Finite Group Databasebeta

← #99846

Subgroups — #99846

Order 512.

538 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 108 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#14314C211yesmaximal, characteristic
3C4×#324C211yesmaximal, characteristic
4#7573C212yesmaximal
5#7024C212yesmaximal
6C2×#432—21no—
7C2×#398C411yescharacteristic
8C2×#389C2211yescharacteristic
9C2×#387—21no—
10C2×C4×C4⋊C4C2211yescharacteristic
11#1940—24no—
12#1797—21no—
13#1797C2212yes—
14C4×C22⋊C8C2212yes—
15C2×#324—21no—
16#1445C411yescharacteristic
17#1443—21no—
18#1442C411yescharacteristic
19#1441—21no—
20#1441C411yescharacteristic
21#1436—21no—
22#1434C2211yescharacteristic
23#1280—21no—
24#1271—24no—
25C22×C4⋊C4—21no—
26C22×C4⋊C4—21no—
27C22×C4⋊C4C2×C411yescharacteristic
28C22×C4⋊C4C2×C411yescharacteristic
29C22×C4⋊C4C2×C411yescharacteristic
30C22×C4⋊C4D411yescharacteristic
31C22×C42D411yescharacteristic
32C22×C42D411yescharacteristic
33C22×C42C2311yescharacteristic
34#432—42no—
35#432—42no—
36C2×C4⋊C8—22no—
37C2×C4⋊C8—22no—
38C2×C4⋊C8—22no—
39C2×C22⋊C8—22no—
40C2×C22⋊C8—22no—
41C2×#97—22no—
42C2×C4×C8—22no—
43#398—22no—
44#398—22no—
45#389—22no—
46#389—22no—
47#387—42no—
48#387—42no—
49C4×C4⋊C4—22no—
50C4×C4⋊C4—22no—
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×#95—21no—
60C2×#95—21no—
61C2×#95C2×C411yescharacteristic
62C2×#95C2×C411yescharacteristic
63C2×#95C2×C411yescharacteristic
64C2×#95D411yescharacteristic
65#336—22no—
66#336—22no—
67#336D414yes—
68#324—24no—
69C23×C4—21no—
70C23×C4—21no—
71C23×C4—21no—
72C23×C4—21no—
73C23×C4C22⋊C411yescharacteristic
74C23×C4C22⋊C411yescharacteristic
75C23×C4C22⋊C411yescharacteristic
76C23×C4C22⋊C411yescharacteristic
77C23×C4C22×C411yescharacteristic
78C23×C4C2×D411yescharacteristic
79C23×C4C2×D411yescharacteristic
80C22×C8—24no—
81C22×C8—42no—
82C2×C4⋊C4—22no—
83C2×C4⋊C4—22no—
84C2×C4⋊C4—24no—
85C2×C4⋊C4—22no—
86C2×C4⋊C4—22no—
87C2×C4⋊C4—22no—
88C2×C4⋊C4—21no—
89C2×C4⋊C4—21no—
90C2×C4⋊C4—21no—
91C2×C4⋊C4—22no—
92C2×C4⋊C4—22no—
93C2×C4⋊C4—41no—
94C2×C4⋊C4—42no—
95C2×C4⋊C4—42no—
96C2×C4⋊C4—41no—
97C2×C4⋊C4—41no—
98C2×C4⋊C4—41no—
99C2×C4⋊C4—41no—
100C2×C4⋊C4—41no—
101C2×C4⋊C4—41no—
102C2×C4⋊C4—81no—
103C2×C4⋊C4M1612yes—
104C2×C42—21no—
105C2×C42—21no—
106C2×C42—21no—
107C2×C42—21no—
108C2×C42—21no—
109C2×C42—21no—
110C2×C42—81no—
111C2×C42—81no—
112C2×C42D812yes—
113C2×C42SD1612yes—
114C2×C42C2×D412yes—
115C2×C42#4112yes—
116C4⋊C8—44no—
117C4⋊C8—82no—
118C4⋊C8—82no—
119C22⋊C8—24no—
120C22⋊C8—42no—
121C22⋊C8—42no—
122C22⋊C8—42no—
123#97—44no—
124C4×C8—82no—
125#95—24no—
126#95—22no—
127#95—22no—
128#95—21no—
129#95—22no—
130#95—42no—
131#95—42no—
132#95—42no—
133#95—42no—
134#95—42no—
135#95—41no—
136#95—41no—
137#95—81no—
138#95—81no—
139#95—81no—
140#95M1612yes—
141C24C2×C22⋊C411yescharacteristic
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—22no—
157C22×C4—22no—
158C22×C4—21no—
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—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#10212yes—
198C22×C4#10212yes—
199C22×C4#10412yes—
200C22×C4C4×D412yes—
201C22×C4#12011yescharacteristic
202C22×C4#12112yes—
203C22×C4#12311yescharacteristic
204C22×C4C2×M1611yescharacteristic
205C22×C4C2×M1611yescharacteristic
206C22×C4#13112yes—
207C22×C4C2×D811yescharacteristic
208C22×C4C2×SD1611yescharacteristic
209C22×C4AGL(1,ℤ/8)11yescharacteristic
210C22×C4#13711yescharacteristic
211C2×C8—44no—
212C2×C8—44no—
213C2×C8—44no—
214C2×C8—44no—
215C2×C8—82no—
216C2×C8—82no—
217C4⋊C4—24no—
218C4⋊C4—44no—
219C4⋊C4—48no—
220C4⋊C4—42no—
221C4⋊C4—42no—
222C4⋊C4—42no—
223C4⋊C4—82no—
224C4⋊C4—81no—
225C4⋊C4—81no—
226C4⋊C4—81no—
227C4⋊C4—81no—
228C42—22no—
229C42—22no—
230C42—22no—
231C42—22no—
232C42—42no—
233C42—42no—
234C42—42no—
235C42—81no—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23#38611yescharacteristic
241C23#40711yescharacteristic
242C23#40811yescharacteristic
243C23C2×#10211yescharacteristic
244C23#41711yescharacteristic
245C23C2×#10411yescharacteristic
246C23#42111yescharacteristic
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—42no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
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—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4#43512yes—
316C2×C4#43612yes—
317C2×C4#44711yescharacteristic
318C2×C4#44811yescharacteristic
319C2×C4#48011yescharacteristic
320C2×C4#48111yescharacteristic
321C8—84no—
322C8—84no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22#148611yescharacteristic
336C22#148911yescharacteristic
337C22#149211yescharacteristic
338C22#149511yescharacteristic
339C22#187011yescharacteristic
340C22#187111yescharacteristic
341C22#187411yescharacteristic
342C22#190911yescharacteristic
343C22#191211yescharacteristic
344C22#191311yescharacteristic
345C22#191511yescharacteristic
346C4—22no—
347C4—22no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—42no—
353C4—42no—
354C4—42no—
355C4—42no—
356C4—82no—
357C4—81no—
358C4—82no—
359C4—161no—
360C4—161no—
361C2—21no—
362C2—21no—
363C2—21no—
364C2—21no—
365C2#894411yescharacteristic
366C2#910411yescharacteristic
367C2#911011yescharacteristic
368C2#918311yescharacteristic
369C2#919011yescharacteristic
370C2#919511yescharacteristic
371C2#920411yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C22 ▷ 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
#143142
C4×#3242
#75732
#70242