Finite Group Databasebeta

← #14676934

Subgroups — #14676934

Order 2816.

2278 conjugacy classes of subgroups.

The subgroup lattice has 1194 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
4C2×#10622278C211yesmaximal, characteristic
5C2×#10622600C211yesmaximal, characteristic, complemented
6C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
7C2×D11×#95C211yesmaximal, characteristic, complemented
8#13066876C211yesmaximal, characteristic, complemented
9#13066873C211yesmaximal, characteristic, complemented
10#13066864C211yesmaximal, characteristic, complemented
11#13066858C211yesmaximal, characteristic, complemented
12#13066854C211yesmaximal, characteristic, complemented
13#13066840C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1436C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
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×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#10622600—24no—
52C4×(C2×D11)⋊C4—24no—
53#10622283—24no—
54#10622278—24no—
55#10622278—24no—
56#10622278C418yescomplemented
57D11×#95—24no—
58C24×D11C2311yescharacteristic
59C24×D11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C22×D44—22no—
74C22×D44—22no—
75C22×D44—22no—
76C22×D44—22no—
77C22×D44—22no—
78C22×D44—22no—
79C22×D44C2×C414yes—
80C22×C4×D11—22no—
81C22×C4×D11—22no—
82C22×C4×D11—22no—
83C22×C4×D11—22no—
84C22×C4×D11—22no—
85C22×C4×D11—22no—
86C22×C4×D11—22no—
87C22×C4×D11—22no—
88C22×C4×D11—22no—
89C22×C4×D11—22no—
90C22×C4×D11—22no—
91C22×C4×D11—22no—
92C22×C4×D11—22no—
93C22×C4×D11—41no—
94C22×C4×D11—41no—
95C22×C4×D11—41no—
96C22×C4×D11—41no—
97C22×C4×D11—41no—
98C22×C4×D11—41no—
99C22×C4×D11C2×C414yes—
100C22×C4×D11D414yes—
101C2×C11×C4⋊C4—22no—
102C2×C11×C4⋊C4—22no—
103C2×C11×C4⋊C4—41no—
104C2×C42×C11—22no—
105C2×C42×C11—41no—
106C2×C42×C11—41no—
107C2×(C2×D11)⋊C4—22no—
108C2×(C2×D11)⋊C4—22no—
109C2×(C2×D11)⋊C4—22no—
110C2×(C2×D11)⋊C4—22no—
111C2×(C2×D11)⋊C4—22no—
112C2×(C2×D11)⋊C4—22no—
113C2×(C2×D11)⋊C4—22no—
114C2×(C2×D11)⋊C4—22no—
115C2×(C2×D11)⋊C4—22no—
116C2×(C2×D11)⋊C4—22no—
117C2×(C2×D11)⋊C4—22no—
118C2×(C2×D11)⋊C4—22no—
119C2×(C2×D11)⋊C4—22no—
120C2×(C2×D11)⋊C4—22no—
121C2×(C2×D11)⋊C4—22no—
122C2×(C2×D11)⋊C4—22no—
123C2×(C2×D11)⋊C4—22no—
124C2×(C2×D11)⋊C4—41no—
125C2×(C2×D11)⋊C4—41no—
126C2×(C2×D11)⋊C4—41no—
127C2×(C2×D11)⋊C4—41no—
128C2×(C2×D11)⋊C4—41no—
129C2×(C2×D11)⋊C4—41no—
130C2×(C2×D11)⋊C4C2×C414yes—
131C2×(C2×D11)⋊C4C2×C414yescomplemented
132C2×(C2×D11)⋊C4C2×C414yescomplemented
133C2×(C2×D11)⋊C4D414yes—
134C2×C4⋊Dic11—22no—
135C2×C4⋊Dic11—22no—
136C2×C4⋊Dic11—41no—
137C2×C4×Dic11—22no—
138C2×C4×Dic11—22no—
139C2×C4×Dic11—22no—
140C11×#95—22no—
141C11×#95—22no—
142C11×#95—41no—
143C11×#95C2×C414yescomplemented
144C11×#95D414yescomplemented
145C11⋊#95—22no—
146C11⋊#95—22no—
147C11⋊#95—22no—
148C11⋊#95—22no—
149C11⋊#95—22no—
150C11⋊#95—22no—
151C11⋊#95—22no—
152C11⋊#95—22no—
153C11⋊#95—22no—
154C11⋊#95—22no—
155C11⋊#95—22no—
156C11⋊#95—41no—
157C11⋊#95C2×C414yescomplemented
158#13999—111nomaximal, Sylow
159C24×C11C2411yescharacteristic
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×D11—21no—
175C23×D11—21no—
176C23×D11—21no—
177C23×D11—21no—
178C23×D11—21no—
179C23×D11—21no—
180C23×D11—21no—
181C23×D11—21no—
182C23×D11C22×C412yes—
183C23×D11C22×C412yes—
184C23×D11C2×D412yes—
185C23×D11C2×D412yes—
186C23×D11#4112yes—
187C23×D11#4112yes—
188C23×D11#4112yes—
189C23×D11#4112yes—
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×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11C22×C412yes—
230C22×C4×C11C22×C412yes—
231C22×C4×C11C22×C412yes—
232C22×C4×C11C2×D412yes—
233C22×C4×C11C2×D412yes—
234C22×C4×C11C2×D412yes—
235C22×C4×C11C2×D412yes—
236C22×C4×C11C2×D412yes—
237C22×C4×C11#4112yes—
238C22×C4×C11#4112yes—
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×Dic11—21no—
266C22×Dic11—21no—
267C22×Dic11—21no—
268C22×Dic11—21no—
269C22×Dic11—21no—
270C22×Dic11—21no—
271C22×Dic11—21no—
272C22×Dic11—21no—
273C22×Dic11—21no—
274C22×Dic11—21no—
275C22×Dic11—21no—
276C22×Dic11C22×C412yes—
277C22×Dic11C22×C412yes—
278C22×Dic11C2×D412yes—
279C22×Dic11C2×D412yes—
280C22×Dic11#4112yes—
281C2×D44—28no—
282C2×D44—28no—
283C2×D44—28no—
284C2×D44—44no—
285C2×D44—44no—
286C2×D44—44no—
287C2×D44—44no—
288C2×C4×D11—28no—
289C2×C4×D11—28no—
290C2×C4×D11—28no—
291C2×C4×D11—28no—
292C2×C4×D11—28no—
293C2×C4×D11—44no—
294C2×C4×D11—44no—
295C2×C4×D11—44no—
296C2×C4×D11—44no—
297C2×C4×D11—44no—
298C2×C4×D11—44no—
299C2×C4×D11—44no—
300C2×C4×D11—44no—
301C2×C4×D11—44no—
302C2×C4×D11—44no—
303C2×C4×D11—44no—
304C2×C4×D11—44no—
305C2×C4×D11—44no—
306C2×C4×D11—44no—
307C2×C4×D11—44no—
308C2×C4×D11—44no—
309C11×C4⋊C4—44no—
310C42×C11—44no—
311(C2×D11)⋊C4—28no—
312(C2×D11)⋊C4—28no—
313(C2×D11)⋊C4—28no—
314(C2×D11)⋊C4—44no—
315(C2×D11)⋊C4—44no—
316(C2×D11)⋊C4—44no—
317(C2×D11)⋊C4—44no—
318(C2×D11)⋊C4—44no—
319(C2×D11)⋊C4—44no—
320C4⋊Dic11—44no—
321C4×Dic11—44no—
322C2×#388—111no—
323C2×#386—111no—
324C2×#386—111no—
325C2×#386—111no—
326C2×#380—111no—
327C2×C4×C22⋊C4—111no—
328C22×#95—111no—
329#1443—111no—
330#1442—111no—
331#1440—111no—
332#1439—111no—
333#1437—111no—
334#1436D1111yescharacteristic, complemented
335#1434—111no—
336C22⋊#95—111no—
337C23×C11C23×C411yescharacteristic
338C23×C11C22×D411yescharacteristic
339C23×C11C22×D411yescharacteristic
340C23×C11C22×D411yescharacteristic
341C23×C11C2×#4111yescharacteristic
342C23×C11C2×#4111yescharacteristic
343C23×C11C2×#4111yescharacteristic
344C23×C11C2×#4111yescharacteristic
345C23×C11C2×#4111yescharacteristic
346C23×C11C2×#4111yescharacteristic
347C23×C11C2×#4111yescharacteristic
348C23×C11H(5,𝔽2)11yescharacteristic
349C23×C11H(5,𝔽2)11yescharacteristic
350C23×C11H(5,𝔽2)11yescharacteristic
351C23×C112−1+411yescharacteristic
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—22no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—22no—
372C22×D11—22no—
373C22×D11—22no—
374C22×D11—22no—
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—22no—
382C22×D11—22no—
383C22×D11—22no—
384C22×D11—22no—
385C22×D11—22no—
386C22×D11—22no—
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—41no—
401C22×D11—41no—
402C22×D11—41no—
403C22×D11—41no—
404C22×D11—41no—
405C22×D11—41no—
406C22×D11—41no—
407C22×D11—41no—
408C22×D11—41no—
409C22×D11—41no—
410C22×D11—41no—
411C22×D11—41no—
412C22×D11—41no—
413C22×D11—41no—
414C22×D11—41no—
415C22×D11#11714yes—
416C22×D11C4×D414yes—
417C22×D11C4×D414yes—
418C22×D11#12114yes—
419C22×D11#12314yes—
420C22×D11#12414yes—
421C22×D11#12614yes—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
431C2×C4×C11—22no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—22no—
446C2×C4×C11—41no—
447C2×C4×C11—41no—
448C2×C4×C11—41no—
449C2×C4×C11—41no—
450C2×C4×C11—41no—
451C2×C4×C11—41no—
452C2×C4×C11—41no—
453C2×C4×C11—41no—
454C2×C4×C11—41no—
455C2×C4×C11—41no—
456C2×C4×C11—41no—
457C2×C4×C11—41no—
458C2×C4×C11—41no—
459C2×C4×C11—41no—
460C2×C4×C11—41no—
461C2×C4×C11—41no—
462C2×C4×C11—41no—
463C2×C4×C11—41no—
464C2×C4×C11—41no—
465C2×C4×C11—41no—
466C2×C4×C11—41no—
467C2×C4×C11—41no—
468C2×C4×C11—41no—
469C2×C4×C11C4×D414yes—
470C2×C4×C11#12114yes—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—22no—
477C2×Dic11—22no—
478C2×Dic11—22no—
479C2×Dic11—22no—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—22no—
483C2×Dic11—22no—
484C2×Dic11—22no—
485C2×Dic11—22no—
486C2×Dic11—41no—
487C2×Dic11—41no—
488C2×Dic11—41no—
489C2×Dic11—41no—
490C2×Dic11—41no—
491C2×Dic11—41no—
492C2×Dic11—41no—
493C2×Dic11—41no—
494C2×Dic11—41no—
495C2×Dic11—41no—
496C2×Dic11—41no—
497C2×Dic11—41no—
498C2×Dic11—41no—
499C2×Dic11—41no—
500C2×Dic11—41no—
501C2×Dic11—41no—
502C2×Dic11—41no—
503C2×Dic11—41no—
504C2×Dic11—41no—
505C2×Dic11—41no—
506C2×Dic11—41no—
507C2×Dic11—41no—
508C2×Dic11—41no—
509C2×Dic11—41no—
510C2×Dic11—41no—
511C2×Dic11—41no—
512C2×Dic11—41no—
513D44—416no—
514C4×D11—416no—
515C4×D11—416no—
516C4×D11—416no—
517C23×D4—111no—
518C24×C4—111no—
519C24×C4—111no—
520C24×C4—111no—
521C22×C4⋊C4—111no—
522C22×C4⋊C4C2×D1111yescharacteristic
523C22×C22⋊C4—111no—
524C22×C22⋊C4—111no—
525C22×C22⋊C4—111no—
526C22×C22⋊C4—111no—
527C22×C22⋊C4—111no—
528C22×C22⋊C4—111no—
529C22×C22⋊C4—111no—
530C22×C22⋊C4—111no—
531C22×C22⋊C4—111no—
532C22×C42—111no—
533C22×C42C2×D1111yescharacteristic
534#388—224no—
535#386—118no—
536#386—224no—
537#386—224no—
538#380—224no—
539C4×C22⋊C4—224no—
540C2×#95—111no—
541C2×#95—111no—
542C2×#95—111no—
543C2×#95—111no—
544C2×#95—111no—
545C2×#95—111no—
546C2×#95—111no—
547C2×#95—111no—
548C2×#95—111no—
549C2×#95—111no—
550C2×#95—111no—
551C2×#95—111no—
552C2×#95—111no—
553C2×#95—224no—
554C2×#95C2×D1111yescharacteristic
555C2×#95C2×D1111yescharacteristic
556C2×#95C2×D1111yescharacteristic
557C2×#95C2×D1111yescharacteristic
558C2×#95C2×D1111yescharacteristic
559C22×C11C2×#11711yescharacteristic
560C22×C11C2×C4×D411yescharacteristic
561C22×C11C2×C4×D411yescharacteristic
562C22×C11C2×C4×D411yescharacteristic
563C22×C11C4×#4111yescharacteristic
564C22×C11#51811yescharacteristic
565C22×C11#52011yescharacteristic
566C22×C11C2×#12111yescharacteristic
567C22×C11C2×#12111yescharacteristic
568C22×C11C2×#12311yescharacteristic
569C22×C11#52511yescharacteristic
570C22×C11C2×#12411yescharacteristic
571C22×C11C2×#12611yescharacteristic
572C22×C11#52911yescharacteristic
573C22×C11#53211yescharacteristic
574C22×C11#53411yescharacteristic
575C22×C11#53711yescharacteristic
576C22×C11#53811yescharacteristic
577C22×C11#53911yescharacteristic
578C22×C11D4211yescharacteristic
579C22×C11#54611yescharacteristic
580C22×C11#54611yescharacteristic
581C22×C11#54611yescharacteristic
582C22×C11#54611yescharacteristic
583C22×C11#54711yescharacteristic
584C22×C11#54811yescharacteristic
585C22×C11#55111yescharacteristic
586C22×C11#55111yescharacteristic
587C22×C11#55111yescharacteristic
588C22×C11#55111yescharacteristic
589C22×C11#55211yescharacteristic
590C22×C11#55211yescharacteristic
591C22×C11#55311yescharacteristic
592C22×C11#55311yescharacteristic
593C22×C11#55311yescharacteristic
594C2×D11—24no—
595C2×D11—24no—
596C2×D11—24no—
597C2×D11—24no—
598C2×D11—24no—
599C2×D11—24no—
600C2×D11—24no—
601C2×D11—24no—
602C2×D11—24no—
603C2×D11—24no—
604C2×D11—24no—
605C2×D11—24no—
606C2×D11—24no—
607C2×D11—24no—
608C2×D11—42no—
609C2×D11—42no—
610C2×D11—42no—
611C2×D11—42no—
612C2×D11—42no—
613C2×D11—42no—
614C2×D11—42no—
615C2×D11—81no—
616C2×D11—81no—
617C2×D11—81no—
618C2×D11—81no—
619C2×D11—81no—
620C2×D11—81no—
621C2×D11—81no—
622C2×D11—81no—
623C2×D11#38818yescomplemented
624C4×C11—24no—
625C4×C11—24no—
626C4×C11—42no—
627C4×C11—42no—
628C4×C11—42no—
629C4×C11—42no—
630C4×C11—81no—
631Dic11—42no—
632Dic11—42no—
633Dic11—42no—
634Dic11—42no—
635Dic11—42no—
636Dic11—81no—
637C25—111no—
638C25—111no—
639C22×D4—114no—
640C22×D4—222no—
641C22×D4—222no—
642C22×D4—222no—
643C22×D4—222no—
644C22×D4—222no—
645C22×D4—222no—
646C23×C4—111no—
647C23×C4—111no—
648C23×C4—111no—
649C23×C4—111no—
650C23×C4—111no—
651C23×C4—114no—
652C23×C4—114no—
653C23×C4—111no—
654C23×C4—222no—
655C23×C4—222no—
656C23×C4—222no—
657C23×C4—222no—
658C23×C4—222no—
659C23×C4—222no—
660C23×C4—222no—
661C23×C4—222no—
662C23×C4—222no—
663C23×C4—222no—
664C23×C4—222no—
665C23×C4—222no—
666C23×C4—222no—
667C23×C4—441no—
668C23×C4—441no—
669C23×C4—441no—
670C23×C4—441no—
671C23×C4—441no—
672C23×C4—441no—
673C23×C4C22×D1111yescharacteristic
674C23×C4C22×D1111yescharacteristic
675C23×C4C22×D1111yescharacteristic
676C23×C4C22×D1111yescharacteristic
677C23×C4C22×D1111yescharacteristic
678C23×C4C22×D1111yescharacteristic
679C23×C4C22×D1111yescharacteristic
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—41no—
683C2×C4⋊C4—222no—
684C2×C4⋊C4—222no—
685C2×C4⋊C4—441no—
686C2×C22⋊C4—114no—
687C2×C22⋊C4—114no—
688C2×C22⋊C4—114no—
689C2×C22⋊C4—114no—
690C2×C22⋊C4—222no—
691C2×C22⋊C4—222no—
692C2×C22⋊C4—222no—
693C2×C22⋊C4—222no—
694C2×C22⋊C4—222no—
695C2×C22⋊C4—222no—
696C2×C22⋊C4—222no—
697C2×C22⋊C4—222no—
698C2×C22⋊C4—222no—
699C2×C22⋊C4—222no—
700C2×C22⋊C4—222no—
701C2×C22⋊C4—222no—
702C2×C22⋊C4—222no—
703C2×C22⋊C4—222no—
704C2×C22⋊C4—222no—
705C2×C22⋊C4—222no—
706C2×C22⋊C4—222no—
707C2×C22⋊C4—441no—
708C2×C22⋊C4—441no—
709C2×C22⋊C4—441no—
710C2×C22⋊C4—441no—
711C2×C22⋊C4—441no—
712C2×C22⋊C4—441no—
713C2×C42—22no—
714C2×C42—41no—
715C2×C42—41no—
716C2×C42—222no—
717C2×C42—222no—
718C2×C42—222no—
719#95—22no—
720#95—22no—
721#95—41no—
722#95—114no—
723#95—222no—
724#95—222no—
725#95—222no—
726#95—222no—
727#95—222no—
728#95—222no—
729#95—222no—
730#95—222no—
731#95—222no—
732#95—222no—
733#95—222no—
734#95—441no—
735#95C4×D1114yescomplemented
736#95D4414yescomplemented
737C2×C11C2×#38811yescharacteristic
738C2×C11C4×#12111yescharacteristic
739C2×C11#232511yescharacteristic
740C2×C11#235211yescharacteristic
741C2×C11#235311yescharacteristic
742C2×C11#235811yescharacteristic
743C2×C11#235911yescharacteristic
744C2×C11#241211yescharacteristic
745C2×C11#241611yescharacteristic
746C2×C11#247211yescharacteristic
747C2×C11#248111yescharacteristic
748C2×C11#248811yescharacteristic
749C2×C11#249811yescharacteristic
750C2×C11#251011yescharacteristic
751C2×C11#254311yescharacteristic
752D11—28no—
753D11—82no—
754C24—112no—
755C24—112no—
756C24—112no—
757C24—112no—
758C24—112no—
759C24—112no—
760C24—112no—
761C24—112no—
762C24—221no—
763C24—221no—
764C24—221no—
765C24—221no—
766C24—221no—
767C24—221no—
768C24—221no—
769C24—221no—
770C24—221no—
771C24—221no—
772C24—221no—
773C24—221no—
774C24—221no—
775C24—221no—
776C24—221no—
777C24—221no—
778C24—221no—
779C24—221no—
780C24—221no—
781C24—221no—
782C24—221no—
783C24—221no—
784C24C23×D1111yescharacteristic
785C2×D4—228no—
786C2×D4—228no—
787C2×D4—228no—
788C2×D4—444no—
789C2×D4—444no—
790C2×D4—444no—
791C2×D4—444no—
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—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—112no—
832C22×C4—112no—
833C22×C4—112no—
834C22×C4—112no—
835C22×C4—112no—
836C22×C4—228no—
837C22×C4—228no—
838C22×C4—228no—
839C22×C4—221no—
840C22×C4—221no—
841C22×C4—221no—
842C22×C4—221no—
843C22×C4—221no—
844C22×C4—221no—
845C22×C4—221no—
846C22×C4—221no—
847C22×C4—221no—
848C22×C4—221no—
849C22×C4—221no—
850C22×C4—221no—
851C22×C4—221no—
852C22×C4—221no—
853C22×C4—221no—
854C22×C4—221no—
855C22×C4—221no—
856C22×C4—221no—
857C22×C4—221no—
858C22×C4—221no—
859C22×C4—221no—
860C22×C4—221no—
861C22×C4—221no—
862C22×C4—221no—
863C22×C4—221no—
864C22×C4—221no—
865C22×C4—221no—
866C22×C4—221no—
867C22×C4—221no—
868C22×C4—221no—
869C22×C4—228no—
870C22×C4—228no—
871C22×C4—221no—
872C22×C4—221no—
873C22×C4—221no—
874C22×C4—221no—
875C22×C4—221no—
876C22×C4—221no—
877C22×C4—221no—
878C22×C4—444no—
879C22×C4—444no—
880C22×C4—444no—
881C22×C4—444no—
882C22×C4—444no—
883C22×C4—444no—
884C22×C4—444no—
885C22×C4—444no—
886C22×C4—444no—
887C22×C4—444no—
888C22×C4—444no—
889C22×C4—444no—
890C22×C4—444no—
891C22×C4—444no—
892C22×C4—444no—
893C22×C4—444no—
894C22×C4C2×C4×D1112yes—
895C22×C4C2×C4×D1112yes—
896C22×C4C2×C4×D1112yes—
897C22×C4C2×D4412yes—
898C22×C4C2×D4412yes—
899C22×C4C2×D4412yes—
900C22×C4#433912yes—
901C22×C4D4×D1112yes—
902C22×C4D4×D1112yes—
903C22×C4#434312yes—
904C4⋊C4—44no—
905C4⋊C4—444no—
906C22⋊C4—228no—
907C22⋊C4—228no—
908C22⋊C4—228no—
909C22⋊C4—444no—
910C22⋊C4—444no—
911C22⋊C4—444no—
912C22⋊C4—444no—
913C22⋊C4—444no—
914C22⋊C4—444no—
915C42—44no—
916C42—444no—
917C11#1399911yescharacteristic, complemented, Sylow
918C23—114no—
919C23—114no—
920C23—114no—
921C23—114no—
922C23—114no—
923C23—114no—
924C23—114no—
925C23—222no—
926C23—222no—
927C23—222no—
928C23—222no—
929C23—222no—
930C23—222no—
931C23—222no—
932C23—222no—
933C23—222no—
934C23—222no—
935C23—222no—
936C23—222no—
937C23—222no—
938C23—222no—
939C23—222no—
940C23—222no—
941C23—222no—
942C23—222no—
943C23—222no—
944C23—222no—
945C23—222no—
946C23—222no—
947C23—222no—
948C23—222no—
949C23—222no—
950C23—222no—
951C23—222no—
952C23—222no—
953C23—222no—
954C23—222no—
955C23—222no—
956C23—222no—
957C23—222no—
958C23—222no—
959C23—222no—
960C23—441no—
961C23—441no—
962C23—441no—
963C23—441no—
964C23—441no—
965C23—441no—
966C23—441no—
967C23—441no—
968C23—441no—
969C23—441no—
970C23—441no—
971C23—441no—
972C23—441no—
973C23—441no—
974C23—441no—
975C23—441no—
976C23—441no—
977C23—441no—
978C23—441no—
979C23—441no—
980C23—441no—
981C23—441no—
982C23—441no—
983C23—441no—
984C23—441no—
985C23—441no—
986C23—441no—
987C23—441no—
988C23C22×C4×D1111yescharacteristic
989C23C22×D4411yescharacteristic
990C23C2×#433911yescharacteristic
991C23C2×D4×D1111yescharacteristic
992C23C2×D4×D1111yescharacteristic
993C23#6703711yescharacteristic
994C23#6703711yescharacteristic
995C23C2×#434311yescharacteristic
996C23#6704011yescharacteristic
997C23#41×D1111yescharacteristic
998C23#41×D1111yescharacteristic
999C23#41×D1111yescharacteristic
1000C23#41×D1111yescharacteristic
1001C23#41×D1111yescharacteristic
1002C23#6704211yescharacteristic
1003D4—4416no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—222no—
1052C2×C4—222no—
1053C2×C4—222no—
1054C2×C4—222no—
1055C2×C4—222no—
1056C2×C4—222no—
1057C2×C4—222no—
1058C2×C4—222no—
1059C2×C4—222no—
1060C2×C4—222no—
1061C2×C4—222no—
1062C2×C4—222no—
1063C2×C4—222no—
1064C2×C4—222no—
1065C2×C4—222no—
1066C2×C4—4416no—
1067C2×C4—4416no—
1068C2×C4—4416no—
1069C2×C4—441no—
1070C2×C4—441no—
1071C2×C4—441no—
1072C2×C4—441no—
1073C2×C4—441no—
1074C2×C4—441no—
1075C2×C4—441no—
1076C2×C4—441no—
1077C2×C4—441no—
1078C2×C4—441no—
1079C2×C4—441no—
1080C2×C4—441no—
1081C2×C4—441no—
1082C2×C4—441no—
1083C2×C4—441no—
1084C2×C4—441no—
1085C2×C4—441no—
1086C2×C4—441no—
1087C2×C4—441no—
1088C2×C4—441no—
1089C2×C4—441no—
1090C2×C4—441no—
1091C2×C4—441no—
1092C2×C4—441no—
1093C2×C4—441no—
1094C2×C4—441no—
1095C2×C4—441no—
1096C2×C4C4×D4414yes—
1097C2×C4#6694814yes—
1098C22—118no—
1099C22—224no—
1100C22—224no—
1101C22—224no—
1102C22—224no—
1103C22—224no—
1104C22—224no—
1105C22—224no—
1106C22—224no—
1107C22—224no—
1108C22—224no—
1109C22—224no—
1110C22—224no—
1111C22—224no—
1112C22—224no—
1113C22—442no—
1114C22—442no—
1115C22—442no—
1116C22—442no—
1117C22—442no—
1118C22—442no—
1119C22—442no—
1120C22—881no—
1121C22—881no—
1122C22—881no—
1123C22—881no—
1124C22—881no—
1125C22—881no—
1126C22—881no—
1127C22—881no—
1128C22C2×C4×D4411yescharacteristic
1129C22#1062302111yescharacteristic
1130C22#1062303511yescharacteristic
1131C22C2×#6694811yescharacteristic
1132C22D11×#11711yescharacteristic
1133C22#1062305511yescharacteristic
1134C22#1062305811yescharacteristic
1135C22C4×D4×D1111yescharacteristic
1136C22C4×D4×D1111yescharacteristic
1137C22#1062307611yescharacteristic
1138C22#1062307911yescharacteristic
1139C22D4×D4411yescharacteristic
1140C22#1062308511yescharacteristic
1141C22#1062308511yescharacteristic
1142C22#1062308911yescharacteristic
1143C22C4×#434311yescharacteristic
1144C22#1062310711yescharacteristic
1145C22#1062311111yescharacteristic
1146C22#1062311211yescharacteristic
1147C22#1062312011yescharacteristic
1148C22D11×#12111yescharacteristic
1149C22#1062314111yescharacteristic
1150C22#1062316011yescharacteristic
1151C22#1062316811yescharacteristic
1152C22#1062316811yescharacteristic
1153C22#1062316911yescharacteristic
1154C22D11×#12311yescharacteristic
1155C22#1062318811yescharacteristic
1156C22#1062319211yescharacteristic
1157C22D11×#12411yescharacteristic
1158C22#1062322411yescharacteristic
1159C22#1062322611yescharacteristic
1160C22D11×#12611yescharacteristic
1161C22#1062323611yescharacteristic
1162C22#1062325711yescharacteristic
1163C4—24no—
1164C4—24no—
1165C4—42no—
1166C4—42no—
1167C4—42no—
1168C4—42no—
1169C4—81no—
1170C4—442no—
1171C4—442no—
1172C4—442no—
1173C4—442no—
1174C4—442no—
1175C4—881no—
1176C2—228no—
1177C2—882no—
1178C2D11×#38811yescharacteristic
1179C2C4×#6694811yescharacteristic
1180C2#1307131311yescharacteristic
1181C2#1307154811yescharacteristic
1182C2#1307155511yescharacteristic
1183C2#1307159811yescharacteristic
1184C2#1307160311yescharacteristic
1185C2#1307201011yescharacteristic
1186C2#1307205411yescharacteristic
1187C2#1307274011yescharacteristic
1188C2#1307287511yescharacteristic
1189C2#1307294911yescharacteristic
1190C2#1307305711yescharacteristic
1191C2#1307317311yescharacteristic
1192C2#1307357511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1436D11
hypocenterC11#13999
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
1. C2×#10622283C2semidirect
5. C2×#10622600C2semidirect
6. C2×C4×(C2×D11)⋊C4C2semidirect
7. C2×D11×#95C2semidirect
8. #13066876C2semidirect
9. #13066873C2semidirect
10. #13066864C2semidirect
11. #13066858C2semidirect
12. #13066854C2semidirect
13. #13066840C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1436C2semidirect
56. #10622278C4semidirect
131. C2×(C2×D11)⋊C4C2×C4semidirect
132. C2×(C2×D11)⋊C4C2×C4semidirect
143. C11×#95C2×C4semidirect
144. C11×#95D4semidirect
157. C11⋊#95C2×C4semidirect
334. #1436D11semidirect
623. C2×D11#388semidirect
735. #95C4×D11semidirect
736. #95D44semidirect
917. C11#13999semidirect

Maximal subgroups

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

subgroupindex
C2×#106222832
C2×#106222782
C2×#106226002
C2×C4×(C2×D11)⋊C42
C2×D11×#952
#130668762
#130668732
#130668642
#130668582
#130668542
#130668402
(C2×D11)⋊#952
C11×#14362
#1399911