Finite Group Databasebeta

← #16844329

Subgroups — #16844329

Order 3968.

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

normal subgroups only

This group has 218 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
1#14521583C211yesmaximal, characteristic
2#14521106C211yesmaximal, characteristic, complemented
3#14520790C212yesmaximal, complemented
4#14520788C212yesmaximal, complemented
5C2×C31×#97C211yesmaximal, characteristic, complemented
6C22×C8×C31—21no—
7C2×C42×C31C2211yescharacteristic
8#11758507C411yescharacteristic
9#11758506—21no—
10C4×C22⋊D31—21no—
11#11758501C411yescharacteristic
12#11758453—21no—
13#11758452C2211yescharacteristic
14C4×D124C411yescharacteristic
15#11758449—21no—
16#11758447C2211yescharacteristic
17C4×Dic62C411yescharacteristic
18C31×#97—21no—
19C31×#97C2212yes—
20C22⋊(C31⋊C8)—21no—
21C4⋊(C31⋊C8)—21no—
22#11758391C2212yes—
23C22×C4×C31C2×C411yescharacteristic
24C22×C4×C31D411yescharacteristic
25C22×C4×C31D411yescharacteristic
26C2×C22⋊D31—21no—
27C2×D124C2×C411yescharacteristic
28C2×C4×D31—21no—
29C2×Dic62C2×C411yescharacteristic
30C2×C8×C31—24no—
31C2×C8×C31—22no—
32C42×C31C2×C411yescharacteristic
33C42×C31D411yescharacteristic
34C42×C31D411yescharacteristic
35C42×C31C2311yescharacteristic
36C22⋊Dic31—21no—
37(C2×D31)⋊C4—21no—
38(C2×D31)⋊C4—21no—
39(C2×D31)⋊C4—21no—
40(C2×D31)⋊C4—21no—
41C4⋊Dic31C2×C411yescharacteristic
42C4⋊Dic31C2×C411yescharacteristic
43Dic31⋊C4—21no—
44Dic31⋊C4—21no—
45Dic31⋊C4—21no—
46Dic31⋊C4—21no—
47C4×Dic31—21no—
48C2×C31⋊C8—22no—
49C23×C31C22⋊C411yescharacteristic
50C22×D31—21no—
51C2×C4×C31—22no—
52C2×C4×C31—41no—
53C2×C4×C31—41no—
54C2×C4×C31C22⋊C411yescharacteristic
55C2×C4×C31C22⋊C411yescharacteristic
56C2×C4×C31C22⋊C411yescharacteristic
57C2×C4×C31C22×C411yescharacteristic
58C2×C4×C31C2×D411yescharacteristic
59C2×C4×C31C2×D411yescharacteristic
60C22⋊D31—42no—
61C2×Dic31—21no—
62C2×Dic31—21no—
63C2×Dic31—21no—
64D124—41no—
65C4×D31—42no—
66Dic62—41no—
67C8×C31—24no—
68C31⋊C8—42no—
69#1532—311nomaximal, Sylow
70C22×C31—21no—
71C22×C31—21no—
72C22×C31#10412yes—
73C22×C31C2×C22⋊C411yescharacteristic
74C2×D31—41no—
75C2×D31—41no—
76C2×D31—41no—
77C4×C31—21no—
78C4×C31—21no—
79C4×C31—21no—
80C4×C31—21no—
81C4×C31—21no—
82C4×C31—21no—
83Dic31—41no—
84Dic31—41no—
85Dic31—41no—
86#529—311no—
87#432—311no—
88C2×#97D3111yescharacteristic, complemented
89#330—312no—
90#329—312no—
91C2×C31—22no—
92C2×C31#41311yescharacteristic
93C2×C31C2×#10411yescharacteristic
94C2×C31#42111yescharacteristic
95D31—81no—
96C22×C8—21no—
97#126—621no—
98#125—311no—
99#124—311no—
100#123—621no—
101C22⋊Q8—311no—
102#121—311no—
103C4×Q8—311no—
104C4×D4—311no—
105C4×D4—621no—
106#117—621no—
107C2×C42C2×D3111yescharacteristic
108C4⋊C8—621no—
109C22⋊C8—621no—
110#97—21no—
111#97—312no—
112#97C2×D3112yes—
113C31#153211yescharacteristic, complemented, Sylow
114C2×Q8—311no—
115C2×D4—311no—
116C2×D4—621no—
117C22×C4—621no—
118C22×C4C4×D3111yescharacteristic
119C22×C4D12411yescharacteristic
120C22×C4C22⋊D3111yescharacteristic
121C2×C8—24no—
122C2×C8—22no—
123C2×C8—622no—
124C4⋊C4—311no—
125C4⋊C4—311no—
126C4⋊C4—621no—
127C4⋊C4—621no—
128C4⋊C4—621no—
129C4⋊C4—621no—
130C22⋊C4—621no—
131C22⋊C4—621no—
132C22⋊C4—621no—
133C22⋊C4—621no—
134C22⋊C4—621no—
135C42—621no—
136C42C4×D3111yescharacteristic
137C42D12411yescharacteristic
138C42C22⋊D3111yescharacteristic
139C42C22×D3111yescharacteristic
140C23—621no—
141C23(C2×D31)⋊C411yescharacteristic
142Q8—1241no—
143D4—1241no—
144D4—1242no—
145C2×C4—22no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—621no—
149C2×C4—621no—
150C2×C4—621no—
151C2×C4—1242no—
152C2×C4(C2×D31)⋊C411yescharacteristic
153C2×C4(C2×D31)⋊C411yescharacteristic
154C2×C4(C2×D31)⋊C411yescharacteristic
155C2×C4C2×C4×D3111yescharacteristic
156C2×C4C2×D12411yescharacteristic
157C2×C4C2×C22⋊D3111yescharacteristic
158C8—24no—
159C8—1242no—
160C22—21no—
161C22—21no—
162C22—1241no—
163C22—1241no—
164C22—1241no—
165C22#1175839312yes—
166C22C2×(C2×D31)⋊C411yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—1241no—
174C4—1241no—
175C4—1241no—
176C2—22no—
177C2—2481no—
178C2#1452103111yescharacteristic
179C2C2×#1175839311yescharacteristic
180C2#1452106511yescharacteristic
subgroupG/H
centerC22C2×(C2×D31)⋊C4
commutatorC2×C4×C31C22×C4
FrattiniC42C22×D31
FittingC2×C31×#97C2
socleC22×C31C2×C22⋊C4
prime radical#11758507C4
cosocleC42×C31C23
hypercenterC2×#97D31
hypocenterC31#1532
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
2. #14521106C2semidirect
3. #14520790C2semidirect
4. #14520788C2semidirect
5. C2×C31×#97C2semidirect
88. C2×#97D31semidirect
113. C31#1532semidirect

Maximal subgroups

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

subgroupindex
#145215832
#145211062
#145207902
#145207882
C2×C31×#972
#153231