Finite Group Databasebeta

← C2×#13079869 #15625962

Subgroups — C2×#13079869 #15625962

Order 2816.

1806 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623066C211yesmaximal, characteristic
2#13079869C2116yesmaximal, direct product factor
3C2×#10622693C211yesmaximal, characteristic, complemented
4C2×#10622677C211yesmaximal, characteristic, complemented
5C2×#10622680C211yesmaximal, characteristic, complemented
6C2×#10622701C211yesmaximal, characteristic, complemented
7C2×#10622581C211yesmaximal, characteristic, complemented
8C2×#10622616C211yesmaximal, characteristic, complemented
9C2×#10622616C211yesmaximal, characteristic, complemented
10C2×#10622580C211yesmaximal, characteristic, complemented
11C2×#10622679C211yesmaximal, characteristic, complemented
12C2×#10622679C211yesmaximal, characteristic, complemented
13C2×#10622697C211yesmaximal, characteristic, complemented
14C2×#10622700C211yesmaximal, characteristic, complemented
15C2×#10622613C211yesmaximal, characteristic, complemented
16C2×C11×#544C211yesmaximal, characteristic, complemented
17C11×#544—24no—
18C11×#544C2218yescomplemented
19C2×C11×C4⋊Q8—21no—
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×C11×C4⋊Q8C2211yescharacteristic
22C2×C11×#125—21no—
23C2×C11×#125C2211yescharacteristic
24C2×C11×#125C2211yescharacteristic
25C2×C11×C22⋊Q8—21no—
26C2×C11×C22⋊Q8—21no—
27C2×C11×#117C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic
29C22×C11×C4⋊C4C2211yescharacteristic
30C2×#66983C2211yescharacteristic
31C2×#66983C2211yescharacteristic
32#10623066—24no—
33#10623066C2218yes—
34C2×#66947—21no—
35C2×#66947—21no—
36C2×#66937—21no—
37C2×#66937—21no—
38C2×#66927C2211yescharacteristic
39C2×C4×D44C2211yescharacteristic
40C2×C4×D44C2211yescharacteristic
41C2×#66923C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44#10622701C2218yescomplemented
45#10622700C2218yescomplemented
46#10622697C2218yescomplemented
47#10622693C2218yescomplemented
48#10622680C2218yescomplemented
49#10622679C2218yescomplemented
50#10622679C2218yescomplemented
51#10622677C2218yescomplemented
52#10622616C2218yescomplemented
53#10622616C2218yescomplemented
54#10622613C2218yescomplemented
55#10622581C2218yescomplemented
56#10622580C2218yescomplemented
57C2×#66873C2211yescharacteristic
58C2×#66873C2211yescharacteristic
59C2×#66873C2211yescharacteristic
60C2×#66873C2211yescharacteristic
61C2×#66873C2211yescharacteristic
62C2×#66873C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66873C2211yescharacteristic
65C2×#66872C2211yescharacteristic
66C2×#66872C2211yescharacteristic
67C2×#66872C2211yescharacteristic
68C2×#66872C2211yescharacteristic
69C2×#66871C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71C2×#66871C2211yescharacteristic
72C2×#66871C2211yescharacteristic
73C2×C4⋊(C11⋊C8)C2211yescharacteristic
74C2×C4⋊(C11⋊C8)C2211yescharacteristic
75C2×#66867C2211yescharacteristic
76C2×C4×C11⋊C8C2211yescharacteristic
77C22×Q8×C11—21no—
78C22×Q8×C11—21no—
79C23×C4×C11—21no—
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C22×D44—21no—
84C22×D44—21no—
85C22×D44C2311yescharacteristic
86C22×D44C2311yescharacteristic
87C22×C4×D11—21no—
88C22×C4×D11—21no—
89C11×C4⋊Q8—28no—
90C11×C4⋊Q8—22no—
91C11×C4⋊Q8—22no—
92C11×C4⋊Q8C2314yes—
93C11×C4⋊Q8C2314yes—
94C11×#125—28no—
95C11×#125—22no—
96C11×#125—22no—
97C11×#125C2314yes—
98C11×#125C2314yes—
99C11×C22⋊Q8—28no—
100C11×C22⋊Q8—28no—
101C11×#117—22no—
102C11×#117D414yes—
103C11×#117C2314yes—
104C11×#117C2314yes—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—22no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4—21no—
112C2×C11×C4⋊C4—21no—
113C2×C11×C4⋊C4D411yescharacteristic
114C2×C11×C4⋊C4D411yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C4⋊C4C2311yescharacteristic
118C2×C11×C4⋊C4C2311yescharacteristic
119C2×C11×C4⋊C4C2314yes—
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4D411yescharacteristic
122C2×C11×C22⋊C4D411yescharacteristic
123C2×C42×C11—21no—
124C2×C42×C11C2311yescharacteristic
125C2×C42×C11C2311yescharacteristic
126#66983—22no—
127#66983—22no—
128#66983C2314yes—
129#66983C2314yes—
130C2×(C2×D11)⋊C4—21no—
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4—21no—
134C2×C4⋊Dic11C2311yescharacteristic
135C2×C4⋊Dic11C2311yescharacteristic
136C2×Dic11⋊C4—21no—
137C2×Dic11⋊C4—21no—
138C22×C11⋊C8C2311yescharacteristic
139C22×C11⋊C8C2311yescharacteristic
140C22×C11⋊C8C2311yescharacteristic
141C22×C11⋊C8C2311yescharacteristic
142#66947—28no—
143#66947—28no—
144#66937—28no—
145#66937—28no—
146#66927—22no—
147#66927C2314yes—
148C4×D44—22no—
149C4×D44—22no—
150C4×D44C2314yes—
151C4×D44C2314yes—
152#66923—22no—
153#66923C2314yes—
154C22⋊(C11⋊C8)C2314yes—
155C22⋊(C11⋊C8)C2314yes—
156#66873C2314yes—
157#66873C2314yes—
158#66873C2314yes—
159#66873C2314yes—
160#66873C2314yes—
161#66873C2314yes—
162#66873C2314yes—
163#66873C2314yes—
164#66872C2314yes—
165#66872C2314yes—
166#66872C2314yes—
167#66872C2314yes—
168#66871C2314yes—
169#66871C2314yes—
170#66871C2314yes—
171#66871C2314yes—
172C4⋊(C11⋊C8)C2314yes—
173C4⋊(C11⋊C8)C2314yes—
174#66867C2314yes—
175C4×C11⋊C8C2314yes—
176C2×#3241—111nomaximal, Sylow
177C24×C11C2×D411yescharacteristic
178C23×D11—21no—
179C23×D11—21no—
180C2×Q8×C11—24no—
181C2×Q8×C11—24no—
182C2×Q8×C11—82no—
183C2×Q8×C11—82no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—24no—
191C22×C4×C11—82no—
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D412yes—
198C22×C4×C11C2412yes—
199C22×C4×C11C2411yescharacteristic
200C2×C22⋊D11—24no—
201C2×C22⋊D11—24no—
202C2×C22⋊D11—82no—
203C2×C22⋊D11—82no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C2×D44—21no—
207C2×D44—21no—
208C2×D44—24no—
209C2×D44—24no—
210C2×D44—22no—
211C2×D44—22no—
212C2×D44—22no—
213C2×D44—22no—
214C2×D44—82no—
215C2×D44—82no—
216C2×D44C2412yes—
217C2×D44C2412yes—
218C2×C4×D11—24no—
219C2×C4×D11—24no—
220C2×C4×D11—82no—
221C2×C4×D11—82no—
222C11×C4⋊C4—24no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—24no—
226C11×C4⋊C4—24no—
227C11×C4⋊C4—24no—
228C11×C4⋊C4—24no—
229C11×C4⋊C4—24no—
230C11×C4⋊C4—24no—
231C11×C4⋊C4—21no—
232C11×C4⋊C4—21no—
233C11×C4⋊C4C2×D414yes—
234C11×C4⋊C4C2×D414yes—
235C11×C4⋊C4C2412yes—
236C11×C4⋊C4C2412yes—
237C11×C4⋊C4C2412yes—
238C11×C4⋊C4C2412yes—
239C11×C22⋊C4—24no—
240C11×C22⋊C4C2×D414yes—
241C11×C22⋊C4C2×D414yes—
242C42×C11—24no—
243C42×C11C2×D412yes—
244C42×C11C2×D412yes—
245C42×C11C2412yes—
246C42×C11C2412yes—
247(C2×D11)⋊C4—24no—
248(C2×D11)⋊C4—24no—
249(C2×D11)⋊C4—24no—
250(C2×D11)⋊C4—24no—
251C4⋊Dic11—21no—
252C4⋊Dic11—21no—
253C4⋊Dic11C2412yes—
254C4⋊Dic11C2412yes—
255Dic11⋊C4—24no—
256Dic11⋊C4—24no—
257C2×C11⋊C8—22no—
258C2×C11⋊C8—22no—
259C2×C11⋊C8—22no—
260C2×C11⋊C8—22no—
261C2×C11⋊C8C2412yes—
262C2×C11⋊C8C2412yes—
263C2×C11⋊C8C2412yes—
264C2×C11⋊C8C2412yes—
265C2×#544D1111yescharacteristic, complemented
266C2×#540—111no—
267#3241—1116no—
268C2×#501—111no—
269C2×#499—111no—
270C2×#490—111no—
271C2×#486—111no—
272C2×#481—111no—
273C2×#482—111no—
274C2×#482—111no—
275C2×#480—111no—
276C2×#478—111no—
277C2×#478—111no—
278C2×#476—111no—
279C2×#474—111no—
280C2×#433—111no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11C22×D412yes—
285C23×C11C22×D411yescharacteristic
286C22×D11—22no—
287C22×D11—22no—
288C22×D11—42no—
289C22×D11—42no—
290C22×D11—42no—
291C22×D11—42no—
292C22×D11—42no—
293C22×D11—42no—
294Q8×C11—84no—
295Q8×C11—84no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—24no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—42no—
309C2×C4×C11—42no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11—84no—
313C2×C4×C11C22×D412yes—
314C2×C4×C11C22×D412yes—
315C2×C4×C11C22×D412yes—
316C2×C4×C11C22×D412yes—
317C2×C4×C11C22×D412yes—
318C2×C4×C11C22×D411yescharacteristic
319C2×C4×C112−1+412yes—
320C2×C4×C112−1+412yes—
321C2×C4×C11C2511yescharacteristic
322C22⋊D11—84no—
323C22⋊D11—84no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—42no—
327C2×Dic11—42no—
328D44—22no—
329D44—22no—
330D44—22no—
331D44—22no—
332D44—42no—
333D44—42no—
334D44—84no—
335D44—84no—
336C4×D11—84no—
337C4×D11—84no—
338C11⋊C8—22no—
339C11⋊C8—22no—
340C11⋊C8—22no—
341C11⋊C8—22no—
342#544—24no—
343#544C2×D1118yescomplemented
344#540—118no—
345#540—224no—
346C2×C4⋊Q8—21no—
347C2×C4⋊Q8C2×D1111yescharacteristic
348C2×C4⋊Q8C2×D1111yescharacteristic
349C2×#127—111no—
350C2×#125—21no—
351C2×#125—111no—
352C2×#125C2×D1111yescharacteristic
353C2×#125C2×D1111yescharacteristic
354C2×#123—221no—
355C2×#123—221no—
356C2×C22⋊Q8—21no—
357C2×C22⋊Q8—21no—
358C2×#121—111no—
359C2×#121—111no—
360C2×#121—221no—
361C2×#121—221no—
362C2×C4×D4—111no—
363C2×C4×D4—111no—
364C2×#117C2×D1111yescharacteristic
365C2×#117C2×D1111yescharacteristic
366C22×C4⋊C4C2×D1111yescharacteristic
367#501—118no—
368#499—118no—
369#490—118no—
370#486—118no—
371#482—118no—
372#482—118no—
373#481—118no—
374#480—118no—
375#478—118no—
376#478—118no—
377#476—118no—
378#474—118no—
379#433—118no—
380C2×#107—111no—
381C2×#107—111no—
382C2×#107—111no—
383C2×#107—111no—
384C2×#106—111no—
385C2×#106—111no—
386C2×#106—111no—
387C2×#106—111no—
388C2×C4⋊C8—111no—
389C2×C4⋊C8—111no—
390C2×#102—111no—
391C2×#102—111no—
392C2×#102—111no—
393C2×#102—111no—
394C2×#102—111no—
395C2×#102—111no—
396C2×#102—111no—
397C2×#102—111no—
398C2×C22⋊C8—111no—
399C2×C22⋊C8—111no—
400C2×#97—111no—
401C2×C4×C8—111no—
402C22×C11—22no—
403C22×C11—22no—
404C22×C11—22no—
405C22×C11—44no—
406C22×C11#53612yes—
407C22×C11#57612yes—
408C22×C11#57712yes—
409C22×C11C23×D411yescharacteristic
410C2×D11—42no—
411C2×D11—42no—
412C2×D11—42no—
413C2×D11—42no—
414C2×D11—42no—
415C2×D11—42no—
416C2×D11—84no—
417C2×D11—84no—
418C4×C11—22no—
419C4×C11—22no—
420C4×C11—22no—
421C4×C11—22no—
422C4×C11—22no—
423C4×C11—42no—
424C4×C11—42no—
425C4×C11—42no—
426C4×C11—42no—
427C4×C11#53612yes—
428C4×C11C2×2−1+411yescharacteristic
429C4×C11C2×2−1+411yescharacteristic
430Dic11—42no—
431Dic11—42no—
432C22×Q8—21no—
433C22×Q8—21no—
434C22×D4—111no—
435C22×D4—111no—
436C22×D4—221no—
437C22×D4—221no—
438C22×D4—221no—
439C22×D4—221no—
440C23×C4—21no—
441C23×C4—221no—
442C23×C4—221no—
443C23×C4C22×D1111yescharacteristic
444C22×C8—111no—
445C22×C8—111no—
446C22×C8—111no—
447C22×C8—111no—
448C4⋊Q8—28no—
449C4⋊Q8—22no—
450C4⋊Q8—22no—
451C4⋊Q8C22×D1114yes—
452C4⋊Q8C22×D1114yes—
453#127—114no—
454#127—222no—
455#125—28no—
456#125—22no—
457#125—22no—
458#125—114no—
459#125—222no—
460#125C22×D1114yes—
461#125C22×D1114yes—
462#123—228no—
463#123—228no—
464C22⋊Q8—28no—
465C22⋊Q8—28no—
466#121—114no—
467#121—114no—
468#121—222no—
469#121—222no—
470#121—228no—
471#121—228no—
472C4×D4—114no—
473C4×D4—114no—
474C4×D4—222no—
475C4×D4—222no—
476#117—22no—
477#117C22⋊D1114yes—
478#117C22×D1114yes—
479#117C22×D1114yes—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—111no—
489C2×C4⋊C4—111no—
490C2×C4⋊C4—221no—
491C2×C4⋊C4—221no—
492C2×C4⋊C4C22⋊D1111yescharacteristic
493C2×C4⋊C4C22⋊D1111yescharacteristic
494C2×C4⋊C4C22×D1111yescharacteristic
495C2×C4⋊C4C22×D1111yescharacteristic
496C2×C4⋊C4C22×D1114yes—
497C2×C4⋊C4C22×D1111yescharacteristic
498C2×C4⋊C4C22×D1111yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—221no—
501C2×C22⋊C4—221no—
502C2×C22⋊C4—221no—
503C2×C22⋊C4—221no—
504C2×C22⋊C4C22⋊D1111yescharacteristic
505C2×C22⋊C4C22⋊D1111yescharacteristic
506C2×C42—21no—
507C2×C42C22×D1111yescharacteristic
508C2×C42C22×D1111yescharacteristic
509#107—114no—
510#107—114no—
511#107—114no—
512#107—114no—
513#106—114no—
514#106—114no—
515#106—114no—
516#106—114no—
517C4⋊C8—114no—
518C4⋊C8—114no—
519#102—114no—
520#102—114no—
521#102—114no—
522#102—114no—
523#102—114no—
524#102—114no—
525#102—114no—
526#102—114no—
527C22⋊C8—114no—
528C22⋊C8—114no—
529#97—114no—
530C4×C8—114no—
531C2×C11—42no—
532C2×C11#324114yescomplemented
533C2×C11C2×#53611yescharacteristic
534C2×C11C2×#57611yescharacteristic
535C2×C11C2×#57711yescharacteristic
536D11—82no—
537D11—82no—
538C24—221no—
539C24—221no—
540C24C2×C22⋊D1111yescharacteristic
541C2×Q8—24no—
542C2×Q8—24no—
543C2×Q8—82no—
544C2×Q8—82no—
545C2×D4—112no—
546C2×D4—112no—
547C2×D4—224no—
548C2×D4—224no—
549C2×D4—222no—
550C2×D4—222no—
551C2×D4—222no—
552C2×D4—222no—
553C2×D4—221no—
554C2×D4—221no—
555C2×D4—224no—
556C2×D4—224no—
557C2×D4—882no—
558C2×D4—882no—
559C2×D4—882no—
560C2×D4—882no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—24no—
568C22×C4—82no—
569C22×C4—221no—
570C22×C4—221no—
571C22×C4—224no—
572C22×C4—224no—
573C22×C4—882no—
574C22×C4—882no—
575C22×C4C2×C22⋊D1112yes—
576C22×C4C2×C22⋊D1111yescharacteristic
577C22×C4C2×C22⋊D1111yescharacteristic
578C22×C4C2×C22⋊D1111yescharacteristic
579C22×C4C2×C22⋊D1111yescharacteristic
580C22×C4C2×C22⋊D1111yescharacteristic
581C22×C4C23×D1112yes—
582C22×C4C23×D1111yescharacteristic
583C2×C8—112no—
584C2×C8—112no—
585C2×C8—112no—
586C2×C8—112no—
587C2×C8—222no—
588C2×C8—222no—
589C2×C8—222no—
590C2×C8—222no—
591C4⋊C4—24no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—24no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—112no—
603C4⋊C4—112no—
604C4⋊C4—221no—
605C4⋊C4—221no—
606C4⋊C4—224no—
607C4⋊C4—224no—
608C4⋊C4C2×C22⋊D1114yes—
609C4⋊C4C2×C22⋊D1114yes—
610C4⋊C4C23×D1112yes—
611C4⋊C4C23×D1112yes—
612C4⋊C4C23×D1112yes—
613C4⋊C4C23×D1112yes—
614C22⋊C4—24no—
615C22⋊C4—224no—
616C22⋊C4—224no—
617C22⋊C4—224no—
618C22⋊C4—224no—
619C22⋊C4C2×C22⋊D1114yes—
620C22⋊C4C2×C22⋊D1114yes—
621C42—24no—
622C42C2×C22⋊D1112yes—
623C42C2×C22⋊D1112yes—
624C42C23×D1112yes—
625C42C23×D1112yes—
626C11C2×#324111yescharacteristic, complemented, Sylow
627C23—22no—
628C23—22no—
629C23—22no—
630C23—222no—
631C23—222no—
632C23—442no—
633C23—442no—
634C23—442no—
635C23—442no—
636C23—442no—
637C23—442no—
638C23C22×C22⋊D1112yes—
639C23C22×C22⋊D1111yescharacteristic
640Q8—84no—
641Q8—84no—
642D4—222no—
643D4—222no—
644D4—222no—
645D4—222no—
646D4—442no—
647D4—442no—
648D4—884no—
649D4—884no—
650D4—884no—
651D4—884no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—84no—
669C2×C4—222no—
670C2×C4—222no—
671C2×C4—442no—
672C2×C4—442no—
673C2×C4—884no—
674C2×C4—884no—
675C2×C4#6704012yes—
676C2×C4#6704012yes—
677C2×C4C22×C22⋊D1112yes—
678C2×C4C22×C22⋊D1112yes—
679C2×C4C22×C22⋊D1112yes—
680C2×C4C22×C22⋊D1112yes—
681C2×C4C22×C22⋊D1112yes—
682C2×C4C22×C22⋊D1111yescharacteristic
683C2×C4C24×D1111yescharacteristic
684C8—222no—
685C8—222no—
686C8—222no—
687C8—222no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—44no—
692C22—442no—
693C22—442no—
694C22—442no—
695C22—442no—
696C22—442no—
697C22—442no—
698C22—884no—
699C22—884no—
700C22#1062334712yes—
701C22#1062336612yes—
702C22#1062336812yes—
703C22C23×C22⋊D1111yescharacteristic
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—42no—
713C4—442no—
714C4—442no—
715C4#1062334712yes—
716C4C2×#6704011yescharacteristic
717C4C2×#6704011yescharacteristic
718C2—42no—
719C2—882no—
720C2—882no—
721C2#1307986914yesdirect product factor
722C2C2×#1062334711yescharacteristic
723C2C2×#1062336611yescharacteristic
724C2C2×#1062336811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#544C2
socleC23×C11C22×D4
prime radicalC2×#10623066C2
hypercenterC2×#544D11
hypocenterC11C2×#3241
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
2. #13079869C2direct (N × H)
3. C2×#10622693C2semidirect
4. C2×#10622677C2semidirect
5. C2×#10622680C2semidirect
6. C2×#10622701C2semidirect
7. C2×#10622581C2semidirect
8. C2×#10622616C2semidirect
9. C2×#10622616C2semidirect
10. C2×#10622580C2semidirect
11. C2×#10622679C2semidirect
12. C2×#10622679C2semidirect
13. C2×#10622697C2semidirect
14. C2×#10622700C2semidirect
15. C2×#10622613C2semidirect
16. C2×C11×#544C2semidirect
18. C11×#544C22semidirect
44. #10622701C22semidirect
45. #10622700C22semidirect
46. #10622697C22semidirect
47. #10622693C22semidirect
48. #10622680C22semidirect
49. #10622679C22semidirect
50. #10622679C22semidirect
51. #10622677C22semidirect
52. #10622616C22semidirect
53. #10622616C22semidirect
54. #10622613C22semidirect
55. #10622581C22semidirect
56. #10622580C22semidirect
265. C2×#544D11semidirect
343. #544C2×D11semidirect
532. C2×C11#3241semidirect
626. C11C2×#3241semidirect
721. C2#13079869direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230662
#130798692
C2×#106226932
C2×#106226772
C2×#106226802
C2×#106227012
C2×#106225812
C2×#106226162
C2×#106225802
C2×#106226792
C2×#106226972
C2×#106227002
C2×#106226132
C2×C11×#5442
C2×#324111