Finite Group Databasebeta

← C3×#81002 #11882231

Subgroups — C3×#81002 #11882231

Order 1152.

832 conjugacy classes of subgroups.

The subgroup lattice has 589 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5725C211yesmaximal, characteristic
2C3×#5578C211yesmaximal, characteristic, complemented
3C32×#475C211yesmaximal, characteristic, complemented
4C3×#5094C211yesmaximal, characteristic, complemented
5C3×#5027C211yesmaximal, characteristic, complemented
6C3×#4870C212yesmaximal, complemented
7C3×#4864C212yesmaximal, complemented
8C3×#4848C211yesmaximal, characteristic, complemented
9C3×D3×C4⋊C8C211yesmaximal, characteristic, complemented
10C3×#4818C212yesmaximal, complemented
11C3×#4807C212yesmaximal, complemented
12C3×#3246—31nomaximal
13#81002C311yesmaximal, characteristic, direct product factor
14C2×C3×#239—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C32×C4×Q8C2211yescharacteristic
17C3×#947—21no—
18C3×#946C2211yescharacteristic
19C3×#944C2211yescharacteristic
20C2×C3×#215C2212yes—
21C2×C3×#204C2212yes—
22C2×C3×D3×C8C2212yes—
23C3×#897C2211yescharacteristic
24C3×#896—21no—
25C3×#895—21no—
26C3×#895C2212yes—
27C3×#893—21no—
28C3×#893C2212yes—
29C3×#889—21no—
30C3×#888C2211yescharacteristic
31C3×#874C2211yescharacteristic
32C3×#872—21no—
33C3×C42×D3C2211yescharacteristic
34C3×C4×Dic6—21no—
35C3×C4×Dic6C2211yescharacteristic
36C32×#106C2212yes—
37C32×C4⋊C8C2211yescharacteristic
38C32×#103C2212yes—
39C3×#821C2212yes—
40C3×Dic3⋊C8C2212yes—
41C3×#810C2212yes—
42C3×#809C2212yes—
43C3×#808C2212yes—
44C3×C4⋊(C3⋊C8)C2211yescharacteristic
45C3×#533—31no—
46C3×#532—31no—
47#5725C2×C311yescharacteristic
48#5578C2×C311yescharacteristic, complemented
49C3×#476—32no—
50C3×#475—21no—
51C3×#475—31no—
52C3×#475D311yescharacteristic, complemented
53C3×#475C2×C311yescharacteristic, complemented
54C3×#465—32no—
55C3×#465—32no—
56C3×#461—32no—
57C3×#460—31no—
58C3×#460—31no—
59C2×C3×C4⋊C8—31no—
60#5094C2×C311yescharacteristic, complemented
61#5027C2×C311yescharacteristic, complemented
62#4870C2×C312yescomplemented
63#4864C2×C312yescomplemented
64#4848C2×C311yescharacteristic, complemented
65D3×C4⋊C8C2×C311yescharacteristic, complemented
66#4818C2×C312yescomplemented
67#4807C2×C312yescomplemented
68C2×C32×Q8—21no—
69C2×C32×Q8C2311yescharacteristic
70C3×#239—44no—
71C2×C3×D12—22no—
72C2×C3×D12—21no—
73C2×C3×D12—21no—
74C2×C3×D12C2312yes—
75C2×C3×C4×D3—22no—
76C2×C3×C4×D3D411yescharacteristic
77C2×C3×C4×D3D411yescharacteristic
78C2×C3×C4×D3C2311yescharacteristic
79C2×C3×Dic6—21no—
80C2×C3×Dic6C2311yescharacteristic
81C2×C32×C8C2312yes—
82C32×C4⋊C4—21no—
83C32×C4⋊C4—21no—
84C32×C4⋊C4C2311yescharacteristic
85C32×C4⋊C4C2312yes—
86C32×C42—21no—
87C32×C42C2311yescharacteristic
88C3×#215—42no—
89C3×(C2×D3)⋊C4—21no—
90C3×(C2×D3)⋊C4—21no—
91C3×(C2×D3)⋊C4—22no—
92C3×(C2×D3)⋊C4—22no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3C2311yescharacteristic
95C3×Dic3⋊C4—21no—
96C3×Dic3⋊C4—21no—
97C3×Dic3⋊C4—21no—
98C3×Dic3⋊C4—21no—
99C3×Dic3⋊C4—21no—
100C3×C4×Dic3—21no—
101C3×C4×Dic3D411yescharacteristic
102C3×C4×Dic3D411yescharacteristic
103C3×C4×Dic3C2311yescharacteristic
104C2×C3×C3⋊C8C2312yes—
105C3×#204—42no—
106C3×D3×C8—42no—
107#3246—31noSylow
108C2×C3×#41—61no—
109C2×#239—21no—
110C2×C3×SD16—32no—
111C2×C3×SD16—32no—
112C22×C3×C8—32no—
113C3×C4⋊Q8—21no—
114C3×C4⋊Q8—31no—
115C3×C4⋊Q8—31no—
116C3×C4⋊Q8C2×D311yescharacteristic
117C3×C4⋊Q8C22×C311yescharacteristic
118C3×#127—31no—
119C3×#125—61no—
120C3×#124—61no—
121C3×C22⋊Q8—31no—
122C3×C22⋊Q8—31no—
123C3×C22⋊Q8—61no—
124C3×#121—32no—
125C3×#121—61no—
126C3×C4×Q8—21no—
127C3×C4×Q8—31no—
128C3×C4×Q8—61no—
129C3×C4×Q8C2×D311yescharacteristic
130C3×C4×Q8C22×C311yescharacteristic
131C3×C4×D4—32no—
132C3×C4×D4—61no—
133C3×#117—61no—
134C2×C3×C42—31no—
135#947—21no—
136#946C22×C311yescharacteristic
137#944C22×C311yescharacteristic
138C2×#215C22×C312yes—
139C2×#204C22×C312yes—
140C2×D3×C8C22×C312yes—
141#897C22×C311yescharacteristic
142#896—21no—
143#895—21no—
144#895C22×C312yes—
145#893—21no—
146#893C22×C312yes—
147#889—21no—
148#888C22×C311yescharacteristic
149#874C22×C311yescharacteristic
150#872—21no—
151C42×D3C22×C311yescharacteristic
152C4×Dic6—21no—
153C4×Dic6C22×C311yescharacteristic
154C3×#106—22no—
155C3×#106—32no—
156C3×#106C2×D312yes—
157C3×#106C22×C312yes—
158C3×C4⋊C8—21no—
159C3×C4⋊C8—32no—
160C3×C4⋊C8—31no—
161C3×C4⋊C8C2×D311yescharacteristic
162C3×C4⋊C8C22×C311yescharacteristic
163C3×#103—22no—
164C3×#103—32no—
165C3×#103C2×D312yes—
166C3×#103C22×C312yes—
167C3×#102—32no—
168C3×#102—32no—
169#821C22×C312yes—
170Dic3⋊C8C22×C312yes—
171#810C22×C312yes—
172#809C22×C312yes—
173#808C22×C312yes—
174C4⋊(C3⋊C8)C22×C311yescharacteristic
175C22×C3×D3—22no—
176C22×C3×D3C2×D411yescharacteristic
177C32×Q8—21no—
178C32×Q8—21no—
179C32×Q8—42no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—22no—
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2411yescharacteristic
186C2×C3×Dic3—21no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3C2×D411yescharacteristic
189C2×C3×Dic3C2×D411yescharacteristic
190C2×C3×Dic3C2×D411yescharacteristic
191C3×D12—22no—
192C3×D12—22no—
193C3×D12—42no—
194C3×D12—44no—
195C3×D12—42no—
196C3×C4×D3—21no—
197C3×C4×D3—21no—
198C3×C4×D3—41no—
199C3×C4×D3—44no—
200C3×C4×D3SD1614yescomplemented
201C3×Dic6—21no—
202C3×Dic6—21no—
203C3×Dic6—42no—
204C32×C8—22no—
205C3×C3⋊C8—22no—
206#533—31no—
207#532—31no—
208#476—32no—
209#475—31no—
210#475C3×D311yescharacteristic, complemented
211#465—32no—
212#465—32no—
213#461—32no—
214#460—31no—
215#460—31no—
216C2×C4⋊C8—31no—
217C3×#41—124no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—31no—
222C2×C3×Q8—41no—
223C2×C3×Q8—61no—
224C2×C3×Q8C22×D311yescharacteristic
225C2×C3×Q8C23×C311yescharacteristic
226C2×C3×D4—32no—
227C2×C3×D4—62no—
228C2×C3×D4—61no—
229C2×C3×D4—61no—
230C22×C3×C4—31no—
231C22×C3×C4—31no—
232C22×C3×C4—31no—
233C22×C3×C4—62no—
234#239—44no—
235C2×D12—22no—
236C2×D12—21no—
237C2×D12—21no—
238C2×D12C23×C312yes—
239C2×C4×D3—22no—
240C2×C4×D3C3×D411yescharacteristic
241C2×C4×D3C3×D411yescharacteristic
242C2×C4×D3C23×C311yescharacteristic
243C2×Dic6—21no—
244C2×Dic6C23×C311yescharacteristic
245C3×SD16—122no—
246C3×SD16—122no—
247C2×C3×C8—22no—
248C2×C3×C8—32no—
249C2×C3×C8—122no—
250C2×C3×C8C22×D312yes—
251C2×C3×C8C23×C312yes—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—21no—
256C3×C4⋊C4—22no—
257C3×C4⋊C4—21no—
258C3×C4⋊C4—31no—
259C3×C4⋊C4—41no—
260C3×C4⋊C4—41no—
261C3×C4⋊C4—61no—
262C3×C4⋊C4—61no—
263C3×C4⋊C4—61no—
264C3×C4⋊C4—61no—
265C3×C4⋊C4—61no—
266C3×C4⋊C4—61no—
267C3×C4⋊C4C22×D311yescharacteristic
268C3×C4⋊C4C22×D312yes—
269C3×C4⋊C4C23×C312yes—
270C3×C4⋊C4C23×C311yescharacteristic
271C3×C22⋊C4—62no—
272C3×C22⋊C4—62no—
273C3×C22⋊C4—61no—
274C3×C22⋊C4—61no—
275C3×C42—21no—
276C3×C42—21no—
277C3×C42—21no—
278C3×C42—31no—
279C3×C42—31no—
280C3×C42—31no—
281C3×C42—41no—
282C3×C42—61no—
283C3×C42C22×D311yescharacteristic
284C3×C42C23×C311yescharacteristic
285#215—42no—
286(C2×D3)⋊C4—21no—
287(C2×D3)⋊C4—21no—
288(C2×D3)⋊C4—22no—
289(C2×D3)⋊C4—22no—
290C4⋊Dic3—21no—
291C4⋊Dic3C23×C311yescharacteristic
292Dic3⋊C4—21no—
293Dic3⋊C4—21no—
294Dic3⋊C4—21no—
295Dic3⋊C4—21no—
296Dic3⋊C4—21no—
297C4×Dic3—21no—
298C4×Dic3C3×D411yescharacteristic
299C4×Dic3C3×D411yescharacteristic
300C4×Dic3C23×C311yescharacteristic
301C2×C3⋊C8C23×C312yes—
302#204—42no—
303D3×C8—42no—
304C22×C32C22×D411yescharacteristic
305C2×C3×D3—21no—
306C2×C3×D3—21no—
307C2×C3×D3—42no—
308C2×C3×D3—42no—
309C2×C3×D3—42no—
310C2×C3×D3C2×SD1612yes—
311C32×C4—21no—
312C32×C4—41no—
313C32×C4—42no—
314C32×C4—41no—
315C32×C4C2×SD1612yes—
316C32×C4H(5,𝔽2)11yescharacteristic
317C32×C42−1+411yescharacteristic
318C3×Dic3—21no—
319C3×Dic3—21no—
320C3×Dic3—41no—
321C3×Dic3—41no—
322C3×Dic3C2×SD1612yes—
323C2×#41—61no—
324C2×SD16—32no—
325C2×SD16—32no—
326C22×C8—32no—
327C4⋊Q8—31no—
328C4⋊Q8—31no—
329C4⋊Q8C2×C3×D311yescharacteristic
330#127—31no—
331#125—61no—
332#124—61no—
333C22⋊Q8—31no—
334C22⋊Q8—31no—
335C22⋊Q8—61no—
336#121—32no—
337#121—61no—
338C4×Q8—31no—
339C4×Q8—61no—
340C4×Q8C2×C3×D311yescharacteristic
341C4×D4—32no—
342C4×D4—61no—
343#117—61no—
344C2×C42—31no—
345#106—32no—
346#106C2×C3×D312yes—
347C4⋊C8—32no—
348C4⋊C8—31no—
349C4⋊C8C2×C3×D311yescharacteristic
350#103—32no—
351#103C2×C3×D312yes—
352#102—32no—
353#102—32no—
354C23×C3—31no—
355C23×C3—62no—
356C22×D3—22no—
357C22×D3C2×C3×D411yescharacteristic
358C3×Q8—22no—
359C3×Q8—21no—
360C3×Q8—21no—
361C3×Q8—21no—
362C3×Q8—21no—
363C3×Q8—41no—
364C3×Q8—42no—
365C3×Q8—42no—
366C3×Q8—61no—
367C3×Q8—61no—
368C3×Q8—82no—
369C3×Q8—122no—
370C3×D4—62no—
371C3×D4—62no—
372C3×D4—122no—
373C3×D4—124no—
374C3×D4—122no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—22no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—22no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—31no—
385C2×C3×C4—34no—
386C2×C3×C4—31no—
387C2×C3×C4—31no—
388C2×C3×C4—41no—
389C2×C3×C4—41no—
390C2×C3×C4—42no—
391C2×C3×C4—61no—
392C2×C3×C4—61no—
393C2×C3×C4—61no—
394C2×C3×C4—61no—
395C2×C3×C4—121no—
396C2×C3×C4—124no—
397C2×C3×C4D3×D411yescharacteristic
398C2×C3×C4D3×D411yescharacteristic
399C2×C3×C4C2×C3×D411yescharacteristic
400C2×C3×C4C2×C3×D411yescharacteristic
401C2×C3×C4C23×D311yescharacteristic
402C2×C3×C4C24×C311yescharacteristic
403C2×Dic3—21no—
404C2×Dic3—21no—
405C2×Dic3C2×C3×D411yescharacteristic
406C2×Dic3C2×C3×D411yescharacteristic
407C2×Dic3C2×C3×D411yescharacteristic
408D12—22no—
409D12—22no—
410D12—42no—
411D12—44no—
412D12—42no—
413C4×D3—21no—
414C4×D3—21no—
415C4×D3—41no—
416C4×D3—44no—
417C4×D3C3×SD1614yescomplemented
418Dic6—21no—
419Dic6—21no—
420Dic6—42no—
421C3×C8—22no—
422C3×C8—22no—
423C3×C8—42no—
424C3×C8—62no—
425C3⋊C8—22no—
426C2×C32#53711yescharacteristic
427C2×C32C22×SD1611yescharacteristic
428C2×C32#57511yescharacteristic
429C3×D3—22no—
430C3×D3—82no—
431#41—124no—
432C2×Q8—21no—
433C2×Q8—31no—
434C2×Q8—61no—
435C2×Q8C22×C3×D311yescharacteristic
436C2×D4—32no—
437C2×D4—62no—
438C2×D4—61no—
439C2×D4—61no—
440C22×C4—31no—
441C22×C4—31no—
442C22×C4—31no—
443C22×C4—62no—
444SD16—122no—
445SD16—122no—
446C2×C8—32no—
447C2×C8—122no—
448C2×C8C22×C3×D312yes—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—31no—
452C4⋊C4—61no—
453C4⋊C4—61no—
454C4⋊C4—61no—
455C4⋊C4—61no—
456C4⋊C4—61no—
457C4⋊C4—61no—
458C4⋊C4C22×C3×D311yescharacteristic
459C4⋊C4C22×C3×D312yes—
460C22⋊C4—62no—
461C22⋊C4—62no—
462C22⋊C4—61no—
463C22⋊C4—61no—
464C42—21no—
465C42—31no—
466C42—31no—
467C42—31no—
468C42—61no—
469C42C22×C3×D311yescharacteristic
470C22×C3—21no—
471C22×C3—32no—
472C22×C3—61no—
473C22×C3—61no—
474C22×C3—122no—
475C22×C3—122no—
476C22×C3—122no—
477C22×C3C2×D3×D411yescharacteristic
478C22×C3C22×C3×D411yescharacteristic
479C2×D3—21no—
480C2×D3—21no—
481C2×D3—42no—
482C2×D3—42no—
483C2×D3—42no—
484C2×D3C2×C3×SD1612yes—
485C3×C4—21no—
486C3×C4—21no—
487C3×C4—22no—
488C3×C4—21no—
489C3×C4—21no—
490C3×C4—32no—
491C3×C4—41no—
492C3×C4—42no—
493C3×C4—42no—
494C3×C4—41no—
495C3×C4—42no—
496C3×C4—41no—
497C3×C4—41no—
498C3×C4—41no—
499C3×C4—61no—
500C3×C4—61no—
501C3×C4—82no—
502C3×C4—81no—
503C3×C4—121no—
504C3×C4—121no—
505C3×C4D3×SD1612yes—
506C3×C4C2×C3×SD1612yes—
507C3×C4#100711yescharacteristic
508C3×C4#100911yescharacteristic
509C3×C4C3×H(5,𝔽2)11yescharacteristic
510C3×C4C3×2−1+411yescharacteristic
511Dic3—21no—
512Dic3—21no—
513Dic3—41no—
514Dic3—41no—
515Dic3C2×C3×SD1612yes—
516C32#324611yescharacteristic, complemented, Sylow
517C23—31no—
518C23—62no—
519Q8—21no—
520Q8—21no—
521Q8—42no—
522Q8—61no—
523Q8—61no—
524Q8—122no—
525D4—62no—
526D4—62no—
527D4—122no—
528D4—124no—
529D4—122no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—31no—
534C2×C4—34no—
535C2×C4—31no—
536C2×C4—31no—
537C2×C4—61no—
538C2×C4—61no—
539C2×C4—61no—
540C2×C4—61no—
541C2×C4—121no—
542C2×C4—124no—
543C2×C4C3×D3×D411yescharacteristic
544C2×C4C3×D3×D411yescharacteristic
545C2×C4C23×C3×D311yescharacteristic
546C8—22no—
547C8—62no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—62no—
552C2×C3—242no—
553C2×C3#562911yescharacteristic
554C2×C3C2×D3×SD1611yescharacteristic
555C2×C3#577711yescharacteristic
556C2×C3C3×#53711yescharacteristic
557C2×C3C22×C3×SD1611yescharacteristic
558C2×C3C3×#57511yescharacteristic
559D3—22no—
560D3—82no—
561C22—32no—
562C22—61no—
563C22—61no—
564C22—122no—
565C22—122no—
566C22—122no—
567C22C2×C3×D3×D411yescharacteristic
568C4—21no—
569C4—32no—
570C4—42no—
571C4—41no—
572C4—41no—
573C4—61no—
574C4—61no—
575C4—121no—
576C4—121no—
577C4C3×D3×SD1612yes—
578C4C3×#100711yescharacteristic
579C4C3×#100911yescharacteristic
580C3—21no—
581C3#8100211yescharacteristic, direct product factor
582C3C3×#324611yescharacteristic, complemented
583C2—62no—
584C2—242no—
585C2C3×#562911yescharacteristic
586C2C2×C3×D3×SD1611yescharacteristic
587C2C3×#577711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#475C2
socleC22×C32C22×D4
prime radicalC3×#5725C2
hypercenterC3×#475D3
hypocenterC3C3×#3246
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#475

Complements

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

NH ≅ G/Ntype
2. C3×#5578C2semidirect
3. C32×#475C2semidirect
4. C3×#5094C2semidirect
5. C3×#5027C2semidirect
6. C3×#4870C2semidirect
7. C3×#4864C2semidirect
8. C3×#4848C2semidirect
9. C3×D3×C4⋊C8C2semidirect
10. C3×#4818C2semidirect
11. C3×#4807C2semidirect
13. #81002C3direct (N × H)
48. #5578C2×C3semidirect
52. C3×#475D3semidirect
53. C3×#475C2×C3semidirect
60. #5094C2×C3semidirect
61. #5027C2×C3semidirect
62. #4870C2×C3semidirect
63. #4864C2×C3semidirect
64. #4848C2×C3semidirect
65. D3×C4⋊C8C2×C3semidirect
66. #4818C2×C3semidirect
67. #4807C2×C3semidirect
200. C3×C4×D3SD16semidirect
210. #475C3×D3semidirect
417. C4×D3C3×SD16semidirect
516. C32#3246semidirect
581. C3#81002direct (N × H)
582. C3C3×#3246semidirect

Maximal subgroups

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

subgroupindex
C3×#57252
C3×#55782
C32×#4752
C3×#50942
C3×#50272
C3×#48702
C3×#48642
C3×#48482
C3×D3×C4⋊C82
C3×#48182
C3×#48072
C3×#32463
#810023