Finite Group Databasebeta

← #14682138

Subgroups — #14682138

Order 2816.

1506 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622558C211yesmaximal, characteristic
2C2×#10622591C211yesmaximal, characteristic, complemented
3#13066877C211yesmaximal, characteristic, complemented
4#13066876C211yesmaximal, characteristic, complemented
5#13066875C211yesmaximal, characteristic, complemented
6#13066870C211yesmaximal, characteristic, complemented
7#13066863C211yesmaximal, characteristic
8#13066861C211yesmaximal, characteristic
9#13066853C211yesmaximal, characteristic
10#13066848C211yesmaximal, characteristic, complemented
11#13066845C211yesmaximal, characteristic, complemented
12#13066842C211yesmaximal, characteristic, complemented
13#13066839C211yesmaximal, characteristic
14#13066839C211yesmaximal, characteristic
15C2×C11×#385C211yesmaximal, characteristic
16C24×C4×C11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
29C11×#385—24no—
30C2×C11×#95C2211yescharacteristic
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
51C2×C11⋊#95C2211yescharacteristic
52#10622591—24no—
53#10622558C418yescomplemented
54C25×C11C2311yescharacteristic
55C23×C4×C11—22no—
56C23×C4×C11—22no—
57C23×C4×C11—22no—
58C23×C4×C11—41no—
59C23×C4×C11—41no—
60C23×C4×C11—41no—
61C23×C4×C11—41no—
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—41no—
79C2×C11×C4⋊C4—41no—
80C2×C11×C4⋊C4—41no—
81C2×C11×C4⋊C4D414yes—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—41no—
87C2×C11×C22⋊C4C2×C414yes—
88C2×C22⋊Dic11—22no—
89C2×C22⋊Dic11—22no—
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11—22no—
92C2×C22⋊Dic11—22no—
93C2×C22⋊Dic11—41no—
94C2×C22⋊Dic11—41no—
95C2×C22⋊Dic11—41no—
96C2×C22⋊Dic11—41no—
97C2×C22⋊Dic11—41no—
98C2×C22⋊Dic11C2×C414yes—
99C2×C22⋊Dic11C2×C414yes—
100C2×C4⋊Dic11—22no—
101C2×C4⋊Dic11—41no—
102C2×C4⋊Dic11—41no—
103C2×Dic11⋊C4—22no—
104C2×Dic11⋊C4—22no—
105C2×Dic11⋊C4C2×C414yescomplemented
106C2×C4×Dic11—22no—
107C2×C4×Dic11—41no—
108C2×C4×Dic11—41no—
109C2×C4×Dic11—41no—
110C2×C4×Dic11—41no—
111C2×C4×Dic11C2×C414yescomplemented
112C11×#95—22no—
113C11×#95—22no—
114C11⋊#95—22no—
115C11⋊#95—22no—
116C11⋊#95—22no—
117C11⋊#95—22no—
118C11⋊#95—22no—
119C11⋊#95—22no—
120C11⋊#95—22no—
121C11⋊#95—41no—
122C11⋊#95—41no—
123C11⋊#95—41no—
124C11⋊#95—41no—
125C11⋊#95—41no—
126C11⋊#95—41no—
127C11⋊#95—41no—
128C11⋊#95—41no—
129C11⋊#95—41no—
130C11⋊#95—41no—
131C11⋊#95—41no—
132C11⋊#95C2×C414yescomplemented
133C11⋊#95C2×C414yescomplemented
134#14436—111nomaximal, Sylow
135C24×C11—21no—
136C24×C11—21no—
137C24×C11—21no—
138C24×C11—21no—
139C24×C11—21no—
140C24×C11—21no—
141C24×C11—21no—
142C24×C11—21no—
143C24×C11—21no—
144C24×C11—21no—
145C24×C11—21no—
146C24×C11—21no—
147C24×C11C22×C412yes—
148C24×C11#4112yes—
149C24×C11#4112yes—
150C24×C11C2411yescharacteristic
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
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—44no—
187C22×C4×C11—44no—
188C22×C4×C11—44no—
189C22×C4×C11—44no—
190C22×C4×C11—44no—
191C22×C4×C11—44no—
192C22×C4×C11—44no—
193C22×C4×C11C22×C412yes—
194C22×C4×C11C22×C412yes—
195C22×C4×C11C2×D412yes—
196C22×C4×C11C2×D412yes—
197C22×C4×C11C2×D412yes—
198C22×C4×C11#4112yes—
199C22×C4×C11#4112yes—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—21no—
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×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11C22×C412yes—
252C22×Dic11C22×C412yes—
253C22×Dic11C22×C412yes—
254C22×Dic11C22×C412yes—
255C22×Dic11#4112yes—
256C11×C4⋊C4—44no—
257C11×C4⋊C4—44no—
258C11×C22⋊C4—28no—
259C11×C22⋊C4—44no—
260C22⋊Dic11—28no—
261C22⋊Dic11—44no—
262C22⋊Dic11—44no—
263C22⋊Dic11—44no—
264C4⋊Dic11—44no—
265Dic11⋊C4—28no—
266C4×Dic11—44no—
267C4×Dic11—44no—
268C2×#388—111no—
269C2×#387—111no—
270C2×#385D1111yescharacteristic
271#1443—111no—
272#1443—111no—
273#1442—111no—
274#1441—111no—
275#1440—111no—
276#1439—111no—
277#1437—111no—
278#1436—111no—
279C4⋊#95—111no—
280#1434—111no—
281C22⋊#95—111no—
282C22⋊#95—111no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—41no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11#11714yes—
318C23×C11C23×C411yescharacteristic
319C23×C11C22×D411yescharacteristic
320C23×C11C2×#4111yescharacteristic
321C23×C11C2×#4111yescharacteristic
322C23×C11C2×#4111yescharacteristic
323C23×C11C2×#4111yescharacteristic
324C23×C11C2×#4111yescharacteristic
325C23×C11H(5,𝔽2)11yescharacteristic
326C23×C11H(5,𝔽2)11yescharacteristic
327C23×C11H(5,𝔽2)11yescharacteristic
328C23×C11H(5,𝔽2)11yescharacteristic
329C23×C11H(5,𝔽2)11yescharacteristic
330C23×C112−1+411yescharacteristic
331C23×C112−1+411yescharacteristic
332C23×C112−1+411yescharacteristic
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
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—416no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—41no—
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×C11C4×D414yes—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—22no—
391C2×Dic11—41no—
392C2×Dic11—41no—
393C2×Dic11—41no—
394C2×Dic11—41no—
395C2×Dic11—41no—
396C2×Dic11—41no—
397C2×Dic11—41no—
398C2×Dic11—41no—
399C2×Dic11—41no—
400C2×Dic11—41no—
401C2×Dic11—41no—
402C2×Dic11—41no—
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—
432C24×C4C2×D1111yescharacteristic
433C22×C4⋊C4—111no—
434C22×C4⋊C4—111no—
435C22×C4⋊C4C2×D1111yescharacteristic
436C22×C4⋊C4C2×D1111yescharacteristic
437C22×C22⋊C4—111no—
438C22×C22⋊C4—111no—
439C22×C22⋊C4—111no—
440C22×C22⋊C4—111no—
441C22×C22⋊C4C2×D1111yescharacteristic
442C22×C22⋊C4C2×D1111yescharacteristic
443C22×C42—111no—
444C22×C42—111no—
445#388—118no—
446#387—224no—
447#385—24no—
448C2×#95—111no—
449C2×#95—111no—
450C2×#95—111no—
451C2×#95—111no—
452C2×#95—111no—
453C2×#95—111no—
454C2×#95—111no—
455C2×#95—111no—
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×#95C2×D1111yescharacteristic
469C2×#95C2×D1111yescharacteristic
470C22×C11—24no—
471C22×C11—24no—
472C22×C11—24no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—42no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11—42no—
484C22×C11—42no—
485C22×C11C2×#11711yescharacteristic
486C22×C11C2×C4×D411yescharacteristic
487C22×C11C4×#4111yescharacteristic
488C22×C11#51811yescharacteristic
489C22×C11#52011yescharacteristic
490C22×C11#52011yescharacteristic
491C22×C11#52011yescharacteristic
492C22×C11#53411yescharacteristic
493C22×C11#53711yescharacteristic
494C22×C11#53811yescharacteristic
495C22×C11#53811yescharacteristic
496C22×C11#53811yescharacteristic
497C22×C11#53811yescharacteristic
498C22×C11#53911yescharacteristic
499C22×C11#53911yescharacteristic
500C22×C11#53911yescharacteristic
501C22×C11#53911yescharacteristic
502C22×C11#54011yescharacteristic
503C22×C11#54211yescharacteristic
504C22×C11#54611yescharacteristic
505C22×C11#54611yescharacteristic
506C22×C11#54811yescharacteristic
507C22×C11#54811yescharacteristic
508C22×C11#55111yescharacteristic
509C22×C11#55111yescharacteristic
510C22×C11#55211yescharacteristic
511C22×C11#55211yescharacteristic
512C22×C11#55211yescharacteristic
513C22×C11#55311yescharacteristic
514C22×C11#55611yescharacteristic
515C22×C11#55911yescharacteristic
516C22×C11#56011yescharacteristic
517C22×C11#56311yescharacteristic
518C22×C11#56311yescharacteristic
519C22×C11#56311yescharacteristic
520C4×C11—24no—
521C4×C11—42no—
522C4×C11—42no—
523C4×C11—42no—
524C4×C11—42no—
525C4×C11—81no—
526Dic11—42no—
527Dic11—42no—
528Dic11—42no—
529Dic11—42no—
530Dic11—42no—
531Dic11—81no—
532Dic11—81no—
533Dic11—81no—
534C25C22×D1111yescharacteristic
535C23×C4—22no—
536C23×C4—22no—
537C23×C4—22no—
538C23×C4—41no—
539C23×C4—41no—
540C23×C4—41no—
541C23×C4—41no—
542C23×C4—111no—
543C23×C4—111no—
544C23×C4—111no—
545C23×C4—111no—
546C23×C4—111no—
547C23×C4—111no—
548C23×C4—111no—
549C23×C4—111no—
550C23×C4C22×D1111yescharacteristic
551C23×C4C22×D1111yescharacteristic
552C23×C4C22×D1111yescharacteristic
553C23×C4C22×D1111yescharacteristic
554C23×C4C22×D1111yescharacteristic
555C23×C4C22×D1111yescharacteristic
556C2×C4⋊C4—22no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—41no—
559C2×C4⋊C4—41no—
560C2×C4⋊C4—41no—
561C2×C4⋊C4—114no—
562C2×C4⋊C4—222no—
563C2×C4⋊C4—222no—
564C2×C4⋊C4—222no—
565C2×C4⋊C4—441no—
566C2×C4⋊C4—441no—
567C2×C4⋊C4C22⋊D1114yes—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—41no—
573C2×C22⋊C4—114no—
574C2×C22⋊C4—114no—
575C2×C22⋊C4—222no—
576C2×C22⋊C4—222no—
577C2×C22⋊C4—222no—
578C2×C22⋊C4—222no—
579C2×C22⋊C4—222no—
580C2×C22⋊C4—441no—
581C2×C22⋊C4—441no—
582C2×C22⋊C4—441no—
583C2×C22⋊C4—441no—
584C2×C22⋊C4—441no—
585C2×C22⋊C4C4×D1114yes—
586C2×C42—114no—
587C2×C42—222no—
588C2×C42—441no—
589C2×C42—441no—
590C2×C42—441no—
591C2×C42—441no—
592#95—22no—
593#95—22no—
594#95—114no—
595#95—114no—
596#95—222no—
597#95—222no—
598#95—222no—
599#95—222no—
600#95—222no—
601#95—222no—
602#95—222no—
603#95—441no—
604#95—441no—
605#95—441no—
606#95—441no—
607#95—441no—
608#95—441no—
609#95—441no—
610#95—441no—
611#95—441no—
612#95—441no—
613#95—441no—
614C2×C11—44no—
615C2×C11#231811yescharacteristic
616C2×C11#232511yescharacteristic
617C2×C11#233511yescharacteristic
618C2×C11#234311yescharacteristic
619C2×C11#235211yescharacteristic
620C2×C11#236711yescharacteristic
621C2×C11#238311yescharacteristic
622C2×C11#269711yescharacteristic
623C2×C11#270211yescharacteristic
624C2×C11#270711yescharacteristic
625C2×C11#272811yescharacteristic
626C2×C11#274511yescharacteristic
627C2×C11#277111yescharacteristic
628C2×C11#278711yescharacteristic
629C2×C11#279711yescharacteristic
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24C2×C4×D1112yes—
643C24#434112yes—
644C24#434312yes—
645C24C23×D1111yescharacteristic
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
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—44no—
682C22×C4—44no—
683C22×C4—44no—
684C22×C4—44no—
685C22×C4—44no—
686C22×C4—44no—
687C22×C4—44no—
688C22×C4—112no—
689C22×C4—112no—
690C22×C4—112no—
691C22×C4—112no—
692C22×C4—112no—
693C22×C4—221no—
694C22×C4—221no—
695C22×C4—221no—
696C22×C4—221no—
697C22×C4—221no—
698C22×C4—221no—
699C22×C4—221no—
700C22×C4—221no—
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—221no—
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×C4C2×C4×D1112yes—
745C22×C4C2×C4×D1112yes—
746C22×C4#433912yes—
747C22×C4#434112yes—
748C22×C4C2×C22⋊D1112yes—
749C22×C4C2×C22⋊D1112yes—
750C22×C4C2×C22⋊D1112yes—
751C4⋊C4—44no—
752C4⋊C4—44no—
753C4⋊C4—228no—
754C4⋊C4—444no—
755C22⋊C4—28no—
756C22⋊C4—44no—
757C22⋊C4—228no—
758C22⋊C4—444no—
759C22⋊C4—444no—
760C22⋊C4—444no—
761C42—444no—
762C42—444no—
763C11#1443611yescharacteristic, complemented, Sylow
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23#6694514yes—
799C23C22×C4×D1111yescharacteristic
800C23C2×#433911yescharacteristic
801C23C2×#434111yescharacteristic
802C23C2×#434111yescharacteristic
803C23#6703711yescharacteristic
804C23#6703711yescharacteristic
805C23#6703711yescharacteristic
806C23#6703711yescharacteristic
807C23C2×#434311yescharacteristic
808C23#6704011yescharacteristic
809C23#41×D1111yescharacteristic
810C23#6704211yescharacteristic
811C23#6704311yescharacteristic
812C23#6704311yescharacteristic
813C23C22×C22⋊D1111yescharacteristic
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—416no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
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—222no—
857C2×C4—222no—
858C2×C4—222no—
859C2×C4—222no—
860C2×C4—222no—
861C2×C4—222no—
862C2×C4—222no—
863C2×C4—222no—
864C2×C4—222no—
865C2×C4—222no—
866C2×C4—222no—
867C2×C4—222no—
868C2×C4—222no—
869C2×C4—222no—
870C2×C4—222no—
871C2×C4—441no—
872C2×C4—441no—
873C2×C4—441no—
874C2×C4—441no—
875C2×C4—441no—
876C2×C4—441no—
877C2×C4—441no—
878C2×C4—441no—
879C2×C4—441no—
880C2×C4—441no—
881C2×C4—441no—
882C2×C4—441no—
883C2×C4—441no—
884C2×C4—441no—
885C2×C4—441no—
886C2×C4—441no—
887C2×C4—441no—
888C2×C4—441no—
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×C4C4×C22⋊D1114yes—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22C2×#6694511yescharacteristic
929C22#1062303511yescharacteristic
930C22#1062304411yescharacteristic
931C22#1062304511yescharacteristic
932C22C4×#434111yescharacteristic
933C22#1062307311yescharacteristic
934C22#1062307611yescharacteristic
935C22#1062307711yescharacteristic
936C22#1062307711yescharacteristic
937C22#1062309011yescharacteristic
938C22#1062309111yescharacteristic
939C22#1062309511yescharacteristic
940C22#1062311811yescharacteristic
941C22#1062312411yescharacteristic
942C22#1062312411yescharacteristic
943C22#1062312611yescharacteristic
944C22#1062316811yescharacteristic
945C22#1062316911yescharacteristic
946C22#1062317311yescharacteristic
947C22#1062317411yescharacteristic
948C22#1062317511yescharacteristic
949C22#1062317611yescharacteristic
950C22#1062317711yescharacteristic
951C22#1062317711yescharacteristic
952C22#1062318111yescharacteristic
953C22#1062318211yescharacteristic
954C22#1062319411yescharacteristic
955C22#1062319611yescharacteristic
956C22C2×C4×C22⋊D1111yescharacteristic
957C22#1062333511yescharacteristic
958C22#1062333711yescharacteristic
959C22#1062333711yescharacteristic
960C22#1062334811yescharacteristic
961C22#1062336211yescharacteristic
962C22#1062336411yescharacteristic
963C4—24no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—81no—
969C4—442no—
970C4—442no—
971C4—442no—
972C4—442no—
973C4—442no—
974C4—881no—
975C4—881no—
976C4—881no—
977C2—44no—
978C2#1307124411yescharacteristic
979C2#1307131411yescharacteristic
980C2#1307140111yescharacteristic
981C2#1307147411yescharacteristic
982C2#1307154111yescharacteristic
983C2#1307168911yescharacteristic
984C2#1307180411yescharacteristic
985C2#1307517711yescharacteristic
986C2#1307524011yescharacteristic
987C2#1307531511yescharacteristic
988C2#1307558311yescharacteristic
989C2#1307578911yescharacteristic
990C2#1307613411yescharacteristic
991C2#1307634711yescharacteristic
992C2#1307647711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#385C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#385D11
hypocenterC11#14436
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C2×#10622591C2semidirect
3. #13066877C2semidirect
4. #13066876C2semidirect
5. #13066875C2semidirect
6. #13066870C2semidirect
10. #13066848C2semidirect
11. #13066845C2semidirect
12. #13066842C2semidirect
53. #10622558C4semidirect
105. C2×Dic11⋊C4C2×C4semidirect
111. C2×C4×Dic11C2×C4semidirect
132. C11⋊#95C2×C4semidirect
133. C11⋊#95C2×C4semidirect
763. C11#14436semidirect

Maximal subgroups

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

subgroupindex
C2×#106225582
C2×#106225912
#130668772
#130668762
#130668752
#130668702
#130668632
#130668612
#130668532
#130668482
#130668452
#130668422
#130668392
C2×C11×#3852
#1443611