Finite Group Databasebeta

← #11802433

Subgroups — #11802433

Order 1152.

1161 conjugacy classes of subgroups; only the 300 normal subgroups are shown.

normal subgroups only

This group has 1161 conjugacy classes of subgroups — too many to draw. Only its 300 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×C3×#876C211yesmaximal, characteristic
2C42×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C3×#4937C211yesmaximal, characteristic, complemented
4#10591368C213yesmaximal
5#10591286C213yesmaximal
6#10591241C213yesmaximal, complemented
7#10591192C213yesmaximal, complemented
8Dic3×#126—31nomaximal
9#74259—31nomaximal
10C22×D3×Dic3C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C2×C4×C3⋊Dic3C2213yes—
13C2×C4×C3⋊Dic3C2213yes—
14C2×C3×(C2×D3)⋊C4C2213yes—
15C2×C3×Dic3⋊C4C2213yes—
16C3×#876C418yescomplemented
17C2×Dic3⋊Dic3C2213yes—
18C2×(C2×D3)⋊Dic3C2213yes—
19C2×Dic32C2213yes—
20C3×C3⋊#95C2213yes—
21C3×C3⋊#95C2213yes—
22#63579C2213yes—
23#63579C2213yes—
24C2×C3×#126—31no—
25C2×#876D311yescharacteristic
26C3×#383—31no—
27#4980—33no—
28Dic3×C4⋊C4—33no—
29#4951—33no—
30Dic3×C22⋊C4—33no—
31#4937D311yescharacteristic, complemented
32C42×Dic3—31no—
33C42×Dic3—31no—
34C42×Dic3—61no—
35#4669—33no—
36#4666—33no—
37#4652—33no—
38#4649—33no—
39C23×C3×D3C2311yescharacteristic
40C22×C32×C4C2313yes—
41C22×C3⋊Dic3C2313yes—
42C22×C3⋊Dic3C2311yescharacteristic
43C22×C3×Dic3C2311yescharacteristic
44C22×C3×Dic3C2313yes—
45C22×C3×Dic3C2313yes—
46C2×D3×Dic3—26no—
47C32×C42C2×C414yescomplemented
48C4×C3⋊Dic3—26no—
49C4×C3⋊Dic3—26no—
50C3×(C2×D3)⋊C4C2×C4112yes—
51C3×Dic3⋊C4C2×C4112yescomplemented
52Dic3⋊Dic3—26no—
53(C2×D3)⋊Dic3—26no—
54Dic32—26no—
55C4×#126—91noSylow
56C23×Dic3—31no—
57C22×C4×D3—31no—
58C3×#126—38no—
59C2×C3×C4⋊C4—33no—
60C2×C3×C22⋊C4—33no—
61C2×C3×C42—21no—
62C2×C3×C42C2×D311yescharacteristic
63C2×C3×C42C2×D311yescharacteristic
64C2×#217—33no—
65C2×(C2×D3)⋊C4—33no—
66C2×(C2×D3)⋊C4C2×D313yes—
67C2×C4⋊Dic3—33no—
68C2×Dic3⋊C4—33no—
69C2×Dic3⋊C4C2×D313yes—
70C2×C4×Dic3—33no—
71C2×C4×Dic3—33no—
72C2×C4×Dic3—33no—
73C2×C4×Dic3—33no—
74C2×C4×Dic3—33no—
75C2×C4×Dic3—33no—
76C2×C4×Dic3—63no—
77C2×C4×Dic3—63no—
78#876Dic318yescomplemented
79C3×#95—33no—
80C3×#95—33no—
81C3⋊#95—33no—
82C3⋊#95—33no—
83C3⋊#95—33no—
84C3⋊#95—33no—
85C3⋊#95C2×D313yes—
86C3⋊#95C2×D313yes—
87C23×C32C2411yescharacteristic
88C22×C3×D3—23no—
89C22×C3×D3—23no—
90C22×C3×D3C22×C412yes—
91C2×C32×C4—23no—
92C2×C32×C4—23no—
93C2×C32×C4C22×C416yes—
94C2×C3⋊Dic3—23no—
95C2×C3⋊Dic3—23no—
96C2×C3⋊Dic3#4116yes—
97C2×C3⋊Dic3#4116yes—
98C2×C3×Dic3—23no—
99C2×C3×Dic3—23no—
100C2×C3×Dic3—23no—
101C2×C3×Dic3—23no—
102C2×C3×Dic3—23no—
103C2×C3×Dic3—23no—
104C2×C3×Dic3C22×C416yes—
105D3×Dic3—44no—
106C2×#126—31no—
107#388—93no—
108#387—93no—
109#383—31no—
110C4×C4⋊C4—93no—
111C4×C22⋊C4—93no—
112C43—91no—
113C24×C3—31no—
114C23×D3C22×D311yescharacteristic
115C22×C3×C4—23no—
116C22×C3×C4—33no—
117C22×C3×C4—31no—
118C22×C3×C4—33no—
119C22×C3×C4C22×D313yes—
120C22×C3×C4C22×D313yes—
121C22×Dic3—31no—
122C22×Dic3—31no—
123C22×Dic3—33no—
124C22×Dic3—33no—
125C22×Dic3—61no—
126C22×Dic3—63no—
127C22×Dic3—66no—
128C22×Dic3C22×D311yescharacteristic
129C22×Dic3C22×D313yes—
130C22×Dic3C22×D313yes—
131C2×C4×D3—66no—
132C3×C4⋊C4—312no—
133C3×C22⋊C4—312no—
134C3×C42—24no—
135C3×C42C4×D314yescomplemented
136C3×C42C2×Dic314yescomplemented
137#217—66no—
138(C2×D3)⋊C4—66no—
139(C2×D3)⋊C4C2×Dic3112yes—
140C4⋊Dic3—66no—
141Dic3⋊C4—66no—
142Dic3⋊C4C2×Dic3112yescomplemented
143C4×Dic3—66no—
144C4×Dic3—66no—
145C4×Dic3—66no—
146C4×Dic3—66no—
147C4×Dic3—66no—
148C4×Dic3—66no—
149C4×Dic3—612no—
150C4×Dic3—612no—
151C22×C32C23×C411yescharacteristic
152C22×C32C2×#4113yes—
153C22×C32C2×#4113yes—
154C2×C3×D3—26no—
155C2×C3×D3—41no—
156C2×C3×D3—43no—
157C32×C4—26no—
158C3⋊Dic3—26no—
159C3⋊Dic3#12614yescomplemented
160C3×Dic3—26no—
161C3×Dic3—41no—
162C3×Dic3—43no—
163C23×C4—91no—
164#126—38no—
165C2×C4⋊C4—33no—
166C2×C4⋊C4—93no—
167C2×C22⋊C4—33no—
168C2×C22⋊C4—93no—
169C2×C42—93no—
170C2×C42—93no—
171C2×C42—93no—
172C2×C42D3211yescharacteristic
173#95—33no—
174#95—33no—
175#95—93no—
176#95—93no—
177C23×C3—21no—
178C23×C3—32no—
179C23×C3—63no—
180C23×C3—63no—
181C23×C3C23×D311yescharacteristic
182C23×C3C23×D311yescharacteristic
183C22×D3—23no—
184C22×D3—23no—
185C22×D3C22×Dic312yes—
186C2×C3×C4—26no—
187C2×C3×C4—26no—
188C2×C3×C4—23no—
189C2×C3×C4—23no—
190C2×C3×C4—23no—
191C2×C3×C4—23no—
192C2×C3×C4—26no—
193C2×C3×C4—36no—
194C2×C3×C4—63no—
195C2×C3×C4—63no—
196C2×C3×C4—63no—
197C2×C3×C4—63no—
198C2×C3×C4—63no—
199C2×C3×C4—63no—
200C2×C3×C4C2×C4×D316yes—
201C2×C3×C4C22×Dic316yes—
202C2×Dic3—23no—
203C2×Dic3—23no—
204C2×Dic3—23no—
205C2×Dic3—23no—
206C2×Dic3—23no—
207C2×Dic3—23no—
208C2×Dic3—36no—
209C2×Dic3—36no—
210C2×Dic3—36no—
211C2×Dic3—36no—
212C2×Dic3—66no—
213C2×Dic3—66no—
214C2×Dic3—66no—
215C2×Dic3—66no—
216C2×Dic3—63no—
217C2×Dic3—63no—
218C2×Dic3—63no—
219C2×Dic3—63no—
220C2×Dic3—124no—
221C2×Dic3C22×Dic316yes—
222C4×D3—124no—
223C2×C32C4×#4113yes—
224C2×C32C2×#12611yescharacteristic
225C2×C32#52913yes—
226C3×D3—42no—
227C24—31no—
228C22×C4—33no—
229C22×C4—31no—
230C22×C4—33no—
231C22×C4—91no—
232C22×C4—93no—
233C22×C4—186no—
234C22×C4C2×D3213yes—
235C4⋊C4—312no—
236C4⋊C4—186no—
237C22⋊C4—312no—
238C22⋊C4—186no—
239C42—186no—
240C42—186no—
241C42—186no—
242C42D3×Dic314yescomplemented
243C22×C3—23no—
244C22×C3—23no—
245C22×C3—21no—
246C22×C3—66no—
247C22×C3—121no—
248C22×C3—123no—
249C22×C3C22×C4×D311yescharacteristic
250C22×C3D3×#4113yes—
251C22×C3D3×#4113yes—
252C22×C3D3×#4113yes—
253C22×C3D3×#4113yes—
254C22×C3C23×Dic311yescharacteristic
255C2×D3—26no—
256C2×D3—41no—
257C2×D3—43no—
258C3×C4—212no—
259C3×C4—26no—
260C3×C4—26no—
261C3×C4—66no—
262C3×C4—121no—
263C3×C4—123no—
264Dic3—26no—
265Dic3—34no—
266Dic3—34no—
267Dic3—41no—
268Dic3—43no—
269Dic3—64no—
270Dic3—612no—
271Dic3—66no—
272Dic3—66no—
273C32C4×#12611yescharacteristic, complemented, Sylow
274C23—32no—
275C23—63no—
276C23—63no—
277C23C22×D3211yescharacteristic
278C2×C4—23no—
279C2×C4—23no—
280C2×C4—36no—
281C2×C4—63no—
282C2×C4—63no—
283C2×C4—63no—
284C2×C4—63no—
285C2×C4—63no—
286C2×C4—63no—
287C2×C4—96no—
288C2×C4—96no—
289C2×C4—183no—
290C2×C4—183no—
291C2×C4—364no—
292C2×C4C2×D3×Dic316yes—
293C2×C3—23no—
294C2×C3—23no—
295C2×C3—21no—
296C2×C3—122no—
297C2×C3#552213yes—
298C2×C3D3×#12611yescharacteristic
299C2×C3D3×#12611yescharacteristic
300C2×C3#570613yes—
301C2×C3#570613yes—
302C2×C3Dic3×#4113yes—
303D3—42no—
304C22—66no—
305C22—123no—
306C22—121no—
307C22#6430613yes—
308C22#6430613yes—
309C22C22×D3×Dic311yescharacteristic
310C4—26no—
311C4—66no—
312C4—94no—
313C4—123no—
314C4—121no—
315C4—186no—
316C3—21no—
317C3#7425911yescharacteristic, complemented
318C3Dic3×#12611yescharacteristic, complemented
319C2—122no—
320C2#1059397913yes—
321C2#1059402011yescharacteristic
322C2#1059495813yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32C4×#126
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C42×C3⋊Dic3C2semidirect
3. C3×#4937C2semidirect
6. #10591241C2semidirect
7. #10591192C2semidirect
16. C3×#876C4semidirect
31. #4937D3semidirect
47. C32×C42C2×C4semidirect
51. C3×Dic3⋊C4C2×C4semidirect
78. #876Dic3semidirect
135. C3×C42C4×D3semidirect
136. C3×C42C2×Dic3semidirect
142. Dic3⋊C4C2×Dic3semidirect
159. C3⋊Dic3#126semidirect
242. C42D3×Dic3semidirect
273. C32C4×#126semidirect
317. C3#74259semidirect
318. C3Dic3×#126semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8762
C42×C3⋊Dic32
C3×#49372
#105913682
#105912862
#105912412
#105911922
Dic3×#1263
#742593