Finite Group Databasebeta

← D3×#64120 #13176713

Subgroups — D3×#64120 #13176713

Order 1728.

2060 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×#3830C211yesmaximal, characteristic, complemented
2D3×D4×C3⋊D3C211yesmaximal, characteristic, complemented
3#11723952C211yesmaximal, characteristic, complemented
4C3×#64120C211yesmaximal, characteristic, complemented
5C32×D3×D8C211yesmaximal, characteristic, complemented
6#11723564C211yesmaximal, characteristic, complemented
7#11723560C211yesmaximal, characteristic, complemented
8D3×#3754C211yesmaximal, characteristic, complemented
9#11723548C211yesmaximal, characteristic, complemented
10#11723546C211yesmaximal, characteristic, complemented
11D3×#3753C211yesmaximal, characteristic, complemented
12#11723324C211yesmaximal, characteristic, complemented
13#11723320C211yesmaximal, characteristic, complemented
14D3×#3744C211yesmaximal, characteristic, complemented
15D3×#3743C211yesmaximal, characteristic, complemented
16C2×#64120—31nomaximal
17D3×#911—34nomaximal
18C22×D3×C3⋊D3—21no—
19#89078C2211yescharacteristic, complemented
20D4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
21C3×#3830C2211yescharacteristic, complemented
22C3×D4×C3⋊D3C2211yescharacteristic, complemented
23C32×D3×D4C2211yescharacteristic
24C32×D3×D4C2211yescharacteristic, complemented
25#89039—21no—
26C3⋊D3×#67—21no—
27D3×#638—21no—
28D3×#638—21no—
29#89029—21no—
30#89028—21no—
31C2×D3×C3⋊Dic3—21no—
32#89026C2211yescharacteristic, complemented
33C3⋊D3×D12C2211yescharacteristic, complemented
34D3×C4⋊(C3⋊D3)C2211yescharacteristic
35C4×D3×C3⋊D3C2211yescharacteristic
36#89015C2211yescharacteristic, complemented
37#89014C2211yescharacteristic, complemented
38D3×#634C2211yescharacteristic, complemented
39C33×D8C2211yescharacteristic, complemented
40#88861C2211yescharacteristic, complemented
41#88860C2211yescharacteristic, complemented
42#88851C2211yescharacteristic, complemented
43#88850C2211yescharacteristic, complemented
44C3×#3754C2211yescharacteristic, complemented
45C3×#3753C2211yescharacteristic, complemented
46C3×#3744C2211yescharacteristic, complemented
47C3×#3743C2211yescharacteristic, complemented
48C32×#213C2211yescharacteristic, complemented
49C32×#213C2211yescharacteristic, complemented
50C32×D24C2211yescharacteristic, complemented
51C32×D3×C8C2211yescharacteristic, complemented
52#88797C2211yescharacteristic, complemented
53#88796C2211yescharacteristic, complemented
54#88794C2211yescharacteristic, complemented
55#88792C2211yescharacteristic, complemented
56#88790C2211yescharacteristic, complemented
57#88789C2211yescharacteristic, complemented
58#88788C2211yescharacteristic, complemented
59#88787C2211yescharacteristic, complemented
60D3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
61C2×#3830—31no—
62C2×D4×C3⋊D3—31no—
63D3×#237—34no—
64D32×D4—34no—
65C2×C32×D8—31no—
66C2×#3754—31no—
67C2×#3753—31no—
68#64120—31no—
69#64120—31no—
70#64120—31no—
71#64120—31no—
72#64120—31no—
73#64120—31no—
74#64120—31no—
75#64120—34no—
76#64120—64no—
77#64120D311yescharacteristic, direct product factor
78C2×#3744—31no—
79C2×#3743—31no—
80C3×#911—34no—
81C3×D3×D8D314yescomplemented
82#63937—34no—
83#63932—34no—
84D3×#214—34no—
85#63927—34no—
86#63925—34no—
87D3×#213—34no—
88#63798—34no—
89#63795—34no—
90D3×#204—34no—
91D3×ΓL(1,𝔽25)—34no—
92C22×C3⋊(C3⋊D3)—21no—
93C22×C3×C3⋊D3—21no—
94C22×C32×D3—21no—
95C22×C32×D3—21no—
96C2×D3×C3⋊D3—21no—
97C2×D3×C3⋊D3—21no—
98C2×D3×C3⋊D3—21no—
99C2×D3×C3⋊D3—44no—
100C2×D3×C3⋊D3D411yescharacteristic
101C33×D4C2311yescharacteristic
102C33×D4C2311yescharacteristic, complemented
103#6312—21no—
104#6312—21no—
105C2×C3⋊(C3⋊Dic3)—21no—
106C4⋊(C3⋊(C3⋊D3))C2311yescharacteristic
107C4×C3⋊(C3⋊D3)C2311yescharacteristic
108#6308C2311yescharacteristic, complemented
109C3×#638—21no—
110C3×#638—21no—
111C2×C3×C3⋊Dic3—21no—
112C3×C4⋊(C3⋊D3)C2311yescharacteristic
113C3×C4×C3⋊D3C2311yescharacteristic
114C3×#634C2311yescharacteristic, complemented
115C32×#67—21no—
116C32×#67—21no—
117C32×D12C2311yescharacteristic
118C32×D12C2311yescharacteristic, complemented
119C32×C4×D3C2311yescharacteristic
120#6293—21no—
121#6292—21no—
122#6291—21no—
123#6291—21no—
124#6290—21no—
125#6290—21no—
126#6289D411yescharacteristic
127Dic3×C3⋊D3D411yescharacteristic
128D3×C3⋊Dic3—21no—
129D3×C3⋊Dic3—21no—
130D3×C3⋊Dic3—21no—
131D3×C3⋊Dic3D411yescharacteristic
132C33×C8C2311yescharacteristic, complemented
133C3⋊(C3⋊(C3⋊C8))C2311yescharacteristic, complemented
134C3×C3⋊(C3⋊C8)C2311yescharacteristic, complemented
135C32×C3⋊C8C2311yescharacteristic, complemented
136D3×AGL(1,ℤ/8)—91no—
137C2×#911—94no—
138C23×C3⋊D3—61no—
139C22×D32—64no—
140C2×C32×D4—31no—
141C2×C32×D4—31no—
142C2×#638—61no—
143C2×#638—61no—
144C22×C3⋊Dic3—61no—
145#3830—31no—
146#3830—34no—
147#3830—31no—
148#3830—31no—
149#3830—61no—
150#3830—61no—
151#3830—64no—
152#3830C2×D311yescharacteristic, complemented
153D4×C3⋊D3—31no—
154D4×C3⋊D3—34no—
155D4×C3⋊D3—31no—
156D4×C3⋊D3—31no—
157D4×C3⋊D3—61no—
158D4×C3⋊D3—61no—
159D4×C3⋊D3—64no—
160D4×C3⋊D3C2×D311yescharacteristic, complemented
161C2×C4⋊(C3⋊D3)—31no—
162C2×C4×C3⋊D3—31no—
163C2×#634—31no—
164C3×#237—34no—
165C3×D3×D4—34no—
166C3×D3×D4C2×D314yes—
167C3×D3×D4C2×D314yescomplemented
168#3811—64no—
169D3×#67—64no—
170D3×#67—64no—
171D3×#67—64no—
172#3805—64no—
173#3804—64no—
174C2×D3×Dic3—64no—
175#3802—34no—
176D3×D12—34no—
177D3×D12—34no—
178C4×D32—34no—
179#3796—34no—
180#3795—34no—
181D3×Dic6—34no—
182C32×D8—24no—
183C32×D8—31no—
184C32×D8—31no—
185C32×D8—31no—
186C32×D8C2×D314yescomplemented
187C32×D8C2×D311yescharacteristic, complemented
188C2×C32×C8—31no—
189#3754—31no—
190#3754—34no—
191#3754—31no—
192#3754—31no—
193#3754—64no—
194#3754C2×D311yescharacteristic, complemented
195#3753—31no—
196#3753—34no—
197#3753—31no—
198#3753—31no—
199#3753—64no—
200#3753C2×D311yescharacteristic, complemented
201C2×C3⋊(C3⋊C8)—31no—
202#3744—31no—
203#3744—31no—
204#3744—31no—
205#3744—34no—
206#3744—64no—
207#3744C2×D311yescharacteristic, complemented
208#3743—31no—
209#3743—31no—
210#3743—34no—
211#3743—31no—
212#3743—64no—
213#3743C2×D311yescharacteristic, complemented
214C3×#214—34no—
215C3×#213—34no—
216C3×#213C2×D314yescomplemented
217C3×#213C2×D314yescomplemented
218C3×D24C2×D314yescomplemented
219C3×#204—34no—
220C3×ΓL(1,𝔽25)—34no—
221C3×D3×C8C2×D314yescomplemented
222#3717—34no—
223#3716—34no—
224#3716—34no—
225#3715—34no—
226#3714—34no—
227#3713—34no—
228#3712—34no—
229#3711—34no—
230D3×C3⋊C8—34no—
231C22×C33—21no—
232C22×C33—21no—
233C2×C3⋊(C3⋊D3)—21no—
234C2×C3⋊(C3⋊D3)—42no—
235C2×C3⋊(C3⋊D3)C2×D411yescharacteristic
236C2×C3×C3⋊D3—21no—
237C2×C3×C3⋊D3—42no—
238C2×C3×C3⋊D3C2×D411yescharacteristic
239C2×C32×D3—21no—
240C2×C32×D3—21no—
241C2×C32×D3—42no—
242C2×C32×D3—42no—
243C2×C32×D3C2×D411yescharacteristic
244D3×C3⋊D3—22no—
245D3×C3⋊D3—42no—
246D3×C3⋊D3—42no—
247D3×C3⋊D3—42no—
248C33×C4C2411yescharacteristic
249C3⋊(C3⋊Dic3)—21no—
250C3⋊(C3⋊Dic3)C2×D411yescharacteristic
251C3×C3⋊Dic3—21no—
252C3×C3⋊Dic3C2×D411yescharacteristic
253C32×Dic3C2×D411yescharacteristic
254D3×#41—91no—
255C2×#237—94no—
256C2×D3×D4—94no—
257C2×D3×D4—91no—
258C3×AGL(1,ℤ/8)—91no—
259C2×C3×D8—34no—
260#949—91no—
261C2×#214—94no—
262#932—91no—
263C2×#213—94no—
264#914—91no—
265#914—91no—
266D3×SD16—91no—
267D3×SD16—91no—
268#911—34no—
269#911—94no—
270#911—94no—
271#911—94no—
272#911—94no—
273#911—94no—
274#911—94no—
275#911—94no—
276#911—91no—
277#911—91no—
278#911—184no—
279D3×D8—91no—
280D3×D8C3⋊D311yescharacteristic, complemented
281#908—91no—
282D3×M16—91no—
283C2×#204—94no—
284C2×ΓL(1,𝔽25)—94no—
285C23×C32—61no—
286C23×C32—61no—
287C22×C3⋊D3—21no—
288C22×C3⋊D3—31no—
289C22×C3⋊D3—61no—
290C22×C3⋊D3—61no—
291C22×C3⋊D3—61no—
292C22×C3⋊D3—61no—
293C22×C3⋊D3—64no—
294C22×C3⋊D3—124no—
295C22×C3⋊D3—124no—
296C22×C3×D3—24no—
297C22×C3×D3—24no—
298C22×C3×D3—64no—
299C2×D32—34no—
300C2×D32—64no—
301C2×D32—64no—
302C2×D32—64no—
303C2×D32—1216no—
304C32×D4—24no—
305C32×D4—24no—
306C32×D4—31no—
307C32×D4—31no—
308C32×D4—61no—
309C32×D4—61no—
310C32×D4C22×D314yes—
311C32×D4C22×D311yescharacteristic
312C32×D4C22×D314yescomplemented
313C32×D4C22×D311yescharacteristic, complemented
314C2×C32×C4—31no—
315#638—21no—
316#638—21no—
317#638—61no—
318#638—61no—
319#638—61no—
320#638—61no—
321#638—61no—
322#638—61no—
323#638—64no—
324#638—64no—
325#638—124no—
326#638—124no—
327C2×C3⋊Dic3—21no—
328C2×C3⋊Dic3—31no—
329C2×C3⋊Dic3—61no—
330C2×C3⋊Dic3—61no—
331C2×C3⋊Dic3—61no—
332C2×C3⋊Dic3—61no—
333C2×C3⋊Dic3—64no—
334C2×C3⋊Dic3—124no—
335C4⋊(C3⋊D3)—31no—
336C4⋊(C3⋊D3)—34no—
337C4⋊(C3⋊D3)—64no—
338C4⋊(C3⋊D3)—61no—
339C4⋊(C3⋊D3)C22×D311yescharacteristic
340C4×C3⋊D3—31no—
341C4×C3⋊D3—31no—
342C4×C3⋊D3—31no—
343C4×C3⋊D3—34no—
344C4×C3⋊D3—64no—
345C4×C3⋊D3C22×D311yescharacteristic
346#634—31no—
347#634—34no—
348#634—64no—
349#634—61no—
350#634C22×D311yescharacteristic, complemented
351C3×#67—24no—
352C3×#67—24no—
353C3×#67—64no—
354C3×#67—64no—
355C2×C3×Dic3—64no—
356C3×D12—34no—
357C3×D12C22×D314yes—
358C3×D12C22×D314yescomplemented
359C3×C4×D3—34no—
360C3×C4×D3C22×D314yes—
361C3×Dic6—34no—
362#627—64no—
363#626—64no—
364#626—64no—
365#626—64no—
366#625—64no—
367#625—64no—
368#624—34no—
369D3×Dic3—34no—
370D3×Dic3—34no—
371D3×Dic3—64no—
372D3×Dic3—64no—
373D3×Dic3—64no—
374C32×C8—24no—
375C32×C8—31no—
376C32×C8C22×D314yescomplemented
377C32×C8C22×D311yescharacteristic, complemented
378C3⋊(C3⋊C8)—31no—
379C3⋊(C3⋊C8)—34no—
380C3⋊(C3⋊C8)—64no—
381C3⋊(C3⋊C8)C22×D311yescharacteristic, complemented
382C3×C3⋊C8—34no—
383C3×C3⋊C8C22×D314yescomplemented
384C2×AGL(1,ℤ/8)—271noSylow
385C2×C33—41no—
386C2×C33—41no—
387C2×C33C22×D411yescharacteristic
388C3⋊(C3⋊D3)—21no—
389C3⋊(C3⋊D3)—41no—
390C3×C3⋊D3—21no—
391C3×C3⋊D3—41no—
392C32×D3—41no—
393C32×D3—41no—
394C32×D3AGL(1,ℤ/8)12yescomplemented
395C23×D3—181no—
396C23×D3—184no—
397C3×#41—91no—
398C2×C3×D4—34no—
399C2×C3×D4—34no—
400C2×C3×D4—91no—
401C2×#67—181no—
402C2×#67—184no—
403C2×#67—184no—
404C22×Dic3—184no—
405#239—91no—
406D3×Q8—91no—
407#237—34no—
408#237—94no—
409#237—94no—
410#237—94no—
411#237—91no—
412#237—184no—
413#237—184no—
414#237—184no—
415#237—181no—
416D3×D4—34no—
417D3×D4—94no—
418D3×D4—94no—
419D3×D4—94no—
420D3×D4—91no—
421D3×D4—91no—
422D3×D4—91no—
423D3×D4—184no—
424D3×D4—181no—
425D3×D4—184no—
426D3×D4—184no—
427D3×D4—181no—
428D3×D4—181no—
429D3×D4C2×C3⋊D311yescharacteristic
430D3×D4C2×C3⋊D311yescharacteristic, complemented
431#235—91no—
432#235—181no—
433C2×D12—94no—
434C2×D12—91no—
435C2×C4×D3—94no—
436C2×C4×D3—91no—
437C2×C4×D3—181no—
438C2×Dic6—94no—
439C3×SD16—91no—
440C3×SD16—91no—
441C3×D8—24no—
442C3×D8—34no—
443C3×D8—34no—
444C3×D8—34no—
445C3×D8—91no—
446C3×D8D3214yescomplemented
447C3×D8C2×C3⋊D311yescharacteristic, complemented
448C3×M16—91no—
449C2×C3×C8—34no—
450#215—91no—
451#215—91no—
452#214—34no—
453#214—94no—
454#214—94no—
455#214—94no—
456#214—91no—
457#214—91no—
458#214—184no—
459#213—34no—
460#213—94no—
461#213—94no—
462#213—94no—
463#213—91no—
464#213—91no—
465#213—184no—
466#213C2×C3⋊D311yescharacteristic, complemented
467#213C2×C3⋊D311yescharacteristic, complemented
468#208—91no—
469C2×C3⋊C8—94no—
470D24—91no—
471D24C2×C3⋊D311yescharacteristic, complemented
472#204—34no—
473#204—94no—
474#204—94no—
475#204—91no—
476#204—94no—
477#204—91no—
478#204—184no—
479ΓL(1,𝔽25)—34no—
480ΓL(1,𝔽25)—94no—
481ΓL(1,𝔽25)—94no—
482ΓL(1,𝔽25)—94no—
483ΓL(1,𝔽25)—91no—
484ΓL(1,𝔽25)—91no—
485ΓL(1,𝔽25)—184no—
486D3×C8—91no—
487D3×C8C2×C3⋊D311yescharacteristic, complemented
488C22×C32—21no—
489C22×C32—21no—
490C22×C32—24no—
491C22×C32—24no—
492C22×C32—31no—
493C22×C32—44no—
494C22×C32—44no—
495C22×C32—61no—
496C22×C32—61no—
497C22×C32—122no—
498C22×C32—122no—
499C2×C3⋊D3—21no—
500C2×C3⋊D3—31no—
501C2×C3⋊D3—34no—
502C2×C3⋊D3—42no—
503C2×C3⋊D3—64no—
504C2×C3⋊D3—62no—
505C2×C3⋊D3—61no—
506C2×C3⋊D3—64no—
507C2×C3⋊D3—124no—
508C2×C3⋊D3—122no—
509C2×C3⋊D3—122no—
510C2×C3⋊D3—122no—
511C2×C3⋊D3—122no—
512C2×C3⋊D3—128no—
513C2×C3⋊D3—248no—
514C2×C3⋊D3D3×D411yescharacteristic
515C2×C3×D3—24no—
516C2×C3×D3—24no—
517C2×C3×D3—34no—
518C2×C3×D3—48no—
519C2×C3×D3—48no—
520C2×C3×D3—64no—
521C2×C3×D3—128no—
522C2×C3×D3D3×D414yes—
523D32—68no—
524D32—128no—
525D32—128no—
526D32—128no—
527C32×C4—24no—
528C32×C4—31no—
529C32×C4C23×D314yes—
530C32×C4C23×D311yescharacteristic
531C3⋊Dic3—21no—
532C3⋊Dic3—31no—
533C3⋊Dic3—34no—
534C3⋊Dic3—64no—
535C3⋊Dic3—61no—
536C3⋊Dic3—64no—
537C3⋊Dic3—124no—
538C3⋊Dic3D3×D411yescharacteristic
539C3×Dic3—34no—
540C3×Dic3—64no—
541C3×Dic3D3×D414yes—
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—
557C33C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
558C23×C3—64no—
559C23×C3—64no—
560C23×C3—181no—
561C22×D3—21no—
562C22×D3—21no—
563C22×D3—64no—
564C22×D3—94no—
565C22×D3—91no—
566C22×D3—181no—
567C22×D3—181no—
568C22×D3—184no—
569C22×D3—184no—
570C22×D3—184no—
571C22×D3—181no—
572C22×D3—184no—
573C22×D3—181no—
574C22×D3—364no—
575C22×D3—364no—
576C22×D3—3616no—
577C3×Q8—91no—
578C3×D4—24no—
579C3×D4—24no—
580C3×D4—34no—
581C3×D4—34no—
582C3×D4—64no—
583C3×D4—64no—
584C3×D4—91no—
585C3×D4—181no—
586C3×D4—181no—
587C3×D4C2×D3214yes—
588C3×D4C2×D3214yescomplemented
589C3×D4C22×C3⋊D311yescharacteristic
590C3×D4C22×C3⋊D311yescharacteristic, complemented
591C2×C3×C4—34no—
592C2×C3×C4—91no—
593C2×C3×C4—181no—
594#67—21no—
595#67—21no—
596#67—64no—
597#67—64no—
598#67—184no—
599#67—184no—
600#67—181no—
601#67—184no—
602#67—181no—
603#67—184no—
604#67—181no—
605#67—184no—
606#67—181no—
607#67—184no—
608#67—181no—
609#67—364no—
610#67—364no—
611C2×Dic3—64no—
612C2×Dic3—94no—
613C2×Dic3—91no—
614C2×Dic3—184no—
615C2×Dic3—184no—
616C2×Dic3—184no—
617C2×Dic3—181no—
618C2×Dic3—184no—
619C2×Dic3—364no—
620D12—34no—
621D12—94no—
622D12—91no—
623D12—184no—
624D12—184no—
625D12—181no—
626D12—181no—
627D12C22×C3⋊D311yescharacteristic
628D12C22×C3⋊D311yescharacteristic, complemented
629C4×D3—34no—
630C4×D3—94no—
631C4×D3—94no—
632C4×D3—91no—
633C4×D3—94no—
634C4×D3—91no—
635C4×D3—91no—
636C4×D3—184no—
637C4×D3—181no—
638C4×D3—181no—
639C4×D3—181no—
640C4×D3C22×C3⋊D311yescharacteristic
641Dic6—34no—
642Dic6—94no—
643Dic6—91no—
644Dic6—184no—
645Dic6—184no—
646Dic6—181no—
647C3×C8—24no—
648C3×C8—34no—
649C3×C8—91no—
650C3×C8C2×D3214yescomplemented
651C3×C8C22×C3⋊D311yescharacteristic, complemented
652C3⋊C8—34no—
653C3⋊C8—94no—
654C3⋊C8—91no—
655C3⋊C8—184no—
656C3⋊C8C22×C3⋊D311yescharacteristic, complemented
657C2×C32—24no—
658C2×C32—32no—
659C2×C32—41no—
660C2×C32—41no—
661C2×C32—44no—
662C2×C32—44no—
663C2×C32—84no—
664C2×C32—84no—
665C2×C32—121no—
666C2×C32—121no—
667C2×C32C2×D3×D414yes—
668C2×C32C2×D3×D411yescharacteristic
669C3⋊D3—21no—
670C3⋊D3—41no—
671C3⋊D3—61no—
672C3⋊D3—64no—
673C3⋊D3—124no—
674C3⋊D3—121no—
675C3⋊D3—124no—
676C3⋊D3—244no—
677C3×D3—44no—
678C3×D3—44no—
679C3×D3—64no—
680C3×D3—124no—
681C3×D3#91118yescomplemented
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×C3⋊D311yescharacteristic, complemented
719M16—91no—
720M16—271no—
721M16—271no—
722M16—271no—
723C2×C8—31no—
724C2×C8—271no—
725C22×C3—24no—
726C22×C3—24no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—34no—
730C22×C3—44no—
731C22×C3—44no—
732C22×C3—64no—
733C22×C3—64no—
734C22×C3—91no—
735C22×C3—128no—
736C22×C3—128no—
737C22×C3—181no—
738C22×C3—362no—
739C2×D3—21no—
740C2×D3—21no—
741C2×D3—34no—
742C2×D3—42no—
743C2×D3—42no—
744C2×D3—64no—
745C2×D3—94no—
746C2×D3—91no—
747C2×D3—128no—
748C2×D3—184no—
749C2×D3—188no—
750C2×D3—182no—
751C2×D3—184no—
752C2×D3—181no—
753C2×D3—364no—
754C2×D3—362no—
755C2×D3—362no—
756C2×D3—368no—
757C2×D3—368no—
758C2×D3—368no—
759C2×D3—362no—
760C2×D3—368no—
761C2×D3—362no—
762C2×D3—728no—
763C2×D3D4×C3⋊D311yescharacteristic
764C3×C4—24no—
765C3×C4—34no—
766C3×C4—91no—
767C3×C4—181no—
768C3×C4C22×D3214yes—
769C3×C4C23×C3⋊D311yescharacteristic
770Dic3—34no—
771Dic3—64no—
772Dic3—94no—
773Dic3—91no—
774Dic3—184no—
775Dic3—184no—
776Dic3—181no—
777Dic3—364no—
778Dic3D4×C3⋊D311yescharacteristic
779C32—24no—
780C32C2×#91114yescomplemented
781C32D3×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×C3⋊D311yescharacteristic
810D4C2×D3×C3⋊D311yescharacteristic, 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×C3⋊D311yescharacteristic, complemented
826C2×C3—24no—
827C2×C3—38no—
828C2×C3—41no—
829C2×C3—41no—
830C2×C3—44no—
831C2×C3—44no—
832C2×C3—84no—
833C2×C3—84no—
834C2×C3—124no—
835C2×C3—124no—
836C2×C3—181no—
837C2×C3—361no—
838C2×C3D32×D414yes—
839C2×C3C2×D4×C3⋊D311yescharacteristic
840D3—41no—
841D3—41no—
842D3—64no—
843D3—124no—
844D3—181no—
845D3—184no—
846D3—364no—
847D3—361no—
848D3—364no—
849D3—724no—
850D3#6412012yesdirect 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×C3⋊D311yescharacteristic
874C3—24no—
875C3D3×#91114yescomplemented
876C3C2×#6412011yescharacteristic, complemented
877C2—32no—
878C2—41no—
879C2—41no—
880C2—121no—
881C2—121no—
882C2—181no—
883C2—361no—
884C2—541no—
885C2—1081no—
886C2D3×D4×C3⋊D311yescharacteristic
subgroupG/H
centerC2D3×D4×C3⋊D3
commutator, cosocleC33×C4C24
FrattiniC4C22×D3×C3⋊D3
FittingC33×D8C22
socleC2×C33C22×D4
hypercenterD8D3×C3⋊D3
hypocenterC33C2×AGL(1,ℤ/8)
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C4 ◁ D8

Complements

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

NH ≅ G/Ntype
1. D3×#3830C2semidirect
2. D3×D4×C3⋊D3C2semidirect
3. #11723952C2semidirect
4. C3×#64120C2semidirect
5. C32×D3×D8C2semidirect
6. #11723564C2semidirect
7. #11723560C2semidirect
8. D3×#3754C2semidirect
9. #11723548C2semidirect
10. #11723546C2semidirect
11. D3×#3753C2semidirect
12. #11723324C2semidirect
13. #11723320C2semidirect
14. D3×#3744C2semidirect
15. D3×#3743C2semidirect
19. #89078C22semidirect
20. D4×C3⋊(C3⋊D3)C22semidirect
21. C3×#3830C22semidirect
22. C3×D4×C3⋊D3C22semidirect
24. C32×D3×D4C22semidirect
32. #89026C22semidirect
33. C3⋊D3×D12C22semidirect
36. #89015C22semidirect
37. #89014C22semidirect
38. D3×#634C22semidirect
39. C33×D8C22semidirect
40. #88861C22semidirect
41. #88860C22semidirect
42. #88851C22semidirect
43. #88850C22semidirect
44. C3×#3754C22semidirect
45. C3×#3753C22semidirect
46. C3×#3744C22semidirect
47. C3×#3743C22semidirect
48. C32×#213C22semidirect
49. C32×#213C22semidirect
50. C32×D24C22semidirect
51. C32×D3×C8C22semidirect
52. #88797C22semidirect
53. #88796C22semidirect
54. #88794C22semidirect
55. #88792C22semidirect
56. #88790C22semidirect
57. #88789C22semidirect
58. #88788C22semidirect
59. #88787C22semidirect
60. D3×C3⋊(C3⋊C8)C22semidirect
77. #64120D3direct (N × H)
81. C3×D3×D8D3semidirect
102. C33×D4C23semidirect
108. #6308C23semidirect
114. C3×#634C23semidirect
118. C32×D12C23semidirect
132. C33×C8C23semidirect
133. C3⋊(C3⋊(C3⋊C8))C23semidirect
134. C3×C3⋊(C3⋊C8)C23semidirect
135. C32×C3⋊C8C23semidirect
152. #3830C2×D3semidirect
160. D4×C3⋊D3C2×D3semidirect
167. C3×D3×D4C2×D3semidirect
186. C32×D8C2×D3semidirect
187. C32×D8C2×D3semidirect
194. #3754C2×D3semidirect
200. #3753C2×D3semidirect
207. #3744C2×D3semidirect
213. #3743C2×D3semidirect
216. C3×#213C2×D3semidirect
217. C3×#213C2×D3semidirect
218. C3×D24C2×D3semidirect
221. C3×D3×C8C2×D3semidirect
280. D3×D8C3⋊D3semidirect
312. C32×D4C22×D3semidirect
313. C32×D4C22×D3semidirect
350. #634C22×D3semidirect
358. C3×D12C22×D3semidirect
376. C32×C8C22×D3semidirect
377. C32×C8C22×D3semidirect
381. C3⋊(C3⋊C8)C22×D3semidirect
383. C3×C3⋊C8C22×D3semidirect
394. C32×D3AGL(1,ℤ/8)semidirect
430. D3×D4C2×C3⋊D3semidirect
446. C3×D8D32semidirect
447. C3×D8C2×C3⋊D3semidirect
466. #213C2×C3⋊D3semidirect
467. #213C2×C3⋊D3semidirect
471. D24C2×C3⋊D3semidirect
487. D3×C8C2×C3⋊D3semidirect
557. C33C2×AGL(1,ℤ/8)semidirect
588. C3×D4C2×D32semidirect
590. C3×D4C22×C3⋊D3semidirect
628. D12C22×C3⋊D3semidirect
650. C3×C8C2×D32semidirect
651. C3×C8C22×C3⋊D3semidirect
656. C3⋊C8C22×C3⋊D3semidirect
681. C3×D3#911semidirect
718. D8D3×C3⋊D3semidirect
780. C32C2×#911semidirect
781. C32D3×AGL(1,ℤ/8)semidirect
810. D4C2×D3×C3⋊D3semidirect
825. C8C2×D3×C3⋊D3semidirect
850. D3#64120direct (N × H)
875. C3D3×#911semidirect
876. C3C2×#64120semidirect

Maximal subgroups

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

subgroupindex
D3×#38302
D3×D4×C3⋊D32
#117239522
C3×#641202
C32×D3×D82
#117235642
#117235602
D3×#37542
#117235482
#117235462
D3×#37532
#117233242
#117233202
D3×#37442
D3×#37432
C2×#641203
D3×#9113