×Dic1111yescharacteristic
731C2#1308235211yescharacteristic
732C2#1308236911yescharacteristic
733C2#1308251911yescharacteristic
734C2#1308253311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC2×C11×#520C2
socle, cosocleC23×C11C25
prime radicalC22×C11×#41C22
hypercenterC2×#520D11
hypocenterC11#34253
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #13071556C2semidirect
2. #13071545C2semidirect
3. #13071509C2semidirect
4. #13071501C2semidirect
5. #13071493C2semidirect
6. #13071485C2semidirect
7. #13071267C2semidirect
8. #13071259C2semidirect
9. #13071234C2semidirect
12. #13071094C2semidirect
13. #13071081C2semidirect
14. C2×#10622598C2semidirect
15. #13070972C2semidirect
16. #117×Dic11C2semidirect
19. C11×#520C4semidirect
97. C4×Q8×C11C2×C4semidirect
99. C4×D4×C11C2×C4semidirect
101. C11×#117C2×C4semidirect
103. C2×C11×C4⋊C4C2×C4semidirect
299. C2×C4×C11#117semidirect
341. #520Dic11semidirect
455. C4×Q8C2×Dic11semidirect
457. C4×D4C2×Dic11semidirect
462. #117C2×Dic11semidirect
476. C2×C4⋊C4C2×Dic11semidirect
619. C11#34253semidirect
679. C2×C4#66979semidirect

Maximal subgroups

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

subgroupindex
#130715562
#130715452
#130715092
#130715012
#130714932
#130714852
#130712672
#130712592
#130712342
#130712082
#130711072
#130710942
#130710812
C2×#106225982
#130709722
#117×Dic112
C2×C11×#5202
#3425311