Finite Group Databasebeta

← C3×#10594757 #13174354

Subgroups — C3×#10594757 #13174354

Order 1728.

1238 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64320C211yesmaximal, characteristic, complemented
2C3×#64309C211yesmaximal, characteristic, complemented
3C3×#64125C211yesmaximal, characteristic, complemented
4C32×#916C212yesmaximal, complemented
5C3×#63945C211yesmaximal, characteristic, complemented
6C3×#63943C212yesmaximal, complemented
7C3×#63927C211yesmaximal, characteristic, complemented
8C3×#63925C212yesmaximal, complemented
9C3×#63803C211yesmaximal, characteristic, complemented
10C3×#63796C211yesmaximal, characteristic, complemented
11C3×D3×#204C212yesmaximal, complemented
12C3×#5770—32nomaximal
13#10594757C311yesmaximal, characteristic, direct product factor
14C3×#3832C2211yescharacteristic
15C3×#3830C2211yescharacteristic, complemented
16C32×#239C2212yes—
17C32×#237C2212yescomplemented
18C2×C3×#627—21no—
19C3×#3805—21no—
20C3×#3804—22no—
21C3×#3802—21no—
22C3×#3802C2211yescharacteristic
23C3×D3×D12—22no—
24C3×D3×D12C2212yes—
25C3×#3798—21no—
26C3×#3798C2211yescharacteristic
27C3×#3797C2211yescharacteristic, complemented
28C3×D3×Dic6C2212yescomplemented
29C33×SD16C2211yescharacteristic, complemented
30C3×#3756C2211yescharacteristic, complemented
31C3×#3753C2211yescharacteristic, complemented
32C3×#3744C2211yescharacteristic, complemented
33C3×C8×C3⋊D3C2211yescharacteristic, complemented
34C32×#216C2212yescomplemented
35C32×#213C2212yescomplemented
36C32×#204C2212yescomplemented
37C32×D3×C8C2212yescomplemented
38C3×#3717C2212yescomplemented
39C3×#3716C2212yescomplemented
40C3×#3715C2212yescomplemented
41C3×#3712C2211yescharacteristic, complemented
42C3×#3711C2212yescomplemented
43C3×#1010—32no—
44C3×#1009—32no—
45#64320C2×C311yescharacteristic, complemented
46#64309C2×C311yescharacteristic, complemented
47C32×#135—32no—
48#64125C2×C311yescharacteristic, complemented
49C3×#951—32no—
50C3×#949—32no—
51C3×#918—32no—
52C3×#918—32no—
53C3×#916—22no—
54C3×#916—32no—
55C3×#916—61no—
56C3×#916D312yescomplemented
57C3×#916C2×C312yescomplemented
58C3×D3×SD16—32no—
59C3×D3×SD16—32no—
60C3×#911—32no—
61C3×#911—32no—
62C2×C3×#204—32no—
63C3×#901—32no—
64#63945C2×C311yescharacteristic, complemented
65#63943C2×C312yescomplemented
66#63927C2×C311yescharacteristic, complemented
67#63925C2×C312yescomplemented
68#63803C2×C311yescharacteristic, complemented
69#63796C2×C311yescharacteristic, complemented
70D3×#204C2×C312yescomplemented
71C2×C3×D32—21no—
72C2×C3×D32—22no—
73C33×Q8C2311yescharacteristic
74C33×D4C2311yescharacteristic
75C3×#638—21no—
76C2×C3×C3⋊Dic3—21no—
77C3×C4⋊(C3⋊D3)—21no—
78C3×C4⋊(C3⋊D3)C2311yescharacteristic
79C3×C4×C3⋊D3—21no—
80C3×C4×C3⋊D3C2311yescharacteristic
81C3×#634C2311yescharacteristic
82C32×#67—22no—
83C2×C32×Dic3—22no—
84C32×D12—22no—
85C32×D12C2312yes—
86C32×C4×D3—22no—
87C32×C4×D3C2312yes—
88C32×Dic6C2312yes—
89C3×#627—21no—
90C3×#627—22no—
91C3×#627D411yescharacteristic
92C3×#626—22no—
93C3×#626D412yes—
94C3×#625—21no—
95C3×#625D411yescharacteristic
96C3×#624—21no—
97C3×D3×Dic3—22no—
98C33×C8C2311yescharacteristic
99C3×C3⋊(C3⋊C8)C2311yescharacteristic
100C32×C3⋊C8C2312yes—
101C3×#577—91no—
102#5770—32no—
103C32×#41—32no—
104C32×#41—32no—
105#3832C22×C311yescharacteristic
106#3830C22×C311yescharacteristic, complemented
107C3×#239—22no—
108C3×#239—32no—
109C3×#239—61no—
110C3×#239C2×D312yes—
111C3×#239C22×C312yes—
112C3×D3×Q8—32no—
113C3×D3×Q8—32no—
114C3×#237—22no—
115C3×#237—32no—
116C3×#237—62no—
117C3×#237—62no—
118C3×#237—61no—
119C3×#237C2×D312yescomplemented
120C3×#237C22×C312yescomplemented
121C3×D3×D4—32no—
122C3×D3×D4—32no—
123C3×D3×D4—62no—
124C3×D3×D4—62no—
125C3×#235—32no—
126C3×#235—62no—
127C3×#235—62no—
128C2×C3×D12—32no—
129C2×C3×D12—62no—
130C2×C3×Dic6—32no—
131C2×C3×Dic6—62no—
132C2×#627—21no—
133#3805—21no—
134#3804—22no—
135#3802—21no—
136#3802C22×C311yescharacteristic
137D3×D12—22no—
138D3×D12C22×C312yes—
139#3798—21no—
140#3798C22×C311yescharacteristic
141#3797C22×C311yescharacteristic, complemented
142D3×Dic6C22×C312yescomplemented
143C32×Q16—32no—
144C32×SD16—21no—
145C32×SD16—22no—
146C32×SD16—32no—
147C32×SD16—41no—
148C32×SD16C2×D312yescomplemented
149C32×SD16C22×C311yescharacteristic, complemented
150C32×D8—32no—
151C2×C32×C8—32no—
152#3756C22×C311yescharacteristic, complemented
153#3753C22×C311yescharacteristic, complemented
154#3744C22×C311yescharacteristic, complemented
155C8×C3⋊D3C22×C311yescharacteristic, complemented
156C3×#216—22no—
157C3×#216—32no—
158C3×#216—61no—
159C3×#216C2×D312yescomplemented
160C3×#216C22×C312yescomplemented
161C3×#215—32no—
162C3×#215—32no—
163C3×#214—32no—
164C3×#214—32no—
165C3×#213—22no—
166C3×#213—32no—
167C3×#213—61no—
168C3×#213C2×D312yescomplemented
169C3×#213C22×C312yescomplemented
170C3×#208—32no—
171C3×#204—22no—
172C3×#204—32no—
173C3×#204—32no—
174C3×#204—32no—
175C3×#204—61no—
176C3×#204C2×D312yescomplemented
177C3×#204C22×C312yescomplemented
178C3×ΓL(1,𝔽25)—32no—
179C3×ΓL(1,𝔽25)—32no—
180C3×D3×C8—22no—
181C3×D3×C8—32no—
182C3×D3×C8—61no—
183C3×D3×C8C2×D312yescomplemented
184C3×D3×C8C22×C312yescomplemented
185#3717C22×C312yescomplemented
186#3716C22×C312yescomplemented
187#3715C22×C312yescomplemented
188#3712C22×C311yescharacteristic, complemented
189#3711C22×C312yescomplemented
190C22×C33—21no—
191C2×C3×C3⋊D3—21no—
192C2×C3×C3⋊D3C2×D411yescharacteristic
193C2×C32×D3—22no—
194C2×C32×D3C2×D412yes—
195C3×D32—82no—
196C3×D32—81no—
197C33×C4—21no—
198C33×C4C2411yescharacteristic
199C3×C3⋊Dic3—21no—
200C3×C3⋊Dic3C2×D411yescharacteristic
201C32×Dic3—22no—
202C32×Dic3C2×D412yes—
203C3×2−1+4—91no—
204C3×H(5,𝔽2)—91no—
205#1010—32no—
206#1009—32no—
207C3×#137—91no—
208C3×#137—92no—
209C3×AGL(1,ℤ/8)—91no—
210C3×AGL(1,ℤ/8)—92no—
211C3×#135—32no—
212C3×#135—32no—
213C3×#135—62no—
214C3×#135—91no—
215C2×C3×SD16—92no—
216C2×C3×SD16—91no—
217C3×#131—91no—
218#951—32no—
219#949—32no—
220#918—32no—
221#918—32no—
222#916—32no—
223#916—61no—
224#916C3×D312yescomplemented
225D3×SD16—32no—
226D3×SD16—32no—
227#911—32no—
228#911—32no—
229C2×#204—32no—
230#901—32no—
231C22×C3×D3—62no—
232C22×C3×D3—62no—
233C22×C3×D3—62no—
234C2×D32—21no—
235C2×D32—22no—
236C32×Q8—21no—
237C32×Q8—22no—
238C32×Q8—32no—
239C32×Q8—41no—
240C32×Q8C22×D312yes—
241C32×Q8C23×C311yescharacteristic
242C32×D4—21no—
243C32×D4—22no—
244C32×D4—32no—
245C32×D4—41no—
246C32×D4—62no—
247C32×D4—62no—
248C32×D4C22×D312yes—
249C32×D4C23×C311yescharacteristic
250C2×C32×C4—32no—
251C2×C32×C4—62no—
252C2×C32×C4—62no—
253#638—21no—
254C2×C3⋊Dic3—21no—
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)C23×C311yescharacteristic
257C4×C3⋊D3—21no—
258C4×C3⋊D3C23×C311yescharacteristic
259#634C23×C311yescharacteristic
260C3×#67—22no—
261C3×#67—22no—
262C3×#67—32no—
263C3×#67—32no—
264C3×#67—42no—
265C3×#67—62no—
266C3×#67—62no—
267C3×#67—62no—
268C3×#67—121no—
269C2×C3×Dic3—22no—
270C2×C3×Dic3—22no—
271C2×C3×Dic3—42no—
272C2×C3×Dic3—62no—
273C2×C3×Dic3—62no—
274C2×C3×Dic3—121no—
275C3×D12—22no—
276C3×D12—22no—
277C3×D12—22no—
278C3×D12—32no—
279C3×D12—32no—
280C3×D12—42no—
281C3×D12—61no—
282C3×D12—62no—
283C3×D12—62no—
284C3×D12—121no—
285C3×D12C22×D312yes—
286C3×D12C23×C312yes—
287C3×C4×D3—22no—
288C3×C4×D3—22no—
289C3×C4×D3—22no—
290C3×C4×D3—32no—
291C3×C4×D3—42no—
292C3×C4×D3—61no—
293C3×C4×D3—62no—
294C3×C4×D3—62no—
295C3×C4×D3—62no—
296C3×C4×D3—121no—
297C3×C4×D3C22×D312yes—
298C3×C4×D3C23×C312yes—
299C3×Dic6—22no—
300C3×Dic6—32no—
301C3×Dic6—32no—
302C3×Dic6—61no—
303C3×Dic6—62no—
304C3×Dic6—62no—
305C3×Dic6—62no—
306C3×Dic6C22×D312yes—
307C3×Dic6C23×C312yes—
308#627—21no—
309#627—22no—
310#627C3×D411yescharacteristic
311#626—22no—
312#626C3×D412yes—
313#625—21no—
314#625C3×D411yescharacteristic
315#624—21no—
316D3×Dic3—22no—
317C32×C8—21no—
318C32×C8—22no—
319C32×C8—32no—
320C32×C8—41no—
321C32×C8C22×D312yes—
322C32×C8C23×C311yescharacteristic
323C3⋊(C3⋊C8)C23×C311yescharacteristic
324C3×C3⋊C8—22no—
325C3×C3⋊C8—32no—
326C3×C3⋊C8—61no—
327C3×C3⋊C8C22×D312yes—
328C3×C3⋊C8C23×C312yes—
329#577—91noSylow
330C2×C33—41no—
331C2×C33C22×D411yescharacteristic
332C3×C3⋊D3—21no—
333C3×C3⋊D3—41no—
334C32×D3—22no—
335C32×D3—42no—
336C3×#41—32no—
337C3×#41—32no—
338C3×#41—32no—
339C3×#41—32no—
340C3×#41—62no—
341C3×#41—62no—
342C3×#41—91no—
343C3×#41—91no—
344C3×#41—91no—
345C3×#41—181no—
346C3×#41—182no—
347C3×#41—181no—
348C2×C3×Q8—92no—
349C2×C3×Q8—91no—
350C2×C3×Q8—181no—
351C2×C3×D4—92no—
352C2×C3×D4—91no—
353C2×C3×D4—182no—
354C2×C3×D4—181no—
355#239—32no—
356#239—61no—
357#239C2×C3×D312yes—
358D3×Q8—32no—
359D3×Q8—32no—
360#237—32no—
361#237—61no—
362#237—62no—
363#237—62no—
364#237C2×C3×D312yescomplemented
365D3×D4—32no—
366D3×D4—32no—
367D3×D4—62no—
368D3×D4—62no—
369#235—32no—
370#235—62no—
371#235—62no—
372C2×D12—32no—
373C2×D12—62no—
374C2×Dic6—32no—
375C2×Dic6—62no—
376C3×Q16—32no—
377C3×Q16—32no—
378C3×Q16—62no—
379C3×Q16—91no—
380C3×SD16—21no—
381C3×SD16—22no—
382C3×SD16—32no—
383C3×SD16—32no—
384C3×SD16—41no—
385C3×SD16—62no—
386C3×SD16—92no—
387C3×SD16—92no—
388C3×SD16—92no—
389C3×SD16—91no—
390C3×SD16D3211yescharacteristic, complemented
391C3×SD16C2×C3×D312yescomplemented
392C3×D8—32no—
393C3×D8—32no—
394C3×D8—62no—
395C3×D8—91no—
396C3×M16—91no—
397C3×M16—92no—
398C2×C3×C8—32no—
399C2×C3×C8—32no—
400C2×C3×C8—62no—
401C2×C3×C8—91no—
402#216—32no—
403#216—61no—
404#216C2×C3×D312yescomplemented
405#215—32no—
406#215—32no—
407#214—32no—
408#214—32no—
409#213—32no—
410#213—61no—
411#213C2×C3×D312yescomplemented
412#208—32no—
413#204—32no—
414#204—32no—
415#204—32no—
416#204—61no—
417#204C2×C3×D312yescomplemented
418ΓL(1,𝔽25)—32no—
419ΓL(1,𝔽25)—32no—
420D3×C8—32no—
421D3×C8—61no—
422D3×C8C2×C3×D312yescomplemented
423C22×C32—22no—
424C22×C32—21no—
425C22×C32—32no—
426C22×C32—42no—
427C22×C32—41no—
428C22×C32—62no—
429C22×C32—81no—
430C2×C3⋊D3—21no—
431C2×C3⋊D3C2×C3×D411yescharacteristic
432C2×C3×D3—22no—
433C2×C3×D3—22no—
434C2×C3×D3—22no—
435C2×C3×D3—32no—
436C2×C3×D3—42no—
437C2×C3×D3—61no—
438C2×C3×D3—62no—
439C2×C3×D3—121no—
440C2×C3×D3—242no—
441C2×C3×D3—242no—
442C2×C3×D3—242no—
443C2×C3×D3D3×D412yes—
444C2×C3×D3C2×C3×D412yes—
445D32—82no—
446D32—81no—
447C32×C4—22no—
448C32×C4—21no—
449C32×C4—21no—
450C32×C4—22no—
451C32×C4—32no—
452C32×C4—41no—
453C32×C4—42no—
454C32×C4—41no—
455C32×C4—62no—
456C32×C4—81no—
457C32×C4C23×D312yes—
458C32×C4C24×C311yescharacteristic
459C3⋊Dic3—21no—
460C3⋊Dic3C2×C3×D411yescharacteristic
461C3×Dic3—22no—
462C3×Dic3—22no—
463C3×Dic3—22no—
464C3×Dic3—32no—
465C3×Dic3—42no—
466C3×Dic3—61no—
467C3×Dic3—62no—
468C3×Dic3—121no—
469C3×Dic3D3×D412yes—
470C3×Dic3C2×C3×D412yes—
4712−1+4—91no—
472H(5,𝔽2)—91no—
473#137—91no—
474#137—92no—
475AGL(1,ℤ/8)—91no—
476AGL(1,ℤ/8)—92no—
477#135—32no—
478#135—91no—
479C2×SD16—92no—
480C2×SD16—91no—
481#131—91no—
482C33#57711yescharacteristic, complemented, Sylow
483C23×C3—182no—
484C23×C3—181no—
485C22×D3—62no—
486C22×D3—62no—
487C22×D3—62no—
488C3×Q8—22no—
489C3×Q8—21no—
490C3×Q8—32no—
491C3×Q8—32no—
492C3×Q8—41no—
493C3×Q8—62no—
494C3×Q8—91no—
495C3×Q8—91no—
496C3×Q8—182no—
497C3×Q8—181no—
498C3×Q8C2×D3211yescharacteristic
499C3×Q8C22×C3×D312yes—
500C3×D4—22no—
501C3×D4—21no—
502C3×D4—32no—
503C3×D4—32no—
504C3×D4—41no—
505C3×D4—62no—
506C3×D4—62no—
507C3×D4—62no—
508C3×D4—62no—
509C3×D4—62no—
510C3×D4—92no—
511C3×D4—91no—
512C3×D4—91no—
513C3×D4—122no—
514C3×D4—122no—
515C3×D4—181no—
516C3×D4—182no—
517C3×D4—181no—
518C3×D4—181no—
519C3×D4C2×D3211yescharacteristic
520C3×D4C22×C3×D312yes—
521C2×C3×C4—32no—
522C2×C3×C4—32no—
523C2×C3×C4—62no—
524C2×C3×C4—62no—
525C2×C3×C4—62no—
526C2×C3×C4—62no—
527C2×C3×C4—62no—
528C2×C3×C4—91no—
529C2×C3×C4—122no—
530C2×C3×C4—122no—
531C2×C3×C4—181no—
532C2×C3×C4—181no—
533C2×C3×C4—182no—
534C2×C3×C4—181no—
535#67—22no—
536#67—32no—
537#67—32no—
538#67—62no—
539#67—62no—
540#67—62no—
541#67—121no—
542C2×Dic3—22no—
543C2×Dic3—62no—
544C2×Dic3—62no—
545C2×Dic3—121no—
546D12—22no—
547D12—32no—
548D12—32no—
549D12—61no—
550D12—62no—
551D12—62no—
552D12—121no—
553D12C22×C3×D312yes—
554C4×D3—22no—
555C4×D3—32no—
556C4×D3—61no—
557C4×D3—62no—
558C4×D3—62no—
559C4×D3—62no—
560C4×D3—121no—
561C4×D3C22×C3×D312yes—
562Dic6—32no—
563Dic6—32no—
564Dic6—61no—
565Dic6—62no—
566Dic6—62no—
567Dic6—62no—
568Dic6C22×C3×D312yes—
569C3×C8—22no—
570C3×C8—21no—
571C3×C8—32no—
572C3×C8—32no—
573C3×C8—41no—
574C3×C8—62no—
575C3×C8—91no—
576C3×C8C2×D3211yescharacteristic
577C3×C8C22×C3×D312yes—
578C3⋊C8—32no—
579C3⋊C8—61no—
580C3⋊C8C22×C3×D312yes—
581C2×C32—21no—
582C2×C32—22no—
583C2×C32—41no—
584C2×C32—41no—
585C2×C32—42no—
586C2×C32—62no—
587C2×C32—82no—
588C2×C32—81no—
589C2×C32—122no—
590C2×C32—161no—
591C2×C32C2×D3×D412yes—
592C2×C32C22×C3×D411yescharacteristic
593C3⋊D3—21no—
594C3⋊D3—41no—
595C3×D3—22no—
596C3×D3—22no—
597C3×D3—42no—
598C3×D3—42no—
599C3×D3—42no—
600C3×D3—62no—
601C3×D3—82no—
602C3×D3—121no—
603C3×D3—122no—
604C3×D3—241no—
605#41—32no—
606#41—32no—
607#41—91no—
608#41—91no—
609#41—91no—
610#41—181no—
611#41—182no—
612#41—181no—
613C2×Q8—92no—
614C2×Q8—91no—
615C2×Q8—181no—
616C2×D4—92no—
617C2×D4—91no—
618C2×D4—182no—
619C2×D4—181no—
620Q16—32no—
621Q16—91no—
622SD16—32no—
623SD16—92no—
624SD16—92no—
625SD16—92no—
626SD16—91no—
627SD16C3×D3211yescharacteristic, complemented
628D8—32no—
629D8—91no—
630M16—91no—
631M16—92no—
632C2×C8—32no—
633C2×C8—91no—
634C22×C3—21no—
635C22×C3—22no—
636C22×C3—32no—
637C22×C3—32no—
638C22×C3—41no—
639C22×C3—42no—
640C22×C3—62no—
641C22×C3—62no—
642C22×C3—62no—
643C22×C3—81no—
644C22×C3—91no—
645C22×C3—122no—
646C22×C3—181no—
647C22×C3—722no—
648C22×C3—721no—
649C2×D3—22no—
650C2×D3—32no—
651C2×D3—61no—
652C2×D3—62no—
653C2×D3—121no—
654C2×D3—242no—
655C2×D3—242no—
656C2×D3—242no—
657C2×D3C3×D3×D412yes—
658C3×C4—21no—
659C3×C4—22no—
660C3×C4—21no—
661C3×C4—22no—
662C3×C4—32no—
663C3×C4—32no—
664C3×C4—41no—
665C3×C4—42no—
666C3×C4—41no—
667C3×C4—62no—
668C3×C4—62no—
669C3×C4—62no—
670C3×C4—81no—
671C3×C4—91no—
672C3×C4—122no—
673C3×C4—181no—
674C3×C4C22×D3211yescharacteristic
675C3×C4C23×C3×D312yes—
676Dic3—22no—
677Dic3—32no—
678Dic3—61no—
679Dic3—62no—
680Dic3—121no—
681Dic3C3×D3×D412yes—
682C32—22no—
683C32—21no—
684C32—41no—
685C32#577012yescomplemented
686C32C3×#57711yescharacteristic, complemented
687C23—182no—
688C23—181no—
689Q8—32no—
690Q8—91no—
691Q8—91no—
692Q8—182no—
693Q8—181no—
694Q8C2×C3×D3211yescharacteristic
695D4—32no—
696D4—62no—
697D4—62no—
698D4—92no—
699D4—91no—
700D4—91no—
701D4—181no—
702D4—182no—
703D4—181no—
704D4—181no—
705D4C2×C3×D3211yescharacteristic
706C2×C4—32no—
707C2×C4—62no—
708C2×C4—62no—
709C2×C4—91no—
710C2×C4—181no—
711C2×C4—181no—
712C2×C4—182no—
713C2×C4—181no—
714C8—32no—
715C8—91no—
716C8C2×C3×D3211yescharacteristic
717C2×C3—21no—
718C2×C3—22no—
719C2×C3—42no—
720C2×C3—41no—
721C2×C3—41no—
722C2×C3—62no—
723C2×C3—62no—
724C2×C3—81no—
725C2×C3—82no—
726C2×C3—122no—
727C2×C3—122no—
728C2×C3—122no—
729C2×C3—161no—
730C2×C3—181no—
731C2×C3—242no—
732C2×C3—361no—
733C2×C3D32×D411yescharacteristic
734C2×C3C2×C3×D3×D412yes—
735D3—22no—
736D3—42no—
737D3—62no—
738D3—121no—
739D3—122no—
740D3—241no—
741C22—21no—
742C22—32no—
743C22—62no—
744C22—91no—
745C22—181no—
746C22—722no—
747C22—721no—
748C4—21no—
749C4—32no—
750C4—62no—
751C4—91no—
752C4—181no—
753C4C22×C3×D3211yescharacteristic
754C3—21no—
755C3—22no—
756C3—41no—
757C3#1059475711yescharacteristic, direct product factor
758C3C3×#577012yescomplemented
759C2—41no—
760C2—62no—
761C2—122no—
762C2—181no—
763C2—361no—
764C2C3×D32×D411yescharacteristic
subgroupG/H
centerC2×C3D32×D4
commutator, cosocleC32×C4C24×C3
FrattiniC4C22×C3×D32
FittingC33×SD16C22
socleC2×C33C22×D4
hypercenterC3×SD16D32
hypocenterC32C3×#577
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×SD16

Complements

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

NH ≅ G/Ntype
1. C3×#64320C2semidirect
2. C3×#64309C2semidirect
3. C3×#64125C2semidirect
4. C32×#916C2semidirect
5. C3×#63945C2semidirect
6. C3×#63943C2semidirect
7. C3×#63927C2semidirect
8. C3×#63925C2semidirect
9. C3×#63803C2semidirect
10. C3×#63796C2semidirect
11. C3×D3×#204C2semidirect
13. #10594757C3direct (N × H)
15. C3×#3830C22semidirect
17. C32×#237C22semidirect
27. C3×#3797C22semidirect
28. C3×D3×Dic6C22semidirect
29. C33×SD16C22semidirect
30. C3×#3756C22semidirect
31. C3×#3753C22semidirect
32. C3×#3744C22semidirect
33. C3×C8×C3⋊D3C22semidirect
34. C32×#216C22semidirect
35. C32×#213C22semidirect
36. C32×#204C22semidirect
37. C32×D3×C8C22semidirect
38. C3×#3717C22semidirect
39. C3×#3716C22semidirect
40. C3×#3715C22semidirect
41. C3×#3712C22semidirect
42. C3×#3711C22semidirect
45. #64320C2×C3semidirect
46. #64309C2×C3semidirect
48. #64125C2×C3semidirect
56. C3×#916D3semidirect
57. C3×#916C2×C3semidirect
64. #63945C2×C3semidirect
65. #63943C2×C3semidirect
66. #63927C2×C3semidirect
67. #63925C2×C3semidirect
68. #63803C2×C3semidirect
69. #63796C2×C3semidirect
70. D3×#204C2×C3semidirect
106. #3830C22×C3semidirect
119. C3×#237C2×D3semidirect
120. C3×#237C22×C3semidirect
141. #3797C22×C3semidirect
142. D3×Dic6C22×C3semidirect
148. C32×SD16C2×D3semidirect
149. C32×SD16C22×C3semidirect
152. #3756C22×C3semidirect
153. #3753C22×C3semidirect
154. #3744C22×C3semidirect
155. C8×C3⋊D3C22×C3semidirect
159. C3×#216C2×D3semidirect
160. C3×#216C22×C3semidirect
168. C3×#213C2×D3semidirect
169. C3×#213C22×C3semidirect
176. C3×#204C2×D3semidirect
177. C3×#204C22×C3semidirect
183. C3×D3×C8C2×D3semidirect
184. C3×D3×C8C22×C3semidirect
185. #3717C22×C3semidirect
186. #3716C22×C3semidirect
187. #3715C22×C3semidirect
188. #3712C22×C3semidirect
189. #3711C22×C3semidirect
224. #916C3×D3semidirect
364. #237C2×C3×D3semidirect
390. C3×SD16D32semidirect
391. C3×SD16C2×C3×D3semidirect
404. #216C2×C3×D3semidirect
411. #213C2×C3×D3semidirect
417. #204C2×C3×D3semidirect
422. D3×C8C2×C3×D3semidirect
482. C33#577semidirect
627. SD16C3×D32semidirect
685. C32#5770semidirect
686. C32C3×#577semidirect
757. C3#10594757direct (N × H)
758. C3C3×#5770semidirect

Maximal subgroups

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

subgroupindex
C3×#643202
C3×#643092
C3×#641252
C32×#9162
C3×#639452
C3×#639432
C3×#639272
C3×#639252
C3×#638032
C3×#637962
C3×D3×#2042
C3×#57703
#105947573