Finite Group Databasebeta

← #13081016

Subgroups — #13081016

Order 1408.

366 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623149C211yesmaximal, characteristic, complemented
2#10623045C211yesmaximal, characteristic, complemented
3C11×#481C211yesmaximal, characteristic, complemented
4#10622651C211yesmaximal, characteristic, complemented
5C2×#66871C211yesmaximal, characteristic, complemented
6#10622484C211yesmaximal, characteristic, complemented
7#10622479C211yesmaximal, characteristic, complemented
8#10622473C211yesmaximal, characteristic, complemented
9#10622471C211yesmaximal, characteristic, complemented
10#10622392C211yesmaximal, characteristic, complemented
11#10622388C211yesmaximal, characteristic, complemented
12#10622376C211yesmaximal, characteristic, complemented
13#10622369C211yesmaximal, characteristic, complemented
14#10622348C211yesmaximal, characteristic, complemented
15(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
16C11×#121C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18#66992—21no—
19#66991C2211yescharacteristic
20D4×Dic11—21no—
21D4×Dic11C2211yescharacteristic
22C2×#4323C2211yescharacteristic
23#66983—21no—
24#66983C2211yescharacteristic
25C4×C22⋊D11—21no—
26C4×C22⋊D11C2211yescharacteristic
27C2×C4⋊Dic11C2211yescharacteristic
28C22×C11⋊C8C2211yescharacteristic
29C2×C8×D11C2211yescharacteristic
30#66951—21no—
31#66948C2211yescharacteristic
32#66947—21no—
33#66946C2211yescharacteristic
34#66945C2211yescharacteristic
35#66945C2211yescharacteristic
36#66943C2211yescharacteristic
37#66943C2211yescharacteristic
38#66939—21no—
39#66932—21no—
40C11×#106C2211yescharacteristic
41C11×#106C2211yescharacteristic
42C11×#102C2211yescharacteristic
43C11×#102C2211yescharacteristic
44C11×C22⋊C8C2211yescharacteristic
45#66896C2211yescharacteristic
46#66885C2211yescharacteristic
47#66885C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49#66881C2211yescharacteristic
50#66881C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52C8×Dic11C2211yescharacteristic
53#66873C2211yescharacteristic
54#66871C2211yescharacteristic
55#66871C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×D4×C11—21no—
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11—21no—
62C22×C4×C11C2311yescharacteristic
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65C2×C22⋊D11D411yescharacteristic
66C22×Dic11—21no—
67C22×Dic11—21no—
68C2×D44—21no—
69C2×D44C2311yescharacteristic
70C2×C4×D11—21no—
71C2×C4×D11C2311yescharacteristic
72C2×C8×C11C2311yescharacteristic
73C2×C8×C11C2311yescharacteristic
74C11×C4⋊C4—21no—
75C11×C4⋊C4C2311yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C11×C4⋊C4C2311yescharacteristic
78C11×C22⋊C4—21no—
79C22⋊Dic11—21no—
80C22⋊Dic11—21no—
81C22⋊Dic11D411yescharacteristic
82#4323—22no—
83(C2×D11)⋊C4—21no—
84(C2×D11)⋊C4—21no—
85(C2×D11)⋊C4—21no—
86(C2×D11)⋊C4—21no—
87(C2×D11)⋊C4—21no—
88(C2×D11)⋊C4D411yescharacteristic
89C4⋊Dic11—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11C2311yescharacteristic
93C4⋊Dic11C2311yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4D411yescharacteristic
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11C2311yescharacteristic
101C2×C11⋊C8—22no—
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C8×D11—22no—
105#3339—111nomaximal, Sylow
106C23×C11—21no—
107C23×C11C2×D411yescharacteristic
108C22×D11—21no—
109C22×D11C2×D411yescharacteristic
110D4×C11—21no—
111D4×C11—21no—
112D4×C11—42no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—81no—
119C2×C4×C11C2×D411yescharacteristic
120C2×C4×C11C2411yescharacteristic
121C22⋊D11—22no—
122C22⋊D11—42no—
123C22⋊D11—81no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—81no—
128C2×Dic11—81no—
129C2×Dic11C2×D411yescharacteristic
130C2×Dic11C2×D411yescharacteristic
131C2×Dic11C2×D411yescharacteristic
132D44—21no—
133D44—21no—
134D44—81no—
135C4×D11—21no—
136C4×D11—21no—
137C4×D11—81no—
138C8×C11—21no—
139C8×C11—21no—
140C11⋊C8—21no—
141C11⋊C8#4112yes—
142#553—111no—
143#553—111no—
144#499—111no—
145#482—111no—
146#482—111no—
147#481—111no—
148#481D1111yescharacteristic, complemented
149#478—111no—
150#478—111no—
151#466—111no—
152#466—111no—
153C4×D8—111no—
154C8×D4—111no—
155#427—111no—
156C2×#107—111no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—41no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11#13512yes—
163C22×C11C22×D411yescharacteristic
164C2×D11—21no—
165C2×D11—21no—
166C2×D11—21no—
167C2×D11—41no—
168C2×D11—41no—
169C2×D11—41no—
170C4×C11—21no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11C2×#4111yescharacteristic
175C4×C112−1+411yescharacteristic
176Dic11—21no—
177Dic11—21no—
178Dic11—21no—
179Dic11—41no—
180Dic11—41no—
181Dic11—41no—
182C2×D8—111no—
183C22×C8—111no—
184C22×C8—111no—
185#126—221no—
186#126—221no—
187#125—111no—
188#125—111no—
189#123—221no—
190#123—221no—
191#121—111no—
192#121—111no—
193#121—111no—
194#121—221no—
195#121—221no—
196#121C2×D1111yescharacteristic
197C4×D4—111no—
198C4×D4—111no—
199C4×D4—111no—
200C4×D4—221no—
201C4×D4—221no—
202#117—111no—
203#117—111no—
204C2×C4⋊C4—111no—
205C2×C4⋊C4C2×D1111yescharacteristic
206#107—111no—
207#107—111no—
208#107—111no—
209#107—111no—
210#107—111no—
211#106—111no—
212#106—111no—
213#106C2×D1111yescharacteristic
214#106C2×D1111yescharacteristic
215C4⋊C8—111no—
216#102—111no—
217#102—111no—
218#102—111no—
219#102—111no—
220#102C2×D1111yescharacteristic
221#102C2×D1111yescharacteristic
222C22⋊C8—111no—
223C22⋊C8C2×D1111yescharacteristic
224C4×C8—111no—
225C2×C11—22no—
226C2×C11—81no—
227C2×C11#54711yescharacteristic
228C2×C11C2×#13511yescharacteristic
229C2×C11#57611yescharacteristic
230D11—41no—
231D11—81no—
232C2×D4—21no—
233C2×D4—111no—
234C2×D4—111no—
235C2×D4—221no—
236C2×D4—221no—
237C2×D4—221no—
238C2×D4C22×D1111yescharacteristic
239C22×C4—21no—
240C22×C4—111no—
241C22×C4—221no—
242C22×C4—221no—
243C22×C4—221no—
244C22×C4C22×D1111yescharacteristic
245D8—222no—
246C2×C8—111no—
247C2×C8—111no—
248C2×C8—222no—
249C2×C8—222no—
250C2×C8C22×D1111yescharacteristic
251C2×C8C22×D1111yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—111no—
254C4⋊C4—111no—
255C4⋊C4—111no—
256C4⋊C4—111no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—221no—
261C4⋊C4—221no—
262C4⋊C4C22×D1111yescharacteristic
263C4⋊C4C22×D1111yescharacteristic
264C4⋊C4C22×D1111yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—111no—
267C22⋊C4—111no—
268C22⋊C4—221no—
269C22⋊C4—221no—
270C22⋊C4—221no—
271C22⋊C4—221no—
272C22⋊C4—221no—
273C22⋊C4—221no—
274C22⋊C4—221no—
275C42—111no—
276C42—221no—
277C42—221no—
278C11#333911yescharacteristic, complemented, Sylow
279C23—21no—
280C23—111no—
281C23—221no—
282C23D4×D1111yescharacteristic
283D4—21no—
284D4—21no—
285D4—42no—
286D4—222no—
287D4—221no—
288D4—221no—
289D4—442no—
290D4—881no—
291D4—881no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—81no—
298C2×C4—111no—
299C2×C4—111no—
300C2×C4—111no—
301C2×C4—221no—
302C2×C4—221no—
303C2×C4—221no—
304C2×C4—221no—
305C2×C4—221no—
306C2×C4—881no—
307C2×C4—881no—
308C2×C4—881no—
309C2×C4D4×D1111yescharacteristic
310C2×C4C23×D1111yescharacteristic
311C8—21no—
312C8—21no—
313C8—112no—
314C8—221no—
315C22—21no—
316C22—21no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—221no—
321C22—221no—
322C22—221no—
323C22—441no—
324C22—441no—
325C22—441no—
326C22#6696912yes—
327C22C2×D4×D1111yescharacteristic
328C4—21no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—221no—
333C4—221no—
334C4—221no—
335C4—441no—
336C4—441no—
337C4—441no—
338C4#41×D1111yescharacteristic
339C4#6704311yescharacteristic
340C2—22no—
341C2—81no—
342C2—441no—
343C2—881no—
344C2#1062318611yescharacteristic
345C2C2×#6696911yescharacteristic
346C2#1062330511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#481C2
socleC22×C11C22×D4
hypercenter#481D11
hypocenterC11#3339
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #10623149C2semidirect
2. #10623045C2semidirect
3. C11×#481C2semidirect
4. #10622651C2semidirect
5. C2×#66871C2semidirect
6. #10622484C2semidirect
7. #10622479C2semidirect
8. #10622473C2semidirect
9. #10622471C2semidirect
10. #10622392C2semidirect
11. #10622388C2semidirect
12. #10622376C2semidirect
13. #10622369C2semidirect
14. #10622348C2semidirect
15. (C22⋊D11)⋊C8C2semidirect
148. #481D11semidirect
278. C11#3339semidirect

Maximal subgroups

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

subgroupindex
#106231492
#106230452
C11×#4812
#106226512
C2×#668712
#106224842
#106224792
#106224732
#106224712
#106223922
#106223882
#106223762
#106223692
#106223482
(C22⋊D11)⋊C82
#333911