Finite Group Databasebeta

← C3×#78927 #11864043

Subgroups — C3×#78927 #11864043

Order 1152.

1611 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#237C211yesmaximal, characteristic, complemented
2C2×C3×#932C211yesmaximal, characteristic, complemented
3C2×C3×#909C211yesmaximal, characteristic, complemented
4C3×#5524C211yesmaximal, characteristic, complemented
5C32×#418C211yesmaximal, characteristic, complemented
6C3×#5126C211yesmaximal, characteristic, complemented
7C3×#5004C211yesmaximal, characteristic, complemented
8C3×#4783C214yesmaximal, complemented
9C3×#4781C214yesmaximal, complemented
10C3×#3005—31nomaximal
11#78927C311yesmaximal, characteristic, direct product factor
12C22×C32×D4C2211yescharacteristic
13C22×C3×#67—21no—
14C23×C3×Dic3—21no—
15C2×C3×#237—24no—
16C2×C3×#237—22no—
17C2×C3×#237—24no—
18C2×C3×#237C2214yes—
19C2×C3×#235C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic
22C2×C32×M16C2211yescharacteristic
23C32×#117C2211yescharacteristic
24C2×C3×#214C2212yescomplemented
25C3×#932—24no—
26C2×C3×#213C2212yescomplemented
27C2×C3×#208C2211yescharacteristic
28C3×#909—24no—
29C2×C3×Dic12C2212yescomplemented
30C2×C3×#204C2212yescomplemented
31C3×#897C2212yescomplemented
32C3×#895C2212yescomplemented
33C3×#886—21no—
34C3×#882—21no—
35C3×C4×D12—22no—
36C32×#102C2214yescomplemented
37C3×(C2×D3)⋊C8C2214yescomplemented
38C3×#810C2214yescomplemented
39C22×C3×#41—31no—
40C22×#237C2×C311yescharacteristic, complemented
41C2×C3×#137—31no—
42C2×C3×AGL(1,ℤ/8)—31no—
43C3×#525—31no—
44C2×#932C2×C311yescharacteristic, complemented
45C2×#909C2×C311yescharacteristic, complemented
46#5524C2×C311yescharacteristic, complemented
47C3×#452—34no—
48C3×#449—34no—
49C3×#419—31no—
50C3×#418—21no—
51C3×#418D311yescharacteristic, complemented
52C3×#418C2×C311yescharacteristic, complemented
53C3×#407—31no—
54#5126C2×C311yescharacteristic, complemented
55#5004C2×C311yescharacteristic, complemented
56#4783C2×C314yescomplemented
57#4781C2×C314yescomplemented
58C24×C32—21no—
59C23×C3×D3D411yescharacteristic
60C2×C32×D4—21no—
61C2×C32×D4—22no—
62C2×C32×D4D414yescomplemented
63C2×C32×D4C2312yes—
64C22×C32×C4C2311yescharacteristic
65C2×C3×#67—28no—
66C2×C3×#67—24no—
67C2×C3×#67—21no—
68C22×C3×Dic3—28no—
69C22×C3×Dic3—21no—
70C22×C3×Dic3—24no—
71C22×C3×Dic3D411yescharacteristic
72C3×#237—216no—
73C3×#237—28no—
74C3×#237—28no—
75C3×#235—22no—
76C3×#235—22no—
77C2×C3×D12—22no—
78C2×C3×D12C2311yescharacteristic
79C2×C3×C4×D3—22no—
80C2×C3×C4×D3—22no—
81C2×C3×C4×D3—21no—
82C2×C3×C4×D3D412yes—
83C2×C3×C4×D3C2312yes—
84C2×C3×Dic6—21no—
85C2×C3×Dic6—22no—
86C2×C3×Dic6D414yescomplemented
87C2×C3×Dic6C2311yescharacteristic
88C2×C3×Dic6C2312yes—
89C32×M16—22no—
90C2×C32×C8C2312yes—
91C32×C4⋊C4C2312yes—
92C32×C22⋊C4—21no—
93C32×C42—21no—
94C3×#214—24no—
95C3×#213—24no—
96C3×(C2×D3)⋊C4—22no—
97C3×(C2×D3)⋊C4—22no—
98C3×C4⋊Dic3—22no—
99C3×#208—22no—
100C2×C3×C3⋊C8C2312yes—
101C3×Dic12—24no—
102C3×#204—24no—
103#3005—31noSylow
104C2×C3×#41—34no—
105C2×C3×#41—31no—
106C2×C3×#41—62no—
107C2×C3×#41—64no—
108C2×C3×#41—64no—
109C22×C3×Q8—31no—
110C22×C3×D4—21no—
111C22×C3×D4—61no—
112C22×C3×D4C2×D311yescharacteristic
113C22×C3×D4C22×C311yescharacteristic
114C23×C3×C4—31no—
115C23×C3×C4—61no—
116C22×#67—21no—
117C23×Dic3—21no—
118C2×#237—24no—
119C2×#237—22no—
120C2×#237—24no—
121C2×#237C22×C314yes—
122C2×#235C22×C311yescharacteristic
123C22×C4×D3C22×C311yescharacteristic
124C22×Dic6C22×C311yescharacteristic
125C3×#137—64no—
126C3×AGL(1,ℤ/8)—64no—
127C2×C3×Q16—32no—
128C2×C3×SD16—32no—
129C2×C3×SD16—32no—
130C2×C3×D8—32no—
131C2×C3×M16—21no—
132C2×C3×M16—31no—
133C2×C3×M16C2×D311yescharacteristic
134C2×C3×M16C22×C311yescharacteristic
135C3×#123—61no—
136C3×C22⋊Q8—32no—
137C3×#121—32no—
138C3×#120—61no—
139C3×C4×D4—62no—
140C3×#117—21no—
141C3×#117C2×D311yescharacteristic
142C3×#117C22×C311yescharacteristic
143C2×#214C22×C312yescomplemented
144#932—24no—
145C2×#213C22×C312yescomplemented
146C2×#208C22×C311yescharacteristic
147#909—24no—
148C2×Dic12C22×C312yescomplemented
149C2×#204C22×C312yescomplemented
150#897C22×C312yescomplemented
151#895C22×C312yescomplemented
152#886—21no—
153#882—21no—
154C4×D12—22no—
155C3×#103—34no—
156C3×#102—24no—
157C3×#102C2×D314yescomplemented
158C3×#102C22×C314yescomplemented
159C3×C22⋊C8—34no—
160(C2×D3)⋊C8C22×C314yescomplemented
161#810C22×C314yescomplemented
162C23×C32—24no—
163C23×C32—22no—
164C23×C32—44no—
165C23×C32C2×D411yescharacteristic
166C22×C3×D3—22no—
167C22×C3×D3—21no—
168C22×C3×D3—42no—
169C22×C3×D3C2×D412yes—
170C32×D4—24no—
171C32×D4—22no—
172C32×D4C2×D414yes—
173C2×C32×C4—22no—
174C2×C32×C4C2×D412yes—
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2×D412yes—
177C2×C32×C4C2411yescharacteristic
178C3×#67—216no—
179C3×#67—42no—
180C2×C3×Dic3—216no—
181C2×C3×Dic3—24no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3C2×D412yes—
186C3×D12—21no—
187C3×D12—21no—
188C3×D12—44no—
189C3×C4×D3—24no—
190C3×C4×D3—22no—
191C3×C4×D3—22no—
192C3×C4×D3—42no—
193C3×Dic6—24no—
194C3×Dic6—22no—
195C3×Dic6—21no—
196C3×Dic6—21no—
197C3×Dic6C2×D414yes—
198C32×C8—22no—
199C3×C3⋊C8—22no—
200C22×#41—31no—
201C2×#137—31no—
202C2×AGL(1,ℤ/8)—31no—
203#525—31no—
204#452—34no—
205#449—34no—
206#419—31no—
207#418C3×D311yescharacteristic, complemented
208#407—31no—
209C24×C3—21no—
210C24×C3—21no—
211C24×C3—31no—
212C24×C3—41no—
213C23×D3C3×D411yescharacteristic
214C3×#41—68no—
215C3×#41—616no—
216C3×#41—68no—
217C3×#41—62no—
218C3×#41—62no—
219C2×C3×Q8—34no—
220C2×C3×Q8—32no—
221C2×C3×Q8—31no—
222C2×C3×Q8—62no—
223C2×C3×Q8—61no—
224C2×C3×D4—21no—
225C2×C3×D4—22no—
226C2×C3×D4—21no—
227C2×C3×D4—22no—
228C2×C3×D4—24no—
229C2×C3×D4—22no—
230C2×C3×D4—31no—
231C2×C3×D4—41no—
232C2×C3×D4—42no—
233C2×C3×D4—62no—
234C2×C3×D4—64no—
235C2×C3×D4—68no—
236C2×C3×D4—61no—
237C2×C3×D4D1214yescomplemented
238C2×C3×D4C3×D414yescomplemented
239C2×C3×D4C22×D312yes—
240C2×C3×D4C23×C312yes—
241C22×C3×C4—21no—
242C22×C3×C4—31no—
243C22×C3×C4—32no—
244C22×C3×C4—32no—
245C22×C3×C4—64no—
246C22×C3×C4—68no—
247C22×C3×C4—61no—
248C22×C3×C4—62no—
249C22×C3×C4—62no—
250C22×C3×C4—61no—
251C22×C3×C4C22×D311yescharacteristic
252C22×C3×C4C23×C311yescharacteristic
253C2×#67—28no—
254C2×#67—24no—
255C2×#67—21no—
256C22×Dic3—28no—
257C22×Dic3—21no—
258C22×Dic3—24no—
259C22×Dic3C3×D411yescharacteristic
260#237—216no—
261#237—28no—
262#237—28no—
263#235—22no—
264#235—22no—
265C2×D12—22no—
266C2×D12C23×C311yescharacteristic
267C2×C4×D3—22no—
268C2×C4×D3—22no—
269C2×C4×D3—21no—
270C2×C4×D3C3×D412yes—
271C2×C4×D3C23×C312yes—
272C2×Dic6—22no—
273C2×Dic6—21no—
274C2×Dic6C3×D414yescomplemented
275C2×Dic6C23×C311yescharacteristic
276C2×Dic6C23×C312yes—
277C3×Q16—64no—
278C3×SD16—64no—
279C3×SD16—64no—
280C3×D8—64no—
281C3×M16—22no—
282C3×M16—22no—
283C3×M16—42no—
284C3×M16—62no—
285C2×C3×C8—22no—
286C2×C3×C8—32no—
287C2×C3×C8C22×D312yes—
288C2×C3×C8C23×C312yes—
289C3×C4⋊C4—22no—
290C3×C4⋊C4—62no—
291C3×C4⋊C4C22×D312yes—
292C3×C4⋊C4C23×C312yes—
293C3×C22⋊C4—21no—
294C3×C22⋊C4—21no—
295C3×C22⋊C4—41no—
296C3×C22⋊C4—62no—
297C3×C22⋊C4—62no—
298C3×C42—21no—
299C3×C42—21no—
300C3×C42—41no—
301#214—24no—
302#213—24no—
303(C2×D3)⋊C4—22no—
304(C2×D3)⋊C4—22no—
305C4⋊Dic3—22no—
306#208—22no—
307C2×C3⋊C8C23×C312yes—
308Dic12—24no—
309#204—24no—
310C22×C32—22no—
311C22×C32—24no—
312C22×C32—48no—
313C22×C32—44no—
314C22×C32#12012yes—
315C22×C32C22×D411yescharacteristic
316C2×C3×D3—22no—
317C2×C3×D3—22no—
318C2×C3×D3—22no—
319C2×C3×D3—44no—
320C2×C3×D3—41no—
321C2×C3×D3—42no—
322C32×C4—42no—
323C32×C4#12012yes—
324C32×C4C22×D411yescharacteristic
325C32×C4C22×D411yescharacteristic
326C3×Dic3—24no—
327C3×Dic3—22no—
328C3×Dic3—41no—
329C2×#41—34no—
330C2×#41—31no—
331C2×#41—62no—
332C2×#41—64no—
333C2×#41—64no—
334C22×Q8—31no—
335C22×D4—61no—
336C22×D4C2×C3×D311yescharacteristic
337C23×C4—31no—
338C23×C4—61no—
339#137—64no—
340AGL(1,ℤ/8)—64no—
341C2×Q16—32no—
342C2×SD16—32no—
343C2×SD16—32no—
344C2×D8—32no—
345C2×M16—31no—
346C2×M16C2×C3×D311yescharacteristic
347#123—61no—
348C22⋊Q8—32no—
349#121—32no—
350#120—61no—
351C4×D4—62no—
352#117C2×C3×D311yescharacteristic
353#103—34no—
354#102C2×C3×D314yescomplemented
355C22⋊C8—34no—
356C23×C3—24no—
357C23×C3—24no—
358C23×C3—22no—
359C23×C3—22no—
360C23×C3—21no—
361C23×C3—32no—
362C23×C3—44no—
363C23×C3—42no—
364C23×C3—44no—
365C23×C3—44no—
366C23×C3—62no—
367C23×C3—61no—
368C23×C3—84no—
369C23×C3—122no—
370C23×C3D3×D411yescharacteristic
371C23×C3C2×C3×D411yescharacteristic
372C22×D3—22no—
373C22×D3—21no—
374C22×D3—42no—
375C22×D3C2×C3×D412yes—
376C3×Q8—34no—
377C3×Q8—64no—
378C3×Q8—62no—
379C3×Q8—61no—
380C3×Q8—61no—
381C3×D4—24no—
382C3×D4—24no—
383C3×D4—22no—
384C3×D4—22no—
385C3×D4—24no—
386C3×D4—44no—
387C3×D4—42no—
388C3×D4—616no—
389C3×D4—61no—
390C3×D4—61no—
391C3×D4—124no—
392C3×D4—122no—
393C3×D4C2×D1214yes—
394C3×D4C2×C3×D414yes—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—21no—
398C2×C3×C4—22no—
399C2×C3×C4—21no—
400C2×C3×C4—22no—
401C2×C3×C4—32no—
402C2×C3×C4—42no—
403C2×C3×C4—616no—
404C2×C3×C4—62no—
405C2×C3×C4—64no—
406C2×C3×C4—62no—
407C2×C3×C4—64no—
408C2×C3×C4—62no—
409C2×C3×C4—62no—
410C2×C3×C4—61no—
411C2×C3×C4—122no—
412C2×C3×C4C2×D1212yes—
413C2×C3×C4D3×D411yescharacteristic
414C2×C3×C4D3×D412yes—
415C2×C3×C4C2×C3×D412yes—
416C2×C3×C4C2×C3×D411yescharacteristic
417C2×C3×C4C2×C3×D412yes—
418C2×C3×C4C23×D311yescharacteristic
419C2×C3×C4C24×C311yescharacteristic
420#67—216no—
421#67—42no—
422C2×Dic3—216no—
423C2×Dic3—24no—
424C2×Dic3—22no—
425C2×Dic3—22no—
426C2×Dic3—21no—
427C2×Dic3C2×C3×D412yes—
428D12—21no—
429D12—21no—
430D12—44no—
431C4×D3—24no—
432C4×D3—22no—
433C4×D3—22no—
434C4×D3—42no—
435Dic6—24no—
436Dic6—22no—
437Dic6—21no—
438Dic6—21no—
439Dic6C2×C3×D414yes—
440C3×C8—22no—
441C3×C8—22no—
442C3×C8—42no—
443C3×C8—62no—
444C3⋊C8—22no—
445C2×C32—22no—
446C2×C32—44no—
447C2×C32C2×#12011yescharacteristic
448C2×C32#57512yes—
449C3×D3—42no—
450C3×D3—81no—
451C24—21no—
452C24—31no—
453#41—68no—
454#41—616no—
455#41—68no—
456#41—62no—
457#41—62no—
458C2×Q8—32no—
459C2×Q8—31no—
460C2×Q8—34no—
461C2×Q8—62no—
462C2×Q8—61no—
463C2×D4—21no—
464C2×D4—22no—
465C2×D4—31no—
466C2×D4—62no—
467C2×D4—64no—
468C2×D4—68no—
469C2×D4—61no—
470C2×D4C3×D1214yescomplemented
471C2×D4C22×C3×D312yes—
472C22×C4—31no—
473C22×C4—32no—
474C22×C4—32no—
475C22×C4—64no—
476C22×C4—68no—
477C22×C4—61no—
478C22×C4—62no—
479C22×C4—62no—
480C22×C4—61no—
481C22×C4C22×C3×D311yescharacteristic
482Q16—64no—
483SD16—64no—
484SD16—64no—
485D8—64no—
486M16—22no—
487M16—62no—
488C2×C8—32no—
489C2×C8C22×C3×D312yes—
490C4⋊C4—62no—
491C4⋊C4C22×C3×D312yes—
492C22⋊C4—21no—
493C22⋊C4—62no—
494C22⋊C4—62no—
495C42—21no—
496C22×C3—22no—
497C22×C3—22no—
498C22×C3—24no—
499C22×C3—24no—
500C22×C3—22no—
501C22×C3—21no—
502C22×C3—42no—
503C22×C3—44no—
504C22×C3—48no—
505C22×C3—48no—
506C22×C3—44no—
507C22×C3—44no—
508C22×C3—62no—
509C22×C3—62no—
510C22×C3—62no—
511C22×C3—84no—
512C22×C3—88no—
513C22×C3—124no—
514C22×C3—121no—
515C22×C3—122no—
516C22×C3#88212yes—
517C22×C3C3×#12012yes—
518C22×C3C2×D3×D411yescharacteristic
519C22×C3C22×C3×D411yescharacteristic
520C2×D3—22no—
521C2×D3—22no—
522C2×D3—22no—
523C2×D3—44no—
524C2×D3—42no—
525C2×D3—41no—
526C3×C4—22no—
527C3×C4—21no—
528C3×C4—21no—
529C3×C4—42no—
530C3×C4—42no—
531C3×C4—62no—
532C3×C4—64no—
533C3×C4—82no—
534C3×C4—121no—
535C3×C4#88212yes—
536C3×C4C3×#12012yes—
537C3×C4C22×D1211yescharacteristic
538C3×C4C2×D3×D411yescharacteristic
539C3×C4C22×C3×D411yescharacteristic
540C3×C4C22×C3×D411yescharacteristic
541Dic3—24no—
542Dic3—22no—
543Dic3—41no—
544C32#300511yescharacteristic, complemented, Sylow
545C23—24no—
546C23—22no—
547C23—32no—
548C23—44no—
549C23—62no—
550C23—61no—
551C23—122no—
552C23C3×D3×D411yescharacteristic
553Q8—34no—
554Q8—64no—
555Q8—62no—
556Q8—61no—
557Q8—61no—
558D4—24no—
559D4—22no—
560D4—616no—
561D4—61no—
562D4—61no—
563D4—124no—
564D4—122no—
565D4C2×C3×D1214yes—
566C2×C4—22no—
567C2×C4—32no—
568C2×C4—616no—
569C2×C4—62no—
570C2×C4—64no—
571C2×C4—62no—
572C2×C4—64no—
573C2×C4—62no—
574C2×C4—62no—
575C2×C4—61no—
576C2×C4—122no—
577C2×C4C2×C3×D1212yes—
578C2×C4C3×D3×D411yescharacteristic
579C2×C4C3×D3×D412yes—
580C2×C4C23×C3×D311yescharacteristic
581C8—22no—
582C8—62no—
583C2×C3—22no—
584C2×C3—22no—
585C2×C3—21no—
586C2×C3—22no—
587C2×C3—42no—
588C2×C3—44no—
589C2×C3—44no—
590C2×C3—84no—
591C2×C3—122no—
592C2×C3—241no—
593C2×C3C2×#88211yescharacteristic
594C2×C3#577312yes—
595C2×C3C2×C3×#12011yescharacteristic
596C2×C3C3×#57512yes—
597D3—42no—
598D3—81no—
599C22—22no—
600C22—24no—
601C22—48no—
602C22—44no—
603C22—62no—
604C22—62no—
605C22—62no—
606C22—124no—
607C22—121no—
608C22—122no—
609C22C3×#88212yes—
610C22C2×C3×D3×D411yescharacteristic
611C4—42no—
612C4—62no—
613C4—64no—
614C4—121no—
615C4C3×#88212yes—
616C4C22×C3×D1211yescharacteristic
617C4C2×C3×D3×D411yescharacteristic
618C3—21no—
619C3#7892711yescharacteristic, direct product factor
620C3C3×#300511yescharacteristic, complemented
621C2—22no—
622C2—44no—
623C2—122no—
624C2—241no—
625C2C2×C3×#88211yescharacteristic
626C2C3×#577312yes—
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#418C2
socleC22×C32C22×D4
hypercenterC3×#418D3
hypocenterC3C3×#3005
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#418

Complements

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

NH ≅ G/Ntype
1. C22×C3×#237C2semidirect
2. C2×C3×#932C2semidirect
3. C2×C3×#909C2semidirect
4. C3×#5524C2semidirect
5. C32×#418C2semidirect
6. C3×#5126C2semidirect
7. C3×#5004C2semidirect
8. C3×#4783C2semidirect
9. C3×#4781C2semidirect
11. #78927C3direct (N × H)
24. C2×C3×#214C22semidirect
26. C2×C3×#213C22semidirect
29. C2×C3×Dic12C22semidirect
30. C2×C3×#204C22semidirect
31. C3×#897C22semidirect
32. C3×#895C22semidirect
36. C32×#102C22semidirect
37. C3×(C2×D3)⋊C8C22semidirect
38. C3×#810C22semidirect
40. C22×#237C2×C3semidirect
44. C2×#932C2×C3semidirect
45. C2×#909C2×C3semidirect
46. #5524C2×C3semidirect
51. C3×#418D3semidirect
52. C3×#418C2×C3semidirect
54. #5126C2×C3semidirect
55. #5004C2×C3semidirect
56. #4783C2×C3semidirect
57. #4781C2×C3semidirect
62. C2×C32×D4D4semidirect
86. C2×C3×Dic6D4semidirect
143. C2×#214C22×C3semidirect
145. C2×#213C22×C3semidirect
148. C2×Dic12C22×C3semidirect
149. C2×#204C22×C3semidirect
150. #897C22×C3semidirect
151. #895C22×C3semidirect
157. C3×#102C2×D3semidirect
158. C3×#102C22×C3semidirect
160. (C2×D3)⋊C8C22×C3semidirect
161. #810C22×C3semidirect
207. #418C3×D3semidirect
237. C2×C3×D4D12semidirect
238. C2×C3×D4C3×D4semidirect
274. C2×Dic6C3×D4semidirect
354. #102C2×C3×D3semidirect
470. C2×D4C3×D12semidirect
544. C32#3005semidirect
619. C3#78927direct (N × H)
620. C3C3×#3005semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2372
C2×C3×#9322
C2×C3×#9092
C3×#55242
C32×#4182
C3×#51262
C3×#50042
C3×#47832
C3×#47812
C3×#30053
#789273