Finite Group Databasebeta

← #100985

Subgroups — #100985

Order 512.

472 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 84 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#21916C211yesmaximal, characteristic
2#15086C211yesmaximal, characteristic
3#8719C212yesmaximal
4#8153C211yesmaximal, characteristic
5#7036C212yesmaximal
6C2×#382C2211yescharacteristic
7C2×C4×C4⋊C4C2211yescharacteristic
8#1917—24no—
9#1817—21no—
10#1797—21no—
11#1749C2212yes—
12#1749C2212yes—
13C2×#324—21no—
14#1445—21no—
15#1444C411yescharacteristic
16#1442—21no—
17#1442C411yescharacteristic
18#1441C411yescharacteristic
19#1441C411yescharacteristic
20#1436—21no—
21#1434—21no—
22#1434C2211yescharacteristic
23#1295—24no—
24#1280—21no—
25C22×C4⋊C4—21no—
26C22×C4⋊C4C2×C411yescharacteristic
27C22×C4⋊C4C2×C411yescharacteristic
28C22×C4⋊C4C2×C411yescharacteristic
29C22×C4⋊C4D411yescharacteristic
30C22×C42D411yescharacteristic
31C22×C42D411yescharacteristic
32C22×C42C2311yescharacteristic
33C2×C4⋊C8—22no—
34C2×C22⋊C8—22no—
35C2×C22⋊C8—22no—
36C2×#97—22no—
37C2×#97D414yes—
38#382—22no—
39#382—22no—
40C4×C4⋊C4—22no—
41C4×C4⋊C4—22no—
42C2×#95—21no—
43C2×#95—21no—
44C2×#95—21no—
45C2×#95—21no—
46C2×#95—21no—
47C2×#95—21no—
48C2×#95—21no—
49C2×#95—21no—
50C2×#95—21no—
51C2×#95—21no—
52C2×#95—21no—
53C2×#95C2×C411yescharacteristic
54C2×#95C2×C411yescharacteristic
55C2×#95C2×C411yescharacteristic
56C2×#95D411yescharacteristic
57#336—22no—
58#336—24no—
59#336—22no—
60#336—22no—
61#324—24no—
62C23×C4—21no—
63C23×C4—21no—
64C23×C4—21no—
65C23×C4—21no—
66C23×C4C22⋊C411yescharacteristic
67C23×C4C22⋊C411yescharacteristic
68C23×C4C22⋊C411yescharacteristic
69C23×C4C22⋊C411yescharacteristic
70C23×C4C22×C411yescharacteristic
71C23×C4C2×D411yescharacteristic
72C23×C4C2×D411yescharacteristic
73C22×C8—24no—
74C22×C8—42no—
75C2×C4⋊C4—22no—
76C2×C4⋊C4—22no—
77C2×C4⋊C4—22no—
78C2×C4⋊C4—22no—
79C2×C4⋊C4—22no—
80C2×C4⋊C4—22no—
81C2×C4⋊C4—41no—
82C2×C4⋊C4—41no—
83C2×C4⋊C4—42no—
84C2×C4⋊C4—42no—
85C2×C4⋊C4—81no—
86C2×C4⋊C4—81no—
87C2×C4⋊C4—81no—
88C2×C42—21no—
89C2×C42—21no—
90C2×C42—21no—
91C2×C42—21no—
92C2×C42—42no—
93C2×C42—41no—
94C2×C42—41no—
95C2×C42—42no—
96C2×C42C2×D412yes—
97C2×C42#4112yes—
98C4⋊C8—82no—
99C22⋊C8—24no—
100C22⋊C8—42no—
101C22⋊C8—42no—
102C22⋊C8—42no—
103#97—44no—
104#97—44no—
105#95—22no—
106#95—22no—
107#95—41no—
108#95—41no—
109#95—42no—
110#95—42no—
111#95—42no—
112#95—42no—
113#95—42no—
114#95—42no—
115#95—41no—
116#95—42no—
117#95—41no—
118#95—81no—
119#95—81no—
120#95—81no—
121C24C2×C22⋊C411yescharacteristic
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—22no—
137C22×C4—22no—
138C22×C4—21no—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—21no—
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—41no—
153C22×C4—41no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—41no—
157C22×C4—41no—
158C22×C4—41no—
159C22×C4—41no—
160C22×C4—41no—
161C22×C4—41no—
162C22×C4—41no—
163C22×C4—41no—
164C22×C4—41no—
165C22×C4—41no—
166C22×C4—41no—
167C22×C4—41no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4—41no—
172C22×C4—41no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4#10112yes—
183C22×C4#10412yes—
184C22×C4C4×D412yes—
185C22×C4#12011yescharacteristic
186C22×C4#12112yes—
187C22×C4#12311yescharacteristic
188C2×C8—44no—
189C2×C8—44no—
190C2×C8—44no—
191C2×C8—44no—
192C2×C8—82no—
193C2×C8—82no—
194C4⋊C4—44no—
195C4⋊C4—44no—
196C4⋊C4—82no—
197C4⋊C4—82no—
198C4⋊C4—84no—
199C42—24no—
200C42—42no—
201C42—42no—
202C42—42no—
203C42—42no—
204C42—81no—
205C23—21no—
206C23—21no—
207C23—21no—
208C23—21no—
209C23#38611yescharacteristic
210C23C2×#10111yescharacteristic
211C23#41311yescharacteristic
212C23C2×#10411yescharacteristic
213C23#42111yescharacteristic
214C23#42111yescharacteristic
215C23#42111yescharacteristic
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—81no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—81no—
257C2×C4—81no—
258C2×C4—81no—
259C2×C4—81no—
260C2×C4—81no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4—81no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4—81no—
267C2×C4—81no—
268C2×C4—81no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4#45812yes—
284C8—84no—
285C8—84no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22#152811yescharacteristic
299C22#153211yescharacteristic
300C22#153511yescharacteristic
301C22#153711yescharacteristic
302C22#187111yescharacteristic
303C22#188411yescharacteristic
304C22#189011yescharacteristic
305C22#189711yescharacteristic
306C22#190111yescharacteristic
307C22#191211yescharacteristic
308C22#191411yescharacteristic
309C4—22no—
310C4—41no—
311C4—42no—
312C4—42no—
313C4—42no—
314C4—42no—
315C4—82no—
316C4—81no—
317C4—81no—
318C4—161no—
319C4—161no—
320C4—161no—
321C2—21no—
322C2—21no—
323C2—21no—
324C2—21no—
325C2#901211yescharacteristic
326C2#912511yescharacteristic
327C2#918811yescharacteristic
328C2#938911yescharacteristic
329C2#945011yescharacteristic
330C2#948211yescharacteristic
331C2#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
#219162
#150862
#87192
#81532
#70362