Finite Group Databasebeta

← #13081148

Subgroups — #13081148

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#10623073C211yesmaximal, characteristic
2#10623072C211yesmaximal, characteristic
3C11×#435C211yesmaximal, characteristic
4#10622750C211yesmaximal, characteristic, complemented
5#10622734C211yesmaximal, characteristic, complemented
6#10622729C211yesmaximal, characteristic, complemented
7#10622719C211yesmaximal, characteristic, complemented
8#10622463C211yesmaximal, characteristic, complemented
9#10622442C211yesmaximal, characteristic, complemented
10#10622336C211yesmaximal, characteristic, complemented
11#10622336C211yesmaximal, characteristic, complemented
12#10622336C211yesmaximal, characteristic, complemented
13#10622335C211yesmaximal, characteristic, complemented
14#10622329C211yesmaximal, characteristic, complemented
15#10622315C211yesmaximal, characteristic, complemented
16C2×C11×M16C2211yescharacteristic
17C22×C8×C11C2211yescharacteristic
18C4×D4×C11C2211yescharacteristic
19#66989—21no—
20#66988—21no—
21#66979C2211yescharacteristic
22#66979C2211yescharacteristic
23#66979C2211yescharacteristic
24C2×C4⋊Dic11C2211yescharacteristic
25#66977C2211yescharacteristic
26#66977C2211yescharacteristic
27#66977C2211yescharacteristic
28#66977C2211yescharacteristic
29C2×Dic44C2211yescharacteristic
30#66942—21no—
31#66940—21no—
32#66932—21no—
33#66932—21no—
34#66932—21no—
35#66930—21no—
36#66923C2211yescharacteristic
37#66922C2211yescharacteristic
38C4×Dic22C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40C11×C4⋊C8C2211yescharacteristic
41C11×C22⋊C8C2211yescharacteristic
42C11×C22⋊C8C2211yescharacteristic
43C11×#97C2211yescharacteristic
44#66882C2211yescharacteristic
45#66882C2211yescharacteristic
46#66882C2211yescharacteristic
47#66882C2211yescharacteristic
48#66882C2211yescharacteristic
49#66881C2211yescharacteristic
50#66881C2211yescharacteristic
51#66881C2211yescharacteristic
52#66881C2211yescharacteristic
53#66880C2211yescharacteristic
54#66880C2211yescharacteristic
55#66880C2211yescharacteristic
56#66880C2211yescharacteristic
57#66880C2211yescharacteristic
58#66880C2211yescharacteristic
59C2×D4×C11D411yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×Dic11—21no—
63C2×Dic22—21no—
64C2×Dic22C2311yescharacteristic
65C2×Dic22C2311yescharacteristic
66C11×M16—22no—
67C2×C8×C11—22no—
68C2×C8×C11C2311yescharacteristic
69C2×C8×C11C2311yescharacteristic
70C2×C8×C11C2311yescharacteristic
71C2×C8×C11C2311yescharacteristic
72C11×C4⋊C4D411yescharacteristic
73C11×C22⋊C4D411yescharacteristic
74C11×C22⋊C4D411yescharacteristic
75C42×C11C2311yescharacteristic
76C22⋊Dic11—21no—
77C22⋊Dic11—21no—
78C22⋊Dic11—21no—
79C22⋊Dic11—21no—
80C22⋊Dic11—21no—
81C22⋊Dic11—21no—
82C22⋊Dic11—21no—
83C4⋊Dic11—21no—
84C4⋊Dic11—21no—
85C4⋊Dic11C2311yescharacteristic
86C4⋊Dic11C2311yescharacteristic
87C4⋊Dic11C2311yescharacteristic
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—
98Dic11⋊C4—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104Dic44—22no—
105#3349—111nomaximal, Sylow
106C23×C11C2×D411yescharacteristic
107C23×C11C2×D411yescharacteristic
108D4×C11—41no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11C2×D411yescharacteristic
114C2×C4×C11C2×D411yescharacteristic
115C2×C4×C11C2×D411yescharacteristic
116C2×C4×C11C2×D411yescharacteristic
117C2×C4×C11C2411yescharacteristic
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11—21no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—42no—
127Dic22—21no—
128Dic22—21no—
129Dic22—21no—
130Dic22—21no—
131Dic22—42no—
132C8×C11—21no—
133C8×C11—21no—
134C8×C11—21no—
135C8×C11#4112yes—
136#556—111no—
137#552—111no—
138#501—111no—
139#485—111no—
140#485—111no—
141#485—111no—
142#484—111no—
143#479—111no—
144#477—111no—
145#470—111no—
146#467—111no—
147#441—111no—
148#435D1111yescharacteristic
149#428—111no—
150#427—111no—
151C22×C11—21no—
152C22×C11—21no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11C22×D411yescharacteristic
158C4×C11—21no—
159C4×C11—21no—
160C4×C11—21no—
161C4×C11—21no—
162C4×C11C2×#4111yescharacteristic
163C4×C112−1+411yescharacteristic
164Dic11—41no—
165Dic11—41no—
166Dic11—41no—
167Dic11—41no—
168Dic11—41no—
169Dic11—41no—
170Dic11—41no—
171Dic11—41no—
172C2×Q16—111no—
173C2×M16C2×D1111yescharacteristic
174C22×C8C2×D1111yescharacteristic
175C4⋊Q8—111no—
176#126—221no—
177#126—221no—
178#126—221no—
179#125—111no—
180#125—221no—
181#124—221no—
182#123—221no—
183C22⋊Q8—111no—
184C22⋊Q8—111no—
185C22⋊Q8—111no—
186C22⋊Q8—111no—
187C4×Q8—111no—
188C4×Q8—111no—
189C4×Q8—221no—
190C4×D4C2×D1111yescharacteristic
191#117—111no—
192#117—111no—
193#117—111no—
194#117—221no—
195C2×C4⋊C4—111no—
196#107—111no—
197#107—111no—
198#107—111no—
199#107—111no—
200#107—111no—
201#106—111no—
202#106—111no—
203#106—111no—
204#106—111no—
205C4⋊C8C2×D1111yescharacteristic
206#103—111no—
207#103—111no—
208#103—111no—
209#103—111no—
210#103—111no—
211#103—111no—
212C22⋊C8C2×D1111yescharacteristic
213C22⋊C8C2×D1111yescharacteristic
214#97C2×D1111yescharacteristic
215C2×C11—41no—
216C2×C11—41no—
217C2×C11#54711yescharacteristic
218C2×C11#57511yescharacteristic
219C2×C11#57811yescharacteristic
220C2×Q8—111no—
221C2×Q8—111no—
222C2×Q8—221no—
223C2×D4D4411yescharacteristic
224C22×C4—221no—
225C22×C4C22×D1111yescharacteristic
226C22×C4C22×D1111yescharacteristic
227Q16—222no—
228M16—22no—
229C2×C8—22no—
230C2×C8C22×D1111yescharacteristic
231C2×C8C22×D1111yescharacteristic
232C2×C8C22×D1111yescharacteristic
233C2×C8C22×D1111yescharacteristic
234C4⋊C4—111no—
235C4⋊C4—111no—
236C4⋊C4—111no—
237C4⋊C4—111no—
238C4⋊C4—111no—
239C4⋊C4—111no—
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⋊C4D4411yescharacteristic
251C22⋊C4—221no—
252C22⋊C4—221no—
253C22⋊C4—221no—
254C22⋊C4—221no—
255C22⋊C4—221no—
256C22⋊C4—221no—
257C22⋊C4—221no—
258C22⋊C4D4411yescharacteristic
259C22⋊C4D4411yescharacteristic
260C42—221no—
261C42—221no—
262C42—221no—
263C42—221no—
264C42—221no—
265C42C22×D1111yescharacteristic
266C11#334911yescharacteristic, complemented, Sylow
267C23C2×D4411yescharacteristic
268C23C2×D4411yescharacteristic
269Q8—221no—
270Q8—221no—
271Q8—221no—
272Q8—221no—
273Q8—442no—
274D4—41no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—221no—
280C2×C4—221no—
281C2×C4—221no—
282C2×C4—221no—
283C2×C4—221no—
284C2×C4—221no—
285C2×C4—221no—
286C2×C4—221no—
287C2×C4—442no—
288C2×C4C2×D4411yescharacteristic
289C2×C4C2×D4411yescharacteristic
290C2×C4C2×D4411yescharacteristic
291C2×C4C2×D4411yescharacteristic
292C2×C4C23×D1111yescharacteristic
293C8—21no—
294C8—21no—
295C8—21no—
296C8#434112yes—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22C22×D4411yescharacteristic
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—441no—
309C4—441no—
310C4—441no—
311C4—441no—
312C4—441no—
313C4—441no—
314C4—441no—
315C4—441no—
316C4C2×#434111yescharacteristic
317C4#6704311yescharacteristic
318C2—41no—
319C2—41no—
320C2#1062308611yescharacteristic
321C2#1062327911yescharacteristic
322C2#1062328411yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#435C2
socleC22×C11C22×D4
prime radicalC2×D4×C11D4
hypercenter#435D11
hypocenterC11#3349
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
4. #10622750C2semidirect
5. #10622734C2semidirect
6. #10622729C2semidirect
7. #10622719C2semidirect
8. #10622463C2semidirect
9. #10622442C2semidirect
10. #10622336C2semidirect
11. #10622336C2semidirect
12. #10622336C2semidirect
13. #10622335C2semidirect
14. #10622329C2semidirect
15. #10622315C2semidirect
266. C11#3349semidirect

Maximal subgroups

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

subgroupindex
#106230732
#106230722
C11×#4352
#106227502
#106227342
#106227292
#106227192
#106224632
#106224422
#106223362
#106223352
#106223292
#106223152
#334911