Finite Group Databasebeta

← C2×#13081701 #15634800

Subgroups — C2×#13081701 #15634800

Order 2816.

2066 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623244C211yesmaximal, characteristic, complemented
2C2×#10623212C211yesmaximal, characteristic, complemented
3#13081701C2116yesmaximal, direct product factor
4C2×#10622767C211yesmaximal, characteristic, complemented
5C2×#10622781C211yesmaximal, characteristic, complemented
6C2×#10622779C211yesmaximal, characteristic, complemented
7C2×#10622667C211yesmaximal, characteristic, complemented
8C2×#10622778C211yesmaximal, characteristic, complemented
9C2×#10622766C211yesmaximal, characteristic, complemented
10C2×#10622763C211yesmaximal, characteristic, complemented
11C2×#10622685C211yesmaximal, characteristic, complemented
12C2×#10622314C211yesmaximal, characteristic, complemented
13C2×#10622323C211yesmaximal, characteristic, complemented
14C2×#10622777C211yesmaximal, characteristic, complemented
15C2×D8×Dic11C211yesmaximal, characteristic, complemented
16C2×C11×#496C211yesmaximal, characteristic, complemented
17C22×C11×SD16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C22×C11×D8C2211yescharacteristic
20C22×C11×D8C2211yescharacteristic
21C2×C11×#127C2211yescharacteristic
22C2×C11×#124C2211yescharacteristic
23C2×#67000C2211yescharacteristic
24C2×Q8×Dic11C2211yescharacteristic
25C22×#4326C2211yescharacteristic
26C2×#66993C2211yescharacteristic
27C2×#66989—21no—
28C2×#66989C2211yescharacteristic
29C2×#66989C2211yescharacteristic
30C2×#66988—21no—
31C2×#66988—21no—
32C2×D4×Dic11—21no—
33C2×D4×Dic11C2211yescharacteristic
34C2×D4×Dic11C2211yescharacteristic
35C2×D4×Dic11C2211yescharacteristic
36C22×#4324C2211yescharacteristic
37C22×#4323C2211yescharacteristic
38C22×#4323C2211yescharacteristic
39C22×#4314C2211yescharacteristic
40#10623244—24no—
41#10623244C2218yescomplemented
42#10623212—24no—
43#10623212C2218yescomplemented
44C2×#66939—21no—
45C2×#66938—21no—
46C2×#66936—21no—
47C2×(C22⋊D11)⋊C4—21no—
48C2×C4×D44C2211yescharacteristic
49C2×C4×Dic22C2211yescharacteristic
50C2×C4×Dic22C2211yescharacteristic
51C11×#496C2218yescomplemented
52C2×C11×#97C2211yescharacteristic
53C2×#66899C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55C2×#66896C2211yescharacteristic
56C2×#66896C2211yescharacteristic
57#10622781C2218yescomplemented
58#10622779C2218yescomplemented
59#10622778C2218yescomplemented
60#10622777C2218yescomplemented
61#10622767C2218yescomplemented
62#10622766C2218yescomplemented
63#10622763C2218yescomplemented
64D8×Dic11C2218yescomplemented
65C2×#66885C2211yescharacteristic
66C2×#66882C2211yescharacteristic
67C2×#66880C2211yescharacteristic
68C2×#66879C2211yescharacteristic
69C2×Dic11⋊C8C2211yescharacteristic
70C2×Dic11⋊C8C2211yescharacteristic
71C2×C8×Dic11C2211yescharacteristic
72#10622685C2218yescomplemented
73#10622667C2218yescomplemented
74C2×C4⋊(C11⋊C8)C2211yescharacteristic
75#10622323C2218yescomplemented
76#10622314C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11C2311yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C23×Dic11—21no—
86C23×Dic11—21no—
87C23×Dic11—21no—
88C22×D44C2311yescharacteristic
89C22×C4×D11—21no—
90C22×Dic22D411yescharacteristic
91C22×Dic22C2311yescharacteristic
92C2×C11×SD16—24no—
93C2×C11×SD16—42no—
94C2×C11×SD16C2314yes—
95C2×C11×SD16C2314yes—
96C2×C11×D8—24no—
97C2×C11×D8—42no—
98C2×C11×D8C2314yes—
99C2×C11×D8C2314yes—
100C22×C8×C11C2311yescharacteristic
101C22×C8×C11C2311yescharacteristic
102C11×#127—22no—
103C11×#127C2314yes—
104C11×#124—22no—
105C11×#124C2314yes—
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C42×C11C2311yescharacteristic
109C2×C22⋊Dic11—21no—
110C2×C22⋊Dic11—21no—
111C2×C22⋊Dic11—21no—
112C2×C22⋊Dic11—21no—
113C2×C22⋊Dic11—21no—
114C2×C22⋊Dic11—21no—
115C2×C22⋊Dic11—21no—
116#67000—22no—
117#67000C2314yes—
118Q8×Dic11—22no—
119Q8×Dic11C2314yes—
120C2×#4326—42no—
121C2×#4326C2314yes—
122#66993—22no—
123#66993C2314yes—
124#66989—28no—
125#66989—22no—
126#66989—22no—
127#66989C2314yes—
128#66989C2314yes—
129#66988—28no—
130#66988—28no—
131D4×Dic11—28no—
132D4×Dic11—22no—
133D4×Dic11—22no—
134D4×Dic11—22no—
135D4×Dic11C2314yes—
136D4×Dic11C2314yes—
137D4×Dic11C2314yes—
138C2×#4324—42no—
139C2×#4324C2314yes—
140C2×#4323—42no—
141C2×#4323—42no—
142C2×#4323C2314yes—
143C2×#4323C2314yes—
144C2×(C2×D11)⋊C4—21no—
145C2×(C2×D11)⋊C4—21no—
146C2×(C2×D11)⋊C4—21no—
147C2×C4⋊Dic11—21no—
148C2×C4⋊Dic11D411yescharacteristic
149C2×C4⋊Dic11C2311yescharacteristic
150C2×C4⋊Dic11C2311yescharacteristic
151C2×Dic11⋊C4—21no—
152C2×Dic11⋊C4D411yescharacteristic
153C2×Dic11⋊C4D411yescharacteristic
154C2×C4×Dic11—21no—
155C2×C4×Dic11—21no—
156C2×C4×Dic11C2311yescharacteristic
157C2×C4×Dic11C2311yescharacteristic
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160C2×#4314—24no—
161C2×#4314C2314yes—
162#66939—28no—
163#66938—28no—
164#66936—28no—
165(C22⋊D11)⋊C4—28no—
166C4×D44—22no—
167C4×D44C2314yes—
168C4×Dic22—22no—
169C4×Dic22D414yes—
170C4×Dic22C2314yes—
171C4×Dic22C2314yes—
172C11×#97C2314yes—
173#66899C2314yes—
174#66896C2314yes—
175#66896C2314yes—
176#66896C2314yes—
177#66885C2314yes—
178#66882C2314yes—
179#66880C2314yes—
180#66879C2314yes—
181Dic11⋊C8C2314yes—
182Dic11⋊C8C2314yes—
183C8×Dic11C2314yes—
184C4⋊(C11⋊C8)C2314yes—
185C2×#3403—111nomaximal, Sylow
186C24×C11—21no—
187C24×C11—21no—
188C24×C11—21no—
189C23×D11—21no—
190C2×Q8×C11—21no—
191C2×Q8×C11—22no—
192C2×Q8×C11—22no—
193C2×Q8×C11C2412yes—
194C2×D4×C11—21no—
195C2×D4×C11—21no—
196C2×D4×C11—24no—
197C2×D4×C11—21no—
198C2×D4×C11—24no—
199C2×D4×C11—22no—
200C2×D4×C11—22no—
201C2×D4×C11—22no—
202C2×D4×C11—22no—
203C2×D4×C11—22no—
204C2×D4×C11—22no—
205C2×D4×C11—44no—
206C2×D4×C11—82no—
207C2×D4×C11C2412yes—
208C2×D4×C11C2412yes—
209C2×D4×C11C2412yes—
210C22×C4×C11—21no—
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2411yescharacteristic
214C2×C22⋊D11—24no—
215C2×C22⋊D11—24no—
216C2×C22⋊D11—44no—
217C2×C22⋊D11—82no—
218C22×Dic11—24no—
219C22×Dic11—24no—
220C22×Dic11—24no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—82no—
225C22×Dic11—82no—
226C22×Dic11—82no—
227C22×Dic11C2×D411yescharacteristic
228C22×Dic11C2×D411yescharacteristic
229C22×Dic11C2×D411yescharacteristic
230C22×Dic11C2×D411yescharacteristic
231C2×D44—21no—
232C2×D44—22no—
233C2×D44—22no—
234C2×D44C2412yes—
235C2×C4×D11—24no—
236C2×C4×D11—82no—
237C2×Dic22—21no—
238C2×Dic22—22no—
239C2×Dic22—22no—
240C2×Dic22—42no—
241C2×Dic22C2×D414yes—
242C2×Dic22C2412yes—
243C11×SD16—28no—
244C11×SD16—44no—
245C11×D8—28no—
246C11×D8—44no—
247C2×C8×C11—22no—
248C2×C8×C11#4114yes—
249C2×C8×C11C2412yes—
250C2×C8×C11C2412yes—
251C11×C22⋊C4—24no—
252C11×C22⋊C4—24no—
253C42×C11C2×D412yes—
254C42×C11C2412yes—
255C22⋊Dic11—24no—
256C22⋊Dic11—24no—
257C22⋊Dic11—24no—
258C22⋊Dic11—24no—
259C22⋊Dic11—24no—
260C22⋊Dic11—24no—
261C22⋊Dic11—24no—
262#4326—44no—
263#4324—44no—
264#4323—44no—
265#4323—44no—
266(C2×D11)⋊C4—24no—
267(C2×D11)⋊C4—24no—
268(C2×D11)⋊C4—24no—
269C4⋊Dic11—24no—
270C4⋊Dic11—21no—
271C4⋊Dic11—21no—
272C4⋊Dic11C2×D414yes—
273C4⋊Dic11C2412yes—
274C4⋊Dic11C2412yes—
275Dic11⋊C4—24no—
276Dic11⋊C4C2×D414yes—
277Dic11⋊C4C2×D414yes—
278C4×Dic11—24no—
279C4×Dic11—24no—
280C4×Dic11C2×D412yes—
281C4×Dic11C2×D412yes—
282C4×Dic11C2412yes—
283C4×Dic11C2412yes—
284C2×C11⋊C8—22no—
285C2×C11⋊C8—22no—
286C2×C11⋊C8C2412yes—
287C2×C11⋊C8C2412yes—
288#4314—28no—
289C2×#559—111no—
290C2×#559—111no—
291#3403—1116no—
292C2×#496—111no—
293C2×#496D1111yescharacteristic, complemented
294C2×#495—111no—
295C2×#464—111no—
296C2×#464—111no—
297C2×#463—111no—
298C2×#463—111no—
299C2×#459—111no—
300C2×#459—111no—
301C2×#446—111no—
302C2×#440—111no—
303C2×#440—111no—
304C2×C4×D8—111no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—42no—
309C23×C11—42no—
310C23×C11—42no—
311C23×C11—42no—
312C23×C11—42no—
313C23×C11—42no—
314C23×C11—42no—
315C23×C11—42no—
316C23×C11—42no—
317C23×C11C22×D411yescharacteristic
318C22×D11—22no—
319C22×D11—42no—
320C22×D11—42no—
321C22×D11—42no—
322Q8×C11—22no—
323Q8×C11—22no—
324Q8×C11—42no—
325D4×C11—22no—
326D4×C11—22no—
327D4×C11—22no—
328D4×C11—22no—
329D4×C11—22no—
330D4×C11—22no—
331D4×C11—48no—
332D4×C11—42no—
333D4×C11—42no—
334D4×C11—42no—
335D4×C11—84no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—42no—
340C2×C4×C11C22×D412yes—
341C2×C4×C11C22×D412yes—
342C2×C4×C11C22×D411yescharacteristic
343C2×C4×C11C2×#4112yes—
344C2×C4×C11H(5,𝔽2)12yes—
345C2×C4×C11C2511yescharacteristic
346C22⋊D11—48no—
347C22⋊D11—84no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—42no—
356C2×Dic11—42no—
357C2×Dic11—42no—
358C2×Dic11—84no—
359C2×Dic11—84no—
360C2×Dic11—84no—
361C2×Dic11C22×D412yes—
362C2×Dic11C22×D412yes—
363C2×Dic11C22×D412yes—
364C2×Dic11C22×D412yes—
365D44—22no—
366D44—22no—
367D44—42no—
368C4×D11—84no—
369Dic22—22no—
370Dic22—22no—
371Dic22—44no—
372Dic22—42no—
373C8×C11—22no—
374C8×C11C2×#4114yes—
375C11⋊C8—22no—
376C11⋊C8—22no—
377C22×Q16—111no—
378C22×SD16—111no—
379C22×SD16—111no—
380C22×SD16C2×D1111yescharacteristic
381C22×SD16C2×D1111yescharacteristic
382C22×D8—111no—
383C22×D8—111no—
384C22×D8C2×D1111yescharacteristic
385C22×D8C2×D1111yescharacteristic
386#559—118no—
387#559—118no—
388#559—224no—
389#559—224no—
390C2×#127—111no—
391C2×#127C2×D1111yescharacteristic
392C2×#124—111no—
393C2×#124—111no—
394C2×#124—111no—
395C2×#124—221no—
396C2×#124—221no—
397C2×#124C2×D1111yescharacteristic
398C2×#123—221no—
399C2×#123—221no—
400C2×#123—221no—
401C2×#123—221no—
402C2×C4×Q8—111no—
403C2×C4×Q8—111no—
404C2×C4×Q8—111no—
405C2×C4×D4—111no—
406C2×C4×D4—111no—
407C2×C4×D4—111no—
408C2×C4×D4—111no—
409C2×C4×D4—221no—
410C2×C4×D4—221no—
411#496—118no—
412#496C2×D1118yescomplemented
413#495—118no—
414#464—118no—
415#464—118no—
416#463—118no—
417#463—118no—
418#459—118no—
419#459—118no—
420#446—118no—
421#440—118no—
422#440—118no—
423C4×D8—118no—
424C2×#107—111no—
425C2×C4⋊C8—111no—
426C2×C4⋊C8—111no—
427C2×C4⋊C8—111no—
428C2×#103—111no—
429C2×#103—111no—
430C2×#102—111no—
431C2×#102—111no—
432C2×#102—111no—
433C2×#102—111no—
434C2×#97—111no—
435C2×#97C2×D1111yescharacteristic
436C2×C4×C8—111no—
437C22×C11—42no—
438C22×C11—42no—
439C22×C11—42no—
440C22×C11—42no—
441C22×C11—42no—
442C22×C11—42no—
443C22×C11—42no—
444C22×C11—42no—
445C22×C11—42no—
446C22×C11—84no—
447C22×C11—84no—
448C22×C11—84no—
449C22×C11#55012yes—
450C22×C11#57512yes—
451C22×C11#57612yes—
452C22×C11C23×D411yescharacteristic
453C2×D11—42no—
454C2×D11—42no—
455C2×D11—42no—
456C2×D11—84no—
457C4×C11—22no—
458C4×C11—22no—
459C4×C11—42no—
460C4×C11#55012yes—
461C4×C11C22×#4111yescharacteristic
462C4×C11C2×H(5,𝔽2)11yescharacteristic
463Dic11—22no—
464Dic11—22no—
465Dic11—22no—
466Dic11—22no—
467Dic11—42no—
468Dic11—42no—
469Dic11—42no—
470C22×Q8—111no—
471C22×Q8—111no—
472C22×Q8C22×D1111yescharacteristic
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—111no—
476C22×D4—221no—
477C22×D4—221no—
478C22×D4C22×D1111yescharacteristic
479C22×D4C22×D1111yescharacteristic
480C22×D4C22×D1111yescharacteristic
481C23×C4—221no—
482C23×C4—221no—
483C23×C4—221no—
484C23×C4—221no—
485C2×Q16—114no—
486C2×Q16—442no—
487C2×SD16—24no—
488C2×SD16—42no—
489C2×SD16—114no—
490C2×SD16—114no—
491C2×SD16—224no—
492C2×SD16—442no—
493C2×SD16C22×D1114yes—
494C2×SD16C22×D1114yes—
495C2×D8—24no—
496C2×D8—42no—
497C2×D8—114no—
498C2×D8—114no—
499C2×D8—442no—
500C2×D8—442no—
501C2×D8C22×D1114yes—
502C2×D8C22×D1114yes—
503C22×C8—111no—
504C22×C8—111no—
505C22×C8C22×D1111yescharacteristic
506C22×C8C22×D1111yescharacteristic
507#127—22no—
508#127—114no—
509#127—222no—
510#127C22×D1114yes—
511#124—22no—
512#124—114no—
513#124—114no—
514#124—114no—
515#124—222no—
516#124—222no—
517#124—222no—
518#124—228no—
519#124—228no—
520#124C22×D1114yes—
521#123—228no—
522#123—228no—
523#123—228no—
524#123—228no—
525C4×Q8—114no—
526C4×Q8—114no—
527C4×Q8—114no—
528C4×Q8—114no—
529C4×Q8—222no—
530C4×Q8—222no—
531C4×D4—114no—
532C4×D4—114no—
533C4×D4—114no—
534C4×D4—114no—
535C4×D4—222no—
536C4×D4—222no—
537C4×D4—222no—
538C4×D4—228no—
539C4×D4—228no—
540C4×D4—222no—
541C2×C4⋊C4—111no—
542C2×C4⋊C4—111no—
543C2×C4⋊C4—111no—
544C2×C4⋊C4—111no—
545C2×C4⋊C4—111no—
546C2×C4⋊C4—221no—
547C2×C4⋊C4—221no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—221no—
551C2×C22⋊C4—221no—
552C2×C22⋊C4—221no—
553C2×C22⋊C4—221no—
554C2×C22⋊C4—221no—
555C2×C22⋊C4—221no—
556C2×C22⋊C4—221no—
557C2×C22⋊C4—221no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C42—111no—
561C2×C42—111no—
562C2×C42—221no—
563C2×C42—221no—
564C2×C42C22×D1111yescharacteristic
565#107—114no—
566C4⋊C8—114no—
567C4⋊C8—114no—
568C4⋊C8—114no—
569#103—114no—
570#103—114no—
571#102—114no—
572#102—114no—
573#102—114no—
574#102—114no—
575#97—114no—
576#97C22×D1114yes—
577C4×C8—114no—
578C2×C11—82no—
579C2×C11—82no—
580C2×C11—82no—
581C2×C11#340314yescomplemented
582C2×C11C2×#55011yescharacteristic
583C2×C11C2×#57511yescharacteristic
584C2×C11C2×#57611yescharacteristic
585D11—82no—
586C24—21no—
587C24—21no—
588C24—21no—
589C24—221no—
590C2×Q8—21no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—114no—
594C2×Q8—112no—
595C2×Q8—221no—
596C2×Q8—222no—
597C2×Q8—222no—
598C2×Q8—442no—
599C2×Q8C23×D1112yes—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—24no—
604C2×D4—24no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—44no—
612C2×D4—82no—
613C2×D4—112no—
614C2×D4—224no—
615C2×D4—224no—
616C2×D4—221no—
617C2×D4—222no—
618C2×D4—222no—
619C2×D4—444no—
620C2×D4—882no—
621C2×D4C23×D1112yes—
622C2×D4C23×D1112yes—
623C2×D4C23×D1112yes—
624C22×C4—21no—
625C22×C4—111no—
626C22×C4—111no—
627C22×C4—111no—
628C22×C4—111no—
629C22×C4—224no—
630C22×C4—224no—
631C22×C4—224no—
632C22×C4—221no—
633C22×C4—221no—
634C22×C4—221no—
635C22×C4—224no—
636C22×C4—882no—
637C22×C4—882no—
638C22×C4—882no—
639C22×C4—882no—
640C22×C4D4×D1111yescharacteristic
641C22×C4D4×D1111yescharacteristic
642C22×C4C23×D1111yescharacteristic
643Q16—444no—
644SD16—28no—
645SD16—44no—
646SD16—228no—
647SD16—444no—
648D8—28no—
649D8—44no—
650D8—444no—
651D8—444no—
652C2×C8—22no—
653C2×C8—112no—
654C2×C8—112no—
655C2×C8—222no—
656C2×C8—222no—
657C2×C8#434114yes—
658C2×C8C23×D1112yes—
659C2×C8C23×D1112yes—
660C4⋊C4—114no—
661C4⋊C4—114no—
662C4⋊C4—114no—
663C4⋊C4—112no—
664C4⋊C4—112no—
665C4⋊C4—224no—
666C4⋊C4—221no—
667C4⋊C4—221no—
668C4⋊C4—224no—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—224no—
672C22⋊C4—224no—
673C22⋊C4—224no—
674C22⋊C4—224no—
675C22⋊C4—224no—
676C22⋊C4—224no—
677C22⋊C4—224no—
678C22⋊C4—224no—
679C22⋊C4—224no—
680C22⋊C4—224no—
681C42—112no—
682C42—112no—
683C42—112no—
684C42—112no—
685C42—224no—
686C42—224no—
687C42D4×D1112yes—
688C42C23×D1112yes—
689C11C2×#340311yescharacteristic, complemented, Sylow
690C23—22no—
691C23—22no—
692C23—22no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—222no—
703C23—442no—
704C23—442no—
705C23—442no—
706C23C2×D4×D1111yescharacteristic
707Q8—22no—
708Q8—22no—
709Q8—42no—
710Q8—222no—
711Q8—222no—
712Q8—444no—
713Q8—442no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—22no—
720D4—48no—
721D4—42no—
722D4—42no—
723D4—42no—
724D4—84no—
725D4—222no—
726D4—222no—
727D4—448no—
728D4—442no—
729D4—884no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—42no—
734C2×C4—112no—
735C2×C4—112no—
736C2×C4—112no—
737C2×C4—112no—
738C2×C4—222no—
739C2×C4—222no—
740C2×C4—222no—
741C2×C4—222no—
742C2×C4—222no—
743C2×C4—222no—
744C2×C4—222no—
745C2×C4—442no—
746C2×C4—442no—
747C2×C4—442no—
748C2×C4—884no—
749C2×C4—884no—
750C2×C4—884no—
751C2×C4—884no—
752C2×C4C2×D4×D1112yes—
753C2×C4C2×D4×D1112yes—
754C2×C4C2×D4×D1111yescharacteristic
755C2×C4C2×#434112yes—
756C2×C4#6703712yes—
757C2×C4C24×D1111yescharacteristic
758C8—22no—
759C8—222no—
760C8—222no—
761C8C2×#434114yes—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—84no—
772C22—84no—
773C22—84no—
774C22—442no—
775C22—442no—
776C22—442no—
777C22—884no—
778C22#1062324912yes—
779C22#1062330412yes—
780C22#1062330512yes—
781C22C22×D4×D1111yescharacteristic
782C4—22no—
783C4—22no—
784C4—42no—
785C4—222no—
786C4—222no—
787C4—222no—
788C4—222no—
789C4—442no—
790C4—442no—
791C4—442no—
792C4#1062324912yes—
793C4C22×#434111yescharacteristic
794C4C2×#6703711yescharacteristic
795C2—82no—
796C2—82no—
797C2—82no—
798C2—882no—
799C2#1308170114yesdirect product factor
800C2C2×#1062324911yescharacteristic
801C2C2×#1062330411yescharacteristic
802C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#496C2
socleC23×C11C22×D4
hypercenterC2×#496D11
hypocenterC11C2×#3403
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#496

Complements

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

NH ≅ G/Ntype
1. C2×#10623244C2semidirect
2. C2×#10623212C2semidirect
3. #13081701C2direct (N × H)
4. C2×#10622767C2semidirect
5. C2×#10622781C2semidirect
6. C2×#10622779C2semidirect
7. C2×#10622667C2semidirect
8. C2×#10622778C2semidirect
9. C2×#10622766C2semidirect
10. C2×#10622763C2semidirect
11. C2×#10622685C2semidirect
12. C2×#10622314C2semidirect
13. C2×#10622323C2semidirect
14. C2×#10622777C2semidirect
15. C2×D8×Dic11C2semidirect
16. C2×C11×#496C2semidirect
41. #10623244C22semidirect
43. #10623212C22semidirect
51. C11×#496C22semidirect
57. #10622781C22semidirect
58. #10622779C22semidirect
59. #10622778C22semidirect
60. #10622777C22semidirect
61. #10622767C22semidirect
62. #10622766C22semidirect
63. #10622763C22semidirect
64. D8×Dic11C22semidirect
72. #10622685C22semidirect
73. #10622667C22semidirect
75. #10622323C22semidirect
76. #10622314C22semidirect
293. C2×#496D11semidirect
412. #496C2×D11semidirect
581. C2×C11#3403semidirect
689. C11C2×#3403semidirect
799. C2#13081701direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232442
C2×#106232122
#130817012
C2×#106227672
C2×#106227812
C2×#106227792
C2×#106226672
C2×#106227782
C2×#106227662
C2×#106227632
C2×#106226852
C2×#106223142
C2×#106223232
C2×#106227772
C2×D8×Dic112
C2×C11×#4962
C2×#340311