Finite Group Databasebeta

← C3×#68546 #11780839

Subgroups — C3×#68546 #11780839

Order 1152.

371 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#4851C211yesmaximal, characteristic, complemented
2C3×#4848C211yesmaximal, characteristic
3C3×#4693C211yesmaximal, characteristic
4C3×C8×Dic6C211yesmaximal, characteristic, complemented
5C32×#334C211yesmaximal, characteristic, complemented
6C3×#4486C211yesmaximal, characteristic, complemented
7C3×#4485C211yesmaximal, characteristic
8C3×#1666—31nomaximal
9#68546C311yesmaximal, characteristic, direct product factor
10C2×C3×#204—21no—
11C2×C3×#204—21no—
12C2×C3×#204—21no—
13C3×#874C2211yescharacteristic
14C3×#869C2211yescharacteristic
15C3×C4×Dic6C2211yescharacteristic
16C32×C4⋊C8C2211yescharacteristic
17C32×C4⋊C8C2211yescharacteristic
18C32×C4×C8C2211yescharacteristic
19C3×#821—21no—
20C3×#817—21no—
21C3×#816—21no—
22C3×Dic3⋊C8—21no—
23C3×C8×Dic3—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×#492—31no—
26C3×#475—31no—
27C3×#460—31no—
28C3×C8×Q8—31no—
29#4851C2×C311yescharacteristic, complemented
30#4848C2×C311yescharacteristic
31#4693C2×C311yescharacteristic
32C8×Dic6C2×C311yescharacteristic, complemented
33C3×#334—21no—
34C3×#334D311yescharacteristic, complemented
35C3×#334C2×C311yescharacteristic, complemented
36C3×#332—31no—
37C3×#331—31no—
38#4486C2×C311yescharacteristic, complemented
39#4485C2×C311yescharacteristic
40C2×C3×D12—21no—
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×C3×Dic6—21no—
44C2×C3×Dic6D411yescharacteristic
45C2×C32×C8—21no—
46C2×C32×C8—21no—
47C2×C32×C8D411yescharacteristic
48C2×C32×C8D411yescharacteristic
49C32×C42C2311yescharacteristic
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3D411yescharacteristic
53C3×Dic3⋊C4—21no—
54C3×C4×Dic3—21no—
55C2×C3×C3⋊C8—21no—
56C3×#204—42no—
57C3×#204—42no—
58C3×#204—42no—
59#1666—31noSylow
60C2×C3×SD16—61no—
61C2×C3×SD16—61no—
62C2×C3×SD16—61no—
63C3×C4⋊Q8—31no—
64C3×#127—31no—
65C3×C4×Q8—31no—
66C2×#204—21no—
67C2×#204—21no—
68C2×#204—21no—
69#874C22×C311yescharacteristic
70#869C22×C311yescharacteristic
71C4×Dic6C22×C311yescharacteristic
72C3×#106—61no—
73C3×C4⋊C8—21no—
74C3×C4⋊C8—21no—
75C3×C4⋊C8—31no—
76C3×C4⋊C8—61no—
77C3×C4⋊C8C2×D311yescharacteristic
78C3×C4⋊C8C2×D311yescharacteristic
79C3×C4⋊C8C22×C311yescharacteristic
80C3×C4⋊C8C22×C311yescharacteristic
81C3×#103—61no—
82C3×#102—61no—
83C3×C4×C8—21no—
84C3×C4×C8—61no—
85C3×C4×C8C2×D311yescharacteristic
86C3×C4×C8C22×C311yescharacteristic
87#821—21no—
88#817—21no—
89#816—21no—
90Dic3⋊C8—21no—
91C8×Dic3—21no—
92C4⋊(C3⋊C8)C22×C311yescharacteristic
93C22×C3×D3—41no—
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4#4111yescharacteristic
97C2×C3×Dic3—21no—
98C2×C3×Dic3—21no—
99C2×C3×Dic3—41no—
100C3×D12—41no—
101C3×D12—41no—
102C3×D12—41no—
103C3×D12—41no—
104C3×D12—81no—
105C3×Dic6—21no—
106C3×Dic6—41no—
107C3×Dic6—41no—
108C3×Dic6SD1612yescomplemented
109C32×C8—21no—
110C32×C8—41no—
111C32×C8—41no—
112C32×C8SD1612yescomplemented
113C3×C3⋊C8—41no—
114#492—31no—
115#475—31no—
116#460—31no—
117C8×Q8—31no—
118#334C3×D311yescharacteristic, complemented
119#332—31no—
120#331—31no—
121C2×C3×Q8—31no—
122C2×C3×Q8—61no—
123C2×C3×D4—61no—
124C2×C3×D4—61no—
125C2×C3×D4—61no—
126C2×D12—21no—
127C2×D12—21no—
128C2×D12—21no—
129C2×Dic6—21no—
130C2×Dic6C3×D411yescharacteristic
131C3×SD16—122no—
132C3×SD16—122no—
133C3×SD16—122no—
134C2×C3×C8—21no—
135C2×C3×C8—21no—
136C2×C3×C8—21no—
137C2×C3×C8—21no—
138C2×C3×C8—21no—
139C2×C3×C8—21no—
140C2×C3×C8—41no—
141C2×C3×C8—41no—
142C2×C3×C8—61no—
143C2×C3×C8D1211yescharacteristic
144C2×C3×C8D1211yescharacteristic
145C2×C3×C8C3×D411yescharacteristic
146C2×C3×C8C3×D411yescharacteristic
147C3×C4⋊C4—31no—
148C3×C4⋊C4—61no—
149C3×C4⋊C4—61no—
150C3×C4⋊C4—61no—
151C3×C42—21no—
152C3×C42—61no—
153C3×C42C22×D311yescharacteristic
154C3×C42C23×C311yescharacteristic
155C4⋊Dic3—21no—
156C4⋊Dic3—21no—
157C4⋊Dic3C3×D411yescharacteristic
158Dic3⋊C4—21no—
159C4×Dic3—21no—
160C2×C3⋊C8—21no—
161#204—42no—
162#204—42no—
163#204—42no—
164C22×C32#12111yescharacteristic
165C2×C3×D3—81no—
166C2×C3×D3—81no—
167C2×C3×D3—81no—
168C32×C4—21no—
169C32×C4C2×SD1611yescharacteristic
170C32×C4C2×SD1611yescharacteristic
171C32×C4#13511yescharacteristic
172C32×C4AGL(1,ℤ/8)11yescharacteristic
173C3×Dic3—22no—
174C3×Dic3—41no—
175C3×Dic3—81no—
176C2×SD16—61no—
177C2×SD16—61no—
178C2×SD16—61no—
179C4⋊Q8—31no—
180#127—31no—
181C4×Q8—31no—
182#106—61no—
183C4⋊C8—31no—
184C4⋊C8—61no—
185C4⋊C8C2×C3×D311yescharacteristic
186C4⋊C8C2×C3×D311yescharacteristic
187#103—61no—
188#102—61no—
189C4×C8—61no—
190C4×C8C2×C3×D311yescharacteristic
191C23×C3—121no—
192C22×D3—41no—
193C3×Q8—32no—
194C3×Q8—61no—
195C3×Q8—121no—
196C3×Q8—121no—
197C3×D4—121no—
198C3×D4—121no—
199C3×D4—121no—
200C3×D4—121no—
201C3×D4—241no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—61no—
206C2×C3×C4—61no—
207C2×C3×C4—121no—
208C2×C3×C4C2×D1211yescharacteristic
209C2×C3×C4D3×D411yescharacteristic
210C2×C3×C4#23911yescharacteristic
211C2×C3×C4C2×C3×D411yescharacteristic
212C2×C3×C4C2×C3×D411yescharacteristic
213C2×C3×C4C3×#4111yescharacteristic
214C2×Dic3—21no—
215C2×Dic3—21no—
216C2×Dic3—41no—
217D12—41no—
218D12—41no—
219D12—41no—
220D12—41no—
221D12—81no—
222Dic6—21no—
223Dic6—41no—
224Dic6—41no—
225Dic6C3×SD1612yescomplemented
226C3×C8—21no—
227C3×C8—21no—
228C3×C8—22no—
229C3×C8—41no—
230C3×C8—41no—
231C3×C8—41no—
232C3×C8—41no—
233C3×C8—41no—
234C3×C8—81no—
235C3×C8—81no—
236C3×C8—121no—
237C3×C8#20412yescomplemented
238C3×C8C3×SD1612yescomplemented
239C3⋊C8—41no—
240C2×C32#46011yescharacteristic
241C2×C32#46511yescharacteristic
242C2×C32#47111yescharacteristic
243C3×D3—161no—
244C2×Q8—31no—
245C2×Q8—61no—
246C2×D4—61no—
247C2×D4—61no—
248C2×D4—61no—
249SD16—122no—
250SD16—122no—
251SD16—122no—
252C2×C8—21no—
253C2×C8—21no—
254C2×C8—61no—
255C2×C8C3×D1211yescharacteristic
256C2×C8C3×D1211yescharacteristic
257C4⋊C4—31no—
258C4⋊C4—61no—
259C4⋊C4—61no—
260C4⋊C4—61no—
261C42—61no—
262C42C22×C3×D311yescharacteristic
263C22×C3—21no—
264C22×C3—241no—
265C22×C3—241no—
266C22×C3—241no—
267C22×C3#89511yescharacteristic
268C22×C3C3×#12111yescharacteristic
269C2×D3—81no—
270C2×D3—81no—
271C2×D3—81no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—41no—
279C3×C4—62no—
280C3×C4—121no—
281C3×C4—241no—
282C3×C4C2×#20411yescharacteristic
283C3×C4#90811yescharacteristic
284C3×C4D3×SD1611yescharacteristic
285C3×C4#91611yescharacteristic
286C3×C4C2×C3×SD1611yescharacteristic
287C3×C4C2×C3×SD1611yescharacteristic
288C3×C4C3×#13511yescharacteristic
289C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
290Dic3—22no—
291Dic3—41no—
292Dic3—81no—
293C32#166611yescharacteristic, complemented, Sylow
294C23—121no—
295Q8—32no—
296Q8—61no—
297Q8—121no—
298Q8—121no—
299D4—121no—
300D4—121no—
301D4—121no—
302D4—121no—
303D4—241no—
304C2×C4—61no—
305C2×C4—61no—
306C2×C4—121no—
307C2×C4C2×C3×D1211yescharacteristic
308C2×C4C3×D3×D411yescharacteristic
309C2×C4C3×#23911yescharacteristic
310C8—21no—
311C8—41no—
312C8—41no—
313C8—121no—
314C8C3×#20412yescomplemented
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—481no—
319C2×C3#484811yescharacteristic
320C2×C3#486411yescharacteristic
321C2×C3#489811yescharacteristic
322C2×C3C3×#46011yescharacteristic
323C2×C3C3×#46511yescharacteristic
324C2×C3C3×#47111yescharacteristic
325D3—161no—
326C22—241no—
327C22—241no—
328C22—241no—
329C22C3×#89511yescharacteristic
330C4—21no—
331C4—62no—
332C4—121no—
333C4—241no—
334C4C2×C3×#20411yescharacteristic
335C4C3×#90811yescharacteristic
336C4C3×D3×SD1611yescharacteristic
337C4C3×#91611yescharacteristic
338C3—21no—
339C3#6854611yescharacteristic, direct product factor
340C3C3×#166611yescharacteristic, complemented
341C2—481no—
342C2C3×#484811yescharacteristic
343C2C3×#486411yescharacteristic
344C2C3×#489811yescharacteristic
subgroupG/H
centerC22×C3#895
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#334C2
socleC22×C32#121
prime radicalC3×#874C22
hypercenterC3×#334D3
hypocenterC3C3×#1666
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#334

Complements

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

NH ≅ G/Ntype
1. C3×#4851C2semidirect
4. C3×C8×Dic6C2semidirect
5. C32×#334C2semidirect
6. C3×#4486C2semidirect
9. #68546C3direct (N × H)
29. #4851C2×C3semidirect
32. C8×Dic6C2×C3semidirect
34. C3×#334D3semidirect
35. C3×#334C2×C3semidirect
38. #4486C2×C3semidirect
108. C3×Dic6SD16semidirect
112. C32×C8SD16semidirect
118. #334C3×D3semidirect
225. Dic6C3×SD16semidirect
237. C3×C8#204semidirect
238. C3×C8C3×SD16semidirect
293. C32#1666semidirect
314. C8C3×#204semidirect
339. C3#68546direct (N × H)
340. C3C3×#1666semidirect

Maximal subgroups

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

subgroupindex
C3×#48512
C3×#48482
C3×#46932
C3×C8×Dic62
C32×#3342
C3×#44862
C3×#44852
C3×#16663
#685463