Finite Group Databasebeta

← #102200

Subgroups — #102200

Order 512.

378 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 98 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#33278C211yesmaximal, characteristic
2#9890C211yesmaximal, characteristic
3#9686C211yesmaximal, characteristic
4#8274C211yesmaximal, characteristic
5#7842C211yesmaximal, characteristic
6#7682C211yesmaximal, characteristic
7#7680C211yesmaximal, characteristic
8#2862C2211yescharacteristic
9#2859C2211yescharacteristic
10#1990C411yescharacteristic
11#1990C411yescharacteristic
12#1956C411yescharacteristic
13#1956C411yescharacteristic
14#1933—21no—
15#1933—21no—
16#1933—21no—
17#1933—21no—
18#1767C2211yescharacteristic
19#1767C2211yescharacteristic
20#1744C2211yescharacteristic
21C4×#97C2211yescharacteristic
22C42×C8C2211yescharacteristic
23C2×#335—21no—
24C2×#330—22no—
25C2×#322—21no—
26C2×#322—21no—
27#1295—22no—
28#1277—21no—
29#1272—22no—
30#1271—22no—
31C2×C4⋊Q8C2×C411yescharacteristic
32C2×C4⋊Q8C2×C411yescharacteristic
33C2×#125—21no—
34C2×C4⋊C8—21no—
35C2×C4⋊C8—21no—
36C2×#103—21no—
37C2×#103—21no—
38C2×#103—21no—
39C2×#103—21no—
40C2×#97—21no—
41C2×#97—21no—
42C2×#97—21no—
43C2×#97D412yes—
44C2×C4×C8—21no—
45C2×C4×C8—21no—
46C2×C4×C8C2×C411yescharacteristic
47C2×C4×C8C2×C411yescharacteristic
48C2×C4×C8D411yescharacteristic
49C2×C4×C8D411yescharacteristic
50C2×C4×C8D411yescharacteristic
51C2×C4×C8D411yescharacteristic
52#391—21no—
53#391—21no—
54#391—21no—
55#391—21no—
56#389—21no—
57#389—21no—
58#389—21no—
59#389—21no—
60#384C2×C411yescharacteristic
61#384C2×C411yescharacteristic
62#382—21no—
63#382—21no—
64#382—21no—
65C43C2311yescharacteristic
66#340—21no—
67#340—21no—
68#340—21no—
69#340—21no—
70#336—21no—
71#336—21no—
72#336—21no—
73#336D412yes—
74#335—24no—
75#330—44no—
76#322—24no—
77#322—24no—
78C22×Q8—21no—
79C22×Q8—21no—
80C22×C8—22no—
81C22×C8—22no—
82C22×C8—41no—
83C22×C8—41no—
84C22×C8C22⋊C411yescharacteristic
85C22×C8C22⋊C411yescharacteristic
86C22×C8C22⋊C411yescharacteristic
87C22×C8C22⋊C411yescharacteristic
88C4⋊Q8—41no—
89C4⋊Q8—41no—
90C4⋊Q8—41no—
91C4⋊Q8—41no—
92#125—42no—
93#125—42no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—41no—
105C2×C4⋊C4—41no—
106C2×C42C22×C411yescharacteristic
107C2×C42C2×D411yescharacteristic
108C2×C42C2×D411yescharacteristic
109C2×C42C2×D411yescharacteristic
110C2×C42C2×D411yescharacteristic
111C2×C42#4111yescharacteristic
112C2×C42#4111yescharacteristic
113C4⋊C8—22no—
114C4⋊C8—22no—
115C4⋊C8—41no—
116C4⋊C8—41no—
117#103—42no—
118#103—42no—
119#103—42no—
120#103—42no—
121#97—22no—
122#97—22no—
123#97—42no—
124#97—42no—
125#97—42no—
126C4×C8—22no—
127C4×C8—22no—
128C4×C8—22no—
129C4×C8—22no—
130C4×C8—22no—
131C4×C8—22no—
132C4×C8—22no—
133C4×C8—41no—
134C4×C8—41no—
135C4×C8—41no—
136#95—41no—
137#95—41no—
138#95—41no—
139#95—41no—
140#95—41no—
141#95—41no—
142C2×Q8—41no—
143C2×Q8—41no—
144C2×Q8—41no—
145C2×Q8—41no—
146C2×Q8—41no—
147C2×Q8—41no—
148C2×Q8—42no—
149C2×Q8—81no—
150C2×Q8—81no—
151C22×C4—41no—
152C22×C4—41no—
153C22×C4—41no—
154C22×C4—41no—
155C22×C4C2×C22⋊C411yescharacteristic
156C22×C4C4×D411yescharacteristic
157C22×C4C4×D411yescharacteristic
158C22×C4#12111yescharacteristic
159C22×C4#12111yescharacteristic
160C22×C4#12411yescharacteristic
161C22×C4#12711yescharacteristic
162C2×C8—21no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—24no—
169C2×C8—24no—
170C2×C8—21no—
171C2×C8—21no—
172C2×C8—21no—
173C2×C8—42no—
174C2×C8—42no—
175C2×C8—42no—
176C2×C8—42no—
177C2×C8—42no—
178C2×C8—42no—
179C2×C8—81no—
180C2×C8—81no—
181C2×C8—81no—
182C2×C8—81no—
183C2×C8#10412yes—
184C2×C8#10412yes—
185C2×C8#10412yes—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—42no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—81no—
196C4⋊C4—81no—
197C4⋊C4—81no—
198C4⋊C4—81no—
199C4⋊C4—82no—
200C4⋊C4—81no—
201C4⋊C4—81no—
202C42—21no—
203C42—21no—
204C42—21no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—22no—
209C42—22no—
210C42—41no—
211C42AGL(1,ℤ/8)12yes—
212C42#13712yes—
213C23#39011yescharacteristic
214Q8—81no—
215Q8—81no—
216Q8—81no—
217Q8—81no—
218Q8—162no—
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—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—81no—
233C2×C4—81no—
234C2×C4—81no—
235C2×C4—81no—
236C2×C4—81no—
237C2×C4—81no—
238C2×C4—81no—
239C2×C4—81no—
240C2×C4—81no—
241C2×C4—81no—
242C2×C4—81no—
243C2×C4—81no—
244C2×C4#41311yescharacteristic
245C2×C4#41311yescharacteristic
246C2×C4C2×#10411yescharacteristic
247C2×C4C2×#10411yescharacteristic
248C2×C4C2×#10411yescharacteristic
249C2×C4#42111yescharacteristic
250C2×C4#44012yes—
251C2×C4#44412yes—
252C2×C4#46812yes—
253C2×C4#47312yes—
254C2×C4#49611yescharacteristic
255C2×C4#49711yescharacteristic
256C8—22no—
257C8—22no—
258C8—22no—
259C8—44no—
260C8—44no—
261C8—41no—
262C8—82no—
263C8—82no—
264C22#196211yescharacteristic
265C22#196711yescharacteristic
266C22#197311yescharacteristic
267C22#197511yescharacteristic
268C22#197611yescharacteristic
269C22#197911yescharacteristic
270C22#198011yescharacteristic
271C4—22no—
272C4—22no—
273C4—22no—
274C4—22no—
275C4—21no—
276C4—21no—
277C4—41no—
278C4—161no—
279C4—161no—
280C4—161no—
281C4—161no—
282C4#152411yescharacteristic
283C4#152411yescharacteristic
284C4#152911yescharacteristic
285C4#153211yescharacteristic
286C2#968711yescharacteristic
287C2#972211yescharacteristic
288C2#972711yescharacteristic
289C2#976311yescharacteristic
290C2#979011yescharacteristic
291C2#980911yescharacteristic
292C2#985111yescharacteristic
subgroupG/H
center, socle, prime radicalC23#390
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
#332782
#98902
#96862
#82742
#78422
#76822
#76802