Finite Group Databasebeta

← C2×#13073064 #14923295

Subgroups — C2×#13073064 #14923295

Order 2816.

2702 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
1C22×#66931C211yesmaximal, characteristic
2C22×#66930C211yesmaximal, characteristic
3#13073064C2116yesmaximal, direct product factor
4C2×#10622565C211yesmaximal, characteristic
5C2×#10622565C211yesmaximal, characteristic
6C2×#10622566C211yesmaximal, characteristic
7C2×#10622259C211yesmaximal, characteristic, complemented
8C2×#10622259C211yesmaximal, characteristic, complemented
9C2×#10622268C211yesmaximal, characteristic, complemented
10C2×#10622594C211yesmaximal, characteristic, complemented
11C2×#10622267C211yesmaximal, characteristic, complemented
12C2×#10622265C211yesmaximal, characteristic, complemented
13C2×#10622589C211yesmaximal, characteristic, complemented
14C2×#10622263C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic11C211yesmaximal, characteristic
16C2×C11×#397C211yesmaximal, characteristic
17C24×Dic11C2211yescharacteristic
18C23×Dic22C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic
38C2×#66931—28no—
39C2×#66931C2218yes—
40C2×#66930—28no—
41C2×#66930C2218yes—
42C11×#397C2218yes—
43C2×C11×#95C2211yescharacteristic
44C2×C11×#95C2211yescharacteristic
45C2×C11×#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57#10622594C2218yescomplemented
58#10622589C2218yescomplemented
59#10622566C2218yes—
60#10622565C2218yes—
61#10622565C2218yes—
62C22⋊C4×Dic11C2218yes—
63#10622268C2218yescomplemented
64#10622267C2218yescomplemented
65#10622265C2218yescomplemented
66#10622263C2218yescomplemented
67#10622259C2218yescomplemented
68#10622259C2218yescomplemented
69C25×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×Dic11—24no—
77C23×Dic11—24no—
78C23×Dic11D418yes—
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2314yes—
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C22×Dic22—24no—
89C22×Dic22—24no—
90C22×Dic22—24no—
91C22×Dic22C2314yes—
92C2×C11×C4⋊C4—24no—
93C2×C11×C4⋊C4C2314yes—
94C2×C11×C22⋊C4—24no—
95C2×C11×C22⋊C4—24no—
96C2×C11×C22⋊C4—24no—
97C2×C11×C22⋊C4C2314yes—
98C2×C11×C22⋊C4C2314yes—
99C2×C11×C22⋊C4C2314yes—
100C2×C22⋊Dic11—24no—
101C2×C22⋊Dic11—24no—
102C2×C22⋊Dic11—24no—
103C2×C22⋊Dic11C2314yes—
104C2×C22⋊Dic11C2314yes—
105C2×C22⋊Dic11C2314yes—
106C2×C4⋊Dic11—24no—
107C2×C4⋊Dic11—24no—
108C2×C4⋊Dic11C2314yes—
109C2×C4⋊Dic11C2314yes—
110C2×Dic11⋊C4—24no—
111C2×Dic11⋊C4—24no—
112C2×Dic11⋊C4—24no—
113C2×Dic11⋊C4—24no—
114C2×Dic11⋊C4—24no—
115C2×Dic11⋊C4—24no—
116C2×Dic11⋊C4C2314yes—
117C2×Dic11⋊C4C2314yes—
118C2×Dic11⋊C4C2314yes—
119C2×Dic11⋊C4C2314yes—
120C2×Dic11⋊C4C2314yes—
121C2×Dic11⋊C4C2314yes—
122C2×C4×Dic11—24no—
123C2×C4×Dic11—24no—
124C2×C4×Dic11—24no—
125C2×C4×Dic11—24no—
126C2×C4×Dic11C2314yes—
127C2×C4×Dic11C2314yes—
128C2×C4×Dic11C2314yes—
129C2×C4×Dic11C2314yes—
130#66931—232no—
131#66930—232no—
132C11×#95C2314yes—
133C11×#95C2314yes—
134C11×#95C2314yes—
135C11⋊#95C2314yes—
136C11⋊#95C2314yes—
137C11⋊#95C2314yes—
138C11⋊#95C2314yes—
139C11⋊#95C2314yes—
140C11⋊#95C2314yes—
141C11⋊#95C2314yes—
142C11⋊#95C2314yes—
143C11⋊#95C2314yes—
144C11⋊#95C2314yes—
145C11⋊#95C2314yes—
146C2×#2499—111nomaximal, Sylow
147C24×C11—22no—
148C24×C11—22no—
149C24×C11—22no—
150C24×C11—22no—
151C24×C11—22no—
152C24×C11—22no—
153C24×C11C2×D414yes—
154C24×C11C2412yes—
155C24×C11C2411yescharacteristic
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11#4114yes—
174C22×C4×C11C2412yes—
175C22×C4×C11C2412yes—
176C22×C4×C11C2412yes—
177C22×C4×C11C2412yes—
178C22×C4×C11C2412yes—
179C22×C4×C11C2412yes—
180C22×Dic11—232no—
181C22×Dic11—28no—
182C22×Dic11—28no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—22no—
195C22×Dic11—22no—
196C22×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11C2×D4116yes—
203C22×Dic11C2×D414yes—
204C22×Dic11C2×D414yes—
205C22×Dic11#4114yes—
206C22×Dic11#4114yes—
207C22×Dic11#4114yes—
208C22×Dic11C2412yes—
209C22×Dic11C2412yes—
210C22×Dic11C2412yes—
211C22×Dic11C2412yes—
212C22×Dic11C2412yes—
213C22×Dic11C2412yes—
214C22×Dic11C2412yes—
215C22×Dic11C2412yes—
216C2×Dic22—28no—
217C2×Dic22—28no—
218C2×Dic22—28no—
219C2×Dic22—416no—
220C11×C4⋊C4—28no—
221C11×C22⋊C4—28no—
222C11×C22⋊C4—28no—
223C11×C22⋊C4—28no—
224C22⋊Dic11—28no—
225C22⋊Dic11—28no—
226C22⋊Dic11—28no—
227C4⋊Dic11—28no—
228C4⋊Dic11—28no—
229Dic11⋊C4—28no—
230Dic11⋊C4—28no—
231Dic11⋊C4—28no—
232Dic11⋊C4—28no—
233Dic11⋊C4—28no—
234Dic11⋊C4—28no—
235C4×Dic11—28no—
236C4×Dic11—28no—
237C4×Dic11—28no—
238C4×Dic11—28no—
239C22×C22⋊Q8—111no—
240C22×#117—111no—
241#2499—1116no—
242C2×#397—111no—
243C2×#397—111no—
244C2×#397—111no—
245C2×#397D1111yescharacteristic
246C2×#391—111no—
247C2×#391—111no—
248C2×#387—111no—
249C2×#387—111no—
250C2×#387—111no—
251C2×#387—111no—
252C2×#384—111no—
253C2×#382—111no—
254C2×C4×C22⋊C4—111no—
255C23×C11—28no—
256C23×C11—28no—
257C23×C11—28no—
258C23×C11—22no—
259C23×C11—22no—
260C23×C11—22no—
261C23×C11—22no—
262C23×C11—22no—
263C23×C11—22no—
264C23×C11—44no—
265C23×C11—44no—
266C23×C11—44no—
267C23×C11—44no—
268C23×C11C22×D414yes—
269C23×C11C22×D412yes—
270C23×C11C2×#4112yes—
271C23×C11C2×#4112yes—
272C23×C11C2×#4112yes—
273C23×C11C2×#4112yes—
274C23×C112−1+412yes—
275C23×C112−1+412yes—
276C23×C11C2511yescharacteristic
277C2×C4×C11—28no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—44no—
296C2×C4×C11—44no—
297C2×C4×C11—44no—
298C2×C4×C11—44no—
299C2×C4×C11—44no—
300C2×C4×C11C2×#4114yes—
301C2×Dic11—28no—
302C2×Dic11—28no—
303C2×Dic11—22no—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11—22no—
307C2×Dic11—232no—
308C2×Dic11—22no—
309C2×Dic11—22no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—44no—
324C2×Dic11—44no—
325C2×Dic11—44no—
326C2×Dic11—44no—
327C2×Dic11—44no—
328C2×Dic11#123116yes—
329C2×Dic11C22×D414yes—
330C2×Dic11C22×D414yes—
331C2×Dic11C2×#4114yes—
332C2×Dic11C2×#4114yes—
333C2×Dic11C2×#4114yes—
334Dic22—416no—
335C23×Q8—111no—
336C24×C4—111no—
337C2×C22⋊Q8—118no—
338C2×C22⋊Q8—228no—
339C2×#117—118no—
340C2×#117—228no—
341C22×C4⋊C4—111no—
342C22×C4⋊C4—111no—
343C22×C4⋊C4—111no—
344C22×C4⋊C4—111no—
345C22×C4⋊C4—111no—
346C22×C4⋊C4—111no—
347C22×C4⋊C4—111no—
348C22×C4⋊C4—111no—
349C22×C4⋊C4C2×D1111yescharacteristic
350C22×C22⋊C4—111no—
351C22×C22⋊C4—111no—
352C22×C22⋊C4—111no—
353C22×C22⋊C4C2×D1111yescharacteristic
354C22×C22⋊C4C2×D1111yescharacteristic
355C22×C22⋊C4C2×D1111yescharacteristic
356C22×C42—111no—
357C22×C42—111no—
358C22×C42—111no—
359C22×C42—111no—
360#397—118no—
361#397—118no—
362#397—118no—
363#397C2×D1118yes—
364#391—118no—
365#391—118no—
366#387—118no—
367#387—118no—
368#387—118no—
369#387—118no—
370#384—118no—
371#382—118no—
372C4×C22⋊C4—118no—
373C2×#95—111no—
374C2×#95—111no—
375C2×#95—111no—
376C2×#95—111no—
377C2×#95—111no—
378C2×#95—111no—
379C2×#95—111no—
380C2×#95—111no—
381C2×#95—111no—
382C2×#95—111no—
383C2×#95—111no—
384C2×#95C2×D1111yescharacteristic
385C2×#95C2×D1111yescharacteristic
386C2×#95C2×D1111yescharacteristic
387C22×C11—24no—
388C22×C11—24no—
389C22×C11—24no—
390C22×C11—42no—
391C22×C11—42no—
392C22×C11—42no—
393C22×C11—42no—
394C22×C11—416no—
395C22×C11C2×#12314yes—
396C22×C11#53214yes—
397C22×C11#53614yes—
398C22×C11#55214yes—
399C22×C11#55214yes—
400C22×C11#55614yes—
401C22×C11#55614yes—
402C22×C11C23×D411yescharacteristic
403C22×C11C22×#4111yescharacteristic
404C22×C11C22×#4111yescharacteristic
405C22×C11C22×#4111yescharacteristic
406C22×C11C22×#4111yescharacteristic
407C22×C11C2×2−1+411yescharacteristic
408C22×C11C2×2−1+411yescharacteristic
409C4×C11—24no—
410C4×C11—42no—
411C4×C11—42no—
412C4×C11—42no—
413C4×C11—42no—
414C4×C11—42no—
415Dic11—24no—
416Dic11—24no—
417Dic11—42no—
418Dic11—42no—
419Dic11—42no—
420Dic11—42no—
421Dic11—42no—
422Dic11C2×#12318yes—
423C25C22×D1111yescharacteristic
424C22×Q8—114no—
425C22×Q8—224no—
426C22×Q8—224no—
427C22×Q8—224no—
428C23×C4—111no—
429C23×C4—118no—
430C23×C4—114no—
431C23×C4—111no—
432C23×C4—111no—
433C23×C4—111no—
434C23×C4—111no—
435C23×C4—111no—
436C23×C4—111no—
437C23×C4—111no—
438C23×C4—224no—
439C23×C4—224no—
440C23×C4C22×D1111yescharacteristic
441C23×C4C22×D1111yescharacteristic
442C23×C4C22×D1111yescharacteristic
443C23×C4C22×D1111yescharacteristic
444C23×C4C22×D1111yescharacteristic
445C23×C4C22×D1111yescharacteristic
446C22⋊Q8—2232no—
447#117—2232no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—114no—
450C2×C4⋊C4—114no—
451C2×C4⋊C4—114no—
452C2×C4⋊C4—114no—
453C2×C4⋊C4—114no—
454C2×C4⋊C4—114no—
455C2×C4⋊C4—114no—
456C2×C4⋊C4—114no—
457C2×C4⋊C4—224no—
458C2×C4⋊C4—224no—
459C2×C4⋊C4—224no—
460C2×C4⋊C4—224no—
461C2×C4⋊C4—224no—
462C2×C4⋊C4—224no—
463C2×C4⋊C4—224no—
464C2×C4⋊C4—224no—
465C2×C4⋊C4C22×D1114yes—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—114no—
470C2×C22⋊C4—114no—
471C2×C22⋊C4—114no—
472C2×C22⋊C4—224no—
473C2×C22⋊C4—224no—
474C2×C22⋊C4—224no—
475C2×C22⋊C4C22×D1114yes—
476C2×C22⋊C4C22×D1114yes—
477C2×C22⋊C4C22×D1114yes—
478C2×C42—114no—
479C2×C42—114no—
480C2×C42—114no—
481C2×C42—114no—
482C2×C42—224no—
483C2×C42—224no—
484C2×C42—224no—
485C2×C42—224no—
486#95—114no—
487#95—114no—
488#95—114no—
489#95—114no—
490#95—114no—
491#95—114no—
492#95—114no—
493#95—114no—
494#95—114no—
495#95—114no—
496#95—114no—
497#95C22×D1114yes—
498#95C22×D1114yes—
499#95C22×D1114yes—
500C2×C11—44no—
501C2×C11#249918yescomplemented
502C2×C11C22×#12311yescharacteristic
503C2×C11C2×#53211yescharacteristic
504C2×C11C2×#53611yescharacteristic
505C2×C11C2×#55211yescharacteristic
506C2×C11C2×#55211yescharacteristic
507C2×C11C2×#55611yescharacteristic
508C2×C11C2×#55611yescharacteristic
509C24—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24D4×D1114yes—
516C24C23×D1112yes—
517C24C23×D1111yescharacteristic
518C2×Q8—228no—
519C2×Q8—228no—
520C2×Q8—228no—
521C2×Q8—4416no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—114no—
540C22×C4—114no—
541C22×C4—114no—
542C22×C4—112no—
543C22×C4—114no—
544C22×C4—1116no—
545C22×C4—114no—
546C22×C4—112no—
547C22×C4—112no—
548C22×C4—112no—
549C22×C4—112no—
550C22×C4—112no—
551C22×C4—112no—
552C22×C4—112no—
553C22×C4—2232no—
554C22×C4—228no—
555C22×C4—228no—
556C22×C4—222no—
557C22×C4—222no—
558C22×C4—222no—
559C22×C4—222no—
560C22×C4—222no—
561C22×C4—222no—
562C22×C4—222no—
563C22×C4—222no—
564C22×C4—222no—
565C22×C4—222no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—222no—
574C22×C4—222no—
575C22×C4#434114yes—
576C22×C4C23×D1112yes—
577C22×C4C23×D1112yes—
578C22×C4C23×D1112yes—
579C22×C4C23×D1112yes—
580C22×C4C23×D1112yes—
581C22×C4C23×D1112yes—
582C4⋊C4—28no—
583C4⋊C4—228no—
584C4⋊C4—228no—
585C4⋊C4—228no—
586C4⋊C4—228no—
587C4⋊C4—228no—
588C4⋊C4—228no—
589C4⋊C4—228no—
590C4⋊C4—228no—
591C22⋊C4—28no—
592C22⋊C4—28no—
593C22⋊C4—28no—
594C22⋊C4—228no—
595C22⋊C4—228no—
596C22⋊C4—228no—
597C42—228no—
598C42—228no—
599C42—228no—
600C42—228no—
601C11C2×#249911yescharacteristic, complemented, Sylow
602C23—28no—
603C23—28no—
604C23—28no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—44no—
612C23—44no—
613C23—44no—
614C23—44no—
615C23C2×D4×D1114yes—
616C23C2×D4×D1112yes—
617C23C2×#434112yes—
618C23#41×D1112yes—
619C23#41×D1112yes—
620C23#41×D1112yes—
621C23#6704312yes—
622C23#6704312yes—
623C23C24×D1111yescharacteristic
624Q8—4416no—
625C2×C4—28no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—44no—
647C2×C4—44no—
648C2×C4—1116no—
649C2×C4—114no—
650C2×C4—114no—
651C2×C4—114no—
652C2×C4—114no—
653C2×C4—114no—
654C2×C4—2232no—
655C2×C4—228no—
656C2×C4—228no—
657C2×C4—222no—
658C2×C4—222no—
659C2×C4—222no—
660C2×C4—222no—
661C2×C4—222no—
662C2×C4—222no—
663C2×C4—222no—
664C2×C4—222no—
665C2×C4—222no—
666C2×C4—222no—
667C2×C4—222no—
668C2×C4—222no—
669C2×C4—222no—
670C2×C4—222no—
671C2×C4—222no—
672C2×C4—222no—
673C2×C4—222no—
674C2×C4—222no—
675C2×C4—222no—
676C2×C4—444no—
677C2×C4—444no—
678C2×C4—444no—
679C2×C4—444no—
680C2×C4—444no—
681C2×C4C2×#434114yes—
682C22—24no—
683C22—24no—
684C22—24no—
685C22—42no—
686C22—42no—
687C22—42no—
688C22—42no—
689C22—416no—
690C22#1062312714yes—
691C22#1062317914yes—
692C22#1062318114yes—
693C22D11×#12314yes—
694C22#1062320214yes—
695C22#1062323314yes—
696C22#1062323914yes—
697C22C22×D4×D1111yescharacteristic
698C22C22×#434111yescharacteristic
699C22C2×#41×D1111yescharacteristic
700C22C2×#41×D1111yescharacteristic
701C22C2×#41×D1111yescharacteristic
702C22C2×#6704311yescharacteristic
703C22C2×#6704311yescharacteristic
704C4—24no—
705C4—42no—
706C4—42no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—118no—
711C4—224no—
712C4—224no—
713C4—442no—
714C4—442no—
715C4—442no—
716C4—442no—
717C4—442no—
718C2—44no—
719C2#1307306418yesdirect product factor
720C2C2×D11×#12311yescharacteristic
721C2C2×#1062312711yescharacteristic
722C2C2×#1062317911yescharacteristic
723C2C2×#1062323911yescharacteristic
724C2C2×#1062318111yescharacteristic
725C2C2×#1062323311yescharacteristic
726C2C2×#1062320211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#397C2
socleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#397D11
hypocenterC11C2×#2499
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
3. #13073064C2direct (N × H)
7. C2×#10622259C2semidirect
8. C2×#10622259C2semidirect
9. C2×#10622268C2semidirect
10. C2×#10622594C2semidirect
11. C2×#10622267C2semidirect
12. C2×#10622265C2semidirect
13. C2×#10622589C2semidirect
14. C2×#10622263C2semidirect
57. #10622594C22semidirect
58. #10622589C22semidirect
63. #10622268C22semidirect
64. #10622267C22semidirect
65. #10622265C22semidirect
66. #10622263C22semidirect
67. #10622259C22semidirect
68. #10622259C22semidirect
501. C2×C11#2499semidirect
601. C11C2×#2499semidirect
719. C2#13073064direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669312
C22×#669302
#130730642
C2×#106225652
C2×#106225662
C2×#106222592
C2×#106222682
C2×#106225942
C2×#106222672
C2×#106222652
C2×#106225892
C2×#106222632
C2×C22⋊C4×Dic112
C2×C11×#3972
C2×#249911