Finite Group Databasebeta

← D3×#5247 #11800964

Subgroups — D3×#5247 #11800964

Order 1152.

7181 conjugacy classes of subgroups; only the 668 normal subgroups are shown.

normal subgroups only

This group has 7181 conjugacy classes of subgroups — too many to draw. Only its 668 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
1C25×C3×D3C211yesmaximal, characteristic
2C2×D3×#217C216yesmaximal, complemented
3#10592946C211yesmaximal, characteristic, complemented
4C3×#5247C211yesmaximal, characteristic, complemented
5#10591706C216yesmaximal, complemented
6C2×#5247—31nomaximal
7D3×#379—31nomaximal
8C25×C32C2211yescharacteristic
9C24×C3×D3—224no—
10C24×C3×D3C418yescomplemented
11C24×C3×D3C2213yes—
12C24×C3×D3C2213yes—
13C22×D3×Dic3C2214yescomplemented
14C2×#3757C2216yescomplemented
15C2×C3×#217C2216yescomplemented
16D3×#217—224no—
17C2×(C2×D3)⋊Dic3C22112yescomplemented
18C26×C3—31no—
19C25×D3D311yescharacteristic
20C22×#217—36no—
21C2×D3×C22⋊C4—36no—
22C3×#379—31no—
23#5247—36no—
24#5247—31no—
25#5247—31no—
26#5247—61no—
27#5247D311yescharacteristic, direct product factor
28#4955—36no—
29C24×C32—212no—
30C24×C32C2×C414yescomplemented
31C24×C32C2313yes—
32C23×C3×D3—2128no—
33C23×C3×D3—212no—
34C23×C3×D3—296no—
35C23×C3×D3—224no—
36C23×C3×D3—224no—
37C23×C3×D3C2×C4112yes—
38C23×C3×D3C2×C4112yescomplemented
39C23×C3×D3D4124yes—
40C23×C3×D3C2313yes—
41C23×C3×D3C2311yescharacteristic
42C22×C3⋊Dic3C2314yescomplemented
43C22×C3×Dic3C2314yescomplemented
44C2×D3×Dic3—224no—
45#3757—212no—
46C3×#217—212no—
47(C2×D3)⋊Dic3—224no—
48C2×#379—91noSylow
49C25×C3—21no—
50C25×C3—33no—
51C25×C3—38no—
52C25×C3—33no—
53C25×C3—624no—
54C25×C3C2×D311yescharacteristic
55C25×C3C2×D311yescharacteristic
56C24×D3—224no—
57C24×D3Dic318yescomplemented
58C24×D3C2×D313yes—
59C24×D3C2×D313yes—
60C23×Dic3—34no—
61C22×C4×D3—34no—
62C2×C3×C22⋊C4—36no—
63C2×#217—36no—
64C2×#217—36no—
65C2×#217—312no—
66C2×#217—66no—
67C2×#217—624no—
68C2×#217C2×D316yescomplemented
69C2×(C2×D3)⋊C4—312no—
70D3×C22⋊C4—624no—
71C23×C32—232no—
72C23×C32—224no—
73C23×C32—212no—
74C23×C32C22×C416yes—
75C23×C32C2×D4112yes—
76C23×C32C2411yescharacteristic
77C22×C3×D3—296no—
78C22×C3×D3—2256no—
79C22×C3×D3—224no—
80C22×C3×D3—212no—
81C22×C3×D3—248no—
82C22×C3×D3—248no—
83C22×C3×D3—296no—
84C22×C3×D3C22⋊C4148yescomplemented
85C22×C3×D3C22×C416yes—
86C22×C3×D3C22×C412yes—
87C22×C3×D3C2×D4112yes—
88C22×C3×D3C2×D4112yes—
89C2×C3⋊Dic3—212no—
90C2×C3×Dic3—212no—
91D3×Dic3—416no—
92C26—31no—
93C22×C22⋊C4—96no—
94#379—31no—
95#379—96no—
96#379—91no—
97C24×C3—212no—
98C24×C3—212no—
99C24×C3—24no—
100C24×C3—23no—
101C24×C3—31no—
102C24×C3—312no—
103C24×C3—324no—
104C24×C3—33no—
105C24×C3—312no—
106C24×C3—412no—
107C24×C3—696no—
108C24×C3—624no—
109C24×C3—624no—
110C24×C3—6128no—
111C24×C3—612no—
112C24×C3C4×D314yescomplemented
113C24×C3C2×Dic314yescomplemented
114C24×C3C22×D313yes—
115C24×C3C22×D313yes—
116C23×D3—2128no—
117C23×D3—212no—
118C23×D3—296no—
119C23×D3—224no—
120C23×D3—224no—
121C23×D3C2×Dic3112yes—
122C23×D3C2×Dic3112yescomplemented
123C23×D3#67124yes—
124C23×D3C22×D313yes—
125C23×D3C22×D311yescharacteristic
126C22×C3×C4—34no—
127C22×Dic3—34no—
128C22×Dic3—34no—
129C22×Dic3—64no—
130C22×Dic3—624no—
131C22×Dic3C22×D314yescomplemented
132C2×C4×D3—624no—
133C3×C22⋊C4—612no—
134#217—212no—
135#217—624no—
136#217—612no—
137#217—612no—
138#217—1212no—
139(C2×D3)⋊C4—624no—
140C22×C32—232no—
141C22×C32—212no—
142C22×C32—224no—
143C22×C32C2×C22⋊C4112yescomplemented
144C22×C32C23×C411yescharacteristic
145C22×C32C22×D416yes—
146C2×C3×D3—296no—
147C2×C3×D3—212no—
148C2×C3×D3—224no—
149C2×C3×D3—296no—
150C2×C3×D3C2×C22⋊C4112yes—
151C2×C3×D3C2×C22⋊C4112yescomplemented
152C2×C3×D3#120116yes—
153C3⋊Dic3—44no—
154C3×Dic3—44no—
155C25—33no—
156C25—38no—
157C25—33no—
158C25—624no—
159C25D3211yescharacteristic
160C23×C4—94no—
161C2×C22⋊C4—36no—
162C2×C22⋊C4—912no—
163C2×C22⋊C4—96no—
164C2×C22⋊C4—1824no—
165C23×C3—232no—
166C23×C3—232no—
167C23×C3—224no—
168C23×C3—224no—
169C23×C3—212no—
170C23×C3—212no—
171C23×C3—21no—
172C23×C3—26no—
173C23×C3—212no—
174C23×C3—32no—
175C23×C3—312no—
176C23×C3—348no—
177C23×C3—36no—
178C23×C3—312no—
179C23×C3—412no—
180C23×C3—424no—
181C23×C3—432no—
182C23×C3—648no—
183C23×C3—648no—
184C23×C3—696no—
185C23×C3—6256no—
186C23×C3—696no—
187C23×C3—624no—
188C23×C3—612no—
189C23×C3C2×C4×D316yes—
190C23×C3D3×D4112yes—
191C23×C3C22×Dic316yes—
192C23×C3C2×#67112yes—
193C23×C3C23×D311yescharacteristic
194C23×C3C23×D311yescharacteristic
195C22×D3—296no—
196C22×D3—2256no—
197C22×D3—224no—
198C22×D3—212no—
199C22×D3—248no—
200C22×D3—248no—
201C22×D3—296no—
202C22×D3#217148yescomplemented
203C22×D3C22×Dic316yes—
204C22×D3C22×Dic312yes—
205C22×D3C2×#67112yes—
206C22×D3C2×#67112yes—
207C2×C3×C4—612no—
208C2×Dic3—212no—
209C2×Dic3—612no—
210C2×Dic3—612no—
211C2×Dic3—1212no—
212C2×Dic3—1216no—
213C4×D3—1216no—
214C2×C32—212no—
215C2×C32C22×C22⋊C413yes—
216C2×C32C2×#12014yes—
217C3×D3—212no—
218C3×D3#37918yescomplemented
219C24—212no—
220C24—31no—
221C24—33no—
222C24—312no—
223C24—324no—
224C24—312no—
225C24—624no—
226C24—624no—
227C24—696no—
228C24—6128no—
229C24—612no—
230C24D3×Dic314yescomplemented
231C24C2×D3213yes—
232C22×C4—34no—
233C22×C4—94no—
234C22×C4—1824no—
235C22⋊C4—612no—
236C22⋊C4—1824no—
237C22⋊C4—1812no—
238C22×C3—232no—
239C22×C3—232no—
240C22×C3—212no—
241C22×C3—212no—
242C22×C3—224no—
243C22×C3—224no—
244C22×C3—21no—
245C22×C3—26no—
246C22×C3—212no—
247C22×C3—312no—
248C22×C3—316no—
249C22×C3—312no—
250C22×C3—412no—
251C22×C3—424no—
252C22×C3—432no—
253C22×C3—696no—
254C22×C3—696no—
255C22×C3—612no—
256C22×C3—624no—
257C22×C3D3×C22⋊C4112yescomplemented
258C22×C3C2×#217112yescomplemented
259C22×C3C22×C4×D311yescharacteristic
260C22×C3C2×D3×D416yes—
261C22×C3C23×Dic311yescharacteristic
262C22×C3C22×#6716yes—
263C2×D3—296no—
264C2×D3—212no—
265C2×D3—224no—
266C2×D3—296no—
267C2×D3C2×#217112yes—
268C2×D3C2×#217112yescomplemented
269C2×D3#953116yes—
270C3×C4—124no—
271Dic3—44no—
272Dic3—124no—
273Dic3—124no—
274Dic3—244no—
275C32C2×#37911yescharacteristic, complemented, Sylow
276C23—232no—
277C23—212no—
278C23—224no—
279C23—32no—
280C23—312no—
281C23—36no—
282C23—312no—
283C23—348no—
284C23—648no—
285C23—648no—
286C23—696no—
287C23—6256no—
288C23—696no—
289C23—612no—
290C23—624no—
291C23C2×D3×Dic316yes—
292C23D3×#67112yes—
293C23C22×D3211yescharacteristic
294C2×C4—612no—
295C2×C4—1812no—
296C2×C4—3616no—
297C2×C3—212no—
298C2×C3—212no—
299C2×C3—23no—
300C2×C3—24no—
301C2×C3—38no—
302C2×C3—412no—
303C2×C3—612no—
304C2×C3C2×D3×C22⋊C413yes—
305C2×C3D3×#12014yes—
306C2×C3C22×#21713yes—
307C2×C3C2×#95314yes—
308D3—212no—
309D3#524718yesdirect product factor
310C22—232no—
311C22—212no—
312C22—224no—
313C22—312no—
314C22—316no—
315C22—312no—
316C22—696no—
317C22—696no—
318C22—612no—
319C22—624no—
320C22D3×#217112yescomplemented
321C22C22×D3×Dic311yescharacteristic
322C22C2×D3×#6716yes—
323C4—124no—
324C4—364no—
325C3—21no—
326C3D3×#37911yescharacteristic, complemented
327C3C2×#524711yescharacteristic, complemented
328C2—212no—
329C2—38no—
330C2—612no—
331C2C2×D3×#21713yes—
332C2D3×#95314yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC25×C32C22
socle, cosocleC23×C32C24
prime radicalC25×C3×D3C2
hypercenterC25D32
hypocenterC32C2×#379
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C25

Complements

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

NH ≅ G/Ntype
2. C2×D3×#217C2semidirect
3. #10592946C2semidirect
4. C3×#5247C2semidirect
5. #10591706C2semidirect
10. C24×C3×D3C4semidirect
13. C22×D3×Dic3C22semidirect
14. C2×#3757C22semidirect
15. C2×C3×#217C22semidirect
17. C2×(C2×D3)⋊Dic3C22semidirect
27. #5247D3direct (N × H)
30. C24×C32C2×C4semidirect
38. C23×C3×D3C2×C4semidirect
42. C22×C3⋊Dic3C23semidirect
43. C22×C3×Dic3C23semidirect
57. C24×D3Dic3semidirect
68. C2×#217C2×D3semidirect
84. C22×C3×D3C22⋊C4semidirect
112. C24×C3C4×D3semidirect
113. C24×C3C2×Dic3semidirect
122. C23×D3C2×Dic3semidirect
131. C22×Dic3C22×D3semidirect
143. C22×C32C2×C22⋊C4semidirect
151. C2×C3×D3C2×C22⋊C4semidirect
202. C22×D3#217semidirect
218. C3×D3#379semidirect
230. C24D3×Dic3semidirect
257. C22×C3D3×C22⋊C4semidirect
258. C22×C3C2×#217semidirect
268. C2×D3C2×#217semidirect
275. C32C2×#379semidirect
309. D3#5247direct (N × H)
320. C22D3×#217semidirect
326. C3D3×#379semidirect
327. C3C2×#5247semidirect

Maximal subgroups

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

subgroupindex
C25×C3×D32
C2×D3×#2172
#105929462
C3×#52472
#105917062
C2×#52473
D3×#3793