Finite Group Databasebeta

← #11661688

Subgroups — #11661688

Order 768.

4938 conjugacy classes of subgroups.

The subgroup lattice has 1232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5964C211yesmaximal, characteristic, complemented
2C2×D3×AGL(1,ℤ/8)C212yesmaximal, complemented
3C2×#5607C211yesmaximal, characteristic, complemented
4C3×#3006C211yesmaximal, characteristic, complemented
5#84082C211yesmaximal, characteristic, complemented
6#83946C212yesmaximal, complemented
7#82624C211yesmaximal, characteristic, complemented
8#80086C214yesmaximal, complemented
9#80085C214yesmaximal, complemented
10#80041C214yesmaximal, complemented
11#80004C214yesmaximal, complemented
12#78884C212yesmaximal, complemented
13#78881C212yesmaximal, complemented
14#78639C211yesmaximal, characteristic, complemented
15#78630C211yesmaximal, characteristic, complemented
16#60369—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic, complemented
18#5964—216no—
19C2×#1010—21no—
20C2×#1010C2212yescomplemented
21C2×#1009—21no—
22C2×#1009C2212yescomplemented
23C2×D3×#41—22no—
24C2×D3×#41C2212yes—
25C2×D3×#41C2212yescomplemented
26C2×#1007C2212yescomplemented
27C2×#1004—21no—
28C2×#1004—21no—
29C2×#1004C2212yescomplemented
30C22×D3×D4C2211yescharacteristic, complemented
31C22×#235—22no—
32C22×#235C2211yescharacteristic
33C22×#235C2211yescharacteristic, complemented
34C2×C3×AGL(1,ℤ/8)C2212yescomplemented
35C2×C3×#121C2211yescharacteristic, complemented
36C2×#949C2212yescomplemented
37C2×#940—21no—
38C2×#938C2211yescharacteristic, complemented
39C2×#937—21no—
40C2×#932C2212yescomplemented
41C2×#930C2211yescharacteristic, complemented
42D3×AGL(1,ℤ/8)—216no—
43C2×#914C2214yescomplemented
44C2×D3×SD16C2214yescomplemented
45C2×#911C2214yescomplemented
46C2×D3×D8C2214yescomplemented
47C2×#908C2212yescomplemented
48C2×D3×M16C2212yescomplemented
49#5607—22no—
50#5607—22no—
51#5607C2214yescomplemented
52#5607C2214yescomplemented
53C2×#895C2211yescharacteristic, complemented
54C2×#892C2211yescharacteristic, complemented
55C2×#885—21no—
56C2×#882—21no—
57C3×#449C2214yescomplemented
58C3×#448C2212yescomplemented
59C3×#447C2212yescomplemented
60C3×#417C2212yescomplemented
61C3×#407C2211yescharacteristic, complemented
62#5238C2214yescomplemented
63#5232C2212yescomplemented
64#5227C2212yescomplemented
65#5217C2212yescomplemented
66#5207C2211yescharacteristic, complemented
67#5172C2214yescomplemented
68#5170C2214yescomplemented
69#5158C2214yescomplemented
70#5156C2214yescomplemented
71#5133C2212yescomplemented
72#5126C2212yescomplemented
73#5040C2212yescomplemented
74#5037C2214yescomplemented
75#5036C2212yescomplemented
76#4966C2212yescomplemented
77#4810C2214yescomplemented
78#4806C2214yescomplemented
79#4804C2214yescomplemented
80#4802C2214yescomplemented
81#4781C2214yescomplemented
82#4773C2214yescomplemented
83#4772C2214yescomplemented
84#4770C2214yescomplemented
85#4738C2212yescomplemented
86#4734C2214yescomplemented
87#4732C2212yescomplemented
88#4727C2214yescomplemented
89#4727C2214yescomplemented
90C2×#585—31no—
91C22×AGL(1,ℤ/8)—32no—
92C2×#535—31no—
93#3010—34no—
94#3010—34no—
95#3008—34no—
96#3008—34no—
97#3006—32no—
98#3006—31no—
99#3006—31no—
100#3006—32no—
101#3006—31no—
102#3006D311yescharacteristic, complemented
103#2896—32no—
104#2879—31no—
105C24×D3—21no—
106C2×C3×#41—28no—
107C2×C3×#41—21no—
108C2×C3×#41—21no—
109C2×C3×#41C2312yes—
110C2×C3×#41C2312yescomplemented
111C22×C3×Q8C2311yescharacteristic, complemented
112C22×C3×D4—21no—
113C22×C3×D4—21no—
114C22×C3×D4C2311yescharacteristic
115C22×C3×D4C2311yescharacteristic, complemented
116C23×C3×C4—21no—
117C23×C3×C4C2311yescharacteristic
118C22×#67—21no—
119C22×#67—22no—
120C22×#67—22no—
121C22×#67—21no—
122C22×#67—21no—
123C22×#67—21no—
124C22×#67D411yescharacteristic
125C22×#67D411yescharacteristic
126#1010—216no—
127#1010—28no—
128#1010—28no—
129#1009—216no—
130#1009—28no—
131#1009—28no—
132D3×#41—232no—
133D3×#41—28no—
134D3×#41—28no—
135D3×#41—28no—
136D3×#41D4116yescomplemented
137#1007—28no—
138#1007—28no—
139C2×#239—22no—
140C2×#239C2312yes—
141C2×#239C2312yescomplemented
142C2×D3×Q8—22no—
143C2×D3×Q8C2312yes—
144C2×D3×Q8C2312yescomplemented
145#1004—216no—
146#1004—216no—
147#1004—28no—
148#1004—28no—
149C2×#237—22no—
150C2×#237—22no—
151C2×#237—22no—
152C2×#237—22no—
153C2×#237—22no—
154C2×#237C2312yes—
155C2×#237C2312yescomplemented
156C2×D3×D4—22no—
157C2×D3×D4—22no—
158C2×D3×D4—22no—
159C2×D3×D4—22no—
160C2×D3×D4—22no—
161C2×D3×D4—28no—
162C2×D3×D4—22no—
163C2×D3×D4C2314yes—
164C2×D3×D4C2312yes—
165C2×D3×D4C2312yescomplemented
166C2×#235—232no—
167C2×#235—21no—
168C2×#235—21no—
169C2×#235—22no—
170C2×#235—22no—
171C2×#235—28no—
172C2×#235—22no—
173C2×#235—22no—
174C2×#235—22no—
175C2×#235—28no—
176C2×#235—22no—
177C2×#235D412yes—
178C2×#235D412yes—
179C2×#235C2312yes—
180C2×#235C2312yes—
181C2×#235C2312yes—
182C2×#235C2312yescomplemented
183C22×D12—22no—
184C22×D12—21no—
185C22×D12D411yescharacteristic
186C22×D12C2311yescharacteristic
187C22×D12C2311yescharacteristic, complemented
188C22×C4×D3—21no—
189C22×C4×D3—22no—
190C22×C4×D3—22no—
191C22×C4×D3C2311yescharacteristic
192C22×C4×D3C2311yescharacteristic
193C22×Dic6—22no—
194C22×Dic6D411yescharacteristic
195C22×Dic6C2311yescharacteristic, complemented
196C3×AGL(1,ℤ/8)—28no—
197C2×C3×SD16C2314yes—
198C2×C3×D8C2314yes—
199C2×C3×M16C2312yes—
200C3×#121—21no—
201C3×#121—21no—
202C3×#121C2312yes—
203C3×#121C2312yes—
204C2×C3×C4⋊C4C2311yescharacteristic
205C2×C3×C22⋊C4—21no—
206C2×#217—21no—
207#949—28no—
208C2×#215C2314yes—
209#940—24no—
210#940—24no—
211#938—22no—
212#938C2314yes—
213#937—24no—
214#937—24no—
215C2×#214C2314yes—
216#932—28no—
217C2×#213C2314yes—
218C2×#213C2314yes—
219#930—21no—
220#930—21no—
221#930C2312yes—
222#930C2312yes—
223C2×(C2×D3)⋊C4—21no—
224C2×(C2×D3)⋊C4—21no—
225C2×(C2×D3)⋊C4—21no—
226C2×C4⋊Dic3C2311yescharacteristic
227C2×C4×Dic3—21no—
228C2×#208C2312yes—
229#914—216no—
230D3×SD16—216no—
231#911—216no—
232D3×D8—216no—
233#908—28no—
234D3×M16—28no—
235C2×D24C2314yes—
236C2×#204C2314yes—
237C2×ΓL(1,𝔽25)C2314yes—
238C2×D3×C8C2314yes—
239#895—22no—
240#895C2314yes—
241#892—22no—
242#892C2314yes—
243#885—24no—
244#885—24no—
245#882—24no—
246#882—24no—
247C3×#103C2314yescomplemented
248C3×#102C2314yescomplemented
249C3×C22⋊C8C2312yescomplemented
250C3×C22⋊C8C2312yescomplemented
251#835C2314yescomplemented
252#832C2314yescomplemented
253#830C2312yescomplemented
254#830C2312yescomplemented
255#821C2314yescomplemented
256(C2×D3)⋊C8C2314yescomplemented
257(C2×D3)⋊C8C2314yescomplemented
258#816C2314yescomplemented
259#810C2314yescomplemented
260#809C2314yescomplemented
261#585—616no—
262C2×2−1+4—32no—
263C2×2−1+4—32no—
264C2×2−1+4—61no—
265C2×H(5,𝔽2)—32no—
266C2×H(5,𝔽2)—32no—
267C2×H(5,𝔽2)—61no—
268C2×H(5,𝔽2)—61no—
269C2×H(5,𝔽2)—61no—
270C22×#41—31no—
271C22×#41—32no—
272C22×#41—32no—
273C22×#41—31no—
274C22×#41—62no—
275C22×#41—62no—
276C22×#41C2×D311yescharacteristic, complemented
277C23×D4—31no—
278C2×AGL(1,ℤ/8)—32no—
279C2×AGL(1,ℤ/8)—32no—
280C2×AGL(1,ℤ/8)—34no—
281C2×AGL(1,ℤ/8)—34no—
282C2×AGL(1,ℤ/8)—32no—
283C2×AGL(1,ℤ/8)—616no—
284C2×AGL(1,ℤ/8)C2×D312yescomplemented
285C22×SD16—34no—
286C22×D8—34no—
287C22×M16—32no—
288#535—34no—
289#535—34no—
290#535—62no—
291#535—62no—
292C2×#127—61no—
293C2×#124—61no—
294C2×#121—31no—
295C2×#121—31no—
296C2×#121—31no—
297C2×#121C2×D311yescharacteristic, complemented
298C2×#120—61no—
299C2×#120—61no—
300C2×#117—31no—
301#449—34no—
302#449—34no—
303#449—34no—
304#449—34no—
305#449—34no—
306#449—34no—
307#449—34no—
308#449C2×D314yescomplemented
309#448—32no—
310#448—34no—
311#448—32no—
312#448—34no—
313#448—32no—
314#448C2×D312yescomplemented
315#447—32no—
316#447—34no—
317#447—32no—
318#447—34no—
319#447—32no—
320#447C2×D312yescomplemented
321#419—34no—
322#418—34no—
323#417—32no—
324#417—32no—
325#417—32no—
326#417C2×D312yescomplemented
327#416—34no—
328#416—34no—
329#408—34no—
330#408—34no—
331#407—31no—
332#407—32no—
333#407C2×D311yescharacteristic, complemented
334C24×C3—21no—
335C24×C3—21no—
336C24×C3C2×D411yescharacteristic
337C23×D3—21no—
338C23×D3—22no—
339C23×D3—22no—
340C23×D3—21no—
341C23×D3—24no—
342C23×D3—44no—
343C23×D3—82no—
344C23×D3—82no—
345C23×D3C2×D411yescharacteristic
346C23×D3C2×D411yescharacteristic
347C3×#41—28no—
348C3×#41—28no—
349C3×#41—24no—
350C3×#41—24no—
351C3×#41—24no—
352C3×#41C2×D418yes—
353C2×C3×Q8—24no—
354C2×C3×Q8—21no—
355C2×C3×Q8C2412yes—
356C2×C3×D4—28no—
357C2×C3×D4—22no—
358C2×C3×D4—22no—
359C2×C3×D4—24no—
360C2×C3×D4—22no—
361C2×C3×D4—22no—
362C2×C3×D4—21no—
363C2×C3×D4—24no—
364C2×C3×D4—21no—
365C2×C3×D4—82no—
366C2×C3×D4C2412yes—
367C2×C3×D4C2412yes—
368C22×C3×C4—28no—
369C22×C3×C4—21no—
370C22×C3×C4—22no—
371C22×C3×C4—22no—
372C22×C3×C4—24no—
373C22×C3×C4—21no—
374C22×C3×C4C2×D411yescharacteristic
375C22×C3×C4C2×D411yescharacteristic
376C22×C3×C4C2×D411yescharacteristic
377C22×C3×C4C2411yescharacteristic
378C22×C3×C4C2411yescharacteristic
379C22×C3×C4C2411yescharacteristic
380C2×#67—28no—
381C2×#67—216no—
382C2×#67—216no—
383C2×#67—22no—
384C2×#67—22no—
385C2×#67—24no—
386C2×#67—22no—
387C2×#67—22no—
388C2×#67—22no—
389C2×#67—22no—
390C2×#67—24no—
391C2×#67—24no—
392C2×#67—22no—
393C2×#67—22no—
394C2×#67—24no—
395C2×#67—44no—
396C2×#67—82no—
397C2×#67—82no—
398C2×#67C2×D412yes—
399C2×#67C2×D412yes—
400C2×#67C2×D412yes—
401C2×#67C2×D412yes—
402C22×Dic3—21no—
403C22×Dic3—22no—
404C22×Dic3—22no—
405C22×Dic3—21no—
406C22×Dic3C2×D411yescharacteristic
407C22×Dic3C2×D411yescharacteristic
408#239—216no—
409#239—24no—
410#239—24no—
411#239—24no—
412#239C2×D418yescomplemented
413D3×Q8—216no—
414D3×Q8—24no—
415D3×Q8—24no—
416D3×Q8—24no—
417D3×Q8C2×D418yescomplemented
418#237—216no—
419#237—216no—
420#237—216no—
421#237—216no—
422#237—24no—
423#237—216no—
424#237—24no—
425#237—24no—
426#237C2×D418yescomplemented
427D3×D4—216no—
428D3×D4—216no—
429D3×D4—216no—
430D3×D4—216no—
431D3×D4—216no—
432D3×D4—24no—
433D3×D4—24no—
434D3×D4—24no—
435D3×D4—28no—
436D3×D4—28no—
437D3×D4—48no—
438D3×D4C2×D418yescomplemented
439#235—28no—
440#235—216no—
441#235—216no—
442#235—216no—
443#235—28no—
444#235—216no—
445#235—216no—
446#235—24no—
447#235—24no—
448#235—28no—
449#235—216no—
450#235—28no—
451#235—24no—
452#235—24no—
453#235—24no—
454#235—24no—
455#235—24no—
456#235C2×D418yes—
457C2×D12—216no—
458C2×D12—24no—
459C2×D12—22no—
460C2×D12—22no—
461C2×D12—21no—
462C2×D12—24no—
463C2×D12—24no—
464C2×D12—21no—
465C2×D12—24no—
466C2×D12—82no—
467C2×D12C2×D412yes—
468C2×D12C2×D412yes—
469C2×D12C2412yes—
470C2×D12C2412yes—
471C2×C4×D3—28no—
472C2×C4×D3—216no—
473C2×C4×D3—22no—
474C2×C4×D3—22no—
475C2×C4×D3—22no—
476C2×C4×D3—22no—
477C2×C4×D3—24no—
478C2×C4×D3—22no—
479C2×C4×D3—22no—
480C2×C4×D3—216no—
481C2×C4×D3C2×D412yes—
482C2×C4×D3C2×D412yes—
483C2×C4×D3C2×D418yes—
484C2×C4×D3C2412yes—
485C2×C4×D3C2412yes—
486C2×Dic6—216no—
487C2×Dic6—21no—
488C2×Dic6—24no—
489C2×Dic6—22no—
490C2×Dic6—22no—
491C2×Dic6—24no—
492C2×Dic6C2×D412yes—
493C2×Dic6C2×D412yes—
494C2×Dic6C2412yes—
495C3×SD16—28no—
496C3×D8—28no—
497C3×M16—24no—
498C2×C3×C8C2414yes—
499C3×C4⋊C4—21no—
500C3×C4⋊C4C2412yes—
501C3×C22⋊C4—22no—
502C3×C22⋊C4—22no—
503#217—24no—
504#215—28no—
505#214—28no—
506#213—28no—
507#213—28no—
508(C2×D3)⋊C4—24no—
509(C2×D3)⋊C4—22no—
510(C2×D3)⋊C4—22no—
511(C2×D3)⋊C4—24no—
512C4⋊Dic3—21no—
513C4⋊Dic3C2412yes—
514C4×Dic3—24no—
515#208—24no—
516C2×C3⋊C8C2414yes—
517D24—28no—
518#204—28no—
519ΓL(1,𝔽25)—28no—
520D3×C8—28no—
521C25—61no—
5222−1+4—68no—
5232−1+4—68no—
5242−1+4—68no—
5252−1+4—68no—
5262−1+4—616no—
527H(5,𝔽2)—68no—
528H(5,𝔽2)—68no—
529H(5,𝔽2)—616no—
530H(5,𝔽2)—616no—
531H(5,𝔽2)—68no—
532H(5,𝔽2)—68no—
533H(5,𝔽2)—616no—
534C2×#41—28no—
535C2×#41—21no—
536C2×#41—21no—
537C2×#41—32no—
538C2×#41—32no—
539C2×#41—32no—
540C2×#41—32no—
541C2×#41—316no—
542C2×#41—32no—
543C2×#41—32no—
544C2×#41—32no—
545C2×#41—32no—
546C2×#41—32no—
547C2×#41—32no—
548C2×#41—62no—
549C2×#41—62no—
550C2×#41—68no—
551C2×#41—62no—
552C2×#41—62no—
553C2×#41—62no—
554C2×#41—62no—
555C2×#41—68no—
556C2×#41—632no—
557C2×#41—62no—
558C2×#41—62no—
559C2×#41—68no—
560C2×#41—62no—
561C2×#41—62no—
562C2×#41—62no—
563C2×#41—62no—
564C2×#41—68no—
565C2×#41—632no—
566C2×#41—68no—
567C2×#41—61no—
568C2×#41—61no—
569C2×#41C22×D312yes—
570C2×#41C22×D312yescomplemented
571C22×Q8—31no—
572C22×Q8—32no—
573C22×Q8—32no—
574C22×Q8—31no—
575C22×Q8—62no—
576C22×Q8—62no—
577C22×Q8C22×D311yescharacteristic, complemented
578C22×D4—21no—
579C22×D4—21no—
580C22×D4—32no—
581C22×D4—31no—
582C22×D4—31no—
583C22×D4—34no—
584C22×D4—32no—
585C22×D4—31no—
586C22×D4—31no—
587C22×D4—31no—
588C22×D4—62no—
589C22×D4—61no—
590C22×D4—68no—
591C22×D4—62no—
592C22×D4—61no—
593C22×D4—62no—
594C22×D4—62no—
595C22×D4—62no—
596C22×D4—62no—
597C22×D4—62no—
598C22×D4—62no—
599C22×D4—62no—
600C22×D4—61no—
601C22×D4—61no—
602C22×D4—61no—
603C22×D4C22×D311yescharacteristic
604C22×D4C22×D311yescharacteristic, complemented
605C23×C4—21no—
606C23×C4—31no—
607C23×C4—31no—
608C23×C4—62no—
609C23×C4—62no—
610C23×C4—61no—
611C23×C4C22×D311yescharacteristic
612AGL(1,ℤ/8)—28no—
613AGL(1,ℤ/8)—68no—
614AGL(1,ℤ/8)—616no—
615AGL(1,ℤ/8)—616no—
616AGL(1,ℤ/8)—68no—
617AGL(1,ℤ/8)—68no—
618C2×SD16—34no—
619C2×SD16—34no—
620C2×SD16—34no—
621C2×SD16—616no—
622C2×SD16C22×D314yes—
623C2×D8—34no—
624C2×D8—34no—
625C2×D8—34no—
626C2×D8—616no—
627C2×D8C22×D314yes—
628C2×M16—32no—
629C2×M16—34no—
630C2×M16—68no—
631C2×M16C22×D312yes—
632C22×C8—34no—
633#127—64no—
634#127—64no—
635#124—64no—
636#124—64no—
637#121—21no—
638#121—21no—
639#121—34no—
640#121—32no—
641#121—32no—
642#121—34no—
643#121—62no—
644#121—62no—
645#121—61no—
646#121—61no—
647#121C22×D312yes—
648#121C22×D312yes—
649#120—64no—
650#120—64no—
651#120—64no—
652#120—64no—
653#117—34no—
654#117—62no—
655C2×C4⋊C4—31no—
656C2×C4⋊C4C22×D311yescharacteristic
657C2×C22⋊C4—21no—
658C2×C22⋊C4—61no—
659C2×C22⋊C4—61no—
660C2×C22⋊C4—61no—
661C2×C22⋊C4—61no—
662C2×C42—61no—
663#103—34no—
664#103—34no—
665#103—34no—
666#103C22×D314yescomplemented
667#102—34no—
668#102—34no—
669#102—34no—
670#102C22×D314yescomplemented
671C22⋊C8—32no—
672C22⋊C8—32no—
673C22⋊C8—34no—
674C22⋊C8—34no—
675C22⋊C8C22×D312yescomplemented
676C22⋊C8C22×D312yescomplemented
677C23×C3—24no—
678C23×C3—22no—
679C23×C3—22no—
680C23×C3—22no—
681C23×C3—41no—
682C23×C3—41no—
683C23×C3—42no—
684C23×C3—42no—
685C23×C3—42no—
686C23×C3—81no—
687C23×C3—81no—
688C23×C3C22×D411yescharacteristic
689C23×C3C22×D411yescharacteristic
690C23×C3C22×D411yescharacteristic
691C22×D3—22no—
692C22×D3—28no—
693C22×D3—24no—
694C22×D3—22no—
695C22×D3—28no—
696C22×D3—22no—
697C22×D3—41no—
698C22×D3—41no—
699C22×D3—41no—
700C22×D3—41no—
701C22×D3—42no—
702C22×D3—42no—
703C22×D3—42no—
704C22×D3—48no—
705C22×D3—82no—
706C22×D3—82no—
707C22×D3—82no—
708C22×D3—82no—
709C22×D3—84no—
710C22×D3—84no—
711C22×D3—81no—
712C22×D3—81no—
713C22×D3—816no—
714C22×D3#12014yes—
715C22×D3C22×D412yes—
716C22×D3C22×D412yes—
717C3×Q8—24no—
718C3×Q8—22no—
719C3×Q8C22×D414yes—
720C3×D4—28no—
721C3×D4—24no—
722C3×D4—28no—
723C3×D4—22no—
724C3×D4—24no—
725C3×D4—42no—
726C3×D4—82no—
727C3×D4—82no—
728C3×D4C22×D414yes—
729C2×C3×C4—28no—
730C2×C3×C4—24no—
731C2×C3×C4—22no—
732C2×C3×C4—22no—
733C2×C3×C4—28no—
734C2×C3×C4—22no—
735C2×C3×C4—22no—
736C2×C3×C4—22no—
737C2×C3×C4—22no—
738C2×C3×C4—22no—
739C2×C3×C4—42no—
740C2×C3×C4C22×D411yescharacteristic
741C2×C3×C4C22×D411yescharacteristic
742C2×C3×C4C22×D411yescharacteristic
743C2×C3×C4C22×D414yes—
744C2×C3×C4C2511yescharacteristic
745#67—28no—
746#67—28no—
747#67—28no—
748#67—28no—
749#67—24no—
750#67—24no—
751#67—28no—
752#67—24no—
753#67—24no—
754#67—28no—
755#67—48no—
756#67—84no—
757#67—82no—
758#67—82no—
759C2×Dic3—28no—
760C2×Dic3—24no—
761C2×Dic3—22no—
762C2×Dic3—22no—
763C2×Dic3—28no—
764C2×Dic3—22no—
765C2×Dic3—42no—
766C2×Dic3#12014yes—
767C2×Dic3C22×D412yes—
768C2×Dic3C22×D412yes—
769D12—24no—
770D12—28no—
771D12—24no—
772D12—28no—
773D12—24no—
774D12—22no—
775D12—24no—
776D12—42no—
777D12—84no—
778D12C22×D414yes—
779C4×D3—28no—
780C4×D3—28no—
781C4×D3—28no—
782C4×D3—28no—
783C4×D3—28no—
784C4×D3—24no—
785C4×D3—22no—
786C4×D3—22no—
787C4×D3—28no—
788C4×D3#12018yes—
789C4×D3C22×D414yes—
790C4×D3C22×D414yes—
791Dic6—24no—
792Dic6—28no—
793Dic6—22no—
794Dic6—24no—
795Dic6—28no—
796Dic6—24no—
797Dic6C22×D414yes—
798C3×C8—24no—
799C3⋊C8—24no—
800C24—21no—
801C24—21no—
802C24—31no—
803C24—31no—
804C24—62no—
805C24—62no—
806C24—64no—
807C24—61no—
808C24—61no—
809C24—124no—
810C24—242no—
811C24—242no—
812C24D3×D411yescharacteristic
813#41—28no—
814#41—28no—
815#41—24no—
816#41—24no—
817#41—24no—
818#41—38no—
819#41—38no—
820#41—38no—
821#41—68no—
822#41—616no—
823#41—68no—
824#41—64no—
825#41—64no—
826#41—64no—
827#41—64no—
828#41—64no—
829#41—64no—
830#41—68no—
831#41—616no—
832#41—616no—
833#41—616no—
834#41—616no—
835#41—616no—
836#41—68no—
837#41—616no—
838#41—64no—
839#41—64no—
840#41—64no—
841#41—616no—
842#41—616no—
843#41—616no—
844#41—616no—
845#41—64no—
846#41—616no—
847#41—64no—
848#41—64no—
849#41—64no—
850#41D3×D418yes—
851C2×Q8—24no—
852C2×Q8—21no—
853C2×Q8—32no—
854C2×Q8—32no—
855C2×Q8—38no—
856C2×Q8—32no—
857C2×Q8—62no—
858C2×Q8—62no—
859C2×Q8—64no—
860C2×Q8—64no—
861C2×Q8—616no—
862C2×Q8—64no—
863C2×Q8—64no—
864C2×Q8—616no—
865C2×Q8—64no—
866C2×Q8—61no—
867C2×Q8C23×D312yes—
868C2×D4—28no—
869C2×D4—22no—
870C2×D4—22no—
871C2×D4—24no—
872C2×D4—22no—
873C2×D4—22no—
874C2×D4—21no—
875C2×D4—24no—
876C2×D4—21no—
877C2×D4—38no—
878C2×D4—32no—
879C2×D4—32no—
880C2×D4—32no—
881C2×D4—32no—
882C2×D4—32no—
883C2×D4—32no—
884C2×D4—32no—
885C2×D4—32no—
886C2×D4—64no—
887C2×D4—64no—
888C2×D4—62no—
889C2×D4—62no—
890C2×D4—616no—
891C2×D4—64no—
892C2×D4—64no—
893C2×D4—68no—
894C2×D4—68no—
895C2×D4—62no—
896C2×D4—62no—
897C2×D4—64no—
898C2×D4—64no—
899C2×D4—64no—
900C2×D4—616no—
901C2×D4—616no—
902C2×D4—616no—
903C2×D4—616no—
904C2×D4—616no—
905C2×D4—64no—
906C2×D4—62no—
907C2×D4—62no—
908C2×D4—616no—
909C2×D4—616no—
910C2×D4—68no—
911C2×D4—62no—
912C2×D4—62no—
913C2×D4—64no—
914C2×D4—64no—
915C2×D4—62no—
916C2×D4—62no—
917C2×D4—61no—
918C2×D4—64no—
919C2×D4—61no—
920C2×D4—82no—
921C2×D4—128no—
922C2×D4—124no—
923C2×D4—242no—
924C2×D4—242no—
925C2×D4—242no—
926C2×D4C23×D312yes—
927C2×D4C23×D312yes—
928C22×C4—28no—
929C22×C4—21no—
930C22×C4—22no—
931C22×C4—22no—
932C22×C4—24no—
933C22×C4—21no—
934C22×C4—31no—
935C22×C4—32no—
936C22×C4—38no—
937C22×C4—32no—
938C22×C4—31no—
939C22×C4—32no—
940C22×C4—32no—
941C22×C4—62no—
942C22×C4—62no—
943C22×C4—616no—
944C22×C4—62no—
945C22×C4—62no—
946C22×C4—616no—
947C22×C4—68no—
948C22×C4—62no—
949C22×C4—62no—
950C22×C4—61no—
951C22×C4—64no—
952C22×C4—62no—
953C22×C4—62no—
954C22×C4—61no—
955C22×C4D3×D411yescharacteristic
956C22×C4D3×D411yescharacteristic
957C22×C4D3×D411yescharacteristic
958C22×C4C23×D311yescharacteristic
959C22×C4C23×D311yescharacteristic
960C22×C4C23×D311yescharacteristic
961SD16—28no—
962SD16—68no—
963SD16—68no—
964SD16—68no—
965D8—28no—
966D8—68no—
967D8—68no—
968D8—68no—
969M16—24no—
970M16—68no—
971M16—64no—
972C2×C8—34no—
973C2×C8—68no—
974C2×C8C23×D314yes—
975C4⋊C4—21no—
976C4⋊C4—32no—
977C4⋊C4—61no—
978C4⋊C4C23×D312yes—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—64no—
982C22⋊C4—64no—
983C22⋊C4—64no—
984C22⋊C4—62no—
985C22⋊C4—62no—
986C42—64no—
987C22×C3—21no—
988C22×C3—21no—
989C22×C3—21no—
990C22×C3—21no—
991C22×C3—21no—
992C22×C3—21no—
993C22×C3—21no—
994C22×C3—24no—
995C22×C3—21no—
996C22×C3—42no—
997C22×C3—42no—
998C22×C3—42no—
999C22×C3—42no—
1000C22×C3—42no—
1001C22×C3—82no—
1002C22×C3—84no—
1003C22×C3—84no—
1004C22×C3C2×#12012yes—
1005C22×C3C23×D411yescharacteristic
1006C2×D3—22no—
1007C2×D3—22no—
1008C2×D3—22no—
1009C2×D3—22no—
1010C2×D3—22no—
1011C2×D3—24no—
1012C2×D3—44no—
1013C2×D3—42no—
1014C2×D3—42no—
1015C2×D3—42no—
1016C2×D3—42no—
1017C2×D3—42no—
1018C2×D3—88no—
1019C2×D3—816no—
1020C2×D3—82no—
1021C2×D3—88no—
1022C2×D3—84no—
1023C2×D3—84no—
1024C2×D3C2×#12014yes—
1025C3×C4—21no—
1026C3×C4—24no—
1027C3×C4—21no—
1028C3×C4—42no—
1029C3×C4C2×#12012yes—
1030C3×C4C23×D412yes—
1031Dic3—22no—
1032Dic3—24no—
1033Dic3—42no—
1034Dic3C2×#12014yes—
1035C23—24no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—32no—
1040C23—34no—
1041C23—32no—
1042C23—41no—
1043C23—41no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—68no—
1048C23—64no—
1049C23—68no—
1050C23—62no—
1051C23—62no—
1052C23—62no—
1053C23—81no—
1054C23—81no—
1055C23—121no—
1056C23—121no—
1057C23—121no—
1058C23—121no—
1059C23—122no—
1060C23—122no—
1061C23—128no—
1062C23—122no—
1063C23—241no—
1064C23—241no—
1065C23—244no—
1066C23—244no—
1067C23—242no—
1068C23—242no—
1069C23—242no—
1070C23—242no—
1071C23—2416no—
1072C23C2×D3×D411yescharacteristic
1073C23C2×D3×D411yescharacteristic
1074C23C2×D3×D411yescharacteristic
1075Q8—24no—
1076Q8—22no—
1077Q8—34no—
1078Q8—64no—
1079Q8—68no—
1080Q8—64no—
1081Q8—64no—
1082Q8—68no—
1083Q8—62no—
1084Q8C2×D3×D414yes—
1085D4—28no—
1086D4—24no—
1087D4—28no—
1088D4—22no—
1089D4—24no—
1090D4—34no—
1091D4—42no—
1092D4—64no—
1093D4—64no—
1094D4—68no—
1095D4—64no—
1096D4—68no—
1097D4—64no—
1098D4—64no—
1099D4—68no—
1100D4—64no—
1101D4—64no—
1102D4—68no—
1103D4—68no—
1104D4—68no—
1105D4—68no—
1106D4—68no—
1107D4—62no—
1108D4—64no—
1109D4—82no—
1110D4—82no—
1111D4—128no—
1112D4—122no—
1113D4—244no—
1114D4—242no—
1115D4—242no—
1116D4—244no—
1117D4C2×D3×D414yes—
1118C2×C4—24no—
1119C2×C4—28no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—28no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—32no—
1129C2×C4—34no—
1130C2×C4—34no—
1131C2×C4—34no—
1132C2×C4—38no—
1133C2×C4—32no—
1134C2×C4—42no—
1135C2×C4—68no—
1136C2×C4—68no—
1137C2×C4—68no—
1138C2×C4—68no—
1139C2×C4—68no—
1140C2×C4—68no—
1141C2×C4—68no—
1142C2×C4—64no—
1143C2×C4—62no—
1144C2×C4—62no—
1145C2×C4—62no—
1146C2×C4—62no—
1147C2×C4—64no—
1148C2×C4—68no—
1149C2×C4—62no—
1150C2×C4—122no—
1151C2×C4C2×D3×D411yescharacteristic
1152C2×C4C2×D3×D411yescharacteristic
1153C2×C4C2×D3×D414yes—
1154C2×C4C2×D3×D411yescharacteristic
1155C2×C4C24×D311yescharacteristic
1156C8—24no—
1157C8—64no—
1158C2×C3—22no—
1159C2×C3—41no—
1160C2×C3—44no—
1161C2×C3—41no—
1162C2×C3—82no—
1163C2×C3C22×#12011yescharacteristic
1164C2×C3#358511yescharacteristic
1165C2×C3#358511yescharacteristic
1166D3—24no—
1167D3—42no—
1168D3—44no—
1169D3—82no—
1170C22—21no—
1171C22—21no—
1172C22—21no—
1173C22—21no—
1174C22—21no—
1175C22—21no—
1176C22—24no—
1177C22—21no—
1178C22—21no—
1179C22—34no—
1180C22—42no—
1181C22—42no—
1182C22—42no—
1183C22—42no—
1184C22—42no—
1185C22—62no—
1186C22—62no—
1187C22—62no—
1188C22—64no—
1189C22—62no—
1190C22—62no—
1191C22—82no—
1192C22—84no—
1193C22—84no—
1194C22—124no—
1195C22—122no—
1196C22—122no—
1197C22—122no—
1198C22—122no—
1199C22—122no—
1200C22—242no—
1201C22—244no—
1202C22—248no—
1203C22—244no—
1204C22—248no—
1205C22—2416no—
1206C22D3×#12012yes—
1207C22C22×D3×D411yescharacteristic
1208C4—21no—
1209C4—24no—
1210C4—21no—
1211C4—34no—
1212C4—42no—
1213C4—62no—
1214C4—64no—
1215C4—122no—
1216C4D3×#12012yes—
1217C4C22×D3×D412yes—
1218C3#6036911yescharacteristic, complemented, Sylow
1219C2—22no—
1220C2—41no—
1221C2—41no—
1222C2—44no—
1223C2—64no—
1224C2—82no—
1225C2—122no—
1226C2—124no—
1227C2—242no—
1228C2C2×D3×#12011yescharacteristic
1229C2#8719211yescharacteristic
1230C2#8720011yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3006C2
socleC22×C3C23×D4
hypercenter#3006D3
hypocenterC3#60369
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3006

Complements

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

NH ≅ G/Ntype
1. C2×#5964C2semidirect
2. C2×D3×AGL(1,ℤ/8)C2semidirect
3. C2×#5607C2semidirect
4. C3×#3006C2semidirect
5. #84082C2semidirect
6. #83946C2semidirect
7. #82624C2semidirect
8. #80086C2semidirect
9. #80085C2semidirect
10. #80041C2semidirect
11. #80004C2semidirect
12. #78884C2semidirect
13. #78881C2semidirect
14. #78639C2semidirect
15. #78630C2semidirect
17. C22×C3×#41C22semidirect
20. C2×#1010C22semidirect
22. C2×#1009C22semidirect
25. C2×D3×#41C22semidirect
26. C2×#1007C22semidirect
29. C2×#1004C22semidirect
30. C22×D3×D4C22semidirect
33. C22×#235C22semidirect
34. C2×C3×AGL(1,ℤ/8)C22semidirect
35. C2×C3×#121C22semidirect
36. C2×#949C22semidirect
38. C2×#938C22semidirect
40. C2×#932C22semidirect
41. C2×#930C22semidirect
43. C2×#914C22semidirect
44. C2×D3×SD16C22semidirect
45. C2×#911C22semidirect
46. C2×D3×D8C22semidirect
47. C2×#908C22semidirect
48. C2×D3×M16C22semidirect
51. #5607C22semidirect
52. #5607C22semidirect
53. C2×#895C22semidirect
54. C2×#892C22semidirect
57. C3×#449C22semidirect
58. C3×#448C22semidirect
59. C3×#447C22semidirect
60. C3×#417C22semidirect
61. C3×#407C22semidirect
62. #5238C22semidirect
63. #5232C22semidirect
64. #5227C22semidirect
65. #5217C22semidirect
66. #5207C22semidirect
67. #5172C22semidirect
68. #5170C22semidirect
69. #5158C22semidirect
70. #5156C22semidirect
71. #5133C22semidirect
72. #5126C22semidirect
73. #5040C22semidirect
74. #5037C22semidirect
75. #5036C22semidirect
76. #4966C22semidirect
77. #4810C22semidirect
78. #4806C22semidirect
79. #4804C22semidirect
80. #4802C22semidirect
81. #4781C22semidirect
82. #4773C22semidirect
83. #4772C22semidirect
84. #4770C22semidirect
85. #4738C22semidirect
86. #4734C22semidirect
87. #4732C22semidirect
88. #4727C22semidirect
89. #4727C22semidirect
102. #3006D3semidirect
110. C2×C3×#41C23semidirect
111. C22×C3×Q8C23semidirect
115. C22×C3×D4C23semidirect
136. D3×#41D4semidirect
141. C2×#239C23semidirect
144. C2×D3×Q8C23semidirect
155. C2×#237C23semidirect
165. C2×D3×D4C23semidirect
182. C2×#235C23semidirect
187. C22×D12C23semidirect
195. C22×Dic6C23semidirect
247. C3×#103C23semidirect
248. C3×#102C23semidirect
249. C3×C22⋊C8C23semidirect
250. C3×C22⋊C8C23semidirect
251. #835C23semidirect
252. #832C23semidirect
253. #830C23semidirect
254. #830C23semidirect
255. #821C23semidirect
256. (C2×D3)⋊C8C23semidirect
257. (C2×D3)⋊C8C23semidirect
258. #816C23semidirect
259. #810C23semidirect
260. #809C23semidirect
276. C22×#41C2×D3semidirect
284. C2×AGL(1,ℤ/8)C2×D3semidirect
297. C2×#121C2×D3semidirect
308. #449C2×D3semidirect
314. #448C2×D3semidirect
320. #447C2×D3semidirect
326. #417C2×D3semidirect
333. #407C2×D3semidirect
412. #239C2×D4semidirect
417. D3×Q8C2×D4semidirect
426. #237C2×D4semidirect
438. D3×D4C2×D4semidirect
570. C2×#41C22×D3semidirect
577. C22×Q8C22×D3semidirect
604. C22×D4C22×D3semidirect
666. #103C22×D3semidirect
670. #102C22×D3semidirect
675. C22⋊C8C22×D3semidirect
676. C22⋊C8C22×D3semidirect
1218. C3#60369semidirect

Maximal subgroups

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

subgroupindex
C2×#59642
C2×D3×AGL(1,ℤ/8)2
C2×#56072
C3×#30062
#840822
#839462
#826242
#800862
#800852
#800412
#800042
#788842
#788812
#786392
#786302
#603693