Finite Group Databasebeta

← #11802434

Subgroups — #11802434

Order 1152.

1155 conjugacy classes of subgroups; only the 276 normal subgroups are shown.

normal subgroups only

This group has 1155 conjugacy classes of subgroups — too many to draw. Only its 276 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×#64085C211yesmaximal, characteristic
2C3×#4937C211yesmaximal, characteristic, complemented
3C3×C42×Dic3C211yesmaximal, characteristic, complemented
4#10591243C213yesmaximal, complemented
5#10591233C213yesmaximal
6#10591202C213yesmaximal
7#10591197C213yesmaximal, complemented
8#74259—31nomaximal
9C4×#876—31nomaximal
10C22×#624C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C2×#3752C2213yes—
13C2×#3750C2213yes—
14#64085C418yescomplemented
15C2×C3×C4×Dic3C2213yes—
16C2×C3×C4×Dic3C2213yes—
17C2×#3724C2213yes—
18C2×#3722C2213yes—
19C2×Dic32C2213yes—
20C3×C3⋊#95C2213yes—
21C3×C3⋊#95C2213yes—
22#63579C2213yes—
23#63579C2213yes—
24C2×#876—31no—
25C2×#876—31no—
26C2×#876—61no—
27C3×#383—31no—
28C3×C43—31no—
29#4940—33no—
30C4×(C2×D3)⋊C4—33no—
31#4937D311yescharacteristic, complemented
32#4933—33no—
33C4×Dic3⋊C4—33no—
34C42×Dic3D311yescharacteristic, complemented
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×Dic3C2313yes—
44C22×C3×Dic3C2313yes—
45C22×C3×Dic3C2311yescharacteristic
46C2×#624—26no—
47C32×C42C2×C414yescomplemented
48#3752C2×C4112yes—
49#3750C2×C4112yescomplemented
50C3×C4×Dic3—26no—
51C3×C4×Dic3—26no—
52#3724—26no—
53#3722—26no—
54Dic32—26no—
55C4×#126—91noSylow
56C22×C4×D3—31no—
57C22×C4×D3—31no—
58C2×C3×C42—21no—
59C2×C3×C42—33no—
60C2×C3×C42—33no—
61C2×C3×C42C2×D311yescharacteristic
62C2×C3×C42C2×D311yescharacteristic
63C2×(C2×D3)⋊C4—33no—
64C2×(C2×D3)⋊C4—33no—
65C2×(C2×D3)⋊C4—33no—
66C2×(C2×D3)⋊C4—33no—
67C2×(C2×D3)⋊C4—63no—
68C2×Dic3⋊C4—33no—
69C2×Dic3⋊C4—33no—
70C2×Dic3⋊C4—33no—
71C2×Dic3⋊C4—33no—
72C2×Dic3⋊C4—63no—
73C2×C4×Dic3—33no—
74C2×C4×Dic3—33no—
75C2×C4×Dic3C2×D313yes—
76C2×C4×Dic3C2×D313yes—
77#876—38no—
78#876—38no—
79#876—68no—
80C3×#95—33no—
81C3×#95—33no—
82C3⋊#95—33no—
83C3⋊#95—33no—
84C3⋊#95—33no—
85C3⋊#95—33no—
86C3⋊#95C2×D313yes—
87C3⋊#95C2×D313yes—
88C23×C32C2411yescharacteristic
89C22×C3⋊D3—23no—
90C22×C3⋊D3—23no—
91C22×C3⋊D3C22×C412yes—
92C2×C32×C4—23no—
93C2×C32×C4—23no—
94C2×C32×C4C22×C416yes—
95C2×C3⋊Dic3—23no—
96C2×C3⋊Dic3—23no—
97C2×C3⋊Dic3C22×C416yes—
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×Dic3#4116yes—
105C2×C3×Dic3#4116yes—
106#624—44no—
107C2×#126—91no—
108#388—93no—
109#387—93no—
110#383—31no—
111C4×C4⋊C4—93no—
112C4×C22⋊C4—93no—
113C43—31no—
114C23×D3—31no—
115C23×D3—31no—
116C23×D3—61no—
117C22×C3×C4—23no—
118C22×C3×C4—31no—
119C22×C3×C4—33no—
120C22×C3×C4—31no—
121C22×C3×C4—33no—
122C22×C3×C4C22×D313yes—
123C22×C3×C4C22×D313yes—
124C22×Dic3—33no—
125C22×Dic3—33no—
126C22×Dic3—63no—
127C22×Dic3C22×D311yescharacteristic
128C22×Dic3C22×D313yes—
129C22×Dic3C22×D313yes—
130C22×Dic3C22×D311yescharacteristic
131C2×C4×D3—66no—
132C2×C4×D3—66no—
133C3×C42—24no—
134C3×C42—66no—
135C3×C42—66no—
136C3×C42C4×D314yescomplemented
137C3×C42C4×D314yescomplemented
138(C2×D3)⋊C4—312no—
139(C2×D3)⋊C4—312no—
140(C2×D3)⋊C4—612no—
141(C2×D3)⋊C4—66no—
142(C2×D3)⋊C4—66no—
143Dic3⋊C4—312no—
144Dic3⋊C4—312no—
145Dic3⋊C4—612no—
146Dic3⋊C4—66no—
147Dic3⋊C4—66no—
148C4×Dic3—26no—
149C4×Dic3—26no—
150C4×Dic3—66no—
151C4×Dic3—66no—
152C22×C32C23×C411yescharacteristic
153C22×C32C2×#4113yes—
154C22×C32C2×#4113yes—
155C2×C3⋊D3—26no—
156C2×C3⋊D3—41no—
157C2×C3⋊D3—43no—
158C32×C4—26no—
159C3⋊Dic3—26no—
160C3×Dic3—26no—
161C3×Dic3—41no—
162C3×Dic3—43no—
163C3×Dic3#12614yescomplemented
164C23×C4—91no—
165#126—98no—
166C2×C4⋊C4—93no—
167C2×C4⋊C4—93no—
168C2×C22⋊C4—93no—
169C2×C22⋊C4—93no—
170C2×C42—33no—
171C2×C42—33no—
172C2×C42—93no—
173C2×C42D3211yescharacteristic
174#95—33no—
175#95—33no—
176#95—93no—
177#95—93no—
178C23×C3—21no—
179C23×C3C23×D311yescharacteristic
180C23×C3C23×D311yescharacteristic
181C22×D3—32no—
182C22×D3—32no—
183C22×D3—62no—
184C22×D3—63no—
185C22×D3—63no—
186C22×D3—63no—
187C22×D3—63no—
188C22×D3—123no—
189C22×D3—123no—
190C2×C3×C4—23no—
191C2×C3×C4—23no—
192C2×C3×C4—23no—
193C2×C3×C4—23no—
194C2×C3×C4—26no—
195C2×C3×C4—36no—
196C2×C3×C4—36no—
197C2×C3×C4—43no—
198C2×C3×C4—43no—
199C2×C3×C4—63no—
200C2×C3×C4—63no—
201C2×C3×C4—63no—
202C2×C3×C4—63no—
203C2×C3×C4—63no—
204C2×C3×C4—63no—
205C2×C3×C4C2×C4×D316yes—
206C2×C3×C4C2×C4×D316yes—
207C2×Dic3—23no—
208C2×Dic3—23no—
209C2×Dic3—23no—
210C2×Dic3—23no—
211C2×Dic3—23no—
212C2×Dic3—23no—
213C2×Dic3—36no—
214C2×Dic3—36no—
215C2×Dic3—66no—
216C2×Dic3—63no—
217C2×Dic3—63no—
218C2×Dic3—63no—
219C2×Dic3—63no—
220C2×Dic3—123no—
221C2×Dic3—123no—
222C2×Dic3#23516yes—
223C2×Dic3#23516yes—
224C4×D3—124no—
225C4×D3—124no—
226C2×C32C4×#4113yes—
227C2×C32C2×#12611yescharacteristic
228C2×C32#52913yes—
229C3⋊D3—42no—
230C24—91no—
231C22×C4—31no—
232C22×C4—33no—
233C22×C4—31no—
234C22×C4—33no—
235C22×C4—93no—
236C22×C4—186no—
237C22×C4C2×D3213yes—
238C4⋊C4—912no—
239C4⋊C4—186no—
240C22⋊C4—912no—
241C22⋊C4—186no—
242C42—66no—
243C42—66no—
244C42—186no—
245C42#62414yescomplemented
246C22×C3—23no—
247C22×C3—23no—
248C22×C3—21no—
249C22×C3C22×C4×D311yescharacteristic
250C22×C3C22×C4×D311yescharacteristic
251C22×C3C2×#23513yes—
252C22×C3C2×#23513yes—
253C22×C3D3×#4113yes—
254C22×C3D3×#4113yes—
255C2×D3—66no—
256C2×D3—66no—
257C2×D3—126no—
258C2×D3—121no—
259C2×D3—123no—
260C2×D3—121no—
261C2×D3—123no—
262C2×D3—243no—
263C2×D3—241no—
264C3×C4—26no—
265C3×C4—26no—
266C3×C4—34no—
267C3×C4—46no—
268C3×C4—66no—
269C3×C4—121no—
270C3×C4—123no—
271Dic3—26no—
272Dic3—41no—
273Dic3—43no—
274Dic3—66no—
275Dic3—66no—
276Dic3—126no—
277Dic3#87614yescomplemented
278C32C4×#12611yescharacteristic, complemented, Sylow
279C23—92no—
280C23—183no—
281C23—183no—
282C23C22×D3211yescharacteristic
283C2×C4—23no—
284C2×C4—23no—
285C2×C4—36no—
286C2×C4—36no—
287C2×C4—63no—
288C2×C4—63no—
289C2×C4—63no—
290C2×C4—63no—
291C2×C4—63no—
292C2×C4—63no—
293C2×C4—96no—
294C2×C4—183no—
295C2×C4—183no—
296C2×C4—364no—
297C2×C4C2×#62416yes—
298C2×C3—23no—
299C2×C3—23no—
300C2×C3—21no—
301C2×C3C4×#23513yes—
302C2×C3C2×#87611yescharacteristic
303C2×C3#547913yes—
304C2×C3#552213yes—
305C2×C3D3×#12611yescharacteristic
306C2×C3#570613yes—
307D3—122no—
308D3—122no—
309D3—242no—
310C22—186no—
311C22—363no—
312C22—361no—
313C22D3×#23513yes—
314C22D3×#23513yes—
315C22C22×#62411yescharacteristic
316C4—26no—
317C4—34no—
318C4—66no—
319C4—123no—
320C4—121no—
321C4—186no—
322C3—21no—
323C3C4×#87611yescharacteristic, complemented
324C3#7425911yescharacteristic, complemented
325C2—362no—
326C2#1059397513yes—
327C2D3×#87611yescharacteristic
328C2#1059495413yes—
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. C3×#4937C2semidirect
3. C3×C42×Dic3C2semidirect
4. #10591243C2semidirect
7. #10591197C2semidirect
14. #64085C4semidirect
31. #4937D3semidirect
34. C42×Dic3D3semidirect
47. C32×C42C2×C4semidirect
49. #3750C2×C4semidirect
136. C3×C42C4×D3semidirect
137. C3×C42C4×D3semidirect
163. C3×Dic3#126semidirect
245. C42#624semidirect
277. Dic3#876semidirect
278. C32C4×#126semidirect
323. C3C4×#876semidirect
324. C3#74259semidirect

Maximal subgroups

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

subgroupindex
C2×#640852
C3×#49372
C3×C42×Dic32
#105912432
#105912332
#105912022
#105911972
#742593
C4×#8763