Finite Group Databasebeta

← C3×#78883 #11858057

Subgroups — C3×#78883 #11858057

Order 1152.

1533 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic
2C2×C3×#907C211yesmaximal, characteristic, complemented
3C3×#5504C211yesmaximal, characteristic, complemented
4C32×#417C211yesmaximal, characteristic, complemented
5C3×#5233C211yesmaximal, characteristic, complemented
6C3×#5120C211yesmaximal, characteristic, complemented
7C2×C3×#810C211yesmaximal, characteristic, complemented
8C3×#4802C212yesmaximal, complemented
9C3×D3×#103C212yesmaximal, complemented
10C3×#4772C212yesmaximal, complemented
11C3×#4771C212yesmaximal, complemented
12C3×#2898—31nomaximal
13#78883C311yesmaximal, characteristic, direct product factor
14C2×C32×#41C2211yescharacteristic
15C3×#1010—24no—
16C3×#1010C418yescomplemented
17C2×C3×D3×Q8C2212yes—
18C2×C3×#237—22no—
19C2×C3×#237C2212yes—
20C2×C3×#235—21no—
21C2×C3×#235C2211yescharacteristic
22C22×C3×Dic6—21no—
23C22×C3×Dic6C2211yescharacteristic
24C2×C32×M16C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic
26C3×C4×#67—22no—
27C3×#926C2211yescharacteristic
28C22×C3×C3⋊C8C2211yescharacteristic
29C3×#907—24no—
30C2×C3×ΓL(1,𝔽25)C2212yes—
31C2×C3×D3×C8C2212yes—
32C3×#893—21no—
33C3×#892C2212yes—
34C3×D3×C4⋊C4C2212yes—
35C3×#887—21no—
36C32×#103C2212yes—
37C32×#102C2212yes—
38C3×#835C2211yescharacteristic
39C3×#835C2211yescharacteristic
40C3×#832C2211yescharacteristic
41C3×#832C2211yescharacteristic
42C3×#816C2212yes—
43C3×#816C2212yes—
44C3×#810C2212yes—
45C3×#810C2212yes—
46C2×C3×2−1+4—31no—
47C2×#1010C2×C311yescharacteristic
48C2×C3×#131—31no—
49C3×#520—31no—
50C2×#907C2×C311yescharacteristic, complemented
51#5504C2×C311yescharacteristic, complemented
52C3×#419—31no—
53C3×#419—32no—
54C3×#417—21no—
55C3×#417—32no—
56C3×#417D311yescharacteristic, complemented
57C3×#417C2×C311yescharacteristic, complemented
58C3×#416—31no—
59C3×#416—32no—
60C2×C3×#103—31no—
61C2×C3×#103—32no—
62#5233C2×C311yescharacteristic, complemented
63#5120C2×C311yescharacteristic, complemented
64C2×#810C2×C311yescharacteristic, complemented
65#4802C2×C312yescomplemented
66D3×#103C2×C312yescomplemented
67#4772C2×C312yescomplemented
68#4771C2×C312yescomplemented
69C32×#41—22no—
70C32×#41C2×C414yescomplemented
71C2×C32×Q8C2311yescharacteristic
72C2×C32×D4—21no—
73C2×C32×D4C2311yescharacteristic
74C22×C32×C4—21no—
75C22×C32×C4—21no—
76C22×C32×C4C2311yescharacteristic
77C2×C3×#67—22no—
78C2×C3×#67D412yes—
79C22×C3×Dic3—21no—
80C22×C3×Dic3—22no—
81C3×D3×Q8—24no—
82C3×D3×Q8C2×C418yescomplemented
83C3×#237—216no—
84C3×#237—24no—
85C3×#237C2×C418yescomplemented
86C3×#235—28no—
87C3×#235C2×C414yes—
88C3×#235D414yes—
89C2×C3×D12D411yescharacteristic
90C2×C3×C4×D3—22no—
91C2×C3×C4×D3—22no—
92C2×C3×C4×D3C2312yes—
93C2×C3×Dic6—21no—
94C2×C3×Dic6—22no—
95C2×C3×Dic6—22no—
96C2×C3×Dic6—28no—
97C2×C3×Dic6C2×C414yescomplemented
98C2×C3×Dic6D411yescharacteristic
99C2×C3×Dic6C2312yes—
100C32×M16—22no—
101C2×C32×C8C2312yes—
102C32×C4⋊C4—21no—
103C32×C4⋊C4C2312yes—
104C3×#217—21no—
105C3×(C2×D3)⋊C4—22no—
106C3×C4⋊Dic3C2311yescharacteristic
107C3×C4⋊Dic3C2311yescharacteristic
108C3×Dic3⋊C4—22no—
109C3×C4×Dic3—21no—
110C3×C4×Dic3—22no—
111C2×C3×C3⋊C8—22no—
112C2×C3×C3⋊C8C2311yescharacteristic
113C2×C3×C3⋊C8C2311yescharacteristic
114C3×ΓL(1,𝔽25)—24no—
115C3×D3×C8—24no—
116#2898—31noSylow
117C3×2−1+4—38no—
118C3×2−1+4—64no—
119C2×C3×#41—21no—
120C2×C3×#41—31no—
121C2×C3×#41—32no—
122C2×C3×#41—61no—
123C2×C3×#41—62no—
124C2×C3×#41C2×D311yescharacteristic
125C2×C3×#41C22×C311yescharacteristic
126C22×C3×Q8—32no—
127C22×C3×Q8—31no—
128C22×C3×Q8—61no—
129#1010—24no—
130#1010C3×C418yescomplemented
131C2×D3×Q8C22×C312yes—
132C2×#237—22no—
133C2×#237C22×C312yes—
134C2×#235—21no—
135C2×#235C22×C311yescharacteristic
136C22×Dic6—21no—
137C22×Dic6C22×C311yescharacteristic
138C3×#131—64no—
139C2×C3×M16—21no—
140C2×C3×M16—32no—
141C2×C3×M16C2×D311yescharacteristic
142C2×C3×M16C22×C311yescharacteristic
143C22×C3×C8—31no—
144C22×C3×C8—32no—
145C3×C4×Q8—61no—
146C3×C4×D4—61no—
147C3×C4×D4—62no—
148C3×#117—31no—
149C3×#117—32no—
150C2×C3×C4⋊C4—21no—
151C2×C3×C4⋊C4—32no—
152C2×C3×C4⋊C4C2×D311yescharacteristic
153C2×C3×C4⋊C4C22×C311yescharacteristic
154C4×#67—22no—
155#926C22×C311yescharacteristic
156C22×C3⋊C8C22×C311yescharacteristic
157#907—24no—
158C2×ΓL(1,𝔽25)C22×C312yes—
159C2×D3×C8C22×C312yes—
160#893—21no—
161#892C22×C312yes—
162D3×C4⋊C4C22×C312yes—
163#887—21no—
164C3×#103—22no—
165C3×#103—31no—
166C3×#103—31no—
167C3×#103—32no—
168C3×#103—32no—
169C3×#103—32no—
170C3×#103—32no—
171C3×#103C2×D312yes—
172C3×#103C22×C312yes—
173C3×#102—22no—
174C3×#102—31no—
175C3×#102—31no—
176C3×#102C2×D312yes—
177C3×#102C22×C312yes—
178#835C22×C311yescharacteristic
179#835C22×C311yescharacteristic
180#832C22×C311yescharacteristic
181#832C22×C311yescharacteristic
182#816C22×C312yes—
183#816C22×C312yes—
184#810C22×C312yes—
185#810C22×C312yes—
186C23×C32—21no—
187C23×C32C2×D411yescharacteristic
188C22×C3×D3C2×D412yes—
189C32×Q8—21no—
190C32×Q8C22×C412yes—
191C32×D4—24no—
192C32×D4—21no—
193C32×D4C22×C412yes—
194C2×C32×C4—21no—
195C2×C32×C4—24no—
196C2×C32×C4—22no—
197C2×C32×C4—81no—
198C2×C32×C4C22×C412yes—
199C2×C32×C4C2×D411yescharacteristic
200C2×C32×C4C2×D412yes—
201C2×C32×C4C2411yescharacteristic
202C3×#67—28no—
203C3×#67C22⋊C418yes—
204C2×C3×Dic3—24no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—28no—
207C2×C3×Dic3—21no—
208C2×C3×Dic3—21no—
209C2×C3×Dic3C2×D412yes—
210C3×D12C22⋊C414yes—
211C3×C4×D3—28no—
212C3×C4×D3—82no—
213C3×C4×D3C22×C414yes—
214C3×C4×D3C2×D414yes—
215C3×Dic6—24no—
216C3×Dic6—22no—
217C3×Dic6—28no—
218C3×Dic6C22⋊C414yes—
219C3×Dic6C22×C414yes—
220C32×C8—22no—
221C3×C3⋊C8—21no—
222C3×C3⋊C8—21no—
223C2×2−1+4—31no—
224C2×#131—31no—
225#520—31no—
226#419—31no—
227#419—32no—
228#417—32no—
229#417C3×D311yescharacteristic, complemented
230#416—31no—
231#416—32no—
232C2×#103—31no—
233C2×#103—32no—
234C3×#41—22no—
235C3×#41—22no—
236C3×#41—24no—
237C3×#41—34no—
238C3×#41—34no—
239C3×#41—38no—
240C3×#41—42no—
241C3×#41—68no—
242C3×#41—64no—
243C3×#41—616no—
244C3×#41C4×D314yescomplemented
245C3×#41C2×C3×C414yescomplemented
246C2×C3×Q8—21no—
247C2×C3×Q8—31no—
248C2×C3×Q8—38no—
249C2×C3×Q8—34no—
250C2×C3×Q8—32no—
251C2×C3×Q8—62no—
252C2×C3×Q8—68no—
253C2×C3×Q8—64no—
254C2×C3×Q8—61no—
255C2×C3×Q8—62no—
256C2×C3×Q8C22×D311yescharacteristic
257C2×C3×Q8C23×C311yescharacteristic
258C2×C3×D4—21no—
259C2×C3×D4—21no—
260C2×C3×D4—21no—
261C2×C3×D4—32no—
262C2×C3×D4—31no—
263C2×C3×D4—41no—
264C2×C3×D4—62no—
265C2×C3×D4C22×D311yescharacteristic
266C2×C3×D4C23×C311yescharacteristic
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—32no—
273C22×C3×C4—41no—
274C22×C3×C4—41no—
275C22×C3×C4—62no—
276C22×C3×C4—62no—
277C22×C3×C4—62no—
278C22×C3×C4—61no—
279C22×C3×C4C22×D311yescharacteristic
280C22×C3×C4C23×C311yescharacteristic
281C2×#67—22no—
282C2×#67C3×D412yes—
283C22×Dic3—21no—
284C22×Dic3—22no—
285D3×Q8—24no—
286D3×Q8C2×C3×C418yescomplemented
287#237—216no—
288#237—24no—
289#237C2×C3×C418yescomplemented
290#235—28no—
291#235C2×C3×C414yes—
292#235C3×D414yes—
293C2×D12C3×D411yescharacteristic
294C2×C4×D3—22no—
295C2×C4×D3—22no—
296C2×C4×D3C23×C312yes—
297C2×Dic6—21no—
298C2×Dic6—22no—
299C2×Dic6—22no—
300C2×Dic6—28no—
301C2×Dic6C2×C3×C414yescomplemented
302C2×Dic6C3×D411yescharacteristic
303C2×Dic6C23×C312yes—
304C3×M16—22no—
305C3×M16—22no—
306C3×M16—42no—
307C3×M16—64no—
308C2×C3×C8—22no—
309C2×C3×C8—31no—
310C2×C3×C8—31no—
311C2×C3×C8—64no—
312C2×C3×C8—62no—
313C2×C3×C8C22×D312yes—
314C2×C3×C8C23×C312yes—
315C3×C4⋊C4—21no—
316C3×C4⋊C4—21no—
317C3×C4⋊C4—22no—
318C3×C4⋊C4—31no—
319C3×C4⋊C4—31no—
320C3×C4⋊C4—41no—
321C3×C4⋊C4—62no—
322C3×C4⋊C4C22×D312yes—
323C3×C4⋊C4C23×C312yes—
324C3×C22⋊C4—62no—
325C3×C22⋊C4—61no—
326C3×C42—62no—
327C3×C42—61no—
328#217—21no—
329(C2×D3)⋊C4—22no—
330C4⋊Dic3C23×C311yescharacteristic
331C4⋊Dic3C23×C311yescharacteristic
332Dic3⋊C4—22no—
333C4×Dic3—21no—
334C4×Dic3—22no—
335C2×C3⋊C8—22no—
336C2×C3⋊C8C23×C311yescharacteristic
337C2×C3⋊C8C23×C311yescharacteristic
338ΓL(1,𝔽25)—24no—
339D3×C8—24no—
340C22×C32—21no—
341C22×C32—21no—
342C22×C32—22no—
343C22×C32—41no—
344C22×C32—41no—
345C22×C32C2×C22⋊C412yes—
346C22×C32C22×D411yescharacteristic
347C2×C3×D3—22no—
348C2×C3×D3—22no—
349C2×C3×D3C2×C22⋊C414yes—
350C32×C4—22no—
351C32×C4—42no—
352C32×C4C2×C22⋊C412yes—
353C32×C4C23×C411yescharacteristic
354C32×C4C22×D411yescharacteristic
355C3×Dic3—24no—
356C3×Dic3—41no—
357C3×Dic3—41no—
358C3×Dic3C2×C22⋊C414yes—
3592−1+4—38no—
3602−1+4—64no—
361C2×#41—31no—
362C2×#41—32no—
363C2×#41—61no—
364C2×#41—62no—
365C2×#41C2×C3×D311yescharacteristic
366C22×Q8—32no—
367C22×Q8—31no—
368C22×Q8—61no—
369#131—64no—
370C2×M16—32no—
371C2×M16C2×C3×D311yescharacteristic
372C22×C8—31no—
373C22×C8—32no—
374C4×Q8—61no—
375C4×D4—61no—
376C4×D4—62no—
377#117—31no—
378#117—32no—
379C2×C4⋊C4—32no—
380C2×C4⋊C4C2×C3×D311yescharacteristic
381#103—31no—
382#103—31no—
383#103—32no—
384#103—32no—
385#103—32no—
386#103—32no—
387#103C2×C3×D312yes—
388#102—31no—
389#102—31no—
390#102C2×C3×D312yes—
391C23×C3—21no—
392C23×C3—21no—
393C23×C3—21no—
394C23×C3—32no—
395C23×C3—41no—
396C23×C3D3×D411yescharacteristic
397C23×C3C2×C3×D411yescharacteristic
398C22×D3C2×C3×D412yes—
399C3×Q8—21no—
400C3×Q8—21no—
401C3×Q8—22no—
402C3×Q8—34no—
403C3×Q8—34no—
404C3×Q8—41no—
405C3×Q8—68no—
406C3×Q8—64no—
407C3×Q8—62no—
408C3×Q8C2×C4×D312yes—
409C3×Q8C22×C3×C412yes—
410C3×D4—24no—
411C3×D4—24no—
412C3×D4—21no—
413C3×D4—21no—
414C3×D4—22no—
415C3×D4—38no—
416C3×D4—34no—
417C3×D4—41no—
418C3×D4—44no—
419C3×D4—68no—
420C3×D4C2×C4×D312yes—
421C3×D4C22×C3×C412yes—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—24no—
425C2×C3×C4—24no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—21no—
429C2×C3×C4—22no—
430C2×C3×C4—21no—
431C2×C3×C4—22no—
432C2×C3×C4—32no—
433C2×C3×C4—34no—
434C2×C3×C4—34no—
435C2×C3×C4—44no—
436C2×C3×C4—41no—
437C2×C3×C4—42no—
438C2×C3×C4—68no—
439C2×C3×C4—68no—
440C2×C3×C4—64no—
441C2×C3×C4—62no—
442C2×C3×C4—61no—
443C2×C3×C4—61no—
444C2×C3×C4—81no—
445C2×C3×C4—81no—
446C2×C3×C4—82no—
447C2×C3×C4—242no—
448C2×C3×C4C2×C4×D312yes—
449C2×C3×C4D3×D411yescharacteristic
450C2×C3×C4D3×D412yes—
451C2×C3×C4C22×C3×C412yes—
452C2×C3×C4C2×C3×D411yescharacteristic
453C2×C3×C4C2×C3×D412yes—
454C2×C3×C4C23×D311yescharacteristic
455C2×C3×C4C24×C311yescharacteristic
456#67—28no—
457#67C3×C22⋊C418yes—
458C2×Dic3—24no—
459C2×Dic3—22no—
460C2×Dic3—28no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3C2×C3×D412yes—
464D12C3×C22⋊C414yes—
465C4×D3—28no—
466C4×D3—82no—
467C4×D3C22×C3×C414yes—
468C4×D3C2×C3×D414yes—
469Dic6—24no—
470Dic6—22no—
471Dic6—28no—
472Dic6C3×C22⋊C414yes—
473Dic6C22×C3×C414yes—
474C3×C8—22no—
475C3×C8—22no—
476C3×C8—42no—
477C3×C8—61no—
478C3×C8—61no—
479C3⋊C8—21no—
480C3⋊C8—21no—
481C2×C32—22no—
482C2×C32—42no—
483C2×C32C22×C22⋊C411yescharacteristic
484C2×C32#57711yescharacteristic
485C2×C32#57811yescharacteristic
486C3×D3—24no—
487#41—22no—
488#41—34no—
489#41—34no—
490#41—38no—
491#41—68no—
492#41—64no—
493#41—616no—
494#41C3×C4×D314yescomplemented
495C2×Q8—31no—
496C2×Q8—38no—
497C2×Q8—32no—
498C2×Q8—34no—
499C2×Q8—62no—
500C2×Q8—68no—
501C2×Q8—64no—
502C2×Q8—61no—
503C2×Q8—62no—
504C2×Q8C22×C3×D311yescharacteristic
505C2×D4—21no—
506C2×D4—32no—
507C2×D4—31no—
508C2×D4—62no—
509C2×D4C22×C3×D311yescharacteristic
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—32no—
513C22×C4—62no—
514C22×C4—62no—
515C22×C4—62no—
516C22×C4—61no—
517C22×C4C22×C3×D311yescharacteristic
518M16—22no—
519M16—64no—
520C2×C8—31no—
521C2×C8—31no—
522C2×C8—64no—
523C2×C8—62no—
524C2×C8C22×C3×D312yes—
525C4⋊C4—21no—
526C4⋊C4—31no—
527C4⋊C4—31no—
528C4⋊C4—62no—
529C4⋊C4C22×C3×D312yes—
530C22⋊C4—62no—
531C22⋊C4—61no—
532C42—62no—
533C42—61no—
534C22×C3—21no—
535C22×C3—21no—
536C22×C3—21no—
537C22×C3—21no—
538C22×C3—22no—
539C22×C3—22no—
540C22×C3—22no—
541C22×C3—21no—
542C22×C3—34no—
543C22×C3—41no—
544C22×C3—41no—
545C22×C3—42no—
546C22×C3—41no—
547C22×C3—41no—
548C22×C3—41no—
549C22×C3—41no—
550C22×C3—62no—
551C22×C3—62no—
552C22×C3—81no—
553C22×C3—81no—
554C22×C3D3×C22⋊C412yes—
555C22×C3C2×C3×C22⋊C412yes—
556C22×C3C2×D3×D411yescharacteristic
557C22×C3C22×C3×D411yescharacteristic
558C2×D3—22no—
559C2×D3—22no—
560C2×D3C2×C3×C22⋊C414yes—
561C3×C4—22no—
562C3×C4—22no—
563C3×C4—22no—
564C3×C4—21no—
565C3×C4—21no—
566C3×C4—34no—
567C3×C4—42no—
568C3×C4—42no—
569C3×C4—42no—
570C3×C4—64no—
571C3×C4—82no—
572C3×C4—121no—
573C3×C4—121no—
574C3×C4D3×C22⋊C412yes—
575C3×C4C2×C3×C22⋊C412yes—
576C3×C4C22×C4×D311yescharacteristic
577C3×C4C2×D3×D411yescharacteristic
578C3×C4C23×C3×C411yescharacteristic
579C3×C4C22×C3×D411yescharacteristic
580Dic3—24no—
581Dic3—41no—
582Dic3—41no—
583Dic3C2×C3×C22⋊C414yes—
584C32#289811yescharacteristic, complemented, Sylow
585C23—21no—
586C23—32no—
587C23C3×D3×D411yescharacteristic
588Q8—21no—
589Q8—34no—
590Q8—34no—
591Q8—68no—
592Q8—64no—
593Q8—62no—
594Q8C2×C3×C4×D312yes—
595D4—24no—
596D4—21no—
597D4—38no—
598D4—34no—
599D4—68no—
600D4C2×C3×C4×D312yes—
601C2×C4—21no—
602C2×C4—24no—
603C2×C4—22no—
604C2×C4—32no—
605C2×C4—34no—
606C2×C4—34no—
607C2×C4—68no—
608C2×C4—68no—
609C2×C4—64no—
610C2×C4—62no—
611C2×C4—61no—
612C2×C4—61no—
613C2×C4—81no—
614C2×C4—242no—
615C2×C4C2×C3×C4×D312yes—
616C2×C4C3×D3×D411yescharacteristic
617C2×C4C3×D3×D412yes—
618C2×C4C23×C3×D311yescharacteristic
619C8—22no—
620C8—61no—
621C8—61no—
622C2×C3—22no—
623C2×C3—22no—
624C2×C3—21no—
625C2×C3—21no—
626C2×C3—21no—
627C2×C3—42no—
628C2×C3—42no—
629C2×C3—42no—
630C2×C3—64no—
631C2×C3—82no—
632C2×C3C2×D3×C22⋊C411yescharacteristic
633C2×C3#577511yescharacteristic
634C2×C3#577911yescharacteristic
635C2×C3C22×C3×C22⋊C411yescharacteristic
636C2×C3C3×#57711yescharacteristic
637C2×C3C3×#57811yescharacteristic
638D3—24no—
639C22—21no—
640C22—21no—
641C22—22no—
642C22—34no—
643C22—41no—
644C22—41no—
645C22—62no—
646C22—62no—
647C22C3×D3×C22⋊C412yes—
648C22C2×C3×D3×D411yescharacteristic
649C4—22no—
650C4—34no—
651C4—42no—
652C4—64no—
653C4—121no—
654C4—121no—
655C4C3×D3×C22⋊C412yes—
656C4C22×C3×C4×D311yescharacteristic
657C4C2×C3×D3×D411yescharacteristic
658C3—21no—
659C3#7888311yescharacteristic, direct product factor
660C3C3×#289811yescharacteristic, complemented
661C2—22no—
662C2—42no—
663C2—64no—
664C2C2×C3×D3×C22⋊C411yescharacteristic
665C2C3×#577511yescharacteristic
666C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC32×#417C2
socleC22×C32C22×D4
prime radicalC2×C3×#1010C2
cosocleC2×C3×C4C24×C3
hypercenterC3×#417D3
hypocenterC3C3×#2898
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#417

Complements

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

NH ≅ G/Ntype
2. C2×C3×#907C2semidirect
3. C3×#5504C2semidirect
4. C32×#417C2semidirect
5. C3×#5233C2semidirect
6. C3×#5120C2semidirect
7. C2×C3×#810C2semidirect
8. C3×#4802C2semidirect
9. C3×D3×#103C2semidirect
10. C3×#4772C2semidirect
11. C3×#4771C2semidirect
13. #78883C3direct (N × H)
16. C3×#1010C4semidirect
50. C2×#907C2×C3semidirect
51. #5504C2×C3semidirect
56. C3×#417D3semidirect
57. C3×#417C2×C3semidirect
62. #5233C2×C3semidirect
63. #5120C2×C3semidirect
64. C2×#810C2×C3semidirect
65. #4802C2×C3semidirect
66. D3×#103C2×C3semidirect
67. #4772C2×C3semidirect
68. #4771C2×C3semidirect
70. C32×#41C2×C4semidirect
82. C3×D3×Q8C2×C4semidirect
85. C3×#237C2×C4semidirect
97. C2×C3×Dic6C2×C4semidirect
130. #1010C3×C4semidirect
229. #417C3×D3semidirect
244. C3×#41C4×D3semidirect
245. C3×#41C2×C3×C4semidirect
286. D3×Q8C2×C3×C4semidirect
289. #237C2×C3×C4semidirect
301. C2×Dic6C2×C3×C4semidirect
494. #41C3×C4×D3semidirect
584. C32#2898semidirect
659. C3#78883direct (N × H)
660. C3C3×#2898semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C2×C3×#9072
C3×#55042
C32×#4172
C3×#52332
C3×#51202
C2×C3×#8102
C3×#48022
C3×D3×#1032
C3×#47722
C3×#47712
C3×#28983
#788833