Finite Group Databasebeta

← #11661725

Subgroups — #11661725

Order 768.

5058 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×H(5,𝔽2)C211yesmaximal, characteristic, complemented
2C2×C3×#577C211yesmaximal, characteristic, complemented
3#87295C211yesmaximal, characteristic, complemented
4C2×#5837C211yesmaximal, characteristic, complemented
5#84099C211yesmaximal, characteristic, complemented
6#83982C213yesmaximal, complemented
7#83981C213yesmaximal, complemented
8#83949C213yesmaximal, complemented
9#83944C213yesmaximal, complemented
10#83912C213yesmaximal, complemented
11#83911C213yesmaximal, complemented
12#83859C213yesmaximal, complemented
13C2×#5169C213yesmaximal, complemented
14#83797C211yesmaximal, characteristic, complemented
15#83793C211yesmaximal, characteristic, complemented
16#60373—31nomaximal, Sylow
17C2×C3×2−1+4C2211yescharacteristic, complemented
18C2×C3×H(5,𝔽2)C2211yescharacteristic
19D3×H(5,𝔽2)—28no—
20D3×H(5,𝔽2)—28no—
21C2×#1009—21no—
22C2×#1009C2213yes—
23C2×#1009C2211yescharacteristic
24C2×D3×#41—21no—
25C2×D3×#41C2213yes—
26C2×D3×#41C2211yescharacteristic
27C2×#1004—23no—
28C2×#1004C2213yes—
29C22×D3×D4—23no—
30C22×D3×D4C2213yes—
31C3×#577—28no—
32C2×C3×#137C2213yescomplemented
33C2×C3×AGL(1,ℤ/8)C2213yescomplemented
34C2×C3×#135C2213yescomplemented
35C22×C3×SD16C2213yescomplemented
36C2×C3×#131C2211yescharacteristic, complemented
37#5837—28no—
38#5833C2213yescomplemented
39#5829—23no—
40#5828C2213yescomplemented
41#5827C2211yescharacteristic, complemented
42#5824—23no—
43C2×#950C2213yescomplemented
44C2×#949C2213yescomplemented
45C2×#948C2211yescharacteristic, complemented
46#5817—21no—
47#5816C2213yescomplemented
48Q8×#67—21no—
49C2×#946C2213yescomplemented
50C2×#942C2213yescomplemented
51C22×#215C2213yescomplemented
52#5233C2213yescomplemented
53#5232C2213yescomplemented
54#5215C2213yescomplemented
55C2×#832C2213yescomplemented
56#5187C2216yescomplemented
57#5187C2213yescomplemented
58#5186C2213yescomplemented
59#5173C2216yescomplemented
60#5173C2213yescomplemented
61#5172C2213yescomplemented
62#5170C2211yescharacteristic, complemented
63#5169C2216yescomplemented
64#5169C2213yescomplemented
65#5169C2216yescomplemented
66#5169C2216yescomplemented
67#5169C2216yescomplemented
68#5158C2213yescomplemented
69#5156C2213yescomplemented
70#5156C2216yescomplemented
71#5133C2213yescomplemented
72#5131C2213yescomplemented
73#5129C2213yescomplemented
74#5126C2213yescomplemented
75#5113C2213yescomplemented
76C2×#821C2213yescomplemented
77#5110C2213yescomplemented
78C2×(C2×D3)⋊C8C2213yescomplemented
79C22×H(5,𝔽2)—31no—
80C2×#577—31no—
81C2×#577D311yescharacteristic, complemented
82#3489—31no—
83#3012—33no—
84#3012—33no—
85#3009—33no—
86#3009—33no—
87#3007—33no—
88#3003—33no—
89#3002—33no—
90C2×#450—33no—
91#2897—31no—
92#2897—31no—
93#2880—31no—
94C24×D3—23no—
95C3×2−1+4—24no—
96C3×2−1+4—24no—
97C3×H(5,𝔽2)—24no—
98C3×H(5,𝔽2)D418yescomplemented
99C2×C3×#41—21no—
100C2×C3×#41—23no—
101C2×C3×#41C2313yes—
102C2×C3×#41C2311yescharacteristic
103C2×C3×#41C2313yescomplemented
104C22×C3×Q8—21no—
105C22×C3×Q8C2313yescomplemented
106C22×C3×D4—23no—
107C22×C3×D4C2313yes—
108C22×#67—26no—
109C22×#67—23no—
110#1009—216no—
111#1009—212no—
112#1009—24no—
113#1009—212no—
114#1009D418yescomplemented
115D3×#41—216no—
116D3×#41—24no—
117D3×#41—212no—
118D3×#41—24no—
119D3×#41—212no—
120C2×#239—21no—
121C2×#239D411yescharacteristic
122C2×#239C2313yes—
123C2×D3×Q8D411yescharacteristic
124C2×D3×Q8C2311yescharacteristic
125#1004—248no—
126#1004—212no—
127#1004—212no—
128C2×#237—23no—
129C2×#237—23no—
130C2×#237D413yes—
131C2×#237C2313yes—
132C2×D3×D4—248no—
133C2×D3×D4—23no—
134C2×D3×D4—23no—
135C2×D3×D4—212no—
136C2×D3×D4—26no—
137C2×D3×D4—23no—
138C2×D3×D4—212no—
139C2×D3×D4—23no—
140C2×D3×D4—23no—
141C2×D3×D4D413yes—
142C2×D3×D4C2313yes—
143C2×D3×D4C2316yes—
144C2×#235—23no—
145C2×#235—23no—
146C2×#235C2313yes—
147C2×#235C2313yes—
148C22×D12—23no—
149C22×D12C2313yes—
150C22×C4×D3—23no—
151C22×C4×D3C2313yes—
152C3×#137—212no—
153C3×AGL(1,ℤ/8)—212no—
154C3×#135—212no—
155C2×C3×Q16C2313yescomplemented
156C2×C3×SD16—212no—
157C2×C3×SD16C2313yescomplemented
158C2×C3×SD16C2316yescomplemented
159C2×C3×SD16C2311yescharacteristic, complemented
160C2×C3×D8C2313yescomplemented
161C3×#131—24no—
162C2×C3×M16C2313yescomplemented
163C22×C3×C8C2313yescomplemented
164#950—212no—
165#949—212no—
166#948—24no—
167#947—23no—
168#946—23no—
169#946—23no—
170#946C2313yes—
171#946C2316yescomplemented
172#946C2313yescomplemented
173Q8×Dic3—21no—
174#944—23no—
175C2×#216C2313yescomplemented
176#942—212no—
177C2×#215—212no—
178C2×#215C2313yescomplemented
179C2×#215C2316yescomplemented
180#939—26no—
181#938C2311yescharacteristic
182#938C2313yescomplemented
183#937—23no—
184#935—23no—
185D4×Dic3—23no—
186C2×#214C2311yescharacteristic, complemented
187C2×#213C2313yescomplemented
188#930—23no—
189#929—26no—
190C4×#67—23no—
191C4×#67—23no—
192C2×(C2×D3)⋊C4—23no—
193#926C2313yescomplemented
194C2×C4⋊Dic3C2313yescomplemented
195#924—23no—
196C2×Dic3⋊C4—23no—
197C2×#208C2313yescomplemented
198C22×C3⋊C8C2313yescomplemented
199#835C2311yescharacteristic, complemented
200#835C2313yescomplemented
201#832C2316yescomplemented
202#832C2313yescomplemented
203#832C2313yescomplemented
204#821C2313yescomplemented
205#821C2316yescomplemented
206#821C2313yescomplemented
207(C2×D3)⋊C8C2313yes—
208(C2×D3)⋊C8C2311yescharacteristic
209(C2×D3)⋊C8C2316yescomplemented
210(C2×D3)⋊C8C2313yescomplemented
211(C2×D3)⋊C8C2313yescomplemented
212#816C2313yescomplemented
213#816C2311yescharacteristic, complemented
214C2×2−1+4C2×D311yescharacteristic, complemented
215C2×H(5,𝔽2)—33no—
216C2×H(5,𝔽2)—31no—
217C2×H(5,𝔽2)—33no—
218C2×H(5,𝔽2)—63no—
219C2×H(5,𝔽2)—61no—
220C2×H(5,𝔽2)—68no—
221C2×H(5,𝔽2)—68no—
222C2×H(5,𝔽2)C2×D311yescharacteristic
223C22×#41—31no—
224C22×#41—33no—
225C22×#41—61no—
226C23×D4—33no—
227C23×D4—63no—
228#577—28no—
229#577—68no—
230C2×#137—33no—
231C2×#137C2×D313yescomplemented
232C2×AGL(1,ℤ/8)—33no—
233C2×AGL(1,ℤ/8)C2×D313yescomplemented
234C2×#135—33no—
235C2×#135C2×D313yescomplemented
236C22×SD16—33no—
237C22×SD16C2×D313yescomplemented
238C2×#131—31no—
239C2×#131C2×D311yescharacteristic, complemented
240D4×Q8—61no—
241#548—61no—
242#547—63no—
243#546—63no—
244#537—33no—
245#536—33no—
246#525—33no—
247C2×C22⋊Q8—33no—
248#520—31no—
249#452—33no—
250#452—36no—
251#452—33no—
252#452—36no—
253#451—33no—
254#450—33no—
255#450—36no—
256#450—36no—
257#450—36no—
258#450—36no—
259#449—33no—
260#449—33no—
261#448—31no—
262#447—33no—
263#447—36no—
264#418—33no—
265#418—33no—
266#417—33no—
267#417—33no—
268#416—33no—
269#416—33no—
270C2×#102—33no—
271C2×#102—33no—
272#408—33no—
273#408—33no—
274#407—33no—
275C2×C22⋊C8—33no—
276C24×C3—23no—
277C23×D3—224no—
278C23×D3—23no—
279C23×D3—23no—
280C23×D3—26no—
281C23×D3—86no—
282C23×D3—86no—
283C23×D3C2×D413yes—
284C3×#41—28no—
285C3×#41—26no—
286C3×#41—26no—
287C3×#41—26no—
288C3×#41—412no—
289C3×#41C2×D414yes—
290C3×#41C2×D4112yes—
291C3×#41C2×D414yes—
292C2×C3×Q8—23no—
293C2×C3×Q8—26no—
294C2×C3×Q8—26no—
295C2×C3×Q8—44no—
296C2×C3×Q8C2×D411yescharacteristic
297C2×C3×Q8C2413yes—
298C2×C3×Q8C2411yescharacteristic
299C2×C3×D4—23no—
300C2×C3×D4—224no—
301C2×C3×D4—23no—
302C2×C3×D4—23no—
303C2×C3×D4—26no—
304C2×C3×D4C2×D413yes—
305C2×C3×D4C2×D4112yes—
306C2×C3×D4C2411yescharacteristic
307C2×C3×D4C2413yes—
308C22×C3×C4—23no—
309C22×C3×C4—23no—
310C22×C3×C4—23no—
311C22×C3×C4C2413yes—
312C2×#67—248no—
313C2×#67—224no—
314C2×#67—23no—
315C2×#67—23no—
316C2×#67—21no—
317C2×#67—23no—
318C2×#67—23no—
319C2×#67—26no—
320C2×#67C2×D416yes—
321C22×Dic3—23no—
322C22×Dic3—23no—
323C22×Dic3C2×D413yes—
324#239—28no—
325#239—24no—
326#239—26no—
327#239—26no—
328D3×Q8—24no—
329D3×Q8—22no—
330D3×Q8—22no—
331#237—224no—
332#237—224no—
333#237—212no—
334#237—26no—
335#237—26no—
336D3×D4—224no—
337D3×D4—224no—
338D3×D4—248no—
339D3×D4—224no—
340D3×D4—224no—
341D3×D4—212no—
342D3×D4—224no—
343D3×D4—26no—
344D3×D4—212no—
345D3×D4—26no—
346D3×D4—212no—
347#235—224no—
348#235—224no—
349#235—26no—
350#235—26no—
351#235—26no—
352#235C2×D4112yes—
353C2×D12—224no—
354C2×D12—23no—
355C2×D12—23no—
356C2×D12—26no—
357C2×D12C2×D413yes—
358C2×D12C2×D4112yes—
359C2×D12C2413yes—
360C2×C4×D3—224no—
361C2×C4×D3—21no—
362C2×C4×D3—23no—
363C2×C4×D3—26no—
364C2×C4×D3—26no—
365C2×C4×D3—23no—
366C2×C4×D3C2×D413yes—
367C2×C4×D3C2×D413yes—
368C2×C4×D3C2411yescharacteristic
369C2×C4×D3C2413yes—
370C2×Dic6—21no—
371C2×Dic6C2×D413yes—
372C2×Dic6C2411yescharacteristic
373C3×Q16—26no—
374C3×SD16—22no—
375C3×SD16—26no—
376C3×SD16—212no—
377C3×D8—26no—
378C3×M16—26no—
379C2×C3×C8—26no—
380C2×C3×C8C2411yescharacteristic
381C2×C3×C8C2413yes—
382#217—23no—
383#217—23no—
384#217—21no—
385#216—26no—
386#215—26no—
387#215—212no—
388#214—22no—
389#213—26no—
390(C2×D3)⋊C4—23no—
391(C2×D3)⋊C4—26no—
392(C2×D3)⋊C4—23no—
393C4⋊Dic3—23no—
394C4⋊Dic3C2413yes—
395C4⋊Dic3C2411yescharacteristic
396Dic3⋊C4—23no—
397Dic3⋊C4—26no—
398Dic3⋊C4—23no—
399C4×Dic3—23no—
400#208—26no—
401C2×C3⋊C8—26no—
402C2×C3⋊C8C2411yescharacteristic
403C2×C3⋊C8C2413yes—
404C25—63no—
4052−1+4—24no—
4062−1+4—24no—
407H(5,𝔽2)—24no—
408H(5,𝔽2)—38no—
409H(5,𝔽2)—612no—
410H(5,𝔽2)—648no—
411H(5,𝔽2)—612no—
412H(5,𝔽2)—616no—
413H(5,𝔽2)—612no—
414H(5,𝔽2)—64no—
415H(5,𝔽2)—612no—
416H(5,𝔽2)#6718yescomplemented
417C2×#41—21no—
418C2×#41—23no—
419C2×#41—31no—
420C2×#41—33no—
421C2×#41—33no—
422C2×#41—33no—
423C2×#41—33no—
424C2×#41—33no—
425C2×#41—63no—
426C2×#41—63no—
427C2×#41—63no—
428C2×#41—63no—
429C2×#41—612no—
430C2×#41—616no—
431C2×#41—64no—
432C2×#41—612no—
433C2×#41—64no—
434C2×#41—61no—
435C2×#41C22×D313yes—
436C2×#41C22×D311yescharacteristic
437C2×#41C22×D313yescomplemented
438C22×Q8—21no—
439C22×Q8—31no—
440C22×Q8—31no—
441C22×Q8C22×D313yescomplemented
442C22×D4—23no—
443C22×D4—33no—
444C22×D4—33no—
445C22×D4—36no—
446C22×D4—33no—
447C22×D4—63no—
448C22×D4—63no—
449C22×D4—63no—
450C22×D4—63no—
451C22×D4—612no—
452C22×D4—66no—
453C22×D4—63no—
454C22×D4—63no—
455C22×D4—648no—
456C22×D4—66no—
457C22×D4—63no—
458C22×D4—612no—
459C22×D4C22×D313yes—
460C23×C4—33no—
461C23×C4—63no—
462#137—212no—
463#137—612no—
464AGL(1,ℤ/8)—212no—
465AGL(1,ℤ/8)—612no—
466#135—212no—
467#135—612no—
468C2×Q16—33no—
469C2×Q16C22×D313yescomplemented
470C2×SD16—212no—
471C2×SD16—33no—
472C2×SD16—36no—
473C2×SD16—31no—
474C2×SD16—612no—
475C2×SD16C22×D313yescomplemented
476C2×SD16C22×D316yescomplemented
477C2×SD16C22×D311yescharacteristic, complemented
478C2×D8—33no—
479C2×D8C22×D313yescomplemented
480#131—24no—
481#131—64no—
482C2×M16—33no—
483C2×M16C22×D313yescomplemented
484C22×C8—33no—
485C22×C8C22×D313yescomplemented
486C4⋊Q8—63no—
487#124—63no—
488#123—66no—
489#123—63no—
490C22⋊Q8—33no—
491C22⋊Q8—36no—
492C22⋊Q8—33no—
493C22⋊Q8—63no—
494C22⋊Q8—63no—
495C22⋊Q8—63no—
496#121—31no—
497#121—33no—
498#121—63no—
499#121—66no—
500#120—63no—
501C4×Q8—61no—
502C4×D4—63no—
503C4×D4—63no—
504C4×D4—63no—
505#117—33no—
506C2×C4⋊C4—33no—
507C2×C4⋊C4—63no—
508C2×C22⋊C4—63no—
509#103—31no—
510#103—33no—
511#103—31no—
512#103—33no—
513#102—33no—
514#102—36no—
515#102—33no—
516#102—33no—
517#102—36no—
518#102—33no—
519C22⋊C8—31no—
520C22⋊C8—33no—
521C22⋊C8—33no—
522C22⋊C8—33no—
523C22⋊C8—36no—
524C23×C3—23no—
525C23×C3—212no—
526C23×C3—21no—
527C23×C3—83no—
528C23×C3—83no—
529C23×C3C22×D413yes—
530C22×D3—212no—
531C22×D3—26no—
532C22×D3—23no—
533C22×D3—224no—
534C22×D3—212no—
535C22×D3—26no—
536C22×D3—43no—
537C22×D3—46no—
538C22×D3—46no—
539C22×D3—86no—
540C22×D3—86no—
541C22×D3—848no—
542C22×D3—83no—
543C22×D3—83no—
544C22×D3C22×D413yes—
545C22×D3C22×D411yescharacteristic
546C3×Q8—21no—
547C3×Q8—23no—
548C3×Q8—23no—
549C3×Q8—46no—
550C3×Q8#12014yes—
551C3×Q8C22×D412yes—
552C3×D4—212no—
553C3×D4—212no—
554C3×D4—23no—
555C3×D4—21no—
556C3×D4—21no—
557C3×D4—46no—
558C3×D4#120112yes—
559C3×D4C22×D416yes—
560C2×C3×C4—21no—
561C2×C3×C4—212no—
562C2×C3×C4—23no—
563C2×C3×C4—46no—
564C2×C3×C4—46no—
565C2×C3×C4C22×D413yes—
566C2×C3×C4C22×D416yes—
567C2×C3×C4C22×D416yes—
568C2×C3×C4C2511yescharacteristic
569#67—224no—
570#67—212no—
571#67—212no—
572#67—212no—
573#67—212no—
574#67—42no—
575#67—83no—
576C2×Dic3—212no—
577C2×Dic3—26no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—23no—
581C2×Dic3—83no—
582C2×Dic3C22×D411yescharacteristic
583C2×Dic3C22×D413yes—
584D12—212no—
585D12—26no—
586D12—212no—
587D12—23no—
588D12C22×D416yes—
589C4×D3—24no—
590C4×D3—212no—
591C4×D3—26no—
592C4×D3—212no—
593C4×D3—26no—
594C4×D3—21no—
595C4×D3—21no—
596C4×D3—23no—
597C4×D3—23no—
598Dic6—24no—
599Dic6—26no—
600Dic6—21no—
601Dic6C22×D412yes—
602C3×C8—21no—
603C3×C8—23no—
604C3⋊C8—21no—
605C3⋊C8—23no—
606C24—23no—
607C24—33no—
608C24—63no—
609C24—66no—
610C24—624no—
611C24—63no—
612C24—246no—
613C24—246no—
614#41—28no—
615#41—26no—
616#41—26no—
617#41—26no—
618#41—312no—
619#41—412no—
620#41—624no—
621#41—624no—
622#41—66no—
623#41—624no—
624#41—624no—
625#41—66no—
626#41—64no—
627#41—68no—
628#41—66no—
629#41—612no—
630#41—66no—
631#41—66no—
632#41—66no—
633#41—66no—
634#41D3×D414yes—
635#41C2×#67112yes—
636#41C2×#6714yes—
637C2×Q8—23no—
638C2×Q8—26no—
639C2×Q8—26no—
640C2×Q8—33no—
641C2×Q8—31no—
642C2×Q8—44no—
643C2×Q8—61no—
644C2×Q8—62no—
645C2×Q8—64no—
646C2×Q8—62no—
647C2×Q8D3×D411yescharacteristic
648C2×Q8C23×D313yes—
649C2×Q8C23×D311yescharacteristic
650C2×D4—23no—
651C2×D4—224no—
652C2×D4—23no—
653C2×D4—23no—
654C2×D4—26no—
655C2×D4—36no—
656C2×D4—312no—
657C2×D4—33no—
658C2×D4—33no—
659C2×D4—63no—
660C2×D4—624no—
661C2×D4—63no—
662C2×D4—66no—
663C2×D4—66no—
664C2×D4—612no—
665C2×D4—624no—
666C2×D4—624no—
667C2×D4—648no—
668C2×D4—624no—
669C2×D4—624no—
670C2×D4—63no—
671C2×D4—648no—
672C2×D4—624no—
673C2×D4—63no—
674C2×D4—612no—
675C2×D4—624no—
676C2×D4—66no—
677C2×D4—612no—
678C2×D4—61no—
679C2×D4—63no—
680C2×D4—63no—
681C2×D4—66no—
682C2×D4D3×D413yes—
683C2×D4C2×#67112yes—
684C2×D4C23×D311yescharacteristic
685C2×D4C23×D313yes—
686C22×C4—23no—
687C22×C4—23no—
688C22×C4—23no—
689C22×C4—33no—
690C22×C4—33no—
691C22×C4—33no—
692C22×C4—31no—
693C22×C4—33no—
694C22×C4—63no—
695C22×C4—61no—
696C22×C4—624no—
697C22×C4—63no—
698C22×C4—66no—
699C22×C4—63no—
700C22×C4—66no—
701C22×C4—63no—
702C22×C4C23×D313yes—
703Q16—26no—
704Q16—66no—
705SD16—22no—
706SD16—26no—
707SD16—212no—
708SD16—62no—
709SD16—66no—
710SD16—612no—
711D8—26no—
712D8—66no—
713M16—26no—
714M16—66no—
715C2×C8—26no—
716C2×C8—31no—
717C2×C8—33no—
718C2×C8—66no—
719C2×C8C23×D311yescharacteristic
720C2×C8C23×D313yes—
721C4⋊C4—33no—
722C4⋊C4—31no—
723C4⋊C4—63no—
724C4⋊C4—66no—
725C4⋊C4—63no—
726C4⋊C4—63no—
727C22⋊C4—63no—
728C22⋊C4—66no—
729C22⋊C4—63no—
730C22⋊C4—61no—
731C22⋊C4—63no—
732C22⋊C4—63no—
733C42—63no—
734C22×C3—23no—
735C22×C3—23no—
736C22×C3—26no—
737C22×C3—43no—
738C22×C3—43no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—812no—
743C22×C3C2×#12016yes—
744C22×C3C23×D411yescharacteristic
745C2×D3—21no—
746C2×D3—21no—
747C2×D3—23no—
748C2×D3—23no—
749C2×D3—26no—
750C2×D3—23no—
751C2×D3—412no—
752C2×D3—424no—
753C2×D3—43no—
754C2×D3—43no—
755C2×D3—812no—
756C2×D3—824no—
757C2×D3#57712yescomplemented
758C3×C4—22no—
759C3×C4—43no—
760C3×C4C2×#12016yes—
761C3×C4C23×D411yescharacteristic
762C3×C4C23×D411yescharacteristic
763Dic3—21no—
764Dic3—23no—
765Dic3—22no—
766Dic3—43no—
767Dic3—41no—
768C23—23no—
769C23—212no—
770C23—21no—
771C23—31no—
772C23—33no—
773C23—66no—
774C23—612no—
775C23—624no—
776C23—63no—
777C23—66no—
778C23—612no—
779C23—83no—
780C23—83no—
781C23—123no—
782C23—126no—
783C23—126no—
784C23—243no—
785C23—243no—
786C23—246no—
787C23—246no—
788C23—2448no—
789C23C2×D3×D413yes—
790Q8—21no—
791Q8—23no—
792Q8—23no—
793Q8—32no—
794Q8—46no—
795Q8—64no—
796Q8—61no—
797Q8—66no—
798Q8#93714yes—
799Q8C22×#6712yes—
800D4—212no—
801D4—23no—
802D4—21no—
803D4—21no—
804D4—212no—
805D4—36no—
806D4—46no—
807D4—612no—
808D4—612no—
809D4—624no—
810D4—612no—
811D4—612no—
812D4—612no—
813D4—63no—
814D4—612no—
815D4—66no—
816D4—122no—
817D4—243no—
818D4#937112yes—
819D4C22×#6716yes—
820C2×C4—21no—
821C2×C4—212no—
822C2×C4—23no—
823C2×C4—31no—
824C2×C4—33no—
825C2×C4—46no—
826C2×C4—46no—
827C2×C4—64no—
828C2×C4—612no—
829C2×C4—612no—
830C2×C4—61no—
831C2×C4—66no—
832C2×C4—61no—
833C2×C4—63no—
834C2×C4—61no—
835C2×C4—63no—
836C2×C4—66no—
837C2×C4—66no—
838C2×C4—612no—
839C2×C4—61no—
840C2×C4—63no—
841C2×C4—243no—
842C2×C4C2×D3×D416yes—
843C2×C4C2×D3×D413yes—
844C2×C4C22×#6716yes—
845C2×C4C24×D311yescharacteristic
846C8—21no—
847C8—23no—
848C8—61no—
849C8—63no—
850C2×C3—26no—
851C2×C3—46no—
852C2×C3—81no—
853C2×C3C22×#12011yescharacteristic
854C2×C3C2×#57711yescharacteristic
855C2×C3#358511yescharacteristic
856D3—22no—
857D3—43no—
858D3—46no—
859C22—23no—
860C22—23no—
861C22—26no—
862C22—32no—
863C22—43no—
864C22—43no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—61no—
869C22—61no—
870C22—63no—
871C22—63no—
872C22—66no—
873C22—63no—
874C22—812no—
875C22—1212no—
876C22—1224no—
877C22—123no—
878C22—123no—
879C22—2412no—
880C22—2424no—
881C22C2×#93716yes—
882C22C22×D3×D411yescharacteristic
883C4—22no—
884C4—43no—
885C4—61no—
886C4—63no—
887C4—62no—
888C4—121no—
889C4—123no—
890C4C2×#93716yes—
891C4C22×D3×D411yescharacteristic
892C4C23×#6711yescharacteristic
893C3#6037311yescharacteristic, complemented, Sylow
894C2—26no—
895C2—46no—
896C2—62no—
897C2—81no—
898C2—123no—
899C2—126no—
900C2D3×#57711yescharacteristic
901C2#8720711yescharacteristic
902C2C22×#93711yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#577C2
socleC22×C3C23×D4
hypercenterC2×#577D3
hypocenterC3#60373
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#577

Complements

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

NH ≅ G/Ntype
1. C2×D3×H(5,𝔽2)C2semidirect
2. C2×C3×#577C2semidirect
3. #87295C2semidirect
4. C2×#5837C2semidirect
5. #84099C2semidirect
6. #83982C2semidirect
7. #83981C2semidirect
8. #83949C2semidirect
9. #83944C2semidirect
10. #83912C2semidirect
11. #83911C2semidirect
12. #83859C2semidirect
13. C2×#5169C2semidirect
14. #83797C2semidirect
15. #83793C2semidirect
17. C2×C3×2−1+4C22semidirect
32. C2×C3×#137C22semidirect
33. C2×C3×AGL(1,ℤ/8)C22semidirect
34. C2×C3×#135C22semidirect
35. C22×C3×SD16C22semidirect
36. C2×C3×#131C22semidirect
38. #5833C22semidirect
40. #5828C22semidirect
41. #5827C22semidirect
43. C2×#950C22semidirect
44. C2×#949C22semidirect
45. C2×#948C22semidirect
47. #5816C22semidirect
49. C2×#946C22semidirect
50. C2×#942C22semidirect
51. C22×#215C22semidirect
52. #5233C22semidirect
53. #5232C22semidirect
54. #5215C22semidirect
55. C2×#832C22semidirect
56. #5187C22semidirect
57. #5187C22semidirect
58. #5186C22semidirect
59. #5173C22semidirect
60. #5173C22semidirect
61. #5172C22semidirect
62. #5170C22semidirect
63. #5169C22semidirect
64. #5169C22semidirect
65. #5169C22semidirect
66. #5169C22semidirect
67. #5169C22semidirect
68. #5158C22semidirect
69. #5156C22semidirect
70. #5156C22semidirect
71. #5133C22semidirect
72. #5131C22semidirect
73. #5129C22semidirect
74. #5126C22semidirect
75. #5113C22semidirect
76. C2×#821C22semidirect
77. #5110C22semidirect
78. C2×(C2×D3)⋊C8C22semidirect
81. C2×#577D3semidirect
98. C3×H(5,𝔽2)D4semidirect
103. C2×C3×#41C23semidirect
105. C22×C3×Q8C23semidirect
114. #1009D4semidirect
155. C2×C3×Q16C23semidirect
157. C2×C3×SD16C23semidirect
158. C2×C3×SD16C23semidirect
159. C2×C3×SD16C23semidirect
160. C2×C3×D8C23semidirect
162. C2×C3×M16C23semidirect
163. C22×C3×C8C23semidirect
171. #946C23semidirect
172. #946C23semidirect
175. C2×#216C23semidirect
178. C2×#215C23semidirect
179. C2×#215C23semidirect
182. #938C23semidirect
186. C2×#214C23semidirect
187. C2×#213C23semidirect
193. #926C23semidirect
194. C2×C4⋊Dic3C23semidirect
197. C2×#208C23semidirect
198. C22×C3⋊C8C23semidirect
199. #835C23semidirect
200. #835C23semidirect
201. #832C23semidirect
202. #832C23semidirect
203. #832C23semidirect
204. #821C23semidirect
205. #821C23semidirect
206. #821C23semidirect
209. (C2×D3)⋊C8C23semidirect
210. (C2×D3)⋊C8C23semidirect
211. (C2×D3)⋊C8C23semidirect
212. #816C23semidirect
213. #816C23semidirect
214. C2×2−1+4C2×D3semidirect
231. C2×#137C2×D3semidirect
233. C2×AGL(1,ℤ/8)C2×D3semidirect
235. C2×#135C2×D3semidirect
237. C22×SD16C2×D3semidirect
239. C2×#131C2×D3semidirect
416. H(5,𝔽2)#67semidirect
437. C2×#41C22×D3semidirect
441. C22×Q8C22×D3semidirect
469. C2×Q16C22×D3semidirect
475. C2×SD16C22×D3semidirect
476. C2×SD16C22×D3semidirect
477. C2×SD16C22×D3semidirect
479. C2×D8C22×D3semidirect
483. C2×M16C22×D3semidirect
485. C22×C8C22×D3semidirect
757. C2×D3#577semidirect
893. C3#60373semidirect

Maximal subgroups

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

subgroupindex
C2×D3×H(5,𝔽2)2
C2×C3×#5772
#872952
C2×#58372
#840992
#839822
#839812
#839492
#839442
#839122
#839112
#838592
C2×#51692
#837972
#837932
#603733