Finite Group Databasebeta

← #14926360

Subgroups — #14926360

Order 2816.

2866 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623014C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D11C211yesmaximal, characteristic
3#13076952C212yesmaximal, complemented
4#13076902C212yesmaximal, complemented
5#13074435C212yesmaximal, complemented
6#13074427C212yesmaximal, complemented
7#13072442C214yesmaximal, complemented
8#13072440C214yesmaximal, complemented
9#13072427C214yesmaximal, complemented
10#13072425C214yesmaximal, complemented
11#13071228C211yesmaximal, characteristic, complemented
12#13071191C211yesmaximal, characteristic
13#13071191C211yesmaximal, characteristic
14C2×#10622823C211yesmaximal, characteristic, complemented
15C2×C11×#385C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C4⋊C4C2212yescomplemented
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C2×C4×C22⋊D11—28no—
26C2×C4×C22⋊D11C2214yes—
27C2×C4×C22⋊D11C2214yes—
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C2×#66977C2212yescomplemented
30C2×#66977C2212yescomplemented
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2212yescomplemented
33C22×C4×Dic11C2211yescharacteristic
34C2×#66949C2214yescomplemented
35#10623014—28no—
36C2×#66931C2212yes—
37C2×#66931C2212yes—
38C2×#66931C2212yescomplemented
39C2×#66931C2212yescomplemented
40C11×#385C2212yes—
41C11×#385C2212yes—
42C11×#385C2214yescomplemented
43C2×C11×#95C2212yescomplemented
44#10622826C2212yes—
45#10622826C2214yes—
46#10622826C2212yes—
47#10622823C2212yes—
48#10622823C2212yes—
49#10622823C2214yescomplemented
50#10622823C2214yescomplemented
51C2×C11⋊#95C2212yescomplemented
52#10622607C2214yescomplemented
53#10622605C2214yescomplemented
54#10622602C2214yescomplemented
55#10622594C2214yescomplemented
56#10622593C2214yescomplemented
57#10622592C2214yescomplemented
58#10622585C2214yescomplemented
59#10622571C2212yes—
60#10622571C2214yes—
61#10622571C2212yes—
62#10622568C2212yes—
63#10622568C2212yes—
64#10622559C2214yescomplemented
65#10622556C2212yes—
66#10622556C2212yes—
67#10622555C2212yes—
68#10622555C2212yes—
69#10622289C2214yescomplemented
70#10622286C2214yescomplemented
71#10622281C2214yescomplemented
72#10622280C2214yescomplemented
73#10622271C2214yescomplemented
74#10622270C2214yescomplemented
75#10622265C2214yescomplemented
76#10622259C2214yescomplemented
77C25×C11C2311yescharacteristic
78C24×D11C2311yescharacteristic
79C23×C4×C11—24no—
80C23×C4×C11—44no—
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2312yes—
83C23×C4×C11C2312yes—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2312yes—
88C22×C22⋊D11—24no—
89C22×C22⋊D11—24no—
90C22×C22⋊D11Q818yescomplemented
91C22×C22⋊D11C2312yes—
92C22×C22⋊D11C2312yes—
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2312yes—
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C22×C4×D11—24no—
100C22×C4×D11—44no—
101C22×C4×D11C2314yes—
102C22×Dic22C2312yes—
103C22×Dic22C2312yes—
104C2×C11×C4⋊C4—44no—
105C2×C11×C4⋊C4C2314yes—
106C2×C11×C4⋊C4C2314yes—
107C2×C11×C22⋊C4—24no—
108C2×C11×C22⋊C4—24no—
109C2×C11×C22⋊C4C2312yes—
110C2×C11×C22⋊C4C2312yes—
111C2×C11×C22⋊C4C2312yes—
112C2×C11×C22⋊C4C2312yes—
113C2×C22⋊Dic11—24no—
114C2×C22⋊Dic11—24no—
115C2×C22⋊Dic11D418yes—
116C2×C22⋊Dic11C2312yes—
117C2×C22⋊Dic11C2312yes—
118C2×C22⋊Dic11C2312yes—
119C2×C22⋊Dic11C2312yes—
120C2×C22⋊Dic11C2312yes—
121C2×C22⋊Dic11C2312yes—
122C4×C22⋊D11—216no—
123C4×C22⋊D11—216no—
124C2×(C2×D11)⋊C4—24no—
125C2×(C2×D11)⋊C4C2314yes—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2314yes—
128C2×(C2×D11)⋊C4C2314yes—
129C2×(C2×D11)⋊C4C2314yes—
130C2×C4⋊Dic11C2312yes—
131C2×C4⋊Dic11C2312yes—
132#66977—28no—
133#66977—28no—
134C2×Dic11⋊C4—24no—
135C2×Dic11⋊C4—44no—
136C2×Dic11⋊C4C2312yes—
137C2×Dic11⋊C4C2312yes—
138C2×Dic11⋊C4C2312yes—
139C2×Dic11⋊C4C2312yes—
140C2×Dic11⋊C4C2314yes—
141C2×Dic11⋊C4C2314yes—
142C2×Dic11⋊C4C2314yes—
143C2×Dic11⋊C4C2314yes—
144C2×Dic11⋊C4C2314yes—
145C2×C4×Dic11—24no—
146C2×C4×Dic11C2314yes—
147#66949—48no—
148#66931—28no—
149#66931—28no—
150#66931—28no—
151#66931—28no—
152C11×#95C2314yes—
153C11×#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162#34985—111nomaximal, Sylow
163C24×C11—42no—
164C24×C11—42no—
165C24×C11C2×D414yes—
166C24×C11C2×Q814yes—
167C24×C11#4114yes—
168C24×C11C2411yescharacteristic
169C24×C11C2411yescharacteristic
170C24×C11C2411yescharacteristic
171C23×D11—22no—
172C23×D11—22no—
173C23×D11—42no—
174C23×D11—42no—
175C23×D11C2×Q814yes—
176C23×D11C2412yes—
177C22×C4×C11—22no—
178C22×C4×C11—24no—
179C22×C4×C11—22no—
180C22×C4×C11—24no—
181C22×C4×C11—24no—
182C22×C4×C11—24no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—24no—
186C22×C4×C11—24no—
187C22×C4×C11—42no—
188C22×C4×C11—42no—
189C22×C4×C11—42no—
190C22×C4×C11—42no—
191C22×C4×C11—42no—
192C22×C4×C11—42no—
193C22×C4×C11—42no—
194C22×C4×C11—416no—
195C22×C4×C11C2414yes—
196C22×C4×C11C2412yes—
197C22×C4×C11C2412yes—
198C22×C4×C11C2412yes—
199C22×C4×C11C2412yes—
200C2×C22⋊D11—232no—
201C2×C22⋊D11—24no—
202C2×C22⋊D11—24no—
203C2×C22⋊D11—24no—
204C2×C22⋊D11—24no—
205C2×C22⋊D11C2×Q818yes—
206C2×C22⋊D11C2×Q818yes—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11—24no—
212C22×Dic11—42no—
213C22×Dic11—42no—
214C22×Dic11—42no—
215C22×Dic11—42no—
216C22×Dic11—42no—
217C22×Dic11—42no—
218C22×Dic11C2×D414yes—
219C22×Dic11C2×D414yes—
220C22×Dic11C2×Q814yes—
221C22×Dic11C2414yes—
222C22×Dic11C2412yes—
223C22×Dic11C2412yes—
224C22×Dic11C2412yes—
225C22×Dic11C2412yes—
226C22×Dic11C2412yes—
227C2×C4×D11—28no—
228C2×C4×D11—28no—
229C2×C4×D11—44no—
230C2×C4×D11—416no—
231C2×Dic22—24no—
232C2×Dic22—24no—
233C2×Dic22—44no—
234C2×Dic22—44no—
235C11×C4⋊C4—28no—
236C11×C4⋊C4—44no—
237C11×C22⋊C4—24no—
238C11×C22⋊C4—24no—
239C11×C22⋊C4—24no—
240C11×C22⋊C4—24no—
241C22⋊Dic11—24no—
242C22⋊Dic11—24no—
243C22⋊Dic11—24no—
244C22⋊Dic11—24no—
245C22⋊Dic11C2×D418yes—
246C22⋊Dic11C2×D418yes—
247(C2×D11)⋊C4—28no—
248(C2×D11)⋊C4—44no—
249(C2×D11)⋊C4—44no—
250(C2×D11)⋊C4—44no—
251(C2×D11)⋊C4—44no—
252C4⋊Dic11—24no—
253C4⋊Dic11—24no—
254Dic11⋊C4—24no—
255Dic11⋊C4—24no—
256Dic11⋊C4—24no—
257Dic11⋊C4—24no—
258Dic11⋊C4—28no—
259Dic11⋊C4—28no—
260Dic11⋊C4—44no—
261Dic11⋊C4—44no—
262Dic11⋊C4—44no—
263C4×Dic11—28no—
264C2×#543—111no—
265C22×C4×D4—111no—
266#2855—112no—
267#2848—112no—
268#2627—112no—
269#2626—112no—
270#2450—114no—
271#2450—114no—
272#2449—114no—
273#2449—114no—
274#2315—111no—
275#2308—111no—
276#2308—111no—
277C2×#385—111no—
278C2×#385D1111yescharacteristic, complemented
279C23×C11—22no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—44no—
286C23×C11—44no—
287C23×C11—48no—
288C23×C11—48no—
289C23×C11C22⋊Q8116yescomplemented
290C23×C11C22×D412yes—
291C23×C11C22×D412yes—
292C23×C11C22×D412yes—
293C23×C11C22×Q812yes—
294C23×C11C22×Q812yes—
295C23×C11C22×Q812yes—
296C23×C11C2×#4112yes—
297C23×C11C2×#4112yes—
298C23×C11C2×#4112yes—
299C23×C11C2511yescharacteristic
300C22×D11—28no—
301C22×D11—22no—
302C22×D11—22no—
303C22×D11—24no—
304C22×D11—24no—
305C22×D11—48no—
306C22×D11—44no—
307C22×D11—48no—
308C22×D11—44no—
309C22×D11C22×Q814yes—
310C2×C4×C11—28no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—24no—
317C2×C4×C11—22no—
318C2×C4×C11—24no—
319C2×C4×C11—24no—
320C2×C4×C11—22no—
321C2×C4×C11—24no—
322C2×C4×C11—24no—
323C2×C4×C11—48no—
324C2×C4×C11—48no—
325C2×C4×C11—48no—
326C2×C4×C11—44no—
327C2×C4×C11—82no—
328C2×C4×C11—82no—
329C2×C4×C11H(5,𝔽2)14yes—
330C22⋊D11—216no—
331C22⋊D11—216no—
332C2×Dic11—28no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—24no—
336C2×Dic11—24no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—24no—
340C2×Dic11—24no—
341C2×Dic11—24no—
342C2×Dic11—24no—
343C2×Dic11—24no—
344C2×Dic11—44no—
345C2×Dic11—44no—
346C2×Dic11—48no—
347C2×Dic11—82no—
348C2×Dic11—82no—
349C2×Dic11C22×D414yes—
350C2×Dic11C22×D414yes—
351C2×Dic11C22×Q814yes—
352C4×D11—416no—
353Dic22—84no—
354Dic22—84no—
355C23×D4—111no—
356C24×C4—111no—
357C24×C4C2×D1111yescharacteristic
358#543—228no—
359C2×C22⋊Q8—112no—
360C2×C22⋊Q8—112no—
361C2×C22⋊Q8—114no—
362C2×C22⋊Q8—112no—
363C2×C22⋊Q8—112no—
364C2×C22⋊Q8—112no—
365C2×C22⋊Q8—112no—
366C2×C4×D4—114no—
367C2×C4×D4—114no—
368C2×C4×D4—228no—
369C22×C4⋊C4—111no—
370C22×C4⋊C4—112no—
371C22×C4⋊C4C2×D1112yescomplemented
372C22×C22⋊C4—111no—
373C22×C22⋊C4—111no—
374C22×C22⋊C4—111no—
375C22×C22⋊C4—111no—
376C22×C22⋊C4C2×D1111yescharacteristic
377C22×C22⋊C4C2×D1111yescharacteristic
378C22×C42—111no—
379#400—114no—
380#399—114no—
381#398—114no—
382#398—114no—
383#396—114no—
384#396—114no—
385#395—114no—
386#393—114no—
387#391—114no—
388#389—114no—
389#387—114no—
390#387—114no—
391#386—112no—
392#386—114no—
393#386—112no—
394#386—112no—
395#386—114no—
396#386—112no—
397#385—114no—
398#385—112no—
399#385—112no—
400#385—114no—
401#385—114no—
402#385—114no—
403#385—114no—
404#385C2×D1112yes—
405#385C2×D1112yes—
406#385C2×D1114yescomplemented
407#381—112no—
408#381—112no—
409#380—112no—
410#380—112no—
411#380—114no—
412#379—112no—
413#379—112no—
414C2×#95—112no—
415C2×#95C2×D1112yescomplemented
416C22×C11—24no—
417C22×C11—24no—
418C22×C11—24no—
419C22×C11—22no—
420C22×C11—22no—
421C22×C11—22no—
422C22×C11—22no—
423C22×C11—22no—
424C22×C11—22no—
425C22×C11—24no—
426C22×C11—24no—
427C22×C11—24no—
428C22×C11—416no—
429C22×C11C2×C22⋊Q814yes—
430C22×C11C2×C22⋊Q814yes—
431C22×C11C2×C22⋊Q814yes—
432C22×C11C23×D411yescharacteristic
433C22×C11C23×Q811yescharacteristic
434C22×C11C22×#4111yescharacteristic
435C22×C11C2×H(5,𝔽2)12yes—
436C22×C11#58512yes—
437C2×D11—24no—
438C2×D11—28no—
439C2×D11—416no—
440C2×D11—44no—
441C2×D11—42no—
442C2×D11—42no—
443C4×C11—24no—
444C4×C11—44no—
445C4×C11—42no—
446C4×C11—42no—
447C4×C11—42no—
448Dic11—24no—
449Dic11—24no—
450Dic11—24no—
451Dic11—44no—
452Dic11—42no—
453Dic11—42no—
454C25—111no—
455C25C22×D1111yescharacteristic
456C22×Q8—112no—
457C22×Q8—112no—
458C22×D4—118no—
459C22×D4—112no—
460C22×D4—112no—
461C22×D4—224no—
462C22×D4—224no—
463C23×C4—24no—
464C23×C4—44no—
465C23×C4—111no—
466C23×C4—111no—
467C23×C4—111no—
468C23×C4—111no—
469C23×C4—112no—
470C23×C4—111no—
471C23×C4—114no—
472C23×C4—224no—
473C23×C4—444no—
474C23×C4C22×D1111yescharacteristic
475C23×C4C22×D1112yes—
476C23×C4C22×D1112yes—
477C23×C4C22×D1111yescharacteristic
478C23×C4C22×D1111yescharacteristic
479C23×C4C22×D1112yes—
480C23×C4C22×D1111yescharacteristic
481C22⋊Q8—228no—
482C22⋊Q8—228no—
483C22⋊Q8—228no—
484C22⋊Q8—228no—
485C22⋊Q8—228no—
486C22⋊Q8—228no—
487C22⋊Q8—448no—
488C4×D4—2216no—
489C4×D4—2216no—
490C2×C4⋊C4—44no—
491C2×C4⋊C4—114no—
492C2×C4⋊C4—114no—
493C2×C4⋊C4—112no—
494C2×C4⋊C4—112no—
495C2×C4⋊C4—112no—
496C2×C4⋊C4—112no—
497C2×C4⋊C4—112no—
498C2×C4⋊C4—112no—
499C2×C4⋊C4—114no—
500C2×C4⋊C4—114no—
501C2×C4⋊C4—114no—
502C2×C4⋊C4—224no—
503C2×C4⋊C4—444no—
504C2×C4⋊C4C22×D1114yes—
505C2×C4⋊C4C22×D1114yes—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—118no—
509C2×C22⋊C4—112no—
510C2×C22⋊C4—112no—
511C2×C22⋊C4—112no—
512C2×C22⋊C4—112no—
513C2×C22⋊C4—112no—
514C2×C22⋊C4—112no—
515C2×C22⋊C4—114no—
516C2×C22⋊C4—114no—
517C2×C22⋊C4—114no—
518C2×C22⋊C4—114no—
519C2×C22⋊C4—114no—
520C2×C22⋊C4—224no—
521C2×C22⋊C4—224no—
522C2×C22⋊C4—224no—
523C2×C22⋊C4C22×D1112yes—
524C2×C22⋊C4C22×D1112yes—
525C2×C22⋊C4C22×D1112yes—
526C2×C22⋊C4C22×D1112yes—
527C2×C42—114no—
528C2×C42—224no—
529#95—114no—
530#95—114no—
531#95—114no—
532#95—114no—
533#95—114no—
534#95—114no—
535#95—114no—
536#95—114no—
537#95C22×D1114yes—
538#95C22×D1114yes—
539C2×C11—24no—
540C2×C11—24no—
541C2×C11—24no—
542C2×C11C22×C22⋊Q811yescharacteristic
543C2×C11#345912yes—
544C2×C11#348411yescharacteristic
545C2×C11#348511yescharacteristic
546C2×C11#350112yes—
547D11—44no—
548C24—42no—
549C24—42no—
550C24—112no—
551C24—114no—
552C24—222no—
553C24—222no—
554C24—442no—
555C24—442no—
556C24#433914yes—
557C24D4×D1114yes—
558C24Q8×D1114yes—
559C24C23×D1111yescharacteristic
560C24C23×D1111yescharacteristic
561C24C23×D1111yescharacteristic
562C2×Q8—224no—
563C2×Q8—224no—
564C2×Q8—444no—
565C2×Q8—444no—
566C2×D4—118no—
567C2×D4—118no—
568C2×D4—2232no—
569C2×D4—224no—
570C2×D4—224no—
571C2×D4—224no—
572C2×D4—224no—
573C22×C4—22no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—416no—
591C22×C4—114no—
592C22×C4—112no—
593C22×C4—112no—
594C22×C4—112no—
595C22×C4—114no—
596C22×C4—114no—
597C22×C4—114no—
598C22×C4—112no—
599C22×C4—112no—
600C22×C4—228no—
601C22×C4—222no—
602C22×C4—222no—
603C22×C4—224no—
604C22×C4—222no—
605C22×C4—222no—
606C22×C4—228no—
607C22×C4—444no—
608C22×C4—4416no—
609C22×C4—442no—
610C22×C4—442no—
611C22×C4—442no—
612C22×C4—442no—
613C22×C4—442no—
614C22×C4—442no—
615C22×C4C23×D1114yes—
616C22×C4C23×D1112yes—
617C22×C4C23×D1112yes—
618C22×C4C23×D1112yes—
619C22×C4C23×D1112yes—
620C4⋊C4—28no—
621C4⋊C4—44no—
622C4⋊C4—228no—
623C4⋊C4—224no—
624C4⋊C4—224no—
625C4⋊C4—224no—
626C4⋊C4—224no—
627C4⋊C4—224no—
628C4⋊C4—224no—
629C4⋊C4—228no—
630C4⋊C4—444no—
631C4⋊C4—444no—
632C4⋊C4—444no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—118no—
638C22⋊C4—118no—
639C22⋊C4—228no—
640C22⋊C4—224no—
641C22⋊C4—224no—
642C22⋊C4—224no—
643C22⋊C4—224no—
644C22⋊C4—444no—
645C22⋊C4—444no—
646C22⋊C4—444no—
647C22⋊C4—444no—
648C42—228no—
649C11#3498511yescharacteristic, complemented, Sylow
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—44no—
657C23—48no—
658C23—44no—
659C23—48no—
660C23—114no—
661C23—228no—
662C23—222no—
663C23—222no—
664C23—224no—
665C23—224no—
666C23—448no—
667C23—444no—
668C23—444no—
669C23—448no—
670C23#66949116yescomplemented
671C23C2×#433912yes—
672C23C2×#433912yes—
673C23C2×#433912yes—
674C23C2×D4×D1112yes—
675C23C2×D4×D1112yes—
676C23C2×D4×D1112yes—
677C23C2×Q8×D1112yes—
678C23C2×Q8×D1112yes—
679C23C2×Q8×D1112yes—
680C23C24×D1111yescharacteristic
681Q8—884no—
682Q8—884no—
683D4—2216no—
684D4—2216no—
685C2×C4—28no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—48no—
699C2×C4—48no—
700C2×C4—48no—
701C2×C4—44no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—114no—
705C2×C4—114no—
706C2×C4—114no—
707C2×C4—228no—
708C2×C4—222no—
709C2×C4—222no—
710C2×C4—224no—
711C2×C4—224no—
712C2×C4—224no—
713C2×C4—222no—
714C2×C4—222no—
715C2×C4—224no—
716C2×C4—224no—
717C2×C4—224no—
718C2×C4—224no—
719C2×C4—4416no—
720C2×C4—444no—
721C2×C4—444no—
722C2×C4—448no—
723C2×C4—882no—
724C2×C4—882no—
725C2×C4#6703714yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—24no—
736C22—24no—
737C22—24no—
738C22—416no—
739C22—228no—
740C22—224no—
741C22—4416no—
742C22—442no—
743C22—442no—
744C22—444no—
745C22C2×#6694914yes—
746C22C2×#6694914yes—
747C22C2×#6694914yes—
748C22C22×#433911yescharacteristic
749C22C22×D4×D1111yescharacteristic
750C22C2×#6703712yes—
751C22C22×Q8×D1111yescharacteristic
752C22#1062345312yes—
753C4—24no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—44no—
758C4—224no—
759C4—224no—
760C4—224no—
761C4—442no—
762C4—442no—
763C4—444no—
764C2—24no—
765C2—24no—
766C2—24no—
767C2—444no—
768C2C22×#6694911yescharacteristic
769C2#1308202512yes—
770C2#1308224511yescharacteristic
771C2#1308225411yescharacteristic
772C2#1308241212yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C11×#385C2
prime radicalC23×C22⋊D11C22
hypercenterC2×#385D11
hypocenterC11#34985
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C2×#10623014C2semidirect
3. #13076952C2semidirect
4. #13076902C2semidirect
5. #13074435C2semidirect
6. #13074427C2semidirect
7. #13072442C2semidirect
8. #13072440C2semidirect
9. #13072427C2semidirect
10. #13072425C2semidirect
11. #13071228C2semidirect
14. C2×#10622823C2semidirect
15. C2×C11×#385C2semidirect
19. C22×C11×C4⋊C4C22semidirect
29. C2×#66977C22semidirect
30. C2×#66977C22semidirect
32. C22×Dic11⋊C4C22semidirect
34. C2×#66949C22semidirect
38. C2×#66931C22semidirect
39. C2×#66931C22semidirect
42. C11×#385C22semidirect
43. C2×C11×#95C22semidirect
49. #10622823C22semidirect
50. #10622823C22semidirect
51. C2×C11⋊#95C22semidirect
52. #10622607C22semidirect
53. #10622605C22semidirect
54. #10622602C22semidirect
55. #10622594C22semidirect
56. #10622593C22semidirect
57. #10622592C22semidirect
58. #10622585C22semidirect
64. #10622559C22semidirect
69. #10622289C22semidirect
70. #10622286C22semidirect
71. #10622281C22semidirect
72. #10622280C22semidirect
73. #10622271C22semidirect
74. #10622270C22semidirect
75. #10622265C22semidirect
76. #10622259C22semidirect
90. C22×C22⋊D11Q8semidirect
278. C2×#385D11semidirect
289. C23×C11C22⋊Q8semidirect
371. C22×C4⋊C4C2×D11semidirect
406. #385C2×D11semidirect
415. C2×#95C2×D11semidirect
649. C11#34985semidirect
670. C23#66949semidirect

Maximal subgroups

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

subgroupindex
C2×#106230142
C22×C4×C22⋊D112
#130769522
#130769022
#130744352
#130744272
#130724422
#130724402
#130724272
#130724252
#130712282
#130711912
C2×#106228232
C2×C11×#3852
#3498511