Finite Group Databasebeta

← #103153

Subgroups — #103153

Order 512.

550 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 130 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#28748C211yesmaximal, characteristic
3#28440C211yesmaximal, characteristic
4#9898C211yesmaximal, characteristic
5#9898C211yesmaximal, characteristic
6#9870C211yesmaximal, characteristic
7#7015C211yesmaximal, characteristic
8C2×#494—21no—
9C2×#487—21no—
10C2×#462—22no—
11#2868C2211yescharacteristic
12#2868C2211yescharacteristic
13C4×C4⋊Q8C2211yescharacteristic
14#2043—22no—
15#2016—22no—
16#1990—22no—
17#1990—22no—
18#1981—22no—
19#1956—21no—
20#1956—21no—
21#1842C2211yescharacteristic
22#1834—22no—
23C4×C4⋊C8C2211yescharacteristic
24C4×C4⋊C8C2211yescharacteristic
25C42×C8C2211yescharacteristic
26#1296—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#487—42no—
41#487—42no—
42#462—44no—
43#462—44no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8—21no—
47C2×C4⋊C8D412yes—
48C2×C4⋊C8D412yes—
49C2×#103—24no—
50C2×#103—24no—
51C2×#103—24no—
52C2×C4×C8—21no—
53C2×C4×C8—21no—
54C2×C4×C8—21no—
55C2×C4×C8—21no—
56C2×C4×C8D412yes—
57#391—21no—
58#389—21no—
59#389—21no—
60#384—21no—
61#384—21no—
62#384—21no—
63#384—21no—
64#384—21no—
65#384—21no—
66#384—21no—
67#384—21no—
68#384D411yescharacteristic
69C4×C4⋊C4—21no—
70C4×C4⋊C4—21no—
71C43C2311yescharacteristic
72#340—28no—
73#336—21no—
74#336—21no—
75C22×Q8—21no—
76C22×Q8—22no—
77C22×Q8—22no—
78C2×Q16—48no—
79C2×Q16—48no—
80C2×Q16—84no—
81C22×C8—22no—
82C22×C8—22no—
83C22×C8—22no—
84C22×C8—41no—
85C4⋊Q8—21no—
86C4⋊Q8—21no—
87C4⋊Q8—21no—
88C4⋊Q8—44no—
89C4⋊Q8—44no—
90C4⋊Q8—41no—
91C4⋊Q8—41no—
92C4⋊Q8—42no—
93C4⋊Q8—41no—
94C4⋊Q8—41no—
95C4⋊Q8—42no—
96C4⋊Q8—41no—
97C4⋊Q8—41no—
98C4⋊Q8—42no—
99C4⋊Q8—41no—
100C4⋊Q8—41no—
101C4⋊Q8—42no—
102C4⋊Q8D812yes—
103C4×Q8—42no—
104C4×Q8—42no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—22no—
109C2×C4⋊C4—22no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—22no—
113C2×C4⋊C4—22no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4—41no—
119C2×C4⋊C4—41no—
120C2×C4⋊C4—41no—
121C2×C4⋊C4—41no—
122C2×C4⋊C4—41no—
123C2×C42—41no—
124C2×C42C2×D411yescharacteristic
125C2×C42C2×D411yescharacteristic
126C2×C42C2×D411yescharacteristic
127C2×C42C2×D411yescharacteristic
128C2×C42C2×D411yescharacteristic
129C2×C42C2×D411yescharacteristic
130C2×C42#4111yescharacteristic
131C4⋊C8—22no—
132C4⋊C8—22no—
133C4⋊C8—22no—
134C4⋊C8—42no—
135C4⋊C8—42no—
136C4⋊C8—42no—
137C4⋊C8SD1614yes—
138#103—48no—
139#103—48no—
140#103—84no—
141C4×C8—22no—
142C4×C8—42no—
143C4×C8—42no—
144C4×C8—41no—
145C4×C8—41no—
146C4×C8—41no—
147C4×C8—41no—
148C4×C8Q1614yescomplemented
149#95—41no—
150#95—41no—
151C2×Q8—22no—
152C2×Q8—41no—
153C2×Q8—42no—
154C2×Q8—42no—
155C2×Q8—42no—
156C2×Q8—42no—
157C2×Q8—42no—
158C2×Q8—44no—
159C2×Q8—44no—
160C2×Q8—42no—
161C2×Q8—44no—
162C2×Q8—44no—
163C22×C4—41no—
164C22×C4—41no—
165C22×C4—42no—
166C22×C4—42no—
167C22×C4#12011yescharacteristic
168C22×C4#12011yescharacteristic
169C22×C4#12011yescharacteristic
170C22×C4#12111yescharacteristic
171C22×C4#12111yescharacteristic
172C22×C4#12111yescharacteristic
173C22×C4#12711yescharacteristic
174Q16—816no—
175C2×C8—24no—
176C2×C8—24no—
177C2×C8—42no—
178C2×C8—42no—
179C2×C8—42no—
180C2×C8—42no—
181C2×C8—42no—
182C2×C8—42no—
183C2×C8—42no—
184C2×C8—81no—
185C2×C8—81no—
186C2×C8—81no—
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—44no—
190C4⋊C4—44no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—82no—
197C4⋊C4—82no—
198C4⋊C4—81no—
199C4⋊C4—81no—
200C4⋊C4—81no—
201C4⋊C4—81no—
202C4⋊C4—82no—
203C4⋊C4—82no—
204C4⋊C4—82no—
205C4⋊C4—81no—
206C4⋊C4—81no—
207C4⋊C4—81no—
208C4⋊C4—81no—
209C4⋊C4—81no—
210C4⋊C4—81no—
211C4⋊C4—81no—
212C4⋊C4—81no—
213C42—22no—
214C42—22no—
215C42—22no—
216C42—81no—
217C42—81no—
218C42C2×D811yescharacteristic
219C42C2×SD1612yes—
220C42C2×Q1612yes—
221C42#13511yescharacteristic
222C42#13512yes—
223C42AGL(1,ℤ/8)11yescharacteristic
224C42AGL(1,ℤ/8)11yescharacteristic
225C42AGL(1,ℤ/8)12yes—
226C42#13712yes—
227C42#13712yes—
228C23#39211yescharacteristic
229Q8—44no—
230Q8—82no—
231Q8—84no—
232Q8—84no—
233Q8—84no—
234Q8—84no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—42no—
242C2×C4—81no—
243C2×C4—81no—
244C2×C4—82no—
245C2×C4—82no—
246C2×C4—82no—
247C2×C4—82no—
248C2×C4—81no—
249C2×C4—81no—
250C2×C4—82no—
251C2×C4—82no—
252C2×C4—81no—
253C2×C4#44711yescharacteristic
254C2×C4#44711yescharacteristic
255C2×C4#44911yescharacteristic
256C2×C4#44911yescharacteristic
257C2×C4#45012yes—
258C2×C4#45112yes—
259C2×C4#45212yes—
260C2×C4#45512yes—
261C2×C4#45512yes—
262C2×C4#46012yes—
263C2×C4#46212yes—
264C2×C4#46412yes—
265C2×C4#46611yescharacteristic
266C2×C4#46911yescharacteristic
267C2×C4#47312yes—
268C2×C4#49211yescharacteristic
269C2×C4#49411yescharacteristic
270C2×C4#49511yescharacteristic
271C2×C4#49611yescharacteristic
272C2×C4#49711yescharacteristic
273C2×C4#49711yescharacteristic
274C8—44no—
275C8—44no—
276C8—82no—
277C8—161no—
278C22#199911yescharacteristic
279C22#200411yescharacteristic
280C22#200411yescharacteristic
281C22#201411yescharacteristic
282C22#201511yescharacteristic
283C22#201611yescharacteristic
284C22#202011yescharacteristic
285C4—22no—
286C4—22no—
287C4—22no—
288C4—82no—
289C4—162no—
290C4—162no—
291C4—161no—
292C4#163912yes—
293C4#164012yes—
294C4#164112yes—
295C4#164212yes—
296C4#167412yes—
297C4#169412yes—
298C4#170711yescharacteristic
299C4#171611yescharacteristic
300C4#172011yescharacteristic
301C4#172311yescharacteristic
302C2#1006211yescharacteristic
303C2#1006311yescharacteristic
304C2#1017011yescharacteristic
305C2#1017111yescharacteristic
306C2#1026511yescharacteristic
307C2#1029711yescharacteristic
308C2#1031811yescharacteristic
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
148. C4×C8Q16semidirect

Maximal subgroups

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

subgroupindex
#332892
#287482
#284402
#98982
#98702
#70152