Finite Group Databasebeta

← #122121

Subgroups — #122121

Order 512.

585 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35345C211yesmaximal, characteristic
2#8110C211yesmaximal, characteristic
3#7951C211yesmaximal, characteristic
4#7948C211yesmaximal, characteristic
5#7926C211yesmaximal, characteristic
6#7870C211yesmaximal, characteristic
7#7857C211yesmaximal, characteristic
8#2920C2211yescharacteristic
9#2920C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×#431C2211yescharacteristic
12#2864—21no—
13#2859—21no—
14#2629—22no—
15#2608—22no—
16#2608C414yes—
17#2606—22no—
18#2606—22no—
19#2330—22no—
20#2283C2211yescharacteristic
21#2283C2211yescharacteristic
22C4×#117C2211yescharacteristic
23#1305—22no—
24#1285—22no—
25#1285—22no—
26#1282—22no—
27#1276—21no—
28#1276—21no—
29#1274—22no—
30C2×#125—22no—
31C2×#117—21no—
32C22×C42C2311yescharacteristic
33#432—21no—
34#432—21no—
35#432—21no—
36#432—21no—
37#432—21no—
38#432—21no—
39#432—21no—
40#432—21no—
41#431—21no—
42#431—21no—
43#431—21no—
44#431—21no—
45#431—21no—
46#431—21no—
47#431Q812yes—
48#431Q812yes—
49#423—21no—
50#423Q812yes—
51C2×C4⋊C8—21no—
52C2×C4⋊C8—21no—
53#407—21no—
54#407—21no—
55C2×C22⋊C8—21no—
56C2×C22⋊C8—21no—
57C4×M16—21no—
58C4×M16—21no—
59C2×#97Q812yes—
60C2×C4×C8—21no—
61#398—24no—
62#398—24no—
63#396—24no—
64#396—24no—
65#389—24no—
66#389—22no—
67#389—22no—
68#389—24no—
69#389—24no—
70#389—24no—
71#387—24no—
72#387—24no—
73#387—24no—
74#387—24no—
75#384—22no—
76#383—21no—
77#383—21no—
78#382—21no—
79#382—21no—
80#381—21no—
81#381C2×C412yes—
82#380—21no—
83#380D412yes—
84C4×C4⋊C4—21no—
85C4×C4⋊C4—21no—
86C4×C4⋊C4D412yes—
87C4×C4⋊C4D412yes—
88C4×C22⋊C4—21no—
89C4×C22⋊C4C2×C412yes—
90C4×C22⋊C4C2×C412yes—
91C4×C22⋊C4D412yes—
92#376—21no—
93#376—21no—
94#376D412yes—
95C43D411yescharacteristic
96C43D411yescharacteristic
97C23×C4C22×C411yescharacteristic
98C23×C4C2×D411yescharacteristic
99C23×C4C2×D411yescharacteristic
100C2×M16—22no—
101C2×M16—41no—
102C22×C8—22no—
103C22×C8—41no—
104#125—48no—
105#117—44no—
106C2×C4⋊C4—24no—
107C2×C4⋊C4—24no—
108C2×C4⋊C4—22no—
109C2×C4⋊C4—22no—
110C2×C4⋊C4—22no—
111C2×C4⋊C4—24no—
112C2×C4⋊C4—24no—
113C2×C4⋊C4—24no—
114C2×C4⋊C4—24no—
115C2×C22⋊C4—22no—
116C2×C22⋊C4—22no—
117C2×C22⋊C4C22⋊C414yes—
118C2×C42—21no—
119C2×C42—21no—
120C2×C42—21no—
121C2×C42—21no—
122C2×C42—22no—
123C2×C42C22⋊C412yes—
124C2×C42C22⋊C412yes—
125C2×C42C22⋊C414yes—
126C2×C42C2×D411yescharacteristic
127C2×C42C2×D411yescharacteristic
128C2×C42C2×D411yescharacteristic
129C2×C42C2×D411yescharacteristic
130C2×C42C2×Q811yescharacteristic
131C2×C42C2×Q811yescharacteristic
132C2×C42C2×Q811yescharacteristic
133C2×C42C2×Q811yescharacteristic
134C2×C42#4111yescharacteristic
135C2×C42#4111yescharacteristic
136C2×C42#4111yescharacteristic
137C2×C42#4111yescharacteristic
138C4⋊C8—22no—
139C4⋊C8—22no—
140C4⋊C8—22no—
141C4⋊C8—22no—
142C4⋊C8—41no—
143C4⋊C8—41no—
144C4⋊C8—41no—
145C4⋊C8—41no—
146C22⋊C8—22no—
147C22⋊C8—22no—
148C22⋊C8—41no—
149C22⋊C8—41no—
150C22⋊C8—41no—
151C22⋊C8—41no—
152C22⋊C8—41no—
153C22⋊C8—41no—
154#97—22no—
155#97—22no—
156#97—41no—
157#97—41no—
158C4×C8—22no—
159C4×C8—22no—
160C4×C8—41no—
161C4×C8—41no—
162#95—24no—
163#95—24no—
164#95—22no—
165#95—22no—
166#95—22no—
167#95—22no—
168#95—22no—
169#95—22no—
170#95—22no—
171#95—22no—
172#95—22no—
173#95—22no—
174C24C2×C22⋊C411yescharacteristic
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—24no—
178C22×C4—24no—
179C22×C4—42no—
180C22×C4—42no—
181C22×C4—81no—
182C22×C4C2×C22⋊C411yescharacteristic
183C22×C4C2×C22⋊C411yescharacteristic
184C22×C4C4×Q811yescharacteristic
185C22×C4C4×Q811yescharacteristic
186C22×C4C4×Q811yescharacteristic
187C22×C4C4×Q811yescharacteristic
188C22×C4#12011yescharacteristic
189C22×C4#12011yescharacteristic
190C22×C4#12011yescharacteristic
191C22×C4#12011yescharacteristic
192C22×C4C22⋊Q811yescharacteristic
193C22×C4C22⋊Q811yescharacteristic
194C22×C4C22⋊Q811yescharacteristic
195C22×C4C22⋊Q811yescharacteristic
196C22×C4#12411yescharacteristic
197C22×C4#12411yescharacteristic
198C22×C4C4⋊Q811yescharacteristic
199C22×C4C4⋊Q811yescharacteristic
200M16—82no—
201M16—82no—
202C2×C8—42no—
203C2×C8—42no—
204C2×C8—42no—
205C2×C8—42no—
206C2×C8—82no—
207C2×C8—82no—
208C4⋊C4—44no—
209C4⋊C4—44no—
210C4⋊C4—44no—
211C4⋊C4—48no—
212C4⋊C4—48no—
213C4⋊C4—84no—
214C4⋊C4—84no—
215C4⋊C4—84no—
216C4⋊C4—84no—
217C22⋊C4—44no—
218C22⋊C4—44no—
219C22⋊C4—82no—
220C42—24no—
221C42—42no—
222C42—42no—
223C42—44no—
224C42—42no—
225C42—81no—
226C42—81no—
227C42—82no—
228C42C22⋊Q811yescharacteristic
229C42C22⋊Q811yescharacteristic
230C42C22⋊Q811yescharacteristic
231C42C22⋊Q811yescharacteristic
232C42C22⋊Q811yescharacteristic
233C42C22⋊Q811yescharacteristic
234C42C22⋊Q811yescharacteristic
235C42C22⋊Q811yescharacteristic
236C42#12411yescharacteristic
237C42#12411yescharacteristic
238C42#12411yescharacteristic
239C42#12411yescharacteristic
240C42C4⋊Q811yescharacteristic
241C42C4⋊Q811yescharacteristic
242C42C4⋊Q811yescharacteristic
243C42C4⋊Q811yescharacteristic
244C23—22no—
245C23—41no—
246C23—41no—
247C23#37911yescharacteristic
248C23#39111yescharacteristic
249C23#39111yescharacteristic
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—24no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—44no—
274C2×C4—44no—
275C2×C4—44no—
276C2×C4—44no—
277C2×C4—42no—
278C2×C4—44no—
279C2×C4—44no—
280C2×C4#39111yescharacteristic
281C2×C4#39111yescharacteristic
282C2×C4#39111yescharacteristic
283C2×C4#39111yescharacteristic
284C2×C4#39311yescharacteristic
285C2×C4#39311yescharacteristic
286C2×C4#39311yescharacteristic
287C2×C4#39311yescharacteristic
288C2×C4#39511yescharacteristic
289C2×C4#39511yescharacteristic
290C2×C4#39511yescharacteristic
291C2×C4#39511yescharacteristic
292C8—82no—
293C8—82no—
294C8—82no—
295C8—82no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—82no—
305C22#144611yescharacteristic
306C22#179112yes—
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—44no—
319C4—82no—
320C4—84no—
321C4—84no—
322C4#203112yes—
323C2—22no—
324C2—41no—
325C2—41no—
326C2#1138711yescharacteristic
327C2#1138911yescharacteristic
328C2#1139111yescharacteristic
subgroupG/H
center, socleC22#1446
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C2×C22⋊C4
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
#353452
#81102
#79512
#79482
#79262
#78702
#78572