Finite Group Databasebeta

← #14677366

Subgroups — #14677366

Order 2816.

1442 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622260C211yesmaximal, characteristic
2C2×#10622591C211yesmaximal, characteristic
3C2×#10622591C211yesmaximal, characteristic
4C2×C4⋊C4×Dic11C211yesmaximal, characteristic
5C2×C4⋊C4×Dic11C211yesmaximal, characteristic
6#13066882C211yesmaximal, characteristic
7#13066875C211yesmaximal, characteristic
8#13066866C211yesmaximal, characteristic
9#13066851C211yesmaximal, characteristic
10#13066850C211yesmaximal, characteristic
11#13066850C211yesmaximal, characteristic
12#13066850C211yesmaximal, characteristic
13#13066847C211yesmaximal, characteristic
14#13066842C211yesmaximal, characteristic
15C11×#1444C211yesmaximal, characteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×Dic11⋊C4C2211yescharacteristic
22C22×Dic11⋊C4C2211yescharacteristic
23C22×Dic11⋊C4C2211yescharacteristic
24C22×C4×Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
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#10622591—24no—
52#10622591—24no—
53C4⋊C4×Dic11—24no—
54C4⋊C4×Dic11—24no—
55#10622260C418yescomplemented
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—41no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11C2×C414yes—
85C2×C4⋊Dic11Q814yes—
86C2×Dic11⋊C4—22no—
87C2×Dic11⋊C4—22no—
88C2×Dic11⋊C4—22no—
89C2×Dic11⋊C4—22no—
90C2×Dic11⋊C4—22no—
91C2×Dic11⋊C4—22no—
92C2×Dic11⋊C4C2×C414yes—
93C2×Dic11⋊C4C2×C414yes—
94C2×Dic11⋊C4C2×C414yes—
95C2×C4×Dic11—22no—
96C2×C4×Dic11—22no—
97C2×C4×Dic11—22no—
98C2×C4×Dic11—22no—
99C2×C4×Dic11—22no—
100C2×C4×Dic11—22no—
101C2×C4×Dic11—22no—
102C2×C4×Dic11—22no—
103C2×C4×Dic11—22no—
104C2×C4×Dic11—22no—
105C2×C4×Dic11—22no—
106C2×C4×Dic11—41no—
107C2×C4×Dic11—41no—
108C2×C4×Dic11—41no—
109C2×C4×Dic11C2×C414yes—
110C11×#95—22no—
111C11×#95—22no—
112C11×#95—41no—
113C11×#95C2×C414yes—
114C11⋊#95—22no—
115C11⋊#95—22no—
116C11⋊#95—22no—
117C11⋊#95—22no—
118C11⋊#95—22no—
119C11⋊#95—22no—
120C11⋊#95—22no—
121C11⋊#95—22no—
122C11⋊#95—22no—
123C11⋊#95—22no—
124C11⋊#95—22no—
125C11⋊#95—22no—
126C11⋊#95—22no—
127C11⋊#95—22no—
128C11⋊#95—41no—
129C11⋊#95C2×C414yes—
130C11⋊#95D414yes—
131C11⋊#95D414yes—
132#14035—111nomaximal, Sylow
133C24×C11C2411yescharacteristic
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×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×C11C22×C412yes—
174C22×C4×C11C22×C412yes—
175C22×C4×C11C22×C412yes—
176C22×C4×C11C2×D412yes—
177C22×C4×C11C2×D412yes—
178C22×C4×C11C2×Q812yes—
179C22×C4×C11#4112yes—
180C22×C4×C11#4112yes—
181C22×C4×C11#4112yes—
182C22×C4×C11#4112yes—
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×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11C22×C412yes—
227C22×Dic11C22×C412yes—
228C22×Dic11C22×C412yes—
229C22×Dic11C22×C412yes—
230C22×Dic11C2×D412yes—
231C22×Dic11C2×D412yes—
232C22×Dic11C2×D412yes—
233C22×Dic11C2×D412yes—
234C22×Dic11C2×Q812yes—
235C22×Dic11C2×Q812yes—
236C22×Dic11#4112yes—
237C22×Dic11#4112yes—
238C22×Dic11#4112yes—
239C11×C4⋊C4—28no—
240C11×C4⋊C4—28no—
241C11×C4⋊C4—44no—
242C4⋊Dic11—28no—
243C4⋊Dic11—28no—
244Dic11⋊C4—28no—
245Dic11⋊C4—28no—
246Dic11⋊C4—28no—
247C4×Dic11—28no—
248C4×Dic11—28no—
249C4×Dic11—44no—
250C4×Dic11—44no—
251C4×Dic11—44no—
252C2×#389—111no—
253C2×#387—111no—
254C2×#387—111no—
255C2×C4×C4⋊C4—111no—
256C2×C4×C4⋊C4—111no—
257#1445—111no—
258#1444D1111yescharacteristic
259#1442—111no—
260#1441—111no—
261#1436—111no—
262#1436—111no—
263#1436—111no—
264#1436—111no—
265#1436—111no—
266#1434—111no—
267C23×C11C23×C411yescharacteristic
268C23×C11C22×D411yescharacteristic
269C23×C11C22×D411yescharacteristic
270C23×C11C22×Q811yescharacteristic
271C23×C11C2×#4111yescharacteristic
272C23×C11C2×#4111yescharacteristic
273C23×C11C2×#4111yescharacteristic
274C23×C11C2×#4111yescharacteristic
275C23×C11C2×#4111yescharacteristic
276C23×C11C2×#4111yescharacteristic
277C23×C11C2×#4111yescharacteristic
278C23×C11H(5,𝔽2)11yescharacteristic
279C23×C112−1+411yescharacteristic
280C23×C112−1+411yescharacteristic
281C23×C112−1+411yescharacteristic
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
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×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11#11714yes—
330C2×C4×C11C4×Q814yes—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
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—41no—
371C2×Dic11—41no—
372C2×Dic11—41no—
373C2×Dic11—41no—
374C2×Dic11—41no—
375C2×Dic11—41no—
376C2×Dic11—41no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380C2×Dic11—41no—
381C2×Dic11—41no—
382C2×Dic11—41no—
383C2×Dic11—41no—
384C2×Dic11C4×D414yes—
385C2×Dic11C4×D414yes—
386C2×Dic11C22⋊Q814yes—
387C22×C4⋊C4—111no—
388C22×C4⋊C4—111no—
389C22×C4⋊C4—111no—
390C22×C4⋊C4—111no—
391C22×C4⋊C4—111no—
392C22×C4⋊C4C2×D1111yescharacteristic
393C22×C4⋊C4C2×D1111yescharacteristic
394C22×C4⋊C4C2×D1111yescharacteristic
395C22×C42—111no—
396C22×C42—111no—
397C22×C42—111no—
398C22×C42—111no—
399C22×C42—111no—
400#389—118no—
401#387—224no—
402#387—224no—
403C4×C4⋊C4—224no—
404C4×C4⋊C4—224no—
405C2×#95—111no—
406C2×#95—111no—
407C2×#95—111no—
408C2×#95—111no—
409C2×#95—111no—
410C2×#95—111no—
411C2×#95—111no—
412C2×#95—111no—
413C2×#95—111no—
414C2×#95—111no—
415C2×#95—111no—
416C2×#95—111no—
417C2×#95—111no—
418C2×#95—111no—
419C2×#95—111no—
420C2×#95—111no—
421C2×#95—111no—
422C2×#95—111no—
423C2×#95C2×D1111yescharacteristic
424C2×#95C2×D1111yescharacteristic
425C2×#95C2×D1111yescharacteristic
426C2×#95C2×D1111yescharacteristic
427C22×C11C2×#11711yescharacteristic
428C22×C11C2×C4×D411yescharacteristic
429C22×C11C2×C4×D411yescharacteristic
430C22×C11C2×C4×Q811yescharacteristic
431C22×C11C4×#4111yescharacteristic
432C22×C11#51911yescharacteristic
433C22×C11#52011yescharacteristic
434C22×C11C2×C22⋊Q811yescharacteristic
435C22×C11#52511yescharacteristic
436C22×C11#52511yescharacteristic
437C22×C11#52511yescharacteristic
438C22×C11#52911yescharacteristic
439C22×C11#52911yescharacteristic
440C22×C11#52911yescharacteristic
441C22×C11#53311yescharacteristic
442C22×C11#53911yescharacteristic
443C22×C11#53911yescharacteristic
444C22×C11#54111yescharacteristic
445C22×C11#54111yescharacteristic
446C22×C11D4211yescharacteristic
447C22×C11#54711yescharacteristic
448C22×C11#54711yescharacteristic
449C22×C11#54711yescharacteristic
450C22×C11#54711yescharacteristic
451C22×C11#54811yescharacteristic
452C22×C11D4×Q811yescharacteristic
453C22×C11#55211yescharacteristic
454C22×C11#55211yescharacteristic
455C22×C11#55311yescharacteristic
456C22×C11#55411yescharacteristic
457C22×C11#55611yescharacteristic
458C22×C11#55611yescharacteristic
459C22×C11#55711yescharacteristic
460C22×C11#55711yescharacteristic
461C22×C11#55911yescharacteristic
462C4×C11—24no—
463C4×C11—24no—
464C4×C11—42no—
465C4×C11—42no—
466C4×C11—42no—
467C4×C11—42no—
468C4×C11—81no—
469Dic11—24no—
470Dic11—24no—
471Dic11—24no—
472Dic11—42no—
473Dic11—42no—
474Dic11—42no—
475Dic11—42no—
476Dic11—81no—
477C23×C4—111no—
478C23×C4—111no—
479C23×C4—111no—
480C23×C4—111no—
481C23×C4—111no—
482C23×C4—111no—
483C23×C4—111no—
484C23×C4—111no—
485C23×C4C22×D1111yescharacteristic
486C23×C4C22×D1111yescharacteristic
487C23×C4C22×D1111yescharacteristic
488C23×C4C22×D1111yescharacteristic
489C23×C4C22×D1111yescharacteristic
490C23×C4C22×D1111yescharacteristic
491C23×C4C22×D1111yescharacteristic
492C2×C4⋊C4—22no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—41no—
501C2×C4⋊C4—114no—
502C2×C4⋊C4—114no—
503C2×C4⋊C4—114no—
504C2×C4⋊C4—114no—
505C2×C4⋊C4—114no—
506C2×C4⋊C4—222no—
507C2×C4⋊C4—222no—
508C2×C4⋊C4—222no—
509C2×C4⋊C4—222no—
510C2×C4⋊C4—222no—
511C2×C4⋊C4—222no—
512C2×C4⋊C4—222no—
513C2×C4⋊C4—222no—
514C2×C4⋊C4—222no—
515C2×C4⋊C4—222no—
516C2×C42—114no—
517C2×C42—222no—
518C2×C42—222no—
519C2×C42—222no—
520C2×C42—222no—
521C2×C42—222no—
522C2×C42—222no—
523C2×C42—222no—
524C2×C42—222no—
525C2×C42—222no—
526C2×C42—222no—
527C2×C42—222no—
528C2×C42—441no—
529C2×C42—441no—
530C2×C42—441no—
531#95—22no—
532#95—22no—
533#95—41no—
534#95—114no—
535#95—114no—
536#95—114no—
537#95—222no—
538#95—222no—
539#95—222no—
540#95—222no—
541#95—222no—
542#95—222no—
543#95—222no—
544#95—222no—
545#95—222no—
546#95—222no—
547#95—222no—
548#95—222no—
549#95—222no—
550#95—222no—
551#95—441no—
552#95C4×D1114yes—
553C2×C11#229011yescharacteristic
554C2×C11C4×C22⋊Q811yescharacteristic
555C2×C11#233611yescharacteristic
556C2×C11#234411yescharacteristic
557C2×C11#235511yescharacteristic
558C2×C11#236111yescharacteristic
559C2×C11#236511yescharacteristic
560C2×C11#244911yescharacteristic
561C2×C11#245311yescharacteristic
562C2×C11#245511yescharacteristic
563C2×C11#246211yescharacteristic
564C2×C11#246911yescharacteristic
565C2×C11#247811yescharacteristic
566C2×C11#258511yescharacteristic
567C2×C11#259611yescharacteristic
568C24C23×D1111yescharacteristic
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—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—112no—
609C22×C4—112no—
610C22×C4—112no—
611C22×C4—112no—
612C22×C4—112no—
613C22×C4—112no—
614C22×C4—112no—
615C22×C4—112no—
616C22×C4—112no—
617C22×C4—112no—
618C22×C4—112no—
619C22×C4—112no—
620C22×C4—112no—
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×C4—221no—
640C22×C4—221no—
641C22×C4—221no—
642C22×C4—221no—
643C22×C4—221no—
644C22×C4—221no—
645C22×C4—221no—
646C22×C4—221no—
647C22×C4—221no—
648C22×C4—221no—
649C22×C4—221no—
650C22×C4—221no—
651C22×C4—221no—
652C22×C4—221no—
653C22×C4—221no—
654C22×C4—221no—
655C22×C4—221no—
656C22×C4—221no—
657C22×C4—221no—
658C22×C4—221no—
659C22×C4—221no—
660C22×C4—221no—
661C22×C4—221no—
662C22×C4—221no—
663C22×C4—221no—
664C22×C4C2×C4×D1112yes—
665C22×C4C2×C4×D1112yes—
666C22×C4C2×C4×D1112yes—
667C22×C4D4×D1112yes—
668C22×C4D4×D1112yes—
669C22×C4#434112yes—
670C22×C4#434112yes—
671C22×C4#434112yes—
672C22×C4Q8×D1112yes—
673C22×C4#434312yes—
674C4⋊C4—28no—
675C4⋊C4—28no—
676C4⋊C4—44no—
677C4⋊C4—228no—
678C4⋊C4—228no—
679C4⋊C4—228no—
680C4⋊C4—228no—
681C4⋊C4—228no—
682C42—228no—
683C42—228no—
684C42—444no—
685C42—444no—
686C42—444no—
687C11#1403511yescharacteristic, complemented, Sylow
688C23C22×C4×D1111yescharacteristic
689C23C2×D4×D1111yescharacteristic
690C23C2×D4×D1111yescharacteristic
691C23C2×#434111yescharacteristic
692C23C2×#434111yescharacteristic
693C23C2×#434111yescharacteristic
694C23#6703711yescharacteristic
695C23C2×Q8×D1111yescharacteristic
696C23C2×#434311yescharacteristic
697C23#6704011yescharacteristic
698C23#6704011yescharacteristic
699C23#41×D1111yescharacteristic
700C23#41×D1111yescharacteristic
701C23#41×D1111yescharacteristic
702C23#6704311yescharacteristic
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—114no—
751C2×C4—114no—
752C2×C4—114no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—222no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—222no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—222no—
766C2×C4—222no—
767C2×C4—222no—
768C2×C4—222no—
769C2×C4—222no—
770C2×C4—222no—
771C2×C4—222no—
772C2×C4—222no—
773C2×C4—222no—
774C2×C4—222no—
775C2×C4—222no—
776C2×C4—222no—
777C2×C4—222no—
778C2×C4—222no—
779C2×C4—222no—
780C2×C4—222no—
781C2×C4—222no—
782C2×C4—222no—
783C2×C4—441no—
784C2×C4—441no—
785C2×C4—441no—
786C2×C4—441no—
787C2×C4—441no—
788C2×C4—441no—
789C2×C4—441no—
790C2×C4—441no—
791C2×C4—441no—
792C2×C4—441no—
793C2×C4—441no—
794C2×C4—441no—
795C2×C4—441no—
796C2×C4—441no—
797C2×C4—441no—
798C2×C4—441no—
799C2×C4—441no—
800C2×C4—441no—
801C2×C4—441no—
802C2×C4—441no—
803C2×C4—441no—
804C2×C4—441no—
805C2×C4—441no—
806C2×C4#6694014yes—
807C2×C4#6694514yes—
808C22C2×#6694011yescharacteristic
809C22C2×#6694511yescharacteristic
810C22#1062303511yescharacteristic
811C22C4×#434111yescharacteristic
812C22C4×D4×D1111yescharacteristic
813C22C4×D4×D1111yescharacteristic
814C22#1062310311yescharacteristic
815C22#1062311711yescharacteristic
816C22#1062311711yescharacteristic
817C22#1062312111yescharacteristic
818C22#1062313311yescharacteristic
819C22#1062314211yescharacteristic
820C22#1062314211yescharacteristic
821C22#1062315311yescharacteristic
822C22#1062315511yescharacteristic
823C22D11×C22⋊Q811yescharacteristic
824C22#1062315811yescharacteristic
825C22#1062316211yescharacteristic
826C22#1062316411yescharacteristic
827C22#1062316911yescharacteristic
828C22#1062317011yescharacteristic
829C22#1062317211yescharacteristic
830C22#1062318011yescharacteristic
831C22#1062318011yescharacteristic
832C22#1062319211yescharacteristic
833C22#1062321611yescharacteristic
834C22#1062322511yescharacteristic
835C22#1062322711yescharacteristic
836C22#1062324411yescharacteristic
837C22#1062325211yescharacteristic
838C22#1062325711yescharacteristic
839C22#1062325811yescharacteristic
840C22#1062326111yescharacteristic
841C22#1062326211yescharacteristic
842C22#1062326311yescharacteristic
843C4—24no—
844C4—24no—
845C4—42no—
846C4—42no—
847C4—42no—
848C4—42no—
849C4—81no—
850C4—224no—
851C4—224no—
852C4—224no—
853C4—442no—
854C4—442no—
855C4—442no—
856C4—442no—
857C4—881no—
858C2#1307105211yescharacteristic
859C2#1307114811yescharacteristic
860C2#1307141411yescharacteristic
861C2#1307148411yescharacteristic
862C2#1307157511yescharacteristic
863C2#1307163511yescharacteristic
864C2#1307166911yescharacteristic
865C2#1307241811yescharacteristic
866C2#1307247211yescharacteristic
867C2#1307249211yescharacteristic
868C2#1307259111yescharacteristic
869C2#1307269011yescharacteristic
870C2#1307283511yescharacteristic
871C2#1307400611yescharacteristic
872C2#1307415311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1444C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1444D11
hypocenterC11#14035
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
55. #10622260C4semidirect
687. C11#14035semidirect

Maximal subgroups

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

subgroupindex
C2×#106222602
C2×#106225912
C2×C4⋊C4×Dic112
#130668822
#130668752
#130668662
#130668512
#130668502
#130668472
#130668422
C11×#14442
#1403511