Finite Group Databasebeta

← C3×#86766 #11902763

Subgroups — C3×#86766 #11902763

Order 1152.

3452 conjugacy classes of subgroups.

The subgroup lattice has 623 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#41C212yesmaximal, complemented
2C32×#550C211yesmaximal, characteristic, complemented
3C3×#5831C212yesmaximal, complemented
4C3×#5717C213yesmaximal, complemented
5C3×#5716C213yesmaximal, complemented
6C3×#5612C216yesmaximal, complemented
7C3×#5606C216yesmaximal, complemented
8C3×Q8×D12C211yesmaximal, characteristic, complemented
9C3×C4×#239C211yesmaximal, characteristic, complemented
10C3×#5551C213yesmaximal, complemented
11C3×C4×D3×D4C213yesmaximal, complemented
12C3×D4×#41—31nomaximal
13#86766C311yesmaximal, characteristic, direct product factor
14C2×C32×#41C2212yescomplemented
15C3×D3×#41—216no—
16C2×C3×#239C2211yescharacteristic
17C2×C3×D3×Q8C2212yescomplemented
18C2×C3×#237C2216yescomplemented
19C2×C3×D3×D4C2213yes—
20C2×C3×D3×D4C2216yescomplemented
21C2×C3×#235C2216yescomplemented
22C22×C3×C4×D3C2216yescomplemented
23C32×#127C2213yescomplemented
24C32×#121C2216yescomplemented
25C32×C4×Q8C2211yescharacteristic, complemented
26C32×C4×D4C2213yescomplemented
27C3×Q8×Dic3C2211yescharacteristic, complemented
28C3×#938C2216yescomplemented
29C3×#938C2216yescomplemented
30C3×#938C2216yescomplemented
31C3×#937C22112yescomplemented
32C3×#936C2216yescomplemented
33C3×D4×Dic3C2213yescomplemented
34C3×D4×Dic3C2216yescomplemented
35C3×C4×#67C2216yescomplemented
36C3×#924C2216yescomplemented
37C3×#897C2216yescomplemented
38C3×#893C2211yescharacteristic
39C3×#893C2213yescomplemented
40C3×#892C2213yescomplemented
41C3×D3×C4⋊C4C2213yescomplemented
42C3×#883C22112yescomplemented
43C3×#67⋊C4C2216yescomplemented
44C3×D3×C22⋊C4C2216yescomplemented
45C3×C4×D12C2213yes—
46C3×C4×D12C2213yescomplemented
47C3×C42×D3C2213yescomplemented
48C3×#869C2213yescomplemented
49C22×C3×#41—32no—
50C2×D3×#41C2×C312yescomplemented
51C3×#550—21no—
52C3×#550D311yescharacteristic, complemented
53C3×#550C2×C311yescharacteristic, complemented
54C3×D4×Q8—31no—
55C3×#548—32no—
56C3×#547—33no—
57C3×#546—36no—
58C3×D42—33no—
59C3×#532—33no—
60C3×#525—36no—
61C3×C4×#41—31no—
62C2×C3×C4×D4—33no—
63#5831C2×C312yescomplemented
64#5717C2×C313yescomplemented
65#5716C2×C313yescomplemented
66#5612C2×C316yescomplemented
67#5606C2×C316yescomplemented
68Q8×D12C2×C311yescharacteristic, complemented
69C4×#239C2×C311yescharacteristic, complemented
70#5551C2×C313yescomplemented
71C4×D3×D4C2×C313yescomplemented
72C23×C3×D3C2316yes—
73C32×#41—28no—
74C2×C32×Q8C2311yescharacteristic
75C2×C32×D4C2313yes—
76C2×C32×D4C2316yes—
77C2×C32×D4C2316yes—
78C22×C32×C4C2316yes—
79C2×C3×#67C2316yes—
80C2×C3×#67C23112yes—
81C22×C3×Dic3C2316yes—
82C3×#239D418yescomplemented
83C3×D3×Q8—28no—
84C3×#237—224no—
85C3×D3×D4—224no—
86C3×D3×D4—212no—
87C3×#235—224no—
88C2×C3×D12C2313yes—
89C2×C3×D12C2311yescharacteristic
90C2×C3×C4×D3—224no—
91C2×C3×C4×D3C2316yes—
92C2×C3×C4×D3C2312yes—
93C2×C3×C4×D3C2313yes—
94C2×C3×C4×D3C2316yes—
95C2×C3×C4×D3C2313yes—
96C2×C3×C4×D3C2313yes—
97C2×C3×Dic6C2316yes—
98C32×C4⋊C4C2311yescharacteristic
99C32×C4⋊C4C2313yes—
100C32×C22⋊C4C2316yes—
101C32×C42C2313yes—
102C3×#217C2316yes—
103C3×#217C23112yes—
104C3×(C2×D3)⋊C4C2312yes—
105C3×(C2×D3)⋊C4C2316yes—
106C3×(C2×D3)⋊C4C2316yes—
107C3×C4⋊Dic3C2316yes—
108C3×C4⋊Dic3C2313yes—
109C3×C4⋊Dic3C2313yes—
110C3×Dic3⋊C4C2316yes—
111C3×C4×Dic3C2313yes—
112C3×C4×Dic3C2311yescharacteristic
113C3×C4×Dic3C2313yes—
114D4×#41—31noSylow
115C2×C3×#41—22no—
116C2×C3×#41—31no—
117C2×C3×#41—36no—
118C2×C3×#41—36no—
119C2×C3×#41—616no—
120C2×C3×#41C2×D312yescomplemented
121C2×C3×#41C22×C312yescomplemented
122C22×C3×Q8—32no—
123C22×C3×D4—36no—
124C22×C3×D4—33no—
125C23×C3×C4—36no—
126D3×#41—216no—
127C2×#239C22×C311yescharacteristic
128C2×D3×Q8C22×C312yescomplemented
129C2×#237C22×C316yescomplemented
130C2×D3×D4C22×C313yes—
131C2×D3×D4C22×C316yescomplemented
132C2×#235C22×C316yescomplemented
133C22×C4×D3C22×C316yescomplemented
134C3×C4⋊Q8—33no—
135C3×#127—23no—
136C3×#127C2×D313yescomplemented
137C3×#127C22×C313yescomplemented
138C3×#124—36no—
139C3×#123—312no—
140C3×C22⋊Q8—36no—
141C3×C22⋊Q8—36no—
142C3×#121—26no—
143C3×#121—36no—
144C3×#121—36no—
145C3×#121—36no—
146C3×#121C2×D316yescomplemented
147C3×#121C22×C316yescomplemented
148C3×#120—312no—
149C3×C4×Q8—21no—
150C3×C4×Q8—31no—
151C3×C4×Q8C2×D311yescharacteristic, complemented
152C3×C4×Q8C22×C311yescharacteristic, complemented
153C3×C4×D4—23no—
154C3×C4×D4—33no—
155C3×C4×D4—36no—
156C3×C4×D4—36no—
157C3×C4×D4—31no—
158C3×C4×D4—33no—
159C3×C4×D4—36no—
160C3×C4×D4—33no—
161C3×C4×D4—33no—
162C3×C4×D4C2×D313yescomplemented
163C3×C4×D4C22×C313yescomplemented
164C3×#117—33no—
165C2×C3×C4⋊C4—33no—
166C2×C3×C22⋊C4—36no—
167C2×C3×C42—33no—
168Q8×Dic3C22×C311yescharacteristic, complemented
169#938C22×C316yescomplemented
170#938C22×C316yescomplemented
171#938C22×C316yescomplemented
172#937C22×C3112yescomplemented
173#936C22×C316yescomplemented
174D4×Dic3C22×C313yescomplemented
175D4×Dic3C22×C316yescomplemented
176C4×#67C22×C316yescomplemented
177#924C22×C316yescomplemented
178#897C22×C316yescomplemented
179#893C22×C311yescharacteristic
180#893C22×C313yescomplemented
181#892C22×C313yescomplemented
182D3×C4⋊C4C22×C313yescomplemented
183#883C22×C3112yescomplemented
184#67⋊C4C22×C316yescomplemented
185D3×C22⋊C4C22×C316yescomplemented
186C4×D12C22×C313yes—
187C4×D12C22×C313yescomplemented
188C42×D3C22×C313yescomplemented
189#869C22×C313yescomplemented
190C23×C32C2416yes—
191C22×C3×D3—212no—
192C22×C3×D3—212no—
193C22×C3×D3—46no—
194C22×C3×D3C2413yes—
195C22×C3×D3C2412yes—
196C32×Q8C2×D414yescomplemented
197C32×D4—212no—
198C32×D4—26no—
199C32×D4—46no—
200C2×C32×C4—212no—
201C2×C32×C4C2413yes—
202C2×C32×C4C2412yes—
203C2×C32×C4C2413yes—
204C2×C32×C4C2411yescharacteristic
205C3×#67—224no—
206C3×#67—212no—
207C2×C3×Dic3—212no—
208C2×C3×Dic3C2411yescharacteristic
209C2×C3×Dic3C2413yes—
210C2×C3×Dic3C2416yes—
211C2×C3×Dic3C2411yescharacteristic
212C3×D12C2×D4112yescomplemented
213C3×D12#4114yescomplemented
214C3×C4×D3—212no—
215C3×C4×D3—212no—
216C3×C4×D3—26no—
217C3×C4×D3—24no—
218C3×C4×D3—43no—
219C3×C4×D3C2×D4112yescomplemented
220C3×Dic6—212no—
221C22×#41—32no—
222#550C3×D311yescharacteristic, complemented
223D4×Q8—31no—
224#548—32no—
225#547—33no—
226#546—36no—
227D42—33no—
228#532—33no—
229#525—36no—
230C4×#41—31no—
231C2×C4×D4—33no—
232C24×C3—36no—
233C23×D3C23×C316yes—
234C3×#41—28no—
235C3×#41—28no—
236C3×#41—38no—
237C3×#41—48no—
238C3×#41—624no—
239C3×#41—624no—
240C2×C3×Q8—21no—
241C2×C3×Q8—36no—
242C2×C3×Q8—68no—
243C2×C3×Q8C22×D311yescharacteristic
244C2×C3×Q8C23×C311yescharacteristic
245C2×C3×D4—23no—
246C2×C3×D4—26no—
247C2×C3×D4—26no—
248C2×C3×D4—36no—
249C2×C3×D4—312no—
250C2×C3×D4—31no—
251C2×C3×D4—33no—
252C2×C3×D4—612no—
253C2×C3×D4—624no—
254C2×C3×D4C22×D313yes—
255C2×C3×D4C22×D316yes—
256C2×C3×D4C22×D316yes—
257C2×C3×D4C23×C313yes—
258C2×C3×D4C23×C316yes—
259C2×C3×D4C23×C316yes—
260C22×C3×C4—26no—
261C22×C3×C4—33no—
262C22×C3×C4—36no—
263C22×C3×C4—33no—
264C22×C3×C4—36no—
265C22×C3×C4—32no—
266C22×C3×C4—36no—
267C22×C3×C4—33no—
268C22×C3×C4—624no—
269C22×C3×C4C22×D316yes—
270C22×C3×C4C23×C316yes—
271C2×#67C23×C316yes—
272C2×#67C23×C3112yes—
273C22×Dic3C23×C316yes—
274#239C3×D418yescomplemented
275D3×Q8—28no—
276#237—224no—
277D3×D4—224no—
278D3×D4—212no—
279#235—224no—
280C2×D12C23×C313yes—
281C2×D12C23×C311yescharacteristic
282C2×C4×D3—224no—
283C2×C4×D3C23×C313yes—
284C2×C4×D3C23×C316yes—
285C2×C4×D3C23×C316yes—
286C2×C4×D3C23×C312yes—
287C2×C4×D3C23×C313yes—
288C2×C4×D3C23×C313yes—
289C2×Dic6C23×C316yes—
290C3×C4⋊C4—21no—
291C3×C4⋊C4—23no—
292C3×C4⋊C4—36no—
293C3×C4⋊C4—33no—
294C3×C4⋊C4—33no—
295C3×C4⋊C4—36no—
296C3×C4⋊C4C22×D311yescharacteristic
297C3×C4⋊C4C22×D313yes—
298C3×C4⋊C4C23×C311yescharacteristic
299C3×C4⋊C4C23×C313yes—
300C3×C22⋊C4—26no—
301C3×C22⋊C4—36no—
302C3×C22⋊C4—312no—
303C3×C22⋊C4—32no—
304C3×C22⋊C4—36no—
305C3×C22⋊C4—36no—
306C3×C22⋊C4C22×D316yes—
307C3×C22⋊C4C23×C316yes—
308C3×C42—23no—
309C3×C42—31no—
310C3×C42—33no—
311C3×C42—33no—
312C3×C42C22×D313yes—
313C3×C42C23×C313yes—
314#217C23×C316yes—
315#217C23×C3112yes—
316(C2×D3)⋊C4C23×C316yes—
317(C2×D3)⋊C4C23×C316yes—
318(C2×D3)⋊C4C23×C312yes—
319C4⋊Dic3C23×C313yes—
320C4⋊Dic3C23×C316yes—
321C4⋊Dic3C23×C313yes—
322Dic3⋊C4C23×C316yes—
323C4×Dic3C23×C311yescharacteristic
324C4×Dic3C23×C313yes—
325C4×Dic3C23×C313yes—
326C22×C32—26no—
327C22×C32—26no—
328C22×C32—26no—
329C22×C32C2511yescharacteristic
330C2×C3×D3—22no—
331C2×C3×D3—23no—
332C2×C3×D3—23no—
333C2×C3×D3—22no—
334C2×C3×D3—424no—
335C2×C3×D3C22×D416yes—
336C2×C3×D3C2×#4114yescomplemented
337C32×C4—22no—
338C32×C4—23no—
339C32×C4C22×D416yes—
340C32×C4C2×#4112yescomplemented
341C3×Dic3—26no—
342C3×Dic3—23no—
343C3×Dic3—21no—
344C3×Dic3C22×D412yes—
345C2×#41—31no—
346C2×#41—36no—
347C2×#41—36no—
348C2×#41—616no—
349C2×#41C2×C3×D312yescomplemented
350C22×Q8—32no—
351C22×D4—33no—
352C22×D4—36no—
353C23×C4—36no—
354C4⋊Q8—33no—
355#127C2×C3×D313yescomplemented
356#124—36no—
357#123—312no—
358C22⋊Q8—36no—
359C22⋊Q8—36no—
360#121—36no—
361#121—36no—
362#121—36no—
363#121C2×C3×D316yescomplemented
364#120—312no—
365C4×Q8—31no—
366C4×Q8C2×C3×D311yescharacteristic, complemented
367C4×D4—33no—
368C4×D4—36no—
369C4×D4—36no—
370C4×D4—31no—
371C4×D4—33no—
372C4×D4—36no—
373C4×D4—33no—
374C4×D4—33no—
375C4×D4C2×C3×D313yescomplemented
376#117—33no—
377C2×C4⋊C4—33no—
378C2×C22⋊C4—36no—
379C2×C42—33no—
380C23×C3—26no—
381C23×C3—32no—
382C23×C3—33no—
383C23×C3—612no—
384C23×C3—612no—
385C23×C3—126no—
386C23×C3C23×D316yes—
387C23×C3C24×C316yes—
388C22×D3—212no—
389C22×D3—212no—
390C22×D3—46no—
391C22×D3C24×C313yes—
392C22×D3C24×C312yes—
393C3×Q8—24no—
394C3×Q8—612no—
395C3×Q8D3×D414yescomplemented
396C3×Q8C2×C3×D414yescomplemented
397C3×D4—212no—
398C3×D4—26no—
399C3×D4—212no—
400C3×D4—26no—
401C3×D4—312no—
402C3×D4—34no—
403C3×D4—46no—
404C3×D4—412no—
405C3×D4—46no—
406C3×D4—46no—
407C3×D4—612no—
408C3×D4—624no—
409C3×D4—86no—
410C2×C3×C4—212no—
411C2×C3×C4—212no—
412C2×C3×C4—21no—
413C2×C3×C4—23no—
414C2×C3×C4—23no—
415C2×C3×C4—22no—
416C2×C3×C4—31no—
417C2×C3×C4—312no—
418C2×C3×C4—31no—
419C2×C3×C4—33no—
420C2×C3×C4—36no—
421C2×C3×C4—412no—
422C2×C3×C4—64no—
423C2×C3×C4—612no—
424C2×C3×C4—612no—
425C2×C3×C4—612no—
426C2×C3×C4—66no—
427C2×C3×C4—123no—
428C2×C3×C4C23×D313yes—
429C2×C3×C4C23×D312yes—
430C2×C3×C4C23×D313yes—
431C2×C3×C4C23×D311yescharacteristic
432C2×C3×C4C24×C313yes—
433C2×C3×C4C24×C312yes—
434C2×C3×C4C24×C313yes—
435C2×C3×C4C24×C311yescharacteristic
436#67—224no—
437#67—212no—
438C2×Dic3—212no—
439C2×Dic3C24×C311yescharacteristic
440C2×Dic3C24×C313yes—
441C2×Dic3C24×C316yes—
442C2×Dic3C24×C311yescharacteristic
443D12C2×C3×D4112yescomplemented
444D12C3×#4114yescomplemented
445C4×D3—212no—
446C4×D3—212no—
447C4×D3—26no—
448C4×D3—24no—
449C4×D3—43no—
450C4×D3C2×C3×D4112yescomplemented
451Dic6—212no—
452C2×C32—46no—
453C2×C32C23×D411yescharacteristic
454C2×C32C22×#4111yescharacteristic
455C2×C32#58511yescharacteristic
456C3×D3—24no—
457C3×D3—26no—
458C24—36no—
459#41—28no—
460#41—38no—
461#41—624no—
462#41—624no—
463C2×Q8—36no—
464C2×Q8—68no—
465C2×Q8C22×C3×D311yescharacteristic
466C2×D4—36no—
467C2×D4—312no—
468C2×D4—31no—
469C2×D4—33no—
470C2×D4—624no—
471C2×D4—612no—
472C2×D4C22×C3×D313yes—
473C2×D4C22×C3×D316yes—
474C2×D4C22×C3×D316yes—
475C22×C4—33no—
476C22×C4—36no—
477C22×C4—33no—
478C22×C4—36no—
479C22×C4—32no—
480C22×C4—36no—
481C22×C4—33no—
482C22×C4—624no—
483C22×C4C22×C3×D316yes—
484C4⋊C4—33no—
485C4⋊C4—36no—
486C4⋊C4—33no—
487C4⋊C4—36no—
488C4⋊C4C22×C3×D311yescharacteristic
489C4⋊C4C22×C3×D313yes—
490C22⋊C4—36no—
491C22⋊C4—312no—
492C22⋊C4—32no—
493C22⋊C4—36no—
494C22⋊C4—36no—
495C22⋊C4C22×C3×D316yes—
496C42—31no—
497C42—33no—
498C42—33no—
499C42C22×C3×D313yes—
500C22×C3—26no—
501C22×C3—26no—
502C22×C3—26no—
503C22×C3—26no—
504C22×C3—26no—
505C22×C3—26no—
506C22×C3—21no—
507C22×C3—36no—
508C22×C3—34no—
509C22×C3—46no—
510C22×C3—46no—
511C22×C3—46no—
512C22×C3—62no—
513C22×C3—63no—
514C22×C3—63no—
515C22×C3—62no—
516C22×C3—1224no—
517C22×C3C24×D311yescharacteristic
518C22×C3C25×C311yescharacteristic
519C2×D3—22no—
520C2×D3—23no—
521C2×D3—23no—
522C2×D3—22no—
523C2×D3—424no—
524C2×D3C22×C3×D416yes—
525C2×D3C2×C3×#4114yescomplemented
526C3×C4—22no—
527C3×C4—23no—
528C3×C4—22no—
529C3×C4—23no—
530C3×C4—26no—
531C3×C4—22no—
532C3×C4—32no—
533C3×C4—42no—
534C3×C4—43no—
535C3×C4—66no—
536C3×C4—63no—
537C3×C4—61no—
538C3×C4C2×D3×D416yes—
539C3×C4D3×#4112yescomplemented
540C3×C4C22×C3×D416yes—
541C3×C4C2×C3×#4112yescomplemented
542Dic3—26no—
543Dic3—23no—
544Dic3—21no—
545Dic3C22×C3×D412yes—
546C32D4×#4111yescharacteristic, complemented, Sylow
547C23—32no—
548C23—33no—
549C23—612no—
550C23—612no—
551C23—126no—
552C23C23×C3×D316yes—
553Q8—612no—
554Q8C3×D3×D414yescomplemented
555D4—212no—
556D4—26no—
557D4—312no—
558D4—34no—
559D4—46no—
560D4—624no—
561D4—612no—
562C2×C4—212no—
563C2×C4—31no—
564C2×C4—312no—
565C2×C4—31no—
566C2×C4—33no—
567C2×C4—36no—
568C2×C4—64no—
569C2×C4—612no—
570C2×C4—612no—
571C2×C4—612no—
572C2×C4—66no—
573C2×C4—123no—
574C2×C4C23×C3×D313yes—
575C2×C4C23×C3×D312yes—
576C2×C4C23×C3×D313yes—
577C2×C4C23×C3×D311yescharacteristic
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—21no—
581C2×C3—46no—
582C2×C3—46no—
583C2×C3—64no—
584C2×C3—66no—
585C2×C3—86no—
586C2×C3C22×D3×D411yescharacteristic
587C2×C3C2×D3×#4111yescharacteristic
588C2×C3#596611yescharacteristic
589C2×C3C23×C3×D411yescharacteristic
590C2×C3C22×C3×#4111yescharacteristic
591C2×C3C3×#58511yescharacteristic
592D3—24no—
593D3—26no—
594C22—26no—
595C22—26no—
596C22—26no—
597C22—36no—
598C22—34no—
599C22—62no—
600C22—63no—
601C22—63no—
602C22—62no—
603C22—1224no—
604C22C24×C3×D311yescharacteristic
605C4—22no—
606C4—23no—
607C4—32no—
608C4—66no—
609C4—63no—
610C4—61no—
611C4C2×C3×D3×D416yes—
612C4C3×D3×#4112yescomplemented
613C3—21no—
614C3#8676611yescharacteristic, direct product factor
615C3C3×D4×#4111yescharacteristic, complemented
616C2—46no—
617C2—64no—
618C2—66no—
619C2C22×C3×D3×D411yescharacteristic
620C2C2×C3×D3×#4111yescharacteristic
621C2C3×#596611yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#550C2
socleC22×C32C25
hypercenterC3×#550D3
hypocenterC3C3×D4×#41
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#550

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×#41C2semidirect
2. C32×#550C2semidirect
3. C3×#5831C2semidirect
4. C3×#5717C2semidirect
5. C3×#5716C2semidirect
6. C3×#5612C2semidirect
7. C3×#5606C2semidirect
8. C3×Q8×D12C2semidirect
9. C3×C4×#239C2semidirect
10. C3×#5551C2semidirect
11. C3×C4×D3×D4C2semidirect
13. #86766C3direct (N × H)
14. C2×C32×#41C22semidirect
17. C2×C3×D3×Q8C22semidirect
18. C2×C3×#237C22semidirect
20. C2×C3×D3×D4C22semidirect
21. C2×C3×#235C22semidirect
22. C22×C3×C4×D3C22semidirect
23. C32×#127C22semidirect
24. C32×#121C22semidirect
25. C32×C4×Q8C22semidirect
26. C32×C4×D4C22semidirect
27. C3×Q8×Dic3C22semidirect
28. C3×#938C22semidirect
29. C3×#938C22semidirect
30. C3×#938C22semidirect
31. C3×#937C22semidirect
32. C3×#936C22semidirect
33. C3×D4×Dic3C22semidirect
34. C3×D4×Dic3C22semidirect
35. C3×C4×#67C22semidirect
36. C3×#924C22semidirect
37. C3×#897C22semidirect
39. C3×#893C22semidirect
40. C3×#892C22semidirect
41. C3×D3×C4⋊C4C22semidirect
42. C3×#883C22semidirect
43. C3×#67⋊C4C22semidirect
44. C3×D3×C22⋊C4C22semidirect
46. C3×C4×D12C22semidirect
47. C3×C42×D3C22semidirect
48. C3×#869C22semidirect
50. C2×D3×#41C2×C3semidirect
52. C3×#550D3semidirect
53. C3×#550C2×C3semidirect
63. #5831C2×C3semidirect
64. #5717C2×C3semidirect
65. #5716C2×C3semidirect
66. #5612C2×C3semidirect
67. #5606C2×C3semidirect
68. Q8×D12C2×C3semidirect
69. C4×#239C2×C3semidirect
70. #5551C2×C3semidirect
71. C4×D3×D4C2×C3semidirect
82. C3×#239D4semidirect
120. C2×C3×#41C2×D3semidirect
121. C2×C3×#41C22×C3semidirect
128. C2×D3×Q8C22×C3semidirect
129. C2×#237C22×C3semidirect
131. C2×D3×D4C22×C3semidirect
132. C2×#235C22×C3semidirect
133. C22×C4×D3C22×C3semidirect
136. C3×#127C2×D3semidirect
137. C3×#127C22×C3semidirect
146. C3×#121C2×D3semidirect
147. C3×#121C22×C3semidirect
151. C3×C4×Q8C2×D3semidirect
152. C3×C4×Q8C22×C3semidirect
162. C3×C4×D4C2×D3semidirect
163. C3×C4×D4C22×C3semidirect
168. Q8×Dic3C22×C3semidirect
169. #938C22×C3semidirect
170. #938C22×C3semidirect
171. #938C22×C3semidirect
172. #937C22×C3semidirect
173. #936C22×C3semidirect
174. D4×Dic3C22×C3semidirect
175. D4×Dic3C22×C3semidirect
176. C4×#67C22×C3semidirect
177. #924C22×C3semidirect
178. #897C22×C3semidirect
180. #893C22×C3semidirect
181. #892C22×C3semidirect
182. D3×C4⋊C4C22×C3semidirect
183. #883C22×C3semidirect
184. #67⋊C4C22×C3semidirect
185. D3×C22⋊C4C22×C3semidirect
187. C4×D12C22×C3semidirect
188. C42×D3C22×C3semidirect
189. #869C22×C3semidirect
196. C32×Q8C2×D4semidirect
212. C3×D12C2×D4semidirect
213. C3×D12#41semidirect
219. C3×C4×D3C2×D4semidirect
222. #550C3×D3semidirect
274. #239C3×D4semidirect
336. C2×C3×D3C2×#41semidirect
340. C32×C4C2×#41semidirect
349. C2×#41C2×C3×D3semidirect
355. #127C2×C3×D3semidirect
363. #121C2×C3×D3semidirect
366. C4×Q8C2×C3×D3semidirect
375. C4×D4C2×C3×D3semidirect
395. C3×Q8D3×D4semidirect
396. C3×Q8C2×C3×D4semidirect
443. D12C2×C3×D4semidirect
444. D12C3×#41semidirect
450. C4×D3C2×C3×D4semidirect
525. C2×D3C2×C3×#41semidirect
539. C3×C4D3×#41semidirect
541. C3×C4C2×C3×#41semidirect
546. C32D4×#41semidirect
554. Q8C3×D3×D4semidirect
612. C4C3×D3×#41semidirect
614. C3#86766direct (N × H)
615. C3C3×D4×#41semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×#412
C32×#5502
C3×#58312
C3×#57172
C3×#57162
C3×#56122
C3×#56062
C3×Q8×D122
C3×C4×#2392
C3×#55512
C3×C4×D3×D42
C3×D4×#413
#867663