Finite Group Databasebeta

← C3×#68444 #11781330

Subgroups — C3×#68444 #11781330

Order 1152.

364 conjugacy classes of subgroups.

The subgroup lattice has 341 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5087C211yesmaximal, characteristic
2C3×#5079C211yesmaximal, characteristic, complemented
3C3×#4841C211yesmaximal, characteristic
4C3×#4834C211yesmaximal, characteristic
5C32×#332C211yesmaximal, characteristic, complemented
6C3×#4486C211yesmaximal, characteristic, complemented
7C3×#4480C211yesmaximal, characteristic, complemented
8C3×#1679—31nomaximal
9#68444C311yesmaximal, characteristic, direct product factor
10C32×C4⋊Q8C2211yescharacteristic
11C2×C3×#204—21no—
12C2×C3×D3×C8—21no—
13C3×C4×D12C2211yescharacteristic
14C3×#869C2211yescharacteristic
15C32×C4⋊C8C2211yescharacteristic
16C32×C4⋊C8C2211yescharacteristic
17C3×#835—21no—
18C3×#835—21no—
19C3×(C2×D3)⋊C8—21no—
20C3×#816—21no—
21C3×#809—21no—
22C3×#807—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#487—31no—
26C3×#474—31no—
27C3×#461—31no—
28C3×C8×D4—31no—
29#5087C2×C311yescharacteristic
30#5079C2×C311yescharacteristic, complemented
31#4841C2×C311yescharacteristic
32#4834C2×C311yescharacteristic
33C3×#334—31no—
34C3×#332—21no—
35C3×#332—31no—
36C3×#332D311yescharacteristic, complemented
37C3×#332C2×C311yescharacteristic, complemented
38#4486C2×C311yescharacteristic, complemented
39#4480C2×C311yescharacteristic, complemented
40C2×C32×Q8—21no—
41C2×C3×D12D411yescharacteristic
42C2×C3×C4×D3—21no—
43C2×C3×Dic6—21no—
44C2×C32×C8—21no—
45C2×C32×C8—21no—
46C32×C4⋊C4—21no—
47C32×C4⋊C4—21no—
48C32×C42C2311yescharacteristic
49C3×(C2×D3)⋊C4—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3D411yescharacteristic
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8D411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
56C3×#204—42no—
57C3×D3×C8—42no—
58#1679—31noSylow
59C2×C3×SD16—61no—
60C22×C3×C8—61no—
61C3×C4⋊Q8—21no—
62C3×C4⋊Q8—31no—
63C3×C4⋊Q8C2×D311yescharacteristic
64C3×C4⋊Q8C22×C311yescharacteristic
65C3×C4×D4—31no—
66C2×#204—21no—
67C2×D3×C8—21no—
68C4×D12C22×C311yescharacteristic
69#869C22×C311yescharacteristic
70C3×#107—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×#103—61no—
79C3×#103—61no—
80C3×#103—61no—
81C3×#102—61no—
82C3×C22⋊C8—61no—
83C3×C4×C8—31no—
84#835—21no—
85#835—21no—
86(C2×D3)⋊C8—21no—
87#816—21no—
88#809—21no—
89#807—21no—
90C4⋊(C3⋊C8)C22×C311yescharacteristic
91C4×C3⋊C8C22×C311yescharacteristic
92C22×C3×D3—21no—
93C32×Q8—41no—
94C32×Q8—41no—
95C2×C32×C4—41no—
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4#4111yescharacteristic
99C2×C3×Dic3—21no—
100C2×C3×Dic3—41no—
101C3×D12—21no—
102C3×D12SD1612yes—
103C3×C4×D3—41no—
104C3×C4×D3—41no—
105C3×Dic6—41no—
106C3×Dic6—41no—
107C32×C8—41no—
108C32×C8—41no—
109C3×C3⋊C8—21no—
110C3×C3⋊C8—21no—
111C3×C3⋊C8—41no—
112#487—31no—
113#474—31no—
114#461—31no—
115C8×D4—31no—
116#334—31no—
117#332—31no—
118#332C3×D311yescharacteristic, complemented
119C2×C3×Q8—21no—
120C2×C3×Q8—21no—
121C2×C3×Q8—41no—
122C2×C3×Q8—61no—
123C2×C3×D4—31no—
124C22×C3×C4—61no—
125C2×D12C3×D411yescharacteristic
126C2×C4×D3—21no—
127C2×Dic6—21no—
128C3×SD16—122no—
129C2×C3×C8—21no—
130C2×C3×C8—21no—
131C2×C3×C8—21no—
132C2×C3×C8—21no—
133C2×C3×C8—31no—
134C2×C3×C8—31no—
135C2×C3×C8—41no—
136C2×C3×C8—41no—
137C2×C3×C8—61no—
138C2×C3×C8—122no—
139C3×C4⋊C4—22no—
140C3×C4⋊C4—21no—
141C3×C4⋊C4—21no—
142C3×C4⋊C4—21no—
143C3×C4⋊C4—21no—
144C3×C4⋊C4—31no—
145C3×C4⋊C4—41no—
146C3×C4⋊C4—61no—
147C3×C4⋊C4—61no—
148C3×C22⋊C4—61no—
149C3×C42—21no—
150C3×C42C22×D311yescharacteristic
151C3×C42C23×C311yescharacteristic
152(C2×D3)⋊C4—21no—
153C4⋊Dic3—21no—
154C4⋊Dic3—21no—
155C4⋊Dic3C3×D411yescharacteristic
156C2×C3⋊C8—21no—
157C2×C3⋊C8C3×D411yescharacteristic
158C2×C3⋊C8C3×D411yescharacteristic
159#204—42no—
160D3×C8—42no—
161C22×C32#12111yescharacteristic
162C2×C3×D3—22no—
163C2×C3×D3—41no—
164C2×C3×D3—41no—
165C32×C4—21no—
166C32×C4—81no—
167C32×C4C2×SD1611yescharacteristic
168C32×C4#13511yescharacteristic
169C32×C4#13511yescharacteristic
170C32×C4AGL(1,ℤ/8)11yescharacteristic
171C3×Dic3—41no—
172C3×Dic3—81no—
173C2×SD16—61no—
174C22×C8—61no—
175C4⋊Q8—31no—
176C4⋊Q8C2×C3×D311yescharacteristic
177C4×D4—31no—
178#107—61no—
179C4⋊C8—31no—
180C4⋊C8C2×C3×D311yescharacteristic
181C4⋊C8C2×C3×D311yescharacteristic
182#103—61no—
183#103—61no—
184#103—61no—
185#102—61no—
186C22⋊C8—61no—
187C4×C8—31no—
188C23×C3—61no—
189C22×D3—21no—
190C3×Q8—41no—
191C3×Q8—41no—
192C3×Q8—41no—
193C3×Q8—41no—
194C3×Q8—81no—
195C3×Q8—81no—
196C3×Q8—121no—
197C3×Q8—121no—
198C3×D4—32no—
199C3×D4—61no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—42no—
204C2×C3×C4—41no—
205C2×C3×C4—41no—
206C2×C3×C4—61no—
207C2×C3×C4—121no—
208C2×C3×C4—121no—
209C2×C3×C4—121no—
210C2×C3×C4#23511yescharacteristic
211C2×C3×C4D3×D411yescharacteristic
212C2×C3×C4D3×D411yescharacteristic
213C2×C3×C4C2×C3×D411yescharacteristic
214C2×C3×C4C2×C3×D411yescharacteristic
215C2×C3×C4C3×#4111yescharacteristic
216C2×Dic3—21no—
217C2×Dic3—41no—
218D12—21no—
219D12C3×SD1612yes—
220C4×D3—41no—
221C4×D3—41no—
222Dic6—41no—
223Dic6—41no—
224C3×C8—41no—
225C3×C8—41no—
226C3×C8—41no—
227C3×C8—41no—
228C3×C8—61no—
229C3×C8—61no—
230C3×C8—81no—
231C3×C8—81no—
232C3×C8—121no—
233C3⋊C8—21no—
234C3⋊C8—21no—
235C3⋊C8—41no—
236C2×C32#46311yescharacteristic
237C2×C32#46511yescharacteristic
238C2×C32#47311yescharacteristic
239C3×D3—42no—
240C2×Q8—21no—
241C2×Q8—61no—
242C2×D4—31no—
243C22×C4—61no—
244SD16—122no—
245C2×C8—21no—
246C2×C8—21no—
247C2×C8—31no—
248C2×C8—31no—
249C2×C8—61no—
250C2×C8—122no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—31no—
254C4⋊C4—61no—
255C4⋊C4—61no—
256C22⋊C4—61no—
257C42C22×C3×D311yescharacteristic
258C22×C3—21no—
259C22×C3—62no—
260C22×C3—121no—
261C22×C3—121no—
262C22×C3#88411yescharacteristic
263C22×C3C3×#12111yescharacteristic
264C2×D3—22no—
265C2×D3—41no—
266C2×D3—41no—
267C3×C4—21no—
268C3×C4—21no—
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—41no—
274C3×C4—82no—
275C3×C4—81no—
276C3×C4—81no—
277C3×C4—121no—
278C3×C4—241no—
279C3×C4#91111yescharacteristic
280C3×C4D3×SD1611yescharacteristic
281C3×C4#91611yescharacteristic
282C3×C4#91911yescharacteristic
283C3×C4C2×C3×SD1611yescharacteristic
284C3×C4C3×#13511yescharacteristic
285C3×C4C3×#13511yescharacteristic
286C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
287Dic3—41no—
288Dic3—81no—
289C32#167911yescharacteristic, complemented, Sylow
290C23—61no—
291Q8—41no—
292Q8—41no—
293Q8—121no—
294Q8—121no—
295D4—32no—
296D4—61no—
297C2×C4—41no—
298C2×C4—61no—
299C2×C4—121no—
300C2×C4—121no—
301C2×C4—121no—
302C2×C4C3×#23511yescharacteristic
303C2×C4C3×D3×D411yescharacteristic
304C2×C4C3×D3×D411yescharacteristic
305C8—41no—
306C8—41no—
307C8—61no—
308C8—61no—
309C8—121no—
310C2×C3—21no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—122no—
314C2×C3#475511yescharacteristic
315C2×C3#478711yescharacteristic
316C2×C3#480711yescharacteristic
317C2×C3C3×#46311yescharacteristic
318C2×C3C3×#46511yescharacteristic
319C2×C3C3×#47311yescharacteristic
320D3—42no—
321C22—62no—
322C22—121no—
323C22—121no—
324C22C3×#88411yescharacteristic
325C4—21no—
326C4—81no—
327C4—121no—
328C4—241no—
329C4C3×#91111yescharacteristic
330C4C3×D3×SD1611yescharacteristic
331C4C3×#91611yescharacteristic
332C4C3×#91911yescharacteristic
333C3—21no—
334C3#6844411yescharacteristic, direct product factor
335C3C3×#167911yescharacteristic, complemented
336C2—122no—
337C2C3×#475511yescharacteristic
338C2C3×#478711yescharacteristic
339C2C3×#480711yescharacteristic
subgroupG/H
centerC22×C3#884
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#332C2
socleC22×C32#121
prime radicalC2×C3×D12D4
hypercenterC3×#332D3
hypocenterC3C3×#1679
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
2. C3×#5079C2semidirect
5. C32×#332C2semidirect
6. C3×#4486C2semidirect
7. C3×#4480C2semidirect
9. #68444C3direct (N × H)
30. #5079C2×C3semidirect
36. C3×#332D3semidirect
37. C3×#332C2×C3semidirect
38. #4486C2×C3semidirect
39. #4480C2×C3semidirect
118. #332C3×D3semidirect
289. C32#1679semidirect
334. C3#68444direct (N × H)
335. C3C3×#1679semidirect

Maximal subgroups

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

subgroupindex
C3×#50872
C3×#50792
C3×#48412
C3×#48342
C32×#3322
C3×#44862
C3×#44802
C3×#16793
#684443