Finite Group Databasebeta

← C3×#68447 #11781516

Subgroups — C3×#68447 #11781516

Order 1152.

352 conjugacy classes of subgroups.

The subgroup lattice has 333 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5087C211yesmaximal, characteristic
2C3×#5079C211yesmaximal, characteristic, complemented
3C3×#4842C211yesmaximal, characteristic
4C3×#4834C211yesmaximal, characteristic
5C32×#332C211yesmaximal, characteristic, complemented
6C3×#4481C211yesmaximal, characteristic, complemented
7C3×#4479C211yesmaximal, characteristic, complemented
8C3×#1683—31nomaximal
9#68447C311yesmaximal, characteristic, direct product factor
10C32×C4⋊Q8C2211yescharacteristic
11C2×C3×D3×C8—21no—
12C3×C4×D12C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C32×C4⋊C8C2211yescharacteristic
15C32×C4⋊C8C2211yescharacteristic
16C3×#835—21no—
17C3×#835—21no—
18C3×#821—21no—
19C3×(C2×D3)⋊C8—21no—
20C3×#817—21no—
21C3×#809—21no—
22C3×#807—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#487—31no—
26C3×#476—31no—
27C3×#474—31no—
28C3×C8×D4—31no—
29#5087C2×C311yescharacteristic
30#5079C2×C311yescharacteristic, complemented
31#4842C2×C311yescharacteristic
32#4834C2×C311yescharacteristic
33C3×#335—31no—
34C3×#333—31no—
35C3×#332—21no—
36C3×#332D311yescharacteristic, complemented
37C3×#332C2×C311yescharacteristic, complemented
38#4481C2×C311yescharacteristic, complemented
39#4479C2×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×D3×C8—42no—
57#1683—31noSylow
58C22×C3×C8—61no—
59C3×C4⋊Q8—21no—
60C3×C4⋊Q8—31no—
61C3×C4⋊Q8C2×D311yescharacteristic
62C3×C4⋊Q8C22×C311yescharacteristic
63C3×C4×D4—31no—
64C2×D3×C8—21no—
65C4×D12C22×C311yescharacteristic
66#869C22×C311yescharacteristic
67C3×#107—61no—
68C3×#106—61no—
69C3×C4⋊C8—21no—
70C3×C4⋊C8—21no—
71C3×C4⋊C8—31no—
72C3×C4⋊C8C2×D311yescharacteristic
73C3×C4⋊C8C2×D311yescharacteristic
74C3×C4⋊C8C22×C311yescharacteristic
75C3×C4⋊C8C22×C311yescharacteristic
76C3×#103—61no—
77C3×#103—61no—
78C3×#102—61no—
79C3×#102—61no—
80C3×C22⋊C8—61no—
81C3×C4×C8—31no—
82#835—21no—
83#835—21no—
84#821—21no—
85(C2×D3)⋊C8—21no—
86#817—21no—
87#809—21no—
88#807—21no—
89C4⋊(C3⋊C8)C22×C311yescharacteristic
90C4×C3⋊C8C22×C311yescharacteristic
91C22×C3×D3—21no—
92C32×Q8—41no—
93C32×Q8—41no—
94C2×C32×C4—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×D12Q1612yes—
102C3×C4×D3—41no—
103C3×C4×D3—41no—
104C3×Dic6—81no—
105C32×C8—41no—
106C32×C8—41no—
107C3×C3⋊C8—21no—
108C3×C3⋊C8—21no—
109C3×C3⋊C8—41no—
110#487—31no—
111#476—31no—
112#474—31no—
113C8×D4—31no—
114#335—31no—
115#333—31no—
116#332C3×D311yescharacteristic, complemented
117C2×C3×Q8—21no—
118C2×C3×Q8—21no—
119C2×C3×Q8—41no—
120C2×C3×Q8—61no—
121C2×C3×D4—31no—
122C22×C3×C4—61no—
123C2×D12C3×D411yescharacteristic
124C2×C4×D3—21no—
125C2×Dic6—21no—
126C2×C3×C8—21no—
127C2×C3×C8—21no—
128C2×C3×C8—21no—
129C2×C3×C8—21no—
130C2×C3×C8—31no—
131C2×C3×C8—31no—
132C2×C3×C8—41no—
133C2×C3×C8—41no—
134C2×C3×C8—61no—
135C2×C3×C8—122no—
136C3×C4⋊C4—22no—
137C3×C4⋊C4—21no—
138C3×C4⋊C4—21no—
139C3×C4⋊C4—21no—
140C3×C4⋊C4—21no—
141C3×C4⋊C4—31no—
142C3×C4⋊C4—41no—
143C3×C4⋊C4—61no—
144C3×C4⋊C4—61no—
145C3×C22⋊C4—61no—
146C3×C42—21no—
147C3×C42C22×D311yescharacteristic
148C3×C42C23×C311yescharacteristic
149(C2×D3)⋊C4—21no—
150C4⋊Dic3—21no—
151C4⋊Dic3—21no—
152C4⋊Dic3C3×D411yescharacteristic
153C2×C3⋊C8—21no—
154C2×C3⋊C8C3×D411yescharacteristic
155C2×C3⋊C8C3×D411yescharacteristic
156D3×C8—42no—
157C22×C32#12111yescharacteristic
158C2×C3×D3—22no—
159C2×C3×D3—41no—
160C2×C3×D3—41no—
161C32×C4—21no—
162C32×C4—81no—
163C32×C4C2×Q1611yescharacteristic
164C32×C4#13511yescharacteristic
165C32×C4#13511yescharacteristic
166C32×C4AGL(1,ℤ/8)11yescharacteristic
167C3×Dic3—41no—
168C3×Dic3—81no—
169C22×C8—61no—
170C4⋊Q8—31no—
171C4⋊Q8C2×C3×D311yescharacteristic
172C4×D4—31no—
173#107—61no—
174#106—61no—
175C4⋊C8—31no—
176C4⋊C8C2×C3×D311yescharacteristic
177C4⋊C8C2×C3×D311yescharacteristic
178#103—61no—
179#103—61no—
180#102—61no—
181#102—61no—
182C22⋊C8—61no—
183C4×C8—31no—
184C23×C3—61no—
185C22×D3—21no—
186C3×Q8—41no—
187C3×Q8—41no—
188C3×Q8—41no—
189C3×Q8—41no—
190C3×Q8—81no—
191C3×Q8—81no—
192C3×Q8—241no—
193C3×D4—32no—
194C3×D4—61no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—42no—
199C2×C3×C4—41no—
200C2×C3×C4—41no—
201C2×C3×C4—61no—
202C2×C3×C4—121no—
203C2×C3×C4—121no—
204C2×C3×C4—121no—
205C2×C3×C4#23511yescharacteristic
206C2×C3×C4D3×D411yescharacteristic
207C2×C3×C4D3×D411yescharacteristic
208C2×C3×C4C2×C3×D411yescharacteristic
209C2×C3×C4C2×C3×D411yescharacteristic
210C2×C3×C4C3×#4111yescharacteristic
211C2×Dic3—21no—
212C2×Dic3—41no—
213D12—21no—
214D12C3×Q1612yes—
215C4×D3—41no—
216C4×D3—41no—
217Dic6—81no—
218C3×C8—41no—
219C3×C8—41no—
220C3×C8—41no—
221C3×C8—41no—
222C3×C8—61no—
223C3×C8—61no—
224C3×C8—81no—
225C3×C8—81no—
226C3×C8—121no—
227C3⋊C8—21no—
228C3⋊C8—21no—
229C3⋊C8—41no—
230C2×C32#46311yescharacteristic
231C2×C32#46711yescharacteristic
232C2×C32#47111yescharacteristic
233C3×D3—42no—
234C2×Q8—21no—
235C2×Q8—61no—
236C2×D4—31no—
237C22×C4—61no—
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—31no—
241C2×C8—31no—
242C2×C8—61no—
243C2×C8—122no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—31no—
247C4⋊C4—61no—
248C4⋊C4—61no—
249C22⋊C4—61no—
250C42C22×C3×D311yescharacteristic
251C22×C3—21no—
252C22×C3—62no—
253C22×C3—121no—
254C22×C3—121no—
255C22×C3#88411yescharacteristic
256C22×C3C3×#12111yescharacteristic
257C2×D3—22no—
258C2×D3—41no—
259C2×D3—41no—
260C3×C4—21no—
261C3×C4—21no—
262C3×C4—21no—
263C3×C4—21no—
264C3×C4—21no—
265C3×C4—21no—
266C3×C4—41no—
267C3×C4—82no—
268C3×C4—81no—
269C3×C4—81no—
270C3×C4—121no—
271C3×C4—241no—
272C3×C4#91111yescharacteristic
273C3×C4#91611yescharacteristic
274C3×C4#91611yescharacteristic
275C3×C4D3×Q1611yescharacteristic
276C3×C4C2×C3×Q1611yescharacteristic
277C3×C4C3×#13511yescharacteristic
278C3×C4C3×#13511yescharacteristic
279C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
280Dic3—41no—
281Dic3—81no—
282C32#168311yescharacteristic, complemented, Sylow
283C23—61no—
284Q8—41no—
285Q8—41no—
286Q8—241no—
287D4—32no—
288D4—61no—
289C2×C4—41no—
290C2×C4—61no—
291C2×C4—121no—
292C2×C4—121no—
293C2×C4—121no—
294C2×C4C3×#23511yescharacteristic
295C2×C4C3×D3×D411yescharacteristic
296C2×C4C3×D3×D411yescharacteristic
297C8—41no—
298C8—41no—
299C8—61no—
300C8—61no—
301C8—121no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3—122no—
306C2×C3#475411yescharacteristic
307C2×C3#478711yescharacteristic
308C2×C3#481311yescharacteristic
309C2×C3C3×#46311yescharacteristic
310C2×C3C3×#46711yescharacteristic
311C2×C3C3×#47111yescharacteristic
312D3—42no—
313C22—62no—
314C22—121no—
315C22—121no—
316C22C3×#88411yescharacteristic
317C4—21no—
318C4—81no—
319C4—121no—
320C4—241no—
321C4C3×#91111yescharacteristic
322C4C3×#91611yescharacteristic
323C4C3×#91611yescharacteristic
324C4C3×D3×Q1611yescharacteristic
325C3—21no—
326C3#6844711yescharacteristic, direct product factor
327C3C3×#168311yescharacteristic, complemented
328C2—122no—
329C2C3×#475411yescharacteristic
330C2C3×#478711yescharacteristic
331C2C3×#481311yescharacteristic
subgroupG/H
centerC22×C3#884
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#332C2
socleC22×C32#121
prime radicalC2×C3×D12D4
hypercenterC3×#332D3
hypocenterC3C3×#1683
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×#4481C2semidirect
7. C3×#4479C2semidirect
9. #68447C3direct (N × H)
30. #5079C2×C3semidirect
36. C3×#332D3semidirect
37. C3×#332C2×C3semidirect
38. #4481C2×C3semidirect
39. #4479C2×C3semidirect
116. #332C3×D3semidirect
282. C32#1683semidirect
326. C3#68447direct (N × H)
327. C3C3×#1683semidirect

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×#48422
C3×#48342
C32×#3322
C3×#44812
C3×#44792
C3×#16833
#684473