Finite Group Databasebeta

← C3×#68580 #11781430

Subgroups — C3×#68580 #11781430

Order 1152.

391 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#4843C211yesmaximal, characteristic
2C3×#4841C211yesmaximal, characteristic, complemented
3C3×#4694C211yesmaximal, characteristic, complemented
4C3×C8×D12C211yesmaximal, characteristic, complemented
5C32×#335C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic, complemented
7C3×#4482C211yesmaximal, characteristic, complemented
8C3×#1681—31nomaximal
9#68580C311yesmaximal, characteristic, direct product factor
10C2×C3×D24—21no—
11C2×C3×#204—21no—
12C2×C3×D3×C8—21no—
13C3×#874C2211yescharacteristic
14C3×C4×D12C2211yescharacteristic
15C3×#869C2211yescharacteristic
16C32×C4⋊C8C2211yescharacteristic
17C32×C4⋊C8C2211yescharacteristic
18C32×C4×C8C2211yescharacteristic
19C3×#821—21no—
20C3×#821—21no—
21C3×#821—21no—
22C3×(C2×D3)⋊C8—21no—
23C3×#816—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×#486—31no—
26C3×#461—31no—
27C3×#459—31no—
28C3×C8×D4—31no—
29#4843C2×C311yescharacteristic
30#4841C2×C311yescharacteristic, complemented
31#4694C2×C311yescharacteristic, complemented
32C8×D12C2×C311yescharacteristic, complemented
33C3×#335—21no—
34C3×#335D311yescharacteristic, complemented
35C3×#335C2×C311yescharacteristic, complemented
36C3×#332—31no—
37C3×#331—31no—
38#4485C2×C311yescharacteristic, complemented
39#4482C2×C311yescharacteristic, complemented
40C2×C3×D12—21no—
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×C3×D12D411yescharacteristic
44C2×C3×C4×D3—21no—
45C2×C3×Dic6—21no—
46C2×C32×C8—21no—
47C2×C32×C8—21no—
48C2×C32×C8D411yescharacteristic
49C2×C32×C8D411yescharacteristic
50C32×C42C2311yescharacteristic
51C3×(C2×D3)⋊C4—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3D411yescharacteristic
55C2×C3×C3⋊C8—21no—
56C3×D24—42no—
57C3×#204—42no—
58C3×D3×C8—42no—
59#1681—31noSylow
60C2×C3×SD16—61no—
61C2×C3×D8—61no—
62C22×C3×C8—61no—
63C3×C4⋊Q8—31no—
64C3×#127—31no—
65C3×C4×D4—31no—
66C2×D24—21no—
67C2×#204—21no—
68C2×D3×C8—21no—
69#874C22×C311yescharacteristic
70C4×D12C22×C311yescharacteristic
71#869C22×C311yescharacteristic
72C3×C4⋊C8—21no—
73C3×C4⋊C8—21no—
74C3×C4⋊C8—31no—
75C3×C4⋊C8C2×D311yescharacteristic
76C3×C4⋊C8C2×D311yescharacteristic
77C3×C4⋊C8C22×C311yescharacteristic
78C3×C4⋊C8C22×C311yescharacteristic
79C3×#103—61no—
80C3×#102—61no—
81C3×#102—61no—
82C3×#102—61no—
83C3×C22⋊C8—61no—
84C3×C4×C8—21no—
85C3×C4×C8C2×D311yescharacteristic
86C3×C4×C8C22×C311yescharacteristic
87#821—21no—
88#821—21no—
89#821—21no—
90(C2×D3)⋊C8—21no—
91#816—21no—
92C4⋊(C3⋊C8)C22×C311yescharacteristic
93C22×C3×D3—21no—
94C22×C3×D3—41no—
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4#4111yescharacteristic
98C2×C3×Dic3—21no—
99C2×C3×Dic3—41no—
100C3×D12—21no—
101C3×D12—41no—
102C3×D12—41no—
103C3×D12—41no—
104C3×D12—41no—
105C3×D12—81no—
106C3×D12D812yes—
107C3×C4×D3—41no—
108C3×C4×D3—41no—
109C3×Dic6—41no—
110C3×Dic6—41no—
111C32×C8—21no—
112C32×C8—21no—
113C32×C8—41no—
114C32×C8—41no—
115C3×C3⋊C8—41no—
116#486—31no—
117#461—31no—
118#459—31no—
119C8×D4—31no—
120#335C3×D311yescharacteristic, complemented
121#332—31no—
122#331—31no—
123C2×C3×Q8—61no—
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—
134C2×Dic6—21no—
135C3×SD16—122no—
136C3×D8—122no—
137C2×C3×C8—21no—
138C2×C3×C8—21no—
139C2×C3×C8—21no—
140C2×C3×C8—21no—
141C2×C3×C8—21no—
142C2×C3×C8—21no—
143C2×C3×C8—41no—
144C2×C3×C8—41no—
145C2×C3×C8—61no—
146C2×C3×C8—122no—
147C2×C3×C8D1211yescharacteristic
148C2×C3×C8D1211yescharacteristic
149C2×C3×C8C3×D411yescharacteristic
150C2×C3×C8C3×D411yescharacteristic
151C3×C4⋊C4—31no—
152C3×C4⋊C4—61no—
153C3×C4⋊C4—61no—
154C3×C22⋊C4—61no—
155C3×C42—21no—
156C3×C42C22×D311yescharacteristic
157C3×C42C23×C311yescharacteristic
158(C2×D3)⋊C4—21no—
159C4⋊Dic3—21no—
160C4⋊Dic3—21no—
161C4⋊Dic3C3×D411yescharacteristic
162C2×C3⋊C8—21no—
163D24—42no—
164#204—42no—
165D3×C8—42no—
166C22×C32#12111yescharacteristic
167C2×C3×D3—22no—
168C2×C3×D3—41no—
169C2×C3×D3—41no—
170C2×C3×D3—81no—
171C2×C3×D3—81no—
172C2×C3×D3—81no—
173C32×C4—21no—
174C32×C4C2×D811yescharacteristic
175C32×C4#13511yescharacteristic
176C32×C4#13511yescharacteristic
177C32×C4AGL(1,ℤ/8)11yescharacteristic
178C3×Dic3—41no—
179C3×Dic3—81no—
180C2×SD16—61no—
181C2×D8—61no—
182C22×C8—61no—
183C4⋊Q8—31no—
184#127—31no—
185C4×D4—31no—
186C4⋊C8—31no—
187C4⋊C8C2×C3×D311yescharacteristic
188C4⋊C8C2×C3×D311yescharacteristic
189#103—61no—
190#102—61no—
191#102—61no—
192#102—61no—
193C22⋊C8—61no—
194C4×C8C2×C3×D311yescharacteristic
195C23×C3—61no—
196C23×C3—121no—
197C22×D3—21no—
198C22×D3—41no—
199C3×Q8—121no—
200C3×Q8—121no—
201C3×D4—32no—
202C3×D4—61no—
203C3×D4—121no—
204C3×D4—121no—
205C3×D4—121no—
206C3×D4—121no—
207C3×D4—241no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—61no—
212C2×C3×C4—121no—
213C2×C3×C4—121no—
214C2×C3×C4—121no—
215C2×C3×C4C2×D1211yescharacteristic
216C2×C3×C4D3×D411yescharacteristic
217C2×C3×C4#23911yescharacteristic
218C2×C3×C4C2×C3×D411yescharacteristic
219C2×C3×C4C2×C3×D411yescharacteristic
220C2×C3×C4C3×#4111yescharacteristic
221C2×Dic3—21no—
222C2×Dic3—41no—
223D12—21no—
224D12—41no—
225D12—41no—
226D12—41no—
227D12—41no—
228D12—81no—
229D12C3×D812yes—
230C4×D3—41no—
231C4×D3—41no—
232Dic6—41no—
233Dic6—41no—
234C3×C8—22no—
235C3×C8—21no—
236C3×C8—21no—
237C3×C8—21no—
238C3×C8—21no—
239C3×C8—41no—
240C3×C8—41no—
241C3×C8—41no—
242C3×C8—41no—
243C3×C8—41no—
244C3×C8—81no—
245C3×C8—81no—
246C3×C8—121no—
247C3⋊C8—41no—
248C2×C32#46311yescharacteristic
249C2×C32#46611yescharacteristic
250C2×C32#47111yescharacteristic
251C3×D3—42no—
252C3×D3—161no—
253C2×Q8—61no—
254C2×D4—31no—
255C2×D4—61no—
256C2×D4—61no—
257C2×D4—61no—
258C22×C4—61no—
259SD16—122no—
260D8—122no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—61no—
264C2×C8—122no—
265C2×C8C3×D1211yescharacteristic
266C2×C8C3×D1211yescharacteristic
267C4⋊C4—31no—
268C4⋊C4—61no—
269C4⋊C4—61no—
270C22⋊C4—61no—
271C42C22×C3×D311yescharacteristic
272C22×C3—21no—
273C22×C3—62no—
274C22×C3—121no—
275C22×C3—121no—
276C22×C3—241no—
277C22×C3—241no—
278C22×C3—241no—
279C22×C3#89511yescharacteristic
280C22×C3C3×#12111yescharacteristic
281C2×D3—22no—
282C2×D3—41no—
283C2×D3—41no—
284C2×D3—81no—
285C2×D3—81no—
286C2×D3—81no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—41no—
294C3×C4—121no—
295C3×C4—241no—
296C3×C4#90411yescharacteristic
297C3×C4#90811yescharacteristic
298C3×C4D3×D811yescharacteristic
299C3×C4#91911yescharacteristic
300C3×C4C2×C3×D811yescharacteristic
301C3×C4C3×#13511yescharacteristic
302C3×C4C3×#13511yescharacteristic
303C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
304Dic3—41no—
305Dic3—81no—
306C32#168111yescharacteristic, complemented, Sylow
307C23—61no—
308C23—121no—
309Q8—121no—
310Q8—121no—
311D4—32no—
312D4—61no—
313D4—121no—
314D4—121no—
315D4—121no—
316D4—121no—
317D4—241no—
318C2×C4—61no—
319C2×C4—121no—
320C2×C4—121no—
321C2×C4—121no—
322C2×C4C2×C3×D1211yescharacteristic
323C2×C4C3×D3×D411yescharacteristic
324C2×C4C3×#23911yescharacteristic
325C8—21no—
326C8—21no—
327C8—41no—
328C8—41no—
329C8—121no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—122no—
334C2×C3—481no—
335C2×C3#484411yescharacteristic
336C2×C3#488311yescharacteristic
337C2×C3#489811yescharacteristic
338C2×C3C3×#46311yescharacteristic
339C2×C3C3×#46611yescharacteristic
340C2×C3C3×#47111yescharacteristic
341D3—42no—
342D3—161no—
343C22—62no—
344C22—121no—
345C22—121no—
346C22—241no—
347C22—241no—
348C22—241no—
349C22C3×#89511yescharacteristic
350C4—21no—
351C4—121no—
352C4—241no—
353C4C3×#90411yescharacteristic
354C4C3×#90811yescharacteristic
355C4C3×D3×D811yescharacteristic
356C4C3×#91911yescharacteristic
357C3—21no—
358C3#6858011yescharacteristic, direct product factor
359C3C3×#168111yescharacteristic, complemented
360C2—122no—
361C2—481no—
362C2C3×#484411yescharacteristic
363C2C3×#488311yescharacteristic
364C2C3×#489811yescharacteristic
subgroupG/H
centerC22×C3#895
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#335C2
socleC22×C32#121
prime radicalC3×#4843C2
hypercenterC3×#335D3
hypocenterC3C3×#1681
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#335

Complements

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

NH ≅ G/Ntype
2. C3×#4841C2semidirect
3. C3×#4694C2semidirect
4. C3×C8×D12C2semidirect
5. C32×#335C2semidirect
6. C3×#4485C2semidirect
7. C3×#4482C2semidirect
9. #68580C3direct (N × H)
30. #4841C2×C3semidirect
31. #4694C2×C3semidirect
32. C8×D12C2×C3semidirect
34. C3×#335D3semidirect
35. C3×#335C2×C3semidirect
38. #4485C2×C3semidirect
39. #4482C2×C3semidirect
120. #335C3×D3semidirect
306. C32#1681semidirect
358. C3#68580direct (N × H)
359. C3C3×#1681semidirect

Maximal subgroups

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

subgroupindex
C3×#48432
C3×#48412
C3×#46942
C3×C8×D122
C32×#3352
C3×#44852
C3×#44822
C3×#16813
#685803