Finite Group Databasebeta

← C3×#10594767 #13174364

Subgroups — C3×#10594767 #13174364

Order 1728.

1232 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64320C211yesmaximal, characteristic, complemented
2C3×#64316C211yesmaximal, characteristic, complemented
3C3×#64128C211yesmaximal, characteristic, complemented
4C32×#918C212yesmaximal, complemented
5C3×#63949C212yesmaximal, complemented
6C3×#63945C211yesmaximal, characteristic, complemented
7C3×#63941C211yesmaximal, characteristic, complemented
8C3×D3×#215C212yesmaximal, complemented
9C3×#63805C211yesmaximal, characteristic, complemented
10C3×#63796C211yesmaximal, characteristic, complemented
11C3×#63794C212yesmaximal, complemented
12C3×#5778—32nomaximal
13#10594767C311yesmaximal, characteristic, direct product factor
14C3×#3832C2211yescharacteristic
15C3×#3832C2211yescharacteristic, complemented
16C32×#239C2212yes—
17C32×D3×Q8C2212yescomplemented
18C3×#3802—21no—
19C3×#3802C2211yescharacteristic
20C3×D3×D12—22no—
21C3×D3×D12C2212yes—
22C3×#3799—22no—
23C3×#3799C2212yescomplemented
24C3×#3798—21no—
25C3×#3798—21no—
26C3×#3798C2211yescharacteristic
27C3×#3797—21no—
28C3×#3797C2211yescharacteristic, complemented
29C33×Q16C2211yescharacteristic, complemented
30C3×#3755C2211yescharacteristic, complemented
31C3×#3755C2211yescharacteristic, complemented
32C3×#3745C2211yescharacteristic, complemented
33C3×C8×C3⋊D3C2211yescharacteristic, complemented
34C32×#216C2212yescomplemented
35C32×#215C2212yescomplemented
36C32×#204C2212yescomplemented
37C32×ΓL(1,𝔽25)C2212yescomplemented
38C3×#3717C2212yescomplemented
39C3×#3715C2212yescomplemented
40C3×#3714C2212yescomplemented
41C3×#3712C2211yescharacteristic, complemented
42C3×D3×C3⋊C8C2212yescomplemented
43C3×#1009—32no—
44C3×#1007—32no—
45#64320C2×C311yescharacteristic, complemented
46#64316C2×C311yescharacteristic, complemented
47C32×#137—32no—
48#64128C2×C311yescharacteristic, complemented
49C3×#950—32no—
50C2×C3×#215—32no—
51C3×#919—32no—
52C3×#919—32no—
53C3×#919—61no—
54C3×#918—22no—
55C3×#918—32no—
56C3×#918D312yescomplemented
57C3×#918C2×C312yescomplemented
58C3×#914—32no—
59C3×#914—32no—
60C3×D3×SD16—32no—
61C3×D3×SD16—32no—
62C3×#908—32no—
63C3×#907—32no—
64#63949C2×C312yescomplemented
65#63945C2×C311yescharacteristic, complemented
66#63941C2×C311yescharacteristic, complemented
67D3×#215C2×C312yescomplemented
68#63805C2×C311yescharacteristic, complemented
69#63796C2×C311yescharacteristic, complemented
70#63794C2×C312yescomplemented
71C2×C3×D32—21no—
72C2×C3×D32—22no—
73C33×Q8C2311yescharacteristic
74C33×Q8C2311yescharacteristic
75C3×C4⋊(C3⋊D3)—21no—
76C3×C4⋊(C3⋊D3)—21no—
77C3×C4⋊(C3⋊D3)C2311yescharacteristic
78C3×C4⋊(C3⋊D3)C2311yescharacteristic
79C3×C4×C3⋊D3—21no—
80C3×C4×C3⋊D3—21no—
81C3×C4×C3⋊D3C2311yescharacteristic
82C32×D12—22no—
83C32×D12C2312yes—
84C32×C4×D3—22no—
85C32×C4×D3—22no—
86C32×C4×D3C2312yes—
87C32×Dic6—22no—
88C32×Dic6C2312yes—
89C3×#627—21no—
90C3×#627D411yescharacteristic
91C3×#626—22no—
92C3×#626—22no—
93C3×#626D412yes—
94C3×#625—21no—
95C3×#625D411yescharacteristic
96C3×#624—21no—
97C3×#624—22no—
98C33×C8C2311yescharacteristic
99C3×C3⋊(C3⋊C8)C2311yescharacteristic
100C32×C3⋊C8C2312yes—
101C3×#577—91no—
102#5778—32no—
103C32×#41—32no—
104C2×C32×Q8—32no—
105#3832C22×C311yescharacteristic
106#3832C22×C311yescharacteristic, complemented
107C3×#239—22no—
108C3×#239—32no—
109C3×#239—32no—
110C3×#239—32no—
111C3×#239—62no—
112C3×#239—61no—
113C3×#239—61no—
114C3×#239C2×D312yes—
115C3×#239C22×C312yes—
116C3×D3×Q8—22no—
117C3×D3×Q8—32no—
118C3×D3×Q8—62no—
119C3×D3×Q8C2×D312yescomplemented
120C3×D3×Q8C22×C312yescomplemented
121C3×D3×D4—32no—
122C3×D3×D4—32no—
123C3×D3×D4—62no—
124C3×D3×D4—62no—
125C3×#235—32no—
126C3×#235—32no—
127C3×#235—62no—
128C3×#235—62no—
129C3×#235—62no—
130C2×C3×D12—32no—
131C2×C3×D12—62no—
132#3802—21no—
133#3802C22×C311yescharacteristic
134D3×D12—22no—
135D3×D12C22×C312yes—
136#3799—22no—
137#3799C22×C312yescomplemented
138#3798—21no—
139#3798—21no—
140#3798C22×C311yescharacteristic
141#3797—21no—
142#3797C22×C311yescharacteristic, complemented
143C32×Q16—21no—
144C32×Q16—22no—
145C32×Q16—32no—
146C32×Q16—41no—
147C32×Q16C2×D312yescomplemented
148C32×Q16C22×C311yescharacteristic, complemented
149C32×SD16—32no—
150C32×SD16—32no—
151C32×M16—32no—
152#3755C22×C311yescharacteristic, complemented
153#3755C22×C311yescharacteristic, complemented
154#3745C22×C311yescharacteristic, complemented
155C8×C3⋊D3C22×C311yescharacteristic, complemented
156C3×#216—22no—
157C3×#216C2×D312yescomplemented
158C3×#216C22×C312yescomplemented
159C3×#215—22no—
160C3×#215—32no—
161C3×#215—32no—
162C3×#215—32no—
163C3×#215—32no—
164C3×#215—61no—
165C3×#215—61no—
166C3×#215C2×D312yescomplemented
167C3×#215C22×C312yescomplemented
168C3×#214—32no—
169C3×#213—32no—
170C2×C3×C3⋊C8—32no—
171C3×D24—32no—
172C3×D24—32no—
173C3×D24—61no—
174C3×#204—22no—
175C3×#204—32no—
176C3×#204C2×D312yescomplemented
177C3×#204C22×C312yescomplemented
178C3×ΓL(1,𝔽25)—22no—
179C3×ΓL(1,𝔽25)—32no—
180C3×ΓL(1,𝔽25)C2×D312yescomplemented
181C3×ΓL(1,𝔽25)C22×C312yescomplemented
182C3×D3×C8—32no—
183C3×D3×C8—32no—
184C3×D3×C8—61no—
185#3717C22×C312yescomplemented
186#3715C22×C312yescomplemented
187#3714C22×C312yescomplemented
188#3712C22×C311yescharacteristic, complemented
189D3×C3⋊C8C22×C312yescomplemented
190C2×C3×C3⋊D3—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×C4—21no—
199C33×C4C2411yescharacteristic
200C3×C3⋊Dic3C2×D411yescharacteristic
201C32×Dic3—22no—
202C32×Dic3C2×D412yes—
203C3×2−1+4—91no—
204C3×H(5,𝔽2)—91no—
205#1009—32no—
206#1007—32no—
207C3×#137—32no—
208C3×#137—32no—
209C3×#137—62no—
210C3×#137—91no—
211C3×AGL(1,ℤ/8)—92no—
212C3×AGL(1,ℤ/8)—91no—
213C3×#135—92no—
214C3×#135—91no—
215C2×C3×SD16—91no—
216C2×C3×SD16—92no—
217C3×#131—91no—
218#950—32no—
219C2×#215—32no—
220#919—32no—
221#919—32no—
222#919—61no—
223#918—32no—
224#918C3×D312yescomplemented
225#914—32no—
226#914—32no—
227D3×SD16—32no—
228D3×SD16—32no—
229#908—32no—
230#907—32no—
231C22×C3×D3—62no—
232C22×C3×D3—62no—
233C22×C3×D3—62no—
234C2×D32—21no—
235C2×D32—22no—
236C32×Q8—21no—
237C32×Q8—21no—
238C32×Q8—22no—
239C32×Q8—22no—
240C32×Q8—32no—
241C32×Q8—41no—
242C32×Q8—41no—
243C32×Q8—62no—
244C32×Q8C22×D312yes—
245C32×Q8C22×D312yes—
246C32×Q8C23×C311yescharacteristic
247C32×Q8C23×C311yescharacteristic
248C32×D4—32no—
249C32×D4—62no—
250C2×C32×C4—32no—
251C2×C32×C4—62no—
252C2×C32×C4—62no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)C23×C311yescharacteristic
256C4⋊(C3⋊D3)C23×C311yescharacteristic
257C4×C3⋊D3—21no—
258C4×C3⋊D3—21no—
259C4×C3⋊D3C23×C311yescharacteristic
260C3×#67—32no—
261C3×#67—32no—
262C3×#67—62no—
263C3×#67—62no—
264C3×#67—62no—
265C3×D12—22no—
266C3×D12—22no—
267C3×D12—22no—
268C3×D12—32no—
269C3×D12—32no—
270C3×D12—32no—
271C3×D12—42no—
272C3×D12—61no—
273C3×D12—61no—
274C3×D12—62no—
275C3×D12—62no—
276C3×D12—62no—
277C3×D12—62no—
278C3×D12—121no—
279C3×D12—121no—
280C3×D12C22×D312yes—
281C3×D12C23×C312yes—
282C3×C4×D3—22no—
283C3×C4×D3—22no—
284C3×C4×D3—22no—
285C3×C4×D3—22no—
286C3×C4×D3—22no—
287C3×C4×D3—32no—
288C3×C4×D3—42no—
289C3×C4×D3—42no—
290C3×C4×D3—61no—
291C3×C4×D3—62no—
292C3×C4×D3—62no—
293C3×C4×D3—62no—
294C3×C4×D3—62no—
295C3×C4×D3—62no—
296C3×C4×D3—121no—
297C3×C4×D3—121no—
298C3×C4×D3C22×D312yes—
299C3×C4×D3C23×C312yes—
300C3×Dic6—22no—
301C3×Dic6—22no—
302C3×Dic6—22no—
303C3×Dic6—32no—
304C3×Dic6—42no—
305C3×Dic6—62no—
306C3×Dic6C22×D312yes—
307C3×Dic6C23×C312yes—
308#627—21no—
309#627C3×D411yescharacteristic
310#626—22no—
311#626—22no—
312#626C3×D412yes—
313#625—21no—
314#625C3×D411yescharacteristic
315#624—21no—
316#624—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×C33C22×D411yescharacteristic
331C3×C3⋊D3—21no—
332C3×C3⋊D3—41no—
333C3×C3⋊D3—41no—
334C32×D3—22no—
335C32×D3—42no—
336C3×#41—32no—
337C3×#41—32no—
338C3×#41—62no—
339C3×#41—91no—
340C3×#41—92no—
341C3×#41—91no—
342C3×#41—91no—
343C3×#41—181no—
344C3×#41—181no—
345C3×#41—182no—
346C2×C3×Q8—32no—
347C2×C3×Q8—32no—
348C2×C3×Q8—62no—
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—32no—
357#239—32no—
358#239—61no—
359#239—61no—
360#239—62no—
361#239C2×C3×D312yes—
362D3×Q8—32no—
363D3×Q8—62no—
364D3×Q8C2×C3×D312yescomplemented
365D3×D4—32no—
366D3×D4—32no—
367D3×D4—62no—
368D3×D4—62no—
369#235—32no—
370#235—32no—
371#235—62no—
372#235—62no—
373#235—62no—
374C2×D12—32no—
375C2×D12—62no—
376C3×Q16—21no—
377C3×Q16—22no—
378C3×Q16—32no—
379C3×Q16—32no—
380C3×Q16—41no—
381C3×Q16—62no—
382C3×Q16D3211yescharacteristic, complemented
383C3×Q16C2×C3×D312yescomplemented
384C3×SD16—32no—
385C3×SD16—32no—
386C3×SD16—32no—
387C3×SD16—32no—
388C3×SD16—62no—
389C3×SD16—62no—
390C3×SD16—92no—
391C3×SD16—92no—
392C3×SD16—91no—
393C3×SD16—91no—
394C3×D8—92no—
395C3×D8—91no—
396C3×M16—32no—
397C3×M16—32no—
398C3×M16—62no—
399C3×M16—91no—
400C2×C3×C8—92no—
401C2×C3×C8—91no—
402#216C2×C3×D312yescomplemented
403#215—32no—
404#215—32no—
405#215—32no—
406#215—32no—
407#215—61no—
408#215—61no—
409#215C2×C3×D312yescomplemented
410#214—32no—
411#213—32no—
412C2×C3⋊C8—32no—
413D24—32no—
414D24—32no—
415D24—61no—
416#204—32no—
417#204C2×C3×D312yescomplemented
418ΓL(1,𝔽25)—32no—
419ΓL(1,𝔽25)C2×C3×D312yescomplemented
420D3×C8—32no—
421D3×C8—32no—
422D3×C8—61no—
423C22×C32—32no—
424C22×C32—62no—
425C2×C3⋊D3—21no—
426C2×C3⋊D3—21no—
427C2×C3⋊D3C2×C3×D411yescharacteristic
428C2×C3×D3—22no—
429C2×C3×D3—22no—
430C2×C3×D3—22no—
431C2×C3×D3—32no—
432C2×C3×D3—42no—
433C2×C3×D3—61no—
434C2×C3×D3—62no—
435C2×C3×D3—62no—
436C2×C3×D3—121no—
437C2×C3×D3—121no—
438C2×C3×D3—242no—
439C2×C3×D3—242no—
440C2×C3×D3—242no—
441C2×C3×D3D3×D412yes—
442C2×C3×D3C2×C3×D412yes—
443D32—82no—
444D32—81no—
445C32×C4—22no—
446C32×C4—22no—
447C32×C4—21no—
448C32×C4—21no—
449C32×C4—21no—
450C32×C4—22no—
451C32×C4—32no—
452C32×C4—41no—
453C32×C4—42no—
454C32×C4—42no—
455C32×C4—41no—
456C32×C4—41no—
457C32×C4—62no—
458C32×C4—81no—
459C32×C4—81no—
460C32×C4C23×D312yes—
461C32×C4C24×C311yescharacteristic
462C3⋊Dic3C2×C3×D411yescharacteristic
463C3×Dic3—22no—
464C3×Dic3—22no—
465C3×Dic3—22no—
466C3×Dic3—32no—
467C3×Dic3—42no—
468C3×Dic3—61no—
469C3×Dic3D3×D412yes—
470C3×Dic3C2×C3×D412yes—
4712−1+4—91no—
472H(5,𝔽2)—91no—
473#137—32no—
474#137—91no—
475AGL(1,ℤ/8)—92no—
476AGL(1,ℤ/8)—91no—
477#135—92no—
478#135—91no—
479C2×SD16—91no—
480C2×SD16—92no—
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—22no—
490C3×Q8—21no—
491C3×Q8—21no—
492C3×Q8—32no—
493C3×Q8—32no—
494C3×Q8—41no—
495C3×Q8—41no—
496C3×Q8—62no—
497C3×Q8—62no—
498C3×Q8—62no—
499C3×Q8—91no—
500C3×Q8—122no—
501C3×Q8—181no—
502C3×Q8C2×D3211yescharacteristic
503C3×Q8C2×D3211yescharacteristic
504C3×Q8C22×C3×D312yes—
505C3×Q8C22×C3×D312yes—
506C3×D4—32no—
507C3×D4—32no—
508C3×D4—62no—
509C3×D4—62no—
510C3×D4—62no—
511C3×D4—92no—
512C3×D4—91no—
513C3×D4—91no—
514C3×D4—91no—
515C3×D4—122no—
516C3×D4—181no—
517C3×D4—181no—
518C3×D4—182no—
519C3×D4—182no—
520C3×D4—181no—
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—32no—
536#67—32no—
537#67—62no—
538#67—62no—
539#67—62no—
540D12—22no—
541D12—32no—
542D12—32no—
543D12—32no—
544D12—61no—
545D12—61no—
546D12—62no—
547D12—62no—
548D12—62no—
549D12—62no—
550D12—121no—
551D12—121no—
552D12C22×C3×D312yes—
553C4×D3—22no—
554C4×D3—22no—
555C4×D3—32no—
556C4×D3—61no—
557C4×D3—62no—
558C4×D3—62no—
559C4×D3—62no—
560C4×D3—62no—
561C4×D3—62no—
562C4×D3—121no—
563C4×D3—121no—
564C4×D3C22×C3×D312yes—
565Dic6—22no—
566Dic6—32no—
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—62no—
585C2×C32—122no—
586C2×C32C2×D3×D412yes—
587C2×C32C22×C3×D411yescharacteristic
588C3⋊D3—21no—
589C3⋊D3—41no—
590C3⋊D3—41no—
591C3×D3—22no—
592C3×D3—22no—
593C3×D3—42no—
594C3×D3—42no—
595C3×D3—42no—
596C3×D3—62no—
597C3×D3—82no—
598C3×D3—121no—
599C3×D3—122no—
600C3×D3—122no—
601C3×D3—241no—
602C3×D3—241no—
603#41—32no—
604#41—91no—
605#41—92no—
606#41—91no—
607#41—91no—
608#41—181no—
609#41—181no—
610#41—182no—
611C2×Q8—32no—
612C2×Q8—91no—
613C2×Q8—181no—
614C2×D4—92no—
615C2×D4—91no—
616C2×D4—182no—
617C2×D4—181no—
618Q16—32no—
619Q16C3×D3211yescharacteristic, complemented
620SD16—32no—
621SD16—32no—
622SD16—92no—
623SD16—92no—
624SD16—91no—
625SD16—91no—
626D8—92no—
627D8—91no—
628M16—32no—
629M16—91no—
630C2×C8—92no—
631C2×C8—91no—
632C22×C3—32no—
633C22×C3—32no—
634C22×C3—62no—
635C22×C3—62no—
636C22×C3—62no—
637C22×C3—91no—
638C22×C3—122no—
639C22×C3—181no—
640C22×C3—181no—
641C22×C3—722no—
642C22×C3—721no—
643C2×D3—22no—
644C2×D3—32no—
645C2×D3—61no—
646C2×D3—62no—
647C2×D3—62no—
648C2×D3—121no—
649C2×D3—121no—
650C2×D3—242no—
651C2×D3—242no—
652C2×D3—242no—
653C2×D3C3×D3×D412yes—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—22no—
657C3×C4—22no—
658C3×C4—21no—
659C3×C4—22no—
660C3×C4—32no—
661C3×C4—32no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—42no—
665C3×C4—42no—
666C3×C4—41no—
667C3×C4—62no—
668C3×C4—62no—
669C3×C4—62no—
670C3×C4—81no—
671C3×C4—81no—
672C3×C4—91no—
673C3×C4—122no—
674C3×C4C22×D3211yescharacteristic
675C3×C4C23×C3×D312yes—
676Dic3—22no—
677Dic3—32no—
678Dic3—61no—
679Dic3C3×D3×D412yes—
680C32—22no—
681C32—21no—
682C32—41no—
683C32#577812yescomplemented
684C32C3×#57711yescharacteristic, complemented
685C23—182no—
686C23—181no—
687Q8—32no—
688Q8—62no—
689Q8—91no—
690Q8—181no—
691Q8C2×C3×D3211yescharacteristic
692Q8C2×C3×D3211yescharacteristic
693D4—32no—
694D4—62no—
695D4—92no—
696D4—91no—
697D4—91no—
698D4—91no—
699D4—181no—
700D4—181no—
701D4—182no—
702D4—182no—
703D4—181no—
704C2×C4—32no—
705C2×C4—62no—
706C2×C4—62no—
707C2×C4—91no—
708C2×C4—181no—
709C2×C4—181no—
710C2×C4—182no—
711C2×C4—181no—
712C8—32no—
713C8—91no—
714C8C2×C3×D3211yescharacteristic
715C2×C3—21no—
716C2×C3—22no—
717C2×C3—41no—
718C2×C3—62no—
719C2×C3—62no—
720C2×C3—122no—
721C2×C3—122no—
722C2×C3—122no—
723C2×C3—181no—
724C2×C3—242no—
725C2×C3—361no—
726C2×C3—361no—
727C2×C3D32×D411yescharacteristic
728C2×C3C2×C3×D3×D412yes—
729D3—22no—
730D3—42no—
731D3—62no—
732D3—121no—
733D3—122no—
734D3—122no—
735D3—241no—
736D3—241no—
737C22—32no—
738C22—62no—
739C22—91no—
740C22—181no—
741C22—181no—
742C22—722no—
743C22—721no—
744C4—21no—
745C4—21no—
746C4—32no—
747C4—62no—
748C4—91no—
749C4C22×C3×D3211yescharacteristic
750C3—21no—
751C3—22no—
752C3—41no—
753C3#1059476711yescharacteristic, direct product factor
754C3C3×#577812yescomplemented
755C2—62no—
756C2—122no—
757C2—181no—
758C2—361no—
759C2—361no—
760C2C3×D32×D411yescharacteristic
subgroupG/H
centerC2×C3D32×D4
commutator, cosocleC32×C4C24×C3
FrattiniC4C22×C3×D32
FittingC33×Q16C22
socleC2×C33C22×D4
hypercenterC3×Q16D32
hypocenterC32C3×#577
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×Q16

Complements

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

NH ≅ G/Ntype
1. C3×#64320C2semidirect
2. C3×#64316C2semidirect
3. C3×#64128C2semidirect
4. C32×#918C2semidirect
5. C3×#63949C2semidirect
6. C3×#63945C2semidirect
7. C3×#63941C2semidirect
8. C3×D3×#215C2semidirect
9. C3×#63805C2semidirect
10. C3×#63796C2semidirect
11. C3×#63794C2semidirect
13. #10594767C3direct (N × H)
15. C3×#3832C22semidirect
17. C32×D3×Q8C22semidirect
23. C3×#3799C22semidirect
28. C3×#3797C22semidirect
29. C33×Q16C22semidirect
30. C3×#3755C22semidirect
31. C3×#3755C22semidirect
32. C3×#3745C22semidirect
33. C3×C8×C3⋊D3C22semidirect
34. C32×#216C22semidirect
35. C32×#215C22semidirect
36. C32×#204C22semidirect
37. C32×ΓL(1,𝔽25)C22semidirect
38. C3×#3717C22semidirect
39. C3×#3715C22semidirect
40. C3×#3714C22semidirect
41. C3×#3712C22semidirect
42. C3×D3×C3⋊C8C22semidirect
45. #64320C2×C3semidirect
46. #64316C2×C3semidirect
48. #64128C2×C3semidirect
56. C3×#918D3semidirect
57. C3×#918C2×C3semidirect
64. #63949C2×C3semidirect
65. #63945C2×C3semidirect
66. #63941C2×C3semidirect
67. D3×#215C2×C3semidirect
68. #63805C2×C3semidirect
69. #63796C2×C3semidirect
70. #63794C2×C3semidirect
106. #3832C22×C3semidirect
119. C3×D3×Q8C2×D3semidirect
120. C3×D3×Q8C22×C3semidirect
137. #3799C22×C3semidirect
142. #3797C22×C3semidirect
147. C32×Q16C2×D3semidirect
148. C32×Q16C22×C3semidirect
152. #3755C22×C3semidirect
153. #3755C22×C3semidirect
154. #3745C22×C3semidirect
155. C8×C3⋊D3C22×C3semidirect
157. C3×#216C2×D3semidirect
158. C3×#216C22×C3semidirect
166. C3×#215C2×D3semidirect
167. C3×#215C22×C3semidirect
176. C3×#204C2×D3semidirect
177. C3×#204C22×C3semidirect
180. C3×ΓL(1,𝔽25)C2×D3semidirect
181. C3×ΓL(1,𝔽25)C22×C3semidirect
185. #3717C22×C3semidirect
186. #3715C22×C3semidirect
187. #3714C22×C3semidirect
188. #3712C22×C3semidirect
189. D3×C3⋊C8C22×C3semidirect
224. #918C3×D3semidirect
364. D3×Q8C2×C3×D3semidirect
382. C3×Q16D32semidirect
383. C3×Q16C2×C3×D3semidirect
402. #216C2×C3×D3semidirect
409. #215C2×C3×D3semidirect
417. #204C2×C3×D3semidirect
419. ΓL(1,𝔽25)C2×C3×D3semidirect
482. C33#577semidirect
619. Q16C3×D32semidirect
683. C32#5778semidirect
684. C32C3×#577semidirect
753. C3#10594767direct (N × H)
754. C3C3×#5778semidirect

Maximal subgroups

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

subgroupindex
C3×#643202
C3×#643162
C3×#641282
C32×#9182
C3×#639492
C3×#639452
C3×#639412
C3×D3×#2152
C3×#638052
C3×#637962
C3×#637942
C3×#57783
#105947673