Finite Group Databasebeta

← #99490

Subgroups — #99490

Order 512.

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

normal subgroups only

This group has 323 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#22824C211yesmaximal, characteristic
2#9604C211yesmaximal, characteristic
3#8809C211yesmaximal, characteristic
4#8568C211yesmaximal, characteristic
5#7562C211yesmaximal, characteristic
6#7031C211yesmaximal, characteristic
7#7027C211yesmaximal, characteristic
8#2295C2211yescharacteristic
9#1985—21no—
10#1917—21no—
11#1916—21no—
12#1842C2211yescharacteristic
13#1842C2211yescharacteristic
14#1832—21no—
15#1771—21no—
16#1768—21no—
17#1767C2211yescharacteristic
18C4×C4⋊C8C2211yescharacteristic
19C4×C4⋊C8C2211yescharacteristic
20#1744C2211yescharacteristic
21C2×#335—21no—
22C2×#334—21no—
23C2×#334—21no—
24C2×Q8⋊C8—21no—
25#1279—21no—
26#1277—21no—
27#1272C411yescharacteristic
28#1272C411yescharacteristic
29#1271C411yescharacteristic
30#1271C411yescharacteristic
31C2×C4×Q8D411yescharacteristic
32C2×C4⋊C8—21no—
33C2×C4⋊C8—21no—
34C2×C4⋊C8—21no—
35C2×C4⋊C8—21no—
36C2×C4⋊C8—21no—
37C2×C4⋊C8—21no—
38C2×C4⋊C8—21no—
39C2×C4⋊C8D411yescharacteristic
40C2×C4⋊C8D411yescharacteristic
41C2×C4⋊C8D411yescharacteristic
42C2×C4⋊C8D411yescharacteristic
43C2×#97—21no—
44C2×#97—21no—
45C2×C4×C8—21no—
46C2×C4×C8—21no—
47C2×C4×C8—21no—
48C2×C4×C8—21no—
49#391C2×C411yescharacteristic
50#391Q811yescharacteristic
51#389C2×C411yescharacteristic
52#389Q811yescharacteristic
53#387—21no—
54#387—21no—
55C4×C4⋊C4—21no—
56C4×C4⋊C4D411yescharacteristic
57#376—21no—
58C43C2311yescharacteristic
59#336—21no—
60#336—21no—
61#336—21no—
62#336—21no—
63#336—21no—
64#336—21no—
65#336—21no—
66#336—21no—
67#336—21no—
68#336C2×C411yescharacteristic
69#336C2×C411yescharacteristic
70#336C2×C411yescharacteristic
71#336C2×C411yescharacteristic
72#335—42no—
73#334—42no—
74#334—42no—
75Q8⋊C8—42no—
76C22×Q8C4⋊C411yescharacteristic
77C22×C8—21no—
78C22×C8—21no—
79C22×C8—21no—
80C22×C8—21no—
81C22×C8—21no—
82C22×C8—21no—
83C22×C8—21no—
84C22×C8—21no—
85C22×C8—41no—
86C22×C8—41no—
87C4×Q8—21no—
88C4×Q8—21no—
89C4×Q8—21no—
90C4×Q8—21no—
91C2×C4⋊C4—21no—
92C2×C4⋊C4—21no—
93C2×C4⋊C4—21no—
94C2×C4⋊C4C4⋊C411yescharacteristic
95C2×C4⋊C4C4⋊C411yescharacteristic
96C2×C4⋊C4C4⋊C411yescharacteristic
97C2×C42—21no—
98C2×C42—21no—
99C2×C42C22×C411yescharacteristic
100C2×C42C2×D411yescharacteristic
101C2×C42C2×D411yescharacteristic
102C2×C42C2×D411yescharacteristic
103C2×C42C2×Q811yescharacteristic
104C2×C42#4111yescharacteristic
105C2×C42#4111yescharacteristic
106C4⋊C8—22no—
107C4⋊C8—21no—
108C4⋊C8—21no—
109C4⋊C8—21no—
110C4⋊C8—41no—
111C4⋊C8—41no—
112C4⋊C8—41no—
113C4⋊C8—41no—
114C4⋊C8—41no—
115C4⋊C8—42no—
116C4⋊C8—41no—
117C4⋊C8—41no—
118C4⋊C8—41no—
119C4⋊C8—41no—
120C4⋊C8—41no—
121C4⋊C8—41no—
122C4⋊C8—41no—
123C4⋊C8—41no—
124C4⋊C8SD1612yes—
125#97—41no—
126#97—41no—
127#97—81no—
128C4×C8—22no—
129C4×C8—22no—
130C4×C8—41no—
131C4×C8—41no—
132C4×C8—41no—
133C4×C8—41no—
134C4×C8—81no—
135#95—21no—
136#95—21no—
137#95—21no—
138#95—21no—
139#95—21no—
140#95—21no—
141#95—21no—
142C2×Q8—21no—
143C2×Q8—21no—
144C2×Q8—41no—
145C2×Q8—41no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4C2×C4⋊C411yescharacteristic
151C22×C4C4×D411yescharacteristic
152C22×C4C4×D411yescharacteristic
153C22×C4#12011yescharacteristic
154C22×C4C22⋊Q811yescharacteristic
155C22×C4C22⋊Q811yescharacteristic
156C22×C4#12311yescharacteristic
157C2×C8—22no—
158C2×C8—22no—
159C2×C8—22no—
160C2×C8—22no—
161C2×C8—41no—
162C2×C8—41no—
163C2×C8—41no—
164C2×C8—41no—
165C2×C8—41no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—41no—
169C2×C8—42no—
170C2×C8—41no—
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—81no—
183C2×C8—81no—
184C2×C8—81no—
185C2×C8—81no—
186C2×C8—81no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—81no—
196C42—21no—
197C42—21no—
198C42—21no—
199C42—21no—
200C42—41no—
201C42—41no—
202C42—41no—
203C42—41no—
204C42—41no—
205C42—41no—
206C42—41no—
207C42C2×SD1611yescharacteristic
208C42#13511yescharacteristic
209C42#13511yescharacteristic
210C42#13511yescharacteristic
211C42AGL(1,ℤ/8)11yescharacteristic
212C42#13711yescharacteristic
213C42#13711yescharacteristic
214C42#13711yescharacteristic
215C23#38511yescharacteristic
216Q8—42no—
217Q8—81no—
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—21no—
230C2×C4—21no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
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#42711yescharacteristic
244C2×C4#42811yescharacteristic
245C2×C4C4×SD1611yescharacteristic
246C2×C4#44111yescharacteristic
247C2×C4#44311yescharacteristic
248C2×C4#44411yescharacteristic
249C2×C4#44811yescharacteristic
250C2×C4#44911yescharacteristic
251C2×C4#45211yescharacteristic
252C2×C4#45211yescharacteristic
253C2×C4#45311yescharacteristic
254C2×C4#45611yescharacteristic
255C2×C4#47511yescharacteristic
256C2×C4#47911yescharacteristic
257C2×C4#48211yescharacteristic
258C2×C4#48511yescharacteristic
259C8—42no—
260C8—42no—
261C8—42no—
262C8—42no—
263C8—81no—
264C8—82no—
265C8—81no—
266C8—81no—
267C8—81no—
268C8—161no—
269C22#185411yescharacteristic
270C22#185811yescharacteristic
271C22#185911yescharacteristic
272C22#186111yescharacteristic
273C22#186511yescharacteristic
274C22#186611yescharacteristic
275C22#186811yescharacteristic
276C4—21no—
277C4—21no—
278C4—21no—
279C4—21no—
280C4—21no—
281C4—21no—
282C4—21no—
283C4—21no—
284C4—21no—
285C4—21no—
286C4—41no—
287C4—81no—
288C4—81no—
289C4—81no—
290C4—81no—
291C4#162211yescharacteristic
292C4#163011yescharacteristic
293C4#165211yescharacteristic
294C4#165311yescharacteristic
295C2#886311yescharacteristic
296C2#887611yescharacteristic
297C2#888111yescharacteristic
298C2#888711yescharacteristic
299C2#890311yescharacteristic
300C2#891611yescharacteristic
301C2#893111yescharacteristic
subgroupG/H
centerC22×C4#120
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
socle, prime radicalC23#385
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ 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
#228242
#96042
#88092
#85682
#75622
#70312
#70272