Finite Group Databasebeta

← #11808065

Subgroups — #11808065

Order 1152.

1005 conjugacy classes of subgroups; only the 284 normal subgroups are shown.

normal subgroups only

This group has 1005 conjugacy classes of subgroups — too many to draw. Only its 284 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
2#10592634C211yesmaximal, characteristic, complemented
3C3×#4937C211yesmaximal, characteristic, complemented
4#10591379C213yesmaximal
5#10591316C213yesmaximal
6#10591272C213yesmaximal, complemented
7#10591268C213yesmaximal, complemented
8#83076—31nomaximal
9#74299—31nomaximal
10C22×D3×Dic3C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2213yes—
13C2×C4⋊(C3⋊Dic3)C2213yes—
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#4984—33no—
28#4980—33no—
29#4951—33no—
30#4950—33no—
31#4937D311yescharacteristic, complemented
32#4935—31no—
33#4935—31no—
34#4935—61no—
35#4670—33no—
36#4668—33no—
37#4655—33no—
38#4647—33no—
39C23×C3×D3C2311yescharacteristic
40C22×C32×C4C2313yes—
41C22×C3⋊Dic3C2311yescharacteristic
42C22×C3⋊Dic3C2313yes—
43C22×C3×Dic3C2311yescharacteristic
44C22×C3×Dic3C2313yes—
45C22×C3×Dic3C2313yes—
46C2×D3×Dic3—43no—
47C32×C42C2×C414yescomplemented
48C4⋊(C3⋊Dic3)—43no—
49C4⋊(C3⋊Dic3)—43no—
50C3×(C2×D3)⋊C4C2×C4112yes—
51C3×Dic3⋊C4C2×C4112yescomplemented
52Dic3⋊Dic3—43no—
53(C2×D3)⋊Dic3—43no—
54Dic32—43no—
55#2383—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×C4⋊Dic3—33no—
69C2×C4⋊Dic3—33no—
70C2×C4⋊Dic3—33no—
71C2×C4⋊Dic3—33no—
72C2×C4⋊Dic3—63no—
73C2×C4⋊Dic3—63no—
74C2×Dic3⋊C4—33no—
75C2×Dic3⋊C4C2×D313yes—
76C2×C4×Dic3—33no—
77C2×C4×Dic3—33no—
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—23no—
97C2×C3⋊Dic3—23no—
98C2×C3×Dic3—23no—
99C2×C3×Dic3—23no—
100C2×C3×Dic3—23no—
101C2×C3×Dic3—23no—
102C2×C3×Dic3—26no—
103C2×C3×Dic3C22×C416yes—
104D3×Dic3—44no—
105C2×#126—31no—
106#389—93no—
107#388—93no—
108#387—93no—
109#385—93no—
110#384—91no—
111#383—31no—
112C24×C3—31no—
113C23×D3C22×D311yescharacteristic
114C22×C3×C4—23no—
115C22×C3×C4—33no—
116C22×C3×C4—33no—
117C22×C3×C4—31no—
118C22×C3×C4C22×D313yes—
119C22×C3×C4C22×D313yes—
120C22×Dic3—31no—
121C22×Dic3—31no—
122C22×Dic3—33no—
123C22×Dic3—33no—
124C22×Dic3—61no—
125C22×Dic3—63no—
126C22×Dic3—123no—
127C22×Dic3C22×D313yes—
128C22×Dic3C22×D311yescharacteristic
129C22×Dic3C22×D313yes—
130C2×C4×D3—123no—
131C3×C4⋊C4—312no—
132C3×C22⋊C4—312no—
133C3×C42—24no—
134C3×C42C4×D314yescomplemented
135C3×C42C2×Dic314yescomplemented
136#217—123no—
137(C2×D3)⋊C4—123no—
138(C2×D3)⋊C4C2×Dic3112yes—
139C4⋊Dic3—123no—
140C4⋊Dic3—123no—
141C4⋊Dic3—123no—
142C4⋊Dic3—123no—
143C4⋊Dic3—123no—
144C4⋊Dic3—126no—
145C4⋊Dic3—126no—
146Dic3⋊C4—123no—
147Dic3⋊C4C2×Dic3112yescomplemented
148C4×Dic3—123no—
149C4×Dic3—123no—
150C22×C32C23×C411yescharacteristic
151C22×C32H(5,𝔽2)13yes—
152C22×C322−1+413yes—
153C2×C3×D3—26no—
154C2×C3×D3—41no—
155C2×C3×D3—43no—
156C32×C4—26no—
157C3⋊Dic3—41no—
158C3⋊Dic3—43no—
159C3×Dic3—26no—
160C3×Dic3—41no—
161C3×Dic3—43no—
162C23×C4—91no—
163#126—38no—
164C2×C4⋊C4—33no—
165C2×C4⋊C4—93no—
166C2×C4⋊C4—93no—
167C2×C4⋊C4—93no—
168C2×C22⋊C4—33no—
169C2×C22⋊C4—93no—
170C2×C42—93no—
171C2×C42D3211yescharacteristic
172#95—33no—
173#95—33no—
174#95—93no—
175#95—93no—
176C23×C3—21no—
177C23×C3—32no—
178C23×C3—63no—
179C23×C3—63no—
180C23×C3C23×D311yescharacteristic
181C23×C3C23×D311yescharacteristic
182C22×D3—23no—
183C22×D3—23no—
184C22×D3C22×Dic312yes—
185C2×C3×C4—26no—
186C2×C3×C4—26no—
187C2×C3×C4—23no—
188C2×C3×C4—23no—
189C2×C3×C4—23no—
190C2×C3×C4—23no—
191C2×C3×C4—26no—
192C2×C3×C4—36no—
193C2×C3×C4—63no—
194C2×C3×C4—63no—
195C2×C3×C4—63no—
196C2×C3×C4—63no—
197C2×C3×C4—66no—
198C2×C3×C4C2×C4×D316yes—
199C2×C3×C4C22×Dic316yes—
200C2×Dic3—23no—
201C2×Dic3—23no—
202C2×Dic3—23no—
203C2×Dic3—23no—
204C2×Dic3—26no—
205C2×Dic3—63no—
206C2×Dic3—63no—
207C2×Dic3—63no—
208C2×Dic3—63no—
209C2×Dic3—63no—
210C2×Dic3—63no—
211C2×Dic3—63no—
212C2×Dic3—63no—
213C2×Dic3—123no—
214C2×Dic3—123no—
215C2×Dic3—123no—
216C2×Dic3—123no—
217C2×Dic3—124no—
218C2×Dic3C22×Dic316yes—
219C4×D3—124no—
220C2×C32#52013yes—
221C2×C32#56011yescharacteristic
222C2×C32#56313yes—
223C3×D3—42no—
224C24—31no—
225C22×C4—33no—
226C22×C4—33no—
227C22×C4—31no—
228C22×C4—91no—
229C22×C4—93no—
230C22×C4—363no—
231C22×C4C2×D3213yes—
232C4⋊C4—312no—
233C4⋊C4—363no—
234C4⋊C4—363no—
235C4⋊C4—363no—
236C22⋊C4—312no—
237C22⋊C4—363no—
238C42—363no—
239C42D3×Dic314yescomplemented
240C22×C3—23no—
241C22×C3—23no—
242C22×C3—21no—
243C22×C3—66no—
244C22×C3—121no—
245C22×C3—123no—
246C22×C3C22×C4×D311yescharacteristic
247C22×C3#100913yes—
248C22×C3#100913yes—
249C22×C3#101013yes—
250C22×C3#101013yes—
251C22×C3C23×Dic311yescharacteristic
252C2×D3—26no—
253C2×D3—41no—
254C2×D3—43no—
255C3×C4—212no—
256C3×C4—26no—
257C3×C4—26no—
258C3×C4—66no—
259C3×C4—121no—
260C3×C4—123no—
261Dic3—26no—
262Dic3—41no—
263Dic3—43no—
264Dic3—121no—
265Dic3—121no—
266Dic3—123no—
267Dic3—123no—
268Dic3—241no—
269Dic3—243no—
270C32#238311yescharacteristic, complemented, Sylow
271C23—32no—
272C23—63no—
273C23—63no—
274C23C22×D3211yescharacteristic
275C2×C4—23no—
276C2×C4—23no—
277C2×C4—36no—
278C2×C4—63no—
279C2×C4—63no—
280C2×C4—66no—
281C2×C4—63no—
282C2×C4—63no—
283C2×C4—183no—
284C2×C4—183no—
285C2×C4—183no—
286C2×C4—183no—
287C2×C4—364no—
288C2×C4C2×D3×Dic316yes—
289C2×C3—23no—
290C2×C3—23no—
291C2×C3—21no—
292C2×C3—122no—
293C2×C3#552313yes—
294C2×C3#571111yescharacteristic
295C2×C3#571111yescharacteristic
296C2×C3#571213yes—
297C2×C3#571213yes—
298C2×C3#582713yes—
299D3—42no—
300C22—66no—
301C22—123no—
302C22—121no—
303C22#6429813yes—
304C22#6430813yes—
305C22C22×D3×Dic311yescharacteristic
306C4—26no—
307C4—66no—
308C4—123no—
309C4—121no—
310C4—361no—
311C4—363no—
312C3—21no—
313C3#7429911yescharacteristic, complemented
314C3#8307611yescharacteristic, complemented
315C2—122no—
316C2#1059396213yes—
317C2#1059402311yescharacteristic
318C2#1059499213yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32#2383
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #10592634C2semidirect
3. C3×#4937C2semidirect
6. #10591272C2semidirect
7. #10591268C2semidirect
16. C3×#876C4semidirect
31. #4937D3semidirect
47. C32×C42C2×C4semidirect
51. C3×Dic3⋊C4C2×C4semidirect
78. #876Dic3semidirect
134. C3×C42C4×D3semidirect
135. C3×C42C2×Dic3semidirect
147. Dic3⋊C4C2×Dic3semidirect
239. C42D3×Dic3semidirect
270. C32#2383semidirect
313. C3#74299semidirect
314. C3#83076semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8762
#105926342
C3×#49372
#105913792
#105913162
#105912722
#105912682
#830763
#742993