Finite Group Databasebeta

← #13079268

Subgroups — #13079268

Order 1408.

338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623156C212yesmaximal
2C11×#467C211yesmaximal, characteristic
3Q16×Dic11C211yesmaximal, characteristic, complemented
4#10622794C211yesmaximal, characteristic, complemented
5#10622729C211yesmaximal, characteristic
6#10622714C211yesmaximal, characteristic
7#10622665C212yesmaximal
8#10622491C211yesmaximal, characteristic, complemented
9#10622486C211yesmaximal, characteristic, complemented
10#10622410C212yesmaximal, complemented
11#10622402C212yesmaximal, complemented
12C2×C11×Q16C2211yescharacteristic
13C22×C8×C11C2211yescharacteristic
14C11×C22⋊Q8C2212yes—
15Q8×Dic11C2212yes—
16#66997C2212yes—
17C2×#4326C2212yes—
18#66979C2211yescharacteristic
19#66977C2212yes—
20C2×#4318C2211yescharacteristic
21C2×Dic44C2211yescharacteristic
22#66943—22no—
23#66943C2212yes—
24#66942—22no—
25#66940C2212yes—
26#66932—22no—
27#66932—22no—
28C11×#107C2211yescharacteristic
29C11×#103C2212yes—
30#66899C2212yes—
31#66882C2211yescharacteristic
32#66880C2212yes—
33#66879C2211yescharacteristic
34#66879C2211yescharacteristic
35C8×Dic11C2211yescharacteristic
36C8×Dic11C2211yescharacteristic
37#66874C2212yes—
38#66872C2212yes—
39C2×Q8×C11C2312yes—
40C22×C4×C11C2311yescharacteristic
41C2×Dic22C2312yes—
42C11×Q16—22no—
43C2×C8×C11—22no—
44C2×C8×C11C2311yescharacteristic
45C2×C8×C11C2311yescharacteristic
46C11×C4⋊C4—22no—
47C11×C4⋊C4C2312yes—
48C11×C22⋊C4—22no—
49C22⋊Dic11—22no—
50C22⋊Dic11D411yescharacteristic
51C22⋊Dic11D411yescharacteristic
52#4326—24no—
53C4⋊Dic11—22no—
54C4⋊Dic11—22no—
55C4⋊Dic11D411yescharacteristic
56C4⋊Dic11D411yescharacteristic
57C4⋊Dic11C2312yes—
58Dic11⋊C4—22no—
59Dic11⋊C4—22no—
60Dic11⋊C4—22no—
61Dic11⋊C4—22no—
62Dic11⋊C4—22no—
63C4×Dic11—22no—
64C4×Dic11—22no—
65C4×Dic11C2311yescharacteristic
66C4×Dic11C2311yescharacteristic
67#4318—22no—
68C2×C11⋊C8C2311yescharacteristic
69C2×C11⋊C8C2311yescharacteristic
70Dic44—22no—
71#3177—111nomaximal, Sylow
72C23×C11C2×D411yescharacteristic
73Q8×C11—22no—
74Q8×C11—22no—
75C2×C4×C11—21no—
76C2×C4×C11—21no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11C2×D411yescharacteristic
80C2×C4×C11C2411yescharacteristic
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11C2×D411yescharacteristic
84C2×Dic11C2×D411yescharacteristic
85C2×Dic11C2×D411yescharacteristic
86C2×Dic11C2×D411yescharacteristic
87Dic22—22no—
88Dic22—22no—
89C8×C11—21no—
90C8×C11#4112yes—
91C11⋊C8—21no—
92C11⋊C8#4112yes—
93#541—112no—
94#499—111no—
95#494—111no—
96#491—112no—
97#470—112no—
98#467—111no—
99#467D1111yescharacteristic
100#441—112no—
101C4×Q16—111no—
102C4×Q16—111no—
103#405—111no—
104C22×C11—21no—
105C22×C11—21no—
106C22×C11—21no—
107C22×C11C22×D411yescharacteristic
108C4×C11—21no—
109C4×C11—42no—
110C4×C11—42no—
111C4×C11C2×#4111yescharacteristic
112C4×C11C2×#4111yescharacteristic
113Dic11—21no—
114Dic11—21no—
115Dic11—21no—
116Dic11—21no—
117Dic11—42no—
118Dic11—42no—
119C2×Q16—112no—
120C2×Q16—111no—
121C2×Q16C2×D1111yescharacteristic
122C2×M16—111no—
123C22×C8C2×D1111yescharacteristic
124C4⋊Q8—112no—
125#126—222no—
126#126—222no—
127#125—112no—
128#125—222no—
129#125—222no—
130C22⋊Q8—112no—
131C22⋊Q8C2×D1112yes—
132C4×Q8—112no—
133C4×Q8—112no—
134#117—111no—
135#107—111no—
136#107C2×D1111yescharacteristic
137#106—112no—
138#103—112no—
139#103—112no—
140#103—112no—
141#103C2×D1112yes—
142#97—111no—
143#97—111no—
144C4×C8—111no—
145C4×C8—111no—
146C2×C11—41no—
147C2×C11#53211yescharacteristic
148C2×C11#57811yescharacteristic
149C2×C11#57811yescharacteristic
150C2×Q8—112no—
151C2×Q8C22×D1112yes—
152C22×C4C22×D1111yescharacteristic
153Q16—22no—
154Q16—224no—
155Q16—222no—
156M16—222no—
157C2×C8—22no—
158C2×C8—111no—
159C2×C8—111no—
160C2×C8C22×D1111yescharacteristic
161C2×C8C22×D1111yescharacteristic
162C4⋊C4—22no—
163C4⋊C4—111no—
164C4⋊C4—111no—
165C4⋊C4—112no—
166C4⋊C4—222no—
167C4⋊C4—222no—
168C4⋊C4—222no—
169C4⋊C4—222no—
170C4⋊C4—222no—
171C4⋊C4—222no—
172C4⋊C4—222no—
173C4⋊C4C22×D1112yes—
174C22⋊C4—22no—
175C22⋊C4—111no—
176C22⋊C4—111no—
177C22⋊C4—222no—
178C42—111no—
179C42—111no—
180C42—222no—
181C42—222no—
182C11#317711yescharacteristic, complemented, Sylow
183C23D4×D1111yescharacteristic
184Q8—22no—
185Q8—22no—
186Q8—222no—
187Q8—222no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—111no—
193C2×C4—111no—
194C2×C4—111no—
195C2×C4—111no—
196C2×C4—222no—
197C2×C4—222no—
198C2×C4D4×D1111yescharacteristic
199C2×C4C23×D1111yescharacteristic
200C8—21no—
201C8—112no—
202C8—221no—
203C8#434112yes—
204C22—21no—
205C22—21no—
206C22—21no—
207C22C2×D4×D1111yescharacteristic
208C4—21no—
209C4—42no—
210C4—42no—
211C4—221no—
212C4—221no—
213C4—221no—
214C4—221no—
215C4—442no—
216C4—442no—
217C4C2×#434111yescharacteristic
218C4#41×D1111yescharacteristic
219C2—41no—
220C2#1062312711yescharacteristic
221C2#1062329711yescharacteristic
222C2#1062330211yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#467C2
socleC22×C11C22×D4
prime radicalC23×C11C2×D4
hypercenter#467D11
hypocenterC11#3177
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
3. Q16×Dic11C2semidirect
4. #10622794C2semidirect
8. #10622491C2semidirect
9. #10622486C2semidirect
10. #10622410C2semidirect
11. #10622402C2semidirect
182. C11#3177semidirect

Maximal subgroups

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

subgroupindex
#106231562
C11×#4672
Q16×Dic112
#106227942
#106227292
#106227142
#106226652
#106224912
#106224862
#106224102
#106224022
#317711