Finite Group Databasebeta

← D3×#63823 #13170524

Subgroups — D3×#63823 #13170524

Order 1728.

1416 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#235C211yesmaximal, characteristic, complemented
2C2×C3×D3×D12C211yesmaximal, characteristic, complemented
3#11723661C211yesmaximal, characteristic, complemented
4#11723365C211yesmaximal, characteristic, complemented
5#11723364C211yesmaximal, characteristic, complemented
6D3×#3748C211yesmaximal, characteristic, complemented
7C3×#63823C211yesmaximal, characteristic, complemented
8#11722867C212yesmaximal, complemented
9#11722866C212yesmaximal, complemented
10D3×#3715C212yesmaximal, complemented
11D3×#3713C212yesmaximal, complemented
12D3×#949—31nomaximal
13D3×#932—31nomaximal
14C2×#63823—31nomaximal
15C22×C3×D32—21no—
16C3×#3828C2211yescharacteristic, complemented
17C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
18C32×#235C2211yescharacteristic, complemented
19C2×C32×D12C2211yescharacteristic, complemented
20C2×C32×C4×D3C2211yescharacteristic
21C3×D3×#67—21no—
22C2×C3×#626—21no—
23C3×#3804—21no—
24C3×D3×D12—21no—
25C3×D3×D12—21no—
26C3×D3×D12C2212yes—
27C3×D3×D12C2212yescomplemented
28C3×D3×D12C2211yescharacteristic, complemented
29C3×C4×D32—21no—
30C3×#3799C2211yescharacteristic, complemented
31C3×#3798—21no—
32C3×#3795C2211yescharacteristic, complemented
33C3×D3×Dic6C2211yescharacteristic, complemented
34#88855C2211yescharacteristic, complemented
35C3×#3748C2211yescharacteristic, complemented
36#88811C2212yescomplemented
37#88810C2212yescomplemented
38#88793C2212yescomplemented
39#88792C2212yescomplemented
40#88789C2212yescomplemented
41#88789C2212yescomplemented
42#88786C2212yescomplemented
43D3×C3⋊(C3⋊C8)C2212yescomplemented
44C3×#3715C2212yescomplemented
45C3×#3713C2212yescomplemented
46C3×D3×#41—31no—
47C2×C3×D3×D4—31no—
48C2×C3×#235—31no—
49C22×C3×D12—31no—
50D3×#235D311yescharacteristic, complemented
51C2×D3×D12D311yescharacteristic, complemented
52#64158—31no—
53#64141—31no—
54C2×#3748—31no—
55C3×#949—31no—
56C3×#932—31no—
57#63939—32no—
58D3×#215—32no—
59#63934—32no—
60#63932—32no—
61D3×#214—32no—
62#63925—32no—
63D3×#213—32no—
64D3×#213—32no—
65#63830—31no—
66C2×#3715—32no—
67#63825—31no—
68#63823—31no—
69#63823—31no—
70#63823—31no—
71#63823—31no—
72#63823—31no—
73#63823—32no—
74#63823—32no—
75#63823—61no—
76#63823—61no—
77#63823D311yescharacteristic, direct product factor
78C2×#3713—32no—
79D3×#208—31no—
80D3×#208—31no—
81D3×#208—61no—
82C22×C3×C3⋊D3—21no—
83C22×C32×D3—21no—
84C22×C32×D3D411yescharacteristic
85C2×C3×D32—22no—
86C2×C3×D32—22no—
87C2×C3×D32—21no—
88C2×C3×D32—44no—
89C2×C33×C4C2311yescharacteristic
90C3×#638—21no—
91C3×C4⋊(C3⋊D3)—21no—
92C3×C4⋊(C3⋊D3)C2312yes—
93C3×C4⋊(C3⋊D3)C2311yescharacteristic, complemented
94C3×C4×C3⋊D3—21no—
95C3×#634C2311yescharacteristic, complemented
96C32×#67—21no—
97C2×C32×Dic3D411yescharacteristic
98C32×D12—21no—
99C32×D12C2312yes—
100C32×D12C2311yescharacteristic, complemented
101C32×C4×D3—21no—
102C32×C4×D3D411yescharacteristic
103C32×C4×D3D411yescharacteristic
104C32×C4×D3C2311yescharacteristic
105C32×C4×D3C2311yescharacteristic
106C32×Dic6C2311yescharacteristic, complemented
107C3×#627—21no—
108C3×#626—21no—
109C3×#626—21no—
110C3×#626—22no—
111C3×#626—22no—
112C3×#625—21no—
113C3×#624—21no—
114C3×D3×Dic3—21no—
115C3×D3×Dic3—21no—
116C3⋊(C3⋊(C3⋊C8))C2312yescomplemented
117C3×C3⋊(C3⋊C8)C2312yescomplemented
118C2×#949—91no—
119C2×#932—91no—
120D3×AGL(1,ℤ/8)—91no—
121C23×C3×D3—61no—
122C23×C3×D3—61no—
123C22×D32—21no—
124C32×#41—31no—
125C2×C32×D4—31no—
126C22×C32×C4—31no—
127#3828C2×D311yescharacteristic, complemented
128C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
129C2×C3×#67—61no—
130C2×C3×#67—61no—
131C3×#239—31no—
132C3×D3×Q8—31no—
133C3×#237—31no—
134C3×#237—61no—
135C3×D3×D4—32no—
136C3×D3×D4—32no—
137C3×D3×D4—31no—
138C3×D3×D4—61no—
139C3×D3×D4—61no—
140C3×D3×D4—61no—
141C3×#235—21no—
142C3×#235—31no—
143C3×#235—31no—
144C3×#235—31no—
145C3×#235—31no—
146C3×#235—61no—
147C3×#235—61no—
148C3×#235—61no—
149C3×#235—61no—
150C3×#235C2×D311yescharacteristic, complemented
151C3×#235C2×D311yescharacteristic, complemented
152C2×C3×D12—21no—
153C2×C3×D12—31no—
154C2×C3×D12—31no—
155C2×C3×D12—32no—
156C2×C3×D12—32no—
157C2×C3×D12—31no—
158C2×C3×D12—61no—
159C2×C3×D12—61no—
160C2×C3×D12—61no—
161C2×C3×D12—61no—
162C2×C3×D12C2×D311yescharacteristic, complemented
163C2×C3×D12C2×D311yescharacteristic, complemented
164C2×C3×C4×D3—21no—
165C2×C3×C4×D3—61no—
166C2×C3×C4×D3—61no—
167C2×C3×C4×D3C2×D311yescharacteristic
168C2×C3×C4×D3C2×D311yescharacteristic
169C2×C3×Dic6—31no—
170D3×#67—21no—
171C2×#626—21no—
172#3804—21no—
173D3×D12—21no—
174D3×D12—21no—
175D3×D12C2×D312yes—
176D3×D12C2×D312yescomplemented
177D3×D12C2×D311yescharacteristic, complemented
178C4×D32—21no—
179#3799C2×D311yescharacteristic, complemented
180#3798—21no—
181#3795C2×D311yescharacteristic, complemented
182D3×Dic6C2×D311yescharacteristic, complemented
183#3755—32no—
184#3754—32no—
185#3753—32no—
186#3753—32no—
187#3748—31no—
188#3748—31no—
189#3748—31no—
190#3748—32no—
191#3748—61no—
192#3748—61no—
193#3748—61no—
194#3748—121no—
195#3748C2×D311yescharacteristic, complemented
196C2×C3⋊(C3⋊C8)—32no—
197C3×#215—32no—
198C3×#214—32no—
199C3×#213—32no—
200C3×#213—32no—
201C3×#208—31no—
202C3×#208—31no—
203C3×#208—61no—
204#3717—32no—
205#3716—32no—
206#3715—32no—
207#3715—32no—
208#3715—32no—
209#3715—32no—
210#3715—32no—
211#3715—62no—
212#3715—62no—
213#3715C2×D312yescomplemented
214#3714—32no—
215#3714—32no—
216#3713—32no—
217#3713—32no—
218#3713—32no—
219#3713—32no—
220#3713—32no—
221#3713—62no—
222#3713—62no—
223#3713C2×D312yescomplemented
224#3711—32no—
225#3711—32no—
226#3711—62no—
227D3×C3⋊C8—32no—
228D3×C3⋊C8—32no—
229D3×C3⋊C8—62no—
230C22×C33C2×D411yescharacteristic
231C2×C3×C3⋊D3—21no—
232C2×C3×C3⋊D3—22no—
233C2×C3×C3⋊D3—42no—
234C2×C32×D3—22no—
235C2×C32×D3—21no—
236C2×C32×D3—22no—
237C2×C32×D3—42no—
238C2×C32×D3C2×D411yescharacteristic
239C2×C32×D3C2×D411yescharacteristic
240C3×D32—44no—
241C3×D32—42no—
242C3×D32—44no—
243C33×C4C2×D411yescharacteristic
244C33×C4C2411yescharacteristic
245C3×C3⋊Dic3—21no—
246C32×Dic3—21no—
247C32×Dic3C2×D411yescharacteristic
248C32×Dic3C2×D411yescharacteristic
249C2×C3×#41—91no—
250C22×C3×D4—91no—
251D3×#41—31no—
252C2×D3×D4—31no—
253C2×#235—31no—
254C22×D12—31no—
255C3×AGL(1,ℤ/8)—91no—
256#949—31no—
257#949—91no—
258#949—92no—
259#949—92no—
260#949—91no—
261#949—91no—
262#949—91no—
263#949—181no—
264C2×#215—92no—
265C2×#214—92no—
266#932—31no—
267#932—91no—
268#932—92no—
269#932—92no—
270#932—91no—
271#932—91no—
272#932—91no—
273#932—181no—
274C2×#213—92no—
275C2×#213—92no—
276C2×#208—91no—
277C2×#208—91no—
278C2×#208—181no—
279#914—92no—
280D3×SD16—92no—
281#911—92no—
282D3×D8—92no—
283#908—91no—
284D3×M16—91no—
285C23×C32—31no—
286C23×C32—61no—
287C22×C3⋊D3—21no—
288C22×C3×D3—21no—
289C22×C3×D3—21no—
290C22×C3×D3—21no—
291C22×C3×D3—41no—
292C22×C3×D3—62no—
293C22×C3×D3—62no—
294C22×C3×D3—61no—
295C22×C3×D3—61no—
296C22×C3×D3—61no—
297C22×C3×D3—62no—
298C22×C3×D3—62no—
299C22×C3×D3—61no—
300C22×C3×D3—121no—
301C22×C3×D3—124no—
302C22×C3×D3—124no—
303C22×C3×D3#6711yescharacteristic
304C22×C3×D3#6711yescharacteristic
305C2×D32—22no—
306C2×D32—22no—
307C2×D32—21no—
308C2×D32—44no—
309C32×Q8—31no—
310C32×D4—31no—
311C32×D4—32no—
312C32×D4—61no—
313C32×D4—61no—
314C2×C32×C4—21no—
315C2×C32×C4—21no—
316C2×C32×C4—21no—
317C2×C32×C4—31no—
318C2×C32×C4—31no—
319C2×C32×C4—31no—
320C2×C32×C4—31no—
321C2×C32×C4—31no—
322C2×C32×C4—41no—
323C2×C32×C4—61no—
324C2×C32×C4C22×D311yescharacteristic
325C2×C32×C4C22×D311yescharacteristic
326C2×C32×C4C22×D311yescharacteristic
327#638—21no—
328C4⋊(C3⋊D3)—21no—
329C4⋊(C3⋊D3)C22×D312yes—
330C4⋊(C3⋊D3)C22×D311yescharacteristic, complemented
331C4×C3⋊D3—21no—
332#634C22×D311yescharacteristic, complemented
333C3×#67—21no—
334C3×#67—21no—
335C3×#67—41no—
336C3×#67—61no—
337C3×#67—61no—
338C3×#67—61no—
339C3×#67—61no—
340C3×#67—61no—
341C3×#67—61no—
342C3×#67—62no—
343C3×#67—62no—
344C3×#67—121no—
345C2×C3×Dic3—21no—
346C2×C3×Dic3—61no—
347C2×C3×Dic3—61no—
348C2×C3×Dic3#6711yescharacteristic
349C2×C3×Dic3#6711yescharacteristic
350C3×D12—21no—
351C3×D12—21no—
352C3×D12—22no—
353C3×D12—21no—
354C3×D12—31no—
355C3×D12—31no—
356C3×D12—32no—
357C3×D12—32no—
358C3×D12—41no—
359C3×D12—61no—
360C3×D12—62no—
361C3×D12—62no—
362C3×D12—62no—
363C3×D12—61no—
364C3×D12—61no—
365C3×D12—61no—
366C3×D12—61no—
367C3×D12—121no—
368C3×D12C22×D312yes—
369C3×D12C22×D312yes—
370C3×D12C22×D311yescharacteristic, complemented
371C3×D12C22×D311yescharacteristic, complemented
372C3×C4×D3—21no—
373C3×C4×D3—21no—
374C3×C4×D3—21no—
375C3×C4×D3—21no—
376C3×C4×D3—21no—
377C3×C4×D3—21no—
378C3×C4×D3—41no—
379C3×C4×D3—61no—
380C3×C4×D3—61no—
381C3×C4×D3—61no—
382C3×C4×D3—61no—
383C3×C4×D3—61no—
384C3×C4×D3—61no—
385C3×C4×D3—121no—
386C3×C4×D3#6711yescharacteristic
387C3×C4×D3#6711yescharacteristic
388C3×C4×D3#6711yescharacteristic
389C3×C4×D3#6711yescharacteristic
390C3×C4×D3C22×D311yescharacteristic
391C3×C4×D3C22×D311yescharacteristic
392C3×C4×D3C22×D311yescharacteristic
393C3×C4×D3C22×D311yescharacteristic
394C3×Dic6—21no—
395C3×Dic6—31no—
396C3×Dic6—31no—
397C3×Dic6—61no—
398C3×Dic6—61no—
399C3×Dic6—61no—
400C3×Dic6C22×D311yescharacteristic, complemented
401C3×Dic6C22×D311yescharacteristic, complemented
402#627—21no—
403#626—21no—
404#626—21no—
405#626—22no—
406#626—22no—
407#625—21no—
408#624—21no—
409D3×Dic3—21no—
410D3×Dic3—21no—
411C3⋊(C3⋊C8)—32no—
412C3⋊(C3⋊C8)—32no—
413C3⋊(C3⋊C8)—32no—
414C3⋊(C3⋊C8)—62no—
415C3⋊(C3⋊C8)—62no—
416C3⋊(C3⋊C8)—62no—
417C3⋊(C3⋊C8)—122no—
418C3⋊(C3⋊C8)C22×D312yescomplemented
419C3×C3⋊C8—32no—
420C3×C3⋊C8—32no—
421C3×C3⋊C8—62no—
422C2×AGL(1,ℤ/8)—271noSylow
423C2×C33—21no—
424C2×C33C22×D411yescharacteristic
425C3×C3⋊D3—42no—
426C3×C3⋊D3—41no—
427C32×D3—21no—
428C32×D3—42no—
429C32×D3—41no—
430C32×D3AGL(1,ℤ/8)12yescomplemented
431C24×C3—181no—
432C23×D3—61no—
433C23×D3—61no—
434C3×#41—31no—
435C3×#41—31no—
436C3×#41—61no—
437C3×#41—91no—
438C3×#41—91no—
439C3×#41—91no—
440C3×#41—181no—
441C3×#41—181no—
442C2×C3×Q8—91no—
443C2×C3×D4—31no—
444C2×C3×D4—31no—
445C2×C3×D4—61no—
446C2×C3×D4—91no—
447C2×C3×D4—92no—
448C2×C3×D4—92no—
449C2×C3×D4—91no—
450C2×C3×D4—181no—
451C2×C3×D4—181no—
452C2×C3×D4—181no—
453C2×C3×D4—181no—
454C22×C3×C4—31no—
455C22×C3×C4—31no—
456C22×C3×C4—61no—
457C22×C3×C4—181no—
458C2×#67—61no—
459C2×#67—61no—
460#239—31no—
461D3×Q8—31no—
462#237—31no—
463#237—61no—
464D3×D4—31no—
465D3×D4—32no—
466D3×D4—32no—
467D3×D4—61no—
468D3×D4—61no—
469D3×D4—61no—
470#235—31no—
471#235—31no—
472#235—31no—
473#235—31no—
474#235—61no—
475#235—61no—
476#235—61no—
477#235—61no—
478#235D3211yescharacteristic, complemented
479C2×D12—31no—
480C2×D12—31no—
481C2×D12—32no—
482C2×D12—32no—
483C2×D12—31no—
484C2×D12—61no—
485C2×D12—61no—
486C2×D12—61no—
487C2×D12—61no—
488C2×D12D3211yescharacteristic, complemented
489C2×C4×D3—61no—
490C2×C4×D3—61no—
491C2×C4×D3D3211yescharacteristic
492C2×Dic6—31no—
493C3×SD16—92no—
494C3×D8—92no—
495C3×M16—91no—
496#215—32no—
497#215—92no—
498#215—92no—
499#215—92no—
500#215—92no—
501#215—182no—
502#214—32no—
503#214—92no—
504#214—92no—
505#214—92no—
506#214—92no—
507#214—182no—
508#213—32no—
509#213—32no—
510#213—92no—
511#213—92no—
512#213—92no—
513#213—92no—
514#213—92no—
515#213—92no—
516#213—92no—
517#213—92no—
518#213—182no—
519#213—182no—
520#208—31no—
521#208—31no—
522#208—61no—
523#208—92no—
524#208—92no—
525#208—91no—
526#208—91no—
527#208—91no—
528#208—182no—
529#208—181no—
530#208—181no—
531#208—181no—
532#208—361no—
533C2×C3⋊C8—92no—
534C2×C3⋊C8—92no—
535C2×C3⋊C8—182no—
536D24—92no—
537#204—92no—
538ΓL(1,𝔽25)—92no—
539D3×C8—92no—
540C22×C32—21no—
541C22×C32—21no—
542C22×C32—21no—
543C22×C32—31no—
544C22×C32—31no—
545C22×C32—41no—
546C22×C32—62no—
547C22×C32—61no—
548C22×C32—62no—
549C22×C32—122no—
550C22×C32D3×D411yescharacteristic
551C22×C32C2×#6711yescharacteristic
552C22×C32C2×#6711yescharacteristic
553C2×C3⋊D3—21no—
554C2×C3⋊D3—22no—
555C2×C3⋊D3—42no—
556C2×C3×D3—22no—
557C2×C3×D3—22no—
558C2×C3×D3—21no—
559C2×C3×D3—22no—
560C2×C3×D3—21no—
561C2×C3×D3—22no—
562C2×C3×D3—21no—
563C2×C3×D3—21no—
564C2×C3×D3—42no—
565C2×C3×D3—41no—
566C2×C3×D3—42no—
567C2×C3×D3—42no—
568C2×C3×D3—42no—
569C2×C3×D3—61no—
570C2×C3×D3—62no—
571C2×C3×D3—61no—
572C2×C3×D3—62no—
573C2×C3×D3—82no—
574C2×C3×D3—121no—
575C2×C3×D3—122no—
576C2×C3×D3—124no—
577C2×C3×D3—122no—
578C2×C3×D3—124no—
579C2×C3×D3—124no—
580C2×C3×D3—122no—
581C2×C3×D3—122no—
582C2×C3×D3—122no—
583C2×C3×D3—124no—
584C2×C3×D3—242no—
585C2×C3×D3C2×#6711yescharacteristic
586C2×C3×D3C2×#6711yescharacteristic
587C2×C3×D3C2×#6711yescharacteristic
588C2×C3×D3C2×#6711yescharacteristic
589D32—44no—
590D32—44no—
591D32—42no—
592C32×C4—21no—
593C32×C4—21no—
594C32×C4—21no—
595C32×C4—21no—
596C32×C4—21no—
597C32×C4—21no—
598C32×C4—31no—
599C32×C4—31no—
600C32×C4—41no—
601C32×C4—41no—
602C32×C4—61no—
603C32×C4D3×D411yescharacteristic
604C32×C4C2×#6711yescharacteristic
605C32×C4C2×#6711yescharacteristic
606C32×C4C23×D311yescharacteristic
607C32×C4C23×D311yescharacteristic
608C32×C4C23×D311yescharacteristic
609C3⋊Dic3—21no—
610C3×Dic3—21no—
611C3×Dic3—21no—
612C3×Dic3—21no—
613C3×Dic3—21no—
614C3×Dic3—41no—
615C3×Dic3—61no—
616C3×Dic3—61no—
617C3×Dic3—121no—
618C3×Dic3C2×#6711yescharacteristic
619C3×Dic3C2×#6711yescharacteristic
620C3×Dic3C2×#6711yescharacteristic
621C3×Dic3C2×#6711yescharacteristic
622C2×#41—91no—
623C22×D4—91no—
624AGL(1,ℤ/8)—91no—
625AGL(1,ℤ/8)—271no—
626AGL(1,ℤ/8)—272no—
627AGL(1,ℤ/8)—272no—
628AGL(1,ℤ/8)—271no—
629AGL(1,ℤ/8)—271no—
630C2×SD16—272no—
631C2×D8—272no—
632C2×M16—271no—
633C33C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
634C23×C3—31no—
635C23×C3—31no—
636C23×C3—61no—
637C23×C3—61no—
638C23×C3—61no—
639C23×C3—121no—
640C23×C3—181no—
641C23×C3—182no—
642C23×C3—182no—
643C23×C3—181no—
644C23×C3—364no—
645C22×D3—21no—
646C22×D3—61no—
647C22×D3—62no—
648C22×D3—62no—
649C22×D3—61no—
650C22×D3—61no—
651C22×D3—61no—
652C22×D3—62no—
653C22×D3—62no—
654C22×D3—121no—
655C22×D3—124no—
656C22×D3—124no—
657C22×D3#62511yescharacteristic
658C3×Q8—31no—
659C3×Q8—31no—
660C3×Q8—61no—
661C3×Q8—91no—
662C3×Q8—181no—
663C3×D4—32no—
664C3×D4—32no—
665C3×D4—31no—
666C3×D4—31no—
667C3×D4—61no—
668C3×D4—62no—
669C3×D4—61no—
670C3×D4—61no—
671C3×D4—61no—
672C3×D4—61no—
673C3×D4—91no—
674C3×D4—92no—
675C3×D4—121no—
676C3×D4—121no—
677C3×D4—182no—
678C3×D4—182no—
679C3×D4—181no—
680C3×D4—181no—
681C3×D4—181no—
682C3×D4—181no—
683C3×D4—181no—
684C2×C3×C4—21no—
685C2×C3×C4—21no—
686C2×C3×C4—21no—
687C2×C3×C4—31no—
688C2×C3×C4—31no—
689C2×C3×C4—31no—
690C2×C3×C4—31no—
691C2×C3×C4—31no—
692C2×C3×C4—31no—
693C2×C3×C4—31no—
694C2×C3×C4—31no—
695C2×C3×C4—31no—
696C2×C3×C4—31no—
697C2×C3×C4—41no—
698C2×C3×C4—61no—
699C2×C3×C4—61no—
700C2×C3×C4—61no—
701C2×C3×C4—61no—
702C2×C3×C4—61no—
703C2×C3×C4—61no—
704C2×C3×C4—61no—
705C2×C3×C4—121no—
706C2×C3×C4—181no—
707C2×C3×C4—181no—
708C2×C3×C4—181no—
709C2×C3×C4—181no—
710C2×C3×C4C2×D3211yescharacteristic
711C2×C3×C4C2×D3211yescharacteristic
712C2×C3×C4C2×D3211yescharacteristic
713#67—21no—
714#67—61no—
715#67—61no—
716#67—61no—
717#67—61no—
718#67—61no—
719#67—61no—
720#67—62no—
721#67—62no—
722#67—121no—
723C2×Dic3—61no—
724C2×Dic3—61no—
725C2×Dic3#62511yescharacteristic
726D12—21no—
727D12—32no—
728D12—32no—
729D12—31no—
730D12—31no—
731D12—62no—
732D12—61no—
733D12—62no—
734D12—62no—
735D12—61no—
736D12—61no—
737D12—61no—
738D12—61no—
739D12—121no—
740D12C2×D3212yes—
741D12C2×D3211yescharacteristic, complemented
742C4×D3—21no—
743C4×D3—61no—
744C4×D3—61no—
745C4×D3—61no—
746C4×D3—61no—
747C4×D3—61no—
748C4×D3—61no—
749C4×D3—121no—
750C4×D3#62511yescharacteristic
751C4×D3#62511yescharacteristic
752C4×D3C2×D3211yescharacteristic
753C4×D3C2×D3211yescharacteristic
754Dic6—31no—
755Dic6—31no—
756Dic6—61no—
757Dic6—61no—
758Dic6—61no—
759Dic6C2×D3211yescharacteristic, complemented
760C3×C8—92no—
761C3⋊C8—32no—
762C3⋊C8—32no—
763C3⋊C8—62no—
764C3⋊C8—92no—
765C3⋊C8—92no—
766C3⋊C8—92no—
767C3⋊C8—182no—
768C3⋊C8—182no—
769C3⋊C8—182no—
770C3⋊C8—362no—
771C2×C32—21no—
772C2×C32—21no—
773C2×C32—21no—
774C2×C32—21no—
775C2×C32—21no—
776C2×C32—21no—
777C2×C32—32no—
778C2×C32—41no—
779C2×C32—41no—
780C2×C32—41no—
781C2×C32—41no—
782C2×C32—61no—
783C2×C32—81no—
784C2×C32—121no—
785C2×C32—122no—
786C2×C32C2×D3×D411yescharacteristic
787C2×C32C22×#6711yescharacteristic
788C2×C32C22×#6711yescharacteristic
789C3⋊D3—42no—
790C3⋊D3—41no—
791C3×D3—21no—
792C3×D3—21no—
793C3×D3—22no—
794C3×D3—41no—
795C3×D3—42no—
796C3×D3—41no—
797C3×D3—42no—
798C3×D3—41no—
799C3×D3—81no—
800C3×D3—82no—
801C3×D3—121no—
802C3×D3—122no—
803C3×D3—121no—
804C3×D3—122no—
805C3×D3—241no—
806C3×D3—242no—
807C3×D3#93212yescomplemented
808C3×D3#94912yescomplemented
809C24—181no—
810#41—31no—
811#41—91no—
812#41—91no—
813#41—91no—
814#41—181no—
815#41—181no—
816C2×Q8—91no—
817C2×D4—31no—
818C2×D4—91no—
819C2×D4—92no—
820C2×D4—92no—
821C2×D4—91no—
822C2×D4—181no—
823C2×D4—181no—
824C2×D4—181no—
825C2×D4—181no—
826C22×C4—31no—
827C22×C4—181no—
828SD16—92no—
829SD16—272no—
830SD16—272no—
831SD16—272no—
832D8—92no—
833D8—272no—
834D8—272no—
835D8—272no—
836M16—91no—
837M16—272no—
838M16—271no—
839C2×C8—272no—
840C22×C3—21no—
841C22×C3—21no—
842C22×C3—21no—
843C22×C3—31no—
844C22×C3—31no—
845C22×C3—31no—
846C22×C3—31no—
847C22×C3—41no—
848C22×C3—61no—
849C22×C3—61no—
850C22×C3—62no—
851C22×C3—62no—
852C22×C3—61no—
853C22×C3—62no—
854C22×C3—61no—
855C22×C3—62no—
856C22×C3—121no—
857C22×C3—122no—
858C22×C3—122no—
859C22×C3—122no—
860C22×C3—122no—
861C22×C3—181no—
862C22×C3—182no—
863C22×C3—242no—
864C22×C3—362no—
865C22×C3—364no—
866C22×C3—362no—
867C22×C3—364no—
868C22×C3C2×#62511yescharacteristic
869C22×C3D3×#6711yescharacteristic
870C22×C3D3×#6711yescharacteristic
871C2×D3—22no—
872C2×D3—21no—
873C2×D3—22no—
874C2×D3—42no—
875C2×D3—61no—
876C2×D3—62no—
877C2×D3—61no—
878C2×D3—62no—
879C2×D3—121no—
880C2×D3—122no—
881C2×D3—124no—
882C2×D3—124no—
883C2×D3—122no—
884C2×D3—124no—
885C2×D3—122no—
886C2×D3—122no—
887C2×D3—124no—
888C2×D3—122no—
889C2×D3—242no—
890C2×D3C2×#62511yescharacteristic
891C2×D3C2×#62511yescharacteristic
892C3×C4—21no—
893C3×C4—21no—
894C3×C4—21no—
895C3×C4—21no—
896C3×C4—21no—
897C3×C4—21no—
898C3×C4—31no—
899C3×C4—31no—
900C3×C4—31no—
901C3×C4—31no—
902C3×C4—41no—
903C3×C4—41no—
904C3×C4—61no—
905C3×C4—61no—
906C3×C4—61no—
907C3×C4—61no—
908C3×C4—121no—
909C3×C4—181no—
910C3×C4C2×#62511yescharacteristic
911C3×C4D3×#6711yescharacteristic
912C3×C4D3×#6711yescharacteristic
913C3×C4C22×D3211yescharacteristic
914C3×C4C22×D3211yescharacteristic
915C3×C4C22×D3211yescharacteristic
916Dic3—21no—
917Dic3—61no—
918Dic3—61no—
919Dic3—121no—
920Dic3C2×#62511yescharacteristic
921Dic3C2×#62511yescharacteristic
922C32—21no—
923C32—21no—
924C32—21no—
925C32—41no—
926C32D3×AGL(1,ℤ/8)11yescharacteristic, complemented
927C32C2×#93211yescharacteristic, complemented
928C32C2×#94911yescharacteristic, complemented
929C23—31no—
930C23—61no—
931C23—181no—
932C23—182no—
933C23—182no—
934C23—181no—
935C23—364no—
936Q8—31no—
937Q8—91no—
938Q8—181no—
939D4—31no—
940D4—32no—
941D4—61no—
942D4—61no—
943D4—91no—
944D4—92no—
945D4—182no—
946D4—182no—
947D4—181no—
948D4—181no—
949D4—181no—
950D4—181no—
951D4—181no—
952C2×C4—31no—
953C2×C4—31no—
954C2×C4—31no—
955C2×C4—31no—
956C2×C4—31no—
957C2×C4—61no—
958C2×C4—181no—
959C2×C4—181no—
960C2×C4—181no—
961C2×C4—181no—
962C2×C4D3311yescharacteristic
963C8—92no—
964C8—272no—
965C2×C3—21no—
966C2×C3—21no—
967C2×C3—21no—
968C2×C3—21no—
969C2×C3—21no—
970C2×C3—21no—
971C2×C3—32no—
972C2×C3—32no—
973C2×C3—41no—
974C2×C3—41no—
975C2×C3—41no—
976C2×C3—41no—
977C2×C3—62no—
978C2×C3—61no—
979C2×C3—61no—
980C2×C3—81no—
981C2×C3—121no—
982C2×C3—121no—
983C2×C3—122no—
984C2×C3—122no—
985C2×C3—121no—
986C2×C3—242no—
987C2×C3—241no—
988C2×C3—361no—
989C2×C3—362no—
990C2×C3C22×#62511yescharacteristic
991C2×C3C2×D3×#6711yescharacteristic
992C2×C3C2×D3×#6711yescharacteristic
993D3—21no—
994D3—42no—
995D3—41no—
996D3—122no—
997D3—121no—
998D3—122no—
999D3—121no—
1000D3—242no—
1001D3—241no—
1002D3#6382312yesdirect product factor
1003C22—31no—
1004C22—31no—
1005C22—62no—
1006C22—61no—
1007C22—62no—
1008C22—122no—
1009C22—181no—
1010C22—182no—
1011C22—362no—
1012C22—364no—
1013C22—362no—
1014C22—364no—
1015C22D3×#62511yescharacteristic
1016C4—31no—
1017C4—31no—
1018C4—61no—
1019C4—181no—
1020C4D3×#62511yescharacteristic
1021C4C2×D3311yescharacteristic
1022C3—21no—
1023C3—21no—
1024C3—21no—
1025C3—41no—
1026C3C2×#6382311yescharacteristic, complemented
1027C3D3×#93211yescharacteristic, complemented
1028C3D3×#94911yescharacteristic, complemented
1029C2—21no—
1030C2—32no—
1031C2—61no—
1032C2—122no—
1033C2—121no—
1034C2—362no—
1035C2—361no—
1036C2C2×D3×#62511yescharacteristic
subgroupG/H
centerC2C2×D3×#625
commutator, cosocleC33×C4C24
FrattiniC4C2×D33
FittingC2×C33×C4C23
socleC2×C33C22×D4
hypercenterC2×C4D33
hypocenterC33C2×AGL(1,ℤ/8)
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C3×D3×#235C2semidirect
2. C2×C3×D3×D12C2semidirect
3. #11723661C2semidirect
4. #11723365C2semidirect
5. #11723364C2semidirect
6. D3×#3748C2semidirect
7. C3×#63823C2semidirect
8. #11722867C2semidirect
9. #11722866C2semidirect
10. D3×#3715C2semidirect
11. D3×#3713C2semidirect
16. C3×#3828C22semidirect
17. C2×C3×C4⋊(C3⋊D3)C22semidirect
18. C32×#235C22semidirect
19. C2×C32×D12C22semidirect
27. C3×D3×D12C22semidirect
28. C3×D3×D12C22semidirect
30. C3×#3799C22semidirect
32. C3×#3795C22semidirect
33. C3×D3×Dic6C22semidirect
34. #88855C22semidirect
35. C3×#3748C22semidirect
36. #88811C22semidirect
37. #88810C22semidirect
38. #88793C22semidirect
39. #88792C22semidirect
40. #88789C22semidirect
41. #88789C22semidirect
42. #88786C22semidirect
43. D3×C3⋊(C3⋊C8)C22semidirect
44. C3×#3715C22semidirect
45. C3×#3713C22semidirect
50. D3×#235D3semidirect
51. C2×D3×D12D3semidirect
77. #63823D3direct (N × H)
93. C3×C4⋊(C3⋊D3)C23semidirect
95. C3×#634C23semidirect
100. C32×D12C23semidirect
106. C32×Dic6C23semidirect
116. C3⋊(C3⋊(C3⋊C8))C23semidirect
117. C3×C3⋊(C3⋊C8)C23semidirect
127. #3828C2×D3semidirect
128. C2×C4⋊(C3⋊D3)C2×D3semidirect
150. C3×#235C2×D3semidirect
151. C3×#235C2×D3semidirect
162. C2×C3×D12C2×D3semidirect
163. C2×C3×D12C2×D3semidirect
176. D3×D12C2×D3semidirect
177. D3×D12C2×D3semidirect
179. #3799C2×D3semidirect
181. #3795C2×D3semidirect
182. D3×Dic6C2×D3semidirect
195. #3748C2×D3semidirect
213. #3715C2×D3semidirect
223. #3713C2×D3semidirect
330. C4⋊(C3⋊D3)C22×D3semidirect
332. #634C22×D3semidirect
370. C3×D12C22×D3semidirect
371. C3×D12C22×D3semidirect
400. C3×Dic6C22×D3semidirect
401. C3×Dic6C22×D3semidirect
418. C3⋊(C3⋊C8)C22×D3semidirect
430. C32×D3AGL(1,ℤ/8)semidirect
478. #235D32semidirect
488. C2×D12D32semidirect
633. C33C2×AGL(1,ℤ/8)semidirect
741. D12C2×D32semidirect
759. Dic6C2×D32semidirect
807. C3×D3#932semidirect
808. C3×D3#949semidirect
926. C32D3×AGL(1,ℤ/8)semidirect
927. C32C2×#932semidirect
928. C32C2×#949semidirect
1002. D3#63823direct (N × H)
1026. C3C2×#63823semidirect
1027. C3D3×#932semidirect
1028. C3D3×#949semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#2352
C2×C3×D3×D122
#117236612
#117233652
#117233642
D3×#37482
C3×#638232
#117228672
#117228662
D3×#37152
D3×#37132
D3×#9493
D3×#9323
C2×#638233