Finite Group Databasebeta

← C3×#10591520 #13158547

Subgroups — C3×#10591520 #13158547

Order 1728.

940 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3796C211yesmaximal, characteristic, complemented
2C3×#64147C211yesmaximal, characteristic, complemented
3C2×C32×#214C211yesmaximal, characteristic, complemented
4C2×C32×#213C211yesmaximal, characteristic, complemented
5C3×#63566C211yesmaximal, characteristic, complemented
6C3×#63563C211yesmaximal, characteristic, complemented
7C3×#63557C211yesmaximal, characteristic, complemented
8C3×#5172—31nomaximal
9C3×#5158—31nomaximal
10#10591520C311yesmaximal, characteristic, direct product factor
11C2×C33×D4C2211yescharacteristic
12C2×C3×#638—21no—
13C2×C3×C4×C3⋊D3C2211yescharacteristic
14C2×C32×D12C2211yescharacteristic
15C2×C32×Dic6C2211yescharacteristic
16C2×C3×#626—21no—
17C2×C3×D3×Dic3—21no—
18C3×#3796—22no—
19C3×#3796—22no—
20C3×#3757—21no—
21C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C32×#214—22no—
23C32×#213—22no—
24C2×C32×C3⋊C8C2211yescharacteristic
25C2×C32×C3⋊C8C2211yescharacteristic
26C2×C3×#239—31no—
27C2×C3×#237—31no—
28C2×#3796C2×C311yescharacteristic, complemented
29C2×C32×SD16—31no—
30C2×C32×D8—31no—
31#64147C2×C311yescharacteristic, complemented
32C3×#938—31no—
33C3×#938—31no—
34C3×#938—61no—
35C2×C3×#214—21no—
36C2×C3×#214D311yescharacteristic, complemented
37C2×C3×#214C2×C311yescharacteristic, complemented
38C2×C3×#213—21no—
39C2×C3×#213D311yescharacteristic, complemented
40C2×C3×#213C2×C311yescharacteristic, complemented
41C3×#835—31no—
42C3×#832—31no—
43C3×#821—31no—
44C3×(C2×D3)⋊C8—31no—
45C3×(C2×D3)⋊C8—31no—
46C3×#816—31no—
47#63566C2×C311yescharacteristic, complemented
48#63563C2×C311yescharacteristic, complemented
49#63557C2×C311yescharacteristic, complemented
50C23×C33—21no—
51C22×C3×C3⋊D3D411yescharacteristic
52C22×C32×D3—21no—
53C33×D4—21no—
54C33×D4—21no—
55C2×C33×C4C2311yescharacteristic
56C3×#638—42no—
57C2×C3×C3⋊Dic3—21no—
58C2×C3×C3⋊Dic3D411yescharacteristic
59C3×C4×C3⋊D3—21no—
60C3×C4×C3⋊D3—21no—
61C2×C32×Dic3—21no—
62C32×D12—21no—
63C32×D12D412yescomplemented
64C32×Dic6—21no—
65C32×Dic6D412yescomplemented
66C3×#626—24no—
67C3×D3×Dic3—24no—
68C32×C3⋊C8—21no—
69C32×C3⋊C8—21no—
70C3×#449—91no—
71#5172—31no—
72#5158—31no—
73C2×C32×Q8—31no—
74C2×C32×D4—21no—
75C2×C32×D4—21no—
76C2×C32×D4—21no—
77C2×C32×D4—31no—
78C2×C32×D4—41no—
79C2×C32×D4C2×D311yescharacteristic
80C2×C32×D4C2×D311yescharacteristic
81C2×C32×D4C22×C311yescharacteristic
82C2×#638—21no—
83C2×C4×C3⋊D3C22×C311yescharacteristic
84C2×C3×#67—61no—
85C2×C3×#67—61no—
86C2×C3×#67—61no—
87C2×C3×#67—62no—
88C22×C3×Dic3—61no—
89C3×#239—62no—
90C3×#239—62no—
91C3×#237—62no—
92C3×#237—62no—
93C2×C3×D12—21no—
94C2×C3×D12—61no—
95C2×C3×D12C2×D311yescharacteristic
96C2×C3×D12C22×C311yescharacteristic
97C2×C3×C4×D3—31no—
98C2×C3×C4×D3—31no—
99C2×C3×C4×D3—61no—
100C2×C3×C4×D3—61no—
101C2×C3×Dic6—21no—
102C2×C3×Dic6C2×D311yescharacteristic
103C2×C3×Dic6C22×C311yescharacteristic
104C2×#626—21no—
105C2×D3×Dic3—21no—
106#3796—22no—
107#3796—22no—
108C32×SD16—62no—
109C32×D8—62no—
110C2×C32×C8—31no—
111C2×C32×C8—31no—
112#3757—21no—
113C4⋊(C3⋊Dic3)C22×C311yescharacteristic
114C3×#217—61no—
115C3×#217—61no—
116C3×#217—62no—
117C3×#214—24no—
118C3×#214—22no—
119C3×#214—22no—
120C3×#213—24no—
121C3×#213—22no—
122C3×#213—22no—
123C3×C4⋊Dic3—31no—
124C3×C4⋊Dic3—31no—
125C3×C4⋊Dic3—61no—
126C2×C3×C3⋊C8—21no—
127C2×C3×C3⋊C8—21no—
128C2×C3×C3⋊C8C2×D311yescharacteristic
129C2×C3×C3⋊C8C2×D311yescharacteristic
130C2×C3×C3⋊C8C22×C311yescharacteristic
131C2×C3×C3⋊C8C22×C311yescharacteristic
132C22×C33—41no—
133C22×C33—41no—
134C22×C33—41no—
135C22×C33C2×D411yescharacteristic
136C2×C3×C3⋊D3—21no—
137C2×C3×C3⋊D3—21no—
138C2×C3×C3⋊D3—21no—
139C2×C32×D3—22no—
140C2×C32×D3—41no—
141C2×C32×D3—41no—
142C33×C4C2×D411yescharacteristic
143C33×C4C2×D411yescharacteristic
144C3×C3⋊Dic3—21no—
145C3×C3⋊Dic3—41no—
146C32×Dic3—22no—
147C2×C3×#41—91no—
148C2×#239—31no—
149C2×#237—31no—
150C2×C3×SD16—31no—
151C2×C3×SD16—31no—
152C2×C3×SD16—61no—
153C2×C3×D8—31no—
154C2×C3×D8—31no—
155C2×C3×D8—61no—
156C3×#121—91no—
157#938—31no—
158#938—31no—
159#938—61no—
160C2×#214C3×D311yescharacteristic, complemented
161C2×#213C3×D311yescharacteristic, complemented
162C3×#103—91no—
163C3×#102—91no—
164C3×C22⋊C8—91no—
165#835—31no—
166#832—31no—
167#821—31no—
168(C2×D3)⋊C8—31no—
169(C2×D3)⋊C8—31no—
170#816—31no—
171C23×C32—21no—
172C23×C32—22no—
173C23×C32—21no—
174C23×C32—21no—
175C23×C32—41no—
176C23×C32—41no—
177C23×C32—42no—
178C23×C32—61no—
179C22×C3⋊D3C3×D411yescharacteristic
180C22×C3×D3—21no—
181C22×C3×D3—21no—
182C22×C3×D3—31no—
183C22×C3×D3—31no—
184C22×C3×D3—41no—
185C22×C3×D3—61no—
186C32×Q8—32no—
187C32×Q8—61no—
188C32×D4—21no—
189C32×D4—21no—
190C32×D4—22no—
191C32×D4—22no—
192C32×D4—21no—
193C32×D4—21no—
194C32×D4—21no—
195C32×D4—21no—
196C32×D4—32no—
197C32×D4—41no—
198C32×D4—41no—
199C32×D4—41no—
200C32×D4—41no—
201C32×D4—42no—
202C32×D4—42no—
203C32×D4—61no—
204C2×C32×C4—21no—
205C2×C32×C4—21no—
206C2×C32×C4—21no—
207C2×C32×C4—41no—
208C2×C32×C4—61no—
209C2×C32×C4C22×D311yescharacteristic
210C2×C32×C4C22×D311yescharacteristic
211C2×C32×C4C23×C311yescharacteristic
212#638—42no—
213C2×C3⋊Dic3—21no—
214C2×C3⋊Dic3C3×D411yescharacteristic
215C4×C3⋊D3—21no—
216C4×C3⋊D3—21no—
217C3×#67—64no—
218C3×#67—124no—
219C3×#67—122no—
220C3×#67—122no—
221C2×C3×Dic3—21no—
222C2×C3×Dic3—21no—
223C2×C3×Dic3—31no—
224C2×C3×Dic3—31no—
225C2×C3×Dic3—41no—
226C2×C3×Dic3—61no—
227C2×C3×Dic3—64no—
228C2×C3×Dic3—62no—
229C2×C3×Dic3—61no—
230C2×C3×Dic3—61no—
231C3×D12—21no—
232C3×D12—21no—
233C3×D12—22no—
234C3×D12—41no—
235C3×D12—64no—
236C3×D12#6712yescomplemented
237C3×D12C3×D412yescomplemented
238C3×C4×D3—64no—
239C3×C4×D3—61no—
240C3×C4×D3—61no—
241C3×C4×D3—61no—
242C3×C4×D3—61no—
243C3×C4×D3—121no—
244C3×C4×D3—121no—
245C3×Dic6—21no—
246C3×Dic6—21no—
247C3×Dic6—22no—
248C3×Dic6—41no—
249C3×Dic6#6712yescomplemented
250C3×Dic6C3×D412yescomplemented
251#626—24no—
252D3×Dic3—24no—
253C32×C8—61no—
254C32×C8—61no—
255C3×C3⋊C8—22no—
256C3×C3⋊C8—22no—
257C3×C3⋊C8—21no—
258C3×C3⋊C8—21no—
259C3×C3⋊C8—21no—
260C3×C3⋊C8—21no—
261#449—91noSylow
262C2×C33—81no—
263C2×C33#12011yescharacteristic
264C2×C33#13511yescharacteristic
265C2×C33AGL(1,ℤ/8)11yescharacteristic
266C3×C3⋊D3—41no—
267C32×D3—42no—
268C3×#41—182no—
269C3×#41—182no—
270C2×C3×Q8—31no—
271C2×C3×Q8—31no—
272C2×C3×Q8—61no—
273C2×C3×D4—21no—
274C2×C3×D4—21no—
275C2×C3×D4—21no—
276C2×C3×D4—31no—
277C2×C3×D4—31no—
278C2×C3×D4—41no—
279C2×C3×D4—61no—
280C2×C3×D4—181no—
281C2×C3×D4—181no—
282C2×C3×D4D3211yescharacteristic
283C2×C3×D4C2×C3×D311yescharacteristic
284C2×C3×D4C2×C3×D311yescharacteristic
285C22×C3×C4—91no—
286C22×C3×C4—181no—
287C2×#67—61no—
288C2×#67—61no—
289C2×#67—61no—
290C2×#67—62no—
291C22×Dic3—61no—
292#239—62no—
293#239—62no—
294#237—62no—
295#237—62no—
296C2×D12—61no—
297C2×D12C2×C3×D311yescharacteristic
298C2×C4×D3—31no—
299C2×C4×D3—31no—
300C2×C4×D3—61no—
301C2×C4×D3—61no—
302C2×Dic6C2×C3×D311yescharacteristic
303C3×SD16—62no—
304C3×SD16—62no—
305C3×SD16—64no—
306C3×D8—62no—
307C3×D8—62no—
308C3×D8—64no—
309C2×C3×C8—31no—
310C2×C3×C8—31no—
311C2×C3×C8—31no—
312C2×C3×C8—31no—
313C2×C3×C8—61no—
314C2×C3×C8—61no—
315C3×C4⋊C4—91no—
316C3×C22⋊C4—181no—
317#217—61no—
318#217—61no—
319#217—62no—
320#214—22no—
321#213—22no—
322C4⋊Dic3—31no—
323C4⋊Dic3—31no—
324C4⋊Dic3—61no—
325C2×C3⋊C8C2×C3×D311yescharacteristic
326C2×C3⋊C8C2×C3×D311yescharacteristic
327C22×C32—21no—
328C22×C32—21no—
329C22×C32—21no—
330C22×C32—41no—
331C22×C32—42no—
332C22×C32—42no—
333C22×C32—42no—
334C22×C32—44no—
335C22×C32—41no—
336C22×C32—41no—
337C22×C32—41no—
338C22×C32—41no—
339C22×C32—41no—
340C22×C32—42no—
341C22×C32—42no—
342C22×C32—41no—
343C22×C32—41no—
344C22×C32—41no—
345C22×C32—41no—
346C22×C32—62no—
347C22×C32—81no—
348C22×C32—81no—
349C22×C32—81no—
350C22×C32—81no—
351C22×C32—82no—
352C22×C32—82no—
353C22×C32—121no—
354C22×C32—121no—
355C22×C32D3×D411yescharacteristic
356C22×C32D3×D411yescharacteristic
357C22×C32C2×C3×D411yescharacteristic
358C2×C3⋊D3—21no—
359C2×C3⋊D3—21no—
360C2×C3⋊D3—21no—
361C2×C3×D3—22no—
362C2×C3×D3—22no—
363C2×C3×D3—42no—
364C2×C3×D3—41no—
365C2×C3×D3—41no—
366C2×C3×D3—41no—
367C2×C3×D3—41no—
368C2×C3×D3—62no—
369C2×C3×D3—61no—
370C2×C3×D3—61no—
371C2×C3×D3—61no—
372C2×C3×D3—61no—
373C2×C3×D3—61no—
374C2×C3×D3—61no—
375C2×C3×D3—81no—
376C2×C3×D3—81no—
377C2×C3×D3—121no—
378C2×C3×D3—121no—
379C32×C4—21no—
380C32×C4—21no—
381C32×C4—21no—
382C32×C4—21no—
383C32×C4—21no—
384C32×C4—21no—
385C32×C4—41no—
386C32×C4—41no—
387C32×C4—62no—
388C32×C4D3×D411yescharacteristic
389C32×C4D3×D411yescharacteristic
390C32×C4C2×#6711yescharacteristic
391C32×C4C2×#6711yescharacteristic
392C32×C4C2×C3×D411yescharacteristic
393C32×C4C2×C3×D411yescharacteristic
394C3⋊Dic3—21no—
395C3⋊Dic3—41no—
396C3×Dic3—22no—
397C3×Dic3—22no—
398C3×Dic3—42no—
399C3×Dic3—61no—
400C3×Dic3—61no—
401C3×Dic3—121no—
402C3×Dic3—122no—
403C3×Dic3—121no—
404C3×Dic3—121no—
405C2×#41—91no—
406C2×SD16—31no—
407C2×D8—31no—
408#121—91no—
409#103—91no—
410#102—91no—
411C22⋊C8—91no—
412C33#44911yescharacteristic, complemented, Sylow
413C23×C3—22no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3—42no—
420C23×C3—61no—
421C23×C3—61no—
422C23×C3—91no—
423C23×C3—121no—
424C22×D3—21no—
425C22×D3—31no—
426C22×D3—31no—
427C22×D3—61no—
428C3×Q8—32no—
429C3×Q8—32no—
430C3×Q8—62no—
431C3×Q8—61no—
432C3×Q8—61no—
433C3×Q8—121no—
434C3×D4—22no—
435C3×D4—22no—
436C3×D4—21no—
437C3×D4—21no—
438C3×D4—21no—
439C3×D4—21no—
440C3×D4—21no—
441C3×D4—21no—
442C3×D4—32no—
443C3×D4—32no—
444C3×D4—41no—
445C3×D4—41no—
446C3×D4—41no—
447C3×D4—41no—
448C3×D4—42no—
449C3×D4—42no—
450C3×D4—62no—
451C3×D4—61no—
452C3×D4—61no—
453C3×D4—121no—
454C3×D4—184no—
455C3×D4—362no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—41no—
460C2×C3×C4—61no—
461C2×C3×C4—61no—
462C2×C3×C4—91no—
463C2×C3×C4—121no—
464C2×C3×C4—184no—
465C2×C3×C4—181no—
466C2×C3×C4—181no—
467C2×C3×C4—181no—
468C2×C3×C4C2×D3211yescharacteristic
469C2×C3×C4C22×C3×D311yescharacteristic
470C2×C3×C4C22×C3×D311yescharacteristic
471#67—64no—
472#67—124no—
473#67—122no—
474#67—122no—
475C2×Dic3—21no—
476C2×Dic3—31no—
477C2×Dic3—31no—
478C2×Dic3—61no—
479C2×Dic3—64no—
480C2×Dic3—62no—
481C2×Dic3—61no—
482C2×Dic3—61no—
483D12—21no—
484D12—64no—
485D12C3×#6712yescomplemented
486C4×D3—64no—
487C4×D3—61no—
488C4×D3—61no—
489C4×D3—61no—
490C4×D3—61no—
491C4×D3—121no—
492C4×D3—121no—
493Dic6—21no—
494Dic6C3×#6712yescomplemented
495C3×C8—62no—
496C3×C8—62no—
497C3×C8—61no—
498C3×C8—61no—
499C3×C8—61no—
500C3×C8—61no—
501C3⋊C8—21no—
502C3⋊C8—21no—
503C2×C32—21no—
504C2×C32—21no—
505C2×C32—21no—
506C2×C32—21no—
507C2×C32—21no—
508C2×C32—21no—
509C2×C32—21no—
510C2×C32—21no—
511C2×C32—21no—
512C2×C32—41no—
513C2×C32—41no—
514C2×C32—41no—
515C2×C32—82no—
516C2×C32—82no—
517C2×C32—82no—
518C2×C32—84no—
519C2×C32—81no—
520C2×C32—81no—
521C2×C32—81no—
522C2×C32—122no—
523C2×C32#91111yescharacteristic
524C2×C32#91211yescharacteristic
525C2×C32#91411yescharacteristic
526C2×C32#91611yescharacteristic
527C2×C32#93711yescharacteristic
528C2×C32#93711yescharacteristic
529C2×C32C3×#12011yescharacteristic
530C2×C32C3×#13511yescharacteristic
531C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
532C3⋊D3—41no—
533C3×D3—42no—
534C3×D3—42no—
535C3×D3—82no—
536C3×D3—122no—
537C3×D3—121no—
538C3×D3—121no—
539#41—182no—
540#41—182no—
541C2×Q8—31no—
542C2×D4—31no—
543C2×D4—181no—
544C2×D4—181no—
545C2×D4C3×D3211yescharacteristic
546C22×C4—91no—
547C22×C4—181no—
548SD16—62no—
549D8—62no—
550C2×C8—31no—
551C2×C8—31no—
552C4⋊C4—91no—
553C22⋊C4—181no—
554C22×C3—21no—
555C22×C3—21no—
556C22×C3—21no—
557C22×C3—42no—
558C22×C3—42no—
559C22×C3—42no—
560C22×C3—42no—
561C22×C3—42no—
562C22×C3—44no—
563C22×C3—41no—
564C22×C3—41no—
565C22×C3—41no—
566C22×C3—41no—
567C22×C3—41no—
568C22×C3—41no—
569C22×C3—41no—
570C22×C3—41no—
571C22×C3—41no—
572C22×C3—41no—
573C22×C3—62no—
574C22×C3—62no—
575C22×C3—81no—
576C22×C3—81no—
577C22×C3—81no—
578C22×C3—81no—
579C22×C3—82no—
580C22×C3—82no—
581C22×C3—122no—
582C22×C3—121no—
583C22×C3—121no—
584C22×C3—121no—
585C22×C3—121no—
586C22×C3—181no—
587C22×C3—181no—
588C22×C3—181no—
589C22×C3—241no—
590C22×C3—241no—
591C22×C3#381111yescharacteristic
592C22×C3C3×D3×D411yescharacteristic
593C22×C3C3×D3×D411yescharacteristic
594C2×D3—22no—
595C2×D3—41no—
596C2×D3—41no—
597C2×D3—62no—
598C2×D3—61no—
599C2×D3—61no—
600C2×D3—61no—
601C2×D3—61no—
602C2×D3—61no—
603C2×D3—61no—
604C2×D3—121no—
605C2×D3—121no—
606C3×C4—21no—
607C3×C4—21no—
608C3×C4—21no—
609C3×C4—21no—
610C3×C4—21no—
611C3×C4—21no—
612C3×C4—41no—
613C3×C4—41no—
614C3×C4—62no—
615C3×C4—62no—
616C3×C4—122no—
617C3×C4—181no—
618C3×C4—361no—
619C3×C4D3×#6711yescharacteristic
620C3×C4D3×#6711yescharacteristic
621C3×C4C3×D3×D411yescharacteristic
622C3×C4C3×D3×D411yescharacteristic
623C3×C4C2×C3×#6711yescharacteristic
624C3×C4C2×C3×#6711yescharacteristic
625Dic3—22no—
626Dic3—61no—
627Dic3—61no—
628Dic3—121no—
629Dic3—122no—
630Dic3—121no—
631Dic3—121no—
632C32—21no—
633C32—21no—
634C32—21no—
635C32—41no—
636C32#515811yescharacteristic, complemented
637C32#517211yescharacteristic, complemented
638C32C3×#44911yescharacteristic, complemented
639C23—21no—
640C23—61no—
641C23—91no—
642Q8—32no—
643Q8—61no—
644D4—21no—
645D4—21no—
646D4—32no—
647D4—61no—
648D4—184no—
649D4—362no—
650C2×C4—61no—
651C2×C4—91no—
652C2×C4—184no—
653C2×C4—181no—
654C2×C4—181no—
655C2×C4—181no—
656C2×C4C2×C3×D3211yescharacteristic
657C8—61no—
658C8—61no—
659C2×C3—21no—
660C2×C3—21no—
661C2×C3—21no—
662C2×C3—21no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—41no—
669C2×C3—41no—
670C2×C3—41no—
671C2×C3—82no—
672C2×C3—82no—
673C2×C3—82no—
674C2×C3—84no—
675C2×C3—81no—
676C2×C3—81no—
677C2×C3—81no—
678C2×C3—122no—
679C2×C3—122no—
680C2×C3—242no—
681C2×C3—361no—
682C2×C3#6393611yescharacteristic
683C2×C3#6393711yescharacteristic
684C2×C3#6398311yescharacteristic
685C2×C3C3×#91111yescharacteristic
686C2×C3C3×#91211yescharacteristic
687C2×C3C3×#91411yescharacteristic
688C2×C3C3×#91611yescharacteristic
689C2×C3C3×#93711yescharacteristic
690C2×C3C3×#93711yescharacteristic
691D3—42no—
692D3—122no—
693D3—121no—
694D3—121no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—62no—
699C22—121no—
700C22—121no—
701C22—181no—
702C22—181no—
703C22—181no—
704C22C3×#381111yescharacteristic
705C4—62no—
706C4—181no—
707C4—361no—
708C4C3×D3×#6711yescharacteristic
709C4C3×D3×#6711yescharacteristic
710C3—21no—
711C3—21no—
712C3—21no—
713C3—41no—
714C3#1059152011yescharacteristic, direct product factor
715C3C3×#515811yescharacteristic, complemented
716C3C3×#517211yescharacteristic, complemented
717C2—81no—
718C2—122no—
719C2—361no—
720C2C3×#6393611yescharacteristic
721C2C3×#6393711yescharacteristic
722C2C3×#6398311yescharacteristic
subgroupG/H
centerC22×C3#3811
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C2×C3×D32
FittingC2×C33×D4C22
socleC22×C33C2×D4
hypercenterC2×C3×D4D32
hypocenterC32C3×#449
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3796C2semidirect
2. C3×#64147C2semidirect
3. C2×C32×#214C2semidirect
4. C2×C32×#213C2semidirect
5. C3×#63566C2semidirect
6. C3×#63563C2semidirect
7. C3×#63557C2semidirect
10. #10591520C3direct (N × H)
28. C2×#3796C2×C3semidirect
31. #64147C2×C3semidirect
36. C2×C3×#214D3semidirect
37. C2×C3×#214C2×C3semidirect
39. C2×C3×#213D3semidirect
40. C2×C3×#213C2×C3semidirect
47. #63566C2×C3semidirect
48. #63563C2×C3semidirect
49. #63557C2×C3semidirect
63. C32×D12D4semidirect
65. C32×Dic6D4semidirect
160. C2×#214C3×D3semidirect
161. C2×#213C3×D3semidirect
236. C3×D12#67semidirect
237. C3×D12C3×D4semidirect
249. C3×Dic6#67semidirect
250. C3×Dic6C3×D4semidirect
412. C33#449semidirect
485. D12C3×#67semidirect
494. Dic6C3×#67semidirect
636. C32#5158semidirect
637. C32#5172semidirect
638. C32C3×#449semidirect
714. C3#10591520direct (N × H)
715. C3C3×#5158semidirect
716. C3C3×#5172semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#37962
C3×#641472
C2×C32×#2142
C2×C32×#2132
C3×#635662
C3×#635632
C3×#635572
C3×#51723
C3×#51583
#105915203