Finite Group Databasebeta

← #14923626

Subgroups — #14923626

Order 2816.

2926 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic11C211yesmaximal, characteristic
2C22×#66930C211yesmaximal, characteristic, complemented
3#13072930C212yesmaximal, complemented
4#13072921C212yesmaximal, complemented
5#13072906C214yesmaximal, complemented
6#13072902C212yesmaximal, complemented
7#13072897C211yesmaximal, characteristic, complemented
8#13072894C211yesmaximal, characteristic, complemented
9#13072887C212yesmaximal, complemented
10#13071939C211yesmaximal, characteristic
11#13071872C214yesmaximal, complemented
12#13071141C212yesmaximal, complemented
13#123×Dic11C212yesmaximal, complemented
14#13071095C212yesmaximal, complemented
15#13070994C211yesmaximal, characteristic, complemented
16#13070994C212yesmaximal, complemented
17C11×#2405C211yesmaximal, characteristic
18C23×D4×C11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C24×Dic11C2211yescharacteristic
21C2×C11×#123C2212yes—
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C2×#66988C2212yes—
27C2×D4×Dic11—28no—
28C2×D4×Dic11C2212yes—
29C2×D4×Dic11C2212yes—
30C2×D4×Dic11C2212yes—
31C2×D4×Dic11C2212yes—
32C22×C4⋊Dic11C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic, complemented
34C22×Dic11⋊C4C2211yescharacteristic, complemented
35C22×C4×Dic11C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic, complemented
37C22×C4×Dic11C2211yescharacteristic, complemented
38C2×#66930—28no—
39C2×#66930C2212yes—
40C2×#66930C2212yes—
41C2×#66930C2212yes—
42C2×#66930C2212yescomplemented
43C2×#66930C2212yescomplemented
44C11×#394C2214yes—
45C11×#386C2212yes—
46C11×#385C2212yes—
47C11×#379C2211yescharacteristic
48C11×#379C2212yes—
49#10622860C2212yes—
50#10622860C2211yescharacteristic
51#10622835C2214yes—
52#10622833C2212yes—
53#10622824C2212yescomplemented
54#10622823C2212yes—
55#10622823C2212yescomplemented
56#10622597C2214yescomplemented
57#10622594C2214yescomplemented
58C4⋊C4×Dic11C2214yescomplemented
59#10622585C2214yescomplemented
60#10622566C2214yescomplemented
61#10622565C2214yescomplemented
62#10622565C2214yescomplemented
63#10622564C2214yescomplemented
64#10622563C2212yes—
65#10622563C2212yescomplemented
66#10622562C2214yescomplemented
67#10622559C2212yes—
68#10622558C2214yescomplemented
69#10622556C2212yes—
70#10622556C2212yes—
71#10622556C2212yes—
72#10622556C2212yescomplemented
73#10622555C2212yescomplemented
74#10622555C2214yescomplemented
75#10622555C2214yescomplemented
76#10622555C2212yescomplemented
77C22⋊C4×Dic11C2212yescomplemented
78C22⋊C4×Dic11C2214yescomplemented
79C22⋊C4×Dic11C2214yescomplemented
80C22⋊C4×Dic11C2212yescomplemented
81#10622273C2214yescomplemented
82#10622268C2214yescomplemented
83#10622262C2214yescomplemented
84#10622260C2214yescomplemented
85C25×C11C2311yescharacteristic
86C25×C11C2311yescharacteristic
87C22×D4×C11—24no—
88C22×D4×C11—28no—
89C22×D4×C11C2312yes—
90C22×D4×C11C2312yes—
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C23×Dic11—28no—
95C23×Dic11—24no—
96C23×Dic11—28no—
97C23×Dic11D418yes—
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2312yes—
101C23×Dic11C2312yes—
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2311yescharacteristic
110C11×#123—28no—
111C2×C11×C4⋊C4C2314yes—
112C2×C11×C22⋊C4—24no—
113C2×C11×C22⋊C4C2312yes—
114C2×C11×C22⋊C4C2312yes—
115C2×C11×C22⋊C4C2312yes—
116C2×C11×C22⋊C4C2312yes—
117C2×C11×C22⋊C4C2314yes—
118C2×C11×C22⋊C4C2314yes—
119C2×C11×C22⋊C4C2312yes—
120C2×C22⋊Dic11—24no—
121C2×C22⋊Dic11—24no—
122C2×C22⋊Dic11—24no—
123C2×C22⋊Dic11C2312yes—
124C2×C22⋊Dic11C2312yes—
125C2×C22⋊Dic11C2312yes—
126C2×C22⋊Dic11C2314yes—
127C2×C22⋊Dic11C2312yes—
128C2×C22⋊Dic11C2312yes—
129C2×C22⋊Dic11C2312yes—
130C2×C22⋊Dic11C2312yes—
131C2×C22⋊Dic11C2312yes—
132C2×C22⋊Dic11C2314yes—
133C2×C22⋊Dic11C2312yes—
134#66988—28no—
135D4×Dic11—28no—
136D4×Dic11—28no—
137D4×Dic11—28no—
138D4×Dic11—28no—
139C2×C4⋊Dic11—24no—
140C2×C4⋊Dic11C2312yes—
141C2×C4⋊Dic11C2312yes—
142C2×C4⋊Dic11C2314yes—
143C2×Dic11⋊C4—24no—
144C2×Dic11⋊C4—24no—
145C2×Dic11⋊C4C2312yes—
146C2×Dic11⋊C4C2312yes—
147C2×Dic11⋊C4C2312yes—
148C2×Dic11⋊C4C2312yes—
149C2×Dic11⋊C4C2314yes—
150C2×Dic11⋊C4C2314yes—
151C2×Dic11⋊C4C2314yes—
152C2×C4×Dic11—24no—
153C2×C4×Dic11—24no—
154C2×C4×Dic11—24no—
155C2×C4×Dic11C2312yes—
156C2×C4×Dic11C2312yes—
157C2×C4×Dic11C2312yes—
158C2×C4×Dic11C2312yes—
159C2×C4×Dic11C2314yes—
160C2×C4×Dic11C2312yes—
161C2×C4×Dic11C2312yes—
162#66930—28no—
163#66930—28no—
164#66930—28no—
165#66930—28no—
166#66930—28no—
167C11×#95C2314yes—
168C11⋊#95C2314yes—
169C11⋊#95C2314yes—
170C11⋊#95C2314yes—
171C11⋊#95C2314yes—
172C11⋊#95C2314yes—
173C11⋊#95C2314yes—
174C11⋊#95C2314yes—
175C11⋊#95C2314yes—
176C11⋊#95C2314yes—
177#34809—111nomaximal, Sylow
178C24×C11—22no—
179C24×C11—24no—
180C24×C11—24no—
181C24×C11—24no—
182C24×C11—24no—
183C24×C11—42no—
184C24×C11—42no—
185C24×C11C2×D414yes—
186C24×C11C2411yescharacteristic
187C24×C11C2412yes—
188C24×C11C2411yescharacteristic
189C24×C11C2411yescharacteristic
190C2×D4×C11—232no—
191C2×D4×C11—24no—
192C2×D4×C11—24no—
193C2×D4×C11—24no—
194C2×D4×C11—24no—
195C2×D4×C11—24no—
196C2×D4×C11#4118yes—
197C22×C4×C11—22no—
198C22×C4×C11—24no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—24no—
202C22×C4×C11—42no—
203C22×C4×C11C2414yes—
204C22×C4×C11C2412yes—
205C22×C4×C11C2412yes—
206C22×C4×C11C2412yes—
207C22×Dic11—232no—
208C22×Dic11—24no—
209C22×Dic11—24no—
210C22×Dic11—24no—
211C22×Dic11—24no—
212C22×Dic11—24no—
213C22×Dic11—24no—
214C22×Dic11—28no—
215C22×Dic11—28no—
216C22×Dic11—22no—
217C22×Dic11—22no—
218C22×Dic11—22no—
219C22×Dic11—22no—
220C22×Dic11—24no—
221C22×Dic11—24no—
222C22×Dic11—24no—
223C22×Dic11—42no—
224C22×Dic11—42no—
225C22×Dic11—416no—
226C22×Dic11C2×D414yes—
227C22×Dic11C2×D414yes—
228C22×Dic11C2×D414yes—
229C22×Dic11C2×D414yes—
230C22×Dic11C2×D414yes—
231C22×Dic11C2×D414yes—
232C22×Dic11#4118yes—
233C22×Dic11C2412yes—
234C22×Dic11C2414yes—
235C22×Dic11C2412yes—
236C22×Dic11C2412yes—
237C22×Dic11C2412yes—
238C22×Dic11C2411yescharacteristic
239C22×Dic11C2411yescharacteristic
240C22×Dic11C2411yescharacteristic
241C22×Dic11C2411yescharacteristic
242C11×C4⋊C4—28no—
243C11×C22⋊C4—24no—
244C11×C22⋊C4—24no—
245C11×C22⋊C4—24no—
246C11×C22⋊C4—24no—
247C11×C22⋊C4—28no—
248C11×C22⋊C4—44no—
249C11×C22⋊C4—42no—
250C22⋊Dic11—24no—
251C22⋊Dic11—24no—
252C22⋊Dic11—24no—
253C22⋊Dic11—24no—
254C22⋊Dic11—24no—
255C22⋊Dic11—24no—
256C22⋊Dic11—24no—
257C22⋊Dic11—28no—
258C22⋊Dic11—24no—
259C22⋊Dic11—42no—
260C22⋊Dic11—44no—
261C4⋊Dic11—24no—
262C4⋊Dic11—24no—
263C4⋊Dic11—44no—
264Dic11⋊C4—24no—
265Dic11⋊C4—24no—
266Dic11⋊C4—24no—
267Dic11⋊C4—24no—
268Dic11⋊C4—28no—
269Dic11⋊C4—28no—
270Dic11⋊C4—44no—
271C4×Dic11—24no—
272C4×Dic11—24no—
273C4×Dic11—24no—
274C4×Dic11—24no—
275C4×Dic11—24no—
276C4×Dic11—24no—
277C4×Dic11—28no—
278C22×C4×D4—111no—
279C22×#117—111no—
280#2487—112no—
281#2486—112no—
282#2485—114no—
283#2484—112no—
284#2483—111no—
285#2483—111no—
286#2482—112no—
287#2405—111no—
288#2405D1111yescharacteristic
289#2395—114no—
290C4×#123—112no—
291C4×#123—112no—
292#2296—112no—
293#2280—112no—
294#2280—111no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—28no—
300C23×C11—28no—
301C23×C11—28no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—24no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—24no—
309C23×C11—44no—
310C23×C11—416no—
311C23×C11—416no—
312C23×C11—44no—
313C23×C11—44no—
314C23×C11C22×D412yes—
315C23×C11C22×D412yes—
316C23×C11C22×D412yes—
317C23×C11C2×#4114yes—
318C23×C11C2×#4114yes—
319C23×C11C2×#4114yes—
320C23×C11C2511yescharacteristic
321D4×C11—216no—
322D4×C11—216no—
323C2×C4×C11—28no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—24no—
329C2×C4×C11—24no—
330C2×C4×C11—24no—
331C2×C4×C11—24no—
332C2×C4×C11—24no—
333C2×C4×C11—44no—
334C2×C4×C11—44no—
335C2×C4×C11C2×#4114yes—
336C2×Dic11—28no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—28no—
340C2×Dic11—28no—
341C2×Dic11—28no—
342C2×Dic11—28no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—24no—
348C2×Dic11—24no—
349C2×Dic11—24no—
350C2×Dic11—24no—
351C2×Dic11—24no—
352C2×Dic11—24no—
353C2×Dic11—24no—
354C2×Dic11—44no—
355C2×Dic11—44no—
356C2×Dic11—44no—
357C2×Dic11—44no—
358C2×Dic11—48no—
359C2×Dic11—48no—
360C2×Dic11#123116yescomplemented
361C2×Dic11C22×D412yes—
362C2×Dic11C22×D412yes—
363C2×Dic11C22×D412yes—
364C2×Dic11C22×D412yes—
365C2×Dic11C2×#4114yes—
366C2×Dic11C2×#4114yes—
367C23×D4C2×D1111yescharacteristic
368C24×C4—111no—
369C24×C4—111no—
370C2×#123—112no—
371C2×#123C2×D1112yes—
372C2×C4×D4—112no—
373C2×C4×D4—112no—
374C2×C4×D4—112no—
375C2×C4×D4—112no—
376C2×C4×D4—228no—
377C2×#117—112no—
378C2×#117—112no—
379C2×#117—112no—
380C2×#117—112no—
381C2×#117—112no—
382C2×#117—228no—
383C22×C4⋊C4—111no—
384C22×C4⋊C4—111no—
385C22×C4⋊C4—111no—
386C22×C22⋊C4—111no—
387C22×C22⋊C4—111no—
388C22×C22⋊C4—111no—
389C22×C22⋊C4C2×D1111yescharacteristic
390C22×C42—111no—
391C22×C42—111no—
392C22×C42—111no—
393#400—114no—
394#399—114no—
395#398—114no—
396#397—114no—
397#397—114no—
398#397—114no—
399#394—114no—
400#394C2×D1114yes—
401#389—114no—
402#389—114no—
403#388—114no—
404#388—114no—
405#387—114no—
406#387—114no—
407#386—112no—
408#386C2×D1112yes—
409#385—112no—
410#385—112no—
411#385—112no—
412#385—112no—
413#385—112no—
414#385C2×D1112yes—
415#381—112no—
416#381—112no—
417#381—112no—
418#381—112no—
419#381—112no—
420#380—112no—
421#380—114no—
422#380—114no—
423#380—112no—
424#379—112no—
425#379—111no—
426#379C2×D1112yes—
427#379C2×D1111yescharacteristic
428C4×C4⋊C4—114no—
429C4×C4⋊C4—114no—
430C4×C22⋊C4—112no—
431C4×C22⋊C4—114no—
432C4×C22⋊C4—114no—
433C4×C22⋊C4—112no—
434C22×C11—22no—
435C22×C11—22no—
436C22×C11—22no—
437C22×C11—22no—
438C22×C11—28no—
439C22×C11—28no—
440C22×C11—22no—
441C22×C11—22no—
442C22×C11—24no—
443C22×C11—22no—
444C22×C11—28no—
445C22×C11—416no—
446C22×C11—416no—
447C22×C11—42no—
448C22×C11—42no—
449C22×C11—44no—
450C22×C11—44no—
451C22×C11C2×#12314yes—
452C22×C11#52514yes—
453C22×C11C23×D411yescharacteristic
454C22×C11C22×#4112yes—
455C22×C11C22×#4112yes—
456C22×C11#58512yes—
457C4×C11—24no—
458C4×C11—42no—
459C4×C11—42no—
460C4×C11—44no—
461Dic11—22no—
462Dic11—22no—
463Dic11—42no—
464Dic11—42no—
465Dic11—42no—
466Dic11—42no—
467Dic11—44no—
468Dic11C2×#12314yes—
469Dic11C2×#12314yes—
470C25C22×D1111yescharacteristic
471C25C22×D1111yescharacteristic
472C22×D4—24no—
473C22×D4—28no—
474C22×D4C22×D1112yes—
475C22×D4C22×D1112yes—
476C23×C4—111no—
477C23×C4—118no—
478C23×C4—111no—
479C23×C4—111no—
480C23×C4—111no—
481C23×C4—111no—
482C23×C4—111no—
483C23×C4—111no—
484C23×C4—111no—
485C23×C4—112no—
486C23×C4—112no—
487C23×C4—111no—
488C23×C4—111no—
489C23×C4—228no—
490C23×C4—224no—
491C23×C4—228no—
492C23×C4C22×D1111yescharacteristic
493C23×C4C22×D1111yescharacteristic
494C23×C4C22×D1111yescharacteristic
495#123—28no—
496#123—228no—
497C4×D4—228no—
498C4×D4—228no—
499C4×D4—228no—
500C4×D4—228no—
501#117—228no—
502#117—228no—
503#117—228no—
504#117—228no—
505#117—228no—
506C2×C4⋊C4—112no—
507C2×C4⋊C4—112no—
508C2×C4⋊C4—112no—
509C2×C4⋊C4—112no—
510C2×C4⋊C4—112no—
511C2×C4⋊C4—112no—
512C2×C4⋊C4—114no—
513C2×C4⋊C4—114no—
514C2×C4⋊C4—114no—
515C2×C4⋊C4—114no—
516C2×C4⋊C4—224no—
517C2×C4⋊C4—224no—
518C2×C4⋊C4—224no—
519C2×C4⋊C4C22×D1114yes—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—112no—
522C2×C22⋊C4—112no—
523C2×C22⋊C4—112no—
524C2×C22⋊C4—112no—
525C2×C22⋊C4—112no—
526C2×C22⋊C4—112no—
527C2×C22⋊C4—112no—
528C2×C22⋊C4—112no—
529C2×C22⋊C4—114no—
530C2×C22⋊C4—114no—
531C2×C22⋊C4—112no—
532C2×C22⋊C4—224no—
533C2×C22⋊C4—224no—
534C2×C22⋊C4—224no—
535C2×C22⋊C4C22×D1112yes—
536C2×C22⋊C4C22×D1112yes—
537C2×C22⋊C4C22×D1112yes—
538C2×C22⋊C4C22×D1112yes—
539C2×C22⋊C4C22×D1114yes—
540C2×C22⋊C4C22×D1114yes—
541C2×C22⋊C4C22×D1112yes—
542C2×C42—112no—
543C2×C42—112no—
544C2×C42—112no—
545C2×C42—112no—
546C2×C42—114no—
547C2×C42—112no—
548C2×C42—112no—
549C2×C42—224no—
550C2×C42—224no—
551C2×C42—224no—
552#95—114no—
553#95—114no—
554#95—114no—
555#95—114no—
556#95—114no—
557#95—114no—
558#95—114no—
559#95—114no—
560#95—114no—
561#95C22×D1114yes—
562C2×C11—24no—
563C2×C11—24no—
564C2×C11—42no—
565C2×C11—44no—
566C2×C11C22×#12311yescharacteristic
567C2×C11C2×#52511yescharacteristic
568C2×C11#344911yescharacteristic
569C2×C11#347514yes—
570C24—22no—
571C24—24no—
572C24—24no—
573C24—24no—
574C24—24no—
575C24—42no—
576C24—42no—
577C24D4×D1114yes—
578C24C23×D1111yescharacteristic
579C24C23×D1112yes—
580C24C23×D1111yescharacteristic
581C24C23×D1111yescharacteristic
582C2×D4—232no—
583C2×D4—24no—
584C2×D4—24no—
585C2×D4—24no—
586C2×D4—24no—
587C2×D4—24no—
588C2×D4#434118yes—
589C22×C4—22no—
590C22×C4—24no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—24no—
594C22×C4—42no—
595C22×C4—114no—
596C22×C4—118no—
597C22×C4—111no—
598C22×C4—111no—
599C22×C4—114no—
600C22×C4—114no—
601C22×C4—114no—
602C22×C4—114no—
603C22×C4—114no—
604C22×C4—111no—
605C22×C4—111no—
606C22×C4—112no—
607C22×C4—114no—
608C22×C4—112no—
609C22×C4—112no—
610C22×C4—112no—
611C22×C4—2232no—
612C22×C4—224no—
613C22×C4—224no—
614C22×C4—224no—
615C22×C4—224no—
616C22×C4—224no—
617C22×C4—224no—
618C22×C4—228no—
619C22×C4—228no—
620C22×C4—224no—
621C22×C4—222no—
622C22×C4—222no—
623C22×C4—222no—
624C22×C4—222no—
625C22×C4—224no—
626C22×C4—224no—
627C22×C4—4416no—
628C22×C4—442no—
629C22×C4—442no—
630C22×C4C23×D1114yes—
631C22×C4C23×D1112yes—
632C22×C4C23×D1112yes—
633C22×C4C23×D1112yes—
634C4⋊C4—28no—
635C4⋊C4—224no—
636C4⋊C4—224no—
637C4⋊C4—224no—
638C4⋊C4—224no—
639C4⋊C4—224no—
640C4⋊C4—224no—
641C4⋊C4—228no—
642C4⋊C4—228no—
643C4⋊C4—444no—
644C4⋊C4—444no—
645C22⋊C4—24no—
646C22⋊C4—24no—
647C22⋊C4—24no—
648C22⋊C4—28no—
649C22⋊C4—24no—
650C22⋊C4—42no—
651C22⋊C4—44no—
652C22⋊C4—224no—
653C22⋊C4—224no—
654C22⋊C4—224no—
655C22⋊C4—224no—
656C22⋊C4—224no—
657C22⋊C4—224no—
658C22⋊C4—224no—
659C22⋊C4—228no—
660C22⋊C4—224no—
661C22⋊C4—442no—
662C22⋊C4—444no—
663C42—224no—
664C42—224no—
665C42—224no—
666C42—224no—
667C42—224no—
668C42—224no—
669C42—228no—
670C11#3480911yescharacteristic, complemented, Sylow
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—28no—
676C23—28no—
677C23—28no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—24no—
682C23—22no—
683C23—24no—
684C23—22no—
685C23—44no—
686C23—416no—
687C23—416no—
688C23—44no—
689C23—44no—
690C23C2×D4×D1112yes—
691C23C2×D4×D1112yes—
692C23C2×D4×D1112yes—
693C23C2×#434114yes—
694C23C2×#434114yes—
695C23#41×D1114yes—
696C23C24×D1111yescharacteristic
697D4—216no—
698D4—216no—
699C2×C4—28no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—1116no—
712C2×C4—112no—
713C2×C4—112no—
714C2×C4—114no—
715C2×C4—114no—
716C2×C4—112no—
717C2×C4—112no—
718C2×C4—228no—
719C2×C4—228no—
720C2×C4—228no—
721C2×C4—228no—
722C2×C4—228no—
723C2×C4—222no—
724C2×C4—222no—
725C2×C4—222no—
726C2×C4—222no—
727C2×C4—222no—
728C2×C4—222no—
729C2×C4—224no—
730C2×C4—224no—
731C2×C4—224no—
732C2×C4—224no—
733C2×C4—224no—
734C2×C4—224no—
735C2×C4—224no—
736C2×C4—448no—
737C2×C4—448no—
738C2×C4—444no—
739C2×C4—444no—
740C2×C4—444no—
741C2×C4—444no—
742C2×C4C2×#434114yes—
743C22—28no—
744C22—28no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—28no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—24no—
754C22—416no—
755C22—416no—
756C22—44no—
757C22—44no—
758C22—42no—
759C22—42no—
760C22#1062311714yes—
761C22D11×#12314yes—
762C22C22×D4×D1111yescharacteristic
763C22C22×#434112yes—
764C22C2×#41×D1112yes—
765C22#1062345512yes—
766C4—24no—
767C4—44no—
768C4—42no—
769C4—42no—
770C4—114no—
771C4—114no—
772C4—222no—
773C4—222no—
774C4—444no—
775C4—442no—
776C4—442no—
777C4—442no—
778C4—442no—
779C2—24no—
780C2—24no—
781C2—44no—
782C2—42no—
783C2C2×D11×#12311yescharacteristic
784C2C2×#1062311711yescharacteristic
785C2#1308194211yescharacteristic
786C2#1308216714yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2405C2
prime radicalC23×D4×C11C22
hypercenter#2405D11
hypocenterC11#34809
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2405

Complements

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

NH ≅ G/Ntype
2. C22×#66930C2semidirect
3. #13072930C2semidirect
4. #13072921C2semidirect
5. #13072906C2semidirect
6. #13072902C2semidirect
7. #13072897C2semidirect
8. #13072894C2semidirect
9. #13072887C2semidirect
11. #13071872C2semidirect
12. #13071141C2semidirect
13. #123×Dic11C2semidirect
14. #13071095C2semidirect
15. #13070994C2semidirect
16. #13070994C2semidirect
33. C22×Dic11⋊C4C22semidirect
34. C22×Dic11⋊C4C22semidirect
36. C22×C4×Dic11C22semidirect
37. C22×C4×Dic11C22semidirect
42. C2×#66930C22semidirect
43. C2×#66930C22semidirect
53. #10622824C22semidirect
55. #10622823C22semidirect
56. #10622597C22semidirect
57. #10622594C22semidirect
58. C4⋊C4×Dic11C22semidirect
59. #10622585C22semidirect
60. #10622566C22semidirect
61. #10622565C22semidirect
62. #10622565C22semidirect
63. #10622564C22semidirect
65. #10622563C22semidirect
66. #10622562C22semidirect
68. #10622558C22semidirect
72. #10622556C22semidirect
73. #10622555C22semidirect
74. #10622555C22semidirect
75. #10622555C22semidirect
76. #10622555C22semidirect
77. C22⋊C4×Dic11C22semidirect
78. C22⋊C4×Dic11C22semidirect
79. C22⋊C4×Dic11C22semidirect
80. C22⋊C4×Dic11C22semidirect
81. #10622273C22semidirect
82. #10622268C22semidirect
83. #10622262C22semidirect
84. #10622260C22semidirect
360. C2×Dic11#123semidirect
670. C11#34809semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic112
C22×#669302
#130729302
#130729212
#130729062
#130729022
#130728972
#130728942
#130728872
#130719392
#130718722
#130711412
#123×Dic112
#130710952
#130709942
C11×#24052
#3480911