Finite Group Databasebeta

← #13178772

Subgroups — #13178772

Order 1728.

1532 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#41×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C4⋊#1113C211yesmaximal, characteristic, complemented
3C3×#64158C212yesmaximal, complemented
4#11723709C212yesmaximal, complemented
5#11723708C212yesmaximal, complemented
6#11723703C212yesmaximal, complemented
7#11723702C212yesmaximal, complemented
8#11723661C212yesmaximal, complemented
9#11723656C211yesmaximal, characteristic, complemented
10#10595458—31nomaximal
11D3×#949—32nomaximal
12C22×#1113—21no—
13C33×#41C2211yescharacteristic, complemented
14C3×#3832C2211yescharacteristic, complemented
15C3×Q8×C3⋊D3C2211yescharacteristic, complemented
16C3×#3830—21no—
17C3×#3830C2211yescharacteristic, complemented
18C3×D4×C3⋊D3—21no—
19C3×D4×C3⋊D3C2211yescharacteristic, complemented
20C3×#3828—21no—
21C3×#3828C2211yescharacteristic, complemented
22C2×C3×C4⋊(C3⋊D3)C2212yescomplemented
23C2×C3×C4×C3⋊D3—21no—
24C2×C3×C4×C3⋊D3C2211yescharacteristic
25C2×#6295—21no—
26C4⋊#1113—21no—
27C4⋊#1113—21no—
28C4⋊#1113C2212yes—
29C4⋊#1113C2212yescomplemented
30C3×#3755C2214yescomplemented
31C3×#3753C2214yescomplemented
32C3×#3748C2212yescomplemented
33#88811C2214yescomplemented
34#88810C2214yescomplemented
35#88809C2212yescomplemented
36#88808C2212yescomplemented
37#41×C3⋊D3D311yescharacteristic, complemented
38C3×D3×#41—32no—
39C3×D3×#41—61no—
40C2×#3802—31no—
41C2×D3×D12—32no—
42#64158D312yescomplemented
43C3×#949—32no—
44C3×#949—32no—
45C3×#949—62no—
46#63941—32no—
47#63940—32no—
48#63939—34no—
49D3×#215—34no—
50#63927—32no—
51#63926—32no—
52#63925—34no—
53D3×#213—34no—
54#63830—32no—
55#63825—32no—
56#63823—32no—
57#63818—31no—
58D3×#208—32no—
59C22×C3×C3⋊D3—22no—
60C22×C3×C3⋊D3—21no—
61C22×C3×C3⋊D3D411yescharacteristic
62C2×#1113—22no—
63C2×#1113—22no—
64C2×#1113—44no—
65C33×Q8C2311yescharacteristic, complemented
66C33×D4—21no—
67C33×D4C2311yescharacteristic, complemented
68C2×C33×C4—21no—
69C2×C33×C4C2311yescharacteristic
70C3×#638—21no—
71C3×#638—21no—
72C3×#638—21no—
73C2×C3×C3⋊Dic3—21no—
74C2×C3×C3⋊Dic3D411yescharacteristic
75C3×C4⋊(C3⋊D3)—21no—
76C3×C4⋊(C3⋊D3)—22no—
77C3×C4⋊(C3⋊D3)C2314yes—
78C3×C4⋊(C3⋊D3)C2311yescharacteristic, complemented
79C3×C4×C3⋊D3—21no—
80C3×C4×C3⋊D3—21no—
81C3×C4×C3⋊D3—21no—
82C3×C4×C3⋊D3D411yescharacteristic
83C3×C4×C3⋊D3D411yescharacteristic
84C3×C4×C3⋊D3C2311yescharacteristic
85C3×C4×C3⋊D3C2311yescharacteristic
86C3×#634—21no—
87C3×#634C2311yescharacteristic, complemented
88#6295—22no—
89#6295—22no—
90C3×C3⋊(C3⋊C8)C2314yescomplemented
91C2×#949—91no—
92D3×AGL(1,ℤ/8)—92no—
93C22×D32—62no—
94C22×D32—61no—
95C32×#41—21no—
96C32×#41—22no—
97C32×#41—41no—
98C32×#41C2×D311yescharacteristic, complemented
99C32×#41C2×D312yescomplemented
100#3832C2×D311yescharacteristic, complemented
101Q8×C3⋊D3C2×D311yescharacteristic, complemented
102#3830—21no—
103#3830C2×D311yescharacteristic, complemented
104D4×C3⋊D3—21no—
105D4×C3⋊D3C2×D311yescharacteristic, complemented
106#3828—21no—
107#3828C2×D311yescharacteristic, complemented
108C2×C4⋊(C3⋊D3)C2×D312yescomplemented
109C2×C4×C3⋊D3—21no—
110C2×C4×C3⋊D3C2×D311yescharacteristic
111C3×#239—32no—
112C3×#239—61no—
113C3×D3×Q8—32no—
114C3×D3×Q8—61no—
115C3×#237—32no—
116C3×#237—62no—
117C3×#237—61no—
118C3×#237—62no—
119C3×D3×D4—32no—
120C3×D3×D4—62no—
121C3×D3×D4—61no—
122C3×D3×D4—62no—
123C3×#235—32no—
124C3×#235—62no—
125C3×#235—61no—
126C3×#235—62no—
127C2×C3×D12—32no—
128C2×C3×D12—32no—
129C2×C3×D12—62no—
130C2×C3×C4×D3—32no—
131C2×C3×C4×D3—62no—
132C2×C3×C4×D3—61no—
133C2×C3×C4×D3—62no—
134C2×#626—62no—
135C2×#625—61no—
136#3802—32no—
137#3802—32no—
138#3802—61no—
139#3802—61no—
140D3×D12—34no—
141D3×D12—34no—
142D3×D12—62no—
143D3×D12—62no—
144#3755C2×D314yescomplemented
145#3753C2×D314yescomplemented
146#3748C2×D312yescomplemented
147C3×#215—34no—
148C3×#215—34no—
149C3×#215—64no—
150C3×#213—34no—
151C3×#213—34no—
152C3×#213—64no—
153C3×#208—32no—
154C3×#208—32no—
155C3×#208—62no—
156#3717—34no—
157#3716—34no—
158#3715—34no—
159#3714—34no—
160#3714—34no—
161#3713—34no—
162#3712—32no—
163#3711—34no—
164#3710—32no—
165D3×C3⋊C8—34no—
166C22×C33—21no—
167C22×C33C2×D411yescharacteristic
168C2×C3×C3⋊D3—22no—
169C2×C3×C3⋊D3—21no—
170C2×C3×C3⋊D3—24no—
171C2×C3×C3⋊D3—44no—
172C2×C3×C3⋊D3—42no—
173C2×C3×C3⋊D3C2×D411yescharacteristic
174C2×C3×C3⋊D3C2×D411yescharacteristic
175#1113—44no—
176#1113—44no—
177C33×C4—21no—
178C33×C4C2×D411yescharacteristic
179C33×C4C2411yescharacteristic
180C3×C3⋊Dic3—21no—
181C3×C3⋊Dic3C2×D411yescharacteristic
182C3×C3⋊Dic3C2×D411yescharacteristic
183C2×C3×#41—91no—
184D3×#41—32no—
185D3×#41—61no—
186C2×D3×D4—92no—
187C22×D12—91no—
188C3×AGL(1,ℤ/8)—92no—
189#949—32no—
190#949—32no—
191#949—62no—
192#949—92no—
193#949—92no—
194#949—92no—
195C2×#215—92no—
196#932—92no—
197C2×#213—92no—
198C2×#208—91no—
199#914—94no—
200D3×SD16—94no—
201#911—94no—
202D3×D8—94no—
203#908—92no—
204D3×M16—92no—
205C22×C3⋊D3—21no—
206C22×C3⋊D3—22no—
207C22×C3⋊D3#6711yescharacteristic
208C22×C3×D3—32no—
209C22×C3×D3—61no—
210C22×C3×D3—62no—
211C22×C3×D3—62no—
212C22×C3×D3—62no—
213C22×C3×D3—62no—
214C22×C3×D3—122no—
215C2×D32—64no—
216C2×D32—64no—
217C2×D32—62no—
218C2×D32—62no—
219C2×D32—128no—
220C2×D32—124no—
221C32×Q8—21no—
222C32×Q8—22no—
223C32×Q8—41no—
224C32×Q8C22×D311yescharacteristic, complemented
225C32×Q8C22×D312yescomplemented
226C32×D4—21no—
227C32×D4—22no—
228C32×D4—22no—
229C32×D4—21no—
230C32×D4—22no—
231C32×D4—41no—
232C32×D4—42no—
233C32×D4—42no—
234C32×D4C22×D311yescharacteristic, complemented
235C32×D4C22×D312yescomplemented
236C2×C32×C4—21no—
237C2×C32×C4—22no—
238C2×C32×C4—22no—
239C2×C32×C4—22no—
240C2×C32×C4—21no—
241C2×C32×C4—41no—
242C2×C32×C4—42no—
243C2×C32×C4—42no—
244C2×C32×C4C22×D312yes—
245C2×C32×C4C22×D311yescharacteristic
246#638—21no—
247#638—21no—
248#638—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3#6711yescharacteristic
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)—22no—
253C4⋊(C3⋊D3)C22×D314yes—
254C4⋊(C3⋊D3)C22×D311yescharacteristic, complemented
255C4×C3⋊D3—21no—
256C4×C3⋊D3—21no—
257C4×C3⋊D3—21no—
258C4×C3⋊D3#6711yescharacteristic
259C4×C3⋊D3#6711yescharacteristic
260C4×C3⋊D3C22×D311yescharacteristic
261C4×C3⋊D3C22×D311yescharacteristic
262#634—21no—
263#634C22×D311yescharacteristic, complemented
264C3×#67—62no—
265C3×#67—62no—
266C3×#67—62no—
267C3×#67—62no—
268C3×#67—62no—
269C3×#67—62no—
270C2×C3×Dic3—32no—
271C2×C3×Dic3—61no—
272C2×C3×Dic3—62no—
273C2×C3×Dic3—62no—
274C3×D12—32no—
275C3×D12—34no—
276C3×D12—34no—
277C3×D12—61no—
278C3×D12—64no—
279C3×D12—62no—
280C3×D12—62no—
281C3×D12—62no—
282C3×D12—62no—
283C3×D12—122no—
284C3×C4×D3—32no—
285C3×C4×D3—32no—
286C3×C4×D3—32no—
287C3×C4×D3—32no—
288C3×C4×D3—61no—
289C3×C4×D3—61no—
290C3×C4×D3—61no—
291C3×C4×D3—61no—
292C3×C4×D3—62no—
293C3×C4×D3—62no—
294C3×C4×D3—62no—
295C3×C4×D3—62no—
296C3×C4×D3—62no—
297C3×C4×D3—62no—
298C3×Dic6—32no—
299C3×Dic6—61no—
300C3×Dic6—62no—
301C3×Dic6—62no—
302#626—64no—
303#626—64no—
304#625—62no—
305#625—62no—
306C3⋊(C3⋊C8)C22×D314yescomplemented
307C3×C3⋊C8—34no—
308C3×C3⋊C8—34no—
309C3×C3⋊C8—64no—
310C2×AGL(1,ℤ/8)—271noSylow
311C2×C33—21no—
312C2×C33—41no—
313C2×C33C22×D411yescharacteristic
314C3×C3⋊D3—21no—
315C3×C3⋊D3—41no—
316C3×C3⋊D3—44no—
317C3×C3⋊D3AGL(1,ℤ/8)12yescomplemented
318C23×D3—182no—
319C23×D3—181no—
320C3×#41—21no—
321C3×#41—22no—
322C3×#41—41no—
323C3×#41—91no—
324C3×#41—91no—
325C3×#41—91no—
326C3×#41—181no—
327C3×#41—181no—
328C3×#41D3211yescharacteristic, complemented
329C3×#41D3212yescomplemented
330C2×C3×Q8—91no—
331C2×C3×D4—91no—
332C2×C3×D4—92no—
333C2×C3×D4—181no—
334C22×C3×C4—91no—
335C22×C3×C4—181no—
336C2×#67—182no—
337#239—32no—
338#239—61no—
339D3×Q8—32no—
340D3×Q8—61no—
341#237—32no—
342#237—61no—
343#237—62no—
344#237—62no—
345D3×D4—32no—
346D3×D4—61no—
347D3×D4—62no—
348D3×D4—62no—
349D3×D4—94no—
350D3×D4—94no—
351D3×D4—182no—
352D3×D4—182no—
353#235—32no—
354#235—61no—
355#235—62no—
356#235—62no—
357C2×D12—32no—
358C2×D12—32no—
359C2×D12—62no—
360C2×D12—92no—
361C2×D12—92no—
362C2×D12—181no—
363C2×D12—181no—
364C2×D12—181no—
365C2×C4×D3—32no—
366C2×C4×D3—61no—
367C2×C4×D3—62no—
368C2×C4×D3—62no—
369C3×SD16—94no—
370C3×D8—94no—
371C3×M16—92no—
372#215—34no—
373#215—34no—
374#215—64no—
375#215—94no—
376#214—94no—
377#213—34no—
378#213—34no—
379#213—64no—
380#213—94no—
381#213—94no—
382#208—32no—
383#208—32no—
384#208—62no—
385#208—92no—
386C2×C3⋊C8—92no—
387D24—94no—
388#204—94no—
389ΓL(1,𝔽25)—94no—
390D3×C8—94no—
391C22×C32—21no—
392C22×C32—22no—
393C22×C32—22no—
394C22×C32—22no—
395C22×C32—21no—
396C22×C32—41no—
397C22×C32—42no—
398C22×C32—42no—
399C22×C32D3×D412yes—
400C22×C32C2×#6711yescharacteristic
401C2×C3⋊D3—21no—
402C2×C3⋊D3—22no—
403C2×C3⋊D3—24no—
404C2×C3⋊D3—42no—
405C2×C3⋊D3—44no—
406C2×C3⋊D3C2×#6711yescharacteristic
407C2×C3⋊D3C2×#6711yescharacteristic
408C2×C3×D3—32no—
409C2×C3×D3—32no—
410C2×C3×D3—61no—
411C2×C3×D3—61no—
412C2×C3×D3—64no—
413C2×C3×D3—62no—
414C2×C3×D3—64no—
415C2×C3×D3—62no—
416C2×C3×D3—64no—
417C2×C3×D3—122no—
418C2×C3×D3—124no—
419C2×C3×D3—124no—
420C2×C3×D3—124no—
421C2×C3×D3—124no—
422C2×C3×D3—124no—
423C2×C3×D3—244no—
424D32—128no—
425D32—128no—
426D32—124no—
427D32—124no—
428C32×C4—21no—
429C32×C4—22no—
430C32×C4—22no—
431C32×C4—22no—
432C32×C4—21no—
433C32×C4—22no—
434C32×C4—21no—
435C32×C4—41no—
436C32×C4—41no—
437C32×C4—42no—
438C32×C4—42no—
439C32×C4D3×D412yes—
440C32×C4C2×#6711yescharacteristic
441C32×C4C23×D312yes—
442C32×C4C23×D311yescharacteristic
443C3⋊Dic3—21no—
444C3⋊Dic3C2×#6711yescharacteristic
445C3⋊Dic3C2×#6711yescharacteristic
446C3×Dic3—32no—
447C3×Dic3—32no—
448C3×Dic3—61no—
449C3×Dic3—61no—
450C3×Dic3—62no—
451C3×Dic3—62no—
452C2×#41—91no—
453C22×D4—271no—
454AGL(1,ℤ/8)—92no—
455AGL(1,ℤ/8)—272no—
456AGL(1,ℤ/8)—272no—
457AGL(1,ℤ/8)—272no—
458C2×SD16—272no—
459C2×D8—272no—
460C2×M16—271no—
461C33C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
462C23×C3—91no—
463C23×C3—181no—
464C23×C3—182no—
465C22×D3—32no—
466C22×D3—61no—
467C22×D3—62no—
468C22×D3—62no—
469C22×D3—62no—
470C22×D3—62no—
471C22×D3—122no—
472C22×D3—184no—
473C22×D3—184no—
474C22×D3—182no—
475C22×D3—182no—
476C22×D3—368no—
477C22×D3—364no—
478C3×Q8—21no—
479C3×Q8—22no—
480C3×Q8—41no—
481C3×Q8—91no—
482C3×Q8—181no—
483C3×Q8C2×D3211yescharacteristic, complemented
484C3×Q8C2×D3212yescomplemented
485C3×D4—22no—
486C3×D4—22no—
487C3×D4—21no—
488C3×D4—21no—
489C3×D4—22no—
490C3×D4—42no—
491C3×D4—42no—
492C3×D4—41no—
493C3×D4—91no—
494C3×D4—94no—
495C3×D4—181no—
496C3×D4—181no—
497C3×D4—181no—
498C3×D4—181no—
499C3×D4—182no—
500C3×D4C2×D3211yescharacteristic, complemented
501C3×D4C2×D3212yescomplemented
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—21no—
505C2×C3×C4—22no—
506C2×C3×C4—21no—
507C2×C3×C4—42no—
508C2×C3×C4—42no—
509C2×C3×C4—41no—
510C2×C3×C4—91no—
511C2×C3×C4—91no—
512C2×C3×C4—91no—
513C2×C3×C4—91no—
514C2×C3×C4—91no—
515C2×C3×C4—181no—
516C2×C3×C4—181no—
517C2×C3×C4—181no—
518C2×C3×C4—181no—
519C2×C3×C4C2×D3212yes—
520C2×C3×C4C2×D3211yescharacteristic
521#67—62no—
522#67—62no—
523#67—62no—
524#67—62no—
525#67—62no—
526#67—62no—
527#67—184no—
528#67—184no—
529C2×Dic3—32no—
530C2×Dic3—61no—
531C2×Dic3—62no—
532C2×Dic3—62no—
533D12—34no—
534D12—34no—
535D12—32no—
536D12—61no—
537D12—64no—
538D12—62no—
539D12—62no—
540D12—62no—
541D12—62no—
542D12—122no—
543D12—182no—
544D12—182no—
545C4×D3—32no—
546C4×D3—32no—
547C4×D3—32no—
548C4×D3—32no—
549C4×D3—61no—
550C4×D3—61no—
551C4×D3—61no—
552C4×D3—61no—
553C4×D3—62no—
554C4×D3—62no—
555C4×D3—62no—
556C4×D3—62no—
557C4×D3—62no—
558C4×D3—62no—
559Dic6—32no—
560Dic6—61no—
561Dic6—62no—
562Dic6—62no—
563C3×C8—94no—
564C3⋊C8—34no—
565C3⋊C8—34no—
566C3⋊C8—64no—
567C2×C32—22no—
568C2×C32—21no—
569C2×C32—22no—
570C2×C32—21no—
571C2×C32—41no—
572C2×C32—41no—
573C2×C32—42no—
574C2×C32—41no—
575C2×C32—42no—
576C2×C32—42no—
577C2×C32—81no—
578C2×C32—82no—
579C2×C32—82no—
580C2×C32C2×D3×D412yes—
581C2×C32C22×#6711yescharacteristic
582C3⋊D3—21no—
583C3⋊D3—41no—
584C3⋊D3—44no—
585C3⋊D3#94912yescomplemented
586C3×D3—34no—
587C3×D3—62no—
588C3×D3—62no—
589C3×D3—121no—
590C3×D3—122no—
591C3×D3—124no—
592C3×D3—122no—
593C3×D3—124no—
594C3×D3—244no—
595C24—541no—
596#41—91no—
597#41—91no—
598#41—91no—
599#41—181no—
600#41—181no—
601#41#111311yescharacteristic, complemented
602C2×Q8—91no—
603C2×D4—91no—
604C2×D4—92no—
605C2×D4—181no—
606C2×D4—272no—
607C2×D4—272no—
608C2×D4—541no—
609C2×D4—541no—
610C2×D4—541no—
611C22×C4—91no—
612C22×C4—181no—
613SD16—94no—
614SD16—274no—
615D8—94no—
616D8—274no—
617M16—92no—
618M16—272no—
619C2×C8—272no—
620C22×C3—22no—
621C22×C3—22no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—22no—
625C22×C3—42no—
626C22×C3—42no—
627C22×C3—41no—
628C22×C3—91no—
629C22×C3—91no—
630C22×C3—182no—
631C22×C3—184no—
632C22×C3—181no—
633C22×C3—364no—
634C22×C3—362no—
635C22×C3D3×#6712yes—
636C22×C3#381111yescharacteristic
637C2×D3—32no—
638C2×D3—32no—
639C2×D3—61no—
640C2×D3—61no—
641C2×D3—64no—
642C2×D3—62no—
643C2×D3—62no—
644C2×D3—64no—
645C2×D3—64no—
646C2×D3—122no—
647C2×D3—124no—
648C2×D3—124no—
649C2×D3—124no—
650C2×D3—124no—
651C2×D3—124no—
652C2×D3—244no—
653C2×D3—368no—
654C2×D3—368no—
655C2×D3—364no—
656C2×D3—364no—
657C3×C4—22no—
658C3×C4—22no—
659C3×C4—21no—
660C3×C4—22no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—22no—
664C3×C4—42no—
665C3×C4—42no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—91no—
669C3×C4—91no—
670C3×C4—181no—
671C3×C4D3×#6712yes—
672C3×C4#381111yescharacteristic
673C3×C4C22×D3212yes—
674C3×C4C22×D3211yescharacteristic
675Dic3—32no—
676Dic3—32no—
677Dic3—61no—
678Dic3—61no—
679Dic3—62no—
680Dic3—62no—
681C32—22no—
682C32—21no—
683C32—41no—
684C32D3×AGL(1,ℤ/8)12yescomplemented
685C32C2×#94911yescharacteristic, complemented
686C23—91no—
687C23—181no—
688C23—182no—
689C23—542no—
690C23—542no—
691C23—1084no—
692Q8—91no—
693Q8—181no—
694Q8C2×#111311yescharacteristic, complemented
695D4—21no—
696D4—94no—
697D4—91no—
698D4—181no—
699D4—181no—
700D4—181no—
701D4—181no—
702D4—182no—
703D4—542no—
704D4—542no—
705D4C2×#111311yescharacteristic, complemented
706C2×C4—21no—
707C2×C4—91no—
708C2×C4—91no—
709C2×C4—91no—
710C2×C4—91no—
711C2×C4—91no—
712C2×C4—181no—
713C2×C4—181no—
714C2×C4—181no—
715C2×C4—181no—
716C2×C4C2×#111311yescharacteristic
717C8—94no—
718C2×C3—22no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—22no—
722C2×C3—41no—
723C2×C3—42no—
724C2×C3—42no—
725C2×C3—42no—
726C2×C3—41no—
727C2×C3—41no—
728C2×C3—81no—
729C2×C3—82no—
730C2×C3—82no—
731C2×C3—92no—
732C2×C3—181no—
733C2×C3—364no—
734C2×C3—361no—
735C2×C3C2×D3×#6712yes—
736C2×C3C2×#381111yescharacteristic
737D3—34no—
738D3—62no—
739D3—62no—
740D3—121no—
741D3—122no—
742D3—124no—
743D3—122no—
744D3—124no—
745D3—244no—
746C22—21no—
747C22—91no—
748C22—91no—
749C22—182no—
750C22—181no—
751C22—184no—
752C22—364no—
753C22—362no—
754C22—1084no—
755C22—1084no—
756C22#8904911yescharacteristic
757C4—21no—
758C4—91no—
759C4—91no—
760C4—181no—
761C4#8904911yescharacteristic
762C4C22×#111311yescharacteristic
763C3—21no—
764C3—22no—
765C3—41no—
766C3D3×#94912yescomplemented
767C3#1059545811yescharacteristic, complemented
768C2—21no—
769C2—41no—
770C2—92no—
771C2—181no—
772C2—364no—
773C2—361no—
774C2C2×#8904911yescharacteristic
subgroupG/H
centerC2C2×#89049
commutator, cosocleC33×C4C24
FrattiniC4C22×#1113
FittingC33×#41C22
socleC2×C33C22×D4
hypercenter#41#1113
hypocenterC33C2×AGL(1,ℤ/8)
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. C3×#41×C3⋊D3C2semidirect
2. C2×C4⋊#1113C2semidirect
3. C3×#64158C2semidirect
4. #11723709C2semidirect
5. #11723708C2semidirect
6. #11723703C2semidirect
7. #11723702C2semidirect
8. #11723661C2semidirect
9. #11723656C2semidirect
13. C33×#41C22semidirect
14. C3×#3832C22semidirect
15. C3×Q8×C3⋊D3C22semidirect
17. C3×#3830C22semidirect
19. C3×D4×C3⋊D3C22semidirect
21. C3×#3828C22semidirect
22. C2×C3×C4⋊(C3⋊D3)C22semidirect
29. C4⋊#1113C22semidirect
30. C3×#3755C22semidirect
31. C3×#3753C22semidirect
32. C3×#3748C22semidirect
33. #88811C22semidirect
34. #88810C22semidirect
35. #88809C22semidirect
36. #88808C22semidirect
37. #41×C3⋊D3D3semidirect
42. #64158D3semidirect
65. C33×Q8C23semidirect
67. C33×D4C23semidirect
78. C3×C4⋊(C3⋊D3)C23semidirect
87. C3×#634C23semidirect
90. C3×C3⋊(C3⋊C8)C23semidirect
98. C32×#41C2×D3semidirect
99. C32×#41C2×D3semidirect
100. #3832C2×D3semidirect
101. Q8×C3⋊D3C2×D3semidirect
103. #3830C2×D3semidirect
105. D4×C3⋊D3C2×D3semidirect
107. #3828C2×D3semidirect
108. C2×C4⋊(C3⋊D3)C2×D3semidirect
144. #3755C2×D3semidirect
145. #3753C2×D3semidirect
146. #3748C2×D3semidirect
224. C32×Q8C22×D3semidirect
225. C32×Q8C22×D3semidirect
234. C32×D4C22×D3semidirect
235. C32×D4C22×D3semidirect
254. C4⋊(C3⋊D3)C22×D3semidirect
263. #634C22×D3semidirect
306. C3⋊(C3⋊C8)C22×D3semidirect
317. C3×C3⋊D3AGL(1,ℤ/8)semidirect
328. C3×#41D32semidirect
329. C3×#41D32semidirect
461. C33C2×AGL(1,ℤ/8)semidirect
483. C3×Q8C2×D32semidirect
484. C3×Q8C2×D32semidirect
500. C3×D4C2×D32semidirect
501. C3×D4C2×D32semidirect
585. C3⋊D3#949semidirect
601. #41#1113semidirect
684. C32D3×AGL(1,ℤ/8)semidirect
685. C32C2×#949semidirect
694. Q8C2×#1113semidirect
705. D4C2×#1113semidirect
766. C3D3×#949semidirect
767. C3#10595458semidirect

Maximal subgroups

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

subgroupindex
C3×#41×C3⋊D32
C2×C4⋊#11132
C3×#641582
#117237092
#117237082
#117237032
#117237022
#117236612
#117236562
#105954583
D3×#9493