Finite Group Databasebeta

← C3×#79260 #11858667

Subgroups — C3×#79260 #11858667

Order 1152.

931 conjugacy classes of subgroups.

The subgroup lattice has 331 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5745C212yesmaximal
2C2×C3×#907C211yesmaximal, characteristic
3C32×#430C211yesmaximal, characteristic, complemented
4C3×#5125C211yesmaximal, characteristic, complemented
5C2×C3×#822C212yesmaximal, complemented
6C3×#4893C214yesmaximal, complemented
7C3×D3×#108C214yesmaximal, complemented
8C3×#2916—31nomaximal
9#79260C311yesmaximal, characteristic, direct product factor
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2212yes—
12C2×C32×M16C2211yescharacteristic
13C2×C3×#208C2212yes—
14C22×C3×C3⋊C8C2211yescharacteristic
15C3×#907—24no—
16C3×#907C418yes—
17C3×D3×M16C2218yes—
18C3×#901—24no—
19C2×C3×ΓL(1,𝔽25)C2212yes—
20C2×C3×D3×C8C2212yes—
21C32×#108C2214yes—
22C3×#822C2214yes—
23C3×#822C2214yes—
24C3×#819C2214yes—
25C3×#568—32no—
26C2×C3×#131—31no—
27#5745C2×C312yes—
28C2×#907C2×C311yescharacteristic
29C3×#430—21no—
30C3×#430—31no—
31C3×#430—34no—
32C3×#430D311yescharacteristic, complemented
33C3×#430C2×C311yescharacteristic, complemented
34C2×C3×#108—32no—
35C2×C3×#108—34no—
36#5125C2×C311yescharacteristic, complemented
37C2×#822C2×C312yescomplemented
38#4893C2×C314yescomplemented
39D3×#108C2×C314yescomplemented
40C22×C32×C4C2311yescharacteristic
41C2×C3×#67Q812yes—
42C3×#235C2×C414yes—
43C3×#235D414yes—
44C2×C3×D12Q811yescharacteristic
45C2×C3×C4×D3C2312yes—
46C2×C3×Dic6Q811yescharacteristic
47C32×M16—22no—
48C32×M16C2×C414yes—
49C32×M16C2314yes—
50C2×C32×C8—22no—
51C2×C32×C8C2312yes—
52C3×#208—22no—
53C3×#208C2314yes—
54C2×C3×C3⋊C8—22no—
55C2×C3×C3⋊C8C2×C414yes—
56C2×C3×C3⋊C8C2311yescharacteristic
57C2×C3×C3⋊C8C2311yescharacteristic
58C3×ΓL(1,𝔽25)—28no—
59C3×ΓL(1,𝔽25)C2×C418yes—
60C3×D3×C8—28no—
61C3×D3×C8C2×C418yes—
62#2916—31noSylow
63C2×C3×#41—31no—
64C2×#235C22×C311yescharacteristic
65C3×#131—38no—
66C3×#131—64no—
67C3×#131—64no—
68C2×C3×M16—21no—
69C2×C3×M16—22no—
70C2×C3×M16—32no—
71C2×C3×M16—32no—
72C2×C3×M16—38no—
73C2×C3×M16C2×D312yes—
74C2×C3×M16C2×D311yescharacteristic
75C2×C3×M16C22×C312yes—
76C2×C3×M16C22×C311yescharacteristic
77C22×C3×C8—31no—
78C22×C3×C8—32no—
79C2×#208C22×C312yes—
80C22×C3⋊C8C22×C311yescharacteristic
81#907—24no—
82#907C3×C418yes—
83D3×M16C22×C318yes—
84#901—24no—
85C2×ΓL(1,𝔽25)C22×C312yes—
86C2×D3×C8C22×C312yes—
87C3×#108—24no—
88C3×#108—34no—
89C3×#108—34no—
90C3×#108—34no—
91C3×#108C2×D314yes—
92C3×#108C22×C314yes—
93#822C22×C314yes—
94#822C22×C314yes—
95#819C22×C314yes—
96C23×C32C2×Q811yescharacteristic
97C22×C3×D3C2×Q812yes—
98C2×C32×C4C22×C412yes—
99C2×C32×C4C2×D412yes—
100C2×C32×C4C2×Q811yescharacteristic
101C2×C32×C4C2411yescharacteristic
102C3×#67C4⋊C418yes—
103C2×C3×Dic3C2×Q812yes—
104C3×D12C4⋊C414yes—
105C3×C4×D3C22×C414yes—
106C3×C4×D3C2×D414yes—
107C3×Dic6C4⋊C414yes—
108C32×C8—24no—
109C32×C8C22×C414yes—
110C3×C3⋊C8—24no—
111C3×C3⋊C8C22×C412yes—
112C3×C3⋊C8C22×C412yes—
113#568—32no—
114C2×#131—31no—
115#430—31no—
116#430—34no—
117#430C3×D311yescharacteristic, complemented
118C2×#108—32no—
119C2×#108—34no—
120C3×#41—34no—
121C3×#41—34no—
122C2×C3×Q8—31no—
123C2×C3×D4—32no—
124C2×C3×D4—31no—
125C22×C3×C4—21no—
126C22×C3×C4—32no—
127C22×C3×C4C22×D311yescharacteristic
128C22×C3×C4C23×C311yescharacteristic
129C2×#67C3×Q812yes—
130#235C2×C3×C414yes—
131#235C3×D414yes—
132C2×D12C3×Q811yescharacteristic
133C2×C4×D3C23×C312yes—
134C2×Dic6C3×Q811yescharacteristic
135C3×M16—22no—
136C3×M16—22no—
137C3×M16—24no—
138C3×M16—24no—
139C3×M16—38no—
140C3×M16—34no—
141C3×M16—42no—
142C3×M16—68no—
143C3×M16—62no—
144C3×M16C4×D314yes—
145C3×M16C2×C3×C414yes—
146C3×M16C22×D314yes—
147C3×M16C23×C314yes—
148C2×C3×C8—22no—
149C2×C3×C8—22no—
150C2×C3×C8—22no—
151C2×C3×C8—34no—
152C2×C3×C8—31no—
153C2×C3×C8—31no—
154C2×C3×C8—38no—
155C2×C3×C8—42no—
156C2×C3×C8—68no—
157C2×C3×C8—62no—
158C2×C3×C8C22×D312yes—
159C2×C3×C8C23×C312yes—
160#208—22no—
161#208C23×C314yes—
162C2×C3⋊C8—22no—
163C2×C3⋊C8C2×C3×C414yes—
164C2×C3⋊C8C23×C311yescharacteristic
165C2×C3⋊C8C23×C311yescharacteristic
166ΓL(1,𝔽25)—28no—
167ΓL(1,𝔽25)C2×C3×C418yes—
168D3×C8—28no—
169D3×C8C2×C3×C418yes—
170C22×C32—41no—
171C22×C32C2×C4⋊C412yes—
172C22×C32C22×Q811yescharacteristic
173C2×C3×D3—42no—
174C2×C3×D3C2×C4⋊C414yes—
175C32×C4C2×C4⋊C412yes—
176C32×C4C23×C411yescharacteristic
177C32×C4C22×D411yescharacteristic
178C3×Dic3C2×C4⋊C414yes—
179C2×#41—31no—
180#131—38no—
181#131—64no—
182#131—64no—
183C2×M16—32no—
184C2×M16—32no—
185C2×M16—38no—
186C2×M16C2×C3×D312yes—
187C2×M16C2×C3×D311yescharacteristic
188C22×C8—31no—
189C22×C8—32no—
190#108—34no—
191#108—34no—
192#108—34no—
193#108C2×C3×D314yes—
194C23×C3—21no—
195C23×C3—32no—
196C23×C3D3×Q811yescharacteristic
197C23×C3C2×C3×Q811yescharacteristic
198C22×D3C2×C3×Q812yes—
199C3×Q8—34no—
200C3×D4—38no—
201C3×D4—34no—
202C2×C3×C4—21no—
203C2×C3×C4—22no—
204C2×C3×C4—22no—
205C2×C3×C4—21no—
206C2×C3×C4—32no—
207C2×C3×C4—34no—
208C2×C3×C4—34no—
209C2×C3×C4C2×C4×D312yes—
210C2×C3×C4D3×D412yes—
211C2×C3×C4D3×Q811yescharacteristic
212C2×C3×C4C22×C3×C412yes—
213C2×C3×C4C2×C3×D412yes—
214C2×C3×C4C2×C3×Q811yescharacteristic
215C2×C3×C4C23×D311yescharacteristic
216C2×C3×C4C24×C311yescharacteristic
217#67C3×C4⋊C418yes—
218C2×Dic3C2×C3×Q812yes—
219D12C3×C4⋊C414yes—
220C4×D3C22×C3×C414yes—
221C4×D3C2×C3×D414yes—
222Dic6C3×C4⋊C414yes—
223C3×C8—24no—
224C3×C8—24no—
225C3×C8—24no—
226C3×C8—32no—
227C3×C8—32no—
228C3×C8—44no—
229C3×C8—64no—
230C3×C8C2×C4×D314yes—
231C3×C8C22×C3×C414yes—
232C3⋊C8—24no—
233C3⋊C8C22×C3×C412yes—
234C3⋊C8C22×C3×C412yes—
235C2×C32—21no—
236C2×C32—22no—
237C2×C32C22×C4⋊C411yescharacteristic
238C3×D3—24no—
239#41—34no—
240#41—34no—
241C2×Q8—31no—
242C2×D4—32no—
243C2×D4—31no—
244C22×C4—32no—
245C22×C4C22×C3×D311yescharacteristic
246M16—22no—
247M16—38no—
248M16—34no—
249M16—68no—
250M16—62no—
251M16C3×C4×D314yes—
252M16C22×C3×D314yes—
253C2×C8—22no—
254C2×C8—31no—
255C2×C8—31no—
256C2×C8—34no—
257C2×C8—38no—
258C2×C8—68no—
259C2×C8—62no—
260C2×C8C22×C3×D312yes—
261C22×C3—22no—
262C22×C3—21no—
263C22×C3—34no—
264C22×C3—41no—
265C22×C3—41no—
266C22×C3—81no—
267C22×C3—122no—
268C22×C3D3×C4⋊C412yes—
269C22×C3C2×C3×C4⋊C412yes—
270C22×C3C2×D3×Q811yescharacteristic
271C22×C3C22×C3×Q811yescharacteristic
272C2×D3—42no—
273C2×D3C2×C3×C4⋊C414yes—
274C3×C4—22no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—34no—
278C3×C4D3×C4⋊C412yes—
279C3×C4C2×C3×C4⋊C412yes—
280C3×C4C22×C4×D311yescharacteristic
281C3×C4C2×D3×D411yescharacteristic
282C3×C4C23×C3×C411yescharacteristic
283C3×C4C22×C3×D411yescharacteristic
284Dic3C2×C3×C4⋊C414yes—
285C32#291611yescharacteristic, complemented, Sylow
286C23—32no—
287C23C3×D3×Q811yescharacteristic
288Q8—34no—
289D4—38no—
290D4—34no—
291C2×C4—32no—
292C2×C4—34no—
293C2×C4—34no—
294C2×C4C2×C3×C4×D312yes—
295C2×C4C3×D3×D412yes—
296C2×C4C3×D3×Q811yescharacteristic
297C2×C4C23×C3×D311yescharacteristic
298C8—24no—
299C8—32no—
300C8—32no—
301C8—64no—
302C8C2×C3×C4×D314yes—
303C2×C3—21no—
304C2×C3—22no—
305C2×C3—21no—
306C2×C3—22no—
307C2×C3—21no—
308C2×C3—41no—
309C2×C3—42no—
310C2×C3—64no—
311C2×C3C2×D3×C4⋊C411yescharacteristic
312C2×C3C22×C3×C4⋊C411yescharacteristic
313D3—24no—
314C22—34no—
315C22—41no—
316C22—122no—
317C22C3×D3×C4⋊C412yes—
318C22C2×C3×D3×Q811yescharacteristic
319C4—34no—
320C4C3×D3×C4⋊C412yes—
321C4C22×C3×C4×D311yescharacteristic
322C4C2×C3×D3×D411yescharacteristic
323C3—21no—
324C3#7926011yescharacteristic, direct product factor
325C3C3×#291611yescharacteristic, complemented
326C2—21no—
327C2—22no—
328C2—64no—
329C2C2×C3×D3×C4⋊C411yescharacteristic
subgroupG/H
centerC3×C4C2×D3×D4
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC32×#430C2
socleC2×C32C22×C4⋊C4
prime radicalC2×C3×#235C22
cosocleC2×C3×C4C24×C3
hypercenterC3×#430D3
hypocenterC3C3×#2916
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×#430

Complements

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

NH ≅ G/Ntype
3. C32×#430C2semidirect
4. C3×#5125C2semidirect
5. C2×C3×#822C2semidirect
6. C3×#4893C2semidirect
7. C3×D3×#108C2semidirect
9. #79260C3direct (N × H)
32. C3×#430D3semidirect
33. C3×#430C2×C3semidirect
36. #5125C2×C3semidirect
37. C2×#822C2×C3semidirect
38. #4893C2×C3semidirect
39. D3×#108C2×C3semidirect
117. #430C3×D3semidirect
285. C32#2916semidirect
324. C3#79260direct (N × H)
325. C3C3×#2916semidirect

Maximal subgroups

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

subgroupindex
C3×#57452
C2×C3×#9072
C32×#4302
C3×#51252
C2×C3×#8222
C3×#48932
C3×D3×#1082
C3×#29163
#792603