Finite Group Databasebeta

← #14681237

Subgroups — #14681237

Order 2816.

1550 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622591C211yesmaximal, characteristic, complemented
2C2×#10622555C211yesmaximal, characteristic
3C2×#10622555C211yesmaximal, characteristic
4#13066882C211yesmaximal, characteristic, complemented
5#13066879C211yesmaximal, characteristic, complemented
6#13066871C211yesmaximal, characteristic, complemented
7#13066867C211yesmaximal, characteristic, complemented
8#13066859C211yesmaximal, characteristic
9#13066853C211yesmaximal, characteristic
10#13066853C211yesmaximal, characteristic
11#13066851C211yesmaximal, characteristic, complemented
12#13066851C211yesmaximal, characteristic, complemented
13#13066847C211yesmaximal, characteristic, complemented
14#13066838C211yesmaximal, characteristic
15C11×#1439C211yesmaximal, characteristic
16C24×Dic11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
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
51#10622591—24no—
52#10622555—24no—
53#10622555C418yescomplemented
54C25×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×Dic11—22no—
62C23×Dic11—22no—
63C23×Dic11—22no—
64C23×Dic11—22no—
65C23×Dic11—41no—
66C23×Dic11—41no—
67C23×Dic11C2×C414yes—
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—41no—
78C2×C11×C4⋊C4—41no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—41no—
83C2×C11×C22⋊C4—41no—
84C2×C11×C22⋊C4—41no—
85C2×C11×C22⋊C4—41no—
86C2×C11×C22⋊C4—41no—
87C2×C11×C22⋊C4C2×C414yes—
88C2×C22⋊Dic11—22no—
89C2×C22⋊Dic11—22no—
90C2×C22⋊Dic11—41no—
91C2×C22⋊Dic11—41no—
92C2×C22⋊Dic11—41no—
93C2×C22⋊Dic11—41no—
94C2×C22⋊Dic11—41no—
95C2×C22⋊Dic11C2×C414yes—
96C2×C22⋊Dic11Q814yes—
97C2×Dic11⋊C4—22no—
98C2×Dic11⋊C4—22no—
99C2×Dic11⋊C4—22no—
100C2×Dic11⋊C4—22no—
101C2×Dic11⋊C4—22no—
102C2×Dic11⋊C4—22no—
103C2×Dic11⋊C4—41no—
104C2×Dic11⋊C4—41no—
105C2×Dic11⋊C4—41no—
106C2×Dic11⋊C4—41no—
107C2×Dic11⋊C4—41no—
108C2×Dic11⋊C4—41no—
109C2×Dic11⋊C4—41no—
110C2×Dic11⋊C4C2×C414yes—
111C2×Dic11⋊C4C2×C414yes—
112C2×C4×Dic11—22no—
113C2×C4×Dic11—41no—
114C2×C4×Dic11—41no—
115C2×C4×Dic11—41no—
116C2×C4×Dic11—41no—
117C2×C4×Dic11—41no—
118C11×#95—41no—
119C11×#95—41no—
120C11×#95—41no—
121C11⋊#95—22no—
122C11⋊#95—22no—
123C11⋊#95—22no—
124C11⋊#95—22no—
125C11⋊#95—22no—
126C11⋊#95—22no—
127C11⋊#95—22no—
128C11⋊#95—41no—
129C11⋊#95—41no—
130C11⋊#95—41no—
131C11⋊#95—41no—
132C11⋊#95—41no—
133C11⋊#95—41no—
134C11⋊#95—41no—
135C11⋊#95C2×C414yes—
136C11⋊#95C2×C414yes—
137C11⋊#95D414yes—
138#14370—111nomaximal, Sylow
139C24×C11—21no—
140C24×C11—21no—
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×C11C22×C412yes—
152C24×C11C2×Q812yes—
153C24×C11#4112yes—
154C24×C11C2411yescharacteristic
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×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×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11C22×C412yes—
195C22×C4×C11C22×C412yes—
196C22×C4×C11C2×D412yes—
197C22×Dic11—28no—
198C22×Dic11—28no—
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—44no—
245C22×Dic11—44no—
246C22×Dic11—44no—
247C22×Dic11—44no—
248C22×Dic11—44no—
249C22×Dic11C22×C412yes—
250C22×Dic11C22×C412yes—
251C22×Dic11C22×C412yes—
252C22×Dic11C22×C412yes—
253C22×Dic11C2×D412yes—
254C22×Dic11C2×D412yes—
255C22×Dic11C2×Q812yes—
256C22×Dic11C2×Q812yes—
257C22×Dic11#4112yes—
258C22×Dic11#4112yes—
259C22×Dic11#4112yes—
260C11×C4⋊C4—44no—
261C11×C22⋊C4—44no—
262C11×C22⋊C4—44no—
263C11×C22⋊C4—44no—
264C22⋊Dic11—44no—
265C22⋊Dic11—44no—
266C22⋊Dic11—44no—
267Dic11⋊C4—28no—
268Dic11⋊C4—44no—
269Dic11⋊C4—44no—
270Dic11⋊C4—44no—
271Dic11⋊C4—44no—
272C4×Dic11—44no—
273C4×Dic11—44no—
274C2×#387—111no—
275C2×#380—111no—
276C2×#380—111no—
277#1445—111no—
278#1444—111no—
279#1442—111no—
280#1441—111no—
281#1439—111no—
282#1439D1111yescharacteristic
283#1437—111no—
284#1437—111no—
285#1436—111no—
286#1436—111no—
287#1436—111no—
288C22⋊#95—111no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
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×C11—41no—
323C23×C11C4×Q814yes—
324C23×C11C23×C411yescharacteristic
325C23×C11C22×D411yescharacteristic
326C23×C11C22×Q811yescharacteristic
327C23×C11C2×#4111yescharacteristic
328C23×C11C2×#4111yescharacteristic
329C23×C11C2×#4111yescharacteristic
330C23×C11C2×#4111yescharacteristic
331C23×C11H(5,𝔽2)11yescharacteristic
332C23×C11H(5,𝔽2)11yescharacteristic
333C23×C11H(5,𝔽2)11yescharacteristic
334C23×C11H(5,𝔽2)11yescharacteristic
335C23×C11H(5,𝔽2)11yescharacteristic
336C23×C11H(5,𝔽2)11yescharacteristic
337C23×C112−1+411yescharacteristic
338C23×C112−1+411yescharacteristic
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—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
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×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
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—22no—
407C2×Dic11—22no—
408C2×Dic11—416no—
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—41no—
435C2×Dic11—41no—
436C2×Dic11#11714yes—
437C2×Dic11C4×D414yes—
438C24×C4—111no—
439C22×C4⋊C4—111no—
440C22×C4⋊C4—111no—
441C22×C4⋊C4—111no—
442C22×C4⋊C4—111no—
443C22×C4⋊C4—111no—
444C22×C4⋊C4C2×D1111yescharacteristic
445C22×C22⋊C4—111no—
446C22×C22⋊C4—111no—
447C22×C22⋊C4—111no—
448C22×C22⋊C4C2×D1111yescharacteristic
449C22×C22⋊C4C2×D1111yescharacteristic
450C22×C22⋊C4C2×D1111yescharacteristic
451C22×C42—111no—
452C22×C42—111no—
453#387—224no—
454#380—118no—
455#380—224no—
456C2×#95—111no—
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
475C2×#95C2×D1111yescharacteristic
476C22×C11—24no—
477C22×C11—24no—
478C22×C11—24no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11—42no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11C2×#11711yescharacteristic
492C22×C11C2×C4×D411yescharacteristic
493C22×C11C2×C4×Q811yescharacteristic
494C22×C11#51811yescharacteristic
495C22×C11#51811yescharacteristic
496C22×C11#52011yescharacteristic
497C22×C11#52011yescharacteristic
498C22×C11#53511yescharacteristic
499C22×C11#53711yescharacteristic
500C22×C11#53811yescharacteristic
501C22×C11#53911yescharacteristic
502C22×C11#54011yescharacteristic
503C22×C11#54011yescharacteristic
504C22×C11#54111yescharacteristic
505C22×C11#54211yescharacteristic
506C22×C11#54211yescharacteristic
507C22×C11#54211yescharacteristic
508C22×C11#54311yescharacteristic
509C22×C11#54411yescharacteristic
510C22×C11#54611yescharacteristic
511C22×C11#54611yescharacteristic
512C22×C11#54611yescharacteristic
513C22×C11D4×Q811yescharacteristic
514C22×C11#55111yescharacteristic
515C22×C11#55111yescharacteristic
516C22×C11#55211yescharacteristic
517C22×C11#55311yescharacteristic
518C22×C11#55311yescharacteristic
519C22×C11#55411yescharacteristic
520C22×C11#55411yescharacteristic
521C22×C11#55411yescharacteristic
522C22×C11#56011yescharacteristic
523C22×C11#56011yescharacteristic
524C22×C11#56211yescharacteristic
525C22×C11#56211yescharacteristic
526C4×C11—42no—
527C4×C11—42no—
528C4×C11—42no—
529C4×C11—81no—
530C4×C11—81no—
531C4×C11—81no—
532Dic11—24no—
533Dic11—24no—
534Dic11—42no—
535Dic11—42no—
536Dic11—42no—
537Dic11—42no—
538Dic11—42no—
539Dic11—81no—
540C25C22×D1111yescharacteristic
541C23×C4—111no—
542C23×C4—111no—
543C23×C4—111no—
544C23×C4—111no—
545C23×C4—111no—
546C23×C4—111no—
547C23×C4—111no—
548C23×C4—114no—
549C23×C4—111no—
550C23×C4—222no—
551C23×C4—222no—
552C23×C4—222no—
553C23×C4—222no—
554C23×C4—441no—
555C23×C4—441no—
556C23×C4C22×D1111yescharacteristic
557C23×C4C22×D1111yescharacteristic
558C23×C4C22×D1111yescharacteristic
559C23×C4C22×D1111yescharacteristic
560C23×C4C22×D1111yescharacteristic
561C23×C4C22×D1111yescharacteristic
562C2×C4⋊C4—22no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4—41no—
565C2×C4⋊C4—114no—
566C2×C4⋊C4—114no—
567C2×C4⋊C4—222no—
568C2×C4⋊C4—222no—
569C2×C4⋊C4—222no—
570C2×C4⋊C4—222no—
571C2×C4⋊C4—222no—
572C2×C4⋊C4—222no—
573C2×C4⋊C4—441no—
574C2×C4⋊C4—441no—
575C2×C4⋊C4—441no—
576C2×C4⋊C4—441no—
577C2×C4⋊C4—441no—
578C2×C4⋊C4—441no—
579C2×C4⋊C4—441no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—22no—
583C2×C22⋊C4—41no—
584C2×C22⋊C4—41no—
585C2×C22⋊C4—41no—
586C2×C22⋊C4—41no—
587C2×C22⋊C4—41no—
588C2×C22⋊C4—114no—
589C2×C22⋊C4—114no—
590C2×C22⋊C4—222no—
591C2×C22⋊C4—222no—
592C2×C22⋊C4—441no—
593C2×C22⋊C4—441no—
594C2×C22⋊C4—441no—
595C2×C22⋊C4—441no—
596C2×C22⋊C4—441no—
597C2×C22⋊C4C4×D1114yes—
598C2×C42—222no—
599C2×C42—441no—
600C2×C42—441no—
601C2×C42—441no—
602C2×C42—441no—
603C2×C42—441no—
604#95—41no—
605#95—41no—
606#95—41no—
607#95—114no—
608#95—114no—
609#95—114no—
610#95—222no—
611#95—222no—
612#95—222no—
613#95—222no—
614#95—222no—
615#95—222no—
616#95—222no—
617#95—441no—
618#95—441no—
619#95—441no—
620#95—441no—
621#95—441no—
622#95—441no—
623#95—441no—
624C2×C11—44no—
625C2×C11#231411yescharacteristic
626C2×C11#232411yescharacteristic
627C2×C11#232911yescharacteristic
628C2×C11#234211yescharacteristic
629C2×C11#234511yescharacteristic
630C2×C11#236011yescharacteristic
631C2×C11#237711yescharacteristic
632C2×C11#269111yescharacteristic
633C2×C11#269211yescharacteristic
634C2×C11#270311yescharacteristic
635C2×C11#270411yescharacteristic
636C2×C11#274111yescharacteristic
637C2×C11#274211yescharacteristic
638C2×C11#274711yescharacteristic
639C2×C11#274811yescharacteristic
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24C2×C4×D1112yes—
653C24#434112yes—
654C24Q8×D1112yes—
655C24C23×D1111yescharacteristic
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—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—112no—
696C22×C4—112no—
697C22×C4—112no—
698C22×C4—112no—
699C22×C4—112no—
700C22×C4—112no—
701C22×C4—112no—
702C22×C4—112no—
703C22×C4—112no—
704C22×C4—112no—
705C22×C4—112no—
706C22×C4—228no—
707C22×C4—228no—
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×C4—221no—
746C22×C4—221no—
747C22×C4—221no—
748C22×C4—221no—
749C22×C4—221no—
750C22×C4—221no—
751C22×C4—221no—
752C22×C4—221no—
753C22×C4—444no—
754C22×C4—444no—
755C22×C4—444no—
756C22×C4—444no—
757C22×C4—444no—
758C22×C4C2×C4×D1112yes—
759C22×C4C2×C4×D1112yes—
760C22×C4D4×D1112yes—
761C4⋊C4—44no—
762C4⋊C4—228no—
763C4⋊C4—444no—
764C4⋊C4—444no—
765C4⋊C4—444no—
766C4⋊C4—444no—
767C22⋊C4—44no—
768C22⋊C4—44no—
769C22⋊C4—44no—
770C22⋊C4—444no—
771C22⋊C4—444no—
772C22⋊C4—444no—
773C42—444no—
774C42—444no—
775C11#1437011yescharacteristic, complemented, Sylow
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23#6694014yes—
811C23C22×C4×D1111yescharacteristic
812C23C2×D4×D1111yescharacteristic
813C23C2×#434111yescharacteristic
814C23#6703711yescharacteristic
815C23#6703711yescharacteristic
816C23#6703711yescharacteristic
817C23#6703711yescharacteristic
818C23#6703711yescharacteristic
819C23C2×Q8×D1111yescharacteristic
820C23#41×D1111yescharacteristic
821C23#41×D1111yescharacteristic
822C23#41×D1111yescharacteristic
823C23#6704211yescharacteristic
824C23#6704311yescharacteristic
825C23#6704311yescharacteristic
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—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
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—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—114no—
869C2×C4—114no—
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—222no—
893C2×C4—222no—
894C2×C4—222no—
895C2×C4—222no—
896C2×C4—222no—
897C2×C4—4416no—
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×C4—441no—
919C2×C4—441no—
920C2×C4—441no—
921C2×C4—441no—
922C2×C4—441no—
923C2×C4—441no—
924C2×C4—441no—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22#1062301711yescharacteristic
941C22C2×#6694011yescharacteristic
942C22D11×#11711yescharacteristic
943C22C4×D4×D1111yescharacteristic
944C22#1062307611yescharacteristic
945C22#1062307711yescharacteristic
946C22#1062307711yescharacteristic
947C22#1062312211yescharacteristic
948C22#1062312311yescharacteristic
949C22#1062312411yescharacteristic
950C22#1062313211yescharacteristic
951C22#1062313211yescharacteristic
952C22#1062313911yescharacteristic
953C22#1062314111yescharacteristic
954C22#1062314611yescharacteristic
955C22#1062314611yescharacteristic
956C22#1062315111yescharacteristic
957C22#1062315211yescharacteristic
958C22#1062315411yescharacteristic
959C22#1062316311yescharacteristic
960C22#1062316511yescharacteristic
961C22#1062316711yescharacteristic
962C22#1062316711yescharacteristic
963C22#1062316711yescharacteristic
964C22#1062318111yescharacteristic
965C22#1062319011yescharacteristic
966C22#1062319311yescharacteristic
967C22#1062319311yescharacteristic
968C22#1062319611yescharacteristic
969C22#1062320011yescharacteristic
970C22#1062320711yescharacteristic
971C22#1062321511yescharacteristic
972C22#1062323211yescharacteristic
973C22#1062323611yescharacteristic
974C22#1062325111yescharacteristic
975C4—42no—
976C4—42no—
977C4—42no—
978C4—81no—
979C4—81no—
980C4—81no—
981C4—224no—
982C4—224no—
983C4—442no—
984C4—442no—
985C4—442no—
986C4—442no—
987C4—442no—
988C4—881no—
989C2—44no—
990C2#1307122011yescharacteristic
991C2#1307130611yescharacteristic
992C2#1307134711yescharacteristic
993C2#1307146411yescharacteristic
994C2#1307148811yescharacteristic
995C2#1307161611yescharacteristic
996C2#1307176711yescharacteristic
997C2#1307510211yescharacteristic
998C2#1307511711yescharacteristic
999C2#1307526411yescharacteristic
1000C2#1307527911yescharacteristic
1001C2#1307573611yescharacteristic
1002C2#1307574611yescharacteristic
1003C2#1307580811yescharacteristic
1004C2#1307582311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenter#1439D11
hypocenterC11#14370
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C2×#10622591C2semidirect
4. #13066882C2semidirect
5. #13066879C2semidirect
6. #13066871C2semidirect
7. #13066867C2semidirect
11. #13066851C2semidirect
12. #13066851C2semidirect
13. #13066847C2semidirect
53. #10622555C4semidirect
775. C11#14370semidirect

Maximal subgroups

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

subgroupindex
C2×#106225912
C2×#106225552
#130668822
#130668792
#130668712
#130668672
#130668592
#130668532
#130668512
#130668472
#130668382
C11×#14392
#1437011