Finite Group Databasebeta

← #16845189

Subgroups — #16845189

Order 3968.

198 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 51 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#14521425C211yesmaximal, characteristic, complemented
2#14521245C211yesmaximal, characteristic, complemented
3#14521241C211yesmaximal, characteristic, complemented
4#14521126C211yesmaximal, characteristic, complemented
5#14520799C211yesmaximal, characteristic, complemented
6#14520792C211yesmaximal, characteristic, complemented
7C31×#331C211yesmaximal, characteristic, complemented
8C31×#127C2211yescharacteristic
9C2×#92479—21no—
10C2×#92479—21no—
11C2×#92479—21no—
12C2×D248—21no—
13C2×#92469—21no—
14#11758451C2211yescharacteristic
15C4×D124C2211yescharacteristic
16C31×C4⋊C8C2211yescharacteristic
17C31×C4⋊C8C2211yescharacteristic
18#11758420—21no—
19#11758409—21no—
20(C2×D31)⋊C8—21no—
21C4⋊(C31⋊C8)C2211yescharacteristic
22C4×C31⋊C8C2211yescharacteristic
23C2×D4×C31—21no—
24C2×D4×C31—21no—
25C2×D4×C31—21no—
26C2×D124—21no—
27C2×D124—21no—
28C2×D124—21no—
29C2×D124D411yescharacteristic
30C2×C4×D31—21no—
31C2×C8×C31—21no—
32C2×C8×C31—21no—
33C42×C31C2311yescharacteristic
34#92479—42no—
35#92479—42no—
36#92479—42no—
37(C2×D31)⋊C4—21no—
38C4⋊Dic31D411yescharacteristic
39C2×C31⋊C8—21no—
40C2×C31⋊C8D411yescharacteristic
41C2×C31⋊C8D411yescharacteristic
42D248—42no—
43#92469—42no—
44C23×C31—41no—
45C22×D31—21no—
46C22×D31—41no—
47D4×C31—41no—
48D4×C31—41no—
49D4×C31—41no—
50D4×C31—41no—
51D4×C31—81no—
52C2×C4×C31C2×D411yescharacteristic
53C2×C4×C31C2×D411yescharacteristic
54C2×C4×C31#4111yescharacteristic
55C2×Dic31—21no—
56D124—21no—
57D124—21no—
58D124—41no—
59D124—41no—
60D124—41no—
61D124—41no—
62D124—81no—
63C4×D31—41no—
64C4×D31—41no—
65C8×C31—41no—
66C8×C31—41no—
67C31⋊C8—21no—
68C31⋊C8—41no—
69C31⋊C8D812yescomplemented
70#1687—311nomaximal, Sylow
71C22×C31—81no—
72C22×C31—81no—
73C22×C31—81no—
74C22×C31#12111yescharacteristic
75C2×D31—41no—
76C2×D31—41no—
77C2×D31—41no—
78C2×D31—81no—
79C2×D31—81no—
80C2×D31—81no—
81C4×C31—21no—
82C4×C31C2×D811yescharacteristic
83C4×C31AGL(1,ℤ/8)11yescharacteristic
84C4×C31AGL(1,ℤ/8)11yescharacteristic
85C4×C31AGL(1,ℤ/8)11yescharacteristic
86Dic31—41no—
87#493—311no—
88#459—311no—
89#459—311no—
90#436—311no—
91#334—311no—
92#331—311no—
93#331D3111yescharacteristic, complemented
94C2×C31—161no—
95C2×C31#45911yescharacteristic
96C2×C31#46911yescharacteristic
97C2×C31#47211yescharacteristic
98D31—81no—
99D31—161no—
100C2×D8—621no—
101C2×D8—621no—
102C2×D8—621no—
103C2×D8—621no—
104C2×M16—621no—
105#127—311no—
106#127C2×D3111yescharacteristic
107C4×D4—311no—
108C4⋊C8—311no—
109C4⋊C8C2×D3111yescharacteristic
110C4⋊C8C2×D3111yescharacteristic
111#102—621no—
112#102—621no—
113C22⋊C8—621no—
114C4×C8—311no—
115C31#168711yescharacteristic, complemented, Sylow
116C2×D4—21no—
117C2×D4—21no—
118C2×D4—21no—
119C2×D4—311no—
120C2×D4—621no—
121C2×D4—621no—
122C2×D4—621no—
123C22×C4—621no—
124D8—1242no—
125D8—1242no—
126D8—1242no—
127D8—1242no—
128M16—1242no—
129C2×C8—21no—
130C2×C8—21no—
131C2×C8—311no—
132C2×C8—311no—
133C2×C8—621no—
134C4⋊C4—311no—
135C22⋊C4—621no—
136C42C22×D3111yescharacteristic
137C23—41no—
138C23—621no—
139C23—1241no—
140D4—41no—
141D4—41no—
142D4—41no—
143D4—41no—
144D4—81no—
145D4—621no—
146D4—621no—
147D4—1241no—
148D4—1241no—
149D4—1241no—
150D4—1241no—
151D4—2481no—
152C2×C4—621no—
153C2×C4—1241no—
154C2×C4—1241no—
155C2×C4#9249511yescharacteristic
156C2×C4D4×D3111yescharacteristic
157C2×C4D4×D3111yescharacteristic
158C8—41no—
159C8—41no—
160C8—312no—
161C8—621no—
162C8—1241no—
163C22—81no—
164C22—81no—
165C22—81no—
166C22—1241no—
167C22—1241no—
168C22—1241no—
169C22—2481no—
170C22—2481no—
171C22—2481no—
172C22#1175846111yescharacteristic
173C4—21no—
174C4—1241no—
175C4D8×D3111yescharacteristic
176C4#1175848811yescharacteristic
177C4#1175849111yescharacteristic
178C4#1175849111yescharacteristic
179C2—161no—
180C2—4961no—
181C2—2481no—
182C2#1452124311yescharacteristic
183C2#1452130111yescharacteristic
184C2#1452131811yescharacteristic
subgroupG/H
centerC22#11758461
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×#331C2
socleC22×C31#121
hypercenter#331D31
hypocenterC31#1687
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
1. #14521425C2semidirect
2. #14521245C2semidirect
3. #14521241C2semidirect
4. #14521126C2semidirect
5. #14520799C2semidirect
6. #14520792C2semidirect
7. C31×#331C2semidirect
69. C31⋊C8D8semidirect
93. #331D31semidirect
115. C31#1687semidirect

Maximal subgroups

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

subgroupindex
#145214252
#145212452
#145212412
#145211262
#145207992
#145207922
C31×#3312
#168731