Finite Group Databasebeta

← #16848427

Subgroups — #16848427

Order 3968.

516 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 205 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×#11758521C211yesmaximal, characteristic
2C2×C4×Dic62C211yesmaximal, characteristic
3#14520956C211yesmaximal, characteristic
4#14520954C211yesmaximal, characteristic
5#14520933C214yesmaximal
6#14520930C214yesmaximal
7#14520914C211yesmaximal, characteristic
8#14520895C211yesmaximal, characteristic
9C2×C4×Q8×C31C211yesmaximal, characteristic
10C22×Q8×C31C2211yescharacteristic
11C22×Dic62C2211yescharacteristic
12C4×Q8×C31—24no—
13C2×C4⋊C4×C31C2211yescharacteristic
14C2×C4⋊C4×C31C2212yes—
15C2×C42×C31C2212yes—
16C2×C42×C31C2211yescharacteristic
17#11758521C418yescomplemented
18C2×C4⋊Dic31C2211yescharacteristic
19C2×Dic31⋊C4C2212yes—
20C2×Dic31⋊C4C2214yes—
21C2×C4×Dic31C2211yescharacteristic
22C2×C4×Dic31C2212yes—
23C2×C4×Dic31C2211yescharacteristic
24C4×Dic62—24no—
25C31⋊#95C2212yes—
26C31⋊#95C2212yes—
27C31⋊#95C2214yes—
28C31⋊#95C2214yes—
29C31⋊#95C2214yes—
30C2×Q8×C31—22no—
31C2×Q8×C31—22no—
32C2×Q8×C31C2×C414yes—
33C22×C4×C31C2312yes—
34C22×C4×C31C2312yes—
35C22×C4×C31C2311yescharacteristic
36C22×C4×C31C2311yescharacteristic
37C22×C4×C31C2311yescharacteristic
38C22×Dic31C2312yes—
39C22×Dic31C2312yes—
40C22×Dic31C2312yes—
41C22×Dic31C2312yes—
42C2×Dic62—22no—
43C2×Dic62—22no—
44C2×Dic62C2×C414yes—
45C4⋊C4×C31—24no—
46C4⋊C4×C31—22no—
47C42×C31—24no—
48C42×C31D414yes—
49C4⋊Dic31—22no—
50Dic31⋊C4—24no—
51Dic31⋊C4C2×C4116yes—
52C4×Dic31—24no—
53C4×Dic31—22no—
54C4×Dic31C2×C414yes—
55C23×C31C2411yescharacteristic
56Q8×C31—28no—
57C2×C4×C31—22no—
58C2×C4×C31—22no—
59C2×C4×C31—22no—
60C2×C4×C31—22no—
61C2×C4×C31—22no—
62C2×C4×C31—24no—
63C2×C4×C31C22×C414yes—
64C2×C4×C31C22×C412yes—
65C2×C4×C31C2×D412yes—
66C2×C4×C31C2×D412yes—
67C2×C4×C31C2×D412yes—
68C2×C4×C31#4112yes—
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×Dic31—22no—
78C2×Dic31C22×C414yes—
79C2×Dic31C22×C414yes—
80Dic62—28no—
81#2327—311nomaximal, Sylow
82C22×C31C23×C411yescharacteristic
83C22×C31C22×D411yescharacteristic
84C22×C31C2×#4111yescharacteristic
85C22×C312−1+412yes—
86C22×C312−1+412yes—
87C4×C31—24no—
88C4×C31—22no—
89C4×C31—22no—
90C4×C31—42no—
91C4×C31C4×D414yes—
92Dic31—24no—
93Dic31—24no—
94Dic31—42no—
95Dic31—42no—
96C2×C4⋊Q8—311no—
97C2×C4×Q8—311no—
98C2×C4×Q8D3111yescharacteristic
99#391—311no—
100#391—311no—
101#387—314no—
102#387—314no—
103#382—311no—
104#376—311no—
105C2×C31C2×C4×D411yescharacteristic
106C2×C31#51912yes—
107C2×C31#53611yescharacteristic
108C2×C31#53611yescharacteristic
109C2×C31#54112yes—
110C22×Q8—311no—
111C22×Q8C2×D3111yescharacteristic
112C4⋊Q8—318no—
113C4×Q8—24no—
114C4×Q8—624no—
115C2×C4⋊C4—314no—
116C2×C4⋊C4—311no—
117C2×C4⋊C4—312no—
118C2×C4⋊C4C2×D3111yescharacteristic
119C2×C4⋊C4C2×D3112yes—
120C2×C42—311no—
121C2×C42—312no—
122C2×C42—311no—
123C2×C42C2×D3112yes—
124C2×C42C2×D3111yescharacteristic
125#95—312no—
126#95—312no—
127#95—314no—
128#95—314no—
129#95—314no—
130C31#232711yescharacteristic, complemented, Sylow
131C2×Q8—22no—
132C2×Q8—22no—
133C2×Q8—314no—
134C2×Q8—622no—
135C2×Q8—622no—
136C2×Q8C4×D3114yes—
137C22×C4—312no—
138C22×C4—312no—
139C22×C4—312no—
140C22×C4—312no—
141C22×C4C22×D3112yes—
142C22×C4C22×D3112yes—
143C22×C4C22×D3111yescharacteristic
144C22×C4C22×D3111yescharacteristic
145C22×C4C22×D3111yescharacteristic
146C4⋊C4—24no—
147C4⋊C4—22no—
148C4⋊C4—3116no—
149C4⋊C4—624no—
150C4⋊C4—622no—
151C42—24no—
152C42—314no—
153C42—622no—
154C42—624no—
155C42C22⋊D3114yes—
156C23C23×D3111yescharacteristic
157Q8—28no—
158Q8—628no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—24no—
164C2×C4—22no—
165C2×C4—314no—
166C2×C4—314no—
167C2×C4—622no—
168C2×C4—622no—
169C2×C4—622no—
170C2×C4—622no—
171C2×C4—622no—
172C2×C4—624no—
173C2×C4—622no—
174C2×C4—622no—
175C2×C4—622no—
176C2×C4C2×C4×D3114yes—
177C2×C4C2×C4×D3112yes—
178C2×C4#9249512yes—
179C2×C4C2×C22⋊D3112yes—
180C2×C4C2×C22⋊D3112yes—
181C2×C4C2×C22⋊D3112yes—
182C22C22×C4×D3111yescharacteristic
183C22C2×#9249511yescharacteristic
184C22#1175856412yes—
185C22#1175856712yes—
186C22C22×C22⋊D3111yescharacteristic
187C4—22no—
188C4—22no—
189C4—24no—
190C4—42no—
191C4—624no—
192C4—624no—
193C4—1242no—
194C4—1242no—
195C4C4×C22⋊D3114yes—
196C2C2×C4×C22⋊D3111yescharacteristic
197C2#1452152512yes—
198C2#1452162011yescharacteristic
199C2#1452162311yescharacteristic
200C2#1452165712yes—
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC2×C4×Q8×C31C2
socle, prime radical, cosocleC23×C31C24
hypercenterC2×C4×Q8D31
hypocenterC31#2327
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
17. #11758521C4semidirect
130. C31#2327semidirect

Maximal subgroups

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

subgroupindex
C2×#117585212
C2×C4×Dic622
#145209562
#145209542
#145209332
#145209302
#145209142
#145208952
C2×C4×Q8×C312
#232731