Finite Group Databasebeta

← C2×C3×#63830 #13174428

Subgroups — C2×C3×#63830 #13174428

Order 1728.

1714 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×#3828C211yesmaximal, characteristic, complemented
2C22×C32×D12C211yesmaximal, characteristic, complemented
3C2×C32×#208C211yesmaximal, characteristic, complemented
4C3×#63830C218yesmaximal, direct product factor
5C2×C3×#3716C212yesmaximal, complemented
6C2×C3×#3714C212yesmaximal, complemented
7C2×C3×#932—31nomaximal
8C2×C3×#908—31nomaximal
9C2×#63830C311yesmaximal, characteristic, direct product factor
10C23×C32×D3—21no—
11C22×C33×C4C2211yescharacteristic
12C2×C3×#638—21no—
13C3×#3828—22no—
14C3×#3828C2214yescomplemented
15C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
16C2×C3×C4×C3⋊D3—21no—
17C2×C3×#634C2211yescharacteristic, complemented
18C2×C32×D12—22no—
19C2×C32×D12—21no—
20C2×C32×D12C2212yes—
21C2×C32×D12C2214yescomplemented
22C32×#208C2214yescomplemented
23C2×C32×C3⋊C8C2212yescomplemented
24C3×#3716C2218yescomplemented
25C3×#3714C2218yescomplemented
26C22×C32×D4—31no—
27C2×#3828C2×C311yescharacteristic, complemented
28C2×C3×#235—31no—
29C2×C3×#235—31no—
30C2×C3×#235—61no—
31C22×C3×D12—21no—
32C22×C3×D12D311yescharacteristic, complemented
33C22×C3×D12C2×C311yescharacteristic, complemented
34C2×C32×M16—31no—
35C2×C3×#214—32no—
36C3×#932—38no—
37C2×C3×#213—32no—
38C2×C3×#208—21no—
39C2×C3×#208D311yescharacteristic, complemented
40C2×C3×#208C2×C311yescharacteristic, complemented
41C3×#908—38no—
42C2×C3×D24—32no—
43C2×C3×#204—32no—
44#63830C2×C318yesdirect product factor
45C2×#3716C2×C312yescomplemented
46C2×#3714C2×C312yescomplemented
47C23×C33D411yescharacteristic
48C22×C3×C3⋊D3—21no—
49C22×C32×D3—22no—
50C22×C32×D3—24no—
51C22×C32×D3—44no—
52C2×C33×C4D411yescharacteristic
53C2×C33×C4D412yes—
54C2×C33×C4C2311yescharacteristic
55C2×C33×C4C2312yes—
56C3×#638—24no—
57C2×C3×C3⋊Dic3—21no—
58C3×C4⋊(C3⋊D3)—21no—
59C3×C4⋊(C3⋊D3)C2312yescomplemented
60C3×C4×C3⋊D3—24no—
61C3×#634—21no—
62C3×#634C2312yescomplemented
63C32×D12—22no—
64C32×D12—24no—
65C32×D12C2314yes—
66C32×C3⋊C8C2314yescomplemented
67C2×C3×AGL(1,ℤ/8)—91no—
68C2×#932—31no—
69C2×#908—31no—
70C24×C32—61no—
71C23×C3×D3—22no—
72C23×C3×D3—21no—
73C23×C3×D3—21no—
74C2×C32×D4—32no—
75C2×C32×D4—34no—
76C2×C32×D4—61no—
77C2×C32×D4—62no—
78C22×C32×C4—21no—
79C22×C32×C4—21no—
80C22×C32×C4—21no—
81C22×C32×C4—41no—
82C22×C32×C4C2×D311yescharacteristic
83C22×C32×C4C2×D311yescharacteristic
84C22×C32×C4C22×C311yescharacteristic
85C2×#638—21no—
86#3828—22no—
87#3828C22×C314yescomplemented
88C2×C4⋊(C3⋊D3)C22×C311yescharacteristic, complemented
89C2×C4×C3⋊D3—21no—
90C2×#634C22×C311yescharacteristic, complemented
91C2×C3×#67—62no—
92C2×C3×#67—61no—
93C2×C3×#67—61no—
94C3×#235—34no—
95C3×#235—34no—
96C3×#235—64no—
97C3×#235—64no—
98C3×#235—62no—
99C3×#235—62no—
100C2×C3×D12—24no—
101C2×C3×D12—22no—
102C2×C3×D12—22no—
103C2×C3×D12—24no—
104C2×C3×D12—22no—
105C2×C3×D12—21no—
106C2×C3×D12—22no—
107C2×C3×D12—21no—
108C2×C3×D12—31no—
109C2×C3×D12—31no—
110C2×C3×D12—61no—
111C2×C3×D12C2×D312yes—
112C2×C3×D12C2×D314yescomplemented
113C2×C3×D12C22×C312yes—
114C2×C3×D12C22×C314yescomplemented
115C2×C3×C4×D3—62no—
116C2×C3×C4×D3—61no—
117C2×C3×C4×D3—61no—
118C2×C3×Dic6—31no—
119C2×C3×Dic6—31no—
120C2×C3×Dic6—61no—
121C32×M16—34no—
122C2×C32×C8—32no—
123C3×#214—38no—
124C3×#213—38no—
125C3×#208—24no—
126C3×#208C2×D314yescomplemented
127C3×#208C22×C314yescomplemented
128C2×C3×C3⋊C8—22no—
129C2×C3×C3⋊C8C2×D312yescomplemented
130C2×C3×C3⋊C8C22×C312yescomplemented
131C3×D24—38no—
132C3×#204—38no—
133#3716C22×C318yescomplemented
134#3714C22×C318yescomplemented
135C22×C33—22no—
136C22×C33C2×D412yes—
137C22×C33C2×D411yescharacteristic
138C2×C3×C3⋊D3—22no—
139C2×C3×C3⋊D3—42no—
140C2×C32×D3—24no—
141C2×C32×D3—48no—
142C2×C32×D3—44no—
143C33×C4C2×D411yescharacteristic
144C33×C4C2×D412yes—
145C33×C4C2411yescharacteristic
146C3×C3⋊Dic3—22no—
147C2×C3×#41—91no—
148C22×C3×D4—31no—
149C22×C3×D4—31no—
150C22×C3×D4—61no—
151C2×#235—31no—
152C2×#235—31no—
153C2×#235—61no—
154C22×D12C3×D311yescharacteristic, complemented
155C3×AGL(1,ℤ/8)—98no—
156C2×C3×SD16—92no—
157C2×C3×D8—92no—
158C2×C3×M16—31no—
159C2×C3×M16—31no—
160C2×C3×M16—61no—
161C2×#214—32no—
162#932—38no—
163C2×#213—32no—
164C2×#208C3×D311yescharacteristic, complemented
165#908—38no—
166C2×D24—32no—
167C2×#204—32no—
168C23×C32—21no—
169C23×C32—21no—
170C23×C32—21no—
171C23×C32—41no—
172C23×C32—64no—
173C23×C32—62no—
174C23×C32—124no—
175C23×C32D1211yescharacteristic
176C23×C32#6711yescharacteristic
177C23×C32C3×D411yescharacteristic
178C22×C3⋊D3—21no—
179C22×C3×D3—24no—
180C22×C3×D3—28no—
181C22×C3×D3—22no—
182C22×C3×D3—24no—
183C22×C3×D3—22no—
184C22×C3×D3—24no—
185C22×C3×D3—48no—
186C22×C3×D3—44no—
187C22×C3×D3—44no—
188C22×C3×D3—62no—
189C22×C3×D3—61no—
190C22×C3×D3—61no—
191C32×D4—34no—
192C32×D4—62no—
193C32×D4—64no—
194C2×C32×C4—21no—
195C2×C32×C4—22no—
196C2×C32×C4—21no—
197C2×C32×C4—22no—
198C2×C32×C4—21no—
199C2×C32×C4—22no—
200C2×C32×C4—21no—
201C2×C32×C4—22no—
202C2×C32×C4—21no—
203C2×C32×C4—22no—
204C2×C32×C4—21no—
205C2×C32×C4—22no—
206C2×C32×C4—41no—
207C2×C32×C4—42no—
208C2×C32×C4—41no—
209C2×C32×C4—42no—
210C2×C32×C4D1211yescharacteristic
211C2×C32×C4D1212yes—
212C2×C32×C4#6711yescharacteristic
213C2×C32×C4#6712yes—
214C2×C32×C4C3×D411yescharacteristic
215C2×C32×C4C3×D412yes—
216C2×C32×C4C22×D311yescharacteristic
217C2×C32×C4C22×D312yes—
218C2×C32×C4C22×D311yescharacteristic
219C2×C32×C4C22×D312yes—
220C2×C32×C4C23×C311yescharacteristic
221C2×C32×C4C23×C312yes—
222#638—24no—
223C2×C3⋊Dic3—21no—
224C4⋊(C3⋊D3)—21no—
225C4⋊(C3⋊D3)C23×C312yescomplemented
226C4×C3⋊D3—24no—
227#634—21no—
228#634C23×C312yescomplemented
229C3×#67—68no—
230C3×#67—64no—
231C3×#67—64no—
232C2×C3×Dic3—62no—
233C2×C3×Dic3—61no—
234C2×C3×Dic3—61no—
235C3×D12—24no—
236C3×D12—28no—
237C3×D12—22no—
238C3×D12—24no—
239C3×D12—22no—
240C3×D12—24no—
241C3×D12—24no—
242C3×D12—32no—
243C3×D12—32no—
244C3×D12—62no—
245C3×D12—62no—
246C3×D12—61no—
247C3×D12—61no—
248C3×D12C22×D314yes—
249C3×D12C23×C314yes—
250C3×C4×D3—68no—
251C3×C4×D3—64no—
252C3×C4×D3—64no—
253C3×Dic6—32no—
254C3×Dic6—32no—
255C3×Dic6—62no—
256C3×Dic6—62no—
257C3×Dic6—61no—
258C3×Dic6—61no—
259C32×C8—34no—
260C3×C3⋊C8—24no—
261C3×C3⋊C8C22×D314yescomplemented
262C3×C3⋊C8C23×C314yescomplemented
263C2×AGL(1,ℤ/8)—91noSylow
264C2×C33—22no—
265C2×C33AGL(1,ℤ/8)12yescomplemented
266C2×C33C22×D411yescharacteristic
267C3×C3⋊D3—42no—
268C32×D3—44no—
269C24×C3—62no—
270C24×C3—61no—
271C24×C3—61no—
272C23×D3—21no—
273C3×#41—94no—
274C3×#41—182no—
275C2×C3×Q8—91no—
276C2×C3×D4—32no—
277C2×C3×D4—34no—
278C2×C3×D4—32no—
279C2×C3×D4—34no—
280C2×C3×D4—62no—
281C2×C3×D4—64no—
282C2×C3×D4—62no—
283C2×C3×D4—64no—
284C2×C3×D4—62no—
285C2×C3×D4—61no—
286C2×C3×D4—61no—
287C2×C3×D4—62no—
288C2×C3×D4—91no—
289C2×C3×D4—181no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—41no—
294C22×C3×C4—181no—
295C22×C3×C4D3211yescharacteristic
296C22×C3×C4C2×C3×D311yescharacteristic
297C22×C3×C4C2×C3×D311yescharacteristic
298C2×#67—62no—
299C2×#67—61no—
300C2×#67—61no—
301#235—34no—
302#235—34no—
303#235—64no—
304#235—64no—
305#235—62no—
306#235—62no—
307C2×D12—22no—
308C2×D12—21no—
309C2×D12—31no—
310C2×D12—31no—
311C2×D12—61no—
312C2×D12C2×C3×D312yes—
313C2×D12C2×C3×D314yescomplemented
314C2×C4×D3—62no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×Dic6—31no—
318C2×Dic6—31no—
319C2×Dic6—61no—
320C3×SD16—98no—
321C3×D8—98no—
322C3×M16—34no—
323C3×M16—34no—
324C3×M16—64no—
325C2×C3×C8—32no—
326C2×C3×C8—32no—
327C2×C3×C8—62no—
328#214—38no—
329#213—38no—
330#208C2×C3×D314yescomplemented
331C2×C3⋊C8C2×C3×D312yescomplemented
332D24—38no—
333#204—38no—
334C22×C32—22no—
335C22×C32—24no—
336C22×C32—22no—
337C22×C32—22no—
338C22×C32—22no—
339C22×C32—21no—
340C22×C32—21no—
341C22×C32—22no—
342C22×C32—22no—
343C22×C32—21no—
344C22×C32—41no—
345C22×C32—42no—
346C22×C32—42no—
347C22×C32—42no—
348C22×C32—44no—
349C22×C32—64no—
350C22×C32—128no—
351C22×C32—124no—
352C22×C32C2×D1212yes—
353C22×C32C2×D1211yescharacteristic
354C22×C32C2×#6712yes—
355C22×C32C2×#6711yescharacteristic
356C22×C32C2×C3×D412yes—
357C22×C32C2×C3×D411yescharacteristic
358C2×C3⋊D3—22no—
359C2×C3⋊D3—42no—
360C2×C3×D3—28no—
361C2×C3×D3—24no—
362C2×C3×D3—24no—
363C2×C3×D3—416no—
364C2×C3×D3—48no—
365C2×C3×D3—48no—
366C2×C3×D3—48no—
367C2×C3×D3—44no—
368C2×C3×D3—44no—
369C2×C3×D3—64no—
370C2×C3×D3—62no—
371C2×C3×D3—62no—
372C2×C3×D3—124no—
373C2×C3×D3—122no—
374C2×C3×D3—122no—
375C32×C4—21no—
376C32×C4—21no—
377C32×C4—21no—
378C32×C4—21no—
379C32×C4—22no—
380C32×C4—21no—
381C32×C4—22no—
382C32×C4—21no—
383C32×C4—22no—
384C32×C4—41no—
385C32×C4—42no—
386C32×C4—41no—
387C32×C4C2×D1211yescharacteristic
388C32×C4C2×D1212yes—
389C32×C4C2×#6711yescharacteristic
390C32×C4C2×#6712yes—
391C32×C4C2×C3×D411yescharacteristic
392C32×C4C2×C3×D412yes—
393C32×C4C23×D311yescharacteristic
394C32×C4C23×D311yescharacteristic
395C32×C4C24×C311yescharacteristic
396C3⋊Dic3—22no—
397C3×Dic3—64no—
398C3×Dic3—62no—
399C3×Dic3—62no—
400C2×#41—91no—
401C22×D4—31no—
402AGL(1,ℤ/8)—98no—
403C2×SD16—92no—
404C2×D8—92no—
405C2×M16—31no—
406C33C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—41no—
411C23×C3—68no—
412C23×C3—64no—
413C23×C3—64no—
414C23×C3—62no—
415C23×C3—64no—
416C23×C3—62no—
417C23×C3—128no—
418C23×C3—124no—
419C23×C3—124no—
420C23×C3—181no—
421C23×C3#62611yescharacteristic
422C23×C3C3×D1211yescharacteristic
423C23×C3C3×#6711yescharacteristic
424C22×D3—22no—
425C22×D3—24no—
426C22×D3—44no—
427C22×D3—62no—
428C22×D3—61no—
429C22×D3—61no—
430C3×Q8—92no—
431C3×Q8—181no—
432C3×D4—34no—
433C3×D4—34no—
434C3×D4—64no—
435C3×D4—68no—
436C3×D4—64no—
437C3×D4—64no—
438C3×D4—62no—
439C3×D4—62no—
440C3×D4—64no—
441C3×D4—92no—
442C3×D4—184no—
443C3×D4—181no—
444C2×C3×C4—21no—
445C2×C3×C4—22no—
446C2×C3×C4—21no—
447C2×C3×C4—22no—
448C2×C3×C4—21no—
449C2×C3×C4—22no—
450C2×C3×C4—21no—
451C2×C3×C4—22no—
452C2×C3×C4—21no—
453C2×C3×C4—22no—
454C2×C3×C4—21no—
455C2×C3×C4—22no—
456C2×C3×C4—41no—
457C2×C3×C4—42no—
458C2×C3×C4—41no—
459C2×C3×C4—42no—
460C2×C3×C4—181no—
461C2×C3×C4—184no—
462C2×C3×C4#62612yes—
463C2×C3×C4#62611yescharacteristic
464C2×C3×C4C3×D1211yescharacteristic
465C2×C3×C4C3×D1212yes—
466C2×C3×C4C3×#6711yescharacteristic
467C2×C3×C4C3×#6712yes—
468C2×C3×C4C2×D3212yes—
469C2×C3×C4C2×D3211yescharacteristic
470C2×C3×C4C22×C3×D311yescharacteristic
471C2×C3×C4C22×C3×D312yes—
472C2×C3×C4C22×C3×D311yescharacteristic
473C2×C3×C4C22×C3×D312yes—
474#67—68no—
475#67—64no—
476#67—64no—
477C2×Dic3—62no—
478C2×Dic3—61no—
479C2×Dic3—61no—
480D12—22no—
481D12—24no—
482D12—32no—
483D12—32no—
484D12—62no—
485D12—62no—
486D12—61no—
487D12—61no—
488D12C22×C3×D314yes—
489C4×D3—68no—
490C4×D3—64no—
491C4×D3—64no—
492Dic6—32no—
493Dic6—32no—
494Dic6—62no—
495Dic6—62no—
496Dic6—61no—
497Dic6—61no—
498C3×C8—34no—
499C3×C8—34no—
500C3×C8—64no—
501C3⋊C8C22×C3×D314yescomplemented
502C2×C32—22no—
503C2×C32—24no—
504C2×C32—22no—
505C2×C32—22no—
506C2×C32—22no—
507C2×C32—22no—
508C2×C32—21no—
509C2×C32—22no—
510C2×C32—21no—
511C2×C32—21no—
512C2×C32—42no—
513C2×C32—41no—
514C2×C32—42no—
515C2×C32—42no—
516C2×C32—44no—
517C2×C32—124no—
518C2×C32#90812yescomplemented
519C2×C32#93212yescomplemented
520C2×C32C3×AGL(1,ℤ/8)12yescomplemented
521C2×C32C22×D1211yescharacteristic
522C2×C32C22×#6711yescharacteristic
523C2×C32C22×C3×D411yescharacteristic
524C3⋊D3—42no—
525C3×D3—48no—
526C3×D3—44no—
527C3×D3—44no—
528C3×D3—124no—
529C3×D3—122no—
530C3×D3—122no—
531C24—61no—
532#41—94no—
533#41—182no—
534C2×Q8—91no—
535C2×D4—32no—
536C2×D4—34no—
537C2×D4—61no—
538C2×D4—62no—
539C2×D4—91no—
540C2×D4—181no—
541C22×C4—181no—
542C22×C4C3×D3211yescharacteristic
543SD16—98no—
544D8—98no—
545M16—34no—
546C2×C8—32no—
547C22×C3—24no—
548C22×C3—22no—
549C22×C3—22no—
550C22×C3—22no—
551C22×C3—21no—
552C22×C3—22no—
553C22×C3—21no—
554C22×C3—21no—
555C22×C3—22no—
556C22×C3—22no—
557C22×C3—42no—
558C22×C3—42no—
559C22×C3—44no—
560C22×C3—42no—
561C22×C3—41no—
562C22×C3—68no—
563C22×C3—64no—
564C22×C3—64no—
565C22×C3—1216no—
566C22×C3—128no—
567C22×C3—128no—
568C22×C3—128no—
569C22×C3—124no—
570C22×C3—124no—
571C22×C3—182no—
572C22×C3—362no—
573C22×C3C2×#62612yes—
574C22×C3C2×#62611yescharacteristic
575C22×C3C2×C3×D1212yes—
576C22×C3C2×C3×D1211yescharacteristic
577C22×C3C2×C3×#6712yes—
578C22×C3C2×C3×#6711yescharacteristic
579C2×D3—24no—
580C2×D3—48no—
581C2×D3—44no—
582C2×D3—64no—
583C2×D3—62no—
584C2×D3—62no—
585C2×D3—124no—
586C2×D3—122no—
587C2×D3—122no—
588C3×C4—21no—
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—21no—
592C3×C4—22no—
593C3×C4—22no—
594C3×C4—21no—
595C3×C4—22no—
596C3×C4—21no—
597C3×C4—41no—
598C3×C4—42no—
599C3×C4—41no—
600C3×C4—182no—
601C3×C4C2×#62612yes—
602C3×C4C2×#62611yescharacteristic
603C3×C4C2×C3×D1211yescharacteristic
604C3×C4C2×C3×D1212yes—
605C3×C4C2×C3×#6711yescharacteristic
606C3×C4C2×C3×#6712yes—
607C3×C4C22×D3211yescharacteristic
608C3×C4C23×C3×D311yescharacteristic
609C3×C4C23×C3×D311yescharacteristic
610Dic3—64no—
611Dic3—62no—
612Dic3—62no—
613C32—21no—
614C32—21no—
615C32—21no—
616C32—41no—
617C32C2×#90811yescharacteristic, complemented
618C32C2×#93211yescharacteristic, complemented
619C32C2×C3×AGL(1,ℤ/8)11yescharacteristic, complemented
620C23—64no—
621C23—62no—
622C23—124no—
623C23—181no—
624C23C3×#62611yescharacteristic
625Q8—92no—
626Q8—181no—
627D4—34no—
628D4—64no—
629D4—62no—
630D4—92no—
631D4—184no—
632D4—181no—
633C2×C4—181no—
634C2×C4—184no—
635C2×C4C3×#62611yescharacteristic
636C2×C4C3×#62612yes—
637C2×C4C2×C3×D3211yescharacteristic
638C2×C4C2×C3×D3212yes—
639C8—34no—
640C2×C3—24no—
641C2×C3—22no—
642C2×C3—22no—
643C2×C3—22no—
644C2×C3—21no—
645C2×C3—21no—
646C2×C3—21no—
647C2×C3—22no—
648C2×C3—22no—
649C2×C3—22no—
650C2×C3—42no—
651C2×C3—42no—
652C2×C3—44no—
653C2×C3—41no—
654C2×C3—42no—
655C2×C3—128no—
656C2×C3—124no—
657C2×C3—124no—
658C2×C3—362no—
659C2×C3#6383012yesdirect product factor
660C2×C3C3×#90812yescomplemented
661C2×C3C3×#93212yescomplemented
662C2×C3C22×#62611yescharacteristic
663C2×C3C22×C3×D1211yescharacteristic
664C2×C3C22×C3×#6711yescharacteristic
665D3—44no—
666D3—124no—
667D3—122no—
668D3—122no—
669C22—22no—
670C22—64no—
671C22—128no—
672C22—124no—
673C22—182no—
674C22—362no—
675C22C2×C3×#62612yes—
676C22C2×C3×#62611yescharacteristic
677C4—182no—
678C4C2×C3×#62612yes—
679C4C2×C3×#62611yescharacteristic
680C4C22×C3×D3211yescharacteristic
681C3—21no—
682C3—21no—
683C3—21no—
684C3—41no—
685C3C2×#6383011yescharacteristic, direct product factor
686C3C2×C3×#90811yescharacteristic, complemented
687C3C2×C3×#93211yescharacteristic, complemented
688C2—22no—
689C2—124no—
690C2—362no—
691C2C3×#6383012yesdirect product factor
692C2C22×C3×#62611yescharacteristic
subgroupG/H
centerC22×C3C2×#626
commutator, cosocleC32×C4C24×C3
FrattiniC4C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C2×D4
hypercenterC22×C3×C4D32
hypocenterC32C2×C3×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×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×#3828C2semidirect
2. C22×C32×D12C2semidirect
3. C2×C32×#208C2semidirect
4. C3×#63830C2direct (N × H)
5. C2×C3×#3716C2semidirect
6. C2×C3×#3714C2semidirect
9. C2×#63830C3direct (N × H)
14. C3×#3828C22semidirect
15. C2×C3×C4⋊(C3⋊D3)C22semidirect
17. C2×C3×#634C22semidirect
21. C2×C32×D12C22semidirect
22. C32×#208C22semidirect
23. C2×C32×C3⋊C8C22semidirect
24. C3×#3716C22semidirect
25. C3×#3714C22semidirect
27. C2×#3828C2×C3semidirect
32. C22×C3×D12D3semidirect
33. C22×C3×D12C2×C3semidirect
39. C2×C3×#208D3semidirect
40. C2×C3×#208C2×C3semidirect
44. #63830C2×C3direct (N × H)
45. C2×#3716C2×C3semidirect
46. C2×#3714C2×C3semidirect
59. C3×C4⋊(C3⋊D3)C23semidirect
62. C3×#634C23semidirect
66. C32×C3⋊C8C23semidirect
87. #3828C22×C3semidirect
88. C2×C4⋊(C3⋊D3)C22×C3semidirect
90. C2×#634C22×C3semidirect
112. C2×C3×D12C2×D3semidirect
114. C2×C3×D12C22×C3semidirect
126. C3×#208C2×D3semidirect
127. C3×#208C22×C3semidirect
129. C2×C3×C3⋊C8C2×D3semidirect
130. C2×C3×C3⋊C8C22×C3semidirect
133. #3716C22×C3semidirect
134. #3714C22×C3semidirect
154. C22×D12C3×D3semidirect
164. C2×#208C3×D3semidirect
225. C4⋊(C3⋊D3)C23×C3semidirect
228. #634C23×C3semidirect
261. C3×C3⋊C8C22×D3semidirect
262. C3×C3⋊C8C23×C3semidirect
265. C2×C33AGL(1,ℤ/8)semidirect
313. C2×D12C2×C3×D3semidirect
330. #208C2×C3×D3semidirect
331. C2×C3⋊C8C2×C3×D3semidirect
406. C33C2×AGL(1,ℤ/8)semidirect
501. C3⋊C8C22×C3×D3semidirect
518. C2×C32#908semidirect
519. C2×C32#932semidirect
520. C2×C32C3×AGL(1,ℤ/8)semidirect
617. C32C2×#908semidirect
618. C32C2×#932semidirect
619. C32C2×C3×AGL(1,ℤ/8)semidirect
659. C2×C3#63830direct (N × H)
660. C2×C3C3×#908semidirect
661. C2×C3C3×#932semidirect
685. C3C2×#63830direct (N × H)
686. C3C2×C3×#908semidirect
687. C3C2×C3×#932semidirect
691. C2C3×#63830direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#38282
C22×C32×D122
C2×C32×#2082
C3×#638302
C2×C3×#37162
C2×C3×#37142
C2×C3×#9323
C2×C3×#9083
C2×#638303