Finite Group Databasebeta

← #94108

Subgroups — #94108

Order 512.

346 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 66 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×#1327C212yesmaximal
2#10839C211yesmaximal, characteristic
3C2×#423C2211yescharacteristic
4#2285C411yescharacteristic
5C2×C43C411yescharacteristic
6C2×#349—22no—
7C2×#339—22no—
8#1327—22no—
9#1327C414yescomplemented
10C22×M16D412yes—
11C2×#117—21no—
12C22×C42—21no—
13C22×C42—41no—
14C22×C42C2×C411yescharacteristic
15C2×M32—42no—
16#423—41no—
17#423C2×C412yes—
18#423D411yescharacteristic
19#423Q811yescharacteristic
20C2×C4⋊C8—41no—
21#384C812yes—
22#382—21no—
23#380—41no—
24C4×C4⋊C4—41no—
25C43—21no—
26C43—41no—
27C43C812yes—
28#349—24no—
29#349—42no—
30#339—44no—
31C23×C4—21no—
32C23×C4—41no—
33C23×C4C22⋊C411yescharacteristic
34C2×M16—22no—
35C2×M16—42no—
36C2×M16—42no—
37C2×M16C22⋊C412yes—
38C2×M16C4⋊C412yes—
39C22×C8—22no—
40#117—42no—
41#117—42no—
42C2×C4⋊C4—22no—
43C2×C4⋊C4—42no—
44C2×C22⋊C4—41no—
45C2×C42—21no—
46C2×C42—21no—
47C2×C42—21no—
48C2×C42—22no—
49C2×C42—22no—
50C2×C42—22no—
51C2×C42—42no—
52C2×C42—42no—
53C2×C42—41no—
54C2×C42—41no—
55C2×C42—48no—
56C2×C42—41no—
57C2×C42—41no—
58C2×C42C4211yescharacteristic
59C2×C42C4⋊C411yescharacteristic
60C2×C42C2×C811yescharacteristic
61C2×C42C2×C811yescharacteristic
62C2×C42M1611yescharacteristic
63C2×C42M1611yescharacteristic
64M32—44no—
65M32—82no—
66C2×C16—82no—
67C4⋊C8—42no—
68C4⋊C8—41no—
69C4⋊C8—41no—
70#95—42no—
71C24#10011yescharacteristic
72C22×C4—21no—
73C22×C4—21no—
74C22×C4—21no—
75C22×C4—21no—
76C22×C4—21no—
77C22×C4—21no—
78C22×C4—21no—
79C22×C4—21no—
80C22×C4—21no—
81C22×C4—21no—
82C22×C4—44no—
83C22×C4—42no—
84C22×C4—42no—
85C22×C4—48no—
86C22×C4—42no—
87C22×C4—42no—
88C22×C4#9511yescharacteristic
89C22×C4C22⋊C811yescharacteristic
90C22×C4C22⋊C811yescharacteristic
91C22×C4#9911yescharacteristic
92C22×C4#9911yescharacteristic
93C22×C4#10111yescharacteristic
94M16—42no—
95M16—42no—
96M16—82no—
97C2×C8—22no—
98C2×C8—22no—
99C2×C8—42no—
100C2×C8—42no—
101C4⋊C4—44no—
102C4⋊C4—84no—
103C22⋊C4—82no—
104C42—21no—
105C42—21no—
106C42—21no—
107C42—21no—
108C42—21no—
109C42—21no—
110C42—24no—
111C42—42no—
112C42—42no—
113C42—42no—
114C42—48no—
115C42—48no—
116C42—81no—
117C42—81no—
118C42C4×C811yescharacteristic
119C42#9711yescharacteristic
120C42C4⋊C811yescharacteristic
121C42C4⋊C811yescharacteristic
122C16—84no—
123C23—21no—
124C23—21no—
125C23—42no—
126C23#32311yescharacteristic
127C23#32311yescharacteristic
128C23#34311yescharacteristic
129C2×C4—24no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—42no—
145C2×C4—42no—
146C2×C4—42no—
147C2×C4—42no—
148C2×C4—44no—
149C2×C4—42no—
150C2×C4—48no—
151C2×C4—48no—
152C2×C4—48no—
153C2×C4—84no—
154C2×C4—82no—
155C2×C4#32411yescharacteristic
156C2×C4#32411yescharacteristic
157C2×C4#33611yescharacteristic
158C2×C4#34211yescharacteristic
159C2×C4#35311yescharacteristic
160C2×C4#35411yescharacteristic
161C2×C4#35511yescharacteristic
162C2×C4#35611yescharacteristic
163C8—42no—
164C8—42no—
165C22—22no—
166C22—21no—
167C22—21no—
168C22—41no—
169C22—41no—
170C22—42no—
171C22—42no—
172C22#128011yescharacteristic
173C22#131811yescharacteristic
174C22#131911yescharacteristic
175C4—22no—
176C4—22no—
177C4—21no—
178C4—21no—
179C4—41no—
180C4—41no—
181C4—48no—
182C4—162no—
183C4#132411yescharacteristic
184C4#132511yescharacteristic
185C4#139311yescharacteristic
186C4#139411yescharacteristic
187C2—21no—
188C2—21no—
189C2—41no—
190C2—41no—
191C2#718911yescharacteristic
192C2#735712yes—
subgroupG/H
centerC2×C4#353
commutatorC42C4×C8
Frattini, cosocleC2×#423C22
socleC22#1318
prime radicalC24#100
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C2×#423 ◁ G
LECSG ▷ C2×#423 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
9. #1327C4semidirect

Maximal subgroups

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

subgroupindex
C2×#13272
#108392