Finite Group Databasebeta

← #140924

Subgroups — #140924

Order 512.

582 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 118 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#15151C211yesmaximal, characteristic
2C2×#1346C214yesmaximal
3#10847C211yesmaximal, characteristic
4C4×#324C211yesmaximal, characteristic
5C2×#423—21no—
6C2×#398—21no—
7C2×#398C2212yes—
8C2×#389—21no—
9C2×#384C411yescharacteristic
10C2×C4×C4⋊C4C2211yescharacteristic
11C4×C22⋊C8—21no—
12C2×#343—21no—
13C2×#343C2212yes—
14C2×#324C2212yes—
15#1445—21no—
16#1445C412yes—
17C4⋊#95—21no—
18C4⋊#95C411yescharacteristic
19#1346—28no—
20#1280—21no—
21C22×M16—22no—
22C22×C4⋊C4—21no—
23C22×C4⋊C4—21no—
24C22×C4⋊C4—21no—
25C22×C4⋊C4—22no—
26C22×C4⋊C4C2×C412yes—
27C22×C4⋊C4D411yescharacteristic
28C22×C4⋊C4C2311yescharacteristic
29C22×C42C2×C411yescharacteristic
30C22×C42D411yescharacteristic
31C22×C42D411yescharacteristic
32#423—24no—
33#423—42no—
34C2×C4⋊C8—41no—
35C2×C4⋊C8—41no—
36C2×C22⋊C8—22no—
37C2×C4×C8—41no—
38#398—24no—
39#398—24no—
40#398—42no—
41#398—42no—
42#389—42no—
43#389—42no—
44#384—41no—
45#384—41no—
46C4×C4⋊C4—41no—
47C4×C4⋊C4—41no—
48C2×#95—22no—
49C2×#95—21no—
50C2×#95—22no—
51C2×#95—22no—
52C2×#95C2×C412yes—
53C2×#95C2×C411yescharacteristic
54C2×#95D411yescharacteristic
55#343—24no—
56#343—42no—
57#336—41no—
58#324—22no—
59#324D414yes—
60C23×C4—22no—
61C23×C4—22no—
62C23×C4C22⋊C411yescharacteristic
63C23×C4C22⋊C411yescharacteristic
64C23×C4C22⋊C411yescharacteristic
65C23×C4C22⋊C411yescharacteristic
66C23×C4C22×C411yescharacteristic
67C23×C4C2×D411yescharacteristic
68C23×C4C2×D411yescharacteristic
69C2×M16—24no—
70C2×M16—42no—
71C2×M16—42no—
72C2×M16—42no—
73C2×M16—42no—
74C2×M16—42no—
75C22×C8—42no—
76C22×C8—42no—
77C2×C4⋊C4—24no—
78C2×C4⋊C4—24no—
79C2×C4⋊C4—41no—
80C2×C4⋊C4—41no—
81C2×C4⋊C4—41no—
82C2×C4⋊C4—41no—
83C2×C4⋊C4—42no—
84C2×C4⋊C4—42no—
85C2×C4⋊C4—42no—
86C2×C4⋊C4—42no—
87C2×C4⋊C4—42no—
88C2×C4⋊C4—42no—
89C2×C4⋊C4—41no—
90C2×C4⋊C4—41no—
91C2×C4⋊C4—42no—
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⋊C4D812yes—
101C2×C4⋊C4SD1612yes—
102C2×C4⋊C4C2×D412yes—
103C2×C4⋊C4#4112yes—
104C2×C42—21no—
105C2×C42—21no—
106C2×C42—22no—
107C2×C42—21no—
108C2×C42—21no—
109C2×C42—21no—
110C2×C42—21no—
111C2×C42—42no—
112C2×C42—42no—
113C2×C42D812yes—
114C2×C42SD1612yes—
115C4⋊C8—44no—
116C4⋊C8—44no—
117C22⋊C8—24no—
118C22⋊C8—42no—
119C4×C8—82no—
120#95—24no—
121#95—41no—
122#95—41no—
123#95—44no—
124#95—42no—
125#95—44no—
126#95—44no—
127C24C2×C22⋊C411yescharacteristic
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—21no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—21no—
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—24no—
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—42no—
156C22×C4—42no—
157C22×C4—42no—
158C22×C4—42no—
159C22×C4—42no—
160C22×C4—42no—
161C22×C4—42no—
162C22×C4—42no—
163C22×C4—42no—
164C22×C4—42no—
165C22×C4—42no—
166C22×C4—42no—
167C22×C4—42no—
168C22×C4#9911yescharacteristic
169C22×C4#9911yescharacteristic
170C22×C4#10212yes—
171C22×C4#10212yes—
172C22×C4#10212yes—
173C22×C4#10212yes—
174C22×C4#10412yes—
175C22×C4C4×D412yes—
176C22×C4#12112yes—
177C22×C4#12411yescharacteristic
178C22×C4#12711yescharacteristic
179C22×C4C2×D811yescharacteristic
180C22×C4C2×D811yescharacteristic
181C22×C4C2×SD1611yescharacteristic
182C22×C4C2×SD1611yescharacteristic
183M16—44no—
184M16—44no—
185M16—82no—
186M16—82no—
187C2×C8—44no—
188C2×C8—44no—
189C2×C8—82no—
190C2×C8—82no—
191C2×C8—82no—
192C2×C8—82no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—42no—
197C4⋊C4—48no—
198C4⋊C4—84no—
199C4⋊C4—84no—
200C4⋊C4—82no—
201C4⋊C4—82no—
202C4⋊C4—82no—
203C4⋊C4—82no—
204C4⋊C4—82no—
205C4⋊C4—82no—
206C42—22no—
207C42—22no—
208C42—22no—
209C42—22no—
210C42—42no—
211C42—42no—
212C42—42no—
213C42—81no—
214C23—21no—
215C23—21no—
216C23—21no—
217C23—21no—
218C23#39011yescharacteristic
219C23C2×#9911yescharacteristic
220C23#41011yescharacteristic
221C23C2×#10211yescharacteristic
222C23C2×#10211yescharacteristic
223C23C2×#10411yescharacteristic
224C23#42111yescharacteristic
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—24no—
240C2×C4—24no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—44no—
264C2×C4—44no—
265C2×C4—44no—
266C2×C4—81no—
267C2×C4—81no—
268C2×C4—81no—
269C2×C4—82no—
270C2×C4—82no—
271C2×C4—82no—
272C2×C4—82no—
273C2×C4—82no—
274C2×C4—82no—
275C2×C4—82no—
276C2×C4—82no—
277C2×C4—82no—
278C2×C4—82no—
279C2×C4—82no—
280C2×C4#32712yes—
281C2×C4#32712yes—
282C2×C4#35212yes—
283C2×C4#35612yes—
284C2×C4#48611yescharacteristic
285C2×C4#48611yescharacteristic
286C2×C4#49211yescharacteristic
287C2×C4#49311yescharacteristic
288C8—84no—
289C8—84no—
290C22—21no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22C2×#32711yescharacteristic
303C22#150211yescharacteristic
304C22#151711yescharacteristic
305C22#151911yescharacteristic
306C22#195711yescharacteristic
307C22#196411yescharacteristic
308C22#198011yescharacteristic
309C22C2×#35211yescharacteristic
310C22#212311yescharacteristic
311C22C2×#35611yescharacteristic
312C22#213511yescharacteristic
313C4—22no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—42no—
319C4—42no—
320C4—42no—
321C4—42no—
322C4—42no—
323C4—84no—
324C4—162no—
325C4#134614yescomplemented
326C2—21no—
327C2—21no—
328C2—21no—
329C2—21no—
330C2#968011yescharacteristic
331C2C2×#134611yescharacteristic
332C2#1170011yescharacteristic
333C2#1188111yescharacteristic
334C2#1188311yescharacteristic
335C2#1322011yescharacteristic
336C2#1322711yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC23×C4C22×C4
Frattini, cosocleC22×C4⋊C4C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
325. C4#1346semidirect

Maximal subgroups

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

subgroupindex
#151512
C2×#13462
#108472
C4×#3242