Finite Group Databasebeta

← #105163

Subgroups — #105163

Order 512.

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

normal subgroups only

This group has 352 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#28518C211yesmaximal, characteristic
2#9900C211yesmaximal, characteristic
3#9605C211yesmaximal, characteristic
4#8589C211yesmaximal, characteristic
5#7663C211yesmaximal, characteristic
6#7570C211yesmaximal, characteristic
7#7022C211yesmaximal, characteristic
8C2×#479—21no—
9C2×#479—21no—
10#2859C2211yescharacteristic
11C4×C4⋊Q8C2211yescharacteristic
12#2096—21no—
13#2095—21no—
14#1960—21no—
15#1847—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#1271—21no—
28#1271—21no—
29#1271—21no—
30#1271—21no—
31C2×C4⋊Q8D411yescharacteristic
32C2×#125—21no—
33C2×C4×Q8—21no—
34#479—42no—
35#479—42no—
36#479—42no—
37#479—42no—
38C2×#107—21no—
39C2×#107—21no—
40C2×#106—21no—
41C2×#106—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8—21no—
47C2×C4⋊C8—21no—
48C2×C4⋊C8D411yescharacteristic
49C2×C4⋊C8D411yescharacteristic
50C2×#103—21no—
51C2×#103—21no—
52C2×#103—21no—
53C2×#103—21no—
54C2×#97—21no—
55C2×C4×C8—21no—
56C2×C4×C8—21no—
57#391—21no—
58#389—21no—
59#389—21no—
60#389—21no—
61#389—21no—
62#389—21no—
63#389—21no—
64#384D411yescharacteristic
65#384D411yescharacteristic
66#384D411yescharacteristic
67#382—21no—
68C4×C4⋊C4—21no—
69C4×C4⋊C4—21no—
70C43C2311yescharacteristic
71#336—21no—
72#336—21no—
73#336—21no—
74#336—21no—
75#336D411yescharacteristic
76#336D411yescharacteristic
77#334—42no—
78#332—42no—
79C22×Q8—21no—
80C22×C8—21no—
81C22×C8—21no—
82C22×C8—21no—
83C22×C8—21no—
84C22×C8—41no—
85C22×C8—41no—
86C22×C8—41no—
87C4⋊Q8—21no—
88C4⋊Q8—21no—
89C4⋊Q8—21no—
90C4⋊Q8SD1612yes—
91#125—41no—
92#125—41no—
93#125—41no—
94#125—41no—
95C4×Q8—41no—
96C4×Q8—41no—
97C4×Q8—41no—
98C4×Q8—41no—
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—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—41no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4—41no—
113C2×C42—41no—
114C2×C42C2×D411yescharacteristic
115C2×C42C2×D411yescharacteristic
116C2×C42C2×D411yescharacteristic
117C2×C42C2×D411yescharacteristic
118C2×C42#4111yescharacteristic
119C2×C42#4111yescharacteristic
120C2×C42#4111yescharacteristic
121#107—42no—
122#107—42no—
123#106—42no—
124#106—42no—
125C4⋊C8—22no—
126C4⋊C8—21no—
127C4⋊C8—21no—
128C4⋊C8—41no—
129C4⋊C8—42no—
130C4⋊C8—42no—
131C4⋊C8—41no—
132C4⋊C8—41no—
133C4⋊C8—41no—
134C4⋊C8—41no—
135C4⋊C8—41no—
136C4⋊C8—41no—
137C4⋊C8D812yes—
138C4⋊C8SD1612yes—
139#103—42no—
140#103—42no—
141#103—42no—
142#103—42no—
143#97—41no—
144#97—41no—
145C4×C8—41no—
146C4×C8—41no—
147C4×C8—81no—
148#95—41no—
149#95—41no—
150#95—41no—
151#95—41no—
152C2×Q8—22no—
153C2×Q8—41no—
154C2×Q8—41no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×Q8—41no—
158C22×C4—41no—
159C22×C4—41no—
160C22×C4—41no—
161C22×C4—41no—
162C22×C4#12011yescharacteristic
163C22×C4#12111yescharacteristic
164C22×C4#12111yescharacteristic
165C22×C4#12111yescharacteristic
166C22×C4#12311yescharacteristic
167C22×C4#12311yescharacteristic
168C22×C4#12411yescharacteristic
169C2×C8—22no—
170C2×C8—22no—
171C2×C8—22no—
172C2×C8—41no—
173C2×C8—41no—
174C2×C8—41no—
175C2×C8—41no—
176C2×C8—41no—
177C2×C8—41no—
178C2×C8—42no—
179C2×C8—41no—
180C2×C8—41no—
181C2×C8—41no—
182C2×C8—81no—
183C2×C8—81no—
184C2×C8—81no—
185C2×C8—81no—
186C2×C8—81no—
187C2×C8—81no—
188C2×C8—81no—
189C2×C8—81no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—81no—
203C4⋊C4—81no—
204C4⋊C4—81no—
205C4⋊C4—81no—
206C4⋊C4—81no—
207C4⋊C4—81no—
208C4⋊C4—81no—
209C4⋊C4—81no—
210C4⋊C4—81no—
211C4⋊C4—81no—
212C4⋊C4—81no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—41no—
218C42—41no—
219C42—41no—
220C42—81no—
221C42—81no—
222C42C2×D811yescharacteristic
223C42C2×SD1611yescharacteristic
224C42C2×SD1611yescharacteristic
225C42#13511yescharacteristic
226C42AGL(1,ℤ/8)11yescharacteristic
227C42AGL(1,ℤ/8)11yescharacteristic
228C42#13711yescharacteristic
229C42#13711yescharacteristic
230C23#39411yescharacteristic
231Q8—42no—
232Q8—42no—
233Q8—81no—
234Q8—81no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—42no—
249C2×C4—81no—
250C2×C4—81no—
251C2×C4—81no—
252C2×C4—81no—
253C2×C4—81no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—81no—
257C2×C4—81no—
258C2×C4—81no—
259C2×C4—81no—
260C2×C4#44711yescharacteristic
261C2×C4#44811yescharacteristic
262C2×C4#45011yescharacteristic
263C2×C4#45211yescharacteristic
264C2×C4#45411yescharacteristic
265C2×C4#45611yescharacteristic
266C2×C4#45911yescharacteristic
267C2×C4#46011yescharacteristic
268C2×C4#46511yescharacteristic
269C2×C4#47011yescharacteristic
270C2×C4#47111yescharacteristic
271C2×C4#47311yescharacteristic
272C2×C4#48311yescharacteristic
273C2×C4#48511yescharacteristic
274C2×C4#48611yescharacteristic
275C2×C4#49011yescharacteristic
276C8—42no—
277C8—42no—
278C8—42no—
279C8—81no—
280C8—82no—
281C8—161no—
282C8—161no—
283C22#203511yescharacteristic
284C22#203811yescharacteristic
285C22#204111yescharacteristic
286C22#204911yescharacteristic
287C22#205011yescharacteristic
288C22#205211yescharacteristic
289C22#205311yescharacteristic
290C4—21no—
291C4—21no—
292C4—21no—
293C4—21no—
294C4—21no—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—21no—
299C4—21no—
300C4—41no—
301C4—82no—
302C4—161no—
303C4—161no—
304C4—161no—
305C4#162711yescharacteristic
306C4#163511yescharacteristic
307C4#164711yescharacteristic
308C4#165111yescharacteristic
309C2#1042011yescharacteristic
310C2#1046211yescharacteristic
311C2#1047011yescharacteristic
312C2#1049911yescharacteristic
313C2#1051111yescharacteristic
314C2#1054611yescharacteristic
315C2#1055011yescharacteristic
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
#285182
#99002
#96052
#85892
#76632
#75702
#70222