Finite Group Databasebeta

← #16853982

Subgroups — #16853982

Order 3968.

356 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 125 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#14520990C212yesmaximal
3#14520987C212yesmaximal
4#14520969C212yesmaximal
5#14520969C211yesmaximal, characteristic
6#14520968C212yesmaximal
7#14520914C211yesmaximal, characteristic
8#14520913C212yesmaximal
9C31×#395C211yesmaximal, characteristic
10C22×Q8×C31C2211yescharacteristic
11C22×Dic62C2211yescharacteristic
12C2×C4⋊C4×C31C2211yescharacteristic
13C2×C4⋊C4×C31C2212yes—
14C2×C4⋊Dic31C2211yescharacteristic
15C2×Dic31⋊C4C2212yes—
16C2×Dic31⋊C4C2212yes—
17C2×Dic31⋊C4C2212yes—
18C2×Dic31⋊C4C2212yes—
19C2×C4×Dic31C2211yescharacteristic
20C31×#95C2212yes—
21C31×#95C2211yescharacteristic
22C31⋊#95C2212yes—
23C31⋊#95C2212yes—
24C31⋊#95C2212yes—
25C31⋊#95C2212yes—
26C31⋊#95C2212yes—
27C31⋊#95C2212yes—
28C31⋊#95C2211yescharacteristic
29C31⋊#95C2212yes—
30C31⋊#95C2212yes—
31C2×Q8×C31—42no—
32C2×Q8×C31—41no—
33C22×C4×C31C2312yes—
34C22×C4×C31C2311yescharacteristic
35C22×C4×C31C2312yes—
36C22×C4×C31C2311yescharacteristic
37C22×C4×C31C2311yescharacteristic
38C22×Dic31C2312yes—
39C22×Dic31C2312yes—
40C22×Dic31C2312yes—
41C22×Dic31C2312yes—
42C2×Dic62—42no—
43C2×Dic62—41no—
44C4⋊C4×C31—41no—
45C4⋊C4×C31—42no—
46C4⋊Dic31—41no—
47Dic31⋊C4—42no—
48Dic31⋊C4—42no—
49Dic31⋊C4—42no—
50Dic31⋊C4—42no—
51C4×Dic31Q814yescomplemented
52C23×C31C2411yescharacteristic
53Q8×C31—44no—
54C2×C4×C31—21no—
55C2×C4×C31—21no—
56C2×C4×C31—22no—
57C2×C4×C31—22no—
58C2×C4×C31—22no—
59C2×C4×C31—22no—
60C2×C4×C31—22no—
61C2×C4×C31—21no—
62C2×C4×C31—22no—
63C2×C4×C31—21no—
64C2×C4×C31—22no—
65C2×C4×C31—22no—
66C2×C4×C31C2×Q812yes—
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—24no—
76C2×Dic31—22no—
77C2×Dic31C2×Q814yes—
78Dic62—44no—
79#2844—311nomaximal, Sylow
80C22×C31C22×Q811yescharacteristic
81C22×C31H(5,𝔽2)12yes—
82C22×C31H(5,𝔽2)11yescharacteristic
83C22×C312−1+412yes—
84C22×C312−1+411yescharacteristic
85C4×C31—22no—
86C4×C31—41no—
87C4×C31—42no—
88C4×C31—41no—
89C4×C31—42no—
90Dic31—24no—
91Dic31—42no—
92Dic31—42no—
93Dic31—42no—
94#400—312no—
95#400—312no—
96#400—312no—
97#395—312no—
98#395—312no—
99#395—311no—
100#395D3111yescharacteristic
101#382—311no—
102#382—312no—
103C2×C31#54412yes—
104C2×C31#54411yescharacteristic
105C2×C31H(3,𝔽4)11yescharacteristic
106C2×C31#56311yescharacteristic
107C2×C31#56312yes—
108C22×Q8—311no—
109C22×Q8C2×D3111yescharacteristic
110C2×C4⋊C4—312no—
111C2×C4⋊C4—312no—
112C2×C4⋊C4—311no—
113C2×C4⋊C4—312no—
114C2×C4⋊C4—312no—
115C2×C4⋊C4C2×D3111yescharacteristic
116C2×C4⋊C4C2×D3112yes—
117C2×C42—311no—
118#95—312no—
119#95—312no—
120#95—312no—
121#95—312no—
122#95—312no—
123#95—311no—
124#95—312no—
125#95—312no—
126#95—312no—
127#95C2×D3112yes—
128#95C2×D3111yescharacteristic
129C31#284411yescharacteristic, complemented, Sylow
130C2×Q8—42no—
131C2×Q8—41no—
132C2×Q8—1242no—
133C2×Q8—1241no—
134C22×C4—312no—
135C22×C4—312no—
136C22×C4—312no—
137C22×C4—312no—
138C22×C4C22×D3112yes—
139C22×C4C22×D3111yescharacteristic
140C22×C4C22×D3111yescharacteristic
141C22×C4C22×D3112yes—
142C22×C4C22×D3111yescharacteristic
143C4⋊C4—41no—
144C4⋊C4—42no—
145C4⋊C4—1242no—
146C4⋊C4—1242no—
147C4⋊C4—1242no—
148C4⋊C4—1242no—
149C4⋊C4—1241no—
150C42—314no—
151C23C23×D3111yescharacteristic
152Q8—44no—
153Q8—1244no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—314no—
167C2×C4—622no—
168C2×C4—622no—
169C2×C4—622no—
170C2×C4—622no—
171C2×C4—622no—
172C2×C4—622no—
173C2×C4—622no—
174C2×C4—624no—
175C2×C4—622no—
176C2×C4—622no—
177C2×C4Q8×D3112yes—
178C22#1175856112yes—
179C22#1175856111yescharacteristic
180C22C2×Q8×D3111yescharacteristic
181C22#1175856412yes—
182C22#1175856711yescharacteristic
183C4—22no—
184C4—42no—
185C4—41no—
186C4—41no—
187C4—42no—
188C4—624no—
189C4—1242no—
190C4—1242no—
191C4—1242no—
192C2#1452167612yes—
193C2#1452167811yescharacteristic
194C2#1452179211yescharacteristic
195C2#1452179811yescharacteristic
196C2#1452180012yes—
subgroupG/H
center, FrattiniC23C23×D31
commutator, socle, prime radical, cosocleC23×C31C24
FittingC31×#395C2
hypercenter#395D31
hypocenterC31#2844
LCSG ▷ C23×C31 ▷ C31
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
51. C4×Dic31Q8semidirect
129. C31#2844semidirect

Maximal subgroups

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

subgroupindex
#145209912
#145209902
#145209872
#145209692
#145209682
#145209142
#145209132
C31×#3952
#284431