Finite Group Databasebeta

← C3×#71233 #11781510

Subgroups — C3×#71233 #11781510

Order 1152.

369 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
1C32×#487C211yesmaximal, characteristic, complemented
2C3×#5087C211yesmaximal, characteristic
3C3×#5084C211yesmaximal, characteristic
4C3×C8×D12C211yesmaximal, characteristic
5C3×#4547C211yesmaximal, characteristic, complemented
6C3×#4546C211yesmaximal, characteristic, complemented
7C3×#4458C211yesmaximal, characteristic, complemented
8C3×#1683—31nomaximal
9#71233C311yesmaximal, characteristic, direct product factor
10C32×C4⋊Q8C2211yescharacteristic
11C32×C4⋊Q8C2211yescharacteristic
12C2×C3×D3×C8—21no—
13C3×C4×D12C2211yescharacteristic
14C32×#103—21no—
15C32×#103—21no—
16C32×C4×C8C2211yescharacteristic
17C3×(C2×D3)⋊C8—21no—
18C3×#809—21no—
19C3×#809—21no—
20C3×#808—21no—
21C3×#807—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×#487—21no—
26C3×#487D311yescharacteristic, complemented
27C3×#487C2×C311yescharacteristic, complemented
28C3×#476—31no—
29C3×#474—31no—
30C3×C8×D4—31no—
31#5087C2×C311yescharacteristic
32#5084C2×C311yescharacteristic
33C8×D12C2×C311yescharacteristic
34C3×#335—31no—
35C3×#333—31no—
36C3×#332—31no—
37#4547C2×C311yescharacteristic, complemented
38#4546C2×C311yescharacteristic, complemented
39#4458C2×C311yescharacteristic, complemented
40C2×C32×Q8—21no—
41C2×C32×Q8—21no—
42C2×C3×D12D411yescharacteristic
43C2×C3×C4×D3—21no—
44C2×C32×C8D411yescharacteristic
45C2×C32×C8D411yescharacteristic
46C32×C4⋊C4—21no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4—21no—
49C32×C4⋊C4—21no—
50C32×C42C2311yescharacteristic
51C3×(C2×D3)⋊C4—21no—
52C3×C4⋊Dic3D411yescharacteristic
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56C3×D3×C8—42no—
57#1683—31noSylow
58C22×C3×C8—61no—
59C3×C4⋊Q8—21no—
60C3×C4⋊Q8—21no—
61C3×C4⋊Q8C2×D311yescharacteristic
62C3×C4⋊Q8C2×D311yescharacteristic
63C3×C4⋊Q8C22×C311yescharacteristic
64C3×C4⋊Q8C22×C311yescharacteristic
65C3×C4×D4—31no—
66C2×D3×C8—21no—
67C4×D12C22×C311yescharacteristic
68C3×#107—61no—
69C3×#106—61no—
70C3×C4⋊C8—31no—
71C3×C4⋊C8—31no—
72C3×C4⋊C8—31no—
73C3×#103—22no—
74C3×#103—22no—
75C3×#103—21no—
76C3×#103—21no—
77C3×#103—21no—
78C3×#103—21no—
79C3×#102—61no—
80C3×#102—61no—
81C3×C22⋊C8—61no—
82C3×C4×C8—21no—
83C3×C4×C8C2×D311yescharacteristic
84C3×C4×C8C22×C311yescharacteristic
85(C2×D3)⋊C8—21no—
86#809—21no—
87#809—21no—
88#808—21no—
89#807—21no—
90C4⋊(C3⋊C8)C22×C311yescharacteristic
91C4⋊(C3⋊C8)C22×C311yescharacteristic
92C4⋊(C3⋊C8)C22×C311yescharacteristic
93C22×C3×D3—21no—
94C32×Q8—41no—
95C32×Q8—41no—
96C32×Q8—81no—
97C2×C32×C4—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×D12Q1612yes—
105C3×C4×D3—41no—
106C3×C4×D3—41no—
107C32×C8—21no—
108C32×C8—21no—
109C3×C3⋊C8—41no—
110C3×C3⋊C8—41no—
111C3×C3⋊C8—41no—
112#487C3×D311yescharacteristic, complemented
113#476—31no—
114#474—31no—
115C8×D4—31no—
116#335—31no—
117#333—31no—
118#332—31no—
119C2×C3×Q8—22no—
120C2×C3×Q8—21no—
121C2×C3×Q8—21no—
122C2×C3×Q8—21no—
123C2×C3×Q8—21no—
124C2×C3×Q8—41no—
125C2×C3×D4—31no—
126C22×C3×C4—61no—
127C2×D12C3×D411yescharacteristic
128C2×C4×D3—21no—
129C2×C3×C8—21no—
130C2×C3×C8—21no—
131C2×C3×C8—61no—
132C2×C3×C8—61no—
133C2×C3×C8—61no—
134C2×C3×C8—122no—
135C2×C3×C8#6711yescharacteristic
136C2×C3×C8#6711yescharacteristic
137C2×C3×C8C3×D411yescharacteristic
138C2×C3×C8C3×D411yescharacteristic
139C3×C4⋊C4—22no—
140C3×C4⋊C4—21no—
141C3×C4⋊C4—21no—
142C3×C4⋊C4—21no—
143C3×C4⋊C4—21no—
144C3×C4⋊C4—21no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—21no—
148C3×C4⋊C4—31no—
149C3×C4⋊C4—41no—
150C3×C4⋊C4—41no—
151C3×C4⋊C4—41no—
152C3×C22⋊C4—61no—
153C3×C42—21no—
154C3×C42C22×D311yescharacteristic
155C3×C42C23×C311yescharacteristic
156(C2×D3)⋊C4—21no—
157C4⋊Dic3C3×D411yescharacteristic
158C2×C3⋊C8—21no—
159C2×C3⋊C8—21no—
160C2×C3⋊C8—21no—
161D3×C8—42no—
162C22×C32#12111yescharacteristic
163C2×C3×D3—22no—
164C2×C3×D3—41no—
165C2×C3×D3—41no—
166C32×C4—21no—
167C32×C4—81no—
168C32×C4—81no—
169C32×C4C2×Q1611yescharacteristic
170C32×C4#13511yescharacteristic
171C32×C4#13511yescharacteristic
172C32×C4AGL(1,ℤ/8)11yescharacteristic
173C3×Dic3—41no—
174C22×C8—61no—
175C4⋊Q8C2×C3×D311yescharacteristic
176C4⋊Q8C2×C3×D311yescharacteristic
177C4×D4—31no—
178#107—61no—
179#106—61no—
180C4⋊C8—31no—
181C4⋊C8—31no—
182C4⋊C8—31no—
183#103—21no—
184#103—21no—
185#102—61no—
186#102—61no—
187C22⋊C8—61no—
188C4×C8C2×C3×D311yescharacteristic
189C23×C3—61no—
190C22×D3—21no—
191C3×Q8—42no—
192C3×Q8—42no—
193C3×Q8—41no—
194C3×Q8—41no—
195C3×Q8—41no—
196C3×Q8—41no—
197C3×Q8—81no—
198C3×Q8—81no—
199C3×Q8—82no—
200C3×D4—32no—
201C3×D4—61no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—42no—
206C2×C3×C4—42no—
207C2×C3×C4—41no—
208C2×C3×C4—41no—
209C2×C3×C4—41no—
210C2×C3×C4—41no—
211C2×C3×C4—61no—
212C2×C3×C4—121no—
213C2×C3×C4—121no—
214C2×C3×C4D3×D411yescharacteristic
215C2×C3×C4#23711yescharacteristic
216C2×C3×C4C2×#6711yescharacteristic
217C2×C3×C4C2×C3×D411yescharacteristic
218C2×C3×C4C2×C3×D411yescharacteristic
219C2×C3×C4C3×#4111yescharacteristic
220C2×Dic3—21no—
221D12—21no—
222D12C3×Q1612yes—
223C4×D3—41no—
224C4×D3—41no—
225C3×C8—21no—
226C3×C8—21no—
227C3×C8—21no—
228C3×C8—21no—
229C3×C8—41no—
230C3×C8—41no—
231C3×C8—121no—
232C3×C8—121no—
233C3×C8—121no—
234C3⋊C8—41no—
235C3⋊C8—41no—
236C3⋊C8—41no—
237C2×C32#46311yescharacteristic
238C2×C32#46711yescharacteristic
239C2×C32#47111yescharacteristic
240C3×D3—42no—
241C2×Q8—21no—
242C2×Q8—21no—
243C2×D4—31no—
244C22×C4—61no—
245C2×C8—61no—
246C2×C8—61no—
247C2×C8—61no—
248C2×C8—122no—
249C2×C8C3×#6711yescharacteristic
250C2×C8C3×#6711yescharacteristic
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—31no—
256C22⋊C4—61no—
257C42C22×C3×D311yescharacteristic
258C22×C3—21no—
259C22×C3—62no—
260C22×C3—121no—
261C22×C3—121no—
262C22×C3#93811yescharacteristic
263C22×C3C3×#12111yescharacteristic
264C2×D3—22no—
265C2×D3—41no—
266C2×D3—41no—
267C3×C4—22no—
268C3×C4—21no—
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—82no—
275C3×C4—82no—
276C3×C4—81no—
277C3×C4—81no—
278C3×C4—81no—
279C3×C4—81no—
280C3×C4—121no—
281C3×C4D3×Q1611yescharacteristic
282C3×C4#91911yescharacteristic
283C3×C4#94911yescharacteristic
284C3×C4#95011yescharacteristic
285C3×C4C2×C3×Q1611yescharacteristic
286C3×C4C3×#13511yescharacteristic
287C3×C4C3×#13511yescharacteristic
288C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
289Dic3—41no—
290C32#168311yescharacteristic, complemented, Sylow
291C23—61no—
292Q8—41no—
293Q8—41no—
294Q8—81no—
295D4—32no—
296D4—61no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—61no—
300C2×C4—121no—
301C2×C4—121no—
302C2×C4C3×D3×D411yescharacteristic
303C2×C4C3×#23711yescharacteristic
304C2×C4C2×C3×#6711yescharacteristic
305C8—21no—
306C8—21no—
307C8—121no—
308C8—121no—
309C8—121no—
310C2×C3—21no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—122no—
314C2×C3#505711yescharacteristic
315C2×C3#517711yescharacteristic
316C2×C3#518811yescharacteristic
317C2×C3C3×#46311yescharacteristic
318C2×C3C3×#46711yescharacteristic
319C2×C3C3×#47111yescharacteristic
320D3—42no—
321C22—62no—
322C22—121no—
323C22—121no—
324C22C3×#93811yescharacteristic
325C4—21no—
326C4—81no—
327C4—81no—
328C4—121no—
329C4C3×D3×Q1611yescharacteristic
330C4C3×#91911yescharacteristic
331C4C3×#94911yescharacteristic
332C4C3×#95011yescharacteristic
333C3—21no—
334C3#7123311yescharacteristic, direct product factor
335C3C3×#168311yescharacteristic, complemented
336C2—122no—
337C2C3×#505711yescharacteristic
338C2C3×#517711yescharacteristic
339C2C3×#518811yescharacteristic
subgroupG/H
centerC22×C3#938
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#487C2
socleC22×C32#121
prime radicalC2×C3×D12D4
hypercenterC3×#487D3
hypocenterC3C3×#1683
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#487

Complements

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

NH ≅ G/Ntype
1. C32×#487C2semidirect
5. C3×#4547C2semidirect
6. C3×#4546C2semidirect
7. C3×#4458C2semidirect
9. #71233C3direct (N × H)
26. C3×#487D3semidirect
27. C3×#487C2×C3semidirect
37. #4547C2×C3semidirect
38. #4546C2×C3semidirect
39. #4458C2×C3semidirect
112. #487C3×D3semidirect
290. C32#1683semidirect
334. C3#71233direct (N × H)
335. C3C3×#1683semidirect

Maximal subgroups

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

subgroupindex
C32×#4872
C3×#50872
C3×#50842
C3×C8×D122
C3×#45472
C3×#45462
C3×#44582
C3×#16833
#712333