Finite Group Databasebeta

← #16844823

Subgroups — #16844823

Order 3968.

216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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#14521769C211yesmaximal, characteristic, complemented
2#14521396C211yesmaximal, characteristic, complemented
3#14521250C211yesmaximal, characteristic, complemented
4#14521244C211yesmaximal, characteristic
5#14520794C211yesmaximal, characteristic, complemented
6#14520781C211yesmaximal, characteristic, complemented
7C31×D4⋊C8C211yesmaximal, characteristic, complemented
8C4×D4×C31C2211yescharacteristic
9#11758513—21no—
10C2×#92479—21no—
11#11758503—21no—
12#11758501—21no—
13C2×#92470—21no—
14#11758464—21no—
15#11758456—22no—
16#11758451C2211yescharacteristic
17#11758446C2211yescharacteristic
18C4×Dic62C2211yescharacteristic
19C31×C4⋊C8C2211yescharacteristic
20C4×C8×C31C2211yescharacteristic
21#11758409—22no—
22#11758409—21no—
23#11758397—21no—
24C4⋊(C31⋊C8)C2211yescharacteristic
25C2×D4×C31D411yescharacteristic
26C22×C4×C31—21no—
27C2×D124—21no—
28C2×D124—21no—
29C2×D124—21no—
30C2×Dic62—21no—
31C2×Dic62D411yescharacteristic
32C2×C8×C31—21no—
33C2×C8×C31—21no—
34C4⋊C4×C31D411yescharacteristic
35C22⋊C4×C31—21no—
36C42×C31C2311yescharacteristic
37C22⋊Dic31—22no—
38C22⋊Dic31—22no—
39#92479—42no—
40C4⋊Dic31—21no—
41C4⋊Dic31D411yescharacteristic
42C4⋊Dic31D412yes—
43Dic31⋊C4—22no—
44Dic31⋊C4—21no—
45C4×Dic31—22no—
46C4×Dic31—21no—
47C2×C31⋊C8—21no—
48#92470—42no—
49C23×C31—21no—
50C22×D31—41no—
51D4×C31—21no—
52D4×C31—21no—
53C2×C4×C31—21no—
54C2×C4×C31—41no—
55C2×C4×C31—41no—
56C2×C4×C31C2×D411yescharacteristic
57C2×C4×C31C2×D411yescharacteristic
58C2×C4×C31C2×D411yescharacteristic
59C2×Dic31—21no—
60C2×Dic31—21no—
61C2×Dic31—22no—
62D124—42no—
63D124—41no—
64D124—41no—
65D124—41no—
66D124—41no—
67Dic62—21no—
68Dic62—21no—
69Dic62—41no—
70Dic62—41no—
71C8×C31—41no—
72C8×C31—41no—
73C31⋊C8—41no—
74#1628—311nomaximal, Sylow
75C22×C31—41no—
76C22×C31—41no—
77C22×C31—41no—
78C22×C31#12011yescharacteristic
79C2×D31—81no—
80C2×D31—81no—
81C2×D31—81no—
82C4×C31—21no—
83C4×C31—41no—
84C4×C31#13511yescharacteristic
85C4×C31#13511yescharacteristic
86C4×C31AGL(1,ℤ/8)11yescharacteristic
87C4×C31AGL(1,ℤ/8)11yescharacteristic
88Dic31—41no—
89Dic31—42no—
90Dic31—41no—
91#556—311no—
92#486—311no—
93#460—311no—
94#459—311no—
95#332—311no—
96Q8⋊C8—311no—
97D4⋊C8D3111yescharacteristic, complemented
98C2×C31—81no—
99C2×C31#44911yescharacteristic
100C2×C31#44911yescharacteristic
101C2×C31#45411yescharacteristic
102D31—161no—
103C2×SD16—621no—
104C2×D8—621no—
105C4⋊Q8—311no—
106#127—311no—
107#126—622no—
108#124—621no—
109C22⋊Q8—621no—
110C4×Q8—311no—
111C4×Q8—621no—
112C4×D4C2×D3111yescharacteristic
113#117—621no—
114C4⋊C8—311no—
115C4⋊C8C2×D3111yescharacteristic
116#102—621no—
117#102—622no—
118#102—621no—
119C4×C8C2×D3111yescharacteristic
120C31#162811yescharacteristic, complemented, Sylow
121C2×Q8—311no—
122C2×Q8—621no—
123C2×D4—621no—
124C2×D4—621no—
125C2×D4—621no—
126C2×D4D12411yescharacteristic
127C22×C4—21no—
128SD16—1242no—
129D8—1242no—
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—621no—
133C4⋊C4—311no—
134C4⋊C4—312no—
135C4⋊C4—622no—
136C4⋊C4—621no—
137C4⋊C4—621no—
138C4⋊C4D12411yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—622no—
141C22⋊C4—622no—
142C42—622no—
143C42—621no—
144C42C22×D3111yescharacteristic
145C23—21no—
146C23—1241no—
147Q8—621no—
148Q8—621no—
149Q8—1241no—
150Q8—1241no—
151D4—21no—
152D4—21no—
153D4—1242no—
154D4—1241no—
155D4—1241no—
156D4—1241no—
157D4—1241no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—621no—
162C2×C4—622no—
163C2×C4—621no—
164C2×C4C2×D12411yescharacteristic
165C2×C4D4×D3111yescharacteristic
166C2×C4D4×D3111yescharacteristic
167C8—41no—
168C8—41no—
169C8—1241no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—2481no—
174C22—2481no—
175C22—2481no—
176C22#1175845911yescharacteristic
177C4—21no—
178C4—41no—
179C4—1241no—
180C4—1242no—
181C4—1241no—
182C4#1175848111yescharacteristic
183C4#1175848511yescharacteristic
184C4#1175848811yescharacteristic
185C4#1175849311yescharacteristic
186C2—81no—
187C2—4961no—
188C2#1452119511yescharacteristic
189C2#1452119611yescharacteristic
190C2#1452122311yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×D4⋊C8C2
socleC22×C31#120
prime radical#14521244C2
hypercenterD4⋊C8D31
hypocenterC31#1628
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
1. #14521769C2semidirect
2. #14521396C2semidirect
3. #14521250C2semidirect
5. #14520794C2semidirect
6. #14520781C2semidirect
7. C31×D4⋊C8C2semidirect
97. D4⋊C8D31semidirect
120. C31#1628semidirect

Maximal subgroups

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

subgroupindex
#145217692
#145213962
#145212502
#145212442
#145207942
#145207812
C31×D4⋊C82
#162831