Finite Group Databasebeta

← #104047

Subgroups — #104047

Order 512.

438 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 92 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#29347C211yesmaximal, characteristic
2#29273C211yesmaximal, characteristic
3#29211C211yesmaximal, characteristic
4#9677C211yesmaximal, characteristic
5#9673C211yesmaximal, characteristic
6#7662C211yesmaximal, characteristic
7#7022C211yesmaximal, characteristic
8#2862C2211yescharacteristic
9C4×C4⋊Q8C2211yescharacteristic
10C4×C4⋊Q8C2211yescharacteristic
11#2099—21no—
12#2072—21no—
13#2058—21no—
14#2058—21no—
15#2057—21no—
16#2024—21no—
17#1993—21no—
18#1987—21no—
19#1987—21no—
20#1981—21no—
21#1949—22no—
22#1948—21no—
23#1933—22no—
24#1919—22no—
25#1847—21no—
26#1831C2211yescharacteristic
27#1767C2211yescharacteristic
28C4×C4⋊C8C2211yescharacteristic
29C4×C4⋊C8C2211yescharacteristic
30C2×Q8⋊C8—22no—
31C2×Q8⋊C8—22no—
32#1272—22no—
33C2×C4⋊Q8D411yescharacteristic
34C2×C4⋊Q8D411yescharacteristic
35C2×C4⋊Q8D411yescharacteristic
36C2×C4⋊Q8D411yescharacteristic
37C2×C4×Q8—21no—
38C2×C4×Q8—21no—
39C2×#107—22no—
40C2×#106—22no—
41C2×#106—22no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8D412yes—
46C2×#103—22no—
47C2×#103—22no—
48C2×#97—21no—
49C2×C4×C8—21no—
50C2×C4×C8D412yes—
51#391—21no—
52#391—21no—
53#391—21no—
54#391—21no—
55#391—21no—
56#391—21no—
57#389—21no—
58#389—21no—
59#389—21no—
60#389—21no—
61#384D411yescharacteristic
62#384D411yescharacteristic
63#382—21no—
64#382—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#340—22no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336D412yes—
82Q8⋊C8—44no—
83Q8⋊C8—44no—
84C22×Q8—21no—
85C22×Q8—21no—
86C22×Q8—21no—
87C22×Q8—21no—
88C22×C8—22no—
89C22×C8—22no—
90C22×C8—22no—
91C22×C8—41no—
92C4⋊Q8—21no—
93C4⋊Q8—21no—
94C4⋊Q8—21no—
95C4⋊Q8—42no—
96C4⋊Q8—42no—
97C4⋊Q8—42no—
98C4⋊Q8Q1612yes—
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—41no—
118C2×C4⋊C4—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—82no—
129#106—44no—
130#106—82no—
131C4⋊C8—22no—
132C4⋊C8—22no—
133C4⋊C8—41no—
134C4⋊C8—42no—
135C4⋊C8—41no—
136C4⋊C8—41no—
137C4⋊C8SD1614yes—
138#103—44no—
139#103—82no—
140#97—41no—
141#97—41no—
142C4×C8—42no—
143C4×C8—42no—
144#95—41no—
145#95—41no—
146#95—41no—
147#95—41no—
148#95—41no—
149#95—41no—
150#95—41no—
151#95—41no—
152C2×Q8—22no—
153C2×Q8—22no—
154C2×Q8—41no—
155C2×Q8—42no—
156C2×Q8—42no—
157C2×Q8—42no—
158C2×Q8—42no—
159C2×Q8—42no—
160C2×Q8—42no—
161C2×Q8—41no—
162C2×Q8—41no—
163C2×Q8—41no—
164C2×Q8—42no—
165C2×Q8—81no—
166C2×Q8—81no—
167C22×C4—41no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4—41no—
172C22×C4—41no—
173C22×C4#12011yescharacteristic
174C22×C4#12011yescharacteristic
175C22×C4#12011yescharacteristic
176C22×C4#12111yescharacteristic
177C22×C4#12111yescharacteristic
178C22×C4#12111yescharacteristic
179C22×C4#12711yescharacteristic
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—42no—
189C2×C8—42no—
190C2×C8—81no—
191C2×C8—81no—
192C4⋊C4—22no—
193C4⋊C4—22no—
194C4⋊C4—22no—
195C4⋊C4—22no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—42no—
199C4⋊C4—42no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C4⋊C4—42no—
210C4⋊C4—81no—
211C4⋊C4—81no—
212C4⋊C4—81no—
213C4⋊C4—81no—
214C4⋊C4—81no—
215C42—21no—
216C42—21no—
217C42—22no—
218C42—41no—
219C42—41no—
220C42—41no—
221C42—82no—
222C42—82no—
223C42C2×SD1612yes—
224C42C2×Q1611yescharacteristic
225C42#13511yescharacteristic
226C42#13712yes—
227C42#13711yescharacteristic
228C42#13711yescharacteristic
229C23#39211yescharacteristic
230Q8—44no—
231Q8—44no—
232Q8—82no—
233Q8—82no—
234Q8—82no—
235Q8—82no—
236Q8—162no—
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—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—42no—
251C2×C4—42no—
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—81no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4—81no—
267C2×C4—81no—
268C2×C4#44812yes—
269C2×C4#45111yescharacteristic
270C2×C4#45111yescharacteristic
271C2×C4#45211yescharacteristic
272C2×C4#45211yescharacteristic
273C2×C4#45311yescharacteristic
274C2×C4#45411yescharacteristic
275C2×C4#45512yes—
276C2×C4#46112yes—
277C2×C4#46711yescharacteristic
278C2×C4#47011yescharacteristic
279C2×C4#49211yescharacteristic
280C2×C4#49711yescharacteristic
281C8—44no—
282C8—82no—
283C8—82no—
284C8—82no—
285C22#200111yescharacteristic
286C22#200411yescharacteristic
287C22#200611yescharacteristic
288C22#200911yescharacteristic
289C22#201011yescharacteristic
290C22#201311yescharacteristic
291C22#201711yescharacteristic
292C4—21no—
293C4—21no—
294C4—21no—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—22no—
299C4—21no—
300C4—21no—
301C4—41no—
302C4—82no—
303C4—82no—
304C4—161no—
305C4—161no—
306C4—161no—
307C4—161no—
308C4#164312yes—
309C4#164512yes—
310C2#1000311yescharacteristic
311C2#1000611yescharacteristic
312C2#1003611yescharacteristic
313C2#1007311yescharacteristic
314C2#1012511yescharacteristic
315C2#1020111yescharacteristic
316C2#1025811yescharacteristic
subgroupG/H
center, socle, prime radicalC23#392
commutator, Frattini, cosocleC43C23
LCSG ▷ C43 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ 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
#293472
#292732
#292112
#96772
#96732
#76622
#70222