Finite Group Databasebeta

← D3×#63473 #13149896

Subgroups — D3×#63473 #13149896

Order 1728.

962 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#3699C211yesmaximal, characteristic, complemented
2D3×D4×D9C211yesmaximal, characteristic, complemented
3#11721790C211yesmaximal, characteristic, complemented
4D3×C9×D8C211yesmaximal, characteristic, complemented
5C3×#63473C211yesmaximal, characteristic, complemented
6#11721179C211yesmaximal, characteristic, complemented
7#11721176C211yesmaximal, characteristic, complemented
8#11721175C211yesmaximal, characteristic, complemented
9#11721173C211yesmaximal, characteristic, complemented
10D3×#3673C211yesmaximal, characteristic, complemented
11D3×#3672C211yesmaximal, characteristic, complemented
12#11720819C211yesmaximal, characteristic, complemented
13#11720816C211yesmaximal, characteristic, complemented
14D3×#3664C211yesmaximal, characteristic, complemented
15D3×#3663C211yesmaximal, characteristic, complemented
16D3×#911—31nomaximal
17C2×#63473—31nomaximal
18C22×D3×D9—21no—
19#88742C2211yescharacteristic, complemented
20D4×C3⋊D9C2211yescharacteristic, complemented
21D3×D4×C9C2211yescharacteristic
22D3×D4×C9C2211yescharacteristic, complemented
23C3×#3699C2211yescharacteristic, complemented
24C3×D4×D9C2211yescharacteristic, complemented
25#88668—21no—
26D9×#67—21no—
27D3×#611—21no—
28D3×#611—21no—
29#88663—21no—
30#88662—21no—
31C2×D3×Dic9—21no—
32#88646C2211yescharacteristic, complemented
33D9×D12C2211yescharacteristic, complemented
34D3×D36C2211yescharacteristic
35C4×D3×D9C2211yescharacteristic
36#88639C2211yescharacteristic, complemented
37#88638C2211yescharacteristic, complemented
38D3×Dic18C2211yescharacteristic, complemented
39C3×C9×D8C2211yescharacteristic, complemented
40#88544C2211yescharacteristic, complemented
41#88543C2211yescharacteristic, complemented
42#88524C2211yescharacteristic, complemented
43#88523C2211yescharacteristic, complemented
44C9×#213C2211yescharacteristic, complemented
45C9×#213C2211yescharacteristic, complemented
46C3×#3673C2211yescharacteristic, complemented
47C3×#3672C2211yescharacteristic, complemented
48C9×D24C2211yescharacteristic, complemented
49D3×C8×C9C2211yescharacteristic, complemented
50C3×#3664C2211yescharacteristic, complemented
51C3×#3663C2211yescharacteristic, complemented
52#88424C2211yescharacteristic, complemented
53#88423C2211yescharacteristic, complemented
54#88422C2211yescharacteristic, complemented
55#88421C2211yescharacteristic, complemented
56D3×C9⋊C8C2211yescharacteristic, complemented
57#88416C2211yescharacteristic, complemented
58#88415C2211yescharacteristic, complemented
59#88414C2211yescharacteristic, complemented
60#88413C2211yescharacteristic, complemented
61D3×#237—31no—
62D32×D4—31no—
63#64120—31no—
64C3×#911—31no—
65C3×D3×D8D311yescharacteristic
66#63937—31no—
67#63932—31no—
68D3×#214—31no—
69#63927—31no—
70#63925—31no—
71D3×#213—31no—
72#63798—31no—
73#63795—31no—
74D3×#204—31no—
75D3×ΓL(1,𝔽25)—31no—
76C2×#3699—31no—
77C2×D4×D9—31no—
78C2×C9×D8—31no—
79C2×#3673—31no—
80C2×#3672—31no—
81#63473—31no—
82#63473—31no—
83#63473—31no—
84#63473—31no—
85#63473—31no—
86#63473—31no—
87#63473—31no—
88#63473—61no—
89#63473D311yescharacteristic, direct product factor
90C2×#3664—31no—
91C2×#3663—31no—
92C22×C3⋊D9—21no—
93C22×D3×C9—21no—
94C22×D3×C9—21no—
95C22×C3×D9—21no—
96C2×D3×D9—21no—
97C2×D3×D9—21no—
98C2×D3×D9—21no—
99C2×D3×D9—44no—
100C2×D3×D9D411yescharacteristic
101C3×D4×C9C2311yescharacteristic
102C3×D4×C9C2311yescharacteristic, complemented
103#6233—21no—
104#6233—21no—
105C2×C3⋊Dic9—21no—
106C4⋊(C3⋊D9)C2311yescharacteristic
107C4×C3⋊D9C2311yescharacteristic
108#6226C2311yescharacteristic, complemented
109C9×#67—21no—
110C9×#67—21no—
111C3×#611—21no—
112C3×#611—21no—
113C2×C3×Dic9—21no—
114C9×D12C2311yescharacteristic
115C9×D12C2311yescharacteristic, complemented
116C4×D3×C9C2311yescharacteristic
117C3×D36C2311yescharacteristic
118C3×C4×D9C2311yescharacteristic
119C3×Dic18C2311yescharacteristic, complemented
120#6195—21no—
121#6195—21no—
122#6194—21no—
123#6194—21no—
124D3×Dic9—21no—
125D3×Dic9—21no—
126D3×Dic9—21no—
127D3×Dic9D411yescharacteristic
128#6192—21no—
129(C3⋊D9)⋊C4D411yescharacteristic
130Dic3×D9D411yescharacteristic
131#6189—21no—
132C3×C8×C9C2311yescharacteristic, complemented
133C3⋊(C9⋊C8)C2311yescharacteristic, complemented
134C9×C3⋊C8C2311yescharacteristic, complemented
135C3×C9⋊C8C2311yescharacteristic, complemented
136D3×AGL(1,ℤ/8)—91no—
137C2×#911—91no—
138C22×D32—61no—
139#3830—31no—
140D4×C3⋊D3—31no—
141C3×#237—31no—
142C3×D3×D4—31no—
143C3×D3×D4C2×D311yescharacteristic
144C3×D3×D4C2×D311yescharacteristic
145#3811—61no—
146D3×#67—61no—
147D3×#67—61no—
148D3×#67—61no—
149#3805—61no—
150#3804—61no—
151C2×D3×Dic3—61no—
152#3802—31no—
153D3×D12—31no—
154D3×D12—31no—
155C4×D32—31no—
156#3796—31no—
157#3795—31no—
158D3×Dic6—31no—
159C23×D9—61no—
160C32×D8C2×D311yescharacteristic
161#3754—31no—
162#3753—31no—
163#3744—31no—
164#3743—31no—
165C3×#214—31no—
166C3×#213—31no—
167C3×#213C2×D311yescharacteristic
168C3×#213C2×D311yescharacteristic
169C3×D24C2×D311yescharacteristic
170C3×#204—31no—
171C3×ΓL(1,𝔽25)—31no—
172C3×D3×C8C2×D311yescharacteristic
173#3717—31no—
174#3716—31no—
175#3716—31no—
176#3715—31no—
177#3714—31no—
178#3713—31no—
179#3712—31no—
180#3711—31no—
181D3×C3⋊C8—31no—
182C2×D4×C9—31no—
183C2×D4×C9—31no—
184C2×#611—61no—
185C2×#611—61no—
186C22×Dic9—61no—
187#3699—31no—
188#3699—31no—
189#3699—31no—
190#3699—61no—
191#3699—61no—
192#3699—61no—
193#3699C2×D311yescharacteristic, complemented
194D4×D9—31no—
195D4×D9—31no—
196D4×D9—31no—
197D4×D9—61no—
198D4×D9—61no—
199D4×D9—61no—
200D4×D9C2×D311yescharacteristic, complemented
201C2×D36—31no—
202C2×C4×D9—31no—
203C2×Dic18—31no—
204C9×D8—21no—
205C9×D8—31no—
206C9×D8—31no—
207C9×D8—31no—
208C9×D8C2×D311yescharacteristic, complemented
209C2×C8×C9—31no—
210#3673—31no—
211#3673—31no—
212#3673—31no—
213#3673—61no—
214#3673C2×D311yescharacteristic, complemented
215#3672—31no—
216#3672—31no—
217#3672—31no—
218#3672—61no—
219#3672C2×D311yescharacteristic, complemented
220C2×C9⋊C8—31no—
221#3664—31no—
222#3664—31no—
223#3664—31no—
224#3664—61no—
225#3664C2×D311yescharacteristic, complemented
226#3663—31no—
227#3663—31no—
228#3663—31no—
229#3663—61no—
230#3663C2×D311yescharacteristic, complemented
231C22×C3×C9—21no—
232C22×C3×C9—21no—
233C2×C3⋊D9—21no—
234C2×C3⋊D9—42no—
235C2×C3⋊D9C2×D411yescharacteristic
236C2×D3×C9—21no—
237C2×D3×C9—21no—
238C2×D3×C9—42no—
239C2×D3×C9—42no—
240C2×D3×C9C2×D411yescharacteristic
241C2×C3×D9—21no—
242C2×C3×D9—42no—
243C2×C3×D9C2×D411yescharacteristic
244D3×D9—22no—
245D3×D9—42no—
246D3×D9—42no—
247D3×D9—42no—
248C3×C4×C9C2411yescharacteristic
249C3⋊Dic9—21no—
250C3⋊Dic9C2×D411yescharacteristic
251C9×Dic3C2×D411yescharacteristic
252C3×Dic9—21no—
253C3×Dic9C2×D411yescharacteristic
254D3×#41—91no—
255C2×#237—91no—
256C2×D3×D4—91no—
257C2×D3×D4—91no—
258C3×AGL(1,ℤ/8)—91no—
259C2×C3×D8—31no—
260#949—91no—
261C2×#214—91no—
262#932—91no—
263C2×#213—91no—
264#914—91no—
265#914—91no—
266D3×SD16—91no—
267D3×SD16—91no—
268#911—31no—
269#911—91no—
270#911—91no—
271#911—91no—
272#911—91no—
273#911—91no—
274#911—91no—
275#911—91no—
276#911—91no—
277#911—91no—
278#911—181no—
279D3×D8—91no—
280D3×D8D911yescharacteristic, complemented
281#908—91no—
282D3×M16—91no—
283C2×#204—91no—
284C2×ΓL(1,𝔽25)—91no—
285C22×C3⋊D3—61no—
286C22×C3×D3—21no—
287C22×C3×D3—21no—
288C22×C3×D3—61no—
289C2×D32—31no—
290C2×D32—61no—
291C2×D32—61no—
292C2×D32—61no—
293C2×D32—124no—
294C32×D4C22×D311yescharacteristic
295C32×D4C22×D311yescharacteristic
296#638—61no—
297#638—61no—
298C2×C3⋊Dic3—61no—
299C4⋊(C3⋊D3)—31no—
300C4×C3⋊D3—31no—
301#634—31no—
302C3×#67—21no—
303C3×#67—21no—
304C3×#67—61no—
305C3×#67—61no—
306C2×C3×Dic3—61no—
307C3×D12—31no—
308C3×D12C22×D311yescharacteristic
309C3×D12C22×D311yescharacteristic
310C3×C4×D3—31no—
311C3×C4×D3C22×D311yescharacteristic
312C3×Dic6—31no—
313#627—61no—
314#626—61no—
315#626—61no—
316#626—61no—
317#625—61no—
318#625—61no—
319#624—31no—
320D3×Dic3—31no—
321D3×Dic3—31no—
322D3×Dic3—61no—
323D3×Dic3—61no—
324D3×Dic3—61no—
325C23×C9—61no—
326C23×C9—61no—
327C22×D9—21no—
328C22×D9—31no—
329C22×D9—61no—
330C22×D9—61no—
331C22×D9—61no—
332C22×D9—61no—
333C22×D9—121no—
334C22×D9—124no—
335C32×C8C22×D311yescharacteristic
336C3⋊(C3⋊C8)—31no—
337C3×C3⋊C8—31no—
338C3×C3⋊C8C22×D311yescharacteristic
339D4×C9—21no—
340D4×C9—21no—
341D4×C9—31no—
342D4×C9—31no—
343D4×C9—61no—
344D4×C9—61no—
345D4×C9C22×D311yescharacteristic
346D4×C9C22×D311yescharacteristic, complemented
347C2×C4×C9—31no—
348#611—21no—
349#611—21no—
350#611—61no—
351#611—61no—
352#611—61no—
353#611—61no—
354#611—61no—
355#611—61no—
356#611—121no—
357#611—121no—
358C2×Dic9—21no—
359C2×Dic9—31no—
360C2×Dic9—61no—
361C2×Dic9—61no—
362C2×Dic9—61no—
363C2×Dic9—61no—
364C2×Dic9—121no—
365D36—31no—
366D36—61no—
367D36—61no—
368D36C22×D311yescharacteristic
369C4×D9—31no—
370C4×D9—31no—
371C4×D9—31no—
372C4×D9—61no—
373C4×D9C22×D311yescharacteristic
374Dic18—31no—
375Dic18—61no—
376Dic18—61no—
377Dic18C22×D311yescharacteristic, complemented
378C8×C9—21no—
379C8×C9—31no—
380C8×C9C22×D311yescharacteristic, complemented
381C9⋊C8—31no—
382C9⋊C8—61no—
383C9⋊C8C22×D311yescharacteristic, complemented
384C2×AGL(1,ℤ/8)—271noSylow
385C2×C3×C9—41no—
386C2×C3×C9—41no—
387C2×C3×C9C22×D411yescharacteristic
388C3⋊D9—21no—
389C3⋊D9—41no—
390D3×C9—41no—
391D3×C9—41no—
392D3×C9AGL(1,ℤ/8)12yescomplemented
393C3×D9—21no—
394C3×D9—41no—
395C23×D3—181no—
396C23×D3—181no—
397C3×#41—91no—
398C2×C3×D4—31no—
399C2×C3×D4—31no—
400C2×C3×D4—91no—
401C2×#67—181no—
402C2×#67—181no—
403C2×#67—181no—
404C22×Dic3—181no—
405#239—91no—
406D3×Q8—91no—
407#237—31no—
408#237—91no—
409#237—91no—
410#237—91no—
411#237—91no—
412#237—181no—
413#237—181no—
414#237—181no—
415#237—181no—
416D3×D4—31no—
417D3×D4—91no—
418D3×D4—91no—
419D3×D4—91no—
420D3×D4—91no—
421D3×D4—91no—
422D3×D4—91no—
423D3×D4—181no—
424D3×D4—181no—
425D3×D4—181no—
426D3×D4—181no—
427D3×D4—181no—
428D3×D4—181no—
429D3×D4C2×D911yescharacteristic
430D3×D4C2×D911yescharacteristic, complemented
431#235—91no—
432#235—181no—
433C2×D12—91no—
434C2×D12—91no—
435C2×C4×D3—91no—
436C2×C4×D3—91no—
437C2×C4×D3—181no—
438C2×Dic6—91no—
439C3×SD16—91no—
440C3×SD16—91no—
441C3×D8—21no—
442C3×D8—31no—
443C3×D8—31no—
444C3×D8—31no—
445C3×D8—91no—
446C3×D8C2×D911yescharacteristic, complemented
447C3×D8D3211yescharacteristic
448C3×M16—91no—
449C2×C3×C8—31no—
450#215—91no—
451#215—91no—
452#214—31no—
453#214—91no—
454#214—91no—
455#214—91no—
456#214—91no—
457#214—91no—
458#214—181no—
459#213—31no—
460#213—91no—
461#213—91no—
462#213—91no—
463#213—91no—
464#213—91no—
465#213—181no—
466#213C2×D911yescharacteristic, complemented
467#213C2×D911yescharacteristic, complemented
468#208—91no—
469C2×C3⋊C8—91no—
470D24—91no—
471D24C2×D911yescharacteristic, complemented
472#204—31no—
473#204—91no—
474#204—91no—
475#204—91no—
476#204—91no—
477#204—91no—
478#204—181no—
479ΓL(1,𝔽25)—31no—
480ΓL(1,𝔽25)—91no—
481ΓL(1,𝔽25)—91no—
482ΓL(1,𝔽25)—91no—
483ΓL(1,𝔽25)—91no—
484ΓL(1,𝔽25)—91no—
485ΓL(1,𝔽25)—181no—
486D3×C8—91no—
487D3×C8C2×D911yescharacteristic, complemented
488C22×C32—21no—
489C22×C32—21no—
490C2×C3⋊D3—31no—
491C2×C3⋊D3—61no—
492C2×C3⋊D3—122no—
493C2×C3×D3—21no—
494C2×C3×D3—21no—
495C2×C3×D3—31no—
496C2×C3×D3—42no—
497C2×C3×D3—42no—
498C2×C3×D3—61no—
499C2×C3×D3—122no—
500C2×C3×D3D3×D411yescharacteristic
501D32—62no—
502D32—122no—
503D32—122no—
504D32—122no—
505C32×C4C23×D311yescharacteristic
506C3⋊Dic3—31no—
507C3⋊Dic3—61no—
508C3×Dic3—31no—
509C3×Dic3—61no—
510C3×Dic3D3×D411yescharacteristic
511C22×C9—21no—
512C22×C9—21no—
513C22×C9—31no—
514C22×C9—41no—
515C22×C9—41no—
516C22×C9—61no—
517C22×C9—61no—
518C22×C9—122no—
519C22×C9—122no—
520C2×D9—21no—
521C2×D9—31no—
522C2×D9—42no—
523C2×D9—61no—
524C2×D9—62no—
525C2×D9—61no—
526C2×D9—121no—
527C2×D9—122no—
528C2×D9—122no—
529C2×D9—122no—
530C2×D9—122no—
531C2×D9—242no—
532C2×D9D3×D411yescharacteristic
533C4×C9—21no—
534C4×C9—31no—
535C4×C9C23×D311yescharacteristic
536Dic9—21no—
537Dic9—31no—
538Dic9—61no—
539Dic9—61no—
540Dic9—121no—
541Dic9D3×D411yescharacteristic
542C2×#41—271no—
543C22×D4—271no—
544AGL(1,ℤ/8)—91no—
545AGL(1,ℤ/8)—271no—
546AGL(1,ℤ/8)—271no—
547AGL(1,ℤ/8)—271no—
548AGL(1,ℤ/8)—271no—
549AGL(1,ℤ/8)—271no—
550AGL(1,ℤ/8)—271no—
551AGL(1,ℤ/8)—271no—
552C2×SD16—271no—
553C2×SD16—271no—
554C2×D8—31no—
555C2×D8—271no—
556C2×M16—271no—
557C3×C9C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
558C23×C3—61no—
559C23×C3—61no—
560C23×C3—181no—
561C22×D3—21no—
562C22×D3—21no—
563C22×D3—61no—
564C22×D3—91no—
565C22×D3—91no—
566C22×D3—181no—
567C22×D3—181no—
568C22×D3—181no—
569C22×D3—181no—
570C22×D3—181no—
571C22×D3—181no—
572C22×D3—181no—
573C22×D3—181no—
574C22×D3—361no—
575C22×D3—364no—
576C22×D3—364no—
577C3×Q8—91no—
578C3×D4—21no—
579C3×D4—21no—
580C3×D4—31no—
581C3×D4—31no—
582C3×D4—61no—
583C3×D4—61no—
584C3×D4—91no—
585C3×D4—181no—
586C3×D4—181no—
587C3×D4C22×D911yescharacteristic
588C3×D4C22×D911yescharacteristic, complemented
589C3×D4C2×D3211yescharacteristic
590C3×D4C2×D3211yescharacteristic
591C2×C3×C4—31no—
592C2×C3×C4—91no—
593C2×C3×C4—181no—
594#67—21no—
595#67—21no—
596#67—61no—
597#67—61no—
598#67—181no—
599#67—181no—
600#67—181no—
601#67—181no—
602#67—181no—
603#67—181no—
604#67—181no—
605#67—181no—
606#67—181no—
607#67—181no—
608#67—181no—
609#67—361no—
610#67—361no—
611C2×Dic3—61no—
612C2×Dic3—91no—
613C2×Dic3—91no—
614C2×Dic3—181no—
615C2×Dic3—181no—
616C2×Dic3—181no—
617C2×Dic3—181no—
618C2×Dic3—181no—
619C2×Dic3—361no—
620D12—31no—
621D12—91no—
622D12—91no—
623D12—181no—
624D12—181no—
625D12—181no—
626D12—181no—
627D12C22×D911yescharacteristic
628D12C22×D911yescharacteristic, complemented
629C4×D3—31no—
630C4×D3—91no—
631C4×D3—91no—
632C4×D3—91no—
633C4×D3—91no—
634C4×D3—91no—
635C4×D3—91no—
636C4×D3—181no—
637C4×D3—181no—
638C4×D3—181no—
639C4×D3—181no—
640C4×D3C22×D911yescharacteristic
641Dic6—31no—
642Dic6—91no—
643Dic6—91no—
644Dic6—181no—
645Dic6—181no—
646Dic6—181no—
647C3×C8—21no—
648C3×C8—31no—
649C3×C8—91no—
650C3×C8C22×D911yescharacteristic, complemented
651C3×C8C2×D3211yescharacteristic
652C3⋊C8—31no—
653C3⋊C8—91no—
654C3⋊C8—91no—
655C3⋊C8—181no—
656C3⋊C8C22×D911yescharacteristic, complemented
657C2×C32—41no—
658C2×C32—41no—
659C2×C32C2×D3×D411yescharacteristic
660C3⋊D3—61no—
661C3⋊D3—121no—
662C3×D3—41no—
663C3×D3—41no—
664C3×D3—61no—
665C3×D3—121no—
666C3×D3#91112yes—
667C2×C9—21no—
668C2×C9—32no—
669C2×C9—41no—
670C2×C9—41no—
671C2×C9—81no—
672C2×C9—81no—
673C2×C9—121no—
674C2×C9—121no—
675C2×C9C2×D3×D411yescharacteristic
676D9—21no—
677D9—41no—
678D9—61no—
679D9—121no—
680D9—121no—
681D9—241no—
682C24—541no—
683#41—91no—
684#41—271no—
685#41—271no—
686#41—271no—
687#41—541no—
688#41—541no—
689C2×Q8—271no—
690C2×D4—31no—
691C2×D4—31no—
692C2×D4—91no—
693C2×D4—271no—
694C2×D4—271no—
695C2×D4—271no—
696C2×D4—271no—
697C2×D4—541no—
698C2×D4—541no—
699C2×D4—541no—
700C2×D4—541no—
701C22×C4—271no—
702C22×C4—541no—
703SD16—91no—
704SD16—91no—
705SD16—271no—
706SD16—271no—
707SD16—271no—
708SD16—271no—
709SD16—271no—
710SD16—271no—
711D8—31no—
712D8—31no—
713D8—31no—
714D8—91no—
715D8—271no—
716D8—271no—
717D8—271no—
718D8D3×D911yescharacteristic, complemented
719M16—91no—
720M16—271no—
721M16—271no—
722M16—271no—
723C2×C8—31no—
724C2×C8—271no—
725C22×C3—21no—
726C22×C3—21no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—31no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—61no—
733C22×C3—61no—
734C22×C3—91no—
735C22×C3—122no—
736C22×C3—122no—
737C22×C3—181no—
738C22×C3—362no—
739C2×D3—21no—
740C2×D3—21no—
741C2×D3—31no—
742C2×D3—42no—
743C2×D3—42no—
744C2×D3—61no—
745C2×D3—91no—
746C2×D3—91no—
747C2×D3—122no—
748C2×D3—181no—
749C2×D3—182no—
750C2×D3—182no—
751C2×D3—181no—
752C2×D3—181no—
753C2×D3—361no—
754C2×D3—362no—
755C2×D3—362no—
756C2×D3—362no—
757C2×D3—362no—
758C2×D3—362no—
759C2×D3—362no—
760C2×D3—362no—
761C2×D3—362no—
762C2×D3—722no—
763C2×D3D4×D911yescharacteristic
764C3×C4—21no—
765C3×C4—31no—
766C3×C4—91no—
767C3×C4—181no—
768C3×C4C23×D911yescharacteristic
769C3×C4C22×D3211yescharacteristic
770Dic3—31no—
771Dic3—61no—
772Dic3—91no—
773Dic3—91no—
774Dic3—181no—
775Dic3—181no—
776Dic3—181no—
777Dic3—361no—
778Dic3D4×D911yescharacteristic
779C32C2×#91111yescharacteristic
780C9—21no—
781C9D3×AGL(1,ℤ/8)11yescharacteristic, complemented
782C23—61no—
783C23—61no—
784C23—181no—
785C23—271no—
786C23—541no—
787C23—541no—
788C23—541no—
789C23—541no—
790C23—1084no—
791Q8—91no—
792Q8—271no—
793Q8—541no—
794D4—31no—
795D4—31no—
796D4—61no—
797D4—61no—
798D4—91no—
799D4—181no—
800D4—181no—
801D4—271no—
802D4—541no—
803D4—541no—
804D4—541no—
805D4—541no—
806D4—541no—
807D4—541no—
808D4—541no—
809D4C2×D3×D911yescharacteristic
810D4C2×D3×D911yescharacteristic, complemented
811C2×C4—31no—
812C2×C4—91no—
813C2×C4—181no—
814C2×C4—271no—
815C2×C4—271no—
816C2×C4—271no—
817C2×C4—271no—
818C2×C4—541no—
819C2×C4—541no—
820C2×C4—541no—
821C2×C4—541no—
822C8—31no—
823C8—91no—
824C8—271no—
825C8C2×D3×D911yescharacteristic, complemented
826C2×C3—21no—
827C2×C3—32no—
828C2×C3—41no—
829C2×C3—41no—
830C2×C3—41no—
831C2×C3—41no—
832C2×C3—81no—
833C2×C3—81no—
834C2×C3—121no—
835C2×C3—121no—
836C2×C3—181no—
837C2×C3—361no—
838C2×C3C2×D4×D911yescharacteristic
839C2×C3D32×D411yescharacteristic
840D3—41no—
841D3—41no—
842D3—61no—
843D3—121no—
844D3—181no—
845D3—181no—
846D3—361no—
847D3—361no—
848D3—361no—
849D3—721no—
850D3#6347312yesdirect product factor
851C22—21no—
852C22—21no—
853C22—31no—
854C22—61no—
855C22—61no—
856C22—91no—
857C22—122no—
858C22—122no—
859C22—181no—
860C22—271no—
861C22—362no—
862C22—542no—
863C22—541no—
864C22—1082no—
865C22—1082no—
866C22—1082no—
867C22—1082no—
868C4—31no—
869C4—91no—
870C4—181no—
871C4—271no—
872C4—541no—
873C4C22×D3×D911yescharacteristic
874C3—21no—
875C3C2×#6347311yescharacteristic, complemented
876C3D3×#91111yescharacteristic
877C2—32no—
878C2—41no—
879C2—41no—
880C2—121no—
881C2—121no—
882C2—181no—
883C2—361no—
884C2—541no—
885C2—1081no—
886C2D3×D4×D911yescharacteristic
subgroupG/H
centerC2D3×D4×D9
commutator, cosocleC3×C4×C9C24
FrattiniC3×C4C22×D32
FittingC3×C9×D8C22
socleC2×C32C2×D3×D4
hypercenterD8D3×D9
hypocenterC3×C9C2×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C9 ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2 ◁ C4 ◁ D8

Complements

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

NH ≅ G/Ntype
1. D3×#3699C2semidirect
2. D3×D4×D9C2semidirect
3. #11721790C2semidirect
4. D3×C9×D8C2semidirect
5. C3×#63473C2semidirect
6. #11721179C2semidirect
7. #11721176C2semidirect
8. #11721175C2semidirect
9. #11721173C2semidirect
10. D3×#3673C2semidirect
11. D3×#3672C2semidirect
12. #11720819C2semidirect
13. #11720816C2semidirect
14. D3×#3664C2semidirect
15. D3×#3663C2semidirect
19. #88742C22semidirect
20. D4×C3⋊D9C22semidirect
22. D3×D4×C9C22semidirect
23. C3×#3699C22semidirect
24. C3×D4×D9C22semidirect
32. #88646C22semidirect
33. D9×D12C22semidirect
36. #88639C22semidirect
37. #88638C22semidirect
38. D3×Dic18C22semidirect
39. C3×C9×D8C22semidirect
40. #88544C22semidirect
41. #88543C22semidirect
42. #88524C22semidirect
43. #88523C22semidirect
44. C9×#213C22semidirect
45. C9×#213C22semidirect
46. C3×#3673C22semidirect
47. C3×#3672C22semidirect
48. C9×D24C22semidirect
49. D3×C8×C9C22semidirect
50. C3×#3664C22semidirect
51. C3×#3663C22semidirect
52. #88424C22semidirect
53. #88423C22semidirect
54. #88422C22semidirect
55. #88421C22semidirect
56. D3×C9⋊C8C22semidirect
57. #88416C22semidirect
58. #88415C22semidirect
59. #88414C22semidirect
60. #88413C22semidirect
89. #63473D3direct (N × H)
102. C3×D4×C9C23semidirect
108. #6226C23semidirect
115. C9×D12C23semidirect
119. C3×Dic18C23semidirect
132. C3×C8×C9C23semidirect
133. C3⋊(C9⋊C8)C23semidirect
134. C9×C3⋊C8C23semidirect
135. C3×C9⋊C8C23semidirect
193. #3699C2×D3semidirect
200. D4×D9C2×D3semidirect
208. C9×D8C2×D3semidirect
214. #3673C2×D3semidirect
219. #3672C2×D3semidirect
225. #3664C2×D3semidirect
230. #3663C2×D3semidirect
280. D3×D8D9semidirect
346. D4×C9C22×D3semidirect
377. Dic18C22×D3semidirect
380. C8×C9C22×D3semidirect
383. C9⋊C8C22×D3semidirect
392. D3×C9AGL(1,ℤ/8)semidirect
430. D3×D4C2×D9semidirect
446. C3×D8C2×D9semidirect
466. #213C2×D9semidirect
467. #213C2×D9semidirect
471. D24C2×D9semidirect
487. D3×C8C2×D9semidirect
557. C3×C9C2×AGL(1,ℤ/8)semidirect
588. C3×D4C22×D9semidirect
628. D12C22×D9semidirect
650. C3×C8C22×D9semidirect
656. C3⋊C8C22×D9semidirect
718. D8D3×D9semidirect
781. C9D3×AGL(1,ℤ/8)semidirect
810. D4C2×D3×D9semidirect
825. C8C2×D3×D9semidirect
850. D3#63473direct (N × H)
875. C3C2×#63473semidirect

Maximal subgroups

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

subgroupindex
D3×#36992
D3×D4×D92
#117217902
D3×C9×D82
C3×#634732
#117211792
#117211762
#117211752
#117211732
D3×#36732
D3×#36722
#117208192
#117208162
D3×#36642
D3×#36632
D3×#9113
C2×#634733