Finite Group Databasebeta

← #14914623

Subgroups — #14914623

Order 2816.

2286 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623111C211yesmaximal, characteristic
2#13071739C214yesmaximal, complemented
3#13071653C212yesmaximal
4#13071639C212yesmaximal, complemented
5#13071573C211yesmaximal, characteristic, complemented
6#13071567C211yesmaximal, characteristic, complemented
7#13071567C212yesmaximal, complemented
8#13071548C212yesmaximal, complemented
9C4⋊C4×D44C211yesmaximal, characteristic, complemented
10#13071409C214yesmaximal, complemented
11#13071224C212yesmaximal, complemented
12#13071175C212yesmaximal, complemented
13C4×#67000C212yesmaximal, complemented
14#13071021C211yesmaximal, characteristic, complemented
15#13070970C212yesmaximal, complemented
16C4×#66945C211yesmaximal, characteristic, complemented
17Q8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
18C2×C4×Q8×C11C2212yes—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×#67000C2211yescharacteristic
21C2×#66999C2211yescharacteristic
22#10623111C4116yescomplemented
23C2×#66951C2212yes—
24C2×#66948C2211yescharacteristic
25C2×#66947C2212yes—
26C2×#66945C2211yescharacteristic
27C2×#66945C2211yescharacteristic
28C2×#66945C2212yes—
29C2×#66945C2212yes—
30C2×C4⋊C4×D11C2212yes—
31C2×#66943C2211yescharacteristic
32C2×C4×D44C2212yes—
33C2×C4×D44C2211yescharacteristic
34C2×C4×D44C2212yes—
35C2×#66925C2212yes—
36C2×C42×D11C2211yescharacteristic
37C11×#389C2212yes—
38C11×#389C2214yes—
39C11×#384C2212yes—
40C11×#384C2211yescharacteristic
41C4×C11×C4⋊C4C2211yescharacteristic
42C4×C11×C4⋊C4C2212yes—
43#10622843C2212yes—
44#10622603C2214yes—
45#10622603C2214yes—
46#10622603C2214yes—
47#10622603C2214yes—
48#10622603C2214yes—
49#10622601C2214yes—
50#10622601C2212yes—
51#10622600C2212yes—
52#10622600C2212yes—
53#10622600C2212yes—
54#10622600C2212yes—
55#10622594C2214yes—
56#10622591C2214yes—
57#10622591C2214yes—
58#10622590C2212yes—
59C4⋊C4×Dic11C2212yes—
60C4⋊C4×Dic11C2212yes—
61C4⋊C4×Dic11C2214yes—
62C4⋊C4×Dic11C2211yescharacteristic
63C4⋊C4×Dic11C2211yescharacteristic
64C4⋊C4×Dic11C2212yes—
65C4⋊C4×Dic11C2212yes—
66#10622553C2214yes—
67C4×(C2×D11)⋊C4C2212yes—
68C4×(C2×D11)⋊C4C2214yes—
69C4×(C2×D11)⋊C4C2214yes—
70#10622549C2212yes—
71#10622548C2211yescharacteristic
72C4×C4⋊Dic11C2211yescharacteristic
73C4×C4⋊Dic11C2212yes—
74C4×Dic11⋊C4C2214yes—
75C42×Dic11C2212yes—
76#10622541C2212yes—
77#10622281C2214yes—
78#10622279C2214yes—
79#10622279C2212yes—
80#10622278C2214yes—
81#10622266C2214yes—
82#10622262C2214yes—
83#10622261C2212yes—
84C22×Q8×C11C2311yescharacteristic
85C22×D44C2311yescharacteristic
86C22×D44C2312yes—
87C22×C4×D11C2311yescharacteristic
88C22×C4×D11C2311yescharacteristic
89C22×C4×D11C2312yes—
90C22×C4×D11C2314yes—
91C22×C4×D11C2311yescharacteristic
92C4×Q8×C11—44no—
93C4×Q8×C11C2×C418yescomplemented
94C2×C11×C4⋊C4C2312yes—
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2312yes—
97C2×C11×C4⋊C4C2314yes—
98C2×C11×C4⋊C4C2312yes—
99C2×C11×C4⋊C4C2314yes—
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2312yes—
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C42×C11C2312yes—
104C2×C42×C11C2314yes—
105C2×C42×C11C2311yescharacteristic
106C2×C42×C11C2312yes—
107#67000C2×C418yes—
108#66999C2×C418yescomplemented
109C2×(C2×D11)⋊C4C2312yes—
110C2×(C2×D11)⋊C4C2312yes—
111C2×(C2×D11)⋊C4C2314yes—
112C2×(C2×D11)⋊C4C2314yes—
113C2×(C2×D11)⋊C4C2314yes—
114C2×(C2×D11)⋊C4C2314yes—
115C2×(C2×D11)⋊C4C2312yes—
116C2×(C2×D11)⋊C4C2312yes—
117C2×(C2×D11)⋊C4C2312yes—
118C2×(C2×D11)⋊C4C2312yes—
119C2×(C2×D11)⋊C4C2312yes—
120C2×C4⋊Dic11C2312yes—
121C2×C4⋊Dic11C2312yes—
122C2×C4⋊Dic11C2311yescharacteristic
123C2×C4⋊Dic11C2312yes—
124C2×C4⋊Dic11C2312yes—
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4⋊Dic11C2311yescharacteristic
127C2×Dic11⋊C4C2314yes—
128C2×Dic11⋊C4C2312yes—
129C2×Dic11⋊C4C2312yes—
130C2×C4×Dic11C2312yes—
131C2×C4×Dic11C2312yes—
132C2×C4×Dic11C2314yes—
133C2×C4×Dic11C2312yes—
134C2×C4×Dic11C2312yes—
135C2×C4×Dic11C2314yes—
136C2×C4×Dic11C2314yes—
137C2×C4×Dic11C2312yes—
138C2×C4×Dic11C2311yescharacteristic
139C2×C4×Dic11C2311yescharacteristic
140C2×C4×Dic11C2311yescharacteristic
141#66951C2×C4116yescomplemented
142#66948C2×C418yes—
143#66947C2×C4116yescomplemented
144#66945—24no—
145#66945—24no—
146#66945—28no—
147#66945—44no—
148C4⋊C4×D11—28no—
149#66943C2×C418yescomplemented
150C4×D44—44no—
151C4×D44C2×C418yes—
152C4×D44C2×C4116yescomplemented
153#66925C2×C4116yescomplemented
154C42×D11C2×C418yescomplemented
155C11×#95C2312yes—
156C11×#95C2314yes—
157C11⋊#95C2312yes—
158C11⋊#95C2312yes—
159C11⋊#95C2312yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C11⋊#95C2314yes—
167#34242—111nomaximal, Sylow
168C23×D11C2411yescharacteristic
169C23×D11C2412yes—
170C2×Q8×C11—22no—
171C2×Q8×C11—22no—
172C2×Q8×C11C22×C414yes—
173C22×C4×C11C2414yes—
174C22×C4×C11C2412yes—
175C22×C4×C11C2412yes—
176C22×C4×C11C2412yes—
177C22×C4×C11C2411yescharacteristic
178C22×C4×C11C2412yes—
179C22×C4×C11C2411yescharacteristic
180C22×C4×C11C2411yescharacteristic
181C22×Dic11C2412yes—
182C22×Dic11C2414yes—
183C22×Dic11C2411yescharacteristic
184C22×Dic11C2411yescharacteristic
185C22×Dic11C2411yescharacteristic
186C22×Dic11C2412yes—
187C22×Dic11C2412yes—
188C2×D44—22no—
189C2×D44—22no—
190C2×D44—42no—
191C2×D44—42no—
192C2×D44C22×C414yes—
193C2×D44C22×C418yes—
194C2×C4×D11—24no—
195C2×C4×D11—22no—
196C2×C4×D11—22no—
197C2×C4×D11—24no—
198C2×C4×D11—28no—
199C2×C4×D11—22no—
200C2×C4×D11—22no—
201C2×C4×D11—41no—
202C2×C4×D11—41no—
203C2×C4×D11—44no—
204C2×C4×D11—44no—
205C2×C4×D11C22×C414yes—
206C2×C4×D11C22×C414yes—
207C2×C4×D11C22×C418yes—
208C2×C4×D11C22×C414yes—
209C11×C4⋊C4—22no—
210C11×C4⋊C4—24no—
211C11×C4⋊C4—24no—
212C11×C4⋊C4—42no—
213C11×C4⋊C4—44no—
214C11×C4⋊C4—44no—
215C11×C4⋊C4C22×C414yes—
216C11×C4⋊C4C22×C418yes—
217C11×C4⋊C4#4114yes—
218C42×C11—24no—
219C42×C11—44no—
220C42×C11C22×C414yes—
221C42×C11C22×C418yes—
222(C2×D11)⋊C4—24no—
223(C2×D11)⋊C4—28no—
224(C2×D11)⋊C4—24no—
225(C2×D11)⋊C4—44no—
226(C2×D11)⋊C4—44no—
227(C2×D11)⋊C4—44no—
228(C2×D11)⋊C4C22×C418yes—
229(C2×D11)⋊C4C22×C418yes—
230(C2×D11)⋊C4C22×C418yes—
231(C2×D11)⋊C4C22×C418yes—
232(C2×D11)⋊C4C22×C418yes—
233C4⋊Dic11—24no—
234C4⋊Dic11—22no—
235C4⋊Dic11—24no—
236C4⋊Dic11—42no—
237C4⋊Dic11C22×C414yes—
238C4⋊Dic11C22×C418yes—
239C4⋊Dic11#4114yes—
240Dic11⋊C4—28no—
241Dic11⋊C4C22×C418yes—
242Dic11⋊C4C22×C418yes—
243C4×Dic11—24no—
244C4×Dic11—28no—
245C4×Dic11—24no—
246C4×Dic11—24no—
247C4×Dic11—44no—
248C4×Dic11—44no—
249C4×Dic11—42no—
250C4×Dic11—42no—
251C4×Dic11C22×C414yes—
252C4×Dic11C22×C414yes—
253C4×Dic11C22×C414yes—
254C2×#529—111no—
255#2373—114no—
256#2363—112no—
257#2362—112no—
258#2355—111no—
259#2354—112no—
260#2354—111no—
261#2352—112no—
262Q8×C4⋊C4D1111yescharacteristic, complemented
263D4×C4⋊C4—111no—
264#2335—114no—
265#2314—112no—
266C4×#125—112no—
267C4×#124—112no—
268#2285—111no—
269#2274—112no—
270C4×#117—111no—
271C23×C11C2511yescharacteristic
272C22×D11—21no—
273C22×D11—21no—
274C22×D11—22no—
275C22×D11—22no—
276C22×D11—21no—
277C22×D11—22no—
278C22×D11—21no—
279C22×D11—22no—
280C22×D11—22no—
281C22×D11—22no—
282C22×D11—21no—
283C22×D11—21no—
284C22×D11C23×C414yes—
285C22×D11C23×C412yes—
286Q8×C11—28no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—22no—
295C2×C4×C11—24no—
296C2×C4×C11—22no—
297C2×C4×C11—24no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—24no—
301C2×C4×C11C23×C412yes—
302C2×C4×C11C23×C414yes—
303C2×C4×C11C23×C414yes—
304C2×C4×C11C23×C412yes—
305C2×C4×C11C23×C412yes—
306C2×C4×C11C2×#4114yes—
307C2×C4×C11C2×#4112yes—
308C2×C4×C11C2×#4112yes—
309C2×C4×C11H(5,𝔽2)12yes—
310C2×C4×C112−1+412yes—
311C2×Dic11—21no—
312C2×Dic11—21no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—21no—
316C2×Dic11—22no—
317C2×Dic11—21no—
318C2×Dic11—22no—
319C2×Dic11—21no—
320C2×Dic11—21no—
321C2×Dic11—22no—
322C2×Dic11—24no—
323C2×Dic11—24no—
324C2×Dic11—22no—
325C2×Dic11—24no—
326C2×Dic11—22no—
327C2×Dic11C23×C412yes—
328C2×Dic11C23×C412yes—
329C2×Dic11C23×C412yes—
330C2×Dic11C23×C414yes—
331C2×Dic11C2×#4114yes—
332D44—28no—
333D44—48no—
334C4×D11—216no—
335C4×D11—28no—
336C4×D11—28no—
337C4×D11—44no—
338C4×D11—88no—
339#529—1116no—
340C2×#126—112no—
341C2×#125—111no—
342C2×#124—111no—
343C2×#123—112no—
344C2×C22⋊Q8—111no—
345C2×#121—111no—
346C2×C4×Q8C2×D1112yes—
347C2×C4×Q8C2×D1111yescharacteristic
348C2×C4×D4—111no—
349C2×C4×D4—112no—
350C2×C4×D4—112no—
351C2×#117—111no—
352C2×#117—111no—
353C2×#117—112no—
354C2×#117—112no—
355C2×#117—112no—
356C22×C4⋊C4—112no—
357C22×C42—111no—
358#391—112no—
359#390—114no—
360#390—112no—
361#389—112no—
362#389C2×D1112yes—
363#389C2×D1114yes—
364#388—114no—
365#388—114no—
366#388—114no—
367#388—114no—
368#388—114no—
369#388—114no—
370#387—114no—
371#387—114no—
372#387—114no—
373#387—114no—
374#386—114no—
375#385—114no—
376#384—111no—
377#384C2×D1112yes—
378#384C2×D1111yescharacteristic
379#382—112no—
380#382—112no—
381#380—112no—
382#380—112no—
383#380—112no—
384#380—112no—
385C4×C4⋊C4—112no—
386C4×C4⋊C4—114no—
387C4×C4⋊C4—112no—
388C4×C4⋊C4—111no—
389C4×C4⋊C4—112no—
390C4×C4⋊C4—112no—
391C4×C4⋊C4—111no—
392C4×C4⋊C4—111no—
393C4×C4⋊C4—112no—
394C4×C4⋊C4—114no—
395C4×C4⋊C4—114no—
396C4×C4⋊C4C2×D1111yescharacteristic
397C4×C4⋊C4C2×D1112yes—
398C4×C22⋊C4—114no—
399C4×C22⋊C4—114no—
400C4×C22⋊C4—112no—
401C4×C22⋊C4—112no—
402C4×C22⋊C4—114no—
403#376—112no—
404C43—112no—
405C22×C11C24×C411yescharacteristic
406C22×C11C22×#4111yescharacteristic
407C22×C11C22×#4111yescharacteristic
408C22×C11C2×H(5,𝔽2)11yescharacteristic
409C22×C11C2×2−1+411yescharacteristic
410C22×C11#58511yescharacteristic
411C22×C11#58511yescharacteristic
412C2×D11—22no—
413C2×D11—24no—
414C2×D11—22no—
415C2×D11—24no—
416C2×D11—22no—
417C2×D11—24no—
418C2×D11—41no—
419C2×D11—42no—
420C2×D11—41no—
421C2×D11—42no—
422C2×D11—41no—
423C2×D11—42no—
424C2×D11—41no—
425C2×D11—42no—
426C4×C11—24no—
427C4×C11—22no—
428C4×C11—24no—
429C4×C11—24no—
430C4×C11—44no—
431C4×C11—42no—
432C4×C11C4×#4114yes—
433C4×C11#52014yes—
434Dic11—22no—
435Dic11—24no—
436Dic11—22no—
437Dic11—22no—
438Dic11—24no—
439Dic11—44no—
440Dic11—42no—
441C22×Q8C22×D1111yescharacteristic
442C22×D4—111no—
443C22×D4—112no—
444C23×C4—112no—
445C23×C4—111no—
446C23×C4—111no—
447C23×C4—111no—
448C23×C4—114no—
449#126—1116no—
450#125—118no—
451#124—118no—
452#123—1116no—
453C22⋊Q8—118no—
454#121—118no—
455C4×Q8—44no—
456C4×Q8C4×D1118yescomplemented
457C4×D4—118no—
458C4×D4—1116no—
459C4×D4—444no—
460#117—1116no—
461#117—224no—
462#117—228no—
463#117—224no—
464#117—444no—
465C2×C4⋊C4—111no—
466C2×C4⋊C4—112no—
467C2×C4⋊C4—112no—
468C2×C4⋊C4—111no—
469C2×C4⋊C4—112no—
470C2×C4⋊C4—112no—
471C2×C4⋊C4—114no—
472C2×C4⋊C4—112no—
473C2×C4⋊C4—111no—
474C2×C4⋊C4—112no—
475C2×C4⋊C4—228no—
476C2×C4⋊C4C22×D1112yes—
477C2×C4⋊C4C22×D1111yescharacteristic
478C2×C4⋊C4C22×D1112yes—
479C2×C4⋊C4C22×D1114yes—
480C2×C4⋊C4C22×D1112yes—
481C2×C4⋊C4C22×D1114yes—
482C2×C4⋊C4C22×D1111yescharacteristic
483C2×C4⋊C4C22×D1112yes—
484C2×C4⋊C4C22×D1111yescharacteristic
485C2×C22⋊C4—112no—
486C2×C22⋊C4—112no—
487C2×C22⋊C4—112no—
488C2×C22⋊C4—112no—
489C2×C22⋊C4—112no—
490C2×C22⋊C4—112no—
491C2×C22⋊C4—112no—
492C2×C22⋊C4—114no—
493C2×C22⋊C4—114no—
494C2×C22⋊C4—114no—
495C2×C22⋊C4—114no—
496C2×C42—111no—
497C2×C42—111no—
498C2×C42—111no—
499C2×C42—118no—
500C2×C42—112no—
501C2×C42—112no—
502C2×C42—114no—
503C2×C42—112no—
504C2×C42—114no—
505C2×C42—112no—
506C2×C42—112no—
507C2×C42—114no—
508C2×C42C22×D1112yes—
509C2×C42C22×D1114yes—
510C2×C42C22×D1112yes—
511C2×C42C22×D1111yescharacteristic
512#95—112no—
513#95—112no—
514#95—112no—
515#95—114no—
516#95—114no—
517#95—114no—
518#95—114no—
519#95—114no—
520#95—114no—
521#95—114no—
522#95C22×D1112yes—
523#95C22×D1114yes—
524C2×C11C2×C4×#4111yescharacteristic
525C2×C11C2×#52011yescharacteristic
526C2×C11#342811yescharacteristic
527C2×C11#351411yescharacteristic
528C2×C11#351511yescharacteristic
529C2×C11#351711yescharacteristic
530C2×C11#351811yescharacteristic
531D11—42no—
532D11—44no—
533C24—112no—
534C24—111no—
535C2×Q8—22no—
536C2×Q8—22no—
537C2×Q8C2×C4×D1114yes—
538C2×D4—114no—
539C2×D4—118no—
540C2×D4—222no—
541C2×D4—222no—
542C2×D4—442no—
543C2×D4—442no—
544C22×C4—112no—
545C22×C4—111no—
546C22×C4—111no—
547C22×C4—111no—
548C22×C4—112no—
549C22×C4—114no—
550C22×C4—114no—
551C22×C4—118no—
552C22×C4—114no—
553C22×C4—112no—
554C22×C4—114no—
555C22×C4—222no—
556C22×C4—224no—
557C22×C4—222no—
558C22×C4—222no—
559C22×C4—224no—
560C22×C4—222no—
561C22×C4—228no—
562C22×C4—441no—
563C22×C4—441no—
564C22×C4—444no—
565C22×C4—444no—
566C22×C4C23×D1112yes—
567C22×C4C23×D1114yes—
568C22×C4C23×D1112yes—
569C22×C4C23×D1112yes—
570C22×C4C23×D1111yescharacteristic
571C22×C4C23×D1112yes—
572C22×C4C23×D1111yescharacteristic
573C22×C4C23×D1111yescharacteristic
574C4⋊C4—24no—
575C4⋊C4—22no—
576C4⋊C4—24no—
577C4⋊C4—44no—
578C4⋊C4—42no—
579C4⋊C4—44no—
580C4⋊C4—118no—
581C4⋊C4—118no—
582C4⋊C4—114no—
583C4⋊C4—118no—
584C4⋊C4—114no—
585C4⋊C4—224no—
586C4⋊C4—228no—
587C4⋊C4—224no—
588C4⋊C4—222no—
589C4⋊C4—442no—
590C4⋊C4C2×C4×D1114yes—
591C4⋊C4C2×C4×D1118yes—
592C4⋊C4#434314yes—
593C22⋊C4—118no—
594C22⋊C4—118no—
595C22⋊C4—118no—
596C22⋊C4—118no—
597C22⋊C4—118no—
598C22⋊C4—224no—
599C22⋊C4—228no—
600C22⋊C4—224no—
601C22⋊C4—444no—
602C22⋊C4—444no—
603C22⋊C4—444no—
604C42—24no—
605C42—44no—
606C42—114no—
607C42—114no—
608C42—114no—
609C42—224no—
610C42—228no—
611C42—224no—
612C42—224no—
613C42—444no—
614C42—444no—
615C42—442no—
616C42—442no—
617C42C2×C4×D1114yes—
618C42C2×C4×D1118yes—
619C11#3424211yescharacteristic, complemented, Sylow
620C23—114no—
621C23—112no—
622C23—221no—
623C23—222no—
624C23—221no—
625C23—222no—
626C23—221no—
627C23—222no—
628C23—222no—
629C23—221no—
630C23—222no—
631C23—221no—
632C23—222no—
633C23—221no—
634C23C24×D1111yescharacteristic
635Q8—28no—
636D4—228no—
637D4—448no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—24no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—24no—
652C2×C4—112no—
653C2×C4—112no—
654C2×C4—112no—
655C2×C4—114no—
656C2×C4—114no—
657C2×C4—221no—
658C2×C4—221no—
659C2×C4—222no—
660C2×C4—222no—
661C2×C4—221no—
662C2×C4—221no—
663C2×C4—222no—
664C2×C4—221no—
665C2×C4—222no—
666C2×C4—221no—
667C2×C4—228no—
668C2×C4—228no—
669C2×C4—2216no—
670C2×C4—224no—
671C2×C4—222no—
672C2×C4—224no—
673C2×C4—222no—
674C2×C4—222no—
675C2×C4—224no—
676C2×C4—444no—
677C2×C4—888no—
678C2×C4C22×C4×D1112yes—
679C2×C4C22×C4×D1114yes—
680C2×C4C22×C4×D1114yes—
681C2×C4C22×C4×D1112yes—
682C2×C4C22×C4×D1112yes—
683C2×C4#6703712yes—
684C2×C4C2×#434314yes—
685C2×C4C2×#434312yes—
686C2×C4#6704012yes—
687C2×C4#41×D1112yes—
688C22—224no—
689C22—222no—
690C22—222no—
691C22—224no—
692C22—222no—
693C22—224no—
694C22—441no—
695C22—442no—
696C22—442no—
697C22—441no—
698C22—441no—
699C22—442no—
700C22—441no—
701C22—442no—
702C22C23×C4×D1111yescharacteristic
703C22C2×#6703711yescharacteristic
704C22C22×#434311yescharacteristic
705C22C2×#6704011yescharacteristic
706C22C2×#41×D1111yescharacteristic
707C22#1062345511yescharacteristic
708C22#1062345711yescharacteristic
709C4—24no—
710C4—24no—
711C4—22no—
712C4—24no—
713C4—42no—
714C4—44no—
715C4—222no—
716C4—224no—
717C4—222no—
718C4—222no—
719C4—224no—
720C4—442no—
721C4—444no—
722C4#1062303514yes—
723C4C4×#434314yes—
724C2—442no—
725C2—444no—
726C2C2×C4×#434311yescharacteristic
727C2C2×#1062303511yescharacteristic
728C2#1308181611yescharacteristic
729C2#1308257811yescharacteristic
730C2#1308259311yescharacteristic
731C2#1308261911yescharacteristic
732C2#1308263411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingQ8×C11×C4⋊C4C2
socle, cosocleC23×C11C25
prime radicalC2×#66948C22
hypercenterQ8×C4⋊C4D11
hypocenterC11#34242
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ Q8×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13071739C2semidirect
4. #13071639C2semidirect
5. #13071573C2semidirect
6. #13071567C2semidirect
7. #13071567C2semidirect
8. #13071548C2semidirect
9. C4⋊C4×D44C2semidirect
10. #13071409C2semidirect
11. #13071224C2semidirect
12. #13071175C2semidirect
13. C4×#67000C2semidirect
14. #13071021C2semidirect
15. #13070970C2semidirect
16. C4×#66945C2semidirect
17. Q8×C11×C4⋊C4C2semidirect
22. #10623111C4semidirect
93. C4×Q8×C11C2×C4semidirect
108. #66999C2×C4semidirect
141. #66951C2×C4semidirect
143. #66947C2×C4semidirect
149. #66943C2×C4semidirect
152. C4×D44C2×C4semidirect
153. #66925C2×C4semidirect
154. C42×D11C2×C4semidirect
262. Q8×C4⋊C4D11semidirect
456. C4×Q8C4×D11semidirect
619. C11#34242semidirect

Maximal subgroups

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

subgroupindex
C2×#106231112
#130717392
#130716532
#130716392
#130715732
#130715672
#130715482
C4⋊C4×D442
#130714092
#130712242
#130711752
C4×#670002
#130710212
#130709702
C4×#669452
Q8×C11×C4⋊C42
#3424211