Finite Group Databasebeta

← #16846249

Subgroups — #16846249

Order 3968.

314 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 93 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#14521527C211yesmaximal, characteristic, complemented
2#14521066C212yesmaximal
3C2×#11758424C211yesmaximal, characteristic, complemented
4#14520805C212yesmaximal, complemented
5C31×#536C211yesmaximal, characteristic
6C2×#41×C31C2211yescharacteristic
7C22×Q8×C31C2211yescharacteristic
8C31×C4⋊Q8C412yescomplemented
9C31×#124C412yescomplemented
10C31×#123—22no—
11C31×C22⋊Q8—22no—
12C31×#117C2211yescharacteristic
13Q8×Dic31—24no—
14#11758503—22no—
15#11758503C2212yes—
16C2×#92474C2212yes—
17#11758425—24no—
18#11758424—22no—
19#41×C31—22no—
20#41×C31—22no—
21C2×Q8×C31—22no—
22C2×Q8×C31—22no—
23C2×Q8×C31C2×C411yescharacteristic
24C2×Q8×C31C2×C412yes—
25C2×Q8×C31D412yes—
26C2×D4×C31—21no—
27C2×D4×C31C2×C411yescharacteristic
28C22×C4×C31—21no—
29C22×C4×C31D412yes—
30C22×C4×C31C2311yescharacteristic
31C4⋊C4×C31—24no—
32C4⋊C4×C31—21no—
33C22⋊C4×C31—21no—
34C22⋊C4×C31—24no—
35C42×C31C2×C412yes—
36C22⋊Dic31—22no—
37C4⋊Dic31—24no—
38C4⋊Dic31—22no—
39C4×Dic31—24no—
40C4×Dic31D414yes—
41#92474—22no—
42#92474—22no—
43C2×C31⋊C8—22no—
44C23×C31—21no—
45C23×C31C2×D411yescharacteristic
46Q8×C31—24no—
47Q8×C31—24no—
48Q8×C31—22no—
49D4×C31—22no—
50D4×C31—41no—
51D4×C31—41no—
52C2×C4×C31—22no—
53C2×C4×C31—22no—
54C2×C4×C31—22no—
55C2×C4×C31—21no—
56C2×C4×C31—42no—
57C2×C4×C31C22⋊C414yes—
58C2×C4×C31C22×C411yescharacteristic
59C2×C4×C31C2×D412yes—
60C2×C4×C31C2×D411yescharacteristic
61C2×C4×C31#4112yes—
62C2×Dic31—24no—
63C31⋊C8—42no—
64#1912—311nomaximal, Sylow
65C22×C31—41no—
66C22×C31—42no—
67C22×C31—41no—
68C22×C31C2×C22⋊C411yescharacteristic
69C22×C31#12011yescharacteristic
70C22×C31#12311yescharacteristic
71C4×C31—24no—
72C4×C31—42no—
73C4×C31—41no—
74C4×C31C4×D412yes—
75C4×C31#12112yes—
76Dic31—44no—
77#536D3111yescharacteristic
78#519—311no—
79#421—312no—
80C2×#101—311no—
81H(3,ℤ/4)—312no—
82C2×C31—21no—
83C2×C31—21no—
84C2×C31—21no—
85C2×C31—81no—
86C2×C31#38611yescharacteristic
87C2×#41C2×D3111yescharacteristic
88C22×Q8C2×D3111yescharacteristic
89C2×M16—312no—
90C4⋊Q8Dic3112yescomplemented
91#124Dic3112yescomplemented
92#123—22no—
93C22⋊Q8—22no—
94C4×Q8—624no—
95#117—312no—
96#117—622no—
97#117C2×D3111yescharacteristic
98#104—624no—
99#101—622no—
100C31#191211yescharacteristic, complemented, Sylow
101#41—22no—
102#41—22no—
103C2×Q8—22no—
104C2×Q8—22no—
105C2×Q8C2×Dic3111yescharacteristic
106C2×Q8C2×Dic3112yes—
107C2×Q8C22⋊D3112yes—
108C2×D4—21no—
109C2×D4C2×Dic3111yescharacteristic
110C22×C4—21no—
111C22×C4C22⋊D3112yes—
112C22×C4C22×D3111yescharacteristic
113M16—622no—
114M16—622no—
115C2×C8—622no—
116C4⋊C4—24no—
117C4⋊C4—21no—
118C4⋊C4—624no—
119C4⋊C4—622no—
120C22⋊C4—21no—
121C22⋊C4—24no—
122C22⋊C4—622no—
123C42—314no—
124C42—624no—
125C42C2×Dic3112yes—
126C23—21no—
127C23C2×C22⋊D3111yescharacteristic
128Q8—24no—
129Q8—24no—
130Q8—22no—
131D4—22no—
132D4—41no—
133D4—41no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—22no—
137C2×C4—21no—
138C2×C4—42no—
139C2×C4—624no—
140C2×C4C22⋊Dic3114yes—
141C2×C4D4×D3112yes—
142C2×C4#9249712yes—
143C2×C4C22×Dic3111yescharacteristic
144C2×C4C2×C22⋊D3111yescharacteristic
145C8—1242no—
146C22—41no—
147C22—42no—
148C22—41no—
149C22#1175851211yescharacteristic
150C22#1175851411yescharacteristic
151C22C2×C22⋊Dic3111yescharacteristic
152C4—24no—
153C4—42no—
154C4—41no—
155C4—1244no—
156C4D4×Dic3112yes—
157C4#1175851612yes—
158C2—21no—
159C2—21no—
160C2—21no—
161C2—81no—
162C2#1452092911yescharacteristic
subgroupG/H
centerC2#14520929
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#536C2
socleC2×C31#386
prime radicalC2×#41×C31C22
cosocleC22×C4×C31C23
hypercenter#536D31
hypocenterC31#1912
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
1. #14521527C2semidirect
3. C2×#11758424C2semidirect
4. #14520805C2semidirect
8. C31×C4⋊Q8C4semidirect
9. C31×#124C4semidirect
90. C4⋊Q8Dic31semidirect
91. #124Dic31semidirect
100. C31#1912semidirect

Maximal subgroups

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

subgroupindex
#145215272
#145210662
C2×#117584242
#145208052
C31×#5362
#191231