Finite Group Databasebeta

← #103157

Subgroups — #103157

Order 512.

540 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 134 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#33289C211yesmaximal, characteristic
2#29208C211yesmaximal, characteristic
3#28440C211yesmaximal, characteristic
4#9898C211yesmaximal, characteristic
5#9870C211yesmaximal, characteristic
6#9691C211yesmaximal, characteristic
7#7015C211yesmaximal, characteristic
8C2×#494—21no—
9C2×#462—22no—
10#2868C2211yescharacteristic
11#2868C2211yescharacteristic
12C4×C4⋊Q8C2211yescharacteristic
13#2057—22no—
14#2016—22no—
15#1990—22no—
16#1990—22no—
17#1990—21no—
18#1956—21no—
19#1947—22no—
20#1845—21no—
21#1842C2211yescharacteristic
22#1834—22no—
23C4×C4⋊C8C2211yescharacteristic
24C4×C4⋊C8C2211yescharacteristic
25C42×C8C2211yescharacteristic
26C2×#333—22no—
27#1296—22no—
28#1279—22no—
29C22×Q16—24no—
30C2×C4⋊Q8—21no—
31C2×C4⋊Q8—21no—
32C2×C4⋊Q8—21no—
33C2×C4⋊Q8—21no—
34C2×C4⋊Q8D411yescharacteristic
35C2×C4⋊Q8D412yes—
36C2×C4⋊Q8D412yes—
37C2×C4×Q8—21no—
38#494—42no—
39#494—42no—
40#462—44no—
41#462—44no—
42C2×#107—24no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8D412yes—
47C2×C4⋊C8D412yes—
48C2×#103—24no—
49C2×C4×C8—21no—
50C2×C4×C8—21no—
51C2×C4×C8—21no—
52C2×C4×C8—21no—
53C2×C4×C8D412yes—
54#391—21no—
55#389—21no—
56#389—21no—
57#384—21no—
58#384—21no—
59#384—21no—
60#384—21no—
61#384—21no—
62#384—21no—
63#384—21no—
64#384—21no—
65#384D411yescharacteristic
66C4×C4⋊C4—21no—
67C4×C4⋊C4—21no—
68C43C2311yescharacteristic
69#340—24no—
70#340—28no—
71#336—21no—
72#336—21no—
73#333—44no—
74C22×Q8—21no—
75C22×Q8—22no—
76C22×Q8—22no—
77C2×Q16—48no—
78C2×Q16—48no—
79C2×Q16—84no—
80C22×C8—22no—
81C22×C8—22no—
82C22×C8—22no—
83C22×C8—41no—
84C4⋊Q8—21no—
85C4⋊Q8—21no—
86C4⋊Q8—21no—
87C4⋊Q8—44no—
88C4⋊Q8—44no—
89C4⋊Q8—42no—
90C4⋊Q8—42no—
91C4⋊Q8—41no—
92C4⋊Q8—41no—
93C4⋊Q8—42no—
94C4⋊Q8—42no—
95C4⋊Q8—41no—
96C4⋊Q8—41no—
97C4⋊Q8—82no—
98C4⋊Q8SD1612yes—
99C4×Q8—42no—
100C4×Q8—42no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—22no—
105C2×C4⋊C4—22no—
106C2×C4⋊C4—22no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—22no—
110C2×C4⋊C4—41no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4—41no—
119C2×C42—41no—
120C2×C42C2×D411yescharacteristic
121C2×C42C2×D411yescharacteristic
122C2×C42C2×D411yescharacteristic
123C2×C42C2×D411yescharacteristic
124C2×C42C2×D411yescharacteristic
125C2×C42C2×D411yescharacteristic
126C2×C42#4111yescharacteristic
127#107—84no—
128C4⋊C8—22no—
129C4⋊C8—22no—
130C4⋊C8—42no—
131C4⋊C8—42no—
132C4⋊C8—42no—
133C4⋊C8D814yes—
134C4⋊C8Q1614yescomplemented
135#103—48no—
136C4×C8—22no—
137C4×C8—42no—
138C4×C8—42no—
139C4×C8—41no—
140C4×C8—41no—
141C4×C8—41no—
142C4×C8—41no—
143C4×C8Q1614yescomplemented
144#95—41no—
145#95—41no—
146C2×Q8—22no—
147C2×Q8—41no—
148C2×Q8—42no—
149C2×Q8—44no—
150C2×Q8—42no—
151C2×Q8—42no—
152C2×Q8—42no—
153C2×Q8—44no—
154C2×Q8—44no—
155C2×Q8—82no—
156C2×Q8—82no—
157C22×C4—41no—
158C22×C4—41no—
159C22×C4—42no—
160C22×C4—42no—
161C22×C4#12011yescharacteristic
162C22×C4#12011yescharacteristic
163C22×C4#12011yescharacteristic
164C22×C4#12111yescharacteristic
165C22×C4#12111yescharacteristic
166C22×C4#12111yescharacteristic
167C22×C4#12711yescharacteristic
168Q16—816no—
169C2×C8—24no—
170C2×C8—24no—
171C2×C8—24no—
172C2×C8—42no—
173C2×C8—42no—
174C2×C8—42no—
175C2×C8—42no—
176C2×C8—42no—
177C2×C8—42no—
178C2×C8—81no—
179C2×C8—81no—
180C2×C8—81no—
181C4⋊C4—22no—
182C4⋊C4—22no—
183C4⋊C4—44no—
184C4⋊C4—44no—
185C4⋊C4—41no—
186C4⋊C4—41no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C4⋊C4—44no—
190C4⋊C4—42no—
191C4⋊C4—82no—
192C4⋊C4—82no—
193C4⋊C4—82no—
194C4⋊C4—81no—
195C4⋊C4—81no—
196C4⋊C4—82no—
197C4⋊C4—82no—
198C4⋊C4—81no—
199C4⋊C4—81no—
200C4⋊C4—82no—
201C4⋊C4—81no—
202C4⋊C4—81no—
203C4⋊C4—81no—
204C4⋊C4—81no—
205C42—22no—
206C42—22no—
207C42—22no—
208C42—81no—
209C42—81no—
210C42C2×D812yes—
211C42C2×SD1611yescharacteristic
212C42C2×Q1612yes—
213C42C2×Q1612yes—
214C42#13511yescharacteristic
215C42AGL(1,ℤ/8)12yes—
216C42AGL(1,ℤ/8)11yescharacteristic
217C42#13711yescharacteristic
218C42#13712yes—
219C42#13712yes—
220C23#39211yescharacteristic
221Q8—44no—
222Q8—82no—
223Q8—84no—
224Q8—84no—
225Q8—164no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—42no—
233C2×C4—81no—
234C2×C4—81no—
235C2×C4—82no—
236C2×C4—82no—
237C2×C4—82no—
238C2×C4—81no—
239C2×C4—81no—
240C2×C4—82no—
241C2×C4—82no—
242C2×C4—81no—
243C2×C4—82no—
244C2×C4#44712yes—
245C2×C4#44811yescharacteristic
246C2×C4#44911yescharacteristic
247C2×C4#45011yescharacteristic
248C2×C4#45112yes—
249C2×C4#45112yes—
250C2×C4#45211yescharacteristic
251C2×C4#45512yes—
252C2×C4#45512yes—
253C2×C4#45912yes—
254C2×C4#46212yes—
255C2×C4#46212yes—
256C2×C4#46511yescharacteristic
257C2×C4#46811yescharacteristic
258C2×C4#47112yes—
259C2×C4#49311yescharacteristic
260C2×C4#49411yescharacteristic
261C2×C4#49411yescharacteristic
262C2×C4#49611yescharacteristic
263C2×C4#49711yescharacteristic
264C2×C4#49711yescharacteristic
265C8—44no—
266C8—44no—
267C8—44no—
268C8—161no—
269C22#200011yescharacteristic
270C22#200411yescharacteristic
271C22#200411yescharacteristic
272C22#201111yescharacteristic
273C22#201611yescharacteristic
274C22#201611yescharacteristic
275C22#201911yescharacteristic
276C4—22no—
277C4—22no—
278C4—22no—
279C4—82no—
280C4—162no—
281C4—161no—
282C4—162no—
283C4#163912yes—
284C4#164112yes—
285C4#164412yes—
286C4#164512yes—
287C4#167212yes—
288C4#169212yes—
289C4#171311yescharacteristic
290C4#172211yescharacteristic
291C4#172311yescharacteristic
292C4#172311yescharacteristic
293C2#1006511yescharacteristic
294C2#1007011yescharacteristic
295C2#1016311yescharacteristic
296C2#1016811yescharacteristic
297C2#1027311yescharacteristic
298C2#1029711yescharacteristic
299C2#1030911yescharacteristic
subgroupG/H
center, socle, prime radicalC23#392
commutator, Frattini, cosocleC43C23
LCSG ▷ C43 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
134. C4⋊C8Q16semidirect
143. C4×C8Q16semidirect

Maximal subgroups

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

subgroupindex
#332892
#292082
#284402
#98982
#98702
#96912
#70152