Finite Group Databasebeta

← #16846876

Subgroups — #16846876

Order 3968.

466 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 67 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#14521675C211yesmaximal, characteristic, complemented
2#14520904C211yesmaximal, characteristic
3#14520904C212yesmaximal
4#14520815C212yesmaximal, complemented
5C31×#342C211yesmaximal, characteristic, complemented
6C24×D31C2211yescharacteristic
7C2×C22⋊C4×C31C2212yes—
8C2×C22⋊C4×C31C2211yescharacteristic
9C2×C22⋊Dic31C2211yescharacteristic
10C2×C22⋊Dic31C2212yes—
11C2×(C2×D31)⋊C4—22no—
12C2×(C2×D31)⋊C4—24no—
13#11758501—22no—
14#11758455—24no—
15C24×C31C2311yescharacteristic
16C23×D31—21no—
17C23×D31—22no—
18C23×D31—22no—
19C23×D31—21no—
20C23×D31—44no—
21C23×D31Q812yescomplemented
22C22×C4×C31—22no—
23C22×C4×C31D412yes—
24C22×Dic31—21no—
25C22×Dic31D414yes—
26C2×Dic62—22no—
27C22⋊C4×C31—22no—
28C22⋊C4×C31—22no—
29C22⋊C4×C31—22no—
30C22⋊Dic31—22no—
31C22⋊Dic31—22no—
32C22⋊Dic31—22no—
33(C2×D31)⋊C4—48no—
34(C2×D31)⋊C4—44no—
35C4⋊Dic31—22no—
36Dic31⋊C4—24no—
37C23×C31—42no—
38C23×C31C2×D411yescharacteristic
39C23×C31C2×D412yes—
40C23×C31C2×Q811yescharacteristic
41C23×C31#4112yes—
42C23×C31#4111yescharacteristic
43C22×D31—24no—
44C22×D31—28no—
45C22×D31—24no—
46C22×D31—22no—
47C22×D31—44no—
48C22×D31—48no—
49C22×D31—44no—
50C22×D31—42no—
51C22×D31—44no—
52C22×D31—41no—
53C22×D31—41no—
54C22×D31—42no—
55C2×C4×C31—22no—
56C2×C4×C31—42no—
57C2×C4×C31—44no—
58C2×C4×C31—42no—
59C2×Dic31—24no—
60C2×Dic31—44no—
61C2×Dic31—42no—
62C2×Dic31—41no—
63Dic62—82no—
64#2029—311nomaximal, Sylow
65C22×C31—22no—
66C22×C31—24no—
67C22×C31—41no—
68C22×C31—42no—
69C22×C31—41no—
70C22×C31#12011yescharacteristic
71C22×C31C22⋊Q812yes—
72C22×C31C22⋊Q811yescharacteristic
73C22×C31#12411yescharacteristic
74C22×C31#12412yes—
75C2×D31—28no—
76C2×D31—24no—
77C2×D31—44no—
78C2×D31—48no—
79C2×D31—44no—
80C2×D31—42no—
81C2×D31—42no—
82C2×D31—44no—
83C4×C31—42no—
84C4×C31—82no—
85Dic31—44no—
86Dic31—81no—
87#543—311no—
88#379—312no—
89#379—311no—
90#342—312no—
91#342D3111yescharacteristic, complemented
92C2×C31—21no—
93C2×C31—22no—
94C2×C31—22no—
95C2×C31—21no—
96C2×C31#39311yescharacteristic
97C2×C31B(4,𝔽2)12yes—
98D31—44no—
99C25—311no—
100C22⋊Q8—624no—
101C22⋊Q8—622no—
102C2×C22⋊C4—312no—
103C2×C22⋊C4—311no—
104C2×C22⋊C4—624no—
105C2×C22⋊C4—622no—
106C2×C22⋊C4C2×D3112yes—
107C2×C22⋊C4C2×D3111yescharacteristic
108C31#202911yescharacteristic, complemented, Sylow
109C24—312no—
110C24—621no—
111C24—622no—
112C24—622no—
113C24—621no—
114C24—1244no—
115C24C22×D3111yescharacteristic
116C2×Q8—622no—
117C22×C4—22no—
118C22×C4—314no—
119C22×C4—621no—
120C22×C4D12412yes—
121C4⋊C4—624no—
122C4⋊C4—622no—
123C22⋊C4—22no—
124C22⋊C4—22no—
125C22⋊C4—22no—
126C22⋊C4—622no—
127C22⋊C4—622no—
128C22⋊C4—622no—
129C22⋊C4—1244no—
130C22⋊C4—1248no—
131C23—42no—
132C23—624no—
133C23—628no—
134C23—624no—
135C23—622no—
136C23—1242no—
137C23—1244no—
138C23—1244no—
139C23—1248no—
140C23—1244no—
141C23—1241no—
142C23—1241no—
143C23—1242no—
144C23C2×D12411yescharacteristic
145C23#9249512yes—
146C23D4×D3112yes—
147C23#9249711yescharacteristic
148C23Q8×D3111yescharacteristic
149Q8—2482no—
150C2×C4—22no—
151C2×C4—42no—
152C2×C4—44no—
153C2×C4—42no—
154C2×C4—624no—
155C2×C4—1244no—
156C2×C4—1242no—
157C2×C4—1241no—
158C22—22no—
159C22—24no—
160C22—42no—
161C22—41no—
162C22—41no—
163C22—628no—
164C22—624no—
165C22—1248no—
166C22—1244no—
167C22—1244no—
168C22—1242no—
169C22—1242no—
170C22—1244no—
171C22#1175845211yescharacteristic
172C22#1175845911yescharacteristic
173C22#1175846212yes—
174C22#1175847312yes—
175C22#1175847411yescharacteristic
176C4—42no—
177C4—82no—
178C4—1244no—
179C4—2481no—
180C2—22no—
181C2—21no—
182C2—22no—
183C2—21no—
184C2—1244no—
185C2#1452096211yescharacteristic
186C2#1452123712yes—
subgroupG/H
centerC22#11758459
commutator, cosocleC24×C31C23
FrattiniC24C22×D31
FittingC31×#342C2
socleC22×C31#120
prime radicalC24×D31C22
hypercenter#342D31
hypocenterC31#2029
LCSG ▷ C24×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
1. #14521675C2semidirect
4. #14520815C2semidirect
5. C31×#342C2semidirect
21. C23×D31Q8semidirect
91. #342D31semidirect
108. C31#2029semidirect

Maximal subgroups

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

subgroupindex
#145216752
#145209042
#145208152
C31×#3422
#202931