Finite Group Databasebeta

← D3×#63830 #13170554

Subgroups — D3×#63830 #13170554

Order 1728.

1532 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#3828C211yesmaximal, characteristic, complemented
2C2×C3×D3×D12C211yesmaximal, characteristic, complemented
3#11723661C211yesmaximal, characteristic, complemented
4#11723378C211yesmaximal, characteristic, complemented
5#11723370C211yesmaximal, characteristic, complemented
6C3×#63830C211yesmaximal, characteristic, complemented
7C3×D3×#208C211yesmaximal, characteristic, complemented
8#11722869C212yesmaximal, complemented
9#11722868C212yesmaximal, complemented
10D3×#3716C212yesmaximal, complemented
11D3×#3714C212yesmaximal, complemented
12D3×#932—31nomaximal
13C2×#63830—31nomaximal
14D3×#908—31nomaximal
15C22×C3×D32—21no—
16#89076C2211yescharacteristic, complemented
17C3×#3828C2211yescharacteristic, complemented
18C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
19C2×C32×D12C2211yescharacteristic, complemented
20C2×C32×C4×D3C2211yescharacteristic
21D3×#638—21no—
22#89031—21no—
23D3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
24C4×D3×C3⋊D3—21no—
25#89022C2211yescharacteristic, complemented
26#89021C2211yescharacteristic, complemented
27#89020—21no—
28D3×#634C2211yescharacteristic, complemented
29C2×C3×#626—21no—
30C3×D3×D12—21no—
31C3×D3×D12—21no—
32C3×D3×D12C2212yes—
33C3×D3×D12C2212yescomplemented
34C3×#3748C2211yescharacteristic, complemented
35C32×#208C2211yescharacteristic, complemented
36#88811C2212yescomplemented
37#88810C2212yescomplemented
38#88796C2212yescomplemented
39#88794C2212yescomplemented
40#88791C2212yescomplemented
41#88790C2212yescomplemented
42C3×#3716C2212yescomplemented
43C3×#3714C2212yescomplemented
44C3×#3711C2212yescomplemented
45C3×D3×C3⋊C8C2212yescomplemented
46C2×#3828—31no—
47C2×C3×D3×D4—31no—
48C22×C3×D12—31no—
49D3×#235—31no—
50D3×#235—31no—
51D3×#235—61no—
52C2×D3×D12D311yescharacteristic, complemented
53#64141—31no—
54#64117—31no—
55C3×#932—31no—
56C2×C3×#208—31no—
57C3×#908—31no—
58C3×D3×M16—31no—
59#63934—32no—
60#63932—32no—
61D3×#214—32no—
62D3×#213—32no—
63#63830—31no—
64#63830—31no—
65#63830—31no—
66#63830—31no—
67#63830—31no—
68#63830—32no—
69#63830—32no—
70#63830—61no—
71#63830—61no—
72#63830D311yescharacteristic, direct product factor
73C2×#3716—32no—
74#63825—31no—
75C2×#3714—32no—
76#63823—31no—
77D3×#208D311yescharacteristic, complemented
78#63795—32no—
79#63794—32no—
80D3×D24—32no—
81D3×#204—32no—
82C22×C3×C3⋊D3—21no—
83C22×C32×D3—21no—
84C22×C32×D3D411yescharacteristic
85C2×D3×C3⋊D3—21no—
86C2×C3×D32—22no—
87C2×C3×D32—22no—
88C2×C3×D32—44no—
89C2×C33×C4C2311yescharacteristic
90#6312—21no—
91C4⋊(C3⋊(C3⋊D3))C2311yescharacteristic, complemented
92C4×C3⋊(C3⋊D3)—21no—
93#6308C2311yescharacteristic, complemented
94C3×#638—21no—
95C3×C4⋊(C3⋊D3)—21no—
96C3×C4⋊(C3⋊D3)C2312yes—
97C3×C4⋊(C3⋊D3)C2311yescharacteristic, complemented
98C3×C4×C3⋊D3—21no—
99C3×#634C2311yescharacteristic, complemented
100C2×C32×Dic3D411yescharacteristic
101C32×D12—21no—
102C32×D12C2312yes—
103C32×C4×D3D411yescharacteristic
104C32×C4×D3D411yescharacteristic
105C32×C4×D3C2311yescharacteristic
106C32×C4×D3C2311yescharacteristic
107#6293—21no—
108#6292—21no—
109#6291—21no—
110#6290—21no—
111#6289—21no—
112Dic3×C3⋊D3—21no—
113D3×C3⋊Dic3—21no—
114C3×#626—22no—
115C3×#626—22no—
116C3×C3⋊(C3⋊C8)C2312yescomplemented
117C32×C3⋊C8C2312yescomplemented
118C2×#932—91no—
119D3×AGL(1,ℤ/8)—91no—
120C2×#908—91no—
121C23×C3×D3—61no—
122C23×C3×D3—61no—
123C22×D32—21no—
124C2×C32×D4—31no—
125C22×C32×C4—31no—
126C2×#638—61no—
127#3828—31no—
128#3828—31no—
129#3828—31no—
130#3828—31no—
131#3828—31no—
132#3828—61no—
133#3828—61no—
134#3828—61no—
135#3828—61no—
136#3828—61no—
137#3828—121no—
138#3828C2×D311yescharacteristic, complemented
139C2×C4⋊(C3⋊D3)—31no—
140C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
141C2×C4×C3⋊D3—61no—
142C2×#634—31no—
143C2×C3×#67—61no—
144C3×D3×D4—32no—
145C3×D3×D4—32no—
146C3×D3×D4—61no—
147C3×D3×D4—61no—
148C3×#235—31no—
149C3×#235—31no—
150C3×#235—61no—
151C2×C3×D12—21no—
152C2×C3×D12—31no—
153C2×C3×D12—31no—
154C2×C3×D12—32no—
155C2×C3×D12—32no—
156C2×C3×D12—61no—
157C2×C3×D12—61no—
158C2×C3×D12—61no—
159C2×C3×D12—61no—
160C2×C3×D12C2×D311yescharacteristic, complemented
161C2×C3×D12C2×D311yescharacteristic, complemented
162C2×C3×C4×D3—21no—
163C2×C3×C4×D3C2×D311yescharacteristic
164C2×C3×C4×D3C2×D311yescharacteristic
165D3×#67—62no—
166D3×#67—61no—
167D3×#67—61no—
168C2×#626—21no—
169#3804—62no—
170#3804—61no—
171#3804—61no—
172D3×D12—21no—
173D3×D12—21no—
174D3×D12—31no—
175D3×D12—31no—
176D3×D12—61no—
177D3×D12C2×D312yes—
178D3×D12C2×D312yescomplemented
179C4×D32—62no—
180C4×D32—61no—
181C4×D32—61no—
182#3799—31no—
183#3799—31no—
184#3799—61no—
185#3798—62no—
186#3798—61no—
187#3798—61no—
188#3795—31no—
189#3795—31no—
190#3795—61no—
191D3×Dic6—31no—
192D3×Dic6—31no—
193D3×Dic6—61no—
194C32×M16—31no—
195#3754—32no—
196#3753—32no—
197#3748C2×D311yescharacteristic, complemented
198#3745—32no—
199#3744—32no—
200C3×#214—32no—
201C3×#213—32no—
202C3×#208—21no—
203C3×#208—31no—
204C3×#208—31no—
205C3×#208—32no—
206C3×#208—61no—
207C3×#208C2×D311yescharacteristic, complemented
208C3×#208C2×D311yescharacteristic, complemented
209C2×C3×C3⋊C8—32no—
210C3×D24—32no—
211C3×#204—32no—
212C3×ΓL(1,𝔽25)—32no—
213C3×D3×C8—32no—
214#3717—32no—
215#3716—32no—
216#3716—32no—
217#3716—32no—
218#3716—32no—
219#3716—32no—
220#3716—62no—
221#3716—62no—
222#3716C2×D312yescomplemented
223#3715—32no—
224#3714—32no—
225#3714—32no—
226#3714—32no—
227#3714—32no—
228#3714—32no—
229#3714—32no—
230#3714—62no—
231#3714—62no—
232#3714C2×D312yescomplemented
233#3713—32no—
234#3711C2×D312yescomplemented
235D3×C3⋊C8C2×D312yescomplemented
236C22×C33C2×D411yescharacteristic
237C2×C3⋊(C3⋊D3)—21no—
238C2×C3×C3⋊D3—21no—
239C2×C3×C3⋊D3—22no—
240C2×C3×C3⋊D3—42no—
241C2×C32×D3—22no—
242C2×C32×D3—22no—
243C2×C32×D3—42no—
244C2×C32×D3C2×D411yescharacteristic
245C2×C32×D3C2×D411yescharacteristic
246D3×C3⋊D3—42no—
247C3×D32—44no—
248C3×D32—44no—
249C33×C4C2×D411yescharacteristic
250C33×C4C2411yescharacteristic
251C3⋊(C3⋊Dic3)—21no—
252C3×C3⋊Dic3—21no—
253C32×Dic3C2×D411yescharacteristic
254C32×Dic3C2×D411yescharacteristic
255C22×C3×D4—91no—
256D3×#41—91no—
257C2×D3×D4—31no—
258C2×#235—91no—
259C2×#235—91no—
260C2×#235—181no—
261C22×D12—31no—
262C3×AGL(1,ℤ/8)—91no—
263C2×C3×M16—91no—
264#949—91no—
265C2×#214—92no—
266#932—31no—
267#932—92no—
268#932—92no—
269#932—91no—
270#932—91no—
271#932—91no—
272#932—91no—
273#932—181no—
274C2×#213—92no—
275C2×#208—31no—
276#914—92no—
277D3×SD16—92no—
278#911—92no—
279D3×D8—92no—
280#908—31no—
281#908—92no—
282#908—92no—
283#908—91no—
284#908—91no—
285#908—91no—
286#908—91no—
287#908—181no—
288D3×M16—31no—
289C2×D24—92no—
290C2×#204—92no—
291C23×C32—31no—
292C23×C32—61no—
293C22×C3⋊D3—21no—
294C22×C3⋊D3—61no—
295C22×C3×D3—21no—
296C22×C3×D3—21no—
297C22×C3×D3—21no—
298C22×C3×D3—41no—
299C22×C3×D3—62no—
300C22×C3×D3—62no—
301C22×C3×D3—61no—
302C22×C3×D3—61no—
303C22×C3×D3—62no—
304C22×C3×D3—62no—
305C22×C3×D3—121no—
306C22×C3×D3—124no—
307C22×C3×D3—124no—
308C22×C3×D3D1211yescharacteristic
309C22×C3×D3#6711yescharacteristic
310C2×D32—22no—
311C2×D32—22no—
312C2×D32—44no—
313C2×D32—62no—
314C2×D32—61no—
315C2×D32—61no—
316C32×D4—32no—
317C32×D4—61no—
318C2×C32×C4—21no—
319C2×C32×C4—21no—
320C2×C32×C4—21no—
321C2×C32×C4—31no—
322C2×C32×C4—31no—
323C2×C32×C4—31no—
324C2×C32×C4—31no—
325C2×C32×C4—31no—
326C2×C32×C4—41no—
327C2×C32×C4C22×D311yescharacteristic
328C2×C32×C4C22×D311yescharacteristic
329C2×C32×C4C22×D311yescharacteristic
330#638—21no—
331#638—61no—
332#638—61no—
333#638—61no—
334#638—62no—
335#638—61no—
336#638—61no—
337#638—121no—
338#638—121no—
339#638—122no—
340C2×C3⋊Dic3—61no—
341C4⋊(C3⋊D3)—21no—
342C4⋊(C3⋊D3)—31no—
343C4⋊(C3⋊D3)—31no—
344C4⋊(C3⋊D3)—31no—
345C4⋊(C3⋊D3)—61no—
346C4⋊(C3⋊D3)—61no—
347C4⋊(C3⋊D3)—61no—
348C4⋊(C3⋊D3)—61no—
349C4⋊(C3⋊D3)—121no—
350C4⋊(C3⋊D3)C22×D312yes—
351C4⋊(C3⋊D3)C22×D311yescharacteristic, complemented
352C4×C3⋊D3—21no—
353C4×C3⋊D3—61no—
354C4×C3⋊D3—61no—
355C4×C3⋊D3—61no—
356C4×C3⋊D3—62no—
357C4×C3⋊D3—61no—
358C4×C3⋊D3—61no—
359C4×C3⋊D3—121no—
360C4×C3⋊D3—121no—
361C4×C3⋊D3—122no—
362#634—31no—
363#634—31no—
364#634—31no—
365#634—61no—
366#634—61no—
367#634—61no—
368#634—61no—
369#634—121no—
370#634C22×D311yescharacteristic, complemented
371C3×#67—62no—
372C3×#67—61no—
373C3×#67—61no—
374C3×#67—62no—
375C3×#67—62no—
376C2×C3×Dic3—21no—
377C2×C3×Dic3D1211yescharacteristic
378C2×C3×Dic3#6711yescharacteristic
379C3×D12—21no—
380C3×D12—21no—
381C3×D12—22no—
382C3×D12—31no—
383C3×D12—32no—
384C3×D12—32no—
385C3×D12—31no—
386C3×D12—41no—
387C3×D12—61no—
388C3×D12—62no—
389C3×D12—62no—
390C3×D12—62no—
391C3×D12—61no—
392C3×D12—61no—
393C3×D12—121no—
394C3×D12C22×D312yes—
395C3×D12C22×D312yes—
396C3×C4×D3—21no—
397C3×C4×D3—21no—
398C3×C4×D3—21no—
399C3×C4×D3—21no—
400C3×C4×D3—62no—
401C3×C4×D3—61no—
402C3×C4×D3—61no—
403C3×C4×D3D1211yescharacteristic
404C3×C4×D3D1211yescharacteristic
405C3×C4×D3#6711yescharacteristic
406C3×C4×D3#6711yescharacteristic
407C3×C4×D3C22×D311yescharacteristic
408C3×C4×D3C22×D311yescharacteristic
409C3×C4×D3C22×D311yescharacteristic
410C3×C4×D3C22×D311yescharacteristic
411C3×Dic6—31no—
412C3×Dic6—31no—
413C3×Dic6—61no—
414#627—62no—
415#627—61no—
416#627—61no—
417#626—22no—
418#626—22no—
419#626—62no—
420#626—62no—
421#626—61no—
422#626—61no—
423#626—61no—
424#626—61no—
425#625—62no—
426#625—61no—
427#625—61no—
428#624—62no—
429#624—61no—
430#624—61no—
431D3×Dic3—62no—
432D3×Dic3—62no—
433D3×Dic3—61no—
434D3×Dic3—61no—
435D3×Dic3—61no—
436D3×Dic3—61no—
437C32×C8—32no—
438C3⋊(C3⋊C8)C22×D312yescomplemented
439C3×C3⋊C8—22no—
440C3×C3⋊C8—32no—
441C3×C3⋊C8—32no—
442C3×C3⋊C8—62no—
443C3×C3⋊C8C22×D312yescomplemented
444C3×C3⋊C8C22×D312yescomplemented
445C2×AGL(1,ℤ/8)—271noSylow
446C2×C33—21no—
447C2×C33C22×D411yescharacteristic
448C3⋊(C3⋊D3)—41no—
449C3×C3⋊D3—41no—
450C3×C3⋊D3—42no—
451C32×D3—21no—
452C32×D3—42no—
453C32×D3AGL(1,ℤ/8)12yescomplemented
454C24×C3—181no—
455C23×D3—61no—
456C23×D3—61no—
457C3×#41—91no—
458C2×C3×D4—31no—
459C2×C3×D4—31no—
460C2×C3×D4—61no—
461C2×C3×D4—92no—
462C2×C3×D4—92no—
463C2×C3×D4—91no—
464C2×C3×D4—181no—
465C2×C3×D4—181no—
466C2×C3×D4—181no—
467C22×C3×C4—31no—
468C22×C3×C4—31no—
469C22×C3×C4—61no—
470C2×#67—61no—
471C2×#67—181no—
472C2×#67—181no—
473C2×#67—182no—
474#239—91no—
475D3×Q8—91no—
476#237—91no—
477#237—181no—
478D3×D4—32no—
479D3×D4—32no—
480D3×D4—61no—
481D3×D4—61no—
482D3×D4—91no—
483D3×D4—181no—
484#235—31no—
485#235—31no—
486#235—61no—
487#235—91no—
488#235—91no—
489#235—91no—
490#235—91no—
491#235—91no—
492#235—91no—
493#235—91no—
494#235—181no—
495#235—181no—
496#235—181no—
497#235—181no—
498#235—181no—
499#235—181no—
500#235—181no—
501#235—182no—
502#235—181no—
503#235—181no—
504#235—182no—
505#235—181no—
506#235—361no—
507C2×D12—31no—
508C2×D12—31no—
509C2×D12—32no—
510C2×D12—32no—
511C2×D12—61no—
512C2×D12—61no—
513C2×D12—61no—
514C2×D12—61no—
515C2×D12—91no—
516C2×D12—91no—
517C2×D12—181no—
518C2×D12D3211yescharacteristic, complemented
519C2×C4×D3—181no—
520C2×C4×D3—181no—
521C2×C4×D3—182no—
522C2×C4×D3—181no—
523C2×C4×D3D3211yescharacteristic
524C2×Dic6—91no—
525C2×Dic6—91no—
526C2×Dic6—181no—
527C3×SD16—92no—
528C3×D8—92no—
529C3×M16—31no—
530C3×M16—31no—
531C3×M16—61no—
532C3×M16—92no—
533C3×M16—91no—
534C2×C3×C8—92no—
535#215—92no—
536#214—32no—
537#214—92no—
538#214—92no—
539#214—92no—
540#214—92no—
541#214—182no—
542#213—32no—
543#213—92no—
544#213—92no—
545#213—92no—
546#213—92no—
547#213—92no—
548#213—182no—
549#208—31no—
550#208—31no—
551#208—32no—
552#208—61no—
553#208D3211yescharacteristic, complemented
554C2×C3⋊C8—32no—
555D24—32no—
556D24—92no—
557D24—92no—
558D24—92no—
559D24—92no—
560D24—182no—
561#204—32no—
562#204—92no—
563#204—92no—
564#204—92no—
565#204—92no—
566#204—182no—
567ΓL(1,𝔽25)—32no—
568D3×C8—32no—
569C22×C32—21no—
570C22×C32—21no—
571C22×C32—21no—
572C22×C32—31no—
573C22×C32—31no—
574C22×C32—41no—
575C22×C32—62no—
576C22×C32—62no—
577C22×C32—122no—
578C22×C32C2×D1211yescharacteristic
579C22×C32D3×D411yescharacteristic
580C22×C32C2×#6711yescharacteristic
581C2×C3⋊D3—21no—
582C2×C3⋊D3—22no—
583C2×C3⋊D3—42no—
584C2×C3⋊D3—61no—
585C2×C3⋊D3—62no—
586C2×C3⋊D3—61no—
587C2×C3⋊D3—61no—
588C2×C3⋊D3—121no—
589C2×C3⋊D3—121no—
590C2×C3⋊D3—122no—
591C2×C3⋊D3—122no—
592C2×C3×D3—22no—
593C2×C3×D3—22no—
594C2×C3×D3—22no—
595C2×C3×D3—22no—
596C2×C3×D3—21no—
597C2×C3×D3—21no—
598C2×C3×D3—42no—
599C2×C3×D3—42no—
600C2×C3×D3—42no—
601C2×C3×D3—42no—
602C2×C3×D3—62no—
603C2×C3×D3—61no—
604C2×C3×D3—62no—
605C2×C3×D3—62no—
606C2×C3×D3—61no—
607C2×C3×D3—82no—
608C2×C3×D3—122no—
609C2×C3×D3—124no—
610C2×C3×D3—124no—
611C2×C3×D3—124no—
612C2×C3×D3—122no—
613C2×C3×D3—122no—
614C2×C3×D3—124no—
615C2×C3×D3—242no—
616C2×C3×D3C2×D1211yescharacteristic
617C2×C3×D3C2×D1211yescharacteristic
618C2×C3×D3C2×#6711yescharacteristic
619C2×C3×D3C2×#6711yescharacteristic
620D32—44no—
621D32—44no—
622D32—124no—
623D32—122no—
624D32—122no—
625C32×C4—21no—
626C32×C4—21no—
627C32×C4—21no—
628C32×C4—21no—
629C32×C4—21no—
630C32×C4—21no—
631C32×C4—31no—
632C32×C4—31no—
633C32×C4—41no—
634C32×C4—41no—
635C32×C4C2×D1211yescharacteristic
636C32×C4D3×D411yescharacteristic
637C32×C4C2×#6711yescharacteristic
638C32×C4C23×D311yescharacteristic
639C32×C4C23×D311yescharacteristic
640C32×C4C23×D311yescharacteristic
641C3⋊Dic3—21no—
642C3⋊Dic3—61no—
643C3⋊Dic3—62no—
644C3⋊Dic3—61no—
645C3⋊Dic3—61no—
646C3⋊Dic3—121no—
647C3⋊Dic3—121no—
648C3⋊Dic3—122no—
649C3×Dic3—21no—
650C3×Dic3—21no—
651C3×Dic3—62no—
652C3×Dic3—61no—
653C3×Dic3—61no—
654C3×Dic3C2×D1211yescharacteristic
655C3×Dic3C2×D1211yescharacteristic
656C3×Dic3C2×#6711yescharacteristic
657C3×Dic3C2×#6711yescharacteristic
658C2×#41—271no—
659C22×D4—91no—
660AGL(1,ℤ/8)—91no—
661AGL(1,ℤ/8)—271no—
662AGL(1,ℤ/8)—272no—
663AGL(1,ℤ/8)—272no—
664AGL(1,ℤ/8)—271no—
665AGL(1,ℤ/8)—271no—
666C2×SD16—272no—
667C2×D8—272no—
668C2×M16—91no—
669C33C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
670C23×C3—31no—
671C23×C3—31no—
672C23×C3—61no—
673C23×C3—61no—
674C23×C3—61no—
675C23×C3—121no—
676C23×C3—182no—
677C23×C3—182no—
678C23×C3—181no—
679C23×C3—364no—
680C22×D3—21no—
681C22×D3—62no—
682C22×D3—62no—
683C22×D3—61no—
684C22×D3—61no—
685C22×D3—62no—
686C22×D3—62no—
687C22×D3—121no—
688C22×D3—124no—
689C22×D3—124no—
690C22×D3—181no—
691C22×D3—181no—
692C22×D3—182no—
693C22×D3—181no—
694C22×D3#62611yescharacteristic
695C3×Q8—91no—
696C3×D4—32no—
697C3×D4—32no—
698C3×D4—62no—
699C3×D4—61no—
700C3×D4—61no—
701C3×D4—92no—
702C3×D4—91no—
703C3×D4—121no—
704C3×D4—182no—
705C3×D4—182no—
706C3×D4—181no—
707C3×D4—181no—
708C2×C3×C4—21no—
709C2×C3×C4—21no—
710C2×C3×C4—21no—
711C2×C3×C4—31no—
712C2×C3×C4—31no—
713C2×C3×C4—31no—
714C2×C3×C4—31no—
715C2×C3×C4—31no—
716C2×C3×C4—31no—
717C2×C3×C4—31no—
718C2×C3×C4—31no—
719C2×C3×C4—31no—
720C2×C3×C4—31no—
721C2×C3×C4—41no—
722C2×C3×C4—61no—
723C2×C3×C4—61no—
724C2×C3×C4—61no—
725C2×C3×C4—61no—
726C2×C3×C4—61no—
727C2×C3×C4—181no—
728C2×C3×C4C2×D3211yescharacteristic
729C2×C3×C4C2×D3211yescharacteristic
730C2×C3×C4C2×D3211yescharacteristic
731#67—62no—
732#67—61no—
733#67—61no—
734#67—62no—
735#67—62no—
736#67—181no—
737#67—181no—
738#67—182no—
739#67—181no—
740#67—181no—
741#67—182no—
742#67—182no—
743#67—181no—
744#67—181no—
745#67—181no—
746#67—181no—
747#67—181no—
748#67—361no—
749#67—361no—
750#67—362no—
751C2×Dic3—181no—
752C2×Dic3—181no—
753C2×Dic3—182no—
754C2×Dic3—181no—
755C2×Dic3#62611yescharacteristic
756D12—21no—
757D12—32no—
758D12—32no—
759D12—31no—
760D12—31no—
761D12—61no—
762D12—62no—
763D12—62no—
764D12—62no—
765D12—61no—
766D12—61no—
767D12—91no—
768D12—91no—
769D12—91no—
770D12—121no—
771D12—181no—
772D12—181no—
773D12—181no—
774D12—181no—
775D12—181no—
776D12—182no—
777D12—181no—
778D12—361no—
779D12C2×D3212yes—
780C4×D3—62no—
781C4×D3—61no—
782C4×D3—61no—
783C4×D3—181no—
784C4×D3—181no—
785C4×D3—182no—
786C4×D3—182no—
787C4×D3—181no—
788C4×D3—181no—
789C4×D3—182no—
790C4×D3—181no—
791C4×D3—181no—
792C4×D3—181no—
793C4×D3—181no—
794C4×D3—181no—
795C4×D3—361no—
796C4×D3—361no—
797C4×D3—362no—
798C4×D3#62611yescharacteristic
799C4×D3#62611yescharacteristic
800C4×D3C2×D3211yescharacteristic
801C4×D3C2×D3211yescharacteristic
802Dic6—31no—
803Dic6—31no—
804Dic6—61no—
805Dic6—91no—
806Dic6—91no—
807Dic6—91no—
808Dic6—181no—
809Dic6—181no—
810Dic6—181no—
811Dic6—181no—
812Dic6—181no—
813Dic6—182no—
814Dic6—181no—
815Dic6—361no—
816C3×C8—32no—
817C3×C8—32no—
818C3×C8—62no—
819C3×C8—92no—
820C3⋊C8—32no—
821C3⋊C8—32no—
822C3⋊C8—62no—
823C3⋊C8C2×D3212yescomplemented
824C2×C32—21no—
825C2×C32—21no—
826C2×C32—21no—
827C2×C32—21no—
828C2×C32—21no—
829C2×C32—21no—
830C2×C32—32no—
831C2×C32—41no—
832C2×C32—41no—
833C2×C32—41no—
834C2×C32—41no—
835C2×C32—61no—
836C2×C32—81no—
837C2×C32—122no—
838C2×C32C22×D1211yescharacteristic
839C2×C32C2×D3×D411yescharacteristic
840C2×C32C22×#6711yescharacteristic
841C3⋊D3—41no—
842C3⋊D3—42no—
843C3⋊D3—121no—
844C3⋊D3—122no—
845C3⋊D3—121no—
846C3⋊D3—121no—
847C3⋊D3—241no—
848C3⋊D3—241no—
849C3⋊D3—242no—
850C3×D3—21no—
851C3×D3—21no—
852C3×D3—22no—
853C3×D3—41no—
854C3×D3—42no—
855C3×D3—42no—
856C3×D3—82no—
857C3×D3—122no—
858C3×D3—121no—
859C3×D3—122no—
860C3×D3—122no—
861C3×D3—121no—
862C3×D3—242no—
863C3×D3#90812yescomplemented
864C3×D3#93212yescomplemented
865C24—181no—
866#41—91no—
867#41—271no—
868#41—271no—
869#41—271no—
870#41—541no—
871#41—541no—
872C2×Q8—271no—
873C2×D4—31no—
874C2×D4—92no—
875C2×D4—92no—
876C2×D4—91no—
877C2×D4—181no—
878C2×D4—181no—
879C2×D4—181no—
880C2×D4—271no—
881C2×D4—541no—
882C22×C4—31no—
883C22×C4—541no—
884SD16—92no—
885SD16—272no—
886SD16—272no—
887SD16—272no—
888D8—92no—
889D8—272no—
890D8—272no—
891D8—272no—
892M16—31no—
893M16—92no—
894M16—91no—
895C2×C8—92no—
896C22×C3—21no—
897C22×C3—21no—
898C22×C3—21no—
899C22×C3—31no—
900C22×C3—31no—
901C22×C3—31no—
902C22×C3—31no—
903C22×C3—41no—
904C22×C3—61no—
905C22×C3—61no—
906C22×C3—62no—
907C22×C3—62no—
908C22×C3—62no—
909C22×C3—62no—
910C22×C3—122no—
911C22×C3—122no—
912C22×C3—122no—
913C22×C3—122no—
914C22×C3—182no—
915C22×C3—181no—
916C22×C3—242no—
917C22×C3—362no—
918C22×C3—364no—
919C22×C3—364no—
920C22×C3D3×D1211yescharacteristic
921C22×C3C2×#62611yescharacteristic
922C22×C3D3×#6711yescharacteristic
923C2×D3—22no—
924C2×D3—22no—
925C2×D3—42no—
926C2×D3—62no—
927C2×D3—61no—
928C2×D3—62no—
929C2×D3—61no—
930C2×D3—62no—
931C2×D3—122no—
932C2×D3—124no—
933C2×D3—124no—
934C2×D3—124no—
935C2×D3—122no—
936C2×D3—122no—
937C2×D3—124no—
938C2×D3—182no—
939C2×D3—181no—
940C2×D3—181no—
941C2×D3—181no—
942C2×D3—242no—
943C2×D3—361no—
944C2×D3—361no—
945C2×D3—362no—
946C2×D3—362no—
947C2×D3—362no—
948C2×D3—364no—
949C2×D3—362no—
950C2×D3C2×#62611yescharacteristic
951C2×D3C2×#62611yescharacteristic
952C3×C4—21no—
953C3×C4—21no—
954C3×C4—21no—
955C3×C4—21no—
956C3×C4—21no—
957C3×C4—21no—
958C3×C4—31no—
959C3×C4—31no—
960C3×C4—31no—
961C3×C4—31no—
962C3×C4—41no—
963C3×C4—41no—
964C3×C4—61no—
965C3×C4—61no—
966C3×C4—181no—
967C3×C4D3×D1211yescharacteristic
968C3×C4C2×#62611yescharacteristic
969C3×C4D3×#6711yescharacteristic
970C3×C4C22×D3211yescharacteristic
971C3×C4C22×D3211yescharacteristic
972C3×C4C22×D3211yescharacteristic
973Dic3—62no—
974Dic3—61no—
975Dic3—61no—
976Dic3—182no—
977Dic3—181no—
978Dic3—181no—
979Dic3—181no—
980Dic3—361no—
981Dic3—361no—
982Dic3—362no—
983Dic3C2×#62611yescharacteristic
984Dic3C2×#62611yescharacteristic
985C32—21no—
986C32—21no—
987C32—21no—
988C32—41no—
989C32C2×#90811yescharacteristic, complemented
990C32D3×AGL(1,ℤ/8)11yescharacteristic, complemented
991C32C2×#93211yescharacteristic, complemented
992C23—31no—
993C23—61no—
994C23—182no—
995C23—182no—
996C23—181no—
997C23—364no—
998C23—541no—
999Q8—91no—
1000Q8—271no—
1001Q8—541no—
1002D4—32no—
1003D4—61no—
1004D4—91no—
1005D4—92no—
1006D4—182no—
1007D4—182no—
1008D4—181no—
1009D4—181no—
1010D4—271no—
1011D4—541no—
1012D4—541no—
1013D4—541no—
1014D4—541no—
1015C2×C4—31no—
1016C2×C4—31no—
1017C2×C4—31no—
1018C2×C4—31no—
1019C2×C4—31no—
1020C2×C4—181no—
1021C2×C4—541no—
1022C2×C4—541no—
1023C2×C4—541no—
1024C2×C4—541no—
1025C2×C4D3311yescharacteristic
1026C8—32no—
1027C8—92no—
1028C2×C3—21no—
1029C2×C3—21no—
1030C2×C3—21no—
1031C2×C3—21no—
1032C2×C3—21no—
1033C2×C3—21no—
1034C2×C3—32no—
1035C2×C3—32no—
1036C2×C3—41no—
1037C2×C3—41no—
1038C2×C3—41no—
1039C2×C3—41no—
1040C2×C3—62no—
1041C2×C3—61no—
1042C2×C3—61no—
1043C2×C3—81no—
1044C2×C3—121no—
1045C2×C3—122no—
1046C2×C3—122no—
1047C2×C3—242no—
1048C2×C3—362no—
1049C2×C3—361no—
1050C2×C3C2×D3×D1211yescharacteristic
1051C2×C3C22×#62611yescharacteristic
1052C2×C3C2×D3×#6711yescharacteristic
1053D3—21no—
1054D3—42no—
1055D3—122no—
1056D3—122no—
1057D3—121no—
1058D3—121no—
1059D3—122no—
1060D3—242no—
1061D3—362no—
1062D3—361no—
1063D3—361no—
1064D3—361no—
1065D3—721no—
1066D3—721no—
1067D3—722no—
1068D3#6383012yesdirect product factor
1069C22—31no—
1070C22—31no—
1071C22—62no—
1072C22—62no—
1073C22—122no—
1074C22—181no—
1075C22—182no—
1076C22—362no—
1077C22—364no—
1078C22—364no—
1079C22—541no—
1080C22—1082no—
1081C22D3×#62611yescharacteristic
1082C4—31no—
1083C4—31no—
1084C4—181no—
1085C4—541no—
1086C4D3×#62611yescharacteristic
1087C4C2×D3311yescharacteristic
1088C3—21no—
1089C3—21no—
1090C3—21no—
1091C3—41no—
1092C3D3×#90811yescharacteristic, complemented
1093C3C2×#6383011yescharacteristic, complemented
1094C3D3×#93211yescharacteristic, complemented
1095C2—21no—
1096C2—32no—
1097C2—61no—
1098C2—122no—
1099C2—362no—
1100C2—361no—
1101C2—1081no—
1102C2C2×D3×#62611yescharacteristic
subgroupG/H
centerC2C2×D3×#626
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. D3×#3828C2semidirect
2. C2×C3×D3×D12C2semidirect
3. #11723661C2semidirect
4. #11723378C2semidirect
5. #11723370C2semidirect
6. C3×#63830C2semidirect
7. C3×D3×#208C2semidirect
8. #11722869C2semidirect
9. #11722868C2semidirect
10. D3×#3716C2semidirect
11. D3×#3714C2semidirect
16. #89076C22semidirect
17. C3×#3828C22semidirect
18. C2×C3×C4⋊(C3⋊D3)C22semidirect
19. C2×C32×D12C22semidirect
23. D3×C4⋊(C3⋊D3)C22semidirect
25. #89022C22semidirect
26. #89021C22semidirect
28. D3×#634C22semidirect
33. C3×D3×D12C22semidirect
34. C3×#3748C22semidirect
35. C32×#208C22semidirect
36. #88811C22semidirect
37. #88810C22semidirect
38. #88796C22semidirect
39. #88794C22semidirect
40. #88791C22semidirect
41. #88790C22semidirect
42. C3×#3716C22semidirect
43. C3×#3714C22semidirect
44. C3×#3711C22semidirect
45. C3×D3×C3⋊C8C22semidirect
52. C2×D3×D12D3semidirect
72. #63830D3direct (N × H)
77. D3×#208D3semidirect
91. C4⋊(C3⋊(C3⋊D3))C23semidirect
93. #6308C23semidirect
97. C3×C4⋊(C3⋊D3)C23semidirect
99. C3×#634C23semidirect
116. C3×C3⋊(C3⋊C8)C23semidirect
117. C32×C3⋊C8C23semidirect
138. #3828C2×D3semidirect
140. C2×C4⋊(C3⋊D3)C2×D3semidirect
160. C2×C3×D12C2×D3semidirect
161. C2×C3×D12C2×D3semidirect
178. D3×D12C2×D3semidirect
197. #3748C2×D3semidirect
207. C3×#208C2×D3semidirect
208. C3×#208C2×D3semidirect
222. #3716C2×D3semidirect
232. #3714C2×D3semidirect
234. #3711C2×D3semidirect
235. D3×C3⋊C8C2×D3semidirect
351. C4⋊(C3⋊D3)C22×D3semidirect
370. #634C22×D3semidirect
438. C3⋊(C3⋊C8)C22×D3semidirect
443. C3×C3⋊C8C22×D3semidirect
444. C3×C3⋊C8C22×D3semidirect
453. C32×D3AGL(1,ℤ/8)semidirect
518. C2×D12D32semidirect
553. #208D32semidirect
669. C33C2×AGL(1,ℤ/8)semidirect
823. C3⋊C8C2×D32semidirect
863. C3×D3#908semidirect
864. C3×D3#932semidirect
989. C32C2×#908semidirect
990. C32D3×AGL(1,ℤ/8)semidirect
991. C32C2×#932semidirect
1068. D3#63830direct (N × H)
1092. C3D3×#908semidirect
1093. C3C2×#63830semidirect
1094. C3D3×#932semidirect

Maximal subgroups

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

subgroupindex
D3×#38282
C2×C3×D3×D122
#117236612
#117233782
#117233702
C3×#638302
C3×D3×#2082
#117228692
#117228682
D3×#37162
D3×#37142
D3×#9323
C2×#638303
D3×#9083