Finite Group Databasebeta

← #100466

Subgroups — #100466

Order 512.

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

normal subgroups only

This group has 425 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#33069C211yesmaximal, characteristic
2#20520C211yesmaximal, characteristic
3#9891C211yesmaximal, characteristic
4#8175C211yesmaximal, characteristic
5#7683C211yesmaximal, characteristic
6#7049C211yesmaximal, characteristic
7#7030C211yesmaximal, characteristic
8C2×#446—21no—
9#2859C2211yescharacteristic
10C42×Q8C2211yescharacteristic
11#1947C411yescharacteristic
12#1947C411yescharacteristic
13#1921—21no—
14#1921—21no—
15#1863—21no—
16#1863—21no—
17#1831C2211yescharacteristic
18#1803C411yescharacteristic
19#1803C411yescharacteristic
20#1771—22no—
21C8×C4⋊C4—21no—
22#1767—21no—
23#1767C2211yescharacteristic
24#1767C2211yescharacteristic
25#1744C2211yescharacteristic
26C4×#97—21no—
27C4×#97C2211yescharacteristic
28C2×Q8⋊C8—21no—
29#1295—21no—
30#1295—21no—
31#1279—21no—
32#1271—22no—
33C2×#125—21no—
34C2×C4×Q8C2×C411yescharacteristic
35C2×C4×Q8D411yescharacteristic
36C2×C4×Q8D411yescharacteristic
37#446—24no—
38#446—24no—
39C2×#107—21no—
40C2×#107—21no—
41C2×C4⋊C8—22no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8C2×C411yescharacteristic
45C2×C4⋊C8C2×C411yescharacteristic
46C2×#103—21no—
47C2×#103—21no—
48C2×#97—22no—
49C2×#97—21no—
50C2×#97—21no—
51C2×#97—21no—
52C2×#97D411yescharacteristic
53C2×#97D411yescharacteristic
54C2×C4×C8—21no—
55C2×C4×C8—21no—
56C2×C4×C8—22no—
57#389—21no—
58#389—21no—
59#389—21no—
60#389—21no—
61#384C2×C411yescharacteristic
62#384C2×C411yescharacteristic
63#382—21no—
64C4×C4⋊C4—21no—
65C4×C4⋊C4—21no—
66C4×C4⋊C4—21no—
67C4×C4⋊C4C2×C411yescharacteristic
68C4×C4⋊C4D411yescharacteristic
69C4×C4⋊C4D411yescharacteristic
70C43—21no—
71C43C2311yescharacteristic
72#340—21no—
73#340—21no—
74#340—21no—
75#340—21no—
76#336—22no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336—21no—
82#336D412yes—
83Q8⋊C8—24no—
84C22×Q8C22⋊C411yescharacteristic
85C22×C8—21no—
86C22×C8—21no—
87C22×C8—22no—
88C22×C8—21no—
89C22×C8—21no—
90C22×C8—41no—
91C22×C8—41no—
92#125—82no—
93C4×Q8—22no—
94C4×Q8—22no—
95C4×Q8—22no—
96C4×Q8—22no—
97C4×Q8—41no—
98C4×Q8—41no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—41no—
109C2×C4⋊C4—41no—
110C2×C4⋊C4C22⋊C411yescharacteristic
111C2×C4⋊C4C22⋊C411yescharacteristic
112C2×C4⋊C4C22⋊C411yescharacteristic
113C2×C42—21no—
114C2×C42—21no—
115C2×C42—21no—
116C2×C42—21no—
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—42no—
127#107—42no—
128C4⋊C8—28no—
129C4⋊C8—22no—
130C4⋊C8—22no—
131C4⋊C8—22no—
132C4⋊C8—41no—
133C4⋊C8—41no—
134C4⋊C8—41no—
135#103—42no—
136#103—42no—
137#97—28no—
138#97—21no—
139#97—21no—
140#97—21no—
141#97—42no—
142#97—41no—
143#97—41no—
144#97—41no—
145#97—41no—
146#97Q1612yes—
147C4×C8—22no—
148C4×C8—22no—
149C4×C8—22no—
150C4×C8—41no—
151C4×C8—44no—
152#95—21no—
153#95—21no—
154#95—21no—
155#95—41no—
156#95—41no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8—21no—
162C2×Q8#10412yes—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—41no—
168C22×C4—41no—
169C22×C4C2×C22⋊C411yescharacteristic
170C22×C4C4×D411yescharacteristic
171C22×C4C4×D411yescharacteristic
172C22×C4#12011yescharacteristic
173C22×C4#12111yescharacteristic
174C22×C4#12111yescharacteristic
175C22×C4#12311yescharacteristic
176C2×C8—22no—
177C2×C8—22no—
178C2×C8—22no—
179C2×C8—22no—
180C2×C8—24no—
181C2×C8—42no—
182C2×C8—41no—
183C2×C8—41no—
184C2×C8—42no—
185C2×C8—42no—
186C2×C8—42no—
187C2×C8—41no—
188C2×C8—41no—
189C2×C8—41no—
190C2×C8—41no—
191C2×C8—41no—
192C2×C8—41no—
193C2×C8—81no—
194C2×C8—81no—
195C2×C8—81no—
196C2×C8—81no—
197C4⋊C4—24no—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—21no—
201C4⋊C4—42no—
202C4⋊C4—42no—
203C4⋊C4—42no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—41no—
208C4⋊C4—81no—
209C4⋊C4—81no—
210C4⋊C4—81no—
211C4⋊C4—82no—
212C4⋊C4—82no—
213C4⋊C4#10112yes—
214C4⋊C4#10412yes—
215C4⋊C4#10412yes—
216C42—24no—
217C42—21no—
218C42—21no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—41no—
224C42—41no—
225C42—41no—
226C42—42no—
227C42—42no—
228C42—42no—
229C42—81no—
230C42—81no—
231C42C2×Q1611yescharacteristic
232C42#13511yescharacteristic
233C42#13711yescharacteristic
234C42#13711yescharacteristic
235C23#38611yescharacteristic
236Q8—22no—
237Q8—22no—
238Q8—41no—
239Q8—41no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—81no—
268C2×C4—81no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4C2×#10111yescharacteristic
274C2×C4#41311yescharacteristic
275C2×C4C2×#10411yescharacteristic
276C2×C4C2×#10411yescharacteristic
277C2×C4C2×#10411yescharacteristic
278C2×C4#42111yescharacteristic
279C2×C4C4×Q1611yescharacteristic
280C2×C4#44111yescharacteristic
281C2×C4#45111yescharacteristic
282C2×C4#45211yescharacteristic
283C2×C4#46211yescharacteristic
284C2×C4#46411yescharacteristic
285C8—24no—
286C8—42no—
287C8—44no—
288C8—82no—
289C8—82no—
290C8—81no—
291C8—81no—
292C22#187111yescharacteristic
293C22#187811yescharacteristic
294C22#188111yescharacteristic
295C22#189611yescharacteristic
296C22#190111yescharacteristic
297C22#190311yescharacteristic
298C22#190611yescharacteristic
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—21no—
305C4—41no—
306C4—42no—
307C4—41no—
308C4—42no—
309C4—42no—
310C4—41no—
311C4—42no—
312C4—161no—
313C4—161no—
314C4#152411yescharacteristic
315C4#152611yescharacteristic
316C4#152811yescharacteristic
317C4#152911yescharacteristic
318C2#899011yescharacteristic
319C2#912211yescharacteristic
320C2#916111yescharacteristic
321C2#923211yescharacteristic
322C2#925011yescharacteristic
323C2#931111yescharacteristic
324C2#935111yescharacteristic
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
#330692
#205202
#98912
#81752
#76832
#70492
#70302