Finite Group Databasebeta

← #102206

Subgroups — #102206

Order 512.

346 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 98 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#9891C212yesmaximal
3#8273C211yesmaximal, characteristic
4#8132C211yesmaximal, characteristic
5#7683C212yesmaximal
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×#334—21no—
19#1295—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—21no—
31C2×#97—22no—
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#334—24no—
55C22×C8—22no—
56C22×C8—22no—
57C22×C8—42no—
58C22×C8C22⋊C411yescharacteristic
59C22×C8C22⋊C411yescharacteristic
60C22×C8C22⋊C411yescharacteristic
61C22×C8C22⋊C411yescharacteristic
62#125—84no—
63C2×C4⋊C4—22no—
64C2×C4⋊C4—22no—
65C2×C4⋊C4—22no—
66C2×C4⋊C4—22no—
67C2×C4⋊C4—22no—
68C2×C4⋊C4—22no—
69C2×C4⋊C4—42no—
70C2×C4⋊C4—42no—
71C2×C42C22×C411yescharacteristic
72C2×C42C2×D411yescharacteristic
73C2×C42C2×D411yescharacteristic
74C2×C42C2×D411yescharacteristic
75C2×C42C2×D411yescharacteristic
76C2×C42#4111yescharacteristic
77C2×C42#4111yescharacteristic
78#107—42no—
79#107—42no—
80#107—42no—
81#107—42no—
82C4⋊C8—24no—
83C4⋊C8—42no—
84#97—24no—
85#97—24no—
86#97—44no—
87C4×C8—22no—
88C4×C8—22no—
89C4×C8—22no—
90C4×C8—41no—
91C4×C8—41no—
92C4×C8—41no—
93C4×C8—41no—
94C4×C8—41no—
95C4×C8—41no—
96C4×C8—41no—
97#95—42no—
98#95—42no—
99C22×C4—42no—
100C22×C4—42no—
101C22×C4C2×C22⋊C411yescharacteristic
102C22×C4C4×D411yescharacteristic
103C22×C4C4×D411yescharacteristic
104C22×C4#12111yescharacteristic
105C22×C4#12111yescharacteristic
106C22×C4#12411yescharacteristic
107C22×C4#12711yescharacteristic
108C2×C8—21no—
109C2×C8—21no—
110C2×C8—21no—
111C2×C8—21no—
112C2×C8—21no—
113C2×C8—21no—
114C2×C8—24no—
115C2×C8—21no—
116C2×C8—21no—
117C2×C8—21no—
118C2×C8—42no—
119C2×C8—42no—
120C2×C8—42no—
121C2×C8—44no—
122C2×C8—42no—
123C2×C8—42no—
124C2×C8—82no—
125C2×C8—82no—
126C2×C8#10112yes—
127C2×C8#10112yes—
128C2×C8#10412yes—
129C4⋊C4—42no—
130C4⋊C4—42no—
131C4⋊C4—42no—
132C4⋊C4—42no—
133C4⋊C4—44no—
134C4⋊C4—82no—
135C4⋊C4—82no—
136C4⋊C4—82no—
137C4⋊C4—84no—
138C4⋊C4—84no—
139C42—21no—
140C42—21no—
141C42—21no—
142C42—21no—
143C42—21no—
144C42—21no—
145C42—22no—
146C42—22no—
147C42—41no—
148C42#13714yes—
149C23#39011yescharacteristic
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—21no—
162C2×C4—21no—
163C2×C4—82no—
164C2×C4—82no—
165C2×C4—82no—
166C2×C4—82no—
167C2×C4—82no—
168C2×C4—82no—
169C2×C4C2×#10111yescharacteristic
170C2×C4C2×#10111yescharacteristic
171C2×C4C2×#10411yescharacteristic
172C2×C4#42111yescharacteristic
173C2×C4#42111yescharacteristic
174C2×C4#42111yescharacteristic
175C2×C4#44112yes—
176C2×C4#44312yes—
177C2×C4#47012yes—
178C2×C4#47212yes—
179C2×C4#49712yes—
180C8—22no—
181C8—22no—
182C8—22no—
183C8—44no—
184C8—41no—
185C8—82no—
186C8—84no—
187C22#196311yescharacteristic
188C22#196611yescharacteristic
189C22#197111yescharacteristic
190C22#197411yescharacteristic
191C22#197611yescharacteristic
192C22#197811yescharacteristic
193C22#198011yescharacteristic
194C4—22no—
195C4—22no—
196C4—22no—
197C4—22no—
198C4—22no—
199C4—41no—
200C4—162no—
201C4—162no—
202C4#152811yescharacteristic
203C4#153111yescharacteristic
204C4#153411yescharacteristic
205C4#153711yescharacteristic
206C2#969011yescharacteristic
207C2#972011yescharacteristic
208C2#972411yescharacteristic
209C2#976411yescharacteristic
210C2#978811yescharacteristic
211C2#981011yescharacteristic
212C2#985311yescharacteristic
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
#98912
#82732
#81322
#76832