Finite Group Databasebeta

← #102871

Subgroups — #102871

Order 512.

495 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 495 conjugacy classes of subgroups — too many to draw. Only its 100 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#23837C211yesmaximal, characteristic
2#23816C211yesmaximal, characteristic
3#23801C211yesmaximal, characteristic
4#9874C211yesmaximal, characteristic
5#9874C211yesmaximal, characteristic
6#9874C211yesmaximal, characteristic
7#7014C211yesmaximal, characteristic
8C2×C4×Q16—22no—
9C4×C4⋊Q8C2211yescharacteristic
10C4×C4⋊Q8C2211yescharacteristic
11C4×C4⋊Q8C2211yescharacteristic
12#2100—21no—
13#2095—21no—
14#2095—21no—
15#2084—21no—
16#2084—21no—
17#2072—21no—
18#2058—21no—
19#2058—21no—
20#2043—21no—
21#2024—21no—
22#2016—21no—
23#2016—21no—
24#1842C2211yescharacteristic
25C4×#106—22no—
26C4×#103—22no—
27#1744C2211yescharacteristic
28#1744C2211yescharacteristic
29#1744C2211yescharacteristic
30#1279—22no—
31#1279—22no—
32#1279—22no—
33C22×Q16—22no—
34C2×C4⋊Q8D411yescharacteristic
35C2×C4⋊Q8D411yescharacteristic
36C2×C4⋊Q8D411yescharacteristic
37C2×C4×Q8—21no—
38C2×C4×Q8—21no—
39C2×C4×Q8—21no—
40C4×Q16—44no—
41C4×Q16—44no—
42C2×#107—22no—
43C2×#106—22no—
44C2×#106—22no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8—21no—
47C2×C4⋊C8—21no—
48C2×#103—22no—
49C2×#103—22no—
50C2×#103—22no—
51C2×#103—22no—
52C2×C4×C8D412yes—
53C2×C4×C8D412yes—
54C2×C4×C8D412yes—
55#391—21no—
56#391—21no—
57#391—21no—
58#389—21no—
59#389—21no—
60#389—21no—
61#389—21no—
62#389—21no—
63#389—21no—
64#384D411yescharacteristic
65#384D411yescharacteristic
66#384D411yescharacteristic
67C4×C4⋊C4—21no—
68C4×C4⋊C4—21no—
69C4×C4⋊C4—21no—
70C4×C4⋊C4—21no—
71C4×C4⋊C4—21no—
72C4×C4⋊C4—21no—
73C43C2311yescharacteristic
74#340—22no—
75#340—22no—
76#340—22no—
77#340—22no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336—21no—
82#336—21no—
83#336—21no—
84C22×Q8—21no—
85C22×Q8—21no—
86C22×Q8—21no—
87C2×Q16—44no—
88C2×Q16—44no—
89C2×Q16—44no—
90C22×C8—22no—
91C22×C8—22no—
92C22×C8—22no—
93C22×C8—41no—
94C4⋊Q8—42no—
95C4⋊Q8—42no—
96C4⋊Q8—42no—
97C4×Q8—42no—
98C4×Q8—42no—
99C4×Q8—42no—
100C4×Q8—42no—
101C4×Q8—42no—
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—21no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—41no—
119C2×C4⋊C4—41no—
120C2×C4⋊C4—41no—
121C2×C42—41no—
122C2×C42—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
131#107—44no—
132#106—44no—
133#106—44no—
134C4⋊C8—42no—
135C4⋊C8—42no—
136C4⋊C8—42no—
137#103—44no—
138#103—44no—
139#103—44no—
140#103—44no—
141C4×C8—22no—
142C4×C8—22no—
143C4×C8—22no—
144C4×C8—22no—
145C4×C8SD1614yes—
146C4×C8Q1614yescomplemented
147#95—41no—
148#95—41no—
149#95—41no—
150#95—41no—
151#95—41no—
152#95—41no—
153C2×Q8—22no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—41no—
157C2×Q8—41no—
158C2×Q8—41no—
159C2×Q8—42no—
160C2×Q8—42no—
161C2×Q8—42no—
162C2×Q8—42no—
163C2×Q8—42no—
164C2×Q8—42no—
165C22×C4—41no—
166C22×C4—41no—
167C22×C4—41no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4#12011yescharacteristic
172C22×C4#12011yescharacteristic
173C22×C4#12011yescharacteristic
174C22×C4#12111yescharacteristic
175C22×C4#12111yescharacteristic
176C22×C4#12111yescharacteristic
177C22×C4#12711yescharacteristic
178Q16—416no—
179C2×C8—24no—
180C2×C8—24no—
181C2×C8—42no—
182C2×C8—42no—
183C2×C8—42no—
184C2×C8—42no—
185C2×C8—42no—
186C2×C8—42no—
187C2×C8—42no—
188C2×C8—81no—
189C2×C8—81no—
190C2×C8—81no—
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—22no—
194C4⋊C4—22no—
195C4⋊C4—22no—
196C4⋊C4—22no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C4⋊C4—42no—
204C4⋊C4—42no—
205C4⋊C4—42no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C4⋊C4—42no—
210C4⋊C4—42no—
211C4⋊C4—42no—
212C4⋊C4—82no—
213C4⋊C4—82no—
214C4⋊C4—82no—
215C42—41no—
216C42—41no—
217C42—41no—
218C42—41no—
219C42—81no—
220C42—81no—
221C42—81no—
222C42—81no—
223C42—81no—
224C42—81no—
225C42C2×SD1612yes—
226C42C2×Q1612yes—
227C42#13512yes—
228C42AGL(1,ℤ/8)12yes—
229C42#13712yes—
230C42#13712yes—
231C23#39211yescharacteristic
232Q8—44no—
233Q8—44no—
234Q8—44no—
235Q8—82no—
236Q8—82no—
237Q8—82no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
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—42no—
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—81no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4—81no—
267C2×C4—81no—
268C2×C4#45012yes—
269C2×C4#45112yes—
270C2×C4#45212yes—
271C2×C4#46012yes—
272C2×C4#46212yes—
273C2×C4#46412yes—
274C2×C4#49211yescharacteristic
275C2×C4#49411yescharacteristic
276C2×C4#49511yescharacteristic
277C2×C4#49611yescharacteristic
278C2×C4#49711yescharacteristic
279C2×C4#49711yescharacteristic
280C8—44no—
281C8—44no—
282C8—82no—
283C8—161no—
284C22#201011yescharacteristic
285C22#201011yescharacteristic
286C22#201011yescharacteristic
287C22#201411yescharacteristic
288C22#201511yescharacteristic
289C22#201611yescharacteristic
290C22#201711yescharacteristic
291C4—22no—
292C4—22no—
293C4—22no—
294C4—22no—
295C4—22no—
296C4—22no—
297C4—82no—
298C4—82no—
299C4—82no—
300C4—161no—
301C4—161no—
302C4—161no—
303C4#170711yescharacteristic
304C4#171611yescharacteristic
305C4#172011yescharacteristic
306C4#172311yescharacteristic
307C2#1001511yescharacteristic
308C2#1001611yescharacteristic
309C2#1001711yescharacteristic
310C2#1003411yescharacteristic
311C2#1003511yescharacteristic
312C2#1003711yescharacteristic
313C2#1031811yescharacteristic
subgroupG/H
centerC22×C4#127
commutator, Frattini, cosocleC43C23
socle, prime radicalC23#392
LCSG ▷ C43 ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
146. C4×C8Q16semidirect

Maximal subgroups

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

subgroupindex
#238372
#238162
#238012
#98742
#70142