Finite Group Databasebeta

← #145962

Subgroups — #145962

Order 512.

224 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 76 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#13286C211yesmaximal, characteristic
2#13160C211yesmaximal, characteristic
3#11999C211yesmaximal, characteristic
4#11934C211yesmaximal, characteristic
5#9749C211yesmaximal, characteristic
6#9628C211yesmaximal, characteristic
7#7277C211yesmaximal, characteristic
8#3160C2211yescharacteristic
9C2×C4⋊C16—21no—
10C2×C4⋊C16C2211yescharacteristic
11C2×#346C2211yescharacteristic
12#1848C2211yescharacteristic
13C8×C4⋊C4C2211yescharacteristic
14#1570—21no—
15#1564C2211yescharacteristic
16#1564C2211yescharacteristic
17#1503—21no—
18#1481—21no—
19#1382—21no—
20#1382—21no—
21#1374—21no—
22#1368—22no—
23#1363—22no—
24#1303—21no—
25#533—21no—
26C22×C16—21no—
27C22×C16D411yescharacteristic
28C22×C16D411yescharacteristic
29#500Q811yescharacteristic
30#500Q811yescharacteristic
31#499—21no—
32#499—21no—
33#498—21no—
34#431—21no—
35#431—21no—
36C2×#108—21no—
37C2×#108—21no—
38#427—21no—
39#427—21no—
40#423—21no—
41C2×C4⋊C8D411yescharacteristic
42C2×C4×C8—21no—
43C2×C4×C8C2311yescharacteristic
44C4×C4⋊C4D411yescharacteristic
45C4⋊C16—21no—
46C4⋊C16—21no—
47C4⋊C16—42no—
48#346—21no—
49#346—21no—
50#336—21no—
51#335—21no—
52#335—21no—
53#334—21no—
54#334—42no—
55#334D412yes—
56#328—41no—
57#328—41no—
58Q8⋊C8—42no—
59C2×M16—41no—
60C22×C8—21no—
61C22×C8C2×D411yescharacteristic
62C22×C8#4111yescharacteristic
63C4⋊Q8—21no—
64C4⋊Q8—21no—
65#125—41no—
66C22⋊Q8—41no—
67C22⋊Q8—41no—
68C4×Q8—41no—
69C4×Q8—41no—
70#117—41no—
71C2×C4⋊C4—21no—
72C2×C42—21no—
73C2×C42C2×D411yescharacteristic
74C2×C16—21no—
75C2×C16—21no—
76C2×C16—21no—
77C2×C16—21no—
78C2×C16—21no—
79C2×C16—41no—
80C2×C16—41no—
81C2×C16—41no—
82C2×C16SD1612yes—
83#108—41no—
84#108—41no—
85#108—81no—
86#107—21no—
87#107—21no—
88#107—21no—
89#107—21no—
90#106—41no—
91#106—41no—
92C4⋊C8—22no—
93C4⋊C8—21no—
94C4⋊C8—21no—
95C4⋊C8—41no—
96C4⋊C8—41no—
97C4⋊C8—41no—
98C22⋊C8—41no—
99C22⋊C8—41no—
100C4×C8—41no—
101C4×C8—41no—
102C4×C8—41no—
103C4×C8—41no—
104C4×C8C2×D411yescharacteristic
105C4×C8C2×Q811yescharacteristic
106C4×C8#4111yescharacteristic
107C4×C8#4111yescharacteristic
108#95SD1611yescharacteristic
109#95SD1611yescharacteristic
110C2×Q8—41no—
111C2×Q8—41no—
112C22×C4—21no—
113C22×C4—21no—
114C22×C4#12111yescharacteristic
115C22×C4C2×SD1611yescharacteristic
116C22×C4#13511yescharacteristic
117M16—81no—
118M16—81no—
119C2×C8—21no—
120C2×C8—21no—
121C2×C8—41no—
122C2×C8—42no—
123C2×C8—41no—
124C2×C8—41no—
125C2×C8—81no—
126C2×C8—81no—
127C2×C8#12111yescharacteristic
128C2×C8C22⋊Q811yescharacteristic
129C2×C8C22⋊Q811yescharacteristic
130C2×C8#12611yescharacteristic
131C2×C8C2×SD1611yescharacteristic
132C2×C8#13511yescharacteristic
133C2×C8#13711yescharacteristic
134C2×C8#13711yescharacteristic
135C4⋊C4—42no—
136C4⋊C4—41no—
137C4⋊C4—41no—
138C4⋊C4—41no—
139C4⋊C4—41no—
140C4⋊C4—81no—
141C4⋊C4—81no—
142C22⋊C4—81no—
143C42—41no—
144C42—41no—
145C42—81no—
146C42#12111yescharacteristic
147C42C22⋊Q811yescharacteristic
148C42AGL(1,ℤ/8)11yescharacteristic
149C42AGL(1,ℤ/8)11yescharacteristic
150C16—22no—
151C16—41no—
152C16—81no—
153C23#46511yescharacteristic
154Q8—82no—
155Q8—161no—
156C2×C4—22no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—81no—
165C2×C4—81no—
166C2×C4#39611yescharacteristic
167C2×C4#46011yescharacteristic
168C2×C4#46111yescharacteristic
169C2×C4#46311yescharacteristic
170C2×C4#46411yescharacteristic
171C2×C4#46911yescharacteristic
172C2×C4#47111yescharacteristic
173C2×C4#47311yescharacteristic
174C2×C4#47611yescharacteristic
175C2×C4#47811yescharacteristic
176C8—21no—
177C8—21no—
178C8—82no—
179C8—81no—
180C8—161no—
181C8—161no—
182C8#46511yescharacteristic
183C8#47011yescharacteristic
184C8#47511yescharacteristic
185C8#47911yescharacteristic
186C22—21no—
187C22—21no—
188C22#167111yescharacteristic
189C22#168011yescharacteristic
190C22#206511yescharacteristic
191C4—21no—
192C4—21no—
193C4—21no—
194C4—21no—
195C4—42no—
196C4—81no—
197C4—161no—
198C4—161no—
199C4#169311yescharacteristic
200C4#170211yescharacteristic
201C4#206411yescharacteristic
202C4#206611yescharacteristic
203C2—21no—
204C2—21no—
205C2#1059811yescharacteristic
206C2#1346611yescharacteristic
207C2#1346811yescharacteristic
subgroupG/H
centerC2×C4#469
commutator, Frattini, cosocleC2×C4×C8C23
socleC22#2065
prime radicalC23#465
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ 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
#132862
#131602
#119992
#119342
#97492
#96282
#72772