Finite Group Databasebeta

← #14677311

Subgroups — #14677311

Order 2816.

1594 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622558C211yesmaximal, characteristic
2C2×#10622557C211yesmaximal, characteristic
3C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
4C2×#10622262C211yesmaximal, characteristic, complemented
5#13066879C211yesmaximal, characteristic, complemented
6#13066876C211yesmaximal, characteristic, complemented
7#13066859C211yesmaximal, characteristic
8#13066859C211yesmaximal, characteristic
9#13066853C211yesmaximal, characteristic
10#13066853C211yesmaximal, characteristic
11#13066849C211yesmaximal, characteristic, complemented
12#13066848C211yesmaximal, characteristic, complemented
13#13066847C211yesmaximal, characteristic, complemented
14#13066841C211yesmaximal, characteristic, complemented
15C2×C11×#388C211yesmaximal, characteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C11×#388—24no—
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#10622558C418yescomplemented
53#10622557—24no—
54C4×Dic11⋊C4—24no—
55#10622262—24no—
56C25×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—41no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—41no—
81C2×C11×C22⋊C4—41no—
82C2×C11×C22⋊C4C2×C414yes—
83C2×C42×C11—22no—
84C2×C42×C11—22no—
85C2×C42×C11—41no—
86C2×C22⋊Dic11—22no—
87C2×C22⋊Dic11—22no—
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—41no—
95C2×C22⋊Dic11—41no—
96C2×C22⋊Dic11C2×C414yes—
97C2×C22⋊Dic11C2×C414yes—
98C2×Dic11⋊C4—22no—
99C2×Dic11⋊C4—22no—
100C2×Dic11⋊C4—22no—
101C2×Dic11⋊C4—22no—
102C2×Dic11⋊C4—22no—
103C2×Dic11⋊C4—22no—
104C2×Dic11⋊C4—22no—
105C2×Dic11⋊C4—22no—
106C2×Dic11⋊C4—22no—
107C2×Dic11⋊C4—22no—
108C2×Dic11⋊C4C2×C414yes—
109C2×Dic11⋊C4D414yes—
110C2×C4×Dic11—22no—
111C2×C4×Dic11—22no—
112C2×C4×Dic11—22no—
113C2×C4×Dic11—22no—
114C2×C4×Dic11—22no—
115C2×C4×Dic11—22no—
116C2×C4×Dic11—22no—
117C2×C4×Dic11—22no—
118C2×C4×Dic11—22no—
119C2×C4×Dic11—41no—
120C2×C4×Dic11—41no—
121C2×C4×Dic11C2×C414yes—
122C11×#95—22no—
123C11×#95D414yes—
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—22no—
134C11⋊#95—41no—
135C11⋊#95—41no—
136C11⋊#95—41no—
137C11⋊#95—41no—
138C11⋊#95C2×C414yes—
139C11⋊#95C2×C414yes—
140#14031—111nomaximal, Sylow
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×C11—21no—
152C24×C11—21no—
153C24×C11—21no—
154C24×C11—21no—
155C24×C11C22×C412yes—
156C24×C11C2411yescharacteristic
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×C11C22×C412yes—
192C22×C4×C11C22×C412yes—
193C22×C4×C11C2×D412yes—
194C22×C4×C11C2×D412yes—
195C22×C4×C11C2×D412yes—
196C22×C4×C11C2×D412yes—
197C22×C4×C11#4112yes—
198C22×C4×C11#4112yes—
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×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×Dic11C22×C412yes—
244C22×Dic11C22×C412yes—
245C22×Dic11C22×C412yes—
246C22×Dic11C22×C412yes—
247C22×Dic11C2×D412yes—
248C22×Dic11C2×D412yes—
249C22×Dic11#4112yes—
250C22×Dic11#4112yes—
251C22×Dic11#4112yes—
252C22×Dic11#4112yes—
253C22×Dic11#4112yes—
254C22×Dic11#4112yes—
255C11×C4⋊C4—44no—
256C11×C22⋊C4—28no—
257C11×C22⋊C4—44no—
258C11×C22⋊C4—44no—
259C42×C11—44no—
260C22⋊Dic11—28no—
261C22⋊Dic11—28no—
262C22⋊Dic11—44no—
263C22⋊Dic11—44no—
264Dic11⋊C4—28no—
265Dic11⋊C4—28no—
266Dic11⋊C4—28no—
267Dic11⋊C4—28no—
268C4×Dic11—28no—
269C4×Dic11—28no—
270C4×Dic11—44no—
271C4×Dic11—44no—
272C2×#388—111no—
273C2×#388—111no—
274C2×#388D1111yescharacteristic
275C2×C4×C4⋊C4—111no—
276C2×C4×C4⋊C4—111no—
277#1444—111no—
278#1443—111no—
279#1439—111no—
280#1439—111no—
281#1437—111no—
282#1437—111no—
283#1436—111no—
284#1436—111no—
285#1436—111no—
286#1434—111no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—41no—
295C23×C11—41no—
296C23×C11—41no—
297C23×C11—41no—
298C23×C11—41no—
299C23×C11—41no—
300C23×C11—41no—
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—41no—
318C23×C11—41no—
319C23×C11—41no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11C23×C411yescharacteristic
323C23×C11C22×D411yescharacteristic
324C23×C11C22×D411yescharacteristic
325C23×C11C2×#4111yescharacteristic
326C23×C11C2×#4111yescharacteristic
327C23×C11C2×#4111yescharacteristic
328C23×C11C2×#4111yescharacteristic
329C23×C11C2×#4111yescharacteristic
330C23×C11C2×#4111yescharacteristic
331C23×C11C2×#4111yescharacteristic
332C23×C11C2×#4111yescharacteristic
333C23×C11H(5,𝔽2)11yescharacteristic
334C23×C11H(5,𝔽2)11yescharacteristic
335C23×C112−1+411yescharacteristic
336C23×C112−1+411yescharacteristic
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—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—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×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11C4×D414yes—
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—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—22no—
404C2×Dic11—22no—
405C2×Dic11—22no—
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#11714yes—
433C2×Dic11C4×D414yes—
434C2×Dic11#12314yes—
435C22×C4⋊C4—111no—
436C22×C4⋊C4—111no—
437C22×C4⋊C4—111no—
438C22×C4⋊C4—111no—
439C22×C4⋊C4C2×D1111yescharacteristic
440C22×C22⋊C4—111no—
441C22×C22⋊C4—111no—
442C22×C22⋊C4—111no—
443C22×C22⋊C4—111no—
444C22×C22⋊C4C2×D1111yescharacteristic
445C22×C22⋊C4C2×D1111yescharacteristic
446C22×C22⋊C4C2×D1111yescharacteristic
447C22×C42—111no—
448C22×C42—111no—
449C22×C42—111no—
450C22×C42—111no—
451C22×C42C2×D1111yescharacteristic
452#388—24no—
453#388—118no—
454#388—224no—
455C4×C4⋊C4—224no—
456C4×C4⋊C4—224no—
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×#95C2×D1111yescharacteristic
474C2×#95C2×D1111yescharacteristic
475C22×C11—42no—
476C22×C11—42no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—81no—
483C22×C11—81no—
484C22×C11—81no—
485C22×C11—81no—
486C22×C11—81no—
487C22×C11—81no—
488C22×C11—81no—
489C22×C11—81no—
490C22×C11C2×#11711yescharacteristic
491C22×C11C2×C4×D411yescharacteristic
492C22×C11C2×C4×D411yescharacteristic
493C22×C11C4×#4111yescharacteristic
494C22×C11C4×#4111yescharacteristic
495C22×C11#52011yescharacteristic
496C22×C11#52011yescharacteristic
497C22×C11C2×#12311yescharacteristic
498C22×C11#52511yescharacteristic
499C22×C11#52511yescharacteristic
500C22×C11#52511yescharacteristic
501C22×C11#52911yescharacteristic
502C22×C11#52911yescharacteristic
503C22×C11#52911yescharacteristic
504C22×C11#52911yescharacteristic
505C22×C11#53811yescharacteristic
506C22×C11#53911yescharacteristic
507C22×C11#54111yescharacteristic
508C22×C11#54211yescharacteristic
509C22×C11D4211yescharacteristic
510C22×C11#54611yescharacteristic
511C22×C11#54711yescharacteristic
512C22×C11#54711yescharacteristic
513C22×C11#54811yescharacteristic
514C22×C11#54811yescharacteristic
515C22×C11#55011yescharacteristic
516C22×C11#55311yescharacteristic
517C22×C11#55311yescharacteristic
518C22×C11#55311yescharacteristic
519C22×C11#55511yescharacteristic
520C22×C11#55611yescharacteristic
521C22×C11#55611yescharacteristic
522C22×C11#55611yescharacteristic
523C22×C11#55611yescharacteristic
524C22×C11#55911yescharacteristic
525C4×C11—24no—
526C4×C11—42no—
527C4×C11—42no—
528C4×C11—42no—
529C4×C11—42no—
530C4×C11—42no—
531Dic11—24no—
532Dic11—24no—
533Dic11—24no—
534Dic11—42no—
535Dic11—42no—
536Dic11—42no—
537Dic11—81no—
538Dic11—81no—
539C25C22×D1111yescharacteristic
540C23×C4—111no—
541C23×C4—111no—
542C23×C4—111no—
543C23×C4—111no—
544C23×C4—111no—
545C23×C4—111no—
546C23×C4—111no—
547C23×C4—111no—
548C23×C4C22×D1111yescharacteristic
549C23×C4C22×D1111yescharacteristic
550C23×C4C22×D1111yescharacteristic
551C23×C4C22×D1111yescharacteristic
552C23×C4C22×D1111yescharacteristic
553C23×C4C22×D1111yescharacteristic
554C2×C4⋊C4—22no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4—41no—
557C2×C4⋊C4—114no—
558C2×C4⋊C4—114no—
559C2×C4⋊C4—222no—
560C2×C4⋊C4—222no—
561C2×C4⋊C4—222no—
562C2×C4⋊C4—222no—
563C2×C4⋊C4—222no—
564C2×C4⋊C4—222no—
565C2×C4⋊C4—222no—
566C2×C4⋊C4—222no—
567C2×C4⋊C4—222no—
568C2×C4⋊C4—222no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4—41no—
576C2×C22⋊C4—41no—
577C2×C22⋊C4—114no—
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—441no—
588C2×C22⋊C4—441no—
589C2×C22⋊C4C4×D1114yes—
590C2×C42—22no—
591C2×C42—22no—
592C2×C42—41no—
593C2×C42—114no—
594C2×C42—222no—
595C2×C42—222no—
596C2×C42—222no—
597C2×C42—222no—
598C2×C42—222no—
599C2×C42—222no—
600C2×C42—222no—
601C2×C42—222no—
602C2×C42—222no—
603C2×C42—441no—
604C2×C42—441no—
605#95—22no—
606#95—114no—
607#95—114no—
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—222no—
618#95—441no—
619#95—441no—
620#95—441no—
621#95—441no—
622#95C22⋊D1114yes—
623C2×C11—82no—
624C2×C11#229011yescharacteristic
625C2×C11C4×#12311yescharacteristic
626C2×C11#233411yescharacteristic
627C2×C11#234711yescharacteristic
628C2×C11#235411yescharacteristic
629C2×C11#236111yescharacteristic
630C2×C11#236711yescharacteristic
631C2×C11#244311yescharacteristic
632C2×C11#244811yescharacteristic
633C2×C11#245611yescharacteristic
634C2×C11#246911yescharacteristic
635C2×C11#246911yescharacteristic
636C2×C11#247411yescharacteristic
637C2×C11#259311yescharacteristic
638C2×C11#259411yescharacteristic
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24C2×C4×D1112yes—
654C24C23×D1111yescharacteristic
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—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—112no—
690C22×C4—112no—
691C22×C4—112no—
692C22×C4—112no—
693C22×C4—112no—
694C22×C4—112no—
695C22×C4—112no—
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—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×C4C2×C4×D1112yes—
746C22×C4C2×C4×D1112yes—
747C22×C4#433912yes—
748C22×C4D4×D1112yes—
749C22×C4#434112yes—
750C22×C4C2×C22⋊D1112yes—
751C22×C4C2×C22⋊D1112yes—
752C22×C4C2×C22⋊D1112yes—
753C4⋊C4—44no—
754C4⋊C4—228no—
755C4⋊C4—228no—
756C4⋊C4—228no—
757C4⋊C4—228no—
758C22⋊C4—28no—
759C22⋊C4—44no—
760C22⋊C4—44no—
761C22⋊C4—228no—
762C22⋊C4—228no—
763C22⋊C4—444no—
764C22⋊C4—444no—
765C42—44no—
766C42—228no—
767C42—228no—
768C42—444no—
769C42—444no—
770C11#1403111yescharacteristic, complemented, Sylow
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
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—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23C22×C4×D1111yescharacteristic
807C23C2×#433911yescharacteristic
808C23C2×D4×D1111yescharacteristic
809C23C2×#434111yescharacteristic
810C23#6703711yescharacteristic
811C23#6703711yescharacteristic
812C23#41×D1111yescharacteristic
813C23#41×D1111yescharacteristic
814C23#41×D1111yescharacteristic
815C23#41×D1111yescharacteristic
816C23#41×D1111yescharacteristic
817C23#41×D1111yescharacteristic
818C23#6704311yescharacteristic
819C23#6704311yescharacteristic
820C23C22×C22⋊D1111yescharacteristic
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—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—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—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—114no—
863C2×C4—114no—
864C2×C4—114no—
865C2×C4—222no—
866C2×C4—222no—
867C2×C4—222no—
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—222no—
890C2×C4—222no—
891C2×C4—222no—
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×C4C4×C22⋊D1114yes—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22D11×#11711yescharacteristic
935C22#1062305311yescharacteristic
936C22#1062305911yescharacteristic
937C22#1062305911yescharacteristic
938C22C4×#434111yescharacteristic
939C22#1062307111yescharacteristic
940C22#1062307311yescharacteristic
941C22C4×D4×D1111yescharacteristic
942C22#1062307711yescharacteristic
943C22#1062307711yescharacteristic
944C22#1062308311yescharacteristic
945C22#1062309011yescharacteristic
946C22#1062313011yescharacteristic
947C22#1062313211yescharacteristic
948C22#1062313711yescharacteristic
949C22#1062314411yescharacteristic
950C22D11×#12311yescharacteristic
951C22#1062318611yescharacteristic
952C22#1062319111yescharacteristic
953C22#1062319211yescharacteristic
954C22#1062320011yescharacteristic
955C22#1062320111yescharacteristic
956C22#1062320211yescharacteristic
957C22#1062321111yescharacteristic
958C22#1062323211yescharacteristic
959C22#1062323311yescharacteristic
960C22#1062323311yescharacteristic
961C22#1062323711yescharacteristic
962C22C2×C4×C22⋊D1111yescharacteristic
963C22D4×C22⋊D1111yescharacteristic
964C22#1062333711yescharacteristic
965C22#1062335511yescharacteristic
966C22#1062335911yescharacteristic
967C22#1062335911yescharacteristic
968C22#1062336211yescharacteristic
969C4—24no—
970C4—42no—
971C4—42no—
972C4—42no—
973C4—42no—
974C4—42no—
975C4—224no—
976C4—224no—
977C4—224no—
978C4—442no—
979C4—442no—
980C4—442no—
981C4—881no—
982C4—881no—
983C2—82no—
984C2#1307105311yescharacteristic
985C2#1307114311yescharacteristic
986C2#1307138911yescharacteristic
987C2#1307150611yescharacteristic
988C2#1307156211yescharacteristic
989C2#1307163311yescharacteristic
990C2#1307168911yescharacteristic
991C2#1307234811yescharacteristic
992C2#1307241311yescharacteristic
993C2#1307251311yescharacteristic
994C2#1307269311yescharacteristic
995C2#1307270211yescharacteristic
996C2#1307276811yescharacteristic
997C2#1307411111yescharacteristic
998C2#1307412011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#388C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#388D11
hypocenterC11#14031
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. C2×C4×Dic11⋊C4C2semidirect
4. C2×#10622262C2semidirect
5. #13066879C2semidirect
6. #13066876C2semidirect
11. #13066849C2semidirect
12. #13066848C2semidirect
13. #13066847C2semidirect
14. #13066841C2semidirect
52. #10622558C4semidirect
770. C11#14031semidirect

Maximal subgroups

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

subgroupindex
C2×#106225582
C2×#106225572
C2×C4×Dic11⋊C42
C2×#106222622
#130668792
#130668762
#130668592
#130668532
#130668492
#130668482
#130668472
#130668412
C2×C11×#3882
#1403111