Finite Group Databasebeta

← C2×#13080917 #15630678

Subgroups — C2×#13080917 #15630678

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×#10623038C211yesmaximal, characteristic, complemented
2C2×#10623355C211yesmaximal, characteristic, complemented
3#13080917C2116yesmaximal, direct product factor
4C2×#10622405C211yesmaximal, characteristic, complemented
5C2×#10622583C211yesmaximal, characteristic, complemented
6C2×#10622422C211yesmaximal, characteristic, complemented
7C2×#10622372C211yesmaximal, characteristic, complemented
8C2×#10622425C211yesmaximal, characteristic, complemented
9C2×#10622747C211yesmaximal, characteristic, complemented
10C2×#10622431C211yesmaximal, characteristic, complemented
11C2×#10622394C211yesmaximal, characteristic, complemented
12C2×#10622851C211yesmaximal, characteristic, complemented
13C2×#10622369C211yesmaximal, characteristic, complemented
14C2×#10622741C211yesmaximal, characteristic, complemented
15C2×#10622384C211yesmaximal, characteristic, complemented
16C2×C11×#417C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×#4341C2211yescharacteristic
19C22×#4339—21no—
20C22×C11×M16C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22#10623355—24no—
23#10623355C2218yescomplemented
24C2×#66999C2211yescharacteristic
25C2×#66997C2211yescharacteristic
26C22×#4325C2211yescharacteristic
27C2×#66992—21no—
28C2×#66988—21no—
29C2×D4×Dic11C2211yescharacteristic
30C22×#4323C2211yescharacteristic
31C2×#66983C2211yescharacteristic
32C2×#66982—21no—
33C2×#66982—21no—
34C2×C4×C22⋊D11C2211yescharacteristic
35C2×#66977C2211yescharacteristic
36C22×Dic11⋊C4—21no—
37C22×#4314C2211yescharacteristic
38C22×#4313C2211yescharacteristic
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#10622741C2218yescomplemented
58C2×#66885C2211yescharacteristic
59C2×(C2×D11)⋊C8C2211yescharacteristic
60C2×#66882C2211yescharacteristic
61C2×#66880C2211yescharacteristic
62C2×Dic11⋊C8C2211yescharacteristic
63C2×C8×Dic11C2211yescharacteristic
64#10622583C2218yescomplemented
65C2×#66874C2211yescharacteristic
66C2×#66874C2211yescharacteristic
67C2×#66871C2211yescharacteristic
68C2×#66871C2211yescharacteristic
69#10622431C2218yescomplemented
70#10622425C2218yescomplemented
71#10622422C2218yescomplemented
72#10622405C2218yescomplemented
73#10622394C2218yescomplemented
74#10622384C2218yescomplemented
75#10622372C2218yescomplemented
76#10622369C2218yescomplemented
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
90C23×Dic11—21no—
91C23×Dic11—21no—
92C2×#4341—24no—
93C2×#4341—22no—
94C2×#4341—42no—
95C2×#4341C2314yes—
96C2×#4339—28no—
97C2×#4339—48no—
98C22×D44—21no—
99C22×D44C2311yescharacteristic
100C22×C4×D11—21no—
101C22×C4×D11—21no—
102C22×C4×D11C2311yescharacteristic
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⋊Dic11D411yescharacteristic
117#66999—22no—
118#66999C2314yes—
119#66997—22no—
120#66997C2314yes—
121C2×#4325—42no—
122C2×#4325C2314yes—
123#66992—28no—
124#66988—28no—
125D4×Dic11—22no—
126D4×Dic11C2314yes—
127C2×#4323—24no—
128C2×#4323C2314yes—
129#66983—22no—
130#66983C2314yes—
131#66982—28no—
132#66982—28no—
133C4×C22⋊D11D414yes—
134C4×C22⋊D11C2314yes—
135C2×(C2×D11)⋊C4—21no—
136C2×(C2×D11)⋊C4—21no—
137C2×(C2×D11)⋊C4—21no—
138C2×(C2×D11)⋊C4—21no—
139C2×(C2×D11)⋊C4D411yescharacteristic
140C2×C4⋊Dic11C2311yescharacteristic
141C2×C4⋊Dic11C2311yescharacteristic
142#66977—22no—
143#66977C2314yes—
144C2×Dic11⋊C4—21no—
145C2×Dic11⋊C4—21no—
146C2×Dic11⋊C4—21no—
147C2×Dic11⋊C4—21no—
148C2×Dic11⋊C4—21no—
149C2×Dic11⋊C4—21no—
150C2×Dic11⋊C4—28no—
151C2×Dic11⋊C4D411yescharacteristic
152C2×C4×Dic11C2311yescharacteristic
153C22×C11⋊C8C2311yescharacteristic
154C22×C11⋊C8C2311yescharacteristic
155C2×#4314—42no—
156C2×#4314C2314yes—
157C2×#4313—42no—
158C2×#4313C2314yes—
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—
180Dic11⋊C8C2314yes—
181C8×Dic11C2314yes—
182#66874C2314yes—
183#66874C2314yes—
184#66871C2314yes—
185#66871C2314yes—
186C2×#3330—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—22no—
197C2×Q8×C11C2412yes—
198C2×D4×C11—24no—
199C2×D4×C11—21no—
200C2×D4×C11—22no—
201C2×D4×C11—44no—
202C2×D4×C11#4114yescomplemented
203C2×D4×C11C2412yes—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—21no—
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—24no—
224C22×Dic11—24no—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11—21no—
228C22×Dic11—44no—
229C22×Dic11—44no—
230C22×Dic11C2×D411yescharacteristic
231C22×Dic11C2×D411yescharacteristic
232C22×Dic11C2×D411yescharacteristic
233#4341—28no—
234#4341—44no—
235#4341—48no—
236#4339—432no—
237C2×D44—24no—
238C2×D44—21no—
239C2×D44—22no—
240C2×D44—22no—
241C2×D44—44no—
242C2×D44C2412yes—
243C2×C4×D11—24no—
244C2×C4×D11—24no—
245C2×C4×D11—22no—
246C2×C4×D11—22no—
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×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⋊Dic11C2×D414yes—
270#4325—44no—
271#4323—28no—
272(C2×D11)⋊C4—24no—
273(C2×D11)⋊C4—24no—
274(C2×D11)⋊C4—24no—
275(C2×D11)⋊C4—24no—
276(C2×D11)⋊C4C2×D414yes—
277C4⋊Dic11—21no—
278C4⋊Dic11—21no—
279C4⋊Dic11C2412yes—
280C4⋊Dic11C2412yes—
281Dic11⋊C4—24no—
282Dic11⋊C4—24no—
283Dic11⋊C4—24no—
284Dic11⋊C4—24no—
285Dic11⋊C4—24no—
286Dic11⋊C4—24no—
287Dic11⋊C4C2×D414yes—
288C4×Dic11C2×D412yes—
289C4×Dic11C2412yes—
290C2×C11⋊C8—22no—
291C2×C11⋊C8—22no—
292C2×C11⋊C8C2412yes—
293C2×C11⋊C8C2412yes—
294#4314—44no—
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×#468—111no—
305C2×#461—111no—
306C2×#449—111no—
307C2×#449—111no—
308C2×C4×D8—111no—
309C2×#436—111no—
310C2×#417—111no—
311C2×#417D1111yescharacteristic, complemented
312C23×C11—24no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—42no—
318C23×C11—42no—
319C23×C11C22×D412yes—
320C23×C11C22×D411yescharacteristic
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—42no—
326C22×D11—42no—
327C22×D11—42no—
328C22×D11C22×D412yes—
329Q8×C11—22no—
330Q8×C11—22no—
331Q8×C11—42no—
332D4×C11—24no—
333D4×C11—22no—
334D4×C11—48no—
335D4×C11C2×#4114yescomplemented
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—48no—
344C2×C4×C11—48no—
345C2×C4×C11—42no—
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—48no—
362C2×Dic11—42no—
363C2×Dic11—42no—
364C2×Dic11—42no—
365C2×Dic11—48no—
366C2×Dic11AGL(1,ℤ/8)14yes—
367C2×Dic11C22×D412yes—
368C2×Dic11C22×D412yes—
369C2×Dic11C22×D412yes—
370D44—22no—
371D44—22no—
372D44—48no—
373D44—42no—
374C4×D11—24no—
375C4×D11—22no—
376C4×D11—22no—
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—221no—
389C22×#41C2×D1111yescharacteristic
390C22×SD16—111no—
391C22×SD16—111no—
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—111no—
407C2×C22⋊Q8—221no—
408C2×#121—111no—
409C2×#121—111no—
410C2×#121—221no—
411C2×C4×D4—111no—
412C2×C4×D4—111no—
413C2×C4×D4—111no—
414C22×C4⋊C4—111no—
415C22×C4⋊C4—221no—
416C22×C4⋊C4C2×D1111yescharacteristic
417#487—118no—
418#484—118no—
419#484—118no—
420#474—118no—
421#468—118no—
422#468—118no—
423#461—118no—
424#449—118no—
425#449—118no—
426C4×D8—118no—
427#436—118no—
428C2×#107—111no—
429C2×#107—111no—
430C2×#107—111no—
431C2×C4⋊C8—111no—
432#417—118no—
433#417C2×D1118yescomplemented
434C2×#103—111no—
435C2×#103—111no—
436C2×#103—111no—
437C2×#103—111no—
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×C4×C8—111no—
447C22×C11—22no—
448C22×C11—24no—
449C22×C11—22no—
450C22×C11—22no—
451C22×C11—44no—
452C22×C11—48no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11#54612yes—
456C22×C11C2×AGL(1,ℤ/8)12yes—
457C22×C11#57812yes—
458C22×C11C23×D411yescharacteristic
459C2×D11—22no—
460C2×D11—22no—
461C2×D11—22no—
462C2×D11—44no—
463C2×D11—42no—
464C2×D11—42no—
465C2×D11—42no—
466C2×D11—84no—
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—22no—
481C2×#41—24no—
482C2×#41—42no—
483C2×#41—114no—
484C2×#41—228no—
485C2×#41—222no—
486C2×#41—224no—
487C2×#41—448no—
488C2×#41—442no—
489C2×#41C22×D1114yes—
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—21no—
501C23×C4—21no—
502C23×C4—111no—
503C23×C4—221no—
504C23×C4—221no—
505C23×C4—221no—
506C23×C4—221no—
507C23×C4C22×D1111yescharacteristic
508C2×SD16—114no—
509C2×SD16—114no—
510C2×SD16—442no—
511C2×SD16—442no—
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—114no—
531C22⋊Q8—114no—
532C22⋊Q8—228no—
533C22⋊Q8—222no—
534C22⋊Q8—222no—
535#121—114no—
536#121—114no—
537#121—222no—
538#121—228no—
539#121—222no—
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—22no—
548C2×C4⋊C4—111no—
549C2×C4⋊C4—111no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4—114no—
552C2×C4⋊C4—222no—
553C2×C4⋊C4—228no—
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⋊C4C22×D1111yescharacteristic
561C2×C4⋊C4C22×D1111yescharacteristic
562C2×C4⋊C4C22×D1114yes—
563C2×C22⋊C4—111no—
564C2×C22⋊C4—111no—
565C2×C22⋊C4—221no—
566C2×C22⋊C4—221no—
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#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—
588C4×C8—114no—
589C2×C11—42no—
590C2×C11—44no—
591C2×C11#333014yescomplemented
592C2×C11C2×#54611yescharacteristic
593C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
594C2×C11C2×#57811yescharacteristic
595D11—42no—
596D11—82no—
597C24—21no—
598C24—111no—
599C24—221no—
600C24D4×D1111yescharacteristic
601#41—28no—
602#41—44no—
603#41—48no—
604#41—228no—
605#41—4432no—
606#41—444no—
607#41—448no—
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—44no—
622C2×D4—114no—
623C2×D4—112no—
624C2×D4—224no—
625C2×D4—224no—
626C2×D4—224no—
627C2×D4—224no—
628C2×D4—222no—
629C2×D4—221no—
630C2×D4—222no—
631C2×D4—444no—
632C2×D4—444no—
633C2×D4—444no—
634C2×D4#433914yescomplemented
635C2×D4C23×D1112yes—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—24no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—44no—
644C22×C4—44no—
645C22×C4—111no—
646C22×C4—111no—
647C22×C4—111no—
648C22×C4—112no—
649C22×C4—112no—
650C22×C4—224no—
651C22×C4—224no—
652C22×C4—224no—
653C22×C4—224no—
654C22×C4—222no—
655C22×C4—222no—
656C22×C4—221no—
657C22×C4—221no—
658C22×C4—221no—
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—444no—
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—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—224no—
690C4⋊C4—224no—
691C4⋊C4—221no—
692C4⋊C4—221no—
693C4⋊C4—224no—
694C4⋊C4C23×D1112yes—
695C4⋊C4C23×D1112yes—
696C22⋊C4—114no—
697C22⋊C4—114no—
698C22⋊C4—224no—
699C22⋊C4—224no—
700C22⋊C4—224no—
701C22⋊C4—224no—
702C22⋊C4—224no—
703C22⋊C4—224no—
704C42—112no—
705C42—112no—
706C11C2×#333011yescharacteristic, complemented, Sylow
707C23—22no—
708C23—24no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—42no—
713C23—42no—
714C23—112no—
715C23—222no—
716C23—222no—
717C23—222no—
718C23—222no—
719C23—442no—
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—24no—
732D4—22no—
733D4—48no—
734D4—228no—
735D4—222no—
736D4—222no—
737D4—448no—
738D4—448no—
739D4—448no—
740D4—442no—
741D4C2×#433914yescomplemented
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—48no—
750C2×C4—48no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—114no—
755C2×C4—112no—
756C2×C4—112no—
757C2×C4—112no—
758C2×C4—222no—
759C2×C4—222no—
760C2×C4—224no—
761C2×C4—222no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—222no—
766C2×C4—448no—
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—24no—
784C22—22no—
785C22—22no—
786C22—44no—
787C22—48no—
788C22—42no—
789C22—42no—
790C22—222no—
791C22—222no—
792C22—222no—
793C22—444no—
794C22—442no—
795C22—442no—
796C22—442no—
797C22—884no—
798C22#1062302112yes—
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#1062302112yes—
813C4C22×#433911yescharacteristic
814C4C2×#6703711yescharacteristic
815C2—42no—
816C2—44no—
817C2—442no—
818C2—882no—
819C2#1308091714yesdirect 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×#3330
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×#10623038C2semidirect
2. C2×#10623355C2semidirect
3. #13080917C2direct (N × H)
4. C2×#10622405C2semidirect
5. C2×#10622583C2semidirect
6. C2×#10622422C2semidirect
7. C2×#10622372C2semidirect
8. C2×#10622425C2semidirect
9. C2×#10622747C2semidirect
10. C2×#10622431C2semidirect
11. C2×#10622394C2semidirect
12. C2×#10622851C2semidirect
13. C2×#10622369C2semidirect
14. C2×#10622741C2semidirect
15. C2×#10622384C2semidirect
16. C2×C11×#417C2semidirect
23. #10623355C22semidirect
41. #10623038C22semidirect
47. C11×#417C22semidirect
52. #10622851C22semidirect
56. #10622747C22semidirect
57. #10622741C22semidirect
64. #10622583C22semidirect
69. #10622431C22semidirect
70. #10622425C22semidirect
71. #10622422C22semidirect
72. #10622405C22semidirect
73. #10622394C22semidirect
74. #10622384C22semidirect
75. #10622372C22semidirect
76. #10622369C22semidirect
202. C2×D4×C11#41semidirect
311. C2×#417D11semidirect
335. D4×C11C2×#41semidirect
433. #417C2×D11semidirect
591. C2×C11#3330semidirect
634. C2×D4#4339semidirect
706. C11C2×#3330semidirect
741. D4C2×#4339semidirect
819. C2#13080917direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230382
C2×#106233552
#130809172
C2×#106224052
C2×#106225832
C2×#106224222
C2×#106223722
C2×#106224252
C2×#106227472
C2×#106224312
C2×#106223942
C2×#106228512
C2×#106223692
C2×#106227412
C2×#106223842
C2×C11×#4172
C2×#333011