Finite Group Databasebeta

← C2×#13080916 #15630677

Subgroups — C2×#13080916 #15630677

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×#10623162C211yesmaximal, characteristic, complemented
2C2×#10623142C211yesmaximal, characteristic, complemented
3#13080916C2116yesmaximal, direct product factor
4C2×#10622405C211yesmaximal, characteristic, complemented
5C2×#10622497C211yesmaximal, characteristic, complemented
6C2×#10622657C211yesmaximal, characteristic, complemented
7C2×#10622503C211yesmaximal, characteristic, complemented
8C2×#10622393C211yesmaximal, characteristic, complemented
9C2×#10622775C211yesmaximal, characteristic, complemented
10C2×#10622785C211yesmaximal, characteristic, complemented
11C2×#10622650C211yesmaximal, characteristic, complemented
12C2×#10622369C211yesmaximal, characteristic, complemented
13C2×#10622741C211yesmaximal, characteristic, complemented
14C2×#10622746C211yesmaximal, characteristic, complemented
15C2×#10622416C211yesmaximal, characteristic, complemented
16C2×C11×#468C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C22×#4341—21no—
19C22×#4339C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic
21C22×C11×M16C2211yescharacteristic
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic
24C2×#66997C2211yescharacteristic
25C2×#66991C2211yescharacteristic
26C2×#66988—21no—
27C2×D4×Dic11C2211yescharacteristic
28C22×#4324C2211yescharacteristic
29C22×#4323C2211yescharacteristic
30C2×C4×C22⋊D11C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×#4313C2211yescharacteristic
33#10623162—24no—
34#10623162C2218yescomplemented
35#10623142—24no—
36#10623142C2218yescomplemented
37C2×#66950C2211yescharacteristic
38C2×#66947—21no—
39C2×#66946C2211yescharacteristic
40C2×C4⋊C4×D11—21no—
41C2×C4⋊C4×D11C2211yescharacteristic
42C2×#66941C2211yescharacteristic
43C2×#66937—21no—
44C2×#66936—21no—
45C2×#66936—21no—
46C2×#66931—21no—
47C11×#468C2218yescomplemented
48C2×C11×#107C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53C2×C22⋊(C11⋊C8)C2211yescharacteristic
54#10622785C2218yescomplemented
55#10622775C2218yescomplemented
56#10622746C2218yescomplemented
57#10622741C2218yescomplemented
58C2×#66885C2211yescharacteristic
59C2×#66885C2211yescharacteristic
60C2×(C2×D11)⋊C8C2211yescharacteristic
61C2×#66880C2211yescharacteristic
62C2×#66880C2211yescharacteristic
63C2×Dic11⋊C8C2211yescharacteristic
64C2×C8×Dic11C2211yescharacteristic
65#10622657C2218yescomplemented
66#10622650C2218yescomplemented
67C2×#66874C2211yescharacteristic
68C2×#66873C2211yescharacteristic
69C2×#66871C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71#10622503C2218yescomplemented
72#10622497C2218yescomplemented
73#10622416C2218yescomplemented
74#10622405C2218yescomplemented
75#10622393C2218yescomplemented
76#10622369C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11—21no—
79C22×D4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C22×C22⋊D11D411yescharacteristic
84C23×Dic11—21no—
85C23×Dic11—21no—
86C2×#4343—22no—
87C2×#4343—24no—
88C2×#4343—42no—
89C2×#4343C2314yes—
90C2×#4341—28no—
91C2×#4341—48no—
92C2×#4339—22no—
93C2×#4339—24no—
94C2×#4339—42no—
95C2×#4339C2314yes—
96C22×D44—21no—
97C22×D44C2311yescharacteristic
98C22×C4×D11—21no—
99C22×C4×D11—21no—
100C22×C4×D11—21no—
101C22×C4×D11—21no—
102C22×C4×D11C2311yescharacteristic
103C22×Dic22—21no—
104C22×Dic22C2311yescharacteristic
105C2×C11×SD16—42no—
106C2×C11×SD16C2314yes—
107C2×C11×M16—42no—
108C2×C11×M16C2314yes—
109C22×C8×C11C2311yescharacteristic
110C22×C8×C11C2311yescharacteristic
111C11×C22⋊Q8—22no—
112C11×C22⋊Q8C2314yes—
113C11×#121—22no—
114C11×#121C2314yes—
115C2×C11×C4⋊C4—21no—
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C4⋊C4C2311yescharacteristic
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C22⋊Dic11—21no—
121C2×C22⋊Dic11—21no—
122C2×C22⋊Dic11D411yescharacteristic
123#66997—22no—
124#66997C2314yes—
125#66991—22no—
126#66991C2314yes—
127#66988—28no—
128D4×Dic11—22no—
129D4×Dic11C2314yes—
130C2×#4324—42no—
131C2×#4324C2314yes—
132C2×#4323—24no—
133C2×#4323C2314yes—
134C4×C22⋊D11D414yes—
135C4×C22⋊D11C2314yes—
136C2×(C2×D11)⋊C4—21no—
137C2×(C2×D11)⋊C4—21no—
138C2×(C2×D11)⋊C4D411yescharacteristic
139C2×C4⋊Dic11—21no—
140C2×C4⋊Dic11—22no—
141C2×C4⋊Dic11—21no—
142C2×C4⋊Dic11C2311yescharacteristic
143C2×C4⋊Dic11C2311yescharacteristic
144C2×C4⋊Dic11C2314yes—
145C2×Dic11⋊C4—21no—
146C2×Dic11⋊C4—21no—
147C2×Dic11⋊C4—21no—
148C2×Dic11⋊C4—21no—
149C2×Dic11⋊C4D411yescharacteristic
150C2×C4×Dic11C2311yescharacteristic
151C22×C11⋊C8C2311yescharacteristic
152C22×C11⋊C8C2311yescharacteristic
153C2×#4313—42no—
154C2×#4313C2314yes—
155#66950—22no—
156#66950C2314yes—
157#66947—28no—
158#66946—22no—
159#66946C2314yes—
160C4⋊C4×D11—22no—
161C4⋊C4×D11—28no—
162C4⋊C4×D11C2314yes—
163#66941—22no—
164#66941C2314yes—
165#66937—28no—
166#66936—28no—
167#66936—28no—
168#66931—28no—
169C11×#107C2314yes—
170C11×#103C2314yes—
171C11×#102C2314yes—
172#66899C2314yes—
173#66899C2314yes—
174C22⋊(C11⋊C8)C2314yes—
175#66885C2314yes—
176#66885C2314yes—
177(C2×D11)⋊C8C2314yes—
178#66880C2314yes—
179#66880C2314yes—
180Dic11⋊C8C2314yes—
181C8×Dic11C2314yes—
182#66874C2314yes—
183#66873C2314yes—
184#66871C2314yes—
185#66871C2314yes—
186C2×#3330—111nomaximal, Sylow
187C24×C11—21no—
188C24×C11C2×D411yescharacteristic
189C23×D11—21no—
190C23×D11C2×D411yescharacteristic
191C2×Q8×C11—21no—
192C2×Q8×C11—22no—
193C2×Q8×C11—22no—
194C2×Q8×C11C2412yes—
195C2×D4×C11—24no—
196C2×D4×C11—21no—
197C2×D4×C11—22no—
198C2×D4×C11—22no—
199C2×D4×C11—44no—
200C2×D4×C11C2412yes—
201C22×C4×C11—22no—
202C22×C4×C11—22no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D412yes—
208C22×C4×C11C2412yes—
209C22×C4×C11C2411yescharacteristic
210C2×C22⋊D11—24no—
211C2×C22⋊D11—24no—
212C2×C22⋊D11—24no—
213C2×C22⋊D11—44no—
214C2×C22⋊D11—44no—
215C2×C22⋊D11C2×D414yes—
216C22×Dic11—24no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—24no—
221C22×Dic11—44no—
222C22×Dic11—44no—
223C22×Dic11C2×D411yescharacteristic
224C22×Dic11C2×D411yescharacteristic
225C22×Dic11C2×D411yescharacteristic
226#4343—28no—
227#4343—44no—
228#4343—48no—
229#4341—432no—
230#4339—28no—
231#4339—44no—
232#4339—48no—
233C2×D44—24no—
234C2×D44—21no—
235C2×D44—22no—
236C2×D44—44no—
237C2×D44#4114yescomplemented
238C2×D44C2412yes—
239C2×C4×D11—24no—
240C2×C4×D11—24no—
241C2×C4×D11—24no—
242C2×C4×D11—24no—
243C2×C4×D11—22no—
244C2×C4×D11—22no—
245C2×C4×D11—44no—
246C2×C4×D11—44no—
247C2×C4×D11—44no—
248C2×C4×D11—44no—
249C2×C4×D11C2×D412yes—
250C2×C4×D11C2412yes—
251C2×Dic22—24no—
252C2×Dic22—21no—
253C2×Dic22—22no—
254C2×Dic22—22no—
255C2×Dic22—44no—
256C2×Dic22C2412yes—
257C11×SD16—44no—
258C11×M16—44no—
259C2×C8×C11—22no—
260C2×C8×C11—22no—
261C2×C8×C11C2412yes—
262C2×C8×C11C2412yes—
263C11×C4⋊C4—21no—
264C11×C4⋊C4—24no—
265C11×C4⋊C4—21no—
266C11×C4⋊C4C2412yes—
267C11×C4⋊C4C2412yes—
268C11×C22⋊C4—24no—
269C11×C22⋊C4—24no—
270C22⋊Dic11—24no—
271C22⋊Dic11—24no—
272C22⋊Dic11C2×D414yes—
273#4324—44no—
274#4323—28no—
275(C2×D11)⋊C4—24no—
276(C2×D11)⋊C4—24no—
277(C2×D11)⋊C4C2×D414yes—
278C4⋊Dic11—24no—
279C4⋊Dic11—24no—
280C4⋊Dic11—21no—
281C4⋊Dic11—21no—
282C4⋊Dic11C2412yes—
283C4⋊Dic11C2412yes—
284Dic11⋊C4—24no—
285Dic11⋊C4—24no—
286Dic11⋊C4—24no—
287Dic11⋊C4—24no—
288Dic11⋊C4C2×D414yes—
289C4×Dic11C2×D412yes—
290C4×Dic11C2412yes—
291C2×C11⋊C8—22no—
292C2×C11⋊C8—22no—
293C2×C11⋊C8C2412yes—
294C2×C11⋊C8C2412yes—
295#4313—44no—
296C2×#547—111no—
297C2×#547—111no—
298#3330—1116no—
299C2×#487—111no—
300C2×#484—111no—
301C2×#484—111no—
302C2×#474—111no—
303C2×#468—111no—
304C2×#468D1111yescharacteristic, complemented
305C2×#461—111no—
306C2×#449—111no—
307C2×#449—111no—
308C2×C4×D8—111no—
309C2×#436—111no—
310C2×#417—111no—
311C2×#417—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—24no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—42no—
327C22×D11—42no—
328C22×D11C22×D412yes—
329Q8×C11—22no—
330Q8×C11—22no—
331Q8×C11—42no—
332D4×C11—22no—
333D4×C11—22no—
334D4×C11—48no—
335D4×C11—42no—
336C2×C4×C11—22no—
337C2×C4×C11—24no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—42no—
344C2×C4×C11—42no—
345C2×C4×C11—42no—
346C2×C4×C11C22×D412yes—
347C2×C4×C11C22×D411yescharacteristic
348C2×C4×C11C2×#4112yes—
349C2×C4×C11H(5,𝔽2)12yes—
350C2×C4×C11C2511yescharacteristic
351C22⋊D11—28no—
352C22⋊D11—48no—
353C22⋊D11—48no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—48no—
360C2×Dic11—42no—
361C2×Dic11—42no—
362C2×Dic11—42no—
363C2×Dic11—48no—
364C2×Dic11AGL(1,ℤ/8)14yes—
365C2×Dic11C22×D412yes—
366C2×Dic11C22×D412yes—
367C2×Dic11C22×D412yes—
368D44—24no—
369D44—22no—
370D44—48no—
371D44C2×#4114yescomplemented
372C4×D11—24no—
373C4×D11—22no—
374C4×D11—22no—
375C4×D11—48no—
376C4×D11—48no—
377C4×D11—48no—
378C4×D11—48no—
379Dic22—22no—
380Dic22—22no—
381Dic22—42no—
382Dic22—48no—
383C8×C11—22no—
384C8×C11—22no—
385C11⋊C8—22no—
386C11⋊C8—22no—
387C22×#41—111no—
388C22×#41—111no—
389C22×#41—221no—
390C22×SD16—111no—
391C22×SD16C2×D1111yescharacteristic
392C22×D8—111no—
393C22×M16—111no—
394C22×M16C2×D1111yescharacteristic
395#547—118no—
396#547—118no—
397#547—224no—
398#547—224no—
399C2×C4⋊Q8—111no—
400C2×C4⋊Q8—111no—
401C2×#123—221no—
402C2×#123—221no—
403C2×#123—221no—
404C2×#123—221no—
405C2×C22⋊Q8—111no—
406C2×C22⋊Q8—221no—
407C2×C22⋊Q8C2×D1111yescharacteristic
408C2×#121—111no—
409C2×#121—221no—
410C2×#121C2×D1111yescharacteristic
411C2×C4×D4—111no—
412C2×C4×D4—111no—
413C2×C4×D4—111no—
414C22×C4⋊C4—111no—
415C22×C4⋊C4—111no—
416C22×C4⋊C4—221no—
417#487—118no—
418#484—118no—
419#484—118no—
420#474—118no—
421#468—118no—
422#468C2×D1118yescomplemented
423#461—118no—
424#449—118no—
425#449—118no—
426C4×D8—118no—
427#436—118no—
428C2×#107—111no—
429C2×#107—111no—
430C2×#107C2×D1111yescharacteristic
431C2×C4⋊C8—111no—
432#417—118no—
433#417—118no—
434C2×#103—111no—
435C2×#103—111no—
436C2×#103—111no—
437C2×#103—111no—
438C2×#103—111no—
439C2×#103C2×D1111yescharacteristic
440C2×#102—111no—
441C2×#102—111no—
442C2×#102—111no—
443C2×#102C2×D1111yescharacteristic
444C2×C22⋊C8—111no—
445C2×C22⋊C8—111no—
446C2×C4×C8—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—24no—
460C2×D11—22no—
461C2×D11—22no—
462C2×D11—22no—
463C2×D11—44no—
464C2×D11—48no—
465C2×D11—42no—
466C2×D11—42no—
467C4×C11—22no—
468C4×C11—42no—
469C4×C11—42no—
470C4×C11—42no—
471C4×C11#54612yes—
472C4×C11C22×#4111yescharacteristic
473C4×C11C2×H(5,𝔽2)11yescharacteristic
474Dic11—22no—
475Dic11—22no—
476Dic11—42no—
477Dic11—42no—
478Dic11—42no—
479Dic11C2×AGL(1,ℤ/8)14yes—
480C2×#41—114no—
481C2×#41—114no—
482C2×#41—224no—
483C2×#41—222no—
484C2×#41—228no—
485C2×#41—222no—
486C2×#41—224no—
487C2×#41—442no—
488C2×#41—442no—
489C2×#41—448no—
490C22×Q8—111no—
491C22×Q8—221no—
492C22×Q8C22×D1111yescharacteristic
493C22×D4—21no—
494C22×D4—111no—
495C22×D4—111no—
496C22×D4—221no—
497C22×D4—221no—
498C22×D4—221no—
499C22×D4C22×D1111yescharacteristic
500C23×C4—111no—
501C23×C4—221no—
502C23×C4—221no—
503C23×C4—221no—
504C23×C4—221no—
505C23×C4—221no—
506C23×C4—221no—
507C23×C4C22×D1111yescharacteristic
508C2×SD16—42no—
509C2×SD16—114no—
510C2×SD16—442no—
511C2×SD16C22×D1114yes—
512C2×D8—114no—
513C2×D8—224no—
514C2×M16—42no—
515C2×M16—114no—
516C2×M16—442no—
517C2×M16C22×D1114yes—
518C22×C8—111no—
519C22×C8—111no—
520C22×C8C22×D1111yescharacteristic
521C22×C8C22×D1111yescharacteristic
522C4⋊Q8—114no—
523C4⋊Q8—114no—
524C4⋊Q8—222no—
525C4⋊Q8—222no—
526#123—228no—
527#123—228no—
528#123—228no—
529#123—228no—
530C22⋊Q8—22no—
531C22⋊Q8—114no—
532C22⋊Q8—228no—
533C22⋊Q8—222no—
534C22⋊Q8C22×D1114yes—
535#121—22no—
536#121—114no—
537#121—228no—
538#121—222no—
539#121C22×D1114yes—
540C4×D4—114no—
541C4×D4—114no—
542C4×D4—114no—
543C4×D4—114no—
544C4×D4—222no—
545C4×D4—222no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—111no—
548C2×C4⋊C4—111no—
549C2×C4⋊C4—111no—
550C2×C4⋊C4—114no—
551C2×C4⋊C4—114no—
552C2×C4⋊C4—228no—
553C2×C4⋊C4—222no—
554C2×C4⋊C4—221no—
555C2×C4⋊C4—221no—
556C2×C4⋊C4—221no—
557C2×C4⋊C4—221no—
558C2×C4⋊C4—221no—
559C2×C4⋊C4—221no—
560C2×C4⋊C4—222no—
561C2×C4⋊C4C22×D1111yescharacteristic
562C2×C4⋊C4C22×D1111yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—111no—
566C2×C22⋊C4—111no—
567C2×C22⋊C4—221no—
568C2×C22⋊C4—221no—
569C2×C22⋊C4—221no—
570C2×C22⋊C4—221no—
571C2×C42—111no—
572#107—114no—
573#107—114no—
574#107C22×D1114yes—
575C4⋊C8—114no—
576#103—114no—
577#103—114no—
578#103—114no—
579#103—114no—
580#103—114no—
581#103C22×D1114yes—
582#102—114no—
583#102—114no—
584#102—114no—
585#102C22×D1114yes—
586C22⋊C8—114no—
587C22⋊C8—114no—
588C4×C8—114no—
589C2×C11—42no—
590C2×C11—82no—
591C2×C11#333014yescomplemented
592C2×C11C2×#54611yescharacteristic
593C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
594C2×C11C2×#57811yescharacteristic
595D11—42no—
596D11—44no—
597C24—21no—
598C24—111no—
599C24—221no—
600C24D4×D1111yescharacteristic
601#41—228no—
602#41—228no—
603#41—444no—
604#41—448no—
605#41—444no—
606#41—448no—
607#41—4432no—
608C2×Q8—21no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—112no—
612C2×Q8—224no—
613C2×Q8—221no—
614C2×Q8—222no—
615C2×Q8—222no—
616C2×Q8—444no—
617C2×Q8C23×D1112yes—
618C2×D4—24no—
619C2×D4—21no—
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—44no—
623C2×D4—114no—
624C2×D4—114no—
625C2×D4—112no—
626C2×D4—224no—
627C2×D4—224no—
628C2×D4—224no—
629C2×D4—224no—
630C2×D4—221no—
631C2×D4—222no—
632C2×D4—444no—
633C2×D4—444no—
634C2×D4—444no—
635C2×D4C23×D1112yes—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—111no—
642C22×C4—111no—
643C22×C4—111no—
644C22×C4—112no—
645C22×C4—112no—
646C22×C4—224no—
647C22×C4—224no—
648C22×C4—224no—
649C22×C4—224no—
650C22×C4—222no—
651C22×C4—222no—
652C22×C4—224no—
653C22×C4—221no—
654C22×C4—221no—
655C22×C4—221no—
656C22×C4—224no—
657C22×C4—444no—
658C22×C4—444no—
659C22×C4—444no—
660C22×C4—444no—
661C22×C4—444no—
662C22×C4—444no—
663C22×C4D4×D1112yes—
664C22×C4D4×D1111yescharacteristic
665C22×C4C23×D1112yes—
666C22×C4C23×D1111yescharacteristic
667SD16—44no—
668SD16—444no—
669D8—228no—
670M16—44no—
671M16—444no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—112no—
675C2×C8—112no—
676C2×C8—222no—
677C2×C8—222no—
678C2×C8C23×D1112yes—
679C2×C8C23×D1112yes—
680C4⋊C4—24no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—114no—
684C4⋊C4—112no—
685C4⋊C4—112no—
686C4⋊C4—224no—
687C4⋊C4—224no—
688C4⋊C4—224no—
689C4⋊C4—224no—
690C4⋊C4—224no—
691C4⋊C4—221no—
692C4⋊C4—221no—
693C4⋊C4—224no—
694C4⋊C4C23×D1112yes—
695C4⋊C4C23×D1112yes—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—114no—
699C22⋊C4—114no—
700C22⋊C4—224no—
701C22⋊C4—224no—
702C22⋊C4—224no—
703C22⋊C4—224no—
704C42—112no—
705C42—112no—
706C11C2×#333011yescharacteristic, complemented, Sylow
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—112no—
715C23—222no—
716C23—222no—
717C23—222no—
718C23—224no—
719C23—222no—
720C23—442no—
721C23—442no—
722C23C2×D4×D1112yes—
723C23C2×D4×D1111yescharacteristic
724Q8—22no—
725Q8—22no—
726Q8—42no—
727Q8—222no—
728Q8—222no—
729Q8—448no—
730Q8—442no—
731D4—22no—
732D4—22no—
733D4—48no—
734D4—42no—
735D4—114no—
736D4—228no—
737D4—224no—
738D4—222no—
739D4—448no—
740D4—448no—
741D4—448no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—114no—
753C2×C4—112no—
754C2×C4—112no—
755C2×C4—112no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—224no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—222no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—448no—
765C2×C4—448no—
766C2×C4—448no—
767C2×C4—448no—
768C2×C4—448no—
769C2×C4—448no—
770C2×C4—442no—
771C2×C4—442no—
772C2×C4—442no—
773C2×C4C2×D4×D1112yes—
774C2×C4C2×D4×D1111yescharacteristic
775C2×C4#6703712yes—
776C2×C4#41×D1112yes—
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—222no—
791C22—224no—
792C22—222no—
793C22—222no—
794C22—444no—
795C22—448no—
796C22—442no—
797C22—442no—
798C22#1062314112yes—
799C22D11×AGL(1,ℤ/8)12yes—
800C22#1062331012yes—
801C22C22×D4×D1111yescharacteristic
802C4—22no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—114no—
807C4—222no—
808C4—222no—
809C4—442no—
810C4—442no—
811C4—442no—
812C4#1062314112yes—
813C4C2×#6703711yescharacteristic
814C4C2×#41×D1111yescharacteristic
815C2—42no—
816C2—82no—
817C2—442no—
818C2—444no—
819C2#1308091614yesdirect product factor
820C2C2×#1062314111yescharacteristic
821C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
822C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#468C2
socleC23×C11C22×D4
hypercenterC2×#468D11
hypocenterC11C2×#3330
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#10623162C2semidirect
2. C2×#10623142C2semidirect
3. #13080916C2direct (N × H)
4. C2×#10622405C2semidirect
5. C2×#10622497C2semidirect
6. C2×#10622657C2semidirect
7. C2×#10622503C2semidirect
8. C2×#10622393C2semidirect
9. C2×#10622775C2semidirect
10. C2×#10622785C2semidirect
11. C2×#10622650C2semidirect
12. C2×#10622369C2semidirect
13. C2×#10622741C2semidirect
14. C2×#10622746C2semidirect
15. C2×#10622416C2semidirect
16. C2×C11×#468C2semidirect
34. #10623162C22semidirect
36. #10623142C22semidirect
47. C11×#468C22semidirect
54. #10622785C22semidirect
55. #10622775C22semidirect
56. #10622746C22semidirect
57. #10622741C22semidirect
65. #10622657C22semidirect
66. #10622650C22semidirect
71. #10622503C22semidirect
72. #10622497C22semidirect
73. #10622416C22semidirect
74. #10622405C22semidirect
75. #10622393C22semidirect
76. #10622369C22semidirect
237. C2×D44#41semidirect
304. C2×#468D11semidirect
371. D44C2×#41semidirect
422. #468C2×D11semidirect
591. C2×C11#3330semidirect
706. C11C2×#3330semidirect
819. C2#13080916direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231622
C2×#106231422
#130809162
C2×#106224052
C2×#106224972
C2×#106226572
C2×#106225032
C2×#106223932
C2×#106227752
C2×#106227852
C2×#106226502
C2×#106223692
C2×#106227412
C2×#106227462
C2×#106224162
C2×C11×#4682
C2×#333011