Finite Group Databasebeta

← C3×#10590472 #13157451

Subgroups — C3×#10590472 #13157451

Order 1728.

612 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64097C211yesmaximal, characteristic, complemented
2C3×#63898C211yesmaximal, characteristic
3C32×#809C211yesmaximal, characteristic
4C32×#808C211yesmaximal, characteristic, complemented
5C3×#63573C211yesmaximal, characteristic, complemented
6C3×#63572C211yesmaximal, characteristic, complemented
7C3×#63563C211yesmaximal, characteristic
8C3×#4870—31nomaximal
9C3×#4761—31nomaximal
10#10590472C311yesmaximal, characteristic, direct product factor
11C2×C3×#634—21no—
12C2×C32×D12C2211yescharacteristic
13C2×C3×D3×Dic3—21no—
14C33×C4⋊C4C2211yescharacteristic
15C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C3×#3750—21no—
17C3×C4×C3⋊Dic3C2211yescharacteristic
18C32×C4⋊Dic3C2211yescharacteristic
19C2×C32×C3⋊C8C2211yescharacteristic
20C2×C32×C3⋊C8C2211yescharacteristic
21C3×(C2×D3)⋊Dic3—21no—
22#64097C2×C311yescharacteristic, complemented
23C3×D4×Dic3—31no—
24C3×#893—31no—
25C3×#888—31no—
26C3×#888—31no—
27C3×#888—61no—
28#63898C2×C311yescharacteristic
29C32×#106—31no—
30C32×#102—31no—
31C3×#832—31no—
32C3×#821—31no—
33C3×#817—31no—
34C3×Dic3⋊C8—31no—
35C3×Dic3⋊C8—31no—
36C3×#809—21no—
37C3×#809D311yescharacteristic
38C3×#809C2×C311yescharacteristic
39C3×#808—21no—
40C3×#808—31no—
41C3×#808D311yescharacteristic, complemented
42C3×#808C2×C311yescharacteristic, complemented
43#63573C2×C311yescharacteristic, complemented
44#63572C2×C311yescharacteristic, complemented
45#63563C2×C311yescharacteristic
46C22×C32×D3—21no—
47C2×C33×C4—21no—
48C2×C33×C4C2311yescharacteristic
49C2×C3×C3⋊Dic3—21no—
50C2×C3×C3⋊Dic3D411yescharacteristic
51C2×C3×C3⋊Dic3D411yescharacteristic
52C3×#634—42no—
53C2×C32×Dic3—21no—
54C32×D12—21no—
55C32×D12Q812yescomplemented
56C3×D3×Dic3—42no—
57C32×C3⋊C8—21no—
58C32×C3⋊C8—21no—
59C3×#476—91no—
60#4870—31no—
61#4761—31no—
62C2×C32×D4—31no—
63C2×#634—21no—
64C22×C3×Dic3—61no—
65C2×C3×D12—21no—
66C2×C3×D12C2×D311yescharacteristic
67C2×C3×D12C22×C311yescharacteristic
68C2×C3×C4×D3—61no—
69C2×C3×Dic6—61no—
70C2×C3×Dic6—61no—
71C2×C3×Dic6—62no—
72C2×D3×Dic3—21no—
73C2×C32×C8—31no—
74C2×C32×C8—31no—
75C32×C4⋊C4—21no—
76C32×C4⋊C4—21no—
77C32×C4⋊C4—21no—
78C32×C4⋊C4—31no—
79C32×C4⋊C4—41no—
80C32×C4⋊C4C2×D311yescharacteristic
81C32×C4⋊C4C2×D311yescharacteristic
82C32×C4⋊C4C22×C311yescharacteristic
83C4⋊(C3⋊Dic3)C22×C311yescharacteristic
84#3750—21no—
85C4×C3⋊Dic3C22×C311yescharacteristic
86C3×#217—61no—
87C3×(C2×D3)⋊C4—61no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—31no—
90C3×C4⋊Dic3—31no—
91C3×C4⋊Dic3—61no—
92C3×C4⋊Dic3C2×D311yescharacteristic
93C3×C4⋊Dic3C22×C311yescharacteristic
94C3×Dic3⋊C4—61no—
95C3×Dic3⋊C4—61no—
96C3×Dic3⋊C4—62no—
97C3×C4×Dic3—31no—
98C3×C4×Dic3—31no—
99C3×C4×Dic3—61no—
100C2×C3×C3⋊C8—21no—
101C2×C3×C3⋊C8—21no—
102C2×C3×C3⋊C8C2×D311yescharacteristic
103C2×C3×C3⋊C8C2×D311yescharacteristic
104C2×C3×C3⋊C8C22×C311yescharacteristic
105C2×C3×C3⋊C8C22×C311yescharacteristic
106(C2×D3)⋊Dic3—21no—
107C22×C33C2×D411yescharacteristic
108C2×C32×D3—22no—
109C2×C32×D3—41no—
110C2×C32×D3—41no—
111C33×C4—41no—
112C33×C4C2×Q811yescharacteristic
113C33×C4#4111yescharacteristic
114C3×C3⋊Dic3—21no—
115C3×C3⋊Dic3—41no—
116C3×C3⋊Dic3SD1612yes—
117C32×Dic3—41no—
118C3×C4⋊Q8—91no—
119C3×C4×D4—91no—
120D4×Dic3—31no—
121#893—31no—
122#888—31no—
123#888—31no—
124#888—61no—
125C3×#106—31no—
126C3×#106—31no—
127C3×#106—61no—
128C3×#106—91no—
129C3×C4⋊C8—91no—
130C3×#102—31no—
131C3×#102—31no—
132C3×#102—61no—
133C3×#102—91no—
134#832—31no—
135#821—31no—
136#817—31no—
137Dic3⋊C8—31no—
138Dic3⋊C8—31no—
139#809C3×D311yescharacteristic
140#808—31no—
141#808C3×D311yescharacteristic, complemented
142C23×C32—61no—
143C22×C3×D3—21no—
144C22×C3×D3—21no—
145C22×C3×D3—41no—
146C32×D4—32no—
147C32×D4—61no—
148C2×C32×C4—21no—
149C2×C32×C4—22no—
150C2×C32×C4—21no—
151C2×C32×C4—21no—
152C2×C32×C4—21no—
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4—41no—
156C2×C32×C4—41no—
157C2×C32×C4—41no—
158C2×C32×C4—42no—
159C2×C32×C4—61no—
160C2×C32×C4C22×D311yescharacteristic
161C2×C32×C4C22×D311yescharacteristic
162C2×C32×C4C23×C311yescharacteristic
163C2×C3⋊Dic3—21no—
164C2×C3⋊Dic3C3×D411yescharacteristic
165C2×C3⋊Dic3C3×D411yescharacteristic
166#634—42no—
167C2×C3×Dic3—21no—
168C2×C3×Dic3—21no—
169C2×C3×Dic3—31no—
170C2×C3×Dic3—31no—
171C2×C3×Dic3—31no—
172C2×C3×Dic3—31no—
173C2×C3×Dic3—41no—
174C2×C3×Dic3—61no—
175C2×C3×Dic3—61no—
176C2×C3×Dic3—62no—
177C2×C3×Dic3—61no—
178C2×C3×Dic3—61no—
179C2×C3×Dic3—122no—
180C3×D12—21no—
181C3×D12—21no—
182C3×D12—22no—
183C3×D12—41no—
184C3×D12Dic612yescomplemented
185C3×D12C3×Q812yescomplemented
186C3×C4×D3—122no—
187C3×Dic6—124no—
188C3×Dic6—122no—
189C3×Dic6—122no—
190D3×Dic3—42no—
191C32×C8—61no—
192C32×C8—61no—
193C3×C3⋊C8—22no—
194C3×C3⋊C8—21no—
195C3×C3⋊C8—21no—
196C3×C3⋊C8—21no—
197C3×C3⋊C8—21no—
198C3×C3⋊C8—41no—
199#476—91noSylow
200C2×C33C22⋊Q811yescharacteristic
201C2×C33C2×SD1611yescharacteristic
202C2×C33AGL(1,ℤ/8)11yescharacteristic
203C32×D3—42no—
204C2×C3×Q8—181no—
205C2×C3×D4—31no—
206C2×C3×D4—31no—
207C2×C3×D4—61no—
208C22×C3×C4—181no—
209C22×Dic3—61no—
210C2×D12C2×C3×D311yescharacteristic
211C2×C4×D3—61no—
212C2×Dic6—61no—
213C2×Dic6—61no—
214C2×Dic6—62no—
215C2×C3×C8—31no—
216C2×C3×C8—31no—
217C2×C3×C8—31no—
218C2×C3×C8—31no—
219C2×C3×C8—61no—
220C2×C3×C8—61no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—31no—
225C3×C4⋊C4—31no—
226C3×C4⋊C4—41no—
227C3×C4⋊C4—61no—
228C3×C4⋊C4—91no—
229C3×C4⋊C4—181no—
230C3×C4⋊C4D3211yescharacteristic
231C3×C4⋊C4C2×C3×D311yescharacteristic
232C3×C4⋊C4C2×C3×D311yescharacteristic
233C3×C22⋊C4—181no—
234C3×C42—91no—
235#217—61no—
236(C2×D3)⋊C4—61no—
237C4⋊Dic3—31no—
238C4⋊Dic3—31no—
239C4⋊Dic3—61no—
240C4⋊Dic3C2×C3×D311yescharacteristic
241Dic3⋊C4—61no—
242Dic3⋊C4—61no—
243Dic3⋊C4—62no—
244C4×Dic3—31no—
245C4×Dic3—31no—
246C4×Dic3—61no—
247C2×C3⋊C8C2×C3×D311yescharacteristic
248C2×C3⋊C8C2×C3×D311yescharacteristic
249C22×C32—21no—
250C22×C32—21no—
251C22×C32—21no—
252C22×C32—41no—
253C22×C32—62no—
254C22×C32—121no—
255C22×C32—121no—
256C22×C32D3×D411yescharacteristic
257C22×C32D3×D411yescharacteristic
258C22×C32C2×C3×D411yescharacteristic
259C2×C3×D3—22no—
260C2×C3×D3—22no—
261C2×C3×D3—42no—
262C2×C3×D3—41no—
263C2×C3×D3—41no—
264C2×C3×D3—41no—
265C2×C3×D3—41no—
266C2×C3×D3—81no—
267C2×C3×D3—81no—
268C32×C4—21no—
269C32×C4—21no—
270C32×C4—21no—
271C32×C4—21no—
272C32×C4—21no—
273C32×C4—21no—
274C32×C4—41no—
275C32×C4—41no—
276C32×C4—41no—
277C32×C4—42no—
278C32×C4—41no—
279C32×C4—41no—
280C32×C4—81no—
281C32×C4—81no—
282C32×C4—82no—
283C32×C4—121no—
284C32×C4C2×Dic611yescharacteristic
285C32×C4#23511yescharacteristic
286C32×C4#23711yescharacteristic
287C32×C4D3×Q811yescharacteristic
288C32×C4C2×C3×Q811yescharacteristic
289C32×C4C3×#4111yescharacteristic
290C3⋊Dic3—21no—
291C3⋊Dic3—41no—
292C3⋊Dic3C3×SD1612yes—
293C3×Dic3—32no—
294C3×Dic3—32no—
295C3×Dic3—41no—
296C3×Dic3—41no—
297C3×Dic3—62no—
298C3×Dic3—62no—
299C3×Dic3—61no—
300C3×Dic3—61no—
301C3×Dic3—81no—
302C3×Dic3—122no—
303C3×Dic3—121no—
304C3×Dic3—121no—
305C4⋊Q8—91no—
306C4×D4—91no—
307#106—31no—
308#106—91no—
309C4⋊C8—91no—
310#102—31no—
311#102—91no—
312C33#47611yescharacteristic, complemented, Sylow
313C23×C3—61no—
314C23×C3—61no—
315C23×C3—121no—
316C22×D3—21no—
317C3×Q8—362no—
318C3×D4—32no—
319C3×D4—32no—
320C3×D4—62no—
321C3×D4—61no—
322C3×D4—61no—
323C3×D4—121no—
324C2×C3×C4—22no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—41no—
332C2×C3×C4—41no—
333C2×C3×C4—42no—
334C2×C3×C4—41no—
335C2×C3×C4—61no—
336C2×C3×C4—61no—
337C2×C3×C4—91no—
338C2×C3×C4—91no—
339C2×C3×C4—121no—
340C2×C3×C4—181no—
341C2×C3×C4—362no—
342C2×C3×C4C2×D3211yescharacteristic
343C2×C3×C4C22×C3×D311yescharacteristic
344C2×C3×C4C22×C3×D311yescharacteristic
345C2×Dic3—21no—
346C2×Dic3—31no—
347C2×Dic3—31no—
348C2×Dic3—31no—
349C2×Dic3—31no—
350C2×Dic3—61no—
351C2×Dic3—61no—
352C2×Dic3—62no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355C2×Dic3—122no—
356D12—21no—
357D12C3×Dic612yescomplemented
358C4×D3—122no—
359Dic6—124no—
360Dic6—122no—
361Dic6—122no—
362C3×C8—62no—
363C3×C8—61no—
364C3×C8—61no—
365C3×C8—61no—
366C3×C8—61no—
367C3×C8—121no—
368C3⋊C8—21no—
369C3⋊C8—21no—
370C2×C32—21no—
371C2×C32—21no—
372C2×C32—21no—
373C2×C32—21no—
374C2×C32—21no—
375C2×C32—21no—
376C2×C32—21no—
377C2×C32—21no—
378C2×C32—21no—
379C2×C32—41no—
380C2×C32—41no—
381C2×C32—41no—
382C2×C32—122no—
383C2×C32#87811yescharacteristic
384C2×C32#89611yescharacteristic
385C2×C32#91111yescharacteristic
386C2×C32D3×SD1611yescharacteristic
387C2×C32D3×SD1611yescharacteristic
388C2×C32#91411yescharacteristic
389C2×C32C3×C22⋊Q811yescharacteristic
390C2×C32C2×C3×SD1611yescharacteristic
391C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
392C3×D3—42no—
393C3×D3—42no—
394C3×D3—82no—
395C2×Q8—181no—
396C2×D4—31no—
397C22×C4—181no—
398C2×C8—31no—
399C2×C8—31no—
400C4⋊C4—31no—
401C4⋊C4—91no—
402C4⋊C4—181no—
403C4⋊C4C3×D3211yescharacteristic
404C22⋊C4—181no—
405C42—91no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—41no—
410C22×C3—62no—
411C22×C3—62no—
412C22×C3—122no—
413C22×C3—121no—
414C22×C3—121no—
415C22×C3—121no—
416C22×C3—121no—
417C22×C3—241no—
418C22×C3—241no—
419C22×C3#381111yescharacteristic
420C22×C3C3×D3×D411yescharacteristic
421C22×C3C3×D3×D411yescharacteristic
422C2×D3—22no—
423C2×D3—41no—
424C2×D3—41no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—42no—
432C3×C4—41no—
433C3×C4—41no—
434C3×C4—41no—
435C3×C4—41no—
436C3×C4—41no—
437C3×C4—81no—
438C3×C4—81no—
439C3×C4—82no—
440C3×C4—92no—
441C3×C4—121no—
442C3×C4—121no—
443C3×C4—181no—
444C3×C4—241no—
445C3×C4—361no—
446C3×C4D3×Dic611yescharacteristic
447C3×C4#379511yescharacteristic
448C3×C4C2×C3×Dic611yescharacteristic
449C3×C4C3×#23511yescharacteristic
450C3×C4C3×#23711yescharacteristic
451C3×C4C3×D3×Q811yescharacteristic
452Dic3—32no—
453Dic3—32no—
454Dic3—41no—
455Dic3—62no—
456Dic3—62no—
457Dic3—61no—
458Dic3—61no—
459Dic3—122no—
460Dic3—121no—
461Dic3—121no—
462C32—21no—
463C32—21no—
464C32—21no—
465C32—41no—
466C32#476111yescharacteristic, complemented
467C32#487011yescharacteristic, complemented
468C32C3×#47611yescharacteristic, complemented
469C23—61no—
470Q8—362no—
471D4—32no—
472D4—61no—
473C2×C4—21no—
474C2×C4—61no—
475C2×C4—91no—
476C2×C4—91no—
477C2×C4—181no—
478C2×C4—362no—
479C2×C4C2×C3×D3211yescharacteristic
480C8—61no—
481C8—61no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—41no—
492C2×C3—41no—
493C2×C3—41no—
494C2×C3—122no—
495C2×C3—122no—
496C2×C3—242no—
497C2×C3#6389611yescharacteristic
498C2×C3#6393711yescharacteristic
499C2×C3#6394011yescharacteristic
500C2×C3C3×#87811yescharacteristic
501C2×C3C3×#89611yescharacteristic
502C2×C3C3×#91111yescharacteristic
503C2×C3C3×D3×SD1611yescharacteristic
504C2×C3C3×D3×SD1611yescharacteristic
505C2×C3C3×#91411yescharacteristic
506D3—42no—
507C22—62no—
508C22—121no—
509C22—121no—
510C22C3×#381111yescharacteristic
511C4—41no—
512C4—92no—
513C4—121no—
514C4—181no—
515C4—361no—
516C4C3×D3×Dic611yescharacteristic
517C4C3×#379511yescharacteristic
518C3—21no—
519C3—21no—
520C3—21no—
521C3—41no—
522C3#1059047211yescharacteristic, direct product factor
523C3C3×#476111yescharacteristic, complemented
524C3C3×#487011yescharacteristic, complemented
525C2—122no—
526C2C3×#6389611yescharacteristic
527C2C3×#6393711yescharacteristic
528C2C3×#6394011yescharacteristic
subgroupG/H
centerC22×C3#3811
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C2×C3×D32
FittingC33×C4⋊C4C22
socleC22×C33C2×D4
prime radicalC2×C32×D12C22
hypercenterC3×C4⋊C4D32
hypocenterC32C3×#476
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#64097C2semidirect
4. C32×#808C2semidirect
5. C3×#63573C2semidirect
6. C3×#63572C2semidirect
10. #10590472C3direct (N × H)
22. #64097C2×C3semidirect
41. C3×#808D3semidirect
42. C3×#808C2×C3semidirect
43. #63573C2×C3semidirect
44. #63572C2×C3semidirect
55. C32×D12Q8semidirect
141. #808C3×D3semidirect
184. C3×D12Dic6semidirect
185. C3×D12C3×Q8semidirect
312. C33#476semidirect
357. D12C3×Dic6semidirect
466. C32#4761semidirect
467. C32#4870semidirect
468. C32C3×#476semidirect
522. C3#10590472direct (N × H)
523. C3C3×#4761semidirect
524. C3C3×#4870semidirect

Maximal subgroups

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

subgroupindex
C3×#640972
C3×#638982
C32×#8092
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