Finite Group Databasebeta

← #14680883

Subgroups — #14680883

Order 2816.

1138 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622273C211yesmaximal, characteristic
2#13066876C211yesmaximal, characteristic
3#13066875C211yesmaximal, characteristic
4#13066875C211yesmaximal, characteristic
5#13066871C211yesmaximal, characteristic
6#13066868C211yesmaximal, characteristic
7#13066866C211yesmaximal, characteristic
8#13066851C211yesmaximal, characteristic
9#13066848C211yesmaximal, characteristic
10#13066848C211yesmaximal, characteristic
11#13066847C211yesmaximal, characteristic
12#13066845C211yesmaximal, characteristic
13#13066841C211yesmaximal, characteristic
14#95×Dic11C211yesmaximal, characteristic
15C11×#1444C211yesmaximal, characteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×Dic11⋊C4C2211yescharacteristic
21C22×Dic11⋊C4C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C22×C4×Dic11C2211yescharacteristic
25C2×C11×#95C2211yescharacteristic
26C2×C11×#95C2211yescharacteristic
27C2×C11×#95C2211yescharacteristic
28C2×C11×#95C2211yescharacteristic
29C2×C11⋊#95C2211yescharacteristic
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
51#10622273C418yescomplemented
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—41no—
71C2×C11×C4⋊C4—41no—
72C2×C11×C4⋊C4—41no—
73C2×C11×C4⋊C4—41no—
74C2×C11×C4⋊C4—41no—
75C2×C11×C4⋊C4—41no—
76C2×C4⋊Dic11—41no—
77C2×C4⋊Dic11—41no—
78C2×C4⋊Dic11C2×C414yes—
79C2×Dic11⋊C4—22no—
80C2×Dic11⋊C4—41no—
81C2×Dic11⋊C4—41no—
82C2×Dic11⋊C4—41no—
83C2×Dic11⋊C4—41no—
84C2×Dic11⋊C4C2×C414yes—
85C2×C4×Dic11—22no—
86C2×C4×Dic11—22no—
87C2×C4×Dic11—41no—
88C2×C4×Dic11—41no—
89C2×C4×Dic11—41no—
90C2×C4×Dic11—41no—
91C2×C4×Dic11—41no—
92C2×C4×Dic11—41no—
93C2×C4×Dic11Q814yes—
94C11×#95—22no—
95C11×#95—41no—
96C11×#95—41no—
97C11×#95C2×C414yes—
98C11⋊#95—22no—
99C11⋊#95—22no—
100C11⋊#95—22no—
101C11⋊#95—22no—
102C11⋊#95—22no—
103C11⋊#95—22no—
104C11⋊#95—22no—
105C11⋊#95—22no—
106C11⋊#95—41no—
107C11⋊#95—41no—
108C11⋊#95—41no—
109C11⋊#95—41no—
110C11⋊#95—41no—
111C11⋊#95—41no—
112C11⋊#95—41no—
113C11⋊#95—41no—
114C11⋊#95—41no—
115C11⋊#95—41no—
116C11⋊#95C2×C414yes—
117C11⋊#95C2×C414yes—
118C11⋊#95C2×C414yes—
119C11⋊#95C2×C414yes—
120#14330—111nomaximal, Sylow
121C24×C11C2411yescharacteristic
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
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×C11C22×C412yes—
165C22×C4×C11C22×C412yes—
166C22×C4×C11C22×C412yes—
167C22×C4×C11C2×Q812yes—
168C22×C4×C11#4112yes—
169C22×C4×C11#4112yes—
170C22×C4×C11#4112yes—
171C22×Dic11—21no—
172C22×Dic11—21no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—21no—
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×Dic11C22×C412yes—
220C22×Dic11C22×C412yes—
221C22×Dic11C22×C412yes—
222C22×Dic11C22×C412yes—
223C22×Dic11C2×Q812yes—
224C22×Dic11C2×Q812yes—
225C22×Dic11#4112yes—
226C22×Dic11#4112yes—
227C11×C4⋊C4—44no—
228C11×C4⋊C4—44no—
229C11×C4⋊C4—44no—
230C4⋊Dic11—44no—
231Dic11⋊C4—44no—
232Dic11⋊C4—44no—
233C4×Dic11—44no—
234C4×Dic11—44no—
235C4×Dic11—44no—
236C2×#400—111no—
237#1444D1111yescharacteristic
238#1443—111no—
239#1442—111no—
240#1442—111no—
241#1442—111no—
242#1441—111no—
243#1441—111no—
244#1436—111no—
245#1436—111no—
246#1436—111no—
247#1436—111no—
248C4⋊#95—111no—
249#1434—111no—
250C4×#95—111no—
251C23×C11C23×C411yescharacteristic
252C23×C11C22×Q811yescharacteristic
253C23×C11C2×#4111yescharacteristic
254C23×C11C2×#4111yescharacteristic
255C23×C11C2×#4111yescharacteristic
256C23×C11C2×#4111yescharacteristic
257C23×C11C2×#4111yescharacteristic
258C23×C11H(5,𝔽2)11yescharacteristic
259C23×C11H(5,𝔽2)11yescharacteristic
260C23×C11H(5,𝔽2)11yescharacteristic
261C23×C11H(5,𝔽2)11yescharacteristic
262C23×C11H(5,𝔽2)11yescharacteristic
263C23×C112−1+411yescharacteristic
264C23×C112−1+411yescharacteristic
265C23×C112−1+411yescharacteristic
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
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—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11C4×Q814yes—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—41no—
337C2×Dic11—41no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355C2×Dic11—41no—
356C2×Dic11—41no—
357C2×Dic11—41no—
358C2×Dic11—41no—
359C2×Dic11—41no—
360C2×Dic11—41no—
361C2×Dic11—41no—
362C2×Dic11—41no—
363C2×Dic11—41no—
364C2×Dic11—41no—
365C2×Dic11—41no—
366C2×Dic11—41no—
367C2×Dic11—41no—
368C2×Dic11—41no—
369C2×Dic11—41no—
370C2×Dic11#12514yes—
371C22×C4⋊C4—111no—
372C22×C4⋊C4—111no—
373C22×C4⋊C4—111no—
374C22×C4⋊C4C2×D1111yescharacteristic
375C22×C4⋊C4C2×D1111yescharacteristic
376C22×C4⋊C4C2×D1111yescharacteristic
377C22×C42—111no—
378C22×C42—111no—
379C22×C42—111no—
380#400—118no—
381C2×#95—111no—
382C2×#95—111no—
383C2×#95—111no—
384C2×#95—111no—
385C2×#95—111no—
386C2×#95—111no—
387C2×#95—111no—
388C2×#95—111no—
389C2×#95—111no—
390C2×#95—111no—
391C2×#95—111no—
392C2×#95—111no—
393C2×#95—111no—
394C2×#95—111no—
395C2×#95—111no—
396C2×#95—111no—
397C2×#95—111no—
398C2×#95—111no—
399C2×#95—111no—
400C2×#95—111no—
401C2×#95—111no—
402C2×#95—111no—
403C2×#95C2×D1111yescharacteristic
404C2×#95C2×D1111yescharacteristic
405C2×#95C2×D1111yescharacteristic
406C2×#95C2×D1111yescharacteristic
407C22×C11C2×C4×Q811yescharacteristic
408C22×C11C4×#4111yescharacteristic
409C22×C11C4×#4111yescharacteristic
410C22×C11#51811yescharacteristic
411C22×C11#52011yescharacteristic
412C22×C11#52011yescharacteristic
413C22×C11#52011yescharacteristic
414C22×C11C2×#12511yescharacteristic
415C22×C11#52911yescharacteristic
416C22×C11#52911yescharacteristic
417C22×C11#53311yescharacteristic
418C22×C11#53811yescharacteristic
419C22×C11#53811yescharacteristic
420C22×C11#53811yescharacteristic
421C22×C11#53811yescharacteristic
422C22×C11#53811yescharacteristic
423C22×C11#53811yescharacteristic
424C22×C11#53911yescharacteristic
425C22×C11#53911yescharacteristic
426C22×C11#53911yescharacteristic
427C22×C11#53911yescharacteristic
428C22×C11#54011yescharacteristic
429C22×C11#54011yescharacteristic
430C22×C11#54111yescharacteristic
431C22×C11#54111yescharacteristic
432C22×C11#54111yescharacteristic
433C22×C11#54211yescharacteristic
434C22×C11#54211yescharacteristic
435C22×C11#54211yescharacteristic
436C22×C11#54211yescharacteristic
437C22×C11#54211yescharacteristic
438C22×C11#54311yescharacteristic
439C22×C11#54411yescharacteristic
440C22×C11#54411yescharacteristic
441C22×C11#54411yescharacteristic
442C4×C11—24no—
443C4×C11—42no—
444C4×C11—42no—
445C4×C11—42no—
446C4×C11—42no—
447C4×C11—81no—
448C4×C11—81no—
449Dic11—24no—
450Dic11—42no—
451Dic11—42no—
452Dic11—42no—
453Dic11—42no—
454Dic11—42no—
455Dic11—81no—
456Dic11—81no—
457C23×C4—111no—
458C23×C4—111no—
459C23×C4—111no—
460C23×C4—111no—
461C23×C4—111no—
462C23×C4—111no—
463C23×C4—111no—
464C23×C4—111no—
465C23×C4C22×D1111yescharacteristic
466C23×C4C22×D1111yescharacteristic
467C23×C4C22×D1111yescharacteristic
468C23×C4C22×D1111yescharacteristic
469C23×C4C22×D1111yescharacteristic
470C23×C4C22×D1111yescharacteristic
471C23×C4C22×D1111yescharacteristic
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—41no—
476C2×C4⋊C4—41no—
477C2×C4⋊C4—41no—
478C2×C4⋊C4—41no—
479C2×C4⋊C4—41no—
480C2×C4⋊C4—41no—
481C2×C4⋊C4—114no—
482C2×C4⋊C4—114no—
483C2×C4⋊C4—222no—
484C2×C4⋊C4—441no—
485C2×C4⋊C4—441no—
486C2×C4⋊C4—441no—
487C2×C4⋊C4—441no—
488C2×C4⋊C4—441no—
489C2×C4⋊C4—441no—
490C2×C42—114no—
491C2×C42—222no—
492C2×C42—222no—
493C2×C42—441no—
494C2×C42—441no—
495C2×C42—441no—
496C2×C42—441no—
497C2×C42—441no—
498C2×C42—441no—
499#95—22no—
500#95—41no—
501#95—41no—
502#95—114no—
503#95—114no—
504#95—114no—
505#95—114no—
506#95—222no—
507#95—222no—
508#95—222no—
509#95—222no—
510#95—222no—
511#95—222no—
512#95—222no—
513#95—222no—
514#95—441no—
515#95—441no—
516#95—441no—
517#95—441no—
518#95—441no—
519#95—441no—
520#95—441no—
521#95—441no—
522#95—441no—
523#95—441no—
524#95C4×D1114yes—
525C2×C11C4×#12511yescharacteristic
526C2×C11#232911yescharacteristic
527C2×C11#233011yescharacteristic
528C2×C11#233411yescharacteristic
529C2×C11#233411yescharacteristic
530C2×C11#233511yescharacteristic
531C2×C11#233711yescharacteristic
532C2×C11#264611yescharacteristic
533C2×C11#264711yescharacteristic
534C2×C11#264811yescharacteristic
535C2×C11#264911yescharacteristic
536C2×C11#265011yescharacteristic
537C2×C11#265511yescharacteristic
538C2×C11#266511yescharacteristic
539C2×C11#266611yescharacteristic
540C24C23×D1111yescharacteristic
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—112no—
584C22×C4—112no—
585C22×C4—112no—
586C22×C4—112no—
587C22×C4—112no—
588C22×C4—112no—
589C22×C4—112no—
590C22×C4—112no—
591C22×C4—221no—
592C22×C4—221no—
593C22×C4—221no—
594C22×C4—221no—
595C22×C4—221no—
596C22×C4—221no—
597C22×C4—221no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—221no—
602C22×C4—221no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—221no—
606C22×C4—221no—
607C22×C4—221no—
608C22×C4—221no—
609C22×C4—221no—
610C22×C4—221no—
611C22×C4—221no—
612C22×C4—221no—
613C22×C4—221no—
614C22×C4—221no—
615C22×C4—221no—
616C22×C4—221no—
617C22×C4—221no—
618C22×C4—221no—
619C22×C4—221no—
620C22×C4—221no—
621C22×C4—221no—
622C22×C4—221no—
623C22×C4—221no—
624C22×C4—221no—
625C22×C4—221no—
626C22×C4—221no—
627C22×C4—221no—
628C22×C4—221no—
629C22×C4—221no—
630C22×C4—221no—
631C22×C4—221no—
632C22×C4—221no—
633C22×C4—221no—
634C22×C4—221no—
635C22×C4—221no—
636C22×C4—221no—
637C22×C4—221no—
638C22×C4—221no—
639C22×C4C2×C4×D1112yes—
640C22×C4C2×C4×D1112yes—
641C22×C4C2×C4×D1112yes—
642C22×C4#434112yes—
643C22×C4#434112yes—
644C22×C4Q8×D1112yes—
645C22×C4#434312yes—
646C4⋊C4—44no—
647C4⋊C4—44no—
648C4⋊C4—44no—
649C4⋊C4—444no—
650C4⋊C4—444no—
651C4⋊C4—444no—
652C42—444no—
653C42—444no—
654C42—444no—
655C11#1433011yescharacteristic, complemented, Sylow
656C23C22×C4×D1111yescharacteristic
657C23C2×#434111yescharacteristic
658C23C2×#434111yescharacteristic
659C23#6703711yescharacteristic
660C23#6703711yescharacteristic
661C23#6703711yescharacteristic
662C23#6703711yescharacteristic
663C23C2×Q8×D1111yescharacteristic
664C23C2×#434311yescharacteristic
665C23#6704011yescharacteristic
666C23#6704011yescharacteristic
667C23#41×D1111yescharacteristic
668C23#41×D1111yescharacteristic
669C23#6704211yescharacteristic
670C23#6704311yescharacteristic
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—114no—
720C2×C4—222no—
721C2×C4—222no—
722C2×C4—222no—
723C2×C4—222no—
724C2×C4—222no—
725C2×C4—222no—
726C2×C4—222no—
727C2×C4—222no—
728C2×C4—222no—
729C2×C4—222no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—222no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—222no—
737C2×C4—222no—
738C2×C4—222no—
739C2×C4—222no—
740C2×C4—222no—
741C2×C4—441no—
742C2×C4—441no—
743C2×C4—441no—
744C2×C4—441no—
745C2×C4—441no—
746C2×C4—441no—
747C2×C4—441no—
748C2×C4—441no—
749C2×C4—441no—
750C2×C4—441no—
751C2×C4—441no—
752C2×C4—441no—
753C2×C4—441no—
754C2×C4—441no—
755C2×C4—441no—
756C2×C4—441no—
757C2×C4—441no—
758C2×C4—441no—
759C2×C4—441no—
760C2×C4—441no—
761C2×C4—441no—
762C2×C4—441no—
763C2×C4—441no—
764C2×C4—441no—
765C2×C4—441no—
766C2×C4—441no—
767C2×C4—441no—
768C2×C4—441no—
769C2×C4—441no—
770C2×C4—441no—
771C2×C4—441no—
772C2×C4—441no—
773C2×C4—441no—
774C2×C4—441no—
775C2×C4#6694014yes—
776C22C2×#6694011yescharacteristic
777C22#1062303511yescharacteristic
778C22#1062303511yescharacteristic
779C22C4×#434111yescharacteristic
780C22#1062307611yescharacteristic
781C22#1062307711yescharacteristic
782C22C4×#434311yescharacteristic
783C22#1062312411yescharacteristic
784C22#1062312411yescharacteristic
785C22#1062312411yescharacteristic
786C22#1062313111yescharacteristic
787C22#1062314411yescharacteristic
788C22#1062314611yescharacteristic
789C22#1062315411yescharacteristic
790C22#1062315511yescharacteristic
791C22#1062315611yescharacteristic
792C22#1062316511yescharacteristic
793C22#1062316911yescharacteristic
794C22#1062317111yescharacteristic
795C22#1062317411yescharacteristic
796C22#1062317511yescharacteristic
797C22#1062317611yescharacteristic
798C22#1062318811yescharacteristic
799C22#1062319311yescharacteristic
800C22#1062319611yescharacteristic
801C22D11×#12511yescharacteristic
802C22#1062322311yescharacteristic
803C22#1062322711yescharacteristic
804C22#1062325011yescharacteristic
805C22#1062325911yescharacteristic
806C22#1062326011yescharacteristic
807C22#1062326011yescharacteristic
808C22#1062326211yescharacteristic
809C22#1062326411yescharacteristic
810C22#1062326411yescharacteristic
811C4—24no—
812C4—42no—
813C4—42no—
814C4—42no—
815C4—42no—
816C4—81no—
817C4—81no—
818C4—224no—
819C4—442no—
820C4—442no—
821C4—442no—
822C4—442no—
823C4—442no—
824C4—881no—
825C4—881no—
826C2#1307117511yescharacteristic
827C2#1307134711yescharacteristic
828C2#1307135511yescharacteristic
829C2#1307139011yescharacteristic
830C2#1307139211yescharacteristic
831C2#1307140911yescharacteristic
832C2#1307143011yescharacteristic
833C2#1307458511yescharacteristic
834C2#1307459011yescharacteristic
835C2#1307460511yescharacteristic
836C2#1307462211yescharacteristic
837C2#1307463711yescharacteristic
838C2#1307471011yescharacteristic
839C2#1307479111yescharacteristic
840C2#1307480211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1444C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1444D11
hypocenterC11#14330
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
51. #10622273C4semidirect
655. C11#14330semidirect

Maximal subgroups

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

subgroupindex
C2×#106222732
#130668762
#130668752
#130668712
#130668682
#130668662
#130668512
#130668482
#130668472
#130668452
#130668412
#95×Dic112
C11×#14442
#1433011