Finite Group Databasebeta

← #14684455

Subgroups — #14684455

Order 2816.

1390 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622286C211yesmaximal, characteristic
2C2×#10622259C211yesmaximal, characteristic, complemented
3C2×#10622283C211yesmaximal, characteristic
4#13066886C211yesmaximal, characteristic, complemented
5#13066879C211yesmaximal, characteristic, complemented
6#13066873C211yesmaximal, characteristic, complemented
7#13066872C211yesmaximal, characteristic, complemented
8#13066871C211yesmaximal, characteristic, complemented
9#13066864C211yesmaximal, characteristic
10#13066864C211yesmaximal, characteristic
11#13066860C211yesmaximal, characteristic
12#13066860C211yesmaximal, characteristic
13#13066858C211yesmaximal, characteristic
14#13066842C211yesmaximal, characteristic, complemented
15C11×#1442C211yesmaximal, characteristic, complemented
16C23×Dic22C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
29C2×C11×#95C2211yescharacteristic
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
51#10622286C418yescomplemented
52#10622283—24no—
53#10622259—24no—
54C24×D11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C22×Dic22—22no—
70C22×Dic22—22no—
71C22×Dic22—41no—
72C22×Dic22—41no—
73C22×Dic22—41no—
74C22×Dic22—41no—
75C22×Dic22C2×C414yes—
76C2×C11×C4⋊C4—41no—
77C2×C11×C4⋊C4—41no—
78C2×C11×C4⋊C4—41no—
79C2×(C2×D11)⋊C4—22no—
80C2×(C2×D11)⋊C4—22no—
81C2×(C2×D11)⋊C4—22no—
82C2×(C2×D11)⋊C4—22no—
83C2×(C2×D11)⋊C4—41no—
84C2×(C2×D11)⋊C4—41no—
85C2×(C2×D11)⋊C4—41no—
86C2×(C2×D11)⋊C4—41no—
87C2×(C2×D11)⋊C4—41no—
88C2×(C2×D11)⋊C4—41no—
89C2×(C2×D11)⋊C4—41no—
90C2×(C2×D11)⋊C4—41no—
91C2×(C2×D11)⋊C4—41no—
92C2×(C2×D11)⋊C4—41no—
93C2×(C2×D11)⋊C4—41no—
94C2×(C2×D11)⋊C4—41no—
95C2×(C2×D11)⋊C4—41no—
96C2×(C2×D11)⋊C4—41no—
97C2×(C2×D11)⋊C4C2×C414yes—
98C2×(C2×D11)⋊C4C2×C414yes—
99C2×(C2×D11)⋊C4C2×C414yes—
100C2×C4⋊Dic11—22no—
101C2×C4⋊Dic11—41no—
102C2×C4⋊Dic11—41no—
103C2×Dic11⋊C4—22no—
104C2×Dic11⋊C4—41no—
105C2×Dic11⋊C4—41no—
106C2×Dic11⋊C4—41no—
107C2×Dic11⋊C4—41no—
108C2×Dic11⋊C4—41no—
109C2×C4×Dic11—41no—
110C2×C4×Dic11—41no—
111C2×C4×Dic11D414yes—
112C11×#95—22no—
113C11×#95—22no—
114C11×#95—41no—
115C11×#95—41no—
116C11×#95—41no—
117C11×#95C2×C414yes—
118C11⋊#95—22no—
119C11⋊#95—22no—
120C11⋊#95—22no—
121C11⋊#95—22no—
122C11⋊#95—22no—
123C11⋊#95—41no—
124C11⋊#95—41no—
125C11⋊#95—41no—
126C11⋊#95—41no—
127C11⋊#95—41no—
128C11⋊#95—41no—
129C11⋊#95—41no—
130C11⋊#95—41no—
131C11⋊#95—41no—
132C11⋊#95C2×C414yes—
133C11⋊#95C2×C414yes—
134#14625—111nomaximal, Sylow
135C24×C11C2411yescharacteristic
136C23×D11—21no—
137C23×D11—21no—
138C23×D11—21no—
139C23×D11—21no—
140C23×D11—21no—
141C23×D11—21no—
142C23×D11—21no—
143C23×D11—21no—
144C23×D11—21no—
145C23×D11—21no—
146C23×D11—21no—
147C23×D11—21no—
148C23×D11—21no—
149C23×D11—21no—
150C23×D11C22×C412yes—
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×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×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11C22×C412yes—
197C22×C4×C11C22×C412yes—
198C22×C4×C11C22×C412yes—
199C22×C4×C11C2×D412yes—
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×Dic11C22×C412yes—
244C22×Dic11C22×C412yes—
245C22×Dic11C22×C412yes—
246C22×Dic11C2×D412yes—
247C22×Dic11C2×D412yes—
248C22×Dic11#4112yes—
249C2×Dic22—28no—
250C2×Dic22—44no—
251C2×Dic22—44no—
252C2×Dic22—44no—
253C2×Dic22—44no—
254C2×Dic22—44no—
255C2×Dic22—44no—
256C11×C4⋊C4—44no—
257(C2×D11)⋊C4—28no—
258(C2×D11)⋊C4—44no—
259(C2×D11)⋊C4—44no—
260(C2×D11)⋊C4—44no—
261(C2×D11)⋊C4—44no—
262(C2×D11)⋊C4—44no—
263(C2×D11)⋊C4—44no—
264C4⋊Dic11—44no—
265Dic11⋊C4—44no—
266Dic11⋊C4—44no—
267C4×Dic11—44no—
268C2×#393—111no—
269C2×#391—111no—
270C2×#388—111no—
271#1446—111no—
272#1444—111no—
273#1442—111no—
274#1442—111no—
275#1442—111no—
276#1442D1111yescharacteristic, complemented
277#1440—111no—
278#1440—111no—
279#1439—111no—
280#1439—111no—
281#1439—111no—
282#1434—111no—
283C23×C11C23×C411yescharacteristic
284C23×C11C22×D411yescharacteristic
285C23×C11C2×#4111yescharacteristic
286C23×C11H(5,𝔽2)11yescharacteristic
287C23×C11H(5,𝔽2)11yescharacteristic
288C23×C11H(5,𝔽2)11yescharacteristic
289C23×C11H(5,𝔽2)11yescharacteristic
290C23×C11H(5,𝔽2)11yescharacteristic
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
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—22no—
302C22×D11—22no—
303C22×D11—22no—
304C22×D11—22no—
305C22×D11—41no—
306C22×D11—41no—
307C22×D11—41no—
308C22×D11—41no—
309C22×D11—41no—
310C22×D11—41no—
311C22×D11—41no—
312C22×D11—41no—
313C22×D11—41no—
314C22×D11—41no—
315C22×D11—41no—
316C22×D11—41no—
317C22×D11—41no—
318C22×D11—41no—
319C22×D11—41no—
320C22×D11—41no—
321C22×D11—41no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—41no—
327C22×D11—41no—
328C22×D11—41no—
329C22×D11—41no—
330C22×D11—41no—
331C22×D11—41no—
332C22×D11—41no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
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—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
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×C4×C11—41no—
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—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×Dic11C4×D414yes—
431Dic22—416no—
432C23×Q8—111no—
433C22×C4⋊C4—111no—
434C22×C4⋊C4—111no—
435C22×C4⋊C4—111no—
436C22×C4⋊C4C2×D1111yescharacteristic
437C22×C22⋊C4—111no—
438C22×C22⋊C4—111no—
439C22×C22⋊C4—111no—
440C22×C22⋊C4—111no—
441C22×C22⋊C4—111no—
442C22×C22⋊C4—111no—
443C22×C22⋊C4—111no—
444C22×C42—111no—
445#393—118no—
446#391—224no—
447#388—224no—
448C2×#95—111no—
449C2×#95—111no—
450C2×#95—111no—
451C2×#95—111no—
452C2×#95—111no—
453C2×#95—111no—
454C2×#95—111no—
455C2×#95—111no—
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×#95C2×D1111yescharacteristic
465C2×#95C2×D1111yescharacteristic
466C2×#95C2×D1111yescharacteristic
467C2×#95C2×D1111yescharacteristic
468C2×#95C2×D1111yescharacteristic
469C2×#95C2×D1111yescharacteristic
470C22×C11C2×C4×D411yescharacteristic
471C22×C11#51811yescharacteristic
472C22×C11#51811yescharacteristic
473C22×C11#51911yescharacteristic
474C22×C11#52011yescharacteristic
475C22×C11#52011yescharacteristic
476C22×C11#52011yescharacteristic
477C22×C11#53411yescharacteristic
478C22×C11#53511yescharacteristic
479C22×C11#53511yescharacteristic
480C22×C11#53611yescharacteristic
481C22×C11#53611yescharacteristic
482C22×C11#53711yescharacteristic
483C22×C11#53811yescharacteristic
484C22×C11#53811yescharacteristic
485C22×C11#54111yescharacteristic
486C22×C11#54211yescharacteristic
487C22×C11#54211yescharacteristic
488C22×C11#54211yescharacteristic
489C22×C11H(3,𝔽4)11yescharacteristic
490C22×C11H(3,𝔽4)11yescharacteristic
491C22×C11#56211yescharacteristic
492C22×C11#56211yescharacteristic
493C22×C11#56211yescharacteristic
494C22×C11#56211yescharacteristic
495C22×C11#56211yescharacteristic
496C22×C11#56211yescharacteristic
497C22×C11#56211yescharacteristic
498C22×C11#56211yescharacteristic
499C22×C11#56311yescharacteristic
500C22×C11#56311yescharacteristic
501C22×C11#56311yescharacteristic
502C22×C11#56311yescharacteristic
503C22×C11#56311yescharacteristic
504C22×C11#56311yescharacteristic
505C2×D11—42no—
506C2×D11—42no—
507C2×D11—42no—
508C2×D11—42no—
509C2×D11—42no—
510C2×D11—42no—
511C2×D11—42no—
512C2×D11—81no—
513C2×D11—81no—
514C2×D11—81no—
515C2×D11—81no—
516C2×D11—81no—
517C2×D11—81no—
518C2×D11—81no—
519C2×D11—81no—
520C4×C11—42no—
521C4×C11—42no—
522C4×C11—42no—
523C4×C11—42no—
524C4×C11—81no—
525C4×C11—81no—
526C4×C11—81no—
527Dic11—24no—
528Dic11—42no—
529Dic11—42no—
530Dic11—42no—
531Dic11—81no—
532Dic11—81no—
533Dic11—81no—
534C25—111no—
535C22×Q8—114no—
536C22×Q8—222no—
537C22×Q8—222no—
538C22×Q8—441no—
539C22×Q8—441no—
540C22×Q8—441no—
541C22×Q8—441no—
542C23×C4—111no—
543C23×C4—111no—
544C23×C4—111no—
545C23×C4—111no—
546C23×C4—111no—
547C23×C4—111no—
548C23×C4—111no—
549C23×C4C22×D1111yescharacteristic
550C23×C4C22×D1111yescharacteristic
551C23×C4C22×D1111yescharacteristic
552C23×C4C22×D1111yescharacteristic
553C23×C4C22×D1111yescharacteristic
554C23×C4C22×D1111yescharacteristic
555C23×C4C22×D1111yescharacteristic
556C2×C4⋊C4—41no—
557C2×C4⋊C4—41no—
558C2×C4⋊C4—41no—
559C2×C4⋊C4—222no—
560C2×C4⋊C4—222no—
561C2×C4⋊C4—441no—
562C2×C4⋊C4—441no—
563C2×C4⋊C4—441no—
564C2×C4⋊C4—441no—
565C2×C4⋊C4—441no—
566C2×C4⋊C4—441no—
567C2×C4⋊C4—441no—
568C2×C22⋊C4—114no—
569C2×C22⋊C4—114no—
570C2×C22⋊C4—114no—
571C2×C22⋊C4—222no—
572C2×C22⋊C4—222no—
573C2×C22⋊C4—222no—
574C2×C22⋊C4—222no—
575C2×C22⋊C4—441no—
576C2×C22⋊C4—441no—
577C2×C22⋊C4—441no—
578C2×C22⋊C4—441no—
579C2×C22⋊C4—441no—
580C2×C22⋊C4—441no—
581C2×C22⋊C4—441no—
582C2×C22⋊C4—441no—
583C2×C22⋊C4—441no—
584C2×C22⋊C4—441no—
585C2×C22⋊C4—441no—
586C2×C22⋊C4—441no—
587C2×C22⋊C4—441no—
588C2×C22⋊C4—441no—
589C2×C42—114no—
590C2×C42—441no—
591C2×C42—441no—
592#95—22no—
593#95—22no—
594#95—41no—
595#95—41no—
596#95—41no—
597#95—114no—
598#95—114no—
599#95—222no—
600#95—222no—
601#95—222no—
602#95—222no—
603#95—222no—
604#95—441no—
605#95—441no—
606#95—441no—
607#95—441no—
608#95—441no—
609#95—441no—
610#95—441no—
611#95—441no—
612#95—441no—
613#95C4×D1114yes—
614C2×C11#232111yescharacteristic
615C2×C11#232311yescharacteristic
616C2×C11#232611yescharacteristic
617C2×C11#237811yescharacteristic
618C2×C11#237811yescharacteristic
619C2×C11#237911yescharacteristic
620C2×C11#237911yescharacteristic
621C2×C11#281411yescharacteristic
622C2×C11#281611yescharacteristic
623C2×C11#281911yescharacteristic
624C2×C11#282111yescharacteristic
625C2×C11#283111yescharacteristic
626C2×C11#283111yescharacteristic
627C2×C11#283211yescharacteristic
628C2×C11#283211yescharacteristic
629D11—82no—
630C24—112no—
631C24—221no—
632C24—221no—
633C24—221no—
634C24—221no—
635C24—221no—
636C24—221no—
637C24—221no—
638C24—221no—
639C24—221no—
640C24—221no—
641C24—221no—
642C24—221no—
643C24—221no—
644C24—221no—
645C24C23×D1111yescharacteristic
646C2×Q8—228no—
647C2×Q8—444no—
648C2×Q8—444no—
649C2×Q8—444no—
650C2×Q8—444no—
651C2×Q8—444no—
652C2×Q8—444no—
653C22×C4—21no—
654C22×C4—21no—
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—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—112no—
699C22×C4—112no—
700C22×C4—112no—
701C22×C4—112no—
702C22×C4—112no—
703C22×C4—112no—
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×C4—221no—
744C22×C4—221no—
745C22×C4—221no—
746C22×C4—221no—
747C22×C4C2×C4×D1112yes—
748C22×C4C2×C4×D1112yes—
749C22×C4C2×C4×D1112yes—
750C22×C4D4×D1112yes—
751C4⋊C4—44no—
752C4⋊C4—444no—
753C4⋊C4—444no—
754C4⋊C4—444no—
755C22⋊C4—228no—
756C22⋊C4—444no—
757C22⋊C4—444no—
758C22⋊C4—444no—
759C22⋊C4—444no—
760C22⋊C4—444no—
761C22⋊C4—444no—
762C42—444no—
763C11#1462511yescharacteristic, complemented, Sylow
764C23—222no—
765C23—222no—
766C23—222no—
767C23—222no—
768C23—222no—
769C23—222no—
770C23—222no—
771C23—441no—
772C23—441no—
773C23—441no—
774C23—441no—
775C23—441no—
776C23—441no—
777C23—441no—
778C23—441no—
779C23—441no—
780C23—441no—
781C23—441no—
782C23—441no—
783C23—441no—
784C23—441no—
785C23—441no—
786C23—441no—
787C23—441no—
788C23—441no—
789C23—441no—
790C23—441no—
791C23—441no—
792C23—441no—
793C23—441no—
794C23—441no—
795C23—441no—
796C23—441no—
797C23—441no—
798C23—441no—
799C23C22×C4×D1111yescharacteristic
800C23C2×D4×D1111yescharacteristic
801C23#6703711yescharacteristic
802C23#6703711yescharacteristic
803C23#6703711yescharacteristic
804C23#6704011yescharacteristic
805C23#6704011yescharacteristic
806C23#41×D1111yescharacteristic
807C23#6704211yescharacteristic
808C23#6704211yescharacteristic
809C23#6704211yescharacteristic
810C23#6704211yescharacteristic
811C23#6704311yescharacteristic
812C23#6704311yescharacteristic
813C23#6704311yescharacteristic
814Q8—4416no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
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—114no—
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—222no—
878C2×C4—222no—
879C2×C4—222no—
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—
913C22—442no—
914C22—442no—
915C22—442no—
916C22—442no—
917C22—442no—
918C22—442no—
919C22—442no—
920C22—881no—
921C22—881no—
922C22—881no—
923C22—881no—
924C22—881no—
925C22—881no—
926C22—881no—
927C22—881no—
928C22#1062303511yescharacteristic
929C22#1062305211yescharacteristic
930C22#1062305411yescharacteristic
931C22C4×D4×D1111yescharacteristic
932C22#1062307611yescharacteristic
933C22#1062307711yescharacteristic
934C22#1062310311yescharacteristic
935C22#1062312511yescharacteristic
936C22#1062312811yescharacteristic
937C22#1062313811yescharacteristic
938C22#1062313811yescharacteristic
939C22#1062317111yescharacteristic
940C22#1062317711yescharacteristic
941C22#1062317711yescharacteristic
942C22#1062317811yescharacteristic
943C22#1062317811yescharacteristic
944C22#1062317911yescharacteristic
945C22#1062318411yescharacteristic
946C22#1062319811yescharacteristic
947C22#1062319811yescharacteristic
948C22#1062319811yescharacteristic
949C22#1062320011yescharacteristic
950C22#1062320911yescharacteristic
951C22#1062321411yescharacteristic
952C22#1062321511yescharacteristic
953C22#1062322711yescharacteristic
954C22#1062323011yescharacteristic
955C22#1062323011yescharacteristic
956C22#1062323111yescharacteristic
957C22#1062323111yescharacteristic
958C22#1062323511yescharacteristic
959C22#1062324111yescharacteristic
960C22#1062324311yescharacteristic
961C22#1062324311yescharacteristic
962C22#1062325511yescharacteristic
963C4—42no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—81no—
968C4—81no—
969C4—81no—
970C4—224no—
971C4—442no—
972C4—442no—
973C4—442no—
974C4—881no—
975C4—881no—
976C4—881no—
977C2—882no—
978C2#1307127811yescharacteristic
979C2#1307129311yescharacteristic
980C2#1307132511yescharacteristic
981C2#1307178011yescharacteristic
982C2#1307178111yescharacteristic
983C2#1307178711yescharacteristic
984C2#1307178911yescharacteristic
985C2#1307663511yescharacteristic
986C2#1307664911yescharacteristic
987C2#1307666011yescharacteristic
988C2#1307667611yescharacteristic
989C2#1307676911yescharacteristic
990C2#1307677111yescharacteristic
991C2#1307678411yescharacteristic
992C2#1307678511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1442C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1442D11
hypocenterC11#14625
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
2. C2×#10622259C2semidirect
4. #13066886C2semidirect
5. #13066879C2semidirect
6. #13066873C2semidirect
7. #13066872C2semidirect
8. #13066871C2semidirect
14. #13066842C2semidirect
15. C11×#1442C2semidirect
51. #10622286C4semidirect
276. #1442D11semidirect
763. C11#14625semidirect

Maximal subgroups

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

subgroupindex
C2×#106222862
C2×#106222592
C2×#106222832
#130668862
#130668792
#130668732
#130668722
#130668712
#130668642
#130668602
#130668582
#130668422
C11×#14422
#1462511