Finite Group Databasebeta

← C2×#13080878 #15630636

Subgroups — C2×#13080878 #15630636

Order 2816.

2114 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623083C211yesmaximal, characteristic
2#13080878C2116yesmaximal, direct product factor
3C2×#10622681C211yesmaximal, characteristic, complemented
4C2×#10622583C211yesmaximal, characteristic, complemented
5C2×#10622616C211yesmaximal, characteristic, complemented
6C2×#10622676C211yesmaximal, characteristic, complemented
7C2×#10622665C211yesmaximal, characteristic, complemented
8C2×#10622662C211yesmaximal, characteristic, complemented
9C2×#10622641C211yesmaximal, characteristic, complemented
10C2×#10622660C211yesmaximal, characteristic, complemented
11C2×#10622663C211yesmaximal, characteristic, complemented
12C2×C4×#4326C211yesmaximal, characteristic, complemented
13C2×#10622625C211yesmaximal, characteristic, complemented
14C2×#10622579C211yesmaximal, characteristic, complemented
15C2×#10622617C211yesmaximal, characteristic, complemented
16C2×C11×#552C211yesmaximal, characteristic, complemented
17C22×#4339C2211yescharacteristic
18C23×Dic22C2211yescharacteristic
19C11×#552—24no—
20C11×#552C2218yescomplemented
21C2×C11×#126—21no—
22C2×C11×#125—21no—
23C2×C11×#125C2211yescharacteristic
24C2×C11×#123—21no—
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C2×C11×#117—21no—
30C2×C11×#117C2211yescharacteristic
31C22×C11×C4⋊C4C2211yescharacteristic
32C22×#4326C2211yescharacteristic
33C22×#4326C2211yescharacteristic
34C22×#4325C2211yescharacteristic
35C2×#66992—21no—
36C2×#66983C2211yescharacteristic
37C2×#66977C2211yescharacteristic
38C22×#4318C2211yescharacteristic
39C22×#4318C2211yescharacteristic
40#10623083—24no—
41#10623083C2218yes—
42C2×#66949—21no—
43C2×#66938—21no—
44C2×(C22⋊D11)⋊C4—21no—
45C2×#66928C2211yescharacteristic
46C2×C4×Dic22C2211yescharacteristic
47C2×#66899C2211yescharacteristic
48C2×C22⋊(C11⋊C8)C2211yescharacteristic
49C2×C22⋊(C11⋊C8)C2211yescharacteristic
50#10622681C2218yescomplemented
51#10622676C2218yescomplemented
52#10622665C2218yescomplemented
53#10622663C2218yescomplemented
54#10622662C2218yescomplemented
55#10622660C2218yescomplemented
56C4×#4326C2218yescomplemented
57#10622641C2218yescomplemented
58#10622625C2218yescomplemented
59#10622617C2218yescomplemented
60#10622616C2218yescomplemented
61#10622583C2218yescomplemented
62C2×#66874C2211yescharacteristic
63C2×#66874C2211yescharacteristic
64C2×#66874C2211yescharacteristic
65C2×#66874C2211yescharacteristic
66C2×#66874C2211yescharacteristic
67C2×#66874C2211yescharacteristic
68#10622579C2218yescomplemented
69C2×#66873C2211yescharacteristic
70C2×#66873C2211yescharacteristic
71C2×#66873C2211yescharacteristic
72C2×#66872C2211yescharacteristic
73C2×#66871C2211yescharacteristic
74C2×#66871C2211yescharacteristic
75C2×C4⋊(C11⋊C8)C2211yescharacteristic
76C2×C4×C11⋊C8C2211yescharacteristic
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11D411yescharacteristic
79C23×C4×C11—21no—
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C23×Dic11—21no—
85C2×#4339—22no—
86C2×#4339—24no—
87C2×#4339—42no—
88C2×#4339C2314yes—
89C22×D44C2311yescharacteristic
90C22×C4×D11—21no—
91C22×Dic22—24no—
92C22×Dic22—21no—
93C22×Dic22—22no—
94C22×Dic22—42no—
95C22×Dic22C2311yescharacteristic
96C22×Dic22C2314yes—
97C22×Dic22C2311yescharacteristic
98C11×#126—28no—
99C11×#125—28no—
100C11×#125—22no—
101C11×#125C2314yes—
102C11×#123—28no—
103C11×C22⋊Q8—22no—
104C11×C22⋊Q8—22no—
105C11×C22⋊Q8C2314yes—
106C11×C22⋊Q8C2314yes—
107C4×Q8×C11—22no—
108C4×Q8×C11C2314yes—
109C4×D4×C11D414yes—
110C4×D4×C11C2314yes—
111C11×#117—22no—
112C11×#117—28no—
113C11×#117C2314yes—
114C2×C11×C4⋊C4—21no—
115C2×C11×C4⋊C4—22no—
116C2×C11×C4⋊C4—21no—
117C2×C11×C4⋊C4—21no—
118C2×C11×C4⋊C4—21no—
119C2×C11×C4⋊C4—21no—
120C2×C11×C4⋊C4—21no—
121C2×C11×C4⋊C4D411yescharacteristic
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C11×C4⋊C4C2311yescharacteristic
124C2×C11×C4⋊C4C2311yescharacteristic
125C2×C11×C4⋊C4C2314yes—
126C2×C11×C22⋊C4—21no—
127C2×C11×C22⋊C4—21no—
128C2×C11×C22⋊C4—21no—
129C2×C11×C22⋊C4D411yescharacteristic
130C2×C11×C22⋊C4D411yescharacteristic
131C2×C42×C11—21no—
132C2×C42×C11—21no—
133C2×C42×C11C2311yescharacteristic
134C2×C22⋊Dic11—21no—
135C2×#4326—24no—
136C2×#4326—42no—
137C2×#4326C2314yes—
138C2×#4326C2314yes—
139C2×#4325—42no—
140C2×#4325C2314yes—
141#66992—28no—
142#66983—22no—
143#66983C2314yes—
144C2×(C2×D11)⋊C4—21no—
145C2×(C2×D11)⋊C4—21no—
146C2×(C2×D11)⋊C4—21no—
147C2×C4⋊Dic11C2311yescharacteristic
148#66977—22no—
149#66977C2314yes—
150C2×Dic11⋊C4—21no—
151C2×Dic11⋊C4—21no—
152C2×C4×Dic11—21no—
153C2×#4318—42no—
154C2×#4318—42no—
155C2×#4318C2314yes—
156C2×#4318C2314yes—
157C22×C11⋊C8C2311yescharacteristic
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160C22×C11⋊C8C2311yescharacteristic
161#66949—28no—
162#66938—28no—
163(C22⋊D11)⋊C4—28no—
164#66928—22no—
165#66928C2314yes—
166C4×Dic22—22no—
167C4×Dic22C2314yes—
168#66899C2314yes—
169C22⋊(C11⋊C8)C2314yes—
170C22⋊(C11⋊C8)C2314yes—
171#66874C2314yes—
172#66874C2314yes—
173#66874C2314yes—
174#66874C2314yes—
175#66874C2314yes—
176#66874C2314yes—
177#66873C2314yes—
178#66873C2314yes—
179#66873C2314yes—
180#66872C2314yes—
181#66871C2314yes—
182#66871C2314yes—
183C4⋊(C11⋊C8)C2314yes—
184C4×C11⋊C8C2314yes—
185C2×#3327—111nomaximal, Sylow
186C24×C11C2×D411yescharacteristic
187C24×C11C2×D411yescharacteristic
188C23×D11—21no—
189C2×Q8×C11—21no—
190C2×Q8×C11—22no—
191C2×Q8×C11—22no—
192C2×Q8×C11C2412yes—
193C2×D4×C11—42no—
194C2×D4×C11C2×D414yes—
195C22×C4×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—24no—
204C22×C4×C11—44no—
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D412yes—
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D412yes—
211C22×C4×C11C2412yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2411yescharacteristic
214C2×C22⋊D11—24no—
215C2×C22⋊D11—24no—
216C2×C22⋊D11—44no—
217C2×C22⋊D11—44no—
218C22×Dic11—21no—
219C22×Dic11—24no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—44no—
223#4339—28no—
224#4339—44no—
225#4339—48no—
226C2×D44—21no—
227C2×D44—22no—
228C2×D44—22no—
229C2×D44C2412yes—
230C2×C4×D11—24no—
231C2×C4×D11—44no—
232C2×Dic22—28no—
233C2×Dic22—21no—
234C2×Dic22—21no—
235C2×Dic22—24no—
236C2×Dic22—22no—
237C2×Dic22—22no—
238C2×Dic22—22no—
239C2×Dic22—44no—
240C2×Dic22—48no—
241C2×Dic22—44no—
242C2×Dic22#4114yes—
243C2×Dic22C2412yes—
244C2×Dic22C2412yes—
245C11×C4⋊C4—21no—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—24no—
248C11×C4⋊C4—24no—
249C11×C4⋊C4—24no—
250C11×C4⋊C4—24no—
251C11×C4⋊C4—24no—
252C11×C4⋊C4—24no—
253C11×C4⋊C4—21no—
254C11×C4⋊C4C2×D414yes—
255C11×C4⋊C4C2412yes—
256C11×C4⋊C4C2412yes—
257C11×C4⋊C4C2412yes—
258C11×C22⋊C4—24no—
259C11×C22⋊C4—24no—
260C11×C22⋊C4—24no—
261C11×C22⋊C4C2×D414yes—
262C11×C22⋊C4C2×D414yes—
263C42×C11—24no—
264C42×C11—24no—
265C42×C11C2×D412yes—
266C42×C11C2412yes—
267C22⋊Dic11—24no—
268#4326—28no—
269#4326—44no—
270#4325—44no—
271(C2×D11)⋊C4—24no—
272(C2×D11)⋊C4—24no—
273(C2×D11)⋊C4—24no—
274C4⋊Dic11—21no—
275C4⋊Dic11C2412yes—
276Dic11⋊C4—24no—
277Dic11⋊C4—24no—
278C4×Dic11—24no—
279#4318—44no—
280#4318—44no—
281C2×C11⋊C8—22no—
282C2×C11⋊C8—22no—
283C2×C11⋊C8—22no—
284C2×C11⋊C8—22no—
285C2×C11⋊C8C2412yes—
286C2×C11⋊C8C2412yes—
287C2×C11⋊C8C2412yes—
288C2×C11⋊C8C2412yes—
289C2×#552D1111yescharacteristic, complemented
290C2×#548—111no—
291#3327—1116no—
292C2×#488—111no—
293C2×#484—111no—
294C2×#482—111no—
295C2×#479—111no—
296C2×#470—111no—
297C2×#468—111no—
298C2×#464—111no—
299C2×#452—111no—
300C2×#451—111no—
301C2×C4×Q16—111no—
302C2×#436—111no—
303C2×#417—111no—
304C2×#419—111no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11C22×D412yes—
312C23×C11C22×D412yes—
313C23×C11C22×D411yescharacteristic
314C22×D11—22no—
315C22×D11—42no—
316C22×D11—42no—
317C22×D11—42no—
318Q8×C11—22no—
319Q8×C11—22no—
320Q8×C11—42no—
321D4×C11—44no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—24no—
327C2×C4×C11—24no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
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—48no—
337C2×C4×C11—42no—
338C2×C4×C11—42no—
339C2×C4×C11—42no—
340C2×C4×C11—42no—
341C2×C4×C11C22×D412yes—
342C2×C4×C11C22×D412yes—
343C2×C4×C11C22×D412yes—
344C2×C4×C11C22×D412yes—
345C2×C4×C11C22×D411yescharacteristic
346C2×C4×C11C2×#4112yes—
347C2×C4×C11H(5,𝔽2)12yes—
348C2×C4×C11C2511yescharacteristic
349C22⋊D11—48no—
350C22⋊D11—48no—
351C2×Dic11—24no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—48no—
356C2×Dic11—42no—
357C2×Dic11—42no—
358D44—22no—
359D44—22no—
360D44—42no—
361C4×D11—48no—
362Dic22—24no—
363Dic22—22no—
364Dic22—22no—
365Dic22—22no—
366Dic22—48no—
367Dic22—42no—
368Dic22C2×#4114yes—
369C11⋊C8—22no—
370C11⋊C8—22no—
371C11⋊C8—22no—
372C11⋊C8—22no—
373C22×#41—111no—
374C23×Q8—111no—
375C22×Q16—111no—
376C22×Q16—111no—
377C22×SD16—111no—
378C22×M16—111no—
379C22×M16—111no—
380#552—24no—
381#552C2×D1118yescomplemented
382#548—118no—
383#548—224no—
384C2×#126—21no—
385C2×#125—21no—
386C2×#125C2×D1111yescharacteristic
387C2×#124—111no—
388C2×#124—221no—
389C2×#123—21no—
390C2×C22⋊Q8—111no—
391C2×C22⋊Q8—221no—
392C2×C22⋊Q8C2×D1111yescharacteristic
393C2×C22⋊Q8C2×D1111yescharacteristic
394C2×#121—111no—
395C2×#121—221no—
396C2×C4×Q8—111no—
397C2×C4×Q8C2×D1111yescharacteristic
398C2×C4×D4—221no—
399C2×C4×D4C2×D1111yescharacteristic
400C2×#117—21no—
401C2×#117C2×D1111yescharacteristic
402C22×C4⋊C4C2×D1111yescharacteristic
403#488—118no—
404#484—118no—
405#482—118no—
406#479—118no—
407#470—118no—
408#468—118no—
409#464—118no—
410#452—118no—
411#451—118no—
412C4×Q16—118no—
413#436—118no—
414C2×#107—111no—
415C2×#107—111no—
416C2×#106—111no—
417C2×C4⋊C8—111no—
418#419—118no—
419#417—118no—
420C2×#103—111no—
421C2×#103—111no—
422C2×#103—111no—
423C2×#103—111no—
424C2×#103—111no—
425C2×#103—111no—
426C2×#103—111no—
427C2×#102—111no—
428C2×#102—111no—
429C2×#102—111no—
430C2×C22⋊C8—111no—
431C2×C22⋊C8—111no—
432C2×C4×C8—111no—
433C22×C11—22no—
434C22×C11—22no—
435C22×C11—22no—
436C22×C11—22no—
437C22×C11—22no—
438C22×C11—22no—
439C22×C11—44no—
440C22×C11—44no—
441C22×C11#54612yes—
442C22×C11#57512yes—
443C22×C11#57812yes—
444C22×C11C23×D411yescharacteristic
445C2×D11—42no—
446C2×D11—42no—
447C2×D11—42no—
448C2×D11—84no—
449C4×C11—22no—
450C4×C11—22no—
451C4×C11—22no—
452C4×C11—22no—
453C4×C11—42no—
454C4×C11—42no—
455C4×C11—42no—
456C4×C11—42no—
457C4×C11#54612yes—
458C4×C11C22×#4111yescharacteristic
459C4×C11C2×H(5,𝔽2)11yescharacteristic
460Dic11—24no—
461Dic11—42no—
462Dic11—42no—
463C2×#41—114no—
464C2×#41—224no—
465C2×#41—222no—
466C2×#41—442no—
467C22×Q8—111no—
468C22×Q8—111no—
469C22×Q8—114no—
470C22×Q8—224no—
471C22×Q8—221no—
472C22×Q8—222no—
473C22×Q8—442no—
474C22×Q8C22×D1111yescharacteristic
475C22×D4—111no—
476C22×D4—221no—
477C22×D4—221no—
478C22×D4C22⋊D1111yescharacteristic
479C23×C4—21no—
480C23×C4—221no—
481C23×C4—221no—
482C23×C4C22×D1111yescharacteristic
483C23×C4C22×D1111yescharacteristic
484C2×Q16—114no—
485C2×Q16—114no—
486C2×Q16—224no—
487C2×Q16—442no—
488C2×SD16—114no—
489C2×SD16—442no—
490C2×M16—114no—
491C2×M16—114no—
492C2×M16—442no—
493C2×M16—442no—
494C22×C8—111no—
495C22×C8—111no—
496C22×C8—111no—
497C22×C8—111no—
498#126—28no—
499#125—28no—
500#125—22no—
501#125C22×D1114yes—
502#124—114no—
503#124—228no—
504#124—222no—
505#123—28no—
506C22⋊Q8—22no—
507C22⋊Q8—22no—
508C22⋊Q8—114no—
509C22⋊Q8—222no—
510C22⋊Q8—228no—
511C22⋊Q8C22×D1114yes—
512C22⋊Q8C22×D1114yes—
513#121—114no—
514#121—228no—
515#121—222no—
516C4×Q8—22no—
517C4×Q8—114no—
518C4×Q8—222no—
519C4×Q8C22×D1114yes—
520C4×D4—228no—
521C4×D4C22⋊D1114yes—
522C4×D4C22×D1114yes—
523#117—22no—
524#117—28no—
525#117C22×D1114yes—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—22no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—111no—
534C2×C4⋊C4—221no—
535C2×C4⋊C4—221no—
536C2×C4⋊C4C22⋊D1111yescharacteristic
537C2×C4⋊C4C22×D1111yescharacteristic
538C2×C4⋊C4C22×D1111yescharacteristic
539C2×C4⋊C4C22×D1114yes—
540C2×C4⋊C4C22×D1111yescharacteristic
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—221no—
545C2×C22⋊C4—221no—
546C2×C22⋊C4—221no—
547C2×C22⋊C4—221no—
548C2×C22⋊C4C22⋊D1111yescharacteristic
549C2×C22⋊C4C22⋊D1111yescharacteristic
550C2×C42—21no—
551C2×C42—21no—
552C2×C42—221no—
553C2×C42C22×D1111yescharacteristic
554#107—114no—
555#107—114no—
556#106—114no—
557C4⋊C8—114no—
558#103—114no—
559#103—114no—
560#103—114no—
561#103—114no—
562#103—114no—
563#103—114no—
564#103—114no—
565#102—114no—
566#102—114no—
567#102—114no—
568C22⋊C8—114no—
569C22⋊C8—114no—
570C4×C8—114no—
571C2×C11—42no—
572C2×C11—42no—
573C2×C11#332714yescomplemented
574C2×C11C2×#54611yescharacteristic
575C2×C11C2×#57511yescharacteristic
576C2×C11C2×#57811yescharacteristic
577D11—82no—
578C24—221no—
579C24C2×C22⋊D1111yescharacteristic
580C24C2×C22⋊D1111yescharacteristic
581#41—228no—
582#41—444no—
583#41—448no—
584C2×Q8—21no—
585C2×Q8—22no—
586C2×Q8—22no—
587C2×Q8—114no—
588C2×Q8—112no—
589C2×Q8—112no—
590C2×Q8—228no—
591C2×Q8—222no—
592C2×Q8—221no—
593C2×Q8—224no—
594C2×Q8—221no—
595C2×Q8—222no—
596C2×Q8—222no—
597C2×Q8—444no—
598C2×Q8—444no—
599C2×Q8—448no—
600C2×Q8C23×D1112yes—
601C2×D4—42no—
602C2×D4—112no—
603C2×D4—224no—
604C2×D4—224no—
605C2×D4—222no—
606C2×D4—222no—
607C2×D4—221no—
608C2×D4—444no—
609C2×D4—444no—
610C2×D4C2×C22⋊D1114yes—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—24no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—44no—
621C22×C4—221no—
622C22×C4—224no—
623C22×C4—221no—
624C22×C4—221no—
625C22×C4—224no—
626C22×C4—444no—
627C22×C4—444no—
628C22×C4C2×C22⋊D1112yes—
629C22×C4C2×C22⋊D1112yes—
630C22×C4C2×C22⋊D1111yescharacteristic
631C22×C4C2×C22⋊D1111yescharacteristic
632C22×C4C2×C22⋊D1111yescharacteristic
633C22×C4C2×C22⋊D1111yescharacteristic
634C22×C4C23×D1112yes—
635C22×C4C23×D1112yes—
636C22×C4C23×D1111yescharacteristic
637Q16—228no—
638Q16—444no—
639SD16—444no—
640M16—444no—
641M16—444no—
642C2×C8—112no—
643C2×C8—112no—
644C2×C8—112no—
645C2×C8—112no—
646C2×C8—222no—
647C2×C8—222no—
648C2×C8—222no—
649C2×C8—222no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—24no—
655C4⋊C4—24no—
656C4⋊C4—24no—
657C4⋊C4—24no—
658C4⋊C4—21no—
659C4⋊C4—112no—
660C4⋊C4—221no—
661C4⋊C4—224no—
662C4⋊C4—224no—
663C4⋊C4C2×C22⋊D1114yes—
664C4⋊C4C23×D1112yes—
665C4⋊C4C23×D1112yes—
666C4⋊C4C23×D1112yes—
667C22⋊C4—24no—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—224no—
671C22⋊C4—224no—
672C22⋊C4—224no—
673C22⋊C4—224no—
674C22⋊C4C2×C22⋊D1114yes—
675C22⋊C4C2×C22⋊D1114yes—
676C42—24no—
677C42—24no—
678C42—224no—
679C42C2×C22⋊D1112yes—
680C42C23×D1112yes—
681C11C2×#332711yescharacteristic, complemented, Sylow
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—222no—
689C23—442no—
690C23—442no—
691C23—442no—
692C23C22×C22⋊D1112yes—
693C23C22×C22⋊D1112yes—
694C23C22×C22⋊D1111yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—42no—
698Q8—114no—
699Q8—224no—
700Q8—222no—
701Q8—222no—
702Q8—222no—
703Q8—448no—
704Q8—442no—
705D4—44no—
706D4—222no—
707D4—222no—
708D4—448no—
709D4—448no—
710D4—442no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—48no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—224no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—222no—
734C2×C4—448no—
735C2×C4—448no—
736C2×C4—442no—
737C2×C4—442no—
738C2×C4#41×D1112yes—
739C2×C4#6704212yes—
740C2×C4C22×C22⋊D1112yes—
741C2×C4C22×C22⋊D1112yes—
742C2×C4C22×C22⋊D1112yes—
743C2×C4C22×C22⋊D1112yes—
744C2×C4C22×C22⋊D1111yescharacteristic
745C2×C4C24×D1111yescharacteristic
746C8—222no—
747C8—222no—
748C8—222no—
749C8—222no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—44no—
758C22—442no—
759C22—442no—
760C22—442no—
761C22—884no—
762C22#1062335312yes—
763C22#1062336012yes—
764C22#1062336912yes—
765C22C23×C22⋊D1111yescharacteristic
766C4—22no—
767C4—22no—
768C4—22no—
769C4—22no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—42no—
774C4—224no—
775C4—442no—
776C4—442no—
777C4#1062336012yes—
778C4C2×#41×D1111yescharacteristic
779C4C2×#6704211yescharacteristic
780C2—42no—
781C2—42no—
782C2—882no—
783C2#1308087814yesdirect product factor
784C2C2×#1062336011yescharacteristic
785C2C2×#1062335311yescharacteristic
786C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#552C2
socleC23×C11C22×D4
prime radicalC2×#10623083C2
hypercenterC2×#552D11
hypocenterC11C2×#3327
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #13080878C2direct (N × H)
3. C2×#10622681C2semidirect
4. C2×#10622583C2semidirect
5. C2×#10622616C2semidirect
6. C2×#10622676C2semidirect
7. C2×#10622665C2semidirect
8. C2×#10622662C2semidirect
9. C2×#10622641C2semidirect
10. C2×#10622660C2semidirect
11. C2×#10622663C2semidirect
12. C2×C4×#4326C2semidirect
13. C2×#10622625C2semidirect
14. C2×#10622579C2semidirect
15. C2×#10622617C2semidirect
16. C2×C11×#552C2semidirect
20. C11×#552C22semidirect
50. #10622681C22semidirect
51. #10622676C22semidirect
52. #10622665C22semidirect
53. #10622663C22semidirect
54. #10622662C22semidirect
55. #10622660C22semidirect
56. C4×#4326C22semidirect
57. #10622641C22semidirect
58. #10622625C22semidirect
59. #10622617C22semidirect
60. #10622616C22semidirect
61. #10622583C22semidirect
68. #10622579C22semidirect
289. C2×#552D11semidirect
381. #552C2×D11semidirect
573. C2×C11#3327semidirect
681. C11C2×#3327semidirect
783. C2#13080878direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230832
#130808782
C2×#106226812
C2×#106225832
C2×#106226162
C2×#106226762
C2×#106226652
C2×#106226622
C2×#106226412
C2×#106226602
C2×#106226632
C2×C4×#43262
C2×#106226252
C2×#106225792
C2×#106226172
C2×C11×#5522
C2×#332711