Finite Group Databasebeta

← #94148

Subgroups — #94148

Order 512.

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

normal subgroups only

This group has 205 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#12982C211yesmaximal, characteristic
2#12633C211yesmaximal, characteristic
3#11491C211yesmaximal, characteristic
4#3407C411yescharacteristic, complemented
5#2931C2211yescharacteristic
6#2163—21no—
7#2132C411yescharacteristic
8#2126C411yescharacteristic
9#2117—21no—
10#2115C411yescharacteristic, complemented
11#1757—21no—
12#1395—21no—
13#1376—21no—
14#1315—21no—
15#1315C412yescomplemented
16C2×#131C2×C411yescharacteristic
17C2×#131D411yescharacteristic
18#532C2×C411yescharacteristic
19#504—42no—
20C2×M32—21no—
21C2×M32—21no—
22C2×M32—41no—
23#436—41no—
24C8×D4—41no—
25#423Q811yescharacteristic
26#413—21no—
27#410—21no—
28#408C2×C411yescharacteristic
29#408D411yescharacteristic
30#405—41no—
31C2×C4×C8D411yescharacteristic
32C4⋊C16—41no—
33#356C812yes—
34#355—21no—
35#354C812yes—
36#353—21no—
37#350—42no—
38#349—41no—
39C22⋊C16—22no—
40#346—41no—
41#344—41no—
42C2×#41C4211yescharacteristic
43C2×#41C22⋊C411yescharacteristic
44#131—41no—
45#131—41no—
46#131—41no—
47#131—41no—
48C2×M16—21no—
49C2×M16—21no—
50C2×M16—41no—
51C2×M16C4⋊C411yescharacteristic
52C2×M16C4⋊C411yescharacteristic
53C22×C8—21no—
54C22×C8—21no—
55C22×C8C22⋊C411yescharacteristic
56C22×C8C22⋊C411yescharacteristic
57C4⋊Q8C2×C811yescharacteristic
58#127M1611yescharacteristic
59#124C2×C811yescharacteristic
60#124M1611yescharacteristic
61#121—41no—
62C4×D4—41no—
63#117—41no—
64C2×C42C4⋊C411yescharacteristic
65M32—22no—
66M32—42no—
67M32—41no—
68M32—41no—
69M32—41no—
70C2×C16—41no—
71C2×C16—42no—
72C2×C16—42no—
73C2×C16—41no—
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×Q8C4×C811yescharacteristic
90C2×Q8C22⋊C811yescharacteristic
91C2×D4—21no—
92C2×D4—21no—
93C2×D4—41no—
94C2×D4#9711yescharacteristic
95C2×D4C22⋊C811yescharacteristic
96C22×C4—21no—
97C22×C4—21no—
98C22×C4—21no—
99C22×C4#9511yescharacteristic
100M16—42no—
101M16—41no—
102M16—41no—
103M16—42no—
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
127C42C4⋊C811yescharacteristic
128C16—42no—
129C16—81no—
130C16—82no—
131C23—21no—
132C23—21no—
133C23#34411yescharacteristic
134Q8—41no—
135Q8—41no—
136D4—41no—
137D4—41no—
138D4—42no—
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—
160C8AΣL(1,𝔽16)11yescharacteristic
161C8#35211yescharacteristic
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#139011yescharacteristic
176C4#139111yescharacteristic
177C2—21no—
178C2—41no—
179C2—81no—
180C2—81no—
181C2#720411yescharacteristic
subgroupG/H
centerC4#1390
commutatorC2×Q8C4×C8
Frattini, cosocle#2931C22
socleC2#7204
prime radical#532C2×C4
LCSG ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4 ◁ 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
4. #3407C4semidirect
10. #2115C4semidirect
15. #1315C4semidirect

Maximal subgroups

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

subgroupindex
#129822
#126332
#114912