Finite Group Databasebeta

← C2×#13080608 #15630348

Subgroups — C2×#13080608 #15630348

Order 2816.

2374 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623362C211yesmaximal, characteristic, complemented
2C2×#10623038C211yesmaximal, characteristic, complemented
3#13080608C2116yesmaximal, direct product factor
4C2×#10622378C211yesmaximal, characteristic, complemented
5C2×#10622583C211yesmaximal, characteristic, complemented
6C2×#10622387C211yesmaximal, characteristic, complemented
7C2×#10622407C211yesmaximal, characteristic, complemented
8C2×#10622747C211yesmaximal, characteristic, complemented
9C2×#10622388C211yesmaximal, characteristic, complemented
10C2×#10622400C211yesmaximal, characteristic, complemented
11C2×#10622851C211yesmaximal, characteristic, complemented
12C2×#10622419C211yesmaximal, characteristic, complemented
13C2×#10622430C211yesmaximal, characteristic, complemented
14C2×#10622740C211yesmaximal, characteristic, complemented
15C2×D11×#103C211yesmaximal, characteristic, complemented
16C2×C11×#417C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×Q8×D11C2211yescharacteristic
19C22×#4339—21no—
20C22×C11×M16C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22#10623362—24no—
23#10623362C2218yescomplemented
24C2×Q8×Dic11C2211yescharacteristic
25C22×#4325C2211yescharacteristic
26C2×#66991—21no—
27C2×#66991C2211yescharacteristic
28C2×#66989—21no—
29C2×#66989C2211yescharacteristic
30C22×#4323C2211yescharacteristic
31C2×#66983C2211yescharacteristic
32C2×#66982—21no—
33C2×C4×C22⋊D11—21no—
34C2×C4×C22⋊D11C2211yescharacteristic
35C2×#66977—21no—
36C2×#66977C2211yescharacteristic
37C22×#4314C2211yescharacteristic
38C22×C8×D11C2211yescharacteristic
39C2×#66949—21no—
40#10623038—24no—
41#10623038C2218yescomplemented
42C2×#66948C2211yescharacteristic
43C2×#66947—21no—
44C2×#66946C2211yescharacteristic
45C2×C4⋊C4×D11C2211yescharacteristic
46C2×#66941C2211yescharacteristic
47C11×#417C2218yescomplemented
48C2×C11×#103C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52#10622851C2218yescomplemented
53C2×#66899C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55C2×C22⋊(C11⋊C8)C2211yescharacteristic
56#10622747C2218yescomplemented
57#10622740C2218yescomplemented
58C2×#66885C2211yescharacteristic
59C2×(C2×D11)⋊C8C2211yescharacteristic
60C2×#66882C2211yescharacteristic
61C2×#66880C2211yescharacteristic
62C2×#66879C2211yescharacteristic
63C2×Dic11⋊C8C2211yescharacteristic
64#10622583C2218yescomplemented
65C2×#66874C2211yescharacteristic
66C2×#66874C2211yescharacteristic
67C2×#66871C2211yescharacteristic
68C2×#66871C2211yescharacteristic
69#10622430C2218yescomplemented
70#10622419C2218yescomplemented
71D11×#103C2218yescomplemented
72#10622407C2218yescomplemented
73#10622400C2218yescomplemented
74#10622388C2218yescomplemented
75#10622387C2218yescomplemented
76#10622378C2218yescomplemented
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⋊D11—21no—
89C22×C22⋊D11D411yescharacteristic
90C2×Q8×D11—22no—
91C2×Q8×D11—24no—
92C2×Q8×D11—42no—
93C2×Q8×D11C2314yes—
94C2×#4339—28no—
95C2×#4339—48no—
96C22×D44—21no—
97C22×D44C2311yescharacteristic
98C22×C4×D11—21no—
99C22×C4×D11—21no—
100C22×C4×D11—21no—
101C22×C4×D11C2311yescharacteristic
102C22×Dic22—21no—
103C22×Dic22—21no—
104C22×Dic22C2311yescharacteristic
105C2×C11×M16—42no—
106C2×C11×M16C2314yes—
107C22×C8×C11C2311yescharacteristic
108C22×C8×C11C2311yescharacteristic
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4—22no—
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2314yes—
114C2×C22⋊Dic11—21no—
115C2×C22⋊Dic11—21no—
116C2×C22⋊Dic11—21no—
117C2×C22⋊Dic11—21no—
118C2×C22⋊Dic11D411yescharacteristic
119Q8×Dic11—22no—
120Q8×Dic11C2314yes—
121C2×#4325—24no—
122C2×#4325C2314yes—
123#66991—28no—
124#66991—22no—
125#66991C2314yes—
126#66989—28no—
127#66989—22no—
128#66989C2314yes—
129C2×#4323—42no—
130C2×#4323C2314yes—
131#66983—22no—
132#66983C2314yes—
133#66982—28no—
134C4×C22⋊D11—28no—
135C4×C22⋊D11D414yes—
136C4×C22⋊D11C2314yes—
137C2×(C2×D11)⋊C4—21no—
138C2×(C2×D11)⋊C4—21no—
139C2×(C2×D11)⋊C4—21no—
140C2×(C2×D11)⋊C4D411yescharacteristic
141C2×C4⋊Dic11—21no—
142C2×C4⋊Dic11C2311yescharacteristic
143C2×C4⋊Dic11C2311yescharacteristic
144#66977—22no—
145#66977—28no—
146#66977C2314yes—
147C2×Dic11⋊C4—21no—
148C2×Dic11⋊C4—21no—
149C2×Dic11⋊C4—21no—
150C2×Dic11⋊C4D411yescharacteristic
151C2×C4×Dic11—21no—
152C2×C4×Dic11C2311yescharacteristic
153C22×C11⋊C8C2311yescharacteristic
154C22×C11⋊C8C2311yescharacteristic
155C2×#4314—42no—
156C2×#4314C2314yes—
157C2×C8×D11—42no—
158C2×C8×D11C2314yes—
159#66949—28no—
160#66948—22no—
161#66948C2314yes—
162#66947—28no—
163#66946—22no—
164#66946C2314yes—
165C4⋊C4×D11—22no—
166C4⋊C4×D11C2314yes—
167#66941—22no—
168#66941C2314yes—
169C11×#103C2314yes—
170C11×#103C2314yes—
171C11×#102C2314yes—
172C11×#102C2314yes—
173#66899C2314yes—
174#66896C2314yes—
175C22⋊(C11⋊C8)C2314yes—
176#66885C2314yes—
177(C2×D11)⋊C8C2314yes—
178#66882C2314yes—
179#66880C2314yes—
180#66879C2314yes—
181Dic11⋊C8C2314yes—
182#66874C2314yes—
183#66874C2314yes—
184#66871C2314yes—
185#66871C2314yes—
186C2×#3308—111nomaximal, Sylow
187C24×C11—21no—
188C24×C11C2×D411yescharacteristic
189C23×D11—21no—
190C23×D11C2×D411yescharacteristic
191C11×#41—28no—
192C11×#41—44no—
193C11×#41—48no—
194C2×Q8×C11—21no—
195C2×Q8×C11—22no—
196C2×Q8×C11#4114yescomplemented
197C2×Q8×C11C2412yes—
198C2×D4×C11—24no—
199C2×D4×C11—21no—
200C2×D4×C11—22no—
201C2×D4×C11—22no—
202C2×D4×C11—44no—
203C2×D4×C11C2412yes—
204C22×C4×C11—21no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—24no—
210C22×C4×C11—24no—
211C22×C4×C11—44no—
212C22×C4×C11—44no—
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2×D412yes—
215C22×C4×C11C2412yes—
216C22×C4×C11C2411yescharacteristic
217C2×C22⋊D11—24no—
218C2×C22⋊D11—24no—
219C2×C22⋊D11—24no—
220C2×C22⋊D11—44no—
221C2×C22⋊D11—44no—
222C2×C22⋊D11C2×D414yes—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11C2×D411yescharacteristic
227C22×Dic11C2×D411yescharacteristic
228C22×Dic11C2×D411yescharacteristic
229Q8×D11—28no—
230Q8×D11—44no—
231Q8×D11—48no—
232#4339—432no—
233C2×D44—24no—
234C2×D44—21no—
235C2×D44—22no—
236C2×D44—22no—
237C2×D44—44no—
238C2×D44C2412yes—
239C2×C4×D11—24no—
240C2×C4×D11—24no—
241C2×C4×D11—24no—
242C2×C4×D11—22no—
243C2×C4×D11—22no—
244C2×C4×D11—44no—
245C2×C4×D11—44no—
246C2×C4×D11—44no—
247C2×C4×D11C2×D412yes—
248C2×C4×D11C2412yes—
249C2×Dic22—24no—
250C2×Dic22—24no—
251C2×Dic22—21no—
252C2×Dic22—22no—
253C2×Dic22—22no—
254C2×Dic22—44no—
255C2×Dic22—44no—
256C2×Dic22C2412yes—
257C11×M16—44no—
258C2×C8×C11—22no—
259C2×C8×C11—22no—
260C2×C8×C11C2412yes—
261C2×C8×C11C2412yes—
262C11×C4⋊C4—21no—
263C11×C4⋊C4—21no—
264C11×C4⋊C4—24no—
265C11×C4⋊C4C2412yes—
266C11×C4⋊C4C2412yes—
267C22⋊Dic11—24no—
268C22⋊Dic11—24no—
269C22⋊Dic11—24no—
270C22⋊Dic11—24no—
271C22⋊Dic11C2×D414yes—
272#4325—28no—
273#4323—44no—
274(C2×D11)⋊C4—24no—
275(C2×D11)⋊C4—24no—
276(C2×D11)⋊C4—24no—
277(C2×D11)⋊C4C2×D414yes—
278C4⋊Dic11—24no—
279C4⋊Dic11—21no—
280C4⋊Dic11—21no—
281C4⋊Dic11C2412yes—
282C4⋊Dic11C2412yes—
283Dic11⋊C4—24no—
284Dic11⋊C4—24no—
285Dic11⋊C4—24no—
286Dic11⋊C4C2×D414yes—
287C4×Dic11—24no—
288C4×Dic11C2×D412yes—
289C4×Dic11C2412yes—
290C2×C11⋊C8—22no—
291C2×C11⋊C8—22no—
292C2×C11⋊C8C2412yes—
293C2×C11⋊C8C2412yes—
294#4314—44no—
295C8×D11—44no—
296C2×#548—111no—
297C2×#547—111no—
298#3308—1116no—
299C2×#489—111no—
300C2×#484—111no—
301C2×#480—111no—
302C2×#477—111no—
303C2×#468—111no—
304C2×#466—111no—
305C2×#463—111no—
306C2×#449—111no—
307C2×#448—111no—
308C2×#440—111no—
309C2×#435—111no—
310C2×#417D1111yescharacteristic, complemented
311C22×#103—111no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—42no—
317C23×C11—42no—
318C23×C11—42no—
319C23×C11C22×D412yes—
320C23×C11C22×D411yescharacteristic
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—42no—
325C22×D11—42no—
326C22×D11—42no—
327C22×D11AGL(1,ℤ/8)14yes—
328C22×D11C22×D412yes—
329Q8×C11—24no—
330Q8×C11—22no—
331Q8×C11C2×#4114yescomplemented
332D4×C11—22no—
333D4×C11—22no—
334D4×C11—48no—
335D4×C11—42no—
336C2×C4×C11—24no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—24no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—48no—
345C2×C4×C11—48no—
346C2×C4×C11—42no—
347C2×C4×C11—42no—
348C2×C4×C11C22×D412yes—
349C2×C4×C11C22×D411yescharacteristic
350C2×C4×C11C2×#4112yes—
351C2×C4×C11H(5,𝔽2)12yes—
352C2×C4×C11C2511yescharacteristic
353C22⋊D11—28no—
354C22⋊D11—48no—
355C22⋊D11—48no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—42no—
363C2×Dic11—42no—
364C2×Dic11—42no—
365C2×Dic11C22×D412yes—
366C2×Dic11C22×D412yes—
367C2×Dic11C22×D412yes—
368D44—22no—
369D44—22no—
370D44—48no—
371D44—42no—
372C4×D11—24no—
373C4×D11—22no—
374C4×D11—22no—
375C4×D11—48no—
376C4×D11—48no—
377C4×D11—48no—
378Dic22—22no—
379Dic22—22no—
380Dic22—48no—
381Dic22—48no—
382Dic22—42no—
383C8×C11—22no—
384C8×C11—22no—
385C11⋊C8—22no—
386C11⋊C8—22no—
387C22×#41—221no—
388C22×#41C2×D1111yescharacteristic
389C23×Q8—111no—
390C22×SD16—111no—
391C22×SD16—111no—
392C22×D8—111no—
393C22×M16C2×D1111yescharacteristic
394C23×C8—111no—
395#548—118no—
396#548—224no—
397#547—118no—
398#547—224no—
399C2×C4⋊Q8—111no—
400C2×#124—111no—
401C2×#124—221no—
402C2×#123—221no—
403C2×#123—221no—
404C2×C22⋊Q8—111no—
405C2×C22⋊Q8—221no—
406C2×C22⋊Q8—221no—
407C2×#121—111no—
408C2×#121—111no—
409C2×#121—111no—
410C2×#121—221no—
411C2×C4×Q8—111no—
412C2×C4×D4—111no—
413C2×C4×D4—111no—
414C2×C4×D4—221no—
415C22×C4⋊C4—111no—
416C22×C4⋊C4C2×D1111yescharacteristic
417#489—118no—
418#484—118no—
419#480—118no—
420#477—118no—
421#468—118no—
422#466—118no—
423#463—118no—
424#449—118no—
425#448—118no—
426#440—118no—
427#435—118no—
428C2×#107—111no—
429C2×#107—111no—
430C2×#107—111no—
431C2×C4⋊C8—111no—
432#417C2×D1118yescomplemented
433C2×#103—111no—
434C2×#103—111no—
435C2×#103—111no—
436C2×#103—111no—
437C2×#103—118no—
438C2×#103C2×D1111yescharacteristic
439C2×#103C2×D1111yescharacteristic
440C2×#102—111no—
441C2×#102—111no—
442C2×#102C2×D1111yescharacteristic
443C2×#102C2×D1111yescharacteristic
444C2×C22⋊C8—111no—
445C2×C22⋊C8—111no—
446C2×#97—111no—
447C22×C11—22no—
448C22×C11—22no—
449C22×C11—22no—
450C22×C11—44no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—84no—
455C22×C11#54612yes—
456C22×C11C2×AGL(1,ℤ/8)12yes—
457C22×C11#57812yes—
458C22×C11C23×D411yescharacteristic
459C2×D11—22no—
460C2×D11—28no—
461C2×D11—22no—
462C2×D11—42no—
463C2×D11—42no—
464C2×D11—42no—
465C2×D11—84no—
466C2×D11C2×AGL(1,ℤ/8)14yes—
467C4×C11—22no—
468C4×C11—24no—
469C4×C11—42no—
470C4×C11—42no—
471C4×C11#54612yes—
472C4×C11C22×#4111yescharacteristic
473C4×C11C2×H(5,𝔽2)11yescharacteristic
474Dic11—22no—
475Dic11—22no—
476Dic11—22no—
477Dic11—42no—
478Dic11—42no—
479Dic11—42no—
480C2×#41—22no—
481C2×#41—24no—
482C2×#41—42no—
483C2×#41—228no—
484C2×#41—448no—
485C2×#41C22×D1114yes—
486C22×Q8—114no—
487C22×Q8—111no—
488C22×Q8—221no—
489C22×Q8—221no—
490C22×Q8—222no—
491C22×Q8—224no—
492C22×Q8—442no—
493C22×Q8C22×D1111yescharacteristic
494C22×D4—21no—
495C22×D4—111no—
496C22×D4—111no—
497C22×D4—221no—
498C22×D4—221no—
499C22×D4—221no—
500C22×D4C22×D1111yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—111no—
504C23×C4—221no—
505C23×C4—221no—
506C23×C4—221no—
507C23×C4C22×D1111yescharacteristic
508C2×SD16—114no—
509C2×SD16—114no—
510C2×SD16—224no—
511C2×SD16—442no—
512C2×D8—114no—
513C2×D8—442no—
514C2×M16—42no—
515C2×M16C22×D1114yes—
516C22×C8—111no—
517C22×C8—111no—
518C22×C8—114no—
519C22×C8—442no—
520C22×C8C22×D1111yescharacteristic
521C22×C8C22×D1111yescharacteristic
522C4⋊Q8—114no—
523C4⋊Q8—222no—
524#124—114no—
525#124—222no—
526#124—228no—
527#123—228no—
528#123—228no—
529C22⋊Q8—114no—
530C22⋊Q8—228no—
531C22⋊Q8—228no—
532C22⋊Q8—222no—
533#121—114no—
534#121—114no—
535#121—114no—
536#121—222no—
537#121—222no—
538#121—228no—
539#121—222no—
540C4×Q8—114no—
541C4×Q8—222no—
542C4×D4—114no—
543C4×D4—114no—
544C4×D4—114no—
545C4×D4—222no—
546C4×D4—228no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—22no—
549C2×C4⋊C4—111no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4—111no—
552C2×C4⋊C4—114no—
553C2×C4⋊C4—222no—
554C2×C4⋊C4—221no—
555C2×C4⋊C4—221no—
556C2×C4⋊C4—221no—
557C2×C4⋊C4—221no—
558C2×C4⋊C4C22×D1111yescharacteristic
559C2×C4⋊C4C22×D1111yescharacteristic
560C2×C4⋊C4C22×D1114yes—
561C2×C22⋊C4—111no—
562C2×C22⋊C4—111no—
563C2×C22⋊C4—221no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—221no—
566C2×C22⋊C4—221no—
567C2×C22⋊C4—221no—
568C2×C22⋊C4—221no—
569C2×C22⋊C4—221no—
570C2×C42—111no—
571C2×C42—221no—
572#107—114no—
573#107—114no—
574#107—114no—
575C4⋊C8—114no—
576#103—114no—
577#103—114no—
578#103—114no—
579#103—114no—
580#103C22×D1114yes—
581#103C22×D1114yes—
582#102—114no—
583#102—114no—
584#102C22×D1114yes—
585#102C22×D1114yes—
586C22⋊C8—114no—
587C22⋊C8—114no—
588#97—114no—
589C2×C11—42no—
590C2×C11—82no—
591C2×C11#330814yescomplemented
592C2×C11C2×#54611yescharacteristic
593C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
594C2×C11C2×#57811yescharacteristic
595D11—24no—
596D11—82no—
597C24—21no—
598C24—111no—
599C24—221no—
600C24D4×D1111yescharacteristic
601#41—28no—
602#41—44no—
603#41—48no—
604#41—4432no—
605C2×Q8—21no—
606C2×Q8—22no—
607C2×Q8—112no—
608C2×Q8—224no—
609C2×Q8—224no—
610C2×Q8—221no—
611C2×Q8—228no—
612C2×Q8—222no—
613C2×Q8—222no—
614C2×Q8—444no—
615C2×Q8—444no—
616C2×Q8—444no—
617C2×Q8—448no—
618C2×Q8#433914yescomplemented
619C2×Q8C23×D1112yes—
620C2×D4—24no—
621C2×D4—22no—
622C2×D4—21no—
623C2×D4—22no—
624C2×D4—44no—
625C2×D4—114no—
626C2×D4—112no—
627C2×D4—224no—
628C2×D4—224no—
629C2×D4—224no—
630C2×D4—224no—
631C2×D4—222no—
632C2×D4—221no—
633C2×D4—222no—
634C2×D4—444no—
635C2×D4—444no—
636C2×D4—444no—
637C2×D4C23×D1112yes—
638C22×C4—21no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—24no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—24no—
645C22×C4—44no—
646C22×C4—44no—
647C22×C4—111no—
648C22×C4—111no—
649C22×C4—111no—
650C22×C4—112no—
651C22×C4—112no—
652C22×C4—224no—
653C22×C4—224no—
654C22×C4—224no—
655C22×C4—222no—
656C22×C4—222no—
657C22×C4—221no—
658C22×C4—221no—
659C22×C4—221no—
660C22×C4—444no—
661C22×C4—444no—
662C22×C4—444no—
663C22×C4D4×D1112yes—
664C22×C4D4×D1111yescharacteristic
665C22×C4C23×D1112yes—
666C22×C4C23×D1111yescharacteristic
667SD16—228no—
668SD16—444no—
669D8—444no—
670M16—44no—
671C2×C8—22no—
672C2×C8—22no—
673C2×C8—112no—
674C2×C8—112no—
675C2×C8—222no—
676C2×C8—222no—
677C2×C8—444no—
678C2×C8C23×D1112yes—
679C2×C8C23×D1112yes—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—24no—
683C4⋊C4—114no—
684C4⋊C4—112no—
685C4⋊C4—112no—
686C4⋊C4—224no—
687C4⋊C4—224no—
688C4⋊C4—224no—
689C4⋊C4—221no—
690C4⋊C4—221no—
691C4⋊C4—224no—
692C4⋊C4C23×D1112yes—
693C4⋊C4C23×D1112yes—
694C22⋊C4—114no—
695C22⋊C4—114no—
696C22⋊C4—224no—
697C22⋊C4—224no—
698C22⋊C4—224no—
699C22⋊C4—224no—
700C22⋊C4—224no—
701C22⋊C4—224no—
702C22⋊C4—224no—
703C42—112no—
704C42—112no—
705C42—224no—
706C11C2×#330811yescharacteristic, complemented, Sylow
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—114no—
715C23—112no—
716C23—222no—
717C23—222no—
718C23—222no—
719C23—442no—
720C23—442no—
721C23—442no—
722C23C2×D4×D1112yes—
723C23C2×D4×D1111yescharacteristic
724Q8—24no—
725Q8—22no—
726Q8—222no—
727Q8—222no—
728Q8—448no—
729Q8—448no—
730Q8—442no—
731Q8C2×#433914yescomplemented
732D4—22no—
733D4—22no—
734D4—48no—
735D4—42no—
736D4—228no—
737D4—222no—
738D4—222no—
739D4—448no—
740D4—448no—
741D4—448no—
742D4—442no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—48no—
752C2×C4—48no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—112no—
756C2×C4—112no—
757C2×C4—112no—
758C2×C4—222no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—224no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—222no—
766C2×C4—222no—
767C2×C4—448no—
768C2×C4—448no—
769C2×C4—448no—
770C2×C4—442no—
771C2×C4—442no—
772C2×C4—442no—
773C2×C4C2×#433912yes—
774C2×C4C2×D4×D1112yes—
775C2×C4C2×D4×D1111yescharacteristic
776C2×C4#6703712yes—
777C2×C4C24×D1111yescharacteristic
778C8—22no—
779C8—22no—
780C8—222no—
781C8—222no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—44no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—84no—
790C22—114no—
791C22—228no—
792C22—222no—
793C22—222no—
794C22—442no—
795C22—442no—
796C22—442no—
797C22—884no—
798C22#1062302112yes—
799C22D11×AGL(1,ℤ/8)12yes—
800C22#1062331012yes—
801C22C22×D4×D1111yescharacteristic
802C4—22no—
803C4—24no—
804C4—42no—
805C4—42no—
806C4—222no—
807C4—222no—
808C4—222no—
809C4—442no—
810C4—442no—
811C4—442no—
812C4#1062302112yes—
813C4C22×#433911yescharacteristic
814C4C2×#6703711yescharacteristic
815C2—42no—
816C2—82no—
817C2—224no—
818C2—882no—
819C2#1308060814yesdirect product factor
820C2C2×#1062302111yescharacteristic
821C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
822C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#417C2
socleC23×C11C22×D4
hypercenterC2×#417D11
hypocenterC11C2×#3308
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×#10623362C2semidirect
2. C2×#10623038C2semidirect
3. #13080608C2direct (N × H)
4. C2×#10622378C2semidirect
5. C2×#10622583C2semidirect
6. C2×#10622387C2semidirect
7. C2×#10622407C2semidirect
8. C2×#10622747C2semidirect
9. C2×#10622388C2semidirect
10. C2×#10622400C2semidirect
11. C2×#10622851C2semidirect
12. C2×#10622419C2semidirect
13. C2×#10622430C2semidirect
14. C2×#10622740C2semidirect
15. C2×D11×#103C2semidirect
16. C2×C11×#417C2semidirect
23. #10623362C22semidirect
41. #10623038C22semidirect
47. C11×#417C22semidirect
52. #10622851C22semidirect
56. #10622747C22semidirect
57. #10622740C22semidirect
64. #10622583C22semidirect
69. #10622430C22semidirect
70. #10622419C22semidirect
71. D11×#103C22semidirect
72. #10622407C22semidirect
73. #10622400C22semidirect
74. #10622388C22semidirect
75. #10622387C22semidirect
76. #10622378C22semidirect
196. C2×Q8×C11#41semidirect
310. C2×#417D11semidirect
331. Q8×C11C2×#41semidirect
432. #417C2×D11semidirect
591. C2×C11#3308semidirect
618. C2×Q8#4339semidirect
706. C11C2×#3308semidirect
731. Q8C2×#4339semidirect
819. C2#13080608direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233622
C2×#106230382
#130806082
C2×#106223782
C2×#106225832
C2×#106223872
C2×#106224072
C2×#106227472
C2×#106223882
C2×#106224002
C2×#106228512
C2×#106224192
C2×#106224302
C2×#106227402
C2×D11×#1032
C2×C11×#4172
C2×#330811