Finite Group Databasebeta

← #16844447

Subgroups — #16844447

Order 3968.

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

normal subgroups only

This group has 210 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
1#14521604C211yesmaximal, characteristic
2#14521071C211yesmaximal, characteristic
3#14521071C211yesmaximal, characteristic
4#14520796C211yesmaximal, characteristic, complemented
5#14520795C211yesmaximal, characteristic, complemented
6#14520794C211yesmaximal, characteristic, complemented
7C31×#332C211yesmaximal, characteristic, complemented
8C31×C4⋊Q8C2211yescharacteristic
9#11758523—21no—
10Q8×Dic31—21no—
11C2×#92469—21no—
12C2×#92469—21no—
13#11758474—21no—
14#11758469C412yes—
15#11758467C412yes—
16#11758464—21no—
17C42×D31C2211yescharacteristic
18#11758446C2211yescharacteristic
19C31×C4⋊C8C2211yescharacteristic
20C31×C4⋊C8C2211yescharacteristic
21Dic31⋊C8—21no—
22Dic31⋊C8—21no—
23C4⋊(C31⋊C8)C2211yescharacteristic
24C4⋊(C31⋊C8)C2211yescharacteristic
25C2×Q8×C31—21no—
26C2×C4×D31C2×C411yescharacteristic
27C2×C4×D31D411yescharacteristic
28C2×C4×D31D411yescharacteristic
29C2×Dic62—21no—
30C2×C8×C31—21no—
31C2×C8×C31—21no—
32C4⋊C4×C31—21no—
33C4⋊C4×C31C2×C412yes—
34C42×C31C2311yescharacteristic
35(C2×D31)⋊C4—22no—
36C4⋊Dic31—21no—
37C4⋊Dic31—22no—
38C4⋊Dic31C2×C412yes—
39Dic31⋊C4—22no—
40C4×Dic31—22no—
41C4×Dic31C2×C411yescharacteristic
42C4×Dic31D411yescharacteristic
43C4×Dic31D411yescharacteristic
44C2×C31⋊C8—21no—
45C2×C31⋊C8—21no—
46#92469—42no—
47#92469—42no—
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—21no—
60C4×D31—21no—
61C4×D31—21no—
62C4×D31—21no—
63C4×D31—22no—
64Dic62—41no—
65Dic62—41no—
66C8×C31—41no—
67C8×C31—41no—
68C31⋊C8—41no—
69C31⋊C8—41no—
70#1561—311nomaximal, Sylow
71C22×C31C2×C22⋊C411yescharacteristic
72C2×D31—21no—
73C2×D31—21no—
74C2×D31—21no—
75C4×C31—21no—
76C4×C31—42no—
77C4×C31AGL(1,ℤ/8)11yescharacteristic
78C4×C31AGL(1,ℤ/8)11yescharacteristic
79C4×C31#13711yescharacteristic
80C4×C31#13711yescharacteristic
81Dic31—21no—
82Dic31—21no—
83Dic31—42no—
84Dic31#10112yes—
85#533—311no—
86#423—311no—
87#423—311no—
88#332—311no—
89#332—311no—
90#332—311no—
91#332D3111yescharacteristic, complemented
92C2×C31C2×#10111yescharacteristic
93C2×C31#41711yescharacteristic
94C2×C31#41711yescharacteristic
95D31—41no—
96C2×M16—621no—
97C2×M16—621no—
98C4⋊Q8—311no—
99C4⋊Q8C2×D3111yescharacteristic
100#125—312no—
101C22⋊Q8—621no—
102C22⋊Q8—621no—
103C4×Q8—621no—
104C4×Q8—621no—
105#117—312no—
106C2×C42—311no—
107C4⋊C8—311no—
108C4⋊C8—311no—
109C4⋊C8—621no—
110C4⋊C8—621no—
111C4⋊C8C2×D3111yescharacteristic
112C4⋊C8C2×D3111yescharacteristic
113C31#156111yescharacteristic, complemented, Sylow
114C2×Q8—21no—
115C2×Q8—621no—
116C22×C4—311no—
117C22×C4—311no—
118C22×C4—311no—
119M16—1242no—
120M16—1242no—
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—621no—
124C2×C8—621no—
125C4⋊C4—21no—
126C4⋊C4—312no—
127C4⋊C4—622no—
128C4⋊C4—622no—
129C4⋊C4—621no—
130C4⋊C4C4×D3112yes—
131C22⋊C4—622no—
132C42—311no—
133C42—311no—
134C42—311no—
135C42—622no—
136C42C22×D3111yescharacteristic
137C23—311no—
138Q8—41no—
139Q8—41no—
140Q8—1241no—
141Q8—1241no—
142C2×C4—22no—
143C2×C4—311no—
144C2×C4—311no—
145C2×C4—311no—
146C2×C4—622no—
147C2×C4—621no—
148C2×C4—621no—
149C2×C4—621no—
150C2×C4—621no—
151C2×C4—622no—
152C2×C4C2×C4×D3111yescharacteristic
153C2×C4D4×D3111yescharacteristic
154C2×C4D4×D3111yescharacteristic
155C8—41no—
156C8—41no—
157C8—1241no—
158C8—1241no—
159C22—621no—
160C22—621no—
161C22—621no—
162C22C22⋊C4×D3111yescharacteristic
163C4—21no—
164C4—42no—
165C4—312no—
166C4—621no—
167C4—621no—
168C4—1242no—
169C4#1175848811yescharacteristic
170C4#1175849111yescharacteristic
171C4#1175849211yescharacteristic
172C4#1175849511yescharacteristic
173C2—1241no—
174C2#101×D3111yescharacteristic
175C2#1452104711yescharacteristic
176C2#1452104911yescharacteristic
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#1561
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
91. #332D31semidirect
113. C31#1561semidirect

Maximal subgroups

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

subgroupindex
#145216042
#145210712
#145207962
#145207952
#145207942
C31×#3322
#156131