Finite Group Databasebeta

← #125599

Subgroups — #125599

Order 512.

442 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 86 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#15152C211yesmaximal, characteristic
2#8701C211yesmaximal, characteristic
3#8560C211yesmaximal, characteristic
4#7122C214yesmaximal
5C2×#400—21no—
6C2×#384C411yescharacteristic
7C2×C4×C4⋊C4C2211yescharacteristic
8#1817—21no—
9#1797—21no—
10C2×#324—21no—
11#1445—21no—
12#1442C2212yes—
13#1441C412yes—
14C4⋊#95—21no—
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⋊C4C2×C411yescharacteristic
24C22×C4⋊C4C2×C412yes—
25C22×C4⋊C4D411yescharacteristic
26C22×C42C2×C411yescharacteristic
27C22×C42D411yescharacteristic
28C22×C42D411yescharacteristic
29C2×C4⋊C8—41no—
30C2×C22⋊C8—22no—
31C2×C22⋊C8—22no—
32#400—42no—
33#400—42no—
34#384—41no—
35#384—41no—
36C4×C4⋊C4—41no—
37C4×C4⋊C4—41no—
38C2×#95—22no—
39C2×#95—21no—
40C2×#95—22no—
41C2×#95—22no—
42C2×#95—22no—
43C2×#95C2×C412yes—
44C2×#95D411yescharacteristic
45C2×#95C2311yescharacteristic
46#336—41no—
47#336—41no—
48#336—41no—
49#324—42no—
50C23×C4—22no—
51C23×C4—22no—
52C23×C4C22⋊C411yescharacteristic
53C23×C4C22⋊C411yescharacteristic
54C23×C4C22⋊C411yescharacteristic
55C23×C4C22⋊C411yescharacteristic
56C23×C4C22×C411yescharacteristic
57C23×C4C2×D411yescharacteristic
58C23×C4C2×D411yescharacteristic
59C22×C8—42no—
60C22×C8—42no—
61C2×C4⋊C4—22no—
62C2×C4⋊C4—22no—
63C2×C4⋊C4—41no—
64C2×C4⋊C4—41no—
65C2×C4⋊C4—41no—
66C2×C4⋊C4—42no—
67C2×C4⋊C4—42no—
68C2×C4⋊C4—42no—
69C2×C4⋊C4—42no—
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—82no—
78C2×C4⋊C4D812yes—
79C2×C4⋊C4SD1612yes—
80C2×C42—21no—
81C2×C42—21no—
82C2×C42—21no—
83C2×C42—21no—
84C2×C42—21no—
85C2×C42—22no—
86C2×C42—21no—
87C2×C42—41no—
88C2×C42—42no—
89C2×C42—42no—
90C4⋊C8—82no—
91C22⋊C8—42no—
92C22⋊C8—42no—
93C22⋊C8—42no—
94C22⋊C8—42no—
95#95—24no—
96#95—41no—
97#95—41no—
98#95—42no—
99#95—44no—
100#95—42no—
101#95—42no—
102#95—82no—
103#95—82no—
104C24C2×C22⋊C411yescharacteristic
105C22×C4—21no—
106C22×C4—21no—
107C22×C4—22no—
108C22×C4—22no—
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—21no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—41no—
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—42no—
136C22×C4—42no—
137C22×C4—42no—
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#9911yescharacteristic
150C22×C4#9911yescharacteristic
151C22×C4#10112yes—
152C22×C4#10212yes—
153C22×C4#10212yes—
154C22×C4#13112yes—
155C22×C4C2×D811yescharacteristic
156C22×C4C2×SD1611yescharacteristic
157C22×C4#13712yes—
158C2×C8—82no—
159C2×C8—82no—
160C2×C8—82no—
161C2×C8—82no—
162C2×C8—82no—
163C2×C8—82no—
164C4⋊C4—42no—
165C4⋊C4—42no—
166C4⋊C4—44no—
167C4⋊C4—84no—
168C4⋊C4—82no—
169C4⋊C4—84no—
170C4⋊C4—84no—
171C4⋊C4—82no—
172C42—42no—
173C42—42no—
174C42—42no—
175C42—42no—
176C42—42no—
177C42—81no—
178C23—21no—
179C23—21no—
180C23—21no—
181C23—21no—
182C23#40811yescharacteristic
183C23C2×#9911yescharacteristic
184C23C2×#10111yescharacteristic
185C23C2×#10211yescharacteristic
186C23#41911yescharacteristic
187C23#42111yescharacteristic
188C23#42111yescharacteristic
189C2×C4—24no—
190C2×C4—24no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—41no—
207C2×C4—41no—
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—41no—
219C2×C4—41no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—42no—
226C2×C4—81no—
227C2×C4—81no—
228C2×C4—81no—
229C2×C4—82no—
230C2×C4—82no—
231C2×C4—82no—
232C2×C4—82no—
233C2×C4—82no—
234C2×C4—82no—
235C2×C4—82no—
236C2×C4—82no—
237C2×C4—82no—
238C2×C4—82no—
239C2×C4—82no—
240C2×C4—82no—
241C2×C4—82no—
242C2×C4—82no—
243C2×C4#35212yes—
244C2×C4#35512yes—
245C8—162no—
246C8—162no—
247C22—21no—
248C22—21no—
249C22—21no—
250C22—21no—
251C22—21no—
252C22—21no—
253C22—21no—
254C22—21no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22#147211yescharacteristic
260C22#148011yescharacteristic
261C22#149711yescharacteristic
262C22#151111yescharacteristic
263C22#151911yescharacteristic
264C22#153711yescharacteristic
265C22#154611yescharacteristic
266C22C2×#35211yescharacteristic
267C22#212211yescharacteristic
268C22#212911yescharacteristic
269C22C2×#35511yescharacteristic
270C4—22no—
271C4—22no—
272C4—42no—
273C4—42no—
274C4—42no—
275C4—42no—
276C4—41no—
277C4—42no—
278C4—41no—
279C4—162no—
280C4—162no—
281C2—21no—
282C2—21no—
283C2—21no—
284C2—21no—
285C2#772811yescharacteristic
286C2#1157311yescharacteristic
287C2#1157611yescharacteristic
288C2#1181211yescharacteristic
289C2#1181411yescharacteristic
290C2#1187411yescharacteristic
291C2#1188211yescharacteristic
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
#151522
#87012
#85602
#71222