Finite Group Databasebeta

← #1393×C181 #37529336

Subgroups — #1393×C181 #37529336

Order 23168.

232 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 64 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
1C2×#99×C181C212yesmaximal
2#390×C181C211yesmaximal, characteristic
3C22×D4×C181C2211yescharacteristic
4C2×C4⋊C4×C181C411yescharacteristic, complemented
5C2×C22⋊C4×C181—22no—
6C2×C22⋊C4×C181—22no—
7C2×C42×C181C411yescharacteristic, complemented
8#99×C181—22no—
9#99×C181C414yescomplemented
10C24×C181D412yes—
11C2×D4×C181—41no—
12C2×D4×C181—41no—
13C2×D4×C181C2×C412yes—
14C2×D4×C181D411yescharacteristic
15C2×D4×C181Q811yescharacteristic
16C22×C4×C181—21no—
17C22×C4×C181—21no—
18C22×C4×C181—42no—
19C22×C4×C181C2×C411yescharacteristic
20C4⋊C4×C181—41no—
21C22⋊C4×C181—24no—
22C22⋊C4×C181—44no—
23C22⋊C4×C181—42no—
24C42×C181—41no—
25C23×C181—22no—
26C23×C181—22no—
27C23×C181—42no—
28C23×C181—42no—
29C23×C181C22⋊C412yes—
30C23×C181C22⋊C411yescharacteristic
31C23×C181C4⋊C412yes—
32D4×C181—42no—
33D4×C181—41no—
34D4×C181—41no—
35C2×C4×C181—21no—
36C2×C4×C181—21no—
37C2×C4×C181—22no—
38C2×C4×C181—41no—
39C2×C4×C181—41no—
40C2×C4×C181—44no—
41C2×C4×C181—42no—
42C2×C4×C181—41no—
43C2×C4×C181—82no—
44C2×C4×C181—82no—
45C2×C4×C181C4211yescharacteristic
46C2×C4×C181C4⋊C411yescharacteristic
47C22×C181—21no—
48C22×C181—21no—
49C22×C181—22no—
50C22×C181—22no—
51C22×C181—42no—
52C22×C181—42no—
53C22×C181—42no—
54C22×C181—42no—
55C22×C181—82no—
56C22×C181#9511yescharacteristic
57C22×C181#9911yescharacteristic
58C22×C181#9911yescharacteristic
59C4×C181—21no—
60C4×C181—21no—
61C4×C181—42no—
62C4×C181—84no—
63C4×C181—81no—
64C2×C181—21no—
65C2×C181—21no—
66C2×C181—42no—
67C2×C181—42no—
68C2×C181#34211yescharacteristic
69C2×C181#35311yescharacteristic
70C2×C181#35411yescharacteristic
71C181#139311yescharacteristic, direct product factor, Sylow
72#1393C18111yesmaximal, characteristic, direct product factor, Sylow
73C2×#99C2×C18112yes—
74#390C2×C18111yescharacteristic
75C22×D4C22×C18111yescharacteristic
76C2×C4⋊C4C4×C18111yescharacteristic, complemented
77C2×C22⋊C4—22no—
78C2×C22⋊C4—22no—
79C2×C42C4×C18111yescharacteristic, complemented
80#99—22no—
81#99C4×C18114yescomplemented
82C24D4×C18112yes—
83C2×D4—41no—
84C2×D4—41no—
85C2×D4C2×C4×C18112yes—
86C2×D4D4×C18111yescharacteristic
87C2×D4Q8×C18111yescharacteristic
88C22×C4—21no—
89C22×C4—21no—
90C22×C4—42no—
91C22×C4C2×C4×C18111yescharacteristic
92C4⋊C4—41no—
93C22⋊C4—24no—
94C22⋊C4—44no—
95C22⋊C4—42no—
96C42—41no—
97C23—22no—
98C23—22no—
99C23—42no—
100C23—42no—
101C23C22⋊C4×C18111yescharacteristic
102C23C22⋊C4×C18112yes—
103C23C4⋊C4×C18112yes—
104D4—42no—
105D4—41no—
106D4—41no—
107C2×C4—21no—
108C2×C4—21no—
109C2×C4—22no—
110C2×C4—41no—
111C2×C4—41no—
112C2×C4—44no—
113C2×C4—42no—
114C2×C4—41no—
115C2×C4—82no—
116C2×C4—82no—
117C2×C4C42×C18111yescharacteristic
118C2×C4C4⋊C4×C18111yescharacteristic
119C22—21no—
120C22—21no—
121C22—22no—
122C22—22no—
123C22—42no—
124C22—42no—
125C22—42no—
126C22—42no—
127C22—82no—
128C22#95×C18111yescharacteristic
129C22#99×C18111yescharacteristic
130C22#99×C18111yescharacteristic
131C4—21no—
132C4—21no—
133C4—42no—
134C4—84no—
135C4—81no—
136C2—21no—
137C2—21no—
138C2—42no—
139C2—42no—
140C2#342×C18111yescharacteristic
141C2#353×C18111yescharacteristic
142C2#354×C18111yescharacteristic
subgroupG/H
center, socleC22×C181#99
commutatorC2×C4C42×C181
Frattini, cosocleC22×D4C22×C181
prime radicalC22×D4×C181C22
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C181 ◁ C23×C181 ◁ C22×D4×C181 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C4⋊C4×C181C4semidirect
7. C2×C42×C181C4semidirect
9. #99×C181C4semidirect
71. C181#1393direct (N × H)
72. #1393C181direct (N × H)
76. C2×C4⋊C4C4×C181semidirect
79. C2×C42C4×C181semidirect
81. #99C4×C181semidirect

Maximal subgroups

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

subgroupindex
C2×#99×C1812
#390×C1812
#1393181