Finite Group Databasebeta

← #119469

Subgroups — #119469

Order 512.

930 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 138 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
1C2×#1821C211yesmaximal, characteristic
2#14342C211yesmaximal, characteristic
3#13904C211yesmaximal, characteristic
4#8015C212yesmaximal
5C2×#1284C212yesmaximal
6C23×C4⋊C4C2211yescharacteristic
7C2×#407C2212yes—
8C2×#381—22no—
9C2×#381C2212yes—
10C2×#380C2211yescharacteristic
11C2×C4×C22⋊C4C2211yescharacteristic
12#1821—24no—
13C2×#343—22no—
14#1445—24no—
15#1445—22no—
16C4⋊#95C414yescomplemented
17C22⋊#95—22no—
18#1294—24no—
19#1284—24no—
20C24×C4D412yes—
21C24×C4C2311yescharacteristic
22C22×M16—22no—
23C22×C4⋊C4—22no—
24C22×C4⋊C4—22no—
25C22×C4⋊C4—22no—
26C22×C4⋊C4—22no—
27C22×C4⋊C4—22no—
28C22×C4⋊C4—22no—
29C22×C4⋊C4C2×C412yes—
30C22×C4⋊C4C2×C412yes—
31C22×C4⋊C4D412yes—
32C22×C22⋊C4—21no—
33C22×C22⋊C4—22no—
34C22×C22⋊C4—21no—
35C22×C42C2×C412yes—
36#407—22no—
37#407—22no—
38#407—22no—
39#407D414yes—
40C2×C22⋊C8—22no—
41C2×C22⋊C8—22no—
42#381—22no—
43#381—22no—
44#381—22no—
45#381—22no—
46#381—48no—
47#380—22no—
48#380—22no—
49C4×C22⋊C4—22no—
50C4×C22⋊C4—22no—
51C2×#95—28no—
52C2×#95—21no—
53C2×#95—21no—
54C2×#95—22no—
55C2×#95—24no—
56C2×#95—24no—
57C2×#95D414yes—
58#343—28no—
59C25C2×D411yescharacteristic
60C23×C4—22no—
61C23×C4—22no—
62C23×C4—24no—
63C23×C4—24no—
64C23×C4—22no—
65C23×C4—22no—
66C23×C4—24no—
67C23×C4—44no—
68C23×C4—44no—
69C23×C4—44no—
70C23×C4C22⋊C414yes—
71C23×C4C22×C411yescharacteristic
72C23×C4C2×D411yescharacteristic
73C23×C4C2×D412yes—
74C23×C4C2×D412yes—
75C23×C4#4112yes—
76C23×C4#4112yes—
77C23×C4#4112yes—
78C23×C4#4112yes—
79C2×M16—24no—
80C2×M16—42no—
81C2×M16—48no—
82C22×C8—42no—
83C2×C4⋊C4—22no—
84C2×C4⋊C4—22no—
85C2×C4⋊C4—24no—
86C2×C4⋊C4—24no—
87C2×C4⋊C4—22no—
88C2×C4⋊C4—24no—
89C2×C4⋊C4—24no—
90C2×C4⋊C4—22no—
91C2×C4⋊C4—24no—
92C2×C4⋊C4—42no—
93C2×C4⋊C4—42no—
94C2×C4⋊C4—42no—
95C2×C4⋊C4—42no—
96C2×C4⋊C4—42no—
97C2×C4⋊C4—42no—
98C2×C4⋊C4—42no—
99C2×C4⋊C4—42no—
100C2×C4⋊C4—44no—
101C2×C22⋊C4—24no—
102C2×C22⋊C4—42no—
103C2×C22⋊C4—42no—
104C2×C22⋊C4—48no—
105C2×C22⋊C4—44no—
106C2×C22⋊C4—41no—
107C2×C22⋊C4—42no—
108C2×C22⋊C4—41no—
109C2×C22⋊C4—42no—
110C2×C42—24no—
111C2×C42—44no—
112C22⋊C8—24no—
113C22⋊C8—24no—
114C22⋊C8—42no—
115C22⋊C8—42no—
116#95—24no—
117#95—24no—
118#95—416no—
119#95—41no—
120#95—42no—
121#95—42no—
122#95—41no—
123#95—42no—
124#95—84no—
125#95—84no—
126C24—24no—
127C24—22no—
128C24—22no—
129C24—42no—
130C24C2×C22⋊C411yescharacteristic
131C24#12011yescharacteristic
132C24#12112yes—
133C24#12311yescharacteristic
134C24#12312yes—
135C22×C4—24no—
136C22×C4—24no—
137C22×C4—24no—
138C22×C4—24no—
139C22×C4—24no—
140C22×C4—24no—
141C22×C4—44no—
142C22×C4—44no—
143C22×C4—44no—
144C22×C4—44no—
145C22×C4—44no—
146C22×C4—44no—
147C22×C4—44no—
148C22×C4—44no—
149C22×C4—42no—
150C22×C4—44no—
151C22×C4—416no—
152C22×C4—42no—
153C22×C4—44no—
154C22×C4—44no—
155C22×C4—44no—
156C22×C4—44no—
157C22×C4—44no—
158C22×C4—44no—
159C22×C4—48no—
160C22×C4—48no—
161C22×C4—44no—
162C22×C4—42no—
163C22×C4—44no—
164C22×C4—44no—
165C22×C4—44no—
166C22×C4—44no—
167C22×C4—82no—
168C22×C4—82no—
169C22×C4—88no—
170C22×C4#11711yescharacteristic
171C22×C4#11711yescharacteristic
172C22×C4C4×D412yes—
173C22×C4C4×D412yes—
174C22×C4#12011yescharacteristic
175C22×C4#12112yes—
176C22×C4#12112yes—
177C22×C4#12112yes—
178C22×C4#12312yes—
179C22×C4#12311yescharacteristic
180C22×C4#12312yes—
181C22×C4#12312yes—
182C22×C4#12412yes—
183C22×C4#12412yes—
184C22×C4#12612yes—
185C22×C4#12612yes—
186M16—48no—
187M16—84no—
188C2×C8—44no—
189C2×C8—84no—
190C4⋊C4—44no—
191C4⋊C4—44no—
192C4⋊C4—44no—
193C4⋊C4—44no—
194C4⋊C4—84no—
195C22⋊C4—48no—
196C22⋊C4—84no—
197C22⋊C4—84no—
198C22⋊C4—82no—
199C22⋊C4—82no—
200C42—84no—
201C23—21no—
202C23—21no—
203C23—22no—
204C23—22no—
205C23—22no—
206C23—24no—
207C23—21no—
208C23—21no—
209C23—24no—
210C23—22no—
211C23—22no—
212C23—24no—
213C23—24no—
214C23—42no—
215C23—42no—
216C23—48no—
217C23—48no—
218C23#38111yescharacteristic
219C23#38611yescharacteristic
220C23#38611yescharacteristic
221C23#39412yes—
222C23#39712yes—
223C23#41014yes—
224C23#45312yes—
225C23#45512yes—
226C2×C4—24no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—24no—
230C2×C4—24no—
231C2×C4—24no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—44no—
243C2×C4—48no—
244C2×C4—48no—
245C2×C4—44no—
246C2×C4—44no—
247C2×C4—44no—
248C2×C4—82no—
249C2×C4—84no—
250C2×C4—88no—
251C2×C4—82no—
252C2×C4—88no—
253C2×C4—84no—
254C2×C4—84no—
255C2×C4—84no—
256C2×C4—88no—
257C2×C4—88no—
258C2×C4—88no—
259C2×C4—82no—
260C2×C4—82no—
261C2×C4—82no—
262C2×C4—84no—
263C2×C4#38812yes—
264C2×C4#38812yes—
265C2×C4#39412yes—
266C2×C4#39712yes—
267C8—84no—
268C22—21no—
269C22—22no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—22no—
274C22—24no—
275C22—24no—
276C22—24no—
277C22—24no—
278C22—22no—
279C22—22no—
280C22—22no—
281C22—48no—
282C22—48no—
283C22—42no—
284C22—42no—
285C22#144011yescharacteristic
286C22#182012yes—
287C22#188511yescharacteristic
288C22#188711yescharacteristic
289C22#189912yes—
290C22#189912yes—
291C22#191212yes—
292C22#203714yes—
293C4—22no—
294C4—22no—
295C4—22no—
296C4—22no—
297C4—84no—
298C4—84no—
299C4—164no—
300C4—162no—
301C2—22no—
302C2—24no—
303C2—22no—
304C2—42no—
305C2#946012yes—
306C2#946412yes—
307C2#1115611yescharacteristic
308C2#1116111yescharacteristic
309C2#1119711yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC23×C4C22×C4
Frattini, cosocleC24×C4C23
prime radicalC25C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C24×C4 ▷ C22 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
16. C4⋊#95C4semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#18212
#143422
#139042
#80152
C2×#12842