Finite Group Databasebeta

← #101037

Subgroups — #101037

Order 512.

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

normal subgroups only

This group has 524 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#15152C211yesmaximal, characteristic
3#8725C212yesmaximal
4#8558C211yesmaximal, characteristic
5#7039C212yesmaximal
6C2×#432—21no—
7C2×#400C412yes—
8C2×#384C2211yescharacteristic
9C2×C4×C4⋊C4C2211yescharacteristic
10#1940—24no—
11#1797—21no—
12#1797C2212yes—
13#1797C2212yes—
14C2×#324—21no—
15#1445C412yes—
16#1442—21no—
17#1441—21no—
18C4⋊#95—21no—
19C4⋊#95—21no—
20C4⋊#95C2211yescharacteristic
21#1296—24no—
22#1280—21no—
23C22×C4⋊C4—21no—
24C22×C4⋊C4—21no—
25C22×C4⋊C4—21no—
26C22×C4⋊C4C2×C411yescharacteristic
27C22×C4⋊C4C2×C412yes—
28C22×C4⋊C4D411yescharacteristic
29C22×C42D411yescharacteristic
30C22×C42D411yescharacteristic
31C22×C42C2311yescharacteristic
32#432—42no—
33#432—42no—
34C2×C4⋊C8—22no—
35C2×C4⋊C8—22no—
36C2×C4⋊C8—22no—
37C2×C4⋊C8D414yes—
38C2×C22⋊C8—22no—
39C2×C22⋊C8—22no—
40C2×#97—22no—
41#400—44no—
42#384—22no—
43#384—22no—
44C4×C4⋊C4—22no—
45C4×C4⋊C4—22no—
46C2×#95—22no—
47C2×#95—22no—
48C2×#95—21no—
49C2×#95—22no—
50C2×#95—22no—
51C2×#95C2×C411yescharacteristic
52C2×#95C2×C412yes—
53C2×#95D411yescharacteristic
54#336—22no—
55#336—22no—
56#336—22no—
57#324—42no—
58C23×C4—22no—
59C23×C4—22no—
60C23×C4C22⋊C411yescharacteristic
61C23×C4C22⋊C411yescharacteristic
62C23×C4C22⋊C411yescharacteristic
63C23×C4C22⋊C411yescharacteristic
64C23×C4C22×C411yescharacteristic
65C23×C4C2×D411yescharacteristic
66C23×C4C2×D411yescharacteristic
67C22×C8—24no—
68C22×C8—42no—
69C2×C4⋊C4—22no—
70C2×C4⋊C4—22no—
71C2×C4⋊C4—22no—
72C2×C4⋊C4—21no—
73C2×C4⋊C4—22no—
74C2×C4⋊C4—21no—
75C2×C4⋊C4—24no—
76C2×C4⋊C4—41no—
77C2×C4⋊C4—42no—
78C2×C4⋊C4—42no—
79C2×C4⋊C4—42no—
80C2×C4⋊C4—42no—
81C2×C4⋊C4—42no—
82C2×C4⋊C4—42no—
83C2×C4⋊C4—41no—
84C2×C4⋊C4—42no—
85C2×C4⋊C4—41no—
86C2×C4⋊C4—41no—
87C2×C4⋊C4—41no—
88C2×C4⋊C4—82no—
89C2×C42—21no—
90C2×C42—21no—
91C2×C42—21no—
92C2×C42—21no—
93C2×C42—21no—
94C2×C42—21no—
95C2×C42—42no—
96C2×C42—42no—
97C2×C42SD1612yes—
98C2×C42Q1612yes—
99C2×C42C2×D412yes—
100C2×C42#4112yes—
101C4⋊C8—44no—
102C4⋊C8—44no—
103C4⋊C8—44no—
104C4⋊C8—82no—
105C22⋊C8—42no—
106C22⋊C8—42no—
107C22⋊C8—42no—
108C22⋊C8—42no—
109#97—44no—
110#95—22no—
111#95—22no—
112#95—42no—
113#95—44no—
114#95—44no—
115#95—41no—
116#95—41no—
117#95—82no—
118#95—82no—
119C24C2×C22⋊C411yescharacteristic
120C22×C4—22no—
121C22×C4—22no—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—21no—
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—41no—
138C22×C4—41no—
139C22×C4—41no—
140C22×C4—41no—
141C22×C4—41no—
142C22×C4—41no—
143C22×C4—41no—
144C22×C4—41no—
145C22×C4—41no—
146C22×C4—41no—
147C22×C4—42no—
148C22×C4—42no—
149C22×C4—42no—
150C22×C4—42no—
151C22×C4—42no—
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#10012yes—
162C22×C4#10312yes—
163C22×C4#10312yes—
164C22×C4C4×D412yes—
165C22×C4#12011yescharacteristic
166C22×C4#12112yes—
167C22×C4#12311yescharacteristic
168C22×C4C2×SD1611yescharacteristic
169C22×C4C2×Q1611yescharacteristic
170C22×C4AGL(1,ℤ/8)11yescharacteristic
171C22×C4AGL(1,ℤ/8)11yescharacteristic
172C22×C4#13711yescharacteristic
173C22×C4#13712yes—
174C22×C4#13711yescharacteristic
175C2×C8—44no—
176C2×C8—44no—
177C2×C8—44no—
178C2×C8—82no—
179C2×C8—82no—
180C2×C8—82no—
181C4⋊C4—44no—
182C4⋊C4—42no—
183C4⋊C4—42no—
184C4⋊C4—84no—
185C4⋊C4—82no—
186C4⋊C4—82no—
187C4⋊C4—82no—
188C4⋊C4—84no—
189C4⋊C4—82no—
190C42—22no—
191C42—22no—
192C42—24no—
193C42—22no—
194C42—22no—
195C42—42no—
196C42—42no—
197C42—81no—
198C23—21no—
199C23—21no—
200C23—21no—
201C23—21no—
202C23#38611yescharacteristic
203C23C2×#10011yescharacteristic
204C23#41311yescharacteristic
205C23C2×#10311yescharacteristic
206C23#41711yescharacteristic
207C23#41711yescharacteristic
208C23#41911yescharacteristic
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—41no—
226C2×C4—42no—
227C2×C4—41no—
228C2×C4—42no—
229C2×C4—42no—
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—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—81no—
245C2×C4—81no—
246C2×C4—81no—
247C2×C4—82no—
248C2×C4—82no—
249C2×C4—82no—
250C2×C4—82no—
251C2×C4—82no—
252C2×C4—82no—
253C2×C4—82no—
254C2×C4—82no—
255C2×C4—82no—
256C2×C4—82no—
257C2×C4—82no—
258C2×C4—82no—
259C2×C4—82no—
260C2×C4—82no—
261C2×C4#45011yescharacteristic
262C2×C4#45111yescharacteristic
263C2×C4#45412yes—
264C2×C4#45812yes—
265C2×C4#46812yes—
266C2×C4#47012yes—
267C2×C4#48311yescharacteristic
268C2×C4#48411yescharacteristic
269C8—84no—
270C8—162no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22#154811yescharacteristic
284C22#155011yescharacteristic
285C22#155911yescharacteristic
286C22#156011yescharacteristic
287C22#187211yescharacteristic
288C22#188811yescharacteristic
289C22#189011yescharacteristic
290C22#189411yescharacteristic
291C22#190011yescharacteristic
292C22#191011yescharacteristic
293C22#191511yescharacteristic
294C4—22no—
295C4—22no—
296C4—21no—
297C4—21no—
298C4—42no—
299C4—42no—
300C4—42no—
301C4—42no—
302C4—81no—
303C4—162no—
304C4—162no—
305C4#161612yes—
306C4#161712yes—
307C2—21no—
308C2—21no—
309C2—21no—
310C2—21no—
311C2#902311yescharacteristic
312C2#913511yescharacteristic
313C2#919311yescharacteristic
314C2#940411yescharacteristic
315C2#945811yescharacteristic
316C2#947311yescharacteristic
317C2#950711yescharacteristic
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
#151522
#87252
#85582
#70392