Finite Group Databasebeta

← #16847381

Subgroups — #16847381

Order 3968.

270 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 55 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#14521612C211yesmaximal, characteristic
2#14521021C212yesmaximal, complemented
3#14520842C211yesmaximal, characteristic, complemented
4#14520841C212yesmaximal, complemented
5C31×#353C211yesmaximal, characteristic, complemented
6C2×#92497C2211yescharacteristic
7C2×D4×D31C411yescharacteristic, complemented
8C31×#127C2211yescharacteristic
9#11758517C2211yescharacteristic
10#11758516—22no—
11#11758514—22no—
12#11758513C411yescharacteristic, complemented
13#11758454—22no—
14#11758452C411yescharacteristic, complemented
15#11758449C411yescharacteristic, complemented
16C31×#99C2212yescomplemented
17#11758422C2212yescomplemented
18#11758394—22no—
19C23×D31—21no—
20C2×D4×C31—22no—
21C2×D4×C31C2×C411yescharacteristic
22C2×D4×C31C2311yescharacteristic
23C2×C22⋊D31—22no—
24C2×C22⋊D31—21no—
25C2×C22⋊D31D412yes—
26C22×Dic31D412yes—
27#92497—42no—
28D4×D31—42no—
29C2×D124C2×C411yescharacteristic
30C2×C4×D31C2×C411yescharacteristic
31C2×Dic62C2×C411yescharacteristic
32C22⋊C4×C31—22no—
33C42×C31C2×C411yescharacteristic
34C22⋊Dic31—22no—
35C22⋊Dic31—22no—
36(C2×D31)⋊C4—21no—
37(C2×D31)⋊C4—22no—
38Dic31⋊C4—21no—
39Dic31⋊C4—42no—
40C4×Dic31—42no—
41C4×Dic31C2×C411yescharacteristic
42C23×C31—21no—
43C23×C31C2×D412yes—
44C22×D31—21no—
45C22×D31—42no—
46C22×D31—82no—
47C22×D31C22⋊C411yescharacteristic
48D4×C31—41no—
49D4×C31—41no—
50D4×C31—82no—
51C2×C4×C31—21no—
52C2×C4×C31—42no—
53C2×C4×C31C22×C411yescharacteristic
54C22⋊D31—42no—
55C22⋊D31—42no—
56C22⋊D31—82no—
57C2×Dic31—22no—
58C2×Dic31—22no—
59C2×Dic31—21no—
60C2×Dic31—42no—
61C2×Dic31C22⋊C412yes—
62C2×Dic31C22⋊C411yescharacteristic
63D124—41no—
64C4×D31—22no—
65Dic62—41no—
66#2128—311nomaximal, Sylow
67C22×C31—22no—
68C22×C31—42no—
69C22×C31—42no—
70C22×C31—41no—
71C22×C31C2×C22⋊C411yescharacteristic
72C2×D31—21no—
73C2×D31—41no—
74C2×D31—42no—
75C2×D31—41no—
76C2×D31—84no—
77C4×C31—21no—
78C4×C31—41no—
79C4×C31—82no—
80Dic31—22no—
81Dic31—41no—
82Dic31—82no—
83Dic31#9912yes—
84#535—311no—
85#410—312no—
86#353—311no—
87#353—312no—
88#353D3111yescharacteristic, complemented
89C2×C31—21no—
90C2×C31—42no—
91C2×C31—81no—
92C2×C31C2×#9911yescharacteristic
93D31—41no—
94D31—81no—
95C2×#41—311no—
96C22×D4—311no—
97#127—311no—
98#127C2×D3111yescharacteristic
99#124—311no—
100#124—311no—
101#121—622no—
102#120—622no—
103#117—311no—
104#117—622no—
105#99—312no—
106#99—622no—
107#99C2×D3112yescomplemented
108C31#212811yescharacteristic, complemented, Sylow
109C24—621no—
110#41—1242no—
111C2×Q8—311no—
112C2×D4—22no—
113C2×D4—312no—
114C2×D4—311no—
115C2×D4—621no—
116C2×D4—622no—
117C2×D4—1242no—
118C2×D4C4×D3111yescharacteristic
119C2×D4C22×D3111yescharacteristic
120C22×C4—312no—
121C22×C4—311no—
122C4⋊C4—621no—
123C4⋊C4—1242no—
124C22⋊C4—22no—
125C22⋊C4—622no—
126C22⋊C4—621no—
127C22⋊C4—622no—
128C22⋊C4—622no—
129C42—311no—
130C42—1242no—
131C42C4×D3111yescharacteristic
132C23—21no—
133C23—311no—
134C23—621no—
135C23—1242no—
136C23—2482no—
137C23D4×D3112yes—
138Q8—1241no—
139D4—41no—
140D4—41no—
141D4—82no—
142D4—1241no—
143D4—1242no—
144D4—1242no—
145D4—2482no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—311no—
149C2×C4—312no—
150C2×C4—622no—
151C2×C4—622no—
152C2×C4—622no—
153C2×C4—621no—
154C2×C4—1242no—
155C2×C4C2×C4×D3111yescharacteristic
156C22—22no—
157C22—42no—
158C22—42no—
159C22—41no—
160C22—621no—
161C22—1241no—
162C22—1242no—
163C22—1241no—
164C22—2484no—
165C22C22⋊C4×D3111yescharacteristic
166C4—21no—
167C4—41no—
168C4—82no—
169C4—312no—
170C4—622no—
171C4—1241no—
172C4—2482no—
173C2—21no—
174C2—42no—
175C2—81no—
176C2—1241no—
177C2—2481no—
178C2#99×D3111yescharacteristic
subgroupG/H
centerC2#99×D31
commutatorC2×C4×C31C22×C4
FrattiniC2×D4C22×D31
FittingC31×#353C2
socleC2×C31C2×#99
prime radical#14521612C2
cosocleC2×D4×C31C23
hypercenter#353D31
hypocenterC31#2128
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #14521021C2semidirect
3. #14520842C2semidirect
4. #14520841C2semidirect
5. C31×#353C2semidirect
7. C2×D4×D31C4semidirect
12. #11758513C4semidirect
14. #11758452C4semidirect
15. #11758449C4semidirect
16. C31×#99C22semidirect
17. #11758422C22semidirect
88. #353D31semidirect
107. #99C2×D31semidirect
108. C31#2128semidirect

Maximal subgroups

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

subgroupindex
#145216122
#145210212
#145208422
#145208412
C31×#3532
#212831