Finite Group Databasebeta

← #101045

Subgroups — #101045

Order 512.

550 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 112 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#21955C211yesmaximal, characteristic
2#15196C211yesmaximal, characteristic
3#8724C212yesmaximal
4#8558C211yesmaximal, characteristic
5#7039C212yesmaximal
6C2×#432—21no—
7C2×#389—21no—
8C2×#384C2211yescharacteristic
9C2×C4×C4⋊C4C2211yescharacteristic
10#1940—24no—
11#1797—21no—
12#1797C2212yes—
13#1797C2212yes—
14C2×#324—21no—
15#1444—21no—
16#1444C412yes—
17#1441—21no—
18#1441C412yes—
19C4⋊#95—21no—
20C4⋊#95C2211yescharacteristic
21#1296—24no—
22#1280—21no—
23C22×C4⋊C4—21no—
24C22×C4⋊C4—21no—
25C22×C4⋊C4—22no—
26C22×C4⋊C4—21no—
27C22×C4⋊C4C2×C411yescharacteristic
28C22×C4⋊C4C2×C412yes—
29C22×C4⋊C4D411yescharacteristic
30C22×C42D411yescharacteristic
31C22×C42D411yescharacteristic
32C22×C42C2311yescharacteristic
33#432—42no—
34#432—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×#97—22no—
42#389—42no—
43#389—42no—
44#384—22no—
45#384—22no—
46C4×C4⋊C4—22no—
47C4×C4⋊C4—22no—
48C2×#95—22no—
49C2×#95—21no—
50C2×#95—22no—
51C2×#95—22no—
52C2×#95C2×C411yescharacteristic
53C2×#95C2×C412yes—
54C2×#95D411yescharacteristic
55#336—22no—
56#336—22no—
57#336—22no—
58#324—42no—
59C23×C4—22no—
60C23×C4—22no—
61C23×C4C22⋊C411yescharacteristic
62C23×C4C22⋊C411yescharacteristic
63C23×C4C22⋊C411yescharacteristic
64C23×C4C22⋊C411yescharacteristic
65C23×C4C22×C411yescharacteristic
66C23×C4C2×D411yescharacteristic
67C23×C4C2×D411yescharacteristic
68C22×C8—24no—
69C22×C8—42no—
70C2×C4⋊C4—24no—
71C2×C4⋊C4—22no—
72C2×C4⋊C4—22no—
73C2×C4⋊C4—22no—
74C2×C4⋊C4—21no—
75C2×C4⋊C4—22no—
76C2×C4⋊C4—21no—
77C2×C4⋊C4—24no—
78C2×C4⋊C4—41no—
79C2×C4⋊C4—42no—
80C2×C4⋊C4—41no—
81C2×C4⋊C4—41no—
82C2×C4⋊C4—44no—
83C2×C4⋊C4—41no—
84C2×C4⋊C4—42no—
85C2×C4⋊C4—41no—
86C2×C4⋊C4—41no—
87C2×C4⋊C4—41no—
88C2×C4⋊C4—41no—
89C2×C4⋊C4—41no—
90C2×C4⋊C4—82no—
91C2×C4⋊C4—82no—
92C2×C4⋊C4—82no—
93C2×C4⋊C4—82no—
94C2×C42—21no—
95C2×C42—21no—
96C2×C42—21no—
97C2×C42—21no—
98C2×C42—21no—
99C2×C42—21no—
100C2×C42—42no—
101C2×C42—42no—
102C2×C42D812yes—
103C2×C42SD1612yes—
104C2×C42C2×D412yes—
105C2×C42#4112yes—
106C4⋊C8—44no—
107C4⋊C8—44no—
108C4⋊C8—44no—
109C4⋊C8—82no—
110C22⋊C8—42no—
111C22⋊C8—42no—
112C22⋊C8—42no—
113C22⋊C8—42no—
114#97—44no—
115#95—22no—
116#95—22no—
117#95—42no—
118#95—44no—
119#95—41no—
120#95—41no—
121#95—82no—
122#95—82no—
123C24C2×C22⋊C411yescharacteristic
124C22×C4—22no—
125C22×C4—22no—
126C22×C4—21no—
127C22×C4—21no—
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4—24no—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—41no—
143C22×C4—41no—
144C22×C4—41no—
145C22×C4—41no—
146C22×C4—41no—
147C22×C4—41no—
148C22×C4—41no—
149C22×C4—41no—
150C22×C4—41no—
151C22×C4—41no—
152C22×C4—42no—
153C22×C4—42no—
154C22×C4—42no—
155C22×C4—42no—
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#10112yes—
166C22×C4#10212yes—
167C22×C4#10212yes—
168C22×C4C4×D412yes—
169C22×C4#12011yescharacteristic
170C22×C4#12112yes—
171C22×C4#12311yescharacteristic
172C22×C4C2×D811yescharacteristic
173C22×C4C2×SD1611yescharacteristic
174C22×C4AGL(1,ℤ/8)11yescharacteristic
175C22×C4AGL(1,ℤ/8)11yescharacteristic
176C22×C4#13711yescharacteristic
177C22×C4#13712yes—
178C22×C4#13711yescharacteristic
179C2×C8—44no—
180C2×C8—44no—
181C2×C8—44no—
182C2×C8—82no—
183C2×C8—82no—
184C2×C8—82no—
185C4⋊C4—44no—
186C4⋊C4—44no—
187C4⋊C4—44no—
188C4⋊C4—42no—
189C4⋊C4—42no—
190C4⋊C4—84no—
191C4⋊C4—84no—
192C4⋊C4—88no—
193C4⋊C4—81no—
194C4⋊C4—81no—
195C4⋊C4—81no—
196C4⋊C4—81no—
197C42—22no—
198C42—22no—
199C42—24no—
200C42—22no—
201C42—22no—
202C42—42no—
203C42—42no—
204C42—81no—
205C23—21no—
206C23—21no—
207C23—21no—
208C23—21no—
209C23#38611yescharacteristic
210C23C2×#10111yescharacteristic
211C23#41311yescharacteristic
212C23C2×#10211yescharacteristic
213C23#41711yescharacteristic
214C23#41711yescharacteristic
215C23#41911yescharacteristic
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—41no—
233C2×C4—42no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—44no—
248C2×C4—44no—
249C2×C4—44no—
250C2×C4—42no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—82no—
257C2×C4—82no—
258C2×C4—82no—
259C2×C4—82no—
260C2×C4—81no—
261C2×C4—82no—
262C2×C4—82no—
263C2×C4—82no—
264C2×C4—82no—
265C2×C4—82no—
266C2×C4—82no—
267C2×C4—82no—
268C2×C4#44711yescharacteristic
269C2×C4#44811yescharacteristic
270C2×C4#45612yes—
271C2×C4#45812yes—
272C2×C4#46812yes—
273C2×C4#47012yes—
274C2×C4#48011yescharacteristic
275C2×C4#48111yescharacteristic
276C8—84no—
277C8—162no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22#154611yescharacteristic
291C22#154711yescharacteristic
292C22#155911yescharacteristic
293C22#156111yescharacteristic
294C22#187411yescharacteristic
295C22#188611yescharacteristic
296C22#189011yescharacteristic
297C22#189411yescharacteristic
298C22#190111yescharacteristic
299C22#191011yescharacteristic
300C22#191411yescharacteristic
301C4—22no—
302C4—22no—
303C4—21no—
304C4—21no—
305C4—42no—
306C4—42no—
307C4—42no—
308C4—42no—
309C4—84no—
310C4—81no—
311C4—162no—
312C4#161012yes—
313C4#161112yes—
314C2—21no—
315C2—21no—
316C2—21no—
317C2—21no—
318C2#902711yescharacteristic
319C2#913911yescharacteristic
320C2#919711yescharacteristic
321C2#940011yescharacteristic
322C2#945411yescharacteristic
323C2#947311yescharacteristic
324C2#950911yescharacteristic
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
#219552
#151962
#87242
#85582
#70392