Finite Group Databasebeta

← #100705

Subgroups — #100705

Order 512.

324 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 80 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#29989C211yesmaximal, characteristic
2#22831C211yesmaximal, characteristic
3#7720C211yesmaximal, characteristic
4#7683C211yesmaximal, characteristic
5#7581C211yesmaximal, characteristic
6#7041C211yesmaximal, characteristic
7#7018C211yesmaximal, characteristic
8#2859C2211yescharacteristic
9#2295C2211yescharacteristic
10#2100C411yescharacteristic
11#2099C411yescharacteristic
12#2096C411yescharacteristic
13#2095C411yescharacteristic
14#2059—21no—
15#2026—21no—
16#1985—21no—
17#1949—21no—
18#1917—21no—
19#1916—21no—
20#1840—21no—
21#1839C2211yescharacteristic
22#1831C2211yescharacteristic
23#1831C2211yescharacteristic
24#1805—21no—
25#1771—21no—
26#1767C2211yescharacteristic
27#1746—21no—
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
37C2×#107—21no—
38C2×#106—21no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×#103—21no—
43C2×#103—21no—
44C2×#97—21no—
45C2×#97—21no—
46C2×C4×C8—21no—
47C2×C4×C8—21no—
48#391C2×C411yescharacteristic
49#391D411yescharacteristic
50#389—21no—
51#389—21no—
52#389—21no—
53#389—21no—
54#389C2×C411yescharacteristic
55#389D411yescharacteristic
56#387—21no—
57#387—21no—
58#384C2×C411yescharacteristic
59#384C2×C411yescharacteristic
60#382—21no—
61C4×C4⋊C4—21no—
62C4×C4⋊C4D411yescharacteristic
63#376—21no—
64C43C2311yescharacteristic
65#340—21no—
66#340—21no—
67#340—21no—
68#340—21no—
69#336—21no—
70#336—21no—
71#336—21no—
72#336—21no—
73#336—21no—
74#336—21no—
75#336—21no—
76#336—21no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336—21no—
82#336C2×C411yescharacteristic
83#336C2×C411yescharacteristic
84#336D411yescharacteristic
85#336D411yescharacteristic
86#336D411yescharacteristic
87#336D411yescharacteristic
88C22×Q8C22⋊C411yescharacteristic
89C22×C8—21no—
90C22×C8—21no—
91C22×C8—21no—
92C22×C8—21no—
93C22×C8—21no—
94C22×C8—21no—
95C22×C8—41no—
96C22×C8—41no—
97#125—81no—
98#125—81no—
99C4×Q8—21no—
100C4×Q8—21no—
101C4×Q8—21no—
102C4×Q8—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—41no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4C22⋊C411yescharacteristic
115C2×C4⋊C4C22⋊C411yescharacteristic
116C2×C4⋊C4C22⋊C411yescharacteristic
117C2×C42—21no—
118C2×C42—21no—
119C2×C42C22×C411yescharacteristic
120C2×C42C2×D411yescharacteristic
121C2×C42C2×D411yescharacteristic
122C2×C42C2×D411yescharacteristic
123C2×C42C2×D411yescharacteristic
124C2×C42#4111yescharacteristic
125C2×C42#4111yescharacteristic
126#107—81no—
127#106—81no—
128C4⋊C8—42no—
129C4⋊C8—41no—
130C4⋊C8—41no—
131C4⋊C8—41no—
132C4⋊C8—41no—
133#103—81no—
134#103—81no—
135#97—42no—
136#97—41no—
137#97—41no—
138C4×C8—22no—
139C4×C8—41no—
140C4×C8—42no—
141#95—21no—
142#95—21no—
143#95—21no—
144#95—21no—
145#95—21no—
146#95—21no—
147#95—21no—
148#95—41no—
149#95—41no—
150C2×Q8—21no—
151C2×Q8—21no—
152C2×Q8—41no—
153C2×Q8—41no—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—21no—
158C22×C4—41no—
159C22×C4—41no—
160C22×C4C2×C22⋊C411yescharacteristic
161C22×C4C4×D411yescharacteristic
162C22×C4C4×D411yescharacteristic
163C22×C4#12011yescharacteristic
164C22×C4#12111yescharacteristic
165C22×C4#12111yescharacteristic
166C22×C4#12311yescharacteristic
167C2×C8—22no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8—42no—
171C2×C8—41no—
172C2×C8—41no—
173C2×C8—41no—
174C2×C8—41no—
175C2×C8—41no—
176C2×C8—41no—
177C2×C8—41no—
178C2×C8—41no—
179C2×C8—41no—
180C2×C8—41no—
181C2×C8—41no—
182C2×C8—41no—
183C2×C8—41no—
184C2×C8—41no—
185C2×C8—41no—
186C2×C8—81no—
187C2×C8—81no—
188C2×C8—81no—
189C2×C8—81no—
190C2×C8—81no—
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—42no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—81no—
207C4⋊C4—81no—
208C4⋊C4—81no—
209C4⋊C4—82no—
210C4⋊C4—82no—
211C42—21no—
212C42—21no—
213C42—41no—
214C42—41no—
215C42—41no—
216C42—41no—
217C42—41no—
218C42—41no—
219C42—41no—
220C42—41no—
221C42—41no—
222C42#13511yescharacteristic
223C42#13511yescharacteristic
224C42#13711yescharacteristic
225C42#13711yescharacteristic
226C23#38611yescharacteristic
227Q8—42no—
228Q8—81no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
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—21no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—81no—
259C2×C4—81no—
260C2×C4—81no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4—81no—
264C2×C4#41611yescharacteristic
265C2×C4#41911yescharacteristic
266C2×C4#44311yescharacteristic
267C2×C4#44411yescharacteristic
268C2×C4#45211yescharacteristic
269C2×C4#45211yescharacteristic
270C2×C4#48511yescharacteristic
271C2×C4#48511yescharacteristic
272C8—42no—
273C8—81no—
274C8—81no—
275C8—81no—
276C8—81no—
277C8—81no—
278C8—82no—
279C8—161no—
280C22#187311yescharacteristic
281C22#187611yescharacteristic
282C22#188111yescharacteristic
283C22#190511yescharacteristic
284C22#190611yescharacteristic
285C22#191011yescharacteristic
286C22#191511yescharacteristic
287C4—21no—
288C4—21no—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—21no—
293C4—21no—
294C4—21no—
295C4—41no—
296C4—41no—
297C4—41no—
298C4—81no—
299C4—81no—
300C4—81no—
301C4—81no—
302C4—161no—
303C4—161no—
304C2#899411yescharacteristic
305C2#917811yescharacteristic
306C2#919411yescharacteristic
307C2#926611yescharacteristic
308C2#928211yescharacteristic
309C2#933611yescharacteristic
310C2#937011yescharacteristic
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
#299892
#228312
#77202
#76832
#75812
#70412
#70182