Finite Group Databasebeta

← D3×#63825 #13170529

Subgroups — D3×#63825 #13170529

Order 1728.

1618 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C3×D3×#235C211yesmaximal, characteristic, complemented
3#11723661C211yesmaximal, characteristic, complemented
4#11723371C211yesmaximal, characteristic, complemented
5#11723367C211yesmaximal, characteristic, complemented
6C3×#63825C211yesmaximal, characteristic, complemented
7C3×D3×#208C211yesmaximal, characteristic, complemented
8#11722871C212yesmaximal, complemented
9#11722870C212yesmaximal, complemented
10D3×#3717C212yesmaximal, complemented
11D3×#3714C212yesmaximal, complemented
12D3×#949—31nomaximal
13C2×#63825—31nomaximal
14D3×#908—31nomaximal
15C22×D3×C3⋊D3—21no—
16C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
17C3×#3828C2211yescharacteristic, complemented
18C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
19C32×#235C2211yescharacteristic, complemented
20C2×C32×C4×D3C2211yescharacteristic
21C2×#6292—21no—
22D3×C4⋊(C3⋊D3)—21no—
23D3×C4⋊(C3⋊D3)—21no—
24D3×C4⋊(C3⋊D3)C2212yes—
25D3×C4⋊(C3⋊D3)C2212yescomplemented
26C3×D3×#67—21no—
27C3×#3804—21no—
28C3×D3×D12C2211yescharacteristic, complemented
29C3×C4×D32—21no—
30C3×#3799C2211yescharacteristic, complemented
31C3×#3798—21no—
32C3×#3795C2211yescharacteristic, complemented
33C3×D3×Dic6C2211yescharacteristic, complemented
34C3×#3748C2211yescharacteristic, complemented
35C32×#208C2211yescharacteristic, complemented
36#88811C2212yescomplemented
37#88810C2212yescomplemented
38#88797C2212yescomplemented
39#88795C2212yescomplemented
40#88791C2212yescomplemented
41#88790C2212yescomplemented
42C3×#3717C2212yescomplemented
43C3×#3714C2212yescomplemented
44C3×#3711C2212yescomplemented
45C3×D3×C3⋊C8C2212yescomplemented
46C22×C4⋊(C3⋊D3)—31no—
47C3×D3×#41—31no—
48C2×C3×#235—31no—
49D3×#235D311yescharacteristic, complemented
50C2×D3×D12—31no—
51C2×D3×D12—31no—
52C2×D3×D12—61no—
53#64158—31no—
54#64117—31no—
55C3×#949—31no—
56C2×C3×#208—31no—
57C3×#908—31no—
58C3×D3×M16—31no—
59#63939—32no—
60D3×#215—32no—
61#63925—32no—
62D3×#213—32no—
63C2×#3717—32no—
64#63830—31no—
65#63825—31no—
66#63825—31no—
67#63825—31no—
68#63825—31no—
69#63825—31no—
70#63825—32no—
71#63825—32no—
72#63825—61no—
73#63825—61no—
74#63825D311yescharacteristic, direct product factor
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×C3×C3⋊D3—21no—
84C22×C32×D3D411yescharacteristic
85C2×D3×C3⋊D3—22no—
86C2×D3×C3⋊D3—22no—
87C2×D3×C3⋊D3—44no—
88C2×C3×D32—21no—
89C2×C33×C4C2311yescharacteristic
90C4⋊(C3⋊(C3⋊D3))—21no—
91C4⋊(C3⋊(C3⋊D3))C2312yes—
92C3×#638—21no—
93C3×C4⋊(C3⋊D3)—21no—
94C3×C4⋊(C3⋊D3)C2312yes—
95C3×C4⋊(C3⋊D3)C2311yescharacteristic, complemented
96C3×C4×C3⋊D3—21no—
97C3×#634C2311yescharacteristic, complemented
98C32×#67—21no—
99C2×C32×Dic3D411yescharacteristic
100C32×D12C2311yescharacteristic, complemented
101C32×C4×D3—21no—
102C32×C4×D3D411yescharacteristic
103C32×C4×D3D411yescharacteristic
104C32×C4×D3C2311yescharacteristic
105C32×C4×D3C2311yescharacteristic
106C32×Dic6C2311yescharacteristic, complemented
107#6292—22no—
108#6292—22no—
109C3×#627—21no—
110C3×#626—21no—
111C3×#626—21no—
112C3×#625—21no—
113C3×#624—21no—
114C3×D3×Dic3—21no—
115C3×D3×Dic3—21no—
116C3×C3⋊(C3⋊C8)C2312yescomplemented
117C32×C3⋊C8C2312yescomplemented
118C2×#949—91no—
119D3×AGL(1,ℤ/8)—91no—
120C2×#908—91no—
121C23×C3⋊D3—61no—
122C22×D32—62no—
123C22×D32—61no—
124C22×D32—61no—
125C32×#41—31no—
126C22×C32×C4—31no—
127#3828C2×D311yescharacteristic, complemented
128C2×C4⋊(C3⋊D3)—31no—
129C2×C4⋊(C3⋊D3)—31no—
130C2×C4⋊(C3⋊D3)—31no—
131C2×C4⋊(C3⋊D3)—32no—
132C2×C4⋊(C3⋊D3)—32no—
133C2×C4⋊(C3⋊D3)—61no—
134C2×C4⋊(C3⋊D3)—61no—
135C2×C4⋊(C3⋊D3)—61no—
136C2×C4⋊(C3⋊D3)—61no—
137C2×C4⋊(C3⋊D3)—61no—
138C2×C4⋊(C3⋊D3)—61no—
139C2×C4⋊(C3⋊D3)—121no—
140C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
141C2×C3×#67—61no—
142C3×#239—31no—
143C3×D3×Q8—31no—
144C3×#237—31no—
145C3×#237—61no—
146C3×D3×D4—31no—
147C3×D3×D4—61no—
148C3×#235—21no—
149C3×#235—31no—
150C3×#235—31no—
151C3×#235—31no—
152C3×#235—31no—
153C3×#235—61no—
154C3×#235—61no—
155C3×#235—61no—
156C3×#235—61no—
157C3×#235C2×D311yescharacteristic, complemented
158C3×#235C2×D311yescharacteristic, complemented
159C2×C3×D12—31no—
160C2×C3×D12—31no—
161C2×C3×D12—31no—
162C2×C3×D12—61no—
163C2×C3×C4×D3—21no—
164C2×C3×C4×D3—61no—
165C2×C3×C4×D3—61no—
166C2×C3×C4×D3C2×D311yescharacteristic
167C2×C3×C4×D3C2×D311yescharacteristic
168C2×C3×Dic6—31no—
169D3×#67—21no—
170C2×#626—62no—
171C2×#626—61no—
172C2×#626—61no—
173#3804—21no—
174D3×D12—32no—
175D3×D12—32no—
176D3×D12—32no—
177D3×D12—32no—
178D3×D12—62no—
179D3×D12—62no—
180D3×D12—62no—
181D3×D12—62no—
182D3×D12—61no—
183D3×D12—61no—
184D3×D12—61no—
185D3×D12—61no—
186D3×D12C2×D311yescharacteristic, complemented
187C4×D32—21no—
188#3799C2×D311yescharacteristic, complemented
189#3798—21no—
190#3795C2×D311yescharacteristic, complemented
191D3×Dic6C2×D311yescharacteristic, complemented
192C32×M16—31no—
193#3755—32no—
194#3753—32no—
195#3748C2×D311yescharacteristic, complemented
196#3745—32no—
197#3744—32no—
198C3×#215—32no—
199C3×#213—32no—
200C3×#208—21no—
201C3×#208—31no—
202C3×#208—31no—
203C3×#208—32no—
204C3×#208—61no—
205C3×#208C2×D311yescharacteristic, complemented
206C3×#208C2×D311yescharacteristic, complemented
207C2×C3×C3⋊C8—32no—
208C3×D24—32no—
209C3×#204—32no—
210C3×ΓL(1,𝔽25)—32no—
211C3×D3×C8—32no—
212#3717—32no—
213#3717—32no—
214#3717—32no—
215#3717—32no—
216#3717—32no—
217#3717—62no—
218#3717—62no—
219#3717C2×D312yescomplemented
220#3716—32no—
221#3715—32no—
222#3714—32no—
223#3714—32no—
224#3714—32no—
225#3714—32no—
226#3714—32no—
227#3714—32no—
228#3714—62no—
229#3714—62no—
230#3714C2×D312yescomplemented
231#3713—32no—
232#3711C2×D312yescomplemented
233D3×C3⋊C8C2×D312yescomplemented
234C22×C33C2×D411yescharacteristic
235C2×C3⋊(C3⋊D3)—22no—
236C2×C3⋊(C3⋊D3)—42no—
237C2×C3×C3⋊D3—22no—
238C2×C3×C3⋊D3—21no—
239C2×C3×C3⋊D3—42no—
240C2×C32×D3—22no—
241C2×C32×D3—21no—
242C2×C32×D3C2×D411yescharacteristic
243C2×C32×D3C2×D411yescharacteristic
244D3×C3⋊D3—44no—
245D3×C3⋊D3—44no—
246C3×D32—42no—
247C33×C4C2×D411yescharacteristic
248C33×C4C2411yescharacteristic
249C3×C3⋊Dic3—21no—
250C32×Dic3—21no—
251C32×Dic3C2×D411yescharacteristic
252C32×Dic3C2×D411yescharacteristic
253C2×C3×#41—91no—
254D3×#41—31no—
255C2×D3×D4—91no—
256C2×#235—31no—
257C22×D12—91no—
258C22×D12—91no—
259C22×D12—181no—
260C3×AGL(1,ℤ/8)—91no—
261C2×C3×M16—91no—
262#949—31no—
263#949—92no—
264#949—92no—
265#949—91no—
266#949—91no—
267#949—91no—
268#949—91no—
269#949—181no—
270C2×#215—92no—
271#932—91no—
272C2×#213—92no—
273C2×#208—31no—
274#914—92no—
275D3×SD16—92no—
276#911—92no—
277D3×D8—92no—
278#908—31no—
279#908—92no—
280#908—92no—
281#908—91no—
282#908—91no—
283#908—91no—
284#908—91no—
285#908—181no—
286D3×M16—31no—
287C2×D24—92no—
288C2×#204—92no—
289C23×C32—31no—
290C22×C3⋊D3—21no—
291C22×C3⋊D3—62no—
292C22×C3⋊D3—62no—
293C22×C3⋊D3—61no—
294C22×C3⋊D3—62no—
295C22×C3⋊D3—61no—
296C22×C3⋊D3—61no—
297C22×C3⋊D3—121no—
298C22×C3⋊D3—121no—
299C22×C3⋊D3—122no—
300C22×C3⋊D3—124no—
301C22×C3×D3—21no—
302C22×C3×D3—61no—
303C22×C3×D3—62no—
304C22×C3×D3—61no—
305C22×C3×D3—61no—
306C22×C3×D3—61no—
307C22×C3×D3D1211yescharacteristic
308C22×C3×D3#6711yescharacteristic
309C2×D32—21no—
310C2×D32—64no—
311C2×D32—64no—
312C2×D32—62no—
313C2×D32—62no—
314C2×D32—62no—
315C2×D32—62no—
316C2×D32—128no—
317C2×D32—124no—
318C2×D32—124no—
319C32×Q8—31no—
320C32×D4—31no—
321C32×D4—61no—
322C2×C32×C4—21no—
323C2×C32×C4—21no—
324C2×C32×C4—21no—
325C2×C32×C4—31no—
326C2×C32×C4—31no—
327C2×C32×C4—31no—
328C2×C32×C4—31no—
329C2×C32×C4—31no—
330C2×C32×C4—41no—
331C2×C32×C4—61no—
332C2×C32×C4C22×D311yescharacteristic
333C2×C32×C4C22×D311yescharacteristic
334C2×C32×C4C22×D311yescharacteristic
335#638—21no—
336C4⋊(C3⋊D3)—21no—
337C4⋊(C3⋊D3)—32no—
338C4⋊(C3⋊D3)—32no—
339C4⋊(C3⋊D3)—32no—
340C4⋊(C3⋊D3)—62no—
341C4⋊(C3⋊D3)—62no—
342C4⋊(C3⋊D3)—62no—
343C4⋊(C3⋊D3)—62no—
344C4⋊(C3⋊D3)—62no—
345C4⋊(C3⋊D3)—61no—
346C4⋊(C3⋊D3)—62no—
347C4⋊(C3⋊D3)—61no—
348C4⋊(C3⋊D3)—61no—
349C4⋊(C3⋊D3)—122no—
350C4⋊(C3⋊D3)—121no—
351C4⋊(C3⋊D3)—121no—
352C4⋊(C3⋊D3)—122no—
353C4⋊(C3⋊D3)C22×D312yes—
354C4⋊(C3⋊D3)C22×D311yescharacteristic, complemented
355C4×C3⋊D3—21no—
356#634C22×D311yescharacteristic, complemented
357C3×#67—21no—
358C3×#67—21no—
359C3×#67—41no—
360C3×#67—61no—
361C3×#67—61no—
362C3×#67—61no—
363C3×#67—61no—
364C3×#67—61no—
365C3×#67—61no—
366C3×#67—121no—
367C2×C3×Dic3—21no—
368C2×C3×Dic3—61no—
369C2×C3×Dic3—61no—
370C2×C3×Dic3D1211yescharacteristic
371C2×C3×Dic3#6711yescharacteristic
372C3×D12—21no—
373C3×D12—31no—
374C3×D12—32no—
375C3×D12—31no—
376C3×D12—32no—
377C3×D12—62no—
378C3×D12—61no—
379C3×D12—62no—
380C3×D12—61no—
381C3×D12—61no—
382C3×D12—61no—
383C3×D12—61no—
384C3×D12C22×D311yescharacteristic, complemented
385C3×D12C22×D311yescharacteristic, complemented
386C3×C4×D3—21no—
387C3×C4×D3—21no—
388C3×C4×D3—21no—
389C3×C4×D3—21no—
390C3×C4×D3—21no—
391C3×C4×D3—21no—
392C3×C4×D3—41no—
393C3×C4×D3—61no—
394C3×C4×D3—61no—
395C3×C4×D3—61no—
396C3×C4×D3—61no—
397C3×C4×D3—61no—
398C3×C4×D3—61no—
399C3×C4×D3—121no—
400C3×C4×D3D1211yescharacteristic
401C3×C4×D3D1211yescharacteristic
402C3×C4×D3#6711yescharacteristic
403C3×C4×D3#6711yescharacteristic
404C3×C4×D3C22×D311yescharacteristic
405C3×C4×D3C22×D311yescharacteristic
406C3×C4×D3C22×D311yescharacteristic
407C3×C4×D3C22×D311yescharacteristic
408C3×Dic6—21no—
409C3×Dic6—31no—
410C3×Dic6—31no—
411C3×Dic6—61no—
412C3×Dic6—61no—
413C3×Dic6—61no—
414C3×Dic6C22×D311yescharacteristic, complemented
415C3×Dic6C22×D311yescharacteristic, complemented
416#627—21no—
417#626—21no—
418#626—21no—
419#626—64no—
420#626—64no—
421#626—62no—
422#626—62no—
423#626—62no—
424#626—62no—
425#625—21no—
426#624—21no—
427D3×Dic3—21no—
428D3×Dic3—21no—
429C32×C8—32no—
430C3⋊(C3⋊C8)C22×D312yescomplemented
431C3×C3⋊C8—22no—
432C3×C3⋊C8—32no—
433C3×C3⋊C8—32no—
434C3×C3⋊C8—62no—
435C3×C3⋊C8C22×D312yescomplemented
436C3×C3⋊C8C22×D312yescomplemented
437C2×AGL(1,ℤ/8)—271noSylow
438C2×C33—21no—
439C2×C33C22×D411yescharacteristic
440C3⋊(C3⋊D3)—42no—
441C3×C3⋊D3—42no—
442C3×C3⋊D3—41no—
443C32×D3—21no—
444C32×D3—41no—
445C32×D3AGL(1,ℤ/8)12yescomplemented
446C23×D3—181no—
447C23×D3—181no—
448C23×D3—182no—
449C23×D3—181no—
450C3×#41—31no—
451C3×#41—31no—
452C3×#41—61no—
453C3×#41—91no—
454C3×#41—91no—
455C3×#41—91no—
456C3×#41—181no—
457C3×#41—181no—
458C2×C3×Q8—91no—
459C2×C3×D4—91no—
460C2×C3×D4—91no—
461C2×C3×D4—181no—
462C22×C3×C4—31no—
463C22×C3×C4—31no—
464C22×C3×C4—61no—
465C22×C3×C4—181no—
466C2×#67—61no—
467C2×#67—181no—
468#239—31no—
469D3×Q8—31no—
470#237—31no—
471#237—61no—
472D3×D4—31no—
473D3×D4—61no—
474D3×D4—92no—
475D3×D4—92no—
476D3×D4—181no—
477D3×D4—181no—
478#235—31no—
479#235—31no—
480#235—31no—
481#235—31no—
482#235—61no—
483#235—61no—
484#235—61no—
485#235—61no—
486#235D3211yescharacteristic, complemented
487C2×D12—31no—
488C2×D12—31no—
489C2×D12—31no—
490C2×D12—61no—
491C2×D12—92no—
492C2×D12—92no—
493C2×D12—92no—
494C2×D12—92no—
495C2×D12—91no—
496C2×D12—91no—
497C2×D12—91no—
498C2×D12—182no—
499C2×D12—182no—
500C2×D12—181no—
501C2×D12—181no—
502C2×D12—181no—
503C2×D12—181no—
504C2×D12—181no—
505C2×D12—181no—
506C2×D12—181no—
507C2×D12—182no—
508C2×D12—182no—
509C2×D12—181no—
510C2×D12—181no—
511C2×D12—182no—
512C2×D12—361no—
513C2×C4×D3—61no—
514C2×C4×D3—61no—
515C2×C4×D3D3211yescharacteristic
516C2×Dic6—31no—
517C3×SD16—92no—
518C3×D8—92no—
519C3×M16—31no—
520C3×M16—31no—
521C3×M16—61no—
522C3×M16—92no—
523C3×M16—91no—
524C2×C3×C8—92no—
525#215—32no—
526#215—92no—
527#215—92no—
528#215—92no—
529#215—92no—
530#215—182no—
531#214—92no—
532#213—32no—
533#213—92no—
534#213—92no—
535#213—92no—
536#213—92no—
537#213—92no—
538#213—182no—
539#208—31no—
540#208—31no—
541#208—32no—
542#208—61no—
543#208D3211yescharacteristic, complemented
544C2×C3⋊C8—32no—
545D24—32no—
546D24—92no—
547D24—92no—
548D24—92no—
549D24—92no—
550D24—182no—
551#204—32no—
552#204—92no—
553#204—92no—
554#204—92no—
555#204—92no—
556#204—182no—
557ΓL(1,𝔽25)—32no—
558D3×C8—32no—
559C22×C32—21no—
560C22×C32—21no—
561C22×C32—21no—
562C22×C32—31no—
563C22×C32—31no—
564C22×C32—41no—
565C22×C32—62no—
566C22×C32—61no—
567C22×C32C2×D1211yescharacteristic
568C22×C32D3×D411yescharacteristic
569C22×C32C2×#6711yescharacteristic
570C2×C3⋊D3—22no—
571C2×C3⋊D3—21no—
572C2×C3⋊D3—42no—
573C2×C3⋊D3—62no—
574C2×C3⋊D3—64no—
575C2×C3⋊D3—62no—
576C2×C3⋊D3—62no—
577C2×C3⋊D3—122no—
578C2×C3⋊D3—122no—
579C2×C3⋊D3—124no—
580C2×C3⋊D3—124no—
581C2×C3⋊D3—124no—
582C2×C3⋊D3—122no—
583C2×C3⋊D3—124no—
584C2×C3⋊D3—122no—
585C2×C3⋊D3—122no—
586C2×C3⋊D3—242no—
587C2×C3⋊D3—242no—
588C2×C3⋊D3—244no—
589C2×C3×D3—24no—
590C2×C3×D3—22no—
591C2×C3×D3—22no—
592C2×C3×D3—21no—
593C2×C3×D3—21no—
594C2×C3×D3—21no—
595C2×C3×D3—21no—
596C2×C3×D3—41no—
597C2×C3×D3—64no—
598C2×C3×D3—62no—
599C2×C3×D3—61no—
600C2×C3×D3—61no—
601C2×C3×D3—62no—
602C2×C3×D3—121no—
603C2×C3×D3—122no—
604C2×C3×D3—124no—
605C2×C3×D3—122no—
606C2×C3×D3—122no—
607C2×C3×D3—122no—
608C2×C3×D3C2×D1211yescharacteristic
609C2×C3×D3C2×D1211yescharacteristic
610C2×C3×D3C2×#6711yescharacteristic
611C2×C3×D3C2×#6711yescharacteristic
612D32—42no—
613D32—128no—
614D32—124no—
615D32—124no—
616D32—128no—
617D32—124no—
618D32—124no—
619C32×C4—21no—
620C32×C4—21no—
621C32×C4—21no—
622C32×C4—21no—
623C32×C4—21no—
624C32×C4—21no—
625C32×C4—31no—
626C32×C4—31no—
627C32×C4—41no—
628C32×C4—41no—
629C32×C4—61no—
630C32×C4C2×D1211yescharacteristic
631C32×C4D3×D411yescharacteristic
632C32×C4C2×#6711yescharacteristic
633C32×C4C23×D311yescharacteristic
634C32×C4C23×D311yescharacteristic
635C32×C4C23×D311yescharacteristic
636C3⋊Dic3—21no—
637C3×Dic3—21no—
638C3×Dic3—21no—
639C3×Dic3—21no—
640C3×Dic3—21no—
641C3×Dic3—41no—
642C3×Dic3—61no—
643C3×Dic3—61no—
644C3×Dic3—121no—
645C3×Dic3C2×D1211yescharacteristic
646C3×Dic3C2×D1211yescharacteristic
647C3×Dic3C2×#6711yescharacteristic
648C3×Dic3C2×#6711yescharacteristic
649C2×#41—91no—
650C22×D4—271no—
651AGL(1,ℤ/8)—91no—
652AGL(1,ℤ/8)—271no—
653AGL(1,ℤ/8)—272no—
654AGL(1,ℤ/8)—272no—
655AGL(1,ℤ/8)—271no—
656AGL(1,ℤ/8)—271no—
657C2×SD16—272no—
658C2×D8—272no—
659C2×M16—91no—
660C33C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
661C23×C3—31no—
662C23×C3—31no—
663C23×C3—61no—
664C23×C3—181no—
665C23×C3—181no—
666C22×D3—61no—
667C22×D3—62no—
668C22×D3—61no—
669C22×D3—61no—
670C22×D3—61no—
671C22×D3—182no—
672C22×D3—182no—
673C22×D3—182no—
674C22×D3—182no—
675C22×D3—184no—
676C22×D3—184no—
677C22×D3—182no—
678C22×D3—181no—
679C22×D3—181no—
680C22×D3—181no—
681C22×D3—182no—
682C22×D3—182no—
683C22×D3—361no—
684C22×D3—361no—
685C22×D3—362no—
686C22×D3—364no—
687C22×D3—364no—
688C22×D3—364no—
689C22×D3—368no—
690C22×D3#62611yescharacteristic
691C3×Q8—31no—
692C3×Q8—31no—
693C3×Q8—61no—
694C3×Q8—91no—
695C3×Q8—181no—
696C3×D4—31no—
697C3×D4—31no—
698C3×D4—61no—
699C3×D4—61no—
700C3×D4—61no—
701C3×D4—91no—
702C3×D4—92no—
703C3×D4—121no—
704C3×D4—181no—
705C3×D4—181no—
706C3×D4—181no—
707C3×D4—181no—
708C3×D4—181no—
709C2×C3×C4—21no—
710C2×C3×C4—21no—
711C2×C3×C4—21no—
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—31no—
722C2×C3×C4—41no—
723C2×C3×C4—61no—
724C2×C3×C4—61no—
725C2×C3×C4—61no—
726C2×C3×C4—61no—
727C2×C3×C4—61no—
728C2×C3×C4—61no—
729C2×C3×C4—61no—
730C2×C3×C4—121no—
731C2×C3×C4—181no—
732C2×C3×C4—181no—
733C2×C3×C4—181no—
734C2×C3×C4—181no—
735C2×C3×C4C2×D3211yescharacteristic
736C2×C3×C4C2×D3211yescharacteristic
737C2×C3×C4C2×D3211yescharacteristic
738#67—21no—
739#67—61no—
740#67—61no—
741#67—61no—
742#67—61no—
743#67—61no—
744#67—61no—
745#67—121no—
746#67—182no—
747#67—182no—
748C2×Dic3—61no—
749C2×Dic3—61no—
750C2×Dic3#62611yescharacteristic
751D12—32no—
752D12—32no—
753D12—31no—
754D12—31no—
755D12—62no—
756D12—61no—
757D12—62no—
758D12—61no—
759D12—61no—
760D12—61no—
761D12—61no—
762D12—92no—
763D12—92no—
764D12—92no—
765D12—182no—
766D12—182no—
767D12—182no—
768D12—182no—
769D12—182no—
770D12—182no—
771D12—182no—
772D12—182no—
773D12—184no—
774D12—184no—
775D12—181no—
776D12—181no—
777D12—181no—
778D12—362no—
779D12—361no—
780D12—361no—
781D12—362no—
782D12C2×D3211yescharacteristic, complemented
783C4×D3—21no—
784C4×D3—61no—
785C4×D3—61no—
786C4×D3—61no—
787C4×D3—61no—
788C4×D3—61no—
789C4×D3—61no—
790C4×D3—121no—
791C4×D3#62611yescharacteristic
792C4×D3#62611yescharacteristic
793C4×D3C2×D3211yescharacteristic
794C4×D3C2×D3211yescharacteristic
795Dic6—31no—
796Dic6—31no—
797Dic6—61no—
798Dic6—61no—
799Dic6—61no—
800Dic6C2×D3211yescharacteristic, complemented
801C3×C8—32no—
802C3×C8—32no—
803C3×C8—62no—
804C3×C8—92no—
805C3⋊C8—32no—
806C3⋊C8—32no—
807C3⋊C8—62no—
808C3⋊C8C2×D3212yescomplemented
809C2×C32—21no—
810C2×C32—22no—
811C2×C32—21no—
812C2×C32—21no—
813C2×C32—21no—
814C2×C32—21no—
815C2×C32—21no—
816C2×C32—32no—
817C2×C32—41no—
818C2×C32—41no—
819C2×C32—41no—
820C2×C32—42no—
821C2×C32—61no—
822C2×C32—121no—
823C2×C32C22×D1211yescharacteristic
824C2×C32C2×D3×D411yescharacteristic
825C2×C32C22×#6711yescharacteristic
826C3⋊D3—42no—
827C3⋊D3—41no—
828C3⋊D3—122no—
829C3⋊D3—124no—
830C3⋊D3—122no—
831C3⋊D3—122no—
832C3⋊D3—242no—
833C3⋊D3—242no—
834C3⋊D3—244no—
835C3×D3—22no—
836C3×D3—21no—
837C3×D3—21no—
838C3×D3—22no—
839C3×D3—41no—
840C3×D3—41no—
841C3×D3—81no—
842C3×D3—124no—
843C3×D3—122no—
844C3×D3—121no—
845C3×D3—121no—
846C3×D3—122no—
847C3×D3—241no—
848C3×D3#90812yescomplemented
849C3×D3#94912yescomplemented
850C24—541no—
851#41—31no—
852#41—91no—
853#41—91no—
854#41—91no—
855#41—181no—
856#41—181no—
857C2×Q8—91no—
858C2×D4—91no—
859C2×D4—91no—
860C2×D4—181no—
861C2×D4—272no—
862C2×D4—272no—
863C2×D4—271no—
864C2×D4—541no—
865C2×D4—541no—
866C2×D4—541no—
867C22×C4—31no—
868C22×C4—181no—
869SD16—92no—
870SD16—272no—
871SD16—272no—
872SD16—272no—
873D8—92no—
874D8—272no—
875D8—272no—
876D8—272no—
877M16—31no—
878M16—92no—
879M16—91no—
880C2×C8—92no—
881C22×C3—21no—
882C22×C3—21no—
883C22×C3—21no—
884C22×C3—31no—
885C22×C3—31no—
886C22×C3—31no—
887C22×C3—31no—
888C22×C3—41no—
889C22×C3—61no—
890C22×C3—61no—
891C22×C3—62no—
892C22×C3—62no—
893C22×C3—64no—
894C22×C3—61no—
895C22×C3—61no—
896C22×C3—121no—
897C22×C3—181no—
898C22×C3—182no—
899C22×C3—362no—
900C22×C3—362no—
901C22×C3D3×D1211yescharacteristic
902C22×C3C2×#62611yescharacteristic
903C22×C3D3×#6711yescharacteristic
904C2×D3—22no—
905C2×D3—21no—
906C2×D3—64no—
907C2×D3—62no—
908C2×D3—61no—
909C2×D3—61no—
910C2×D3—62no—
911C2×D3—121no—
912C2×D3—122no—
913C2×D3—124no—
914C2×D3—122no—
915C2×D3—122no—
916C2×D3—122no—
917C2×D3—184no—
918C2×D3—182no—
919C2×D3—182no—
920C2×D3—182no—
921C2×D3—362no—
922C2×D3—362no—
923C2×D3—364no—
924C2×D3—364no—
925C2×D3—364no—
926C2×D3—364no—
927C2×D3—368no—
928C2×D3—368no—
929C2×D3—364no—
930C2×D3—364no—
931C2×D3—362no—
932C2×D3—364no—
933C2×D3—362no—
934C2×D3—362no—
935C2×D3—364no—
936C2×D3—722no—
937C2×D3—722no—
938C2×D3—724no—
939C2×D3C2×#62611yescharacteristic
940C2×D3C2×#62611yescharacteristic
941C3×C4—21no—
942C3×C4—21no—
943C3×C4—21no—
944C3×C4—21no—
945C3×C4—21no—
946C3×C4—21no—
947C3×C4—31no—
948C3×C4—31no—
949C3×C4—31no—
950C3×C4—31no—
951C3×C4—41no—
952C3×C4—41no—
953C3×C4—61no—
954C3×C4—61no—
955C3×C4—61no—
956C3×C4—61no—
957C3×C4—121no—
958C3×C4—181no—
959C3×C4D3×D1211yescharacteristic
960C3×C4C2×#62611yescharacteristic
961C3×C4D3×#6711yescharacteristic
962C3×C4C22×D3211yescharacteristic
963C3×C4C22×D3211yescharacteristic
964C3×C4C22×D3211yescharacteristic
965Dic3—21no—
966Dic3—61no—
967Dic3—61no—
968Dic3—121no—
969Dic3C2×#62611yescharacteristic
970Dic3C2×#62611yescharacteristic
971C32—21no—
972C32—21no—
973C32—21no—
974C32—41no—
975C32C2×#90811yescharacteristic, complemented
976C32D3×AGL(1,ℤ/8)11yescharacteristic, complemented
977C32C2×#94911yescharacteristic, complemented
978C23—31no—
979C23—181no—
980C23—181no—
981C23—542no—
982C23—542no—
983C23—541no—
984C23—1084no—
985Q8—31no—
986Q8—91no—
987Q8—181no—
988D4—31no—
989D4—61no—
990D4—92no—
991D4—91no—
992D4—181no—
993D4—181no—
994D4—181no—
995D4—181no—
996D4—181no—
997D4—272no—
998D4—542no—
999D4—542no—
1000D4—541no—
1001C2×C4—31no—
1002C2×C4—31no—
1003C2×C4—31no—
1004C2×C4—31no—
1005C2×C4—31no—
1006C2×C4—61no—
1007C2×C4—181no—
1008C2×C4—181no—
1009C2×C4—181no—
1010C2×C4—181no—
1011C2×C4D3311yescharacteristic
1012C8—32no—
1013C8—92no—
1014C2×C3—22no—
1015C2×C3—21no—
1016C2×C3—21no—
1017C2×C3—21no—
1018C2×C3—21no—
1019C2×C3—21no—
1020C2×C3—21no—
1021C2×C3—32no—
1022C2×C3—32no—
1023C2×C3—41no—
1024C2×C3—41no—
1025C2×C3—42no—
1026C2×C3—41no—
1027C2×C3—62no—
1028C2×C3—62no—
1029C2×C3—61no—
1030C2×C3—61no—
1031C2×C3—121no—
1032C2×C3—121no—
1033C2×C3—241no—
1034C2×C3—361no—
1035C2×C3—362no—
1036C2×C3C2×D3×D1211yescharacteristic
1037C2×C3C22×#62611yescharacteristic
1038C2×C3C2×D3×#6711yescharacteristic
1039D3—21no—
1040D3—41no—
1041D3—124no—
1042D3—122no—
1043D3—121no—
1044D3—122no—
1045D3—121no—
1046D3—241no—
1047D3—364no—
1048D3—362no—
1049D3—362no—
1050D3—362no—
1051D3—722no—
1052D3—722no—
1053D3—724no—
1054D3#6382512yesdirect product factor
1055C22—31no—
1056C22—31no—
1057C22—62no—
1058C22—61no—
1059C22—181no—
1060C22—182no—
1061C22—362no—
1062C22—362no—
1063C22—542no—
1064C22—1082no—
1065C22—1084no—
1066C22—1084no—
1067C22D3×#62611yescharacteristic
1068C4—31no—
1069C4—31no—
1070C4—61no—
1071C4—181no—
1072C4D3×#62611yescharacteristic
1073C4C2×D3311yescharacteristic
1074C3—21no—
1075C3—21no—
1076C3—21no—
1077C3—41no—
1078C3D3×#90811yescharacteristic, complemented
1079C3C2×#6382511yescharacteristic, complemented
1080C3D3×#94911yescharacteristic, complemented
1081C2—21no—
1082C2—32no—
1083C2—61no—
1084C2—121no—
1085C2—362no—
1086C2—361no—
1087C2—1082no—
1088C2C2×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. C2×D3×C4⋊(C3⋊D3)C2semidirect
2. C3×D3×#235C2semidirect
3. #11723661C2semidirect
4. #11723371C2semidirect
5. #11723367C2semidirect
6. C3×#63825C2semidirect
7. C3×D3×#208C2semidirect
8. #11722871C2semidirect
9. #11722870C2semidirect
10. D3×#3717C2semidirect
11. D3×#3714C2semidirect
16. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
17. C3×#3828C22semidirect
18. C2×C3×C4⋊(C3⋊D3)C22semidirect
19. C32×#235C22semidirect
25. D3×C4⋊(C3⋊D3)C22semidirect
28. C3×D3×D12C22semidirect
30. C3×#3799C22semidirect
32. C3×#3795C22semidirect
33. C3×D3×Dic6C22semidirect
34. C3×#3748C22semidirect
35. C32×#208C22semidirect
36. #88811C22semidirect
37. #88810C22semidirect
38. #88797C22semidirect
39. #88795C22semidirect
40. #88791C22semidirect
41. #88790C22semidirect
42. C3×#3717C22semidirect
43. C3×#3714C22semidirect
44. C3×#3711C22semidirect
45. C3×D3×C3⋊C8C22semidirect
49. D3×#235D3semidirect
74. #63825D3direct (N × H)
77. D3×#208D3semidirect
95. C3×C4⋊(C3⋊D3)C23semidirect
97. C3×#634C23semidirect
100. C32×D12C23semidirect
106. C32×Dic6C23semidirect
116. C3×C3⋊(C3⋊C8)C23semidirect
117. C32×C3⋊C8C23semidirect
127. #3828C2×D3semidirect
140. C2×C4⋊(C3⋊D3)C2×D3semidirect
157. C3×#235C2×D3semidirect
158. C3×#235C2×D3semidirect
186. D3×D12C2×D3semidirect
188. #3799C2×D3semidirect
190. #3795C2×D3semidirect
191. D3×Dic6C2×D3semidirect
195. #3748C2×D3semidirect
205. C3×#208C2×D3semidirect
206. C3×#208C2×D3semidirect
219. #3717C2×D3semidirect
230. #3714C2×D3semidirect
232. #3711C2×D3semidirect
233. D3×C3⋊C8C2×D3semidirect
354. C4⋊(C3⋊D3)C22×D3semidirect
356. #634C22×D3semidirect
384. C3×D12C22×D3semidirect
385. C3×D12C22×D3semidirect
414. C3×Dic6C22×D3semidirect
415. C3×Dic6C22×D3semidirect
430. C3⋊(C3⋊C8)C22×D3semidirect
435. C3×C3⋊C8C22×D3semidirect
436. C3×C3⋊C8C22×D3semidirect
445. C32×D3AGL(1,ℤ/8)semidirect
486. #235D32semidirect
543. #208D32semidirect
660. C33C2×AGL(1,ℤ/8)semidirect
782. D12C2×D32semidirect
800. Dic6C2×D32semidirect
808. C3⋊C8C2×D32semidirect
848. C3×D3#908semidirect
849. C3×D3#949semidirect
975. C32C2×#908semidirect
976. C32D3×AGL(1,ℤ/8)semidirect
977. C32C2×#949semidirect
1054. D3#63825direct (N × H)
1078. C3D3×#908semidirect
1079. C3C2×#63825semidirect
1080. C3D3×#949semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C4⋊(C3⋊D3)2
C3×D3×#2352
#117236612
#117233712
#117233672
C3×#638252
C3×D3×#2082
#117228712
#117228702
D3×#37172
D3×#37142
D3×#9493
C2×#638253
D3×#9083