Finite Group Databasebeta

← #100482

Subgroups — #100482

Order 512.

377 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 377 conjugacy classes of subgroups — too many to draw. Only its 94 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#21345C211yesmaximal, characteristic
3#9891C211yesmaximal, characteristic
4#8175C211yesmaximal, characteristic
5#7683C211yesmaximal, characteristic
6#7049C211yesmaximal, characteristic
7#7030C211yesmaximal, characteristic
8#2859C2211yescharacteristic
9C42×Q8C2211yescharacteristic
10#1984—21no—
11#1947C411yescharacteristic
12#1947C411yescharacteristic
13#1939—21no—
14#1921—21no—
15#1921—21no—
16#1917—22no—
17#1863—21no—
18#1863—21no—
19#1831C2211yescharacteristic
20#1803C411yescharacteristic
21#1803C411yescharacteristic
22#1767—21no—
23#1767C2211yescharacteristic
24#1767C2211yescharacteristic
25#1745—21no—
26#1744C2211yescharacteristic
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
37C2×#107—21no—
38C2×#107—21no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8—22no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8C2×C411yescharacteristic
43C2×C4⋊C8C2×C411yescharacteristic
44C2×#103—21no—
45C2×#103—21no—
46C2×#97—21no—
47C2×#97—21no—
48C2×#97—21no—
49C2×#97D411yescharacteristic
50C2×#97D411yescharacteristic
51C2×C4×C8—21no—
52C2×C4×C8—21no—
53#389—21no—
54#389—21no—
55#389—21no—
56#389—21no—
57#384C2×C411yescharacteristic
58#384C2×C411yescharacteristic
59#382—21no—
60C4×C4⋊C4—21no—
61C4×C4⋊C4—21no—
62C4×C4⋊C4—21no—
63C4×C4⋊C4C2×C411yescharacteristic
64C4×C4⋊C4D411yescharacteristic
65C4×C4⋊C4D411yescharacteristic
66C43—21no—
67C43C2311yescharacteristic
68#340—21no—
69#340—21no—
70#340—21no—
71#340—21no—
72#336—22no—
73#336—22no—
74#336—22no—
75#336—21no—
76#336—21no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336D412yes—
81Q8⋊C8—24no—
82C22×Q8C22⋊C411yescharacteristic
83C22×C8—21no—
84C22×C8—21no—
85C22×C8—21no—
86C22×C8—21no—
87C22×C8—22no—
88C22×C8—41no—
89C22×C8—41no—
90#125—82no—
91C4×Q8—22no—
92C4×Q8—22no—
93C4×Q8—41no—
94C4×Q8—41no—
95C4×Q8—41no—
96C4×Q8—41no—
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—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—41no—
107C2×C4⋊C4—41no—
108C2×C4⋊C4C22⋊C411yescharacteristic
109C2×C4⋊C4C22⋊C411yescharacteristic
110C2×C4⋊C4C22⋊C411yescharacteristic
111C2×C42—21no—
112C2×C42—21no—
113C2×C42—21no—
114C2×C42—21no—
115C2×C42—21no—
116C2×C42—21no—
117C2×C42C22×C411yescharacteristic
118C2×C42C2×D411yescharacteristic
119C2×C42C2×D411yescharacteristic
120C2×C42C2×D411yescharacteristic
121C2×C42C2×D411yescharacteristic
122C2×C42#4111yescharacteristic
123C2×C42#4111yescharacteristic
124#107—42no—
125#107—42no—
126C4⋊C8—22no—
127C4⋊C8—41no—
128C4⋊C8—41no—
129C4⋊C8—41no—
130C4⋊C8—41no—
131C4⋊C8—41no—
132C4⋊C8—44no—
133#103—42no—
134#103—42no—
135#97—21no—
136#97—21no—
137#97—21no—
138#97—42no—
139#97—41no—
140#97—41no—
141#97—41no—
142#97—41no—
143#97Q1612yes—
144C4×C8—22no—
145C4×C8—41no—
146C4×C8—41no—
147C4×C8—41no—
148#95—21no—
149#95—21no—
150#95—21no—
151#95—41no—
152#95—41no—
153C2×Q8—21no—
154C2×Q8—21no—
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8#10112yes—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—41no—
164C22×C4—41no—
165C22×C4C2×C22⋊C411yescharacteristic
166C22×C4C4×D411yescharacteristic
167C22×C4C4×D411yescharacteristic
168C22×C4#12011yescharacteristic
169C22×C4#12111yescharacteristic
170C22×C4#12111yescharacteristic
171C22×C4#12311yescharacteristic
172C2×C8—22no—
173C2×C8—22no—
174C2×C8—41no—
175C2×C8—41no—
176C2×C8—41no—
177C2×C8—41no—
178C2×C8—42no—
179C2×C8—42no—
180C2×C8—42no—
181C2×C8—42no—
182C2×C8—41no—
183C2×C8—41no—
184C2×C8—41no—
185C2×C8—41no—
186C2×C8—41no—
187C2×C8—41no—
188C2×C8—42no—
189C2×C8—81no—
190C2×C8—81no—
191C2×C8—81no—
192C2×C8—81no—
193C4⋊C4—21no—
194C4⋊C4—21no—
195C4⋊C4—21no—
196C4⋊C4—21no—
197C4⋊C4—21no—
198C4⋊C4—42no—
199C4⋊C4—42no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—81no—
207C4⋊C4—81no—
208C4⋊C4—81no—
209C4⋊C4—82no—
210C4⋊C4—82no—
211C4⋊C4#10412yes—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—21no—
218C42—41no—
219C42—41no—
220C42—41no—
221C42—42no—
222C42—42no—
223C42—42no—
224C42—42no—
225C42—81no—
226C42—81no—
227C42C2×Q1611yescharacteristic
228C42#13511yescharacteristic
229C42#13711yescharacteristic
230C42#13711yescharacteristic
231C23#38611yescharacteristic
232Q8—22no—
233Q8—22no—
234Q8—41no—
235Q8—41no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—81no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4—81no—
267C2×C4—81no—
268C2×C4—81no—
269C2×C4C2×#10111yescharacteristic
270C2×C4#41311yescharacteristic
271C2×C4C2×#10411yescharacteristic
272C2×C4#42111yescharacteristic
273C2×C4#42111yescharacteristic
274C2×C4#42111yescharacteristic
275C2×C4C4×Q1611yescharacteristic
276C2×C4#44111yescharacteristic
277C2×C4#45111yescharacteristic
278C2×C4#45211yescharacteristic
279C2×C4#46211yescharacteristic
280C2×C4#46411yescharacteristic
281C8—42no—
282C8—42no—
283C8—82no—
284C8—82no—
285C8—82no—
286C8—81no—
287C8—81no—
288C22#187111yescharacteristic
289C22#187811yescharacteristic
290C22#188111yescharacteristic
291C22#189711yescharacteristic
292C22#190111yescharacteristic
293C22#190311yescharacteristic
294C22#190611yescharacteristic
295C4—21no—
296C4—21no—
297C4—21no—
298C4—21no—
299C4—21no—
300C4—21no—
301C4—41no—
302C4—41no—
303C4—42no—
304C4—41no—
305C4—42no—
306C4—81no—
307C4—81no—
308C4—161no—
309C4—161no—
310C4#152911yescharacteristic
311C4#153111yescharacteristic
312C4#153411yescharacteristic
313C4#153511yescharacteristic
314C2#899011yescharacteristic
315C2#912611yescharacteristic
316C2#916111yescharacteristic
317C2#923611yescharacteristic
318C2#925011yescharacteristic
319C2#931311yescharacteristic
320C2#935211yescharacteristic
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
#213452
#98912
#81752
#76832
#70492
#70302