Finite Group Databasebeta

← #14680707

Subgroups — #14680707

Order 2816.

1558 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622607C211yesmaximal, characteristic
2C2×#10622546C211yesmaximal, characteristic, complemented
3C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
4#13066883C211yesmaximal, characteristic, complemented
5#13066871C211yesmaximal, characteristic, complemented
6#13066869C211yesmaximal, characteristic, complemented
7#13066866C211yesmaximal, characteristic, complemented
8#13066862C211yesmaximal, characteristic
9#13066860C211yesmaximal, characteristic
10#13066858C211yesmaximal, characteristic
11#13066850C211yesmaximal, characteristic, complemented
12#13066850C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic
14(C2×D11)⋊#95C211yesmaximal, characteristic
15C11×C4⋊#95C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C2×C11×#95C2211yescharacteristic
32C2×C11×#95C2211yescharacteristic
33C2×C11×#95C2211yescharacteristic
34C2×C11×#95C2211yescharacteristic
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51#10622607C418yescomplemented
52C4×(C2×D11)⋊C4—24no—
53#10622546—24no—
54C24×D11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C22×C4×D11—22no—
70C22×C4×D11—22no—
71C22×C4×D11—41no—
72C22×C4×D11—41no—
73C22×C4×D11—41no—
74C22×C4×D11—41no—
75C22×C4×D11Q814yes—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—41no—
78C2×C11×C4⋊C4—41no—
79C2×C11×C4⋊C4—41no—
80C2×C11×C4⋊C4—41no—
81C2×C11×C4⋊C4C2×C414yescomplemented
82C2×C42×C11—41no—
83C2×C42×C11—41no—
84C2×C42×C11D414yes—
85C2×(C2×D11)⋊C4—22no—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—22no—
88C2×(C2×D11)⋊C4—22no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—22no—
92C2×(C2×D11)⋊C4—41no—
93C2×(C2×D11)⋊C4—41no—
94C2×(C2×D11)⋊C4—41no—
95C2×(C2×D11)⋊C4—41no—
96C2×(C2×D11)⋊C4—41no—
97C2×(C2×D11)⋊C4—41no—
98C2×(C2×D11)⋊C4—41no—
99C2×(C2×D11)⋊C4—41no—
100C2×(C2×D11)⋊C4C2×C414yes—
101C2×(C2×D11)⋊C4C2×C414yes—
102C2×(C2×D11)⋊C4C2×C414yes—
103C2×C4⋊Dic11—22no—
104C2×C4⋊Dic11—41no—
105C2×C4⋊Dic11—41no—
106C2×C4⋊Dic11—41no—
107C2×C4⋊Dic11—41no—
108C2×C4⋊Dic11C2×C414yescomplemented
109C2×Dic11⋊C4—22no—
110C2×Dic11⋊C4—22no—
111C2×Dic11⋊C4—22no—
112C2×Dic11⋊C4—41no—
113C2×Dic11⋊C4—41no—
114C2×Dic11⋊C4C2×C414yescomplemented
115C2×C4×Dic11—22no—
116C2×C4×Dic11—41no—
117C2×C4×Dic11—41no—
118C11×#95—22no—
119C11×#95—22no—
120C11×#95—41no—
121C11×#95—41no—
122C11⋊#95—22no—
123C11⋊#95—22no—
124C11⋊#95—22no—
125C11⋊#95—22no—
126C11⋊#95—22no—
127C11⋊#95—22no—
128C11⋊#95—22no—
129C11⋊#95—41no—
130C11⋊#95—41no—
131C11⋊#95—41no—
132C11⋊#95—41no—
133C11⋊#95—41no—
134C11⋊#95—41no—
135C11⋊#95—41no—
136C11⋊#95—41no—
137C11⋊#95C2×C414yescomplemented
138#14315—111nomaximal, Sylow
139C24×C11C2411yescharacteristic
140C23×D11—21no—
141C23×D11—21no—
142C23×D11—21no—
143C23×D11—21no—
144C23×D11—21no—
145C23×D11—21no—
146C23×D11—21no—
147C23×D11—21no—
148C23×D11—21no—
149C23×D11—21no—
150C23×D11—21no—
151C23×D11—21no—
152C23×D11C22×C412yes—
153C23×D11C2×Q812yes—
154C23×D11#4112yes—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11C22×C412yes—
196C22×C4×C11C22×C412yes—
197C22×C4×C11C22×C412yes—
198C22×C4×C11C2×D412yes—
199C22×C4×C11C2×D412yes—
200C22×C4×C11C2×D412yes—
201C22×C4×C11C2×Q812yes—
202C22×C4×C11#4112yes—
203C22×C4×C11#4112yes—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11—21no—
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11C22×C412yes—
249C22×Dic11C22×C412yes—
250C22×Dic11C22×C412yes—
251C22×Dic11C2×Q812yes—
252C22×Dic11#4112yes—
253C2×C4×D11—28no—
254C2×C4×D11—44no—
255C2×C4×D11—44no—
256C2×C4×D11—44no—
257C2×C4×D11—44no—
258C2×C4×D11—44no—
259C2×C4×D11—44no—
260C11×C4⋊C4—44no—
261C11×C4⋊C4—44no—
262C42×C11—44no—
263(C2×D11)⋊C4—28no—
264(C2×D11)⋊C4—28no—
265(C2×D11)⋊C4—44no—
266(C2×D11)⋊C4—44no—
267(C2×D11)⋊C4—44no—
268(C2×D11)⋊C4—44no—
269C4⋊Dic11—44no—
270C4⋊Dic11—44no—
271Dic11⋊C4—28no—
272Dic11⋊C4—44no—
273C4×Dic11—44no—
274C2×#396—111no—
275C2×#387—111no—
276C2×C4×C22⋊C4—111no—
277#1445—111no—
278#1442—111no—
279#1441—111no—
280#1441—111no—
281#1439—111no—
282#1439—111no—
283#1439—111no—
284#1436—111no—
285#1436—111no—
286C4⋊#95D1111yescharacteristic, complemented
287C22⋊#95—111no—
288C22⋊#95—111no—
289C23×C11C23×C411yescharacteristic
290C23×C11C22×D411yescharacteristic
291C23×C11C22×Q811yescharacteristic
292C23×C11C2×#4111yescharacteristic
293C23×C11C2×#4111yescharacteristic
294C23×C11C2×#4111yescharacteristic
295C23×C11C2×#4111yescharacteristic
296C23×C11H(5,𝔽2)11yescharacteristic
297C23×C11H(5,𝔽2)11yescharacteristic
298C23×C11H(5,𝔽2)11yescharacteristic
299C23×C11H(5,𝔽2)11yescharacteristic
300C23×C11H(5,𝔽2)11yescharacteristic
301C23×C11H(5,𝔽2)11yescharacteristic
302C23×C112−1+411yescharacteristic
303C23×C112−1+411yescharacteristic
304C22×D11—22no—
305C22×D11—22no—
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—22no—
309C22×D11—22no—
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—41no—
327C22×D11—41no—
328C22×D11—41no—
329C22×D11—41no—
330C22×D11—41no—
331C22×D11—41no—
332C22×D11—41no—
333C22×D11—41no—
334C22×D11—41no—
335C22×D11—41no—
336C22×D11—41no—
337C22×D11—41no—
338C22×D11C4×Q814yes—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11C4×D414yes—
387C2×C4×C11C22⋊Q814yes—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—41no—
404C2×Dic11—41no—
405C2×Dic11—41no—
406C2×Dic11—41no—
407C2×Dic11—41no—
408C2×Dic11—41no—
409C2×Dic11—41no—
410C2×Dic11—41no—
411C2×Dic11—41no—
412C2×Dic11—41no—
413C2×Dic11—41no—
414C2×Dic11—41no—
415C2×Dic11—41no—
416C2×Dic11—41no—
417C2×Dic11—41no—
418C2×Dic11—41no—
419C2×Dic11—41no—
420C2×Dic11—41no—
421C2×Dic11—41no—
422C2×Dic11—41no—
423C2×Dic11—41no—
424C2×Dic11—41no—
425C2×Dic11—41no—
426C2×Dic11—41no—
427C2×Dic11—41no—
428C2×Dic11—41no—
429C2×Dic11—41no—
430C2×Dic11—41no—
431C2×Dic11—41no—
432C2×Dic11—41no—
433C2×Dic11—41no—
434C2×Dic11—41no—
435C2×Dic11—41no—
436C2×Dic11—41no—
437C4×D11—416no—
438C24×C4—111no—
439C22×C4⋊C4—111no—
440C22×C4⋊C4—111no—
441C22×C4⋊C4—111no—
442C22×C4⋊C4—111no—
443C22×C4⋊C4C2×D1111yescharacteristic
444C22×C4⋊C4C2×D1111yescharacteristic
445C22×C22⋊C4—111no—
446C22×C22⋊C4—111no—
447C22×C22⋊C4—111no—
448C22×C22⋊C4—111no—
449C22×C22⋊C4—111no—
450C22×C22⋊C4—111no—
451C22×C42—111no—
452C22×C42C2×D1111yescharacteristic
453#396—118no—
454#387—224no—
455C4×C22⋊C4—224no—
456C2×#95—111no—
457C2×#95—111no—
458C2×#95—111no—
459C2×#95—111no—
460C2×#95—111no—
461C2×#95—111no—
462C2×#95—111no—
463C2×#95—111no—
464C2×#95—111no—
465C2×#95—111no—
466C2×#95—111no—
467C2×#95—111no—
468C2×#95—111no—
469C2×#95—111no—
470C2×#95—111no—
471C2×#95—111no—
472C2×#95C2×D1111yescharacteristic
473C2×#95C2×D1111yescharacteristic
474C2×#95C2×D1111yescharacteristic
475C2×#95C2×D1111yescharacteristic
476C22×C11C2×C4×D411yescharacteristic
477C22×C11C2×C4×Q811yescharacteristic
478C22×C11C4×#4111yescharacteristic
479C22×C11#51811yescharacteristic
480C22×C11#51811yescharacteristic
481C22×C11#52011yescharacteristic
482C22×C11#52011yescharacteristic
483C22×C11C2×C22⋊Q811yescharacteristic
484C22×C11#52511yescharacteristic
485C22×C11#52911yescharacteristic
486C22×C11#53311yescharacteristic
487C22×C11#53411yescharacteristic
488C22×C11#53511yescharacteristic
489C22×C11#53711yescharacteristic
490C22×C11#53711yescharacteristic
491C22×C11#53811yescharacteristic
492C22×C11#53811yescharacteristic
493C22×C11#53811yescharacteristic
494C22×C11#53811yescharacteristic
495C22×C11#53811yescharacteristic
496C22×C11#53811yescharacteristic
497C22×C11#53911yescharacteristic
498C22×C11#53911yescharacteristic
499C22×C11#53911yescharacteristic
500C22×C11#53911yescharacteristic
501C22×C11#54011yescharacteristic
502C22×C11#54011yescharacteristic
503C22×C11#54011yescharacteristic
504C22×C11#54111yescharacteristic
505C22×C11#54211yescharacteristic
506C22×C11#54211yescharacteristic
507C22×C11#54311yescharacteristic
508C22×C11#54311yescharacteristic
509C22×C11#54411yescharacteristic
510C22×C11#54411yescharacteristic
511C2×D11—24no—
512C2×D11—24no—
513C2×D11—24no—
514C2×D11—42no—
515C2×D11—42no—
516C2×D11—42no—
517C2×D11—42no—
518C2×D11—42no—
519C2×D11—42no—
520C2×D11—42no—
521C2×D11—42no—
522C2×D11—42no—
523C2×D11—42no—
524C2×D11—42no—
525C2×D11—42no—
526C4×C11—24no—
527C4×C11—24no—
528C4×C11—42no—
529C4×C11—42no—
530C4×C11—42no—
531C4×C11—81no—
532C4×C11—81no—
533Dic11—42no—
534Dic11—42no—
535Dic11—42no—
536Dic11—42no—
537Dic11—42no—
538Dic11—81no—
539Dic11—81no—
540C25—111no—
541C23×C4—111no—
542C23×C4—111no—
543C23×C4—111no—
544C23×C4—111no—
545C23×C4—111no—
546C23×C4—114no—
547C23×C4—111no—
548C23×C4—111no—
549C23×C4—222no—
550C23×C4—222no—
551C23×C4—441no—
552C23×C4—441no—
553C23×C4—441no—
554C23×C4—441no—
555C23×C4C22×D1111yescharacteristic
556C23×C4C22×D1111yescharacteristic
557C23×C4C22×D1111yescharacteristic
558C23×C4C22×D1111yescharacteristic
559C23×C4C22×D1111yescharacteristic
560C23×C4C22×D1111yescharacteristic
561C23×C4C22×D1111yescharacteristic
562C2×C4⋊C4—22no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4—41no—
565C2×C4⋊C4—41no—
566C2×C4⋊C4—41no—
567C2×C4⋊C4—114no—
568C2×C4⋊C4—114no—
569C2×C4⋊C4—222no—
570C2×C4⋊C4—222no—
571C2×C4⋊C4—222no—
572C2×C4⋊C4—222no—
573C2×C4⋊C4—441no—
574C2×C4⋊C4—441no—
575C2×C4⋊C4—441no—
576C2×C4⋊C4—441no—
577C2×C4⋊C4—441no—
578C2×C4⋊C4—441no—
579C2×C4⋊C4C4×D1114yescomplemented
580C2×C22⋊C4—114no—
581C2×C22⋊C4—114no—
582C2×C22⋊C4—114no—
583C2×C22⋊C4—222no—
584C2×C22⋊C4—222no—
585C2×C22⋊C4—222no—
586C2×C22⋊C4—222no—
587C2×C22⋊C4—222no—
588C2×C22⋊C4—222no—
589C2×C22⋊C4—222no—
590C2×C22⋊C4—441no—
591C2×C22⋊C4—441no—
592C2×C22⋊C4—441no—
593C2×C22⋊C4—441no—
594C2×C22⋊C4—441no—
595C2×C22⋊C4—441no—
596C2×C22⋊C4—441no—
597C2×C22⋊C4—441no—
598C2×C42—41no—
599C2×C42—41no—
600C2×C42—222no—
601C2×C42—441no—
602C2×C42—441no—
603C2×C42D4414yes—
604#95—22no—
605#95—22no—
606#95—41no—
607#95—41no—
608#95—114no—
609#95—222no—
610#95—222no—
611#95—222no—
612#95—222no—
613#95—222no—
614#95—222no—
615#95—222no—
616#95—441no—
617#95—441no—
618#95—441no—
619#95—441no—
620#95—441no—
621#95—441no—
622#95—441no—
623#95—441no—
624C2×C11C4×C22⋊Q811yescharacteristic
625C2×C11#232411yescharacteristic
626C2×C11#232511yescharacteristic
627C2×C11#232911yescharacteristic
628C2×C11#232911yescharacteristic
629C2×C11#233311yescharacteristic
630C2×C11#233411yescharacteristic
631C2×C11#262611yescharacteristic
632C2×C11#262911yescharacteristic
633C2×C11#263011yescharacteristic
634C2×C11#263611yescharacteristic
635C2×C11#264811yescharacteristic
636C2×C11#265211yescharacteristic
637C2×C11#266511yescharacteristic
638C2×C11#266711yescharacteristic
639D11—44no—
640C24—112no—
641C24—112no—
642C24—112no—
643C24—221no—
644C24—221no—
645C24—221no—
646C24—221no—
647C24—221no—
648C24—221no—
649C24—221no—
650C24—221no—
651C24—221no—
652C24—221no—
653C24—221no—
654C24—221no—
655C24C23×D1111yescharacteristic
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—112no—
697C22×C4—112no—
698C22×C4—112no—
699C22×C4—112no—
700C22×C4—112no—
701C22×C4—221no—
702C22×C4—221no—
703C22×C4—221no—
704C22×C4—221no—
705C22×C4—221no—
706C22×C4—221no—
707C22×C4—221no—
708C22×C4—221no—
709C22×C4—221no—
710C22×C4—221no—
711C22×C4—221no—
712C22×C4—221no—
713C22×C4—221no—
714C22×C4—221no—
715C22×C4—221no—
716C22×C4—221no—
717C22×C4—221no—
718C22×C4—221no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4—221no—
722C22×C4—221no—
723C22×C4—221no—
724C22×C4—221no—
725C22×C4—221no—
726C22×C4—221no—
727C22×C4—221no—
728C22×C4—221no—
729C22×C4—221no—
730C22×C4—221no—
731C22×C4—228no—
732C22×C4—221no—
733C22×C4—221no—
734C22×C4—221no—
735C22×C4—221no—
736C22×C4—221no—
737C22×C4—221no—
738C22×C4—221no—
739C22×C4—221no—
740C22×C4—221no—
741C22×C4—221no—
742C22×C4—221no—
743C22×C4—221no—
744C22×C4—221no—
745C22×C4—221no—
746C22×C4—444no—
747C22×C4—444no—
748C22×C4—444no—
749C22×C4—444no—
750C22×C4—444no—
751C22×C4—444no—
752C22×C4C2×C4×D1112yes—
753C22×C4C2×C4×D1112yes—
754C22×C4C2×C4×D1112yes—
755C22×C4C2×D4412yes—
756C22×C4C2×D4412yes—
757C22×C4C2×D4412yes—
758C22×C4#433912yes—
759C22×C4#434112yes—
760C22×C4Q8×D1112yes—
761C4⋊C4—44no—
762C4⋊C4—44no—
763C4⋊C4—228no—
764C4⋊C4—444no—
765C4⋊C4—444no—
766C4⋊C4—444no—
767C22⋊C4—228no—
768C22⋊C4—228no—
769C22⋊C4—444no—
770C22⋊C4—444no—
771C22⋊C4—444no—
772C22⋊C4—444no—
773C42—44no—
774C42—444no—
775C11#1431511yescharacteristic, complemented, Sylow
776C23—114no—
777C23—222no—
778C23—222no—
779C23—222no—
780C23—222no—
781C23—222no—
782C23—222no—
783C23—222no—
784C23—222no—
785C23—222no—
786C23—222no—
787C23—222no—
788C23—222no—
789C23—222no—
790C23—222no—
791C23—222no—
792C23—222no—
793C23—222no—
794C23—222no—
795C23—441no—
796C23—441no—
797C23—441no—
798C23—441no—
799C23—441no—
800C23—441no—
801C23—441no—
802C23—441no—
803C23—441no—
804C23—441no—
805C23—441no—
806C23—441no—
807C23—441no—
808C23—441no—
809C23—441no—
810C23—441no—
811C23C22×C4×D1111yescharacteristic
812C23C22×D4411yescharacteristic
813C23C2×#433911yescharacteristic
814C23C2×#434111yescharacteristic
815C23#6703711yescharacteristic
816C23#6703711yescharacteristic
817C23#6703711yescharacteristic
818C23#6703711yescharacteristic
819C23C2×Q8×D1111yescharacteristic
820C23#6704011yescharacteristic
821C23#6704011yescharacteristic
822C23#41×D1111yescharacteristic
823C23#41×D1111yescharacteristic
824C23#6704211yescharacteristic
825C23#6704211yescharacteristic
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—222no—
874C2×C4—222no—
875C2×C4—222no—
876C2×C4—222no—
877C2×C4—222no—
878C2×C4—222no—
879C2×C4—222no—
880C2×C4—222no—
881C2×C4—222no—
882C2×C4—222no—
883C2×C4—222no—
884C2×C4—222no—
885C2×C4—222no—
886C2×C4—222no—
887C2×C4—222no—
888C2×C4—4416no—
889C2×C4—441no—
890C2×C4—441no—
891C2×C4—441no—
892C2×C4—441no—
893C2×C4—441no—
894C2×C4—441no—
895C2×C4—441no—
896C2×C4—441no—
897C2×C4—441no—
898C2×C4—441no—
899C2×C4—441no—
900C2×C4—441no—
901C2×C4—441no—
902C2×C4—441no—
903C2×C4—441no—
904C2×C4—441no—
905C2×C4—441no—
906C2×C4—441no—
907C2×C4—441no—
908C2×C4—441no—
909C2×C4—441no—
910C2×C4—441no—
911C2×C4—441no—
912C2×C4—441no—
913C2×C4—441no—
914C2×C4—441no—
915C2×C4—441no—
916C2×C4—441no—
917C2×C4—441no—
918C2×C4—441no—
919C2×C4—441no—
920C2×C4—441no—
921C2×C4—441no—
922C2×C4—441no—
923C2×C4C4×D4414yes—
924C2×C4#6695014yes—
925C22—224no—
926C22—224no—
927C22—224no—
928C22—442no—
929C22—442no—
930C22—442no—
931C22—442no—
932C22—442no—
933C22—442no—
934C22—442no—
935C22—442no—
936C22—442no—
937C22—442no—
938C22—442no—
939C22—442no—
940C22C2×C4×D4411yescharacteristic
941C22#1062301711yescharacteristic
942C22#1062302411yescharacteristic
943C22#1062302511yescharacteristic
944C22#1062303511yescharacteristic
945C22C2×#6695011yescharacteristic
946C22#1062304111yescharacteristic
947C22#1062304111yescharacteristic
948C22#1062304611yescharacteristic
949C22#1062305511yescharacteristic
950C22#1062305611yescharacteristic
951C22C4×#434111yescharacteristic
952C22#1062307611yescharacteristic
953C22#1062308811yescharacteristic
954C22#1062309311yescharacteristic
955C22C4×Q8×D1111yescharacteristic
956C22#1062310511yescharacteristic
957C22#1062310911yescharacteristic
958C22#1062311311yescharacteristic
959C22#1062314411yescharacteristic
960C22#1062314611yescharacteristic
961C22#1062314811yescharacteristic
962C22#1062314811yescharacteristic
963C22#1062316511yescharacteristic
964C22#1062316511yescharacteristic
965C22#1062316911yescharacteristic
966C22#1062317111yescharacteristic
967C22#1062320911yescharacteristic
968C22#1062320911yescharacteristic
969C22#1062322311yescharacteristic
970C22#1062322311yescharacteristic
971C22#1062325011yescharacteristic
972C22#1062326011yescharacteristic
973C22#1062326011yescharacteristic
974C22#1062326211yescharacteristic
975C4—24no—
976C4—24no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—81no—
981C4—81no—
982C4—442no—
983C4—442no—
984C4—442no—
985C4—442no—
986C4—442no—
987C4—881no—
988C4—881no—
989C2—444no—
990C2C4×#6695011yescharacteristic
991C2#1307131011yescharacteristic
992C2#1307131911yescharacteristic
993C2#1307134811yescharacteristic
994C2#1307135011yescharacteristic
995C2#1307137511yescharacteristic
996C2#1307138411yescharacteristic
997C2#1307442411yescharacteristic
998C2#1307444911yescharacteristic
999C2#1307445711yescharacteristic
1000C2#1307451511yescharacteristic
1001C2#1307460811yescharacteristic
1002C2#1307466811yescharacteristic
1003C2#1307479011yescharacteristic
1004C2#1307481411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC4⋊#95D11
hypocenterC11#14315
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#10622546C2semidirect
4. #13066883C2semidirect
5. #13066871C2semidirect
6. #13066869C2semidirect
7. #13066866C2semidirect
11. #13066850C2semidirect
12. #13066850C2semidirect
15. C11×C4⋊#95C2semidirect
51. #10622607C4semidirect
81. C2×C11×C4⋊C4C2×C4semidirect
108. C2×C4⋊Dic11C2×C4semidirect
114. C2×Dic11⋊C4C2×C4semidirect
137. C11⋊#95C2×C4semidirect
286. C4⋊#95D11semidirect
579. C2×C4⋊C4C4×D11semidirect
775. C11#14315semidirect

Maximal subgroups

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

subgroupindex
C2×#106226072
C2×#106225462
C2×C4×(C2×D11)⋊C42
#130668832
#130668712
#130668692
#130668662
#130668622
#130668602
#130668582
#130668502
(C2×D11)⋊#952
C11×C4⋊#952
#1431511