Finite Group Databasebeta

← #15618999

Subgroups — #15618999

Order 2816.

1882 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082172C211yesmaximal, characteristic
2#13077774C212yesmaximal, complemented
3#13077771C212yesmaximal, complemented
4#13077771C211yesmaximal, characteristic, complemented
5#13077765C211yesmaximal, characteristic, complemented
6#13077760C211yesmaximal, characteristic, complemented
7#13077751C212yesmaximal, complemented
8#13077750C212yesmaximal, complemented
9#13077740C211yesmaximal, characteristic, complemented
10#13077737C211yesmaximal, characteristic, complemented
11#13077726C211yesmaximal, characteristic, complemented
12#13077725C211yesmaximal, characteristic, complemented
13#13077558C211yesmaximal, characteristic, complemented
14#13077547C211yesmaximal, characteristic, complemented
15#13077352C211yesmaximal, characteristic, complemented
16#13077339C212yesmaximal, complemented
17#13077305C212yesmaximal, complemented
18C8×D4×D11C211yesmaximal, characteristic, complemented
19#13077272C212yesmaximal, complemented
20#13077255C211yesmaximal, characteristic, complemented
21#13077181C211yesmaximal, characteristic, complemented
22D11×#424C212yesmaximal, complemented
23C11×#2994C211yesmaximal, characteristic, complemented
24C11×#529C2211yescharacteristic
25C2×M16×D11C2212yes—
26C2×#66954C2212yes—
27C22×C8×D11C2212yes—
28#10623239C412yes—
29#10623236C412yes—
30#10623225C411yescharacteristic
31#10623221C411yescharacteristic
32#10623207C411yescharacteristic
33#10623202C411yescharacteristic
34#10623192C412yes—
35#10623190C412yes—
36#10623170C411yescharacteristic
37#10623162C411yescharacteristic
38#10623147C411yescharacteristic
39#10623143C411yescharacteristic
40#10623109C2211yescharacteristic
41C4×#4343C2211yescharacteristic
42#10623088C2211yescharacteristic
43#10623088C2212yes—
44#10623078C2212yes—
45C4×D4×D11C2211yescharacteristic
46#10623059C2212yes—
47D11×#117C2212yes—
48C4×#4339C2211yescharacteristic
49C4×#4339C2211yescharacteristic
50C11×#446C2211yescharacteristic, complemented
51C8×Q8×C11C2211yescharacteristic, complemented
52C11×#436C2211yescharacteristic
53C11×#435C2212yescomplemented
54C8×D4×C11C2211yescharacteristic
55C8×D4×C11C2212yescomplemented
56C11×#433C2212yescomplemented
57C11×#431C2211yescharacteristic, complemented
58C11×#424C2212yescomplemented
59C2×C11×C4⋊C8C2211yescharacteristic, complemented
60#10622741C2212yescomplemented
61#10622740C2212yes—
62#10622732C2212yescomplemented
63C8×C22⋊D11C2212yes—
64C8×C22⋊D11C2212yescomplemented
65C8×C22⋊D11C2212yescomplemented
66C8×C22⋊D11C2212yescomplemented
67#10622715C2212yescomplemented
68#10622715C2212yescomplemented
69#10622637C2211yescharacteristic, complemented
70Q8×C11⋊C8C2211yescharacteristic, complemented
71#10622625C2211yescharacteristic
72#10622625C2212yescomplemented
73#10622624C2212yescomplemented
74D4×C11⋊C8C2211yescharacteristic
75#10622613C2212yescomplemented
76#10622612C2212yescomplemented
77#10622538C2211yescharacteristic, complemented
78#10622537C2211yescharacteristic, complemented
79#10622453C2211yescharacteristic, complemented
80#10622453C2211yescharacteristic, complemented
81#10622452C2211yescharacteristic
82#10622452C2211yescharacteristic
83#10622452C2212yes—
84#10622452C2212yes—
85#10622452C2212yes—
86#10622452C2212yescomplemented
87#10622450C2211yescharacteristic
88#10622450C2211yescharacteristic, complemented
89#10622449C2212yescomplemented
90#10622448C2212yescomplemented
91#10622447C2211yescharacteristic
92#10622447C2211yescharacteristic
93#10622447C2212yescomplemented
94#10622446C2212yescomplemented
95D11×C4⋊C8C2211yescharacteristic
96D11×C4⋊C8C2212yescomplemented
97D11×C4⋊C8C2211yescharacteristic, complemented
98D11×C4⋊C8C2212yescomplemented
99D11×C4⋊C8C2212yescomplemented
100D11×C4⋊C8C2212yescomplemented
101#10622443C2211yescharacteristic, complemented
102#10622443C2212yescomplemented
103#10622443C2211yescharacteristic, complemented
104#10622441C2212yescomplemented
105#10622343C2212yescomplemented
106#10622341C2212yes—
107#10622341C2212yescomplemented
108#10622341C2212yescomplemented
109#10622341C2212yescomplemented
110#10622340C2211yescharacteristic
111#10622340C2211yescharacteristic
112#10622339C2212yes—
113(C22⋊D11)⋊C8C2212yes—
114D11×C22⋊C8C2212yes—
115#10622333C2212yescomplemented
116#10622333C2211yescharacteristic, complemented
117#10622333C2211yescharacteristic, complemented
118#10622333C2212yescomplemented
119#10622321C2212yes—
120#10622319C2212yescomplemented
121#10622318C2212yescomplemented
122#10622314C2212yescomplemented
123#10622302C2212yes—
124C4×#4313C2211yescharacteristic
125C8×D44C2211yescharacteristic
126C8×D44C2211yescharacteristic
127C8×D44C2212yescomplemented
128#10622298C2211yescharacteristic, complemented
129#10622298C2211yescharacteristic, complemented
130#10622298C2212yescomplemented
131C4×C8×D11C2211yescharacteristic
132#10622292C2211yescharacteristic, complemented
133#10622292C2211yescharacteristic, complemented
134#10622292C2212yescomplemented
135C2×#4343C2×C411yescharacteristic
136C2×D4×D11C2×C411yescharacteristic
137C2×#4339C2×C411yescharacteristic
138C2×#4339C2311yescharacteristic
139C22×C4×D11C2312yes—
140C2×C11×M16C2312yes—
141C22×C8×C11C2312yes—
142C22×C8×C11C2312yes—
143C11×#126C2×C412yes—
144C11×#125C2×C411yescharacteristic
145C11×#124C2×C411yescharacteristic
146C11×#123C2×C412yes—
147C11×C22⋊Q8C2×C411yescharacteristic
148C11×#121C2×C411yescharacteristic
149C4×Q8×C11C2311yescharacteristic
150C4×D4×C11C2311yescharacteristic
151C4×D4×C11C2312yes—
152C11×#117C2312yes—
153C2×C42×C11C2311yescharacteristic
154#66999C2×C411yescharacteristic
155Q8×Dic11C2×C411yescharacteristic
156#66997C2×C411yescharacteristic
157#66992C2×C412yes—
158#66991C2×C412yes—
159#66991C2×C411yescharacteristic
160#66990C2×C412yes—
161#66989C2×C411yescharacteristic
162#66989C2×C412yes—
163D4×Dic11C2×C411yescharacteristic
164C4×C22⋊D11C2×C411yescharacteristic
165C4×C22⋊D11C2×C411yescharacteristic
166C4×C22⋊D11C2×C411yescharacteristic
167C4×C22⋊D11C2×C412yes—
168C4×C22⋊D11C2×C411yescharacteristic
169C4×C22⋊D11C2312yes—
170C4×C22⋊D11C2312yes—
171C4×C22⋊D11C2312yes—
172#66979C2×C411yescharacteristic
173#66979C2312yes—
174#66979C2311yescharacteristic
175C2×#4318C2312yes—
176C2×#4318C2312yes—
177C22×C11⋊C8C2312yes—
178M16×D11—44no—
179#66954—44no—
180C2×#4313C2312yes—
181C2×#4313C2311yescharacteristic
182C2×#4313C2311yescharacteristic
183C2×#4313C2312yes—
184C2×C8×D11—44no—
185C2×C8×D11C2311yescharacteristic
186C2×C8×D11C2312yes—
187C2×C8×D11C2311yescharacteristic
188C2×C8×D11C2312yes—
189C2×C8×D11C2312yes—
190C2×C8×D11C2312yes—
191C2×C8×D11C2312yes—
192C2×C8×D11C2312yes—
193#66951C2×C412yes—
194#66950C2×C412yes—
195#66950C2×C411yescharacteristic
196#66950C2×C411yescharacteristic
197#66949C2×C412yes—
198#66949C2×C412yes—
199#66949C2×C412yes—
200#66947C2×C412yes—
201#66947C2×C412yes—
202#66946C2×C412yes—
203#66946C2×C411yescharacteristic
204#66946C2×C411yescharacteristic
205#66945C2×C412yes—
206#66945C2×C412yes—
207#66945C2×C412yes—
208#66945C2×C411yescharacteristic
209C4⋊C4×D11C2×C412yes—
210C4⋊C4×D11C2×C412yes—
211C4⋊C4×D11C2×C411yescharacteristic
212#66943C2×C412yes—
213#66943C2×C411yescharacteristic
214#66942C2×C412yes—
215#66942C2×C412yes—
216#66941C2×C411yescharacteristic
217#66938C2×C412yes—
218#66937C2×C412yes—
219#66937C2×C412yes—
220#66936C2×C412yes—
221#66936C2×C412yes—
222#66936C2×C412yes—
223#66936C2×C412yes—
224#66936C2×C412yes—
225#66935C2×C412yes—
226(C22⋊D11)⋊C4C2×C412yes—
227C22⋊C4×D11C2×C412yes—
228C22⋊C4×D11C2×C412yes—
229C22⋊C4×D11C2×C412yes—
230#66932C2×C412yes—
231#66932C2×C412yes—
232#66932C2×C412yes—
233#66932C2×C412yes—
234#66931C2×C412yes—
235#66930C2×C412yes—
236#66930C2×C412yes—
237C4×D44C2×C411yescharacteristic
238C4×D44C2×C411yescharacteristic
239C4×D44C2×C411yescharacteristic
240C4×D44C2311yescharacteristic
241C4×D44C2312yes—
242#66925C2×C412yes—
243#66925C2311yescharacteristic
244#66925C2311yescharacteristic
245#66925C2312yes—
246C42×D11C2312yes—
247C42×D11C2311yescharacteristic
248C42×D11C2311yescharacteristic
249C42×D11C2312yes—
250C4×Dic22C2×C411yescharacteristic
251C4×Dic22C2×C411yescharacteristic
252C4×Dic22C2×C411yescharacteristic
253C4×Dic22C2311yescharacteristic
254C4×Dic22C2312yes—
255C11×C4⋊C8C2312yes—
256C11×C4⋊C8C2311yescharacteristic
257C11×C4⋊C8C2311yescharacteristic
258C11×C4⋊C8C2311yescharacteristic
259C11×C4⋊C8C2312yes—
260C11×C4⋊C8C2312yes—
261C11×C4⋊C8C2311yescharacteristic
262C11×C22⋊C8C2312yes—
263C11×C22⋊C8C2312yes—
264C11×C22⋊C8C2311yescharacteristic
265C11×C22⋊C8C2311yescharacteristic
266C11×#97C2312yes—
267C4×C8×C11C2311yescharacteristic
268C4×C8×C11C2311yescharacteristic
269C4×C8×C11C2312yes—
270C22⋊(C11⋊C8)C2312yes—
271C22⋊(C11⋊C8)C2311yescharacteristic
272C22⋊(C11⋊C8)C2311yescharacteristic
273C22⋊(C11⋊C8)C2312yes—
274(C2×D11)⋊C8C2312yes—
275(C2×D11)⋊C8C2311yescharacteristic
276(C2×D11)⋊C8C2312yes—
277(C2×D11)⋊C8C2311yescharacteristic
278(C2×D11)⋊C8C2312yes—
279(C2×D11)⋊C8C2311yescharacteristic
280(C2×D11)⋊C8C2311yescharacteristic
281(C2×D11)⋊C8C2312yes—
282#66879C2311yescharacteristic
283#66879C2311yescharacteristic
284#66879C2312yes—
285#66879C2312yes—
286Dic11⋊C8C2312yes—
287Dic11⋊C8C2312yes—
288Dic11⋊C8C2312yes—
289Dic11⋊C8C2312yes—
290Dic11⋊C8C2311yescharacteristic
291Dic11⋊C8C2312yes—
292Dic11⋊C8C2312yes—
293Dic11⋊C8C2312yes—
294Dic11⋊C8C2311yescharacteristic
295Dic11⋊C8C2311yescharacteristic
296Dic11⋊C8C2311yescharacteristic
297Dic11⋊C8C2312yes—
298C8×Dic11C2311yescharacteristic
299C8×Dic11C2312yes—
300C8×Dic11C2312yes—
301C8×Dic11C2311yescharacteristic
302C4⋊(C11⋊C8)C2311yescharacteristic
303C4⋊(C11⋊C8)C2311yescharacteristic
304C4⋊(C11⋊C8)C2312yes—
305C4⋊(C11⋊C8)C2311yescharacteristic
306C4⋊(C11⋊C8)C2311yescharacteristic
307C4⋊(C11⋊C8)C2312yes—
308C4⋊(C11⋊C8)C2312yes—
309#66867C2312yes—
310C4×C11⋊C8C2311yescharacteristic
311C4×C11⋊C8C2311yescharacteristic
312C4×C11⋊C8C2312yes—
313#60271—111nomaximal, Sylow
314C23×D11C22×C412yes—
315C2×Q8×C11C22×C411yescharacteristic
316C2×D4×C11C22×C411yescharacteristic
317C2×D4×C11C22×C412yes—
318C22×C4×C11C22×C411yescharacteristic
319C22×C4×C11C22×C411yescharacteristic
320C22×C4×C11C2412yes—
321C22×C4×C11C2411yescharacteristic
322C2×C22⋊D11C22×C412yes—
323C2×C22⋊D11C22×C411yescharacteristic
324C2×C22⋊D11C22×C412yes—
325C2×C22⋊D11C22×C411yescharacteristic
326C2×C22⋊D11C22×C412yes—
327C22×Dic11C22×C412yes—
328#4343—24no—
329D4×D11—24no—
330#4339—24no—
331#4339—22no—
332#4339—22no—
333C2×D44C22×C411yescharacteristic
334C2×D44C22×C412yes—
335C2×D44C22×C411yescharacteristic
336C2×C4×D11—24no—
337C2×C4×D11—24no—
338C2×C4×D11C22×C412yes—
339C2×C4×D11C22×C411yescharacteristic
340C2×C4×D11C22×C411yescharacteristic
341C2×C4×D11C22×C412yes—
342C2×C4×D11C22×C412yes—
343C2×C4×D11C22×C412yes—
344C2×C4×D11C22×C411yescharacteristic
345C2×C4×D11C22×C412yes—
346C2×C4×D11C22×C411yescharacteristic
347C2×C4×D11C22×C412yes—
348C2×C4×D11C2412yes—
349C2×C4×D11C2411yescharacteristic
350C2×C4×D11C2411yescharacteristic
351C2×Dic22C22×C411yescharacteristic
352C2×Dic22C22×C411yescharacteristic
353C2×Dic22C22×C412yes—
354C11×M16—42no—
355C2×C8×C11—42no—
356C2×C8×C11—42no—
357C2×C8×C11C2411yescharacteristic
358C2×C8×C11C2412yes—
359C2×C8×C11C2412yes—
360C2×C8×C11C2411yescharacteristic
361C2×C8×C11C2411yescharacteristic
362C2×C8×C11C2411yescharacteristic
363C11×C4⋊C4C22×C411yescharacteristic
364C11×C4⋊C4C22×C412yes—
365C11×C4⋊C4C22×C412yes—
366C11×C4⋊C4C22×C411yescharacteristic
367C11×C4⋊C4C22×C412yes—
368C11×C4⋊C4C22×C412yes—
369C11×C22⋊C4C22×C412yes—
370C11×C22⋊C4C22×C412yes—
371C11×C22⋊C4C22×C412yes—
372C11×C22⋊C4C22×C412yes—
373C11×C22⋊C4C22×C412yes—
374C42×C11C22×C411yescharacteristic
375C42×C11C22×C411yescharacteristic
376C42×C11C2411yescharacteristic
377C42×C11C2412yes—
378C42×C11C2411yescharacteristic
379C22⋊Dic11C22×C412yes—
380C22⋊Dic11C22×C412yes—
381C22⋊Dic11C22×C412yes—
382C22⋊Dic11C22×C412yes—
383C22⋊Dic11C22×C411yescharacteristic
384C22⋊Dic11C22×C412yes—
385C22⋊Dic11C22×C411yescharacteristic
386(C2×D11)⋊C4C22×C412yes—
387(C2×D11)⋊C4C22×C412yes—
388(C2×D11)⋊C4C22×C411yescharacteristic
389(C2×D11)⋊C4C22×C411yescharacteristic
390(C2×D11)⋊C4C22×C411yescharacteristic
391(C2×D11)⋊C4C22×C411yescharacteristic
392(C2×D11)⋊C4C22×C412yes—
393(C2×D11)⋊C4C22×C412yes—
394(C2×D11)⋊C4C22×C412yes—
395(C2×D11)⋊C4C22×C412yes—
396(C2×D11)⋊C4C22×C412yes—
397(C2×D11)⋊C4C22×C412yes—
398C4⋊Dic11C22×C411yescharacteristic
399C4⋊Dic11C22×C411yescharacteristic
400C4⋊Dic11C22×C411yescharacteristic
401C4⋊Dic11C22×C411yescharacteristic
402C4⋊Dic11C22×C412yes—
403C4⋊Dic11C22×C412yes—
404C4⋊Dic11C22×C412yes—
405C4⋊Dic11C22×C412yes—
406Dic11⋊C4C22×C412yes—
407Dic11⋊C4C22×C411yescharacteristic
408Dic11⋊C4C22×C411yescharacteristic
409Dic11⋊C4C22×C411yescharacteristic
410Dic11⋊C4C22×C411yescharacteristic
411Dic11⋊C4C22×C412yes—
412Dic11⋊C4C22×C412yes—
413Dic11⋊C4C22×C412yes—
414Dic11⋊C4C22×C412yes—
415Dic11⋊C4C22×C412yes—
416Dic11⋊C4C22×C412yes—
417Dic11⋊C4C22×C412yes—
418C4×Dic11C22×C412yes—
419C4×Dic11C22×C411yescharacteristic
420C4×Dic11C22×C411yescharacteristic
421C4×Dic11C22×C411yescharacteristic
422C4×Dic11C22×C411yescharacteristic
423C4×Dic11C22×C412yes—
424C4×Dic11C22×C412yes—
425C4×Dic11C22×C412yes—
426C4×Dic11C2411yescharacteristic
427C4×Dic11C2412yes—
428C4×Dic11C2411yescharacteristic
429#4318—42no—
430#4318—42no—
431C2×C11⋊C8—42no—
432C2×C11⋊C8C2411yescharacteristic
433C2×C11⋊C8C2411yescharacteristic
434C2×C11⋊C8C2411yescharacteristic
435C2×C11⋊C8C2411yescharacteristic
436C2×C11⋊C8C2412yes—
437C2×C11⋊C8C2412yes—
438#4313—24no—
439#4313—22no—
440#4313—22no—
441#4313—42no—
442C8×D11—22no—
443C8×D11—24no—
444C8×D11—22no—
445C8×D11—42no—
446C8×D11—42no—
447C8×D11—42no—
448C8×D11—42no—
449C8×D11—42no—
450#3475—111no—
451#2994—111no—
452#2994—112no—
453#2994—112no—
454#2994D1111yescharacteristic, complemented
455#2993—111no—
456#2993—111no—
457#2992—112no—
458#2992—112no—
459#2990—111no—
460#2990—111no—
461#2988—111no—
462#2988—111no—
463#2962—111no—
464#2960—111no—
465D4×M16—111no—
466#2933—112no—
467#2929—112no—
468C2×C8×D4—111no—
469#2924—112no—
470#2922—111no—
471#2906—111no—
472C2×#424—112no—
473C23×C11C23×C412yes—
474C23×C11C23×C411yescharacteristic
475C22×D11—24no—
476C22×D11—24no—
477C22×D11—42no—
478C22×D11C23×C411yescharacteristic
479C22×D11C23×C411yescharacteristic
480C22×D11C23×C412yes—
481Q8×C11—22no—
482D4×C11—22no—
483D4×C11—42no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11—21no—
487C2×C4×C11—22no—
488C2×C4×C11—21no—
489C2×C4×C11—41no—
490C2×C4×C11C23×C411yescharacteristic
491C2×C4×C11C23×C411yescharacteristic
492C2×C4×C11C23×C411yescharacteristic
493C2×C4×C11C23×C412yes—
494C2×C4×C11C23×C412yes—
495C2×C4×C11C23×C411yescharacteristic
496C2×C4×C11C23×C412yes—
497C2×C4×C11C23×C411yescharacteristic
498C2×C4×C11C2511yescharacteristic
499C22⋊D11—22no—
500C22⋊D11—24no—
501C22⋊D11—24no—
502C22⋊D11—22no—
503C22⋊D11—42no—
504C2×Dic11—24no—
505C2×Dic11C23×C412yes—
506C2×Dic11C23×C411yescharacteristic
507C2×Dic11C23×C411yescharacteristic
508C2×Dic11C23×C411yescharacteristic
509C2×Dic11C23×C411yescharacteristic
510C2×Dic11C23×C412yes—
511C2×Dic11C23×C412yes—
512C2×Dic11C23×C411yescharacteristic
513C2×Dic11C23×C411yescharacteristic
514D44—22no—
515D44—24no—
516D44#13114yescomplemented
517C4×D11—24no—
518C4×D11—24no—
519C4×D11—24no—
520C4×D11—22no—
521C4×D11—22no—
522C4×D11—22no—
523C4×D11—21no—
524C4×D11—22no—
525C4×D11—21no—
526C4×D11—24no—
527C4×D11—41no—
528C4×D11—42no—
529C4×D11—41no—
530C4×D11—42no—
531C4×D11H(5,𝔽2)12yes—
532C4×D112−1+412yes—
533Dic22—22no—
534Dic22—22no—
535Dic22—42no—
536C8×C11—21no—
537C8×C11—22no—
538C8×C11—21no—
539C8×C11—22no—
540C8×C11—21no—
541C8×C11—21no—
542C11⋊C8—21no—
543C11⋊C8—22no—
544C11⋊C8—22no—
545C11⋊C8—21no—
546C11⋊C8—21no—
547C11⋊C8—21no—
548C2×#131—112no—
549C22×M16—112no—
550C23×C8—112no—
551#556—111no—
552#555—111no—
553#554—111no—
554#553—112no—
555#552—112no—
556#552—111no—
557#552—111no—
558#551—112no—
559#551—112no—
560#547—111no—
561#546—111no—
562#546—111no—
563#533—111no—
564#529—112no—
565#529—111no—
566#529—112no—
567#529C2×D1111yescharacteristic
568#525—112no—
569C4×#41—111no—
570C4×#41—111no—
571C4×#41—111no—
572C2×C4×D4—111no—
573C2×#117—112no—
574#446—111no—
575#446—112no—
576#446—112no—
577#446—111no—
578#446—111no—
579#446—112no—
580#446C2×D1111yescharacteristic, complemented
581C8×Q8—111no—
582C8×Q8—111no—
583C8×Q8—112no—
584C8×Q8—111no—
585C8×Q8C2×D1111yescharacteristic, complemented
586#436—112no—
587#436—112no—
588#436—111no—
589#436C2×D1111yescharacteristic
590#435—112no—
591#435—112no—
592#435—112no—
593#435—112no—
594#435—112no—
595#435—112no—
596#435—112no—
597#435—112no—
598#435—112no—
599#435C2×D1112yescomplemented
600C8×D4—112no—
601C8×D4—112no—
602C8×D4—112no—
603C8×D4—112no—
604C8×D4—111no—
605C8×D4—111no—
606C8×D4—112no—
607C8×D4—111no—
608C8×D4—112no—
609C8×D4—111no—
610C8×D4—111no—
611C8×D4—112no—
612C8×D4C2×D1111yescharacteristic
613C8×D4C2×D1112yescomplemented
614#433—112no—
615#433—111no—
616#433—111no—
617#433—111no—
618#433—111no—
619#433—112no—
620#433—112no—
621#433C2×D1112yescomplemented
622#432—112no—
623#432—112no—
624#431—111no—
625#431—112no—
626#431—111no—
627#431—111no—
628#431—112no—
629#431C2×D1111yescharacteristic, complemented
630#424—112no—
631#424—112no—
632#424—112no—
633#424—112no—
634#424—111no—
635#424—112no—
636#424—112no—
637#424—112no—
638#424—112no—
639#424—111no—
640#424C2×D1112yescomplemented
641#423—111no—
642#423—111no—
643#423—111no—
644C2×C4⋊C8—112no—
645C2×C4⋊C8—112no—
646C2×C4⋊C8—112no—
647C2×C4⋊C8—112no—
648C2×C4⋊C8—111no—
649C2×C4⋊C8—111no—
650C2×C4⋊C8C2×D1111yescharacteristic, complemented
651#408—111no—
652#408—111no—
653#407—112no—
654C2×C22⋊C8—112no—
655#405—112no—
656#405—112no—
657C4×M16—111no—
658C2×C4×C8—111no—
659C22×C11—22no—
660C22×C11—21no—
661C22×C11—21no—
662C22×C11—22no—
663C22×C11—21no—
664C22×C11—22no—
665C22×C11C24×C411yescharacteristic
666C2×D11—22no—
667C2×D11—21no—
668C2×D11—21no—
669C2×D11—22no—
670C2×D11—21no—
671C2×D11—21no—
672C2×D11—21no—
673C2×D11—48no—
674C2×D11#52012yes—
675C2×D11C2×#13114yes—
676C4×C11—21no—
677C4×C11—22no—
678C4×C11—21no—
679C4×C11—22no—
680C4×C11—21no—
681C4×C11—21no—
682C4×C11—22no—
683C4×C11C2×#13112yes—
684C4×C11C2×H(5,𝔽2)11yescharacteristic
685C4×C11C2×2−1+411yescharacteristic
686Dic11—21no—
687Dic11—22no—
688Dic11—22no—
689Dic11—21no—
690Dic11—21no—
691Dic11—21no—
692Dic11—22no—
693Dic11—21no—
694Dic11#52012yes—
695C2×#41—111no—
696C2×#41—111no—
697C2×#41—111no—
698C22×D4—111no—
699C23×C4—112no—
700#131—444no—
701C2×M16—112no—
702C2×M16—112no—
703C2×M16—111no—
704C2×M16—112no—
705C2×M16—111no—
706C2×M16—112no—
707C2×M16—444no—
708C2×M16C22×D1112yes—
709C22×C8—112no—
710C22×C8—111no—
711C22×C8—112no—
712C22×C8—111no—
713C22×C8—112no—
714C22×C8—112no—
715C22×C8—112no—
716C22×C8—112no—
717C22×C8—112no—
718C22×C8—444no—
719C22×C8C22×D1112yes—
720C22×C8C22×D1112yes—
721C4⋊Q8—111no—
722C4⋊Q8—111no—
723#126—112no—
724#126—112no—
725#126—112no—
726#126—112no—
727#126—112no—
728#126C4×D1112yes—
729#125—112no—
730#125—112no—
731#125—111no—
732#125—112no—
733#125C4×D1111yescharacteristic
734#124—111no—
735#124—112no—
736#124—112no—
737#124C4×D1111yescharacteristic
738#123—112no—
739#123—112no—
740#123—112no—
741#123—112no—
742#123—112no—
743#123—112no—
744#123—112no—
745#123C4×D1112yes—
746C22⋊Q8—111no—
747C22⋊Q8—112no—
748C22⋊Q8—111no—
749C22⋊Q8—112no—
750C22⋊Q8—112no—
751C22⋊Q8—111no—
752C22⋊Q8—112no—
753C22⋊Q8—112no—
754C22⋊Q8C4×D1111yescharacteristic
755#121—112no—
756#121—112no—
757#121—111no—
758#121—112no—
759#121—112no—
760#121C4×D1111yescharacteristic
761#120—112no—
762#120—112no—
763C4×Q8—111no—
764C4×Q8—111no—
765C4×Q8—111no—
766C4×Q8—111no—
767C4×Q8—111no—
768C4×Q8—112no—
769C4×Q8C22×D1111yescharacteristic
770C4×D4—111no—
771C4×D4—111no—
772C4×D4—111no—
773C4×D4—111no—
774C4×D4—112no—
775C4×D4—111no—
776C4×D4—112no—
777C4×D4—112no—
778C4×D4—112no—
779C4×D4—111no—
780C4×D4—111no—
781C4×D4—112no—
782C4×D4—112no—
783C4×D4—111no—
784C4×D4—111no—
785C4×D4—111no—
786C4×D4—111no—
787C4×D4—112no—
788C4×D4C22×D1111yescharacteristic
789C4×D4C22×D1112yes—
790#117—111no—
791#117—112no—
792#117—111no—
793#117—112no—
794#117—112no—
795#117—112no—
796#117—111no—
797#117—112no—
798#117—112no—
799#117—112no—
800#117—111no—
801#117—112no—
802#117—111no—
803#117C22×D1112yes—
804C2×C4⋊C4—112no—
805C2×C4⋊C4—112no—
806C2×C4⋊C4—111no—
807C2×C22⋊C4—112no—
808C2×C22⋊C4—112no—
809C2×C22⋊C4—112no—
810C2×C42—112no—
811C2×C42—112no—
812C2×C42—111no—
813C2×C42—111no—
814C2×C42C22×D1111yescharacteristic
815C4⋊C8—111no—
816C4⋊C8—112no—
817C4⋊C8—111no—
818C4⋊C8—112no—
819C4⋊C8—112no—
820C4⋊C8—112no—
821C4⋊C8—112no—
822C4⋊C8—112no—
823C4⋊C8—112no—
824C4⋊C8—112no—
825C4⋊C8—111no—
826C4⋊C8—111no—
827C4⋊C8—111no—
828C4⋊C8—111no—
829C4⋊C8—111no—
830C4⋊C8—112no—
831C4⋊C8—112no—
832C4⋊C8—112no—
833C4⋊C8—111no—
834C4⋊C8C22×D1111yescharacteristic
835C4⋊C8C22×D1111yescharacteristic
836C4⋊C8C22×D1112yes—
837C4⋊C8C22×D1112yes—
838C4⋊C8C22×D1112yes—
839C4⋊C8C22×D1111yescharacteristic
840C4⋊C8C22×D1111yescharacteristic
841C22⋊C8—112no—
842C22⋊C8—112no—
843C22⋊C8—111no—
844C22⋊C8—111no—
845C22⋊C8—112no—
846C22⋊C8—112no—
847C22⋊C8—112no—
848C22⋊C8—112no—
849C22⋊C8—111no—
850C22⋊C8—111no—
851C22⋊C8—111no—
852C22⋊C8—111no—
853C22⋊C8C22×D1112yes—
854C22⋊C8C22×D1112yes—
855C22⋊C8C22×D1111yescharacteristic
856C22⋊C8C22×D1111yescharacteristic
857#97—111no—
858#97—111no—
859#97—112no—
860#97—112no—
861#97—112no—
862#97C22×D1112yes—
863C4×C8—111no—
864C4×C8—111no—
865C4×C8—112no—
866C4×C8—112no—
867C4×C8—111no—
868C4×C8—111no—
869C4×C8—112no—
870C4×C8C22×D1111yescharacteristic
871C4×C8C22×D1111yescharacteristic
872C4×C8C22×D1112yes—
873C2×C11—42no—
874C2×C11—41no—
875C2×C11C2×#52011yescharacteristic
876C2×C11C22×#13111yescharacteristic
877C2×C11#357311yescharacteristic
878D11—22no—
879D11—24no—
880D11—41no—
881C24—112no—
882#41—222no—
883#41—222no—
884#41—224no—
885#41—224no—
886C2×Q8—111no—
887C2×Q8—111no—
888C2×Q8—112no—
889C2×Q8C2×C4×D1111yescharacteristic
890C2×D4—111no—
891C2×D4—112no—
892C2×D4—111no—
893C2×D4—112no—
894C2×D4—112no—
895C2×D4—111no—
896C2×D4—111no—
897C2×D4—112no—
898C2×D4—224no—
899C2×D4C2×C4×D1111yescharacteristic
900C2×D4C2×C4×D1112yes—
901C22×C4—111no—
902C22×C4—112no—
903C22×C4—112no—
904C22×C4—112no—
905C22×C4—111no—
906C22×C4—111no—
907C22×C4—112no—
908C22×C4—112no—
909C22×C4—112no—
910C22×C4—111no—
911C22×C4—111no—
912C22×C4—112no—
913C22×C4—112no—
914C22×C4—111no—
915C22×C4—224no—
916C22×C4—224no—
917C22×C4C2×C4×D1111yescharacteristic
918C22×C4C2×C4×D1111yescharacteristic
919C22×C4C23×D1111yescharacteristic
920C22×C4C23×D1112yes—
921M16—42no—
922M16—222no—
923M16—224no—
924M16—222no—
925M16—442no—
926M16—442no—
927M16—442no—
928C2×C8—42no—
929C2×C8—42no—
930C2×C8—111no—
931C2×C8—111no—
932C2×C8—111no—
933C2×C8—111no—
934C2×C8—112no—
935C2×C8—112no—
936C2×C8—222no—
937C2×C8—224no—
938C2×C8—222no—
939C2×C8—442no—
940C2×C8—442no—
941C2×C8—442no—
942C2×C8—442no—
943C2×C8—442no—
944C2×C8—442no—
945C2×C8C23×D1111yescharacteristic
946C2×C8C23×D1111yescharacteristic
947C2×C8C23×D1112yes—
948C2×C8C23×D1112yes—
949C2×C8C23×D1111yescharacteristic
950C2×C8C23×D1111yescharacteristic
951C4⋊C4—111no—
952C4⋊C4—111no—
953C4⋊C4—111no—
954C4⋊C4—112no—
955C4⋊C4—112no—
956C4⋊C4—112no—
957C4⋊C4—112no—
958C4⋊C4—112no—
959C4⋊C4—111no—
960C4⋊C4—111no—
961C4⋊C4—111no—
962C4⋊C4—112no—
963C4⋊C4—112no—
964C4⋊C4—112no—
965C4⋊C4—111no—
966C4⋊C4—111no—
967C4⋊C4—112no—
968C4⋊C4—112no—
969C4⋊C4—112no—
970C4⋊C4—112no—
971C4⋊C4C2×C4×D1112yes—
972C4⋊C4C2×C4×D1112yes—
973C4⋊C4C2×C4×D1111yescharacteristic
974C4⋊C4C2×C4×D1111yescharacteristic
975C4⋊C4C2×C4×D1112yes—
976C4⋊C4C2×C4×D1112yes—
977C22⋊C4—112no—
978C22⋊C4—112no—
979C22⋊C4—112no—
980C22⋊C4—111no—
981C22⋊C4—112no—
982C22⋊C4—111no—
983C22⋊C4—112no—
984C22⋊C4—111no—
985C22⋊C4—111no—
986C22⋊C4—112no—
987C22⋊C4—112no—
988C22⋊C4—112no—
989C22⋊C4—112no—
990C22⋊C4—112no—
991C22⋊C4—112no—
992C22⋊C4—111no—
993C22⋊C4—112no—
994C22⋊C4—111no—
995C22⋊C4—112no—
996C22⋊C4C2×C4×D1112yes—
997C22⋊C4C2×C4×D1112yes—
998C22⋊C4C2×C4×D1112yes—
999C22⋊C4C2×C4×D1112yes—
1000C22⋊C4C2×C4×D1112yes—
1001C42—112no—
1002C42—112no—
1003C42—112no—
1004C42—112no—
1005C42—111no—
1006C42—111no—
1007C42—111no—
1008C42—111no—
1009C42—111no—
1010C42—112no—
1011C42—111no—
1012C42C2×C4×D1111yescharacteristic
1013C42C2×C4×D1111yescharacteristic
1014C42C23×D1111yescharacteristic
1015C42C23×D1112yes—
1016C42C23×D1111yescharacteristic
1017C11#6027111yescharacteristic, complemented, Sylow
1018C23—111no—
1019C23—112no—
1020C23—111no—
1021C23—224no—
1022C23—224no—
1023C23—442no—
1024C23C22×C4×D1112yes—
1025C23C22×C4×D1111yescharacteristic
1026Q8—22no—
1027Q8—222no—
1028Q8—222no—
1029Q8—442no—
1030D4—22no—
1031D4—42no—
1032D4—114no—
1033D4—224no—
1034D4—222no—
1035D4—222no—
1036D4—224no—
1037D4—224no—
1038D4—222no—
1039D4—442no—
1040C2×C4—22no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—21no—
1045C2×C4—41no—
1046C2×C4—111no—
1047C2×C4—112no—
1048C2×C4—112no—
1049C2×C4—111no—
1050C2×C4—111no—
1051C2×C4—112no—
1052C2×C4—111no—
1053C2×C4—112no—
1054C2×C4—112no—
1055C2×C4—111no—
1056C2×C4—111no—
1057C2×C4—224no—
1058C2×C4—224no—
1059C2×C4—224no—
1060C2×C4—224no—
1061C2×C4—224no—
1062C2×C4—222no—
1063C2×C4—222no—
1064C2×C4—222no—
1065C2×C4—221no—
1066C2×C4—222no—
1067C2×C4—221no—
1068C2×C4—441no—
1069C2×C4—442no—
1070C2×C4—441no—
1071C2×C4—442no—
1072C2×C4C22×C4×D1111yescharacteristic
1073C2×C4C22×C4×D1111yescharacteristic
1074C2×C4C22×C4×D1111yescharacteristic
1075C2×C4C22×C4×D1112yes—
1076C2×C4C22×C4×D1112yes—
1077C2×C4C22×C4×D1111yescharacteristic
1078C2×C4C22×C4×D1112yes—
1079C2×C4C22×C4×D1111yescharacteristic
1080C2×C4C24×D1111yescharacteristic
1081C8—21no—
1082C8—22no—
1083C8—22no—
1084C8—21no—
1085C8—21no—
1086C8—21no—
1087C8—221no—
1088C8—222no—
1089C8—221no—
1090C8—222no—
1091C8—221no—
1092C8—221no—
1093C22—21no—
1094C22—22no—
1095C22—21no—
1096C22—22no—
1097C22—22no—
1098C22—21no—
1099C22—114no—
1100C22—112no—
1101C22—221no—
1102C22—222no—
1103C22—221no—
1104C22—222no—
1105C22—221no—
1106C22—221no—
1107C22—221no—
1108C22—448no—
1109C22C23×C4×D1111yescharacteristic
1110C4—21no—
1111C4—22no—
1112C4—21no—
1113C4—21no—
1114C4—22no—
1115C4—22no—
1116C4—21no—
1117C4—112no—
1118C4—221no—
1119C4—221no—
1120C4—222no—
1121C4—221no—
1122C4—222no—
1123C4—221no—
1124C4—222no—
1125C4—221no—
1126C4D11×#13112yes—
1127C4D11×H(5,𝔽2)11yescharacteristic
1128C4D11×2−1+411yescharacteristic
1129C2—42no—
1130C2—41no—
1131C2—222no—
1132C2—224no—
1133C2—441no—
1134C2D11×#52011yescharacteristic
1135C2C2×D11×#13111yescharacteristic
1136C2#1308332711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2994C2
prime radical#13082172C2
cosocleC2×C4×C11C25
hypercenter#2994D11
hypocenterC11#60271
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2994

Complements

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

NH ≅ G/Ntype
2. #13077774C2semidirect
3. #13077771C2semidirect
4. #13077771C2semidirect
5. #13077765C2semidirect
6. #13077760C2semidirect
7. #13077751C2semidirect
8. #13077750C2semidirect
9. #13077740C2semidirect
10. #13077737C2semidirect
11. #13077726C2semidirect
12. #13077725C2semidirect
13. #13077558C2semidirect
14. #13077547C2semidirect
15. #13077352C2semidirect
16. #13077339C2semidirect
17. #13077305C2semidirect
18. C8×D4×D11C2semidirect
19. #13077272C2semidirect
20. #13077255C2semidirect
21. #13077181C2semidirect
22. D11×#424C2semidirect
23. C11×#2994C2semidirect
50. C11×#446C22semidirect
51. C8×Q8×C11C22semidirect
53. C11×#435C22semidirect
55. C8×D4×C11C22semidirect
56. C11×#433C22semidirect
57. C11×#431C22semidirect
58. C11×#424C22semidirect
59. C2×C11×C4⋊C8C22semidirect
60. #10622741C22semidirect
62. #10622732C22semidirect
64. C8×C22⋊D11C22semidirect
65. C8×C22⋊D11C22semidirect
66. C8×C22⋊D11C22semidirect
67. #10622715C22semidirect
68. #10622715C22semidirect
69. #10622637C22semidirect
70. Q8×C11⋊C8C22semidirect
72. #10622625C22semidirect
73. #10622624C22semidirect
75. #10622613C22semidirect
76. #10622612C22semidirect
77. #10622538C22semidirect
78. #10622537C22semidirect
79. #10622453C22semidirect
80. #10622453C22semidirect
86. #10622452C22semidirect
88. #10622450C22semidirect
89. #10622449C22semidirect
90. #10622448C22semidirect
93. #10622447C22semidirect
94. #10622446C22semidirect
96. D11×C4⋊C8C22semidirect
97. D11×C4⋊C8C22semidirect
98. D11×C4⋊C8C22semidirect
99. D11×C4⋊C8C22semidirect
100. D11×C4⋊C8C22semidirect
101. #10622443C22semidirect
102. #10622443C22semidirect
103. #10622443C22semidirect
104. #10622441C22semidirect
105. #10622343C22semidirect
107. #10622341C22semidirect
108. #10622341C22semidirect
109. #10622341C22semidirect
115. #10622333C22semidirect
116. #10622333C22semidirect
117. #10622333C22semidirect
118. #10622333C22semidirect
120. #10622319C22semidirect
121. #10622318C22semidirect
122. #10622314C22semidirect
127. C8×D44C22semidirect
128. #10622298C22semidirect
129. #10622298C22semidirect
130. #10622298C22semidirect
132. #10622292C22semidirect
133. #10622292C22semidirect
134. #10622292C22semidirect
454. #2994D11semidirect
516. D44#131semidirect
580. #446C2×D11semidirect
585. C8×Q8C2×D11semidirect
599. #435C2×D11semidirect
613. C8×D4C2×D11semidirect
621. #433C2×D11semidirect
629. #431C2×D11semidirect
640. #424C2×D11semidirect
650. C2×C4⋊C8C2×D11semidirect
1017. C11#60271semidirect

Maximal subgroups

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

subgroupindex
#130821722
#130777742
#130777712
#130777652
#130777602
#130777512
#130777502
#130777402
#130777372
#130777262
#130777252
#130775582
#130775472
#130773522
#130773392
#130773052
C8×D4×D112
#130772722
#130772552
#130771812
D11×#4242
C11×#29942
#6027111