Finite Group Databasebeta

← #94102

Subgroups — #94102

Order 512.

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

normal subgroups only

This group has 352 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
1#11447C212yesmaximal
2#10839C211yesmaximal, characteristic
3C2×#423C411yescharacteristic
4#2285C2211yescharacteristic
5C2×C43C411yescharacteristic
6C2×#339—22no—
7#1458—22no—
8#1325—22no—
9#1324C414yescomplemented
10C22×M16—21no—
11C2×#117D412yes—
12C22×C42—21no—
13C22×C42—41no—
14C22×C42C2×C411yescharacteristic
15#431—42no—
16#423—21no—
17#423—41no—
18#423C812yescomplemented
19C2×C4⋊C8—41no—
20#384D411yescharacteristic
21#384Q811yescharacteristic
22#382C2×C412yes—
23#380—41no—
24C4×C4⋊C4—41no—
25C43—21no—
26C43—41no—
27C43C812yescomplemented
28#339—44no—
29#324—24no—
30#323—42no—
31C23×C4—21no—
32C23×C4—41no—
33C23×C4C22⋊C411yescharacteristic
34C2×M16—22no—
35C2×M16—41no—
36C2×M16—42no—
37C2×M16—42no—
38C22×C8—41no—
39#117—42no—
40#117—42no—
41C2×C4⋊C4—41no—
42C2×C4⋊C4—41no—
43C2×C4⋊C4C22⋊C412yes—
44C2×C4⋊C4C4⋊C412yes—
45C2×C22⋊C4—22no—
46C2×C42—21no—
47C2×C42—21no—
48C2×C42—21no—
49C2×C42—22no—
50C2×C42—22no—
51C2×C42—22no—
52C2×C42—22no—
53C2×C42—42no—
54C2×C42—42no—
55C2×C42—41no—
56C2×C42—41no—
57C2×C42—44no—
58C2×C42—44no—
59C2×C42—41no—
60C2×C42C4211yescharacteristic
61C2×C42C4⋊C411yescharacteristic
62C2×C42C2×C811yescharacteristic
63C2×C42C2×C811yescharacteristic
64C2×C42M1611yescharacteristic
65C2×C42M1611yescharacteristic
66C4⋊C8—42no—
67C4⋊C8—42no—
68C4⋊C8—82no—
69C22⋊C8—44no—
70C4×C8—82no—
71#95—42no—
72C24#9911yescharacteristic
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—21no—
83C22×C4—22no—
84C22×C4—22no—
85C22×C4—42no—
86C22×C4—42no—
87C22×C4—42no—
88C22×C4—42no—
89C22×C4—44no—
90C22×C4—44no—
91C22×C4—42no—
92C22×C4#9511yescharacteristic
93C22×C4C22⋊C811yescharacteristic
94C22×C4C22⋊C811yescharacteristic
95C22×C4#9911yescharacteristic
96C22×C4#10011yescharacteristic
97C22×C4#10111yescharacteristic
98M16—44no—
99M16—82no—
100C2×C8—42no—
101C2×C8—81no—
102C2×C8—81no—
103C2×C8—84no—
104C4⋊C4—42no—
105C4⋊C4—42no—
106C4⋊C4—82no—
107C4⋊C4—82no—
108C22⋊C4—82no—
109C42—21no—
110C42—21no—
111C42—21no—
112C42—21no—
113C42—21no—
114C42—21no—
115C42—24no—
116C42—42no—
117C42—42no—
118C42—42no—
119C42—48no—
120C42—48no—
121C42—42no—
122C42—42no—
123C42C4×C811yescharacteristic
124C42#9711yescharacteristic
125C42C4⋊C811yescharacteristic
126C42C4⋊C811yescharacteristic
127C23—21no—
128C23—21no—
129C23—41no—
130C23—41no—
131C23#32311yescharacteristic
132C23#32411yescharacteristic
133C23#34211yescharacteristic
134C2×C4—22no—
135C2×C4—22no—
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—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—42no—
151C2×C4—42no—
152C2×C4—42no—
153C2×C4—42no—
154C2×C4—44no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—48no—
158C2×C4—48no—
159C2×C4—44no—
160C2×C4—44no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—82no—
164C2×C4—82no—
165C2×C4#32311yescharacteristic
166C2×C4#32411yescharacteristic
167C2×C4#33611yescharacteristic
168C2×C4#34311yescharacteristic
169C2×C4#35311yescharacteristic
170C2×C4#35411yescharacteristic
171C2×C4#35511yescharacteristic
172C2×C4#35611yescharacteristic
173C8—82no—
174C8—164no—
175C22—21no—
176C22—21no—
177C22—21no—
178C22—21no—
179C22—41no—
180C22—41no—
181C22—42no—
182C22—41no—
183C22—41no—
184C22#128011yescharacteristic
185C22#139311yescharacteristic
186C22#139411yescharacteristic
187C4—22no—
188C4—22no—
189C4—21no—
190C4—21no—
191C4—41no—
192C4—41no—
193C4—48no—
194C4—82no—
195C4—82no—
196C4#131811yescharacteristic
197C4#131911yescharacteristic
198C4#132411yescharacteristic
199C4#132511yescharacteristic
200C2—21no—
201C2—21no—
202C2—41no—
203C2—41no—
204C2#718911yescharacteristic
205C2#750011yescharacteristic
206C2#750111yescharacteristic
subgroupG/H
centerC2×C4#354
commutatorC42C4×C8
Frattini, cosocle#2285C22
socleC22#1393
prime radicalC24#99
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ #2285 ◁ G
LECSG ▷ #2285 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
9. #1324C4semidirect
18. #423C8semidirect
27. C43C8semidirect

Maximal subgroups

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

subgroupindex
#114472
#108392