Finite Group Databasebeta

← #14684475

Subgroups — #14684475

Order 2816.

1434 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×#10622565C211yesmaximal, characteristic
2C2×#10622823C211yesmaximal, characteristic
3#13066879C211yesmaximal, characteristic, complemented
4#13066879C211yesmaximal, characteristic, complemented
5#13066877C211yesmaximal, characteristic, complemented
6#13066876C211yesmaximal, characteristic, complemented
7#13066875C211yesmaximal, characteristic, complemented
8#13066874C211yesmaximal, characteristic, complemented
9#13066867C211yesmaximal, characteristic, complemented
10#13066866C211yesmaximal, characteristic, complemented
11#13066865C211yesmaximal, characteristic
12#13066863C211yesmaximal, characteristic
13#13066859C211yesmaximal, characteristic
14#13066839C211yesmaximal, characteristic
15C2×C11×#385C211yesmaximal, characteristic
16C24×C4×C11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C11×#385—24no—
30C2×C11×#95C2211yescharacteristic
31C2×C11×#95C2211yescharacteristic
32#10622823—24no—
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
53#10622565C418yescomplemented
54C25×C11C2311yescharacteristic
55C23×C4×C11—41no—
56C23×C4×C11—41no—
57C23×C4×C11—41no—
58C23×C4×C11—41no—
59C23×C4×C11—41no—
60C23×C4×C11—41no—
61C23×C4×C11D414yes—
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
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—22no—
78C2×C11×C4⋊C4—41no—
79C2×C11×C4⋊C4—41no—
80C2×C11×C4⋊C4—41no—
81C2×C11×C4⋊C4—41no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
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—22no—
91C2×C22⋊Dic11—22no—
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⋊Dic11C2×C414yes—
99C2×C22⋊Dic11C2×C414yes—
100C2×Dic11⋊C4—22no—
101C2×Dic11⋊C4—22no—
102C2×Dic11⋊C4—41no—
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⋊C4—41no—
111C2×Dic11⋊C4C2×C414yescomplemented
112C11×#95—22no—
113C11×#95—22no—
114C11⋊#95—22no—
115C11⋊#95—22no—
116C11⋊#95—41no—
117C11⋊#95—41no—
118C11⋊#95—41no—
119C11⋊#95—41no—
120C11⋊#95—41no—
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⋊#95C2×C414yescomplemented
132C11⋊#95C2×C414yescomplemented
133C11⋊#95C2×C414yescomplemented
134#14627—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×C11C22×C412yes—
148C24×C11C2×D412yes—
149C24×C11#4112yes—
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×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—44no—
190C22×C4×C11—44no—
191C22×C4×C11—44no—
192C22×C4×C11—44no—
193C22×C4×C11—44no—
194C22×C4×C11—44no—
195C22×C4×C11—44no—
196C22×C4×C11C22×C412yes—
197C22×C4×C11C22×C412yes—
198C22×C4×C11C2×D412yes—
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×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11C22×C412yes—
253C22×Dic11C22×C412yes—
254C22×Dic11C22×C412yes—
255C22×Dic11C22×C412yes—
256C11×C4⋊C4—44no—
257C11×C4⋊C4—44no—
258C11×C22⋊C4—28no—
259C11×C22⋊C4—44no—
260C22⋊Dic11—28no—
261C22⋊Dic11—44no—
262C22⋊Dic11—44no—
263C22⋊Dic11—44no—
264Dic11⋊C4—44no—
265Dic11⋊C4—44no—
266Dic11⋊C4—44no—
267Dic11⋊C4—44no—
268C2×#397—111no—
269C2×#385—111no—
270C2×#385D1111yescharacteristic
271#1444—111no—
272#1444—111no—
273#1443—111no—
274#1443—111no—
275#1442—111no—
276#1442—111no—
277#1441—111no—
278#1441—111no—
279#1440—111no—
280#1440—111no—
281#1439—111no—
282C22⋊#95—111no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—22no—
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—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×C11—41no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11C4×D414yes—
318C23×C11C23×C411yescharacteristic
319C23×C11C22×D411yescharacteristic
320C23×C11C2×#4111yescharacteristic
321C23×C11H(5,𝔽2)11yescharacteristic
322C23×C11H(5,𝔽2)11yescharacteristic
323C23×C11H(5,𝔽2)11yescharacteristic
324C23×C11H(5,𝔽2)11yescharacteristic
325C23×C11H(5,𝔽2)11yescharacteristic
326C23×C11H(5,𝔽2)11yescharacteristic
327C23×C11H(5,𝔽2)11yescharacteristic
328C23×C112−1+411yescharacteristic
329C23×C112−1+411yescharacteristic
330C23×C112−1+411yescharacteristic
331C23×C112−1+411yescharacteristic
332C23×C112−1+411yescharacteristic
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—416no—
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×Dic11—22no—
377C2×Dic11—22no—
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—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—
427C2×Dic11—41no—
428C2×Dic11—41no—
429C2×Dic11—41no—
430C2×Dic11—41no—
431C2×Dic11—41no—
432C24×C4C2×D1111yescharacteristic
433C22×C4⋊C4—111no—
434C22×C4⋊C4—111no—
435C22×C4⋊C4—111no—
436C22×C4⋊C4—111no—
437C22×C4⋊C4C2×D1111yescharacteristic
438C22×C4⋊C4C2×D1111yescharacteristic
439C22×C22⋊C4—111no—
440C22×C22⋊C4—111no—
441C22×C22⋊C4—111no—
442C22×C22⋊C4—111no—
443C22×C22⋊C4C2×D1111yescharacteristic
444C22×C22⋊C4C2×D1111yescharacteristic
445#397—118no—
446#385—24no—
447#385—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×#95—111no—
465C2×#95—111no—
466C2×#95—111no—
467C2×#95—111no—
468C2×#95C2×D1111yescharacteristic
469C2×#95C2×D1111yescharacteristic
470C22×C11—24no—
471C22×C11—24no—
472C22×C11—24no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—42no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11—42no—
484C22×C11—42no—
485C22×C11C2×C4×D411yescharacteristic
486C22×C11#51811yescharacteristic
487C22×C11#52011yescharacteristic
488C22×C11#52011yescharacteristic
489C22×C11#52011yescharacteristic
490C22×C11#52011yescharacteristic
491C22×C11#52011yescharacteristic
492C22×C11#53411yescharacteristic
493C22×C11#53411yescharacteristic
494C22×C11#53411yescharacteristic
495C22×C11#53611yescharacteristic
496C22×C11#53611yescharacteristic
497C22×C11#53711yescharacteristic
498C22×C11#53811yescharacteristic
499C22×C11#53911yescharacteristic
500C22×C11#53911yescharacteristic
501C22×C11#53911yescharacteristic
502C22×C11#53911yescharacteristic
503C22×C11#53911yescharacteristic
504C22×C11#56011yescharacteristic
505C22×C11#56011yescharacteristic
506C22×C11#56011yescharacteristic
507C22×C11H(3,𝔽4)11yescharacteristic
508C22×C11#56211yescharacteristic
509C22×C11#56211yescharacteristic
510C22×C11#56211yescharacteristic
511C22×C11#56211yescharacteristic
512C22×C11#56311yescharacteristic
513C22×C11#56311yescharacteristic
514C22×C11#56311yescharacteristic
515C22×C11#56311yescharacteristic
516C22×C11#56311yescharacteristic
517C22×C11#56311yescharacteristic
518C22×C11#56311yescharacteristic
519C22×C11#56311yescharacteristic
520C4×C11—42no—
521C4×C11—42no—
522C4×C11—42no—
523C4×C11—42no—
524C4×C11—81no—
525C4×C11—81no—
526Dic11—42no—
527Dic11—42no—
528Dic11—42no—
529Dic11—42no—
530Dic11—81no—
531Dic11—81no—
532Dic11—81no—
533Dic11—81no—
534C25C22×D1111yescharacteristic
535C23×C4—41no—
536C23×C4—41no—
537C23×C4—41no—
538C23×C4—41no—
539C23×C4—41no—
540C23×C4—41no—
541C23×C4—111no—
542C23×C4—111no—
543C23×C4—111no—
544C23×C4—111no—
545C23×C4—111no—
546C23×C4—111no—
547C23×C4—111no—
548C23×C4—111no—
549C23×C4C22⋊D1114yes—
550C23×C4C22×D1111yescharacteristic
551C23×C4C22×D1111yescharacteristic
552C23×C4C22×D1111yescharacteristic
553C23×C4C22×D1111yescharacteristic
554C23×C4C22×D1111yescharacteristic
555C23×C4C22×D1111yescharacteristic
556C2×C4⋊C4—22no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—41no—
559C2×C4⋊C4—41no—
560C2×C4⋊C4—41no—
561C2×C4⋊C4—41no—
562C2×C4⋊C4—114no—
563C2×C4⋊C4—222no—
564C2×C4⋊C4—222no—
565C2×C4⋊C4—441no—
566C2×C4⋊C4—441no—
567C2×C4⋊C4—441no—
568C2×C4⋊C4—441no—
569C2×C4⋊C4—441no—
570C2×C4⋊C4—441no—
571C2×C4⋊C4—441no—
572C2×C4⋊C4—441no—
573C2×C4⋊C4—441no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4—22no—
576C2×C22⋊C4—22no—
577C2×C22⋊C4—41no—
578C2×C22⋊C4—41no—
579C2×C22⋊C4—114no—
580C2×C22⋊C4—114no—
581C2×C22⋊C4—222no—
582C2×C22⋊C4—222no—
583C2×C22⋊C4—222no—
584C2×C22⋊C4—222no—
585C2×C22⋊C4—441no—
586C2×C22⋊C4—441no—
587C2×C22⋊C4—441no—
588C2×C22⋊C4—441no—
589C2×C22⋊C4—441no—
590C2×C22⋊C4—441no—
591C2×C22⋊C4C4×D1114yes—
592#95—22no—
593#95—22no—
594#95—114no—
595#95—114no—
596#95—114no—
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—
609#95—441no—
610#95—441no—
611#95—441no—
612#95—441no—
613#95—441no—
614C2×C11—44no—
615C2×C11#232211yescharacteristic
616C2×C11#232211yescharacteristic
617C2×C11#232511yescharacteristic
618C2×C11#237611yescharacteristic
619C2×C11#237911yescharacteristic
620C2×C11#238311yescharacteristic
621C2×C11#238311yescharacteristic
622C2×C11#281211yescharacteristic
623C2×C11#281411yescharacteristic
624C2×C11#281411yescharacteristic
625C2×C11#281711yescharacteristic
626C2×C11#282711yescharacteristic
627C2×C11#282711yescharacteristic
628C2×C11#283411yescharacteristic
629C2×C11#283511yescharacteristic
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24C2×C4×D1112yes—
643C24#433912yes—
644C24C2×C22⋊D1112yes—
645C24C23×D1111yescharacteristic
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—44no—
685C22×C4—44no—
686C22×C4—44no—
687C22×C4—44no—
688C22×C4—44no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—112no—
692C22×C4—112no—
693C22×C4—112no—
694C22×C4—112no—
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×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×C22⋊D1112yes—
750C22×C4C2×C22⋊D1112yes—
751C4⋊C4—44no—
752C4⋊C4—44no—
753C4⋊C4—444no—
754C4⋊C4—444no—
755C4⋊C4—444no—
756C4⋊C4—444no—
757C22⋊C4—28no—
758C22⋊C4—44no—
759C22⋊C4—228no—
760C22⋊C4—444no—
761C22⋊C4—444no—
762C22⋊C4—444no—
763C11#1462711yescharacteristic, complemented, Sylow
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23C4×C22⋊D1114yes—
799C23C22×C4×D1111yescharacteristic
800C23C2×#433911yescharacteristic
801C23#6703711yescharacteristic
802C23#6703711yescharacteristic
803C23#6703711yescharacteristic
804C23#6703711yescharacteristic
805C23#6703711yescharacteristic
806C23#6703711yescharacteristic
807C23#6704011yescharacteristic
808C23#6704011yescharacteristic
809C23#6704211yescharacteristic
810C23#6704311yescharacteristic
811C23#6704311yescharacteristic
812C23#6704311yescharacteristic
813C23C22×C22⋊D1111yescharacteristic
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—416no—
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—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—222no—
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—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—24no—
914C22—24no—
915C22—24no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22#1062303511yescharacteristic
929C22#1062303511yescharacteristic
930C22#1062304611yescharacteristic
931C22#1062304611yescharacteristic
932C22#1062307611yescharacteristic
933C22#1062307711yescharacteristic
934C22#1062307711yescharacteristic
935C22#1062307711yescharacteristic
936C22#1062309111yescharacteristic
937C22#1062309511yescharacteristic
938C22#1062309511yescharacteristic
939C22#1062309511yescharacteristic
940C22#1062312511yescharacteristic
941C22#1062312611yescharacteristic
942C22#1062312611yescharacteristic
943C22#1062312611yescharacteristic
944C22#1062317711yescharacteristic
945C22#1062317711yescharacteristic
946C22#1062317711yescharacteristic
947C22#1062317711yescharacteristic
948C22#1062317711yescharacteristic
949C22#1062317711yescharacteristic
950C22#1062317811yescharacteristic
951C22#1062317811yescharacteristic
952C22#1062318211yescharacteristic
953C22#1062318211yescharacteristic
954C22#1062319811yescharacteristic
955C22#1062319811yescharacteristic
956C22C2×C4×C22⋊D1111yescharacteristic
957C22#1062333511yescharacteristic
958C22#1062333511yescharacteristic
959C22#1062333511yescharacteristic
960C22#1062334711yescharacteristic
961C22#1062335611yescharacteristic
962C22#1062336411yescharacteristic
963C4—42no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—81no—
968C4—81no—
969C4—442no—
970C4—442no—
971C4—442no—
972C4—442no—
973C4—881no—
974C4—881no—
975C4—881no—
976C4—881no—
977C2—44no—
978C2#1307128111yescharacteristic
979C2#1307128511yescharacteristic
980C2#1307131411yescharacteristic
981C2#1307176511yescharacteristic
982C2#1307178911yescharacteristic
983C2#1307180411yescharacteristic
984C2#1307180411yescharacteristic
985C2#1307661111yescharacteristic
986C2#1307662711yescharacteristic
987C2#1307662911yescharacteristic
988C2#1307665111yescharacteristic
989C2#1307671811yescharacteristic
990C2#1307672211yescharacteristic
991C2#1307679911yescharacteristic
992C2#1307680411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#385C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#385D11
hypocenterC11#14627
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
3. #13066879C2semidirect
4. #13066879C2semidirect
5. #13066877C2semidirect
6. #13066876C2semidirect
7. #13066875C2semidirect
8. #13066874C2semidirect
9. #13066867C2semidirect
10. #13066866C2semidirect
53. #10622565C4semidirect
111. C2×Dic11⋊C4C2×C4semidirect
131. C11⋊#95C2×C4semidirect
132. C11⋊#95C2×C4semidirect
133. C11⋊#95C2×C4semidirect
763. C11#14627semidirect

Maximal subgroups

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

subgroupindex
C2×#106225652
C2×#106228232
#130668792
#130668772
#130668762
#130668752
#130668742
#130668672
#130668662
#130668652
#130668632
#130668592
#130668392
C2×C11×#3852
#1462711