Finite Group Databasebeta

← C3×#68498 #11781248

Subgroups — C3×#68498 #11781248

Order 1152.

384 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5088C211yesmaximal, characteristic, complemented
2C3×#5084C211yesmaximal, characteristic, complemented
3C3×#4843C211yesmaximal, characteristic
4C3×#4834C211yesmaximal, characteristic, complemented
5C32×#333C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic, complemented
7C3×#4480C211yesmaximal, characteristic, complemented
8C3×#1677—31nomaximal
9#68498C311yesmaximal, characteristic, direct product factor
10C32×C4⋊Q8C2211yescharacteristic
11C2×C3×D24—21no—
12C2×C3×D3×C8—21no—
13C3×#874C2211yescharacteristic
14C3×C4×D12C2211yescharacteristic
15C32×C4⋊C8C2211yescharacteristic
16C32×C4⋊C8C2211yescharacteristic
17C3×#821—21no—
18C3×(C2×D3)⋊C8—21no—
19C3×#809—21no—
20C3×#809—21no—
21C3×#809—21no—
22C3×#808—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#486—31no—
26C3×#476—31no—
27C3×#459—31no—
28C3×C8×D4—31no—
29#5088C2×C311yescharacteristic, complemented
30#5084C2×C311yescharacteristic, complemented
31#4843C2×C311yescharacteristic
32#4834C2×C311yescharacteristic, complemented
33C3×#334—31no—
34C3×#333—21no—
35C3×#333D311yescharacteristic, complemented
36C3×#333C2×C311yescharacteristic, complemented
37C3×#331—31no—
38#4485C2×C311yescharacteristic, complemented
39#4480C2×C311yescharacteristic, complemented
40C2×C32×Q8—21no—
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×C3×D12—21no—
44C2×C3×D12D411yescharacteristic
45C2×C3×C4×D3—21no—
46C2×C32×C8—21no—
47C2×C32×C8—21no—
48C32×C4⋊C4—21no—
49C32×C4⋊C4—21no—
50C32×C42C2311yescharacteristic
51C3×(C2×D3)⋊C4—21no—
52C3×C4⋊Dic3D411yescharacteristic
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8D411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
56C3×D24—42no—
57C3×D3×C8—42no—
58#1677—31noSylow
59C2×C3×D8—61no—
60C22×C3×C8—61no—
61C3×C4⋊Q8—21no—
62C3×C4⋊Q8C2×D311yescharacteristic
63C3×C4⋊Q8C22×C311yescharacteristic
64C3×#127—31no—
65C3×C4×D4—31no—
66C2×D24—21no—
67C2×D3×C8—21no—
68#874C22×C311yescharacteristic
69C4×D12C22×C311yescharacteristic
70C3×#106—61no—
71C3×C4⋊C8—21no—
72C3×C4⋊C8—21no—
73C3×C4⋊C8—31no—
74C3×C4⋊C8C2×D311yescharacteristic
75C3×C4⋊C8C2×D311yescharacteristic
76C3×C4⋊C8C22×C311yescharacteristic
77C3×C4⋊C8C22×C311yescharacteristic
78C3×#102—61no—
79C3×#102—61no—
80C3×#102—61no—
81C3×#102—61no—
82C3×C22⋊C8—61no—
83C3×C4×C8—31no—
84#821—21no—
85(C2×D3)⋊C8—21no—
86#809—21no—
87#809—21no—
88#809—21no—
89#808—21no—
90C4⋊(C3⋊C8)C22×C311yescharacteristic
91C4×C3⋊C8C22×C311yescharacteristic
92C22×C3×D3—21no—
93C22×C3×D3—41no—
94C32×Q8—81no—
95C2×C32×C4—41no—
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4#4111yescharacteristic
99C2×C3×Dic3—21no—
100C3×D12—21no—
101C3×D12—41no—
102C3×D12—41no—
103C3×D12—41no—
104C3×D12—41no—
105C3×D12—81no—
106C3×D12SD1612yes—
107C3×C4×D3—41no—
108C3×C4×D3—41no—
109C32×C8—41no—
110C32×C8—41no—
111C3×C3⋊C8—21no—
112C3×C3⋊C8—21no—
113C3×C3⋊C8—41no—
114#486—31no—
115#476—31no—
116#459—31no—
117C8×D4—31no—
118#334—31no—
119#333C3×D311yescharacteristic, complemented
120#331—31no—
121C2×C3×Q8—22no—
122C2×C3×Q8—21no—
123C2×C3×Q8—21no—
124C2×C3×D4—31no—
125C2×C3×D4—61no—
126C2×C3×D4—61no—
127C2×C3×D4—61no—
128C22×C3×C4—61no—
129C2×D12—21no—
130C2×D12—21no—
131C2×D12—21no—
132C2×D12C3×D411yescharacteristic
133C2×C4×D3—21no—
134C3×D8—122no—
135C2×C3×C8—21no—
136C2×C3×C8—21no—
137C2×C3×C8—21no—
138C2×C3×C8—21no—
139C2×C3×C8—31no—
140C2×C3×C8—31no—
141C2×C3×C8—41no—
142C2×C3×C8—41no—
143C2×C3×C8—61no—
144C2×C3×C8—122no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—21no—
148C3×C4⋊C4—21no—
149C3×C4⋊C4—31no—
150C3×C4⋊C4—41no—
151C3×C4⋊C4—41no—
152C3×C22⋊C4—61no—
153C3×C42—21no—
154C3×C42C22×D311yescharacteristic
155C3×C42C23×C311yescharacteristic
156(C2×D3)⋊C4—21no—
157C4⋊Dic3C3×D411yescharacteristic
158C2×C3⋊C8—21no—
159C2×C3⋊C8C3×D411yescharacteristic
160C2×C3⋊C8C3×D411yescharacteristic
161D24—42no—
162D3×C8—42no—
163C22×C32#12111yescharacteristic
164C2×C3×D3—22no—
165C2×C3×D3—41no—
166C2×C3×D3—41no—
167C2×C3×D3—81no—
168C2×C3×D3—81no—
169C2×C3×D3—81no—
170C32×C4—21no—
171C32×C4—81no—
172C32×C4C2×SD1611yescharacteristic
173C32×C4#13511yescharacteristic
174C32×C4#13511yescharacteristic
175C32×C4AGL(1,ℤ/8)11yescharacteristic
176C3×Dic3—41no—
177C2×D8—61no—
178C22×C8—61no—
179C4⋊Q8C2×C3×D311yescharacteristic
180#127—31no—
181C4×D4—31no—
182#106—61no—
183C4⋊C8—31no—
184C4⋊C8C2×C3×D311yescharacteristic
185C4⋊C8C2×C3×D311yescharacteristic
186#102—61no—
187#102—61no—
188#102—61no—
189#102—61no—
190C22⋊C8—61no—
191C4×C8—31no—
192C23×C3—61no—
193C23×C3—121no—
194C22×D3—21no—
195C22×D3—41no—
196C3×Q8—81no—
197C3×Q8—81no—
198C3×Q8—82no—
199C3×D4—32no—
200C3×D4—61no—
201C3×D4—121no—
202C3×D4—121no—
203C3×D4—121no—
204C3×D4—121no—
205C3×D4—241no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—42no—
210C2×C3×C4—41no—
211C2×C3×C4—41no—
212C2×C3×C4—61no—
213C2×C3×C4—121no—
214C2×C3×C4—121no—
215C2×C3×C4#23511yescharacteristic
216C2×C3×C4D3×D411yescharacteristic
217C2×C3×C4D3×D411yescharacteristic
218C2×C3×C4C2×C3×D411yescharacteristic
219C2×C3×C4C2×C3×D411yescharacteristic
220C2×C3×C4C3×#4111yescharacteristic
221C2×Dic3—21no—
222D12—21no—
223D12—41no—
224D12—41no—
225D12—41no—
226D12—41no—
227D12—81no—
228D12C3×SD1612yes—
229C4×D3—41no—
230C4×D3—41no—
231C3×C8—41no—
232C3×C8—41no—
233C3×C8—41no—
234C3×C8—41no—
235C3×C8—61no—
236C3×C8—61no—
237C3×C8—81no—
238C3×C8—81no—
239C3×C8—121no—
240C3⋊C8—21no—
241C3⋊C8—21no—
242C3⋊C8—41no—
243C2×C32#46311yescharacteristic
244C2×C32#46511yescharacteristic
245C2×C32#47211yescharacteristic
246C3×D3—42no—
247C3×D3—161no—
248C2×Q8—21no—
249C2×D4—31no—
250C2×D4—61no—
251C2×D4—61no—
252C2×D4—61no—
253C22×C4—61no—
254D8—122no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—31no—
258C2×C8—31no—
259C2×C8—61no—
260C2×C8—122no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—31no—
264C22⋊C4—61no—
265C42C22×C3×D311yescharacteristic
266C22×C3—21no—
267C22×C3—62no—
268C22×C3—121no—
269C22×C3—121no—
270C22×C3—241no—
271C22×C3—241no—
272C22×C3—241no—
273C22×C3#88411yescharacteristic
274C22×C3C3×#12111yescharacteristic
275C2×D3—22no—
276C2×D3—41no—
277C2×D3—41no—
278C2×D3—81no—
279C2×D3—81no—
280C2×D3—81no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—41no—
288C3×C4—82no—
289C3×C4—81no—
290C3×C4—81no—
291C3×C4—121no—
292C3×C4D3×SD1611yescharacteristic
293C3×C4#91411yescharacteristic
294C3×C4#91911yescharacteristic
295C3×C4#91911yescharacteristic
296C3×C4C2×C3×SD1611yescharacteristic
297C3×C4C3×#13511yescharacteristic
298C3×C4C3×#13511yescharacteristic
299C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
300Dic3—41no—
301C32#167711yescharacteristic, complemented, Sylow
302C23—61no—
303C23—121no—
304Q8—81no—
305D4—32no—
306D4—61no—
307D4—121no—
308D4—121no—
309D4—121no—
310D4—121no—
311D4—241no—
312C2×C4—41no—
313C2×C4—61no—
314C2×C4—121no—
315C2×C4—121no—
316C2×C4C3×#23511yescharacteristic
317C2×C4C3×D3×D411yescharacteristic
318C2×C4C3×D3×D411yescharacteristic
319C8—41no—
320C8—41no—
321C8—61no—
322C8—61no—
323C8—121no—
324C2×C3—21no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—122no—
328C2×C3—481no—
329C2×C3#474911yescharacteristic
330C2×C3#480711yescharacteristic
331C2×C3#481911yescharacteristic
332C2×C3C3×#46311yescharacteristic
333C2×C3C3×#46511yescharacteristic
334C2×C3C3×#47211yescharacteristic
335D3—42no—
336D3—161no—
337C22—62no—
338C22—121no—
339C22—121no—
340C22—241no—
341C22—241no—
342C22—241no—
343C22C3×#88411yescharacteristic
344C4—21no—
345C4—81no—
346C4—121no—
347C4C3×D3×SD1611yescharacteristic
348C4C3×#91411yescharacteristic
349C4C3×#91911yescharacteristic
350C4C3×#91911yescharacteristic
351C3—21no—
352C3#6849811yescharacteristic, direct product factor
353C3C3×#167711yescharacteristic, complemented
354C2—122no—
355C2—481no—
356C2C3×#474911yescharacteristic
357C2C3×#480711yescharacteristic
358C2C3×#481911yescharacteristic
subgroupG/H
centerC22×C3#884
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#333C2
socleC22×C32#121
prime radicalC3×#4843C2
hypercenterC3×#333D3
hypocenterC3C3×#1677
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#333

Complements

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

NH ≅ G/Ntype
1. C3×#5088C2semidirect
2. C3×#5084C2semidirect
4. C3×#4834C2semidirect
5. C32×#333C2semidirect
6. C3×#4485C2semidirect
7. C3×#4480C2semidirect
9. #68498C3direct (N × H)
29. #5088C2×C3semidirect
30. #5084C2×C3semidirect
32. #4834C2×C3semidirect
35. C3×#333D3semidirect
36. C3×#333C2×C3semidirect
38. #4485C2×C3semidirect
39. #4480C2×C3semidirect
119. #333C3×D3semidirect
301. C32#1677semidirect
352. C3#68498direct (N × H)
353. C3C3×#1677semidirect

Maximal subgroups

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

subgroupindex
C3×#50882
C3×#50842
C3×#48432
C3×#48342
C32×#3332
C3×#44852
C3×#44802
C3×#16773
#684983