Finite Group Databasebeta

← #16844879

Subgroups — #16844879

Order 3968.

228 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×Dic62C211yesmaximal, characteristic
2#14521400C211yesmaximal, characteristic, complemented
3#14521345C211yesmaximal, characteristic, complemented
4#14521339C211yesmaximal, characteristic
5#14520796C211yesmaximal, characteristic, complemented
6#14520781C211yesmaximal, characteristic, complemented
7C31×D4⋊C8C211yesmaximal, characteristic
8C22×Dic62—21no—
9C4×D4×C31C2211yescharacteristic
10D4×Dic31—21no—
11#11758501—21no—
12#11758465—21no—
13#11758455—22no—
14#11758446C2211yescharacteristic
15#11758446C2211yescharacteristic
16C4×Dic62C2211yescharacteristic
17C31×C4⋊C8C2211yescharacteristic
18C4×C8×C31C2211yescharacteristic
19#11758420—21no—
20#11758406—21no—
21#11758404—21no—
22#11758404—22no—
23#11758396—21no—
24C4⋊(C31⋊C8)C2211yescharacteristic
25C2×D4×C31D411yescharacteristic
26C22×C4×C31—21no—
27C22×Dic31—22no—
28C2×Dic62—22no—
29C2×Dic62—21no—
30C2×Dic62—21no—
31C2×Dic62—42no—
32C2×Dic62—42no—
33C2×Dic62D411yescharacteristic
34C2×C8×C31—21no—
35C2×C8×C31—21no—
36C4⋊C4×C31D411yescharacteristic
37C22⋊C4×C31—21no—
38C42×C31C2311yescharacteristic
39C22⋊Dic31—22no—
40C4⋊Dic31—21no—
41C4⋊Dic31—21no—
42C4⋊Dic31—21no—
43C4⋊Dic31D412yes—
44C4⋊Dic31D411yescharacteristic
45Dic31⋊C4—22no—
46Dic31⋊C4—21no—
47C4×Dic31—21no—
48C2×C31⋊C8—21no—
49C23×C31—21no—
50D4×C31—21no—
51D4×C31Q1612yes—
52C2×C4×C31—21no—
53C2×C4×C31—41no—
54C2×C4×C31—41no—
55C2×C4×C31C2×D411yescharacteristic
56C2×C4×C31C2×D411yescharacteristic
57C2×C4×C31C2×D411yescharacteristic
58C2×Dic31—21no—
59C2×Dic31—21no—
60C2×Dic31—22no—
61C2×Dic31—44no—
62C2×Dic31—41no—
63Dic62—21no—
64Dic62—44no—
65Dic62—41no—
66Dic62—41no—
67Dic62—42no—
68Dic62SD1612yes—
69C8×C31—41no—
70C8×C31—41no—
71C31⋊C8—41no—
72#1637—311nomaximal, Sylow
73C22×C31—22no—
74C22×C31—41no—
75C22×C31—41no—
76C22×C31#12011yescharacteristic
77C4×C31—21no—
78C4×C31—41no—
79C4×C31C2×SD1611yescharacteristic
80C4×C31C2×Q1611yescharacteristic
81C4×C31AGL(1,ℤ/8)11yescharacteristic
82C4×C31#13711yescharacteristic
83Dic31—22no—
84Dic31—42no—
85Dic31—41no—
86Dic31—81no—
87D4×Q8—311no—
88#487—311no—
89#477—311no—
90#476—311no—
91#332—311no—
92Q8⋊C8—311no—
93D4⋊C8D3111yescharacteristic
94C2×C31—42no—
95C2×C31#45011yescharacteristic
96C2×C31#45111yescharacteristic
97C2×C31#45411yescharacteristic
98C22×Q8—621no—
99C4⋊Q8—311no—
100C4⋊Q8—311no—
101C4⋊Q8—621no—
102C22⋊Q8—622no—
103C22⋊Q8—621no—
104C4×Q8—311no—
105C4×D4—621no—
106C4×D4C2×D3111yescharacteristic
107#107—621no—
108#106—621no—
109C4⋊C8—311no—
110C4⋊C8C2×D3111yescharacteristic
111#103—622no—
112#103—621no—
113#102—621no—
114C4×C8C2×D3111yescharacteristic
115C31#163711yescharacteristic, complemented, Sylow
116C2×Q8—311no—
117C2×Q8—622no—
118C2×Q8—621no—
119C2×Q8—621no—
120C2×Q8—1242no—
121C2×Q8—1242no—
122C2×D4D12411yescharacteristic
123C22×C4—21no—
124C22×C4—622no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—621no—
128C4⋊C4—312no—
129C4⋊C4—311no—
130C4⋊C4—622no—
131C4⋊C4—621no—
132C4⋊C4—621no—
133C4⋊C4—621no—
134C4⋊C4—621no—
135C4⋊C4D12411yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—622no—
138C42—621no—
139C42C22×D3111yescharacteristic
140C23—21no—
141Q8—312no—
142Q8—621no—
143Q8—1242no—
144Q8—1244no—
145Q8—1241no—
146Q8—1241no—
147D4—21no—
148D4Dic12412yes—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—621no—
153C2×C4—621no—
154C2×C4—622no—
155C2×C4—1244no—
156C2×C4—1241no—
157C2×C4C2×D12411yescharacteristic
158C2×C4D4×D3111yescharacteristic
159C2×C4D4×D3111yescharacteristic
160C8—41no—
161C8—41no—
162C8—1241no—
163C22—22no—
164C22—41no—
165C22—41no—
166C22#1175845911yescharacteristic
167C4—21no—
168C4—41no—
169C4—622no—
170C4—1242no—
171C4—1241no—
172C4—2481no—
173C4C2×Dic12411yescharacteristic
174C4#1175848611yescharacteristic
175C4#1175848811yescharacteristic
176C4SD16×D3111yescharacteristic
177C2—42no—
178C2#1452120111yescharacteristic
179C2#1452120711yescharacteristic
180C2#1452122311yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×D4⋊C8C2
socleC22×C31#120
prime radicalC2×D4×C31D4
hypercenterD4⋊C8D31
hypocenterC31#1637
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #14521400C2semidirect
3. #14521345C2semidirect
5. #14520796C2semidirect
6. #14520781C2semidirect
115. C31#1637semidirect

Maximal subgroups

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

subgroupindex
D4×Dic622
#145214002
#145213452
#145213392
#145207962
#145207812
C31×D4⋊C82
#163731