Finite Group Databasebeta

← C3×#6499867 #72271889

Subgroups — C3×#6499867 #72271889

Order 1536.

23636 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#62817C211yesmaximal, characteristic, complemented
2C2×C3×#2846C213yesmaximal, complemented
3C3×#23984C2112yesmaximal, complemented
4C3×#23900C2112yesmaximal, complemented
5C3×#21746C213yesmaximal, complemented
6#6499867C311yesmaximal, characteristic, direct product factor, Sylow
7C27×C3C2211yescharacteristic, complemented
8C3×#3532—212no—
9C3×#3490—26no—
10C3×#3490C2216yescomplemented
11C3×#3484—26no—
12C3×#3484C2216yescomplemented
13C22×C3×#120—26no—
14C22×C3×#120C2213yes—
15C22×C3×#120C2216yescomplemented
16C2×C3×B(4,𝔽2)C2218yescomplemented
17C3×#2846—212no—
18C3×#2846C22124yescomplemented
19C2×C3×#379—26no—
20C2×C3×#379C2216yescomplemented
21C2×C3×#379C2213yescomplemented
22C3×#2029C2218yescomplemented
23C3×#2021C22124yescomplemented
24C3×#1898C22124yescomplemented
25C3×#1889C22124yescomplemented
26C3×#1819C2216yescomplemented
27C3×#1781C2216yescomplemented
28#62817C2×C311yescharacteristic, complemented
29C2×#2846C2×C313yescomplemented
30#23984C2×C3112yescomplemented
31#23900C2×C3112yescomplemented
32#21746C2×C313yescomplemented
33C26×C3—26no—
34C26×C3—26no—
35C26×C3—416no—
36C26×C3—48no—
37C26×C3C2316yes—
38C26×C3C2311yescharacteristic
39C2×C3×H(5,𝔽2)—22no—
40C2×C3×H(5,𝔽2)C2312yescomplemented
41C23×C3×D4—26no—
42C23×C3×D4D416yescomplemented
43C23×C3×D4C2313yes—
44C3×H(3,𝔽4)—24no—
45C3×#560—212no—
46C3×#551—212no—
47C3×#551—224no—
48C3×#546—224no—
49C3×#546—224no—
50C3×#546—224no—
51C3×D42—212no—
52C3×D42—224no—
53C3×#543—22no—
54C3×#543C2312yescomplemented
55C3×#538—212no—
56C3×#538—212no—
57C3×#538—212no—
58C3×#535—212no—
59C3×#535—26no—
60C3×#534—26no—
61C3×#534—212no—
62C3×#534—26no—
63C3×#534C2316yescomplemented
64C3×#525—212no—
65C3×#525—26no—
66C2×C3×#120—248no—
67C2×C3×#120—212no—
68C2×C3×#120—212no—
69C2×C3×#120—212no—
70C2×C3×#120—26no—
71C2×C3×#120—424no—
72C2×C3×#120—448no—
73C2×C3×#120D4112yescomplemented
74C2×C3×#120C23124yes—
75C2×C3×#120C23112yes—
76C3×#518—26no—
77C3×#518C2316yescomplemented
78C22×C3×C22⋊C4—212no—
79C22×C3×C22⋊C4—26no—
80C22×C3×C22⋊C4—26no—
81C22×C3×C22⋊C4D416yescomplemented
82C22×C3×C22⋊C4C2313yes—
83C22×C3×C22⋊C4C2316yes—
84C3×B(4,𝔽2)—416no—
85C2×C3×#99C23124yescomplemented
86C3×#379—248no—
87C3×#379—212no—
88C3×#379—26no—
89C3×#379C23124yes—
90C3×#379C23112yes—
91C3×#342C23124yescomplemented
92C27C22×C311yescharacteristic, complemented
93#3532—212no—
94#3490—26no—
95#3490C22×C316yescomplemented
96#3484—26no—
97#3484C22×C316yescomplemented
98C22×#120—26no—
99C22×#120C22×C313yes—
100C22×#120C22×C316yescomplemented
101C2×B(4,𝔽2)C22×C318yescomplemented
102#2846—212no—
103#2846C22×C3124yescomplemented
104C2×#379—26no—
105C2×#379C22×C316yescomplemented
106C2×#379C22×C313yescomplemented
107#2029C22×C318yescomplemented
108#2021C22×C3124yescomplemented
109#1898C22×C3124yescomplemented
110#1889C22×C3124yescomplemented
111#1819C22×C316yescomplemented
112#1781C22×C316yescomplemented
113C25×C3—26no—
114C25×C3—248no—
115C25×C3—224no—
116C25×C3—26no—
117C25×C3—224no—
118C25×C3—448no—
119C25×C3—412no—
120C25×C3—44no—
121C25×C3—48no—
122C25×C3—448no—
123C25×C3—448no—
124C25×C3—424no—
125C25×C3—448no—
126C25×C3—496no—
127C25×C3—4256no—
128C25×C3—46no—
129C25×C3—46no—
130C25×C3—42no—
131C25×C3—42no—
132C25×C3C2×D416yes—
133C25×C3C2×D416yes—
134C25×C3C2×D413yescomplemented
135C25×C3C2414yes—
136C25×C3C2413yes—
137C3×H(5,𝔽2)—48no—
138C3×H(5,𝔽2)—88no—
139C2×C3×#41—212no—
140C2×C3×#41—26no—
141C22×C3×D4—26no—
142C22×C3×D4—212no—
143C22×C3×D4—26no—
144C22×C3×D4—212no—
145C22×C3×D4—212no—
146C22×C3×D4—26no—
147C22×C3×D4—224no—
148C22×C3×D4—412no—
149C22×C3×D4—424no—
150C22×C3×D4—424no—
151C22×C3×D4—448no—
152C22×C3×D4C2×D4124yescomplemented
153C22×C3×D4C2×D416yescomplemented
154C22×C3×D4C2416yes—
155C23×C3×C4—26no—
156C23×C3×C4C2×D416yescomplemented
157C23×C3×C4C2×D413yescomplemented
158C3×#127—212no—
159C3×#126—224no—
160C3×#124—224no—
161C3×#124—212no—
162C3×#123—224no—
163C3×#123—212no—
164C3×#123—224no—
165C3×#123—212no—
166C3×C22⋊Q8—212no—
167C3×C22⋊Q8—212no—
168C3×C22⋊Q8—212no—
169C3×#121—224no—
170C3×#121—224no—
171C3×#121—224no—
172C3×#121—212no—
173C3×#121—212no—
174C3×#121—212no—
175C3×#120—212no—
176C3×#120—224no—
177C3×#120—212no—
178C3×#120—224no—
179C3×#120—212no—
180C3×#120—212no—
181C3×#120—212no—
182C3×#120—224no—
183C3×#120—212no—
184C3×#120—248no—
185C3×#120—424no—
186C3×#120—448no—
187C3×#120—4192no—
188C3×C4×D4—224no—
189C3×C4×D4—224no—
190C3×C4×D4—224no—
191C3×#117—212no—
192C3×#117—26no—
193C2×C3×C22⋊C4—212no—
194C2×C3×C22⋊C4—26no—
195C2×C3×C22⋊C4—26no—
196C2×C3×C22⋊C4—212no—
197C2×C3×C22⋊C4—212no—
198C2×C3×C22⋊C4—26no—
199C2×C3×C22⋊C4—26no—
200C2×C3×C22⋊C4—224no—
201C2×C3×C22⋊C4—224no—
202C2×C3×C22⋊C4—248no—
203C2×C3×C22⋊C4—412no—
204C2×C3×C22⋊C4—424no—
205C2×C3×C22⋊C4—448no—
206C2×C3×C22⋊C4—424no—
207C2×C3×C22⋊C4C2×D4124yescomplemented
208C2×C3×C22⋊C4C2×D416yescomplemented
209C2×C3×C22⋊C4C24112yes—
210C2×C3×C22⋊C4C2416yes—
211C3×#99—424no—
212C26—26no—
213C26—26no—
214C26—416no—
215C26—48no—
216C26C23×C316yes—
217C26C23×C311yescharacteristic
218C2×H(5,𝔽2)—22no—
219C2×H(5,𝔽2)C23×C312yescomplemented
220C23×D4—26no—
221C23×D4C3×D416yescomplemented
222C23×D4C23×C313yes—
223H(3,𝔽4)—24no—
224#560—212no—
225#551—212no—
226#551—224no—
227#546—224no—
228#546—224no—
229#546—224no—
230D42—212no—
231D42—224no—
232#543—22no—
233#543C23×C312yescomplemented
234#538—212no—
235#538—212no—
236#538—212no—
237#535—212no—
238#535—26no—
239#534—26no—
240#534—212no—
241#534—26no—
242#534C23×C316yescomplemented
243#525—212no—
244#525—26no—
245C2×#120—212no—
246C2×#120—212no—
247C2×#120—26no—
248C2×#120—212no—
249C2×#120—248no—
250C2×#120—424no—
251C2×#120—448no—
252C2×#120C3×D4112yescomplemented
253C2×#120C23×C3124yes—
254C2×#120C23×C3112yes—
255#518—26no—
256#518C23×C316yescomplemented
257C22×C22⋊C4—26no—
258C22×C22⋊C4—212no—
259C22×C22⋊C4—26no—
260C22×C22⋊C4C3×D416yescomplemented
261C22×C22⋊C4C23×C313yes—
262C22×C22⋊C4C23×C316yes—
263B(4,𝔽2)—416no—
264C2×#99C23×C3124yescomplemented
265#379—26no—
266#379—212no—
267#379—248no—
268#379C23×C3112yes—
269#379C23×C3124yes—
270#342C23×C3124yescomplemented
271C24×C3—224no—
272C24×C3—248no—
273C24×C3—212no—
274C24×C3—212no—
275C24×C3—224no—
276C24×C3—296no—
277C24×C3—224no—
278C24×C3—22no—
279C24×C3—212no—
280C24×C3—26no—
281C24×C3—412no—
282C24×C3—412no—
283C24×C3—412no—
284C24×C3—424no—
285C24×C3—412no—
286C24×C3—416no—
287C24×C3—46no—
288C24×C3—496no—
289C24×C3—412no—
290C24×C3—424no—
291C24×C3—496no—
292C24×C3—448no—
293C24×C3—4192no—
294C24×C3—4384no—
295C24×C3—412no—
296C24×C3—448no—
297C24×C3—496no—
298C24×C3—448no—
299C24×C3—412no—
300C24×C3—416no—
301C24×C3—448no—
302C24×C3—448no—
303C24×C3—416no—
304C24×C3—448no—
305C24×C3—416no—
306C24×C3—432no—
307C24×C3—4192no—
308C24×C3—464no—
309C24×C3—4384no—
310C24×C3—4768no—
311C24×C3—412no—
312C24×C3—412no—
313C24×C3—416no—
314C24×C3#12016yes—
315C24×C3#12016yes—
316C24×C3#12012yes—
317C24×C3#12012yes—
318C24×C3C22×D413yes—
319C24×C3C22×D4112yes—
320C24×C3C22×D416yes—
321C24×C3C22×D413yes—
322C24×C3H(5,𝔽2)18yescomplemented
323C24×C3C2511yescharacteristic
324C3×#41—812no—
325C3×#41—824no—
326C2×C3×Q8—22no—
327C2×C3×Q8—24no—
328C2×C3×D4—224no—
329C2×C3×D4—212no—
330C2×C3×D4—224no—
331C2×C3×D4—26no—
332C2×C3×D4—212no—
333C2×C3×D4—212no—
334C2×C3×D4—224no—
335C2×C3×D4—412no—
336C2×C3×D4—424no—
337C2×C3×D4—448no—
338C2×C3×D4—448no—
339C2×C3×D4—496no—
340C2×C3×D4—812no—
341C2×C3×D4—824no—
342C2×C3×D4—824no—
343C2×C3×D4—812no—
344C2×C3×D4—824no—
345C2×C3×D4—896no—
346C22×C3×C4—26no—
347C22×C3×C4—26no—
348C22×C3×C4—212no—
349C22×C3×C4—26no—
350C22×C3×C4—26no—
351C22×C3×C4—212no—
352C22×C3×C4—46no—
353C22×C3×C4—412no—
354C22×C3×C4—424no—
355C22×C3×C4—412no—
356C22×C3×C4C22×D416yes—
357C22×C3×C4C22×D4112yes—
358C3×C4⋊C4—212no—
359C3×C4⋊C4—212no—
360C3×C4⋊C4—212no—
361C3×C22⋊C4—224no—
362C3×C22⋊C4—212no—
363C3×C22⋊C4—224no—
364C3×C22⋊C4—224no—
365C3×C22⋊C4—212no—
366C3×C22⋊C4—212no—
367C3×C22⋊C4—224no—
368C3×C22⋊C4—448no—
369C3×C22⋊C4—496no—
370C3×C22⋊C4—448no—
371C3×C22⋊C4—412no—
372C3×C42—212no—
373C25—26no—
374C25—248no—
375C25—224no—
376C25—26no—
377C25—224no—
378C25—448no—
379C25—44no—
380C25—412no—
381C25—48no—
382C25—448no—
383C25—448no—
384C25—424no—
385C25—448no—
386C25—496no—
387C25—4256no—
388C25—46no—
389C25—46no—
390C25—42no—
391C25—42no—
392C25C2×C3×D416yes—
393C25C2×C3×D416yes—
394C25C2×C3×D413yescomplemented
395C25C24×C314yes—
396C25C24×C313yes—
397H(5,𝔽2)—48no—
398H(5,𝔽2)—88no—
399C2×#41—212no—
400C2×#41—26no—
401C22×D4—26no—
402C22×D4—212no—
403C22×D4—26no—
404C22×D4—212no—
405C22×D4—212no—
406C22×D4—26no—
407C22×D4—224no—
408C22×D4—412no—
409C22×D4—424no—
410C22×D4—424no—
411C22×D4—448no—
412C22×D4C2×C3×D416yescomplemented
413C22×D4C2×C3×D4124yescomplemented
414C22×D4C24×C316yes—
415C23×C4—26no—
416C23×C4C2×C3×D413yescomplemented
417C23×C4C2×C3×D416yescomplemented
418#127—212no—
419#126—224no—
420#124—224no—
421#124—212no—
422#123—224no—
423#123—224no—
424#123—212no—
425#123—212no—
426C22⋊Q8—212no—
427C22⋊Q8—212no—
428C22⋊Q8—212no—
429#121—212no—
430#121—212no—
431#121—224no—
432#121—224no—
433#121—224no—
434#121—212no—
435#120—224no—
436#120—212no—
437#120—224no—
438#120—212no—
439#120—212no—
440#120—212no—
441#120—212no—
442#120—224no—
443#120—212no—
444#120—248no—
445#120—424no—
446#120—448no—
447#120—4192no—
448C4×D4—224no—
449C4×D4—224no—
450C4×D4—224no—
451#117—212no—
452#117—26no—
453C2×C22⋊C4—212no—
454C2×C22⋊C4—26no—
455C2×C22⋊C4—26no—
456C2×C22⋊C4—212no—
457C2×C22⋊C4—212no—
458C2×C22⋊C4—26no—
459C2×C22⋊C4—224no—
460C2×C22⋊C4—26no—
461C2×C22⋊C4—248no—
462C2×C22⋊C4—224no—
463C2×C22⋊C4—412no—
464C2×C22⋊C4—424no—
465C2×C22⋊C4—448no—
466C2×C22⋊C4—424no—
467C2×C22⋊C4C2×C3×D4124yescomplemented
468C2×C22⋊C4C2×C3×D416yescomplemented
469C2×C22⋊C4C24×C3112yes—
470C2×C22⋊C4C24×C316yes—
471#99—424no—
472C23×C3—26no—
473C23×C3—212no—
474C23×C3—248no—
475C23×C3—296no—
476C23×C3—26no—
477C23×C3—224no—
478C23×C3—224no—
479C23×C3—224no—
480C23×C3—224no—
481C23×C3—212no—
482C23×C3—26no—
483C23×C3—212no—
484C23×C3—42no—
485C23×C3—46no—
486C23×C3—46no—
487C23×C3—42no—
488C23×C3—46no—
489C23×C3—42no—
490C23×C3—44no—
491C23×C3—412no—
492C23×C3—46no—
493C23×C3—416no—
494C23×C3—42no—
495C23×C3—448no—
496C23×C3—496no—
497C23×C3—496no—
498C23×C3—448no—
499C23×C3—448no—
500C23×C3—424no—
501C23×C3—448no—
502C23×C3—448no—
503C23×C3—4384no—
504C23×C3—496no—
505C23×C3—448no—
506C23×C3—496no—
507C23×C3—412no—
508C23×C3—4128no—
509C23×C3—496no—
510C23×C3—4384no—
511C23×C3—4384no—
512C23×C3—496no—
513C23×C3—4384no—
514C23×C3—4128no—
515C23×C3—44no—
516C23×C3—412no—
517C23×C3—448no—
518C23×C3—412no—
519C23×C3—86no—
520C23×C3—86no—
521C23×C3—824no—
522C23×C3—82no—
523C23×C3—84no—
524C23×C3B(4,𝔽2)18yescomplemented
525C23×C3C2×#12016yes—
526C23×C3C2×#12016yes—
527C23×C3C23×D413yes—
528C23×C3C2×H(5,𝔽2)14yes—
529C3×Q8—82no—
530C3×Q8—84no—
531C3×D4—424no—
532C3×D4—448no—
533C3×D4—812no—
534C3×D4—824no—
535C3×D4—86no—
536C3×D4—812no—
537C3×D4—896no—
538C2×C3×C4—26no—
539C2×C3×C4—212no—
540C2×C3×C4—212no—
541C2×C3×C4—412no—
542C2×C3×C4—412no—
543C2×C3×C4—424no—
544C2×C3×C4—412no—
545C2×C3×C4—86no—
546C2×C3×C4—86no—
547C2×C3×C4—86no—
548C2×C3×C4—812no—
549C2×C3×C4—824no—
550C24—224no—
551C24—248no—
552C24—212no—
553C24—212no—
554C24—224no—
555C24—296no—
556C24—224no—
557C24—22no—
558C24—212no—
559C24—26no—
560C24—412no—
561C24—412no—
562C24—412no—
563C24—424no—
564C24—412no—
565C24—416no—
566C24—46no—
567C24—496no—
568C24—412no—
569C24—424no—
570C24—496no—
571C24—448no—
572C24—4192no—
573C24—4384no—
574C24—412no—
575C24—448no—
576C24—496no—
577C24—448no—
578C24—412no—
579C24—416no—
580C24—448no—
581C24—448no—
582C24—416no—
583C24—448no—
584C24—416no—
585C24—432no—
586C24—464no—
587C24—4192no—
588C24—4384no—
589C24—4768no—
590C24—416no—
591C24—412no—
592C24—412no—
593C24C3×#12016yes—
594C24C3×#12016yes—
595C24C3×#12012yes—
596C24C3×#12012yes—
597C24C22×C3×D413yes—
598C24C22×C3×D4112yes—
599C24C22×C3×D416yes—
600C24C22×C3×D413yes—
601C24C3×H(5,𝔽2)18yescomplemented
602C24C25×C311yescharacteristic
603#41—812no—
604#41—824no—
605C2×Q8—22no—
606C2×Q8—24no—
607C2×D4—212no—
608C2×D4—224no—
609C2×D4—224no—
610C2×D4—26no—
611C2×D4—212no—
612C2×D4—212no—
613C2×D4—224no—
614C2×D4—412no—
615C2×D4—424no—
616C2×D4—448no—
617C2×D4—448no—
618C2×D4—496no—
619C2×D4—812no—
620C2×D4—824no—
621C2×D4—824no—
622C2×D4—812no—
623C2×D4—824no—
624C2×D4—896no—
625C22×C4—26no—
626C22×C4—26no—
627C22×C4—212no—
628C22×C4—26no—
629C22×C4—26no—
630C22×C4—212no—
631C22×C4—46no—
632C22×C4—412no—
633C22×C4—424no—
634C22×C4—412no—
635C22×C4C22×C3×D416yes—
636C22×C4C22×C3×D4112yes—
637C4⋊C4—212no—
638C4⋊C4—212no—
639C4⋊C4—212no—
640C22⋊C4—224no—
641C22⋊C4—212no—
642C22⋊C4—212no—
643C22⋊C4—224no—
644C22⋊C4—224no—
645C22⋊C4—212no—
646C22⋊C4—224no—
647C22⋊C4—448no—
648C22⋊C4—496no—
649C22⋊C4—448no—
650C22⋊C4—412no—
651C42—212no—
652C22×C3—224no—
653C22×C3—26no—
654C22×C3—26no—
655C22×C3—26no—
656C22×C3—248no—
657C22×C3—26no—
658C22×C3—212no—
659C22×C3—44no—
660C22×C3—48no—
661C22×C3—448no—
662C22×C3—424no—
663C22×C3—448no—
664C22×C3—412no—
665C22×C3—424no—
666C22×C3—4192no—
667C22×C3—424no—
668C22×C3—48no—
669C22×C3—4192no—
670C22×C3—48no—
671C22×C3—416no—
672C22×C3—46no—
673C22×C3—412no—
674C22×C3—812no—
675C22×C3—1612no—
676C22×C3—322no—
677C22×C3C2×B(4,𝔽2)112yes—
678C22×C3C22×#12011yescharacteristic
679C22×C3#348416yes—
680C3×C4—46no—
681C3×C4—412no—
682C3×C4—812no—
683C23—26no—
684C23—212no—
685C23—248no—
686C23—296no—
687C23—26no—
688C23—224no—
689C23—224no—
690C23—224no—
691C23—224no—
692C23—212no—
693C23—26no—
694C23—212no—
695C23—42no—
696C23—42no—
697C23—46no—
698C23—46no—
699C23—42no—
700C23—46no—
701C23—42no—
702C23—44no—
703C23—412no—
704C23—46no—
705C23—416no—
706C23—448no—
707C23—496no—
708C23—496no—
709C23—448no—
710C23—448no—
711C23—424no—
712C23—448no—
713C23—448no—
714C23—4384no—
715C23—496no—
716C23—448no—
717C23—496no—
718C23—412no—
719C23—4128no—
720C23—496no—
721C23—4384no—
722C23—4384no—
723C23—496no—
724C23—4384no—
725C23—4128no—
726C23—44no—
727C23—412no—
728C23—448no—
729C23—412no—
730C23—86no—
731C23—86no—
732C23—824no—
733C23—82no—
734C23—84no—
735C23C3×B(4,𝔽2)18yescomplemented
736C23C2×C3×#12016yes—
737C23C2×C3×#12016yes—
738C23C23×C3×D413yes—
739C23C2×C3×H(5,𝔽2)14yes—
740Q8—82no—
741Q8—84no—
742D4—424no—
743D4—448no—
744D4—812no—
745D4—824no—
746D4—86no—
747D4—812no—
748D4—896no—
749C2×C4—26no—
750C2×C4—212no—
751C2×C4—212no—
752C2×C4—412no—
753C2×C4—412no—
754C2×C4—424no—
755C2×C4—412no—
756C2×C4—86no—
757C2×C4—86no—
758C2×C4—86no—
759C2×C4—812no—
760C2×C4—824no—
761C2×C3—26no—
762C2×C3—212no—
763C2×C3—416no—
764C2×C3—46no—
765C2×C3—86no—
766C2×C3#3534611yescharacteristic
767C2×C3C22×B(4,𝔽2)12yes—
768C22—224no—
769C22—26no—
770C22—26no—
771C22—26no—
772C22—248no—
773C22—26no—
774C22—212no—
775C22—44no—
776C22—48no—
777C22—448no—
778C22—424no—
779C22—448no—
780C22—412no—
781C22—424no—
782C22—4192no—
783C22—424no—
784C22—48no—
785C22—4192no—
786C22—48no—
787C22—416no—
788C22—46no—
789C22—412no—
790C22—812no—
791C22—1612no—
792C22—322no—
793C22C2×C3×B(4,𝔽2)112yes—
794C22C22×C3×#12011yescharacteristic
795C22C3×#348416yes—
796C4—46no—
797C4—412no—
798C4—812no—
799C3#649986711yescharacteristic, direct product factor, Sylow
800C2—26no—
801C2—212no—
802C2—416no—
803C2—46no—
804C2—86no—
805C2C3×#3534611yescharacteristic
806C2C22×C3×B(4,𝔽2)12yes—
subgroupG/H
center, socleC22×C3C22×#120
commutator, Frattini, cosocleC24C25×C3
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C26×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#62817C2semidirect
2. C2×C3×#2846C2semidirect
3. C3×#23984C2semidirect
4. C3×#23900C2semidirect
5. C3×#21746C2semidirect
6. #6499867C3direct (N × H)
7. C27×C3C22semidirect
10. C3×#3490C22semidirect
12. C3×#3484C22semidirect
15. C22×C3×#120C22semidirect
16. C2×C3×B(4,𝔽2)C22semidirect
18. C3×#2846C22semidirect
20. C2×C3×#379C22semidirect
21. C2×C3×#379C22semidirect
22. C3×#2029C22semidirect
23. C3×#2021C22semidirect
24. C3×#1898C22semidirect
25. C3×#1889C22semidirect
26. C3×#1819C22semidirect
27. C3×#1781C22semidirect
28. #62817C2×C3semidirect
29. C2×#2846C2×C3semidirect
30. #23984C2×C3semidirect
31. #23900C2×C3semidirect
32. #21746C2×C3semidirect
40. C2×C3×H(5,𝔽2)C23semidirect
42. C23×C3×D4D4semidirect
54. C3×#543C23semidirect
63. C3×#534C23semidirect
73. C2×C3×#120D4semidirect
77. C3×#518C23semidirect
81. C22×C3×C22⋊C4D4semidirect
85. C2×C3×#99C23semidirect
91. C3×#342C23semidirect
92. C27C22×C3semidirect
95. #3490C22×C3semidirect
97. #3484C22×C3semidirect
100. C22×#120C22×C3semidirect
101. C2×B(4,𝔽2)C22×C3semidirect
103. #2846C22×C3semidirect
105. C2×#379C22×C3semidirect
106. C2×#379C22×C3semidirect
107. #2029C22×C3semidirect
108. #2021C22×C3semidirect
109. #1898C22×C3semidirect
110. #1889C22×C3semidirect
111. #1819C22×C3semidirect
112. #1781C22×C3semidirect
134. C25×C3C2×D4semidirect
152. C22×C3×D4C2×D4semidirect
153. C22×C3×D4C2×D4semidirect
156. C23×C3×C4C2×D4semidirect
157. C23×C3×C4C2×D4semidirect
207. C2×C3×C22⋊C4C2×D4semidirect
208. C2×C3×C22⋊C4C2×D4semidirect
219. C2×H(5,𝔽2)C23×C3semidirect
221. C23×D4C3×D4semidirect
233. #543C23×C3semidirect
242. #534C23×C3semidirect
252. C2×#120C3×D4semidirect
256. #518C23×C3semidirect
260. C22×C22⋊C4C3×D4semidirect
264. C2×#99C23×C3semidirect
270. #342C23×C3semidirect
322. C24×C3H(5,𝔽2)semidirect
394. C25C2×C3×D4semidirect
412. C22×D4C2×C3×D4semidirect
413. C22×D4C2×C3×D4semidirect
416. C23×C4C2×C3×D4semidirect
417. C23×C4C2×C3×D4semidirect
467. C2×C22⋊C4C2×C3×D4semidirect
468. C2×C22⋊C4C2×C3×D4semidirect
524. C23×C3B(4,𝔽2)semidirect
601. C24C3×H(5,𝔽2)semidirect
735. C23C3×B(4,𝔽2)semidirect
799. C3#6499867direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#628172
C2×C3×#28462
C3×#239842
C3×#239002
C3×#217462
#64998673