Finite Group Databasebeta

← #102867

Subgroups — #102867

Order 512.

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

normal subgroups only

This group has 463 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#23835C211yesmaximal, characteristic
3#23816C211yesmaximal, characteristic
4#9874C211yesmaximal, characteristic
5#9643C211yesmaximal, characteristic
6#9643C211yesmaximal, characteristic
7#7014C211yesmaximal, characteristic
8C4×C4⋊Q8C2211yescharacteristic
9C4×C4⋊Q8C2211yescharacteristic
10C4×C4⋊Q8C2211yescharacteristic
11#2100—21no—
12#2084—21no—
13#2084—21no—
14#2083—21no—
15#2083—21no—
16#2072—21no—
17#2058—21no—
18#2058—21no—
19#2057—21no—
20#2057—21no—
21#2043—21no—
22#2024—21no—
23#1842C2211yescharacteristic
24C4×#107—22no—
25C4×#106—22no—
26C4×#103—22no—
27#1744C2211yescharacteristic
28#1744C2211yescharacteristic
29#1744C2211yescharacteristic
30C2×Q8⋊C8—22no—
31C2×Q8⋊C8—22no—
32#1279—22no—
33C2×C4⋊Q8D411yescharacteristic
34C2×C4⋊Q8D411yescharacteristic
35C2×C4⋊Q8D411yescharacteristic
36C2×C4×Q8—21no—
37C2×C4×Q8—21no—
38C2×C4×Q8—21no—
39C2×#107—22no—
40C2×#107—22no—
41C2×#106—22no—
42C2×#106—22no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×#103—22no—
47C2×#103—22no—
48C2×C4×C8D412yes—
49C2×C4×C8D412yes—
50C2×C4×C8D412yes—
51#391—21no—
52#391—21no—
53#391—21no—
54#389—21no—
55#389—21no—
56#389—21no—
57#389—21no—
58#389—21no—
59#389—21no—
60#384D411yescharacteristic
61#384D411yescharacteristic
62#384D411yescharacteristic
63C4×C4⋊C4—21no—
64C4×C4⋊C4—21no—
65C4×C4⋊C4—21no—
66C4×C4⋊C4—21no—
67C4×C4⋊C4—21no—
68C4×C4⋊C4—21no—
69C43C2311yescharacteristic
70#340—22no—
71#340—22no—
72#340—22no—
73#340—22no—
74#340—22no—
75#340—22no—
76#336—21no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336—21no—
82Q8⋊C8—44no—
83Q8⋊C8—44no—
84C22×Q8—21no—
85C22×Q8—21no—
86C22×Q8—21no—
87C22×C8—22no—
88C22×C8—22no—
89C22×C8—22no—
90C22×C8—41no—
91C4⋊Q8—42no—
92C4⋊Q8—42no—
93C4⋊Q8—42no—
94C4×Q8—42no—
95C4×Q8—42no—
96C4×Q8—42no—
97C4×Q8—42no—
98C4×Q8—42no—
99C4×Q8—42no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
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—41no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—41no—
118C2×C42—41no—
119C2×C42—41no—
120C2×C42—41no—
121C2×C42C2×D411yescharacteristic
122C2×C42C2×D411yescharacteristic
123C2×C42C2×D411yescharacteristic
124C2×C42C2×D411yescharacteristic
125C2×C42C2×D411yescharacteristic
126C2×C42C2×D411yescharacteristic
127C2×C42#4111yescharacteristic
128#107—44no—
129#107—44no—
130#106—44no—
131#106—44no—
132C4⋊C8—42no—
133C4⋊C8—42no—
134C4⋊C8—42no—
135#103—44no—
136#103—44no—
137C4×C8—22no—
138C4×C8—22no—
139C4×C8—22no—
140C4×C8—22no—
141C4×C8SD1614yes—
142C4×C8Q1614yes—
143#95—41no—
144#95—41no—
145#95—41no—
146#95—41no—
147#95—41no—
148#95—41no—
149C2×Q8—22no—
150C2×Q8—22no—
151C2×Q8—22no—
152C2×Q8—41no—
153C2×Q8—41no—
154C2×Q8—41no—
155C2×Q8—42no—
156C2×Q8—42no—
157C2×Q8—42no—
158C2×Q8—42no—
159C2×Q8—42no—
160C2×Q8—42no—
161C22×C4—41no—
162C22×C4—41no—
163C22×C4—41no—
164C22×C4—41no—
165C22×C4—41no—
166C22×C4—41no—
167C22×C4#12011yescharacteristic
168C22×C4#12011yescharacteristic
169C22×C4#12011yescharacteristic
170C22×C4#12111yescharacteristic
171C22×C4#12111yescharacteristic
172C22×C4#12111yescharacteristic
173C22×C4#12711yescharacteristic
174C2×C8—24no—
175C2×C8—24no—
176C2×C8—42no—
177C2×C8—42no—
178C2×C8—42no—
179C2×C8—42no—
180C2×C8—42no—
181C2×C8—42no—
182C2×C8—42no—
183C2×C8—81no—
184C2×C8—81no—
185C2×C8—81no—
186C4⋊C4—22no—
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—42no—
199C4⋊C4—42no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C4⋊C4—42no—
203C4⋊C4—42no—
204C4⋊C4—42no—
205C4⋊C4—42no—
206C4⋊C4—42no—
207C4⋊C4—82no—
208C4⋊C4—82no—
209C4⋊C4—82no—
210C42—41no—
211C42—41no—
212C42—41no—
213C42—41no—
214C42—81no—
215C42—81no—
216C42—81no—
217C42—81no—
218C42—81no—
219C42—81no—
220C42C2×SD1612yes—
221C42C2×Q1612yes—
222C42#13512yes—
223C42AGL(1,ℤ/8)12yes—
224C42#13712yes—
225C42#13712yes—
226C23#39211yescharacteristic
227Q8—44no—
228Q8—44no—
229Q8—44no—
230Q8—82no—
231Q8—82no—
232Q8—82no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—81no—
249C2×C4—81no—
250C2×C4—81no—
251C2×C4—81no—
252C2×C4—81no—
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#44812yes—
264C2×C4#44912yes—
265C2×C4#45112yes—
266C2×C4#46112yes—
267C2×C4#46212yes—
268C2×C4#46312yes—
269C2×C4#49211yescharacteristic
270C2×C4#49411yescharacteristic
271C2×C4#49511yescharacteristic
272C2×C4#49611yescharacteristic
273C2×C4#49711yescharacteristic
274C2×C4#49711yescharacteristic
275C8—44no—
276C8—44no—
277C8—82no—
278C8—161no—
279C22#201011yescharacteristic
280C22#201011yescharacteristic
281C22#201011yescharacteristic
282C22#201211yescharacteristic
283C22#201311yescharacteristic
284C22#201611yescharacteristic
285C22#201711yescharacteristic
286C4—22no—
287C4—22no—
288C4—22no—
289C4—22no—
290C4—22no—
291C4—22no—
292C4—82no—
293C4—82no—
294C4—82no—
295C4—161no—
296C4—161no—
297C4—161no—
298C4#170711yescharacteristic
299C4#171411yescharacteristic
300C4#171811yescharacteristic
301C4#172311yescharacteristic
302C2#1001311yescharacteristic
303C2#1001411yescharacteristic
304C2#1001711yescharacteristic
305C2#1003311yescharacteristic
306C2#1003611yescharacteristic
307C2#1003711yescharacteristic
308C2#1031411yescharacteristic
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

Maximal subgroups

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

subgroupindex
#238372
#238352
#238162
#98742
#96432
#70142