Finite Group Databasebeta

← C2×#13072983 #14922990

Subgroups — C2×#13072983 #14922990

Order 2816.

2854 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66997C211yesmaximal, characteristic, complemented
2C22×#66931C211yesmaximal, characteristic
3#13072983C2116yesmaximal, direct product factor
4C2×#10622271C211yesmaximal, characteristic, complemented
5C2×#10622272C211yesmaximal, characteristic, complemented
6C2×#10622560C211yesmaximal, characteristic
7C2×#10622843C211yesmaximal, characteristic, complemented
8C2×#10622259C211yesmaximal, characteristic, complemented
9C2×#10622259C211yesmaximal, characteristic, complemented
10C2×#10622259C211yesmaximal, characteristic, complemented
11C2×#10622558C211yesmaximal, characteristic
12C2×#10622557C211yesmaximal, characteristic
13C2×#10622555C211yesmaximal, characteristic
14C2×#10622262C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic11C211yesmaximal, characteristic
16C2×C11×#393C211yesmaximal, characteristic
17C23×Q8×C11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C23×Dic22C2211yescharacteristic
20C23×Dic22C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C2×#66997—28no—
28C2×#66997C2218yescomplemented
29C22×C4⋊Dic11C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C2×#66931—28no—
41C2×#66931C2218yes—
42C11×#393C2218yes—
43C2×C11×#95C2211yescharacteristic
44C2×C11×#95C2211yescharacteristic
45C2×C11×#95C2211yescharacteristic
46#10622843C2218yescomplemented
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
57C2×C11⋊#95C2211yescharacteristic
58#10622560C2218yes—
59#10622558C2218yes—
60#10622557C2218yes—
61#10622555C2218yes—
62C22⋊C4×Dic11C2218yes—
63#10622272C2218yescomplemented
64#10622271C2218yescomplemented
65#10622262C2218yescomplemented
66#10622259C2218yescomplemented
67#10622259C2218yescomplemented
68#10622259C2218yescomplemented
69C25×C11C2311yescharacteristic
70C22×Q8×C11—24no—
71C22×Q8×C11—24no—
72C22×Q8×C11—42no—
73C22×Q8×C11C2314yes—
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×Dic11—24no—
81C23×Dic11—24no—
82C23×Dic11—24no—
83C23×Dic11C2314yes—
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C22×Dic22—24no—
93C22×Dic22—24no—
94C22×Dic22—24no—
95C22×Dic22—24no—
96C22×Dic22—24no—
97C22×Dic22—42no—
98C22×Dic22C2314yes—
99C22×Dic22C2314yes—
100C2×C11×C22⋊C4—24no—
101C2×C11×C22⋊C4—24no—
102C2×C11×C22⋊C4—42no—
103C2×C11×C22⋊C4C2314yes—
104C2×C11×C22⋊C4C2314yes—
105C2×C11×C22⋊C4C2314yes—
106C2×C22⋊Dic11—24no—
107C2×C22⋊Dic11—42no—
108C2×C22⋊Dic11Q818yescomplemented
109C2×C22⋊Dic11C2314yes—
110C2×C22⋊Dic11C2314yes—
111C2×C22⋊Dic11C2314yes—
112#66997—232no—
113C2×C4⋊Dic11—24no—
114C2×C4⋊Dic11C2314yes—
115C2×Dic11⋊C4—24no—
116C2×Dic11⋊C4—24no—
117C2×Dic11⋊C4—24no—
118C2×Dic11⋊C4—24no—
119C2×Dic11⋊C4—24no—
120C2×Dic11⋊C4D418yes—
121C2×Dic11⋊C4C2314yes—
122C2×Dic11⋊C4C2314yes—
123C2×Dic11⋊C4C2314yes—
124C2×Dic11⋊C4C2314yes—
125C2×Dic11⋊C4C2314yes—
126C2×Dic11⋊C4C2314yes—
127C2×C4×Dic11—24no—
128C2×C4×Dic11—24no—
129C2×C4×Dic11—42no—
130C2×C4×Dic11—42no—
131C2×C4×Dic11C2314yes—
132C2×C4×Dic11C2314yes—
133C2×C4×Dic11C2314yes—
134C2×C4×Dic11C2314yes—
135#66931—232no—
136C11×#95C2314yes—
137C11×#95C2314yes—
138C11×#95C2314yes—
139C11⋊#95C2314yes—
140C11⋊#95C2314yes—
141C11⋊#95C2314yes—
142C11⋊#95C2314yes—
143C11⋊#95C2314yes—
144C11⋊#95C2314yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C2×#2492—111nomaximal, Sylow
151C24×C11—22no—
152C24×C11—22no—
153C24×C11—22no—
154C24×C11—22no—
155C24×C11—22no—
156C24×C11—22no—
157C24×C11C2×Q814yes—
158C24×C11C2412yes—
159C24×C11C2411yescharacteristic
160C2×Q8×C11—28no—
161C2×Q8×C11—28no—
162C2×Q8×C11—44no—
163C2×Q8×C11—416no—
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—22no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11C2×D414yes—
181C22×C4×C11#4114yes—
182C22×C4×C11C2412yes—
183C22×C4×C11C2412yes—
184C22×C4×C11C2412yes—
185C22×C4×C11C2412yes—
186C22×C4×C11C2412yes—
187C22×C4×C11C2412yes—
188C22×Dic11—28no—
189C22×Dic11—28no—
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×Dic11—22no—
205C22×Dic11—22no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—416no—
210C22×Dic11C2×D414yes—
211C22×Dic11C2×D414yes—
212C22×Dic11C2×Q814yes—
213C22×Dic11C2×Q814yes—
214C22×Dic11#4114yes—
215C22×Dic11#4114yes—
216C22×Dic11C2412yes—
217C22×Dic11C2412yes—
218C22×Dic11C2412yes—
219C22×Dic11C2412yes—
220C22×Dic11C2412yes—
221C22×Dic11C2412yes—
222C22×Dic11C2412yes—
223C22×Dic11C2412yes—
224C2×Dic22—28no—
225C2×Dic22—28no—
226C2×Dic22—28no—
227C2×Dic22—28no—
228C2×Dic22—28no—
229C2×Dic22—44no—
230C2×Dic22—416no—
231C2×Dic22—416no—
232C11×C22⋊C4—28no—
233C11×C22⋊C4—28no—
234C11×C22⋊C4—44no—
235C22⋊Dic11—28no—
236C22⋊Dic11—44no—
237C22⋊Dic11C2×Q8116yescomplemented
238C4⋊Dic11—28no—
239Dic11⋊C4—28no—
240Dic11⋊C4—28no—
241Dic11⋊C4—28no—
242Dic11⋊C4—28no—
243Dic11⋊C4—28no—
244Dic11⋊C4C2×D4116yes—
245C4×Dic11—28no—
246C4×Dic11—28no—
247C4×Dic11—44no—
248C4×Dic11—44no—
249C22×C4⋊Q8—111no—
250C22×C22⋊Q8—111no—
251#2492—1116no—
252C2×#400—111no—
253C2×#400—111no—
254C2×#393—111no—
255C2×#393D1111yescharacteristic
256C2×#391—111no—
257C2×#391—111no—
258C2×#391—111no—
259C2×#391—111no—
260C2×#388—111no—
261C2×#388—111no—
262C2×#380—111no—
263C2×C4×C4⋊C4—111no—
264C2×C4×C22⋊C4—111no—
265C23×C11—28no—
266C23×C11—28no—
267C23×C11—28no—
268C23×C11—22no—
269C23×C11—22no—
270C23×C11—22no—
271C23×C11—22no—
272C23×C11—22no—
273C23×C11—22no—
274C23×C11—44no—
275C23×C11—44no—
276C23×C11—44no—
277C23×C11—44no—
278C23×C11C22×D412yes—
279C23×C11C22×Q814yes—
280C23×C11C22×Q812yes—
281C23×C11C2×#4112yes—
282C23×C11C2×#4112yes—
283C23×C11C2×#4112yes—
284C23×C11H(5,𝔽2)12yes—
285C23×C112−1+412yes—
286C23×C11C2511yescharacteristic
287Q8×C11—416no—
288C2×C4×C11—28no—
289C2×C4×C11—28no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—44no—
307C2×C4×C11—44no—
308C2×C4×C11—44no—
309C2×C4×C11—44no—
310C2×C4×C11C22×D414yes—
311C2×C4×C11C2×#4114yes—
312C2×Dic11—28no—
313C2×Dic11—28no—
314C2×Dic11—28no—
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—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—44no—
334C2×Dic11—44no—
335C2×Dic11—44no—
336C2×Dic11—44no—
337C2×Dic11—416no—
338C2×Dic11#124116yes—
339C2×Dic11C22×D414yes—
340C2×Dic11C22×D414yes—
341C2×Dic11C22×Q814yes—
342C2×Dic11C22×Q814yes—
343C2×Dic11C2×#4114yes—
344C2×Dic11C2×#4114yes—
345Dic22—416no—
346Dic22—416no—
347C23×Q8—111no—
348C23×Q8—111no—
349C23×Q8C2×D1111yescharacteristic
350C24×C4—111no—
351C2×C4⋊Q8—118no—
352C2×C4⋊Q8—228no—
353C2×C22⋊Q8—118no—
354C2×C22⋊Q8—228no—
355C22×C4⋊C4—111no—
356C22×C4⋊C4—111no—
357C22×C4⋊C4—111no—
358C22×C4⋊C4—111no—
359C22×C4⋊C4—111no—
360C22×C4⋊C4—111no—
361C22×C4⋊C4—111no—
362C22×C22⋊C4—111no—
363C22×C22⋊C4—111no—
364C22×C22⋊C4—111no—
365C22×C22⋊C4C2×D1111yescharacteristic
366C22×C22⋊C4C2×D1111yescharacteristic
367C22×C22⋊C4C2×D1111yescharacteristic
368C22×C42—111no—
369C22×C42—111no—
370C22×C42—111no—
371C22×C42—111no—
372#400—118no—
373#400—118no—
374#393—118no—
375#393C2×D1118yes—
376#391—118no—
377#391—118no—
378#391—118no—
379#391—118no—
380#388—118no—
381#388—118no—
382#380—118no—
383C4×C4⋊C4—118no—
384C4×C22⋊C4—118no—
385C2×#95—111no—
386C2×#95—111no—
387C2×#95—111no—
388C2×#95—111no—
389C2×#95—111no—
390C2×#95—111no—
391C2×#95—111no—
392C2×#95—111no—
393C2×#95—111no—
394C2×#95—111no—
395C2×#95—111no—
396C2×#95C2×D1111yescharacteristic
397C2×#95C2×D1111yescharacteristic
398C2×#95C2×D1111yescharacteristic
399C22×C11—24no—
400C22×C11—24no—
401C22×C11—24no—
402C22×C11—42no—
403C22×C11—42no—
404C22×C11—42no—
405C22×C11—42no—
406C22×C11—416no—
407C22×C11C2×#12414yes—
408C22×C11#53314yes—
409C22×C11#54214yes—
410C22×C11#54614yes—
411C22×C11D4×Q814yes—
412C22×C11#55414yes—
413C22×C11#55614yes—
414C22×C11C23×D411yescharacteristic
415C22×C11C23×Q811yescharacteristic
416C22×C11C22×#4111yescharacteristic
417C22×C11C22×#4111yescharacteristic
418C22×C11C22×#4111yescharacteristic
419C22×C11C2×H(5,𝔽2)11yescharacteristic
420C22×C11C2×2−1+411yescharacteristic
421C4×C11—24no—
422C4×C11—24no—
423C4×C11—42no—
424C4×C11—42no—
425C4×C11—42no—
426C4×C11—42no—
427Dic11—24no—
428Dic11—24no—
429Dic11—24no—
430Dic11—42no—
431Dic11—42no—
432Dic11—42no—
433Dic11—42no—
434Dic11C2×#12418yes—
435C25C22×D1111yescharacteristic
436C22×Q8—24no—
437C22×Q8—24no—
438C22×Q8—42no—
439C22×Q8—114no—
440C22×Q8—114no—
441C22×Q8—224no—
442C22×Q8—224no—
443C22×Q8—224no—
444C22×Q8—224no—
445C22×Q8—224no—
446C22×Q8—442no—
447C22×Q8C22×D1114yes—
448C23×C4—111no—
449C23×C4—111no—
450C23×C4—111no—
451C23×C4—111no—
452C23×C4—114no—
453C23×C4—111no—
454C23×C4—111no—
455C23×C4—111no—
456C23×C4—111no—
457C23×C4—224no—
458C23×C4—224no—
459C23×C4—224no—
460C23×C4C22×D1111yescharacteristic
461C23×C4C22×D1111yescharacteristic
462C23×C4C22×D1111yescharacteristic
463C23×C4C22×D1111yescharacteristic
464C23×C4C22×D1111yescharacteristic
465C23×C4C22×D1111yescharacteristic
466C4⋊Q8—2232no—
467C22⋊Q8—2232no—
468C2×C4⋊C4—118no—
469C2×C4⋊C4—114no—
470C2×C4⋊C4—114no—
471C2×C4⋊C4—114no—
472C2×C4⋊C4—114no—
473C2×C4⋊C4—114no—
474C2×C4⋊C4—114no—
475C2×C4⋊C4—114no—
476C2×C4⋊C4—224no—
477C2×C4⋊C4—224no—
478C2×C4⋊C4—224no—
479C2×C4⋊C4—224no—
480C2×C4⋊C4—224no—
481C2×C4⋊C4—224no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—42no—
485C2×C22⋊C4—118no—
486C2×C22⋊C4—114no—
487C2×C22⋊C4—114no—
488C2×C22⋊C4—114no—
489C2×C22⋊C4—224no—
490C2×C22⋊C4—442no—
491C2×C22⋊C4C22×D1114yes—
492C2×C22⋊C4C22×D1114yes—
493C2×C22⋊C4C22×D1114yes—
494C2×C42—114no—
495C2×C42—114no—
496C2×C42—114no—
497C2×C42—114no—
498C2×C42—224no—
499C2×C42—224no—
500C2×C42—442no—
501C2×C42—442no—
502#95—114no—
503#95—114no—
504#95—114no—
505#95—114no—
506#95—114no—
507#95—114no—
508#95—114no—
509#95—114no—
510#95—114no—
511#95—114no—
512#95—114no—
513#95C22×D1114yes—
514#95C22×D1114yes—
515#95C22×D1114yes—
516C2×C11—44no—
517C2×C11#249218yescomplemented
518C2×C11C22×#12411yescharacteristic
519C2×C11C2×#53311yescharacteristic
520C2×C11C2×#54211yescharacteristic
521C2×C11C2×#54611yescharacteristic
522C2×C11C2×D4×Q811yescharacteristic
523C2×C11C2×#55411yescharacteristic
524C2×C11C2×#55611yescharacteristic
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24Q8×D1114yes—
532C24C23×D1112yes—
533C24C23×D1111yescharacteristic
534C2×Q8—28no—
535C2×Q8—28no—
536C2×Q8—44no—
537C2×Q8—416no—
538C2×Q8—228no—
539C2×Q8—228no—
540C2×Q8—228no—
541C2×Q8—228no—
542C2×Q8—228no—
543C2×Q8—444no—
544C2×Q8—4416no—
545C2×Q8—4416no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—114no—
563C22×C4—114no—
564C22×C4—114no—
565C22×C4—112no—
566C22×C4—114no—
567C22×C4—114no—
568C22×C4—114no—
569C22×C4—112no—
570C22×C4—112no—
571C22×C4—112no—
572C22×C4—112no—
573C22×C4—112no—
574C22×C4—112no—
575C22×C4—112no—
576C22×C4—228no—
577C22×C4—228no—
578C22×C4—228no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—222no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—222no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—4416no—
598C22×C4D4×D1114yes—
599C22×C4#434114yes—
600C22×C4C23×D1112yes—
601C22×C4C23×D1112yes—
602C22×C4C23×D1112yes—
603C22×C4C23×D1112yes—
604C22×C4C23×D1112yes—
605C22×C4C23×D1112yes—
606C4⋊C4—1116no—
607C4⋊C4—228no—
608C4⋊C4—228no—
609C4⋊C4—228no—
610C4⋊C4—228no—
611C4⋊C4—228no—
612C4⋊C4—228no—
613C22⋊C4—28no—
614C22⋊C4—28no—
615C22⋊C4—44no—
616C22⋊C4—1116no—
617C22⋊C4—228no—
618C22⋊C4—444no—
619C42—228no—
620C42—228no—
621C42—444no—
622C42—444no—
623C11C2×#249211yescharacteristic, complemented, Sylow
624C23—28no—
625C23—28no—
626C23—28no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—44no—
634C23—44no—
635C23—44no—
636C23—44no—
637C23C2×D4×D1112yes—
638C23C2×#434112yes—
639C23#6703712yes—
640C23C2×Q8×D1114yes—
641C23C2×Q8×D1112yes—
642C23#41×D1112yes—
643C23#41×D1112yes—
644C23#6704312yes—
645C23C24×D1111yescharacteristic
646Q8—416no—
647Q8—4416no—
648Q8—4416no—
649C2×C4—28no—
650C2×C4—28no—
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—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—44no—
668C2×C4—44no—
669C2×C4—44no—
670C2×C4—44no—
671C2×C4—114no—
672C2×C4—114no—
673C2×C4—114no—
674C2×C4—1116no—
675C2×C4—114no—
676C2×C4—114no—
677C2×C4—114no—
678C2×C4—228no—
679C2×C4—228no—
680C2×C4—228no—
681C2×C4—222no—
682C2×C4—222no—
683C2×C4—222no—
684C2×C4—222no—
685C2×C4—222no—
686C2×C4—222no—
687C2×C4—222no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—222no—
694C2×C4—222no—
695C2×C4—222no—
696C2×C4—222no—
697C2×C4—222no—
698C2×C4—222no—
699C2×C4—4416no—
700C2×C4—444no—
701C2×C4—444no—
702C2×C4—444no—
703C2×C4—444no—
704C2×C4C2×D4×D1114yes—
705C2×C4C2×#434114yes—
706C22—24no—
707C22—24no—
708C22—24no—
709C22—42no—
710C22—42no—
711C22—416no—
712C22—42no—
713C22—42no—
714C22#1062312214yes—
715C22#1062315314yes—
716C22#1062316314yes—
717C22#1062316714yes—
718C22#1062320014yes—
719C22#1062320214yes—
720C22D11×#12414yes—
721C22C22×D4×D1111yescharacteristic
722C22C22×#434111yescharacteristic
723C22C2×#6703711yescharacteristic
724C22C22×Q8×D1111yescharacteristic
725C22C2×#41×D1111yescharacteristic
726C22C2×#41×D1111yescharacteristic
727C22C2×#6704311yescharacteristic
728C4—24no—
729C4—24no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—118no—
735C4—224no—
736C4—224no—
737C4—224no—
738C4—442no—
739C4—442no—
740C4—442no—
741C4—442no—
742C2—44no—
743C2#1307298318yesdirect product factor
744C2C2×D11×#12411yescharacteristic
745C2C2×#1062315311yescharacteristic
746C2C2×#1062320011yescharacteristic
747C2C2×#1062312211yescharacteristic
748C2C2×#1062316311yescharacteristic
749C2C2×#1062316711yescharacteristic
750C2C2×#1062320211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#393C2
socleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#393D11
hypocenterC11C2×#2492
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C22×#66997C2semidirect
3. #13072983C2direct (N × H)
4. C2×#10622271C2semidirect
5. C2×#10622272C2semidirect
7. C2×#10622843C2semidirect
8. C2×#10622259C2semidirect
9. C2×#10622259C2semidirect
10. C2×#10622259C2semidirect
14. C2×#10622262C2semidirect
28. C2×#66997C22semidirect
46. #10622843C22semidirect
63. #10622272C22semidirect
64. #10622271C22semidirect
65. #10622262C22semidirect
66. #10622259C22semidirect
67. #10622259C22semidirect
68. #10622259C22semidirect
108. C2×C22⋊Dic11Q8semidirect
237. C22⋊Dic11C2×Q8semidirect
517. C2×C11#2492semidirect
623. C11C2×#2492semidirect
743. C2#13072983direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669972
C22×#669312
#130729832
C2×#106222712
C2×#106222722
C2×#106225602
C2×#106228432
C2×#106222592
C2×#106225582
C2×#106225572
C2×#106225552
C2×#106222622
C2×C22⋊C4×Dic112
C2×C11×#3932
C2×#249211