Finite Group Databasebeta

← #93043

Subgroups — #93043

Order 512.

268 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 72 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#11459C211yesmaximal, characteristic
2#8599C211yesmaximal, characteristic
3#7981C211yesmaximal, characteristic
4C2×#431C2211yescharacteristic
5#2285—21no—
6#2162—21no—
7#1797—21no—
8C2×#335C411yescharacteristic, complemented
9C2×#335C411yescharacteristic, complemented
10#1322C412yescomplemented
11#1314—21no—
12#1289—21no—
13#1289C412yes—
14#1277—21no—
15C2×#117—41no—
16C22×C42D411yescharacteristic
17#431—41no—
18#431—41no—
19C2×C4⋊C8—21no—
20C2×C4⋊C8—21no—
21C2×C4⋊C8C2×C411yescharacteristic
22C2×C4⋊C8Q811yescharacteristic
23C2×C22⋊C8—41no—
24C2×C22⋊C8C2×C411yescharacteristic
25C2×C22⋊C8D411yescharacteristic
26C2×C4×C8C2×C411yescharacteristic
27C2×C4×C8D411yescharacteristic
28#384—41no—
29#382—22no—
30#380—22no—
31#380—41no—
32C4×C4⋊C4—22no—
33C4×C4⋊C4—41no—
34C4⋊C16—41no—
35C22⋊C16—22no—
36C4×C16—41no—
37#336—41no—
38#335—41no—
39#335—41no—
40C23×C4C22⋊C411yescharacteristic
41C23×C4D811yescharacteristic
42C23×C4SD1611yescharacteristic
43C22×C8—41no—
44C22×C8—41no—
45C22×C8C4211yescharacteristic
46C22×C8C22⋊C411yescharacteristic
47C22×C8C4⋊C411yescharacteristic
48C22×C8C4⋊C411yescharacteristic
49#117—81no—
50#117—81no—
51#117—81no—
52#117—81no—
53C2×C4⋊C4—42no—
54C2×C4⋊C4—42no—
55C2×C4⋊C4—42no—
56C2×C22⋊C4—42no—
57C2×C42—21no—
58C2×C42—21no—
59C2×C42—21no—
60C2×C42—21no—
61C2×C42—42no—
62C2×C42C22⋊C411yescharacteristic
63C2×C42C4⋊C411yescharacteristic
64C2×C42SD1611yescharacteristic
65C2×C42Q1611yescharacteristic
66C2×C16—42no—
67C4⋊C8—41no—
68C4⋊C8—41no—
69C4⋊C8—41no—
70C4⋊C8—41no—
71C4⋊C8—41no—
72C4⋊C8—41no—
73C22⋊C8—41no—
74C22⋊C8—41no—
75C22⋊C8—81no—
76C22⋊C8—81no—
77C4×C8—21no—
78C4×C8—21no—
79C4×C8—21no—
80C4×C8—21no—
81#95—24no—
82#95—42no—
83C24#10211yescharacteristic
84C22×C4—21no—
85C22×C4—21no—
86C22×C4—21no—
87C22×C4—21no—
88C22×C4—21no—
89C22×C4—21no—
90C22×C4—21no—
91C22×C4—21no—
92C22×C4—41no—
93C22×C4—41no—
94C22×C4—44no—
95C22×C4—81no—
96C22×C4#9511yescharacteristic
97C22×C4#10211yescharacteristic
98C22×C4#10311yescharacteristic
99C22×C4#10311yescharacteristic
100C22×C4#10611yescharacteristic
101C22×C4#10711yescharacteristic
102C22×C4D1611yescharacteristic
103C22×C4SD3211yescharacteristic
104C22×C4SD3211yescharacteristic
105C22×C4Q3211yescharacteristic
106C2×C8—21no—
107C2×C8—21no—
108C2×C8—21no—
109C2×C8—21no—
110C2×C8—41no—
111C2×C8—41no—
112C2×C8—41no—
113C2×C8—41no—
114C2×C8—81no—
115C2×C8—81no—
116C2×C8—81no—
117C2×C8—81no—
118C2×C8—81no—
119C2×C8—81no—
120C4⋊C4—82no—
121C4⋊C4—82no—
122C4⋊C4—84no—
123C4⋊C4—82no—
124C4⋊C4—82no—
125C22⋊C4—82no—
126C22⋊C4—82no—
127C42—21no—
128C42—21no—
129C42—21no—
130C42—21no—
131C42—21no—
132C42—21no—
133C42—82no—
134C42—82no—
135C42#9911yescharacteristic
136C42#9911yescharacteristic
137C42#10411yescharacteristic
138C42#10411yescharacteristic
139C16—82no—
140C23—21no—
141C23—21no—
142C23—41no—
143C23—41no—
144C23#34011yescharacteristic
145C23#35711yescharacteristic
146C23#35811yescharacteristic
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—42no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—81no—
168C2×C4—81no—
169C2×C4—84no—
170C2×C4—84no—
171C2×C4—84no—
172C2×C4#32711yescharacteristic
173C2×C4#32711yescharacteristic
174C2×C4#32811yescharacteristic
175C2×C4#32811yescharacteristic
176C2×C4#33911yescharacteristic
177C2×C4#34211yescharacteristic
178C2×C4#35711yescharacteristic
179C2×C4#35811yescharacteristic
180C2×C4#36011yescharacteristic
181C2×C4#36011yescharacteristic
182C2×C4#36611yescharacteristic
183C2×C4#36711yescharacteristic
184C8—41no—
185C8—41no—
186C8—41no—
187C8—41no—
188C8—161no—
189C8—161no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—41no—
195C22—41no—
196C22—41no—
197C22—41no—
198C22—81no—
199C22#129411yescharacteristic
200C22#138011yescharacteristic
201C22#138611yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—21no—
206C4—21no—
207C4—41no—
208C4—41no—
209C4—164no—
210C4#134711yescharacteristic
211C4#134711yescharacteristic
212C4#134811yescharacteristic
213C4#134811yescharacteristic
214C4#139111yescharacteristic
215C4#139511yescharacteristic
216C2—21no—
217C2—21no—
218C2—41no—
219C2—41no—
220C2#725211yescharacteristic
221C2#725611yescharacteristic
222C2#725811yescharacteristic
subgroupG/H
centerC2×C4#327
commutatorC22×C8C42
Frattini, cosocleC2×#431C22
socleC22#1294
prime radicalC24#102
LCSG ▷ C22×C8 ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×#431 ◁ G
LECSG ▷ C2×#431 ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
8. C2×#335C4semidirect
9. C2×#335C4semidirect
10. #1322C4semidirect

Maximal subgroups

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

subgroupindex
#114592
#85992
#79812