Finite Group Databasebeta

← #145093

Subgroups — #145093

Order 512.

306 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 86 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#28680C211yesmaximal, characteristic
2#13284C211yesmaximal, characteristic
3#13177C211yesmaximal, characteristic
4C2×#1363C211yesmaximal, characteristic
5C2×#1338C211yesmaximal, characteristic
6#8653C211yesmaximal, characteristic
7#7178C211yesmaximal, characteristic
8C2×#499C2211yescharacteristic
9C2×#446C2211yescharacteristic
10#2584—21no—
11C2×#367—21no—
12C2×C4⋊C16C2211yescharacteristic
13C2×#346C2211yescharacteristic
14#2087—21no—
15#2086—21no—
16#1989—21no—
17#1943—21no—
18#1943—21no—
19#1845C2211yescharacteristic
20#1803—21no—
21C4×#107C2211yescharacteristic
22C2×#334C2211yescharacteristic
23#1380—21no—
24#1380—21no—
25#1380—21no—
26#1363—22no—
27#1338—22no—
28#1296—21no—
29C2×#125—21no—
30C2×C4×Q8D411yescharacteristic
31C22×C16—21no—
32C22×C16—21no—
33#499—21no—
34#499—21no—
35#499—21no—
36#499—21no—
37#446—21no—
38#446—21no—
39#446—21no—
40#446—21no—
41C2×#107—21no—
42C2×#107—21no—
43C2×#107D411yescharacteristic
44C2×#107D411yescharacteristic
45C2×#107D411yescharacteristic
46C2×#107D411yescharacteristic
47C2×#106—21no—
48C2×C4⋊C8—21no—
49C2×C4⋊C8—21no—
50C2×C4⋊C8D411yescharacteristic
51C2×#103—41no—
52C2×#97—21no—
53C2×C4×C8C2311yescharacteristic
54#398—41no—
55#395—41no—
56#389—21no—
57#389—21no—
58#389—21no—
59#389—21no—
60#389—41no—
61#389—41no—
62#384—21no—
63C4×C4⋊C4—21no—
64#367—42no—
65C4⋊C16—21no—
66C4⋊C16D412yes—
67#346—21no—
68#346—21no—
69#340—21no—
70#340—21no—
71#340—21no—
72#340—21no—
73#340—21no—
74#340—41no—
75#334—21no—
76#334—21no—
77C22×Q8D811yescharacteristic
78C22×C8—21no—
79C22×C8—41no—
80C22×C8C2×D411yescharacteristic
81C22×C8C2×D411yescharacteristic
82#125—41no—
83#125—41no—
84#125—41no—
85#125—41no—
86C4×Q8—21no—
87C4×Q8—21no—
88C4×Q8—21no—
89C4×Q8—21no—
90C2×C4⋊C4—21no—
91C2×C4⋊C4—21no—
92C2×C4⋊C4—21no—
93C2×C4⋊C4—21no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—41no—
96C2×C4⋊C4—41no—
97C2×C4⋊C4—41no—
98C2×C4⋊C4—41no—
99C2×C4⋊C4—41no—
100C2×C4⋊C4—41no—
101C2×C4⋊C4—41no—
102C2×C4⋊C4—41no—
103C2×C4⋊C4—41no—
104C2×C4⋊C4D811yescharacteristic
105C2×C42—21no—
106C2×C42—41no—
107C2×C42C2×D411yescharacteristic
108C2×C16—22no—
109C2×C16—22no—
110C2×C16—41no—
111C2×C16—41no—
112C2×C16—41no—
113C2×C16—41no—
114#107—21no—
115#107—21no—
116#107—21no—
117#107—21no—
118#107—21no—
119#107—21no—
120#107—42no—
121#107—41no—
122#107—41no—
123#107SD1612yes—
124#107Q1612yes—
125#106—41no—
126#106—41no—
127C4⋊C8—21no—
128C4⋊C8—21no—
129C4⋊C8—41no—
130C4⋊C8—41no—
131C4⋊C8—41no—
132C4⋊C8—41no—
133#103—82no—
134#97—41no—
135#97—41no—
136C4×C8C2×D411yescharacteristic
137C4×C8#4111yescharacteristic
138C4×C8#4111yescharacteristic
139C4×C8#4111yescharacteristic
140#95—41no—
141#95—41no—
142#95—41no—
143#95—41no—
144#95—41no—
145C2×Q8—21no—
146C2×Q8—21no—
147C2×Q8—41no—
148C2×Q8—41no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—41no—
152C22×C4—41no—
153C22×C4—41no—
154C22×C4—41no—
155C22×C4—81no—
156C22×C4#12011yescharacteristic
157C22×C4C2×D811yescharacteristic
158C22×C4AGL(1,ℤ/8)11yescharacteristic
159C2×C8—21no—
160C2×C8—21no—
161C2×C8—41no—
162C2×C8—41no—
163C2×C8—41no—
164C2×C8—81no—
165C2×C8—81no—
166C2×C8—81no—
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—22no—
176C4⋊C4—22no—
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—41no—
186C4⋊C4—41no—
187C4⋊C4—81no—
188C4⋊C4—81no—
189C4⋊C4—82no—
190C4⋊C4—82no—
191C4⋊C4—81no—
192C4⋊C4—81no—
193C4⋊C4—81no—
194C4⋊C4—81no—
195C4⋊C4—81no—
196C4⋊C4—81no—
197C4⋊C4—161no—
198C4⋊C4—161no—
199C4⋊C4—161no—
200C42—41no—
201C42—41no—
202C42—161no—
203C42#12111yescharacteristic
204C42#12311yescharacteristic
205C42#13511yescharacteristic
206C42#13711yescharacteristic
207C16—42no—
208C16—42no—
209C23#44711yescharacteristic
210Q8—42no—
211Q8—81no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—81no—
225C2×C4—81no—
226C2×C4—81no—
227C2×C4—81no—
228C2×C4—81no—
229C2×C4—81no—
230C2×C4—81no—
231C2×C4—81no—
232C2×C4—81no—
233C2×C4—81no—
234C2×C4—161no—
235C2×C4—161no—
236C2×C4—161no—
237C2×C4#39411yescharacteristic
238C2×C4#44811yescharacteristic
239C2×C4#45111yescharacteristic
240C2×C4#45211yescharacteristic
241C2×C4#45411yescharacteristic
242C2×C4#45611yescharacteristic
243C2×C4#46611yescharacteristic
244C2×C4#46811yescharacteristic
245C2×C4#48011yescharacteristic
246C2×C4#48211yescharacteristic
247C8—21no—
248C8—21no—
249C8—81no—
250C8—161no—
251C8#46111yescharacteristic
252C8#46211yescharacteristic
253C8#48711yescharacteristic
254C8#49111yescharacteristic
255C22#162711yescharacteristic
256C22#164911yescharacteristic
257C22#203311yescharacteristic
258C22#219011yescharacteristic
259C22#219111yescharacteristic
260C22#219311yescharacteristic
261C22#219411yescharacteristic
262C4—21no—
263C4—21no—
264C4—21no—
265C4—21no—
266C4—81no—
267C4—82no—
268C4—81no—
269C4—82no—
270C4—161no—
271C4—161no—
272C4—321no—
273C4#163611yescharacteristic
274C4#165311yescharacteristic
275C4#203811yescharacteristic
276C4#204311yescharacteristic
277C2#1041911yescharacteristic
278C2#1236111yescharacteristic
279C2#1236211yescharacteristic
280C2#1241311yescharacteristic
281C2#1241411yescharacteristic
282C2#1338511yescharacteristic
283C2#1338611yescharacteristic
subgroupG/H
center, socle, prime radicalC23#447
commutator, Frattini, cosocleC2×C4×C8C23
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#446 ◁ 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
#286802
#132842
#131772
C2×#13632
C2×#13382
#86532
#71782