Finite Group Databasebeta

← C3×D3×#823 #13158017

Subgroups — C3×D3×#823 #13158017

Order 1728.

924 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×D12C211yesmaximal, characteristic
2C32×D3×M16C211yesmaximal, characteristic, complemented
3C3×D3×#208C211yesmaximal, characteristic, complemented
4C3×#63650C211yesmaximal, characteristic, complemented
5C32×#823C211yesmaximal, characteristic, complemented
6C3×#63559C211yesmaximal, characteristic, complemented
7C3×#63558C211yesmaximal, characteristic, complemented
8C2×C3×#823—31nomaximal
9C3×D3×#100—31nomaximal
10D3×#823C311yesmaximal, characteristic, direct product factor
11C22×C3×D32C412yes—
12C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
13C2×C32×D12C2211yescharacteristic
14C2×C32×C4×D3C2211yescharacteristic
15C2×C3×#626C412yes—
16C3×D3×D12—21no—
17C3×D3×D12—21no—
18C3×D3×D12—21no—
19C3×D3×D12—21no—
20C33×M16C2211yescharacteristic, complemented
21C3×#3748C2211yescharacteristic, complemented
22C32×#208C2211yescharacteristic, complemented
23C32×#208C2211yescharacteristic, complemented
24C32×ΓL(1,𝔽25)—21no—
25C32×D3×C8—21no—
26C3×#3711—21no—
27C3×D3×C3⋊C8—21no—
28C2×C3×D3×D4—31no—
29C22×C3×D12—31no—
30C2×D3×D12C2×C311yescharacteristic
31C2×C32×M16—31no—
32C2×C3×#208—31no—
33C3×D3×M16—21no—
34C3×D3×M16—31no—
35C3×D3×M16D311yescharacteristic, complemented
36C3×D3×M16C2×C311yescharacteristic, complemented
37D3×#208C2×C311yescharacteristic, complemented
38C32×#100—31no—
39#63650C2×C311yescharacteristic, complemented
40C3×#833—31no—
41C3×#823—21no—
42C3×#823—31no—
43C3×#823—31no—
44C3×#823—31no—
45C3×#823—31no—
46C3×#823—31no—
47C3×#823—61no—
48C3×#823D311yescharacteristic, direct product factor
49C3×#823C2×C311yescharacteristic, complemented
50#63559C2×C311yescharacteristic, complemented
51#63558C2×C311yescharacteristic, complemented
52C22×C3×C3⋊D3C2×C412yes—
53C22×C32×D3C2×C411yescharacteristic
54C22×C32×D3C2×C412yes—
55C2×C3×D32—22no—
56C2×C3×D32—22no—
57C2×C3×D32—44no—
58C2×C33×C4C2311yescharacteristic
59C3×C4⋊(C3⋊D3)—21no—
60C3×C4⋊(C3⋊D3)—21no—
61C2×C32×Dic3C2×C411yescharacteristic
62C32×D12—21no—
63C32×D12—21no—
64C32×C4×D3D411yescharacteristic
65C32×C4×D3D411yescharacteristic
66C32×C4×D3D411yescharacteristic
67C32×C4×D3D411yescharacteristic
68C3×#626—22no—
69C3×#626—22no—
70C33×C8—21no—
71C3×C3⋊(C3⋊C8)—21no—
72C32×C3⋊C8—21no—
73C32×C3⋊C8—21no—
74C2×C3×#100—91no—
75C2×#823—31no—
76D3×#100—31no—
77C23×C3×D3—32no—
78C23×C3×D3—32no—
79C22×D32C3×C412yes—
80C2×C32×D4—31no—
81C22×C32×C4—31no—
82C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
83C2×C3×#67—32no—
84C3×D3×D4—61no—
85C3×D3×D4—61no—
86C3×D3×D4—61no—
87C3×D3×D4—61no—
88C2×C3×D12—21no—
89C2×C3×D12—32no—
90C2×C3×D12—31no—
91C2×C3×D12—31no—
92C2×C3×D12—61no—
93C2×C3×D12—61no—
94C2×C3×D12—61no—
95C2×C3×D12—61no—
96C2×C3×D12—61no—
97C2×C3×D12C2×D311yescharacteristic
98C2×C3×D12C22×C311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3C2×D311yescharacteristic
101C2×C3×C4×D3C22×C311yescharacteristic
102C2×#626C3×C412yes—
103D3×D12—21no—
104D3×D12—21no—
105D3×D12—21no—
106D3×D12—21no—
107C32×M16—21no—
108C32×M16—21no—
109C32×M16—21no—
110C32×M16—31no—
111C32×M16—31no—
112C32×M16—41no—
113C32×M16—61no—
114C32×M16C2×D311yescharacteristic, complemented
115C32×M16C2×D311yescharacteristic, complemented
116C32×M16C22×C311yescharacteristic, complemented
117C2×C32×C8—61no—
118#3748C22×C311yescharacteristic, complemented
119C3×#208—21no—
120C3×#208—21no—
121C3×#208—31no—
122C3×#208—31no—
123C3×#208—61no—
124C3×#208—61no—
125C3×#208C2×D311yescharacteristic, complemented
126C3×#208C2×D311yescharacteristic, complemented
127C3×#208C22×C311yescharacteristic, complemented
128C3×#208C22×C311yescharacteristic, complemented
129C2×C3×C3⋊C8—61no—
130C3×ΓL(1,𝔽25)—22no—
131C3×ΓL(1,𝔽25)—21no—
132C3×ΓL(1,𝔽25)—21no—
133C3×ΓL(1,𝔽25)—61no—
134C3×D3×C8—22no—
135C3×D3×C8—21no—
136C3×D3×C8—21no—
137C3×D3×C8—61no—
138#3711—21no—
139D3×C3⋊C8—21no—
140C22×C33C22×C411yescharacteristic
141C2×C3×C3⋊D3—22no—
142C2×C3×C3⋊D3—42no—
143C2×C32×D3—22no—
144C2×C32×D3—22no—
145C2×C32×D3—42no—
146C2×C32×D3C22⋊C411yescharacteristic
147C2×C32×D3C22⋊C411yescharacteristic
148C3×D32—44no—
149C3×D32—44no—
150C33×C4C2×D411yescharacteristic
151C33×C4C2×D411yescharacteristic
152C32×Dic3C22⋊C411yescharacteristic
153C32×Dic3C22⋊C411yescharacteristic
154C22×C3×D4—91no—
155C2×D3×D4—31no—
156C22×D12—31no—
157C2×C3×M16—31no—
158C2×C3×M16—31no—
159C2×C3×M16—61no—
160C2×C3×M16—91no—
161C2×#208—31no—
162D3×M16—31no—
163D3×M16C3×D311yescharacteristic, complemented
164C3×#100—31no—
165C3×#100—31no—
166C3×#100—61no—
167C3×#100—91no—
168C3×#100—91no—
169C3×#100—91no—
170#833—31no—
171#823—31no—
172#823—31no—
173#823—31no—
174#823—31no—
175#823—31no—
176#823—61no—
177#823C3×D311yescharacteristic, direct product factor
178C23×C32—31no—
179C23×C32—32no—
180C22×C3⋊D3C2×C3×C412yes—
181C22×C3×D3—21no—
182C22×C3×D3—22no—
183C22×C3×D3—32no—
184C22×C3×D3—32no—
185C22×C3×D3—62no—
186C22×C3×D3—62no—
187C22×C3×D3—62no—
188C22×C3×D3—62no—
189C22×C3×D3—62no—
190C22×C3×D3—124no—
191C22×C3×D3—124no—
192C22×C3×D3C4×D311yescharacteristic
193C22×C3×D3C4×D312yes—
194C22×C3×D3C2×C3×C411yescharacteristic
195C22×C3×D3C2×C3×C412yes—
196C2×D32—22no—
197C2×D32—22no—
198C2×D32—44no—
199C32×D4—61no—
200C32×D4—61no—
201C2×C32×C4—21no—
202C2×C32×C4—21no—
203C2×C32×C4—21no—
204C2×C32×C4—31no—
205C2×C32×C4—31no—
206C2×C32×C4—31no—
207C2×C32×C4—31no—
208C2×C32×C4—31no—
209C2×C32×C4—41no—
210C2×C32×C4C22×D311yescharacteristic
211C2×C32×C4C22×D311yescharacteristic
212C2×C32×C4C23×C311yescharacteristic
213C4⋊(C3⋊D3)—21no—
214C4⋊(C3⋊D3)—21no—
215C3×#67—62no—
216C3×#67—62no—
217C2×C3×Dic3—21no—
218C2×C3×Dic3C4×D311yescharacteristic
219C2×C3×Dic3C2×C3×C411yescharacteristic
220C3×D12—21no—
221C3×D12—21no—
222C3×D12—21no—
223C3×D12—21no—
224C3×D12—41no—
225C3×D12—41no—
226C3×D12—62no—
227C3×D12—62no—
228C3×D12—61no—
229C3×D12—61no—
230C3×D12—61no—
231C3×D12—61no—
232C3×D12—121no—
233C3×D12—121no—
234C3×C4×D3—21no—
235C3×C4×D3—21no—
236C3×C4×D3—21no—
237C3×C4×D3—21no—
238C3×C4×D3D1211yescharacteristic
239C3×C4×D3D1211yescharacteristic
240C3×C4×D3#6711yescharacteristic
241C3×C4×D3#6711yescharacteristic
242C3×C4×D3C3×D411yescharacteristic
243C3×C4×D3C3×D411yescharacteristic
244C3×C4×D3C3×D411yescharacteristic
245C3×C4×D3C3×D411yescharacteristic
246#626—22no—
247#626—22no—
248C32×C8—21no—
249C32×C8—22no—
250C32×C8—21no—
251C32×C8—21no—
252C32×C8—41no—
253C32×C8—41no—
254C32×C8—42no—
255C32×C8—61no—
256C32×C8—61no—
257C3⋊(C3⋊C8)—21no—
258C3×C3⋊C8—22no—
259C3×C3⋊C8—21no—
260C3×C3⋊C8—21no—
261C3×C3⋊C8—21no—
262C3×C3⋊C8—21no—
263C3×C3⋊C8—41no—
264C3×C3⋊C8—61no—
265C3×C3⋊C8—61no—
266C3×C3⋊C8—121no—
267C2×#100—91noSylow
268C2×C33—21no—
269C2×C33C2×C22⋊C411yescharacteristic
270C3×C3⋊D3—42no—
271C32×D3—21no—
272C32×D3—42no—
273C32×D3#10012yescomplemented
274C24×C3—92no—
275C23×D3—32no—
276C23×D3—32no—
277C2×C3×D4—31no—
278C2×C3×D4—31no—
279C2×C3×D4—61no—
280C2×C3×D4—92no—
281C2×C3×D4—91no—
282C2×C3×D4—181no—
283C2×C3×D4—181no—
284C2×C3×D4—181no—
285C2×C3×D4—181no—
286C22×C3×C4—31no—
287C22×C3×C4—31no—
288C22×C3×C4—61no—
289C2×#67—32no—
290D3×D4—61no—
291D3×D4—61no—
292D3×D4—61no—
293D3×D4—61no—
294C2×D12—32no—
295C2×D12—31no—
296C2×D12—31no—
297C2×D12—61no—
298C2×D12—61no—
299C2×D12—61no—
300C2×D12—61no—
301C2×D12—61no—
302C2×D12C2×C3×D311yescharacteristic
303C2×C4×D3C2×C3×D311yescharacteristic
304C3×M16—21no—
305C3×M16—21no—
306C3×M16—21no—
307C3×M16—31no—
308C3×M16—31no—
309C3×M16—31no—
310C3×M16—31no—
311C3×M16—41no—
312C3×M16—61no—
313C3×M16—61no—
314C3×M16—61no—
315C3×M16—61no—
316C3×M16—62no—
317C3×M16—91no—
318C3×M16—181no—
319C3×M16D3211yescharacteristic, complemented
320C3×M16C2×C3×D311yescharacteristic, complemented
321C3×M16C2×C3×D311yescharacteristic, complemented
322C2×C3×C8—61no—
323C2×C3×C8—61no—
324C2×C3×C8—62no—
325C2×C3×C8—181no—
326#208—31no—
327#208—31no—
328#208—61no—
329#208—61no—
330#208C2×C3×D311yescharacteristic, complemented
331#208C2×C3×D311yescharacteristic, complemented
332C2×C3⋊C8—61no—
333ΓL(1,𝔽25)—21no—
334ΓL(1,𝔽25)—61no—
335D3×C8—21no—
336D3×C8—61no—
337C22×C32—21no—
338C22×C32—21no—
339C22×C32—21no—
340C22×C32—31no—
341C22×C32—31no—
342C22×C32—41no—
343C22×C32—62no—
344C22×C32—62no—
345C22×C32—122no—
346C22×C32C2×C4×D311yescharacteristic
347C22×C32C2×C4×D311yescharacteristic
348C22×C32C22×C3×C411yescharacteristic
349C2×C3⋊D3—22no—
350C2×C3⋊D3—42no—
351C2×C3×D3—22no—
352C2×C3×D3—22no—
353C2×C3×D3—22no—
354C2×C3×D3—22no—
355C2×C3×D3—21no—
356C2×C3×D3—21no—
357C2×C3×D3—42no—
358C2×C3×D3—42no—
359C2×C3×D3—42no—
360C2×C3×D3—42no—
361C2×C3×D3—62no—
362C2×C3×D3—62no—
363C2×C3×D3—82no—
364C2×C3×D3—122no—
365C2×C3×D3—124no—
366C2×C3×D3—124no—
367C2×C3×D3—124no—
368C2×C3×D3—124no—
369C2×C3×D3—122no—
370C2×C3×D3—122no—
371C2×C3×D3—242no—
372C2×C3×D3(C2×D3)⋊C411yescharacteristic
373C2×C3×D3(C2×D3)⋊C411yescharacteristic
374C2×C3×D3C3×C22⋊C411yescharacteristic
375C2×C3×D3C3×C22⋊C411yescharacteristic
376D32—44no—
377D32—44no—
378C32×C4—21no—
379C32×C4—21no—
380C32×C4—21no—
381C32×C4—21no—
382C32×C4—21no—
383C32×C4—21no—
384C32×C4—31no—
385C32×C4—31no—
386C32×C4—41no—
387C32×C4—41no—
388C32×C4C2×D1211yescharacteristic
389C32×C4D3×D411yescharacteristic
390C32×C4D3×D411yescharacteristic
391C32×C4C2×#6711yescharacteristic
392C32×C4C2×C3×D411yescharacteristic
393C32×C4C2×C3×D411yescharacteristic
394C3×Dic3—21no—
395C3×Dic3—21no—
396C3×Dic3(C2×D3)⋊C411yescharacteristic
397C3×Dic3(C2×D3)⋊C411yescharacteristic
398C3×Dic3C3×C22⋊C411yescharacteristic
399C3×Dic3C3×C22⋊C411yescharacteristic
400C22×D4—91no—
401C2×M16—31no—
402C2×M16—91no—
403#100—31no—
404#100—91no—
405#100—91no—
406#100—91no—
407C33C2×#10011yescharacteristic, complemented, Sylow
408C23×C3—31no—
409C23×C3—31no—
410C23×C3—32no—
411C23×C3—32no—
412C23×C3—61no—
413C23×C3—62no—
414C23×C3—92no—
415C23×C3—182no—
416C23×C3—182no—
417C23×C3—364no—
418C22×D3—32no—
419C22×D3—32no—
420C22×D3—62no—
421C22×D3—62no—
422C22×D3—62no—
423C22×D3—62no—
424C22×D3—62no—
425C22×D3—124no—
426C22×D3—124no—
427C22×D3C3×C4×D311yescharacteristic
428C22×D3C3×C4×D312yes—
429C3×D4—61no—
430C3×D4—61no—
431C3×D4—61no—
432C3×D4—61no—
433C3×D4—121no—
434C3×D4—121no—
435C3×D4—182no—
436C3×D4—182no—
437C3×D4—181no—
438C3×D4—181no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—31no—
443C2×C3×C4—31no—
444C2×C3×C4—31no—
445C2×C3×C4—31no—
446C2×C3×C4—31no—
447C2×C3×C4—31no—
448C2×C3×C4—31no—
449C2×C3×C4—31no—
450C2×C3×C4—31no—
451C2×C3×C4—31no—
452C2×C3×C4—41no—
453C2×C3×C4—61no—
454C2×C3×C4—61no—
455C2×C3×C4—61no—
456C2×C3×C4—61no—
457C2×C3×C4—61no—
458C2×C3×C4C2×D3211yescharacteristic
459C2×C3×C4C22×C3×D311yescharacteristic
460C2×C3×C4C22×C3×D311yescharacteristic
461#67—62no—
462#67—62no—
463C2×Dic3C3×C4×D311yescharacteristic
464D12—21no—
465D12—21no—
466D12—62no—
467D12—62no—
468D12—61no—
469D12—61no—
470D12—61no—
471D12—61no—
472D12—121no—
473D12—121no—
474C4×D3C3×D1211yescharacteristic
475C4×D3C3×D1211yescharacteristic
476C4×D3C3×#6711yescharacteristic
477C4×D3C3×#6711yescharacteristic
478C3×C8—22no—
479C3×C8—21no—
480C3×C8—21no—
481C3×C8—21no—
482C3×C8—41no—
483C3×C8—41no—
484C3×C8—42no—
485C3×C8—62no—
486C3×C8—61no—
487C3×C8—61no—
488C3×C8—61no—
489C3×C8—61no—
490C3×C8—121no—
491C3×C8—181no—
492C3⋊C8—21no—
493C3⋊C8—21no—
494C3⋊C8—61no—
495C3⋊C8—61no—
496C3⋊C8—121no—
497C2×C32—21no—
498C2×C32—21no—
499C2×C32—21no—
500C2×C32—21no—
501C2×C32—21no—
502C2×C32—21no—
503C2×C32—32no—
504C2×C32—41no—
505C2×C32—41no—
506C2×C32—41no—
507C2×C32—41no—
508C2×C32—61no—
509C2×C32—81no—
510C2×C32—122no—
511C2×C32D3×C22⋊C411yescharacteristic
512C2×C32C2×(C2×D3)⋊C411yescharacteristic
513C2×C32C2×C3×C22⋊C411yescharacteristic
514C3⋊D3—42no—
515C3×D3—21no—
516C3×D3—21no—
517C3×D3—22no—
518C3×D3—41no—
519C3×D3—42no—
520C3×D3—42no—
521C3×D3—82no—
522C3×D3—122no—
523C3×D3—122no—
524C3×D3—242no—
525C3×D3#82312yesdirect product factor
526C3×D3C3×#10012yescomplemented
527C24—92no—
528C2×D4—31no—
529C2×D4—92no—
530C2×D4—91no—
531C2×D4—181no—
532C2×D4—181no—
533C2×D4—181no—
534C2×D4—181no—
535C22×C4—31no—
536M16—31no—
537M16—31no—
538M16—61no—
539M16—91no—
540M16—181no—
541M16C3×D3211yescharacteristic, complemented
542C2×C8—61no—
543C2×C8—181no—
544C22×C3—21no—
545C22×C3—21no—
546C22×C3—21no—
547C22×C3—31no—
548C22×C3—31no—
549C22×C3—31no—
550C22×C3—31no—
551C22×C3—41no—
552C22×C3—61no—
553C22×C3—61no—
554C22×C3—62no—
555C22×C3—62no—
556C22×C3—62no—
557C22×C3—62no—
558C22×C3—122no—
559C22×C3—122no—
560C22×C3—122no—
561C22×C3—122no—
562C22×C3—182no—
563C22×C3—242no—
564C22×C3—362no—
565C22×C3—364no—
566C22×C3—364no—
567C22×C3C4×D3211yescharacteristic
568C22×C3C2×C3×C4×D311yescharacteristic
569C22×C3C2×C3×C4×D311yescharacteristic
570C2×D3—22no—
571C2×D3—22no—
572C2×D3—42no—
573C2×D3—62no—
574C2×D3—62no—
575C2×D3—122no—
576C2×D3—124no—
577C2×D3—124no—
578C2×D3—124no—
579C2×D3—124no—
580C2×D3—122no—
581C2×D3—122no—
582C2×D3—242no—
583C2×D3C3×(C2×D3)⋊C411yescharacteristic
584C2×D3C3×(C2×D3)⋊C411yescharacteristic
585C3×C4—21no—
586C3×C4—21no—
587C3×C4—21no—
588C3×C4—21no—
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—31no—
592C3×C4—31no—
593C3×C4—31no—
594C3×C4—31no—
595C3×C4—41no—
596C3×C4—41no—
597C3×C4—61no—
598C3×C4—61no—
599C3×C4D3×D1211yescharacteristic
600C3×C4D3×#6711yescharacteristic
601C3×C4C2×C3×D1211yescharacteristic
602C3×C4C3×D3×D411yescharacteristic
603C3×C4C3×D3×D411yescharacteristic
604C3×C4C2×C3×#6711yescharacteristic
605Dic3C3×(C2×D3)⋊C411yescharacteristic
606Dic3C3×(C2×D3)⋊C411yescharacteristic
607C32—21no—
608C32—21no—
609C32—21no—
610C32—41no—
611C32D3×#10011yescharacteristic, complemented
612C32C2×#82311yescharacteristic, complemented
613C32C2×C3×#10011yescharacteristic, complemented
614C23—31no—
615C23—32no—
616C23—92no—
617C23—182no—
618C23—182no—
619C23—364no—
620D4—61no—
621D4—61no—
622D4—182no—
623D4—182no—
624D4—181no—
625D4—181no—
626C2×C4—31no—
627C2×C4—31no—
628C2×C4—31no—
629C2×C4—31no—
630C2×C4—31no—
631C2×C4C2×C3×D3211yescharacteristic
632C8—21no—
633C8—61no—
634C8—61no—
635C8—181no—
636C2×C3—21no—
637C2×C3—21no—
638C2×C3—21no—
639C2×C3—21no—
640C2×C3—21no—
641C2×C3—21no—
642C2×C3—32no—
643C2×C3—32no—
644C2×C3—41no—
645C2×C3—41no—
646C2×C3—41no—
647C2×C3—41no—
648C2×C3—62no—
649C2×C3—61no—
650C2×C3—61no—
651C2×C3—81no—
652C2×C3—121no—
653C2×C3—122no—
654C2×C3—122no—
655C2×C3—242no—
656C2×C3—362no—
657C2×C3D3×(C2×D3)⋊C411yescharacteristic
658C2×C3C3×D3×C22⋊C411yescharacteristic
659C2×C3C2×C3×(C2×D3)⋊C411yescharacteristic
660D3—21no—
661D3—42no—
662D3—122no—
663D3—122no—
664D3—242no—
665D3C3×#82312yesdirect product factor
666C22—31no—
667C22—31no—
668C22—62no—
669C22—62no—
670C22—122no—
671C22—182no—
672C22—362no—
673C22—364no—
674C22—364no—
675C22C3×C4×D3211yescharacteristic
676C4—31no—
677C4—31no—
678C4C3×D3×D1211yescharacteristic
679C4C3×D3×#6711yescharacteristic
680C3—21no—
681C3—21no—
682C3—21no—
683C3—41no—
684C3D3×#82311yescharacteristic, direct product factor
685C3C3×D3×#10011yescharacteristic, complemented
686C3C2×C3×#82311yescharacteristic, complemented
687C2—21no—
688C2—32no—
689C2—61no—
690C2—122no—
691C2—362no—
692C2C3×D3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC2×C3D3×(C2×D3)⋊C4
commutatorC22×C32C22×C3×C4
FrattiniC2×C4C2×C3×D32
FittingC33×M16C22
socleC2×C33C2×C22⋊C4
prime radicalC2×C3×D3×D12C2
cosocleC2×C32×C4C23×C3
hypercenterC3×M16D32
hypocenterC32C2×C3×#100
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×M16

Complements

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

NH ≅ G/Ntype
2. C32×D3×M16C2semidirect
3. C3×D3×#208C2semidirect
4. C3×#63650C2semidirect
5. C32×#823C2semidirect
6. C3×#63559C2semidirect
7. C3×#63558C2semidirect
10. D3×#823C3direct (N × H)
20. C33×M16C22semidirect
21. C3×#3748C22semidirect
22. C32×#208C22semidirect
23. C32×#208C22semidirect
35. C3×D3×M16D3semidirect
36. C3×D3×M16C2×C3semidirect
37. D3×#208C2×C3semidirect
39. #63650C2×C3semidirect
48. C3×#823D3direct (N × H)
49. C3×#823C2×C3semidirect
50. #63559C2×C3semidirect
51. #63558C2×C3semidirect
114. C32×M16C2×D3semidirect
115. C32×M16C2×D3semidirect
116. C32×M16C22×C3semidirect
118. #3748C22×C3semidirect
125. C3×#208C2×D3semidirect
126. C3×#208C2×D3semidirect
127. C3×#208C22×C3semidirect
128. C3×#208C22×C3semidirect
163. D3×M16C3×D3semidirect
177. #823C3×D3direct (N × H)
273. C32×D3#100semidirect
319. C3×M16D32semidirect
320. C3×M16C2×C3×D3semidirect
321. C3×M16C2×C3×D3semidirect
330. #208C2×C3×D3semidirect
331. #208C2×C3×D3semidirect
407. C33C2×#100semidirect
525. C3×D3#823direct (N × H)
526. C3×D3C3×#100semidirect
541. M16C3×D32semidirect
611. C32D3×#100semidirect
612. C32C2×#823semidirect
613. C32C2×C3×#100semidirect
665. D3C3×#823direct (N × H)
684. C3D3×#823direct (N × H)
685. C3C3×D3×#100semidirect
686. C3C2×C3×#823semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×D122
C32×D3×M162
C3×D3×#2082
C3×#636502
C32×#8232
C3×#635592
C3×#635582
C2×C3×#8233
C3×D3×#1003
D3×#8233