Finite Group Databasebeta

← #98849

Subgroups — #98849

Order 512.

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

normal subgroups only

This group has 376 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#21020C211yesmaximal, characteristic
2#8596C211yesmaximal, characteristic
3#8595C211yesmaximal, characteristic
4#7598C212yesmaximal
5#7034C212yesmaximal
6C2×#424C411yescharacteristic
7C22×C4×C8C2211yescharacteristic
8#2296C2211yescharacteristic
9#1916—21no—
10#1916—21no—
11#1916—21no—
12#1916—21no—
13#1797C2212yes—
14#1797C2212yes—
15#1729C411yescharacteristic
16#1729C411yescharacteristic
17#1729C411yescharacteristic
18#1728C2211yescharacteristic
19C2×#335—21no—
20C2×#334—21no—
21#1277—21no—
22#1277—21no—
23#1271—22no—
24#1271—22no—
25C22×M16C2×C411yescharacteristic
26C22×M16C2×C411yescharacteristic
27C23×C8C2×C411yescharacteristic
28C23×C8C2×C411yescharacteristic
29C2×#117C2×C411yescharacteristic
30C2×#117C2×C411yescharacteristic
31C22×C42C2311yescharacteristic
32#424—42no—
33C2×C4⋊C8—21no—
34C2×C4⋊C8—21no—
35C2×C4⋊C8—22no—
36C2×C4⋊C8—22no—
37C2×C22⋊C8—22no—
38C2×C22⋊C8—22no—
39C2×C4×C8—42no—
40C2×C4×C8D411yescharacteristic
41C2×C4×C8D411yescharacteristic
42C2×C4×C8D411yescharacteristic
43C2×C4×C8D411yescharacteristic
44#389D411yescharacteristic
45#389D411yescharacteristic
46#389Q811yescharacteristic
47#389Q811yescharacteristic
48#385—21no—
49#385—21no—
50C4×C4⋊C4—21no—
51C4×C4⋊C4—21no—
52#336—21no—
53#336—21no—
54#336—21no—
55#336—21no—
56#336—21no—
57#336—21no—
58#336—21no—
59#336—21no—
60#336—22no—
61#336—22no—
62#335—42no—
63#334—42no—
64C23×C4C22×C411yescharacteristic
65C23×C4#4111yescharacteristic
66C23×C4#4111yescharacteristic
67C2×M16—22no—
68C2×M16—22no—
69C2×M16—41no—
70C2×M16—41no—
71C2×M16—41no—
72C2×M16—41no—
73C22×C8—22no—
74C22×C8—22no—
75C22×C8—22no—
76C22×C8—22no—
77C22×C8—21no—
78C22×C8—21no—
79C22×C8—41no—
80C22×C8—41no—
81C22×C8—42no—
82C22×C8—42no—
83C22×C8C22⋊C411yescharacteristic
84C22×C8C22⋊C411yescharacteristic
85C22×C8C22⋊C411yescharacteristic
86C22×C8C22⋊C411yescharacteristic
87#117—22no—
88#117—22no—
89#117—41no—
90#117—41no—
91C2×C4⋊C4—21no—
92C2×C4⋊C4—21no—
93C2×C4⋊C4—21no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4C4⋊C411yescharacteristic
96C2×C4⋊C4C4⋊C411yescharacteristic
97C2×C4⋊C4C4⋊C411yescharacteristic
98C2×C4⋊C4C4⋊C411yescharacteristic
99C2×C22⋊C4—21no—
100C2×C22⋊C4—21no—
101C2×C42—21no—
102C2×C42—21no—
103C2×C42—41no—
104C2×C42—41no—
105C2×C42C2×D411yescharacteristic
106C2×C42C2×D411yescharacteristic
107C2×C42C2×D411yescharacteristic
108C2×C42C2×Q811yescharacteristic
109C4⋊C8—42no—
110C4⋊C8—42no—
111C4⋊C8—42no—
112C4⋊C8—42no—
113C4⋊C8—42no—
114C4⋊C8—42no—
115C22⋊C8—82no—
116C22⋊C8—82no—
117C4×C8—22no—
118C4×C8—22no—
119C4×C8—41no—
120C4×C8—41no—
121#95—21no—
122#95—21no—
123#95—21no—
124#95—21no—
125C24#11711yescharacteristic
126C22×C4—21no—
127C22×C4—21no—
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—22no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—41no—
138C22×C4—41no—
139C22×C4—41no—
140C22×C4—41no—
141C22×C4C2×C22⋊C411yescharacteristic
142C22×C4C2×C4⋊C411yescharacteristic
143C22×C4#12111yescharacteristic
144C22×C4#12111yescharacteristic
145C22×C4C22⋊Q811yescharacteristic
146C22×C4C22⋊Q811yescharacteristic
147C22×C4#13112yes—
148C22×C4#13112yes—
149M16—82no—
150M16—82no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—21no—
157C2×C8—21no—
158C2×C8—21no—
159C2×C8—21no—
160C2×C8—21no—
161C2×C8—44no—
162C2×C8—44no—
163C2×C8—41no—
164C2×C8—41no—
165C2×C8—41no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—41no—
169C2×C8—82no—
170C2×C8—82no—
171C2×C8—82no—
172C2×C8—82no—
173C2×C8—82no—
174C2×C8—82no—
175C2×C8#9912yes—
176C2×C8#10112yes—
177C4⋊C4—22no—
178C4⋊C4—22no—
179C4⋊C4—41no—
180C4⋊C4—41no—
181C4⋊C4—42no—
182C4⋊C4—42no—
183C4⋊C4—42no—
184C4⋊C4—41no—
185C4⋊C4—41no—
186C22⋊C4—42no—
187C22⋊C4—42no—
188C42—21no—
189C42—21no—
190C42—21no—
191C42—21no—
192C42—41no—
193C42—41no—
194C42—41no—
195C42—41no—
196C42—41no—
197C42—41no—
198C23—21no—
199C23—21no—
200C23—21no—
201C23—21no—
202C23—21no—
203C23—21no—
204C23#38011yescharacteristic
205C23#43312yes—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—44no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4#40811yescharacteristic
238C2×C4#40811yescharacteristic
239C2×C4C2×#9911yescharacteristic
240C2×C4#41011yescharacteristic
241C2×C4C2×#10111yescharacteristic
242C2×C4#41311yescharacteristic
243C2×C4#42412yes—
244C2×C4#47112yes—
245C2×C4#47211yescharacteristic
246C2×C4#47311yescharacteristic
247C8—22no—
248C8—22no—
249C8—41no—
250C8—41no—
251C8—81no—
252C8—81no—
253C8—162no—
254C8—162no—
255C22—22no—
256C22—22no—
257C22—22no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22#179811yescharacteristic
263C22#179911yescharacteristic
264C22#180111yescharacteristic
265C22#181411yescharacteristic
266C22#181411yescharacteristic
267C22#181511yescharacteristic
268C22#181611yescharacteristic
269C4—22no—
270C4—22no—
271C4—21no—
272C4—21no—
273C4—41no—
274C4—41no—
275C4—81no—
276C4—81no—
277C4—81no—
278C4—81no—
279C4#146811yescharacteristic
280C4#147011yescharacteristic
281C4#147211yescharacteristic
282C4#147311yescharacteristic
283C2—42no—
284C2#856211yescharacteristic
285C2#860611yescharacteristic
286C2#860711yescharacteristic
287C2#862611yescharacteristic
288C2#862811yescharacteristic
289C2#863311yescharacteristic
290C2#864111yescharacteristic
subgroupG/H
center, socleC23#380
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#117
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#210202
#85962
#85952
#75982
#70342