Finite Group Databasebeta

← C2×#13080590 #15630409

Subgroups — C2×#13080590 #15630409

Order 2816.

2190 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623061C211yesmaximal, characteristic, complemented
2C2×#10623162C211yesmaximal, characteristic, complemented
3#13080590C2116yesmaximal, direct product factor
4C2×#10622410C211yesmaximal, characteristic, complemented
5C2×#10622475C211yesmaximal, characteristic, complemented
6C2×#10622504C211yesmaximal, characteristic, complemented
7C2×#10622499C211yesmaximal, characteristic, complemented
8C2×#10622661C211yesmaximal, characteristic, complemented
9C2×#10622431C211yesmaximal, characteristic, complemented
10C2×#10622424C211yesmaximal, characteristic, complemented
11C2×#10622347C211yesmaximal, characteristic, complemented
12C2×#10622482C211yesmaximal, characteristic, complemented
13C2×#10622343C211yesmaximal, characteristic, complemented
14C2×#10622416C211yesmaximal, characteristic, complemented
15C2×#10622615C211yesmaximal, characteristic, complemented
16C2×C11×#485C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C22×#4339C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C2×#66997C2211yescharacteristic
22C22×#4325C2211yescharacteristic
23C2×#66983C2211yescharacteristic
24C2×C4×C22⋊D11C2211yescharacteristic
25C23×C11⋊C8C2211yescharacteristic
26C22×D88C2211yescharacteristic
27C22×#4314C2211yescharacteristic
28C22×#4313C2211yescharacteristic
29#10623162—24no—
30#10623162C2218yescomplemented
31#10623061—24no—
32#10623061C2218yescomplemented
33C2×#66950C2211yescharacteristic
34C2×#66948C2211yescharacteristic
35C2×#66947—21no—
36C2×#66946C2211yescharacteristic
37C2×#66946C2211yescharacteristic
38C2×C4⋊C4×D11—21no—
39C2×C4⋊C4×D11C2211yescharacteristic
40C2×#66943C2211yescharacteristic
41C2×#66937—21no—
42C2×#66937—21no—
43C2×#66936—21no—
44C2×#66936—21no—
45C2×#66929—21no—
46C2×C4×D44—21no—
47C11×#485C2218yescomplemented
48C2×C11×#107C2211yescharacteristic
49C2×C11×#106C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic
51C2×C11×#103C2211yescharacteristic
52C2×C11×C22⋊C8C2211yescharacteristic
53C2×#66899C2211yescharacteristic
54C2×#66885C2211yescharacteristic
55C2×(C2×D11)⋊C8C2211yescharacteristic
56C2×#66880C2211yescharacteristic
57C2×#66879C2211yescharacteristic
58C2×Dic11⋊C8C2211yescharacteristic
59#10622661C2218yescomplemented
60#10622615C2218yescomplemented
61C2×#66874C2211yescharacteristic
62C2×#66874C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66873C2211yescharacteristic
65C2×#66873C2211yescharacteristic
66C2×#66872C2211yescharacteristic
67#10622504C2218yescomplemented
68#10622499C2218yescomplemented
69#10622482C2218yescomplemented
70#10622475C2218yescomplemented
71#10622431C2218yescomplemented
72#10622424C2218yescomplemented
73#10622416C2218yescomplemented
74#10622410C2218yescomplemented
75#10622347C2218yescomplemented
76#10622343C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C22×C22⋊D11—21no—
80C22×C22⋊D11—21no—
81C22×C22⋊D11D411yescharacteristic
82C2×#4343—22no—
83C2×#4343—24no—
84C2×#4343—42no—
85C2×#4343C2314yes—
86C2×#4339—22no—
87C2×#4339—24no—
88C2×#4339—42no—
89C2×#4339C2314yes—
90C22×D44—21no—
91C22×D44—21no—
92C22×D44C2311yescharacteristic
93C22×D44C2311yescharacteristic
94C22×C4×D11—21no—
95C22×C4×D11—21no—
96C22×C4×D11—21no—
97C22×C4×D11—21no—
98C22×C4×D11—21no—
99C22×C4×D11C2311yescharacteristic
100C22×Dic22C2311yescharacteristic
101C22×C8×C11C2311yescharacteristic
102C22×C8×C11C2311yescharacteristic
103C11×C22⋊Q8—22no—
104C11×C22⋊Q8C2314yes—
105C11×#117—22no—
106C11×#117C2314yes—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C42×C11—21no—
114C2×C22⋊Dic11D411yescharacteristic
115#66997—22no—
116#66997C2314yes—
117C2×#4325—42no—
118C2×#4325C2314yes—
119#66983—22no—
120#66983C2314yes—
121C4×C22⋊D11D414yes—
122C4×C22⋊D11C2314yes—
123C2×(C2×D11)⋊C4—21no—
124C2×(C2×D11)⋊C4—21no—
125C2×(C2×D11)⋊C4—21no—
126C2×(C2×D11)⋊C4—21no—
127C2×(C2×D11)⋊C4—21no—
128C2×(C2×D11)⋊C4D411yescharacteristic
129C2×C4⋊Dic11—21no—
130C2×C4⋊Dic11—21no—
131C2×C4⋊Dic11C2311yescharacteristic
132C2×Dic11⋊C4—21no—
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4—21no—
135C2×Dic11⋊C4—21no—
136C2×Dic11⋊C4D411yescharacteristic
137C2×C4×Dic11C2311yescharacteristic
138C22×C11⋊C8—42no—
139C22×C11⋊C8C2311yescharacteristic
140C22×C11⋊C8C2311yescharacteristic
141C22×C11⋊C8C2314yes—
142C2×D88—24no—
143C2×D88C2314yes—
144C2×#4314—42no—
145C2×#4314C2314yes—
146C2×#4313—42no—
147C2×#4313C2314yes—
148#66950—22no—
149#66950C2314yes—
150#66948—22no—
151#66948C2314yes—
152#66947—28no—
153#66946—22no—
154#66946—22no—
155#66946C2314yes—
156#66946C2314yes—
157C4⋊C4×D11—22no—
158C4⋊C4×D11—28no—
159C4⋊C4×D11C2314yes—
160#66943—22no—
161#66943C2314yes—
162#66937—28no—
163#66937—28no—
164#66936—28no—
165#66936—28no—
166#66929—28no—
167C4×D44—28no—
168C11×#107C2314yes—
169C11×#106C2314yes—
170C11×#103C2314yes—
171C11×#103C2314yes—
172C11×C22⋊C8C2314yes—
173#66899C2314yes—
174#66885C2314yes—
175(C2×D11)⋊C8C2314yes—
176#66880C2314yes—
177#66879C2314yes—
178Dic11⋊C8C2314yes—
179#66874C2314yes—
180#66874C2314yes—
181#66873C2314yes—
182#66873C2314yes—
183#66873C2314yes—
184#66872C2314yes—
185C2×#3307—111nomaximal, Sylow
186C24×C11C2×D411yescharacteristic
187C23×D11—21no—
188C23×D11—21no—
189C23×D11C2×D411yescharacteristic
190C2×Q8×C11—21no—
191C2×Q8×C11—22no—
192C2×Q8×C11—22no—
193C2×Q8×C11C2412yes—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2×D412yes—
202C22×C4×C11C2412yes—
203C22×C4×C11C2411yescharacteristic
204C2×C22⋊D11—24no—
205C2×C22⋊D11—24no—
206C2×C22⋊D11—42no—
207C2×C22⋊D11—44no—
208C2×C22⋊D11—82no—
209C2×C22⋊D11C2×D414yes—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11C2×D411yescharacteristic
213C22×Dic11C2×D411yescharacteristic
214C22×Dic11C2×D411yescharacteristic
215#4343—28no—
216#4343—44no—
217#4343—48no—
218#4339—28no—
219#4339—44no—
220#4339—48no—
221C2×D44—24no—
222C2×D44—24no—
223C2×D44—21no—
224C2×D44—21no—
225C2×D44—22no—
226C2×D44—22no—
227C2×D44—22no—
228C2×D44—44no—
229C2×D44—44no—
230C2×D44#4114yes—
231C2×D44C2412yes—
232C2×D44C2412yes—
233C2×C4×D11—24no—
234C2×C4×D11—24no—
235C2×C4×D11—24no—
236C2×C4×D11—24no—
237C2×C4×D11—24no—
238C2×C4×D11—22no—
239C2×C4×D11—22no—
240C2×C4×D11—44no—
241C2×C4×D11—44no—
242C2×C4×D11—44no—
243C2×C4×D11—82no—
244C2×C4×D11—82no—
245C2×C4×D11C2×D412yes—
246C2×C4×D11C2412yes—
247C2×Dic22—21no—
248C2×Dic22—22no—
249C2×Dic22—22no—
250C2×Dic22C2412yes—
251C2×C8×C11—22no—
252C2×C8×C11—22no—
253C2×C8×C11C2412yes—
254C2×C8×C11C2412yes—
255C11×C4⋊C4—21no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4—24no—
258C11×C4⋊C4—21no—
259C11×C4⋊C4C2412yes—
260C11×C4⋊C4C2412yes—
261C11×C4⋊C4C2412yes—
262C11×C22⋊C4—24no—
263C11×C22⋊C4—24no—
264C42×C11—24no—
265C22⋊Dic11C2×D414yes—
266#4325—44no—
267(C2×D11)⋊C4—24no—
268(C2×D11)⋊C4—24no—
269(C2×D11)⋊C4—24no—
270(C2×D11)⋊C4—24no—
271(C2×D11)⋊C4—24no—
272(C2×D11)⋊C4C2×D414yes—
273C4⋊Dic11—24no—
274C4⋊Dic11—24no—
275C4⋊Dic11—21no—
276C4⋊Dic11C2412yes—
277Dic11⋊C4—24no—
278Dic11⋊C4—24no—
279Dic11⋊C4—24no—
280Dic11⋊C4—24no—
281Dic11⋊C4C2×D414yes—
282C4×Dic11C2×D412yes—
283C4×Dic11C2412yes—
284C2×C11⋊C8—22no—
285C2×C11⋊C8—22no—
286C2×C11⋊C8—44no—
287C2×C11⋊C8C2412yes—
288C2×C11⋊C8C2412yes—
289D88—28no—
290#4314—44no—
291#4313—44no—
292C2×#553—111no—
293C2×#547—111no—
294#3307—1116no—
295C2×#491—111no—
296C2×#485D1111yescharacteristic, complemented
297C2×#483—111no—
298C2×#478—111no—
299C2×#468—111no—
300C2×#465—111no—
301C2×#461—111no—
302C2×#449—111no—
303C2×#449—111no—
304C2×#442—111no—
305C2×#435—111no—
306C2×#417—111no—
307C2×#416—111no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11C22×D412yes—
312C23×C11C22×D411yescharacteristic
313C22×D11—22no—
314C22×D11—24no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—42no—
320C22×D11—42no—
321C22×D11—42no—
322C22×D11—42no—
323C22×D11—42no—
324C22×D11C22×D412yes—
325Q8×C11—22no—
326Q8×C11—22no—
327Q8×C11—42no—
328C2×C4×C11—22no—
329C2×C4×C11—24no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—42no—
337C2×C4×C11—42no—
338C2×C4×C11—42no—
339C2×C4×C11—42no—
340C2×C4×C11C22×D412yes—
341C2×C4×C11C22×D411yescharacteristic
342C2×C4×C11C2×#4112yes—
343C2×C4×C11H(5,𝔽2)12yes—
344C2×C4×C11C2511yescharacteristic
345C22⋊D11—44no—
346C22⋊D11—48no—
347C22⋊D11—84no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—42no—
354C2×Dic11—42no—
355C2×Dic11C22×D412yes—
356C2×Dic11C22×D412yes—
357C2×Dic11C22×D412yes—
358D44—24no—
359D44—22no—
360D44—22no—
361D44—22no—
362D44—48no—
363D44—48no—
364D44—42no—
365D44C2×#4114yes—
366C4×D11—24no—
367C4×D11—22no—
368C4×D11—22no—
369C4×D11—48no—
370C4×D11—48no—
371C4×D11—48no—
372C4×D11—84no—
373C4×D11—84no—
374Dic22—22no—
375Dic22—22no—
376Dic22—42no—
377C8×C11—22no—
378C8×C11—22no—
379C11⋊C8—22no—
380C11⋊C8—22no—
381C22×#41—111no—
382C22×#41—111no—
383C22×SD16—111no—
384C22×SD16—111no—
385C22×D8—111no—
386C22×M16—111no—
387C23×C8—111no—
388#553—118no—
389#553—224no—
390#547—118no—
391#547—224no—
392C2×C4⋊Q8—111no—
393C2×#126—221no—
394C2×#125—111no—
395C2×#123—221no—
396C2×#123—221no—
397C2×#123—221no—
398C2×C22⋊Q8—111no—
399C2×C22⋊Q8C2×D1111yescharacteristic
400C2×#121—111no—
401C2×#121—111no—
402C2×#121—221no—
403C2×#121—221no—
404C2×C4×D4—111no—
405C2×C4×D4—111no—
406C2×C4×D4—111no—
407C2×C4×D4—221no—
408C2×#117C2×D1111yescharacteristic
409C22×C4⋊C4—111no—
410C22×C4⋊C4—221no—
411#491—118no—
412#485C2×D1118yescomplemented
413#483—118no—
414#478—118no—
415#468—118no—
416#465—118no—
417#461—118no—
418#449—118no—
419#449—118no—
420#442—118no—
421#435—118no—
422C2×#107C2×D1111yescharacteristic
423C2×#106—111no—
424C2×#106C2×D1111yescharacteristic
425C2×C4⋊C8—111no—
426#417—118no—
427#416—118no—
428C2×#103—111no—
429C2×#103—111no—
430C2×#103—111no—
431C2×#103—111no—
432C2×#103C2×D1111yescharacteristic
433C2×#103C2×D1111yescharacteristic
434C2×#102—111no—
435C2×#102—111no—
436C2×#102—111no—
437C2×#102—111no—
438C2×C22⋊C8—111no—
439C2×C22⋊C8C2×D1111yescharacteristic
440C2×#97—111no—
441C22×C11—22no—
442C22×C11—22no—
443C22×C11—22no—
444C22×C11—44no—
445C22×C11#54612yes—
446C22×C11#57512yes—
447C22×C11#57712yes—
448C22×C11C23×D411yescharacteristic
449C2×D11—24no—
450C2×D11—22no—
451C2×D11—22no—
452C2×D11—22no—
453C2×D11—44no—
454C2×D11—48no—
455C2×D11—42no—
456C2×D11—42no—
457C2×D11—42no—
458C2×D11—42no—
459C2×D11—42no—
460C2×D11—84no—
461C4×C11—22no—
462C4×C11—42no—
463C4×C11—42no—
464C4×C11—42no—
465C4×C11—42no—
466C4×C11#54612yes—
467C4×C11C22×#4111yescharacteristic
468C4×C11C2×H(5,𝔽2)11yescharacteristic
469Dic11—22no—
470Dic11—22no—
471Dic11—22no—
472Dic11—42no—
473Dic11—42no—
474C2×#41—114no—
475C2×#41—114no—
476C2×#41—224no—
477C2×#41—222no—
478C2×#41—222no—
479C2×#41—224no—
480C2×#41—442no—
481C2×#41—442no—
482C22×Q8—111no—
483C22×Q8C22×D1111yescharacteristic
484C22×D4—111no—
485C22×D4—111no—
486C22×D4—111no—
487C22×D4—221no—
488C22×D4—221no—
489C22×D4—221no—
490C22×D4—221no—
491C23×C4—111no—
492C23×C4—221no—
493C23×C4—221no—
494C23×C4—221no—
495C23×C4—221no—
496C23×C4—221no—
497C23×C4C22×D1111yescharacteristic
498C2×SD16—114no—
499C2×SD16—114no—
500C2×SD16—442no—
501C2×SD16—442no—
502C2×D8—114no—
503C2×D8—224no—
504C2×M16—114no—
505C2×M16—442no—
506C22×C8—111no—
507C22×C8—111no—
508C22×C8—114no—
509C22×C8—442no—
510C22×C8C22×D1111yescharacteristic
511C22×C8C22×D1111yescharacteristic
512C4⋊Q8—114no—
513C4⋊Q8—222no—
514#126—228no—
515#125—114no—
516#125—222no—
517#123—228no—
518#123—228no—
519#123—228no—
520C22⋊Q8—22no—
521C22⋊Q8—114no—
522C22⋊Q8—222no—
523C22⋊Q8C22×D1114yes—
524#121—114no—
525#121—114no—
526#121—228no—
527#121—228no—
528#121—222no—
529#121—222no—
530C4×D4—114no—
531C4×D4—114no—
532C4×D4—114no—
533C4×D4—114no—
534C4×D4—228no—
535C4×D4—222no—
536C4×D4—222no—
537#117—22no—
538#117C22×D1114yes—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—111no—
541C2×C4⋊C4—111no—
542C2×C4⋊C4—114no—
543C2×C4⋊C4—228no—
544C2×C4⋊C4—222no—
545C2×C4⋊C4—221no—
546C2×C4⋊C4—221no—
547C2×C4⋊C4—221no—
548C2×C4⋊C4—221no—
549C2×C4⋊C4—221no—
550C2×C4⋊C4—221no—
551C2×C4⋊C4C22×D1111yescharacteristic
552C2×C4⋊C4C22×D1111yescharacteristic
553C2×C4⋊C4C22×D1111yescharacteristic
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—111no—
557C2×C22⋊C4—111no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C22⋊C4—221no—
561C2×C22⋊C4—221no—
562C2×C22⋊C4—221no—
563C2×C42—21no—
564C2×C42—111no—
565#107C22×D1114yes—
566#106—114no—
567#106C22×D1114yes—
568C4⋊C8—114no—
569#103—114no—
570#103—114no—
571#103—114no—
572#103—114no—
573#103C22×D1114yes—
574#103C22×D1114yes—
575#102—114no—
576#102—114no—
577#102—114no—
578#102—114no—
579C22⋊C8—114no—
580C22⋊C8C22×D1114yes—
581#97—114no—
582C2×C11—42no—
583C2×C11#330714yescomplemented
584C2×C11C2×#54611yescharacteristic
585C2×C11C2×#57511yescharacteristic
586C2×C11C2×#57711yescharacteristic
587D11—42no—
588D11—44no—
589D11—82no—
590C24—111no—
591C24—221no—
592C24—221no—
593C24D4×D1111yescharacteristic
594#41—228no—
595#41—228no—
596#41—444no—
597#41—448no—
598#41—444no—
599#41—448no—
600C2×Q8—21no—
601C2×Q8—22no—
602C2×Q8—22no—
603C2×Q8—112no—
604C2×Q8—221no—
605C2×Q8—222no—
606C2×Q8—222no—
607C2×Q8C23×D1112yes—
608C2×D4—114no—
609C2×D4—114no—
610C2×D4—112no—
611C2×D4—112no—
612C2×D4—224no—
613C2×D4—224no—
614C2×D4—224no—
615C2×D4—224no—
616C2×D4—221no—
617C2×D4—221no—
618C2×D4—222no—
619C2×D4—222no—
620C2×D4—222no—
621C2×D4—444no—
622C2×D4—444no—
623C2×D4—442no—
624C2×D4—444no—
625C2×D4—882no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—111no—
633C22×C4—111no—
634C22×C4—111no—
635C22×C4—112no—
636C22×C4—112no—
637C22×C4—224no—
638C22×C4—224no—
639C22×C4—224no—
640C22×C4—224no—
641C22×C4—222no—
642C22×C4—222no—
643C22×C4—221no—
644C22×C4—221no—
645C22×C4—224no—
646C22×C4—444no—
647C22×C4—444no—
648C22×C4—444no—
649C22×C4—882no—
650C22×C4—882no—
651C22×C4D4×D1112yes—
652C22×C4D4×D1111yescharacteristic
653C22×C4C23×D1112yes—
654C22×C4C23×D1111yescharacteristic
655SD16—444no—
656SD16—444no—
657D8—228no—
658M16—444no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—112no—
662C2×C8—112no—
663C2×C8—222no—
664C2×C8—222no—
665C2×C8—444no—
666C2×C8C23×D1112yes—
667C2×C8C23×D1112yes—
668C4⋊C4—24no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—114no—
673C4⋊C4—112no—
674C4⋊C4—224no—
675C4⋊C4—224no—
676C4⋊C4—224no—
677C4⋊C4—224no—
678C4⋊C4—224no—
679C4⋊C4—224no—
680C4⋊C4—221no—
681C4⋊C4C23×D1112yes—
682C4⋊C4C23×D1112yes—
683C4⋊C4C23×D1112yes—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—114no—
687C22⋊C4—114no—
688C22⋊C4—224no—
689C22⋊C4—224no—
690C22⋊C4—224no—
691C22⋊C4—224no—
692C22⋊C4—224no—
693C42—24no—
694C42—112no—
695C42—112no—
696C11C2×#330711yescharacteristic, complemented, Sylow
697C23—22no—
698C23—22no—
699C23—22no—
700C23—112no—
701C23—222no—
702C23—222no—
703C23—222no—
704C23—224no—
705C23—222no—
706C23—222no—
707C23—442no—
708C23—442no—
709C23—442no—
710C23—442no—
711C23—442no—
712C23C2×D4×D1112yes—
713C23C2×D4×D1111yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—222no—
718Q8—222no—
719Q8—442no—
720D4—114no—
721D4—224no—
722D4—222no—
723D4—222no—
724D4—222no—
725D4—448no—
726D4—448no—
727D4—444no—
728D4—448no—
729D4—442no—
730D4—884no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—112no—
744C2×C4—112no—
745C2×C4—112no—
746C2×C4—222no—
747C2×C4—222no—
748C2×C4—222no—
749C2×C4—224no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—448no—
755C2×C4—448no—
756C2×C4—448no—
757C2×C4—442no—
758C2×C4—442no—
759C2×C4—884no—
760C2×C4—884no—
761C2×C4C2×D4×D1112yes—
762C2×C4C2×D4×D1111yescharacteristic
763C2×C4#41×D1112yes—
764C2×C4#6704212yes—
765C2×C4C24×D1111yescharacteristic
766C8—22no—
767C8—22no—
768C8—222no—
769C8—222no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—44no—
774C22—222no—
775C22—224no—
776C22—222no—
777C22—222no—
778C22—444no—
779C22—448no—
780C22—442no—
781C22—442no—
782C22—442no—
783C22—442no—
784C22—442no—
785C22—884no—
786C22#1062318512yes—
787C22#1062329912yes—
788C22#1062330912yes—
789C22C22×D4×D1111yescharacteristic
790C4—22no—
791C4—42no—
792C4—42no—
793C4—42no—
794C4—42no—
795C4—222no—
796C4—222no—
797C4—222no—
798C4—442no—
799C4—442no—
800C4#1062318512yes—
801C4C2×#41×D1111yescharacteristic
802C4C2×#6704211yescharacteristic
803C2—42no—
804C2—442no—
805C2—444no—
806C2—882no—
807C2#1308059014yesdirect product factor
808C2C2×#1062318511yescharacteristic
809C2C2×#1062329911yescharacteristic
810C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#485C2
socleC23×C11C22×D4
hypercenterC2×#485D11
hypocenterC11C2×#3307
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
1. C2×#10623061C2semidirect
2. C2×#10623162C2semidirect
3. #13080590C2direct (N × H)
4. C2×#10622410C2semidirect
5. C2×#10622475C2semidirect
6. C2×#10622504C2semidirect
7. C2×#10622499C2semidirect
8. C2×#10622661C2semidirect
9. C2×#10622431C2semidirect
10. C2×#10622424C2semidirect
11. C2×#10622347C2semidirect
12. C2×#10622482C2semidirect
13. C2×#10622343C2semidirect
14. C2×#10622416C2semidirect
15. C2×#10622615C2semidirect
16. C2×C11×#485C2semidirect
30. #10623162C22semidirect
32. #10623061C22semidirect
47. C11×#485C22semidirect
59. #10622661C22semidirect
60. #10622615C22semidirect
67. #10622504C22semidirect
68. #10622499C22semidirect
69. #10622482C22semidirect
70. #10622475C22semidirect
71. #10622431C22semidirect
72. #10622424C22semidirect
73. #10622416C22semidirect
74. #10622410C22semidirect
75. #10622347C22semidirect
76. #10622343C22semidirect
296. C2×#485D11semidirect
412. #485C2×D11semidirect
583. C2×C11#3307semidirect
696. C11C2×#3307semidirect
807. C2#13080590direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230612
C2×#106231622
#130805902
C2×#106224102
C2×#106224752
C2×#106225042
C2×#106224992
C2×#106226612
C2×#106224312
C2×#106224242
C2×#106223472
C2×#106224822
C2×#106223432
C2×#106224162
C2×#106226152
C2×C11×#4852
C2×#330711