Finite Group Databasebeta

← #14769287

Subgroups — #14769287

Order 2816.

1530 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623348C211yesmaximal, characteristic
2C2×#10622343C211yesmaximal, characteristic, complemented
3C2×#10622416C211yesmaximal, characteristic, complemented
4C22×#66899C211yesmaximal, characteristic, complemented
5#13071512C211yesmaximal, characteristic, complemented
6#13069545C211yesmaximal, characteristic, complemented
7#13069429C211yesmaximal, characteristic, complemented
8#13069046C211yesmaximal, characteristic, complemented
9#13069042C211yesmaximal, characteristic, complemented
10#13068931C211yesmaximal, characteristic, complemented
11#13068920C211yesmaximal, characteristic, complemented
12#13068619C211yesmaximal, characteristic, complemented
13#13068555C211yesmaximal, characteristic, complemented
14#13068448C211yesmaximal, characteristic, complemented
15C11×#1787C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C22×#4343C2211yescharacteristic
18#10623348—24no—
19#10623348C418yescomplemented
20C2×#67000—21no—
21C2×#67000C2211yescharacteristic
22C2×#66999—21no—
23C2×#66999C2211yescharacteristic
24C2×Q8×Dic11C2211yescharacteristic
25C2×#66983—21no—
26C2×#66983C2211yescharacteristic
27C2×C4×C22⋊D11—21no—
28C2×C4×C22⋊D11C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C23×C11⋊C8C2211yescharacteristic
31C22×#4313C2211yescharacteristic
32C2×C4⋊C4×D11C2211yescharacteristic
33C2×(C22⋊D11)⋊C4—21no—
34C2×C11×#103C2211yescharacteristic
35C2×C11×#103C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#103C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic
39C11×#380C2211yescharacteristic
40C2×#66899—24no—
41C2×#66899C2211yescharacteristic
42C2×#66899C2211yescharacteristic
43C2×#66899C2211yescharacteristic
44C2×#66899C2211yescharacteristic
45C2×#66885C2211yescharacteristic
46C2×#66885C2211yescharacteristic
47C2×(C2×D11)⋊C8C2211yescharacteristic
48C2×#66879C2211yescharacteristic
49C2×Dic11⋊C8C2211yescharacteristic
50#10622600C2211yescharacteristic
51#10622589C2211yescharacteristic
52C4⋊C4×Dic11C2211yescharacteristic
53C2×#66873C2211yescharacteristic
54C2×#66873C2211yescharacteristic
55#10622559—21no—
56#10622416—24no—
57#10622343—24no—
58#10622281—21no—
59#10622260—21no—
60#10622189C2211yescharacteristic
61#10622189C2211yescharacteristic
62#10622167C2211yescharacteristic
63#10622167C2211yescharacteristic
64C22×Q8×C11—21no—
65C22×Q8×C11—22no—
66C22×Q8×C11—22no—
67C22×Q8×C11—22no—
68C22×Q8×C11—41no—
69C22×Q8×C11—41no—
70C22×Q8×C11C2×C414yescomplemented
71C22×Q8×C11C2311yescharacteristic
72C22×Q8×C11C2311yescharacteristic
73C23×C4×C11—21no—
74C23×C4×C11C2311yescharacteristic
75C22×C22⋊D11—21no—
76C22×C22⋊D11D411yescharacteristic
77C23×Dic11—21no—
78C2×#4343—22no—
79C2×#4343—22no—
80C2×#4343—22no—
81C2×#4343—41no—
82C2×#4343—41no—
83C2×#4343C2×C414yescomplemented
84C22×D44—21no—
85C22×D44C2311yescharacteristic
86C22×C4×D11—21no—
87C22×C4×D11—21no—
88C22×C4×D11C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C22⋊C4—21no—
94C2×C22⋊Dic11D411yescharacteristic
95#67000—28no—
96#67000—22no—
97#67000C2×C414yescomplemented
98#66999—22no—
99#66999—28no—
100#66999C2×C414yescomplemented
101Q8×Dic11—22no—
102Q8×Dic11C2×C414yescomplemented
103#66983—22no—
104#66983—28no—
105#66983C2×C414yescomplemented
106C4×C22⋊D11—28no—
107C4×C22⋊D11C2×C414yes—
108C4×C22⋊D11D414yes—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4—21no—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4D411yescharacteristic
115C2×C4⋊Dic11—21no—
116C2×C4⋊Dic11—22no—
117C2×C4⋊Dic11—21no—
118C2×C4⋊Dic11—41no—
119C2×C4⋊Dic11C2311yescharacteristic
120C2×C4⋊Dic11C2311yescharacteristic
121C2×C4⋊Dic11C2311yescharacteristic
122C2×Dic11⋊C4—21no—
123C2×Dic11⋊C4—21no—
124C2×Dic11⋊C4—21no—
125C2×Dic11⋊C4—21no—
126C2×Dic11⋊C4D411yescharacteristic
127C2×C4×Dic11—21no—
128C2×C4×Dic11—21no—
129C2×C4×Dic11C2311yescharacteristic
130C22×C11⋊C8—22no—
131C22×C11⋊C8—22no—
132C22×C11⋊C8—41no—
133C22×C11⋊C8C2311yescharacteristic
134C22×C11⋊C8C2311yescharacteristic
135C2×#4313—22no—
136C2×#4313—22no—
137C2×#4313—41no—
138C4⋊C4×D11—22no—
139C4⋊C4×D11—41no—
140(C22⋊D11)⋊C4—44no—
141C11×#103—22no—
142C11×#103—22no—
143C11×#103—41no—
144C11×#103—41no—
145C11×C22⋊C8—22no—
146C11×#95—21no—
147#66899—22no—
148#66899—22no—
149#66899—22no—
150#66899D414yescomplemented
151C11⋊#95—21no—
152C11⋊#95—21no—
153#66885—22no—
154#66885—41no—
155(C2×D11)⋊C8—22no—
156#66879—22no—
157Dic11⋊C8—22no—
158#66873—22no—
159#66873—41no—
160#22421—111nomaximal, Sylow
161C24×C11C2×D411yescharacteristic
162C23×D11—21no—
163C23×D11C2×D411yescharacteristic
164C2×Q8×C11—24no—
165C2×Q8×C11—21no—
166C2×Q8×C11—21no—
167C2×Q8×C11—21no—
168C2×Q8×C11—21no—
169C2×Q8×C11—28no—
170C2×Q8×C11—21no—
171C2×Q8×C11—21no—
172C2×Q8×C11—21no—
173C2×Q8×C11—21no—
174C2×Q8×C11—42no—
175C2×Q8×C11—42no—
176C2×Q8×C11—44no—
177C2×Q8×C11—44no—
178C2×Q8×C11—44no—
179C2×Q8×C11C22×C412yes—
180C2×Q8×C11C22×C412yes—
181C2×Q8×C11C2×D412yes—
182C2×Q8×C11#4112yes—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—24no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—42no—
193C22×C4×C11—42no—
194C22×C4×C11C22×C412yes—
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D412yes—
197C22×C4×C11C2411yescharacteristic
198C2×C22⋊D11—24no—
199C2×C22⋊D11—22no—
200C2×C22⋊D11—22no—
201C2×C22⋊D11—42no—
202C2×C22⋊D11—42no—
203C2×C22⋊D11C22⋊C414yes—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—42no—
208C22×Dic11—42no—
209C22×Dic11—81no—
210C22×Dic11C2×D411yescharacteristic
211C22×Dic11C2×D411yescharacteristic
212C22×Dic11C2×D411yescharacteristic
213#4343—28no—
214#4343—44no—
215#4343—44no—
216#4343—44no—
217C2×D44—24no—
218C2×D44—21no—
219C2×D44—21no—
220C2×D44—21no—
221C2×D44—21no—
222C2×D44—21no—
223C2×D44—42no—
224C2×D44—42no—
225C2×D44C22×C412yes—
226C2×C4×D11—24no—
227C2×C4×D11—21no—
228C2×C4×D11—21no—
229C2×C4×D11—21no—
230C2×C4×D11—21no—
231C2×C4×D11—42no—
232C2×C4×D11—42no—
233C2×C4×D11—42no—
234C2×C4×D11—42no—
235C2×C4×D11—81no—
236C2×C4×D11C22×C412yes—
237C2×C4×D11C2×D412yes—
238C2×C8×C11—21no—
239C2×C8×C11—21no—
240C2×C8×C11—21no—
241C2×C8×C11—21no—
242C2×C8×C11—21no—
243C2×C8×C11—21no—
244C11×C4⋊C4—21no—
245C11×C4⋊C4—21no—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—21no—
248C11×C22⋊C4—42no—
249C22⋊Dic11C22⋊C414yes—
250(C2×D11)⋊C4—24no—
251(C2×D11)⋊C4—24no—
252(C2×D11)⋊C4—24no—
253(C2×D11)⋊C4—24no—
254(C2×D11)⋊C4—42no—
255(C2×D11)⋊C4C22⋊C414yes—
256C4⋊Dic11—24no—
257C4⋊Dic11—21no—
258C4⋊Dic11—21no—
259C4⋊Dic11—21no—
260C4⋊Dic11—21no—
261C4⋊Dic11—42no—
262C4⋊Dic11C22×C412yes—
263C4⋊Dic11C2×D412yes—
264Dic11⋊C4—24no—
265Dic11⋊C4—42no—
266Dic11⋊C4—42no—
267Dic11⋊C4—81no—
268Dic11⋊C4C22⋊C414yes—
269C4×Dic11—24no—
270C4×Dic11—42no—
271C4×Dic11C22×C412yes—
272C4×Dic11C2×D412yes—
273C2×C11⋊C8—21no—
274C2×C11⋊C8—21no—
275C2×C11⋊C8—21no—
276C2×C11⋊C8—21no—
277C2×C11⋊C8—21no—
278C2×C11⋊C8—44no—
279C2×C11⋊C8C2×D412yes—
280#4313—44no—
281C2×#548—111no—
282C2×#435—111no—
283C2×#417—111no—
284C22×#103—111no—
285D4×C4⋊C4—111no—
286#1983—111no—
287#1959—111no—
288#1894—111no—
289#1893—111no—
290#1874—111no—
291#1872—111no—
292#1803—111no—
293#1788—111no—
294#1787D1111yescharacteristic, complemented
295#1763—111no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11C2×C22⋊C412yes—
301C23×C11AGL(1,ℤ/8)12yes—
302C23×C11#13712yes—
303C23×C11C22×D411yescharacteristic
304C22×D11—21no—
305C22×D11—21no—
306C22×D11—21no—
307C22×D11—21no—
308C22×D11—21no—
309C22×D11—21no—
310C22×D11—22no—
311C22×D11—41no—
312C22×D11—41no—
313C22×D11—41no—
314C22×D11—41no—
315C22×D11—41no—
316C22×D11—41no—
317C22×D11C2×C22⋊C412yes—
318Q8×C11—22no—
319Q8×C11—22no—
320Q8×C11—22no—
321Q8×C11—22no—
322Q8×C11—22no—
323Q8×C11—48no—
324Q8×C11—41no—
325Q8×C11—41no—
326Q8×C11C4×D414yescomplemented
327C2×C4×C11—22no—
328C2×C4×C11—21no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—21no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—48no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11C2×C22⋊C412yes—
347C2×C4×C11C23×C411yescharacteristic
348C2×C4×C11C22×D411yescharacteristic
349C2×C4×C11C22×D411yescharacteristic
350C2×C4×C11C2×#4111yescharacteristic
351C2×C4×C11H(5,𝔽2)11yescharacteristic
352C2×C4×C11H(5,𝔽2)11yescharacteristic
353C22⋊D11—28no—
354C22⋊D11—48no—
355C2×Dic11—21no—
356C2×Dic11—21no—
357C2×Dic11—21no—
358C2×Dic11—21no—
359C2×Dic11—21no—
360C2×Dic11—21no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—41no—
364C2×Dic11—41no—
365C2×Dic11—41no—
366C2×Dic11—41no—
367C2×Dic11—41no—
368C2×Dic11—41no—
369C2×Dic11—41no—
370C2×Dic11—84no—
371C2×Dic11C2×C22⋊C412yes—
372C2×Dic11C2×C22⋊C412yes—
373C2×Dic11C2×C22⋊C412yes—
374D44—22no—
375D44—22no—
376D44—48no—
377D44—41no—
378D44—41no—
379C4×D11—22no—
380C4×D11—22no—
381C4×D11—22no—
382C4×D11—22no—
383C4×D11—48no—
384C4×D11—84no—
385C8×C11—41no—
386C8×C11—41no—
387C11⋊C8—22no—
388C11⋊C8—41no—
389C22×#41—111no—
390C23×Q8C2×D1111yescharacteristic
391C22×M16—111no—
392C23×C8—111no—
393#548—118no—
394#548—224no—
395C2×#124—111no—
396C2×#124—221no—
397C2×C22⋊Q8—111no—
398C2×C22⋊Q8—221no—
399C2×#121—111no—
400C2×#121—221no—
401C2×C4×Q8—111no—
402C2×C4×D4—111no—
403C2×C4×D4—221no—
404C2×C4×D4—221no—
405C22×C4⋊C4—111no—
406C22×C4⋊C4—111no—
407#435—224no—
408C2×C4⋊C8—111no—
409#417—224no—
410C2×#103—111no—
411C2×#103—111no—
412C2×#103—111no—
413C2×#103—111no—
414C2×#103—224no—
415C2×#103C2×D1111yescharacteristic
416C2×#103C2×D1111yescharacteristic
417C2×#103C2×D1111yescharacteristic
418C2×#103C2×D1111yescharacteristic
419C2×#102—111no—
420C2×#102—111no—
421C2×#102—111no—
422C2×#102—111no—
423C2×C22⋊C8—111no—
424C2×C22⋊C8C2×D1111yescharacteristic
425C2×#97—111no—
426#389—221no—
427#385—221no—
428#385—221no—
429#384—111no—
430#380—111no—
431#380C2×D1111yescharacteristic
432C4×C4⋊C4—111no—
433#340—111no—
434#340—111no—
435#340—111no—
436#340—111no—
437C22×C11—22no—
438C22×C11—22no—
439C22×C11—22no—
440C22×C11—22no—
441C22×C11—22no—
442C22×C11—22no—
443C22×C11#41714yescomplemented
444C22×C11C22×C22⋊C411yescharacteristic
445C22×C11D4211yescharacteristic
446C22×C11#54611yescharacteristic
447C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
448C22×C11C2×#13711yescharacteristic
449C22×C11#57711yescharacteristic
450C22×C11#57811yescharacteristic
451C2×D11—22no—
452C2×D11—22no—
453C2×D11—22no—
454C2×D11—41no—
455C2×D11—41no—
456C2×D11—41no—
457C2×D11—41no—
458C2×D11—42no—
459C2×D11—42no—
460C2×D11—42no—
461C2×D11—81no—
462C2×D11—81no—
463C2×D11—81no—
464C2×D11—81no—
465C4×C11—22no—
466C4×C11—24no—
467C4×C11—42no—
468C4×C11—81no—
469C4×C11—81no—
470C4×C11C2×C4×D411yescharacteristic
471C4×C11#51811yescharacteristic
472C4×C11D4211yescharacteristic
473C4×C11#54611yescharacteristic
474Dic11—22no—
475Dic11—22no—
476Dic11—22no—
477Dic11—42no—
478Dic11—42no—
479Dic11—81no—
480C2×#41—114no—
481C2×#41—222no—
482C2×#41—222no—
483C2×#41—222no—
484C2×#41—441no—
485C2×#41—441no—
486C22×Q8—21no—
487C22×Q8—22no—
488C22×Q8—22no—
489C22×Q8—22no—
490C22×Q8—41no—
491C22×Q8—41no—
492C22×Q8C4×D1114yescomplemented
493C22×Q8C22×D1111yescharacteristic
494C22×Q8C22×D1111yescharacteristic
495C22×D4—111no—
496C22×D4—111no—
497C22×D4—221no—
498C22×D4—221no—
499C23×C4—21no—
500C23×C4—111no—
501C23×C4—221no—
502C23×C4—221no—
503C23×C4—221no—
504C23×C4C22×D1111yescharacteristic
505C2×M16—222no—
506C2×M16—222no—
507C2×M16—441no—
508C22×C8—111no—
509C22×C8—111no—
510C22×C8—222no—
511C22×C8—222no—
512C22×C8—441no—
513C22×C8C22×D1111yescharacteristic
514C22×C8C22×D1111yescharacteristic
515#124—114no—
516#124—222no—
517#124—228no—
518C22⋊Q8—114no—
519C22⋊Q8—228no—
520C22⋊Q8—222no—
521#121—114no—
522#121—228no—
523#121—222no—
524C4×Q8—114no—
525C4×Q8—222no—
526C4×D4—114no—
527C4×D4—114no—
528C4×D4—228no—
529C4×D4—444no—
530C2×C4⋊C4—111no—
531C2×C4⋊C4—111no—
532C2×C4⋊C4—111no—
533C2×C4⋊C4—111no—
534C2×C4⋊C4—222no—
535C2×C4⋊C4—222no—
536C2×C4⋊C4—221no—
537C2×C4⋊C4—221no—
538C2×C4⋊C4—221no—
539C2×C4⋊C4—221no—
540C2×C4⋊C4—221no—
541C2×C4⋊C4—221no—
542C2×C4⋊C4—441no—
543C2×C4⋊C4—441no—
544C2×C4⋊C4C22×D1111yescharacteristic
545C2×C4⋊C4C22×D1111yescharacteristic
546C2×C22⋊C4—21no—
547C2×C22⋊C4—111no—
548C2×C22⋊C4—111no—
549C2×C22⋊C4—221no—
550C2×C22⋊C4—221no—
551C2×C22⋊C4—221no—
552C2×C22⋊C4—221no—
553C2×C22⋊C4—221no—
554C2×C42—111no—
555C2×C42—221no—
556C2×C42—221no—
557C4⋊C8—222no—
558#103—22no—
559#103—22no—
560#103—41no—
561#103—41no—
562#103—114no—
563#103—222no—
564#103—222no—
565#103—222no—
566#102—222no—
567#102—222no—
568#102—441no—
569#102—441no—
570C22⋊C8—22no—
571C22⋊C8—222no—
572#97—222no—
573#95—21no—
574#95—221no—
575#95—221no—
576C2×C11—24no—
577C2×C11D4×C22⋊C411yescharacteristic
578C2×C11C2×#41711yescharacteristic
579C2×C11#289811yescharacteristic
580C2×C11#326511yescharacteristic
581C2×C11#327011yescharacteristic
582C2×C11#330811yescharacteristic
583C2×C11#331611yescharacteristic
584D11—42no—
585D11—82no—
586C24—111no—
587C24—221no—
588C24D4×D1111yescharacteristic
589#41—228no—
590#41—444no—
591#41—444no—
592#41—444no—
593C2×Q8—24no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—28no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—42no—
604C2×Q8—42no—
605C2×Q8—44no—
606C2×Q8—44no—
607C2×Q8—44no—
608C2×Q8C2×C4×D1112yes—
609C2×Q8C2×C4×D1112yes—
610C2×Q8D4×D1112yes—
611C2×Q8#434112yes—
612C2×D4—114no—
613C2×D4—112no—
614C2×D4—224no—
615C2×D4—222no—
616C2×D4—222no—
617C2×D4—224no—
618C2×D4—221no—
619C2×D4—221no—
620C2×D4—221no—
621C2×D4—221no—
622C2×D4—221no—
623C2×D4—442no—
624C2×D4—442no—
625C2×D4—442no—
626C2×D4—442no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—24no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—111no—
639C22×C4—111no—
640C22×C4—111no—
641C22×C4—112no—
642C22×C4—112no—
643C22×C4—224no—
644C22×C4—221no—
645C22×C4—221no—
646C22×C4—221no—
647C22×C4—221no—
648C22×C4—221no—
649C22×C4—221no—
650C22×C4—221no—
651C22×C4—442no—
652C22×C4—442no—
653C22×C4—442no—
654C22×C4—442no—
655C22×C4—442no—
656C22×C4—442no—
657C22×C4—881no—
658C22×C4—881no—
659C22×C4C2×C4×D1112yes—
660C22×C4D4×D1111yescharacteristic
661C22×C4D4×D1112yes—
662C22×C4C23×D1111yescharacteristic
663M16—444no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—112no—
671C2×C8—221no—
672C2×C8—221no—
673C2×C8—221no—
674C2×C8—221no—
675C2×C8—221no—
676C2×C8—444no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—114no—
682C4⋊C4—112no—
683C4⋊C4—112no—
684C4⋊C4—224no—
685C4⋊C4—224no—
686C4⋊C4—221no—
687C4⋊C4—221no—
688C4⋊C4—221no—
689C4⋊C4—221no—
690C4⋊C4—442no—
691C4⋊C4—442no—
692C4⋊C4—442no—
693C4⋊C4—881no—
694C22⋊C4—42no—
695C22⋊C4—114no—
696C22⋊C4—114no—
697C22⋊C4—224no—
698C22⋊C4—224no—
699C22⋊C4—224no—
700C22⋊C4—224no—
701C22⋊C4—442no—
702C42—112no—
703C42—112no—
704C42—224no—
705C42—442no—
706C11#2242111yescharacteristic, complemented, Sylow
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—112no—
712C23—221no—
713C23—221no—
714C23—221no—
715C23—221no—
716C23—221no—
717C23—221no—
718C23—222no—
719C23—441no—
720C23—441no—
721C23—441no—
722C23—441no—
723C23—441no—
724C23—441no—
725C23C22⋊C4×D1112yes—
726C23#6696712yes—
727C23#6697112yes—
728C23C2×D4×D1111yescharacteristic
729Q8—22no—
730Q8—22no—
731Q8—22no—
732Q8—22no—
733Q8—22no—
734Q8—48no—
735Q8—41no—
736Q8—41no—
737Q8(C22⋊D11)⋊C414yescomplemented
738D4—228no—
739D4—222no—
740D4—222no—
741D4—448no—
742D4—448no—
743D4—441no—
744D4—441no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—48no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—112no—
765C2×C4—112no—
766C2×C4—112no—
767C2×C4—221no—
768C2×C4—221no—
769C2×C4—221no—
770C2×C4—221no—
771C2×C4—221no—
772C2×C4—221no—
773C2×C4—222no—
774C2×C4—222no—
775C2×C4—222no—
776C2×C4—222no—
777C2×C4—222no—
778C2×C4—222no—
779C2×C4—448no—
780C2×C4—441no—
781C2×C4—441no—
782C2×C4—441no—
783C2×C4—441no—
784C2×C4—441no—
785C2×C4—441no—
786C2×C4—441no—
787C2×C4—884no—
788C2×C4—884no—
789C2×C4C22⋊C4×D1112yes—
790C2×C4C22×C4×D1111yescharacteristic
791C2×C4C2×D4×D1111yescharacteristic
792C2×C4C2×D4×D1111yescharacteristic
793C2×C4C2×#434111yescharacteristic
794C2×C4#6703711yescharacteristic
795C2×C4#6703711yescharacteristic
796C8—41no—
797C8—41no—
798C8—222no—
799C8—441no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—222no—
807C22—222no—
808C22—222no—
809C22—441no—
810C22—441no—
811C22—441no—
812C22—441no—
813C22—442no—
814C22—442no—
815C22—442no—
816C22—881no—
817C22—881no—
818C22—881no—
819C22—881no—
820C22#1062241614yescomplemented
821C22C2×C22⋊C4×D1111yescharacteristic
822C22#1062312111yescharacteristic
823C22#1062312211yescharacteristic
824C22C2×#6696711yescharacteristic
825C22C2×#6697111yescharacteristic
826C22#1062330911yescharacteristic
827C22#1062331011yescharacteristic
828C4—22no—
829C4—24no—
830C4—42no—
831C4—81no—
832C4—81no—
833C4—222no—
834C4—222no—
835C4—222no—
836C4—442no—
837C4—442no—
838C4—881no—
839C4C2×(C22⋊D11)⋊C411yescharacteristic
840C4#1062301711yescharacteristic
841C4#1062312111yescharacteristic
842C4#1062312211yescharacteristic
843C2—24no—
844C2—442no—
845C2—882no—
846C2#1307143211yescharacteristic
847C2C2×#1062241611yescharacteristic
848C2#1307714811yescharacteristic
849C2#1308010411yescharacteristic
850C2#1308019011yescharacteristic
851C2#1308061111yescharacteristic
852C2#1308073111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1787C2
socleC23×C11C22×D4
prime radicalC2×#10623348C2
cosocleC22×C4×C11C24
hypercenter#1787D11
hypocenterC11#22421
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
2. C2×#10622343C2semidirect
3. C2×#10622416C2semidirect
4. C22×#66899C2semidirect
5. #13071512C2semidirect
6. #13069545C2semidirect
7. #13069429C2semidirect
8. #13069046C2semidirect
9. #13069042C2semidirect
10. #13068931C2semidirect
11. #13068920C2semidirect
12. #13068619C2semidirect
13. #13068555C2semidirect
14. #13068448C2semidirect
15. C11×#1787C2semidirect
19. #10623348C4semidirect
70. C22×Q8×C11C2×C4semidirect
83. C2×#4343C2×C4semidirect
97. #67000C2×C4semidirect
100. #66999C2×C4semidirect
102. Q8×Dic11C2×C4semidirect
105. #66983C2×C4semidirect
150. #66899D4semidirect
294. #1787D11semidirect
326. Q8×C11C4×D4semidirect
443. C22×C11#417semidirect
492. C22×Q8C4×D11semidirect
706. C11#22421semidirect
737. Q8(C22⋊D11)⋊C4semidirect
820. C22#10622416semidirect

Maximal subgroups

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

subgroupindex
C2×#106233482
C2×#106223432
C2×#106224162
C22×#668992
#130715122
#130695452
#130694292
#130690462
#130690422
#130689312
#130689202
#130686192
#130685552
#130684482
C11×#17872
#2242111