Finite Group Databasebeta

← C2×C3×AΣL(1,𝔽64) #72274953

Subgroups — C2×C3×AΣL(1,𝔽64) #72274953

Order 2304.

11566 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 11566 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C22⋊A4C211yesmaximal, characteristic, complemented
2C22×C3×#120⋊C3C211yesmaximal, characteristic, complemented
3C3×AΣL(1,𝔽64)C214yesmaximal, direct product factor
4C2×C3×#379⋊C3C211yesmaximal, characteristic, complemented
5C2×AΣL(1,𝔽64)C313yesmaximal, direct product factor
6C2×C3×#2846C311yesmaximal, characteristic, complemented
7C22×C3×C22⋊A4—22no—
8C22×C3×C22⋊A4C2211yescharacteristic
9C22×C3×C22⋊A4C2212yescomplemented
10C2×C3×D4×A4—41nomaximal
11C2×C3×#120⋊C3—22no—
12C2×C3×#120⋊C3C2212yescomplemented
13C3×#379⋊C3C2212yescomplemented
14C27×C3C2×C311yescharacteristic, complemented
15C23×C22⋊A4C2×C313yescomplemented
16C22×C3×#120—31no—
17C22×C3×#120—31no—
18C22×C3×#120C2×C311yescharacteristic, complemented
19C22×#120⋊C3C2×C313yescomplemented
20C3×#2846—34no—
21C3×#2846C2×C314yescomplemented
22C2×C3×#379—31no—
23C2×C3×#379—31no—
24C2×C3×#379C2×C311yescharacteristic, complemented
25AΣL(1,𝔽64)C2×C3112yesdirect product factor
26C2×#379⋊C3C2×C313yescomplemented
27C2×C3×C22⋊A4—22no—
28C2×C3×C22⋊A4D412yescomplemented
29C2×C3×C22⋊A4C2311yescharacteristic
30C23×C3×A4—41no—
31C23×C3×A4—41no—
32C23×C3×A4—82no—
33C3×D4×A4—44no—
34C2×C3×C4×A4—41no—
35C3×#120⋊C3—22no—
36C2×#2846C3211yescharacteristic, complemented, Sylow
37C26×C3—22no—
38C26×C3—31no—
39C26×C3—31no—
40C26×C3—32no—
41C26×C3—62no—
42C26×C3—62no—
43C26×C3—64no—
44C26×C3—68no—
45C26×C3—62no—
46C26×C3C22×C311yescharacteristic
47C26×C3C22×C312yescomplemented
48C22×C22⋊A4—26no—
49C22×C22⋊A4C22×C313yes—
50C22×C22⋊A4C22×C316yescomplemented
51C23×C3×D4—31no—
52C23×C3×D4—31no—
53C23×C3×D4A411yescharacteristic, complemented
54C2×D4×A4—43no—
55C2×C3×#120—22no—
56C2×C3×#120—34no—
57C2×C3×#120—32no—
58C2×C3×#120—34no—
59C2×C3×#120—34no—
60C2×C3×#120—34no—
61C2×C3×#120—62no—
62C2×C3×#120—68no—
63C2×C3×#120—62no—
64C2×C3×#120—64no—
65C2×C3×#120—62no—
66C2×C3×#120C22×C312yescomplemented
67C22×C3×C22⋊C4—31no—
68C22×C3×C22⋊C4—31no—
69C22×C3×C22⋊C4—32no—
70C22×C3×C22⋊C4—31no—
71C22×C3×C22⋊C4—31no—
72C22×C3×C22⋊C4—31no—
73C2×#120⋊C3—26no—
74C2×#120⋊C3C22×C316yescomplemented
75C3×#379—34no—
76C3×#379—34no—
77C3×#379—32no—
78C3×#379—34no—
79C3×#379—34no—
80C3×#379C22×C312yescomplemented
81#379⋊C3C22×C316yescomplemented
82C3×C22⋊A4C2×D411yescharacteristic, complemented
83C22×C3×A4—41no—
84C22×C3×A4—42no—
85C22×C3×A4—42no—
86C22×C3×A4—82no—
87C22×C3×A4—82no—
88C22×C3×A4—82no—
89C22×C3×A4—84no—
90C22×C3×A4—88no—
91C2×C32×D4—161no—
92C3×C4×A4—42no—
93C27C2×C3211yescharacteristic, complemented
94C22×#120—31no—
95C22×#120—31no—
96C22×#120C2×C3211yescharacteristic, complemented
97#2846—34no—
98#2846C2×C3214yescomplemented
99C2×#379—31no—
100C2×#379—31no—
101C2×#379C2×C3211yescharacteristic, complemented
102C25×C3—22no—
103C25×C3—22no—
104C25×C3—31no—
105C25×C3—31no—
106C25×C3—32no—
107C25×C3—38no—
108C25×C3—34no—
109C25×C3—32no—
110C25×C3—32no—
111C25×C3—31no—
112C25×C3—32no—
113C25×C3—32no—
114C25×C3—32no—
115C25×C3—32no—
116C25×C3—62no—
117C25×C3—64no—
118C25×C3—62no—
119C25×C3—62no—
120C25×C3—68no—
121C25×C3—68no—
122C25×C3—62no—
123C25×C3—64no—
124C25×C3—64no—
125C25×C3—62no—
126C25×C3—64no—
127C25×C3—68no—
128C25×C3—62no—
129C25×C3—62no—
130C25×C3—64no—
131C25×C3—62no—
132C25×C3—64no—
133C25×C3—68no—
134C25×C3—62no—
135C25×C3—64no—
136C25×C3—62no—
137C25×C3—64no—
138C25×C3—68no—
139C25×C3—64no—
140C25×C3—62no—
141C25×C3—62no—
142C25×C3—64no—
143C25×C3—64no—
144C25×C3—68no—
145C25×C3—616no—
146C25×C3—68no—
147C25×C3—64no—
148C25×C3—68no—
149C25×C3—68no—
150C25×C3—616no—
151C25×C3—62no—
152C25×C3—64no—
153C25×C3—68no—
154C25×C3—62no—
155C25×C3—64no—
156C25×C3—68no—
157C25×C3—616no—
158C25×C3—68no—
159C25×C3—68no—
160C25×C3—64no—
161C25×C3—68no—
162C25×C3—616no—
163C25×C3—616no—
164C25×C3—616no—
165C25×C3—64no—
166C25×C3—68no—
167C25×C3—616no—
168C25×C3—68no—
169C25×C3—616no—
170C25×C3—632no—
171C25×C3—616no—
172C25×C3—632no—
173C25×C3C3×D412yescomplemented
174C25×C3C2×A411yescharacteristic
175C25×C3C2×A411yescharacteristic, complemented
176C25×C3C23×C311yescharacteristic
177C2×C22⋊A4—26no—
178C2×C22⋊A4C3×D416yescomplemented
179C2×C22⋊A4C23×C313yes—
180C23×A4—43no—
181C23×A4—43no—
182C23×A4—86no—
183C22×C3×D4—32no—
184C22×C3×D4—34no—
185C22×C3×D4—32no—
186C22×C3×D4—61no—
187C22×C3×D4—62no—
188C22×C3×D4—62no—
189C22×C3×D4—62no—
190C22×C3×D4—62no—
191C22×C3×D4—62no—
192C22×C3×D4—68no—
193C22×C3×D4—62no—
194C22×C3×D4—64no—
195C22×C3×D4—61no—
196C22×C3×D4—62no—
197C22×C3×D4C2×A414yescomplemented
198C23×C3×C4—31no—
199C23×C3×C4—31no—
200C23×C3×C4C2×A411yescharacteristic, complemented
201D4×A4—412no—
202C2×C4×A4—43no—
203C3×#120—22no—
204C3×#120—68no—
205C3×#120—68no—
206C3×#120—616no—
207C3×#120—616no—
208C3×#120—68no—
209C3×#120—68no—
210C3×#120—64no—
211C3×#120—64no—
212C3×#120—62no—
213C2×C3×C22⋊C4—38no—
214C2×C3×C22⋊C4—32no—
215C2×C3×C22⋊C4—32no—
216C2×C3×C22⋊C4—34no—
217C2×C3×C22⋊C4—32no—
218C2×C3×C22⋊C4—34no—
219C2×C3×C22⋊C4—32no—
220C2×C3×C22⋊C4—32no—
221C2×C3×C22⋊C4—32no—
222C2×C3×C22⋊C4—62no—
223C2×C3×C22⋊C4—62no—
224C2×C3×C22⋊C4—64no—
225C2×C3×C22⋊C4—68no—
226C2×C3×C22⋊C4—61no—
227C2×C3×C22⋊C4—62no—
228C2×C3×C22⋊C4—61no—
229C2×C3×C22⋊C4—62no—
230C2×C3×C22⋊C4—62no—
231C2×C3×C22⋊C4—62no—
232C2×C3×C22⋊C4—62no—
233#120⋊C3—26no—
234C23×C32—161no—
235C23×C32—161no—
236C2×C3×A4—42no—
237C2×C3×A4—41no—
238C2×C3×A4—84no—
239C2×C3×A4—82no—
240C2×C3×A4—82no—
241C2×C3×A4—82no—
242C2×C3×A4—88no—
243C32×D4—164no—
244C2×C32×C4—161no—
245C26—22no—
246C26—31no—
247C26—31no—
248C26—32no—
249C26—62no—
250C26—62no—
251C26—64no—
252C26—68no—
253C26—62no—
254C26C22×C3211yescharacteristic
255C26C22×C3212yescomplemented
256C23×D4—31no—
257C23×D4—31no—
258C23×D4C3×A411yescharacteristic, complemented
259C2×#120—22no—
260C2×#120—34no—
261C2×#120—34no—
262C2×#120—34no—
263C2×#120—32no—
264C2×#120—34no—
265C2×#120—62no—
266C2×#120—68no—
267C2×#120—62no—
268C2×#120—64no—
269C2×#120—62no—
270C2×#120C22×C3212yescomplemented
271C22×C22⋊C4—32no—
272C22×C22⋊C4—31no—
273C22×C22⋊C4—31no—
274C22×C22⋊C4—31no—
275C22×C22⋊C4—31no—
276C22×C22⋊C4—31no—
277#379—34no—
278#379—34no—
279#379—32no—
280#379—34no—
281#379—34no—
282#379C22×C3212yescomplemented
283C24×C3—28no—
284C24×C3—22no—
285C24×C3—24no—
286C24×C3—22no—
287C24×C3—22no—
288C24×C3—34no—
289C24×C3—32no—
290C24×C3—38no—
291C24×C3—32no—
292C24×C3—32no—
293C24×C3—32no—
294C24×C3—32no—
295C24×C3—31no—
296C24×C3—31no—
297C24×C3—32no—
298C24×C3—32no—
299C24×C3—31no—
300C24×C3—32no—
301C24×C3—31no—
302C24×C3—38no—
303C24×C3—38no—
304C24×C3—34no—
305C24×C3—34no—
306C24×C3—34no—
307C24×C3—34no—
308C24×C3—32no—
309C24×C3—32no—
310C24×C3—31no—
311C24×C3—64no—
312C24×C3—62no—
313C24×C3—62no—
314C24×C3—62no—
315C24×C3—64no—
316C24×C3—68no—
317C24×C3—62no—
318C24×C3—64no—
319C24×C3—68no—
320C24×C3—64no—
321C24×C3—616no—
322C24×C3—68no—
323C24×C3—61no—
324C24×C3—64no—
325C24×C3—62no—
326C24×C3—62no—
327C24×C3—62no—
328C24×C3—62no—
329C24×C3—64no—
330C24×C3—62no—
331C24×C3—62no—
332C24×C3—62no—
333C24×C3—62no—
334C24×C3—62no—
335C24×C3—64no—
336C24×C3—68no—
337C24×C3—64no—
338C24×C3—68no—
339C24×C3—62no—
340C24×C3—64no—
341C24×C3—64no—
342C24×C3—68no—
343C24×C3—68no—
344C24×C3—68no—
345C24×C3—64no—
346C24×C3—62no—
347C24×C3—64no—
348C24×C3—68no—
349C24×C3—64no—
350C24×C3—64no—
351C24×C3—68no—
352C24×C3—68no—
353C24×C3—64no—
354C24×C3—68no—
355C24×C3—64no—
356C24×C3—68no—
357C24×C3—616no—
358C24×C3—64no—
359C24×C3—68no—
360C24×C3—68no—
361C24×C3—68no—
362C24×C3—68no—
363C24×C3—68no—
364C24×C3—616no—
365C24×C3—632no—
366C24×C3—68no—
367C24×C3—64no—
368C24×C3—616no—
369C24×C3—64no—
370C24×C3—68no—
371C24×C3—64no—
372C24×C3—64no—
373C24×C3—64no—
374C24×C3—62no—
375C24×C3—64no—
376C24×C3—64no—
377C24×C3—64no—
378C24×C3—68no—
379C24×C3—64no—
380C24×C3—61no—
381C24×C3—62no—
382C24×C3—68no—
383C24×C3—68no—
384C24×C3—62no—
385C24×C3—64no—
386C24×C3—62no—
387C24×C3—64no—
388C24×C3—64no—
389C24×C3—68no—
390C24×C3—68no—
391C24×C3—62no—
392C24×C3—62no—
393C24×C3—64no—
394C24×C3—64no—
395C24×C3—68no—
396C24×C3—68no—
397C24×C3—616no—
398C24×C3—68no—
399C24×C3—68no—
400C24×C3—616no—
401C24×C3—64no—
402C24×C3—68no—
403C24×C3—616no—
404C24×C3—616no—
405C24×C3—68no—
406C24×C3—616no—
407C24×C3—68no—
408C24×C3—616no—
409C24×C3—64no—
410C24×C3—68no—
411C24×C3—68no—
412C24×C3—68no—
413C24×C3—68no—
414C24×C3—64no—
415C24×C3—64no—
416C24×C3—64no—
417C24×C3—616no—
418C24×C3—616no—
419C24×C3—616no—
420C24×C3—616no—
421C24×C3—632no—
422C24×C3—68no—
423C24×C3—68no—
424C24×C3—616no—
425C24×C3—632no—
426C24×C3—68no—
427C24×C3—68no—
428C24×C3—68no—
429C24×C3—64no—
430C24×C3—616no—
431C24×C3—616no—
432C24×C3—68no—
433C24×C3—68no—
434C24×C3—68no—
435C24×C3—68no—
436C24×C3—68no—
437C24×C3—616no—
438C24×C3—616no—
439C24×C3—616no—
440C24×C3—632no—
441C24×C3—616no—
442C24×C3—616no—
443C24×C3—632no—
444C24×C3—632no—
445C24×C3—616no—
446C24×C3—64no—
447C24×C3—616no—
448C24×C3—632no—
449C24×C3—616no—
450C24×C3—632no—
451C24×C3—616no—
452C24×C3—632no—
453C24×C3—616no—
454C24×C3—632no—
455C24×C3—68no—
456C24×C3—616no—
457C24×C3—68no—
458C24×C3—616no—
459C24×C3—616no—
460C24×C3—616no—
461C24×C3—632no—
462C24×C3—616no—
463C24×C3—632no—
464C24×C3—632no—
465C24×C3—68no—
466C24×C3—616no—
467C24×C3—616no—
468C24×C3—632no—
469C24×C3—616no—
470C24×C3—616no—
471C24×C3—632no—
472C24×C3—632no—
473C24×C3—616no—
474C24×C3—632no—
475C24×C3—632no—
476C24×C3—616no—
477C24×C3—632no—
478C24×C3—632no—
479C24×C3—632no—
480C24×C3—632no—
481C24×C3—616no—
482C24×C3—64no—
483C24×C3—68no—
484C24×C3—62no—
485C24×C3—62no—
486C24×C3C2×C3×D411yescharacteristic, complemented
487C24×C3C22×A412yes—
488C24×C3C22×A411yescharacteristic
489C24×C3C22×A412yescomplemented
490C22⋊A4C2×C3×D413yescomplemented
491C22×A4—43no—
492C22×A4—46no—
493C22×A4—46no—
494C22×A4—86no—
495C22×A4—812no—
496C22×A4—86no—
497C22×A4—86no—
498C22×A4—824no—
499C2×C3×D4—41no—
500C2×C3×D4—64no—
501C2×C3×D4—62no—
502C2×C3×D4—64no—
503C2×C3×D4—62no—
504C2×C3×D4—64no—
505C2×C3×D4—68no—
506C2×C3×D4—64no—
507C2×C3×D4—64no—
508C2×C3×D4—616no—
509C2×C3×D4—64no—
510C2×C3×D4—64no—
511C2×C3×D4—121no—
512C2×C3×D4—122no—
513C2×C3×D4—122no—
514C2×C3×D4—124no—
515C2×C3×D4—124no—
516C2×C3×D4—128no—
517C2×C3×D4—124no—
518C2×C3×D4—124no—
519C2×C3×D4—128no—
520C2×C3×D4—163no—
521C22×C3×C4—32no—
522C22×C3×C4—32no—
523C22×C3×C4—61no—
524C22×C3×C4—62no—
525C22×C3×C4—64no—
526C22×C3×C4—61no—
527C22×C3×C4—61no—
528C22×C3×C4—61no—
529C22×C3×C4—61no—
530C22×C3×C4—62no—
531C22×C3×C4—61no—
532C22×C3×C4C22×A412yescomplemented
533C4×A4—46no—
534C3×C22⋊C4—64no—
535C3×C22⋊C4—68no—
536C3×C22⋊C4—64no—
537C3×C22⋊C4—616no—
538C3×C22⋊C4—64no—
539C3×C22⋊C4—64no—
540C3×C22⋊C4—64no—
541C3×C22⋊C4—64no—
542C3×C22⋊C4—64no—
543C3×C22⋊C4—62no—
544C3×C22⋊C4—62no—
545C22×C32—162no—
546C22×C32—161no—
547C22×C32—162no—
548C22×C32—322no—
549C22×C32—322no—
550C3×A4—41no—
551C3×A4—82no—
552C32×C4—162no—
553C25—22no—
554C25—22no—
555C25—31no—
556C25—31no—
557C25—32no—
558C25—38no—
559C25—34no—
560C25—32no—
561C25—32no—
562C25—31no—
563C25—32no—
564C25—32no—
565C25—32no—
566C25—32no—
567C25—62no—
568C25—64no—
569C25—62no—
570C25—62no—
571C25—68no—
572C25—68no—
573C25—62no—
574C25—64no—
575C25—64no—
576C25—62no—
577C25—64no—
578C25—68no—
579C25—62no—
580C25—62no—
581C25—64no—
582C25—62no—
583C25—68no—
584C25—64no—
585C25—62no—
586C25—64no—
587C25—64no—
588C25—68no—
589C25—62no—
590C25—64no—
591C25—62no—
592C25—62no—
593C25—64no—
594C25—64no—
595C25—68no—
596C25—616no—
597C25—68no—
598C25—64no—
599C25—68no—
600C25—68no—
601C25—616no—
602C25—62no—
603C25—64no—
604C25—68no—
605C25—62no—
606C25—64no—
607C25—68no—
608C25—616no—
609C25—68no—
610C25—68no—
611C25—64no—
612C25—68no—
613C25—616no—
614C25—616no—
615C25—616no—
616C25—64no—
617C25—68no—
618C25—616no—
619C25—68no—
620C25—616no—
621C25—632no—
622C25—616no—
623C25—632no—
624C25C32×D412yescomplemented
625C25C2×C3×A411yescharacteristic
626C25C2×C3×A411yescharacteristic, complemented
627C25C23×C3211yescharacteristic
628C22×D4—32no—
629C22×D4—32no—
630C22×D4—34no—
631C22×D4—61no—
632C22×D4—62no—
633C22×D4—62no—
634C22×D4—62no—
635C22×D4—62no—
636C22×D4—62no—
637C22×D4—68no—
638C22×D4—62no—
639C22×D4—64no—
640C22×D4—61no—
641C22×D4—62no—
642C22×D4C2×C3×A414yescomplemented
643C23×C4—31no—
644C23×C4—31no—
645C23×C4C2×C3×A411yescharacteristic, complemented
646#120—22no—
647#120—68no—
648#120—68no—
649#120—616no—
650#120—616no—
651#120—68no—
652#120—68no—
653#120—64no—
654#120—64no—
655#120—62no—
656C2×C22⋊C4—38no—
657C2×C22⋊C4—32no—
658C2×C22⋊C4—32no—
659C2×C22⋊C4—34no—
660C2×C22⋊C4—32no—
661C2×C22⋊C4—34no—
662C2×C22⋊C4—32no—
663C2×C22⋊C4—32no—
664C2×C22⋊C4—32no—
665C2×C22⋊C4—62no—
666C2×C22⋊C4—62no—
667C2×C22⋊C4—68no—
668C2×C22⋊C4—64no—
669C2×C22⋊C4—61no—
670C2×C22⋊C4—62no—
671C2×C22⋊C4—61no—
672C2×C22⋊C4—62no—
673C2×C22⋊C4—62no—
674C2×C22⋊C4—62no—
675C2×C22⋊C4—62no—
676C23×C3—28no—
677C23×C3—22no—
678C23×C3—24no—
679C23×C3—22no—
680C23×C3—22no—
681C23×C3—32no—
682C23×C3—31no—
683C23×C3—31no—
684C23×C3—32no—
685C23×C3—38no—
686C23×C3—32no—
687C23×C3—32no—
688C23×C3—34no—
689C23×C3—32no—
690C23×C3—34no—
691C23×C3—34no—
692C23×C3—38no—
693C23×C3—32no—
694C23×C3—38no—
695C23×C3—34no—
696C23×C3—34no—
697C23×C3—32no—
698C23×C3—32no—
699C23×C3—31no—
700C23×C3—31no—
701C23×C3—31no—
702C23×C3—32no—
703C23×C3—32no—
704C23×C3—41no—
705C23×C3—62no—
706C23×C3—62no—
707C23×C3—62no—
708C23×C3—68no—
709C23×C3—68no—
710C23×C3—64no—
711C23×C3—62no—
712C23×C3—68no—
713C23×C3—62no—
714C23×C3—62no—
715C23×C3—64no—
716C23×C3—62no—
717C23×C3—62no—
718C23×C3—62no—
719C23×C3—62no—
720C23×C3—62no—
721C23×C3—64no—
722C23×C3—68no—
723C23×C3—64no—
724C23×C3—64no—
725C23×C3—64no—
726C23×C3—68no—
727C23×C3—64no—
728C23×C3—68no—
729C23×C3—62no—
730C23×C3—64no—
731C23×C3—62no—
732C23×C3—64no—
733C23×C3—62no—
734C23×C3—64no—
735C23×C3—62no—
736C23×C3—68no—
737C23×C3—64no—
738C23×C3—68no—
739C23×C3—64no—
740C23×C3—68no—
741C23×C3—64no—
742C23×C3—64no—
743C23×C3—64no—
744C23×C3—68no—
745C23×C3—64no—
746C23×C3—68no—
747C23×C3—68no—
748C23×C3—64no—
749C23×C3—64no—
750C23×C3—68no—
751C23×C3—68no—
752C23×C3—68no—
753C23×C3—616no—
754C23×C3—64no—
755C23×C3—68no—
756C23×C3—62no—
757C23×C3—64no—
758C23×C3—68no—
759C23×C3—68no—
760C23×C3—616no—
761C23×C3—632no—
762C23×C3—616no—
763C23×C3—64no—
764C23×C3—68no—
765C23×C3—64no—
766C23×C3—68no—
767C23×C3—68no—
768C23×C3—64no—
769C23×C3—62no—
770C23×C3—616no—
771C23×C3—68no—
772C23×C3—62no—
773C23×C3—64no—
774C23×C3—68no—
775C23×C3—64no—
776C23×C3—64no—
777C23×C3—62no—
778C23×C3—68no—
779C23×C3—62no—
780C23×C3—62no—
781C23×C3—64no—
782C23×C3—64no—
783C23×C3—64no—
784C23×C3—68no—
785C23×C3—68no—
786C23×C3—616no—
787C23×C3—68no—
788C23×C3—616no—
789C23×C3—616no—
790C23×C3—632no—
791C23×C3—616no—
792C23×C3—632no—
793C23×C3—616no—
794C23×C3—68no—
795C23×C3—616no—
796C23×C3—68no—
797C23×C3—616no—
798C23×C3—632no—
799C23×C3—616no—
800C23×C3—616no—
801C23×C3—632no—
802C23×C3—68no—
803C23×C3—68no—
804C23×C3—616no—
805C23×C3—616no—
806C23×C3—616no—
807C23×C3—68no—
808C23×C3—64no—
809C23×C3—64no—
810C23×C3—64no—
811C23×C3—64no—
812C23×C3—616no—
813C23×C3—68no—
814C23×C3—68no—
815C23×C3—68no—
816C23×C3—68no—
817C23×C3—616no—
818C23×C3—632no—
819C23×C3—616no—
820C23×C3—68no—
821C23×C3—68no—
822C23×C3—68no—
823C23×C3—68no—
824C23×C3—632no—
825C23×C3—616no—
826C23×C3—64no—
827C23×C3—616no—
828C23×C3—632no—
829C23×C3—632no—
830C23×C3—616no—
831C23×C3—68no—
832C23×C3—632no—
833C23×C3—616no—
834C23×C3—616no—
835C23×C3—632no—
836C23×C3—616no—
837C23×C3—632no—
838C23×C3—68no—
839C23×C3—616no—
840C23×C3—616no—
841C23×C3—616no—
842C23×C3—68no—
843C23×C3—616no—
844C23×C3—616no—
845C23×C3—632no—
846C23×C3—632no—
847C23×C3—616no—
848C23×C3—616no—
849C23×C3—632no—
850C23×C3—632no—
851C23×C3—616no—
852C23×C3—616no—
853C23×C3—632no—
854C23×C3—632no—
855C23×C3—616no—
856C23×C3—632no—
857C23×C3—632no—
858C23×C3—632no—
859C23×C3—632no—
860C23×C3—64no—
861C23×C3—68no—
862C23×C3—64no—
863C23×C3—64no—
864C23×C3—68no—
865C23×C3—68no—
866C23×C3—68no—
867C23×C3—68no—
868C23×C3—616no—
869C23×C3—616no—
870C23×C3—68no—
871C23×C3—616no—
872C23×C3—616no—
873C23×C3—68no—
874C23×C3—62no—
875C23×C3—62no—
876C23×C3—62no—
877C23×C3—64no—
878C23×C3—64no—
879C23×C3—121no—
880C23×C3—122no—
881C23×C3—122no—
882C23×C3—122no—
883C23×C3—122no—
884C23×C3—163no—
885C23×C3—163no—
886C23×C3#120⋊C311yescharacteristic, complemented
887C23×C3D4×A412yes—
888C23×C3C23×A411yescharacteristic
889C2×A4—46no—
890C2×A4—43no—
891C2×A4—812no—
892C2×A4—86no—
893C2×A4—86no—
894C2×A4—86no—
895C2×A4—824no—
896C3×D4—44no—
897C3×D4—124no—
898C3×D4—124no—
899C3×D4—128no—
900C3×D4—124no—
901C3×D4—1216no—
902C3×D4—1612no—
903C2×C3×C4—41no—
904C2×C3×C4—62no—
905C2×C3×C4—64no—
906C2×C3×C4—62no—
907C2×C3×C4—62no—
908C2×C3×C4—62no—
909C2×C3×C4—62no—
910C2×C3×C4—121no—
911C2×C3×C4—122no—
912C2×C3×C4—122no—
913C2×C3×C4—122no—
914C2×C3×C4—122no—
915C2×C3×C4—163no—
916C2×C32—161no—
917C2×C32—162no—
918C2×C32—322no—
919C2×C32—322no—
920C24—28no—
921C24—22no—
922C24—24no—
923C24—22no—
924C24—22no—
925C24—38no—
926C24—32no—
927C24—34no—
928C24—32no—
929C24—32no—
930C24—32no—
931C24—32no—
932C24—31no—
933C24—32no—
934C24—32no—
935C24—31no—
936C24—32no—
937C24—31no—
938C24—31no—
939C24—38no—
940C24—38no—
941C24—34no—
942C24—34no—
943C24—34no—
944C24—34no—
945C24—32no—
946C24—32no—
947C24—31no—
948C24—64no—
949C24—62no—
950C24—62no—
951C24—62no—
952C24—64no—
953C24—68no—
954C24—62no—
955C24—64no—
956C24—68no—
957C24—64no—
958C24—616no—
959C24—68no—
960C24—61no—
961C24—64no—
962C24—62no—
963C24—62no—
964C24—62no—
965C24—62no—
966C24—62no—
967C24—62no—
968C24—64no—
969C24—62no—
970C24—62no—
971C24—62no—
972C24—64no—
973C24—68no—
974C24—64no—
975C24—68no—
976C24—62no—
977C24—64no—
978C24—64no—
979C24—68no—
980C24—68no—
981C24—64no—
982C24—68no—
983C24—62no—
984C24—64no—
985C24—68no—
986C24—64no—
987C24—64no—
988C24—68no—
989C24—68no—
990C24—64no—
991C24—68no—
992C24—64no—
993C24—68no—
994C24—616no—
995C24—64no—
996C24—68no—
997C24—68no—
998C24—68no—
999C24—68no—
1000C24—68no—
1001C24—616no—
1002C24—632no—
1003C24—68no—
1004C24—64no—
1005C24—616no—
1006C24—64no—
1007C24—68no—
1008C24—64no—
1009C24—64no—
1010C24—64no—
1011C24—62no—
1012C24—64no—
1013C24—64no—
1014C24—64no—
1015C24—68no—
1016C24—64no—
1017C24—61no—
1018C24—62no—
1019C24—68no—
1020C24—68no—
1021C24—62no—
1022C24—64no—
1023C24—62no—
1024C24—64no—
1025C24—64no—
1026C24—68no—
1027C24—68no—
1028C24—62no—
1029C24—62no—
1030C24—64no—
1031C24—64no—
1032C24—68no—
1033C24—68no—
1034C24—616no—
1035C24—68no—
1036C24—68no—
1037C24—616no—
1038C24—64no—
1039C24—68no—
1040C24—616no—
1041C24—616no—
1042C24—68no—
1043C24—616no—
1044C24—68no—
1045C24—616no—
1046C24—64no—
1047C24—68no—
1048C24—68no—
1049C24—68no—
1050C24—68no—
1051C24—64no—
1052C24—64no—
1053C24—64no—
1054C24—616no—
1055C24—616no—
1056C24—616no—
1057C24—616no—
1058C24—632no—
1059C24—68no—
1060C24—68no—
1061C24—616no—
1062C24—632no—
1063C24—68no—
1064C24—68no—
1065C24—68no—
1066C24—64no—
1067C24—616no—
1068C24—616no—
1069C24—68no—
1070C24—68no—
1071C24—68no—
1072C24—68no—
1073C24—68no—
1074C24—616no—
1075C24—616no—
1076C24—616no—
1077C24—632no—
1078C24—616no—
1079C24—616no—
1080C24—632no—
1081C24—632no—
1082C24—616no—
1083C24—64no—
1084C24—616no—
1085C24—632no—
1086C24—616no—
1087C24—632no—
1088C24—616no—
1089C24—632no—
1090C24—616no—
1091C24—632no—
1092C24—68no—
1093C24—616no—
1094C24—68no—
1095C24—616no—
1096C24—616no—
1097C24—616no—
1098C24—632no—
1099C24—616no—
1100C24—632no—
1101C24—632no—
1102C24—68no—
1103C24—616no—
1104C24—616no—
1105C24—632no—
1106C24—616no—
1107C24—616no—
1108C24—632no—
1109C24—632no—
1110C24—616no—
1111C24—632no—
1112C24—632no—
1113C24—616no—
1114C24—632no—
1115C24—632no—
1116C24—632no—
1117C24—632no—
1118C24—616no—
1119C24—64no—
1120C24—68no—
1121C24—62no—
1122C24—62no—
1123C24C2×C32×D411yescharacteristic, complemented
1124C24C22×C3×A412yes—
1125C24C22×C3×A411yescharacteristic
1126C24C22×C3×A412yescomplemented
1127C2×D4—41no—
1128C2×D4—64no—
1129C2×D4—62no—
1130C2×D4—64no—
1131C2×D4—62no—
1132C2×D4—64no—
1133C2×D4—64no—
1134C2×D4—68no—
1135C2×D4—64no—
1136C2×D4—64no—
1137C2×D4—616no—
1138C2×D4—64no—
1139C2×D4—121no—
1140C2×D4—122no—
1141C2×D4—122no—
1142C2×D4—124no—
1143C2×D4—124no—
1144C2×D4—128no—
1145C2×D4—124no—
1146C2×D4—124no—
1147C2×D4—128no—
1148C22×C4—32no—
1149C22×C4—32no—
1150C22×C4—61no—
1151C22×C4—62no—
1152C22×C4—64no—
1153C22×C4—61no—
1154C22×C4—61no—
1155C22×C4—61no—
1156C22×C4—61no—
1157C22×C4—62no—
1158C22×C4—61no—
1159C22×C4C22×C3×A412yescomplemented
1160C22⋊C4—64no—
1161C22⋊C4—68no—
1162C22⋊C4—64no—
1163C22⋊C4—616no—
1164C22⋊C4—64no—
1165C22⋊C4—64no—
1166C22⋊C4—64no—
1167C22⋊C4—64no—
1168C22⋊C4—64no—
1169C22⋊C4—62no—
1170C22⋊C4—62no—
1171C22×C3—22no—
1172C22×C3—22no—
1173C22×C3—31no—
1174C22×C3—32no—
1175C22×C3—32no—
1176C22×C3—31no—
1177C22×C3—31no—
1178C22×C3—32no—
1179C22×C3—32no—
1180C22×C3—38no—
1181C22×C3—32no—
1182C22×C3—32no—
1183C22×C3—34no—
1184C22×C3—32no—
1185C22×C3—42no—
1186C22×C3—62no—
1187C22×C3—62no—
1188C22×C3—64no—
1189C22×C3—68no—
1190C22×C3—616no—
1191C22×C3—68no—
1192C22×C3—62no—
1193C22×C3—62no—
1194C22×C3—64no—
1195C22×C3—62no—
1196C22×C3—68no—
1197C22×C3—64no—
1198C22×C3—62no—
1199C22×C3—62no—
1200C22×C3—68no—
1201C22×C3—64no—
1202C22×C3—62no—
1203C22×C3—64no—
1204C22×C3—68no—
1205C22×C3—64no—
1206C22×C3—64no—
1207C22×C3—616no—
1208C22×C3—68no—
1209C22×C3—68no—
1210C22×C3—64no—
1211C22×C3—68no—
1212C22×C3—62no—
1213C22×C3—64no—
1214C22×C3—62no—
1215C22×C3—62no—
1216C22×C3—64no—
1217C22×C3—68no—
1218C22×C3—68no—
1219C22×C3—68no—
1220C22×C3—64no—
1221C22×C3—68no—
1222C22×C3—616no—
1223C22×C3—616no—
1224C22×C3—68no—
1225C22×C3—616no—
1226C22×C3—64no—
1227C22×C3—616no—
1228C22×C3—616no—
1229C22×C3—64no—
1230C22×C3—68no—
1231C22×C3—616no—
1232C22×C3—632no—
1233C22×C3—68no—
1234C22×C3—616no—
1235C22×C3—632no—
1236C22×C3—62no—
1237C22×C3—62no—
1238C22×C3—64no—
1239C22×C3—64no—
1240C22×C3—68no—
1241C22×C3—64no—
1242C22×C3—62no—
1243C22×C3—82no—
1244C22×C3—122no—
1245C22×C3—122no—
1246C22×C3—166no—
1247C22×C3—163no—
1248C22×C3—166no—
1249C22×C3—242no—
1250C22×C3—326no—
1251C22×C3—326no—
1252C22×C3C2×#120⋊C311yescharacteristic
1253C22×C3C2×#120⋊C312yescomplemented
1254C22×C3C2×D4×A411yescharacteristic
1255A4—43no—
1256A4—86no—
1257C3×C4—42no—
1258C3×C4—122no—
1259C3×C4—122no—
1260C3×C4—166no—
1261C32—161noSylow
1262C23—28no—
1263C23—22no—
1264C23—24no—
1265C23—22no—
1266C23—22no—
1267C23—32no—
1268C23—31no—
1269C23—31no—
1270C23—32no—
1271C23—32no—
1272C23—38no—
1273C23—32no—
1274C23—32no—
1275C23—34no—
1276C23—34no—
1277C23—34no—
1278C23—38no—
1279C23—32no—
1280C23—34no—
1281C23—34no—
1282C23—38no—
1283C23—32no—
1284C23—31no—
1285C23—32no—
1286C23—31no—
1287C23—31no—
1288C23—32no—
1289C23—32no—
1290C23—41no—
1291C23—62no—
1292C23—62no—
1293C23—62no—
1294C23—68no—
1295C23—68no—
1296C23—64no—
1297C23—62no—
1298C23—68no—
1299C23—62no—
1300C23—62no—
1301C23—64no—
1302C23—62no—
1303C23—62no—
1304C23—62no—
1305C23—62no—
1306C23—62no—
1307C23—64no—
1308C23—68no—
1309C23—64no—
1310C23—64no—
1311C23—64no—
1312C23—68no—
1313C23—64no—
1314C23—68no—
1315C23—62no—
1316C23—64no—
1317C23—62no—
1318C23—64no—
1319C23—62no—
1320C23—64no—
1321C23—62no—
1322C23—64no—
1323C23—68no—
1324C23—64no—
1325C23—64no—
1326C23—68no—
1327C23—64no—
1328C23—68no—
1329C23—64no—
1330C23—68no—
1331C23—64no—
1332C23—68no—
1333C23—68no—
1334C23—64no—
1335C23—64no—
1336C23—68no—
1337C23—68no—
1338C23—68no—
1339C23—616no—
1340C23—64no—
1341C23—68no—
1342C23—62no—
1343C23—64no—
1344C23—68no—
1345C23—68no—
1346C23—616no—
1347C23—64no—
1348C23—68no—
1349C23—616no—
1350C23—632no—
1351C23—64no—
1352C23—68no—
1353C23—68no—
1354C23—64no—
1355C23—62no—
1356C23—616no—
1357C23—68no—
1358C23—62no—
1359C23—64no—
1360C23—68no—
1361C23—64no—
1362C23—64no—
1363C23—62no—
1364C23—68no—
1365C23—62no—
1366C23—62no—
1367C23—64no—
1368C23—64no—
1369C23—64no—
1370C23—68no—
1371C23—68no—
1372C23—616no—
1373C23—68no—
1374C23—616no—
1375C23—616no—
1376C23—632no—
1377C23—616no—
1378C23—632no—
1379C23—616no—
1380C23—68no—
1381C23—616no—
1382C23—68no—
1383C23—616no—
1384C23—632no—
1385C23—616no—
1386C23—616no—
1387C23—632no—
1388C23—68no—
1389C23—68no—
1390C23—616no—
1391C23—616no—
1392C23—616no—
1393C23—68no—
1394C23—64no—
1395C23—64no—
1396C23—64no—
1397C23—64no—
1398C23—616no—
1399C23—68no—
1400C23—68no—
1401C23—68no—
1402C23—68no—
1403C23—616no—
1404C23—632no—
1405C23—616no—
1406C23—68no—
1407C23—68no—
1408C23—68no—
1409C23—68no—
1410C23—632no—
1411C23—616no—
1412C23—632no—
1413C23—64no—
1414C23—616no—
1415C23—632no—
1416C23—616no—
1417C23—68no—
1418C23—632no—
1419C23—616no—
1420C23—616no—
1421C23—632no—
1422C23—616no—
1423C23—632no—
1424C23—68no—
1425C23—616no—
1426C23—616no—
1427C23—616no—
1428C23—68no—
1429C23—616no—
1430C23—616no—
1431C23—632no—
1432C23—632no—
1433C23—616no—
1434C23—616no—
1435C23—632no—
1436C23—632no—
1437C23—616no—
1438C23—616no—
1439C23—632no—
1440C23—632no—
1441C23—616no—
1442C23—632no—
1443C23—632no—
1444C23—632no—
1445C23—632no—
1446C23—64no—
1447C23—68no—
1448C23—64no—
1449C23—64no—
1450C23—68no—
1451C23—68no—
1452C23—68no—
1453C23—68no—
1454C23—616no—
1455C23—616no—
1456C23—68no—
1457C23—616no—
1458C23—616no—
1459C23—68no—
1460C23—62no—
1461C23—62no—
1462C23—62no—
1463C23—64no—
1464C23—64no—
1465C23—121no—
1466C23—122no—
1467C23—122no—
1468C23—122no—
1469C23—122no—
1470C23C3×#120⋊C311yescharacteristic, complemented
1471C23C3×D4×A412yes—
1472C23C23×C3×A411yescharacteristic
1473D4—44no—
1474D4—124no—
1475D4—124no—
1476D4—128no—
1477D4—124no—
1478D4—1216no—
1479C2×C4—41no—
1480C2×C4—62no—
1481C2×C4—62no—
1482C2×C4—64no—
1483C2×C4—62no—
1484C2×C4—62no—
1485C2×C4—62no—
1486C2×C4—121no—
1487C2×C4—122no—
1488C2×C4—122no—
1489C2×C4—122no—
1490C2×C4—122no—
1491C2×C3—22no—
1492C2×C3—31no—
1493C2×C3—31no—
1494C2×C3—32no—
1495C2×C3—62no—
1496C2×C3—68no—
1497C2×C3—62no—
1498C2×C3—64no—
1499C2×C3—62no—
1500C2×C3—82no—
1501C2×C3—163no—
1502C2×C3—166no—
1503C2×C3—326no—
1504C2×C3—326no—
1505C2×C3AΣL(1,𝔽64)12yesdirect product factor
1506C2×C3C22×#120⋊C311yescharacteristic
1507C22—22no—
1508C22—22no—
1509C22—31no—
1510C22—32no—
1511C22—32no—
1512C22—31no—
1513C22—31no—
1514C22—32no—
1515C22—32no—
1516C22—32no—
1517C22—32no—
1518C22—34no—
1519C22—38no—
1520C22—32no—
1521C22—42no—
1522C22—62no—
1523C22—62no—
1524C22—64no—
1525C22—68no—
1526C22—616no—
1527C22—68no—
1528C22—62no—
1529C22—62no—
1530C22—62no—
1531C22—68no—
1532C22—64no—
1533C22—62no—
1534C22—64no—
1535C22—64no—
1536C22—62no—
1537C22—68no—
1538C22—64no—
1539C22—62no—
1540C22—68no—
1541C22—64no—
1542C22—64no—
1543C22—616no—
1544C22—68no—
1545C22—68no—
1546C22—64no—
1547C22—68no—
1548C22—62no—
1549C22—64no—
1550C22—62no—
1551C22—62no—
1552C22—64no—
1553C22—68no—
1554C22—68no—
1555C22—68no—
1556C22—64no—
1557C22—68no—
1558C22—616no—
1559C22—616no—
1560C22—68no—
1561C22—616no—
1562C22—64no—
1563C22—616no—
1564C22—616no—
1565C22—64no—
1566C22—68no—
1567C22—616no—
1568C22—632no—
1569C22—68no—
1570C22—616no—
1571C22—632no—
1572C22—62no—
1573C22—62no—
1574C22—64no—
1575C22—64no—
1576C22—68no—
1577C22—64no—
1578C22—62no—
1579C22—82no—
1580C22—122no—
1581C22—122no—
1582C22—242no—
1583C22C2×C3×#120⋊C311yescharacteristic
1584C22C2×C3×#120⋊C312yescomplemented
1585C22C2×C3×D4×A411yescharacteristic
1586C4—42no—
1587C4—122no—
1588C4—122no—
1589C3—163no—
1590C3C2×AΣL(1,𝔽64)11yescharacteristic, direct product factor
1591C2—22no—
1592C2—31no—
1593C2—31no—
1594C2—32no—
1595C2—62no—
1596C2—68no—
1597C2—62no—
1598C2—64no—
1599C2—62no—
1600C2—82no—
1601C2C3×AΣL(1,𝔽64)12yesdirect product factor
1602C2C22×C3×#120⋊C311yescharacteristic
subgroupG/H
centerC22×C3C2×#120⋊C3
commutator, cosocleC25C23×C32
FrattiniC23C23×C3×A4
FittingC2×C3×#2846C3
socleC24×C3C22×A4
hypercenterC23×C3#120⋊C3
hypocenterC24C2×C32×D4
LCSG ▷ C25 ▷ C24
UCSC1 ◁ C22×C3 ◁ C23×C3

Complements

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

NH ≅ G/Ntype
1. C23×C3×C22⋊A4C2semidirect
2. C22×C3×#120⋊C3C2semidirect
3. C3×AΣL(1,𝔽64)C2direct (N × H)
4. C2×C3×#379⋊C3C2semidirect
5. C2×AΣL(1,𝔽64)C3direct (N × H)
6. C2×C3×#2846C3semidirect
9. C22×C3×C22⋊A4C22semidirect
12. C2×C3×#120⋊C3C22semidirect
13. C3×#379⋊C3C22semidirect
14. C27×C3C2×C3semidirect
15. C23×C22⋊A4C2×C3semidirect
18. C22×C3×#120C2×C3semidirect
19. C22×#120⋊C3C2×C3semidirect
21. C3×#2846C2×C3semidirect
24. C2×C3×#379C2×C3semidirect
25. AΣL(1,𝔽64)C2×C3direct (N × H)
26. C2×#379⋊C3C2×C3semidirect
28. C2×C3×C22⋊A4D4semidirect
36. C2×#2846C32semidirect
47. C26×C3C22×C3semidirect
50. C22×C22⋊A4C22×C3semidirect
53. C23×C3×D4A4semidirect
66. C2×C3×#120C22×C3semidirect
74. C2×#120⋊C3C22×C3semidirect
80. C3×#379C22×C3semidirect
81. #379⋊C3C22×C3semidirect
82. C3×C22⋊A4C2×D4semidirect
93. C27C2×C32semidirect
96. C22×#120C2×C32semidirect
98. #2846C2×C32semidirect
101. C2×#379C2×C32semidirect
173. C25×C3C3×D4semidirect
175. C25×C3C2×A4semidirect
178. C2×C22⋊A4C3×D4semidirect
197. C22×C3×D4C2×A4semidirect
200. C23×C3×C4C2×A4semidirect
255. C26C22×C32semidirect
258. C23×D4C3×A4semidirect
270. C2×#120C22×C32semidirect
282. #379C22×C32semidirect
486. C24×C3C2×C3×D4semidirect
489. C24×C3C22×A4semidirect
490. C22⋊A4C2×C3×D4semidirect
532. C22×C3×C4C22×A4semidirect
624. C25C32×D4semidirect
626. C25C2×C3×A4semidirect
642. C22×D4C2×C3×A4semidirect
645. C23×C4C2×C3×A4semidirect
886. C23×C3#120⋊C3semidirect
1123. C24C2×C32×D4semidirect
1126. C24C22×C3×A4semidirect
1159. C22×C4C22×C3×A4semidirect
1253. C22×C3C2×#120⋊C3semidirect
1470. C23C3×#120⋊C3semidirect
1505. C2×C3AΣL(1,𝔽64)direct (N × H)
1584. C22C2×C3×#120⋊C3semidirect
1590. C3C2×AΣL(1,𝔽64)direct (N × H)
1601. C2C3×AΣL(1,𝔽64)direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C22⋊A42
C22×C3×#120⋊C32
C3×AΣL(1,𝔽64)2
C2×C3×#379⋊C32
C2×AΣL(1,𝔽64)3
C2×C3×#28463
C2×C3×D4×A44