Finite Group Databasebeta

← #100799

Subgroups — #100799

Order 512.

335 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 335 conjugacy classes of subgroups — too many to draw. Only its 88 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#29223C211yesmaximal, characteristic
2#23363C211yesmaximal, characteristic
3#8593C211yesmaximal, characteristic
4#7720C211yesmaximal, characteristic
5#7720C211yesmaximal, characteristic
6#7041C211yesmaximal, characteristic
7#7041C211yesmaximal, characteristic
8#2859C2211yescharacteristic
9C4×C4⋊Q8C2211yescharacteristic
10#2100C412yes—
11#2099C412yes—
12#1993—21no—
13#1989—22no—
14#1984—22no—
15#1916—22no—
16#1916—22no—
17#1839C2211yescharacteristic
18#1839C2211yescharacteristic
19#1836—21no—
20#1831C2211yescharacteristic
21#1831C2211yescharacteristic
22#1767C2211yescharacteristic
23C2×#332—21no—
24#1296—21no—
25#1271—22no—
26#1271—22no—
27C2×C4⋊Q8D411yescharacteristic
28C2×#125—21no—
29C2×C4×Q8—21no—
30C2×C4⋊C8—21no—
31C2×C4⋊C8—21no—
32C2×C4⋊C8—21no—
33C2×C4⋊C8—22no—
34C2×#97—21no—
35C2×C4×C8—22no—
36#391—21no—
37#389—21no—
38#389—21no—
39#389—21no—
40#389—21no—
41#389—21no—
42#389C2×C412yes—
43#384C2×C411yescharacteristic
44#384C2×C411yescharacteristic
45#384D411yescharacteristic
46#382—21no—
47C4×C4⋊C4—21no—
48C4×C4⋊C4D412yes—
49C43C2311yescharacteristic
50#340—22no—
51#340—22no—
52#340—22no—
53#340—22no—
54#336—24no—
55#336—21no—
56#336—21no—
57#336—21no—
58#336—21no—
59#336—21no—
60#336—21no—
61#336—21no—
62#336—21no—
63#336C2×C412yes—
64#336D412yes—
65#336D412yes—
66#332—42no—
67C22×Q8—21no—
68C22×C8—22no—
69C22×C8—22no—
70C22×C8—22no—
71C22×C8—41no—
72C22×C8—41no—
73C4⋊Q8—21no—
74C4⋊Q8—21no—
75C4⋊Q8SD1612yes—
76C4⋊Q8Q1612yes—
77#125—44no—
78C4×Q8—81no—
79C4×Q8—81no—
80C2×C4⋊C4—21no—
81C2×C4⋊C4—21no—
82C2×C4⋊C4—21no—
83C2×C4⋊C4—21no—
84C2×C4⋊C4—21no—
85C2×C4⋊C4—22no—
86C2×C4⋊C4—21no—
87C2×C4⋊C4—21no—
88C2×C4⋊C4—21no—
89C2×C4⋊C4—21no—
90C2×C4⋊C4—41no—
91C2×C4⋊C4—41no—
92C2×C4⋊C4C22⋊C412yes—
93C2×C4⋊C4C22⋊C412yes—
94C2×C42—22no—
95C2×C42C22×C411yescharacteristic
96C2×C42C2×D411yescharacteristic
97C2×C42C2×D411yescharacteristic
98C2×C42C2×D411yescharacteristic
99C2×C42C2×D411yescharacteristic
100C2×C42#4111yescharacteristic
101C2×C42#4111yescharacteristic
102C4⋊C8—42no—
103C4⋊C8—41no—
104C4⋊C8—41no—
105C4⋊C8—41no—
106C4⋊C8—41no—
107C4⋊C8—82no—
108#97—41no—
109#97—41no—
110C4×C8—82no—
111#95—22no—
112#95—22no—
113#95—41no—
114#95—41no—
115C2×Q8—22no—
116C2×Q8—22no—
117C2×Q8—81no—
118C2×Q8—81no—
119C22×C4—22no—
120C22×C4—22no—
121C22×C4—41no—
122C22×C4—41no—
123C22×C4C2×C22⋊C411yescharacteristic
124C22×C4C4×D411yescharacteristic
125C22×C4C4×D411yescharacteristic
126C22×C4#12011yescharacteristic
127C22×C4#12111yescharacteristic
128C22×C4#12111yescharacteristic
129C22×C4#12311yescharacteristic
130C2×C8—42no—
131C2×C8—42no—
132C2×C8—42no—
133C2×C8—42no—
134C2×C8—42no—
135C2×C8—42no—
136C2×C8—42no—
137C2×C8—42no—
138C2×C8—42no—
139C2×C8—81no—
140C2×C8—81no—
141C2×C8—81no—
142C2×C8—81no—
143C2×C8—81no—
144C2×C8—81no—
145C4⋊C4—22no—
146C4⋊C4—22no—
147C4⋊C4—22no—
148C4⋊C4—42no—
149C4⋊C4—42no—
150C4⋊C4—42no—
151C4⋊C4—42no—
152C4⋊C4—42no—
153C4⋊C4—81no—
154C4⋊C4—81no—
155C4⋊C4—82no—
156C4⋊C4—81no—
157C4⋊C4—81no—
158C4⋊C4—82no—
159C4⋊C4—82no—
160C4⋊C4#10314yes—
161C42—22no—
162C42—41no—
163C42—41no—
164C42—41no—
165C42—41no—
166C42—41no—
167C42—42no—
168C42—42no—
169C42C2×SD1611yescharacteristic
170C42C2×Q1611yescharacteristic
171C42#13511yescharacteristic
172C42#13511yescharacteristic
173C23#38611yescharacteristic
174Q8—82no—
175Q8—82no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—24no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—81no—
200C2×C4—81no—
201C2×C4—81no—
202C2×C4—81no—
203C2×C4—81no—
204C2×C4—81no—
205C2×C4C2×#10311yescharacteristic
206C2×C4#41611yescharacteristic
207C2×C4#45412yes—
208C2×C4#46511yescharacteristic
209C2×C4#46511yescharacteristic
210C2×C4#46711yescharacteristic
211C2×C4#46711yescharacteristic
212C8—82no—
213C8—82no—
214C8—82no—
215C8—161no—
216C8—161no—
217C22#188111yescharacteristic
218C22#188111yescharacteristic
219C22#188811yescharacteristic
220C22#189211yescharacteristic
221C22#190411yescharacteristic
222C22#190511yescharacteristic
223C22#191511yescharacteristic
224C4—21no—
225C4—21no—
226C4—21no—
227C4—21no—
228C4—21no—
229C4—21no—
230C4—22no—
231C4—41no—
232C4—44no—
233C4—41no—
234C4—41no—
235C4—82no—
236C4—161no—
237C4—161no—
238C2#900811yescharacteristic
239C2#930311yescharacteristic
240C2#930411yescharacteristic
241C2#933511yescharacteristic
242C2#933611yescharacteristic
243C2#939611yescharacteristic
244C2#943011yescharacteristic
subgroupG/H
center, socle, prime radicalC23#386
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
#292232
#233632
#85932
#77202
#70412