Finite Group Databasebeta

← #13073808

Subgroups — #13073808

Order 1408.

452 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 161 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×#125C211yesmaximal, characteristic
2C2×C4×Dic22C211yesmaximal, characteristic
3#10622597C214yesmaximal
4#10622591C214yesmaximal
5#10622590C211yesmaximal, characteristic
6#10622589C211yesmaximal, characteristic
7#10622587C211yesmaximal, characteristic
8#10622587C211yesmaximal, characteristic
9C4×C4⋊Dic11C211yesmaximal, characteristic
10C22×Dic22C2211yescharacteristic
11C11×#125—24no—
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C4⋊C4C2212yes—
15C2×C11×C4⋊C4C2212yes—
16C2×C42×C11C2211yescharacteristic
17C2×C4⋊Dic11C2211yescharacteristic
18C2×C4⋊Dic11C2212yes—
19C2×Dic11⋊C4C2212yes—
20C2×Dic11⋊C4C2214yes—
21C2×C4×Dic11C2212yes—
22C2×C4×Dic11C2211yescharacteristic
23C2×C4×Dic11C2211yescharacteristic
24C4×Dic22—24no—
25C11⋊#95C2212yes—
26C11⋊#95C2214yes—
27C11⋊#95C2214yes—
28C11⋊#95C2214yes—
29C22×C4×C11C2312yes—
30C22×C4×C11C2312yes—
31C22×C4×C11C2311yescharacteristic
32C22×C4×C11C2311yescharacteristic
33C22×C4×C11C2311yescharacteristic
34C22×Dic11C2312yes—
35C22×Dic11C2312yes—
36C22×Dic11C2312yes—
37C22×Dic11C2312yes—
38C2×Dic22—22no—
39C2×Dic22—22no—
40C2×Dic22Q814yes—
41C11×C4⋊C4—24no—
42C11×C4⋊C4—24no—
43C11×C4⋊C4—22no—
44C11×C4⋊C4—22no—
45C42×C11D414yes—
46C4⋊Dic11—24no—
47C4⋊Dic11—22no—
48Dic11⋊C4—28no—
49Dic11⋊C4—24no—
50C4×Dic11—24no—
51C4×Dic11—22no—
52C4×Dic11—22no—
53#2565—111nomaximal, Sylow
54C23×C11C2411yescharacteristic
55C2×C4×C11—22no—
56C2×C4×C11—22no—
57C2×C4×C11—22no—
58C2×C4×C11—22no—
59C2×C4×C11—24no—
60C2×C4×C11—24no—
61C2×C4×C11C2×D412yes—
62C2×C4×C11C2×D412yes—
63C2×C4×C11C2×D412yes—
64C2×C4×C11C2×Q812yes—
65C2×C4×C11#4112yes—
66C2×Dic11—22no—
67C2×Dic11—22no—
68C2×Dic11—22no—
69C2×Dic11—22no—
70C2×Dic11—22no—
71C2×Dic11—22no—
72C2×Dic11—24no—
73C2×Dic11—22no—
74C2×Dic11—22no—
75C2×Dic11C2×Q814yes—
76C2×Dic11#4114yes—
77Dic22—28no—
78C2×#125D1111yescharacteristic
79C2×C4×Q8—111no—
80#398—114no—
81#391—111no—
82#391—111no—
83#387—114no—
84#384—111no—
85#382—111no—
86C4×C4⋊C4—111no—
87C22×C11C22×D411yescharacteristic
88C22×C11C22×Q811yescharacteristic
89C22×C11C2×#4111yescharacteristic
90C22×C11C2×#4112yes—
91C22×C112−1+412yes—
92C4×C11—22no—
93C4×C11—22no—
94C4×C11—42no—
95C4×C11—42no—
96C4×C11C22⋊Q814yes—
97Dic11—24no—
98Dic11—24no—
99Dic11—42no—
100Dic11—42no—
101C22×Q8—111no—
102#125—24no—
103C4×Q8—224no—
104C2×C4⋊C4—111no—
105C2×C4⋊C4—112no—
106C2×C4⋊C4—112no—
107C2×C4⋊C4—114no—
108C2×C4⋊C4C2×D1111yescharacteristic
109C2×C4⋊C4C2×D1111yescharacteristic
110C2×C4⋊C4C2×D1112yes—
111C2×C4⋊C4C2×D1112yes—
112C2×C42—112no—
113C2×C42—111no—
114C2×C42—111no—
115C2×C42C2×D1111yescharacteristic
116#95—112no—
117#95—114no—
118#95—114no—
119#95—114no—
120C2×C11C2×C22⋊Q811yescharacteristic
121C2×C11#53211yescharacteristic
122C2×C11#53611yescharacteristic
123C2×C11#55212yes—
124C2×C11#55712yes—
125C2×Q8—114no—
126C2×Q8—222no—
127C2×Q8—222no—
128C22×C4—112no—
129C22×C4—112no—
130C22×C4—112no—
131C22×C4—112no—
132C22×C4C22×D1112yes—
133C22×C4C22×D1112yes—
134C22×C4C22×D1111yescharacteristic
135C22×C4C22×D1111yescharacteristic
136C22×C4C22×D1111yescharacteristic
137C4⋊C4—24no—
138C4⋊C4—24no—
139C4⋊C4—22no—
140C4⋊C4—22no—
141C4⋊C4—228no—
142C4⋊C4—224no—
143C4⋊C4—224no—
144C4⋊C4—222no—
145C42—222no—
146C42—222no—
147C42—224no—
148C42C22⋊D1114yes—
149C11#256511yescharacteristic, complemented, Sylow
150C23C23×D1111yescharacteristic
151Q8—228no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—24no—
155C2×C4—24no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—114no—
159C2×C4—114no—
160C2×C4—222no—
161C2×C4—222no—
162C2×C4—222no—
163C2×C4—222no—
164C2×C4—222no—
165C2×C4—224no—
166C2×C4—222no—
167C2×C4—222no—
168C2×C4—222no—
169C2×C4Q8×D1112yes—
170C2×C4#434312yes—
171C2×C4C2×C22⋊D1112yes—
172C2×C4C2×C22⋊D1112yes—
173C2×C4C2×C22⋊D1112yes—
174C22C2×Q8×D1111yescharacteristic
175C22C2×#434311yescharacteristic
176C22#41×D1112yes—
177C22#6704312yes—
178C22C22×C22⋊D1111yescharacteristic
179C4—22no—
180C4—22no—
181C4—42no—
182C4—42no—
183C4—224no—
184C4—224no—
185C4—442no—
186C4—442no—
187C4#6699914yes—
188C2#1062321612yes—
189C2#1062322512yes—
190C2C2×#6699911yescharacteristic
191C2#1062335611yescharacteristic
192C2#1062336311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC2×C11×#125C2
hypercenterC2×#125D11
hypocenterC11#2565
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
149. C11#2565semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1252
C2×C4×Dic222
#106225972
#106225912
#106225902
#106225892
#106225872
C4×C4⋊Dic112
#256511