Finite Group Databasebeta

← #11707323

Subgroups — #11707323

Order 768.

7686 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3496C211yesmaximal, characteristic, complemented
2#87281C212yesmaximal, complemented
3Dic3×H(5,𝔽2)C212yesmaximal, complemented
4#86685C214yesmaximal, complemented
5#86676C214yesmaximal, complemented
6#86641C218yesmaximal, complemented
7#86637C218yesmaximal, complemented
8#86610C214yesmaximal, complemented
9D4×#237C214yesmaximal, complemented
10#86368C214yesmaximal, complemented
11#86299C218yesmaximal, complemented
12#86225C212yesmaximal, complemented
13#86220C212yesmaximal, complemented
14#85937C214yesmaximal, complemented
15C2×#5598C214yesmaximal, complemented
16C2×D4×Dic6C211yesmaximal, characteristic, complemented
17C4×#1004C211yesmaximal, characteristic, complemented
18#62984—31nomaximal, Sylow
19C2×C3×H(5,𝔽2)C2212yes—
20C2×#1004C2211yescharacteristic
21C22×#237C2214yescomplemented
22C23×Dic6C2212yescomplemented
23C3×#547C2214yescomplemented
24C3×#546C2218yescomplemented
25C3×D42C2214yescomplemented
26C3×#537C2212yescomplemented
27C3×#534C2214yescomplemented
28C3×#532C2212yescomplemented
29C2×C3×#121C2214yescomplemented
30C2×C3×C4×D4C2211yescharacteristic
31#5833C2214yescomplemented
32#5832C2214yescomplemented
33#5829C2218yescomplemented
34#5827C2214yescomplemented
35#5827C2218yescomplemented
36Dic3×#41C2214yescomplemented
37Dic3×#41C2218yescomplemented
38#5824C2218yescomplemented
39#5806C2218yescomplemented
40#5806C2218yescomplemented
41#5804C2218yescomplemented
42C2×#939C2218yescomplemented
43D4×#67C2218yescomplemented
44#5798C2211yescharacteristic
45#5798C2218yescomplemented
46#5798C2218yescomplemented
47C2×#936C2214yescomplemented
48C2×D4×Dic3C2212yes—
49C2×D4×Dic3C2218yescomplemented
50C2×D4×Dic3C2218yescomplemented
51C2×C4×#67C2214yescomplemented
52C2×#924C2212yescomplemented
53#5732C2212yescomplemented
54#5728C2214yescomplemented
55#5721C2212yescomplemented
56#5718C2212yescomplemented
57#5716C2214yescomplemented
58#5713C2212yescomplemented
59#5682C2218yescomplemented
60#5681C2214yescomplemented
61#5671C2214yescomplemented
62#5665C22116yescomplemented
63#5658C22116yescomplemented
64#5650C22116yescomplemented
65#5649C22116yescomplemented
66#5643C2218yescomplemented
67#5641C2218yescomplemented
68#5635C2218yescomplemented
69#5622C2218yescomplemented
70#5618C2218yescomplemented
71#5618C2214yescomplemented
72#5617C2218yescomplemented
73#5616C2218yescomplemented
74#5611C2218yescomplemented
75#5606C2218yescomplemented
76#5603C2218yescomplemented
77#5602C2218yescomplemented
78#5601C2218yescomplemented
79#5601C22116yescomplemented
80#5600C2218yescomplemented
81#5598C22116yescomplemented
82#5598C2218yescomplemented
83#5598C2218yescomplemented
84#5598C22116yescomplemented
85#5598C2214yescomplemented
86#5598C2218yescomplemented
87#5596C2218yescomplemented
88#5593C22116yescomplemented
89#5591C22116yescomplemented
90#5587C22116yescomplemented
91#5586C22116yescomplemented
92#5563C2214yescomplemented
93#5557C2214yescomplemented
94#5555C2214yescomplemented
95#5546C2214yescomplemented
96#5545C2214yescomplemented
97C4×D3×D4C2214yescomplemented
98#5543C2214yescomplemented
99#5542C2214yescomplemented
100#5538C2218yescomplemented
101D4×Dic6C2214yescomplemented
102D4×Dic6C2214yescomplemented
103D4×Dic6C2218yescomplemented
104C4×#237C2214yescomplemented
105C4×#237C2214yescomplemented
106#5513C2218yescomplemented
107C2×#897C2214yescomplemented
108#5504C2212yescomplemented
109C2×#888C2212yescomplemented
110C2×#887C2214yescomplemented
111#5495C22116yescomplemented
112C2×#885C2218yescomplemented
113#5486C2214yescomplemented
114C2×#878C2214yescomplemented
115C2×#878C2218yescomplemented
116C4×#235C2212yescomplemented
117C2×#869C2211yescharacteristic, complemented
118C2×C4×Dic6C2211yescharacteristic, complemented
119#3520—34no—
120#3520—38no—
121#3514—38no—
122#3514—34no—
123#3511—34no—
124#3511—32no—
125#3505—38no—
126#3505—34no—
127#3496—32no—
128#3496D311yescharacteristic, complemented
129#3482—34no—
130#3480—32no—
131D4×#41—34no—
132C2×D4×Q8—31no—
133C2×#548—34no—
134C4×H(5,𝔽2)—32no—
135C4×H(5,𝔽2)—31no—
136C3×H(5,𝔽2)—216no—
137C2×C3×#41C2318yes—
138C2×C3×#41C2314yes—
139C22×C3×D4C2318yes—
140C22×C3×D4C2318yes—
141C22×C3×D4C2314yes—
142C22×C3×D4C2311yescharacteristic
143C23×C3×C4C2312yes—
144C22×#67C2314yes—
145C22×#67C2318yes—
146C23×Dic3C2314yes—
147C23×Dic3C2318yes—
148#1004—28no—
149C2×#237—416no—
150C2×#237C2314yes—
151C2×#237C2314yes—
152C2×#237C2318yes—
153C2×#237C23116yes—
154C2×D3×D4C2314yes—
155C2×#235C2312yes—
156C22×C4×D3C2314yes—
157C22×Dic6—48no—
158C22×Dic6C2311yescharacteristic
159C22×Dic6C2314yes—
160C22×Dic6C2312yes—
161C22×Dic6C2318yes—
162C22×Dic6C2314yes—
163C22×Dic6C2314yes—
164C3×C4⋊Q8C2312yes—
165C3×#127C2312yes—
166C3×#124C2314yes—
167C3×#123C23116yes—
168C3×C22⋊Q8C2318yes—
169C3×#121C2318yes—
170C3×#121C2314yes—
171C3×#121C2318yes—
172C3×#121C2318yes—
173C3×#121C2318yes—
174C3×#121C2314yes—
175C3×#120C23116yes—
176C3×C4×D4C2314yes—
177C3×C4×D4C2314yes—
178C3×C4×D4C2314yes—
179C3×C4×D4C2314yes—
180C2×C3×C4⋊C4C2314yes—
181C2×C3×C4⋊C4C2311yescharacteristic
182C2×C3×C22⋊C4C2312yes—
183C2×C3×C22⋊C4C2318yes—
184C2×C3×C42C2311yescharacteristic
185#953C23116yes—
186C2×#217C2314yes—
187C2×#217C2318yes—
188C2×#217C2314yes—
189C2×#217C2318yes—
190C2×#217C23116yes—
191#947C2314yes—
192#946C2318yes—
193Q8×Dic3C2314yes—
194Q8×Dic3C2314yes—
195Q8×Dic3C2318yes—
196#944C2314yes—
197#940C2314yes—
198#939C23116yes—
199#939C23116yes—
200#939C2318yes—
201#939C2318yes—
202#939C23116yes—
203#939C2318yes—
204#939C23116yes—
205#938C2318yes—
206#938C2318yes—
207#938C2314yes—
208#937C23116yes—
209#936C2314yes—
210#936C2314yes—
211#936C2318yes—
212#936C23116yes—
213#935C23116yes—
214#935C2318yes—
215#935C23116yes—
216D4×Dic3C23116yes—
217D4×Dic3C23116yes—
218D4×Dic3C23116yes—
219D4×Dic3C23116yes—
220D4×Dic3C2314yes—
221D4×Dic3C2314yes—
222D4×Dic3C2318yes—
223D4×Dic3C2314yes—
224D4×Dic3C2318yes—
225D4×Dic3C2314yes—
226D4×Dic3C2318yes—
227D4×Dic3C2318yes—
228D4×Dic3C2314yes—
229D4×Dic3C2318yes—
230D4×Dic3C23116yes—
231D4×Dic3C2318yes—
232#930C2318yes—
233#929C23116yes—
234C4×#67C2318yes—
235C4×#67C2318yes—
236C4×#67C2314yes—
237C4×#67C2314yes—
238C4×#67C2318yes—
239C4×#67C2318yes—
240C4×#67C2318yes—
241C2×(C2×D3)⋊C4C2318yes—
242C2×(C2×D3)⋊C4C2314yes—
243#926C2318yes—
244#926C2318yes—
245#926C23116yes—
246#926C2312yes—
247C2×C4⋊Dic3C2318yes—
248C2×C4⋊Dic3C2318yes—
249C2×C4⋊Dic3C2311yescharacteristic
250C2×C4⋊Dic3C2312yes—
251C2×C4⋊Dic3C2312yes—
252#924C2318yes—
253#924C2318yes—
254#924C2318yes—
255C2×Dic3⋊C4C2318yes—
256C2×Dic3⋊C4C2312yes—
257C2×Dic3⋊C4C2314yes—
258C2×Dic3⋊C4C2314yes—
259C2×C4×Dic3C2318yes—
260C2×C4×Dic3C2312yes—
261C2×C4×Dic3C2314yes—
262C2×C4×Dic3C2318yes—
263#898C23116yes—
264#898C2318yes—
265#897C23116yes—
266#897C2318yes—
267#897C2314yes—
268#893C2314yes—
269#892C2314yes—
270#892C2318yes—
271#892C2314yes—
272D3×C4⋊C4C2314yes—
273#890C2318yes—
274#890C2314yes—
275#889C23116yes—
276#889C2318yes—
277#888C2318yes—
278#888C2318yes—
279#887C23116yes—
280#887C2314yes—
281#887C2318yes—
282#887C2314yes—
283#886C23116yes—
284#886C2318yes—
285#885C23116yes—
286#885C23116yes—
287#885C2318yes—
288#885C23116yes—
289#883C23116yes—
290#883C2318yes—
291#67⋊C4C23116yes—
292#67⋊C4C2318yes—
293#67⋊C4C2318yes—
294#67⋊C4C2318yes—
295D3×C22⋊C4C2318yes—
296#879C23116yes—
297#879C23116yes—
298#879C2318yes—
299#879C2318yes—
300#878C23116yes—
301#878C23116yes—
302#878C23116yes—
303#878C23116yes—
304#878C2318yes—
305#878C23116yes—
306#877C23116yes—
307#877C2318yes—
308#877C2318yes—
309C4×D12C2312yes—
310C4×D12C2312yes—
311#872C2314yes—
312C42×D3C2314yes—
313#869C2314yes—
314#869C2314yes—
315C4×Dic6C2312yes—
316C4×Dic6C2314yes—
317C4×Dic6C2312yes—
318C4×Dic6C2312yes—
319C4×Dic6C2312yes—
320C2×H(5,𝔽2)—31no—
321C2×H(5,𝔽2)C2×D312yes—
322C22×#41—34no—
323C23×Q8—32no—
324#559—32no—
325#559—34no—
326#557—32no—
327#556—32no—
328#556—34no—
329#556—38no—
330#556—34no—
331#555—38no—
332#555—34no—
333#554—38no—
334#554—34no—
335#553—38no—
336#553—34no—
337#553—316no—
338#553—38no—
339#552—316no—
340#552—38no—
341#551—316no—
342#551—316no—
343#551—316no—
344#550—32no—
345D4×Q8—34no—
346D4×Q8—38no—
347D4×Q8—34no—
348#548—34no—
349#548—38no—
350#548—316no—
351#548—38no—
352#548—316no—
353#548—38no—
354#547—38no—
355#547—38no—
356#547—34no—
357#547C2×D314yescomplemented
358#546—38no—
359#546—38no—
360#546—38no—
361#546—316no—
362#546C2×D318yescomplemented
363D42—38no—
364D42C2×D314yescomplemented
365#542—38no—
366#542—38no—
367#542—38no—
368#539—316no—
369#539—38no—
370#538—38no—
371#538—316no—
372#537—34no—
373#537C2×D312yescomplemented
374#534—38no—
375#534C2×D314yescomplemented
376#533—34no—
377#533—38no—
378#532—34no—
379#532—34no—
380#532—38no—
381#532C2×D312yescomplemented
382C2×C4⋊Q8—32no—
383C2×C4⋊Q8—31no—
384#529—316no—
385#529—38no—
386#529—38no—
387#529—34no—
388C2×#124—34no—
389C2×#124—38no—
390#525—38no—
391#525—316no—
392C2×C22⋊Q8—32no—
393C2×C22⋊Q8—34no—
394C2×C22⋊Q8—38no—
395C2×C22⋊Q8—34no—
396C2×#121—38no—
397C2×#121C2×D314yescomplemented
398#520—34no—
399#520—38no—
400#520—34no—
401#520—32no—
402#518—31no—
403#518—38no—
404#518—38no—
405#518—34no—
406#518—34no—
407C4×#41—34no—
408C4×#41—38no—
409C4×#41—34no—
410C4×#41—34no—
411C4×#41—32no—
412C2×C4×Q8—34no—
413C2×C4×Q8—31no—
414C2×C4×D4—38no—
415C2×C4×D4—32no—
416C2×C4×D4—38no—
417C2×C4×D4—34no—
418C2×C4×D4—34no—
419C2×C4×D4C2×D311yescharacteristic
420C24×C3C2418yes—
421C24×C3C2412yes—
422C23×D3C2414yes—
423C3×#41—232no—
424C3×#41—216no—
425C2×C3×Q8C2414yes—
426C2×C3×D4—232no—
427C2×C3×D4—232no—
428C2×C3×D4—48no—
429C2×C3×D4#4118yescomplemented
430C2×C3×D4C24116yes—
431C2×C3×D4C2414yes—
432C2×C3×D4C2418yes—
433C2×C3×D4C2414yes—
434C2×C3×D4C2414yes—
435C2×C3×D4C2418yes—
436C2×C3×D4C2414yes—
437C22×C3×C4—44no—
438C22×C3×C4C2418yes—
439C22×C3×C4C2414yes—
440C22×C3×C4C2418yes—
441C22×C3×C4C2411yescharacteristic
442C22×C3×C4C2411yescharacteristic
443C22×C3×C4C2412yes—
444C22×C3×C4C2414yes—
445C22×C3×C4C2411yescharacteristic
446C2×#67—216no—
447C2×#67—416no—
448C2×#67C2418yes—
449C2×#67C2418yes—
450C2×#67C2414yes—
451C2×#67C2418yes—
452C2×#67C24116yes—
453C22×Dic3—48no—
454C22×Dic3—416no—
455C22×Dic3C2414yes—
456C22×Dic3C2418yes—
457C22×Dic3C2418yes—
458C22×Dic3C2412yes—
459C22×Dic3C2418yes—
460C22×Dic3C24116yes—
461C22×Dic3C2418yes—
462C22×Dic3C2414yes—
463C22×Dic3C2414yes—
464C22×Dic3C2412yes—
465C22×Dic3C2414yes—
466#237—216no—
467#237—216no—
468#237—416no—
469#237—432no—
470D3×D4—216no—
471#235—28no—
472C2×D12C2412yes—
473C2×C4×D3—48no—
474C2×C4×D3C2414yes—
475C2×C4×D3C2414yes—
476C2×C4×D3C2414yes—
477C2×C4×D3C2418yes—
478C2×Dic6—24no—
479C2×Dic6—216no—
480C2×Dic6—416no—
481C2×Dic6—48no—
482C2×Dic6—48no—
483C2×Dic6—44no—
484C2×Dic6C2412yes—
485C2×Dic6C2412yes—
486C2×Dic6C2411yescharacteristic
487C2×Dic6C2414yes—
488C2×Dic6C2418yes—
489C2×Dic6C2414yes—
490C2×Dic6C2418yes—
491C2×Dic6C2411yescharacteristic
492C3×C4⋊C4C2414yes—
493C3×C4⋊C4C2418yes—
494C3×C4⋊C4C2414yes—
495C3×C4⋊C4C2414yes—
496C3×C22⋊C4C2418yes—
497C3×C22⋊C4C24116yes—
498C3×C22⋊C4C2418yes—
499C3×C22⋊C4C2418yes—
500C3×C42C2412yes—
501C3×C42C2412yes—
502#217C24116yes—
503#217C2418yes—
504#217C2418yes—
505#217C2418yes—
506#217C24116yes—
507#217C2418yes—
508#217C24116yes—
509#217C2418yes—
510#217C2414yes—
511(C2×D3)⋊C4C2414yes—
512(C2×D3)⋊C4C2414yes—
513(C2×D3)⋊C4C2418yes—
514(C2×D3)⋊C4C2418yes—
515(C2×D3)⋊C4C24116yes—
516(C2×D3)⋊C4C2418yes—
517C4⋊Dic3C2412yes—
518C4⋊Dic3C2412yes—
519C4⋊Dic3C2412yes—
520C4⋊Dic3C2412yes—
521C4⋊Dic3C2418yes—
522C4⋊Dic3C2418yes—
523C4⋊Dic3C2418yes—
524C4⋊Dic3C24116yes—
525C4⋊Dic3C2418yes—
526Dic3⋊C4C2414yes—
527Dic3⋊C4C2414yes—
528Dic3⋊C4C2414yes—
529Dic3⋊C4C2414yes—
530Dic3⋊C4C2418yes—
531Dic3⋊C4C2418yes—
532Dic3⋊C4C2418yes—
533Dic3⋊C4C24116yes—
534Dic3⋊C4C24116yes—
535C4×Dic3C2414yes—
536C4×Dic3C2414yes—
537C4×Dic3C2414yes—
538C4×Dic3C2414yes—
539C4×Dic3C2414yes—
540C4×Dic3C2418yes—
541C4×Dic3C2418yes—
542C4×Dic3C24116yes—
543C4×Dic3C2418yes—
544H(5,𝔽2)—216no—
545H(5,𝔽2)—68no—
546C2×#41—34no—
547C2×#41—34no—
548C2×#41—316no—
549C2×#41—38no—
550C2×#41—32no—
551C2×#41—1216no—
552C2×#41C22×D314yes—
553C2×#41C22×D318yes—
554C22×Q8—31no—
555C22×Q8—34no—
556C22×Q8—38no—
557C22×Q8—34no—
558C22×Q8—34no—
559C22×Q8—32no—
560C22×Q8—128no—
561C22×D4—34no—
562C22×D4—38no—
563C22×D4—34no—
564C22×D4C22×D318yes—
565C22×D4C22×D318yes—
566C22×D4C22×D314yes—
567C22×D4C22×D311yescharacteristic
568C23×C4—34no—
569C23×C4—38no—
570C23×C4—34no—
571C23×C4C22×D312yes—
572C4⋊Q8—34no—
573C4⋊Q8—38no—
574C4⋊Q8—38no—
575C4⋊Q8—34no—
576C4⋊Q8—34no—
577C4⋊Q8C22×D312yes—
578#127—34no—
579#127C22×D312yes—
580#126—316no—
581#126—38no—
582#126—316no—
583#126—316no—
584#126—38no—
585#126—38no—
586#125—38no—
587#125—34no—
588#125—316no—
589#125—38no—
590#124—34no—
591#124—34no—
592#124—38no—
593#124—316no—
594#124—34no—
595#124—38no—
596#124—316no—
597#124—316no—
598#124—316no—
599#124C22×D314yes—
600#123—316no—
601#123—316no—
602#123—38no—
603#123—316no—
604#123—316no—
605#123—316no—
606#123—38no—
607#123—38no—
608#123C22×D3116yes—
609C22⋊Q8—38no—
610C22⋊Q8—38no—
611C22⋊Q8—38no—
612C22⋊Q8—38no—
613C22⋊Q8—34no—
614C22⋊Q8—38no—
615C22⋊Q8—316no—
616C22⋊Q8—38no—
617C22⋊Q8—316no—
618C22⋊Q8—316no—
619C22⋊Q8—316no—
620C22⋊Q8—316no—
621C22⋊Q8—316no—
622C22⋊Q8C22×D318yes—
623#121—38no—
624#121—316no—
625#121—316no—
626#121—316no—
627#121—34no—
628#121—38no—
629#121—38no—
630#121—38no—
631#121—38no—
632#121—316no—
633#121—38no—
634#121C22×D314yes—
635#121C22×D318yes—
636#121C22×D318yes—
637#121C22×D318yes—
638#121C22×D318yes—
639#121C22×D314yes—
640#120—316no—
641#120—316no—
642#120C22×D3116yes—
643C4×Q8—34no—
644C4×Q8—38no—
645C4×Q8—34no—
646C4×Q8—34no—
647C4×Q8—316no—
648C4×Q8—38no—
649C4×Q8—34no—
650C4×Q8—32no—
651C4×Q8—34no—
652C4×Q8—32no—
653C4×Q8—32no—
654C4×Q8—32no—
655C4×D4—34no—
656C4×D4—38no—
657C4×D4—316no—
658C4×D4—34no—
659C4×D4—38no—
660C4×D4—316no—
661C4×D4—38no—
662C4×D4—38no—
663C4×D4—316no—
664C4×D4—316no—
665C4×D4—34no—
666C4×D4—316no—
667C4×D4—38no—
668C4×D4—34no—
669C4×D4—34no—
670C4×D4—38no—
671C4×D4—38no—
672C4×D4—34no—
673C4×D4—38no—
674C4×D4—38no—
675C4×D4—34no—
676C4×D4—38no—
677C4×D4—38no—
678C4×D4—34no—
679C4×D4—38no—
680C4×D4—38no—
681C4×D4—38no—
682C4×D4—316no—
683C4×D4—32no—
684C4×D4—32no—
685C4×D4C22×D314yes—
686C4×D4C22×D314yes—
687C4×D4C22×D314yes—
688C4×D4C22×D314yes—
689#117—32no—
690#117—38no—
691#117—316no—
692#117—38no—
693#117—34no—
694#117—34no—
695#117—38no—
696#117—38no—
697#117—38no—
698#117—316no—
699#117—34no—
700C2×C4⋊C4—34no—
701C2×C4⋊C4—38no—
702C2×C4⋊C4—32no—
703C2×C4⋊C4—38no—
704C2×C4⋊C4—38no—
705C2×C4⋊C4—32no—
706C2×C4⋊C4—31no—
707C2×C4⋊C4—34no—
708C2×C4⋊C4—32no—
709C2×C4⋊C4—34no—
710C2×C4⋊C4C22×D311yescharacteristic
711C2×C4⋊C4C22×D314yes—
712C2×C22⋊C4—34no—
713C2×C22⋊C4—34no—
714C2×C22⋊C4—38no—
715C2×C22⋊C4—316no—
716C2×C22⋊C4—38no—
717C2×C22⋊C4—34no—
718C2×C22⋊C4—38no—
719C2×C22⋊C4—38no—
720C2×C22⋊C4C22×D312yes—
721C2×C22⋊C4C22×D318yes—
722C2×C42—34no—
723C2×C42—38no—
724C2×C42—32no—
725C2×C42—38no—
726C2×C42—34no—
727C2×C42C22×D311yescharacteristic
728C23×C3—216no—
729C23×C3—42no—
730C23×C3—42no—
731C23×C3—48no—
732C23×C3—48no—
733C23×C3C2×#4118yescomplemented
734C23×C3C2518yes—
735C23×C3C2514yes—
736C23×C3C2511yescharacteristic
737C22×D3—28no—
738C22×D3—44no—
739C22×D3—44no—
740C22×D3C2514yes—
741C3×Q8—28no—
742C3×D4—232no—
743C3×D4—216no—
744C3×D4—28no—
745C3×D4—28no—
746C3×D4—48no—
747C3×D4—44no—
748C3×D4C2×#41116yescomplemented
749C2×C3×C4—216no—
750C2×C3×C4—216no—
751C2×C3×C4—22no—
752C2×C3×C4—28no—
753C2×C3×C4—44no—
754C2×C3×C4—42no—
755C2×C3×C4—41no—
756C2×C3×C4C2×#4114yescomplemented
757C2×C3×C4C2518yes—
758C2×C3×C4C2512yes—
759C2×C3×C4C2514yes—
760C2×C3×C4C2511yescharacteristic
761C2×C3×C4C2512yes—
762C2×C3×C4C2511yescharacteristic
763#67—28no—
764#67—216no—
765#67—216no—
766#67—416no—
767#67—48no—
768C2×Dic3—28no—
769C2×Dic3—24no—
770C2×Dic3—216no—
771C2×Dic3—216no—
772C2×Dic3—48no—
773C2×Dic3—44no—
774C2×Dic3—44no—
775C2×Dic3—416no—
776C2×Dic3—44no—
777C2×Dic3—48no—
778C2×Dic3—42no—
779C2×Dic3C2514yes—
780C2×Dic3C2514yes—
781C2×Dic3C2514yes—
782C2×Dic3C2514yes—
783C2×Dic3C2518yes—
784C2×Dic3C2512yes—
785C2×Dic3C2512yes—
786D12—24no—
787C4×D3—28no—
788C4×D3—28no—
789C4×D3—48no—
790C4×D3—44no—
791Dic6—24no—
792Dic6—22no—
793Dic6—28no—
794Dic6—24no—
795Dic6—216no—
796Dic6—48no—
797Dic6—44no—
798Dic6H(5,𝔽2)14yescomplemented
799C24—34no—
800C24C23×D318yes—
801C24C23×D312yes—
802#41—232no—
803#41—216no—
804#41—616no—
805#41—616no—
806#41—68no—
807#41—1216no—
808#41—1232no—
809C2×Q8—31no—
810C2×Q8—32no—
811C2×Q8—32no—
812C2×Q8—31no—
813C2×Q8—38no—
814C2×Q8—34no—
815C2×Q8—38no—
816C2×Q8—34no—
817C2×Q8—64no—
818C2×Q8—616no—
819C2×Q8—124no—
820C2×Q8—128no—
821C2×Q8—1216no—
822C2×Q8—128no—
823C2×Q8C23×D314yes—
824C2×D4—232no—
825C2×D4—232no—
826C2×D4—38no—
827C2×D4—34no—
828C2×D4—38no—
829C2×D4—38no—
830C2×D4—316no—
831C2×D4—32no—
832C2×D4—48no—
833C2×D4—616no—
834C2×D4—616no—
835C2×D4—1216no—
836C2×D4#23718yescomplemented
837C2×D4C23×D3116yes—
838C2×D4C23×D318yes—
839C2×D4C23×D314yes—
840C2×D4C23×D314yes—
841C2×D4C23×D314yes—
842C2×D4C23×D318yes—
843C2×D4C23×D314yes—
844C22×C4—34no—
845C22×C4—32no—
846C22×C4—38no—
847C22×C4—38no—
848C22×C4—34no—
849C22×C4—32no—
850C22×C4—38no—
851C22×C4—38no—
852C22×C4—34no—
853C22×C4—34no—
854C22×C4—316no—
855C22×C4—34no—
856C22×C4—34no—
857C22×C4—34no—
858C22×C4—38no—
859C22×C4—44no—
860C22×C4—128no—
861C22×C4—128no—
862C22×C4—1216no—
863C22×C4C23×D318yes—
864C22×C4C23×D318yes—
865C22×C4C23×D314yes—
866C22×C4C23×D311yescharacteristic
867C22×C4C23×D311yescharacteristic
868C22×C4C23×D314yes—
869C22×C4C23×D312yes—
870C22×C4C23×D311yescharacteristic
871C4⋊C4—32no—
872C4⋊C4—38no—
873C4⋊C4—34no—
874C4⋊C4—38no—
875C4⋊C4—38no—
876C4⋊C4—316no—
877C4⋊C4—38no—
878C4⋊C4—34no—
879C4⋊C4—32no—
880C4⋊C4—316no—
881C4⋊C4—38no—
882C4⋊C4—316no—
883C4⋊C4—34no—
884C4⋊C4—32no—
885C4⋊C4—32no—
886C4⋊C4—34no—
887C4⋊C4—38no—
888C4⋊C4—38no—
889C4⋊C4C23×D314yes—
890C4⋊C4C23×D314yes—
891C4⋊C4C23×D318yes—
892C4⋊C4C23×D314yes—
893C22⋊C4—38no—
894C22⋊C4—34no—
895C22⋊C4—316no—
896C22⋊C4—38no—
897C22⋊C4—316no—
898C22⋊C4—38no—
899C22⋊C4—38no—
900C22⋊C4—316no—
901C22⋊C4—38no—
902C22⋊C4—34no—
903C22⋊C4—38no—
904C22⋊C4—34no—
905C22⋊C4—38no—
906C22⋊C4—316no—
907C22⋊C4—38no—
908C22⋊C4C23×D318yes—
909C22⋊C4C23×D318yes—
910C22⋊C4C23×D3116yes—
911C22⋊C4C23×D318yes—
912C42—34no—
913C42—34no—
914C42—38no—
915C42—34no—
916C42—38no—
917C42—34no—
918C42—38no—
919C42—316no—
920C42—34no—
921C42C23×D312yes—
922C42C23×D312yes—
923C22×C3—21no—
924C22×C3—24no—
925C22×C3—21no—
926C22×C3—24no—
927C22×C3—28no—
928C22×C3—28no—
929C22×C3—28no—
930C22×C3—48no—
931C22×C3—816no—
932C22×C3C22×#4118yes—
933C22×C3C22×#4112yes—
934C22×C3C2611yescharacteristic
935C2×D3—24no—
936C2×D3—24no—
937C2×D3—24no—
938C2×D3—88no—
939C3×C4—28no—
940C3×C4—21no—
941C3×C4—24no—
942C3×C4—22no—
943C3×C4C22×#4114yes—
944C3×C4C2×H(5,𝔽2)12yes—
945Dic3—24no—
946Dic3—22no—
947Dic3—28no—
948Dic3—24no—
949Dic3—24no—
950Dic3—24no—
951Dic3C2×H(5,𝔽2)14yes—
952C23—216no—
953C23—34no—
954C23—42no—
955C23—42no—
956C23—48no—
957C23—48no—
958C23—68no—
959C23—124no—
960C23—124no—
961C23C2×#23718yescomplemented
962C23C24×D318yes—
963C23C24×D314yes—
964C23C24×D311yescharacteristic
965Q8—28no—
966Q8—34no—
967Q8—64no—
968Q8—616no—
969Q8—64no—
970Q8—62no—
971Q8—68no—
972Q8—124no—
973Q8—128no—
974D4—232no—
975D4—216no—
976D4—28no—
977D4—28no—
978D4—48no—
979D4—44no—
980D4—616no—
981D4—616no—
982D4—68no—
983D4—64no—
984D4—1216no—
985D4—128no—
986D4C2×#237116yescomplemented
987C2×C4—216no—
988C2×C4—216no—
989C2×C4—22no—
990C2×C4—28no—
991C2×C4—32no—
992C2×C4—34no—
993C2×C4—34no—
994C2×C4—34no—
995C2×C4—34no—
996C2×C4—32no—
997C2×C4—38no—
998C2×C4—44no—
999C2×C4—42no—
1000C2×C4—41no—
1001C2×C4—616no—
1002C2×C4—64no—
1003C2×C4—616no—
1004C2×C4—68no—
1005C2×C4—68no—
1006C2×C4—68no—
1007C2×C4—128no—
1008C2×C4—124no—
1009C2×C4—124no—
1010C2×C4—124no—
1011C2×C4—128no—
1012C2×C4—1216no—
1013C2×C4—124no—
1014C2×C4—128no—
1015C2×C4—122no—
1016C2×C4C2×#23714yescomplemented
1017C2×C4C24×D318yes—
1018C2×C4C24×D312yes—
1019C2×C4C24×D314yes—
1020C2×C4C24×D311yescharacteristic
1021C2×C4C24×D312yes—
1022C2×C4C24×D311yescharacteristic
1023C2×C3—28no—
1024C2×C3—22no—
1025C2×C3—48no—
1026C2×C3C23×#4111yescharacteristic
1027C2×C3C22×H(5,𝔽2)11yescharacteristic
1028C2×C32−1+611yescharacteristic
1029D3—44no—
1030C22—21no—
1031C22—24no—
1032C22—21no—
1033C22—24no—
1034C22—28no—
1035C22—28no—
1036C22—28no—
1037C22—48no—
1038C22—64no—
1039C22—64no—
1040C22—64no—
1041C22—816no—
1042C22—248no—
1043C22C22×#23718yes—
1044C22C22×#23712yes—
1045C22C25×D311yescharacteristic
1046C4—28no—
1047C4—21no—
1048C4—24no—
1049C4—22no—
1050C4—34no—
1051C4—64no—
1052C4—64no—
1053C4—68no—
1054C4—62no—
1055C4—64no—
1056C4—64no—
1057C4C22×#23714yes—
1058C4D3×H(5,𝔽2)12yes—
1059C3#6298411yescharacteristic, complemented, Sylow
1060C2—22no—
1061C2—28no—
1062C2—48no—
1063C2—124no—
1064C2C23×#23711yescharacteristic
1065C2C2×D3×H(5,𝔽2)11yescharacteristic
1066C2#8757211yescharacteristic
subgroupG/H
center, FrattiniC22C25×D3
commutator, socle, cosocleC22×C3C26
FittingC3×#3496C2
hypercenter#3496D3
hypocenterC3#62984
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #3496

Complements

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

NH ≅ G/Ntype
1. C3×#3496C2semidirect
2. #87281C2semidirect
3. Dic3×H(5,𝔽2)C2semidirect
4. #86685C2semidirect
5. #86676C2semidirect
6. #86641C2semidirect
7. #86637C2semidirect
8. #86610C2semidirect
9. D4×#237C2semidirect
10. #86368C2semidirect
11. #86299C2semidirect
12. #86225C2semidirect
13. #86220C2semidirect
14. #85937C2semidirect
15. C2×#5598C2semidirect
16. C2×D4×Dic6C2semidirect
17. C4×#1004C2semidirect
21. C22×#237C22semidirect
22. C23×Dic6C22semidirect
23. C3×#547C22semidirect
24. C3×#546C22semidirect
25. C3×D42C22semidirect
26. C3×#537C22semidirect
27. C3×#534C22semidirect
28. C3×#532C22semidirect
29. C2×C3×#121C22semidirect
31. #5833C22semidirect
32. #5832C22semidirect
33. #5829C22semidirect
34. #5827C22semidirect
35. #5827C22semidirect
36. Dic3×#41C22semidirect
37. Dic3×#41C22semidirect
38. #5824C22semidirect
39. #5806C22semidirect
40. #5806C22semidirect
41. #5804C22semidirect
42. C2×#939C22semidirect
43. D4×#67C22semidirect
45. #5798C22semidirect
46. #5798C22semidirect
47. C2×#936C22semidirect
49. C2×D4×Dic3C22semidirect
50. C2×D4×Dic3C22semidirect
51. C2×C4×#67C22semidirect
52. C2×#924C22semidirect
53. #5732C22semidirect
54. #5728C22semidirect
55. #5721C22semidirect
56. #5718C22semidirect
57. #5716C22semidirect
58. #5713C22semidirect
59. #5682C22semidirect
60. #5681C22semidirect
61. #5671C22semidirect
62. #5665C22semidirect
63. #5658C22semidirect
64. #5650C22semidirect
65. #5649C22semidirect
66. #5643C22semidirect
67. #5641C22semidirect
68. #5635C22semidirect
69. #5622C22semidirect
70. #5618C22semidirect
71. #5618C22semidirect
72. #5617C22semidirect
73. #5616C22semidirect
74. #5611C22semidirect
75. #5606C22semidirect
76. #5603C22semidirect
77. #5602C22semidirect
78. #5601C22semidirect
79. #5601C22semidirect
80. #5600C22semidirect
81. #5598C22semidirect
82. #5598C22semidirect
83. #5598C22semidirect
84. #5598C22semidirect
85. #5598C22semidirect
86. #5598C22semidirect
87. #5596C22semidirect
88. #5593C22semidirect
89. #5591C22semidirect
90. #5587C22semidirect
91. #5586C22semidirect
92. #5563C22semidirect
93. #5557C22semidirect
94. #5555C22semidirect
95. #5546C22semidirect
96. #5545C22semidirect
97. C4×D3×D4C22semidirect
98. #5543C22semidirect
99. #5542C22semidirect
100. #5538C22semidirect
101. D4×Dic6C22semidirect
102. D4×Dic6C22semidirect
103. D4×Dic6C22semidirect
104. C4×#237C22semidirect
105. C4×#237C22semidirect
106. #5513C22semidirect
107. C2×#897C22semidirect
108. #5504C22semidirect
109. C2×#888C22semidirect
110. C2×#887C22semidirect
111. #5495C22semidirect
112. C2×#885C22semidirect
113. #5486C22semidirect
114. C2×#878C22semidirect
115. C2×#878C22semidirect
116. C4×#235C22semidirect
117. C2×#869C22semidirect
118. C2×C4×Dic6C22semidirect
128. #3496D3semidirect
357. #547C2×D3semidirect
362. #546C2×D3semidirect
364. D42C2×D3semidirect
373. #537C2×D3semidirect
375. #534C2×D3semidirect
381. #532C2×D3semidirect
397. C2×#121C2×D3semidirect
429. C2×C3×D4#41semidirect
733. C23×C3C2×#41semidirect
748. C3×D4C2×#41semidirect
756. C2×C3×C4C2×#41semidirect
798. Dic6H(5,𝔽2)semidirect
836. C2×D4#237semidirect
961. C23C2×#237semidirect
986. D4C2×#237semidirect
1016. C2×C4C2×#237semidirect
1059. C3#62984semidirect

Maximal subgroups

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

subgroupindex
C3×#34962
#872812
Dic3×H(5,𝔽2)2
#866852
#866762
#866412
#866372
#866102
D4×#2372
#863682
#862992
#862252
#862202
#859372
C2×#55982
C2×D4×Dic62
C4×#10042
#629843