Finite Group Databasebeta

← #102021

Subgroups — #102021

Order 512.

408 conjugacy classes of subgroups.

The subgroup lattice has 325 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#487C211yesmaximal, characteristic
2#9865C211yesmaximal, characteristic
3#9864C211yesmaximal, characteristic
4C4×#334C211yesmaximal, characteristic
5#8261C211yesmaximal, characteristic
6#7571C211yesmaximal, characteristic
7#7570C211yesmaximal, characteristic
8C2×#487C411yescharacteristic
9C4×C4⋊Q8C2211yescharacteristic
10C4×C4⋊Q8C2211yescharacteristic
11#1990C411yescharacteristic
12#1956C411yescharacteristic
13#1933—21no—
14#1933—21no—
15#1834C411yescharacteristic
16C4×C4⋊C8C2211yescharacteristic
17C4×C4⋊C8C2211yescharacteristic
18C4×C4⋊C8C2211yescharacteristic
19C4×C4⋊C8C2211yescharacteristic
20C4×#103—21no—
21C4×#103—21no—
22C42×C8C2211yescharacteristic
23C2×#334—21no—
24C2×#322—21no—
25#1279—22no—
26#1279—22no—
27#1277—21no—
28#1273—21no—
29#1272—22no—
30#1271—22no—
31C2×C4⋊Q8C2×C411yescharacteristic
32C2×C4⋊Q8C2×C411yescharacteristic
33C2×C4×Q8—21no—
34C2×C4×Q8—21no—
35#487—22no—
36#487—22no—
37C2×C4⋊C8—21no—
38C2×C4⋊C8—21no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8D412yes—
41C2×#103—21no—
42C2×#103—21no—
43C2×#103—21no—
44C2×#103—21no—
45C2×C4×C8—21no—
46C2×C4×C8—21no—
47C2×C4×C8—21no—
48C2×C4×C8—21no—
49C2×C4×C8C2×C411yescharacteristic
50C2×C4×C8C2×C411yescharacteristic
51C2×C4×C8D411yescharacteristic
52C2×C4×C8D411yescharacteristic
53C2×C4×C8D411yescharacteristic
54C2×C4×C8D411yescharacteristic
55#391—21no—
56#391—21no—
57#389—21no—
58#389—21no—
59#389—21no—
60#389—21no—
61#384C2×C411yescharacteristic
62#384C2×C411yescharacteristic
63C4×C4⋊C4—21no—
64C4×C4⋊C4—21no—
65C4×C4⋊C4—21no—
66C4×C4⋊C4—21no—
67C43C2311yescharacteristic
68#340—21no—
69#340—21no—
70#340—21no—
71#340—21no—
72#336—21no—
73#336—21no—
74#336—21no—
75#336D412yes—
76#334—24no—
77#322—42no—
78C22×Q8—21no—
79C22×Q8—21no—
80C22×C8—22no—
81C22×C8—22no—
82C22×C8—41no—
83C22×C8—41no—
84C22×C8C22⋊C411yescharacteristic
85C22×C8C22⋊C411yescharacteristic
86C22×C8C22⋊C411yescharacteristic
87C22×C8C22⋊C411yescharacteristic
88C4⋊Q8—21no—
89C4⋊Q8—21no—
90C4⋊Q8—21no—
91C4⋊Q8—21no—
92C4⋊Q8—21no—
93C4⋊Q8—21no—
94C4⋊Q8M1612yes—
95C4⋊Q8M1612yes—
96C4×Q8—41no—
97C4×Q8—41no—
98C4×Q8—41no—
99C4×Q8—41no—
100C4×Q8—82no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4—41no—
113C2×C42—41no—
114C2×C42—41no—
115C2×C42C22×C411yescharacteristic
116C2×C42C2×D411yescharacteristic
117C2×C42C2×D411yescharacteristic
118C2×C42C2×D411yescharacteristic
119C2×C42C2×D411yescharacteristic
120C2×C42#4111yescharacteristic
121C2×C42#4111yescharacteristic
122C4⋊C8—24no—
123C4⋊C8—22no—
124C4⋊C8—22no—
125C4⋊C8—22no—
126C4⋊C8—22no—
127C4⋊C8—41no—
128C4⋊C8—41no—
129#103—24no—
130#103—24no—
131#103—42no—
132#103—42no—
133C4×C8—22no—
134C4×C8—21no—
135C4×C8—21no—
136C4×C8—21no—
137C4×C8—21no—
138C4×C8—21no—
139C4×C8—21no—
140C4×C8—21no—
141C4×C8—21no—
142C4×C8—41no—
143C4×C8—41no—
144C4×C8—41no—
145C4×C8—41no—
146C4×C8—41no—
147C4×C8—42no—
148C4×C8—42no—
149#95—41no—
150#95—41no—
151#95—41no—
152#95—41no—
153C2×Q8—22no—
154C2×Q8—22no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×Q8—41no—
158C2×Q8—41no—
159C2×Q8—41no—
160C2×Q8—41no—
161C2×Q8—81no—
162C2×Q8—81no—
163C22×C4—41no—
164C22×C4—41no—
165C22×C4—41no—
166C22×C4—41no—
167C22×C4C2×C22⋊C411yescharacteristic
168C22×C4C4×D411yescharacteristic
169C22×C4C4×D411yescharacteristic
170C22×C4#12111yescharacteristic
171C22×C4#12111yescharacteristic
172C22×C4#12411yescharacteristic
173C22×C4#12711yescharacteristic
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—24no—
177C2×C8—21no—
178C2×C8—21no—
179C2×C8—21no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—21no—
183C2×C8—21no—
184C2×C8—21no—
185C2×C8—21no—
186C2×C8—42no—
187C2×C8—42no—
188C2×C8—42no—
189C2×C8—42no—
190C2×C8—42no—
191C2×C8—42no—
192C2×C8—42no—
193C2×C8—81no—
194C2×C8—81no—
195C2×C8—81no—
196C2×C8—81no—
197C2×C8#10412yes—
198C4⋊C4—22no—
199C4⋊C4—22no—
200C4⋊C4—22no—
201C4⋊C4—22no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—42no—
211C4⋊C4—42no—
212C4⋊C4—81no—
213C4⋊C4—81no—
214C4⋊C4—82no—
215C4⋊C4—81no—
216C4⋊C4—81no—
217C42—21no—
218C42—21no—
219C42—22no—
220C42—22no—
221C42—41no—
222C42—81no—
223C42—81no—
224C42—82no—
225C42C2×M1611yescharacteristic
226C42C2×M1611yescharacteristic
227C42#13111yescharacteristic
228C42#13111yescharacteristic
229C42#13511yescharacteristic
230C42#13511yescharacteristic
231C42AGL(1,ℤ/8)11yescharacteristic
232C42#13711yescharacteristic
233C42#13712yes—
234C42#13712yes—
235C23#39011yescharacteristic
236Q8—42no—
237Q8—42no—
238Q8—82no—
239Q8—82no—
240Q8—81no—
241Q8—81no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—81no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—81no—
257C2×C4—81no—
258C2×C4—81no—
259C2×C4—81no—
260C2×C4—81no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4#40711yescharacteristic
264C2×C4#40811yescharacteristic
265C2×C4#41611yescharacteristic
266C2×C4#41711yescharacteristic
267C2×C4C2×#10411yescharacteristic
268C2×C4#42111yescharacteristic
269C2×C4#43511yescharacteristic
270C2×C4#43511yescharacteristic
271C2×C4#43511yescharacteristic
272C2×C4#43511yescharacteristic
273C2×C4#44112yes—
274C2×C4#44312yes—
275C2×C4#46311yescharacteristic
276C2×C4#46311yescharacteristic
277C2×C4#46411yescharacteristic
278C2×C4#46411yescharacteristic
279C2×C4#47012yes—
280C2×C4#47112yes—
281C2×C4#49711yescharacteristic
282C2×C4#49711yescharacteristic
283C8—22no—
284C8—44no—
285C8—41no—
286C8—41no—
287C8—41no—
288C8—82no—
289C8—82no—
290C8—82no—
291C22#195511yescharacteristic
292C22#197111yescharacteristic
293C22#197411yescharacteristic
294C22#197611yescharacteristic
295C22#197711yescharacteristic
296C22#198011yescharacteristic
297C22#198311yescharacteristic
298C4—21no—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—41no—
305C4—82no—
306C4—82no—
307C4—161no—
308C4—161no—
309C4#148811yescharacteristic
310C4#148911yescharacteristic
311C4#149411yescharacteristic
312C4#149511yescharacteristic
313C4#158712yes—
314C4#158712yes—
315C4#170312yes—
316C4#170412yes—
317C2#966411yescharacteristic
318C2#967211yescharacteristic
319C2#967611yescharacteristic
320C2#972011yescharacteristic
321C2#972311yescharacteristic
322C2#974511yescharacteristic
323C2#975111yescharacteristic
subgroupG/H
centerC22×C4#121
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
socle, prime radicalC23#390
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C4×#4872
#98652
#98642
C4×#3342
#82612
#75712
#75702