Finite Group Databasebeta

← #13081423

Subgroups — #13081423

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#10623252C211yesmaximal, characteristic
2#10623101C211yesmaximal, characteristic
3C11×#462C211yesmaximal, characteristic
4#10622797C212yesmaximal
5#10622795C212yesmaximal
6#10622694C211yesmaximal, characteristic
7C4×#4326C211yesmaximal, characteristic
8#10622464C211yesmaximal, characteristic
9#10622444C211yesmaximal, characteristic
10#10622412C212yesmaximal
11#10622410C212yesmaximal
12C2×C11×Q16C2212yes—
13C11×C4⋊Q8C2211yescharacteristic
14C4×Q8×C11C2211yescharacteristic
15Q8×Dic11C2212yes—
16Q8×Dic11C2212yes—
17#66997C2212yes—
18C2×#4326C2211yescharacteristic
19#66943—21no—
20#66943—22no—
21#66943C2212yes—
22#66942—22no—
23#66940—21no—
24#66922—21no—
25#66922C2211yescharacteristic
26C4×Dic22—21no—
27C4×Dic22C2211yescharacteristic
28C4×Dic22C2211yescharacteristic
29C11×C4⋊C8C2211yescharacteristic
30C11×#103C2212yes—
31#66899C2212yes—
32#66899C2211yescharacteristic
33#66899C2212yes—
34#66881C2212yes—
35#66880C2212yes—
36#66879C2212yes—
37Dic11⋊C8C2212yes—
38#66874C2211yescharacteristic
39#66871C2211yescharacteristic
40C4×C11⋊C8C2211yescharacteristic
41C2×Q8×C11C2312yes—
42C2×Q8×C11C2311yescharacteristic
43C2×Dic22—21no—
44C2×Dic22D411yescharacteristic
45C2×Dic22C2311yescharacteristic
46C11×Q16—24no—
47C2×C8×C11C2312yes—
48C11×C4⋊C4—21no—
49C11×C4⋊C4—21no—
50C11×C4⋊C4—21no—
51C11×C4⋊C4C2311yescharacteristic
52C42×C11—21no—
53C42×C11C2311yescharacteristic
54#4326—22no—
55C4⋊Dic11—22no—
56C4⋊Dic11—22no—
57C4⋊Dic11—22no—
58C4⋊Dic11—21no—
59C4⋊Dic11D411yescharacteristic
60C4⋊Dic11C2311yescharacteristic
61C4⋊Dic11C2312yes—
62Dic11⋊C4—22no—
63Dic11⋊C4—22no—
64Dic11⋊C4—22no—
65Dic11⋊C4—21no—
66Dic11⋊C4D412yes—
67C4×Dic11—22no—
68C4×Dic11—22no—
69C4×Dic11—21no—
70C4×Dic11C2312yes—
71C2×C11⋊C8C2311yescharacteristic
72C2×C11⋊C8C2311yescharacteristic
73#3374—111nomaximal, Sylow
74Q8×C11—21no—
75Q8×C11—22no—
76Q8×C11—22no—
77Q8×C11#4112yes—
78C2×C4×C11—21no—
79C2×C4×C11—22no—
80C2×C4×C11—21no—
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11C2×D411yescharacteristic
83C2×C4×C11C2411yescharacteristic
84C2×Dic11—21no—
85C2×Dic11—21no—
86C2×Dic11—22no—
87C2×Dic11C2×D412yes—
88C2×Dic11C2×D412yes—
89Dic22—22no—
90Dic22—21no—
91Dic22—21no—
92Dic22—42no—
93C8×C11—22no—
94C11⋊C8—21no—
95C11⋊C8—21no—
96#557—111no—
97#557—111no—
98#491—112no—
99#487—111no—
100#479—112no—
101#475—111no—
102#462—112no—
103#462D1111yescharacteristic
104#446—111no—
105#441—112no—
106C4×Q16—111no—
107C22×C11C22×D411yescharacteristic
108C4×C11—22no—
109C4×C11—21no—
110C4×C11—42no—
111C4×C11—41no—
112C4×C11#13712yes—
113C4×C11C2×#4111yescharacteristic
114C4×C112−1+411yescharacteristic
115Dic11—22no—
116Dic11—22no—
117Dic11—41no—
118Dic11—42no—
119Dic11—41no—
120C2×Q16—111no—
121C2×Q16C2×D1112yes—
122C4⋊Q8—112no—
123C4⋊Q8—111no—
124C4⋊Q8—221no—
125C4⋊Q8C2×D1111yescharacteristic
126#125—112no—
127#125—222no—
128#125—222no—
129#125—221no—
130C4×Q8—111no—
131C4×Q8—112no—
132C4×Q8—112no—
133C4×Q8—111no—
134C4×Q8—221no—
135C4×Q8—221no—
136C4×Q8C2×D1111yescharacteristic
137#107—111no—
138#106—112no—
139C4⋊C8—112no—
140C4⋊C8C2×D1111yescharacteristic
141#103—111no—
142#103—112no—
143#103—112no—
144#103—112no—
145#103—111no—
146#103C2×D1112yes—
147#97—112no—
148C4×C8—111no—
149C2×C11#54811yescharacteristic
150C2×C11C2×#13711yescharacteristic
151C2×C11#57811yescharacteristic
152C2×Q8—111no—
153C2×Q8—111no—
154C2×Q8—221no—
155C2×Q8C22×D1112yes—
156C2×Q8C22×D1111yescharacteristic
157Q16—24no—
158Q16—222no—
159C2×C8—111no—
160C2×C8—111no—
161C2×C8C22×D1112yes—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—111no—
166C4⋊C4—112no—
167C4⋊C4—112no—
168C4⋊C4—111no—
169C4⋊C4—222no—
170C4⋊C4—222no—
171C4⋊C4—222no—
172C4⋊C4—222no—
173C4⋊C4—222no—
174C4⋊C4—222no—
175C4⋊C4—221no—
176C4⋊C4—221no—
177C4⋊C4C22×D1111yescharacteristic
178C42—21no—
179C42—112no—
180C42—222no—
181C42—222no—
182C42—221no—
183C42C22×D1111yescharacteristic
184C11#337411yescharacteristic, complemented, Sylow
185Q8—21no—
186Q8—22no—
187Q8—22no—
188Q8—222no—
189Q8—221no—
190Q8—221no—
191Q8—442no—
192Q8#434112yes—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—112no—
197C2×C4—112no—
198C2×C4—221no—
199C2×C4—222no—
200C2×C4—221no—
201C2×C4D4×D1111yescharacteristic
202C2×C4D4×D1111yescharacteristic
203C2×C4C23×D1111yescharacteristic
204C8—22no—
205C8—221no—
206C8—221no—
207C22C2×D4×D1111yescharacteristic
208C4—21no—
209C4—22no—
210C4—41no—
211C4—42no—
212C4—222no—
213C4—222no—
214C4—442no—
215C4—441no—
216C4—441no—
217C4#6697112yes—
218C4C2×#434111yescharacteristic
219C4#6704311yescharacteristic
220C2#1062312911yescharacteristic
221C2C2×#6697111yescharacteristic
222C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#462C2
socle, prime radicalC22×C11C22×D4
hypercenter#462D11
hypocenterC11#3374
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #462

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
#106232522
#106231012
C11×#4622
#106227972
#106227952
#106226942
C4×#43262
#106224642
#106224442
#106224122
#106224102
#337411