Finite Group Databasebeta

← #16844957

Subgroups — #16844957

Order 3968.

234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 57 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#14521714C211yesmaximal, characteristic
2#14521326C211yesmaximal, characteristic
3#14521256C211yesmaximal, characteristic, complemented
4#14520795C211yesmaximal, characteristic, complemented
5#14520781C211yesmaximal, characteristic, complemented
6#14520778C211yesmaximal, characteristic
7C31×#500C211yesmaximal, characteristic, complemented
8C2×Q8×D31—21no—
9C31×C4⋊Q8C2211yescharacteristic
10C31×C4⋊Q8C2211yescharacteristic
11#11758523—21no—
12C2×#92482—21no—
13#11758473—22no—
14#11758470—21no—
15#11758465—21no—
16C4×D124C2211yescharacteristic
17C4×Dic62C2211yescharacteristic
18C31×#107—22no—
19C4×C8×C31C2211yescharacteristic
20#11758423—21no—
21#11758397—21no—
22#11758395—21no—
23C4⋊(C31⋊C8)C2211yescharacteristic
24C4⋊(C31⋊C8)C2211yescharacteristic
25C2×Q8×C31—21no—
26C2×Q8×C31—21no—
27Q8×D31—42no—
28Q8×D31—42no—
29C2×D124D411yescharacteristic
30C2×C4×D31—22no—
31C2×C4×D31—21no—
32C2×Dic62—22no—
33C2×Dic62D411yescharacteristic
34C2×C8×C31—21no—
35C4⋊C4×C31—21no—
36C4⋊C4×C31—21no—
37C4⋊C4×C31—21no—
38C4⋊C4×C31D412yes—
39C42×C31C2311yescharacteristic
40#92482—42no—
41(C2×D31)⋊C4—22no—
42(C2×D31)⋊C4—21no—
43C4⋊Dic31D411yescharacteristic
44C4⋊Dic31D411yescharacteristic
45Dic31⋊C4—22no—
46Dic31⋊C4—21no—
47C4×Dic31—21no—
48C2×C31⋊C8—21no—
49C2×C31⋊C8—21no—
50C22×D31—21no—
51Q8×C31—41no—
52Q8×C31—41no—
53Q8×C31—41no—
54Q8×C31—41no—
55C2×C4×C31—22no—
56C2×C4×C31—41no—
57C2×C4×C31C2×D411yescharacteristic
58C2×C4×C31C2×D411yescharacteristic
59C2×C4×C31C2×D411yescharacteristic
60C2×Dic31—21no—
61C2×Dic31—21no—
62C2×Dic31—21no—
63D124—21no—
64D124Q1612yescomplemented
65C4×D31—44no—
66C4×D31—41no—
67C4×D31—41no—
68Dic62—21no—
69Dic62—44no—
70Dic62D812yes—
71C8×C31—22no—
72C31⋊C8—41no—
73C31⋊C8—41no—
74#1649—311nomaximal, Sylow
75C22×C31#12011yescharacteristic
76C2×D31—22no—
77C2×D31—41no—
78C2×D31—41no—
79C4×C31—21no—
80C4×C31—42no—
81C4×C31—81no—
82C4×C31C2×D811yescharacteristic
83C4×C31C2×Q1611yescharacteristic
84C4×C31AGL(1,ℤ/8)11yescharacteristic
85C4×C31#13711yescharacteristic
86Dic31—22no—
87Dic31—41no—
88Dic31—41no—
89D4×Q8—311no—
90#500D3111yescharacteristic, complemented
91#474—311no—
92#462—311no—
93#332—311no—
94Q8⋊C8—311no—
95D4⋊C8—311no—
96C2×C31#44711yescharacteristic
97C2×C31#45111yescharacteristic
98C2×C31#45611yescharacteristic
99D31—42no—
100C22×Q8—621no—
101C2×Q16—621no—
102C4⋊Q8—621no—
103C4⋊Q8C2×D3111yescharacteristic
104C4⋊Q8C2×D3111yescharacteristic
105C22⋊Q8—621no—
106C22⋊Q8—622no—
107C4×Q8—311no—
108C4×D4—311no—
109C4×D4—621no—
110#107—22no—
111#107—621no—
112C4⋊C8—311no—
113C4⋊C8—311no—
114#103—621no—
115#102—621no—
116C4×C8C2×D3111yescharacteristic
117C31#164911yescharacteristic, complemented, Sylow
118C2×Q8—21no—
119C2×Q8—21no—
120C2×Q8—311no—
121C2×Q8—622no—
122C2×Q8—1242no—
123C2×Q8—1242no—
124C2×D4—311no—
125C22×C4—622no—
126C22×C4—621no—
127Q16—1242no—
128C2×C8—21no—
129C2×C8—621no—
130C2×C8—621no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—311no—
135C4⋊C4—311no—
136C4⋊C4—622no—
137C4⋊C4—621no—
138C4⋊C4C22⋊D3112yes—
139C22⋊C4—622no—
140C22⋊C4—621no—
141C42—621no—
142C42C22×D3111yescharacteristic
143C23—621no—
144Q8—41no—
145Q8—41no—
146Q8—41no—
147Q8—41no—
148Q8—312no—
149Q8—621no—
150Q8—1244no—
151D4—312no—
152D4—621no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—621no—
156C2×C4—621no—
157C2×C4—621no—
158C2×C4—1244no—
159C2×C4—1241no—
160C2×C4—1241no—
161C2×C4D4×D3111yescharacteristic
162C2×C4D4×D3111yescharacteristic
163C2×C4C2×C22⋊D3111yescharacteristic
164C8—22no—
165C8—1241no—
166C8—1241no—
167C22—622no—
168C22—1241no—
169C22—1241no—
170C22#1175851411yescharacteristic
171C4—21no—
172C4—42no—
173C4—81no—
174C4—622no—
175C4—1241no—
176C4—1241no—
177C4D8×D3111yescharacteristic
178C4#1175848811yescharacteristic
179C4Q16×D3111yescharacteristic
180C4#1175849511yescharacteristic
181C2—1242no—
182C2#1452118111yescharacteristic
183C2#1452120311yescharacteristic
184C2#1452123111yescharacteristic
subgroupG/H
centerC22#11758514
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×#500C2
socleC22×C31#120
prime radicalC2×D124D4
hypercenter#500D31
hypocenterC31#1649
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
3. #14521256C2semidirect
4. #14520795C2semidirect
5. #14520781C2semidirect
7. C31×#500C2semidirect
64. D124Q16semidirect
90. #500D31semidirect
117. C31#1649semidirect

Maximal subgroups

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

subgroupindex
#145217142
#145213262
#145212562
#145207952
#145207812
#145207782
C31×#5002
#164931