Finite Group Databasebeta

← #102010

Subgroups — #102010

Order 512.

420 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#487C211yesmaximal, characteristic
2#9865C211yesmaximal, characteristic
3#9673C211yesmaximal, characteristic
4C4×#335C211yesmaximal, characteristic
5#8260C211yesmaximal, characteristic
6#7570C211yesmaximal, 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×#335—21no—
24C2×Q8⋊C8—22no—
25C2×#322—21no—
26#1279—22no—
27#1277—21no—
28#1273—21no—
29#1271—22no—
30#1271—22no—
31C2×C4⋊Q8C2×C411yescharacteristic
32C2×C4⋊Q8C2×C411yescharacteristic
33C2×C4×Q8—21no—
34C2×C4×Q8—21no—
35#487—22no—
36#487C814yescomplemented
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#335—24no—
77Q8⋊C8—44no—
78#322—42no—
79C22×Q8—21no—
80C22×Q8—21no—
81C22×C8—22no—
82C22×C8—22no—
83C22×C8—41no—
84C22×C8—41no—
85C22×C8C22⋊C411yescharacteristic
86C22×C8C22⋊C411yescharacteristic
87C22×C8C22⋊C411yescharacteristic
88C22×C8C22⋊C411yescharacteristic
89C4⋊Q8—21no—
90C4⋊Q8—21no—
91C4⋊Q8—21no—
92C4⋊Q8—21no—
93C4⋊Q8—21no—
94C4⋊Q8—21no—
95C4⋊Q8C2×C812yes—
96C4⋊Q8C2×C812yes—
97C4×Q8—41no—
98C4×Q8—41no—
99C4×Q8—41no—
100C4×Q8—42no—
101C4×Q8—41no—
102C4×Q8—42no—
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—21no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4—41no—
115C2×C42—41no—
116C2×C42—41no—
117C2×C42C22×C411yescharacteristic
118C2×C42C2×D411yescharacteristic
119C2×C42C2×D411yescharacteristic
120C2×C42C2×D411yescharacteristic
121C2×C42C2×D411yescharacteristic
122C2×C42#4111yescharacteristic
123C2×C42#4111yescharacteristic
124C4⋊C8—22no—
125C4⋊C8—22no—
126C4⋊C8—22no—
127C4⋊C8—22no—
128C4⋊C8—41no—
129C4⋊C8—41no—
130C4⋊C8—42no—
131#103—24no—
132#103—24no—
133#103—42no—
134#103—42no—
135C4×C8—22no—
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—
149C4×C8C2×C812yes—
150C4×C8M1612yes—
151#95—41no—
152#95—41no—
153#95—41no—
154#95—41no—
155C2×Q8—22no—
156C2×Q8—22no—
157C2×Q8—41no—
158C2×Q8—41no—
159C2×Q8—41no—
160C2×Q8—41no—
161C2×Q8—41no—
162C2×Q8—41no—
163C2×Q8—42no—
164C2×Q8—42no—
165C22×C4—41no—
166C22×C4—41no—
167C22×C4—41no—
168C22×C4—41no—
169C22×C4C2×C22⋊C411yescharacteristic
170C22×C4C4×D411yescharacteristic
171C22×C4C4×D411yescharacteristic
172C22×C4#12111yescharacteristic
173C22×C4#12111yescharacteristic
174C22×C4#12411yescharacteristic
175C22×C4#12711yescharacteristic
176C2×C8—21no—
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—42no—
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×C8C22⋊C812yes—
198C2×C8C22⋊C812yes—
199C2×C8#10412yes—
200C4⋊C4—22no—
201C4⋊C4—22no—
202C4⋊C4—22no—
203C4⋊C4—22no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—42no—
213C4⋊C4—42no—
214C4⋊C4—81no—
215C4⋊C4—81no—
216C4⋊C4—81no—
217C4⋊C4—81no—
218C4⋊C4—81no—
219C4⋊C4—81no—
220C42—21no—
221C42—21no—
222C42—22no—
223C42—22no—
224C42—41no—
225C42—81no—
226C42—81no—
227C42—82no—
228C42C22×C811yescharacteristic
229C42C2×M1611yescharacteristic
230C42#13111yescharacteristic
231C42#13111yescharacteristic
232C42#13511yescharacteristic
233C42#13511yescharacteristic
234C42AGL(1,ℤ/8)11yescharacteristic
235C42AGL(1,ℤ/8)12yes—
236C42#13711yescharacteristic
237C42#13712yes—
238C23#39011yescharacteristic
239Q8—44no—
240Q8—42no—
241Q8—42no—
242Q8—82no—
243Q8—81no—
244Q8—81no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—81no—
257C2×C4—81no—
258C2×C4—81no—
259C2×C4—81no—
260C2×C4—81no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4—81no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4C2×C22⋊C811yescharacteristic
267C2×C4#40811yescharacteristic
268C2×C4#41611yescharacteristic
269C2×C4#41711yescharacteristic
270C2×C4C2×#10411yescharacteristic
271C2×C4#42111yescharacteristic
272C2×C4C8×D411yescharacteristic
273C2×C4C8×D411yescharacteristic
274C2×C4#43611yescharacteristic
275C2×C4#43611yescharacteristic
276C2×C4#44012yes—
277C2×C4#44412yes—
278C2×C4#46311yescharacteristic
279C2×C4#46311yescharacteristic
280C2×C4#46411yescharacteristic
281C2×C4#46411yescharacteristic
282C2×C4#46812yes—
283C2×C4#47312yes—
284C2×C4#49611yescharacteristic
285C2×C4#49711yescharacteristic
286C8—22no—
287C8—22no—
288C8—22no—
289C8—41no—
290C8—82no—
291C8—82no—
292C8—82no—
293C8—82no—
294C22#195411yescharacteristic
295C22#197311yescharacteristic
296C22#197511yescharacteristic
297C22#197611yescharacteristic
298C22#197911yescharacteristic
299C22#198011yescharacteristic
300C22#198311yescharacteristic
301C4—21no—
302C4—21no—
303C4—21no—
304C4—21no—
305C4—21no—
306C4—21no—
307C4—41no—
308C4—82no—
309C4—82no—
310C4—161no—
311C4—161no—
312C4#147611yescharacteristic
313C4#147711yescharacteristic
314C4#148211yescharacteristic
315C4#148311yescharacteristic
316C4SD16⋊C812yes—
317C4#159212yes—
318C4#169912yes—
319C4#170012yes—
320C2#966011yescharacteristic
321C2#966911yescharacteristic
322C2#967511yescharacteristic
323C2#972211yescharacteristic
324C2#972711yescharacteristic
325C2#974811yescharacteristic
326C2#975411yescharacteristic
subgroupG/H
centerC22×C4#121
commutatorC42C22×C8
Frattini, cosocleC43C23
socle, prime radicalC23#390
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
36. #487C8semidirect

Maximal subgroups

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

subgroupindex
C4×#4872
#98652
#96732
C4×#3352
#82602
#75702