Finite Group Databasebeta

← C3×#78680 #11864677

Subgroups — C3×#78680 #11864677

Order 1152.

1503 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic, complemented
2C3×#5833C211yesmaximal, characteristic, complemented
3C2×C3×#909C211yesmaximal, characteristic, complemented
4C2×C3×#904C211yesmaximal, characteristic, complemented
5C32×#408C211yesmaximal, characteristic, complemented
6C3×#5133C211yesmaximal, characteristic, complemented
7C2×C3×#816C211yesmaximal, characteristic, complemented
8C3×#4739C212yesmaximal, complemented
9C3×#4738C212yesmaximal, complemented
10C3×#4734C212yesmaximal, complemented
11C3×#4733C212yesmaximal, complemented
12C3×#3013—31nomaximal
13#78680C311yesmaximal, characteristic, direct product factor
14C2×C32×#41C2211yescharacteristic
15C3×#1010—24no—
16C3×#1010—24no—
17C2×C3×D3×Q8—21no—
18C2×C3×#237—21no—
19C2×C3×#237—22no—
20C2×C3×#235C2211yescharacteristic
21C2×C3×#235C2212yes—
22C2×C3×#235C2211yescharacteristic
23C22×C3×Dic6C2212yes—
24C22×C3×Dic6C2211yescharacteristic
25C2×C32×M16C2211yescharacteristic
26C22×C32×C8C2211yescharacteristic
27C3×#946—21no—
28C3×#939—22no—
29C3×#938—21no—
30C3×#930C2212yes—
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C3×#924C2212yes—
33C3×#909—24no—
34C2×C3×Dic12C2212yes—
35C2×C3×Dic12C2211yescharacteristic
36C3×#904—24no—
37C2×C3×D24C2211yescharacteristic
38C2×C3×#204C2212yes—
39C2×C3×#204C2211yescharacteristic
40C2×C3×#204C2211yescharacteristic
41C32×C22⋊C8C2212yes—
42C32×C22⋊C8C2212yes—
43C3×#821C2212yes—
44C3×#816C2212yes—
45C3×#816C2212yes—
46C3×#816C2212yes—
47C2×C3×2−1+4—31no—
48C2×#1010C2×C311yescharacteristic, complemented
49C2×C3×#137—31no—
50C2×C3×#135—31no—
51C3×#537—31no—
52#5833C2×C311yescharacteristic, complemented
53C2×#909C2×C311yescharacteristic, complemented
54C2×#904C2×C311yescharacteristic, complemented
55C3×#452—32no—
56C3×#451—32no—
57C3×#449—32no—
58C3×#448—32no—
59C3×#417—31no—
60C2×C3×#103—31no—
61C3×#408—21no—
62C3×#408D311yescharacteristic, complemented
63C3×#408C2×C311yescharacteristic, complemented
64#5133C2×C311yescharacteristic, complemented
65C2×#816C2×C311yescharacteristic, complemented
66#4739C2×C312yescomplemented
67#4738C2×C312yescomplemented
68#4734C2×C312yescomplemented
69#4733C2×C312yescomplemented
70C32×#41—22no—
71C32×#41—22no—
72C2×C32×Q8D411yescharacteristic
73C2×C32×D4D411yescharacteristic
74C2×C32×D4D412yes—
75C22×C32×C4C2312yes—
76C22×C32×C4C2311yescharacteristic
77C2×C3×#67—22no—
78C2×C3×#67—21no—
79C2×C3×#67—21no—
80C2×C3×#67—22no—
81C22×C3×Dic3—22no—
82C22×C3×Dic3—21no—
83C22×C3×Dic3—21no—
84C3×D3×Q8—28no—
85C3×#237—216no—
86C3×#237—28no—
87C3×#235—22no—
88C3×#235—24no—
89C3×#235—22no—
90C3×#235—22no—
91C3×#235—24no—
92C3×#235D414yescomplemented
93C2×C3×D12C2311yescharacteristic
94C2×C3×D12C2311yescharacteristic
95C2×C3×C4×D3—22no—
96C2×C3×C4×D3—21no—
97C2×C3×C4×D3—21no—
98C2×C3×Dic6—22no—
99C2×C3×Dic6—21no—
100C2×C3×Dic6—22no—
101C2×C3×Dic6—24no—
102C2×C3×Dic6—24no—
103C2×C3×Dic6D414yescomplemented
104C2×C3×Dic6C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×C3×Dic6C2312yes—
107C32×M16—22no—
108C2×C32×C8—22no—
109C2×C32×C8C2311yescharacteristic
110C2×C32×C8C2312yes—
111C2×C32×C8C2311yescharacteristic
112C3×#217—22no—
113C3×(C2×D3)⋊C4—22no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3C2312yes—
116C3×Dic3⋊C4—22no—
117C3×Dic12—22no—
118C3×Dic12—24no—
119C3×D24—22no—
120C3×#204—22no—
121C3×#204—22no—
122C3×#204—24no—
123#3013—31noSylow
124C3×2−1+4—64no—
125C3×2−1+4—64no—
126C2×C3×#41—21no—
127C2×C3×#41—31no—
128C2×C3×#41—31no—
129C2×C3×#41—32no—
130C2×C3×#41—61no—
131C2×C3×#41—62no—
132C2×C3×#41C2×D311yescharacteristic
133C2×C3×#41C22×C311yescharacteristic
134C22×C3×Q8—31no—
135C22×C3×Q8—32no—
136C22×C3×Q8—61no—
137#1010—24no—
138#1010—24no—
139C2×D3×Q8—21no—
140C2×#237—21no—
141C2×#237—22no—
142C2×#235C22×C312yes—
143C2×#235C22×C311yescharacteristic
144C2×#235C22×C311yescharacteristic
145C22×Dic6C22×C312yes—
146C22×Dic6C22×C311yescharacteristic
147C3×#137—64no—
148C3×#135—64no—
149C2×C3×Q16—31no—
150C2×C3×Q16—32no—
151C2×C3×SD16—31no—
152C2×C3×SD16—31no—
153C2×C3×SD16—32no—
154C2×C3×D8—31no—
155C2×C3×M16—21no—
156C2×C3×M16C2×D311yescharacteristic
157C2×C3×M16C22×C311yescharacteristic
158C22×C3×C8—21no—
159C22×C3×C8C2×D311yescharacteristic
160C22×C3×C8C22×C311yescharacteristic
161C3×C22⋊Q8—32no—
162C3×C22⋊Q8—61no—
163C3×#121—32no—
164C3×#121—61no—
165C3×#121—62no—
166C2×C3×C4⋊C4—31no—
167#946—21no—
168#939—22no—
169#938—21no—
170#930C22×C312yes—
171C2×C4⋊Dic3C22×C311yescharacteristic
172#924C22×C312yes—
173#909—24no—
174C2×Dic12C22×C311yescharacteristic
175C2×Dic12C22×C312yes—
176#904—24no—
177C2×D24C22×C311yescharacteristic
178C2×#204C22×C311yescharacteristic
179C2×#204C22×C311yescharacteristic
180C2×#204C22×C312yes—
181C3×#103—32no—
182C3×#103—32no—
183C3×#103—32no—
184C3×#102—32no—
185C3×C22⋊C8—22no—
186C3×C22⋊C8—22no—
187C3×C22⋊C8C2×D312yes—
188C3×C22⋊C8C2×D312yes—
189C3×C22⋊C8C22×C312yes—
190C3×C22⋊C8C22×C312yes—
191#821C22×C312yes—
192#816C22×C312yes—
193#816C22×C312yes—
194#816C22×C312yes—
195C23×C32C2×D412yes—
196C23×C32C2×D411yescharacteristic
197C22×C3×D3—21no—
198C22×C3×D3—21no—
199C32×Q8—22no—
200C32×D4—24no—
201C32×D4—22no—
202C2×C32×C4—22no—
203C2×C32×C4—22no—
204C2×C32×C4C2×D412yes—
205C2×C32×C4C2×D411yescharacteristic
206C2×C32×C4C2×D412yes—
207C2×C32×C4C2×D412yes—
208C2×C32×C4C2411yescharacteristic
209C3×#67—28no—
210C3×#67—24no—
211C3×#67—42no—
212C3×#67—82no—
213C2×C3×Dic3—28no—
214C2×C3×Dic3—24no—
215C2×C3×Dic3—21no—
216C2×C3×Dic3—22no—
217C2×C3×Dic3—21no—
218C2×C3×Dic3—22no—
219C2×C3×Dic3—81no—
220C3×D12—21no—
221C3×D12—21no—
222C3×D12—21no—
223C3×D12C2×D412yes—
224C3×C4×D3—28no—
225C3×C4×D3—24no—
226C3×C4×D3—42no—
227C3×Dic6—28no—
228C3×Dic6—24no—
229C3×Dic6—22no—
230C3×Dic6—21no—
231C3×Dic6—21no—
232C3×Dic6—21no—
233C3×Dic6C2×D412yes—
234C3×Dic6C2×D414yes—
235C32×C8—21no—
236C32×C8—22no—
237C32×C8—21no—
238C2×2−1+4—31no—
239C2×#137—31no—
240C2×#135—31no—
241#537—31no—
242#452—32no—
243#451—32no—
244#449—32no—
245#448—32no—
246#417—31no—
247C2×#103—31no—
248#408C3×D311yescharacteristic, complemented
249C3×#41—22no—
250C3×#41—22no—
251C3×#41—22no—
252C3×#41—22no—
253C3×#41—34no—
254C3×#41—42no—
255C3×#41—42no—
256C3×#41—64no—
257C3×#41—64no—
258C3×#41—616no—
259C3×#41—68no—
260C3×#41—62no—
261C3×#41—62no—
262C3×#41—62no—
263C2×C3×Q8—21no—
264C2×C3×Q8—34no—
265C2×C3×Q8—32no—
266C2×C3×Q8—31no—
267C2×C3×Q8—31no—
268C2×C3×Q8—64no—
269C2×C3×Q8—64no—
270C2×C3×Q8—68no—
271C2×C3×Q8—62no—
272C2×C3×Q8—61no—
273C2×C3×Q8—62no—
274C2×C3×Q8D1211yescharacteristic
275C2×C3×Q8C3×D411yescharacteristic
276C2×C3×D4—21no—
277C2×C3×D4—22no—
278C2×C3×D4—31no—
279C2×C3×D4—31no—
280C2×C3×D4—62no—
281C2×C3×D4—61no—
282C2×C3×D4—61no—
283C2×C3×D4—62no—
284C2×C3×D4D1212yes—
285C2×C3×D4D1211yescharacteristic
286C2×C3×D4C3×D411yescharacteristic
287C2×C3×D4C3×D412yes—
288C22×C3×C4—21no—
289C22×C3×C4—22no—
290C22×C3×C4—62no—
291C22×C3×C4—61no—
292C22×C3×C4—62no—
293C22×C3×C4—61no—
294C22×C3×C4—61no—
295C22×C3×C4—61no—
296C22×C3×C4C22×D312yes—
297C22×C3×C4C22×D311yescharacteristic
298C22×C3×C4C23×C312yes—
299C22×C3×C4C23×C311yescharacteristic
300C2×#67—22no—
301C2×#67—21no—
302C2×#67—21no—
303C2×#67—22no—
304C22×Dic3—22no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307D3×Q8—28no—
308#237—216no—
309#237—28no—
310#235—22no—
311#235—24no—
312#235—22no—
313#235—22no—
314#235—24no—
315#235C3×D414yescomplemented
316C2×D12C23×C311yescharacteristic
317C2×D12C23×C311yescharacteristic
318C2×C4×D3—22no—
319C2×C4×D3—21no—
320C2×C4×D3—21no—
321C2×Dic6—22no—
322C2×Dic6—21no—
323C2×Dic6—22no—
324C2×Dic6—24no—
325C2×Dic6—24no—
326C2×Dic6C3×D414yescomplemented
327C2×Dic6C23×C311yescharacteristic
328C2×Dic6C23×C311yescharacteristic
329C2×Dic6C23×C312yes—
330C3×Q16—62no—
331C3×Q16—64no—
332C3×SD16—62no—
333C3×SD16—62no—
334C3×SD16—64no—
335C3×D8—62no—
336C3×M16—22no—
337C3×M16—22no—
338C3×M16—42no—
339C2×C3×C8—22no—
340C2×C3×C8—22no—
341C2×C3×C8—21no—
342C2×C3×C8—21no—
343C2×C3×C8—22no—
344C2×C3×C8—42no—
345C2×C3×C8C22×D312yes—
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C23×C311yescharacteristic
349C2×C3×C8C23×C311yescharacteristic
350C2×C3×C8C23×C312yes—
351C3×C4⋊C4—32no—
352C3×C4⋊C4—62no—
353C3×C4⋊C4—61no—
354C3×C22⋊C4—62no—
355C3×C22⋊C4—62no—
356#217—22no—
357(C2×D3)⋊C4—22no—
358C4⋊Dic3—21no—
359C4⋊Dic3C23×C312yes—
360Dic3⋊C4—22no—
361Dic12—22no—
362Dic12—24no—
363D24—22no—
364#204—22no—
365#204—22no—
366#204—24no—
367C22×C32—21no—
368C22×C32—21no—
369C22×C32—22no—
370C22×C32—22no—
371C22×C32—22no—
372C22×C32#12012yes—
373C22×C32C22×D411yescharacteristic
374C2×C3×D3—22no—
375C2×C3×D3—41no—
376C2×C3×D3—41no—
377C2×C3×D3—41no—
378C2×C3×D3—41no—
379C2×C3×D3—41no—
380C32×C4—22no—
381C32×C4#12012yes—
382C32×C4C22×D411yescharacteristic
383C32×C4C22×D411yescharacteristic
384C3×Dic3—22no—
385C3×Dic3—24no—
386C3×Dic3—41no—
387C3×Dic3—42no—
3882−1+4—64no—
3892−1+4—64no—
390C2×#41—31no—
391C2×#41—31no—
392C2×#41—32no—
393C2×#41—61no—
394C2×#41—62no—
395C2×#41C2×C3×D311yescharacteristic
396C22×Q8—31no—
397C22×Q8—32no—
398C22×Q8—61no—
399#137—64no—
400#135—64no—
401C2×Q16—31no—
402C2×Q16—32no—
403C2×SD16—31no—
404C2×SD16—31no—
405C2×SD16—32no—
406C2×D8—31no—
407C2×M16C2×C3×D311yescharacteristic
408C22×C8C2×C3×D311yescharacteristic
409C22⋊Q8—32no—
410C22⋊Q8—61no—
411#121—32no—
412#121—61no—
413#121—62no—
414C2×C4⋊C4—31no—
415#103—32no—
416#103—32no—
417#103—32no—
418#102—32no—
419C22⋊C8C2×C3×D312yes—
420C22⋊C8C2×C3×D312yes—
421C23×C3—21no—
422C23×C3—22no—
423C23×C3—61no—
424C23×C3—61no—
425C23×C3C2×D1212yes—
426C23×C3C2×D1211yescharacteristic
427C23×C3C2×C3×D412yes—
428C23×C3C2×C3×D411yescharacteristic
429C22×D3—21no—
430C22×D3—21no—
431C3×Q8—22no—
432C3×Q8—22no—
433C3×Q8—34no—
434C3×Q8—32no—
435C3×Q8—42no—
436C3×Q8—68no—
437C3×Q8—64no—
438C3×Q8—62no—
439C3×Q8—61no—
440C3×Q8—61no—
441C3×Q8—61no—
442C3×D4—24no—
443C3×D4—24no—
444C3×D4—22no—
445C3×D4—22no—
446C3×D4—32no—
447C3×D4—42no—
448C3×D4—44no—
449C3×D4—68no—
450C3×D4—64no—
451C3×D4—61no—
452C3×D4—61no—
453C3×D4—61no—
454C3×D4—122no—
455C3×D4—242no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—42no—
466C2×C3×C4—42no—
467C2×C3×C4—68no—
468C2×C3×C4—68no—
469C2×C3×C4—64no—
470C2×C3×C4—62no—
471C2×C3×C4—61no—
472C2×C3×C4—64no—
473C2×C3×C4—62no—
474C2×C3×C4—61no—
475C2×C3×C4—122no—
476C2×C3×C4—241no—
477C2×C3×C4C2×D1212yes—
478C2×C3×C4C2×D1211yescharacteristic
479C2×C3×C4D3×D412yes—
480C2×C3×C4D3×D412yes—
481C2×C3×C4C2×C3×D412yes—
482C2×C3×C4C2×C3×D411yescharacteristic
483C2×C3×C4C2×C3×D412yes—
484C2×C3×C4C2×C3×D412yes—
485C2×C3×C4C23×D311yescharacteristic
486C2×C3×C4C24×C311yescharacteristic
487#67—28no—
488#67—24no—
489#67—42no—
490#67—82no—
491C2×Dic3—28no—
492C2×Dic3—24no—
493C2×Dic3—21no—
494C2×Dic3—22no—
495C2×Dic3—21no—
496C2×Dic3—22no—
497C2×Dic3—81no—
498D12—21no—
499D12—21no—
500D12—21no—
501D12C2×C3×D412yes—
502C4×D3—28no—
503C4×D3—24no—
504C4×D3—42no—
505Dic6—28no—
506Dic6—24no—
507Dic6—22no—
508Dic6—21no—
509Dic6—21no—
510Dic6—21no—
511Dic6C2×C3×D412yes—
512Dic6C2×C3×D414yes—
513C3×C8—21no—
514C3×C8—21no—
515C3×C8—22no—
516C3×C8—21no—
517C3×C8—22no—
518C3×C8—21no—
519C3×C8—41no—
520C3×C8—41no—
521C3×C8—42no—
522C2×C32—22no—
523C2×C32—42no—
524C2×C32C2×#12011yescharacteristic
525C2×C32#57711yescharacteristic
526C2×C32#57811yescharacteristic
527C3×D3—42no—
528C3×D3—81no—
529#41—22no—
530#41—22no—
531#41—34no—
532#41—64no—
533#41—64no—
534#41—616no—
535#41—68no—
536#41—62no—
537#41—62no—
538#41—62no—
539C2×Q8—32no—
540C2×Q8—31no—
541C2×Q8—31no—
542C2×Q8—34no—
543C2×Q8—64no—
544C2×Q8—64no—
545C2×Q8—68no—
546C2×Q8—62no—
547C2×Q8—61no—
548C2×Q8—62no—
549C2×Q8C3×D1211yescharacteristic
550C2×D4—31no—
551C2×D4—31no—
552C2×D4—62no—
553C2×D4—61no—
554C2×D4—61no—
555C2×D4—62no—
556C2×D4C3×D1212yes—
557C2×D4C3×D1211yescharacteristic
558C22×C4—62no—
559C22×C4—61no—
560C22×C4—62no—
561C22×C4—61no—
562C22×C4—61no—
563C22×C4—61no—
564C22×C4C22×C3×D312yes—
565C22×C4C22×C3×D311yescharacteristic
566Q16—62no—
567Q16—64no—
568SD16—62no—
569SD16—62no—
570SD16—64no—
571D8—62no—
572M16—22no—
573C2×C8—22no—
574C2×C8C22×C3×D312yes—
575C2×C8C22×C3×D311yescharacteristic
576C2×C8C22×C3×D311yescharacteristic
577C4⋊C4—32no—
578C4⋊C4—61no—
579C4⋊C4—62no—
580C22⋊C4—62no—
581C22⋊C4—62no—
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—21no—
586C22×C3—22no—
587C22×C3—22no—
588C22×C3—22no—
589C22×C3—22no—
590C22×C3—22no—
591C22×C3—22no—
592C22×C3—22no—
593C22×C3—21no—
594C22×C3—41no—
595C22×C3—41no—
596C22×C3—42no—
597C22×C3—42no—
598C22×C3—42no—
599C22×C3—62no—
600C22×C3—121no—
601C22×C3—121no—
602C22×C3—121no—
603C22×C3—121no—
604C22×C3—121no—
605C22×C3#88212yes—
606C22×C3C3×#12012yes—
607C22×C3C22×D1211yescharacteristic
608C22×C3C22×C3×D411yescharacteristic
609C2×D3—22no—
610C2×D3—41no—
611C2×D3—41no—
612C2×D3—41no—
613C2×D3—41no—
614C2×D3—41no—
615C3×C4—22no—
616C3×C4—22no—
617C3×C4—22no—
618C3×C4—21no—
619C3×C4—21no—
620C3×C4—42no—
621C3×C4—64no—
622C3×C4—62no—
623C3×C4—121no—
624C3×C4—122no—
625C3×C4#88212yes—
626C3×C4C3×#12012yes—
627C3×C4C2×D3×D411yescharacteristic
628C3×C4C2×D3×D411yescharacteristic
629C3×C4C22×C3×D411yescharacteristic
630C3×C4C22×C3×D411yescharacteristic
631Dic3—22no—
632Dic3—24no—
633Dic3—42no—
634Dic3—41no—
635C32#301311yescharacteristic, complemented, Sylow
636C23—61no—
637C23—61no—
638C23C2×C3×D1212yes—
639C23C2×C3×D1211yescharacteristic
640Q8—22no—
641Q8—34no—
642Q8—32no—
643Q8—68no—
644Q8—64no—
645Q8—62no—
646Q8—61no—
647Q8—61no—
648Q8—61no—
649D4—24no—
650D4—22no—
651D4—32no—
652D4—68no—
653D4—64no—
654D4—61no—
655D4—61no—
656D4—61no—
657D4—122no—
658D4—242no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—68no—
662C2×C4—68no—
663C2×C4—64no—
664C2×C4—62no—
665C2×C4—61no—
666C2×C4—64no—
667C2×C4—62no—
668C2×C4—61no—
669C2×C4—122no—
670C2×C4—241no—
671C2×C4C2×C3×D1212yes—
672C2×C4C2×C3×D1211yescharacteristic
673C2×C4C3×D3×D412yes—
674C2×C4C3×D3×D412yes—
675C2×C4C23×C3×D311yescharacteristic
676C8—21no—
677C8—21no—
678C8—22no—
679C2×C3—22no—
680C2×C3—22no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—42no—
685C2×C3—42no—
686C2×C3—42no—
687C2×C3—82no—
688C2×C3—122no—
689C2×C3—241no—
690C2×C3C2×#88211yescharacteristic
691C2×C3#575111yescharacteristic
692C2×C3#575311yescharacteristic
693C2×C3C2×C3×#12011yescharacteristic
694C2×C3C3×#57711yescharacteristic
695C2×C3C3×#57811yescharacteristic
696D3—42no—
697D3—81no—
698C22—21no—
699C22—21no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—62no—
704C22—121no—
705C22—121no—
706C22—121no—
707C22—121no—
708C22—121no—
709C22C3×#88212yes—
710C22C22×C3×D1211yescharacteristic
711C4—22no—
712C4—64no—
713C4—62no—
714C4—121no—
715C4—122no—
716C4C3×#88212yes—
717C4C2×C3×D3×D411yescharacteristic
718C4C2×C3×D3×D411yescharacteristic
719C3—21no—
720C3#7868011yescharacteristic, direct product factor
721C3C3×#301311yescharacteristic, complemented
722C2—22no—
723C2—42no—
724C2—122no—
725C2—241no—
726C2C2×C3×#88211yescharacteristic
727C2C3×#575111yescharacteristic
728C2C3×#575311yescharacteristic
subgroupG/H
centerC22×C3C22×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#408C2
socleC22×C32C22×D4
hypercenterC3×#408D3
hypocenterC3C3×#3013
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×#41 ◁ C3×#408

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1010C2semidirect
2. C3×#5833C2semidirect
3. C2×C3×#909C2semidirect
4. C2×C3×#904C2semidirect
5. C32×#408C2semidirect
6. C3×#5133C2semidirect
7. C2×C3×#816C2semidirect
8. C3×#4739C2semidirect
9. C3×#4738C2semidirect
10. C3×#4734C2semidirect
11. C3×#4733C2semidirect
13. #78680C3direct (N × H)
48. C2×#1010C2×C3semidirect
52. #5833C2×C3semidirect
53. C2×#909C2×C3semidirect
54. C2×#904C2×C3semidirect
62. C3×#408D3semidirect
63. C3×#408C2×C3semidirect
64. #5133C2×C3semidirect
65. C2×#816C2×C3semidirect
66. #4739C2×C3semidirect
67. #4738C2×C3semidirect
68. #4734C2×C3semidirect
69. #4733C2×C3semidirect
92. C3×#235D4semidirect
103. C2×C3×Dic6D4semidirect
248. #408C3×D3semidirect
315. #235C3×D4semidirect
326. C2×Dic6C3×D4semidirect
635. C32#3013semidirect
720. C3#78680direct (N × H)
721. C3C3×#3013semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C3×#58332
C2×C3×#9092
C2×C3×#9042
C32×#4082
C3×#51332
C2×C3×#8162
C3×#47392
C3×#47382
C3×#47342
C3×#47332
C3×#30133
#786803