Finite Group Databasebeta

← #16847740

Subgroups — #16847740

Order 3968.

224 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 41 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#14521779C211yesmaximal, characteristic, complemented
2#14521232C212yesmaximal
3#14520848C211yesmaximal, characteristic, complemented
4#14520847C212yesmaximal, complemented
5C31×#456C211yesmaximal, characteristic
6C31×2−1+4C2211yescharacteristic
7C31×#137—21no—
8C31×C4⋊Q8C2211yescharacteristic
9#11758528—22no—
10#11758521—21no—
11#11758521C2212yes—
12#11758465—22no—
13#11758464—22no—
14C4×Dic62—21no—
15C31×#104—21no—
16C31×#101C2211yescharacteristic
17#11758425—22no—
18#11758424C2212yes—
19#41×C31—22no—
20#41×C31—21no—
21#41×C31—41no—
22C2×Q8×C31—41no—
23C2×Q8×C31D411yescharacteristic
24C2×Q8×C31C2311yescharacteristic
25C2×Dic62—21no—
26C2×Dic62—21no—
27C2×Dic62D412yes—
28Q16×C31—41no—
29SD16×C31—41no—
30M16×C31—21no—
31C4⋊C4×C31—22no—
32C42×C31D411yescharacteristic
33#92482—42no—
34#92480—42no—
35C4⋊Dic31—21no—
36Dic31⋊C4—22no—
37Dic31⋊C4—22no—
38Dic31⋊C4—22no—
39C4×Dic31—22no—
40C4×Dic31—21no—
41C4×Dic31D412yes—
42#92474—22no—
43Q8×C31—22no—
44Q8×C31—21no—
45Q8×C31—41no—
46Q8×C31—41no—
47D4×C31—22no—
48D4×C31—21no—
49D4×C31—41no—
50C2×C4×C31—21no—
51C2×C4×C31—21no—
52C2×C4×C31—42no—
53C2×C4×C31—41no—
54C2×C4×C31C2×D412yes—
55C2×C4×C31C2×D411yescharacteristic
56C2×Dic31—22no—
57C2×Dic31—22no—
58Dic62—24no—
59Dic62—42no—
60Dic62—81no—
61C8×C31—41no—
62C31⋊C8—42no—
63#2205—311nomaximal, Sylow
64C22×C31—41no—
65C22×C31#12011yescharacteristic
66C4×C31—22no—
67C4×C31—22no—
68C4×C31—21no—
69C4×C31—41no—
70C4×C31—41no—
71Dic31—24no—
72Dic31—42no—
73Q82—311no—
74#456—312no—
75#456D3111yescharacteristic
76#356—311no—
77#356—312no—
78C2×C31—21no—
79C2×C31—81no—
80C2×C31B(4,𝔽2)11yescharacteristic
812−1+4C2×D3111yescharacteristic
82#137—21no—
83#137—622no—
84C4⋊Q8—312no—
85C4⋊Q8—622no—
86C4⋊Q8—621no—
87C4⋊Q8C2×D3111yescharacteristic
88C4×Q8—622no—
89C4×Q8—621no—
90#104—21no—
91#104—622no—
92#101—312no—
93#101C2×D3111yescharacteristic
94C31#220511yescharacteristic, complemented, Sylow
95#41—22no—
96#41—21no—
97#41—41no—
98C2×Q8—41no—
99C2×Q8—312no—
100C2×Q8—621no—
101C2×Q8—621no—
102C2×Q8C22⋊D3111yescharacteristic
103C2×Q8C22×D3111yescharacteristic
104Q16—41no—
105Q16—1242no—
106SD16—41no—
107SD16—1242no—
108M16—21no—
109M16—622no—
110C4⋊C4—22no—
111C4⋊C4—622no—
112C4⋊C4—621no—
113C4⋊C4—622no—
114C4⋊C4—622no—
115C42—312no—
116C42—622no—
117C42—621no—
118C42C22⋊D3111yescharacteristic
119Q8—21no—
120Q8—22no—
121Q8—41no—
122Q8—41no—
123Q8—624no—
124Q8—1242no—
125Q8—2481no—
126D4—21no—
127D4—22no—
128D4—41no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—41no—
132C2×C4—42no—
133C2×C4—622no—
134C2×C4—622no—
135C2×C4D4×D3112yes—
136C2×C4C2×C22⋊D3111yescharacteristic
137C8—41no—
138C8—1242no—
139C22—41no—
140C22#1175851411yescharacteristic
141C4—22no—
142C4—21no—
143C4—22no—
144C4—41no—
145C4—41no—
146C4—624no—
147C4—1242no—
148C2—21no—
149C2—81no—
150C2#1452123511yescharacteristic
subgroupG/H
centerC2#14521235
commutator, cosocleC2×Q8×C31C23
FrattiniC2×Q8C22×D31
FittingC31×#456C2
socleC2×C31B(4,𝔽2)
prime radicalC31×2−1+4C22
hypercenter#456D31
hypocenterC31#2205
LCSG ▷ C2×Q8×C31 ▷ C22×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #14521779C2semidirect
3. #14520848C2semidirect
4. #14520847C2semidirect
94. C31#2205semidirect

Maximal subgroups

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

subgroupindex
#145217792
#145212322
#145208482
#145208472
C31×#4562
#220531