Finite Group Databasebeta

← C3×#83860 #11864399

Subgroups — C3×#83860 #11864399

Order 1152.

1613 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1007C211yesmaximal, characteristic, complemented
2C22×C32×SD16C211yesmaximal, characteristic, complemented
3C3×#5805C211yesmaximal, characteristic, complemented
4C2×C3×#932C211yesmaximal, characteristic, complemented
5C3×#5225C211yesmaximal, characteristic, complemented
6C3×#5172C214yesmaximal, complemented
7C3×#5170C214yesmaximal, complemented
8C3×#5113C211yesmaximal, characteristic, complemented
9C3×#5110C211yesmaximal, characteristic, complemented
10C3×#3010—31nomaximal
11#83860C311yesmaximal, characteristic, direct product factor
12C22×C32×Q8C2211yescharacteristic
13C22×C32×D4C2211yescharacteristic
14C3×#1007—24no—
15C3×#1007—24no—
16C2×C3×#239—21no—
17C2×C3×#239C2212yescomplemented
18C2×C3×D3×Q8—21no—
19C2×C3×D3×Q8C2212yescomplemented
20C2×C3×#235—22no—
21C2×C3×#235C2211yescharacteristic
22C2×C3×#235C2211yescharacteristic
23C2×C32×SD16—24no—
24C2×C32×SD16C2214yes—
25C22×C32×C8C2211yescharacteristic
26C3×#953—22no—
27C3×#940—21no—
28C3×#938C2214yes—
29C3×#936—21no—
30C2×C3×#214C2212yes—
31C3×#932—24no—
32C2×C3×#213C2212yes—
33C3×#926C2211yescharacteristic
34C2×C3×#208C2211yescharacteristic
35C3×#835C2214yescomplemented
36C3×#821C2212yescomplemented
37C3×(C2×D3)⋊C8C2214yescomplemented
38C3×#816C2212yescomplemented
39C2×C3×2−1+4—31no—
40C2×#1007C2×C311yescharacteristic, complemented
41C2×C3×AGL(1,ℤ/8)—31no—
42C22×C3×SD16—21no—
43C22×C3×SD16D311yescharacteristic, complemented
44C22×C3×SD16C2×C311yescharacteristic, complemented
45C3×#535—31no—
46#5805C2×C311yescharacteristic, complemented
47C2×#932C2×C311yescharacteristic, complemented
48C3×#449—34no—
49C3×#448—34no—
50C3×#419—31no—
51C3×#416—31no—
52C3×#408—31no—
53#5225C2×C311yescharacteristic, complemented
54#5172C2×C314yescomplemented
55#5170C2×C314yescomplemented
56#5113C2×C311yescharacteristic, complemented
57#5110C2×C311yescharacteristic, complemented
58C24×C32—21no—
59C2×C32×Q8—21no—
60C2×C32×Q8—22no—
61C2×C32×Q8D414yescomplemented
62C2×C32×Q8C2312yes—
63C2×C32×D4—22no—
64C2×C32×D4—22no—
65C2×C32×D4—21no—
66C2×C32×D4C2312yes—
67C22×C32×C4—21no—
68C22×C32×C4C2311yescharacteristic
69C2×C3×#67—21no—
70C2×C3×#67—24no—
71C2×C3×#67D412yes—
72C3×#239—28no—
73C3×#239—24no—
74C3×#239—24no—
75C3×D3×Q8—28no—
76C3×D3×Q8—24no—
77C3×D3×Q8—24no—
78C3×#235—216no—
79C3×#235—22no—
80C3×#235—22no—
81C3×#235—22no—
82C3×#235D414yescomplemented
83C2×C3×D12—22no—
84C2×C3×D12D411yescharacteristic
85C2×C3×D12C2311yescharacteristic
86C2×C3×C4×D3—22no—
87C2×C3×C4×D3—21no—
88C2×C3×C4×D3—22no—
89C2×C3×C4×D3C2312yes—
90C2×C3×Dic6—22no—
91C2×C3×Dic6D411yescharacteristic
92C2×C3×Dic6C2311yescharacteristic
93C32×SD16—28no—
94C2×C32×C8—22no—
95C2×C32×C8C2312yes—
96C3×#217—21no—
97C3×#217—24no—
98C3×#214—24no—
99C3×#213—24no—
100C3×C4⋊Dic3C2312yes—
101C3×C4×Dic3—21no—
102C3×#208—22no—
103C2×C3×C3⋊C8C2312yes—
104#3010—31noSylow
105C3×2−1+4—64no—
106C3×2−1+4—64no—
107C2×C3×#41—31no—
108C2×C3×#41—32no—
109C2×C3×#41—31no—
110C2×C3×#41—62no—
111C2×C3×#41—61no—
112C22×C3×Q8—21no—
113C22×C3×Q8—32no—
114C22×C3×Q8—61no—
115C22×C3×Q8C2×D311yescharacteristic
116C22×C3×Q8C22×C311yescharacteristic
117C22×C3×D4—21no—
118C22×C3×D4C2×D311yescharacteristic
119C22×C3×D4C22×C311yescharacteristic
120#1007—24no—
121#1007—24no—
122C2×#239—21no—
123C2×#239C22×C312yescomplemented
124C2×D3×Q8—21no—
125C2×D3×Q8C22×C312yescomplemented
126C2×#235—22no—
127C2×#235C22×C311yescharacteristic
128C2×#235C22×C311yescharacteristic
129C3×AGL(1,ℤ/8)—64no—
130C2×C3×SD16—28no—
131C2×C3×SD16—24no—
132C2×C3×SD16—24no—
133C2×C3×SD16—24no—
134C2×C3×SD16—32no—
135C2×C3×SD16C2×D314yes—
136C2×C3×SD16C22×C314yes—
137C2×C3×D8—32no—
138C2×C3×M16—31no—
139C22×C3×C8—21no—
140C22×C3×C8C2×D311yescharacteristic
141C22×C3×C8C22×C311yescharacteristic
142C3×#127—61no—
143C3×#124—61no—
144C3×#121—34no—
145C3×#120—62no—
146C3×#117—31no—
147#953—22no—
148#940—21no—
149#938C22×C314yes—
150#936—21no—
151C2×#214C22×C312yes—
152#932—24no—
153C2×#213C22×C312yes—
154#926C22×C311yescharacteristic
155C2×#208C22×C311yescharacteristic
156C3×#103—34no—
157C3×#103—32no—
158C3×#102—32no—
159C3×C22⋊C8—34no—
160#835C22×C314yescomplemented
161#821C22×C312yescomplemented
162(C2×D3)⋊C8C22×C314yescomplemented
163#816C22×C312yescomplemented
164C23×C32—22no—
165C23×C32—42no—
166C23×C32—82no—
167C23×C32C2×D411yescharacteristic
168C22×C3×D3—21no—
169C22×C3×D3C2×D412yes—
170C32×Q8—24no—
171C32×Q8—22no—
172C32×Q8C2×D414yes—
173C32×D4—22no—
174C32×D4—22no—
175C32×D4—42no—
176C2×C32×C4—24no—
177C2×C32×C4—22no—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×D412yes—
180C2×C32×C4C2×D412yes—
181C2×C32×C4C2411yescharacteristic
182C3×#67—24no—
183C3×#67—24no—
184C3×#67—84no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3C2×D412yes—
188C3×D12—28no—
189C3×D12—22no—
190C3×D12—21no—
191C3×D12C2×D412yes—
192C3×C4×D3—28no—
193C3×C4×D3—28no—
194C3×C4×D3—24no—
195C3×C4×D3—22no—
196C3×C4×D3—22no—
197C3×Dic6—28no—
198C3×Dic6—22no—
199C3×Dic6—21no—
200C3×Dic6C2×D412yes—
201C32×C8—22no—
202C3×C3⋊C8—22no—
203C2×2−1+4—31no—
204C2×AGL(1,ℤ/8)—31no—
205C22×SD16C3×D311yescharacteristic, complemented
206#535—31no—
207#449—34no—
208#448—34no—
209#419—31no—
210#416—31no—
211#408—31no—
212C24×C3—21no—
213C24×C3—21no—
214C24×C3—41no—
215C3×#41—34no—
216C3×#41—616no—
217C3×#41—64no—
218C3×#41—68no—
219C3×#41—64no—
220C3×#41—62no—
221C3×#41—62no—
222C3×#41—62no—
223C2×C3×Q8—21no—
224C2×C3×Q8—22no—
225C2×C3×Q8—21no—
226C2×C3×Q8—22no—
227C2×C3×Q8—24no—
228C2×C3×Q8—22no—
229C2×C3×Q8—31no—
230C2×C3×Q8—31no—
231C2×C3×Q8—41no—
232C2×C3×Q8—42no—
233C2×C3×Q8—62no—
234C2×C3×Q8—64no—
235C2×C3×Q8—68no—
236C2×C3×Q8—64no—
237C2×C3×Q8#6714yescomplemented
238C2×C3×Q8C3×D414yescomplemented
239C2×C3×Q8C22×D312yes—
240C2×C3×Q8C23×C312yes—
241C2×C3×D4—24no—
242C2×C3×D4—22no—
243C2×C3×D4—21no—
244C2×C3×D4—22no—
245C2×C3×D4—22no—
246C2×C3×D4—22no—
247C2×C3×D4—21no—
248C2×C3×D4—22no—
249C2×C3×D4—32no—
250C2×C3×D4—31no—
251C2×C3×D4—31no—
252C2×C3×D4—42no—
253C2×C3×D4—41no—
254C2×C3×D4—62no—
255C2×C3×D4—61no—
256C2×C3×D4—64no—
257C2×C3×D4C22×D312yes—
258C2×C3×D4C23×C312yes—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—32no—
263C22×C3×C4—41no—
264C22×C3×C4—62no—
265C22×C3×C4—62no—
266C22×C3×C4—61no—
267C22×C3×C4C22×D311yescharacteristic
268C22×C3×C4C23×C311yescharacteristic
269C2×#67—21no—
270C2×#67—24no—
271C2×#67C3×D412yes—
272#239—28no—
273#239—24no—
274#239—24no—
275D3×Q8—28no—
276D3×Q8—24no—
277D3×Q8—24no—
278#235—216no—
279#235—22no—
280#235—22no—
281#235—22no—
282#235C3×D414yescomplemented
283C2×D12—22no—
284C2×D12C3×D411yescharacteristic
285C2×D12C23×C311yescharacteristic
286C2×C4×D3—22no—
287C2×C4×D3—21no—
288C2×C4×D3—22no—
289C2×C4×D3C23×C312yes—
290C2×Dic6—22no—
291C2×Dic6C3×D411yescharacteristic
292C2×Dic6C23×C311yescharacteristic
293C3×SD16—216no—
294C3×SD16—28no—
295C3×SD16—28no—
296C3×SD16—64no—
297C3×D8—64no—
298C3×M16—62no—
299C2×C3×C8—24no—
300C2×C3×C8—22no—
301C2×C3×C8—22no—
302C2×C3×C8—22no—
303C2×C3×C8—32no—
304C2×C3×C8C22×D312yes—
305C2×C3×C8C23×C312yes—
306C3×C4⋊C4—32no—
307C3×C22⋊C4—64no—
308C3×C22⋊C4—61no—
309C3×C42—61no—
310#217—21no—
311#217—24no—
312#214—24no—
313#213—24no—
314C4⋊Dic3C23×C312yes—
315C4×Dic3—21no—
316#208—22no—
317C2×C3⋊C8C23×C312yes—
318C22×C32—22no—
319C22×C32—42no—
320C22×C32—44no—
321C22×C32—84no—
322C22×C32#12012yes—
323C22×C32C22×D411yescharacteristic
324C2×C3×D3—22no—
325C2×C3×D3—22no—
326C2×C3×D3—24no—
327C2×C3×D3—42no—
328C32×C4—24no—
329C32×C4#12012yes—
330C32×C4C22×D411yescharacteristic
331C32×C4C22×D411yescharacteristic
332C3×Dic3—22no—
333C3×Dic3—22no—
334C3×Dic3—42no—
3352−1+4—64no—
3362−1+4—64no—
337C2×#41—31no—
338C2×#41—32no—
339C2×#41—31no—
340C2×#41—62no—
341C2×#41—61no—
342C22×Q8—32no—
343C22×Q8—61no—
344C22×Q8C2×C3×D311yescharacteristic
345C22×D4C2×C3×D311yescharacteristic
346AGL(1,ℤ/8)—64no—
347C2×SD16—24no—
348C2×SD16—32no—
349C2×SD16C2×C3×D314yes—
350C2×D8—32no—
351C2×M16—31no—
352C22×C8C2×C3×D311yescharacteristic
353#127—61no—
354#124—61no—
355#121—34no—
356#120—62no—
357#117—31no—
358#103—34no—
359#103—32no—
360#102—32no—
361C22⋊C8—34no—
362C23×C3—22no—
363C23×C3—22no—
364C23×C3—21no—
365C23×C3—32no—
366C23×C3—42no—
367C23×C3—44no—
368C23×C3—42no—
369C23×C3—42no—
370C23×C3—61no—
371C23×C3—82no—
372C23×C3—82no—
373C23×C3—84no—
374C23×C3D3×D411yescharacteristic
375C23×C3C2×C3×D411yescharacteristic
376C22×D3—21no—
377C22×D3C2×C3×D412yes—
378C3×Q8—24no—
379C3×Q8—24no—
380C3×Q8—22no—
381C3×Q8—22no—
382C3×Q8—24no—
383C3×Q8—32no—
384C3×Q8—44no—
385C3×Q8—42no—
386C3×Q8—68no—
387C3×Q8—62no—
388C3×Q8—61no—
389C3×Q8C2×#6714yes—
390C3×Q8C2×C3×D414yes—
391C3×D4—24no—
392C3×D4—22no—
393C3×D4—22no—
394C3×D4—22no—
395C3×D4—22no—
396C3×D4—32no—
397C3×D4—42no—
398C3×D4—44no—
399C3×D4—42no—
400C3×D4—42no—
401C3×D4—68no—
402C3×D4—64no—
403C3×D4—64no—
404C3×D4—62no—
405C3×D4—61no—
406C3×D4—244no—
407C2×C3×C4—24no—
408C2×C3×C4—24no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—32no—
416C2×C3×C4—44no—
417C2×C3×C4—42no—
418C2×C3×C4—68no—
419C2×C3×C4—68no—
420C2×C3×C4—61no—
421C2×C3×C4—64no—
422C2×C3×C4—62no—
423C2×C3×C4—62no—
424C2×C3×C4—62no—
425C2×C3×C4D3×D411yescharacteristic
426C2×C3×C4D3×D412yes—
427C2×C3×C4C2×#6712yes—
428C2×C3×C4C2×C3×D411yescharacteristic
429C2×C3×C4C2×C3×D412yes—
430C2×C3×C4C2×C3×D412yes—
431C2×C3×C4C23×D311yescharacteristic
432C2×C3×C4C24×C311yescharacteristic
433#67—24no—
434#67—24no—
435#67—84no—
436C2×Dic3—21no—
437C2×Dic3—22no—
438C2×Dic3C2×C3×D412yes—
439D12—28no—
440D12—22no—
441D12—21no—
442D12C2×C3×D412yes—
443C4×D3—28no—
444C4×D3—28no—
445C4×D3—24no—
446C4×D3—22no—
447C4×D3—22no—
448Dic6—28no—
449Dic6—22no—
450Dic6—21no—
451Dic6C2×C3×D412yes—
452C3×C8—24no—
453C3×C8—22no—
454C3×C8—22no—
455C3×C8—62no—
456C3⋊C8—22no—
457C2×C32—22no—
458C2×C32—82no—
459C2×C32C2×#12011yescharacteristic
460C2×C32#57712yes—
461C3×D3—42no—
462C3×D3—42no—
463C24—21no—
464#41—34no—
465#41—616no—
466#41—64no—
467#41—68no—
468#41—64no—
469#41—62no—
470#41—62no—
471#41—62no—
472C2×Q8—21no—
473C2×Q8—22no—
474C2×Q8—31no—
475C2×Q8—31no—
476C2×Q8—62no—
477C2×Q8—64no—
478C2×Q8—68no—
479C2×Q8—64no—
480C2×Q8C3×#6714yescomplemented
481C2×Q8C22×C3×D312yes—
482C2×D4—22no—
483C2×D4—21no—
484C2×D4—22no—
485C2×D4—32no—
486C2×D4—31no—
487C2×D4—31no—
488C2×D4—62no—
489C2×D4—61no—
490C2×D4—64no—
491C2×D4C22×C3×D312yes—
492C22×C4—21no—
493C22×C4—32no—
494C22×C4—62no—
495C22×C4—62no—
496C22×C4—61no—
497C22×C4C22×C3×D311yescharacteristic
498SD16—28no—
499SD16—64no—
500D8—64no—
501M16—62no—
502C2×C8—22no—
503C2×C8—32no—
504C2×C8C22×C3×D312yes—
505C4⋊C4—32no—
506C22⋊C4—64no—
507C22⋊C4—61no—
508C42—61no—
509C22×C3—24no—
510C22×C3—22no—
511C22×C3—22no—
512C22×C3—22no—
513C22×C3—21no—
514C22×C3—44no—
515C22×C3—44no—
516C22×C3—44no—
517C22×C3—42no—
518C22×C3—42no—
519C22×C3—64no—
520C22×C3—62no—
521C22×C3—62no—
522C22×C3—84no—
523C22×C3—88no—
524C22×C3—84no—
525C22×C3—84no—
526C22×C3—122no—
527C22×C3#93712yes—
528C22×C3C3×#12012yes—
529C22×C3C2×D3×D411yescharacteristic
530C22×C3C22×C3×D411yescharacteristic
531C2×D3—24no—
532C2×D3—22no—
533C2×D3—22no—
534C2×D3—42no—
535C3×C4—24no—
536C3×C4—24no—
537C3×C4—22no—
538C3×C4—21no—
539C3×C4—21no—
540C3×C4—44no—
541C3×C4—62no—
542C3×C4—62no—
543C3×C4—122no—
544C3×C4#93712yes—
545C3×C4C3×#12012yes—
546C3×C4C2×D3×D411yescharacteristic
547C3×C4C22×#6711yescharacteristic
548C3×C4C22×C3×D411yescharacteristic
549C3×C4C22×C3×D411yescharacteristic
550Dic3—22no—
551Dic3—22no—
552Dic3—42no—
553C32#301011yescharacteristic, complemented, Sylow
554C23—22no—
555C23—32no—
556C23—42no—
557C23—61no—
558C23—82no—
559C23C3×D3×D411yescharacteristic
560Q8—24no—
561Q8—22no—
562Q8—32no—
563Q8—68no—
564Q8—62no—
565Q8—61no—
566Q8C2×C3×#6714yes—
567D4—22no—
568D4—22no—
569D4—32no—
570D4—42no—
571D4—68no—
572D4—64no—
573D4—64no—
574D4—62no—
575D4—61no—
576D4—244no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—32no—
580C2×C4—68no—
581C2×C4—68no—
582C2×C4—61no—
583C2×C4—64no—
584C2×C4—62no—
585C2×C4—62no—
586C2×C4—62no—
587C2×C4C3×D3×D411yescharacteristic
588C2×C4C3×D3×D412yes—
589C2×C4C2×C3×#6712yes—
590C2×C4C23×C3×D311yescharacteristic
591C8—22no—
592C8—62no—
593C2×C3—24no—
594C2×C3—22no—
595C2×C3—22no—
596C2×C3—22no—
597C2×C3—21no—
598C2×C3—84no—
599C2×C3—82no—
600C2×C3—82no—
601C2×C3—122no—
602C2×C3—122no—
603C2×C3#576212yes—
604C2×C3C2×#93711yescharacteristic
605C2×C3C2×C3×#12011yescharacteristic
606C2×C3C3×#57712yes—
607D3—42no—
608D3—42no—
609C22—22no—
610C22—44no—
611C22—42no—
612C22—64no—
613C22—62no—
614C22—62no—
615C22—84no—
616C22—122no—
617C22C3×#93712yes—
618C22C2×C3×D3×D411yescharacteristic
619C4—24no—
620C4—62no—
621C4—62no—
622C4—122no—
623C4C3×#93712yes—
624C4C2×C3×D3×D411yescharacteristic
625C4C22×C3×#6711yescharacteristic
626C3—21no—
627C3#8386011yescharacteristic, direct product factor
628C3C3×#301011yescharacteristic, complemented
629C2—22no—
630C2—82no—
631C2—122no—
632C2—122no—
633C2C3×#576212yes—
634C2C2×C3×#93711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC22×C32×SD16C2
socleC22×C32C22×D4
hypercenterC22×C3×SD16D3
hypocenterC3C3×#3010
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C22×C3×SD16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1007C2semidirect
2. C22×C32×SD16C2semidirect
3. C3×#5805C2semidirect
4. C2×C3×#932C2semidirect
5. C3×#5225C2semidirect
6. C3×#5172C2semidirect
7. C3×#5170C2semidirect
8. C3×#5113C2semidirect
9. C3×#5110C2semidirect
11. #83860C3direct (N × H)
17. C2×C3×#239C22semidirect
19. C2×C3×D3×Q8C22semidirect
35. C3×#835C22semidirect
36. C3×#821C22semidirect
37. C3×(C2×D3)⋊C8C22semidirect
38. C3×#816C22semidirect
40. C2×#1007C2×C3semidirect
43. C22×C3×SD16D3semidirect
44. C22×C3×SD16C2×C3semidirect
46. #5805C2×C3semidirect
47. C2×#932C2×C3semidirect
53. #5225C2×C3semidirect
54. #5172C2×C3semidirect
55. #5170C2×C3semidirect
56. #5113C2×C3semidirect
57. #5110C2×C3semidirect
61. C2×C32×Q8D4semidirect
82. C3×#235D4semidirect
123. C2×#239C22×C3semidirect
125. C2×D3×Q8C22×C3semidirect
160. #835C22×C3semidirect
161. #821C22×C3semidirect
162. (C2×D3)⋊C8C22×C3semidirect
163. #816C22×C3semidirect
205. C22×SD16C3×D3semidirect
237. C2×C3×Q8#67semidirect
238. C2×C3×Q8C3×D4semidirect
282. #235C3×D4semidirect
480. C2×Q8C3×#67semidirect
553. C32#3010semidirect
627. C3#83860direct (N × H)
628. C3C3×#3010semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10072
C22×C32×SD162
C3×#58052
C2×C3×#9322
C3×#52252
C3×#51722
C3×#51702
C3×#51132
C3×#51102
C3×#30103
#838603