Finite Group Databasebeta

← C3×#85845 #11904237

Subgroups — C3×#85845 #11904237

Order 1152.

2559 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C4×#41C211yesmaximal, characteristic, complemented
2C3×#5834C212yesmaximal, complemented
3C3×#5577C211yesmaximal, characteristic, complemented
4C3×C4×#239C212yesmaximal, complemented
5C3×Q8×Dic6C211yesmaximal, characteristic, complemented
6C3×#5563C213yesmaximal, complemented
7C3×#5553C213yesmaximal, complemented
8C3×#5548C216yesmaximal, complemented
9C3×#5532C216yesmaximal, complemented
10C3×#5477C213yesmaximal, complemented
11C3×C4×#235C213yesmaximal, complemented
12C3×#3483—31nomaximal
13#85845C311yesmaximal, characteristic, direct product factor
14C2×C32×#41C2211yescharacteristic
15C2×C3×#239C2212yes—
16C2×C3×#235C2213yes—
17C2×C3×#235C2216yes—
18C32×C4×Q8C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20C32×C4×D4C2213yes—
21C32×C4×D4C2213yes—
22C32×#117C2213yes—
23C2×C32×C42C2213yes—
24C3×Q8×Dic3C2212yes—
25C3×#940C2216yes—
26C3×#938C2216yes—
27C3×#930C2216yes—
28C3×#930C2216yes—
29C3×C4×#67C2216yes—
30C3×C4×#67C2216yes—
31C3×#926C2213yes—
32C3×#895C2216yes—
33C3×#893C2216yes—
34C3×#892C2216yes—
35C3×#888C2216yes—
36C3×#885C22112yes—
37C3×#884C22112yes—
38C3×#875C2216yes—
39C3×#874C2213yes—
40C3×C4×D12C2216yes—
41C3×C4×D12C2213yes—
42C3×C4×D12C2213yes—
43C3×#872C2216yes—
44C3×C42×D3C2216yes—
45C3×#869C2213yes—
46C3×C4×Dic6C2213yes—
47C3×C4×Dic6C2211yescharacteristic
48C3×Q82—31no—
49C3×#555—33no—
50C3×#555—36no—
51C3×#550—32no—
52C3×#550—31no—
53C3×#550—33no—
54C3×#532—36no—
55C3×#532—33no—
56C3×C4×#41—21no—
57C3×C4×#41—32no—
58C3×C4×#41—33no—
59C3×C4×#41D311yescharacteristic, complemented
60C3×C4×#41C2×C311yescharacteristic, complemented
61#5834C2×C312yescomplemented
62#5577C2×C311yescharacteristic, complemented
63C4×#239C2×C312yescomplemented
64Q8×Dic6C2×C311yescharacteristic, complemented
65#5563C2×C313yescomplemented
66#5553C2×C313yescomplemented
67#5548C2×C316yescomplemented
68#5532C2×C316yescomplemented
69#5477C2×C313yescomplemented
70C4×#235C2×C313yescomplemented
71C32×#41—24no—
72C2×C32×Q8C2311yescharacteristic
73C2×C32×D4C2313yes—
74C22×C32×C4C2313yes—
75C22×C32×C4C2313yes—
76C22×C32×C4C2313yes—
77C2×C3×#67C2316yes—
78C2×C3×#67C23112yes—
79C3×#239—28no—
80C3×#235—212no—
81C3×#235—412no—
82C2×C3×D12C2316yes—
83C2×C3×D12C2313yes—
84C2×C3×D12C2316yes—
85C2×C3×C4×D3C2316yes—
86C2×C3×C4×D3C2316yes—
87C2×C3×C4×D3C2316yes—
88C2×C3×Dic6C2316yes—
89C2×C3×Dic6C2311yescharacteristic
90C32×C4⋊C4C2313yes—
91C32×C4⋊C4C2313yes—
92C32×C22⋊C4C2316yes—
93C32×C42C2311yescharacteristic
94C32×C42C2313yes—
95C32×C42C2313yes—
96C32×C42C2313yes—
97C3×#217C2316yes—
98C3×(C2×D3)⋊C4C23112yes—
99C3×(C2×D3)⋊C4C2316yes—
100C3×(C2×D3)⋊C4C2316yes—
101C3×C4⋊Dic3C2316yes—
102C3×C4⋊Dic3C2311yescharacteristic
103C3×C4⋊Dic3C2313yes—
104C3×Dic3⋊C4C2316yes—
105C3×Dic3⋊C4C2312yes—
106C3×C4×Dic3C2316yes—
107C3×C4×Dic3C2316yes—
108C3×C4×Dic3C2312yes—
109#3483—31noSylow
110C2×C3×#41—21no—
111C2×C3×#41—32no—
112C2×C3×#41—33no—
113C2×C3×#41—36no—
114C2×C3×#41C2×D311yescharacteristic
115C2×C3×#41C22×C311yescharacteristic
116C2×#239C22×C312yes—
117C2×#235C22×C313yes—
118C2×#235C22×C316yes—
119C3×C4⋊Q8—36no—
120C3×C4⋊Q8—33no—
121C3×#127—36no—
122C3×#127—33no—
123C3×#124—312no—
124C3×#124—36no—
125C3×#121—36no—
126C3×#121—36no—
127C3×#121—36no—
128C3×#121—36no—
129C3×#121—312no—
130C3×C4×Q8—21no—
131C3×C4×Q8—21no—
132C3×C4×Q8—32no—
133C3×C4×Q8—33no—
134C3×C4×Q8—31no—
135C3×C4×Q8C2×D311yescharacteristic
136C3×C4×Q8C2×D311yescharacteristic
137C3×C4×Q8C22×C311yescharacteristic
138C3×C4×Q8C22×C311yescharacteristic
139C3×C4×D4—23no—
140C3×C4×D4—23no—
141C3×C4×D4—36no—
142C3×C4×D4—36no—
143C3×C4×D4—36no—
144C3×C4×D4—36no—
145C3×C4×D4—33no—
146C3×C4×D4—33no—
147C3×C4×D4C2×D313yes—
148C3×C4×D4C2×D313yes—
149C3×C4×D4C22×C313yes—
150C3×C4×D4C22×C313yes—
151C3×#117—23no—
152C3×#117—33no—
153C3×#117—36no—
154C3×#117—36no—
155C3×#117C2×D313yes—
156C3×#117C22×C313yes—
157C2×C3×C42—23no—
158C2×C3×C42—36no—
159C2×C3×C42C2×D313yes—
160C2×C3×C42C22×C313yes—
161Q8×Dic3C22×C312yes—
162#940C22×C316yes—
163#938C22×C316yes—
164#930C22×C316yes—
165#930C22×C316yes—
166C4×#67C22×C316yes—
167C4×#67C22×C316yes—
168#926C22×C313yes—
169#895C22×C316yes—
170#893C22×C316yes—
171#892C22×C316yes—
172#888C22×C316yes—
173#885C22×C3112yes—
174#884C22×C3112yes—
175#875C22×C316yes—
176#874C22×C313yes—
177C4×D12C22×C313yes—
178C4×D12C22×C313yes—
179C4×D12C22×C316yes—
180#872C22×C316yes—
181C42×D3C22×C316yes—
182#869C22×C313yes—
183C4×Dic6C22×C311yescharacteristic
184C4×Dic6C22×C313yes—
185C23×C32C2413yes—
186C22×C3×D3C2416yes—
187C32×Q8#4114yescomplemented
188C32×D4—26no—
189C2×C32×C4—26no—
190C2×C32×C4—26no—
191C2×C32×C4—26no—
192C2×C32×C4C2413yes—
193C2×C32×C4C2411yescharacteristic
194C2×C32×C4C2413yes—
195C2×C32×C4C2413yes—
196C2×C32×C4C2411yescharacteristic
197C2×C32×C4C2411yescharacteristic
198C3×#67—212no—
199C3×#67—412no—
200C2×C3×Dic3C2412yes—
201C2×C3×Dic3C2416yes—
202C2×C3×Dic3C2412yes—
203C3×D12—26no—
204C3×D12—212no—
205C3×D12—46no—
206C3×C4×D3—212no—
207C3×C4×D3—212no—
208C3×C4×D3—212no—
209C3×Dic6—46no—
210C3×Dic6#4114yescomplemented
211Q82—31no—
212#555—33no—
213#555—36no—
214#550—32no—
215#550—31no—
216#550—33no—
217#532—36no—
218#532—33no—
219C4×#41—32no—
220C4×#41—33no—
221C4×#41C3×D311yescharacteristic, complemented
222C3×#41—28no—
223C3×#41—24no—
224C3×#41—24no—
225C3×#41—612no—
226C3×#41—68no—
227C3×#41—1212no—
228C2×C3×Q8—21no—
229C2×C3×Q8—31no—
230C2×C3×Q8—36no—
231C2×C3×Q8C22×D311yescharacteristic
232C2×C3×Q8C23×C311yescharacteristic
233C2×C3×D4—23no—
234C2×C3×D4—36no—
235C2×C3×D4—312no—
236C2×C3×D4—36no—
237C2×C3×D4—33no—
238C2×C3×D4—36no—
239C2×C3×D4C22×D313yes—
240C2×C3×D4C23×C313yes—
241C22×C3×C4—23no—
242C22×C3×C4—23no—
243C22×C3×C4—23no—
244C22×C3×C4—36no—
245C22×C3×C4—36no—
246C22×C3×C4—36no—
247C22×C3×C4C22×D313yes—
248C22×C3×C4C22×D313yes—
249C22×C3×C4C22×D313yes—
250C22×C3×C4C23×C313yes—
251C22×C3×C4C23×C313yes—
252C22×C3×C4C23×C313yes—
253C2×#67C23×C316yes—
254C2×#67C23×C3112yes—
255#239—28no—
256#235—212no—
257#235—412no—
258C2×D12C23×C313yes—
259C2×D12C23×C316yes—
260C2×D12C23×C316yes—
261C2×C4×D3C23×C316yes—
262C2×C4×D3C23×C316yes—
263C2×C4×D3C23×C316yes—
264C2×Dic6C23×C316yes—
265C2×Dic6C23×C311yescharacteristic
266C3×C4⋊C4—23no—
267C3×C4⋊C4—23no—
268C3×C4⋊C4—32no—
269C3×C4⋊C4—36no—
270C3×C4⋊C4—31no—
271C3×C4⋊C4—36no—
272C3×C4⋊C4—33no—
273C3×C4⋊C4C22×D313yes—
274C3×C4⋊C4C22×D313yes—
275C3×C4⋊C4C23×C313yes—
276C3×C4⋊C4C23×C313yes—
277C3×C22⋊C4—26no—
278C3×C22⋊C4—36no—
279C3×C22⋊C4—36no—
280C3×C22⋊C4—312no—
281C3×C22⋊C4—36no—
282C3×C22⋊C4C22×D316yes—
283C3×C22⋊C4C23×C316yes—
284C3×C42—21no—
285C3×C42—23no—
286C3×C42—23no—
287C3×C42—23no—
288C3×C42—36no—
289C3×C42—36no—
290C3×C42—32no—
291C3×C42C22×D313yes—
292C3×C42C22×D313yes—
293C3×C42C22×D313yes—
294C3×C42C22×D311yescharacteristic
295C3×C42C23×C313yes—
296C3×C42C23×C311yescharacteristic
297C3×C42C23×C313yes—
298C3×C42C23×C313yes—
299#217C23×C316yes—
300(C2×D3)⋊C4C23×C316yes—
301(C2×D3)⋊C4C23×C316yes—
302(C2×D3)⋊C4C23×C3112yes—
303C4⋊Dic3C23×C313yes—
304C4⋊Dic3C23×C311yescharacteristic
305C4⋊Dic3C23×C316yes—
306Dic3⋊C4C23×C312yes—
307Dic3⋊C4C23×C316yes—
308C4×Dic3C23×C312yes—
309C4×Dic3C23×C316yes—
310C4×Dic3C23×C316yes—
311C22×C32—23no—
312C22×C32—23no—
313C22×C32—23no—
314C22×C32C2511yescharacteristic
315C2×C3×D3—26no—
316C2×C3×D3—26no—
317C2×C3×D3—26no—
318C32×C4—21no—
319C32×C4—23no—
320C32×C4—23no—
321C32×C4C2×#4116yes—
322C32×C4C2×#4112yes—
323C32×C4H(5,𝔽2)12yes—
324C3×Dic3—22no—
325C3×Dic3—26no—
326C3×Dic3C2×#4114yes—
327C2×#41—32no—
328C2×#41—33no—
329C2×#41—36no—
330C2×#41C2×C3×D311yescharacteristic
331C4⋊Q8—36no—
332C4⋊Q8—33no—
333#127—36no—
334#127—33no—
335#124—312no—
336#124—36no—
337#121—36no—
338#121—36no—
339#121—36no—
340#121—36no—
341#121—312no—
342C4×Q8—32no—
343C4×Q8—31no—
344C4×Q8—33no—
345C4×Q8C2×C3×D311yescharacteristic
346C4×Q8C2×C3×D311yescharacteristic
347C4×D4—36no—
348C4×D4—36no—
349C4×D4—36no—
350C4×D4—36no—
351C4×D4—33no—
352C4×D4—33no—
353C4×D4C2×C3×D313yes—
354C4×D4C2×C3×D313yes—
355#117—33no—
356#117—36no—
357#117—36no—
358#117C2×C3×D313yes—
359C2×C42—36no—
360C2×C42C2×C3×D313yes—
361C23×C3—23no—
362C23×C3—36no—
363C23×C3C23×D313yes—
364C23×C3C24×C313yes—
365C22×D3C24×C316yes—
366C3×Q8—24no—
367C3×Q8—34no—
368C3×Q8—126no—
369C3×Q8#23514yescomplemented
370C3×Q8C3×#4114yescomplemented
371C3×D4—212no—
372C3×D4—26no—
373C3×D4—26no—
374C3×D4—612no—
375C3×D4—612no—
376C3×D4—66no—
377C3×D4—126no—
378C3×D4—1212no—
379C2×C3×C4—212no—
380C2×C3×C4—26no—
381C2×C3×C4—26no—
382C2×C3×C4—26no—
383C2×C3×C4—26no—
384C2×C3×C4—26no—
385C2×C3×C4—26no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—23no—
390C2×C3×C4—23no—
391C2×C3×C4—23no—
392C2×C3×C4—32no—
393C2×C3×C4—32no—
394C2×C3×C4—36no—
395C2×C3×C4—46no—
396C2×C3×C4—46no—
397C2×C3×C4—612no—
398C2×C3×C4—612no—
399C2×C3×C4—612no—
400C2×C3×C4C23×D313yes—
401C2×C3×C4C23×D311yescharacteristic
402C2×C3×C4C23×D313yes—
403C2×C3×C4C23×D313yes—
404C2×C3×C4C23×D311yescharacteristic
405C2×C3×C4C23×D311yescharacteristic
406C2×C3×C4C24×C313yes—
407C2×C3×C4C24×C311yescharacteristic
408C2×C3×C4C24×C313yes—
409C2×C3×C4C24×C313yes—
410C2×C3×C4C24×C311yescharacteristic
411C2×C3×C4C24×C311yescharacteristic
412#67—212no—
413#67—412no—
414C2×Dic3C24×C312yes—
415C2×Dic3C24×C316yes—
416C2×Dic3C24×C312yes—
417D12—26no—
418D12—212no—
419D12—46no—
420C4×D3—212no—
421C4×D3—212no—
422C4×D3—212no—
423Dic6—46no—
424Dic6C3×#4114yescomplemented
425C2×C32—43no—
426C2×C32C22×#4111yescharacteristic
427C2×C32C22×#4111yescharacteristic
428C2×C32C2×H(5,𝔽2)11yescharacteristic
429C3×D3—46no—
430#41—24no—
431#41—612no—
432#41—68no—
433#41—1212no—
434C2×Q8—31no—
435C2×Q8—36no—
436C2×Q8C22×C3×D311yescharacteristic
437C2×D4—36no—
438C2×D4—312no—
439C2×D4—36no—
440C2×D4—33no—
441C2×D4—36no—
442C2×D4C22×C3×D313yes—
443C22×C4—36no—
444C22×C4—36no—
445C22×C4—36no—
446C22×C4C22×C3×D313yes—
447C22×C4C22×C3×D313yes—
448C22×C4C22×C3×D313yes—
449C4⋊C4—32no—
450C4⋊C4—31no—
451C4⋊C4—36no—
452C4⋊C4—36no—
453C4⋊C4—33no—
454C4⋊C4C22×C3×D313yes—
455C4⋊C4C22×C3×D313yes—
456C22⋊C4—36no—
457C22⋊C4—36no—
458C22⋊C4—312no—
459C22⋊C4—36no—
460C22⋊C4C22×C3×D316yes—
461C42—32no—
462C42—36no—
463C42—36no—
464C42C22×C3×D313yes—
465C42C22×C3×D311yescharacteristic
466C42C22×C3×D313yes—
467C42C22×C3×D313yes—
468C22×C3—26no—
469C22×C3—23no—
470C22×C3—23no—
471C22×C3—23no—
472C22×C3—23no—
473C22×C3—23no—
474C22×C3—23no—
475C22×C3—21no—
476C22×C3—43no—
477C22×C3—43no—
478C22×C3—66no—
479C22×C3—66no—
480C22×C3—66no—
481C22×C3C24×D311yescharacteristic
482C22×C3C25×C311yescharacteristic
483C2×D3—26no—
484C2×D3—26no—
485C2×D3—26no—
486C3×C4—22no—
487C3×C4—21no—
488C3×C4—23no—
489C3×C4—23no—
490C3×C4—23no—
491C3×C4—21no—
492C3×C4—23no—
493C3×C4—26no—
494C3×C4—22no—
495C3×C4—22no—
496C3×C4—34no—
497C3×C4—43no—
498C3×C4—43no—
499C3×C4—62no—
500C3×C4—66no—
501C3×C4C2×#23516yes—
502C3×C4D3×#4112yes—
503C3×C4#100912yes—
504C3×C4C2×C3×#4116yes—
505C3×C4C2×C3×#4112yes—
506C3×C4C3×H(5,𝔽2)12yes—
507Dic3—22no—
508Dic3—26no—
509Dic3C2×C3×#4114yes—
510C32#348311yescharacteristic, complemented, Sylow
511C23—36no—
512C23C23×C3×D313yes—
513Q8—34no—
514Q8—126no—
515Q8C3×#23514yescomplemented
516D4—26no—
517D4—612no—
518D4—612no—
519D4—66no—
520D4—126no—
521D4—1212no—
522C2×C4—26no—
523C2×C4—26no—
524C2×C4—26no—
525C2×C4—32no—
526C2×C4—32no—
527C2×C4—36no—
528C2×C4—612no—
529C2×C4—612no—
530C2×C4—612no—
531C2×C4C23×C3×D313yes—
532C2×C4C23×C3×D311yescharacteristic
533C2×C4C23×C3×D313yes—
534C2×C4C23×C3×D313yes—
535C2×C4C23×C3×D311yescharacteristic
536C2×C4C23×C3×D311yescharacteristic
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—46no—
541C2×C3—43no—
542C2×C3—43no—
543C2×C3—126no—
544C2×C3C22×#23511yescharacteristic
545C2×C3C2×D3×#4111yescharacteristic
546C2×C3C2×#100911yescharacteristic
547C2×C3C22×C3×#4111yescharacteristic
548C2×C3C22×C3×#4111yescharacteristic
549C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
550D3—46no—
551C22—23no—
552C22—23no—
553C22—23no—
554C22—66no—
555C22—66no—
556C22—66no—
557C22C24×C3×D311yescharacteristic
558C4—21no—
559C4—23no—
560C4—23no—
561C4—34no—
562C4—62no—
563C4—66no—
564C4C2×C3×#23516yes—
565C4C3×D3×#4112yes—
566C4C3×#100912yes—
567C3—21no—
568C3#8584511yescharacteristic, direct product factor
569C3C3×#348311yescharacteristic, complemented
570C2—43no—
571C2—126no—
572C2C22×C3×#23511yescharacteristic
573C2C2×C3×D3×#4111yescharacteristic
574C2C2×C3×#100911yescharacteristic
subgroupG/H
centerC2×C3×C4C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×C4×#41C2
socleC22×C32C25
hypercenterC3×C4×#41D3
hypocenterC3C3×#3483
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C3×C4×#41

Complements

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

NH ≅ G/Ntype
1. C32×C4×#41C2semidirect
2. C3×#5834C2semidirect
3. C3×#5577C2semidirect
4. C3×C4×#239C2semidirect
5. C3×Q8×Dic6C2semidirect
6. C3×#5563C2semidirect
7. C3×#5553C2semidirect
8. C3×#5548C2semidirect
9. C3×#5532C2semidirect
10. C3×#5477C2semidirect
11. C3×C4×#235C2semidirect
13. #85845C3direct (N × H)
59. C3×C4×#41D3semidirect
60. C3×C4×#41C2×C3semidirect
61. #5834C2×C3semidirect
62. #5577C2×C3semidirect
63. C4×#239C2×C3semidirect
64. Q8×Dic6C2×C3semidirect
65. #5563C2×C3semidirect
66. #5553C2×C3semidirect
67. #5548C2×C3semidirect
68. #5532C2×C3semidirect
69. #5477C2×C3semidirect
70. C4×#235C2×C3semidirect
187. C32×Q8#41semidirect
210. C3×Dic6#41semidirect
221. C4×#41C3×D3semidirect
369. C3×Q8#235semidirect
370. C3×Q8C3×#41semidirect
424. Dic6C3×#41semidirect
510. C32#3483semidirect
515. Q8C3×#235semidirect
568. C3#85845direct (N × H)
569. C3C3×#3483semidirect

Maximal subgroups

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

subgroupindex
C32×C4×#412
C3×#58342
C3×#55772
C3×C4×#2392
C3×Q8×Dic62
C3×#55632
C3×#55532
C3×#55482
C3×#55322
C3×#54772
C3×C4×#2352
C3×#34833
#858453