Finite Group Databasebeta

← #11670754

Subgroups — #11670754

Order 768.

2818 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5752C211yesmaximal, characteristic, complemented
2C2×#5748C211yesmaximal, characteristic, complemented
3#86041C212yesmaximal, complemented
4C3×#2930C211yesmaximal, characteristic, complemented
5#83800C211yesmaximal, characteristic, complemented
6C2×#5135C211yesmaximal, characteristic, complemented
7#79551C214yesmaximal, complemented
8#79550C214yesmaximal, complemented
9#79508C214yesmaximal, complemented
10#79493C214yesmaximal, complemented
11#79088C212yesmaximal, complemented
12#78672C212yesmaximal, complemented
13#78639C212yesmaximal, complemented
14#78574C211yesmaximal, characteristic, complemented
15#78565C211yesmaximal, characteristic, complemented
16#61063—31nomaximal, Sylow
17C2×#1009C2212yescomplemented
18C22×#235C2212yescomplemented
19C2×C3×#131C2211yescharacteristic, complemented
20C22×C3×M16C2211yescharacteristic, complemented
21C3×#525C2211yescharacteristic
22#5833C2212yescomplemented
23C2×#930C2212yescomplemented
24#5752—28no—
25#5748—28no—
26C2×#909C2212yescomplemented
27C2×#909C2212yescomplemented
28C2×#908C2212yescomplemented
29C2×#908C2212yescomplemented
30C2×#908C2212yescomplemented
31C2×#908C2214yescomplemented
32C2×#908C2212yescomplemented
33C2×#904C2211yescharacteristic
34C2×#904C2212yescomplemented
35C2×#904C2211yescharacteristic, complemented
36C2×#904C2212yescomplemented
37C22×D24C2211yescharacteristic, complemented
38C22×D24C2212yescomplemented
39#5654—24no—
40#5629—22no—
41#5627—22no—
42#5607—22no—
43D3×#121—22no—
44#5590—24no—
45#5553C2214yescomplemented
46#5552C2214yescomplemented
47#5550C2214yescomplemented
48D4×D12C2214yescomplemented
49#5525C2212yescomplemented
50#5523C2212yescomplemented
51C3×#436C2214yescomplemented
52C3×#435C2214yescomplemented
53C3×#424C2211yescharacteristic, complemented
54C3×#408C2211yescharacteristic, complemented
55C3×#407C2211yescharacteristic, complemented
56C3×#405C2211yescharacteristic, complemented
57#5137C2212yescomplemented
58#5135C2214yescomplemented
59#5135C2214yescomplemented
60#5135C2212yescomplemented
61#5133C2212yescomplemented
62#5133C2212yescomplemented
63#5114C2214yescomplemented
64C2×#821C2212yescomplemented
65C2×#817C2211yescharacteristic, complemented
66#4848C2214yescomplemented
67#4845C2214yescomplemented
68#4844C2214yescomplemented
69#4843C2214yescomplemented
70#4738C2214yescomplemented
71#4734C2214yescomplemented
72#4734C2214yescomplemented
73#4734C2214yescomplemented
74#4733C2214yescomplemented
75#4732C2214yescomplemented
76#4732C2214yescomplemented
77#4731C2214yescomplemented
78#4716C2212yescomplemented
79#4712C2214yescomplemented
80#4711C2212yescomplemented
81#4696C2212yescomplemented
82#4695C2212yescomplemented
83C4×#204C2214yescomplemented
84C2×#576—31no—
85C2×#575—31no—
86#3488—32no—
87#3275—34no—
88#3274—34no—
89#3271—34no—
90#3264—34no—
91#3155—31no—
92#3060—31no—
93C2×#469—31no—
94#3045—32no—
95#3012—32no—
96#3006—32no—
97#2952—31no—
98#2930D311yescharacteristic, complemented
99C2×C3×#41C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C22×#67—22no—
102C22×#67—22no—
103#1009—28no—
104#1009—44no—
105C2×#239—22no—
106C2×D3×D4—24no—
107C2×D3×D4—22no—
108C2×D3×D4—24no—
109C2×#235—22no—
110C2×#235—22no—
111C2×#235—28no—
112C2×#235—44no—
113C2×#235C2312yes—
114C2×#235C2312yes—
115C2×#235C2312yes—
116C2×#235C2314yes—
117C2×#235C2312yes—
118C22×D12C2312yes—
119C22×D12C2312yes—
120C22×D12C2314yes—
121C22×C4×D3—22no—
122C22×Dic6C2312yes—
123C3×#131—24no—
124C2×C3×M16—24no—
125C2×C3×M16C2312yes—
126C2×C3×M16C2312yes—
127C2×C3×M16C2311yescharacteristic
128C2×C3×M16C2312yes—
129C2×C3×M16C2311yescharacteristic
130C22×C3×C8C2311yescharacteristic
131C22×C3×C8C2312yes—
132C22×C3×C8C2311yescharacteristic
133C3×#123D412yes—
134C3×C22⋊Q8D412yes—
135C3×#121D412yes—
136C3×#120D412yes—
137C3×C4×D4C2314yes—
138C3×#117C2311yescharacteristic
139#946—22no—
140#940—24no—
141#939—24no—
142#939—24no—
143#938—22no—
144#937—24no—
145#930—22no—
146#930—22no—
147#930C2314yes—
148#930C2314yes—
149#930C2314yes—
150C2×(C2×D3)⋊C4—22no—
151C2×C4⋊Dic3C2312yes—
152#924C2314yes—
153#909—28no—
154#909—28no—
155#908—28no—
156#908—28no—
157#908—28no—
158#908—216no—
159#908—44no—
160C2×Dic12C2311yescharacteristic
161C2×Dic12C2312yes—
162C2×Dic12C2311yescharacteristic
163#904—28no—
164#904—24no—
165#904—28no—
166#904D418yescomplemented
167C2×D24—24no—
168C2×D24—28no—
169C2×D24C2311yescharacteristic
170C2×D24C2312yes—
171C2×D24C2312yes—
172C2×D24C2314yes—
173C2×D24C2312yes—
174C2×D24C2314yes—
175C2×D24C2311yescharacteristic
176C2×#204C2312yes—
177C2×#204C2314yes—
178C2×#204C2312yes—
179C2×#204C2312yes—
180C2×#204C2314yes—
181C2×#204C2312yes—
182#896—24no—
183#895—24no—
184#895—22no—
185#895—22no—
186#894—24no—
187#893—24no—
188#892—22no—
189D3×C4⋊C4—22no—
190#885—24no—
191#884—24no—
192#884—24no—
193#884—24no—
194#882—24no—
195#882—24no—
196#882—24no—
197#67⋊C4—24no—
198#67⋊C4—24no—
199D3×C22⋊C4—24no—
200#875C2314yes—
201#874C2314yes—
202C4×D12C2314yes—
203C4×Dic6C2314yes—
204C3×C4⋊C8C2314yes—
205C3×C22⋊C8C2314yes—
206C3×C22⋊C8C2314yes—
207C3×#97C2312yes—
208C3×C4×C8C2312yes—
209#821C2314yes—
210#821C2314yes—
211#821C2314yes—
212#821C2314yes—
213#817C2312yes—
214#817C2312yes—
215#816C2314yes—
216#816C2314yes—
217C2×H(5,𝔽2)—32no—
218C22×#41—32no—
219#576—68no—
220#575—68no—
221C2×#137—32no—
222C2×#137—32no—
223C2×AGL(1,ℤ/8)—32no—
224C2×AGL(1,ℤ/8)—32no—
225C2×AGL(1,ℤ/8)—32no—
226C2×AGL(1,ℤ/8)—34no—
227C2×AGL(1,ℤ/8)—32no—
228C2×#135—31no—
229C2×#135—31no—
230C2×#135—32no—
231C2×#135—32no—
232C22×D8—31no—
233C22×D8—32no—
234C2×#131C2×D311yescharacteristic, complemented
235C22×M16C2×D311yescharacteristic, complemented
236#550—34no—
237#548—34no—
238#546—34no—
239#546—64no—
240D42—34no—
241D42—64no—
242#537—32no—
243#537—62no—
244#535—32no—
245#535—62no—
246#525—62no—
247#525C2×D311yescharacteristic
248C2×#121—32no—
249C2×#121—62no—
250#520—32no—
251#496—34no—
252#495—32no—
253#493—32no—
254#470—32no—
255#469—34no—
256#469—32no—
257#469—34no—
258#465—34no—
259#464—34no—
260#463—34no—
261#460—34no—
262#459—34no—
263#452—34no—
264#450—34no—
265#449—34no—
266#449—34no—
267#449—34no—
268#448—34no—
269#447—34no—
270#447—34no—
271#442—32no—
272#441—32no—
273C4×SD16—34no—
274#436C2×D314yescomplemented
275#435C2×D314yescomplemented
276C2×#106—31no—
277#424C2×D311yescharacteristic, complemented
278#417—32no—
279#417—32no—
280C2×#102—32no—
281#408C2×D311yescharacteristic, complemented
282#407C2×D311yescharacteristic, complemented
283#405C2×D311yescharacteristic, complemented
284C24×C3C2×D411yescharacteristic
285C23×D3—22no—
286C23×D3—24no—
287C23×D3—22no—
288C3×#41—22no—
289C3×#41—22no—
290C2×C3×Q8C2×D411yescharacteristic
291C2×C3×D4C2×D411yescharacteristic
292C2×C3×D4C2×D412yes—
293C2×C3×D4C2×D414yes—
294C22×C3×C4—22no—
295C22×C3×C4—22no—
296C22×C3×C4C2×D411yescharacteristic
297C22×C3×C4C2×D412yes—
298C22×C3×C4C2412yes—
299C22×C3×C4C2412yes—
300C22×C3×C4C2411yescharacteristic
301C2×#67—22no—
302C2×#67—24no—
303C2×#67—22no—
304C2×#67—22no—
305C2×#67—22no—
306C2×#67—24no—
307C2×#67—24no—
308C2×#67—24no—
309C2×#67—48no—
310C2×#67—84no—
311C22×Dic3—22no—
312C22×Dic3—22no—
313#239—48no—
314D3×D4—48no—
315D3×D4—416no—
316D3×D4—88no—
317#235—24no—
318#235—24no—
319#235—24no—
320#235—24no—
321#235—28no—
322#235—24no—
323#235—42no—
324#235—42no—
325#235—44no—
326#235—48no—
327#235—48no—
328#235C2×D418yescomplemented
329C2×D12—24no—
330C2×D12—24no—
331C2×D12—28no—
332C2×D12—24no—
333C2×D12—22no—
334C2×D12—24no—
335C2×D12—22no—
336C2×D12—24no—
337C2×D12—24no—
338C2×D12—42no—
339C2×D12—44no—
340C2×D12C2412yes—
341C2×D12C2414yes—
342C2×D12C2412yes—
343C2×C4×D3—22no—
344C2×C4×D3—22no—
345C2×C4×D3—24no—
346C2×C4×D3—22no—
347C2×C4×D3—22no—
348C2×C4×D3—24no—
349C2×C4×D3—48no—
350C2×Dic6—24no—
351C2×Dic6—22no—
352C2×Dic6—42no—
353C2×Dic6C2412yes—
354C2×Dic6C2412yes—
355C3×M16—22no—
356C3×M16—22no—
357C3×M16—24no—
358C3×M16—24no—
359C3×M16—24no—
360C2×C3×C8—22no—
361C2×C3×C8—24no—
362C2×C3×C8C2×D414yescomplemented
363C2×C3×C8C2412yes—
364C2×C3×C8C2412yes—
365C2×C3×C8C2412yes—
366C2×C3×C8C2411yescharacteristic
367C2×C3×C8C2411yescharacteristic
368C3×C4⋊C4C2×D412yes—
369C3×C4⋊C4C2×D414yes—
370C3×C22⋊C4C2×D414yes—
371C3×C22⋊C4C2×D412yes—
372C3×C22⋊C4C2×D414yes—
373C3×C42C2412yes—
374#217—24no—
375(C2×D3)⋊C4—24no—
376(C2×D3)⋊C4—24no—
377(C2×D3)⋊C4—24no—
378(C2×D3)⋊C4—24no—
379(C2×D3)⋊C4—24no—
380(C2×D3)⋊C4—24no—
381C4⋊Dic3—22no—
382C4⋊Dic3C2414yes—
383Dic3⋊C4—24no—
384Dic3⋊C4—24no—
385C4×Dic3—24no—
386Dic12—24no—
387Dic12—22no—
388Dic12C2×D414yescomplemented
389D24—28no—
390D24—24no—
391D24—24no—
392D24—24no—
393D24—22no—
394D24—44no—
395D24C2×D414yescomplemented
396#204—24no—
397#204—28no—
398#204—24no—
399#204—24no—
400#204—44no—
401#204C2×D418yescomplemented
402H(5,𝔽2)—68no—
403H(5,𝔽2)—124no—
404C2×#41—32no—
405C2×#41—32no—
406C2×#41—32no—
407C2×#41—34no—
408C2×#41—32no—
409C2×#41—68no—
410C2×#41—62no—
411C2×#41—62no—
412C2×#41—62no—
413C2×#41—124no—
414C2×#41C22×D311yescharacteristic
415C22×Q8—32no—
416C22×D4—32no—
417C22×D4—32no—
418C22×D4—34no—
419C22×D4—62no—
420C22×D4—62no—
421C22×D4—62no—
422C22×D4—64no—
423C22×D4—64no—
424C23×C4—62no—
425C23×C4C22×D311yescharacteristic
426#137—68no—
427#137—68no—
428AGL(1,ℤ/8)—68no—
429AGL(1,ℤ/8)—68no—
430AGL(1,ℤ/8)—616no—
431AGL(1,ℤ/8)—68no—
432AGL(1,ℤ/8)—124no—
433#135—38no—
434#135—68no—
435#135—68no—
436#135—64no—
437C2×Q16—31no—
438C2×Q16—32no—
439C2×Q16—31no—
440C2×SD16—32no—
441C2×SD16—34no—
442C2×SD16—32no—
443C2×SD16—32no—
444C2×SD16—32no—
445C2×SD16—34no—
446C2×D8—31no—
447C2×D8—32no—
448C2×D8—34no—
449C2×D8—32no—
450C2×D8—32no—
451C2×D8—31no—
452C2×D8—34no—
453C2×D8—68no—
454C2×D8—64no—
455#131—24no—
456C2×M16—24no—
457C2×M16C22×D312yes—
458C2×M16C22×D312yes—
459C2×M16C22×D311yescharacteristic
460C2×M16C22×D312yes—
461C2×M16C22×D311yescharacteristic
462C22×C8C22×D311yescharacteristic
463C22×C8C22×D312yes—
464C22×C8C22×D311yescharacteristic
465#127—34no—
466#127—64no—
467#124—34no—
468#124—64no—
469#123—64no—
470#123D1212yes—
471C22⋊Q8—34no—
472C22⋊Q8—62no—
473C22⋊Q8—64no—
474C22⋊Q8D1212yes—
475#121—34no—
476#121—34no—
477#121—34no—
478#121—62no—
479#121—64no—
480#121—64no—
481#121—62no—
482#121—62no—
483#121—62no—
484#121—62no—
485#121—64no—
486#121—64no—
487#121—64no—
488#121—64no—
489#121D1212yes—
490#120—64no—
491#120—64no—
492#120—64no—
493#120—64no—
494#120D1212yes—
495C4×Q8—34no—
496C4×D4—34no—
497C4×D4—64no—
498C4×D4—64no—
499C4×D4—64no—
500C4×D4C22×D314yes—
501#117—62no—
502#117C22×D311yescharacteristic
503C2×C4⋊C4—32no—
504C2×C4⋊C4—62no—
505C2×C22⋊C4—62no—
506C2×C22⋊C4—64no—
507#106—32no—
508#106—32no—
509C4⋊C8C22×D314yes—
510#103—34no—
511#103—34no—
512#102—34no—
513#102—34no—
514#102—34no—
515#102—34no—
516C22⋊C8C22×D314yes—
517C22⋊C8C22×D314yes—
518#97C22×D312yes—
519C4×C8C22×D312yes—
520C23×C3—22no—
521C23×C3—42no—
522C23×C3C22×D412yes—
523C23×C3C22×D412yes—
524C23×C3C22×D411yescharacteristic
525C22×D3—22no—
526C22×D3—24no—
527C22×D3—22no—
528C22×D3—44no—
529C22×D3—48no—
530C22×D3—44no—
531C22×D3—44no—
532C22×D3—82no—
533C22×D3—84no—
534C22×D3—82no—
535C22×D3—84no—
536C22×D3—82no—
537C3×Q8—22no—
538C3×D4—24no—
539C3×D4—22no—
540C3×D4—44no—
541C2×C3×C4—22no—
542C2×C3×C4—24no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
547C2×C3×C4C22×D414yes—
548C2×C3×C4C22×D412yes—
549C2×C3×C4C22×D412yes—
550C2×C3×C4C22×D411yescharacteristic
551C2×C3×C4C22×D412yes—
552C2×C3×C4H(5,𝔽2)12yes—
553C2×C3×C4C2511yescharacteristic
554#67—28no—
555#67—44no—
556#67—48no—
557#67—44no—
558#67—48no—
559#67—44no—
560#67—84no—
561#67—84no—
562C2×Dic3—22no—
563C2×Dic3—24no—
564C2×Dic3—22no—
565C2×Dic3—44no—
566C2×Dic3—82no—
567D12—22no—
568D12—24no—
569D12—22no—
570D12—24no—
571D12—22no—
572D12—44no—
573D12—48no—
574D12—44no—
575D12—84no—
576D12—84no—
577D12C22×D414yes—
578C4×D3—28no—
579C4×D3—44no—
580C4×D3—48no—
581C4×D3—44no—
582C4×D3—44no—
583C4×D3—84no—
584Dic6—22no—
585Dic6—22no—
586Dic6—22no—
587Dic6—44no—
588Dic6C22×D414yes—
589C3×C8—22no—
590C3×C8—22no—
591C3×C8—22no—
592C3×C8C22×D412yes—
593C3×C8C22×D412yes—
594C24—62no—
595C24—64no—
596C24—62no—
597C24C2×D1211yescharacteristic
598#41—22no—
599#41—22no—
600#41—38no—
601#41—64no—
602#41—68no—
603#41—64no—
604#41—64no—
605#41—64no—
606#41—64no—
607#41—128no—
608#41—122no—
609#41—122no—
610#41—124no—
611#41—128no—
612#41—128no—
613C2×Q8—32no—
614C2×Q8—32no—
615C2×Q8—64no—
616C2×Q8—62no—
617C2×Q8—122no—
618C2×Q8C2×D1211yescharacteristic
619C2×D4—32no—
620C2×D4—34no—
621C2×D4—32no—
622C2×D4—68no—
623C2×D4—64no—
624C2×D4—62no—
625C2×D4—64no—
626C2×D4—62no—
627C2×D4—62no—
628C2×D4—64no—
629C2×D4—62no—
630C2×D4—64no—
631C2×D4—64no—
632C2×D4—62no—
633C2×D4—64no—
634C2×D4—62no—
635C2×D4—64no—
636C2×D4—64no—
637C2×D4—64no—
638C2×D4—64no—
639C2×D4—122no—
640C2×D4—124no—
641C2×D4—128no—
642C2×D4—1216no—
643C2×D4—128no—
644C2×D4—248no—
645C2×D4—244no—
646C2×D4C2×D1212yes—
647C2×D4C2×D1211yescharacteristic
648C2×D4C2×D1214yes—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—62no—
652C22×C4—62no—
653C22×C4—62no—
654C22×C4—62no—
655C22×C4—62no—
656C22×C4—64no—
657C22×C4—62no—
658C22×C4—64no—
659C22×C4—128no—
660C22×C4C2×D1211yescharacteristic
661C22×C4C2×D1212yes—
662C22×C4C23×D312yes—
663C22×C4C23×D312yes—
664C22×C4C23×D311yescharacteristic
665Q16—34no—
666Q16—64no—
667Q16—62no—
668SD16—38no—
669SD16—64no—
670SD16—68no—
671SD16—64no—
672SD16—64no—
673SD16—124no—
674D8—34no—
675D8—68no—
676D8—64no—
677D8—64no—
678D8—64no—
679D8—62no—
680D8—124no—
681M16—22no—
682M16—22no—
683M16—24no—
684M16—24no—
685M16—24no—
686C2×C8—22no—
687C2×C8—24no—
688C2×C8D3×D414yescomplemented
689C2×C8C23×D312yes—
690C2×C8C23×D312yes—
691C2×C8C23×D312yes—
692C2×C8C23×D311yescharacteristic
693C2×C8C23×D311yescharacteristic
694C4⋊C4—34no—
695C4⋊C4—62no—
696C4⋊C4—64no—
697C4⋊C4—64no—
698C4⋊C4C2×D1212yes—
699C4⋊C4C2×D1214yes—
700C22⋊C4—64no—
701C22⋊C4—64no—
702C22⋊C4—64no—
703C22⋊C4—64no—
704C22⋊C4—64no—
705C22⋊C4—64no—
706C22⋊C4—64no—
707C22⋊C4C2×D1214yes—
708C22⋊C4C2×D1212yes—
709C22⋊C4C2×D1214yes—
710C42—64no—
711C42C23×D312yes—
712C22×C3—22no—
713C22×C3—22no—
714C22×C3—22no—
715C22×C3—24no—
716C22×C3—22no—
717C22×C3—22no—
718C22×C3—82no—
719C22×C3D4212yes—
720C22×C3C23×D411yescharacteristic
721C2×D3—24no—
722C2×D3—42no—
723C2×D3—42no—
724C2×D3—42no—
725C2×D3—42no—
726C2×D3—44no—
727C2×D3—44no—
728C2×D3—42no—
729C2×D3—44no—
730C2×D3—88no—
731C2×D3—168no—
732C2×D3—164no—
733C3×C4—24no—
734C3×C4—22no—
735C3×C4—22no—
736C3×C4D4212yes—
737C3×C4C23×D411yescharacteristic
738C3×C4C2×H(5,𝔽2)11yescharacteristic
739Dic3—24no—
740Dic3—44no—
741Dic3—42no—
742C23—22no—
743C23—42no—
744C23—62no—
745C23—64no—
746C23—62no—
747C23—124no—
748C23—128no—
749C23—124no—
750C23—124no—
751C23—242no—
752C23—242no—
753C23—244no—
754C23—242no—
755C23—244no—
756C23C22×D1212yes—
757C23C22×D1212yes—
758C23C22×D1211yescharacteristic
759Q8—22no—
760Q8—34no—
761Q8—62no—
762Q8—62no—
763Q8—62no—
764Q8—124no—
765D4—24no—
766D4—22no—
767D4—34no—
768D4—44no—
769D4—68no—
770D4—64no—
771D4—62no—
772D4—62no—
773D4—62no—
774D4—64no—
775D4—128no—
776D4—124no—
777D4—128no—
778D4—124no—
779D4—124no—
780D4—128no—
781D4—124no—
782D4—124no—
783D4—244no—
784D4—244no—
785D4—244no—
786D4—244no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—24no—
793C2×C4—62no—
794C2×C4—68no—
795C2×C4—64no—
796C2×C4—62no—
797C2×C4—124no—
798C2×C4—128no—
799C2×C4—124no—
800C2×C4—124no—
801C2×C4—124no—
802C2×C4—244no—
803C2×C4—242no—
804C2×C4C22×D1214yes—
805C2×C4C22×D1212yes—
806C2×C4C22×D1212yes—
807C2×C4C22×D1211yescharacteristic
808C2×C4C2×D3×D412yes—
809C2×C4#100912yes—
810C2×C4C24×D311yescharacteristic
811C8—22no—
812C8—22no—
813C8—22no—
814C8C2×D3×D412yes—
815C8C2×D3×D412yes—
816C2×C3—22no—
817C2×C3—42no—
818C2×C3—42no—
819C2×C3C2×D4211yescharacteristic
820C2×C3#358512yes—
821D3—44no—
822D3—82no—
823D3—84no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—24no—
829C22—22no—
830C22—64no—
831C22—82no—
832C22—122no—
833C22—122no—
834C22—122no—
835C22—124no—
836C22—124no—
837C22—122no—
838C22—122no—
839C22—124no—
840C22—248no—
841C22—484no—
842C22—488no—
843C22D4×D1212yes—
844C22C23×D1211yescharacteristic
845C4—22no—
846C4—22no—
847C4—24no—
848C4—64no—
849C4—122no—
850C4—124no—
851C4D4×D1212yes—
852C4C22×D3×D411yescharacteristic
853C4C2×#100911yescharacteristic
854C3#6106311yescharacteristic, complemented, Sylow
855C2—22no—
856C2—42no—
857C2—42no—
858C2—124no—
859C2—242no—
860C2—244no—
861C2C2×D4×D1211yescharacteristic
862C2#8716712yes—
subgroupG/H
centerC22C23×D12
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#2930C2
socleC22×C3C23×D4
hypercenter#2930D3
hypocenterC3#61063
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #525 ◁ #2930

Complements

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

NH ≅ G/Ntype
1. C2×#5752C2semidirect
2. C2×#5748C2semidirect
3. #86041C2semidirect
4. C3×#2930C2semidirect
5. #83800C2semidirect
6. C2×#5135C2semidirect
7. #79551C2semidirect
8. #79550C2semidirect
9. #79508C2semidirect
10. #79493C2semidirect
11. #79088C2semidirect
12. #78672C2semidirect
13. #78639C2semidirect
14. #78574C2semidirect
15. #78565C2semidirect
17. C2×#1009C22semidirect
18. C22×#235C22semidirect
19. C2×C3×#131C22semidirect
20. C22×C3×M16C22semidirect
22. #5833C22semidirect
23. C2×#930C22semidirect
26. C2×#909C22semidirect
27. C2×#909C22semidirect
28. C2×#908C22semidirect
29. C2×#908C22semidirect
30. C2×#908C22semidirect
31. C2×#908C22semidirect
32. C2×#908C22semidirect
34. C2×#904C22semidirect
35. C2×#904C22semidirect
36. C2×#904C22semidirect
37. C22×D24C22semidirect
38. C22×D24C22semidirect
45. #5553C22semidirect
46. #5552C22semidirect
47. #5550C22semidirect
48. D4×D12C22semidirect
49. #5525C22semidirect
50. #5523C22semidirect
51. C3×#436C22semidirect
52. C3×#435C22semidirect
53. C3×#424C22semidirect
54. C3×#408C22semidirect
55. C3×#407C22semidirect
56. C3×#405C22semidirect
57. #5137C22semidirect
58. #5135C22semidirect
59. #5135C22semidirect
60. #5135C22semidirect
61. #5133C22semidirect
62. #5133C22semidirect
63. #5114C22semidirect
64. C2×#821C22semidirect
65. C2×#817C22semidirect
66. #4848C22semidirect
67. #4845C22semidirect
68. #4844C22semidirect
69. #4843C22semidirect
70. #4738C22semidirect
71. #4734C22semidirect
72. #4734C22semidirect
73. #4734C22semidirect
74. #4733C22semidirect
75. #4732C22semidirect
76. #4732C22semidirect
77. #4731C22semidirect
78. #4716C22semidirect
79. #4712C22semidirect
80. #4711C22semidirect
81. #4696C22semidirect
82. #4695C22semidirect
83. C4×#204C22semidirect
98. #2930D3semidirect
166. #904D4semidirect
234. C2×#131C2×D3semidirect
235. C22×M16C2×D3semidirect
274. #436C2×D3semidirect
275. #435C2×D3semidirect
277. #424C2×D3semidirect
281. #408C2×D3semidirect
282. #407C2×D3semidirect
283. #405C2×D3semidirect
328. #235C2×D4semidirect
362. C2×C3×C8C2×D4semidirect
388. Dic12C2×D4semidirect
395. D24C2×D4semidirect
401. #204C2×D4semidirect
688. C2×C8D3×D4semidirect
854. C3#61063semidirect

Maximal subgroups

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

subgroupindex
C2×#57522
C2×#57482
#860412
C3×#29302
#838002
C2×#51352
#795512
#795502
#795082
#794932
#790882
#786722
#786392
#785742
#785652
#610633