Finite Group Databasebeta

← C3×#80427 #11865751

Subgroups — C3×#80427 #11865751

Order 1152.

1052 conjugacy classes of subgroups.

The subgroup lattice has 647 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#916C212yesmaximal, complemented
2C3×#5725C211yesmaximal, characteristic, complemented
3C3×C4×#237C211yesmaximal, characteristic, complemented
4C32×#461C211yesmaximal, characteristic, complemented
5C3×#5165C212yesmaximal, complemented
6C3×#5090C211yesmaximal, characteristic, complemented
7C3×#5015C211yesmaximal, characteristic, complemented
8C3×#4848C211yesmaximal, characteristic, complemented
9C3×D3×C4⋊C8C211yesmaximal, characteristic, complemented
10C3×#4804C212yesmaximal, complemented
11C3×#4798C212yesmaximal, complemented
12C3×#3035—31nomaximal
13#80427C311yesmaximal, characteristic, direct product factor
14C2×C3×#239C2212yes—
15C2×C3×#237C2211yescharacteristic
16C2×C32×SD16C2212yes—
17C32×C4⋊Q8C2211yescharacteristic
18C32×C4×D4C2211yescharacteristic
19C3×#947C2212yes—
20C2×C3×#216C2212yes—
21C3×D4×Dic3C2211yescharacteristic
22C2×C3×#213C2212yes—
23C3×C4×#67—21no—
24C2×C3×C4×Dic3—21no—
25C3×#916—28no—
26C2×C3×#204C2212yes—
27C2×C3×D3×C8C2212yes—
28C3×#895—21no—
29C3×#895—21no—
30C3×#893—21no—
31C3×#893—21no—
32C3×#892C2211yescharacteristic
33C3×#887C2211yescharacteristic
34C3×#67⋊C4—21no—
35C3×#877—21no—
36C3×#874C2211yescharacteristic
37C3×C42×D3C2211yescharacteristic
38C3×C4×Dic6C2211yescharacteristic
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×#916C2×C312yescomplemented
50#5725C2×C311yescharacteristic, complemented
51C4×#237C2×C311yescharacteristic, complemented
52C3×#464—32no—
53C3×#463—32no—
54C3×#462—31no—
55C3×#461—21no—
56C3×#461D311yescharacteristic, complemented
57C3×#461C2×C311yescharacteristic, complemented
58C3×#460—31no—
59C3×#459—31no—
60C2×C3×C4⋊C8—31no—
61C3×#416—32no—
62#5165C2×C312yescomplemented
63#5090C2×C311yescharacteristic, complemented
64#5015C2×C311yescharacteristic, complemented
65#4848C2×C311yescharacteristic, complemented
66D3×C4⋊C8C2×C311yescharacteristic, complemented
67#4804C2×C312yescomplemented
68#4798C2×C312yescomplemented
69C2×C32×Q8C2312yes—
70C2×C32×D4C2311yescharacteristic
71C22×C32×C4—21no—
72C2×C3×#67—21no—
73C22×C3×Dic3—21no—
74C22×C3×Dic3—21no—
75C3×#239—24no—
76C3×#239—24no—
77C3×#237—22no—
78C3×#237D414yescomplemented
79C2×C3×D12—22no—
80C2×C3×D12—21no—
81C2×C3×D12—21no—
82C2×C3×D12C2312yes—
83C2×C3×C4×D3—22no—
84C2×C3×C4×D3D411yescharacteristic
85C2×C3×C4×D3D411yescharacteristic
86C2×C3×C4×D3C2311yescharacteristic
87C2×C3×Dic6C2311yescharacteristic
88C32×SD16—24no—
89C2×C32×C8C2312yes—
90C32×C4⋊C4—21no—
91C32×C4⋊C4—21no—
92C32×C4⋊C4C2311yescharacteristic
93C32×C22⋊C4—21no—
94C32×C42C2311yescharacteristic
95C3×#217—21no—
96C3×#216—24no—
97C3×#213—24no—
98C3×(C2×D3)⋊C4—21no—
99C3×(C2×D3)⋊C4—22no—
100C3×(C2×D3)⋊C4—22no—
101C3×C4⋊Dic3C2311yescharacteristic
102C3×Dic3⋊C4—21no—
103C3×Dic3⋊C4—21no—
104C3×C4×Dic3—21no—
105C3×C4×Dic3—21no—
106C3×C4×Dic3—21no—
107C3×C4×Dic3D411yescharacteristic
108C3×C4×Dic3D411yescharacteristic
109C3×C4×Dic3C2311yescharacteristic
110C2×C3×C3⋊C8C2312yes—
111C3×#204—24no—
112C3×D3×C8—24no—
113#3035—31noSylow
114C2×C3×#41—32no—
115C2×C3×#41—31no—
116C2×#239C22×C312yes—
117C2×#237C22×C311yescharacteristic
118C3×#135—68no—
119C2×C3×Q16—32no—
120C2×C3×SD16—22no—
121C2×C3×SD16—32no—
122C2×C3×SD16C2×D312yes—
123C2×C3×SD16C22×C312yes—
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—31no—
134C3×C4×Q8—31no—
135C3×C4×D4—21no—
136C3×C4×D4—31no—
137C3×C4×D4—61no—
138C3×C4×D4—61no—
139C3×C4×D4—61no—
140C3×C4×D4—61no—
141C3×C4×D4C2×D311yescharacteristic
142C3×C4×D4C22×C311yescharacteristic
143C3×#117—31no—
144C3×#117—61no—
145C2×C3×C42—31no—
146C2×C3×C42—61no—
147#947C22×C312yes—
148C2×#216C22×C312yes—
149D4×Dic3C22×C311yescharacteristic
150C2×#213C22×C312yes—
151C4×#67—21no—
152C2×C4×Dic3—21no—
153#916—28no—
154C2×#204C22×C312yes—
155C2×D3×C8C22×C312yes—
156#895—21no—
157#895—21no—
158#893—21no—
159#893—21no—
160#892C22×C311yescharacteristic
161#887C22×C311yescharacteristic
162#67⋊C4—21no—
163#877—21no—
164#874C22×C311yescharacteristic
165C42×D3C22×C311yescharacteristic
166C4×Dic6C22×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
183C23×C32—21no—
184C22×C3×D3—22no—
185C22×C3×D3C2×D411yescharacteristic
186C32×Q8—22no—
187C32×Q8—22no—
188C32×D4—21no—
189C32×D4C2×D412yes—
190C2×C32×C4—21no—
191C2×C32×C4—22no—
192C2×C32×C4—42no—
193C2×C32×C4C2×D411yescharacteristic
194C2×C32×C4C2×D411yescharacteristic
195C2×C32×C4C2411yescharacteristic
196C3×#67—24no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—24no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3—42no—
201C2×C3×Dic3C2×D411yescharacteristic
202C2×C3×Dic3C2×D411yescharacteristic
203C2×C3×Dic3C2×D411yescharacteristic
204C3×D12—22no—
205C3×D12—22no—
206C3×D12—42no—
207C3×D12—44no—
208C3×D12—42no—
209C3×C4×D3—22no—
210C3×C4×D3—41no—
211C3×C4×D3—44no—
212C3×C4×D3C2×D412yes—
213C3×C4×D3#4112yes—
214C3×Dic6—21no—
215C3×Dic6C2×D412yes—
216C32×C8—22no—
217C3×C3⋊C8—22no—
218C2×#135—32no—
219#532—31no—
220C4×#41—31no—
221#464—32no—
222#463—32no—
223#462—31no—
224#461C3×D311yescharacteristic, complemented
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—22no—
234C2×C3×Q8—31no—
235C2×C3×Q8C22×D312yes—
236C2×C3×Q8C23×C312yes—
237C2×C3×D4—21no—
238C2×C3×D4—32no—
239C2×C3×D4—62no—
240C2×C3×D4—61no—
241C2×C3×D4—61no—
242C2×C3×D4—61no—
243C2×C3×D4C22×D311yescharacteristic
244C2×C3×D4C23×C311yescharacteristic
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—31no—
248C22×C3×C4—31no—
249C22×C3×C4—31no—
250C22×C3×C4—41no—
251C22×C3×C4—62no—
252C22×C3×C4—61no—
253C22×C3×C4—61no—
254C2×#67—21no—
255C22×Dic3—21no—
256C22×Dic3—21no—
257#239—24no—
258#239—24no—
259#237—22no—
260#237C3×D414yescomplemented
261C2×D12—22no—
262C2×D12—21no—
263C2×D12—21no—
264C2×D12C23×C312yes—
265C2×C4×D3—22no—
266C2×C4×D3C3×D411yescharacteristic
267C2×C4×D3C3×D411yescharacteristic
268C2×C4×D3C23×C311yescharacteristic
269C2×Dic6C23×C311yescharacteristic
270C3×Q16—64no—
271C3×SD16—24no—
272C3×SD16—24no—
273C3×SD16—44no—
274C3×SD16—64no—
275C3×D8—64no—
276C2×C3×C8—22no—
277C2×C3×C8—32no—
278C2×C3×C8—64no—
279C2×C3×C8C22×D312yes—
280C2×C3×C8C23×C312yes—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—31no—
287C3×C4⋊C4—41no—
288C3×C4⋊C4—41no—
289C3×C4⋊C4—61no—
290C3×C4⋊C4—61no—
291C3×C4⋊C4C22×D311yescharacteristic
292C3×C4⋊C4C23×C311yescharacteristic
293C3×C22⋊C4—21no—
294C3×C22⋊C4—21no—
295C3×C22⋊C4—41no—
296C3×C22⋊C4—62no—
297C3×C22⋊C4—62no—
298C3×C22⋊C4—61no—
299C3×C22⋊C4—61no—
300C3×C42—21no—
301C3×C42—31no—
302C3×C42—31no—
303C3×C42—31no—
304C3×C42—61no—
305C3×C42—61no—
306C3×C42—61no—
307C3×C42C22×D311yescharacteristic
308C3×C42C23×C311yescharacteristic
309#217—21no—
310#216—24no—
311#213—24no—
312(C2×D3)⋊C4—21no—
313(C2×D3)⋊C4—22no—
314(C2×D3)⋊C4—22no—
315C4⋊Dic3C23×C311yescharacteristic
316Dic3⋊C4—21no—
317Dic3⋊C4—21no—
318C4×Dic3—21no—
319C4×Dic3—21no—
320C4×Dic3—21no—
321C4×Dic3C3×D411yescharacteristic
322C4×Dic3C3×D411yescharacteristic
323C4×Dic3C23×C311yescharacteristic
324C2×C3⋊C8C23×C312yes—
325#204—24no—
326D3×C8—24no—
327C22×C32—22no—
328C22×C32—41no—
329C22×C32—41no—
330C22×C32C22×D411yescharacteristic
331C2×C3×D3—21no—
332C2×C3×D3—21no—
333C2×C3×D3—42no—
334C2×C3×D3—42no—
335C2×C3×D3—42no—
336C2×C3×D3#12112yes—
337C32×C4—21no—
338C32×C4—42no—
339C32×C4—41no—
340C32×C4#13512yescomplemented
341C32×C4C22×D411yescharacteristic
342C32×C4C2×#4111yescharacteristic
343C3×Dic3—22no—
344C3×Dic3—21no—
345C3×Dic3—21no—
346C3×Dic3—41no—
347C3×Dic3#12112yes—
348C2×#41—32no—
349C2×#41—31no—
350#135—68no—
351C2×Q16—32no—
352C2×SD16—32no—
353C2×SD16C2×C3×D312yes—
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×Q8—31no—
363C4×D4—31no—
364C4×D4—61no—
365C4×D4—61no—
366C4×D4—61no—
367C4×D4—61no—
368C4×D4C2×C3×D311yescharacteristic
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—21no—
381C23×C3—21no—
382C23×C3—31no—
383C23×C3—41no—
384C23×C3—62no—
385C22×D3—22no—
386C22×D3C2×C3×D411yescharacteristic
387C3×Q8—22no—
388C3×Q8—22no—
389C3×Q8—22no—
390C3×Q8—22no—
391C3×Q8—32no—
392C3×Q8—42no—
393C3×Q8—42no—
394C3×Q8—61no—
395C3×D4—21no—
396C3×D4—21no—
397C3×D4—22no—
398C3×D4—41no—
399C3×D4—64no—
400C3×D4—62no—
401C3×D4—62no—
402C3×D4—122no—
403C3×D4—124no—
404C3×D4—122no—
405C3×D4D3×D412yes—
406C3×D4C2×C3×D412yes—
407C2×C3×C4—21no—
408C2×C3×C4—22no—
409C2×C3×C4—21no—
410C2×C3×C4—22no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—31no—
415C2×C3×C4—32no—
416C2×C3×C4—32no—
417C2×C3×C4—31no—
418C2×C3×C4—31no—
419C2×C3×C4—41no—
420C2×C3×C4—42no—
421C2×C3×C4—42no—
422C2×C3×C4—42no—
423C2×C3×C4—64no—
424C2×C3×C4—61no—
425C2×C3×C4—62no—
426C2×C3×C4—61no—
427C2×C3×C4—82no—
428C2×C3×C4—121no—
429C2×C3×C4—124no—
430C2×C3×C4—122no—
431C2×C3×C4D3×D411yescharacteristic
432C2×C3×C4D3×D411yescharacteristic
433C2×C3×C4C2×C3×D411yescharacteristic
434C2×C3×C4C2×C3×D411yescharacteristic
435C2×C3×C4C23×D311yescharacteristic
436C2×C3×C4C24×C311yescharacteristic
437#67—24no—
438C2×Dic3—21no—
439C2×Dic3—24no—
440C2×Dic3—21no—
441C2×Dic3—42no—
442C2×Dic3C2×C3×D411yescharacteristic
443C2×Dic3C2×C3×D411yescharacteristic
444C2×Dic3C2×C3×D411yescharacteristic
445D12—22no—
446D12—22no—
447D12—42no—
448D12—44no—
449D12—42no—
450C4×D3—22no—
451C4×D3—41no—
452C4×D3—44no—
453C4×D3C2×C3×D412yes—
454C4×D3C3×#4112yes—
455Dic6—21no—
456Dic6C2×C3×D412yes—
457C3×C8—22no—
458C3×C8—22no—
459C3×C8—42no—
460C3×C8—62no—
461C3⋊C8—22no—
462C2×C32—42no—
463C2×C32C2×#12111yescharacteristic
464C2×C32C2×#13511yescharacteristic
465C2×C32#57511yescharacteristic
466C3×D3—22no—
467C3×D3—82no—
468#41—34no—
469#41—62no—
470#41—64no—
471#41—64no—
472C2×Q8—31no—
473C2×Q8C22×C3×D312yes—
474C2×D4—32no—
475C2×D4—62no—
476C2×D4—61no—
477C2×D4—61no—
478C2×D4—61no—
479C2×D4C22×C3×D311yescharacteristic
480C22×C4—21no—
481C22×C4—31no—
482C22×C4—31no—
483C22×C4—31no—
484C22×C4—62no—
485C22×C4—61no—
486C22×C4—61no—
487Q16—64no—
488SD16—24no—
489SD16—64no—
490D8—64no—
491C2×C8—32no—
492C2×C8—64no—
493C2×C8C22×C3×D312yes—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—31no—
497C4⋊C4—61no—
498C4⋊C4—61no—
499C4⋊C4C22×C3×D311yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—62no—
502C22⋊C4—62no—
503C22⋊C4—61no—
504C22⋊C4—61no—
505C42—31no—
506C42—31no—
507C42—31no—
508C42—61no—
509C42—61no—
510C42—61no—
511C42C22×C3×D311yescharacteristic
512C22×C3—22no—
513C22×C3—22no—
514C22×C3—21no—
515C22×C3—32no—
516C22×C3—42no—
517C22×C3—41no—
518C22×C3—41no—
519C22×C3—41no—
520C22×C3—41no—
521C22×C3—61no—
522C22×C3—61no—
523C22×C3—81no—
524C22×C3—81no—
525C22×C3—122no—
526C22×C3—122no—
527C22×C3—122no—
528C22×C3C2×D3×D411yescharacteristic
529C22×C3C22×C3×D411yescharacteristic
530C2×D3—21no—
531C2×D3—21no—
532C2×D3—42no—
533C2×D3—42no—
534C2×D3—42no—
535C2×D3C3×#12112yes—
536C3×C4—21no—
537C3×C4—21no—
538C3×C4—22no—
539C3×C4—21no—
540C3×C4—21no—
541C3×C4—32no—
542C3×C4—41no—
543C3×C4—41no—
544C3×C4—41no—
545C3×C4—42no—
546C3×C4—42no—
547C3×C4—61no—
548C3×C4—61no—
549C3×C4—62no—
550C3×C4—81no—
551C3×C4—82no—
552C3×C4—121no—
553C3×C4#91612yescomplemented
554C3×C4C3×#13512yescomplemented
555C3×C4C2×D3×D411yescharacteristic
556C3×C4D3×#4111yescharacteristic
557C3×C4C22×C3×D411yescharacteristic
558C3×C4C2×C3×#4111yescharacteristic
559Dic3—21no—
560Dic3—21no—
561Dic3—22no—
562Dic3—41no—
563Dic3C3×#12112yes—
564C32#303511yescharacteristic, complemented, Sylow
565C23—21no—
566C23—31no—
567C23—62no—
568Q8—22no—
569Q8—22no—
570Q8—32no—
571Q8—61no—
572D4—21no—
573D4—64no—
574D4—62no—
575D4—62no—
576D4—122no—
577D4—124no—
578D4—122no—
579D4C3×D3×D412yes—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—31no—
583C2×C4—32no—
584C2×C4—32no—
585C2×C4—31no—
586C2×C4—31no—
587C2×C4—42no—
588C2×C4—64no—
589C2×C4—61no—
590C2×C4—62no—
591C2×C4—61no—
592C2×C4—121no—
593C2×C4—124no—
594C2×C4—122no—
595C2×C4C3×D3×D411yescharacteristic
596C2×C4C3×D3×D411yescharacteristic
597C2×C4C23×C3×D311yescharacteristic
598C8—22no—
599C8—62no—
600C2×C3—21no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—42no—
604C2×C3—42no—
605C2×C3—62no—
606C2×C3—82no—
607C2×C3—242no—
608C2×C3D3×#12111yescharacteristic
609C2×C3C2×#91611yescharacteristic
610C2×C3#577711yescharacteristic
611C2×C3C2×C3×#12111yescharacteristic
612C2×C3C2×C3×#13511yescharacteristic
613C2×C3C3×#57511yescharacteristic
614D3—22no—
615D3—82no—
616C22—22no—
617C22—32no—
618C22—41no—
619C22—41no—
620C22—61no—
621C22—61no—
622C22—122no—
623C22—122no—
624C22—122no—
625C22C2×C3×D3×D411yescharacteristic
626C4—21no—
627C4—32no—
628C4—41no—
629C4—42no—
630C4—61no—
631C4—61no—
632C4—62no—
633C4—121no—
634C4C3×#91612yescomplemented
635C4C2×C3×D3×D411yescharacteristic
636C4C3×D3×#4111yescharacteristic
637C3—21no—
638C3#8042711yescharacteristic, direct product factor
639C3C3×#303511yescharacteristic, complemented
640C2—42no—
641C2—62no—
642C2—242no—
643C2C3×D3×#12111yescharacteristic
644C2C2×C3×#91611yescharacteristic
645C2C3×#577711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#461C2
socleC22×C32C22×D4
hypercenterC3×#461D3
hypocenterC3C3×#3035
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#461

Complements

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

NH ≅ G/Ntype
1. C2×C3×#916C2semidirect
2. C3×#5725C2semidirect
3. C3×C4×#237C2semidirect
4. C32×#461C2semidirect
5. C3×#5165C2semidirect
6. C3×#5090C2semidirect
7. C3×#5015C2semidirect
8. C3×#4848C2semidirect
9. C3×D3×C4⋊C8C2semidirect
10. C3×#4804C2semidirect
11. C3×#4798C2semidirect
13. #80427C3direct (N × H)
49. C2×#916C2×C3semidirect
50. #5725C2×C3semidirect
51. C4×#237C2×C3semidirect
56. C3×#461D3semidirect
57. C3×#461C2×C3semidirect
62. #5165C2×C3semidirect
63. #5090C2×C3semidirect
64. #5015C2×C3semidirect
65. #4848C2×C3semidirect
66. D3×C4⋊C8C2×C3semidirect
67. #4804C2×C3semidirect
68. #4798C2×C3semidirect
78. C3×#237D4semidirect
224. #461C3×D3semidirect
260. #237C3×D4semidirect
340. C32×C4#135semidirect
553. C3×C4#916semidirect
554. C3×C4C3×#135semidirect
564. C32#3035semidirect
634. C4C3×#916semidirect
638. C3#80427direct (N × H)
639. C3C3×#3035semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9162
C3×#57252
C3×C4×#2372
C32×#4612
C3×#51652
C3×#50902
C3×#50152
C3×#48482
C3×D3×C4⋊C82
C3×#48042
C3×#47982
C3×#30353
#804273