Finite Group Databasebeta

← #13073809

Subgroups — #13073809

Order 1408.

452 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 165 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×Q8×Dic11C211yesmaximal, characteristic
2C2×#66943C211yesmaximal, characteristic
3C11×#391C211yesmaximal, characteristic
4#10622843C211yesmaximal, characteristic
5#10622590C211yesmaximal, characteristic
6#10622548C211yesmaximal, characteristic
7C4×Dic11⋊C4C211yesmaximal, characteristic
8#10622274C214yesmaximal
9#10622267C214yesmaximal
10C22×Q8×C11C2211yescharacteristic
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×C42×C11C2211yescharacteristic
13Q8×Dic11—24no—
14C2×C4⋊Dic11C2212yes—
15C2×C4⋊Dic11C2211yescharacteristic
16C2×C4⋊Dic11C2214yes—
17C2×C4⋊Dic11C2212yes—
18C2×C4⋊Dic11C2211yescharacteristic
19C2×Dic11⋊C4C2212yes—
20C2×Dic11⋊C4C2212yes—
21C2×C4×Dic11C2212yes—
22C2×C4×Dic11C2211yescharacteristic
23C2×C4×Dic11C2211yescharacteristic
24#66943—24no—
25C11×#95C2214yes—
26C11⋊#95C2212yes—
27C11⋊#95C2214yes—
28C11⋊#95C2214yes—
29C2×Q8×C11—22no—
30C2×Q8×C11—22no—
31C2×Q8×C11Q814yes—
32C22×C4×C11C2312yes—
33C22×C4×C11C2312yes—
34C22×C4×C11C2312yes—
35C22×C4×C11C2311yescharacteristic
36C22×Dic11C2312yes—
37C22×Dic11C2312yes—
38C22×Dic11C2312yes—
39C22×Dic11C2311yescharacteristic
40C22×Dic11C2311yescharacteristic
41C11×C4⋊C4—22no—
42C42×C11—22no—
43C4⋊Dic11—24no—
44C4⋊Dic11—24no—
45C4⋊Dic11—22no—
46C4⋊Dic11—22no—
47C4⋊Dic11—28no—
48Dic11⋊C4—24no—
49Dic11⋊C4—24no—
50C4×Dic11—24no—
51C4×Dic11—22no—
52C4×Dic11D414yes—
53#2565—111nomaximal, Sylow
54C23×C11C2411yescharacteristic
55Q8×C11—28no—
56C2×C4×C11—22no—
57C2×C4×C11—22no—
58C2×C4×C11—22no—
59C2×C4×C11—22no—
60C2×C4×C11—22no—
61C2×C4×C11—24no—
62C2×C4×C11C2×D412yes—
63C2×C4×C11C2×Q814yes—
64C2×C4×C11C2×Q812yes—
65C2×C4×C11#4112yes—
66C2×C4×C11#4114yes—
67C2×Dic11—22no—
68C2×Dic11—22no—
69C2×Dic11—22no—
70C2×Dic11—22no—
71C2×Dic11—22no—
72C2×Dic11—22no—
73C2×Dic11—24no—
74C2×Dic11—24no—
75C2×Dic11—22no—
76C2×Dic11C2×D412yes—
77C2×Dic11C2×D412yes—
78C2×#125—111no—
79C2×C4×Q8—111no—
80#398—114no—
81#391—111no—
82#391D1111yescharacteristic
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—24no—
93C4×C11—24no—
94C4×C11—42no—
95C4×C11C22⋊Q814yes—
96Dic11—22no—
97Dic11—22no—
98Dic11—42no—
99Dic11—42no—
100Dic11—42no—
101C22×Q8C2×D1111yescharacteristic
102#125—224no—
103C4×Q8—224no—
104C2×C4⋊C4—111no—
105C2×C4⋊C4—112no—
106C2×C4⋊C4—111no—
107C2×C4⋊C4—112no—
108C2×C4⋊C4—112no—
109C2×C4⋊C4—112no—
110C2×C4⋊C4—114no—
111C2×C4⋊C4C2×D1111yescharacteristic
112C2×C42—111no—
113C2×C42—112no—
114C2×C42—111no—
115C2×C42C2×D1111yescharacteristic
116#95—112no—
117#95—114no—
118#95—114no—
119#95C2×D1114yes—
120C2×C11C2×C22⋊Q811yescharacteristic
121C2×C11#53211yescharacteristic
122C2×C11#53611yescharacteristic
123C2×C11#55212yes—
124C2×C11#55712yes—
125C2×Q8—22no—
126C2×Q8—22no—
127C2×Q8Dic2214yes—
128C22×C4—111no—
129C22×C4—111no—
130C22×C4—112no—
131C22×C4—112no—
132C22×C4—112no—
133C22×C4C22×D1112yes—
134C22×C4C22×D1112yes—
135C22×C4C22×D1112yes—
136C22×C4C22×D1111yescharacteristic
137C4⋊C4—22no—
138C4⋊C4—224no—
139C4⋊C4—224no—
140C4⋊C4—224no—
141C4⋊C4—222no—
142C4⋊C4—222no—
143C4⋊C4—224no—
144C4⋊C4—228no—
145C42—22no—
146C42—114no—
147C42—224no—
148C42—222no—
149C11#256511yescharacteristic, complemented, Sylow
150C23C23×D1111yescharacteristic
151Q8—28no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—112no—
159C2×C4—112no—
160C2×C4—222no—
161C2×C4—222no—
162C2×C4—222no—
163C2×C4—222no—
164C2×C4—222no—
165C2×C4—224no—
166C2×C4—224no—
167C2×C4—222no—
168C2×C4—222no—
169C2×C4C2×Dic2214yes—
170C2×C4C2×Dic2212yes—
171C2×C4D4×D1112yes—
172C2×C4#434112yes—
173C2×C4#434314yes—
174C22C22×Dic2211yescharacteristic
175C22C2×D4×D1111yescharacteristic
176C22C2×#434111yescharacteristic
177C22C2×#434312yes—
178C22#6704312yes—
179C4—24no—
180C4—24no—
181C4—42no—
182C4—222no—
183C4—222no—
184C4—442no—
185C4—442no—
186C4—442no—
187C4#6693114yes—
188C2C2×#6693111yescharacteristic
189C2#1062310112yes—
190C2#1062317312yes—
191C2#1062320611yescharacteristic
192C2#1062325611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#391C2
hypercenter#391D11
hypocenterC11#2565
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #391

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×Q8×Dic112
C2×#669432
C11×#3912
#106228432
#106225902
#106225482
C4×Dic11⋊C42
#106222742
#106222672
#256511