Finite Group Databasebeta

← #13079773

Subgroups — #13079773

Order 1408.

326 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623153C211yesmaximal, characteristic
2#10623048C211yesmaximal, characteristic
3C11×#485C211yesmaximal, characteristic
4#10622658C211yesmaximal, characteristic
5#10622609C211yesmaximal, characteristic
6#10622490C211yesmaximal, characteristic, complemented
7#10622487C211yesmaximal, characteristic, complemented
8#10622470C211yesmaximal, characteristic, complemented
9#10622468C211yesmaximal, characteristic, complemented
10#10622412C211yesmaximal, characteristic, complemented
11#10622409C211yesmaximal, characteristic, complemented
12#10622405C211yesmaximal, characteristic, complemented
13#10622405C211yesmaximal, characteristic, complemented
14#10622336C211yesmaximal, characteristic
15#10622331C211yesmaximal, characteristic
16C11×C22⋊Q8C2211yescharacteristic
17C11×#117C2211yescharacteristic
18Q8×Dic11C2211yescharacteristic
19#66997C2211yescharacteristic
20#66979C2211yescharacteristic
21#66977C2211yescharacteristic
22C2×C4×Dic11C2211yescharacteristic
23#66943C2211yescharacteristic
24#66943C2211yescharacteristic
25#66942—21no—
26#66941C2211yescharacteristic
27#66941C2211yescharacteristic
28#66941C2211yescharacteristic
29#66940—21no—
30#66940C2211yescharacteristic
31#66931—21no—
32#66931—21no—
33#66931—21no—
34#66930—21no—
35C4×Dic22—21no—
36C4×Dic22—21no—
37C11×#107C2211yescharacteristic
38C11×#106C2211yescharacteristic
39C11×#103C2211yescharacteristic
40C11×#103C2211yescharacteristic
41C11×C22⋊C8C2211yescharacteristic
42#66899C2211yescharacteristic
43#66899C2211yescharacteristic
44C22⋊(C11⋊C8)C2211yescharacteristic
45#66882C2211yescharacteristic
46#66881C2211yescharacteristic
47#66880C2211yescharacteristic
48#66880C2211yescharacteristic
49Dic11⋊C8C2211yescharacteristic
50Dic11⋊C8C2211yescharacteristic
51C8×Dic11C2211yescharacteristic
52C8×Dic11C2211yescharacteristic
53#66874C2211yescharacteristic
54#66874C2211yescharacteristic
55#66872C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×Dic11D411yescharacteristic
62C22×Dic11D411yescharacteristic
63C2×Dic22—21no—
64C2×Dic22—21no—
65C2×Dic22—21no—
66C2×Dic22C2311yescharacteristic
67C2×C8×C11C2311yescharacteristic
68C2×C8×C11C2311yescharacteristic
69C11×C4⋊C4—21no—
70C11×C4⋊C4C2311yescharacteristic
71C11×C4⋊C4C2311yescharacteristic
72C11×C4⋊C4C2311yescharacteristic
73C11×C22⋊C4—21no—
74C11×C22⋊C4—21no—
75C42×C11—21no—
76C22⋊Dic11—21no—
77C22⋊Dic11—21no—
78C4⋊Dic11—21no—
79C4⋊Dic11—21no—
80C4⋊Dic11—21no—
81C4⋊Dic11C2311yescharacteristic
82C4⋊Dic11C2311yescharacteristic
83C4⋊Dic11C2311yescharacteristic
84Dic11⋊C4—21no—
85Dic11⋊C4—21no—
86Dic11⋊C4—21no—
87Dic11⋊C4—21no—
88Dic11⋊C4—21no—
89Dic11⋊C4—21no—
90Dic11⋊C4—21no—
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93C4×Dic11—21no—
94C4×Dic11—21no—
95C4×Dic11—21no—
96C4×Dic11D411yescharacteristic
97C4×Dic11D411yescharacteristic
98C4×Dic11C2311yescharacteristic
99C4×Dic11C2311yescharacteristic
100C2×C11⋊C8C2311yescharacteristic
101C2×C11⋊C8C2311yescharacteristic
102#3231—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—22no—
115C2×Dic11—22no—
116C2×Dic11—21no—
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11C2×D411yescharacteristic
121C2×Dic11C2×D411yescharacteristic
122C2×Dic11C2×D411yescharacteristic
123C2×Dic11C2×D411yescharacteristic
124Dic22—21no—
125Dic22—21no—
126Dic22—42no—
127Dic22—42no—
128Dic22—42no—
129C8×C11—21no—
130C8×C11—21no—
131C11⋊C8—21no—
132C11⋊C8—21no—
133#533—111no—
134#533—111no—
135#500—111no—
136#498—111no—
137#487—111no—
138#487—111no—
139#485—111no—
140#485—111no—
141#485—111no—
142#485D1111yescharacteristic
143#479—111no—
144#479—111no—
145#479—111no—
146#479—111no—
147#431—111no—
148C22×C11—21no—
149C22×C11—21no—
150C22×C11—21no—
151C22×C11C22×D411yescharacteristic
152C4×C11—21no—
153C4×C11—41no—
154C4×C11—41no—
155C4×C11—41no—
156C4×C11—41no—
157C4×C112−1+411yescharacteristic
158C4×C112−1+411yescharacteristic
159Dic11—21no—
160Dic11—21no—
161Dic11—41no—
162Dic11—41no—
163Dic11—41no—
164Dic11—41no—
165Dic11#13512yes—
166Dic11#13712yes—
167C4⋊Q8—111no—
168C4⋊Q8—111no—
169C4⋊Q8—111no—
170C4⋊Q8—111no—
171#125—111no—
172#125—111no—
173#125—221no—
174C22⋊Q8—111no—
175C22⋊Q8—221no—
176C22⋊Q8—221no—
177C22⋊Q8—221no—
178C22⋊Q8C2×D1111yescharacteristic
179C4×Q8—111no—
180C4×Q8—111no—
181C4×Q8—221no—
182C4×Q8—221no—
183C4×Q8—221no—
184#117—111no—
185#117—221no—
186#117C2×D1111yescharacteristic
187C2×C42—111no—
188#107—111no—
189#107—111no—
190#107—111no—
191#107C2×D1111yescharacteristic
192#106—111no—
193#106—111no—
194#106—111no—
195#106C2×D1111yescharacteristic
196C4⋊C8—111no—
197C4⋊C8—111no—
198#103—111no—
199#103—111no—
200#103—111no—
201#103—111no—
202#103—111no—
203#103—111no—
204#103C2×D1111yescharacteristic
205#103C2×D1111yescharacteristic
206C22⋊C8—111no—
207C22⋊C8C2×D1111yescharacteristic
208C4×C8—111no—
209C4×C8—111no—
210C2×C11—41no—
211C2×C11#53611yescharacteristic
212C2×C11C2×#13511yescharacteristic
213C2×C11C2×#13711yescharacteristic
214C2×Q8—111no—
215C2×Q8—221no—
216C2×Q8—221no—
217C2×Q8—221no—
218C2×Q8C22×D1111yescharacteristic
219C22×C4—111no—
220C22×C4—111no—
221C22×C4C22×D1111yescharacteristic
222C2×C8—111no—
223C2×C8—111no—
224C2×C8C22×D1111yescharacteristic
225C2×C8C22×D1111yescharacteristic
226C4⋊C4—21no—
227C4⋊C4—111no—
228C4⋊C4—111no—
229C4⋊C4—111no—
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—221no—
248C22⋊C4—221no—
249C42—21no—
250C42—111no—
251C42—111no—
252C42—111no—
253C42—111no—
254C42—221no—
255C42—221no—
256C42—221no—
257C11#323111yescharacteristic, complemented, Sylow
258C23D4×D1111yescharacteristic
259Q8—21no—
260Q8—21no—
261Q8—221no—
262Q8—221no—
263Q8—442no—
264Q8—442no—
265Q8—442no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—111no—
273C2×C4—111no—
274C2×C4—111no—
275C2×C4—111no—
276C2×C4—222no—
277C2×C4—222no—
278C2×C4—221no—
279C2×C4—221no—
280C2×C4—221no—
281C2×C4—221no—
282C2×C4D4×D1111yescharacteristic
283C2×C4C23×D1111yescharacteristic
284C8—21no—
285C8—21no—
286C8—221no—
287C8—221no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22C2×D4×D1111yescharacteristic
292C4—21no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—112no—
298C4—112no—
299C4—221no—
300C4—221no—
301C4—441no—
302C4—441no—
303C4—441no—
304C4—441no—
305C4#6704311yescharacteristic
306C4#6704311yescharacteristic
307C2—41no—
308C2#1062317911yescharacteristic
309C2D11×#13511yescharacteristic
310C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#485C2
socleC22×C11C22×D4
prime radicalC23×C11C2×D4
hypercenter#485D11
hypocenterC11#3231
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. #10622490C2semidirect
7. #10622487C2semidirect
8. #10622470C2semidirect
9. #10622468C2semidirect
10. #10622412C2semidirect
11. #10622409C2semidirect
12. #10622405C2semidirect
13. #10622405C2semidirect
257. C11#3231semidirect

Maximal subgroups

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

subgroupindex
#106231532
#106230482
C11×#4852
#106226582
#106226092
#106224902
#106224872
#106224702
#106224682
#106224122
#106224092
#106224052
#106223362
#106223312
#323111