Finite Group Databasebeta

← C3×#78491 #11859526

Subgroups — C3×#78491 #11859526

Order 1152.

1041 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#901C212yesmaximal, complemented
2C3×#5477C211yesmaximal, characteristic
3C2×C32×#97C211yesmaximal, characteristic, complemented
4C3×#5110C212yesmaximal, complemented
5C3×#4924C211yesmaximal, characteristic, complemented
6C3×#4706C218yesmaximal, complemented
7C3×#2932—31nomaximal
8#78491C311yesmaximal, characteristic, direct product factor
9C2×C3×#235C2212yes—
10C22×C32×C8C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C3×#930C414yes—
14C2×C3×#208C2212yes—
15C3×#901—28no—
16C2×C3×ΓL(1,𝔽25)C2214yes—
17C2×C3×D3×C8C2214yes—
18C3×#875C412yes—
19C3×#874C411yescharacteristic
20C3×C4×D12C2214yes—
21C3×#869C411yescharacteristic
22C32×#97C2214yes—
23C3×(C2×D3)⋊C8C2218yes—
24C3×C4⋊(C3⋊C8)C2214yes—
25C2×C3×#131—32no—
26C3×#532—31no—
27C2×#901C2×C312yescomplemented
28#5477C2×C311yescharacteristic
29C3×#435—38no—
30C3×#423—31no—
31C3×#408—32no—
32C2×C3×#97—21no—
33C2×C3×#97D311yescharacteristic, complemented
34C2×C3×#97C2×C311yescharacteristic, complemented
35#5110C2×C312yescomplemented
36#4924C2×C311yescharacteristic, complemented
37#4706C2×C318yescomplemented
38C22×C32×C4C2×C412yes—
39C22×C32×C4C2311yescharacteristic
40C2×C3×#67C2×C414yes—
41C3×#235—24no—
42C3×#235—24no—
43C2×C3×D12C2×C412yes—
44C2×C3×D12C2×C414yes—
45C2×C3×C4×D3C2314yes—
46C2×C3×Dic6C2×C412yes—
47C2×C32×C8—22no—
48C2×C32×C8D414yescomplemented
49C2×C32×C8C2312yes—
50C2×C32×C8C2312yes—
51C32×C42C2×C411yescharacteristic
52C32×C42C2×C411yescharacteristic
53C32×C42C2312yes—
54C3×(C2×D3)⋊C4C2×C418yes—
55C3×C4⋊Dic3C2×C414yes—
56C3×#208—24no—
57C2×C3×C3⋊C8C2314yes—
58C3×ΓL(1,𝔽25)—28no—
59C3×D3×C8—28no—
60#2932—31noSylow
61C2×C3×#41—32no—
62C2×#235C22×C312yes—
63C3×#131—68no—
64C2×C3×M16—32no—
65C2×C3×M16—34no—
66C22×C3×C8—21no—
67C22×C3×C8—21no—
68C22×C3×C8—34no—
69C22×C3×C8C2×D311yescharacteristic
70C22×C3×C8C2×D311yescharacteristic
71C22×C3×C8C22×C311yescharacteristic
72C22×C3×C8C22×C311yescharacteristic
73C3×C4⋊Q8—31no—
74C3×#127—31no—
75C3×#124—32no—
76C3×#121—34no—
77C3×C4×D4—34no—
78C2×C3×C42—21no—
79C2×C3×C42C2×D311yescharacteristic
80C2×C3×C42C22×C311yescharacteristic
81#930C3×C414yes—
82C2×#208C22×C312yes—
83#901—28no—
84C2×ΓL(1,𝔽25)C22×C314yes—
85C2×D3×C8C22×C314yes—
86#875C3×C412yes—
87#874C3×C411yescharacteristic
88C4×D12C22×C314yes—
89#869C3×C411yescharacteristic
90C3×C4⋊C8—34no—
91C3×C22⋊C8—38no—
92C3×#97—24no—
93C3×#97C2×D314yes—
94C3×#97C22×C314yes—
95(C2×D3)⋊C8C22×C318yes—
96C4⋊(C3⋊C8)C22×C314yes—
97C23×C32C22×C411yescharacteristic
98C22×C3×D3C22×C414yes—
99C2×C32×C4—42no—
100C2×C32×C4C22×C412yes—
101C2×C32×C4C22×C412yes—
102C2×C32×C4C22×C411yescharacteristic
103C2×C32×C4C2×D412yes—
104C2×C32×C4#4112yes—
105C2×C32×C4C2411yescharacteristic
106C3×#67—28no—
107C2×C3×Dic3C22×C414yes—
108C3×D12—24no—
109C3×D12—44no—
110C3×C4×D3—24no—
111C3×C4×D3—24no—
112C3×Dic6—24no—
113C32×C8—22no—
114C32×C8C2×D414yes—
115C3×C3⋊C8—24no—
116C2×#131—32no—
117#532—31no—
118#435—38no—
119#423—31no—
120#408—32no—
121C2×#97C3×D311yescharacteristic, complemented
122C3×#41—64no—
123C3×#41—64no—
124C2×C3×Q8—32no—
125C2×C3×D4—34no—
126C2×C3×D4—32no—
127C2×C3×D4—34no—
128C22×C3×C4—22no—
129C22×C3×C4—21no—
130C22×C3×C4—34no—
131C22×C3×C4C4×D312yes—
132C22×C3×C4C2×C3×C412yes—
133C22×C3×C4C22×D311yescharacteristic
134C22×C3×C4C23×C311yescharacteristic
135C2×#67C2×C3×C414yes—
136#235—24no—
137#235—24no—
138C2×D12C2×C3×C412yes—
139C2×D12C2×C3×C414yes—
140C2×C4×D3C23×C314yes—
141C2×Dic6C2×C3×C412yes—
142C3×M16—64no—
143C3×M16—68no—
144C2×C3×C8—24no—
145C2×C3×C8—22no—
146C2×C3×C8—22no—
147C2×C3×C8—24no—
148C2×C3×C8—22no—
149C2×C3×C8—22no—
150C2×C3×C8—34no—
151C2×C3×C8—68no—
152C2×C3×C8D1214yescomplemented
153C2×C3×C8C3×D414yescomplemented
154C2×C3×C8C22×D312yes—
155C2×C3×C8C22×D312yes—
156C2×C3×C8C23×C312yes—
157C2×C3×C8C23×C312yes—
158C3×C4⋊C4—34no—
159C3×C22⋊C4—38no—
160C3×C42—21no—
161C3×C42—21no—
162C3×C42—22no—
163C3×C42C4×D311yescharacteristic
164C3×C42C4×D311yescharacteristic
165C3×C42C2×C3×C411yescharacteristic
166C3×C42C2×C3×C411yescharacteristic
167C3×C42C22×D312yes—
168C3×C42C23×C312yes—
169(C2×D3)⋊C4C2×C3×C418yes—
170C4⋊Dic3C2×C3×C414yes—
171#208—24no—
172C2×C3⋊C8C23×C314yes—
173ΓL(1,𝔽25)—28no—
174D3×C8—28no—
175C22×C32—22no—
176C22×C32C4×D412yes—
177C22×C32C23×C411yescharacteristic
178C2×C3×D3—24no—
179C2×C3×D3—28no—
180C32×C4—22no—
181C32×C4—22no—
182C32×C4C4×D412yes—
183C32×C4C22×D411yescharacteristic
184C32×C4C2×#4111yescharacteristic
185C3×Dic3—24no—
186C2×#41—32no—
187#131—68no—
188C2×M16—32no—
189C2×M16—34no—
190C22×C8—34no—
191C22×C8C2×C3×D311yescharacteristic
192C22×C8C2×C3×D311yescharacteristic
193C4⋊Q8—31no—
194#127—31no—
195#124—32no—
196#121—34no—
197C4×D4—34no—
198C2×C42C2×C3×D311yescharacteristic
199C4⋊C8—34no—
200C22⋊C8—38no—
201#97C2×C3×D314yes—
202C23×C3—21no—
203C23×C3—34no—
204C23×C3C2×C4×D311yescharacteristic
205C23×C3C22×C3×C411yescharacteristic
206C22×D3C22×C3×C414yes—
207C3×Q8—64no—
208C3×D4—68no—
209C3×D4—64no—
210C3×D4—124no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—22no—
214C2×C3×C4—22no—
215C2×C3×C4—22no—
216C2×C3×C4—22no—
217C2×C3×C4—34no—
218C2×C3×C4—42no—
219C2×C3×C4—42no—
220C2×C3×C4—44no—
221C2×C3×C4—64no—
222C2×C3×C4—64no—
223C2×C3×C4C2×C4×D312yes—
224C2×C3×C4C2×C4×D312yes—
225C2×C3×C4C2×C4×D311yescharacteristic
226C2×C3×C4C2×D1212yes—
227C2×C3×C4#23512yes—
228C2×C3×C4C22×C3×C412yes—
229C2×C3×C4C22×C3×C412yes—
230C2×C3×C4C22×C3×C411yescharacteristic
231C2×C3×C4C2×C3×D412yes—
232C2×C3×C4C3×#4112yes—
233C2×C3×C4C23×D311yescharacteristic
234C2×C3×C4C24×C311yescharacteristic
235#67—28no—
236C2×Dic3C22×C3×C414yes—
237D12—24no—
238D12—44no—
239C4×D3—24no—
240C4×D3—24no—
241Dic6—24no—
242C3×C8—24no—
243C3×C8—22no—
244C3×C8—22no—
245C3×C8—24no—
246C3×C8—64no—
247C3×C8C2×D1214yes—
248C3×C8C2×C3×D414yes—
249C3⋊C8—24no—
250C2×C32—22no—
251C2×C32C2×C4×D411yescharacteristic
252C2×C32#56812yes—
253C3×D3—44no—
254#41—64no—
255#41—64no—
256C2×Q8—32no—
257C2×D4—34no—
258C2×D4—32no—
259C2×D4—34no—
260C22×C4—34no—
261C22×C4C3×C4×D312yes—
262C22×C4C22×C3×D311yescharacteristic
263M16—64no—
264M16—68no—
265C2×C8—22no—
266C2×C8—34no—
267C2×C8—68no—
268C2×C8C3×D1214yescomplemented
269C2×C8C22×C3×D312yes—
270C2×C8C22×C3×D312yes—
271C4⋊C4—34no—
272C22⋊C4—38no—
273C42C3×C4×D311yescharacteristic
274C42C3×C4×D311yescharacteristic
275C42C22×C3×D312yes—
276C22×C3—24no—
277C22×C3—22no—
278C22×C3—22no—
279C22×C3—21no—
280C22×C3—22no—
281C22×C3—64no—
282C22×C3—68no—
283C22×C3C4×D1212yes—
284C22×C3C3×C4×D412yes—
285C22×C3C22×C4×D311yescharacteristic
286C22×C3C23×C3×C411yescharacteristic
287C2×D3—28no—
288C2×D3—24no—
289C3×C4—22no—
290C3×C4—22no—
291C3×C4—22no—
292C3×C4—22no—
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—22no—
296C3×C4—42no—
297C3×C4—42no—
298C3×C4—64no—
299C3×C4C4×D1212yes—
300C3×C4C3×C4×D412yes—
301C3×C4C22×D1211yescharacteristic
302C3×C4C2×#23511yescharacteristic
303C3×C4C22×C3×D411yescharacteristic
304C3×C4C2×C3×#4111yescharacteristic
305Dic3—24no—
306C32#293211yescharacteristic, complemented, Sylow
307C23—34no—
308C23C2×C3×C4×D311yescharacteristic
309Q8—64no—
310D4—68no—
311D4—64no—
312D4—124no—
313C2×C4—34no—
314C2×C4—42no—
315C2×C4—64no—
316C2×C4—64no—
317C2×C4C2×C3×C4×D312yes—
318C2×C4C2×C3×C4×D312yes—
319C2×C4C2×C3×C4×D311yescharacteristic
320C2×C4C2×C3×D1212yes—
321C2×C4C3×#23512yes—
322C2×C4C23×C3×D311yescharacteristic
323C8—22no—
324C8—64no—
325C8C2×C3×D1214yes—
326C2×C3—24no—
327C2×C3—22no—
328C2×C3—22no—
329C2×C3—22no—
330C2×C3—21no—
331C2×C3—124no—
332C2×C3C2×C4×D1211yescharacteristic
333C2×C3#574512yes—
334C2×C3C2×C3×C4×D411yescharacteristic
335C2×C3C3×#56812yes—
336D3—44no—
337C22—22no—
338C22—68no—
339C22—64no—
340C22C3×C4×D1212yes—
341C22C22×C3×C4×D311yescharacteristic
342C4—22no—
343C4—22no—
344C4—64no—
345C4C3×C4×D1212yes—
346C4C22×C3×D1211yescharacteristic
347C4C2×C3×#23511yescharacteristic
348C3—21no—
349C3#7849111yescharacteristic, direct product factor
350C3C3×#293211yescharacteristic, complemented
351C2—22no—
352C2—124no—
353C2C2×C3×C4×D1211yescharacteristic
354C2C3×#574512yes—
subgroupG/H
centerC2×C3×C4C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#97C2
socleC22×C32C23×C4
prime radicalC3×#5477C2
cosocleC2×C3×C4C24×C3
hypercenterC2×C3×#97D3
hypocenterC3C3×#2932
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×#97

Complements

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

NH ≅ G/Ntype
1. C2×C3×#901C2semidirect
3. C2×C32×#97C2semidirect
4. C3×#5110C2semidirect
5. C3×#4924C2semidirect
6. C3×#4706C2semidirect
8. #78491C3direct (N × H)
27. C2×#901C2×C3semidirect
33. C2×C3×#97D3semidirect
34. C2×C3×#97C2×C3semidirect
35. #5110C2×C3semidirect
36. #4924C2×C3semidirect
37. #4706C2×C3semidirect
48. C2×C32×C8D4semidirect
121. C2×#97C3×D3semidirect
152. C2×C3×C8D12semidirect
153. C2×C3×C8C3×D4semidirect
268. C2×C8C3×D12semidirect
306. C32#2932semidirect
349. C3#78491direct (N × H)
350. C3C3×#2932semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9012
C3×#54772
C2×C32×#972
C3×#51102
C3×#49242
C3×#47062
C3×#29323
#784913