Finite Group Databasebeta

← #124698

Subgroups — #124698

Order 512.

484 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 92 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#14277C211yesmaximal, characteristic
2#8699C211yesmaximal, characteristic
3#7910C211yesmaximal, characteristic
4#7122C214yesmaximal
5C2×#432—21no—
6C2×#389—21no—
7C2×#384C411yescharacteristic
8C2×#382C411yescharacteristic
9C2×#376C2211yescharacteristic
10#1817—21no—
11#1444—21no—
12#1444C412yes—
13#1442—21no—
14#1442C2212yes—
15C4⋊#95—21no—
16#1280—21no—
17#1280—21no—
18#1280C2212yes—
19#1280C2212yes—
20C22×C4⋊C4—21no—
21C22×C4⋊C4—21no—
22C22×C4⋊C4—21no—
23C22×C4⋊C4—22no—
24C22×C4⋊C4C2×C412yes—
25C22×C42C2×C411yescharacteristic
26C22×C42D411yescharacteristic
27C22×C42D411yescharacteristic
28#432—24no—
29#432—42no—
30C2×C4⋊C8—41no—
31C2×C22⋊C8—22no—
32C2×C22⋊C8—22no—
33C2×#97—41no—
34#389—42no—
35#389—42no—
36#384—41no—
37#384—41no—
38#382—24no—
39#376—41no—
40#376—41no—
41C2×#95—21no—
42C2×#95—22no—
43C2×#95—22no—
44C2×#95—22no—
45C2×#95C2×C412yes—
46C2×#95C2×C411yescharacteristic
47C2×#95D411yescharacteristic
48C2×#95D411yescharacteristic
49C2×#95C2311yescharacteristic
50#336—41no—
51#336—41no—
52C23×C4—22no—
53C23×C4—22no—
54C23×C4C22⋊C411yescharacteristic
55C23×C4C22⋊C411yescharacteristic
56C23×C4C22⋊C411yescharacteristic
57C23×C4C22⋊C411yescharacteristic
58C23×C4C22×C411yescharacteristic
59C23×C4C2×D411yescharacteristic
60C23×C4C2×D411yescharacteristic
61C22×C8—42no—
62C22×C8—42no—
63C2×C4⋊C4—24no—
64C2×C4⋊C4—42no—
65C2×C4⋊C4—42no—
66C2×C4⋊C4—42no—
67C2×C4⋊C4—42no—
68C2×C4⋊C4—41no—
69C2×C4⋊C4—41no—
70C2×C4⋊C4—44no—
71C2×C4⋊C4—42no—
72C2×C4⋊C4—42no—
73C2×C4⋊C4—82no—
74C2×C4⋊C4—82no—
75C2×C4⋊C4—82no—
76C2×C4⋊C4—82no—
77C2×C42—21no—
78C2×C42—21no—
79C2×C42—21no—
80C2×C42—21no—
81C2×C42—22no—
82C2×C42—22no—
83C2×C42—22no—
84C2×C42—21no—
85C2×C42—21no—
86C2×C42—22no—
87C2×C42—41no—
88C2×C42D812yes—
89C2×C42SD1612yes—
90C4⋊C8—44no—
91C22⋊C8—24no—
92C22⋊C8—42no—
93C22⋊C8—42no—
94C22⋊C8—42no—
95#97—44no—
96#95—24no—
97#95—22no—
98#95—41no—
99#95—41no—
100#95—41no—
101#95—41no—
102#95—42no—
103#95—42no—
104#95—82no—
105#95—82no—
106#95M1614yes—
107C24C2×C22⋊C411yescharacteristic
108C22×C4—21no—
109C22×C4—21no—
110C22×C4—21no—
111C22×C4—21no—
112C22×C4—21no—
113C22×C4—21no—
114C22×C4—21no—
115C22×C4—21no—
116C22×C4—21no—
117C22×C4—21no—
118C22×C4—21no—
119C22×C4—21no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—24no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—21no—
126C22×C4—41no—
127C22×C4—41no—
128C22×C4—41no—
129C22×C4—41no—
130C22×C4—41no—
131C22×C4—41no—
132C22×C4—41no—
133C22×C4—41no—
134C22×C4—41no—
135C22×C4—41no—
136C22×C4—41no—
137C22×C4—41no—
138C22×C4—42no—
139C22×C4—42no—
140C22×C4—42no—
141C22×C4—42no—
142C22×C4—42no—
143C22×C4—42no—
144C22×C4—42no—
145C22×C4—42no—
146C22×C4—42no—
147C22×C4—42no—
148C22×C4—42no—
149C22×C4—42no—
150C22×C4—42no—
151C22×C4#9911yescharacteristic
152C22×C4#9911yescharacteristic
153C22×C4#10112yes—
154C22×C4#10212yes—
155C22×C4#10212yes—
156C22×C4#10412yes—
157C22×C4C2×M1612yes—
158C22×C4C2×D811yescharacteristic
159C22×C4C2×SD1611yescharacteristic
160C22×C4#13712yes—
161C2×C8—44no—
162C2×C8—82no—
163C2×C8—82no—
164C2×C8—82no—
165C2×C8—82no—
166C2×C8—82no—
167C4⋊C4—48no—
168C4⋊C4—84no—
169C4⋊C4—84no—
170C4⋊C4—88no—
171C4⋊C4—82no—
172C4⋊C4—82no—
173C42—24no—
174C42—24no—
175C42—22no—
176C42—22no—
177C42—22no—
178C42—22no—
179C42—42no—
180C42—42no—
181C23—21no—
182C23—21no—
183C23—21no—
184C23—21no—
185C23#40711yescharacteristic
186C23C2×#9911yescharacteristic
187C23C2×#10111yescharacteristic
188C23C2×#10211yescharacteristic
189C23#41911yescharacteristic
190C23C2×#10411yescharacteristic
191C23#42111yescharacteristic
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—44no—
225C2×C4—44no—
226C2×C4—42no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—44no—
230C2×C4—41no—
231C2×C4—81no—
232C2×C4—81no—
233C2×C4—81no—
234C2×C4—82no—
235C2×C4—82no—
236C2×C4—82no—
237C2×C4—82no—
238C2×C4—81no—
239C2×C4—82no—
240C2×C4—82no—
241C2×C4—82no—
242C2×C4—82no—
243C2×C4—82no—
244C2×C4—82no—
245C2×C4—82no—
246C2×C4#32712yes—
247C2×C4#32712yes—
248C8—84no—
249C8—162no—
250C22—21no—
251C22—21no—
252C22—21no—
253C22—21no—
254C22—21no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22#146311yescharacteristic
263C22#148611yescharacteristic
264C22#149111yescharacteristic
265C22C2×#32711yescharacteristic
266C22#151111yescharacteristic
267C22#152811yescharacteristic
268C22#154611yescharacteristic
269C22#212211yescharacteristic
270C22#212311yescharacteristic
271C22#212911yescharacteristic
272C22#213411yescharacteristic
273C4—22no—
274C4—22no—
275C4—42no—
276C4—42no—
277C4—41no—
278C4—41no—
279C4—42no—
280C4—42no—
281C4—84no—
282C4—81no—
283C4—162no—
284C2—21no—
285C2—21no—
286C2—21no—
287C2—21no—
288C2#761011yescharacteristic
289C2#1151511yescharacteristic
290C2#1152011yescharacteristic
291C2#1169411yescharacteristic
292C2#1169911yescharacteristic
293C2#1181211yescharacteristic
294C2#1181811yescharacteristic
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
#142772
#86992
#79102
#71222