Finite Group Databasebeta

← #14681694

Subgroups — #14681694

Order 2816.

2118 conjugacy classes of subgroups.

The subgroup lattice has 1196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622552C211yesmaximal, characteristic
2C2×#10622278C211yesmaximal, characteristic
3C2×#10622278C211yesmaximal, characteristic
4C2×#10622281C211yesmaximal, characteristic, complemented
5C2×#10622281C211yesmaximal, characteristic, complemented
6C2×#10622280C211yesmaximal, characteristic, complemented
7C2×#10622600C211yesmaximal, characteristic, complemented
8#13066881C211yesmaximal, characteristic, complemented
9#13066880C211yesmaximal, characteristic, complemented
10#13066862C211yesmaximal, characteristic, complemented
11#13066860C211yesmaximal, characteristic, complemented
12#13066860C211yesmaximal, characteristic, complemented
13#13066858C211yesmaximal, characteristic, complemented
14#13066849C211yesmaximal, characteristic, complemented
15C11×#1436C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
32C22×C4⋊Dic11C2211yescharacteristic
33C22×C4⋊Dic11C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
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—
52#10622552—24no—
53#10622281—24no—
54#10622281—24no—
55#10622280—24no—
56#10622278—24no—
57#10622278C418yescomplemented
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—41no—
74C22×D44—41no—
75C22×D44—41no—
76C22×D44—41no—
77C22×D44C2×C414yes—
78C22×D44D414yes—
79C22×D44Q814yes—
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—41no—
88C22×C4×D11—41no—
89C22×C4×D11—41no—
90C22×C4×D11—41no—
91C22×C4×D11—41no—
92C22×C4×D11—41no—
93C22×C4×D11C2×C414yescomplemented
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4—41no—
97C2×C42×C11—22no—
98C2×C42×C11—41no—
99C2×C42×C11—41no—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4—22no—
102C2×(C2×D11)⋊C4—22no—
103C2×(C2×D11)⋊C4—22no—
104C2×(C2×D11)⋊C4—22no—
105C2×(C2×D11)⋊C4—22no—
106C2×(C2×D11)⋊C4—22no—
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—41no—
118C2×(C2×D11)⋊C4—41no—
119C2×(C2×D11)⋊C4—41no—
120C2×(C2×D11)⋊C4—41no—
121C2×(C2×D11)⋊C4—41no—
122C2×(C2×D11)⋊C4—41no—
123C2×(C2×D11)⋊C4—41no—
124C2×(C2×D11)⋊C4—41no—
125C2×(C2×D11)⋊C4—41no—
126C2×(C2×D11)⋊C4—41no—
127C2×(C2×D11)⋊C4C2×C414yes—
128C2×(C2×D11)⋊C4C2×C414yes—
129C2×(C2×D11)⋊C4C2×C414yescomplemented
130C2×C4⋊Dic11—22no—
131C2×C4⋊Dic11—22no—
132C2×C4⋊Dic11—22no—
133C2×C4⋊Dic11—22no—
134C2×C4⋊Dic11—41no—
135C2×C4⋊Dic11—41no—
136C2×C4⋊Dic11—41no—
137C2×C4⋊Dic11—41no—
138C2×C4⋊Dic11—41no—
139C2×Dic11⋊C4—22no—
140C2×Dic11⋊C4—22no—
141C2×Dic11⋊C4—22no—
142C2×Dic11⋊C4—22no—
143C2×Dic11⋊C4—22no—
144C2×Dic11⋊C4—41no—
145C2×Dic11⋊C4—41no—
146C2×Dic11⋊C4—41no—
147C2×Dic11⋊C4—41no—
148C11×#95—22no—
149C11×#95—22no—
150C11×#95—41no—
151C11×#95C2×C414yescomplemented
152C11×#95D414yescomplemented
153C11⋊#95—22no—
154C11⋊#95—22no—
155C11⋊#95—22no—
156C11⋊#95—22no—
157C11⋊#95—41no—
158C11⋊#95—41no—
159C11⋊#95—41no—
160C11⋊#95C2×C414yescomplemented
161C11⋊#95D414yescomplemented
162#14401—111nomaximal, Sylow
163C24×C11C2411yescharacteristic
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×D11—21no—
183C23×D11—21no—
184C23×D11—21no—
185C23×D11—21no—
186C23×D11—21no—
187C23×D11—21no—
188C23×D11C22×C412yes—
189C23×D11C22×C412yes—
190C23×D11C2×D412yes—
191C23×D11C2×D412yes—
192C23×D11C2×Q812yes—
193C23×D11C2×Q812yes—
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×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11C22×C412yes—
234C22×C4×C11C22×C412yes—
235C22×C4×C11C22×C412yes—
236C22×C4×C11C2×D412yes—
237C22×C4×C11C2×D412yes—
238C22×C4×C11C2×D412yes—
239C22×C4×C11C2×D412yes—
240C22×C4×C11C2×D412yes—
241C22×C4×C11C2×Q812yes—
242C22×C4×C11#4112yes—
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×Dic11—21no—
277C22×Dic11—21no—
278C22×Dic11—21no—
279C22×Dic11—21no—
280C22×Dic11C22×C412yes—
281C22×Dic11C22×C412yes—
282C22×Dic11C2×D412yes—
283C22×Dic11C2×D412yes—
284C22×Dic11#4112yes—
285C2×D44—44no—
286C2×D44—44no—
287C2×D44—44no—
288C2×D44—44no—
289C2×D44—44no—
290C2×D44—44no—
291C2×D44C4⋊C4116yescomplemented
292C2×C4×D11—28no—
293C2×C4×D11—28no—
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—
306C11×C4⋊C4—44no—
307C42×C11—44no—
308(C2×D11)⋊C4—28no—
309(C2×D11)⋊C4—28no—
310(C2×D11)⋊C4—44no—
311(C2×D11)⋊C4—44no—
312(C2×D11)⋊C4—44no—
313(C2×D11)⋊C4—44no—
314(C2×D11)⋊C4—44no—
315(C2×D11)⋊C4—44no—
316(C2×D11)⋊C4—44no—
317(C2×D11)⋊C4—44no—
318C4⋊Dic11—44no—
319C4⋊Dic11—44no—
320C4⋊Dic11—44no—
321Dic11⋊C4—44no—
322Dic11⋊C4—44no—
323Dic11⋊C4—44no—
324C2×#390—111no—
325C2×#386—111no—
326C2×#386—111no—
327C2×#385—111no—
328C2×#385—111no—
329C2×#380—111no—
330C2×#380—111no—
331#1444—111no—
332#1444—111no—
333#1439—111no—
334#1439—111no—
335#1439—111no—
336#1439—111no—
337#1436—111no—
338#1436D1111yescharacteristic, complemented
339C23×C11C23×C411yescharacteristic
340C23×C11C22×D411yescharacteristic
341C23×C11C22×D411yescharacteristic
342C23×C11C22×D411yescharacteristic
343C23×C11C22×Q811yescharacteristic
344C23×C11C2×#4111yescharacteristic
345C23×C11C2×#4111yescharacteristic
346C23×C11H(5,𝔽2)11yescharacteristic
347C23×C11H(5,𝔽2)11yescharacteristic
348C23×C11H(5,𝔽2)11yescharacteristic
349C23×C11H(5,𝔽2)11yescharacteristic
350C23×C11H(5,𝔽2)11yescharacteristic
351C23×C11H(5,𝔽2)11yescharacteristic
352C23×C112−1+411yescharacteristic
353C23×C112−1+411yescharacteristic
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—22no—
388C22×D11—22no—
389C22×D11—22no—
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—41no—
416C22×D11—41no—
417C22×D11—41no—
418C22×D11—41no—
419C22×D11—41no—
420C22×D11—41no—
421C22×D11—41no—
422C22×D11C2×C4⋊C414yes—
423C22×D11C2×C4⋊C414yes—
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—22no—
447C2×C4×C11—22no—
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×C11—41no—
470C2×C4×C11—41no—
471C2×C4×C11C2×C4⋊C414yes—
472C2×C4×C11C4×D414yes—
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—41no—
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—
513C2×Dic11—41no—
514C2×Dic11C4×D414yes—
515D44—416no—
516C4×D11—416no—
517C4×D11—416no—
518C23×D4—111no—
519C24×C4—111no—
520C24×C4—111no—
521C22×C4⋊C4—111no—
522C22×C4⋊C4—111no—
523C22×C4⋊C4—111no—
524C22×C4⋊C4—111no—
525C22×C4⋊C4—111no—
526C22×C4⋊C4—111no—
527C22×C4⋊C4C2×D1111yescharacteristic
528C22×C22⋊C4—111no—
529C22×C22⋊C4—111no—
530C22×C22⋊C4—111no—
531C22×C22⋊C4—111no—
532C22×C22⋊C4—111no—
533C22×C22⋊C4—111no—
534C22×C22⋊C4—111no—
535C22×C22⋊C4—111no—
536C22×C22⋊C4—111no—
537C22×C22⋊C4—111no—
538C22×C42C2×D1111yescharacteristic
539#390—224no—
540#386—118no—
541#386—224no—
542#385—224no—
543#385—224no—
544#380—224no—
545#380—224no—
546C2×#95—111no—
547C2×#95—111no—
548C2×#95—111no—
549C2×#95—111no—
550C2×#95—111no—
551C2×#95—111no—
552C2×#95—111no—
553C2×#95—111no—
554C2×#95—111no—
555C2×#95C2×D1111yescharacteristic
556C2×#95C2×D1111yescharacteristic
557C2×#95C2×D1111yescharacteristic
558C2×#95C2×D1111yescharacteristic
559C2×#95C2×D1111yescharacteristic
560C22×C11C22×C4⋊C411yescharacteristic
561C22×C11C2×C4×D411yescharacteristic
562C22×C11C2×C4×D411yescharacteristic
563C22×C11#51811yescharacteristic
564C22×C11#51811yescharacteristic
565C22×C11#52011yescharacteristic
566C22×C11#52011yescharacteristic
567C22×C11#53411yescharacteristic
568C22×C11#53411yescharacteristic
569C22×C11#53511yescharacteristic
570C22×C11#53511yescharacteristic
571C22×C11#53711yescharacteristic
572C22×C11#53711yescharacteristic
573C22×C11#54011yescharacteristic
574C22×C11#54011yescharacteristic
575C22×C11#54211yescharacteristic
576C22×C11#54211yescharacteristic
577C22×C11#54311yescharacteristic
578C22×C11#54311yescharacteristic
579C22×C11D4211yescharacteristic
580C22×C11D4211yescharacteristic
581C22×C11D4211yescharacteristic
582C22×C11#54611yescharacteristic
583C22×C11#54611yescharacteristic
584C22×C11#54711yescharacteristic
585C22×C11#54711yescharacteristic
586C22×C11D4×Q811yescharacteristic
587C22×C11D4×Q811yescharacteristic
588C22×C11#55111yescharacteristic
589C22×C11#55411yescharacteristic
590C22×C11#55411yescharacteristic
591C22×C11#56011yescharacteristic
592C22×C11#56211yescharacteristic
593C22×C11#56211yescharacteristic
594C22×C11#56311yescharacteristic
595C2×D11—24no—
596C2×D11—24no—
597C2×D11—24no—
598C2×D11—24no—
599C2×D11—24no—
600C2×D11—24no—
601C2×D11—42no—
602C2×D11—42no—
603C2×D11—42no—
604C2×D11—42no—
605C2×D11—42no—
606C2×D11—42no—
607C2×D11—42no—
608C2×D11—42no—
609C2×D11—42no—
610C2×D11—42no—
611C2×D11—42no—
612C2×D11—42no—
613C2×D11—42no—
614C2×D11—42no—
615C2×D11—42no—
616C2×D11—42no—
617C2×D11—42no—
618C2×D11—42no—
619C2×D11—42no—
620C2×D11—42no—
621C2×D11—42no—
622C2×D11—42no—
623C2×D11—42no—
624C2×D11—42no—
625C4×C11—24no—
626C4×C11—24no—
627C4×C11—42no—
628C4×C11—42no—
629C4×C11—42no—
630C4×C11—42no—
631C4×C11—81no—
632Dic11—24no—
633Dic11—42no—
634Dic11—42no—
635Dic11—81no—
636Dic11—81no—
637Dic11—81no—
638C25—111no—
639C25—111no—
640C22×D4—114no—
641C22×D4—114no—
642C22×D4—114no—
643C22×D4—441no—
644C22×D4—441no—
645C22×D4—441no—
646C22×D4—441no—
647C23×C4—111no—
648C23×C4—111no—
649C23×C4—111no—
650C23×C4—114no—
651C23×C4—111no—
652C23×C4—111no—
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—441no—
662C23×C4—441no—
663C23×C4—441no—
664C23×C4—441no—
665C23×C4—441no—
666C23×C4—441no—
667C23×C4C22×D1111yescharacteristic
668C23×C4C22×D1111yescharacteristic
669C23×C4C22×D1111yescharacteristic
670C23×C4C22×D1111yescharacteristic
671C23×C4C22×D1111yescharacteristic
672C23×C4C22×D1111yescharacteristic
673C23×C4C22×D1111yescharacteristic
674C2×C4⋊C4—22no—
675C2×C4⋊C4—22no—
676C2×C4⋊C4—41no—
677C2×C4⋊C4—222no—
678C2×C4⋊C4—222no—
679C2×C4⋊C4—222no—
680C2×C4⋊C4—222no—
681C2×C4⋊C4—222no—
682C2×C4⋊C4—222no—
683C2×C4⋊C4—222no—
684C2×C4⋊C4—222no—
685C2×C4⋊C4—222no—
686C2×C4⋊C4—441no—
687C2×C4⋊C4—441no—
688C2×C4⋊C4—441no—
689C2×C4⋊C4—441no—
690C2×C4⋊C4—441no—
691C2×C4⋊C4—441no—
692C2×C4⋊C4—441no—
693C2×C4⋊C4—441no—
694C2×C4⋊C4—441no—
695C2×C22⋊C4—114no—
696C2×C22⋊C4—114no—
697C2×C22⋊C4—114no—
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—222no—
708C2×C22⋊C4—222no—
709C2×C22⋊C4—222no—
710C2×C22⋊C4—222no—
711C2×C22⋊C4—222no—
712C2×C22⋊C4—222no—
713C2×C22⋊C4—222no—
714C2×C22⋊C4—222no—
715C2×C22⋊C4—441no—
716C2×C22⋊C4—441no—
717C2×C22⋊C4—441no—
718C2×C22⋊C4—441no—
719C2×C22⋊C4—441no—
720C2×C22⋊C4—441no—
721C2×C22⋊C4—441no—
722C2×C22⋊C4—441no—
723C2×C22⋊C4—441no—
724C2×C22⋊C4—441no—
725C2×C42—22no—
726C2×C42—41no—
727C2×C42—41no—
728#95—22no—
729#95—22no—
730#95—41no—
731#95—114no—
732#95—114no—
733#95—222no—
734#95—222no—
735#95—222no—
736#95—222no—
737#95—441no—
738#95—441no—
739#95—441no—
740#95C4×D1114yescomplemented
741#95D4414yescomplemented
742C2×C11#231511yescharacteristic
743C2×C11#232411yescharacteristic
744C2×C11#232411yescharacteristic
745C2×C11D4×C4⋊C411yescharacteristic
746C2×C11D4×C4⋊C411yescharacteristic
747C2×C11#235811yescharacteristic
748C2×C11#237611yescharacteristic
749C2×C11#266911yescharacteristic
750C2×C11#267111yescharacteristic
751C2×C11#267111yescharacteristic
752C2×C11#268311yescharacteristic
753C2×C11#269211yescharacteristic
754C2×C11#269211yescharacteristic
755C2×C11#271711yescharacteristic
756C2×C11#274811yescharacteristic
757D11—44no—
758D11—44no—
759C24—112no—
760C24—112no—
761C24—112no—
762C24—112no—
763C24—112no—
764C24—112no—
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—
784C24—221no—
785C24—221no—
786C24—221no—
787C24—221no—
788C24—221no—
789C24C23×D1111yescharacteristic
790C2×D4—1116no—
791C2×D4—444no—
792C2×D4—444no—
793C2×D4—444no—
794C2×D4—444no—
795C2×D4—444no—
796C2×D4—444no—
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—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—112no—
837C22×C4—112no—
838C22×C4—112no—
839C22×C4—112no—
840C22×C4—112no—
841C22×C4—228no—
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—228no—
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—221no—
870C22×C4—221no—
871C22×C4—221no—
872C22×C4—221no—
873C22×C4—221no—
874C22×C4—221no—
875C22×C4—221no—
876C22×C4—221no—
877C22×C4—221no—
878C22×C4—221no—
879C22×C4—221no—
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×C4C2×C4×D1112yes—
893C22×C4C2×C4×D1112yes—
894C22×C4C2×C4×D1112yes—
895C22×C4C2×D4412yes—
896C22×C4C2×D4412yes—
897C22×C4C2×D4412yes—
898C22×C4#433912yes—
899C22×C4D4×D1112yes—
900C22×C4D4×D1112yes—
901C22×C4Q8×D1112yes—
902C4⋊C4—44no—
903C4⋊C4—444no—
904C4⋊C4—444no—
905C4⋊C4—444no—
906C4⋊C4—444no—
907C4⋊C4—444no—
908C4⋊C4—444no—
909C22⋊C4—228no—
910C22⋊C4—228no—
911C22⋊C4—444no—
912C22⋊C4—444no—
913C22⋊C4—444no—
914C22⋊C4—444no—
915C22⋊C4—444no—
916C22⋊C4—444no—
917C22⋊C4—444no—
918C22⋊C4—444no—
919C42—44no—
920C11#1440111yescharacteristic, complemented, Sylow
921C23—114no—
922C23—114no—
923C23—222no—
924C23—222no—
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—441no—
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—
988C23—441no—
989C23—441no—
990C23—441no—
991C23C22×C4×D1111yescharacteristic
992C23C22×D4411yescharacteristic
993C23C2×#433911yescharacteristic
994C23C2×D4×D1111yescharacteristic
995C23C2×D4×D1111yescharacteristic
996C23#6703711yescharacteristic
997C23#6703711yescharacteristic
998C23C2×Q8×D1111yescharacteristic
999C23#6704011yescharacteristic
1000C23#41×D1111yescharacteristic
1001C23#6704211yescharacteristic
1002C23#6704211yescharacteristic
1003C23#6704211yescharacteristic
1004C23#6704211yescharacteristic
1005C23#6704311yescharacteristic
1006D4—4416no—
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—22no—
1029C2×C4—22no—
1030C2×C4—22no—
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—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—114no—
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—222no—
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×C4—441no—
1097C2×C4—441no—
1098C2×C4C4×D4414yes—
1099C2×C4C4⋊C4×D1114yes—
1100C22—224no—
1101C22—224no—
1102C22—224no—
1103C22—224no—
1104C22—224no—
1105C22—224no—
1106C22—442no—
1107C22—442no—
1108C22—442no—
1109C22—442no—
1110C22—442no—
1111C22—442no—
1112C22—442no—
1113C22—442no—
1114C22—442no—
1115C22—442no—
1116C22—442no—
1117C22—442no—
1118C22—442no—
1119C22—442no—
1120C22—442no—
1121C22—442no—
1122C22—442no—
1123C22—442no—
1124C22—442no—
1125C22—442no—
1126C22—442no—
1127C22—442no—
1128C22—442no—
1129C22—442no—
1130C22C2×C4×D4411yescharacteristic
1131C22#1062302111yescharacteristic
1132C22C2×C4⋊C4×D1111yescharacteristic
1133C22#1062304111yescharacteristic
1134C22#1062305411yescharacteristic
1135C22#1062305611yescharacteristic
1136C22#1062305811yescharacteristic
1137C22C4×D4×D1111yescharacteristic
1138C22#1062307611yescharacteristic
1139C22#1062307611yescharacteristic
1140C22D4×D4411yescharacteristic
1141C22D4×D4411yescharacteristic
1142C22#1062308211yescharacteristic
1143C22#1062308511yescharacteristic
1144C22#1062309311yescharacteristic
1145C22#1062310511yescharacteristic
1146C22Q8×D4411yescharacteristic
1147C22#1062311011yescharacteristic
1148C22#1062311311yescharacteristic
1149C22#1062312011yescharacteristic
1150C22#1062312811yescharacteristic
1151C22#1062314011yescharacteristic
1152C22#1062316211yescharacteristic
1153C22#1062316511yescharacteristic
1154C22#1062316511yescharacteristic
1155C22#1062317811yescharacteristic
1156C22#1062318411yescharacteristic
1157C22#1062319411yescharacteristic
1158C22#1062319811yescharacteristic
1159C22#1062320511yescharacteristic
1160C22#1062322111yescharacteristic
1161C22#1062323011yescharacteristic
1162C22#1062324111yescharacteristic
1163C22#1062324211yescharacteristic
1164C22#1062325811yescharacteristic
1165C4—24no—
1166C4—24no—
1167C4—42no—
1168C4—42no—
1169C4—42no—
1170C4—42no—
1171C4—81no—
1172C4—224no—
1173C4—442no—
1174C4—442no—
1175C4—881no—
1176C4—881no—
1177C4—881no—
1178C2—444no—
1179C2—444no—
1180C2#1307122711yescharacteristic
1181C2#1307130411yescharacteristic
1182C2#1307131011yescharacteristic
1183C2#1307151711yescharacteristic
1184C2C4⋊C4×D4411yescharacteristic
1185C2#1307159811yescharacteristic
1186C2#1307176311yescharacteristic
1187C2#1307483111yescharacteristic
1188C2#1307485311yescharacteristic
1189C2#1307485511yescharacteristic
1190C2#1307498711yescharacteristic
1191C2#1307510711yescharacteristic
1192C2#1307511011yescharacteristic
1193C2#1307545611yescharacteristic
1194C2#1307582411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1436D11
hypocenterC11#14401
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
4. C2×#10622281C2semidirect
5. C2×#10622281C2semidirect
6. C2×#10622280C2semidirect
7. C2×#10622600C2semidirect
8. #13066881C2semidirect
9. #13066880C2semidirect
10. #13066862C2semidirect
11. #13066860C2semidirect
12. #13066860C2semidirect
13. #13066858C2semidirect
14. #13066849C2semidirect
15. C11×#1436C2semidirect
57. #10622278C4semidirect
93. C22×C4×D11C2×C4semidirect
129. C2×(C2×D11)⋊C4C2×C4semidirect
151. C11×#95C2×C4semidirect
152. C11×#95D4semidirect
160. C11⋊#95C2×C4semidirect
161. C11⋊#95D4semidirect
291. C2×D44C4⋊C4semidirect
338. #1436D11semidirect
740. #95C4×D11semidirect
741. #95D44semidirect
920. C11#14401semidirect

Maximal subgroups

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

subgroupindex
C2×#106225522
C2×#106222782
C2×#106222812
C2×#106222802
C2×#106226002
#130668812
#130668802
#130668622
#130668602
#130668582
#130668492
C11×#14362
#1440111