Finite Group Databasebeta

← #145983

Subgroups — #145983

Order 512.

239 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 239 conjugacy classes of subgroups — too many to draw. Only its 78 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#13290C211yesmaximal, characteristic
2#13163C211yesmaximal, characteristic
3#12009C211yesmaximal, characteristic
4#11940C211yesmaximal, characteristic
5#9731C211yesmaximal, characteristic
6#9628C211yesmaximal, characteristic
7#7281C211yesmaximal, characteristic
8C2×#500C2211yescharacteristic
9C2×#364—21no—
10#2150C2211yescharacteristic
11C4×M32C2211yescharacteristic
12#1981—21no—
13#1848C2211yescharacteristic
14C8×C4⋊C4C2211yescharacteristic
15#1570—21no—
16#1564C2211yescharacteristic
17C2×#335C2211yescharacteristic
18C2×#332—21no—
19#1387—21no—
20#1387—21no—
21#1376—21no—
22#1372—21no—
23#1371—21no—
24#1364—21no—
25#1364—21no—
26#1303—21no—
27C2×C4⋊Q8—21no—
28C2×M32—21no—
29C2×M32D411yescharacteristic
30C2×M32D411yescharacteristic
31#500—21no—
32#500—21no—
33#500—21no—
34#500Q812yes—
35#431—21no—
36C2×#108—21no—
37C2×#108—21no—
38C2×#107—21no—
39C2×#107—21no—
40#423—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8D411yescharacteristic
43C2×#103—42no—
44C2×C4×C8—21no—
45C2×C4×C8C2311yescharacteristic
46C4×C4⋊C4D411yescharacteristic
47#364—42no—
48C4⋊C16—21no—
49C4⋊C16—21no—
50#346—21no—
51C4×C16—21no—
52#336—21no—
53#335—21no—
54#335—21no—
55#335D411yescharacteristic
56#335D411yescharacteristic
57#334—21no—
58#334—42no—
59#332—42no—
60C22×Q8—41no—
61C2×M16—41no—
62C22×C8—21no—
63C22×C8—41no—
64C22×C8C2×D411yescharacteristic
65C22×C8#4111yescharacteristic
66C4⋊Q8—22no—
67C4⋊Q8—41no—
68C4⋊Q8—41no—
69C4⋊Q8—41no—
70C2×C4⋊C4—21no—
71C2×C4⋊C4—41no—
72C2×C4⋊C4—41no—
73C2×C42—21no—
74C2×C42C2×D411yescharacteristic
75M32—21no—
76M32—21no—
77M32—21no—
78M32—41no—
79M32—41no—
80M32SD1612yes—
81C2×C16—21no—
82C2×C16—21no—
83C2×C16—41no—
84#108—41no—
85#108—41no—
86#108—81no—
87#107—22no—
88#107—22no—
89#107—41no—
90#107—41no—
91C4⋊C8—21no—
92C4⋊C8—21no—
93C4⋊C8—21no—
94C4⋊C8—41no—
95C4⋊C8—41no—
96C4⋊C8—41no—
97C4⋊C8—41no—
98C4⋊C8D812yes—
99#103—84no—
100C22⋊C8—41no—
101C4×C8—41no—
102C4×C8—41no—
103C4×C8—41no—
104C4×C8C2×D411yescharacteristic
105C4×C8C2×Q811yescharacteristic
106C4×C8#4111yescharacteristic
107C4×C8#4111yescharacteristic
108#95—21no—
109C2×Q8—42no—
110C2×Q8—82no—
111C2×Q8—82no—
112C2×Q8—81no—
113C22×C4—41no—
114C22×C4—81no—
115C22×C4#12111yescharacteristic
116C22×C4AGL(1,ℤ/8)11yescharacteristic
117C22×C4#13711yescharacteristic
118M16—81no—
119M16—81no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—22no—
123C2×C8—41no—
124C2×C8—41no—
125C2×C8—41no—
126C2×C8—41no—
127C2×C8—82no—
128C2×C8—81no—
129C2×C8—81no—
130C2×C8#12111yescharacteristic
131C2×C8C22⋊Q811yescharacteristic
132C2×C8C22⋊Q811yescharacteristic
133C2×C8#12611yescharacteristic
134C2×C8C2×SD1611yescharacteristic
135C2×C8#13511yescharacteristic
136C2×C8#13711yescharacteristic
137C2×C8#13711yescharacteristic
138C4⋊C4—22no—
139C4⋊C4—41no—
140C4⋊C4—42no—
141C4⋊C4—42no—
142C4⋊C4—81no—
143C4⋊C4—81no—
144C42—41no—
145C42—41no—
146C42#12111yescharacteristic
147C42C22⋊Q811yescharacteristic
148C42C2×D811yescharacteristic
149C42#13511yescharacteristic
150C16—22no—
151C16—41no—
152C16—81no—
153C23#46811yescharacteristic
154Q8—84no—
155Q8—161no—
156Q8—161no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—42no—
161C2×C4—81no—
162C2×C4—81no—
163C2×C4—82no—
164C2×C4—162no—
165C2×C4#39611yescharacteristic
166C2×C4#45911yescharacteristic
167C2×C4#46111yescharacteristic
168C2×C4#46411yescharacteristic
169C2×C4#46411yescharacteristic
170C2×C4#46611yescharacteristic
171C2×C4#47111yescharacteristic
172C2×C4#47311yescharacteristic
173C2×C4#47411yescharacteristic
174C2×C4#47811yescharacteristic
175C8—21no—
176C8—21no—
177C8—42no—
178C8—81no—
179C8—81no—
180C8—161no—
181C8—161no—
182C8#46511yescharacteristic
183C8#47011yescharacteristic
184C8#47511yescharacteristic
185C8#47911yescharacteristic
186C22—21no—
187C22—21no—
188C22#169111yescharacteristic
189C22#170011yescharacteristic
190C22#206711yescharacteristic
191C4—21no—
192C4—21no—
193C4—21no—
194C4—82no—
195C4—162no—
196C4#167311yescharacteristic
197C4#168211yescharacteristic
198C4#206411yescharacteristic
199C4#206611yescharacteristic
200C4#221211yescharacteristic
201C4#221311yescharacteristic
202C2—21no—
203C2—21no—
204C2#1060211yescharacteristic
205C2#1347311yescharacteristic
206C2#1347811yescharacteristic
subgroupG/H
center, socleC22#2067
commutator, Frattini, cosocleC2×C4×C8C23
prime radicalC23#468
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ C8×C4⋊C4 ◁ 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
#132902
#131632
#120092
#119402
#97312
#96282
#72812