Finite Group Databasebeta

← #13079820

Subgroups — #13079820

Order 1408.

324 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
1D11×#125C211yesmaximal, characteristic
2#10623109C211yesmaximal, characteristic
3C11×#479C211yesmaximal, characteristic, complemented
4#10622676C211yesmaximal, characteristic, complemented
5#10622635C211yesmaximal, characteristic, complemented
6#10622497C211yesmaximal, characteristic
7#10622489C211yesmaximal, characteristic, complemented
8#10622475C211yesmaximal, characteristic
9#10622469C211yesmaximal, characteristic, complemented
10#10622448C211yesmaximal, characteristic
11#10622442C211yesmaximal, characteristic, complemented
12#10622422C211yesmaximal, characteristic
13#10622418C211yesmaximal, characteristic
14#10622410C211yesmaximal, characteristic, complemented
15#10622410C211yesmaximal, characteristic, complemented
16C11×#125C2211yescharacteristic
17C4×Q8×C11C2211yescharacteristic
18#66999C2211yescharacteristic
19#66997C2211yescharacteristic
20#66950C2211yescharacteristic
21#66949—21no—
22C4⋊C4×D11—21no—
23C4⋊C4×D11—21no—
24C4⋊C4×D11C2211yescharacteristic
25C4⋊C4×D11C2211yescharacteristic
26#66943C2211yescharacteristic
27#66943C2211yescharacteristic
28#66942—21no—
29#66942—21no—
30#66942—21no—
31#66941C2211yescharacteristic
32#66925—21no—
33C42×D11C2211yescharacteristic
34#66923C2211yescharacteristic
35C4×Dic22—21no—
36C4×Dic22C2211yescharacteristic
37C11×#107C2211yescharacteristic
38C11×#106C2211yescharacteristic
39C11×C4⋊C8C2211yescharacteristic
40C11×#103C2211yescharacteristic
41C11×#103C2211yescharacteristic
42#66899C2211yescharacteristic
43#66899C2211yescharacteristic
44(C2×D11)⋊C8C2211yescharacteristic
45(C2×D11)⋊C8C2211yescharacteristic
46#66882C2211yescharacteristic
47#66881C2211yescharacteristic
48#66880C2211yescharacteristic
49#66880C2211yescharacteristic
50#66879C2211yescharacteristic
51#66879C2211yescharacteristic
52#66874C2211yescharacteristic
53#66874C2211yescharacteristic
54#66872C2211yescharacteristic
55#66872C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×C4×D11—21no—
61C2×C4×D11—21no—
62C2×C4×D11D411yescharacteristic
63C2×C4×D11D411yescharacteristic
64C2×C4×D11C2311yescharacteristic
65C2×Dic22—21no—
66C2×Dic22C2311yescharacteristic
67C2×C8×C11C2311yescharacteristic
68C2×C8×C11C2311yescharacteristic
69C11×C4⋊C4—21no—
70C11×C4⋊C4—21no—
71C11×C4⋊C4—21no—
72C11×C4⋊C4C2311yescharacteristic
73C11×C4⋊C4C2311yescharacteristic
74C11×C4⋊C4C2311yescharacteristic
75C42×C11—21no—
76C42×C11C2311yescharacteristic
77(C2×D11)⋊C4—21no—
78(C2×D11)⋊C4—21no—
79C4⋊Dic11—21no—
80C4⋊Dic11—21no—
81C4⋊Dic11—21no—
82C4⋊Dic11C2311yescharacteristic
83C4⋊Dic11C2311yescharacteristic
84C4⋊Dic11C2311yescharacteristic
85Dic11⋊C4—21no—
86Dic11⋊C4—21no—
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×Dic11D411yescharacteristic
98C4×Dic11D411yescharacteristic
99C4×Dic11C2311yescharacteristic
100C2×C11⋊C8C2311yescharacteristic
101C2×C11⋊C8C2311yescharacteristic
102#3236—111nomaximal, Sylow
103C22×D11C2×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×C11C2×D411yescharacteristic
111C2×C4×C11C2×D411yescharacteristic
112C2×C4×C11C2411yescharacteristic
113C2×Dic11—21no—
114C2×Dic11—21no—
115C2×Dic11—21no—
116C2×Dic11—21no—
117C2×Dic11C2×D411yescharacteristic
118C2×Dic11C2×D411yescharacteristic
119C2×Dic11C2×D411yescharacteristic
120C4×D11—22no—
121C4×D11—21no—
122C4×D11—21no—
123C4×D11—41no—
124C4×D11—42no—
125C4×D11—42no—
126Dic22—21no—
127Dic22—21no—
128Dic22—42no—
129C8×C11—21no—
130C8×C11—21no—
131C11⋊C8—21no—
132C11⋊C8—21no—
133#533—111no—
134C2×#125—111no—
135#501—111no—
136#501—111no—
137#491—111no—
138#491—111no—
139#484—111no—
140#484—111no—
141#483—111no—
142#483—111no—
143#479—111no—
144#479—111no—
145#479—111no—
146#479D1111yescharacteristic, complemented
147#432—111no—
148C22×C11C22×D411yescharacteristic
149C2×D11—21no—
150C2×D11—21no—
151C2×D11#13712yes—
152C4×C11—21no—
153C4×C11—21no—
154C4×C11—41no—
155C4×C11—41no—
156C4×C11—41no—
157C4×C11—41no—
158C4×C112−1+411yescharacteristic
159C4×C112−1+411yescharacteristic
160Dic11—21no—
161Dic11—21no—
162Dic11—21no—
163Dic11—41no—
164Dic11—41no—
165Dic11—41no—
166Dic11—41no—
167C4⋊Q8—111no—
168C4⋊Q8—111no—
169#125—111no—
170#125—111no—
171#125—111no—
172#125—221no—
173#125—221no—
174#125—221no—
175#125C2×D1111yescharacteristic
176C22⋊Q8—111no—
177C22⋊Q8—111no—
178C22⋊Q8—221no—
179C4×Q8—111no—
180C4×Q8—221no—
181C4×Q8C2×D1111yescharacteristic
182#117—221no—
183C2×C4⋊C4—111no—
184C2×C4⋊C4—111no—
185C2×C4⋊C4—221no—
186C2×C4⋊C4—221no—
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⋊C8C2×D1111yescharacteristic
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⋊C8—111no—
208#97—111no—
209#97—111no—
210C2×C11#53611yescharacteristic
211C2×C11C2×#13711yescharacteristic
212C2×C11#57511yescharacteristic
213D11—22no—
214C2×Q8—111no—
215C2×Q8—221no—
216C2×Q8C22×D1111yescharacteristic
217C22×C4—111no—
218C22×C4—111no—
219C22×C4—111no—
220C22×C4—221no—
221C22×C4—221no—
222C2×C8—111no—
223C2×C8—111no—
224C2×C8C22×D1111yescharacteristic
225C2×C8C22×D1111yescharacteristic
226C4⋊C4—21no—
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—111no—
230C4⋊C4—111no—
231C4⋊C4—111no—
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⋊C4—221no—
243C4⋊C4—221no—
244C4⋊C4—221no—
245C4⋊C4—221no—
246C4⋊C4C22×D1111yescharacteristic
247C4⋊C4C22×D1111yescharacteristic
248C4⋊C4C22×D1111yescharacteristic
249C22⋊C4—221no—
250C22⋊C4—221no—
251C42—21no—
252C42—111no—
253C42—111no—
254C42—111no—
255C42—221no—
256C42C22×D1111yescharacteristic
257C11#323611yescharacteristic, complemented, Sylow
258C23—111no—
259Q8—21no—
260Q8—21no—
261Q8—221no—
262Q8—221no—
263Q8—442no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—111no—
269C2×C4—111no—
270C2×C4—111no—
271C2×C4—222no—
272C2×C4—221no—
273C2×C4—221no—
274C2×C4—221no—
275C2×C4—221no—
276C2×C4—221no—
277C2×C4—221no—
278C2×C4—441no—
279C2×C4—442no—
280C2×C4—442no—
281C2×C4D4×D1111yescharacteristic
282C2×C4D4×D1111yescharacteristic
283C2×C4C23×D1111yescharacteristic
284C8—21no—
285C8—21no—
286C8—221no—
287C8—221no—
288C22—112no—
289C22—221no—
290C22—221no—
291C22C2×D4×D1111yescharacteristic
292C4—21no—
293C4—21no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—41no—
298C4—221no—
299C4—221no—
300C4—221no—
301C4—441no—
302C4—441no—
303C4—441no—
304C4—441no—
305C4#6704011yescharacteristic
306C4#6704311yescharacteristic
307C2—222no—
308C2#1062315911yescharacteristic
309C2#1062329911yescharacteristic
310C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#479C2
socleC22×C11C22×D4
prime radicalC22×D11C2×D4
hypercenter#479D11
hypocenterC11#3236
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
3. C11×#479C2semidirect
4. #10622676C2semidirect
5. #10622635C2semidirect
7. #10622489C2semidirect
9. #10622469C2semidirect
11. #10622442C2semidirect
14. #10622410C2semidirect
15. #10622410C2semidirect
146. #479D11semidirect
257. C11#3236semidirect

Maximal subgroups

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

subgroupindex
D11×#1252
#106231092
C11×#4792
#106226762
#106226352
#106224972
#106224892
#106224752
#106224692
#106224482
#106224422
#106224222
#106224182
#106224102
#323611