Finite Group Databasebeta

← C2×#13080713 #15630428

Subgroups — C2×#13080713 #15630428

Order 2816.

2126 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×#10623044C211yesmaximal, characteristic, complemented
2C2×#10623355C211yesmaximal, characteristic
3#13080713C2116yesmaximal, direct product factor
4C2×#10622410C211yesmaximal, characteristic, complemented
5C2×#10622583C211yesmaximal, characteristic, complemented
6C2×#10622428C211yesmaximal, characteristic, complemented
7C2×#10622376C211yesmaximal, characteristic, complemented
8C2×#10622750C211yesmaximal, characteristic, complemented
9C2×#10622426C211yesmaximal, characteristic, complemented
10C2×#10622406C211yesmaximal, characteristic, complemented
11C2×#10622396C211yesmaximal, characteristic, complemented
12C2×#10622852C211yesmaximal, characteristic, complemented
13C2×#10622370C211yesmaximal, characteristic, complemented
14C2×#10622740C211yesmaximal, characteristic, complemented
15C2×#10622385C211yesmaximal, characteristic, complemented
16C2×C11×#417C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×#4341C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21#10623355—24no—
22#10623355C2218yes—
23C2×#66999C2211yescharacteristic
24C2×#66997C2211yescharacteristic
25C22×#4326C2211yescharacteristic
26C2×#66992—21no—
27C2×#66988—21no—
28C2×D4×Dic11C2211yescharacteristic
29C22×#4324C2211yescharacteristic
30C2×#66982—21no—
31C2×#66982—21no—
32C2×C4×C22⋊D11C2211yescharacteristic
33C2×#66979—21no—
34C2×#66977C2211yescharacteristic
35C2×#66977C2211yescharacteristic
36C22×Dic11⋊C4—21no—
37C22×Dic44C2211yescharacteristic
38C22×C8×D11C2211yescharacteristic
39#10623044—24no—
40#10623044C2218yescomplemented
41C2×#66951—21no—
42C2×#66950C2211yescharacteristic
43C2×#66945C2211yescharacteristic
44C2×#66943C2211yescharacteristic
45C2×#66942—21no—
46C2×#66940C2211yescharacteristic
47C11×#417C2218yescomplemented
48C2×C11×#103C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52#10622852C2218yescomplemented
53C2×#66899C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55C2×C22⋊(C11⋊C8)C2211yescharacteristic
56#10622750C2218yescomplemented
57#10622740C2218yescomplemented
58C2×(C2×D11)⋊C8C2211yescharacteristic
59C2×#66881C2211yescharacteristic
60C2×#66880C2211yescharacteristic
61C2×#66880C2211yescharacteristic
62C2×#66879C2211yescharacteristic
63C2×Dic11⋊C8C2211yescharacteristic
64#10622583C2218yescomplemented
65C2×#66874C2211yescharacteristic
66C2×#66874C2211yescharacteristic
67C2×#66871C2211yescharacteristic
68C2×#66871C2211yescharacteristic
69#10622428C2218yescomplemented
70#10622426C2218yescomplemented
71#10622410C2218yescomplemented
72#10622406C2218yescomplemented
73#10622396C2218yescomplemented
74#10622385C2218yescomplemented
75#10622376C2218yescomplemented
76#10622370C2218yescomplemented
77C2×C11×#41—22no—
78C2×C11×#41—24no—
79C2×C11×#41—42no—
80C2×C11×#41C2314yes—
81C22×Q8×C11C2311yescharacteristic
82C22×D4×C11—21no—
83C22×D4×C11C2311yescharacteristic
84C23×C4×C11—21no—
85C23×C4×C11—21no—
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11—21no—
88C22×C22⋊D11D411yescharacteristic
89C23×Dic11—21no—
90C23×Dic11—21no—
91C2×#4341—24no—
92C2×#4341—22no—
93C2×#4341—42no—
94C2×#4341C2314yes—
95C22×C4×D11C2311yescharacteristic
96C22×Dic22C2311yescharacteristic
97C22×Dic22C2311yescharacteristic
98C2×C11×M16—42no—
99C2×C11×M16C2314yes—
100C22×C8×C11C2311yescharacteristic
101C22×C8×C11C2311yescharacteristic
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—22no—
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C4⋊C4C2314yes—
107C2×C22⋊Dic11—21no—
108C2×C22⋊Dic11—21no—
109C2×C22⋊Dic11—21no—
110C2×C22⋊Dic11D411yescharacteristic
111#66999—22no—
112#66999C2314yes—
113#66997—22no—
114#66997C2314yes—
115C2×#4326—42no—
116C2×#4326C2314yes—
117#66992—28no—
118#66988—28no—
119D4×Dic11—22no—
120D4×Dic11C2314yes—
121C2×#4324—24no—
122C2×#4324C2314yes—
123#66982—28no—
124#66982—28no—
125C4×C22⋊D11D414yes—
126C4×C22⋊D11C2314yes—
127C2×(C2×D11)⋊C4—21no—
128C2×(C2×D11)⋊C4—21no—
129C2×(C2×D11)⋊C4—21no—
130C2×(C2×D11)⋊C4D411yescharacteristic
131#66979—28no—
132C2×C4⋊Dic11—21no—
133C2×C4⋊Dic11—21no—
134C2×C4⋊Dic11C2311yescharacteristic
135C2×C4⋊Dic11C2311yescharacteristic
136#66977—22no—
137#66977—22no—
138#66977C2314yes—
139#66977C2314yes—
140C2×Dic11⋊C4—21no—
141C2×Dic11⋊C4—21no—
142C2×Dic11⋊C4—21no—
143C2×Dic11⋊C4—21no—
144C2×Dic11⋊C4—21no—
145C2×Dic11⋊C4—21no—
146C2×Dic11⋊C4—21no—
147C2×Dic11⋊C4—28no—
148C2×Dic11⋊C4D411yescharacteristic
149C2×C4×Dic11—21no—
150C2×C4×Dic11—21no—
151C2×C4×Dic11C2311yescharacteristic
152C22×C11⋊C8C2311yescharacteristic
153C22×C11⋊C8C2311yescharacteristic
154C2×Dic44—42no—
155C2×Dic44C2314yes—
156C2×C8×D11—42no—
157C2×C8×D11C2314yes—
158#66951—28no—
159#66950—22no—
160#66950C2314yes—
161#66945—22no—
162#66945C2314yes—
163#66943—22no—
164#66943C2314yes—
165#66942—28no—
166#66940—22no—
167#66940C2314yes—
168C11×#103C2314yes—
169C11×#103C2314yes—
170C11×#102C2314yes—
171C11×#102C2314yes—
172#66899C2314yes—
173#66896C2314yes—
174C22⋊(C11⋊C8)C2314yes—
175(C2×D11)⋊C8C2314yes—
176#66881C2314yes—
177#66880C2314yes—
178#66880C2314yes—
179#66879C2314yes—
180Dic11⋊C8C2314yes—
181#66874C2314yes—
182#66874C2314yes—
183#66871C2314yes—
184#66871C2314yes—
185C2×#3315—111nomaximal, Sylow
186C24×C11—21no—
187C24×C11C2×D411yescharacteristic
188C23×D11C2×D411yescharacteristic
189C11×#41—28no—
190C11×#41—44no—
191C11×#41—48no—
192C2×Q8×C11—21no—
193C2×Q8×C11—22no—
194C2×Q8×C11—22no—
195C2×Q8×C11C2412yes—
196C2×D4×C11—24no—
197C2×D4×C11—21no—
198C2×D4×C11—22no—
199C2×D4×C11—44no—
200C2×D4×C11#4114yes—
201C2×D4×C11C2412yes—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—24no—
208C22×C4×C11—24no—
209C22×C4×C11—44no—
210C22×C4×C11—44no—
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D412yes—
213C22×C4×C11C2412yes—
214C22×C4×C11C2411yescharacteristic
215C2×C22⋊D11—24no—
216C2×C22⋊D11—42no—
217C2×C22⋊D11—44no—
218C2×C22⋊D11C2×D414yes—
219C22×Dic11—24no—
220C22×Dic11—24no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—44no—
226C22×Dic11—44no—
227C22×Dic11C2×D411yescharacteristic
228C22×Dic11C2×D411yescharacteristic
229C22×Dic11C2×D411yescharacteristic
230#4341—28no—
231#4341—44no—
232#4341—48no—
233C2×C4×D11—22no—
234C2×C4×D11—22no—
235C2×C4×D11C2×D412yes—
236C2×C4×D11C2412yes—
237C2×Dic22—21no—
238C2×Dic22—21no—
239C2×Dic22—22no—
240C2×Dic22—22no—
241C2×Dic22—22no—
242C2×Dic22—22no—
243C2×Dic22C2412yes—
244C2×Dic22C2412yes—
245C11×M16—44no—
246C2×C8×C11—22no—
247C2×C8×C11—22no—
248C2×C8×C11C2412yes—
249C2×C8×C11C2412yes—
250C11×C4⋊C4—21no—
251C11×C4⋊C4—24no—
252C11×C4⋊C4—21no—
253C11×C4⋊C4C2412yes—
254C11×C4⋊C4C2412yes—
255C22⋊Dic11—24no—
256C22⋊Dic11—24no—
257C22⋊Dic11—24no—
258C22⋊Dic11C2×D414yes—
259#4326—44no—
260#4324—28no—
261(C2×D11)⋊C4—24no—
262(C2×D11)⋊C4—24no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4C2×D414yes—
265C4⋊Dic11—24no—
266C4⋊Dic11—24no—
267C4⋊Dic11—21no—
268C4⋊Dic11—21no—
269C4⋊Dic11C2412yes—
270C4⋊Dic11C2412yes—
271Dic11⋊C4—24no—
272Dic11⋊C4—24no—
273Dic11⋊C4—24no—
274Dic11⋊C4—24no—
275Dic11⋊C4—24no—
276Dic11⋊C4—24no—
277Dic11⋊C4—24no—
278Dic11⋊C4C2×D414yes—
279C4×Dic11—24no—
280C4×Dic11—24no—
281C4×Dic11C2×D412yes—
282C4×Dic11C2412yes—
283C2×C11⋊C8—22no—
284C2×C11⋊C8—22no—
285C2×C11⋊C8C2412yes—
286C2×C11⋊C8C2412yes—
287Dic44—44no—
288C8×D11—44no—
289C2×#552—111no—
290C2×#547—111no—
291#3315—1116no—
292C2×#491—111no—
293C2×#484—111no—
294C2×#485—111no—
295C2×#478—111no—
296C2×#470—111no—
297C2×#467—111no—
298C2×#462—111no—
299C2×#452—111no—
300C2×#452—111no—
301C2×#440—111no—
302C2×#435—111no—
303C2×#417D1111yescharacteristic, complemented
304C2×#416—111no—
305C23×C11—24no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—42no—
311C23×C11—42no—
312C23×C11C22×D412yes—
313C23×C11C22×D411yescharacteristic
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11C22×D412yes—
318Q8×C11—22no—
319Q8×C11—22no—
320Q8×C11—42no—
321D4×C11—24no—
322D4×C11—22no—
323D4×C11—48no—
324D4×C11C2×#4114yes—
325C2×C4×C11—22no—
326C2×C4×C11—24no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—48no—
333C2×C4×C11—48no—
334C2×C4×C11—42no—
335C2×C4×C11—42no—
336C2×C4×C11—42no—
337C2×C4×C11C22×D412yes—
338C2×C4×C11C22×D411yescharacteristic
339C2×C4×C11C2×#4112yes—
340C2×C4×C11H(5,𝔽2)12yes—
341C2×C4×C11C2511yescharacteristic
342C22⋊D11—44no—
343C22⋊D11—48no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—48no—
352C2×Dic11—48no—
353C2×Dic11—42no—
354C2×Dic11—42no—
355C2×Dic11—42no—
356C2×Dic11—42no—
357C2×Dic11C22×D412yes—
358C2×Dic11C22×D412yes—
359C2×Dic11C22×D412yes—
360C4×D11—24no—
361C4×D11—22no—
362C4×D11—22no—
363Dic22—22no—
364Dic22—22no—
365Dic22—22no—
366Dic22—22no—
367Dic22—42no—
368Dic22—42no—
369C8×C11—22no—
370C8×C11—22no—
371C11⋊C8—22no—
372C11⋊C8—22no—
373C22×#41—111no—
374C22×#41C2×D1111yescharacteristic
375C22×Q16—111no—
376C22×Q16—111no—
377C22×SD16—111no—
378C22×M16C2×D1111yescharacteristic
379C23×C8—111no—
380#552—118no—
381#552—224no—
382#547—118no—
383#547—224no—
384C2×C4⋊Q8—111no—
385C2×#126—221no—
386C2×#125—111no—
387C2×#125—221no—
388C2×#123—221no—
389C2×#123—221no—
390C2×#123—221no—
391C2×C22⋊Q8—111no—
392C2×C22⋊Q8—111no—
393C2×C22⋊Q8—111no—
394C2×C22⋊Q8—111no—
395C2×#121—221no—
396C2×C4×Q8—111no—
397C2×C4×D4—111no—
398C2×C4×D4—111no—
399C2×#117—111no—
400C2×#117—221no—
401C22×C4⋊C4—221no—
402C22×C4⋊C4C2×D1111yescharacteristic
403#491—118no—
404#485—118no—
405#484—118no—
406#478—118no—
407#470—118no—
408#467—118no—
409#462—118no—
410#452—118no—
411#452—118no—
412#440—118no—
413#435—118no—
414C2×#107—111no—
415C2×#107—111no—
416C2×#106—111no—
417C2×C4⋊C8—111no—
418#417C2×D1118yescomplemented
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×#102C2×D1111yescharacteristic
429C2×#102C2×D1111yescharacteristic
430C2×C22⋊C8—111no—
431C2×C22⋊C8—111no—
432C2×#97—111no—
433C22×C11—22no—
434C22×C11—24no—
435C22×C11—22no—
436C22×C11—22no—
437C22×C11—44no—
438C22×C11—48no—
439C22×C11—42no—
440C22×C11—42no—
441C22×C11#54612yes—
442C22×C11#57512yes—
443C22×C11#57812yes—
444C22×C11C23×D411yescharacteristic
445C2×D11—22no—
446C2×D11—22no—
447C2×D11—22no—
448C2×D11—44no—
449C4×C11—22no—
450C4×C11—42no—
451C4×C11—42no—
452C4×C11—42no—
453C4×C11#54612yes—
454C4×C11C22×#4111yescharacteristic
455C4×C11C2×H(5,𝔽2)11yescharacteristic
456Dic11—22no—
457Dic11—22no—
458Dic11—22no—
459Dic11—42no—
460Dic11—42no—
461Dic11—42no—
462Dic11—42no—
463C2×#41—22no—
464C2×#41—24no—
465C2×#41—42no—
466C2×#41—114no—
467C2×#41—222no—
468C2×#41—224no—
469C2×#41—442no—
470C2×#41C22×D1114yes—
471C22×Q8—111no—
472C22×Q8—111no—
473C22×Q8C22×D1111yescharacteristic
474C22×D4—21no—
475C22×D4—111no—
476C22×D4—221no—
477C22×D4C22×D1111yescharacteristic
478C23×C4—21no—
479C23×C4—21no—
480C23×C4—111no—
481C23×C4—221no—
482C23×C4—221no—
483C23×C4C22×D1111yescharacteristic
484C2×Q16—114no—
485C2×Q16—114no—
486C2×Q16—442no—
487C2×Q16—442no—
488C2×SD16—114no—
489C2×SD16—224no—
490C2×M16—42no—
491C2×M16C22×D1114yes—
492C22×C8—111no—
493C22×C8—111no—
494C22×C8—114no—
495C22×C8—442no—
496C22×C8C22×D1111yescharacteristic
497C22×C8C22×D1111yescharacteristic
498C4⋊Q8—114no—
499C4⋊Q8—222no—
500#126—228no—
501#125—114no—
502#125—222no—
503#125—228no—
504#123—228no—
505#123—228no—
506#123—228no—
507C22⋊Q8—114no—
508C22⋊Q8—114no—
509C22⋊Q8—114no—
510C22⋊Q8—114no—
511C22⋊Q8—222no—
512C22⋊Q8—222no—
513C22⋊Q8—222no—
514C22⋊Q8—222no—
515#121—228no—
516C4×Q8—114no—
517C4×Q8—222no—
518C4×D4—114no—
519C4×D4—114no—
520C4×D4—114no—
521C4×D4—222no—
522#117—114no—
523#117—228no—
524#117—222no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—22no—
527C2×C4⋊C4—111no—
528C2×C4⋊C4—111no—
529C2×C4⋊C4—111no—
530C2×C4⋊C4—228no—
531C2×C4⋊C4—221no—
532C2×C4⋊C4—221no—
533C2×C4⋊C4—221no—
534C2×C4⋊C4—221no—
535C2×C4⋊C4—221no—
536C2×C4⋊C4—221no—
537C2×C4⋊C4—221no—
538C2×C4⋊C4—221no—
539C2×C4⋊C4—221no—
540C2×C4⋊C4C22×D1111yescharacteristic
541C2×C4⋊C4C22×D1111yescharacteristic
542C2×C4⋊C4C22×D1114yes—
543C2×C22⋊C4—111no—
544C2×C22⋊C4—111no—
545C2×C22⋊C4—221no—
546C2×C22⋊C4—221no—
547C2×C22⋊C4—221no—
548C2×C22⋊C4—221no—
549C2×C22⋊C4—221no—
550C2×C22⋊C4—221no—
551C2×C42—111no—
552C2×C42—221no—
553C2×C42—221no—
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#103C22×D1114yes—
564#103C22×D1114yes—
565#102—114no—
566#102C22×D1114yes—
567#102C22×D1114yes—
568C22⋊C8—114no—
569C22⋊C8—114no—
570#97—114no—
571C2×C11—42no—
572C2×C11—44no—
573C2×C11#331514yescomplemented
574C2×C11C2×#54611yescharacteristic
575C2×C11C2×#57511yescharacteristic
576C2×C11C2×#57811yescharacteristic
577D11—42no—
578C24—21no—
579C24—111no—
580C24D4×D1111yescharacteristic
581#41—28no—
582#41—44no—
583#41—48no—
584#41—228no—
585#41—444no—
586#41—448no—
587C2×Q8—21no—
588C2×Q8—22no—
589C2×Q8—22no—
590C2×Q8—112no—
591C2×Q8—112no—
592C2×Q8—221no—
593C2×Q8—221no—
594C2×Q8—222no—
595C2×Q8—222no—
596C2×Q8—222no—
597C2×Q8—222no—
598C2×Q8C23×D1112yes—
599C2×D4—24no—
600C2×D4—21no—
601C2×D4—22no—
602C2×D4—44no—
603C2×D4—114no—
604C2×D4—224no—
605C2×D4—442no—
606C2×D4—444no—
607C2×D4#433914yes—
608C2×D4C23×D1112yes—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—24no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—111no—
619C22×C4—111no—
620C22×C4—111no—
621C22×C4—112no—
622C22×C4—112no—
623C22×C4—224no—
624C22×C4—224no—
625C22×C4—222no—
626C22×C4—222no—
627C22×C4—221no—
628C22×C4—221no—
629C22×C4—221no—
630C22×C4—221no—
631C22×C4—444no—
632C22×C4—444no—
633C22×C4D4×D1112yes—
634C22×C4D4×D1111yescharacteristic
635C22×C4C23×D1112yes—
636C22×C4C23×D1111yescharacteristic
637Q16—444no—
638Q16—444no—
639SD16—228no—
640M16—44no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—112no—
644C2×C8—112no—
645C2×C8—222no—
646C2×C8—222no—
647C2×C8—444no—
648C2×C8C23×D1112yes—
649C2×C8C23×D1112yes—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—24no—
653C4⋊C4—114no—
654C4⋊C4—112no—
655C4⋊C4—112no—
656C4⋊C4—224no—
657C4⋊C4—224no—
658C4⋊C4—224no—
659C4⋊C4—224no—
660C4⋊C4—224no—
661C4⋊C4—224no—
662C4⋊C4—224no—
663C4⋊C4—221no—
664C4⋊C4—221no—
665C4⋊C4—224no—
666C4⋊C4—224no—
667C4⋊C4C23×D1112yes—
668C4⋊C4C23×D1112yes—
669C22⋊C4—114no—
670C22⋊C4—114no—
671C22⋊C4—224no—
672C22⋊C4—224no—
673C22⋊C4—224no—
674C22⋊C4—224no—
675C22⋊C4—224no—
676C22⋊C4—224no—
677C42—112no—
678C42—112no—
679C42—224no—
680C42—224no—
681C11C2×#331511yescharacteristic, complemented, Sylow
682C23—22no—
683C23—24no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—42no—
688C23—42no—
689C23—112no—
690C23—222no—
691C23—222no—
692C23—222no—
693C23C2×D4×D1112yes—
694C23C2×D4×D1111yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—42no—
698Q8—222no—
699Q8—222no—
700Q8—222no—
701Q8—222no—
702Q8—442no—
703Q8—442no—
704D4—24no—
705D4—22no—
706D4—48no—
707D4—444no—
708D4—448no—
709D4C2×#433914yes—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—48no—
718C2×C4—48no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—112no—
723C2×C4—112no—
724C2×C4—112no—
725C2×C4—222no—
726C2×C4—222no—
727C2×C4—222no—
728C2×C4—224no—
729C2×C4—222no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—222no—
734C2×C4—222no—
735C2×C4—448no—
736C2×C4—448no—
737C2×C4—442no—
738C2×C4—442no—
739C2×C4—442no—
740C2×C4—442no—
741C2×C4C2×#433912yes—
742C2×C4C2×D4×D1112yes—
743C2×C4C2×D4×D1111yescharacteristic
744C2×C4#6703712yes—
745C2×C4C24×D1111yescharacteristic
746C8—22no—
747C8—22no—
748C8—222no—
749C8—222no—
750C22—22no—
751C22—24no—
752C22—22no—
753C22—22no—
754C22—44no—
755C22—48no—
756C22—42no—
757C22—42no—
758C22—222no—
759C22—222no—
760C22—222no—
761C22—444no—
762C22#1062302112yes—
763C22#1062330412yes—
764C22#1062331012yes—
765C22C22×D4×D1111yescharacteristic
766C4—22no—
767C4—42no—
768C4—42no—
769C4—42no—
770C4—222no—
771C4—222no—
772C4—222no—
773C4—442no—
774C4—442no—
775C4—442no—
776C4—442no—
777C4#1062302112yes—
778C4C22×#433911yescharacteristic
779C4C2×#6703711yescharacteristic
780C2—42no—
781C2—44no—
782C2—442no—
783C2#1308071314yesdirect product factor
784C2C2×#1062302111yescharacteristic
785C2C2×#1062330411yescharacteristic
786C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#417C2
socleC23×C11C22×D4
prime radicalC2×#10623355C2
hypercenterC2×#417D11
hypocenterC11C2×#3315
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#10623044C2semidirect
3. #13080713C2direct (N × H)
4. C2×#10622410C2semidirect
5. C2×#10622583C2semidirect
6. C2×#10622428C2semidirect
7. C2×#10622376C2semidirect
8. C2×#10622750C2semidirect
9. C2×#10622426C2semidirect
10. C2×#10622406C2semidirect
11. C2×#10622396C2semidirect
12. C2×#10622852C2semidirect
13. C2×#10622370C2semidirect
14. C2×#10622740C2semidirect
15. C2×#10622385C2semidirect
16. C2×C11×#417C2semidirect
40. #10623044C22semidirect
47. C11×#417C22semidirect
52. #10622852C22semidirect
56. #10622750C22semidirect
57. #10622740C22semidirect
64. #10622583C22semidirect
69. #10622428C22semidirect
70. #10622426C22semidirect
71. #10622410C22semidirect
72. #10622406C22semidirect
73. #10622396C22semidirect
74. #10622385C22semidirect
75. #10622376C22semidirect
76. #10622370C22semidirect
303. C2×#417D11semidirect
418. #417C2×D11semidirect
573. C2×C11#3315semidirect
681. C11C2×#3315semidirect
783. C2#13080713direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230442
C2×#106233552
#130807132
C2×#106224102
C2×#106225832
C2×#106224282
C2×#106223762
C2×#106227502
C2×#106224262
C2×#106224062
C2×#106223962
C2×#106228522
C2×#106223702
C2×#106227402
C2×#106223852
C2×C11×#4172
C2×#331511