Finite Group Databasebeta

← #16844122

Subgroups — #16844122

Order 3968.

234 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 77 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
2C4×#92474C211yesmaximal, characteristic, complemented
3#14520779C212yesmaximal, complemented
4#14520776C212yesmaximal, complemented
5C2×C31×C4⋊C8C211yesmaximal, characteristic, complemented
6C22×C8×C31—21no—
7C2×C42×C31C2211yescharacteristic
8#11758507C411yescharacteristic
9#11758506—21no—
10C4×C22⋊D31—21no—
11#11758501C411yescharacteristic
12C2×#92474—21no—
13#11758453—21no—
14#11758452C411yescharacteristic
15C4×D124C2211yescharacteristic
16#11758449—21no—
17#11758447C411yescharacteristic
18C4×Dic62C2211yescharacteristic
19C31×C4⋊C8—21no—
20C31×C4⋊C8C2212yes—
21#11758391—21no—
22C4×C31⋊C8C2212yes—
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—22no—
31C2×C8×C31—42no—
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—
48#92474—24no—
49C2×C31⋊C8—22no—
50C23×C31C22⋊C411yescharacteristic
51C22×D31—21no—
52C2×C4×C31—22no—
53C2×C4×C31—22no—
54C2×C4×C31—21no—
55C2×C4×C31—21no—
56C2×C4×C31C22⋊C411yescharacteristic
57C2×C4×C31C22⋊C411yescharacteristic
58C2×C4×C31C22⋊C411yescharacteristic
59C2×C4×C31C22×C411yescharacteristic
60C2×C4×C31C2×D411yescharacteristic
61C2×C4×C31C2×D411yescharacteristic
62C22⋊D31—42no—
63C2×Dic31—21no—
64C2×Dic31—21no—
65C2×Dic31—21no—
66D124—22no—
67C4×D31—41no—
68C4×D31—41no—
69Dic62—22no—
70C8×C31—42no—
71C31⋊C8—24no—
72#1483—311nomaximal, Sylow
73C22×C31—21no—
74C22×C31—21no—
75C22×C31#10412yes—
76C22×C31C2×C22⋊C411yescharacteristic
77C2×D31—41no—
78C2×D31—41no—
79C2×D31—41no—
80C4×C31—21no—
81C4×C31—21no—
82C4×C31—21no—
83C4×C31—21no—
84C4×C31#13112yes—
85C4×C31AGL(1,ℤ/8)11yescharacteristic
86C4×C31#13711yescharacteristic
87Dic31—41no—
88Dic31—41no—
89Dic31—41no—
90#529—311no—
91C2×C4⋊C8D3111yescharacteristic, complemented
92C4×M16—311no—
93Q8⋊C8—312no—
94D4⋊C8—312no—
95C2×C31—22no—
96C2×C31#40811yescharacteristic
97C2×C31#41711yescharacteristic
98C2×C31C2×#10411yescharacteristic
99D31—81no—
100C2×M16—621no—
101C22×C8—21no—
102#126—621no—
103#125—311no—
104#124—311no—
105#123—621no—
106C22⋊Q8—311no—
107#121—311no—
108C4×Q8—311no—
109C4×D4—311no—
110C4×D4—621no—
111#117—621no—
112C2×C42C2×D3111yescharacteristic
113C4⋊C8—21no—
114C4⋊C8C2×D3112yes—
115#97—621no—
116C4×C8—312no—
117C31#148311yescharacteristic, complemented, Sylow
118C2×Q8—311no—
119C2×D4—311no—
120C2×D4—621no—
121C22×C4—621no—
122C22×C4C4×D3111yescharacteristic
123C22×C4D12411yescharacteristic
124C22×C4C22⋊D3111yescharacteristic
125M16—624no—
126C2×C8—22no—
127C2×C8—42no—
128C2×C8—622no—
129C4⋊C4—311no—
130C4⋊C4—311no—
131C4⋊C4—621no—
132C4⋊C4—621no—
133C4⋊C4—621no—
134C4⋊C4—621no—
135C22⋊C4—621no—
136C22⋊C4—621no—
137C22⋊C4—621no—
138C22⋊C4—621no—
139C22⋊C4—621no—
140C42—621no—
141C42C4×D3111yescharacteristic
142C42D12411yescharacteristic
143C42C22⋊D3111yescharacteristic
144C42C22×D3111yescharacteristic
145C23—621no—
146C23(C2×D31)⋊C411yescharacteristic
147Q8—622no—
148D4—622no—
149D4—1242no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—621no—
155C2×C4—621no—
156C2×C4—621no—
157C2×C4—1241no—
158C2×C4—1241no—
159C2×C4(C2×D31)⋊C411yescharacteristic
160C2×C4(C2×D31)⋊C411yescharacteristic
161C2×C4(C2×D31)⋊C411yescharacteristic
162C2×C4C2×C4×D3111yescharacteristic
163C2×C4C2×D12411yescharacteristic
164C2×C4C2×C22⋊D3111yescharacteristic
165C8—42no—
166C8—624no—
167C22—21no—
168C22—21no—
169C22—1241no—
170C22—1241no—
171C22—1241no—
172C22#1175841312yes—
173C22C2×(C2×D31)⋊C411yescharacteristic
174C4—21no—
175C4—21no—
176C4—21no—
177C4—21no—
178C4—1241no—
179C4—1241no—
180C4—1241no—
181C4#1175847812yes—
182C4#1175850911yescharacteristic
183C4#1175851911yescharacteristic
184C2—22no—
185C2—2481no—
186C2#1452101511yescharacteristic
187C2#1452104811yescharacteristic
188C2C2×#1175841311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D31
commutatorC2×C4×C31C22×C4
FrattiniC42C22×D31
FittingC2×C31×C4⋊C8C2
socleC22×C31C2×C22⋊C4
prime radical#11758507C4
cosocleC42×C31C23
hypercenterC2×C4⋊C8D31
hypocenterC31#1483
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C4×#92474C2semidirect
3. #14520779C2semidirect
4. #14520776C2semidirect
5. C2×C31×C4⋊C8C2semidirect
91. C2×C4⋊C8D31semidirect
117. C31#1483semidirect

Maximal subgroups

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

subgroupindex
#145215832
C4×#924742
#145207792
#145207762
C2×C31×C4⋊C82
#148331