Finite Group Databasebeta

← C3×#10590424 #13157474

Subgroups — C3×#10590424 #13157474

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×#63909C211yesmaximal, characteristic
3C3×#63636C211yesmaximal, characteristic, complemented
4C32×#807C211yesmaximal, characteristic, complemented
5C3×#63574C211yesmaximal, characteristic, complemented
6C3×#63564C211yesmaximal, characteristic, complemented
7C3×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C3×#5003—31nomaximal
9C3×#4885—31nomaximal
10#10590424C311yesmaximal, characteristic, direct product factor
11C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
12C2×C32×C4×D3C2211yescharacteristic
13C2×C3×#626—21no—
14C33×C4⋊C4C2211yescharacteristic
15C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
16C32×(C2×D3)⋊C4—21no—
17C32×C4⋊Dic3C2211yescharacteristic
18C32×C4⋊Dic3C2211yescharacteristic
19C32×C4×Dic3—21no—
20C2×C32×C3⋊C8C2211yescharacteristic
21C3×#3722—21no—
22C32×#117—31no—
23C3×#930—31no—
24C3×#895—31no—
25C3×#892—21no—
26C3×#892D311yescharacteristic, complemented
27C3×#892C2×C311yescharacteristic, complemented
28#63909C2×C311yescharacteristic
29C32×#107—31no—
30#63636C2×C311yescharacteristic, complemented
31C3×#830—31no—
32C3×#821—31no—
33C3×(C2×D3)⋊C8—31no—
34C3×#809—31no—
35C3×#809—31no—
36C3×#809—31no—
37C3×#809—61no—
38C3×#808—31no—
39C3×#808—31no—
40C3×#807—21no—
41C3×#807D311yescharacteristic, complemented
42C3×#807C2×C311yescharacteristic, complemented
43#63574C2×C311yescharacteristic, complemented
44#63564C2×C311yescharacteristic, complemented
45(C2×D3)⋊(C3⋊C8)C2×C311yescharacteristic, complemented
46C22×C3×C3⋊D3—21no—
47C22×C32×D3D411yescharacteristic
48C2×C33×C4—21no—
49C2×C33×C4C2311yescharacteristic
50C3×C4⋊(C3⋊D3)—21no—
51C3×C4⋊(C3⋊D3)—21no—
52C2×C32×Dic3—21no—
53C2×C32×Dic3—21no—
54C2×C32×Dic3D411yescharacteristic
55C32×C4×D3—21no—
56C32×C4×D3—21no—
57C3×#626—42no—
58C3×C3⋊(C3⋊C8)—21no—
59C32×C3⋊C8—21no—
60C3×#482—91no—
61#5003—31no—
62#4885—31no—
63C22×C32×C4—31no—
64C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
65C2×C3×#67—61no—
66C2×C3×D12—31no—
67C2×C3×D12—31no—
68C2×C3×D12—61no—
69C2×C3×D12—61no—
70C2×C3×C4×D3—21no—
71C2×C3×C4×D3C2×D311yescharacteristic
72C2×C3×C4×D3C22×C311yescharacteristic
73C2×#626—21no—
74C2×C32×C8—31no—
75C32×C4⋊C4—21no—
76C32×C4⋊C4—21no—
77C32×C4⋊C4—21no—
78C32×C4⋊C4—31no—
79C32×C4⋊C4—31no—
80C32×C4⋊C4—41no—
81C32×C4⋊C4C2×D311yescharacteristic
82C32×C4⋊C4C2×D311yescharacteristic
83C32×C4⋊C4C22×C311yescharacteristic
84C32×C22⋊C4—61no—
85C32×C42—61no—
86C2×C3⋊(C3⋊C8)C22×C311yescharacteristic
87C3×(C2×D3)⋊C4—22no—
88C3×(C2×D3)⋊C4—21no—
89C3×(C2×D3)⋊C4—21no—
90C3×(C2×D3)⋊C4—61no—
91C3×(C2×D3)⋊C4—61no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3C2×D311yescharacteristic
95C3×C4⋊Dic3C2×D311yescharacteristic
96C3×C4⋊Dic3C22×C311yescharacteristic
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#3722—21no—
108C22×C33C2×D411yescharacteristic
109C2×C3×C3⋊D3—41no—
110C2×C3×C3⋊D3—41no—
111C2×C3×C3⋊D3—41no—
112C2×C32×D3—21no—
113C2×C32×D3—21no—
114C2×C32×D3—21no—
115C33×C4—41no—
116C33×C4#4111yescharacteristic
117C33×C4#4111yescharacteristic
118C32×Dic3—21no—
119C32×Dic3—41no—
120C32×Dic3—41no—
121C3×#121—91no—
122C3×#117—31no—
123C3×#117—31no—
124C3×#117—61no—
125#930—31no—
126#895—31no—
127#892C3×D311yescharacteristic, complemented
128C3×#107—31no—
129C3×#107—31no—
130C3×#107—61no—
131C3×#106—91no—
132C3×#102—91no—
133C3×#102—91no—
134C3×C22⋊C8—91no—
135#830—31no—
136#821—31no—
137(C2×D3)⋊C8—31no—
138#809—31no—
139#809—31no—
140#809—31no—
141#809—61no—
142#808—31no—
143#808—31no—
144#807C3×D311yescharacteristic, complemented
145C23×C32—31no—
146C22×C3⋊D3—21no—
147C22×C3×D3—21no—
148C22×C3×D3—61no—
149C22×C3×D3—61no—
150C22×C3×D3—121no—
151C22×C3×D3#6711yescharacteristic
152C22×C3×D3C3×D411yescharacteristic
153C2×C32×C4—21no—
154C2×C32×C4—22no—
155C2×C32×C4—21no—
156C2×C32×C4—21no—
157C2×C32×C4—21no—
158C2×C32×C4—21no—
159C2×C32×C4—21no—
160C2×C32×C4—31no—
161C2×C32×C4—41no—
162C2×C32×C4—41no—
163C2×C32×C4—41no—
164C2×C32×C4—42no—
165C2×C32×C4—61no—
166C2×C32×C4—61no—
167C2×C32×C4—61no—
168C2×C32×C4—61no—
169C2×C32×C4C22×D311yescharacteristic
170C2×C32×C4C22×D311yescharacteristic
171C2×C32×C4C23×C311yescharacteristic
172C4⋊(C3⋊D3)—21no—
173C4⋊(C3⋊D3)—21no—
174C3×#67—122no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—41no—
182C2×C3×Dic3#6711yescharacteristic
183C2×C3×Dic3C3×D411yescharacteristic
184C3×D12—62no—
185C3×D12—61no—
186C3×D12—61no—
187C3×D12—61no—
188C3×D12—61no—
189C3×D12—121no—
190C3×D12—122no—
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#626—42no—
198C32×C8—61no—
199C3⋊(C3⋊C8)—21no—
200C3×C3⋊C8—22no—
201C3×C3⋊C8—21no—
202C3×C3⋊C8—21no—
203C3×C3⋊C8—61no—
204C3×C3⋊C8—61no—
205C3×C3⋊C8—121no—
206#482—91noSylow
207C2×C33#12311yescharacteristic
208C2×C33#13511yescharacteristic
209C2×C33AGL(1,ℤ/8)11yescharacteristic
210C3×C3⋊D3—81no—
211C32×D3—41no—
212C2×C3×D4—91no—
213C2×C3×D4—181no—
214C22×C3×C4—31no—
215C22×C3×C4—31no—
216C22×C3×C4—61no—
217C2×#67—61no—
218C2×D12—31no—
219C2×D12—31no—
220C2×D12—61no—
221C2×D12—61no—
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—31no—
233C3×C4⋊C4—31no—
234C3×C4⋊C4—41no—
235C3×C4⋊C4—61no—
236C3×C4⋊C4—61no—
237C3×C4⋊C4D3211yescharacteristic
238C3×C4⋊C4C2×C3×D311yescharacteristic
239C3×C4⋊C4C2×C3×D311yescharacteristic
240C3×C22⋊C4—61no—
241C3×C22⋊C4—61no—
242C3×C22⋊C4—62no—
243C3×C22⋊C4—181no—
244C3×C42—61no—
245C3×C42—61no—
246C3×C42—62no—
247(C2×D3)⋊C4—21no—
248(C2×D3)⋊C4—61no—
249(C2×D3)⋊C4—61no—
250C4⋊Dic3C2×C3×D311yescharacteristic
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×C32D3×D411yescharacteristic
265C22×C32C2×#6711yescharacteristic
266C22×C32C2×C3×D411yescharacteristic
267C2×C3⋊D3—41no—
268C2×C3⋊D3—41no—
269C2×C3⋊D3—41no—
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—122no—
280C2×C3×D3—121no—
281C2×C3×D3—121no—
282C2×C3×D3—121no—
283C2×C3×D3—121no—
284C2×C3×D3—121no—
285C2×C3×D3—121no—
286C2×C3×D3—241no—
287C2×C3×D3—241no—
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—121no—
306C32×C4#23511yescharacteristic
307C32×C4#23511yescharacteristic
308C32×C4#23511yescharacteristic
309C32×C4#23911yescharacteristic
310C32×C4C3×#4111yescharacteristic
311C32×C4C3×#4111yescharacteristic
312C3×Dic3—22no—
313C3×Dic3—21no—
314C3×Dic3—21no—
315C3×Dic3—42no—
316C3×Dic3—41no—
317C3×Dic3—41no—
318C3×Dic3—41no—
319C3×Dic3—41no—
320C3×Dic3—81no—
321#121—91no—
322#117—31no—
323#107—31no—
324#106—91no—
325#102—91no—
326#102—91no—
327C22⋊C8—91no—
328C33#48211yescharacteristic, complemented, Sylow
329C23×C3—31no—
330C23×C3—31no—
331C23×C3—61no—
332C23×C3—181no—
333C22×D3—61no—
334C22×D3—61no—
335C22×D3—121no—
336C22×D3C3×#6711yescharacteristic
337C3×D4—181no—
338C3×D4—181no—
339C3×D4—362no—
340C2×C3×C4—22no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—31no—
348C2×C3×C4—31no—
349C2×C3×C4—41no—
350C2×C3×C4—41no—
351C2×C3×C4—42no—
352C2×C3×C4—41no—
353C2×C3×C4—61no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—61no—
357C2×C3×C4—61no—
358C2×C3×C4—61no—
359C2×C3×C4—61no—
360C2×C3×C4—62no—
361C2×C3×C4—61no—
362C2×C3×C4—61no—
363C2×C3×C4—61no—
364C2×C3×C4—61no—
365C2×C3×C4—121no—
366C2×C3×C4C2×D3211yescharacteristic
367C2×C3×C4C22×C3×D311yescharacteristic
368C2×C3×C4C22×C3×D311yescharacteristic
369#67—122no—
370C2×Dic3—21no—
371C2×Dic3—21no—
372C2×Dic3C3×#6711yescharacteristic
373D12—62no—
374D12—61no—
375D12—61no—
376D12—61no—
377D12—61no—
378D12—121no—
379D12—122no—
380C4×D3—21no—
381C4×D3—21no—
382C3×C8—62no—
383C3×C8—61no—
384C3×C8—61no—
385C3×C8—181no—
386C3⋊C8—21no—
387C3⋊C8—61no—
388C3⋊C8—61no—
389C3⋊C8—121no—
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#89411yescharacteristic
404C2×C32#91111yescharacteristic
405C2×C32#91911yescharacteristic
406C2×C32#92911yescharacteristic
407C2×C32#94911yescharacteristic
408C2×C32#95011yescharacteristic
409C2×C32C3×#12311yescharacteristic
410C2×C32C3×#13511yescharacteristic
411C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
412C3⋊D3—81no—
413C3×D3—42no—
414C3×D3—41no—
415C3×D3—41no—
416C3×D3—242no—
417C3×D3—241no—
418C3×D3—241no—
419C2×D4—91no—
420C2×D4—181no—
421C22×C4—31no—
422C2×C8—31no—
423C2×C8—91no—
424C4⋊C4—31no—
425C4⋊C4—31no—
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—361no—
444C22×C3—361no—
445C22×C3—361no—
446C22×C3D3×#6711yescharacteristic
447C22×C3C3×D3×D411yescharacteristic
448C22×C3C2×C3×#6711yescharacteristic
449C2×D3—21no—
450C2×D3—21no—
451C2×D3—21no—
452C2×D3—122no—
453C2×D3—121no—
454C2×D3—121no—
455C2×D3—121no—
456C2×D3—121no—
457C2×D3—121no—
458C2×D3—121no—
459C2×D3—241no—
460C2×D3—241no—
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—121no—
483C3×C4—121no—
484C3×C4—241no—
485C3×C4#379811yescharacteristic
486C3×C4#379911yescharacteristic
487C3×C4C3×#23511yescharacteristic
488C3×C4C3×#23511yescharacteristic
489C3×C4C3×#23511yescharacteristic
490C3×C4C3×#23911yescharacteristic
491Dic3—21no—
492Dic3—41no—
493Dic3—41no—
494C32—21no—
495C32—21no—
496C32—21no—
497C32—41no—
498C32#488511yescharacteristic, complemented
499C32#500311yescharacteristic, complemented
500C32C3×#48211yescharacteristic, complemented
501C23—31no—
502C23—181no—
503D4—181no—
504D4—181no—
505D4—362no—
506C2×C4—21no—
507C2×C4—31no—
508C2×C4—61no—
509C2×C4—61no—
510C2×C4—61no—
511C2×C4—61no—
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—721no—
531C2×C3#6385011yescharacteristic
532C2×C3#6392511yescharacteristic
533C2×C3#6394911yescharacteristic
534C2×C3C3×#89411yescharacteristic
535C2×C3C3×#91111yescharacteristic
536C2×C3C3×#91911yescharacteristic
537C2×C3C3×#92911yescharacteristic
538C2×C3C3×#94911yescharacteristic
539C2×C3C3×#95011yescharacteristic
540D3—41no—
541D3—242no—
542D3—241no—
543D3—241no—
544C22—61no—
545C22—61no—
546C22—61no—
547C22—361no—
548C22—361no—
549C22—361no—
550C22C3×D3×#6711yescharacteristic
551C4—41no—
552C4—61no—
553C4—121no—
554C4—121no—
555C4C3×#379811yescharacteristic
556C4C3×#379911yescharacteristic
557C3—21no—
558C3—21no—
559C3—21no—
560C3—41no—
561C3#1059042411yescharacteristic, direct product factor
562C3C3×#488511yescharacteristic, complemented
563C3C3×#500311yescharacteristic, complemented
564C2—121no—
565C2—721no—
566C2C3×#6385011yescharacteristic
567C2C3×#6392511yescharacteristic
568C2C3×#6394911yescharacteristic
subgroupG/H
centerC22×C3D3×#67
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C2×C3×D32
FittingC33×C4⋊C4C22
socleC22×C33C2×D4
prime radicalC3×#63909C2
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×#63636C2semidirect
4. C32×#807C2semidirect
5. C3×#63574C2semidirect
6. C3×#63564C2semidirect
7. C3×(C2×D3)⋊(C3⋊C8)C2semidirect
10. #10590424C3direct (N × H)
26. C3×#892D3semidirect
27. C3×#892C2×C3semidirect
30. #63636C2×C3semidirect
41. C3×#807D3semidirect
42. C3×#807C2×C3semidirect
43. #63574C2×C3semidirect
44. #63564C2×C3semidirect
45. (C2×D3)⋊(C3⋊C8)C2×C3semidirect
127. #892C3×D3semidirect
144. #807C3×D3semidirect
328. C33#482semidirect
498. C32#4885semidirect
499. C32#5003semidirect
500. C32C3×#482semidirect
561. C3#10590424direct (N × H)
562. C3C3×#4885semidirect
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×#639092
C3×#636362
C32×#8072
C3×#635742
C3×#635642
C3×(C2×D3)⋊(C3⋊C8)2
C3×#50033
C3×#48853
#105904243