Finite Group Databasebeta

← #120811

Subgroups — #120811

Order 512.

397 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17820C211yesmaximal, characteristic
2#8119C211yesmaximal, characteristic
3#8109C211yesmaximal, characteristic
4#8082C211yesmaximal, characteristic
5#8045C211yesmaximal, characteristic
6#7961C211yesmaximal, characteristic
7#7935C211yesmaximal, characteristic
8#2920C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11#2920C2211yescharacteristic
12C2×#423C2211yescharacteristic
13C22×C4⋊C8C2211yescharacteristic
14#2285C2211yescharacteristic
15#1574—22no—
16#1571—21no—
17#1570—21no—
18#1569—22no—
19#1307—22no—
20#1305C414yes—
21#1301—22no—
22#1296—22no—
23#1286—21no—
24#1286—21no—
25#1283—22no—
26C22×M16—21no—
27C23×C8—21no—
28C2×#117—21no—
29C22×C42C2311yescharacteristic
30#432—21no—
31#432—21no—
32#432—21no—
33#432—21no—
34#432—21no—
35#432—21no—
36#432—21no—
37#432Q812yes—
38#431—21no—
39#431—21no—
40#431—21no—
41#431—21no—
42#431—21no—
43#431—21no—
44#431D412yes—
45#431Q812yes—
46#423—21no—
47#423—21no—
48#423—21no—
49#423—21no—
50#423—21no—
51#423—21no—
52#423D411yescharacteristic
53#423D411yescharacteristic
54#423D412yes—
55C2×C4⋊C8—21no—
56C2×C4⋊C8—21no—
57C2×C4⋊C8—21no—
58C2×C4⋊C8—21no—
59C2×C4⋊C8—21no—
60C2×C4⋊C8—21no—
61C2×C4⋊C8—21no—
62C2×C4⋊C8D412yes—
63#407—21no—
64#407—21no—
65#407C2×C412yes—
66#407C2×C412yes—
67C4×M16—21no—
68C4×M16—21no—
69C4×M16—21no—
70C4×M16—21no—
71#384—21no—
72#382—21no—
73#380—21no—
74#380C2×C412yes—
75C4×C4⋊C4—21no—
76C4×C4⋊C4—21no—
77#335—24no—
78#334—24no—
79C23×C4C22×C411yescharacteristic
80C23×C4#4111yescharacteristic
81C23×C4#4111yescharacteristic
82C2×M16—22no—
83C2×M16—21no—
84C2×M16—21no—
85C2×M16—22no—
86C2×M16—22no—
87C2×M16—41no—
88C2×M16—41no—
89C2×M16—81no—
90C2×M16—81no—
91C22×C8—22no—
92C22×C8—41no—
93C22×C8—41no—
94C22×C8—41no—
95C22×C8—82no—
96#117—81no—
97#117—81no—
98C2×C4⋊C4—22no—
99C2×C4⋊C4—41no—
100C2×C4⋊C4—41no—
101C2×C22⋊C4—22no—
102C2×C42—41no—
103C2×C42C2×D411yescharacteristic
104C2×C42C2×D411yescharacteristic
105C2×C42C2×D411yescharacteristic
106C2×C42C2×D411yescharacteristic
107C2×C42C2×Q811yescharacteristic
108C2×C42C2×Q811yescharacteristic
109C2×C42#4111yescharacteristic
110C2×C42#4111yescharacteristic
111C2×C42#4111yescharacteristic
112C2×C42#4111yescharacteristic
113C2×C42#4111yescharacteristic
114C2×C42#4111yescharacteristic
115C4⋊C8—21no—
116C4⋊C8—22no—
117C4⋊C8—21no—
118C4⋊C8—22no—
119C4⋊C8—22no—
120C4⋊C8—22no—
121C4⋊C8—22no—
122C4⋊C8—22no—
123C4⋊C8—22no—
124C4⋊C8—21no—
125C4⋊C8—21no—
126C4⋊C8—41no—
127C4⋊C8—41no—
128C4⋊C8—41no—
129C4⋊C8—41no—
130C4⋊C8—41no—
131C4⋊C8—41no—
132C4⋊C8—41no—
133C22⋊C8—22no—
134C22⋊C8—22no—
135C22⋊C8—22no—
136C22⋊C8—22no—
137C22⋊C8—41no—
138C22⋊C8—41no—
139C22⋊C8—41no—
140C22⋊C8C4⋊C414yes—
141#97—22no—
142#97—41no—
143#97—41no—
144#97—41no—
145C4×C8—22no—
146C4×C8—22no—
147C4×C8—41no—
148C4×C8—41no—
149#95—22no—
150#95—41no—
151C24#11711yescharacteristic
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—41no—
157C22×C4—41no—
158C22×C4—42no—
159C22×C4—81no—
160C22×C4C2×C4⋊C411yescharacteristic
161C22×C4#11711yescharacteristic
162C22×C4C4×D411yescharacteristic
163C22×C4C4×D411yescharacteristic
164C22×C4C4×D411yescharacteristic
165C22×C4C4×Q811yescharacteristic
166C22×C4#12111yescharacteristic
167C22×C4C22⋊Q811yescharacteristic
168C22×C4#12311yescharacteristic
169C22×C4#12311yescharacteristic
170C22×C4#12411yescharacteristic
171C22×C4#12411yescharacteristic
172C22×C4#12411yescharacteristic
173C22×C4#12511yescharacteristic
174C22×C4#12511yescharacteristic
175C22×C4#12511yescharacteristic
176C22×C4#12611yescharacteristic
177C22×C4#12611yescharacteristic
178M16—41no—
179M16—41no—
180M16—41no—
181M16—41no—
182M16—82no—
183M16—81no—
184M16—81no—
185M16—82no—
186M16—82no—
187M16—82no—
188C2×C8—24no—
189C2×C8—42no—
190C2×C8—42no—
191C2×C8—41no—
192C2×C8—41no—
193C2×C8—42no—
194C2×C8—42no—
195C2×C8—82no—
196C2×C8—82no—
197C2×C8—81no—
198C2×C8—81no—
199C2×C8—82no—
200C4⋊C4—81no—
201C4⋊C4—81no—
202C4⋊C4—82no—
203C4⋊C4—81no—
204C4⋊C4—81no—
205C22⋊C4—82no—
206C42—82no—
207C42#12011yescharacteristic
208C42#12111yescharacteristic
209C42#12111yescharacteristic
210C42C22⋊Q811yescharacteristic
211C42C22⋊Q811yescharacteristic
212C42C22⋊Q811yescharacteristic
213C42C22⋊Q811yescharacteristic
214C42#12311yescharacteristic
215C42#12311yescharacteristic
216C42#12311yescharacteristic
217C42#12411yescharacteristic
218C42#12511yescharacteristic
219C42#12511yescharacteristic
220C42#12611yescharacteristic
221C42#12611yescharacteristic
222C42C4⋊Q811yescharacteristic
223C23—21no—
224C23—21no—
225C23—41no—
226C23—41no—
227C23#38211yescharacteristic
228C23#38711yescharacteristic
229C23#38811yescharacteristic
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—82no—
256C2×C4—82no—
257C2×C4—82no—
258C2×C4#38511yescharacteristic
259C2×C4#38711yescharacteristic
260C2×C4#38811yescharacteristic
261C2×C4#38911yescharacteristic
262C2×C4#39311yescharacteristic
263C2×C4#39411yescharacteristic
264C2×C4#39711yescharacteristic
265C2×C4#39811yescharacteristic
266C2×C4#39811yescharacteristic
267C2×C4#40011yescharacteristic
268C2×C4#40011yescharacteristic
269C2×C4#40011yescharacteristic
270C2×C4#47111yescharacteristic
271C2×C4#47111yescharacteristic
272C2×C4#47211yescharacteristic
273C2×C4#47311yescharacteristic
274C8—44no—
275C8—82no—
276C8—82no—
277C8—82no—
278C8—81no—
279C8—81no—
280C8—82no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—42no—
290C22—42no—
291C22#144211yescharacteristic
292C22#193011yescharacteristic
293C22#193111yescharacteristic
294C4—21no—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—21no—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—162no—
304C4#205111yescharacteristic
305C4#205211yescharacteristic
306C4#208111yescharacteristic
307C4#208211yescharacteristic
308C4#208911yescharacteristic
309C4#209011yescharacteristic
310C2—21no—
311C2—21no—
312C2—41no—
313C2—41no—
314C2#1128011yescharacteristic
315C2#1128311yescharacteristic
316C2#1129011yescharacteristic
subgroupG/H
center, socleC22#1442
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#117
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
#178202
#81192
#81092
#80822
#80452
#79612
#79352