Finite Group Databasebeta

← C2×C3×#5945 #11919880

Subgroups — C2×C3×#5945 #11919880

Order 1152.

2780 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5945C218yesmaximal, direct product factor
2C2×C3×2−1+4⋊C3C213yesmaximal, complemented
3C2×C3×#994C211yesmaximal, characteristic, complemented
4C22×C3×#41⋊C3C213yesmaximal, complemented
5C2×C3×#585C311yesmaximal, characteristic, complemented
6C2×#5945C313yesmaximal, direct product factor
7C2×C32×#41—41nomaximal
8C3×2−1+4⋊C3C22112yescomplemented
9C3×#994C2214yescomplemented
10C2×C3×#41⋊C3C2211yescharacteristic, complemented
11C2×C3×#41⋊C3C2213yescomplemented
12C2×C3×#41⋊C3C22112yescomplemented
13C22×C3×SL(2,𝔽3)C2213yescomplemented
14C3×#585—38no—
15C3×#585C2×C318yescomplemented
16C2×C3×2−1+4—31no—
17C2×C3×2−1+4C2×C313yescomplemented
18C2×C3×H(5,𝔽2)—33no—
19C2×C3×H(5,𝔽2)C2×C311yescharacteristic, complemented
20C22×C3×#41—33no—
21C22×C3×#41—31no—
22C22×C3×#41C2×C313yescomplemented
23#5945C2×C3124yesdirect product factor
24C2×2−1+4⋊C3C2×C319yescomplemented
25C2×#994C2×C313yescomplemented
26C22×#41⋊C3C2×C319yescomplemented
27C32×#41—48no—
28C2×C32×Q8—41no—
29C2×C32×D4—43no—
30C22×C32×C4—43no—
31C3×#41⋊C3C2312yescomplemented
32C3×#41⋊C3C2316yescomplemented
33C2×C3×SL(2,𝔽3)C2311yescharacteristic
34C2×C3×SL(2,𝔽3)C2316yescomplemented
35C2×#585C3211yescharacteristic, complemented, Sylow
36C3×2−1+4—312no—
37C3×2−1+4—38no—
38C3×2−1+4—38no—
39C3×2−1+4C22×C3112yescomplemented
40C3×H(5,𝔽2)—34no—
41C3×H(5,𝔽2)—324no—
42C3×H(5,𝔽2)—324no—
43C3×H(5,𝔽2)C22×C314yescomplemented
44C2×C3×#41—324no—
45C2×C3×#41—36no—
46C2×C3×#41—324no—
47C2×C3×#41—38no—
48C2×C3×#41—38no—
49C2×C3×#41—31no—
50C2×C3×#41—33no—
51C2×C3×#41—36no—
52C2×C3×#41—33no—
53C2×C3×#41—33no—
54C2×C3×#41—33no—
55C2×C3×#41—312no—
56C2×C3×#41—43no—
57C2×C3×#41A411yescharacteristic
58C2×C3×#41C22×C311yescharacteristic
59C2×C3×#41C22×C313yes—
60C2×C3×#41C22×C3112yescomplemented
61C22×C3×Q8—33no—
62C22×C3×Q8—31no—
63C22×C3×Q8C22×C313yes—
64C22×C3×D4—33no—
65C22×C3×D4—36no—
66C22×C3×D4—33no—
67C22×C3×D4—33no—
68C23×C3×C4—32no—
69C23×C3×C4—33no—
702−1+4⋊C3C22×C3136yescomplemented
71#994C22×C3112yescomplemented
72C2×#41⋊C3C22×C313yescomplemented
73C2×#41⋊C3C22×C319yescomplemented
74C2×#41⋊C3C22×C3136yescomplemented
75C22×SL(2,𝔽3)C22×C319yescomplemented
76C23×C32—43no—
77C32×Q8—44no—
78C32×D4—412no—
79C2×C32×C4—43no—
80C2×C32×C4—412no—
81C2×C32×C4—41no—
82C3×SL(2,𝔽3)C2411yescharacteristic
83#585—38no—
84#585C2×C3218yescomplemented
85C2×2−1+4—31no—
86C2×2−1+4C2×C3213yescomplemented
87C2×H(5,𝔽2)—33no—
88C2×H(5,𝔽2)C2×C3211yescharacteristic, complemented
89C22×#41—33no—
90C22×#41—31no—
91C22×#41C2×C3213yescomplemented
92C24×C3—32no—
93C24×C3—33no—
94C3×#41—312no—
95C3×#41—324no—
96C3×#41—348no—
97C3×#41—312no—
98C3×#41—34no—
99C3×#41—34no—
100C3×#41—312no—
101C3×#41—312no—
102C3×#41—324no—
103C3×#41—324no—
104C3×#41—32no—
105C3×#41—312no—
106C3×#41—36no—
107C3×#41—312no—
108C3×#41—424no—
109C3×#41C2×A418yes—
110C3×#41C23×C312yes—
111C3×#41C23×C316yes—
112C2×C3×Q8—312no—
113C2×C3×Q8—312no—
114C2×C3×Q8—38no—
115C2×C3×Q8—33no—
116C2×C3×Q8—33no—
117C2×C3×Q8—36no—
118C2×C3×Q8—43no—
119C2×C3×Q8C2×A411yescharacteristic
120C2×C3×Q8C23×C311yescharacteristic
121C2×C3×Q8C23×C316yes—
122C2×C3×D4—31no—
123C2×C3×D4—33no—
124C2×C3×D4—312no—
125C2×C3×D4—36no—
126C2×C3×D4—348no—
127C2×C3×D4—312no—
128C2×C3×D4—312no—
129C2×C3×D4—36no—
130C2×C3×D4—324no—
131C2×C3×D4—312no—
132C2×C3×D4—33no—
133C2×C3×D4—49no—
134C2×C3×D4C2×A413yes—
135C22×C3×C4—36no—
136C22×C3×C4—316no—
137C22×C3×C4—33no—
138C22×C3×C4—33no—
139C22×C3×C4—33no—
140C22×C3×C4—312no—
141C22×C3×C4—312no—
142C22×C3×C4—33no—
143C22×C3×C4—31no—
144C22×C3×C4—49no—
145C22×C3×C4C2×A413yes—
146#41⋊C3C23×C316yescomplemented
147#41⋊C3C23×C3118yescomplemented
148C2×SL(2,𝔽3)C23×C313yes—
149C2×SL(2,𝔽3)C23×C3118yescomplemented
150C22×C32—41no—
151C22×C32—46no—
152C22×C32—86no—
153C32×C4—42no—
154C32×C4—46no—
1552−1+4—312no—
1562−1+4—38no—
1572−1+4—38no—
1582−1+4C22×C32112yescomplemented
159H(5,𝔽2)—34no—
160H(5,𝔽2)—324no—
161H(5,𝔽2)—324no—
162H(5,𝔽2)C22×C3214yescomplemented
163C2×#41—324no—
164C2×#41—36no—
165C2×#41—324no—
166C2×#41—38no—
167C2×#41—38no—
168C2×#41—31no—
169C2×#41—33no—
170C2×#41—36no—
171C2×#41—33no—
172C2×#41—33no—
173C2×#41—33no—
174C2×#41—312no—
175C2×#41C3×A411yescharacteristic
176C2×#41C22×C3211yescharacteristic
177C2×#41C22×C3213yes—
178C2×#41C22×C32112yescomplemented
179C22×Q8—33no—
180C22×Q8—31no—
181C22×Q8C22×C3213yes—
182C22×D4—33no—
183C22×D4—36no—
184C22×D4—33no—
185C22×D4—33no—
186C23×C4—32no—
187C23×C4—33no—
188C23×C3—38no—
189C23×C3—33no—
190C23×C3—31no—
191C23×C3—312no—
192C23×C3—49no—
193C23×C3—126no—
194C23×C3—124no—
195C23×C3C22×A413yes—
196C3×Q8—36no—
197C3×Q8—31no—
198C3×Q8—36no—
199C3×Q8—312no—
200C3×Q8—412no—
201C3×Q8C22×A414yes—
202C3×Q8C24×C311yescharacteristic
203C3×D4—32no—
204C3×D4—36no—
205C3×D4—36no—
206C3×D4—32no—
207C3×D4—324no—
208C3×D4—324no—
209C3×D4—312no—
210C3×D4—436no—
211C3×D4C22×A4112yes—
212C2×C3×C4—324no—
213C2×C3×C4—33no—
214C2×C3×C4—31no—
215C2×C3×C4—36no—
216C2×C3×C4—36no—
217C2×C3×C4—312no—
218C2×C3×C4—32no—
219C2×C3×C4—32no—
220C2×C3×C4—312no—
221C2×C3×C4—36no—
222C2×C3×C4—36no—
223C2×C3×C4—43no—
224C2×C3×C4—49no—
225C2×C3×C4—436no—
226C2×C3×C4C22×A413yes—
227C2×C3×C4C22×A4112yes—
228C2×C3×C4C22×A411yescharacteristic
229SL(2,𝔽3)C24×C313yes—
230C2×C32—42no—
231C2×C32—41no—
232C2×C32—86no—
233C24—32no—
234C24—33no—
235#41—312no—
236#41—324no—
237#41—348no—
238#41—312no—
239#41—34no—
240#41—34no—
241#41—312no—
242#41—312no—
243#41—324no—
244#41—324no—
245#41—32no—
246#41—312no—
247#41—36no—
248#41—312no—
249#41C2×C3×A418yes—
250#41C23×C3212yes—
251#41C23×C3216yes—
252C2×Q8—312no—
253C2×Q8—312no—
254C2×Q8—38no—
255C2×Q8—33no—
256C2×Q8—33no—
257C2×Q8—36no—
258C2×Q8C2×C3×A411yescharacteristic
259C2×Q8C23×C3211yescharacteristic
260C2×Q8C23×C3216yes—
261C2×D4—31no—
262C2×D4—33no—
263C2×D4—312no—
264C2×D4—36no—
265C2×D4—348no—
266C2×D4—312no—
267C2×D4—312no—
268C2×D4—36no—
269C2×D4—324no—
270C2×D4—312no—
271C2×D4—33no—
272C2×D4C2×C3×A413yes—
273C22×C4—36no—
274C22×C4—316no—
275C22×C4—33no—
276C22×C4—31no—
277C22×C4—33no—
278C22×C4—33no—
279C22×C4—33no—
280C22×C4—312no—
281C22×C4—312no—
282C22×C4C2×C3×A413yes—
283C22×C3—26no—
284C22×C3—36no—
285C22×C3—32no—
286C22×C3—43no—
287C22×C3—418no—
288C22×C3—62no—
289C22×C3—66no—
290C22×C3—818no—
291C22×C3—1212no—
292C22×C3—128no—
293C22×C3C23×A416yes—
294C22×C3C23×A411yescharacteristic
295C3×C4—36no—
296C3×C4—31no—
297C3×C4—31no—
298C3×C4—46no—
299C3×C4—418no—
300C3×C4C23×A412yes—
301C3×C4C23×A416yes—
302C32—41noSylow
303C23—38no—
304C23—33no—
305C23—31no—
306C23—312no—
307C23—126no—
308C23—124no—
309C23C22×C3×A413yes—
310Q8—36no—
311Q8—31no—
312Q8—36no—
313Q8—312no—
314Q8C22×C3×A414yes—
315Q8C24×C3211yescharacteristic
316D4—32no—
317D4—36no—
318D4—36no—
319D4—32no—
320D4—324no—
321D4—324no—
322D4—312no—
323D4C22×C3×A4112yes—
324C2×C4—324no—
325C2×C4—31no—
326C2×C4—33no—
327C2×C4—36no—
328C2×C4—36no—
329C2×C4—32no—
330C2×C4—312no—
331C2×C4—32no—
332C2×C4—36no—
333C2×C4—36no—
334C2×C4—312no—
335C2×C4C22×C3×A411yescharacteristic
336C2×C4C22×C3×A413yes—
337C2×C4C22×C3×A4112yes—
338C2×C3—26no—
339C2×C3—46no—
340C2×C3—43no—
341C2×C3—62no—
342C2×C3—66no—
343C2×C3—818no—
344C2×C3#594512yesdirect product factor
345C2×C3C24×A411yescharacteristic
346C22—26no—
347C22—36no—
348C22—32no—
349C22—62no—
350C22—66no—
351C22—1212no—
352C22—128no—
353C22C23×C3×A416yes—
354C22C23×C3×A411yescharacteristic
355C4—31no—
356C4—36no—
357C4—31no—
358C4C23×C3×A412yes—
359C4C23×C3×A416yes—
360C3—43no—
361C3C2×#594511yescharacteristic, direct product factor
362C2—26no—
363C2—62no—
364C2—66no—
365C2C3×#594512yesdirect product factor
366C2C24×C3×A411yescharacteristic
subgroupG/H
centerC2×C3×C4C22×A4
commutator, cosocle, hypocenterQ8C24×C32
FrattiniC2C24×C3×A4
FittingC2×C3×#585C3
socleC22×C3C23×A4
hypercenterC2×C3×#41A4
LCSG ▷ Q8
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×#41

Complements

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

NH ≅ G/Ntype
1. C3×#5945C2direct (N × H)
2. C2×C3×2−1+4⋊C3C2semidirect
3. C2×C3×#994C2semidirect
4. C22×C3×#41⋊C3C2semidirect
5. C2×C3×#585C3semidirect
6. C2×#5945C3direct (N × H)
8. C3×2−1+4⋊C3C22semidirect
9. C3×#994C22semidirect
10. C2×C3×#41⋊C3C22semidirect
11. C2×C3×#41⋊C3C22semidirect
12. C2×C3×#41⋊C3C22semidirect
13. C22×C3×SL(2,𝔽3)C22semidirect
15. C3×#585C2×C3semidirect
17. C2×C3×2−1+4C2×C3semidirect
19. C2×C3×H(5,𝔽2)C2×C3semidirect
22. C22×C3×#41C2×C3semidirect
23. #5945C2×C3direct (N × H)
24. C2×2−1+4⋊C3C2×C3semidirect
25. C2×#994C2×C3semidirect
26. C22×#41⋊C3C2×C3semidirect
31. C3×#41⋊C3C23semidirect
32. C3×#41⋊C3C23semidirect
34. C2×C3×SL(2,𝔽3)C23semidirect
35. C2×#585C32semidirect
39. C3×2−1+4C22×C3semidirect
43. C3×H(5,𝔽2)C22×C3semidirect
60. C2×C3×#41C22×C3semidirect
70. 2−1+4⋊C3C22×C3semidirect
71. #994C22×C3semidirect
72. C2×#41⋊C3C22×C3semidirect
73. C2×#41⋊C3C22×C3semidirect
74. C2×#41⋊C3C22×C3semidirect
75. C22×SL(2,𝔽3)C22×C3semidirect
84. #585C2×C32semidirect
86. C2×2−1+4C2×C32semidirect
88. C2×H(5,𝔽2)C2×C32semidirect
91. C22×#41C2×C32semidirect
146. #41⋊C3C23×C3semidirect
147. #41⋊C3C23×C3semidirect
149. C2×SL(2,𝔽3)C23×C3semidirect
158. 2−1+4C22×C32semidirect
162. H(5,𝔽2)C22×C32semidirect
178. C2×#41C22×C32semidirect
344. C2×C3#5945direct (N × H)
361. C3C2×#5945direct (N × H)
365. C2C3×#5945direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#59452
C2×C3×2−1+4⋊C32
C2×C3×#9942
C22×C3×#41⋊C32
C2×C3×#5853
C2×#59453
C2×C32×#414