Finite Group Databasebeta

← #120043

Subgroups — #120043

Order 512.

606 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21955C211yesmaximal, characteristic
2#13911C211yesmaximal, characteristic
3#8040C212yesmaximal
4C2×#1285C212yesmaximal
5#7912C211yesmaximal, characteristic
6C2×#432C2212yes—
7C2×#432C2212yes—
8C2×#384C2211yescharacteristic
9C2×#382C412yes—
10C2×C4×C4⋊C4C2211yescharacteristic
11C2×C4×C4⋊C4C2211yescharacteristic
12#1940—24no—
13#1797—21no—
14#1797—21no—
15#1442—21no—
16#1442—21no—
17C4⋊#95—21no—
18C4⋊#95—21no—
19C4⋊#95C412yes—
20#1296—24no—
21#1285—24no—
22#1280—21no—
23#1280—21no—
24C22×C4⋊C4—21no—
25C22×C4⋊C4—21no—
26C22×C4⋊C4—21no—
27C22×C4⋊C4C2×C411yescharacteristic
28C22×C4⋊C4C2×C411yescharacteristic
29C22×C4⋊C4C2×C412yes—
30C22×C42C2×C412yes—
31C22×C42D411yescharacteristic
32C22×C42D411yescharacteristic
33C22×C42C2311yescharacteristic
34#432—22no—
35#432—22no—
36#432—22no—
37#432—22no—
38#432—22no—
39#432—22no—
40#432—22no—
41#432Q814yes—
42C2×C4⋊C8—22no—
43C2×C4⋊C8—22no—
44C2×C4⋊C8—22no—
45C2×C4⋊C8D414yes—
46C2×C22⋊C8—22no—
47C2×C22⋊C8—22no—
48C2×#97—22no—
49C2×#97—22no—
50#384—22no—
51#384—22no—
52#382—44no—
53C4×C4⋊C4—22no—
54C4×C4⋊C4—21no—
55C4×C4⋊C4—22no—
56C4×C4⋊C4—21no—
57C4×C4⋊C4D412yes—
58C4×C4⋊C4Q812yes—
59C2×#95—21no—
60C2×#95—22no—
61C2×#95—22no—
62C2×#95—22no—
63C2×#95—22no—
64C2×#95D411yescharacteristic
65C2×#95D411yescharacteristic
66#336—22no—
67#336—22no—
68C23×C4—22no—
69C23×C4—22no—
70C23×C4C22⋊C411yescharacteristic
71C23×C4C22⋊C411yescharacteristic
72C23×C4C22⋊C411yescharacteristic
73C23×C4C22⋊C411yescharacteristic
74C23×C4C22×C411yescharacteristic
75C23×C4C2×D411yescharacteristic
76C23×C4C2×D411yescharacteristic
77C22×C8—24no—
78C22×C8—42no—
79C2×C4⋊C4—22no—
80C2×C4⋊C4—22no—
81C2×C4⋊C4—22no—
82C2×C4⋊C4—22no—
83C2×C4⋊C4—22no—
84C2×C4⋊C4—22no—
85C2×C4⋊C4—24no—
86C2×C4⋊C4—41no—
87C2×C4⋊C4—41no—
88C2×C4⋊C4—42no—
89C2×C4⋊C4—42no—
90C2×C4⋊C4—42no—
91C2×C4⋊C4—42no—
92C2×C4⋊C4—42no—
93C2×C4⋊C4—42no—
94C2×C4⋊C4—41no—
95C2×C4⋊C4—42no—
96C2×C4⋊C4—41no—
97C2×C4⋊C4—82no—
98C2×C42—22no—
99C2×C42—21no—
100C2×C42—21no—
101C2×C42—21no—
102C2×C42—21no—
103C2×C42—42no—
104C2×C42—42no—
105C2×C42—42no—
106C2×C42—42no—
107C2×C42C4⋊C414yes—
108C2×C42C2×D411yescharacteristic
109C2×C42C2×D412yes—
110C2×C42C2×Q812yes—
111C2×C42C2×Q811yescharacteristic
112C2×C42#4112yes—
113C2×C42#4111yescharacteristic
114C2×C42#4112yes—
115C2×C42#4111yescharacteristic
116C4⋊C8—24no—
117C4⋊C8—24no—
118C4⋊C8—24no—
119C4⋊C8—42no—
120C4⋊C8—82no—
121C4⋊C8—82no—
122C22⋊C8—24no—
123C22⋊C8—42no—
124C22⋊C8—42no—
125C22⋊C8—42no—
126#97—24no—
127#97—42no—
128#97—42no—
129#97—42no—
130#95—22no—
131#95—22no—
132#95—22no—
133#95—22no—
134#95—44no—
135#95—44no—
136#95—82no—
137#95—82no—
138C24C2×C22⋊C411yescharacteristic
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—22no—
144C22×C4—22no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—24no—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—41no—
157C22×C4—41no—
158C22×C4—41no—
159C22×C4—41no—
160C22×C4—41no—
161C22×C4—41no—
162C22×C4—41no—
163C22×C4—41no—
164C22×C4—41no—
165C22×C4—41no—
166C22×C4—42no—
167C22×C4—42no—
168C22×C4—42no—
169C22×C4—42no—
170C22×C4—42no—
171C22×C4—42no—
172C22×C4—42no—
173C22×C4—42no—
174C22×C4—42no—
175C22×C4—42no—
176C22×C4—42no—
177C22×C4—42no—
178C22×C4—42no—
179C22×C4#10012yes—
180C22×C4#10112yes—
181C22×C4C2×C4⋊C411yescharacteristic
182C22×C4#11711yescharacteristic
183C22×C4C4×D412yes—
184C22×C4C4×Q812yes—
185C22×C4#12011yescharacteristic
186C22×C4#12111yescharacteristic
187C22×C4#12112yes—
188C22×C4#12111yescharacteristic
189C22×C4C22⋊Q811yescharacteristic
190C22×C4C22⋊Q812yes—
191C22×C4C22⋊Q811yescharacteristic
192C22×C4#12311yescharacteristic
193C22×C4#12411yescharacteristic
194C22×C4C4⋊Q811yescharacteristic
195C2×C8—44no—
196C2×C8—44no—
197C2×C8—44no—
198C2×C8—44no—
199C2×C8—82no—
200C2×C8—82no—
201C4⋊C4—44no—
202C4⋊C4—44no—
203C4⋊C4—44no—
204C4⋊C4—44no—
205C4⋊C4—84no—
206C4⋊C4—82no—
207C4⋊C4—84no—
208C4⋊C4—82no—
209C42—44no—
210C42—44no—
211C42—42no—
212C42—42no—
213C42—81no—
214C42—81no—
215C42#12112yes—
216C42C22⋊Q812yes—
217C42C22⋊Q812yes—
218C42#12312yes—
219C42#12512yes—
220C42#12512yes—
221C42#12612yes—
222C42C4⋊Q812yes—
223C23—21no—
224C23—21no—
225C23—21no—
226C23—21no—
227C23#38011yescharacteristic
228C23#38611yescharacteristic
229C23#39111yescharacteristic
230C23C2×#10011yescharacteristic
231C23C2×#10111yescharacteristic
232C23#41311yescharacteristic
233C23#41311yescharacteristic
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—44no—
262C2×C4—44no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—44no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—82no—
275C2×C4—82no—
276C2×C4—82no—
277C2×C4—82no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—82no—
281C2×C4—82no—
282C2×C4—82no—
283C2×C4—82no—
284C2×C4—82no—
285C2×C4—82no—
286C2×C4—82no—
287C2×C4#38712yes—
288C2×C4#38912yes—
289C2×C4#39411yescharacteristic
290C2×C4#39511yescharacteristic
291C2×C4#39612yes—
292C2×C4#39811yescharacteristic
293C2×C4#39812yes—
294C2×C4#40011yescharacteristic
295C2×C4#45412yes—
296C2×C4#45512yes—
297C8—84no—
298C8—84no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22#144111yescharacteristic
312C22#180011yescharacteristic
313C22#180111yescharacteristic
314C22#188511yescharacteristic
315C22#188811yescharacteristic
316C22#190011yescharacteristic
317C22#190111yescharacteristic
318C22#190911yescharacteristic
319C22#191011yescharacteristic
320C22#199711yescharacteristic
321C22#199811yescharacteristic
322C4—22no—
323C4—22no—
324C4—21no—
325C4—21no—
326C4—22no—
327C4—22no—
328C4—42no—
329C4—42no—
330C4—84no—
331C4—81no—
332C4—81no—
333C4—162no—
334C4#204012yes—
335C4#206112yes—
336C2—21no—
337C2—21no—
338C2—21no—
339C2—21no—
340C2#945111yescharacteristic
341C2#945311yescharacteristic
342C2#945611yescharacteristic
343C2#945811yescharacteristic
344C2#1120411yescharacteristic
345C2#1121111yescharacteristic
346C2#1122511yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ 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
#219552
#139112
#80402
C2×#12852
#79122