Finite Group Databasebeta

← #145890

Subgroups — #145890

Order 512.

262 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 80 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#28834C211yesmaximal, characteristic
2#13185C211yesmaximal, characteristic
3#12904C211yesmaximal, characteristic
4#9630C211yesmaximal, characteristic
5#7279C211yesmaximal, characteristic
6#7174C211yesmaximal, characteristic
7#7168C211yesmaximal, characteristic
8#2570—21no—
9C2×#365—21no—
10C2×#365—21no—
11C2×#365—21no—
12#2150C2211yescharacteristic
13C4×M32C2211yescharacteristic
14#2085—21no—
15#2084—21no—
16#1949—21no—
17#1943—21no—
18#1848C2211yescharacteristic
19#1847—21no—
20#1846C2211yescharacteristic
21C4×#106C2211yescharacteristic
22#1770C2211yescharacteristic
23#1571—21no—
24#1564C2211yescharacteristic
25#1383—21no—
26#1303—21no—
27C2×M32—21no—
28C2×M32—21no—
29#431—21no—
30C2×#108—21no—
31C2×#108—21no—
32C2×#107—21no—
33C2×#107—21no—
34C2×#106—21no—
35C2×#106D411yescharacteristic
36C2×#106D411yescharacteristic
37C2×#106D411yescharacteristic
38C2×#106D411yescharacteristic
39#423—21no—
40C2×C4⋊C8D411yescharacteristic
41C2×#97—21no—
42C2×C4×C8C2311yescharacteristic
43#400—41no—
44#398—41no—
45#389—21no—
46#389—21no—
47#387—41no—
48#387—41no—
49#384—21no—
50#382—21no—
51#382—21no—
52C4×C4⋊C4—21no—
53C4×C4⋊C4D411yescharacteristic
54#365—42no—
55#365—42no—
56#365—42no—
57C4⋊C16—21no—
58C4⋊C16Q812yes—
59#346—21no—
60C4×C16Q812yes—
61#340—21no—
62#340—21no—
63#340—21no—
64#336—21no—
65#335—21no—
66#335—42no—
67#334Q812yes—
68C2×M16—41no—
69C22×C8—21no—
70C22×C8C2×D411yescharacteristic
71C22×C8C2×D411yescharacteristic
72C2×C4⋊C4—21no—
73C2×C4⋊C4—21no—
74C2×C4⋊C4—21no—
75C2×C4⋊C4—21no—
76C2×C4⋊C4—21no—
77C2×C4⋊C4—41no—
78C2×C4⋊C4—41no—
79C2×C4⋊C4—41no—
80C2×C4⋊C4—41no—
81C2×C42—21no—
82C2×C42—41no—
83C2×C42C2×D411yescharacteristic
84M32—22no—
85M32—22no—
86M32—41no—
87M32—41no—
88C2×C16—22no—
89C2×C16—22no—
90#108—41no—
91#108—41no—
92#108—41no—
93#108—41no—
94#107—41no—
95#107—41no—
96#107—81no—
97#106—21no—
98#106—21no—
99#106—21no—
100#106—21no—
101#106—41no—
102#106—41no—
103#106—81no—
104C4⋊C8—22no—
105C4⋊C8—21no—
106C4⋊C8—41no—
107C4⋊C8—41no—
108C4⋊C8SD1612yes—
109C22⋊C8—41no—
110#97—41no—
111#97—41no—
112C4×C8—41no—
113C4×C8C2×Q811yescharacteristic
114C4×C8C2×Q811yescharacteristic
115C4×C8C2×Q811yescharacteristic
116C4×C8#4111yescharacteristic
117#95—41no—
118#95—41no—
119#95—41no—
120#95—41no—
121#95—41no—
122#95—41no—
123#95—41no—
124#95SD1611yescharacteristic
125#95SD1611yescharacteristic
126C22×C4—21no—
127C22×C4—21no—
128C22×C4—41no—
129C22×C4—41no—
130C22×C4—41no—
131C22×C4—41no—
132C22×C4#12011yescharacteristic
133C22×C4C2×SD1611yescharacteristic
134C22×C4AGL(1,ℤ/8)11yescharacteristic
135M16—81no—
136M16—81no—
137C2×C8—21no—
138C2×C8—21no—
139C2×C8—22no—
140C2×C8—41no—
141C2×C8—41no—
142C2×C8—42no—
143C2×C8—81no—
144C2×C8C22⋊Q811yescharacteristic
145C2×C8C22⋊Q811yescharacteristic
146C2×C8C4⋊Q811yescharacteristic
147C2×C8C4⋊Q811yescharacteristic
148C2×C8#13511yescharacteristic
149C2×C8#13511yescharacteristic
150C2×C8AGL(1,ℤ/8)11yescharacteristic
151C2×C8#13711yescharacteristic
152C4⋊C4—41no—
153C4⋊C4—41no—
154C4⋊C4—41no—
155C4⋊C4—41no—
156C4⋊C4—41no—
157C4⋊C4—41no—
158C4⋊C4—41no—
159C4⋊C4—41no—
160C4⋊C4—81no—
161C4⋊C4—82no—
162C4⋊C4—82no—
163C4⋊C4—161no—
164C4⋊C4—161no—
165C42—41no—
166C42—41no—
167C42—161no—
168C42C22⋊Q811yescharacteristic
169C42C4⋊Q811yescharacteristic
170C42C2×SD1611yescharacteristic
171C42#13711yescharacteristic
172C16—24no—
173C16—42no—
174C23#45011yescharacteristic
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—81no—
184C2×C4—81no—
185C2×C4—81no—
186C2×C4—81no—
187C2×C4—81no—
188C2×C4—81no—
189C2×C4—81no—
190C2×C4—81no—
191C2×C4—81no—
192C2×C4—81no—
193C2×C4—81no—
194C2×C4—81no—
195C2×C4#39511yescharacteristic
196C2×C4#44811yescharacteristic
197C2×C4#44911yescharacteristic
198C2×C4#45211yescharacteristic
199C2×C4#45311yescharacteristic
200C2×C4#45611yescharacteristic
201C2×C4#47511yescharacteristic
202C2×C4#47611yescharacteristic
203C2×C4#49811yescharacteristic
204C2×C4#50111yescharacteristic
205C8—21no—
206C8—21no—
207C8—42no—
208C8—82no—
209C8—161no—
210C8#47811yescharacteristic
211C8#47911yescharacteristic
212C8#49911yescharacteristic
213C8#50111yescharacteristic
214C22—21no—
215C22—21no—
216C22#163111yescharacteristic
217C22#165411yescharacteristic
218C22#205811yescharacteristic
219C4—21no—
220C4—21no—
221C4—21no—
222C4—21no—
223C4—81no—
224C4—81no—
225C4—161no—
226C4—161no—
227C4—161no—
228C4—161no—
229C4#162211yescharacteristic
230C4#165311yescharacteristic
231C4#205911yescharacteristic
232C4#206011yescharacteristic
233C2—21no—
234C2—21no—
235C2#1058011yescharacteristic
236C2#1345911yescharacteristic
237C2#1346011yescharacteristic
subgroupG/H
center, socleC22#2058
commutator, Frattini, cosocleC2×C4×C8C23
prime radicalC23#450
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1770 ◁ 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
#288342
#131852
#129042
#96302
#72792
#71742
#71682