Finite Group Databasebeta

← #16846872

Subgroups — #16846872

Order 3968.

246 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 69 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#14521680C211yesmaximal, characteristic
2#14521058C212yesmaximal
3#14520818C211yesmaximal, characteristic
4#14520809C212yesmaximal
5C31×#391C211yesmaximal, characteristic
6C22×Q8×C31C2211yescharacteristic
7C2×C4⋊C4×C31C2211yescharacteristic
8C2×C42×C31C2211yescharacteristic
9#11758503C2212yes—
10#11758501—22no—
11C2×#92474C2212yes—
12#11758467—22no—
13#11758465—22no—
14C31×#95—22no—
15#11758423—22no—
16#11758423—22no—
17C2×Q8×C31—21no—
18C2×Q8×C31—22no—
19C2×Q8×C31—22no—
20C2×Q8×C31Q812yescomplemented
21C22×C4×C31—21no—
22C22×C4×C31—21no—
23C22×C4×C31D412yes—
24C22×C4×C31C2311yescharacteristic
25C2×Dic62—22no—
26C4⋊C4×C31—22no—
27C42×C31—22no—
28C22⋊Dic31—22no—
29C4⋊Dic31—22no—
30C4⋊Dic31D412yes—
31C4⋊Dic31D412yes—
32Dic31⋊C4—24no—
33C4×Dic31—22no—
34#92474—22no—
35#92474—22no—
36C2×C31⋊C8—22no—
37C23×C31C2×D411yescharacteristic
38Q8×C31—24no—
39Q8×C31—42no—
40C2×C4×C31—22no—
41C2×C4×C31—22no—
42C2×C4×C31—22no—
43C2×C4×C31—41no—
44C2×C4×C31—41no—
45C2×C4×C31—41no—
46C2×C4×C31—41no—
47C2×C4×C31—42no—
48C2×C4×C31C2×D412yes—
49C2×C4×C31C2×Q811yescharacteristic
50C2×C4×C31#4111yescharacteristic
51C2×C4×C31#4112yes—
52C2×Dic31—22no—
53C2×Dic31—22no—
54Dic62—82no—
55C31⋊C8—42no—
56#2028—311nomaximal, Sylow
57C22×C31—21no—
58C22×C31—21no—
59C22×C31#12011yescharacteristic
60C22×C31C22⋊Q811yescharacteristic
61C22×C31#12411yescharacteristic
62C4×C31—42no—
63C4×C31—42no—
64C4×C31—42no—
65C4×C31C22⋊Q812yes—
66C4×C31#12412yes—
67Dic31—42no—
68Dic31—42no—
69#544—311no—
70#419—312no—
71#391D3111yescharacteristic
72#343—311no—
73#339—312no—
74C2×C31—21no—
75C2×C31—21no—
76C2×C31#39311yescharacteristic
77C2×C31#45511yescharacteristic
78C2×C31#45611yescharacteristic
79C22×Q8C2×D3111yescharacteristic
80C2×M16—312no—
81C4⋊Q8—622no—
82#125—622no—
83C22⋊Q8—622no—
84#117—312no—
85C2×C4⋊C4C2×D3111yescharacteristic
86C2×C42C2×D3111yescharacteristic
87#103—622no—
88#103—622no—
89#95—22no—
90C31#202811yescharacteristic, complemented, Sylow
91C2×Q8—21no—
92C2×Q8—22no—
93C2×Q8—22no—
94C2×Q8—622no—
95C2×Q8Dic6212yescomplemented
96C22×C4—21no—
97C22×C4—21no—
98C22×C4C22⋊D3112yes—
99C22×C4C22×D3111yescharacteristic
100M16—622no—
101M16—622no—
102C2×C8—622no—
103C4⋊C4—22no—
104C4⋊C4—312no—
105C4⋊C4—312no—
106C4⋊C4—624no—
107C4⋊C4—622no—
108C22⋊C4—622no—
109C42—22no—
110C42—622no—
111C23C2×C22⋊D3111yescharacteristic
112Q8—24no—
113Q8—42no—
114Q8—2482no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—22no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4—42no—
123C2×C4—622no—
124C2×C4—622no—
125C2×C4C2×Dic6211yescharacteristic
126C2×C4#9249511yescharacteristic
127C2×C4D4×D3112yes—
128C2×C4#9249712yes—
129C8—1242no—
130C22—21no—
131C22—21no—
132C22#1175850111yescharacteristic
133C22#1175851311yescharacteristic
134C22#1175851411yescharacteristic
135C4—42no—
136C4—42no—
137C4—42no—
138C4—1242no—
139C4—1242no—
140C4#1175845512yes—
141C4#1175846212yes—
142C2—21no—
143C2—21no—
144C2#1452096111yescharacteristic
145C2#1452122611yescharacteristic
146C2#1452123111yescharacteristic
subgroupG/H
centerC22#11758514
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#391C2
socleC22×C31#120
prime radicalC23×C31C2×D4
hypercenter#391D31
hypocenterC31#2028
LCSG ▷ C22×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
20. C2×Q8×C31Q8semidirect
90. C31#2028semidirect
95. C2×Q8Dic62semidirect

Maximal subgroups

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

subgroupindex
#145216802
#145210582
#145208182
#145208092
C31×#3912
#202831