Finite Group Databasebeta

← #11808922

Subgroups — #11808922

Order 1152.

957 conjugacy classes of subgroups; only the 192 normal subgroups are shown.

normal subgroups only

This group has 957 conjugacy classes of subgroups — too many to draw. Only its 192 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#10592375C211yesmaximal, characteristic
2C3×C3⋊#401C211yesmaximal, characteristic, complemented
3C3×#4648C211yesmaximal, characteristic, complemented
4#10591243C213yesmaximal, complemented
5#10591233C213yesmaximal
6#10591217C213yesmaximal, complemented
7#10591216C213yesmaximal
8#78409—31nomaximal
9#73420—31nomaximal
10C22×#624C2211yescharacteristic
11C2×#3752C2213yes—
12C2×#3750C2213yes—
13C2×C3×C4×Dic3C2213yes—
14C2×#3724C2213yes—
15C2×#3722C2213yes—
16C2×Dic32C2213yes—
17C32×#95C2211yescharacteristic
18C3×C3⋊#95C2213yes—
19C3×C3⋊#95C2213yes—
20C3×C3⋊#95C2213yes—
21#63579C2213yes—
22#63579C2213yes—
23C3×#401—31no—
24C3×#376—31no—
25C4×(C2×D3)⋊C4—33no—
26C4×Dic3⋊C4—33no—
27#4676—31no—
28#4676—31no—
29#4676—61no—
30#4675—33no—
31#4675—33no—
32#4666—33no—
33C3⋊#401D311yescharacteristic, complemented
34#4658—33no—
35#4658—33no—
36#4649—33no—
37#4648D311yescharacteristic, complemented
38C23×C3⋊D3C2311yescharacteristic
39C22×C32×C4C2313yes—
40C22×C3⋊Dic3C2313yes—
41C22×C3×Dic3C2313yes—
42C22×C3×Dic3C2311yescharacteristic
43C22×C3×Dic3C2313yes—
44C22×C3×Dic3C2311yescharacteristic
45C2×#624—26no—
46#3752—26no—
47#3750—26no—
48C3×C4×Dic3—26no—
49#3724—26no—
50#3722—26no—
51Dic32—26no—
52#2401—91noSylow
53C22×C4×D3—31no—
54C22×C4×D3—31no—
55C2×C3×C42—33no—
56C2×(C2×D3)⋊C4—33no—
57C2×(C2×D3)⋊C4—33no—
58C2×(C2×D3)⋊C4—33no—
59C2×(C2×D3)⋊C4—33no—
60C2×(C2×D3)⋊C4—63no—
61C2×Dic3⋊C4—33no—
62C2×Dic3⋊C4—33no—
63C2×Dic3⋊C4—33no—
64C2×Dic3⋊C4—33no—
65C2×Dic3⋊C4—63no—
66C2×C4×Dic3—33no—
67C2×C4×Dic3—33no—
68C2×C4×Dic3C2×D313yes—
69C3×#95—21no—
70C3×#95—33no—
71C3×#95—33no—
72C3×#95—33no—
73C3×#95C2×D311yescharacteristic
74C3×#95C2×D311yescharacteristic
75C3⋊#95—33no—
76C3⋊#95—33no—
77C3⋊#95—33no—
78C3⋊#95—33no—
79C3⋊#95C2×D313yes—
80C3⋊#95C2×D313yes—
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#4116yes—
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—23no—
99C2×C3×Dic3#4116yes—
100#624—44no—
101#401—31no—
102#400—93no—
103#397—93no—
104#396—91no—
105C4×C4⋊C4—93no—
106C4×C22⋊C4—93no—
107#376—31no—
108C23×D3—31no—
109C23×D3—31no—
110C23×D3—61no—
111C22×C3×C4—23no—
112C22×C3×C4—31no—
113C22×C3×C4—31no—
114C22×C3×C4—33no—
115C22×C3×C4—33no—
116C22×C3×C4C22×D313yes—
117C22×C3×C4C22×D313yes—
118C22×Dic3—33no—
119C22×Dic3—33no—
120C22×Dic3—63no—
121C22×Dic3C22×D311yescharacteristic
122C22×Dic3C22×D313yes—
123C22×Dic3C22×D313yes—
124C22×Dic3C22×D311yescharacteristic
125C2×C4×D3—66no—
126C2×C4×D3—66no—
127C3×C42—66no—
128(C2×D3)⋊C4—66no—
129(C2×D3)⋊C4—66no—
130(C2×D3)⋊C4—66no—
131(C2×D3)⋊C4—66no—
132(C2×D3)⋊C4—126no—
133Dic3⋊C4—66no—
134Dic3⋊C4—66no—
135Dic3⋊C4—66no—
136Dic3⋊C4—66no—
137Dic3⋊C4—126no—
138C4×Dic3—26no—
139C4×Dic3—66no—
140C4×Dic3—66no—
141C22×C32C2×#4113yes—
142C22×C32C2×#4111yescharacteristic
143C22×C32C2×#4113yes—
144C2×C3⋊D3—26no—
145C2×C3⋊D3—41no—
146C2×C3⋊D3—43no—
147C32×C4—43no—
148C3⋊Dic3—26no—
149C3×Dic3—41no—
150C3×Dic3—43no—
151C3×Dic3—43no—
152C3×Dic3#12614yes—
153C23×C4—91no—
154C2×C4⋊C4—93no—
155C2×C4⋊C4—93no—
156C2×C22⋊C4—93no—
157C2×C22⋊C4—93no—
158C2×C42—33no—
159C2×C42—93no—
160#95—33no—
161#95—33no—
162#95—33no—
163#95—93no—
164#95—93no—
165#95D3211yescharacteristic
166C23×C3—21no—
167C23×C3C23×D311yescharacteristic
168C23×C3C23×D311yescharacteristic
169C22×D3—32no—
170C22×D3—32no—
171C22×D3—62no—
172C22×D3—63no—
173C22×D3—63no—
174C22×D3—63no—
175C22×D3—63no—
176C22×D3—123no—
177C22×D3—123no—
178C2×C3×C4—23no—
179C2×C3×C4—23no—
180C2×C3×C4—23no—
181C2×C3×C4—23no—
182C2×C3×C4—23no—
183C2×C3×C4—23no—
184C2×C3×C4—36no—
185C2×C3×C4—43no—
186C2×C3×C4—43no—
187C2×C3×C4—43no—
188C2×C3×C4—63no—
189C2×C3×C4—63no—
190C2×C3×C4—63no—
191C2×C3×C4—63no—
192C2×C3×C4—63no—
193C2×C3×C4—63no—
194C2×C3×C4—63no—
195C2×Dic3—23no—
196C2×Dic3—23no—
197C2×Dic3—23no—
198C2×Dic3—23no—
199C2×Dic3—23no—
200C2×Dic3—23no—
201C2×Dic3—23no—
202C2×Dic3—36no—
203C2×Dic3—36no—
204C2×Dic3—66no—
205C2×Dic3—63no—
206C2×Dic3—63no—
207C2×Dic3—63no—
208C2×Dic3—63no—
209C2×Dic3—123no—
210C2×Dic3—123no—
211C2×Dic3#23516yes—
212C4×D3—124no—
213C4×D3—124no—
214C2×C32C2×#12611yescharacteristic
215C2×C32#52913yes—
216C2×C32#52913yes—
217C3⋊D3—42no—
218C24—91no—
219C22×C4—31no—
220C22×C4—31no—
221C22×C4—33no—
222C22×C4—33no—
223C22×C4—93no—
224C22×C4—186no—
225C22×C4C2×D3213yes—
226C4⋊C4—186no—
227C4⋊C4—186no—
228C22⋊C4—186no—
229C22⋊C4—186no—
230C42—66no—
231C42—186no—
232C22×C3—23no—
233C22×C3—23no—
234C22×C3—21no—
235C22×C3C2×#23513yes—
236C22×C3D3×#4113yes—
237C22×C3D3×#4113yes—
238C22×C3D3×#4113yes—
239C22×C3D3×#4111yescharacteristic
240C22×C3D3×#4111yescharacteristic
241C2×D3—66no—
242C2×D3—66no—
243C2×D3—126no—
244C2×D3—121no—
245C2×D3—123no—
246C2×D3—121no—
247C2×D3—123no—
248C2×D3—243no—
249C2×D3—241no—
250C3×C4—34no—
251C3×C4—43no—
252C3×C4—43no—
253C3×C4—83no—
254C3×C4—123no—
255C3×C4—121no—
256C3×C4—123no—
257Dic3—41no—
258Dic3—43no—
259Dic3—43no—
260Dic3—66no—
261Dic3—66no—
262Dic3—126no—
263Dic3#87614yes—
264C32#240111yescharacteristic, complemented, Sylow
265C23—92no—
266C23—183no—
267C23—183no—
268C23C22×D3211yescharacteristic
269C2×C4—23no—
270C2×C4—23no—
271C2×C4—23no—
272C2×C4—36no—
273C2×C4—63no—
274C2×C4—63no—
275C2×C4—63no—
276C2×C4—63no—
277C2×C4—63no—
278C2×C4—63no—
279C2×C4—63no—
280C2×C4—96no—
281C2×C4—183no—
282C2×C4—183no—
283C2×C4—364no—
284C2×C3—23no—
285C2×C3—23no—
286C2×C3—21no—
287C2×C3C2×#87611yescharacteristic
288C2×C3#552813yes—
289C2×C3#552813yes—
290C2×C3D3×#12611yescharacteristic
291C2×C3#570613yes—
292C2×C3#570613yes—
293D3—122no—
294D3—122no—
295D3—242no—
296C22—186no—
297C22—363no—
298C22—361no—
299C22D3×#23513yes—
300C22#6431213yes—
301C22#6431911yescharacteristic
302C4—34no—
303C4—43no—
304C4—123no—
305C4—123no—
306C4—121no—
307C4—186no—
308C3—21no—
309C3#7342011yescharacteristic, complemented
310C3#7840911yescharacteristic, complemented
311C2—362no—
312C2D3×#87611yescharacteristic
313C2#1059410613yes—
314C2#1059441713yes—
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
2. C3×C3⋊#401C2semidirect
3. C3×#4648C2semidirect
4. #10591243C2semidirect
6. #10591217C2semidirect
33. C3⋊#401D3semidirect
37. #4648D3semidirect
264. C32#2401semidirect
309. C3#73420semidirect
310. C3#78409semidirect

Maximal subgroups

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

subgroupindex
#105923752
C3×C3⋊#4012
C3×#46482
#105912432
#105912332
#105912172
#105912162
#784093
#734203