Finite Group Databasebeta

← #13081003

Subgroups — #13081003

Order 1408.

356 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623166C211yesmaximal, characteristic
2#10623042C211yesmaximal, characteristic
3C11×#484C211yesmaximal, characteristic, complemented
4#10622664C211yesmaximal, characteristic, complemented
5C2×#66871C211yesmaximal, characteristic, complemented
6#10622497C211yesmaximal, characteristic, complemented
7D11×#107C211yesmaximal, characteristic, complemented
8#10622488C211yesmaximal, characteristic, complemented
9#10622487C211yesmaximal, characteristic, complemented
10#10622426C211yesmaximal, characteristic, complemented
11#10622422C211yesmaximal, characteristic, complemented
12#10622407C211yesmaximal, characteristic, complemented
13#10622403C211yesmaximal, characteristic, complemented
14(C22⋊D11)⋊C8C211yesmaximal, characteristic
15#10622335C211yesmaximal, characteristic, complemented
16C11×C22⋊Q8C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18#66999C2211yescharacteristic
19Q8×Dic11C2211yescharacteristic
20C2×#4326C2211yescharacteristic
21C4×C22⋊D11—21no—
22C4×C22⋊D11C2211yescharacteristic
23C2×C4⋊Dic11C2211yescharacteristic
24#66977—21no—
25#66977C2211yescharacteristic
26C22×C11⋊C8C2211yescharacteristic
27C2×C8×D11C2211yescharacteristic
28#66950—21no—
29#66950C2211yescharacteristic
30#66949—21no—
31C4⋊C4×D11C2211yescharacteristic
32C4⋊C4×D11C2211yescharacteristic
33#66942—21no—
34#66942—21no—
35#66941C2211yescharacteristic
36#66941C2211yescharacteristic
37#66940C2211yescharacteristic
38(C22⋊D11)⋊C4—21no—
39#66931—21no—
40C11×#107C2211yescharacteristic
41C11×#107C2211yescharacteristic
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#66871C2211yescharacteristic
55#66871C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C22×C4×C11—21no—
61C22×C4×C11C2311yescharacteristic
62C2×C22⋊D11D411yescharacteristic
63C22×Dic11—21no—
64C2×C4×D11—21no—
65C2×C4×D11—21no—
66C2×C4×D11C2311yescharacteristic
67C2×Dic22—21no—
68C2×Dic22—21no—
69C2×Dic22C2311yescharacteristic
70C2×C8×C11C2311yescharacteristic
71C2×C8×C11C2311yescharacteristic
72C11×C4⋊C4—21no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4C2311yescharacteristic
75C11×C4⋊C4C2311yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C11×C22⋊C4—21no—
78C22⋊Dic11—21no—
79C22⋊Dic11D411yescharacteristic
80#4326—22no—
81(C2×D11)⋊C4—21no—
82(C2×D11)⋊C4—21no—
83(C2×D11)⋊C4D411yescharacteristic
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⋊C4—21no—
97Dic11⋊C4D411yescharacteristic
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11C2311yescharacteristic
101C2×C11⋊C8—22no—
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C8×D11—22no—
105#3338—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×C11—81no—
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2411yescharacteristic
119C22⋊D11Q1614yescomplemented
120C2×Dic11—21no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—81no—
125C2×Dic11C2×D411yescharacteristic
126C2×Dic11C2×D411yescharacteristic
127C2×Dic11C2×D411yescharacteristic
128C4×D11—21no—
129C4×D11—21no—
130C4×D11—81no—
131C4×D11—81no—
132Dic22—21no—
133Dic22—21no—
134Dic22—81no—
135Dic22—81no—
136C8×C11—21no—
137C8×C11—21no—
138C11⋊C8—21no—
139C11⋊C8#4112yes—
140#554—111no—
141#554—111no—
142#500—111no—
143#484—111no—
144#484—111no—
145#484—111no—
146#484D1111yescharacteristic, complemented
147#477—111no—
148#477—111no—
149#467—111no—
150#467—111no—
151C4×Q16—111no—
152C8×D4—111no—
153C2×#107—111no—
154C2×#107—111no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11C2×Q1612yes—
158C22×C11C22×D411yescharacteristic
159C2×D11—21no—
160C2×D11—21no—
161C2×D11C2×Q1612yes—
162C4×C11—21no—
163C4×C11—41no—
164C4×C11—41no—
165C4×C11—41no—
166C4×C11—41no—
167C4×C11C2×#4111yescharacteristic
168C4×C112−1+411yescharacteristic
169Dic11—21no—
170Dic11—21no—
171Dic11—41no—
172Dic11—41no—
173Dic11—41no—
174Dic11—41no—
175Dic11C2×Q1612yes—
176C2×Q16—111no—
177C22×C8—111no—
178C22×C8—111no—
179C4⋊Q8—111no—
180C4⋊Q8—111no—
181#125—221no—
182#125—221no—
183C22⋊Q8—111no—
184C22⋊Q8—111no—
185C22⋊Q8—111no—
186C22⋊Q8—221no—
187C22⋊Q8—221no—
188C22⋊Q8—221no—
189C22⋊Q8—221no—
190C22⋊Q8C2×D1111yescharacteristic
191C4×Q8—111no—
192C4×Q8—111no—
193C4×D4—111no—
194C4×D4—221no—
195C4×D4—221no—
196C2×C4⋊C4—111no—
197C2×C4⋊C4—111no—
198C2×C4⋊C4—111no—
199C2×C4⋊C4C2×D1111yescharacteristic
200#107—111no—
201#107—111no—
202#107—111no—
203#107—111no—
204#107—111no—
205#107—111no—
206#107—111no—
207#107C2×D1111yescharacteristic
208#107C2×D1111yescharacteristic
209C4⋊C8—111no—
210#103—111no—
211#103—111no—
212#103—111no—
213#103—111no—
214#103C2×D1111yescharacteristic
215#103C2×D1111yescharacteristic
216C22⋊C8—111no—
217C22⋊C8C2×D1111yescharacteristic
218C4×C8—111no—
219C2×C11—22no—
220C2×C11#54711yescharacteristic
221C2×C11C22×Q1611yescharacteristic
222C2×C11#57611yescharacteristic
223D11—22no—
224C2×Q8—111no—
225C2×Q8—221no—
226C2×Q8—221no—
227C2×Q8C22×D1111yescharacteristic
228C2×D4—111no—
229C22×C4—21no—
230C22×C4—111no—
231C22×C4—221no—
232C22×C4—221no—
233C22×C4—221no—
234C22×C4C22×D1111yescharacteristic
235Q16—222no—
236C2×C8—111no—
237C2×C8—111no—
238C2×C8—222no—
239C2×C8—222no—
240C2×C8C22×D1111yescharacteristic
241C2×C8C22×D1111yescharacteristic
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—111no—
245C4⋊C4—111no—
246C4⋊C4—111no—
247C4⋊C4—111no—
248C4⋊C4—221no—
249C4⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4C22×D1111yescharacteristic
259C4⋊C4C22×D1111yescharacteristic
260C4⋊C4C22×D1111yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—111no—
263C22⋊C4—111no—
264C22⋊C4—221no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C42—111no—
268C42—221no—
269C42—221no—
270C11#333811yescharacteristic, complemented, Sylow
271C23—111no—
272C23D4×D1111yescharacteristic
273Q8—21no—
274Q8—21no—
275Q8—221no—
276Q8—221no—
277Q8—881no—
278Q8—881no—
279D4—114no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—81no—
287C2×C4—111no—
288C2×C4—111no—
289C2×C4—111no—
290C2×C4—221no—
291C2×C4—221no—
292C2×C4—221no—
293C2×C4—221no—
294C2×C4—221no—
295C2×C4—221no—
296C2×C4—881no—
297C2×C4—881no—
298C2×C4—881no—
299C2×C4D4×D1111yescharacteristic
300C2×C4C23×D1111yescharacteristic
301C8—21no—
302C8—21no—
303C8—112no—
304C8—221no—
305C22—21no—
306C22—21no—
307C22—112no—
308C22—221no—
309C22—221no—
310C22Q16×D1112yes—
311C22C2×D4×D1111yescharacteristic
312C4—21no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—112no—
318C4—221no—
319C4—221no—
320C4—441no—
321C4—441no—
322C4—441no—
323C4—441no—
324C4#41×D1111yescharacteristic
325C4#6704311yescharacteristic
326C2—22no—
327C2—222no—
328C2#1062318611yescharacteristic
329C2C2×Q16×D1111yescharacteristic
330C2#1062330511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#484C2
socleC22×C11C22×D4
prime radicalC2×C22⋊D11D4
hypercenter#484D11
hypocenterC11#3338
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. C11×#484C2semidirect
4. #10622664C2semidirect
5. C2×#66871C2semidirect
6. #10622497C2semidirect
7. D11×#107C2semidirect
8. #10622488C2semidirect
9. #10622487C2semidirect
10. #10622426C2semidirect
11. #10622422C2semidirect
12. #10622407C2semidirect
13. #10622403C2semidirect
15. #10622335C2semidirect
119. C22⋊D11Q16semidirect
146. #484D11semidirect
270. C11#3338semidirect

Maximal subgroups

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

subgroupindex
#106231662
#106230422
C11×#4842
#106226642
C2×#668712
#106224972
D11×#1072
#106224882
#106224872
#106224262
#106224222
#106224072
#106224032
(C22⋊D11)⋊C82
#106223352
#333811