Finite Group Databasebeta

← Dic3×#577 #11659423

Subgroups — Dic3×#577 #11659423

Order 768.

2742 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#577C211yesmaximal, characteristic
2Dic3×2−1+4C211yesmaximal, characteristic, complemented
3Dic3×H(5,𝔽2)C211yesmaximal, characteristic, complemented
4#84111C211yesmaximal, characteristic, complemented
5#84099C211yesmaximal, characteristic, complemented
6#83965C213yesmaximal, complemented
7Dic3×#137C213yesmaximal, complemented
8#83930C213yesmaximal, complemented
9Dic3×AGL(1,ℤ/8)C213yesmaximal, complemented
10#83899C213yesmaximal, complemented
11Dic3×#135C213yesmaximal, complemented
12#83843C213yesmaximal, complemented
13C2×Dic3×SD16C213yesmaximal, complemented
14#83784C211yesmaximal, characteristic, complemented
15Dic3×#131C211yesmaximal, characteristic, complemented
16C4×#577—31nomaximal, Sylow
17C2×C3×2−1+4C2211yescharacteristic
18C2×C3×H(5,𝔽2)C2211yescharacteristic
19C3×#577C4116yescomplemented
20C2×C3×#137C2213yes—
21C2×C3×AGL(1,ℤ/8)C2213yes—
22C2×C3×#135C2213yes—
23C22×C3×SD16C2213yes—
24C2×C3×#131C2211yescharacteristic
25#5827—21no—
26#5827—23no—
27#5827C2213yes—
28#5827C2211yescharacteristic
29#5827C2211yescharacteristic
30#5827C2213yescomplemented
31Dic3×#41—21no—
32Dic3×#41—23no—
33Dic3×#41C2213yes—
34Dic3×#41C2211yescharacteristic
35Dic3×#41C2213yescomplemented
36C2×#948C2211yescharacteristic
37#5812—21no—
38#5812C2213yescomplemented
39C2×Q8×Dic3—21no—
40C2×Q8×Dic3C2213yescomplemented
41#5798—23no—
42#5798C2213yes—
43C2×D4×Dic3—23no—
44C2×D4×Dic3C2213yes—
45#5233C2213yes—
46#5233C2213yescomplemented
47#5232C2213yes—
48#5232C2213yescomplemented
49#5225C2213yescomplemented
50C2×#835C2213yescomplemented
51#5215C2213yes—
52C2×#832C2213yes—
53#5184C2216yescomplemented
54Dic3×Q16C2213yescomplemented
55Dic3×Q16C2213yescomplemented
56#5164C2216yescomplemented
57#5164C2216yescomplemented
58Dic3×SD16C2213yescomplemented
59Dic3×SD16C2216yescomplemented
60Dic3×SD16C2216yescomplemented
61Dic3×SD16C2216yescomplemented
62Dic3×SD16C2213yescomplemented
63Dic3×SD16C2211yescharacteristic, complemented
64Dic3×SD16C2213yescomplemented
65#5152C2216yescomplemented
66Dic3×D8C2213yescomplemented
67Dic3×D8C2213yescomplemented
68#5122C2213yescomplemented
69#5121C2213yescomplemented
70#5121C2213yescomplemented
71Dic3×M16C2213yescomplemented
72#5106C2213yescomplemented
73C2×#817C2213yescomplemented
74#5101C2213yescomplemented
75C2×C8×Dic3C2213yescomplemented
76C2×#577D311yescharacteristic
77C4×2−1+4—31no—
78C4×H(5,𝔽2)—31no—
79#2952—33no—
80#2949—33no—
81#2947—33no—
82#2946—33no—
83C4×#137—33no—
84C4×AGL(1,ℤ/8)—33no—
85C4×#135—33no—
86C2×C4×SD16—33no—
87#2912—31no—
88#2898—31no—
89#2897—31no—
90C4×#131—31no—
91C3×2−1+4—24no—
92C3×2−1+4C2×C418yescomplemented
93C3×H(5,𝔽2)—24no—
94C3×H(5,𝔽2)C2×C418yescomplemented
95C2×C3×#41—21no—
96C2×C3×#41—23no—
97C2×C3×#41C2313yes—
98C2×C3×#41C2313yes—
99C2×C3×#41C2311yescharacteristic
100C22×C3×Q8—21no—
101C22×C3×Q8C2313yes—
102C22×C3×D4—23no—
103C22×C3×D4C2313yes—
104C23×Dic3—23no—
105C3×#137C2×C4124yescomplemented
106C3×AGL(1,ℤ/8)C2×C4124yescomplemented
107C3×#135C2×C4124yescomplemented
108C2×C3×Q16C2313yes—
109C2×C3×SD16C2×C4124yescomplemented
110C2×C3×SD16C2313yes—
111C2×C3×SD16C2316yes—
112C2×C3×SD16C2311yescharacteristic
113C2×C3×D8C2313yes—
114C3×#131C2×C418yescomplemented
115C2×C3×M16C2313yes—
116C22×C3×C8C2313yes—
117C2×#217—23no—
118C2×#217—26no—
119#948—24no—
120Q8×Dic3—21no—
121Q8×Dic3—21no—
122Q8×Dic3—23no—
123Q8×Dic3—23no—
124Q8×Dic3—23no—
125Q8×Dic3—23no—
126Q8×Dic3D411yescharacteristic
127Q8×Dic3D411yescharacteristic
128Q8×Dic3C2313yes—
129Q8×Dic3C2316yes—
130Q8×Dic3C2313yes—
131Q8×Dic3C2311yescharacteristic
132Q8×Dic3C2313yes—
133D4×Dic3—23no—
134D4×Dic3—23no—
135D4×Dic3—23no—
136D4×Dic3—23no—
137D4×Dic3—23no—
138D4×Dic3—23no—
139D4×Dic3—26no—
140D4×Dic3—26no—
141D4×Dic3—23no—
142D4×Dic3—23no—
143D4×Dic3—23no—
144D4×Dic3—23no—
145D4×Dic3D413yes—
146D4×Dic3D413yes—
147D4×Dic3C2311yescharacteristic
148D4×Dic3C2313yes—
149D4×Dic3C2313yes—
150D4×Dic3C2313yes—
151D4×Dic3C2316yes—
152#926—26no—
153#926—23no—
154#926—23no—
155#926—23no—
156#926—23no—
157#926C2313yes—
158#926C2313yes—
159#926C2313yes—
160C2×C4⋊Dic3—23no—
161C2×C4⋊Dic3—23no—
162C2×C4⋊Dic3—23no—
163C2×C4⋊Dic3C2313yes—
164C2×C4⋊Dic3C2313yes—
165C2×C4×Dic3—23no—
166C2×C4×Dic3—23no—
167C2×C4×Dic3—23no—
168C2×C4×Dic3C2313yes—
169C2×#208C2313yes—
170C22×C3⋊C8C2313yes—
171#835C2313yes—
172#835C2316yes—
173#835C2313yes—
174#835C2311yescharacteristic
175#835C2313yes—
176#832C2311yescharacteristic
177#832C2313yes—
178#832C2313yes—
179#832C2313yes—
180#832C2316yes—
181#818C2313yes—
182#818C2313yes—
183#817C2316yes—
184#817C2313yes—
185#817C2311yescharacteristic
186#815C2316yes—
187C8×Dic3C2313yes—
188C8×Dic3C2313yes—
189C8×Dic3C2311yescharacteristic
190C8×Dic3C2313yes—
191C2×2−1+4C2×D311yescharacteristic
192C2×H(5,𝔽2)C2×D311yescharacteristic
193#577Dic3116yesdirect product factor
194C2×#137C2×D313yes—
195C2×AGL(1,ℤ/8)C2×D313yes—
196C2×#135C2×D313yes—
197C22×SD16C2×D313yes—
198C2×#131—31no—
199C2×#131C2×D311yescharacteristic
200#520—31no—
201#520—31no—
202#520—33no—
203#520—33no—
204#520—63no—
205#520—61no—
206#519—33no—
207#519—61no—
208#518—33no—
209#518—63no—
210C4×#41—31no—
211C4×#41—33no—
212C4×#41—33no—
213C4×#41—63no—
214C4×#41—61no—
215C2×C4×Q8—33no—
216C2×C4×Q8—61no—
217C2×C4×D4—33no—
218C2×C4×D4—63no—
219#442—36no—
220#441—36no—
221#440—36no—
222#440—36no—
223C4×Q16—33no—
224C4×Q16—33no—
225C4×SD16—33no—
226C4×SD16—36no—
227C4×SD16—36no—
228C4×SD16—36no—
229C4×SD16—31no—
230C4×SD16—33no—
231C4×SD16—33no—
232C4×D8—33no—
233C4×D8—33no—
234#428—33no—
235#428—33no—
236#427—33no—
237C2×#106—33no—
238#419—33no—
239#418—33no—
240#417—33no—
241#417—33no—
242#416—33no—
243#416—33no—
244C2×#103—33no—
245C2×#102—33no—
246#405—33no—
247#405—33no—
248C4×M16—33no—
249C2×C4×C8—33no—
250C24×C3—23no—
251C3×#41—28no—
252C3×#41—224no—
253C3×#41—26no—
254C3×#41—26no—
255C3×#41C22×C4112yes—
256C3×#41C22×C414yes—
257C3×#41C22×C4112yescomplemented
258C3×#41#4114yes—
259C2×C3×Q8—28no—
260C2×C3×Q8—23no—
261C2×C3×Q8—26no—
262C2×C3×Q8C22×C4112yescomplemented
263C2×C3×Q8C2×D411yescharacteristic
264C2×C3×Q8C2413yes—
265C2×C3×Q8C2411yescharacteristic
266C2×C3×D4—23no—
267C2×C3×D4—23no—
268C2×C3×D4—224no—
269C2×C3×D4—23no—
270C2×C3×D4—26no—
271C2×C3×D4C22×C4112yes—
272C2×C3×D4C2×D413yes—
273C2×C3×D4C2411yescharacteristic
274C2×C3×D4C2413yes—
275C22×C3×C4—23no—
276C22×C3×C4—23no—
277C22×C3×C4—23no—
278C22×C3×C4C2413yes—
279C22×Dic3—23no—
280C22×Dic3—23no—
281C22×Dic3—21no—
282C22×Dic3—23no—
283C22×Dic3—23no—
284C22×Dic3—23no—
285C22×Dic3—26no—
286C22×Dic3—86no—
287C22×Dic3C2×D413yes—
288C22×Dic3C2×D413yes—
289C3×Q16C22×C4112yescomplemented
290C3×SD16C22×C4112yescomplemented
291C3×SD16C22×C4124yescomplemented
292C3×SD16C22×C414yescomplemented
293C3×D8C22×C4112yescomplemented
294C3×M16C22×C4112yescomplemented
295C2×C3×C8C22×C4112yescomplemented
296C2×C3×C8C2411yescharacteristic
297C2×C3×C8C2413yes—
298#217—23no—
299#217—23no—
300#217—21no—
301#217—23no—
302#217—23no—
303#217—26no—
304#217—23no—
305#217C2×D416yes—
306C4⋊Dic3—23no—
307C4⋊Dic3—23no—
308C4⋊Dic3—23no—
309C4⋊Dic3—26no—
310C4⋊Dic3—23no—
311C4⋊Dic3—21no—
312C4⋊Dic3—23no—
313C4⋊Dic3C2×D413yes—
314C4⋊Dic3C2×D413yes—
315C4⋊Dic3C2413yes—
316C4⋊Dic3C2413yes—
317C4⋊Dic3C2411yescharacteristic
318C4⋊Dic3C2411yescharacteristic
319C4×Dic3—23no—
320C4×Dic3—23no—
321C4×Dic3—21no—
322C4×Dic3—23no—
323C4×Dic3—23no—
324C4×Dic3—23no—
325C4×Dic3—26no—
326C4×Dic3C2×D413yes—
327C4×Dic3C2×D413yes—
328C4×Dic3C2411yescharacteristic
329C4×Dic3C2413yes—
330#208—26no—
331C2×C3⋊C8—26no—
332C2×C3⋊C8C2411yescharacteristic
333C2×C3⋊C8C2413yes—
3342−1+4—24no—
3352−1+4C2×Dic318yescomplemented
336H(5,𝔽2)—24no—
337H(5,𝔽2)C2×Dic318yescomplemented
338C2×#41—21no—
339C2×#41—23no—
340C2×#41C22×D313yes—
341C2×#41C22×D313yes—
342C2×#41C22×D311yescharacteristic
343C22×Q8—21no—
344C22×Q8C22×D313yes—
345C22×D4—23no—
346C22×D4C22×D313yes—
347C23×C4—63no—
348#137C2×Dic3124yescomplemented
349AGL(1,ℤ/8)C2×Dic3124yescomplemented
350#135C2×Dic3124yescomplemented
351C2×Q16C22×D313yes—
352C2×SD16C2×Dic3124yescomplemented
353C2×SD16C22×D313yes—
354C2×SD16C22×D316yes—
355C2×SD16C22×D311yescharacteristic
356C2×D8C22×D313yes—
357#131—64no—
358#131C2×Dic318yescomplemented
359C2×M16—33no—
360C2×M16C22×D313yes—
361C22×C8—33no—
362C22×C8C22×D313yes—
363C4×Q8—31no—
364C4×Q8—31no—
365C4×Q8—33no—
366C4×Q8—36no—
367C4×Q8—31no—
368C4×Q8—33no—
369C4×Q8—33no—
370C4×Q8—63no—
371C4×Q8—63no—
372C4×Q8—63no—
373C4×Q8—63no—
374C4×Q8—61no—
375C4×Q8—61no—
376C4×D4—33no—
377C4×D4—33no—
378C4×D4—33no—
379C4×D4—36no—
380C4×D4—31no—
381C4×D4—33no—
382C4×D4—33no—
383C4×D4—63no—
384C4×D4—63no—
385C4×D4—66no—
386C4×D4—66no—
387C4×D4—63no—
388C4×D4—63no—
389C4×D4—63no—
390C4×D4—63no—
391C4×D4—63no—
392C4×D4—63no—
393C4×D4—63no—
394C4×D4—63no—
395#117—33no—
396#117—33no—
397#117—33no—
398#117—63no—
399#117—63no—
400#117—66no—
401#117—63no—
402#117—63no—
403C2×C4⋊C4—33no—
404C2×C4⋊C4—33no—
405C2×C4⋊C4—63no—
406C2×C4⋊C4—63no—
407C2×C4⋊C4—63no—
408C2×C22⋊C4—66no—
409C2×C22⋊C4—63no—
410C2×C42—33no—
411C2×C42—63no—
412C2×C42—63no—
413C2×C42—63no—
414#107—33no—
415#107—33no—
416#106—33no—
417#106—36no—
418#106—31no—
419#103—33no—
420#103—36no—
421#103—31no—
422#103—33no—
423#103—33no—
424#102—33no—
425#102—36no—
426#102—31no—
427#102—33no—
428#102—33no—
429#97—36no—
430C4×C8—31no—
431C4×C8—33no—
432C4×C8—33no—
433C4×C8—33no—
434C23×C3—21no—
435C23×C3—23no—
436C23×C3—212no—
437C23×C3—83no—
438C23×C3—83no—
439C23×C3C22×D413yes—
440C3×Q8—212no—
441C3×Q8—23no—
442C3×Q8—21no—
443C3×Q8C4×D414yes—
444C3×Q8C23×C416yes—
445C3×Q8C23×C412yes—
446C3×D4—212no—
447C3×D4—212no—
448C3×D4—212no—
449C3×D4—23no—
450C3×D4—21no—
451C3×D4C4×D4112yes—
452C3×D4C23×C412yes—
453C3×D4C23×C416yes—
454C2×C3×C4—212no—
455C2×C3×C4—21no—
456C2×C3×C4—23no—
457C2×C3×C4—212no—
458C2×C3×C4—212no—
459C2×C3×C4C23×C416yes—
460C2×C3×C4C22×D413yes—
461C2×C3×C4C2×#4116yes—
462C2×C3×C4C2511yescharacteristic
463C2×Dic3—26no—
464C2×Dic3—21no—
465C2×Dic3—23no—
466C2×Dic3—21no—
467C2×Dic3—23no—
468C2×Dic3—43no—
469C2×Dic3—42no—
470C2×Dic3—46no—
471C2×Dic3—83no—
472C2×Dic3—83no—
473C2×Dic3—86no—
474C2×Dic3—83no—
475C2×Dic3—83no—
476C2×Dic3C22×D413yes—
477C2×Dic3C22×D413yes—
478C2×Dic3C22×D411yescharacteristic
479C2×Dic3C22×D411yescharacteristic
480C3×C8C23×C412yes—
481C3×C8C23×C416yes—
482C3⋊C8—21no—
483C3⋊C8—23no—
484C24—23no—
485#41—28no—
486#41—224no—
487#41—26no—
488#41—26no—
489#41#23714yes—
490#41C22×Dic3112yes—
491#41C22×Dic314yes—
492#41C22×Dic3112yescomplemented
493C2×Q8—28no—
494C2×Q8—23no—
495C2×Q8—26no—
496C2×Q8D3×D411yescharacteristic
497C2×Q8C22×Dic3112yescomplemented
498C2×Q8C23×D313yes—
499C2×Q8C23×D311yescharacteristic
500C2×D4—23no—
501C2×D4—23no—
502C2×D4—224no—
503C2×D4—23no—
504C2×D4—26no—
505C2×D4D3×D413yes—
506C2×D4C22×Dic3112yes—
507C2×D4C23×D311yescharacteristic
508C2×D4C23×D313yes—
509C22×C4—23no—
510C22×C4—23no—
511C22×C4—23no—
512C22×C4—33no—
513C22×C4—33no—
514C22×C4—61no—
515C22×C4—63no—
516C22×C4—63no—
517C22×C4—63no—
518C22×C4—66no—
519C22×C4—63no—
520C22×C4—63no—
521C22×C4—246no—
522C22×C4C23×D313yes—
523Q16C22×Dic3112yescomplemented
524SD16C22×Dic3112yescomplemented
525SD16C22×Dic3124yescomplemented
526SD16C22×Dic314yescomplemented
527D8C22×Dic3112yescomplemented
528M16—66no—
529M16C22×Dic3112yescomplemented
530C2×C8—31no—
531C2×C8—33no—
532C2×C8—66no—
533C2×C8C22×Dic3112yescomplemented
534C2×C8C23×D311yescharacteristic
535C2×C8C23×D313yes—
536C4⋊C4—33no—
537C4⋊C4—33no—
538C4⋊C4—33no—
539C4⋊C4—31no—
540C4⋊C4—33no—
541C4⋊C4—31no—
542C4⋊C4—63no—
543C4⋊C4—63no—
544C4⋊C4—66no—
545C4⋊C4—61no—
546C4⋊C4—63no—
547C4⋊C4—63no—
548C4⋊C4—63no—
549C22⋊C4—36no—
550C22⋊C4—63no—
551C22⋊C4—63no—
552C22⋊C4—66no—
553C22⋊C4—61no—
554C22⋊C4—63no—
555C22⋊C4—63no—
556C22⋊C4—63no—
557C42—33no—
558C42—33no—
559C42—31no—
560C42—33no—
561C42—61no—
562C42—63no—
563C42—63no—
564C42—63no—
565C42—66no—
566C42—63no—
567C42—63no—
568C22×C3—23no—
569C22×C3—23no—
570C22×C3—22no—
571C22×C3—26no—
572C22×C3—41no—
573C22×C3—43no—
574C22×C3—43no—
575C22×C3—41no—
576C22×C3—812no—
577C22×C3C2×C4×D416yes—
578C22×C3C23×D411yescharacteristic
579C3×C4—22no—
580C3×C4—26no—
581C3×C4C2×C4×D416yes—
582C3×C4C24×C411yescharacteristic
583C3×C4C22×#4111yescharacteristic
584Dic3—21no—
585Dic3—23no—
586Dic3—23no—
587Dic3—43no—
588Dic3—41no—
589Dic3—41no—
590Dic3—43no—
591Dic3#57712yesdirect product factor
592C23—21no—
593C23—23no—
594C23—212no—
595C23—83no—
596C23—83no—
597C23C2×D3×D413yes—
598Q8—23no—
599Q8—21no—
600Q8—212no—
601Q8D4×Dic314yes—
602Q8C23×Dic316yes—
603Q8C23×Dic312yes—
604D4—212no—
605D4—212no—
606D4—23no—
607D4—21no—
608D4—212no—
609D4D4×Dic3112yes—
610D4C23×Dic312yes—
611D4C23×Dic316yes—
612C2×C4—21no—
613C2×C4—23no—
614C2×C4—212no—
615C2×C4—212no—
616C2×C4—212no—
617C2×C4—31no—
618C2×C4—31no—
619C2×C4—33no—
620C2×C4—33no—
621C2×C4—66no—
622C2×C4—61no—
623C2×C4—61no—
624C2×C4—63no—
625C2×C4—63no—
626C2×C4—126no—
627C2×C4—122no—
628C2×C4—123no—
629C2×C4—246no—
630C2×C4—243no—
631C2×C4—243no—
632C2×C4—243no—
633C2×C4—243no—
634C2×C4C2×D3×D413yes—
635C2×C4C2×#23716yes—
636C2×C4C23×Dic316yes—
637C2×C4C24×D311yescharacteristic
638C8—61no—
639C8—63no—
640C8C23×Dic312yes—
641C8C23×Dic316yes—
642C2×C3—26no—
643C2×C3—42no—
644C2×C3—46no—
645C2×C3C22×C4×D411yescharacteristic
646C2×C3C2×#57711yescharacteristic
647C2×C3#358411yescharacteristic
648C22—23no—
649C22—23no—
650C22—22no—
651C22—26no—
652C22—43no—
653C22—41no—
654C22—41no—
655C22—43no—
656C22—812no—
657C22C2×D4×Dic316yes—
658C22C22×D3×D411yescharacteristic
659C4—22no—
660C4—26no—
661C4—32no—
662C4—63no—
663C4—61no—
664C4—63no—
665C4—123no—
666C4—121no—
667C4—121no—
668C4—123no—
669C4C2×D4×Dic316yes—
670C4C22×#23711yescharacteristic
671C4C24×Dic311yescharacteristic
672C3C4×#57711yescharacteristic, complemented, Sylow
673C2—26no—
674C2—46no—
675C2—42no—
676C2D3×#57711yescharacteristic
677C2#8720611yescharacteristic
678C2C22×D4×Dic311yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutatorC3×C4C24×C4
FrattiniC2×C4C24×D3
Fitting, prime radicalC2×C3×#577C2
socleC22×C3C23×D4
cosocleC2×C3×C4C25
hypercenterC2×#577D3
hypocenterC3C4×#577
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#577

Complements

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

NH ≅ G/Ntype
2. Dic3×2−1+4C2semidirect
3. Dic3×H(5,𝔽2)C2semidirect
4. #84111C2semidirect
5. #84099C2semidirect
6. #83965C2semidirect
7. Dic3×#137C2semidirect
8. #83930C2semidirect
9. Dic3×AGL(1,ℤ/8)C2semidirect
10. #83899C2semidirect
11. Dic3×#135C2semidirect
12. #83843C2semidirect
13. C2×Dic3×SD16C2semidirect
14. #83784C2semidirect
15. Dic3×#131C2semidirect
19. C3×#577C4semidirect
30. #5827C22semidirect
35. Dic3×#41C22semidirect
38. #5812C22semidirect
40. C2×Q8×Dic3C22semidirect
46. #5233C22semidirect
48. #5232C22semidirect
49. #5225C22semidirect
50. C2×#835C22semidirect
53. #5184C22semidirect
54. Dic3×Q16C22semidirect
55. Dic3×Q16C22semidirect
56. #5164C22semidirect
57. #5164C22semidirect
58. Dic3×SD16C22semidirect
59. Dic3×SD16C22semidirect
60. Dic3×SD16C22semidirect
61. Dic3×SD16C22semidirect
62. Dic3×SD16C22semidirect
63. Dic3×SD16C22semidirect
64. Dic3×SD16C22semidirect
65. #5152C22semidirect
66. Dic3×D8C22semidirect
67. Dic3×D8C22semidirect
68. #5122C22semidirect
69. #5121C22semidirect
70. #5121C22semidirect
71. Dic3×M16C22semidirect
72. #5106C22semidirect
73. C2×#817C22semidirect
74. #5101C22semidirect
75. C2×C8×Dic3C22semidirect
92. C3×2−1+4C2×C4semidirect
94. C3×H(5,𝔽2)C2×C4semidirect
105. C3×#137C2×C4semidirect
106. C3×AGL(1,ℤ/8)C2×C4semidirect
107. C3×#135C2×C4semidirect
109. C2×C3×SD16C2×C4semidirect
114. C3×#131C2×C4semidirect
193. #577Dic3direct (N × H)
257. C3×#41C22×C4semidirect
262. C2×C3×Q8C22×C4semidirect
289. C3×Q16C22×C4semidirect
290. C3×SD16C22×C4semidirect
291. C3×SD16C22×C4semidirect
292. C3×SD16C22×C4semidirect
293. C3×D8C22×C4semidirect
294. C3×M16C22×C4semidirect
295. C2×C3×C8C22×C4semidirect
335. 2−1+4C2×Dic3semidirect
337. H(5,𝔽2)C2×Dic3semidirect
348. #137C2×Dic3semidirect
349. AGL(1,ℤ/8)C2×Dic3semidirect
350. #135C2×Dic3semidirect
352. C2×SD16C2×Dic3semidirect
358. #131C2×Dic3semidirect
492. #41C22×Dic3semidirect
497. C2×Q8C22×Dic3semidirect
523. Q16C22×Dic3semidirect
524. SD16C22×Dic3semidirect
525. SD16C22×Dic3semidirect
526. SD16C22×Dic3semidirect
527. D8C22×Dic3semidirect
529. M16C22×Dic3semidirect
533. C2×C8C22×Dic3semidirect
591. Dic3#577direct (N × H)
672. C3C4×#577semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5772
Dic3×2−1+42
Dic3×H(5,𝔽2)2
#841112
#840992
#839652
Dic3×#1372
#839302
Dic3×AGL(1,ℤ/8)2
#838992
Dic3×#1352
#838432
C2×Dic3×SD162
#837842
Dic3×#1312
C4×#5773