Finite Group Databasebeta

← #13081560

Subgroups — #13081560

Order 1408.

334 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
1#10623261C211yesmaximal, characteristic
2#10623216C211yesmaximal, characteristic, complemented
3C11×#501C211yesmaximal, characteristic, complemented
4#10622707C211yesmaximal, characteristic, complemented
5#10622679C211yesmaximal, characteristic
6#10622504C211yesmaximal, characteristic
7#10622502C211yesmaximal, characteristic
8#10622491C211yesmaximal, characteristic, complemented
9#10622490C211yesmaximal, characteristic, complemented
10#10622483C211yesmaximal, characteristic
11#10622470C211yesmaximal, characteristic, complemented
12#10622469C211yesmaximal, characteristic, complemented
13#10622465C211yesmaximal, characteristic
14#10622323C211yesmaximal, characteristic
15#10622314C211yesmaximal, characteristic, complemented
16C11×C4⋊Q8C2211yescharacteristic
17C11×#125C2211yescharacteristic
18#66999—21no—
19#66999—21no—
20C2×#4314C2211yescharacteristic
21#66950—21no—
22#66946C2211yescharacteristic
23#66946C2211yescharacteristic
24C4⋊C4×D11—21no—
25#66943C2211yescharacteristic
26#66943C2211yescharacteristic
27#66943C2211yescharacteristic
28#66942—21no—
29#66942—21no—
30#66941—21no—
31#66941C2211yescharacteristic
32#66940—21no—
33#66940C2211yescharacteristic
34#66940C2211yescharacteristic
35C4×D44C2211yescharacteristic
36C4×Dic22C2211yescharacteristic
37C4×Dic22C2211yescharacteristic
38C11×#107C2211yescharacteristic
39C11×#107C2211yescharacteristic
40C11×#106C2211yescharacteristic
41C11×#106C2211yescharacteristic
42C11×#97C2211yescharacteristic
43#66885C2211yescharacteristic
44#66882C2211yescharacteristic
45#66880C2211yescharacteristic
46#66879C2211yescharacteristic
47Dic11⋊C8C2211yescharacteristic
48Dic11⋊C8C2211yescharacteristic
49C8×Dic11C2211yescharacteristic
50#66874C2211yescharacteristic
51#66874C2211yescharacteristic
52#66873C2211yescharacteristic
53#66873C2211yescharacteristic
54#66872C2211yescharacteristic
55#66872C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×D44C2311yescharacteristic
61C2×C4×D11—21no—
62C2×C4×D11—21no—
63C2×C4×D11—21no—
64C2×Dic22—21no—
65C2×Dic22D411yescharacteristic
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
75C11×C4⋊C4C2311yescharacteristic
76C42×C11C2311yescharacteristic
77(C2×D11)⋊C4—21no—
78(C2×D11)⋊C4—21no—
79(C2×D11)⋊C4—21no—
80C4⋊Dic11—21no—
81C4⋊Dic11—21no—
82C4⋊Dic11—21no—
83C4⋊Dic11D411yescharacteristic
84C4⋊Dic11C2311yescharacteristic
85C4⋊Dic11C2311yescharacteristic
86Dic11⋊C4—21no—
87Dic11⋊C4—21no—
88Dic11⋊C4—21no—
89Dic11⋊C4—21no—
90Dic11⋊C4—21no—
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4D411yescharacteristic
94Dic11⋊C4D411yescharacteristic
95C4×Dic11—21no—
96C4×Dic11—21no—
97C4×Dic11—21no—
98C4×Dic11C2311yescharacteristic
99C4×Dic11C2311yescharacteristic
100C2×C11⋊C8C2311yescharacteristic
101C2×C11⋊C8C2311yescharacteristic
102#4314Q814yescomplemented
103#3388—111nomaximal, Sylow
104C22×D11—21no—
105Q8×C11—81no—
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×Dic11C2×D411yescharacteristic
117C2×Dic11C2×D411yescharacteristic
118C2×Dic11C2×D411yescharacteristic
119C2×Dic11C2×D411yescharacteristic
120D44—21no—
121D44C2×Q812yes—
122C4×D11—42no—
123C4×D11—81no—
124C4×D11—81no—
125Dic22—21no—
126Dic22—41no—
127Dic22—42no—
128Dic22C2×Q812yes—
129C8×C11—21no—
130C8×C11C2×Q812yes—
131C11⋊C8—21no—
132C11⋊C8—21no—
133#557—111no—
134#554—111no—
135#501—111no—
136#501D1111yescharacteristic, complemented
137#499—111no—
138#479—111no—
139#479—111no—
140#478—111no—
141#478—111no—
142#476—111no—
143#475—111no—
144#446—111no—
145#440—111no—
146#440—111no—
147C4×SD16—111no—
148C22×C11C22×D411yescharacteristic
149C2×D11—22no—
150C2×D11—41no—
151C2×D11—41no—
152C4×C11—21no—
153C4×C11—21no—
154C4×C11—41no—
155C4×C11—41no—
156C4×C11—41no—
157C4×C11—41no—
158C4×C11C22×Q811yescharacteristic
159C4×C112−1+411yescharacteristic
160Dic11—22no—
161Dic11—21no—
162Dic11—21no—
163Dic11—21no—
164Dic11—21no—
165Dic11—41no—
166Dic11—41no—
167C2×SD16—111no—
168C4⋊Q8—111no—
169C4⋊Q8—221no—
170C4⋊Q8C2×D1111yescharacteristic
171#125—111no—
172#125—111no—
173#125—111no—
174#125—221no—
175#125—221no—
176#125C2×D1111yescharacteristic
177C22⋊Q8—221no—
178C22⋊Q8—221no—
179C22⋊Q8—221no—
180C4×Q8—111no—
181C4×Q8—111no—
182C4×Q8—111no—
183C4×Q8—111no—
184C4×Q8—221no—
185C4×D4—111no—
186C4×D4—111no—
187C4×D4—111no—
188C2×C4⋊C4—221no—
189#107—111no—
190#107—111no—
191#107C2×D1111yescharacteristic
192#107C2×D1111yescharacteristic
193#106—111no—
194#106—111no—
195#106—111no—
196#106C2×D1111yescharacteristic
197#106C2×D1111yescharacteristic
198C4⋊C8—111no—
199C4⋊C8—111no—
200C4⋊C8—111no—
201#103—111no—
202#103—111no—
203#103—111no—
204#102—111no—
205#102—111no—
206#102—111no—
207#97—111no—
208#97C2×D1111yescharacteristic
209C4×C8—111no—
210C2×C11D4×Q811yescharacteristic
211C2×C11#57511yescharacteristic
212C2×C11#57711yescharacteristic
213D11—42no—
214C2×Q8—21no—
215C2×Q8—111no—
216C2×Q8—111no—
217C2×Q8—221no—
218C2×D4—111no—
219C22×C4—221no—
220C22×C4—221no—
221C22×C4—221no—
222SD16—114no—
223C2×C8—111no—
224C2×C8—111no—
225C2×C8C22×D1111yescharacteristic
226C2×C8C22×D1111yescharacteristic
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—21no—
230C4⋊C4—111no—
231C4⋊C4—111no—
232C4⋊C4—111no—
233C4⋊C4—111no—
234C4⋊C4—111no—
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⋊C4C22×D1111yescharacteristic
246C4⋊C4C22×D1111yescharacteristic
247C4⋊C4C22×D1111yescharacteristic
248C4⋊C4C22×D1111yescharacteristic
249C22⋊C4—221no—
250C22⋊C4—221no—
251C22⋊C4—221no—
252C42—111no—
253C42—111no—
254C42—221no—
255C42—221no—
256C42—221no—
257C42C22×D1111yescharacteristic
258C11#338811yescharacteristic, complemented, Sylow
259C23—221no—
260Q8—81no—
261Q8—112no—
262Q8—221no—
263Q8—441no—
264Q8—442no—
265D4—112no—
266D4—221no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—111no—
272C2×C4—111no—
273C2×C4—111no—
274C2×C4—111no—
275C2×C4—221no—
276C2×C4—221no—
277C2×C4—221no—
278C2×C4—442no—
279C2×C4—881no—
280C2×C4—881no—
281C2×C4D4×D1111yescharacteristic
282C2×C4D4×D1111yescharacteristic
283C2×C4C23×D1111yescharacteristic
284C8—21no—
285C8—221no—
286C8—221no—
287C8Q8×D1112yes—
288C22—222no—
289C22—441no—
290C22—441no—
291C22C2×D4×D1111yescharacteristic
292C4—21no—
293C4—21no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—41no—
298C4—222no—
299C4—221no—
300C4—221no—
301C4—221no—
302C4—221no—
303C4—441no—
304C4—441no—
305C4C2×Q8×D1111yescharacteristic
306C4#6704011yescharacteristic
307C2—442no—
308C2#1062325811yescharacteristic
309C2#1062330611yescharacteristic
310C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#501C2
socleC22×C11C22×D4
prime radicalC2×D44C23
hypercenter#501D11
hypocenterC11#3388
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. #10623216C2semidirect
3. C11×#501C2semidirect
4. #10622707C2semidirect
8. #10622491C2semidirect
9. #10622490C2semidirect
11. #10622470C2semidirect
12. #10622469C2semidirect
15. #10622314C2semidirect
102. #4314Q8semidirect
136. #501D11semidirect
258. C11#3388semidirect

Maximal subgroups

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

subgroupindex
#106232612
#106232162
C11×#5012
#106227072
#106226792
#106225042
#106225022
#106224912
#106224902
#106224832
#106224702
#106224692
#106224652
#106223232
#106223142
#338811