Finite Group Databasebeta

← C3×#86581 #11901938

Subgroups — C3×#86581 #11901938

Order 1152.

2095 conjugacy classes of subgroups.

The subgroup lattice has 585 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#544C211yesmaximal, characteristic, complemented
2C3×#5729C214yesmaximal, complemented
3C3×#5728C214yesmaximal, complemented
4C3×#5689C214yesmaximal, complemented
5C3×#5688C214yesmaximal, complemented
6C3×#5634C214yesmaximal
7C3×#5622C214yesmaximal, complemented
8C3×D3×#117C212yesmaximal
9C3×#5519C212yesmaximal, complemented
10C2×C3×#892C211yesmaximal, characteristic
11C3×#5500C211yesmaximal, characteristic, complemented
12C3×#3458—31nomaximal
13#86581C311yesmaximal, characteristic, direct product factor
14C22×C3×C4×D3C2211yescharacteristic
15C32×C4⋊Q8C2214yescomplemented
16C32×#125C2214yescomplemented
17C32×C22⋊Q8C2214yes—
18C32×#117C2212yes—
19C2×C32×C4⋊C4C2211yescharacteristic
20C3×#946C2218yes—
21C3×Q8×Dic3C2214yescomplemented
22C3×#944C2214yescomplemented
23C2×C3×(C2×D3)⋊C4C2212yes—
24C3×#926C2212yes—
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C3×#924C2214yes—
27C2×C3×C4×Dic3C2212yes—
28C3×#897C2218yes—
29C3×#896C2218yes—
30C3×#896C2218yes—
31C3×#892C2214yes—
32C3×#892C2214yes—
33C3×#892C2212yes—
34C3×#892C2212yes—
35C3×D3×C4⋊C4C2212yes—
36C3×D3×C4⋊C4C2212yes—
37C3×#890C2214yescomplemented
38C3×#890C2214yescomplemented
39C3×#889C2218yescomplemented
40C3×#888C2214yescomplemented
41C3×#888C2214yescomplemented
42C3×#888C2214yescomplemented
43C3×#887C2214yescomplemented
44C3×#887C2218yescomplemented
45C3×D3×C22⋊C4C2214yes—
46C3×#878C2218yes—
47C3×#877C2214yes—
48C3×#872C2214yes—
49C3×C42×D3C2214yes—
50C3×#870C2214yescomplemented
51C3×#869C2214yescomplemented
52C3×#544—21no—
53C3×#544—34no—
54C3×#544—34no—
55C3×#544—32no—
56C3×#544—31no—
57C3×#544D311yescharacteristic, complemented
58C3×#544C2×C311yescharacteristic, complemented
59C3×#543—34no—
60C3×#533—34no—
61C3×#533—34no—
62C3×#533—34no—
63C2×C3×#117—32no—
64C2×C3×#117—31no—
65#5729C2×C314yescomplemented
66#5728C2×C314yescomplemented
67#5689C2×C314yescomplemented
68#5688C2×C314yescomplemented
69#5634C2×C314yes—
70#5622C2×C314yescomplemented
71D3×#117C2×C312yes—
72#5519C2×C312yescomplemented
73C2×#892C2×C311yescharacteristic
74#5500C2×C311yescharacteristic, complemented
75C23×C3×D3C2311yescharacteristic
76C2×C32×Q8C2314yes—
77C22×C32×C4C2312yes—
78C22×C32×C4C2311yescharacteristic
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2311yescharacteristic
81C2×C3×C4×D3Q818yescomplemented
82C2×C3×C4×D3C2314yes—
83C2×C3×C4×D3C2314yes—
84C2×C3×C4×D3C2312yes—
85C2×C3×C4×D3C2312yes—
86C2×C3×Dic6C2318yes—
87C2×C3×Dic6C2314yes—
88C32×C4⋊C4C2314yes—
89C32×C4⋊C4C2318yes—
90C32×C4⋊C4C2312yes—
91C32×C4⋊C4C2314yes—
92C32×C4⋊C4C2312yes—
93C32×C22⋊C4C2314yes—
94C32×C42C2314yes—
95C3×#217C2314yes—
96C3×(C2×D3)⋊C4C2314yes—
97C3×(C2×D3)⋊C4C2314yes—
98C3×(C2×D3)⋊C4C2318yes—
99C3×C4⋊Dic3C2318yes—
100C3×C4⋊Dic3C2312yes—
101C3×C4⋊Dic3C2314yes—
102C3×C4⋊Dic3C2314yes—
103C3×C4⋊Dic3C2312yes—
104C3×Dic3⋊C4C2314yes—
105C3×Dic3⋊C4C2314yes—
106C3×Dic3⋊C4C2318yes—
107C3×Dic3⋊C4C2318yes—
108C3×Dic3⋊C4C2318yes—
109C3×C4×Dic3C2314yes—
110C3×C4×Dic3C2314yes—
111C3×C4×Dic3C2314yes—
112C3×C4×Dic3C2314yes—
113C3×C4×Dic3C2314yes—
114#3458—31noSylow
115C23×C3×C4—31no—
116C22×C4×D3C22×C311yescharacteristic
117C3×C4⋊Q8—24no—
118C3×C4⋊Q8—34no—
119C3×C4⋊Q8—34no—
120C3×C4⋊Q8—34no—
121C3×C4⋊Q8—34no—
122C3×C4⋊Q8—34no—
123C3×C4⋊Q8C2×D314yescomplemented
124C3×C4⋊Q8C22×C314yescomplemented
125C3×#125—24no—
126C3×#125—38no—
127C3×#125—34no—
128C3×#125—34no—
129C3×#125—34no—
130C3×#125C2×D314yescomplemented
131C3×#125C22×C314yescomplemented
132C3×C22⋊Q8—24no—
133C3×C22⋊Q8—38no—
134C3×C22⋊Q8—34no—
135C3×C22⋊Q8—38no—
136C3×C22⋊Q8—38no—
137C3×C22⋊Q8—38no—
138C3×C22⋊Q8—38no—
139C3×C22⋊Q8C2×D314yes—
140C3×C22⋊Q8C22×C314yes—
141C3×C4×Q8—34no—
142C3×C4×Q8—38no—
143C3×C4×Q8—34no—
144C3×#117—22no—
145C3×#117—32no—
146C3×#117—32no—
147C3×#117—32no—
148C3×#117—34no—
149C3×#117—34no—
150C3×#117—34no—
151C3×#117—34no—
152C3×#117C2×D312yes—
153C3×#117C22×C312yes—
154C2×C3×C4⋊C4—21no—
155C2×C3×C4⋊C4—31no—
156C2×C3×C4⋊C4—32no—
157C2×C3×C4⋊C4—32no—
158C2×C3×C4⋊C4C2×D311yescharacteristic
159C2×C3×C4⋊C4C22×C311yescharacteristic
160C2×C3×C22⋊C4—32no—
161C2×C3×C22⋊C4—34no—
162C2×C3×C42—32no—
163C2×C3×C42—34no—
164#946C22×C318yes—
165Q8×Dic3C22×C314yescomplemented
166#944C22×C314yescomplemented
167C2×(C2×D3)⋊C4C22×C312yes—
168#926C22×C312yes—
169C2×C4⋊Dic3C22×C311yescharacteristic
170#924C22×C314yes—
171C2×C4×Dic3C22×C312yes—
172#897C22×C318yes—
173#896C22×C318yes—
174#896C22×C318yes—
175#892C22×C312yes—
176#892C22×C314yes—
177#892C22×C314yes—
178#892C22×C312yes—
179D3×C4⋊C4C22×C312yes—
180D3×C4⋊C4C22×C312yes—
181#890C22×C314yescomplemented
182#890C22×C314yescomplemented
183#889C22×C318yescomplemented
184#888C22×C314yescomplemented
185#888C22×C314yescomplemented
186#888C22×C314yescomplemented
187#887C22×C314yescomplemented
188#887C22×C318yescomplemented
189D3×C22⋊C4C22×C314yes—
190#878C22×C318yes—
191#877C22×C314yes—
192#872C22×C314yes—
193C42×D3C22×C314yes—
194#870C22×C314yescomplemented
195#869C22×C314yescomplemented
196C23×C32C2411yescharacteristic
197C22×C3×D3—41no—
198C22×C3×D3—41no—
199C22×C3×D3C2×Q814yes—
200C22×C3×D3C2412yes—
201C32×Q8—44no—
202C2×C32×C4—42no—
203C2×C32×C4C2×Q814yes—
204C2×C32×C4C2414yes—
205C2×C32×C4C2414yes—
206C2×C32×C4C2414yes—
207C2×C32×C4C2412yes—
208C2×C3×Dic3—42no—
209C2×C3×Dic3C2×Q814yes—
210C2×C3×Dic3C2414yes—
211C2×C3×Dic3C2414yes—
212C2×C3×Dic3C2414yes—
213C2×C3×Dic3C2411yescharacteristic
214C2×C3×Dic3C2411yescharacteristic
215C3×C4×D3—44no—
216C3×C4×D3—44no—
217C3×C4×D3C2×Q818yes—
218C3×C4×D3C2×Q818yes—
219C3×Dic6—44no—
220C3×Dic6—48no—
221#544—34no—
222#544—34no—
223#544—32no—
224#544—31no—
225#544C3×D311yescharacteristic, complemented
226#543—34no—
227#533—34no—
228#533—34no—
229#533—34no—
230C2×#117—32no—
231C2×#117—31no—
232C24×C3—31no—
233C23×D3C23×C311yescharacteristic
234C2×C3×Q8—24no—
235C2×C3×Q8—34no—
236C2×C3×Q8—38no—
237C2×C3×Q8C22×D314yes—
238C2×C3×Q8C23×C314yes—
239C22×C3×C4—21no—
240C22×C3×C4—22no—
241C22×C3×C4—31no—
242C22×C3×C4—38no—
243C22×C3×C4—32no—
244C22×C3×C4—32no—
245C22×C3×C4—32no—
246C22×C3×C4—34no—
247C22×C3×C4—34no—
248C22×C3×C4C22×D312yes—
249C22×C3×C4C22×D311yescharacteristic
250C22×C3×C4C23×C312yes—
251C22×C3×C4C23×C311yescharacteristic
252C22×Dic3C23×C312yes—
253C22×Dic3C23×C311yescharacteristic
254C2×C4×D3C3×Q818yescomplemented
255C2×C4×D3C23×C314yes—
256C2×C4×D3C23×C314yes—
257C2×C4×D3C23×C312yes—
258C2×C4×D3C23×C312yes—
259C2×Dic6C23×C318yes—
260C2×Dic6C23×C314yes—
261C3×C4⋊C4—24no—
262C3×C4⋊C4—22no—
263C3×C4⋊C4—22no—
264C3×C4⋊C4—24no—
265C3×C4⋊C4—28no—
266C3×C4⋊C4—34no—
267C3×C4⋊C4—34no—
268C3×C4⋊C4—38no—
269C3×C4⋊C4—38no—
270C3×C4⋊C4—38no—
271C3×C4⋊C4—32no—
272C3×C4⋊C4—34no—
273C3×C4⋊C4—32no—
274C3×C4⋊C4—34no—
275C3×C4⋊C4—38no—
276C3×C4⋊C4C22×D312yes—
277C3×C4⋊C4C22×D312yes—
278C3×C4⋊C4C22×D314yes—
279C3×C4⋊C4C22×D318yes—
280C3×C4⋊C4C22×D314yes—
281C3×C4⋊C4C23×C314yes—
282C3×C4⋊C4C23×C318yes—
283C3×C4⋊C4C23×C312yes—
284C3×C4⋊C4C23×C314yes—
285C3×C4⋊C4C23×C312yes—
286C3×C22⋊C4—24no—
287C3×C22⋊C4—34no—
288C3×C22⋊C4—38no—
289C3×C22⋊C4—34no—
290C3×C22⋊C4—34no—
291C3×C22⋊C4C22×D314yes—
292C3×C22⋊C4C23×C314yes—
293C3×C42—24no—
294C3×C42—34no—
295C3×C42—34no—
296C3×C42—34no—
297C3×C42—34no—
298C3×C42—34no—
299C3×C42C22×D314yes—
300C3×C42C23×C314yes—
301#217C23×C314yes—
302(C2×D3)⋊C4C23×C314yes—
303(C2×D3)⋊C4C23×C314yes—
304(C2×D3)⋊C4C23×C318yes—
305C4⋊Dic3C23×C312yes—
306C4⋊Dic3C23×C314yes—
307C4⋊Dic3C23×C318yes—
308C4⋊Dic3C23×C312yes—
309C4⋊Dic3C23×C314yes—
310Dic3⋊C4C23×C318yes—
311Dic3⋊C4C23×C318yes—
312Dic3⋊C4C23×C314yes—
313Dic3⋊C4C23×C314yes—
314Dic3⋊C4C23×C318yes—
315C4×Dic3C23×C314yes—
316C4×Dic3C23×C314yes—
317C4×Dic3C23×C314yes—
318C4×Dic3C23×C314yes—
319C4×Dic3C23×C314yes—
320C22×C32—21no—
321C22×C32—21no—
322C22×C32C22×Q812yes—
323C22×C32C2511yescharacteristic
324C2×C3×D3—22no—
325C2×C3×D3—22no—
326C2×C3×D3—44no—
327C2×C3×D3C22×Q814yes—
328C32×C4—24no—
329C32×C4—24no—
330C32×C4—24no—
331C32×C4C22×Q814yes—
332C3×Dic3—24no—
333C3×Dic3—24no—
334C3×Dic3—24no—
335C3×Dic3C22×Q812yes—
336C3×Dic3C22×Q812yes—
337C23×C4—31no—
338C4⋊Q8—34no—
339C4⋊Q8—34no—
340C4⋊Q8—34no—
341C4⋊Q8—34no—
342C4⋊Q8—34no—
343C4⋊Q8C2×C3×D314yescomplemented
344#125—38no—
345#125—34no—
346#125—34no—
347#125—34no—
348#125C2×C3×D314yescomplemented
349C22⋊Q8—38no—
350C22⋊Q8—34no—
351C22⋊Q8—38no—
352C22⋊Q8—38no—
353C22⋊Q8—38no—
354C22⋊Q8—38no—
355C22⋊Q8C2×C3×D314yes—
356C4×Q8—34no—
357C4×Q8—38no—
358C4×Q8—34no—
359#117—32no—
360#117—32no—
361#117—32no—
362#117—34no—
363#117—34no—
364#117—34no—
365#117—34no—
366#117C2×C3×D312yes—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—32no—
369C2×C4⋊C4—32no—
370C2×C4⋊C4C2×C3×D311yescharacteristic
371C2×C22⋊C4—32no—
372C2×C22⋊C4—34no—
373C2×C42—32no—
374C2×C42—34no—
375C23×C3—21no—
376C23×C3—32no—
377C23×C3—34no—
378C23×C3—121no—
379C23×C3—121no—
380C23×C3C23×D311yescharacteristic
381C23×C3C24×C311yescharacteristic
382C22×D3—41no—
383C22×D3—41no—
384C22×D3C2×C3×Q814yes—
385C22×D3C24×C312yes—
386C3×Q8—44no—
387C3×Q8—44no—
388C3×Q8—84no—
389C3×Q8—124no—
390C3×Q8—128no—
391C2×C3×C4—22no—
392C2×C3×C4—24no—
393C2×C3×C4—24no—
394C2×C3×C4—24no—
395C2×C3×C4—24no—
396C2×C3×C4—34no—
397C2×C3×C4—31no—
398C2×C3×C4—31no—
399C2×C3×C4—38no—
400C2×C3×C4—38no—
401C2×C3×C4—34no—
402C2×C3×C4—34no—
403C2×C3×C4—34no—
404C2×C3×C4—42no—
405C2×C3×C4—42no—
406C2×C3×C4—82no—
407C2×C3×C4—124no—
408C2×C3×C4—124no—
409C2×C3×C4—122no—
410C2×C3×C4D3×Q814yes—
411C2×C3×C4C2×C3×Q814yes—
412C2×C3×C4C23×D314yes—
413C2×C3×C4C23×D314yes—
414C2×C3×C4C23×D314yes—
415C2×C3×C4C23×D312yes—
416C2×C3×C4C24×C314yes—
417C2×C3×C4C24×C314yes—
418C2×C3×C4C24×C314yes—
419C2×C3×C4C24×C312yes—
420C2×Dic3—42no—
421C2×Dic3C2×C3×Q814yes—
422C2×Dic3C24×C314yes—
423C2×Dic3C24×C314yes—
424C2×Dic3C24×C314yes—
425C2×Dic3C24×C311yescharacteristic
426C2×Dic3C24×C311yescharacteristic
427C4×D3—44no—
428C4×D3—44no—
429C4×D3C2×C3×Q818yes—
430C4×D3C2×C3×Q818yes—
431Dic6—44no—
432Dic6—48no—
433C2×C32—22no—
434C2×C32C23×Q811yescharacteristic
435C2×C32#58511yescharacteristic
436C2×C32#58511yescharacteristic
437C3×D3—24no—
438C24—31no—
439C2×Q8—34no—
440C2×Q8—38no—
441C2×Q8C22×C3×D314yes—
442C22×C4—31no—
443C22×C4—32no—
444C22×C4—32no—
445C22×C4—38no—
446C22×C4—32no—
447C22×C4—34no—
448C22×C4—34no—
449C22×C4C22×C3×D312yes—
450C22×C4C22×C3×D311yescharacteristic
451C4⋊C4—34no—
452C4⋊C4—34no—
453C4⋊C4—34no—
454C4⋊C4—32no—
455C4⋊C4—32no—
456C4⋊C4—38no—
457C4⋊C4—38no—
458C4⋊C4—38no—
459C4⋊C4—34no—
460C4⋊C4—38no—
461C4⋊C4C22×C3×D312yes—
462C4⋊C4C22×C3×D312yes—
463C4⋊C4C22×C3×D314yes—
464C4⋊C4C22×C3×D318yes—
465C4⋊C4C22×C3×D314yes—
466C22⋊C4—34no—
467C22⋊C4—38no—
468C22⋊C4—34no—
469C22⋊C4—34no—
470C22⋊C4C22×C3×D314yes—
471C42—34no—
472C42—34no—
473C42—34no—
474C42—34no—
475C42—34no—
476C42C22×C3×D314yes—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3—22no—
482C22×C3—21no—
483C22×C3—34no—
484C22×C3—41no—
485C22×C3—41no—
486C22×C3—62no—
487C22×C3—62no—
488C22×C3—124no—
489C22×C3C2×D3×Q812yes—
490C22×C3C22×C3×Q812yes—
491C22×C3C24×D311yescharacteristic
492C22×C3C25×C311yescharacteristic
493C2×D3—22no—
494C2×D3—22no—
495C2×D3—44no—
496C2×D3C22×C3×Q814yes—
497C3×C4—24no—
498C3×C4—24no—
499C3×C4—24no—
500C3×C4—24no—
501C3×C4—24no—
502C3×C4—24no—
503C3×C4—24no—
504C3×C4—32no—
505C3×C4—32no—
506C3×C4—44no—
507C3×C4—44no—
508C3×C4—44no—
509C3×C4—64no—
510C3×C4—64no—
511C3×C4—64no—
512C3×C4C2×D3×Q814yes—
513C3×C4C22×C3×Q814yes—
514Dic3—24no—
515Dic3—24no—
516Dic3—24no—
517Dic3C22×C3×Q812yes—
518Dic3C22×C3×Q812yes—
519C32#345811yescharacteristic, complemented, Sylow
520C23—32no—
521C23—34no—
522C23—121no—
523C23—121no—
524C23C23×C3×D311yescharacteristic
525Q8—44no—
526Q8—124no—
527Q8—128no—
528C2×C4—34no—
529C2×C4—31no—
530C2×C4—31no—
531C2×C4—38no—
532C2×C4—38no—
533C2×C4—34no—
534C2×C4—34no—
535C2×C4—34no—
536C2×C4—42no—
537C2×C4—124no—
538C2×C4—124no—
539C2×C4—122no—
540C2×C4C3×D3×Q814yes—
541C2×C4C23×C3×D314yes—
542C2×C4C23×C3×D314yes—
543C2×C4C23×C3×D314yes—
544C2×C4C23×C3×D312yes—
545C2×C3—22no—
546C2×C3—22no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—42no—
551C2×C3—64no—
552C2×C3C22×D3×Q811yescharacteristic
553C2×C3#596611yescharacteristic
554C2×C3#596811yescharacteristic
555C2×C3C23×C3×Q811yescharacteristic
556C2×C3C3×#58511yescharacteristic
557C2×C3C3×#58511yescharacteristic
558D3—24no—
559C22—21no—
560C22—21no—
561C22—34no—
562C22—62no—
563C22—62no—
564C22—124no—
565C22C2×C3×D3×Q812yes—
566C22C24×C3×D311yescharacteristic
567C4—24no—
568C4—24no—
569C4—24no—
570C4—32no—
571C4—32no—
572C4—64no—
573C4—64no—
574C4—64no—
575C4C2×C3×D3×Q814yes—
576C3—21no—
577C3#8658111yescharacteristic, direct product factor
578C3C3×#345811yescharacteristic, complemented
579C2—22no—
580C2—64no—
581C2C22×C3×D3×Q811yescharacteristic
582C2C3×#596611yescharacteristic
583C2C3×#596811yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#544C2
socleC22×C32C25
prime radicalC23×C3×D3C23
hypercenterC3×#544D3
hypocenterC3C3×#3458
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#544

Complements

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

NH ≅ G/Ntype
1. C32×#544C2semidirect
2. C3×#5729C2semidirect
3. C3×#5728C2semidirect
4. C3×#5689C2semidirect
5. C3×#5688C2semidirect
7. C3×#5622C2semidirect
9. C3×#5519C2semidirect
11. C3×#5500C2semidirect
13. #86581C3direct (N × H)
15. C32×C4⋊Q8C22semidirect
16. C32×#125C22semidirect
21. C3×Q8×Dic3C22semidirect
22. C3×#944C22semidirect
37. C3×#890C22semidirect
38. C3×#890C22semidirect
39. C3×#889C22semidirect
40. C3×#888C22semidirect
41. C3×#888C22semidirect
42. C3×#888C22semidirect
43. C3×#887C22semidirect
44. C3×#887C22semidirect
50. C3×#870C22semidirect
51. C3×#869C22semidirect
57. C3×#544D3semidirect
58. C3×#544C2×C3semidirect
65. #5729C2×C3semidirect
66. #5728C2×C3semidirect
67. #5689C2×C3semidirect
68. #5688C2×C3semidirect
70. #5622C2×C3semidirect
72. #5519C2×C3semidirect
74. #5500C2×C3semidirect
81. C2×C3×C4×D3Q8semidirect
123. C3×C4⋊Q8C2×D3semidirect
124. C3×C4⋊Q8C22×C3semidirect
130. C3×#125C2×D3semidirect
131. C3×#125C22×C3semidirect
165. Q8×Dic3C22×C3semidirect
166. #944C22×C3semidirect
181. #890C22×C3semidirect
182. #890C22×C3semidirect
183. #889C22×C3semidirect
184. #888C22×C3semidirect
185. #888C22×C3semidirect
186. #888C22×C3semidirect
187. #887C22×C3semidirect
188. #887C22×C3semidirect
194. #870C22×C3semidirect
195. #869C22×C3semidirect
225. #544C3×D3semidirect
254. C2×C4×D3C3×Q8semidirect
343. C4⋊Q8C2×C3×D3semidirect
348. #125C2×C3×D3semidirect
519. C32#3458semidirect
577. C3#86581direct (N × H)
578. C3C3×#3458semidirect

Maximal subgroups

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

subgroupindex
C32×#5442
C3×#57292
C3×#57282
C3×#56892
C3×#56882
C3×#56342
C3×#56222
C3×D3×#1172
C3×#55192
C2×C3×#8922
C3×#55002
C3×#34583
#865813