Finite Group Databasebeta

← #94192

Subgroups — #94192

Order 512.

170 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 38 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#12864C211yesmaximal, characteristic
2#11524C211yesmaximal, characteristic
3#8187C211yesmaximal, characteristic
4#2922C2211yescharacteristic
5#2165—21no—
6#1827—21no—
7#1476—21no—
8#1452C411yescharacteristic, complemented
9C2×C82C411yescharacteristic, complemented
10#1395—21no—
11#1392C411yescharacteristic
12#1391C411yescharacteristic
13#1328C412yescomplemented
14#1321—21no—
15#1278—21no—
16C4×#41D411yescharacteristic
17#433—41no—
18#431—21no—
19#431—41no—
20#424C2×C411yescharacteristic
21#424Q811yescharacteristic
22#413—21no—
23#410—21no—
24#408C2×C411yescharacteristic
25#408D411yescharacteristic
26C4×M16D411yescharacteristic
27C2×C4×C8—21no—
28C2×C4×C8C2×C411yescharacteristic
29#364—41no—
30#349—22no—
31#347—41no—
32#339—41no—
33H(3,ℤ/4)—41no—
34Q8⋊C8—22no—
35D4⋊C8—22no—
36#322—41no—
37C82—41no—
38C2×#41C22⋊C411yescharacteristic
39C2×M16—41no—
40C2×M16C22⋊C411yescharacteristic
41C2×M16C4⋊C411yescharacteristic
42C22×C8—41no—
43C22×C8C4211yescharacteristic
44C22×C8C4⋊C411yescharacteristic
45C4×Q8—21no—
46C4×D4—21no—
47C4×D4—41no—
48#117—21no—
49#117—41no—
50#117C4⋊C411yescharacteristic
51C2×C42—21no—
52C2×C42C22⋊C411yescharacteristic
53M32—42no—
54C4⋊C8—22no—
55C4⋊C8—41no—
56C4⋊C8—41no—
57#101—41no—
58#100—41no—
59#99—41no—
60#99—41no—
61C22⋊C8—41no—
62C22⋊C8—41no—
63C22⋊C8—41no—
64#97—21no—
65C4×C8—22no—
66C4×C8—21no—
67C4×C8—21no—
68C4×C8—21no—
69C4×C8—41no—
70C4×C8—41no—
71#41—41no—
72#41—41no—
73C2×Q8#10411yescharacteristic
74C2×D4—21no—
75C2×D4#10411yescharacteristic
76C22×C4—21no—
77C22×C4—21no—
78C22×C4—41no—
79C22×C4#9511yescharacteristic
80M16—41no—
81M16—41no—
82M16—81no—
83M16—81no—
84C2×C8—21no—
85C2×C8—21no—
86C2×C8—21no—
87C2×C8—21no—
88C2×C8—42no—
89C2×C8—44no—
90C2×C8—41no—
91C2×C8—41no—
92C2×C8—42no—
93C2×C8—81no—
94C4⋊C4—21no—
95C4⋊C4—41no—
96C4⋊C4—81no—
97C22⋊C4—21no—
98C22⋊C4—41no—
99C22⋊C4—81no—
100C42—21no—
101C42—21no—
102C42—41no—
103C42—81no—
104C42#9911yescharacteristic
105C42#9911yescharacteristic
106C16—82no—
107C23—21no—
108C23H(3,ℤ/4)11yescharacteristic
109Q8—41no—
110D4—41no—
111D4—81no—
112C2×C4—21no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—21no—
117C2×C4—42no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—82no—
122C2×C4—161no—
123C2×C4#33911yescharacteristic
124C2×C4#34211yescharacteristic
125C8—44no—
126C8—41no—
127C8—41no—
128C8—41no—
129C8—41no—
130C8—82no—
131C8—161no—
132C22—21no—
133C22—41no—
134C22—41no—
135C22—81no—
136C22#128411yescharacteristic
137C4—22no—
138C4—21no—
139C4—41no—
140C4—41no—
141C4—81no—
142C4—321no—
143C4#139111yescharacteristic
144C4#139511yescharacteristic
145C2—21no—
146C2—41no—
147C2—81no—
148C2#721411yescharacteristic
subgroupG/H
centerC4#1391
commutatorC22×C8C42
Frattini, cosocle#2922C22
socleC2#7214
prime radicalC2×#41C22⋊C4
LCSG ▷ C22×C8 ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4 ◁ C42 ◁ C2×C42 ◁ #2922 ◁ G
LECSG ▷ #2922 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
8. #1452C4semidirect
9. C2×C82C4semidirect
13. #1328C4semidirect

Maximal subgroups

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

subgroupindex
#128642
#115242
#81872