Finite Group Databasebeta

← #16844820

Subgroups — #16844820

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#14521772C211yesmaximal, characteristic, complemented
2#14521395C211yesmaximal, characteristic, complemented
3#14521241C211yesmaximal, characteristic
4#14520794C211yesmaximal, characteristic, complemented
5Q8⋊(C31⋊C8)C211yesmaximal, characteristic, complemented
6#14520776C211yesmaximal, characteristic, complemented
7C31×#460C211yesmaximal, characteristic, complemented
8C2×SD16×C31—21no—
9C31×#127C2211yescharacteristic
10C4×Q8×C31C2211yescharacteristic
11#11758523—21no—
12C2×#92479—21no—
13#11758475—22no—
14#11758469—21no—
15#11758452—21no—
16C4×D124C2211yescharacteristic
17#11758446C2211yescharacteristic
18C4×Dic62—21no—
19C31×C4⋊C8C2211yescharacteristic
20C31×#102—21no—
21#11758420—22no—
22#11758420—21no—
23C4⋊(C31⋊C8)C2211yescharacteristic
24C4×C31⋊C8C2211yescharacteristic
25C2×Q8×C31D411yescharacteristic
26C2×D4×C31—21no—
27C2×D4×C31—21no—
28C2×D4×C31—21no—
29C2×D124D411yescharacteristic
30C2×C4×D31—21no—
31C2×Dic62—21no—
32SD16×C31—42no—
33C2×C8×C31—21no—
34C4⋊C4×C31—21no—
35C4⋊C4×C31D411yescharacteristic
36C42×C31—21no—
37C42×C31C2311yescharacteristic
38#92479—42no—
39(C2×D31)⋊C4—22no—
40(C2×D31)⋊C4—22no—
41(C2×D31)⋊C4—21no—
42C4⋊Dic31—21no—
43C4⋊Dic31D411yescharacteristic
44C4⋊Dic31D412yes—
45Dic31⋊C4—22no—
46C4×Dic31—22no—
47C2×C31⋊C8—21no—
48C2×C31⋊C8—21no—
49C23×C31—41no—
50C22×D31—21no—
51Q8×C31—21no—
52Q8×C31—21no—
53D4×C31—42no—
54D4×C31—41no—
55D4×C31—41no—
56D4×C31—41no—
57D4×C31—41no—
58C2×C4×C31—21no—
59C2×C4×C31—21no—
60C2×C4×C31C2×D411yescharacteristic
61C2×C4×C31C2×D411yescharacteristic
62C2×C4×C31C2×D411yescharacteristic
63C2×Dic31—21no—
64C2×Dic31—22no—
65D124—21no—
66D124—21no—
67C4×D31—41no—
68C4×D31—41no—
69Dic62—41no—
70Dic62—41no—
71C8×C31—41no—
72C31⋊C8—41no—
73C31⋊C8—41no—
74#1628—311nomaximal, Sylow
75C22×C31—81no—
76C22×C31—81no—
77C22×C31—81no—
78C22×C31#12011yescharacteristic
79C2×D31—41no—
80C2×D31—41no—
81C2×D31—41no—
82C4×C31—21no—
83C4×C31—41no—
84C4×C31—41no—
85C4×C31#13511yescharacteristic
86C4×C31#13511yescharacteristic
87C4×C31AGL(1,ℤ/8)11yescharacteristic
88C4×C31AGL(1,ℤ/8)11yescharacteristic
89Dic31—42no—
90Dic31—41no—
91#556—311no—
92#486—311no—
93#460D3111yescharacteristic, complemented
94#459—311no—
95#332—311no—
96Q8⋊C8—311no—
97D4⋊C8—311no—
98C2×C31—161no—
99C2×C31#44911yescharacteristic
100C2×C31#44911yescharacteristic
101C2×C31#45411yescharacteristic
102D31—81no—
103C2×SD16—21no—
104C2×D8—621no—
105C4⋊Q8—311no—
106#127C2×D3111yescharacteristic
107#126—622no—
108#124—621no—
109C22⋊Q8—621no—
110C4×Q8—621no—
111C4×Q8C2×D3111yescharacteristic
112C4×D4—311no—
113#117—621no—
114C4⋊C8—311no—
115C4⋊C8C2×D3111yescharacteristic
116#102—21no—
117#102—621no—
118#102—622no—
119C4×C8—311no—
120C31#162811yescharacteristic, complemented, Sylow
121C2×Q8—621no—
122C2×Q8C22⋊D3111yescharacteristic
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—311no—
127C22×C4—621no—
128SD16—42no—
129D8—1242no—
130C2×C8—21no—
131C2×C8—621no—
132C2×C8—621no—
133C4⋊C4—21no—
134C4⋊C4—311no—
135C4⋊C4—312no—
136C4⋊C4—622no—
137C4⋊C4—621no—
138C4⋊C4C22⋊D3111yescharacteristic
139C22⋊C4—622no—
140C22⋊C4—622no—
141C22⋊C4—621no—
142C42—21no—
143C42—622no—
144C42C22×D3111yescharacteristic
145C23—41no—
146C23—621no—
147Q8—21no—
148Q8—21no—
149Q8—1241no—
150Q8—1241no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—621no—
157D4—621no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—621no—
161C2×C4—622no—
162C2×C4—1241no—
163C2×C4—1241no—
164C2×C4D4×D3111yescharacteristic
165C2×C4D4×D3111yescharacteristic
166C2×C4C2×C22⋊D3111yescharacteristic
167C8—41no—
168C8—1241no—
169C8—1241no—
170C22—81no—
171C22—81no—
172C22—81no—
173C22—1241no—
174C22—1241no—
175C22—1241no—
176C22#1175851411yescharacteristic
177C4—21no—
178C4—41no—
179C4—41no—
180C4—1241no—
181C4—1242no—
182C4#1175849111yescharacteristic
183C4#1175849311yescharacteristic
184C4#1175850911yescharacteristic
185C4#1175852711yescharacteristic
186C2—161no—
187C2—2481no—
188C2#1452119211yescharacteristic
189C2#1452119311yescharacteristic
190C2#1452122011yescharacteristic
subgroupG/H
centerC22#11758514
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×#460C2
socleC22×C31#120
prime radical#14521241C2
hypercenter#460D31
hypocenterC31#1628
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #14521772C2semidirect
2. #14521395C2semidirect
4. #14520794C2semidirect
5. Q8⋊(C31⋊C8)C2semidirect
6. #14520776C2semidirect
7. C31×#460C2semidirect
93. #460D31semidirect
120. C31#1628semidirect

Maximal subgroups

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

subgroupindex
#145217722
#145213952
#145212412
#145207942
Q8⋊(C31⋊C8)2
#145207762
C31×#4602
#162831