Finite Group Databasebeta

← #13079890

Subgroups — #13079890

Order 1408.

308 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623156C211yesmaximal, characteristic
2#10623050C211yesmaximal, characteristic
3C11×#485C211yesmaximal, characteristic
4#10622657C211yesmaximal, characteristic
5#10622609C211yesmaximal, characteristic
6#10622489C211yesmaximal, characteristic, complemented
7#10622488C211yesmaximal, characteristic, complemented
8#10622471C211yesmaximal, characteristic, complemented
9#10622470C211yesmaximal, characteristic, complemented
10#10622412C211yesmaximal, characteristic, complemented
11#10622410C211yesmaximal, characteristic, complemented
12#10622405C211yesmaximal, characteristic, complemented
13#10622404C211yesmaximal, characteristic, complemented
14#10622334C211yesmaximal, characteristic
15#10622333C211yesmaximal, characteristic
16C11×C22⋊Q8C2211yescharacteristic
17C11×#117C2211yescharacteristic
18Q8×Dic11C2211yescharacteristic
19#66997C2211yescharacteristic
20#66979C2211yescharacteristic
21C2×C4⋊Dic11C2211yescharacteristic
22#66977C2211yescharacteristic
23#66943—21no—
24#66943C2211yescharacteristic
25#66943C2211yescharacteristic
26#66943C2211yescharacteristic
27#66942—21no—
28#66941C2211yescharacteristic
29#66941C2211yescharacteristic
30#66940C2211yescharacteristic
31#66932—21no—
32#66932—21no—
33#66931—21no—
34#66931—21no—
35#66923—21no—
36#66922—21no—
37C11×#107C2211yescharacteristic
38C11×#106C2211yescharacteristic
39C11×#103C2211yescharacteristic
40C11×#103C2211yescharacteristic
41C11×C22⋊C8C2211yescharacteristic
42#66899C2211yescharacteristic
43#66899C2211yescharacteristic
44C22⋊(C11⋊C8)C2211yescharacteristic
45#66881C2211yescharacteristic
46#66881C2211yescharacteristic
47#66880C2211yescharacteristic
48#66880C2211yescharacteristic
49#66879C2211yescharacteristic
50Dic11⋊C8C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52C8×Dic11C2211yescharacteristic
53#66874C2211yescharacteristic
54#66874C2211yescharacteristic
55#66872C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×Dic11—21no—
62C2×Dic22—21no—
63C2×Dic22—21no—
64C2×Dic22C2311yescharacteristic
65C2×C8×C11C2311yescharacteristic
66C2×C8×C11C2311yescharacteristic
67C11×C4⋊C4—21no—
68C11×C4⋊C4C2311yescharacteristic
69C11×C4⋊C4C2311yescharacteristic
70C11×C4⋊C4C2311yescharacteristic
71C11×C22⋊C4—21no—
72C11×C22⋊C4—21no—
73C42×C11—21no—
74C22⋊Dic11—21no—
75C22⋊Dic11D411yescharacteristic
76C22⋊Dic11D411yescharacteristic
77C4⋊Dic11—21no—
78C4⋊Dic11—21no—
79C4⋊Dic11—21no—
80C4⋊Dic11—21no—
81C4⋊Dic11—21no—
82C4⋊Dic11D411yescharacteristic
83C4⋊Dic11D411yescharacteristic
84C4⋊Dic11C2311yescharacteristic
85C4⋊Dic11C2311yescharacteristic
86C4⋊Dic11C2311yescharacteristic
87Dic11⋊C4—21no—
88Dic11⋊C4—21no—
89Dic11⋊C4—21no—
90Dic11⋊C4—21no—
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96C4×Dic11—21no—
97C4×Dic11—21no—
98C4×Dic11C2311yescharacteristic
99C4×Dic11C2311yescharacteristic
100C2×C11⋊C8C2311yescharacteristic
101C2×C11⋊C8C2311yescharacteristic
102#3242—111nomaximal, Sylow
103C23×C11C2×D411yescharacteristic
104Q8×C11—21no—
105Q8×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11C2×D411yescharacteristic
113C2×C4×C11C2411yescharacteristic
114C2×Dic11—21no—
115C2×Dic11—21no—
116C2×Dic11—21no—
117C2×Dic11—21no—
118C2×Dic11—81no—
119C2×Dic11C2×D411yescharacteristic
120C2×Dic11C2×D411yescharacteristic
121C2×Dic11C2×D411yescharacteristic
122C2×Dic11C2×D411yescharacteristic
123Dic22—21no—
124Dic22—21no—
125Dic22—81no—
126Dic22—81no—
127C8×C11—21no—
128C8×C11—21no—
129C11⋊C8—21no—
130C11⋊C8—21no—
131#544—111no—
132#541—111no—
133#501—111no—
134#499—111no—
135#491—111no—
136#487—111no—
137#485—111no—
138#485D1111yescharacteristic
139#484—111no—
140#483—111no—
141#479—111no—
142#479—111no—
143#477—111no—
144#475—111no—
145#433—111no—
146C22×C11—21no—
147C22×C11—21no—
148C22×C11—21no—
149C22×C11C22×D411yescharacteristic
150C4×C11—21no—
151C4×C11—41no—
152C4×C11—41no—
153C4×C11—41no—
154C4×C11—41no—
155C4×C112−1+411yescharacteristic
156C4×C112−1+411yescharacteristic
157Dic11—21no—
158Dic11—21no—
159Dic11—21no—
160Dic11—21no—
161Dic11—41no—
162Dic11—41no—
163Dic11—41no—
164Dic11—41no—
165C4⋊Q8—111no—
166C4⋊Q8—111no—
167C4⋊Q8—111no—
168C4⋊Q8—221no—
169#126—221no—
170#126—221no—
171#125—111no—
172#125—111no—
173#125—111no—
174#125—221no—
175#125—221no—
176#125—221no—
177C22⋊Q8—111no—
178C22⋊Q8—221no—
179C22⋊Q8—221no—
180C22⋊Q8C2×D1111yescharacteristic
181C4×Q8—111no—
182C4×Q8—111no—
183#117—111no—
184#117C2×D1111yescharacteristic
185C2×C4⋊C4—111no—
186#107—111no—
187#107—111no—
188#107—111no—
189#107C2×D1111yescharacteristic
190#106—111no—
191#106—111no—
192#106—111no—
193#106C2×D1111yescharacteristic
194C4⋊C8—111no—
195C4⋊C8—111no—
196#103—111no—
197#103—111no—
198#103—111no—
199#103—111no—
200#103—111no—
201#103—111no—
202#103C2×D1111yescharacteristic
203#103C2×D1111yescharacteristic
204C22⋊C8—111no—
205C22⋊C8C2×D1111yescharacteristic
206#97—111no—
207C4×C8—111no—
208C2×C11—41no—
209C2×C11#53611yescharacteristic
210C2×C11#57711yescharacteristic
211C2×C11#57811yescharacteristic
212C2×Q8—111no—
213C2×Q8—221no—
214C2×Q8—221no—
215C2×Q8C22×D1111yescharacteristic
216C22×C4—221no—
217C22×C4C22×D1111yescharacteristic
218C2×C8—111no—
219C2×C8—111no—
220C2×C8C22×D1111yescharacteristic
221C2×C8C22×D1111yescharacteristic
222C4⋊C4—21no—
223C4⋊C4—111no—
224C4⋊C4—111no—
225C4⋊C4—111no—
226C4⋊C4—111no—
227C4⋊C4—111no—
228C4⋊C4—221no—
229C4⋊C4—221no—
230C4⋊C4—221no—
231C4⋊C4—221no—
232C4⋊C4—221no—
233C4⋊C4—221no—
234C4⋊C4—221no—
235C4⋊C4—221no—
236C4⋊C4—221no—
237C4⋊C4—221no—
238C4⋊C4—221no—
239C4⋊C4—221no—
240C4⋊C4—221no—
241C4⋊C4—221no—
242C4⋊C4C22×D1111yescharacteristic
243C4⋊C4C22×D1111yescharacteristic
244C4⋊C4C22×D1111yescharacteristic
245C22⋊C4—21no—
246C22⋊C4—21no—
247C22⋊C4—111no—
248C22⋊C4—111no—
249C22⋊C4—221no—
250C42—21no—
251C42—111no—
252C42—111no—
253C42—221no—
254C42—221no—
255C11#324211yescharacteristic, complemented, Sylow
256C23D4×D1111yescharacteristic
257Q8—21no—
258Q8—21no—
259Q8—221no—
260Q8—221no—
261Q8—881no—
262Q8—881no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—111no—
270C2×C4—111no—
271C2×C4—111no—
272C2×C4—111no—
273C2×C4—221no—
274C2×C4—221no—
275C2×C4—221no—
276C2×C4—221no—
277C2×C4—881no—
278C2×C4D4×D1111yescharacteristic
279C2×C4C23×D1111yescharacteristic
280C8—21no—
281C8—21no—
282C8—221no—
283C8—221no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22C2×D4×D1111yescharacteristic
288C4—21no—
289C4—41no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—221no—
294C4—221no—
295C4—221no—
296C4—221no—
297C4—441no—
298C4—441no—
299C4—441no—
300C4—441no—
301C4#6704311yescharacteristic
302C4#6704311yescharacteristic
303C2—41no—
304C2#1062317911yescharacteristic
305C2#1062330111yescharacteristic
306C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#485C2
socleC22×C11C22×D4
prime radicalC23×C11C2×D4
hypercenter#485D11
hypocenterC11#3242
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
6. #10622489C2semidirect
7. #10622488C2semidirect
8. #10622471C2semidirect
9. #10622470C2semidirect
10. #10622412C2semidirect
11. #10622410C2semidirect
12. #10622405C2semidirect
13. #10622404C2semidirect
255. C11#3242semidirect

Maximal subgroups

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

subgroupindex
#106231562
#106230502
C11×#4852
#106226572
#106226092
#106224892
#106224882
#106224712
#106224702
#106224122
#106224102
#106224052
#106224042
#106223342
#106223332
#324211