Finite Group Databasebeta

← #120888

Subgroups — #120888

Order 512.

387 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 387 conjugacy classes of subgroups — too many to draw. Only its 114 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#17823C211yesmaximal, characteristic
2#8113C211yesmaximal, characteristic
3#8110C211yesmaximal, characteristic
4#7974C211yesmaximal, characteristic
5#7973C211yesmaximal, characteristic
6#7944C211yesmaximal, characteristic
7#7920C211yesmaximal, characteristic
8#2920C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11#2920C2211yescharacteristic
12C2×C4×M16C2211yescharacteristic
13#2283C2211yescharacteristic
14#2283C2211yescharacteristic
15#1574—22no—
16#1572—22no—
17#1569—22no—
18#1306—22no—
19#1305—22no—
20#1288—22no—
21#1288—22no—
22#1284C414yes—
23#1281—22no—
24C22×M16—21no—
25C22×C42C2311yescharacteristic
26#432—21no—
27#432—21no—
28#432—21no—
29#432—21no—
30#432—21no—
31#432D412yes—
32#432D412yes—
33#432Q812yes—
34#431—21no—
35#431—21no—
36#431—21no—
37#431—21no—
38#431—21no—
39#431—21no—
40#431—21no—
41#431D412yes—
42#423—21no—
43#423—21no—
44#423—21no—
45#423—21no—
46#407—21no—
47#407—21no—
48#407C2×C412yes—
49#407D412yes—
50C4×M16—21no—
51C4×M16—21no—
52C4×M16—21no—
53C4×M16—21no—
54C4×M16—21no—
55C4×M16—21no—
56C4×M16—21no—
57C4×M16—21no—
58C2×#97—21no—
59C2×C4×C8Q812yes—
60#383—21no—
61#383—21no—
62#382—21no—
63#382—21no—
64#381—21no—
65#381C2×C412yes—
66#380—21no—
67#380—21no—
68C4×C4⋊C4—21no—
69C4×C4⋊C4—21no—
70C4×C22⋊C4—21no—
71C4×C22⋊C4C2×C412yes—
72#376—21no—
73#376—21no—
74#335—24no—
75#334—24no—
76C23×C4C22×C411yescharacteristic
77C23×C4C2×D411yescharacteristic
78C23×C4#4111yescharacteristic
79C2×M16—22no—
80C2×M16—22no—
81C2×M16—44no—
82C2×M16—41no—
83C2×M16—41no—
84C2×M16—41no—
85C2×M16—41no—
86C22×C8—22no—
87C2×C4⋊C4—41no—
88C2×C4⋊C4—41no—
89C2×C22⋊C4—22no—
90C2×C22⋊C4—22no—
91C2×C42—22no—
92C2×C42—41no—
93C2×C42C2×D411yescharacteristic
94C2×C42C2×D411yescharacteristic
95C2×C42C2×D411yescharacteristic
96C2×C42C2×Q811yescharacteristic
97C2×C42C2×Q811yescharacteristic
98C2×C42#4111yescharacteristic
99C2×C42#4111yescharacteristic
100C2×C42#4111yescharacteristic
101C2×C42#4111yescharacteristic
102C2×C42#4111yescharacteristic
103C2×C42#4111yescharacteristic
104C2×C42#4111yescharacteristic
105C4⋊C8—22no—
106C4⋊C8—22no—
107C4⋊C8—22no—
108C4⋊C8—22no—
109C4⋊C8—41no—
110C4⋊C8—41no—
111C4⋊C8—41no—
112C4⋊C8—41no—
113C22⋊C8—22no—
114C22⋊C8—22no—
115C22⋊C8—22no—
116C22⋊C8—22no—
117C22⋊C8—22no—
118C22⋊C8—41no—
119C22⋊C8—41no—
120C22⋊C8C4⋊C414yes—
121#97—22no—
122#97—22no—
123#97—22no—
124#97—41no—
125#97—41no—
126#97—41no—
127C4×C8—22no—
128C4×C8—22no—
129C4×C8—22no—
130C4×C8—41no—
131C4×C8—41no—
132C4×C8—41no—
133#95—22no—
134#95—22no—
135#95—22no—
136#95—41no—
137#95—41no—
138#95—41no—
139#95—41no—
140#95—41no—
141C24C4×D411yescharacteristic
142C22×C4—42no—
143C22×C4—42no—
144C22×C4—42no—
145C22×C4—81no—
146C22×C4—81no—
147C22×C4C2×C4⋊C411yescharacteristic
148C22×C4#11711yescharacteristic
149C22×C4#11711yescharacteristic
150C22×C4C4×D411yescharacteristic
151C22×C4C4×D411yescharacteristic
152C22×C4C4×Q811yescharacteristic
153C22×C4#12111yescharacteristic
154C22×C4#12111yescharacteristic
155C22×C4#12111yescharacteristic
156C22×C4C22⋊Q811yescharacteristic
157C22×C4#12311yescharacteristic
158C22×C4#12311yescharacteristic
159C22×C4#12411yescharacteristic
160C22×C4#12411yescharacteristic
161C22×C4#12511yescharacteristic
162C22×C4#12611yescharacteristic
163C22×C4#12611yescharacteristic
164C22×C4C4⋊Q811yescharacteristic
165M16—44no—
166M16—44no—
167M16—82no—
168M16—82no—
169M16—82no—
170M16—82no—
171C2×C8—24no—
172C2×C8—24no—
173C2×C8—42no—
174C2×C8—42no—
175C2×C8—42no—
176C2×C8—42no—
177C2×C8—42no—
178C4⋊C4—82no—
179C4⋊C4—82no—
180C22⋊C4—82no—
181C22⋊C4—82no—
182C42—82no—
183C42—82no—
184C42#12011yescharacteristic
185C42C22⋊Q811yescharacteristic
186C42C22⋊Q811yescharacteristic
187C42C22⋊Q811yescharacteristic
188C42C22⋊Q811yescharacteristic
189C42#12311yescharacteristic
190C42#12311yescharacteristic
191C42#12311yescharacteristic
192C42#12411yescharacteristic
193C42#12411yescharacteristic
194C42#12511yescharacteristic
195C42#12511yescharacteristic
196C42#12511yescharacteristic
197C42#12511yescharacteristic
198C42#12611yescharacteristic
199C42#12611yescharacteristic
200C23—41no—
201C23—41no—
202C23—41no—
203C23#38811yescharacteristic
204C23#38811yescharacteristic
205C23#38911yescharacteristic
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
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—41no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—82no—
225C2×C4—82no—
226C2×C4—82no—
227C2×C4—82no—
228C2×C4—82no—
229C2×C4—82no—
230C2×C4#38211yescharacteristic
231C2×C4#38511yescharacteristic
232C2×C4#38711yescharacteristic
233C2×C4#38711yescharacteristic
234C2×C4#39311yescharacteristic
235C2×C4#39411yescharacteristic
236C2×C4#39711yescharacteristic
237C2×C4#39811yescharacteristic
238C2×C4#39811yescharacteristic
239C2×C4#40011yescharacteristic
240C2×C4#40011yescharacteristic
241C2×C4#40011yescharacteristic
242C8—44no—
243C8—44no—
244C8—82no—
245C8—82no—
246C8—82no—
247C22—21no—
248C22—21no—
249C22—21no—
250C22—21no—
251C22—21no—
252C22—21no—
253C22—21no—
254C22—21no—
255C22—21no—
256C22—82no—
257C22#144211yescharacteristic
258C4—21no—
259C4—21no—
260C4—21no—
261C4—21no—
262C4—21no—
263C4—21no—
264C4—21no—
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—162no—
270C4—162no—
271C4#210212yes—
272C2—41no—
273C2—41no—
274C2—41no—
275C2#1127711yescharacteristic
276C2#1128011yescharacteristic
277C2#1128611yescharacteristic
subgroupG/H
center, socleC22#1442
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C4×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#178232
#81132
#81102
#79742
#79732
#79442
#79202