Finite Group Databasebeta

← C3×#10590505 #13157476

Subgroups — C3×#10590505 #13157476

Order 1728.

612 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#892C211yesmaximal, characteristic, complemented
2C3×#63908C211yesmaximal, characteristic
3C3×#63635C211yesmaximal, characteristic, complemented
4C32×#809C211yesmaximal, characteristic, complemented
5C3×#63575C211yesmaximal, characteristic, complemented
6C3×#63562C211yesmaximal, characteristic, complemented
7C3×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C3×#5003—31nomaximal
9C3×#4784—31nomaximal
10#10590505C311yesmaximal, characteristic, direct product factor
11C2×C32×D12C2211yescharacteristic
12C2×C32×C4×D3C2211yescharacteristic
13C2×C3×#625—21no—
14C33×C4⋊C4C2211yescharacteristic
15C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
17C32×(C2×D3)⋊C4—21no—
18C32×C4⋊Dic3C2211yescharacteristic
19C32×C4×Dic3—21no—
20C2×C32×C3⋊C8C2211yescharacteristic
21C3×(C2×D3)⋊Dic3—21no—
22C32×#117—31no—
23C3×#938—31no—
24C3×#930—31no—
25C3×#892—21no—
26C3×#892D311yescharacteristic, complemented
27C3×#892C2×C311yescharacteristic, complemented
28#63908C2×C311yescharacteristic
29C32×#102—31no—
30#63635C2×C311yescharacteristic, complemented
31C3×#832—31no—
32C3×#830—31no—
33C3×(C2×D3)⋊C8—31no—
34C3×#818—31no—
35C3×#809—21no—
36C3×#809—31no—
37C3×#809D311yescharacteristic, complemented
38C3×#809C2×C311yescharacteristic, complemented
39C3×#808—31no—
40C3×#808—31no—
41C3×#808—61no—
42C3×#807—31no—
43#63575C2×C311yescharacteristic, complemented
44#63562C2×C311yescharacteristic, complemented
45(C2×D3)⋊(C3⋊C8)C2×C311yescharacteristic, complemented
46C22×C32×D3—21no—
47C22×C32×D3D411yescharacteristic
48C2×C33×C4—21no—
49C2×C33×C4C2311yescharacteristic
50C2×C3×C3⋊Dic3—21no—
51C2×C32×Dic3—21no—
52C2×C32×Dic3D411yescharacteristic
53C32×D12—21no—
54C32×D12—21no—
55C32×C4×D3—21no—
56C32×C4×D3—21no—
57C3×#625—42no—
58C3×C3⋊(C3⋊C8)—21no—
59C32×C3⋊C8—21no—
60C3×#482—91no—
61#5003—31no—
62#4784—31no—
63C2×C32×D4—31no—
64C22×C32×C4—31no—
65C2×C3×#67—61no—
66C2×C3×#67—61no—
67C2×C3×D12—21no—
68C2×C3×D12C2×D311yescharacteristic
69C2×C3×D12C22×C311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×C4×D3C2×D311yescharacteristic
72C2×C3×C4×D3C22×C311yescharacteristic
73C2×#625—21no—
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
83C32×C22⋊C4—61no—
84C32×C42—61no—
85C4⋊(C3⋊Dic3)C22×C311yescharacteristic
86C2×C3⋊(C3⋊C8)C22×C311yescharacteristic
87C3×#217—61no—
88C3×(C2×D3)⋊C4—22no—
89C3×(C2×D3)⋊C4—21no—
90C3×(C2×D3)⋊C4—21no—
91C3×(C2×D3)⋊C4—61no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3—31no—
94C3×C4⋊Dic3—31no—
95C3×C4⋊Dic3—61no—
96C3×C4⋊Dic3C2×D311yescharacteristic
97C3×C4⋊Dic3C22×C311yescharacteristic
98C3×C4×Dic3—22no—
99C3×C4×Dic3—21no—
100C3×C4×Dic3—21no—
101C2×C3×C3⋊C8—21no—
102C2×C3×C3⋊C8—31no—
103C2×C3×C3⋊C8—31no—
104C2×C3×C3⋊C8—61no—
105C2×C3×C3⋊C8C2×D311yescharacteristic
106C2×C3×C3⋊C8C22×C311yescharacteristic
107(C2×D3)⋊Dic3—21no—
108C22×C33C2×D411yescharacteristic
109C2×C32×D3—21no—
110C2×C32×D3—21no—
111C2×C32×D3—21no—
112C2×C32×D3—41no—
113C2×C32×D3—41no—
114C2×C32×D3—41no—
115C33×C4—41no—
116C33×C4#4111yescharacteristic
117C33×C4#4111yescharacteristic
118C3×C3⋊Dic3—41no—
119C32×Dic3—21no—
120C32×Dic3—41no—
121C3×#121—91no—
122C3×#117—31no—
123C3×#117—31no—
124C3×#117—61no—
125#938—31no—
126#930—31no—
127#892C3×D311yescharacteristic, complemented
128C3×#107—91no—
129C3×#106—91no—
130C3×#102—31no—
131C3×#102—31no—
132C3×#102—61no—
133C3×#102—91no—
134C3×C22⋊C8—91no—
135#832—31no—
136#830—31no—
137(C2×D3)⋊C8—31no—
138#818—31no—
139#809—31no—
140#809C3×D311yescharacteristic, complemented
141#808—31no—
142#808—31no—
143#808—61no—
144#807—31no—
145C23×C32—31no—
146C23×C32—61no—
147C22×C3×D3—21no—
148C22×C3×D3—21no—
149C22×C3×D3—21no—
150C22×C3×D3—41no—
151C22×C3×D3#6711yescharacteristic
152C22×C3×D3C3×D411yescharacteristic
153C32×D4—61no—
154C32×D4—61no—
155C2×C32×C4—21no—
156C2×C32×C4—22no—
157C2×C32×C4—21no—
158C2×C32×C4—21no—
159C2×C32×C4—21no—
160C2×C32×C4—21no—
161C2×C32×C4—21no—
162C2×C32×C4—31no—
163C2×C32×C4—41no—
164C2×C32×C4—41no—
165C2×C32×C4—41no—
166C2×C32×C4—42no—
167C2×C32×C4—61no—
168C2×C32×C4—61no—
169C2×C32×C4—61no—
170C2×C32×C4C22×D311yescharacteristic
171C2×C32×C4C22×D311yescharacteristic
172C2×C32×C4C23×C311yescharacteristic
173C2×C3⋊Dic3—21no—
174C3×#67—122no—
175C3×#67—122no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—61no—
181C2×C3×Dic3—61no—
182C2×C3×Dic3—121no—
183C2×C3×Dic3#6711yescharacteristic
184C2×C3×Dic3C3×D411yescharacteristic
185C3×D12—22no—
186C3×D12—21no—
187C3×D12—21no—
188C3×D12—21no—
189C3×D12—21no—
190C3×D12—41no—
191C3×C4×D3—22no—
192C3×C4×D3—22no—
193C3×C4×D3—21no—
194C3×C4×D3—21no—
195C3×C4×D3—21no—
196C3×C4×D3—21no—
197#625—42no—
198C32×C8—61no—
199C3⋊(C3⋊C8)—21no—
200C3×C3⋊C8—21no—
201C3×C3⋊C8—21no—
202C3×C3⋊C8—41no—
203C3×C3⋊C8—62no—
204C3×C3⋊C8—61no—
205C3×C3⋊C8—61no—
206#482—91noSylow
207C2×C33#12311yescharacteristic
208C2×C33#13511yescharacteristic
209C2×C33AGL(1,ℤ/8)11yescharacteristic
210C32×D3—41no—
211C32×D3—81no—
212C2×C3×D4—31no—
213C2×C3×D4—31no—
214C2×C3×D4—61no—
215C2×C3×D4—181no—
216C22×C3×C4—31no—
217C22×C3×C4—31no—
218C22×C3×C4—61no—
219C2×#67—61no—
220C2×#67—61no—
221C2×D12C2×C3×D311yescharacteristic
222C2×C4×D3C2×C3×D311yescharacteristic
223C2×C3×C8—31no—
224C2×C3×C8—31no—
225C2×C3×C8—61no—
226C2×C3×C8—91no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—31no—
231C3×C4⋊C4—31no—
232C3×C4⋊C4—41no—
233C3×C4⋊C4—61no—
234C3×C4⋊C4—91no—
235C3×C4⋊C4D3211yescharacteristic
236C3×C4⋊C4C2×C3×D311yescharacteristic
237C3×C4⋊C4C2×C3×D311yescharacteristic
238C3×C22⋊C4—61no—
239C3×C22⋊C4—61no—
240C3×C22⋊C4—62no—
241C3×C22⋊C4—181no—
242C3×C42—61no—
243C3×C42—61no—
244C3×C42—62no—
245#217—61no—
246(C2×D3)⋊C4—21no—
247(C2×D3)⋊C4—61no—
248C4⋊Dic3—31no—
249C4⋊Dic3—31no—
250C4⋊Dic3—61no—
251C4⋊Dic3C2×C3×D311yescharacteristic
252C4×Dic3—21no—
253C2×C3⋊C8—31no—
254C2×C3⋊C8—31no—
255C2×C3⋊C8—61no—
256C2×C3⋊C8C2×C3×D311yescharacteristic
257C22×C32—21no—
258C22×C32—21no—
259C22×C32—21no—
260C22×C32—41no—
261C22×C32—61no—
262C22×C32—61no—
263C22×C32—61no—
264C22×C32—121no—
265C22×C32—121no—
266C22×C32—121no—
267C22×C32D3×D411yescharacteristic
268C22×C32C2×#6711yescharacteristic
269C22×C32C2×C3×D411yescharacteristic
270C2×C3×D3—22no—
271C2×C3×D3—21no—
272C2×C3×D3—21no—
273C2×C3×D3—21no—
274C2×C3×D3—21no—
275C2×C3×D3—21no—
276C2×C3×D3—21no—
277C2×C3×D3—41no—
278C2×C3×D3—41no—
279C2×C3×D3—42no—
280C2×C3×D3—41no—
281C2×C3×D3—41no—
282C2×C3×D3—41no—
283C2×C3×D3—41no—
284C2×C3×D3—41no—
285C2×C3×D3—41no—
286C2×C3×D3—81no—
287C2×C3×D3—81no—
288C32×C4—21no—
289C32×C4—21no—
290C32×C4—21no—
291C32×C4—21no—
292C32×C4—21no—
293C32×C4—21no—
294C32×C4—41no—
295C32×C4—41no—
296C32×C4—41no—
297C32×C4—42no—
298C32×C4—41no—
299C32×C4—41no—
300C32×C4—61no—
301C32×C4—81no—
302C32×C4—81no—
303C32×C4—82no—
304C32×C4—121no—
305C32×C4#23511yescharacteristic
306C32×C4#23511yescharacteristic
307C32×C4#23511yescharacteristic
308C32×C4#23711yescharacteristic
309C32×C4C3×#4111yescharacteristic
310C32×C4C3×#4111yescharacteristic
311C3⋊Dic3—41no—
312C3×Dic3—22no—
313C3×Dic3—21no—
314C3×Dic3—21no—
315C3×Dic3—42no—
316C3×Dic3—41no—
317C3×Dic3—41no—
318C3×Dic3—121no—
319C3×Dic3—121no—
320C3×Dic3—241no—
321#121—91no—
322#117—31no—
323#107—91no—
324#106—91no—
325#102—31no—
326#102—91no—
327C22⋊C8—91no—
328C33#48211yescharacteristic, complemented, Sylow
329C23×C3—31no—
330C23×C3—31no—
331C23×C3—61no—
332C23×C3—61no—
333C23×C3—61no—
334C23×C3—121no—
335C22×D3—21no—
336C22×D3C3×#6711yescharacteristic
337C3×D4—62no—
338C3×D4—61no—
339C3×D4—61no—
340C3×D4—61no—
341C3×D4—61no—
342C3×D4—121no—
343C3×D4—362no—
344C2×C3×C4—22no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—31no—
352C2×C3×C4—31no—
353C2×C3×C4—41no—
354C2×C3×C4—41no—
355C2×C3×C4—42no—
356C2×C3×C4—41no—
357C2×C3×C4—61no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4—61no—
361C2×C3×C4—61no—
362C2×C3×C4—61no—
363C2×C3×C4—61no—
364C2×C3×C4—62no—
365C2×C3×C4—61no—
366C2×C3×C4—61no—
367C2×C3×C4—181no—
368C2×C3×C4C2×D3211yescharacteristic
369C2×C3×C4C22×C3×D311yescharacteristic
370C2×C3×C4C22×C3×D311yescharacteristic
371#67—122no—
372#67—122no—
373C2×Dic3—21no—
374C2×Dic3—61no—
375C2×Dic3—61no—
376C2×Dic3—121no—
377C2×Dic3C3×#6711yescharacteristic
378D12—21no—
379D12—21no—
380C4×D3—21no—
381C4×D3—21no—
382C3×C8—61no—
383C3×C8—61no—
384C3×C8—121no—
385C3×C8—181no—
386C3⋊C8—21no—
387C3⋊C8—62no—
388C3⋊C8—61no—
389C3⋊C8—61no—
390C2×C32—21no—
391C2×C32—21no—
392C2×C32—21no—
393C2×C32—21no—
394C2×C32—21no—
395C2×C32—21no—
396C2×C32—21no—
397C2×C32—21no—
398C2×C32—21no—
399C2×C32—41no—
400C2×C32—41no—
401C2×C32—41no—
402C2×C32—121no—
403C2×C32—241no—
404C2×C32#88311yescharacteristic
405C2×C32#91211yescharacteristic
406C2×C32#91411yescharacteristic
407C2×C32#92911yescharacteristic
408C2×C32#94911yescharacteristic
409C2×C32#95011yescharacteristic
410C2×C32C3×#12311yescharacteristic
411C2×C32C3×#13511yescharacteristic
412C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
413C3×D3—42no—
414C3×D3—41no—
415C3×D3—41no—
416C3×D3—82no—
417C3×D3—81no—
418C3×D3—81no—
419C2×D4—31no—
420C2×D4—181no—
421C22×C4—31no—
422C2×C8—31no—
423C2×C8—91no—
424C4⋊C4—31no—
425C4⋊C4—91no—
426C4⋊C4C3×D3211yescharacteristic
427C22⋊C4—61no—
428C22⋊C4—181no—
429C42—61no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—41no—
434C22×C3—62no—
435C22×C3—61no—
436C22×C3—61no—
437C22×C3—61no—
438C22×C3—61no—
439C22×C3—61no—
440C22×C3—61no—
441C22×C3—121no—
442C22×C3—121no—
443C22×C3—122no—
444C22×C3—121no—
445C22×C3—121no—
446C22×C3—121no—
447C22×C3—121no—
448C22×C3—121no—
449C22×C3—121no—
450C22×C3—241no—
451C22×C3—241no—
452C22×C3D3×#6711yescharacteristic
453C22×C3C3×D3×D411yescharacteristic
454C22×C3C2×C3×#6711yescharacteristic
455C2×D3—21no—
456C2×D3—21no—
457C2×D3—21no—
458C2×D3—41no—
459C2×D3—41no—
460C2×D3—41no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—42no—
468C3×C4—41no—
469C3×C4—41no—
470C3×C4—41no—
471C3×C4—41no—
472C3×C4—41no—
473C3×C4—62no—
474C3×C4—61no—
475C3×C4—61no—
476C3×C4—81no—
477C3×C4—81no—
478C3×C4—82no—
479C3×C4—122no—
480C3×C4—121no—
481C3×C4—121no—
482C3×C4—361no—
483C3×C4#379511yescharacteristic
484C3×C4#379811yescharacteristic
485C3×C4C3×#23511yescharacteristic
486C3×C4C3×#23511yescharacteristic
487C3×C4C3×#23511yescharacteristic
488C3×C4C3×#23711yescharacteristic
489Dic3—21no—
490Dic3—41no—
491Dic3—121no—
492Dic3—121no—
493Dic3—241no—
494C32—21no—
495C32—21no—
496C32—21no—
497C32—41no—
498C32#478411yescharacteristic, complemented
499C32#500311yescharacteristic, complemented
500C32C3×#48211yescharacteristic, complemented
501C23—31no—
502C23—61no—
503D4—61no—
504D4—61no—
505D4—362no—
506C2×C4—21no—
507C2×C4—31no—
508C2×C4—61no—
509C2×C4—61no—
510C2×C4—61no—
511C2×C4—181no—
512C2×C4C2×C3×D3211yescharacteristic
513C8—61no—
514C8—181no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—41no—
525C2×C3—41no—
526C2×C3—41no—
527C2×C3—122no—
528C2×C3—121no—
529C2×C3—121no—
530C2×C3—242no—
531C2×C3—241no—
532C2×C3—241no—
533C2×C3#6390511yescharacteristic
534C2×C3#6393311yescharacteristic
535C2×C3#6393911yescharacteristic
536C2×C3C3×#88311yescharacteristic
537C2×C3C3×#91211yescharacteristic
538C2×C3C3×#91411yescharacteristic
539C2×C3C3×#92911yescharacteristic
540C2×C3C3×#94911yescharacteristic
541C2×C3C3×#95011yescharacteristic
542D3—41no—
543D3—81no—
544C22—61no—
545C22—61no—
546C22—61no—
547C22—121no—
548C22—121no—
549C22—121no—
550C22C3×D3×#6711yescharacteristic
551C4—41no—
552C4—61no—
553C4—121no—
554C4—361no—
555C4C3×#379511yescharacteristic
556C4C3×#379811yescharacteristic
557C3—21no—
558C3—21no—
559C3—21no—
560C3—41no—
561C3#1059050511yescharacteristic, direct product factor
562C3C3×#478411yescharacteristic, complemented
563C3C3×#500311yescharacteristic, complemented
564C2—121no—
565C2—241no—
566C2C3×#6390511yescharacteristic
567C2C3×#6393311yescharacteristic
568C2C3×#6393911yescharacteristic
subgroupG/H
centerC22×C3D3×#67
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C2×C3×D32
FittingC33×C4⋊C4C22
socleC22×C33C2×D4
prime radicalC3×#63908C2
hypercenterC3×C4⋊C4D32
hypocenterC32C3×#482
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. C32×#892C2semidirect
3. C3×#63635C2semidirect
4. C32×#809C2semidirect
5. C3×#63575C2semidirect
6. C3×#63562C2semidirect
7. C3×(C2×D3)⋊(C3⋊C8)C2semidirect
10. #10590505C3direct (N × H)
26. C3×#892D3semidirect
27. C3×#892C2×C3semidirect
30. #63635C2×C3semidirect
37. C3×#809D3semidirect
38. C3×#809C2×C3semidirect
43. #63575C2×C3semidirect
44. #63562C2×C3semidirect
45. (C2×D3)⋊(C3⋊C8)C2×C3semidirect
127. #892C3×D3semidirect
140. #809C3×D3semidirect
328. C33#482semidirect
498. C32#4784semidirect
499. C32#5003semidirect
500. C32C3×#482semidirect
561. C3#10590505direct (N × H)
562. C3C3×#4784semidirect
563. C3C3×#5003semidirect

Maximal subgroups

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

subgroupindex
C32×#8922
C3×#639082
C3×#636352
C32×#8092
C3×#635752
C3×#635622
C3×(C2×D3)⋊(C3⋊C8)2
C3×#50033
C3×#47843
#105905053