Finite Group Databasebeta

← C3×#83581 #11895711

Subgroups — C3×#83581 #11895711

Order 1152.

948 conjugacy classes of subgroups.

The subgroup lattice has 585 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#550C211yesmaximal, characteristic, complemented
2C3×#5579C211yesmaximal, characteristic, complemented
3C3×#5072C212yesmaximal, complemented
4C3×#5072C211yesmaximal, characteristic, complemented
5C3×#5071C212yesmaximal, complemented
6C3×#5070C211yesmaximal, characteristic, complemented
7C3×#5024C211yesmaximal, characteristic, complemented
8C3×#5014C212yesmaximal, complemented
9C3×C4×#213C211yesmaximal, characteristic, complemented
10C3×#5009C212yesmaximal, complemented
11C3×#5008C211yesmaximal, characteristic, complemented
12C3×#3366—31nomaximal
13#83581C311yesmaximal, characteristic, direct product factor
14C2×C32×#41—21no—
15C32×#127C2211yescharacteristic
16C32×#127C2212yes—
17C32×#121—21no—
18C32×#121—22no—
19C32×C4×Q8C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C32×C4×D4C2212yes—
22C3×#946—21no—
23C2×C3×#213C2211yescharacteristic
24C2×C3×#213C2212yes—
25C3×#896—22no—
26C3×D3×C4⋊C4—21no—
27C3×C4×D12C2211yescharacteristic
28C3×C4×D12C2212yes—
29C3×#870C2212yes—
30C3×#869C2211yescharacteristic
31C3×#832C2212yes—
32C3×#832C2212yes—
33C3×#832C2212yes—
34C3×#832C2211yescharacteristic
35C3×#832C2212yes—
36C3×#809C2211yescharacteristic
37C3×#808C2212yes—
38C3×#807C2211yescharacteristic
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40C3×C4⋊(C3⋊C8)C2212yes—
41C3×#803C2212yes—
42C3×C4×C3⋊C8C2211yescharacteristic
43C3×#554—31no—
44C3×#550—21no—
45C3×#550D311yescharacteristic, complemented
46C3×#550C2×C311yescharacteristic, complemented
47#5579C2×C311yescharacteristic, complemented
48C3×#490—32no—
49C3×#486—31no—
50C3×#478—32no—
51C3×#476—31no—
52C3×#459—32no—
53C3×#459—31no—
54C3×#446—31no—
55C3×#442—32no—
56C3×C4×D8—31no—
57#5072C2×C311yescharacteristic, complemented
58#5072C2×C312yescomplemented
59#5071C2×C312yescomplemented
60#5070C2×C311yescharacteristic, complemented
61#5024C2×C311yescharacteristic, complemented
62#5014C2×C312yescomplemented
63C4×#213C2×C311yescharacteristic, complemented
64#5009C2×C312yescomplemented
65#5008C2×C311yescharacteristic, complemented
66C32×#41—44no—
67C2×C32×Q8D411yescharacteristic
68C2×C32×D4—22no—
69C2×C32×D4—21no—
70C2×C32×D4—22no—
71C2×C32×D4—21no—
72C2×C32×D4C2311yescharacteristic
73C2×C32×D4C2312yes—
74C22×C32×C4—22no—
75C22×C32×C4—21no—
76C2×C3×D12C2311yescharacteristic
77C2×C3×C4×D3—21no—
78C2×C3×C4×D3—22no—
79C2×C3×Dic6—21no—
80C32×C4⋊C4D411yescharacteristic
81C32×C4⋊C4D412yes—
82C32×C4⋊C4C2311yescharacteristic
83C32×C22⋊C4—22no—
84C32×C22⋊C4—21no—
85C32×C42C2311yescharacteristic
86C32×C42C2312yes—
87C3×#213—22no—
88C3×#213—24no—
89C3×(C2×D3)⋊C4—21no—
90C3×(C2×D3)⋊C4—22no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3C2311yescharacteristic
93C3×C4⋊Dic3C2312yes—
94C3×Dic3⋊C4—22no—
95C3×Dic3⋊C4—22no—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2312yes—
98C2×C3×C3⋊C8C2311yescharacteristic
99#3366—31noSylow
100C2×C3×#41—22no—
101C2×C3×#41—21no—
102C2×C3×#41—21no—
103C2×C3×D8—31no—
104C2×C3×D8—32no—
105C3×C4⋊Q8—31no—
106C3×#127—21no—
107C3×#127—22no—
108C3×#127C2×D311yescharacteristic
109C3×#127C2×D312yes—
110C3×#127C22×C311yescharacteristic
111C3×#127C22×C312yes—
112C3×#125—32no—
113C3×C22⋊Q8—61no—
114C3×C22⋊Q8—62no—
115C3×#121—22no—
116C3×#121—24no—
117C3×#121—21no—
118C3×#121—22no—
119C3×#121—21no—
120C3×#121—22no—
121C3×C4×Q8—21no—
122C3×C4×Q8C2×D311yescharacteristic
123C3×C4×Q8C22×C311yescharacteristic
124C3×C4×D4—21no—
125C3×C4×D4—22no—
126C3×C4×D4—31no—
127C3×C4×D4—32no—
128C3×C4×D4C2×D311yescharacteristic
129C3×C4×D4C2×D312yes—
130C3×C4×D4C22×C311yescharacteristic
131C3×C4×D4C22×C312yes—
132C2×C3×C4⋊C4—61no—
133#946—21no—
134C2×#213C22×C311yescharacteristic
135C2×#213C22×C312yes—
136#896—22no—
137D3×C4⋊C4—21no—
138C4×D12C22×C311yescharacteristic
139C4×D12C22×C312yes—
140#870C22×C312yes—
141#869C22×C311yescharacteristic
142C3×#107—31no—
143C3×#106—32no—
144C3×C4⋊C8—31no—
145C3×C4⋊C8—32no—
146C3×#102—31no—
147C3×#102—32no—
148C3×#102—32no—
149C3×#102—32no—
150C3×#102—32no—
151C3×#102—31no—
152C3×#97—32no—
153C3×C4×C8—31no—
154#832C22×C312yes—
155#832C22×C312yes—
156#832C22×C312yes—
157#832C22×C311yescharacteristic
158#832C22×C312yes—
159#809C22×C311yescharacteristic
160#808C22×C312yes—
161#807C22×C311yescharacteristic
162C4⋊(C3⋊C8)C22×C311yescharacteristic
163C4⋊(C3⋊C8)C22×C312yes—
164#803C22×C312yes—
165C4×C3⋊C8C22×C311yescharacteristic
166C23×C32—22no—
167C23×C32—21no—
168C22×C3×D3—21no—
169C32×Q8—22no—
170C32×D4—21no—
171C32×D4—22no—
172C32×D4—21no—
173C32×D4—22no—
174C32×D4—44no—
175C32×D4—42no—
176C32×D4—81no—
177C32×D4—82no—
178C2×C32×C4—21no—
179C2×C32×C4—44no—
180C2×C32×C4—42no—
181C2×C32×C4C2×D412yes—
182C2×C32×C4C2×D412yes—
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2411yescharacteristic
186C2×C3×Dic3—21no—
187C2×C3×Dic3—22no—
188C3×D12—21no—
189C3×D12#4112yescomplemented
190C3×C4×D3—42no—
191C3×C4×D3—82no—
192C3×Dic6—81no—
193C3×C3⋊C8—21no—
194C3×C3⋊C8—22no—
195C3×C3⋊C8—21no—
196#554—31no—
197#550C3×D311yescharacteristic, complemented
198#490—32no—
199#486—31no—
200#478—32no—
201#476—31no—
202#459—32no—
203#459—31no—
204#446—31no—
205#442—32no—
206C4×D8—31no—
207C3×#41—48no—
208C3×#41—44no—
209C3×#41—44no—
210C2×C3×Q8—21no—
211C2×C3×Q8—61no—
212C2×C3×Q8#6711yescharacteristic
213C2×C3×Q8C3×D411yescharacteristic
214C2×C3×D4—24no—
215C2×C3×D4—22no—
216C2×C3×D4—22no—
217C2×C3×D4—24no—
218C2×C3×D4—22no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—22no—
222C2×C3×D4—22no—
223C2×C3×D4—21no—
224C2×C3×D4—22no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—22no—
228C2×C3×D4—31no—
229C2×C3×D4C22×D311yescharacteristic
230C2×C3×D4C22×D312yes—
231C2×C3×D4C23×C311yescharacteristic
232C2×C3×D4C23×C312yes—
233C22×C3×C4—24no—
234C22×C3×C4—22no—
235C22×C3×C4—22no—
236C22×C3×C4—21no—
237C22×C3×C4—22no—
238C22×C3×C4—21no—
239C22×C3×C4—61no—
240C22×C3×C4—62no—
241C2×D12C23×C311yescharacteristic
242C2×C4×D3—21no—
243C2×C4×D3—22no—
244C2×Dic6—21no—
245C3×D8—62no—
246C3×D8—64no—
247C2×C3×C8—31no—
248C2×C3×C8—31no—
249C2×C3×C8—32no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—22no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—32no—
254C3×C4⋊C4—31no—
255C3×C4⋊C4—62no—
256C3×C4⋊C4—62no—
257C3×C4⋊C4—61no—
258C3×C4⋊C4#6711yescharacteristic
259C3×C4⋊C4#6712yes—
260C3×C4⋊C4C3×D411yescharacteristic
261C3×C4⋊C4C3×D412yes—
262C3×C4⋊C4C22×D311yescharacteristic
263C3×C4⋊C4C23×C311yescharacteristic
264C3×C22⋊C4—22no—
265C3×C22⋊C4—24no—
266C3×C22⋊C4—21no—
267C3×C22⋊C4—22no—
268C3×C22⋊C4—22no—
269C3×C22⋊C4—21no—
270C3×C22⋊C4—61no—
271C3×C22⋊C4—62no—
272C3×C42—21no—
273C3×C42—22no—
274C3×C42C22×D311yescharacteristic
275C3×C42C22×D312yes—
276C3×C42C23×C311yescharacteristic
277C3×C42C23×C312yes—
278#213—22no—
279#213—24no—
280(C2×D3)⋊C4—21no—
281(C2×D3)⋊C4—22no—
282C4⋊Dic3—21no—
283C4⋊Dic3C23×C311yescharacteristic
284C4⋊Dic3C23×C312yes—
285Dic3⋊C4—22no—
286Dic3⋊C4—22no—
287C2×C3⋊C8C23×C311yescharacteristic
288C2×C3⋊C8C23×C311yescharacteristic
289C2×C3⋊C8C23×C312yes—
290C22×C32—42no—
291C22×C32—41no—
292C22×C32—42no—
293C22×C32—41no—
294C22×C32—42no—
295C22×C32—41no—
296C22×C32C22×D411yescharacteristic
297C2×C3×D3—22no—
298C2×C3×D3—41no—
299C2×C3×D3—41no—
300C32×C4—22no—
301C32×C4—21no—
302C32×C4—22no—
303C32×C4—41no—
304C32×C4AGL(1,ℤ/8)12yes—
305C32×C4C2×#4111yescharacteristic
306C32×C42−1+411yescharacteristic
307C3×Dic3—41no—
308C3×Dic3—42no—
309C2×#41—21no—
310C2×D8—31no—
311C2×D8—32no—
312C4⋊Q8—31no—
313#127C2×C3×D311yescharacteristic
314#127C2×C3×D312yes—
315#125—32no—
316C22⋊Q8—61no—
317C22⋊Q8—62no—
318#121—21no—
319#121—22no—
320C4×Q8C2×C3×D311yescharacteristic
321C4×D4—31no—
322C4×D4—32no—
323C4×D4C2×C3×D311yescharacteristic
324C4×D4C2×C3×D312yes—
325C2×C4⋊C4—61no—
326#107—31no—
327#106—32no—
328C4⋊C8—31no—
329C4⋊C8—32no—
330#102—31no—
331#102—32no—
332#102—32no—
333#102—32no—
334#102—32no—
335#102—31no—
336#97—32no—
337C4×C8—31no—
338C23×C3—24no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—21no—
342C23×C3—22no—
343C23×C3—21no—
344C23×C3—61no—
345C22×D3—21no—
346C3×Q8—24no—
347C3×Q8—22no—
348C3×Q8—22no—
349C3×Q8—241no—
350C3×D4—21no—
351C3×D4—22no—
352C3×D4—21no—
353C3×D4—22no—
354C3×D4—21no—
355C3×D4—22no—
356C3×D4—21no—
357C3×D4—22no—
358C3×D4—32no—
359C3×D4—41no—
360C3×D4—42no—
361C3×D4—41no—
362C3×D4—42no—
363C3×D4—48no—
364C3×D4—44no—
365C3×D4—44no—
366C3×D4—44no—
367C3×D4—42no—
368C3×D4—42no—
369C3×D4—61no—
370C3×D4—81no—
371C3×D4—82no—
372C3×D4—82no—
373C3×D4—81no—
374C3×D4—84no—
375C3×D4—82no—
376C2×C3×C4—22no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—22no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—22no—
384C2×C3×C4—48no—
385C2×C3×C4—44no—
386C2×C3×C4—44no—
387C2×C3×C4—44no—
388C2×C3×C4—42no—
389C2×C3×C4—42no—
390C2×C3×C4—61no—
391C2×C3×C4—62no—
392C2×C3×C4—122no—
393C2×C3×C4—242no—
394C2×C3×C4C2×#6711yescharacteristic
395C2×C3×C4C2×#6712yes—
396C2×C3×C4C2×#6712yes—
397C2×C3×C4C2×#6711yescharacteristic
398C2×C3×C4C2×C3×D412yes—
399C2×C3×C4C2×C3×D412yes—
400C2×C3×C4C2×C3×D411yescharacteristic
401C2×C3×C4C2×C3×D411yescharacteristic
402C2×C3×C4C23×D311yescharacteristic
403C2×C3×C4C24×C311yescharacteristic
404C2×Dic3—21no—
405C2×Dic3—22no—
406D12—21no—
407D12C3×#4112yescomplemented
408C4×D3—42no—
409C4×D3—82no—
410Dic6—81no—
411C3×C8—61no—
412C3×C8—62no—
413C3×C8—61no—
414C3⋊C8—21no—
415C3⋊C8—22no—
416C3⋊C8—21no—
417C2×C32—82no—
418C2×C32—81no—
419C2×C32#54811yescharacteristic
420C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
421C2×C32#57611yescharacteristic
422C3×D3—42no—
423#41—44no—
424C2×Q8—61no—
425C2×Q8C3×#6711yescharacteristic
426C2×D4—22no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—22no—
430C2×D4—31no—
431C2×D4C22×C3×D311yescharacteristic
432C2×D4C22×C3×D312yes—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—61no—
436C22×C4—62no—
437D8—62no—
438D8—64no—
439C2×C8—31no—
440C2×C8—31no—
441C2×C8—32no—
442C4⋊C4—32no—
443C4⋊C4—31no—
444C4⋊C4—62no—
445C4⋊C4—61no—
446C4⋊C4—62no—
447C4⋊C4C3×#6711yescharacteristic
448C4⋊C4C3×#6712yes—
449C4⋊C4C22×C3×D311yescharacteristic
450C22⋊C4—21no—
451C22⋊C4—22no—
452C22⋊C4—61no—
453C22⋊C4—62no—
454C42C22×C3×D311yescharacteristic
455C42C22×C3×D312yes—
456C22×C3—21no—
457C22×C3—44no—
458C22×C3—42no—
459C22×C3—44no—
460C22×C3—42no—
461C22×C3—42no—
462C22×C3—44no—
463C22×C3—42no—
464C22×C3—41no—
465C22×C3—42no—
466C22×C3—41no—
467C22×C3—42no—
468C22×C3—41no—
469C22×C3—42no—
470C22×C3—41no—
471C22×C3—41no—
472C22×C3—42no—
473C22×C3—42no—
474C22×C3—41no—
475C22×C3—62no—
476C22×C3—121no—
477C22×C3—121no—
478C22×C3C22×#6711yescharacteristic
479C22×C3C22×C3×D411yescharacteristic
480C2×D3—22no—
481C2×D3—41no—
482C2×D3—41no—
483C3×C4—24no—
484C3×C4—22no—
485C3×C4—21no—
486C3×C4—22no—
487C3×C4—22no—
488C3×C4—22no—
489C3×C4—21no—
490C3×C4—22no—
491C3×C4—21no—
492C3×C4—21no—
493C3×C4—42no—
494C3×C4—41no—
495C3×C4—42no—
496C3×C4—41no—
497C3×C4—41no—
498C3×C4—121no—
499C3×C4—122no—
500C3×C4#93212yes—
501C3×C4C3×AGL(1,ℤ/8)12yes—
502C3×C4D3×#4111yescharacteristic
503C3×C4#101011yescharacteristic
504C3×C4C2×C3×#4111yescharacteristic
505C3×C4C3×2−1+411yescharacteristic
506Dic3—41no—
507Dic3—42no—
508C32#336611yescharacteristic, complemented, Sylow
509C23—22no—
510C23—21no—
511C23—61no—
512Q8—22no—
513Q8—241no—
514D4—21no—
515D4—22no—
516D4—21no—
517D4—22no—
518D4—32no—
519D4—44no—
520D4—42no—
521D4—61no—
522D4—82no—
523D4—81no—
524C2×C4—21no—
525C2×C4—44no—
526C2×C4—42no—
527C2×C4—61no—
528C2×C4—62no—
529C2×C4—122no—
530C2×C4—242no—
531C2×C4C2×C3×#6711yescharacteristic
532C2×C4C2×C3×#6712yes—
533C2×C4C2×C3×#6712yes—
534C2×C4C2×C3×#6711yescharacteristic
535C2×C4C23×C3×D311yescharacteristic
536C8—61no—
537C8—62no—
538C8—61no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—84no—
543C2×C3—82no—
544C2×C3—82no—
545C2×C3—81no—
546C2×C3—82no—
547C2×C3—81no—
548C2×C3—122no—
549C2×C3C2×#93211yescharacteristic
550C2×C3#583111yescharacteristic
551C2×C3#583511yescharacteristic
552C2×C3C3×#54811yescharacteristic
553C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
554C2×C3C3×#57611yescharacteristic
555D3—42no—
556C22—42no—
557C22—41no—
558C22—42no—
559C22—41no—
560C22—41no—
561C22—42no—
562C22—62no—
563C22—121no—
564C22—121no—
565C22C22×C3×#6711yescharacteristic
566C4—22no—
567C4—22no—
568C4—21no—
569C4—41no—
570C4—121no—
571C4—122no—
572C4C3×#93212yes—
573C4C3×D3×#4111yescharacteristic
574C4C3×#101011yescharacteristic
575C3—21no—
576C3#8358111yescharacteristic, direct product factor
577C3C3×#336611yescharacteristic, complemented
578C2—82no—
579C2—81no—
580C2—122no—
581C2C2×C3×#93211yescharacteristic
582C2C3×#583111yescharacteristic
583C2C3×#583511yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#550C2
socleC22×C32C22×D4
hypercenterC3×#550D3
hypocenterC3C3×#3366
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×Q8 ◁ C3×#550

Complements

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

NH ≅ G/Ntype
1. C32×#550C2semidirect
2. C3×#5579C2semidirect
3. C3×#5072C2semidirect
4. C3×#5072C2semidirect
5. C3×#5071C2semidirect
6. C3×#5070C2semidirect
7. C3×#5024C2semidirect
8. C3×#5014C2semidirect
9. C3×C4×#213C2semidirect
10. C3×#5009C2semidirect
11. C3×#5008C2semidirect
13. #83581C3direct (N × H)
45. C3×#550D3semidirect
46. C3×#550C2×C3semidirect
47. #5579C2×C3semidirect
57. #5072C2×C3semidirect
58. #5072C2×C3semidirect
59. #5071C2×C3semidirect
60. #5070C2×C3semidirect
61. #5024C2×C3semidirect
62. #5014C2×C3semidirect
63. C4×#213C2×C3semidirect
64. #5009C2×C3semidirect
65. #5008C2×C3semidirect
189. C3×D12#41semidirect
197. #550C3×D3semidirect
407. D12C3×#41semidirect
508. C32#3366semidirect
576. C3#83581direct (N × H)
577. C3C3×#3366semidirect

Maximal subgroups

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

subgroupindex
C32×#5502
C3×#55792
C3×#50722
C3×#50712
C3×#50702
C3×#50242
C3×#50142
C3×C4×#2132
C3×#50092
C3×#50082
C3×#33663
#835813