Finite Group Databasebeta

← C2×#13079516 #15624479

Subgroups — C2×#13079516 #15624479

Order 2816.

2250 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623041C211yesmaximal, characteristic, complemented
2C2×#10623139C211yesmaximal, characteristic, complemented
3#13079516C2116yesmaximal, direct product factor
4C2×#10622497C211yesmaximal, characteristic, complemented
5C2×#10622583C211yesmaximal, characteristic, complemented
6C2×#10622495C211yesmaximal, characteristic, complemented
7C2×#10622499C211yesmaximal, characteristic, complemented
8C2×#10622393C211yesmaximal, characteristic, complemented
9C2×#10622500C211yesmaximal, characteristic, complemented
10C2×#10622388C211yesmaximal, characteristic, complemented
11C2×#10622346C211yesmaximal, characteristic, complemented
12C2×#10622396C211yesmaximal, characteristic, complemented
13C2×#10622394C211yesmaximal, characteristic, complemented
14C2×#10622650C211yesmaximal, characteristic, complemented
15C2×#10622340C211yesmaximal, characteristic, complemented
16C2×C11×#480C211yesmaximal, characteristic, complemented
17C22×#4341C2211yescharacteristic
18C22×#4339C2211yescharacteristic
19C22×#4339C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C2×#66992—21no—
23C2×#66991—21no—
24C2×#66991C2211yescharacteristic
25C22×#4324C2211yescharacteristic
26C22×#4323C2211yescharacteristic
27C2×#66983—21no—
28C2×#66983—21no—
29C2×#66977C2211yescharacteristic
30C22×Dic44C2211yescharacteristic
31C22×#4314C2211yescharacteristic
32C22×#4313C2211yescharacteristic
33C22×C8×D11C2211yescharacteristic
34#10623139—24no—
35#10623139C2218yescomplemented
36#10623041—24no—
37#10623041C2218yescomplemented
38C2×#66950—21no—
39C2×#66950C2211yescharacteristic
40C2×#66950C2211yescharacteristic
41C2×#66950C2211yescharacteristic
42C2×#66948—21no—
43C2×#66948C2211yescharacteristic
44C2×#66948C2211yescharacteristic
45C2×C4⋊C4×D11C2211yescharacteristic
46C2×#66937—21no—
47C2×#66931—21no—
48C11×#480C2218yescomplemented
49C2×C11×#107C2211yescharacteristic
50C2×C11×#107C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×C11×#102C2211yescharacteristic
53C2×C11×C22⋊C8C2211yescharacteristic
54C2×C22⋊(C11⋊C8)C2211yescharacteristic
55C2×#66885C2211yescharacteristic
56C2×(C2×D11)⋊C8C2211yescharacteristic
57C2×(C2×D11)⋊C8C2211yescharacteristic
58C2×#66880C2211yescharacteristic
59#10622650C2218yescomplemented
60#10622583C2218yescomplemented
61C2×#66874C2211yescharacteristic
62C2×#66874C2211yescharacteristic
63C2×#66874C2211yescharacteristic
64C2×#66873C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×#66871C2211yescharacteristic
67#10622500C2218yescomplemented
68#10622499C2218yescomplemented
69#10622497C2218yescomplemented
70#10622495C2218yescomplemented
71#10622396C2218yescomplemented
72#10622394C2218yescomplemented
73#10622393C2218yescomplemented
74#10622388C2218yescomplemented
75#10622346C2218yescomplemented
76#10622340C2218yescomplemented
77C22×D4×C11—21no—
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11—21no—
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11D411yescharacteristic
85C22×C22⋊D11D411yescharacteristic
86C23×Dic11—21no—
87C2×#4341—22no—
88C2×#4341—42no—
89C2×#4341—42no—
90C2×#4341C2314yes—
91C2×#4339—22no—
92C2×#4339—42no—
93C2×#4339—42no—
94C2×#4339—42no—
95C2×#4339—42no—
96C2×#4339D414yes—
97C2×#4339C2314yes—
98C2×#4339C2314yes—
99C22×D44—21no—
100C22×D44—21no—
101C22×D44D411yescharacteristic
102C22×D44C2311yescharacteristic
103C22×C4×D11—21no—
104C22×C4×D11—21no—
105C22×C4×D11C2311yescharacteristic
106C22×C4×D11C2311yescharacteristic
107C22×Dic22D411yescharacteristic
108C22×Dic22C2311yescharacteristic
109C22×Dic22C2311yescharacteristic
110C22×C8×C11C2311yescharacteristic
111C22×C8×C11C2311yescharacteristic
112C11×#121—22no—
113C11×#121C2314yes—
114C2×C11×C4⋊C4—21no—
115C2×C11×C4⋊C4—22no—
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C4⋊C4C2311yescharacteristic
118C2×C11×C4⋊C4C2311yescharacteristic
119C2×C11×C4⋊C4C2314yes—
120C2×C11×C22⋊C4—21no—
121C2×C22⋊Dic11—21no—
122C2×C22⋊Dic11—21no—
123#66992—28no—
124#66991—28no—
125#66991—22no—
126#66991C2314yes—
127C2×#4324—42no—
128C2×#4324C2314yes—
129C2×#4323—42no—
130C2×#4323C2314yes—
131#66983—28no—
132#66983—28no—
133C2×(C2×D11)⋊C4—21no—
134C2×(C2×D11)⋊C4—21no—
135C2×(C2×D11)⋊C4—21no—
136C2×(C2×D11)⋊C4—21no—
137C2×(C2×D11)⋊C4—21no—
138C2×C4⋊Dic11—21no—
139C2×C4⋊Dic11—21no—
140C2×C4⋊Dic11—21no—
141C2×C4⋊Dic11C2311yescharacteristic
142#66977—22no—
143#66977C2314yes—
144C2×Dic11⋊C4—21no—
145C2×Dic11⋊C4—21no—
146C22×C11⋊C8C2311yescharacteristic
147C22×C11⋊C8C2311yescharacteristic
148C2×Dic44—42no—
149C2×Dic44C2314yes—
150C2×#4314—42no—
151C2×#4314C2314yes—
152C2×#4313—42no—
153C2×#4313C2314yes—
154C2×C8×D11—42no—
155C2×C8×D11C2314yes—
156#66950—22no—
157#66950—22no—
158#66950—22no—
159#66950—28no—
160#66950C2314yes—
161#66950C2314yes—
162#66950C2314yes—
163#66948—28no—
164#66948—22no—
165#66948—22no—
166#66948C2314yes—
167#66948C2314yes—
168C4⋊C4×D11—22no—
169C4⋊C4×D11C2314yes—
170#66937—28no—
171#66931—28no—
172C11×#107C2314yes—
173C11×#107C2314yes—
174C11×#102C2314yes—
175C11×#102C2314yes—
176C11×C22⋊C8C2314yes—
177C22⋊(C11⋊C8)C2314yes—
178#66885C2314yes—
179(C2×D11)⋊C8C2314yes—
180(C2×D11)⋊C8C2314yes—
181#66880C2314yes—
182#66874C2314yes—
183#66874C2314yes—
184#66874C2314yes—
185#66873C2314yes—
186#66871C2314yes—
187#66871C2314yes—
188C2×#3203—111nomaximal, Sylow
189C24×C11—21no—
190C24×C11C2×D411yescharacteristic
191C23×D11—21no—
192C23×D11C2×D411yescharacteristic
193C23×D11C2×D411yescharacteristic
194C2×D4×C11—24no—
195C2×D4×C11—21no—
196C2×D4×C11—22no—
197C2×D4×C11—22no—
198C2×D4×C11—82no—
199C2×D4×C11C2412yes—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—24no—
206C22×C4×C11—82no—
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D412yes—
209C22×C4×C11C2412yes—
210C22×C4×C11C2411yescharacteristic
211C2×C22⋊D11—24no—
212C2×C22⋊D11—24no—
213C2×C22⋊D11—24no—
214C2×C22⋊D11—42no—
215C2×C22⋊D11—42no—
216C2×C22⋊D11—44no—
217C2×C22⋊D11—44no—
218C2×C22⋊D11—82no—
219C2×C22⋊D11C2×D414yes—
220C2×C22⋊D11C2×D414yes—
221C22×Dic11—24no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—44no—
226C22×Dic11C2×D411yescharacteristic
227C22×Dic11C2×D411yescharacteristic
228#4341—44no—
229#4341—44no—
230#4341—48no—
231#4339—44no—
232#4339—44no—
233#4339—48no—
234#4339—44no—
235#4339—44no—
236#4339—48no—
237C2×D44—24no—
238C2×D44—24no—
239C2×D44—21no—
240C2×D44—22no—
241C2×D44—22no—
242C2×D44—42no—
243C2×D44—82no—
244C2×D44—82no—
245C2×D44C2×D414yes—
246C2×D44C2412yes—
247C2×C4×D11—24no—
248C2×C4×D11—24no—
249C2×C4×D11—22no—
250C2×C4×D11—22no—
251C2×C4×D11—22no—
252C2×C4×D11—22no—
253C2×C4×D11—44no—
254C2×C4×D11—82no—
255C2×C4×D11C2×D412yes—
256C2×C4×D11C2×D412yes—
257C2×C4×D11C2412yes—
258C2×C4×D11C2412yes—
259C2×Dic22—21no—
260C2×Dic22—21no—
261C2×Dic22—22no—
262C2×Dic22—22no—
263C2×Dic22—22no—
264C2×Dic22—22no—
265C2×Dic22—42no—
266C2×Dic22C2×D414yes—
267C2×Dic22C2412yes—
268C2×Dic22C2412yes—
269C2×C8×C11—22no—
270C2×C8×C11—22no—
271C2×C8×C11C2412yes—
272C2×C8×C11C2412yes—
273C11×C4⋊C4—21no—
274C11×C4⋊C4—24no—
275C11×C4⋊C4—21no—
276C11×C4⋊C4—21no—
277C11×C4⋊C4C2412yes—
278C11×C4⋊C4C2412yes—
279C11×C4⋊C4C2412yes—
280C11×C22⋊C4—24no—
281C22⋊Dic11—24no—
282C22⋊Dic11—24no—
283#4324—44no—
284#4323—44no—
285(C2×D11)⋊C4—24no—
286(C2×D11)⋊C4—24no—
287(C2×D11)⋊C4—24no—
288(C2×D11)⋊C4—24no—
289(C2×D11)⋊C4—24no—
290C4⋊Dic11—24no—
291C4⋊Dic11—24no—
292C4⋊Dic11—24no—
293C4⋊Dic11—21no—
294C4⋊Dic11C2412yes—
295Dic11⋊C4—24no—
296Dic11⋊C4—24no—
297C2×C11⋊C8—22no—
298C2×C11⋊C8—22no—
299C2×C11⋊C8C2412yes—
300C2×C11⋊C8C2412yes—
301Dic44—44no—
302#4314—44no—
303#4313—44no—
304C8×D11—44no—
305C2×#537—111no—
306C2×#537—111no—
307#3203—1116no—
308C2×#484—111no—
309C2×#484—111no—
310C2×#480—111no—
311C2×#480D1111yescharacteristic, complemented
312C2×#468—111no—
313C2×#468—111no—
314C2×#467—111no—
315C2×#466—111no—
316C2×#452—111no—
317C2×#452—111no—
318C2×#449—111no—
319C2×#449—111no—
320C2×#408—111no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—42no—
326C23×C11—42no—
327C23×C11—42no—
328C23×C11C22×D412yes—
329C23×C11C22×D411yescharacteristic
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—42no—
338C22×D11—42no—
339C22×D11—42no—
340C22×D11C22×D412yes—
341C22×D11C22×D412yes—
342D4×C11—22no—
343D4×C11—22no—
344D4×C11—42no—
345D4×C11—84no—
346C2×C4×C11—22no—
347C2×C4×C11—24no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—42no—
354C2×C4×C11—42no—
355C2×C4×C11—42no—
356C2×C4×C11—84no—
357C2×C4×C11C22×D412yes—
358C2×C4×C11C22×D411yescharacteristic
359C2×C4×C11H(5,𝔽2)12yes—
360C2×C4×C11H(5,𝔽2)12yes—
361C2×C4×C11C2511yescharacteristic
362C22⋊D11—44no—
363C22⋊D11—44no—
364C22⋊D11—48no—
365C22⋊D11—48no—
366C22⋊D11—84no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—48no—
373C2×Dic11—42no—
374C2×Dic11—42no—
375C2×Dic11—42no—
376C2×Dic11C22×D412yes—
377C2×Dic11C22×D412yes—
378D44—22no—
379D44—22no—
380D44—44no—
381D44—42no—
382D44—84no—
383D44—84no—
384C4×D11—24no—
385C4×D11—24no—
386C4×D11—22no—
387C4×D11—22no—
388C4×D11—22no—
389C4×D11—22no—
390C4×D11—48no—
391C4×D11—84no—
392Dic22—22no—
393Dic22—22no—
394Dic22—22no—
395Dic22—22no—
396Dic22—44no—
397Dic22—42no—
398Dic22—42no—
399C8×C11—22no—
400C8×C11—22no—
401C11⋊C8—22no—
402C11⋊C8—22no—
403C22×#41—111no—
404C22×#41—111no—
405C22×#41—111no—
406C22×Q16—111no—
407C22×SD16—111no—
408C22×SD16—111no—
409C22×D8—111no—
410C22×M16—111no—
411C23×C8—111no—
412#537—118no—
413#537—118no—
414#537—224no—
415#537—224no—
416C2×C22⋊Q8—111no—
417C2×C22⋊Q8—111no—
418C2×C22⋊Q8—111no—
419C2×C22⋊Q8—111no—
420C2×C22⋊Q8—221no—
421C2×C22⋊Q8—221no—
422C2×#121—111no—
423C2×#121—111no—
424C2×#121—111no—
425C2×#121—221no—
426C2×#121—221no—
427C2×#121—221no—
428C2×#121—221no—
429C2×#121—221no—
430C2×#121—221no—
431C2×#121C2×D1111yescharacteristic
432C22×C4⋊C4—111no—
433C22×C4⋊C4C2×D1111yescharacteristic
434#484—118no—
435#484—118no—
436#480—118no—
437#480C2×D1118yescomplemented
438#468—118no—
439#468—118no—
440#467—118no—
441#466—118no—
442#452—118no—
443#452—118no—
444#449—118no—
445#449—118no—
446C2×#107—111no—
447C2×#107—111no—
448C2×#107C2×D1111yescharacteristic
449C2×#107C2×D1111yescharacteristic
450C2×#103—111no—
451C2×#103—111no—
452C2×#103—111no—
453C2×#103—111no—
454C2×#102—111no—
455C2×#102—111no—
456C2×#102C2×D1111yescharacteristic
457C2×#102C2×D1111yescharacteristic
458#408—118no—
459C2×C22⋊C8—111no—
460C2×C22⋊C8—111no—
461C2×C22⋊C8—111no—
462C2×C22⋊C8C2×D1111yescharacteristic
463C22×C11—22no—
464C22×C11—22no—
465C22×C11—22no—
466C22×C11—44no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—84no—
471C22×C11#53412yes—
472C22×C11#57612yes—
473C22×C11#57812yes—
474C22×C11C23×D411yescharacteristic
475C2×D11—22no—
476C2×D11—22no—
477C2×D11—22no—
478C2×D11—22no—
479C2×D11—22no—
480C2×D11—22no—
481C2×D11—44no—
482C2×D11—44no—
483C2×D11—42no—
484C2×D11—42no—
485C2×D11—42no—
486C2×D11—84no—
487C4×C11—22no—
488C4×C11—42no—
489C4×C11—42no—
490C4×C11—42no—
491C4×C11#53412yes—
492C4×C11C2×H(5,𝔽2)11yescharacteristic
493C4×C11C2×H(5,𝔽2)11yescharacteristic
494Dic11—22no—
495Dic11—22no—
496Dic11—42no—
497Dic11—42no—
498Dic11—42no—
499C2×#41—114no—
500C2×#41—114no—
501C2×#41—114no—
502C2×#41—114no—
503C2×#41—222no—
504C2×#41—222no—
505C2×#41—442no—
506C2×#41—442no—
507C2×#41—442no—
508C2×#41—442no—
509C2×#41—442no—
510C2×#41—442no—
511C22×Q8—111no—
512C22×Q8—111no—
513C22×Q8—111no—
514C22×D4—21no—
515C22×D4—111no—
516C22×D4—111no—
517C22×D4—111no—
518C22×D4—111no—
519C22×D4—221no—
520C22×D4—221no—
521C22×D4—221no—
522C22×D4—221no—
523C22×D4—221no—
524C22×D4C22×D1111yescharacteristic
525C23×C4—21no—
526C23×C4—111no—
527C23×C4—111no—
528C23×C4—221no—
529C23×C4—221no—
530C23×C4—221no—
531C23×C4C22×D1111yescharacteristic
532C2×Q16—114no—
533C2×Q16—442no—
534C2×SD16—114no—
535C2×SD16—114no—
536C2×SD16—442no—
537C2×SD16—442no—
538C2×D8—114no—
539C2×D8—442no—
540C2×M16—114no—
541C2×M16—442no—
542C22×C8—111no—
543C22×C8—111no—
544C22×C8—114no—
545C22×C8—442no—
546C22×C8C22×D1111yescharacteristic
547C22×C8C22×D1111yescharacteristic
548C22⋊Q8—114no—
549C22⋊Q8—114no—
550C22⋊Q8—114no—
551C22⋊Q8—114no—
552C22⋊Q8—228no—
553C22⋊Q8—222no—
554C22⋊Q8—222no—
555C22⋊Q8—222no—
556C22⋊Q8—228no—
557C22⋊Q8—222no—
558#121—22no—
559#121—114no—
560#121—114no—
561#121—114no—
562#121—228no—
563#121—222no—
564#121—222no—
565#121—228no—
566#121—228no—
567#121—228no—
568#121—222no—
569#121—228no—
570#121—228no—
571#121C22×D1114yes—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—111no—
575C2×C4⋊C4—114no—
576C2×C4⋊C4—222no—
577C2×C4⋊C4—221no—
578C2×C4⋊C4—221no—
579C2×C4⋊C4—221no—
580C2×C4⋊C4—221no—
581C2×C4⋊C4—221no—
582C2×C4⋊C4C22×D1111yescharacteristic
583C2×C4⋊C4C22×D1111yescharacteristic
584C2×C4⋊C4C22×D1111yescharacteristic
585C2×C4⋊C4C22×D1114yes—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—221no—
588C2×C22⋊C4—221no—
589C2×C22⋊C4—221no—
590C2×C22⋊C4—221no—
591C2×C22⋊C4—221no—
592C2×C22⋊C4—221no—
593C2×C22⋊C4—221no—
594#107—114no—
595#107—114no—
596#107C22×D1114yes—
597#107C22×D1114yes—
598#103—114no—
599#103—114no—
600#103—114no—
601#103—114no—
602#102—114no—
603#102—114no—
604#102C22×D1114yes—
605#102C22×D1114yes—
606C22⋊C8—114no—
607C22⋊C8—114no—
608C22⋊C8—114no—
609C22⋊C8C22×D1114yes—
610C2×C11—42no—
611C2×C11—82no—
612C2×C11#320314yescomplemented
613C2×C11C2×#53411yescharacteristic
614C2×C11C2×#57611yescharacteristic
615C2×C11C2×#57811yescharacteristic
616D11—42no—
617D11—42no—
618D11—82no—
619C24—21no—
620C24—111no—
621C24—111no—
622C24—221no—
623C24D4×D1111yescharacteristic
624#41—448no—
625#41—444no—
626#41—444no—
627#41—444no—
628#41—444no—
629#41—448no—
630#41—444no—
631#41—444no—
632#41—448no—
633C2×Q8—114no—
634C2×Q8—112no—
635C2×Q8—112no—
636C2×Q8—221no—
637C2×Q8—221no—
638C2×Q8—222no—
639C2×Q8—222no—
640C2×Q8—222no—
641C2×Q8—222no—
642C2×Q8—442no—
643C2×D4—24no—
644C2×D4—21no—
645C2×D4—22no—
646C2×D4—22no—
647C2×D4—82no—
648C2×D4—114no—
649C2×D4—114no—
650C2×D4—114no—
651C2×D4—112no—
652C2×D4—224no—
653C2×D4—224no—
654C2×D4—224no—
655C2×D4—224no—
656C2×D4—224no—
657C2×D4—221no—
658C2×D4—222no—
659C2×D4—222no—
660C2×D4—442no—
661C2×D4—442no—
662C2×D4—442no—
663C2×D4—444no—
664C2×D4—444no—
665C2×D4—882no—
666C2×D4—882no—
667C2×D4—882no—
668C2×D4C23×D1112yes—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—24no—
675C22×C4—82no—
676C22×C4—111no—
677C22×C4—111no—
678C22×C4—112no—
679C22×C4—112no—
680C22×C4—112no—
681C22×C4—112no—
682C22×C4—224no—
683C22×C4—224no—
684C22×C4—222no—
685C22×C4—222no—
686C22×C4—222no—
687C22×C4—222no—
688C22×C4—221no—
689C22×C4—221no—
690C22×C4—221no—
691C22×C4—224no—
692C22×C4—444no—
693C22×C4—444no—
694C22×C4—882no—
695C22×C4D4×D1112yes—
696C22×C4D4×D1111yescharacteristic
697C22×C4C23×D1112yes—
698C22×C4C23×D1111yescharacteristic
699Q16—444no—
700SD16—444no—
701SD16—444no—
702D8—444no—
703M16—444no—
704C2×C8—22no—
705C2×C8—22no—
706C2×C8—112no—
707C2×C8—112no—
708C2×C8—222no—
709C2×C8—222no—
710C2×C8—444no—
711C2×C8C23×D1112yes—
712C2×C8C23×D1112yes—
713C4⋊C4—24no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—112no—
718C4⋊C4—224no—
719C4⋊C4—224no—
720C4⋊C4—224no—
721C4⋊C4—224no—
722C4⋊C4—221no—
723C4⋊C4—224no—
724C4⋊C4C23×D1112yes—
725C4⋊C4C23×D1112yes—
726C4⋊C4C23×D1112yes—
727C22⋊C4—24no—
728C22⋊C4—224no—
729C22⋊C4—224no—
730C22⋊C4—224no—
731C22⋊C4—224no—
732C22⋊C4—224no—
733C22⋊C4—224no—
734C22⋊C4—224no—
735C11C2×#320311yescharacteristic, complemented, Sylow
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—112no—
744C23—112no—
745C23—222no—
746C23—222no—
747C23—222no—
748C23—222no—
749C23—222no—
750C23—222no—
751C23—222no—
752C23—442no—
753C23—442no—
754C23—442no—
755C23C2×D4×D1112yes—
756C23C2×D4×D1111yescharacteristic
757Q8—222no—
758Q8—222no—
759Q8—222no—
760Q8—222no—
761Q8—444no—
762Q8—442no—
763Q8—442no—
764D4—22no—
765D4—22no—
766D4—42no—
767D4—84no—
768D4—222no—
769D4—222no—
770D4—444no—
771D4—444no—
772D4—444no—
773D4—448no—
774D4—448no—
775D4—442no—
776D4—884no—
777D4—884no—
778D4—884no—
779C2×C4—22no—
780C2×C4—24no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—84no—
790C2×C4—112no—
791C2×C4—112no—
792C2×C4—222no—
793C2×C4—222no—
794C2×C4—224no—
795C2×C4—224no—
796C2×C4—222no—
797C2×C4—222no—
798C2×C4—222no—
799C2×C4—222no—
800C2×C4—222no—
801C2×C4—222no—
802C2×C4—222no—
803C2×C4—448no—
804C2×C4—448no—
805C2×C4—442no—
806C2×C4—442no—
807C2×C4—442no—
808C2×C4—884no—
809C2×C4C2×D4×D1112yes—
810C2×C4C2×D4×D1111yescharacteristic
811C2×C4#6704212yes—
812C2×C4#6704212yes—
813C2×C4C24×D1111yescharacteristic
814C8—22no—
815C8—22no—
816C8—222no—
817C8—222no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—44no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—84no—
826C22—222no—
827C22—222no—
828C22—222no—
829C22—222no—
830C22—222no—
831C22—222no—
832C22—444no—
833C22—444no—
834C22—442no—
835C22—442no—
836C22—442no—
837C22—884no—
838C22#1062318412yes—
839C22#1062328812yes—
840C22#1062331012yes—
841C22C22×D4×D1111yescharacteristic
842C4—22no—
843C4—42no—
844C4—42no—
845C4—42no—
846C4—222no—
847C4—222no—
848C4—442no—
849C4—442no—
850C4—442no—
851C4#1062318412yes—
852C4C2×#6704211yescharacteristic
853C4C2×#6704211yescharacteristic
854C2—42no—
855C2—82no—
856C2—442no—
857C2—442no—
858C2—882no—
859C2#1307951614yesdirect product factor
860C2C2×#1062318411yescharacteristic
861C2C2×#1062328811yescharacteristic
862C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#480C2
socleC23×C11C22×D4
hypercenterC2×#480D11
hypocenterC11C2×#3203
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#10623041C2semidirect
2. C2×#10623139C2semidirect
3. #13079516C2direct (N × H)
4. C2×#10622497C2semidirect
5. C2×#10622583C2semidirect
6. C2×#10622495C2semidirect
7. C2×#10622499C2semidirect
8. C2×#10622393C2semidirect
9. C2×#10622500C2semidirect
10. C2×#10622388C2semidirect
11. C2×#10622346C2semidirect
12. C2×#10622396C2semidirect
13. C2×#10622394C2semidirect
14. C2×#10622650C2semidirect
15. C2×#10622340C2semidirect
16. C2×C11×#480C2semidirect
35. #10623139C22semidirect
37. #10623041C22semidirect
48. C11×#480C22semidirect
59. #10622650C22semidirect
60. #10622583C22semidirect
67. #10622500C22semidirect
68. #10622499C22semidirect
69. #10622497C22semidirect
70. #10622495C22semidirect
71. #10622396C22semidirect
72. #10622394C22semidirect
73. #10622393C22semidirect
74. #10622388C22semidirect
75. #10622346C22semidirect
76. #10622340C22semidirect
311. C2×#480D11semidirect
437. #480C2×D11semidirect
612. C2×C11#3203semidirect
735. C11C2×#3203semidirect
859. C2#13079516direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230412
C2×#106231392
#130795162
C2×#106224972
C2×#106225832
C2×#106224952
C2×#106224992
C2×#106223932
C2×#106225002
C2×#106223882
C2×#106223462
C2×#106223962
C2×#106223942
C2×#106226502
C2×#106223402
C2×C11×#4802
C2×#320311