Finite Group Databasebeta

← #94162

Subgroups — #94162

Order 512.

201 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 201 conjugacy classes of subgroups — too many to draw. Only its 52 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#13192C211yesmaximal, characteristic
2#12633C211yesmaximal, characteristic
3#11485C211yesmaximal, characteristic
4#2931C2211yescharacteristic
5#2150C411yescharacteristic, complemented
6#2132C411yescharacteristic
7#2126C411yescharacteristic
8C2×#350—21no—
9C2×#350—21no—
10#2115—21no—
11C2×#346C411yescharacteristic, complemented
12#1757—21no—
13#1395—21no—
14#1327C412yescomplemented
15#1321—21no—
16C2×#131D411yescharacteristic
17C2×#131D411yescharacteristic
18#532C2×C411yescharacteristic
19C2×M32—21no—
20C2×M32—41no—
21C22×C16—21no—
22#436—41no—
23C8×D4—41no—
24#423C2×C411yescharacteristic
25#413—21no—
26#410—21no—
27#408D411yescharacteristic
28#408Q811yescharacteristic
29#405—41no—
30C2×C4×C8C2×C411yescharacteristic
31C4⋊C16—41no—
32#356C812yes—
33#355—21no—
34#354—21no—
35#353C812yes—
36#350—42no—
37#350—42no—
38#349—22no—
39#349—41no—
40#346—41no—
41#344—41no—
42C2×#41C22⋊C411yescharacteristic
43C2×#41C4⋊C411yescharacteristic
44#131—41no—
45#131—41no—
46#131—41no—
47#131—41no—
48C2×M16—21no—
49C2×M16—21no—
50C2×M16—41no—
51C2×M16C22⋊C411yescharacteristic
52C2×M16C4⋊C411yescharacteristic
53C22×C8—21no—
54C22×C8—21no—
55C22×C8C22⋊C411yescharacteristic
56C22×C8C4⋊C411yescharacteristic
57C4⋊Q8C2×C811yescharacteristic
58#127C2×C811yescharacteristic
59#124M1611yescharacteristic
60#124M1611yescharacteristic
61#121—41no—
62C4×D4—41no—
63#117—41no—
64C2×C42C4211yescharacteristic
65M32—42no—
66M32—41no—
67M32—41no—
68M32—81no—
69C2×C16—22no—
70C2×C16—41no—
71C2×C16—41no—
72C2×C16—41no—
73C2×C16—81no—
74C4⋊C8—41no—
75#101—22no—
76#100—41no—
77#99—22no—
78#99—41no—
79C22⋊C8—41no—
80C22⋊C8—41no—
81#97—81no—
82C4×C8—21no—
83C4×C8—21no—
84C4×C8—81no—
85#41—41no—
86#41—41no—
87#41—41no—
88#41—41no—
89C2×Q8C22⋊C811yescharacteristic
90C2×Q8C4⋊C811yescharacteristic
91C2×D4—21no—
92C2×D4—21no—
93C2×D4—41no—
94C2×D4C22⋊C811yescharacteristic
95C2×D4C4⋊C811yescharacteristic
96C22×C4—21no—
97C22×C4—21no—
98C22×C4—21no—
99C22×C4#9511yescharacteristic
100M16—41no—
101M16—41no—
102M16—42no—
103M16—81no—
104M16—81no—
105M16—81no—
106C2×C8—21no—
107C2×C8—21no—
108C2×C8—21no—
109C2×C8—21no—
110C2×C8—21no—
111C2×C8—41no—
112C2×C8—41no—
113C2×C8—41no—
114C2×C8—41no—
115C2×C8—41no—
116C2×C8—81no—
117C2×C8#9911yescharacteristic
118C2×C8#9911yescharacteristic
119C4⋊C4—41no—
120C4⋊C4—81no—
121C22⋊C4—41no—
122C22⋊C4—41no—
123C22⋊C4—42no—
124C42—21no—
125C42—81no—
126C42C4×C811yescharacteristic
127C42#9711yescharacteristic
128C16—42no—
129C16—82no—
130C16—81no—
131C23—21no—
132C23—21no—
133C23#34411yescharacteristic
134Q8—41no—
135Q8—41no—
136D4—41no—
137D4—41no—
138D4—81no—
139D4—81no—
140D4—82no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—81no—
152C2×C4—82no—
153C2×C4#33611yescharacteristic
154C2×C4#34211yescharacteristic
155C8—21no—
156C8—41no—
157C8—41no—
158C8—41no—
159C8—82no—
160C8#35311yescharacteristic
161C8#35411yescharacteristic
162C22—21no—
163C22—41no—
164C22—41no—
165C22—41no—
166C22—81no—
167C22—81no—
168C22#128211yescharacteristic
169C4—21no—
170C4—41no—
171C4—41no—
172C4—41no—
173C4—41no—
174C4—162no—
175C4#139311yescharacteristic
176C4#139511yescharacteristic
177C2—21no—
178C2—41no—
179C2—81no—
180C2—81no—
181C2#720511yescharacteristic
subgroupG/H
centerC8#354
commutatorC42C4×C8
Frattini, cosocle#2931C22
socleC2#7205
prime radical#532C2×C4
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C8 ◁ C2×C8 ◁ C22×C8 ◁ #2931 ◁ G
LECSG ▷ #2931 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
5. #2150C4semidirect
11. C2×#346C4semidirect
14. #1327C4semidirect

Maximal subgroups

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

subgroupindex
#131922
#126332
#114852