Finite Group Databasebeta

← C2×#13081146 #15632400

Subgroups — C2×#13081146 #15632400

Order 2816.

1834 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623073C211yesmaximal, characteristic
2#13081146C2116yesmaximal, direct product factor
3C2×#10622678C211yesmaximal, characteristic, complemented
4C2×#10622583C211yesmaximal, characteristic, complemented
5C2×#10622609C211yesmaximal, characteristic, complemented
6C2×#10622658C211yesmaximal, characteristic, complemented
7C2×#10622658C211yesmaximal, characteristic, complemented
8C2×#10622676C211yesmaximal, characteristic, complemented
9C2×#10622634C211yesmaximal, characteristic, complemented
10C2×#10622665C211yesmaximal, characteristic, complemented
11C2×#10622664C211yesmaximal, characteristic, complemented
12C2×#10622643C211yesmaximal, characteristic, complemented
13C2×#10622624C211yesmaximal, characteristic
14C2×#10622577C211yesmaximal, characteristic, complemented
15C2×#10622611C211yesmaximal, characteristic, complemented
16C2×C11×#552C211yesmaximal, characteristic
17C11×#552—24no—
18C11×#552C2218yes—
19C2×C11×#126—21no—
20C2×C11×#125—21no—
21C2×C11×#125C2211yescharacteristic
22C2×C11×#123—21no—
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×C22⋊Q8C2211yescharacteristic
25C2×C4×Q8×C11C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×C11×#117—21no—
28C2×C11×#117C2211yescharacteristic
29C22×C11×C4⋊C4C2211yescharacteristic
30C22×#4326C2211yescharacteristic
31C2×#66989—21no—
32C2×#66979C2211yescharacteristic
33C2×#66979C2211yescharacteristic
34C2×#66977C2211yescharacteristic
35C2×#66977C2211yescharacteristic
36C22×#4318C2211yescharacteristic
37C23×C11⋊C8C2211yescharacteristic
38#10623073—24no—
39#10623073C2218yes—
40C2×#66940—21no—
41C2×#66932—21no—
42C2×#66932—21no—
43C2×#66922C2211yescharacteristic
44C2×C4×Dic22C2211yescharacteristic
45C2×#66899C2211yescharacteristic
46C2×#66899C2211yescharacteristic
47C2×#66899C2211yescharacteristic
48C2×C22⋊(C11⋊C8)C2211yescharacteristic
49C2×C22⋊(C11⋊C8)C2211yescharacteristic
50#10622678C2218yescomplemented
51#10622676C2218yescomplemented
52#10622665C2218yescomplemented
53#10622664C2218yescomplemented
54#10622658C2218yescomplemented
55#10622658C2218yescomplemented
56#10622643C2218yescomplemented
57#10622634C2218yescomplemented
58#10622624C2218yes—
59#10622611C2218yescomplemented
60#10622609C2218yescomplemented
61#10622583C2218yescomplemented
62C2×#66874C2211yescharacteristic
63C2×#66874C2211yescharacteristic
64C2×#66874C2211yescharacteristic
65#10622577C2218yescomplemented
66C2×#66872C2211yescharacteristic
67C2×#66872C2211yescharacteristic
68C2×#66872C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71C2×#66871C2211yescharacteristic
72C2×#66871C2211yescharacteristic
73C2×#66871C2211yescharacteristic
74C2×#66871C2211yescharacteristic
75C2×C4⋊(C11⋊C8)C2211yescharacteristic
76C2×#66867C2211yescharacteristic
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11D411yescharacteristic
79C23×C4×C11—21no—
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C22×Dic22—21no—
83C22×Dic22C2311yescharacteristic
84C11×#126—28no—
85C11×#125—28no—
86C11×#125—22no—
87C11×#125C2314yes—
88C11×#123—28no—
89C11×C22⋊Q8—22no—
90C11×C22⋊Q8—22no—
91C11×C22⋊Q8C2314yes—
92C11×C22⋊Q8C2314yes—
93C4×Q8×C11—22no—
94C4×Q8×C11C2314yes—
95C4×D4×C11D414yes—
96C4×D4×C11C2314yes—
97C11×#117—22no—
98C11×#117—28no—
99C11×#117C2314yes—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—22no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4D411yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2314yes—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4D411yescharacteristic
116C2×C11×C22⋊C4D411yescharacteristic
117C2×C42×C11—21no—
118C2×C42×C11—21no—
119C2×C42×C11C2311yescharacteristic
120C2×C22⋊Dic11—21no—
121C2×C22⋊Dic11—21no—
122C2×C22⋊Dic11—21no—
123C2×C22⋊Dic11—21no—
124C2×#4326—24no—
125C2×#4326C2314yes—
126#66989—28no—
127#66979—22no—
128#66979—22no—
129#66979C2314yes—
130#66979C2314yes—
131C2×C4⋊Dic11—21no—
132C2×C4⋊Dic11C2311yescharacteristic
133C2×C4⋊Dic11C2311yescharacteristic
134C2×C4⋊Dic11C2311yescharacteristic
135#66977—22no—
136#66977—22no—
137#66977C2314yes—
138#66977C2314yes—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C2×Dic11⋊C4—21no—
142C2×C4×Dic11—21no—
143C2×C4×Dic11—21no—
144C2×C4×Dic11—21no—
145C2×#4318—24no—
146C2×#4318C2314yes—
147C22×C11⋊C8—24no—
148C22×C11⋊C8C2311yescharacteristic
149C22×C11⋊C8C2311yescharacteristic
150C22×C11⋊C8C2311yescharacteristic
151C22×C11⋊C8C2314yes—
152C22×C11⋊C8C2311yescharacteristic
153#66940—28no—
154#66932—28no—
155#66932—28no—
156#66922—22no—
157#66922C2314yes—
158C4×Dic22—22no—
159C4×Dic22C2314yes—
160#66899C2314yes—
161#66899C2314yes—
162#66899C2314yes—
163C22⋊(C11⋊C8)C2314yes—
164C22⋊(C11⋊C8)C2314yes—
165#66874C2314yes—
166#66874C2314yes—
167#66874C2314yes—
168#66872C2314yes—
169#66872C2314yes—
170#66872C2314yes—
171#66872C2314yes—
172#66871C2314yes—
173#66871C2314yes—
174#66871C2314yes—
175#66871C2314yes—
176#66871C2314yes—
177C4⋊(C11⋊C8)C2314yes—
178#66867C2314yes—
179C2×#3349—111nomaximal, Sylow
180C24×C11C2×D411yescharacteristic
181C24×C11C2×D411yescharacteristic
182C2×Q8×C11—21no—
183C2×Q8×C11—22no—
184C2×Q8×C11—22no—
185C2×Q8×C11C2412yes—
186C2×D4×C11—42no—
187C2×D4×C11C2×D414yes—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—24no—
197C22×C4×C11—44no—
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D412yes—
203C22×C4×C11C2×D412yes—
204C22×C4×C11C2412yes—
205C22×C4×C11C2412yes—
206C22×C4×C11C2411yescharacteristic
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C2×Dic22—21no—
212C2×Dic22—24no—
213C2×Dic22—22no—
214C2×Dic22—22no—
215C2×Dic22—44no—
216C2×Dic22C2412yes—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—24no—
220C11×C4⋊C4—24no—
221C11×C4⋊C4—24no—
222C11×C4⋊C4—24no—
223C11×C4⋊C4—24no—
224C11×C4⋊C4—24no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4C2×D414yes—
227C11×C4⋊C4C2412yes—
228C11×C4⋊C4C2412yes—
229C11×C4⋊C4C2412yes—
230C11×C22⋊C4—24no—
231C11×C22⋊C4—24no—
232C11×C22⋊C4—24no—
233C11×C22⋊C4C2×D414yes—
234C11×C22⋊C4C2×D414yes—
235C42×C11—24no—
236C42×C11—24no—
237C42×C11C2×D412yes—
238C42×C11C2412yes—
239C22⋊Dic11—24no—
240C22⋊Dic11—24no—
241C22⋊Dic11—24no—
242C22⋊Dic11—24no—
243#4326—28no—
244C4⋊Dic11—21no—
245C4⋊Dic11—21no—
246C4⋊Dic11—21no—
247C4⋊Dic11—24no—
248C4⋊Dic11C2412yes—
249C4⋊Dic11C2412yes—
250C4⋊Dic11C2412yes—
251Dic11⋊C4—24no—
252Dic11⋊C4—24no—
253Dic11⋊C4—24no—
254C4×Dic11—24no—
255C4×Dic11—24no—
256C4×Dic11—24no—
257#4318—28no—
258C2×C11⋊C8—28no—
259C2×C11⋊C8—22no—
260C2×C11⋊C8—22no—
261C2×C11⋊C8—22no—
262C2×C11⋊C8#4114yes—
263C2×C11⋊C8C2412yes—
264C2×C11⋊C8C2412yes—
265C2×C11⋊C8C2412yes—
266C2×C11⋊C8C2412yes—
267C2×#556—111no—
268C2×#552D1111yescharacteristic
269#3349—1116no—
270C2×#501—111no—
271C2×#484—111no—
272C2×#485—111no—
273C2×#485—111no—
274C2×#485—111no—
275C2×#479—111no—
276C2×#477—111no—
277C2×#470—111no—
278C2×#467—111no—
279C2×#441—111no—
280C2×#435—111no—
281C2×#428—111no—
282C2×#427—111no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11C22×D412yes—
290C23×C11C22×D412yes—
291C23×C11C22×D411yescharacteristic
292Q8×C11—22no—
293Q8×C11—22no—
294Q8×C11—42no—
295D4×C11—44no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—24no—
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—22no—
309C2×C4×C11—22no—
310C2×C4×C11—48no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11C22×D412yes—
316C2×C4×C11C22×D412yes—
317C2×C4×C11C22×D412yes—
318C2×C4×C11C22×D412yes—
319C2×C4×C11C22×D411yescharacteristic
320C2×C4×C11C2×#4112yes—
321C2×C4×C112−1+412yes—
322C2×C4×C11C2511yescharacteristic
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11—42no—
330C2×Dic11—42no—
331Dic22—22no—
332Dic22—22no—
333Dic22—48no—
334Dic22—42no—
335C11⋊C8—22no—
336C11⋊C8—22no—
337C11⋊C8—22no—
338C11⋊C8C2×#4114yes—
339C22×Q16—111no—
340C22×M16—111no—
341C23×C8—111no—
342#556—118no—
343#556—224no—
344#552—24no—
345#552C2×D1118yes—
346C2×C4⋊Q8—111no—
347C2×#126—21no—
348C2×#126—221no—
349C2×#126—221no—
350C2×#125—21no—
351C2×#125C2×D1111yescharacteristic
352C2×#124—221no—
353C2×#123—21no—
354C2×C22⋊Q8—111no—
355C2×C22⋊Q8—111no—
356C2×C22⋊Q8C2×D1111yescharacteristic
357C2×C22⋊Q8C2×D1111yescharacteristic
358C2×C4×Q8—111no—
359C2×C4×Q8—221no—
360C2×C4×Q8C2×D1111yescharacteristic
361C2×C4×D4C2×D1111yescharacteristic
362C2×#117—21no—
363C2×#117—111no—
364C2×#117—111no—
365C2×#117C2×D1111yescharacteristic
366C22×C4⋊C4C2×D1111yescharacteristic
367#501—118no—
368#485—118no—
369#485—118no—
370#485—118no—
371#484—118no—
372#479—118no—
373#477—118no—
374#470—118no—
375#467—118no—
376#441—118no—
377#435—118no—
378#428—118no—
379#427—118no—
380C2×#107—111no—
381C2×#107—111no—
382C2×#107—111no—
383C2×#107—111no—
384C2×#107—111no—
385C2×#106—111no—
386C2×#106—111no—
387C2×#106—111no—
388C2×#106—111no—
389C2×C4⋊C8—111no—
390C2×#103—111no—
391C2×#103—111no—
392C2×#103—111no—
393C2×#103—111no—
394C2×#103—111no—
395C2×#103—111no—
396C2×C22⋊C8—111no—
397C2×C22⋊C8—111no—
398C2×#97—111no—
399C22×C11—22no—
400C22×C11—22no—
401C22×C11—22no—
402C22×C11—22no—
403C22×C11—22no—
404C22×C11—22no—
405C22×C11—44no—
406C22×C11—44no—
407C22×C11#54712yes—
408C22×C11#57512yes—
409C22×C11#57812yes—
410C22×C11C23×D411yescharacteristic
411C4×C11—22no—
412C4×C11—22no—
413C4×C11—22no—
414C4×C11—22no—
415C4×C11—42no—
416C4×C11—42no—
417C4×C11—42no—
418C4×C11—42no—
419C4×C11#54712yes—
420C4×C11C22×#4111yescharacteristic
421C4×C11C2×2−1+411yescharacteristic
422Dic11—42no—
423Dic11—42no—
424Dic11—42no—
425Dic11—42no—
426C22×Q8—111no—
427C22×Q8—221no—
428C22×Q8C22×D1111yescharacteristic
429C22×D4C22⋊D1111yescharacteristic
430C23×C4—21no—
431C23×C4C22×D1111yescharacteristic
432C23×C4C22×D1111yescharacteristic
433C2×Q16—114no—
434C2×Q16—224no—
435C2×M16—114no—
436C2×M16—224no—
437C22×C8—111no—
438C22×C8—111no—
439C22×C8—114no—
440C22×C8—111no—
441C22×C8—111no—
442C22×C8—224no—
443C4⋊Q8—114no—
444C4⋊Q8—222no—
445#126—28no—
446#126—228no—
447#126—228no—
448#125—28no—
449#125—22no—
450#125C22×D1114yes—
451#124—228no—
452#123—28no—
453C22⋊Q8—22no—
454C22⋊Q8—22no—
455C22⋊Q8—114no—
456C22⋊Q8—114no—
457C22⋊Q8—222no—
458C22⋊Q8—222no—
459C22⋊Q8C22×D1114yes—
460C22⋊Q8C22×D1114yes—
461C4×Q8—22no—
462C4×Q8—114no—
463C4×Q8—228no—
464C4×Q8—222no—
465C4×Q8C22×D1114yes—
466C4×D4C22⋊D1114yes—
467C4×D4C22×D1114yes—
468#117—22no—
469#117—28no—
470#117—114no—
471#117—114no—
472#117—222no—
473#117—222no—
474#117C22×D1114yes—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—111no—
483C2×C4⋊C4—111no—
484C2×C4⋊C4—111no—
485C2×C4⋊C4—221no—
486C2×C4⋊C4—221no—
487C2×C4⋊C4—221no—
488C2×C4⋊C4—221no—
489C2×C4⋊C4C22⋊D1111yescharacteristic
490C2×C4⋊C4C22×D1111yescharacteristic
491C2×C4⋊C4C22×D1111yescharacteristic
492C2×C4⋊C4C22×D1114yes—
493C2×C4⋊C4C22×D1111yescharacteristic
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—221no—
498C2×C22⋊C4—221no—
499C2×C22⋊C4—221no—
500C2×C22⋊C4—221no—
501C2×C22⋊C4C22⋊D1111yescharacteristic
502C2×C22⋊C4C22⋊D1111yescharacteristic
503C2×C42—21no—
504C2×C42—21no—
505C2×C42—221no—
506C2×C42—221no—
507C2×C42—221no—
508C2×C42C22×D1111yescharacteristic
509#107—114no—
510#107—114no—
511#107—114no—
512#107—114no—
513#107—114no—
514#106—114no—
515#106—114no—
516#106—114no—
517#106—114no—
518C4⋊C8—114no—
519#103—114no—
520#103—114no—
521#103—114no—
522#103—114no—
523#103—114no—
524#103—114no—
525C22⋊C8—114no—
526C22⋊C8—114no—
527#97—114no—
528C2×C11—42no—
529C2×C11—42no—
530C2×C11#334914yescomplemented
531C2×C11C2×#54711yescharacteristic
532C2×C11C2×#57511yescharacteristic
533C2×C11C2×#57811yescharacteristic
534C24C2×C22⋊D1111yescharacteristic
535C24C2×C22⋊D1111yescharacteristic
536C2×Q8—21no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—112no—
540C2×Q8—221no—
541C2×Q8—224no—
542C2×Q8—222no—
543C2×Q8—222no—
544C2×Q8—444no—
545C2×Q8C23×D1112yes—
546C2×D4—42no—
547C2×D4C2×C22⋊D1114yes—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—24no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—44no—
558C22×C4—221no—
559C22×C4—221no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4C2×C22⋊D1112yes—
563C22×C4C2×C22⋊D1112yes—
564C22×C4C2×C22⋊D1111yescharacteristic
565C22×C4C2×C22⋊D1111yescharacteristic
566C22×C4C2×C22⋊D1111yescharacteristic
567C22×C4C2×C22⋊D1111yescharacteristic
568C22×C4C23×D1112yes—
569C22×C4C23×D1112yes—
570C22×C4C23×D1111yescharacteristic
571Q16—228no—
572M16—228no—
573C2×C8—114no—
574C2×C8—112no—
575C2×C8—112no—
576C2×C8—112no—
577C2×C8—112no—
578C2×C8—228no—
579C2×C8—222no—
580C2×C8—222no—
581C2×C8—222no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—21no—
591C4⋊C4—112no—
592C4⋊C4—112no—
593C4⋊C4—112no—
594C4⋊C4—221no—
595C4⋊C4—221no—
596C4⋊C4—221no—
597C4⋊C4—224no—
598C4⋊C4—224no—
599C4⋊C4—224no—
600C4⋊C4—224no—
601C4⋊C4C2×C22⋊D1114yes—
602C4⋊C4C23×D1112yes—
603C4⋊C4C23×D1112yes—
604C4⋊C4C23×D1112yes—
605C22⋊C4—24no—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—224no—
609C22⋊C4—224no—
610C22⋊C4—224no—
611C22⋊C4—224no—
612C22⋊C4C2×C22⋊D1114yes—
613C22⋊C4C2×C22⋊D1114yes—
614C42—24no—
615C42—24no—
616C42—224no—
617C42—224no—
618C42—224no—
619C42C2×C22⋊D1112yes—
620C42C23×D1112yes—
621C11C2×#334911yescharacteristic, complemented, Sylow
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23C22×C22⋊D1112yes—
629C23C22×C22⋊D1112yes—
630C23C22×C22⋊D1111yescharacteristic
631Q8—22no—
632Q8—22no—
633Q8—42no—
634Q8—222no—
635Q8—222no—
636Q8—448no—
637Q8—442no—
638D4—44no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—48no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—222no—
659C2×C4—222no—
660C2×C4—222no—
661C2×C4—222no—
662C2×C4—442no—
663C2×C4—442no—
664C2×C4—442no—
665C2×C4—442no—
666C2×C4#41×D1112yes—
667C2×C4#6704312yes—
668C2×C4C22×C22⋊D1112yes—
669C2×C4C22×C22⋊D1112yes—
670C2×C4C22×C22⋊D1112yes—
671C2×C4C22×C22⋊D1112yes—
672C2×C4C22×C22⋊D1111yescharacteristic
673C2×C4C24×D1111yescharacteristic
674C8—114no—
675C8—222no—
676C8—222no—
677C8—222no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—44no—
685C22—44no—
686C22#1062335312yes—
687C22#1062335512yes—
688C22#1062336912yes—
689C22C23×C22⋊D1111yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—42no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—442no—
699C4—442no—
700C4—442no—
701C4—442no—
702C4#1062335512yes—
703C4C2×#41×D1111yescharacteristic
704C4C2×#6704311yescharacteristic
705C2—42no—
706C2—42no—
707C2#1308114614yesdirect product factor
708C2C2×#1062335511yescharacteristic
709C2C2×#1062335311yescharacteristic
710C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#552C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenterC2×#552D11
hypocenterC11C2×#3349
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #13081146C2direct (N × H)
3. C2×#10622678C2semidirect
4. C2×#10622583C2semidirect
5. C2×#10622609C2semidirect
6. C2×#10622658C2semidirect
7. C2×#10622658C2semidirect
8. C2×#10622676C2semidirect
9. C2×#10622634C2semidirect
10. C2×#10622665C2semidirect
11. C2×#10622664C2semidirect
12. C2×#10622643C2semidirect
14. C2×#10622577C2semidirect
15. C2×#10622611C2semidirect
50. #10622678C22semidirect
51. #10622676C22semidirect
52. #10622665C22semidirect
53. #10622664C22semidirect
54. #10622658C22semidirect
55. #10622658C22semidirect
56. #10622643C22semidirect
57. #10622634C22semidirect
59. #10622611C22semidirect
60. #10622609C22semidirect
61. #10622583C22semidirect
65. #10622577C22semidirect
530. C2×C11#3349semidirect
621. C11C2×#3349semidirect
707. C2#13081146direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230732
#130811462
C2×#106226782
C2×#106225832
C2×#106226092
C2×#106226582
C2×#106226762
C2×#106226342
C2×#106226652
C2×#106226642
C2×#106226432
C2×#106226242
C2×#106225772
C2×#106226112
C2×C11×#5522
C2×#334911