Finite Group Databasebeta

← #105166

Subgroups — #105166

Order 512.

316 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 84 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#29223C211yesmaximal, characteristic
2#9900C211yesmaximal, characteristic
3#9605C211yesmaximal, characteristic
4#8591C211yesmaximal, characteristic
5#7663C211yesmaximal, characteristic
6#7571C211yesmaximal, characteristic
7#7022C211yesmaximal, characteristic
8#2859C2211yescharacteristic
9C4×C4⋊Q8C2211yescharacteristic
10#2100—21no—
11#2099—21no—
12#1993—21no—
13#1989—21no—
14#1989—21no—
15#1842C2211yescharacteristic
16#1836—21no—
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—
34C2×C4⋊C8—21no—
35C2×C4⋊C8—21no—
36C2×C4⋊C8—21no—
37C2×C4⋊C8—21no—
38C2×C4⋊C8—21no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8D411yescharacteristic
41C2×C4⋊C8D411yescharacteristic
42C2×#97—21no—
43C2×C4×C8—21no—
44C2×C4×C8—21no—
45#391—21no—
46#389—21no—
47#389—21no—
48#389—21no—
49#389—21no—
50#389—21no—
51#389—21no—
52#384D411yescharacteristic
53#384D411yescharacteristic
54#384D411yescharacteristic
55#382—21no—
56C4×C4⋊C4—21no—
57C4×C4⋊C4—21no—
58C43C2311yescharacteristic
59#340—21no—
60#340—21no—
61#340—21no—
62#340—21no—
63#340—21no—
64#340—21no—
65#340—21no—
66#340—21no—
67#336—21no—
68#336—21no—
69#336—21no—
70#336—21no—
71#336D411yescharacteristic
72#336D411yescharacteristic
73#334—42no—
74#332—42no—
75C22×Q8—21no—
76C22×C8—21no—
77C22×C8—21no—
78C22×C8—21no—
79C22×C8—21no—
80C22×C8—41no—
81C22×C8—41no—
82C22×C8—41no—
83C4⋊Q8—21no—
84C4⋊Q8—21no—
85C4⋊Q8—21no—
86C4⋊Q8SD1612yes—
87#125—41no—
88#125—41no—
89#125—41no—
90#125—41no—
91C4×Q8—82no—
92C2×C4⋊C4—21no—
93C2×C4⋊C4—21no—
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—41no—
104C2×C4⋊C4—41no—
105C2×C4⋊C4—41no—
106C2×C42—41no—
107C2×C42C2×D411yescharacteristic
108C2×C42C2×D411yescharacteristic
109C2×C42C2×D411yescharacteristic
110C2×C42C2×D411yescharacteristic
111C2×C42#4111yescharacteristic
112C2×C42#4111yescharacteristic
113C2×C42#4111yescharacteristic
114C4⋊C8—22no—
115C4⋊C8—21no—
116C4⋊C8—21no—
117C4⋊C8—21no—
118C4⋊C8—21no—
119C4⋊C8—41no—
120C4⋊C8—42no—
121C4⋊C8—42no—
122C4⋊C8—41no—
123C4⋊C8—41no—
124C4⋊C8—41no—
125C4⋊C8—41no—
126C4⋊C8—41no—
127C4⋊C8—41no—
128#97—41no—
129#97—41no—
130C4×C8—41no—
131C4×C8—41no—
132C4×C8—81no—
133#95—41no—
134#95—41no—
135#95—41no—
136#95—41no—
137C2×Q8—22no—
138C2×Q8—41no—
139C2×Q8—81no—
140C2×Q8—81no—
141C22×C4—41no—
142C22×C4—41no—
143C22×C4—41no—
144C22×C4—41no—
145C22×C4#12011yescharacteristic
146C22×C4#12111yescharacteristic
147C22×C4#12111yescharacteristic
148C22×C4#12111yescharacteristic
149C22×C4#12311yescharacteristic
150C22×C4#12311yescharacteristic
151C22×C4#12411yescharacteristic
152C2×C8—22no—
153C2×C8—41no—
154C2×C8—41no—
155C2×C8—42no—
156C2×C8—41no—
157C2×C8—41no—
158C2×C8—41no—
159C2×C8—41no—
160C2×C8—41no—
161C2×C8—41no—
162C2×C8—41no—
163C2×C8—41no—
164C2×C8—41no—
165C2×C8—81no—
166C2×C8—81no—
167C2×C8—81no—
168C2×C8—81no—
169C2×C8—81no—
170C2×C8—81no—
171C2×C8—81no—
172C2×C8—81no—
173C4⋊C4—22no—
174C4⋊C4—22no—
175C4⋊C4—41no—
176C4⋊C4—41no—
177C4⋊C4—41no—
178C4⋊C4—41no—
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—
189C4⋊C4—81no—
190C4⋊C4—82no—
191C4⋊C4—81no—
192C4⋊C4—81no—
193C4⋊C4—81no—
194C4⋊C4—81no—
195C42—21no—
196C42—21no—
197C42—21no—
198C42—21no—
199C42—41no—
200C42—41no—
201C42—41no—
202C42—82no—
203C42C2×SD1611yescharacteristic
204C42#13511yescharacteristic
205C42#13511yescharacteristic
206C42#13511yescharacteristic
207C42AGL(1,ℤ/8)11yescharacteristic
208C42#13711yescharacteristic
209C42#13711yescharacteristic
210C42#13711yescharacteristic
211C23#39411yescharacteristic
212Q8—82no—
213Q8—82no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—42no—
228C2×C4—81no—
229C2×C4—81no—
230C2×C4—81no—
231C2×C4—81no—
232C2×C4—81no—
233C2×C4—81no—
234C2×C4—81no—
235C2×C4—81no—
236C2×C4—81no—
237C2×C4—81no—
238C2×C4—81no—
239C2×C4#44811yescharacteristic
240C2×C4#44911yescharacteristic
241C2×C4#45211yescharacteristic
242C2×C4#45211yescharacteristic
243C2×C4#45411yescharacteristic
244C2×C4#45611yescharacteristic
245C2×C4#46311yescharacteristic
246C2×C4#46411yescharacteristic
247C2×C4#46511yescharacteristic
248C2×C4#47011yescharacteristic
249C2×C4#47111yescharacteristic
250C2×C4#47311yescharacteristic
251C2×C4#48311yescharacteristic
252C2×C4#48511yescharacteristic
253C2×C4#48811yescharacteristic
254C2×C4#48911yescharacteristic
255C8—42no—
256C8—81no—
257C8—82no—
258C8—81no—
259C8—81no—
260C8—161no—
261C8—161no—
262C22#203511yescharacteristic
263C22#203811yescharacteristic
264C22#204211yescharacteristic
265C22#204811yescharacteristic
266C22#205011yescharacteristic
267C22#205211yescharacteristic
268C22#205311yescharacteristic
269C4—21no—
270C4—21no—
271C4—21no—
272C4—21no—
273C4—21no—
274C4—21no—
275C4—21no—
276C4—21no—
277C4—21no—
278C4—21no—
279C4—41no—
280C4—82no—
281C4—161no—
282C4—161no—
283C4—161no—
284C4#162611yescharacteristic
285C4#163811yescharacteristic
286C4#165011yescharacteristic
287C4#165311yescharacteristic
288C2#1042311yescharacteristic
289C2#1046211yescharacteristic
290C2#1046811yescharacteristic
291C2#1049711yescharacteristic
292C2#1051111yescharacteristic
293C2#1054711yescharacteristic
294C2#1055111yescharacteristic
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
#292232
#99002
#96052
#85912
#76632
#75712
#70222