Finite Group Databasebeta

← #13073602

Subgroups — #13073602

Order 1408.

540 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 185 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
1C2×C11×C4⋊Q8C211yesmaximal, characteristic
2C2×Q8×Dic11C211yesmaximal, characteristic
3C2×#66997C211yesmaximal, characteristic
4C2×#66997C211yesmaximal, characteristic
5#10622843C211yesmaximal, characteristic
6#10622597C214yesmaximal
7#10622585C214yesmaximal
8C4×Dic11⋊C4C211yesmaximal, characteristic
9#10622542C211yesmaximal, characteristic
10C22×Q8×C11C2211yescharacteristic
11C22×Q8×C11C2211yescharacteristic
12C22×Dic22C2211yescharacteristic
13C11×C4⋊Q8—24no—
14C2×C11×C4⋊C4C2214yes—
15C2×C42×C11C2211yescharacteristic
16Q8×Dic11—24no—
17#66997—24no—
18#66997—24no—
19C2×C4⋊Dic11C2211yescharacteristic
20C2×C4⋊Dic11C2212yes—
21C2×Dic11⋊C4C2212yes—
22C2×Dic11⋊C4C2214yes—
23C2×Dic11⋊C4C2212yes—
24C2×Dic11⋊C4C2212yes—
25C2×C4×Dic11C2211yescharacteristic
26C2×C4×Dic11C2212yes—
27C2×C4×Dic11C2211yescharacteristic
28C11⋊#95C2214yes—
29C11⋊#95C2212yes—
30C11⋊#95C2214yes—
31C2×Q8×C11—22no—
32C2×Q8×C11—22no—
33C2×Q8×C11—22no—
34C2×Q8×C11—22no—
35C2×Q8×C11—22no—
36C2×Q8×C11D414yes—
37C22×C4×C11C2312yes—
38C22×C4×C11C2312yes—
39C22×C4×C11C2312yes—
40C22×C4×C11C2311yescharacteristic
41C22×Dic11C2312yes—
42C22×Dic11C2312yes—
43C22×Dic11C2311yescharacteristic
44C22×Dic11C2312yes—
45C22×Dic11C2311yescharacteristic
46C2×Dic22—22no—
47C2×Dic22—22no—
48C2×Dic22—22no—
49C11×C4⋊C4—28no—
50C42×C11—22no—
51C4⋊Dic11—24no—
52C4⋊Dic11—22no—
53Dic11⋊C4—24no—
54Dic11⋊C4—24no—
55Dic11⋊C4—28no—
56Dic11⋊C4Q818yescomplemented
57C4×Dic11—24no—
58C4×Dic11—22no—
59C4×Dic11D414yes—
60#2546—111nomaximal, Sylow
61C23×C11C2411yescharacteristic
62Q8×C11—28no—
63Q8×C11—44no—
64C2×C4×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—22no—
68C2×C4×C11—22no—
69C2×C4×C11—22no—
70C2×C4×C11—22no—
71C2×C4×C11C2×D412yes—
72C2×C4×C11C2×D414yes—
73C2×C4×C11C2×D412yes—
74C2×C4×C11C2×Q814yes—
75C2×C4×C11#4112yes—
76C2×Dic11—22no—
77C2×Dic11—22no—
78C2×Dic11—22no—
79C2×Dic11—22no—
80C2×Dic11—22no—
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11—24no—
84C2×Dic11C2×D412yes—
85C2×Dic11C2×D412yes—
86C2×Dic11C2×Q814yes—
87C2×Dic11C2×Q814yes—
88Dic22—44no—
89C2×C4⋊Q8—111no—
90C2×C4⋊Q8—111no—
91C2×C4⋊Q8D1111yescharacteristic
92C2×C4×Q8—111no—
93#398—114no—
94#391—111no—
95#391—111no—
96#389—114no—
97C4×C4⋊C4—111no—
98C22×C11C22×D411yescharacteristic
99C22×C11C22×D411yescharacteristic
100C22×C11C22×Q812yes—
101C22×C11C2×#4111yescharacteristic
102C22×C112−1+412yes—
103C4×C11—24no—
104C4×C11—24no—
105C4×C11—42no—
106C4×C11#12114yes—
107Dic11—22no—
108Dic11—24no—
109Dic11—42no—
110Dic11—42no—
111Dic11C4⋊Q814yescomplemented
112C22×Q8—111no—
113C22×Q8C2×D1111yescharacteristic
114C22×Q8C2×D1111yescharacteristic
115C4⋊Q8—24no—
116C4⋊Q8—224no—
117C4⋊Q8—224no—
118C4×Q8—224no—
119C2×C4⋊C4—112no—
120C2×C4⋊C4—111no—
121C2×C4⋊C4—112no—
122C2×C4⋊C4—112no—
123C2×C4⋊C4—114no—
124C2×C4⋊C4—112no—
125C2×C4⋊C4C2×D1114yes—
126C2×C42—111no—
127C2×C42—112no—
128C2×C42—111no—
129C2×C42C2×D1111yescharacteristic
130#95—112no—
131#95—114no—
132#95—114no—
133C2×C11C2×#12111yescharacteristic
134C2×C11C2×C4⋊Q811yescharacteristic
135C2×C11#53611yescharacteristic
136C2×C11D4×Q812yes—
137C2×C11#55712yes—
138C2×Q8—22no—
139C2×Q8—22no—
140C2×Q8—22no—
141C2×Q8—22no—
142C2×Q8—22no—
143C2×Q8—222no—
144C2×Q8—222no—
145C2×Q8—222no—
146C2×Q8C22⋊D1114yes—
147C22×C4—111no—
148C22×C4—112no—
149C22×C4—111no—
150C22×C4—112no—
151C22×C4—112no—
152C22×C4C22×D1112yes—
153C22×C4C22×D1112yes—
154C22×C4C22×D1112yes—
155C22×C4C22×D1111yescharacteristic
156C4⋊C4—28no—
157C4⋊C4—118no—
158C4⋊C4—224no—
159C4⋊C4—224no—
160C4⋊C4—224no—
161C4⋊C4—222no—
162C4⋊C4—228no—
163C42—22no—
164C42—114no—
165C42—224no—
166C42—222no—
167C11#254611yescharacteristic, complemented, Sylow
168C23C23×D1111yescharacteristic
169Q8—28no—
170Q8—44no—
171Q8—444no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—112no—
180C2×C4—114no—
181C2×C4—112no—
182C2×C4—114no—
183C2×C4—222no—
184C2×C4—222no—
185C2×C4—222no—
186C2×C4—222no—
187C2×C4—222no—
188C2×C4—222no—
189C2×C4—224no—
190C2×C4—222no—
191C2×C4D4×D1112yes—
192C2×C4#434112yes—
193C2×C4Q8×D1114yes—
194C2×C4C2×C22⋊D1114yes—
195C2×C4C2×C22⋊D1112yes—
196C22C2×D4×D1111yescharacteristic
197C22C2×#434111yescharacteristic
198C22C2×Q8×D1112yes—
199C22#6704012yes—
200C22C22×C22⋊D1111yescharacteristic
201C4—24no—
202C4—24no—
203C4—42no—
204C4—114no—
205C4—222no—
206C4—224no—
207C4—442no—
208C4—442no—
209C4#6699214yes—
210C2#1062325212yes—
211C2D11×C4⋊Q811yescharacteristic
212C2#1062325511yescharacteristic
213C2C2×#6699211yescharacteristic
214C2Q8×C22⋊D1112yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC2×C11×C4⋊Q8C2
hypercenterC2×C4⋊Q8D11
hypocenterC11#2546
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
56. Dic11⋊C4Q8semidirect
111. Dic11C4⋊Q8semidirect
167. C11#2546semidirect

Maximal subgroups

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

subgroupindex
C2×C11×C4⋊Q82
C2×Q8×Dic112
C2×#669972
#106228432
#106225972
#106225852
C4×Dic11⋊C42
#106225422
#254611