Finite Group Databasebeta

← #13081184

Subgroups — #13081184

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#10623173C211yesmaximal, characteristic
2#10623060C211yesmaximal, characteristic
3C11×#485C211yesmaximal, characteristic, complemented
4#10622665C211yesmaximal, characteristic, complemented
5#10622608C211yesmaximal, characteristic, complemented
6#10622501C211yesmaximal, characteristic, complemented
7#10622491C211yesmaximal, characteristic, complemented
8#10622474C211yesmaximal, characteristic, complemented
9#10622470C211yesmaximal, characteristic, complemented
10#10622429C211yesmaximal, characteristic, complemented
11#10622422C211yesmaximal, characteristic, complemented
12#10622409C211yesmaximal, characteristic, complemented
13#10622403C211yesmaximal, characteristic, complemented
14#10622342C211yesmaximal, characteristic
15#10622335C211yesmaximal, characteristic, complemented
16C11×C22⋊Q8C2211yescharacteristic
17C11×#117C2211yescharacteristic
18#66999C2211yescharacteristic
19Q8×Dic11C2211yescharacteristic
20C2×#4326C2211yescharacteristic
21C4×C22⋊D11C2211yescharacteristic
22C2×C4⋊Dic11C2211yescharacteristic
23#66977C2211yescharacteristic
24C2×#4318C2211yescharacteristic
25C2×#4313C2211yescharacteristic
26#66951—21no—
27#66950C2211yescharacteristic
28#66945C2211yescharacteristic
29C4⋊C4×D11C2211yescharacteristic
30#66943—21no—
31#66943C2211yescharacteristic
32#66943C2211yescharacteristic
33#66940C2211yescharacteristic
34#66939—21no—
35#66936—21no—
36#66932—21no—
37#66930—21no—
38#66925—21no—
39#66923—21no—
40C11×#107C2211yescharacteristic
41C11×#106C2211yescharacteristic
42C11×#103C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×C22⋊C8C2211yescharacteristic
45#66899C2211yescharacteristic
46(C2×D11)⋊C8C2211yescharacteristic
47#66882C2211yescharacteristic
48#66882C2211yescharacteristic
49#66880C2211yescharacteristic
50#66880C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52C8×Dic11C2211yescharacteristic
53#66874C2211yescharacteristic
54#66872C2211yescharacteristic
55#66872C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C2×C22⋊D11D411yescharacteristic
62C22×Dic11—21no—
63C2×C4×D11—21no—
64C2×C4×D11C2311yescharacteristic
65C2×Dic22C2311yescharacteristic
66C2×C8×C11C2311yescharacteristic
67C2×C8×C11C2311yescharacteristic
68C11×C4⋊C4—21no—
69C11×C4⋊C4C2311yescharacteristic
70C11×C4⋊C4C2311yescharacteristic
71C11×C4⋊C4C2311yescharacteristic
72C11×C22⋊C4—21no—
73C11×C22⋊C4—21no—
74C42×C11—21no—
75C22⋊Dic11—21no—
76C22⋊Dic11D411yescharacteristic
77#4326—22no—
78(C2×D11)⋊C4—21no—
79(C2×D11)⋊C4—21no—
80(C2×D11)⋊C4—21no—
81(C2×D11)⋊C4D411yescharacteristic
82C4⋊Dic11—21no—
83C4⋊Dic11—21no—
84C4⋊Dic11—21no—
85C4⋊Dic11—21no—
86C4⋊Dic11—21no—
87C4⋊Dic11C2311yescharacteristic
88C4⋊Dic11C2311yescharacteristic
89C4⋊Dic11C2311yescharacteristic
90Dic11⋊C4—21no—
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4D411yescharacteristic
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11C2311yescharacteristic
101#4318—22no—
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104#4313—22no—
105#3352—111nomaximal, Sylow
106C23×C11C2×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×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11C2×D411yescharacteristic
117C2×C4×C11C2411yescharacteristic
118C22⋊D11—41no—
119C2×Dic11—21no—
120C2×Dic11—21no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—42no—
124C2×Dic11C2×D411yescharacteristic
125C2×Dic11C2×D411yescharacteristic
126C2×Dic11C2×D411yescharacteristic
127C4×D11—21no—
128C4×D11—21no—
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#485D1111yescharacteristic, complemented
141#484—111no—
142#484—111no—
143#479—111no—
144#479—111no—
145#470—111no—
146#470—111no—
147C4×Q16—111no—
148#436—111no—
149#428—111no—
150#428—111no—
151C22×C11—21no—
152C22×C11—21no—
153C22×C11—21no—
154C22×C11C22×D411yescharacteristic
155C2×D11—21no—
156C2×D11—21no—
157C2×D11—21no—
158C4×C11—21no—
159C4×C11—41no—
160C4×C11—41no—
161C4×C11—41no—
162C4×C11—41no—
163C4×C11C2×#4111yescharacteristic
164C4×C112−1+411yescharacteristic
165Dic11—21no—
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—111no—
179#125—221no—
180#125—221no—
181#123—221no—
182#123—221no—
183C22⋊Q8—111no—
184C22⋊Q8—111no—
185C22⋊Q8—111no—
186C22⋊Q8C2×D1111yescharacteristic
187C4×Q8—111no—
188C4×Q8—111no—
189C4×D4—111no—
190#117—111no—
191#117—221no—
192#117—221no—
193#117C2×D1111yescharacteristic
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⋊C8—111no—
206#103—111no—
207#103—111no—
208#103—111no—
209#103—111no—
210#103C2×D1111yescharacteristic
211#103C2×D1111yescharacteristic
212C22⋊C8—111no—
213C22⋊C8C2×D1111yescharacteristic
214C4×C8—111no—
215C2×C11—41no—
216C2×C11#54711yescharacteristic
217C2×C11#57511yescharacteristic
218C2×C11#57811yescharacteristic
219D11—41no—
220C2×Q8—111no—
221C2×Q8C22×D1111yescharacteristic
222C2×D4—111no—
223C22×C4—111no—
224C22×C4—221no—
225C22×C4—221no—
226C22×C4C22×D1111yescharacteristic
227Q16—222no—
228M16—222no—
229M16—222no—
230C2×C8—111no—
231C2×C8—111no—
232C2×C8C22×D1111yescharacteristic
233C2×C8C22×D1111yescharacteristic
234C4⋊C4—21no—
235C4⋊C4—111no—
236C4⋊C4—111no—
237C4⋊C4—111no—
238C4⋊C4—111no—
239C4⋊C4—221no—
240C4⋊C4—221no—
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—21no—
254C22⋊C4—21no—
255C22⋊C4—111no—
256C22⋊C4—111no—
257C22⋊C4—221no—
258C22⋊C4—221no—
259C22⋊C4—221no—
260C22⋊C4—221no—
261C42—21no—
262C42—111no—
263C42—221no—
264C42—221no—
265C42—221no—
266C11#335211yescharacteristic, complemented, Sylow
267C23—111no—
268C23D4×D1111yescharacteristic
269Q8—21no—
270Q8—21no—
271Q8—221no—
272Q8—221no—
273D4—441no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—111no—
281C2×C4—111no—
282C2×C4—111no—
283C2×C4—221no—
284C2×C4—221no—
285C2×C4—221no—
286C2×C4—221no—
287C2×C4—221no—
288C2×C4—221no—
289C2×C4—442no—
290C2×C4—442no—
291C2×C4D4×D1111yescharacteristic
292C2×C4C23×D1111yescharacteristic
293C8—21no—
294C8—21no—
295C8—112no—
296C8—221no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—221no—
301C22—221no—
302C22—221no—
303C22C2×D4×D1111yescharacteristic
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—221no—
310C4—221no—
311C4—221no—
312C4—441no—
313C4—441no—
314C4—441no—
315C4—441no—
316C4#41×D1111yescharacteristic
317C4#6704311yescharacteristic
318C2—41no—
319C2—441no—
320C2#1062318611yescharacteristic
321C2#1062330211yescharacteristic
322C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#485C2
socleC22×C11C22×D4
prime radicalC2×C22⋊D11D4
hypercenter#485D11
hypocenterC11#3352
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
3. C11×#485C2semidirect
4. #10622665C2semidirect
5. #10622608C2semidirect
6. #10622501C2semidirect
7. #10622491C2semidirect
8. #10622474C2semidirect
9. #10622470C2semidirect
10. #10622429C2semidirect
11. #10622422C2semidirect
12. #10622409C2semidirect
13. #10622403C2semidirect
15. #10622335C2semidirect
140. #485D11semidirect
266. C11#3352semidirect

Maximal subgroups

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

subgroupindex
#106231732
#106230602
C11×#4852
#106226652
#106226082
#106225012
#106224912
#106224742
#106224702
#106224292
#106224222
#106224092
#106224032
#106223422
#106223352
#335211