Finite Group Databasebeta

← C3×#83390 #11864405

Subgroups — C3×#83390 #11864405

Order 1152.

1631 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic, complemented
2C32×#535C211yesmaximal, characteristic, complemented
3C22×C3×#214C211yesmaximal, characteristic, complemented
4C2×C3×#932C211yesmaximal, characteristic, complemented
5C3×#5234C211yesmaximal, characteristic, complemented
6C3×#5040C214yesmaximal, complemented
7C3×#5037C214yesmaximal, complemented
8C3×#5004C211yesmaximal, characteristic, complemented
9C3×#5002C211yesmaximal, characteristic, complemented
10C3×#3010—31nomaximal
11#83390C311yesmaximal, characteristic, direct product factor
12C2×C32×#41C2211yescharacteristic
13C22×C32×D4C2211yescharacteristic
14C3×#1010—24no—
15C3×#1010—24no—
16C2×C3×D3×Q8—21no—
17C2×C3×#237—21no—
18C2×C3×#237—22no—
19C2×C3×#235C2211yescharacteristic
20C2×C3×#235C2212yescomplemented
21C22×C3×Dic6C2211yescharacteristic
22C22×C3×Dic6C2212yescomplemented
23C32×#127—21no—
24C32×#124—21no—
25C32×#121C2214yes—
26C32×#120—22no—
27C32×#117C2211yescharacteristic
28C2×C3×#214—24no—
29C2×C3×#214C2212yes—
30C2×C3×#214C2214yes—
31C3×#932—24no—
32C2×C3×#213C2212yes—
33C2×C3×#208C2211yescharacteristic
34C22×C3×C3⋊C8C2211yescharacteristic
35C3×#830C2214yescomplemented
36C3×#810C2212yescomplemented
37C3×#810C2214yescomplemented
38C3×#809C2212yescomplemented
39C2×C3×2−1+4—31no—
40C2×#1010C2×C311yescharacteristic, complemented
41C2×C3×AGL(1,ℤ/8)—31no—
42C22×C3×SD16—31no—
43C3×#535—21no—
44C3×#535D311yescharacteristic, complemented
45C3×#535C2×C311yescharacteristic, complemented
46C22×#214C2×C311yescharacteristic, complemented
47C2×#932C2×C311yescharacteristic, complemented
48C3×#449—34no—
49C3×#448—34no—
50C3×#419—31no—
51C3×#416—31no—
52C3×#408—31no—
53#5234C2×C311yescharacteristic, complemented
54#5040C2×C314yescomplemented
55#5037C2×C314yescomplemented
56#5004C2×C311yescharacteristic, complemented
57#5002C2×C311yescharacteristic, complemented
58C24×C32—21no—
59C32×#41—22no—
60C32×#41—22no—
61C2×C32×Q8D411yescharacteristic
62C2×C32×D4—24no—
63C2×C32×D4—22no—
64C2×C32×D4—22no—
65C2×C32×D4—21no—
66C2×C32×D4D412yes—
67C2×C32×D4D411yescharacteristic
68C2×C32×D4C2312yes—
69C22×C32×C4C2312yes—
70C22×C32×C4C2311yescharacteristic
71C2×C3×#67—21no—
72C2×C3×#67—22no—
73C22×C3×Dic3—21no—
74C22×C3×Dic3—22no—
75C3×D3×Q8—28no—
76C3×#237—216no—
77C3×#237—28no—
78C3×#235—22no—
79C3×#235—24no—
80C3×#235—24no—
81C3×#235D414yescomplemented
82C2×C3×D12C2311yescharacteristic
83C2×C3×C4×D3—21no—
84C2×C3×C4×D3—22no—
85C2×C3×Dic6—21no—
86C2×C3×Dic6—22no—
87C2×C3×Dic6—22no—
88C2×C3×Dic6—24no—
89C2×C3×Dic6—24no—
90C2×C3×Dic6D414yescomplemented
91C2×C3×Dic6C2312yes—
92C2×C3×Dic6C2311yescharacteristic
93C32×C4⋊C4C2312yes—
94C32×C22⋊C4—21no—
95C32×C22⋊C4—24no—
96C32×C42—21no—
97C3×#214—24no—
98C3×#214—28no—
99C3×#213—24no—
100C3×#208—22no—
101C2×C3×C3⋊C8—22no—
102C2×C3×C3⋊C8C2312yes—
103C2×C3×C3⋊C8C2312yes—
104#3010—31noSylow
105C3×2−1+4—64no—
106C3×2−1+4—64no—
107C2×C3×#41—21no—
108C2×C3×#41—31no—
109C2×C3×#41—32no—
110C2×C3×#41—62no—
111C2×C3×#41—61no—
112C2×C3×#41C2×D311yescharacteristic
113C2×C3×#41C22×C311yescharacteristic
114C22×C3×Q8—31no—
115C22×C3×Q8—32no—
116C22×C3×Q8—61no—
117C22×C3×D4—21no—
118C22×C3×D4C2×D311yescharacteristic
119C22×C3×D4C22×C311yescharacteristic
120#1010—24no—
121#1010—24no—
122C2×D3×Q8—21no—
123C2×#237—21no—
124C2×#237—22no—
125C2×#235C22×C311yescharacteristic
126C2×#235C22×C312yescomplemented
127C22×Dic6C22×C311yescharacteristic
128C22×Dic6C22×C312yescomplemented
129C3×AGL(1,ℤ/8)—64no—
130C2×C3×SD16—34no—
131C2×C3×SD16—32no—
132C2×C3×SD16—64no—
133C2×C3×D8—32no—
134C2×C3×M16—31no—
135C22×C3×C8—31no—
136C3×#127—22no—
137C3×#127—21no—
138C3×#127—21no—
139C3×#124—22no—
140C3×#124—21no—
141C3×#124—21no—
142C3×#121—24no—
143C3×#121C2×D314yes—
144C3×#121C22×C314yes—
145C3×#120—24no—
146C3×#120—22no—
147C3×#120—22no—
148C3×#117—21no—
149C3×#117C2×D311yescharacteristic
150C3×#117C22×C311yescharacteristic
151C2×#214—24no—
152C2×#214C22×C312yes—
153C2×#214C22×C314yes—
154#932—24no—
155C2×#213C22×C312yes—
156C2×#208C22×C311yescharacteristic
157C22×C3⋊C8C22×C311yescharacteristic
158C3×#103—32no—
159C3×#103—34no—
160C3×#102—32no—
161C3×C22⋊C8—34no—
162#830C22×C314yescomplemented
163#810C22×C312yescomplemented
164#810C22×C314yescomplemented
165#809C22×C312yescomplemented
166C23×C32—22no—
167C23×C32—42no—
168C23×C32—82no—
169C23×C32C2×D412yes—
170C23×C32C2×D411yescharacteristic
171C22×C3×D3—21no—
172C32×Q8—22no—
173C32×D4—24no—
174C32×D4—22no—
175C32×D4—22no—
176C32×D4—22no—
177C32×D4—42no—
178C32×D4—84no—
179C2×C32×C4—22no—
180C2×C32×C4—22no—
181C2×C32×C4—22no—
182C2×C32×C4C2×D412yes—
183C2×C32×C4C2×D412yes—
184C2×C32×C4C2×D412yes—
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2411yescharacteristic
187C3×#67—28no—
188C3×#67—24no—
189C2×C3×Dic3—28no—
190C2×C3×Dic3—24no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—21no—
193C3×D12—21no—
194C3×D12C2×D412yes—
195C3×C4×D3—28no—
196C3×C4×D3—24no—
197C3×Dic6—28no—
198C3×Dic6—24no—
199C3×Dic6—22no—
200C3×Dic6—21no—
201C3×Dic6C2×D412yes—
202C3×Dic6C2×D414yes—
203C3×C3⋊C8—22no—
204C3×C3⋊C8—22no—
205C2×2−1+4—31no—
206C2×AGL(1,ℤ/8)—31no—
207C22×SD16—31no—
208#535C3×D311yescharacteristic, complemented
209#449—34no—
210#448—34no—
211#419—31no—
212#416—31no—
213#408—31no—
214C24×C3—22no—
215C24×C3—21no—
216C24×C3—21no—
217C3×#41—22no—
218C3×#41—22no—
219C3×#41—22no—
220C3×#41—22no—
221C3×#41—34no—
222C3×#41—42no—
223C3×#41—42no—
224C3×#41—64no—
225C3×#41—64no—
226C3×#41—616no—
227C3×#41—68no—
228C3×#41—62no—
229C2×C3×Q8—21no—
230C2×C3×Q8—34no—
231C2×C3×Q8—32no—
232C2×C3×Q8—31no—
233C2×C3×Q8—64no—
234C2×C3×Q8—64no—
235C2×C3×Q8—68no—
236C2×C3×Q8—62no—
237C2×C3×Q8—62no—
238C2×C3×Q8—61no—
239C2×C3×Q8#6711yescharacteristic
240C2×C3×Q8C3×D411yescharacteristic
241C2×C3×D4—22no—
242C2×C3×D4—28no—
243C2×C3×D4—24no—
244C2×C3×D4—24no—
245C2×C3×D4—22no—
246C2×C3×D4—22no—
247C2×C3×D4—21no—
248C2×C3×D4—22no—
249C2×C3×D4—22no—
250C2×C3×D4—21no—
251C2×C3×D4—22no—
252C2×C3×D4—21no—
253C2×C3×D4—22no—
254C2×C3×D4—31no—
255C2×C3×D4—42no—
256C2×C3×D4—42no—
257C2×C3×D4—62no—
258C2×C3×D4—61no—
259C2×C3×D4#6712yes—
260C2×C3×D4#6711yescharacteristic
261C2×C3×D4C3×D412yes—
262C2×C3×D4C3×D411yescharacteristic
263C2×C3×D4C22×D312yes—
264C2×C3×D4C23×C312yes—
265C22×C3×C4—21no—
266C22×C3×C4—22no—
267C22×C3×C4—62no—
268C22×C3×C4—61no—
269C22×C3×C4—62no—
270C22×C3×C4—61no—
271C22×C3×C4C22×D312yes—
272C22×C3×C4C22×D311yescharacteristic
273C22×C3×C4C23×C312yes—
274C22×C3×C4C23×C311yescharacteristic
275C2×#67—21no—
276C2×#67—22no—
277C22×Dic3—21no—
278C22×Dic3—22no—
279D3×Q8—28no—
280#237—216no—
281#237—28no—
282#235—22no—
283#235—24no—
284#235—24no—
285#235C3×D414yescomplemented
286C2×D12C23×C311yescharacteristic
287C2×C4×D3—21no—
288C2×C4×D3—22no—
289C2×Dic6—21no—
290C2×Dic6—22no—
291C2×Dic6—22no—
292C2×Dic6—24no—
293C2×Dic6—24no—
294C2×Dic6C3×D414yescomplemented
295C2×Dic6C23×C312yes—
296C2×Dic6C23×C311yescharacteristic
297C3×SD16—68no—
298C3×SD16—64no—
299C3×D8—64no—
300C3×M16—62no—
301C2×C3×C8—32no—
302C2×C3×C8—32no—
303C2×C3×C8—62no—
304C3×C4⋊C4—22no—
305C3×C4⋊C4C22×D312yes—
306C3×C4⋊C4C23×C312yes—
307C3×C22⋊C4—22no—
308C3×C22⋊C4—28no—
309C3×C22⋊C4—21no—
310C3×C22⋊C4—21no—
311C3×C22⋊C4—24no—
312C3×C22⋊C4—24no—
313C3×C42—22no—
314C3×C42—21no—
315C3×C42—21no—
316#214—24no—
317#214—28no—
318#213—24no—
319#208—22no—
320C2×C3⋊C8—22no—
321C2×C3⋊C8C23×C312yes—
322C2×C3⋊C8C23×C312yes—
323C22×C32—22no—
324C22×C32—22no—
325C22×C32—24no—
326C22×C32—42no—
327C22×C32—44no—
328C22×C32—84no—
329C22×C32#12012yes—
330C22×C32C22×D411yescharacteristic
331C2×C3×D3—22no—
332C2×C3×D3—42no—
333C32×C4—22no—
334C32×C4—42no—
335C32×C4#12012yes—
336C32×C4C22×D411yescharacteristic
337C32×C4C22×D411yescharacteristic
338C3×Dic3—22no—
339C3×Dic3—24no—
3402−1+4—64no—
3412−1+4—64no—
342C2×#41—31no—
343C2×#41—32no—
344C2×#41—62no—
345C2×#41—61no—
346C2×#41C2×C3×D311yescharacteristic
347C22×Q8—31no—
348C22×Q8—32no—
349C22×Q8—61no—
350C22×D4C2×C3×D311yescharacteristic
351AGL(1,ℤ/8)—64no—
352C2×SD16—34no—
353C2×SD16—32no—
354C2×SD16—64no—
355C2×D8—32no—
356C2×M16—31no—
357C22×C8—31no—
358#127—21no—
359#124—21no—
360#121C2×C3×D314yes—
361#120—22no—
362#117C2×C3×D311yescharacteristic
363#103—32no—
364#103—34no—
365#102—32no—
366C22⋊C8—34no—
367C23×C3—24no—
368C23×C3—22no—
369C23×C3—22no—
370C23×C3—21no—
371C23×C3—22no—
372C23×C3—44no—
373C23×C3—42no—
374C23×C3—42no—
375C23×C3—61no—
376C23×C3—82no—
377C23×C3—82no—
378C23×C3—84no—
379C23×C3C2×#6712yes—
380C23×C3C2×#6711yescharacteristic
381C23×C3C2×C3×D412yes—
382C23×C3C2×C3×D411yescharacteristic
383C22×D3—21no—
384C3×Q8—22no—
385C3×Q8—22no—
386C3×Q8—34no—
387C3×Q8—32no—
388C3×Q8—42no—
389C3×Q8—68no—
390C3×Q8—64no—
391C3×Q8—62no—
392C3×Q8—61no—
393C3×D4—24no—
394C3×D4—24no—
395C3×D4—22no—
396C3×D4—22no—
397C3×D4—22no—
398C3×D4—22no—
399C3×D4—22no—
400C3×D4—22no—
401C3×D4—32no—
402C3×D4—42no—
403C3×D4—42no—
404C3×D4—42no—
405C3×D4—44no—
406C3×D4—44no—
407C3×D4—42no—
408C3×D4—42no—
409C3×D4—68no—
410C3×D4—64no—
411C3×D4—61no—
412C3×D4—84no—
413C3×D4—84no—
414C3×D4—88no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—24no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—21no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—21no—
426C2×C3×C4—22no—
427C2×C3×C4—42no—
428C2×C3×C4—42no—
429C2×C3×C4—68no—
430C2×C3×C4—68no—
431C2×C3×C4—64no—
432C2×C3×C4—62no—
433C2×C3×C4—61no—
434C2×C3×C4—64no—
435C2×C3×C4D3×D412yes—
436C2×C3×C4D3×D412yes—
437C2×C3×C4C2×#6712yes—
438C2×C3×C4C2×#6711yescharacteristic
439C2×C3×C4C2×C3×D412yes—
440C2×C3×C4C2×C3×D412yes—
441C2×C3×C4C2×C3×D412yes—
442C2×C3×C4C2×C3×D411yescharacteristic
443C2×C3×C4C23×D311yescharacteristic
444C2×C3×C4C24×C311yescharacteristic
445#67—28no—
446#67—24no—
447C2×Dic3—28no—
448C2×Dic3—24no—
449C2×Dic3—22no—
450C2×Dic3—21no—
451D12—21no—
452D12C2×C3×D412yes—
453C4×D3—28no—
454C4×D3—24no—
455Dic6—28no—
456Dic6—24no—
457Dic6—22no—
458Dic6—21no—
459Dic6C2×C3×D412yes—
460Dic6C2×C3×D414yes—
461C3×C8—62no—
462C3×C8—62no—
463C3⋊C8—22no—
464C3⋊C8—22no—
465C2×C32—22no—
466C2×C32—42no—
467C2×C32—82no—
468C2×C32C2×#12011yescharacteristic
469C2×C32#57712yes—
470C3×D3—42no—
471C24—21no—
472#41—22no—
473#41—22no—
474#41—34no—
475#41—64no—
476#41—64no—
477#41—616no—
478#41—68no—
479#41—62no—
480C2×Q8—32no—
481C2×Q8—31no—
482C2×Q8—34no—
483C2×Q8—64no—
484C2×Q8—64no—
485C2×Q8—68no—
486C2×Q8—62no—
487C2×Q8—62no—
488C2×Q8—61no—
489C2×Q8C3×#6711yescharacteristic
490C2×D4—24no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—21no—
494C2×D4—31no—
495C2×D4—62no—
496C2×D4—61no—
497C2×D4C3×#6712yes—
498C2×D4C3×#6711yescharacteristic
499C2×D4C22×C3×D312yes—
500C22×C4—62no—
501C22×C4—61no—
502C22×C4—62no—
503C22×C4—61no—
504C22×C4C22×C3×D312yes—
505C22×C4C22×C3×D311yescharacteristic
506SD16—68no—
507SD16—64no—
508D8—64no—
509M16—62no—
510C2×C8—32no—
511C2×C8—32no—
512C2×C8—62no—
513C4⋊C4C22×C3×D312yes—
514C22⋊C4—21no—
515C22⋊C4—24no—
516C42—21no—
517C22×C3—22no—
518C22×C3—22no—
519C22×C3—24no—
520C22×C3—22no—
521C22×C3—24no—
522C22×C3—22no—
523C22×C3—22no—
524C22×C3—21no—
525C22×C3—42no—
526C22×C3—42no—
527C22×C3—44no—
528C22×C3—44no—
529C22×C3—48no—
530C22×C3—44no—
531C22×C3—42no—
532C22×C3—44no—
533C22×C3—42no—
534C22×C3—62no—
535C22×C3—84no—
536C22×C3—84no—
537C22×C3—88no—
538C22×C3—122no—
539C22×C3#93712yes—
540C22×C3C3×#12012yes—
541C22×C3C22×#6711yescharacteristic
542C22×C3C22×C3×D411yescharacteristic
543C2×D3—22no—
544C2×D3—42no—
545C3×C4—22no—
546C3×C4—22no—
547C3×C4—22no—
548C3×C4—21no—
549C3×C4—21no—
550C3×C4—42no—
551C3×C4—44no—
552C3×C4—42no—
553C3×C4—42no—
554C3×C4—64no—
555C3×C4—62no—
556C3×C4#93712yes—
557C3×C4C3×#12012yes—
558C3×C4C2×D3×D411yescharacteristic
559C3×C4C2×D3×D411yescharacteristic
560C3×C4C22×C3×D411yescharacteristic
561C3×C4C22×C3×D411yescharacteristic
562Dic3—22no—
563Dic3—24no—
564C32#301011yescharacteristic, complemented, Sylow
565C23—22no—
566C23—42no—
567C23—61no—
568C23—82no—
569C23C2×C3×#6712yes—
570C23C2×C3×#6711yescharacteristic
571Q8—22no—
572Q8—34no—
573Q8—32no—
574Q8—68no—
575Q8—64no—
576Q8—62no—
577Q8—61no—
578D4—24no—
579D4—22no—
580D4—22no—
581D4—22no—
582D4—32no—
583D4—42no—
584D4—68no—
585D4—64no—
586D4—61no—
587D4—84no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—68no—
592C2×C4—68no—
593C2×C4—64no—
594C2×C4—62no—
595C2×C4—61no—
596C2×C4—64no—
597C2×C4C3×D3×D412yes—
598C2×C4C3×D3×D412yes—
599C2×C4C2×C3×#6712yes—
600C2×C4C2×C3×#6711yescharacteristic
601C2×C4C23×C3×D311yescharacteristic
602C8—62no—
603C8—62no—
604C2×C3—22no—
605C2×C3—22no—
606C2×C3—21no—
607C2×C3—22no—
608C2×C3—42no—
609C2×C3—42no—
610C2×C3—42no—
611C2×C3—82no—
612C2×C3—84no—
613C2×C3—82no—
614C2×C3—82no—
615C2×C3—122no—
616C2×C3C2×#93711yescharacteristic
617C2×C3#583612yes—
618C2×C3C2×C3×#12011yescharacteristic
619C2×C3C3×#57712yes—
620D3—42no—
621C22—22no—
622C22—22no—
623C22—24no—
624C22—42no—
625C22—44no—
626C22—62no—
627C22—84no—
628C22—122no—
629C22C3×#93712yes—
630C22C22×C3×#6711yescharacteristic
631C4—22no—
632C4—42no—
633C4—64no—
634C4—62no—
635C4C3×#93712yes—
636C4C2×C3×D3×D411yescharacteristic
637C4C2×C3×D3×D411yescharacteristic
638C3—21no—
639C3#8339011yescharacteristic, direct product factor
640C3C3×#301011yescharacteristic, complemented
641C2—22no—
642C2—42no—
643C2—82no—
644C2—122no—
645C2C2×C3×#93711yescharacteristic
646C2C3×#583612yes—
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#535C2
socleC22×C32C22×D4
hypercenterC3×#535D3
hypocenterC3C3×#3010
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×#41 ◁ C3×#535

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1010C2semidirect
2. C32×#535C2semidirect
3. C22×C3×#214C2semidirect
4. C2×C3×#932C2semidirect
5. C3×#5234C2semidirect
6. C3×#5040C2semidirect
7. C3×#5037C2semidirect
8. C3×#5004C2semidirect
9. C3×#5002C2semidirect
11. #83390C3direct (N × H)
20. C2×C3×#235C22semidirect
22. C22×C3×Dic6C22semidirect
35. C3×#830C22semidirect
36. C3×#810C22semidirect
37. C3×#810C22semidirect
38. C3×#809C22semidirect
40. C2×#1010C2×C3semidirect
44. C3×#535D3semidirect
45. C3×#535C2×C3semidirect
46. C22×#214C2×C3semidirect
47. C2×#932C2×C3semidirect
53. #5234C2×C3semidirect
54. #5040C2×C3semidirect
55. #5037C2×C3semidirect
56. #5004C2×C3semidirect
57. #5002C2×C3semidirect
81. C3×#235D4semidirect
90. C2×C3×Dic6D4semidirect
126. C2×#235C22×C3semidirect
128. C22×Dic6C22×C3semidirect
162. #830C22×C3semidirect
163. #810C22×C3semidirect
164. #810C22×C3semidirect
165. #809C22×C3semidirect
208. #535C3×D3semidirect
285. #235C3×D4semidirect
294. C2×Dic6C3×D4semidirect
564. C32#3010semidirect
639. C3#83390direct (N × H)
640. C3C3×#3010semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C32×#5352
C22×C3×#2142
C2×C3×#9322
C3×#52342
C3×#50402
C3×#50372
C3×#50042
C3×#50022
C3×#30103
#833903