Finite Group Databasebeta

← #121841

Subgroups — #121841

Order 512.

417 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21961C211yesmaximal, characteristic
2#8109C211yesmaximal, characteristic
3#8105C211yesmaximal, characteristic
4#8094C211yesmaximal, characteristic
5#7988C211yesmaximal, characteristic
6#7961C211yesmaximal, characteristic
7#7935C211yesmaximal, characteristic
8#2920C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11#2920C2211yescharacteristic
12C22×C4⋊C8C2211yescharacteristic
13#2285C2211yescharacteristic
14#2285C2211yescharacteristic
15#1947—22no—
16#1947—22no—
17#1808C414yes—
18#1305—22no—
19#1305—22no—
20#1303—22no—
21#1290—22no—
22#1286—22no—
23#1283—22no—
24C23×C8C2×C412yes—
25C2×#117—21no—
26C2×#117—21no—
27C22×C42C2311yescharacteristic
28#432—21no—
29#432—21no—
30#432—21no—
31#432—21no—
32#432—21no—
33#432—21no—
34#432—21no—
35#432Q812yes—
36#431—21no—
37#431—21no—
38#431—21no—
39#431—21no—
40#431—21no—
41#431—21no—
42#431—21no—
43#431—21no—
44C2×#107—24no—
45#423—21no—
46#423—21no—
47#423—21no—
48#423D412yes—
49C2×C4⋊C8—21no—
50C2×C4⋊C8—21no—
51C2×C4⋊C8—21no—
52C2×C4⋊C8—21no—
53C2×C4⋊C8D412yes—
54C2×C4⋊C8D412yes—
55#407—21no—
56#407—21no—
57#407—21no—
58#407D412yes—
59C4×M16—21no—
60C4×M16—21no—
61C4×M16—21no—
62C4×M16Q812yes—
63#384—21no—
64#384—21no—
65#382—21no—
66#382—21no—
67#380—21no—
68#380—21no—
69#380C2×C412yes—
70#380C2×C412yes—
71C4×C4⋊C4—21no—
72C4×C4⋊C4—21no—
73C4×C4⋊C4—21no—
74C4×C4⋊C4—21no—
75#340—24no—
76C23×C4C22×C411yescharacteristic
77C23×C4C2×D411yescharacteristic
78C23×C4#4111yescharacteristic
79C2×M16—22no—
80C2×M16—22no—
81C2×M16—22no—
82C2×M16—41no—
83C22×C8—22no—
84C22×C8—22no—
85C22×C8—82no—
86C22×C8C22⋊C414yes—
87#117—82no—
88#117—82no—
89C2×C4⋊C4—22no—
90C2×C4⋊C4—22no—
91C2×C4⋊C4—41no—
92C2×C4⋊C4—41no—
93C2×C4⋊C4—41no—
94C2×C4⋊C4—41no—
95C2×C22⋊C4—22no—
96C2×C22⋊C4—22no—
97C2×C42—41no—
98C2×C42—41no—
99C2×C42C2×D411yescharacteristic
100C2×C42C2×D411yescharacteristic
101C2×C42C2×D411yescharacteristic
102C2×C42C2×Q811yescharacteristic
103C2×C42C2×Q811yescharacteristic
104C2×C42#4111yescharacteristic
105C2×C42#4111yescharacteristic
106C2×C42#4111yescharacteristic
107C2×C42#4111yescharacteristic
108C2×C42#4111yescharacteristic
109C2×C42#4111yescharacteristic
110C2×C42#4111yescharacteristic
111#107—84no—
112C4⋊C8—22no—
113C4⋊C8—22no—
114C4⋊C8—22no—
115C4⋊C8—22no—
116C4⋊C8—22no—
117C4⋊C8—22no—
118C4⋊C8—22no—
119C4⋊C8—41no—
120C4⋊C8—41no—
121C4⋊C8—41no—
122C4⋊C8—41no—
123C4⋊C8—41no—
124C22⋊C8—22no—
125C22⋊C8—22no—
126C22⋊C8—22no—
127C22⋊C8—41no—
128C22⋊C8—41no—
129C22⋊C8—41no—
130C22⋊C8—41no—
131C22⋊C8—41no—
132#97—22no—
133#97—22no—
134#97—41no—
135#97—41no—
136C4×C8—22no—
137C4×C8—41no—
138C4×C8—41no—
139C4×C8—41no—
140#95—22no—
141#95—22no—
142#95—41no—
143#95—41no—
144C24C4×D411yescharacteristic
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—41no—
148C22×C4—41no—
149C22×C4—42no—
150C22×C4—42no—
151C22×C4—81no—
152C22×C4C2×C22⋊C411yescharacteristic
153C22×C4#11711yescharacteristic
154C22×C4#11711yescharacteristic
155C22×C4C4×D411yescharacteristic
156C22×C4C4×Q811yescharacteristic
157C22×C4C4×Q811yescharacteristic
158C22×C4#12111yescharacteristic
159C22×C4#12111yescharacteristic
160C22×C4C22⋊Q811yescharacteristic
161C22×C4C22⋊Q811yescharacteristic
162C22×C4#12311yescharacteristic
163C22×C4#12311yescharacteristic
164C22×C4#12411yescharacteristic
165C22×C4#12511yescharacteristic
166C22×C4#12511yescharacteristic
167C22×C4#12611yescharacteristic
168C22×C4#12611yescharacteristic
169C22×C4#12711yescharacteristic
170M16—42no—
171M16—42no—
172M16—82no—
173M16—82no—
174M16—82no—
175C2×C8—24no—
176C2×C8—44no—
177C2×C8—42no—
178C2×C8—42no—
179C2×C8—42no—
180C2×C8—42no—
181C2×C8—82no—
182C2×C8—82no—
183C4⋊C4—42no—
184C4⋊C4—42no—
185C4⋊C4—42no—
186C4⋊C4—42no—
187C4⋊C4—82no—
188C4⋊C4—82no—
189C4⋊C4—82no—
190C4⋊C4—82no—
191C22⋊C4—82no—
192C22⋊C4—82no—
193C42—82no—
194C42—82no—
195C42C22⋊Q811yescharacteristic
196C42C22⋊Q811yescharacteristic
197C42C22⋊Q811yescharacteristic
198C42C22⋊Q811yescharacteristic
199C42#12311yescharacteristic
200C42#12311yescharacteristic
201C42#12311yescharacteristic
202C42#12311yescharacteristic
203C42#12311yescharacteristic
204C42#12311yescharacteristic
205C42#12411yescharacteristic
206C42#12511yescharacteristic
207C42#12511yescharacteristic
208C42#12611yescharacteristic
209C42#12611yescharacteristic
210C42C4⋊Q811yescharacteristic
211C23—21no—
212C23—21no—
213C23—41no—
214C23—41no—
215C23#38711yescharacteristic
216C23#38711yescharacteristic
217C23#39011yescharacteristic
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—82no—
240C2×C4—82no—
241C2×C4—82no—
242C2×C4—82no—
243C2×C4—82no—
244C2×C4—82no—
245C2×C4#38111yescharacteristic
246C2×C4#38711yescharacteristic
247C2×C4#38711yescharacteristic
248C2×C4#39111yescharacteristic
249C2×C4#39711yescharacteristic
250C2×C4#39711yescharacteristic
251C2×C4#39811yescharacteristic
252C2×C4#39811yescharacteristic
253C2×C4#39911yescharacteristic
254C2×C4#39911yescharacteristic
255C2×C4#40011yescharacteristic
256C2×C4#40011yescharacteristic
257C2×C4#47212yes—
258C2×C4#47312yes—
259C8—44no—
260C8—82no—
261C8—82no—
262C8—82no—
263C8—82no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—42no—
273C22—42no—
274C22#144511yescharacteristic
275C22#197811yescharacteristic
276C22#197911yescharacteristic
277C4—21no—
278C4—21no—
279C4—21no—
280C4—21no—
281C4—21no—
282C4—21no—
283C4—21no—
284C4—21no—
285C4—21no—
286C4—162no—
287C4—162no—
288C4#182911yescharacteristic
289C4#183011yescharacteristic
290C4#207812yes—
291C4#208912yes—
292C2—21no—
293C2—21no—
294C2—41no—
295C2—41no—
296C2#1135211yescharacteristic
297C2#1136111yescharacteristic
298C2#1136511yescharacteristic
subgroupG/H
center, socleC22#1445
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
#219612
#81092
#81052
#80942
#79882
#79612
#79352