Finite Group Databasebeta

← #14677913

Subgroups — #14677913

Order 2816.

1630 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×#10622594C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊Dic11C211yesmaximal, characteristic
3#13066878C211yesmaximal, characteristic, complemented
4#13066869C211yesmaximal, characteristic, complemented
5#13066861C211yesmaximal, characteristic
6#13066861C211yesmaximal, characteristic
7#13066853C211yesmaximal, characteristic
8#13066853C211yesmaximal, characteristic
9#13066850C211yesmaximal, characteristic, complemented
10#13066848C211yesmaximal, characteristic, complemented
11#13066845C211yesmaximal, characteristic, complemented
12#13066841C211yesmaximal, characteristic, complemented
13#13066839C211yesmaximal, characteristic
14#95×Dic11C211yesmaximal, characteristic, complemented
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×C4⋊Dic11C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C11×#385C418yescomplemented
32C2×C11×#95C2211yescharacteristic
33C2×C11×#95C2211yescharacteristic
34C4×C22⋊Dic11—24no—
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
52C2×C11⋊#95C2211yescharacteristic
53#10622594—24no—
54C25×C11C2311yescharacteristic
55C23×C4×C11—22no—
56C23×C4×C11—22no—
57C23×C4×C11—41no—
58C23×C4×C11—41no—
59C23×C4×C11—41no—
60C23×C4×C11—41no—
61C23×C4×C11C2×C414yes—
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⋊C4C2×C414yes—
81C2×C11×C4⋊C4C2×C414yes—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—41no—
85C2×C11×C22⋊C4—41no—
86C2×C11×C22⋊C4C2×C414yes—
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—22no—
94C2×C22⋊Dic11—22no—
95C2×C22⋊Dic11—22no—
96C2×C22⋊Dic11—22no—
97C2×C22⋊Dic11—41no—
98C2×C22⋊Dic11—41no—
99C2×C22⋊Dic11Q814yes—
100C2×C4⋊Dic11—22no—
101C2×C4⋊Dic11—22no—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11—41no—
104C2×C4⋊Dic11—41no—
105C2×C4⋊Dic11—41no—
106C2×C4×Dic11—22no—
107C2×C4×Dic11—22no—
108C2×C4×Dic11—22no—
109C2×C4×Dic11—22no—
110C2×C4×Dic11—22no—
111C2×C4×Dic11—41no—
112C2×C4×Dic11—41no—
113C2×C4×Dic11—41no—
114C2×C4×Dic11—41no—
115C2×C4×Dic11—41no—
116C2×C4×Dic11—41no—
117C2×C4×Dic11D414yes—
118C11×#95C2×C414yes—
119C11×#95C2×C414yes—
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—22no—
129C11⋊#95—22no—
130C11⋊#95—22no—
131C11⋊#95—22no—
132C11⋊#95—22no—
133C11⋊#95—41no—
134C11⋊#95—41no—
135C11⋊#95—41no—
136C11⋊#95—41no—
137C11⋊#95—41no—
138#14075—111nomaximal, Sylow
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×C11—21no—
148C24×C11—21no—
149C24×C11—21no—
150C24×C11—21no—
151C24×C11C22×C412yes—
152C24×C11C2×Q812yes—
153C24×C11#4112yes—
154C24×C11C2411yescharacteristic
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—28no—
188C22×C4×C11—44no—
189C22×C4×C11—44no—
190C22×C4×C11—44no—
191C22×C4×C11—44no—
192C22×C4×C11—44no—
193C22×C4×C11—44no—
194C22×C4×C11C22×C412yes—
195C22×C4×C11C22×C412yes—
196C22×C4×C11C22×C412yes—
197C22×C4×C11C22×C412yes—
198C22×C4×C11C22×C412yes—
199C22×C4×C11C22×C412yes—
200C22×C4×C11C2×D412yes—
201C22×C4×C11#4112yes—
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×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11C2×D412yes—
253C22×Dic11C2×D412yes—
254C22×Dic11C2×Q812yes—
255C22×Dic11C2×Q812yes—
256C22×Dic11#4112yes—
257C22×Dic11#4112yes—
258C22×Dic11#4112yes—
259C22×Dic11#4112yes—
260C11×C4⋊C4—28no—
261C11×C4⋊C4—44no—
262C11×C22⋊C4—28no—
263C11×C22⋊C4—44no—
264C22⋊Dic11—28no—
265C22⋊Dic11—28no—
266C22⋊Dic11—44no—
267C22⋊Dic11—44no—
268C4⋊Dic11—44no—
269C4⋊Dic11—44no—
270C4×Dic11—44no—
271C4×Dic11—44no—
272C4×Dic11—44no—
273C4×Dic11—44no—
274C2×#387—111no—
275C2×#385D1111yescharacteristic
276C2×C4×C22⋊C4—111no—
277#1443—111no—
278#1441—111no—
279#1439—111no—
280#1439—111no—
281#1437—111no—
282#1437—111no—
283#1436—111no—
284#1436—111no—
285C4⋊#95—111no—
286#1434—111no—
287C22⋊#95—111no—
288C4×#95—111no—
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—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
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—41no—
318C23×C11—41no—
319C23×C11—41no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11—41no—
323C23×C11C4×Q814yes—
324C23×C11C23×C411yescharacteristic
325C23×C11C22×D411yescharacteristic
326C23×C11C22×Q811yescharacteristic
327C23×C11C2×#4111yescharacteristic
328C23×C11C2×#4111yescharacteristic
329C23×C11C2×#4111yescharacteristic
330C23×C11C2×#4111yescharacteristic
331C23×C11C2×#4111yescharacteristic
332C23×C11C2×#4111yescharacteristic
333C23×C11C2×#4111yescharacteristic
334C23×C11C2×#4111yescharacteristic
335C23×C11H(5,𝔽2)11yescharacteristic
336C23×C11H(5,𝔽2)11yescharacteristic
337C23×C11H(5,𝔽2)11yescharacteristic
338C23×C11H(5,𝔽2)11yescharacteristic
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—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—416no—
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#11714yes—
381C2×C4×C11C4×D414yes—
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—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—
437C2×Dic11C22⋊Q814yes—
438C24×C4C2×D1111yescharacteristic
439C22×C4⋊C4—111no—
440C22×C4⋊C4—111no—
441C22×C4⋊C4C2×D1111yescharacteristic
442C22×C4⋊C4C2×D1111yescharacteristic
443C22×C22⋊C4—111no—
444C22×C22⋊C4—111no—
445C22×C22⋊C4—111no—
446C22×C22⋊C4—111no—
447C22×C22⋊C4C2×D1111yescharacteristic
448C22×C22⋊C4C2×D1111yescharacteristic
449C22×C42—111no—
450C22×C42—111no—
451C22×C42—111no—
452C22×C42—111no—
453#387—224no—
454#385Dic1118yescomplemented
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×#95—111no—
473C2×#95—111no—
474C2×#95C2×D1111yescharacteristic
475C2×#95C2×D1111yescharacteristic
476C22×C11—24no—
477C22×C11—24no—
478C22×C11—24no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11—42no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11C2×#11711yescharacteristic
492C22×C11C2×C4×D411yescharacteristic
493C22×C11C2×C4×Q811yescharacteristic
494C22×C11C4×#4111yescharacteristic
495C22×C11C4×#4111yescharacteristic
496C22×C11#51811yescharacteristic
497C22×C11#51811yescharacteristic
498C22×C11C2×C22⋊Q811yescharacteristic
499C22×C11#52511yescharacteristic
500C22×C11#52911yescharacteristic
501C22×C11#52911yescharacteristic
502C22×C11#52911yescharacteristic
503C22×C11#53211yescharacteristic
504C22×C11#53211yescharacteristic
505C22×C11#53311yescharacteristic
506C22×C11#53411yescharacteristic
507C22×C11#53511yescharacteristic
508C22×C11#53811yescharacteristic
509C22×C11#53811yescharacteristic
510C22×C11#55111yescharacteristic
511C22×C11#55111yescharacteristic
512C22×C11#55111yescharacteristic
513C22×C11#55111yescharacteristic
514C22×C11#55111yescharacteristic
515C22×C11#55311yescharacteristic
516C22×C11#55311yescharacteristic
517C22×C11#55311yescharacteristic
518C22×C11#55311yescharacteristic
519C22×C11#55311yescharacteristic
520C22×C11#55311yescharacteristic
521C22×C11#55411yescharacteristic
522C22×C11#55411yescharacteristic
523C22×C11#55411yescharacteristic
524C22×C11#55411yescharacteristic
525C22×C11#55911yescharacteristic
526C4×C11—24no—
527C4×C11—24no—
528C4×C11—42no—
529C4×C11—42no—
530C4×C11—42no—
531C4×C11—42no—
532Dic11—24no—
533Dic11—42no—
534Dic11—42no—
535Dic11—42no—
536Dic11—42no—
537Dic11—42no—
538Dic11—81no—
539Dic11—81no—
540C25C22×D1111yescharacteristic
541C23×C4—22no—
542C23×C4—22no—
543C23×C4—41no—
544C23×C4—41no—
545C23×C4—41no—
546C23×C4—41no—
547C23×C4—111no—
548C23×C4—111no—
549C23×C4—111no—
550C23×C4—111no—
551C23×C4—111no—
552C23×C4—111no—
553C23×C4—111no—
554C23×C4—111no—
555C23×C4C2×Dic1114yes—
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—22no—
564C2×C4⋊C4—41no—
565C2×C4⋊C4—41no—
566C2×C4⋊C4—222no—
567C2×C4⋊C4—222no—
568C2×C4⋊C4—222no—
569C2×C4⋊C4—441no—
570C2×C4⋊C4—441no—
571C2×C4⋊C4—441no—
572C2×C4⋊C4C2×Dic1114yes—
573C2×C4⋊C4C2×Dic1114yes—
574C2×C22⋊C4—22no—
575C2×C22⋊C4—22no—
576C2×C22⋊C4—41no—
577C2×C22⋊C4—41no—
578C2×C22⋊C4—114no—
579C2×C22⋊C4—222no—
580C2×C22⋊C4—222no—
581C2×C22⋊C4—222no—
582C2×C22⋊C4—222no—
583C2×C22⋊C4—222no—
584C2×C22⋊C4—222no—
585C2×C22⋊C4—222no—
586C2×C22⋊C4—222no—
587C2×C22⋊C4—222no—
588C2×C22⋊C4—441no—
589C2×C22⋊C4—441no—
590C2×C22⋊C4C2×Dic1114yes—
591C2×C22⋊C4C2×Dic1114yes—
592C2×C42—114no—
593C2×C42—222no—
594C2×C42—222no—
595C2×C42—222no—
596C2×C42—222no—
597C2×C42—222no—
598C2×C42—441no—
599C2×C42—441no—
600C2×C42—441no—
601C2×C42—441no—
602C2×C42—441no—
603C2×C42—441no—
604#95—222no—
605#95—222no—
606#95—222no—
607#95—222no—
608#95—222no—
609#95—222no—
610#95—222no—
611#95—222no—
612#95—222no—
613#95—222no—
614#95—222no—
615#95—222no—
616#95—222no—
617#95—441no—
618#95—441no—
619#95—441no—
620#95—441no—
621#95—441no—
622#95C2×Dic1114yes—
623#95C2×Dic1114yes—
624C2×C11—44no—
625C2×C11#229311yescharacteristic
626C2×C11C4×C22⋊Q811yescharacteristic
627C2×C11#232111yescharacteristic
628C2×C11#234511yescharacteristic
629C2×C11#235311yescharacteristic
630C2×C11#236811yescharacteristic
631C2×C11#237411yescharacteristic
632C2×C11#256411yescharacteristic
633C2×C11#256611yescharacteristic
634C2×C11#257611yescharacteristic
635C2×C11#257811yescharacteristic
636C2×C11#258711yescharacteristic
637C2×C11#258911yescharacteristic
638C2×C11#260211yescharacteristic
639C2×C11#260311yescharacteristic
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24Q8×D1112yes—
653C24#434312yes—
654C24C22×Dic1112yes—
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—28no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—44no—
692C22×C4—44no—
693C22×C4—44no—
694C22×C4—44no—
695C22×C4—112no—
696C22×C4—112no—
697C22×C4—112no—
698C22×C4—112no—
699C22×C4—112no—
700C22×C4—112no—
701C22×C4—112no—
702C22×C4—112no—
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×C4—221no—
745C22×C4—221no—
746C22×C4—221no—
747C22×C4—221no—
748C22×C4—221no—
749C22×C4—221no—
750C22×C4—221no—
751C22×C4#433912yes—
752C22×C4#433912yes—
753C22×C4D4×D1112yes—
754C22×C4#434112yes—
755C22×C4C22×Dic1112yes—
756C22×C4C22×Dic1112yes—
757C22×C4C22×Dic1112yes—
758C22×C4C22×Dic1112yes—
759C22×C4C22×Dic1112yes—
760C22×C4C22×Dic1112yes—
761C4⋊C4—28no—
762C4⋊C4—44no—
763C4⋊C4—444no—
764C4⋊C4—444no—
765C22⋊C4—28no—
766C22⋊C4—44no—
767C22⋊C4—228no—
768C22⋊C4—228no—
769C22⋊C4—444no—
770C22⋊C4—444no—
771C42—444no—
772C42—444no—
773C42—444no—
774C42—444no—
775C11#1407511yescharacteristic, complemented, Sylow
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23Q8×Dic1114yes—
811C23C2×#433911yescharacteristic
812C23C2×#433911yescharacteristic
813C23C2×D4×D1111yescharacteristic
814C23C2×#434111yescharacteristic
815C23#6703711yescharacteristic
816C23#6703711yescharacteristic
817C23#6703711yescharacteristic
818C23#6703711yescharacteristic
819C23C2×Q8×D1111yescharacteristic
820C23C2×#434311yescharacteristic
821C23#41×D1111yescharacteristic
822C23#41×D1111yescharacteristic
823C23#41×D1111yescharacteristic
824C23#41×D1111yescharacteristic
825C23C23×Dic1111yescharacteristic
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—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—416no—
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—114no—
868C2×C4—222no—
869C2×C4—222no—
870C2×C4—222no—
871C2×C4—222no—
872C2×C4—222no—
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—222no—
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×C4#6697914yes—
924C2×C4D4×Dic1114yes—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22#1062304211yescharacteristic
941C22#1062304211yescharacteristic
942C22#1062304511yescharacteristic
943C22#1062304511yescharacteristic
944C22#1062307111yescharacteristic
945C22#1062307111yescharacteristic
946C22#1062307911yescharacteristic
947C22#1062307911yescharacteristic
948C22#1062308711yescharacteristic
949C22#1062308711yescharacteristic
950C22#1062308811yescharacteristic
951C22#1062308811yescharacteristic
952C22#1062312011yescharacteristic
953C22#1062312311yescharacteristic
954C22#1062312411yescharacteristic
955C22#1062312411yescharacteristic
956C22#1062315311yescharacteristic
957C22#1062315511yescharacteristic
958C22D11×C22⋊Q811yescharacteristic
959C22#1062315811yescharacteristic
960C22#1062316711yescharacteristic
961C22#1062316711yescharacteristic
962C22#1062316811yescharacteristic
963C22#1062316811yescharacteristic
964C22#1062319011yescharacteristic
965C22#1062319211yescharacteristic
966C22#1062319211yescharacteristic
967C22#1062319511yescharacteristic
968C22C2×#6697911yescharacteristic
969C22C2×D4×Dic1111yescharacteristic
970C22#1062332911yescharacteristic
971C22#1062332911yescharacteristic
972C22C2×Q8×Dic1111yescharacteristic
973C22#41×Dic1111yescharacteristic
974C22#41×Dic1111yescharacteristic
975C4—24no—
976C4—24no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—224no—
982C4—442no—
983C4—442no—
984C4—442no—
985C4—442no—
986C4—442no—
987C4—881no—
988C4—881no—
989C2—44no—
990C2#1307108111yescharacteristic
991C2C22⋊Q8×Dic1111yescharacteristic
992C2#1307127711yescharacteristic
993C2#1307149311yescharacteristic
994C2#1307155611yescharacteristic
995C2#1307170111yescharacteristic
996C2#1307175211yescharacteristic
997C2#1307380111yescharacteristic
998C2#1307381411yescharacteristic
999C2#1307391911yescharacteristic
1000C2#1307394911yescharacteristic
1001C2#1307403611yescharacteristic
1002C2#1307406611yescharacteristic
1003C2#1307423211yescharacteristic
1004C2#1307424211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#385C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#385D11
hypocenterC11#14075
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C2×#10622594C2semidirect
3. #13066878C2semidirect
4. #13066869C2semidirect
9. #13066850C2semidirect
10. #13066848C2semidirect
11. #13066845C2semidirect
12. #13066841C2semidirect
14. #95×Dic11C2semidirect
31. C11×#385C4semidirect
454. #385Dic11semidirect
775. C11#14075semidirect

Maximal subgroups

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

subgroupindex
C2×#106225942
C2×C4×C22⋊Dic112
#130668782
#130668692
#130668612
#130668532
#130668502
#130668482
#130668452
#130668412
#130668392
#95×Dic112
C2×C11×#3852
#1407511