Finite Group Databasebeta

← #14681690

Subgroups — #14681690

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×#10622570C211yesmaximal, characteristic
2C2×#10622571C211yesmaximal, characteristic
3C2×#10622569C211yesmaximal, characteristic
4C2×#10622563C211yesmaximal, characteristic, complemented
5C2×#10622559C211yesmaximal, characteristic, complemented
6C2×#10622280C211yesmaximal, characteristic, complemented
7C2×#10622600C211yesmaximal, characteristic, complemented
8#13066880C211yesmaximal, characteristic, complemented
9#13066880C211yesmaximal, characteristic, complemented
10#13066862C211yesmaximal, characteristic, complemented
11#13066860C211yesmaximal, characteristic, complemented
12#13066859C211yesmaximal, characteristic, complemented
13#13066848C211yesmaximal, characteristic, complemented
14#13066847C211yesmaximal, characteristic, complemented
15C11×#1439C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
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#10622571—24no—
53#10622570—24no—
54#10622569C418yescomplemented
55#10622563—24no—
56#10622559—24no—
57#10622280—24no—
58C25×C11C2311yescharacteristic
59C24×D11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11—41no—
67C22×C22⋊D11—41no—
68C22×C22⋊D11—41no—
69C22×C22⋊D11—41no—
70C22×C22⋊D11C2×C414yes—
71C22×C22⋊D11D414yes—
72C22×C22⋊D11Q814yes—
73C23×Dic11—22no—
74C23×Dic11—22no—
75C23×Dic11—22no—
76C23×Dic11—41no—
77C23×Dic11—41no—
78C23×Dic11—41no—
79C23×Dic11—41no—
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C22×C4×D11—22no—
88C22×C4×D11—22no—
89C22×C4×D11—22no—
90C22×C4×D11—22no—
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×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4—22no—
99C2×C11×C22⋊C4—22no—
100C2×C11×C22⋊C4—22no—
101C2×C11×C22⋊C4—22no—
102C2×C11×C22⋊C4—41no—
103C2×C11×C22⋊C4—41no—
104C2×C11×C22⋊C4—41no—
105C2×C11×C22⋊C4C2×C414yes—
106C2×C22⋊Dic11—22no—
107C2×C22⋊Dic11—22no—
108C2×C22⋊Dic11—22no—
109C2×C22⋊Dic11—22no—
110C2×C22⋊Dic11—41no—
111C2×C22⋊Dic11C2×C414yes—
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—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)⋊C4C2×C414yescomplemented
127C2×C4⋊Dic11—22no—
128C2×C4⋊Dic11—22no—
129C2×C4⋊Dic11—22no—
130C2×C4⋊Dic11—41no—
131C2×C4⋊Dic11—41no—
132C2×C4⋊Dic11—41no—
133C2×Dic11⋊C4—22no—
134C2×Dic11⋊C4—22no—
135C2×Dic11⋊C4—22no—
136C2×Dic11⋊C4—22no—
137C2×Dic11⋊C4—22no—
138C2×Dic11⋊C4—22no—
139C2×Dic11⋊C4—41no—
140C2×Dic11⋊C4—41no—
141C2×Dic11⋊C4—41no—
142C2×Dic11⋊C4—41no—
143C2×Dic11⋊C4—41no—
144C2×Dic11⋊C4—41no—
145C2×C4×Dic11—22no—
146C2×C4×Dic11—41no—
147C2×C4×Dic11—41no—
148C11×#95—22no—
149C11×#95—41no—
150C11×#95—41no—
151C11⋊#95—22no—
152C11⋊#95—22no—
153C11⋊#95—22no—
154C11⋊#95—22no—
155C11⋊#95—22no—
156C11⋊#95—41no—
157C11⋊#95—41no—
158C11⋊#95C2×C414yescomplemented
159C11⋊#95C2×C414yescomplemented
160C11⋊#95D414yescomplemented
161C11⋊#95D414yescomplemented
162#14401—111nomaximal, Sylow
163C24×C11—21no—
164C24×C11—21no—
165C24×C11—21no—
166C24×C11—21no—
167C24×C11—21no—
168C24×C11—21no—
169C24×C11—21no—
170C24×C11—21no—
171C24×C11—21no—
172C24×C11—21no—
173C24×C11—21no—
174C24×C11—21no—
175C24×C11C22×C412yes—
176C24×C11C2×D412yes—
177C24×C11C2×Q812yes—
178C24×C11C2411yescharacteristic
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×D11—21no—
189C23×D11—21no—
190C23×D11—21no—
191C23×D11C22×C412yes—
192C23×D11C2×D412yes—
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×C11C22×C412yes—
232C22×C4×C11C22×C412yes—
233C22×C4×C11C2×D412yes—
234C22×C4×C11C2×D412yes—
235C22×C4×C11#4112yes—
236C2×C22⋊D11—44no—
237C2×C22⋊D11—44no—
238C2×C22⋊D11—44no—
239C2×C22⋊D11—44no—
240C2×C22⋊D11—44no—
241C2×C22⋊D11—44no—
242C2×C22⋊D11C4⋊C4116yescomplemented
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×Dic11—21no—
281C22×Dic11—21no—
282C22×Dic11—44no—
283C22×Dic11—44no—
284C22×Dic11—44no—
285C22×Dic11—44no—
286C22×Dic11—44no—
287C22×Dic11—44no—
288C22×Dic11—44no—
289C22×Dic11C22×C412yes—
290C22×Dic11C22×C412yes—
291C22×Dic11C22×C412yes—
292C22×Dic11C2×D412yes—
293C22×Dic11C2×D412yes—
294C22×Dic11C2×D412yes—
295C22×Dic11C2×D412yes—
296C22×Dic11C2×D412yes—
297C22×Dic11C2×Q812yes—
298C22×Dic11#4112yes—
299C2×C4×D11—28no—
300C2×C4×D11—28no—
301C2×C4×D11—44no—
302C2×C4×D11—44no—
303C2×C4×D11—44no—
304C2×C4×D11—44no—
305C2×C4×D11—44no—
306C11×C4⋊C4—44no—
307C11×C22⋊C4—28no—
308C11×C22⋊C4—44no—
309C11×C22⋊C4—44no—
310C22⋊Dic11—28no—
311C22⋊Dic11—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—
317C4⋊Dic11—44no—
318C4⋊Dic11—44no—
319Dic11⋊C4—44no—
320Dic11⋊C4—44no—
321Dic11⋊C4—44no—
322Dic11⋊C4—44no—
323C4×Dic11—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#1439D1111yescharacteristic, complemented
337#1436—111no—
338#1436—111no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—22no—
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—22no—
352C23×C11—22no—
353C23×C11—22no—
354C23×C11—22no—
355C23×C11—22no—
356C23×C11—22no—
357C23×C11—41no—
358C23×C11—41no—
359C23×C11—41no—
360C23×C11—41no—
361C23×C11—41no—
362C23×C11—41no—
363C23×C11—41no—
364C23×C11—41no—
365C23×C11—41no—
366C23×C11—41no—
367C23×C11—41no—
368C23×C11—41no—
369C23×C11—41no—
370C23×C11—41no—
371C23×C11—41no—
372C23×C11—41no—
373C23×C11C2×C4⋊C414yes—
374C23×C11C23×C411yescharacteristic
375C23×C11C22×D411yescharacteristic
376C23×C11C22×D411yescharacteristic
377C23×C11C22×D411yescharacteristic
378C23×C11C22×Q811yescharacteristic
379C23×C11C2×#4111yescharacteristic
380C23×C11C2×#4111yescharacteristic
381C23×C11H(5,𝔽2)11yescharacteristic
382C23×C11H(5,𝔽2)11yescharacteristic
383C23×C11H(5,𝔽2)11yescharacteristic
384C23×C11H(5,𝔽2)11yescharacteristic
385C23×C11H(5,𝔽2)11yescharacteristic
386C23×C11H(5,𝔽2)11yescharacteristic
387C23×C112−1+411yescharacteristic
388C23×C112−1+411yescharacteristic
389C22×D11—22no—
390C22×D11—22no—
391C22×D11—22no—
392C22×D11—22no—
393C22×D11—22no—
394C22×D11—22no—
395C22×D11—22no—
396C22×D11—22no—
397C22×D11—22no—
398C22×D11—22no—
399C22×D11—22no—
400C22×D11—22no—
401C22×D11—22no—
402C22×D11—22no—
403C22×D11—22no—
404C22×D11—22no—
405C22×D11—22no—
406C22×D11—22no—
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×D11—41no—
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—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×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×C11C4×D414yes—
466C22⋊D11—416no—
467C2×Dic11—22no—
468C2×Dic11—22no—
469C2×Dic11—22no—
470C2×Dic11—22no—
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—22no—
487C2×Dic11—22no—
488C2×Dic11—22no—
489C2×Dic11—22no—
490C2×Dic11—22no—
491C2×Dic11—416no—
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×Dic11—41no—
515C2×Dic11C2×C4⋊C414yes—
516C2×Dic11C4×D414yes—
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⋊C4C2×D1111yescharacteristic
536C22×C22⋊C4C2×D1111yescharacteristic
537C22×C22⋊C4C2×D1111yescharacteristic
538C22×C42—111no—
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×#95—111no—
556C2×#95—111no—
557C2×#95C2×D1111yescharacteristic
558C2×#95C2×D1111yescharacteristic
559C2×#95C2×D1111yescharacteristic
560C22×C11—24no—
561C22×C11—24no—
562C22×C11—24no—
563C22×C11—42no—
564C22×C11—42no—
565C22×C11—42no—
566C22×C11—42no—
567C22×C11—42no—
568C22×C11—42no—
569C22×C11—42no—
570C22×C11—42no—
571C22×C11—42no—
572C22×C11—42no—
573C22×C11—42no—
574C22×C11—42no—
575C22×C11C22×C4⋊C411yescharacteristic
576C22×C11C2×C4×D411yescharacteristic
577C22×C11C2×C4×D411yescharacteristic
578C22×C11#51811yescharacteristic
579C22×C11#51811yescharacteristic
580C22×C11#52011yescharacteristic
581C22×C11#52011yescharacteristic
582C22×C11#53411yescharacteristic
583C22×C11#53411yescharacteristic
584C22×C11#53511yescharacteristic
585C22×C11#53511yescharacteristic
586C22×C11#53711yescharacteristic
587C22×C11#53711yescharacteristic
588C22×C11#54011yescharacteristic
589C22×C11#54011yescharacteristic
590C22×C11#54211yescharacteristic
591C22×C11#54211yescharacteristic
592C22×C11#54311yescharacteristic
593C22×C11#54311yescharacteristic
594C22×C11D4211yescharacteristic
595C22×C11D4211yescharacteristic
596C22×C11D4211yescharacteristic
597C22×C11#54611yescharacteristic
598C22×C11#54611yescharacteristic
599C22×C11#54711yescharacteristic
600C22×C11#54711yescharacteristic
601C22×C11D4×Q811yescharacteristic
602C22×C11D4×Q811yescharacteristic
603C22×C11#55111yescharacteristic
604C22×C11#55411yescharacteristic
605C22×C11#55411yescharacteristic
606C22×C11#56011yescharacteristic
607C22×C11#56211yescharacteristic
608C22×C11#56211yescharacteristic
609C22×C11#56311yescharacteristic
610C2×D11—24no—
611C2×D11—24no—
612C2×D11—24no—
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—42no—
627C4×C11—42no—
628C4×C11—81no—
629C4×C11—81no—
630C4×C11—81no—
631Dic11—24no—
632Dic11—24no—
633Dic11—42no—
634Dic11—42no—
635Dic11—42no—
636Dic11—42no—
637Dic11—81no—
638C25—111no—
639C25C22×D1111yescharacteristic
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—111no—
651C23×C4—111no—
652C23×C4—111no—
653C23×C4—114no—
654C23×C4—111no—
655C23×C4—222no—
656C23×C4—222no—
657C23×C4—222no—
658C23×C4—222no—
659C23×C4—222no—
660C23×C4—222no—
661C23×C4—222no—
662C23×C4—441no—
663C23×C4—441no—
664C23×C4—441no—
665C23×C4—441no—
666C23×C4—441no—
667C23×C4—441no—
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—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—41no—
701C2×C22⋊C4—41no—
702C2×C22⋊C4—41no—
703C2×C22⋊C4—114no—
704C2×C22⋊C4—114no—
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—222no—
716C2×C22⋊C4—222no—
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⋊C4C4×D1114yes—
725C2×C42—222no—
726C2×C42—441no—
727C2×C42—441no—
728#95—22no—
729#95—41no—
730#95—41no—
731#95—114no—
732#95—114no—
733#95—114no—
734#95—114no—
735#95—222no—
736#95—222no—
737#95—222no—
738#95—222no—
739#95—222no—
740#95—441no—
741#95—441no—
742C2×C11—44no—
743C2×C11#231511yescharacteristic
744C2×C11#232411yescharacteristic
745C2×C11#232411yescharacteristic
746C2×C11D4×C4⋊C411yescharacteristic
747C2×C11D4×C4⋊C411yescharacteristic
748C2×C11#235811yescharacteristic
749C2×C11#237611yescharacteristic
750C2×C11#266911yescharacteristic
751C2×C11#267111yescharacteristic
752C2×C11#267111yescharacteristic
753C2×C11#268311yescharacteristic
754C2×C11#269211yescharacteristic
755C2×C11#269211yescharacteristic
756C2×C11#271711yescharacteristic
757C2×C11#274811yescharacteristic
758D11—44no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—112no—
772C24—112no—
773C24—112no—
774C24—221no—
775C24—221no—
776C24—221no—
777C24—221no—
778C24—221no—
779C24—221no—
780C24—221no—
781C24—221no—
782C24—221no—
783C24—221no—
784C24—221no—
785C24—221no—
786C24C2×C4×D1112yes—
787C24D4×D1112yes—
788C24Q8×D1112yes—
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—112no—
835C22×C4—112no—
836C22×C4—112no—
837C22×C4—112no—
838C22×C4—112no—
839C22×C4—112no—
840C22×C4—112no—
841C22×C4—112no—
842C22×C4—112no—
843C22×C4—112no—
844C22×C4—228no—
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—221no—
870C22×C4—221no—
871C22×C4—221no—
872C22×C4—221no—
873C22×C4—221no—
874C22×C4—221no—
875C22×C4—221no—
876C22×C4—221no—
877C22×C4—228no—
878C22×C4—221no—
879C22×C4—221no—
880C22×C4—221no—
881C22×C4—221no—
882C22×C4—221no—
883C22×C4—221no—
884C22×C4—221no—
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×C4—444no—
895C22×C4—444no—
896C22×C4—444no—
897C22×C4C2×C4×D1112yes—
898C22×C4C2×C4×D1112yes—
899C22×C4D4×D1112yes—
900C22×C4D4×D1112yes—
901C22×C4#434112yes—
902C4⋊C4—44no—
903C4⋊C4—444no—
904C4⋊C4—444no—
905C4⋊C4—444no—
906C4⋊C4—444no—
907C4⋊C4—444no—
908C4⋊C4—444no—
909C22⋊C4—28no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—228no—
913C22⋊C4—444no—
914C22⋊C4—444no—
915C22⋊C4—444no—
916C22⋊C4—444no—
917C22⋊C4—444no—
918C22⋊C4—444no—
919C42—444no—
920C11#1440111yescharacteristic, complemented, Sylow
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—114no—
956C23—222no—
957C23—222no—
958C23—222no—
959C23—222no—
960C23—222no—
961C23—222no—
962C23—222no—
963C23—222no—
964C23—222no—
965C23—222no—
966C23—222no—
967C23—222no—
968C23—222no—
969C23—222no—
970C23—222no—
971C23—222no—
972C23—222no—
973C23—222no—
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—
990C23C4⋊C4×D1114yes—
991C23C22×C4×D1111yescharacteristic
992C23C2×D4×D1111yescharacteristic
993C23C2×D4×D1111yescharacteristic
994C23C2×D4×D1111yescharacteristic
995C23C2×#434111yescharacteristic
996C23#6703711yescharacteristic
997C23#6703711yescharacteristic
998C23#6703711yescharacteristic
999C23C2×Q8×D1111yescharacteristic
1000C23#41×D1111yescharacteristic
1001C23#6704211yescharacteristic
1002C23#6704211yescharacteristic
1003C23#6704211yescharacteristic
1004C23#6704311yescharacteristic
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—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
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—114no—
1049C2×C4—114no—
1050C2×C4—222no—
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—222no—
1067C2×C4—222no—
1068C2×C4—222no—
1069C2×C4—222no—
1070C2×C4—222no—
1071C2×C4—222no—
1072C2×C4—222no—
1073C2×C4—222no—
1074C2×C4—4416no—
1075C2×C4—4416no—
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×C4—441no—
1099C2×C4(C22⋊D11)⋊C414yes—
1100C22—24no—
1101C22—24no—
1102C22—24no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—224no—
1116C22—224no—
1117C22—224no—
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×(C22⋊D11)⋊C411yescharacteristic
1131C22C2×C4⋊C4×D1111yescharacteristic
1132C22#1062305411yescharacteristic
1133C22C4×D4×D1111yescharacteristic
1134C22#1062307611yescharacteristic
1135C22#1062307611yescharacteristic
1136C22#1062307711yescharacteristic
1137C22#1062312011yescharacteristic
1138C22#1062312111yescharacteristic
1139C22#1062312211yescharacteristic
1140C22#1062312811yescharacteristic
1141C22#1062313811yescharacteristic
1142C22#1062313911yescharacteristic
1143C22#1062314011yescharacteristic
1144C22#1062314011yescharacteristic
1145C22#1062314111yescharacteristic
1146C22#1062314211yescharacteristic
1147C22#1062315211yescharacteristic
1148C22#1062316311yescharacteristic
1149C22#1062316311yescharacteristic
1150C22#1062316511yescharacteristic
1151C22#1062316511yescharacteristic
1152C22#1062316611yescharacteristic
1153C22#1062316711yescharacteristic
1154C22#1062318411yescharacteristic
1155C22#1062318611yescharacteristic
1156C22#1062318911yescharacteristic
1157C22#1062319411yescharacteristic
1158C22#1062319711yescharacteristic
1159C22#1062320511yescharacteristic
1160C22#1062321311yescharacteristic
1161C22#1062321511yescharacteristic
1162C22#1062324111yescharacteristic
1163C22#1062324311yescharacteristic
1164C22#1062325011yescharacteristic
1165C4—24no—
1166C4—42no—
1167C4—42no—
1168C4—81no—
1169C4—81no—
1170C4—81no—
1171C4—224no—
1172C4—224no—
1173C4—442no—
1174C4—442no—
1175C4—442no—
1176C4—442no—
1177C4—881no—
1178C2—44no—
1179C2—444no—
1180C2#1307122711yescharacteristic
1181C2#1307130411yescharacteristic
1182C2#1307131211yescharacteristic
1183C2#1307151211yescharacteristic
1184C2#1307151411yescharacteristic
1185C2#1307159611yescharacteristic
1186C2#1307175811yescharacteristic
1187C2#1307483211yescharacteristic
1188C2#1307485411yescharacteristic
1189C2#1307485811yescharacteristic
1190C2#1307498511yescharacteristic
1191C2#1307511111yescharacteristic
1192C2#1307511811yescharacteristic
1193C2#1307545711yescharacteristic
1194C2#1307583011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenter#1439D11
hypocenterC11#14401
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
4. C2×#10622563C2semidirect
5. C2×#10622559C2semidirect
6. C2×#10622280C2semidirect
7. C2×#10622600C2semidirect
8. #13066880C2semidirect
9. #13066880C2semidirect
10. #13066862C2semidirect
11. #13066860C2semidirect
12. #13066859C2semidirect
13. #13066848C2semidirect
14. #13066847C2semidirect
15. C11×#1439C2semidirect
54. #10622569C4semidirect
93. C22×C4×D11C2×C4semidirect
126. C2×(C2×D11)⋊C4C2×C4semidirect
158. C11⋊#95C2×C4semidirect
159. C11⋊#95C2×C4semidirect
160. C11⋊#95D4semidirect
161. C11⋊#95D4semidirect
242. C2×C22⋊D11C4⋊C4semidirect
336. #1439D11semidirect
920. C11#14401semidirect

Maximal subgroups

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

subgroupindex
C2×#106225702
C2×#106225712
C2×#106225692
C2×#106225632
C2×#106225592
C2×#106222802
C2×#106226002
#130668802
#130668622
#130668602
#130668592
#130668482
#130668472
C11×#14392
#1440111