Finite Group Databasebeta

← C2×#13078169 #15620713

Subgroups — C2×#13078169 #15620713

Order 2816.

2742 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66971C211yesmaximal, characteristic, complemented
2C22×#66969C211yesmaximal, characteristic
3C2×#10623206C211yesmaximal, characteristic, complemented
4C2×#10623105C211yesmaximal, characteristic, complemented
5#13078169C2116yesmaximal, direct product factor
6C2×#10622779C211yesmaximal, characteristic, complemented
7C2×#10622644C211yesmaximal, characteristic, complemented
8C2×#10622795C211yesmaximal, characteristic, complemented
9C2×#10622400C211yesmaximal, characteristic, complemented
10C2×#10622670C211yesmaximal, characteristic, complemented
11C2×#10622454C211yesmaximal, characteristic, complemented
12C2×#10622431C211yesmaximal, characteristic, complemented
13C2×#10622452C211yesmaximal, characteristic, complemented
14C2×#10622384C211yesmaximal, characteristic, complemented
15C2×D11×#103C211yesmaximal, characteristic, complemented
16C2×C11×#464C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C22×Q8×D11C2211yescharacteristic
19C22×#4341C2211yescharacteristic
20C22×C11×Q16C2211yescharacteristic
21C22×C11×SD16C2211yescharacteristic
22C2×C11×#124C2211yescharacteristic
23C2×C4×Q8×C11C2211yescharacteristic
24C2×Q8×Dic11C2211yescharacteristic
25C2×#66997C2211yescharacteristic
26C22×#4326C2211yescharacteristic
27C22×#4326C2211yescharacteristic
28C22×#4325C2211yescharacteristic
29C2×#66989C2211yescharacteristic
30C22×#4323C2211yescharacteristic
31C2×#66971—28no—
32C2×#66971C2218yescomplemented
33C2×#66969—28no—
34C2×#66969C2218yes—
35C22×#4314C2211yescharacteristic
36C22×#4314C2211yescharacteristic
37C22×#4313C2211yescharacteristic
38C22×C8×D11C2211yescharacteristic
39#10623206—24no—
40#10623206C2218yescomplemented
41#10623105—24no—
42#10623105C2218yescomplemented
43C2×#66946—21no—
44C2×#66946C2211yescharacteristic
45C2×C4⋊C4×D11—21no—
46C2×C4⋊C4×D11C2211yescharacteristic
47C2×#66936—21no—
48C2×#66936—21no—
49C2×#66931—21no—
50C2×#66931—21no—
51C2×C4×D44—21no—
52C2×C4×D44C2211yescharacteristic
53C2×#66925—21no—
54C2×#66925C2211yescharacteristic
55C2×#66922C2211yescharacteristic
56C11×#464C2218yescomplemented
57C2×C11×C4⋊C8C2211yescharacteristic
58C2×C11×#103C2211yescharacteristic
59C2×C11×#102C2211yescharacteristic
60C2×#66899C2211yescharacteristic
61C2×#66896C2211yescharacteristic
62#10622795C2218yescomplemented
63#10622779C2218yescomplemented
64C2×#66880C2211yescharacteristic
65C2×#66880C2211yescharacteristic
66C2×Dic11⋊C8C2211yescharacteristic
67C2×Dic11⋊C8C2211yescharacteristic
68#10622670C2218yescomplemented
69#10622644C2218yescomplemented
70C2×#66874C2211yescharacteristic
71C2×#66874C2211yescharacteristic
72C2×C4⋊(C11⋊C8)C2211yescharacteristic
73#10622454C2218yescomplemented
74#10622452C2218yescomplemented
75#10622431C2218yescomplemented
76D11×#103C2218yescomplemented
77#10622400C2218yescomplemented
78#10622384C2218yescomplemented
79C22×Q8×C11C2311yescharacteristic
80C22×Q8×C11C2311yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C22×C22⋊D11—21no—
83C23×Dic11—21no—
84C2×#4343—22no—
85C2×#4343—24no—
86C2×#4343D418yes—
87C2×#4343C2314yes—
88C2×Q8×D11—22no—
89C2×Q8×D11—24no—
90C2×Q8×D11—24no—
91C2×Q8×D11C2314yes—
92C2×#4341—24no—
93C2×#4341—22no—
94C2×#4341—24no—
95C2×#4341C2314yes—
96C22×D44—21no—
97C22×D44C2311yescharacteristic
98C22×C4×D11—21no—
99C22×C4×D11—21no—
100C22×C4×D11—21no—
101C22×C4×D11—21no—
102C22×C4×D11—21no—
103C22×C4×D11C2311yescharacteristic
104C22×Dic22—21no—
105C22×Dic22C2311yescharacteristic
106C22×Dic22C2311yescharacteristic
107C2×C11×Q16—24no—
108C2×C11×Q16C2314yes—
109C2×C11×SD16—24no—
110C2×C11×SD16C2314yes—
111C22×C8×C11C2311yescharacteristic
112C22×C8×C11C2311yescharacteristic
113C11×#124—22no—
114C11×#124C2314yes—
115C4×Q8×C11—22no—
116C4×Q8×C11C2314yes—
117C2×C11×C4⋊C4—21no—
118C2×C11×C4⋊C4C2311yescharacteristic
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C42×C11—21no—
122C2×C42×C11C2311yescharacteristic
123C2×C22⋊Dic11—21no—
124C2×C22⋊Dic11—21no—
125Q8×Dic11—22no—
126Q8×Dic11C2314yes—
127#66997—22no—
128#66997C2314yes—
129C2×#4326—24no—
130C2×#4326—24no—
131C2×#4326C2314yes—
132C2×#4326C2314yes—
133C2×#4325—24no—
134C2×#4325C2314yes—
135#66989—22no—
136#66989C2314yes—
137C2×#4323—24no—
138C2×#4323C2314yes—
139C2×(C2×D11)⋊C4—21no—
140C2×(C2×D11)⋊C4—21no—
141C2×(C2×D11)⋊C4D411yescharacteristic
142C2×(C2×D11)⋊C4D411yescharacteristic
143C2×C4⋊Dic11—21no—
144C2×C4⋊Dic11—21no—
145C2×C4⋊Dic11—21no—
146C2×C4⋊Dic11C2311yescharacteristic
147C2×Dic11⋊C4—21no—
148C2×Dic11⋊C4—21no—
149C2×Dic11⋊C4—21no—
150C2×Dic11⋊C4D411yescharacteristic
151C2×Dic11⋊C4D411yescharacteristic
152C2×C4×Dic11—21no—
153C2×C4×Dic11C2311yescharacteristic
154C22×C11⋊C8C2311yescharacteristic
155C22×C11⋊C8C2311yescharacteristic
156#66971—232no—
157#66969—232no—
158C2×#4314—24no—
159C2×#4314—24no—
160C2×#4314C2314yes—
161C2×#4314C2314yes—
162C2×#4313—24no—
163C2×#4313C2314yes—
164C2×C8×D11—24no—
165C2×C8×D11C2314yes—
166#66946—28no—
167#66946—22no—
168#66946C2314yes—
169C4⋊C4×D11—22no—
170C4⋊C4×D11—28no—
171C4⋊C4×D11C2314yes—
172#66936—28no—
173#66936—28no—
174#66931—28no—
175#66931—28no—
176C4×D44—22no—
177C4×D44—28no—
178C4×D44C2314yes—
179#66925—28no—
180#66925D414yes—
181#66925C2314yes—
182#66922—22no—
183#66922C2314yes—
184C11×C4⋊C8C2314yes—
185C11×#103C2314yes—
186C11×#102C2314yes—
187#66899C2314yes—
188#66896C2314yes—
189#66880C2314yes—
190#66880C2314yes—
191Dic11⋊C8C2314yes—
192Dic11⋊C8C2314yes—
193#66874C2314yes—
194#66874C2314yes—
195C4⋊(C11⋊C8)C2314yes—
196C2×#3046—111nomaximal, Sylow
197C24×C11—21no—
198C23×D11—21no—
199C23×D11C2×D411yescharacteristic
200C2×Q8×C11—21no—
201C2×Q8×C11—21no—
202C2×Q8×C11—22no—
203C2×Q8×C11—22no—
204C2×Q8×C11—22no—
205C2×Q8×C11C2×D414yes—
206C2×Q8×C11C2412yes—
207C2×Q8×C11C2412yes—
208C2×D4×C11—22no—
209C2×D4×C11—21no—
210C2×D4×C11—22no—
211C2×D4×C11C2412yes—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2411yescharacteristic
218C2×C22⋊D11—24no—
219C2×C22⋊D11—44no—
220C22×Dic11—24no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—44no—
225C22×Dic11C2×D411yescharacteristic
226C22×Dic11C2×D411yescharacteristic
227C22×Dic11C2×D411yescharacteristic
228#4343—216no—
229#4343—28no—
230#4343C2×D4116yes—
231Q8×D11—28no—
232Q8×D11—28no—
233Q8×D11—48no—
234#4341—28no—
235#4341—28no—
236#4341—48no—
237C2×D44—28no—
238C2×D44—24no—
239C2×D44—21no—
240C2×D44—22no—
241C2×D44C2×D414yes—
242C2×D44C2412yes—
243C2×C4×D11—28no—
244C2×C4×D11—24no—
245C2×C4×D11—24no—
246C2×C4×D11—24no—
247C2×C4×D11—24no—
248C2×C4×D11—24no—
249C2×C4×D11—44no—
250C2×C4×D11—82no—
251C2×C4×D11—82no—
252C2×C4×D11—82no—
253C2×C4×D11C2×D414yes—
254C2×C4×D11C2×D412yes—
255C2×C4×D11#4114yes—
256C2×C4×D11C2412yes—
257C2×Dic22—24no—
258C2×Dic22—22no—
259C2×Dic22—22no—
260C2×Dic22—21no—
261C2×Dic22—21no—
262C2×Dic22—22no—
263C2×Dic22—22no—
264C2×Dic22—44no—
265C2×Dic22C2412yes—
266C2×Dic22C2412yes—
267C11×Q16—28no—
268C11×SD16—28no—
269C2×C8×C11—22no—
270C2×C8×C11—22no—
271C2×C8×C11C2412yes—
272C2×C8×C11C2412yes—
273C11×C4⋊C4—24no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4C2412yes—
276C11×C22⋊C4—24no—
277C11×C22⋊C4—24no—
278C42×C11—24no—
279C42×C11C2×D412yes—
280C42×C11C2412yes—
281C22⋊Dic11—24no—
282C22⋊Dic11—24no—
283#4326—28no—
284#4326—28no—
285#4325—28no—
286#4323—28no—
287(C2×D11)⋊C4—24no—
288(C2×D11)⋊C4—24no—
289(C2×D11)⋊C4C2×D414yes—
290(C2×D11)⋊C4C2×D414yes—
291C4⋊Dic11—24no—
292C4⋊Dic11—24no—
293C4⋊Dic11—24no—
294C4⋊Dic11—21no—
295C4⋊Dic11C2412yes—
296Dic11⋊C4—24no—
297Dic11⋊C4—24no—
298Dic11⋊C4—24no—
299Dic11⋊C4C2×D414yes—
300Dic11⋊C4C2×D414yes—
301C4×Dic11—24no—
302C4×Dic11C2×D412yes—
303C4×Dic11C2412yes—
304C2×C11⋊C8—22no—
305C2×C11⋊C8—22no—
306C2×C11⋊C8C2412yes—
307C2×C11⋊C8C2412yes—
308#4314—28no—
309#4314—28no—
310#4313—28no—
311C8×D11—28no—
312C22×#137—111no—
313C22×#135—111no—
314C2×#536—111no—
315C2×#520—111no—
316#3046—1116no—
317C2×#464—111no—
318C2×#464D1111yescharacteristic, complemented
319C2×#462—111no—
320C2×#462—111no—
321C2×#463—111no—
322C2×#463—111no—
323C2×#461—111no—
324C2×#461—111no—
325C2×#424—111no—
326C2×#417—111no—
327C22×#103—111no—
328C23×C11—22no—
329C23×C11—42no—
330C23×C11—42no—
331C23×C11—42no—
332C23×C11C22×D411yescharacteristic
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—24no—
336C22×D11—22no—
337C22×D11—42no—
338C22×D11—42no—
339C22×D11#12114yes—
340C22×D11C22×D412yes—
341Q8×C11—24no—
342Q8×C11—22no—
343Q8×C11—22no—
344Q8×C11—22no—
345Q8×C11—42no—
346Q8×C11C22×D414yes—
347D4×C11—22no—
348D4×C11—22no—
349D4×C11—42no—
350C2×C4×C11—24no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—42no—
357C2×C4×C11—42no—
358C2×C4×C11C22×D412yes—
359C2×C4×C11C22×D412yes—
360C2×C4×C11C22×D411yescharacteristic
361C2×C4×C11C22×D412yes—
362C2×C4×C11C2×#4112yes—
363C2×C4×C11C2511yescharacteristic
364C22⋊D11—48no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—42no—
371C2×Dic11—42no—
372C2×Dic11—42no—
373C2×Dic11—48no—
374C2×Dic11#12114yes—
375C2×Dic11C22×D412yes—
376C2×Dic11C22×D412yes—
377C2×Dic11C22×D412yes—
378D44—216no—
379D44—24no—
380D44—22no—
381D44C22×D414yes—
382C4×D11—216no—
383C4×D11—48no—
384C4×D11—84no—
385C4×D11—84no—
386C4×D11—84no—
387C4×D11#12118yes—
388C4×D11C22×D414yes—
389C4×D11C2×#4114yes—
390Dic22—22no—
391Dic22—22no—
392Dic22—22no—
393Dic22—22no—
394Dic22—42no—
395Dic22—42no—
396Dic22—48no—
397C8×C11—22no—
398C8×C11—22no—
399C11⋊C8—22no—
400C11⋊C8—22no—
401C22×#41—111no—
402C22×#41—111no—
403C23×Q8—111no—
404C2×#137—118no—
405C2×#137—228no—
406C2×#135—118no—
407C2×#135—228no—
408C22×Q16—111no—
409C22×Q16—111no—
410C22×Q16C2×D1111yescharacteristic
411C22×SD16—111no—
412C22×SD16—111no—
413C22×SD16—111no—
414C22×SD16C2×D1111yescharacteristic
415C22×D8—111no—
416C22×M16—111no—
417C23×C8—111no—
418#536—118no—
419#536—224no—
420C2×C4⋊Q8—111no—
421C2×C4⋊Q8—111no—
422C2×#124—111no—
423C2×#124C2×D1111yescharacteristic
424C2×#123—221no—
425C2×#123—221no—
426C2×C22⋊Q8—221no—
427C2×C22⋊Q8—221no—
428#520—118no—
429#520—224no—
430C2×C4×Q8—111no—
431C2×C4×Q8C2×D1111yescharacteristic
432C2×C4×D4—111no—
433C2×C4×D4—111no—
434C2×C4×D4—221no—
435C2×C4×D4—221no—
436C2×#117—111no—
437C2×#117—221no—
438C22×C4⋊C4—111no—
439C22×C4⋊C4—221no—
440#464—118no—
441#464C2×D1118yescomplemented
442#463—118no—
443#463—118no—
444#462—118no—
445#462—118no—
446#461—118no—
447#461—118no—
448#424—118no—
449C2×C4⋊C8—111no—
450C2×C4⋊C8—111no—
451C2×C4⋊C8—111no—
452C2×C4⋊C8C2×D1111yescharacteristic
453#417—118no—
454C2×#103—111no—
455C2×#103—111no—
456C2×#103—111no—
457C2×#103—111no—
458C2×#103—111no—
459C2×#103—118no—
460C2×#103C2×D1111yescharacteristic
461C2×#102—111no—
462C2×#102C2×D1111yescharacteristic
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—84no—
467C22×C11C2×#12112yes—
468C22×C11#57712yes—
469C22×C11#57812yes—
470C22×C11C23×D411yescharacteristic
471C2×D11—28no—
472C2×D11—22no—
473C2×D11—22no—
474C2×D11—24no—
475C2×D11—48no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11C2×#12114yes—
479C4×C11—24no—
480C4×C11—22no—
481C4×C11—22no—
482C4×C11—42no—
483C4×C11—42no—
484C4×C11C2×#12112yes—
485C4×C11C23×D411yescharacteristic
486C4×C11C22×#4111yescharacteristic
487Dic11—22no—
488Dic11—22no—
489Dic11—42no—
490Dic11—42no—
491Dic11—42no—
492Dic11C2×#12114yes—
493C2×#41—118no—
494C2×#41—114no—
495C2×#41—114no—
496C2×#41—222no—
497C2×#41—222no—
498C2×#41—224no—
499C2×#41—224no—
500C2×#41—224no—
501C22×Q8—114no—
502C22×Q8—111no—
503C22×Q8—111no—
504C22×Q8—221no—
505C22×Q8—222no—
506C22×Q8—224no—
507C22×Q8—224no—
508C22×Q8C22×D1111yescharacteristic
509C22×Q8C22×D1111yescharacteristic
510C22×D4—111no—
511C22×D4—221no—
512C22×D4—221no—
513C22×D4C22×D1111yescharacteristic
514C23×C4—111no—
515C23×C4—221no—
516C23×C4—221no—
517C23×C4—221no—
518C23×C4—221no—
519C23×C4—221no—
520C23×C4—221no—
521#137—2232no—
522#135—2232no—
523C2×Q16—24no—
524C2×Q16—114no—
525C2×Q16—114no—
526C2×Q16—224no—
527C2×Q16—224no—
528C2×Q16C22×D1114yes—
529C2×SD16—24no—
530C2×SD16—114no—
531C2×SD16—114no—
532C2×SD16—114no—
533C2×SD16—224no—
534C2×SD16—224no—
535C2×SD16—224no—
536C2×SD16C22×D1114yes—
537C2×D8—114no—
538C2×D8—224no—
539C2×M16—114no—
540C2×M16—224no—
541C22×C8—111no—
542C22×C8—111no—
543C22×C8—114no—
544C22×C8—224no—
545C22×C8C22×D1111yescharacteristic
546C22×C8C22×D1111yescharacteristic
547C4⋊Q8—114no—
548C4⋊Q8—114no—
549C4⋊Q8—222no—
550C4⋊Q8—222no—
551#124—22no—
552#124—114no—
553#124—222no—
554#124C22×D1114yes—
555#123—228no—
556#123—228no—
557C22⋊Q8—228no—
558C22⋊Q8—228no—
559C4×Q8—22no—
560C4×Q8—114no—
561C4×Q8—222no—
562C4×Q8C22×D1114yes—
563C4×D4—114no—
564C4×D4—114no—
565C4×D4—228no—
566C4×D4—222no—
567C4×D4—228no—
568C4×D4—222no—
569#117—114no—
570#117—114no—
571#117—228no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—111no—
574C2×C4⋊C4—111no—
575C2×C4⋊C4—111no—
576C2×C4⋊C4—114no—
577C2×C4⋊C4—228no—
578C2×C4⋊C4—222no—
579C2×C4⋊C4—221no—
580C2×C4⋊C4—221no—
581C2×C4⋊C4—221no—
582C2×C4⋊C4—221no—
583C2×C4⋊C4—221no—
584C2×C4⋊C4—221no—
585C2×C4⋊C4C22×D1111yescharacteristic
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—111no—
589C2×C22⋊C4—111no—
590C2×C22⋊C4—221no—
591C2×C22⋊C4—221no—
592C2×C22⋊C4—221no—
593C2×C22⋊C4—221no—
594C2×C42—21no—
595C2×C42—111no—
596C2×C42—221no—
597C2×C42C22×D1111yescharacteristic
598C4⋊C8—114no—
599C4⋊C8—114no—
600C4⋊C8—114no—
601C4⋊C8C22×D1114yes—
602#103—114no—
603#103—114no—
604#103—114no—
605#103—114no—
606#103—114no—
607#103C22×D1114yes—
608#102—114no—
609#102C22×D1114yes—
610C2×C11—82no—
611C2×C11#304614yescomplemented
612C2×C11C22×#12111yescharacteristic
613C2×C11C2×#57711yescharacteristic
614C2×C11C2×#57811yescharacteristic
615D11—24no—
616D11—44no—
617C24—21no—
618C24—111no—
619C24—221no—
620#41—1116no—
621#41—2216no—
622#41—228no—
623#41—228no—
624#41—228no—
625#41—448no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—22no—
629C2×Q8—22no—
630C2×Q8—22no—
631C2×Q8—112no—
632C2×Q8—112no—
633C2×Q8—224no—
634C2×Q8—228no—
635C2×Q8—228no—
636C2×Q8—221no—
637C2×Q8—221no—
638C2×Q8—222no—
639C2×Q8—222no—
640C2×Q8—222no—
641C2×Q8—222no—
642C2×Q8—444no—
643C2×Q8—448no—
644C2×Q8D4×D1114yes—
645C2×Q8C23×D1112yes—
646C2×Q8C23×D1112yes—
647C2×D4—22no—
648C2×D4—21no—
649C2×D4—22no—
650C2×D4—114no—
651C2×D4—112no—
652C2×D4—224no—
653C2×D4—228no—
654C2×D4—224no—
655C2×D4—221no—
656C2×D4—222no—
657C2×D4—444no—
658C2×D4C23×D1112yes—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—111no—
663C22×C4—112no—
664C22×C4—114no—
665C22×C4—114no—
666C22×C4—112no—
667C22×C4—111no—
668C22×C4—111no—
669C22×C4—224no—
670C22×C4—228no—
671C22×C4—224no—
672C22×C4—224no—
673C22×C4—224no—
674C22×C4—224no—
675C22×C4—221no—
676C22×C4—221no—
677C22×C4—221no—
678C22×C4—224no—
679C22×C4—444no—
680C22×C4—444no—
681C22×C4—882no—
682C22×C4—882no—
683C22×C4—882no—
684C22×C4D4×D1111yescharacteristic
685C22×C4D4×D1111yescharacteristic
686C22×C4C23×D1111yescharacteristic
687Q16—28no—
688Q16—228no—
689Q16—228no—
690SD16—28no—
691SD16—228no—
692SD16—228no—
693SD16—228no—
694D8—228no—
695M16—228no—
696C2×C8—22no—
697C2×C8—22no—
698C2×C8—112no—
699C2×C8—112no—
700C2×C8—228no—
701C2×C8—222no—
702C2×C8—222no—
703C2×C8C23×D1112yes—
704C2×C8C23×D1112yes—
705C4⋊C4—24no—
706C4⋊C4—21no—
707C4⋊C4—114no—
708C4⋊C4—114no—
709C4⋊C4—112no—
710C4⋊C4—224no—
711C4⋊C4—224no—
712C4⋊C4—224no—
713C4⋊C4—224no—
714C4⋊C4—221no—
715C4⋊C4—224no—
716C4⋊C4—224no—
717C4⋊C4C23×D1112yes—
718C22⋊C4—24no—
719C22⋊C4—24no—
720C22⋊C4—114no—
721C22⋊C4—114no—
722C22⋊C4—224no—
723C22⋊C4—224no—
724C22⋊C4—224no—
725C22⋊C4—224no—
726C42—24no—
727C42—112no—
728C42—112no—
729C42—224no—
730C42D4×D1112yes—
731C42C23×D1112yes—
732C11C2×#304611yescharacteristic, complemented, Sylow
733C23—22no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—114no—
738C23—112no—
739C23—222no—
740C23—222no—
741C23—224no—
742C23—222no—
743C23—442no—
744C23—442no—
745C23C2×D4×D1111yescharacteristic
746Q8—24no—
747Q8—22no—
748Q8—22no—
749Q8—22no—
750Q8—42no—
751Q8—222no—
752Q8—222no—
753Q8—222no—
754Q8—222no—
755Q8—448no—
756Q8—442no—
757Q8—442no—
758Q8C2×D4×D1114yes—
759D4—22no—
760D4—22no—
761D4—42no—
762D4—114no—
763D4—2216no—
764D4—224no—
765D4—222no—
766D4—448no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—114no—
776C2×C4—112no—
777C2×C4—118no—
778C2×C4—114no—
779C2×C4—114no—
780C2×C4—112no—
781C2×C4—112no—
782C2×C4—2216no—
783C2×C4—222no—
784C2×C4—222no—
785C2×C4—222no—
786C2×C4—222no—
787C2×C4—222no—
788C2×C4—448no—
789C2×C4—448no—
790C2×C4—442no—
791C2×C4—442no—
792C2×C4—442no—
793C2×C4—884no—
794C2×C4—884no—
795C2×C4—884no—
796C2×C4C2×D4×D1112yes—
797C2×C4C2×D4×D1112yes—
798C2×C4C2×D4×D1111yescharacteristic
799C2×C4C2×D4×D1112yes—
800C2×C4#41×D1112yes—
801C2×C4C24×D1111yescharacteristic
802C8—22no—
803C8—22no—
804C8—222no—
805C8—222no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—84no—
810C22—114no—
811C22—228no—
812C22—222no—
813C22—222no—
814C22—224no—
815C22—448no—
816C22—442no—
817C22—442no—
818C22D11×#12112yes—
819C22#1062330112yes—
820C22#1062331012yes—
821C22C22×D4×D1111yescharacteristic
822C4—24no—
823C4—22no—
824C4—22no—
825C4—42no—
826C4—42no—
827C4—114no—
828C4—222no—
829C4—222no—
830C4—442no—
831C4—442no—
832C4—442no—
833C4D11×#12112yes—
834C4C22×D4×D1111yescharacteristic
835C4C2×#41×D1111yescharacteristic
836C2—82no—
837C2—224no—
838C2—444no—
839C2#1307816914yesdirect product factor
840C2C2×D11×#12111yescharacteristic
841C2C2×#1062330111yescharacteristic
842C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#464C2
socleC23×C11C22×D4
prime radicalC22×#66969C2
hypercenterC2×#464D11
hypocenterC11C2×#3046
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C22×#66971C2semidirect
3. C2×#10623206C2semidirect
4. C2×#10623105C2semidirect
5. #13078169C2direct (N × H)
6. C2×#10622779C2semidirect
7. C2×#10622644C2semidirect
8. C2×#10622795C2semidirect
9. C2×#10622400C2semidirect
10. C2×#10622670C2semidirect
11. C2×#10622454C2semidirect
12. C2×#10622431C2semidirect
13. C2×#10622452C2semidirect
14. C2×#10622384C2semidirect
15. C2×D11×#103C2semidirect
16. C2×C11×#464C2semidirect
32. C2×#66971C22semidirect
40. #10623206C22semidirect
42. #10623105C22semidirect
56. C11×#464C22semidirect
62. #10622795C22semidirect
63. #10622779C22semidirect
68. #10622670C22semidirect
69. #10622644C22semidirect
73. #10622454C22semidirect
74. #10622452C22semidirect
75. #10622431C22semidirect
76. D11×#103C22semidirect
77. #10622400C22semidirect
78. #10622384C22semidirect
318. C2×#464D11semidirect
441. #464C2×D11semidirect
611. C2×C11#3046semidirect
732. C11C2×#3046semidirect
839. C2#13078169direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669712
C22×#669692
C2×#106232062
C2×#106231052
#130781692
C2×#106227792
C2×#106226442
C2×#106227952
C2×#106224002
C2×#106226702
C2×#106224542
C2×#106224312
C2×#106224522
C2×#106223842
C2×D11×#1032
C2×C11×#4642
C2×#304611