Finite Group Databasebeta

← #16844426

Subgroups — #16844426

Order 3968.

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

normal subgroups only

This group has 228 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
1C4⋊Q8×D31C211yesmaximal, characteristic
2#14521105C211yesmaximal, characteristic
3#14521105C211yesmaximal, characteristic
4#14520796C211yesmaximal, characteristic, complemented
5#14520795C211yesmaximal, characteristic, complemented
6#14520794C211yesmaximal, characteristic, complemented
7C31×#332C211yesmaximal, characteristic, complemented
8C2×Q8×D31—21no—
9C31×C4⋊Q8C2211yescharacteristic
10#11758521—21no—
11C4⋊C4×D31—21no—
12C4⋊C4×D31C412yes—
13#11758465—21no—
14#11758465C412yes—
15C42×D31C2211yescharacteristic
16#11758446C2211yescharacteristic
17C31×C4⋊C8C2211yescharacteristic
18C31×C4⋊C8C2211yescharacteristic
19(C2×D31)⋊C8—21no—
20(C2×D31)⋊C8—21no—
21#11758403—21no—
22#11758403—21no—
23C4⋊(C31⋊C8)C2211yescharacteristic
24C4⋊(C31⋊C8)C2211yescharacteristic
25C2×Q8×C31—21no—
26Q8×D31—42no—
27Q8×D31—42no—
28C2×C4×D31—22no—
29C2×C4×D31C2×C411yescharacteristic
30C2×C4×D31D411yescharacteristic
31C2×C4×D31D411yescharacteristic
32C2×Dic62—21no—
33C2×Dic62—22no—
34C2×C8×C31—21no—
35C2×C8×C31—21no—
36C4⋊C4×C31—21no—
37C4⋊C4×C31C2×C412yes—
38C42×C31C2311yescharacteristic
39C4⋊Dic31—21no—
40C4⋊Dic31C2×C412yes—
41Dic31⋊C4—22no—
42Dic31⋊C4—22no—
43C4×Dic31C2×C411yescharacteristic
44C4×Dic31D411yescharacteristic
45C4×Dic31D411yescharacteristic
46C2×C31⋊C8—21no—
47C2×C31⋊C8—21no—
48C22×D31C22⋊C411yescharacteristic
49Q8×C31—41no—
50Q8×C31—41no—
51C2×C4×C31—22no—
52C2×C4×C31C22×C411yescharacteristic
53C2×C4×C31C2×D411yescharacteristic
54C2×C4×C31C2×D411yescharacteristic
55C2×Dic31—22no—
56C2×Dic31C22⋊C411yescharacteristic
57C2×Dic31C22⋊C411yescharacteristic
58C2×Dic31C22⋊C411yescharacteristic
59C4×D31—22no—
60C4×D31—21no—
61C4×D31—21no—
62C4×D31—21no—
63C4×D31—21no—
64C4×D31—44no—
65Dic62—44no—
66Dic62—41no—
67Dic62—41no—
68C8×C31—41no—
69C8×C31—41no—
70C31⋊C8—41no—
71C31⋊C8—41no—
72#1556—311nomaximal, Sylow
73C22×C31C2×C22⋊C411yescharacteristic
74C2×D31—21no—
75C2×D31—21no—
76C2×D31#10112yes—
77C4×C31—21no—
78C4×C31—42no—
79C4×C31AGL(1,ℤ/8)11yescharacteristic
80C4×C31AGL(1,ℤ/8)11yescharacteristic
81C4×C31#13711yescharacteristic
82C4×C31#13711yescharacteristic
83Dic31—21no—
84Dic31—21no—
85Dic31—21no—
86Dic31—42no—
87C2×C4⋊Q8—311no—
88#432—311no—
89#432—311no—
90#332—311no—
91#332—311no—
92#332—311no—
93#332D3111yescharacteristic, complemented
94C2×C31C2×#10111yescharacteristic
95C2×C31#41811yescharacteristic
96C2×C31#41911yescharacteristic
97D31—22no—
98C22×Q8—621no—
99C4⋊Q8—312no—
100C4⋊Q8—311no—
101C4⋊Q8—621no—
102C4⋊Q8—621no—
103C4⋊Q8C2×D3111yescharacteristic
104C2×C4⋊C4—312no—
105C2×C4⋊C4—621no—
106C2×C42—311no—
107C4⋊C8—311no—
108C4⋊C8—311no—
109C4⋊C8C2×D3111yescharacteristic
110C4⋊C8C2×D3111yescharacteristic
111C22⋊C8—621no—
112C22⋊C8—621no—
113#97—621no—
114#97—621no—
115C31#155611yescharacteristic, complemented, Sylow
116C2×Q8—21no—
117C2×Q8—622no—
118C2×Q8—621no—
119C2×Q8—1242no—
120C2×Q8—1242no—
121C22×C4—311no—
122C22×C4—311no—
123C22×C4—311no—
124C22×C4—622no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—621no—
128C2×C8—621no—
129C4⋊C4—21no—
130C4⋊C4—312no—
131C4⋊C4—622no—
132C4⋊C4—622no—
133C4⋊C4—621no—
134C4⋊C4C4×D3112yes—
135C42—311no—
136C42—311no—
137C42—311no—
138C42C22×D3111yescharacteristic
139C23—311no—
140Q8—41no—
141Q8—41no—
142Q8—1244no—
143Q8—1241no—
144Q8—1241no—
145C2×C4—22no—
146C2×C4—311no—
147C2×C4—311no—
148C2×C4—311no—
149C2×C4—622no—
150C2×C4—621no—
151C2×C4—621no—
152C2×C4—621no—
153C2×C4—621no—
154C2×C4—622no—
155C2×C4—1244no—
156C2×C4C2×C4×D3111yescharacteristic
157C2×C4D4×D3111yescharacteristic
158C2×C4D4×D3111yescharacteristic
159C8—41no—
160C8—41no—
161C8—1241no—
162C8—1241no—
163C22—312no—
164C22—621no—
165C22—621no—
166C22C22⋊C4×D3111yescharacteristic
167C4—21no—
168C4—42no—
169C4—621no—
170C4—621no—
171C4—621no—
172C4—1242no—
173C4#1175848811yescharacteristic
174C4#1175849111yescharacteristic
175C4#1175849211yescharacteristic
176C4#1175849511yescharacteristic
177C2—622no—
178C2#101×D3111yescharacteristic
179C2#1452105211yescharacteristic
180C2#1452105611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D31
commutatorC2×C4×C31C22×C4
FrattiniC42C22×D31
FittingC31×#332C2
socleC22×C31C2×C22⋊C4
prime radicalC22×D31C22⋊C4
cosocleC42×C31C23
hypercenter#332D31
hypocenterC31#1556
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
4. #14520796C2semidirect
5. #14520795C2semidirect
6. #14520794C2semidirect
7. C31×#332C2semidirect
93. #332D31semidirect
115. C31#1556semidirect

Maximal subgroups

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

subgroupindex
C4⋊Q8×D312
#145211052
#145207962
#145207952
#145207942
C31×#3322
#155631