Finite Group Databasebeta

← #134816

Subgroups — #134816

Order 512.

320 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 78 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
1C8×C4⋊Q8C211yesmaximal, characteristic
2#11532C212yesmaximal
3#8623C212yesmaximal
4#7248C212yesmaximal
5C2×C8×Q8C411yescharacteristic
6C2×C8×Q8C2211yescharacteristic
7C4×C4⋊Q8C2211yescharacteristic
8#1984C411yescharacteristic
9#1984C2211yescharacteristic
10#1939—22no—
11#1842C411yescharacteristic
12C8×C4⋊C4—22no—
13C42×C8C411yescharacteristic
14#1568—22no—
15#1467C2214yes—
16#1325—22no—
17#1319—22no—
18#1290—22no—
19C2×C4⋊Q8Q811yescharacteristic
20C2×C4×Q8C2×C411yescharacteristic
21C2×C4×Q8C2311yescharacteristic
22C8×Q8—41no—
23C8×Q8—41no—
24C8×Q8—41no—
25C8×Q8—41no—
26#432—24no—
27C2×C4⋊C8—22no—
28C2×C4⋊C8—21no—
29C2×C4⋊C8C2×C411yescharacteristic
30C2×C4⋊C8C2×C411yescharacteristic
31C2×C4⋊C8D412yes—
32C2×C4×C8—21no—
33C2×C4×C8—21no—
34C2×C4×C8—21no—
35C2×C4×C8C2×C411yescharacteristic
36C2×C4×C8C2×C411yescharacteristic
37C2×C4×C8D412yes—
38#391D411yescharacteristic
39#391Q811yescharacteristic
40#389—22no—
41#384D411yescharacteristic
42C4×C4⋊C4—22no—
43C43C2×C411yescharacteristic
44#336—22no—
45#336—22no—
46#335—42no—
47#334—42no—
48#324—24no—
49#324—24no—
50C22×Q8C4⋊C411yescharacteristic
51C22×Q8C2×Q811yescharacteristic
52C22×C8—21no—
53C22×C8—21no—
54C22×C8C22⋊C411yescharacteristic
55C22×C8C22⋊C412yes—
56C22×C8C22⋊C411yescharacteristic
57C4⋊Q8—22no—
58C4⋊Q8—22no—
59C4×Q8—41no—
60C4×Q8—41no—
61C4×Q8—41no—
62C4×Q8—41no—
63C2×C4⋊C4—22no—
64C2×C4⋊C4—21no—
65C2×C4⋊C4—22no—
66C2×C4⋊C4C4⋊C411yescharacteristic
67C2×C4⋊C4C2×D411yescharacteristic
68C2×C4⋊C4#4112yes—
69C2×C42—21no—
70C2×C42—21no—
71C2×C42—21no—
72C2×C42C4⋊C411yescharacteristic
73C2×C42C4⋊C411yescharacteristic
74C2×C42C22×C411yescharacteristic
75C2×C42C2×D412yes—
76C4⋊C8—41no—
77C4⋊C8—42no—
78C4⋊C8—41no—
79C4⋊C8—44no—
80C4⋊C8—44no—
81C4⋊C8—42no—
82C22⋊C8—44no—
83#97—44no—
84C4×C8—24no—
85C4×C8—22no—
86C4×C8—22no—
87C4×C8—21no—
88C4×C8—21no—
89C4×C8—41no—
90C4×C8—42no—
91C4×C8—41no—
92C4×C8—41no—
93#95—22no—
94#95—22no—
95C2×Q8—21no—
96C2×Q8—21no—
97C2×Q8—21no—
98C2×Q8—41no—
99C2×Q8—41no—
100C2×Q8—41no—
101C2×Q8—41no—
102C2×Q8#10812yes—
103C22×C4—21no—
104C22×C4—21no—
105C22×C4—21no—
106C22×C4—21no—
107C22×C4C2×C22⋊C411yescharacteristic
108C22×C4C2×C4⋊C411yescharacteristic
109C22×C4#11711yescharacteristic
110C22×C4#12112yes—
111C22×C4C22⋊Q812yes—
112C2×C8—22no—
113C2×C8—22no—
114C2×C8—21no—
115C2×C8—22no—
116C2×C8—41no—
117C2×C8—41no—
118C2×C8—41no—
119C2×C8—42no—
120C2×C8—42no—
121C2×C8—41no—
122C2×C8—84no—
123C2×C8#9911yescharacteristic
124C2×C8#9911yescharacteristic
125C4⋊C4—28no—
126C4⋊C4—41no—
127C4⋊C4—42no—
128C4⋊C4—41no—
129C4⋊C4—44no—
130C4⋊C4—42no—
131C42—22no—
132C42—22no—
133C42—22no—
134C42—21no—
135C42—21no—
136C42—22no—
137C42—21no—
138C42—41no—
139C42—42no—
140C42—41no—
141C42—41no—
142C42#10812yes—
143C23#38011yescharacteristic
144Q8—42no—
145Q8—42no—
146Q8—42no—
147Q8—42no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—21no—
151C2×C4—22no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—41no—
170C2×C4C2×#9911yescharacteristic
171C2×C4#41011yescharacteristic
172C2×C4C2×#10811yescharacteristic
173C2×C4C2×#10811yescharacteristic
174C8—21no—
175C8—42no—
176C8—41no—
177C8—42no—
178C8—81no—
179C8—164no—
180C8#35612yes—
181C22—21no—
182C22—21no—
183C22#179911yescharacteristic
184C22#181011yescharacteristic
185C22#181311yescharacteristic
186C4—24no—
187C4—21no—
188C4—21no—
189C4—21no—
190C4—42no—
191C4—42no—
192C4—41no—
193C4—42no—
194C4—42no—
195C4—81no—
196C4C2×#35611yescharacteristic
197C4#213211yescharacteristic
198C2—21no—
199C2—21no—
200C2#861211yescharacteristic
201C2#1280211yescharacteristic
202C2#1280711yescharacteristic
subgroupG/H
center, socleC22#1799
commutatorC2×C42C22×C4
Frattini, cosocleC2×C4×Q8C23
prime radicalC23#380
LCSG ▷ C2×C42 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C8×Q8 ◁ G
LECSG ▷ C2×C4×Q8 ▷ C23 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
C8×C4⋊Q82
#115322
#86232
#72482