Finite Group Databasebeta

← #16844324

Subgroups — #16844324

Order 3968.

212 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 61 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#14521605C211yesmaximal, characteristic
2#14521104C211yesmaximal, characteristic
3#97×D31C211yesmaximal, characteristic
4#14520791C211yesmaximal, characteristic, complemented
5#14520790C211yesmaximal, characteristic, complemented
6#14520790C211yesmaximal, characteristic, complemented
7C31×#330C211yesmaximal, characteristic, complemented
8C31×#125C2211yescharacteristic
9C2×C8×D31—21no—
10#11758473—21no—
11#11758473—21no—
12#11758469C411yescharacteristic
13#11758469C411yescharacteristic
14#11758465C411yescharacteristic
15#11758465C411yescharacteristic
16#11758464—21no—
17#11758464—21no—
18C42×D31C2211yescharacteristic
19#11758447C2211yescharacteristic
20C31×#97C2211yescharacteristic
21C31×#97C2211yescharacteristic
22(C2×D31)⋊C8—21no—
23#11758403—21no—
24Dic31⋊C8—21no—
25#11758391C2211yescharacteristic
26#11758391C2211yescharacteristic
27C2×C4×D31C2×C411yescharacteristic
28C2×C4×D31D411yescharacteristic
29C2×C4×D31D411yescharacteristic
30C2×Dic62—21no—
31C2×Dic62—21no—
32C2×C8×C31—21no—
33C2×C8×C31—21no—
34C4⋊C4×C31—21no—
35C4⋊C4×C31—21no—
36C4⋊C4×C31C2×C411yescharacteristic
37C4⋊C4×C31C2×C411yescharacteristic
38C42×C31C2311yescharacteristic
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—
48C4×Dic31—21no—
49C4×Dic31C2×C411yescharacteristic
50C4×Dic31D411yescharacteristic
51C4×Dic31D411yescharacteristic
52C2×C31⋊C8—21no—
53C2×C31⋊C8—21no—
54C8×D31—24no—
55C22×D31C22⋊C411yescharacteristic
56C2×C4×C31—21no—
57C2×C4×C31—21no—
58C2×C4×C31C22×C411yescharacteristic
59C2×C4×C31C2×D411yescharacteristic
60C2×C4×C31C2×D411yescharacteristic
61C2×Dic31—21no—
62C2×Dic31—21no—
63C2×Dic31C22⋊C411yescharacteristic
64C2×Dic31C22⋊C411yescharacteristic
65C2×Dic31C22⋊C411yescharacteristic
66C4×D31—22no—
67C4×D31—22no—
68C4×D31—41no—
69Dic62—42no—
70Dic62—42no—
71C8×C31—22no—
72C8×C31—41no—
73C31⋊C8—22no—
74C31⋊C8—41no—
75#1531—311nomaximal, Sylow
76C22×C31C2×C22⋊C411yescharacteristic
77C2×D31—21no—
78C2×D31—21no—
79C2×D31#10112yes—
80C4×C31—21no—
81C4×C31—21no—
82C4×C31—21no—
83C4×C31—41no—
84C4×C31—41no—
85Dic31—21no—
86Dic31—21no—
87Dic31—41no—
88Dic31—41no—
89Dic31#10412yes—
90#533—311no—
91#432—311no—
92C2×#97—311no—
93#330—311no—
94#330—311no—
95#330—311no—
96#330D3111yescharacteristic, complemented
97C2×C31C2×#10111yescharacteristic
98C2×C31C2×#10411yescharacteristic
99C2×C31#42111yescharacteristic
100D31—22no—
101C22×C8—621no—
102C4⋊Q8—311no—
103C4⋊Q8—311no—
104#125—311no—
105#125C2×D3111yescharacteristic
106C22⋊Q8—621no—
107C22⋊Q8—621no—
108C4×Q8—621no—
109C4×Q8—621no—
110#117—311no—
111#117—311no—
112C2×C42—311no—
113C4⋊C8—621no—
114C22⋊C8—621no—
115#97—311no—
116#97—311no—
117#97—621no—
118#97C2×D3111yescharacteristic
119#97C2×D3111yescharacteristic
120C31#153111yescharacteristic, complemented, Sylow
121C2×Q8—621no—
122C2×Q8—621no—
123C22×C4—311no—
124C22×C4—311no—
125C22×C4—311no—
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—624no—
129C2×C8—621no—
130C2×C8—621no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—311no—
134C4⋊C4—311no—
135C4⋊C4—621no—
136C4⋊C4—621no—
137C4⋊C4—621no—
138C4⋊C4—621no—
139C4⋊C4C4×D3111yescharacteristic
140C4⋊C4C4×D3111yescharacteristic
141C22⋊C4—621no—
142C22⋊C4—621no—
143C42—311no—
144C42—311no—
145C42—311no—
146C42—621no—
147C42—621no—
148C42C22×D3111yescharacteristic
149C23—311no—
150Q8—1242no—
151Q8—1242no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—311no—
155C2×C4—311no—
156C2×C4—311no—
157C2×C4—622no—
158C2×C4—622no—
159C2×C4—621no—
160C2×C4—621no—
161C2×C4—1241no—
162C2×C4C2×C4×D3111yescharacteristic
163C2×C4D4×D3111yescharacteristic
164C2×C4D4×D3111yescharacteristic
165C8—22no—
166C8—41no—
167C8—622no—
168C8—1241no—
169C22—312no—
170C22—621no—
171C22—621no—
172C22C22⋊C4×D3111yescharacteristic
173C4—21no—
174C4—21no—
175C4—21no—
176C4—41no—
177C4—41no—
178C4—312no—
179C4—621no—
180C4—621no—
181C4—1241no—
182C4—1241no—
183C2—622no—
184C2#101×D3111yescharacteristic
185C2#104×D3111yescharacteristic
186C2#1452106411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D31
commutatorC2×C4×C31C22×C4
FrattiniC42C22×D31
FittingC31×#330C2
socleC22×C31C2×C22⋊C4
prime radicalC22×D31C22⋊C4
cosocleC42×C31C23
hypercenter#330D31
hypocenterC31#1531
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
4. #14520791C2semidirect
5. #14520790C2semidirect
6. #14520790C2semidirect
7. C31×#330C2semidirect
96. #330D31semidirect
120. C31#1531semidirect

Maximal subgroups

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

subgroupindex
#145216052
#145211042
#97×D312
#145207912
#145207902
C31×#3302
#153131