Finite Group Databasebeta

← #14926359

Subgroups — #14926359

Order 2816.

2866 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623165C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D11C211yesmaximal, characteristic
3#13076952C212yesmaximal, complemented
4#13076903C211yesmaximal, characteristic, complemented
5#13074432C211yesmaximal, characteristic, complemented
6#13074431C211yesmaximal, characteristic, complemented
7#13074425C212yesmaximal, complemented
8#13072447C214yesmaximal, complemented
9#13072445C214yesmaximal, complemented
10#13072424C214yesmaximal, complemented
11#13072422C214yesmaximal, complemented
12#13071229C211yesmaximal, characteristic, complemented
13#13071192C212yesmaximal
14D11×#385C212yesmaximal, complemented
15C11×#2848C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×C22⋊Q8C2212yescomplemented
21C22×C22⋊Dic11C2211yescharacteristic
22C2×#66999C2212yescomplemented
23C2×C4×C22⋊D11—28no—
24C2×C4×C22⋊D11C2214yes—
25C2×C4×C22⋊D11C2214yes—
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C2×#66977C2211yescharacteristic
28C2×#66977C2212yescomplemented
29C22×Dic11⋊C4C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31#10623165—28no—
32C2×#66950C2212yescomplemented
33C2×#66949C2212yescomplemented
34C2×#66949C2212yescomplemented
35C2×C4⋊C4×D11C2214yescomplemented
36C2×C22⋊C4×D11C2212yes—
37C2×C22⋊C4×D11C2212yes—
38C2×#66931C2212yes—
39C11×#385C2212yes—
40C11×#385C2214yescomplemented
41C11×#380C2211yescharacteristic
42C11×#380C2212yescomplemented
43C11×#379C2212yes—
44#10622860C2212yes—
45#10622842C2212yescomplemented
46#10622825C2211yescharacteristic
47#10622825C2212yescomplemented
48#10622823C2212yes—
49#10622823C2214yescomplemented
50#10622602C2214yescomplemented
51#10622602C2214yescomplemented
52#10622597C2214yescomplemented
53#10622596C2214yescomplemented
54#10622595C2212yescomplemented
55#10622594C2214yescomplemented
56#10622585C2214yescomplemented
57#10622569C2214yes—
58#10622569C2214yes—
59#10622569C2214yes—
60#10622569C2214yes—
61#10622563C2212yes—
62#10622562C2214yescomplemented
63#10622561C2214yescomplemented
64#10622561C2214yescomplemented
65#10622560C2214yescomplemented
66#10622559C2212yes—
67#10622556C2212yes—
68#10622556C2212yes—
69#10622555C2212yes—
70#10622281C2214yescomplemented
71#10622281C2214yescomplemented
72D11×#95C2214yescomplemented
73#10622272C2212yescomplemented
74#10622269C2212yescomplemented
75#10622265C2214yescomplemented
76#10622259C2214yescomplemented
77C25×C11C2311yescharacteristic
78C24×D11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C23×C4×C11—24no—
81C23×C4×C11—44no—
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2312yes—
84C23×C4×C11C2312yes—
85C23×C4×C11C2311yescharacteristic
86C22×C22⋊D11—24no—
87C22×C22⋊D11—24no—
88C22×C22⋊D11Q818yescomplemented
89C22×C22⋊D11C2314yes—
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C22×C4×D11—24no—
94C22×C4×D11—44no—
95C22×C4×D11C2314yes—
96C22×C4×D11C2312yes—
97C22×C4×D11C2314yes—
98C22×C4×D11C2312yes—
99C22×Dic22C2312yes—
100C22×Dic22C2311yescharacteristic
101C11×C22⋊Q8—24no—
102C11×C22⋊Q8—44no—
103C2×C11×C4⋊C4C2314yes—
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2312yes—
106C2×C11×C4⋊C4C2312yes—
107C2×C11×C22⋊C4C2312yes—
108C2×C11×C22⋊C4C2312yes—
109C2×C11×C22⋊C4C2314yes—
110C2×C11×C22⋊C4C2314yes—
111C2×C22⋊Dic11—24no—
112C2×C22⋊Dic11C2312yes—
113C2×C22⋊Dic11C2312yes—
114C2×C22⋊Dic11C2314yes—
115C2×C22⋊Dic11C2314yes—
116C2×C22⋊Dic11C2314yes—
117#66999—28no—
118C4×C22⋊D11—216no—
119C4×C22⋊D11—216no—
120C2×(C2×D11)⋊C4D418yes—
121C2×(C2×D11)⋊C4C2312yes—
122C2×(C2×D11)⋊C4C2312yes—
123C2×(C2×D11)⋊C4C2314yes—
124C2×(C2×D11)⋊C4C2312yes—
125C2×(C2×D11)⋊C4C2312yes—
126C2×C4⋊Dic11C2312yes—
127C2×C4⋊Dic11C2311yescharacteristic
128C2×C4⋊Dic11C2314yes—
129C2×C4⋊Dic11C2312yes—
130#66977—24no—
131#66977—44no—
132C2×Dic11⋊C4—24no—
133C2×Dic11⋊C4C2312yes—
134C2×Dic11⋊C4C2312yes—
135C2×Dic11⋊C4C2314yes—
136C2×Dic11⋊C4C2312yes—
137C2×Dic11⋊C4C2312yes—
138C2×Dic11⋊C4C2312yes—
139C2×Dic11⋊C4C2314yes—
140C2×Dic11⋊C4C2314yes—
141C2×C4×Dic11—24no—
142C2×C4×Dic11C2314yes—
143#66950—28no—
144#66949—28no—
145#66949—28no—
146C4⋊C4×D11—48no—
147C22⋊C4×D11—28no—
148C22⋊C4×D11—28no—
149#66931—28no—
150C11×#95C2314yes—
151C11×#95C2312yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2312yes—
161#34985—111nomaximal, Sylow
162C24×C11—22no—
163C24×C11—22no—
164C24×C11—42no—
165C24×C11—42no—
166C24×C11C2×Q814yes—
167C24×C11C2412yes—
168C24×C11C2411yescharacteristic
169C23×D11—42no—
170C23×D11—42no—
171C23×D11C2×D414yes—
172C23×D11C2×Q814yes—
173C23×D11#4114yes—
174C23×D11C2412yes—
175C2×Q8×C11—22no—
176C2×Q8×C11—42no—
177C22×C4×C11—22no—
178C22×C4×C11—24no—
179C22×C4×C11—24no—
180C22×C4×C11—24no—
181C22×C4×C11—24no—
182C22×C4×C11—24no—
183C22×C4×C11—42no—
184C22×C4×C11—42no—
185C22×C4×C11—42no—
186C22×C4×C11—416no—
187C22×C4×C11C2×D414yes—
188C22×C4×C11C2414yes—
189C22×C4×C11C2412yes—
190C22×C4×C11C2412yes—
191C22×C4×C11C2411yescharacteristic
192C22×C4×C11C2411yescharacteristic
193C22×C4×C11C2412yes—
194C2×C22⋊D11—232no—
195C2×C22⋊D11—28no—
196C2×C22⋊D11—28no—
197C2×C22⋊D11C2×Q8116yes—
198C22×Dic11—22no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—42no—
202C22×Dic11—42no—
203C22×Dic11C2×D414yes—
204C22×Dic11C2×Q814yes—
205C22×Dic11C2414yes—
206C22×Dic11C2412yes—
207C22×Dic11C2412yes—
208C22×Dic11C2412yes—
209C22×Dic11C2412yes—
210C22×Dic11C2412yes—
211C2×C4×D11—28no—
212C2×C4×D11—24no—
213C2×C4×D11—24no—
214C2×C4×D11—28no—
215C2×C4×D11—28no—
216C2×C4×D11—44no—
217C2×C4×D11—44no—
218C2×C4×D11—44no—
219C2×C4×D11—44no—
220C2×C4×D11—44no—
221C2×C4×D11—416no—
222C2×Dic22—24no—
223C2×Dic22—22no—
224C2×Dic22—42no—
225C2×Dic22—44no—
226C11×C4⋊C4—22no—
227C11×C4⋊C4—24no—
228C11×C4⋊C4—28no—
229C11×C4⋊C4—42no—
230C11×C22⋊C4—24no—
231C11×C22⋊C4—24no—
232C11×C22⋊C4—44no—
233C11×C22⋊C4—44no—
234C22⋊Dic11—28no—
235C22⋊Dic11—24no—
236C22⋊Dic11—24no—
237C22⋊Dic11—44no—
238C22⋊Dic11—44no—
239(C2×D11)⋊C4—24no—
240(C2×D11)⋊C4—24no—
241(C2×D11)⋊C4—28no—
242(C2×D11)⋊C4C2×D418yes—
243(C2×D11)⋊C4C2×D418yes—
244C4⋊Dic11—24no—
245C4⋊Dic11—22no—
246C4⋊Dic11—44no—
247C4⋊Dic11—42no—
248Dic11⋊C4—24no—
249Dic11⋊C4—24no—
250Dic11⋊C4—24no—
251Dic11⋊C4—24no—
252Dic11⋊C4—24no—
253Dic11⋊C4—28no—
254Dic11⋊C4—44no—
255Dic11⋊C4—44no—
256C4×Dic11—28no—
257C2×#543—111no—
258C22×C4×D4—111no—
259#2855—112no—
260#2848—111no—
261#2848D1111yescharacteristic, complemented
262#2627—111no—
263#2627—111no—
264#2626—112no—
265#2450—114no—
266#2450—114no—
267#2449—114no—
268#2449—114no—
269#2315—111no—
270#2308—112no—
271C2×#385—112no—
272C23×C11—22no—
273C23×C11—22no—
274C23×C11—28no—
275C23×C11—22no—
276C23×C11—22no—
277C23×C11—22no—
278C23×C11—22no—
279C23×C11—22no—
280C23×C11—22no—
281C23×C11—48no—
282C23×C11—44no—
283C23×C11—48no—
284C23×C11—44no—
285C23×C11C22×D412yes—
286C23×C11C22×Q814yes—
287C23×C11C22×Q812yes—
288C23×C11C2×#4112yes—
289C23×C11C2511yescharacteristic
290C22×D11—24no—
291C22×D11—24no—
292C22×D11—44no—
293C22×D11—44no—
294C22×D11—48no—
295C22×D11—48no—
296C22×D11C22⋊Q8116yescomplemented
297C22×D11C22×D414yes—
298C22×D11C22×Q814yes—
299C22×D11C2×#4114yes—
300Q8×C11—82no—
301C2×C4×C11—28no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—24no—
309C2×C4×C11—24no—
310C2×C4×C11—24no—
311C2×C4×C11—24no—
312C2×C4×C11—24no—
313C2×C4×C11—44no—
314C2×C4×C11—48no—
315C2×C4×C11—48no—
316C2×C4×C11C22×D412yes—
317C2×C4×C11C22×D412yes—
318C2×C4×C11H(5,𝔽2)14yes—
319C22⋊D11—232no—
320C2×Dic11—28no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—24no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—24no—
328C2×Dic11—24no—
329C2×Dic11—24no—
330C2×Dic11—24no—
331C2×Dic11—24no—
332C2×Dic11—24no—
333C2×Dic11—44no—
334C2×Dic11—44no—
335C2×Dic11C22×D414yes—
336C2×Dic11C22×Q814yes—
337C4×D11—416no—
338C4×D11—416no—
339C4×D11—84no—
340C4×D11—84no—
341Dic22—84no—
342Dic22—82no—
343C23×D4—111no—
344C24×C4—111no—
345C24×C4C2×D1111yescharacteristic
346#543—228no—
347C2×C22⋊Q8—112no—
348C2×C22⋊Q8—111no—
349C2×C22⋊Q8—112no—
350C2×C22⋊Q8—112no—
351C2×C22⋊Q8—112no—
352C2×C22⋊Q8—112no—
353C2×C22⋊Q8—112no—
354C2×C22⋊Q8C2×D1111yescharacteristic
355C2×C22⋊Q8C2×D1112yescomplemented
356C2×C4×D4—114no—
357C2×C4×D4—114no—
358C2×C4×D4—228no—
359C22×C4⋊C4—111no—
360C22×C4⋊C4—114no—
361C22×C22⋊C4—111no—
362C22×C22⋊C4—111no—
363C22×C22⋊C4—112no—
364C22×C22⋊C4—112no—
365C22×C42—111no—
366#400—112no—
367#400—112no—
368#399—114no—
369#398—114no—
370#398—114no—
371#396—114no—
372#396—114no—
373#395—112no—
374#395—112no—
375#393—114no—
376#391—114no—
377#389—114no—
378#387—114no—
379#387—114no—
380#386—114no—
381#386—114no—
382#386—114no—
383#386—114no—
384#385—112no—
385#385—114no—
386#385—114no—
387#385—114no—
388#385—112no—
389#385—112no—
390#385—114no—
391#385—114no—
392#385C2×D1112yes—
393#385C2×D1114yescomplemented
394#381—112no—
395#381—112no—
396#380—111no—
397#380—112no—
398#380—112no—
399#380C2×D1111yescharacteristic
400#380C2×D1112yescomplemented
401#379—112no—
402#379C2×D1112yes—
403C2×#95—114no—
404C22×C11—24no—
405C22×C11—22no—
406C22×C11—22no—
407C22×C11—24no—
408C22×C11—24no—
409C22×C11—24no—
410C22×C11—24no—
411C22×C11—416no—
412C22×C11—42no—
413C22×C11—42no—
414C22×C11—42no—
415C22×C11—42no—
416C22×C11C2×C22⋊Q814yes—
417C22×C11C23×D411yescharacteristic
418C22×C11C23×Q811yescharacteristic
419C22×C11C22×#4111yescharacteristic
420C22×C11C2×H(5,𝔽2)12yes—
421C22×C11#58512yes—
422C2×D11—28no—
423C2×D11—24no—
424C2×D11—24no—
425C2×D11—28no—
426C2×D11—416no—
427C2×D11C2×C22⋊Q818yes—
428C4×C11—24no—
429C4×C11—22no—
430C4×C11—22no—
431C4×C11—44no—
432C4×C11—42no—
433C4×C11—42no—
434Dic11—24no—
435Dic11—24no—
436Dic11—44no—
437Dic11—42no—
438Dic11—42no—
439Dic11—42no—
440C25—111no—
441C25C22×D1111yescharacteristic
442C22×Q8—111no—
443C22×Q8—112no—
444C22×Q8C22×D1111yescharacteristic
445C22×D4—118no—
446C22×D4—114no—
447C22×D4—224no—
448C22×D4—224no—
449C23×C4—24no—
450C23×C4—44no—
451C23×C4—111no—
452C23×C4—111no—
453C23×C4—111no—
454C23×C4—114no—
455C23×C4—112no—
456C23×C4—114no—
457C23×C4—112no—
458C23×C4—224no—
459C23×C4—444no—
460C23×C4C22×D1111yescharacteristic
461C23×C4C22×D1112yes—
462C23×C4C22×D1112yes—
463C23×C4C22×D1111yescharacteristic
464C22⋊Q8—24no—
465C22⋊Q8—44no—
466C22⋊Q8—228no—
467C22⋊Q8—228no—
468C22⋊Q8—228no—
469C22⋊Q8—228no—
470C22⋊Q8—228no—
471C22⋊Q8—224no—
472C22⋊Q8—444no—
473C4×D4—2216no—
474C4×D4—2216no—
475C2×C4⋊C4—112no—
476C2×C4⋊C4—112no—
477C2×C4⋊C4—114no—
478C2×C4⋊C4—111no—
479C2×C4⋊C4—112no—
480C2×C4⋊C4—112no—
481C2×C4⋊C4—112no—
482C2×C4⋊C4—112no—
483C2×C4⋊C4—114no—
484C2×C4⋊C4—114no—
485C2×C4⋊C4—112no—
486C2×C4⋊C4—114no—
487C2×C4⋊C4—224no—
488C2×C4⋊C4—448no—
489C2×C4⋊C4C22×D1114yes—
490C2×C4⋊C4C22×D1111yescharacteristic
491C2×C4⋊C4C22×D1112yes—
492C2×C4⋊C4C22×D1112yes—
493C2×C22⋊C4—118no—
494C2×C22⋊C4—112no—
495C2×C22⋊C4—112no—
496C2×C22⋊C4—114no—
497C2×C22⋊C4—112no—
498C2×C22⋊C4—112no—
499C2×C22⋊C4—112no—
500C2×C22⋊C4—112no—
501C2×C22⋊C4—114no—
502C2×C22⋊C4—114no—
503C2×C22⋊C4—114no—
504C2×C22⋊C4—228no—
505C2×C22⋊C4—228no—
506C2×C22⋊C4—224no—
507C2×C22⋊C4C22×D1112yes—
508C2×C22⋊C4C22×D1112yes—
509C2×C22⋊C4C22×D1114yes—
510C2×C22⋊C4C22×D1114yes—
511C2×C42—114no—
512C2×C42—224no—
513#95—114no—
514#95—114no—
515#95—114no—
516#95—112no—
517#95—114no—
518#95—114no—
519#95—114no—
520#95—114no—
521#95—114no—
522#95C22×D1114yes—
523#95C22×D1112yes—
524C2×C11—24no—
525C2×C11—44no—
526C2×C11C22×C22⋊Q811yescharacteristic
527C2×C11#345912yes—
528C2×C11#348411yescharacteristic
529C2×C11#348511yescharacteristic
530C2×C11#350112yes—
531D11—28no—
532C24—22no—
533C24—22no—
534C24—42no—
535C24—42no—
536C24—112no—
537C24—114no—
538C24—114no—
539C24—114no—
540C24—442no—
541C24—442no—
542C24Q8×D1114yes—
543C24C23×D1112yes—
544C24C23×D1111yescharacteristic
545C2×Q8—22no—
546C2×Q8—42no—
547C2×Q8—224no—
548C2×Q8—222no—
549C2×Q8—442no—
550C2×Q8—444no—
551C2×D4—1116no—
552C2×D4—228no—
553C2×D4—2232no—
554C2×D4—228no—
555C22×C4—22no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—416no—
565C22×C4—114no—
566C22×C4—112no—
567C22×C4—112no—
568C22×C4—114no—
569C22×C4—114no—
570C22×C4—112no—
571C22×C4—112no—
572C22×C4—112no—
573C22×C4—228no—
574C22×C4—228no—
575C22×C4—224no—
576C22×C4—224no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—222no—
580C22×C4—228no—
581C22×C4—444no—
582C22×C4—444no—
583C22×C4—444no—
584C22×C4—444no—
585C22×C4—444no—
586C22×C4—4416no—
587C22×C4—442no—
588C22×C4—442no—
589C22×C4D4×D1114yes—
590C22×C4C23×D1114yes—
591C22×C4C23×D1112yes—
592C22×C4C23×D1112yes—
593C22×C4C23×D1111yescharacteristic
594C22×C4C23×D1111yescharacteristic
595C22×C4C23×D1112yes—
596C4⋊C4—22no—
597C4⋊C4—24no—
598C4⋊C4—28no—
599C4⋊C4—42no—
600C4⋊C4—224no—
601C4⋊C4—224no—
602C4⋊C4—224no—
603C4⋊C4—224no—
604C4⋊C4—224no—
605C4⋊C4—224no—
606C4⋊C4—222no—
607C4⋊C4—228no—
608C4⋊C4—444no—
609C4⋊C4—444no—
610C4⋊C4—442no—
611C4⋊C4—444no—
612C22⋊C4—24no—
613C22⋊C4—24no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—118no—
617C22⋊C4—118no—
618C22⋊C4—224no—
619C22⋊C4—224no—
620C22⋊C4—228no—
621C22⋊C4—228no—
622C22⋊C4—224no—
623C22⋊C4—224no—
624C22⋊C4—444no—
625C22⋊C4—444no—
626C42—228no—
627C11#3498511yescharacteristic, complemented, Sylow
628C23—22no—
629C23—22no—
630C23—28no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—48no—
638C23—44no—
639C23—44no—
640C23—48no—
641C23—114no—
642C23—114no—
643C23—114no—
644C23—1116no—
645C23—224no—
646C23—224no—
647C23—444no—
648C23—448no—
649C23—444no—
650C23—448no—
651C23C2×D4×D1112yes—
652C23C2×Q8×D1114yes—
653C23C2×Q8×D1112yes—
654C23#41×D1112yes—
655C23C24×D1111yescharacteristic
656Q8—82no—
657Q8—882no—
658Q8—884no—
659D4—2232no—
660C2×C4—28no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—44no—
673C2×C4—48no—
674C2×C4—48no—
675C2×C4—114no—
676C2×C4—114no—
677C2×C4—228no—
678C2×C4—222no—
679C2×C4—222no—
680C2×C4—224no—
681C2×C4—222no—
682C2×C4—222no—
683C2×C4—222no—
684C2×C4—224no—
685C2×C4—224no—
686C2×C4—224no—
687C2×C4—224no—
688C2×C4—224no—
689C2×C4—224no—
690C2×C4—4416no—
691C2×C4—4416no—
692C2×C4—444no—
693C2×C4—444no—
694C2×C4—884no—
695C2×C4—884no—
696C2×C4C2×D4×D1112yes—
697C2×C4C2×D4×D1112yes—
698C2×C4#6703714yes—
699C22—24no—
700C22—22no—
701C22—22no—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—24no—
706C22—416no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—118no—
712C22—228no—
713C22—224no—
714C22—224no—
715C22—228no—
716C22—4416no—
717C22D11×C22⋊Q814yes—
718C22C22×D4×D1111yescharacteristic
719C22C2×#6703712yes—
720C22C22×Q8×D1111yescharacteristic
721C22C2×#41×D1111yescharacteristic
722C22#1062345312yes—
723C4—24no—
724C4—22no—
725C4—22no—
726C4—42no—
727C4—42no—
728C4—44no—
729C4—224no—
730C4—224no—
731C4—442no—
732C4—442no—
733C4—442no—
734C4—444no—
735C2—24no—
736C2—44no—
737C2—228no—
738C2C2×D11×C22⋊Q811yescharacteristic
739C2#1308202312yes—
740C2#1308224511yescharacteristic
741C2#1308225811yescharacteristic
742C2#1308241212yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2848C2
prime radicalC23×C22⋊D11C22
hypercenter#2848D11
hypocenterC11#34985
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2848

Complements

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

NH ≅ G/Ntype
1. C2×#10623165C2semidirect
3. #13076952C2semidirect
4. #13076903C2semidirect
5. #13074432C2semidirect
6. #13074431C2semidirect
7. #13074425C2semidirect
8. #13072447C2semidirect
9. #13072445C2semidirect
10. #13072424C2semidirect
11. #13072422C2semidirect
12. #13071229C2semidirect
14. D11×#385C2semidirect
15. C11×#2848C2semidirect
20. C2×C11×C22⋊Q8C22semidirect
22. C2×#66999C22semidirect
28. C2×#66977C22semidirect
32. C2×#66950C22semidirect
33. C2×#66949C22semidirect
34. C2×#66949C22semidirect
35. C2×C4⋊C4×D11C22semidirect
40. C11×#385C22semidirect
42. C11×#380C22semidirect
45. #10622842C22semidirect
47. #10622825C22semidirect
49. #10622823C22semidirect
50. #10622602C22semidirect
51. #10622602C22semidirect
52. #10622597C22semidirect
53. #10622596C22semidirect
54. #10622595C22semidirect
55. #10622594C22semidirect
56. #10622585C22semidirect
62. #10622562C22semidirect
63. #10622561C22semidirect
64. #10622561C22semidirect
65. #10622560C22semidirect
70. #10622281C22semidirect
71. #10622281C22semidirect
72. D11×#95C22semidirect
73. #10622272C22semidirect
74. #10622269C22semidirect
75. #10622265C22semidirect
76. #10622259C22semidirect
88. C22×C22⋊D11Q8semidirect
261. #2848D11semidirect
296. C22×D11C22⋊Q8semidirect
355. C2×C22⋊Q8C2×D11semidirect
393. #385C2×D11semidirect
400. #380C2×D11semidirect
627. C11#34985semidirect

Maximal subgroups

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

subgroupindex
C2×#106231652
C22×C4×C22⋊D112
#130769522
#130769032
#130744322
#130744312
#130744252
#130724472
#130724452
#130724242
#130724222
#130712292
#130711922
D11×#3852
C11×#28482
#3498511