Finite Group Databasebeta

← #16844862

Subgroups — #16844862

Order 3968.

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

normal subgroups only

This group has 234 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#14521401C211yesmaximal, characteristic, complemented
2#14521339C211yesmaximal, characteristic, complemented
3#14521339C211yesmaximal, characteristic, complemented
4#14520795C211yesmaximal, characteristic, complemented
5D4⋊(C31⋊C8)C211yesmaximal, characteristic, complemented
6D4⋊(C31⋊C8)C211yesmaximal, characteristic, complemented
7C31×#547C211yesmaximal, characteristic
8C2×#41×C31—21no—
9C31×C4⋊Q8C2211yescharacteristic
10C31×#123—22no—
11C31×C22⋊Q8—21no—
12C31×#121—21no—
13C4×D4×C31C2211yescharacteristic
14C4×D4×C31C2211yescharacteristic
15C2×C4⋊C4×C31—21no—
16#11758446C2211yescharacteristic
17#11758420—21no—
18#11758420—21no—
19#11758398—22no—
20#11758396—21no—
21#11758396—21no—
22C4⋊(C31⋊C8)C2211yescharacteristic
23C4⋊(C31⋊C8)C2211yescharacteristic
24C4×C31⋊C8C2211yescharacteristic
25#41×C31—42no—
26#41×C31—42no—
27C2×Q8×C31—21no—
28C2×D4×C31—22no—
29C2×D4×C31D411yescharacteristic
30C2×D4×C31D411yescharacteristic
31C22×C4×C31—22no—
32C22×C4×C31—21no—
33C22×C4×C31—21no—
34C2×Dic62—21no—
35C4⋊C4×C31—22no—
36C4⋊C4×C31—21no—
37C4⋊C4×C31D411yescharacteristic
38C4⋊C4×C31D411yescharacteristic
39C4⋊C4×C31D412yes—
40C22⋊C4×C31—22no—
41C22⋊C4×C31—21no—
42C22⋊C4×C31—21no—
43C42×C31C2311yescharacteristic
44C4⋊Dic31—21no—
45C4⋊Dic31—21no—
46C2×C31⋊C8—21no—
47C2×C31⋊C8—21no—
48C2×C31⋊C8—21no—
49C23×C31—21no—
50C23×C31—21no—
51Q8×C31—41no—
52Q8×C31—41no—
53D4×C31—21no—
54D4×C31—21no—
55D4×C31—21no—
56D4×C31—44no—
57D4×C31SD1612yes—
58C2×C4×C31—21no—
59C2×C4×C31—21no—
60C2×C4×C31—22no—
61C2×C4×C31—44no—
62C2×C4×C31—41no—
63C2×C4×C31—41no—
64C2×C4×C31—41no—
65C2×C4×C31—41no—
66C2×C4×C31C2×D411yescharacteristic
67C2×C4×C31C2×D411yescharacteristic
68C2×C4×C31C2×D411yescharacteristic
69C2×Dic31—41no—
70Dic62—42no—
71C31⋊C8—41no—
72C31⋊C8—41no—
73C31⋊C8—41no—
74#1635—311nomaximal, Sylow
75C22×C31—22no—
76C22×C31—41no—
77C22×C31—41no—
78C22×C31—41no—
79C22×C31—41no—
80C22×C31—41no—
81C22×C31#12011yescharacteristic
82C4×C31—21no—
83C4×C31—41no—
84C4×C31—42no—
85C4×C31—41no—
86C4×C31C2×SD1611yescharacteristic
87C4×C31#13511yescharacteristic
88C4×C31AGL(1,ℤ/8)11yescharacteristic
89C4×C31#13711yescharacteristic
90Dic31—81no—
91#547D3111yescharacteristic
92#487—311no—
93#476—311no—
94#476—311no—
95#332—311no—
96D4⋊C8—311no—
97D4⋊C8—311no—
98C2×C31—42no—
99C2×C31—81no—
100C2×C31#45011yescharacteristic
101C2×C31#45211yescharacteristic
102C2×C31#45411yescharacteristic
103C2×#41—21no—
104C4⋊Q8—311no—
105C4⋊Q8C2×D3111yescharacteristic
106#123—22no—
107C22⋊Q8—21no—
108#121—21no—
109C4×D4C2×D3111yescharacteristic
110C4×D4C2×D3111yescharacteristic
111C2×C4⋊C4—21no—
112#106—621no—
113#106—621no—
114C4⋊C8—311no—
115C4⋊C8—311no—
116#103—622no—
117#102—621no—
118#102—621no—
119C4×C8—311no—
120C31#163511yescharacteristic, complemented, Sylow
121#41—42no—
122#41—42no—
123C2×Q8—21no—
124C2×Q8—621no—
125C2×D4—22no—
126C2×D4C22⋊D3111yescharacteristic
127C2×D4C22⋊D3111yescharacteristic
128C22×C4—22no—
129C22×C4—21no—
130C22×C4—21no—
131C2×C8—621no—
132C2×C8—621no—
133C2×C8—621no—
134C4⋊C4—22no—
135C4⋊C4—21no—
136C4⋊C4—621no—
137C4⋊C4—621no—
138C4⋊C4C22⋊D3112yes—
139C4⋊C4C22⋊D3111yescharacteristic
140C4⋊C4C22⋊D3111yescharacteristic
141C22⋊C4—22no—
142C22⋊C4—21no—
143C22⋊C4—21no—
144C42C22×D3111yescharacteristic
145C23—21no—
146C23—21no—
147Q8—41no—
148Q8—41no—
149Q8—1242no—
150D4—21no—
151D4—21no—
152D4—21no—
153D4—44no—
154D4#9248012yes—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—44no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—1241no—
164C2×C4C2×C22⋊D3111yescharacteristic
165C2×C4C2×C22⋊D3111yescharacteristic
166C2×C4C2×C22⋊D3111yescharacteristic
167C8—1241no—
168C8—1241no—
169C8—1241no—
170C22—22no—
171C22—41no—
172C22—41no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22#1175853011yescharacteristic
177C4—21no—
178C4—41no—
179C4—42no—
180C4—41no—
181C4—2481no—
182C4#1175850911yescharacteristic
183C4C2×#9248011yescharacteristic
184C4#1175852711yescharacteristic
185C4#1175852811yescharacteristic
186C2—42no—
187C2—81no—
188C2#1452120011yescharacteristic
189C2#1452121111yescharacteristic
190C2#1452122211yescharacteristic
subgroupG/H
centerC22#11758530
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
Fitting, prime radicalC31×#547C2
socleC22×C31#120
hypercenter#547D31
hypocenterC31#1635
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #14521401C2semidirect
2. #14521339C2semidirect
3. #14521339C2semidirect
4. #14520795C2semidirect
5. D4⋊(C31⋊C8)C2semidirect
6. D4⋊(C31⋊C8)C2semidirect
120. C31#1635semidirect

Maximal subgroups

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

subgroupindex
#145214012
#145213392
#145207952
D4⋊(C31⋊C8)2
C31×#5472
#163531