Finite Group Databasebeta

← C2×#13080688 #15630513

Subgroups — C2×#13080688 #15630513

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×#10623172C211yesmaximal, characteristic, complemented
2C2×#10623164C211yesmaximal, characteristic
3#13080688C2116yesmaximal, direct product factor
4C2×#10622408C211yesmaximal, characteristic, complemented
5C2×#10622658C211yesmaximal, characteristic, complemented
6C2×#10622498C211yesmaximal, characteristic, complemented
7C2×#10622488C211yesmaximal, characteristic, complemented
8C2×#10622425C211yesmaximal, characteristic, complemented
9C2×#10622798C211yesmaximal, characteristic, complemented
10C2×#10622660C211yesmaximal, characteristic, complemented
11C2×#10622799C211yesmaximal, characteristic, complemented
12C2×#10622402C211yesmaximal, characteristic, complemented
13C2×#10622724C211yesmaximal, characteristic, complemented
14C2×#10622415C211yesmaximal, characteristic, complemented
15C2×#10622726C211yesmaximal, characteristic, complemented
16C2×C11×#467C211yesmaximal, characteristic, complemented
17C22×Q8×D11C2211yescharacteristic
18C22×#4339C2211yescharacteristic
19C22×C11×Q16C2211yescharacteristic
20C23×C8×C11C2211yescharacteristic
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×#67000C2211yescharacteristic
24C2×#66999C2211yescharacteristic
25C2×Q8×Dic11C2211yescharacteristic
26C22×#4326C2211yescharacteristic
27C22×#4325C2211yescharacteristic
28C2×C4×C22⋊D11C2211yescharacteristic
29C2×#66979C2211yescharacteristic
30C22×#4313C2211yescharacteristic
31#10623172—24no—
32#10623172C2218yescomplemented
33#10623164—24no—
34#10623164C2218yes—
35C2×#66951—21no—
36C2×#66949—21no—
37C2×#66948C2211yescharacteristic
38C2×#66946—21no—
39C2×#66945C2211yescharacteristic
40C2×#66941C2211yescharacteristic
41C2×#66940—21no—
42C2×#66940C2211yescharacteristic
43C2×#66938—21no—
44C2×#66938—21no—
45C2×#66937—21no—
46C2×#66932—21no—
47C11×#467C2218yescomplemented
48C2×C11×#107C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53C2×C22⋊(C11⋊C8)C2211yescharacteristic
54#10622799C2218yescomplemented
55#10622798C2218yescomplemented
56#10622726C2218yescomplemented
57C2×#66885C2211yescharacteristic
58C2×#66885C2211yescharacteristic
59#10622724C2218yescomplemented
60C2×(C2×D11)⋊C8C2211yescharacteristic
61C2×#66880C2211yescharacteristic
62C2×#66880C2211yescharacteristic
63C2×#66879C2211yescharacteristic
64C2×Dic11⋊C8C2211yescharacteristic
65#10622660C2218yescomplemented
66#10622658C2218yescomplemented
67C2×#66874C2211yescharacteristic
68C2×#66873C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71#10622498C2218yescomplemented
72#10622488C2218yescomplemented
73#10622425C2218yescomplemented
74#10622415C2218yescomplemented
75#10622408C2218yescomplemented
76#10622402C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11—21no—
81C22×C22⋊D11D411yescharacteristic
82C2×Q8×D11—22no—
83C2×Q8×D11—24no—
84C2×Q8×D11—42no—
85C2×Q8×D11C2314yes—
86C2×#4339—22no—
87C2×#4339—24no—
88C2×#4339—42no—
89C2×#4339C2314yes—
90C22×D44—21no—
91C22×D44C2311yescharacteristic
92C22×C4×D11—21no—
93C22×C4×D11—21no—
94C22×C4×D11C2311yescharacteristic
95C22×Dic22—21no—
96C22×Dic22—21no—
97C22×Dic22C2311yescharacteristic
98C2×C11×Q16—42no—
99C2×C11×Q16C2314yes—
100C22×C8×C11—42no—
101C22×C8×C11C2311yescharacteristic
102C22×C8×C11C2311yescharacteristic
103C22×C8×C11C2314yes—
104C11×C22⋊Q8—22no—
105C11×C22⋊Q8—22no—
106C11×C22⋊Q8C2314yes—
107C11×C22⋊Q8C2314yes—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C22⋊Dic11—21no—
115C2×C22⋊Dic11D411yescharacteristic
116#67000—22no—
117#67000C2314yes—
118#66999—22no—
119#66999C2314yes—
120Q8×Dic11—22no—
121Q8×Dic11C2314yes—
122C2×#4326—24no—
123C2×#4326C2314yes—
124C2×#4325—42no—
125C2×#4325C2314yes—
126C4×C22⋊D11D414yes—
127C4×C22⋊D11C2314yes—
128C2×(C2×D11)⋊C4—21no—
129C2×(C2×D11)⋊C4—21no—
130C2×(C2×D11)⋊C4—21no—
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4D411yescharacteristic
134#66979—22no—
135#66979C2314yes—
136C2×C4⋊Dic11—21no—
137C2×C4⋊Dic11C2311yescharacteristic
138C2×C4⋊Dic11C2311yescharacteristic
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C2×Dic11⋊C4—21no—
142C2×Dic11⋊C4D411yescharacteristic
143C2×C4×Dic11—21no—
144C2×C4×Dic11—21no—
145C2×C4×Dic11—21no—
146C2×C4×Dic11—21no—
147C2×C4×Dic11C2311yescharacteristic
148C22×C11⋊C8C2311yescharacteristic
149C22×C11⋊C8C2311yescharacteristic
150C2×#4313—42no—
151C2×#4313C2314yes—
152#66951—28no—
153#66949—28no—
154#66948—22no—
155#66948C2314yes—
156#66946—28no—
157#66945—22no—
158#66945C2314yes—
159#66941—22no—
160#66941C2314yes—
161#66940—28no—
162#66940—22no—
163#66940C2314yes—
164#66938—28no—
165#66938—28no—
166#66937—28no—
167#66932—28no—
168C11×#107C2314yes—
169C11×#103C2314yes—
170C11×#103C2314yes—
171#66899C2314yes—
172#66899C2314yes—
173C22⋊(C11⋊C8)C2314yes—
174#66885C2314yes—
175#66885C2314yes—
176(C2×D11)⋊C8C2314yes—
177#66880C2314yes—
178#66880C2314yes—
179#66879C2314yes—
180Dic11⋊C8C2314yes—
181#66874C2314yes—
182#66873C2314yes—
183#66872C2314yes—
184#66871C2314yes—
185C2×#3313—111nomaximal, Sylow
186C24×C11C2×D411yescharacteristic
187C23×D11—21no—
188C23×D11C2×D411yescharacteristic
189C2×Q8×C11—21no—
190C2×Q8×C11—21no—
191C2×Q8×C11—22no—
192C2×Q8×C11—22no—
193C2×Q8×C11—22no—
194C2×Q8×C11—22no—
195C2×Q8×C11C2412yes—
196C2×Q8×C11C2412yes—
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×C11C2×D411yescharacteristic
204C22×C4×C11C2×D412yes—
205C22×C4×C11C2412yes—
206C22×C4×C11C2411yescharacteristic
207C2×C22⋊D11—24no—
208C2×C22⋊D11—42no—
209C2×C22⋊D11—44no—
210C2×C22⋊D11C2×D414yes—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11C2×D411yescharacteristic
215C22×Dic11C2×D411yescharacteristic
216C22×Dic11C2×D411yescharacteristic
217Q8×D11—28no—
218Q8×D11—44no—
219Q8×D11—48no—
220#4339—28no—
221#4339—44no—
222#4339—48no—
223C2×D44—24no—
224C2×D44—21no—
225C2×D44—22no—
226C2×D44—22no—
227C2×D44—44no—
228C2×D44C2412yes—
229C2×C4×D11—24no—
230C2×C4×D11—24no—
231C2×C4×D11—22no—
232C2×C4×D11—22no—
233C2×C4×D11—44no—
234C2×C4×D11—44no—
235C2×C4×D11C2×D412yes—
236C2×C4×D11C2412yes—
237C2×Dic22—24no—
238C2×Dic22—24no—
239C2×Dic22—21no—
240C2×Dic22—22no—
241C2×Dic22—44no—
242C2×Dic22—44no—
243C2×Dic22#4114yes—
244C2×Dic22C2412yes—
245C11×Q16—44no—
246C2×C8×C11—22no—
247C2×C8×C11—22no—
248C2×C8×C11—44no—
249C2×C8×C11C2412yes—
250C2×C8×C11C2412yes—
251C11×C4⋊C4—21no—
252C11×C4⋊C4—24no—
253C11×C4⋊C4—21no—
254C11×C4⋊C4—24no—
255C11×C4⋊C4C2412yes—
256C11×C4⋊C4C2412yes—
257C11×C22⋊C4—24no—
258C11×C22⋊C4—24no—
259C22⋊Dic11—24no—
260C22⋊Dic11C2×D414yes—
261#4326—28no—
262#4325—44no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—24no—
265(C2×D11)⋊C4—24no—
266(C2×D11)⋊C4—24no—
267(C2×D11)⋊C4—24no—
268(C2×D11)⋊C4C2×D414yes—
269C4⋊Dic11—24no—
270C4⋊Dic11—21no—
271C4⋊Dic11—21no—
272C4⋊Dic11C2412yes—
273C4⋊Dic11C2412yes—
274Dic11⋊C4—24no—
275Dic11⋊C4—24no—
276Dic11⋊C4—24no—
277Dic11⋊C4C2×D414yes—
278C4×Dic11—24no—
279C4×Dic11—24no—
280C4×Dic11—24no—
281C4×Dic11—24no—
282C4×Dic11C2×D412yes—
283C4×Dic11C2412yes—
284C2×C11⋊C8—22no—
285C2×C11⋊C8—22no—
286C2×C11⋊C8C2412yes—
287C2×C11⋊C8C2412yes—
288#4313—44no—
289C2×#556—111no—
290C2×#548—111no—
291#3313—1116no—
292C2×#489—111no—
293C2×#485—111no—
294C2×#482—111no—
295C2×#477—111no—
296C2×#468—111no—
297C2×#467D1111yescharacteristic, complemented
298C2×#464—111no—
299C2×#452—111no—
300C2×#451—111no—
301C2×#441—111no—
302C2×#435—111no—
303C2×#419—111no—
304C2×#416—111no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11C22×D412yes—
309C23×C11C22×D411yescharacteristic
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—42no—
315C22×D11—42no—
316C22×D11—42no—
317C22×D11C22×D412yes—
318Q8×C11—22no—
319Q8×C11—22no—
320Q8×C11—22no—
321Q8×C11—22no—
322Q8×C11—42no—
323Q8×C11—42no—
324C2×C4×C11—22no—
325C2×C4×C11—24no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—42no—
333C2×C4×C11—42no—
334C2×C4×C11—42no—
335C2×C4×C11—42no—
336C2×C4×C11C22×D412yes—
337C2×C4×C11C22×D411yescharacteristic
338C2×C4×C11C2×#4112yes—
339C2×C4×C11H(5,𝔽2)12yes—
340C2×C4×C11C2511yescharacteristic
341C22⋊D11—44no—
342C22⋊D11—48no—
343C2×Dic11—24no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—42no—
351C2×Dic11—42no—
352C2×Dic11C22×D412yes—
353C2×Dic11C22×D412yes—
354C2×Dic11C22×D412yes—
355D44—22no—
356D44—22no—
357D44—48no—
358D44—42no—
359C4×D11—24no—
360C4×D11—22no—
361C4×D11—22no—
362C4×D11—48no—
363C4×D11—48no—
364Dic22—24no—
365Dic22—22no—
366Dic22—48no—
367Dic22—48no—
368Dic22C2×#4114yes—
369C8×C11—22no—
370C8×C11—22no—
371C11⋊C8—22no—
372C11⋊C8—22no—
373C22×#41—111no—
374C23×Q8—111no—
375C22×Q16—111no—
376C22×Q16C2×D1111yescharacteristic
377C22×SD16—111no—
378C22×M16—111no—
379C23×C8C2×D1111yescharacteristic
380#556—118no—
381#556—224no—
382#548—118no—
383#548—224no—
384C2×C4⋊Q8—111no—
385C2×#126—221no—
386C2×#126—221no—
387C2×#124—111no—
388C2×#124—221no—
389C2×#124—221no—
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×Q8—111no—
398C2×C4×Q8—221no—
399C2×C4×D4—111no—
400C2×C4×D4—221no—
401C2×#117—111no—
402C2×#117—111no—
403#489—118no—
404#485—118no—
405#482—118no—
406#477—118no—
407#468—118no—
408#467C2×D1118yescomplemented
409#464—118no—
410#452—118no—
411#451—118no—
412#441—118no—
413#435—118no—
414C2×#107—111no—
415C2×#107C2×D1111yescharacteristic
416C2×#106—111no—
417C2×C4⋊C8—111no—
418#419—118no—
419#416—118no—
420C2×#103—111no—
421C2×#103—111no—
422C2×#103—111no—
423C2×#103—111no—
424C2×#103—111no—
425C2×#103C2×D1111yescharacteristic
426C2×#103C2×D1111yescharacteristic
427C2×#102—111no—
428C2×#102—111no—
429C2×#102—111no—
430C2×C22⋊C8—111no—
431C2×C22⋊C8—111no—
432C2×#97—111no—
433C22×C11—22no—
434C22×C11—22no—
435C22×C11—22no—
436C22×C11—44no—
437C22×C11#54612yes—
438C22×C11#57512yes—
439C22×C11#57812yes—
440C22×C11C23×D411yescharacteristic
441C2×D11—22no—
442C2×D11—22no—
443C2×D11—22no—
444C2×D11—44no—
445C2×D11—42no—
446C2×D11—42no—
447C2×D11—42no—
448C2×D11—84no—
449C4×C11—22no—
450C4×C11—42no—
451C4×C11—42no—
452C4×C11—42no—
453C4×C11—42no—
454C4×C11#54612yes—
455C4×C11C22×#4111yescharacteristic
456C4×C11C2×H(5,𝔽2)11yescharacteristic
457Dic11—24no—
458Dic11—22no—
459Dic11—22no—
460Dic11—22no—
461Dic11—42no—
462Dic11—42no—
463C2×#41—114no—
464C2×#41—224no—
465C2×#41—222no—
466C2×#41—442no—
467C22×Q8—114no—
468C22×Q8—111no—
469C22×Q8—221no—
470C22×Q8—221no—
471C22×Q8—222no—
472C22×Q8—224no—
473C22×Q8—442no—
474C22×Q8C22×D1111yescharacteristic
475C22×Q8C22×D1111yescharacteristic
476C22×D4—111no—
477C22×D4—111no—
478C22×D4—221no—
479C22×D4—221no—
480C23×C4—111no—
481C23×C4—221no—
482C23×C4—221no—
483C23×C4C22×D1111yescharacteristic
484C2×Q16—42no—
485C2×Q16—114no—
486C2×Q16—224no—
487C2×Q16C22×D1114yes—
488C2×SD16—114no—
489C2×SD16—442no—
490C2×M16—114no—
491C2×M16—442no—
492C22×C8—42no—
493C22×C8—111no—
494C22×C8—111no—
495C22×C8C22×D1111yescharacteristic
496C22×C8C22×D1111yescharacteristic
497C22×C8C22×D1114yes—
498C4⋊Q8—114no—
499C4⋊Q8—222no—
500#126—228no—
501#126—228no—
502#124—114no—
503#124—222no—
504#124—228no—
505#124—228no—
506C22⋊Q8—22no—
507C22⋊Q8—22no—
508C22⋊Q8—114no—
509C22⋊Q8—228no—
510C22⋊Q8—222no—
511C22⋊Q8C22×D1114yes—
512C22⋊Q8C22×D1114yes—
513#121—114no—
514#121—228no—
515#121—222no—
516C4×Q8—114no—
517C4×Q8—114no—
518C4×Q8—222no—
519C4×Q8—222no—
520C4×Q8—228no—
521C4×D4—114no—
522C4×D4—114no—
523C4×D4—228no—
524#117—114no—
525#117—114no—
526#117—222no—
527#117—222no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—111no—
531C2×C4⋊C4—111no—
532C2×C4⋊C4—111no—
533C2×C4⋊C4—221no—
534C2×C4⋊C4—221no—
535C2×C4⋊C4—221no—
536C2×C4⋊C4—221no—
537C2×C4⋊C4C22×D1111yescharacteristic
538C2×C4⋊C4C22×D1111yescharacteristic
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—111no—
542C2×C22⋊C4—111no—
543C2×C22⋊C4—221no—
544C2×C22⋊C4—221no—
545C2×C22⋊C4—221no—
546C2×C22⋊C4—221no—
547C2×C22⋊C4—221no—
548C2×C22⋊C4—221no—
549C2×C42—111no—
550C2×C42—221no—
551C2×C42—221no—
552C2×C42—221no—
553C2×C42—221no—
554#107—114no—
555#107C22×D1114yes—
556#106—114no—
557C4⋊C8—114no—
558#103—114no—
559#103—114no—
560#103—114no—
561#103—114no—
562#103—114no—
563#103C22×D1114yes—
564#103C22×D1114yes—
565#102—114no—
566#102—114no—
567#102—114no—
568C22⋊C8—114no—
569C22⋊C8—114no—
570#97—114no—
571C2×C11—42no—
572C2×C11#331314yescomplemented
573C2×C11C2×#54611yescharacteristic
574C2×C11C2×#57511yescharacteristic
575C2×C11C2×#57811yescharacteristic
576D11—42no—
577D11—82no—
578C24—111no—
579C24—221no—
580C24D4×D1111yescharacteristic
581#41—228no—
582#41—444no—
583#41—448no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—22no—
589C2×Q8—22no—
590C2×Q8—114no—
591C2×Q8—112no—
592C2×Q8—224no—
593C2×Q8—224no—
594C2×Q8—221no—
595C2×Q8—222no—
596C2×Q8—228no—
597C2×Q8—444no—
598C2×Q8—444no—
599C2×Q8—444no—
600C2×Q8—448no—
601C2×Q8C23×D1112yes—
602C2×Q8C23×D1112yes—
603C2×D4—114no—
604C2×D4—112no—
605C2×D4—224no—
606C2×D4—224no—
607C2×D4—221no—
608C2×D4—222no—
609C2×D4—222no—
610C2×D4—444no—
611C2×D4—442no—
612C2×D4—444no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—111no—
620C22×C4—111no—
621C22×C4—111no—
622C22×C4—112no—
623C22×C4—112no—
624C22×C4—224no—
625C22×C4—221no—
626C22×C4—222no—
627C22×C4—222no—
628C22×C4—221no—
629C22×C4—221no—
630C22×C4—224no—
631C22×C4—444no—
632C22×C4—444no—
633C22×C4D4×D1112yes—
634C22×C4D4×D1111yescharacteristic
635C22×C4C23×D1112yes—
636C22×C4C23×D1111yescharacteristic
637Q16—44no—
638Q16—228no—
639SD16—444no—
640M16—444no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—44no—
644C2×C8—112no—
645C2×C8—112no—
646C2×C8—222no—
647C2×C8—222no—
648C2×C8C23×D1112yes—
649C2×C8C23×D1112yes—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—114no—
655C4⋊C4—112no—
656C4⋊C4—112no—
657C4⋊C4—224no—
658C4⋊C4—224no—
659C4⋊C4—224no—
660C4⋊C4—224no—
661C4⋊C4—221no—
662C4⋊C4—221no—
663C4⋊C4C23×D1112yes—
664C4⋊C4C23×D1112yes—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—114no—
668C22⋊C4—114no—
669C22⋊C4—224no—
670C22⋊C4—224no—
671C22⋊C4—224no—
672C22⋊C4—224no—
673C22⋊C4—224no—
674C22⋊C4—224no—
675C42—112no—
676C42—112no—
677C42—224no—
678C42—224no—
679C42—224no—
680C42—224no—
681C11C2×#331311yescharacteristic, complemented, Sylow
682C23—22no—
683C23—22no—
684C23—22no—
685C23—112no—
686C23—222no—
687C23—222no—
688C23—222no—
689C23—222no—
690C23—442no—
691C23—442no—
692C23—442no—
693C23C2×D4×D1112yes—
694C23C2×D4×D1111yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—42no—
700Q8—42no—
701Q8—114no—
702Q8—224no—
703Q8—222no—
704Q8—448no—
705Q8—448no—
706D4—222no—
707D4—222no—
708D4—448no—
709D4—444no—
710D4—448no—
711D4—442no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—112no—
725C2×C4—112no—
726C2×C4—112no—
727C2×C4—222no—
728C2×C4—222no—
729C2×C4—222no—
730C2×C4—224no—
731C2×C4—222no—
732C2×C4—224no—
733C2×C4—222no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—222no—
737C2×C4—448no—
738C2×C4—448no—
739C2×C4—442no—
740C2×C4—442no—
741C2×C4C2×D4×D1112yes—
742C2×C4C2×D4×D1111yescharacteristic
743C2×C4#6703712yes—
744C2×C4#41×D1112yes—
745C2×C4C24×D1111yescharacteristic
746C8—22no—
747C8—22no—
748C8—222no—
749C8—222no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—44no—
754C22—222no—
755C22—222no—
756C22—222no—
757C22—444no—
758C22—442no—
759C22—442no—
760C22—442no—
761C22—884no—
762C22#1062314112yes—
763C22#1062329712yes—
764C22#1062329912yes—
765C22C22×D4×D1111yescharacteristic
766C4—22no—
767C4—42no—
768C4—42no—
769C4—42no—
770C4—42no—
771C4—222no—
772C4—224no—
773C4—222no—
774C4—222no—
775C4—442no—
776C4—442no—
777C4#1062314112yes—
778C4C2×#6703711yescharacteristic
779C4C2×#41×D1111yescharacteristic
780C2—42no—
781C2—442no—
782C2—882no—
783C2#1308068814yesdirect product factor
784C2C2×#1062314111yescharacteristic
785C2C2×#1062329911yescharacteristic
786C2C2×#1062329711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#467C2
socleC23×C11C22×D4
prime radicalC2×#10623164C2
hypercenterC2×#467D11
hypocenterC11C2×#3313
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C2×#10623172C2semidirect
3. #13080688C2direct (N × H)
4. C2×#10622408C2semidirect
5. C2×#10622658C2semidirect
6. C2×#10622498C2semidirect
7. C2×#10622488C2semidirect
8. C2×#10622425C2semidirect
9. C2×#10622798C2semidirect
10. C2×#10622660C2semidirect
11. C2×#10622799C2semidirect
12. C2×#10622402C2semidirect
13. C2×#10622724C2semidirect
14. C2×#10622415C2semidirect
15. C2×#10622726C2semidirect
16. C2×C11×#467C2semidirect
32. #10623172C22semidirect
47. C11×#467C22semidirect
54. #10622799C22semidirect
55. #10622798C22semidirect
56. #10622726C22semidirect
59. #10622724C22semidirect
65. #10622660C22semidirect
66. #10622658C22semidirect
71. #10622498C22semidirect
72. #10622488C22semidirect
73. #10622425C22semidirect
74. #10622415C22semidirect
75. #10622408C22semidirect
76. #10622402C22semidirect
297. C2×#467D11semidirect
408. #467C2×D11semidirect
572. C2×C11#3313semidirect
681. C11C2×#3313semidirect
783. C2#13080688direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231722
C2×#106231642
#130806882
C2×#106224082
C2×#106226582
C2×#106224982
C2×#106224882
C2×#106224252
C2×#106227982
C2×#106226602
C2×#106227992
C2×#106224022
C2×#106227242
C2×#106224152
C2×#106227262
C2×C11×#4672
C2×#331311