Finite Group Databasebeta

← #144539

Subgroups — #144539

Order 512.

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

normal subgroups only

This group has 264 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#29230C211yesmaximal, characteristic
2#13262C211yesmaximal, characteristic
3#13262C211yesmaximal, characteristic
4#9772C211yesmaximal, characteristic
5#7270C211yesmaximal, characteristic
6#7181C211yesmaximal, characteristic
7#7180C211yesmaximal, characteristic
8C2×#494C2211yescharacteristic
9C2×#364C2211yescharacteristic
10C2×#364C2211yescharacteristic
11C2×#362—21no—
12C2×#362—21no—
13#2141—21no—
14#2141—21no—
15#2102—22no—
16#1953—21no—
17#1953—21no—
18#1848C2211yescharacteristic
19#1833—21no—
20#1833—21no—
21#1772C2211yescharacteristic
22#1772C2211yescharacteristic
23#1546—22no—
24#1450C2211yescharacteristic
25C22×Q16—21no—
26C22×Q16—21no—
27C2×C4⋊Q8—21no—
28C2×M32—21no—
29C2×M32—21no—
30#494—21no—
31#494—21no—
32#494—21no—
33#494Q812yes—
34#431—21no—
35#430—22no—
36C2×#108—21no—
37C2×#108—21no—
38C2×#108D411yescharacteristic
39C2×#108D411yescharacteristic
40#427D411yescharacteristic
41#427D411yescharacteristic
42#423D412yes—
43#405—21no—
44#405—21no—
45C2×C4×C8C2311yescharacteristic
46#364—21no—
47#364—21no—
48#364—21no—
49#364—21no—
50#362—42no—
51#362—42no—
52#358—42no—
53#358—42no—
54#344—22no—
55#344—22no—
56#339—21no—
57#339—21no—
58H(3,ℤ/4)—22no—
59#332—44no—
60#322—21no—
61C82—21no—
62C22×Q8—41no—
63C2×Q16—22no—
64C2×Q16—22no—
65C2×Q16—41no—
66C2×Q16—41no—
67C2×Q16—41no—
68C2×Q16—41no—
69C2×Q16—41no—
70C2×Q16—41no—
71C2×Q16—41no—
72C2×Q16—41no—
73C2×Q16—41no—
74C2×Q16—41no—
75C2×M16—22no—
76C2×M16—21no—
77C2×M16—21no—
78C22×C8C2×D411yescharacteristic
79C22×C8C2×D411yescharacteristic
80C4⋊Q8—22no—
81C4⋊Q8—42no—
82C4⋊Q8—41no—
83#117—21no—
84#117—21no—
85C2×C4⋊C4—42no—
86C2×C42C2×D411yescharacteristic
87M32—41no—
88M32—41no—
89M32—41no—
90M32—41no—
91C2×C16—41no—
92C2×C16—41no—
93#108—21no—
94#108—21no—
95#108—21no—
96#108—21no—
97#108—41no—
98#108—41no—
99#108—41no—
100#108—41no—
101#108—82no—
102#107—21no—
103#107—21no—
104#106—21no—
105#106—21no—
106C4⋊C8—22no—
107C4⋊C8—42no—
108C22⋊C8—41no—
109#97—41no—
110#97—41no—
111C4×C8—41no—
112C4×C8—41no—
113C4×C8—41no—
114C4×C8C2×Q811yescharacteristic
115C4×C8#4111yescharacteristic
116C4×C8#4111yescharacteristic
117C4×C8#4111yescharacteristic
118C2×Q8—42no—
119C2×Q8—81no—
120C2×Q8—81no—
121C2×Q8—81no—
122C2×Q8—81no—
123C2×Q8—81no—
124C22×C4—21no—
125C22×C4—81no—
126C22×C4#12011yescharacteristic
127Q16—42no—
128Q16—42no—
129Q16—42no—
130Q16—42no—
131Q16—81no—
132Q16—81no—
133Q16—81no—
134Q16—81no—
135M16—41no—
136M16—41no—
137M16—42no—
138M16—42no—
139M16—41no—
140M16—41no—
141C2×C8—42no—
142C2×C8—41no—
143C2×C8—41no—
144C2×C8—42no—
145C2×C8C22⋊Q811yescharacteristic
146C2×C8C22⋊Q811yescharacteristic
147C2×C8#12411yescharacteristic
148C2×C8#12411yescharacteristic
149C2×C8#13511yescharacteristic
150C2×C8#13511yescharacteristic
151C2×C8#13511yescharacteristic
152C2×C8#13511yescharacteristic
153C2×C8AGL(1,ℤ/8)11yescharacteristic
154C2×C8AGL(1,ℤ/8)11yescharacteristic
155C2×C8AGL(1,ℤ/8)11yescharacteristic
156C2×C8AGL(1,ℤ/8)11yescharacteristic
157C4⋊C4—44no—
158C4⋊C4—41no—
159C4⋊C4—41no—
160C4⋊C4—82no—
161C22⋊C4—41no—
162C22⋊C4—41no—
163C42—21no—
164C42—41no—
165C42—41no—
166C42C22⋊Q811yescharacteristic
167C42#12411yescharacteristic
168C16—81no—
169C16—81no—
170C23#45411yescharacteristic
171Q8—82no—
172Q8—82no—
173Q8—161no—
174Q8—161no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—42no—
178C2×C4—81no—
179C2×C4—81no—
180C2×C4—82no—
181C2×C4—161no—
182C2×C4—161no—
183C2×C4#39311yescharacteristic
184C2×C4#44911yescharacteristic
185C2×C4#44911yescharacteristic
186C2×C4#44911yescharacteristic
187C2×C4#44911yescharacteristic
188C2×C4#45311yescharacteristic
189C8—82no—
190C8—82no—
191C8—81no—
192C8—81no—
193C8#47811yescharacteristic
194C8#47811yescharacteristic
195C8#47811yescharacteristic
196C8#47811yescharacteristic
197C8#48811yescharacteristic
198C8#48811yescharacteristic
199C8#49011yescharacteristic
200C8#49011yescharacteristic
201C22—41no—
202C22#162811yescharacteristic
203C22#162811yescharacteristic
204C22#202711yescharacteristic
205C4—22no—
206C4—41no—
207C4—161no—
208C4—161no—
209C4—162no—
210C4#162011yescharacteristic
211C4#162411yescharacteristic
212C4#202511yescharacteristic
213C4#202511yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2#1035111yescharacteristic
subgroupG/H
center, socleC2#10351
commutator, Frattini, cosocleC2×C4×C8C23
prime radicalC23#454
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×C4×C8 ◁ 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
#292302
#132622
#97722
#72702
#71812
#71802