Finite Group Databasebeta

← #14914206

Subgroups — #14914206

Order 2816.

2226 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623048C211yesmaximal, characteristic
2#13071714C212yesmaximal, complemented
3#13071708C212yesmaximal, complemented
4#13071703C212yesmaximal, complemented
5#13071675C212yesmaximal, complemented
6#13071574C212yesmaximal, complemented
7#13071574C212yesmaximal, complemented
8#13071571C212yesmaximal, complemented
9C4⋊C4×Dic22C212yesmaximal, complemented
10#13071344C214yesmaximal
11#13071239C211yesmaximal, characteristic
12#13071236C211yesmaximal, characteristic
13C4×#66931C214yesmaximal
14#13071019C211yesmaximal, characteristic
15#13070973C211yesmaximal, characteristic
16C2×C4⋊C4×Dic11C211yesmaximal, characteristic
17C11×#2274C211yesmaximal, characteristic
18C2×C11×#117C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C2×#66979C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4×Dic11C2212yes—
25C22×C4×Dic11C2211yescharacteristic
26#10623048C4116yescomplemented
27C2×#66943C2211yescharacteristic
28C2×#66943C2211yescharacteristic
29C2×#66941C2211yescharacteristic
30C2×#66941C2211yescharacteristic
31C2×#66931C2212yes—
32C2×#66931C2212yes—
33C2×C4×Dic22C2214yes—
34C2×C4×Dic22C2212yes—
35C2×C4×Dic22C2212yes—
36C4×C11×C4⋊C4C2212yes—
37C4×C11×C4⋊C4C2212yes—
38C4×C11×C4⋊C4C2212yes—
39C4×C11×C4⋊C4C2212yes—
40C4×C11×C22⋊C4C2214yes—
41C4×C22⋊Dic11C2214yes—
42C2×C11⋊#95C2212yes—
43#10622598C2212yes—
44#10622598C2212yes—
45#10622590C2212yes—
46#10622590C2211yescharacteristic
47#10622590C2211yescharacteristic
48#10622589C2212yes—
49#10622589C2211yescharacteristic
50#10622589C2211yescharacteristic
51C4⋊C4×Dic11C2212yes—
52C4⋊C4×Dic11C2212yes—
53C4⋊C4×Dic11C2212yes—
54C4⋊C4×Dic11C2212yes—
55C4⋊C4×Dic11C2212yes—
56C4⋊C4×Dic11C2212yes—
57C4⋊C4×Dic11C2212yes—
58C4⋊C4×Dic11C2212yes—
59#10622563C2214yes—
60#10622559C2214yes—
61#10622555C2212yes—
62#10622555C2212yes—
63#10622549C2212yes—
64#10622548C2212yes—
65C4×C4⋊Dic11C2214yes—
66#10622546C2214yes—
67#10622546C2214yes—
68C4×Dic11⋊C4C2214yes—
69C4×Dic11⋊C4C2214yes—
70C4×Dic11⋊C4C2212yes—
71C4×Dic11⋊C4C2212yes—
72#10622542C2214yes—
73#10622541C2212yes—
74#10622541C2212yes—
75#10622541C2214yes—
76#10622268C2214yes—
77#10622268C2214yes—
78#10622267C2214yes—
79#10622267C2214yes—
80#10622260C2214yes—
81#10622260C2214yes—
82#10622259C2214yes—
83#10622259C2214yes—
84C23×C4×C11C2312yes—
85C23×C4×C11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2312yes—
88C23×Dic11C2311yescharacteristic
89C22×Dic22C2312yes—
90C22×Dic22C2312yes—
91C11×#117—24no—
92C11×#117C2×C418yes—
93C2×C11×C4⋊C4Q818yescomplemented
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2312yes—
99C2×C11×C4⋊C4C2312yes—
100C2×C11×C22⋊C4C2312yes—
101C2×C11×C22⋊C4C2312yes—
102C2×C42×C11C2312yes—
103C2×C42×C11C2314yes—
104C2×C42×C11C2314yes—
105C2×C42×C11C2312yes—
106C2×C22⋊Dic11C2312yes—
107C2×C22⋊Dic11C2312yes—
108#66979—24no—
109#66979C2×C418yes—
110C2×C4⋊Dic11—24no—
111C2×C4⋊Dic11C2312yes—
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2312yes—
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4⋊Dic11C2314yes—
116C2×C4⋊Dic11C2314yes—
117C2×C4⋊Dic11C2312yes—
118C2×C4⋊Dic11C2312yes—
119C2×C4⋊Dic11C2311yescharacteristic
120C2×C4⋊Dic11C2311yescharacteristic
121C2×Dic11⋊C4C2312yes—
122C2×Dic11⋊C4C2312yes—
123C2×Dic11⋊C4C2314yes—
124C2×Dic11⋊C4C2314yes—
125C2×Dic11⋊C4C2312yes—
126C2×Dic11⋊C4C2312yes—
127C2×Dic11⋊C4C2312yes—
128C2×Dic11⋊C4C2312yes—
129C2×Dic11⋊C4C2312yes—
130C2×Dic11⋊C4C2312yes—
131C2×C4×Dic11—44no—
132C2×C4×Dic11C2×C418yes—
133C2×C4×Dic11C2314yes—
134C2×C4×Dic11C2312yes—
135C2×C4×Dic11C2314yes—
136C2×C4×Dic11C2314yes—
137C2×C4×Dic11C2314yes—
138C2×C4×Dic11C2311yescharacteristic
139C2×C4×Dic11C2311yescharacteristic
140C2×C4×Dic11C2312yes—
141C2×C4×Dic11C2311yescharacteristic
142C2×C4×Dic11C2311yescharacteristic
143#66943C2×C418yescomplemented
144#66943C2×C418yescomplemented
145#66941C2×C418yescomplemented
146#66941C2×C418yescomplemented
147#66931C2×C4116yes—
148#66931C2×C4116yes—
149C4×Dic22—48no—
150C4×Dic22C2×C4116yescomplemented
151C4×Dic22C2×C4116yescomplemented
152C11×#95C2314yes—
153C11×#95C2314yes—
154C11⋊#95C2312yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2312yes—
163C11⋊#95C2314yes—
164C11⋊#95C2312yes—
165C11⋊#95C2312yes—
166#34213—111nomaximal, Sylow
167C24×C11C2411yescharacteristic
168C22×C4×C11—42no—
169C22×C4×C11—42no—
170C22×C4×C11C22×C414yes—
171C22×C4×C11C2×Q818yes—
172C22×C4×C11C2×Q814yes—
173C22×C4×C11#4114yes—
174C22×C4×C11C2412yes—
175C22×C4×C11C2412yes—
176C22×C4×C11C2412yes—
177C22×C4×C11C2412yes—
178C22×C4×C11C2414yes—
179C22×C4×C11C2411yescharacteristic
180C22×C4×C11C2411yescharacteristic
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—24no—
184C22×Dic11—42no—
185C22×Dic11—41no—
186C22×Dic11—42no—
187C22×Dic11—41no—
188C22×Dic11C22×C414yes—
189C22×Dic11C22×C414yes—
190C22×Dic11C2412yes—
191C22×Dic11C2414yes—
192C22×Dic11C2412yes—
193C22×Dic11C2411yescharacteristic
194C22×Dic11C2411yescharacteristic
195C22×Dic11C2412yes—
196C22×Dic11C2412yes—
197C22×Dic11C2411yescharacteristic
198C22×Dic11C2411yescharacteristic
199C2×Dic22—24no—
200C2×Dic22—24no—
201C2×Dic22—42no—
202C2×Dic22—42no—
203C2×Dic22C22×C418yes—
204C2×Dic22C22×C418yes—
205C11×C4⋊C4—22no—
206C11×C4⋊C4—22no—
207C11×C4⋊C4C22×C414yes—
208C11×C4⋊C4C22×C414yes—
209C11×C4⋊C4C2×Q818yes—
210C11×C4⋊C4C2×Q818yes—
211C11×C22⋊C4—24no—
212C11×C22⋊C4C22×C418yes—
213C42×C11—24no—
214C42×C11—44no—
215C42×C11—44no—
216C42×C11C22×C418yes—
217C22⋊Dic11—24no—
218C22⋊Dic11C22×C418yes—
219C4⋊Dic11—24no—
220C4⋊Dic11—24no—
221C4⋊Dic11—22no—
222C4⋊Dic11—22no—
223C4⋊Dic11—44no—
224C4⋊Dic11—44no—
225C4⋊Dic11C22×C418yes—
226C4⋊Dic11C22×C418yes—
227C4⋊Dic11C22×C414yes—
228C4⋊Dic11C22×C414yes—
229Dic11⋊C4—24no—
230Dic11⋊C4—24no—
231Dic11⋊C4—44no—
232Dic11⋊C4—44no—
233Dic11⋊C4—42no—
234Dic11⋊C4—42no—
235Dic11⋊C4C22×C418yes—
236Dic11⋊C4C22×C418yes—
237Dic11⋊C4C22×C418yes—
238Dic11⋊C4C22×C418yes—
239C4×Dic11—28no—
240C4×Dic11—24no—
241C4×Dic11—44no—
242C4×Dic11—44no—
243C4×Dic11—44no—
244C4×Dic11C22×C414yes—
245C4×Dic11C22×C414yes—
246C4×Dic11C22×C418yes—
247C4×Dic11C22×C414yes—
248C4×Dic11C22×C414yes—
249C2×#533—111no—
250#2370—112no—
251#2370—112no—
252#2369—112no—
253#2365—112no—
254#2355—112no—
255#2355—112no—
256#2355—112no—
257Q8×C4⋊C4—112no—
258#2329—114no—
259#2317—111no—
260#2317—111no—
261C4×C22⋊Q8—114no—
262#2285—111no—
263#2274—111no—
264#2274D1111yescharacteristic
265C2×C4×C4⋊C4—111no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11C23×C412yes—
271C23×C11C22×Q812yes—
272C23×C11C2×#4112yes—
273C23×C11C2511yescharacteristic
274C2×C4×C11—24no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—24no—
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—48no—
287C2×C4×C11C4×Q8116yescomplemented
288C2×C4×C11C23×C414yes—
289C2×C4×C11C23×C414yes—
290C2×C4×C11C23×C412yes—
291C2×C4×C11C23×C412yes—
292C2×C4×C11C22×Q818yes—
293C2×C4×C11C22×Q812yes—
294C2×C4×C11C22×Q812yes—
295C2×C4×C11C2×#4112yes—
296C2×C4×C11C2×#4112yes—
297C2×Dic11—21no—
298C2×Dic11—22no—
299C2×Dic11—22no—
300C2×Dic11—21no—
301C2×Dic11—22no—
302C2×Dic11—22no—
303C2×Dic11—21no—
304C2×Dic11—21no—
305C2×Dic11—21no—
306C2×Dic11—21no—
307C2×Dic11—28no—
308C2×Dic11—22no—
309C2×Dic11—22no—
310C2×Dic11—24no—
311C2×Dic11—24no—
312C2×Dic11—22no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—22no—
316C2×Dic11—24no—
317C2×Dic11—44no—
318C2×Dic11—48no—
319C2×Dic11C23×C412yes—
320C2×Dic11C23×C412yes—
321C2×Dic11C23×C412yes—
322C2×Dic11C23×C414yes—
323C2×Dic11C23×C414yes—
324C2×Dic11C23×C412yes—
325C2×Dic11H(5,𝔽2)12yes—
326C2×Dic112−1+412yes—
327Dic22—216no—
328Dic22—48no—
329#533—1116no—
330C2×C4⋊Q8—111no—
331C2×C4⋊Q8—111no—
332C2×#125—111no—
333C2×#125—111no—
334C2×C22⋊Q8—112no—
335C2×C22⋊Q8—112no—
336C2×C4×Q8—112no—
337C2×C4×Q8—112no—
338C2×C4×Q8—114no—
339C2×#117—111no—
340C2×#117—111no—
341C2×#117C2×D1111yescharacteristic
342C2×#117C2×D1111yescharacteristic
343C22×C4⋊C4—111no—
344C22×C4⋊C4C2×D1111yescharacteristic
345C22×C42—111no—
346C22×C42—112no—
347#391—114no—
348#391—114no—
349#391—114no—
350#389—112no—
351#389—112no—
352#389—112no—
353#389—112no—
354#389—114no—
355#389—114no—
356#389—114no—
357#387—114no—
358#387—114no—
359#387—114no—
360#387—114no—
361#387—114no—
362#387—114no—
363#385—114no—
364#385—114no—
365#384—112no—
366#384—111no—
367#384—111no—
368#384—112no—
369#382—112no—
370#382—111no—
371#382—111no—
372#382—112no—
373#380—112no—
374#380—112no—
375C4×C4⋊C4—112no—
376C4×C4⋊C4—112no—
377C4×C4⋊C4—112no—
378C4×C4⋊C4—112no—
379C4×C4⋊C4—112no—
380C4×C4⋊C4—112no—
381C4×C4⋊C4—112no—
382C4×C4⋊C4—112no—
383C4×C4⋊C4—114no—
384C4×C4⋊C4—114no—
385C4×C4⋊C4—114no—
386C4×C4⋊C4—112no—
387C4×C4⋊C4—112no—
388C4×C4⋊C4C2×D1112yes—
389C4×C4⋊C4C2×D1112yes—
390C4×C4⋊C4C2×D1112yes—
391C4×C4⋊C4C2×D1112yes—
392C4×C22⋊C4—114no—
393C4×C22⋊C4C2×D1114yes—
394C2×#95—112no—
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—22no—
398C22×C11—22no—
399C22×C11—22no—
400C22×C11—22no—
401C22×C11C2×C4×Q814yes—
402C22×C11C24×C411yescharacteristic
403C22×C11C23×Q811yescharacteristic
404C22×C11C22×#4111yescharacteristic
405C22×C11C2×H(5,𝔽2)11yescharacteristic
406C22×C11C2×2−1+411yescharacteristic
407C22×C11#58511yescharacteristic
408C22×C11#58511yescharacteristic
409C4×C11—24no—
410C4×C11—24no—
411C4×C11—28no—
412C4×C11—42no—
413C4×C11—42no—
414C4×C11C2×C4×Q814yes—
415C4×C11C2×C4×Q814yes—
416Dic11—24no—
417Dic11—22no—
418Dic11—22no—
419Dic11—24no—
420Dic11—22no—
421Dic11—42no—
422Dic11—44no—
423Dic11—42no—
424Dic11#52014yes—
425C22×Q8—112no—
426C22×Q8—112no—
427C23×C4—111no—
428C23×C4—111no—
429C23×C4—112no—
430C23×C4C22×D1112yes—
431C23×C4C22×D1111yescharacteristic
432C4⋊Q8—118no—
433C4⋊Q8—118no—
434#125—118no—
435#125—118no—
436C22⋊Q8—1116no—
437C22⋊Q8—1116no—
438C4×Q8—1116no—
439C4×Q8—1116no—
440C4×Q8—448no—
441#117—24no—
442#117—118no—
443#117—224no—
444#117C4×D1118yes—
445C2×C4⋊C4—111no—
446C2×C4⋊C4—111no—
447C2×C4⋊C4—112no—
448C2×C4⋊C4—112no—
449C2×C4⋊C4—112no—
450C2×C4⋊C4—112no—
451C2×C4⋊C4—112no—
452C2×C4⋊C4—112no—
453C2×C4⋊C4—112no—
454C2×C4⋊C4—112no—
455C2×C4⋊C4—111no—
456C2×C4⋊C4—111no—
457C2×C4⋊C4—112no—
458C2×C4⋊C4—112no—
459C2×C4⋊C4—114no—
460C2×C4⋊C4—114no—
461C2×C4⋊C4—112no—
462C2×C4⋊C4—112no—
463C2×C4⋊C4—114no—
464C2×C4⋊C4—114no—
465C2×C4⋊C4—224no—
466C2×C4⋊C4Dic2218yescomplemented
467C2×C4⋊C4C22×D1111yescharacteristic
468C2×C4⋊C4C22×D1111yescharacteristic
469C2×C4⋊C4C22×D1112yes—
470C2×C4⋊C4C22×D1112yes—
471C2×C4⋊C4C22×D1111yescharacteristic
472C2×C4⋊C4C22×D1111yescharacteristic
473C2×C22⋊C4—112no—
474C2×C22⋊C4—112no—
475C2×C22⋊C4C22×D1112yes—
476C2×C22⋊C4C22×D1112yes—
477C2×C42—118no—
478C2×C42—112no—
479C2×C42—111no—
480C2×C42—111no—
481C2×C42—111no—
482C2×C42—111no—
483C2×C42—112no—
484C2×C42—114no—
485C2×C42—114no—
486C2×C42—114no—
487C2×C42—114no—
488C2×C42—444no—
489C2×C42C22×D1112yes—
490C2×C42C22×D1114yes—
491C2×C42C22×D1114yes—
492C2×C42C22×D1112yes—
493#95—114no—
494#95—114no—
495#95—114no—
496#95—114no—
497#95—112no—
498#95—112no—
499#95—112no—
500#95—112no—
501#95—114no—
502#95—114no—
503#95—114no—
504#95—114no—
505#95C22×D1114yes—
506#95C22×D1114yes—
507C2×C11—24no—
508C2×C11C22×C4×Q811yescharacteristic
509C2×C11C2×#52011yescharacteristic
510C2×C11#342811yescharacteristic
511C2×C11#350111yescharacteristic
512C2×C11#350211yescharacteristic
513C2×C11#350611yescharacteristic
514C2×C11#350711yescharacteristic
515C24C23×D1111yescharacteristic
516C2×Q8—118no—
517C2×Q8—118no—
518C2×Q8—224no—
519C2×Q8—224no—
520C2×Q8—442no—
521C2×Q8—442no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—111no—
525C22×C4—114no—
526C22×C4—111no—
527C22×C4—111no—
528C22×C4—112no—
529C22×C4—112no—
530C22×C4—111no—
531C22×C4—114no—
532C22×C4—112no—
533C22×C4—114no—
534C22×C4—112no—
535C22×C4—222no—
536C22×C4—222no—
537C22×C4—224no—
538C22×C4—442no—
539C22×C4—441no—
540C22×C4—441no—
541C22×C4—442no—
542C22×C4C2×Dic2218yes—
543C22×C4C2×Dic2214yes—
544C22×C4C2×C4×D1114yes—
545C22×C4#433914yes—
546C22×C4C23×D1112yes—
547C22×C4C23×D1112yes—
548C22×C4C23×D1114yes—
549C22×C4C23×D1112yes—
550C22×C4C23×D1112yes—
551C22×C4C23×D1111yescharacteristic
552C22×C4C23×D1111yescharacteristic
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—114no—
556C4⋊C4—114no—
557C4⋊C4—118no—
558C4⋊C4—118no—
559C4⋊C4—118no—
560C4⋊C4—118no—
561C4⋊C4—118no—
562C4⋊C4—118no—
563C4⋊C4—224no—
564C4⋊C4—224no—
565C4⋊C4—224no—
566C4⋊C4—224no—
567C4⋊C4—222no—
568C4⋊C4—222no—
569C4⋊C4—444no—
570C4⋊C4—444no—
571C4⋊C4—442no—
572C4⋊C4—442no—
573C4⋊C4—444no—
574C4⋊C4—444no—
575C4⋊C4C2×Dic2218yes—
576C4⋊C4C2×Dic2218yes—
577C4⋊C4C2×C4×D1114yes—
578C4⋊C4C2×C4×D1114yes—
579C22⋊C4—24no—
580C22⋊C4—118no—
581C22⋊C4—224no—
582C22⋊C4C2×C4×D1118yes—
583C42—24no—
584C42—44no—
585C42—44no—
586C42—114no—
587C42—114no—
588C42—114no—
589C42—114no—
590C42—118no—
591C42—228no—
592C42—224no—
593C42—444no—
594C42—444no—
595C42—444no—
596C42C2×C4×D1118yes—
597C11#3421311yescharacteristic, complemented, Sylow
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23C22×Dic2212yes—
603C23C22×C4×D1112yes—
604C23C2×#433912yes—
605C23C24×D1111yescharacteristic
606Q8—2216no—
607Q8—448no—
608C2×C4—22no—
609C2×C4—24no—
610C2×C4—22no—
611C2×C4—24no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—48no—
621C2×C4—112no—
622C2×C4—112no—
623C2×C4—112no—
624C2×C4—112no—
625C2×C4—112no—
626C2×C4—112no—
627C2×C4—114no—
628C2×C4—114no—
629C2×C4—228no—
630C2×C4—221no—
631C2×C4—222no—
632C2×C4—222no—
633C2×C4—221no—
634C2×C4—221no—
635C2×C4—221no—
636C2×C4—222no—
637C2×C4—221no—
638C2×C4—222no—
639C2×C4—221no—
640C2×C4—222no—
641C2×C4—222no—
642C2×C4—224no—
643C2×C4—224no—
644C2×C4—222no—
645C2×C4—222no—
646C2×C4—222no—
647C2×C4—222no—
648C2×C4—224no—
649C2×C4—444no—
650C2×C4—448no—
651C2×C4C4×Dic22116yescomplemented
652C2×C4C22×Dic2218yes—
653C2×C4C22×Dic2212yes—
654C2×C4C22×Dic2212yes—
655C2×C4C22×C4×D1114yes—
656C2×C4C22×C4×D1114yes—
657C2×C4C22×C4×D1112yes—
658C2×C4C22×C4×D1112yes—
659C2×C4C2×#433912yes—
660C2×C4C2×#433912yes—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22C2×C4×Dic2214yes—
668C22C23×Dic2211yescharacteristic
669C22C23×C4×D1111yescharacteristic
670C22C22×#433911yescharacteristic
671C22D11×H(5,𝔽2)11yescharacteristic
672C22#1062345511yescharacteristic
673C22D11×2−1+411yescharacteristic
674C22#1062345711yescharacteristic
675C4—28no—
676C4—24no—
677C4—24no—
678C4—42no—
679C4—42no—
680C4—114no—
681C4—222no—
682C4—224no—
683C4—222no—
684C4—222no—
685C4—224no—
686C4—444no—
687C4—442no—
688C4—442no—
689C4C2×C4×Dic2214yes—
690C4C2×C4×Dic2214yes—
691C2—24no—
692C2C22×C4×Dic2211yescharacteristic
693C2D11×#52011yescharacteristic
694C2#1308181611yescharacteristic
695C2#1308241411yescharacteristic
696C2#1308242211yescharacteristic
697C2#1308246111yescharacteristic
698C2#1308247411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2274C2
socle, cosocleC23×C11C25
prime radicalC24×C11C24
hypercenter#2274D11
hypocenterC11#34213
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2274

Complements

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

NH ≅ G/Ntype
2. #13071714C2semidirect
3. #13071708C2semidirect
4. #13071703C2semidirect
5. #13071675C2semidirect
6. #13071574C2semidirect
7. #13071574C2semidirect
8. #13071571C2semidirect
9. C4⋊C4×Dic22C2semidirect
26. #10623048C4semidirect
93. C2×C11×C4⋊C4Q8semidirect
143. #66943C2×C4semidirect
144. #66943C2×C4semidirect
145. #66941C2×C4semidirect
146. #66941C2×C4semidirect
150. C4×Dic22C2×C4semidirect
151. C4×Dic22C2×C4semidirect
287. C2×C4×C11C4×Q8semidirect
466. C2×C4⋊C4Dic22semidirect
597. C11#34213semidirect
651. C2×C4C4×Dic22semidirect

Maximal subgroups

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

subgroupindex
C2×#106230482
#130717142
#130717082
#130717032
#130716752
#130715742
#130715712
C4⋊C4×Dic222
#130713442
#130712392
#130712362
C4×#669312
#130710192
#130709732
C2×C4⋊C4×Dic112
C11×#22742
#3421311