Finite Group Databasebeta

← #14683854

Subgroups — #14683854

Order 2816.

1358 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622842C211yesmaximal, characteristic
2C2×#10622843C211yesmaximal, characteristic
3C2×#10622268C211yesmaximal, characteristic
4C2×#10622591C211yesmaximal, characteristic
5#13066882C211yesmaximal, characteristic
6#13066877C211yesmaximal, characteristic
7#13066876C211yesmaximal, characteristic
8#13066875C211yesmaximal, characteristic
9#13066872C211yesmaximal, characteristic
10#13066851C211yesmaximal, characteristic
11#13066849C211yesmaximal, characteristic
12#13066847C211yesmaximal, characteristic
13#13066843C211yesmaximal, characteristic
14#13066841C211yesmaximal, characteristic
15C2×C11×#391C211yesmaximal, characteristic
16C23×Q8×C11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×Dic11⋊C4C2211yescharacteristic
21C22×Dic11⋊C4C2211yescharacteristic
22C22×Dic11⋊C4C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C22×C4×Dic11C2211yescharacteristic
25C11×#391—24no—
26C2×C11×#95C2211yescharacteristic
27C2×C11×#95C2211yescharacteristic
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2211yescharacteristic
30#10622843—24no—
31#10622842C418yescomplemented
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
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54#10622591—24no—
55#10622268—24no—
56C22×Q8×C11—22no—
57C22×Q8×C11—22no—
58C22×Q8×C11—22no—
59C22×Q8×C11—22no—
60C22×Q8×C11—41no—
61C22×Q8×C11—41no—
62C22×Q8×C11C2×C414yes—
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—41no—
81C2×C42×C11—22no—
82C2×C42×C11—22no—
83C2×C42×C11—41no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11—41no—
87C2×Dic11⋊C4—22no—
88C2×Dic11⋊C4—22no—
89C2×Dic11⋊C4—22no—
90C2×Dic11⋊C4—22no—
91C2×Dic11⋊C4—41no—
92C2×Dic11⋊C4—41no—
93C2×Dic11⋊C4C2×C414yes—
94C2×Dic11⋊C4C2×C414yes—
95C2×Dic11⋊C4C2×C414yes—
96C2×C4×Dic11—22no—
97C2×C4×Dic11—22no—
98C2×C4×Dic11—22no—
99C2×C4×Dic11—22no—
100C2×C4×Dic11—41no—
101C2×C4×Dic11—41no—
102C11×#95—22no—
103C11×#95—22no—
104C11×#95—22no—
105C11×#95D414yes—
106C11⋊#95—22no—
107C11⋊#95—22no—
108C11⋊#95—22no—
109C11⋊#95—22no—
110C11⋊#95—22no—
111C11⋊#95—22no—
112C11⋊#95—22no—
113C11⋊#95—22no—
114C11⋊#95—22no—
115C11⋊#95—22no—
116C11⋊#95—22no—
117C11⋊#95—22no—
118C11⋊#95—22no—
119C11⋊#95—22no—
120C11⋊#95—22no—
121C11⋊#95—41no—
122C11⋊#95—41no—
123C11⋊#95—41no—
124C11⋊#95C2×C414yes—
125C11⋊#95C2×C414yes—
126C11⋊#95C2×C414yes—
127C11⋊#95D414yes—
128#14574—111nomaximal, Sylow
129C24×C11C2411yescharacteristic
130C2×Q8×C11—28no—
131C2×Q8×C11—28no—
132C2×Q8×C11—44no—
133C2×Q8×C11—44no—
134C2×Q8×C11—44no—
135C2×Q8×C11—44no—
136C2×Q8×C11—44no—
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×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11C22×C412yes—
177C22×C4×C11C22×C412yes—
178C22×C4×C11C22×C412yes—
179C22×C4×C11C2×D412yes—
180C22×C4×C11C2×D412yes—
181C22×C4×C11C2×D412yes—
182C22×C4×C11C2×D412yes—
183C22×C4×C11#4112yes—
184C22×C4×C11#4112yes—
185C22×C4×C11#4112yes—
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×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×Dic11C22×C412yes—
236C22×Dic11C22×C412yes—
237C22×Dic11C22×C412yes—
238C22×Dic11C22×C412yes—
239C22×Dic11C2×D412yes—
240C22×Dic11C2×D412yes—
241C22×Dic11#4112yes—
242C11×C4⋊C4—44no—
243C42×C11—44no—
244C4⋊Dic11—44no—
245Dic11⋊C4—28no—
246Dic11⋊C4—28no—
247Dic11⋊C4—44no—
248C4×Dic11—44no—
249C4×Dic11—44no—
250C2×#395—111no—
251C2×#391—111no—
252C2×#391D1111yescharacteristic
253C2×#387—111no—
254C2×#387—111no—
255#1445—111no—
256#1443—111no—
257#1443—111no—
258#1442—111no—
259#1442—111no—
260#1436—111no—
261#1436—111no—
262#1436—111no—
263#1434—111no—
264#1434—111no—
265C23×C11C23×C411yescharacteristic
266C23×C11C22×D411yescharacteristic
267C23×C11C22×D411yescharacteristic
268C23×C11C2×#4111yescharacteristic
269C23×C11C2×#4111yescharacteristic
270C23×C11C2×#4111yescharacteristic
271C23×C11C2×#4111yescharacteristic
272C23×C11H(5,𝔽2)11yescharacteristic
273C23×C11H(5,𝔽2)11yescharacteristic
274C23×C112−1+411yescharacteristic
275C23×C112−1+411yescharacteristic
276C23×C112−1+411yescharacteristic
277C23×C112−1+411yescharacteristic
278C23×C112−1+411yescharacteristic
279C23×C112−1+411yescharacteristic
280Q8×C11—416no—
281C2×C4×C11—22no—
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—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×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×C11C4×D414yes—
329C2×C4×C11C4×D414yes—
330C2×Dic11—22no—
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—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—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×Dic11—41no—
385C2×Dic11—41no—
386C23×Q8C2×D1111yescharacteristic
387C22×C4⋊C4—111no—
388C22×C4⋊C4—111no—
389C22×C4⋊C4—111no—
390C22×C4⋊C4—111no—
391C22×C4⋊C4C2×D1111yescharacteristic
392C22×C42—111no—
393C22×C42—111no—
394C22×C42C2×D1111yescharacteristic
395#395—118no—
396#391—24no—
397#391—224no—
398#387—224no—
399#387—224no—
400C2×#95—111no—
401C2×#95—111no—
402C2×#95—111no—
403C2×#95—111no—
404C2×#95—111no—
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×#95C2×D1111yescharacteristic
423C2×#95C2×D1111yescharacteristic
424C2×#95C2×D1111yescharacteristic
425C2×#95C2×D1111yescharacteristic
426C22×C11C2×C4×D411yescharacteristic
427C22×C11C2×C4×D411yescharacteristic
428C22×C11C4×#4111yescharacteristic
429C22×C11#51811yescharacteristic
430C22×C11#51911yescharacteristic
431C22×C11#51911yescharacteristic
432C22×C11#51911yescharacteristic
433C22×C11#53611yescharacteristic
434C22×C11#53611yescharacteristic
435C22×C11#53611yescharacteristic
436C22×C11#53611yescharacteristic
437C22×C11#53911yescharacteristic
438C22×C11#53911yescharacteristic
439C22×C11#54111yescharacteristic
440C22×C11#54111yescharacteristic
441C22×C11#54111yescharacteristic
442C22×C11#54111yescharacteristic
443C22×C11#54211yescharacteristic
444C22×C11#54211yescharacteristic
445C22×C11D4211yescharacteristic
446C22×C11#54611yescharacteristic
447C22×C11#54611yescharacteristic
448C22×C11#54711yescharacteristic
449C22×C11#54711yescharacteristic
450C22×C11#54811yescharacteristic
451C22×C11#54811yescharacteristic
452C22×C11#55111yescharacteristic
453C22×C11#55211yescharacteristic
454C22×C11#55211yescharacteristic
455C22×C11#55611yescharacteristic
456C22×C11#55611yescharacteristic
457C22×C11#56311yescharacteristic
458C22×C11#56311yescharacteristic
459C22×C11#56311yescharacteristic
460C22×C11#56311yescharacteristic
461C4×C11—24no—
462C4×C11—24no—
463C4×C11—42no—
464C4×C11—42no—
465C4×C11—42no—
466C4×C11—42no—
467C4×C11—81no—
468Dic11—42no—
469Dic11—42no—
470Dic11—42no—
471Dic11—42no—
472Dic11—42no—
473Dic11—42no—
474Dic11—42no—
475Dic11—81no—
476C22×Q8—22no—
477C22×Q8—22no—
478C22×Q8—22no—
479C22×Q8—22no—
480C22×Q8—41no—
481C22×Q8—41no—
482C22×Q8C4×D1114yes—
483C23×C4—111no—
484C23×C4—111no—
485C23×C4—111no—
486C23×C4—111no—
487C23×C4—111no—
488C23×C4—111no—
489C23×C4—111no—
490C23×C4—111no—
491C23×C4C22×D1111yescharacteristic
492C23×C4C22×D1111yescharacteristic
493C23×C4C22×D1111yescharacteristic
494C23×C4C22×D1111yescharacteristic
495C23×C4C22×D1111yescharacteristic
496C23×C4C22×D1111yescharacteristic
497C23×C4C22×D1111yescharacteristic
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—222no—
505C2×C4⋊C4—222no—
506C2×C4⋊C4—222no—
507C2×C4⋊C4—222no—
508C2×C4⋊C4—222no—
509C2×C4⋊C4—222no—
510C2×C4⋊C4—441no—
511C2×C4⋊C4—441no—
512C2×C4⋊C4—441no—
513C2×C42—22no—
514C2×C42—22no—
515C2×C42—41no—
516C2×C42—222no—
517C2×C42—222no—
518C2×C42—222no—
519C2×C42—222no—
520C2×C42—441no—
521C2×C42—441no—
522#95—22no—
523#95—22no—
524#95—22no—
525#95—114no—
526#95—114no—
527#95—114no—
528#95—114no—
529#95—222no—
530#95—222no—
531#95—222no—
532#95—222no—
533#95—222no—
534#95—222no—
535#95—222no—
536#95—222no—
537#95—222no—
538#95—222no—
539#95—222no—
540#95—222no—
541#95—222no—
542#95—222no—
543#95—222no—
544#95—441no—
545#95—441no—
546#95—441no—
547#95C22⋊D1114yes—
548C2×C11#232711yescharacteristic
549C2×C11#232711yescharacteristic
550C2×C11#233211yescharacteristic
551C2×C11#235811yescharacteristic
552C2×C11#236211yescharacteristic
553C2×C11#236211yescharacteristic
554C2×C11#238111yescharacteristic
555C2×C11#267411yescharacteristic
556C2×C11#267411yescharacteristic
557C2×C11#268911yescharacteristic
558C2×C11#268911yescharacteristic
559C2×C11#269011yescharacteristic
560C2×C11#269011yescharacteristic
561C2×C11#276211yescharacteristic
562C2×C11#276211yescharacteristic
563C24C23×D1111yescharacteristic
564C2×Q8—28no—
565C2×Q8—28no—
566C2×Q8—44no—
567C2×Q8—44no—
568C2×Q8—44no—
569C2×Q8—44no—
570C2×Q8—44no—
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—21no—
609C22×C4—21no—
610C22×C4—112no—
611C22×C4—112no—
612C22×C4—112no—
613C22×C4—112no—
614C22×C4—112no—
615C22×C4—112no—
616C22×C4—112no—
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×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×C4—221no—
665C22×C4—221no—
666C22×C4C2×C4×D1112yes—
667C22×C4C2×C4×D1112yes—
668C22×C4C2×C4×D1112yes—
669C22×C4#433912yes—
670C22×C4D4×D1112yes—
671C22×C4#434112yes—
672C22×C4#434312yes—
673C22×C4C2×C22⋊D1112yes—
674C22×C4C2×C22⋊D1112yes—
675C22×C4C2×C22⋊D1112yes—
676C4⋊C4—44no—
677C4⋊C4—228no—
678C4⋊C4—228no—
679C4⋊C4—444no—
680C4⋊C4—444no—
681C42—44no—
682C42—444no—
683C42—444no—
684C11#1457411yescharacteristic, complemented, Sylow
685C23C22×C4×D1111yescharacteristic
686C23C2×#433911yescharacteristic
687C23C2×D4×D1111yescharacteristic
688C23C2×#434111yescharacteristic
689C23#6703711yescharacteristic
690C23#6703711yescharacteristic
691C23C2×#434311yescharacteristic
692C23#6704011yescharacteristic
693C23#6704011yescharacteristic
694C23#6704011yescharacteristic
695C23#41×D1111yescharacteristic
696C23#6704311yescharacteristic
697C23#6704311yescharacteristic
698C23#6704311yescharacteristic
699C23C22×C22⋊D1111yescharacteristic
700Q8—416no—
701C2×C4—22no—
702C2×C4—22no—
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—41no—
726C2×C4—41no—
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—222no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
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—441no—
770C2×C4—441no—
771C2×C4—441no—
772C2×C4—441no—
773C2×C4—441no—
774C2×C4—441no—
775C2×C4—441no—
776C2×C4—441no—
777C2×C4—441no—
778C2×C4—441no—
779C2×C4—441no—
780C2×C4—441no—
781C2×C4—441no—
782C2×C4—441no—
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(C22⋊D11)⋊C414yes—
805C2×C4C4×C22⋊D1114yes—
806C22C2×(C22⋊D11)⋊C411yescharacteristic
807C22#1062301711yescharacteristic
808C22#1062302111yescharacteristic
809C22#1062302611yescharacteristic
810C22#1062310311yescharacteristic
811C22#1062310311yescharacteristic
812C22#1062310311yescharacteristic
813C22C4×#434311yescharacteristic
814C22#1062311211yescharacteristic
815C22#1062311411yescharacteristic
816C22#1062311411yescharacteristic
817C22#1062311511yescharacteristic
818C22#1062315611yescharacteristic
819C22#1062315611yescharacteristic
820C22#1062316911yescharacteristic
821C22#1062317211yescharacteristic
822C22#1062317311yescharacteristic
823C22#1062317611yescharacteristic
824C22#1062317711yescharacteristic
825C22#1062317711yescharacteristic
826C22#1062320011yescharacteristic
827C22#1062320311yescharacteristic
828C22#1062320611yescharacteristic
829C22#1062320811yescharacteristic
830C22#1062325511yescharacteristic
831C22#1062325711yescharacteristic
832C22#1062326411yescharacteristic
833C22#1062326611yescharacteristic
834C22C2×C4×C22⋊D1111yescharacteristic
835C22D4×C22⋊D1111yescharacteristic
836C22#1062333711yescharacteristic
837C22#1062334711yescharacteristic
838C22#1062334811yescharacteristic
839C22#1062335511yescharacteristic
840C22#1062335611yescharacteristic
841C4—24no—
842C4—24no—
843C4—42no—
844C4—42no—
845C4—42no—
846C4—42no—
847C4—81no—
848C4—442no—
849C4—442no—
850C4—442no—
851C4—442no—
852C4—442no—
853C4—442no—
854C4—442no—
855C4—881no—
856C2#1307133211yescharacteristic
857C2#1307133411yescharacteristic
858C2#1307137111yescharacteristic
859C2#1307159511yescharacteristic
860C2#1307163911yescharacteristic
861C2#1307164811yescharacteristic
862C2#1307179511yescharacteristic
863C2#1307489111yescharacteristic
864C2#1307489211yescharacteristic
865C2#1307506211yescharacteristic
866C2#1307506311yescharacteristic
867C2#1307507711yescharacteristic
868C2#1307507811yescharacteristic
869C2#1307601211yescharacteristic
870C2#1307601811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#391C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×#391D11
hypocenterC11#14574
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
31. #10622842C4semidirect
684. C11#14574semidirect

Maximal subgroups

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

subgroupindex
C2×#106228422
C2×#106228432
C2×#106222682
C2×#106225912
#130668822
#130668772
#130668762
#130668752
#130668722
#130668512
#130668492
#130668472
#130668432
#130668412
C2×C11×#3912
#1457411