Finite Group Databasebeta

← #100877

Subgroups — #100877

Order 512.

347 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 347 conjugacy classes of subgroups — too many to draw. Only its 86 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#29226C211yesmaximal, characteristic
2#23371C211yesmaximal, characteristic
3#9905C211yesmaximal, characteristic
4#9905C211yesmaximal, characteristic
5#7636C211yesmaximal, characteristic
6#7042C211yesmaximal, characteristic
7#7042C211yesmaximal, characteristic
8#2868C2211yescharacteristic
9C4×#125C2211yescharacteristic
10#2099—21no—
11#2099—21no—
12#1992C412yes—
13#1987—21no—
14#1987—21no—
15#1940—21no—
16#1939—21no—
17#1917—21no—
18#1917—21no—
19#1916—21no—
20#1916—21no—
21#1836C412yes—
22#1831C2211yescharacteristic
23#1831C2211yescharacteristic
24#1767C2211yescharacteristic
25#1767C2211yescharacteristic
26#1767C2211yescharacteristic
27#1296—21no—
28#1296—21no—
29#1296—21no—
30#1296—21no—
31#1271—21no—
32#1271—21no—
33C2×C4⋊Q8—21no—
34C2×C4⋊Q8—21no—
35C2×C4⋊Q8—21no—
36C2×#125C2×C411yescharacteristic
37C2×C4⋊C8—21no—
38C2×C4⋊C8—21no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8D411yescharacteristic
43C2×C4⋊C8D411yescharacteristic
44C2×C4⋊C8D411yescharacteristic
45C2×C4⋊C8D411yescharacteristic
46C2×#97—21no—
47C2×#97—21no—
48C2×#97—21no—
49C2×#97C2×C412yes—
50C2×C4×C8—21no—
51#389D411yescharacteristic
52#389D411yescharacteristic
53#387—21no—
54#387—21no—
55#384—21no—
56#384—21no—
57#384—21no—
58#384C2×C412yes—
59#382C2×C411yescharacteristic
60C4×C4⋊C4—21no—
61C4×C4⋊C4—21no—
62C4×C4⋊C4D411yescharacteristic
63C4×C4⋊C4D411yescharacteristic
64C43C2311yescharacteristic
65#340—22no—
66#340—22no—
67#340—22no—
68#340—22no—
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—
80C22×Q8—41no—
81C22×C8—22no—
82C22×C8—21no—
83C22×C8—21no—
84C22×C8—21no—
85C22×C8—21no—
86C22×C8—41no—
87C22×C8—41no—
88C4⋊Q8—42no—
89C4⋊Q8—42no—
90C4⋊Q8—81no—
91C4⋊Q8—81no—
92C4⋊Q8—81no—
93C4⋊Q8—81no—
94#125—22no—
95#125—41no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—22no—
101C2×C4⋊C4—22no—
102C2×C4⋊C4—22no—
103C2×C4⋊C4—41no—
104C2×C4⋊C4—41no—
105C2×C4⋊C4—41no—
106C2×C4⋊C4C22⋊C411yescharacteristic
107C2×C4⋊C4C22⋊C411yescharacteristic
108C2×C4⋊C4C22⋊C411yescharacteristic
109C2×C4⋊C4C22⋊C411yescharacteristic
110C2×C42—21no—
111C2×C42—21no—
112C2×C42C22×C411yescharacteristic
113C2×C42C2×D411yescharacteristic
114C2×C42C2×D411yescharacteristic
115C2×C42C2×D411yescharacteristic
116C2×C42C2×D411yescharacteristic
117C2×C42#4111yescharacteristic
118C2×C42#4111yescharacteristic
119C4⋊C8—22no—
120C4⋊C8—22no—
121C4⋊C8—41no—
122C4⋊C8—41no—
123C4⋊C8—41no—
124C4⋊C8—41no—
125C4⋊C8—41no—
126C4⋊C8—41no—
127C4⋊C8—41no—
128C4⋊C8—41no—
129C4⋊C8—81no—
130C4⋊C8—81no—
131#97—42no—
132#97—81no—
133#97—81no—
134#97—81no—
135C4×C8—81no—
136#95—21no—
137#95—21no—
138#95—21no—
139#95—21no—
140#95—21no—
141#95—21no—
142C2×Q8—82no—
143C2×Q8—82no—
144C2×Q8—82no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—42no—
150C22×C4C2×C22⋊C411yescharacteristic
151C22×C4C4×D411yescharacteristic
152C22×C4C4×D411yescharacteristic
153C22×C4#12011yescharacteristic
154C22×C4#12111yescharacteristic
155C22×C4#12111yescharacteristic
156C22×C4#12311yescharacteristic
157C2×C8—42no—
158C2×C8—42no—
159C2×C8—42no—
160C2×C8—42no—
161C2×C8—42no—
162C2×C8—41no—
163C2×C8—41no—
164C2×C8—41no—
165C2×C8—41no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8—41no—
171C2×C8—41no—
172C2×C8—41no—
173C2×C8—41no—
174C2×C8—81no—
175C2×C8—81no—
176C2×C8—81no—
177C2×C8—81no—
178C4⋊C4—21no—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—42no—
182C4⋊C4—42no—
183C4⋊C4—41no—
184C4⋊C4—41no—
185C4⋊C4—44no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—82no—
191C4⋊C4—82no—
192C4⋊C4—81no—
193C4⋊C4—81no—
194C4⋊C4—81no—
195C4⋊C4—81no—
196C4⋊C4—81no—
197C4⋊C4—81no—
198C4⋊C4#10112yes—
199C42—21no—
200C42—21no—
201C42—21no—
202C42—21no—
203C42—21no—
204C42—21no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—41no—
212C42—41no—
213C42—41no—
214C42—41no—
215C42—41no—
216C23#38611yescharacteristic
217Q8—164no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—82no—
246C2×C4—82no—
247C2×C4—82no—
248C2×C4C2×#10111yescharacteristic
249C2×C4#41311yescharacteristic
250C2×C4#45411yescharacteristic
251C2×C4#45411yescharacteristic
252C2×C4#45511yescharacteristic
253C2×C4#45511yescharacteristic
254C2×C4#45611yescharacteristic
255C2×C4#45611yescharacteristic
256C2×C4#47111yescharacteristic
257C2×C4#47111yescharacteristic
258C2×C4#47211yescharacteristic
259C2×C4#47211yescharacteristic
260C8—82no—
261C8—82no—
262C8—82no—
263C8—81no—
264C8—81no—
265C8—81no—
266C8—81no—
267C22#188211yescharacteristic
268C22#188211yescharacteristic
269C22#188811yescharacteristic
270C22#190111yescharacteristic
271C22#190711yescharacteristic
272C22#190711yescharacteristic
273C22#190911yescharacteristic
274C4—21no—
275C4—21no—
276C4—21no—
277C4—21no—
278C4—21no—
279C4—21no—
280C4—41no—
281C4—42no—
282C4—41no—
283C4—41no—
284C4—81no—
285C4—81no—
286C4—81no—
287C4—162no—
288C4#166211yescharacteristic
289C4#166311yescharacteristic
290C4#166411yescharacteristic
291C4#166411yescharacteristic
292C2#900411yescharacteristic
293C2#935511yescharacteristic
294C2#935611yescharacteristic
295C2#937511yescharacteristic
296C2#937511yescharacteristic
297C2#943811yescharacteristic
298C2#945611yescharacteristic
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
#292262
#233712
#99052
#76362
#70422