Finite Group Databasebeta

← C2×#13079526 #15624490

Subgroups — C2×#13079526 #15624490

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×#10623160C211yesmaximal, characteristic, complemented
3#13079526C2116yesmaximal, direct product factor
4C2×#10622476C211yesmaximal, characteristic, complemented
5C2×#10622581C211yesmaximal, characteristic, complemented
6C2×#10622475C211yesmaximal, characteristic, complemented
7C2×#10622429C211yesmaximal, characteristic, complemented
8C2×#10622478C211yesmaximal, characteristic, complemented
9C2×#10622420C211yesmaximal, characteristic, complemented
10C2×#10622477C211yesmaximal, characteristic, complemented
11C2×#10622423C211yesmaximal, characteristic, complemented
12C2×#10622660C211yesmaximal, characteristic, complemented
13C2×#10622424C211yesmaximal, characteristic, complemented
14C2×#10622347C211yesmaximal, characteristic, complemented
15C2×#10622340C211yesmaximal, characteristic, complemented
16C2×C11×#483C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C22×#4339C2211yescharacteristic
19C22×#4339C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C2×#66999C2211yescharacteristic
23C22×#4326C2211yescharacteristic
24C22×#4325C2211yescharacteristic
25C2×#66983—21no—
26C2×#66983—21no—
27C2×#66983C2211yescharacteristic
28C22×D88C2211yescharacteristic
29C22×#4314C2211yescharacteristic
30C22×#4313C2211yescharacteristic
31C22×C8×D11C2211yescharacteristic
32#10623160—24no—
33#10623160C2218yescomplemented
34#10623041—24no—
35#10623041C2218yescomplemented
36C2×#66950—21no—
37C2×#66950C2211yescharacteristic
38C2×#66950C2211yescharacteristic
39C2×#66949—21no—
40C2×#66948—21no—
41C2×#66948—21no—
42C2×#66948C2211yescharacteristic
43C2×#66948C2211yescharacteristic
44C2×#66948C2211yescharacteristic
45C2×C4⋊C4×D11C2211yescharacteristic
46C2×#66937—21no—
47C2×#66937—21no—
48C11×#483C2218yescomplemented
49C2×C11×#106C2211yescharacteristic
50C2×C11×#106C2211yescharacteristic
51C2×C11×#103C2211yescharacteristic
52C2×C11×#103C2211yescharacteristic
53C2×C11×C22⋊C8C2211yescharacteristic
54C2×C22⋊(C11⋊C8)C2211yescharacteristic
55C2×#66885C2211yescharacteristic
56C2×(C2×D11)⋊C8C2211yescharacteristic
57C2×(C2×D11)⋊C8C2211yescharacteristic
58C2×#66880C2211yescharacteristic
59#10622660C2218yescomplemented
60C2×#66874C2211yescharacteristic
61#10622581C2218yescomplemented
62C2×#66873C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66873C2211yescharacteristic
65C2×#66872C2211yescharacteristic
66C2×#66872C2211yescharacteristic
67#10622478C2218yescomplemented
68#10622477C2218yescomplemented
69#10622476C2218yescomplemented
70#10622475C2218yescomplemented
71#10622429C2218yescomplemented
72#10622424C2218yescomplemented
73#10622423C2218yescomplemented
74#10622420C2218yescomplemented
75#10622347C2218yescomplemented
76#10622340C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C23×C4×C11—21no—
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C22×C22⋊D11D411yescharacteristic
83C22×C22⋊D11D411yescharacteristic
84C2×#4343—22no—
85C2×#4343—42no—
86C2×#4343—42no—
87C2×#4343C2314yes—
88C2×#4339—22no—
89C2×#4339—42no—
90C2×#4339—42no—
91C2×#4339—42no—
92C2×#4339—42no—
93C2×#4339D414yes—
94C2×#4339C2314yes—
95C2×#4339C2314yes—
96C22×D44—21no—
97C22×D44—21no—
98C22×D44—21no—
99C22×D44—21no—
100C22×D44D411yescharacteristic
101C22×D44C2311yescharacteristic
102C22×D44C2311yescharacteristic
103C22×C4×D11—21no—
104C22×C4×D11—21no—
105C22×C4×D11—21no—
106C22×C4×D11C2311yescharacteristic
107C22×C4×D11C2311yescharacteristic
108C22×Dic22D411yescharacteristic
109C22×Dic22C2311yescharacteristic
110C22×C8×C11C2311yescharacteristic
111C22×C8×C11C2311yescharacteristic
112C11×C22⋊Q8—22no—
113C11×C22⋊Q8C2314yes—
114C2×C11×C4⋊C4—21no—
115C2×C11×C4⋊C4—21no—
116C2×C11×C4⋊C4—22no—
117C2×C11×C4⋊C4C2311yescharacteristic
118C2×C11×C4⋊C4C2311yescharacteristic
119C2×C11×C4⋊C4C2311yescharacteristic
120C2×C11×C4⋊C4C2314yes—
121C2×C11×C22⋊C4—21no—
122#66999—22no—
123#66999C2314yes—
124C2×#4326—42no—
125C2×#4326C2314yes—
126C2×#4325—42no—
127C2×#4325C2314yes—
128#66983—22no—
129#66983—28no—
130#66983—28no—
131#66983C2314yes—
132C2×(C2×D11)⋊C4—21no—
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×(C2×D11)⋊C4—21no—
139C2×C4⋊Dic11—21no—
140C2×C4⋊Dic11—21no—
141C2×C4⋊Dic11C2311yescharacteristic
142C2×Dic11⋊C4—21no—
143C2×Dic11⋊C4—21no—
144C22×C11⋊C8C2311yescharacteristic
145C22×C11⋊C8C2311yescharacteristic
146C2×D88—42no—
147C2×D88C2314yes—
148C2×#4314—42no—
149C2×#4314C2314yes—
150C2×#4313—42no—
151C2×#4313C2314yes—
152C2×C8×D11—42no—
153C2×C8×D11C2314yes—
154#66950—22no—
155#66950—22no—
156#66950—28no—
157#66950C2314yes—
158#66950C2314yes—
159#66949—28no—
160#66948—28no—
161#66948—28no—
162#66948—22no—
163#66948—22no—
164#66948—22no—
165#66948C2314yes—
166#66948C2314yes—
167#66948C2314yes—
168C4⋊C4×D11—22no—
169C4⋊C4×D11C2314yes—
170#66937—28no—
171#66937—28no—
172C11×#106C2314yes—
173C11×#106C2314yes—
174C11×#103C2314yes—
175C11×#103C2314yes—
176C11×C22⋊C8C2314yes—
177C22⋊(C11⋊C8)C2314yes—
178#66885C2314yes—
179(C2×D11)⋊C8C2314yes—
180(C2×D11)⋊C8C2314yes—
181#66880C2314yes—
182#66874C2314yes—
183#66873C2314yes—
184#66873C2314yes—
185#66873C2314yes—
186#66872C2314yes—
187#66872C2314yes—
188C2×#3204—111nomaximal, Sylow
189C24×C11C2×D411yescharacteristic
190C23×D11—21no—
191C23×D11—21no—
192C23×D11C2×D411yescharacteristic
193C23×D11C2×D411yescharacteristic
194C2×Q8×C11—21no—
195C2×Q8×C11—22no—
196C2×Q8×C11—22no—
197C2×Q8×C11C2412yes—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—24no—
205C22×C4×C11—82no—
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—42no—
213C2×C22⋊D11—42no—
214C2×C22⋊D11—44no—
215C2×C22⋊D11—82no—
216C2×C22⋊D11C2×D414yes—
217C2×C22⋊D11C2×D414yes—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11C2×D411yescharacteristic
221C22×Dic11C2×D411yescharacteristic
222#4343—44no—
223#4343—44no—
224#4343—48no—
225#4339—44no—
226#4339—44no—
227#4339—48no—
228#4339—44no—
229#4339—44no—
230#4339—48no—
231C2×D44—24no—
232C2×D44—24no—
233C2×D44—24no—
234C2×D44—24no—
235C2×D44—21no—
236C2×D44—21no—
237C2×D44—22no—
238C2×D44—22no—
239C2×D44—22no—
240C2×D44—22no—
241C2×D44—42no—
242C2×D44—44no—
243C2×D44—82no—
244C2×D44—82no—
245C2×D44—82no—
246C2×D44C2×D414yes—
247C2×D44C2412yes—
248C2×D44C2412yes—
249C2×C4×D11—24no—
250C2×C4×D11—24no—
251C2×C4×D11—24no—
252C2×C4×D11—22no—
253C2×C4×D11—22no—
254C2×C4×D11—22no—
255C2×C4×D11—22no—
256C2×C4×D11—44no—
257C2×C4×D11—44no—
258C2×C4×D11—82no—
259C2×C4×D11C2×D412yes—
260C2×C4×D11C2×D412yes—
261C2×C4×D11C2412yes—
262C2×C4×D11C2412yes—
263C2×Dic22—21no—
264C2×Dic22—22no—
265C2×Dic22—22no—
266C2×Dic22—42no—
267C2×Dic22C2×D414yes—
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—24no—
276C11×C4⋊C4—21no—
277C11×C4⋊C4—21no—
278C11×C4⋊C4C2412yes—
279C11×C4⋊C4C2412yes—
280C11×C4⋊C4C2412yes—
281C11×C22⋊C4—24no—
282#4326—44no—
283#4325—44no—
284(C2×D11)⋊C4—24no—
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—
290(C2×D11)⋊C4—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—
301D88—44no—
302#4314—44no—
303#4313—44no—
304C8×D11—44no—
305C2×#537—111no—
306C2×#537—111no—
307#3204—1116no—
308C2×#481—111no—
309C2×#481—111no—
310C2×#483—111no—
311C2×#483D1111yescharacteristic, complemented
312C2×#470—111no—
313C2×#469—111no—
314C2×#465—111no—
315C2×#465—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×C11C22×D412yes—
325C23×C11C22×D411yescharacteristic
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—42no—
335C22×D11—42no—
336C22×D11—42no—
337C22×D11—42no—
338C22×D11—42no—
339C22×D11—42no—
340C22×D11C22×D412yes—
341C22×D11C22×D412yes—
342Q8×C11—22no—
343Q8×C11—22no—
344Q8×C11—42no—
345C2×C4×C11—22no—
346C2×C4×C11—24no—
347C2×C4×C11—22no—
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—42no—
357C2×C4×C11—84no—
358C2×C4×C11C22×D412yes—
359C2×C4×C11C22×D411yescharacteristic
360C2×C4×C11H(5,𝔽2)12yes—
361C2×C4×C11H(5,𝔽2)12yes—
362C2×C4×C11C2511yescharacteristic
363C22⋊D11—44no—
364C22⋊D11—44no—
365C22⋊D11—48no—
366C22⋊D11—84no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—42no—
372C2×Dic11—42no—
373C2×Dic11C22×D412yes—
374C2×Dic11C22×D412yes—
375D44—22no—
376D44—22no—
377D44—22no—
378D44—22no—
379D44—44no—
380D44—48no—
381D44—42no—
382D44—42no—
383D44—84no—
384D44—84no—
385D44—84no—
386C4×D11—24no—
387C4×D11—24no—
388C4×D11—22no—
389C4×D11—22no—
390C4×D11—22no—
391C4×D11—22no—
392C4×D11—48no—
393C4×D11—48no—
394C4×D11—84no—
395Dic22—22no—
396Dic22—22no—
397Dic22—44no—
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—221no—
420C2×C22⋊Q8—221no—
421C2×C22⋊Q8C2×D1111yescharacteristic
422C2×#121—111no—
423C2×#121—111no—
424C2×#121—111no—
425C2×#121—111no—
426C2×#121—221no—
427C2×#121—221no—
428C2×#121—221no—
429C2×#121—221no—
430C2×#121—221no—
431C2×#121—221no—
432C22×C4⋊C4—111no—
433C22×C4⋊C4C2×D1111yescharacteristic
434#483—118no—
435#483C2×D1118yescomplemented
436#481—118no—
437#481—118no—
438#470—118no—
439#469—118no—
440#465—118no—
441#465—118no—
442#452—118no—
443#452—118no—
444#449—118no—
445#449—118no—
446C2×#106—111no—
447C2×#106—111no—
448C2×#106C2×D1111yescharacteristic
449C2×#106C2×D1111yescharacteristic
450C2×#103—111no—
451C2×#103—111no—
452C2×#103C2×D1111yescharacteristic
453C2×#103C2×D1111yescharacteristic
454C2×#102—111no—
455C2×#102—111no—
456C2×#102—111no—
457C2×#102—111no—
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#53412yes—
468C22×C11#57712yes—
469C22×C11#57712yes—
470C22×C11C23×D411yescharacteristic
471C2×D11—22no—
472C2×D11—22no—
473C2×D11—22no—
474C2×D11—22no—
475C2×D11—22no—
476C2×D11—22no—
477C2×D11—44no—
478C2×D11—44no—
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—42no—
482C2×D11—42no—
483C2×D11—42no—
484C2×D11—42no—
485C2×D11—84no—
486C2×D11—84no—
487C4×C11—22no—
488C4×C11—42no—
489C4×C11—42no—
490C4×C11—42no—
491C4×C11—42no—
492C4×C11#53412yes—
493C4×C11C2×H(5,𝔽2)11yescharacteristic
494C4×C11C2×H(5,𝔽2)11yescharacteristic
495Dic11—22no—
496Dic11—22no—
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×Q8C22×D1111yescharacteristic
514C22×D4—111no—
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×D4—221no—
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—22no—
549C22⋊Q8—114no—
550C22⋊Q8—114no—
551C22⋊Q8—114no—
552C22⋊Q8—222no—
553C22⋊Q8—222no—
554C22⋊Q8—228no—
555C22⋊Q8—228no—
556C22⋊Q8—222no—
557C22⋊Q8C22×D1114yes—
558#121—114no—
559#121—114no—
560#121—114no—
561#121—114no—
562#121—228no—
563#121—228no—
564#121—222no—
565#121—222no—
566#121—222no—
567#121—228no—
568#121—228no—
569#121—228no—
570#121—228no—
571#121—222no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—111no—
576C2×C4⋊C4—114no—
577C2×C4⋊C4—222no—
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#106—114no—
595#106—114no—
596#106C22×D1114yes—
597#106C22×D1114yes—
598#103—114no—
599#103—114no—
600#103C22×D1114yes—
601#103C22×D1114yes—
602#102—114no—
603#102—114no—
604#102—114no—
605#102—114no—
606C22⋊C8—114no—
607C22⋊C8—114no—
608C22⋊C8—114no—
609C22⋊C8C22×D1114yes—
610C2×C11—42no—
611C2×C11#320414yescomplemented
612C2×C11C2×#53411yescharacteristic
613C2×C11C2×#57711yescharacteristic
614C2×C11C2×#57711yescharacteristic
615D11—42no—
616D11—42no—
617D11—82no—
618D11—82no—
619C24—111no—
620C24—111no—
621C24—221no—
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—21no—
634C2×Q8—22no—
635C2×Q8—22no—
636C2×Q8—114no—
637C2×Q8—112no—
638C2×Q8—221no—
639C2×Q8—222no—
640C2×Q8—222no—
641C2×Q8—442no—
642C2×Q8C23×D1112yes—
643C2×D4—114no—
644C2×D4—114no—
645C2×D4—114no—
646C2×D4—112no—
647C2×D4—112no—
648C2×D4—224no—
649C2×D4—224no—
650C2×D4—224no—
651C2×D4—224no—
652C2×D4—224no—
653C2×D4—224no—
654C2×D4—221no—
655C2×D4—221no—
656C2×D4—222no—
657C2×D4—222no—
658C2×D4—222no—
659C2×D4—222no—
660C2×D4—442no—
661C2×D4—444no—
662C2×D4—442no—
663C2×D4—442no—
664C2×D4—444no—
665C2×D4—882no—
666C2×D4—882no—
667C2×D4—882no—
668C2×D4—882no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—24no—
676C22×C4—82no—
677C22×C4—111no—
678C22×C4—111no—
679C22×C4—112no—
680C22×C4—112no—
681C22×C4—112no—
682C22×C4—112no—
683C22×C4—224no—
684C22×C4—224no—
685C22×C4—222no—
686C22×C4—222no—
687C22×C4—222no—
688C22×C4—222no—
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—24no—
717C4⋊C4—21no—
718C4⋊C4—112no—
719C4⋊C4—224no—
720C4⋊C4—224no—
721C4⋊C4—224no—
722C4⋊C4—224no—
723C4⋊C4—221no—
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×#320411yescharacteristic, complemented, Sylow
736C23—22no—
737C23—22no—
738C23—22no—
739C23—112no—
740C23—112no—
741C23—222no—
742C23—222no—
743C23—222no—
744C23—222no—
745C23—222no—
746C23—222no—
747C23—222no—
748C23—222no—
749C23—442no—
750C23—442no—
751C23—442no—
752C23—442no—
753C23—442no—
754C23—442no—
755C23C2×D4×D1112yes—
756C23C2×D4×D1111yescharacteristic
757Q8—22no—
758Q8—22no—
759Q8—42no—
760Q8—222no—
761Q8—222no—
762Q8—444no—
763Q8—442no—
764D4—222no—
765D4—222no—
766D4—222no—
767D4—222no—
768D4—444no—
769D4—448no—
770D4—444no—
771D4—444no—
772D4—448no—
773D4—442no—
774D4—442no—
775D4—884no—
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—22no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—84no—
792C2×C4—112no—
793C2×C4—112no—
794C2×C4—222no—
795C2×C4—222no—
796C2×C4—224no—
797C2×C4—224no—
798C2×C4—222no—
799C2×C4—222no—
800C2×C4—222no—
801C2×C4—222no—
802C2×C4—222no—
803C2×C4—222no—
804C2×C4—448no—
805C2×C4—448no—
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—222no—
823C22—222no—
824C22—222no—
825C22—222no—
826C22—222no—
827C22—222no—
828C22—444no—
829C22—444no—
830C22—442no—
831C22—442no—
832C22—442no—
833C22—442no—
834C22—442no—
835C22—442no—
836C22—884no—
837C22—884no—
838C22#1062318412yes—
839C22#1062329312yes—
840C22#1062330912yes—
841C22C22×D4×D1111yescharacteristic
842C4—22no—
843C4—42no—
844C4—42no—
845C4—42no—
846C4—42no—
847C4—222no—
848C4—222no—
849C4—442no—
850C4—442no—
851C4#1062318412yes—
852C4C2×#6704211yescharacteristic
853C4C2×#6704211yescharacteristic
854C2—42no—
855C2—442no—
856C2—442no—
857C2—882no—
858C2—882no—
859C2#1307952614yesdirect product factor
860C2C2×#1062318411yescharacteristic
861C2C2×#1062329311yescharacteristic
862C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#483C2
socleC23×C11C22×D4
hypercenterC2×#483D11
hypocenterC11C2×#3204
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
1. C2×#10623041C2semidirect
2. C2×#10623160C2semidirect
3. #13079526C2direct (N × H)
4. C2×#10622476C2semidirect
5. C2×#10622581C2semidirect
6. C2×#10622475C2semidirect
7. C2×#10622429C2semidirect
8. C2×#10622478C2semidirect
9. C2×#10622420C2semidirect
10. C2×#10622477C2semidirect
11. C2×#10622423C2semidirect
12. C2×#10622660C2semidirect
13. C2×#10622424C2semidirect
14. C2×#10622347C2semidirect
15. C2×#10622340C2semidirect
16. C2×C11×#483C2semidirect
33. #10623160C22semidirect
35. #10623041C22semidirect
48. C11×#483C22semidirect
59. #10622660C22semidirect
61. #10622581C22semidirect
67. #10622478C22semidirect
68. #10622477C22semidirect
69. #10622476C22semidirect
70. #10622475C22semidirect
71. #10622429C22semidirect
72. #10622424C22semidirect
73. #10622423C22semidirect
74. #10622420C22semidirect
75. #10622347C22semidirect
76. #10622340C22semidirect
311. C2×#483D11semidirect
435. #483C2×D11semidirect
611. C2×C11#3204semidirect
735. C11C2×#3204semidirect
859. C2#13079526direct (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×#106231602
#130795262
C2×#106224762
C2×#106225812
C2×#106224752
C2×#106224292
C2×#106224782
C2×#106224202
C2×#106224772
C2×#106224232
C2×#106226602
C2×#106224242
C2×#106223472
C2×#106223402
C2×C11×#4832
C2×#320411