Finite Group Databasebeta

← C2×#13081065 #15632314

Subgroups — C2×#13081065 #15632314

Order 2816.

1878 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623072C211yesmaximal, characteristic
2#13081065C2116yesmaximal, direct product factor
3C2×#10622693C211yesmaximal, characteristic, complemented
4C2×#10622583C211yesmaximal, characteristic, complemented
5C2×#10622658C211yesmaximal, characteristic, complemented
6C2×#10622584C211yesmaximal, characteristic, complemented
7C2×#10622656C211yesmaximal, characteristic, complemented
8C2×#10622635C211yesmaximal, characteristic, complemented
9C2×#10622707C211yesmaximal, characteristic, complemented
10C2×#10622665C211yesmaximal, characteristic, complemented
11C2×#10622664C211yesmaximal, characteristic, complemented
12C2×#10622643C211yesmaximal, characteristic, complemented
13C2×#10622624C211yesmaximal, characteristic
14C2×#10622577C211yesmaximal, characteristic, complemented
15C22×#66872C211yesmaximal, characteristic, complemented
16C2×C11×#554C211yesmaximal, characteristic
17C11×#554—24no—
18C11×#554C2218yes—
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C11×#125—21no—
21C2×C11×C22⋊Q8—21no—
22C2×C11×C22⋊Q8—21no—
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×C22⋊Q8C2211yescharacteristic
25C2×C4×Q8×C11C2211yescharacteristic
26C2×C4×D4×C11—21no—
27C2×C4×D4×C11C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic
29C22×C11×C4⋊C4C2211yescharacteristic
30C22×#4326C2211yescharacteristic
31C2×#66988—21no—
32C2×#66979C2211yescharacteristic
33C22×C4⋊Dic11C2211yescharacteristic
34C2×#66977C2211yescharacteristic
35C2×#66977C2211yescharacteristic
36C22×#4318C2211yescharacteristic
37C23×C11⋊C8C2211yescharacteristic
38#10623072—24no—
39#10623072C2218yes—
40C2×#66942—21no—
41C2×#66932—21no—
42C2×#66930—21no—
43C2×#66923C2211yescharacteristic
44C2×C4×Dic22C2211yescharacteristic
45C2×#66899C2211yescharacteristic
46C2×#66899C2211yescharacteristic
47C2×#66899C2211yescharacteristic
48C2×C22⋊(C11⋊C8)C2211yescharacteristic
49C2×C22⋊(C11⋊C8)C2211yescharacteristic
50#10622707C2218yescomplemented
51#10622693C2218yescomplemented
52#10622665C2218yescomplemented
53#10622664C2218yescomplemented
54#10622658C2218yescomplemented
55#10622656C2218yescomplemented
56#10622643C2218yescomplemented
57#10622635C2218yescomplemented
58#10622624C2218yes—
59#10622584C2218yescomplemented
60#10622583C2218yescomplemented
61C2×#66874C2211yescharacteristic
62C2×#66874C2211yescharacteristic
63C2×#66874C2211yescharacteristic
64#10622577C2218yescomplemented
65C2×#66872C2211yescharacteristic
66C2×#66872C2211yescharacteristic
67C2×#66872C2211yescharacteristic
68C2×#66872C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×#66872C2211yescharacteristic
71C2×#66872C2218yescomplemented
72C2×#66871C2211yescharacteristic
73C2×#66871C2211yescharacteristic
74C2×#66871C2211yescharacteristic
75C2×C4⋊(C11⋊C8)C2211yescharacteristic
76C2×#66867C2211yescharacteristic
77C22×Q8×C11—21no—
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11D411yescharacteristic
80C23×C4×C11—21no—
81C23×C4×C11—21no—
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×Dic11—21no—
85C22×Dic22C2311yescharacteristic
86C11×C4⋊Q8—22no—
87C11×C4⋊Q8C2314yes—
88C11×#125—28no—
89C11×C22⋊Q8—22no—
90C11×C22⋊Q8—22no—
91C11×C22⋊Q8—28no—
92C11×C22⋊Q8—28no—
93C11×C22⋊Q8C2314yes—
94C11×C22⋊Q8C2314yes—
95C4×Q8×C11—22no—
96C4×Q8×C11C2314yes—
97C4×D4×C11—28no—
98C4×D4×C11D414yes—
99C4×D4×C11C2314yes—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4—22no—
103C2×C11×C4⋊C4—22no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4D411yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2314yes—
113C2×C11×C4⋊C4C2314yes—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4D411yescharacteristic
117C2×C11×C22⋊C4D411yescharacteristic
118C2×C42×C11—21no—
119C2×C42×C11C2311yescharacteristic
120C2×C22⋊Dic11—21no—
121C2×C22⋊Dic11—21no—
122C2×C22⋊Dic11—21no—
123C2×#4326—24no—
124C2×#4326C2314yes—
125#66988—28no—
126#66979—22no—
127#66979C2314yes—
128C2×C4⋊Dic11—21no—
129C2×C4⋊Dic11—22no—
130C2×C4⋊Dic11C2311yescharacteristic
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4⋊Dic11C2311yescharacteristic
133C2×C4⋊Dic11C2314yes—
134#66977—22no—
135#66977—22no—
136#66977C2314yes—
137#66977C2314yes—
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C2×Dic11⋊C4—21no—
142C2×Dic11⋊C4—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#66942—28no—
154#66932—28no—
155#66930—28no—
156#66923—22no—
157#66923C2314yes—
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#66872C2314yes—
173#66872C2314yes—
174#66871C2314yes—
175#66871C2314yes—
176#66871C2314yes—
177C4⋊(C11⋊C8)C2314yes—
178#66867C2314yes—
179C2×#3344—111nomaximal, Sylow
180C24×C11C2×D411yescharacteristic
181C24×C11C2×D411yescharacteristic
182C2×Q8×C11—21no—
183C2×Q8×C11—24no—
184C2×Q8×C11—22no—
185C2×Q8×C11—22no—
186C2×Q8×C11—82no—
187C2×Q8×C11C2412yes—
188C2×D4×C11—24no—
189C2×D4×C11C2×D414yes—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—22no—
193C22×C4×C11—22no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—24no—
199C22×C4×C11—24no—
200C22×C4×C11—82no—
201C22×C4×C11—82no—
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D412yes—
207C22×C4×C11C2×D412yes—
208C22×C4×C11C2412yes—
209C22×C4×C11C2412yes—
210C22×C4×C11C2411yescharacteristic
211C22×Dic11—24no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—44no—
217C2×Dic22—21no—
218C2×Dic22—22no—
219C2×Dic22—22no—
220C2×Dic22C2412yes—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—24no—
223C11×C4⋊C4—24no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—24no—
227C11×C4⋊C4—24no—
228C11×C4⋊C4—24no—
229C11×C4⋊C4—24no—
230C11×C4⋊C4C2×D414yes—
231C11×C4⋊C4C2412yes—
232C11×C4⋊C4C2412yes—
233C11×C4⋊C4C2412yes—
234C11×C22⋊C4—24no—
235C11×C22⋊C4—24no—
236C11×C22⋊C4C2×D414yes—
237C11×C22⋊C4C2×D414yes—
238C42×C11—24no—
239C42×C11C2×D412yes—
240C42×C11C2412yes—
241C22⋊Dic11—24no—
242C22⋊Dic11—24no—
243C22⋊Dic11—24no—
244#4326—28no—
245C4⋊Dic11—21no—
246C4⋊Dic11—21no—
247C4⋊Dic11—21no—
248C4⋊Dic11—24no—
249C4⋊Dic11C2412yes—
250C4⋊Dic11C2412yes—
251C4⋊Dic11C2412yes—
252Dic11⋊C4—24no—
253Dic11⋊C4—24no—
254Dic11⋊C4—24no—
255Dic11⋊C4—24no—
256Dic11⋊C4—24no—
257C4×Dic11—24no—
258C4×Dic11—24no—
259#4318—28no—
260C2×C11⋊C8—28no—
261C2×C11⋊C8—22no—
262C2×C11⋊C8—22no—
263C2×C11⋊C8—22no—
264C2×C11⋊C8#4114yes—
265C2×C11⋊C8C2412yes—
266C2×C11⋊C8C2412yes—
267C2×C11⋊C8C2412yes—
268C2×C11⋊C8C2412yes—
269C2×#554D1111yescharacteristic
270C2×#552—111no—
271#3344—1116no—
272C2×#501—111no—
273C2×#484—111no—
274C2×#485—111no—
275C2×#483—111no—
276C2×#483—111no—
277C2×#479—111no—
278C2×#475—111no—
279C2×#470—111no—
280C2×#467—111no—
281C2×#441—111no—
282C2×#435—111no—
283C2×#428—111no—
284C22×#106—111no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11—22no—
290C23×C11#13714yes—
291C23×C11C22×D412yes—
292C23×C11C22×D412yes—
293C23×C11C22×D411yescharacteristic
294Q8×C11—22no—
295Q8×C11—22no—
296Q8×C11—42no—
297Q8×C11—84no—
298D4×C11—28no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—24no—
304C2×C4×C11—24no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11—42no—
317C2×C4×C11—84no—
318C2×C4×C11—84no—
319C2×C4×C11C22×D412yes—
320C2×C4×C11C22×D412yes—
321C2×C4×C11C22×D412yes—
322C2×C4×C11C22×D412yes—
323C2×C4×C11C22×D411yescharacteristic
324C2×C4×C11C2×#4112yes—
325C2×C4×C112−1+412yes—
326C2×C4×C11C2511yescharacteristic
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—42no—
332C2×Dic11—48no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336Dic22—22no—
337Dic22—22no—
338Dic22—42no—
339C11⋊C8—22no—
340C11⋊C8—22no—
341C11⋊C8—22no—
342C11⋊C8C2×#4114yes—
343C22×Q16—111no—
344C22×M16—111no—
345C23×C8—111no—
346#554—24no—
347#554C2×D1118yes—
348#552—118no—
349#552—224no—
350C2×C4⋊Q8C2×D1111yescharacteristic
351C2×#126—221no—
352C2×#125—21no—
353C2×#125—111no—
354C2×#125—221no—
355C2×#123—221no—
356C2×C22⋊Q8—21no—
357C2×C22⋊Q8—21no—
358C2×C22⋊Q8—111no—
359C2×C22⋊Q8—111no—
360C2×C22⋊Q8C2×D1111yescharacteristic
361C2×C22⋊Q8C2×D1111yescharacteristic
362C2×C4×Q8—111no—
363C2×C4×Q8C2×D1111yescharacteristic
364C2×C4×D4—21no—
365C2×C4×D4C2×D1111yescharacteristic
366C2×#117—111no—
367C2×#117—221no—
368C22×C4⋊C4—111no—
369C22×C4⋊C4C2×D1111yescharacteristic
370C22×C4⋊C4C2×D1111yescharacteristic
371#501—118no—
372#485—118no—
373#484—118no—
374#483—118no—
375#483—118no—
376#479—118no—
377#475—118no—
378#470—118no—
379#467—118no—
380#441—118no—
381#435—118no—
382#428—118no—
383C2×#107—111no—
384C2×#107—111no—
385C2×#107—111no—
386C2×#106—111no—
387C2×#106—111no—
388C2×#106—111no—
389C2×#106—111no—
390C2×#106—118no—
391C2×#106—111no—
392C2×#106—111no—
393C2×C4⋊C8—111no—
394C2×#103—111no—
395C2×#103—111no—
396C2×#103—111no—
397C2×#103—111no—
398C2×#103—111no—
399C2×#103—111no—
400C2×C22⋊C8—111no—
401C2×C22⋊C8—111no—
402C2×#97—111no—
403C22×C11—28no—
404C22×C11—22no—
405C22×C11—22no—
406C22×C11—22no—
407C22×C11—22no—
408C22×C11—22no—
409C22×C11—44no—
410C22×C11#54712yes—
411C22×C11C2×#13714yes—
412C22×C11C2×#13712yes—
413C22×C11#57712yes—
414C22×C11C23×D411yescharacteristic
415C4×C11—22no—
416C4×C11—22no—
417C4×C11—22no—
418C4×C11—22no—
419C4×C11—42no—
420C4×C11—42no—
421C4×C11—42no—
422C4×C11—42no—
423C4×C11#54712yes—
424C4×C11C22×#4111yescharacteristic
425C4×C11C2×2−1+411yescharacteristic
426Dic11—42no—
427Dic11—42no—
428Dic11—42no—
429Dic11—42no—
430C22×Q8—21no—
431C22×Q8—111no—
432C22×Q8C22×D1111yescharacteristic
433C22×D4C22⋊D1111yescharacteristic
434C23×C4—21no—
435C23×C4—21no—
436C23×C4—221no—
437C23×C4C22×D1111yescharacteristic
438C23×C4C22×D1111yescharacteristic
439C2×Q16—114no—
440C2×Q16—224no—
441C2×M16—114no—
442C2×M16—224no—
443C22×C8—111no—
444C22×C8—111no—
445C22×C8—114no—
446C22×C8—111no—
447C22×C8—111no—
448C22×C8—224no—
449C4⋊Q8—22no—
450C4⋊Q8C22×D1114yes—
451#126—228no—
452#125—28no—
453#125—114no—
454#125—228no—
455#125—222no—
456#123—228no—
457C22⋊Q8—22no—
458C22⋊Q8—22no—
459C22⋊Q8—28no—
460C22⋊Q8—28no—
461C22⋊Q8—114no—
462C22⋊Q8—114no—
463C22⋊Q8—222no—
464C22⋊Q8—222no—
465C22⋊Q8C22×D1114yes—
466C22⋊Q8C22×D1114yes—
467C4×Q8—22no—
468C4×Q8—114no—
469C4×Q8—222no—
470C4×Q8C22×D1114yes—
471C4×D4—28no—
472C4×D4C22⋊D1114yes—
473C4×D4C22×D1114yes—
474#117—114no—
475#117—222no—
476#117—228no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—111no—
486C2×C4⋊C4—111no—
487C2×C4⋊C4—114no—
488C2×C4⋊C4—111no—
489C2×C4⋊C4—221no—
490C2×C4⋊C4—222no—
491C2×C4⋊C4—221no—
492C2×C4⋊C4—221no—
493C2×C4⋊C4—221no—
494C2×C4⋊C4—221no—
495C2×C4⋊C4—221no—
496C2×C4⋊C4C22⋊D1111yescharacteristic
497C2×C4⋊C4C22×D1111yescharacteristic
498C2×C4⋊C4C22×D1111yescharacteristic
499C2×C4⋊C4C22×D1111yescharacteristic
500C2×C4⋊C4C22×D1114yes—
501C2×C4⋊C4C22×D1114yes—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—221no—
505C2×C22⋊C4—221no—
506C2×C22⋊C4—221no—
507C2×C22⋊C4C22⋊D1111yescharacteristic
508C2×C22⋊C4C22⋊D1111yescharacteristic
509C2×C42—21no—
510C2×C42—221no—
511C2×C42—221no—
512C2×C42C22×D1111yescharacteristic
513#107—114no—
514#107—114no—
515#107—114no—
516#106—114no—
517#106—114no—
518#106—114no—
519#106—114no—
520#106—114no—
521#106—114no—
522C4⋊C8—114no—
523#103—114no—
524#103—114no—
525#103—114no—
526#103—114no—
527#103—114no—
528#103—114no—
529C22⋊C8—114no—
530C22⋊C8—114no—
531#97—114no—
532C2×C11—24no—
533C2×C11—42no—
534C2×C11#334414yescomplemented
535C2×C11C2×#54711yescharacteristic
536C2×C11C22×#13711yescharacteristic
537C2×C11C2×#57711yescharacteristic
538C24C2×C22⋊D1111yescharacteristic
539C24C2×C22⋊D1111yescharacteristic
540C2×Q8—21no—
541C2×Q8—24no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—82no—
545C2×Q8—112no—
546C2×Q8—221no—
547C2×Q8—222no—
548C2×Q8—222no—
549C2×Q8C23×D1112yes—
550C2×D4—24no—
551C2×D4C2×C22⋊D1114yes—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—82no—
563C22×C4—82no—
564C22×C4—224no—
565C22×C4—221no—
566C22×C4—221no—
567C22×C4—221no—
568C22×C4—221no—
569C22×C4—444no—
570C22×C4C2×C22⋊D1112yes—
571C22×C4C2×C22⋊D1112yes—
572C22×C4C2×C22⋊D1111yescharacteristic
573C22×C4C2×C22⋊D1111yescharacteristic
574C22×C4C2×C22⋊D1111yescharacteristic
575C22×C4C2×C22⋊D1111yescharacteristic
576C22×C4C23×D1112yes—
577C22×C4C23×D1112yes—
578C22×C4C23×D1111yescharacteristic
579Q16—228no—
580M16—228no—
581C2×C8—114no—
582C2×C8—112no—
583C2×C8—112no—
584C2×C8—112no—
585C2×C8—112no—
586C2×C8—228no—
587C2×C8—222no—
588C2×C8—222no—
589C2×C8—222no—
590C4⋊C4—21no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—112no—
600C4⋊C4—112no—
601C4⋊C4—112no—
602C4⋊C4—221no—
603C4⋊C4—221no—
604C4⋊C4—224no—
605C4⋊C4—221no—
606C4⋊C4—224no—
607C4⋊C4—224no—
608C4⋊C4—224no—
609C4⋊C4—224no—
610C4⋊C4—224no—
611C4⋊C4C2×C22⋊D1114yes—
612C4⋊C4C23×D1112yes—
613C4⋊C4C23×D1112yes—
614C4⋊C4C23×D1112yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—224no—
618C22⋊C4—224no—
619C22⋊C4—224no—
620C22⋊C4C2×C22⋊D1114yes—
621C22⋊C4C2×C22⋊D1114yes—
622C42—24no—
623C42—224no—
624C42—224no—
625C42C2×C22⋊D1112yes—
626C42C23×D1112yes—
627C11C2×#334411yescharacteristic, complemented, Sylow
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23#6699514yes—
634C23C22×C22⋊D1112yes—
635C23C22×C22⋊D1112yes—
636C23C22×C22⋊D1111yescharacteristic
637Q8—22no—
638Q8—22no—
639Q8—42no—
640Q8—84no—
641Q8—222no—
642Q8—222no—
643Q8—442no—
644D4—28no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—84no—
664C2×C4—84no—
665C2×C4—222no—
666C2×C4—222no—
667C2×C4—222no—
668C2×C4—222no—
669C2×C4—448no—
670C2×C4—442no—
671C2×C4—442no—
672C2×C4—442no—
673C2×C4—442no—
674C2×C4#41×D1112yes—
675C2×C4#6704312yes—
676C2×C4C22×C22⋊D1112yes—
677C2×C4C22×C22⋊D1112yes—
678C2×C4C22×C22⋊D1112yes—
679C2×C4C22×C22⋊D1112yes—
680C2×C4C22×C22⋊D1111yescharacteristic
681C2×C4C24×D1111yescharacteristic
682C8—114no—
683C8—222no—
684C8—222no—
685C8—222no—
686C22—22no—
687C22—28no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—44no—
693C22C2×#6699514yes—
694C22C2×#6699512yes—
695C22#1062335512yes—
696C22#1062336712yes—
697C22C23×C22⋊D1111yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—442no—
707C4—442no—
708C4—442no—
709C4—442no—
710C4#1062335512yes—
711C4C2×#41×D1111yescharacteristic
712C4C2×#6704311yescharacteristic
713C2—24no—
714C2—42no—
715C2#1308106514yesdirect product factor
716C2C2×#1062335511yescharacteristic
717C2C22×#6699511yescharacteristic
718C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#554C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenterC2×#554D11
hypocenterC11C2×#3344
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
2. #13081065C2direct (N × H)
3. C2×#10622693C2semidirect
4. C2×#10622583C2semidirect
5. C2×#10622658C2semidirect
6. C2×#10622584C2semidirect
7. C2×#10622656C2semidirect
8. C2×#10622635C2semidirect
9. C2×#10622707C2semidirect
10. C2×#10622665C2semidirect
11. C2×#10622664C2semidirect
12. C2×#10622643C2semidirect
14. C2×#10622577C2semidirect
15. C22×#66872C2semidirect
50. #10622707C22semidirect
51. #10622693C22semidirect
52. #10622665C22semidirect
53. #10622664C22semidirect
54. #10622658C22semidirect
55. #10622656C22semidirect
56. #10622643C22semidirect
57. #10622635C22semidirect
59. #10622584C22semidirect
60. #10622583C22semidirect
64. #10622577C22semidirect
71. C2×#66872C22semidirect
534. C2×C11#3344semidirect
627. C11C2×#3344semidirect
715. C2#13081065direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230722
#130810652
C2×#106226932
C2×#106225832
C2×#106226582
C2×#106225842
C2×#106226562
C2×#106226352
C2×#106227072
C2×#106226652
C2×#106226642
C2×#106226432
C2×#106226242
C2×#106225772
C22×#668722
C2×C11×#5542
C2×#334411