Finite Group Databasebeta

← #145087

Subgroups — #145087

Order 512.

267 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 267 conjugacy classes of subgroups — too many to draw. Only its 78 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#28701C211yesmaximal, characteristic
2#13289C211yesmaximal, characteristic
3#13179C211yesmaximal, characteristic
4C2×#1363C211yesmaximal, characteristic
5#11610C211yesmaximal, characteristic
6#8683C211yesmaximal, characteristic
7#7173C211yesmaximal, characteristic
8#3166—21no—
9C2×#499C2211yescharacteristic
10#2960C2211yescharacteristic
11C2×#368—21no—
12C2×C4⋊C16C2211yescharacteristic
13C4×M32C2211yescharacteristic
14#2089—21no—
15#2089—21no—
16#1998—21no—
17#1951—21no—
18#1951—21no—
19#1848C2211yescharacteristic
20C4×#108C2211yescharacteristic
21C2×#334C2211yescharacteristic
22#1550—21no—
23#1387—21no—
24#1387—21no—
25#1381—21no—
26#1363—22no—
27#1338—22no—
28#1292—21no—
29#533D411yescharacteristic
30C2×#125—21no—
31C2×M32—21no—
32C22×C16—21no—
33#501—41no—
34#501—41no—
35#499—21no—
36#499—21no—
37#499—21no—
38#499—21no—
39#499—41no—
40#499—41no—
41#446—21no—
42#446—21no—
43C8×Q8—21no—
44C8×Q8—21no—
45C2×#108—21no—
46C2×#108—21no—
47C2×#108D411yescharacteristic
48C2×#108D411yescharacteristic
49#428—21no—
50#428—21no—
51#428—21no—
52#428—21no—
53C2×#107D411yescharacteristic
54C2×#107D411yescharacteristic
55C2×#106—21no—
56#424—21no—
57#423—21no—
58#423D411yescharacteristic
59C2×C4⋊C8—21no—
60#405—21no—
61C4×M16—21no—
62C2×C4×C8C2311yescharacteristic
63#368—42no—
64C4⋊C16—21no—
65C4⋊C16D412yes—
66#346—21no—
67C4×C16—21no—
68#343—21no—
69#343—21no—
70#343—21no—
71#343—21no—
72#341—21no—
73#334—21no—
74#334—21no—
75#333—41no—
76#332—41no—
77C2×M16—21no—
78C2×M16—21no—
79C2×M16—21no—
80C2×M16—41no—
81C22×C8—41no—
82C22×C8C2×D411yescharacteristic
83C22×C8C2×D411yescharacteristic
84C4⋊Q8D811yescharacteristic
85C4⋊Q8D811yescharacteristic
86#125—21no—
87#125—41no—
88#125—41no—
89#125—41no—
90#125—41no—
91C22⋊Q8—21no—
92C22⋊Q8—21no—
93C4×Q8—21no—
94C4×Q8—21no—
95#117—21no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—41no—
99C2×C4⋊C4—41no—
100C2×C42C2×D411yescharacteristic
101M32—22no—
102M32—41no—
103C2×C16—22no—
104C2×C16—41no—
105C2×C16—41no—
106C2×C16—41no—
107#108—21no—
108#108—21no—
109#108—42no—
110#108—41no—
111#108—41no—
112#108SD1612yes—
113#108Q1612yes—
114#107—21no—
115#107—21no—
116#107—21no—
117#107—21no—
118#107—41no—
119#107—41no—
120#107—41no—
121#107—41no—
122#106—41no—
123#106—41no—
124#106—41no—
125#106—41no—
126#106—41no—
127#106—41no—
128C4⋊C8—21no—
129C4⋊C8—21no—
130C4⋊C8—41no—
131C4⋊C8—41no—
132C4⋊C8—41no—
133C4⋊C8—41no—
134C4⋊C8—41no—
135C4⋊C8—41no—
136#97—41no—
137#97—41no—
138C4×C8—41no—
139C4×C8—41no—
140C4×C8C2×D411yescharacteristic
141C4×C8#4111yescharacteristic
142C4×C8#4111yescharacteristic
143C4×C8#4111yescharacteristic
144C2×Q8—21no—
145C2×Q8—21no—
146C22×C4—41no—
147C22×C4—41no—
148C22×C4#12011yescharacteristic
149C22×C4#13511yescharacteristic
150C22×C4#13711yescharacteristic
151M16—22no—
152M16—22no—
153M16—41no—
154M16—41no—
155M16—41no—
156M16—41no—
157M16—81no—
158M16—81no—
159C2×C8—21no—
160C2×C8—21no—
161C2×C8—41no—
162C2×C8—41no—
163C2×C8—41no—
164C2×C8—81no—
165C2×C8—81no—
166C2×C8—161no—
167C2×C8#12111yescharacteristic
168C2×C8#12111yescharacteristic
169C2×C8#12311yescharacteristic
170C2×C8#12411yescharacteristic
171C2×C8C2×SD1611yescharacteristic
172C2×C8C2×Q1611yescharacteristic
173C2×C8#13711yescharacteristic
174C2×C8#13711yescharacteristic
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—21no—
178C4⋊C4—21no—
179C4⋊C4—41no—
180C4⋊C4—41no—
181C4⋊C4—41no—
182C4⋊C4—41no—
183C4⋊C4—41no—
184C4⋊C4—41no—
185C4⋊C4—81no—
186C4⋊C4—81no—
187C4⋊C4—81no—
188C4⋊C4—81no—
189C22⋊C4—41no—
190C42—41no—
191C42#12111yescharacteristic
192C42#12311yescharacteristic
193C42C2×D811yescharacteristic
194C42AGL(1,ℤ/8)11yescharacteristic
195C16—42no—
196C16—42no—
197C23#45211yescharacteristic
198Q8—81no—
199Q8—81no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—81no—
205C2×C4—81no—
206C2×C4—161no—
207C2×C4—161no—
208C2×C4#39411yescharacteristic
209C2×C4#44711yescharacteristic
210C2×C4#44811yescharacteristic
211C2×C4#45111yescharacteristic
212C2×C4#45411yescharacteristic
213C2×C4#45611yescharacteristic
214C2×C4#46611yescharacteristic
215C2×C4#46811yescharacteristic
216C2×C4#48011yescharacteristic
217C2×C4#48211yescharacteristic
218C8—21no—
219C8—21no—
220C8—42no—
221C8—42no—
222C8—81no—
223C8—161no—
224C8—161no—
225C8#46111yescharacteristic
226C8#46211yescharacteristic
227C8#48711yescharacteristic
228C8#49111yescharacteristic
229C22—21no—
230C22—21no—
231C22#163611yescharacteristic
232C22#165311yescharacteristic
233C22#203311yescharacteristic
234C4—21no—
235C4—21no—
236C4—21no—
237C4—21no—
238C4—81no—
239C4—81no—
240C4—161no—
241C4—161no—
242C4#162711yescharacteristic
243C4#164911yescharacteristic
244C4#203811yescharacteristic
245C4#204311yescharacteristic
246C2—21no—
247C2—21no—
248C2#1041911yescharacteristic
249C2#1339111yescharacteristic
250C2#1339211yescharacteristic
subgroupG/H
center, socleC22#2033
commutator, Frattini, cosocleC2×C4×C8C23
prime radicalC23#452
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2960 ◁ 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
#287012
#132892
#131792
C2×#13632
#116102
#86832
#71732