Finite Group Databasebeta

← #14916813

Subgroups — #14916813

Order 2816.

2318 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071808C214yesmaximal, complemented
2#13071636C212yesmaximal
3#13071625C212yesmaximal, complemented
4#13071573C211yesmaximal, characteristic, complemented
5#13071565C211yesmaximal, characteristic, complemented
6#13071545C212yesmaximal, complemented
7Q8×C4⋊Dic11C211yesmaximal, characteristic, complemented
8D4×C4⋊Dic11C212yesmaximal, complemented
9D4×C4⋊Dic11C211yesmaximal, characteristic, complemented
10#13071358C212yesmaximal, complemented
11#13071329C212yesmaximal, complemented
12#13071288C214yesmaximal, complemented
13#13071239C212yesmaximal, complemented
14#13071225C212yesmaximal, complemented
15C2×#10622548C211yesmaximal, characteristic, complemented
16#13071014C211yesmaximal, characteristic, complemented
17C2×C11×#529C211yesmaximal, characteristic
18C11×#529C4116yescomplemented
19C2×C11×#126C2212yes—
20C2×C11×#125C2211yescharacteristic
21C2×C11×#124C2211yescharacteristic
22C2×C11×#123C2212yes—
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×#121C2211yescharacteristic
25C2×C4×Q8×C11C2211yescharacteristic
26C2×C4×D4×C11C2212yes—
27C2×C4×D4×C11C2211yescharacteristic
28C2×C11×#117C2212yes—
29C22×C42×C11C2211yescharacteristic
30C2×Q8×Dic11C2212yes—
31C2×D4×Dic11C2214yes—
32C2×D4×Dic11C2212yes—
33C2×#66979C2212yes—
34C22×C4⋊Dic11C2212yes—
35C22×C4⋊Dic11C2212yes—
36C22×C4⋊Dic11C2212yes—
37C22×C4⋊Dic11C2212yes—
38#10622843C2212yes—
39#10622834C2212yes—
40#10622833C2214yes—
41#10622825C2212yes—
42#10622825C2212yes—
43#10622825C2211yescharacteristic
44#10622825C2211yescharacteristic
45#10622824C2212yes—
46C4×C22⋊Dic11C2212yes—
47#10622598C2214yes—
48#10622598C2212yes—
49#10622598C2212yes—
50#10622598C2214yes—
51#10622598C2214yes—
52#10622598C2214yes—
53#10622594C2214yes—
54#10622594C2214yes—
55#10622594C2214yes—
56#10622594C2214yes—
57C4⋊C4×Dic11C2212yes—
58C4⋊C4×Dic11C2212yes—
59#10622564C2214yes—
60#10622564C2214yes—
61#10622564C2214yes—
62#10622564C2214yes—
63#10622563C2214yes—
64#10622563C2214yes—
65#10622563C2214yes—
66#10622563C2214yes—
67#10622563C2214yes—
68C22⋊C4×Dic11C2214yes—
69#10622550C2212yes—
70#10622549C2211yescharacteristic
71#10622549C2211yescharacteristic
72#10622549C2212yes—
73#10622548C2212yes—
74#10622548C2212yes—
75#10622548C2211yescharacteristic
76#10622548C2211yescharacteristic
77#10622548C2212yes—
78#10622548C2212yes—
79C4×C4⋊Dic11C2212yes—
80C4×C4⋊Dic11C2212yes—
81C4×C4⋊Dic11C2211yescharacteristic
82C4×C4⋊Dic11C2211yescharacteristic
83#10622545C2212yes—
84C22×Q8×C11C2311yescharacteristic
85C22×D4×C11C2312yes—
86C22×D4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2312yes—
91C23×Dic11C2314yes—
92C23×Dic11C2314yes—
93C11×#126C2×C4116yescomplemented
94C11×#125C2×C418yescomplemented
95C11×#124C2×C418yescomplemented
96C11×#123C2×C4116yescomplemented
97C11×C22⋊Q8C2×C418yescomplemented
98C11×#121C2×C418yes—
99C4×Q8×C11C2×C418yescomplemented
100C4×D4×C11C2×C418yescomplemented
101C4×D4×C11C2×C4116yescomplemented
102C11×#117C2×C4116yescomplemented
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2312yes—
106C2×C11×C4⋊C4C2312yes—
107C2×C11×C4⋊C4C2312yes—
108C2×C11×C4⋊C4C2312yes—
109C2×C11×C22⋊C4C2312yes—
110C2×C11×C22⋊C4C2312yes—
111C2×C11×C22⋊C4C2312yes—
112C2×C11×C22⋊C4C2312yes—
113C2×C11×C22⋊C4C2312yes—
114C2×C42×C11C2×C418yescomplemented
115C2×C42×C11C2311yescharacteristic
116C2×C42×C11C2311yescharacteristic
117C2×C42×C11C2312yes—
118C2×C42×C11C2311yescharacteristic
119C2×C42×C11C2311yescharacteristic
120C2×C22⋊Dic11C2312yes—
121C2×C22⋊Dic11C2312yes—
122C2×C22⋊Dic11C2314yes—
123C2×C22⋊Dic11C2314yes—
124C2×C22⋊Dic11C2314yes—
125Q8×Dic11—44no—
126D4×Dic11—44no—
127D4×Dic11—48no—
128#66979—44no—
129C2×C4⋊Dic11—44no—
130C2×C4⋊Dic11—44no—
131C2×C4⋊Dic11—44no—
132C2×C4⋊Dic11—44no—
133C2×C4⋊Dic11C2311yescharacteristic
134C2×C4⋊Dic11C2311yescharacteristic
135C2×C4⋊Dic11C2312yes—
136C2×C4⋊Dic11C2312yes—
137C2×C4⋊Dic11C2311yescharacteristic
138C2×C4⋊Dic11C2311yescharacteristic
139C2×C4⋊Dic11C2312yes—
140C2×C4⋊Dic11C2312yes—
141C2×C4⋊Dic11C2312yes—
142C2×C4⋊Dic11C2314yes—
143C2×C4⋊Dic11C2314yes—
144C2×C4⋊Dic11C2314yes—
145C2×C4⋊Dic11C2312yes—
146C2×C4⋊Dic11C2314yes—
147C2×C4⋊Dic11C2314yes—
148C2×C4⋊Dic11C2314yes—
149C2×C4×Dic11C2312yes—
150C2×C4×Dic11C2312yes—
151C2×C4×Dic11C2314yes—
152C2×C4×Dic11C2314yes—
153C2×C4×Dic11C2314yes—
154C11⋊#95C2312yes—
155C11⋊#95C2312yes—
156C11⋊#95C2312yes—
157C11⋊#95C2312yes—
158C11⋊#95C2312yes—
159C11⋊#95C2312yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2312yes—
163C11⋊#95C2312yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C11⋊#95C2314yes—
167C11⋊#95C2314yes—
168#34384—111nomaximal, Sylow
169C24×C11C2412yes—
170C24×C11C2411yescharacteristic
171C2×Q8×C11—22no—
172C2×Q8×C11—22no—
173C2×Q8×C11C22×C414yes—
174C2×D4×C11—24no—
175C2×D4×C11—24no—
176C2×D4×C11—22no—
177C2×D4×C11—22no—
178C2×D4×C11C22×C418yes—
179C2×D4×C11C22×C414yes—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—24no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—24no—
188C22×C4×C11C22×C414yes—
189C22×C4×C11C22×C414yes—
190C22×C4×C11C22×C414yes—
191C22×C4×C11C22×C418yes—
192C22×C4×C11C2412yes—
193C22×C4×C11C2412yes—
194C22×C4×C11C2412yes—
195C22×C4×C11C2411yescharacteristic
196C22×C4×C11C2411yescharacteristic
197C22×C4×C11C2411yescharacteristic
198C22×C4×C11C2411yescharacteristic
199C22×C4×C11C2411yescharacteristic
200C22×C4×C11C2411yescharacteristic
201C22×Dic11—28no—
202C22×Dic11—44no—
203C22×Dic11—44no—
204C22×Dic11—44no—
205C22×Dic11—44no—
206C22×Dic11—44no—
207C22×Dic11C2412yes—
208C22×Dic11C2412yes—
209C22×Dic11C2412yes—
210C22×Dic11C2412yes—
211C22×Dic11C2414yes—
212C22×Dic11C2414yes—
213C11×C4⋊C4C22×C418yes—
214C11×C4⋊C4C22×C418yes—
215C11×C4⋊C4C22×C414yes—
216C11×C4⋊C4C22×C418yes—
217C11×C4⋊C4C22×C414yes—
218C11×C4⋊C4C22×C418yes—
219C11×C22⋊C4C22×C418yes—
220C11×C22⋊C4C22×C418yes—
221C11×C22⋊C4C22×C418yes—
222C11×C22⋊C4C22×C418yes—
223C11×C22⋊C4C22×C418yes—
224C42×C11C22×C414yes—
225C42×C11C22×C414yes—
226C42×C11C22×C414yes—
227C42×C11C22×C414yes—
228C42×C11C22×C418yes—
229C22⋊Dic11—24no—
230C22⋊Dic11—24no—
231C22⋊Dic11—44no—
232C22⋊Dic11—44no—
233C22⋊Dic11—44no—
234C4⋊Dic11—22no—
235C4⋊Dic11—24no—
236C4⋊Dic11—24no—
237C4⋊Dic11—24no—
238C4⋊Dic11—24no—
239C4⋊Dic11—22no—
240C4⋊Dic11—22no—
241C4⋊Dic11—22no—
242C4⋊Dic11—44no—
243C4⋊Dic11—44no—
244C4⋊Dic11—44no—
245C4⋊Dic11—42no—
246C4⋊Dic11—44no—
247C4⋊Dic11—42no—
248C4⋊Dic11—44no—
249C4⋊Dic11—44no—
250C4×Dic11—24no—
251C4×Dic11—24no—
252C4×Dic11—44no—
253C4×Dic11—44no—
254C4×Dic11—44no—
255C2×#529D1111yescharacteristic
256#2383—114no—
257#2361—112no—
258#2360—112no—
259#2355—111no—
260#2354—111no—
261#2352—112no—
262Q8×C4⋊C4—111no—
263D4×C4⋊C4—111no—
264D4×C4⋊C4—112no—
265#2330—112no—
266#2326—112no—
267#2322—114no—
268#2317—112no—
269#2314—112no—
270C2×#384—111no—
271#2283—111no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—22no—
277C23×C11—22no—
278C23×C11—22no—
279C23×C11—22no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11C23×C414yes—
283C23×C11C23×C412yes—
284C23×C11H(5,𝔽2)12yes—
285C23×C112−1+412yes—
286C23×C11C2511yescharacteristic
287Q8×C11—28no—
288D4×C11—216no—
289D4×C11—28no—
290C2×C4×C11—28no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—22no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—28no—
306C2×C4×C11—216no—
307C2×C4×C11—28no—
308C2×C4×C11C23×C412yes—
309C2×C4×C11C23×C412yes—
310C2×C4×C11C23×C412yes—
311C2×C4×C11C23×C412yes—
312C2×C4×C11C23×C414yes—
313C2×C4×C11C23×C414yes—
314C2×C4×C11C23×C414yes—
315C2×C4×C11C23×C412yes—
316C2×C4×C11C23×C412yes—
317C2×C4×C11H(5,𝔽2)12yes—
318C2×C4×C11H(5,𝔽2)12yes—
319C2×C4×C112−1+412yes—
320C2×C4×C112−1+412yes—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—24no—
326C2×Dic11—24no—
327C2×Dic11—24no—
328C2×Dic11—22no—
329C2×Dic11—24no—
330C2×Dic11—24no—
331C2×Dic11—24no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—88no—
340C2×Dic11—88no—
341#529Dic11116yescomplemented
342C2×#126C2×D1112yes—
343C2×#125C2×D1111yescharacteristic
344C2×#124C2×D1111yescharacteristic
345C2×#123C2×D1112yes—
346C2×C22⋊Q8C2×D1111yescharacteristic
347C2×#121C2×D1111yescharacteristic
348C2×C4×Q8—112no—
349C2×C4×Q8C2×D1111yescharacteristic
350C2×C4×D4—114no—
351C2×C4×D4—112no—
352C2×C4×D4C2×D1112yes—
353C2×C4×D4C2×D1111yescharacteristic
354C2×#117—112no—
355C2×#117C2×D1112yes—
356C22×C4⋊C4—112no—
357C22×C4⋊C4—112no—
358C22×C4⋊C4—112no—
359C22×C4⋊C4—112no—
360C22×C42C2×D1111yescharacteristic
361#391—112no—
362#390—112no—
363#389—114no—
364#389—114no—
365#389—114no—
366#389—112no—
367#389—114no—
368#389—112no—
369#388—114no—
370#388—114no—
371#388—114no—
372#388—114no—
373#387—114no—
374#387—114no—
375#387—114no—
376#387—114no—
377#386—114no—
378#385—114no—
379#385—114no—
380#385—114no—
381#385—114no—
382#385—114no—
383#384—112no—
384#384—112no—
385#384—112no—
386#384—111no—
387#384—111no—
388#384—112no—
389#383—112no—
390#382—111no—
391#382—111no—
392#382—112no—
393#381—112no—
394#380—112no—
395#380—112no—
396#380—111no—
397#380—111no—
398C4×C4⋊C4—112no—
399C4×C4⋊C4—112no—
400C4×C4⋊C4—112no—
401C4×C4⋊C4—112no—
402C4×C4⋊C4—111no—
403C4×C4⋊C4—111no—
404C4×C22⋊C4—112no—
405C4×C22⋊C4—114no—
406#376—112no—
407C22×C11—22no—
408C22×C11—22no—
409C22×C11—22no—
410C22×C11—22no—
411C22×C11—22no—
412C22×C11—22no—
413C22×C11—24no—
414C22×C11—24no—
415C22×C11—24no—
416C22×C11—42no—
417C22×C11—42no—
418C22×C11—42no—
419C22×C11—42no—
420C22×C11#52014yes—
421C22×C11C24×C411yescharacteristic
422C22×C11C2×H(5,𝔽2)11yescharacteristic
423C22×C11C2×H(5,𝔽2)11yescharacteristic
424C22×C11C2×H(5,𝔽2)11yescharacteristic
425C22×C11C2×2−1+411yescharacteristic
426C22×C11C2×2−1+411yescharacteristic
427C22×C11C2×2−1+411yescharacteristic
428C4×C11—22no—
429C4×C11—22no—
430C4×C11—24no—
431C4×C11—22no—
432C4×C11—22no—
433C4×C11—24no—
434C4×C11—24no—
435C4×C11#52014yes—
436C4×C11#52014yes—
437Dic11—44no—
438Dic11—42no—
439Dic11—44no—
440Dic11—42no—
441Dic11—42no—
442Dic11—42no—
443C22×Q8C22×D1111yescharacteristic
444C22×D4C22×D1112yes—
445C22×D4C22×D1111yescharacteristic
446C23×C4—114no—
447C23×C4—114no—
448C23×C4C22×D1111yescharacteristic
449C23×C4C22×D1111yescharacteristic
450C23×C4C22×D1111yescharacteristic
451C23×C4C22×D1112yes—
452#126C2×Dic11116yescomplemented
453#125C2×Dic1118yescomplemented
454#124C2×Dic1118yescomplemented
455#123C2×Dic11116yescomplemented
456C22⋊Q8C2×Dic1118yescomplemented
457#121C2×Dic1118yes—
458C4×Q8—444no—
459C4×Q8C2×Dic1118yescomplemented
460C4×D4—444no—
461C4×D4—448no—
462C4×D4C2×Dic1118yescomplemented
463C4×D4C2×Dic11116yescomplemented
464#117—444no—
465#117C2×Dic11116yescomplemented
466C2×C4⋊C4—111no—
467C2×C4⋊C4—112no—
468C2×C4⋊C4—112no—
469C2×C4⋊C4—112no—
470C2×C4⋊C4—112no—
471C2×C4⋊C4—111no—
472C2×C4⋊C4—111no—
473C2×C4⋊C4—111no—
474C2×C4⋊C4—112no—
475C2×C4⋊C4—114no—
476C2×C4⋊C4—114no—
477C2×C4⋊C4—114no—
478C2×C4⋊C4—112no—
479C2×C4⋊C4—114no—
480C2×C4⋊C4—114no—
481C2×C4⋊C4—114no—
482C2×C4⋊C4—444no—
483C2×C4⋊C4—444no—
484C2×C4⋊C4—444no—
485C2×C4⋊C4—444no—
486C2×C4⋊C4C22×D1112yes—
487C2×C4⋊C4C22×D1112yes—
488C2×C4⋊C4C22×D1111yescharacteristic
489C2×C4⋊C4C22×D1112yes—
490C2×C4⋊C4C22×D1111yescharacteristic
491C2×C4⋊C4C22×D1112yes—
492C2×C22⋊C4—112no—
493C2×C22⋊C4—112no—
494C2×C22⋊C4—114no—
495C2×C22⋊C4—114no—
496C2×C22⋊C4—114no—
497C2×C22⋊C4C22×D1112yes—
498C2×C22⋊C4C22×D1112yes—
499C2×C22⋊C4C22×D1112yes—
500C2×C22⋊C4C22×D1112yes—
501C2×C22⋊C4C22×D1112yes—
502C2×C42—112no—
503C2×C42—112no—
504C2×C42—114no—
505C2×C42—114no—
506C2×C42—114no—
507C2×C42C2×Dic1118yescomplemented
508C2×C42C22×D1111yescharacteristic
509C2×C42C22×D1112yes—
510C2×C42C22×D1111yescharacteristic
511C2×C42C22×D1111yescharacteristic
512C2×C42C22×D1111yescharacteristic
513#95—112no—
514#95—112no—
515#95—112no—
516#95—112no—
517#95—114no—
518#95—112no—
519#95—112no—
520#95—114no—
521#95—114no—
522#95—112no—
523#95—112no—
524#95—114no—
525#95—114no—
526#95—114no—
527C2×C11—24no—
528C2×C11—44no—
529C2×C11C2×#52011yescharacteristic
530C2×C11C2×#52011yescharacteristic
531C2×C11C2×#52011yescharacteristic
532C2×C11#354311yescharacteristic
533C2×C11#354411yescharacteristic
534C2×C11#355211yescharacteristic
535C2×C11#355211yescharacteristic
536C24C23×D1112yes—
537C24C23×D1111yescharacteristic
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8C22×Dic1114yes—
541C2×D4—24no—
542C2×D4—24no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4C22×Dic1118yes—
546C2×D4C22×Dic1114yes—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—112no—
556C22×C4—112no—
557C22×C4—112no—
558C22×C4—112no—
559C22×C4—114no—
560C22×C4—114no—
561C22×C4—228no—
562C22×C4—444no—
563C22×C4—444no—
564C22×C4—444no—
565C22×C4—444no—
566C22×C4—444no—
567C22×C4C22×Dic1114yes—
568C22×C4C22×Dic1114yes—
569C22×C4C22×Dic1114yes—
570C22×C4C22×Dic1118yes—
571C22×C4C23×D1112yes—
572C22×C4C23×D1112yes—
573C22×C4C23×D1112yes—
574C22×C4C23×D1111yescharacteristic
575C22×C4C23×D1111yescharacteristic
576C22×C4C23×D1111yescharacteristic
577C22×C4C23×D1111yescharacteristic
578C22×C4C23×D1111yescharacteristic
579C22×C4C23×D1111yescharacteristic
580C4⋊C4—222no—
581C4⋊C4—224no—
582C4⋊C4—224no—
583C4⋊C4—224no—
584C4⋊C4—224no—
585C4⋊C4—222no—
586C4⋊C4—222no—
587C4⋊C4—222no—
588C4⋊C4—444no—
589C4⋊C4—444no—
590C4⋊C4—444no—
591C4⋊C4—442no—
592C4⋊C4—444no—
593C4⋊C4—442no—
594C4⋊C4—444no—
595C4⋊C4—444no—
596C4⋊C4C22×Dic1118yes—
597C4⋊C4C22×Dic1118yes—
598C4⋊C4C22×Dic1114yes—
599C4⋊C4C22×Dic1118yes—
600C4⋊C4C22×Dic1114yes—
601C4⋊C4C22×Dic1118yes—
602C22⋊C4—224no—
603C22⋊C4—224no—
604C22⋊C4—444no—
605C22⋊C4—444no—
606C22⋊C4—444no—
607C22⋊C4C22×Dic1118yes—
608C22⋊C4C22×Dic1118yes—
609C22⋊C4C22×Dic1118yes—
610C22⋊C4C22×Dic1118yes—
611C22⋊C4C22×Dic1118yes—
612C42—224no—
613C42—224no—
614C42—444no—
615C42—444no—
616C42—444no—
617C42C22×Dic1114yes—
618C42C22×Dic1114yes—
619C42C22×Dic1114yes—
620C42C22×Dic1114yes—
621C42C22×Dic1118yes—
622C11#3438411yescharacteristic, complemented, Sylow
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23#6704212yes—
634C23#6704312yes—
635C23C23×Dic1114yes—
636C23C23×Dic1112yes—
637C23C24×D1111yescharacteristic
638Q8—28no—
639D4—216no—
640D4—28no—
641C2×C4—28no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—28no—
657C2×C4—216no—
658C2×C4—28no—
659C2×C4—222no—
660C2×C4—222no—
661C2×C4—222no—
662C2×C4—222no—
663C2×C4—224no—
664C2×C4—224no—
665C2×C4—224no—
666C2×C4—222no—
667C2×C4—224no—
668C2×C4—224no—
669C2×C4—222no—
670C2×C4—224no—
671C2×C4—222no—
672C2×C4—222no—
673C2×C4—222no—
674C2×C4—222no—
675C2×C4—222no—
676C2×C4—222no—
677C2×C4—888no—
678C2×C4—888no—
679C2×C4#6704212yes—
680C2×C4#6704212yes—
681C2×C4#6704312yes—
682C2×C4#6704312yes—
683C2×C4C23×Dic1112yes—
684C2×C4C23×Dic1112yes—
685C2×C4C23×Dic1112yes—
686C2×C4C23×Dic1112yes—
687C2×C4C23×Dic1114yes—
688C2×C4C23×Dic1114yes—
689C2×C4C23×Dic1114yes—
690C2×C4C23×Dic1112yes—
691C2×C4C23×Dic1112yes—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—24no—
699C22—24no—
700C22—24no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22#1062335814yes—
706C22C2×#6704211yescharacteristic
707C22C2×#6704211yescharacteristic
708C22C2×#6704211yescharacteristic
709C22C2×#6704311yescharacteristic
710C22C2×#6704311yescharacteristic
711C22C2×#6704311yescharacteristic
712C22C24×Dic1111yescharacteristic
713C4—22no—
714C4—22no—
715C4—24no—
716C4—22no—
717C4—22no—
718C4—24no—
719C4—24no—
720C4—442no—
721C4—444no—
722C4—444no—
723C4—442no—
724C4—442no—
725C4—442no—
726C4#1062335814yes—
727C4#1062335814yes—
728C2—24no—
729C2—44no—
730C2C2×#1062335811yescharacteristic
731C2C2×#1062335811yescharacteristic
732C2C2×#1062335811yescharacteristic
733C2#1308294611yescharacteristic
734C2#1308295611yescharacteristic
735C2#1308305311yescharacteristic
736C2#1308306111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC2×C11×#529C2
socle, cosocleC23×C11C25
prime radicalC2×C11×#121C22
hypercenterC2×#529D11
hypocenterC11#34384
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #13071808C2semidirect
3. #13071625C2semidirect
4. #13071573C2semidirect
5. #13071565C2semidirect
6. #13071545C2semidirect
7. Q8×C4⋊Dic11C2semidirect
8. D4×C4⋊Dic11C2semidirect
9. D4×C4⋊Dic11C2semidirect
10. #13071358C2semidirect
11. #13071329C2semidirect
12. #13071288C2semidirect
13. #13071239C2semidirect
14. #13071225C2semidirect
15. C2×#10622548C2semidirect
16. #13071014C2semidirect
18. C11×#529C4semidirect
93. C11×#126C2×C4semidirect
94. C11×#125C2×C4semidirect
95. C11×#124C2×C4semidirect
96. C11×#123C2×C4semidirect
97. C11×C22⋊Q8C2×C4semidirect
99. C4×Q8×C11C2×C4semidirect
100. C4×D4×C11C2×C4semidirect
101. C4×D4×C11C2×C4semidirect
102. C11×#117C2×C4semidirect
114. C2×C42×C11C2×C4semidirect
341. #529Dic11semidirect
452. #126C2×Dic11semidirect
453. #125C2×Dic11semidirect
454. #124C2×Dic11semidirect
455. #123C2×Dic11semidirect
456. C22⋊Q8C2×Dic11semidirect
459. C4×Q8C2×Dic11semidirect
462. C4×D4C2×Dic11semidirect
463. C4×D4C2×Dic11semidirect
465. #117C2×Dic11semidirect
507. C2×C42C2×Dic11semidirect
622. C11#34384semidirect

Maximal subgroups

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

subgroupindex
#130718082
#130716362
#130716252
#130715732
#130715652
#130715452
Q8×C4⋊Dic112
D4×C4⋊Dic112
#130713582
#130713292
#130712882
#130712392
#130712252
C2×#106225482
#130710142
C2×C11×#5292
#3438411