Finite Group Databasebeta

← #16846021

Subgroups — #16846021

Order 3968.

360 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 105 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×#11758501C211yesmaximal, characteristic
2C2×#11758503C211yesmaximal, characteristic
3C2×#11758404C212yesmaximal, complemented
4#14520812C212yesmaximal, complemented
5C2×C31×C22⋊C8C211yesmaximal, characteristic
6C23×C4×C31C2211yescharacteristic
7C22×Dic62C2211yescharacteristic
8C22×C8×C31C2212yes—
9C2×C22⋊Dic31—21no—
10C2×C22⋊Dic31—21no—
11#11758503—24no—
12C2×C4⋊Dic31C2211yescharacteristic
13C2×C4⋊Dic31C2212yes—
14#11758501—22no—
15#11758501C414yescomplemented
16C2×Dic31⋊C4—21no—
17C2×C4×Dic31—21no—
18C31×C22⋊C8—22no—
19#11758404—24no—
20C24×C31D411yescharacteristic
21C22×C4×C31—22no—
22C22×C4×C31—22no—
23C22×C4×C31C2×C412yes—
24C22×C4×C31D411yescharacteristic
25C22×C4×C31D412yes—
26C22×C4×C31C2311yescharacteristic
27C22×Dic31—22no—
28C22×Dic31—21no—
29C22×Dic31—21no—
30C2×Dic62—22no—
31C2×Dic62—22no—
32C2×Dic62—21no—
33C2×Dic62C2×C412yes—
34C2×C8×C31—22no—
35C2×C8×C31—22no—
36C2×C8×C31—22no—
37C22⋊Dic31—24no—
38C22⋊Dic31—24no—
39C4⋊Dic31—21no—
40C4⋊Dic31—22no—
41C4⋊Dic31C2×C412yes—
42C4⋊Dic31D414yes—
43Dic31⋊C4—24no—
44C4×Dic31—24no—
45C23×C31—21no—
46C23×C31—21no—
47C23×C31—22no—
48C23×C31—22no—
49C23×C31C22⋊C412yes—
50C23×C31C2×D411yescharacteristic
51C2×C4×C31—21no—
52C2×C4×C31—21no—
53C2×C4×C31—24no—
54C2×C4×C31—24no—
55C2×C4×C31C22⋊C412yes—
56C2×C4×C31C22×C411yescharacteristic
57C2×C4×C31C2×D412yes—
58C2×C4×C31C2×D411yescharacteristic
59C2×C4×C31#4112yes—
60C2×Dic31—22no—
61C2×Dic31—22no—
62C2×Dic31—24no—
63C2×Dic31—41no—
64C2×Dic31—41no—
65C2×Dic31—42no—
66C2×Dic31—42no—
67C2×Dic31—42no—
68Dic62—24no—
69Dic62—42no—
70C8×C31—42no—
71#1873—311nomaximal, Sylow
72C22×C31—22no—
73C22×C31—22no—
74C22×C31—22no—
75C22×C31—42no—
76C22×C31—42no—
77C22×C31C2×C22⋊C411yescharacteristic
78C22×C31#12011yescharacteristic
79C22×C31#12311yescharacteristic
80C22×C31#13512yes—
81C22×C31#13712yes—
82C4×C31—22no—
83C4×C31C4×D412yes—
84C4×C31#12112yes—
85Dic31—42no—
86Dic31—42no—
87Dic31—44no—
88C2×C22⋊Q8—311no—
89C2×#117—311no—
90C2×#103—312no—
91C2×C22⋊C8D3111yescharacteristic
92#340—312no—
93C2×C31—42no—
94C2×C31#38611yescharacteristic
95C2×C31#41611yescharacteristic
96C2×C31#41911yescharacteristic
97C2×C31#45212yes—
98C2×C31#48512yes—
99C22×Q8—311no—
100C23×C4C2×D3111yescharacteristic
101C22×C8C2×D3112yes—
102C22⋊Q8—314no—
103C22⋊Q8—622no—
104#117—624no—
105C2×C4⋊C4—312no—
106C2×C4⋊C4—311no—
107C2×C4⋊C4—621no—
108C2×C22⋊C4—621no—
109C2×C22⋊C4—621no—
110C2×C42—621no—
111#103—624no—
112C22⋊C8—22no—
113C31#187311yescharacteristic, complemented, Sylow
114C24D12411yescharacteristic
115C2×Q8—312no—
116C2×Q8—621no—
117C2×Q8—622no—
118C2×Q8—622no—
119C22×C4—22no—
120C22×C4—22no—
121C22×C4—622no—
122C22×C4—621no—
123C22×C4—621no—
124C22×C4C4×D3112yes—
125C22×C4D12411yescharacteristic
126C22×C4C22⋊D3112yes—
127C22×C4C22×D3111yescharacteristic
128C2×C8—22no—
129C2×C8—22no—
130C2×C8—22no—
131C4⋊C4—312no—
132C4⋊C4—314no—
133C4⋊C4—624no—
134C4⋊C4—622no—
135C4⋊C4—621no—
136C22⋊C4—624no—
137C22⋊C4—624no—
138C42—624no—
139C23—21no—
140C23—21no—
141C23—22no—
142C23—22no—
143C23(C2×D31)⋊C412yes—
144C23C2×D12411yescharacteristic
145Q8—624no—
146Q8—1242no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—24no—
150C2×C4—24no—
151C2×C4—624no—
152C2×C4—622no—
153C2×C4—622no—
154C2×C4—1241no—
155C2×C4—1241no—
156C2×C4—1242no—
157C2×C4—1242no—
158C2×C4—1242no—
159C2×C4(C2×D31)⋊C412yes—
160C2×C4C2×C4×D3111yescharacteristic
161C2×C4D4×D3112yes—
162C2×C4#9249712yes—
163C2×C4C2×C22⋊D3111yescharacteristic
164C8—42no—
165C22—22no—
166C22—22no—
167C22—22no—
168C22—42no—
169C22—42no—
170C22#1175845911yescharacteristic
171C22#1175846311yescharacteristic
172C22#1175848112yes—
173C22#1175848612yes—
174C22C2×(C2×D31)⋊C411yescharacteristic
175C4—22no—
176C4—1242no—
177C4—1244no—
178C4—1242no—
179C4(C22⋊D31)⋊C412yes—
180C4#1175851612yes—
181C2—42no—
182C2#1452092611yescharacteristic
183C2#1452104611yescharacteristic
184C2#1452105911yescharacteristic
185C2#1452121312yes—
186C2#1452139112yes—
subgroupG/H
centerC23C2×D124
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC2×C31×C22⋊C8C2
socleC23×C31C2×D4
prime radicalC24×C31D4
cosocleC22×C4×C31C23
hypercenterC2×C22⋊C8D31
hypocenterC31#1873
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. C2×#11758404C2semidirect
4. #14520812C2semidirect
15. #11758501C4semidirect
113. C31#1873semidirect

Maximal subgroups

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

subgroupindex
C2×#117585012
C2×#117585032
C2×#117584042
#145208122
C2×C31×C22⋊C82
#187331