Finite Group Databasebeta

← #101017

Subgroups — #101017

Order 512.

586 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 124 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#21951C211yesmaximal, characteristic
2#15151C211yesmaximal, characteristic
3#8723C212yesmaximal
4#8558C211yesmaximal, characteristic
5#7039C212yesmaximal
6C2×#431—21no—
7C2×#398—21no—
8C2×#398C412yes—
9C2×#389—21no—
10C2×#384C2211yescharacteristic
11C2×C4×C4⋊C4C2211yescharacteristic
12#1939—24no—
13#1797—21no—
14#1797C2212yes—
15#1797C2212yes—
16C2×#324—21no—
17#1445—21no—
18#1445C412yes—
19C4⋊#95—21no—
20C4⋊#95C2211yescharacteristic
21#1296—24no—
22#1280—21no—
23C22×C4⋊C4—21no—
24C22×C4⋊C4—22no—
25C22×C4⋊C4—21no—
26C22×C4⋊C4—21no—
27C22×C4⋊C4C2×C411yescharacteristic
28C22×C4⋊C4C2×C412yes—
29C22×C4⋊C4D411yescharacteristic
30C22×C42D411yescharacteristic
31C22×C42D411yescharacteristic
32C22×C42C2311yescharacteristic
33#431—42no—
34#431—42no—
35C2×C4⋊C8—22no—
36C2×C4⋊C8—22no—
37C2×C4⋊C8—22no—
38C2×C4⋊C8D414yes—
39C2×C22⋊C8—22no—
40C2×C22⋊C8—22no—
41C2×C4×C8—22no—
42#398—44no—
43#398—42no—
44#398—42no—
45#389—42no—
46#389—42no—
47#384—22no—
48#384—22no—
49C4×C4⋊C4—22no—
50C4×C4⋊C4—22no—
51C2×#95—22no—
52C2×#95—22no—
53C2×#95—22no—
54C2×#95—21no—
55C2×#95C2×C411yescharacteristic
56C2×#95C2×C412yes—
57C2×#95D411yescharacteristic
58#336—22no—
59#336—22no—
60#336—22no—
61#324—42no—
62C23×C4—22no—
63C23×C4—22no—
64C23×C4C22⋊C411yescharacteristic
65C23×C4C22⋊C411yescharacteristic
66C23×C4C22⋊C411yescharacteristic
67C23×C4C22⋊C411yescharacteristic
68C23×C4C22×C411yescharacteristic
69C23×C4C2×D411yescharacteristic
70C23×C4C2×D411yescharacteristic
71C22×C8—24no—
72C22×C8—42no—
73C2×C4⋊C4—22no—
74C2×C4⋊C4—22no—
75C2×C4⋊C4—24no—
76C2×C4⋊C4—22no—
77C2×C4⋊C4—22no—
78C2×C4⋊C4—24no—
79C2×C4⋊C4—41no—
80C2×C4⋊C4—42no—
81C2×C4⋊C4—41no—
82C2×C4⋊C4—41no—
83C2×C4⋊C4—42no—
84C2×C4⋊C4—42no—
85C2×C4⋊C4—44no—
86C2×C4⋊C4—44no—
87C2×C4⋊C4—44no—
88C2×C4⋊C4—41no—
89C2×C4⋊C4—42no—
90C2×C4⋊C4—41no—
91C2×C4⋊C4—41no—
92C2×C4⋊C4—41no—
93C2×C4⋊C4—41no—
94C2×C4⋊C4—41no—
95C2×C4⋊C4—42no—
96C2×C4⋊C4—41no—
97C2×C4⋊C4—41no—
98C2×C4⋊C4D812yes—
99C2×C4⋊C4SD1612yes—
100C2×C42—21no—
101C2×C42—21no—
102C2×C42—21no—
103C2×C42—21no—
104C2×C42—21no—
105C2×C42—21no—
106C2×C42—42no—
107C2×C42—42no—
108C2×C42D812yes—
109C2×C42SD1612yes—
110C2×C42C2×D412yes—
111C2×C42#4112yes—
112C4⋊C8—44no—
113C4⋊C8—44no—
114C4⋊C8—44no—
115C4⋊C8—82no—
116C22⋊C8—42no—
117C22⋊C8—42no—
118C22⋊C8—42no—
119C22⋊C8—42no—
120C4×C8—44no—
121#95—22no—
122#95—22no—
123#95—42no—
124#95—44no—
125#95—44no—
126#95—44no—
127#95—41no—
128#95—41no—
129C24C2×C22⋊C411yescharacteristic
130C22×C4—21no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—21no—
134C22×C4—22no—
135C22×C4—22no—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—24no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—21no—
146C22×C4—41no—
147C22×C4—41no—
148C22×C4—41no—
149C22×C4—41no—
150C22×C4—41no—
151C22×C4—41no—
152C22×C4—41no—
153C22×C4—41no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—42no—
157C22×C4—42no—
158C22×C4—42no—
159C22×C4—42no—
160C22×C4—42no—
161C22×C4—42no—
162C22×C4—42no—
163C22×C4—42no—
164C22×C4—42no—
165C22×C4—42no—
166C22×C4—42no—
167C22×C4—42no—
168C22×C4—42no—
169C22×C4#10012yes—
170C22×C4#10212yes—
171C22×C4#10212yes—
172C22×C4#10212yes—
173C22×C4#10212yes—
174C22×C4C4×D412yes—
175C22×C4#12011yescharacteristic
176C22×C4#12112yes—
177C22×C4#12311yescharacteristic
178C22×C4C2×D811yescharacteristic
179C22×C4C2×D811yescharacteristic
180C22×C4C2×SD1611yescharacteristic
181C22×C4C2×SD1611yescharacteristic
182C22×C4#13512yes—
183C22×C4AGL(1,ℤ/8)11yescharacteristic
184C22×C4#13711yescharacteristic
185C2×C8—44no—
186C2×C8—44no—
187C2×C8—44no—
188C2×C8—82no—
189C2×C8—82no—
190C2×C8—82no—
191C4⋊C4—24no—
192C4⋊C4—24no—
193C4⋊C4—44no—
194C4⋊C4—44no—
195C4⋊C4—44no—
196C4⋊C4—84no—
197C4⋊C4—88no—
198C4⋊C4—81no—
199C4⋊C4—81no—
200C4⋊C4—82no—
201C4⋊C4—82no—
202C4⋊C4—81no—
203C4⋊C4—81no—
204C42—22no—
205C42—22no—
206C42—24no—
207C42—22no—
208C42—22no—
209C42—42no—
210C42—42no—
211C42—81no—
212C23—21no—
213C23—21no—
214C23—21no—
215C23—21no—
216C23#38611yescharacteristic
217C23C2×#10011yescharacteristic
218C23#41311yescharacteristic
219C23C2×#10211yescharacteristic
220C23C2×#10211yescharacteristic
221C23#41611yescharacteristic
222C23#41711yescharacteristic
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—44no—
254C2×C4—44no—
255C2×C4—44no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—81no—
261C2×C4—81no—
262C2×C4—82no—
263C2×C4—82no—
264C2×C4—82no—
265C2×C4—82no—
266C2×C4—81no—
267C2×C4—82no—
268C2×C4—82no—
269C2×C4—82no—
270C2×C4—82no—
271C2×C4—82no—
272C2×C4—82no—
273C2×C4—82no—
274C2×C4#33114yes—
275C2×C4#44711yescharacteristic
276C2×C4#44811yescharacteristic
277C2×C4#45612yes—
278C2×C4#45812yes—
279C2×C4#46512yes—
280C2×C4#46612yes—
281C2×C4#48011yescharacteristic
282C2×C4#48111yescharacteristic
283C8—84no—
284C8—162no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22C2×#33111yescharacteristic
298C22#154011yescharacteristic
299C22#154711yescharacteristic
300C22#155111yescharacteristic
301C22#187411yescharacteristic
302C22#188611yescharacteristic
303C22#189011yescharacteristic
304C22#189311yescharacteristic
305C22#190011yescharacteristic
306C22#190911yescharacteristic
307C22#191511yescharacteristic
308C4—21no—
309C4—21no—
310C4—24no—
311C4—22no—
312C4—22no—
313C4—42no—
314C4—42no—
315C4—42no—
316C4—84no—
317C4—81no—
318C4—162no—
319C4#161012yes—
320C4#161112yes—
321C2—21no—
322C2—21no—
323C2—21no—
324C2—21no—
325C2#902711yescharacteristic
326C2#913311yescharacteristic
327C2#919511yescharacteristic
328C2#939411yescharacteristic
329C2#945211yescharacteristic
330C2#947011yescharacteristic
331C2#950811yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#219512
#151512
#87232
#85582
#70392