Finite Group Databasebeta

← #125346

Subgroups — #125346

Order 512.

508 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 98 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#15196C211yesmaximal, characteristic
2C4×#324C211yesmaximal, characteristic
3#7912C211yesmaximal, characteristic
4#7123C214yesmaximal
5C2×#432—21no—
6C2×#389—21no—
7C2×#384C411yescharacteristic
8C2×C4×C4⋊C4C2211yescharacteristic
9C4×C22⋊C8—21no—
10C2×#324—21no—
11#1444—21no—
12#1444C2212yes—
13#1441—21no—
14#1441C412yes—
15C4⋊#95—21no—
16C4⋊#95C411yescharacteristic
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×C411yescharacteristic
25C22×C4⋊C4C2×C412yes—
26C22×C4⋊C4D411yescharacteristic
27C22×C42C2×C411yescharacteristic
28C22×C42D411yescharacteristic
29C22×C42D411yescharacteristic
30#432—24no—
31#432—42no—
32C2×C4⋊C8—41no—
33C2×C22⋊C8—22no—
34C2×C22⋊C8—22no—
35C2×#97—41no—
36C2×C4×C8—41no—
37#389—42no—
38#389—42no—
39#384—41no—
40#384—41no—
41C4×C4⋊C4—41no—
42C4×C4⋊C4—41no—
43C2×#95—21no—
44C2×#95—22no—
45C2×#95—22no—
46C2×#95—22no—
47C2×#95C2×C412yes—
48C2×#95D411yescharacteristic
49C2×#95C2311yescharacteristic
50#336—41no—
51#324—24no—
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—22no—
65C2×C4⋊C4—22no—
66C2×C4⋊C4—22no—
67C2×C4⋊C4—22no—
68C2×C4⋊C4—41no—
69C2×C4⋊C4—41no—
70C2×C4⋊C4—42no—
71C2×C4⋊C4—42no—
72C2×C4⋊C4—42no—
73C2×C4⋊C4—42no—
74C2×C4⋊C4—41no—
75C2×C4⋊C4—41no—
76C2×C4⋊C4—42no—
77C2×C4⋊C4—42no—
78C2×C4⋊C4—42no—
79C2×C4⋊C4—42no—
80C2×C4⋊C4—82no—
81C2×C4⋊C4—82no—
82C2×C4⋊C4—82no—
83C2×C4⋊C4—82no—
84C2×C42—21no—
85C2×C42—21no—
86C2×C42—22no—
87C2×C42—21no—
88C2×C42—21no—
89C2×C42—21no—
90C2×C42—21no—
91C2×C42—42no—
92C2×C42—42no—
93C2×C42D812yes—
94C2×C42SD1612yes—
95C4⋊C8—44no—
96C22⋊C8—24no—
97C22⋊C8—24no—
98C22⋊C8—42no—
99C22⋊C8—42no—
100#97—44no—
101C4×C8—82no—
102#95—24no—
103#95—41no—
104#95—41no—
105#95—44no—
106#95—42no—
107#95—82no—
108#95—82no—
109C24C2×C22⋊C411yescharacteristic
110C22×C4—22no—
111C22×C4—22no—
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—21no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—21no—
126C22×C4—21no—
127C22×C4—21no—
128C22×C4—24no—
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—41no—
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—42no—
152C22×C4#9911yescharacteristic
153C22×C4#9911yescharacteristic
154C22×C4#10112yes—
155C22×C4#10212yes—
156C22×C4#10212yes—
157C22×C4#10412yes—
158C22×C4#10412yes—
159C22×C4#13112yes—
160C22×C4C2×D811yescharacteristic
161C22×C4C2×SD1611yescharacteristic
162C22×C4#13712yes—
163C2×C8—44no—
164C2×C8—44no—
165C2×C8—82no—
166C2×C8—82no—
167C2×C8—82no—
168C2×C8—82no—
169C4⋊C4—44no—
170C4⋊C4—44no—
171C4⋊C4—48no—
172C4⋊C4—84no—
173C4⋊C4—84no—
174C4⋊C4—84no—
175C4⋊C4—84no—
176C4⋊C4—82no—
177C4⋊C4—82no—
178C42—22no—
179C42—22no—
180C42—22no—
181C42—22no—
182C42—42no—
183C42—42no—
184C42—42no—
185C42—81no—
186C23—21no—
187C23—21no—
188C23—21no—
189C23—21no—
190C23#40811yescharacteristic
191C23C2×#9911yescharacteristic
192C23C2×#10111yescharacteristic
193C23C2×#10211yescharacteristic
194C23#41911yescharacteristic
195C23C2×#10411yescharacteristic
196C23C2×#10411yescharacteristic
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—24no—
200C2×C4—24no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
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—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—44no—
233C2×C4—44no—
234C2×C4—44no—
235C2×C4—81no—
236C2×C4—81no—
237C2×C4—81no—
238C2×C4—82no—
239C2×C4—82no—
240C2×C4—82no—
241C2×C4—82no—
242C2×C4—82no—
243C2×C4—82no—
244C2×C4—82no—
245C2×C4—82no—
246C2×C4—82no—
247C2×C4—82no—
248C2×C4—82no—
249C2×C4#32712yes—
250C2×C4#32712yes—
251C2×C4#35212yes—
252C2×C4#35612yes—
253C8—84no—
254C8—84no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22#147211yescharacteristic
268C22#148511yescharacteristic
269C22#149211yescharacteristic
270C22C2×#32711yescharacteristic
271C22#150811yescharacteristic
272C22#152611yescharacteristic
273C22#154611yescharacteristic
274C22C2×#35211yescharacteristic
275C22#212211yescharacteristic
276C22#212811yescharacteristic
277C22C2×#35611yescharacteristic
278C4—22no—
279C4—42no—
280C4—42no—
281C4—42no—
282C4—42no—
283C4—42no—
284C4—41no—
285C4—41no—
286C4—84no—
287C4—162no—
288C4#134614yes—
289C2—21no—
290C2—21no—
291C2—21no—
292C2—21no—
293C2#768511yescharacteristic
294C2#1157411yescharacteristic
295C2#1157611yescharacteristic
296C2#1169311yescharacteristic
297C2C2×#134611yescharacteristic
298C2#1178611yescharacteristic
299C2#1179511yescharacteristic
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
#151962
C4×#3242
#79122
#71232