Finite Group Databasebeta

← #14684543

Subgroups — #14684543

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×#10622564C211yesmaximal, characteristic
2C2×#10622594C211yesmaximal, characteristic, complemented
3#13066884C211yesmaximal, characteristic, complemented
4#13066881C211yesmaximal, characteristic, complemented
5#13066878C211yesmaximal, characteristic, complemented
6#13066869C211yesmaximal, characteristic, complemented
7#13066869C211yesmaximal, characteristic, complemented
8#13066869C211yesmaximal, characteristic, complemented
9#13066865C211yesmaximal, characteristic
10#13066865C211yesmaximal, characteristic
11#13066861C211yesmaximal, characteristic
12#13066861C211yesmaximal, characteristic
13#13066861C211yesmaximal, characteristic
14#13066845C211yesmaximal, characteristic, complemented
15C2×C11×#396C211yesmaximal, characteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×C4⋊Dic11C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C11×#396C418yescomplemented
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
52#10622594—24no—
53#10622564—24no—
54C25×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—41no—
72C2×C11×C4⋊C4—41no—
73C2×C11×C4⋊C4—41no—
74C2×C11×C4⋊C4—41no—
75C2×C11×C4⋊C4C2×C414yes—
76C2×C11×C4⋊C4C2×C414yes—
77C2×C11×C4⋊C4C2×C414yes—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—41no—
81C2×C11×C22⋊C4—41no—
82C2×C11×C22⋊C4—41no—
83C2×C11×C22⋊C4—41no—
84C2×C11×C22⋊C4C2×C414yes—
85C2×C11×C22⋊C4C2×C414yes—
86C2×C11×C22⋊C4C2×C414yes—
87C2×C22⋊Dic11—22no—
88C2×C22⋊Dic11—22no—
89C2×C22⋊Dic11—41no—
90C2×C22⋊Dic11—41no—
91C2×C22⋊Dic11—41no—
92C2×C22⋊Dic11—41no—
93C2×C22⋊Dic11—41no—
94C2×C22⋊Dic11—41no—
95C2×C22⋊Dic11—41no—
96C2×C22⋊Dic11—41no—
97C2×C22⋊Dic11—41no—
98C2×C22⋊Dic11—41no—
99C2×C4⋊Dic11—22no—
100C2×C4⋊Dic11—22no—
101C2×C4⋊Dic11—22no—
102C2×C4⋊Dic11—41no—
103C2×C4⋊Dic11—41no—
104C2×C4⋊Dic11—41no—
105C2×C4⋊Dic11—41no—
106C2×C4⋊Dic11—41no—
107C2×C4⋊Dic11—41no—
108C2×C4⋊Dic11—41no—
109C2×C4⋊Dic11—41no—
110C2×C4⋊Dic11—41no—
111C2×C4×Dic11—41no—
112C2×C4×Dic11—41no—
113C2×C4×Dic11D414yes—
114C11×#95C2×C414yes—
115C11⋊#95—22no—
116C11⋊#95—22no—
117C11⋊#95—22no—
118C11⋊#95—22no—
119C11⋊#95—22no—
120C11⋊#95—22no—
121C11⋊#95—41no—
122C11⋊#95—41no—
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⋊#95—41no—
134#14633—111nomaximal, Sylow
135C24×C11—21no—
136C24×C11—21no—
137C24×C11—21no—
138C24×C11—21no—
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×C11C22×C412yes—
150C24×C11C2411yescharacteristic
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×C11C22×C412yes—
186C22×C4×C11C22×C412yes—
187C22×C4×C11C22×C412yes—
188C22×C4×C11C22×C412yes—
189C22×C4×C11C22×C412yes—
190C22×C4×C11C22×C412yes—
191C22×C4×C11C2×D412yes—
192C22×C4×C11#4112yes—
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×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—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11C2×D412yes—
248C22×Dic11C2×D412yes—
249C11×C4⋊C4—28no—
250C11×C4⋊C4—44no—
251C11×C4⋊C4—44no—
252C11×C22⋊C4—28no—
253C11×C22⋊C4—44no—
254C11×C22⋊C4—44no—
255C22⋊Dic11—44no—
256C22⋊Dic11—44no—
257C22⋊Dic11—44no—
258C22⋊Dic11—44no—
259C4⋊Dic11—44no—
260C4⋊Dic11—44no—
261C4⋊Dic11—44no—
262C4⋊Dic11—44no—
263C4×Dic11—44no—
264C2×#396D1111yescharacteristic
265C2×#388—111no—
266C2×#387—111no—
267#1445—111no—
268#1444—111no—
269#1443—111no—
270#1441—111no—
271#1441—111no—
272#1441—111no—
273#1440—111no—
274#1440—111no—
275#1439—111no—
276#1439—111no—
277#1439—111no—
278C4⋊#95—111no—
279C23×C11—22no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—41no—
287C23×C11—41no—
288C23×C11—41no—
289C23×C11—41no—
290C23×C11—41no—
291C23×C11—41no—
292C23×C11—41no—
293C23×C11—41no—
294C23×C11—41no—
295C23×C11—41no—
296C23×C11—41no—
297C23×C11—41no—
298C23×C11—41no—
299C23×C11—41no—
300C23×C11—41no—
301C23×C11—41no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11C23×C411yescharacteristic
315C23×C11C22×D411yescharacteristic
316C23×C11C2×#4111yescharacteristic
317C23×C11H(5,𝔽2)11yescharacteristic
318C23×C11H(5,𝔽2)11yescharacteristic
319C23×C11H(5,𝔽2)11yescharacteristic
320C23×C11H(5,𝔽2)11yescharacteristic
321C23×C11H(5,𝔽2)11yescharacteristic
322C23×C11H(5,𝔽2)11yescharacteristic
323C23×C11H(5,𝔽2)11yescharacteristic
324C23×C112−1+411yescharacteristic
325C23×C112−1+411yescharacteristic
326C23×C112−1+411yescharacteristic
327C23×C112−1+411yescharacteristic
328C23×C112−1+411yescharacteristic
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—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—22no—
349C2×C4×C11—22no—
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×C11C4×D414yes—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
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×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×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⋊C4C2×D1111yescharacteristic
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⋊C4C2×D1111yescharacteristic
439C22×C22⋊C4C2×D1111yescharacteristic
440C22×C22⋊C4C2×D1111yescharacteristic
441C22×C42—111no—
442#396Dic1118yescomplemented
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×#95—111no—
461C2×#95—111no—
462C2×#95—111no—
463C2×#95—111no—
464C2×#95C2×D1111yescharacteristic
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11—81no—
473C22×C11—81no—
474C22×C11—81no—
475C22×C11—81no—
476C22×C11—81no—
477C22×C11—81no—
478C22×C11—81no—
479C22×C11—81no—
480C22×C11C2×C4×D411yescharacteristic
481C22×C11#51811yescharacteristic
482C22×C11#51811yescharacteristic
483C22×C11#51911yescharacteristic
484C22×C11#52011yescharacteristic
485C22×C11#52011yescharacteristic
486C22×C11#52011yescharacteristic
487C22×C11#53411yescharacteristic
488C22×C11#53511yescharacteristic
489C22×C11#53611yescharacteristic
490C22×C11#53711yescharacteristic
491C22×C11#53711yescharacteristic
492C22×C11#53711yescharacteristic
493C22×C11#53811yescharacteristic
494C22×C11#53911yescharacteristic
495C22×C11#54011yescharacteristic
496C22×C11#54111yescharacteristic
497C22×C11#54211yescharacteristic
498C22×C11#54211yescharacteristic
499C22×C11#56011yescharacteristic
500C22×C11#56011yescharacteristic
501C22×C11#56011yescharacteristic
502C22×C11#56211yescharacteristic
503C22×C11#56211yescharacteristic
504C22×C11#56211yescharacteristic
505C22×C11#56211yescharacteristic
506C22×C11#56211yescharacteristic
507C22×C11#56211yescharacteristic
508C22×C11#56311yescharacteristic
509C22×C11#56311yescharacteristic
510C22×C11#56311yescharacteristic
511C22×C11#56311yescharacteristic
512C22×C11#56311yescharacteristic
513C22×C11#56311yescharacteristic
514C22×C11#56311yescharacteristic
515C4×C11—24no—
516C4×C11—42no—
517C4×C11—42no—
518C4×C11—42no—
519C4×C11—42no—
520C4×C11—42no—
521Dic11—42no—
522Dic11—42no—
523Dic11—81no—
524Dic11—81no—
525Dic11—81no—
526Dic11—81no—
527Dic11—81no—
528Dic11—81no—
529C25C22×D1111yescharacteristic
530C23×C4—111no—
531C23×C4—111no—
532C23×C4—111no—
533C23×C4—111no—
534C23×C4—111no—
535C23×C4—111no—
536C23×C4—111no—
537C23×C4—111no—
538C23×C4C22×D1111yescharacteristic
539C23×C4C22×D1111yescharacteristic
540C23×C4C22×D1111yescharacteristic
541C23×C4C22×D1111yescharacteristic
542C23×C4C22×D1111yescharacteristic
543C23×C4C22×D1111yescharacteristic
544C2×C4⋊C4—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—41no—
547C2×C4⋊C4—41no—
548C2×C4⋊C4—41no—
549C2×C4⋊C4—41no—
550C2×C4⋊C4—222no—
551C2×C4⋊C4—222no—
552C2×C4⋊C4—222no—
553C2×C4⋊C4—441no—
554C2×C4⋊C4—441no—
555C2×C4⋊C4—441no—
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⋊C4C2×Dic1114yes—
563C2×C4⋊C4C2×Dic1114yes—
564C2×C4⋊C4C2×Dic1114yes—
565C2×C22⋊C4—22no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—41no—
568C2×C22⋊C4—41no—
569C2×C22⋊C4—41no—
570C2×C22⋊C4—41no—
571C2×C22⋊C4—222no—
572C2×C22⋊C4—222no—
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⋊C4C2×Dic1114yes—
584C2×C22⋊C4C2×Dic1114yes—
585C2×C22⋊C4C2×Dic1114yes—
586C2×C42—114no—
587C2×C42—441no—
588C2×C42—441no—
589#95—222no—
590#95—222no—
591#95—222no—
592#95—222no—
593#95—222no—
594#95—222no—
595#95—441no—
596#95—441no—
597#95—441no—
598#95—441no—
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#95C2×Dic1114yes—
609C2×C11—82no—
610C2×C11#232311yescharacteristic
611C2×C11#232411yescharacteristic
612C2×C11#232511yescharacteristic
613C2×C11#237711yescharacteristic
614C2×C11#237811yescharacteristic
615C2×C11#237811yescharacteristic
616C2×C11#238311yescharacteristic
617C2×C11#281311yescharacteristic
618C2×C11#281411yescharacteristic
619C2×C11#282011yescharacteristic
620C2×C11#282311yescharacteristic
621C2×C11#282911yescharacteristic
622C2×C11#283111yescharacteristic
623C2×C11#283611yescharacteristic
624C2×C11#283811yescharacteristic
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24C22×Dic1112yes—
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—112no—
676C22×C4—112no—
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×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×C4D4×D1112yes—
732C22×C4#434112yes—
733C22×C4C22×Dic1112yes—
734C22×C4C22×Dic1112yes—
735C22×C4C22×Dic1112yes—
736C22×C4C22×Dic1112yes—
737C22×C4C22×Dic1112yes—
738C22×C4C22×Dic1112yes—
739C4⋊C4—28no—
740C4⋊C4—44no—
741C4⋊C4—44no—
742C4⋊C4—444no—
743C4⋊C4—444no—
744C4⋊C4—444no—
745C4⋊C4—444no—
746C22⋊C4—28no—
747C22⋊C4—44no—
748C22⋊C4—44no—
749C22⋊C4—444no—
750C22⋊C4—444no—
751C22⋊C4—444no—
752C22⋊C4—444no—
753C42—444no—
754C11#1463311yescharacteristic, complemented, Sylow
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23C2×D4×D1111yescharacteristic
791C23C2×#434111yescharacteristic
792C23#6703711yescharacteristic
793C23#6703711yescharacteristic
794C23#6703711yescharacteristic
795C23#6703711yescharacteristic
796C23#6704011yescharacteristic
797C23#6704011yescharacteristic
798C23#6704211yescharacteristic
799C23#6704211yescharacteristic
800C23#6704211yescharacteristic
801C23#6704311yescharacteristic
802C23#6704311yescharacteristic
803C23#6704311yescharacteristic
804C23C23×Dic1111yescharacteristic
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—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—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—222no—
847C2×C4—222no—
848C2×C4—222no—
849C2×C4—222no—
850C2×C4—222no—
851C2×C4—222no—
852C2×C4—441no—
853C2×C4—441no—
854C2×C4—441no—
855C2×C4—441no—
856C2×C4—441no—
857C2×C4—441no—
858C2×C4—441no—
859C2×C4—441no—
860C2×C4—441no—
861C2×C4—441no—
862C2×C4—441no—
863C2×C4—441no—
864C2×C4—441no—
865C2×C4—441no—
866C2×C4—441no—
867C2×C4—441no—
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×C4D4×Dic1114yes—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22#1062312811yescharacteristic
919C22#1062313311yescharacteristic
920C22#1062313411yescharacteristic
921C22#1062313611yescharacteristic
922C22#1062313811yescharacteristic
923C22#1062313911yescharacteristic
924C22#1062314811yescharacteristic
925C22#1062315011yescharacteristic
926C22#1062315111yescharacteristic
927C22#1062315111yescharacteristic
928C22#1062315211yescharacteristic
929C22#1062315211yescharacteristic
930C22#1062315611yescharacteristic
931C22#1062315911yescharacteristic
932C22#1062316011yescharacteristic
933C22#1062317411yescharacteristic
934C22#1062317711yescharacteristic
935C22#1062317711yescharacteristic
936C22#1062317711yescharacteristic
937C22#1062317711yescharacteristic
938C22#1062317811yescharacteristic
939C22#1062317811yescharacteristic
940C22#1062317811yescharacteristic
941C22#1062317811yescharacteristic
942C22#1062324211yescharacteristic
943C22#1062324311yescharacteristic
944C22#1062324311yescharacteristic
945C22#1062324311yescharacteristic
946C22C2×D4×Dic1111yescharacteristic
947C22#1062332911yescharacteristic
948C22#1062332911yescharacteristic
949C22#1062334311yescharacteristic
950C22#1062335811yescharacteristic
951C22#1062335811yescharacteristic
952C22#1062335811yescharacteristic
953C4—24no—
954C4—42no—
955C4—42no—
956C4—42no—
957C4—42no—
958C4—42no—
959C4—442no—
960C4—442no—
961C4—881no—
962C4—881no—
963C4—881no—
964C4—881no—
965C4—881no—
966C4—881no—
967C2—82no—
968C2#1307130011yescharacteristic
969C2#1307131111yescharacteristic
970C2#1307132111yescharacteristic
971C2#1307177311yescharacteristic
972C2#1307178211yescharacteristic
973C2#1307178211yescharacteristic
974C2#1307180811yescharacteristic
975C2#1307662511yescharacteristic
976C2#1307663411yescharacteristic
977C2#1307666511yescharacteristic
978C2#1307668911yescharacteristic
979C2#1307675011yescharacteristic
980C2#1307677411yescharacteristic
981C2#1307681711yescharacteristic
982C2#1307684711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#396C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#396D11
hypocenterC11#14633
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
2. C2×#10622594C2semidirect
3. #13066884C2semidirect
4. #13066881C2semidirect
5. #13066878C2semidirect
6. #13066869C2semidirect
7. #13066869C2semidirect
8. #13066869C2semidirect
14. #13066845C2semidirect
31. C11×#396C4semidirect
442. #396Dic11semidirect
754. C11#14633semidirect

Maximal subgroups

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

subgroupindex
C2×#106225642
C2×#106225942
#130668842
#130668812
#130668782
#130668692
#130668652
#130668612
#130668452
C2×C11×#3962
#1463311