Finite Group Databasebeta

← #121840

Subgroups — #121840

Order 512.

395 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#21960C211yesmaximal, characteristic
2#8116C211yesmaximal, characteristic
3#8113C211yesmaximal, characteristic
4#8070C211yesmaximal, characteristic
5#8002C211yesmaximal, characteristic
6#7976C211yesmaximal, characteristic
7#7935C211yesmaximal, characteristic
8#2920C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11#2920C2211yescharacteristic
12C22×C4⋊C8C2211yescharacteristic
13#2283C2211yescharacteristic
14#2283C2211yescharacteristic
15#1949—22no—
16#1949—22no—
17#1808C412yes—
18#1807C412yes—
19#1306—22no—
20#1306—22no—
21#1300—22no—
22#1292—22no—
23#1288—22no—
24#1283—22no—
25C23×C8C2×C411yescharacteristic
26C23×C8C2×C411yescharacteristic
27C22×C42C2311yescharacteristic
28#432—21no—
29#432—21no—
30#432—21no—
31#432—21no—
32#432—21no—
33#432—21no—
34#432D412yes—
35#432Q812yes—
36#431—21no—
37#431—21no—
38#431—21no—
39#431—21no—
40#431—21no—
41#431—21no—
42#431—21no—
43#431Q812yes—
44C2×#107—22no—
45C2×#106—22no—
46#423—21no—
47#423—21no—
48#423—21no—
49#423—21no—
50C2×C4⋊C8—21no—
51C2×C4⋊C8—21no—
52C2×C4⋊C8—21no—
53C2×C4⋊C8—21no—
54C2×C4⋊C8D412yes—
55C2×C4⋊C8D412yes—
56#407—21no—
57#407—21no—
58#407—21no—
59#407D412yes—
60C4×M16—21no—
61C4×M16—21no—
62C4×M16—21no—
63C4×M16—21no—
64#383—21no—
65#383—21no—
66#382—21no—
67#382—21no—
68#381—21no—
69#381—21no—
70#380C2×C412yes—
71#380C2×C412yes—
72C4×C4⋊C4—21no—
73C4×C4⋊C4—21no—
74C4×C22⋊C4—21no—
75C4×C22⋊C4—21no—
76#376—21no—
77#376—21no—
78#340—22no—
79#340—22no—
80C23×C4C22×C411yescharacteristic
81C23×C4C2×D411yescharacteristic
82C23×C4#4111yescharacteristic
83C2×M16—22no—
84C2×M16—41no—
85C2×M16—41no—
86C2×M16—41no—
87C22×C8—21no—
88C22×C8—21no—
89C22×C8—21no—
90C22×C8—21no—
91C22×C8—81no—
92C22×C8—81no—
93C22×C8C22⋊C412yes—
94C22×C8C22⋊C412yes—
95C2×C4⋊C4—22no—
96C2×C4⋊C4—22no—
97C2×C22⋊C4—22no—
98C2×C22⋊C4—22no—
99C2×C42—41no—
100C2×C42—41no—
101C2×C42C2×D411yescharacteristic
102C2×C42C2×D411yescharacteristic
103C2×C42C2×D411yescharacteristic
104C2×C42C2×Q811yescharacteristic
105C2×C42C2×Q811yescharacteristic
106C2×C42#4111yescharacteristic
107C2×C42#4111yescharacteristic
108C2×C42#4111yescharacteristic
109C2×C42#4111yescharacteristic
110C2×C42#4111yescharacteristic
111C2×C42#4111yescharacteristic
112C2×C42#4111yescharacteristic
113#107—82no—
114#106—82no—
115C4⋊C8—22no—
116C4⋊C8—22no—
117C4⋊C8—22no—
118C4⋊C8—22no—
119C4⋊C8—22no—
120C4⋊C8—22no—
121C4⋊C8—22no—
122C4⋊C8—41no—
123C4⋊C8—41no—
124C4⋊C8—41no—
125C4⋊C8—41no—
126C4⋊C8—41no—
127C22⋊C8—22no—
128C22⋊C8—22no—
129C22⋊C8—22no—
130C22⋊C8—22no—
131C22⋊C8—22no—
132C22⋊C8—41no—
133C22⋊C8—41no—
134C22⋊C8—41no—
135#97—22no—
136#97—22no—
137#97—41no—
138#97—41no—
139C4×C8—22no—
140C4×C8—41no—
141C4×C8—41no—
142C4×C8—41no—
143#95—22no—
144#95—22no—
145#95—41no—
146#95—41no—
147#95—41no—
148#95—41no—
149#95—41no—
150#95—41no—
151C24C4×D411yescharacteristic
152C22×C4—41no—
153C22×C4—41no—
154C22×C4—42no—
155C22×C4—42no—
156C22×C4—42no—
157C22×C4—81no—
158C22×C4C2×C22⋊C411yescharacteristic
159C22×C4#11711yescharacteristic
160C22×C4#11711yescharacteristic
161C22×C4C4×D411yescharacteristic
162C22×C4C4×Q811yescharacteristic
163C22×C4C4×Q811yescharacteristic
164C22×C4#12111yescharacteristic
165C22×C4#12111yescharacteristic
166C22×C4C22⋊Q811yescharacteristic
167C22×C4C22⋊Q811yescharacteristic
168C22×C4#12311yescharacteristic
169C22×C4#12311yescharacteristic
170C22×C4#12411yescharacteristic
171C22×C4#12511yescharacteristic
172C22×C4#12511yescharacteristic
173C22×C4#12611yescharacteristic
174C22×C4#12611yescharacteristic
175C22×C4#12711yescharacteristic
176M16—44no—
177M16—82no—
178M16—82no—
179M16—82no—
180C2×C8—22no—
181C2×C8—22no—
182C2×C8—42no—
183C2×C8—42no—
184C2×C8—42no—
185C2×C8—42no—
186C2×C8—42no—
187C2×C8—42no—
188C2×C8—81no—
189C2×C8—81no—
190C2×C8—81no—
191C2×C8—81no—
192C4⋊C4—42no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C22⋊C4—82no—
197C22⋊C4—82no—
198C42—82no—
199C42—82no—
200C42C22⋊Q811yescharacteristic
201C42C22⋊Q811yescharacteristic
202C42C22⋊Q811yescharacteristic
203C42C22⋊Q811yescharacteristic
204C42#12311yescharacteristic
205C42#12311yescharacteristic
206C42#12311yescharacteristic
207C42#12311yescharacteristic
208C42#12311yescharacteristic
209C42#12311yescharacteristic
210C42#12411yescharacteristic
211C42#12511yescharacteristic
212C42#12511yescharacteristic
213C42#12611yescharacteristic
214C42#12611yescharacteristic
215C42C4⋊Q811yescharacteristic
216C23—22no—
217C23—41no—
218C23—41no—
219C23#38711yescharacteristic
220C23#38711yescharacteristic
221C23#39011yescharacteristic
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
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—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—82no—
244C2×C4—82no—
245C2×C4—82no—
246C2×C4—82no—
247C2×C4—82no—
248C2×C4—82no—
249C2×C4#38111yescharacteristic
250C2×C4#38711yescharacteristic
251C2×C4#38711yescharacteristic
252C2×C4#39111yescharacteristic
253C2×C4#39711yescharacteristic
254C2×C4#39711yescharacteristic
255C2×C4#39811yescharacteristic
256C2×C4#39811yescharacteristic
257C2×C4#39911yescharacteristic
258C2×C4#39911yescharacteristic
259C2×C4#40011yescharacteristic
260C2×C4#40011yescharacteristic
261C8—42no—
262C8—42no—
263C8—82no—
264C8—82no—
265C8—82no—
266C8—82no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—44no—
276C22#144511yescharacteristic
277C22#197612yes—
278C4—21no—
279C4—21no—
280C4—21no—
281C4—21no—
282C4—21no—
283C4—21no—
284C4—21no—
285C4—21no—
286C4—21no—
287C4—21no—
288C4—21no—
289C4—162no—
290C4—162no—
291C4#182911yescharacteristic
292C4#183011yescharacteristic
293C2—22no—
294C2—41no—
295C2—41no—
296C2#1135211yescharacteristic
297C2#1136011yescharacteristic
298C2#1136411yescharacteristic
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
#219602
#81162
#81132
#80702
#80022
#79762
#79352