Finite Group Databasebeta

← #16845920

Subgroups — #16845920

Order 3968.

324 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 89 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#14521524C211yesmaximal, characteristic
2#14521089C212yesmaximal, complemented
3C2×#11758421C211yesmaximal, characteristic
4#14520809C212yesmaximal, complemented
5C31×#390C211yesmaximal, characteristic
6C22×D4×C31C2211yescharacteristic
7C2×C4⋊C4×C31C2211yescharacteristic
8C2×C22⋊C4×C31—22no—
9C2×C42×C31C2211yescharacteristic
10C2×C22⋊Dic31—22no—
11D4×Dic31—22no—
12D4×Dic31—22no—
13#11758503C2212yes—
14C2×#92474C2212yes—
15#11758421C414yescomplemented
16#11758396—22no—
17#11758395—22no—
18C24×C31D412yes—
19C2×D4×C31—22no—
20C2×D4×C31—22no—
21C2×D4×C31C2×C412yes—
22C2×D4×C31Q812yes—
23C22×C4×C31—21no—
24C22×C4×C31—21no—
25C22×C4×C31C2311yescharacteristic
26C22×Dic31—22no—
27C22×Dic31—22no—
28C4⋊C4×C31—22no—
29C22⋊C4×C31—44no—
30C42×C31—22no—
31C22⋊Dic31—24no—
32C22⋊Dic31—22no—
33C4⋊Dic31D412yes—
34C4⋊Dic31D412yes—
35C4×Dic31—22no—
36#92474—22no—
37#92474C2×C414yescomplemented
38C2×C31⋊C8—22no—
39C23×C31—22no—
40C23×C31—22no—
41C23×C31—42no—
42C23×C31—42no—
43C23×C31C4⋊C414yes—
44C23×C31C2×D411yescharacteristic
45D4×C31—24no—
46D4×C31—24no—
47C2×C4×C31—22no—
48C2×C4×C31—41no—
49C2×C4×C31—41no—
50C2×C4×C31—42no—
51C2×C4×C31—41no—
52C2×C4×C31C22×C411yescharacteristic
53C2×C4×C31C2×D412yes—
54C2×C4×C31C2×Q811yescharacteristic
55C2×C4×C31#4112yes—
56C2×Dic31—22no—
57C2×Dic31—22no—
58C2×Dic31—82no—
59C2×Dic31—82no—
60C31⋊C8—24no—
61#1856—311nomaximal, Sylow
62C22×C31—21no—
63C22×C31—21no—
64C22×C31—24no—
65C22×C31—44no—
66C22×C31—42no—
67C22×C31—42no—
68C22×C31—82no—
69C22×C31C2×C4⋊C411yescharacteristic
70C22×C31#12011yescharacteristic
71C22×C31#12311yescharacteristic
72C4×C31—42no—
73C4×C31—81no—
74C4×C31C4×D412yes—
75C4×C31C22⋊Q812yes—
76Dic31—42no—
77Dic31—42no—
78#518—311no—
79#428—312no—
80C2×#100—311no—
81#390D3111yescharacteristic
82#339—312no—
83C2×C31—21no—
84C2×C31—21no—
85C2×C31—44no—
86C2×C31#38511yescharacteristic
87C2×C31#45311yescharacteristic
88C2×C31#45511yescharacteristic
89C22×D4C2×D3111yescharacteristic
90C2×M16—312no—
91C4×D4—622no—
92C4×D4—622no—
93#117—312no—
94C2×C4⋊C4C2×D3111yescharacteristic
95C2×C22⋊C4—22no—
96C2×C22⋊C4—622no—
97C2×C42C2×D3111yescharacteristic
98#107—622no—
99#106—622no—
100#100—314no—
101C31#185611yescharacteristic, complemented, Sylow
102C24C22⋊D3112yes—
103C2×D4—22no—
104C2×D4—22no—
105C2×D4Dic6212yes—
106C2×D4C4×D3112yes—
107C22×C4—21no—
108C22×C4—21no—
109C22×C4—622no—
110C22×C4—622no—
111C22×C4C22×D3111yescharacteristic
112M16—314no—
113M16—622no—
114C2×C8—622no—
115C4⋊C4—22no—
116C4⋊C4—312no—
117C4⋊C4—312no—
118C22⋊C4—44no—
119C22⋊C4—624no—
120C22⋊C4—622no—
121C42—22no—
122C42—622no—
123C23—22no—
124C23—22no—
125C23—42no—
126C23—42no—
127C23Dic31⋊C414yes—
128C23C2×C22⋊D3111yescharacteristic
129D4—24no—
130D4—24no—
131C2×C4—22no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—42no—
135C2×C4—41no—
136C2×C4—622no—
137C2×C4—622no—
138C2×C4—2482no—
139C2×C4—2482no—
140C2×C4C2×Dic6211yescharacteristic
141C2×C4C2×C4×D3111yescharacteristic
142C2×C4D4×D3112yes—
143C2×C4#9249712yes—
144C8—624no—
145C22—21no—
146C22—21no—
147C22—24no—
148C22—44no—
149C22—42no—
150C22—42no—
151C22—82no—
152C22C2×Dic31⋊C411yescharacteristic
153C22#1175851211yescharacteristic
154C22#1175851411yescharacteristic
155C4—42no—
156C4—81no—
157C4—1242no—
158C4—1242no—
159C4#1175845512yes—
160C4(C22⋊D31)⋊C412yes—
161C2—21no—
162C2—21no—
163C2—44no—
164C2#1452092111yescharacteristic
165C2#1452121611yescharacteristic
166C2#1452122611yescharacteristic
subgroupG/H
centerC22#11758514
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#390C2
socleC22×C31#120
prime radicalC22×D4×C31C22
cosocleC22×C4×C31C23
hypercenter#390D31
hypocenterC31#1856
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
2. #14521089C2semidirect
4. #14520809C2semidirect
15. #11758421C4semidirect
37. #92474C2×C4semidirect
101. C31#1856semidirect

Maximal subgroups

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

subgroupindex
#145215242
#145210892
C2×#117584212
#145208092
C31×#3902
#185631