Finite Group Databasebeta

← C3×#68448 #11781620

Subgroups — C3×#68448 #11781620

Order 1152.

396 conjugacy classes of subgroups.

The subgroup lattice has 373 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5087C211yesmaximal, characteristic, complemented
2C3×#5085C211yesmaximal, characteristic, complemented
3C3×#4843C211yesmaximal, characteristic
4C3×#4838C211yesmaximal, characteristic, complemented
5C32×#332C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic, complemented
7C3×#4479C211yesmaximal, characteristic, complemented
8C3×#1685—31nomaximal
9#68448C311yesmaximal, characteristic, direct product factor
10C32×C4⋊Q8C2211yescharacteristic
11C2×C3×#215—21no—
12C2×C3×#215—21no—
13C2×C3×D24—21no—
14C2×C3×ΓL(1,𝔽25)—21no—
15C3×#874C2211yescharacteristic
16C3×C4×D12C2211yescharacteristic
17C32×C4⋊C8C2211yescharacteristic
18C32×C4⋊C8C2211yescharacteristic
19C3×#821—21no—
20C3×(C2×D3)⋊C8—21no—
21C3×#809—21no—
22C3×#807—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#492—31no—
26C3×#474—31no—
27C3×#459—31no—
28C3×#436—31no—
29#5087C2×C311yescharacteristic, complemented
30#5085C2×C311yescharacteristic, complemented
31#4843C2×C311yescharacteristic
32#4838C2×C311yescharacteristic, complemented
33C3×#335—31no—
34C3×#332—21no—
35C3×#332D311yescharacteristic, complemented
36C3×#332C2×C311yescharacteristic, complemented
37C3×#331—31no—
38#4485C2×C311yescharacteristic, complemented
39#4479C2×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×#215—42no—
52C3×#215—42no—
53C3×(C2×D3)⋊C4—21no—
54C3×C4⋊Dic3D411yescharacteristic
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8D411yescharacteristic
57C2×C3×C3⋊C8D411yescharacteristic
58C3×D24—42no—
59C3×ΓL(1,𝔽25)—42no—
60#1685—31noSylow
61C2×C3×SD16—61no—
62C2×C3×SD16—61no—
63C2×C3×D8—61no—
64C2×C3×M16—61no—
65C3×C4⋊Q8—21no—
66C3×C4⋊Q8C2×D311yescharacteristic
67C3×C4⋊Q8C22×C311yescharacteristic
68C3×#127—31no—
69C3×C4×D4—31no—
70C2×#215—21no—
71C2×#215—21no—
72C2×D24—21no—
73C2×ΓL(1,𝔽25)—21no—
74#874C22×C311yescharacteristic
75C4×D12C22×C311yescharacteristic
76C3×#107—61no—
77C3×C4⋊C8—21no—
78C3×C4⋊C8—21no—
79C3×C4⋊C8—31no—
80C3×C4⋊C8C2×D311yescharacteristic
81C3×C4⋊C8C2×D311yescharacteristic
82C3×C4⋊C8C22×C311yescharacteristic
83C3×C4⋊C8C22×C311yescharacteristic
84C3×#102—61no—
85C3×#102—61no—
86C3×C22⋊C8—61no—
87C3×C4×C8—31no—
88#821—21no—
89(C2×D3)⋊C8—21no—
90#809—21no—
91#807—21no—
92C4⋊(C3⋊C8)C22×C311yescharacteristic
93C4×C3⋊C8C22×C311yescharacteristic
94C22×C3×D3—21no—
95C22×C3×D3—41no—
96C32×Q8—41no—
97C32×Q8—41no—
98C2×C32×C4—41no—
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C3×Dic3—21no—
103C3×D12—21no—
104C3×D12—21no—
105C3×D12—41no—
106C3×D12—41no—
107C3×D12—41no—
108C3×D12—41no—
109C3×D12—81no—
110C3×C4×D3—41no—
111C3×C4×D3—41no—
112C32×C8—41no—
113C32×C8—41no—
114C3×C3⋊C8—21no—
115C3×C3⋊C8—41no—
116C3×C3⋊C8D812yescomplemented
117#492—31no—
118#474—31no—
119#459—31no—
120#436—31no—
121#335—31no—
122#332C3×D311yescharacteristic, complemented
123#331—31no—
124C2×C3×Q8—21no—
125C2×C3×Q8—21no—
126C2×C3×Q8—41no—
127C2×C3×D4—31no—
128C2×C3×D4—61no—
129C2×C3×D4—61no—
130C2×C3×D4—61no—
131C22×C3×C4—61no—
132C2×D12—21no—
133C2×D12—21no—
134C2×D12—21no—
135C2×D12C3×D411yescharacteristic
136C2×C4×D3—21no—
137C3×SD16—122no—
138C3×SD16—122no—
139C3×D8—122no—
140C3×M16—122no—
141C2×C3×C8—21no—
142C2×C3×C8—21no—
143C2×C3×C8—21no—
144C2×C3×C8—21no—
145C2×C3×C8—31no—
146C2×C3×C8—31no—
147C2×C3×C8—41no—
148C2×C3×C8—41no—
149C2×C3×C8—61no—
150C3×C4⋊C4—22no—
151C3×C4⋊C4—21no—
152C3×C4⋊C4—21no—
153C3×C4⋊C4—21no—
154C3×C4⋊C4—21no—
155C3×C4⋊C4—31no—
156C3×C4⋊C4—41no—
157C3×C22⋊C4—61no—
158C3×C42—21no—
159C3×C42C22×D311yescharacteristic
160C3×C42C23×C311yescharacteristic
161#215—42no—
162#215—42no—
163(C2×D3)⋊C4—21no—
164C4⋊Dic3C3×D411yescharacteristic
165C2×C3⋊C8—21no—
166C2×C3⋊C8C3×D411yescharacteristic
167C2×C3⋊C8C3×D411yescharacteristic
168D24—42no—
169ΓL(1,𝔽25)—42no—
170C22×C32#12111yescharacteristic
171C2×C3×D3—41no—
172C2×C3×D3—41no—
173C2×C3×D3—41no—
174C2×C3×D3—81no—
175C2×C3×D3—81no—
176C2×C3×D3—81no—
177C32×C4—21no—
178C32×C4—81no—
179C32×C4C2×D811yescharacteristic
180C32×C4AGL(1,ℤ/8)11yescharacteristic
181C32×C4AGL(1,ℤ/8)11yescharacteristic
182C32×C4#13711yescharacteristic
183C3×Dic3—41no—
184C2×SD16—61no—
185C2×SD16—61no—
186C2×D8—61no—
187C2×M16—61no—
188C4⋊Q8C2×C3×D311yescharacteristic
189#127—31no—
190C4×D4—31no—
191#107—61no—
192C4⋊C8—31no—
193C4⋊C8C2×C3×D311yescharacteristic
194C4⋊C8C2×C3×D311yescharacteristic
195#102—61no—
196#102—61no—
197C22⋊C8—61no—
198C4×C8—31no—
199C23×C3—61no—
200C23×C3—121no—
201C22×D3—21no—
202C22×D3—41no—
203C3×Q8—41no—
204C3×Q8—41no—
205C3×Q8—41no—
206C3×Q8—41no—
207C3×Q8—81no—
208C3×Q8—81no—
209C3×D4—61no—
210C3×D4—61no—
211C3×D4—121no—
212C3×D4—121no—
213C3×D4—121no—
214C3×D4—121no—
215C3×D4—241no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—42no—
220C2×C3×C4—41no—
221C2×C3×C4—41no—
222C2×C3×C4—61no—
223C2×C3×C4—121no—
224C2×C3×C4—121no—
225C2×C3×C4#23511yescharacteristic
226C2×C3×C4D3×D411yescharacteristic
227C2×C3×C4D3×D411yescharacteristic
228C2×C3×C4C2×C3×D411yescharacteristic
229C2×C3×C4C2×C3×D411yescharacteristic
230C2×C3×C4C3×#4111yescharacteristic
231C2×Dic3—21no—
232D12—21no—
233D12—21no—
234D12—41no—
235D12—41no—
236D12—41no—
237D12—41no—
238D12—81no—
239C4×D3—41no—
240C4×D3—41no—
241C3×C8—32no—
242C3×C8—41no—
243C3×C8—41no—
244C3×C8—41no—
245C3×C8—41no—
246C3×C8—61no—
247C3×C8—81no—
248C3×C8—81no—
249C3×C8—121no—
250C3⋊C8—21no—
251C3⋊C8—41no—
252C3⋊C8C3×D812yescomplemented
253C2×C32#45911yescharacteristic
254C2×C32#46811yescharacteristic
255C2×C32#47111yescharacteristic
256C3×D3—81no—
257C3×D3—161no—
258C2×Q8—21no—
259C2×D4—31no—
260C2×D4—61no—
261C2×D4—61no—
262C2×D4—61no—
263C22×C4—61no—
264SD16—122no—
265SD16—122no—
266D8—122no—
267M16—122no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—31no—
271C2×C8—31no—
272C2×C8—61no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—31no—
276C22⋊C4—61no—
277C42C22×C3×D311yescharacteristic
278C22×C3—21no—
279C22×C3—121no—
280C22×C3—121no—
281C22×C3—121no—
282C22×C3—241no—
283C22×C3—241no—
284C22×C3—241no—
285C22×C3#88411yescharacteristic
286C22×C3C3×#12111yescharacteristic
287C2×D3—41no—
288C2×D3—41no—
289C2×D3—41no—
290C2×D3—81no—
291C2×D3—81no—
292C2×D3—81no—
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—41no—
300C3×C4—82no—
301C3×C4—81no—
302C3×C4—81no—
303C3×C4—121no—
304C3×C4D3×D811yescharacteristic
305C3×C4#91411yescharacteristic
306C3×C4#91411yescharacteristic
307C3×C4#91811yescharacteristic
308C3×C4C2×C3×D811yescharacteristic
309C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
310C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
311C3×C4C3×#13711yescharacteristic
312Dic3—41no—
313C32#168511yescharacteristic, complemented, Sylow
314C23—61no—
315C23—121no—
316Q8—41no—
317Q8—41no—
318D4—61no—
319D4—61no—
320D4—121no—
321D4—121no—
322D4—121no—
323D4—121no—
324D4—241no—
325C2×C4—41no—
326C2×C4—61no—
327C2×C4—121no—
328C2×C4—121no—
329C2×C4C3×#23511yescharacteristic
330C2×C4C3×D3×D411yescharacteristic
331C2×C4C3×D3×D411yescharacteristic
332C8—32no—
333C8—41no—
334C8—41no—
335C8—61no—
336C8—121no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—241no—
341C2×C3—481no—
342C2×C3#475411yescharacteristic
343C2×C3#478611yescharacteristic
344C2×C3#481211yescharacteristic
345C2×C3C3×#45911yescharacteristic
346C2×C3C3×#46811yescharacteristic
347C2×C3C3×#47111yescharacteristic
348D3—81no—
349D3—161no—
350C22—121no—
351C22—121no—
352C22—121no—
353C22—241no—
354C22—241no—
355C22—241no—
356C22C3×#88411yescharacteristic
357C4—21no—
358C4—81no—
359C4—121no—
360C4C3×D3×D811yescharacteristic
361C4C3×#91411yescharacteristic
362C4C3×#91411yescharacteristic
363C4C3×#91811yescharacteristic
364C3—21no—
365C3#6844811yescharacteristic, direct product factor
366C3C3×#168511yescharacteristic, complemented
367C2—241no—
368C2—481no—
369C2C3×#475411yescharacteristic
370C2C3×#478611yescharacteristic
371C2C3×#481211yescharacteristic
subgroupG/H
centerC22×C3#884
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#332C2
socleC22×C32#121
prime radicalC3×#4843C2
hypercenterC3×#332D3
hypocenterC3C3×#1685
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#332

Complements

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

NH ≅ G/Ntype
1. C3×#5087C2semidirect
2. C3×#5085C2semidirect
4. C3×#4838C2semidirect
5. C32×#332C2semidirect
6. C3×#4485C2semidirect
7. C3×#4479C2semidirect
9. #68448C3direct (N × H)
29. #5087C2×C3semidirect
30. #5085C2×C3semidirect
32. #4838C2×C3semidirect
35. C3×#332D3semidirect
36. C3×#332C2×C3semidirect
38. #4485C2×C3semidirect
39. #4479C2×C3semidirect
116. C3×C3⋊C8D8semidirect
122. #332C3×D3semidirect
252. C3⋊C8C3×D8semidirect
313. C32#1685semidirect
365. C3#68448direct (N × H)
366. C3C3×#1685semidirect

Maximal subgroups

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

subgroupindex
C3×#50872
C3×#50852
C3×#48432
C3×#48382
C32×#3322
C3×#44852
C3×#44792
C3×#16853
#684483