Finite Group Databasebeta

← #100708

Subgroups — #100708

Order 512.

358 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 88 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#29871C211yesmaximal, characteristic
2#22737C211yesmaximal, characteristic
3#7723C211yesmaximal, characteristic
4#7680C211yesmaximal, characteristic
5#7581C211yesmaximal, characteristic
6#7041C211yesmaximal, characteristic
7#7018C211yesmaximal, characteristic
8C2×#479—21no—
9C2×#446—21no—
10#2859C2211yescharacteristic
11#2295C2211yescharacteristic
12#2085—21no—
13#2084C411yescharacteristic
14#2083C411yescharacteristic
15#2074—21no—
16#2072C411yescharacteristic
17#2072C411yescharacteristic
18#1989—21no—
19#1940—21no—
20#1940—21no—
21#1939—21no—
22#1839C2211yescharacteristic
23#1832—21no—
24#1831C2211yescharacteristic
25#1831C2211yescharacteristic
26#1768—21no—
27#1767C2211yescharacteristic
28#1744C2211yescharacteristic
29#1272—21no—
30#1271—21no—
31#1271—21no—
32#1271—21no—
33#1271—21no—
34#1271—21no—
35C2×#125—21no—
36C2×C4×Q8D411yescharacteristic
37#479—42no—
38#479—42no—
39#446—42no—
40#446—42no—
41C2×#107—21no—
42C2×#106—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8—21no—
47C2×C4⋊C8—21no—
48C2×C4⋊C8—21no—
49C2×C4⋊C8—21no—
50C2×#103—21no—
51C2×#103—21no—
52C2×#97—21no—
53C2×#97—21no—
54C2×C4×C8—21no—
55C2×C4×C8—21no—
56#391C2×C411yescharacteristic
57#391D411yescharacteristic
58#389—21no—
59#389—21no—
60#389—21no—
61#389—21no—
62#389C2×C411yescharacteristic
63#389D411yescharacteristic
64#387—21no—
65#387—21no—
66#384C2×C411yescharacteristic
67#384C2×C411yescharacteristic
68#382—21no—
69C4×C4⋊C4—21no—
70C4×C4⋊C4D411yescharacteristic
71#376—21no—
72C43C2311yescharacteristic
73#340—21no—
74#340—21no—
75#340—21no—
76#340—21no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336—21no—
82#336—21no—
83#336—21no—
84#336—21no—
85#336—21no—
86#336C2×C411yescharacteristic
87#336C2×C411yescharacteristic
88#336D411yescharacteristic
89#336D411yescharacteristic
90#336D411yescharacteristic
91#336D411yescharacteristic
92C22×Q8C22⋊C411yescharacteristic
93C22×C8—21no—
94C22×C8—21no—
95C22×C8—21no—
96C22×C8—21no—
97C22×C8—21no—
98C22×C8—21no—
99C22×C8—41no—
100C22×C8—41no—
101#125—41no—
102#125—41no—
103#125—41no—
104#125—41no—
105C4×Q8—21no—
106C4×Q8—21no—
107C4×Q8D812yes—
108C4×Q8SD1612yes—
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⋊C4C22⋊C411yescharacteristic
121C2×C4⋊C4C22⋊C411yescharacteristic
122C2×C4⋊C4C22⋊C411yescharacteristic
123C2×C42—21no—
124C2×C42—21no—
125C2×C42C22×C411yescharacteristic
126C2×C42C2×D411yescharacteristic
127C2×C42C2×D411yescharacteristic
128C2×C42C2×D411yescharacteristic
129C2×C42C2×D411yescharacteristic
130C2×C42#4111yescharacteristic
131C2×C42#4111yescharacteristic
132#107—42no—
133#106—42no—
134C4⋊C8—42no—
135C4⋊C8—42no—
136C4⋊C8—42no—
137C4⋊C8—42no—
138C4⋊C8—42no—
139C4⋊C8—41no—
140C4⋊C8—41no—
141C4⋊C8—41no—
142C4⋊C8—41no—
143#103—42no—
144#103—42no—
145#97—42no—
146#97—41no—
147#97—41no—
148C4×C8—22no—
149C4×C8—41no—
150C4×C8—42no—
151#95—21no—
152#95—21no—
153#95—21no—
154#95—21no—
155#95—21no—
156#95—21no—
157#95—21no—
158#95—41no—
159#95—41no—
160C2×Q8—21no—
161C2×Q8—41no—
162C2×Q8—41no—
163C2×Q8#10212yes—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4C2×C22⋊C411yescharacteristic
171C22×C4C4×D411yescharacteristic
172C22×C4C4×D411yescharacteristic
173C22×C4#12011yescharacteristic
174C22×C4#12111yescharacteristic
175C22×C4#12111yescharacteristic
176C22×C4#12311yescharacteristic
177C2×C8—22no—
178C2×C8—41no—
179C2×C8—41no—
180C2×C8—42no—
181C2×C8—41no—
182C2×C8—41no—
183C2×C8—41no—
184C2×C8—41no—
185C2×C8—41no—
186C2×C8—41no—
187C2×C8—41no—
188C2×C8—41no—
189C2×C8—41no—
190C2×C8—41no—
191C2×C8—41no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8—41no—
195C2×C8—41no—
196C2×C8—81no—
197C2×C8—81no—
198C2×C8—81no—
199C2×C8—81no—
200C2×C8—81no—
201C4⋊C4—21no—
202C4⋊C4—22no—
203C4⋊C4—22no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—42no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—81no—
216C4⋊C4—81no—
217C4⋊C4—81no—
218C4⋊C4—81no—
219C4⋊C4—81no—
220C4⋊C4—81no—
221C4⋊C4—81no—
222C4⋊C4#10212yes—
223C42—21no—
224C42—21no—
225C42—22no—
226C42—22no—
227C42—41no—
228C42—41no—
229C42—41no—
230C42—41no—
231C42—41no—
232C42—41no—
233C42—41no—
234C42C2×D811yescharacteristic
235C42C2×SD1611yescharacteristic
236C42AGL(1,ℤ/8)11yescharacteristic
237C42#13711yescharacteristic
238C23#38611yescharacteristic
239Q8—42no—
240Q8—81no—
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—22no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4C2×#10211yescharacteristic
277C2×C4#41711yescharacteristic
278C2×C4#44311yescharacteristic
279C2×C4#44411yescharacteristic
280C2×C4#44711yescharacteristic
281C2×C4#44811yescharacteristic
282C2×C4#48011yescharacteristic
283C2×C4#48111yescharacteristic
284C8—42no—
285C8—81no—
286C8—81no—
287C8—81no—
288C8—81no—
289C8—81no—
290C8—82no—
291C8—161no—
292C22#187411yescharacteristic
293C22#187611yescharacteristic
294C22#188111yescharacteristic
295C22#190511yescharacteristic
296C22#190611yescharacteristic
297C22#190911yescharacteristic
298C22#191511yescharacteristic
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—21no—
305C4—21no—
306C4—21no—
307C4—42no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—42no—
312C4—81no—
313C4—81no—
314C4—161no—
315C4—161no—
316C2#899511yescharacteristic
317C2#918011yescharacteristic
318C2#919511yescharacteristic
319C2#926611yescharacteristic
320C2#928011yescharacteristic
321C2#933611yescharacteristic
322C2#936911yescharacteristic
subgroupG/H
center, socle, prime radicalC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
LCSG ▷ C2×C42 ▷ 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
#298712
#227372
#77232
#76802
#75812
#70412
#70182