Finite Group Databasebeta

← #99498

Subgroups — #99498

Order 512.

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

normal subgroups only

This group has 313 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#8787C211yesmaximal, 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×Q8⋊C8—21no—
23#1279—21no—
24#1277—21no—
25#1277—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—
73Q8⋊C8—42no—
74C22×Q8C4⋊C411yescharacteristic
75C22×C8—21no—
76C22×C8—21no—
77C22×C8—21no—
78C22×C8—21no—
79C22×C8—21no—
80C22×C8—21no—
81C22×C8—21no—
82C22×C8—21no—
83C22×C8—41no—
84C22×C8—41no—
85C4×Q8—21no—
86C4×Q8—21no—
87C4×Q8—21no—
88C4×Q8—21no—
89C2×C4⋊C4—21no—
90C2×C4⋊C4—21no—
91C2×C4⋊C4—21no—
92C2×C4⋊C4C4⋊C411yescharacteristic
93C2×C4⋊C4C4⋊C411yescharacteristic
94C2×C4⋊C4C4⋊C411yescharacteristic
95C2×C42—21no—
96C2×C42—21no—
97C2×C42C22×C411yescharacteristic
98C2×C42C2×D411yescharacteristic
99C2×C42C2×D411yescharacteristic
100C2×C42C2×D411yescharacteristic
101C2×C42C2×Q811yescharacteristic
102C2×C42#4111yescharacteristic
103C2×C42#4111yescharacteristic
104C4⋊C8—22no—
105C4⋊C8—21no—
106C4⋊C8—21no—
107C4⋊C8—21no—
108C4⋊C8—41no—
109C4⋊C8—41no—
110C4⋊C8—41no—
111C4⋊C8—42no—
112C4⋊C8—42no—
113C4⋊C8—41no—
114C4⋊C8—41no—
115C4⋊C8—41no—
116C4⋊C8—41no—
117C4⋊C8—41no—
118C4⋊C8—41no—
119C4⋊C8—41no—
120C4⋊C8—41no—
121C4⋊C8Q1612yes—
122#97—41no—
123#97—41no—
124#97—81no—
125C4×C8—41no—
126C4×C8—41no—
127C4×C8—41no—
128C4×C8—41no—
129C4×C8—41no—
130C4×C8—41no—
131C4×C8—81no—
132#95—21no—
133#95—21no—
134#95—21no—
135#95—21no—
136#95—21no—
137#95—21no—
138#95—21no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—41no—
142C2×Q8—41no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4C2×C4⋊C411yescharacteristic
148C22×C4C4×D411yescharacteristic
149C22×C4C4×D411yescharacteristic
150C22×C4#12011yescharacteristic
151C22×C4C22⋊Q811yescharacteristic
152C22×C4C22⋊Q811yescharacteristic
153C22×C4#12311yescharacteristic
154C2×C8—22no—
155C2×C8—22no—
156C2×C8—41no—
157C2×C8—41no—
158C2×C8—41no—
159C2×C8—41no—
160C2×C8—41no—
161C2×C8—41no—
162C2×C8—42no—
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—41no—
175C2×C8—41no—
176C2×C8—41no—
177C2×C8—41no—
178C2×C8—41no—
179C2×C8—81no—
180C2×C8—81no—
181C2×C8—81no—
182C2×C8—81no—
183C2×C8—81no—
184C4⋊C4—21no—
185C4⋊C4—21no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—81no—
193C42—21no—
194C42—21no—
195C42—21no—
196C42—21no—
197C42—41no—
198C42—41no—
199C42—41no—
200C42—41no—
201C42—41no—
202C42—41no—
203C42—41no—
204C42C2×Q1611yescharacteristic
205C42#13511yescharacteristic
206C42#13511yescharacteristic
207C42#13511yescharacteristic
208C42AGL(1,ℤ/8)11yescharacteristic
209C42AGL(1,ℤ/8)11yescharacteristic
210C42#13711yescharacteristic
211C42#13711yescharacteristic
212C23#38511yescharacteristic
213Q8—42no—
214Q8—81no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
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—41no—
229C2×C4—41no—
230C2×C4—41no—
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#42711yescharacteristic
241C2×C4#42811yescharacteristic
242C2×C4C4×Q1611yescharacteristic
243C2×C4#44011yescharacteristic
244C2×C4#44311yescharacteristic
245C2×C4#44411yescharacteristic
246C2×C4#44911yescharacteristic
247C2×C4#44911yescharacteristic
248C2×C4#45111yescharacteristic
249C2×C4#45211yescharacteristic
250C2×C4#45411yescharacteristic
251C2×C4#45511yescharacteristic
252C2×C4#47711yescharacteristic
253C2×C4#47911yescharacteristic
254C2×C4#48211yescharacteristic
255C2×C4#48511yescharacteristic
256C8—42no—
257C8—42no—
258C8—81no—
259C8—81no—
260C8—81no—
261C8—82no—
262C8—81no—
263C8—81no—
264C8—81no—
265C8—161no—
266C22#185411yescharacteristic
267C22#185811yescharacteristic
268C22#186011yescharacteristic
269C22#186111yescharacteristic
270C22#186311yescharacteristic
271C22#186611yescharacteristic
272C22#186811yescharacteristic
273C4—21no—
274C4—21no—
275C4—21no—
276C4—21no—
277C4—21no—
278C4—21no—
279C4—21no—
280C4—21no—
281C4—21no—
282C4—21no—
283C4—41no—
284C4—81no—
285C4—81no—
286C4—81no—
287C4—81no—
288C4#162811yescharacteristic
289C4#163611yescharacteristic
290C4#164011yescharacteristic
291C4#164411yescharacteristic
292C2#886311yescharacteristic
293C2#887711yescharacteristic
294C2#887911yescharacteristic
295C2#889511yescharacteristic
296C2#890311yescharacteristic
297C2#891711yescharacteristic
298C2#893311yescharacteristic
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
#87872
#85682
#75622
#70312
#70272