Finite Group Databasebeta

← #145991

Subgroups — #145991

Order 512.

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

normal subgroups only

This group has 217 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#12036C211yesmaximal, characteristic
2#12018C211yesmaximal, characteristic
3#11962C211yesmaximal, characteristic
4#11932C211yesmaximal, characteristic
5#9798C211yesmaximal, characteristic
6#9634C211yesmaximal, characteristic
7#7245C211yesmaximal, characteristic
8C2×#494C2211yescharacteristic
9#2162C2211yescharacteristic
10#2150C2211yescharacteristic
11#1997—21no—
12#1574—21no—
13#1567C2211yescharacteristic
14#1567C2211yescharacteristic
15#1564C2211yescharacteristic
16#1548—21no—
17C8×M16C2211yescharacteristic
18#1372—21no—
19#1371—21no—
20#1370—21no—
21#1367—21no—
22#1362—21no—
23#1362—21no—
24#1362—21no—
25#1362—21no—
26#1299—21no—
27C22×Q16—21no—
28C22×Q16Q812yes—
29C2×C4⋊Q8—21no—
30C2×M32—21no—
31#494—21no—
32#494—21no—
33#494—21no—
34#494—21no—
35#431—21no—
36#431D411yescharacteristic
37#423—21no—
38#423—21no—
39C4×M16D411yescharacteristic
40C2×C4×C8C2311yescharacteristic
41C4⋊C16—21no—
42C4⋊C16—21no—
43C4⋊C16D411yescharacteristic
44C4⋊C16D411yescharacteristic
45C22⋊C16—21no—
46C4×C16—21no—
47#343—42no—
48#335—21no—
49#335—21no—
50#335—21no—
51#335—21no—
52#335—41no—
53#335D411yescharacteristic
54#335D411yescharacteristic
55#334—21no—
56#334—41no—
57#333—41no—
58#333—41no—
59#322—21no—
60C82—21no—
61C22×Q8—22no—
62C2×Q16—22no—
63C2×Q16—22no—
64C2×Q16—41no—
65C2×Q16—41no—
66C2×Q16—81no—
67C2×Q16—81no—
68C2×Q16—82no—
69C2×M16—21no—
70C2×M16—41no—
71C2×M16—41no—
72C22×C8C2×Q811yescharacteristic
73C22×C8#4111yescharacteristic
74C4⋊Q8—41no—
75C4⋊Q8—41no—
76C4⋊Q8—41no—
77C4⋊Q8—41no—
78C2×C4⋊C4—41no—
79C2×C4⋊C4—41no—
80C2×C42C2×D411yescharacteristic
81M32—81no—
82C2×C16—21no—
83C2×C16—21no—
84C2×C16—41no—
85C4⋊C8—21no—
86C4⋊C8—21no—
87C4⋊C8—41no—
88C4⋊C8—41no—
89C4⋊C8—41no—
90C4⋊C8—41no—
91C4⋊C8D811yescharacteristic
92C4⋊C8D811yescharacteristic
93C22⋊C8—21no—
94C22⋊C8—41no—
95#97—21no—
96C4×C8—21no—
97C4×C8—21no—
98C4×C8—41no—
99C4×C8C2×D411yescharacteristic
100C4×C8C2×D411yescharacteristic
101C4×C8#4111yescharacteristic
102C4×C8#4111yescharacteristic
103C2×Q8—42no—
104C2×Q8—42no—
105C2×Q8—82no—
106C2×Q8—82no—
107C22×C4—42no—
108C22×C4C22⋊Q811yescharacteristic
109C22×C4#13511yescharacteristic
110C22×C4AGL(1,ℤ/8)11yescharacteristic
111Q16—82no—
112Q16—82no—
113Q16—82no—
114Q16—81no—
115Q16—81no—
116M16—22no—
117M16—41no—
118M16—82no—
119M16—161no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—41no—
125C2×C8—41no—
126C2×C8—41no—
127C2×C8—41no—
128C2×C8—81no—
129C2×C8—81no—
130C2×C8#12111yescharacteristic
131C2×C8C22⋊Q811yescharacteristic
132C2×C8C22⋊Q811yescharacteristic
133C2×C8#12611yescharacteristic
134C4⋊C4—81no—
135C4⋊C4—81no—
136C4⋊C4—81no—
137C4⋊C4—81no—
138C42#12111yescharacteristic
139C42#12111yescharacteristic
140C42C2×D811yescharacteristic
141C42#13711yescharacteristic
142C16—41no—
143C16—41no—
144C16—81no—
145C23#47811yescharacteristic
146Q8—82no—
147Q8—82no—
148Q8—162no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—82no—
156C2×C4—162no—
157C2×C4#39611yescharacteristic
158C2×C4#45911yescharacteristic
159C2×C4#46411yescharacteristic
160C2×C4#46611yescharacteristic
161C2×C4#46811yescharacteristic
162C2×C4#47411yescharacteristic
163C8—21no—
164C8—21no—
165C8—21no—
166C8—42no—
167C8—41no—
168C8—41no—
169C8—81no—
170C8—81no—
171C8—161no—
172C8—161no—
173C8#47111yescharacteristic
174C8#47211yescharacteristic
175C22—21no—
176C22—21no—
177C22—21no—
178C22#206711yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—162no—
183C4#206311yescharacteristic
184C4#206911yescharacteristic
185C4#221211yescharacteristic
186C4#221411yescharacteristic
187C4#222211yescharacteristic
188C4#222311yescharacteristic
189C2—41no—
190C2#1060311yescharacteristic
191C2#1347111yescharacteristic
192C2#1347911yescharacteristic
subgroupG/H
center, socleC22#2067
commutator, Frattini, cosocleC2×C4×C8C23
prime radicalC23#478
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ C8×M16 ◁ 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
#120362
#120182
#119622
#119322
#97982
#96342
#72452