Finite Group Databasebeta

← #13081049

Subgroups — #13081049

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#10623142C211yesmaximal, characteristic
2#10623060C211yesmaximal, characteristic, complemented
3C11×#482C211yesmaximal, characteristic, complemented
4#10622655C211yesmaximal, characteristic, complemented
5#10622608C211yesmaximal, characteristic, complemented
6D11×#107C211yesmaximal, characteristic, complemented
7#10622488C211yesmaximal, characteristic, complemented
8#10622475C211yesmaximal, characteristic, complemented
9#10622469C211yesmaximal, characteristic, complemented
10#10622391C211yesmaximal, characteristic, complemented
11#10622387C211yesmaximal, characteristic, complemented
12#10622379C211yesmaximal, characteristic, complemented
13#10622370C211yesmaximal, characteristic, complemented
14#10622341C211yesmaximal, characteristic, complemented
15#10622335C211yesmaximal, characteristic, complemented
16C2×#4341—21no—
17C11×#121C2211yescharacteristic
18C11×#117C2211yescharacteristic
19#66991C2211yescharacteristic
20#66988—21no—
21D4×Dic11C2211yescharacteristic
22C2×#4324C2211yescharacteristic
23C4×C22⋊D11C2211yescharacteristic
24C2×C4⋊Dic11C2211yescharacteristic
25#66977C2211yescharacteristic
26C2×#4318C2211yescharacteristic
27C2×C8×D11C2211yescharacteristic
28#66950C2211yescharacteristic
29C4⋊C4×D11C2211yescharacteristic
30C4⋊C4×D11C2211yescharacteristic
31#66943C2211yescharacteristic
32#66941C2211yescharacteristic
33#66940C2211yescharacteristic
34#66936—21no—
35#66936—21no—
36#66932—21no—
37#66931—21no—
38#66925—21no—
39#66923—21no—
40C11×#107C2211yescharacteristic
41C11×#106C2211yescharacteristic
42C11×#102C2211yescharacteristic
43C11×#102C2211yescharacteristic
44C11×C22⋊C8C2211yescharacteristic
45#66896C2211yescharacteristic
46(C2×D11)⋊C8C2211yescharacteristic
47#66882C2211yescharacteristic
48#66882C2211yescharacteristic
49#66880C2211yescharacteristic
50#66880C2211yescharacteristic
51#66879C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53#66874C2211yescharacteristic
54#66872C2211yescharacteristic
55#66872C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×D4×C11—21no—
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C2×C22⋊D11D411yescharacteristic
64C22×Dic11—21no—
65C22×Dic11—21no—
66#4341—44no—
67C2×C4×D11—21no—
68C2×C4×D11—21no—
69C2×C4×D11C2311yescharacteristic
70C2×Dic22—21no—
71C2×Dic22C2311yescharacteristic
72C2×C8×C11C2311yescharacteristic
73C2×C8×C11C2311yescharacteristic
74C11×C4⋊C4C2311yescharacteristic
75C11×C4⋊C4C2311yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C11×C22⋊C4—21no—
78C11×C22⋊C4—21no—
79C42×C11—21no—
80C22⋊Dic11—21no—
81C22⋊Dic11—21no—
82C22⋊Dic11—21no—
83C22⋊Dic11D411yescharacteristic
84#4324—22no—
85(C2×D11)⋊C4—21no—
86(C2×D11)⋊C4D411yescharacteristic
87C4⋊Dic11—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11C2311yescharacteristic
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
102#4318—22no—
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105C8×D11—22no—
106#3343—111nomaximal, Sylow
107C23×C11—21no—
108C23×C11C2×D411yescharacteristic
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×C11C2×D411yescharacteristic
119C2×C4×C11C2411yescharacteristic
120C22⋊D11—22no—
121C22⋊D11—42no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—42no—
127C2×Dic11—42no—
128C2×Dic11C2×D411yescharacteristic
129C2×Dic11C2×D411yescharacteristic
130C2×Dic11C2×D411yescharacteristic
131C4×D11—21no—
132C4×D11—21no—
133C4×D11—42no—
134C4×D11—42no—
135Dic22—21no—
136Dic22—21no—
137Dic22—42no—
138C8×C11—21no—
139C8×C11—21no—
140C11⋊C8—21no—
141C11⋊C8#4112yescomplemented
142#552—111no—
143#547—111no—
144#501—111no—
145#484—111no—
146#483—111no—
147#482D1111yescharacteristic, complemented
148#480—111no—
149#478—111no—
150#477—111no—
151#468—111no—
152#465—111no—
153#440—111no—
154#435—111no—
155#428—111no—
156C2×#107—111no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11C22×D411yescharacteristic
164C2×D11—21no—
165C2×D11—21no—
166C2×D11AGL(1,ℤ/8)12yes—
167C4×C11—21no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11C2×#4111yescharacteristic
172C4×C112−1+411yescharacteristic
173Dic11—21no—
174Dic11—21no—
175Dic11—21no—
176Dic11—41no—
177Dic11—41no—
178Dic11—41no—
179Dic11—41no—
180C2×#41—221no—
181C2×SD16—111no—
182C2×M16—111no—
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#121C2×D1111yescharacteristic
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⋊C4—111no—
204#107—111no—
205#107—111no—
206#107—111no—
207#107—111no—
208#107—111no—
209#107C2×D1111yescharacteristic
210#106—111no—
211#106—111no—
212#106C2×D1111yescharacteristic
213C4⋊C8—111no—
214#103—111no—
215#103—111no—
216#103—111no—
217#102—111no—
218#102C2×D1111yescharacteristic
219#102C2×D1111yescharacteristic
220C22⋊C8—111no—
221C22⋊C8C2×D1111yescharacteristic
222#97—111no—
223C2×C11—41no—
224C2×C11—81no—
225C2×C11#54711yescharacteristic
226C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
227C2×C11#57811yescharacteristic
228D11—22no—
229#41—444no—
230C2×Q8—111no—
231C2×Q8—221no—
232C2×D4—21no—
233C2×D4—111no—
234C2×D4—221no—
235C2×D4C22×D1111yescharacteristic
236C22×C4—111no—
237C22×C4—221no—
238C22×C4—221no—
239C22×C4—221no—
240C22×C4—221no—
241C22×C4C22×D1111yescharacteristic
242SD16—222no—
243M16—222no—
244C2×C8—111no—
245C2×C8—111no—
246C2×C8—222no—
247C2×C8C22×D1111yescharacteristic
248C2×C8C22×D1111yescharacteristic
249C4⋊C4—111no—
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⋊C4—221no—
262C4⋊C4C22×D1111yescharacteristic
263C4⋊C4C22×D1111yescharacteristic
264C4⋊C4C22×D1111yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—111no—
268C22⋊C4—111no—
269C22⋊C4—221no—
270C22⋊C4—221no—
271C22⋊C4—221no—
272C22⋊C4—221no—
273C42—21no—
274C42—111no—
275C42—221no—
276C11#334311yescharacteristic, complemented, Sylow
277C23—21no—
278C23—111no—
279C23D4×D1111yescharacteristic
280Q8—221no—
281Q8—221no—
282Q8—442no—
283D4—21no—
284D4—21no—
285D4—42no—
286D4—222no—
287D4—442no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—111no—
294C2×C4—111no—
295C2×C4—111no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4—221no—
302C2×C4—442no—
303C2×C4—442no—
304C2×C4—442no—
305C2×C4—442no—
306C2×C4D4×D1111yescharacteristic
307C2×C4C23×D1111yescharacteristic
308C8—21no—
309C8—21no—
310C8—112no—
311C8—221no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—112no—
319C22—221no—
320C22—221no—
321C22C2×D4×D1111yescharacteristic
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—221no—
327C4—221no—
328C4—221no—
329C4—441no—
330C4—441no—
331C4—441no—
332C4—441no—
333C4#41×D1111yescharacteristic
334C4#6704311yescharacteristic
335C2—41no—
336C2—81no—
337C2—222no—
338C2#1062318611yescharacteristic
339C2#1062330211yescharacteristic
340C2D11×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#482C2
socleC22×C11C22×D4
prime radical#10623142C2
hypercenter#482D11
hypocenterC11#3343
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #10623060C2semidirect
3. C11×#482C2semidirect
4. #10622655C2semidirect
5. #10622608C2semidirect
6. D11×#107C2semidirect
7. #10622488C2semidirect
8. #10622475C2semidirect
9. #10622469C2semidirect
10. #10622391C2semidirect
11. #10622387C2semidirect
12. #10622379C2semidirect
13. #10622370C2semidirect
14. #10622341C2semidirect
15. #10622335C2semidirect
141. C11⋊C8#41semidirect
147. #482D11semidirect
276. C11#3343semidirect

Maximal subgroups

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

subgroupindex
#106231422
#106230602
C11×#4822
#106226552
#106226082
D11×#1072
#106224882
#106224752
#106224692
#106223912
#106223872
#106223792
#106223702
#106223412
#106223352
#334311