Finite Group Databasebeta

← Dic3×#918 #11860396

Subgroups — Dic3×#918 #11860396

Order 1152.

1022 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#918C211yesmaximal, characteristic
2Dic3×#239C211yesmaximal, characteristic
3D3×Q8×Dic3C211yesmaximal, characteristic, complemented
4#10592883C211yesmaximal, characteristic, complemented
5C3×Dic3×Q16C211yesmaximal, characteristic, complemented
6#10591582C211yesmaximal, characteristic, complemented
7Dic3×#216C211yesmaximal, characteristic, complemented
8#10591572C211yesmaximal, characteristic, complemented
9Dic3×#215C211yesmaximal, characteristic, complemented
10#10591557C211yesmaximal, characteristic, complemented
11#10591550C211yesmaximal, characteristic
12#10590779C211yesmaximal, characteristic, complemented
13Dic3×#204C211yesmaximal, characteristic, complemented
14#10590683C211yesmaximal, characteristic, complemented
15Dic3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
16Dic3×#137—31nomaximal
17C4×#918—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic
21Q8×C3⋊Dic3C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C2×C3×#216C2211yescharacteristic
26C2×C3×#215C2211yescharacteristic
27C3×#918C418yescomplemented
28C2×C3×#204C2211yescharacteristic
29C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
30#63898—21no—
31#63898C2211yescharacteristic
32Dic3×D12—21no—
33Dic3×D12C2211yescharacteristic
34D3×C4⋊Dic3—21no—
35D3×C4⋊Dic3C2211yescharacteristic
36C4×D3×Dic3—21no—
37C4×D3×Dic3—21no—
38C4×D3×Dic3C2211yescharacteristic
39#63843—21no—
40#63843C2211yescharacteristic
41Dic3×Dic6—21no—
42Dic3×Dic6C2211yescharacteristic
43#63841—21no—
44#63841C2211yescharacteristic
45C2×#3711C2211yescharacteristic
46#63662C2211yescharacteristic
47#63662C2211yescharacteristic
48#63644C2211yescharacteristic
49#63642C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#835C2211yescharacteristic
52C3×#818C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54#63575C2211yescharacteristic
55#63573C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63563C2211yescharacteristic
59#63562C2211yescharacteristic
60#63555C2211yescharacteristic
61Dic3×C3⋊C8C2211yescharacteristic
62C2×C3×#137—31no—
63Dic3×#41—31no—
64C2×Q8×Dic3—31no—
65C2×#918D311yescharacteristic
66C4×#239—31no—
67C4×D3×Q8—31no—
68C3×C4×Q16—31no—
69#5232—31no—
70#5225—31no—
71#5184—31no—
72#5184—31no—
73#5184—31no—
74#5184—61no—
75Dic3×Q16—31no—
76Dic3×Q16D311yescharacteristic, complemented
77#5164—31no—
78#5164—31no—
79Dic3×SD16—31no—
80Dic3×SD16—31no—
81#5121—31no—
82Dic3×M16—31no—
83C4×#216—31no—
84C4×#215—31no—
85#4889—31no—
86#4881—31no—
87#4817—31no—
88#4803—31no—
89#4802—31no—
90#4789—31no—
91C4×#204—31no—
92C4×ΓL(1,𝔽25)—31no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×Q8C2311yescharacteristic
95C3×#239—22no—
96C3×#239C2×C414yes—
97C3×D3×Q8—22no—
98C3×D3×Q8C2×C414yescomplemented
99C2×C3×D12—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6—21no—
105C2×C3×Dic6C2311yescharacteristic
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3D411yescharacteristic
110C2×D3×Dic3D411yescharacteristic
111C32×Q16C2×C414yescomplemented
112C2×C32×C8C2311yescharacteristic
113C4⋊(C3⋊Dic3)—21no—
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4×C3⋊Dic3—21no—
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#216C2×C414yescomplemented
122C3×#215C2×C414yescomplemented
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4×Dic3—21no—
128C3×C4×Dic3—21no—
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×#204C2×C414yescomplemented
133C3×ΓL(1,𝔽25)C2×C414yescomplemented
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141Dic32—21no—
142Dic32—21no—
143Dic32D411yescharacteristic
144Dic32D411yescharacteristic
145#3711—22no—
146C4×#137—91noSylow
147C2×C3×#41—31no—
148C22×C3×Q8—31no—
149C2×#239C2×D311yescharacteristic
150C2×D3×Q8C2×D311yescharacteristic
151C3×#137—38no—
152C2×C3×Q16—21no—
153C2×C3×Q16—31no—
154C2×C3×Q16C2×D311yescharacteristic
155C2×C3×Q16C2×D311yescharacteristic
156C2×C3×SD16—31no—
157C2×C3×SD16—31no—
158C2×C3×M16—31no—
159C3×C4×Q8—31no—
160C3×C4×Q8—31no—
161Q8×Dic3—31no—
162Q8×Dic3—31no—
163Q8×Dic3—31no—
164Q8×Dic3—31no—
165Q8×Dic3—31no—
166Q8×Dic3—31no—
167Q8×Dic3—61no—
168Q8×Dic3—61no—
169Q8×Dic3—61no—
170Q8×Dic3—61no—
171Q8×Dic3C2×D311yescharacteristic
172Q8×Dic3C2×D311yescharacteristic
173C2×#216C2×D311yescharacteristic
174C2×#215C2×D311yescharacteristic
175D4×Dic3—31no—
176D4×Dic3—31no—
177D4×Dic3—61no—
178D4×Dic3—61no—
179#926—31no—
180#926—61no—
181C2×C4⋊Dic3—31no—
182C2×C4⋊Dic3—61no—
183C2×C4×Dic3—31no—
184C2×C4×Dic3—61no—
185C2×C4×Dic3—61no—
186C2×#208—31no—
187#918Dic318yesdirect product factor
188C2×#204C2×D311yescharacteristic
189C2×ΓL(1,𝔽25)—31no—
190C2×ΓL(1,𝔽25)C2×D311yescharacteristic
191#893—31no—
192#893—61no—
193#892—31no—
194#892—61no—
195D3×C4⋊C4—31no—
196D3×C4⋊C4—61no—
197#887—31no—
198#887—61no—
199C4×D12—31no—
200C4×D12—61no—
201C42×D3—31no—
202C42×D3—61no—
203C42×D3—61no—
204C4×Dic6—31no—
205C4×Dic6—61no—
206C3×#107—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×C4×C8—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#835—31no—
214#835—31no—
215#835—31no—
216#835—61no—
217#835—61no—
218#835C2×D311yescharacteristic
219#835C2×D311yescharacteristic
220#832—31no—
221#832—31no—
222#821—31no—
223#818—31no—
224#818C2×D311yescharacteristic
225#817—31no—
226#817—31no—
227#817—31no—
228#817—61no—
229#816—31no—
230#815—31no—
231#815—31no—
232#815—31no—
233#815—31no—
234#815—61no—
235C8×Dic3—31no—
236C8×Dic3C2×D311yescharacteristic
237#810—31no—
238#809—31no—
239#808—31no—
240#807—31no—
241C4×C3⋊C8—31no—
242C22×C3×D3—21no—
243C22×C3×D3C2×D411yescharacteristic
244C32×Q8—21no—
245C32×Q8—21no—
246C32×Q8C22×C412yes—
247C32×Q8C22×C412yes—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2411yescharacteristic
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3C2×D411yescharacteristic
254C2×C3⋊Dic3C2×D411yescharacteristic
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—24no—
262C3×D12—21no—
263C3×D12C22×C412yes—
264C3×C4×D3—24no—
265C3×C4×D3—24no—
266C3×C4×D3C22×C412yes—
267C3×C4×D3#4112yes—
268C3×Dic6—21no—
269C3×Dic6—24no—
270C3×Dic6C22×C412yes—
271D3×Dic3—22no—
272D3×Dic3—41no—
273D3×Dic3—42no—
274D3×Dic3—42no—
275D3×Dic3—42no—
276C32×C8C22×C412yes—
277C3⋊(C3⋊C8)—21no—
278C3×C3⋊C8—21no—
279C3×C3⋊C8C22×C412yes—
280C2×#137—31no—
281C4×#41—91no—
282C2×C4×Q8—91no—
283#441—91no—
284#441—91no—
285#440—91no—
286#440—91no—
287C4×Q16—31no—
288C4×Q16—91no—
289C4×SD16—91no—
290C4×SD16—91no—
291#428—91no—
292#419—91no—
293#417—91no—
294C4×M16—91no—
295C3×#41—34no—
296C3×#41—62no—
297C2×C3×Q8—21no—
298C2×C3×Q8—21no—
299C2×C3×Q8—34no—
300C2×C3×Q8—31no—
301C2×C3×Q8—61no—
302C2×C3×Q8—62no—
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×Q8C22×D311yescharacteristic
305C2×C3×Q8C22×D311yescharacteristic
306C2×C3×Q8C22×D311yescharacteristic
307C2×C3×D4—31no—
308C2×C3×D4—61no—
309C22×C3×C4—31no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C22×Dic3—31no—
313C22×Dic3—31no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317#239—22no—
318#239C2×Dic314yes—
319D3×Q8—22no—
320D3×Q8C2×Dic314yescomplemented
321C2×D12—21no—
322C2×D12C22×D311yescharacteristic
323C2×C4×D3—21no—
324C2×C4×D3—21no—
325C2×C4×D3—31no—
326C2×C4×D3—31no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3C22×D311yescharacteristic
331C2×Dic6—21no—
332C2×Dic6C22×D311yescharacteristic
333C3×Q16—24no—
334C3×Q16—34no—
335C3×Q16C4×D314yescomplemented
336C3×Q16C2×Dic314yescomplemented
337C3×SD16—34no—
338C3×SD16—34no—
339C3×M16—34no—
340C2×C3×C8—21no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C2×C3×C8C22×D311yescharacteristic
344C2×C3×C8C22×D311yescharacteristic
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C42—31no—
350C3×C42—61no—
351C3×C42—61no—
352#217—61no—
353#217—61no—
354#217—61no—
355#216C2×Dic314yescomplemented
356#215C2×Dic314yescomplemented
357(C2×D3)⋊C4—61no—
358(C2×D3)⋊C4—61no—
359(C2×D3)⋊C4—61no—
360C4⋊Dic3—21no—
361C4⋊Dic3—21no—
362C4⋊Dic3—31no—
363C4⋊Dic3—31no—
364C4⋊Dic3—31no—
365C4⋊Dic3—31no—
366C4⋊Dic3—61no—
367C4⋊Dic3—61no—
368C4⋊Dic3—61no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—121no—
376C4⋊Dic3—121no—
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382C4×Dic3—21no—
383C4×Dic3—21no—
384C4×Dic3—31no—
385C4×Dic3—31no—
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—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—121no—
402C4×Dic3—121no—
403C4×Dic3C22×D311yescharacteristic
404#208—62no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410#204C2×Dic314yescomplemented
411ΓL(1,𝔽25)—62no—
412ΓL(1,𝔽25)C2×Dic314yescomplemented
413C22×C32C22×D411yescharacteristic
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—22no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419C2×C3×D3C4×D412yes—
420C32×C4—22no—
421C32×C4—22no—
422C32×C4C23×C411yescharacteristic
423C32×C4C2×#4111yescharacteristic
424C3⋊Dic3—21no—
425C3⋊Dic3—21no—
426C3⋊Dic3—41no—
427C3⋊Dic3—41no—
428C3×Dic3—22no—
429C3×Dic3—21no—
430C3×Dic3—41no—
431C3×Dic3—41no—
432C3×Dic3C4×D412yes—
433C3×Dic3#13712yescomplemented
434C2×#41—31no—
435C22×Q8—31no—
436#137—38no—
437C2×Q16—31no—
438C2×Q16D3211yescharacteristic
439C2×SD16—31no—
440C2×SD16—31no—
441C2×M16—31no—
442C2×M16—91no—
443C4×Q8—31no—
444C4×Q8—31no—
445C4×Q8—91no—
446C4×Q8—91no—
447C4×Q8—91no—
448C4×Q8—91no—
449C4×Q8—181no—
450C4×Q8—181no—
451C4×D4—91no—
452C4×D4—91no—
453C4×D4—181no—
454C4×D4—181no—
455#117—91no—
456#117—181no—
457C2×C4⋊C4—91no—
458C2×C4⋊C4—181no—
459C2×C42—91no—
460C2×C42—181no—
461C2×C42—181no—
462#107—31no—
463#107—91no—
464#106—91no—
465#106—91no—
466#103—31no—
467#103—31no—
468#103—91no—
469#103—91no—
470#103—91no—
471#103—91no—
472#102—91no—
473#102—91no—
474#97—91no—
475#97—91no—
476C4×C8—31no—
477C4×C8—91no—
478C23×C3—31no—
479C23×C3—61no—
480C22×D3—21no—
481C22×D3D3×D411yescharacteristic
482C3×Q8—21no—
483C3×Q8—21no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—22no—
487C3×Q8—22no—
488C3×Q8—32no—
489C3×Q8—41no—
490C3×Q8—41no—
491C3×Q8—64no—
492C3×Q8—61no—
493C3×Q8C2×C4×D312yes—
494C3×Q8C2×C4×D312yes—
495C3×Q8C22×Dic312yes—
496C3×Q8C22×Dic312yes—
497C3×D4—32no—
498C3×D4—64no—
499C3×D4—61no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—32no—
508C2×C3×C4—32no—
509C2×C3×C4—31no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—64no—
513C2×C3×C4—64no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4C23×D311yescharacteristic
518C2×C3×C4C23×D311yescharacteristic
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—62no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—121no—
534C2×Dic3—121no—
535C2×Dic3—121no—
536C2×Dic3—122no—
537C2×Dic3—122no—
538C2×Dic3—122no—
539C2×Dic3D3×D411yescharacteristic
540C2×Dic3D3×D411yescharacteristic
541C2×Dic3D3×D411yescharacteristic
542D12—24no—
543D12—21no—
544D12C22×Dic312yes—
545C4×D3—24no—
546C4×D3—24no—
547C4×D3—62no—
548C4×D3—121no—
549C4×D3—122no—
550C4×D3—122no—
551C4×D3—122no—
552C4×D3#23712yes—
553C4×D3C22×Dic312yes—
554Dic6—21no—
555Dic6—24no—
556Dic6C22×Dic312yes—
557C3×C8—22no—
558C3×C8—32no—
559C3×C8—61no—
560C3×C8C2×C4×D312yes—
561C3×C8C22×Dic312yes—
562C3⋊C8—21no—
563C3⋊C8—61no—
564C3⋊C8—61no—
565C3⋊C8—121no—
566C3⋊C8C22×Dic312yes—
567C2×C32C2×C4×D411yescharacteristic
568C2×C32C2×#13711yescharacteristic
569C2×C32#57511yescharacteristic
570C3×D3—22no—
571C3×D3—42no—
572#41—34no—
573#41—62no—
574C2×Q8—34no—
575C2×Q8—31no—
576C2×Q8—61no—
577C2×Q8—62no—
578C2×Q8C2×D3211yescharacteristic
579C2×Q8C2×D3211yescharacteristic
580C2×D4—31no—
581C2×D4—61no—
582C22×C4—31no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4—91no—
586C22×C4—91no—
587C22×C4—181no—
588C22×C4—181no—
589C22×C4—181no—
590Q16—34no—
591Q16D3×Dic314yescomplemented
592SD16—34no—
593SD16—34no—
594M16—34no—
595M16—182no—
596C2×C8—31no—
597C2×C8—31no—
598C2×C8—91no—
599C2×C8C2×D3211yescharacteristic
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—91no—
605C4⋊C4—91no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C42—31no—
615C42—61no—
616C42—61no—
617C42—91no—
618C42—91no—
619C42—91no—
620C42—181no—
621C42—181no—
622C42—181no—
623C42—181no—
624C42—181no—
625C22×C3—21no—
626C22×C3—32no—
627C22×C3—61no—
628C22×C3—61no—
629C22×C3—62no—
630C22×C3—121no—
631C22×C3—121no—
632C22×C3C2×D3×D411yescharacteristic
633C22×C3C2×D3×D411yescharacteristic
634C2×D3—21no—
635C2×D3—21no—
636C2×D3—22no—
637C2×D3—41no—
638C2×D3—41no—
639C2×D3D4×Dic312yes—
640C3×C4—22no—
641C3×C4—22no—
642C3×C4—22no—
643C3×C4—22no—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—32no—
647C3×C4—32no—
648C3×C4—42no—
649C3×C4—42no—
650C3×C4—61no—
651C3×C4—62no—
652C3×C4—121no—
653C3×C4—121no—
654C3×C4C22×C4×D311yescharacteristic
655C3×C4C2×#23711yescharacteristic
656C3×C4D3×#4111yescharacteristic
657C3×C4C23×Dic311yescharacteristic
658Dic3—21no—
659Dic3—22no—
660Dic3—41no—
661Dic3—41no—
662Dic3—61no—
663Dic3—61no—
664Dic3—61no—
665Dic3—61no—
666Dic3—121no—
667Dic3—121no—
668Dic3—121no—
669Dic3—121no—
670Dic3—121no—
671Dic3—121no—
672Dic3—241no—
673Dic3—241no—
674Dic3#91812yesdirect product factor
675Dic3D4×Dic312yes—
676C32C4×#13711yescharacteristic, complemented, Sylow
677C23—31no—
678C23—61no—
679Q8—21no—
680Q8—21no—
681Q8—32no—
682Q8—64no—
683Q8—61no—
684Q8C2×D3×Dic312yes—
685Q8C2×D3×Dic312yes—
686D4—32no—
687D4—64no—
688D4—61no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—31no—
692C2×C4—31no—
693C2×C4—32no—
694C2×C4—32no—
695C2×C4—31no—
696C2×C4—64no—
697C2×C4—64no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—91no—
702C2×C4—91no—
703C2×C4—182no—
704C2×C4—181no—
705C2×C4—181no—
706C2×C4—362no—
707C2×C4—361no—
708C2×C4—362no—
709C2×C4—362no—
710C2×C4C22×D3211yescharacteristic
711C8—32no—
712C8—61no—
713C8—181no—
714C8C2×D3×Dic312yes—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—62no—
719C2×C3—122no—
720C2×C3C4×D3×D411yescharacteristic
721C2×C3C2×#91811yescharacteristic
722C2×C3#576811yescharacteristic
723C2×C3D3×#13711yescharacteristic
724C2×C3#577711yescharacteristic
725C2×C3C2×D4×Dic311yescharacteristic
726D3—22no—
727D3—42no—
728C22—32no—
729C22—61no—
730C22—61no—
731C22—62no—
732C22—121no—
733C22—121no—
734C22D32×D411yescharacteristic
735C4—22no—
736C4—22no—
737C4—32no—
738C4—32no—
739C4—62no—
740C4—61no—
741C4—121no—
742C4—121no—
743C4—181no—
744C4—181no—
745C4—361no—
746C4—361no—
747C4D3×#23711yescharacteristic
748C4C22×D3×Dic311yescharacteristic
749C3—21no—
750C3C4×#91811yescharacteristic, complemented
751C3Dic3×#13711yescharacteristic, complemented
752C2—62no—
753C2—122no—
754C2D3×#91811yescharacteristic
755C2#1059476311yescharacteristic
756C2D3×D4×Dic311yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC2×C3×#239C22
cosocleC2×C32×C4C24
hypercenterC2×Q16D32
hypocenterC32C4×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
3. D3×Q8×Dic3C2semidirect
4. #10592883C2semidirect
5. C3×Dic3×Q16C2semidirect
6. #10591582C2semidirect
7. Dic3×#216C2semidirect
8. #10591572C2semidirect
9. Dic3×#215C2semidirect
10. #10591557C2semidirect
12. #10590779C2semidirect
13. Dic3×#204C2semidirect
14. #10590683C2semidirect
15. Dic3×ΓL(1,𝔽25)C2semidirect
27. C3×#918C4semidirect
76. Dic3×Q16D3semidirect
98. C3×D3×Q8C2×C4semidirect
111. C32×Q16C2×C4semidirect
121. C3×#216C2×C4semidirect
122. C3×#215C2×C4semidirect
132. C3×#204C2×C4semidirect
133. C3×ΓL(1,𝔽25)C2×C4semidirect
187. #918Dic3direct (N × H)
320. D3×Q8C2×Dic3semidirect
335. C3×Q16C4×D3semidirect
336. C3×Q16C2×Dic3semidirect
355. #216C2×Dic3semidirect
356. #215C2×Dic3semidirect
410. #204C2×Dic3semidirect
412. ΓL(1,𝔽25)C2×Dic3semidirect
433. C3×Dic3#137semidirect
591. Q16D3×Dic3semidirect
674. Dic3#918direct (N × H)
676. C32C4×#137semidirect
750. C3C4×#918semidirect
751. C3Dic3×#137semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9182
Dic3×#2392
D3×Q8×Dic32
#105928832
C3×Dic3×Q162
#105915822
Dic3×#2162
#105915722
Dic3×#2152
#105915572
#105915502
#105907792
Dic3×#2042
#105906832
Dic3×ΓL(1,𝔽25)2
Dic3×#1373
C4×#9183