Finite Group Databasebeta

← #101445

Subgroups — #101445

Order 512.

405 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 405 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#28161C211yesmaximal, characteristic
2#22307C211yesmaximal, characteristic
3#9874C211yesmaximal, characteristic
4#8590C211yesmaximal, characteristic
5#7652C211yesmaximal, characteristic
6#7040C211yesmaximal, characteristic
7#7018C211yesmaximal, characteristic
8C2×#462—21no—
9C4×C4⋊Q8C2211yescharacteristic
10C4×C4⋊Q8C2211yescharacteristic
11#2072C412yes—
12#2016C412yes—
13#1984—22no—
14#1939—21no—
15#1916—22no—
16#1878—22no—
17#1842C2211yescharacteristic
18#1831C2211yescharacteristic
19#1831C2211yescharacteristic
20#1831C2211yescharacteristic
21#1803—21no—
22C8×C4⋊C4—21no—
23#1744C2211yescharacteristic
24C2×#333—21no—
25#1296—21no—
26#1279—21no—
27#1279—21no—
28#1271—22no—
29C22×Q16—22no—
30C2×C4⋊Q8C2×C411yescharacteristic
31C2×C4⋊Q8D411yescharacteristic
32C2×C4×Q8—21no—
33C2×C4×Q8D412yes—
34#462—42no—
35#462—42no—
36C2×C4⋊C8—21no—
37C2×C4⋊C8—21no—
38C2×C4⋊C8—21no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—22no—
42C2×C4⋊C8—21no—
43C2×#103—22no—
44C2×#103—22no—
45C2×C4×C8—22no—
46C2×C4×C8D411yescharacteristic
47C2×C4×C8D411yescharacteristic
48#391—21no—
49#391C2×C412yes—
50#389—21no—
51#389—21no—
52#389—21no—
53#389—21no—
54#384C2×C411yescharacteristic
55#384D411yescharacteristic
56C4×C4⋊C4—21no—
57C4×C4⋊C4—21no—
58C4×C4⋊C4—21no—
59C4×C4⋊C4—21no—
60C43C2311yescharacteristic
61#340—22no—
62#336—22no—
63#336—22no—
64#336—21no—
65#336—21no—
66#336—21no—
67#336—21no—
68#336—21no—
69#336—21no—
70#336C2×C412yes—
71#336D412yes—
72#333—42no—
73C22×Q8—21no—
74C22×Q8C22⋊C412yes—
75C2×Q16—44no—
76C2×Q16—44no—
77C2×Q16—82no—
78C22×C8—21no—
79C22×C8—22no—
80C22×C8—21no—
81C22×C8—22no—
82C22×C8—41no—
83C22×C8—41no—
84C4⋊Q8—21no—
85C4⋊Q8—21no—
86C4⋊Q8—42no—
87C4⋊Q8D812yes—
88C4⋊Q8SD1612yes—
89C4×Q8—41no—
90C4×Q8—41no—
91C4×Q8—41no—
92C4×Q8—41no—
93C4×Q8—82no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—22no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—41no—
105C2×C4⋊C4C22⋊C412yes—
106C2×C42—22no—
107C2×C42—41no—
108C2×C42C22×C411yescharacteristic
109C2×C42C2×D411yescharacteristic
110C2×C42C2×D411yescharacteristic
111C2×C42C2×D411yescharacteristic
112C2×C42C2×D411yescharacteristic
113C2×C42#4111yescharacteristic
114C2×C42#4111yescharacteristic
115C4⋊C8—41no—
116C4⋊C8—41no—
117C4⋊C8—41no—
118C4⋊C8—41no—
119C4⋊C8—41no—
120C4⋊C8—41no—
121C4⋊C8—41no—
122C4⋊C8—41no—
123C4⋊C8—41no—
124C4⋊C8—41no—
125C4⋊C8—81no—
126C4⋊C8—82no—
127#103—44no—
128#103—82no—
129C4×C8—21no—
130C4×C8—21no—
131C4×C8—21no—
132C4×C8—82no—
133C4×C8Q1612yescomplemented
134#95—22no—
135#95—22no—
136#95—41no—
137#95—41no—
138C2×Q8—22no—
139C2×Q8—22no—
140C2×Q8—41no—
141C2×Q8—42no—
142C2×Q8—42no—
143C2×Q8—41no—
144C2×Q8—41no—
145C2×Q8—41no—
146C2×Q8—41no—
147C2×Q8#10214yes—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—41no—
151C22×C4—41no—
152C22×C4C2×C22⋊C411yescharacteristic
153C22×C4C4×D411yescharacteristic
154C22×C4C4×D411yescharacteristic
155C22×C4#12011yescharacteristic
156C22×C4#12111yescharacteristic
157C22×C4#12111yescharacteristic
158C22×C4#12311yescharacteristic
159Q16—88no—
160C2×C8—22no—
161C2×C8—41no—
162C2×C8—41no—
163C2×C8—42no—
164C2×C8—42no—
165C2×C8—41no—
166C2×C8—41no—
167C2×C8—42no—
168C2×C8—42no—
169C2×C8—42no—
170C2×C8—41no—
171C2×C8—42no—
172C2×C8—81no—
173C2×C8—81no—
174C2×C8—81no—
175C2×C8—81no—
176C2×C8—81no—
177C2×C8—81no—
178C4⋊C4—22no—
179C4⋊C4—22no—
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4—22no—
183C4⋊C4—22no—
184C4⋊C4—42no—
185C4⋊C4—41no—
186C4⋊C4—41no—
187C4⋊C4—42no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—81no—
193C4⋊C4—82no—
194C4⋊C4—81no—
195C4⋊C4—81no—
196C4⋊C4—81no—
197C42—21no—
198C42—21no—
199C42—41no—
200C42—41no—
201C42—41no—
202C42—41no—
203C42—42no—
204C42—42no—
205C42—81no—
206C42—81no—
207C42C2×D811yescharacteristic
208C42C2×SD1611yescharacteristic
209C42C2×Q1611yescharacteristic
210C42#13511yescharacteristic
211C42#13511yescharacteristic
212C42#13511yescharacteristic
213C42#13711yescharacteristic
214C42#13711yescharacteristic
215C23#38611yescharacteristic
216Q8—44no—
217Q8—42no—
218Q8—42no—
219Q8—82no—
220Q8—81no—
221Q8—81no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—24no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—81no—
244C2×C4—81no—
245C2×C4—81no—
246C2×C4—81no—
247C2×C4—81no—
248C2×C4C2×#10211yescharacteristic
249C2×C4#41611yescharacteristic
250C2×C4C4×Q1611yescharacteristic
251C2×C4#44111yescharacteristic
252C2×C4#45111yescharacteristic
253C2×C4#45211yescharacteristic
254C2×C4#46211yescharacteristic
255C2×C4#46411yescharacteristic
256C2×C4#46511yescharacteristic
257C2×C4#46511yescharacteristic
258C2×C4#46611yescharacteristic
259C2×C4#46611yescharacteristic
260C2×C4#47111yescharacteristic
261C2×C4#47311yescharacteristic
262C8—42no—
263C8—82no—
264C8—81no—
265C8—82no—
266C8—161no—
267C8—161no—
268C22#187811yescharacteristic
269C22#188111yescharacteristic
270C22#189111yescharacteristic
271C22#189311yescharacteristic
272C22#190511yescharacteristic
273C22#190811yescharacteristic
274C22#191111yescharacteristic
275C4—21no—
276C4—21no—
277C4—21no—
278C4—21no—
279C4—21no—
280C4—21no—
281C4—21no—
282C4—21no—
283C4—44no—
284C4—41no—
285C4—41no—
286C4—82no—
287C4—82no—
288C4—161no—
289C4#167211yescharacteristic
290C4#167411yescharacteristic
291C4#168011yescharacteristic
292C4#168211yescharacteristic
293C2#904811yescharacteristic
294C2#921811yescharacteristic
295C2#929711yescharacteristic
296C2#930611yescharacteristic
297C2#937311yescharacteristic
298C2#948511yescharacteristic
299C2#952811yescharacteristic
subgroupG/H
center, socle, prime radicalC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
133. C4×C8Q16semidirect

Maximal subgroups

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

subgroupindex
#281612
#223072
#98742
#85902
#76522
#70402
#70182