Finite Group Databasebeta

← #100178

Subgroups — #100178

Order 512.

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

normal subgroups only

This group has 540 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#21912C211yesmaximal, characteristic
2#14223C211yesmaximal, characteristic
3#8706C212yesmaximal
4#8560C211yesmaximal, characteristic
5#7024C212yesmaximal
6C2×#398C411yescharacteristic
7C2×#387—21no—
8C2×C4×C4⋊C4C2211yescharacteristic
9C2×C4×C4⋊C4C2211yescharacteristic
10#1916—24no—
11#1817—21no—
12#1797—21no—
13#1797C2212yes—
14C4×C22⋊C8C2212yes—
15C2×#324—21no—
16#1445C411yescharacteristic
17#1442C411yescharacteristic
18#1441C411yescharacteristic
19#1436—21no—
20#1434—21no—
21#1434—21no—
22#1434C2211yescharacteristic
23#1280—21no—
24#1279—24no—
25C22×C4⋊C4—21no—
26C22×C4⋊C4C2×C411yescharacteristic
27C22×C4⋊C4C2×C411yescharacteristic
28C22×C4⋊C4C2×C411yescharacteristic
29C22×C4⋊C4D411yescharacteristic
30C22×C42—21no—
31C22×C42D411yescharacteristic
32C22×C42D411yescharacteristic
33C22×C42C2311yescharacteristic
34C2×C4⋊C8—22no—
35C2×C4⋊C8—22no—
36C2×C22⋊C8—22no—
37C2×C22⋊C8—22no—
38C2×C4×C8D414yes—
39#398—22no—
40#398—22no—
41#387—42no—
42#387—42no—
43C4×C4⋊C4—22no—
44C4×C4⋊C4—22no—
45C4×C4⋊C4—22no—
46C4×C4⋊C4—22no—
47C2×#95—21no—
48C2×#95—21no—
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×#95C2×C411yescharacteristic
58C2×#95C2×C411yescharacteristic
59C2×#95C2×C411yescharacteristic
60C2×#95D411yescharacteristic
61#336—22no—
62#336—24no—
63#336—22no—
64#336—22no—
65#324—42no—
66C23×C4—21no—
67C23×C4—21no—
68C23×C4—21no—
69C23×C4—21no—
70C23×C4C22⋊C411yescharacteristic
71C23×C4C22⋊C411yescharacteristic
72C23×C4C22⋊C411yescharacteristic
73C23×C4C22⋊C411yescharacteristic
74C23×C4C22×C411yescharacteristic
75C23×C4C2×D411yescharacteristic
76C23×C4C2×D411yescharacteristic
77C22×C8—24no—
78C22×C8—42no—
79C2×C4⋊C4—22no—
80C2×C4⋊C4—22no—
81C2×C4⋊C4—22no—
82C2×C4⋊C4—22no—
83C2×C4⋊C4—22no—
84C2×C4⋊C4—24no—
85C2×C4⋊C4—22no—
86C2×C4⋊C4—21no—
87C2×C4⋊C4—21no—
88C2×C4⋊C4—21no—
89C2×C4⋊C4—22no—
90C2×C4⋊C4—42no—
91C2×C4⋊C4—42no—
92C2×C4⋊C4—42no—
93C2×C4⋊C4M1612yes—
94C2×C4⋊C4D812yes—
95C2×C4⋊C4SD1612yes—
96C2×C42—21no—
97C2×C42—21no—
98C2×C42—21no—
99C2×C42—21no—
100C2×C42—42no—
101C2×C42—41no—
102C2×C42—41no—
103C2×C42—42no—
104C2×C42—42no—
105C2×C42—41no—
106C2×C42—41no—
107C2×C42—42no—
108C2×C42C2×D412yes—
109C2×C42#4112yes—
110C4⋊C8—44no—
111C4⋊C8—82no—
112C22⋊C8—42no—
113C22⋊C8—42no—
114C22⋊C8—42no—
115C22⋊C8—42no—
116C4×C8—44no—
117#95—24no—
118#95—22no—
119#95—22no—
120#95—21no—
121#95—22no—
122#95—42no—
123#95—42no—
124#95—42no—
125#95—42no—
126#95—42no—
127#95—42no—
128#95—42no—
129#95—41no—
130#95—41no—
131#95—41no—
132#95—41no—
133#95M1612yes—
134C24C2×C22⋊C411yescharacteristic
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—21no—
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—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#10212yes—
192C22×C4#10212yes—
193C22×C4C4×D412yes—
194C22×C4#12011yescharacteristic
195C22×C4#12112yes—
196C22×C4#12311yescharacteristic
197C22×C4C2×M1611yescharacteristic
198C22×C4C2×M1611yescharacteristic
199C22×C4#13112yes—
200C22×C4C2×D811yescharacteristic
201C22×C4C2×SD1611yescharacteristic
202C22×C4#13512yes—
203C2×C8—44no—
204C2×C8—44no—
205C2×C8—44no—
206C2×C8—82no—
207C2×C8—82no—
208C2×C8—82no—
209C4⋊C4—24no—
210C4⋊C4—24no—
211C4⋊C4—24no—
212C4⋊C4—24no—
213C4⋊C4—42no—
214C4⋊C4—48no—
215C4⋊C4—42no—
216C4⋊C4—42no—
217C4⋊C4—42no—
218C42—24no—
219C42—42no—
220C42—42no—
221C42—42no—
222C42—42no—
223C42—81no—
224C42—82no—
225C42—82no—
226C23—21no—
227C23—21no—
228C23—21no—
229C23—21no—
230C23#38611yescharacteristic
231C23#40711yescharacteristic
232C23#40811yescharacteristic
233C23C2×#10211yescharacteristic
234C23#41611yescharacteristic
235C23#42111yescharacteristic
236C23#42111yescharacteristic
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
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#43512yes—
305C2×C4#43612yes—
306C2×C4#45812yes—
307C2×C4#46512yes—
308C2×C4#46612yes—
309C8—84no—
310C8—162no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22#148011yescharacteristic
324C22#148211yescharacteristic
325C22#148611yescharacteristic
326C22#148811yescharacteristic
327C22#187011yescharacteristic
328C22#189011yescharacteristic
329C22#189111yescharacteristic
330C22#189311yescharacteristic
331C22#189711yescharacteristic
332C22#190911yescharacteristic
333C22#191211yescharacteristic
334C4—22no—
335C4—22no—
336C4—22no—
337C4—22no—
338C4—22no—
339C4—41no—
340C4—42no—
341C4—42no—
342C4—82no—
343C4—81no—
344C4—82no—
345C4—81no—
346C4—82no—
347C4—161no—
348C2—21no—
349C2—21no—
350C2—21no—
351C2—21no—
352C2#896811yescharacteristic
353C2#907611yescharacteristic
354C2#910411yescharacteristic
355C2#947011yescharacteristic
356C2#948211yescharacteristic
357C2#948611yescharacteristic
358C2#949311yescharacteristic
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
#219122
#142232
#87062
#85602
#70242