Finite Group Databasebeta

← #72271719

Subgroups — #72271719

Order 1536.

46820 conjugacy classes of subgroups.

The subgroup lattice has 1312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#1009C211yesmaximal, characteristic, complemented
2C2×#87298C212yesmaximal, complemented
3#11661728C2116yesmaximal, complemented
4#11661717C2116yesmaximal, complemented
5#11661668C2112yesmaximal, complemented
6#11661579C216yesmaximal, complemented
7C2×#82927C216yesmaximal, complemented
8#11658757C212yesmaximal, complemented
9#11658639C211yesmaximal, characteristic, complemented
10C3×#62811C211yesmaximal, characteristic, complemented
11#10574840—31nomaximal, Sylow
12C2×C3×#585C2211yescharacteristic, complemented
13C23×C3×#41C2211yescharacteristic
14C22×#1009—23no—
15C22×#1009—21no—
16C22×#1009—28no—
17C22×#1009—232no—
18C22×#1009C2212yes—
19C22×#1009C2216yescomplemented
20C22×#1009C22116yescomplemented
21C23×#239—21no—
22C23×D3×D4—23no—
23C23×#235C2213yescomplemented
24C24×D12C2213yescomplemented
25C3×#3489C2218yescomplemented
26C3×#3488C2218yescomplemented
27C3×#3487—21no—
28C3×#3486—21no—
29C3×#3485—23no—
30C3×#3484—23no—
31C3×D4×#41—28no—
32C3×#3449C2216yescomplemented
33C2×C3×#525C2216yescomplemented
34C3×#3428C2211yescharacteristic, complemented
35#87298—232no—
36C2×#5837C22116yescomplemented
37C2×#5835C22116yescomplemented
38C2×#5822C22112yescomplemented
39C22×#949C22112yescomplemented
40C2×#5819C2212yescomplemented
41#84075C22116yescomplemented
42#84074C2216yescomplemented
43C2×#5207C2216yescomplemented
44#83424C22196yescomplemented
45#83404C22148yescomplemented
46#83383C22148yescomplemented
47#82933C2214yescomplemented
48#82928C22124yescomplemented
49#82927C22112yescomplemented
50#82927C22124yescomplemented
51#82927C22148yescomplemented
52#82926C22148yescomplemented
53#82735C22124yescomplemented
54C2×#5046C22124yescomplemented
55#82624C22124yescomplemented
56C2×#5036C22124yescomplemented
57#82563C22132yescomplemented
58#82213C22112yescomplemented
59C2×#5001C22112yescomplemented
60C23×H(5,𝔽2)—31no—
61C2×#3585—32no—
62#62811D311yescharacteristic, complemented
63#60373—316no—
64#60372—316no—
65#60367—312no—
66#60359—36no—
67C2×#3003—36no—
68#60087—32no—
69#60064—31no—
70C25×D3—23no—
71C3×#585—216no—
72C2×C3×2−1+4—21no—
73C2×C3×2−1+4C2314yescomplemented
74C2×C3×H(5,𝔽2)—23no—
75C2×C3×H(5,𝔽2)C2314yescomplemented
76C22×C3×#41—216no—
77C22×C3×#41—24no—
78C22×C3×#41D418yes—
79C22×C3×#41D413yes—
80C22×C3×#41D411yescharacteristic
81C22×C3×#41C2313yes—
82C22×C3×#41C2318yes—
83C22×C3×#41C2311yescharacteristic
84C22×C3×#41C2316yescomplemented
85C23×C3×Q8D411yescharacteristic
86C23×C3×D4D413yes—
87C24×C3×C4C2313yes—
88C23×#67—23no—
89C2×#1009—2256no—
90C2×#1009—232no—
91C2×#1009—296no—
92C2×#1009—216no—
93C2×#1009—28no—
94C2×#1009—224no—
95C2×#1009—248no—
96C2×#1009—216no—
97C2×#1009—2256no—
98C2×#1009—248no—
99C2×#1009—248no—
100C2×#1009D4132yescomplemented
101C2×#1009C23148yes—
102C2×#1009C23116yes—
103C22×#239—232no—
104C22×#239—22no—
105C22×#239—26no—
106C22×#239—216no—
107C22×D3×D4—296no—
108C22×D3×D4—26no—
109C22×D3×D4—212no—
110C22×D3×D4—26no—
111C22×D3×D4—248no—
112C22×#235—212no—
113C22×#235—23no—
114C22×#235—23no—
115C22×#235—248no—
116C22×#235C23124yes—
117C22×#235C2316yes—
118C22×#235C2316yes—
119C23×D12—23no—
120C23×D12—212no—
121C23×D12—23no—
122C23×D12—23no—
123C23×D12—248no—
124C23×D12C2313yes—
125C23×D12C23124yes—
126C23×D12C2316yes—
127C23×D12C2316yes—
128C23×C4×D3—23no—
129C23×Dic6C2311yescharacteristic
130C3×#550—28no—
131C3×D4×Q8—28no—
132C3×#548—28no—
133C3×#548—28no—
134C3×#547—224no—
135C3×#546—224no—
136C3×#546—224no—
137C3×D42—224no—
138C3×#537C23124yescomplemented
139C3×#536—26no—
140C3×#536C23112yescomplemented
141C3×#535—26no—
142C3×#535C23112yescomplemented
143C3×#534—212no—
144C3×#532—212no—
145C3×#525—212no—
146C3×#525—212no—
147C3×#525—26no—
148C3×#525—26no—
149C3×#525C2314yes—
150C3×#525C23112yescomplemented
151C3×#525C23124yescomplemented
152C2×C3×#123—26no—
153C2×C3×C22⋊Q8C23112yescomplemented
154C2×C3×#121C23112yescomplemented
155C2×C3×#120—26no—
156C3×#520C2318yescomplemented
157C3×#519—21no—
158C3×#518—23no—
159C3×C4×#41—24no—
160C2×C3×C4×D4—212no—
161C2×C3×#117C2316yescomplemented
162#5837—2128no—
163#5835—2128no—
164C2×#951C2318yescomplemented
165#5822—296no—
166C2×#950C23148yescomplemented
167C2×#949—296no—
168C2×#949C23124yescomplemented
169C2×#949C23148yescomplemented
170#5819—216no—
171C2×#948C23116yescomplemented
172C2×#942C23124yescomplemented
173C22×#215C23124yescomplemented
174C2×#932C23124yescomplemented
175C22×#213C23124yescomplemented
176C22×#208C23112yescomplemented
177#5234C23148yescomplemented
178#5207C2314yes—
179#5207C23124yescomplemented
180#5207C23112yescomplemented
181C2×#830C23124yescomplemented
182#5050C23116yescomplemented
183#5047C23196yescomplemented
184#5046C23148yescomplemented
185#5046C23196yescomplemented
186#5040C23116yescomplemented
187#5037C23196yescomplemented
188#5036C23148yescomplemented
189#5036C23196yescomplemented
190#5004C2318yescomplemented
191#5002C23148yescomplemented
192#5001C23124yescomplemented
193#5001C23148yescomplemented
194#4966C23148yescomplemented
195C2×#809C23148yescomplemented
196C2×#585C2×D311yescharacteristic, complemented
197C22×H(5,𝔽2)—32no—
198C22×H(5,𝔽2)—36no—
199C22×H(5,𝔽2)—316no—
200C22×H(5,𝔽2)—632no—
201C22×H(5,𝔽2)—68no—
202C22×H(5,𝔽2)—63no—
203C22×H(5,𝔽2)—61no—
204C23×#41—33no—
205C23×#41—61no—
206C23×#41C2×D311yescharacteristic
207C24×D4—33no—
208C24×D4—63no—
209#3585—632no—
210C2×#577—316no—
211C2×#576—316no—
212C2×#575—312no—
213C22×AGL(1,ℤ/8)—312no—
214C2×#568—32no—
215#3489C2×D318yescomplemented
216#3488C2×D318yescomplemented
217#3487—21no—
218#3486—21no—
219#3485—23no—
220#3484—23no—
221D4×#41—28no—
222#3449C2×D316yescomplemented
223C2×#525C2×D316yescomplemented
224#3428C2×D311yescharacteristic, complemented
225#3012—396no—
226#3009—348no—
227#3008—348no—
228#3007—324no—
229#3006—324no—
230#3005—324no—
231#3004—34no—
232#3003—312no—
233#3003—324no—
234#3003—348no—
235#3002—348no—
236C2×#450—324no—
237C2×#447—324no—
238#2897—332no—
239#2896—312no—
240C2×#418—312no—
241#2880—316no—
242#2879—36no—
243C2×#407—36no—
244C25×C3C2×D413yes—
245C24×D3—23no—
246C24×D3—248no—
247C24×D3—224no—
248C24×D3—26no—
249C24×D3—26no—
250C24×D3—824no—
251C3×2−1+4—232no—
252C3×2−1+4—48no—
253C3×H(5,𝔽2)—232no—
254C3×H(5,𝔽2)—424no—
255C2×C3×#41—264no—
256C2×C3×#41—264no—
257C2×C3×#41—28no—
258C2×C3×#41—24no—
259C2×C3×#41—224no—
260C2×C3×#41—212no—
261C2×C3×#41—224no—
262C2×C3×#41—26no—
263C2×C3×#41—26no—
264C2×C3×#41—248no—
265C2×C3×#41—432no—
266C2×C3×#41C2×D4116yes—
267C2×C3×#41C2×D4112yes—
268C2×C3×#41C2×D4124yes—
269C2×C3×#41C2×D418yes—
270C2×C3×#41C2×D414yes—
271C2×C3×#41C2414yes—
272C2×C3×#41C24112yes—
273C2×C3×#41C2414yes—
274C2×C3×#41C24112yescomplemented
275C22×C3×Q8—28no—
276C22×C3×Q8—24no—
277C22×C3×Q8C2×D413yes—
278C22×C3×Q8C2×D418yes—
279C22×C3×Q8C2×D411yescharacteristic
280C22×C3×Q8C2416yescomplemented
281C22×C3×D4—224no—
282C22×C3×D4—26no—
283C22×C3×D4—212no—
284C22×C3×D4—212no—
285C22×C3×D4C2×D416yes—
286C22×C3×D4C2×D413yes—
287C22×C3×D4C2×D4124yes—
288C22×C3×D4C2×D413yes—
289C22×C3×D4C2416yescomplemented
290C23×C3×C4—224no—
291C23×C3×C4—26no—
292C23×C3×C4C2×D413yes—
293C23×C3×C4C2×D4112yes—
294C23×C3×C4C2×D413yes—
295C23×C3×C4C2×D413yes—
296C23×C3×C4C2411yescharacteristic
297C23×C3×C4C24112yes—
298C23×C3×C4C2413yes—
299C23×C3×C4C2413yes—
300C22×#67—248no—
301C22×#67—224no—
302C22×#67—26no—
303C22×#67—26no—
304C23×Dic3—21no—
305#1009—2256no—
306#1009—2768no—
307#1009—2384no—
308#1009—2128no—
309#1009—264no—
310#1009—2192no—
311#1009—2192no—
312#1009C2×D41128yescomplemented
313C2×#239—2256no—
314C2×#239—296no—
315C2×#239—232no—
316C2×#239—248no—
317C2×#239—216no—
318C2×D3×D4—2192no—
319C2×D3×D4—2768no—
320C2×D3×D4—296no—
321C2×D3×D4—296no—
322C2×D3×D4—296no—
323C2×D3×D4—248no—
324C2×D3×D4—248no—
325C2×#235—248no—
326C2×#235—2192no—
327C2×#235—248no—
328C2×#235—224no—
329C2×#235—224no—
330C2×#235—212no—
331C2×#235—224no—
332C2×#235—212no—
333C2×#235—2192no—
334C2×#235—224no—
335C2×#235—224no—
336C2×#235C2×D4148yescomplemented
337C2×#235C24124yes—
338C2×#235C24124yes—
339C22×D12—248no—
340C22×D12—248no—
341C22×D12—2192no—
342C22×D12—248no—
343C22×D12—26no—
344C22×D12—23no—
345C22×D12—224no—
346C22×D12—26no—
347C22×D12—26no—
348C22×D12—224no—
349C22×D12—224no—
350C22×D12—212no—
351C22×D12—224no—
352C22×D12—212no—
353C22×D12—224no—
354C22×D12—248no—
355C22×D12—2192no—
356C22×D12C2×D4148yescomplemented
357C22×D12C24112yes—
358C22×D12C24124yes—
359C22×D12C2416yes—
360C22×D12C24124yes—
361C22×C4×D3—248no—
362C22×C4×D3—224no—
363C22×C4×D3—26no—
364C22×C4×D3—26no—
365C22×Dic6—22no—
366C22×Dic6—21no—
367C22×Dic6—28no—
368C22×Dic6C2414yes—
369C22×Dic6C2412yes—
370C3×C4⋊Q8—212no—
371C3×#127—212no—
372C3×#124—212no—
373C3×#124—212no—
374C3×#123—224no—
375C3×#123—24no—
376C3×#123—212no—
377C3×#123—224no—
378C3×C22⋊Q8—224no—
379C3×C22⋊Q8—212no—
380C3×C22⋊Q8—212no—
381C3×C22⋊Q8C2418yes—
382C3×C22⋊Q8C24124yescomplemented
383C3×#121—224no—
384C3×#121—248no—
385C3×#121—212no—
386C3×#121—212no—
387C3×#121C2418yes—
388C3×#121C24124yescomplemented
389C3×#120—24no—
390C3×#120—212no—
391C3×#120—224no—
392C3×#120—224no—
393C3×C4×Q8—28no—
394C3×C4×D4—224no—
395C3×C4×D4—28no—
396C3×C4×D4—224no—
397C3×C4×D4—224no—
398C3×C4×D4—224no—
399C3×#117—26no—
400C3×#117—26no—
401C3×#117C2414yes—
402C3×#117C24112yescomplemented
403C2×C3×C4⋊C4—212no—
404C2×C3×C4⋊C4C24112yescomplemented
405C2×C3×C22⋊C4—26no—
406C2×C3×C22⋊C4—212no—
407C2×C3×C22⋊C4—212no—
408C2×C3×C42—26no—
409#951—232no—
410#950—2192no—
411#949—296no—
412#949—2192no—
413#948—264no—
414C2×#216C24116yescomplemented
415#942—296no—
416C2×#215—296no—
417C2×#215C24148yescomplemented
418C2×#214C24116yescomplemented
419#932—296no—
420C2×#213—296no—
421C2×#213C24148yescomplemented
422C2×#208—248no—
423C2×#208C2418yes—
424C2×#208C24124yescomplemented
425C22×C3⋊C8C24124yescomplemented
426#830C24116yes—
427#830C24148yescomplemented
428#810C24132yescomplemented
429#809C24196yescomplemented
430C26—63no—
431#585—216no—
432C2×2−1+4—21no—
433C2×2−1+4C22×D314yescomplemented
434C2×H(5,𝔽2)—23no—
435C2×H(5,𝔽2)—332no—
436C2×H(5,𝔽2)—316no—
437C2×H(5,𝔽2)—348no—
438C2×H(5,𝔽2)—648no—
439C2×H(5,𝔽2)—648no—
440C2×H(5,𝔽2)—6256no—
441C2×H(5,𝔽2)—6256no—
442C2×H(5,𝔽2)—632no—
443C2×H(5,𝔽2)—696no—
444C2×H(5,𝔽2)—616no—
445C2×H(5,𝔽2)—624no—
446C2×H(5,𝔽2)—648no—
447C2×H(5,𝔽2)—616no—
448C2×H(5,𝔽2)—68no—
449C2×H(5,𝔽2)C22×D314yescomplemented
450C22×#41—216no—
451C22×#41—24no—
452C22×#41—36no—
453C22×#41—324no—
454C22×#41—36no—
455C22×#41—648no—
456C22×#41—632no—
457C22×#41—66no—
458C22×#41—616no—
459C22×#41—62no—
460C22×#41—612no—
461C22×#41—63no—
462C22×#41—63no—
463C22×#41#6718yes—
464C22×#41#6713yes—
465C22×#41#6711yescharacteristic
466C22×#41C22×D313yes—
467C22×#41C22×D318yes—
468C22×#41C22×D311yescharacteristic
469C22×#41C22×D316yescomplemented
470C23×Q8—31no—
471C23×Q8#6711yescharacteristic
472C23×D4—36no—
473C23×D4—33no—
474C23×D4—324no—
475C23×D4—36no—
476C23×D4—648no—
477C23×D4—696no—
478C23×D4—63no—
479C23×D4—612no—
480C23×D4—66no—
481C23×D4—648no—
482C23×D4—66no—
483C23×D4—63no—
484C23×D4—612no—
485C23×D4—63no—
486C23×D4—63no—
487C23×D4#6713yes—
488C24×C4—63no—
489C24×C4C22×D313yes—
490#577—6128no—
491#576—6128no—
492#575—696no—
493C2×#137—38no—
494C2×#137—324no—
495C2×AGL(1,ℤ/8)—324no—
496C2×AGL(1,ℤ/8)—348no—
497C2×AGL(1,ℤ/8)—324no—
498C2×AGL(1,ℤ/8)—696no—
499C2×#135—348no—
500C22×SD16—324no—
501C22×D8—324no—
502#568—616no—
503C2×#131—316no—
504C22×M16—312no—
505#550—28no—
506D4×Q8—28no—
507#548—28no—
508#548—28no—
509#547—224no—
510#546—224no—
511#546—224no—
512D42—224no—
513#537C22×D3124yescomplemented
514#536—26no—
515#536C22×D3112yescomplemented
516#535—26no—
517#535C22×D3112yescomplemented
518#534—212no—
519#532—212no—
520#525—212no—
521#525—212no—
522#525—26no—
523#525—26no—
524#525C22×D314yes—
525#525C22×D3112yescomplemented
526#525C22×D3124yescomplemented
527C2×#123—26no—
528C2×C22⋊Q8C22×D3112yescomplemented
529C2×#121C22×D3112yescomplemented
530C2×#120—26no—
531#520C22×D318yescomplemented
532#519—21no—
533#518—23no—
534C4×#41—24no—
535C2×C4×D4—212no—
536C2×#117C22×D316yescomplemented
537#452—396no—
538#451—316no—
539#450—348no—
540#450—396no—
541#449—396no—
542#448—316no—
543#447—348no—
544#447—396no—
545#419—38no—
546#418—324no—
547#418—348no—
548#417—348no—
549#416—348no—
550C2×#102—348no—
551#408—348no—
552#407—34no—
553#407—312no—
554#407—324no—
555C2×C22⋊C8—324no—
556C24×C3—212no—
557C24×C3—26no—
558C24×C3—412no—
559C24×C3C22×D411yescharacteristic
560C24×C3C22×D4112yes—
561C24×C3C22×D413yes—
562C24×C3C22×D413yes—
563C23×D3—224no—
564C23×D3—212no—
565C23×D3—26no—
566C23×D3—2192no—
567C23×D3—248no—
568C23×D3—248no—
569C23×D3—224no—
570C23×D3—224no—
571C23×D3—424no—
572C23×D3—848no—
573C23×D3—824no—
574C23×D3—848no—
575C23×D3—824no—
576C23×D3—8192no—
577C3×#41—232no—
578C3×#41—296no—
579C3×#41—248no—
580C3×#41—248no—
581C3×#41—216no—
582C3×#41—248no—
583C3×#41—416no—
584C3×#41—448no—
585C3×#41—424no—
586C3×#41—424no—
587C3×#41#120132yes—
588C3×#41C22×D4132yes—
589C2×C3×Q8—232no—
590C2×C3×Q8—212no—
591C2×C3×Q8—26no—
592C2×C3×Q8—224no—
593C2×C3×Q8—416no—
594C2×C3×Q8#12018yes—
595C2×C3×Q8C22×D4112yes—
596C2×C3×Q8C22×D414yes—
597C2×C3×Q8C2514yes—
598C2×C3×D4—224no—
599C2×C3×D4—296no—
600C2×C3×D4—28no—
601C2×C3×D4—24no—
602C2×C3×D4—212no—
603C2×C3×D4—224no—
604C2×C3×D4—212no—
605C2×C3×D4—224no—
606C2×C3×D4—26no—
607C2×C3×D4—424no—
608C2×C3×D4—448no—
609C2×C3×D4—824no—
610C2×C3×D4#120124yes—
611C2×C3×D4C22×D4124yes—
612C2×C3×D4C22×D4112yes—
613C2×C3×D4C22×D4112yes—
614C2×C3×D4C2514yes—
615C22×C3×C4—212no—
616C22×C3×C4—212no—
617C22×C3×C4—212no—
618C22×C3×C4—248no—
619C22×C3×C4—24no—
620C22×C3×C4—212no—
621C22×C3×C4—248no—
622C22×C3×C4—26no—
623C22×C3×C4—212no—
624C22×C3×C4—24no—
625C22×C3×C4—212no—
626C22×C3×C4—424no—
627C22×C3×C4C22×D4124yes—
628C22×C3×C4C22×D4112yes—
629C22×C3×C4C22×D412yes—
630C22×C3×C4C22×D416yes—
631C22×C3×C4C22×D4112yes—
632C22×C3×C4C22×D4112yes—
633C22×C3×C4C22×D411yescharacteristic
634C22×C3×C4C22×D413yes—
635C22×C3×C4C22×D416yes—
636C22×C3×C4C22×D413yes—
637C22×C3×C4C2512yes—
638C22×C3×C4C2516yes—
639C22×C3×C4C2516yes—
640C22×C3×C4C2511yescharacteristic
641C2×#67—2192no—
642C2×#67—248no—
643C2×#67—248no—
644C2×#67—224no—
645C2×#67—224no—
646C22×Dic3—28no—
647C22×Dic3—24no—
648C22×Dic3—22no—
649#239—2384no—
650#239—2128no—
651D3×D4—2768no—
652D3×D4—2384no—
653D3×D4—2384no—
654#235—2192no—
655#235—2192no—
656#235—296no—
657#235—296no—
658#235—248no—
659#235—248no—
660#235—248no—
661#235C22×D4196yes—
662C2×D12—224no—
663C2×D12—248no—
664C2×D12—248no—
665C2×D12—2192no—
666C2×D12—2192no—
667C2×D12—2192no—
668C2×D12—296no—
669C2×D12—248no—
670C2×D12—296no—
671C2×D12—212no—
672C2×D12—212no—
673C2×D12—26no—
674C2×D12—224no—
675C2×D12—224no—
676C2×D12—248no—
677C2×D12—248no—
678C2×D12—296no—
679C2×D12C22×D4196yes—
680C2×D12C22×D4124yes—
681C2×D12C25112yes—
682C2×C4×D3—248no—
683C2×C4×D3—2192no—
684C2×C4×D3—248no—
685C2×C4×D3—224no—
686C2×C4×D3—224no—
687C2×Dic6—28no—
688C2×Dic6—216no—
689C2×Dic6—24no—
690C2×Dic6—24no—
691C2×Dic6—22no—
692C2×Dic6—216no—
693C2×Dic6C22×D418yes—
694C2×Dic6C2514yes—
695C3×C4⋊C4—28no—
696C3×C4⋊C4—224no—
697C3×C4⋊C4—212no—
698C3×C4⋊C4C2518yes—
699C3×C22⋊C4—24no—
700C3×C22⋊C4—28no—
701C3×C22⋊C4—212no—
702C3×C22⋊C4—224no—
703C3×C22⋊C4—28no—
704C3×C22⋊C4—224no—
705C3×C42—24no—
706C3×C42—212no—
707#216—232no—
708#215—296no—
709#214—232no—
710#213—296no—
711#208—216no—
712#208—248no—
713C2×C3⋊C8—248no—
714C2×C3⋊C8C25116yes—
715C25—648no—
716C25—63no—
717C25—624no—
718C25—66no—
719C25—66no—
720C25—2424no—
721C25C2×#6713yes—
7222−1+4—232no—
7232−1+4—48no—
724H(5,𝔽2)—232no—
725H(5,𝔽2)—3128no—
726H(5,𝔽2)—424no—
727H(5,𝔽2)—6192no—
728H(5,𝔽2)—6192no—
729H(5,𝔽2)—6256no—
730H(5,𝔽2)—6768no—
731H(5,𝔽2)—6384no—
732H(5,𝔽2)—6128no—
733H(5,𝔽2)—664no—
734C2×#41—264no—
735C2×#41—264no—
736C2×#41—28no—
737C2×#41—24no—
738C2×#41—224no—
739C2×#41—212no—
740C2×#41—224no—
741C2×#41—26no—
742C2×#41—26no—
743C2×#41—248no—
744C2×#41—348no—
745C2×#41—324no—
746C2×#41—324no—
747C2×#41—432no—
748C2×#41—624no—
749C2×#41—624no—
750C2×#41—6192no—
751C2×#41—648no—
752C2×#41—6192no—
753C2×#41—648no—
754C2×#41—6256no—
755C2×#41—696no—
756C2×#41—632no—
757C2×#41—648no—
758C2×#41—616no—
759C2×#41—624no—
760C2×#41—624no—
761C2×#41—612no—
762C2×#41—624no—
763C2×#41—612no—
764C2×#41D3×D4116yes—
765C2×#41C2×#67112yes—
766C2×#41C2×#67124yes—
767C2×#41C2×#6718yes—
768C2×#41C2×#6714yes—
769C2×#41C23×D314yes—
770C2×#41C23×D3112yes—
771C2×#41C23×D314yes—
772C2×#41C23×D3112yescomplemented
773C22×Q8—28no—
774C22×Q8—24no—
775C22×Q8—32no—
776C22×Q8—34no—
777C22×Q8—68no—
778C22×Q8—62no—
779C22×Q8—61no—
780C22×Q8C2×#6713yes—
781C22×Q8C2×#6718yes—
782C22×Q8C2×#6711yescharacteristic
783C22×Q8C23×D316yescomplemented
784C22×D4—224no—
785C22×D4—26no—
786C22×D4—212no—
787C22×D4—212no—
788C22×D4—348no—
789C22×D4—324no—
790C22×D4—36no—
791C22×D4—312no—
792C22×D4—324no—
793C22×D4—624no—
794C22×D4—6192no—
795C22×D4—648no—
796C22×D4—648no—
797C22×D4—648no—
798C22×D4—6192no—
799C22×D4—648no—
800C22×D4—6192no—
801C22×D4—6768no—
802C22×D4—696no—
803C22×D4—648no—
804C22×D4—624no—
805C22×D4—66no—
806C22×D4—66no—
807C22×D4—696no—
808C22×D4—696no—
809C22×D4—648no—
810C22×D4—648no—
811C22×D4—624no—
812C22×D4—66no—
813C22×D4—624no—
814C22×D4—66no—
815C22×D4—63no—
816C22×D4—66no—
817C22×D4—624no—
818C22×D4—612no—
819C22×D4—624no—
820C22×D4—612no—
821C22×D4C2×#6716yes—
822C22×D4C2×#6713yes—
823C22×D4C2×#67124yes—
824C22×D4C2×#6713yes—
825C22×D4C23×D316yescomplemented
826C23×C4—224no—
827C23×C4—26no—
828C23×C4—648no—
829C23×C4—61no—
830C23×C4—624no—
831C23×C4—66no—
832C23×C4—66no—
833C23×C4C2×#67112yes—
834C23×C4C2×#6713yes—
835C23×C4C2×#6713yes—
836C23×C4C2×#6713yes—
837C23×C4C23×D3112yes—
838C23×C4C23×D311yescharacteristic
839C23×C4C23×D313yes—
840C23×C4C23×D313yes—
841#137—696no—
842#137—632no—
843AGL(1,ℤ/8)—696no—
844AGL(1,ℤ/8)—696no—
845AGL(1,ℤ/8)—6192no—
846#135—6192no—
847C2×Q16—316no—
848C2×SD16—348no—
849C2×SD16—316no—
850C2×SD16—696no—
851C2×D8—348no—
852C2×D8—696no—
853#131—664no—
854C2×M16—38no—
855C2×M16—324no—
856C2×M16—648no—
857C22×C8—324no—
858C4⋊Q8—212no—
859#127—212no—
860#124—212no—
861#124—212no—
862#123—224no—
863#123—24no—
864#123—212no—
865#123—224no—
866C22⋊Q8—224no—
867C22⋊Q8—212no—
868C22⋊Q8—212no—
869C22⋊Q8C23×D318yes—
870C22⋊Q8C23×D3124yescomplemented
871#121—224no—
872#121—248no—
873#121—212no—
874#121—212no—
875#121C23×D318yes—
876#121C23×D3124yescomplemented
877#120—24no—
878#120—212no—
879#120—224no—
880#120—224no—
881C4×Q8—28no—
882C4×D4—224no—
883C4×D4—28no—
884C4×D4—224no—
885C4×D4—224no—
886C4×D4—224no—
887#117—26no—
888#117—26no—
889#117C23×D314yes—
890#117C23×D3112yescomplemented
891C2×C4⋊C4—212no—
892C2×C4⋊C4C23×D3112yescomplemented
893C2×C22⋊C4—26no—
894C2×C22⋊C4—212no—
895C2×C22⋊C4—212no—
896C2×C42—26no—
897#103—332no—
898#102—396no—
899C22⋊C8—316no—
900C22⋊C8—348no—
901C23×C3—24no—
902C23×C3—22no—
903C23×C3—224no—
904C23×C3—224no—
905C23×C3—26no—
906C23×C3—24no—
907C23×C3—46no—
908C23×C3—412no—
909C23×C3—46no—
910C23×C3—448no—
911C23×C3—412no—
912C23×C3—812no—
913C23×C3C2×#120112yes—
914C23×C3C23×D416yes—
915C23×C3C23×D412yes—
916C23×C3C23×D411yescharacteristic
917C23×C3C23×D416yes—
918C22×D3—248no—
919C22×D3—212no—
920C22×D3—224no—
921C22×D3—296no—
922C22×D3—296no—
923C22×D3—496no—
924C22×D3—424no—
925C22×D3—424no—
926C22×D3—424no—
927C22×D3—848no—
928C22×D3—848no—
929C22×D3—896no—
930C22×D3—8384no—
931C22×D3—896no—
932C3×Q8—224no—
933C3×Q8—28no—
934C3×Q8—412no—
935C3×Q8C2×#120116yes—
936C3×D4—248no—
937C3×D4—28no—
938C3×D4—224no—
939C3×D4—416no—
940C3×D4—48no—
941C3×D4—424no—
942C3×D4—412no—
943C3×D4—824no—
944C3×D4C2×#120148yes—
945C2×C3×C4—22no—
946C2×C3×C4—26no—
947C2×C3×C4—224no—
948C2×C3×C4—24no—
949C2×C3×C4—212no—
950C2×C3×C4—24no—
951C2×C3×C4—224no—
952C2×C3×C4—224no—
953C2×C3×C4—212no—
954C2×C3×C4—28no—
955C2×C3×C4—24no—
956C2×C3×C4—412no—
957C2×C3×C4—48no—
958C2×C3×C4—424no—
959C2×C3×C4—812no—
960C2×C3×C4C2×#120112yes—
961C2×C3×C4C2×#120124yes—
962C2×C3×C4C23×D4124yes—
963C2×C3×C4C23×D414yes—
964C2×C3×C4C23×D412yes—
965C2×C3×C4C23×D416yes—
966C2×C3×C4C23×D411yescharacteristic
967C2×C3×C4C23×D416yes—
968C2×C3×C4C2611yescharacteristic
969#67—296no—
970#67—296no—
971C2×Dic3—216no—
972C2×Dic3—24no—
973C2×Dic3—28no—
974D12—248no—
975D12—296no—
976D12—212no—
977D12—224no—
978D12—296no—
979D12C23×D4124yes—
980C4×D3—296no—
981C4×D3—296no—
982Dic6—216no—
983Dic6—24no—
984Dic6—28no—
985Dic6C23×D418yes—
986C3⋊C8—216no—
987C24—212no—
988C24—26no—
989C24—412no—
990C24—624no—
991C24—6192no—
992C24—648no—
993C24—612no—
994C24—66no—
995C24—624no—
996C24—624no—
997C24—648no—
998C24—1224no—
999C24—2448no—
1000C24—2424no—
1001C24—2448no—
1002C24—2424no—
1003C24—24192no—
1004C24C22×#6711yescharacteristic
1005C24C22×#67112yes—
1006C24C22×#6713yes—
1007C24C22×#6713yes—
1008#41—232no—
1009#41—296no—
1010#41—248no—
1011#41—248no—
1012#41—248no—
1013#41—216no—
1014#41—396no—
1015#41—416no—
1016#41—448no—
1017#41—424no—
1018#41—424no—
1019#41—648no—
1020#41—648no—
1021#41—6192no—
1022#41—696no—
1023#41—6192no—
1024#41—6384no—
1025#41—6128no—
1026#41—648no—
1027#41—696no—
1028#41#937132yes—
1029#41C2×D3×D4132yes—
1030C2×Q8—232no—
1031C2×Q8—26no—
1032C2×Q8—212no—
1033C2×Q8—224no—
1034C2×Q8—38no—
1035C2×Q8—34no—
1036C2×Q8—416no—
1037C2×Q8—616no—
1038C2×Q8—68no—
1039C2×Q8—616no—
1040C2×Q8—64no—
1041C2×Q8—64no—
1042C2×Q8—62no—
1043C2×Q8#93718yes—
1044C2×Q8C22×#67112yes—
1045C2×Q8C22×#6714yes—
1046C2×Q8C24×D314yes—
1047C2×D4—224no—
1048C2×D4—296no—
1049C2×D4—28no—
1050C2×D4—24no—
1051C2×D4—212no—
1052C2×D4—224no—
1053C2×D4—224no—
1054C2×D4—26no—
1055C2×D4—212no—
1056C2×D4—396no—
1057C2×D4—324no—
1058C2×D4—312no—
1059C2×D4—424no—
1060C2×D4—448no—
1061C2×D4—648no—
1062C2×D4—696no—
1063C2×D4—624no—
1064C2×D4—648no—
1065C2×D4—648no—
1066C2×D4—6192no—
1067C2×D4—6192no—
1068C2×D4—6192no—
1069C2×D4—696no—
1070C2×D4—6768no—
1071C2×D4—6384no—
1072C2×D4—6192no—
1073C2×D4—648no—
1074C2×D4—624no—
1075C2×D4—624no—
1076C2×D4—648no—
1077C2×D4—6384no—
1078C2×D4—612no—
1079C2×D4—648no—
1080C2×D4—624no—
1081C2×D4—612no—
1082C2×D4—66no—
1083C2×D4—624no—
1084C2×D4—648no—
1085C2×D4—696no—
1086C2×D4—824no—
1087C2×D4#937124yes—
1088C2×D4C22×#67124yes—
1089C2×D4C22×#67112yes—
1090C2×D4C22×#67112yes—
1091C2×D4C24×D314yes—
1092C22×C4—212no—
1093C22×C4—24no—
1094C22×C4—212no—
1095C22×C4—248no—
1096C22×C4—212no—
1097C22×C4—212no—
1098C22×C4—248no—
1099C22×C4—26no—
1100C22×C4—212no—
1101C22×C4—24no—
1102C22×C4—212no—
1103C22×C4—424no—
1104C22×C4—648no—
1105C22×C4—6192no—
1106C22×C4—68no—
1107C22×C4—64no—
1108C22×C4—62no—
1109C22×C4—624no—
1110C22×C4—624no—
1111C22×C4—648no—
1112C22×C4C2×D3×D4124yes—
1113C22×C4C22×#67112yes—
1114C22×C4C22×#6712yes—
1115C22×C4C22×#6716yes—
1116C22×C4C22×#67112yes—
1117C22×C4C22×#67112yes—
1118C22×C4C22×#6713yes—
1119C22×C4C22×#6711yescharacteristic
1120C22×C4C22×#6716yes—
1121C22×C4C22×#6713yes—
1122C22×C4C24×D312yes—
1123C22×C4C24×D316yes—
1124C22×C4C24×D316yes—
1125C22×C4C24×D311yescharacteristic
1126Q16—632no—
1127SD16—632no—
1128SD16—696no—
1129D8—696no—
1130M16—616no—
1131M16—648no—
1132C2×C8—316no—
1133C2×C8—648no—
1134C4⋊C4—28no—
1135C4⋊C4—224no—
1136C4⋊C4—212no—
1137C4⋊C4C24×D318yes—
1138C22⋊C4—24no—
1139C22⋊C4—28no—
1140C22⋊C4—212no—
1141C22⋊C4—224no—
1142C22⋊C4—28no—
1143C22⋊C4—224no—
1144C42—24no—
1145C42—212no—
1146C22×C3—28no—
1147C22×C3—212no—
1148C22×C3—22no—
1149C22×C3—22no—
1150C22×C3—22no—
1151C22×C3—212no—
1152C22×C3—26no—
1153C22×C3—412no—
1154C22×C3—448no—
1155C22×C3—412no—
1156C22×C3—48no—
1157C22×C3—44no—
1158C22×C3—1612no—
1159C22×C3C22×#12012yes—
1160C22×C3C22×#120112yes—
1161C22×C3#358514yescomplemented
1162C22×C3C24×D411yescharacteristic
1163C2×D3—224no—
1164C2×D3—496no—
1165C2×D3—448no—
1166C2×D3—424no—
1167C2×D3—896no—
1168C2×D3—896no—
1169C3×C4—22no—
1170C3×C4—26no—
1171C3×C4—48no—
1172C3×C4—44no—
1173C3×C4C22×#12012yes—
1174C3×C4C22×#120112yes—
1175C3×C4C24×D412yes—
1176Dic3—28no—
1177C23—24no—
1178C23—22no—
1179C23—224no—
1180C23—224no—
1181C23—26no—
1182C23—24no—
1183C23—46no—
1184C23—412no—
1185C23—46no—
1186C23—448no—
1187C23—412no—
1188C23—648no—
1189C23—696no—
1190C23—612no—
1191C23—624no—
1192C23—696no—
1193C23—812no—
1194C23—1296no—
1195C23—1224no—
1196C23—1224no—
1197C23—1224no—
1198C23—2448no—
1199C23—2448no—
1200C23—2496no—
1201C23—24384no—
1202C23—2496no—
1203C23C2×#937112yes—
1204C23C23×#6716yes—
1205C23C23×#6712yes—
1206C23C23×#6711yescharacteristic
1207C23C23×#6716yes—
1208Q8—224no—
1209Q8—28no—
1210Q8—38no—
1211Q8—412no—
1212Q8—616no—
1213Q8—64no—
1214Q8—68no—
1215Q8C2×#937116yes—
1216D4—248no—
1217D4—28no—
1218D4—224no—
1219D4—324no—
1220D4—416no—
1221D4—48no—
1222D4—424no—
1223D4—412no—
1224D4—648no—
1225D4—696no—
1226D4—696no—
1227D4—696no—
1228D4—612no—
1229D4—624no—
1230D4—696no—
1231D4—824no—
1232D4C2×#937148yes—
1233C2×C4—22no—
1234C2×C4—26no—
1235C2×C4—224no—
1236C2×C4—24no—
1237C2×C4—212no—
1238C2×C4—24no—
1239C2×C4—224no—
1240C2×C4—224no—
1241C2×C4—212no—
1242C2×C4—28no—
1243C2×C4—24no—
1244C2×C4—412no—
1245C2×C4—48no—
1246C2×C4—424no—
1247C2×C4—696no—
1248C2×C4—616no—
1249C2×C4—64no—
1250C2×C4—68no—
1251C2×C4—696no—
1252C2×C4—812no—
1253C2×C4C2×#937124yes—
1254C2×C4C2×#937112yes—
1255C2×C4C22×D3×D4124yes—
1256C2×C4C22×D3×D414yes—
1257C2×C4C23×#6716yes—
1258C2×C4C23×#6712yes—
1259C2×C4C23×#6711yescharacteristic
1260C2×C4C23×#6716yes—
1261C2×C4C25×D311yescharacteristic
1262C8—616no—
1263C2×C3—24no—
1264C2×C3—22no—
1265C2×C3—212no—
1266C2×C3—46no—
1267C2×C3—84no—
1268C2×C3C23×#12011yescharacteristic
1269C2×C3C2×#358512yes—
1270D3—424no—
1271C22—28no—
1272C22—22no—
1273C22—212no—
1274C22—22no—
1275C22—22no—
1276C22—26no—
1277C22—212no—
1278C22—412no—
1279C22—448no—
1280C22—412no—
1281C22—44no—
1282C22—48no—
1283C22—624no—
1284C22—1296no—
1285C22—1248no—
1286C22—1224no—
1287C22—1612no—
1288C22—2496no—
1289C22—2496no—
1290C22C22×#93712yes—
1291C22C22×#937112yes—
1292C22#8729814yescomplemented
1293C22C24×#6711yescharacteristic
1294C4—22no—
1295C4—26no—
1296C4—44no—
1297C4—48no—
1298C4—68no—
1299C4C22×#93712yes—
1300C4C22×#937112yes—
1301C4C23×D3×D412yes—
1302C3#1057484011yescharacteristic, complemented, Sylow
1303C2—24no—
1304C2—22no—
1305C2—212no—
1306C2—46no—
1307C2—84no—
1308C2—1224no—
1309C2C23×#93711yescharacteristic
1310C2C2×#8729812yes—
subgroupG/H
centerC22C24×#67
commutator, cosocleC2×C3×C4C26
FrattiniC2×C4C25×D3
FittingC3×#62811C2
socleC22×C3C24×D4
hypercenter#62811D3
hypocenterC3#10574840
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×#41 ◁ #62811

Complements

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

NH ≅ G/Ntype
1. C23×#1009C2semidirect
2. C2×#87298C2semidirect
3. #11661728C2semidirect
4. #11661717C2semidirect
5. #11661668C2semidirect
6. #11661579C2semidirect
7. C2×#82927C2semidirect
8. #11658757C2semidirect
9. #11658639C2semidirect
10. C3×#62811C2semidirect
12. C2×C3×#585C22semidirect
19. C22×#1009C22semidirect
20. C22×#1009C22semidirect
23. C23×#235C22semidirect
24. C24×D12C22semidirect
25. C3×#3489C22semidirect
26. C3×#3488C22semidirect
32. C3×#3449C22semidirect
33. C2×C3×#525C22semidirect
34. C3×#3428C22semidirect
36. C2×#5837C22semidirect
37. C2×#5835C22semidirect
38. C2×#5822C22semidirect
39. C22×#949C22semidirect
40. C2×#5819C22semidirect
41. #84075C22semidirect
42. #84074C22semidirect
43. C2×#5207C22semidirect
44. #83424C22semidirect
45. #83404C22semidirect
46. #83383C22semidirect
47. #82933C22semidirect
48. #82928C22semidirect
49. #82927C22semidirect
50. #82927C22semidirect
51. #82927C22semidirect
52. #82926C22semidirect
53. #82735C22semidirect
54. C2×#5046C22semidirect
55. #82624C22semidirect
56. C2×#5036C22semidirect
57. #82563C22semidirect
58. #82213C22semidirect
59. C2×#5001C22semidirect
62. #62811D3semidirect
73. C2×C3×2−1+4C23semidirect
75. C2×C3×H(5,𝔽2)C23semidirect
84. C22×C3×#41C23semidirect
100. C2×#1009D4semidirect
138. C3×#537C23semidirect
140. C3×#536C23semidirect
142. C3×#535C23semidirect
150. C3×#525C23semidirect
151. C3×#525C23semidirect
153. C2×C3×C22⋊Q8C23semidirect
154. C2×C3×#121C23semidirect
156. C3×#520C23semidirect
161. C2×C3×#117C23semidirect
164. C2×#951C23semidirect
166. C2×#950C23semidirect
168. C2×#949C23semidirect
169. C2×#949C23semidirect
171. C2×#948C23semidirect
172. C2×#942C23semidirect
173. C22×#215C23semidirect
174. C2×#932C23semidirect
175. C22×#213C23semidirect
176. C22×#208C23semidirect
177. #5234C23semidirect
179. #5207C23semidirect
180. #5207C23semidirect
181. C2×#830C23semidirect
182. #5050C23semidirect
183. #5047C23semidirect
184. #5046C23semidirect
185. #5046C23semidirect
186. #5040C23semidirect
187. #5037C23semidirect
188. #5036C23semidirect
189. #5036C23semidirect
190. #5004C23semidirect
191. #5002C23semidirect
192. #5001C23semidirect
193. #5001C23semidirect
194. #4966C23semidirect
195. C2×#809C23semidirect
196. C2×#585C2×D3semidirect
215. #3489C2×D3semidirect
216. #3488C2×D3semidirect
222. #3449C2×D3semidirect
223. C2×#525C2×D3semidirect
224. #3428C2×D3semidirect
274. C2×C3×#41C24semidirect
280. C22×C3×Q8C24semidirect
289. C22×C3×D4C24semidirect
312. #1009C2×D4semidirect
336. C2×#235C2×D4semidirect
356. C22×D12C2×D4semidirect
382. C3×C22⋊Q8C24semidirect
388. C3×#121C24semidirect
402. C3×#117C24semidirect
404. C2×C3×C4⋊C4C24semidirect
414. C2×#216C24semidirect
417. C2×#215C24semidirect
418. C2×#214C24semidirect
421. C2×#213C24semidirect
424. C2×#208C24semidirect
425. C22×C3⋊C8C24semidirect
427. #830C24semidirect
428. #810C24semidirect
429. #809C24semidirect
433. C2×2−1+4C22×D3semidirect
449. C2×H(5,𝔽2)C22×D3semidirect
469. C22×#41C22×D3semidirect
513. #537C22×D3semidirect
515. #536C22×D3semidirect
517. #535C22×D3semidirect
525. #525C22×D3semidirect
526. #525C22×D3semidirect
528. C2×C22⋊Q8C22×D3semidirect
529. C2×#121C22×D3semidirect
531. #520C22×D3semidirect
536. C2×#117C22×D3semidirect
772. C2×#41C23×D3semidirect
783. C22×Q8C23×D3semidirect
825. C22×D4C23×D3semidirect
870. C22⋊Q8C23×D3semidirect
876. #121C23×D3semidirect
890. #117C23×D3semidirect
892. C2×C4⋊C4C23×D3semidirect
1161. C22×C3#3585semidirect
1292. C22#87298semidirect
1302. C3#10574840semidirect

Maximal subgroups

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

subgroupindex
C23×#10092
C2×#872982
#116617282
#116617172
#116616682
#116615792
C2×#829272
#116587572
#116586392
C3×#628112
#105748403