Finite Group Databasebeta

← #121948

Subgroups — #121948

Order 512.

464 conjugacy classes of subgroups.

The subgroup lattice has 327 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20799C211yesmaximal, characteristic
2#8109C211yesmaximal, characteristic
3#8109C211yesmaximal, characteristic
4#7953C211yesmaximal, characteristic
5#7953C211yesmaximal, characteristic
6#7919C211yesmaximal, characteristic
7#7861C211yesmaximal, characteristic
8#2920C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11#2920C2211yescharacteristic
12C2×#427C412yes—
13C2×#427C412yes—
14C22×#97C2211yescharacteristic
15#2285C2211yescharacteristic
16#2285C2211yescharacteristic
17#1847—21no—
18#1847—21no—
19#1847—22no—
20#1305—22no—
21#1305—22no—
22#1285—22no—
23#1285—22no—
24#1281—21no—
25#1281—21no—
26#1275—22no—
27C23×C8C2×C412yes—
28C2×#117C2×C411yescharacteristic
29C2×#117C2×C412yes—
30C2×#117C2×C411yescharacteristic
31C22×C42C2311yescharacteristic
32#432—21no—
33#432—21no—
34#432—21no—
35#432—21no—
36#432—21no—
37#432—21no—
38#432—21no—
39#432D412yes—
40#431—21no—
41#431—21no—
42#431—21no—
43#431—21no—
44#431—21no—
45#431—21no—
46#431—21no—
47#431Q812yes—
48#427—44no—
49#427—44no—
50C2×#107—22no—
51C2×#107—22no—
52C2×#106—22no—
53C2×#106—22no—
54#423—21no—
55#423—21no—
56#423—21no—
57#423—21no—
58#407—21no—
59#407—21no—
60#407—21no—
61#407D412yes—
62C4×M16—21no—
63C4×M16—21no—
64C4×M16—21no—
65C4×M16Q812yes—
66C2×#97—21no—
67C2×#97—21no—
68C2×#97—21no—
69C2×#97—21no—
70C2×#97D411yescharacteristic
71C2×#97D411yescharacteristic
72C2×#97D412yes—
73#384—21no—
74#384—21no—
75#382—21no—
76#382—21no—
77#380—21no—
78#380—21no—
79#380—21no—
80#380—21no—
81C4×C4⋊C4—21no—
82C4×C4⋊C4—21no—
83C4×C4⋊C4—21no—
84C4×C4⋊C4—21no—
85C23×C4C22×C411yescharacteristic
86C23×C4C2×D411yescharacteristic
87C23×C4#4111yescharacteristic
88C2×M16—22no—
89C2×M16—22no—
90C2×M16—41no—
91C2×M16—41no—
92C22×C8—22no—
93C22×C8—22no—
94C22×C8—24no—
95C22×C8—24no—
96C22×C8C22⋊C412yes—
97C22×C8C22⋊C412yes—
98#117—42no—
99#117—42no—
100#117—42no—
101#117—42no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—22no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—41no—
106C2×C4⋊C4—41no—
107C2×C4⋊C4—41no—
108C2×C4⋊C4—41no—
109C2×C22⋊C4—21no—
110C2×C22⋊C4—21no—
111C2×C22⋊C4—22no—
112C2×C42—21no—
113C2×C42—21no—
114C2×C42—22no—
115C2×C42C2×D411yescharacteristic
116C2×C42C2×D411yescharacteristic
117C2×C42C2×D411yescharacteristic
118C2×C42C2×Q811yescharacteristic
119C2×C42C2×Q811yescharacteristic
120C2×C42#4111yescharacteristic
121C2×C42#4111yescharacteristic
122C2×C42#4111yescharacteristic
123C2×C42#4111yescharacteristic
124C2×C42#4111yescharacteristic
125C2×C42#4111yescharacteristic
126C2×C42#4111yescharacteristic
127#107—44no—
128#107—44no—
129#106—44no—
130#106—44no—
131C4⋊C8—22no—
132C4⋊C8—22no—
133C4⋊C8—41no—
134C4⋊C8—41no—
135C4⋊C8—41no—
136C4⋊C8—41no—
137C4⋊C8—41no—
138C4⋊C8—41no—
139C22⋊C8—22no—
140C22⋊C8—22no—
141C22⋊C8—22no—
142C22⋊C8—22no—
143C22⋊C8—41no—
144C22⋊C8—41no—
145C22⋊C8—41no—
146C22⋊C8—41no—
147#97—22no—
148#97—21no—
149#97—21no—
150#97—21no—
151#97—21no—
152#97—22no—
153#97—22no—
154#97—22no—
155#97—41no—
156#97—41no—
157C4×C8—22no—
158C4×C8—22no—
159C4×C8—41no—
160C4×C8—41no—
161#95—41no—
162#95—41no—
163#95—41no—
164#95—41no—
165C24C4×D411yescharacteristic
166C22×C4—22no—
167C22×C4—22no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4—42no—
171C22×C4—81no—
172C22×C4—81no—
173C22×C4C2×C22⋊C411yescharacteristic
174C22×C4#11711yescharacteristic
175C22×C4#11711yescharacteristic
176C22×C4C4×D411yescharacteristic
177C22×C4C4×Q811yescharacteristic
178C22×C4C4×Q811yescharacteristic
179C22×C4#12111yescharacteristic
180C22×C4#12111yescharacteristic
181C22×C4C22⋊Q811yescharacteristic
182C22×C4C22⋊Q811yescharacteristic
183C22×C4#12311yescharacteristic
184C22×C4#12311yescharacteristic
185C22×C4#12411yescharacteristic
186C22×C4#12511yescharacteristic
187C22×C4#12511yescharacteristic
188C22×C4#12611yescharacteristic
189C22×C4#12611yescharacteristic
190C22×C4#12711yescharacteristic
191M16—82no—
192M16—82no—
193M16—82no—
194M16—82no—
195C2×C8—28no—
196C2×C8—28no—
197C2×C8—22no—
198C2×C8—22no—
199C2×C8—22no—
200C2×C8—22no—
201C2×C8—42no—
202C2×C8—42no—
203C2×C8—42no—
204C2×C8—42no—
205C2×C8#10014yes—
206C2×C8#10114yes—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C4⋊C4—42no—
210C4⋊C4—42no—
211C4⋊C4—82no—
212C4⋊C4—82no—
213C4⋊C4—82no—
214C4⋊C4—82no—
215C22⋊C4—81no—
216C22⋊C4—82no—
217C22⋊C4—81no—
218C42—81no—
219C42—82no—
220C42—81no—
221C42C22⋊Q811yescharacteristic
222C42C22⋊Q811yescharacteristic
223C42C22⋊Q811yescharacteristic
224C42C22⋊Q811yescharacteristic
225C42#12311yescharacteristic
226C42#12311yescharacteristic
227C42#12311yescharacteristic
228C42#12311yescharacteristic
229C42#12311yescharacteristic
230C42#12311yescharacteristic
231C42#12411yescharacteristic
232C42#12511yescharacteristic
233C42#12511yescharacteristic
234C42#12611yescharacteristic
235C42#12611yescharacteristic
236C42C4⋊Q811yescharacteristic
237C23—21no—
238C23—21no—
239C23—41no—
240C23—41no—
241C23#38711yescharacteristic
242C23#38711yescharacteristic
243C23#39011yescharacteristic
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—82no—
263C2×C4—81no—
264C2×C4—81no—
265C2×C4—82no—
266C2×C4—81no—
267C2×C4—81no—
268C2×C4—81no—
269C2×C4—82no—
270C2×C4—81no—
271C2×C4#38111yescharacteristic
272C2×C4#38711yescharacteristic
273C2×C4#38711yescharacteristic
274C2×C4#39111yescharacteristic
275C2×C4#39711yescharacteristic
276C2×C4#39711yescharacteristic
277C2×C4#39811yescharacteristic
278C2×C4#39811yescharacteristic
279C2×C4#39911yescharacteristic
280C2×C4#39911yescharacteristic
281C2×C4#40011yescharacteristic
282C2×C4#40011yescharacteristic
283C2×C4C2×#10012yes—
284C2×C4C2×#10112yes—
285C8—24no—
286C8—24no—
287C8—82no—
288C8—82no—
289C8—82no—
290C8—82no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22—42no—
300C22—42no—
301C22#144511yescharacteristic
302C22#196511yescharacteristic
303C22#196611yescharacteristic
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—162no—
315C4—161no—
316C4—161no—
317C4#182112yes—
318C4#199712yes—
319C2—21no—
320C2—21no—
321C2—41no—
322C2—41no—
323C2#1135411yescharacteristic
324C2#1136011yescharacteristic
325C2#1136111yescharacteristic
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
#207992
#81092
#79532
#79192
#78612