Finite Group Databasebeta

← C3×#10591523 #13158550

Subgroups — C3×#10591523 #13158550

Order 1728.

970 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64307C211yesmaximal, characteristic, complemented
2C3×#64141C211yesmaximal, characteristic, complemented
3C32×#940C211yesmaximal, characteristic, complemented
4C32×#932C211yesmaximal, characteristic, complemented
5C3×#63570C211yesmaximal, characteristic, complemented
6C3×#63569C211yesmaximal, characteristic, complemented
7C3×#63558C211yesmaximal, characteristic, complemented
8C3×#5198—31nomaximal
9C3×#5077—31nomaximal
10#10591523C311yesmaximal, characteristic, direct product factor
11C2×C33×D4C2211yescharacteristic, complemented
12C3×#3828C2211yescharacteristic
13C2×C32×#67—22no—
14C32×#235C2211yescharacteristic
15C2×C32×D12C2211yescharacteristic
16C3×D3×#67—22no—
17C3×#3802—21no—
18C3×D3×D12—21no—
19C3×#3796—21no—
20C3×#3795—21no—
21C3×#3754—21no—
22C3×#3753—21no—
23C3×#3748C2211yescharacteristic, complemented
24C32×#214—21no—
25C32×#213—21no—
26C32×C4×Dic3C2211yescharacteristic, complemented
27C32×#208C2211yescharacteristic, complemented
28C3×#1009—31no—
29C3×#1004—31no—
30#64307C2×C311yescharacteristic, complemented
31C32×AGL(1,ℤ/8)—31no—
32C32×#127—31no—
33#64141C2×C311yescharacteristic, complemented
34C3×#940—21no—
35C3×#940D311yescharacteristic, complemented
36C3×#940C2×C311yescharacteristic, complemented
37C3×#932—21no—
38C3×#932—31no—
39C3×#932—31no—
40C3×#932—61no—
41C3×#932D311yescharacteristic, complemented
42C3×#932C2×C311yescharacteristic, complemented
43C3×#837—31no—
44C3×#833—31no—
45C3×#825—31no—
46C3×#823—31no—
47C3×#805—31no—
48C3×#805—31no—
49#63570C2×C311yescharacteristic, complemented
50#63569C2×C311yescharacteristic, complemented
51#63558C2×C311yescharacteristic, complemented
52C23×C33—21no—
53C22×C32×D3D412yes—
54C2×C3×D32—22no—
55C33×D4—21no—
56C33×D4—21no—
57C2×C33×C4C2311yescharacteristic
58C3×#638—21no—
59C3×C4⋊(C3⋊D3)D411yescharacteristic, complemented
60C3×C4×C3⋊D3—21no—
61C3×#634D411yescharacteristic, complemented
62C32×#67—21no—
63C32×#67—44no—
64C2×C32×Dic3—21no—
65C32×D12—21no—
66C32×D12—21no—
67C32×D12D411yescharacteristic, complemented
68C32×C4×D3—21no—
69C32×Dic6D411yescharacteristic, complemented
70C3×#626—22no—
71C3×#625—22no—
72C3×D3×Dic3—22no—
73C3×C3⋊(C3⋊C8)—21no—
74C32×C3⋊C8—21no—
75C3×#453—91no—
76#5198—31no—
77#5077—31no—
78C32×#41—31no—
79C2×C32×D4—21no—
80C2×C32×D4—21no—
81C2×C32×D4—21no—
82C2×C32×D4—31no—
83C2×C32×D4—41no—
84C2×C32×D4—62no—
85C2×C32×D4C2×D311yescharacteristic, complemented
86C2×C32×D4C2×D311yescharacteristic, complemented
87C2×C32×D4C22×C311yescharacteristic, complemented
88#3828C22×C311yescharacteristic
89C2×C3×#67—24no—
90C2×C3×#67—22no—
91C2×C3×#67—22no—
92C2×C3×#67—62no—
93C3×#239—61no—
94C3×#237—61no—
95C3×#237—61no—
96C3×D3×D4—61no—
97C3×D3×D4—61no—
98C3×D3×D4—62no—
99C3×D3×D4—61no—
100C3×#235—21no—
101C3×#235—31no—
102C3×#235—31no—
103C3×#235—61no—
104C3×#235—61no—
105C3×#235C2×D311yescharacteristic
106C3×#235C22×C311yescharacteristic
107C2×C3×D12—21no—
108C2×C3×D12—61no—
109C2×C3×D12C2×D311yescharacteristic
110C2×C3×D12C22×C311yescharacteristic
111D3×#67—22no—
112#3802—21no—
113D3×D12—21no—
114#3796—21no—
115#3795—21no—
116C32×SD16—61no—
117C32×D8—61no—
118C32×M16—31no—
119C32×C42—31no—
120#3754—21no—
121#3753—21no—
122#3748C22×C311yescharacteristic, complemented
123C3×#214—22no—
124C3×#214—21no—
125C3×#214—21no—
126C3×#214—61no—
127C3×#214—61no—
128C3×#214—62no—
129C3×#213—22no—
130C3×#213—21no—
131C3×#213—21no—
132C3×#213—61no—
133C3×#213—61no—
134C3×#213—62no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3C2×D311yescharacteristic, complemented
137C3×C4×Dic3C22×C311yescharacteristic, complemented
138C3×#208—21no—
139C3×#208—31no—
140C3×#208—31no—
141C3×#208—61no—
142C3×#208C2×D311yescharacteristic, complemented
143C3×#208C22×C311yescharacteristic, complemented
144C22×C33—42no—
145C22×C33—41no—
146C22×C33C2×D411yescharacteristic
147C2×C3×C3⋊D3—21no—
148C2×C32×D3—22no—
149C2×C32×D3—21no—
150C2×C32×D3—42no—
151C3×D32—82no—
152C33×C4C2×D411yescharacteristic
153C33×C4C2×D411yescharacteristic
154C3×C3⋊Dic3—21no—
155C32×Dic3—22no—
156C32×Dic3—21no—
157C3×H(5,𝔽2)—91no—
158#1009—31no—
159#1004—31no—
160C3×AGL(1,ℤ/8)—31no—
161C3×AGL(1,ℤ/8)—31no—
162C3×AGL(1,ℤ/8)—61no—
163C3×AGL(1,ℤ/8)—91no—
164C3×#127—31no—
165C3×#127—31no—
166C3×#127—61no—
167#940C3×D311yescharacteristic, complemented
168#932—31no—
169#932—31no—
170#932—61no—
171#932C3×D311yescharacteristic, complemented
172C3×#104—91no—
173C3×#104—91no—
174C3×#100—91no—
175#837—31no—
176#833—31no—
177#825—31no—
178#823—31no—
179#805—31no—
180#805—31no—
181C23×C32—21no—
182C23×C32—22no—
183C23×C32—21no—
184C23×C32—21no—
185C23×C32—32no—
186C23×C32—41no—
187C23×C32—41no—
188C23×C32—42no—
189C22×C3×D3—22no—
190C22×C3×D3—62no—
191C22×C3×D3—62no—
192C22×C3×D3#6712yes—
193C22×C3×D3C3×D412yes—
194C2×D32—22no—
195C32×Q8—31no—
196C32×D4—21no—
197C32×D4—21no—
198C32×D4—22no—
199C32×D4—22no—
200C32×D4—21no—
201C32×D4—21no—
202C32×D4—21no—
203C32×D4—21no—
204C32×D4—31no—
205C32×D4—41no—
206C32×D4—41no—
207C32×D4—41no—
208C32×D4—41no—
209C32×D4—42no—
210C32×D4—42no—
211C32×D4—61no—
212C32×D4—61no—
213C32×D4—61no—
214C32×D4—124no—
215C2×C32×C4—21no—
216C2×C32×C4—21no—
217C2×C32×C4—21no—
218C2×C32×C4—41no—
219C2×C32×C4—61no—
220C2×C32×C4—61no—
221C2×C32×C4C22×D311yescharacteristic
222C2×C32×C4C22×D311yescharacteristic
223C2×C32×C4C23×C311yescharacteristic
224#638—21no—
225C4⋊(C3⋊D3)C3×D411yescharacteristic, complemented
226C4×C3⋊D3—21no—
227#634C3×D411yescharacteristic, complemented
228C3×#67—21no—
229C3×#67—21no—
230C3×#67—41no—
231C3×#67—44no—
232C3×#67—44no—
233C3×#67—48no—
234C3×#67—62no—
235C3×#67—62no—
236C3×#67—62no—
237C3×#67—61no—
238C3×#67—61no—
239C3×#67—121no—
240C2×C3×Dic3—22no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—62no—
244C3×D12—21no—
245C3×D12—21no—
246C3×D12—21no—
247C3×D12—21no—
248C3×D12—21no—
249C3×D12—31no—
250C3×D12—31no—
251C3×D12—41no—
252C3×D12—41no—
253C3×D12—61no—
254C3×D12—62no—
255C3×D12#6711yescharacteristic, complemented
256C3×D12C3×D411yescharacteristic, complemented
257C3×C4×D3—21no—
258C3×C4×D3—21no—
259C3×C4×D3—41no—
260C3×C4×D3—62no—
261C3×C4×D3—61no—
262C3×C4×D3—61no—
263C3×C4×D3—121no—
264C3×Dic6—21no—
265C3×Dic6—31no—
266C3×Dic6—31no—
267C3×Dic6—61no—
268C3×Dic6#6711yescharacteristic, complemented
269C3×Dic6C3×D411yescharacteristic, complemented
270#626—22no—
271#625—22no—
272D3×Dic3—22no—
273C32×C8—61no—
274C3⋊(C3⋊C8)—21no—
275C3×C3⋊C8—22no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—62no—
279C3×C3⋊C8—61no—
280C3×C3⋊C8—61no—
281#453—91noSylow
282C2×C33—21no—
283C2×C33—81no—
284C2×C33#12011yescharacteristic
285C3×C3⋊D3—41no—
286C32×D3—41no—
287C32×D3—42no—
288C3×#41—31no—
289C3×#41—31no—
290C3×#41—61no—
291C3×#41—91no—
292C3×#41—181no—
293C3×#41—181no—
294C2×C3×D4—21no—
295C2×C3×D4—21no—
296C2×C3×D4—21no—
297C2×C3×D4—31no—
298C2×C3×D4—31no—
299C2×C3×D4—41no—
300C2×C3×D4—61no—
301C2×C3×D4—62no—
302C2×C3×D4—62no—
303C2×C3×D4—64no—
304C2×C3×D4—181no—
305C2×C3×D4—181no—
306C2×C3×D4—182no—
307C2×C3×D4D3211yescharacteristic, complemented
308C2×C3×D4C2×C3×D311yescharacteristic, complemented
309C2×C3×D4C2×C3×D311yescharacteristic, complemented
310C2×#67—22no—
311C2×#67—62no—
312#239—61no—
313#237—61no—
314#237—61no—
315D3×D4—61no—
316D3×D4—61no—
317D3×D4—62no—
318D3×D4—61no—
319#235—31no—
320#235—31no—
321#235—61no—
322#235—61no—
323#235C2×C3×D311yescharacteristic
324C2×D12—61no—
325C2×D12C2×C3×D311yescharacteristic
326C3×SD16—61no—
327C3×SD16—61no—
328C3×SD16—62no—
329C3×SD16—181no—
330C3×D8—61no—
331C3×D8—61no—
332C3×D8—62no—
333C3×D8—181no—
334C3×M16—31no—
335C3×M16—31no—
336C3×M16—61no—
337C3×M16—91no—
338C3×C42—31no—
339C3×C42—31no—
340C3×C42—61no—
341#214—21no—
342#214—61no—
343#214—61no—
344#214—62no—
345#213—21no—
346#213—61no—
347#213—61no—
348#213—62no—
349C4×Dic3C2×C3×D311yescharacteristic, complemented
350#208—31no—
351#208—31no—
352#208—61no—
353#208C2×C3×D311yescharacteristic, complemented
354C22×C32—21no—
355C22×C32—21no—
356C22×C32—21no—
357C22×C32—41no—
358C22×C32—42no—
359C22×C32—42no—
360C22×C32—42no—
361C22×C32—42no—
362C22×C32—44no—
363C22×C32—41no—
364C22×C32—41no—
365C22×C32—41no—
366C22×C32—44no—
367C22×C32—42no—
368C22×C32—42no—
369C22×C32—62no—
370C22×C32—61no—
371C22×C32—82no—
372C22×C32—82no—
373C22×C32—84no—
374C22×C32—122no—
375C22×C32D3×D411yescharacteristic
376C22×C32C2×#6711yescharacteristic
377C22×C32C2×C3×D411yescharacteristic
378C2×C3⋊D3—21no—
379C2×C3×D3—21no—
380C2×C3×D3—22no—
381C2×C3×D3—22no—
382C2×C3×D3—21no—
383C2×C3×D3—41no—
384C2×C3×D3—42no—
385C2×C3×D3—42no—
386C2×C3×D3—42no—
387C2×C3×D3—44no—
388C2×C3×D3—61no—
389C2×C3×D3—61no—
390C2×C3×D3—121no—
391C2×C3×D3—242no—
392C2×C3×D3—242no—
393D32—82no—
394C32×C4—21no—
395C32×C4—21no—
396C32×C4—21no—
397C32×C4—21no—
398C32×C4—21no—
399C32×C4—21no—
400C32×C4—41no—
401C32×C4—41no—
402C32×C4—62no—
403C32×C4—61no—
404C32×C4D3×D411yescharacteristic
405C32×C4D3×D411yescharacteristic
406C32×C4D3×D411yescharacteristic
407C32×C4C2×#6711yescharacteristic
408C32×C4C2×C3×D411yescharacteristic
409C32×C4C2×C3×D411yescharacteristic
410C3⋊Dic3—21no—
411C3×Dic3—24no—
412C3×Dic3—22no—
413C3×Dic3—22no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—41no—
417C3×Dic3—61no—
418C3×Dic3—61no—
419C3×Dic3—121no—
420H(5,𝔽2)—91no—
421AGL(1,ℤ/8)—31no—
422AGL(1,ℤ/8)—91no—
423#127—31no—
424#104—91no—
425#104—91no—
426#100—91no—
427C33#45311yescharacteristic, complemented, Sylow
428C23×C3—22no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3—21no—
432C23×C3—32no—
433C23×C3—32no—
434C23×C3—41no—
435C23×C3—41no—
436C23×C3—42no—
437C23×C3—62no—
438C23×C3—182no—
439C22×D3—62no—
440C22×D3—62no—
441C22×D3C3×#6712yes—
442C3×Q8—31no—
443C3×Q8—31no—
444C3×Q8—61no—
445C3×Q8—91no—
446C3×D4—22no—
447C3×D4—22no—
448C3×D4—21no—
449C3×D4—21no—
450C3×D4—21no—
451C3×D4—21no—
452C3×D4—21no—
453C3×D4—21no—
454C3×D4—31no—
455C3×D4—31no—
456C3×D4—41no—
457C3×D4—41no—
458C3×D4—41no—
459C3×D4—41no—
460C3×D4—42no—
461C3×D4—42no—
462C3×D4—61no—
463C3×D4—61no—
464C3×D4—61no—
465C3×D4—61no—
466C3×D4—61no—
467C3×D4—61no—
468C3×D4—61no—
469C3×D4—91no—
470C3×D4—121no—
471C3×D4—121no—
472C3×D4—121no—
473C3×D4—124no—
474C3×D4—124no—
475C3×D4—128no—
476C3×D4—182no—
477C3×D4—182no—
478C3×D4—181no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—41no—
483C2×C3×C4—62no—
484C2×C3×C4—61no—
485C2×C3×C4—61no—
486C2×C3×C4—61no—
487C2×C3×C4—61no—
488C2×C3×C4—121no—
489C2×C3×C4—182no—
490C2×C3×C4—181no—
491C2×C3×C4C2×D3211yescharacteristic
492C2×C3×C4C22×C3×D311yescharacteristic
493C2×C3×C4C22×C3×D311yescharacteristic
494#67—21no—
495#67—44no—
496#67—62no—
497#67—62no—
498#67—62no—
499#67—61no—
500#67—61no—
501#67—121no—
502C2×Dic3—21no—
503C2×Dic3—62no—
504D12—21no—
505D12—21no—
506D12—31no—
507D12—31no—
508D12—61no—
509D12—62no—
510D12C3×#6711yescharacteristic, complemented
511C4×D3—21no—
512C4×D3—62no—
513C4×D3—61no—
514C4×D3—61no—
515C4×D3—121no—
516Dic6—31no—
517Dic6—31no—
518Dic6—61no—
519Dic6C3×#6711yescharacteristic, complemented
520C3×C8—62no—
521C3×C8—61no—
522C3×C8—61no—
523C3×C8—181no—
524C3⋊C8—21no—
525C3⋊C8—62no—
526C3⋊C8—61no—
527C3⋊C8—61no—
528C2×C32—21no—
529C2×C32—22no—
530C2×C32—21no—
531C2×C32—21no—
532C2×C32—21no—
533C2×C32—21no—
534C2×C32—21no—
535C2×C32—41no—
536C2×C32—41no—
537C2×C32—41no—
538C2×C32—42no—
539C2×C32—82no—
540C2×C32—82no—
541C2×C32—82no—
542C2×C32—84no—
543C2×C32—81no—
544C2×C32—81no—
545C2×C32—81no—
546C2×C32—122no—
547C2×C32—121no—
548C2×C32#93711yescharacteristic
549C2×C32#93711yescharacteristic
550C2×C32C3×#12011yescharacteristic
551C3⋊D3—41no—
552C3×D3—41no—
553C3×D3—41no—
554C3×D3—42no—
555C3×D3—42no—
556C3×D3—81no—
557C3×D3—82no—
558C3×D3—121no—
559C3×D3—121no—
560C3×D3—241no—
561#41—31no—
562#41—91no—
563#41—181no—
564#41—181no—
565C2×D4—31no—
566C2×D4—62no—
567C2×D4—181no—
568C2×D4—181no—
569C2×D4—182no—
570C2×D4C3×D3211yescharacteristic, complemented
571SD16—61no—
572SD16—181no—
573D8—61no—
574D8—181no—
575M16—31no—
576M16—91no—
577C42—31no—
578C22×C3—21no—
579C22×C3—21no—
580C22×C3—21no—
581C22×C3—42no—
582C22×C3—42no—
583C22×C3—42no—
584C22×C3—42no—
585C22×C3—44no—
586C22×C3—42no—
587C22×C3—42no—
588C22×C3—44no—
589C22×C3—41no—
590C22×C3—41no—
591C22×C3—41no—
592C22×C3—41no—
593C22×C3—62no—
594C22×C3—61no—
595C22×C3—61no—
596C22×C3—62no—
597C22×C3—82no—
598C22×C3—82no—
599C22×C3—84no—
600C22×C3—121no—
601C22×C3—122no—
602C22×C3—122no—
603C22×C3—122no—
604C22×C3—124no—
605C22×C3—181no—
606C22×C3—722no—
607C22×C3D3×#6711yescharacteristic
608C22×C3C3×D3×D411yescharacteristic
609C22×C3C2×C3×#6711yescharacteristic
610C2×D3—21no—
611C2×D3—22no—
612C2×D3—42no—
613C2×D3—61no—
614C2×D3—61no—
615C2×D3—121no—
616C2×D3—242no—
617C2×D3—242no—
618C3×C4—21no—
619C3×C4—21no—
620C3×C4—21no—
621C3×C4—21no—
622C3×C4—21no—
623C3×C4—21no—
624C3×C4—41no—
625C3×C4—41no—
626C3×C4—64no—
627C3×C4—62no—
628C3×C4—62no—
629C3×C4—61no—
630C3×C4—61no—
631C3×C4—121no—
632C3×C4—181no—
633C3×C4D3×#6711yescharacteristic
634C3×C4#381111yescharacteristic
635C3×C4C3×D3×D411yescharacteristic
636C3×C4C3×D3×D411yescharacteristic
637C3×C4C3×D3×D411yescharacteristic
638C3×C4C2×C3×#6711yescharacteristic
639Dic3—22no—
640Dic3—21no—
641Dic3—61no—
642Dic3—61no—
643Dic3—121no—
644C32—21no—
645C32—21no—
646C32—21no—
647C32—41no—
648C32#507711yescharacteristic, complemented
649C32#519811yescharacteristic, complemented
650C32C3×#45311yescharacteristic, complemented
651C23—21no—
652C23—32no—
653C23—182no—
654Q8—31no—
655Q8—91no—
656D4—21no—
657D4—21no—
658D4—31no—
659D4—61no—
660D4—61no—
661D4—61no—
662D4—91no—
663D4—124no—
664D4—182no—
665D4—182no—
666D4—181no—
667C2×C4—61no—
668C2×C4—61no—
669C2×C4—182no—
670C2×C4—181no—
671C2×C4C2×C3×D3211yescharacteristic
672C8—61no—
673C8—181no—
674C2×C3—22no—
675C2×C3—21no—
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—41no—
682C2×C3—41no—
683C2×C3—42no—
684C2×C3—41no—
685C2×C3—82no—
686C2×C3—82no—
687C2×C3—82no—
688C2×C3—84no—
689C2×C3—81no—
690C2×C3—81no—
691C2×C3—81no—
692C2×C3—122no—
693C2×C3—121no—
694C2×C3—122no—
695C2×C3—121no—
696C2×C3—242no—
697C2×C3—241no—
698C2×C3—361no—
699C2×C3#6398311yescharacteristic
700C2×C3C3×#93711yescharacteristic
701C2×C3C3×#93711yescharacteristic
702D3—41no—
703D3—42no—
704D3—121no—
705D3—121no—
706D3—241no—
707C22—42no—
708C22—41no—
709C22—61no—
710C22—62no—
711C22—122no—
712C22—181no—
713C22—722no—
714C22C3×D3×#6711yescharacteristic
715C4—62no—
716C4—61no—
717C4—181no—
718C4C3×D3×#6711yescharacteristic
719C4C3×#381111yescharacteristic
720C3—21no—
721C3—21no—
722C3—21no—
723C3—41no—
724C3#1059152311yescharacteristic, direct product factor
725C3C3×#507711yescharacteristic, complemented
726C3C3×#519811yescharacteristic, complemented
727C2—21no—
728C2—81no—
729C2—122no—
730C2—121no—
731C2—361no—
732C2C3×#6398311yescharacteristic
subgroupG/H
centerC2×C3#63983
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C2×C3×D32
FittingC2×C33×D4C22
socleC2×C33#120
hypercenterC2×C3×D4D32
hypocenterC32C3×#453
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C3×#64307C2semidirect
2. C3×#64141C2semidirect
3. C32×#940C2semidirect
4. C32×#932C2semidirect
5. C3×#63570C2semidirect
6. C3×#63569C2semidirect
7. C3×#63558C2semidirect
10. #10591523C3direct (N × H)
11. C2×C33×D4C22semidirect
23. C3×#3748C22semidirect
26. C32×C4×Dic3C22semidirect
27. C32×#208C22semidirect
30. #64307C2×C3semidirect
33. #64141C2×C3semidirect
35. C3×#940D3semidirect
36. C3×#940C2×C3semidirect
41. C3×#932D3semidirect
42. C3×#932C2×C3semidirect
49. #63570C2×C3semidirect
50. #63569C2×C3semidirect
51. #63558C2×C3semidirect
59. C3×C4⋊(C3⋊D3)D4semidirect
61. C3×#634D4semidirect
67. C32×D12D4semidirect
69. C32×Dic6D4semidirect
85. C2×C32×D4C2×D3semidirect
86. C2×C32×D4C2×D3semidirect
87. C2×C32×D4C22×C3semidirect
122. #3748C22×C3semidirect
136. C3×C4×Dic3C2×D3semidirect
137. C3×C4×Dic3C22×C3semidirect
142. C3×#208C2×D3semidirect
143. C3×#208C22×C3semidirect
167. #940C3×D3semidirect
171. #932C3×D3semidirect
225. C4⋊(C3⋊D3)C3×D4semidirect
227. #634C3×D4semidirect
255. C3×D12#67semidirect
256. C3×D12C3×D4semidirect
268. C3×Dic6#67semidirect
269. C3×Dic6C3×D4semidirect
307. C2×C3×D4D32semidirect
308. C2×C3×D4C2×C3×D3semidirect
309. C2×C3×D4C2×C3×D3semidirect
349. C4×Dic3C2×C3×D3semidirect
353. #208C2×C3×D3semidirect
427. C33#453semidirect
510. D12C3×#67semidirect
519. Dic6C3×#67semidirect
570. C2×D4C3×D32semidirect
648. C32#5077semidirect
649. C32#5198semidirect
650. C32C3×#453semidirect
724. C3#10591523direct (N × H)
725. C3C3×#5077semidirect
726. C3C3×#5198semidirect

Maximal subgroups

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

subgroupindex
C3×#643072
C3×#641412
C32×#9402
C32×#9322
C3×#635702
C3×#635692
C3×#635582
C3×#51983
C3×#50773
#105915233