Finite Group Databasebeta

← C2×#13078464 #15621351

Subgroups — C2×#13078464 #15621351

Order 2816.

2094 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623260C211yesmaximal, characteristic, complemented
2C2×#10623105C211yesmaximal, characteristic
3#13078464C2116yesmaximal, direct product factor
4C2×#10622635C211yesmaximal, characteristic, complemented
5C2×#10622412C211yesmaximal, characteristic, complemented
6C2×#10622407C211yesmaximal, characteristic, complemented
7C2×#10622504C211yesmaximal, characteristic, complemented
8C2×#10622460C211yesmaximal, characteristic, complemented
9C2×#10622503C211yesmaximal, characteristic, complemented
10C2×#10622700C211yesmaximal, characteristic, complemented
11C2×#10622494C211yesmaximal, characteristic, complemented
12C2×D11×#107C211yesmaximal, characteristic, complemented
13C2×#10622452C211yesmaximal, characteristic, complemented
14C2×#10622416C211yesmaximal, characteristic
15C2×#10622417C211yesmaximal, characteristic
16C2×C11×#477C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×#66999—21no—
21C2×Q8×Dic11C2211yescharacteristic
22C2×#66997—21no—
23C22×#4313C2211yescharacteristic
24C22×C8×D11C2211yescharacteristic
25#10623260—24no—
26#10623260C2218yescomplemented
27#10623105—24no—
28#10623105C2218yes—
29C2×#66949—21no—
30C2×#66946—21no—
31C2×#66946C2211yescharacteristic
32C2×#66945C2211yescharacteristic
33C2×C4⋊C4×D11—21no—
34C2×C4⋊C4×D11C2211yescharacteristic
35C2×C4⋊C4×D11C2211yescharacteristic
36C2×#66943C2211yescharacteristic
37C2×#66942—21no—
38C2×#66941C2211yescharacteristic
39C2×C4×D44—21no—
40C2×C4×D44C2211yescharacteristic
41C2×#66925—21no—
42C2×#66925C2211yescharacteristic
43C2×#66923C2211yescharacteristic
44C11×#477C2218yescomplemented
45C2×C11×#107C2211yescharacteristic
46C2×C11×#107C2211yescharacteristic
47C2×C11×C4⋊C8C2211yescharacteristic
48C2×C11×#103C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×#66899C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×#66885C2211yescharacteristic
53C2×#66885C2211yescharacteristic
54C2×#66882C2211yescharacteristic
55C2×#66881C2211yescharacteristic
56C2×Dic11⋊C8C2211yescharacteristic
57C2×Dic11⋊C8C2211yescharacteristic
58#10622700C2218yescomplemented
59#10622635C2218yescomplemented
60C2×#66873C2211yescharacteristic
61C2×#66873C2211yescharacteristic
62C2×#66872C2211yescharacteristic
63C2×#66871C2211yescharacteristic
64C2×#66871C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×C4⋊(C11⋊C8)C2211yescharacteristic
67#10622504C2218yescomplemented
68#10622503C2218yescomplemented
69#10622494C2218yescomplemented
70D11×#107C2218yescomplemented
71#10622460C2218yescomplemented
72#10622452C2218yescomplemented
73#10622417C2218yes—
74#10622416C2218yes—
75#10622412C2218yescomplemented
76#10622407C2218yescomplemented
77C22×Q8×C11—21no—
78C22×Q8×C11C2311yescharacteristic
79C2×#4343—22no—
80C2×#4343—24no—
81C2×#4343Q818yescomplemented
82C2×#4343C2314yes—
83C22×D44—21no—
84C22×D44C2311yescharacteristic
85C22×C4×D11—21no—
86C22×C4×D11—21no—
87C22×C4×D11—21no—
88C22×C4×D11—21no—
89C22×C4×D11—21no—
90C22×C4×D11C2311yescharacteristic
91C22×Dic22—21no—
92C22×C8×C11C2311yescharacteristic
93C22×C8×C11C2311yescharacteristic
94C11×C4⋊Q8—22no—
95C11×C4⋊Q8C2314yes—
96C4×Q8×C11—22no—
97C4×Q8×C11C2314yes—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C42×C11—21no—
104C2×C42×C11C2311yescharacteristic
105#66999—28no—
106Q8×Dic11—22no—
107Q8×Dic11C2314yes—
108#66997—28no—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4—21no—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4D411yescharacteristic
113C2×(C2×D11)⋊C4D411yescharacteristic
114C2×C4⋊Dic11—21no—
115C2×C4⋊Dic11—21no—
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2311yescharacteristic
119C2×Dic11⋊C4—21no—
120C2×Dic11⋊C4—21no—
121C2×Dic11⋊C4—21no—
122C2×Dic11⋊C4—21no—
123C2×Dic11⋊C4—21no—
124C2×Dic11⋊C4—21no—
125C2×Dic11⋊C4D411yescharacteristic
126C2×Dic11⋊C4D411yescharacteristic
127C2×C4×Dic11—21no—
128C2×C4×Dic11—21no—
129C2×C4×Dic11C2311yescharacteristic
130C22×C11⋊C8C2311yescharacteristic
131C22×C11⋊C8C2311yescharacteristic
132C2×#4313—24no—
133C2×#4313C2314yes—
134C2×C8×D11—24no—
135C2×C8×D11C2314yes—
136#66949—28no—
137#66946—28no—
138#66946—22no—
139#66946C2314yes—
140#66945—22no—
141#66945C2314yes—
142C4⋊C4×D11—22no—
143C4⋊C4×D11—22no—
144C4⋊C4×D11—28no—
145C4⋊C4×D11C2314yes—
146C4⋊C4×D11C2314yes—
147#66943—22no—
148#66943C2314yes—
149#66942—28no—
150#66941—22no—
151#66941C2314yes—
152C4×D44—22no—
153C4×D44—28no—
154C4×D44C2314yes—
155#66925—28no—
156#66925D414yes—
157#66925C2314yes—
158#66923—22no—
159#66923C2314yes—
160C11×#107C2314yes—
161C11×#107C2314yes—
162C11×C4⋊C8C2314yes—
163C11×#103C2314yes—
164C11×#103C2314yes—
165#66899C2314yes—
166#66899C2314yes—
167#66885C2314yes—
168#66885C2314yes—
169#66882C2314yes—
170#66881C2314yes—
171Dic11⋊C8C2314yes—
172Dic11⋊C8C2314yes—
173#66873C2314yes—
174#66873C2314yes—
175#66872C2314yes—
176#66871C2314yes—
177#66871C2314yes—
178#66871C2314yes—
179C4⋊(C11⋊C8)C2314yes—
180C2×#3083—111nomaximal, Sylow
181C23×D11—21no—
182C23×D11C2×D411yescharacteristic
183C2×Q8×C11—21no—
184C2×Q8×C11—24no—
185C2×Q8×C11—22no—
186C2×Q8×C11—82no—
187C2×Q8×C11C2×Q814yes—
188C2×Q8×C11C2412yes—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2411yescharacteristic
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11C2×D411yescharacteristic
200C22×Dic11C2×D411yescharacteristic
201C22×Dic11C2×D411yescharacteristic
202#4343—216no—
203#4343—28no—
204#4343C2×Q8116yescomplemented
205C2×D44—28no—
206C2×D44—24no—
207C2×D44—21no—
208C2×D44—22no—
209C2×D44C2×Q814yes—
210C2×D44C2412yes—
211C2×C4×D11—28no—
212C2×C4×D11—24no—
213C2×C4×D11—24no—
214C2×C4×D11—24no—
215C2×C4×D11—24no—
216C2×C4×D11—24no—
217C2×C4×D11—82no—
218C2×C4×D11—82no—
219C2×C4×D11—82no—
220C2×C4×D11—82no—
221C2×C4×D11C2×D412yes—
222C2×C4×D11C2×Q814yes—
223C2×C4×D11#4114yes—
224C2×C4×D11C2412yes—
225C2×Dic22—24no—
226C2×Dic22—82no—
227C2×C8×C11—22no—
228C2×C8×C11—22no—
229C2×C8×C11C2412yes—
230C2×C8×C11C2412yes—
231C11×C4⋊C4—21no—
232C11×C4⋊C4—24no—
233C11×C4⋊C4—21no—
234C11×C4⋊C4—24no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4C2412yes—
237C11×C4⋊C4C2412yes—
238C11×C4⋊C4C2412yes—
239C42×C11—24no—
240C42×C11C2×D412yes—
241C42×C11C2412yes—
242(C2×D11)⋊C4—24no—
243(C2×D11)⋊C4—24no—
244(C2×D11)⋊C4—24no—
245(C2×D11)⋊C4C2×D414yes—
246(C2×D11)⋊C4C2×D414yes—
247C4⋊Dic11—24no—
248C4⋊Dic11—24no—
249C4⋊Dic11—21no—
250C4⋊Dic11—21no—
251C4⋊Dic11—21no—
252C4⋊Dic11C2412yes—
253C4⋊Dic11C2412yes—
254C4⋊Dic11C2412yes—
255Dic11⋊C4—24no—
256Dic11⋊C4—24no—
257Dic11⋊C4—24no—
258Dic11⋊C4—24no—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261Dic11⋊C4C2×D414yes—
262Dic11⋊C4C2×D414yes—
263C4×Dic11—24no—
264C4×Dic11—24no—
265C4×Dic11C2×D412yes—
266C4×Dic11C2412yes—
267C2×C11⋊C8—22no—
268C2×C11⋊C8—22no—
269C2×C11⋊C8C2412yes—
270C2×C11⋊C8C2412yes—
271#4313—28no—
272C8×D11—28no—
273C2×#544—111no—
274C2×#520—111no—
275#3083—1116no—
276C2×#479—111no—
277C2×#479—111no—
278C2×#477—111no—
279C2×#477D1111yescharacteristic, complemented
280C2×#478—111no—
281C2×#478—111no—
282C2×#474—111no—
283C2×#474—111no—
284C2×#428—111no—
285C22×#107—111no—
286C2×#424—111no—
287C2×#417—111no—
288C2×#416—111no—
289C23×C11C22×D411yescharacteristic
290C22×D11—22no—
291C22×D11—22no—
292C22×D11—24no—
293C22×D11—22no—
294C22×D11—42no—
295C22×D11—42no—
296C22×D11C22⋊Q814yes—
297C22×D11C22×D412yes—
298Q8×C11—24no—
299Q8×C11—22no—
300Q8×C11—84no—
301Q8×C11C22×Q814yes—
302C2×C4×C11—24no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—42no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11C22×D412yes—
313C2×C4×C11C22×D412yes—
314C2×C4×C11C22×D411yescharacteristic
315C2×C4×C11C22×Q812yes—
316C2×C4×C11C2×#4112yes—
317C2×C4×C11C2511yescharacteristic
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—42no—
324C2×Dic11—42no—
325C2×Dic11—42no—
326C2×Dic11C22⋊Q814yes—
327C2×Dic11C22×D412yes—
328C2×Dic11C22×D412yes—
329C2×Dic11C22×D412yes—
330D44—216no—
331D44—24no—
332D44—22no—
333D44C22×Q814yes—
334C4×D11—216no—
335C4×D11—84no—
336C4×D11—84no—
337C4×D11—84no—
338C4×D11—84no—
339C4×D11C22⋊Q818yes—
340C4×D11C22×Q814yes—
341C4×D11C2×#4114yes—
342Dic22—84no—
343C8×C11—22no—
344C8×C11—22no—
345C11⋊C8—22no—
346C11⋊C8—22no—
347C22×#41—111no—
348C22×M16—111no—
349C23×C8—111no—
350#544—118no—
351#544—224no—
352C2×C4⋊Q8—111no—
353C2×C4⋊Q8—221no—
354C2×C4⋊Q8C2×D1111yescharacteristic
355C2×#125—111no—
356C2×#125—111no—
357C2×#125—221no—
358C2×C22⋊Q8—221no—
359C2×C22⋊Q8—221no—
360#520—118no—
361#520—224no—
362C2×C4×Q8—111no—
363C2×C4×Q8C2×D1111yescharacteristic
364C2×C4×D4—111no—
365C2×C4×D4—111no—
366C2×C4×D4—221no—
367C2×C4×D4—221no—
368C2×#117—111no—
369C2×#117—111no—
370C2×#117—221no—
371C22×C4⋊C4—111no—
372C22×C4⋊C4—111no—
373C22×C4⋊C4—221no—
374#479—118no—
375#479—118no—
376#478—118no—
377#478—118no—
378#477—118no—
379#477C2×D1118yescomplemented
380#474—118no—
381#474—118no—
382#428—118no—
383C2×#107—111no—
384C2×#107—111no—
385C2×#107—111no—
386C2×#107—111no—
387C2×#107—118no—
388C2×#107C2×D1111yescharacteristic
389C2×#107C2×D1111yescharacteristic
390C2×#106—111no—
391C2×#106—111no—
392#424—118no—
393C2×C4⋊C8—111no—
394C2×C4⋊C8—111no—
395C2×C4⋊C8—111no—
396C2×C4⋊C8C2×D1111yescharacteristic
397#417—118no—
398#416—118no—
399C2×#103—111no—
400C2×#103—111no—
401C2×#103C2×D1111yescharacteristic
402C2×#103C2×D1111yescharacteristic
403C2×#102—111no—
404C2×#102—111no—
405C2×#102—111no—
406C2×#102—111no—
407C22×C11C2×C22⋊Q812yes—
408C22×C11#57612yes—
409C22×C11#57812yes—
410C22×C11C23×D411yescharacteristic
411C2×D11—28no—
412C2×D11—22no—
413C2×D11—22no—
414C2×D11—24no—
415C2×D11—48no—
416C2×D11—42no—
417C2×D11—42no—
418C2×D11C2×C22⋊Q814yes—
419C4×C11—24no—
420C4×C11—22no—
421C4×C11—22no—
422C4×C11—42no—
423C4×C11—42no—
424C4×C11—42no—
425C4×C11C2×C22⋊Q812yes—
426C4×C11C23×Q811yescharacteristic
427C4×C11C22×#4111yescharacteristic
428Dic11—22no—
429Dic11—22no—
430Dic11—42no—
431Dic11—42no—
432Dic11—42no—
433Dic11C2×C22⋊Q814yes—
434C2×#41—118no—
435C2×#41—114no—
436C2×#41—222no—
437C2×#41—224no—
438C22×Q8—21no—
439C22×Q8—221no—
440C22×Q8C22×D1111yescharacteristic
441C22×D4—111no—
442C22×D4—221no—
443C23×C4—111no—
444C23×C4—221no—
445C23×C4—221no—
446C23×C4—221no—
447C23×C4—221no—
448C23×C4—221no—
449C2×M16—114no—
450C2×M16—224no—
451C22×C8—111no—
452C22×C8—111no—
453C22×C8—114no—
454C22×C8—224no—
455C22×C8C22×D1111yescharacteristic
456C22×C8C22×D1111yescharacteristic
457C4⋊Q8—22no—
458C4⋊Q8—114no—
459C4⋊Q8—222no—
460C4⋊Q8—228no—
461C4⋊Q8C22×D1114yes—
462#125—114no—
463#125—114no—
464#125—222no—
465#125—228no—
466#125—222no—
467C22⋊Q8—228no—
468C22⋊Q8—228no—
469C4×Q8—22no—
470C4×Q8—114no—
471C4×Q8—222no—
472C4×Q8C22×D1114yes—
473C4×D4—114no—
474C4×D4—114no—
475C4×D4—228no—
476C4×D4—222no—
477C4×D4—228no—
478C4×D4—222no—
479#117—114no—
480#117—114no—
481#117—114no—
482#117—228no—
483#117—222no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—111no—
487C2×C4⋊C4—111no—
488C2×C4⋊C4—111no—
489C2×C4⋊C4—111no—
490C2×C4⋊C4—111no—
491C2×C4⋊C4—114no—
492C2×C4⋊C4—114no—
493C2×C4⋊C4—228no—
494C2×C4⋊C4—222no—
495C2×C4⋊C4—222no—
496C2×C4⋊C4—221no—
497C2×C4⋊C4—221no—
498C2×C4⋊C4—221no—
499C2×C4⋊C4—221no—
500C2×C4⋊C4—221no—
501C2×C4⋊C4—221no—
502C2×C4⋊C4—221no—
503C2×C4⋊C4—221no—
504C2×C4⋊C4C22×D1111yescharacteristic
505C2×C4⋊C4C22×D1111yescharacteristic
506C2×C4⋊C4C22×D1111yescharacteristic
507C2×C22⋊C4—111no—
508C2×C22⋊C4—111no—
509C2×C22⋊C4—221no—
510C2×C22⋊C4—221no—
511C2×C22⋊C4—221no—
512C2×C42—21no—
513C2×C42—111no—
514C2×C42—221no—
515C2×C42—221no—
516C2×C42C22×D1111yescharacteristic
517#107—114no—
518#107—114no—
519#107—114no—
520#107—114no—
521#107C22×D1114yes—
522#107C22×D1114yes—
523#106—114no—
524#106—114no—
525C4⋊C8—114no—
526C4⋊C8—114no—
527C4⋊C8—114no—
528C4⋊C8C22×D1114yes—
529#103—114no—
530#103—114no—
531#103C22×D1114yes—
532#103C22×D1114yes—
533#102—114no—
534#102—114no—
535#102—114no—
536#102—114no—
537C2×C11#308314yescomplemented
538C2×C11C22×C22⋊Q811yescharacteristic
539C2×C11C2×#57611yescharacteristic
540C2×C11C2×#57811yescharacteristic
541D11—24no—
542D11—44no—
543C24—111no—
544C24—221no—
545#41—1116no—
546#41—2216no—
547#41—228no—
548C2×Q8—21no—
549C2×Q8—24no—
550C2×Q8—22no—
551C2×Q8—82no—
552C2×Q8—224no—
553C2×Q8—882no—
554C2×Q8Q8×D1114yes—
555C2×Q8C23×D1112yes—
556C2×D4—114no—
557C2×D4—112no—
558C2×D4—224no—
559C2×D4—228no—
560C2×D4—221no—
561C2×D4—222no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—111no—
567C22×C4—112no—
568C22×C4—114no—
569C22×C4—114no—
570C22×C4—112no—
571C22×C4—111no—
572C22×C4—111no—
573C22×C4—224no—
574C22×C4—228no—
575C22×C4—224no—
576C22×C4—224no—
577C22×C4—224no—
578C22×C4—221no—
579C22×C4—221no—
580C22×C4—221no—
581C22×C4—224no—
582C22×C4—882no—
583C22×C4—882no—
584C22×C4—882no—
585C22×C4—882no—
586C22×C4D4×D1111yescharacteristic
587C22×C4D4×D1111yescharacteristic
588C22×C4C23×D1111yescharacteristic
589M16—228no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—112no—
593C2×C8—112no—
594C2×C8—228no—
595C2×C8—222no—
596C2×C8—222no—
597C2×C8C23×D1112yes—
598C2×C8C23×D1112yes—
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—114no—
605C4⋊C4—114no—
606C4⋊C4—112no—
607C4⋊C4—112no—
608C4⋊C4—112no—
609C4⋊C4—224no—
610C4⋊C4—224no—
611C4⋊C4—224no—
612C4⋊C4—224no—
613C4⋊C4—224no—
614C4⋊C4—224no—
615C4⋊C4—221no—
616C4⋊C4—221no—
617C4⋊C4—221no—
618C4⋊C4—224no—
619C4⋊C4—224no—
620C4⋊C4C23×D1112yes—
621C4⋊C4C23×D1112yes—
622C4⋊C4C23×D1112yes—
623C22⋊C4—114no—
624C22⋊C4—114no—
625C22⋊C4—224no—
626C22⋊C4—224no—
627C22⋊C4—224no—
628C42—24no—
629C42—112no—
630C42—112no—
631C42—224no—
632C42—224no—
633C42D4×D1112yes—
634C42C23×D1112yes—
635C11C2×#308311yescharacteristic, complemented, Sylow
636C23—114no—
637C23—112no—
638C23—222no—
639C23—222no—
640C23—224no—
641C23—222no—
642C23—442no—
643C23—442no—
644C23C2×D4×D1111yescharacteristic
645Q8—24no—
646Q8—22no—
647Q8—84no—
648Q8—884no—
649Q8C2×Q8×D1114yes—
650D4—114no—
651D4—2216no—
652D4—224no—
653D4—222no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—114no—
665C2×C4—112no—
666C2×C4—118no—
667C2×C4—114no—
668C2×C4—114no—
669C2×C4—112no—
670C2×C4—112no—
671C2×C4—2216no—
672C2×C4—222no—
673C2×C4—222no—
674C2×C4—222no—
675C2×C4—222no—
676C2×C4—222no—
677C2×C4—442no—
678C2×C4—442no—
679C2×C4—442no—
680C2×C4—884no—
681C2×C4—884no—
682C2×C4—884no—
683C2×C4—884no—
684C2×C4C2×D4×D1112yes—
685C2×C4C2×D4×D1112yes—
686C2×C4C2×D4×D1111yescharacteristic
687C2×C4C2×Q8×D1112yes—
688C2×C4#41×D1112yes—
689C2×C4C24×D1111yescharacteristic
690C8—22no—
691C8—22no—
692C8—222no—
693C8—222no—
694C22—114no—
695C22—228no—
696C22—222no—
697C22—222no—
698C22—224no—
699C22—448no—
700C22—442no—
701C22—442no—
702C22D11×C22⋊Q812yes—
703C22#1062329712yes—
704C22#1062330512yes—
705C22C22×D4×D1111yescharacteristic
706C4—22no—
707C4—24no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—114no—
713C4—222no—
714C4—222no—
715C4—442no—
716C4—442no—
717C4—442no—
718C4D11×C22⋊Q812yes—
719C4C22×Q8×D1111yescharacteristic
720C4C2×#41×D1111yescharacteristic
721C2—224no—
722C2—444no—
723C2#1307846414yesdirect product factor
724C2C2×D11×C22⋊Q811yescharacteristic
725C2C2×#1062330511yescharacteristic
726C2C2×#1062329711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#477C2
socleC23×C11C22×D4
prime radicalC22×#4343C22
hypercenterC2×#477D11
hypocenterC11C2×#3083
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
1. C2×#10623260C2semidirect
3. #13078464C2direct (N × H)
4. C2×#10622635C2semidirect
5. C2×#10622412C2semidirect
6. C2×#10622407C2semidirect
7. C2×#10622504C2semidirect
8. C2×#10622460C2semidirect
9. C2×#10622503C2semidirect
10. C2×#10622700C2semidirect
11. C2×#10622494C2semidirect
12. C2×D11×#107C2semidirect
13. C2×#10622452C2semidirect
16. C2×C11×#477C2semidirect
26. #10623260C22semidirect
44. C11×#477C22semidirect
58. #10622700C22semidirect
59. #10622635C22semidirect
67. #10622504C22semidirect
68. #10622503C22semidirect
69. #10622494C22semidirect
70. D11×#107C22semidirect
71. #10622460C22semidirect
72. #10622452C22semidirect
75. #10622412C22semidirect
76. #10622407C22semidirect
81. C2×#4343Q8semidirect
204. #4343C2×Q8semidirect
279. C2×#477D11semidirect
379. #477C2×D11semidirect
537. C2×C11#3083semidirect
635. C11C2×#3083semidirect
723. C2#13078464direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232602
C2×#106231052
#130784642
C2×#106226352
C2×#106224122
C2×#106224072
C2×#106225042
C2×#106224602
C2×#106225032
C2×#106227002
C2×#106224942
C2×D11×#1072
C2×#106224522
C2×#106224162
C2×#106224172
C2×C11×#4772
C2×#308311