Finite Group Databasebeta

← #16847404

Subgroups — #16847404

Order 3968.

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

normal subgroups only

This group has 230 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#14521624C211yesmaximal, characteristic
2#14521032C212yesmaximal
3#14520848C211yesmaximal, characteristic, complemented
4#14520847C212yesmaximal, complemented
5C31×#356C211yesmaximal, characteristic, complemented
6C2×#92499C2211yescharacteristic
7C2×Q8×D31C411yescharacteristic
8C31×C4⋊Q8C2211yescharacteristic
9#11758524C411yescharacteristic
10#11758521C2211yescharacteristic
11M16×D31—22no—
12#11758473—22no—
13#11758471—22no—
14#11758452C411yescharacteristic
15#11758449C411yescharacteristic
16C31×#101C2212yes—
17#11758424C2212yes—
18#11758411—22no—
19C2×Q8×C31C2×C411yescharacteristic
20C2×Q8×C31C2311yescharacteristic
21#92499—42no—
22Q8×D31—42no—
23C2×D124C2×C411yescharacteristic
24C2×D124D412yes—
25C2×C4×D31—21no—
26C2×C4×D31C2×C411yescharacteristic
27C2×C4×D31D412yes—
28C2×Dic62—21no—
29C2×Dic62C2×C411yescharacteristic
30M16×C31—22no—
31C4⋊C4×C31—22no—
32C42×C31C2×C411yescharacteristic
33(C2×D31)⋊C4—21no—
34(C2×D31)⋊C4—22no—
35(C2×D31)⋊C4—22no—
36Dic31⋊C4—22no—
37Dic31⋊C4—21no—
38C4×Dic31C2×C411yescharacteristic
39#92474—22no—
40#92469—42no—
41C8×D31—42no—
42C22×D31C22⋊C412yes—
43C22×D31C22⋊C411yescharacteristic
44Q8×C31—41no—
45Q8×C31—41no—
46C2×C4×C31—21no—
47C2×C4×C31—21no—
48C2×C4×C31C22×C411yescharacteristic
49C2×C4×C31C2×D412yes—
50C2×Dic31—21no—
51C2×Dic31—21no—
52C2×Dic31C22⋊C411yescharacteristic
53D124—41no—
54D124—42no—
55C4×D31—22no—
56C4×D31—22no—
57C4×D31—22no—
58C4×D31—42no—
59Dic62—42no—
60Dic62—41no—
61C8×C31—42no—
62C31⋊C8—42no—
63#2135—311nomaximal, Sylow
64C22×C31C2×C22⋊C411yescharacteristic
65C2×D31—21no—
66C2×D31—22no—
67C2×D31—42no—
68C2×D31—41no—
69C4×C31—22no—
70C4×C31—21no—
71C4×C31—41no—
72C4×C31—41no—
73Dic31—41no—
74Dic31—41no—
75Dic31#9912yes—
76#536—311no—
77#413—312no—
78#356—311no—
79#356—312no—
80#356D3111yescharacteristic, complemented
81C2×C31—21no—
82C2×C31C2×#9911yescharacteristic
83D31—41no—
84D31—42no—
85C2×#41—311no—
86C22×Q8—311no—
87C2×M16—622no—
88C4⋊Q8—311no—
89C4⋊Q8C2×D3111yescharacteristic
90#124—311no—
91#124—311no—
92#123—622no—
93C22⋊Q8—622no—
94#117—311no—
95#101—312no—
96#101C2×D3112yes—
97#100—622no—
98C31#213511yescharacteristic, complemented, Sylow
99#41—1242no—
100C2×Q8—311no—
101C2×Q8—621no—
102C2×Q8—1242no—
103C2×Q8C4×D3111yescharacteristic
104C2×Q8C22×D3111yescharacteristic
105C2×D4—311no—
106C2×D4—312no—
107C22×C4—311no—
108C22×C4—312no—
109C22×C4—621no—
110M16—22no—
111M16—622no—
112M16—1242no—
113C2×C8—1242no—
114C4⋊C4—22no—
115C4⋊C4—621no—
116C4⋊C4—622no—
117C22⋊C4—621no—
118C22⋊C4—622no—
119C22⋊C4—622no—
120C42—311no—
121C42C4×D3111yescharacteristic
122C23—312no—
123C23—311no—
124Q8—41no—
125Q8—41no—
126Q8—1241no—
127Q8—1242no—
128D4—1242no—
129D4—1241no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—311no—
133C2×C4—622no—
134C2×C4—622no—
135C2×C4—622no—
136C2×C4—621no—
137C2×C4—621no—
138C2×C4—1242no—
139C2×C4C2×C4×D3111yescharacteristic
140C2×C4D4×D3112yes—
141C8—42no—
142C8—1242no—
143C22—621no—
144C22—622no—
145C22—1242no—
146C22—1241no—
147C22C22⋊C4×D3111yescharacteristic
148C4—22no—
149C4—21no—
150C4—41no—
151C4—41no—
152C4—312no—
153C4—1241no—
154C4—1241no—
155C2—21no—
156C2—1241no—
157C2—1242no—
158C2#99×D3111yescharacteristic
subgroupG/H
centerC2#99×D31
commutatorC2×C4×C31C22×C4
FrattiniC2×Q8C22×D31
FittingC31×#356C2
socleC2×C31C2×#99
prime radicalC2×#92499C22
cosocleC2×Q8×C31C23
hypercenter#356D31
hypocenterC31#2135
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
3. #14520848C2semidirect
4. #14520847C2semidirect
5. C31×#356C2semidirect
80. #356D31semidirect
98. C31#2135semidirect

Maximal subgroups

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

subgroupindex
#145216242
#145210322
#145208482
#145208472
C31×#3562
#213531