Finite Group Databasebeta

← #124997

Subgroups — #124997

Order 512.

440 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 78 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#13963C211yesmaximal, characteristic
2#8699C211yesmaximal, characteristic
3#8699C211yesmaximal, characteristic
4#7123C212yesmaximal
5#7122C212yesmaximal
6C2×#382C411yescharacteristic
7C2×#376C411yescharacteristic
8C2×#376C2211yescharacteristic
9#1817—21no—
10#1817—21no—
11#1444C411yescharacteristic
12#1444C2211yescharacteristic
13#1442C411yescharacteristic
14#1442C2211yescharacteristic
15#1436—21no—
16#1436—21no—
17C4⋊#95—21no—
18#1434—21no—
19#1280—21no—
20#1280—21no—
21#1280C2212yes—
22#1280C2212yes—
23C22×C4⋊C4—21no—
24C22×C4⋊C4—21no—
25C22×C4⋊C4C2×C411yescharacteristic
26C22×C4⋊C4C2×C411yescharacteristic
27C22×C42—21no—
28C22×C42C2×C411yescharacteristic
29C22×C42D411yescharacteristic
30C22×C42D411yescharacteristic
31C2×C22⋊C8—22no—
32C2×C22⋊C8—22no—
33#382—42no—
34#376—22no—
35#376—22no—
36#376—42no—
37C2×#95—21no—
38C2×#95—21no—
39C2×#95—21no—
40C2×#95—21no—
41C2×#95—21no—
42C2×#95—21no—
43C2×#95—21no—
44C2×#95—21no—
45C2×#95—21no—
46C2×#95C2×C411yescharacteristic
47C2×#95C2×C411yescharacteristic
48C2×#95C2×C411yescharacteristic
49C2×#95D411yescharacteristic
50C2×#95D411yescharacteristic
51C2×#95C2311yescharacteristic
52#336—42no—
53#336—42no—
54C23×C4—21no—
55C23×C4—21no—
56C23×C4—21no—
57C23×C4—21no—
58C23×C4C22⋊C411yescharacteristic
59C23×C4C22⋊C411yescharacteristic
60C23×C4C22⋊C411yescharacteristic
61C23×C4C22⋊C411yescharacteristic
62C23×C4C22×C411yescharacteristic
63C23×C4C2×D411yescharacteristic
64C23×C4C2×D411yescharacteristic
65C22×C8—42no—
66C22×C8—42no—
67C2×C4⋊C4—41no—
68C2×C4⋊C4—41no—
69C2×C4⋊C4—42no—
70C2×C4⋊C4—42no—
71C2×C4⋊C4—42no—
72C2×C4⋊C4—42no—
73C2×C4⋊C4—81no—
74C2×C4⋊C4—81no—
75C2×C4⋊C4—81no—
76C2×C4⋊C4—81no—
77C2×C42—22no—
78C2×C42—22no—
79C2×C42—21no—
80C2×C42—21no—
81C2×C42—24no—
82C2×C42—22no—
83C2×C42—22no—
84C2×C42—22no—
85C2×C42—22no—
86C2×C42—41no—
87C2×C42—41no—
88C2×C42—42no—
89C2×C42—42no—
90C22⋊C8—42no—
91C22⋊C8—42no—
92C22⋊C8—42no—
93C22⋊C8—42no—
94#95—24no—
95#95—21no—
96#95—21no—
97#95—41no—
98#95—41no—
99#95—41no—
100#95—41no—
101#95—42no—
102#95—42no—
103#95—42no—
104#95—42no—
105#95—42no—
106#95—42no—
107#95—81no—
108#95—81no—
109#95M1612yes—
110#95M1612yes—
111C24C2×C22⋊C411yescharacteristic
112C22×C4—22no—
113C22×C4—22no—
114C22×C4—21no—
115C22×C4—22no—
116C22×C4—21no—
117C22×C4—21no—
118C22×C4—21no—
119C22×C4—21no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—21no—
126C22×C4—21no—
127C22×C4—21no—
128C22×C4—21no—
129C22×C4—22no—
130C22×C4—21no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—21no—
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—41no—
150C22×C4—41no—
151C22×C4—41no—
152C22×C4—41no—
153C22×C4—41no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—41no—
157C22×C4—41no—
158C22×C4—41no—
159C22×C4—41no—
160C22×C4—41no—
161C22×C4—41no—
162C22×C4—41no—
163C22×C4—41no—
164C22×C4—41no—
165C22×C4—41no—
166C22×C4—41no—
167C22×C4—41no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4—41no—
172C22×C4#9912yes—
173C22×C4#10112yes—
174C22×C4C2×M1611yescharacteristic
175C22×C4C2×M1611yescharacteristic
176C22×C4#13512yes—
177C22×C4#13512yes—
178C2×C8—82no—
179C2×C8—82no—
180C2×C8—82no—
181C2×C8—82no—
182C2×C8—82no—
183C2×C8—82no—
184C4⋊C4—84no—
185C4⋊C4—84no—
186C4⋊C4—82no—
187C4⋊C4—82no—
188C42—24no—
189C42—24no—
190C42—44no—
191C42—44no—
192C42—48no—
193C23—21no—
194C23—21no—
195C23—21no—
196C23—21no—
197C23#40711yescharacteristic
198C23C2×#9911yescharacteristic
199C23C2×#10111yescharacteristic
200C23#41611yescharacteristic
201C23#41611yescharacteristic
202C23#42111yescharacteristic
203C23#42111yescharacteristic
204C2×C4—24no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4—41no—
248C2×C4—41no—
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—81no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4—81no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4—81no—
267C2×C4—81no—
268C2×C4—81no—
269C2×C4—81no—
270C2×C4—81no—
271C8—162no—
272C8—162no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22#146311yescharacteristic
286C22#148811yescharacteristic
287C22#148811yescharacteristic
288C22#151611yescharacteristic
289C22#151611yescharacteristic
290C22#153711yescharacteristic
291C22#154411yescharacteristic
292C22#212211yescharacteristic
293C22#212311yescharacteristic
294C22#212611yescharacteristic
295C22#213211yescharacteristic
296C4—44no—
297C4—41no—
298C4—41no—
299C4—42no—
300C4—42no—
301C4—42no—
302C4—42no—
303C4—82no—
304C4—81no—
305C4—81no—
306C4—161no—
307C4—161no—
308C2—21no—
309C2—21no—
310C2—21no—
311C2—21no—
312C2#764611yescharacteristic
313C2#1151311yescharacteristic
314C2#1152011yescharacteristic
315C2#1184411yescharacteristic
316C2#1184611yescharacteristic
317C2#1185111yescharacteristic
318C2#1185311yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC23×C4C22×C4
Frattini, cosocleC2×#95C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#376 ◁ G
LECSG ▷ C2×#95 ▷ C24 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#139632
#86992
#71232
#71222