Finite Group Databasebeta

← #13081417

Subgroups — #13081417

Order 1408.

326 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 117 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#10623101C211yesmaximal, characteristic
2#10623098C211yesmaximal, characteristic
3C4×C11×Q16C211yesmaximal, characteristic
4#10622795C212yesmaximal
5#10622644C211yesmaximal, characteristic
6#10622633C211yesmaximal, characteristic
7#10622490C212yesmaximal
8#10622410C212yesmaximal
9#10622402C212yesmaximal
10#10622294C211yesmaximal, characteristic
11#10622292C211yesmaximal, characteristic
12C2×C11×Q16C2211yescharacteristic
13C4×Q8×C11C2211yescharacteristic
14C4×Q8×C11C2211yescharacteristic
15Q8×Dic11C2212yes—
16#66997C2212yes—
17C2×#4326C2212yes—
18#66943—22no—
19#66943C2212yes—
20#66942—22no—
21#66940C2212yes—
22#66923—21no—
23#66922—21no—
24#66922C2211yescharacteristic
25#66922C2211yescharacteristic
26C4×Dic22—21no—
27C4×Dic22—21no—
28C4×Dic22C2211yescharacteristic
29C11×#107C2211yescharacteristic
30C11×#103C2211yescharacteristic
31C11×#103C2211yescharacteristic
32C4×C8×C11C2211yescharacteristic
33#66899C2212yes—
34#66880C2212yes—
35#66880C2212yes—
36#66879C2212yes—
37Dic11⋊C8C2212yes—
38#66874C2212yes—
39#66872C2212yes—
40C4⋊(C11⋊C8)C2211yescharacteristic
41C2×Q8×C11C2311yescharacteristic
42C2×Q8×C11C2311yescharacteristic
43C2×Dic22—21no—
44C2×Dic22D411yescharacteristic
45C2×Dic22C2312yes—
46C11×Q16—22no—
47C2×C8×C11C2311yescharacteristic
48C2×C8×C11C2311yescharacteristic
49C11×C4⋊C4—21no—
50C11×C4⋊C4—21no—
51C11×C4⋊C4C2311yescharacteristic
52C11×C4⋊C4C2311yescharacteristic
53C42×C11—21no—
54C42×C11—21no—
55C42×C11C2311yescharacteristic
56#4326—24no—
57C4⋊Dic11—22no—
58C4⋊Dic11—22no—
59C4⋊Dic11—21no—
60C4⋊Dic11—21no—
61C4⋊Dic11—21no—
62C4⋊Dic11D411yescharacteristic
63C4⋊Dic11C2312yes—
64Dic11⋊C4—22no—
65Dic11⋊C4—22no—
66Dic11⋊C4—22no—
67Dic11⋊C4—22no—
68Dic11⋊C4D412yes—
69C4×Dic11—22no—
70C4×Dic11—22no—
71C4×Dic11C2312yes—
72C2×C11⋊C8C2312yes—
73#3374—111nomaximal, Sylow
74Q8×C11—21no—
75Q8×C11—21no—
76Q8×C11—21no—
77Q8×C11#4112yes—
78C2×C4×C11—21no—
79C2×C4×C11—21no—
80C2×C4×C11—21no—
81C2×C4×C11—21no—
82C2×C4×C11C2×D411yescharacteristic
83C2×C4×C11C2×D411yescharacteristic
84C2×C4×C11C2411yescharacteristic
85C2×Dic11—22no—
86C2×Dic11—22no—
87C2×Dic11C2×D412yes—
88C2×Dic11C2×D412yes—
89Dic22—22no—
90Dic22—22no—
91Dic22—22no—
92Dic22—42no—
93C8×C11—21no—
94C8×C11—21no—
95C11⋊C8—22no—
96#557—111no—
97#557—111no—
98#491—112no—
99#487—111no—
100#479—112no—
101#475—111no—
102#462—112no—
103#462—111no—
104#446—111no—
105#441—112no—
106C4×Q16D1111yescharacteristic
107C22×C11C22×D411yescharacteristic
108C4×C11—22no—
109C4×C11—21no—
110C4×C11—41no—
111C4×C11—41no—
112C4×C11—41no—
113C4×C11#13712yes—
114C4×C11C2×#4111yescharacteristic
115C4×C112−1+411yescharacteristic
116Dic11—22no—
117Dic11—22no—
118Dic11—42no—
119Dic11—42no—
120C2×Q16—112no—
121C2×Q16C2×D1111yescharacteristic
122C4⋊Q8—112no—
123C4⋊Q8—111no—
124C4⋊Q8—111no—
125C4⋊Q8—221no—
126#125—112no—
127#125—221no—
128#125—222no—
129#125—222no—
130C4×Q8—111no—
131C4×Q8—112no—
132C4×Q8—112no—
133C4×Q8—221no—
134C4×Q8—221no—
135C4×Q8C2×D1111yescharacteristic
136C4×Q8C2×D1111yescharacteristic
137#107C2×D1111yescharacteristic
138#106—112no—
139C4⋊C8—112no—
140C4⋊C8—111no—
141#103—112no—
142#103—112no—
143#103—112no—
144#103—112no—
145#103C2×D1111yescharacteristic
146#103C2×D1111yescharacteristic
147#97—112no—
148C4×C8C2×D1111yescharacteristic
149C2×C11#54811yescharacteristic
150C2×C11C2×#13711yescharacteristic
151C2×C11#57811yescharacteristic
152C2×Q8—111no—
153C2×Q8—112no—
154C2×Q8—221no—
155C2×Q8C22×D1111yescharacteristic
156C2×Q8C22×D1111yescharacteristic
157Q16—22no—
158Q16—224no—
159C2×C8—112no—
160C2×C8C22×D1111yescharacteristic
161C2×C8C22×D1111yescharacteristic
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—111no—
165C4⋊C4—112no—
166C4⋊C4—112no—
167C4⋊C4—222no—
168C4⋊C4—222no—
169C4⋊C4—222no—
170C4⋊C4—222no—
171C4⋊C4—222no—
172C4⋊C4—222no—
173C4⋊C4—221no—
174C4⋊C4—221no—
175C4⋊C4—221no—
176C4⋊C4C22×D1111yescharacteristic
177C4⋊C4C22×D1111yescharacteristic
178C42—21no—
179C42—21no—
180C42—112no—
181C42—222no—
182C42—222no—
183C42C22×D1111yescharacteristic
184C11#337411yescharacteristic, complemented, Sylow
185Q8—21no—
186Q8—21no—
187Q8—21no—
188Q8—222no—
189Q8—222no—
190Q8—222no—
191Q8—442no—
192Q8#433912yes—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—112no—
198C2×C4—112no—
199C2×C4—222no—
200C2×C4—222no—
201C2×C4D4×D1111yescharacteristic
202C2×C4D4×D1111yescharacteristic
203C2×C4C23×D1111yescharacteristic
204C8—21no—
205C8—21no—
206C8—222no—
207C22C2×D4×D1111yescharacteristic
208C4—21no—
209C4—22no—
210C4—41no—
211C4—41no—
212C4—41no—
213C4—222no—
214C4—222no—
215C4—442no—
216C4—442no—
217C4#6697112yes—
218C4C2×#433911yescharacteristic
219C4#6704311yescharacteristic
220C2#1062308311yescharacteristic
221C2C2×#6697111yescharacteristic
222C2#1062330211yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC4×C11×Q16C2
socle, prime radicalC22×C11C22×D4
hypercenterC4×Q16D11
hypocenterC11#3374
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
184. C11#3374semidirect

Maximal subgroups

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

subgroupindex
#106231012
#106230982
C4×C11×Q162
#106227952
#106226442
#106226332
#106224902
#106224102
#106224022
#106222942
#106222922
#337411