Finite Group Databasebeta

← #16845733

Subgroups — #16845733

Order 3968.

336 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C22×C8×D31C211yesmaximal, characteristic
2C2×#11758405C211yesmaximal, characteristic, complemented
3#14520906C212yesmaximal
4#14520811C212yesmaximal, complemented
5C2×C31×#106C211yesmaximal, characteristic, complemented
6C22×C4×D31C2211yescharacteristic
7C22×C8×C31C2211yescharacteristic
8C2×C4⋊C4×C31C2212yes—
9C2×(C2×D31)⋊C4—22no—
10C2×C4⋊Dic31C2212yes—
11C22×C31⋊C8C2211yescharacteristic
12C2×C8×D31—22no—
13C2×C8×D31—22no—
14C2×C8×D31C414yescomplemented
15C31×#106—22no—
16C31⋊#95—22no—
17#11758405—22no—
18C23×D31D411yescharacteristic
19C22×C4×C31—22no—
20C22×C4×C31C2311yescharacteristic
21C22×Dic31—22no—
22C22×Dic31D411yescharacteristic
23C2×C4×D31—21no—
24C2×C4×D31—21no—
25C2×C4×D31—21no—
26C2×C4×D31—21no—
27C2×C4×D31C2×C412yes—
28C2×C4×D31Q812yes—
29C2×C8×C31C2×C412yes—
30C2×C8×C31D412yes—
31C2×C8×C31D412yes—
32C4⋊C4×C31—22no—
33C4⋊C4×C31—22no—
34(C2×D31)⋊C4—44no—
35C4⋊Dic31—22no—
36C4⋊Dic31—22no—
37C2×C31⋊C8—21no—
38C2×C31⋊C8—21no—
39C2×C31⋊C8C2×C412yes—
40C8×D31—28no—
41C23×C31C2×D411yescharacteristic
42C22×D31—21no—
43C22×D31—21no—
44C22×D31—22no—
45C22×D31C4⋊C412yes—
46C22×D31SD1614yes—
47C2×C4×C31—42no—
48C2×C4×C31—42no—
49C2×C4×C31—42no—
50C2×C4×C31C22×C411yescharacteristic
51C2×C4×C31C2×D411yescharacteristic
52C2×C4×C31C2×D411yescharacteristic
53C2×C4×C31C2×Q811yescharacteristic
54C2×C4×C31#4111yescharacteristic
55C2×C4×C31#4111yescharacteristic
56C2×Dic31—21no—
57C2×Dic31—21no—
58C2×Dic31—42no—
59C2×Dic31—42no—
60C2×Dic31—42no—
61C2×Dic31C4⋊C412yes—
62C4×D31—22no—
63C4×D31—22no—
64C4×D31—22no—
65C4×D31—22no—
66C8×C31C22⋊C414yescomplemented
67C31⋊C8—22no—
68#1807—311nomaximal, Sylow
69C22×C31C2×C4⋊C411yescharacteristic
70C22×C31#12111yescharacteristic
71C22×C31#12111yescharacteristic
72C22×C31C2×SD1612yes—
73C22×C31#13512yes—
74C2×D31—22no—
75C2×D31—22no—
76C2×D31—24no—
77C2×D31—24no—
78C2×D31#10614yescomplemented
79C4×C31—82no—
80C4×C31C2×C22⋊C411yescharacteristic
81C4×C31#11711yescharacteristic
82C4×C31C22⋊Q811yescharacteristic
83C4×C31C22⋊Q811yescharacteristic
84Dic31—22no—
85Dic31—82no—
86C23×C8—311no—
87C2×#106—311no—
88C2×#106D3111yescharacteristic, complemented
89#380—312no—
90#340—312no—
91C2×C31#38011yescharacteristic
92C2×C31C2×#10611yescharacteristic
93C2×C31#42711yescharacteristic
94C2×C31#46512yes—
95C2×C31#46512yes—
96D31—24no—
97C23×C4—311no—
98C22×C8—311no—
99C22×C8—314no—
100C22×C8—622no—
101C22×C8—622no—
102C22×C8C2×D3111yescharacteristic
103C2×C4⋊C4—312no—
104C2×C4⋊C4C2×D3112yes—
105C2×C22⋊C4—622no—
106#106—22no—
107#106—622no—
108#95—622no—
109C31#180711yescharacteristic, complemented, Sylow
110C24—311no—
111C22×C4—22no—
112C22×C4—311no—
113C22×C4—312no—
114C22×C4—312no—
115C22×C4—621no—
116C22×C4—621no—
117C22×C4—621no—
118C22×C4—621no—
119C22×C4—622no—
120C22×C4C22×D3111yescharacteristic
121C2×C8—312no—
122C2×C8—621no—
123C2×C8—621no—
124C2×C8—628no—
125C2×C8C4×D3112yes—
126C2×C8D12412yes—
127C2×C8C22⋊D3112yes—
128C4⋊C4—22no—
129C4⋊C4—22no—
130C4⋊C4—622no—
131C4⋊C4—622no—
132C22⋊C4—1244no—
133C23—312no—
134C23—314no—
135C23—621no—
136C23—622no—
137C23—621no—
138C23D4×D3111yescharacteristic
139C2×C4—42no—
140C2×C4—42no—
141C2×C4—42no—
142C2×C4—312no—
143C2×C4—621no—
144C2×C4—621no—
145C2×C4—622no—
146C2×C4—622no—
147C2×C4—622no—
148C2×C4—622no—
149C2×C4—1242no—
150C2×C4—1242no—
151C2×C4—1242no—
152C2×C4C2×C4×D3111yescharacteristic
153C2×C4C2×D12411yescharacteristic
154C2×C4#9249711yescharacteristic
155C2×C4Q8×D3111yescharacteristic
156C2×C4#9249911yescharacteristic
157C2×C4C2×C22⋊D3111yescharacteristic
158C8—622no—
159C8(C2×D31)⋊C414yescomplemented
160C22—314no—
161C22—622no—
162C22—624no—
163C22—624no—
164C22—622no—
165C22C4⋊C4×D3111yescharacteristic
166C22#1175847211yescharacteristic
167C22SD16×D3112yes—
168C22#1175849312yes—
169C22#1175851511yescharacteristic
170C4—82no—
171C4—622no—
172C4—2482no—
173C4#1175846911yescharacteristic
174C4#1175847411yescharacteristic
175C4C2×(C2×D31)⋊C411yescharacteristic
176C4#1175852311yescharacteristic
177C2—624no—
178C2#1452090611yescharacteristic
179C2#106×D3111yescharacteristic
180C2#1452108411yescharacteristic
181C2#1452127512yes—
182C2#1452127912yes—
subgroupG/H
centerC23D4×D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC2×C31×#106C2
socleC23×C31C2×D4
prime radicalC23×D31D4
cosocleC22×C4×C31C23
hypercenterC2×#106D31
hypocenterC31#1807
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
2. C2×#11758405C2semidirect
4. #14520811C2semidirect
5. C2×C31×#106C2semidirect
14. C2×C8×D31C4semidirect
66. C8×C31C22⋊C4semidirect
78. C2×D31#106semidirect
88. C2×#106D31semidirect
109. C31#1807semidirect
159. C8(C2×D31)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×C8×D312
C2×#117584052
#145209062
#145208112
C2×C31×#1062
#180731