Finite Group Databasebeta

← #14684549

Subgroups — #14684549

Order 2816.

1326 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622607C211yesmaximal, characteristic
2C2×#10622282C211yesmaximal, characteristic
3C2×#10622265C211yesmaximal, characteristic, complemented
4#13066885C211yesmaximal, characteristic, complemented
5#13066879C211yesmaximal, characteristic, complemented
6#13066877C211yesmaximal, characteristic, complemented
7#13066870C211yesmaximal, characteristic, complemented
8#13066868C211yesmaximal, characteristic, complemented
9#13066864C211yesmaximal, characteristic
10#13066864C211yesmaximal, characteristic
11#13066862C211yesmaximal, characteristic
12#13066860C211yesmaximal, characteristic
13#13066858C211yesmaximal, characteristic
14#13066845C211yesmaximal, characteristic, complemented
15C11×#1441C211yesmaximal, characteristic, complemented
16C22×C11×C4⋊C4C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
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#10622607C418yescomplemented
52#10622282—24no—
53#10622265—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
69C2×C11×C4⋊C4—41no—
70C2×C11×C4⋊C4—41no—
71C2×C11×C4⋊C4—41no—
72C2×C11×C4⋊C4—41no—
73C2×C11×C4⋊C4—41no—
74C2×C11×C4⋊C4C2×C414yes—
75C2×(C2×D11)⋊C4—22no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4—22no—
78C2×(C2×D11)⋊C4—22no—
79C2×(C2×D11)⋊C4—41no—
80C2×(C2×D11)⋊C4—41no—
81C2×(C2×D11)⋊C4—41no—
82C2×(C2×D11)⋊C4—41no—
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)⋊C4C2×C414yes—
94C2×(C2×D11)⋊C4C2×C414yes—
95C2×(C2×D11)⋊C4C2×C414yes—
96C2×C4⋊Dic11—22no—
97C2×C4⋊Dic11—41no—
98C2×C4⋊Dic11—41no—
99C2×C4⋊Dic11—41no—
100C2×C4⋊Dic11—41no—
101C2×C4⋊Dic11C2×C414yes—
102C2×Dic11⋊C4—22no—
103C2×Dic11⋊C4—22no—
104C2×Dic11⋊C4—22no—
105C2×Dic11⋊C4—22no—
106C2×Dic11⋊C4—41no—
107C2×Dic11⋊C4—41no—
108C2×Dic11⋊C4—41no—
109C2×Dic11⋊C4—41no—
110C2×Dic11⋊C4C2×C414yes—
111C2×C4×Dic11—41no—
112C2×C4×Dic11—41no—
113C2×C4×Dic11D414yes—
114C11×#95—22no—
115C11×#95—22no—
116C11×#95—41no—
117C11×#95—41no—
118C11×#95—41no—
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⋊#95—41no—
133C11⋊#95C2×C414yes—
134#14633—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×C11C22×C412yes—
196C22×C4×C11C22×C412yes—
197C22×C4×C11C22×C412yes—
198C22×C4×C11C2×D412yes—
199C22×C4×C11#4112yes—
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×Dic11C22×C412yes—
245C22×Dic11C22×C412yes—
246C22×Dic11C22×C412yes—
247C22×Dic11C2×D412yes—
248C22×Dic11C2×D412yes—
249C11×C4⋊C4—44no—
250C11×C4⋊C4—44no—
251(C2×D11)⋊C4—28no—
252(C2×D11)⋊C4—44no—
253(C2×D11)⋊C4—44no—
254(C2×D11)⋊C4—44no—
255(C2×D11)⋊C4—44no—
256(C2×D11)⋊C4—44no—
257(C2×D11)⋊C4—44no—
258C4⋊Dic11—44no—
259C4⋊Dic11—44no—
260Dic11⋊C4—28no—
261Dic11⋊C4—44no—
262Dic11⋊C4—44no—
263C4×Dic11—44no—
264C2×#396—111no—
265C2×#388—111no—
266C2×#387—111no—
267#1445—111no—
268#1444—111no—
269#1443—111no—
270#1441—111no—
271#1441—111no—
272#1441D1111yescharacteristic, complemented
273#1440—111no—
274#1440—111no—
275#1439—111no—
276#1439—111no—
277#1439—111no—
278C4⋊#95—111no—
279C23×C11C23×C411yescharacteristic
280C23×C11C22×D411yescharacteristic
281C23×C11C2×#4111yescharacteristic
282C23×C11H(5,𝔽2)11yescharacteristic
283C23×C11H(5,𝔽2)11yescharacteristic
284C23×C11H(5,𝔽2)11yescharacteristic
285C23×C11H(5,𝔽2)11yescharacteristic
286C23×C11H(5,𝔽2)11yescharacteristic
287C23×C11H(5,𝔽2)11yescharacteristic
288C23×C11H(5,𝔽2)11yescharacteristic
289C23×C112−1+411yescharacteristic
290C23×C112−1+411yescharacteristic
291C23×C112−1+411yescharacteristic
292C23×C112−1+411yescharacteristic
293C23×C112−1+411yescharacteristic
294C22×D11—22no—
295C22×D11—22no—
296C22×D11—22no—
297C22×D11—22no—
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—41no—
302C22×D11—41no—
303C22×D11—41no—
304C22×D11—41no—
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—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
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—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
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×C11C4×D414yes—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
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—41no—
394C2×Dic11—41no—
395C2×Dic11—41no—
396C2×Dic11—41no—
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—
427C22×C4⋊C4—111no—
428C22×C4⋊C4—111no—
429C22×C4⋊C4—111no—
430C22×C4⋊C4—111no—
431C22×C4⋊C4—111no—
432C22×C4⋊C4C2×D1111yescharacteristic
433C22×C4⋊C4C2×D1111yescharacteristic
434C22×C22⋊C4—111no—
435C22×C22⋊C4—111no—
436C22×C22⋊C4—111no—
437C22×C22⋊C4—111no—
438C22×C22⋊C4—111no—
439C22×C22⋊C4—111no—
440C22×C22⋊C4—111no—
441C22×C42—111no—
442#396—118no—
443#388—224no—
444#387—224no—
445C2×#95—111no—
446C2×#95—111no—
447C2×#95—111no—
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×#95C2×D1111yescharacteristic
461C2×#95C2×D1111yescharacteristic
462C2×#95C2×D1111yescharacteristic
463C2×#95C2×D1111yescharacteristic
464C2×#95C2×D1111yescharacteristic
465C22×C11C2×C4×D411yescharacteristic
466C22×C11#51811yescharacteristic
467C22×C11#51811yescharacteristic
468C22×C11#51911yescharacteristic
469C22×C11#52011yescharacteristic
470C22×C11#52011yescharacteristic
471C22×C11#52011yescharacteristic
472C22×C11#53411yescharacteristic
473C22×C11#53511yescharacteristic
474C22×C11#53611yescharacteristic
475C22×C11#53711yescharacteristic
476C22×C11#53711yescharacteristic
477C22×C11#53711yescharacteristic
478C22×C11#53811yescharacteristic
479C22×C11#53911yescharacteristic
480C22×C11#54011yescharacteristic
481C22×C11#54111yescharacteristic
482C22×C11#54211yescharacteristic
483C22×C11#54211yescharacteristic
484C22×C11#56011yescharacteristic
485C22×C11#56011yescharacteristic
486C22×C11#56011yescharacteristic
487C22×C11#56211yescharacteristic
488C22×C11#56211yescharacteristic
489C22×C11#56211yescharacteristic
490C22×C11#56211yescharacteristic
491C22×C11#56211yescharacteristic
492C22×C11#56211yescharacteristic
493C22×C11#56311yescharacteristic
494C22×C11#56311yescharacteristic
495C22×C11#56311yescharacteristic
496C22×C11#56311yescharacteristic
497C22×C11#56311yescharacteristic
498C22×C11#56311yescharacteristic
499C22×C11#56311yescharacteristic
500C2×D11—42no—
501C2×D11—42no—
502C2×D11—42no—
503C2×D11—42no—
504C2×D11—42no—
505C2×D11—42no—
506C2×D11—42no—
507C2×D11—81no—
508C2×D11—81no—
509C2×D11—81no—
510C2×D11—81no—
511C2×D11—81no—
512C2×D11—81no—
513C2×D11—81no—
514C2×D11—81no—
515C4×C11—24no—
516C4×C11—42no—
517C4×C11—42no—
518C4×C11—81no—
519C4×C11—81no—
520C4×C11—81no—
521C4×C11—81no—
522Dic11—42no—
523Dic11—42no—
524Dic11—42no—
525Dic11—42no—
526Dic11—42no—
527Dic11—81no—
528Dic11—81no—
529C25—111no—
530C23×C4—111no—
531C23×C4—111no—
532C23×C4—111no—
533C23×C4—111no—
534C23×C4—111no—
535C23×C4—111no—
536C23×C4—111no—
537C23×C4C22×D1111yescharacteristic
538C23×C4C22×D1111yescharacteristic
539C23×C4C22×D1111yescharacteristic
540C23×C4C22×D1111yescharacteristic
541C23×C4C22×D1111yescharacteristic
542C23×C4C22×D1111yescharacteristic
543C23×C4C22×D1111yescharacteristic
544C2×C4⋊C4—41no—
545C2×C4⋊C4—41no—
546C2×C4⋊C4—41no—
547C2×C4⋊C4—41no—
548C2×C4⋊C4—41no—
549C2×C4⋊C4—114no—
550C2×C4⋊C4—114no—
551C2×C4⋊C4—222no—
552C2×C4⋊C4—222no—
553C2×C4⋊C4—222no—
554C2×C4⋊C4—222no—
555C2×C4⋊C4—222no—
556C2×C4⋊C4—441no—
557C2×C4⋊C4—441no—
558C2×C4⋊C4—441no—
559C2×C4⋊C4—441no—
560C2×C4⋊C4—441no—
561C2×C4⋊C4—441no—
562C2×C4⋊C4—441no—
563C2×C4⋊C4—441no—
564C2×C4⋊C4C4×D1114yes—
565C2×C22⋊C4—114no—
566C2×C22⋊C4—114no—
567C2×C22⋊C4—114no—
568C2×C22⋊C4—222no—
569C2×C22⋊C4—222no—
570C2×C22⋊C4—222no—
571C2×C22⋊C4—222no—
572C2×C22⋊C4—441no—
573C2×C22⋊C4—441no—
574C2×C22⋊C4—441no—
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×C42—114no—
587C2×C42—441no—
588C2×C42—441no—
589#95—22no—
590#95—22no—
591#95—41no—
592#95—41no—
593#95—41no—
594#95—114no—
595#95—222no—
596#95—222no—
597#95—222no—
598#95—222no—
599#95—441no—
600#95—441no—
601#95—441no—
602#95—441no—
603#95—441no—
604#95—441no—
605#95—441no—
606#95—441no—
607#95—441no—
608#95—441no—
609C2×C11#232311yescharacteristic
610C2×C11#232411yescharacteristic
611C2×C11#232511yescharacteristic
612C2×C11#237711yescharacteristic
613C2×C11#237811yescharacteristic
614C2×C11#237811yescharacteristic
615C2×C11#238311yescharacteristic
616C2×C11#281311yescharacteristic
617C2×C11#281411yescharacteristic
618C2×C11#282011yescharacteristic
619C2×C11#282311yescharacteristic
620C2×C11#282911yescharacteristic
621C2×C11#283111yescharacteristic
622C2×C11#283611yescharacteristic
623C2×C11#283811yescharacteristic
624D11—82no—
625C24—112no—
626C24—221no—
627C24—221no—
628C24—221no—
629C24—221no—
630C24—221no—
631C24—221no—
632C24—221no—
633C24—221no—
634C24—221no—
635C24—221no—
636C24—221no—
637C24—221no—
638C24—221no—
639C24—221no—
640C24C23×D1111yescharacteristic
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—21no—
651C22×C4—21no—
652C22×C4—21no—
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—112no—
686C22×C4—112no—
687C22×C4—112no—
688C22×C4—112no—
689C22×C4—112no—
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×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×C4C2×C4×D1112yes—
735C22×C4C2×C4×D1112yes—
736C22×C4C2×C4×D1112yes—
737C22×C4D4×D1112yes—
738C22×C4#434312yes—
739C4⋊C4—44no—
740C4⋊C4—44no—
741C4⋊C4—228no—
742C4⋊C4—444no—
743C4⋊C4—444no—
744C4⋊C4—444no—
745C4⋊C4—444no—
746C22⋊C4—228no—
747C22⋊C4—444no—
748C22⋊C4—444no—
749C22⋊C4—444no—
750C22⋊C4—444no—
751C22⋊C4—444no—
752C22⋊C4—444no—
753C42—444no—
754C11#1463311yescharacteristic, complemented, Sylow
755C23—222no—
756C23—222no—
757C23—222no—
758C23—222no—
759C23—222no—
760C23—222no—
761C23—222no—
762C23—441no—
763C23—441no—
764C23—441no—
765C23—441no—
766C23—441no—
767C23—441no—
768C23—441no—
769C23—441no—
770C23—441no—
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—
790C23C22×C4×D1111yescharacteristic
791C23C2×D4×D1111yescharacteristic
792C23#6703711yescharacteristic
793C23#6703711yescharacteristic
794C23#6703711yescharacteristic
795C23#6703711yescharacteristic
796C23C2×#434311yescharacteristic
797C23#6704011yescharacteristic
798C23#6704011yescharacteristic
799C23#6704211yescharacteristic
800C23#6704211yescharacteristic
801C23#6704211yescharacteristic
802C23#6704311yescharacteristic
803C23#6704311yescharacteristic
804C23#6704311yescharacteristic
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
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—222no—
854C2×C4—222no—
855C2×C4—222no—
856C2×C4—222no—
857C2×C4—222no—
858C2×C4—222no—
859C2×C4—222no—
860C2×C4—222no—
861C2×C4—222no—
862C2×C4—222no—
863C2×C4—222no—
864C2×C4—222no—
865C2×C4—222no—
866C2×C4—222no—
867C2×C4—222no—
868C2×C4—441no—
869C2×C4—441no—
870C2×C4—441no—
871C2×C4—441no—
872C2×C4—441no—
873C2×C4—441no—
874C2×C4—441no—
875C2×C4—441no—
876C2×C4—441no—
877C2×C4—441no—
878C2×C4—441no—
879C2×C4—441no—
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#6694614yes—
903C22—442no—
904C22—442no—
905C22—442no—
906C22—442no—
907C22—442no—
908C22—442no—
909C22—442no—
910C22—881no—
911C22—881no—
912C22—881no—
913C22—881no—
914C22—881no—
915C22—881no—
916C22—881no—
917C22—881no—
918C22#1062301711yescharacteristic
919C22C2×#6694611yescharacteristic
920C22#1062305411yescharacteristic
921C22#1062307611yescharacteristic
922C22#1062307711yescharacteristic
923C22#1062310311yescharacteristic
924C22#1062310511yescharacteristic
925C22#1062312611yescharacteristic
926C22#1062312811yescharacteristic
927C22#1062313611yescharacteristic
928C22#1062313811yescharacteristic
929C22#1062313911yescharacteristic
930C22#1062315111yescharacteristic
931C22#1062315211yescharacteristic
932C22#1062315911yescharacteristic
933C22#1062316011yescharacteristic
934C22#1062317511yescharacteristic
935C22#1062317611yescharacteristic
936C22#1062317711yescharacteristic
937C22#1062317711yescharacteristic
938C22#1062317711yescharacteristic
939C22#1062317811yescharacteristic
940C22#1062319711yescharacteristic
941C22#1062319811yescharacteristic
942C22#1062319811yescharacteristic
943C22#1062321511yescharacteristic
944C22#1062322811yescharacteristic
945C22#1062322911yescharacteristic
946C22#1062323011yescharacteristic
947C22#1062323111yescharacteristic
948C22#1062324311yescharacteristic
949C22#1062324311yescharacteristic
950C22#1062326411yescharacteristic
951C22#1062326411yescharacteristic
952C22#1062326611yescharacteristic
953C4—24no—
954C4—42no—
955C4—42no—
956C4—81no—
957C4—81no—
958C4—81no—
959C4—81no—
960C4—442no—
961C4—442no—
962C4—442no—
963C4—442no—
964C4—442no—
965C4—881no—
966C4—881no—
967C2—882no—
968C2#1307129611yescharacteristic
969C2#1307130711yescharacteristic
970C2#1307131611yescharacteristic
971C2#1307177411yescharacteristic
972C2#1307177711yescharacteristic
973C2#1307178111yescharacteristic
974C2#1307180611yescharacteristic
975C2#1307662311yescharacteristic
976C2#1307663611yescharacteristic
977C2#1307666511yescharacteristic
978C2#1307668911yescharacteristic
979C2#1307675411yescharacteristic
980C2#1307677811yescharacteristic
981C2#1307682111yescharacteristic
982C2#1307685111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1441C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1441D11
hypocenterC11#14633
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
3. C2×#10622265C2semidirect
4. #13066885C2semidirect
5. #13066879C2semidirect
6. #13066877C2semidirect
7. #13066870C2semidirect
8. #13066868C2semidirect
14. #13066845C2semidirect
15. C11×#1441C2semidirect
51. #10622607C4semidirect
272. #1441D11semidirect
754. C11#14633semidirect

Maximal subgroups

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

subgroupindex
C2×#106226072
C2×#106222822
C2×#106222652
#130668852
#130668792
#130668772
#130668702
#130668682
#130668642
#130668622
#130668602
#130668582
#130668452
C11×#14412
#1463311