Finite Group Databasebeta

← C2×#13080724 #15630360

Subgroups — C2×#13080724 #15630360

Order 2816.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623261C211yesmaximal, characteristic, complemented
2C2×#10623107C211yesmaximal, characteristic
3#13080724C2116yesmaximal, direct product factor
4C2×#10622702C211yesmaximal, characteristic, complemented
5C2×#10622476C211yesmaximal, characteristic, complemented
6C2×#10622475C211yesmaximal, characteristic, complemented
7C2×#10622481C211yesmaximal, characteristic, complemented
8C2×#10622477C211yesmaximal, characteristic, complemented
9C2×#10622458C211yesmaximal, characteristic, complemented
10C2×#10622423C211yesmaximal, characteristic, complemented
11C2×#10622421C211yesmaximal, characteristic, complemented
12C2×#10622643C211yesmaximal, characteristic, complemented
13C2×#10622449C211yesmaximal, characteristic, complemented
14C2×#10622416C211yesmaximal, characteristic, complemented
15C2×D11×#103C211yesmaximal, characteristic, complemented
16C2×C11×#475C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C22×Q8×D11C2211yescharacteristic
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×#66999—21no—
22C2×#66999—21no—
23C22×#4326C2211yescharacteristic
24C22×Dic44C2211yescharacteristic
25C22×#4314C2211yescharacteristic
26C22×#4313C2211yescharacteristic
27C22×C8×D11C2211yescharacteristic
28#10623261—24no—
29#10623261C2218yescomplemented
30#10623107—24no—
31#10623107C2218yes—
32C2×#66950—21no—
33C2×#66950C2211yescharacteristic
34C2×#66950C2211yescharacteristic
35C2×#66950C2211yescharacteristic
36C2×#66948—21no—
37C2×#66948C2211yescharacteristic
38C2×#66946—21no—
39C2×C4⋊C4×D11C2211yescharacteristic
40C2×C4⋊C4×D11C2211yescharacteristic
41C2×#66943—21no—
42C2×#66928—21no—
43C2×#66928C2211yescharacteristic
44C2×C4×D44—21no—
45C2×C4×D44C2211yescharacteristic
46C2×C4×Dic22C2211yescharacteristic
47C11×#475C2218yescomplemented
48C2×C11×#106C2211yescharacteristic
49C2×C11×#106C2211yescharacteristic
50C2×C11×C4⋊C8C2211yescharacteristic
51C2×C11×#103C2211yescharacteristic
52C2×C11×#103C2211yescharacteristic
53C2×#66899C2211yescharacteristic
54C2×#66885C2211yescharacteristic
55C2×(C2×D11)⋊C8C2211yescharacteristic
56C2×(C2×D11)⋊C8C2211yescharacteristic
57C2×#66880C2211yescharacteristic
58#10622702C2218yescomplemented
59#10622643C2218yescomplemented
60C2×#66874C2211yescharacteristic
61C2×#66874C2211yescharacteristic
62C2×#66874C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66873C2211yescharacteristic
65C2×#66872C2211yescharacteristic
66C2×#66867C2211yescharacteristic
67#10622481C2218yescomplemented
68#10622477C2218yescomplemented
69#10622476C2218yescomplemented
70#10622475C2218yescomplemented
71#10622458C2218yescomplemented
72#10622449C2218yescomplemented
73#10622423C2218yescomplemented
74#10622421C2218yescomplemented
75#10622416C2218yescomplemented
76D11×#103C2218yescomplemented
77C22×Q8×C11—21no—
78C22×Q8×C11C2311yescharacteristic
79C2×#4343—22no—
80C2×#4343—24no—
81C2×#4343—42no—
82C2×#4343C2314yes—
83C2×Q8×D11—22no—
84C2×Q8×D11—24no—
85C2×Q8×D11—42no—
86C2×Q8×D11C2314yes—
87C22×D44—21no—
88C22×D44—21no—
89C22×D44D411yescharacteristic
90C22×D44C2311yescharacteristic
91C22×C4×D11—21no—
92C22×C4×D11—21no—
93C22×C4×D11—21no—
94C22×C4×D11—21no—
95C22×C4×D11C2311yescharacteristic
96C22×C4×D11C2311yescharacteristic
97C22×Dic22—21no—
98C22×Dic22C2311yescharacteristic
99C22×Dic22C2311yescharacteristic
100C22×C8×C11C2311yescharacteristic
101C22×C8×C11C2311yescharacteristic
102C11×C4⋊Q8—22no—
103C11×C4⋊Q8C2314yes—
104C4×Q8×C11—22no—
105C4×Q8×C11C2314yes—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C42×C11—21no—
112C2×C42×C11C2311yescharacteristic
113#66999—28no—
114#66999—28no—
115C2×#4326—24no—
116C2×#4326C2314yes—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4—21no—
122C2×(C2×D11)⋊C4—21no—
123C2×(C2×D11)⋊C4D411yescharacteristic
124C2×(C2×D11)⋊C4D411yescharacteristic
125C2×C4⋊Dic11—21no—
126C2×C4⋊Dic11—21no—
127C2×C4⋊Dic11—21no—
128C2×C4⋊Dic11D411yescharacteristic
129C2×C4⋊Dic11C2311yescharacteristic
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—21no—
133C2×C4×Dic11—21no—
134C22×C11⋊C8C2311yescharacteristic
135C22×C11⋊C8C2311yescharacteristic
136C2×Dic44—42no—
137C2×Dic44C2314yes—
138C2×#4314—42no—
139C2×#4314C2314yes—
140C2×#4313—42no—
141C2×#4313C2314yes—
142C2×C8×D11—42no—
143C2×C8×D11C2314yes—
144#66950—22no—
145#66950—22no—
146#66950—22no—
147#66950—28no—
148#66950C2314yes—
149#66950C2314yes—
150#66950C2314yes—
151#66948—28no—
152#66948—22no—
153#66948C2314yes—
154#66946—28no—
155C4⋊C4×D11—22no—
156C4⋊C4×D11—22no—
157C4⋊C4×D11C2314yes—
158C4⋊C4×D11C2314yes—
159#66943—28no—
160#66928—22no—
161#66928—28no—
162#66928C2314yes—
163C4×D44—28no—
164C4×D44D414yes—
165C4×D44C2314yes—
166C4×Dic22—22no—
167C4×Dic22C2314yes—
168C11×#106C2314yes—
169C11×#106C2314yes—
170C11×C4⋊C8C2314yes—
171C11×#103C2314yes—
172C11×#103C2314yes—
173#66899C2314yes—
174#66885C2314yes—
175(C2×D11)⋊C8C2314yes—
176(C2×D11)⋊C8C2314yes—
177#66880C2314yes—
178#66874C2314yes—
179#66874C2314yes—
180#66874C2314yes—
181#66873C2314yes—
182#66873C2314yes—
183#66872C2314yes—
184#66867C2314yes—
185C2×#3316—111nomaximal, Sylow
186C23×D11—21no—
187C23×D11C2×D411yescharacteristic
188C23×D11C2×D411yescharacteristic
189C2×Q8×C11—21no—
190C2×Q8×C11—24no—
191C2×Q8×C11—22no—
192C2×Q8×C11—82no—
193C2×Q8×C11#4114yes—
194C2×Q8×C11C2412yes—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2411yescharacteristic
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11C2×D411yescharacteristic
206C22×Dic11C2×D411yescharacteristic
207#4343—28no—
208#4343—44no—
209#4343—48no—
210Q8×D11—28no—
211Q8×D11—44no—
212Q8×D11—48no—
213C2×D44—24no—
214C2×D44—24no—
215C2×D44—24no—
216C2×D44—21no—
217C2×D44—22no—
218C2×D44—22no—
219C2×D44—44no—
220C2×D44—44no—
221C2×D44C2×D414yes—
222C2×D44C2412yes—
223C2×C4×D11—24no—
224C2×C4×D11—24no—
225C2×C4×D11—24no—
226C2×C4×D11—24no—
227C2×C4×D11—22no—
228C2×C4×D11—22no—
229C2×C4×D11—22no—
230C2×C4×D11—22no—
231C2×C4×D11—44no—
232C2×C4×D11—44no—
233C2×C4×D11—82no—
234C2×C4×D11—82no—
235C2×C4×D11C2×D412yes—
236C2×C4×D11C2×D412yes—
237C2×C4×D11C2412yes—
238C2×C4×D11C2412yes—
239C2×Dic22—24no—
240C2×Dic22—21no—
241C2×Dic22—21no—
242C2×Dic22—22no—
243C2×Dic22—22no—
244C2×Dic22—22no—
245C2×Dic22—22no—
246C2×Dic22—44no—
247C2×Dic22C2412yes—
248C2×Dic22C2412yes—
249C2×C8×C11—22no—
250C2×C8×C11—22no—
251C2×C8×C11C2412yes—
252C2×C8×C11C2412yes—
253C11×C4⋊C4—24no—
254C11×C4⋊C4—21no—
255C11×C4⋊C4—21no—
256C11×C4⋊C4—24no—
257C11×C4⋊C4—21no—
258C11×C4⋊C4C2412yes—
259C11×C4⋊C4C2412yes—
260C11×C4⋊C4C2412yes—
261C42×C11—24no—
262C42×C11C2×D412yes—
263C42×C11C2412yes—
264#4326—28no—
265(C2×D11)⋊C4—24no—
266(C2×D11)⋊C4—24no—
267(C2×D11)⋊C4—24no—
268(C2×D11)⋊C4—24no—
269(C2×D11)⋊C4—24no—
270(C2×D11)⋊C4—24no—
271(C2×D11)⋊C4C2×D414yes—
272(C2×D11)⋊C4C2×D414yes—
273C4⋊Dic11—24no—
274C4⋊Dic11—24no—
275C4⋊Dic11—24no—
276C4⋊Dic11—21no—
277C4⋊Dic11C2×D414yes—
278C4⋊Dic11C2412yes—
279Dic11⋊C4—24no—
280Dic11⋊C4—24no—
281Dic11⋊C4—24no—
282C4×Dic11—24no—
283C2×C11⋊C8—22no—
284C2×C11⋊C8—22no—
285C2×C11⋊C8C2412yes—
286C2×C11⋊C8C2412yes—
287Dic44—44no—
288#4314—44no—
289#4313—44no—
290C8×D11—44no—
291C2×#554—111no—
292C2×#548—111no—
293#3316—1116no—
294C2×#489—111no—
295C2×#481—111no—
296C2×#483—111no—
297C2×#475D1111yescharacteristic, complemented
298C2×#470—111no—
299C2×#465—111no—
300C2×#464—111no—
301C2×#452—111no—
302C2×#451—111no—
303C2×#441—111no—
304C2×#435—111no—
305C2×#417—111no—
306C22×#103—111no—
307C23×C11C22×D411yescharacteristic
308C22×D11—22no—
309C22×D11—22no—
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—42no—
315C22×D11—42no—
316C22×D11—42no—
317C22×D11#13714yes—
318C22×D11C22×D412yes—
319C22×D11C22×D412yes—
320Q8×C11—24no—
321Q8×C11—22no—
322Q8×C11—84no—
323Q8×C11C2×#4114yes—
324C2×C4×C11—24no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—42no—
332C2×C4×C11—42no—
333C2×C4×C11—42no—
334C2×C4×C11C22×D412yes—
335C2×C4×C11C22×D412yes—
336C2×C4×C11C22×D411yescharacteristic
337C2×C4×C11C2×#4112yes—
338C2×C4×C11H(5,𝔽2)12yes—
339C2×C4×C11C2511yescharacteristic
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—42no—
346C2×Dic11—42no—
347C2×Dic11—42no—
348C2×Dic11C22×D412yes—
349C2×Dic11C22×D412yes—
350D44—28no—
351D44—22no—
352D44—22no—
353D44—48no—
354D44—48no—
355D44—42no—
356C4×D11—24no—
357C4×D11—24no—
358C4×D11—22no—
359C4×D11—22no—
360C4×D11—22no—
361C4×D11—22no—
362C4×D11—48no—
363C4×D11—48no—
364C4×D11—84no—
365C4×D11—84no—
366Dic22—22no—
367Dic22—22no—
368Dic22—22no—
369Dic22—22no—
370Dic22—48no—
371Dic22—42no—
372Dic22—42no—
373C8×C11—22no—
374C8×C11—22no—
375C11⋊C8—22no—
376C11⋊C8—22no—
377C22×#41—111no—
378C23×Q8—111no—
379C22×Q16—111no—
380C22×Q16—111no—
381C22×SD16—111no—
382C22×M16—111no—
383C23×C8—111no—
384#554—118no—
385#554—224no—
386#548—118no—
387#548—224no—
388C2×C4⋊Q8C2×D1111yescharacteristic
389C2×#125—221no—
390C2×#124—111no—
391C2×#124—221no—
392C2×C22⋊Q8—111no—
393C2×C22⋊Q8—111no—
394C2×C22⋊Q8—111no—
395C2×C22⋊Q8—221no—
396C2×C22⋊Q8—221no—
397C2×C22⋊Q8—221no—
398C2×#121—111no—
399C2×#121—221no—
400C2×C4×Q8—111no—
401C2×C4×Q8C2×D1111yescharacteristic
402C2×C4×D4—111no—
403C2×C4×D4—221no—
404C2×C4×D4—221no—
405C22×C4⋊C4—111no—
406C22×C4⋊C4—111no—
407#489—118no—
408#483—118no—
409#481—118no—
410#475C2×D1118yescomplemented
411#470—118no—
412#465—118no—
413#464—118no—
414#452—118no—
415#451—118no—
416#441—118no—
417#435—118no—
418C2×#106—111no—
419C2×#106C2×D1111yescharacteristic
420C2×#106C2×D1111yescharacteristic
421C2×C4⋊C8C2×D1111yescharacteristic
422#417—118no—
423C2×#103—111no—
424C2×#103—111no—
425C2×#103—111no—
426C2×#103—111no—
427C2×#103—111no—
428C2×#103—118no—
429C2×#103C2×D1111yescharacteristic
430C2×#103C2×D1111yescharacteristic
431C2×#102—111no—
432C2×#102—111no—
433C2×#102—111no—
434C2×C22⋊C8—111no—
435C2×C22⋊C8—111no—
436C2×#97—111no—
437C22×C11#54612yes—
438C22×C11C2×#13712yes—
439C22×C11#57712yes—
440C22×C11C23×D411yescharacteristic
441C2×D11—22no—
442C2×D11—28no—
443C2×D11—22no—
444C2×D11—22no—
445C2×D11—22no—
446C2×D11—22no—
447C2×D11—44no—
448C2×D11—42no—
449C2×D11—42no—
450C2×D11—42no—
451C2×D11—84no—
452C2×D11C2×#13714yes—
453C4×C11—24no—
454C4×C11—22no—
455C4×C11—22no—
456C4×C11—42no—
457C4×C11—42no—
458C4×C11—42no—
459C4×C11#54612yes—
460C4×C11C22×#4111yescharacteristic
461C4×C11C2×H(5,𝔽2)11yescharacteristic
462Dic11—22no—
463Dic11—22no—
464Dic11—42no—
465Dic11—42no—
466Dic11—42no—
467C2×#41—114no—
468C2×#41—222no—
469C2×#41—224no—
470C2×#41—442no—
471C22×Q8—21no—
472C22×Q8—114no—
473C22×Q8—111no—
474C22×Q8—111no—
475C22×Q8—221no—
476C22×Q8—222no—
477C22×Q8—224no—
478C22×Q8—442no—
479C22×Q8C22×D1111yescharacteristic
480C22×D4—111no—
481C22×D4—111no—
482C22×D4—221no—
483C22×D4—221no—
484C23×C4—111no—
485C23×C4—111no—
486C23×C4—221no—
487C23×C4—221no—
488C23×C4—221no—
489C23×C4—221no—
490C2×Q16—114no—
491C2×Q16—114no—
492C2×Q16—224no—
493C2×Q16—442no—
494C2×SD16—114no—
495C2×SD16—442no—
496C2×M16—114no—
497C2×M16—442no—
498C22×C8—111no—
499C22×C8—111no—
500C22×C8—114no—
501C22×C8—442no—
502C22×C8C22×D1111yescharacteristic
503C22×C8C22×D1111yescharacteristic
504C4⋊Q8—22no—
505C4⋊Q8C22×D1114yes—
506#125—228no—
507#124—114no—
508#124—228no—
509#124—222no—
510C22⋊Q8—114no—
511C22⋊Q8—114no—
512C22⋊Q8—114no—
513C22⋊Q8—228no—
514C22⋊Q8—228no—
515C22⋊Q8—228no—
516C22⋊Q8—222no—
517C22⋊Q8—222no—
518C22⋊Q8—222no—
519#121—114no—
520#121—222no—
521#121—228no—
522C4×Q8—22no—
523C4×Q8—114no—
524C4×Q8—222no—
525C4×Q8C22×D1114yes—
526C4×D4—114no—
527C4×D4—114no—
528C4×D4—228no—
529C4×D4—228no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—111no—
533C2×C4⋊C4—111no—
534C2×C4⋊C4—114no—
535C2×C4⋊C4—114no—
536C2×C4⋊C4—222no—
537C2×C4⋊C4—222no—
538C2×C4⋊C4—221no—
539C2×C4⋊C4—221no—
540C2×C4⋊C4—221no—
541C2×C4⋊C4—221no—
542C2×C4⋊C4—221no—
543C2×C4⋊C4—221no—
544C2×C4⋊C4C22×D1111yescharacteristic
545C2×C4⋊C4C22×D1111yescharacteristic
546C2×C4⋊C4C22×D1111yescharacteristic
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×C22⋊C4—221no—
555C2×C42—21no—
556C2×C42—221no—
557C2×C42C22×D1111yescharacteristic
558#106—114no—
559#106C22×D1114yes—
560#106C22×D1114yes—
561C4⋊C8C22×D1114yes—
562#103—114no—
563#103—114no—
564#103—114no—
565#103—114no—
566#103—114no—
567#103C22×D1114yes—
568#103C22×D1114yes—
569#102—114no—
570#102—114no—
571#102—114no—
572C22⋊C8—114no—
573C22⋊C8—114no—
574#97—114no—
575C2×C11#331614yescomplemented
576C2×C11C2×#54611yescharacteristic
577C2×C11C22×#13711yescharacteristic
578C2×C11C2×#57711yescharacteristic
579D11—24no—
580D11—42no—
581D11—82no—
582C24—111no—
583C24—111no—
584C24—221no—
585#41—228no—
586#41—444no—
587#41—448no—
588C2×Q8—21no—
589C2×Q8—24no—
590C2×Q8—22no—
591C2×Q8—82no—
592C2×Q8—112no—
593C2×Q8—112no—
594C2×Q8—224no—
595C2×Q8—221no—
596C2×Q8—221no—
597C2×Q8—228no—
598C2×Q8—222no—
599C2×Q8—222no—
600C2×Q8—222no—
601C2×Q8—222no—
602C2×Q8—444no—
603C2×Q8—444no—
604C2×Q8—448no—
605C2×Q8#434314yes—
606C2×Q8C23×D1112yes—
607C2×D4—114no—
608C2×D4—112no—
609C2×D4—224no—
610C2×D4—224no—
611C2×D4—224no—
612C2×D4—221no—
613C2×D4—222no—
614C2×D4—222no—
615C2×D4—444no—
616C2×D4—444no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—111no—
622C22×C4—111no—
623C22×C4—112no—
624C22×C4—112no—
625C22×C4—112no—
626C22×C4—112no—
627C22×C4—224no—
628C22×C4—224no—
629C22×C4—224no—
630C22×C4—224no—
631C22×C4—222no—
632C22×C4—222no—
633C22×C4—222no—
634C22×C4—222no—
635C22×C4—221no—
636C22×C4—221no—
637C22×C4—221no—
638C22×C4—444no—
639C22×C4—444no—
640C22×C4—882no—
641C22×C4—882no—
642C22×C4D4×D1111yescharacteristic
643C22×C4D4×D1111yescharacteristic
644C22×C4C23×D1111yescharacteristic
645Q16—228no—
646Q16—444no—
647SD16—444no—
648M16—444no—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—112no—
652C2×C8—112no—
653C2×C8—222no—
654C2×C8—222no—
655C2×C8—444no—
656C2×C8C23×D1112yes—
657C2×C8C23×D1112yes—
658C4⋊C4—24no—
659C4⋊C4—24no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—114no—
664C4⋊C4—112no—
665C4⋊C4—224no—
666C4⋊C4—224no—
667C4⋊C4—224no—
668C4⋊C4—224no—
669C4⋊C4—224no—
670C4⋊C4—221no—
671C4⋊C4—224no—
672C4⋊C4C23×D1112yes—
673C4⋊C4C23×D1112yes—
674C4⋊C4C23×D1112yes—
675C22⋊C4—114no—
676C22⋊C4—114no—
677C22⋊C4—224no—
678C22⋊C4—224no—
679C22⋊C4—224no—
680C22⋊C4—224no—
681C22⋊C4—224no—
682C22⋊C4—224no—
683C42—24no—
684C42—224no—
685C42D4×D1112yes—
686C42C23×D1112yes—
687C11C2×#331611yescharacteristic, complemented, Sylow
688C23—114no—
689C23—112no—
690C23—112no—
691C23—222no—
692C23—222no—
693C23—222no—
694C23—222no—
695C23—222no—
696C23—222no—
697C23—442no—
698C23—442no—
699C23—442no—
700C23C2×D4×D1111yescharacteristic
701Q8—24no—
702Q8—22no—
703Q8—84no—
704Q8—222no—
705Q8—222no—
706Q8—222no—
707Q8—222no—
708Q8—448no—
709Q8—442no—
710Q8—442no—
711Q8C2×#434314yes—
712D4—228no—
713D4—222no—
714D4—222no—
715D4—448no—
716D4—448no—
717D4—442no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—112no—
729C2×C4—112no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—224no—
733C2×C4—224no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—222no—
737C2×C4—222no—
738C2×C4—222no—
739C2×C4—222no—
740C2×C4—222no—
741C2×C4—448no—
742C2×C4—448no—
743C2×C4—442no—
744C2×C4—442no—
745C2×C4—442no—
746C2×C4—884no—
747C2×C4—884no—
748C2×C4C2×D4×D1112yes—
749C2×C4C2×D4×D1112yes—
750C2×C4C2×D4×D1111yescharacteristic
751C2×C4C2×#434312yes—
752C2×C4#6704212yes—
753C2×C4C24×D1111yescharacteristic
754C8—22no—
755C8—22no—
756C8—222no—
757C8—222no—
758C22—114no—
759C22—228no—
760C22—222no—
761C22—222no—
762C22—222no—
763C22—222no—
764C22—222no—
765C22—444no—
766C22—442no—
767C22—442no—
768C22—442no—
769C22—884no—
770C22#1062316112yes—
771C22#1062329312yes—
772C22D11×#13712yes—
773C22C22×D4×D1111yescharacteristic
774C4—24no—
775C4—22no—
776C4—22no—
777C4—42no—
778C4—42no—
779C4—42no—
780C4—222no—
781C4—222no—
782C4—442no—
783C4—442no—
784C4—442no—
785C4#1062316112yes—
786C4C22×#434311yescharacteristic
787C4C2×#6704211yescharacteristic
788C2—224no—
789C2—442no—
790C2—882no—
791C2#1308072414yesdirect product factor
792C2C2×#1062316111yescharacteristic
793C2C2×D11×#13711yescharacteristic
794C2C2×#1062329311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#475C2
socleC23×C11C22×D4
prime radicalC2×#10623107C2
hypercenterC2×#475D11
hypocenterC11C2×#3316
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
1. C2×#10623261C2semidirect
3. #13080724C2direct (N × H)
4. C2×#10622702C2semidirect
5. C2×#10622476C2semidirect
6. C2×#10622475C2semidirect
7. C2×#10622481C2semidirect
8. C2×#10622477C2semidirect
9. C2×#10622458C2semidirect
10. C2×#10622423C2semidirect
11. C2×#10622421C2semidirect
12. C2×#10622643C2semidirect
13. C2×#10622449C2semidirect
14. C2×#10622416C2semidirect
15. C2×D11×#103C2semidirect
16. C2×C11×#475C2semidirect
29. #10623261C22semidirect
47. C11×#475C22semidirect
58. #10622702C22semidirect
59. #10622643C22semidirect
67. #10622481C22semidirect
68. #10622477C22semidirect
69. #10622476C22semidirect
70. #10622475C22semidirect
71. #10622458C22semidirect
72. #10622449C22semidirect
73. #10622423C22semidirect
74. #10622421C22semidirect
75. #10622416C22semidirect
76. D11×#103C22semidirect
297. C2×#475D11semidirect
410. #475C2×D11semidirect
575. C2×C11#3316semidirect
687. C11C2×#3316semidirect
791. C2#13080724direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232612
C2×#106231072
#130807242
C2×#106227022
C2×#106224762
C2×#106224752
C2×#106224812
C2×#106224772
C2×#106224582
C2×#106224232
C2×#106224212
C2×#106226432
C2×#106224492
C2×#106224162
C2×D11×#1032
C2×C11×#4752
C2×#331611