Finite Group Databasebeta

← C2×#13072985 #14922994

Subgroups — C2×#13072985 #14922994

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×#66941C211yesmaximal, characteristic, complemented
2C22×#66949C211yesmaximal, characteristic
3#13072985C2116yesmaximal, direct product factor
4C2×#10622273C211yesmaximal, characteristic, complemented
5C2×#10622286C211yesmaximal, characteristic
6C2×#10622286C211yesmaximal, characteristic
7C2×#10622587C211yesmaximal, characteristic, complemented
8C2×#10622259C211yesmaximal, characteristic, complemented
9C2×#10622259C211yesmaximal, characteristic, complemented
10C2×#10622259C211yesmaximal, characteristic, complemented
11C2×#10622283C211yesmaximal, characteristic
12C2×#10622603C211yesmaximal, characteristic
13C2×#10622280C211yesmaximal, characteristic
14C2×#10622262C211yesmaximal, characteristic, complemented
15C2×#10622279C211yesmaximal, characteristic
16C2×C11×#400C211yesmaximal, characteristic, complemented
17C23×C4×D11C2211yescharacteristic
18C23×Dic22C2211yescharacteristic
19C23×Dic22C2211yescharacteristic
20C23×Dic22C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
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×#66949—28no—
39C2×#66949C2218yes—
40C2×#66941—28no—
41C2×#66941C2218yescomplemented
42C11×#400C2218yescomplemented
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#10622603C2218yes—
58#10622587C2218yescomplemented
59#10622286C2218yes—
60#10622286C2218yes—
61#10622283C2218yes—
62#10622280C2218yes—
63#10622279C2218yes—
64#10622273C2218yescomplemented
65#10622262C2218yescomplemented
66#10622259C2218yescomplemented
67#10622259C2218yescomplemented
68#10622259C2218yescomplemented
69C24×D11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C22×C4×D11—24no—
85C22×C4×D11—24no—
86C22×C4×D11—24no—
87C22×C4×D11C2314yes—
88C22×Dic22—24no—
89C22×Dic22—24no—
90C22×Dic22—24no—
91C22×Dic22—24no—
92C22×Dic22—24no—
93C22×Dic22—24no—
94C22×Dic22—24no—
95C22×Dic22—42no—
96C22×Dic22—42no—
97C22×Dic22C2314yes—
98C22×Dic22C2314yes—
99C22×Dic22C2314yes—
100C2×C11×C4⋊C4—24no—
101C2×C11×C4⋊C4—24no—
102C2×C11×C4⋊C4C2314yes—
103C2×C11×C4⋊C4C2314yes—
104C2×(C2×D11)⋊C4—24no—
105C2×(C2×D11)⋊C4—24no—
106C2×(C2×D11)⋊C4—24no—
107C2×(C2×D11)⋊C4—42no—
108C2×(C2×D11)⋊C4—42no—
109C2×(C2×D11)⋊C4Q818yescomplemented
110C2×(C2×D11)⋊C4C2314yes—
111C2×(C2×D11)⋊C4C2314yes—
112C2×(C2×D11)⋊C4C2314yes—
113C2×(C2×D11)⋊C4C2314yes—
114C2×(C2×D11)⋊C4C2314yes—
115C2×(C2×D11)⋊C4C2314yes—
116C2×C4⋊Dic11—24no—
117C2×C4⋊Dic11C2314yes—
118C2×Dic11⋊C4—24no—
119C2×Dic11⋊C4—24no—
120C2×Dic11⋊C4—24no—
121C2×Dic11⋊C4D418yes—
122C2×Dic11⋊C4C2314yes—
123C2×Dic11⋊C4C2314yes—
124C2×Dic11⋊C4C2314yes—
125C2×Dic11⋊C4C2314yes—
126C2×C4×Dic11—24no—
127C2×C4×Dic11—24no—
128C2×C4×Dic11—42no—
129C2×C4×Dic11—42no—
130C2×C4×Dic11C2314yes—
131C2×C4×Dic11C2314yes—
132C2×C4×Dic11C2314yes—
133C2×C4×Dic11C2314yes—
134#66949—232no—
135#66941—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×C11C2411yescharacteristic
152C23×D11—22no—
153C23×D11—22no—
154C23×D11—22no—
155C23×D11—22no—
156C23×D11—22no—
157C23×D11—22no—
158C23×D11C2×Q814yes—
159C23×D11C2412yes—
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—22no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11C2×D414yes—
180C22×C4×C11C2×Q814yes—
181C22×C4×C11C2412yes—
182C22×C4×C11C2412yes—
183C22×C4×C11C2412yes—
184C22×C4×C11C2412yes—
185C22×C4×C11C2412yes—
186C22×C4×C11C2412yes—
187C22×C4×C11C2412yes—
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×Dic11—22no—
203C22×Dic11C2×D414yes—
204C22×Dic11C2×D414yes—
205C22×Dic11C2×Q814yes—
206C22×Dic11#4114yes—
207C22×Dic11#4114yes—
208C22×Dic11#4114yes—
209C22×Dic11C2412yes—
210C22×Dic11C2412yes—
211C22×Dic11C2412yes—
212C22×Dic11C2412yes—
213C22×Dic11C2412yes—
214C22×Dic11C2412yes—
215C22×Dic11C2412yes—
216C2×C4×D11—28no—
217C2×C4×D11—28no—
218C2×C4×D11—28no—
219C2×C4×D11—416no—
220C2×Dic22—28no—
221C2×Dic22—28no—
222C2×Dic22—28no—
223C2×Dic22—28no—
224C2×Dic22—28no—
225C2×Dic22—28no—
226C2×Dic22—28no—
227C2×Dic22—44no—
228C2×Dic22—44no—
229C2×Dic22—416no—
230C2×Dic22—416no—
231C2×Dic22—416no—
232C11×C4⋊C4—28no—
233C11×C4⋊C4—28no—
234(C2×D11)⋊C4—28no—
235(C2×D11)⋊C4—28no—
236(C2×D11)⋊C4—28no—
237(C2×D11)⋊C4—44no—
238(C2×D11)⋊C4—44no—
239(C2×D11)⋊C4C2×Q8116yescomplemented
240C4⋊Dic11—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×#400D1111yescharacteristic, complemented
254C2×#393—111no—
255C2×#393—111no—
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×C11C22×D412yes—
266C23×C11C22×Q812yes—
267C23×C11C2×#4112yes—
268C23×C11C2×#4112yes—
269C23×C11C2×#4112yes—
270C23×C11H(5,𝔽2)12yes—
271C23×C112−1+412yes—
272C23×C11C2511yescharacteristic
273C22×D11—28no—
274C22×D11—28no—
275C22×D11—28no—
276C22×D11—22no—
277C22×D11—22no—
278C22×D11—22no—
279C22×D11—22no—
280C22×D11—22no—
281C22×D11—22no—
282C22×D11—44no—
283C22×D11—44no—
284C22×D11—44no—
285C22×D11—44no—
286C22×D11C22×Q814yes—
287C2×C4×C11—28no—
288C2×C4×C11—28no—
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—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—22no—
307C2×C4×C11—22no—
308C2×C4×C11—44no—
309C2×C4×C11—44no—
310C2×C4×C11—44no—
311C2×C4×C11—44no—
312C2×C4×C11—44no—
313C2×C4×C11C22×D414yes—
314C2×C4×C11C22×Q814yes—
315C2×Dic11—28no—
316C2×Dic11—28no—
317C2×Dic11—28no—
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#124116yes—
337C2×Dic11C22×D414yes—
338C2×Dic11C22×D414yes—
339C2×Dic11C22×Q814yes—
340C2×Dic11C2×#4114yes—
341C2×Dic11C2×#4114yes—
342C2×Dic11C2×#4114yes—
343C4×D11—416no—
344Dic22—416no—
345Dic22—416no—
346Dic22—416no—
347C23×Q8—111no—
348C23×Q8—111no—
349C23×Q8—111no—
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⋊C4C2×D1111yescharacteristic
361C22×C4⋊C4C2×D1111yescharacteristic
362C22×C22⋊C4—111no—
363C22×C22⋊C4—111no—
364C22×C22⋊C4—111no—
365C22×C22⋊C4—111no—
366C22×C22⋊C4—111no—
367C22×C22⋊C4—111no—
368C22×C42—111no—
369C22×C42—111no—
370C22×C42—111no—
371C22×C42—111no—
372#400—118no—
373#400C2×D1118yescomplemented
374#393—118no—
375#393—118no—
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×#95C2×D1111yescharacteristic
395C2×#95C2×D1111yescharacteristic
396C2×#95C2×D1111yescharacteristic
397C2×#95C2×D1111yescharacteristic
398C2×#95C2×D1111yescharacteristic
399C22×C11C2×#12414yes—
400C22×C11#53314yes—
401C22×C11#54214yes—
402C22×C11#54614yes—
403C22×C11D4×Q814yes—
404C22×C11#55414yes—
405C22×C11#55614yes—
406C22×C11C23×D411yescharacteristic
407C22×C11C23×Q811yescharacteristic
408C22×C11C22×#4111yescharacteristic
409C22×C11C22×#4111yescharacteristic
410C22×C11C22×#4111yescharacteristic
411C22×C11C2×H(5,𝔽2)11yescharacteristic
412C22×C11C2×2−1+411yescharacteristic
413C2×D11—24no—
414C2×D11—24no—
415C2×D11—24no—
416C2×D11—42no—
417C2×D11—42no—
418C2×D11—42no—
419C2×D11—42no—
420C2×D11—416no—
421C4×C11—24no—
422C4×C11—24no—
423C4×C11—42no—
424C4×C11—42no—
425C4×C11—42no—
426C4×C11—42no—
427C4×C11—42no—
428Dic11—24no—
429Dic11—24no—
430Dic11—24no—
431Dic11—42no—
432Dic11—42no—
433Dic11—42no—
434Dic11C2×#12418yes—
435C25—111no—
436C22×Q8—114no—
437C22×Q8—114no—
438C22×Q8—114no—
439C22×Q8—224no—
440C22×Q8—224no—
441C22×Q8—224no—
442C22×Q8—224no—
443C22×Q8—224no—
444C22×Q8—224no—
445C22×Q8—224no—
446C22×Q8—442no—
447C22×Q8—442no—
448C23×C4—111no—
449C23×C4—111no—
450C23×C4—111no—
451C23×C4—111no—
452C23×C4—111no—
453C23×C4—111no—
454C23×C4—111no—
455C23×C4—114no—
456C23×C4—224no—
457C23×C4—224no—
458C23×C4—224no—
459C23×C4C22×D1111yescharacteristic
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—24no—
469C2×C4⋊C4—24no—
470C2×C4⋊C4—118no—
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⋊C4C22×D1114yes—
481C2×C4⋊C4C22×D1114yes—
482C2×C22⋊C4—118no—
483C2×C22⋊C4—114no—
484C2×C22⋊C4—114no—
485C2×C22⋊C4—114no—
486C2×C22⋊C4—114no—
487C2×C22⋊C4—114no—
488C2×C22⋊C4—114no—
489C2×C22⋊C4—224no—
490C2×C22⋊C4—224no—
491C2×C22⋊C4—224no—
492C2×C22⋊C4—442no—
493C2×C22⋊C4—442no—
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#95C22×D1114yes—
512#95C22×D1114yes—
513#95C22×D1114yes—
514#95C22×D1114yes—
515#95C22×D1114yes—
516C2×C11#249218yescomplemented
517C2×C11C22×#12411yescharacteristic
518C2×C11C2×#53311yescharacteristic
519C2×C11C2×#54211yescharacteristic
520C2×C11C2×#54611yescharacteristic
521C2×C11C2×D4×Q811yescharacteristic
522C2×C11C2×#55411yescharacteristic
523C2×C11C2×#55611yescharacteristic
524D11—44no—
525C24—114no—
526C24—112no—
527C24—222no—
528C24—222no—
529C24—222no—
530C24—222no—
531C24—222no—
532C24—222no—
533C24C23×D1111yescharacteristic
534C2×Q8—228no—
535C2×Q8—228no—
536C2×Q8—228no—
537C2×Q8—228no—
538C2×Q8—228no—
539C2×Q8—228no—
540C2×Q8—228no—
541C2×Q8—444no—
542C2×Q8—444no—
543C2×Q8—4416no—
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—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—114no—
566C22×C4—114no—
567C22×C4—114no—
568C22×C4—112no—
569C22×C4—114no—
570C22×C4—114no—
571C22×C4—114no—
572C22×C4—112no—
573C22×C4—112no—
574C22×C4—112no—
575C22×C4—112no—
576C22×C4—112no—
577C22×C4—112no—
578C22×C4—228no—
579C22×C4—228no—
580C22×C4—228no—
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—4416no—
597C22×C4D4×D1114yes—
598C22×C4Q8×D1114yes—
599C22×C4C23×D1112yes—
600C22×C4C23×D1112yes—
601C22×C4C23×D1112yes—
602C22×C4C23×D1112yes—
603C22×C4C23×D1112yes—
604C22×C4C23×D1112yes—
605C22×C4C23×D1112yes—
606C4⋊C4—28no—
607C4⋊C4—28no—
608C4⋊C4—1116no—
609C4⋊C4—228no—
610C4⋊C4—228no—
611C4⋊C4—228no—
612C4⋊C4—228no—
613C22⋊C4—1116no—
614C22⋊C4—228no—
615C22⋊C4—228no—
616C22⋊C4—228no—
617C22⋊C4—444no—
618C22⋊C4—444no—
619C42—228no—
620C42—228no—
621C42—444no—
622C42—444no—
623C11C2×#249211yescharacteristic, complemented, Sylow
624C23—114no—
625C23—228no—
626C23—222no—
627C23—222no—
628C23—222no—
629C23—222no—
630C23—222no—
631C23—222no—
632C23—228no—
633C23—228no—
634C23—444no—
635C23—444no—
636C23—444no—
637C23—444no—
638C23C2×D4×D1112yes—
639C23C2×Q8×D1112yes—
640C23#41×D1112yes—
641C23#41×D1112yes—
642C23#41×D1112yes—
643C23#6704212yes—
644C23#6704312yes—
645C23C24×D1111yescharacteristic
646Q8—4416no—
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—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—44no—
671C2×C4—44no—
672C2×C4—44no—
673C2×C4—44no—
674C2×C4—44no—
675C2×C4—114no—
676C2×C4—114no—
677C2×C4—114no—
678C2×C4—1116no—
679C2×C4—114no—
680C2×C4—114no—
681C2×C4—114no—
682C2×C4—228no—
683C2×C4—228no—
684C2×C4—222no—
685C2×C4—222no—
686C2×C4—222no—
687C2×C4—222no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—228no—
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—222no—
700C2×C4—4416no—
701C2×C4—444no—
702C2×C4—444no—
703C2×C4—444no—
704C2×C4C2×D4×D1114yes—
705C2×C4C2×Q8×D1114yes—
706C22—224no—
707C22—224no—
708C22—224no—
709C22—442no—
710C22—442no—
711C22—4416no—
712C22—442no—
713C22—442no—
714C22#1062316314yes—
715C22#1062318514yes—
716C22D11×#12414yes—
717C22#1062321914yes—
718C22#1062322114yes—
719C22#1062323314yes—
720C22#1062324114yes—
721C22C22×D4×D1111yescharacteristic
722C22C22×Q8×D1111yescharacteristic
723C22C2×#41×D1111yescharacteristic
724C22C2×#41×D1111yescharacteristic
725C22C2×#41×D1111yescharacteristic
726C22C2×#6704211yescharacteristic
727C22C2×#6704311yescharacteristic
728C4—24no—
729C4—24no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—118no—
736C4—224no—
737C4—224no—
738C4—224no—
739C4—442no—
740C4—442no—
741C4—442no—
742C2—444no—
743C2#1307298518yesdirect product factor
744C2C2×D11×#12411yescharacteristic
745C2C2×#1062321911yescharacteristic
746C2C2×#1062324111yescharacteristic
747C2C2×#1062318511yescharacteristic
748C2C2×#1062316311yescharacteristic
749C2C2×#1062322111yescharacteristic
750C2C2×#1062323311yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#400C2
socleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#400D11
hypocenterC11C2×#2492
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. C22×#66941C2semidirect
3. #13072985C2direct (N × H)
4. C2×#10622273C2semidirect
7. C2×#10622587C2semidirect
8. C2×#10622259C2semidirect
9. C2×#10622259C2semidirect
10. C2×#10622259C2semidirect
14. C2×#10622262C2semidirect
16. C2×C11×#400C2semidirect
41. C2×#66941C22semidirect
42. C11×#400C22semidirect
58. #10622587C22semidirect
64. #10622273C22semidirect
65. #10622262C22semidirect
66. #10622259C22semidirect
67. #10622259C22semidirect
68. #10622259C22semidirect
109. C2×(C2×D11)⋊C4Q8semidirect
239. (C2×D11)⋊C4C2×Q8semidirect
253. C2×#400D11semidirect
373. #400C2×D11semidirect
516. C2×C11#2492semidirect
623. C11C2×#2492semidirect
743. C2#13072985direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669412
C22×#669492
#130729852
C2×#106222732
C2×#106222862
C2×#106225872
C2×#106222592
C2×#106222832
C2×#106226032
C2×#106222802
C2×#106222622
C2×#106222792
C2×C11×#4002
C2×#249211