Finite Group Databasebeta

← #16849019

Subgroups — #16849019

Order 3968.

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

normal subgroups only

This group has 400 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
1#14520991C212yesmaximal
2#14520988C212yesmaximal
3#14520982C212yesmaximal
4#14520981C212yesmaximal
5C4×Dic31⋊C4C212yesmaximal
6C4×C4⋊Dic31C211yesmaximal, characteristic
7C4×C4⋊Dic31C212yesmaximal
8#14520895C211yesmaximal, characteristic
9C4×C4⋊C4×C31C211yesmaximal, characteristic
10C2×C4⋊C4×C31C2212yes—
11C2×C42×C31C2212yes—
12C2×C42×C31C2211yescharacteristic
13C2×C4⋊Dic31C2212yes—
14C2×C4⋊Dic31C2212yes—
15C2×C4⋊Dic31C2212yes—
16C2×Dic31⋊C4C2212yes—
17C2×Dic31⋊C4C2212yes—
18C2×C4×Dic31C2211yescharacteristic
19C2×C4×Dic31C2211yescharacteristic
20C2×C4×Dic31C2212yes—
21C31×#95C2211yescharacteristic
22C31×#95C2211yescharacteristic
23C31⋊#95C2212yes—
24C31⋊#95C2212yes—
25C31⋊#95C2211yescharacteristic
26C31⋊#95C2212yes—
27C31⋊#95C2211yescharacteristic
28C31⋊#95C2212yes—
29C31⋊#95C2212yes—
30C31⋊#95C2212yes—
31C22×C4×C31C2312yes—
32C22×C4×C31C2311yescharacteristic
33C22×C4×C31C2311yescharacteristic
34C22×C4×C31C2312yes—
35C22×C4×C31C2311yescharacteristic
36C22×Dic31C2312yes—
37C22×Dic31C2312yes—
38C22×Dic31C2312yes—
39C22×Dic31C2312yes—
40C4⋊C4×C31—24no—
41C42×C31—24no—
42C42×C31Q814yes—
43C4⋊Dic31—24no—
44C4⋊Dic31—24no—
45C4⋊Dic31—24no—
46Dic31⋊C4—24no—
47Dic31⋊C4—24no—
48C4×Dic31—24no—
49C4×Dic31—22no—
50C4×Dic31—22no—
51C23×C31C2411yescharacteristic
52C2×C4×C31—22no—
53C2×C4×C31—22no—
54C2×C4×C31—22no—
55C2×C4×C31—22no—
56C2×C4×C31—22no—
57C2×C4×C31—22no—
58C2×C4×C31—22no—
59C2×C4×C31C2×Q812yes—
60C2×C4×C31C2×Q812yes—
61C2×C4×C31C2×Q812yes—
62C2×C4×C31#4114yes—
63C2×C4×C31#4112yes—
64C2×C4×C31#4112yes—
65C2×Dic31—22no—
66C2×Dic31—22no—
67C2×Dic31—22no—
68C2×Dic31—22no—
69C2×Dic31—22no—
70C2×Dic31—22no—
71C2×Dic31—22no—
72C2×Dic31—22no—
73C2×Dic31—22no—
74C2×Dic31—22no—
75C2×Dic31—22no—
76C2×Dic31#4114yes—
77#2402—311nomaximal, Sylow
78C22×C31C22×Q811yescharacteristic
79C22×C31C2×#4112yes—
80C22×C31C2×#4111yescharacteristic
81C22×C31C2×#4111yescharacteristic
82C22×C31C2×#4112yes—
83C4×C31—24no—
84C4×C31—22no—
85C4×C31—22no—
86C4×C31—42no—
87C4×C31#12514yes—
88Dic31—24no—
89Dic31—42no—
90Dic31—42no—
91Dic31—42no—
92#400—312no—
93#400—312no—
94#398—312no—
95#398—312no—
96C4×C4⋊C4—311no—
97C4×C4⋊C4—312no—
98C4×C4⋊C4—312no—
99C4×C4⋊C4D3111yescharacteristic
100#376—311no—
101C2×C31C2×#12511yescharacteristic
102C2×C31#52912yes—
103C2×C31#52912yes—
104C2×C31#53311yescharacteristic
105C2×C31#53311yescharacteristic
106C2×C4⋊C4—312no—
107C2×C4⋊C4—312no—
108C2×C4⋊C4—312no—
109C2×C4⋊C4—312no—
110C2×C4⋊C4—312no—
111C2×C4⋊C4C2×D3112yes—
112C2×C42—311no—
113C2×C42—311no—
114C2×C42—312no—
115C2×C42C2×D3112yes—
116C2×C42C2×D3111yescharacteristic
117#95—312no—
118#95—312no—
119#95—311no—
120#95—312no—
121#95—312no—
122#95—312no—
123#95—312no—
124#95—311no—
125#95C2×D3111yescharacteristic
126#95C2×D3111yescharacteristic
127C31#240211yescharacteristic, complemented, Sylow
128C22×C4—312no—
129C22×C4—312no—
130C22×C4—312no—
131C22×C4—312no—
132C22×C4C22×D3112yes—
133C22×C4C22×D3111yescharacteristic
134C22×C4C22×D3111yescharacteristic
135C22×C4C22×D3112yes—
136C22×C4C22×D3111yescharacteristic
137C4⋊C4—24no—
138C4⋊C4—624no—
139C4⋊C4—624no—
140C4⋊C4—624no—
141C4⋊C4—624no—
142C4⋊C4—624no—
143C42—24no—
144C42—622no—
145C42—624no—
146C42—622no—
147C42Dic6214yes—
148C23C23×D3111yescharacteristic
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—314no—
157C2×C4—622no—
158C2×C4—622no—
159C2×C4—622no—
160C2×C4—622no—
161C2×C4—622no—
162C2×C4—622no—
163C2×C4—622no—
164C2×C4—622no—
165C2×C4—622no—
166C2×C4—622no—
167C2×C4—622no—
168C2×C4C2×Dic6212yes—
169C2×C4C2×Dic6212yes—
170C2×C4C2×Dic6212yes—
171C2×C4#9249514yes—
172C2×C4#9249712yes—
173C2×C4#9249912yes—
174C22C22×Dic6211yescharacteristic
175C22C2×#9249512yes—
176C22C2×#9249711yescharacteristic
177C22C2×#9249911yescharacteristic
178C22#41×D3112yes—
179C4—22no—
180C4—22no—
181C4—24no—
182C4—42no—
183C4—624no—
184C4—1242no—
185C4—1242no—
186C4—1242no—
187C4#1175846714yes—
188C2C2×#1175846711yescharacteristic
189C2#1452157912yes—
190C2#1452158612yes—
191C2#1452160211yescharacteristic
192C2#1452160611yescharacteristic
subgroupG/H
centerC22×C4C22×D31
commutator, socle, prime radical, cosocleC23×C31C24
FrattiniC23C23×D31
FittingC4×C4⋊C4×C31C2
hypercenterC4×C4⋊C4D31
hypocenterC31#2402
LCSG ▷ C23×C31 ▷ C31
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
127. C31#2402semidirect

Maximal subgroups

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

subgroupindex
#145209912
#145209882
#145209822
#145209812
C4×Dic31⋊C42
C4×C4⋊Dic312
#145208952
C4×C4⋊C4×C312
#240231