Finite Group Databasebeta

← #13081188

Subgroups — #13081188

Order 1408.

336 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623225C211yesmaximal, characteristic
2#10623112C211yesmaximal, characteristic
3C11×#479C211yesmaximal, characteristic, complemented
4#10622677C211yesmaximal, characteristic, complemented
5C4×#4326C211yesmaximal, characteristic, complemented
6#10622497C211yesmaximal, characteristic, complemented
7#10622494C211yesmaximal, characteristic, complemented
8#10622480C211yesmaximal, characteristic, complemented
9#10622474C211yesmaximal, characteristic, complemented
10#10622451C211yesmaximal, characteristic
11#10622442C211yesmaximal, characteristic, complemented
12#10622429C211yesmaximal, characteristic, complemented
13#10622429C211yesmaximal, characteristic, complemented
14#10622428C211yesmaximal, characteristic, complemented
15#10622422C211yesmaximal, characteristic, complemented
16C11×#125C2211yescharacteristic
17C4×Q8×C11C2211yescharacteristic
18#66999C2211yescharacteristic
19#66999C2211yescharacteristic
20C2×#4326C2211yescharacteristic
21C2×#4313C2211yescharacteristic
22C2×#4313C2211yescharacteristic
23#66951—21no—
24#66950C2211yescharacteristic
25#66950C2211yescharacteristic
26#66947—21no—
27#66947—21no—
28#66945—21no—
29#66945C2211yescharacteristic
30#66945C2211yescharacteristic
31C4⋊C4×D11C2211yescharacteristic
32C4⋊C4×D11C2211yescharacteristic
33#66943—21no—
34#66942—21no—
35#66929—21no—
36C4×D44C2211yescharacteristic
37#66925—21no—
38#66923C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40C11×#107C2211yescharacteristic
41C11×#106C2211yescharacteristic
42C11×C4⋊C8C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×#103C2211yescharacteristic
45#66899C2211yescharacteristic
46(C2×D11)⋊C8C2211yescharacteristic
47(C2×D11)⋊C8C2211yescharacteristic
48#66882C2211yescharacteristic
49#66881C2211yescharacteristic
50#66880C2211yescharacteristic
51#66880C2211yescharacteristic
52#66874C2211yescharacteristic
53#66872C2211yescharacteristic
54#66872C2211yescharacteristic
55#66871C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58C4×C11⋊C8C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D44D411yescharacteristic
61C2×C4×D11—21no—
62C2×C4×D11—21no—
63C2×C4×D11C2311yescharacteristic
64C2×C4×D11C2311yescharacteristic
65C2×Dic22C2311yescharacteristic
66C2×C8×C11C2311yescharacteristic
67C2×C8×C11C2311yescharacteristic
68C11×C4⋊C4—21no—
69C11×C4⋊C4—21no—
70C11×C4⋊C4—21no—
71C11×C4⋊C4C2311yescharacteristic
72C11×C4⋊C4C2311yescharacteristic
73C11×C4⋊C4C2311yescharacteristic
74C42×C11—21no—
75C42×C11C2311yescharacteristic
76#4326—22no—
77(C2×D11)⋊C4—21no—
78(C2×D11)⋊C4—21no—
79(C2×D11)⋊C4—21no—
80(C2×D11)⋊C4—21no—
81(C2×D11)⋊C4—21no—
82(C2×D11)⋊C4—21no—
83(C2×D11)⋊C4D411yescharacteristic
84(C2×D11)⋊C4D411yescharacteristic
85C4⋊Dic11—21no—
86C4⋊Dic11—21no—
87C4⋊Dic11D411yescharacteristic
88C4⋊Dic11C2311yescharacteristic
89C4⋊Dic11C2311yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C2×C11⋊C8C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103#4313—22no—
104#4313—22no—
105#3352—111nomaximal, Sylow
106C22×D11C2×D411yescharacteristic
107C22×D11C2×D411yescharacteristic
108Q8×C11—21no—
109Q8×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11C2×D411yescharacteristic
115C2×C4×C11C2×D411yescharacteristic
116C2×C4×C11C2411yescharacteristic
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11—21no—
121C2×Dic11C2×D411yescharacteristic
122C2×Dic11C2×D411yescharacteristic
123D44—41no—
124C4×D11—21no—
125C4×D11—21no—
126C4×D11—21no—
127C4×D11—21no—
128C4×D11—42no—
129C4×D11—42no—
130Dic22—21no—
131Dic22—21no—
132C8×C11—21no—
133C8×C11—21no—
134C11⋊C8—21no—
135C11⋊C8#4112yes—
136#552—111no—
137#552—111no—
138#499—111no—
139#485—111no—
140#485—111no—
141#484—111no—
142#484—111no—
143#479—111no—
144#479D1111yescharacteristic, complemented
145#470—111no—
146#470—111no—
147C4×Q16—111no—
148#436—111no—
149#428—111no—
150#428—111no—
151C22×C11C22×D411yescharacteristic
152C2×D11—21no—
153C2×D11—21no—
154C2×D11—21no—
155C2×D11—21no—
156C2×D11—21no—
157C2×D11—21no—
158C4×C11—21no—
159C4×C11—21no—
160C4×C11—41no—
161C4×C11—41no—
162C4×C11—41no—
163C4×C11—41no—
164C4×C11C2×#4111yescharacteristic
165C4×C112−1+411yescharacteristic
166Dic11—21no—
167Dic11—21no—
168Dic11—41no—
169Dic11—41no—
170Dic11—41no—
171Dic11—41no—
172C2×Q16—111no—
173C2×M16—111no—
174C2×M16—111no—
175#126—221no—
176#126—221no—
177#125—111no—
178#125—221no—
179#125—221no—
180#125C2×D1111yescharacteristic
181#123—221no—
182#123—221no—
183C22⋊Q8—111no—
184C22⋊Q8—111no—
185C22⋊Q8—111no—
186C22⋊Q8—111no—
187C4×Q8—111no—
188C4×Q8C2×D1111yescharacteristic
189C4×D4—111no—
190#117—111no—
191#117—111no—
192#117—221no—
193#117—221no—
194C2×C4⋊C4—111no—
195C2×C4⋊C4—111no—
196#107—111no—
197#107—111no—
198#107—111no—
199#107—111no—
200#107C2×D1111yescharacteristic
201#106—111no—
202#106—111no—
203#106—111no—
204#106C2×D1111yescharacteristic
205C4⋊C8C2×D1111yescharacteristic
206#103—111no—
207#103—111no—
208#103—111no—
209#103—111no—
210#103C2×D1111yescharacteristic
211#103C2×D1111yescharacteristic
212C22⋊C8—111no—
213C22⋊C8—111no—
214C4×C8—111no—
215C2×C11#54711yescharacteristic
216C2×C11#57511yescharacteristic
217C2×C11#57811yescharacteristic
218D11—41no—
219D11—41no—
220C2×Q8—111no—
221C2×Q8C22×D1111yescharacteristic
222C2×D4—111no—
223C22×C4—111no—
224C22×C4—111no—
225C22×C4—221no—
226C22×C4—221no—
227Q16—222no—
228M16—222no—
229M16—222no—
230C2×C8—111no—
231C2×C8—111no—
232C2×C8C22×D1111yescharacteristic
233C2×C8C22×D1111yescharacteristic
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—111no—
238C4⋊C4—111no—
239C4⋊C4—111no—
240C4⋊C4—111no—
241C4⋊C4—221no—
242C4⋊C4—221no—
243C4⋊C4—221no—
244C4⋊C4—221no—
245C4⋊C4—221no—
246C4⋊C4—221no—
247C4⋊C4—221no—
248C4⋊C4—221no—
249C4⋊C4—221no—
250C4⋊C4C22×D1111yescharacteristic
251C4⋊C4C22×D1111yescharacteristic
252C4⋊C4C22×D1111yescharacteristic
253C22⋊C4—111no—
254C22⋊C4—111no—
255C22⋊C4—221no—
256C22⋊C4—221no—
257C22⋊C4—221no—
258C22⋊C4—221no—
259C22⋊C4—221no—
260C22⋊C4—221no—
261C42—21no—
262C42—221no—
263C42—221no—
264C42—221no—
265C42C22×D1111yescharacteristic
266C11#335211yescharacteristic, complemented, Sylow
267C23—111no—
268C23—111no—
269Q8—21no—
270Q8—21no—
271Q8—221no—
272Q8—221no—
273D4—441no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—111no—
279C2×C4—111no—
280C2×C4—221no—
281C2×C4—221no—
282C2×C4—221no—
283C2×C4—221no—
284C2×C4—221no—
285C2×C4—221no—
286C2×C4—221no—
287C2×C4—221no—
288C2×C4—442no—
289C2×C4—442no—
290C2×C4D4×D1111yescharacteristic
291C2×C4D4×D1111yescharacteristic
292C2×C4C23×D1111yescharacteristic
293C8—21no—
294C8—21no—
295C8—112no—
296C8—221no—
297C22—221no—
298C22—221no—
299C22—221no—
300C22—221no—
301C22—221no—
302C22—221no—
303C22C2×D4×D1111yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—221no—
311C4—221no—
312C4—441no—
313C4—441no—
314C4—441no—
315C4—441no—
316C4#6704011yescharacteristic
317C4#41×D1111yescharacteristic
318C2—441no—
319C2—441no—
320C2#1062316211yescharacteristic
321C2#1062329911yescharacteristic
322C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#479C2
socleC22×C11C22×D4
prime radicalC2×D44D4
hypercenter#479D11
hypocenterC11#3352
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. #10622677C2semidirect
5. C4×#4326C2semidirect
6. #10622497C2semidirect
7. #10622494C2semidirect
8. #10622480C2semidirect
9. #10622474C2semidirect
11. #10622442C2semidirect
12. #10622429C2semidirect
13. #10622429C2semidirect
14. #10622428C2semidirect
15. #10622422C2semidirect
144. #479D11semidirect
266. C11#3352semidirect

Maximal subgroups

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

subgroupindex
#106232252
#106231122
C11×#4792
#106226772
C4×#43262
#106224972
#106224942
#106224802
#106224742
#106224512
#106224422
#106224292
#106224282
#106224222
#335211