Finite Group Databasebeta

← #101150

Subgroups — #101150

Order 512.

566 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 88 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#20534C211yesmaximal, characteristic
2#15097C211yesmaximal, characteristic
3#8153C211yesmaximal, characteristic
4#7629C212yesmaximal
5#7036C212yesmaximal
6C2×#432—21no—
7C2×#398C411yescharacteristic
8C2×#395C411yescharacteristic
9C2×#391C2211yescharacteristic
10C2×C4×C4⋊C4C2211yescharacteristic
11#1771—24no—
12#1749C2212yes—
13#1749C2212yes—
14C4×C22⋊C8—21no—
15C2×#324—21no—
16#1446C411yescharacteristic
17#1445C411yescharacteristic
18#1442—21no—
19#1441—21no—
20#1436—21no—
21#1436—21no—
22#1434C2211yescharacteristic
23#1280—21no—
24#1272—24no—
25C23×Q8C2×C411yescharacteristic
26C22×C4⋊C4—21no—
27C22×C4⋊C4—21no—
28C22×C4⋊C4C2×C411yescharacteristic
29C22×C4⋊C4C2×C411yescharacteristic
30C22×C4⋊C4D411yescharacteristic
31C22×C42D411yescharacteristic
32C22×C42D411yescharacteristic
33C22×C42C2311yescharacteristic
34#432—24no—
35#432—24no—
36C2×C4⋊C8—22no—
37C2×C22⋊C8—22no—
38C2×C22⋊C8—22no—
39C2×#97—22no—
40C2×#97—22no—
41C2×#97—22no—
42C2×C4×C8—22no—
43#398—42no—
44#395—42no—
45#391—22no—
46#391—22no—
47C4×C4⋊C4—22no—
48C4×C4⋊C4—22no—
49C2×#95—21no—
50C2×#95—21no—
51C2×#95—21no—
52C2×#95—21no—
53C2×#95—21no—
54C2×#95—21no—
55C2×#95—21no—
56C2×#95—21no—
57C2×#95—21no—
58C2×#95—21no—
59C2×#95C2×C411yescharacteristic
60C2×#95C2×C411yescharacteristic
61C2×#95C2×C411yescharacteristic
62C2×#95D411yescharacteristic
63#336—22no—
64#336—22no—
65#336D414yes—
66#324—24no—
67C22×Q8—22no—
68C22×Q8—42no—
69C22×Q8—41no—
70C22×Q8—41no—
71C22×Q8—81no—
72C23×C4—21no—
73C23×C4—21no—
74C23×C4—21no—
75C23×C4—21no—
76C23×C4C22⋊C411yescharacteristic
77C23×C4C22⋊C411yescharacteristic
78C23×C4C22⋊C411yescharacteristic
79C23×C4C22⋊C411yescharacteristic
80C23×C4C22×C411yescharacteristic
81C23×C4C2×D411yescharacteristic
82C23×C4C2×D411yescharacteristic
83C22×C8—24no—
84C22×C8—42no—
85C2×C4⋊C4—22no—
86C2×C4⋊C4—22no—
87C2×C4⋊C4—22no—
88C2×C4⋊C4—22no—
89C2×C4⋊C4—22no—
90C2×C4⋊C4—41no—
91C2×C4⋊C4—41no—
92C2×C4⋊C4—41no—
93C2×C4⋊C4—41no—
94C2×C4⋊C4—42no—
95C2×C4⋊C4—42no—
96C2×C4⋊C4—42no—
97C2×C4⋊C4—42no—
98C2×C4⋊C4—42no—
99C2×C4⋊C4—81no—
100C2×C42—22no—
101C2×C42—22no—
102C2×C42—21no—
103C2×C42—21no—
104C2×C42—21no—
105C2×C42—21no—
106C2×C42—81no—
107C2×C42—81no—
108C2×C42C2×D412yes—
109C2×C42#4112yes—
110C4⋊C8—28no—
111C22⋊C8—24no—
112C22⋊C8—24no—
113C22⋊C8—24no—
114C22⋊C8—42no—
115#97—28no—
116#97—82no—
117#97—82no—
118C4×C8—82no—
119#95—24no—
120#95—22no—
121#95—22no—
122#95—41no—
123#95—41no—
124#95—42no—
125#95—42no—
126#95—42no—
127#95—42no—
128#95—42no—
129#95—41no—
130#95—42no—
131#95—41no—
132#95—81no—
133#95—81no—
134C24C2×C22⋊C411yescharacteristic
135C2×Q8—24no—
136C2×Q8—42no—
137C2×Q8—82no—
138C2×Q8—82no—
139C2×Q8—84no—
140C2×Q8—84no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—22no—
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—41no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4—41no—
186C22×C4—41no—
187C22×C4—41no—
188C22×C4—41no—
189C22×C4—41no—
190C22×C4—41no—
191C22×C4—41no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4#10012yes—
200C22×C4#10412yes—
201C22×C4#10412yes—
202C22×C4#10412yes—
203C22×C4C4×D412yes—
204C22×C4#12011yescharacteristic
205C22×C4#12112yes—
206C22×C4#12311yescharacteristic
207C2×C8—28no—
208C2×C8—44no—
209C2×C8—44no—
210C2×C8—44no—
211C2×C8—82no—
212C2×C8—82no—
213C4⋊C4—44no—
214C4⋊C4—44no—
215C4⋊C4—82no—
216C4⋊C4—84no—
217C4⋊C4—84no—
218C42—22no—
219C42—22no—
220C42—24no—
221C42—42no—
222C42—42no—
223C42—42no—
224C42—81no—
225C23—21no—
226C23—21no—
227C23—21no—
228C23—21no—
229C23#38611yescharacteristic
230C23C2×#10011yescharacteristic
231C23#41311yescharacteristic
232C23C2×#10411yescharacteristic
233C23C2×#10411yescharacteristic
234C23C2×#10411yescharacteristic
235C23#42111yescharacteristic
236Q8—84no—
237Q8—84no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4#45612yes—
306C8—48no—
307C8—84no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22#152411yescharacteristic
321C22#152511yescharacteristic
322C22#152711yescharacteristic
323C22#152911yescharacteristic
324C22#187111yescharacteristic
325C22#188611yescharacteristic
326C22#189111yescharacteristic
327C22#189611yescharacteristic
328C22#190011yescharacteristic
329C22#190911yescharacteristic
330C22#191311yescharacteristic
331C4—22no—
332C4—42no—
333C4—42no—
334C4—42no—
335C4—42no—
336C4—41no—
337C4—42no—
338C4—42no—
339C4—82no—
340C4—82no—
341C4—82no—
342C4—161no—
343C2—21no—
344C2—21no—
345C2—21no—
346C2—21no—
347C2#903011yescharacteristic
348C2#912011yescharacteristic
349C2#918311yescharacteristic
350C2#940811yescharacteristic
351C2#945211yescharacteristic
352C2#949111yescharacteristic
353C2#951511yescharacteristic
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
#205342
#150972
#81532
#76292
#70362