Finite Group Databasebeta

← #14913751

Subgroups — #14913751

Order 2816.

2516 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623074C211yesmaximal, characteristic
2#13071711C212yesmaximal, complemented
3#13071705C211yesmaximal, characteristic, complemented
4#13071697C214yesmaximal, complemented
5#13071621C212yesmaximal, complemented
6#13071575C211yesmaximal, characteristic, complemented
7#13071521C212yesmaximal
8#13071495C212yesmaximal, complemented
9#13071183C211yesmaximal, characteristic, complemented
10#13071175C212yesmaximal, complemented
11#13071148C214yesmaximal, complemented
12#13071144C212yesmaximal, complemented
13C4×#66940C211yesmaximal, characteristic, complemented
14C4×D4×Dic11C212yesmaximal
15C4×D4×Dic11C211yesmaximal, characteristic
16C2×C4⋊C4×Dic11C212yesmaximal, complemented
17D4×C11×C4⋊C4C211yesmaximal, characteristic
18C2×C4×D4×C11C2212yes—
19C2×C4×D4×C11C2211yescharacteristic
20C22×C11×C4⋊C4C2212yes—
21C2×D4×Dic11C2211yescharacteristic
22C2×D4×Dic11C2212yes—
23C2×D4×Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2212yes—
25C2×#66977C2212yes—
26C22×C4×Dic11C2212yes—
27C22×C4×Dic11C2214yes—
28#10623074C4116yescomplemented
29C2×#66943C2212yes—
30C2×#66940C2211yescharacteristic
31C2×#66940C2211yescharacteristic
32C2×#66940C2212yes—
33C2×#66931C2214yes—
34C2×#66922C2211yescharacteristic
35C2×C4×Dic22C2211yescharacteristic
36C11×#389C2212yes—
37C11×#385C2214yes—
38C11×#384C2211yescharacteristic
39C11×#380C2212yes—
40C4×C11×C4⋊C4C2211yescharacteristic
41#10622823C2214yes—
42C4×C22⋊Dic11C2214yes—
43C4×C22⋊Dic11C2212yes—
44C2×C11⋊#95C2214yes—
45#10622591C2214yes—
46#10622591C2214yes—
47#10622590C2212yes—
48C4⋊C4×Dic11C2212yes—
49C4⋊C4×Dic11C2212yes—
50C4⋊C4×Dic11C2214yes—
51C4⋊C4×Dic11C2211yescharacteristic
52C4⋊C4×Dic11C2212yes—
53C4⋊C4×Dic11C2214yes—
54C4⋊C4×Dic11C2211yescharacteristic
55C4⋊C4×Dic11C2212yes—
56C4⋊C4×Dic11C2211yescharacteristic
57C4⋊C4×Dic11C2212yes—
58C4⋊C4×Dic11C2211yescharacteristic
59#10622587C2212yes—
60#10622587C2212yes—
61#10622586C2212yes—
62#10622586C2212yes—
63#10622586C2212yes—
64#10622585C2214yes—
65#10622559C2214yes—
66#10622555C2214yes—
67C22⋊C4×Dic11C2214yes—
68C22⋊C4×Dic11C2212yes—
69C22⋊C4×Dic11C2212yes—
70C22⋊C4×Dic11C2214yes—
71C4×C4⋊Dic11C2212yes—
72C4×C4⋊Dic11C2211yescharacteristic
73C4×Dic11⋊C4C2212yes—
74C42×Dic11C2212yes—
75C42×Dic11C2211yescharacteristic
76#10622541C2212yes—
77#10622266C2214yes—
78#10622266C2214yes—
79#10622265C2214yes—
80#10622262C2214yes—
81#10622262C2212yes—
82#10622262C2212yes—
83#10622259C2214yes—
84C22×D4×C11C2311yescharacteristic
85C23×C4×C11C2314yes—
86C23×C4×C11C2312yes—
87C23×Dic11C2312yes—
88C23×Dic11C2312yes—
89C23×Dic11C2314yes—
90C22×Dic22C2311yescharacteristic
91C22×Dic22C2312yes—
92C4×D4×C11—28no—
93C4×D4×C11C2×C418yes—
94C2×C11×C4⋊C4—28no—
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2314yes—
97C2×C11×C4⋊C4C2312yes—
98C2×C11×C4⋊C4C2312yes—
99C2×C11×C4⋊C4C2312yes—
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C22⋊C4C2314yes—
103C2×C11×C22⋊C4C2312yes—
104C2×C42×C11C2312yes—
105C2×C42×C11C2311yescharacteristic
106C2×C22⋊Dic11C2312yes—
107C2×C22⋊Dic11C2314yes—
108C2×C22⋊Dic11C2312yes—
109D4×Dic11—24no—
110D4×Dic11C2×C4116yes—
111D4×Dic11Q818yescomplemented
112C2×C4⋊Dic11C2×C4116yescomplemented
113C2×C4⋊Dic11C2311yescharacteristic
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4⋊Dic11C2312yes—
116C2×C4⋊Dic11C2312yes—
117C2×C4⋊Dic11C2314yes—
118C2×C4⋊Dic11C2311yescharacteristic
119#66977C2×C4116yescomplemented
120C2×Dic11⋊C4C2312yes—
121C2×Dic11⋊C4C2312yes—
122C2×Dic11⋊C4C2314yes—
123C2×Dic11⋊C4C2314yes—
124C2×Dic11⋊C4C2312yes—
125C2×Dic11⋊C4C2314yes—
126C2×C4×Dic11—28no—
127C2×C4×Dic11—48no—
128C2×C4×Dic11C2311yescharacteristic
129C2×C4×Dic11C2312yes—
130C2×C4×Dic11C2312yes—
131C2×C4×Dic11C2314yes—
132C2×C4×Dic11C2311yescharacteristic
133C2×C4×Dic11C2312yes—
134C2×C4×Dic11C2312yes—
135C2×C4×Dic11C2312yes—
136C2×C4×Dic11C2311yescharacteristic
137C2×C4×Dic11C2312yes—
138C2×C4×Dic11C2314yes—
139C2×C4×Dic11C2311yescharacteristic
140C2×C4×Dic11C2312yes—
141C2×C4×Dic11C2314yes—
142C2×C4×Dic11C2312yes—
143C2×C4×Dic11C2311yescharacteristic
144C2×C4×Dic11C2311yescharacteristic
145#66943C2×C4116yescomplemented
146#66940—24no—
147#66940—24no—
148#66940—44no—
149#66931C2×C4132yescomplemented
150#66922C2×C418yescomplemented
151C4×Dic22C2×C418yescomplemented
152C11×#95C2312yes—
153C11×#95C2314yes—
154C11⋊#95C2312yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2312yes—
158C11⋊#95C2312yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2312yes—
163C11⋊#95C2312yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C4×#554—111nomaximal, Sylow
167C24×C11C2412yes—
168C2×D4×C11C22×C414yes—
169C2×D4×C11C2×Q814yes—
170C2×D4×C11#4114yes—
171C22×C4×C11—24no—
172C22×C4×C11—24no—
173C22×C4×C11—28no—
174C22×C4×C11—28no—
175C22×C4×C11—44no—
176C22×C4×C11C22×C418yes—
177C22×C4×C11C2414yes—
178C22×C4×C11C2412yes—
179C22×C4×C11C2412yes—
180C22×C4×C11C2411yescharacteristic
181C22×C4×C11C2412yes—
182C22×C4×C11C2411yescharacteristic
183C22×C4×C11C2411yescharacteristic
184C22×Dic11—24no—
185C22×Dic11—24no—
186C22×Dic11—24no—
187C22×Dic11—24no—
188C22×Dic11—44no—
189C22×Dic11—44no—
190C22×Dic11—42no—
191C22×Dic11C22×C4116yes—
192C22×Dic11C2×Q818yes—
193C22×Dic11C2412yes—
194C22×Dic11C2411yescharacteristic
195C22×Dic11C2412yes—
196C22×Dic11C2412yes—
197C22×Dic11C2414yes—
198C22×Dic11C2411yescharacteristic
199C22×Dic11C2412yes—
200C22×Dic11C2411yescharacteristic
201C22×Dic11C2411yescharacteristic
202C2×Dic22—22no—
203C2×Dic22—22no—
204C2×Dic22—42no—
205C2×Dic22—42no—
206C2×Dic22C22×C414yes—
207C2×Dic22C22×C418yes—
208C11×C4⋊C4—22no—
209C11×C4⋊C4—28no—
210C11×C4⋊C4—24no—
211C11×C4⋊C4—24no—
212C11×C4⋊C4—42no—
213C11×C4⋊C4C22×C414yes—
214C11×C4⋊C4#4114yes—
215C11×C22⋊C4—28no—
216C11×C22⋊C4C22×C418yes—
217C42×C11—24no—
218C42×C11C22×C414yes—
219C22⋊Dic11—24no—
220C22⋊Dic11C22×C4116yes—
221C22⋊Dic11C2×Q818yes—
222C4⋊Dic11—22no—
223C4⋊Dic11C22×C414yes—
224C4⋊Dic11C22×C418yes—
225C4⋊Dic11C22×C418yes—
226C4⋊Dic11C22×C4116yes—
227C4⋊Dic11C2×Q814yes—
228Dic11⋊C4—24no—
229Dic11⋊C4—24no—
230Dic11⋊C4—44no—
231Dic11⋊C4—44no—
232Dic11⋊C4C22×C418yes—
233Dic11⋊C4C22×C4116yes—
234C4×Dic11—24no—
235C4×Dic11—24no—
236C4×Dic11—24no—
237C4×Dic11—22no—
238C4×Dic11—28no—
239C4×Dic11—24no—
240C4×Dic11—24no—
241C4×Dic11—22no—
242C4×Dic11—24no—
243C4×Dic11—22no—
244C4×Dic11—44no—
245C4×Dic11—44no—
246C4×Dic11—41no—
247C4×Dic11—42no—
248C4×Dic11C22×C418yes—
249C4×Dic11C2×Q814yes—
250C4×Dic11#4114yes—
251C2×#554—111no—
252#2370—112no—
253#2369—111no—
254#2368—114no—
255#2360—112no—
256#2355—111no—
257#2349—112no—
258D4×C4⋊C4D1111yescharacteristic
259#2345—112no—
260C4×C4⋊Q8—111no—
261C4×#125—112no—
262C4×C22⋊Q8—114no—
263C4×C22⋊Q8—112no—
264C42×Q8—111no—
265C42×D4—112no—
266C42×D4—111no—
267C2×C4×C4⋊C4—112no—
268C23×C11—22no—
269C23×C11—22no—
270C23×C11—22no—
271C23×C11—22no—
272C23×C11C23×C414yes—
273C23×C11C22×Q814yes—
274C23×C11C2×#4114yes—
275C23×C11C2511yescharacteristic
276D4×C11C4×Q8116yescomplemented
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—216no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—24no—
287C2×C4×C11—24no—
288C2×C4×C11—24no—
289C2×C4×C11—22no—
290C2×C4×C11—416no—
291C2×C4×C11C23×C414yes—
292C2×C4×C11C23×C412yes—
293C2×C4×C11C23×C412yes—
294C2×C4×C11C23×C412yes—
295C2×C4×C11C22×Q812yes—
296C2×C4×C11C2×#4114yes—
297C2×C4×C11C2×#4112yes—
298C2×C4×C11C2×#4112yes—
299C2×C4×C11C2×#4112yes—
300C2×Dic11—21no—
301C2×Dic11—22no—
302C2×Dic11—22no—
303C2×Dic11—22no—
304C2×Dic11—21no—
305C2×Dic11—22no—
306C2×Dic11—24no—
307C2×Dic11—22no—
308C2×Dic11—21no—
309C2×Dic11—22no—
310C2×Dic11—21no—
311C2×Dic11—24no—
312C2×Dic11—216no—
313C2×Dic11—22no—
314C2×Dic11—21no—
315C2×Dic11—21no—
316C2×Dic11—22no—
317C2×Dic11—21no—
318C2×Dic11—22no—
319C2×Dic11—416no—
320C2×Dic11—48no—
321C2×Dic11C23×C414yes—
322C2×Dic11C23×C414yes—
323C2×Dic11C23×C418yes—
324C2×Dic11C22×Q812yes—
325C2×Dic11C22×Q814yes—
326C2×Dic11C22×Q812yes—
327C2×Dic11C2×#4112yes—
328C2×Dic11C2×#4112yes—
329C2×Dic11H(5,𝔽2)12yes—
330Dic22—28no—
331Dic22—48no—
332#554—1116no—
333C2×C4⋊Q8—111no—
334C2×#125—112no—
335C2×C22⋊Q8—112no—
336C2×C22⋊Q8—114no—
337C2×C4×Q8—111no—
338C2×C4×Q8—111no—
339C2×C4×Q8—112no—
340C2×C4×Q8—111no—
341C2×C4×D4—112no—
342C2×C4×D4—111no—
343C2×C4×D4—111no—
344C2×C4×D4C2×D1112yes—
345C2×C4×D4C2×D1111yescharacteristic
346C22×C4⋊C4—112no—
347C22×C4⋊C4C2×D1112yes—
348C22×C42—112no—
349C22×C42—114no—
350#391—112no—
351#391—112no—
352#391—114no—
353#389—112no—
354#389—112no—
355#389—112no—
356#389—114no—
357#389—112no—
358#389C2×D1112yes—
359#387—114no—
360#387—114no—
361#387—114no—
362#387—114no—
363#387—114no—
364#385—114no—
365#385—114no—
366#385C2×D1114yes—
367#384C2×D1111yescharacteristic
368#382—112no—
369#380—114no—
370#380C2×D1112yes—
371C4×C4⋊C4—111no—
372C4×C4⋊C4—112no—
373C4×C4⋊C4—114no—
374C4×C4⋊C4—112no—
375C4×C4⋊C4—111no—
376C4×C4⋊C4—112no—
377C4×C4⋊C4—112no—
378C4×C4⋊C4—112no—
379C4×C4⋊C4—114no—
380C4×C4⋊C4—111no—
381C4×C4⋊C4—111no—
382C4×C4⋊C4—112no—
383C4×C4⋊C4—111no—
384C4×C4⋊C4—112no—
385C4×C4⋊C4—114no—
386C4×C4⋊C4—112no—
387C4×C4⋊C4—112no—
388C4×C4⋊C4C2×D1111yescharacteristic
389C4×C22⋊C4—112no—
390C4×C22⋊C4—114no—
391C4×C22⋊C4—114no—
392C4×C22⋊C4—112no—
393C4×C22⋊C4—112no—
394C4×C22⋊C4—114no—
395C2×#95—114no—
396C43—112no—
397C43—111no—
398C22×C11—24no—
399C22×C11—24no—
400C22×C11—24no—
401C22×C11—24no—
402C22×C11—24no—
403C22×C11—24no—
404C22×C11C2×C4×Q818yes—
405C22×C11C24×C411yescharacteristic
406C22×C11C23×Q811yescharacteristic
407C22×C11C22×#4111yescharacteristic
408C22×C11C22×#4111yescharacteristic
409C22×C11C22×#4111yescharacteristic
410C22×C11C2×H(5,𝔽2)11yescharacteristic
411C22×C11#58511yescharacteristic
412C4×C11—24no—
413C4×C11—22no—
414C4×C11—24no—
415C4×C11—42no—
416C4×C11—44no—
417C4×C11C2×C4×Q814yes—
418C4×C11C4×#4114yes—
419Dic11—24no—
420Dic11—28no—
421Dic11—24no—
422Dic11—24no—
423Dic11—22no—
424Dic11—22no—
425Dic11—42no—
426Dic11—41no—
427Dic11#55414yescomplemented
428C22×Q8—111no—
429C22×Q8—112no—
430C22×D4C22×D1111yescharacteristic
431C23×C4—112no—
432C23×C4—114no—
433C23×C4—112no—
434C23×C4C22×D1114yes—
435C23×C4C22×D1112yes—
436C4⋊Q8—118no—
437#125—1116no—
438C22⋊Q8—1116no—
439C22⋊Q8—1132no—
440C4×Q8—118no—
441C4×Q8—224no—
442C4×Q8—224no—
443C4×Q8—444no—
444C4×D4—28no—
445C4×D4—1116no—
446C4×D4—118no—
447C4×D4—224no—
448C4×D4C4×D1118yes—
449C2×C4⋊C4—28no—
450C2×C4⋊C4—1116no—
451C2×C4⋊C4—111no—
452C2×C4⋊C4—114no—
453C2×C4⋊C4—112no—
454C2×C4⋊C4—112no—
455C2×C4⋊C4—111no—
456C2×C4⋊C4—112no—
457C2×C4⋊C4—114no—
458C2×C4⋊C4—111no—
459C2×C4⋊C4—112no—
460C2×C4⋊C4—112no—
461C2×C4⋊C4—114no—
462C2×C4⋊C4—114no—
463C2×C4⋊C4C22×D1112yes—
464C2×C4⋊C4C22×D1114yes—
465C2×C4⋊C4C22×D1112yes—
466C2×C4⋊C4C22×D1111yescharacteristic
467C2×C4⋊C4C22×D1112yes—
468C2×C4⋊C4C22×D1111yescharacteristic
469C2×C4⋊C4C22×D1111yescharacteristic
470C2×C22⋊C4—114no—
471C2×C22⋊C4—112no—
472C2×C22⋊C4—112no—
473C2×C22⋊C4C22×D1114yes—
474C2×C22⋊C4C22×D1112yes—
475C2×C42—112no—
476C2×C42—111no—
477C2×C42—111no—
478C2×C42—111no—
479C2×C42—111no—
480C2×C42—112no—
481C2×C42—112no—
482C2×C42—111no—
483C2×C42—114no—
484C2×C42—112no—
485C2×C42—112no—
486C2×C42—112no—
487C2×C42—112no—
488C2×C42—112no—
489C2×C42—111no—
490C2×C42—114no—
491C2×C42—114no—
492C2×C42—228no—
493C2×C42—448no—
494C2×C42C22×D1112yes—
495C2×C42C22×D1111yescharacteristic
496#95—112no—
497#95—114no—
498#95—114no—
499#95—114no—
500#95—112no—
501#95—112no—
502#95—114no—
503#95—114no—
504#95—114no—
505#95—112no—
506#95—112no—
507#95—114no—
508#95C22×D1112yes—
509#95C22×D1114yes—
510C2×C11—28no—
511C2×C11C22×C4×Q811yescharacteristic
512C2×C11C2×C4×#4111yescharacteristic
513C2×C11C4×H(5,𝔽2)11yescharacteristic
514C2×C11C2×#55411yescharacteristic
515C2×C11#347511yescharacteristic
516C2×C11Q8×#4111yescharacteristic
517C2×C11#348111yescharacteristic
518C24C23×D1112yes—
519C2×Q8—114no—
520C2×Q8—118no—
521C2×Q8—222no—
522C2×Q8—222no—
523C2×Q8—442no—
524C2×Q8—442no—
525C2×D4C2×C4×D1114yes—
526C2×D4#434114yes—
527C2×D4Q8×D1114yes—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—44no—
533C22×C4—111no—
534C22×C4—118no—
535C22×C4—111no—
536C22×C4—112no—
537C22×C4—111no—
538C22×C4—112no—
539C22×C4—112no—
540C22×C4—114no—
541C22×C4—1116no—
542C22×C4—112no—
543C22×C4—111no—
544C22×C4—224no—
545C22×C4—224no—
546C22×C4—224no—
547C22×C4—224no—
548C22×C4—444no—
549C22×C4—444no—
550C22×C4—442no—
551C22×C4C2×C4×D1118yes—
552C22×C4C23×D1114yes—
553C22×C4C23×D1112yes—
554C22×C4C23×D1111yescharacteristic
555C22×C4C23×D1112yes—
556C22×C4C23×D1112yes—
557C22×C4C23×D1111yescharacteristic
558C22×C4C23×D1111yescharacteristic
559C4⋊C4—28no—
560C4⋊C4—24no—
561C4⋊C4—24no—
562C4⋊C4—22no—
563C4⋊C4—42no—
564C4⋊C4—114no—
565C4⋊C4—1116no—
566C4⋊C4—118no—
567C4⋊C4—118no—
568C4⋊C4—118no—
569C4⋊C4—1116no—
570C4⋊C4—114no—
571C4⋊C4—224no—
572C4⋊C4—222no—
573C4⋊C4—224no—
574C4⋊C4—444no—
575C4⋊C4—444no—
576C4⋊C4C2×C4×D1114yes—
577C4⋊C4#434114yes—
578C22⋊C4—28no—
579C22⋊C4—1116no—
580C22⋊C4—118no—
581C22⋊C4—224no—
582C22⋊C4C2×C4×D1118yes—
583C42—24no—
584C42—118no—
585C42—114no—
586C42—114no—
587C42—224no—
588C42—224no—
589C42—224no—
590C42—228no—
591C42—224no—
592C42—222no—
593C42—222no—
594C42—224no—
595C42—222no—
596C42—224no—
597C42—444no—
598C42—444no—
599C42—441no—
600C42—442no—
601C42C2×C4×D1114yes—
602C11C4×#55411yescharacteristic, complemented, Sylow
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23C22×C4×D1114yes—
608C23C2×#434114yes—
609C23C2×Q8×D1114yes—
610C23C24×D1111yescharacteristic
611Q8—228no—
612Q8—448no—
613D4#66940116yescomplemented
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—216no—
621C2×C4—22no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—22no—
625C2×C4—24no—
626C2×C4—22no—
627C2×C4—416no—
628C2×C4—112no—
629C2×C4—112no—
630C2×C4—112no—
631C2×C4—114no—
632C2×C4—114no—
633C2×C4—118no—
634C2×C4—112no—
635C2×C4—114no—
636C2×C4—112no—
637C2×C4—2216no—
638C2×C4—221no—
639C2×C4—222no—
640C2×C4—221no—
641C2×C4—222no—
642C2×C4—222no—
643C2×C4—222no—
644C2×C4—224no—
645C2×C4—222no—
646C2×C4—221no—
647C2×C4—221no—
648C2×C4—222no—
649C2×C4—224no—
650C2×C4—221no—
651C2×C4—221no—
652C2×C4—222no—
653C2×C4—222no—
654C2×C4—221no—
655C2×C4—222no—
656C2×C4—4416no—
657C2×C4—448no—
658C2×C4C22×C4×D1112yes—
659C2×C4C22×C4×D1114yes—
660C2×C4C22×C4×D1112yes—
661C2×C4C22×C4×D1112yes—
662C2×C4C2×#434114yes—
663C2×C4C2×#434112yes—
664C2×C4C2×#434112yes—
665C2×C4C2×Q8×D1112yes—
666C2×C4#41×D1112yes—
667C22—24no—
668C22—24no—
669C22—24no—
670C22—24no—
671C22—24no—
672C22—24no—
673C22C2×#6694018yes—
674C22C23×C4×D1111yescharacteristic
675C22C22×#434111yescharacteristic
676C22C22×#434111yescharacteristic
677C22C22×Q8×D1111yescharacteristic
678C22C2×#41×D1111yescharacteristic
679C22D11×H(5,𝔽2)11yescharacteristic
680C22#1062345711yescharacteristic
681C4—24no—
682C4—24no—
683C4—22no—
684C4—42no—
685C4—44no—
686C4—114no—
687C4—224no—
688C4—222no—
689C4—222no—
690C4—224no—
691C4—224no—
692C4—228no—
693C4—442no—
694C4—441no—
695C4C2×#6694014yes—
696C4C4×#434114yes—
697C2—28no—
698C2C22×#6694011yescharacteristic
699C2C2×C4×#434111yescharacteristic
700C2#1308182211yescharacteristic
701C2D11×#55411yescharacteristic
702C2#1308217911yescharacteristic
703C2Q8×#434111yescharacteristic
704C2#1308221711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingD4×C11×C4⋊C4C2
socle, cosocleC23×C11C25
prime radicalC22×D4×C11C23
hypercenterD4×C4⋊C4D11
hypocenterC11C4×#554
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13071711C2semidirect
3. #13071705C2semidirect
4. #13071697C2semidirect
5. #13071621C2semidirect
6. #13071575C2semidirect
8. #13071495C2semidirect
9. #13071183C2semidirect
10. #13071175C2semidirect
11. #13071148C2semidirect
12. #13071144C2semidirect
13. C4×#66940C2semidirect
16. C2×C4⋊C4×Dic11C2semidirect
28. #10623074C4semidirect
111. D4×Dic11Q8semidirect
112. C2×C4⋊Dic11C2×C4semidirect
119. #66977C2×C4semidirect
145. #66943C2×C4semidirect
149. #66931C2×C4semidirect
150. #66922C2×C4semidirect
151. C4×Dic22C2×C4semidirect
276. D4×C11C4×Q8semidirect
427. Dic11#554semidirect
602. C11C4×#554semidirect
613. D4#66940semidirect

Maximal subgroups

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

subgroupindex
C2×#106230742
#130717112
#130717052
#130716972
#130716212
#130715752
#130715212
#130714952
#130711832
#130711752
#130711482
#130711442
C4×#669402
C4×D4×Dic112
C2×C4⋊C4×Dic112
D4×C11×C4⋊C42
C4×#55411