Finite Group Databasebeta

← #14680651

Subgroups — #14680651

Order 2816.

1506 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×#10622564C211yesmaximal, characteristic
2C2×#10622564C211yesmaximal, characteristic
3C2×#10622594C211yesmaximal, characteristic, complemented
4C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
5#13066873C211yesmaximal, characteristic, complemented
6#13066869C211yesmaximal, characteristic, complemented
7#13066869C211yesmaximal, characteristic, complemented
8#13066869C211yesmaximal, characteristic, complemented
9#13066865C211yesmaximal, characteristic
10#13066861C211yesmaximal, characteristic
11#13066861C211yesmaximal, characteristic
12#13066853C211yesmaximal, characteristic
13#13066850C211yesmaximal, characteristic, complemented
14#13066845C211yesmaximal, characteristic, complemented
15C2×C11×#396C211yesmaximal, characteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×C4⋊Dic11C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C11×#396C418yescomplemented
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#10622594—24no—
53C4⋊C4×Dic11—24no—
54#10622564—24no—
55#10622564—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—22no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—41no—
76C2×C11×C4⋊C4—41no—
77C2×C11×C4⋊C4C2×C414yes—
78C2×C11×C4⋊C4C2×C414yes—
79C2×C11×C4⋊C4C2×C414yes—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
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×C11×C22⋊C4C2×C414yes—
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—41no—
96C2×C22⋊Dic11—41no—
97C2×C22⋊Dic11—41no—
98C2×C22⋊Dic11—41no—
99C2×C22⋊Dic11—41no—
100C2×C22⋊Dic11—41no—
101C2×C4⋊Dic11—22no—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11—22no—
104C2×C4⋊Dic11—22no—
105C2×C4⋊Dic11—22no—
106C2×C4⋊Dic11—22no—
107C2×C4⋊Dic11—22no—
108C2×C4⋊Dic11—22no—
109C2×C4⋊Dic11—41no—
110C2×C4⋊Dic11—41no—
111C2×C4⋊Dic11—41no—
112C2×C4⋊Dic11—41no—
113C2×C4×Dic11—22no—
114C2×C4×Dic11—22no—
115C2×C4×Dic11—22no—
116C2×C4×Dic11—41no—
117C2×C4×Dic11—41no—
118C2×C4×Dic11—41no—
119C2×C4×Dic11—41no—
120C2×C4×Dic11D414yes—
121C2×C4×Dic11D414yes—
122C11×#95C2×C414yes—
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—22no—
134C11⋊#95—41no—
135C11⋊#95—41no—
136C11⋊#95—41no—
137C11⋊#95—41no—
138C11⋊#95—41no—
139C11⋊#95—41no—
140#14310—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×C11C22×C412yes—
190C22×C4×C11C22×C412yes—
191C22×C4×C11C22×C412yes—
192C22×C4×C11C22×C412yes—
193C22×C4×C11C22×C412yes—
194C22×C4×C11C22×C412yes—
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×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11C2×D412yes—
250C22×Dic11C2×D412yes—
251C22×Dic11C2×D412yes—
252C22×Dic11C2×D412yes—
253C22×Dic11#4112yes—
254C22×Dic11#4112yes—
255C11×C4⋊C4—28no—
256C11×C4⋊C4—28no—
257C11×C4⋊C4—44no—
258C11×C22⋊C4—28no—
259C11×C22⋊C4—28no—
260C11×C22⋊C4—44no—
261C22⋊Dic11—44no—
262C22⋊Dic11—44no—
263C22⋊Dic11—44no—
264C22⋊Dic11—44no—
265C4⋊Dic11—28no—
266C4⋊Dic11—44no—
267C4⋊Dic11—44no—
268C4⋊Dic11—44no—
269C4×Dic11—28no—
270C4×Dic11—44no—
271C4×Dic11—44no—
272C2×#396D1111yescharacteristic
273C2×#388—111no—
274C2×#388—111no—
275C2×#387—111no—
276C2×C4×C4⋊C4—111no—
277#1442—111no—
278#1441—111no—
279#1441—111no—
280#1441—111no—
281#1440—111no—
282#1439—111no—
283#1439—111no—
284#1437—111no—
285#1436—111no—
286C4⋊#95—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×C11H(5,𝔽2)11yescharacteristic
330C23×C11H(5,𝔽2)11yescharacteristic
331C23×C11H(5,𝔽2)11yescharacteristic
332C23×C11H(5,𝔽2)11yescharacteristic
333C23×C112−1+411yescharacteristic
334C23×C112−1+411yescharacteristic
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—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
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×C11C4×D414yes—
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—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—
432C2×Dic11—41no—
433C2×Dic11—41no—
434C2×Dic11#12114yes—
435C22×C4⋊C4—111no—
436C22×C4⋊C4—111no—
437C22×C4⋊C4—111no—
438C22×C4⋊C4—111no—
439C22×C4⋊C4C2×D1111yescharacteristic
440C22×C4⋊C4C2×D1111yescharacteristic
441C22×C4⋊C4C2×D1111yescharacteristic
442C22×C22⋊C4—111no—
443C22×C22⋊C4—111no—
444C22×C22⋊C4—111no—
445C22×C22⋊C4—111no—
446C22×C22⋊C4C2×D1111yescharacteristic
447C22×C22⋊C4C2×D1111yescharacteristic
448C22×C22⋊C4C2×D1111yescharacteristic
449C22×C42—111no—
450C22×C42—111no—
451C22×C42—111no—
452#396Dic1118yescomplemented
453#388—224no—
454#388—224no—
455#387—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×#95—111no—
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×C4×D411yescharacteristic
491C22×C11C2×C4×D411yescharacteristic
492C22×C11C4×#4111yescharacteristic
493C22×C11#51811yescharacteristic
494C22×C11#51911yescharacteristic
495C22×C11#52011yescharacteristic
496C22×C11#52011yescharacteristic
497C22×C11C2×#12111yescharacteristic
498C22×C11#52511yescharacteristic
499C22×C11#52911yescharacteristic
500C22×C11#53211yescharacteristic
501C22×C11#53411yescharacteristic
502C22×C11#53511yescharacteristic
503C22×C11#53611yescharacteristic
504C22×C11#53611yescharacteristic
505C22×C11#53711yescharacteristic
506C22×C11#53711yescharacteristic
507C22×C11#53711yescharacteristic
508C22×C11#53711yescharacteristic
509C22×C11#53811yescharacteristic
510C22×C11#53811yescharacteristic
511C22×C11#53911yescharacteristic
512C22×C11#53911yescharacteristic
513C22×C11#53911yescharacteristic
514C22×C11#53911yescharacteristic
515C22×C11#54011yescharacteristic
516C22×C11#54111yescharacteristic
517C22×C11#54111yescharacteristic
518C22×C11#54111yescharacteristic
519C22×C11#54211yescharacteristic
520C22×C11#54211yescharacteristic
521C22×C11#54211yescharacteristic
522C22×C11#54211yescharacteristic
523C22×C11#54211yescharacteristic
524C22×C11#54211yescharacteristic
525C4×C11—24no—
526C4×C11—24no—
527C4×C11—42no—
528C4×C11—42no—
529C4×C11—42no—
530C4×C11—42no—
531Dic11—24no—
532Dic11—42no—
533Dic11—42no—
534Dic11—42no—
535Dic11—81no—
536Dic11—81no—
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—22no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—41no—
559C2×C4⋊C4—41no—
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—441no—
569C2×C4⋊C4—441no—
570C2×C4⋊C4—441no—
571C2×C4⋊C4—441no—
572C2×C4⋊C4C2×Dic1114yes—
573C2×C4⋊C4C2×Dic1114yes—
574C2×C4⋊C4C2×Dic1114yes—
575C2×C22⋊C4—22no—
576C2×C22⋊C4—22no—
577C2×C22⋊C4—22no—
578C2×C22⋊C4—22no—
579C2×C22⋊C4—41no—
580C2×C22⋊C4—41no—
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⋊C4—441no—
590C2×C22⋊C4—441no—
591C2×C22⋊C4—441no—
592C2×C22⋊C4—441no—
593C2×C22⋊C4C2×Dic1114yes—
594C2×C22⋊C4C2×Dic1114yes—
595C2×C22⋊C4C2×Dic1114yes—
596C2×C42—114no—
597C2×C42—114no—
598C2×C42—222no—
599C2×C42—222no—
600C2×C42—222no—
601C2×C42—441no—
602C2×C42—441no—
603C2×C42—441no—
604C2×C42—441no—
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—441no—
617#95—441no—
618#95—441no—
619#95—441no—
620#95—441no—
621#95—441no—
622#95C2×Dic1114yes—
623C2×C11—82no—
624C2×C11C4×#12111yescharacteristic
625C2×C11#232311yescharacteristic
626C2×C11#232311yescharacteristic
627C2×C11#232411yescharacteristic
628C2×C11#232511yescharacteristic
629C2×C11#233211yescharacteristic
630C2×C11#233411yescharacteristic
631C2×C11#261811yescharacteristic
632C2×C11#262011yescharacteristic
633C2×C11#263011yescharacteristic
634C2×C11#263711yescharacteristic
635C2×C11#265011yescharacteristic
636C2×C11#265411yescharacteristic
637C2×C11#266211yescharacteristic
638C2×C11#266411yescharacteristic
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—
653C24C22×Dic1112yes—
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—112no—
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×C4D4×D1112yes—
744C22×C4D4×D1112yes—
745C22×C4#434112yes—
746C22×C4#434112yes—
747C22×C4C22×Dic1112yes—
748C22×C4C22×Dic1112yes—
749C22×C4C22×Dic1112yes—
750C22×C4C22×Dic1112yes—
751C22×C4C22×Dic1112yes—
752C22×C4C22×Dic1112yes—
753C4⋊C4—28no—
754C4⋊C4—28no—
755C4⋊C4—44no—
756C4⋊C4—228no—
757C4⋊C4—444no—
758C4⋊C4—444no—
759C4⋊C4—444no—
760C22⋊C4—28no—
761C22⋊C4—28no—
762C22⋊C4—44no—
763C22⋊C4—444no—
764C22⋊C4—444no—
765C22⋊C4—444no—
766C22⋊C4—444no—
767C42—228no—
768C42—444no—
769C42—444no—
770C11#1431011yescharacteristic, 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—
806C23C2×D4×D1111yescharacteristic
807C23C2×D4×D1111yescharacteristic
808C23C2×#434111yescharacteristic
809C23C2×#434111yescharacteristic
810C23#6703711yescharacteristic
811C23#6703711yescharacteristic
812C23#6704011yescharacteristic
813C23#6704011yescharacteristic
814C23#41×D1111yescharacteristic
815C23#41×D1111yescharacteristic
816C23#6704211yescharacteristic
817C23#6704211yescharacteristic
818C23#6704311yescharacteristic
819C23#6704311yescharacteristic
820C23C23×Dic1111yescharacteristic
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—22no—
843C2×C4—22no—
844C2×C4—22no—
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—114no—
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—222no—
872C2×C4—222no—
873C2×C4—222no—
874C2×C4—222no—
875C2×C4—222no—
876C2×C4—222no—
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×C4—441no—
913C2×C4—441no—
914C2×C4—441no—
915C2×C4—441no—
916C2×C4—441no—
917C2×C4D4×Dic1114yes—
918C2×C4D4×Dic1114yes—
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—
934C22#1062312711yescharacteristic
935C22#1062312811yescharacteristic
936C22#1062313111yescharacteristic
937C22#1062313311yescharacteristic
938C22#1062313411yescharacteristic
939C22D11×#12111yescharacteristic
940C22#1062313611yescharacteristic
941C22#1062313711yescharacteristic
942C22#1062313811yescharacteristic
943C22#1062313911yescharacteristic
944C22#1062314811yescharacteristic
945C22#1062315011yescharacteristic
946C22#1062315611yescharacteristic
947C22#1062315611yescharacteristic
948C22#1062315911yescharacteristic
949C22#1062315911yescharacteristic
950C22#1062316011yescharacteristic
951C22#1062316011yescharacteristic
952C22#1062316911yescharacteristic
953C22#1062316911yescharacteristic
954C22#1062317111yescharacteristic
955C22#1062317111yescharacteristic
956C22#1062317411yescharacteristic
957C22#1062317411yescharacteristic
958C22#1062323211yescharacteristic
959C22#1062323511yescharacteristic
960C22#1062323811yescharacteristic
961C22#1062324111yescharacteristic
962C22C2×D4×Dic1111yescharacteristic
963C22C2×D4×Dic1111yescharacteristic
964C22#1062332911yescharacteristic
965C22#1062334311yescharacteristic
966C22#41×Dic1111yescharacteristic
967C22#1062335811yescharacteristic
968C22#1062335811yescharacteristic
969C4—24no—
970C4—24no—
971C4—42no—
972C4—42no—
973C4—42no—
974C4—42no—
975C4—224no—
976C4—442no—
977C4—442no—
978C4—442no—
979C4—881no—
980C4—881no—
981C4—881no—
982C4—881no—
983C2—82no—
984C2#121×Dic1111yescharacteristic
985C2#1307130011yescharacteristic
986C2#1307130011yescharacteristic
987C2#1307131111yescharacteristic
988C2#1307132111yescharacteristic
989C2#1307137411yescharacteristic
990C2#1307139511yescharacteristic
991C2#1307436311yescharacteristic
992C2#1307437511yescharacteristic
993C2#1307446411yescharacteristic
994C2#1307452911yescharacteristic
995C2#1307463511yescharacteristic
996C2#1307469511yescharacteristic
997C2#1307475411yescharacteristic
998C2#1307477611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#396C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#396D11
hypocenterC11#14310
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
3. C2×#10622594C2semidirect
4. C2×C4⋊C4×Dic11C2semidirect
5. #13066873C2semidirect
6. #13066869C2semidirect
7. #13066869C2semidirect
8. #13066869C2semidirect
13. #13066850C2semidirect
14. #13066845C2semidirect
33. C11×#396C4semidirect
452. #396Dic11semidirect
770. C11#14310semidirect

Maximal subgroups

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

subgroupindex
C2×#106225642
C2×#106225942
C2×C4⋊C4×Dic112
#130668732
#130668692
#130668652
#130668612
#130668532
#130668502
#130668452
C2×C11×#3962
#1431011