Finite Group Databasebeta

← C3×#78832 #11858051

Subgroups — C3×#78832 #11858051

Order 1152.

1531 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic
2C2×C3×#901C211yesmaximal, characteristic, complemented
3C3×#5523C211yesmaximal, characteristic, complemented
4C32×#416C211yesmaximal, characteristic, complemented
5C3×#5232C211yesmaximal, characteristic, complemented
6C2×C3×#816C211yesmaximal, characteristic, complemented
7C3×#5004C211yesmaximal, characteristic, complemented
8C3×#4802C212yesmaximal, complemented
9C3×D3×#103C212yesmaximal, complemented
10C3×#4772C212yesmaximal, complemented
11C3×#4771C212yesmaximal, complemented
12C3×#2898—31nomaximal
13#78832C311yesmaximal, 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
24C22×C32×C8C2211yescharacteristic
25C32×#117C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28C3×#901—24no—
29C2×C3×ΓL(1,𝔽25)C2212yes—
30C2×C3×D3×C8C2212yes—
31C3×#892C2212yes—
32C3×D3×C4⋊C4C2212yes—
33C3×#67⋊C4—22no—
34C3×C4×D12—21no—
35C3×C4×Dic6—21no—
36C32×#103C2211yescharacteristic
37C32×#103C2211yescharacteristic
38C32×#102C2211yescharacteristic
39C32×#102C2211yescharacteristic
40C3×#835C2212yes—
41C3×#832C2212yes—
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×#901C2×C311yescharacteristic, complemented
51#5523C2×C311yescharacteristic, complemented
52C3×#419—31no—
53C3×#419—32no—
54C3×#417—31no—
55C3×#417—32no—
56C3×#416—21no—
57C3×#416—32no—
58C3×#416D311yescharacteristic, complemented
59C3×#416C2×C311yescharacteristic, complemented
60C2×C3×#103—31no—
61C2×C3×#103—32no—
62#5232C2×C311yescharacteristic, complemented
63C2×#816C2×C311yescharacteristic, complemented
64#5004C2×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×C4C2311yescharacteristic
76C2×C3×#67—22no—
77C2×C3×#67D412yes—
78C22×C3×Dic3—21no—
79C22×C3×Dic3—22no—
80C22×C3×Dic3—21no—
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—
100C2×C32×C8—22no—
101C2×C32×C8C2311yescharacteristic
102C2×C32×C8C2311yescharacteristic
103C32×C4⋊C4C2311yescharacteristic
104C32×C4⋊C4C2311yescharacteristic
105C32×C22⋊C4—21no—
106C32×C42—21no—
107C3×(C2×D3)⋊C4—22no—
108C3×C4⋊Dic3—21no—
109C3×C4⋊Dic3C2312yes—
110C3×Dic3⋊C4—22no—
111C3×C4×Dic3—22no—
112C3×#208—22no—
113C2×C3×C3⋊C8C2312yes—
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—31no—
140C2×C3×M16—32no—
141C22×C3×C8—21no—
142C22×C3×C8—32no—
143C22×C3×C8C2×D311yescharacteristic
144C22×C3×C8C22×C311yescharacteristic
145C3×C4×Q8—61no—
146C3×C4×D4—61no—
147C3×C4×D4—62no—
148C3×#117—21no—
149C3×#117—32no—
150C3×#117C2×D311yescharacteristic
151C3×#117C22×C311yescharacteristic
152C2×C3×C4⋊C4—31no—
153C2×C3×C4⋊C4—32no—
154C2×C4⋊Dic3C22×C311yescharacteristic
155C2×#208C22×C311yescharacteristic
156#901—24no—
157C2×ΓL(1,𝔽25)C22×C312yes—
158C2×D3×C8C22×C312yes—
159#892C22×C312yes—
160D3×C4⋊C4C22×C312yes—
161#67⋊C4—22no—
162C4×D12—21no—
163C4×Dic6—21no—
164C3×#103—21no—
165C3×#103—21no—
166C3×#103—32no—
167C3×#103—32no—
168C3×#103—32no—
169C3×#103—32no—
170C3×#103—32no—
171C3×#103C2×D311yescharacteristic
172C3×#103C2×D311yescharacteristic
173C3×#103C22×C311yescharacteristic
174C3×#103C22×C311yescharacteristic
175C3×#102—21no—
176C3×#102—21no—
177C3×#102—32no—
178C3×#102C2×D311yescharacteristic
179C3×#102C2×D311yescharacteristic
180C3×#102C22×C311yescharacteristic
181C3×#102C22×C311yescharacteristic
182#835C22×C312yes—
183#832C22×C312yes—
184#816C22×C312yes—
185#816C22×C312yes—
186#810C22×C312yes—
187#810C22×C312yes—
188C23×C32—21no—
189C23×C32C2×D411yescharacteristic
190C22×C3×D3C2×D412yes—
191C32×Q8—21no—
192C32×Q8C22×C412yes—
193C32×D4—24no—
194C32×D4—21no—
195C32×D4C22×C412yes—
196C2×C32×C4—21no—
197C2×C32×C4—24no—
198C2×C32×C4—21no—
199C2×C32×C4—21no—
200C2×C32×C4C22×C412yes—
201C2×C32×C4C2×D411yescharacteristic
202C2×C32×C4C2×D412yes—
203C2×C32×C4C2411yescharacteristic
204C3×#67—28no—
205C3×#67C22⋊C418yes—
206C2×C3×Dic3—24no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3—28no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—81no—
211C2×C3×Dic3C2×D412yes—
212C3×D12C22⋊C414yes—
213C3×C4×D3—28no—
214C3×C4×D3—82no—
215C3×C4×D3C22×C414yes—
216C3×C4×D3C2×D414yes—
217C3×Dic6—24no—
218C3×Dic6—22no—
219C3×Dic6—28no—
220C3×Dic6C22⋊C414yes—
221C3×Dic6C22×C414yes—
222C32×C8—21no—
223C32×C8—21no—
224C3×C3⋊C8—22no—
225C2×2−1+4—31no—
226C2×#131—31no—
227#520—31no—
228#419—31no—
229#419—32no—
230#417—31no—
231#417—32no—
232#416—32no—
233#416C3×D311yescharacteristic, complemented
234C2×#103—31no—
235C2×#103—32no—
236C3×#41—22no—
237C3×#41—22no—
238C3×#41—24no—
239C3×#41—34no—
240C3×#41—34no—
241C3×#41—38no—
242C3×#41—42no—
243C3×#41—68no—
244C3×#41—64no—
245C3×#41—616no—
246C3×#41C4×D314yescomplemented
247C3×#41C2×C3×C414yescomplemented
248C2×C3×Q8—21no—
249C2×C3×Q8—31no—
250C2×C3×Q8—38no—
251C2×C3×Q8—34no—
252C2×C3×Q8—32no—
253C2×C3×Q8—62no—
254C2×C3×Q8—68no—
255C2×C3×Q8—64no—
256C2×C3×Q8—61no—
257C2×C3×Q8—62no—
258C2×C3×Q8C22×D311yescharacteristic
259C2×C3×Q8C23×C311yescharacteristic
260C2×C3×D4—21no—
261C2×C3×D4—21no—
262C2×C3×D4—21no—
263C2×C3×D4—32no—
264C2×C3×D4—31no—
265C2×C3×D4—41no—
266C2×C3×D4—62no—
267C2×C3×D4C22×D311yescharacteristic
268C2×C3×D4C23×C311yescharacteristic
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—32no—
273C22×C3×C4—41no—
274C22×C3×C4—62no—
275C22×C3×C4—62no—
276C22×C3×C4—62no—
277C22×C3×C4—61no—
278C22×C3×C4—61no—
279C22×C3×C4C22×D311yescharacteristic
280C22×C3×C4C23×C311yescharacteristic
281C2×#67—22no—
282C2×#67C3×D412yes—
283C22×Dic3—21no—
284C22×Dic3—22no—
285C22×Dic3—21no—
286D3×Q8—24no—
287D3×Q8C2×C3×C418yescomplemented
288#237—216no—
289#237—24no—
290#237C2×C3×C418yescomplemented
291#235—28no—
292#235C2×C3×C414yes—
293#235C3×D414yes—
294C2×D12C3×D411yescharacteristic
295C2×C4×D3—22no—
296C2×C4×D3—22no—
297C2×C4×D3C23×C312yes—
298C2×Dic6—21no—
299C2×Dic6—22no—
300C2×Dic6—22no—
301C2×Dic6—28no—
302C2×Dic6C2×C3×C414yescomplemented
303C2×Dic6C3×D411yescharacteristic
304C2×Dic6C23×C312yes—
305C3×M16—64no—
306C3×M16—62no—
307C2×C3×C8—22no—
308C2×C3×C8—22no—
309C2×C3×C8—21no—
310C2×C3×C8—21no—
311C2×C3×C8—32no—
312C2×C3×C8—42no—
313C2×C3×C8—64no—
314C2×C3×C8C22×D311yescharacteristic
315C2×C3×C8C22×D311yescharacteristic
316C2×C3×C8C23×C311yescharacteristic
317C2×C3×C8C23×C311yescharacteristic
318C3×C4⋊C4—21no—
319C3×C4⋊C4—21no—
320C3×C4⋊C4—32no—
321C3×C4⋊C4—62no—
322C3×C4⋊C4—61no—
323C3×C4⋊C4C22×D311yescharacteristic
324C3×C4⋊C4C22×D311yescharacteristic
325C3×C4⋊C4C23×C311yescharacteristic
326C3×C4⋊C4C23×C311yescharacteristic
327C3×C22⋊C4—21no—
328C3×C22⋊C4—21no—
329C3×C22⋊C4—41no—
330C3×C22⋊C4—62no—
331C3×C42—21no—
332C3×C42—21no—
333C3×C42—41no—
334C3×C42—62no—
335(C2×D3)⋊C4—22no—
336C4⋊Dic3—21no—
337C4⋊Dic3C23×C312yes—
338Dic3⋊C4—22no—
339C4×Dic3—22no—
340#208—22no—
341C2×C3⋊C8C23×C312yes—
342ΓL(1,𝔽25)—24no—
343D3×C8—24no—
344C22×C32—21no—
345C22×C32—21no—
346C22×C32—22no—
347C22×C32—41no—
348C22×C32—41no—
349C22×C32C2×C22⋊C412yes—
350C22×C32C22×D411yescharacteristic
351C2×C3×D3—22no—
352C2×C3×D3—22no—
353C2×C3×D3C2×C22⋊C414yes—
354C32×C4—22no—
355C32×C4—41no—
356C32×C4—41no—
357C32×C4C2×C22⋊C412yes—
358C32×C4C23×C411yescharacteristic
359C32×C4C22×D411yescharacteristic
360C3×Dic3—24no—
361C3×Dic3—42no—
362C3×Dic3C2×C22⋊C414yes—
3632−1+4—38no—
3642−1+4—64no—
365C2×#41—31no—
366C2×#41—32no—
367C2×#41—61no—
368C2×#41—62no—
369C2×#41C2×C3×D311yescharacteristic
370C22×Q8—32no—
371C22×Q8—31no—
372C22×Q8—61no—
373#131—64no—
374C2×M16—31no—
375C2×M16—32no—
376C22×C8—32no—
377C22×C8C2×C3×D311yescharacteristic
378C4×Q8—61no—
379C4×D4—61no—
380C4×D4—62no—
381#117—32no—
382#117C2×C3×D311yescharacteristic
383C2×C4⋊C4—31no—
384C2×C4⋊C4—32no—
385#103—32no—
386#103—32no—
387#103—32no—
388#103—32no—
389#103—32no—
390#103C2×C3×D311yescharacteristic
391#103C2×C3×D311yescharacteristic
392#102—32no—
393#102C2×C3×D311yescharacteristic
394#102C2×C3×D311yescharacteristic
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—32no—
399C23×C3—41no—
400C23×C3D3×D411yescharacteristic
401C23×C3C2×C3×D411yescharacteristic
402C22×D3C2×C3×D412yes—
403C3×Q8—21no—
404C3×Q8—21no—
405C3×Q8—22no—
406C3×Q8—34no—
407C3×Q8—34no—
408C3×Q8—41no—
409C3×Q8—68no—
410C3×Q8—64no—
411C3×Q8—62no—
412C3×Q8C2×C4×D312yes—
413C3×Q8C22×C3×C412yes—
414C3×D4—24no—
415C3×D4—24no—
416C3×D4—21no—
417C3×D4—21no—
418C3×D4—22no—
419C3×D4—38no—
420C3×D4—34no—
421C3×D4—41no—
422C3×D4—44no—
423C3×D4—68no—
424C3×D4C2×C4×D312yes—
425C3×D4C22×C3×C412yes—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—24no—
429C2×C3×C4—24no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—22no—
436C2×C3×C4—21no—
437C2×C3×C4—22no—
438C2×C3×C4—32no—
439C2×C3×C4—34no—
440C2×C3×C4—34no—
441C2×C3×C4—44no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—68no—
446C2×C3×C4—68no—
447C2×C3×C4—64no—
448C2×C3×C4—62no—
449C2×C3×C4—62no—
450C2×C3×C4—242no—
451C2×C3×C4—241no—
452C2×C3×C4C2×C4×D312yes—
453C2×C3×C4D3×D411yescharacteristic
454C2×C3×C4D3×D412yes—
455C2×C3×C4C22×C3×C412yes—
456C2×C3×C4C2×C3×D411yescharacteristic
457C2×C3×C4C2×C3×D412yes—
458C2×C3×C4C23×D311yescharacteristic
459C2×C3×C4C24×C311yescharacteristic
460#67—28no—
461#67C3×C22⋊C418yes—
462C2×Dic3—24no—
463C2×Dic3—22no—
464C2×Dic3—28no—
465C2×Dic3—22no—
466C2×Dic3—81no—
467C2×Dic3C2×C3×D412yes—
468D12C3×C22⋊C414yes—
469C4×D3—28no—
470C4×D3—82no—
471C4×D3C22×C3×C414yes—
472C4×D3C2×C3×D414yes—
473Dic6—24no—
474Dic6—22no—
475Dic6—28no—
476Dic6C3×C22⋊C414yes—
477Dic6C22×C3×C414yes—
478C3×C8—21no—
479C3×C8—21no—
480C3×C8—21no—
481C3×C8—21no—
482C3×C8—41no—
483C3×C8—41no—
484C3×C8—62no—
485C3⋊C8—22no—
486C2×C32—22no—
487C2×C32—42no—
488C2×C32C22×C22⋊C411yescharacteristic
489C2×C32#57711yescharacteristic
490C2×C32#57811yescharacteristic
491C3×D3—24no—
492#41—22no—
493#41—34no—
494#41—34no—
495#41—38no—
496#41—68no—
497#41—64no—
498#41—616no—
499#41C3×C4×D314yescomplemented
500C2×Q8—31no—
501C2×Q8—38no—
502C2×Q8—32no—
503C2×Q8—34no—
504C2×Q8—62no—
505C2×Q8—68no—
506C2×Q8—64no—
507C2×Q8—61no—
508C2×Q8—62no—
509C2×Q8C22×C3×D311yescharacteristic
510C2×D4—21no—
511C2×D4—32no—
512C2×D4—31no—
513C2×D4—62no—
514C2×D4C22×C3×D311yescharacteristic
515C22×C4—21no—
516C22×C4—32no—
517C22×C4—62no—
518C22×C4—62no—
519C22×C4—62no—
520C22×C4—61no—
521C22×C4—61no—
522C22×C4C22×C3×D311yescharacteristic
523M16—64no—
524M16—62no—
525C2×C8—22no—
526C2×C8—32no—
527C2×C8—64no—
528C2×C8C22×C3×D311yescharacteristic
529C2×C8C22×C3×D311yescharacteristic
530C4⋊C4—32no—
531C4⋊C4—62no—
532C4⋊C4—61no—
533C4⋊C4C22×C3×D311yescharacteristic
534C4⋊C4C22×C3×D311yescharacteristic
535C22⋊C4—21no—
536C22⋊C4—62no—
537C42—21no—
538C42—62no—
539C22×C3—21no—
540C22×C3—21no—
541C22×C3—21no—
542C22×C3—21no—
543C22×C3—22no—
544C22×C3—22no—
545C22×C3—22no—
546C22×C3—21no—
547C22×C3—34no—
548C22×C3—41no—
549C22×C3—41no—
550C22×C3—42no—
551C22×C3—41no—
552C22×C3—41no—
553C22×C3—41no—
554C22×C3—41no—
555C22×C3—62no—
556C22×C3—62no—
557C22×C3—81no—
558C22×C3—81no—
559C22×C3D3×C22⋊C412yes—
560C22×C3C2×C3×C22⋊C412yes—
561C22×C3C2×D3×D411yescharacteristic
562C22×C3C22×C3×D411yescharacteristic
563C2×D3—22no—
564C2×D3—22no—
565C2×D3C2×C3×C22⋊C414yes—
566C3×C4—22no—
567C3×C4—22no—
568C3×C4—22no—
569C3×C4—21no—
570C3×C4—21no—
571C3×C4—34no—
572C3×C4—42no—
573C3×C4—41no—
574C3×C4—41no—
575C3×C4—41no—
576C3×C4—41no—
577C3×C4—64no—
578C3×C4—81no—
579C3×C4—81no—
580C3×C4—122no—
581C3×C4D3×C22⋊C412yes—
582C3×C4C2×C3×C22⋊C412yes—
583C3×C4C22×C4×D311yescharacteristic
584C3×C4C2×D3×D411yescharacteristic
585C3×C4C23×C3×C411yescharacteristic
586C3×C4C22×C3×D411yescharacteristic
587Dic3—24no—
588Dic3—42no—
589Dic3C2×C3×C22⋊C414yes—
590C32#289811yescharacteristic, complemented, Sylow
591C23—21no—
592C23—32no—
593C23C3×D3×D411yescharacteristic
594Q8—21no—
595Q8—34no—
596Q8—34no—
597Q8—68no—
598Q8—64no—
599Q8—62no—
600Q8C2×C3×C4×D312yes—
601D4—24no—
602D4—21no—
603D4—38no—
604D4—34no—
605D4—68no—
606D4C2×C3×C4×D312yes—
607C2×C4—21no—
608C2×C4—24no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—32no—
612C2×C4—34no—
613C2×C4—34no—
614C2×C4—68no—
615C2×C4—68no—
616C2×C4—64no—
617C2×C4—62no—
618C2×C4—62no—
619C2×C4—242no—
620C2×C4—241no—
621C2×C4C2×C3×C4×D312yes—
622C2×C4C3×D3×D411yescharacteristic
623C2×C4C3×D3×D412yes—
624C2×C4C23×C3×D311yescharacteristic
625C8—21no—
626C8—21no—
627C8—62no—
628C2×C3—22no—
629C2×C3—22no—
630C2×C3—21no—
631C2×C3—21no—
632C2×C3—21no—
633C2×C3—42no—
634C2×C3—42no—
635C2×C3—42no—
636C2×C3—64no—
637C2×C3—82no—
638C2×C3C2×D3×C22⋊C411yescharacteristic
639C2×C3#577011yescharacteristic
640C2×C3#577111yescharacteristic
641C2×C3C22×C3×C22⋊C411yescharacteristic
642C2×C3C3×#57711yescharacteristic
643C2×C3C3×#57811yescharacteristic
644D3—24no—
645C22—21no—
646C22—21no—
647C22—22no—
648C22—34no—
649C22—41no—
650C22—41no—
651C22—62no—
652C22—62no—
653C22C3×D3×C22⋊C412yes—
654C22C2×C3×D3×D411yescharacteristic
655C4—22no—
656C4—34no—
657C4—41no—
658C4—41no—
659C4—64no—
660C4—122no—
661C4C3×D3×C22⋊C412yes—
662C4C22×C3×C4×D311yescharacteristic
663C4C2×C3×D3×D411yescharacteristic
664C3—21no—
665C3#7883211yescharacteristic, direct product factor
666C3C3×#289811yescharacteristic, complemented
667C2—22no—
668C2—42no—
669C2—64no—
670C2C2×C3×D3×C22⋊C411yescharacteristic
671C2C3×#577011yescharacteristic
672C2C3×#577111yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC32×#416C2
socleC22×C32C22×D4
prime radicalC2×C3×#1010C2
cosocleC2×C3×C4C24×C3
hypercenterC3×#416D3
hypocenterC3C3×#2898
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#416

Complements

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

NH ≅ G/Ntype
2. C2×C3×#901C2semidirect
3. C3×#5523C2semidirect
4. C32×#416C2semidirect
5. C3×#5232C2semidirect
6. C2×C3×#816C2semidirect
7. C3×#5004C2semidirect
8. C3×#4802C2semidirect
9. C3×D3×#103C2semidirect
10. C3×#4772C2semidirect
11. C3×#4771C2semidirect
13. #78832C3direct (N × H)
16. C3×#1010C4semidirect
50. C2×#901C2×C3semidirect
51. #5523C2×C3semidirect
58. C3×#416D3semidirect
59. C3×#416C2×C3semidirect
62. #5232C2×C3semidirect
63. C2×#816C2×C3semidirect
64. #5004C2×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
233. #416C3×D3semidirect
246. C3×#41C4×D3semidirect
247. C3×#41C2×C3×C4semidirect
287. D3×Q8C2×C3×C4semidirect
290. #237C2×C3×C4semidirect
302. C2×Dic6C2×C3×C4semidirect
499. #41C3×C4×D3semidirect
590. C32#2898semidirect
665. C3#78832direct (N × H)
666. 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×#9012
C3×#55232
C32×#4162
C3×#52322
C2×C3×#8162
C3×#50042
C3×#48022
C3×D3×#1032
C3×#47722
C3×#47712
C3×#28983
#788323