Finite Group Databasebeta

← #14682017

Subgroups — #14682017

Order 2816.

1766 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622601C211yesmaximal, characteristic
2C2×#10622283C211yesmaximal, characteristic, complemented
3C2×#10622278C211yesmaximal, characteristic
4#13066864C211yesmaximal, characteristic, complemented
5#13066864C211yesmaximal, characteristic, complemented
6#13066864C211yesmaximal, characteristic, complemented
7#13066862C211yesmaximal, characteristic, complemented
8#13066856C211yesmaximal, characteristic
9#13066852C211yesmaximal, characteristic, complemented
10#13066850C211yesmaximal, characteristic, complemented
11#13066848C211yesmaximal, characteristic, complemented
12#13066841C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1442C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C22×C11×C4⋊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×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
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#10622601—24no—
52#10622283—24no—
53#10622278C418yescomplemented
54C24×D11C2311yescharacteristic
55C24×D11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C22×D44—22no—
70C22×D44—22no—
71C22×D44—22no—
72C22×D44—22no—
73C22×D44—41no—
74C22×D44—41no—
75C22×D44C2×C414yes—
76C22×C4×D11—41no—
77C22×C4×D11—41no—
78C22×C4×D11—41no—
79C22×C4×D11—41no—
80C22×C4×D11—41no—
81C22×C4×D11—41no—
82C22×C4×D11C2×C414yes—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—41no—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—22no—
88C2×(C2×D11)⋊C4—22no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—22no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—22no—
97C2×(C2×D11)⋊C4—41no—
98C2×(C2×D11)⋊C4—41no—
99C2×(C2×D11)⋊C4—41no—
100C2×(C2×D11)⋊C4—41no—
101C2×(C2×D11)⋊C4—41no—
102C2×(C2×D11)⋊C4—41no—
103C2×(C2×D11)⋊C4—41no—
104C2×(C2×D11)⋊C4—41no—
105C2×(C2×D11)⋊C4—41no—
106C2×(C2×D11)⋊C4—41no—
107C2×(C2×D11)⋊C4—41no—
108C2×(C2×D11)⋊C4—41no—
109C2×(C2×D11)⋊C4—41no—
110C2×(C2×D11)⋊C4—41no—
111C2×(C2×D11)⋊C4—41no—
112C2×(C2×D11)⋊C4—41no—
113C2×(C2×D11)⋊C4—41no—
114C2×(C2×D11)⋊C4—41no—
115C2×(C2×D11)⋊C4C2×C414yes—
116C2×(C2×D11)⋊C4C2×C414yes—
117C2×(C2×D11)⋊C4C2×C414yes—
118C2×(C2×D11)⋊C4D414yes—
119C2×C4⋊Dic11—22no—
120C2×C4⋊Dic11—22no—
121C2×C4⋊Dic11—41no—
122C2×C4×Dic11—22no—
123C2×C4×Dic11—22no—
124C2×C4×Dic11—22no—
125C2×C4×Dic11—41no—
126C2×C4×Dic11—41no—
127C2×C4×Dic11—41no—
128C11×#95—22no—
129C11×#95—22no—
130C11×#95—41no—
131C11×#95—41no—
132C11×#95—41no—
133C11×#95C2×C414yes—
134C11⋊#95—22no—
135C11⋊#95—22no—
136C11⋊#95—22no—
137C11⋊#95—41no—
138C11⋊#95—41no—
139C11⋊#95—41no—
140C11⋊#95—41no—
141C11⋊#95—41no—
142C11⋊#95—41no—
143C11⋊#95—41no—
144C11⋊#95—41no—
145C11⋊#95C2×C414yes—
146#14428—111nomaximal, Sylow
147C24×C11C2411yescharacteristic
148C23×D11—21no—
149C23×D11—21no—
150C23×D11—21no—
151C23×D11—21no—
152C23×D11—21no—
153C23×D11—21no—
154C23×D11—21no—
155C23×D11—21no—
156C23×D11—21no—
157C23×D11—21no—
158C23×D11—21no—
159C23×D11—21no—
160C23×D11—21no—
161C23×D11—21no—
162C23×D11—21no—
163C23×D11—21no—
164C23×D11—21no—
165C23×D11—21no—
166C23×D11—21no—
167C23×D11—21no—
168C23×D11—21no—
169C23×D11—21no—
170C23×D11—21no—
171C23×D11—21no—
172C23×D11—21no—
173C23×D11—21no—
174C23×D11C22×C412yes—
175C23×D11C22×C412yes—
176C23×D11C2×D412yes—
177C23×D11#4112yes—
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×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11C22×C412yes—
222C22×C4×C11C22×C412yes—
223C22×C4×C11C22×C412yes—
224C22×C4×C11C2×D412yes—
225C22×C4×C11#4112yes—
226C22×C4×C11#4112yes—
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×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11—21no—
264C22×Dic11C22×C412yes—
265C22×Dic11C22×C412yes—
266C22×Dic11C2×D412yes—
267C22×Dic11#4112yes—
268C22×Dic11#4112yes—
269C2×D44—28no—
270C2×D44—28no—
271C2×D44—44no—
272C2×D44—44no—
273C2×D44—44no—
274C2×D44—44no—
275C2×D44—44no—
276C2×C4×D11—44no—
277C2×C4×D11—44no—
278C2×C4×D11—44no—
279C2×C4×D11—44no—
280C2×C4×D11—44no—
281C2×C4×D11—44no—
282C2×C4×D11—44no—
283C11×C4⋊C4—44no—
284(C2×D11)⋊C4—28no—
285(C2×D11)⋊C4—44no—
286(C2×D11)⋊C4—44no—
287(C2×D11)⋊C4—44no—
288(C2×D11)⋊C4—44no—
289(C2×D11)⋊C4—44no—
290(C2×D11)⋊C4—44no—
291(C2×D11)⋊C4—44no—
292(C2×D11)⋊C4—44no—
293(C2×D11)⋊C4—44no—
294(C2×D11)⋊C4—44no—
295C4⋊Dic11—44no—
296C4×Dic11—44no—
297C4×Dic11—44no—
298C2×#390—111no—
299C2×#388—111no—
300C2×#386—111no—
301#1442D1111yescharacteristic, complemented
302#1440—111no—
303#1440—111no—
304#1440—111no—
305#1439—111no—
306#1438—111no—
307#1437—111no—
308#1436—111no—
309#1436—111no—
310#1434—111no—
311C22⋊#95—111no—
312C22⋊#95—111no—
313C23×C11C23×C411yescharacteristic
314C23×C11C22×D411yescharacteristic
315C23×C11C2×#4111yescharacteristic
316C23×C11C2×#4111yescharacteristic
317C23×C11C2×#4111yescharacteristic
318C23×C11C2×#4111yescharacteristic
319C23×C11C2×#4111yescharacteristic
320C23×C11H(5,𝔽2)11yescharacteristic
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×C112−1+411yescharacteristic
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—22no—
349C22×D11—22no—
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—41no—
354C22×D11—41no—
355C22×D11—41no—
356C22×D11—41no—
357C22×D11—41no—
358C22×D11—41no—
359C22×D11—41no—
360C22×D11—41no—
361C22×D11—41no—
362C22×D11—41no—
363C22×D11—41no—
364C22×D11—41no—
365C22×D11—41no—
366C22×D11—41no—
367C22×D11—41no—
368C22×D11—41no—
369C22×D11—41no—
370C22×D11—41no—
371C22×D11—41no—
372C22×D11—41no—
373C22×D11—41no—
374C22×D11—41no—
375C22×D11—41no—
376C22×D11—41no—
377C22×D11—41no—
378C22×D11—41no—
379C22×D11—41no—
380C22×D11—41no—
381C22×D11—41no—
382C22×D11—41no—
383C22×D11—41no—
384C22×D11—41no—
385C22×D11—41no—
386C22×D11—41no—
387C22×D11—41no—
388C22×D11—41no—
389C22×D11—41no—
390C22×D11—41no—
391C22×D11—41no—
392C22×D11—41no—
393C22×D11—41no—
394C22×D11—41no—
395C22×D11—41no—
396C22×D11—41no—
397C22×D11C4×D414yes—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—41no—
414C2×C4×C11—41no—
415C2×C4×C11—41no—
416C2×C4×C11—41no—
417C2×C4×C11—41no—
418C2×C4×C11—41no—
419C2×C4×C11—41no—
420C2×C4×C11—41no—
421C2×C4×C11—41no—
422C2×C4×C11—41no—
423C2×C4×C11—41no—
424C2×C4×C11—41no—
425C2×C4×C11—41no—
426C2×C4×C11—41no—
427C2×C4×C11—41no—
428C2×C4×C11—41no—
429C2×C4×C11—41no—
430C2×C4×C11—41no—
431C2×C4×C11—41no—
432C2×C4×C11—41no—
433C2×C4×C11—41no—
434C2×C4×C11—41no—
435C2×C4×C11—41no—
436C2×C4×C11—41no—
437C2×C4×C11—41no—
438C2×C4×C11—41no—
439C2×C4×C11—41no—
440C2×C4×C11—41no—
441C2×C4×C11—41no—
442C2×C4×C11—41no—
443C2×C4×C11—41no—
444C2×C4×C11—41no—
445C2×C4×C11—41no—
446C2×C4×C11#11714yes—
447C2×Dic11—22no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—22no—
452C2×Dic11—22no—
453C2×Dic11—22no—
454C2×Dic11—22no—
455C2×Dic11—22no—
456C2×Dic11—22no—
457C2×Dic11—22no—
458C2×Dic11—22no—
459C2×Dic11—22no—
460C2×Dic11—22no—
461C2×Dic11—22no—
462C2×Dic11—41no—
463C2×Dic11—41no—
464C2×Dic11—41no—
465C2×Dic11—41no—
466C2×Dic11—41no—
467C2×Dic11—41no—
468C2×Dic11—41no—
469C2×Dic11—41no—
470C2×Dic11—41no—
471C2×Dic11—41no—
472C2×Dic11—41no—
473C2×Dic11—41no—
474C2×Dic11—41no—
475C2×Dic11—41no—
476C2×Dic11—41no—
477C2×Dic11—41no—
478C2×Dic11—41no—
479C2×Dic11—41no—
480C2×Dic11—41no—
481C2×Dic11—41no—
482C2×Dic11—41no—
483C2×Dic11—41no—
484C2×Dic11—41no—
485C2×Dic11—41no—
486C2×Dic11—41no—
487C2×Dic11—41no—
488C2×Dic11—41no—
489D44—416no—
490C4×D11—416no—
491C23×D4—111no—
492C24×C4—111no—
493C22×C4⋊C4—111no—
494C22×C4⋊C4C2×D1111yescharacteristic
495C22×C22⋊C4—111no—
496C22×C22⋊C4—111no—
497C22×C22⋊C4—111no—
498C22×C22⋊C4—111no—
499C22×C22⋊C4—111no—
500C22×C22⋊C4—111no—
501C22×C22⋊C4—111no—
502C22×C22⋊C4—111no—
503C22×C22⋊C4—111no—
504C22×C22⋊C4—111no—
505C22×C22⋊C4—111no—
506C22×C42—111no—
507C22×C42—111no—
508#390—224no—
509#388—224no—
510#386—118no—
511C2×#95—111no—
512C2×#95—111no—
513C2×#95—111no—
514C2×#95—111no—
515C2×#95—111no—
516C2×#95—111no—
517C2×#95—111no—
518C2×#95—111no—
519C2×#95—111no—
520C2×#95—111no—
521C2×#95—111no—
522C2×#95—111no—
523C2×#95C2×D1111yescharacteristic
524C2×#95C2×D1111yescharacteristic
525C2×#95C2×D1111yescharacteristic
526C2×#95C2×D1111yescharacteristic
527C2×#95C2×D1111yescharacteristic
528C2×#95C2×D1111yescharacteristic
529C22×C11C2×#11711yescharacteristic
530C22×C11C2×C4×D411yescharacteristic
531C22×C11C4×#4111yescharacteristic
532C22×C11#51811yescharacteristic
533C22×C11#51811yescharacteristic
534C22×C11#51811yescharacteristic
535C22×C11#52011yescharacteristic
536C22×C11#53411yescharacteristic
537C22×C11#53711yescharacteristic
538C22×C11#53811yescharacteristic
539C22×C11#53811yescharacteristic
540C22×C11#53911yescharacteristic
541C22×C11#53911yescharacteristic
542C22×C11#54011yescharacteristic
543C22×C11#54011yescharacteristic
544C22×C11#54011yescharacteristic
545C22×C11#54211yescharacteristic
546C22×C11#54211yescharacteristic
547C22×C11#54211yescharacteristic
548C22×C11#54611yescharacteristic
549C22×C11#54611yescharacteristic
550C22×C11#54611yescharacteristic
551C22×C11#54611yescharacteristic
552C22×C11#55111yescharacteristic
553C22×C11#55111yescharacteristic
554C22×C11#55311yescharacteristic
555C22×C11#55311yescharacteristic
556C22×C11#55311yescharacteristic
557C22×C11#55311yescharacteristic
558C22×C11#55911yescharacteristic
559C22×C11#55911yescharacteristic
560C22×C11#56011yescharacteristic
561C22×C11#56011yescharacteristic
562C22×C11#56011yescharacteristic
563C22×C11H(3,𝔽4)11yescharacteristic
564C2×D11—24no—
565C2×D11—24no—
566C2×D11—24no—
567C2×D11—42no—
568C2×D11—42no—
569C2×D11—42no—
570C2×D11—42no—
571C2×D11—42no—
572C2×D11—42no—
573C2×D11—42no—
574C2×D11—42no—
575C2×D11—42no—
576C2×D11—42no—
577C2×D11—42no—
578C2×D11—42no—
579C2×D11—42no—
580C2×D11—42no—
581C2×D11—42no—
582C2×D11—42no—
583C2×D11—42no—
584C2×D11—42no—
585C2×D11—42no—
586C2×D11—81no—
587C2×D11—81no—
588C2×D11—81no—
589C2×D11—81no—
590C2×D11—81no—
591C2×D11—81no—
592C2×D11—81no—
593C2×D11—81no—
594C4×C11—24no—
595C4×C11—42no—
596C4×C11—42no—
597C4×C11—42no—
598C4×C11—81no—
599C4×C11—81no—
600C4×C11—81no—
601Dic11—42no—
602Dic11—42no—
603Dic11—42no—
604Dic11—42no—
605Dic11—42no—
606Dic11—81no—
607C25—111no—
608C25—111no—
609C22×D4—114no—
610C22×D4—222no—
611C22×D4—222no—
612C22×D4—222no—
613C22×D4—222no—
614C22×D4—441no—
615C22×D4—441no—
616C23×C4—111no—
617C23×C4—111no—
618C23×C4—111no—
619C23×C4—111no—
620C23×C4—111no—
621C23×C4—114no—
622C23×C4—111no—
623C23×C4—441no—
624C23×C4—441no—
625C23×C4—441no—
626C23×C4—441no—
627C23×C4—441no—
628C23×C4—441no—
629C23×C4C22×D1111yescharacteristic
630C23×C4C22×D1111yescharacteristic
631C23×C4C22×D1111yescharacteristic
632C23×C4C22×D1111yescharacteristic
633C23×C4C22×D1111yescharacteristic
634C23×C4C22×D1111yescharacteristic
635C23×C4C22×D1111yescharacteristic
636C2×C4⋊C4—22no—
637C2×C4⋊C4—22no—
638C2×C4⋊C4—41no—
639C2×C4⋊C4—222no—
640C2×C4⋊C4—222no—
641C2×C4⋊C4—441no—
642C2×C22⋊C4—114no—
643C2×C22⋊C4—114no—
644C2×C22⋊C4—114no—
645C2×C22⋊C4—114no—
646C2×C22⋊C4—222no—
647C2×C22⋊C4—222no—
648C2×C22⋊C4—222no—
649C2×C22⋊C4—222no—
650C2×C22⋊C4—222no—
651C2×C22⋊C4—222no—
652C2×C22⋊C4—222no—
653C2×C22⋊C4—222no—
654C2×C22⋊C4—222no—
655C2×C22⋊C4—222no—
656C2×C22⋊C4—222no—
657C2×C22⋊C4—441no—
658C2×C22⋊C4—441no—
659C2×C22⋊C4—441no—
660C2×C22⋊C4—441no—
661C2×C22⋊C4—441no—
662C2×C22⋊C4—441no—
663C2×C22⋊C4—441no—
664C2×C22⋊C4—441no—
665C2×C22⋊C4—441no—
666C2×C22⋊C4—441no—
667C2×C22⋊C4—441no—
668C2×C22⋊C4—441no—
669C2×C22⋊C4—441no—
670C2×C22⋊C4—441no—
671C2×C22⋊C4—441no—
672C2×C22⋊C4—441no—
673C2×C22⋊C4—441no—
674C2×C22⋊C4—441no—
675C2×C42—222no—
676C2×C42—222no—
677C2×C42—222no—
678C2×C42—441no—
679C2×C42—441no—
680C2×C42—441no—
681#95—22no—
682#95—22no—
683#95—41no—
684#95—41no—
685#95—41no—
686#95—114no—
687#95—222no—
688#95—222no—
689#95—222no—
690#95—441no—
691#95—441no—
692#95—441no—
693#95—441no—
694#95—441no—
695#95—441no—
696#95—441no—
697#95—441no—
698#95C4×D1114yes—
699C2×C11#231911yescharacteristic
700C2×C11#232511yescharacteristic
701C2×C11#233511yescharacteristic
702C2×C11#234211yescharacteristic
703C2×C11#235711yescharacteristic
704C2×C11#236411yescharacteristic
705C2×C11#237511yescharacteristic
706C2×C11#268811yescharacteristic
707C2×C11#269111yescharacteristic
708C2×C11#270911yescharacteristic
709C2×C11#271211yescharacteristic
710C2×C11#275311yescharacteristic
711C2×C11#275711yescharacteristic
712C2×C11#279611yescharacteristic
713C2×C11#279711yescharacteristic
714D11—44no—
715D11—82no—
716C24—112no—
717C24—112no—
718C24—112no—
719C24—112no—
720C24—221no—
721C24—221no—
722C24—221no—
723C24—221no—
724C24—221no—
725C24—221no—
726C24—221no—
727C24—221no—
728C24—221no—
729C24—221no—
730C24—221no—
731C24—221no—
732C24—221no—
733C24—221no—
734C24—221no—
735C24—221no—
736C24—221no—
737C24—221no—
738C24—221no—
739C24—221no—
740C24—221no—
741C24—221no—
742C24—221no—
743C24—221no—
744C24—221no—
745C24—221no—
746C24C23×D1111yescharacteristic
747C2×D4—228no—
748C2×D4—228no—
749C2×D4—444no—
750C2×D4—444no—
751C2×D4—444no—
752C2×D4—444no—
753C2×D4—444no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—112no—
798C22×C4—112no—
799C22×C4—112no—
800C22×C4—112no—
801C22×C4—112no—
802C22×C4—221no—
803C22×C4—221no—
804C22×C4—221no—
805C22×C4—221no—
806C22×C4—221no—
807C22×C4—221no—
808C22×C4—221no—
809C22×C4—221no—
810C22×C4—221no—
811C22×C4—221no—
812C22×C4—221no—
813C22×C4—221no—
814C22×C4—221no—
815C22×C4—221no—
816C22×C4—221no—
817C22×C4—221no—
818C22×C4—221no—
819C22×C4—221no—
820C22×C4—221no—
821C22×C4—221no—
822C22×C4—221no—
823C22×C4—221no—
824C22×C4—221no—
825C22×C4—221no—
826C22×C4—221no—
827C22×C4—221no—
828C22×C4—221no—
829C22×C4—221no—
830C22×C4—221no—
831C22×C4—221no—
832C22×C4—221no—
833C22×C4—221no—
834C22×C4—221no—
835C22×C4—221no—
836C22×C4—221no—
837C22×C4—221no—
838C22×C4—221no—
839C22×C4—444no—
840C22×C4—444no—
841C22×C4—444no—
842C22×C4—444no—
843C22×C4—444no—
844C22×C4—444no—
845C22×C4—444no—
846C22×C4C2×C4×D1112yes—
847C22×C4C2×C4×D1112yes—
848C22×C4C2×C4×D1112yes—
849C22×C4D4×D1112yes—
850C22×C4#434112yes—
851C22×C4#434312yes—
852C4⋊C4—44no—
853C4⋊C4—444no—
854C22⋊C4—228no—
855C22⋊C4—444no—
856C22⋊C4—444no—
857C22⋊C4—444no—
858C22⋊C4—444no—
859C22⋊C4—444no—
860C22⋊C4—444no—
861C22⋊C4—444no—
862C22⋊C4—444no—
863C22⋊C4—444no—
864C22⋊C4—444no—
865C42—444no—
866C42—444no—
867C11#1442811yescharacteristic, complemented, Sylow
868C23—114no—
869C23—222no—
870C23—222no—
871C23—222no—
872C23—222no—
873C23—222no—
874C23—222no—
875C23—222no—
876C23—222no—
877C23—222no—
878C23—222no—
879C23—222no—
880C23—222no—
881C23—222no—
882C23—222no—
883C23—222no—
884C23—222no—
885C23—222no—
886C23—222no—
887C23—222no—
888C23—222no—
889C23—222no—
890C23—222no—
891C23—222no—
892C23—222no—
893C23—222no—
894C23—441no—
895C23—441no—
896C23—441no—
897C23—441no—
898C23—441no—
899C23—441no—
900C23—441no—
901C23—441no—
902C23—441no—
903C23—441no—
904C23—441no—
905C23—441no—
906C23—441no—
907C23—441no—
908C23—441no—
909C23—441no—
910C23—441no—
911C23—441no—
912C23—441no—
913C23—441no—
914C23—441no—
915C23—441no—
916C23—441no—
917C23—441no—
918C23—441no—
919C23—441no—
920C23—441no—
921C23—441no—
922C23—441no—
923C23—441no—
924C23—441no—
925C23—441no—
926C23—441no—
927C23—441no—
928C23—441no—
929C23—441no—
930C23—441no—
931C23—441no—
932C23—441no—
933C23—441no—
934C23—441no—
935C23—441no—
936C23—441no—
937C23—441no—
938C23C22×C4×D1111yescharacteristic
939C23C2×D4×D1111yescharacteristic
940C23C2×#434111yescharacteristic
941C23#6703711yescharacteristic
942C23#6703711yescharacteristic
943C23C2×#434311yescharacteristic
944C23#6704011yescharacteristic
945C23#41×D1111yescharacteristic
946C23#41×D1111yescharacteristic
947C23#41×D1111yescharacteristic
948C23#6704211yescharacteristic
949C23#6704211yescharacteristic
950C23#6704211yescharacteristic
951C23#6704211yescharacteristic
952C23#6704211yescharacteristic
953D4—4416no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—222no—
1003C2×C4—222no—
1004C2×C4—222no—
1005C2×C4—222no—
1006C2×C4—222no—
1007C2×C4—222no—
1008C2×C4—222no—
1009C2×C4—222no—
1010C2×C4—222no—
1011C2×C4—222no—
1012C2×C4—222no—
1013C2×C4—222no—
1014C2×C4—222no—
1015C2×C4—222no—
1016C2×C4—222no—
1017C2×C4—4416no—
1018C2×C4—441no—
1019C2×C4—441no—
1020C2×C4—441no—
1021C2×C4—441no—
1022C2×C4—441no—
1023C2×C4—441no—
1024C2×C4—441no—
1025C2×C4—441no—
1026C2×C4—441no—
1027C2×C4—441no—
1028C2×C4—441no—
1029C2×C4—441no—
1030C2×C4—441no—
1031C2×C4—441no—
1032C2×C4—441no—
1033C2×C4—441no—
1034C2×C4—441no—
1035C2×C4—441no—
1036C2×C4—441no—
1037C2×C4—441no—
1038C2×C4—441no—
1039C2×C4—441no—
1040C2×C4—441no—
1041C2×C4—441no—
1042C2×C4—441no—
1043C2×C4—441no—
1044C2×C4—441no—
1045C2×C4#6694514yes—
1046C22—224no—
1047C22—224no—
1048C22—224no—
1049C22—442no—
1050C22—442no—
1051C22—442no—
1052C22—442no—
1053C22—442no—
1054C22—442no—
1055C22—442no—
1056C22—442no—
1057C22—442no—
1058C22—442no—
1059C22—442no—
1060C22—442no—
1061C22—442no—
1062C22—442no—
1063C22—442no—
1064C22—442no—
1065C22—442no—
1066C22—442no—
1067C22—442no—
1068C22—881no—
1069C22—881no—
1070C22—881no—
1071C22—881no—
1072C22—881no—
1073C22—881no—
1074C22—881no—
1075C22—881no—
1076C22C2×#6694511yescharacteristic
1077C22#1062305211yescharacteristic
1078C22#1062305311yescharacteristic
1079C22C4×D4×D1111yescharacteristic
1080C22#1062307611yescharacteristic
1081C22#1062307611yescharacteristic
1082C22#1062310511yescharacteristic
1083C22#1062312211yescharacteristic
1084C22#1062314111yescharacteristic
1085C22#1062315011yescharacteristic
1086C22#1062315111yescharacteristic
1087C22#1062316011yescharacteristic
1088C22#1062316111yescharacteristic
1089C22#1062316811yescharacteristic
1090C22#1062317111yescharacteristic
1091C22#1062317411yescharacteristic
1092C22#1062318411yescharacteristic
1093C22#1062318911yescharacteristic
1094C22#1062319211yescharacteristic
1095C22#1062319411yescharacteristic
1096C22#1062319711yescharacteristic
1097C22#1062320711yescharacteristic
1098C22#1062321211yescharacteristic
1099C22#1062321211yescharacteristic
1100C22#1062321411yescharacteristic
1101C22#1062322311yescharacteristic
1102C22#1062322311yescharacteristic
1103C22#1062322611yescharacteristic
1104C22#1062322611yescharacteristic
1105C22#1062322911yescharacteristic
1106C22#1062323511yescharacteristic
1107C22#1062323511yescharacteristic
1108C22#1062324011yescharacteristic
1109C22#1062324211yescharacteristic
1110C22#1062326411yescharacteristic
1111C4—24no—
1112C4—42no—
1113C4—42no—
1114C4—42no—
1115C4—81no—
1116C4—81no—
1117C4—81no—
1118C4—442no—
1119C4—442no—
1120C4—442no—
1121C4—442no—
1122C4—442no—
1123C4—881no—
1124C2—444no—
1125C2—882no—
1126C2#1307125511yescharacteristic
1127C2#1307131511yescharacteristic
1128C2#1307141211yescharacteristic
1129C2#1307146311yescharacteristic
1130C2#1307159111yescharacteristic
1131C2#1307166011yescharacteristic
1132C2#1307175611yescharacteristic
1133C2#1307505911yescharacteristic
1134C2#1307510411yescharacteristic
1135C2#1307534911yescharacteristic
1136C2#1307538711yescharacteristic
1137C2#1307589911yescharacteristic
1138C2#1307595911yescharacteristic
1139C2#1307645111yescharacteristic
1140C2#1307646611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1442C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1442D11
hypocenterC11#14428
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
2. C2×#10622283C2semidirect
4. #13066864C2semidirect
5. #13066864C2semidirect
6. #13066864C2semidirect
7. #13066862C2semidirect
9. #13066852C2semidirect
10. #13066850C2semidirect
11. #13066848C2semidirect
12. #13066841C2semidirect
13. (C2×D11)⋊#95C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1442C2semidirect
53. #10622278C4semidirect
301. #1442D11semidirect
867. C11#14428semidirect

Maximal subgroups

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

subgroupindex
C2×#106226012
C2×#106222832
C2×#106222782
#130668642
#130668622
#130668562
#130668522
#130668502
#130668482
#130668412
(C2×D11)⋊#952
C11×#14422
#1442811