Finite Group Databasebeta

← #104875

Subgroups — #104875

Order 512.

482 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 94 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#30291C211yesmaximal, characteristic
2#11322C211yesmaximal, characteristic
3#9711C212yesmaximal
4#9129C212yesmaximal
5#7020C211yesmaximal, characteristic
6C22×C4⋊C8—21no—
7C22×C4⋊C8C2211yescharacteristic
8#2857C2212yes—
9#2083—22no—
10#2057—22no—
11#1808—21no—
12#1808—21no—
13#1797C2212yes—
14C2×#336—21no—
15C2×#336C2211yescharacteristic
16C2×#332—22no—
17C2×#328—22no—
18C2×#328—22no—
19C4×#95C2211yescharacteristic
20#1296—22no—
21C23×C8—21no—
22C23×C8D411yescharacteristic
23C23×C8D411yescharacteristic
24C2×C4⋊Q8D412yes—
25C2×C22⋊Q8—22no—
26C22×C42—21no—
27C22×C42C2311yescharacteristic
28C2×#107—21no—
29C2×#107—21no—
30C2×#107—21no—
31C2×#107—21no—
32C2×C4⋊C8—22no—
33C2×C4⋊C8—22no—
34C2×C4⋊C8—42no—
35C2×C4⋊C8—42no—
36C2×C4⋊C8—42no—
37C2×C4⋊C8—42no—
38C2×C22⋊C8—22no—
39#391—22no—
40#389—22no—
41#389—22no—
42#384D412yes—
43#380—22no—
44#380—22no—
45C2×#95—21no—
46C2×#95D411yescharacteristic
47C2×#95D411yescharacteristic
48#340—22no—
49#340—22no—
50#336—22no—
51#336—22no—
52#336—42no—
53#332—44no—
54#328—44no—
55#328—44no—
56C22×Q8—22no—
57C23×C4—21no—
58C23×C4—21no—
59C23×C4C2×D411yescharacteristic
60C23×C4C2×D411yescharacteristic
61C23×C4#4111yescharacteristic
62C22×C8—21no—
63C22×C8—21no—
64C22×C8—21no—
65C22×C8—21no—
66C22×C8—22no—
67C22×C8—41no—
68C22×C8—41no—
69C22×C8—41no—
70C22×C8—41no—
71C22×C8—41no—
72C22×C8—41no—
73C22×C8—41no—
74C22×C8—41no—
75C22×C8—41no—
76C22×C8—41no—
77C22×C8—42no—
78C22×C8SD1612yes—
79C22×C8Q1612yes—
80C4⋊Q8—42no—
81C4⋊Q8—42no—
82C22⋊Q8—42no—
83C22⋊Q8—42no—
84C22⋊Q8—42no—
85C22⋊Q8—42no—
86C2×C4⋊C4—22no—
87C2×C4⋊C4—22no—
88C2×C4⋊C4—22no—
89C2×C4⋊C4—22no—
90C2×C4⋊C4—22no—
91C2×C4⋊C4—42no—
92C2×C22⋊C4—42no—
93C2×C42—22no—
94C2×C42—22no—
95C2×C42—41no—
96C2×C42—41no—
97C2×C42—41no—
98C2×C42—41no—
99C2×C42—41no—
100C2×C42—41no—
101C2×C42C2×D412yes—
102C2×C42#4112yes—
103#107—81no—
104#107—81no—
105#107—81no—
106#107—81no—
107C4⋊C8—24no—
108C4⋊C8—42no—
109C4⋊C8—42no—
110C4⋊C8—42no—
111C4⋊C8—48no—
112C22⋊C8—42no—
113C22⋊C8—42no—
114#95—21no—
115#95—22no—
116#95—42no—
117#95—42no—
118#95—42no—
119#95D812yes—
120C24#12111yescharacteristic
121C2×Q8—42no—
122C2×Q8—42no—
123C2×Q8—82no—
124C2×Q8—82no—
125C22×C4—21no—
126C22×C4—21no—
127C22×C4—21no—
128C22×C4—21no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—22no—
132C22×C4—21no—
133C22×C4—21no—
134C22×C4—22no—
135C22×C4—41no—
136C22×C4—41no—
137C22×C4—41no—
138C22×C4—41no—
139C22×C4—41no—
140C22×C4—41no—
141C22×C4—41no—
142C22×C4—41no—
143C22×C4—41no—
144C22×C4—41no—
145C22×C4—41no—
146C22×C4—41no—
147C22×C4—41no—
148C22×C4—41no—
149C22×C4—42no—
150C22×C4—42no—
151C22×C4#12011yescharacteristic
152C22×C4#12112yes—
153C22×C4#12312yes—
154C22×C4#12411yescharacteristic
155C22×C4C2×D811yescharacteristic
156C22×C4C2×SD1611yescharacteristic
157C22×C4C2×Q1611yescharacteristic
158C22×C4#13511yescharacteristic
159C22×C4AGL(1,ℤ/8)12yes—
160C22×C4#13711yescharacteristic
161C22×C4#13711yescharacteristic
162C2×C8—22no—
163C2×C8—22no—
164C2×C8—41no—
165C2×C8—41no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—42no—
169C2×C8—42no—
170C2×C8—42no—
171C2×C8—42no—
172C2×C8—42no—
173C2×C8—81no—
174C2×C8—81no—
175C2×C8—81no—
176C2×C8—81no—
177C2×C8—81no—
178C2×C8—81no—
179C2×C8—82no—
180C2×C8—82no—
181C2×C8—82no—
182C4⋊C4—44no—
183C4⋊C4—42no—
184C4⋊C4—42no—
185C4⋊C4—42no—
186C4⋊C4—42no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C4⋊C4—82no—
190C4⋊C4—82no—
191C4⋊C4—82no—
192C22⋊C4—82no—
193C22⋊C4—82no—
194C42—22no—
195C42—22no—
196C42—42no—
197C42—42no—
198C42—42no—
199C42—42no—
200C42—42no—
201C23—21no—
202C23—21no—
203C23—21no—
204C23—21no—
205C23#39411yescharacteristic
206C23#46111yescharacteristic
207C23#46211yescharacteristic
208C23#46611yescharacteristic
209C23#46911yescharacteristic
210C23#47311yescharacteristic
211C23#47311yescharacteristic
212Q8—162no—
213Q8—162no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—22no—
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—24no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—81no—
243C2×C4—81no—
244C2×C4—81no—
245C2×C4—81no—
246C2×C4—81no—
247C2×C4—81no—
248C2×C4—82no—
249C2×C4—82no—
250C2×C4—82no—
251C2×C4—82no—
252C2×C4—82no—
253C2×C4—82no—
254C2×C4#44811yescharacteristic
255C2×C4#45111yescharacteristic
256C2×C4#45311yescharacteristic
257C2×C4#45611yescharacteristic
258C2×C4B(4,𝔽2)11yescharacteristic
259C2×C4#45811yescharacteristic
260C2×C4#45912yes—
261C2×C4#46312yes—
262C2×C4#48711yescharacteristic
263C2×C4#49111yescharacteristic
264C8—42no—
265C8—42no—
266C8—82no—
267C8—162no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22#167311yescharacteristic
281C22#167411yescharacteristic
282C22#169311yescharacteristic
283C22#169411yescharacteristic
284C22#203911yescharacteristic
285C22#204311yescharacteristic
286C22#204411yescharacteristic
287C22#204711yescharacteristic
288C22#205011yescharacteristic
289C22#205311yescharacteristic
290C22#205411yescharacteristic
291C4—22no—
292C4—22no—
293C4—21no—
294C4—21no—
295C4—44no—
296C4—42no—
297C4—82no—
298C4—162no—
299C4—162no—
300C4#159611yescharacteristic
301C4#160511yescharacteristic
302C4#161111yescharacteristic
303C4#161411yescharacteristic
304C2—21no—
305C2—21no—
306C2—21no—
307C2—21no—
308C2#1040611yescharacteristic
309C2#1051611yescharacteristic
310C2#1051811yescharacteristic
311C2#1054511yescharacteristic
312C2#1054811yescharacteristic
313C2#1055911yescharacteristic
314C2#1056411yescharacteristic
subgroupG/H
center, socleC23#394
commutator, Frattini, cosocleC22×C42C23
prime radicalC24#121
LCSG ▷ C22×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#302912
#113222
#97112
#91292
#70202