Finite Group Databasebeta

← #11664490

Subgroups — #11664490

Order 768.

2170 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#532C211yesmaximal, characteristic
2C2×#5728C211yesmaximal, characteristic, complemented
3C3×#3141C211yesmaximal, characteristic, complemented
4#83283C211yesmaximal, characteristic, complemented
5#83199C211yesmaximal, characteristic, complemented
6#81682C214yesmaximal, complemented
7#81679C214yesmaximal, complemented
8#81600C212yesmaximal, complemented
9#81598C212yesmaximal, complemented
10#81564C212yesmaximal, complemented
11#81562C212yesmaximal, complemented
12#78881C214yesmaximal, complemented
13#78879C214yesmaximal, complemented
14#78528C211yesmaximal, characteristic, complemented
15C4×D3×M16C211yesmaximal, characteristic, complemented
16#60618—31nomaximal, Sylow
17C2×D3×#41C2212yes—
18C3×#532C2211yescharacteristic
19C2×C3×C4⋊Q8C2211yescharacteristic, complemented
20#5832C2212yes—
21C2×#946—21no—
22C2×Q8×Dic3—21no—
23C2×D3×M16C2212yes—
24#5728—21no—
25#5728—21no—
26#5728—21no—
27#5728—21no—
28#5728C2212yes—
29#5728C2212yes—
30#5728C2212yescomplemented
31#5728C2212yescomplemented
32#5725C2211yescharacteristic
33D3×C4⋊Q8C2211yescharacteristic
34#5716C2211yescharacteristic
35D3×#127C2211yescharacteristic
36D3×#124C2212yes—
37#5668C2212yes—
38D3×#121—21no—
39D3×#121—21no—
40#5596—21no—
41#5596—21no—
42#5548—21no—
43#5548—21no—
44C4×D3×D4—21no—
45C4×D3×D4—21no—
46C2×#897—21no—
47C2×#892C2212yes—
48C2×#890C2212yescomplemented
49C2×#887—21no—
50#5477C2211yescharacteristic
51C2×C42×D3C2211yescharacteristic
52C2×#869C2211yescharacteristic, complemented
53C3×#489C2214yescomplemented
54C3×#487C2212yescomplemented
55C3×#486C2212yescomplemented
56C3×#417C2214yescomplemented
57C3×C4×M16C2211yescharacteristic, complemented
58#5232C2214yescomplemented
59#5133C2214yescomplemented
60Dic3×M16C2212yescomplemented
61#5093C2212yescomplemented
62#5089C2214yescomplemented
63#5088C2212yescomplemented
64#5079C2212yescomplemented
65#5070C2212yescomplemented
66#5055C2214yescomplemented
67#4966C2214yescomplemented
68C4×#208C2211yescharacteristic, complemented
69#4804C2218yescomplemented
70#4802C2218yes—
71#4800C2218yescomplemented
72#4797C2218yescomplemented
73#4772C2218yescomplemented
74#4770C2218yes—
75#4768C2218yescomplemented
76#4764C2218yescomplemented
77#4714C2214yescomplemented
78#4707C2212yes—
79D3×#97C2212yescomplemented
80#4694C2212yescomplemented
81C4×ΓL(1,𝔽25)C2212yes—
82C4×D3×C8C2212yescomplemented
83#4681C2212yescomplemented
84C2×#533—31no—
85C2×#532—31no—
86#3142—34no—
87#3141—31no—
88#3141—31no—
89#3141—31no—
90#3141D311yescharacteristic, complemented
91#3140—34no—
92#3139—32no—
93#3138—32no—
94#3135—34no—
95#3131—32no—
96#3131—32no—
97#2896—34no—
98C2×C4×M16—31no—
99C2×C3×#41C2312yes—
100C22×C3×Q8—21no—
101D3×#41—216no—
102C2×#239C2312yes—
103C2×D3×Q8C2312yes—
104C2×#237—22no—
105C2×#237C2312yes—
106C2×D3×D4—22no—
107C2×D3×D4—21no—
108C2×D3×D4—21no—
109C2×D3×D4C2312yes—
110C2×#235—22no—
111C2×#235C2312yes—
112C22×C4×D3—22no—
113C22×C4×D3D411yescharacteristic
114C22×C4×D3D411yescharacteristic
115C22×C4×D3C2311yescharacteristic
116C22×Dic6—21no—
117C2×C3×M16C2312yes—
118C3×C4⋊Q8—21no—
119C3×C4⋊Q8—21no—
120C3×C4⋊Q8C2311yescharacteristic
121C3×C4⋊Q8C2312yes—
122C3×C4⋊Q8C2312yes—
123C3×#127C2311yescharacteristic
124C3×#124C2312yes—
125C3×#121—21no—
126C3×#121—21no—
127C3×C4×D4—21no—
128C3×C4×D4—21no—
129C2×C3×C4⋊C4—21no—
130C2×C3×C4⋊C4C2312yes—
131C2×C3×C42C2311yescharacteristic
132#947C2312yes—
133#946—22no—
134#946—22no—
135#946—22no—
136#946—22no—
137Q8×Dic3—22no—
138Q8×Dic3—22no—
139Q8×Dic3—22no—
140Q8×Dic3—22no—
141#944C2312yes—
142#940—21no—
143#940—21no—
144#940C2312yes—
145#939—22no—
146#939—22no—
147#938—21no—
148#938—21no—
149#936C2312yes—
150D4×Dic3—21no—
151D4×Dic3—21no—
152#930—21no—
153#930—21no—
154C4×#67—22no—
155C4×#67—22no—
156C2×(C2×D3)⋊C4—22no—
157C2×C4⋊Dic3—21no—
158C2×C4⋊Dic3—22no—
159C2×C4⋊Dic3C2312yes—
160C2×Dic3⋊C4—22no—
161C2×C4×Dic3—22no—
162C2×C4×Dic3D411yescharacteristic
163C2×C4×Dic3D411yescharacteristic
164C2×C4×Dic3C2311yescharacteristic
165C2×#208C2312yes—
166D3×M16—28no—
167C2×ΓL(1,𝔽25)C2314yes—
168C2×D3×C8C2314yes—
169#897—22no—
170#897—22no—
171#897—22no—
172#897—22no—
173#895—21no—
174#895—21no—
175#893—21no—
176#893—21no—
177#892—22no—
178#892—22no—
179#892C2314yes—
180#892C2314yes—
181D3×C4⋊C4—21no—
182D3×C4⋊C4—21no—
183#890—22no—
184#890—22no—
185#890C2314yes—
186#890C2314yes—
187#888—21no—
188#888—21no—
189#887—22no—
190#887—22no—
191#887—22no—
192#887—22no—
193#885—22no—
194#885—22no—
195#884—22no—
196#884—22no—
197#67⋊C4—22no—
198#67⋊C4—22no—
199D3×C22⋊C4—22no—
200D3×C22⋊C4—22no—
201#875C2312yes—
202#874C2311yescharacteristic
203C4×D12—21no—
204C4×D12—21no—
205C42×D3D411yescharacteristic
206C42×D3D411yescharacteristic
207C42×D3D411yescharacteristic
208C42×D3D411yescharacteristic
209C42×D3C2311yescharacteristic
210C42×D3C2311yescharacteristic
211C42×D3C2311yescharacteristic
212C42×D3C2311yescharacteristic
213#869—21no—
214#869—21no—
215#869C2311yescharacteristic
216#869C2312yes—
217#869C2312yes—
218C3×#103C2318yes—
219C3×#102C2318yes—
220C3×#97C2312yes—
221C3×C4×C8C2312yes—
222#835C2318yes—
223#832C2318yes—
224#821C2318yes—
225#816C2318yes—
226#815C2314yes—
227C8×Dic3C2314yes—
228#810C2318yes—
229#809C2318yes—
230#803C2312yes—
231C4×C3⋊C8C2312yes—
232C22×#41—32no—
233C22×M16—32no—
234#533—32no—
235#533—32no—
236#533—32no—
237#533—32no—
238#533—61no—
239#533—61no—
240#533—61no—
241#533—61no—
242#532—32no—
243#532—31no—
244#532—31no—
245#532—32no—
246#532—31no—
247#532—61no—
248#532—61no—
249#532—61no—
250#532—61no—
251#532C2×D311yescharacteristic
252C2×C4⋊Q8—31no—
253C2×C4⋊Q8—31no—
254C2×C4⋊Q8C2×D311yescharacteristic, complemented
255C2×#127—31no—
256C2×#125—32no—
257C2×#124—32no—
258C2×C22⋊Q8—61no—
259C2×C22⋊Q8—61no—
260C2×#121—61no—
261C2×#121—61no—
262C2×C4×Q8—61no—
263C2×C4×Q8—61no—
264C2×C4×D4—61no—
265C2×C4×D4—61no—
266C2×#117—32no—
267C22×C42—31no—
268#491—38no—
269#490—38no—
270#489—34no—
271#489—34no—
272#489—34no—
273#489C2×D314yescomplemented
274#488—38no—
275#488—38no—
276#487—32no—
277#487—32no—
278#487—32no—
279#487C2×D312yescomplemented
280#486—32no—
281#486—32no—
282#486—32no—
283#486C2×D312yescomplemented
284#419—38no—
285#418—38no—
286#417—34no—
287#417—34no—
288#417—34no—
289#417C2×D314yescomplemented
290#416—38no—
291#416—38no—
292C4×M16—32no—
293C4×M16—31no—
294C4×M16—32no—
295C4×M16—32no—
296C4×M16C2×D311yescharacteristic, complemented
297C2×#97—32no—
298C2×C4×C8—32no—
299C23×D3—22no—
300C23×D3C2×D411yescharacteristic
301C3×#41—28no—
302C2×C3×Q8—22no—
303C2×C3×Q8—22no—
304C2×C3×Q8—44no—
305C2×C3×Q8C2412yes—
306C2×C3×D4—22no—
307C2×C3×D4—21no—
308C2×C3×D4—21no—
309C2×C3×D4C2412yes—
310C22×C3×C4—22no—
311C22×C3×C4—22no—
312C22×C3×C4C2×D411yescharacteristic
313C22×C3×C4C2×D411yescharacteristic
314C22×C3×C4C2411yescharacteristic
315C2×#67—22no—
316C2×#67—22no—
317C2×#67—22no—
318C2×#67—22no—
319C2×#67—22no—
320C22×Dic3—22no—
321C22×Dic3—22no—
322C22×Dic3C2×D411yescharacteristic
323C22×Dic3C2×D411yescharacteristic
324C22×Dic3C2×D411yescharacteristic
325#239—28no—
326D3×Q8—28no—
327#237—28no—
328#237—48no—
329D3×D4—28no—
330D3×D4—44no—
331D3×D4—44no—
332D3×D4—48no—
333#235—28no—
334#235—48no—
335C2×D12—22no—
336C2×D12—21no—
337C2×D12—21no—
338C2×D12C2412yes—
339C2×C4×D3—22no—
340C2×C4×D3—22no—
341C2×C4×D3—22no—
342C2×C4×D3—42no—
343C2×C4×D3—42no—
344C2×C4×D3—48no—
345C2×C4×D3C2×D411yescharacteristic
346C2×C4×D3C2×D411yescharacteristic
347C2×C4×D3C2×D411yescharacteristic
348C2×C4×D3C2×D411yescharacteristic
349C2×C4×D3C2×D411yescharacteristic
350C2×C4×D3C2×D411yescharacteristic
351C2×C4×D3C2×D411yescharacteristic
352C2×C4×D3C2×D411yescharacteristic
353C2×C4×D3C2×D411yescharacteristic
354C2×C4×D3C2×D411yescharacteristic
355C2×C4×D3#4118yes—
356C2×C4×D3C2411yescharacteristic
357C2×C4×D3C2411yescharacteristic
358C2×Dic6—22no—
359C2×Dic6—22no—
360C2×Dic6—22no—
361C2×Dic6—44no—
362C2×Dic6C2412yes—
363C3×M16—24no—
364C2×C3×C8C2414yes—
365C3×C4⋊C4—22no—
366C3×C4⋊C4—22no—
367C3×C4⋊C4—21no—
368C3×C4⋊C4—21no—
369C3×C4⋊C4—22no—
370C3×C4⋊C4C2414yes—
371C3×C22⋊C4—22no—
372C3×C22⋊C4—22no—
373C3×C42C2×D411yescharacteristic
374C3×C42C2×D411yescharacteristic
375C3×C42C2411yescharacteristic
376C3×C42C2411yescharacteristic
377#217—22no—
378#217—22no—
379(C2×D3)⋊C4—24no—
380(C2×D3)⋊C4—24no—
381(C2×D3)⋊C4—22no—
382(C2×D3)⋊C4—22no—
383(C2×D3)⋊C4—22no—
384(C2×D3)⋊C4—22no—
385C4⋊Dic3—22no—
386C4⋊Dic3—22no—
387C4⋊Dic3—22no—
388C4⋊Dic3—21no—
389C4⋊Dic3—21no—
390C4⋊Dic3—24no—
391C4⋊Dic3—24no—
392C4⋊Dic3C2414yes—
393Dic3⋊C4—22no—
394Dic3⋊C4—22no—
395Dic3⋊C4—24no—
396Dic3⋊C4—24no—
397C4×Dic3—24no—
398C4×Dic3—24no—
399C4×Dic3C2×D411yescharacteristic
400C4×Dic3C2×D411yescharacteristic
401C4×Dic3C2×D411yescharacteristic
402C4×Dic3C2×D411yescharacteristic
403C4×Dic3C2×D411yescharacteristic
404C4×Dic3C2×D411yescharacteristic
405C4×Dic3C2×D411yescharacteristic
406C4×Dic3C2×D411yescharacteristic
407C4×Dic3C2×D411yescharacteristic
408C4×Dic3C2×D411yescharacteristic
409C4×Dic3C2411yescharacteristic
410C4×Dic3C2411yescharacteristic
411#208—24no—
412C2×C3⋊C8C2414yes—
413ΓL(1,𝔽25)—28no—
414D3×C8—28no—
415C2×#41—32no—
416C2×#41—32no—
417C2×#41—32no—
418C2×#41—62no—
419C2×#41—62no—
420C2×#41—616no—
421C2×#41C22×D312yes—
422C22×Q8—21no—
423C22×Q8—32no—
424C22×Q8—61no—
425C22×D4—32no—
426C22×D4—61no—
427C22×D4—61no—
428C22×D4—62no—
429C23×C4—31no—
430C23×C4—31no—
431C23×C4—31no—
432C23×C4—62no—
433C2×M16—32no—
434C2×M16—34no—
435C2×M16—68no—
436C2×M16C22×D312yes—
437C22×C8—34no—
438C4⋊Q8—21no—
439C4⋊Q8—21no—
440C4⋊Q8—32no—
441C4⋊Q8—32no—
442C4⋊Q8—32no—
443C4⋊Q8—31no—
444C4⋊Q8—61no—
445C4⋊Q8—61no—
446C4⋊Q8—61no—
447C4⋊Q8—61no—
448C4⋊Q8C22×D311yescharacteristic
449C4⋊Q8C22×D312yes—
450C4⋊Q8C22×D312yes—
451#127—32no—
452#127—31no—
453#127—61no—
454#127—61no—
455#127C22×D311yescharacteristic
456#125—34no—
457#125—34no—
458#125—62no—
459#125—62no—
460#124—32no—
461#124—32no—
462#124—32no—
463#124—62no—
464#124—62no—
465#124C22×D312yes—
466C22⋊Q8—62no—
467C22⋊Q8—62no—
468C22⋊Q8—62no—
469C22⋊Q8—62no—
470C22⋊Q8—62no—
471C22⋊Q8—62no—
472C22⋊Q8—62no—
473C22⋊Q8—62no—
474#121—21no—
475#121—21no—
476#121—62no—
477#121—62no—
478#121—61no—
479#121—61no—
480#121—61no—
481#121—61no—
482#121—62no—
483#121—62no—
484#121—61no—
485#121—61no—
486C4×Q8—62no—
487C4×Q8—62no—
488C4×Q8—62no—
489C4×Q8—62no—
490C4×Q8—62no—
491C4×Q8—62no—
492C4×Q8—62no—
493C4×Q8—62no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—62no—
497C4×D4—62no—
498C4×D4—61no—
499C4×D4—61no—
500C4×D4—62no—
501C4×D4—62no—
502C4×D4—61no—
503C4×D4—61no—
504C4×D4—61no—
505C4×D4—61no—
506#117—34no—
507#117—34no—
508#117—62no—
509#117—62no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—32no—
512C2×C4⋊C4—61no—
513C2×C4⋊C4—61no—
514C2×C4⋊C4—62no—
515C2×C4⋊C4—62no—
516C2×C4⋊C4—61no—
517C2×C4⋊C4C22×D312yes—
518C2×C22⋊C4—62no—
519C2×C22⋊C4—62no—
520C2×C22⋊C4—62no—
521C2×C42—31no—
522C2×C42—31no—
523C2×C42—31no—
524C2×C42—31no—
525C2×C42—31no—
526C2×C42—31no—
527C2×C42—31no—
528C2×C42—31no—
529C2×C42—31no—
530C2×C42—31no—
531C2×C42—31no—
532C2×C42—62no—
533C2×C42C22×D311yescharacteristic
534#103—38no—
535#103—38no—
536#103—38no—
537#103C22×D318yes—
538#102—38no—
539#102—38no—
540#102—38no—
541#102C22×D318yes—
542#97—34no—
543#97—32no—
544#97C22×D312yes—
545C4×C8—34no—
546C4×C8—32no—
547C4×C8C22×D312yes—
548C23×C3—22no—
549C23×C3C22×D411yescharacteristic
550C22×D3—22no—
551C22×D3—41no—
552C22×D3—41no—
553C22×D3—44no—
554C22×D3—44no—
555C22×D3—44no—
556C22×D3#12414yes—
557C22×D3C22×D411yescharacteristic
558C22×D3C22×D411yescharacteristic
559C3×Q8—24no—
560C3×Q8—44no—
561C3×Q8—44no—
562C3×D4—24no—
563C3×D4—44no—
564C3×D4—42no—
565C3×D4—42no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—24no—
569C2×C3×C4—22no—
570C2×C3×C4—44no—
571C2×C3×C4—44no—
572C2×C3×C4C22×D411yescharacteristic
573C2×C3×C4C22×D411yescharacteristic
574C2×C3×C4C22×D411yescharacteristic
575C2×C3×C4C22×D411yescharacteristic
576C2×C3×C4C22×D411yescharacteristic
577C2×C3×C4C2×#4114yes—
578C2×C3×C4C2511yescharacteristic
579#67—44no—
580#67—44no—
581#67—44no—
582#67—44no—
583#67—44no—
584C2×Dic3—24no—
585C2×Dic3—22no—
586C2×Dic3—41no—
587C2×Dic3—41no—
588C2×Dic3—44no—
589C2×Dic3—44no—
590C2×Dic3#12414yes—
591C2×Dic3C22×D411yescharacteristic
592C2×Dic3C22×D411yescharacteristic
593C2×Dic3C22×D411yescharacteristic
594C2×Dic3C22×D411yescharacteristic
595C2×Dic3C22×D411yescharacteristic
596C2×Dic3C22×D411yescharacteristic
597D12—24no—
598D12—44no—
599D12—42no—
600D12—42no—
601C4×D3—22no—
602C4×D3—22no—
603C4×D3—22no—
604C4×D3—22no—
605C4×D3—41no—
606C4×D3—41no—
607C4×D3—41no—
608C4×D3—41no—
609C4×D3—44no—
610C4×D3—44no—
611C4×D3—44no—
612C4×D3#12414yes—
613C4×D3#12414yes—
614C4×D3C2×#4114yes—
615C4×D3C2×#4114yes—
616Dic6—24no—
617Dic6—44no—
618Dic6—44no—
619Dic6—44no—
620C3×C8—24no—
621C3⋊C8—24no—
622C24—31no—
623C24—62no—
624#41—28no—
625#41—68no—
626#41—68no—
627#41—68no—
628#41—128no—
629#41—128no—
630C2×Q8—22no—
631C2×Q8—22no—
632C2×Q8—32no—
633C2×Q8—44no—
634C2×Q8—62no—
635C2×Q8—68no—
636C2×Q8—62no—
637C2×Q8—62no—
638C2×Q8—124no—
639C2×Q8C23×D312yes—
640C2×D4—22no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—32no—
644C2×D4—62no—
645C2×D4—68no—
646C2×D4—62no—
647C2×D4—62no—
648C2×D4—62no—
649C2×D4—62no—
650C2×D4—62no—
651C2×D4—61no—
652C2×D4—61no—
653C2×D4—124no—
654C2×D4—124no—
655C2×D4—128no—
656C2×D4C23×D312yes—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—31no—
660C22×C4—31no—
661C22×C4—31no—
662C22×C4—38no—
663C22×C4—31no—
664C22×C4—31no—
665C22×C4—31no—
666C22×C4—31no—
667C22×C4—31no—
668C22×C4—31no—
669C22×C4—31no—
670C22×C4—31no—
671C22×C4—31no—
672C22×C4—31no—
673C22×C4—31no—
674C22×C4—31no—
675C22×C4—62no—
676C22×C4—62no—
677C22×C4—62no—
678C22×C4—62no—
679C22×C4—62no—
680C22×C4—122no—
681C22×C4—122no—
682C22×C4—128no—
683C22×C4D3×D411yescharacteristic
684C22×C4D3×D411yescharacteristic
685C22×C4C23×D311yescharacteristic
686M16—24no—
687M16—68no—
688M16—64no—
689C2×C8—34no—
690C2×C8—68no—
691C2×C8C23×D314yes—
692C4⋊C4—22no—
693C4⋊C4—22no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—22no—
697C4⋊C4—34no—
698C4⋊C4—62no—
699C4⋊C4—62no—
700C4⋊C4—64no—
701C4⋊C4—64no—
702C4⋊C4—64no—
703C4⋊C4—64no—
704C4⋊C4—62no—
705C4⋊C4—61no—
706C4⋊C4—61no—
707C4⋊C4—62no—
708C4⋊C4—62no—
709C4⋊C4C23×D314yes—
710C22⋊C4—22no—
711C22⋊C4—22no—
712C22⋊C4—62no—
713C22⋊C4—62no—
714C22⋊C4—64no—
715C22⋊C4—64no—
716C22⋊C4—62no—
717C22⋊C4—62no—
718C22⋊C4—62no—
719C22⋊C4—62no—
720C42—31no—
721C42—31no—
722C42—31no—
723C42—31no—
724C42—31no—
725C42—31no—
726C42—31no—
727C42—31no—
728C42—31no—
729C42—31no—
730C42—31no—
731C42—31no—
732C42—64no—
733C42—64no—
734C42D3×D411yescharacteristic
735C42D3×D411yescharacteristic
736C42C23×D311yescharacteristic
737C42C23×D311yescharacteristic
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—42no—
741C22×C3—42no—
742C22×C3—42no—
743C22×C3C2×#12412yes—
744C22×C3C23×D411yescharacteristic
745C2×D3—21no—
746C2×D3—21no—
747C2×D3—21no—
748C2×D3—21no—
749C2×D3—44no—
750C2×D3—42no—
751C2×D3—42no—
752C2×D3—42no—
753C2×D3—88no—
754C2×D3C2×#12412yes—
755C2×D3C2×#12412yes—
756C3×C4—21no—
757C3×C4—21no—
758C3×C4—42no—
759C3×C4—44no—
760C3×C4C2×#12412yes—
761C3×C4#57512yes—
762C3×C4#57512yes—
763C3×C4C22×#4112yes—
764Dic3—21no—
765Dic3—21no—
766Dic3—21no—
767Dic3—21no—
768Dic3—42no—
769Dic3—44no—
770Dic3C2×#12412yes—
771Dic3C2×#12412yes—
772C23—22no—
773C23—31no—
774C23—31no—
775C23—34no—
776C23—62no—
777C23—121no—
778C23—121no—
779C23—124no—
780C23—124no—
781C23—124no—
782C23C2×D3×D411yescharacteristic
783Q8—24no—
784Q8—44no—
785Q8—44no—
786Q8—64no—
787Q8—124no—
788Q8—124no—
789Q8—124no—
790D4—24no—
791D4—44no—
792D4—42no—
793D4—42no—
794D4—64no—
795D4—124no—
796D4—124no—
797D4—124no—
798D4—124no—
799D4—124no—
800D4—124no—
801D4—122no—
802D4—122no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—24no—
806C2×C4—22no—
807C2×C4—34no—
808C2×C4—31no—
809C2×C4—31no—
810C2×C4—34no—
811C2×C4—34no—
812C2×C4—34no—
813C2×C4—34no—
814C2×C4—31no—
815C2×C4—31no—
816C2×C4—31no—
817C2×C4—31no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—62no—
821C2×C4—62no—
822C2×C4—62no—
823C2×C4—62no—
824C2×C4—64no—
825C2×C4—62no—
826C2×C4—121no—
827C2×C4—121no—
828C2×C4—121no—
829C2×C4—121no—
830C2×C4—124no—
831C2×C4—124no—
832C2×C4—124no—
833C2×C4—121no—
834C2×C4—121no—
835C2×C4—124no—
836C2×C4—124no—
837C2×C4C2×D3×D411yescharacteristic
838C2×C4C2×D3×D411yescharacteristic
839C2×C4C2×D3×D411yescharacteristic
840C2×C4C2×D3×D411yescharacteristic
841C2×C4C2×D3×D411yescharacteristic
842C2×C4D3×#4114yes—
843C2×C4C24×D311yescharacteristic
844C8—24no—
845C8—64no—
846C2×C3—22no—
847C2×C3—82no—
848C2×C3C22×#12411yescharacteristic
849C2×C3C2×#57511yescharacteristic
850C2×C3C2×#57511yescharacteristic
851D3—22no—
852D3—22no—
853D3—82no—
854C22—21no—
855C22—21no—
856C22—32no—
857C22—32no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—61no—
862C22—61no—
863C22—61no—
864C22—61no—
865C22—124no—
866C22—122no—
867C22—122no—
868C22—122no—
869C22—248no—
870C22D3×#12412yes—
871C22C22×D3×D411yescharacteristic
872C4—21no—
873C4—21no—
874C4—32no—
875C4—32no—
876C4—42no—
877C4—44no—
878C4—61no—
879C4—61no—
880C4—61no—
881C4—61no—
882C4—122no—
883C4—124no—
884C4D3×#12412yes—
885C4#577312yes—
886C4#577712yes—
887C4C2×D3×#4112yes—
888C3#6061811yescharacteristic, complemented, Sylow
889C2—22no—
890C2—62no—
891C2—62no—
892C2—82no—
893C2—242no—
894C2C2×D3×#12411yescharacteristic
895C2C2×#577311yescharacteristic
896C2C2×#577711yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3141C2
socleC22×C3C23×D4
prime radicalD3×#532C2
hypercenter#3141D3
hypocenterC3#60618
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3141

Complements

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

NH ≅ G/Ntype
2. C2×#5728C2semidirect
3. C3×#3141C2semidirect
4. #83283C2semidirect
5. #83199C2semidirect
6. #81682C2semidirect
7. #81679C2semidirect
8. #81600C2semidirect
9. #81598C2semidirect
10. #81564C2semidirect
11. #81562C2semidirect
12. #78881C2semidirect
13. #78879C2semidirect
14. #78528C2semidirect
15. C4×D3×M16C2semidirect
19. C2×C3×C4⋊Q8C22semidirect
30. #5728C22semidirect
31. #5728C22semidirect
48. C2×#890C22semidirect
52. C2×#869C22semidirect
53. C3×#489C22semidirect
54. C3×#487C22semidirect
55. C3×#486C22semidirect
56. C3×#417C22semidirect
57. C3×C4×M16C22semidirect
58. #5232C22semidirect
59. #5133C22semidirect
60. Dic3×M16C22semidirect
61. #5093C22semidirect
62. #5089C22semidirect
63. #5088C22semidirect
64. #5079C22semidirect
65. #5070C22semidirect
66. #5055C22semidirect
67. #4966C22semidirect
68. C4×#208C22semidirect
69. #4804C22semidirect
71. #4800C22semidirect
72. #4797C22semidirect
73. #4772C22semidirect
75. #4768C22semidirect
76. #4764C22semidirect
77. #4714C22semidirect
79. D3×#97C22semidirect
80. #4694C22semidirect
82. C4×D3×C8C22semidirect
83. #4681C22semidirect
90. #3141D3semidirect
254. C2×C4⋊Q8C2×D3semidirect
273. #489C2×D3semidirect
279. #487C2×D3semidirect
283. #486C2×D3semidirect
289. #417C2×D3semidirect
296. C4×M16C2×D3semidirect
888. C3#60618semidirect

Maximal subgroups

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

subgroupindex
D3×#5322
C2×#57282
C3×#31412
#832832
#831992
#816822
#816792
#816002
#815982
#815642
#815622
#788812
#788792
#785282
C4×D3×M162
#606183