Finite Group Databasebeta

← #102187

Subgroups — #102187

Order 512.

362 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 102 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#33258C211yesmaximal, characteristic
2#9686C212yesmaximal
3#8274C211yesmaximal, characteristic
4#8132C211yesmaximal, characteristic
5#7680C212yesmaximal
6#2859C2212yes—
7#1942—21no—
8#1942—21no—
9#1942—21no—
10#1942—21no—
11#1845C411yescharacteristic
12#1845C411yescharacteristic
13#1834C412yes—
14#1767C2212yes—
15#1744C2211yescharacteristic
16C4×#97C2211yescharacteristic
17C42×C8C2211yescharacteristic
18C2×#335—21no—
19C2×#330—24no—
20#1277—21no—
21#1273—21no—
22#1273—21no—
23#1271—24no—
24C2×#125—22no—
25C2×#107—21no—
26C2×#107—21no—
27C2×#107—21no—
28C2×#107—21no—
29C2×C4⋊C8—22no—
30C2×#97—22no—
31C2×#97—21no—
32C2×#97D412yes—
33C2×C4×C8—21no—
34C2×C4×C8—21no—
35C2×C4×C8C2×C411yescharacteristic
36C2×C4×C8C2×C411yescharacteristic
37C2×C4×C8D411yescharacteristic
38C2×C4×C8D411yescharacteristic
39C2×C4×C8D411yescharacteristic
40C2×C4×C8D411yescharacteristic
41#389—22no—
42#389—22no—
43#389—22no—
44#389—22no—
45#384C2×C412yes—
46#384C2×C412yes—
47#382—22no—
48C43C2311yescharacteristic
49#340—22no—
50#340—22no—
51#336—22no—
52#336—21no—
53#336D412yes—
54#335—24no—
55#330—48no—
56C22×C8—22no—
57C22×C8—22no—
58C22×C8—42no—
59C22×C8C22⋊C411yescharacteristic
60C22×C8C22⋊C411yescharacteristic
61C22×C8C22⋊C411yescharacteristic
62C22×C8C22⋊C411yescharacteristic
63#125—44no—
64#125—44no—
65C2×C4⋊C4—22no—
66C2×C4⋊C4—22no—
67C2×C4⋊C4—22no—
68C2×C4⋊C4—22no—
69C2×C4⋊C4—22no—
70C2×C4⋊C4—22no—
71C2×C4⋊C4—42no—
72C2×C4⋊C4—42no—
73C2×C42C22×C411yescharacteristic
74C2×C42C2×D411yescharacteristic
75C2×C42C2×D411yescharacteristic
76C2×C42C2×D411yescharacteristic
77C2×C42C2×D411yescharacteristic
78C2×C42#4111yescharacteristic
79C2×C42#4111yescharacteristic
80#107—42no—
81#107—42no—
82#107—42no—
83#107—42no—
84C4⋊C8—24no—
85C4⋊C8—42no—
86#97—22no—
87#97—42no—
88#97—44no—
89#97D814yes—
90C4×C8—22no—
91C4×C8—22no—
92C4×C8—22no—
93C4×C8—41no—
94C4×C8—41no—
95C4×C8—41no—
96C4×C8—41no—
97C4×C8—41no—
98C4×C8—41no—
99C4×C8—41no—
100#95—42no—
101#95—42no—
102C22×C4—42no—
103C22×C4—42no—
104C22×C4C2×C22⋊C411yescharacteristic
105C22×C4C4×D411yescharacteristic
106C22×C4C4×D411yescharacteristic
107C22×C4#12111yescharacteristic
108C22×C4#12111yescharacteristic
109C22×C4#12411yescharacteristic
110C22×C4#12711yescharacteristic
111C2×C8—21no—
112C2×C8—21no—
113C2×C8—21no—
114C2×C8—21no—
115C2×C8—21no—
116C2×C8—21no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—21no—
120C2×C8—24no—
121C2×C8—42no—
122C2×C8—42no—
123C2×C8—42no—
124C2×C8—44no—
125C2×C8—42no—
126C2×C8—42no—
127C2×C8—82no—
128C2×C8—82no—
129C2×C8#10112yes—
130C2×C8#10112yes—
131C2×C8#10412yes—
132C4⋊C4—42no—
133C4⋊C4—42no—
134C4⋊C4—42no—
135C4⋊C4—42no—
136C4⋊C4—44no—
137C4⋊C4—44no—
138C4⋊C4—44no—
139C4⋊C4—82no—
140C4⋊C4—84no—
141C4⋊C4—82no—
142C4⋊C4—82no—
143C42—21no—
144C42—21no—
145C42—21no—
146C42—21no—
147C42—21no—
148C42—21no—
149C42—22no—
150C42—22no—
151C42—41no—
152C42C2×D812yes—
153C42#13512yes—
154C23#39011yescharacteristic
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—82no—
169C2×C4—82no—
170C2×C4—82no—
171C2×C4—82no—
172C2×C4—82no—
173C2×C4—82no—
174C2×C4C2×#10111yescharacteristic
175C2×C4C2×#10111yescharacteristic
176C2×C4C2×#10411yescharacteristic
177C2×C4#42111yescharacteristic
178C2×C4#42111yescharacteristic
179C2×C4#42111yescharacteristic
180C2×C4C4×D812yes—
181C2×C4#44412yes—
182C2×C4#46612yes—
183C2×C4#47312yes—
184C2×C4#49311yescharacteristic
185C2×C4#49511yescharacteristic
186C8—22no—
187C8—22no—
188C8—22no—
189C8—44no—
190C8—41no—
191C8—82no—
192C8—84no—
193C22#196311yescharacteristic
194C22#196611yescharacteristic
195C22#197011yescharacteristic
196C22#197511yescharacteristic
197C22#197611yescharacteristic
198C22#197911yescharacteristic
199C22#198011yescharacteristic
200C4—22no—
201C4—22no—
202C4—22no—
203C4—22no—
204C4—21no—
205C4—21no—
206C4—41no—
207C4—162no—
208C4—162no—
209C4#152811yescharacteristic
210C4#153111yescharacteristic
211C4#153411yescharacteristic
212C4#153711yescharacteristic
213C2#969011yescharacteristic
214C2#971911yescharacteristic
215C2#972711yescharacteristic
216C2#976511yescharacteristic
217C2#979211yescharacteristic
218C2#979911yescharacteristic
219C2#984711yescharacteristic
subgroupG/H
center, socle, prime radicalC23#390
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#332582
#96862
#82742
#81322
#76802