Finite Group Databasebeta

← #13081342

Subgroups — #13081342

Order 1408.

382 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#10623249C211yesmaximal, characteristic
2#10623216C211yesmaximal, characteristic, complemented
3C11×#490C211yesmaximal, characteristic, complemented
4#10622688C211yesmaximal, characteristic, complemented
5#10622679C211yesmaximal, characteristic, complemented
6#10622379C211yesmaximal, characteristic, complemented
7#10622377C211yesmaximal, characteristic, complemented
8#10622375C211yesmaximal, characteristic, complemented
9#10622375C211yesmaximal, characteristic, complemented
10#10622373C211yesmaximal, characteristic, complemented
11#10622372C211yesmaximal, characteristic, complemented
12#10622371C211yesmaximal, characteristic, complemented
13#10622370C211yesmaximal, characteristic, complemented
14#10622323C211yesmaximal, characteristic, complemented
15#10622314C211yesmaximal, characteristic, complemented
16C2×#4341—21no—
17C11×#127C2211yescharacteristic
18C11×#125C2211yescharacteristic
19#66993C2211yescharacteristic
20#66993C2211yescharacteristic
21#66992—21no—
22#66992—21no—
23#66991—21no—
24D4×Dic11C2211yescharacteristic
25D4×Dic11C2211yescharacteristic
26C2×#4324C2211yescharacteristic
27C2×#4324C2211yescharacteristic
28C2×#4314C2211yescharacteristic
29#66943C2211yescharacteristic
30#66942—21no—
31#66942—21no—
32#66941—21no—
33#66941C2211yescharacteristic
34#66940—21no—
35#66940C2211yescharacteristic
36#66940C2211yescharacteristic
37C4×D44C2211yescharacteristic
38C4×Dic22C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40C11×#102C2211yescharacteristic
41C11×#102C2211yescharacteristic
42C11×#102C2211yescharacteristic
43C11×#102C2211yescharacteristic
44C11×#97C2211yescharacteristic
45#66896C2211yescharacteristic
46#66896C2211yescharacteristic
47#66885C2211yescharacteristic
48#66882C2211yescharacteristic
49#66880C2211yescharacteristic
50#66879C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53C8×Dic11C2211yescharacteristic
54#66873C2211yescharacteristic
55#66873C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×D4×C11—21no—
60C2×D4×C11—21no—
61C2×D4×C11C2311yescharacteristic
62C2×D4×C11C2311yescharacteristic
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C2×C22⋊D11—21no—
67C22×Dic11—21no—
68C22×Dic11—21no—
69#4341—44no—
70C2×D44C2311yescharacteristic
71C2×C4×D11—21no—
72C2×Dic22—21no—
73C2×Dic22D411yescharacteristic
74C2×Dic22C2311yescharacteristic
75C2×C8×C11C2311yescharacteristic
76C2×C8×C11C2311yescharacteristic
77C11×C4⋊C4—21no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4C2311yescharacteristic
80C11×C4⋊C4C2311yescharacteristic
81C42×C11C2311yescharacteristic
82C22⋊Dic11—21no—
83C22⋊Dic11—21no—
84#4324—22no—
85#4324—22no—
86(C2×D11)⋊C4—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11D411yescharacteristic
89C4⋊Dic11C2311yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4D411yescharacteristic
97Dic11⋊C4D411yescharacteristic
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11C2311yescharacteristic
102C4×Dic11C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105#4314—22no—
106#3368—111nomaximal, Sylow
107C23×C11—21no—
108C23×C11—21no—
109C22×D11—21no—
110D4×C11—21no—
111D4×C11—21no—
112D4×C11—21no—
113D4×C11—21no—
114D4×C11—42no—
115D4×C11—81no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11C2×D411yescharacteristic
119C2×C4×C11C2×D411yescharacteristic
120C2×C4×C11C2411yescharacteristic
121C22⋊D11—42no—
122C22⋊D11—42no—
123C22⋊D11—81no—
124C22⋊D11—81no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—42no—
129C2×Dic11—42no—
130C2×Dic11C2×D411yescharacteristic
131C2×Dic11C2×D411yescharacteristic
132C2×Dic11C2×D411yescharacteristic
133C2×Dic11C2×D411yescharacteristic
134D44—21no—
135D44—21no—
136C4×D11—42no—
137Dic22—21no—
138Dic22—22no—
139Dic22—42no—
140Dic22#4112yescomplemented
141C8×C11—21no—
142C8×C11—21no—
143C11⋊C8—21no—
144C11⋊C8—21no—
145#557—111no—
146#550—111no—
147#490—111no—
148#490D1111yescharacteristic, complemented
149#486—111no—
150#478—111no—
151#478—111no—
152#474—111no—
153#460—111no—
154#460—111no—
155#460—111no—
156#446—111no—
157#440—111no—
158#440—111no—
159C4×SD16—111no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11C22×D411yescharacteristic
167C2×D11—41no—
168C2×D11—41no—
169C2×D11—41no—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11C2×#4111yescharacteristic
175C4×C112−1+411yescharacteristic
176Dic11—22no—
177Dic11—21no—
178Dic11—21no—
179Dic11—21no—
180Dic11—41no—
181Dic11—41no—
182Dic11AGL(1,ℤ/8)12yes—
183C2×#41—221no—
184C2×SD16—111no—
185C2×SD16—111no—
186C2×SD16—111no—
187C4⋊Q8—111no—
188C4⋊Q8—221no—
189#127—111no—
190#127—111no—
191#127C2×D1111yescharacteristic
192#125—111no—
193#125—221no—
194#125—221no—
195#125C2×D1111yescharacteristic
196#121—221no—
197#121—221no—
198#121—221no—
199C4×Q8—111no—
200C4×Q8—111no—
201C4×Q8—111no—
202C4×Q8—111no—
203C4×Q8—221no—
204C4×D4—111no—
205C4×D4—111no—
206C4×D4—111no—
207#107—111no—
208#107—111no—
209#106—111no—
210C4⋊C8—111no—
211C4⋊C8—111no—
212C4⋊C8—111no—
213#103—111no—
214#102—111no—
215#102—111no—
216#102—111no—
217#102—111no—
218#102—111no—
219#102C2×D1111yescharacteristic
220#102C2×D1111yescharacteristic
221#102C2×D1111yescharacteristic
222#102C2×D1111yescharacteristic
223#97—111no—
224#97C2×D1111yescharacteristic
225C4×C8—111no—
226C2×C11—81no—
227C2×C11—81no—
228C2×C11#54811yescharacteristic
229C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
230C2×C11#57711yescharacteristic
231D11—81no—
232#41—444no—
233C2×Q8—111no—
234C2×Q8—111no—
235C2×Q8—221no—
236C2×D4—21no—
237C2×D4—21no—
238C2×D4—111no—
239C2×D4—221no—
240C2×D4—221no—
241C2×D4—221no—
242C2×D4—221no—
243C2×D4C22×D1111yescharacteristic
244C2×D4C22×D1111yescharacteristic
245C22×C4—221no—
246C22×C4—221no—
247C22×C4—221no—
248SD16—222no—
249SD16—222no—
250SD16—222no—
251C2×C8—111no—
252C2×C8—111no—
253C2×C8C22×D1111yescharacteristic
254C2×C8C22×D1111yescharacteristic
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—111no—
258C4⋊C4—111no—
259C4⋊C4—111no—
260C4⋊C4—111no—
261C4⋊C4—111no—
262C4⋊C4—221no—
263C4⋊C4—221no—
264C4⋊C4—221no—
265C4⋊C4—221no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C4⋊C4C22×D1111yescharacteristic
269C4⋊C4C22×D1111yescharacteristic
270C22⋊C4—221no—
271C22⋊C4—221no—
272C22⋊C4—221no—
273C42—111no—
274C42—111no—
275C42—221no—
276C42—221no—
277C42—221no—
278C42C22×D1111yescharacteristic
279C11#336811yescharacteristic, complemented, Sylow
280C23—21no—
281C23—21no—
282C23—221no—
283Q8—112no—
284Q8—222no—
285Q8—221no—
286Q8—442no—
287D4—21no—
288D4—21no—
289D4—21no—
290D4—21no—
291D4—42no—
292D4—81no—
293D4—221no—
294D4—221no—
295D4—442no—
296D4—442no—
297D4—881no—
298D4—881no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—111no—
302C2×C4—111no—
303C2×C4—111no—
304C2×C4—111no—
305C2×C4—221no—
306C2×C4—221no—
307C2×C4—221no—
308C2×C4—442no—
309C2×C4—442no—
310C2×C4—442no—
311C2×C4D4×D1111yescharacteristic
312C2×C4D4×D1111yescharacteristic
313C2×C4C23×D1111yescharacteristic
314C8—21no—
315C8—21no—
316C8—221no—
317C8—221no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—441no—
325C22—441no—
326C22—441no—
327C22C2×D4×D1111yescharacteristic
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—112no—
333C4—221no—
334C4—221no—
335C4—221no—
336C4—222no—
337C4—441no—
338C4—441no—
339C4#41×D1111yescharacteristic
340C4#6704311yescharacteristic
341C2—81no—
342C2—81no—
343C2—881no—
344C2#1062320811yescharacteristic
345C2D11×AGL(1,ℤ/8)11yescharacteristic
346C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#490C2
socleC22×C11C22×D4
prime radical#10623249C2
hypercenter#490D11
hypocenterC11#3368
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
2. #10623216C2semidirect
3. C11×#490C2semidirect
4. #10622688C2semidirect
5. #10622679C2semidirect
6. #10622379C2semidirect
7. #10622377C2semidirect
8. #10622375C2semidirect
9. #10622375C2semidirect
10. #10622373C2semidirect
11. #10622372C2semidirect
12. #10622371C2semidirect
13. #10622370C2semidirect
14. #10622323C2semidirect
15. #10622314C2semidirect
140. Dic22#41semidirect
148. #490D11semidirect
279. C11#3368semidirect

Maximal subgroups

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

subgroupindex
#106232492
#106232162
C11×#4902
#106226882
#106226792
#106223792
#106223772
#106223752
#106223732
#106223722
#106223712
#106223702
#106223232
#106223142
#336811