Finite Group Databasebeta

← C2×#13072791 #14922228

Subgroups — C2×#13072791 #14922228

Order 2816.

2638 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66923C211yesmaximal, characteristic, complemented
2C22×#66930C211yesmaximal, characteristic
3#13072791C2116yesmaximal, direct product factor
4C2×#10622271C211yesmaximal, characteristic, complemented
5C2×#10622597C211yesmaximal, characteristic, complemented
6C2×#10622565C211yesmaximal, characteristic
7C2×#10622561C211yesmaximal, characteristic
8C2×#10622260C211yesmaximal, characteristic, complemented
9C2×#10622558C211yesmaximal, characteristic
10C2×#10622594C211yesmaximal, characteristic, complemented
11C2×#10622266C211yesmaximal, characteristic, complemented
12C2×#10622265C211yesmaximal, characteristic, complemented
13C2×#10622563C211yesmaximal, characteristic
14C2×#10622559C211yesmaximal, characteristic
15C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
16C2×C11×#388C211yesmaximal, characteristic
17C24×Dic11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C42×C11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×C4⋊Dic11C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C2×#66930—28no—
41C2×#66930C2218yes—
42C2×#66923—28no—
43C2×#66923C2218yescomplemented
44C11×#388C2218yes—
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#10622597C2218yescomplemented
58#10622594C2218yescomplemented
59#10622565C2218yes—
60#10622563C2218yes—
61#10622561C2218yes—
62#10622559C2218yes—
63#10622558C2218yes—
64C4×Dic11⋊C4C2218yescomplemented
65#10622271C2218yescomplemented
66#10622266C2218yescomplemented
67#10622265C2218yescomplemented
68#10622260C2218yescomplemented
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×Dic11—24no—
79C23×Dic11C2314yes—
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C2×C11×C4⋊C4—24no—
89C2×C11×C4⋊C4C2314yes—
90C2×C11×C22⋊C4—24no—
91C2×C11×C22⋊C4—24no—
92C2×C11×C22⋊C4—24no—
93C2×C11×C22⋊C4C2314yes—
94C2×C11×C22⋊C4C2314yes—
95C2×C11×C22⋊C4C2314yes—
96C2×C42×C11—24no—
97C2×C42×C11C2314yes—
98C2×C22⋊Dic11—24no—
99C2×C22⋊Dic11—24no—
100C2×C22⋊Dic11—24no—
101C2×C22⋊Dic11C2314yes—
102C2×C22⋊Dic11C2314yes—
103C2×C22⋊Dic11C2314yes—
104C2×C4⋊Dic11—24no—
105C2×C4⋊Dic11—24no—
106C2×C4⋊Dic11—24no—
107C2×C4⋊Dic11C2314yes—
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⋊C4—24no—
117C2×Dic11⋊C4D418yes—
118C2×Dic11⋊C4C2314yes—
119C2×Dic11⋊C4C2314yes—
120C2×Dic11⋊C4C2314yes—
121C2×Dic11⋊C4C2314yes—
122C2×Dic11⋊C4C2314yes—
123C2×Dic11⋊C4C2314yes—
124C2×Dic11⋊C4C2314yes—
125C2×Dic11⋊C4C2314yes—
126C2×C4×Dic11—24no—
127C2×C4×Dic11—24no—
128C2×C4×Dic11—24no—
129C2×C4×Dic11C2314yes—
130C2×C4×Dic11C2314yes—
131C2×C4×Dic11C2314yes—
132#66930—232no—
133#66923—232no—
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×#2475—111nomaximal, Sylow
147C24×C11—22no—
148C24×C11—22no—
149C24×C11—22no—
150C24×C11—22no—
151C24×C11—22no—
152C24×C11—22no—
153C24×C11#4114yes—
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×C11C2×D414yes—
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—28no—
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×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11C2×D414yes—
205C22×Dic11C2×D414yes—
206C22×Dic11#4114yes—
207C22×Dic11#4114yes—
208C22×Dic11C2412yes—
209C22×Dic11C2412yes—
210C22×Dic11C2412yes—
211C22×Dic11C2412yes—
212C22×Dic11C2412yes—
213C22×Dic11C2412yes—
214C22×Dic11C2412yes—
215C22×Dic11C2412yes—
216C11×C4⋊C4—28no—
217C11×C22⋊C4—28no—
218C11×C22⋊C4—28no—
219C11×C22⋊C4—28no—
220C42×C11—28no—
221C22⋊Dic11—28no—
222C22⋊Dic11—28no—
223C22⋊Dic11—28no—
224C4⋊Dic11—28no—
225C4⋊Dic11—28no—
226C4⋊Dic11—28no—
227Dic11⋊C4—28no—
228Dic11⋊C4—28no—
229Dic11⋊C4—28no—
230Dic11⋊C4—28no—
231Dic11⋊C4—28no—
232Dic11⋊C4—28no—
233Dic11⋊C4—28no—
234Dic11⋊C4C2×D4116yes—
235C4×Dic11—28no—
236C4×Dic11—28no—
237C4×Dic11—28no—
238C22×#125—111no—
239C22×#117—111no—
240#2475—1116no—
241C2×#400—111no—
242C2×#398—111no—
243C2×#397—111no—
244C2×#396—111no—
245C2×#389—111no—
246C2×#388—111no—
247C2×#388D1111yescharacteristic
248C2×#387—111no—
249C2×#387—111no—
250C2×#387—111no—
251C2×#385—111no—
252C2×#385—111no—
253C2×C4×C4⋊C4—111no—
254C23×C11—28no—
255C23×C11—28no—
256C23×C11—28no—
257C23×C11—22no—
258C23×C11—22no—
259C23×C11—22no—
260C23×C11—22no—
261C23×C11—22no—
262C23×C11—22no—
263C23×C11—44no—
264C23×C11—44no—
265C23×C11—44no—
266C23×C11—44no—
267C23×C11C22×D412yes—
268C23×C11C2×#4114yes—
269C23×C11C2×#4112yes—
270C23×C11C2×#4112yes—
271C23×C11C2×#4112yes—
272C23×C11C2×#4112yes—
273C23×C112−1+412yes—
274C23×C112−1+412yes—
275C23×C11C2511yescharacteristic
276C2×C4×C11—28no—
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—44no—
295C2×C4×C11—44no—
296C2×C4×C11—44no—
297C2×C4×C11—44no—
298C2×C4×C11C22×D414yes—
299C2×C4×C11C2×#4114yes—
300C2×Dic11—232no—
301C2×Dic11—28no—
302C2×Dic11—28no—
303C2×Dic11—28no—
304C2×Dic11—28no—
305C2×Dic11—22no—
306C2×Dic11—22no—
307C2×Dic11—22no—
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—22no—
324C2×Dic11—22no—
325C2×Dic11—44no—
326C2×Dic11—44no—
327C2×Dic11—44no—
328C2×Dic11—44no—
329C2×Dic11C22×D414yes—
330C2×Dic11C22×D414yes—
331C2×Dic11C2×#4114yes—
332C2×Dic11C2×#4114yes—
333C24×C4—111no—
334C2×#125—118no—
335C2×#125—228no—
336C2×#117—118no—
337C2×#117—228no—
338C22×C4⋊C4—111no—
339C22×C4⋊C4—111no—
340C22×C4⋊C4—111no—
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×C42C2×D1111yescharacteristic
360#400—118no—
361#398—118no—
362#397—118no—
363#396—118no—
364#389—118no—
365#388—118no—
366#388C2×D1118yes—
367#387—118no—
368#387—118no—
369#387—118no—
370#385—118no—
371#385—118no—
372C4×C4⋊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×#95C2×D1111yescharacteristic
384C2×#95C2×D1111yescharacteristic
385C22×C11—24no—
386C22×C11—24no—
387C22×C11—24no—
388C22×C11—42no—
389C22×C11—42no—
390C22×C11—42no—
391C22×C11—42no—
392C22×C11—416no—
393C22×C11#52514yes—
394C22×C11#52914yes—
395C22×C11#54114yes—
396C22×C11#54714yes—
397C22×C11#54814yes—
398C22×C11#55214yes—
399C22×C11#55214yes—
400C22×C11C23×D411yescharacteristic
401C22×C11C22×#4111yescharacteristic
402C22×C11C22×#4111yescharacteristic
403C22×C11C22×#4111yescharacteristic
404C22×C11C22×#4111yescharacteristic
405C22×C11C2×2−1+411yescharacteristic
406C22×C11C2×2−1+411yescharacteristic
407C4×C11—24no—
408C4×C11—24no—
409C4×C11—42no—
410C4×C11—42no—
411C4×C11—42no—
412C4×C11—42no—
413Dic11—24no—
414Dic11—24no—
415Dic11—24no—
416Dic11—24no—
417Dic11—42no—
418Dic11—42no—
419Dic11—42no—
420Dic11—42no—
421C25C22×D1111yescharacteristic
422C23×C4—111no—
423C23×C4—111no—
424C23×C4—111no—
425C23×C4—111no—
426C23×C4—114no—
427C23×C4—111no—
428C23×C4—111no—
429C23×C4—111no—
430C23×C4—111no—
431C23×C4—224no—
432C23×C4—224no—
433C23×C4—224no—
434C23×C4C22×D1111yescharacteristic
435C23×C4C22×D1111yescharacteristic
436C23×C4C22×D1111yescharacteristic
437C23×C4C22×D1111yescharacteristic
438C23×C4C22×D1111yescharacteristic
439C23×C4C22×D1111yescharacteristic
440#125—2232no—
441#117—2232no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—118no—
444C2×C4⋊C4—114no—
445C2×C4⋊C4—114no—
446C2×C4⋊C4—114no—
447C2×C4⋊C4—114no—
448C2×C4⋊C4—114no—
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—224no—
456C2×C4⋊C4—224no—
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—24no—
479C2×C42—114no—
480C2×C42—114no—
481C2×C42—114no—
482C2×C42—224no—
483C2×C42—224no—
484C2×C42—224no—
485C2×C42C22×D1114yes—
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#95C22×D1114yes—
497#95C22×D1114yes—
498C2×C11—44no—
499C2×C11#247518yescomplemented
500C2×C11C2×#52511yescharacteristic
501C2×C11C2×#52911yescharacteristic
502C2×C11C2×#54111yescharacteristic
503C2×C11C2×#54711yescharacteristic
504C2×C11C2×#54811yescharacteristic
505C2×C11C2×#55211yescharacteristic
506C2×C11C2×#55211yescharacteristic
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24#433914yes—
514C24C23×D1112yes—
515C24C23×D1111yescharacteristic
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
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—114no—
533C22×C4—114no—
534C22×C4—114no—
535C22×C4—114no—
536C22×C4—112no—
537C22×C4—112no—
538C22×C4—112no—
539C22×C4—112no—
540C22×C4—112no—
541C22×C4—112no—
542C22×C4—112no—
543C22×C4—112no—
544C22×C4—228no—
545C22×C4—228no—
546C22×C4—2232no—
547C22×C4—228no—
548C22×C4—222no—
549C22×C4—222no—
550C22×C4—222no—
551C22×C4—222no—
552C22×C4—222no—
553C22×C4—222no—
554C22×C4—222no—
555C22×C4—222no—
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×C4D4×D1114yes—
569C22×C4#434114yes—
570C22×C4C23×D1112yes—
571C22×C4C23×D1112yes—
572C22×C4C23×D1112yes—
573C22×C4C23×D1112yes—
574C22×C4C23×D1112yes—
575C22×C4C23×D1112yes—
576C4⋊C4—28no—
577C4⋊C4—1116no—
578C4⋊C4—228no—
579C4⋊C4—228no—
580C4⋊C4—228no—
581C4⋊C4—228no—
582C4⋊C4—228no—
583C4⋊C4—228no—
584C4⋊C4—228no—
585C4⋊C4—228no—
586C4⋊C4—228no—
587C4⋊C4—228no—
588C22⋊C4—28no—
589C22⋊C4—28no—
590C22⋊C4—28no—
591C22⋊C4—228no—
592C22⋊C4—228no—
593C22⋊C4—228no—
594C42—28no—
595C42—228no—
596C42—228no—
597C42—228no—
598C11C2×#247511yescharacteristic, complemented, Sylow
599C23—28no—
600C23—28no—
601C23—28no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—44no—
609C23—44no—
610C23—44no—
611C23—44no—
612C23C2×#433914yes—
613C23C2×#433912yes—
614C23C2×D4×D1112yes—
615C23C2×#434112yes—
616C23#41×D1112yes—
617C23#41×D1112yes—
618C23#6704312yes—
619C23#6704312yes—
620C23C24×D1111yescharacteristic
621C2×C4—28no—
622C2×C4—28no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
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—44no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—114no—
644C2×C4—114no—
645C2×C4—114no—
646C2×C4—114no—
647C2×C4—2232no—
648C2×C4—228no—
649C2×C4—228no—
650C2×C4—228no—
651C2×C4—222no—
652C2×C4—222no—
653C2×C4—222no—
654C2×C4—222no—
655C2×C4—222no—
656C2×C4—222no—
657C2×C4—222no—
658C2×C4—222no—
659C2×C4—228no—
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—444no—
673C2×C4—444no—
674C2×C4—444no—
675C2×C4—444no—
676C2×C4C2×D4×D1114yes—
677C2×C4C2×#434114yes—
678C22—24no—
679C22—24no—
680C22—24no—
681C22—42no—
682C22—42no—
683C22—416no—
684C22—42no—
685C22—42no—
686C22#1062306214yes—
687C22#1062307214yes—
688C22#1062307814yes—
689C22#1062312914yes—
690C22#1062318614yes—
691C22#1062321114yes—
692C22#1062323214yes—
693C22C22×#433911yescharacteristic
694C22C22×D4×D1111yescharacteristic
695C22C22×#434111yescharacteristic
696C22C2×#41×D1111yescharacteristic
697C22C2×#41×D1111yescharacteristic
698C22C2×#6704311yescharacteristic
699C22C2×#6704311yescharacteristic
700C4—24no—
701C4—24no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—224no—
707C4—224no—
708C4—224no—
709C4—224no—
710C4—442no—
711C4—442no—
712C4—442no—
713C4—442no—
714C2—44no—
715C2#1307279118yesdirect product factor
716C2C2×#1062307811yescharacteristic
717C2C2×#1062321111yescharacteristic
718C2C2×#1062323211yescharacteristic
719C2C2×#1062318611yescharacteristic
720C2C2×#1062312911yescharacteristic
721C2C2×#1062306211yescharacteristic
722C2C2×#1062307211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#388C2
socleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#388D11
hypocenterC11C2×#2475
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#66923C2semidirect
3. #13072791C2direct (N × H)
4. C2×#10622271C2semidirect
5. C2×#10622597C2semidirect
8. C2×#10622260C2semidirect
10. C2×#10622594C2semidirect
11. C2×#10622266C2semidirect
12. C2×#10622265C2semidirect
15. C2×C4×Dic11⋊C4C2semidirect
43. C2×#66923C22semidirect
57. #10622597C22semidirect
58. #10622594C22semidirect
64. C4×Dic11⋊C4C22semidirect
65. #10622271C22semidirect
66. #10622266C22semidirect
67. #10622265C22semidirect
68. #10622260C22semidirect
499. C2×C11#2475semidirect
598. C11C2×#2475semidirect
715. C2#13072791direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669232
C22×#669302
#130727912
C2×#106222712
C2×#106225972
C2×#106225652
C2×#106225612
C2×#106222602
C2×#106225582
C2×#106225942
C2×#106222662
C2×#106222652
C2×#106225632
C2×#106225592
C2×C4×Dic11⋊C42
C2×C11×#3882
C2×#247511