Finite Group Databasebeta

← #126459

Subgroups — #126459

Order 512.

249 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 249 conjugacy classes of subgroups — too many to draw. Only its 56 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#32692C211yesmaximal, characteristic
2#13510C211yesmaximal, characteristic
3#13510C211yesmaximal, characteristic
4#10663C211yesmaximal, characteristic
5#7133C211yesmaximal, characteristic
6#7127C211yesmaximal, characteristic
7#7126C211yesmaximal, characteristic
8#2584—21no—
9C2×#365—21no—
10C2×#365—21no—
11#2088—21no—
12#2059—21no—
13#2059—21no—
14#1985C2211yescharacteristic
15#1944C2211yescharacteristic
16#1944C2211yescharacteristic
17#1920—21no—
18#1919—21no—
19#1849C2211yescharacteristic
20#1570—21no—
21#1487—21no—
22#1387—21no—
23#1387—21no—
24#1377C2211yescharacteristic
25#1377C2211yescharacteristic
26#1275C2211yescharacteristic
27C2×#125—21no—
28C2×C4×Q8D411yescharacteristic
29C2×M32—21no—
30C2×M32—21no—
31#431—21no—
32C2×#108—21no—
33C2×#108—21no—
34C2×#107D411yescharacteristic
35C2×#107D411yescharacteristic
36C2×#106—21no—
37C2×#106D411yescharacteristic
38C2×#106D411yescharacteristic
39#423—21no—
40C2×C4⋊C8D411yescharacteristic
41C2×#97C2311yescharacteristic
42#398—41no—
43#395—41no—
44#389—21no—
45#389—21no—
46#389—21no—
47#389—21no—
48#389—41no—
49#389—41no—
50C4×C4⋊C4—21no—
51#365—42no—
52#365—42no—
53#340—21no—
54#340—21no—
55#340—21no—
56#340—21no—
57#340—21no—
58#336—21no—
59#336—21no—
60#334—42no—
61Q8⋊C8—42no—
62C22×Q8SD1611yescharacteristic
63C2×M16—41no—
64C22×C8—21no—
65C22×C8C2×D411yescharacteristic
66C22×C8C2×D411yescharacteristic
67#125—81no—
68#125—81no—
69C4×Q8—41no—
70C4×Q8—41no—
71C2×C4⋊C4—21no—
72C2×C4⋊C4—21no—
73C2×C4⋊C4—21no—
74C2×C4⋊C4—21no—
75C2×C4⋊C4—21no—
76C2×C4⋊C4—41no—
77C2×C4⋊C4—41no—
78C2×C4⋊C4—41no—
79C2×C4⋊C4—41no—
80C2×C4⋊C4—41no—
81C2×C4⋊C4—41no—
82C2×C4⋊C4SD1611yescharacteristic
83C2×C42—21no—
84C2×C42—41no—
85C2×C42C2×D411yescharacteristic
86M32—22no—
87M32—22no—
88M32—41no—
89M32—41no—
90C2×C16—41no—
91C2×C16—41no—
92#108—41no—
93#108—41no—
94#108—41no—
95#108—41no—
96#107—41no—
97#107—41no—
98#106—21no—
99#106—21no—
100#106—81no—
101#106SD1612yes—
102#106SD1612yes—
103C4⋊C8—41no—
104C4⋊C8—41no—
105C4⋊C8—41no—
106C4⋊C8—41no—
107C22⋊C8—41no—
108#97—41no—
109C4×C8—22no—
110#95—41no—
111#95—41no—
112#95—41no—
113#95—41no—
114#95—41no—
115C2×Q8—41no—
116C2×Q8—81no—
117C22×C4—21no—
118C22×C4—21no—
119C22×C4—41no—
120C22×C4—41no—
121C22×C4—41no—
122C22×C4—41no—
123C22×C4#12011yescharacteristic
124C22×C4C2×SD1611yescharacteristic
125C22×C4AGL(1,ℤ/8)11yescharacteristic
126M16—81no—
127M16—81no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—42no—
133C2×C8—41no—
134C2×C8—41no—
135C2×C8—41no—
136C2×C8—81no—
137C2×C8C2×SD1611yescharacteristic
138C2×C8C2×SD1611yescharacteristic
139C2×C8#13711yescharacteristic
140C2×C8#13711yescharacteristic
141C4⋊C4—22no—
142C4⋊C4—22no—
143C4⋊C4—41no—
144C4⋊C4—41no—
145C4⋊C4—41no—
146C4⋊C4—41no—
147C4⋊C4—41no—
148C4⋊C4—41no—
149C4⋊C4—41no—
150C4⋊C4—81no—
151C4⋊C4—82no—
152C4⋊C4—82no—
153C4⋊C4—82no—
154C4⋊C4—82no—
155C4⋊C4—161no—
156C4⋊C4—161no—
157C42—21no—
158C42—21no—
159C42—41no—
160C42—41no—
161C42—161no—
162C16—42no—
163C16—42no—
164C23#45011yescharacteristic
165Q8—42no—
166Q8—81no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—81no—
180C2×C4—81no—
181C2×C4—81no—
182C2×C4—81no—
183C2×C4—81no—
184C2×C4—81no—
185C2×C4—81no—
186C2×C4—81no—
187C2×C4—81no—
188C2×C4—81no—
189C2×C4#44811yescharacteristic
190C2×C4#44811yescharacteristic
191C2×C4#45311yescharacteristic
192C2×C4#45611yescharacteristic
193C2×C4#45611yescharacteristic
194C2×C4#45811yescharacteristic
195C8—21no—
196C8—21no—
197C8—21no—
198C8—21no—
199C8—82no—
200C8—81no—
201C8—161no—
202C22—21no—
203C22—21no—
204C22#161311yescharacteristic
205C22#165111yescharacteristic
206C22#165111yescharacteristic
207C4—41no—
208C4—41no—
209C4—82no—
210C4—82no—
211C4—81no—
212C4—81no—
213C4—161no—
214C4—161no—
215C4#161111yescharacteristic
216C4#161111yescharacteristic
217C4#162311yescharacteristic
218C4#166011yescharacteristic
219C2—21no—
220C2—21no—
221C2#781711yescharacteristic
222C2#1230011yescharacteristic
223C2#1230311yescharacteristic
subgroupG/H
center, socleC22#1613
commutator, Frattini, cosocleC2×#97C23
prime radicalC23#450
LCSG ▷ C2×#97 ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#97 ◁ G
LECSG ▷ C2×#97 ▷ C22×C4 ▷ C2 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#326922
#135102
#106632
#71332
#71272
#71262