Finite Group Databasebeta

← C3×#81803 #11878938

Subgroups — C3×#81803 #11878938

Order 1152.

849 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5728C211yesmaximal, characteristic, complemented
2C3×#5725C211yesmaximal, characteristic
3C32×#494C211yesmaximal, characteristic, complemented
4C3×#5187C214yesmaximal, complemented
5C3×#5185C214yesmaximal, complemented
6C3×#5085C211yesmaximal, characteristic, complemented
7C3×#5079C211yesmaximal, characteristic, complemented
8C3×#4694C211yesmaximal, characteristic, complemented
9C3×#4685C211yesmaximal, characteristic, complemented
10C3×#3210—31nomaximal
11#81803C311yesmaximal, characteristic, direct product factor
12C2×C3×#239C2212yes—
13C2×C32×Q16C2214yes—
14C32×C4⋊Q8C2211yescharacteristic
15C32×C4⋊Q8C2211yescharacteristic
16C3×#947C2212yes—
17C3×#946C2212yes—
18C3×Q8×Dic3C2212yes—
19C2×C3×#215C2214yes—
20C3×#897—21no—
21C3×#895—21no—
22C3×#895—21no—
23C3×#893—21no—
24C3×#893—21no—
25C3×#892—21no—
26C3×#890—21no—
27C3×#887—21no—
28C3×#874C2211yescharacteristic
29C3×C42×D3C2211yescharacteristic
30C3×#869C2211yescharacteristic
31C32×C4×C8C2211yescharacteristic
32C3×#835C2214yes—
33C3×#821C2214yes—
34C3×(C2×D3)⋊C8C2212yes—
35C3×Dic3⋊C8C2212yes—
36C3×C4×C3⋊C8C2211yescharacteristic
37C3×#533—31no—
38C3×#532—31no—
39#5728C2×C311yescharacteristic, complemented
40#5725C2×C311yescharacteristic
41C3×#494—21no—
42C3×#494D311yescharacteristic, complemented
43C3×#494C2×C311yescharacteristic, complemented
44C3×#492—31no—
45C3×#487—31no—
46C3×#486—31no—
47C3×#464—34no—
48C3×#452—34no—
49C3×#431—31no—
50#5187C2×C314yescomplemented
51#5185C2×C314yescomplemented
52#5085C2×C311yescharacteristic, complemented
53#5079C2×C311yescharacteristic, complemented
54#4694C2×C311yescharacteristic, complemented
55#4685C2×C311yescharacteristic, complemented
56C2×C32×Q8C2312yes—
57C2×C32×Q8C2312yes—
58C3×#239—44no—
59C2×C3×D12—22no—
60C2×C3×D12—21no—
61C2×C3×D12—21no—
62C2×C3×D12C2312yes—
63C2×C3×C4×D3—22no—
64C2×C3×C4×D3D411yescharacteristic
65C2×C3×C4×D3D411yescharacteristic
66C2×C3×C4×D3C2311yescharacteristic
67C2×C3×Dic6—21no—
68C32×Q16—44no—
69C2×C32×C8C2312yes—
70C32×C4⋊C4—21no—
71C32×C4⋊C4—21no—
72C32×C4⋊C4—21no—
73C32×C4⋊C4—21no—
74C32×C42C2311yescharacteristic
75C3×#215—44no—
76C3×(C2×D3)⋊C4—22no—
77C3×(C2×D3)⋊C4—22no—
78C3×(C2×D3)⋊C4—22no—
79C3×C4⋊Dic3—21no—
80C3×C4⋊Dic3—22no—
81C3×C4⋊Dic3C2312yes—
82C3×Dic3⋊C4—22no—
83C3×C4×Dic3—22no—
84C3×C4×Dic3D411yescharacteristic
85C3×C4×Dic3D411yescharacteristic
86C3×C4×Dic3C2311yescharacteristic
87C2×C3×C3⋊C8C2312yes—
88#3210—31noSylow
89C2×C3×#41—32no—
90C2×#239C22×C312yes—
91C2×C3×Q16—24no—
92C2×C3×Q16C2×D314yes—
93C2×C3×Q16C22×C314yes—
94C2×C3×SD16—34no—
95C3×C4⋊Q8—21no—
96C3×C4⋊Q8—21no—
97C3×C4⋊Q8—31no—
98C3×C4⋊Q8C2×D311yescharacteristic
99C3×C4⋊Q8C2×D311yescharacteristic
100C3×C4⋊Q8C22×C311yescharacteristic
101C3×C4⋊Q8C22×C311yescharacteristic
102C3×#127—31no—
103C3×#125—61no—
104C3×#124—32no—
105C3×C22⋊Q8—32no—
106C3×C22⋊Q8—61no—
107C3×#121—61no—
108C3×#121—61no—
109C3×C4×Q8—32no—
110C3×C4×Q8—61no—
111C3×C4×D4—61no—
112C3×C4×D4—61no—
113C3×#117—61no—
114C2×C3×C42—31no—
115#947C22×C312yes—
116#946C22×C312yes—
117Q8×Dic3C22×C312yes—
118C2×#215C22×C314yes—
119#897—21no—
120#895—21no—
121#895—21no—
122#893—21no—
123#893—21no—
124#892—21no—
125#890—21no—
126#887—21no—
127#874C22×C311yescharacteristic
128C42×D3C22×C311yescharacteristic
129#869C22×C311yescharacteristic
130C3×C4⋊C8—32no—
131C3×#103—34no—
132C3×#102—34no—
133C3×C22⋊C8—32no—
134C3×C4×C8—21no—
135C3×C4×C8—31no—
136C3×C4×C8C2×D311yescharacteristic
137C3×C4×C8C22×C311yescharacteristic
138#835C22×C314yes—
139#821C22×C314yes—
140(C2×D3)⋊C8C22×C312yes—
141Dic3⋊C8C22×C312yes—
142C4×C3⋊C8C22×C311yescharacteristic
143C22×C3×D3—22no—
144C22×C3×D3C2×D411yescharacteristic
145C32×Q8—24no—
146C32×Q8—24no—
147C2×C32×C4—22no—
148C2×C32×C4—22no—
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2411yescharacteristic
152C2×C3×Dic3—22no—
153C2×C3×Dic3C2×D411yescharacteristic
154C2×C3×Dic3C2×D411yescharacteristic
155C2×C3×Dic3C2×D411yescharacteristic
156C3×D12—24no—
157C3×D12—44no—
158C3×D12—42no—
159C3×D12—42no—
160C3×C4×D3—22no—
161C3×C4×D3—22no—
162C3×C4×D3—22no—
163C3×C4×D3—44no—
164C3×Dic6—42no—
165C32×C8—22no—
166C3×C3⋊C8—22no—
167#533—31no—
168#532—31no—
169#494C3×D311yescharacteristic, complemented
170#492—31no—
171#487—31no—
172#486—31no—
173#464—34no—
174#452—34no—
175#431—31no—
176C3×#41—124no—
177C2×C3×Q8—22no—
178C2×C3×Q8—22no—
179C2×C3×Q8—61no—
180C2×C3×Q8C22×D312yes—
181C2×C3×Q8C22×D312yes—
182C2×C3×Q8C23×C312yes—
183C2×C3×Q8C23×C312yes—
184C2×C3×D4—32no—
185C2×C3×D4—62no—
186C2×C3×D4—61no—
187C2×C3×D4—61no—
188C22×C3×C4—31no—
189C22×C3×C4—31no—
190C22×C3×C4—31no—
191C22×C3×C4—62no—
192#239—44no—
193C2×D12—22no—
194C2×D12—21no—
195C2×D12—21no—
196C2×D12C23×C312yes—
197C2×C4×D3—22no—
198C2×C4×D3C3×D411yescharacteristic
199C2×C4×D3C3×D411yescharacteristic
200C2×C4×D3C23×C311yescharacteristic
201C2×Dic6—21no—
202C3×Q16—44no—
203C3×Q16—44no—
204C3×Q16—48no—
205C3×SD16—124no—
206C2×C3×C8—22no—
207C2×C3×C8—32no—
208C2×C3×C8C22×D312yes—
209C2×C3×C8C23×C312yes—
210C3×C4⋊C4—21no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—21no—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—21no—
216C3×C4⋊C4—21no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—32no—
219C3×C4⋊C4—41no—
220C3×C4⋊C4—41no—
221C3×C4⋊C4—41no—
222C3×C4⋊C4—41no—
223C3×C4⋊C4—62no—
224C3×C4⋊C4—62no—
225C3×C4⋊C4—61no—
226C3×C22⋊C4—62no—
227C3×C22⋊C4—62no—
228C3×C22⋊C4—62no—
229C3×C42—21no—
230C3×C42—31no—
231C3×C42—31no—
232C3×C42—31no—
233C3×C42—62no—
234C3×C42C22×D311yescharacteristic
235C3×C42C23×C311yescharacteristic
236#215—44no—
237(C2×D3)⋊C4—22no—
238(C2×D3)⋊C4—22no—
239(C2×D3)⋊C4—22no—
240C4⋊Dic3—21no—
241C4⋊Dic3—22no—
242C4⋊Dic3C23×C312yes—
243Dic3⋊C4—22no—
244C4×Dic3—22no—
245C4×Dic3C3×D411yescharacteristic
246C4×Dic3C3×D411yescharacteristic
247C4×Dic3C23×C311yescharacteristic
248C2×C3⋊C8C23×C312yes—
249C22×C32C22×D411yescharacteristic
250C2×C3×D3—21no—
251C2×C3×D3—21no—
252C2×C3×D3—21no—
253C2×C3×D3—42no—
254C2×C3×D3—42no—
255C2×C3×D3—42no—
256C32×C4—42no—
257C32×C4—42no—
258C32×C4#13512yes—
259C32×C4#13712yes—
260C32×C4H(5,𝔽2)12yes—
261C3×Dic3—21no—
262C3×Dic3—21no—
263C3×Dic3—21no—
264C3×Dic3—42no—
265C2×#41—32no—
266C2×Q16C2×C3×D314yes—
267C2×SD16—34no—
268C4⋊Q8—31no—
269C4⋊Q8C2×C3×D311yescharacteristic
270C4⋊Q8C2×C3×D311yescharacteristic
271#127—31no—
272#125—61no—
273#124—32no—
274C22⋊Q8—32no—
275C22⋊Q8—61no—
276#121—61no—
277#121—61no—
278C4×Q8—32no—
279C4×Q8—61no—
280C4×D4—61no—
281C4×D4—61no—
282#117—61no—
283C2×C42—31no—
284C4⋊C8—32no—
285#103—34no—
286#102—34no—
287C22⋊C8—32no—
288C4×C8—31no—
289C4×C8C2×C3×D311yescharacteristic
290C23×C3—31no—
291C23×C3—62no—
292C22×D3—22no—
293C22×D3C2×C3×D411yescharacteristic
294C3×Q8—24no—
295C3×Q8—24no—
296C3×Q8—24no—
297C3×Q8—24no—
298C3×Q8—44no—
299C3×Q8—44no—
300C3×Q8—122no—
301C3×D4—64no—
302C3×D4—124no—
303C3×D4—122no—
304C3×D4—122no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—31no—
313C2×C3×C4—31no—
314C2×C3×C4—31no—
315C2×C3×C4—42no—
316C2×C3×C4—42no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4—62no—
320C2×C3×C4—62no—
321C2×C3×C4—124no—
322C2×C3×C4D3×D411yescharacteristic
323C2×C3×C4D3×D411yescharacteristic
324C2×C3×C4C2×C3×D411yescharacteristic
325C2×C3×C4C2×C3×D411yescharacteristic
326C2×C3×C4C23×D311yescharacteristic
327C2×C3×C4C24×C311yescharacteristic
328C2×Dic3—22no—
329C2×Dic3C2×C3×D411yescharacteristic
330C2×Dic3C2×C3×D411yescharacteristic
331C2×Dic3C2×C3×D411yescharacteristic
332D12—24no—
333D12—44no—
334D12—42no—
335D12—42no—
336C4×D3—22no—
337C4×D3—22no—
338C4×D3—22no—
339C4×D3—44no—
340Dic6—42no—
341C3×C8—24no—
342C3×C8—22no—
343C3×C8—22no—
344C3×C8—62no—
345C3⋊C8—22no—
346C2×C32#53511yescharacteristic
347C2×C32C2×#13511yescharacteristic
348C2×C32C2×#13711yescharacteristic
349C3×D3—41no—
350C3×D3—82no—
351#41—124no—
352C2×Q8—61no—
353C2×Q8C22×C3×D312yes—
354C2×Q8C22×C3×D312yes—
355C2×D4—32no—
356C2×D4—62no—
357C2×D4—61no—
358C2×D4—61no—
359C22×C4—31no—
360C22×C4—31no—
361C22×C4—31no—
362C22×C4—62no—
363Q16—44no—
364SD16—124no—
365C2×C8—32no—
366C2×C8C22×C3×D312yes—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—32no—
372C4⋊C4—62no—
373C4⋊C4—62no—
374C4⋊C4—61no—
375C22⋊C4—62no—
376C22⋊C4—62no—
377C22⋊C4—62no—
378C42—31no—
379C42—31no—
380C42—31no—
381C42—62no—
382C42C22×C3×D311yescharacteristic
383C22×C3—21no—
384C22×C3—61no—
385C22×C3—61no—
386C22×C3—61no—
387C22×C3—122no—
388C22×C3—122no—
389C22×C3—122no—
390C22×C3C2×D3×D411yescharacteristic
391C22×C3C22×C3×D411yescharacteristic
392C2×D3—21no—
393C2×D3—21no—
394C2×D3—21no—
395C2×D3—42no—
396C2×D3—42no—
397C2×D3—42no—
398C3×C4—22no—
399C3×C4—22no—
400C3×C4—22no—
401C3×C4—42no—
402C3×C4—42no—
403C3×C4—42no—
404C3×C4—42no—
405C3×C4—61no—
406C3×C4—61no—
407C3×C4—61no—
408C3×C4—82no—
409C3×C4—82no—
410C3×C4—122no—
411C3×C4#91812yes—
412C3×C4#91912yes—
413C3×C4C3×#13512yes—
414C3×C4C3×#13712yes—
415C3×C4#100412yes—
416C3×C4C3×H(5,𝔽2)12yes—
417Dic3—21no—
418Dic3—21no—
419Dic3—21no—
420Dic3—42no—
421C32#321011yescharacteristic, complemented, Sylow
422C23—31no—
423C23—62no—
424Q8—24no—
425Q8—24no—
426Q8—122no—
427D4—64no—
428D4—124no—
429D4—122no—
430D4—122no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—31no—
434C2×C4—31no—
435C2×C4—31no—
436C2×C4—62no—
437C2×C4—62no—
438C2×C4—62no—
439C2×C4—62no—
440C2×C4—124no—
441C2×C4C3×D3×D411yescharacteristic
442C2×C4C3×D3×D411yescharacteristic
443C2×C4C23×C3×D311yescharacteristic
444C8—22no—
445C8—62no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—121no—
450C2×C3—242no—
451C2×C3#571511yescharacteristic
452C2×C3C2×#91811yescharacteristic
453C2×C3C2×#91911yescharacteristic
454C2×C3C3×#53511yescharacteristic
455C2×C3C2×C3×#13511yescharacteristic
456C2×C3C2×C3×#13711yescharacteristic
457D3—41no—
458D3—82no—
459C22—61no—
460C22—61no—
461C22—61no—
462C22—122no—
463C22—122no—
464C22—122no—
465C22C2×C3×D3×D411yescharacteristic
466C4—42no—
467C4—42no—
468C4—61no—
469C4—61no—
470C4—61no—
471C4—122no—
472C4C3×#91812yes—
473C4C3×#91912yes—
474C4C3×#100412yes—
475C3—21no—
476C3#8180311yescharacteristic, direct product factor
477C3C3×#321011yescharacteristic, complemented
478C2—121no—
479C2—242no—
480C2C3×#571511yescharacteristic
481C2C2×C3×#91811yescharacteristic
482C2C2×C3×#91911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#494C2
socleC22×C32C22×D4
prime radicalC3×#5725C2
hypercenterC3×#494D3
hypocenterC3C3×#3210
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#494

Complements

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

NH ≅ G/Ntype
1. C3×#5728C2semidirect
3. C32×#494C2semidirect
4. C3×#5187C2semidirect
5. C3×#5185C2semidirect
6. C3×#5085C2semidirect
7. C3×#5079C2semidirect
8. C3×#4694C2semidirect
9. C3×#4685C2semidirect
11. #81803C3direct (N × H)
39. #5728C2×C3semidirect
42. C3×#494D3semidirect
43. C3×#494C2×C3semidirect
50. #5187C2×C3semidirect
51. #5185C2×C3semidirect
52. #5085C2×C3semidirect
53. #5079C2×C3semidirect
54. #4694C2×C3semidirect
55. #4685C2×C3semidirect
169. #494C3×D3semidirect
421. C32#3210semidirect
476. C3#81803direct (N × H)
477. C3C3×#3210semidirect

Maximal subgroups

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

subgroupindex
C3×#57282
C3×#57252
C32×#4942
C3×#51872
C3×#51852
C3×#50852
C3×#50792
C3×#46942
C3×#46852
C3×#32103
#818033