Finite Group Databasebeta

← #145562

Subgroups — #145562

Order 512.

262 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C2×#2245C211yesmaximal, characteristic
2#13273C211yesmaximal, characteristic
3#13262C211yesmaximal, characteristic
4#13162C211yesmaximal, characteristic
5C2×#1366C211yesmaximal, characteristic
6C2×#1358C211yesmaximal, characteristic
7#7161C211yesmaximal, characteristic
8C2×#499C2211yescharacteristic
9C2×#494C2211yescharacteristic
10#2245—22no—
11#2245—22no—
12C2×#364C2211yescharacteristic
13C2×#364C2211yescharacteristic
14C2×#364C2211yescharacteristic
15#2151—21no—
16C2×#362—21no—
17#2141—21no—
18C2×#358—21no—
19C2×#358—21no—
20C2×#346C2211yescharacteristic
21#1772C2211yescharacteristic
22#1386—21no—
23#1383—21no—
24#1379—21no—
25#1366—22no—
26#1358—22no—
27C22×Q16—21no—
28C22×Q16—21no—
29C2×C4⋊Q8—21no—
30C2×#125—21no—
31C2×M32—21no—
32C2×M32—21no—
33C2×M32—21no—
34C22×C16D411yescharacteristic
35C22×C16D411yescharacteristic
36#499—21no—
37#499—21no—
38#499—21no—
39#499D412yes—
40#494—21no—
41#494—21no—
42#494—21no—
43#494D412yes—
44C2×#108D411yescharacteristic
45#427D411yescharacteristic
46C2×#107—21no—
47C2×#106—21no—
48#405—21no—
49C2×C4×C8C2311yescharacteristic
50#364—21no—
51#364—21no—
52#364—21no—
53#364—21no—
54#364—21no—
55#364—21no—
56C4⋊C16—42no—
57#362—42no—
58#358—24no—
59#358—24no—
60#358—42no—
61#346—21no—
62#346—21no—
63#339—21no—
64C22×Q8—41no—
65C2×Q16—22no—
66C2×Q16—22no—
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×Q16—41no—
76C2×Q16—41no—
77C2×M16—21no—
78C22×C8C2×D411yescharacteristic
79C22×C8C2×D411yescharacteristic
80C4⋊Q8—22no—
81C4⋊Q8—41no—
82C4⋊Q8—81no—
83#125—22no—
84#125—41no—
85#125—81no—
86#117—21no—
87C2×C4⋊C4—41no—
88C2×C4⋊C4—81no—
89C2×C4⋊C4—81no—
90C2×C42#4111yescharacteristic
91M32—41no—
92M32—41no—
93M32—41no—
94M32—41no—
95M32—41no—
96M32—41no—
97C2×C16—21no—
98C2×C16—21no—
99C2×C16—21no—
100C2×C16—21no—
101C2×C16—21no—
102C2×C16—21no—
103C2×C16—41no—
104C2×C16—41no—
105C2×C16—41no—
106#108—21no—
107#108—21no—
108#107—22no—
109#107—41no—
110#107SD1612yes—
111#106—21no—
112#106—22no—
113#106—41no—
114#97—41no—
115C4×C8—41no—
116C4×C8C2×D411yescharacteristic
117C4×C8C2×D411yescharacteristic
118C4×C8#4111yescharacteristic
119C4×C8#4111yescharacteristic
120C2×Q8—42no—
121C2×Q8—81no—
122C2×Q8—81no—
123C2×Q8—81no—
124C2×Q8—81no—
125C2×Q8—81no—
126C22×C4—21no—
127C22×C4—81no—
128C22×C4—81no—
129C22×C4#12111yescharacteristic
130Q16—42no—
131Q16—42no—
132Q16—42no—
133Q16—42no—
134Q16—81no—
135Q16—81no—
136Q16—81no—
137Q16—81no—
138M16—41no—
139M16—41no—
140C2×C8—41no—
141C2×C8#12011yescharacteristic
142C2×C8#12111yescharacteristic
143C2×C8#12111yescharacteristic
144C2×C8#12411yescharacteristic
145C2×C8C2×SD1611yescharacteristic
146C2×C8#13511yescharacteristic
147C2×C8#13511yescharacteristic
148C2×C8#13511yescharacteristic
149C2×C8AGL(1,ℤ/8)11yescharacteristic
150C2×C8AGL(1,ℤ/8)11yescharacteristic
151C2×C8#13711yescharacteristic
152C2×C8#13711yescharacteristic
153C4⋊C4—22no—
154C4⋊C4—42no—
155C4⋊C4—82no—
156C4⋊C4—82no—
157C4⋊C4—82no—
158C4⋊C4—82no—
159C4⋊C4—81no—
160C22⋊C4—41no—
161C42—21no—
162C42—41no—
163C42#12311yescharacteristic
164C42#12311yescharacteristic
165C16—41no—
166C16—41no—
167C16—81no—
168C16—81no—
169C16—81no—
170C23#47211yescharacteristic
171Q8—82no—
172Q8—82no—
173Q8—161no—
174Q8—161no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—82no—
180C2×C4—82no—
181C2×C4—162no—
182C2×C4—161no—
183C2×C4—161no—
184C2×C4#39411yescharacteristic
185C2×C4#46311yescharacteristic
186C2×C4#46411yescharacteristic
187C2×C4#46511yescharacteristic
188C2×C4#46811yescharacteristic
189C2×C4#47211yescharacteristic
190C8—81no—
191C8#44911yescharacteristic
192C8#45211yescharacteristic
193C8#46011yescharacteristic
194C8#46111yescharacteristic
195C8#46311yescharacteristic
196C8#46411yescharacteristic
197C8#48811yescharacteristic
198C8#48911yescharacteristic
199C22—22no—
200C22#167711yescharacteristic
201C22#169811yescharacteristic
202C22#204511yescharacteristic
203C4—41no—
204C4—41no—
205C4—82no—
206C4—162no—
207C4—162no—
208C4#167811yescharacteristic
209C4#169711yescharacteristic
210C4#204211yescharacteristic
211C4#205511yescharacteristic
212C2—21no—
213C2—21no—
214C2#1053911yescharacteristic
215C2#1246612yes—
subgroupG/H
center, socleC22#1677
commutator, Frattini, cosocleC2×C4×C8C23
prime radicalC23#472
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ 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
C2×#22452
#132732
#132622
#131622
C2×#13662
C2×#13582
#71612