Finite Group Databasebeta

← #14769360

Subgroups — #14769360

Order 2816.

1458 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623083C211yesmaximal, characteristic
2C2×#10622733C211yesmaximal, characteristic, complemented
3C2×#10622726C211yesmaximal, characteristic, complemented
4#13071565C211yesmaximal, characteristic, complemented
5#13069546C211yesmaximal, characteristic, complemented
6#13069432C211yesmaximal, characteristic, complemented
7#13069054C211yesmaximal, characteristic, complemented
8#13069039C211yesmaximal, characteristic, complemented
9#13068936C211yesmaximal, characteristic, complemented
10#13068926C211yesmaximal, characteristic, complemented
11#13068622C211yesmaximal, characteristic, complemented
12#13068557C211yesmaximal, characteristic, complemented
13#13068552C211yesmaximal, characteristic, complemented
14#13068447C211yesmaximal, characteristic, complemented
15C2×C11×#435C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×#66992—21no—
22C2×#66983C2211yescharacteristic
23C2×#66979C2211yescharacteristic
24C2×#66979C2211yescharacteristic
25C2×#66977C2211yescharacteristic
26#10623083—24no—
27#10623083C418yescomplemented
28C2×#66949—21no—
29C2×#66938—21no—
30C2×(C22⋊D11)⋊C4—21no—
31C2×#66928C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C11×#435—24no—
34C2×C11×C4⋊C8C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×C11×#97C2211yescharacteristic
38#10622834—21no—
39#10622825C2211yescharacteristic
40#10622825C2211yescharacteristic
41#10622733—24no—
42#10622726—24no—
43C2×#66885C2211yescharacteristic
44C2×#66885C2211yescharacteristic
45C2×#66885C2211yescharacteristic
46C2×#66885C2211yescharacteristic
47C2×#66880C2211yescharacteristic
48C2×#66880C2211yescharacteristic
49C2×#66880C2211yescharacteristic
50C2×#66880C2211yescharacteristic
51C2×#66880C2211yescharacteristic
52C2×#66880C2211yescharacteristic
53C2×#66880C2211yescharacteristic
54C2×#66880C2211yescharacteristic
55C4⋊C4×Dic11—21no—
56#10622564—21no—
57#10622564—21no—
58#10622548C2211yescharacteristic
59C4×C4⋊Dic11C2211yescharacteristic
60#10622189C2211yescharacteristic
61#10622189C2211yescharacteristic
62#10622189C2211yescharacteristic
63#10622189C2211yescharacteristic
64C22×D4×C11D411yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—21no—
68C22×C22⋊D11—21no—
69C23×Dic11—21no—
70C2×#4339—22no—
71C2×#4339—22no—
72C2×#4339—22no—
73C2×#4339—41no—
74C2×#4339—41no—
75C2×#4339C2×C414yes—
76C22×D44C2311yescharacteristic
77C22×C4×D11—21no—
78C22×Dic22—22no—
79C22×Dic22—22no—
80C22×Dic22—21no—
81C22×Dic22—22no—
82C22×Dic22—41no—
83C22×Dic22—41no—
84C22×Dic22C2×C414yes—
85C22×Dic22C2311yescharacteristic
86C22×Dic22C2311yescharacteristic
87C2×C11×M16—22no—
88C2×C11×M16—22no—
89C2×C11×M16—41no—
90C22×C8×C11—22no—
91C22×C8×C11—22no—
92C22×C8×C11—41no—
93C22×C8×C11C2311yescharacteristic
94C22×C8×C11C2311yescharacteristic
95C22×C8×C11C2311yescharacteristic
96C22×C8×C11C2311yescharacteristic
97C4×D4×C11C2×C414yes—
98C4×D4×C11D414yes—
99C2×C11×C4⋊C4D411yescharacteristic
100C2×C11×C22⋊C4D411yescharacteristic
101C2×C11×C22⋊C4D411yescharacteristic
102C2×C42×C11C2311yescharacteristic
103C2×C22⋊Dic11—21no—
104C2×C22⋊Dic11—21no—
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11—21no—
107C2×C22⋊Dic11—21no—
108#66992—28no—
109#66983—22no—
110#66983C2×C414yes—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114#66979—22no—
115#66979—22no—
116#66979—41no—
117#66979—41no—
118C2×C4⋊Dic11—21no—
119C2×C4⋊Dic11—21no—
120C2×C4⋊Dic11C2311yescharacteristic
121C2×C4⋊Dic11C2311yescharacteristic
122C2×C4⋊Dic11C2311yescharacteristic
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125#66977—22no—
126#66977C2×C414yes—
127C2×Dic11⋊C4—21no—
128C2×Dic11⋊C4—21no—
129C2×C4×Dic11—21no—
130C2×C4×Dic11—21no—
131C2×C4×Dic11—21no—
132C2×C4×Dic11—21no—
133#66949—28no—
134#66938—28no—
135(C22⋊D11)⋊C4—28no—
136#66928—22no—
137#66928C2×C414yes—
138C4×Dic22—22no—
139C4×Dic22C2×C414yes—
140C11×C4⋊C8—22no—
141C11×C22⋊C8—22no—
142C11×C22⋊C8—22no—
143C11×#97—22no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146C11⋊#95—21no—
147#66885—22no—
148#66885—22no—
149#66885—41no—
150#66885—41no—
151#66880—22no—
152#66880—22no—
153#66880—22no—
154#66880—22no—
155#66880—22no—
156#66880—41no—
157#66880—41no—
158#66880D414yescomplemented
159#22426—111nomaximal, Sylow
160C24×C11C2×D411yescharacteristic
161C24×C11C2×D411yescharacteristic
162C23×D11—21no—
163C2×D4×C11—41no—
164C2×D4×C11—41no—
165C2×D4×C11C22⋊C414yes—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11C22×C412yes—
175C22×C4×C11C22×C412yes—
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D412yes—
181C22×C4×C11C2×D412yes—
182C22×C4×C11C2411yescharacteristic
183C2×C22⋊D11—24no—
184C2×C22⋊D11—24no—
185C2×C22⋊D11—42no—
186C2×C22⋊D11—42no—
187C2×C22⋊D11—42no—
188C2×C22⋊D11—42no—
189C22×Dic11—24no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11—42no—
198C22×Dic11—42no—
199#4339—28no—
200#4339—44no—
201#4339—44no—
202#4339—44no—
203C2×D44—21no—
204C2×D44—21no—
205C2×D44—21no—
206C2×D44—21no—
207C2×D44—21no—
208C2×D44C22×C412yes—
209C2×C4×D11—24no—
210C2×C4×D11—42no—
211C2×C4×D11—42no—
212C2×Dic22—28no—
213C2×Dic22—24no—
214C2×Dic22—21no—
215C2×Dic22—21no—
216C2×Dic22—21no—
217C2×Dic22—21no—
218C2×Dic22—21no—
219C2×Dic22—21no—
220C2×Dic22—21no—
221C2×Dic22—21no—
222C2×Dic22—44no—
223C2×Dic22—44no—
224C2×Dic22—44no—
225C2×Dic22—42no—
226C2×Dic22—42no—
227C2×Dic22C22×C412yes—
228C2×Dic22C22×C412yes—
229C2×Dic22C2×D412yes—
230C2×Dic22#4112yes—
231C11×M16—44no—
232C2×C8×C11—21no—
233C2×C8×C11—21no—
234C2×C8×C11—21no—
235C2×C8×C11—21no—
236C2×C8×C11—21no—
237C2×C8×C11—21no—
238C2×C8×C11—21no—
239C2×C8×C11—21no—
240C2×C8×C11—21no—
241C2×C8×C11—21no—
242C2×C8×C11—21no—
243C2×C8×C11—44no—
244C2×C8×C11C2×D412yes—
245C11×C4⋊C4C22⋊C414yes—
246C11×C22⋊C4C22⋊C414yes—
247C11×C22⋊C4C22⋊C414yes—
248C42×C11C22×C412yes—
249C42×C11C2×D412yes—
250C22⋊Dic11—24no—
251C22⋊Dic11—42no—
252C22⋊Dic11—42no—
253C22⋊Dic11—81no—
254C22⋊Dic11—81no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—24no—
258C4⋊Dic11—21no—
259C4⋊Dic11—21no—
260C4⋊Dic11—21no—
261C4⋊Dic11—21no—
262C4⋊Dic11—21no—
263C4⋊Dic11—21no—
264C4⋊Dic11—21no—
265C4⋊Dic11—21no—
266C4⋊Dic11—42no—
267C4⋊Dic11—81no—
268C4⋊Dic11C22×C412yes—
269C4⋊Dic11C2×D412yes—
270Dic11⋊C4—24no—
271Dic11⋊C4—24no—
272C4×Dic11—24no—
273C4×Dic11—42no—
274C4×Dic11—42no—
275C4×Dic11—42no—
276C2×#548—111no—
277C2×#435D1111yescharacteristic, complemented
278C2×#419—111no—
279C2×#416—111no—
280#2354—111no—
281#1983—111no—
282#1959—111no—
283#1895—111no—
284#1892—111no—
285#1875—111no—
286#1873—111no—
287#1803—111no—
288#1788—111no—
289#1787—111no—
290#1763—111no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11C2×C22⋊C412yes—
304C23×C11C2×C22⋊C412yes—
305C23×C11C22×D411yescharacteristic
306C22×D11—22no—
307C22×D11—41no—
308C22×D11—41no—
309C22×D11—41no—
310C22×D11—41no—
311C22×D11—41no—
312C22×D11—41no—
313D4×C11—44no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11C2×C22⋊C412yes—
331C2×C4×C11C2×C22⋊C412yes—
332C2×C4×C11C2×C22⋊C412yes—
333C2×C4×C11C2×C22⋊C412yes—
334C2×C4×C11C23×C411yescharacteristic
335C2×C4×C11C22×D411yescharacteristic
336C2×C4×C11C22×D411yescharacteristic
337C2×C4×C11C2×#4111yescharacteristic
338C2×C4×C11H(5,𝔽2)11yescharacteristic
339C2×C4×C11H(5,𝔽2)11yescharacteristic
340C22⋊D11—48no—
341C22⋊D11—48no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—48no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355C2×Dic11—41no—
356C2×Dic11—41no—
357C2×Dic11—41no—
358C2×Dic11—41no—
359C2×Dic11—41no—
360C2×Dic11—41no—
361C2×Dic11—41no—
362C2×Dic11—41no—
363C2×Dic11—41no—
364D44—22no—
365D44—22no—
366D44—41no—
367D44—41no—
368C4×D11—48no—
369Dic22—22no—
370Dic22—22no—
371Dic22—22no—
372Dic22—22no—
373Dic22—22no—
374Dic22—48no—
375Dic22—41no—
376Dic22—41no—
377Dic22C4×D414yes—
378C8×C11—22no—
379C8×C11—41no—
380C8×C11—41no—
381C8×C11—41no—
382C22×#41—111no—
383C23×Q8—111no—
384C22×M16C2×D1111yescharacteristic
385C23×C8C2×D1111yescharacteristic
386#548—118no—
387#548—224no—
388C2×#124—111no—
389C2×#124—221no—
390C2×C22⋊Q8—111no—
391C2×C22⋊Q8—221no—
392C2×#121—111no—
393C2×#121—221no—
394C2×C4×Q8—111no—
395C2×C4×D4—221no—
396C2×C4×D4C2×D1111yescharacteristic
397C2×#117—111no—
398C2×#117—111no—
399#435—24no—
400C2×C4⋊C8C2×D1111yescharacteristic
401#419—224no—
402#416—224no—
403C2×#103—111no—
404C2×#103—111no—
405C2×#103—111no—
406C2×#103—111no—
407C2×#103—111no—
408C2×#103—111no—
409C2×#103—111no—
410C2×#103—111no—
411C2×#102—111no—
412C2×#102—111no—
413C2×#102—111no—
414C2×#102—111no—
415C2×C22⋊C8C2×D1111yescharacteristic
416C2×C22⋊C8C2×D1111yescharacteristic
417C2×#97C2×D1111yescharacteristic
418#390—221no—
419#388—221no—
420#388—221no—
421#384—111no—
422#380—111no—
423#380—111no—
424C4×C4⋊C4—111no—
425C4×C4⋊C4—221no—
426#340—111no—
427#340—111no—
428#340—111no—
429#340—111no—
430C22×C11—22no—
431C22×C11—22no—
432C22×C11—22no—
433C22×C11—22no—
434C22×C11—22no—
435C22×C11—22no—
436C22×C11—41no—
437C22×C11—41no—
438C22×C11—41no—
439C22×C11—41no—
440C22×C11—41no—
441C22×C11—41no—
442C22×C11—41no—
443C22×C11—41no—
444C22×C11C22×C22⋊C411yescharacteristic
445C22×C11D4211yescharacteristic
446C22×C11#54611yescharacteristic
447C22×C11#57511yescharacteristic
448C22×C11#57511yescharacteristic
449C22×C11#57711yescharacteristic
450C22×C11#57811yescharacteristic
451C2×D11—42no—
452C2×D11—42no—
453C2×D11—42no—
454C2×D11—81no—
455C2×D11—81no—
456C2×D11—81no—
457C2×D11—81no—
458C4×C11—22no—
459C4×C11—22no—
460C4×C11—22no—
461C4×C11—22no—
462C4×C11C2×C4×D411yescharacteristic
463C4×C11#51811yescharacteristic
464C4×C11D4211yescharacteristic
465C4×C11#54611yescharacteristic
466Dic11—24no—
467Dic11—42no—
468Dic11—42no—
469Dic11—42no—
470Dic11—81no—
471Dic11—81no—
472Dic11—81no—
473C2×#41—114no—
474C2×#41—222no—
475C2×#41—222no—
476C2×#41—222no—
477C2×#41—441no—
478C2×#41—441no—
479C22×Q8—114no—
480C22×Q8—111no—
481C22×Q8—111no—
482C22×Q8—222no—
483C22×Q8—222no—
484C22×Q8—221no—
485C22×Q8—222no—
486C22×Q8—441no—
487C22×Q8—441no—
488C22×D4—111no—
489C22×D4—221no—
490C22×D4—221no—
491C22×D4D4411yescharacteristic
492C23×C4—221no—
493C23×C4—221no—
494C23×C4C22×D1111yescharacteristic
495C23×C4C22×D1111yescharacteristic
496C2×M16—22no—
497C2×M16—22no—
498C2×M16—41no—
499C22×C8—22no—
500C22×C8—22no—
501C22×C8—41no—
502C22×C8C22×D1111yescharacteristic
503C22×C8C22×D1111yescharacteristic
504C22×C8C22×D1111yescharacteristic
505C22×C8C22×D1111yescharacteristic
506#124—114no—
507#124—228no—
508#124—222no—
509C22⋊Q8—114no—
510C22⋊Q8—222no—
511C22⋊Q8—228no—
512#121—114no—
513#121—228no—
514#121—222no—
515C4×Q8—114no—
516C4×Q8—222no—
517C4×D4—228no—
518C4×D4C4×D1114yes—
519C4×D4C22⋊D1114yes—
520#117—222no—
521#117—222no—
522#117—441no—
523#117—441no—
524C2×C4⋊C4—111no—
525C2×C4⋊C4—111no—
526C2×C4⋊C4—111no—
527C2×C4⋊C4—111no—
528C2×C4⋊C4—111no—
529C2×C4⋊C4—221no—
530C2×C4⋊C4—221no—
531C2×C4⋊C4—221no—
532C2×C4⋊C4—221no—
533C2×C4⋊C4D4411yescharacteristic
534C2×C22⋊C4—221no—
535C2×C22⋊C4—221no—
536C2×C22⋊C4—221no—
537C2×C22⋊C4—221no—
538C2×C22⋊C4—221no—
539C2×C22⋊C4—221no—
540C2×C22⋊C4—221no—
541C2×C22⋊C4—221no—
542C2×C22⋊C4D4411yescharacteristic
543C2×C22⋊C4D4411yescharacteristic
544C2×C42—221no—
545C2×C42—221no—
546C2×C42—221no—
547C2×C42—221no—
548C2×C42C22×D1111yescharacteristic
549C4⋊C8—22no—
550#103—114no—
551#103—222no—
552#103—222no—
553#103—222no—
554#103—222no—
555#103—222no—
556#103—441no—
557#103—441no—
558#102—222no—
559#102—222no—
560#102—441no—
561#102—441no—
562C22⋊C8—22no—
563C22⋊C8—22no—
564#97—22no—
565#95—221no—
566#95—221no—
567#95—221no—
568C2×C11—42no—
569C2×C11—42no—
570C2×C11D4×C22⋊C411yescharacteristic
571C2×C11#289611yescharacteristic
572C2×C11#289811yescharacteristic
573C2×C11#326911yescharacteristic
574C2×C11#327111yescharacteristic
575C2×C11#331311yescharacteristic
576C2×C11#332111yescharacteristic
577D11—82no—
578C24—221no—
579C24C2×D4411yescharacteristic
580C24C2×D4411yescharacteristic
581#41—228no—
582#41—444no—
583#41—444no—
584#41—444no—
585C2×Q8—112no—
586C2×Q8—112no—
587C2×Q8—112no—
588C2×Q8—112no—
589C2×Q8—228no—
590C2×Q8—224no—
591C2×Q8—221no—
592C2×Q8—221no—
593C2×Q8—221no—
594C2×Q8—221no—
595C2×Q8—221no—
596C2×Q8—221no—
597C2×Q8—221no—
598C2×Q8—221no—
599C2×Q8—442no—
600C2×Q8—442no—
601C2×Q8—444no—
602C2×Q8—444no—
603C2×Q8—444no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—112no—
607C2×D4—224no—
608C2×D4—224no—
609C2×D4—221no—
610C2×D4—221no—
611C2×D4—221no—
612C2×D4—221no—
613C2×D4—221no—
614C2×D4—442no—
615C2×D4—442no—
616C2×D4—442no—
617C2×D4—442no—
618C2×D4(C2×D11)⋊C414yes—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—221no—
628C22×C4—224no—
629C22×C4—221no—
630C22×C4—221no—
631C22×C4—221no—
632C22×C4—224no—
633C22×C4—221no—
634C22×C4—221no—
635C22×C4—221no—
636C22×C4—442no—
637C22×C4—442no—
638C22×C4—442no—
639C22×C4—442no—
640C22×C4C2×C4×D1112yes—
641C22×C4C2×C4×D1112yes—
642C22×C4C2×D4411yescharacteristic
643C22×C4C2×D4411yescharacteristic
644C22×C4C2×D4411yescharacteristic
645C22×C4C2×D4411yescharacteristic
646C22×C4C2×C22⋊D1112yes—
647C22×C4C2×C22⋊D1112yes—
648C22×C4C23×D1111yescharacteristic
649M16—44no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—44no—
662C2×C8D4×D1112yes—
663C4⋊C4—112no—
664C4⋊C4—112no—
665C4⋊C4—224no—
666C4⋊C4—224no—
667C4⋊C4—221no—
668C4⋊C4—221no—
669C4⋊C4—221no—
670C4⋊C4—221no—
671C4⋊C4—221no—
672C4⋊C4—221no—
673C4⋊C4—221no—
674C4⋊C4—221no—
675C4⋊C4—442no—
676C4⋊C4—881no—
677C4⋊C4(C2×D11)⋊C414yes—
678C22⋊C4—224no—
679C22⋊C4—224no—
680C22⋊C4—224no—
681C22⋊C4—224no—
682C22⋊C4—442no—
683C22⋊C4—442no—
684C22⋊C4—881no—
685C22⋊C4—881no—
686C22⋊C4(C2×D11)⋊C414yes—
687C22⋊C4(C2×D11)⋊C414yes—
688C42—224no—
689C42—442no—
690C42—442no—
691C42—442no—
692C42C2×C4×D1112yes—
693C42C2×C22⋊D1112yes—
694C11#2242611yescharacteristic, complemented, Sylow
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—222no—
708C23—441no—
709C23—441no—
710C23—441no—
711C23—441no—
712C23—441no—
713C23—441no—
714C23C2×(C2×D11)⋊C412yes—
715C23C2×(C2×D11)⋊C412yes—
716C23C22×D4411yescharacteristic
717Q8—114no—
718Q8—222no—
719Q8—222no—
720Q8—222no—
721Q8—222no—
722Q8—222no—
723Q8—448no—
724Q8—441no—
725Q8—441no—
726D4—44no—
727D4—222no—
728D4—222no—
729D4—448no—
730D4—448no—
731D4—441no—
732D4—441no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—448no—
756C2×C4—448no—
757C2×C4—441no—
758C2×C4—441no—
759C2×C4—441no—
760C2×C4—441no—
761C2×C4—441no—
762C2×C4—441no—
763C2×C4—441no—
764C2×C4—441no—
765C2×C4—441no—
766C2×C4—441no—
767C2×C4—441no—
768C2×C4—441no—
769C2×C4—441no—
770C2×C4—441no—
771C2×C4—441no—
772C2×C4C2×(C2×D11)⋊C412yes—
773C2×C4C2×(C2×D11)⋊C412yes—
774C2×C4C2×(C2×D11)⋊C412yes—
775C2×C4C2×(C2×D11)⋊C412yes—
776C2×C4C22×C4×D1111yescharacteristic
777C2×C4C2×D4×D1111yescharacteristic
778C2×C4#6703711yescharacteristic
779C2×C4#41×D1111yescharacteristic
780C2×C4#6704211yescharacteristic
781C2×C4C22×C22⋊D1111yescharacteristic
782C8—22no—
783C8—41no—
784C8—41no—
785C8—41no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—442no—
801C22—442no—
802C22—442no—
803C22—881no—
804C22—881no—
805C22—881no—
806C22—881no—
807C22D4×D4411yescharacteristic
808C22#1062308511yescharacteristic
809C22#1062327911yescharacteristic
810C22#1062327911yescharacteristic
811C22#1062328211yescharacteristic
812C22#1062328411yescharacteristic
813C22C22×(C2×D11)⋊C411yescharacteristic
814C4—22no—
815C4—22no—
816C4—22no—
817C4—22no—
818C4—224no—
819C4—442no—
820C4—442no—
821C4—442no—
822C4—881no—
823C4—881no—
824C4—881no—
825C4C4×D4×D1111yescharacteristic
826C4#1062307611yescharacteristic
827C4D4×C22⋊D1111yescharacteristic
828C4#1062336011yescharacteristic
829C2—42no—
830C2—42no—
831C2—882no—
832C2D4×(C2×D11)⋊C411yescharacteristic
833C2#1307713611yescharacteristic
834C2#1307715011yescharacteristic
835C2#1308017611yescharacteristic
836C2#1308020611yescharacteristic
837C2#1308068411yescharacteristic
838C2#1308080411yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#435C2
socleC23×C11C22×D4
prime radicalC2×#10623083C2
cosocleC22×C4×C11C24
hypercenterC2×#435D11
hypocenterC11#22426
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×#10622733C2semidirect
3. C2×#10622726C2semidirect
4. #13071565C2semidirect
5. #13069546C2semidirect
6. #13069432C2semidirect
7. #13069054C2semidirect
8. #13069039C2semidirect
9. #13068936C2semidirect
10. #13068926C2semidirect
11. #13068622C2semidirect
12. #13068557C2semidirect
13. #13068552C2semidirect
14. #13068447C2semidirect
15. C2×C11×#435C2semidirect
27. #10623083C4semidirect
158. #66880D4semidirect
277. C2×#435D11semidirect
694. C11#22426semidirect

Maximal subgroups

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

subgroupindex
C2×#106230832
C2×#106227332
C2×#106227262
#130715652
#130695462
#130694322
#130690542
#130690392
#130689362
#130689262
#130686222
#130685572
#130685522
#130684472
C2×C11×#4352
#2242611