Finite Group Databasebeta

← Dic3×#914 #11860293

Subgroups — Dic3×#914 #11860293

Order 1152.

1156 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#914C211yesmaximal, characteristic
2Dic3×#239C211yesmaximal, characteristic, complemented
3D3×D4×Dic3C211yesmaximal, characteristic, complemented
4#10592863C211yesmaximal, characteristic, complemented
5C3×Dic3×SD16C211yesmaximal, characteristic, complemented
6#10591572C211yesmaximal, characteristic, complemented
7Dic3×#215C211yesmaximal, characteristic, complemented
8#10591550C211yesmaximal, characteristic, complemented
9#10591436C211yesmaximal, characteristic, complemented
10Dic3×#213C211yesmaximal, characteristic, complemented
11#10591421C211yesmaximal, characteristic, complemented
12#10590781C211yesmaximal, characteristic, complemented
13Dic3×D24C211yesmaximal, characteristic, complemented
14#10590681C211yesmaximal, characteristic, complemented
15Dic3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
16Dic3×AGL(1,ℤ/8)—31nomaximal
17C4×#914—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C22×D3×Dic3—21no—
21C2×C32×SD16C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic, complemented
23D4×C3⋊Dic3C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic, complemented
25C2×C3×#215C2211yescharacteristic
26C3×D4×Dic3C2211yescharacteristic
27C2×C3×#213C2211yescharacteristic
28C3×#914C418yescomplemented
29C2×C3×D24C2211yescharacteristic
30C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
31#67⋊Dic3—21no—
32Dic3×#67—21no—
33D3×#217—21no—
34#63898—21no—
35#63898C2211yescharacteristic
36#63898C2211yescharacteristic, complemented
37Dic3×D12—21no—
38Dic3×D12C2211yescharacteristic
39Dic3×D12C2211yescharacteristic, complemented
40D3×C4⋊Dic3C2211yescharacteristic
41C4×D3×Dic3—21no—
42C4×D3×Dic3C2211yescharacteristic
43#63841—21no—
44#63841C2211yescharacteristic
45C2×#3711C2211yescharacteristic
46#63662C2211yescharacteristic, complemented
47#63659C2211yescharacteristic
48#63645C2211yescharacteristic, complemented
49#63642C2211yescharacteristic, complemented
50C3×#835C2211yescharacteristic, complemented
51C3×#832C2211yescharacteristic
52C3×#817C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59#63562C2211yescharacteristic, complemented
60#63555C2211yescharacteristic, complemented
61Dic3×C3⋊C8C2211yescharacteristic, complemented
62C2×C3×AGL(1,ℤ/8)—31no—
63Dic3×#41—31no—
64C2×D4×Dic3—31no—
65C2×#914D311yescharacteristic
66C4×#239—31no—
67C4×D3×D4—31no—
68C3×C4×SD16—31no—
69#5232—31no—
70#5215—31no—
71#5164—31no—
72#5164—31no—
73#5164—31no—
74#5164—61no—
75Dic3×SD16—31no—
76Dic3×SD16D311yescharacteristic, complemented
77#5152—31no—
78#5152—31no—
79Dic3×D8—31no—
80Dic3×D8—31no—
81#5121—31no—
82Dic3×M16—31no—
83C4×#215—31no—
84C4×#213—31no—
85#4869—31no—
86#4861—31no—
87#4817—31no—
88#4803—31no—
89#4785—31no—
90#4770—31no—
91C4×D24—31no—
92C4×ΓL(1,𝔽25)—31no—
93C23×C3×D3—21no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C22×C3⋊Dic3—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C3×#239—22no—
100C3×#239C2×C414yescomplemented
101C3×D3×D4—22no—
102C3×D3×D4C2×C414yescomplemented
103C2×C3×D12—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111C2×D3×Dic3—21no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3—44no—
114C2×D3×Dic3D411yescharacteristic
115C2×D3×Dic3D411yescharacteristic
116C32×SD16C2×C414yescomplemented
117C2×C32×C8C2311yescharacteristic
118#3757—21no—
119C4⋊(C3⋊Dic3)—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122C4×C3⋊Dic3—21no—
123C4×C3⋊Dic3C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C3×#217—21no—
126C3×#215C2×C414yescomplemented
127C3×#213C2×C414yescomplemented
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4×Dic3—21no—
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C3×D24C2×C414yescomplemented
136C3×ΓL(1,𝔽25)C2×C414yescomplemented
137Dic3⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143Dic32—21no—
144Dic32D411yescharacteristic
145Dic32D411yescharacteristic
146#3711—22no—
147C4×AGL(1,ℤ/8)—91noSylow
148C2×C3×#41—31no—
149C22×C3×D4—31no—
150C23×Dic3—61no—
151C2×#239C2×D311yescharacteristic
152C2×D3×D4C2×D311yescharacteristic
153C22×C4×D3—61no—
154C3×AGL(1,ℤ/8)—38no—
155C2×C3×SD16—21no—
156C2×C3×SD16—31no—
157C2×C3×SD16C2×D311yescharacteristic
158C2×C3×SD16C2×D311yescharacteristic
159C2×C3×D8—31no—
160C2×C3×D8—31no—
161C2×C3×M16—31no—
162C3×C4×Q8—31no—
163C3×C4×D4—31no—
164C2×#217—61no—
165Q8×Dic3—31no—
166Q8×Dic3—31no—
167Q8×Dic3—61no—
168Q8×Dic3C2×D311yescharacteristic, complemented
169C2×#215C2×D311yescharacteristic
170D4×Dic3—31no—
171D4×Dic3—31no—
172D4×Dic3—31no—
173D4×Dic3—31no—
174D4×Dic3—31no—
175D4×Dic3—31no—
176D4×Dic3—61no—
177D4×Dic3—61no—
178D4×Dic3—61no—
179D4×Dic3—61no—
180D4×Dic3—61no—
181D4×Dic3C2×D311yescharacteristic
182C2×#213C2×D311yescharacteristic
183C4×#67—61no—
184#926—31no—
185#926—61no—
186C2×C4⋊Dic3—31no—
187C2×C4×Dic3—31no—
188C2×C4×Dic3—61no—
189C2×#208—31no—
190#914Dic318yesdirect product factor
191C2×D24C2×D311yescharacteristic
192C2×ΓL(1,𝔽25)—31no—
193C2×ΓL(1,𝔽25)C2×D311yescharacteristic
194#893—31no—
195#893—31no—
196#893—61no—
197#892—31no—
198#892—61no—
199D3×C4⋊C4—31no—
200#67⋊C4—61no—
201D3×C22⋊C4—61no—
202C4×D12—31no—
203C4×D12—31no—
204C4×D12—61no—
205C42×D3—31no—
206C42×D3—61no—
207C3×#106—31no—
208C3×#103—31no—
209C3×#102—31no—
210C3×C4×C8—31no—
211#835—31no—
212#835—31no—
213#835—61no—
214#835C2×D311yescharacteristic, complemented
215#832—31no—
216#832—31no—
217#832—31no—
218#832—31no—
219#832—31no—
220#832—31no—
221#832—61no—
222#832C2×D311yescharacteristic
223#821—31no—
224#821—31no—
225#818—31no—
226#818—31no—
227#818—31no—
228#818—61no—
229#817—31no—
230#817C2×D311yescharacteristic, complemented
231#815—31no—
232#815—31no—
233#815—31no—
234#815—31no—
235#815—61no—
236C8×Dic3—31no—
237C8×Dic3C2×D311yescharacteristic, complemented
238#809—31no—
239#809—31no—
240#808—31no—
241#807—31no—
242C4×C3⋊C8—31no—
243C23×C32—21no—
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—24no—
247C22×C3×D3—42no—
248C22×C3×D3—42no—
249C22×C3×D3C2×D411yescharacteristic
250C32×Q8—21no—
251C32×Q8C22×C412yescomplemented
252C32×D4—21no—
253C32×D4C22×C412yes—
254C2×C32×C4—21no—
255C2×C32×C4C2411yescharacteristic
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3—42no—
259C2×C3⋊Dic3C2×D411yescharacteristic
260C2×C3⋊Dic3C2×D411yescharacteristic
261C3×#67—24no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—42no—
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C3×D12—24no—
269C3×D12—21no—
270C3×D12—21no—
271C3×D12C22×C412yes—
272C3×D12C22×C412yescomplemented
273C3×C4×D3—24no—
274C3×C4×D3C22×C412yes—
275C3×C4×D3#4112yes—
276D3×Dic3—22no—
277D3×Dic3—41no—
278D3×Dic3—42no—
279D3×Dic3—42no—
280D3×Dic3—42no—
281D3×Dic3—42no—
282D3×Dic3—42no—
283C32×C8C22×C412yescomplemented
284C3⋊(C3⋊C8)—21no—
285C3×C3⋊C8—21no—
286C3×C3⋊C8C22×C412yescomplemented
287C2×AGL(1,ℤ/8)—31no—
288C4×#41—91no—
289C2×C4×D4—91no—
290#442—91no—
291#442—91no—
292#440—91no—
293#440—91no—
294C4×SD16—31no—
295C4×SD16—91no—
296C4×D8—91no—
297C4×D8—91no—
298#428—91no—
299#418—91no—
300#417—91no—
301C4×M16—91no—
302C24×C3—61no—
303C23×D3—21no—
304C3×#41—34no—
305C3×#41—62no—
306C2×C3×Q8—21no—
307C2×C3×Q8C22×D311yescharacteristic
308C2×C3×Q8C22×D311yescharacteristic
309C2×C3×D4—21no—
310C2×C3×D4—34no—
311C2×C3×D4—31no—
312C2×C3×D4—31no—
313C2×C3×D4—61no—
314C2×C3×D4—62no—
315C2×C3×D4—61no—
316C2×C3×D4C22×D311yescharacteristic
317C2×C3×D4C22×D311yescharacteristic
318C22×C3×C4—31no—
319C22×C3×C4—61no—
320C22×C3×C4—61no—
321C2×#67—21no—
322C22×Dic3—21no—
323C22×Dic3—31no—
324C22×Dic3—31no—
325C22×Dic3—61no—
326C22×Dic3—61no—
327C22×Dic3—61no—
328C22×Dic3—61no—
329C22×Dic3—61no—
330C22×Dic3—61no—
331C22×Dic3—61no—
332C22×Dic3—121no—
333C22×Dic3—124no—
334#239—22no—
335#239C2×Dic314yescomplemented
336D3×D4—22no—
337D3×D4C2×Dic314yescomplemented
338C2×D12—21no—
339C2×D12C22×D311yescharacteristic
340C2×D12C22×D311yescharacteristic
341C2×C4×D3—21no—
342C2×C4×D3—31no—
343C2×C4×D3—31no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3—124no—
350C2×C4×D3C22×D311yescharacteristic
351C3×SD16—24no—
352C3×SD16—34no—
353C3×SD16C4×D314yescomplemented
354C3×SD16C2×Dic314yescomplemented
355C3×D8—34no—
356C3×D8—34no—
357C3×M16—34no—
358C2×C3×C8—21no—
359C2×C3×C8—31no—
360C2×C3×C8—31no—
361C2×C3×C8C22×D311yescharacteristic
362C2×C3×C8C22×D311yescharacteristic
363C3×C4⋊C4—31no—
364C3×C4⋊C4—31no—
365C3×C4⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C42—31no—
368C3×C42—61no—
369#217—21no—
370#217—61no—
371#217—61no—
372#217—61no—
373#217—61no—
374#217—61no—
375#217—61no—
376#217—61no—
377#217—121no—
378#215C2×Dic314yescomplemented
379#213C2×Dic314yescomplemented
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385C4⋊Dic3—21no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3—121no—
396C4⋊Dic3C22×D311yescharacteristic
397C4⋊Dic3C22×D311yescharacteristic
398Dic3⋊C4—61no—
399C4×Dic3—21no—
400C4×Dic3—31no—
401C4×Dic3—31no—
402C4×Dic3—31no—
403C4×Dic3—31no—
404C4×Dic3—31no—
405C4×Dic3—31no—
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3—61no—
409C4×Dic3—61no—
410C4×Dic3—61no—
411C4×Dic3—121no—
412C4×Dic3C22×D311yescharacteristic
413#208—62no—
414C2×C3⋊C8—31no—
415C2×C3⋊C8—31no—
416C2×C3⋊C8—61no—
417C2×C3⋊C8C22×D311yescharacteristic
418C2×C3⋊C8C22×D311yescharacteristic
419D24C2×Dic314yescomplemented
420ΓL(1,𝔽25)—62no—
421ΓL(1,𝔽25)C2×Dic314yescomplemented
422C22×C32—22no—
423C22×C32—41no—
424C22×C32—41no—
425C22×C32C22×D411yescharacteristic
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—22no—
429C2×C3×D3—22no—
430C2×C3×D3—48no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3C4×D412yes—
436C32×C4—22no—
437C32×C4C23×C411yescharacteristic
438C32×C4C2×#4111yescharacteristic
439C3⋊Dic3—21no—
440C3⋊Dic3—21no—
441C3⋊Dic3—41no—
442C3⋊Dic3—41no—
443C3×Dic3—21no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C3×Dic3C4×D412yes—
447C3×Dic3AGL(1,ℤ/8)12yescomplemented
448C2×#41—31no—
449C22×D4—31no—
450C23×C4—181no—
451AGL(1,ℤ/8)—38no—
452C2×SD16—31no—
453C2×SD16D3211yescharacteristic
454C2×D8—31no—
455C2×D8—31no—
456C2×M16—31no—
457C2×M16—91no—
458C4×Q8—31no—
459C4×Q8—91no—
460C4×D4—31no—
461C4×D4—91no—
462C4×D4—91no—
463C4×D4—91no—
464C4×D4—91no—
465C4×D4—91no—
466C4×D4—181no—
467C4×D4—181no—
468C4×D4—181no—
469C4×D4—181no—
470#117—91no—
471#117—181no—
472C2×C4⋊C4—91no—
473C2×C22⋊C4—181no—
474C2×C42—91no—
475C2×C42—181no—
476#107—91no—
477#107—91no—
478#106—31no—
479#106—91no—
480#103—31no—
481#103—91no—
482#102—31no—
483#102—91no—
484#102—91no—
485#102—91no—
486#102—91no—
487#102—91no—
488#97—91no—
489#97—91no—
490C4×C8—31no—
491C4×C8—91no—
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—31no—
495C23×C3—41no—
496C23×C3—64no—
497C23×C3—61no—
498C23×C3—61no—
499C23×C3—122no—
500C23×C3—122no—
501C22×D3—21no—
502C22×D3—21no—
503C22×D3—24no—
504C22×D3—42no—
505C22×D3—42no—
506C22×D3D3×D411yescharacteristic
507C3×Q8—21no—
508C3×Q8—21no—
509C3×Q8—22no—
510C3×Q8—41no—
511C3×Q8C2×C4×D312yescomplemented
512C3×Q8C22×Dic312yescomplemented
513C3×D4—21no—
514C3×D4—21no—
515C3×D4—22no—
516C3×D4—32no—
517C3×D4—32no—
518C3×D4—41no—
519C3×D4—64no—
520C3×D4—64no—
521C3×D4—61no—
522C3×D4—61no—
523C3×D4C2×C4×D312yes—
524C3×D4C22×Dic312yes—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—31no—
529C2×C3×C4—31no—
530C2×C3×C4—32no—
531C2×C3×C4—32no—
532C2×C3×C4—31no—
533C2×C3×C4—41no—
534C2×C3×C4—64no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—122no—
538C2×C3×C4C23×D311yescharacteristic
539C2×C3×C4C23×D311yescharacteristic
540#67—24no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—31no—
544C2×Dic3—31no—
545C2×Dic3—31no—
546C2×Dic3—31no—
547C2×Dic3—42no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—62no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—121no—
556C2×Dic3—121no—
557C2×Dic3—121no—
558C2×Dic3—122no—
559C2×Dic3—122no—
560C2×Dic3—122no—
561C2×Dic3—122no—
562C2×Dic3—122no—
563C2×Dic3—122no—
564C2×Dic3—122no—
565C2×Dic3—242no—
566C2×Dic3D3×D411yescharacteristic
567C2×Dic3D3×D411yescharacteristic
568C2×Dic3D3×D411yescharacteristic
569D12—24no—
570D12—21no—
571D12—21no—
572D12C22×Dic312yes—
573D12C22×Dic312yescomplemented
574C4×D3—24no—
575C4×D3—62no—
576C4×D3—121no—
577C4×D3—122no—
578C4×D3—122no—
579C4×D3—122no—
580C4×D3—122no—
581C4×D3—122no—
582C4×D3#23712yes—
583C4×D3C22×Dic312yes—
584C3×C8—22no—
585C3×C8—32no—
586C3×C8—61no—
587C3×C8C2×C4×D312yescomplemented
588C3×C8C22×Dic312yescomplemented
589C3⋊C8—21no—
590C3⋊C8—61no—
591C3⋊C8—61no—
592C3⋊C8—121no—
593C3⋊C8C22×Dic312yescomplemented
594C2×C32—42no—
595C2×C32C2×C4×D411yescharacteristic
596C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
597C2×C32#57511yescharacteristic
598C3×D3—22no—
599C3×D3—42no—
600C3×D3—42no—
601C24—61no—
602#41—34no—
603#41—62no—
604C2×Q8C2×D3211yescharacteristic
605C2×D4—34no—
606C2×D4—31no—
607C2×D4—31no—
608C2×D4—61no—
609C2×D4—62no—
610C2×D4—61no—
611C2×D4C2×D3211yescharacteristic
612C22×C4—31no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—91no—
616C22×C4—91no—
617C22×C4—181no—
618C22×C4—181no—
619C22×C4—181no—
620C22×C4—181no—
621C22×C4—181no—
622C22×C4—181no—
623C22×C4—364no—
624SD16—34no—
625SD16D3×Dic314yescomplemented
626D8—34no—
627D8—34no—
628M16—34no—
629M16—182no—
630C2×C8—31no—
631C2×C8—31no—
632C2×C8—91no—
633C2×C8C2×D3211yescharacteristic
634C4⋊C4—31no—
635C4⋊C4—31no—
636C4⋊C4—61no—
637C4⋊C4—91no—
638C4⋊C4—91no—
639C4⋊C4—181no—
640C4⋊C4—181no—
641C22⋊C4—61no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C42—31no—
649C42—61no—
650C42—91no—
651C42—91no—
652C42—91no—
653C42—181no—
654C42—181no—
655C22×C3—22no—
656C22×C3—22no—
657C22×C3—21no—
658C22×C3—32no—
659C22×C3—42no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—61no—
665C22×C3—61no—
666C22×C3—62no—
667C22×C3—62no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3—128no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3—121no—
674C22×C3—121no—
675C22×C3C2×D3×D411yescharacteristic
676C22×C3C2×D3×D411yescharacteristic
677C2×D3—21no—
678C2×D3—21no—
679C2×D3—22no—
680C2×D3—22no—
681C2×D3—48no—
682C2×D3—41no—
683C2×D3—41no—
684C2×D3—41no—
685C2×D3—41no—
686C2×D3D4×Dic312yes—
687C3×C4—22no—
688C3×C4—22no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—32no—
692C3×C4—32no—
693C3×C4—42no—
694C3×C4—61no—
695C3×C4—121no—
696C3×C4—121no—
697C3×C4C22×C4×D311yescharacteristic
698C3×C4C2×#23711yescharacteristic
699C3×C4D3×#4111yescharacteristic
700C3×C4C23×Dic311yescharacteristic
701Dic3—21no—
702Dic3—41no—
703Dic3—41no—
704Dic3—61no—
705Dic3—61no—
706Dic3—61no—
707Dic3—61no—
708Dic3—121no—
709Dic3—121no—
710Dic3—121no—
711Dic3—121no—
712Dic3—121no—
713Dic3—121no—
714Dic3—241no—
715Dic3—241no—
716Dic3#91412yesdirect product factor
717Dic3D4×Dic312yes—
718C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
719C23—21no—
720C23—31no—
721C23—64no—
722C23—61no—
723C23—61no—
724C23—122no—
725C23—122no—
726Q8—21no—
727Q8C2×D3×Dic312yescomplemented
728D4—21no—
729D4—32no—
730D4—32no—
731D4—64no—
732D4—64no—
733D4—61no—
734D4—61no—
735D4C2×D3×Dic312yes—
736C2×C4—21no—
737C2×C4—31no—
738C2×C4—31no—
739C2×C4—32no—
740C2×C4—32no—
741C2×C4—31no—
742C2×C4—64no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—91no—
746C2×C4—91no—
747C2×C4—122no—
748C2×C4—182no—
749C2×C4—181no—
750C2×C4—181no—
751C2×C4—362no—
752C2×C4—362no—
753C2×C4—361no—
754C2×C4—362no—
755C2×C4—362no—
756C2×C4—362no—
757C2×C4—362no—
758C2×C4C22×D3211yescharacteristic
759C8—32no—
760C8—61no—
761C8—181no—
762C8C2×D3×Dic312yescomplemented
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—42no—
767C2×C3—42no—
768C2×C3—62no—
769C2×C3—82no—
770C2×C3—122no—
771C2×C3—122no—
772C2×C3C4×D3×D411yescharacteristic
773C2×C3C2×#91411yescharacteristic
774C2×C3#576811yescharacteristic
775C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
776C2×C3#577311yescharacteristic
777C2×C3C2×D4×Dic311yescharacteristic
778D3—22no—
779D3—42no—
780D3—42no—
781C22—22no—
782C22—32no—
783C22—41no—
784C22—41no—
785C22—61no—
786C22—61no—
787C22—62no—
788C22—62no—
789C22—128no—
790C22—121no—
791C22—121no—
792C22—121no—
793C22—121no—
794C22D32×D411yescharacteristic
795C4—22no—
796C4—32no—
797C4—32no—
798C4—61no—
799C4—121no—
800C4—121no—
801C4—181no—
802C4—181no—
803C4—361no—
804C4—361no—
805C4D3×#23711yescharacteristic
806C4C22×D3×Dic311yescharacteristic
807C3—21no—
808C3C4×#91411yescharacteristic, complemented
809C3Dic3×AGL(1,ℤ/8)11yescharacteristic, complemented
810C2—42no—
811C2—62no—
812C2—122no—
813C2—122no—
814C2D3×#91411yescharacteristic
815C2#1059474511yescharacteristic
816C2D3×D4×Dic311yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radicalC2×C3×#914C2
cosocleC2×C32×C4C24
hypercenterC2×SD16D32
hypocenterC32C4×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
2. Dic3×#239C2semidirect
3. D3×D4×Dic3C2semidirect
4. #10592863C2semidirect
5. C3×Dic3×SD16C2semidirect
6. #10591572C2semidirect
7. Dic3×#215C2semidirect
8. #10591550C2semidirect
9. #10591436C2semidirect
10. Dic3×#213C2semidirect
11. #10591421C2semidirect
12. #10590781C2semidirect
13. Dic3×D24C2semidirect
14. #10590681C2semidirect
15. Dic3×ΓL(1,𝔽25)C2semidirect
22. Q8×C3⋊Dic3C22semidirect
24. C3×Q8×Dic3C22semidirect
28. C3×#914C4semidirect
36. #63898C22semidirect
39. Dic3×D12C22semidirect
46. #63662C22semidirect
48. #63645C22semidirect
49. #63642C22semidirect
50. C3×#835C22semidirect
52. C3×#817C22semidirect
53. C3×C8×Dic3C22semidirect
54. #63575C22semidirect
55. #63573C22semidirect
57. #63563C22semidirect
59. #63562C22semidirect
60. #63555C22semidirect
61. Dic3×C3⋊C8C22semidirect
76. Dic3×SD16D3semidirect
100. C3×#239C2×C4semidirect
102. C3×D3×D4C2×C4semidirect
116. C32×SD16C2×C4semidirect
126. C3×#215C2×C4semidirect
127. C3×#213C2×C4semidirect
135. C3×D24C2×C4semidirect
136. C3×ΓL(1,𝔽25)C2×C4semidirect
168. Q8×Dic3C2×D3semidirect
190. #914Dic3direct (N × H)
214. #835C2×D3semidirect
230. #817C2×D3semidirect
237. C8×Dic3C2×D3semidirect
251. C32×Q8C22×C4semidirect
272. C3×D12C22×C4semidirect
283. C32×C8C22×C4semidirect
286. C3×C3⋊C8C22×C4semidirect
335. #239C2×Dic3semidirect
337. D3×D4C2×Dic3semidirect
353. C3×SD16C4×D3semidirect
354. C3×SD16C2×Dic3semidirect
378. #215C2×Dic3semidirect
379. #213C2×Dic3semidirect
419. D24C2×Dic3semidirect
421. ΓL(1,𝔽25)C2×Dic3semidirect
447. C3×Dic3AGL(1,ℤ/8)semidirect
511. C3×Q8C2×C4×D3semidirect
512. C3×Q8C22×Dic3semidirect
573. D12C22×Dic3semidirect
587. C3×C8C2×C4×D3semidirect
588. C3×C8C22×Dic3semidirect
593. C3⋊C8C22×Dic3semidirect
625. SD16D3×Dic3semidirect
716. Dic3#914direct (N × H)
718. C32C4×AGL(1,ℤ/8)semidirect
727. Q8C2×D3×Dic3semidirect
762. C8C2×D3×Dic3semidirect
808. C3C4×#914semidirect
809. C3Dic3×AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9142
Dic3×#2392
D3×D4×Dic32
#105928632
C3×Dic3×SD162
#105915722
Dic3×#2152
#105915502
#105914362
Dic3×#2132
#105914212
#105907812
Dic3×D242
#105906812
Dic3×ΓL(1,𝔽25)2
Dic3×AGL(1,ℤ/8)3
C4×#9143