Finite Group Databasebeta

← C3×#70848 #11781239

Subgroups — C3×#70848 #11781239

Order 1152.

419 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C8×D4C211yesmaximal, characteristic, complemented
2C3×#5015C211yesmaximal, characteristic
3C3×#5008C211yesmaximal, characteristic, complemented
4C3×#4694C211yesmaximal, characteristic, complemented
5C3×#4485C211yesmaximal, characteristic, complemented
6C3×#4481C211yesmaximal, characteristic, complemented
7C3×#4457C211yesmaximal, characteristic, complemented
8C3×#1677—31nomaximal
9#70848C311yesmaximal, characteristic, direct product factor
10C22×C32×C8—21no—
11C32×C4×D4C2211yescharacteristic
12C2×C3×#213—21no—
13C3×#874C2211yescharacteristic
14C3×#869C2211yescharacteristic
15C32×C4⋊C8C2211yescharacteristic
16C32×C22⋊C8—21no—
17C32×C4×C8C2211yescharacteristic
18C3×#832—21no—
19C3×#821—21no—
20C3×#821—21no—
21C3×#809—21no—
22C3×#808—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×#486—31no—
26C3×#476—31no—
27C3×#459—31no—
28C3×C8×D4—21no—
29C3×C8×D4D311yescharacteristic, complemented
30C3×C8×D4C2×C311yescharacteristic, complemented
31#5015C2×C311yescharacteristic
32#5008C2×C311yescharacteristic, complemented
33#4694C2×C311yescharacteristic, complemented
34C3×#334—31no—
35C3×#333—31no—
36C3×#331—31no—
37#4485C2×C311yescharacteristic, complemented
38#4481C2×C311yescharacteristic, complemented
39#4457C2×C311yescharacteristic, complemented
40C2×C32×D4D411yescharacteristic
41C22×C32×C4—21no—
42C2×C3×D12—21no—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×Dic6—21no—
46C2×C32×C8—21no—
47C2×C32×C8—42no—
48C2×C32×C8D411yescharacteristic
49C2×C32×C8D411yescharacteristic
50C32×C4⋊C4D411yescharacteristic
51C32×C22⋊C4—21no—
52C32×C42C2311yescharacteristic
53C3×#213—42no—
54C3×C4⋊Dic3—21no—
55C3×C4⋊Dic3—21no—
56C2×C3×C3⋊C8—21no—
57C2×C3×C3⋊C8—21no—
58#1677—31noSylow
59C2×C3×D8—61no—
60C22×C3×C8—22no—
61C22×C3×C8—21no—
62C22×C3×C8—21no—
63C3×C4⋊Q8—31no—
64C3×#127—31no—
65C3×C4×D4—21no—
66C3×C4×D4C2×D311yescharacteristic
67C3×C4×D4C22×C311yescharacteristic
68C2×#213—21no—
69#874C22×C311yescharacteristic
70#869C22×C311yescharacteristic
71C3×#106—61no—
72C3×C4⋊C8—21no—
73C3×C4⋊C8—31no—
74C3×C4⋊C8—31no—
75C3×C4⋊C8C2×D311yescharacteristic
76C3×C4⋊C8C22×C311yescharacteristic
77C3×#102—61no—
78C3×#102—61no—
79C3×#102—61no—
80C3×#102—61no—
81C3×C22⋊C8—22no—
82C3×C22⋊C8—21no—
83C3×C22⋊C8—21no—
84C3×C4×C8—21no—
85C3×C4×C8C2×D311yescharacteristic
86C3×C4×C8C22×C311yescharacteristic
87#832—21no—
88#821—21no—
89#821—21no—
90#809—21no—
91#808—21no—
92C4⋊(C3⋊C8)C22×C311yescharacteristic
93C4⋊(C3⋊C8)C22×C311yescharacteristic
94C23×C32—21no—
95C22×C3×D3—41no—
96C32×D4—21no—
97C32×D4SD1612yes—
98C2×C32×C4—21no—
99C2×C32×C4—41no—
100C2×C32×C4—41no—
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4#4111yescharacteristic
104C2×C3×Dic3—41no—
105C3×D12—41no—
106C3×D12—41no—
107C3×D12—41no—
108C3×D12—41no—
109C3×D12—81no—
110C3×Dic6—81no—
111C32×C8—21no—
112C32×C8—21no—
113C32×C8—41no—
114C3×C3⋊C8—41no—
115C3×C3⋊C8—41no—
116#486—31no—
117#476—31no—
118#459—31no—
119C8×D4C3×D311yescharacteristic, complemented
120#334—31no—
121#333—31no—
122#331—31no—
123C2×C3×Q8—61no—
124C2×C3×D4—21no—
125C2×C3×D4—61no—
126C2×C3×D4—61no—
127C2×C3×D4—61no—
128C2×C3×D4D1211yescharacteristic
129C2×C3×D4C3×D411yescharacteristic
130C22×C3×C4—22no—
131C22×C3×C4—21no—
132C22×C3×C4—21no—
133C2×D12—21no—
134C2×D12—21no—
135C2×D12—21no—
136C2×Dic6—21no—
137C3×D8—122no—
138C2×C3×C8—22no—
139C2×C3×C8—21no—
140C2×C3×C8—21no—
141C2×C3×C8—21no—
142C2×C3×C8—21no—
143C2×C3×C8—44no—
144C2×C3×C8—42no—
145C2×C3×C8—42no—
146C2×C3×C8—61no—
147C2×C3×C8—61no—
148C2×C3×C8#6711yescharacteristic
149C2×C3×C8#6711yescharacteristic
150C2×C3×C8C3×D411yescharacteristic
151C2×C3×C8C3×D411yescharacteristic
152C3×C4⋊C4—21no—
153C3×C4⋊C4—61no—
154C3×C4⋊C4—61no—
155C3×C4⋊C4D1211yescharacteristic
156C3×C4⋊C4C3×D411yescharacteristic
157C3×C22⋊C4—22no—
158C3×C22⋊C4—21no—
159C3×C22⋊C4—21no—
160C3×C42—21no—
161C3×C42C22×D311yescharacteristic
162C3×C42C23×C311yescharacteristic
163#213—42no—
164C4⋊Dic3—21no—
165C4⋊Dic3—21no—
166C2×C3⋊C8—21no—
167C2×C3⋊C8—21no—
168C22×C32—22no—
169C22×C32—41no—
170C22×C32—41no—
171C22×C32#12111yescharacteristic
172C2×C3×D3—81no—
173C2×C3×D3—81no—
174C2×C3×D3—81no—
175C32×C4—21no—
176C32×C4—41no—
177C32×C4C2×SD1611yescharacteristic
178C32×C4#13511yescharacteristic
179C32×C4#13511yescharacteristic
180C32×C4AGL(1,ℤ/8)11yescharacteristic
181C3×Dic3—81no—
182C2×D8—61no—
183C22×C8—21no—
184C4⋊Q8—31no—
185#127—31no—
186C4×D4C2×C3×D311yescharacteristic
187#106—61no—
188C4⋊C8—31no—
189C4⋊C8—31no—
190C4⋊C8C2×C3×D311yescharacteristic
191#102—61no—
192#102—61no—
193#102—61no—
194#102—61no—
195C22⋊C8—21no—
196C4×C8C2×C3×D311yescharacteristic
197C23×C3—22no—
198C23×C3—21no—
199C23×C3—21no—
200C23×C3—121no—
201C22×D3—41no—
202C3×Q8—241no—
203C3×D4—22no—
204C3×D4—21no—
205C3×D4—21no—
206C3×D4—22no—
207C3×D4—121no—
208C3×D4—121no—
209C3×D4—121no—
210C3×D4—121no—
211C3×D4—241no—
212C3×D4#20412yes—
213C3×D4C3×SD1612yes—
214C2×C3×C4—22no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—42no—
221C2×C3×C4—42no—
222C2×C3×C4—41no—
223C2×C3×C4—41no—
224C2×C3×C4—41no—
225C2×C3×C4—41no—
226C2×C3×C4—121no—
227C2×C3×C4C2×D1211yescharacteristic
228C2×C3×C4#23511yescharacteristic
229C2×C3×C4C2×#6711yescharacteristic
230C2×C3×C4C2×C3×D411yescharacteristic
231C2×C3×C4C2×C3×D411yescharacteristic
232C2×C3×C4C3×#4111yescharacteristic
233C2×Dic3—41no—
234D12—41no—
235D12—41no—
236D12—41no—
237D12—41no—
238D12—81no—
239Dic6—81no—
240C3×C8—22no—
241C3×C8—21no—
242C3×C8—21no—
243C3×C8—21no—
244C3×C8—21no—
245C3×C8—41no—
246C3×C8—42no—
247C3×C8—41no—
248C3×C8—41no—
249C3×C8—121no—
250C3×C8—121no—
251C3⋊C8—41no—
252C3⋊C8—41no—
253C2×C32—42no—
254C2×C32#46311yescharacteristic
255C2×C32#46511yescharacteristic
256C2×C32#47211yescharacteristic
257C3×D3—161no—
258C2×Q8—61no—
259C2×D4—61no—
260C2×D4—61no—
261C2×D4—61no—
262C2×D4C3×D1211yescharacteristic
263C22×C4—21no—
264D8—122no—
265C2×C8—21no—
266C2×C8—42no—
267C2×C8—61no—
268C2×C8—61no—
269C2×C8C3×#6711yescharacteristic
270C2×C8C3×#6711yescharacteristic
271C4⋊C4—61no—
272C4⋊C4—61no—
273C4⋊C4C3×D1211yescharacteristic
274C22⋊C4—21no—
275C42C22×C3×D311yescharacteristic
276C22×C3—24no—
277C22×C3—22no—
278C22×C3—22no—
279C22×C3—21no—
280C22×C3—42no—
281C22×C3—42no—
282C22×C3—41no—
283C22×C3—41no—
284C22×C3—41no—
285C22×C3—41no—
286C22×C3—241no—
287C22×C3—241no—
288C22×C3—241no—
289C22×C3#93011yescharacteristic
290C22×C3C3×#12111yescharacteristic
291C2×D3—81no—
292C2×D3—81no—
293C2×D3—81no—
294C3×C4—21no—
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—41no—
301C3×C4—42no—
302C3×C4—41no—
303C3×C4—41no—
304C3×C4—241no—
305C3×C4C2×#20411yescharacteristic
306C3×C4#90411yescharacteristic
307C3×C4#93211yescharacteristic
308C3×C4#95011yescharacteristic
309C3×C4C2×C3×SD1611yescharacteristic
310C3×C4C3×#13511yescharacteristic
311C3×C4C3×#13511yescharacteristic
312C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
313Dic3—81no—
314C32#167711yescharacteristic, complemented, Sylow
315C23—21no—
316C23—121no—
317Q8—241no—
318D4—21no—
319D4—121no—
320D4—121no—
321D4—121no—
322D4—121no—
323D4—241no—
324D4C3×#20412yes—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—121no—
329C2×C4C2×C3×D1211yescharacteristic
330C2×C4C3×#23511yescharacteristic
331C2×C4C2×C3×#6711yescharacteristic
332C8—21no—
333C8—21no—
334C8—41no—
335C8—121no—
336C8—121no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—44no—
341C2×C3—42no—
342C2×C3—42no—
343C2×C3—481no—
344C2×C3#501611yescharacteristic
345C2×C3#511411yescharacteristic
346C2×C3#514211yescharacteristic
347C2×C3C3×#46311yescharacteristic
348C2×C3C3×#46511yescharacteristic
349C2×C3C3×#47211yescharacteristic
350D3—161no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—241no—
355C22—241no—
356C22—241no—
357C22C3×#93011yescharacteristic
358C4—21no—
359C4—41no—
360C4—241no—
361C4C2×C3×#20411yescharacteristic
362C4C3×#90411yescharacteristic
363C4C3×#93211yescharacteristic
364C4C3×#95011yescharacteristic
365C3—21no—
366C3#7084811yescharacteristic, direct product factor
367C3C3×#167711yescharacteristic, complemented
368C2—42no—
369C2—481no—
370C2C3×#501611yescharacteristic
371C2C3×#511411yescharacteristic
372C2C3×#514211yescharacteristic
subgroupG/H
centerC22×C3#930
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×C8×D4C2
socleC22×C32#121
prime radicalC3×#5015C2
hypercenterC3×C8×D4D3
hypocenterC3C3×#1677
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C8×D4

Complements

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

NH ≅ G/Ntype
1. C32×C8×D4C2semidirect
3. C3×#5008C2semidirect
4. C3×#4694C2semidirect
5. C3×#4485C2semidirect
6. C3×#4481C2semidirect
7. C3×#4457C2semidirect
9. #70848C3direct (N × H)
29. C3×C8×D4D3semidirect
30. C3×C8×D4C2×C3semidirect
32. #5008C2×C3semidirect
33. #4694C2×C3semidirect
37. #4485C2×C3semidirect
38. #4481C2×C3semidirect
39. #4457C2×C3semidirect
119. C8×D4C3×D3semidirect
314. C32#1677semidirect
366. C3#70848direct (N × H)
367. C3C3×#1677semidirect

Maximal subgroups

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

subgroupindex
C32×C8×D42
C3×#50152
C3×#50082
C3×#46942
C3×#44852
C3×#44812
C3×#44572
C3×#16773
#708483