Finite Group Databasebeta

← C3×#10590377 #13157390

Subgroups — C3×#10590377 #13157390

Order 1728.

758 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#634C211yesmaximal, characteristic, complemented
2C32×#874C211yesmaximal, characteristic
3C2×C3×#3716C212yesmaximal, complemented
4C32×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
5C3×#63563C212yesmaximal, complemented
6C3×#5075—31nomaximal
7C3×#4848—31nomaximal
8#10590377C311yesmaximal, characteristic, direct product factor
9C2×C3×#634C2211yescharacteristic
10C2×C32×D12—21no—
11C2×C32×D12—21no—
12C2×C32×D12C2212yes—
13C33×C42C2211yescharacteristic
14C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C3×#3750—21no—
16C3×C4×C3⋊Dic3—21no—
17C2×C32×C3⋊C8C2212yes—
18C3×#3716—24no—
19C32×#127—31no—
20C4×#634C2×C311yescharacteristic, complemented
21C2×C3×#214—32no—
22C2×C3×#204—32no—
23C3×#874—21no—
24C3×#874D311yescharacteristic
25C3×#874C2×C311yescharacteristic
26C3×C4×Dic6—31no—
27C3×C4×Dic6—31no—
28C3×C4×Dic6—61no—
29C2×#3716C2×C312yescomplemented
30C32×C4⋊C8—31no—
31C3×#832—32no—
32C3×#821—32no—
33C3×C4⋊(C3⋊C8)—21no—
34C3×C4⋊(C3⋊C8)D311yescharacteristic, complemented
35C3×C4⋊(C3⋊C8)C2×C311yescharacteristic, complemented
36#63563C2×C312yescomplemented
37C22×C32×D3—22no—
38C2×C33×C4D411yescharacteristic
39C2×C33×C4D411yescharacteristic
40C2×C33×C4C2311yescharacteristic
41C2×C3×C3⋊Dic3—21no—
42C2×C3×C3⋊Dic3—21no—
43C3×#634—21no—
44C3×#634D412yescomplemented
45C32×D12—22no—
46C32×D12—22no—
47C32×D12—42no—
48C32×D12—42no—
49C32×C3⋊C8—22no—
50C3×#460—91no—
51#5075—31no—
52#4848—31no—
53C2×C32×D4—32no—
54C2×C32×D4—61no—
55C2×C32×D4—61no—
56C2×#634C22×C311yescharacteristic
57C2×C3×D12—22no—
58C2×C3×D12—22no—
59C2×C3×D12—22no—
60C2×C3×D12—21no—
61C2×C3×D12—21no—
62C2×C3×D12—21no—
63C2×C3×D12—21no—
64C2×C3×D12C2×D312yes—
65C2×C3×D12C22×C312yes—
66C2×C3×Dic6—31no—
67C2×C3×Dic6—31no—
68C2×C3×Dic6—61no—
69C2×C32×C8—32no—
70C32×C42—21no—
71C32×C42—21no—
72C32×C42—21no—
73C32×C42—41no—
74C32×C42C2×D311yescharacteristic
75C32×C42C2×D311yescharacteristic
76C32×C42C22×C311yescharacteristic
77C4⋊(C3⋊Dic3)C22×C311yescharacteristic
78#3750—21no—
79C4×C3⋊Dic3—21no—
80C3×#214—64no—
81C3×C4⋊Dic3—31no—
82C3×C4⋊Dic3—31no—
83C3×C4⋊Dic3—61no—
84C3×Dic3⋊C4—62no—
85C3×Dic3⋊C4—61no—
86C3×Dic3⋊C4—61no—
87C3×C4×Dic3—62no—
88C3×C4×Dic3—61no—
89C3×C4×Dic3—61no—
90C2×C3×C3⋊C8—22no—
91C2×C3×C3⋊C8C2×D312yes—
92C2×C3×C3⋊C8C22×C312yes—
93C3×#204—64no—
94#3716—24no—
95C22×C33C2×D411yescharacteristic
96C2×C32×D3—42no—
97C2×C32×D3—42no—
98C2×C32×D3—42no—
99C33×C4—21no—
100C33×C4SD1612yescomplemented
101C33×C4C2×D411yescharacteristic
102C33×C4#4111yescharacteristic
103C3×C3⋊Dic3—22no—
104C3×C3⋊Dic3—41no—
105C2×C3×SD16—92no—
106C3×#127—31no—
107C3×#127—31no—
108C3×#127—61no—
109C3×C4×Q8—91no—
110C2×#214—32no—
111C2×#204—32no—
112#874C3×D311yescharacteristic
113C4×Dic6—31no—
114C4×Dic6—31no—
115C4×Dic6—61no—
116C3×C4⋊C8—31no—
117C3×C4⋊C8—31no—
118C3×C4⋊C8—61no—
119C3×#102—92no—
120#832—32no—
121#821—32no—
122C4⋊(C3⋊C8)C3×D311yescharacteristic, complemented
123C23×C32—62no—
124C22×C3×D3—24no—
125C22×C3×D3—22no—
126C22×C3×D3—22no—
127C32×D4—62no—
128C32×D4—62no—
129C32×D4—122no—
130C32×D4—122no—
131C2×C32×C4—21no—
132C2×C32×C4—21no—
133C2×C32×C4—21no—
134C2×C32×C4—21no—
135C2×C32×C4—21no—
136C2×C32×C4—21no—
137C2×C32×C4—21no—
138C2×C32×C4—21no—
139C2×C32×C4—21no—
140C2×C32×C4—41no—
141C2×C32×C4—41no—
142C2×C32×C4—41no—
143C2×C32×C4D1211yescharacteristic
144C2×C32×C4D1211yescharacteristic
145C2×C32×C4#6711yescharacteristic
146C2×C32×C4#6711yescharacteristic
147C2×C32×C4C3×D411yescharacteristic
148C2×C32×C4C3×D411yescharacteristic
149C2×C32×C4C22×D311yescharacteristic
150C2×C32×C4C22×D311yescharacteristic
151C2×C32×C4C23×C311yescharacteristic
152C2×C3⋊Dic3—21no—
153C2×C3⋊Dic3—21no—
154#634—21no—
155#634C3×D412yescomplemented
156C2×C3×Dic3—62no—
157C2×C3×Dic3—61no—
158C2×C3×Dic3—61no—
159C2×C3×Dic3—62no—
160C2×C3×Dic3—61no—
161C2×C3×Dic3—61no—
162C3×D12—22no—
163C3×D12—22no—
164C3×D12—22no—
165C3×D12—22no—
166C3×D12—42no—
167C3×D12—42no—
168C3×D12—44no—
169C3×D12—42no—
170C3×D12—42no—
171C3×D12—44no—
172C3×D12—42no—
173C3×D12—42no—
174C3×Dic6—32no—
175C3×Dic6—32no—
176C3×Dic6—62no—
177C3×Dic6—62no—
178C3×Dic6—61no—
179C3×Dic6—61no—
180C32×C8—62no—
181C3×C3⋊C8—22no—
182C3×C3⋊C8—22no—
183C3×C3⋊C8—42no—
184#460—91noSylow
185C2×C33#12111yescharacteristic
186C2×C33C2×SD1611yescharacteristic
187C2×C33AGL(1,ℤ/8)11yescharacteristic
188C32×D3—82no—
189C2×C3×Q8—91no—
190C2×C3×D4—32no—
191C2×C3×D4—32no—
192C2×C3×D4—62no—
193C2×C3×D4—62no—
194C2×C3×D4—62no—
195C2×C3×D4—61no—
196C2×C3×D4—61no—
197C2×C3×D4—61no—
198C2×C3×D4—61no—
199C2×D12—21no—
200C2×D12—21no—
201C2×D12C2×C3×D312yes—
202C2×Dic6—31no—
203C2×Dic6—31no—
204C2×Dic6—61no—
205C3×SD16—184no—
206C2×C3×C8—32no—
207C2×C3×C8—32no—
208C2×C3×C8—62no—
209C3×C4⋊C4—91no—
210C3×C4⋊C4—181no—
211C3×C42—21no—
212C3×C42—21no—
213C3×C42—21no—
214C3×C42—41no—
215C3×C42—181no—
216C3×C42D3211yescharacteristic
217C3×C42C2×C3×D311yescharacteristic
218C3×C42C2×C3×D311yescharacteristic
219#214—64no—
220C4⋊Dic3—31no—
221C4⋊Dic3—31no—
222C4⋊Dic3—61no—
223Dic3⋊C4—62no—
224Dic3⋊C4—61no—
225Dic3⋊C4—61no—
226C4×Dic3—62no—
227C4×Dic3—61no—
228C4×Dic3—61no—
229C2×C3⋊C8C2×C3×D312yes—
230#204—64no—
231C22×C32—21no—
232C22×C32—21no—
233C22×C32—21no—
234C22×C32—41no—
235C22×C32—122no—
236C22×C32—122no—
237C22×C32—122no—
238C22×C32C2×D1211yescharacteristic
239C22×C32C2×#6711yescharacteristic
240C22×C32C2×C3×D411yescharacteristic
241C2×C3×D3—44no—
242C2×C3×D3—44no—
243C2×C3×D3—44no—
244C2×C3×D3—42no—
245C2×C3×D3—42no—
246C2×C3×D3—42no—
247C2×C3×D3—42no—
248C2×C3×D3—42no—
249C2×C3×D3—42no—
250C32×C4—21no—
251C32×C4—22no—
252C32×C4—21no—
253C32×C4—21no—
254C32×C4—22no—
255C32×C4—22no—
256C32×C4—22no—
257C32×C4—21no—
258C32×C4—21no—
259C32×C4—21no—
260C32×C4—21no—
261C32×C4—21no—
262C32×C4—21no—
263C32×C4—42no—
264C32×C4—41no—
265C32×C4—41no—
266C32×C4—41no—
267C32×C4—41no—
268C32×C4—42no—
269C32×C4#20412yescomplemented
270C32×C4#21412yescomplemented
271C32×C4C3×SD1612yescomplemented
272C32×C4D3×D411yescharacteristic
273C32×C4D3×D411yescharacteristic
274C32×C4#23711yescharacteristic
275C32×C4#23911yescharacteristic
276C32×C4C2×C3×D411yescharacteristic
277C32×C4C3×#4111yescharacteristic
278C3⋊Dic3—22no—
279C3⋊Dic3—41no—
280C3×Dic3—64no—
281C3×Dic3—62no—
282C3×Dic3—62no—
283C3×Dic3—122no—
284C3×Dic3—121no—
285C3×Dic3—121no—
286C2×SD16—92no—
287#127—31no—
288C4×Q8—91no—
289C4⋊C8—31no—
290#102—92no—
291C33#46011yescharacteristic, complemented, Sylow
292C23×C3—64no—
293C23×C3—62no—
294C23×C3—62no—
295C22×D3—22no—
296C3×Q8—92no—
297C3×Q8—181no—
298C3×D4—62no—
299C3×D4—62no—
300C3×D4—62no—
301C3×D4—62no—
302C3×D4—122no—
303C3×D4—122no—
304C3×D4—124no—
305C3×D4—122no—
306C3×D4—122no—
307C3×D4—124no—
308C3×D4—122no—
309C3×D4—122no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—181no—
323C2×C3×C4—181no—
324C2×C3×C4#62611yescharacteristic
325C2×C3×C4#62611yescharacteristic
326C2×C3×C4C3×D1211yescharacteristic
327C2×C3×C4C3×D1211yescharacteristic
328C2×C3×C4C3×#6711yescharacteristic
329C2×C3×C4C3×#6711yescharacteristic
330C2×C3×C4C2×D3211yescharacteristic
331C2×C3×C4C22×C3×D311yescharacteristic
332C2×C3×C4C22×C3×D311yescharacteristic
333C2×Dic3—62no—
334C2×Dic3—61no—
335C2×Dic3—61no—
336C2×Dic3—62no—
337C2×Dic3—61no—
338C2×Dic3—61no—
339D12—22no—
340D12—22no—
341D12—42no—
342D12—42no—
343Dic6—32no—
344Dic6—32no—
345Dic6—62no—
346Dic6—62no—
347Dic6—61no—
348Dic6—61no—
349C3×C8—62no—
350C3×C8—62no—
351C3×C8—122no—
352C3⋊C8—22no—
353C2×C32—21no—
354C2×C32—21no—
355C2×C32—21no—
356C2×C32—21no—
357C2×C32—21no—
358C2×C32—21no—
359C2×C32—21no—
360C2×C32—21no—
361C2×C32—21no—
362C2×C32—41no—
363C2×C32—41no—
364C2×C32—41no—
365C2×C32—242no—
366C2×C32#89511yescharacteristic
367C2×C32C2×#20411yescharacteristic
368C2×C32#90811yescharacteristic
369C2×C32#93211yescharacteristic
370C2×C32C2×#21411yescharacteristic
371C2×C32#93811yescharacteristic
372C2×C32C3×#12111yescharacteristic
373C2×C32C2×C3×SD1611yescharacteristic
374C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
375C3×D3—84no—
376C3×D3—82no—
377C3×D3—82no—
378C2×Q8—91no—
379C2×D4—32no—
380C2×D4—61no—
381C2×D4—61no—
382SD16—184no—
383C2×C8—32no—
384C4⋊C4—91no—
385C4⋊C4—181no—
386C42—181no—
387C42C3×D3211yescharacteristic
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—41no—
392C22×C3—124no—
393C22×C3—124no—
394C22×C3—124no—
395C22×C3—122no—
396C22×C3—122no—
397C22×C3—122no—
398C22×C3—122no—
399C22×C3—122no—
400C22×C3—122no—
401C22×C3C2×#62611yescharacteristic
402C22×C3C2×C3×D1211yescharacteristic
403C22×C3C2×C3×#6711yescharacteristic
404C2×D3—42no—
405C2×D3—42no—
406C2×D3—42no—
407C3×C4—22no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—22no—
418C3×C4—22no—
419C3×C4—22no—
420C3×C4—41no—
421C3×C4—41no—
422C3×C4—42no—
423C3×C4—41no—
424C3×C4—41no—
425C3×C4—42no—
426C3×C4—182no—
427C3×C4—361no—
428C3×C4#371612yescomplemented
429C3×C4C3×#20412yescomplemented
430C3×C4C3×#21412yescomplemented
431C3×C4#379611yescharacteristic
432C3×C4#380211yescharacteristic
433C3×C4C3×D3×D411yescharacteristic
434C3×C4C3×D3×D411yescharacteristic
435C3×C4C3×#23711yescharacteristic
436C3×C4C3×#23911yescharacteristic
437Dic3—64no—
438Dic3—62no—
439Dic3—62no—
440Dic3—122no—
441Dic3—121no—
442Dic3—121no—
443C32—21no—
444C32—21no—
445C32—21no—
446C32—41no—
447C32#484811yescharacteristic, complemented
448C32#507511yescharacteristic, complemented
449C32C3×#46011yescharacteristic, complemented
450C23—62no—
451Q8—92no—
452Q8—181no—
453D4—62no—
454D4—62no—
455D4—122no—
456D4—122no—
457C2×C4—181no—
458C2×C4—181no—
459C2×C4C3×#62611yescharacteristic
460C2×C4C3×#62611yescharacteristic
461C2×C4C2×C3×D3211yescharacteristic
462C8—62no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—41no—
473C2×C3—41no—
474C2×C3—41no—
475C2×C3—244no—
476C2×C3—242no—
477C2×C3—242no—
478C2×C3C2×#371611yescharacteristic
479C2×C3#6383011yescharacteristic
480C2×C3#6391611yescharacteristic
481C2×C3C3×#89511yescharacteristic
482C2×C3C2×C3×#20411yescharacteristic
483C2×C3C3×#90811yescharacteristic
484C2×C3C3×#93211yescharacteristic
485C2×C3C2×C3×#21411yescharacteristic
486C2×C3C3×#93811yescharacteristic
487D3—82no—
488C22—122no—
489C22—122no—
490C22—122no—
491C22C2×C3×#62611yescharacteristic
492C4—21no—
493C4—182no—
494C4—361no—
495C4C3×#371612yescomplemented
496C4C3×#379611yescharacteristic
497C4C3×#380211yescharacteristic
498C3—21no—
499C3—21no—
500C3—21no—
501C3—41no—
502C3#1059037711yescharacteristic, direct product factor
503C3C3×#484811yescharacteristic, complemented
504C3C3×#507511yescharacteristic, complemented
505C2—242no—
506C2C2×C3×#371611yescharacteristic
507C2C3×#6383011yescharacteristic
508C2C3×#6391611yescharacteristic
subgroupG/H
centerC22×C3C2×#626
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C2×C3×D32
FittingC33×C42C22
socleC22×C33C2×D4
prime radicalC32×#874C2
hypercenterC3×C42D32
hypocenterC32C3×#460
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C3×C42

Complements

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

NH ≅ G/Ntype
1. C3×C4×#634C2semidirect
3. C2×C3×#3716C2semidirect
4. C32×C4⋊(C3⋊C8)C2semidirect
5. C3×#63563C2semidirect
8. #10590377C3direct (N × H)
20. C4×#634C2×C3semidirect
29. C2×#3716C2×C3semidirect
34. C3×C4⋊(C3⋊C8)D3semidirect
35. C3×C4⋊(C3⋊C8)C2×C3semidirect
36. #63563C2×C3semidirect
44. C3×#634D4semidirect
100. C33×C4SD16semidirect
122. C4⋊(C3⋊C8)C3×D3semidirect
155. #634C3×D4semidirect
269. C32×C4#204semidirect
270. C32×C4#214semidirect
271. C32×C4C3×SD16semidirect
291. C33#460semidirect
428. C3×C4#3716semidirect
429. C3×C4C3×#204semidirect
430. C3×C4C3×#214semidirect
447. C32#4848semidirect
448. C32#5075semidirect
449. C32C3×#460semidirect
495. C4C3×#3716semidirect
502. C3#10590377direct (N × H)
503. C3C3×#4848semidirect
504. C3C3×#5075semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#6342
C32×#8742
C2×C3×#37162
C32×C4⋊(C3⋊C8)2
C3×#635632
C3×#50753
C3×#48483
#105903773