Finite Group Databasebeta

← #13081057

Subgroups — #13081057

Order 1408.

376 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623060C211yesmaximal, characteristic, complemented
2#10623038C211yesmaximal, characteristic
3C11×#428C211yesmaximal, characteristic, complemented
4#10622747C211yesmaximal, characteristic, complemented
5#10622740C211yesmaximal, characteristic, complemented
6#10622616C211yesmaximal, characteristic, complemented
7#10622583C211yesmaximal, characteristic, complemented
8#10622502C211yesmaximal, characteristic, complemented
9#10622495C211yesmaximal, characteristic, complemented
10D11×#107C211yesmaximal, characteristic, complemented
11#10622488C211yesmaximal, characteristic, complemented
12#10622484C211yesmaximal, characteristic, complemented
13#10622477C211yesmaximal, characteristic, complemented
14#10622475C211yesmaximal, characteristic, complemented
15#10622469C211yesmaximal, characteristic, complemented
16C2×#4339—21no—
17C2×C11×M16C2211yescharacteristic
18C11×#117C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20#66983C2211yescharacteristic
21#66982—21no—
22C4×C22⋊D11C2211yescharacteristic
23#66977C2211yescharacteristic
24C2×#4314C2211yescharacteristic
25C2×C8×D11C2211yescharacteristic
26#66950C2211yescharacteristic
27#66949—21no—
28#66948C2211yescharacteristic
29#66947—21no—
30#66946C2211yescharacteristic
31C4⋊C4×D11C2211yescharacteristic
32C4⋊C4×D11C2211yescharacteristic
33#66943C2211yescharacteristic
34#66941C2211yescharacteristic
35#66940C2211yescharacteristic
36#66936—21no—
37#66932—21no—
38#66925—21no—
39#66923—21no—
40C11×#107C2211yescharacteristic
41C11×#107C2211yescharacteristic
42C11×#106C2211yescharacteristic
43C11×#106C2211yescharacteristic
44C22⋊(C11⋊C8)C2211yescharacteristic
45#66885C2211yescharacteristic
46(C2×D11)⋊C8C2211yescharacteristic
47#66882C2211yescharacteristic
48#66880C2211yescharacteristic
49#66879C2211yescharacteristic
50Dic11⋊C8C2211yescharacteristic
51#66874C2211yescharacteristic
52#66874C2211yescharacteristic
53#66873C2211yescharacteristic
54#66873C2211yescharacteristic
55#66872C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58#66871C2211yescharacteristic
59C22×C4×C11—21no—
60C22×C4×C11C2311yescharacteristic
61C2×C22⋊D11—21no—
62C2×C22⋊D11D411yescharacteristic
63#4339—44no—
64C2×D44—21no—
65C2×D44C2311yescharacteristic
66C2×C4×D11—21no—
67C2×C4×D11—21no—
68C2×C4×D11—21no—
69C2×C4×D11C2311yescharacteristic
70C2×Dic22—21no—
71C2×Dic22C2311yescharacteristic
72C11×M16—22no—
73C2×C8×C11C2311yescharacteristic
74C2×C8×C11C2311yescharacteristic
75C11×C4⋊C4—21no—
76C11×C4⋊C4C2311yescharacteristic
77C11×C4⋊C4C2311yescharacteristic
78C11×C4⋊C4C2311yescharacteristic
79C11×C4⋊C4C2311yescharacteristic
80C11×C22⋊C4—21no—
81C42×C11—21no—
82C22⋊Dic11—21no—
83C22⋊Dic11D411yescharacteristic
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⋊Dic11C2311yescharacteristic
92C4⋊Dic11C2311yescharacteristic
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4D411yescharacteristic
100C4×Dic11—21no—
101C4×Dic11C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104#4314—22no—
105C8×D11—22no—
106#3343—111nomaximal, Sylow
107C23×C11C2×D411yescharacteristic
108C22×D11—21no—
109C22×D11C2×D411yescharacteristic
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—42no—
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2411yescharacteristic
119C22⋊D11—22no—
120C22⋊D11—42no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11C2×D411yescharacteristic
125C2×Dic11C2×D411yescharacteristic
126C2×Dic11C2×D411yescharacteristic
127D44—21no—
128D44—21no—
129D44—42no—
130C4×D11—21no—
131C4×D11—21no—
132C4×D11—42no—
133C4×D11—42no—
134C4×D11—42no—
135Dic22—21no—
136Dic22—21no—
137Dic22—42no—
138C8×C11—21no—
139C8×C11#4112yescomplemented
140C11⋊C8—21no—
141C11⋊C8—21no—
142#552—111no—
143#547—111no—
144#501—111no—
145#484—111no—
146#483—111no—
147#482—111no—
148#480—111no—
149#478—111no—
150#477—111no—
151#468—111no—
152#465—111no—
153#440—111no—
154#435—111no—
155#428D1111yescharacteristic, complemented
156C2×#107—111no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11C22×D411yescharacteristic
161C2×D11—21no—
162C2×D11—21no—
163C2×D11—41no—
164C2×D11—41no—
165C2×D11—41no—
166C2×D11AGL(1,ℤ/8)12yes—
167C4×C11—21no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11C2×#4111yescharacteristic
173C4×C112−1+411yescharacteristic
174Dic11—21no—
175Dic11—21no—
176Dic11—21no—
177Dic11—41no—
178Dic11—41no—
179Dic11—41no—
180C2×#41—221no—
181C2×SD16—111no—
182C2×M16C2×D1111yescharacteristic
183C22×C8—111no—
184C4⋊Q8—111no—
185#126—221no—
186#125—111no—
187#125—221no—
188#123—221no—
189#123—221no—
190#123—221no—
191C22⋊Q8—111no—
192C22⋊Q8—111no—
193C22⋊Q8—221no—
194#121—111no—
195#121—111no—
196C4×Q8—111no—
197C4×D4—111no—
198C4×D4—111no—
199#117—221no—
200#117C2×D1111yescharacteristic
201C2×C4⋊C4—111no—
202C2×C4⋊C4—111no—
203C2×C4⋊C4C2×D1111yescharacteristic
204#107—111no—
205#107—111no—
206#107—111no—
207#107—111no—
208#107C2×D1111yescharacteristic
209#107C2×D1111yescharacteristic
210#106—111no—
211#106C2×D1111yescharacteristic
212#106C2×D1111yescharacteristic
213C4⋊C8—111no—
214#103—111no—
215#103—111no—
216#103—111no—
217#102—111no—
218#102—111no—
219#102—111no—
220C22⋊C8—111no—
221C22⋊C8—111no—
222#97—111no—
223C2×C11—41no—
224C2×C11#54711yescharacteristic
225C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
226C2×C11#57811yescharacteristic
227D11—22no—
228D11—81no—
229#41—444no—
230C2×Q8—111no—
231C2×Q8—221no—
232C2×D4—111no—
233C2×D4—111no—
234C2×D4—221no—
235C2×D4—221no—
236C22×C4—21no—
237C22×C4—111no—
238C22×C4—221no—
239C22×C4—221no—
240C22×C4—221no—
241C22×C4C22×D1111yescharacteristic
242SD16—222no—
243M16—22no—
244C2×C8—111no—
245C2×C8—111no—
246C2×C8—222no—
247C2×C8C22×D1111yescharacteristic
248C2×C8C22×D1111yescharacteristic
249C4⋊C4—21no—
250C4⋊C4—111no—
251C4⋊C4—111no—
252C4⋊C4—111no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—221no—
261C4⋊C4C22×D1111yescharacteristic
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—
273C42—21no—
274C42—111no—
275C42—221no—
276C11#334311yescharacteristic, complemented, Sylow
277C23—111no—
278C23—221no—
279C23D4×D1111yescharacteristic
280Q8—221no—
281Q8—221no—
282Q8—442no—
283D4—222no—
284D4—221no—
285D4—221no—
286D4—442no—
287D4—442no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—42no—
295C2×C4—111no—
296C2×C4—111no—
297C2×C4—111no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4—221no—
302C2×C4—221no—
303C2×C4—442no—
304C2×C4—442no—
305C2×C4—442no—
306C2×C4D4×D1111yescharacteristic
307C2×C4C23×D1111yescharacteristic
308C8—21no—
309C8—221no—
310C8—221no—
311C8#433912yescomplemented
312C22—21no—
313C22—21no—
314C22—21no—
315C22—112no—
316C22—221no—
317C22—221no—
318C22—441no—
319C22—441no—
320C22—441no—
321C22C2×D4×D1111yescharacteristic
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—221no—
328C4—221no—
329C4—221no—
330C4—441no—
331C4—441no—
332C4—441no—
333C4C2×#433911yescharacteristic
334C4#6704011yescharacteristic
335C2—41no—
336C2—222no—
337C2—881no—
338C2#1062303811yescharacteristic
339C2D11×AGL(1,ℤ/8)11yescharacteristic
340C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#428C2
socleC22×C11C22×D4
prime radical#10623038C2
hypercenter#428D11
hypocenterC11#3343
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. #10623060C2semidirect
3. C11×#428C2semidirect
4. #10622747C2semidirect
5. #10622740C2semidirect
6. #10622616C2semidirect
7. #10622583C2semidirect
8. #10622502C2semidirect
9. #10622495C2semidirect
10. D11×#107C2semidirect
11. #10622488C2semidirect
12. #10622484C2semidirect
13. #10622477C2semidirect
14. #10622475C2semidirect
15. #10622469C2semidirect
139. C8×C11#41semidirect
155. #428D11semidirect
276. C11#3343semidirect
311. C8#4339semidirect

Maximal subgroups

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

subgroupindex
#106230602
#106230382
C11×#4282
#106227472
#106227402
#106226162
#106225832
#106225022
#106224952
D11×#1072
#106224882
#106224842
#106224772
#106224752
#106224692
#334311