Finite Group Databasebeta

← #16847401

Subgroups — #16847401

Order 3968.

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

normal subgroups only

This group has 262 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#14521617C211yesmaximal, characteristic
2#14521032C212yesmaximal, complemented
3#14520846C211yesmaximal, characteristic, complemented
4#14520845C212yesmaximal, complemented
5C31×#355C211yesmaximal, characteristic, complemented
6C2×#92499C2211yescharacteristic
7C2×D4×D31C411yescharacteristic
8C31×#124C2211yescharacteristic
9#11758524C2211yescharacteristic
10#11758517C411yescharacteristic
11M16×D31—22no—
12#11758461—22no—
13#11758459—22no—
14#11758451C411yescharacteristic
15#11758449C411yescharacteristic
16C31×#101C2212yescomplemented
17#11758424C2212yescomplemented
18#11758411—22no—
19C23×D31—21no—
20C2×Q8×C31C2311yescharacteristic
21C2×D4×C31C2×C411yescharacteristic
22C2×C22⋊D31—22no—
23C2×C22⋊D31—21no—
24#92499—42no—
25D4×D31—42no—
26C2×D124—22no—
27C2×D124C2×C411yescharacteristic
28C2×D124C2×C411yescharacteristic
29C2×D124D412yes—
30C2×C4×D31C2×C411yescharacteristic
31C2×C4×D31D412yes—
32M16×C31—22no—
33C22⋊C4×C31—22no—
34C42×C31C2×C411yescharacteristic
35(C2×D31)⋊C4—21no—
36(C2×D31)⋊C4—22no—
37Dic31⋊C4—21no—
38C4×Dic31C2×C411yescharacteristic
39#92474—22no—
40#92469—42no—
41C8×D31—42no—
42C23×C31—21no—
43C22×D31—21no—
44C22×D31—42no—
45C22×D31—82no—
46C22×D31C22⋊C411yescharacteristic
47C22×D31C22⋊C412yes—
48Q8×C31—41no—
49D4×C31—41no—
50C2×C4×C31—21no—
51C2×C4×C31C22×C411yescharacteristic
52C2×C4×C31C2×D412yes—
53C22⋊D31—42no—
54C22⋊D31—82no—
55C2×Dic31—21no—
56C2×Dic31C22⋊C411yescharacteristic
57D124—41no—
58D124—42no—
59D124—41no—
60D124—82no—
61C4×D31—22no—
62C4×D31—22no—
63C4×D31—22no—
64C8×C31—42no—
65C31⋊C8—42no—
66#2134—311nomaximal, Sylow
67C22×C31—42no—
68C22×C31—41no—
69C22×C31C2×C22⋊C411yescharacteristic
70C2×D31—21no—
71C2×D31—22no—
72C2×D31—42no—
73C2×D31—41no—
74C2×D31—42no—
75C2×D31—41no—
76C2×D31—84no—
77C4×C31—22no—
78C4×C31—21no—
79C4×C31—41no—
80Dic31—41no—
81Dic31#9912yes—
82#535—311no—
83#413—312no—
84#355—311no—
85#355—312no—
86#355D3111yescharacteristic, complemented
87C2×C31—21no—
88C2×C31—81no—
89C2×C31C2×#9911yescharacteristic
90D31—42no—
91D31—41no—
92D31—81no—
93C2×#41—311no—
94C22×D4—311no—
95C2×M16—622no—
96#127—311no—
97#127—311no—
98#124—311no—
99#124C2×D3111yescharacteristic
100#121—622no—
101#120—622no—
102#117—311no—
103#101—312no—
104#101C2×D3112yescomplemented
105#100—622no—
106C31#213411yescharacteristic, complemented, Sylow
107C24—621no—
108#41—1242no—
109C2×Q8C22×D3111yescharacteristic
110C2×D4—311no—
111C2×D4—311no—
112C2×D4—312no—
113C2×D4—622no—
114C2×D4—621no—
115C2×D4—622no—
116C2×D4—1242no—
117C2×D4C4×D3111yescharacteristic
118C22×C4—311no—
119C22×C4—312no—
120M16—22no—
121M16—622no—
122M16—1242no—
123C2×C8—1242no—
124C4⋊C4—621no—
125C22⋊C4—22no—
126C22⋊C4—621no—
127C22⋊C4—622no—
128C42—311no—
129C42C4×D3111yescharacteristic
130C23—21no—
131C23—311no—
132C23—312no—
133C23—621no—
134C23—1242no—
135C23—2482no—
136Q8—41no—
137D4—41no—
138D4—1242no—
139D4—1241no—
140D4—1241no—
141D4—1242no—
142D4—2482no—
143D4—2482no—
144C2×C4—21no—
145C2×C4—311no—
146C2×C4—622no—
147C2×C4—622no—
148C2×C4—622no—
149C2×C4—621no—
150C2×C4C2×C4×D3111yescharacteristic
151C2×C4D4×D3112yes—
152C8—42no—
153C8—1242no—
154C22—42no—
155C22—41no—
156C22—621no—
157C22—622no—
158C22—1242no—
159C22—1241no—
160C22—1242no—
161C22—1241no—
162C22—2484no—
163C22C22⋊C4×D3111yescharacteristic
164C4—22no—
165C4—21no—
166C4—41no—
167C4—312no—
168C4—1241no—
169C2—21no—
170C2—81no—
171C2—1241no—
172C2—1242no—
173C2—2481no—
174C2#99×D3111yescharacteristic
subgroupG/H
centerC2#99×D31
commutatorC2×C4×C31C22×C4
FrattiniC2×Q8C22×D31
FittingC31×#355C2
socleC2×C31C2×#99
prime radical#14521617C2
cosocleC2×Q8×C31C23
hypercenter#355D31
hypocenterC31#2134
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #14521032C2semidirect
3. #14520846C2semidirect
4. #14520845C2semidirect
5. C31×#355C2semidirect
16. C31×#101C22semidirect
17. #11758424C22semidirect
86. #355D31semidirect
104. #101C2×D31semidirect
106. C31#2134semidirect

Maximal subgroups

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

subgroupindex
#145216172
#145210322
#145208462
#145208452
C31×#3552
#213431