Finite Group Databasebeta

← #11865062

Subgroups — #11865062

Order 1152.

1617 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64308C211yesmaximal, characteristic, complemented
2C3×#5748C211yesmaximal, characteristic, complemented
3#10595045C211yesmaximal, characteristic, complemented
4#10594786C211yesmaximal, characteristic, complemented
5C2×#63650C211yesmaximal, characteristic, complemented
6C3×#5139C211yesmaximal, characteristic, complemented
7#10591111C211yesmaximal, characteristic, complemented
8#10591013C214yesmaximal, complemented
9#10591011C214yesmaximal, complemented
10#84005—31nomaximal
11#78993—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C2×C3×#235C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic, complemented
16C2×#3811—22no—
17#64308—22no—
18#64308—22no—
19#64308—22no—
20#64308C2214yes—
21C2×D3×D12—21no—
22C2×D3×D12—21no—
23C2×#3799—21no—
24C2×#3799—21no—
25C2×C32×M16C2211yescharacteristic, complemented
26C2×#3748C2211yescharacteristic, complemented
27C3×#926C2211yescharacteristic, complemented
28C3×#909—21no—
29C3×#909C2212yescomplemented
30C3×#908—21no—
31C3×#908C2212yescomplemented
32C3×#904—22no—
33#63981—22no—
34#63911C2212yescomplemented
35#63909—22no—
36#63864C2212yescomplemented
37#63827—21no—
38#63827C2212yescomplemented
39#63823—21no—
40#63823C2212yescomplemented
41#63822—22no—
42#63650C2214yescomplemented
43C3×#825C2214yescomplemented
44#63569C2214yescomplemented
45C2×#1009—31no—
46C2×#1009—31no—
47C3×#575—31no—
48#5830—31no—
49#5822—31no—
50#5822—31no—
51#5748D311yescharacteristic, complemented
52#5525—31no—
53C3×#421—31no—
54#5236—31no—
55#5202—34no—
56#5198—34no—
57#5139D311yescharacteristic, complemented
58C2×#823—31no—
59C2×#823—31no—
60C2×#823—61no—
61#5005—31no—
62#4825—34no—
63#4822—34no—
64C23×C3⋊D3D412yes—
65C22×D32—22no—
66C22×C32×C4C2311yescharacteristic
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)—21no—
70C2×C4⋊(C3⋊D3)—21no—
71C2×C4⋊(C3⋊D3)D412yes—
72C2×C4⋊(C3⋊D3)C2312yes—
73C2×C3×#67—21no—
74C2×C3×#67—21no—
75C2×C3×#67—21no—
76C3×#235—21no—
77C3×#235—21no—
78C3×#235—21no—
79C3×#235—21no—
80C3×#235—21no—
81C3×#235—21no—
82C3×#235—21no—
83C3×#235—21no—
84C3×#235D412yescomplemented
85C3×#235D412yescomplemented
86C3×#235C2312yes—
87C3×#235C2312yes—
88C2×C3×D12D411yescharacteristic, complemented
89C2×C3×D12D411yescharacteristic, complemented
90C2×C3×D12C2311yescharacteristic, complemented
91C2×C3×C4×D3—21no—
92C2×C3×C4×D3—21no—
93C2×C3×C4×D3—21no—
94C2×C3×Dic6D411yescharacteristic, complemented
95C2×C3×Dic6D411yescharacteristic, complemented
96C2×C3×Dic6C2311yescharacteristic, complemented
97#3811—28no—
98#3811—28no—
99C2×#626—22no—
100C2×#626—22no—
101C2×#626—24no—
102C2×#624—22no—
103D3×D12—24no—
104D3×D12—24no—
105D3×D12—24no—
106D3×D12—24no—
107#3799—24no—
108#3799—24no—
109#3799—24no—
110#3799—24no—
111C32×M16—21no—
112C32×M16C2312yescomplemented
113C2×C32×C8—21no—
114#3748—21no—
115#3748C2312yescomplemented
116C2×C3⋊(C3⋊C8)—21no—
117C3×#217—21no—
118C3×C4⋊Dic3—21no—
119C3×C4×Dic3C2312yescomplemented
120C3×Dic12—22no—
121C3×D24—22no—
122C3×#204—22no—
123C3×#204—22no—
124#3722—24no—
125#3718—22no—
126#3715—22no—
127#3715—22no—
128#3713—22no—
129#3019—91noSylow
130C2×C3×#41—31no—
131C2×C3×#41—31no—
132C2×C3×#41—31no—
133#1009—34no—
134#1009—34no—
135#1009—62no—
136#1009—62no—
137#1009—62no—
138#1009—62no—
139#1009—62no—
140#1009—62no—
141C2×#239—61no—
142C2×#239—61no—
143C2×D3×D4—61no—
144C2×D3×D4—61no—
145C2×D3×D4—62no—
146C2×D3×D4—62no—
147C2×#235—61no—
148C2×#235—61no—
149C2×#235C2×D311yescharacteristic
150C2×#235C2×D311yescharacteristic
151C2×#235C2×D311yescharacteristic, complemented
152C22×D12—31no—
153C22×D12—31no—
154C22×D12—61no—
155C22×D12—61no—
156C22×D12—61no—
157C3×#137—32no—
158C3×#137—61no—
159C3×AGL(1,ℤ/8)—32no—
160C3×AGL(1,ℤ/8)—61no—
161C3×#135—62no—
162C2×C3×M16—21no—
163C2×C3×M16C2×D311yescharacteristic, complemented
164C2×C3×M16C2×D311yescharacteristic, complemented
165C3×#117—31no—
166#951—32no—
167#951—61no—
168#950—62no—
169#950—62no—
170#949—32no—
171#949—61no—
172#947—32no—
173#942—32no—
174#942—61no—
175#940—32no—
176#937—62no—
177#932—32no—
178#932—61no—
179#930—62no—
180#926C2×D311yescharacteristic, complemented
181C2×#208—31no—
182C2×#208—31no—
183C2×#208—61no—
184#909—21no—
185#909C2×D312yescomplemented
186#908—21no—
187#908C2×D312yescomplemented
188#904—22no—
189#895—62no—
190#882—62no—
191#875—32no—
192#874—32no—
193C3×#104—34no—
194#837—34no—
195#825C2×D314yescomplemented
196#823—34no—
197#823—34no—
198#823—64no—
199#805—34no—
200C23×C32C2×D411yescharacteristic
201C22×C3⋊D3—22no—
202C22×C3⋊D3—22no—
203C22×C3⋊D3—82no—
204C22×C3⋊D3C2×D414yes—
205C22×C3×D3—21no—
206C22×C3×D3—21no—
207C22×C3×D3—21no—
208C2×D32—28no—
209C2×D32—84no—
210C2×C32×C4C2×D411yescharacteristic
211C2×C32×C4C2×D411yescharacteristic
212C2×C32×C4C2×D411yescharacteristic
213C2×C32×C4C2×D411yescharacteristic
214C2×C32×C4C2×D411yescharacteristic
215C2×C32×C4C2411yescharacteristic
216C4⋊(C3⋊D3)—22no—
217C4⋊(C3⋊D3)—22no—
218C4⋊(C3⋊D3)—22no—
219C4⋊(C3⋊D3)—22no—
220C3×#67—22no—
221C3×#67—22no—
222C3×#67—22no—
223C3×#67—22no—
224C3×#67—41no—
225C3×#67—41no—
226C2×C3×Dic3—21no—
227C2×C3×Dic3—21no—
228C2×C3×Dic3—21no—
229C2×C3×Dic3—22no—
230C3×D12—21no—
231C3×D12—21no—
232C3×D12—21no—
233C3×D12—21no—
234C3×D12C2×D412yes—
235C3×D12C2×D412yes—
236C3×C4×D3—22no—
237C3×C4×D3—22no—
238C3×C4×D3—22no—
239C3×C4×D3—22no—
240C3×C4×D3—41no—
241C3×C4×D3—41no—
242C3×Dic6—21no—
243C3×Dic6—21no—
244C3×Dic6—21no—
245C3×Dic6—21no—
246C3×Dic6C2×D412yes—
247C3×Dic6C2×D412yes—
248#626—28no—
249#626—28no—
250#626—84no—
251#624—28no—
252C32×C8—22no—
253C3⋊(C3⋊C8)—22no—
254C2×H(5,𝔽2)—91no—
255#575—31no—
256#575—91no—
257#535—91no—
258#455—94no—
259#453—94no—
260#421—31no—
261#421—91no—
262C2×#100—91no—
263C23×D3—32no—
264C23×D3—32no—
265C23×D3—62no—
266C23×D3—62no—
267C23×D3—62no—
268C3×#41—32no—
269C3×#41—32no—
270C3×#41—32no—
271C3×#41—32no—
272C3×#41—61no—
273C3×#41—61no—
274C3×#41—61no—
275C3×#41—61no—
276C3×#41—61no—
277C3×#41—61no—
278C3×#41—61no—
279C3×#41—61no—
280C2×C3×Q8—31no—
281C2×C3×Q8—31no—
282C2×C3×Q8—31no—
283C2×C3×D4—31no—
284C2×C3×D4—31no—
285C2×C3×D4—31no—
286C2×C3×D4—61no—
287C2×C3×D4—61no—
288C2×C3×D4—61no—
289C22×C3×C4—21no—
290C22×C3×C4—61no—
291C22×C3×C4—61no—
292C22×C3×C4—61no—
293C22×C3×C4C22×D311yescharacteristic
294C22×C3×C4C22×D311yescharacteristic
295C2×#67—21no—
296C2×#67—21no—
297C2×#67—21no—
298C2×#67—62no—
299C2×#67—62no—
300C2×#67—64no—
301#239—64no—
302#239—64no—
303#239—64no—
304#239—64no—
305D3×D4—64no—
306D3×D4—64no—
307D3×D4—64no—
308D3×D4—64no—
309D3×D4—68no—
310D3×D4—68no—
311D3×D4—68no—
312D3×D4—68no—
313#235—21no—
314#235—21no—
315#235—21no—
316#235—21no—
317#235—21no—
318#235—21no—
319#235—21no—
320#235—21no—
321#235—64no—
322#235—64no—
323#235—64no—
324#235—64no—
325#235D1212yescomplemented
326#235#6712yescomplemented
327#235C22×D312yes—
328#235C22×D312yes—
329C2×D12—32no—
330C2×D12—32no—
331C2×D12—32no—
332C2×D12—32no—
333C2×D12—62no—
334C2×D12—62no—
335C2×D12—64no—
336C2×D12—64no—
337C2×D12—62no—
338C2×D12—62no—
339C2×D12—61no—
340C2×D12—61no—
341C2×D12—61no—
342C2×D12—61no—
343C2×D12—61no—
344C2×D12—61no—
345C2×D12—61no—
346C2×D12—61no—
347C2×D12—64no—
348C2×D12—64no—
349C2×D12—64no—
350C2×D12—121no—
351C2×D12—121no—
352C2×D12—121no—
353C2×D12—121no—
354C2×D12D1211yescharacteristic, complemented
355C2×D12#6711yescharacteristic, complemented
356C2×D12C22×D311yescharacteristic, complemented
357C2×C4×D3—21no—
358C2×C4×D3—21no—
359C2×C4×D3—21no—
360C2×C4×D3—62no—
361C2×C4×D3—62no—
362C2×Dic6D1211yescharacteristic, complemented
363C2×Dic6#6711yescharacteristic, complemented
364C2×Dic6C22×D311yescharacteristic, complemented
365C3×Q16—62no—
366C3×SD16—62no—
367C3×SD16—62no—
368C3×D8—62no—
369C3×M16—21no—
370C3×M16—21no—
371C3×M16—22no—
372C3×M16—41no—
373C3×M16C22×D312yescomplemented
374C3×M16C22×D312yescomplemented
375C2×C3×C8—21no—
376C2×C3×C8—21no—
377C2×C3×C8—41no—
378C3×C4⋊C4—61no—
379C3×C22⋊C4—61no—
380C3×C42—32no—
381#217—21no—
382#216—62no—
383#216—62no—
384#215—62no—
385#215—62no—
386#214—62no—
387#214—62no—
388#213—62no—
389#213—62no—
390(C2×D3)⋊C4—64no—
391(C2×D3)⋊C4—64no—
392C4⋊Dic3—21no—
393C4×Dic3C22×D312yescomplemented
394#208—32no—
395#208—32no—
396#208—62no—
397#208—61no—
398#208—61no—
399#208—121no—
400C2×C3⋊C8—61no—
401C2×C3⋊C8—61no—
402C2×C3⋊C8—121no—
403Dic12—22no—
404D24—22no—
405#204—22no—
406#204—22no—
407C22×C32—41no—
408C22×C32#12011yescharacteristic
409C22×C32#12011yescharacteristic
410C22×C32C22×D411yescharacteristic
411C2×C3⋊D3—24no—
412C2×C3⋊D3—44no—
413C2×C3⋊D3—44no—
414C2×C3⋊D3—82no—
415C2×C3×D3—22no—
416C2×C3×D3—22no—
417C2×C3×D3—42no—
418C2×C3×D3—42no—
419C2×C3×D3—42no—
420C2×C3×D3—41no—
421D32—88no—
422C32×C4#12011yescharacteristic
423C32×C4#12011yescharacteristic
424C32×C4C22×D411yescharacteristic
425C32×C4C22×D411yescharacteristic
426C3×Dic3—22no—
427C3×Dic3—22no—
428C3×Dic3—42no—
429C3×Dic3—41no—
430H(5,𝔽2)—94no—
431H(5,𝔽2)—182no—
432H(5,𝔽2)—182no—
433H(5,𝔽2)—182no—
434C2×#41—31no—
435C2×#41—31no—
436C2×#41—31no—
437C2×#41—181no—
438C2×#41—181no—
439C22×D4—91no—
440C22×D4—181no—
441C22×D4—181no—
442C22×D4—182no—
443#137—32no—
444#137—61no—
445#137—92no—
446#137—181no—
447AGL(1,ℤ/8)—32no—
448AGL(1,ℤ/8)—61no—
449AGL(1,ℤ/8)—92no—
450AGL(1,ℤ/8)—181no—
451#135—62no—
452#135—182no—
453C2×M16—91no—
454C2×M16D3211yescharacteristic, complemented
455#127—92no—
456#124—92no—
457#121—182no—
458#120—182no—
459#117—31no—
460#104—34no—
461#104—94no—
462#100—94no—
463C23×C3—21no—
464C23×C3—61no—
465C23×C3—61no—
466C23×C3—61no—
467C23×C3D3×D411yescharacteristic
468C23×C3D3×D411yescharacteristic
469C22×D3—21no—
470C22×D3—21no—
471C22×D3—21no—
472C22×D3—34no—
473C22×D3—34no—
474C22×D3—64no—
475C22×D3—68no—
476C22×D3—68no—
477C22×D3—62no—
478C22×D3—62no—
479C22×D3—62no—
480C22×D3—62no—
481C22×D3—122no—
482C22×D3—122no—
483C22×D3—244no—
484C22×D3—244no—
485C22×D3—242no—
486C22×D3—242no—
487C22×D3—244no—
488C3×Q8—32no—
489C3×Q8—32no—
490C3×Q8—61no—
491C3×Q8—61no—
492C3×Q8—61no—
493C3×Q8—61no—
494C3×D4—32no—
495C3×D4—32no—
496C3×D4—62no—
497C3×D4—62no—
498C3×D4—62no—
499C3×D4—62no—
500C3×D4—61no—
501C3×D4—61no—
502C3×D4—61no—
503C3×D4—61no—
504C3×D4—121no—
505C3×D4—121no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—62no—
515C2×C3×C4—62no—
516C2×C3×C4—62no—
517C2×C3×C4—62no—
518C2×C3×C4—61no—
519C2×C3×C4—62no—
520C2×C3×C4—121no—
521C2×C3×C4—121no—
522C2×C3×C4C2×D1211yescharacteristic
523C2×C3×C4C2×D1211yescharacteristic
524C2×C3×C4D3×D411yescharacteristic
525C2×C3×C4D3×D411yescharacteristic
526C2×C3×C4D3×D411yescharacteristic
527C2×C3×C4D3×D411yescharacteristic
528C2×C3×C4D3×D411yescharacteristic
529C2×C3×C4D3×D411yescharacteristic
530C2×C3×C4C2×#6711yescharacteristic
531C2×C3×C4C2×#6711yescharacteristic
532C2×C3×C4C23×D311yescharacteristic
533C2×C3×C4C23×D311yescharacteristic
534#67—22no—
535#67—22no—
536#67—22no—
537#67—22no—
538#67—41no—
539#67—41no—
540#67—68no—
541#67—68no—
542#67—244no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—22no—
546C2×Dic3—21no—
547D12—21no—
548D12—21no—
549D12—21no—
550D12—21no—
551D12—68no—
552D12—68no—
553D12—62no—
554D12—62no—
555D12—62no—
556D12—62no—
557D12—62no—
558D12—62no—
559D12—62no—
560D12—62no—
561D12—122no—
562D12—122no—
563D12—122no—
564D12—122no—
565D12—244no—
566D12C2×D1212yes—
567D12C2×#6712yes—
568C4×D3—22no—
569C4×D3—22no—
570C4×D3—22no—
571C4×D3—22no—
572C4×D3—41no—
573C4×D3—41no—
574C4×D3—68no—
575C4×D3—68no—
576Dic6—21no—
577Dic6—21no—
578Dic6—21no—
579Dic6—21no—
580Dic6C2×D1212yes—
581Dic6C2×#6712yes—
582C3×C8—22no—
583C3×C8—22no—
584C3×C8—42no—
585C3⋊C8—62no—
586C3⋊C8—62no—
587C3⋊C8—122no—
588C2×C32—21no—
589C2×C32—21no—
590C2×C32—21no—
591C2×C32C2×#12011yescharacteristic
592C3⋊D3—44no—
593C3×D3—42no—
594C3×D3—42no—
595C3×D3—81no—
596C24—92no—
597C24—182no—
598#41—32no—
599#41—32no—
600#41—32no—
601#41—32no—
602#41—61no—
603#41—61no—
604#41—61no—
605#41—61no—
606#41—61no—
607#41—61no—
608#41—61no—
609#41—61no—
610#41—184no—
611#41—184no—
612#41—184no—
613#41—184no—
614C2×Q8—31no—
615C2×Q8—31no—
616C2×Q8—31no—
617C2×D4—31no—
618C2×D4—31no—
619C2×D4—31no—
620C2×D4—61no—
621C2×D4—61no—
622C2×D4—61no—
623C2×D4—92no—
624C2×D4—92no—
625C2×D4—184no—
626C2×D4—184no—
627C2×D4—184no—
628C2×D4—184no—
629C2×D4—182no—
630C2×D4—182no—
631C2×D4—184no—
632C2×D4—188no—
633C2×D4—188no—
634C2×D4—181no—
635C2×D4—181no—
636C2×D4—181no—
637C2×D4—181no—
638C22×C4—61no—
639C22×C4—61no—
640C22×C4—61no—
641C22×C4—182no—
642C22×C4C2×D3211yescharacteristic
643Q16—62no—
644Q16—182no—
645SD16—62no—
646SD16—62no—
647SD16—182no—
648SD16—182no—
649D8—62no—
650D8—182no—
651M16—21no—
652M16—92no—
653M16—181no—
654M16C2×D3212yescomplemented
655C2×C8—21no—
656C2×C8—181no—
657C4⋊C4—61no—
658C22⋊C4—61no—
659C22⋊C4—184no—
660C42—32no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—42no—
667C22×C3—62no—
668C22×C3—62no—
669C22×C3—122no—
670C22×C3—122no—
671C22×C3—122no—
672C22×C3—121no—
673C22×C3#88211yescharacteristic
674C22×C3#88211yescharacteristic
675C22×C3#93711yescharacteristic
676C22×C3#93711yescharacteristic
677C22×C3C2×D3×D411yescharacteristic
678C22×C3C2×D3×D411yescharacteristic
679C2×D3—22no—
680C2×D3—22no—
681C2×D3—42no—
682C2×D3—42no—
683C2×D3—42no—
684C2×D3—41no—
685C2×D3—64no—
686C2×D3—64no—
687C2×D3—124no—
688C2×D3—124no—
689C2×D3—124no—
690C2×D3—124no—
691C2×D3—124no—
692C2×D3—244no—
693C2×D3—244no—
694C2×D3—248no—
695C2×D3—248no—
696C2×D3—242no—
697C2×D3—242no—
698C2×D3—244no—
699C3×C4—21no—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—62no—
704C3×C4—62no—
705C3×C4—122no—
706C3×C4—121no—
707C3×C4#88211yescharacteristic
708C3×C4#88211yescharacteristic
709C3×C4#93711yescharacteristic
710C3×C4#93711yescharacteristic
711C3×C4C22×D1211yescharacteristic
712C3×C4C2×D3×D411yescharacteristic
713C3×C4C2×D3×D411yescharacteristic
714C3×C4C22×#6711yescharacteristic
715Dic3—22no—
716Dic3—22no—
717Dic3—42no—
718Dic3—41no—
719C32#301911yescharacteristic, complemented, Sylow
720C23—61no—
721C23—61no—
722C23—61no—
723C23—94no—
724C23—188no—
725C23—182no—
726C23—182no—
727C23—722no—
728C23—724no—
729C23#380211yescharacteristic
730Q8—32no—
731Q8—32no—
732Q8—61no—
733Q8—61no—
734Q8—61no—
735Q8—61no—
736D4—32no—
737D4—32no—
738D4—62no—
739D4—62no—
740D4—62no—
741D4—62no—
742D4—61no—
743D4—61no—
744D4—61no—
745D4—61no—
746D4—121no—
747D4—121no—
748D4—188no—
749D4—188no—
750D4—182no—
751D4—182no—
752D4—182no—
753D4—182no—
754D4—724no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—62no—
758C2×C4—62no—
759C2×C4—62no—
760C2×C4—62no—
761C2×C4—62no—
762C2×C4—61no—
763C2×C4—121no—
764C2×C4—121no—
765C2×C4—188no—
766C2×C4D3×D1211yescharacteristic
767C2×C4D3×D1211yescharacteristic
768C2×C4#380211yescharacteristic
769C2×C4D3×#6711yescharacteristic
770C2×C4D3×#6711yescharacteristic
771C2×C4C22×D3211yescharacteristic
772C8—22no—
773C8—182no—
774C2×C3—22no—
775C2×C3—21no—
776C2×C3—21no—
777C2×C3—21no—
778C2×C3—21no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—41no—
783C2×C3—41no—
784C2×C3—122no—
785C2×C3—122no—
786C2×C3—241no—
787C2×C3C2×#88211yescharacteristic
788C2×C3C2×#93711yescharacteristic
789D3—42no—
790D3—42no—
791D3—81no—
792D3—124no—
793D3—124no—
794D3—244no—
795C22—41no—
796C22—62no—
797C22—62no—
798C22—122no—
799C22—122no—
800C22—122no—
801C22—121no—
802C22—184no—
803C22—364no—
804C22—364no—
805C22—722no—
806C22—728no—
807C22#6392211yescharacteristic
808C22#6392211yescharacteristic
809C22C2×#380211yescharacteristic
810C4—62no—
811C4—62no—
812C4—122no—
813C4—121no—
814C4#6392211yescharacteristic
815C4#6392211yescharacteristic
816C4C2×D3×D1211yescharacteristic
817C4C2×D3×#6711yescharacteristic
818C3—21no—
819C3#7899311yescharacteristic, complemented
820C3#8400511yescharacteristic, complemented
821C2—21no—
822C2—21no—
823C2—21no—
824C2—122no—
825C2—122no—
826C2—241no—
827C2—364no—
828C2C2×#6392211yescharacteristic
subgroupG/H
centerC2C2×#63922
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC2×C32C2×#120
hypercenterC2×M16D32
hypocenterC32#3019
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×#64308C2semidirect
2. C3×#5748C2semidirect
3. #10595045C2semidirect
4. #10594786C2semidirect
5. C2×#63650C2semidirect
6. C3×#5139C2semidirect
7. #10591111C2semidirect
8. #10591013C2semidirect
9. #10591011C2semidirect
15. C2×C3×#235C22semidirect
25. C2×C32×M16C22semidirect
26. C2×#3748C22semidirect
27. C3×#926C22semidirect
29. C3×#909C22semidirect
31. C3×#908C22semidirect
34. #63911C22semidirect
36. #63864C22semidirect
38. #63827C22semidirect
40. #63823C22semidirect
42. #63650C22semidirect
43. C3×#825C22semidirect
44. #63569C22semidirect
51. #5748D3semidirect
57. #5139D3semidirect
84. C3×#235D4semidirect
85. C3×#235D4semidirect
88. C2×C3×D12D4semidirect
89. C2×C3×D12D4semidirect
90. C2×C3×D12C23semidirect
94. C2×C3×Dic6D4semidirect
95. C2×C3×Dic6D4semidirect
96. C2×C3×Dic6C23semidirect
112. C32×M16C23semidirect
115. #3748C23semidirect
119. C3×C4×Dic3C23semidirect
151. C2×#235C2×D3semidirect
163. C2×C3×M16C2×D3semidirect
164. C2×C3×M16C2×D3semidirect
180. #926C2×D3semidirect
185. #909C2×D3semidirect
187. #908C2×D3semidirect
195. #825C2×D3semidirect
325. #235D12semidirect
326. #235#67semidirect
354. C2×D12D12semidirect
355. C2×D12#67semidirect
356. C2×D12C22×D3semidirect
362. C2×Dic6D12semidirect
363. C2×Dic6#67semidirect
364. C2×Dic6C22×D3semidirect
373. C3×M16C22×D3semidirect
374. C3×M16C22×D3semidirect
393. C4×Dic3C22×D3semidirect
454. C2×M16D32semidirect
654. M16C2×D32semidirect
719. C32#3019semidirect
819. C3#78993semidirect
820. C3#84005semidirect

Maximal subgroups

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

subgroupindex
C2×#643082
C3×#57482
#105950452
#105947862
C2×#636502
C3×#51392
#105911112
#105910132
#105910112
#840053
#789933