Finite Group Databasebeta

← #14676659

Subgroups — #14676659

Order 2816.

1750 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66940C211yesmaximal, characteristic
2C2×#10622259C211yesmaximal, characteristic
3C2×#10622259C211yesmaximal, characteristic
4C2×#10622260C211yesmaximal, characteristic
5C2×#10622263C211yesmaximal, characteristic
6#13066875C211yesmaximal, characteristic
7#13066874C211yesmaximal, characteristic
8#13066871C211yesmaximal, characteristic
9#13066850C211yesmaximal, characteristic
10#13066850C211yesmaximal, characteristic
11#13066847C211yesmaximal, characteristic
12#13066847C211yesmaximal, characteristic
13Dic11⋊#95C211yesmaximal, characteristic
14#95×Dic11C211yesmaximal, characteristic
15C11×#1442C211yesmaximal, characteristic
16C23×Dic22C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×Dic11⋊C4C2211yescharacteristic
20C22×Dic11⋊C4C2211yescharacteristic
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×#66940—24no—
30C2×#66940—24no—
31C2×#66940—24no—
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#10622263—24no—
55#10622260—24no—
56#10622259—24no—
57#10622259C418yescomplemented
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C22×Dic22—22no—
74C22×Dic22—22no—
75C22×Dic22—22no—
76C22×Dic22—22no—
77C22×Dic22C2×C414yes—
78C22×Dic22D414yes—
79C22×Dic22Q814yes—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—22no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—22no—
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⋊C4—22no—
93C2×Dic11⋊C4—22no—
94C2×Dic11⋊C4—22no—
95C2×Dic11⋊C4—22no—
96C2×Dic11⋊C4—22no—
97C2×Dic11⋊C4—22no—
98C2×Dic11⋊C4—22no—
99C2×Dic11⋊C4C2×C414yes—
100C2×Dic11⋊C4D414yes—
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—22no—
110C2×C4×Dic11—22no—
111C2×C4×Dic11—22no—
112C2×C4×Dic11—22no—
113C2×C4×Dic11—22no—
114C2×C4×Dic11C2×C414yes—
115C2×C4×Dic11D414yes—
116#66940—232no—
117C11×#95—22no—
118C11×#95—22no—
119C11×#95—22no—
120C11×#95—22no—
121C11×#95—22no—
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—22no—
135C11⋊#95—22no—
136C11⋊#95C2×C414yes—
137C11⋊#95C2×C414yes—
138C11⋊#95C2×C414yes—
139#13978—111nomaximal, Sylow
140C24×C11C2411yescharacteristic
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×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11C22×C412yes—
183C22×C4×C11C22×C412yes—
184C22×C4×C11C22×C412yes—
185C22×C4×C11C2×D412yes—
186C22×C4×C11C2×D412yes—
187C22×C4×C11C2×D412yes—
188C22×C4×C11C2×Q812yes—
189C22×C4×C11#4112yes—
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×Dic11C22×C412yes—
230C22×Dic11C22×C412yes—
231C22×Dic11C22×C412yes—
232C22×Dic11C22×C412yes—
233C22×Dic11C2×D412yes—
234C22×Dic11C2×D412yes—
235C22×Dic11C2×D412yes—
236C22×Dic11C2×D412yes—
237C22×Dic11C2×D412yes—
238C22×Dic11C2×D412yes—
239C22×Dic11C2×Q812yes—
240C22×Dic11C2×Q812yes—
241C22×Dic11#4112yes—
242C22×Dic11#4112yes—
243C22×Dic11#4112yes—
244C22×Dic11#4112yes—
245C22×Dic11#4112yes—
246C2×Dic22—28no—
247C2×Dic22—28no—
248C2×Dic22—28no—
249C2×Dic22—28no—
250C2×Dic22—28no—
251C2×Dic22—28no—
252C2×Dic22C4⋊C4116yescomplemented
253C11×C4⋊C4—28no—
254C4⋊Dic11—44no—
255Dic11⋊C4—28no—
256Dic11⋊C4—28no—
257Dic11⋊C4—28no—
258Dic11⋊C4—44no—
259Dic11⋊C4—44no—
260C4×Dic11—28no—
261C4×Dic11—28no—
262C4×Dic11—28no—
263C4×Dic11—28no—
264C4×Dic11—44no—
265C22×C4×Q8—111no—
266C2×#391—111no—
267C2×#391—111no—
268C2×#389—111no—
269C2×#382—111no—
270#1442—111no—
271#1442—111no—
272#1442—111no—
273#1442D1111yescharacteristic
274#1436—111no—
275#1436—111no—
276#1436—111no—
277#1436—111no—
278C4⋊#95—111no—
279C4×#95—111no—
280C23×C11C23×C411yescharacteristic
281C23×C11C22×D411yescharacteristic
282C23×C11C22×D411yescharacteristic
283C23×C11C22×D411yescharacteristic
284C23×C11C22×Q811yescharacteristic
285C23×C11C2×#4111yescharacteristic
286C23×C11C2×#4111yescharacteristic
287C23×C11C2×#4111yescharacteristic
288C23×C11C2×#4111yescharacteristic
289C23×C11C2×#4111yescharacteristic
290C23×C11C2×#4111yescharacteristic
291C23×C112−1+411yescharacteristic
292C23×C112−1+411yescharacteristic
293C23×C112−1+411yescharacteristic
294C23×C112−1+411yescharacteristic
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—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
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—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11C2×C4⋊C414yes—
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—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
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—
386C2×Dic11—41no—
387C2×Dic11—41no—
388C2×Dic11—41no—
389C2×Dic11—41no—
390C2×Dic11—41no—
391C2×Dic11C2×C4⋊C414yes—
392C2×Dic11C2×C4⋊C414yes—
393C2×Dic11C4×D414yes—
394C2×Dic11C4×D414yes—
395C2×Dic11#12014yes—
396C2×Dic11C22⋊Q814yes—
397C2×Dic11C22⋊Q814yes—
398C2×Dic11#12314yes—
399C2×Dic11#12414yes—
400Dic22—232no—
401C23×Q8—111no—
402C2×C4×Q8—224no—
403C2×C4×Q8—224no—
404C2×C4×Q8—224no—
405C22×C4⋊C4—111no—
406C22×C4⋊C4—111no—
407C22×C4⋊C4—111no—
408C22×C4⋊C4—111no—
409C22×C4⋊C4—111no—
410C22×C4⋊C4—111no—
411C22×C4⋊C4C2×D1111yescharacteristic
412C22×C42—111no—
413C22×C42—111no—
414C22×C42—111no—
415C22×C42—111no—
416C22×C42—111no—
417#391—118no—
418#391—224no—
419#389—224no—
420#382—224no—
421C2×#95—111no—
422C2×#95—111no—
423C2×#95—111no—
424C2×#95—111no—
425C2×#95—111no—
426C2×#95—111no—
427C2×#95—111no—
428C2×#95—111no—
429C2×#95—111no—
430C2×#95—111no—
431C2×#95—111no—
432C2×#95—111no—
433C2×#95—111no—
434C2×#95—111no—
435C2×#95—111no—
436C2×#95—111no—
437C2×#95C2×D1111yescharacteristic
438C2×#95C2×D1111yescharacteristic
439C2×#95C2×D1111yescharacteristic
440C2×#95C2×D1111yescharacteristic
441C2×#95C2×D1111yescharacteristic
442C2×#95C2×D1111yescharacteristic
443C22×C11C22×C4⋊C411yescharacteristic
444C22×C11C2×C4×D411yescharacteristic
445C22×C11C2×C4×D411yescharacteristic
446C22×C11C4×#4111yescharacteristic
447C22×C11C4×#4111yescharacteristic
448C22×C11#51911yescharacteristic
449C22×C11#51911yescharacteristic
450C22×C11C2×#12011yescharacteristic
451C22×C11C2×C22⋊Q811yescharacteristic
452C22×C11C2×C22⋊Q811yescharacteristic
453C22×C11C2×#12311yescharacteristic
454C22×C11C2×#12411yescharacteristic
455C22×C11#52911yescharacteristic
456C22×C11#52911yescharacteristic
457C22×C11#53211yescharacteristic
458C22×C11#53611yescharacteristic
459C22×C11#53611yescharacteristic
460C22×C11#54111yescharacteristic
461C22×C11#54111yescharacteristic
462C22×C11#54711yescharacteristic
463C22×C11#54711yescharacteristic
464C22×C11#54811yescharacteristic
465C22×C11#54811yescharacteristic
466C22×C11#54811yescharacteristic
467C22×C11#54811yescharacteristic
468C22×C11#54811yescharacteristic
469C22×C11#54811yescharacteristic
470C22×C11#55211yescharacteristic
471C22×C11#55211yescharacteristic
472C22×C11#55611yescharacteristic
473C22×C11#55611yescharacteristic
474C22×C11#55711yescharacteristic
475C22×C11#55711yescharacteristic
476C22×C11#55711yescharacteristic
477C22×C11#55711yescharacteristic
478C4×C11—24no—
479C4×C11—42no—
480C4×C11—42no—
481C4×C11—42no—
482C4×C11—42no—
483C4×C11—42no—
484C4×C11—81no—
485Dic11—24no—
486Dic11—24no—
487Dic11—42no—
488Dic11—42no—
489Dic11—42no—
490Dic11—42no—
491Dic11—81no—
492Dic11#38518yes—
493C22×Q8—114no—
494C22×Q8—114no—
495C22×Q8—114no—
496C22×Q8—222no—
497C22×Q8—222no—
498C22×Q8—222no—
499C22×Q8—222no—
500C23×C4—111no—
501C23×C4—111no—
502C23×C4—111no—
503C23×C4—111no—
504C23×C4—111no—
505C23×C4—111no—
506C23×C4—111no—
507C23×C4—111no—
508C23×C4C22×D1111yescharacteristic
509C23×C4C22×D1111yescharacteristic
510C23×C4C22×D1111yescharacteristic
511C23×C4C22×D1111yescharacteristic
512C23×C4C22×D1111yescharacteristic
513C23×C4C22×D1111yescharacteristic
514C23×C4C22×D1111yescharacteristic
515C4×Q8—2232no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—114no—
520C2×C4⋊C4—114no—
521C2×C4⋊C4—222no—
522C2×C4⋊C4—222no—
523C2×C4⋊C4—222no—
524C2×C4⋊C4—222no—
525C2×C4⋊C4—222no—
526C2×C4⋊C4—222no—
527C2×C4⋊C4—222no—
528C2×C4⋊C4—222no—
529C2×C4⋊C4—222no—
530C2×C4⋊C4—222no—
531C2×C4⋊C4—222no—
532C2×C4⋊C4—222no—
533C2×C4⋊C4—222no—
534C2×C4⋊C4—222no—
535C2×C4⋊C4—222no—
536C2×C4⋊C4—222no—
537C2×C42—114no—
538C2×C42—114no—
539C2×C42—222no—
540C2×C42—222no—
541C2×C42—222no—
542C2×C42—222no—
543C2×C42—222no—
544C2×C42—222no—
545C2×C42—222no—
546C2×C42—222no—
547C2×C42—222no—
548C2×C42—222no—
549C2×C42—222no—
550C2×C42—222no—
551C2×C42—222no—
552#95—22no—
553#95—22no—
554#95—22no—
555#95—22no—
556#95—22no—
557#95—114no—
558#95—114no—
559#95—114no—
560#95—222no—
561#95—222no—
562#95—222no—
563#95—222no—
564#95—222no—
565#95—222no—
566#95—222no—
567#95—222no—
568#95—222no—
569#95—222no—
570#95—222no—
571#95—222no—
572#95—222no—
573#95C4×D1114yes—
574C2×C11C2×#38511yescharacteristic
575C2×C11C4×#12411yescharacteristic
576C2×C11#232711yescharacteristic
577C2×C11#235111yescharacteristic
578C2×C11#235111yescharacteristic
579C2×C11#236211yescharacteristic
580C2×C11#236211yescharacteristic
581C2×C11#242111yescharacteristic
582C2×C11#242111yescharacteristic
583C2×C11#243211yescharacteristic
584C2×C11#243611yescharacteristic
585C2×C11#245311yescharacteristic
586C2×C11#245311yescharacteristic
587C2×C11#256511yescharacteristic
588C2×C11#256811yescharacteristic
589C24C23×D1111yescharacteristic
590C2×Q8—1116no—
591C2×Q8—228no—
592C2×Q8—228no—
593C2×Q8—228no—
594C2×Q8—228no—
595C2×Q8—228no—
596C2×Q8—228no—
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—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—112no—
639C22×C4—112no—
640C22×C4—112no—
641C22×C4—112no—
642C22×C4—112no—
643C22×C4—112no—
644C22×C4—112no—
645C22×C4—112no—
646C22×C4—112no—
647C22×C4—112no—
648C22×C4—112no—
649C22×C4—112no—
650C22×C4—112no—
651C22×C4—112no—
652C22×C4—112no—
653C22×C4—112no—
654C22×C4—112no—
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×C4—221no—
667C22×C4—221no—
668C22×C4—221no—
669C22×C4—221no—
670C22×C4—221no—
671C22×C4—221no—
672C22×C4—221no—
673C22×C4—221no—
674C22×C4—221no—
675C22×C4—221no—
676C22×C4—221no—
677C22×C4—221no—
678C22×C4—221no—
679C22×C4—221no—
680C22×C4—221no—
681C22×C4—221no—
682C22×C4—221no—
683C22×C4—221no—
684C22×C4—221no—
685C22×C4—221no—
686C22×C4—221no—
687C22×C4—221no—
688C22×C4—221no—
689C22×C4—221no—
690C22×C4—221no—
691C22×C4—221no—
692C22×C4—221no—
693C22×C4—221no—
694C22×C4C2×C4×D1112yes—
695C22×C4C2×C4×D1112yes—
696C22×C4C2×C4×D1112yes—
697C22×C4D4×D1112yes—
698C22×C4D4×D1112yes—
699C22×C4D4×D1112yes—
700C22×C4#434112yes—
701C22×C4Q8×D1112yes—
702C4⋊C4—28no—
703C4⋊C4—228no—
704C4⋊C4—228no—
705C4⋊C4—228no—
706C4⋊C4—444no—
707C4⋊C4—444no—
708C4⋊C4—444no—
709C42—228no—
710C42—228no—
711C42—228no—
712C42—228no—
713C42—444no—
714C11#1397811yescharacteristic, complemented, Sylow
715C23C22×C4×D1111yescharacteristic
716C23C2×D4×D1111yescharacteristic
717C23C2×D4×D1111yescharacteristic
718C23C2×D4×D1111yescharacteristic
719C23C2×#434111yescharacteristic
720C23C2×Q8×D1111yescharacteristic
721C23#6704011yescharacteristic
722C23#41×D1111yescharacteristic
723C23#41×D1111yescharacteristic
724C23#41×D1111yescharacteristic
725C23#41×D1111yescharacteristic
726C23#41×D1111yescharacteristic
727C23#6704311yescharacteristic
728C23#6704311yescharacteristic
729C23#6704311yescharacteristic
730Q8—2232no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—114no—
780C2×C4—114no—
781C2×C4—114no—
782C2×C4—114no—
783C2×C4—114no—
784C2×C4—114no—
785C2×C4—114no—
786C2×C4—114no—
787C2×C4—114no—
788C2×C4—222no—
789C2×C4—222no—
790C2×C4—222no—
791C2×C4—222no—
792C2×C4—222no—
793C2×C4—222no—
794C2×C4—222no—
795C2×C4—222no—
796C2×C4—222no—
797C2×C4—222no—
798C2×C4—222no—
799C2×C4—222no—
800C2×C4—222no—
801C2×C4—222no—
802C2×C4—222no—
803C2×C4—222no—
804C2×C4—222no—
805C2×C4—222no—
806C2×C4—222no—
807C2×C4—222no—
808C2×C4—222no—
809C2×C4—222no—
810C2×C4—222no—
811C2×C4—222no—
812C2×C4—441no—
813C2×C4—441no—
814C2×C4—441no—
815C2×C4—441no—
816C2×C4—441no—
817C2×C4—441no—
818C2×C4—441no—
819C2×C4—441no—
820C2×C4—441no—
821C2×C4—441no—
822C2×C4—441no—
823C2×C4—441no—
824C2×C4—441no—
825C2×C4—441no—
826C2×C4—441no—
827C2×C4—441no—
828C2×C4—441no—
829C2×C4—441no—
830C2×C4—441no—
831C2×C4—441no—
832C2×C4—441no—
833C2×C4—441no—
834C2×C4—441no—
835C2×C4C4⋊C4×D1114yes—
836C22C2×C4⋊C4×D1111yescharacteristic
837C22#1062304711yescharacteristic
838C22#1062305311yescharacteristic
839C22C4×#434111yescharacteristic
840C22C4×D4×D1111yescharacteristic
841C22C4×D4×D1111yescharacteristic
842C22#1062310311yescharacteristic
843C22D11×#12011yescharacteristic
844C22#1062312711yescharacteristic
845C22#1062312911yescharacteristic
846C22#1062314211yescharacteristic
847C22D11×C22⋊Q811yescharacteristic
848C22D11×C22⋊Q811yescharacteristic
849C22#1062315911yescharacteristic
850C22#1062316411yescharacteristic
851C22#1062316411yescharacteristic
852C22#1062317911yescharacteristic
853C22#1062318011yescharacteristic
854C22#1062318111yescharacteristic
855C22D11×#12311yescharacteristic
856C22#1062318611yescharacteristic
857C22D11×#12411yescharacteristic
858C22#1062320811yescharacteristic
859C22#1062320811yescharacteristic
860C22#1062320811yescharacteristic
861C22#1062321611yescharacteristic
862C22#1062321611yescharacteristic
863C22#1062321611yescharacteristic
864C22#1062322411yescharacteristic
865C22#1062322711yescharacteristic
866C22#1062323211yescharacteristic
867C22#1062323311yescharacteristic
868C22#1062323311yescharacteristic
869C22#1062323711yescharacteristic
870C22#1062325211yescharacteristic
871C4—24no—
872C4—42no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—81no—
878C4—118no—
879C4—224no—
880C4—224no—
881C4—442no—
882C4—442no—
883C4—442no—
884C4—442no—
885C4—881no—
886C2D11×#38511yescharacteristic
887C2#1307115711yescharacteristic
888C2#1307133111yescharacteristic
889C2#1307153311yescharacteristic
890C2#1307153511yescharacteristic
891C2#1307163811yescharacteristic
892C2#1307164011yescharacteristic
893C2#1307211211yescharacteristic
894C2#1307211411yescharacteristic
895C2#1307223911yescharacteristic
896C2#1307226911yescharacteristic
897C2#1307247011yescharacteristic
898C2#1307247211yescharacteristic
899C2#1307380211yescharacteristic
900C2#1307382711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1442C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1442D11
hypocenterC11#13978
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
57. #10622259C4semidirect
252. C2×Dic22C4⋊C4semidirect
714. C11#13978semidirect

Maximal subgroups

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

subgroupindex
C22×#669402
C2×#106222592
C2×#106222602
C2×#106222632
#130668752
#130668742
#130668712
#130668502
#130668472
Dic11⋊#952
#95×Dic112
C11×#14422
#1397811