Finite Group Databasebeta

← #145899

Subgroups — #145899

Order 512.

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

normal subgroups only

This group has 254 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#12887C211yesmaximal, characteristic
4#9631C211yesmaximal, characteristic
5#7279C211yesmaximal, characteristic
6#7174C211yesmaximal, characteristic
7#7168C211yesmaximal, characteristic
8#2570—21no—
9C2×#365—21no—
10#2150C2211yescharacteristic
11C4×M32C2211yescharacteristic
12#2085—21no—
13#2084—21no—
14#1949—21no—
15#1943—21no—
16#1848C2211yescharacteristic
17#1847—21no—
18#1846C2211yescharacteristic
19C4×#106C2211yescharacteristic
20#1770C2211yescharacteristic
21#1570—21no—
22#1564C2211yescharacteristic
23#1383—21no—
24#1383—21no—
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—
55C4⋊C16—21no—
56C4⋊C16Q812yes—
57#346—21no—
58C4×C16Q812yes—
59#340—21no—
60#340—21no—
61#340—21no—
62#336—21no—
63#335—21no—
64#334—42no—
65#334Q812yes—
66C2×M16—41no—
67C22×C8—21no—
68C22×C8C2×D411yescharacteristic
69C22×C8C2×D411yescharacteristic
70C2×C4⋊C4—21no—
71C2×C4⋊C4—21no—
72C2×C4⋊C4—21no—
73C2×C4⋊C4—21no—
74C2×C4⋊C4—21no—
75C2×C4⋊C4—41no—
76C2×C4⋊C4—41no—
77C2×C4⋊C4—41no—
78C2×C4⋊C4—41no—
79C2×C42—21no—
80C2×C42—41no—
81C2×C42C2×D411yescharacteristic
82M32—41no—
83M32—41no—
84M32—41no—
85M32—41no—
86C2×C16—22no—
87C2×C16—22no—
88#108—42no—
89#108—41no—
90#108—41no—
91#107—41no—
92#107—41no—
93#107—81no—
94#106—21no—
95#106—21no—
96#106—21no—
97#106—21no—
98#106—41no—
99#106—41no—
100#106—81no—
101C4⋊C8—22no—
102C4⋊C8—21no—
103C4⋊C8—41no—
104C4⋊C8—41no—
105C4⋊C8SD1612yes—
106C22⋊C8—41no—
107#97—41no—
108#97—41no—
109C4×C8—41no—
110C4×C8C2×Q811yescharacteristic
111C4×C8C2×Q811yescharacteristic
112C4×C8C2×Q811yescharacteristic
113C4×C8#4111yescharacteristic
114#95—41no—
115#95—41no—
116#95—41no—
117#95—41no—
118#95—41no—
119#95—41no—
120#95—41no—
121#95SD1611yescharacteristic
122#95SD1611yescharacteristic
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—41no—
126C22×C4—41no—
127C22×C4—41no—
128C22×C4—41no—
129C22×C4#12011yescharacteristic
130C22×C4C2×SD1611yescharacteristic
131C22×C4AGL(1,ℤ/8)11yescharacteristic
132M16—81no—
133M16—81no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—22no—
137C2×C8—41no—
138C2×C8—41no—
139C2×C8—42no—
140C2×C8—81no—
141C2×C8C22⋊Q811yescharacteristic
142C2×C8C22⋊Q811yescharacteristic
143C2×C8C4⋊Q811yescharacteristic
144C2×C8C4⋊Q811yescharacteristic
145C2×C8#13511yescharacteristic
146C2×C8#13511yescharacteristic
147C2×C8AGL(1,ℤ/8)11yescharacteristic
148C2×C8#13711yescharacteristic
149C4⋊C4—41no—
150C4⋊C4—41no—
151C4⋊C4—41no—
152C4⋊C4—41no—
153C4⋊C4—41no—
154C4⋊C4—41no—
155C4⋊C4—41no—
156C4⋊C4—41no—
157C4⋊C4—81no—
158C4⋊C4—82no—
159C4⋊C4—82no—
160C4⋊C4—161no—
161C4⋊C4—161no—
162C42—41no—
163C42—41no—
164C42—161no—
165C42C22⋊Q811yescharacteristic
166C42C4⋊Q811yescharacteristic
167C42C2×SD1611yescharacteristic
168C42#13711yescharacteristic
169C16—42no—
170C16—42no—
171C23#45011yescharacteristic
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—41no—
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—81no—
190C2×C4—81no—
191C2×C4—81no—
192C2×C4#39511yescharacteristic
193C2×C4#44811yescharacteristic
194C2×C4#44911yescharacteristic
195C2×C4#45211yescharacteristic
196C2×C4#45411yescharacteristic
197C2×C4#45511yescharacteristic
198C2×C4#47511yescharacteristic
199C2×C4#47611yescharacteristic
200C2×C4#49811yescharacteristic
201C2×C4#50111yescharacteristic
202C8—21no—
203C8—21no—
204C8—42no—
205C8—82no—
206C8—161no—
207C8#47811yescharacteristic
208C8#47911yescharacteristic
209C8#49911yescharacteristic
210C8#50111yescharacteristic
211C22—21no—
212C22—21no—
213C22#163511yescharacteristic
214C22#164211yescharacteristic
215C22#205811yescharacteristic
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—81no—
221C4—81no—
222C4—161no—
223C4—161no—
224C4—161no—
225C4—161no—
226C4#162611yescharacteristic
227C4#164311yescharacteristic
228C4#205911yescharacteristic
229C4#206111yescharacteristic
230C2—21no—
231C2—21no—
232C2#1058211yescharacteristic
233C2#1345911yescharacteristic
234C2#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
#128872
#96312
#72792
#71742
#71682