Finite Group Databasebeta

← #11808924

Subgroups — #11808924

Order 1152.

923 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 923 conjugacy classes of subgroups — too many to draw. Only its 200 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#10592361C211yesmaximal, characteristic, complemented
2C3×#4676C211yesmaximal, characteristic
3C3×#4648C211yesmaximal, characteristic, complemented
4Dic3×(C2×D3)⋊C4C213yesmaximal
5#10591341C213yesmaximal, complemented
6#10591297C213yesmaximal
7Dic3×Dic3⋊C4C213yesmaximal, complemented
8#77283—31nomaximal
9#73420—31nomaximal
10C22×D3×Dic3C2211yescharacteristic
11C2×C3×(C2×D3)⋊C4C2213yes—
12C2×C3×Dic3⋊C4C2213yes—
13C2×C3×C4×Dic3C2213yes—
14C2×Dic3⋊Dic3C2213yes—
15C2×(C2×D3)⋊Dic3C2213yes—
16C2×Dic32C2213yes—
17C32×#95C2211yescharacteristic
18#63658C2213yes—
19#63658C2213yes—
20C3×C3⋊#95C2213yes—
21#63579C2213yes—
22#63579C2213yes—
23C3×#396—31no—
24C3×#376—31no—
25#4986—33no—
26Dic3×C4⋊C4—33no—
27#4953—33no—
28Dic3×C22⋊C4—33no—
29C4×(C2×D3)⋊C4—33no—
30C4×Dic3⋊C4—33no—
31#4676D311yescharacteristic
32#4675—33no—
33C3⋊#401—31no—
34C3⋊#401—31no—
35C3⋊#401—61no—
36#4658—33no—
37#4648D311yescharacteristic, complemented
38C23×C3×D3C2311yescharacteristic
39C22×C32×C4C2313yes—
40C22×C3⋊Dic3C2311yescharacteristic
41C22×C3⋊Dic3C2313yes—
42C22×C3×Dic3C2313yes—
43C22×C3×Dic3C2313yes—
44C22×C3×Dic3C2311yescharacteristic
45C2×D3×Dic3—26no—
46C3×(C2×D3)⋊C4—26no—
47C3×Dic3⋊C4—26no—
48C3×C4×Dic3—26no—
49Dic3⋊Dic3—26no—
50(C2×D3)⋊Dic3—26no—
51Dic32—26no—
52#2401—91noSylow
53C23×Dic3—31no—
54C22×C4×D3—31no—
55C2×C3×C4⋊C4—33no—
56C2×C3×C22⋊C4—33no—
57C2×C3×C42—33no—
58C2×#217—33no—
59C2×(C2×D3)⋊C4—33no—
60C2×(C2×D3)⋊C4C2×D313yes—
61C2×C4⋊Dic3—33no—
62C2×Dic3⋊C4—33no—
63C2×Dic3⋊C4C2×D313yes—
64C2×C4×Dic3—33no—
65C2×C4×Dic3—33no—
66C2×C4×Dic3C2×D313yes—
67C3×#95—21no—
68C3×#95—33no—
69C3×#95C2×D311yescharacteristic
70C3×#95C2×D311yescharacteristic
71C3⋊#95—33no—
72C3⋊#95—33no—
73C3⋊#95—33no—
74C3⋊#95—33no—
75C3⋊#95—33no—
76C3⋊#95—33no—
77C3⋊#95—33no—
78C3⋊#95—33no—
79C3⋊#95—63no—
80C3⋊#95—63no—
81C3⋊#95C2×D313yes—
82C23×C32C2411yescharacteristic
83C22×C3×D3—23no—
84C22×C3×D3—23no—
85C22×C3×D3#4112yes—
86C2×C32×C4—23no—
87C2×C32×C4—23no—
88C2×C32×C4—23no—
89C2×C3⋊Dic3—23no—
90C2×C3⋊Dic3—23no—
91C2×C3⋊Dic3—23no—
92C2×C3⋊Dic3—23no—
93C2×C3×Dic3—23no—
94C2×C3×Dic3—23no—
95C2×C3×Dic3—23no—
96C2×C3×Dic3—23no—
97C2×C3×Dic3—23no—
98C2×C3×Dic3#4116yes—
99C2×C3×Dic3#4116yes—
100D3×Dic3—44no—
101#401—91no—
102#400—93no—
103#397—93no—
104#396—31no—
105C4×C4⋊C4—93no—
106C4×C22⋊C4—93no—
107#376—31no—
108C24×C3—31no—
109C23×D3C22×D311yescharacteristic
110C22×C3×C4—23no—
111C22×C3×C4—31no—
112C22×C3×C4—33no—
113C22×C3×C4—33no—
114C22×C3×C4C22×D313yes—
115C22×C3×C4C22×D313yes—
116C22×Dic3—31no—
117C22×Dic3—31no—
118C22×Dic3—33no—
119C22×Dic3—33no—
120C22×Dic3—61no—
121C22×Dic3—63no—
122C22×Dic3—66no—
123C22×Dic3C22×D313yes—
124C22×Dic3C22×D313yes—
125C22×Dic3C22×D311yescharacteristic
126C2×C4×D3—66no—
127C3×C4⋊C4—66no—
128C3×C22⋊C4—66no—
129C3×C42—66no—
130#217—66no—
131(C2×D3)⋊C4—26no—
132(C2×D3)⋊C4—66no—
133C4⋊Dic3—66no—
134Dic3⋊C4—26no—
135Dic3⋊C4—66no—
136C4×Dic3—26no—
137C4×Dic3—66no—
138C4×Dic3—66no—
139C22×C32C2×#4113yes—
140C22×C32C2×#4113yes—
141C22×C32C2×#4111yescharacteristic
142C2×C3×D3—26no—
143C2×C3×D3—41no—
144C2×C3×D3—43no—
145C32×C4—43no—
146C3⋊Dic3—41no—
147C3⋊Dic3—43no—
148C3×Dic3—26no—
149C3×Dic3—43no—
150C3×Dic3#12614yes—
151C23×C4—91no—
152C2×C4⋊C4—33no—
153C2×C4⋊C4—93no—
154C2×C22⋊C4—33no—
155C2×C22⋊C4—93no—
156C2×C42—33no—
157C2×C42—93no—
158#95—33no—
159#95—93no—
160#95—93no—
161#95—93no—
162#95—93no—
163#95D3211yescharacteristic
164C23×C3—21no—
165C23×C3—32no—
166C23×C3—63no—
167C23×C3—63no—
168C23×C3C23×D311yescharacteristic
169C23×C3C23×D311yescharacteristic
170C22×D3—23no—
171C22×D3—23no—
172C22×D3#23912yes—
173C2×C3×C4—23no—
174C2×C3×C4—23no—
175C2×C3×C4—23no—
176C2×C3×C4—23no—
177C2×C3×C4—23no—
178C2×C3×C4—23no—
179C2×C3×C4—36no—
180C2×C3×C4—36no—
181C2×C3×C4—43no—
182C2×C3×C4—43no—
183C2×C3×C4—43no—
184C2×C3×C4—63no—
185C2×C3×C4—63no—
186C2×C3×C4—63no—
187C2×C3×C4—63no—
188C2×C3×C4—63no—
189C2×Dic3—23no—
190C2×Dic3—23no—
191C2×Dic3—23no—
192C2×Dic3—23no—
193C2×Dic3—23no—
194C2×Dic3—63no—
195C2×Dic3—63no—
196C2×Dic3—63no—
197C2×Dic3—63no—
198C2×Dic3—63no—
199C2×Dic3—63no—
200C2×Dic3—63no—
201C2×Dic3—63no—
202C2×Dic3—123no—
203C2×Dic3—123no—
204C2×Dic3—123no—
205C2×Dic3—123no—
206C2×Dic3—124no—
207C2×Dic3#23516yes—
208C2×Dic3#23716yes—
209C4×D3—124no—
210C2×C32C2×#12611yescharacteristic
211C2×C32#52913yes—
212C2×C32#52913yes—
213C3×D3—42no—
214C24—31no—
215C22×C4—31no—
216C22×C4—33no—
217C22×C4—33no—
218C22×C4—91no—
219C22×C4—93no—
220C22×C4—186no—
221C22×C4C2×D3213yes—
222C4⋊C4—66no—
223C4⋊C4—186no—
224C22⋊C4—66no—
225C22⋊C4—186no—
226C42—66no—
227C42—186no—
228C22×C3—23no—
229C22×C3—23no—
230C22×C3—21no—
231C22×C3—66no—
232C22×C3—121no—
233C22×C3—123no—
234C22×C3C2×#23513yes—
235C22×C3C2×#23713yes—
236C22×C3C2×#23911yescharacteristic
237C22×C3D3×#4113yes—
238C22×C3D3×#4113yes—
239C22×C3D3×#4111yescharacteristic
240C2×D3—26no—
241C2×D3—41no—
242C2×D3—43no—
243C3×C4—34no—
244C3×C4—43no—
245C3×C4—43no—
246C3×C4—66no—
247C3×C4—83no—
248C3×C4—123no—
249Dic3—26no—
250Dic3—43no—
251Dic3—121no—
252Dic3—121no—
253Dic3—123no—
254Dic3—123no—
255Dic3—243no—
256Dic3—241no—
257Dic3#87614yes—
258C32#240111yescharacteristic, complemented, Sylow
259C23—32no—
260C23—63no—
261C23—63no—
262C23C22×D3211yescharacteristic
263C2×C4—23no—
264C2×C4—23no—
265C2×C4—23no—
266C2×C4—36no—
267C2×C4—36no—
268C2×C4—63no—
269C2×C4—63no—
270C2×C4—63no—
271C2×C4—63no—
272C2×C4—63no—
273C2×C4—183no—
274C2×C4—183no—
275C2×C4—183no—
276C2×C4—183no—
277C2×C4—364no—
278C2×C3—23no—
279C2×C3—23no—
280C2×C3—21no—
281C2×C3—122no—
282C2×C3C2×#87611yescharacteristic
283C2×C3#552813yes—
284C2×C3#552813yes—
285C2×C3#560013yes—
286C2×C3#562413yes—
287C2×C3D3×#12611yescharacteristic
288D3—42no—
289C22—66no—
290C22—123no—
291C22—121no—
292C22D3×#23513yes—
293C22D3×#23713yes—
294C22D3×#23911yescharacteristic
295C4—34no—
296C4—43no—
297C4—66no—
298C4—123no—
299C4—363no—
300C4—361no—
301C3—21no—
302C3#7342011yescharacteristic, complemented
303C3#7728311yescharacteristic, complemented
304C2—122no—
305C2D3×#87611yescharacteristic
306C2#1059408613yes—
307C2#1059440213yes—
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC23×C3×D3C23
hypercenter#95D32
hypocenterC32#2401
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
1. #10592361C2semidirect
3. C3×#4648C2semidirect
5. #10591341C2semidirect
7. Dic3×Dic3⋊C4C2semidirect
37. #4648D3semidirect
258. C32#2401semidirect
302. C3#73420semidirect
303. C3#77283semidirect

Maximal subgroups

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

subgroupindex
#105923612
C3×#46762
C3×#46482
Dic3×(C2×D3)⋊C42
#105913412
#105912972
Dic3×Dic3⋊C42
#772833
#734203