Finite Group Databasebeta

← C3×#80475 #11865757

Subgroups — C3×#80475 #11865757

Order 1152.

1046 conjugacy classes of subgroups.

The subgroup lattice has 643 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#919C212yesmaximal, complemented
2C3×#5725C211yesmaximal, characteristic, complemented
3C3×C4×#239C211yesmaximal, characteristic, complemented
4C32×#462C211yesmaximal, characteristic, complemented
5C3×#5185C212yesmaximal, complemented
6C3×#5083C211yesmaximal, characteristic, complemented
7C3×#5027C211yesmaximal, characteristic, complemented
8C3×#4843C211yesmaximal, characteristic, complemented
9C3×D3×C4⋊C8C211yesmaximal, characteristic, complemented
10C3×#4819C212yesmaximal, complemented
11C3×#4804C212yesmaximal, complemented
12C3×#3035—31nomaximal
13#80475C311yesmaximal, characteristic, direct product factor
14C2×C3×#239C2212yes—
15C2×C3×#239C2211yescharacteristic
16C2×C32×Q16C2212yes—
17C32×C4⋊Q8C2211yescharacteristic
18C32×C4×Q8C2211yescharacteristic
19C3×#947C2212yes—
20C3×Q8×Dic3C2211yescharacteristic
21C2×C3×#215C2212yes—
22C2×C3×#215C2212yes—
23C3×#919—28no—
24C2×C3×D24C2212yes—
25C2×C3×D3×C8C2212yes—
26C3×#895—21no—
27C3×#895—21no—
28C3×#893—21no—
29C3×#893—21no—
30C3×#893—21no—
31C3×#893C2211yescharacteristic
32C3×#892—21no—
33C3×#892C2211yescharacteristic
34C3×#874C2211yescharacteristic
35C3×C4×D12—21no—
36C3×C4×D12C2211yescharacteristic
37C3×C42×D3—21no—
38C3×C42×D3C2211yescharacteristic
39C32×C4⋊C8C2211yescharacteristic
40C32×#103C2212yes—
41C3×#835C2212yes—
42C3×#821C2212yes—
43C3×Dic3⋊C8C2212yes—
44C3×#809C2212yes—
45C3×C4⋊(C3⋊C8)C2211yescharacteristic
46C2×C3×#135—32no—
47C3×#532—31no—
48C3×C4×#41—31no—
49C2×#919C2×C312yescomplemented
50#5725C2×C311yescharacteristic, complemented
51C4×#239C2×C311yescharacteristic, complemented
52C3×#464—32no—
53C3×#463—32no—
54C3×#462—21no—
55C3×#462D311yescharacteristic, complemented
56C3×#462C2×C311yescharacteristic, complemented
57C3×#461—31no—
58C3×#460—31no—
59C3×#459—31no—
60C2×C3×C4⋊C8—31no—
61C3×#416—32no—
62#5185C2×C312yescomplemented
63#5083C2×C311yescharacteristic, complemented
64#5027C2×C311yescharacteristic, complemented
65#4843C2×C311yescharacteristic, complemented
66D3×C4⋊C8C2×C311yescharacteristic, complemented
67#4819C2×C312yescomplemented
68#4804C2×C312yescomplemented
69C2×C32×Q8C2312yes—
70C2×C32×Q8C2311yescharacteristic
71C3×#239—22no—
72C3×#239—24no—
73C3×#239—24no—
74C3×#239D414yescomplemented
75C2×C3×D12—21no—
76C2×C3×D12—22no—
77C2×C3×D12—21no—
78C2×C3×D12—21no—
79C2×C3×D12C2312yes—
80C2×C3×D12C2311yescharacteristic
81C2×C3×C4×D3—21no—
82C2×C3×C4×D3—21no—
83C2×C3×C4×D3—22no—
84C2×C3×C4×D3—21no—
85C2×C3×C4×D3D411yescharacteristic
86C2×C3×C4×D3D411yescharacteristic
87C2×C3×C4×D3C2311yescharacteristic
88C32×Q16—24no—
89C2×C32×C8C2312yes—
90C32×C4⋊C4—21no—
91C32×C4⋊C4—21no—
92C32×C4⋊C4—21no—
93C32×C4⋊C4C2311yescharacteristic
94C32×C42—21no—
95C32×C42C2311yescharacteristic
96C3×#215—24no—
97C3×#215—24no—
98C3×(C2×D3)⋊C4—21no—
99C3×(C2×D3)⋊C4—21no—
100C3×(C2×D3)⋊C4—21no—
101C3×(C2×D3)⋊C4—22no—
102C3×(C2×D3)⋊C4—22no—
103C3×C4⋊Dic3—21no—
104C3×C4⋊Dic3C2311yescharacteristic
105C3×C4×Dic3—21no—
106C3×C4×Dic3—21no—
107C3×C4×Dic3D411yescharacteristic
108C3×C4×Dic3D411yescharacteristic
109C3×C4×Dic3C2311yescharacteristic
110C2×C3×C3⋊C8C2312yes—
111C3×D24—24no—
112C3×D3×C8—24no—
113#3035—31noSylow
114C2×C3×#41—31no—
115C2×C3×#41—32no—
116C2×#239C22×C312yes—
117C2×#239C22×C311yescharacteristic
118C3×#135—68no—
119C2×C3×Q16—22no—
120C2×C3×Q16C2×D312yes—
121C2×C3×Q16C22×C312yes—
122C2×C3×SD16—32no—
123C2×C3×SD16—32no—
124C2×C3×D8—32no—
125C22×C3×C8—32no—
126C3×C4⋊Q8—21no—
127C3×C4⋊Q8C2×D311yescharacteristic
128C3×C4⋊Q8C22×C311yescharacteristic
129C3×#127—31no—
130C3×#124—32no—
131C3×#121—61no—
132C3×#121—61no—
133C3×C4×Q8—21no—
134C3×C4×Q8—31no—
135C3×C4×Q8C2×D311yescharacteristic
136C3×C4×Q8C22×C311yescharacteristic
137C3×C4×D4—31no—
138C3×C4×D4—31no—
139C3×C4×D4—61no—
140C3×C4×D4—61no—
141C3×C4×D4—61no—
142C3×C4×D4—61no—
143C3×#117—31no—
144C3×#117—61no—
145C2×C3×C42—31no—
146C2×C3×C42—61no—
147#947C22×C312yes—
148Q8×Dic3C22×C311yescharacteristic
149C2×#215C22×C312yes—
150C2×#215C22×C312yes—
151#919—28no—
152C2×D24C22×C312yes—
153C2×D3×C8C22×C312yes—
154#895—21no—
155#895—21no—
156#893—21no—
157#893—21no—
158#893—21no—
159#893C22×C311yescharacteristic
160#892—21no—
161#892C22×C311yescharacteristic
162#874C22×C311yescharacteristic
163C4×D12—21no—
164C4×D12C22×C311yescharacteristic
165C42×D3—21no—
166C42×D3C22×C311yescharacteristic
167C3×C4⋊C8—21no—
168C3×C4⋊C8—32no—
169C3×C4⋊C8—31no—
170C3×C4⋊C8C2×D311yescharacteristic
171C3×C4⋊C8C22×C311yescharacteristic
172C3×#103—22no—
173C3×#103—32no—
174C3×#103C2×D312yes—
175C3×#103C22×C312yes—
176C3×#102—32no—
177C3×#102—32no—
178#835C22×C312yes—
179#821C22×C312yes—
180Dic3⋊C8C22×C312yes—
181#809C22×C312yes—
182C4⋊(C3⋊C8)C22×C311yescharacteristic
183C22×C3×D3—21no—
184C22×C3×D3—22no—
185C22×C3×D3C2×D411yescharacteristic
186C32×Q8—21no—
187C32×Q8—22no—
188C32×Q8—22no—
189C32×Q8C2×D412yes—
190C2×C32×C4—21no—
191C2×C32×C4—21no—
192C2×C32×C4—22no—
193C2×C32×C4C2×D411yescharacteristic
194C2×C32×C4C2×D411yescharacteristic
195C2×C32×C4C2411yescharacteristic
196C2×C3×Dic3—21no—
197C2×C3×Dic3C2×D411yescharacteristic
198C2×C3×Dic3C2×D411yescharacteristic
199C2×C3×Dic3C2×D411yescharacteristic
200C3×D12—24no—
201C3×D12—22no—
202C3×D12—21no—
203C3×D12—22no—
204C3×D12—42no—
205C3×D12—44no—
206C3×D12—42no—
207C3×D12C2×D412yes—
208C3×C4×D3—22no—
209C3×C4×D3—24no—
210C3×C4×D3—41no—
211C3×C4×D3—42no—
212C3×C4×D3—42no—
213C3×C4×D3—44no—
214C3×C4×D3C2×D412yes—
215C3×C4×D3#4112yes—
216C32×C8—22no—
217C3×C3⋊C8—22no—
218C2×#135—32no—
219#532—31no—
220C4×#41—31no—
221#464—32no—
222#463—32no—
223#462C3×D311yescharacteristic, complemented
224#461—31no—
225#460—31no—
226#459—31no—
227C2×C4⋊C8—31no—
228#416—32no—
229C3×#41—34no—
230C3×#41—62no—
231C3×#41—64no—
232C3×#41—64no—
233C2×C3×Q8—21no—
234C2×C3×Q8—22no—
235C2×C3×Q8C22×D312yes—
236C2×C3×Q8C22×D311yescharacteristic
237C2×C3×Q8C23×C312yes—
238C2×C3×Q8C23×C311yescharacteristic
239C2×C3×D4—31no—
240C2×C3×D4—32no—
241C2×C3×D4—61no—
242C2×C3×D4—62no—
243C2×C3×D4—61no—
244C2×C3×D4—61no—
245C22×C3×C4—31no—
246C22×C3×C4—31no—
247C22×C3×C4—31no—
248C22×C3×C4—61no—
249C22×C3×C4—61no—
250C22×C3×C4—62no—
251C22×C3×C4—61no—
252#239—22no—
253#239—24no—
254#239—24no—
255#239C3×D414yescomplemented
256C2×D12—21no—
257C2×D12—22no—
258C2×D12—21no—
259C2×D12—21no—
260C2×D12C23×C312yes—
261C2×D12C23×C311yescharacteristic
262C2×C4×D3—21no—
263C2×C4×D3—21no—
264C2×C4×D3—21no—
265C2×C4×D3—22no—
266C2×C4×D3C3×D411yescharacteristic
267C2×C4×D3C3×D411yescharacteristic
268C2×C4×D3C23×C311yescharacteristic
269C3×Q16—24no—
270C3×Q16—24no—
271C3×Q16—44no—
272C3×SD16—64no—
273C3×SD16—64no—
274C3×D8—64no—
275C2×C3×C8—22no—
276C2×C3×C8—32no—
277C2×C3×C8—64no—
278C2×C3×C8C22×D312yes—
279C2×C3×C8C23×C312yes—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—31no—
288C3×C4⋊C4—41no—
289C3×C4⋊C4—41no—
290C3×C4⋊C4—41no—
291C3×C4⋊C4—61no—
292C3×C4⋊C4C22×D311yescharacteristic
293C3×C4⋊C4C23×C311yescharacteristic
294C3×C22⋊C4—61no—
295C3×C22⋊C4—62no—
296C3×C22⋊C4—62no—
297C3×C22⋊C4—61no—
298C3×C22⋊C4—61no—
299C3×C42—21no—
300C3×C42—21no—
301C3×C42—21no—
302C3×C42—31no—
303C3×C42—31no—
304C3×C42—31no—
305C3×C42—41no—
306C3×C42—61no—
307C3×C42—61no—
308C3×C42C22×D311yescharacteristic
309C3×C42C23×C311yescharacteristic
310#215—24no—
311#215—24no—
312(C2×D3)⋊C4—21no—
313(C2×D3)⋊C4—21no—
314(C2×D3)⋊C4—21no—
315(C2×D3)⋊C4—22no—
316(C2×D3)⋊C4—22no—
317C4⋊Dic3—21no—
318C4⋊Dic3C23×C311yescharacteristic
319C4×Dic3—21no—
320C4×Dic3—21no—
321C4×Dic3C3×D411yescharacteristic
322C4×Dic3C3×D411yescharacteristic
323C4×Dic3C23×C311yescharacteristic
324C2×C3⋊C8C23×C312yes—
325D24—24no—
326D3×C8—24no—
327C22×C32C22×D411yescharacteristic
328C2×C3×D3—21no—
329C2×C3×D3—21no—
330C2×C3×D3—22no—
331C2×C3×D3—41no—
332C2×C3×D3—41no—
333C2×C3×D3—42no—
334C2×C3×D3—42no—
335C2×C3×D3—42no—
336C2×C3×D3#12112yes—
337C32×C4—22no—
338C32×C4—21no—
339C32×C4—42no—
340C32×C4—41no—
341C32×C4#13512yescomplemented
342C32×C4C22×D411yescharacteristic
343C32×C4C2×#4111yescharacteristic
344C3×Dic3—21no—
345C3×Dic3—21no—
346C3×Dic3—41no—
347C3×Dic3#12112yes—
348C2×#41—31no—
349C2×#41—32no—
350#135—68no—
351C2×Q16C2×C3×D312yes—
352C2×SD16—32no—
353C2×SD16—32no—
354C2×D8—32no—
355C22×C8—32no—
356C4⋊Q8C2×C3×D311yescharacteristic
357#127—31no—
358#124—32no—
359#121—61no—
360#121—61no—
361C4×Q8—31no—
362C4×Q8C2×C3×D311yescharacteristic
363C4×D4—31no—
364C4×D4—31no—
365C4×D4—61no—
366C4×D4—61no—
367C4×D4—61no—
368C4×D4—61no—
369#117—31no—
370#117—61no—
371C2×C42—31no—
372C2×C42—61no—
373C4⋊C8—32no—
374C4⋊C8—31no—
375C4⋊C8C2×C3×D311yescharacteristic
376#103—32no—
377#103C2×C3×D312yes—
378#102—32no—
379#102—32no—
380C23×C3—31no—
381C23×C3—61no—
382C23×C3—62no—
383C22×D3—21no—
384C22×D3—22no—
385C22×D3C2×C3×D411yescharacteristic
386C3×Q8—21no—
387C3×Q8—21no—
388C3×Q8—22no—
389C3×Q8—22no—
390C3×Q8—22no—
391C3×Q8—22no—
392C3×Q8—22no—
393C3×Q8—41no—
394C3×Q8—42no—
395C3×Q8—42no—
396C3×Q8D3×D412yes—
397C3×Q8C2×C3×D412yes—
398C3×D4—32no—
399C3×D4—64no—
400C3×D4—62no—
401C3×D4—61no—
402C3×D4—62no—
403C3×D4—122no—
404C3×D4—124no—
405C3×D4—122no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—22no—
410C2×C3×C4—21no—
411C2×C3×C4—22no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—31no—
416C2×C3×C4—32no—
417C2×C3×C4—32no—
418C2×C3×C4—31no—
419C2×C3×C4—31no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—42no—
423C2×C3×C4—64no—
424C2×C3×C4—62no—
425C2×C3×C4—61no—
426C2×C3×C4—121no—
427C2×C3×C4—124no—
428C2×C3×C4—122no—
429C2×C3×C4—122no—
430C2×C3×C4D3×D411yescharacteristic
431C2×C3×C4D3×D411yescharacteristic
432C2×C3×C4C2×C3×D411yescharacteristic
433C2×C3×C4C2×C3×D411yescharacteristic
434C2×C3×C4C23×D311yescharacteristic
435C2×C3×C4C24×C311yescharacteristic
436C2×Dic3—21no—
437C2×Dic3C2×C3×D411yescharacteristic
438C2×Dic3C2×C3×D411yescharacteristic
439C2×Dic3C2×C3×D411yescharacteristic
440D12—24no—
441D12—22no—
442D12—21no—
443D12—22no—
444D12—42no—
445D12—44no—
446D12—42no—
447D12C2×C3×D412yes—
448C4×D3—22no—
449C4×D3—24no—
450C4×D3—41no—
451C4×D3—42no—
452C4×D3—42no—
453C4×D3—44no—
454C4×D3C2×C3×D412yes—
455C4×D3C3×#4112yes—
456C3×C8—22no—
457C3×C8—22no—
458C3×C8—42no—
459C3×C8—62no—
460C3⋊C8—22no—
461C2×C32C2×#12111yescharacteristic
462C2×C32C2×#13511yescharacteristic
463C2×C32#57511yescharacteristic
464C3×D3—22no—
465C3×D3—42no—
466C3×D3—82no—
467#41—34no—
468#41—62no—
469#41—64no—
470#41—64no—
471C2×Q8C22×C3×D312yes—
472C2×Q8C22×C3×D311yescharacteristic
473C2×D4—31no—
474C2×D4—32no—
475C2×D4—61no—
476C2×D4—62no—
477C2×D4—61no—
478C2×D4—61no—
479C22×C4—31no—
480C22×C4—31no—
481C22×C4—31no—
482C22×C4—61no—
483C22×C4—61no—
484C22×C4—62no—
485C22×C4—61no—
486Q16—24no—
487SD16—64no—
488SD16—64no—
489D8—64no—
490C2×C8—32no—
491C2×C8—64no—
492C2×C8C22×C3×D312yes—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—31no—
497C4⋊C4—61no—
498C4⋊C4C22×C3×D311yescharacteristic
499C22⋊C4—61no—
500C22⋊C4—62no—
501C22⋊C4—62no—
502C22⋊C4—61no—
503C22⋊C4—61no—
504C42—21no—
505C42—31no—
506C42—31no—
507C42—31no—
508C42—61no—
509C42—61no—
510C42C22×C3×D311yescharacteristic
511C22×C3—21no—
512C22×C3—32no—
513C22×C3—61no—
514C22×C3—61no—
515C22×C3—62no—
516C22×C3—121no—
517C22×C3—121no—
518C22×C3—122no—
519C22×C3—122no—
520C22×C3—122no—
521C22×C3C2×D3×D411yescharacteristic
522C22×C3C22×C3×D411yescharacteristic
523C2×D3—21no—
524C2×D3—21no—
525C2×D3—22no—
526C2×D3—41no—
527C2×D3—41no—
528C2×D3—42no—
529C2×D3—42no—
530C2×D3—42no—
531C2×D3C3×#12112yes—
532C3×C4—21no—
533C3×C4—21no—
534C3×C4—22no—
535C3×C4—22no—
536C3×C4—22no—
537C3×C4—21no—
538C3×C4—21no—
539C3×C4—32no—
540C3×C4—41no—
541C3×C4—42no—
542C3×C4—41no—
543C3×C4—41no—
544C3×C4—42no—
545C3×C4—42no—
546C3×C4—61no—
547C3×C4—61no—
548C3×C4—82no—
549C3×C4—81no—
550C3×C4—121no—
551C3×C4#91912yescomplemented
552C3×C4C3×#13512yescomplemented
553C3×C4C2×D3×D411yescharacteristic
554C3×C4D3×#4111yescharacteristic
555C3×C4C22×C3×D411yescharacteristic
556C3×C4C2×C3×#4111yescharacteristic
557Dic3—21no—
558Dic3—21no—
559Dic3—41no—
560Dic3C3×#12112yes—
561C32#303511yescharacteristic, complemented, Sylow
562C23—31no—
563C23—61no—
564C23—62no—
565Q8—21no—
566Q8—22no—
567Q8—22no—
568Q8C3×D3×D412yes—
569D4—32no—
570D4—64no—
571D4—62no—
572D4—61no—
573D4—62no—
574D4—122no—
575D4—124no—
576D4—122no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—31no—
581C2×C4—32no—
582C2×C4—32no—
583C2×C4—31no—
584C2×C4—31no—
585C2×C4—64no—
586C2×C4—62no—
587C2×C4—61no—
588C2×C4—121no—
589C2×C4—124no—
590C2×C4—122no—
591C2×C4—122no—
592C2×C4C3×D3×D411yescharacteristic
593C2×C4C3×D3×D411yescharacteristic
594C2×C4C23×C3×D311yescharacteristic
595C8—22no—
596C8—62no—
597C2×C3—21no—
598C2×C3—21no—
599C2×C3—21no—
600C2×C3—62no—
601C2×C3—122no—
602C2×C3—242no—
603C2×C3D3×#12111yescharacteristic
604C2×C3C2×#91911yescharacteristic
605C2×C3#577711yescharacteristic
606C2×C3C2×C3×#12111yescharacteristic
607C2×C3C2×C3×#13511yescharacteristic
608C2×C3C3×#57511yescharacteristic
609D3—22no—
610D3—42no—
611D3—82no—
612C22—32no—
613C22—61no—
614C22—61no—
615C22—62no—
616C22—121no—
617C22—121no—
618C22—122no—
619C22—122no—
620C22—122no—
621C22C2×C3×D3×D411yescharacteristic
622C4—21no—
623C4—22no—
624C4—32no—
625C4—41no—
626C4—42no—
627C4—61no—
628C4—61no—
629C4—121no—
630C4C3×#91912yescomplemented
631C4C2×C3×D3×D411yescharacteristic
632C4C3×D3×#4111yescharacteristic
633C3—21no—
634C3#8047511yescharacteristic, direct product factor
635C3C3×#303511yescharacteristic, complemented
636C2—62no—
637C2—122no—
638C2—242no—
639C2C3×D3×#12111yescharacteristic
640C2C2×C3×#91911yescharacteristic
641C2C3×#577711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#462C2
socleC22×C32C22×D4
hypercenterC3×#462D3
hypocenterC3C3×#3035
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#462

Complements

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

NH ≅ G/Ntype
1. C2×C3×#919C2semidirect
2. C3×#5725C2semidirect
3. C3×C4×#239C2semidirect
4. C32×#462C2semidirect
5. C3×#5185C2semidirect
6. C3×#5083C2semidirect
7. C3×#5027C2semidirect
8. C3×#4843C2semidirect
9. C3×D3×C4⋊C8C2semidirect
10. C3×#4819C2semidirect
11. C3×#4804C2semidirect
13. #80475C3direct (N × H)
49. C2×#919C2×C3semidirect
50. #5725C2×C3semidirect
51. C4×#239C2×C3semidirect
55. C3×#462D3semidirect
56. C3×#462C2×C3semidirect
62. #5185C2×C3semidirect
63. #5083C2×C3semidirect
64. #5027C2×C3semidirect
65. #4843C2×C3semidirect
66. D3×C4⋊C8C2×C3semidirect
67. #4819C2×C3semidirect
68. #4804C2×C3semidirect
74. C3×#239D4semidirect
223. #462C3×D3semidirect
255. #239C3×D4semidirect
341. C32×C4#135semidirect
551. C3×C4#919semidirect
552. C3×C4C3×#135semidirect
561. C32#3035semidirect
630. C4C3×#919semidirect
634. C3#80475direct (N × H)
635. C3C3×#3035semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9192
C3×#57252
C3×C4×#2392
C32×#4622
C3×#51852
C3×#50832
C3×#50272
C3×#48432
C3×D3×C4⋊C82
C3×#48192
C3×#48042
C3×#30353
#804753