Finite Group Databasebeta

← #16844078

Subgroups — #16844078

Order 3968.

214 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 69 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×#11758453C211yesmaximal, characteristic
2#14521106C211yesmaximal, characteristic, complemented
3#14520774C212yesmaximal, complemented
4#14520772C212yesmaximal
5C31×#431C211yesmaximal, characteristic, complemented
6C2×C42×C31C2211yescharacteristic
7C2×(C2×D31)⋊C4C411yescharacteristic
8C2×(C2×D31)⋊C4C411yescharacteristic
9C2×(C2×D31)⋊C4C2211yescharacteristic
10C2×Dic31⋊C4C411yescharacteristic
11C2×Dic31⋊C4C411yescharacteristic
12C2×Dic31⋊C4C2211yescharacteristic
13#11758453—21no—
14#11758453—21no—
15#11758453—21no—
16#11758453—21no—
17C31×C4⋊C8—21no—
18C31×C22⋊C8C2212yes—
19C4×C8×C31—21no—
20C22⋊(C31⋊C8)C2212yes—
21C4⋊(C31⋊C8)—21no—
22#11758391—21no—
23C23×D31C2×C411yescharacteristic
24C22×C4×C31C2×C411yescharacteristic
25C22×C4×C31C2×C411yescharacteristic
26C22×C4×C31C2311yescharacteristic
27C22×Dic31C2×C411yescharacteristic
28C22×Dic31C2×C411yescharacteristic
29C22×Dic31C2×C411yescharacteristic
30C2×C8×C31—22no—
31C42×C31D411yescharacteristic
32C42×C31D411yescharacteristic
33C42×C31D411yescharacteristic
34C42×C31D411yescharacteristic
35(C2×D31)⋊C4—21no—
36(C2×D31)⋊C4—21no—
37(C2×D31)⋊C4—21no—
38(C2×D31)⋊C4—21no—
39(C2×D31)⋊C4—21no—
40(C2×D31)⋊C4—21no—
41Dic31⋊C4—21no—
42Dic31⋊C4—21no—
43Dic31⋊C4—21no—
44Dic31⋊C4—21no—
45Dic31⋊C4—21no—
46Dic31⋊C4—21no—
47C2×C31⋊C8—22no—
48C23×C31C22×C411yescharacteristic
49C22×D31—21no—
50C22×D31—22no—
51C22×D31—41no—
52C22×D31—41no—
53C2×C4×C31—22no—
54C2×C4×C31—41no—
55C2×C4×C31—41no—
56C2×C4×C31C22⋊C411yescharacteristic
57C2×C4×C31C22⋊C411yescharacteristic
58C2×C4×C31C22⋊C411yescharacteristic
59C2×C4×C31C22⋊C411yescharacteristic
60C2×C4×C31C2×D411yescharacteristic
61C2×C4×C31C2×D411yescharacteristic
62C2×Dic31—21no—
63C2×Dic31—21no—
64C2×Dic31—21no—
65C2×Dic31—22no—
66C2×Dic31—41no—
67C2×Dic31—41no—
68C8×C31—42no—
69C31⋊C8—42no—
70#1473—311nomaximal, Sylow
71C22×C31—21no—
72C22×C31—21no—
73C22×C31C2×C22⋊C411yescharacteristic
74C22×C31#13112yes—
75C2×D31—41no—
76C2×D31—41no—
77C2×D31—41no—
78C2×D31—82no—
79C4×C31—21no—
80C4×C31—21no—
81C4×C31—21no—
82C4×C31—21no—
83C4×C31—21no—
84C4×C31—21no—
85Dic31—41no—
86Dic31—41no—
87Dic31—41no—
88C2×#126—311no—
89#432—311no—
90#431D3111yescharacteristic, complemented
91#324—312no—
92#323—312no—
93C2×C31—22no—
94C2×C31#40811yescharacteristic
95C2×C31#41011yescharacteristic
96C2×C31#41311yescharacteristic
97D31—81no—
98#126—621no—
99#126—621no—
100#126—621no—
101#126—621no—
102C2×C4⋊C4—311no—
103C2×C4⋊C4—311no—
104C2×C4⋊C4—311no—
105C2×C22⋊C4—311no—
106C2×C22⋊C4—311no—
107C2×C22⋊C4—311no—
108C2×C42C2×D3111yescharacteristic
109C4⋊C8—21no—
110C4⋊C8—621no—
111C22⋊C8—312no—
112C22⋊C8C2×D3112yes—
113#97—621no—
114C4×C8—21no—
115C31#147311yescharacteristic, complemented, Sylow
116C24—311no—
117C22×C4—311no—
118C22×C4—311no—
119C22×C4—311no—
120C22×C4C4×D3111yescharacteristic
121C22×C4C4×D3111yescharacteristic
122C22×C4C22×D3111yescharacteristic
123C2×C8—22no—
124C2×C8—622no—
125C4⋊C4—621no—
126C4⋊C4—621no—
127C4⋊C4—621no—
128C4⋊C4—621no—
129C4⋊C4—621no—
130C4⋊C4—621no—
131C22⋊C4—621no—
132C22⋊C4—621no—
133C22⋊C4—621no—
134C22⋊C4—621no—
135C22⋊C4—621no—
136C22⋊C4—621no—
137C42D12411yescharacteristic
138C42D12411yescharacteristic
139C42C22⋊D3111yescharacteristic
140C42C22⋊D3111yescharacteristic
141C23—621no—
142C23—622no—
143C23—1241no—
144C23—1241no—
145C23C2×C4×D3111yescharacteristic
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—622no—
150C2×C4—621no—
151C2×C4—621no—
152C2×C4—621no—
153C2×C4—1241no—
154C2×C4—1241no—
155C2×C4(C2×D31)⋊C411yescharacteristic
156C2×C4(C2×D31)⋊C411yescharacteristic
157C2×C4(C2×D31)⋊C411yescharacteristic
158C2×C4(C2×D31)⋊C411yescharacteristic
159C2×C4C2×D12411yescharacteristic
160C2×C4C2×C22⋊D3111yescharacteristic
161C8—42no—
162C8—1242no—
163C22—21no—
164C22—21no—
165C22—1241no—
166C22—1241no—
167C22—1241no—
168C22—2482no—
169C22#1175847812yes—
170C22C2×(C2×D31)⋊C411yescharacteristic
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—1241no—
178C4—1241no—
179C4—1241no—
180C2—22no—
181C2—2481no—
182C2#1452101511yescharacteristic
183C2#1452102211yescharacteristic
184C2#1452103111yescharacteristic
subgroupG/H
centerC22C2×(C2×D31)⋊C4
commutatorC23×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#431C2
socleC22×C31C2×C22⋊C4
prime radicalC23×D31C2×C4
cosocleC22×C4×C31C23
hypercenter#431D31
hypocenterC31#1473
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #14521106C2semidirect
3. #14520774C2semidirect
5. C31×#431C2semidirect
90. #431D31semidirect
115. C31#1473semidirect

Maximal subgroups

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

subgroupindex
C2×#117584532
#145211062
#145207742
#145207722
C31×#4312
#147331