Finite Group Databasebeta

← #13081379

Subgroups — #13081379

Order 1408.

344 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623244C211yesmaximal, characteristic
2#10623216C211yesmaximal, characteristic, complemented
3C11×#490C211yesmaximal, characteristic
4#10622688C211yesmaximal, characteristic
5#10622676C211yesmaximal, characteristic, complemented
6#10622381C211yesmaximal, characteristic, complemented
7#10622380C211yesmaximal, characteristic, complemented
8#10622380C211yesmaximal, characteristic, complemented
9#10622378C211yesmaximal, characteristic, complemented
10#10622376C211yesmaximal, characteristic, complemented
11#10622374C211yesmaximal, characteristic, complemented
12#10622371C211yesmaximal, characteristic, complemented
13#10622370C211yesmaximal, characteristic, complemented
14#10622329C211yesmaximal, characteristic, complemented
15#10622314C211yesmaximal, characteristic, complemented
16C11×#127C2211yescharacteristic
17C11×#125C2211yescharacteristic
18#66989—21no—
19#66989C2211yescharacteristic
20#66989C2211yescharacteristic
21#66988—21no—
22#66988—21no—
23D4×Dic11—21no—
24D4×Dic11C2211yescharacteristic
25D4×Dic11C2211yescharacteristic
26C2×#4324C2211yescharacteristic
27C2×#4324C2211yescharacteristic
28C2×Dic44C2211yescharacteristic
29#66943C2211yescharacteristic
30#66942—21no—
31#66942—21no—
32#66941—21no—
33#66941C2211yescharacteristic
34#66940—21no—
35#66940C2211yescharacteristic
36#66940C2211yescharacteristic
37C4×Dic22C2211yescharacteristic
38C4×Dic22C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40C11×#102C2211yescharacteristic
41C11×#102C2211yescharacteristic
42C11×#102C2211yescharacteristic
43C11×#102C2211yescharacteristic
44C11×#97C2211yescharacteristic
45#66896C2211yescharacteristic
46#66896C2211yescharacteristic
47#66881C2211yescharacteristic
48#66880C2211yescharacteristic
49#66880C2211yescharacteristic
50#66879C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53C8×Dic11C2211yescharacteristic
54#66874C2211yescharacteristic
55#66874C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×D4×C11—21no—
60C2×D4×C11—21no—
61C2×D4×C11C2311yescharacteristic
62C2×D4×C11C2311yescharacteristic
63C22×Dic11—21no—
64C22×Dic11—21no—
65C2×Dic22—21no—
66C2×Dic22D411yescharacteristic
67C2×Dic22C2311yescharacteristic
68C2×Dic22C2311yescharacteristic
69C2×C8×C11C2311yescharacteristic
70C2×C8×C11C2311yescharacteristic
71C11×C4⋊C4—21no—
72C11×C4⋊C4—21no—
73C11×C4⋊C4C2311yescharacteristic
74C11×C4⋊C4C2311yescharacteristic
75C42×C11C2311yescharacteristic
76C22⋊Dic11—21no—
77C22⋊Dic11—21no—
78C22⋊Dic11—21no—
79C22⋊Dic11—21no—
80C22⋊Dic11—21no—
81C22⋊Dic11—21no—
82#4324—22no—
83#4324—22no—
84C4⋊Dic11—21no—
85C4⋊Dic11D411yescharacteristic
86C4⋊Dic11C2311yescharacteristic
87C4⋊Dic11C2311yescharacteristic
88Dic11⋊C4—21no—
89Dic11⋊C4—21no—
90Dic11⋊C4—21no—
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4D411yescharacteristic
95Dic11⋊C4D411yescharacteristic
96C4×Dic11—21no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11C2311yescharacteristic
101C4×Dic11C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104Dic44—22no—
105#3371—111nomaximal, Sylow
106C23×C11—21no—
107C23×C11—21no—
108D4×C11—21no—
109D4×C11—21no—
110D4×C11—21no—
111D4×C11—21no—
112D4×C11—42no—
113D4×C11—81no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11C2×D411yescharacteristic
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2411yescharacteristic
119C2×Dic11—21no—
120C2×Dic11—21no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—81no—
124C2×Dic11—81no—
125C2×Dic11C2×D411yescharacteristic
126C2×Dic11C2×D411yescharacteristic
127C2×Dic11C2×D411yescharacteristic
128C2×Dic11C2×D411yescharacteristic
129Dic22—21no—
130Dic22—21no—
131Dic22—21no—
132Dic22—41no—
133Dic22—42no—
134Dic22#4112yes—
135C8×C11—21no—
136C8×C11—21no—
137C11⋊C8—21no—
138C11⋊C8—21no—
139#559—111no—
140#557—111no—
141#490D1111yescharacteristic
142#489—111no—
143#488—111no—
144#479—111no—
145#478—111no—
146#476—111no—
147#464—111no—
148#464—111no—
149#460—111no—
150#446—111no—
151#441—111no—
152#440—111no—
153C4×SD16—111no—
154C22×C11—41no—
155C22×C11—41no—
156C22×C11—41no—
157C22×C11—41no—
158C22×C11—41no—
159C22×C11—41no—
160C22×C11C22×D411yescharacteristic
161C4×C11—21no—
162C4×C11—21no—
163C4×C11—41no—
164C4×C11—41no—
165C4×C11C2×#4111yescharacteristic
166C4×C112−1+411yescharacteristic
167Dic11—22no—
168Dic11—21no—
169Dic11—21no—
170Dic11—21no—
171Dic11—21no—
172Dic11—41no—
173Dic11—41no—
174Dic11—41no—
175C2×Q16—111no—
176C2×SD16—111no—
177C2×SD16—111no—
178C4⋊Q8—111no—
179C4⋊Q8—221no—
180#127C2×D1111yescharacteristic
181#125—111no—
182#125—221no—
183#125—221no—
184#125C2×D1111yescharacteristic
185#124—111no—
186#124—111no—
187#124—221no—
188#123—221no—
189#123—221no—
190C4×Q8—111no—
191C4×Q8—111no—
192C4×Q8—111no—
193C4×Q8—111no—
194C4×Q8—111no—
195C4×Q8—221no—
196C4×D4—111no—
197C4×D4—111no—
198C4×D4—221no—
199#107—111no—
200#106—111no—
201#106—111no—
202C4⋊C8—111no—
203C4⋊C8—111no—
204C4⋊C8—111no—
205#103—111no—
206#103—111no—
207#103—111no—
208#103—111no—
209#102—111no—
210#102—111no—
211#102C2×D1111yescharacteristic
212#102C2×D1111yescharacteristic
213#102C2×D1111yescharacteristic
214#102C2×D1111yescharacteristic
215#97—111no—
216#97C2×D1111yescharacteristic
217C4×C8—111no—
218C2×C11—81no—
219C2×C11—81no—
220C2×C11#54811yescharacteristic
221C2×C11#57511yescharacteristic
222C2×C11#57711yescharacteristic
223C2×Q8—111no—
224C2×Q8—111no—
225C2×Q8—111no—
226C2×Q8—221no—
227C2×D4—21no—
228C2×D4—21no—
229C2×D4C22×D1111yescharacteristic
230C2×D4C22×D1111yescharacteristic
231C22×C4—221no—
232C22×C4—221no—
233Q16—222no—
234SD16—222no—
235SD16—222no—
236C2×C8—111no—
237C2×C8—111no—
238C2×C8C22×D1111yescharacteristic
239C2×C8C22×D1111yescharacteristic
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—111no—
243C4⋊C4—111no—
244C4⋊C4—111no—
245C4⋊C4—111no—
246C4⋊C4—111no—
247C4⋊C4—221no—
248C4⋊C4—221no—
249C4⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4C22×D1111yescharacteristic
255C4⋊C4C22×D1111yescharacteristic
256C22⋊C4—221no—
257C22⋊C4—221no—
258C22⋊C4—221no—
259C22⋊C4—221no—
260C22⋊C4—221no—
261C22⋊C4—221no—
262C42—111no—
263C42—111no—
264C42—221no—
265C42—221no—
266C42—221no—
267C42—221no—
268C42C22×D1111yescharacteristic
269C11#337111yescharacteristic, complemented, Sylow
270C23—21no—
271C23—21no—
272Q8—112no—
273Q8—221no—
274Q8—221no—
275Q8—221no—
276Q8—441no—
277Q8—442no—
278D4—21no—
279D4—21no—
280D4—21no—
281D4—21no—
282D4—42no—
283D4—81no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—111no—
287C2×C4—111no—
288C2×C4—111no—
289C2×C4—111no—
290C2×C4—221no—
291C2×C4—221no—
292C2×C4—221no—
293C2×C4—221no—
294C2×C4—881no—
295C2×C4—881no—
296C2×C4D4×D1111yescharacteristic
297C2×C4D4×D1111yescharacteristic
298C2×C4C23×D1111yescharacteristic
299C8—21no—
300C8—21no—
301C8—221no—
302C8—221no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22C2×D4×D1111yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—221no—
315C4—221no—
316C4—221no—
317C4—221no—
318C4—222no—
319C4—441no—
320C4—441no—
321C4—441no—
322C4#41×D1111yescharacteristic
323C4#6704311yescharacteristic
324C2—81no—
325C2—81no—
326C2#1062320811yescharacteristic
327C2#1062330411yescharacteristic
328C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#490C2
socleC22×C11C22×D4
prime radicalC11×#127C22
hypercenter#490D11
hypocenterC11#3371
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
5. #10622676C2semidirect
6. #10622381C2semidirect
7. #10622380C2semidirect
8. #10622380C2semidirect
9. #10622378C2semidirect
10. #10622376C2semidirect
11. #10622374C2semidirect
12. #10622371C2semidirect
13. #10622370C2semidirect
14. #10622329C2semidirect
15. #10622314C2semidirect
269. C11#3371semidirect

Maximal subgroups

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

subgroupindex
#106232442
#106232162
C11×#4902
#106226882
#106226762
#106223812
#106223802
#106223782
#106223762
#106223742
#106223712
#106223702
#106223292
#106223142
#337111