Finite Group Databasebeta

← #129693

Subgroups — #129693

Order 512.

536 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 112 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×#2985C211yesmaximal, characteristic
2#11644C214yesmaximal, complemented
3#11460C212yesmaximal
4C2×#533C411yescharacteristic
5#2985—28no—
6C2×#446—22no—
7C2×#446C2212yes—
8C2×C8×Q8C412yes—
9C2×#433—22no—
10C2×#432C411yescharacteristic
11C2×#431C2211yescharacteristic
12#2163C2214yes—
13#1338—28no—
14#1322—22no—
15#1314—22no—
16#533—24no—
17#533—24no—
18C2×C4⋊Q8C811yescharacteristic
19C2×C4⋊Q8C811yescharacteristic
20C2×#125—21no—
21C2×C22⋊Q8—21no—
22C2×C22⋊Q8C812yes—
23C2×C4×Q8—21no—
24C2×C4×Q8C2×C412yes—
25C2×#117—21no—
26C22×C42C2×C411yescharacteristic
27#446—216no—
28#446—24no—
29#446D418yes—
30C8×Q8—24no—
31C8×Q8—24no—
32#433—216no—
33#432—24no—
34#431—24no—
35C2×C4⋊C8—22no—
36C2×C4⋊C8—22no—
37C2×C4⋊C8C2×C412yes—
38C2×C4⋊C8D412yes—
39C2×C22⋊C8—21no—
40C2×C22⋊C8D412yes—
41C2×#97—22no—
42C2×#97—21no—
43C2×C4×C8—22no—
44C2×C4×C8C2×C411yescharacteristic
45C2×C4×C8C2311yescharacteristic
46C4⋊C16—24no—
47C22⋊C16—24no—
48#346—24no—
49C22×Q8—21no—
50C22×Q8C2×C812yes—
51C23×C4C22⋊C411yescharacteristic
52C23×C4C2×C811yescharacteristic
53C23×C4M1611yescharacteristic
54C22×C8—22no—
55C22×C8C22⋊C412yes—
56C22×C8C2×D412yes—
57C4⋊Q8—24no—
58C4⋊Q8—24no—
59#125—28no—
60C22⋊Q8—28no—
61C22⋊Q8—24no—
62C22⋊Q8—24no—
63C4×Q8—24no—
64C4×Q8—24no—
65C4×Q8—22no—
66C4×Q8—22no—
67C4×Q8C22⋊C414yes—
68C4×Q8M1614yes—
69#117—24no—
70#117—24no—
71C2×C4⋊C4—21no—
72C2×C4⋊C4—21no—
73C2×C4⋊C4—21no—
74C2×C4⋊C4—22no—
75C2×C4⋊C4—22no—
76C2×C4⋊C4C2×C812yes—
77C2×C22⋊C4—22no—
78C2×C42—22no—
79C2×C42—22no—
80C2×C42—22no—
81C2×C42C22⋊C411yescharacteristic
82C2×C42C2×C811yescharacteristic
83C2×C42M1611yescharacteristic
84C2×C42C22×C411yescharacteristic
85C2×C16—44no—
86C4⋊C8—28no—
87C4⋊C8—28no—
88C4⋊C8—24no—
89C4⋊C8—22no—
90C4⋊C8C22⋊C414yes—
91C22⋊C8—24no—
92C22⋊C8—24no—
93#97—24no—
94#97—28no—
95C4×C8—28no—
96C4×C8—22no—
97C4×C8C2×D414yes—
98C24C22⋊C811yescharacteristic
99C2×Q8—24no—
100C2×Q8—22no—
101C2×Q8—44no—
102C2×Q8—82no—
103C2×Q8C22⋊C814yes—
104C22×C4—22no—
105C22×C4—22no—
106C22×C4—21no—
107C22×C4—22no—
108C22×C4—21no—
109C22×C4—22no—
110C22×C4—42no—
111C22×C4—42no—
112C22×C4—81no—
113C22×C4C22⋊C811yescharacteristic
114C22×C4C22⋊C811yescharacteristic
115C22×C4C22⋊C811yescharacteristic
116C22×C4C2×C22⋊C411yescharacteristic
117C22×C4C22×C811yescharacteristic
118C22×C4C2×M1611yescharacteristic
119C2×C8—22no—
120C2×C8—24no—
121C2×C8—42no—
122C2×C8—44no—
123C2×C8—42no—
124C2×C8#12014yes—
125C4⋊C4—24no—
126C4⋊C4—24no—
127C4⋊C4—28no—
128C4⋊C4—24no—
129C4⋊C4—22no—
130C4⋊C4—24no—
131C4⋊C4—24no—
132C4⋊C4C22⋊C814yes—
133C22⋊C4—28no—
134C42—24no—
135C42—21no—
136C42—22no—
137C42—21no—
138C42—22no—
139C42—24no—
140C42C2×C22⋊C412yes—
141C42C2×M1612yes—
142C16—84no—
143C23—21no—
144C23—22no—
145C23—41no—
146C23—41no—
147C23C2×C22⋊C811yescharacteristic
148Q8—44no—
149Q8—44no—
150Q8—84no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—41no—
160C2×C4—42no—
161C2×C4—44no—
162C2×C4—44no—
163C2×C4—44no—
164C2×C4—42no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—82no—
168C2×C4#37911yescharacteristic
169C2×C4C2×C22⋊C812yes—
170C2×C4#40711yescharacteristic
171C2×C4#40712yes—
172C8—24no—
173C8—42no—
174C8—44no—
175C22—21no—
176C22—21no—
177C22—41no—
178C22—41no—
179C22—41no—
180C22—82no—
181C22#177911yescharacteristic
182C22#211512yes—
183C4—21no—
184C4—22no—
185C4—22no—
186C4—41no—
187C4—41no—
188C4—44no—
189C4—44no—
190C4—41no—
191C4#179612yes—
192C2—22no—
193C2—81no—
194C2#832311yescharacteristic
195C2#1268211yescharacteristic
196C2#1268611yescharacteristic
subgroupG/H
centerC2×C4#379
commutatorC22×C4C22×C8
Frattini, cosocleC2×C4×C8C23
socleC22#1779
prime radicalC24C22⋊C8
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ G
LECSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #11644C2semidirect

Maximal subgroups

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

subgroupindex
C2×#29852
#116442
#114602