Finite Group Databasebeta

← #14682016

Subgroups — #14682016

Order 2816.

1874 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622283C211yesmaximal, characteristic, complemented
2C2×#10622278C211yesmaximal, characteristic
3C2×#10622278C211yesmaximal, characteristic
4#13066877C211yesmaximal, characteristic, complemented
5#13066873C211yesmaximal, characteristic, complemented
6#13066864C211yesmaximal, characteristic, complemented
7#13066862C211yesmaximal, characteristic, complemented
8#13066856C211yesmaximal, characteristic
9#13066852C211yesmaximal, characteristic, complemented
10#13066842C211yesmaximal, characteristic, complemented
11(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
12(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1443C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C2×C11×#95C2211yescharacteristic
32C2×C11×#95C2211yescharacteristic
33C2×C11×#95C2211yescharacteristic
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51#10622283—24no—
52#10622278—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—22no—
77C22×C4×D11—22no—
78C22×C4×D11—22no—
79C22×C4×D11—41no—
80C22×C4×D11—41no—
81C22×C4×D11—41no—
82C22×C4×D11—41no—
83C22×C4×D11—41no—
84C22×C4×D11—41no—
85C22×C4×D11—41no—
86C22×C4×D11—41no—
87C22×C4×D11—41no—
88C22×C4×D11—41no—
89C22×C4×D11C2×C414yescomplemented
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)⋊C4C2×C414yes—
117C2×(C2×D11)⋊C4C2×C414yes—
118C2×(C2×D11)⋊C4C2×C414yescomplemented
119C2×(C2×D11)⋊C4D414yes—
120C2×C4⋊Dic11—22no—
121C2×C4⋊Dic11—41no—
122C2×C4⋊Dic11—41no—
123C2×C4×Dic11—22no—
124C2×C4×Dic11—22no—
125C2×C4×Dic11—41no—
126C11×#95—22no—
127C11×#95—22no—
128C11×#95—41no—
129C11×#95—41no—
130C11×#95—41no—
131C11×#95—41no—
132C11×#95C2×C414yescomplemented
133C11⋊#95—22no—
134C11⋊#95—22no—
135C11⋊#95—22no—
136C11⋊#95—41no—
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×C414yescomplemented
146#14427—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×D11C22×C412yes—
173C23×D11C22×C412yes—
174C23×D11C2×D412yes—
175C23×D11#4112yes—
176C23×D11#4112yes—
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×C11—21no—
222C22×C4×C11C22×C412yes—
223C22×C4×C11C22×C412yes—
224C22×C4×C11C22×C412yes—
225C22×C4×C11C2×D412yes—
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—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—
283C2×C4×D11—44no—
284C2×C4×D11—44no—
285C2×C4×D11—44no—
286C2×C4×D11—44no—
287C2×C4×D11—44no—
288C2×C4×D11—44no—
289C2×C4×D11—44no—
290(C2×D11)⋊C4—28no—
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—
296(C2×D11)⋊C4—44no—
297(C2×D11)⋊C4—44no—
298(C2×D11)⋊C4—44no—
299(C2×D11)⋊C4—44no—
300C4⋊Dic11—44no—
301C4×Dic11—44no—
302C2×#388—111no—
303C2×#386—111no—
304C2×#386—111no—
305#1443—111no—
306#1443D1111yescharacteristic, complemented
307#1442—111no—
308#1440—111no—
309#1439—111no—
310#1438—111no—
311#1437—111no—
312#1434—111no—
313C22⋊#95—111no—
314C22⋊#95—111no—
315C22⋊#95—111no—
316C22⋊#95—111no—
317C23×C11C23×C411yescharacteristic
318C23×C11C22×D411yescharacteristic
319C23×C11C2×#4111yescharacteristic
320C23×C11C2×#4111yescharacteristic
321C23×C11C2×#4111yescharacteristic
322C23×C11C2×#4111yescharacteristic
323C23×C11C2×#4111yescharacteristic
324C23×C11H(5,𝔽2)11yescharacteristic
325C23×C11H(5,𝔽2)11yescharacteristic
326C23×C11H(5,𝔽2)11yescharacteristic
327C23×C11H(5,𝔽2)11yescharacteristic
328C23×C11H(5,𝔽2)11yescharacteristic
329C23×C11H(5,𝔽2)11yescharacteristic
330C23×C11H(5,𝔽2)11yescharacteristic
331C23×C112−1+411yescharacteristic
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—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—22no—
360C22×D11—22no—
361C22×D11—22no—
362C22×D11—22no—
363C22×D11—22no—
364C22×D11—22no—
365C22×D11—22no—
366C22×D11—22no—
367C22×D11—22no—
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×D11—41no—
398C22×D11—41no—
399C22×D11—41no—
400C22×D11#11714yes—
401C22×D11C4×D414yes—
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—22no—
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—41no—
447C2×C4×C11—41no—
448C2×C4×C11—41no—
449C2×C4×C11—41no—
450C2×C4×C11—41no—
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—22no—
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—
489C2×Dic11—41no—
490C2×Dic11—41no—
491C2×Dic11—41no—
492C2×Dic11—41no—
493D44—416no—
494C4×D11—416no—
495C4×D11—416no—
496C23×D4—111no—
497C24×C4—111no—
498C24×C4—111no—
499C22×C4⋊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×C22⋊C4—111no—
507C22×C22⋊C4—111no—
508C22×C22⋊C4—111no—
509C22×C22⋊C4—111no—
510C22×C42—111no—
511#388—224no—
512#386—118no—
513#386—224no—
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×#95—111no—
525C2×#95—111no—
526C2×#95—111no—
527C2×#95C2×D1111yescharacteristic
528C2×#95C2×D1111yescharacteristic
529C2×#95C2×D1111yescharacteristic
530C2×#95C2×D1111yescharacteristic
531C2×#95C2×D1111yescharacteristic
532C2×#95C2×D1111yescharacteristic
533C2×#95C2×D1111yescharacteristic
534C22×C11C2×#11711yescharacteristic
535C22×C11C2×C4×D411yescharacteristic
536C22×C11C4×#4111yescharacteristic
537C22×C11#51811yescharacteristic
538C22×C11#51811yescharacteristic
539C22×C11#51811yescharacteristic
540C22×C11#52011yescharacteristic
541C22×C11#53411yescharacteristic
542C22×C11#53711yescharacteristic
543C22×C11#53811yescharacteristic
544C22×C11#53811yescharacteristic
545C22×C11#53811yescharacteristic
546C22×C11#53811yescharacteristic
547C22×C11#53911yescharacteristic
548C22×C11#53911yescharacteristic
549C22×C11#53911yescharacteristic
550C22×C11#53911yescharacteristic
551C22×C11#54011yescharacteristic
552C22×C11#54211yescharacteristic
553C22×C11#54611yescharacteristic
554C22×C11#54611yescharacteristic
555C22×C11#54611yescharacteristic
556C22×C11#54611yescharacteristic
557C22×C11#55111yescharacteristic
558C22×C11#55111yescharacteristic
559C22×C11#55111yescharacteristic
560C22×C11#55111yescharacteristic
561C22×C11#55311yescharacteristic
562C22×C11#55311yescharacteristic
563C22×C11#55311yescharacteristic
564C22×C11#55311yescharacteristic
565C22×C11#56011yescharacteristic
566C22×C11#56011yescharacteristic
567C22×C11#56011yescharacteristic
568C22×C11H(3,𝔽4)11yescharacteristic
569C2×D11—24no—
570C2×D11—24no—
571C2×D11—24no—
572C2×D11—24no—
573C2×D11—24no—
574C2×D11—24no—
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—42no—
587C2×D11—42no—
588C2×D11—42no—
589C2×D11—42no—
590C2×D11—42no—
591C2×D11—42no—
592C2×D11—42no—
593C2×D11—42no—
594C2×D11—42no—
595C2×D11—42no—
596C2×D11—42no—
597C2×D11—42no—
598C2×D11—42no—
599C4×C11—42no—
600C4×C11—42no—
601C4×C11—42no—
602C4×C11—42no—
603C4×C11—42no—
604C4×C11—81no—
605C4×C11—81no—
606Dic11—42no—
607Dic11—42no—
608Dic11—42no—
609Dic11—42no—
610Dic11—81no—
611Dic11—81no—
612C25—111no—
613C25—111no—
614C22×D4—114no—
615C22×D4—222no—
616C22×D4—222no—
617C22×D4—222no—
618C22×D4—222no—
619C22×D4—441no—
620C22×D4—441no—
621C23×C4—111no—
622C23×C4—111no—
623C23×C4—111no—
624C23×C4—111no—
625C23×C4—114no—
626C23×C4—111no—
627C23×C4—111no—
628C23×C4—222no—
629C23×C4—222no—
630C23×C4—222no—
631C23×C4—441no—
632C23×C4—441no—
633C23×C4—441no—
634C23×C4—441no—
635C23×C4—441no—
636C23×C4—441no—
637C23×C4—441no—
638C23×C4—441no—
639C23×C4—441no—
640C23×C4—441no—
641C23×C4C22×D1111yescharacteristic
642C23×C4C22×D1111yescharacteristic
643C23×C4C22×D1111yescharacteristic
644C23×C4C22×D1111yescharacteristic
645C23×C4C22×D1111yescharacteristic
646C23×C4C22×D1111yescharacteristic
647C23×C4C22×D1111yescharacteristic
648C2×C4⋊C4—222no—
649C2×C4⋊C4—441no—
650C2×C4⋊C4—441no—
651C2×C22⋊C4—114no—
652C2×C22⋊C4—114no—
653C2×C22⋊C4—114no—
654C2×C22⋊C4—114no—
655C2×C22⋊C4—222no—
656C2×C22⋊C4—222no—
657C2×C22⋊C4—222no—
658C2×C22⋊C4—222no—
659C2×C22⋊C4—222no—
660C2×C22⋊C4—222no—
661C2×C22⋊C4—222no—
662C2×C22⋊C4—222no—
663C2×C22⋊C4—222no—
664C2×C22⋊C4—222no—
665C2×C22⋊C4—222no—
666C2×C22⋊C4—222no—
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×C22⋊C4—441no—
676C2×C22⋊C4—441no—
677C2×C22⋊C4—441no—
678C2×C22⋊C4—441no—
679C2×C22⋊C4—441no—
680C2×C22⋊C4—441no—
681C2×C42—222no—
682C2×C42—222no—
683C2×C42—441no—
684#95—22no—
685#95—22no—
686#95—41no—
687#95—41no—
688#95—41no—
689#95—41no—
690#95—114no—
691#95—222no—
692#95—222no—
693#95—222no—
694#95—441no—
695#95—441no—
696#95—441no—
697#95—441no—
698#95—441no—
699#95—441no—
700#95—441no—
701#95—441no—
702#95—441no—
703#95C4×D1114yescomplemented
704C2×C11#231811yescharacteristic
705C2×C11#232511yescharacteristic
706C2×C11#233511yescharacteristic
707C2×C11#234211yescharacteristic
708C2×C11#235311yescharacteristic
709C2×C11#236411yescharacteristic
710C2×C11#237511yescharacteristic
711C2×C11#268411yescharacteristic
712C2×C11#268811yescharacteristic
713C2×C11#269111yescharacteristic
714C2×C11#269311yescharacteristic
715C2×C11#274611yescharacteristic
716C2×C11#274911yescharacteristic
717C2×C11#277811yescharacteristic
718C2×C11#278211yescharacteristic
719D11—44no—
720D11—44no—
721C24—112no—
722C24—112no—
723C24—112no—
724C24—112no—
725C24—112no—
726C24—112no—
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—
746C24—221no—
747C24—221no—
748C24—221no—
749C24—221no—
750C24—221no—
751C24C23×D1111yescharacteristic
752C2×D4—228no—
753C2×D4—228no—
754C2×D4—444no—
755C2×D4—444no—
756C2×D4—444no—
757C2×D4—444no—
758C2×D4—444no—
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—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—112no—
804C22×C4—112no—
805C22×C4—112no—
806C22×C4—112no—
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—221no—
840C22×C4—221no—
841C22×C4—221no—
842C22×C4—221no—
843C22×C4—221no—
844C22×C4—221no—
845C22×C4—444no—
846C22×C4—444no—
847C22×C4—444no—
848C22×C4—444no—
849C22×C4—444no—
850C22×C4—444no—
851C22×C4—444no—
852C22×C4—444no—
853C22×C4—444no—
854C22×C4—444no—
855C22×C4—444no—
856C22×C4—444no—
857C22×C4—444no—
858C22×C4—444no—
859C22×C4C2×C4×D1112yes—
860C22×C4C2×C4×D1112yes—
861C22×C4C2×C4×D1112yes—
862C22×C4D4×D1112yes—
863C22×C4#434312yes—
864C4⋊C4—444no—
865C22⋊C4—228no—
866C22⋊C4—444no—
867C22⋊C4—444no—
868C22⋊C4—444no—
869C22⋊C4—444no—
870C22⋊C4—444no—
871C22⋊C4—444no—
872C22⋊C4—444no—
873C22⋊C4—444no—
874C22⋊C4—444no—
875C42—444no—
876C11#1442711yescharacteristic, complemented, Sylow
877C23—114no—
878C23—114no—
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—222no—
895C23—222no—
896C23—222no—
897C23—222no—
898C23—222no—
899C23—222no—
900C23—222no—
901C23—222no—
902C23—222no—
903C23—222no—
904C23—222no—
905C23—222no—
906C23—222no—
907C23—222no—
908C23—222no—
909C23—222no—
910C23—222no—
911C23—222no—
912C23—222no—
913C23—222no—
914C23—222no—
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—
938C23—441no—
939C23—441no—
940C23—441no—
941C23—441no—
942C23—441no—
943C23—441no—
944C23—441no—
945C23—441no—
946C23—441no—
947C23C22×C4×D1111yescharacteristic
948C23C2×D4×D1111yescharacteristic
949C23#6703711yescharacteristic
950C23#6703711yescharacteristic
951C23C2×#434311yescharacteristic
952C23#41×D1111yescharacteristic
953C23#41×D1111yescharacteristic
954C23#41×D1111yescharacteristic
955C23#41×D1111yescharacteristic
956C23#6704211yescharacteristic
957C23#6704211yescharacteristic
958C23#6704211yescharacteristic
959C23#6704211yescharacteristic
960C23#6704211yescharacteristic
961C23#6704311yescharacteristic
962D4—4416no—
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—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
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—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—222no—
1013C2×C4—222no—
1014C2×C4—222no—
1015C2×C4—222no—
1016C2×C4—222no—
1017C2×C4—222no—
1018C2×C4—222no—
1019C2×C4—222no—
1020C2×C4—222no—
1021C2×C4—222no—
1022C2×C4—222no—
1023C2×C4—222no—
1024C2×C4—4416no—
1025C2×C4—4416no—
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—441no—
1046C2×C4—441no—
1047C2×C4—441no—
1048C2×C4—441no—
1049C2×C4—441no—
1050C2×C4—441no—
1051C2×C4—441no—
1052C2×C4—441no—
1053C2×C4—441no—
1054C2×C4—441no—
1055C2×C4—441no—
1056C22—224no—
1057C22—224no—
1058C22—224no—
1059C22—224no—
1060C22—224no—
1061C22—224no—
1062C22—442no—
1063C22—442no—
1064C22—442no—
1065C22—442no—
1066C22—442no—
1067C22—442no—
1068C22—442no—
1069C22—442no—
1070C22—442no—
1071C22—442no—
1072C22—442no—
1073C22—442no—
1074C22—442no—
1075C22—442no—
1076C22—442no—
1077C22—442no—
1078C22—442no—
1079C22—442no—
1080C22—442no—
1081C22—442no—
1082C22—442no—
1083C22—442no—
1084C22—442no—
1085C22—442no—
1086C22D11×#11711yescharacteristic
1087C22#1062305211yescharacteristic
1088C22#1062305411yescharacteristic
1089C22C4×D4×D1111yescharacteristic
1090C22#1062307611yescharacteristic
1091C22#1062307611yescharacteristic
1092C22C4×#434311yescharacteristic
1093C22#1062313911yescharacteristic
1094C22#1062314111yescharacteristic
1095C22#1062315111yescharacteristic
1096C22#1062316111yescharacteristic
1097C22#1062316811yescharacteristic
1098C22#1062317611yescharacteristic
1099C22#1062318411yescharacteristic
1100C22#1062318511yescharacteristic
1101C22#1062318811yescharacteristic
1102C22#1062319011yescharacteristic
1103C22#1062319211yescharacteristic
1104C22#1062319711yescharacteristic
1105C22#1062320711yescharacteristic
1106C22#1062320911yescharacteristic
1107C22#1062321411yescharacteristic
1108C22#1062322611yescharacteristic
1109C22#1062322611yescharacteristic
1110C22#1062322911yescharacteristic
1111C22#1062323511yescharacteristic
1112C22#1062323511yescharacteristic
1113C22#1062323611yescharacteristic
1114C22#1062323611yescharacteristic
1115C22#1062323811yescharacteristic
1116C22#1062323811yescharacteristic
1117C22#1062323811yescharacteristic
1118C22#1062324011yescharacteristic
1119C22#1062324111yescharacteristic
1120C22#1062324211yescharacteristic
1121C4—42no—
1122C4—42no—
1123C4—42no—
1124C4—42no—
1125C4—42no—
1126C4—81no—
1127C4—81no—
1128C4—442no—
1129C4—442no—
1130C4—442no—
1131C4—442no—
1132C4—881no—
1133C4—881no—
1134C2—444no—
1135C2—444no—
1136C2#1307124711yescharacteristic
1137C2#1307132011yescharacteristic
1138C2#1307140511yescharacteristic
1139C2#1307146411yescharacteristic
1140C2#1307155511yescharacteristic
1141C2#1307166211yescharacteristic
1142C2#1307175611yescharacteristic
1143C2#1307499811yescharacteristic
1144C2#1307505911yescharacteristic
1145C2#1307509911yescharacteristic
1146C2#1307512811yescharacteristic
1147C2#1307579311yescharacteristic
1148C2#1307584611yescharacteristic
1149C2#1307623311yescharacteristic
1150C2#1307629511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1443C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1443D11
hypocenterC11#14427
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1443

Complements

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

NH ≅ G/Ntype
1. C2×#10622283C2semidirect
4. #13066877C2semidirect
5. #13066873C2semidirect
6. #13066864C2semidirect
7. #13066862C2semidirect
9. #13066852C2semidirect
10. #13066842C2semidirect
11. (C2×D11)⋊#95C2semidirect
12. (C2×D11)⋊#95C2semidirect
13. (C2×D11)⋊#95C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1443C2semidirect
53. #10622278C4semidirect
89. C22×C4×D11C2×C4semidirect
118. C2×(C2×D11)⋊C4C2×C4semidirect
132. C11×#95C2×C4semidirect
145. C11⋊#95C2×C4semidirect
306. #1443D11semidirect
703. #95C4×D11semidirect
876. C11#14427semidirect

Maximal subgroups

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

subgroupindex
C2×#106222832
C2×#106222782
#130668772
#130668732
#130668642
#130668622
#130668562
#130668522
#130668422
(C2×D11)⋊#952
C11×#14432
#1442711