Finite Group Databasebeta

← #14681930

Subgroups — #14681930

Order 2816.

1670 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66941C211yesmaximal, characteristic
2C2×#10622587C211yesmaximal, characteristic
3C2×#10622259C211yesmaximal, characteristic
4C2×#10622265C211yesmaximal, characteristic
5C2×#10622591C211yesmaximal, characteristic
6#13066886C211yesmaximal, characteristic
7#13066886C211yesmaximal, characteristic
8#13066882C211yesmaximal, characteristic
9#13066882C211yesmaximal, characteristic
10#13066868C211yesmaximal, characteristic
11#13066850C211yesmaximal, characteristic
12#13066848C211yesmaximal, characteristic
13#13066842C211yesmaximal, characteristic
14#13066841C211yesmaximal, characteristic
15C11×#1441C211yesmaximal, characteristic
16C23×Dic22C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×Dic11⋊C4C2211yescharacteristic
22C22×Dic11⋊C4C2211yescharacteristic
23C22×Dic11⋊C4C2211yescharacteristic
24C22×C4×Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C2×#66941—24no—
28C2×#66941—24no—
29C2×#66941C418yescomplemented
30C2×C11×#95C2211yescharacteristic
31C2×C11×#95C2211yescharacteristic
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#10622587—24no—
56#10622265—24no—
57#10622259—24no—
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×Dic22—22no—
78C22×Dic22—22no—
79C22×Dic22—22no—
80C22×Dic22—22no—
81C22×Dic22—41no—
82C22×Dic22—41no—
83C22×Dic22—41no—
84C22×Dic22—41no—
85C22×Dic22C2×C414yes—
86C22×Dic22C2×C414yes—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4—41no—
92C2×C11×C4⋊C4C2×C414yes—
93C2×C4⋊Dic11—22no—
94C2×C4⋊Dic11—22no—
95C2×C4⋊Dic11C2×C414yes—
96C2×Dic11⋊C4—22no—
97C2×Dic11⋊C4—22no—
98C2×Dic11⋊C4—22no—
99C2×Dic11⋊C4—22no—
100C2×Dic11⋊C4—41no—
101C2×Dic11⋊C4C2×C414yes—
102C2×Dic11⋊C4C2×C414yes—
103C2×Dic11⋊C4D414yes—
104C2×Dic11⋊C4D414yes—
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—41no—
112C2×C4×Dic11—41no—
113C2×C4×Dic11C2×C414yes—
114#66941—232no—
115C11×#95—22no—
116C11×#95—22no—
117C11×#95—22no—
118C11×#95—22no—
119C11×#95—41no—
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—22no—
134C11⋊#95—41no—
135C11⋊#95—41no—
136C11⋊#95—41no—
137C11⋊#95D414yes—
138C11⋊#95Q814yescomplemented
139#14420—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×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11C22×C412yes—
234C22×Dic11C22×C412yes—
235C22×Dic11C22×C412yes—
236C22×Dic11C22×C412yes—
237C22×Dic11C2×D412yes—
238C22×Dic11C2×D412yes—
239C22×Dic11C2×D412yes—
240C22×Dic11C2×D412yes—
241C22×Dic11C2×D412yes—
242C22×Dic11C2×D412yes—
243C22×Dic11C2×Q812yes—
244C22×Dic11C2×Q812yes—
245C22×Dic11#4112yes—
246C2×Dic22—28no—
247C2×Dic22—28no—
248C2×Dic22—28no—
249C2×Dic22—28no—
250C2×Dic22—44no—
251C2×Dic22—44no—
252C2×Dic22—44no—
253C2×Dic22—44no—
254C2×Dic22—44no—
255C2×Dic22—44no—
256C2×Dic22—44no—
257C2×Dic22—44no—
258C2×Dic22—44no—
259C2×Dic22—44no—
260C11×C4⋊C4—28no—
261C11×C4⋊C4—44no—
262C4⋊Dic11—28no—
263Dic11⋊C4—28no—
264Dic11⋊C4—44no—
265Dic11⋊C4C22⋊C4116yes—
266C4×Dic11—28no—
267C4×Dic11—44no—
268C4×Dic11—44no—
269C22×C4⋊Q8—111no—
270C2×#391—111no—
271C2×#391—111no—
272C2×#387—111no—
273C2×#387—111no—
274#1446—111no—
275#1446—111no—
276#1445—111no—
277#1445—111no—
278#1441—111no—
279#1441D1111yescharacteristic
280#1436—111no—
281#1436—111no—
282#1434—111no—
283#1434—111no—
284C23×C11C23×C411yescharacteristic
285C23×C11C22×D411yescharacteristic
286C23×C11C22×D411yescharacteristic
287C23×C11C22×D411yescharacteristic
288C23×C11C22×Q811yescharacteristic
289C23×C11C2×#4111yescharacteristic
290C23×C11C2×#4111yescharacteristic
291C23×C11H(5,𝔽2)11yescharacteristic
292C23×C11H(5,𝔽2)11yescharacteristic
293C23×C112−1+411yescharacteristic
294C23×C112−1+411yescharacteristic
295C23×C112−1+411yescharacteristic
296C23×C112−1+411yescharacteristic
297C23×C112−1+411yescharacteristic
298C23×C112−1+411yescharacteristic
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—22no—
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×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11C2×C22⋊C414yes—
347C2×C4×C11C4×Q814yes—
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—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
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×Dic11—41no—
392C2×Dic11—41no—
393C2×Dic11—41no—
394C2×Dic11—41no—
395C2×Dic11—41no—
396C2×Dic11—41no—
397C2×Dic11—41no—
398C2×Dic11—41no—
399C2×Dic11—41no—
400C2×Dic11—41no—
401C2×Dic11C2×C22⋊C414yes—
402C2×Dic11C2×C22⋊C414yes—
403C2×Dic11C4×D414yes—
404Dic22—416no—
405Dic22—416no—
406C23×Q8—111no—
407C23×Q8—111no—
408C2×C4⋊Q8—118no—
409C2×C4⋊Q8—224no—
410C2×C4⋊Q8—224no—
411C22×C4⋊C4—111no—
412C22×C4⋊C4—111no—
413C22×C4⋊C4—111no—
414C22×C4⋊C4—111no—
415C22×C4⋊C4C2×D1111yescharacteristic
416C22×C4⋊C4C2×D1111yescharacteristic
417C22×C42—111no—
418C22×C42—111no—
419C22×C42—111no—
420#391—224no—
421#391—224no—
422#387—224no—
423#387—224no—
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×#95—111no—
438C2×#95—111no—
439C2×#95—111no—
440C2×#95—111no—
441C2×#95—111no—
442C2×#95—111no—
443C2×#95C2×D1111yescharacteristic
444C2×#95C2×D1111yescharacteristic
445C2×#95C2×D1111yescharacteristic
446C2×#95C2×D1111yescharacteristic
447C2×#95C2×D1111yescharacteristic
448C22×C11C22×C22⋊C411yescharacteristic
449C22×C11C2×C4×D411yescharacteristic
450C22×C11C2×C4×Q811yescharacteristic
451C22×C11#51811yescharacteristic
452C22×C11#51911yescharacteristic
453C22×C11#51911yescharacteristic
454C22×C11#51911yescharacteristic
455C22×C11#53611yescharacteristic
456C22×C11#53611yescharacteristic
457C22×C11#53611yescharacteristic
458C22×C11#53611yescharacteristic
459C22×C11#53611yescharacteristic
460C22×C11#53611yescharacteristic
461C22×C11#54111yescharacteristic
462C22×C11#54111yescharacteristic
463C22×C11#54211yescharacteristic
464C22×C11#54211yescharacteristic
465C22×C11#54411yescharacteristic
466C22×C11#54411yescharacteristic
467C22×C11D4211yescharacteristic
468C22×C11D4211yescharacteristic
469C22×C11#54611yescharacteristic
470C22×C11#54611yescharacteristic
471C22×C11#54711yescharacteristic
472C22×C11#54811yescharacteristic
473C22×C11#54811yescharacteristic
474C22×C11D4×Q811yescharacteristic
475C22×C11D4×Q811yescharacteristic
476C22×C11D4×Q811yescharacteristic
477C22×C11#55611yescharacteristic
478C22×C11#55711yescharacteristic
479C22×C11#56311yescharacteristic
480C22×C11#56311yescharacteristic
481C22×C11#56311yescharacteristic
482C22×C11#56311yescharacteristic
483C4×C11—24no—
484C4×C11—24no—
485C4×C11—42no—
486C4×C11—42no—
487C4×C11—81no—
488C4×C11—81no—
489C4×C11—81no—
490Dic11—24no—
491Dic11—24no—
492Dic11—24no—
493Dic11—42no—
494Dic11—42no—
495Dic11—42no—
496Dic11—42no—
497Dic11—81no—
498C22×Q8—114no—
499C22×Q8—114no—
500C22×Q8—222no—
501C22×Q8—222no—
502C22×Q8—222no—
503C22×Q8—222no—
504C22×Q8—222no—
505C22×Q8—222no—
506C22×Q8—222no—
507C22×Q8—222no—
508C22×Q8—441no—
509C22×Q8—441no—
510C22×Q8—441no—
511C22×Q8—441no—
512C23×C4—111no—
513C23×C4—111no—
514C23×C4—111no—
515C23×C4—111no—
516C23×C4—111no—
517C23×C4—111no—
518C23×C4—111no—
519C23×C4—111no—
520C23×C4C22×D1111yescharacteristic
521C23×C4C22×D1111yescharacteristic
522C23×C4C22×D1111yescharacteristic
523C23×C4C22×D1111yescharacteristic
524C23×C4C22×D1111yescharacteristic
525C23×C4C22×D1111yescharacteristic
526C23×C4C22×D1111yescharacteristic
527C4⋊Q8—2232no—
528C2×C4⋊C4—22no—
529C2×C4⋊C4—22no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—22no—
532C2×C4⋊C4—41no—
533C2×C4⋊C4—114no—
534C2×C4⋊C4—114no—
535C2×C4⋊C4—114no—
536C2×C4⋊C4—114no—
537C2×C4⋊C4—114no—
538C2×C4⋊C4—222no—
539C2×C4⋊C4—222no—
540C2×C4⋊C4—222no—
541C2×C4⋊C4—222no—
542C2×C4⋊C4—222no—
543C2×C4⋊C4—222no—
544C2×C4⋊C4—441no—
545C2×C4⋊C4C4×D1114yes—
546C2×C42—114no—
547C2×C42—222no—
548C2×C42—222no—
549C2×C42—222no—
550C2×C42—222no—
551C2×C42—222no—
552C2×C42—222no—
553C2×C42—441no—
554C2×C42—441no—
555#95—22no—
556#95—22no—
557#95—22no—
558#95—22no—
559#95—41no—
560#95—114no—
561#95—114no—
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#95—222no—
574#95—222no—
575#95—222no—
576#95—441no—
577#95—441no—
578#95—441no—
579C2×C11#231011yescharacteristic
580C2×C11#232711yescharacteristic
581C2×C11#233111yescharacteristic
582C2×C11D4×C22⋊C411yescharacteristic
583C2×C11Q8×C22⋊C411yescharacteristic
584C2×C11#236511yescharacteristic
585C2×C11#238111yescharacteristic
586C2×C11#267411yescharacteristic
587C2×C11#267411yescharacteristic
588C2×C11#267711yescharacteristic
589C2×C11#267711yescharacteristic
590C2×C11#271311yescharacteristic
591C2×C11#271311yescharacteristic
592C2×C11#271611yescharacteristic
593C2×C11#271611yescharacteristic
594C24C23×D1111yescharacteristic
595C2×Q8—228no—
596C2×Q8—228no—
597C2×Q8—228no—
598C2×Q8—228no—
599C2×Q8—444no—
600C2×Q8—444no—
601C2×Q8—444no—
602C2×Q8—444no—
603C2×Q8—444no—
604C2×Q8—444no—
605C2×Q8—444no—
606C2×Q8—444no—
607C2×Q8—444no—
608C2×Q8—444no—
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—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—112no—
651C22×C4—112no—
652C22×C4—112no—
653C22×C4—112no—
654C22×C4—112no—
655C22×C4—112no—
656C22×C4—112no—
657C22×C4—112no—
658C22×C4—112no—
659C22×C4—112no—
660C22×C4—112no—
661C22×C4—112no—
662C22×C4—112no—
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×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×C4C2×C4×D1112yes—
707C22×C4C2×C4×D1112yes—
708C22×C4C2×C4×D1112yes—
709C22×C4D4×D1112yes—
710C22×C4D4×D1112yes—
711C22×C4D4×D1112yes—
712C22×C4#434112yes—
713C22×C4Q8×D1112yes—
714C4⋊C4—28no—
715C4⋊C4—44no—
716C4⋊C4—1116no—
717C4⋊C4—228no—
718C4⋊C4—228no—
719C4⋊C4—444no—
720C42—228no—
721C42—444no—
722C42—444no—
723C11#1442011yescharacteristic, complemented, Sylow
724C23C22×C4×D1111yescharacteristic
725C23C2×D4×D1111yescharacteristic
726C23C2×D4×D1111yescharacteristic
727C23C2×D4×D1111yescharacteristic
728C23C2×#434111yescharacteristic
729C23#6703711yescharacteristic
730C23C2×Q8×D1111yescharacteristic
731C23#6704011yescharacteristic
732C23#6704011yescharacteristic
733C23#41×D1111yescharacteristic
734C23#6704211yescharacteristic
735C23#6704311yescharacteristic
736C23#6704311yescharacteristic
737C23#6704311yescharacteristic
738C23#6704311yescharacteristic
739Q8—4416no—
740Q8—4416no—
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—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
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—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—114no—
789C2×C4—114no—
790C2×C4—114no—
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—222no—
813C2×C4—222no—
814C2×C4—222no—
815C2×C4—222no—
816C2×C4—222no—
817C2×C4—222no—
818C2×C4—222no—
819C2×C4—222no—
820C2×C4—222no—
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×C4—441no—
836C2×C4—441no—
837C2×C4—441no—
838C2×C4—441no—
839C2×C4—441no—
840C2×C4—441no—
841C2×C4—441no—
842C2×C4—441no—
843C2×C4—441no—
844C2×C4C22⋊C4×D1114yes—
845C2×C4#6694014yes—
846C22C2×C22⋊C4×D1111yescharacteristic
847C22C2×#6694011yescharacteristic
848C22#1062304711yescharacteristic
849C22C4×D4×D1111yescharacteristic
850C22#1062307611yescharacteristic
851C22#1062310311yescharacteristic
852C22#1062310311yescharacteristic
853C22#1062312111yescharacteristic
854C22#1062312911yescharacteristic
855C22#1062312911yescharacteristic
856C22#1062313411yescharacteristic
857C22#1062314011yescharacteristic
858C22#1062314111yescharacteristic
859C22#1062314211yescharacteristic
860C22#1062315911yescharacteristic
861C22#1062315911yescharacteristic
862C22#1062315911yescharacteristic
863C22#1062316311yescharacteristic
864C22#1062316311yescharacteristic
865C22#1062317211yescharacteristic
866C22#1062317411yescharacteristic
867C22#1062317711yescharacteristic
868C22#1062317911yescharacteristic
869C22#1062318211yescharacteristic
870C22#1062318511yescharacteristic
871C22#1062320611yescharacteristic
872C22#1062321611yescharacteristic
873C22#1062322011yescharacteristic
874C22#1062322711yescharacteristic
875C22#1062323011yescharacteristic
876C22#1062323211yescharacteristic
877C22#1062324311yescharacteristic
878C22#1062325511yescharacteristic
879C22#1062325811yescharacteristic
880C22#1062326011yescharacteristic
881C4—24no—
882C4—24no—
883C4—42no—
884C4—42no—
885C4—81no—
886C4—81no—
887C4—81no—
888C4—224no—
889C4—224no—
890C4—224no—
891C4—442no—
892C4—442no—
893C4—442no—
894C4—442no—
895C4—881no—
896C2#1307119911yescharacteristic
897C2#1307133111yescharacteristic
898C2#1307136311yescharacteristic
899C2#1307143411yescharacteristic
900C2#1307144811yescharacteristic
901C2#1307166911yescharacteristic
902C2#1307179411yescharacteristic
903C2#1307489911yescharacteristic
904C2#1307490411yescharacteristic
905C2#1307493011yescharacteristic
906C2#1307493311yescharacteristic
907C2#1307539611yescharacteristic
908C2#1307540311yescharacteristic
909C2#1307544111yescharacteristic
910C2#1307544811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1441C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1441D11
hypocenterC11#14420
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
29. C2×#66941C4semidirect
138. C11⋊#95Q8semidirect
723. C11#14420semidirect

Maximal subgroups

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

subgroupindex
C22×#669412
C2×#106225872
C2×#106222592
C2×#106222652
C2×#106225912
#130668862
#130668822
#130668682
#130668502
#130668482
#130668422
#130668412
C11×#14412
#1442011