Finite Group Databasebeta

← #122849

Subgroups — #122849

Order 512.

276 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 74 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#28676C211yesmaximal, characteristic
2#11493C211yesmaximal, characteristic
3#8617C211yesmaximal, characteristic
4#7089C214yesmaximal
5C2×#500C411yescharacteristic
6C2×C8×Q8C2211yescharacteristic
7#2567—21no—
8#2162—21no—
9#2087C412yes—
10#2087C2212yes—
11#1987—21no—
12#1942—21no—
13#1942—21no—
14#1801—21no—
15C4×#107C411yescharacteristic
16#1567—21no—
17#1322—21no—
18#1322C2212yes—
19#1292C2212yes—
20C2×C4⋊Q8—21no—
21C2×C4×Q8D411yescharacteristic
22#500—41no—
23#500—41no—
24C8×Q8—41no—
25C8×Q8—41no—
26C2×#107—21no—
27C2×#107—21no—
28C2×#107C2×C412yes—
29#423—22no—
30C2×C4⋊C8C2×C411yescharacteristic
31C2×C4⋊C8D411yescharacteristic
32C2×C4⋊C8C2311yescharacteristic
33C2×#101—41no—
34C2×C4×C8C2×C411yescharacteristic
35C2×C4×C8D411yescharacteristic
36C2×C4×C8D411yescharacteristic
37#395—41no—
38#395—41no—
39#391—41no—
40#389—22no—
41#389—22no—
42#384—41no—
43C4×C4⋊C4—21no—
44C4⋊C16—41no—
45C22⋊C16—22no—
46C4×C16—41no—
47#343—41no—
48#340—22no—
49#340—22no—
50#340C2×C412yes—
51#335—41no—
52#335—41no—
53C22×Q8—41no—
54C22×Q8D811yescharacteristic
55C2×M16—42no—
56C22×C8C22⋊C411yescharacteristic
57C22×C8C22⋊C411yescharacteristic
58C22×C8C22×C411yescharacteristic
59C22×C8C2×D411yescharacteristic
60C4⋊Q8—42no—
61C4⋊Q8—42no—
62C4×Q8—41no—
63C4×Q8—41no—
64C2×C4⋊C4—22no—
65C2×C4⋊C4—22no—
66C2×C4⋊C4—41no—
67C2×C4⋊C4—42no—
68C2×C4⋊C4—42no—
69C2×C4⋊C4D811yescharacteristic
70C2×C4⋊C4SD1611yescharacteristic
71C2×C4⋊C4SD1611yescharacteristic
72C2×C42—41no—
73C2×C42C22⋊C411yescharacteristic
74C2×C42C22⋊C411yescharacteristic
75C2×C42C2×D411yescharacteristic
76C2×C16—42no—
77#107—24no—
78#107—41no—
79#107—41no—
80#107—42no—
81C4⋊C8—41no—
82C4⋊C8—41no—
83C4⋊C8—41no—
84C4⋊C8—42no—
85C4⋊C8—42no—
86#101—82no—
87C4×C8—21no—
88C4×C8—21no—
89C4×C8—21no—
90C4×C8—21no—
91C4×C8—21no—
92C4×C8—21no—
93#95—41no—
94#95—42no—
95#95—42no—
96C2×Q8—41no—
97C2×Q8—41no—
98C2×Q8—82no—
99C2×Q8—162no—
100C2×Q8SD3212yes—
101C2×Q8Q3212yes—
102C22×C4—42no—
103C22×C4—42no—
104C22×C4#10211yescharacteristic
105C22×C4#10211yescharacteristic
106C22×C4#10211yescharacteristic
107C22×C4#10211yescharacteristic
108C22×C4C2×C22⋊C411yescharacteristic
109C22×C4C2×D811yescharacteristic
110C22×C4C2×SD1611yescharacteristic
111M16—82no—
112M16—82no—
113C2×C8—22no—
114C2×C8—21no—
115C2×C8—21no—
116C2×C8—21no—
117C2×C8—41no—
118C2×C8—41no—
119C2×C8—41no—
120C2×C8—82no—
121C2×C8#9911yescharacteristic
122C2×C8#9911yescharacteristic
123C4⋊C4—24no—
124C4⋊C4—41no—
125C4⋊C4—41no—
126C4⋊C4—41no—
127C4⋊C4—42no—
128C4⋊C4—42no—
129C4⋊C4—42no—
130C4⋊C4—82no—
131C4⋊C4—162no—
132C4⋊C4—162no—
133C42—21no—
134C42—21no—
135C42—21no—
136C42—21no—
137C42—21no—
138C42—21no—
139C42—82no—
140C16—82no—
141C23C2×#10211yescharacteristic
142Q8—42no—
143Q8—42no—
144Q8—164no—
145C2×C4—21no—
146C2×C4—21no—
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—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—44no—
160C2×C4—82no—
161C2×C4—82no—
162C2×C4—82no—
163C2×C4—82no—
164C2×C4—82no—
165C2×C4#35812yes—
166C2×C4#35812yes—
167C2×C4C2×#9911yescharacteristic
168C2×C4#42111yescharacteristic
169C2×C4C2×SD3211yescharacteristic
170C2×C4C2×Q3211yescharacteristic
171C8—21no—
172C8—41no—
173C8—41no—
174C8—41no—
175C8—162no—
176C8#35612yes—
177C22—21no—
178C22—21no—
179C22#151911yescharacteristic
180C22C2×#35811yescharacteristic
181C22#214511yescharacteristic
182C4—21no—
183C4—21no—
184C4—22no—
185C4—22no—
186C4—21no—
187C4—41no—
188C4—41no—
189C4—41no—
190C4—84no—
191C4—162no—
192C4#212311yescharacteristic
193C4C2×#35611yescharacteristic
194C2—21no—
195C2—21no—
196C2#1187011yescharacteristic
197C2#1188311yescharacteristic
198C2#1188711yescharacteristic
subgroupG/H
center, socleC22#1519
commutatorC22×C8C22×C4
Frattini, cosocleC2×C4⋊C8C23
prime radicalC23C2×#102
LCSG ▷ C22×C8 ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C8×Q8 ◁ G
LECSG ▷ C2×C4⋊C8 ▷ C22×C4 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#286762
#114932
#86172
#70892