Finite Group Databasebeta

← #14680563

Subgroups — #14680563

Order 2816.

1774 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×#10622285C211yesmaximal, characteristic
2C2×#10622278C211yesmaximal, characteristic
3C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
4#13066882C211yesmaximal, characteristic, complemented
5#13066878C211yesmaximal, characteristic, complemented
6#13066864C211yesmaximal, characteristic, complemented
7#13066864C211yesmaximal, characteristic, complemented
8#13066858C211yesmaximal, characteristic, complemented
9#13066858C211yesmaximal, characteristic, complemented
10#13066856C211yesmaximal, characteristic
11#13066854C211yesmaximal, characteristic, complemented
12#13066852C211yesmaximal, characteristic, complemented
13#13066847C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1436C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
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
51C4×(C2×D11)⋊C4—24no—
52#10622285C418yescomplemented
53#10622278—24no—
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—41no—
72C22×D44—41no—
73C22×D44—41no—
74C22×D44—41no—
75C22×D44C2×C414yes—
76C22×C4×D11—22no—
77C22×C4×D11—22no—
78C22×C4×D11—41no—
79C22×C4×D11—41no—
80C22×C4×D11—41no—
81C22×C4×D11—41no—
82C22×C4×D11D414yes—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—41no—
85C2×C11×C4⋊C4—41no—
86C2×C42×C11—22no—
87C2×C42×C11—41no—
88C2×C42×C11—41no—
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—22no—
98C2×(C2×D11)⋊C4—22no—
99C2×(C2×D11)⋊C4—22no—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4—22no—
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)⋊C4—41no—
116C2×(C2×D11)⋊C4—41no—
117C2×(C2×D11)⋊C4—41no—
118C2×(C2×D11)⋊C4C2×C414yes—
119C2×(C2×D11)⋊C4C2×C414yes—
120C2×(C2×D11)⋊C4C2×C414yescomplemented
121C2×(C2×D11)⋊C4C2×C414yescomplemented
122C2×Dic11⋊C4—41no—
123C2×Dic11⋊C4—41no—
124C2×Dic11⋊C4C2×C414yescomplemented
125C2×C4×Dic11—22no—
126C2×C4×Dic11—41no—
127C2×C4×Dic11—41no—
128C11×#95—22no—
129C11×#95—22no—
130C11×#95—41no—
131C11×#95—41no—
132C11×#95C2×C414yescomplemented
133C11⋊#95—22no—
134C11⋊#95—22no—
135C11⋊#95—22no—
136C11⋊#95—22no—
137C11⋊#95—22no—
138C11⋊#95—41no—
139C11⋊#95—41no—
140C11⋊#95—41no—
141C11⋊#95—41no—
142C11⋊#95—41no—
143C11⋊#95—41no—
144C11⋊#95—41no—
145C11⋊#95—41no—
146#14303—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×C11C22×C412yes—
221C22×C4×C11C22×C412yes—
222C22×C4×C11C22×C412yes—
223C22×C4×C11C2×D412yes—
224C22×C4×C11#4112yes—
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×Dic11—21no—
265C22×Dic11C22×C412yes—
266C22×Dic11C22×C412yes—
267C22×Dic11C2×D412yes—
268C22×Dic11#4112yes—
269C2×D44—28no—
270C2×D44—44no—
271C2×D44—44no—
272C2×D44—44no—
273C2×D44—44no—
274C2×D44—44no—
275C2×D44—44no—
276C2×C4×D11—28no—
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—
284C42×C11—44no—
285(C2×D11)⋊C4—28no—
286(C2×D11)⋊C4—28no—
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—
295(C2×D11)⋊C4—44no—
296Dic11⋊C4—44no—
297C4×Dic11—44no—
298C2×#394—111no—
299C2×#386—111no—
300C2×C4×C22⋊C4—111no—
301#1445—111no—
302#1443—111no—
303#1440—111no—
304#1440—111no—
305#1439—111no—
306#1439—111no—
307#1438—111no—
308#1437—111no—
309#1437—111no—
310#1436—111no—
311#1436D1111yescharacteristic, complemented
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—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
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#12314yes—
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—41no—
460C2×Dic11—41no—
461C2×Dic11—41no—
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×C42C2×D1111yescharacteristic
508#394—118no—
509#386—224no—
510C4×C22⋊C4—224no—
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×#95—111no—
524C2×#95C2×D1111yescharacteristic
525C2×#95C2×D1111yescharacteristic
526C2×#95C2×D1111yescharacteristic
527C2×#95C2×D1111yescharacteristic
528C2×#95C2×D1111yescharacteristic
529C22×C11C2×C4×D411yescharacteristic
530C22×C11C4×#4111yescharacteristic
531C22×C11C4×#4111yescharacteristic
532C22×C11#51811yescharacteristic
533C22×C11#51811yescharacteristic
534C22×C11#51811yescharacteristic
535C22×C11#52011yescharacteristic
536C22×C11C2×#12311yescharacteristic
537C22×C11#52511yescharacteristic
538C22×C11#52911yescharacteristic
539C22×C11#52911yescharacteristic
540C22×C11#53411yescharacteristic
541C22×C11#53411yescharacteristic
542C22×C11#53511yescharacteristic
543C22×C11#53711yescharacteristic
544C22×C11#53811yescharacteristic
545C22×C11#53811yescharacteristic
546C22×C11#53811yescharacteristic
547C22×C11#53811yescharacteristic
548C22×C11#53811yescharacteristic
549C22×C11#53811yescharacteristic
550C22×C11#53811yescharacteristic
551C22×C11#53811yescharacteristic
552C22×C11#53811yescharacteristic
553C22×C11#53811yescharacteristic
554C22×C11#53911yescharacteristic
555C22×C11#53911yescharacteristic
556C22×C11#54011yescharacteristic
557C22×C11#54011yescharacteristic
558C22×C11#54011yescharacteristic
559C22×C11#54011yescharacteristic
560C22×C11#54011yescharacteristic
561C22×C11#54211yescharacteristic
562C22×C11#54211yescharacteristic
563C22×C11#54211yescharacteristic
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—42no—
599C4×C11—81no—
600C4×C11—81no—
601Dic11—42no—
602Dic11—42no—
603Dic11—42no—
604Dic11—42no—
605Dic11—81no—
606Dic11—81no—
607C25—111no—
608C25—111no—
609C22×D4—114no—
610C22×D4—222no—
611C22×D4—222no—
612C22×D4—441no—
613C22×D4—441no—
614C22×D4—441no—
615C22×D4—441no—
616C23×C4—111no—
617C23×C4—111no—
618C23×C4—111no—
619C23×C4—111no—
620C23×C4—114no—
621C23×C4—111no—
622C23×C4—111no—
623C23×C4—222no—
624C23×C4—222no—
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—41no—
638C2×C4⋊C4—41no—
639C2×C4⋊C4—114no—
640C2×C4⋊C4—441no—
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—222no—
658C2×C22⋊C4—222no—
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—22no—
676C2×C42—41no—
677C2×C42—41no—
678C2×C42—222no—
679C2×C42—441no—
680C2×C42—441no—
681#95—22no—
682#95—22no—
683#95—41no—
684#95—41no—
685#95—222no—
686#95—222no—
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×D1114yescomplemented
699C2×C11C4×#12311yescharacteristic
700C2×C11#232111yescharacteristic
701C2×C11#232511yescharacteristic
702C2×C11#233311yescharacteristic
703C2×C11#233311yescharacteristic
704C2×C11#233511yescharacteristic
705C2×C11#233711yescharacteristic
706C2×C11#262211yescharacteristic
707C2×C11#262411yescharacteristic
708C2×C11#263011yescharacteristic
709C2×C11#263511yescharacteristic
710C2×C11#264811yescharacteristic
711C2×C11#264811yescharacteristic
712C2×C11#264911yescharacteristic
713C2×C11#265311yescharacteristic
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—444no—
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—112no—
797C22×C4—112no—
798C22×C4—112no—
799C22×C4—112no—
800C22×C4—221no—
801C22×C4—221no—
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—228no—
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×C4C2×C4×D1112yes—
846C22×C4C2×C4×D1112yes—
847C22×C4C2×C4×D1112yes—
848C22×C4#433912yes—
849C22×C4#433912yes—
850C22×C4D4×D1112yes—
851C22×C4#434312yes—
852C4⋊C4—44no—
853C4⋊C4—444no—
854C22⋊C4—228no—
855C22⋊C4—228no—
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—44no—
866C42—444no—
867C11#1430311yescharacteristic, 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×#433911yescharacteristic
940C23C2×#433911yescharacteristic
941C23C2×D4×D1111yescharacteristic
942C23#6703711yescharacteristic
943C23#6703711yescharacteristic
944C23#6703711yescharacteristic
945C23C2×#434311yescharacteristic
946C23#6704011yescharacteristic
947C23#41×D1111yescharacteristic
948C23#41×D1111yescharacteristic
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—22no—
970C2×C4—22no—
971C2×C4—22no—
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—4416no—
1015C2×C4—441no—
1016C2×C4—441no—
1017C2×C4—441no—
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#6694714yes—
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—
1076C22C4×#433911yescharacteristic
1077C22#1062302511yescharacteristic
1078C22#1062303511yescharacteristic
1079C22C2×#6694711yescharacteristic
1080C22#1062305211yescharacteristic
1081C22#1062305911yescharacteristic
1082C22#1062306611yescharacteristic
1083C22C4×D4×D1111yescharacteristic
1084C22#1062307611yescharacteristic
1085C22#1062307611yescharacteristic
1086C22#1062307811yescharacteristic
1087C22#1062309111yescharacteristic
1088C22#1062309111yescharacteristic
1089C22#1062309111yescharacteristic
1090C22#1062309311yescharacteristic
1091C22C4×#434311yescharacteristic
1092C22#1062311111yescharacteristic
1093C22#1062311311yescharacteristic
1094C22#1062311311yescharacteristic
1095C22#1062312011yescharacteristic
1096C22#1062313811yescharacteristic
1097C22#1062314611yescharacteristic
1098C22#1062316011yescharacteristic
1099C22#1062316911yescharacteristic
1100C22#1062317511yescharacteristic
1101C22#1062317511yescharacteristic
1102C22#1062318411yescharacteristic
1103C22#1062318811yescharacteristic
1104C22#1062319411yescharacteristic
1105C22#1062320911yescharacteristic
1106C22#1062322311yescharacteristic
1107C22#1062322911yescharacteristic
1108C22#1062323511yescharacteristic
1109C22#1062323511yescharacteristic
1110C22#1062326411yescharacteristic
1111C4—24no—
1112C4—42no—
1113C4—42no—
1114C4—42no—
1115C4—42no—
1116C4—81no—
1117C4—81no—
1118C4—442no—
1119C4—442no—
1120C4—442no—
1121C4—442no—
1122C4—881no—
1123C4—881no—
1124C2—444no—
1125C2—882no—
1126C2C4×#6694711yescharacteristic
1127C2#1307127811yescharacteristic
1128C2#1307131311yescharacteristic
1129C2#1307137611yescharacteristic
1130C2#1307138011yescharacteristic
1131C2#1307140911yescharacteristic
1132C2#1307142911yescharacteristic
1133C2#1307439411yescharacteristic
1134C2#1307441011yescharacteristic
1135C2#1307446511yescharacteristic
1136C2#1307450411yescharacteristic
1137C2#1307460011yescharacteristic
1138C2#1307461011yescharacteristic
1139C2#1307461711yescharacteristic
1140C2#1307468511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1436D11
hypocenterC11#14303
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
3. C2×C4×(C2×D11)⋊C4C2semidirect
4. #13066882C2semidirect
5. #13066878C2semidirect
6. #13066864C2semidirect
7. #13066864C2semidirect
8. #13066858C2semidirect
9. #13066858C2semidirect
11. #13066854C2semidirect
12. #13066852C2semidirect
13. #13066847C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1436C2semidirect
52. #10622285C4semidirect
120. C2×(C2×D11)⋊C4C2×C4semidirect
121. C2×(C2×D11)⋊C4C2×C4semidirect
124. C2×Dic11⋊C4C2×C4semidirect
132. C11×#95C2×C4semidirect
311. #1436D11semidirect
698. #95C4×D11semidirect
867. C11#14303semidirect

Maximal subgroups

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

subgroupindex
C2×#106222852
C2×#106222782
C2×C4×(C2×D11)⋊C42
#130668822
#130668782
#130668642
#130668582
#130668562
#130668542
#130668522
#130668472
(C2×D11)⋊#952
C11×#14362
#1430311