Finite Group Databasebeta

← C3×#10595039 #13174620

Subgroups — C3×#10595039 #13174620

Order 1728.

1374 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3752C211yesmaximal, characteristic, complemented
2C32×C4×#67C212yesmaximal, complemented
3C3×#63982C211yesmaximal, characteristic, complemented
4C3×#63981C212yesmaximal, complemented
5C3×#63980C211yesmaximal, characteristic, complemented
6C3×#63906C212yesmaximal, complemented
7C3×#63868C212yesmaximal, complemented
8C3×#63852C212yesmaximal, complemented
9C3×#63850C212yesmaximal, complemented
10C3×#5560—32nomaximal
11#10595039C311yesmaximal, characteristic, direct product factor
12C23×C3×C3⋊D3C2211yescharacteristic
13C22×C33×C4C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C2×C32×#67C2212yes—
16C2×C32×C4×D3C2212yescomplemented
17C2×C3×#627C2211yescharacteristic, complemented
18C2×C3×#626C2212yes—
19C2×C3×#626C2212yes—
20C2×C3×#625C2211yescharacteristic, complemented
21C3×#3752C2212yes—
22C3×#3752C2212yes—
23C32×#217C2212yes—
24C32×(C2×D3)⋊C4C2212yescomplemented
25C32×Dic3⋊C4C2212yescomplemented
26C32×C4×Dic3C2212yescomplemented
27C3×#3724C2211yescharacteristic, complemented
28C3×#3724C2211yescharacteristic, complemented
29C3×Dic3⋊Dic3C2212yescomplemented
30C3×#3722C2212yes—
31C3×#3722C2212yes—
32C3×(C2×D3)⋊Dic3C2212yescomplemented
33C32×C4×D4—32no—
34C2×#3752C2×C311yescharacteristic, complemented
35C3×#939—32no—
36C3×#937—32no—
37C3×#930—32no—
38C3×#929—32no—
39C3×C4×#67—22no—
40C3×C4×#67D312yescomplemented
41C3×C4×#67C2×C312yescomplemented
42C2×C3×(C2×D3)⋊C4—32no—
43C2×C3×(C2×D3)⋊C4—61no—
44C3×#898—32no—
45C3×#894—32no—
46C3×#885—32no—
47C3×#884—32no—
48C3×#882—32no—
49C3×#878—32no—
50C3×#876—32no—
51C3×#875—32no—
52#63982C2×C311yescharacteristic, complemented
53#63981C2×C312yescomplemented
54#63980C2×C311yescharacteristic, complemented
55#63906C2×C312yescomplemented
56#63868C2×C312yescomplemented
57#63852C2×C312yescomplemented
58#63850C2×C312yescomplemented
59C23×C33C2311yescharacteristic
60C22×C3×C3⋊D3—22no—
61C22×C3×C3⋊D3—41no—
62C22×C3×C3⋊D3—41no—
63C22×C3×C3⋊D3C2312yes—
64C22×C32×D3C2312yes—
65C2×C33×C4—41no—
66C2×C33×C4C2312yes—
67C2×C3×C3⋊Dic3—41no—
68C2×C3×C3⋊Dic3C2311yescharacteristic
69C2×C3×C3⋊Dic3C2311yescharacteristic
70C32×#67—24no—
71C2×C32×Dic3C2312yes—
72C2×C32×Dic3C2312yes—
73C2×C32×Dic3C2312yes—
74C32×C4×D3—42no—
75C3×#627—41no—
76C3×#626—42no—
77C3×#626—42no—
78C3×#625—41no—
79C3×#538—91no—
80#5560—32no—
81C23×C3⋊D3C22×C311yescharacteristic
82C23×C3×D3—32no—
83C23×C3×D3—61no—
84C2×C32×D4—32no—
85C22×C32×C4—21no—
86C22×C32×C4—22no—
87C22×C32×C4—32no—
88C22×C32×C4—41no—
89C22×C32×C4C2×D312yes—
90C22×C32×C4C22×C311yescharacteristic
91C22×C3⋊Dic3C22×C311yescharacteristic
92C2×C3×#67—22no—
93C2×C3×#67—32no—
94C2×C3×#67—32no—
95C2×C3×#67—32no—
96C2×C3×#67C2×D312yes—
97C2×C3×#67C22×C312yes—
98C22×C3×Dic3—32no—
99C22×C3×Dic3—61no—
100C2×C3×D12—32no—
101C2×C3×D12—32no—
102C2×C3×C4×D3—22no—
103C2×C3×C4×D3C2×D312yescomplemented
104C2×C3×C4×D3C22×C312yescomplemented
105C2×C3×Dic6—32no—
106C2×#627C22×C311yescharacteristic, complemented
107C2×#626C22×C312yes—
108C2×#626C22×C312yes—
109C2×#625C22×C311yescharacteristic, complemented
110C32×C4⋊C4—32no—
111C32×C22⋊C4—32no—
112C32×C22⋊C4—32no—
113C32×C42—32no—
114#3752C22×C312yes—
115#3752C22×C312yes—
116C3×#217—22no—
117C3×#217—32no—
118C3×#217C2×D312yes—
119C3×#217C22×C312yes—
120C3×(C2×D3)⋊C4—22no—
121C3×(C2×D3)⋊C4—32no—
122C3×(C2×D3)⋊C4—32no—
123C3×(C2×D3)⋊C4—32no—
124C3×(C2×D3)⋊C4—32no—
125C3×(C2×D3)⋊C4—32no—
126C3×(C2×D3)⋊C4—32no—
127C3×(C2×D3)⋊C4—32no—
128C3×(C2×D3)⋊C4—32no—
129C3×(C2×D3)⋊C4—32no—
130C3×(C2×D3)⋊C4—62no—
131C3×(C2×D3)⋊C4—62no—
132C3×(C2×D3)⋊C4C2×D312yescomplemented
133C3×(C2×D3)⋊C4C22×C312yescomplemented
134C3×C4⋊Dic3—32no—
135C3×Dic3⋊C4—22no—
136C3×Dic3⋊C4—32no—
137C3×Dic3⋊C4—32no—
138C3×Dic3⋊C4—32no—
139C3×Dic3⋊C4C2×D312yescomplemented
140C3×Dic3⋊C4C22×C312yescomplemented
141C3×C4×Dic3—22no—
142C3×C4×Dic3C2×D312yescomplemented
143C3×C4×Dic3C22×C312yescomplemented
144#3724C22×C311yescharacteristic, complemented
145#3724C22×C311yescharacteristic, complemented
146Dic3⋊Dic3C22×C312yescomplemented
147#3722C22×C312yes—
148#3722C22×C312yes—
149(C2×D3)⋊Dic3C22×C312yescomplemented
150C22×C33—21no—
151C22×C33—21no—
152C22×C33#4112yes—
153C22×C33C2411yescharacteristic
154C2×C3×C3⋊D3—22no—
155C2×C3×C3⋊D3—22no—
156C2×C3×C3⋊D3—22no—
157C2×C3×C3⋊D3—44no—
158C2×C32×D3—22no—
159C2×C32×D3—22no—
160C2×C32×D3—22no—
161C33×C4—22no—
162C3×C3⋊Dic3—21no—
163C3×C3⋊Dic3—21no—
164C32×Dic3—22no—
165C32×Dic3—22no—
166C32×Dic3—22no—
167C3×#126—92no—
168C3×#124—92no—
169C3×#123—92no—
170C3×C22⋊Q8—91no—
171C3×#121—92no—
172C3×#121—91no—
173C3×#120—92no—
174C3×C4×D4—32no—
175C3×C4×D4—32no—
176C3×C4×D4—62no—
177C2×C3×C22⋊C4—91no—
178#939—32no—
179#937—32no—
180#930—32no—
181#929—32no—
182C4×#67C3×D312yescomplemented
183C2×(C2×D3)⋊C4—32no—
184C2×(C2×D3)⋊C4—61no—
185#898—32no—
186#894—32no—
187#885—32no—
188#884—32no—
189#882—32no—
190#878—32no—
191#876—32no—
192#875—32no—
193C23×C32—21no—
194C23×C32—22no—
195C23×C32—32no—
196C23×C32—41no—
197C23×C32C22×D312yes—
198C23×C32C23×C311yescharacteristic
199C22×C3⋊D3—22no—
200C22×C3⋊D3—41no—
201C22×C3⋊D3—41no—
202C22×C3⋊D3C23×C312yes—
203C22×C3×D3—22no—
204C22×C3×D3—32no—
205C22×C3×D3—32no—
206C22×C3×D3—62no—
207C22×C3×D3—64no—
208C22×C3×D3—64no—
209C22×C3×D3—122no—
210C22×C3×D3—122no—
211C22×C3×D3—122no—
212C22×C3×D3—122no—
213C22×C3×D3C22×D312yes—
214C22×C3×D3C23×C312yes—
215C32×D4—64no—
216C2×C32×C4—22no—
217C2×C32×C4—22no—
218C2×C32×C4—22no—
219C2×C32×C4—32no—
220C2×C32×C4—32no—
221C2×C32×C4—32no—
222C2×C32×C4—42no—
223C2×C32×C4—42no—
224C2×C32×C4—41no—
225C2×C32×C4—44no—
226C2×C32×C4—42no—
227C2×C32×C4—44no—
228C2×C32×C4—122no—
229C2×C32×C4C22×D312yes—
230C2×C32×C4C22×D312yes—
231C2×C32×C4C23×C312yes—
232C2×C3⋊Dic3—41no—
233C2×C3⋊Dic3C23×C311yescharacteristic
234C2×C3⋊Dic3C23×C311yescharacteristic
235C3×#67—28no—
236C3×#67—24no—
237C3×#67—24no—
238C3×#67—122no—
239C3×#67—122no—
240C3×#67—122no—
241C2×C3×Dic3—22no—
242C2×C3×Dic3—22no—
243C2×C3×Dic3—22no—
244C2×C3×Dic3—32no—
245C2×C3×Dic3—32no—
246C2×C3×Dic3—61no—
247C2×C3×Dic3—61no—
248C2×C3×Dic3—122no—
249C2×C3×Dic3—122no—
250C2×C3×Dic3C22×D312yes—
251C2×C3×Dic3C22×D312yes—
252C2×C3×Dic3C22×D312yes—
253C2×C3×Dic3C23×C312yes—
254C2×C3×Dic3C23×C312yes—
255C2×C3×Dic3C23×C312yes—
256C3×D12—122no—
257C3×D12—122no—
258C3×C4×D3—42no—
259C3×C4×D3—42no—
260C3×C4×D3—44no—
261C3×Dic6—122no—
262#627—41no—
263#626—42no—
264#626—42no—
265#625—41no—
266#538—91noSylow
267C2×C33—22no—
268C2×C33C2×#4111yescharacteristic
269C2×C33H(5,𝔽2)11yescharacteristic
270C2×C33H(5,𝔽2)11yescharacteristic
271C3×C3⋊D3—42no—
272C32×D3—42no—
273C24×C3—91no—
274C23×D3—32no—
275C23×D3—61no—
276C2×C3×Q8—91no—
277C2×C3×D4—32no—
278C2×C3×D4—32no—
279C2×C3×D4—62no—
280C2×C3×D4—92no—
281C2×C3×D4—92no—
282C2×C3×D4—91no—
283C22×C3×C4—21no—
284C22×C3×C4—22no—
285C22×C3×C4—32no—
286C22×C3×C4—32no—
287C22×C3×C4—41no—
288C22×C3×C4—62no—
289C22×C3×C4—91no—
290C22×C3×C4D3211yescharacteristic
291C22×C3×C4C2×C3×D312yes—
292C2×#67—32no—
293C2×#67—32no—
294C2×#67—32no—
295C2×#67C2×C3×D312yes—
296C22×Dic3—32no—
297C22×Dic3—61no—
298C2×D12—32no—
299C2×D12—32no—
300C2×C4×D3C2×C3×D312yescomplemented
301C2×Dic6—32no—
302C3×C4⋊C4—32no—
303C3×C4⋊C4—32no—
304C3×C4⋊C4—62no—
305C3×C4⋊C4—91no—
306C3×C4⋊C4—91no—
307C3×C4⋊C4—92no—
308C3×C22⋊C4—32no—
309C3×C22⋊C4—32no—
310C3×C22⋊C4—32no—
311C3×C22⋊C4—32no—
312C3×C22⋊C4—62no—
313C3×C22⋊C4—62no—
314C3×C22⋊C4—92no—
315C3×C22⋊C4—92no—
316C3×C22⋊C4—92no—
317C3×C22⋊C4—92no—
318C3×C22⋊C4—92no—
319C3×C42—32no—
320C3×C42—32no—
321C3×C42—62no—
322#217—32no—
323#217C2×C3×D312yes—
324(C2×D3)⋊C4—32no—
325(C2×D3)⋊C4—32no—
326(C2×D3)⋊C4—32no—
327(C2×D3)⋊C4—32no—
328(C2×D3)⋊C4—32no—
329(C2×D3)⋊C4—32no—
330(C2×D3)⋊C4—32no—
331(C2×D3)⋊C4—32no—
332(C2×D3)⋊C4—32no—
333(C2×D3)⋊C4—62no—
334(C2×D3)⋊C4—62no—
335(C2×D3)⋊C4C2×C3×D312yescomplemented
336C4⋊Dic3—32no—
337Dic3⋊C4—32no—
338Dic3⋊C4—32no—
339Dic3⋊C4—32no—
340Dic3⋊C4C2×C3×D312yescomplemented
341C4×Dic3C2×C3×D312yescomplemented
342C22×C32—21no—
343C22×C32—21no—
344C22×C32—22no—
345C22×C32—22no—
346C22×C32—22no—
347C22×C32—22no—
348C22×C32—21no—
349C22×C32—22no—
350C22×C32—22no—
351C22×C32—24no—
352C22×C32—42no—
353C22×C32—41no—
354C22×C32—42no—
355C22×C32—42no—
356C22×C32—42no—
357C22×C32—42no—
358C22×C32—62no—
359C22×C32—62no—
360C22×C32—62no—
361C22×C32#23514yes—
362C22×C32C3×#4112yes—
363C22×C32C23×D312yes—
364C22×C32C24×C311yescharacteristic
365C2×C3⋊D3—22no—
366C2×C3⋊D3—22no—
367C2×C3⋊D3—22no—
368C2×C3⋊D3—44no—
369C2×C3×D3—24no—
370C2×C3×D3—22no—
371C2×C3×D3—22no—
372C2×C3×D3—22no—
373C2×C3×D3—22no—
374C2×C3×D3—22no—
375C2×C3×D3—22no—
376C2×C3×D3—42no—
377C2×C3×D3—42no—
378C2×C3×D3—64no—
379C2×C3×D3—62no—
380C2×C3×D3—62no—
381C2×C3×D3—62no—
382C2×C3×D3—62no—
383C2×C3×D3—62no—
384C2×C3×D3—62no—
385C2×C3×D3—122no—
386C2×C3×D3—122no—
387C2×C3×D3—128no—
388C2×C3×D3—128no—
389C32×C4—22no—
390C32×C4—24no—
391C32×C4—22no—
392C32×C4—22no—
393C32×C4—42no—
394C32×C4—42no—
395C32×C4—44no—
396C32×C4—62no—
397C32×C4—62no—
398C32×C4—62no—
399C3⋊Dic3—21no—
400C3⋊Dic3—21no—
401C3×Dic3—24no—
402C3×Dic3—22no—
403C3×Dic3—22no—
404C3×Dic3—22no—
405C3×Dic3—22no—
406C3×Dic3—22no—
407C3×Dic3—22no—
408C3×Dic3—42no—
409C3×Dic3—42no—
410C3×Dic3—62no—
411C3×Dic3—62no—
412C3×Dic3—121no—
413C3×Dic3—121no—
414#126—92no—
415#124—92no—
416#123—92no—
417C22⋊Q8—91no—
418#121—92no—
419#121—91no—
420#120—92no—
421C4×D4—32no—
422C2×C22⋊C4—91no—
423C33#53811yescharacteristic, complemented, Sylow
424C23×C3—21no—
425C23×C3—22no—
426C23×C3—32no—
427C23×C3—32no—
428C23×C3—41no—
429C23×C3—62no—
430C23×C3—92no—
431C23×C3—182no—
432C23×C3—361no—
433C23×C3—361no—
434C23×C3C2×D3211yescharacteristic
435C23×C3C22×C3×D312yes—
436C22×D3—32no—
437C22×D3—32no—
438C22×D3—62no—
439C22×D3—64no—
440C22×D3—64no—
441C22×D3—122no—
442C22×D3—122no—
443C22×D3—122no—
444C22×D3—122no—
445C22×D3C22×C3×D312yes—
446C3×Q8—361no—
447C3×D4—68no—
448C3×D4—64no—
449C3×D4—64no—
450C3×D4—362no—
451C3×D4—362no—
452C3×D4—361no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—32no—
457C2×C3×C4—32no—
458C2×C3×C4—32no—
459C2×C3×C4—32no—
460C2×C3×C4—32no—
461C2×C3×C4—32no—
462C2×C3×C4—41no—
463C2×C3×C4—42no—
464C2×C3×C4—44no—
465C2×C3×C4—42no—
466C2×C3×C4—44no—
467C2×C3×C4—42no—
468C2×C3×C4—62no—
469C2×C3×C4—62no—
470C2×C3×C4—62no—
471C2×C3×C4—91no—
472C2×C3×C4—91no—
473C2×C3×C4—122no—
474C2×C3×C4—122no—
475C2×C3×C4—124no—
476C2×C3×C4—361no—
477C2×C3×C4C2×D3212yes—
478C2×C3×C4C22×C3×D312yes—
479C2×C3×C4C22×C3×D312yes—
480#67—24no—
481#67—122no—
482#67—122no—
483#67—122no—
484C2×Dic3—32no—
485C2×Dic3—32no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—122no—
489C2×Dic3—122no—
490C2×Dic3C22×C3×D312yes—
491C2×Dic3C22×C3×D312yes—
492C2×Dic3C22×C3×D312yes—
493D12—122no—
494D12—122no—
495C4×D3—42no—
496Dic6—122no—
497C2×C32—22no—
498C2×C32—24no—
499C2×C32—24no—
500C2×C32—21no—
501C2×C32—21no—
502C2×C32—21no—
503C2×C32—22no—
504C2×C32—22no—
505C2×C32—22no—
506C2×C32—41no—
507C2×C32—41no—
508C2×C32—41no—
509C2×C32—44no—
510C2×C32—44no—
511C2×C32—122no—
512C2×C32C2×#23512yes—
513C2×C32#100412yes—
514C2×C32#100912yes—
515C2×C32C2×C3×#4111yescharacteristic
516C2×C32C3×H(5,𝔽2)11yescharacteristic
517C2×C32C3×H(5,𝔽2)11yescharacteristic
518C3⋊D3—42no—
519C3×D3—44no—
520C3×D3—42no—
521C3×D3—42no—
522C3×D3—124no—
523C3×D3—122no—
524C3×D3—122no—
525C24—91no—
526C2×Q8—91no—
527C2×D4—32no—
528C2×D4—92no—
529C2×D4—92no—
530C2×D4—91no—
531C22×C4—32no—
532C22×C4—91no—
533C22×C4C3×D3211yescharacteristic
534C4⋊C4—32no—
535C4⋊C4—92no—
536C4⋊C4—91no—
537C4⋊C4—91no—
538C22⋊C4—32no—
539C22⋊C4—32no—
540C22⋊C4—92no—
541C22⋊C4—92no—
542C22⋊C4—92no—
543C22⋊C4—92no—
544C22⋊C4—92no—
545C42—32no—
546C22×C3—22no—
547C22×C3—22no—
548C22×C3—21no—
549C22×C3—21no—
550C22×C3—22no—
551C22×C3—22no—
552C22×C3—21no—
553C22×C3—22no—
554C22×C3—22no—
555C22×C3—24no—
556C22×C3—42no—
557C22×C3—42no—
558C22×C3—42no—
559C22×C3—42no—
560C22×C3—41no—
561C22×C3—42no—
562C22×C3—64no—
563C22×C3—62no—
564C22×C3—62no—
565C22×C3—62no—
566C22×C3—62no—
567C22×C3—62no—
568C22×C3—62no—
569C22×C3—122no—
570C22×C3—122no—
571C22×C3—182no—
572C22×C3—182no—
573C22×C3—182no—
574C22×C3—364no—
575C22×C3#379812yes—
576C22×C3C3×#23514yes—
577C22×C3C22×D3211yescharacteristic
578C22×C3C23×C3×D312yes—
579C2×D3—22no—
580C2×D3—22no—
581C2×D3—22no—
582C2×D3—64no—
583C2×D3—62no—
584C2×D3—62no—
585C2×D3—62no—
586C2×D3—62no—
587C2×D3—62no—
588C2×D3—62no—
589C2×D3—122no—
590C2×D3—122no—
591C2×D3—128no—
592C2×D3—128no—
593C3×C4—24no—
594C3×C4—22no—
595C3×C4—22no—
596C3×C4—22no—
597C3×C4—42no—
598C3×C4—42no—
599C3×C4—44no—
600C3×C4—64no—
601C3×C4—62no—
602C3×C4—62no—
603C3×C4—62no—
604C3×C4—62no—
605C3×C4—62no—
606C3×C4—62no—
607C3×C4—122no—
608C3×C4—122no—
609C3×C4—181no—
610C3×C4—181no—
611Dic3—22no—
612Dic3—22no—
613Dic3—22no—
614Dic3—62no—
615Dic3—62no—
616Dic3—121no—
617Dic3—121no—
618C32—22no—
619C32—21no—
620C32—41no—
621C32#556012yescomplemented
622C32C3×#53811yescharacteristic, complemented
623C23—32no—
624C23—92no—
625C23—182no—
626C23—361no—
627C23—361no—
628C23C2×C3×D3211yescharacteristic
629Q8—361no—
630D4—64no—
631D4—362no—
632D4—362no—
633D4—361no—
634C2×C4—32no—
635C2×C4—32no—
636C2×C4—32no—
637C2×C4—41no—
638C2×C4—91no—
639C2×C4—91no—
640C2×C4—122no—
641C2×C4—361no—
642C2×C4C2×C3×D3212yes—
643C2×C3—24no—
644C2×C3—24no—
645C2×C3—22no—
646C2×C3—22no—
647C2×C3—21no—
648C2×C3—22no—
649C2×C3—21no—
650C2×C3—21no—
651C2×C3—22no—
652C2×C3—44no—
653C2×C3—44no—
654C2×C3—41no—
655C2×C3—41no—
656C2×C3—41no—
657C2×C3—124no—
658C2×C3—122no—
659C2×C3—122no—
660C2×C3—362no—
661C2×C3C2×#379811yescharacteristic
662C2×C3#6430811yescharacteristic
663C2×C3#6433011yescharacteristic
664C2×C3C2×C3×#23512yes—
665C2×C3C3×#100412yes—
666C2×C3C3×#100912yes—
667D3—42no—
668D3—124no—
669D3—122no—
670D3—122no—
671C22—21no—
672C22—21no—
673C22—62no—
674C22—62no—
675C22—62no—
676C22—182no—
677C22—182no—
678C22—182no—
679C22—364no—
680C22C3×#379812yes—
681C22C22×C3×D3211yescharacteristic
682C4—22no—
683C4—62no—
684C4—62no—
685C4—62no—
686C4—181no—
687C4—181no—
688C3—21no—
689C3—22no—
690C3—41no—
691C3#1059503911yescharacteristic, direct product factor
692C3C3×#556012yescomplemented
693C2—22no—
694C2—122no—
695C2—362no—
696C2C2×C3×#379811yescharacteristic
697C2C3×#6430811yescharacteristic
698C2C3×#6433011yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
hypercenterC22×C3×C4D32
hypocenterC32C3×#538
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3752C2semidirect
2. C32×C4×#67C2semidirect
3. C3×#63982C2semidirect
4. C3×#63981C2semidirect
5. C3×#63980C2semidirect
6. C3×#63906C2semidirect
7. C3×#63868C2semidirect
8. C3×#63852C2semidirect
9. C3×#63850C2semidirect
11. #10595039C3direct (N × H)
16. C2×C32×C4×D3C22semidirect
17. C2×C3×#627C22semidirect
20. C2×C3×#625C22semidirect
24. C32×(C2×D3)⋊C4C22semidirect
25. C32×Dic3⋊C4C22semidirect
26. C32×C4×Dic3C22semidirect
27. C3×#3724C22semidirect
28. C3×#3724C22semidirect
29. C3×Dic3⋊Dic3C22semidirect
32. C3×(C2×D3)⋊Dic3C22semidirect
34. C2×#3752C2×C3semidirect
40. C3×C4×#67D3semidirect
41. C3×C4×#67C2×C3semidirect
52. #63982C2×C3semidirect
53. #63981C2×C3semidirect
54. #63980C2×C3semidirect
55. #63906C2×C3semidirect
56. #63868C2×C3semidirect
57. #63852C2×C3semidirect
58. #63850C2×C3semidirect
103. C2×C3×C4×D3C2×D3semidirect
104. C2×C3×C4×D3C22×C3semidirect
106. C2×#627C22×C3semidirect
109. C2×#625C22×C3semidirect
132. C3×(C2×D3)⋊C4C2×D3semidirect
133. C3×(C2×D3)⋊C4C22×C3semidirect
139. C3×Dic3⋊C4C2×D3semidirect
140. C3×Dic3⋊C4C22×C3semidirect
142. C3×C4×Dic3C2×D3semidirect
143. C3×C4×Dic3C22×C3semidirect
144. #3724C22×C3semidirect
145. #3724C22×C3semidirect
146. Dic3⋊Dic3C22×C3semidirect
149. (C2×D3)⋊Dic3C22×C3semidirect
182. C4×#67C3×D3semidirect
300. C2×C4×D3C2×C3×D3semidirect
335. (C2×D3)⋊C4C2×C3×D3semidirect
340. Dic3⋊C4C2×C3×D3semidirect
341. C4×Dic3C2×C3×D3semidirect
423. C33#538semidirect
621. C32#5560semidirect
622. C32C3×#538semidirect
691. C3#10595039direct (N × H)
692. C3C3×#5560semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#37522
C32×C4×#672
C3×#639822
C3×#639812
C3×#639802
C3×#639062
C3×#638682
C3×#638522
C3×#638502
C3×#55603
#105950393