Finite Group Databasebeta

← #105157

Subgroups — #105157

Order 512.

334 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 88 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#28692C211yesmaximal, characteristic
2#9900C211yesmaximal, characteristic
3#9605C211yesmaximal, characteristic
4#8591C211yesmaximal, characteristic
5#7660C211yesmaximal, characteristic
6#7571C211yesmaximal, characteristic
7#7022C211yesmaximal, characteristic
8C2×#501—21no—
9#2859C2211yescharacteristic
10C4×C4⋊Q8C2211yescharacteristic
11#2084—21no—
12#2083—21no—
13#1992—21no—
14#1949—21no—
15#1949—21no—
16#1842C2211yescharacteristic
17#1831C2211yescharacteristic
18#1767C2211yescharacteristic
19C4×C4⋊C8C2211yescharacteristic
20C4×C4⋊C8C2211yescharacteristic
21C2×#334—21no—
22C2×#332—21no—
23#1296—21no—
24#1296—21no—
25#1296—21no—
26#1277—21no—
27#1272—21no—
28#1272—21no—
29#1271—21no—
30#1271—21no—
31C2×C4⋊Q8D411yescharacteristic
32C2×#125—21no—
33C2×C4×Q8—21no—
34#501—42no—
35#501—42no—
36C2×#107—21no—
37C2×#107—21no—
38C2×#106—21no—
39C2×#106—21no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8D411yescharacteristic
47C2×C4⋊C8D411yescharacteristic
48C2×#97—21no—
49C2×C4×C8—21no—
50C2×C4×C8—21no—
51#391—21no—
52#389—21no—
53#389—21no—
54#389—21no—
55#389—21no—
56#389—21no—
57#389—21no—
58#384D411yescharacteristic
59#384D411yescharacteristic
60#384D411yescharacteristic
61#382—21no—
62C4×C4⋊C4—21no—
63C4×C4⋊C4—21no—
64C43C2311yescharacteristic
65#340—21no—
66#340—21no—
67#340—21no—
68#340—21no—
69#336—21no—
70#336—21no—
71#336—21no—
72#336—21no—
73#336D411yescharacteristic
74#336D411yescharacteristic
75#334—42no—
76#332—42no—
77C22×Q8—21no—
78C22×C8—21no—
79C22×C8—21no—
80C22×C8—21no—
81C22×C8—21no—
82C22×C8—41no—
83C22×C8—41no—
84C22×C8—41no—
85C4⋊Q8—21no—
86C4⋊Q8—21no—
87C4⋊Q8—21no—
88C4⋊Q8SD1612yes—
89#125—41no—
90#125—41no—
91#125—41no—
92#125—41no—
93C4×Q8—82no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—41no—
106C2×C4⋊C4—41no—
107C2×C4⋊C4—41no—
108C2×C42—41no—
109C2×C42C2×D411yescharacteristic
110C2×C42C2×D411yescharacteristic
111C2×C42C2×D411yescharacteristic
112C2×C42C2×D411yescharacteristic
113C2×C42#4111yescharacteristic
114C2×C42#4111yescharacteristic
115C2×C42#4111yescharacteristic
116#107—42no—
117#107—42no—
118#106—42no—
119#106—42no—
120C4⋊C8—22no—
121C4⋊C8—21no—
122C4⋊C8—21no—
123C4⋊C8—41no—
124C4⋊C8—42no—
125C4⋊C8—42no—
126C4⋊C8—41no—
127C4⋊C8—41no—
128C4⋊C8—41no—
129C4⋊C8—41no—
130C4⋊C8—41no—
131C4⋊C8—41no—
132C4⋊C8SD1612yes—
133C4⋊C8Q1612yes—
134#97—41no—
135#97—41no—
136C4×C8—41no—
137C4×C8—41no—
138C4×C8—81no—
139#95—41no—
140#95—41no—
141#95—41no—
142#95—41no—
143C2×Q8—22no—
144C2×Q8—41no—
145C2×Q8—81no—
146C2×Q8—81no—
147C22×C4—41no—
148C22×C4—41no—
149C22×C4—41no—
150C22×C4—41no—
151C22×C4#12011yescharacteristic
152C22×C4#12111yescharacteristic
153C22×C4#12111yescharacteristic
154C22×C4#12111yescharacteristic
155C22×C4#12311yescharacteristic
156C22×C4#12311yescharacteristic
157C22×C4#12411yescharacteristic
158C2×C8—22no—
159C2×C8—22no—
160C2×C8—22no—
161C2×C8—41no—
162C2×C8—41no—
163C2×C8—41no—
164C2×C8—41no—
165C2×C8—41no—
166C2×C8—41no—
167C2×C8—42no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8—41no—
171C2×C8—81no—
172C2×C8—81no—
173C2×C8—81no—
174C2×C8—81no—
175C2×C8—81no—
176C2×C8—81no—
177C2×C8—81no—
178C2×C8—81no—
179C4⋊C4—22no—
180C4⋊C4—22no—
181C4⋊C4—41no—
182C4⋊C4—41no—
183C4⋊C4—41no—
184C4⋊C4—41no—
185C4⋊C4—41no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—81no—
192C4⋊C4—81no—
193C4⋊C4—81no—
194C4⋊C4—81no—
195C4⋊C4—81no—
196C4⋊C4—82no—
197C4⋊C4—81no—
198C4⋊C4—81no—
199C4⋊C4—81no—
200C4⋊C4—81no—
201C42—21no—
202C42—21no—
203C42—21no—
204C42—21no—
205C42—41no—
206C42—41no—
207C42—41no—
208C42—82no—
209C42C2×SD1611yescharacteristic
210C42C2×SD1611yescharacteristic
211C42C2×Q1611yescharacteristic
212C42#13511yescharacteristic
213C42AGL(1,ℤ/8)11yescharacteristic
214C42AGL(1,ℤ/8)11yescharacteristic
215C42#13711yescharacteristic
216C42#13711yescharacteristic
217C23#39411yescharacteristic
218Q8—82no—
219Q8—82no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—42no—
234C2×C4—81no—
235C2×C4—81no—
236C2×C4—81no—
237C2×C4—81no—
238C2×C4—81no—
239C2×C4—81no—
240C2×C4—81no—
241C2×C4—81no—
242C2×C4—81no—
243C2×C4—81no—
244C2×C4—81no—
245C2×C4#44811yescharacteristic
246C2×C4#44911yescharacteristic
247C2×C4#45011yescharacteristic
248C2×C4#45111yescharacteristic
249C2×C4#45411yescharacteristic
250C2×C4#45611yescharacteristic
251C2×C4#46111yescharacteristic
252C2×C4#46211yescharacteristic
253C2×C4#46511yescharacteristic
254C2×C4#46911yescharacteristic
255C2×C4#47111yescharacteristic
256C2×C4#47311yescharacteristic
257C2×C4#48111yescharacteristic
258C2×C4#48211yescharacteristic
259C2×C4#48711yescharacteristic
260C2×C4#49111yescharacteristic
261C8—42no—
262C8—42no—
263C8—42no—
264C8—81no—
265C8—82no—
266C8—161no—
267C8—161no—
268C22#203411yescharacteristic
269C22#203811yescharacteristic
270C22#204311yescharacteristic
271C22#204811yescharacteristic
272C22#205011yescharacteristic
273C22#205211yescharacteristic
274C22#205311yescharacteristic
275C4—21no—
276C4—21no—
277C4—21no—
278C4—21no—
279C4—21no—
280C4—21no—
281C4—21no—
282C4—21no—
283C4—21no—
284C4—21no—
285C4—41no—
286C4—82no—
287C4—161no—
288C4—161no—
289C4—161no—
290C4#162611yescharacteristic
291C4#163711yescharacteristic
292C4#164811yescharacteristic
293C4#165111yescharacteristic
294C2#1041811yescharacteristic
295C2#1045911yescharacteristic
296C2#1046511yescharacteristic
297C2#1049711yescharacteristic
298C2#1051111yescharacteristic
299C2#1054811yescharacteristic
300C2#1055511yescharacteristic
subgroupG/H
center, socle, prime radicalC23#394
commutator, Frattini, cosocleC43C23
LCSG ▷ C43 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#286922
#99002
#96052
#85912
#76602
#75712
#70222