Finite Group Databasebeta

← C3×#70958 #11781657

Subgroups — C3×#70958 #11781657

Order 1152.

383 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#446C211yesmaximal, characteristic, complemented
2C3×#5027C211yesmaximal, characteristic
3C3×#5020C211yesmaximal, characteristic, complemented
4C3×#4693C211yesmaximal, characteristic
5C3×#4485C211yesmaximal, characteristic
6C3×#4482C211yesmaximal, characteristic, complemented
7C3×#4458C211yesmaximal, characteristic, complemented
8C3×#1686—31nomaximal
9#70958C311yesmaximal, characteristic, direct product factor
10C32×C4×Q8C2211yescharacteristic
11C2×C3×#215—21no—
12C2×C3×#204—21no—
13C2×C3×#204—21no—
14C3×#874C2211yescharacteristic
15C3×#869C2211yescharacteristic
16C32×C4⋊C8—21no—
17C32×C4⋊C8C2211yescharacteristic
18C32×#97—21no—
19C32×C4×C8C2211yescharacteristic
20C3×#835—21no—
21C3×#809—21no—
22C3×#808—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×#492—31no—
26C3×#475—31no—
27C3×#460—31no—
28C3×#446—21no—
29C3×#446D311yescharacteristic, complemented
30C3×#446C2×C311yescharacteristic, complemented
31#5027C2×C311yescharacteristic
32#5020C2×C311yescharacteristic, complemented
33#4693C2×C311yescharacteristic
34C3×#335—31no—
35C3×#332—31no—
36C3×#331—31no—
37#4485C2×C311yescharacteristic
38#4482C2×C311yescharacteristic, complemented
39#4458C2×C311yescharacteristic, complemented
40C2×C32×Q8D411yescharacteristic
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×C3×D12—21no—
44C2×C3×Dic6—21no—
45C2×C32×C8—21no—
46C2×C32×C8D411yescharacteristic
47C2×C32×C8D411yescharacteristic
48C32×C4⋊C4—21no—
49C32×C4⋊C4D411yescharacteristic
50C32×C42—21no—
51C32×C42C2311yescharacteristic
52C3×#215—42no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3—21no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8—21no—
57C3×#204—42no—
58C3×#204—42no—
59#1686—31noSylow
60C2×C3×SD16—61no—
61C2×C3×SD16—61no—
62C2×C3×SD16—61no—
63C3×C4⋊Q8—31no—
64C3×#127—31no—
65C3×C4×Q8—21no—
66C3×C4×Q8C2×D311yescharacteristic
67C3×C4×Q8C22×C311yescharacteristic
68C2×#215—21no—
69C2×#204—21no—
70C2×#204—21no—
71#874C22×C311yescharacteristic
72#869C22×C311yescharacteristic
73C3×#106—61no—
74C3×C4⋊C8—22no—
75C3×C4⋊C8—21no—
76C3×C4⋊C8—21no—
77C3×C4⋊C8—21no—
78C3×C4⋊C8—31no—
79C3×C4⋊C8—31no—
80C3×C4⋊C8C2×D311yescharacteristic
81C3×C4⋊C8C22×C311yescharacteristic
82C3×#103—61no—
83C3×#102—61no—
84C3×#97—22no—
85C3×#97—21no—
86C3×#97—21no—
87C3×C4×C8—21no—
88C3×C4×C8C2×D311yescharacteristic
89C3×C4×C8C22×C311yescharacteristic
90#835—21no—
91#809—21no—
92#808—21no—
93C4⋊(C3⋊C8)C22×C311yescharacteristic
94C4⋊(C3⋊C8)C22×C311yescharacteristic
95C22×C3×D3—41no—
96C32×Q8—21no—
97C32×Q8—21no—
98C2×C32×C4—21no—
99C2×C32×C4—21no—
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4#4111yescharacteristic
103C2×C3×Dic3—41no—
104C3×D12—41no—
105C3×D12—41no—
106C3×D12—41no—
107C3×D12—41no—
108C3×D12—81no—
109C3×Dic6—41no—
110C3×Dic6—41no—
111C32×C8—21no—
112C32×C8—41no—
113C32×C8SD1612yescomplemented
114C3×C3⋊C8—41no—
115C3×C3⋊C8—41no—
116#492—31no—
117#475—31no—
118#460—31no—
119#446C3×D311yescharacteristic, complemented
120#335—31no—
121#332—31no—
122#331—31no—
123C2×C3×Q8—21no—
124C2×C3×Q8—61no—
125C2×C3×Q8D1211yescharacteristic
126C2×C3×Q8C3×D411yescharacteristic
127C2×C3×D4—61no—
128C2×C3×D4—61no—
129C2×C3×D4—61no—
130C2×D12—21no—
131C2×D12—21no—
132C2×D12—21no—
133C2×Dic6—21no—
134C3×SD16—122no—
135C3×SD16—122no—
136C3×SD16—122no—
137C2×C3×C8—22no—
138C2×C3×C8—21no—
139C2×C3×C8—21no—
140C2×C3×C8—21no—
141C2×C3×C8—21no—
142C2×C3×C8—61no—
143C2×C3×C8—61no—
144C2×C3×C8#6711yescharacteristic
145C2×C3×C8#6711yescharacteristic
146C2×C3×C8C3×D411yescharacteristic
147C2×C3×C8C3×D411yescharacteristic
148C3×C4⋊C4—22no—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—21no—
151C3×C4⋊C4—21no—
152C3×C4⋊C4—61no—
153C3×C4⋊C4—61no—
154C3×C4⋊C4D1211yescharacteristic
155C3×C4⋊C4C3×D411yescharacteristic
156C3×C42—22no—
157C3×C42—21no—
158C3×C42—21no—
159C3×C42—21no—
160C3×C42C22×D311yescharacteristic
161C3×C42C23×C311yescharacteristic
162#215—42no—
163C4⋊Dic3—21no—
164C4⋊Dic3—21no—
165C2×C3⋊C8—21no—
166C2×C3⋊C8—21no—
167#204—42no—
168#204—42no—
169C22×C32#12111yescharacteristic
170C2×C3×D3—81no—
171C2×C3×D3—81no—
172C2×C3×D3—81no—
173C32×C4—21no—
174C32×C4—41no—
175C32×C4—41no—
176C32×C4C2×SD1611yescharacteristic
177C32×C4AGL(1,ℤ/8)11yescharacteristic
178C32×C4AGL(1,ℤ/8)11yescharacteristic
179C32×C4#13711yescharacteristic
180C3×Dic3—81no—
181C2×SD16—61no—
182C2×SD16—61no—
183C2×SD16—61no—
184C4⋊Q8—31no—
185#127—31no—
186C4×Q8C2×C3×D311yescharacteristic
187#106—61no—
188C4⋊C8—21no—
189C4⋊C8—31no—
190C4⋊C8—31no—
191C4⋊C8C2×C3×D311yescharacteristic
192#103—61no—
193#102—61no—
194#97—21no—
195C4×C8C2×C3×D311yescharacteristic
196C23×C3—121no—
197C22×D3—41no—
198C3×Q8—21no—
199C3×Q8—21no—
200C3×Q8—21no—
201C3×Q8—21no—
202C3×Q8—41no—
203C3×Q8—41no—
204C3×Q8—121no—
205C3×Q8—121no—
206C3×D4—121no—
207C3×D4—121no—
208C3×D4—121no—
209C3×D4—121no—
210C3×D4—241no—
211C2×C3×C4—22no—
212C2×C3×C4—22no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—121no—
221C2×C3×C4C2×D1211yescharacteristic
222C2×C3×C4#23511yescharacteristic
223C2×C3×C4C2×#6711yescharacteristic
224C2×C3×C4C2×C3×D411yescharacteristic
225C2×C3×C4C2×C3×D411yescharacteristic
226C2×C3×C4C3×#4111yescharacteristic
227C2×Dic3—41no—
228D12—41no—
229D12—41no—
230D12—41no—
231D12—41no—
232D12—81no—
233Dic6—41no—
234Dic6—41no—
235C3×C8—21no—
236C3×C8—21no—
237C3×C8—22no—
238C3×C8—41no—
239C3×C8—42no—
240C3×C8—41no—
241C3×C8—41no—
242C3×C8—121no—
243C3×C8—121no—
244C3×C8#21512yescomplemented
245C3×C8C3×SD1612yescomplemented
246C3⋊C8—41no—
247C3⋊C8—41no—
248C2×C32#46011yescharacteristic
249C2×C32#46811yescharacteristic
250C2×C32#47111yescharacteristic
251C3×D3—161no—
252C2×Q8—61no—
253C2×Q8C3×D1211yescharacteristic
254C2×D4—61no—
255C2×D4—61no—
256C2×D4—61no—
257SD16—122no—
258SD16—122no—
259SD16—122no—
260C2×C8—21no—
261C2×C8—61no—
262C2×C8—61no—
263C2×C8C3×#6711yescharacteristic
264C2×C8C3×#6711yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—61no—
267C4⋊C4—61no—
268C4⋊C4C3×D1211yescharacteristic
269C42—21no—
270C42C22×C3×D311yescharacteristic
271C22×C3—21no—
272C22×C3—241no—
273C22×C3—241no—
274C22×C3—241no—
275C22×C3#93011yescharacteristic
276C22×C3C3×#12111yescharacteristic
277C2×D3—81no—
278C2×D3—81no—
279C2×D3—81no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—41no—
287C3×C4—42no—
288C3×C4—42no—
289C3×C4—41no—
290C3×C4—41no—
291C3×C4—41no—
292C3×C4—41no—
293C3×C4—241no—
294C3×C4#90811yescharacteristic
295C3×C4#90911yescharacteristic
296C3×C4C2×#21511yescharacteristic
297C3×C4#94911yescharacteristic
298C3×C4C2×C3×SD1611yescharacteristic
299C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
300C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
301C3×C4C3×#13711yescharacteristic
302Dic3—81no—
303C32#168611yescharacteristic, complemented, Sylow
304C23—121no—
305Q8—21no—
306Q8—21no—
307Q8—121no—
308Q8—121no—
309D4—121no—
310D4—121no—
311D4—121no—
312D4—121no—
313D4—241no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—121no—
317C2×C4C2×C3×D1211yescharacteristic
318C2×C4C3×#23511yescharacteristic
319C2×C4C2×C3×#6711yescharacteristic
320C8—21no—
321C8—41no—
322C8—121no—
323C8—121no—
324C8C3×#21512yescomplemented
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—481no—
329C2×C3#502711yescharacteristic
330C2×C3#513411yescharacteristic
331C2×C3#514111yescharacteristic
332C2×C3C3×#46011yescharacteristic
333C2×C3C3×#46811yescharacteristic
334C2×C3C3×#47111yescharacteristic
335D3—161no—
336C22—241no—
337C22—241no—
338C22—241no—
339C22C3×#93011yescharacteristic
340C4—21no—
341C4—41no—
342C4—41no—
343C4—241no—
344C4C3×#90811yescharacteristic
345C4C3×#90911yescharacteristic
346C4C2×C3×#21511yescharacteristic
347C4C3×#94911yescharacteristic
348C3—21no—
349C3#7095811yescharacteristic, direct product factor
350C3C3×#168611yescharacteristic, complemented
351C2—481no—
352C2C3×#502711yescharacteristic
353C2C3×#513411yescharacteristic
354C2C3×#514111yescharacteristic
subgroupG/H
centerC22×C3#930
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#446C2
socleC22×C32#121
prime radicalC3×#874C22
hypercenterC3×#446D3
hypocenterC3C3×#1686
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#446

Complements

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

NH ≅ G/Ntype
1. C32×#446C2semidirect
3. C3×#5020C2semidirect
6. C3×#4482C2semidirect
7. C3×#4458C2semidirect
9. #70958C3direct (N × H)
29. C3×#446D3semidirect
30. C3×#446C2×C3semidirect
32. #5020C2×C3semidirect
38. #4482C2×C3semidirect
39. #4458C2×C3semidirect
113. C32×C8SD16semidirect
119. #446C3×D3semidirect
244. C3×C8#215semidirect
245. C3×C8C3×SD16semidirect
303. C32#1686semidirect
324. C8C3×#215semidirect
349. C3#70958direct (N × H)
350. C3C3×#1686semidirect

Maximal subgroups

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

subgroupindex
C32×#4462
C3×#50272
C3×#50202
C3×#46932
C3×#44852
C3×#44822
C3×#44582
C3×#16863
#709583