Finite Group Databasebeta

← C3×#79169 #11860802

Subgroups — C3×#79169 #11860802

Order 1152.

969 conjugacy classes of subgroups.

The subgroup lattice has 323 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×Dic12C211yesmaximal, characteristic
2C3×#5516C212yesmaximal
3C32×#427C211yesmaximal, characteristic
4C3×#5101C211yesmaximal, characteristic
5C3×#5004C212yesmaximal
6C3×#4873C214yesmaximal, complemented
7C3×#4853C214yesmaximal, complemented
8C3×#2950—31nomaximal
9#79169C311yesmaximal, characteristic, direct product factor
10C22×C3×Dic6C2212yes—
11C22×C32×C8C2211yescharacteristic
12C32×#117C2212yes—
13C3×#926C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×Dic12C418yescomplemented
16C2×C3×Dic12C2212yes—
17C2×C3×Dic12C2212yes—
18C3×#887C2218yes—
19C3×#877—24no—
20C3×C4×Dic6—24no—
21C32×#107C2212yes—
22C32×#106C2212yes—
23C3×#815C2212yes—
24C3×C8×Dic3C2212yes—
25C3×#810C2218yes—
26C22×C3×Q16—31no—
27C3×#519—32no—
28C22×Dic12C2×C311yescharacteristic
29#5516C2×C312yes—
30C3×#441—34no—
31C3×C4×Q16—34no—
32C3×#427—21no—
33C3×#427D311yescharacteristic
34C3×#427C2×C311yescharacteristic
35C3×#419—32no—
36C3×#405—31no—
37#5101C2×C311yescharacteristic
38#5004C2×C312yes—
39#4873C2×C314yescomplemented
40#4853C2×C314yescomplemented
41C22×C32×C4C2311yescharacteristic
42C22×C3×Dic3—22no—
43C2×C3×Dic6—22no—
44C2×C3×Dic6—24no—
45C2×C3×Dic6C2×C418yes—
46C2×C3×Dic6C2314yes—
47C2×C32×C8C2×C414yes—
48C2×C32×C8C2311yescharacteristic
49C2×C32×C8C2311yescharacteristic
50C32×C4⋊C4C2314yes—
51C32×C22⋊C4—22no—
52C32×C42—22no—
53C3×#217D412yes—
54C3×C4⋊Dic3D412yes—
55C3×Dic3⋊C4—28no—
56C3×C4×Dic3—28no—
57C3×C4×Dic3C2312yes—
58C3×#208—22no—
59C2×C3×C3⋊C8C2312yes—
60C3×Dic12C2×C418yes—
61C3×Dic12C2×C418yes—
62#2950—31noSylow
63C22×C3×Q8—32no—
64C22×Dic6C22×C312yes—
65C2×C3×Q16—38no—
66C2×C3×Q16—32no—
67C2×C3×Q16—32no—
68C2×C3×M16—31no—
69C22×C3×C8—21no—
70C22×C3×C8C2×D311yescharacteristic
71C22×C3×C8C22×C311yescharacteristic
72C3×C4×Q8—38no—
73C3×C4×Q8—64no—
74C3×#117—22no—
75C3×#117—31no—
76C3×#117—64no—
77C3×#117C2×D312yes—
78C3×#117C22×C312yes—
79#926C22×C311yescharacteristic
80C2×#208C22×C311yescharacteristic
81C2×Dic12C3×C418yescomplemented
82C2×Dic12C22×C312yes—
83C2×Dic12C22×C312yes—
84#887C22×C318yes—
85#877—24no—
86C4×Dic6—24no—
87C3×#107—22no—
88C3×#107C2×D312yes—
89C3×#107C22×C312yes—
90C3×#106—22no—
91C3×#106C2×D312yes—
92C3×#106C22×C312yes—
93C3×#103—38no—
94C3×#97—32no—
95C3×C4×C8—32no—
96#815C22×C312yes—
97C8×Dic3C22×C312yes—
98#810C22×C318yes—
99C23×C32C2×D411yescharacteristic
100C2×C32×C4—24no—
101C2×C32×C4C22×C412yes—
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4#4112yes—
104C2×C32×C4C2411yescharacteristic
105C2×C3×Dic3—28no—
106C2×C3×Dic3—24no—
107C2×C3×Dic3C2×D414yes—
108C3×Dic6—28no—
109C3×Dic6—24no—
110C3×Dic6C22×C418yes—
111C32×C8C22×C412yes—
112C32×C8C22×C412yes—
113C3×C3⋊C8—22no—
114C22×Q16—31no—
115#519—32no—
116#441—34no—
117C4×Q16—34no—
118#427C3×D311yescharacteristic
119#419—32no—
120#405—31no—
121C2×C3×Q8—38no—
122C2×C3×Q8—34no—
123C2×C3×Q8—62no—
124C2×C3×Q8—64no—
125C22×C3×C4—21no—
126C22×C3×C4—62no—
127C22×C3×C4C22×D311yescharacteristic
128C22×C3×C4C23×C311yescharacteristic
129C22×Dic3—22no—
130C2×Dic6—22no—
131C2×Dic6—24no—
132C2×Dic6C2×C3×C418yes—
133C2×Dic6C23×C314yes—
134C3×Q16—38no—
135C3×Q16—38no—
136C3×M16—62no—
137C2×C3×C8—24no—
138C2×C3×C8—21no—
139C2×C3×C8—21no—
140C2×C3×C8—32no—
141C2×C3×C8C4×D314yes—
142C2×C3×C8C2×C3×C414yes—
143C2×C3×C8C22×D311yescharacteristic
144C2×C3×C8C22×D311yescharacteristic
145C2×C3×C8C23×C311yescharacteristic
146C2×C3×C8C23×C311yescharacteristic
147C3×C4⋊C4—24no—
148C3×C4⋊C4—32no—
149C3×C4⋊C4—68no—
150C3×C4⋊C4C22×D314yes—
151C3×C4⋊C4C23×C314yes—
152C3×C22⋊C4—22no—
153C3×C22⋊C4—22no—
154C3×C22⋊C4—32no—
155C3×C22⋊C4—42no—
156C3×C42—22no—
157C3×C42—22no—
158C3×C42—32no—
159C3×C42—42no—
160C3×C42—68no—
161#217C3×D412yes—
162C4⋊Dic3C3×D412yes—
163Dic3⋊C4—28no—
164C4×Dic3—28no—
165C4×Dic3C23×C312yes—
166#208—22no—
167C2×C3⋊C8C23×C312yes—
168Dic12C2×C3×C418yes—
169Dic12C2×C3×C418yes—
170C22×C32—22no—
171C22×C32C4×D412yes—
172C22×C32C22×D411yescharacteristic
173C32×C4—44no—
174C32×C4C4×D412yes—
175C32×C4C23×C411yescharacteristic
176C32×C4C2×#4111yescharacteristic
177C3×Dic3—28no—
178C3×Dic3—24no—
179C22×Q8—32no—
180C2×Q16—38no—
181C2×Q16—32no—
182C2×Q16—32no—
183C2×M16—31no—
184C22×C8C2×C3×D311yescharacteristic
185C4×Q8—38no—
186C4×Q8—64no—
187#117—31no—
188#117—64no—
189#117C2×C3×D312yes—
190#107C2×C3×D312yes—
191#106C2×C3×D312yes—
192#103—38no—
193#97—32no—
194C4×C8—32no—
195C23×C3—21no—
196C23×C3D3×D411yescharacteristic
197C23×C3C2×C3×D411yescharacteristic
198C3×Q8—38no—
199C3×Q8—68no—
200C3×Q8—64no—
201C2×C3×C4—24no—
202C2×C3×C4—24no—
203C2×C3×C4—21no—
204C2×C3×C4—22no—
205C2×C3×C4—21no—
206C2×C3×C4—22no—
207C2×C3×C4—34no—
208C2×C3×C4—44no—
209C2×C3×C4—68no—
210C2×C3×C4—64no—
211C2×C3×C4C2×C4×D312yes—
212C2×C3×C4D3×D411yescharacteristic
213C2×C3×C4#23912yes—
214C2×C3×C4C22×C3×C412yes—
215C2×C3×C4C2×C3×D411yescharacteristic
216C2×C3×C4C3×#4112yes—
217C2×C3×C4C23×D311yescharacteristic
218C2×C3×C4C24×C311yescharacteristic
219C2×Dic3—28no—
220C2×Dic3—24no—
221C2×Dic3C2×C3×D414yes—
222Dic6—28no—
223Dic6—24no—
224Dic6C22×C3×C418yes—
225C3×C8—22no—
226C3×C8—22no—
227C3×C8—62no—
228C3×C8C2×C4×D312yes—
229C3×C8C2×C4×D312yes—
230C3×C8C22×C3×C412yes—
231C3×C8C22×C3×C412yes—
232C3⋊C8—22no—
233C2×C32—22no—
234C2×C32C2×C4×D411yescharacteristic
235C2×C32#57812yes—
236C2×Q8—34no—
237C2×Q8—38no—
238C2×Q8—62no—
239C2×Q8—64no—
240C22×C4—62no—
241C22×C4C22×C3×D311yescharacteristic
242Q16—38no—
243Q16—38no—
244M16—62no—
245C2×C8—32no—
246C2×C8C3×C4×D314yes—
247C2×C8C22×C3×D311yescharacteristic
248C2×C8C22×C3×D311yescharacteristic
249C4⋊C4—32no—
250C4⋊C4—68no—
251C4⋊C4C22×C3×D314yes—
252C22⋊C4—22no—
253C22⋊C4—32no—
254C42—22no—
255C42—32no—
256C42—68no—
257C22×C3—22no—
258C22×C3—22no—
259C22×C3—22no—
260C22×C3—21no—
261C22×C3—42no—
262C22×C3#89312yes—
263C22×C3C3×C4×D412yes—
264C22×C3C2×D3×D411yescharacteristic
265C22×C3C22×C3×D411yescharacteristic
266C3×C4—22no—
267C3×C4—21no—
268C3×C4—21no—
269C3×C4—44no—
270C3×C4—44no—
271C3×C4—68no—
272C3×C4—64no—
273C3×C4—84no—
274C3×C4#89312yes—
275C3×C4C3×C4×D412yes—
276C3×C4C22×C4×D311yescharacteristic
277C3×C4C2×#23911yescharacteristic
278C3×C4C23×C3×C411yescharacteristic
279C3×C4C2×C3×#4111yescharacteristic
280Dic3—24no—
281Dic3—28no—
282C32#295011yescharacteristic, complemented, Sylow
283C23C3×D3×D411yescharacteristic
284Q8—38no—
285Q8—68no—
286Q8—64no—
287C2×C4—24no—
288C2×C4—34no—
289C2×C4—68no—
290C2×C4—64no—
291C2×C4C2×C3×C4×D312yes—
292C2×C4C3×D3×D411yescharacteristic
293C2×C4C3×#23912yes—
294C2×C4C23×C3×D311yescharacteristic
295C8—62no—
296C8C2×C3×C4×D312yes—
297C8C2×C3×C4×D312yes—
298C2×C3—22no—
299C2×C3—22no—
300C2×C3—21no—
301C2×C3—22no—
302C2×C3—42no—
303C2×C3C2×#89311yescharacteristic
304C2×C3#577112yes—
305C2×C3C2×C3×C4×D411yescharacteristic
306C2×C3C3×#57812yes—
307C22—22no—
308C22C3×#89312yes—
309C22C2×C3×D3×D411yescharacteristic
310C4—44no—
311C4—68no—
312C4—64no—
313C4C3×#89312yes—
314C4C22×C3×C4×D311yescharacteristic
315C4C2×C3×#23911yescharacteristic
316C3—21no—
317C3#7916911yescharacteristic, direct product factor
318C3C3×#295011yescharacteristic, complemented
319C2—22no—
320C2C2×C3×#89311yescharacteristic
321C2C3×#577112yes—
subgroupG/H
centerC22×C3C2×D3×D4
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC32×#427C2
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
cosocleC2×C3×C4C24×C3
hypercenterC3×#427D3
hypocenterC3C3×#2950
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#427

Complements

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

NH ≅ G/Ntype
6. C3×#4873C2semidirect
7. C3×#4853C2semidirect
9. #79169C3direct (N × H)
15. C2×C3×Dic12C4semidirect
39. #4873C2×C3semidirect
40. #4853C2×C3semidirect
81. C2×Dic12C3×C4semidirect
282. C32#2950semidirect
317. C3#79169direct (N × H)
318. C3C3×#2950semidirect

Maximal subgroups

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

subgroupindex
C22×C3×Dic122
C3×#55162
C32×#4272
C3×#51012
C3×#50042
C3×#48732
C3×#48532
C3×#29503
#791693