Finite Group Databasebeta

← C3×#71267 #11780780

Subgroups — C3×#71267 #11780780

Order 1152.

447 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#492C211yesmaximal, characteristic, complemented
2C3×#5087C211yesmaximal, characteristic, complemented
3C3×#5072C211yesmaximal, characteristic
4C3×C8×D12C211yesmaximal, characteristic, complemented
5C3×#4547C211yesmaximal, characteristic, complemented
6C3×#4544C211yesmaximal, characteristic, complemented
7C3×#4457C211yesmaximal, characteristic, complemented
8C3×#1665—31nomaximal
9#71267C311yesmaximal, characteristic, direct product factor
10C2×C32×SD16—21no—
11C2×C32×SD16—21no—
12C32×C4⋊Q8C2211yescharacteristic
13C32×#127C2211yescharacteristic
14C2×C3×#213—21no—
15C2×C3×D3×C8—21no—
16C3×C4×D12C2211yescharacteristic
17C32×C4×C8C2211yescharacteristic
18C3×#832—21no—
19C3×(C2×D3)⋊C8—21no—
20C3×#809—21no—
21C3×#807—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×#492—21no—
26C3×#492D311yescharacteristic, complemented
27C3×#492C2×C311yescharacteristic, complemented
28C3×#474—31no—
29C3×#459—31no—
30C3×C8×D4—31no—
31#5087C2×C311yescharacteristic, complemented
32#5072C2×C311yescharacteristic
33C8×D12C2×C311yescharacteristic, complemented
34C3×#334—31no—
35C3×#332—31no—
36C3×#331—31no—
37#4547C2×C311yescharacteristic, complemented
38#4544C2×C311yescharacteristic, complemented
39#4457C2×C311yescharacteristic, complemented
40C2×C32×Q8—21no—
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C3×D12D411yescharacteristic
45C2×C3×C4×D3—21no—
46C32×SD16—42no—
47C32×SD16—42no—
48C2×C32×C8D411yescharacteristic
49C2×C32×C8D411yescharacteristic
50C32×C4⋊C4—21no—
51C32×C4⋊C4—21no—
52C32×C42C2311yescharacteristic
53C3×#213—42no—
54C3×(C2×D3)⋊C4—21no—
55C3×C4⋊Dic3D411yescharacteristic
56C2×C3×C3⋊C8—21no—
57C2×C3×C3⋊C8—21no—
58C2×C3×C3⋊C8—21no—
59C3×D3×C8—42no—
60#1665—31noSylow
61C2×C3×SD16—22no—
62C2×C3×SD16—22no—
63C2×C3×SD16—21no—
64C2×C3×SD16—21no—
65C2×C3×SD16—21no—
66C2×C3×SD16—21no—
67C2×C3×D8—61no—
68C22×C3×C8—61no—
69C3×C4⋊Q8—21no—
70C3×C4⋊Q8C2×D311yescharacteristic
71C3×C4⋊Q8C22×C311yescharacteristic
72C3×#127—21no—
73C3×#127C2×D311yescharacteristic
74C3×#127C22×C311yescharacteristic
75C3×C4×D4—31no—
76C2×#213—21no—
77C2×D3×C8—21no—
78C4×D12C22×C311yescharacteristic
79C3×#107—61no—
80C3×C4⋊C8—31no—
81C3×C4⋊C8—31no—
82C3×C4⋊C8—31no—
83C3×#102—61no—
84C3×#102—61no—
85C3×C22⋊C8—61no—
86C3×C4×C8—21no—
87C3×C4×C8C2×D311yescharacteristic
88C3×C4×C8C22×C311yescharacteristic
89#832—21no—
90(C2×D3)⋊C8—21no—
91#809—21no—
92#807—21no—
93C4⋊(C3⋊C8)C22×C311yescharacteristic
94C4⋊(C3⋊C8)C22×C311yescharacteristic
95C4⋊(C3⋊C8)C22×C311yescharacteristic
96C23×C32—41no—
97C22×C3×D3—21no—
98C32×Q8—41no—
99C32×Q8—41no—
100C32×D4—41no—
101C32×D4—41no—
102C32×D4—41no—
103C32×D4—41no—
104C32×D4—81no—
105C2×C32×C4—41no—
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4#4111yescharacteristic
109C2×C3×Dic3—21no—
110C3×D12—21no—
111C3×D12SD1612yescomplemented
112C3×C4×D3—41no—
113C3×C4×D3—41no—
114C32×C8—21no—
115C32×C8D812yescomplemented
116C3×C3⋊C8—41no—
117C3×C3⋊C8—41no—
118C3×C3⋊C8—41no—
119#492C3×D311yescharacteristic, complemented
120#474—31no—
121#459—31no—
122C8×D4—31no—
123#334—31no—
124#332—31no—
125#331—31no—
126C2×C3×Q8—22no—
127C2×C3×Q8—21no—
128C2×C3×Q8—21no—
129C2×C3×D4—22no—
130C2×C3×D4—21no—
131C2×C3×D4—21no—
132C2×C3×D4—21no—
133C2×C3×D4—21no—
134C2×C3×D4—21no—
135C2×C3×D4—21no—
136C2×C3×D4—31no—
137C2×C3×D4—41no—
138C2×C3×D4—41no—
139C22×C3×C4—61no—
140C2×D12C3×D411yescharacteristic
141C2×C4×D3—21no—
142C3×SD16—44no—
143C3×SD16—42no—
144C3×SD16—42no—
145C3×SD16—44no—
146C3×SD16—42no—
147C3×SD16—42no—
148C3×D8—122no—
149C2×C3×C8—21no—
150C2×C3×C8—21no—
151C2×C3×C8—61no—
152C2×C3×C8—61no—
153C2×C3×C8—61no—
154C2×C3×C8—122no—
155C2×C3×C8#6711yescharacteristic
156C2×C3×C8#6711yescharacteristic
157C2×C3×C8C3×D411yescharacteristic
158C2×C3×C8C3×D411yescharacteristic
159C3×C4⋊C4—21no—
160C3×C4⋊C4—21no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4—21no—
163C3×C4⋊C4—31no—
164C3×C4⋊C4—41no—
165C3×C4⋊C4—41no—
166C3×C22⋊C4—61no—
167C3×C42—21no—
168C3×C42C22×D311yescharacteristic
169C3×C42C23×C311yescharacteristic
170#213—42no—
171(C2×D3)⋊C4—21no—
172C4⋊Dic3C3×D411yescharacteristic
173C2×C3⋊C8—21no—
174C2×C3⋊C8—21no—
175C2×C3⋊C8—21no—
176D3×C8—42no—
177C22×C32—81no—
178C22×C32—81no—
179C22×C32—81no—
180C22×C32#12111yescharacteristic
181C2×C3×D3—22no—
182C2×C3×D3—41no—
183C2×C3×D3—41no—
184C32×C4—21no—
185C32×C4—81no—
186C32×C4C2×D811yescharacteristic
187C32×C4C2×SD1611yescharacteristic
188C32×C4#13511yescharacteristic
189C32×C4AGL(1,ℤ/8)11yescharacteristic
190C3×Dic3—41no—
191C2×SD16—21no—
192C2×SD16—21no—
193C2×D8—61no—
194C22×C8—61no—
195C4⋊Q8C2×C3×D311yescharacteristic
196#127C2×C3×D311yescharacteristic
197C4×D4—31no—
198#107—61no—
199C4⋊C8—31no—
200C4⋊C8—31no—
201C4⋊C8—31no—
202#102—61no—
203#102—61no—
204C22⋊C8—61no—
205C4×C8C2×C3×D311yescharacteristic
206C23×C3—42no—
207C23×C3—41no—
208C23×C3—41no—
209C23×C3—61no—
210C22×D3—21no—
211C3×Q8—42no—
212C3×Q8—42no—
213C3×Q8—41no—
214C3×Q8—41no—
215C3×Q8—41no—
216C3×Q8—41no—
217C3×D4—32no—
218C3×D4—42no—
219C3×D4—42no—
220C3×D4—41no—
221C3×D4—41no—
222C3×D4—41no—
223C3×D4—41no—
224C3×D4—41no—
225C3×D4—41no—
226C3×D4—41no—
227C3×D4—41no—
228C3×D4—61no—
229C3×D4—81no—
230C3×D4—81no—
231C3×D4—81no—
232C3×D4—81no—
233C3×D4—82no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—42no—
238C2×C3×C4—41no—
239C2×C3×C4—41no—
240C2×C3×C4—61no—
241C2×C3×C4—121no—
242C2×C3×C4—121no—
243C2×C3×C4D3×D411yescharacteristic
244C2×C3×C4#23711yescharacteristic
245C2×C3×C4C2×#6711yescharacteristic
246C2×C3×C4C2×C3×D411yescharacteristic
247C2×C3×C4C2×C3×D411yescharacteristic
248C2×C3×C4C3×#4111yescharacteristic
249C2×Dic3—21no—
250D12—21no—
251D12C3×SD1612yescomplemented
252C4×D3—41no—
253C4×D3—41no—
254C3×C8—22no—
255C3×C8—21no—
256C3×C8—21no—
257C3×C8—22no—
258C3×C8—121no—
259C3×C8—121no—
260C3×C8—121no—
261C3×C8#21312yescomplemented
262C3×C8C3×D812yescomplemented
263C3⋊C8—41no—
264C3⋊C8—41no—
265C3⋊C8—41no—
266C2×C32—161no—
267C2×C32#45911yescharacteristic
268C2×C32#46511yescharacteristic
269C2×C32#47111yescharacteristic
270C3×D3—42no—
271C2×Q8—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—31no—
276C22×C4—61no—
277SD16—42no—
278SD16—42no—
279D8—122no—
280C2×C8—61no—
281C2×C8—61no—
282C2×C8—61no—
283C2×C8—122no—
284C2×C8C3×#6711yescharacteristic
285C2×C8C3×#6711yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—31no—
289C22⋊C4—61no—
290C42C22×C3×D311yescharacteristic
291C22×C3—21no—
292C22×C3—62no—
293C22×C3—82no—
294C22×C3—82no—
295C22×C3—82no—
296C22×C3—81no—
297C22×C3—81no—
298C22×C3—81no—
299C22×C3—81no—
300C22×C3—81no—
301C22×C3—81no—
302C22×C3—121no—
303C22×C3—121no—
304C22×C3#93811yescharacteristic
305C22×C3C3×#12111yescharacteristic
306C2×D3—22no—
307C2×D3—41no—
308C2×D3—41no—
309C3×C4—22no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—82no—
317C3×C4—81no—
318C3×C4—81no—
319C3×C4—121no—
320C3×C4D3×SD1611yescharacteristic
321C3×C4#91611yescharacteristic
322C3×C4C2×#21311yescharacteristic
323C3×C4#93211yescharacteristic
324C3×C4C2×C3×D811yescharacteristic
325C3×C4C2×C3×SD1611yescharacteristic
326C3×C4C3×#13511yescharacteristic
327C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
328Dic3—41no—
329C32#166511yescharacteristic, complemented, Sylow
330C23—41no—
331C23—61no—
332Q8—41no—
333Q8—41no—
334D4—32no—
335D4—41no—
336D4—41no—
337D4—41no—
338D4—41no—
339D4—61no—
340D4—81no—
341C2×C4—41no—
342C2×C4—61no—
343C2×C4—121no—
344C2×C4—121no—
345C2×C4C3×D3×D411yescharacteristic
346C2×C4C3×#23711yescharacteristic
347C2×C4C2×C3×#6711yescharacteristic
348C8—21no—
349C8—121no—
350C8—121no—
351C8—121no—
352C8C3×#21312yescomplemented
353C2×C3—21no—
354C2×C3—21no—
355C2×C3—21no—
356C2×C3—122no—
357C2×C3—162no—
358C2×C3—161no—
359C2×C3—161no—
360C2×C3#507211yescharacteristic
361C2×C3#517111yescharacteristic
362C2×C3#517711yescharacteristic
363C2×C3C3×#45911yescharacteristic
364C2×C3C3×#46511yescharacteristic
365C2×C3C3×#47111yescharacteristic
366D3—42no—
367C22—62no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22—121no—
372C22—121no—
373C22C3×#93811yescharacteristic
374C4—21no—
375C4—81no—
376C4—121no—
377C4C3×D3×SD1611yescharacteristic
378C4C3×#91611yescharacteristic
379C4C2×C3×#21311yescharacteristic
380C4C3×#93211yescharacteristic
381C3—21no—
382C3#7126711yescharacteristic, direct product factor
383C3C3×#166511yescharacteristic, complemented
384C2—122no—
385C2—161no—
386C2C3×#507211yescharacteristic
387C2C3×#517111yescharacteristic
388C2C3×#517711yescharacteristic
subgroupG/H
centerC22×C3#938
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#492C2
socleC22×C32#121
prime radicalC3×#5072C2
hypercenterC3×#492D3
hypocenterC3C3×#1665
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#492

Complements

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

NH ≅ G/Ntype
1. C32×#492C2semidirect
2. C3×#5087C2semidirect
4. C3×C8×D12C2semidirect
5. C3×#4547C2semidirect
6. C3×#4544C2semidirect
7. C3×#4457C2semidirect
9. #71267C3direct (N × H)
26. C3×#492D3semidirect
27. C3×#492C2×C3semidirect
31. #5087C2×C3semidirect
33. C8×D12C2×C3semidirect
37. #4547C2×C3semidirect
38. #4544C2×C3semidirect
39. #4457C2×C3semidirect
111. C3×D12SD16semidirect
115. C32×C8D8semidirect
119. #492C3×D3semidirect
251. D12C3×SD16semidirect
261. C3×C8#213semidirect
262. C3×C8C3×D8semidirect
329. C32#1665semidirect
352. C8C3×#213semidirect
382. C3#71267direct (N × H)
383. C3C3×#1665semidirect

Maximal subgroups

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

subgroupindex
C32×#4922
C3×#50872
C3×#50722
C3×C8×D122
C3×#45472
C3×#45442
C3×#44572
C3×#16653
#712673