Finite Group Databasebeta

← #14720148

Subgroups — #14720148

Order 2816.

1314 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622538C211yesmaximal, characteristic, complemented
2C2×#10622538C211yesmaximal, characteristic, complemented
3#13067011C212yesmaximal, complemented
4#13067007C212yesmaximal, complemented
5#13067003C214yesmaximal, complemented
6#13066998C214yesmaximal, complemented
7C2×C4×C11×#41C211yesmaximal, characteristic
8C22×C11×#41C411yescharacteristic
9C4×C11×#41—21no—
10C4×C11×#41—21no—
11C4×C11×#41—21no—
12C4×C11×#41—21no—
13C4×C11×#41C412yes—
14C4×C11×#41C412yes—
15C4×C11×#41C2212yes—
16C4×C11×#41C2212yes—
17C2×C4×Q8×C11C411yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11—21no—
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11C411yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C11×#117—21no—
24C2×C11×#117C411yescharacteristic
25C22×C42×C11—21no—
26C22×C42×C11C2211yescharacteristic
27C2×C22⋊(C11⋊C8)—21no—
28C2×C22⋊(C11⋊C8)—21no—
29#10622538—21no—
30#10622538—21no—
31#10622538—21no—
32#10622538—21no—
33#10622538C2212yes—
34#10622538C2212yes—
35#10622538C2212yescomplemented
36#10622538C2212yescomplemented
37C2×C4⋊(C11⋊C8)—21no—
38C2×C4⋊(C11⋊C8)C2212yescomplemented
39C2×C4×C11⋊C8—21no—
40C2×C4×C11⋊C8C2212yescomplemented
41Q8⋊(C11⋊C8)C2218yescomplemented
42D4⋊(C11⋊C8)C2218yescomplemented
43C2×C11×#41—21no—
44C2×C11×#41—21no—
45C2×C11×#41—24no—
46C2×C11×#41C818yescomplemented
47C2×C11×#41C2×C412yes—
48C2×C11×#41C2×C412yes—
49C22×Q8×C11C2×C411yescharacteristic
50C22×D4×C11—21no—
51C22×D4×C11C2×C411yescharacteristic
52C23×C4×C11—21no—
53C23×C4×C11—21no—
54C23×C4×C11—21no—
55C23×C4×C11C2×C411yescharacteristic
56C23×C4×C11D411yescharacteristic
57C23×C4×C11D411yescharacteristic
58C4×Q8×C11—21no—
59C4×Q8×C11—21no—
60C4×Q8×C11—21no—
61C4×Q8×C11—21no—
62C4×Q8×C11C2×C412yes—
63C4×Q8×C11C2×C412yes—
64C4×Q8×C11C2×C412yes—
65C4×Q8×C11C2312yes—
66C4×D4×C11—22no—
67C4×D4×C11—22no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C4×D4×C11—21no—
75C4×D4×C11—21no—
76C4×D4×C11—21no—
77C4×D4×C11—21no—
78C4×D4×C11C2×C412yes—
79C4×D4×C11C2×C412yes—
80C4×D4×C11C2×C412yes—
81C4×D4×C11C2312yes—
82C11×#117—21no—
83C11×#117—21no—
84C11×#117—22no—
85C11×#117—22no—
86C11×#117—22no—
87C11×#117—22no—
88C11×#117C2×C412yes—
89C11×#117C2×C412yes—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4C2×C411yescharacteristic
93C2×C11×C4⋊C4C2×C411yescharacteristic
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C42×C11—21no—
98C2×C42×C11—21no—
99C2×C42×C11—21no—
100C2×C42×C11—22no—
101C2×C42×C11—22no—
102C2×C42×C11—22no—
103C2×C42×C11—22no—
104C2×C42×C11C2×C411yescharacteristic
105C2×C42×C11C2×C411yescharacteristic
106C2×C42×C11C2×C411yescharacteristic
107C2×C42×C11D411yescharacteristic
108C2×C42×C11D411yescharacteristic
109C2×C42×C11D411yescharacteristic
110C2×C42×C11D411yescharacteristic
111C2×C42×C11D411yescharacteristic
112C2×C42×C11D411yescharacteristic
113C2×C42×C11C2311yescharacteristic
114C2×C42×C11C2311yescharacteristic
115C2×C42×C11C2311yescharacteristic
116C22×C11⋊C8—22no—
117C22×C11⋊C8—22no—
118C22⋊(C11⋊C8)—22no—
119C22⋊(C11⋊C8)—22no—
120C22⋊(C11⋊C8)—22no—
121C22⋊(C11⋊C8)—22no—
122C4⋊(C11⋊C8)—22no—
123C4⋊(C11⋊C8)—22no—
124C4⋊(C11⋊C8)—22no—
125C4⋊(C11⋊C8)C2314yes—
126C4×C11⋊C8—22no—
127C4×C11⋊C8—22no—
128C4×C11⋊C8—22no—
129C4×C11⋊C8C2314yes—
130#17437—111nomaximal, Sylow
131C24×C11—21no—
132C24×C11C22⋊C411yescharacteristic
133C11×#41—28no—
134C11×#41—28no—
135C11×#41—24no—
136C11×#41—24no—
137C11×#41C2×C818yescomplemented
138C11×#41C2×C818yescomplemented
139C2×Q8×C11—21no—
140C2×Q8×C11—22no—
141C2×Q8×C11C2×C814yescomplemented
142C2×Q8×C11C22×C412yes—
143C2×D4×C11—28no—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—21no—
147C2×D4×C11—22no—
148C2×D4×C11C2×C814yescomplemented
149C2×D4×C11C22×C412yes—
150C22×C4×C11—21no—
151C22×C4×C11—28no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—42no—
161C22×C4×C11—42no—
162C22×C4×C11—44no—
163C22×C4×C11—44no—
164C22×C4×C11C22⋊C411yescharacteristic
165C22×C4×C11C22⋊C411yescharacteristic
166C22×C4×C11C22⋊C411yescharacteristic
167C22×C4×C11C22⋊C411yescharacteristic
168C22×C4×C11C22⋊C411yescharacteristic
169C22×C4×C11C22⋊C411yescharacteristic
170C22×C4×C11C22⋊C411yescharacteristic
171C22×C4×C11C22⋊C411yescharacteristic
172C22×C4×C11C22⋊C411yescharacteristic
173C22×C4×C11C2×C814yes—
174C22×C4×C11M1614yes—
175C22×C4×C11C22×C411yescharacteristic
176C22×C4×C11C22×C411yescharacteristic
177C22×C4×C11C22×C411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4C22×C412yes—
191C11×C4⋊C4C22×C412yes—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—22no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—22no—
198C42×C11—22no—
199C42×C11—22no—
200C42×C11—22no—
201C42×C11—22no—
202C42×C11—22no—
203C42×C11—22no—
204C42×C11C22⋊C411yescharacteristic
205C42×C11C22⋊C411yescharacteristic
206C42×C11C22⋊C411yescharacteristic
207C42×C11C22⋊C411yescharacteristic
208C42×C11C22⋊C411yescharacteristic
209C42×C11C22⋊C411yescharacteristic
210C42×C11C22×C411yescharacteristic
211C42×C11C22×C411yescharacteristic
212C42×C11C22×C411yescharacteristic
213C42×C11C2×D411yescharacteristic
214C42×C11C2×D411yescharacteristic
215C42×C11C2×D411yescharacteristic
216C42×C11C2×D411yescharacteristic
217C42×C11C2×D411yescharacteristic
218C42×C11C2×D411yescharacteristic
219C42×C11C2411yescharacteristic
220C2×C11⋊C8—24no—
221C2×C11⋊C8—24no—
222C2×C11⋊C8—44no—
223C2×C11⋊C8—44no—
224C2×C4×#41D1111yescharacteristic
225C2×#431—111no—
226C2×#431—111no—
227#1479—112no—
228#1478—112no—
229#1477—114no—
230#1476—114no—
231C23×C11—22no—
232C23×C11—24no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—42no—
236C23×C11—42no—
237C23×C11C22⋊C814yes—
238C23×C11C2×C22⋊C411yescharacteristic
239C23×C11C2×C22⋊C411yescharacteristic
240C23×C11C2×C22⋊C411yescharacteristic
241Q8×C11—22no—
242Q8×C11—24no—
243Q8×C11C22×C814yes—
244D4×C11—28no—
245D4×C11—28no—
246D4×C11—22no—
247D4×C11—24no—
248D4×C11C22×C814yes—
249C2×C4×C11—22no—
250C2×C4×C11—24no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—28no—
255C2×C4×C11—28no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—44no—
268C2×C4×C11—44no—
269C2×C4×C11—42no—
270C2×C4×C11—42no—
271C2×C4×C11—44no—
272C2×C4×C11—44no—
273C2×C4×C11C22⋊C814yes—
274C2×C4×C11C22⋊C814yes—
275C2×C4×C11C22⋊C814yes—
276C2×C4×C11C2×C22⋊C411yescharacteristic
277C2×C4×C11C2×C22⋊C411yescharacteristic
278C2×C4×C11C2×C22⋊C411yescharacteristic
279C2×C4×C11C2×C22⋊C411yescharacteristic
280C2×C4×C11C2×C22⋊C411yescharacteristic
281C2×C4×C11C2×C22⋊C411yescharacteristic
282C2×C4×C11C2×C22⋊C411yescharacteristic
283C2×C4×C11C2×C22⋊C411yescharacteristic
284C2×C4×C11C2×C22⋊C411yescharacteristic
285C2×C4×C11C22×C812yes—
286C2×C4×C11C22×C812yes—
287C2×C4×C11C22×C812yes—
288C2×C4×C11C2×M1612yes—
289C2×C4×C11C2×M1612yes—
290C2×C4×C11C2×M1612yes—
291C2×C4×C11C23×C411yescharacteristic
292C2×C4×C11C22×D411yescharacteristic
293C2×C4×C11C22×D411yescharacteristic
294C11⋊C8—44no—
295C11⋊C8—44no—
296C22×#41Dic1111yescharacteristic
297C4×#41—21no—
298C4×#41—21no—
299C4×#41—21no—
300C4×#41—21no—
301C4×#41Dic1112yes—
302C4×#41Dic1112yes—
303C4×#41C2×D1112yes—
304C4×#41C2×D1112yes—
305C2×C4×Q8Dic1111yescharacteristic
306C2×C4×Q8C2×D1111yescharacteristic
307C2×C4×D4—21no—
308C2×C4×D4—21no—
309C2×C4×D4Dic1111yescharacteristic
310C2×C4×D4C2×D1111yescharacteristic
311C2×#117—21no—
312C2×#117Dic1111yescharacteristic
313C22×C42—21no—
314C22×C42C2×D1111yescharacteristic
315#431—112no—
316#431—112no—
317#431—112no—
318#431—112no—
319#431—221no—
320#431—221no—
321#431—221no—
322#431—221no—
323C2×C4⋊C8—112no—
324C2×C4⋊C8—221no—
325C2×C22⋊C8—221no—
326C2×C22⋊C8—221no—
327C2×C4×C8—112no—
328C2×C4×C8—221no—
329Q8⋊C8—118no—
330D4⋊C8—118no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—21no—
334C22×C11—21no—
335C22×C11—21no—
336C22×C11—21no—
337C22×C11—24no—
338C22×C11—44no—
339C22×C11—48no—
340C22×C11—42no—
341C22×C11—42no—
342C22×C11C2×C22⋊C812yes—
343C22×C11C2×C22⋊C812yes—
344C22×C11C2×C22⋊C812yes—
345C22×C11C22×C22⋊C411yescharacteristic
346C4×C11—24no—
347C4×C11—21no—
348C4×C11—21no—
349C4×C11—21no—
350C4×C11—21no—
351C4×C11—21no—
352C4×C11—21no—
353C4×C11—42no—
354C4×C11—42no—
355C4×C11C2×C22⋊C812yes—
356C4×C11C2×C22⋊C812yes—
357C4×C11C2×C22⋊C812yes—
358C4×C11#42112yes—
359C4×C11C23×C811yescharacteristic
360C4×C11C22×M1611yescharacteristic
361C4×C11#57512yes—
362C2×#41—24no—
363C2×#41—21no—
364C2×#41—21no—
365C2×#41C11⋊C818yescomplemented
366C2×#41C2×Dic1112yes—
367C2×#41C2×Dic1112yes—
368C22×Q8C2×Dic1111yescharacteristic
369C22×D4—21no—
370C22×D4C2×Dic1111yescharacteristic
371C23×C4—21no—
372C23×C4—21no—
373C23×C4—21no—
374C23×C4C2×Dic1111yescharacteristic
375C23×C4C22⋊D1111yescharacteristic
376C23×C4C22⋊D1111yescharacteristic
377C22×C8—222no—
378C22×C8—222no—
379C4×Q8—21no—
380C4×Q8—21no—
381C4×Q8—21no—
382C4×Q8—21no—
383C4×Q8C2×Dic1112yes—
384C4×Q8C2×Dic1112yes—
385C4×Q8C2×Dic1112yes—
386C4×Q8C22×D1112yes—
387C4×D4—22no—
388C4×D4—22no—
389C4×D4—22no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—22no—
393C4×D4—22no—
394C4×D4—22no—
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4C2×Dic1112yes—
400C4×D4C2×Dic1112yes—
401C4×D4C2×Dic1112yes—
402C4×D4C22×D1112yes—
403#117—21no—
404#117—21no—
405#117—22no—
406#117—22no—
407#117—22no—
408#117—22no—
409#117C2×Dic1112yes—
410#117C2×Dic1112yes—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4C2×Dic1111yescharacteristic
414C2×C4⋊C4C2×Dic1111yescharacteristic
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C42—21no—
419C2×C42—21no—
420C2×C42—21no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42C2×Dic1111yescharacteristic
426C2×C42C2×Dic1111yescharacteristic
427C2×C42C2×Dic1111yescharacteristic
428C2×C42C22⋊D1111yescharacteristic
429C2×C42C22⋊D1111yescharacteristic
430C2×C42C22⋊D1111yescharacteristic
431C2×C42C22⋊D1111yescharacteristic
432C2×C42C22⋊D1111yescharacteristic
433C2×C42C22⋊D1111yescharacteristic
434C2×C42C22×D1111yescharacteristic
435C2×C42C22×D1111yescharacteristic
436C2×C42C22×D1111yescharacteristic
437C4⋊C8—114no—
438C4⋊C8—222no—
439C4⋊C8—222no—
440C4⋊C8—222no—
441C22⋊C8—222no—
442C22⋊C8—222no—
443C22⋊C8—222no—
444C22⋊C8—222no—
445C4×C8—114no—
446C4×C8—222no—
447C4×C8—222no—
448C4×C8—222no—
449C2×C11—22no—
450C2×C11—22no—
451C2×C11—22no—
452C2×C11—44no—
453C2×C11C22×C22⋊C811yescharacteristic
454C2×C11#289611yescharacteristic
455C2×C11C2×#42111yescharacteristic
456C24—21no—
457C24C22⋊Dic1111yescharacteristic
458#41—28no—
459#41—28no—
460#41—24no—
461#41—24no—
462#41C2×C11⋊C818yescomplemented
463#41C2×C11⋊C818yescomplemented
464C2×Q8—22no—
465C2×Q8—21no—
466C2×Q8C2×C11⋊C814yescomplemented
467C2×Q8C22×Dic1112yes—
468C2×D4—28no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—21no—
473C2×D4C2×C11⋊C814yescomplemented
474C2×D4C22×Dic1112yes—
475C22×C4—21no—
476C22×C4—28no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—44no—
488C22×C4—44no—
489C22×C4C2×C11⋊C814yes—
490C22×C4#431814yes—
491C22×C4C22⋊Dic1111yescharacteristic
492C22×C4C22⋊Dic1111yescharacteristic
493C22×C4C22⋊Dic1111yescharacteristic
494C22×C4C22⋊Dic1111yescharacteristic
495C22×C4C22⋊Dic1111yescharacteristic
496C22×C4C22⋊Dic1111yescharacteristic
497C22×C4C22⋊Dic1111yescharacteristic
498C22×C4C22⋊Dic1111yescharacteristic
499C22×C4C22⋊Dic1111yescharacteristic
500C22×C4C22×Dic1111yescharacteristic
501C22×C4C22×Dic1111yescharacteristic
502C22×C4C22×Dic1111yescharacteristic
503C22×C4C2×C22⋊D1111yescharacteristic
504C22×C4C2×C22⋊D1111yescharacteristic
505C22×C4C2×C22⋊D1111yescharacteristic
506C22×C4C2×C22⋊D1111yescharacteristic
507C22×C4C2×C22⋊D1111yescharacteristic
508C22×C4C2×C22⋊D1111yescharacteristic
509C2×C8—224no—
510C2×C8—224no—
511C2×C8—444no—
512C2×C8—444no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—22no—
519C4⋊C4C22×Dic1112yes—
520C4⋊C4C22×Dic1112yes—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C42—22no—
528C42—22no—
529C42—22no—
530C42—22no—
531C42—22no—
532C42—22no—
533C42C22⋊Dic1111yescharacteristic
534C42C22⋊Dic1111yescharacteristic
535C42C22⋊Dic1111yescharacteristic
536C42C22⋊Dic1111yescharacteristic
537C42C22⋊Dic1111yescharacteristic
538C42C22⋊Dic1111yescharacteristic
539C42C22×Dic1111yescharacteristic
540C42C22×Dic1111yescharacteristic
541C42C22×Dic1111yescharacteristic
542C42C2×C22⋊D1111yescharacteristic
543C42C2×C22⋊D1111yescharacteristic
544C42C2×C22⋊D1111yescharacteristic
545C42C2×C22⋊D1111yescharacteristic
546C42C2×C22⋊D1111yescharacteristic
547C42C2×C22⋊D1111yescharacteristic
548C42C23×D1111yescharacteristic
549C11#1743711yescharacteristic, complemented, Sylow
550C23—24no—
551C23—22no—
552C23—41no—
553C23—41no—
554C23—42no—
555C23—42no—
556C23C22⋊(C11⋊C8)14yes—
557C23C2×C22⋊Dic1111yescharacteristic
558C23C2×C22⋊Dic1111yescharacteristic
559C23C2×C22⋊Dic1111yescharacteristic
560Q8—22no—
561Q8—24no—
562Q8C22×C11⋊C814yes—
563D4—28no—
564D4—28no—
565D4—22no—
566D4—24no—
567D4C22×C11⋊C814yes—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—28no—
571C2×C4—28no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—44no—
587C2×C4—44no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—44no—
591C2×C4—44no—
592C2×C4C22⋊(C11⋊C8)14yes—
593C2×C4C22⋊(C11⋊C8)14yes—
594C2×C4C22⋊(C11⋊C8)14yes—
595C2×C4C22×C11⋊C812yes—
596C2×C4C22×C11⋊C812yes—
597C2×C4C22×C11⋊C812yes—
598C2×C4C2×#431812yes—
599C2×C4C2×#431812yes—
600C2×C4C2×#431812yes—
601C2×C4C2×C22⋊Dic1111yescharacteristic
602C2×C4C2×C22⋊Dic1111yescharacteristic
603C2×C4C2×C22⋊Dic1111yescharacteristic
604C2×C4C2×C22⋊Dic1111yescharacteristic
605C2×C4C2×C22⋊Dic1111yescharacteristic
606C2×C4C2×C22⋊Dic1111yescharacteristic
607C2×C4C2×C22⋊Dic1111yescharacteristic
608C2×C4C2×C22⋊Dic1111yescharacteristic
609C2×C4C2×C22⋊Dic1111yescharacteristic
610C2×C4C23×Dic1111yescharacteristic
611C2×C4C22×C22⋊D1111yescharacteristic
612C2×C4C22×C22⋊D1111yescharacteristic
613C8—444no—
614C8—444no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—21no—
620C22—21no—
621C22—24no—
622C22—44no—
623C22—48no—
624C22—42no—
625C22—42no—
626C22C2×C22⋊(C11⋊C8)12yes—
627C22C2×C22⋊(C11⋊C8)12yes—
628C22C2×C22⋊(C11⋊C8)12yes—
629C22C22×C22⋊Dic1111yescharacteristic
630C4—24no—
631C4—21no—
632C4—21no—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—21no—
637C4—42no—
638C4—42no—
639C4C2×C22⋊(C11⋊C8)12yes—
640C4C2×C22⋊(C11⋊C8)12yes—
641C4C2×C22⋊(C11⋊C8)12yes—
642C4#1062284912yes—
643C4C23×C11⋊C811yescharacteristic
644C4C22×#431811yescharacteristic
645C4#1062335312yes—
646C2—22no—
647C2—22no—
648C2—22no—
649C2—44no—
650C2C22×C22⋊(C11⋊C8)11yescharacteristic
651C2#1307713511yescharacteristic
652C2C2×#1062284911yescharacteristic
subgroupG/H
centerC42C2×C22⋊D11
commutatorC4×C11C23×C8
FrattiniC42C23×D11
FittingC2×C4×C11×#41C2
socleC22×C11C22×C22⋊C4
prime radicalC22×C11×#41C4
cosocleC42×C11C24
hypercenterC2×C4×#41D11
hypocenterC11#17437
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C42 ◁ C22×C42 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#10622538C2semidirect
2. C2×#10622538C2semidirect
3. #13067011C2semidirect
4. #13067007C2semidirect
5. #13067003C2semidirect
6. #13066998C2semidirect
35. #10622538C22semidirect
36. #10622538C22semidirect
38. C2×C4⋊(C11⋊C8)C22semidirect
40. C2×C4×C11⋊C8C22semidirect
41. Q8⋊(C11⋊C8)C22semidirect
42. D4⋊(C11⋊C8)C22semidirect
46. C2×C11×#41C8semidirect
137. C11×#41C2×C8semidirect
138. C11×#41C2×C8semidirect
141. C2×Q8×C11C2×C8semidirect
148. C2×D4×C11C2×C8semidirect
365. C2×#41C11⋊C8semidirect
462. #41C2×C11⋊C8semidirect
463. #41C2×C11⋊C8semidirect
466. C2×Q8C2×C11⋊C8semidirect
473. C2×D4C2×C11⋊C8semidirect
549. C11#17437semidirect

Maximal subgroups

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

subgroupindex
C2×#106225382
#130670112
#130670072
#130670032
#130669982
C2×C4×C11×#412
#1743711