Finite Group Databasebeta

← #16845188

Subgroups — #16845188

Order 3968.

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

normal subgroups only

This group has 198 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#14521425C211yesmaximal, characteristic, complemented
2#14521244C211yesmaximal, characteristic, complemented
3#14521127C211yesmaximal, characteristic, complemented
4#14520799C211yesmaximal, characteristic, complemented
5#14520793C211yesmaximal, characteristic, complemented
6#14520792C211yesmaximal, characteristic, complemented
7C31×#459C211yesmaximal, characteristic, complemented
8C2×D8×C31—21no—
9C31×#127C2211yescharacteristic
10C4×D4×C31C2211yescharacteristic
11C2×#92479—21no—
12C2×#92479—21no—
13C2×#92479—21no—
14C2×#92474—21no—
15#11758451C2211yescharacteristic
16C31×C4⋊C8C2211yescharacteristic
17C31×#102—21no—
18C22⋊(C31⋊C8)—21no—
19#11758397—21no—
20C4⋊(C31⋊C8)C2211yescharacteristic
21C4⋊(C31⋊C8)C2211yescharacteristic
22C4×C31⋊C8C2211yescharacteristic
23C2×D4×C31—21no—
24C2×D4×C31—21no—
25C2×D4×C31—21no—
26C2×D4×C31D411yescharacteristic
27C22×C4×C31—21no—
28C2×D124—21no—
29C2×D124—21no—
30C2×D124—21no—
31D8×C31—42no—
32C2×C8×C31—21no—
33C4⋊C4×C31D411yescharacteristic
34C22⋊C4×C31—21no—
35C42×C31C2311yescharacteristic
36#92479—42no—
37#92479—42no—
38#92479—42no—
39#92474—42no—
40C2×C31⋊C8—21no—
41C2×C31⋊C8—21no—
42C2×C31⋊C8D411yescharacteristic
43C2×C31⋊C8D411yescharacteristic
44C23×C31—21no—
45C23×C31—41no—
46C22×D31—41no—
47D4×C31—21no—
48D4×C31—21no—
49D4×C31—41no—
50D4×C31—41no—
51D4×C31—41no—
52D4×C31—41no—
53D4×C31—81no—
54C2×C4×C31—21no—
55C2×C4×C31—41no—
56C2×C4×C31—41no—
57C2×C4×C31C2×D411yescharacteristic
58C2×C4×C31C2×D411yescharacteristic
59C2×C4×C31#4111yescharacteristic
60D124—41no—
61D124—41no—
62D124—41no—
63D124—41no—
64D124—81no—
65C8×C31—41no—
66C31⋊C8—21no—
67C31⋊C8—41no—
68C31⋊C8—41no—
69C31⋊C8D812yescomplemented
70#1687—311nomaximal, Sylow
71C22×C31—41no—
72C22×C31—41no—
73C22×C31—41no—
74C22×C31—81no—
75C22×C31—81no—
76C22×C31—81no—
77C22×C31#12111yescharacteristic
78C2×D31—81no—
79C2×D31—81no—
80C2×D31—81no—
81C4×C31—21no—
82C4×C31—41no—
83C4×C31C2×D811yescharacteristic
84C4×C31AGL(1,ℤ/8)11yescharacteristic
85C4×C31AGL(1,ℤ/8)11yescharacteristic
86C4×C31AGL(1,ℤ/8)11yescharacteristic
87#493—311no—
88#459—311no—
89#459D3111yescharacteristic, complemented
90#436—311no—
91#334—311no—
92#331—311no—
93#331—311no—
94C2×C31—81no—
95C2×C31—161no—
96C2×C31#45911yescharacteristic
97C2×C31#46911yescharacteristic
98C2×C31#47211yescharacteristic
99D31—161no—
100C2×D8—21no—
101C2×D8—621no—
102C2×D8—621no—
103C2×D8—621no—
104C2×M16—621no—
105#127—311no—
106#127C2×D3111yescharacteristic
107C4×D4C2×D3111yescharacteristic
108C4⋊C8—311no—
109C4⋊C8—311no—
110C4⋊C8C2×D3111yescharacteristic
111#102—21no—
112#102—621no—
113C22⋊C8—621no—
114C4×C8—311no—
115C31#168711yescharacteristic, complemented, Sylow
116C2×D4—21no—
117C2×D4—21no—
118C2×D4—21no—
119C2×D4—621no—
120C2×D4—621no—
121C2×D4—621no—
122C2×D4C22⋊D3111yescharacteristic
123C22×C4—21no—
124D8—42no—
125D8—1242no—
126D8—1242no—
127D8—1242no—
128M16—1242no—
129C2×C8—21no—
130C2×C8—311no—
131C2×C8—311no—
132C2×C8—621no—
133C2×C8—621no—
134C4⋊C4C22⋊D3111yescharacteristic
135C22⋊C4—21no—
136C42C22×D3111yescharacteristic
137C23—21no—
138C23—41no—
139C23—1241no—
140D4—21no—
141D4—21no—
142D4—41no—
143D4—41no—
144D4—41no—
145D4—41no—
146D4—81no—
147D4—1241no—
148D4—1241no—
149D4—1241no—
150D4—1241no—
151D4—2481no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4D4×D3111yescharacteristic
156C2×C4#9249711yescharacteristic
157C2×C4C2×C22⋊D3111yescharacteristic
158C8—41no—
159C8—312no—
160C8—621no—
161C8—1241no—
162C8—1241no—
163C22—41no—
164C22—41no—
165C22—41no—
166C22—81no—
167C22—81no—
168C22—81no—
169C22—2481no—
170C22—2481no—
171C22—2481no—
172C22#1175851611yescharacteristic
173C4—21no—
174C4—41no—
175C4D8×D3111yescharacteristic
176C4#1175848811yescharacteristic
177C4#1175850911yescharacteristic
178C4#1175852611yescharacteristic
179C2—81no—
180C2—161no—
181C2—4961no—
182C2#1452124211yescharacteristic
183C2#1452130011yescharacteristic
184C2#1452131711yescharacteristic
subgroupG/H
centerC22#11758516
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×#459C2
socleC22×C31#121
hypercenter#459D31
hypocenterC31#1687
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #14521425C2semidirect
2. #14521244C2semidirect
3. #14521127C2semidirect
4. #14520799C2semidirect
5. #14520793C2semidirect
6. #14520792C2semidirect
7. C31×#459C2semidirect
69. C31⋊C8D8semidirect
89. #459D31semidirect
115. C31#1687semidirect

Maximal subgroups

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

subgroupindex
#145214252
#145212442
#145211272
#145207992
#145207932
#145207922
C31×#4592
#168731