Finite Group Databasebeta

← #122841

Subgroups — #122841

Order 512.

273 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 273 conjugacy classes of subgroups — too many to draw. Only its 64 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#28190C211yesmaximal, characteristic
2#11494C211yesmaximal, characteristic
3#8617C211yesmaximal, characteristic
4#7091C212yesmaximal
5#7090C212yesmaximal
6C2×C8×Q8C2211yescharacteristic
7C2×C4×Q16C411yescharacteristic
8#2581—21no—
9#2163—21no—
10#2086C411yescharacteristic
11#2086C2211yescharacteristic
12#2056C411yescharacteristic
13#2056C2211yescharacteristic
14#1933—21no—
15#1933—21no—
16#1835C411yescharacteristic
17#1805—21no—
18#1801—21no—
19#1567—21no—
20#1322—21no—
21#1322C2212yes—
22#1292C2212yes—
23C22×Q16C2×C411yescharacteristic
24C2×C4×Q8—21no—
25C2×C4×Q8D411yescharacteristic
26C8×Q8—41no—
27C8×Q8—41no—
28C4×Q16—41no—
29C4×Q16—41no—
30C2×#107C2×C411yescharacteristic
31#423—22no—
32C2×C4⋊C8C2×C411yescharacteristic
33C2×C4⋊C8D411yescharacteristic
34C2×C4⋊C8C2311yescharacteristic
35C2×#103—21no—
36C2×#103—21no—
37C2×#103—21no—
38C2×#101—41no—
39C2×C4×C8C2×C411yescharacteristic
40C2×C4×C8D411yescharacteristic
41C2×C4×C8D411yescharacteristic
42#400—41no—
43#395—41no—
44#391—21no—
45#391—21no—
46#389—21no—
47#389—21no—
48#387—41no—
49#387—41no—
50#382—21no—
51C4⋊C16—41no—
52C22⋊C16—22no—
53#346—41no—
54#343—41no—
55#340—21no—
56#340—21no—
57#340—21no—
58#340C2×C411yescharacteristic
59#340C2×C411yescharacteristic
60#335—41no—
61#335—41no—
62C22×Q8—21no—
63C22×Q8D811yescharacteristic
64C2×Q16—41no—
65C2×Q16—42no—
66C2×M16—42no—
67C22×C8C22⋊C411yescharacteristic
68C22×C8C22⋊C411yescharacteristic
69C22×C8C22×C411yescharacteristic
70C22×C8C2×D411yescharacteristic
71C4×Q8—41no—
72C4×Q8—41no—
73C4×Q8—42no—
74C4×Q8—42no—
75C2×C4⋊C4—21no—
76C2×C4⋊C4—21no—
77C2×C4⋊C4—21no—
78C2×C4⋊C4—41no—
79C2×C4⋊C4—41no—
80C2×C4⋊C4—41no—
81C2×C4⋊C4D811yescharacteristic
82C2×C4⋊C4SD1611yescharacteristic
83C2×C4⋊C4SD1611yescharacteristic
84C2×C42—41no—
85C2×C42C22⋊C411yescharacteristic
86C2×C42C22⋊C411yescharacteristic
87C2×C42C2×D411yescharacteristic
88C2×C16—42no—
89#107—41no—
90C4⋊C8—41no—
91C4⋊C8—41no—
92C4⋊C8—41no—
93C4⋊C8—42no—
94C4⋊C8—42no—
95#103—42no—
96#103—42no—
97#103—41no—
98#103—41no—
99#101—82no—
100C4×C8—21no—
101C4×C8—21no—
102C4×C8—21no—
103C4×C8—21no—
104C4×C8—21no—
105C4×C8—21no—
106#95—41no—
107#95—41no—
108#95—41no—
109#95—41no—
110#95—41no—
111#95—41no—
112#95—41no—
113#95—41no—
114C2×Q8—21no—
115C2×Q8—21no—
116C2×Q8—22no—
117C2×Q8—41no—
118C2×Q8—41no—
119C2×Q8—41no—
120C2×Q8—41no—
121C2×Q8—41no—
122C2×Q8—41no—
123C2×Q8—41no—
124C22×C4—41no—
125C22×C4—41no—
126C22×C4—41no—
127C22×C4—41no—
128C22×C4#10211yescharacteristic
129C22×C4#10211yescharacteristic
130C22×C4#10211yescharacteristic
131C22×C4#10211yescharacteristic
132C22×C4C2×C22⋊C411yescharacteristic
133C22×C4C2×D811yescharacteristic
134C22×C4C2×SD1611yescharacteristic
135Q16—42no—
136Q16—42no—
137M16—82no—
138M16—82no—
139C2×C8—21no—
140C2×C8—21no—
141C2×C8—21no—
142C2×C8—41no—
143C2×C8—41no—
144C2×C8—41no—
145C2×C8—41no—
146C2×C8—82no—
147C2×C8#9911yescharacteristic
148C2×C8#9911yescharacteristic
149C4⋊C4—41no—
150C4⋊C4—41no—
151C4⋊C4—41no—
152C4⋊C4—41no—
153C4⋊C4—41no—
154C4⋊C4—41no—
155C4⋊C4—41no—
156C4⋊C4—41no—
157C4⋊C4—41no—
158C4⋊C4—82no—
159C4⋊C4—82no—
160C4⋊C4—81no—
161C4⋊C4—81no—
162C42—21no—
163C42—21no—
164C42—21no—
165C42—21no—
166C42—21no—
167C42—21no—
168C42—82no—
169C16—82no—
170C23C2×#10211yescharacteristic
171Q8—42no—
172Q8—42no—
173Q8—42no—
174Q8—42no—
175Q8—81no—
176Q8—81no—
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—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—42no—
194C2×C4—81no—
195C2×C4—81no—
196C2×C4—81no—
197C2×C4—81no—
198C2×C4—81no—
199C2×C4—81no—
200C2×C4—81no—
201C2×C4—81no—
202C2×C4—81no—
203C2×C4—81no—
204C2×C4—81no—
205C2×C4C2×#9911yescharacteristic
206C2×C4#42111yescharacteristic
207C2×C4#50911yescharacteristic
208C2×C4#51011yescharacteristic
209C8—21no—
210C8—21no—
211C8—41no—
212C8—41no—
213C8—41no—
214C8—162no—
215C22—21no—
216C22—21no—
217C22#151911yescharacteristic
218C22#213911yescharacteristic
219C22#214511yescharacteristic
220C4—21no—
221C4—21no—
222C4—21no—
223C4—41no—
224C4—41no—
225C4—41no—
226C4—41no—
227C4—41no—
228C4—82no—
229C4—161no—
230C4—161no—
231C4—161no—
232C4#212011yescharacteristic
233C4#213311yescharacteristic
234C2—21no—
235C2—21no—
236C2#1187111yescharacteristic
237C2#1187911yescharacteristic
238C2#1189011yescharacteristic
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
#281902
#114942
#86172
#70912
#70902