Finite Group Databasebeta

← #124957

Subgroups — #124957

Order 512.

568 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 102 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#13910C211yesmaximal, characteristic
2#8560C211yesmaximal, characteristic
3#8560C211yesmaximal, characteristic
4#7123C214yesmaximal
5C2×#389—21no—
6C2×#389—21no—
7C2×#384—21no—
8C2×#384C411yescharacteristic
9C2×C4×C4⋊C4C411yescharacteristic
10C2×C4×C4⋊C4C2211yescharacteristic
11#1797—21no—
12#1797—21no—
13C2×#324—21no—
14C2×#324—21no—
15#1444C412yes—
16#1444C2212yes—
17C4⋊#95—21no—
18#1280C2212yes—
19#1280C2212yes—
20C22×C4⋊C4—21no—
21C22×C4⋊C4—21no—
22C22×C4⋊C4—21no—
23C22×C4⋊C4—22no—
24C22×C4⋊C4—22no—
25C22×C4⋊C4C2×C412yes—
26C22×C4⋊C4D411yescharacteristic
27C22×C4⋊C4D411yescharacteristic
28C22×C42—21no—
29C22×C42C2×C411yescharacteristic
30C22×C42D411yescharacteristic
31C22×C42D411yescharacteristic
32C2×C4⋊C8—41no—
33C2×C4⋊C8—41no—
34C2×C22⋊C8—22no—
35C2×C22⋊C8—22no—
36#389—44no—
37#389—44no—
38#384—41no—
39#384—41no—
40#384—42no—
41#384—42no—
42C4×C4⋊C4—24no—
43C4×C4⋊C4—41no—
44C4×C4⋊C4—41no—
45C2×#95—22no—
46C2×#95—22no—
47C2×#95C2×C412yes—
48C2×#95C2×C411yescharacteristic
49C2×#95C2311yescharacteristic
50#336—41no—
51#336—41no—
52#324—42no—
53#324—42no—
54C23×C4—22no—
55C23×C4—22no—
56C23×C4C22⋊C411yescharacteristic
57C23×C4C22⋊C411yescharacteristic
58C23×C4C22⋊C411yescharacteristic
59C23×C4C22⋊C411yescharacteristic
60C23×C4C22×C411yescharacteristic
61C23×C4C2×D411yescharacteristic
62C23×C4C2×D411yescharacteristic
63C22×C8—42no—
64C22×C8—42no—
65C2×C4⋊C4—24no—
66C2×C4⋊C4—24no—
67C2×C4⋊C4—24no—
68C2×C4⋊C4—41no—
69C2×C4⋊C4—41no—
70C2×C4⋊C4—41no—
71C2×C4⋊C4—41no—
72C2×C4⋊C4—42no—
73C2×C4⋊C4—42no—
74C2×C4⋊C4—42no—
75C2×C4⋊C4—42no—
76C2×C4⋊C4—42no—
77C2×C4⋊C4—44no—
78C2×C4⋊C4—44no—
79C2×C4⋊C4—41no—
80C2×C4⋊C4—41no—
81C2×C4⋊C4—42no—
82C2×C4⋊C4—44no—
83C2×C4⋊C4—42no—
84C2×C4⋊C4—42no—
85C2×C4⋊C4—82no—
86C2×C4⋊C4—82no—
87C2×C4⋊C4—82no—
88C2×C4⋊C4D812yes—
89C2×C4⋊C4SD1612yes—
90C2×C4⋊C4SD1612yes—
91C2×C4⋊C4Q1612yes—
92C2×C42—21no—
93C2×C42—21no—
94C2×C42—22no—
95C2×C42—22no—
96C2×C42—24no—
97C2×C42—21no—
98C2×C42—21no—
99C2×C42—21no—
100C2×C42—21no—
101C2×C42—42no—
102C2×C42—42no—
103C2×C42—42no—
104C2×C42—42no—
105C4⋊C8—82no—
106C4⋊C8—82no—
107C22⋊C8—42no—
108C22⋊C8—42no—
109C22⋊C8—42no—
110C22⋊C8—42no—
111#95—22no—
112#95—41no—
113#95—41no—
114#95—44no—
115#95—44no—
116#95M1614yes—
117C24C2×C22⋊C411yescharacteristic
118C22×C4—21no—
119C22×C4—21no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—22no—
125C22×C4—22no—
126C22×C4—24no—
127C22×C4—24no—
128C22×C4—24no—
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—42no—
140C22×C4—42no—
141C22×C4—42no—
142C22×C4—42no—
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—42no—
154C22×C4—42no—
155C22×C4—42no—
156C22×C4—42no—
157C22×C4—42no—
158C22×C4—42no—
159C22×C4—42no—
160C22×C4#9911yescharacteristic
161C22×C4#9911yescharacteristic
162C22×C4#10112yes—
163C22×C4#10212yes—
164C22×C4#10212yes—
165C22×C4#10312yes—
166C22×C4#10312yes—
167C22×C4C2×M1612yes—
168C22×C4C2×D811yescharacteristic
169C22×C4C2×SD1611yescharacteristic
170C22×C4C2×SD1611yescharacteristic
171C22×C4C2×Q1611yescharacteristic
172C2×C8—82no—
173C2×C8—82no—
174C2×C8—82no—
175C2×C8—82no—
176C2×C8—82no—
177C2×C8—82no—
178C4⋊C4—216no—
179C4⋊C4—42no—
180C4⋊C4—42no—
181C4⋊C4—42no—
182C4⋊C4—42no—
183C4⋊C4—82no—
184C4⋊C4—84no—
185C4⋊C4—88no—
186C4⋊C4—84no—
187C4⋊C4—84no—
188C4⋊C4—84no—
189C4⋊C4—82no—
190C42—24no—
191C42—24no—
192C42—48no—
193C42—42no—
194C42—42no—
195C42—81no—
196C42—81no—
197C23—21no—
198C23—21no—
199C23—21no—
200C23—21no—
201C23#40711yescharacteristic
202C23C2×#9911yescharacteristic
203C23C2×#10111yescharacteristic
204C23C2×#10211yescharacteristic
205C23C2×#10311yescharacteristic
206C23#42111yescharacteristic
207C23#42111yescharacteristic
208C2×C4—24no—
209C2×C4—24no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—28no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—44no—
229C2×C4—44no—
230C2×C4—44no—
231C2×C4—44no—
232C2×C4—44no—
233C2×C4—42no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—44no—
245C2×C4—42no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—81no—
253C2×C4—81no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—82no—
257C2×C4—82no—
258C2×C4—82no—
259C2×C4—82no—
260C2×C4—82no—
261C2×C4—82no—
262C2×C4—82no—
263C2×C4#33214yes—
264C2×C4#35312yes—
265C2×C4#35612yes—
266C8—162no—
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#146311yescharacteristic
281C22#148611yescharacteristic
282C22#148711yescharacteristic
283C22#151911yescharacteristic
284C22#152011yescharacteristic
285C22#153411yescharacteristic
286C22C2×#33211yescharacteristic
287C22#212211yescharacteristic
288C22#212311yescharacteristic
289C22C2×#35311yescharacteristic
290C22C2×#35611yescharacteristic
291C4—24no—
292C4—22no—
293C4—22no—
294C4—48no—
295C4—42no—
296C4—41no—
297C4—42no—
298C4—41no—
299C4—41no—
300C4—42no—
301C4—41no—
302C4—162no—
303C2—21no—
304C2—21no—
305C2—21no—
306C2—21no—
307C2#764111yescharacteristic
308C2#1151211yescharacteristic
309C2#1152011yescharacteristic
310C2#1187711yescharacteristic
311C2#1188311yescharacteristic
312C2#1190111yescharacteristic
313C2#1190811yescharacteristic
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×C4×C4⋊C4 ◁ 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
#139102
#85602
#71232