Finite Group Databasebeta

← #16848816

Subgroups — #16848816

Order 3968.

448 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 185 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×#11758447C211yesmaximal, characteristic
2#14520934C212yesmaximal
3#14520933C212yesmaximal
4#14520932C212yesmaximal
5#14520931C212yesmaximal
6C4×Dic31⋊C4C212yesmaximal
7#14520900C212yesmaximal
8#14520895C211yesmaximal, characteristic
9C31×#376C211yesmaximal, characteristic
10C2×C42×C31C2212yes—
11C2×C42×C31C2211yescharacteristic
12C2×C4⋊Dic31C2211yescharacteristic
13C2×C4⋊Dic31C2211yescharacteristic
14C2×Dic31⋊C4C2212yes—
15C2×Dic31⋊C4C2212yes—
16C2×Dic31⋊C4C2212yes—
17C2×Dic31⋊C4C2212yes—
18C2×C4×Dic31C2212yes—
19C2×C4×Dic31C2212yes—
20C2×C4×Dic31C2212yes—
21#11758447C418yescomplemented
22C31×#95C2211yescharacteristic
23C31×#95C2211yescharacteristic
24C31×#95C2212yes—
25C31⋊#95C2211yescharacteristic
26C31⋊#95C2212yes—
27C31⋊#95C2211yescharacteristic
28C31⋊#95C2212yes—
29C31⋊#95C2212yes—
30C31⋊#95C2212yes—
31C31⋊#95C2212yes—
32C22×C4×C31C2312yes—
33C22×C4×C31C2311yescharacteristic
34C22×C4×C31C2311yescharacteristic
35C22×C4×C31C2311yescharacteristic
36C22×C4×C31C2312yes—
37C22×Dic31C2312yes—
38C22×Dic31C2312yes—
39C22×Dic31C2312yes—
40C22×Dic31C2312yes—
41C42×C31—24no—
42C42×C31C2×C414yes—
43C4⋊Dic31C2×C414yes—
44C4⋊Dic31C2×C414yes—
45Dic31⋊C4—24no—
46Dic31⋊C4—24no—
47Dic31⋊C4C2×C418yes—
48Dic31⋊C4C2×C418yes—
49C4×Dic31—24no—
50C4×Dic31—24no—
51C4×Dic31—24no—
52C23×C31C2411yescharacteristic
53C2×C4×C31—22no—
54C2×C4×C31—22no—
55C2×C4×C31—22no—
56C2×C4×C31—21no—
57C2×C4×C31—21no—
58C2×C4×C31—22no—
59C2×C4×C31—22no—
60C2×C4×C31—22no—
61C2×C4×C31—22no—
62C2×C4×C31C22×C412yes—
63C2×C4×C31C22×C412yes—
64C2×C4×C31C22×C412yes—
65C2×C4×C31#4114yes—
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×Dic31C22×C414yes—
76C2×Dic31C22×C414yes—
77C2×Dic31#4114yes—
78#2371—311nomaximal, Sylow
79C22×C31C23×C411yescharacteristic
80C22×C31C2×#4112yes—
81C22×C31C2×#4112yes—
82C22×C312−1+411yescharacteristic
83C22×C312−1+411yescharacteristic
84C4×C31—22no—
85C4×C31—22no—
86C4×C31—22no—
87C4×C31—24no—
88C4×C31—42no—
89Dic31—24no—
90Dic31—24no—
91Dic31—24no—
92Dic31—42no—
93C2×#125—311no—
94#387—312no—
95#387—312no—
96#387—312no—
97#387—312no—
98C4×C4⋊C4—312no—
99C4×C4⋊C4—312no—
100#376—311no—
101#376D3111yescharacteristic
102C2×C31C4×#4111yescharacteristic
103C2×C31C4×#4111yescharacteristic
104C2×C31#51911yescharacteristic
105C2×C31#55212yes—
106C2×C31#55212yes—
107#125—318no—
108C2×C4⋊C4—312no—
109C2×C4⋊C4—312no—
110C2×C4⋊C4—311no—
111C2×C4⋊C4—311no—
112C2×C4⋊C4—312no—
113C2×C4⋊C4—312no—
114C2×C42—312no—
115C2×C42—312no—
116C2×C42—312no—
117C2×C42C2×D3112yes—
118C2×C42C2×D3111yescharacteristic
119#95—311no—
120#95—312no—
121#95—311no—
122#95—312no—
123#95—312no—
124#95—312no—
125#95—312no—
126#95C2×D3111yescharacteristic
127#95C2×D3111yescharacteristic
128#95C2×D3112yes—
129C31#237111yescharacteristic, complemented, Sylow
130C22×C4—312no—
131C22×C4—312no—
132C22×C4—312no—
133C22×C4—312no—
134C22×C4C22×D3112yes—
135C22×C4C22×D3111yescharacteristic
136C22×C4C22×D3111yescharacteristic
137C22×C4C22×D3111yescharacteristic
138C22×C4C22×D3112yes—
139C4⋊C4—318no—
140C4⋊C4—318no—
141C4⋊C4—314no—
142C4⋊C4—314no—
143C4⋊C4—624no—
144C4⋊C4—624no—
145C42—24no—
146C42—624no—
147C42—624no—
148C42—624no—
149C42C4×D3114yes—
150C23C23×D3111yescharacteristic
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—314no—
161C2×C4—314no—
162C2×C4—314no—
163C2×C4—622no—
164C2×C4—622no—
165C2×C4—622no—
166C2×C4—622no—
167C2×C4—622no—
168C2×C4—622no—
169C2×C4—622no—
170C2×C4—622no—
171C2×C4—622no—
172C2×C4C2×C4×D3112yes—
173C2×C4C2×C4×D3112yes—
174C2×C4C2×C4×D3112yes—
175C2×C4#9249514yes—
176C22C22×C4×D3111yescharacteristic
177C22C2×#9249512yes—
178C22#41×D3112yes—
179C22#1175856711yescharacteristic
180C22#1175856711yescharacteristic
181C4—24no—
182C4—22no—
183C4—22no—
184C4—22no—
185C4—42no—
186C4—624no—
187C4—624no—
188C4—624no—
189C4—1242no—
190C2#1452151711yescharacteristic
191C2C4×#9249511yescharacteristic
192C2#1452152611yescharacteristic
193C2#1452173212yes—
194C2#1452173812yes—
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC31×#376C2
socle, prime radical, cosocleC23×C31C24
hypercenter#376D31
hypocenterC31#2371
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ #376

Complements

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

NH ≅ G/Ntype
21. #11758447C4semidirect
129. C31#2371semidirect

Maximal subgroups

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

subgroupindex
C2×#117584472
#145209342
#145209332
#145209322
#145209312
C4×Dic31⋊C42
#145209002
#145208952
C31×#3762
#237131