Finite Group Databasebeta

← #13074565

Subgroups — #13074565

Order 1408.

416 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 141 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×#66997C211yesmaximal, characteristic
2C2×#66943C211yesmaximal, characteristic
3C11×#391C211yesmaximal, characteristic
4#10622843C211yesmaximal, characteristic
5#10622587C211yesmaximal, characteristic
6#10622545C211yesmaximal, characteristic
7#10622542C211yesmaximal, characteristic
8#10622273C214yesmaximal
9#10622271C214yesmaximal
10C22×Q8×C11C2211yescharacteristic
11C22×Dic22C2211yescharacteristic
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C42×C11C2211yescharacteristic
14#66997—24no—
15C2×C4⋊Dic11C2212yes—
16C2×C4⋊Dic11C2211yescharacteristic
17C2×Dic11⋊C4C2212yes—
18C2×Dic11⋊C4C2212yes—
19C2×Dic11⋊C4C2212yes—
20C2×C4×Dic11C2211yescharacteristic
21C2×C4×Dic11C2211yescharacteristic
22#66943—24no—
23C11×#95C2214yes—
24C11⋊#95C2212yes—
25C11⋊#95C2214yes—
26C11⋊#95C2214yes—
27C11⋊#95C2214yes—
28C11⋊#95C2212yes—
29C2×Q8×C11—22no—
30C2×Q8×C11—22no—
31C2×Q8×C11—22no—
32C22×C4×C11C2312yes—
33C22×C4×C11C2312yes—
34C22×C4×C11C2312yes—
35C22×C4×C11C2311yescharacteristic
36C22×Dic11C2312yes—
37C22×Dic11C2312yes—
38C22×Dic11C2312yes—
39C22×Dic11C2311yescharacteristic
40C22×Dic11C2311yescharacteristic
41C2×Dic22—22no—
42C2×Dic22—22no—
43C2×Dic22—22no—
44C11×C4⋊C4—22no—
45C42×C11—22no—
46C4⋊Dic11—24no—
47C4⋊Dic11—22no—
48Dic11⋊C4—24no—
49Dic11⋊C4—24no—
50Dic11⋊C4—24no—
51C4×Dic11—22no—
52C4×Dic11D414yes—
53#2642—111nomaximal, Sylow
54C23×C11C2411yescharacteristic
55Q8×C11—44no—
56C2×C4×C11—22no—
57C2×C4×C11—22no—
58C2×C4×C11—22no—
59C2×C4×C11—22no—
60C2×C4×C11—22no—
61C2×C4×C11—22no—
62C2×C4×C11—24no—
63C2×C4×C11—22no—
64C2×C4×C11C2×D412yes—
65C2×C4×C11#4112yes—
66C2×C4×C11#4112yes—
67C2×Dic11—22no—
68C2×Dic11—22no—
69C2×Dic11—22no—
70C2×Dic11—22no—
71C2×Dic11—22no—
72C2×Dic11—22no—
73C2×Dic11—22no—
74C2×Dic11—24no—
75C2×Dic11—22no—
76C2×Dic11—22no—
77C2×Dic11C2×D412yes—
78C2×Dic11C2×D412yes—
79Dic22—44no—
80C2×C4⋊Q8—111no—
81C2×#125—111no—
82#400—114no—
83#400—114no—
84#391—111no—
85#391—111no—
86#391—111no—
87#391D1111yescharacteristic
88#376—111no—
89C22×C11C22×D411yescharacteristic
90C22×C11C2×#4111yescharacteristic
91C22×C11C2×#4111yescharacteristic
92C22×C112−1+412yes—
93C22×C112−1+412yes—
94C4×C11—42no—
95C4×C11—42no—
96C4×C11—42no—
97C4×C11#12414yes—
98Dic11—22no—
99Dic11—22no—
100Dic11—42no—
101Dic11—42no—
102Dic11—42no—
103C22×Q8—111no—
104C22×Q8C2×D1111yescharacteristic
105C4⋊Q8—224no—
106#125—224no—
107C2×C4⋊C4—111no—
108C2×C4⋊C4—112no—
109C2×C4⋊C4—112no—
110C2×C4⋊C4—112no—
111C2×C4⋊C4—112no—
112C2×C4⋊C4C2×D1111yescharacteristic
113C2×C42—111no—
114C2×C42—111no—
115C2×C42C2×D1111yescharacteristic
116#95—112no—
117#95—112no—
118#95—114no—
119#95—114no—
120#95—114no—
121#95C2×D1114yes—
122C2×C11C2×#12411yescharacteristic
123C2×C11#53611yescharacteristic
124C2×C11#53611yescharacteristic
125C2×C11#54112yes—
126C2×C11#54112yes—
127C2×Q8—22no—
128C2×Q8—22no—
129C2×Q8—22no—
130C2×Q8—222no—
131C2×Q8—222no—
132C2×Q8—222no—
133C22×C4—111no—
134C22×C4—111no—
135C22×C4—112no—
136C22×C4—112no—
137C22×C4—112no—
138C22×C4C22×D1112yes—
139C22×C4C22×D1112yes—
140C22×C4C22×D1112yes—
141C22×C4C22×D1111yescharacteristic
142C4⋊C4—22no—
143C4⋊C4—224no—
144C4⋊C4—224no—
145C4⋊C4—224no—
146C4⋊C4—224no—
147C4⋊C4—222no—
148C42—22no—
149C42—114no—
150C42—222no—
151C11#264211yescharacteristic, complemented, Sylow
152C23C23×D1111yescharacteristic
153Q8—44no—
154Q8—444no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—24no—
163C2×C4—112no—
164C2×C4—112no—
165C2×C4—222no—
166C2×C4—222no—
167C2×C4—222no—
168C2×C4—222no—
169C2×C4—222no—
170C2×C4—222no—
171C2×C4—222no—
172C2×C4—224no—
173C2×C4—222no—
174C2×C4—222no—
175C2×C4#433912yes—
176C2×C4D4×D1112yes—
177C2×C4#434112yes—
178C22C2×#433911yescharacteristic
179C22C2×D4×D1111yescharacteristic
180C22C2×#434111yescharacteristic
181C22#6704012yes—
182C22#6704312yes—
183C4—42no—
184C4—42no—
185C4—42no—
186C4—222no—
187C4—222no—
188C4—442no—
189C4—442no—
190C4—442no—
191C4#6693814yes—
192C2C2×#6693811yescharacteristic
193C2#1062311412yes—
194C2#1062315612yes—
195C2#1062320611yescharacteristic
196C2#1062325511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#391C2
hypercenter#391D11
hypocenterC11#2642
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
151. C11#2642semidirect

Maximal subgroups

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

subgroupindex
C2×#669972
C2×#669432
C11×#3912
#106228432
#106225872
#106225452
#106225422
#106222732
#106222712
#264211