Finite Group Databasebeta

← #146071

Subgroups — #146071

Order 512.

222 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 70 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#12819C211yesmaximal, characteristic
2#12814C211yesmaximal, characteristic
3#9669C211yesmaximal, characteristic
4#8790C211yesmaximal, characteristic
5#7279C211yesmaximal, characteristic
6#7277C211yesmaximal, characteristic
7#7153C211yesmaximal, characteristic
8C2×C4×Q16C2211yescharacteristic
9#2150C2211yescharacteristic
10C2×C4⋊C16C2211yescharacteristic
11C2×#362—21no—
12C2×#358—21no—
13#1848C2211yescharacteristic
14#1846C2211yescharacteristic
15#1564C2211yescharacteristic
16#1479—21no—
17#1461—21no—
18#1450C2211yescharacteristic
19#1387—21no—
20#1380—21no—
21#1286—21no—
22#1286—21no—
23C22×Q16D411yescharacteristic
24C2×C4×Q8—21no—
25C2×M32—21no—
26C22×C16—21no—
27C4×Q16—21no—
28C4×Q16—21no—
29C4×Q16—21no—
30C4×Q16—21no—
31#431—21no—
32#431D411yescharacteristic
33#431D411yescharacteristic
34C2×#108—21no—
35C2×#108—21no—
36C2×#107—21no—
37C2×#107D411yescharacteristic
38C2×#106—21no—
39#423—21no—
40C2×#103—21no—
41C2×C4×C8C2311yescharacteristic
42#382—21no—
43C4⋊C16—21no—
44C4⋊C16—21no—
45C4⋊C16—21no—
46C4⋊C16—21no—
47#362—42no—
48#358—42no—
49#335—21no—
50#334—21no—
51Q8⋊C8—42no—
52#324—42no—
53#322—21no—
54C82—21no—
55C22×Q8—21no—
56C2×Q16—21no—
57C2×Q16—21no—
58C2×Q16—21no—
59C2×Q16—21no—
60C2×Q16—21no—
61C2×Q16SD1612yes—
62C2×M16—41no—
63C22×C8C2×D411yescharacteristic
64C22×C8#4111yescharacteristic
65C4×Q8—41no—
66C4×Q8—41no—
67C4×Q8—41no—
68C4×Q8—41no—
69C2×C4⋊C4—21no—
70C2×C4⋊C4—41no—
71C2×C4⋊C4—41no—
72C2×C42—41no—
73C2×C42C2×D411yescharacteristic
74M32—41no—
75M32—41no—
76C2×C16—41no—
77C2×C16—41no—
78C2×C16—41no—
79C2×C16—41no—
80#108—41no—
81#108—41no—
82#108—81no—
83#107—21no—
84#107—21no—
85#107—41no—
86#107—41no—
87#106—81no—
88C4⋊C8—21no—
89C4⋊C8—21no—
90C4⋊C8—41no—
91C4⋊C8—41no—
92C4⋊C8—41no—
93#103—41no—
94#103—41no—
95C22⋊C8—21no—
96C22⋊C8—21no—
97C22⋊C8—41no—
98C4×C8—21no—
99C4×C8—21no—
100C4×C8—41no—
101C4×C8#4111yescharacteristic
102C4×C8#4111yescharacteristic
103C4×C8#4111yescharacteristic
104C4×C8#4111yescharacteristic
105#95—41no—
106#95—41no—
107C2×Q8—22no—
108C2×Q8—41no—
109C2×Q8—41no—
110C2×Q8—41no—
111C2×Q8—41no—
112C2×Q8—41no—
113C22×C4—41no—
114C22×C4—41no—
115C22×C4—81no—
116C22×C4#12111yescharacteristic
117C22×C4#13511yescharacteristic
118C22×C4AGL(1,ℤ/8)11yescharacteristic
119Q16—22no—
120Q16—22no—
121Q16—41no—
122Q16—41no—
123M16—81no—
124M16—81no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—41no—
128C2×C8—41no—
129C2×C8—81no—
130C2×C8—81no—
131C2×C8#12311yescharacteristic
132C2×C8#12311yescharacteristic
133C2×C8#12611yescharacteristic
134C2×C8#12611yescharacteristic
135C2×C8C2×SD1611yescharacteristic
136C2×C8#13511yescharacteristic
137C2×C8AGL(1,ℤ/8)11yescharacteristic
138C2×C8#13711yescharacteristic
139C4⋊C4—41no—
140C4⋊C4—41no—
141C4⋊C4—81no—
142C4⋊C4—81no—
143C4⋊C4—81no—
144C4⋊C4—81no—
145C42—81no—
146C42—81no—
147C42#12311yescharacteristic
148C42#12411yescharacteristic
149C42#13511yescharacteristic
150C42AGL(1,ℤ/8)11yescharacteristic
151C16—81no—
152C16—81no—
153C23#46311yescharacteristic
154Q8—42no—
155Q8—42no—
156Q8—81no—
157Q8—81no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—42no—
161C2×C4—81no—
162C2×C4—81no—
163C2×C4—81no—
164C2×C4—161no—
165C2×C4—161no—
166C2×C4—161no—
167C2×C4—161no—
168C2×C4#39711yescharacteristic
169C2×C4#46311yescharacteristic
170C2×C4#46511yescharacteristic
171C2×C4#46811yescharacteristic
172C2×C4#47211yescharacteristic
173C2×C4#47311yescharacteristic
174C2×C4#48211yescharacteristic
175C2×C4#48211yescharacteristic
176C2×C4#48811yescharacteristic
177C2×C4#49011yescharacteristic
178C8—21no—
179C8—21no—
180C8—81no—
181C8—81no—
182C8—161no—
183C8—161no—
184C8#48111yescharacteristic
185C8#48211yescharacteristic
186C8#48311yescharacteristic
187C8#48511yescharacteristic
188C22—21no—
189C22—21no—
190C22#167911yescharacteristic
191C22#169711yescharacteristic
192C22#207311yescharacteristic
193C4—21no—
194C4—21no—
195C4—21no—
196C4—21no—
197C4—82no—
198C4—161no—
199C4—321no—
200C4#167711yescharacteristic
201C4#169911yescharacteristic
202C4#207711yescharacteristic
203C4#207811yescharacteristic
204C2—21no—
205C2—21no—
206C2#1062511yescharacteristic
207C2#1348911yescharacteristic
208C2#1349111yescharacteristic
subgroupG/H
center, socleC22#2073
commutator, Frattini, cosocleC2×C4×C8C23
prime radicalC23#463
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1450 ◁ G
LECSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#128192
#128142
#96692
#87902
#72792
#72772
#71532