Finite Group Databasebeta

← #11864609

Subgroups — #11864609

Order 1152.

1661 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1009C211yesmaximal, characteristic, complemented
2C2×#64159C211yesmaximal, characteristic, complemented
3#10595043C211yesmaximal, characteristic, complemented
4C2×#63830C211yesmaximal, characteristic, complemented
5C3×#5232C211yesmaximal, characteristic, complemented
6#10591599C212yesmaximal, complemented
7#10591588C212yesmaximal, complemented
8#10591459C212yesmaximal, complemented
9#10591448C212yesmaximal, complemented
10C2×#63562C211yesmaximal, characteristic, complemented
11#10591071C211yesmaximal, characteristic, complemented
12#84102—31nomaximal
13#78886—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C2×#3828C2211yescharacteristic, complemented
16C3×#1009—24no—
17C3×#1009—24no—
18C2×C3×#239C2212yes—
19C2×C3×D3×D4—22no—
20C2×C3×D3×D4C2212yes—
21C2×C3×#235—21no—
22C2×C3×#235C2211yescharacteristic
23C22×C3×D12—21no—
24C22×C3×D12C2211yescharacteristic
25#64159—24no—
26C2×#3756C2211yescharacteristic, complemented
27C2×#3755C2211yescharacteristic, complemented
28C2×#3754C2211yescharacteristic, complemented
29C2×#3753C2211yescharacteristic, complemented
30C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
31C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
32C2×C3×#208C2211yescharacteristic, complemented
33#63978—22no—
34#63916—21no—
35#63909C2212yescomplemented
36#63871—21no—
37#63857C2212yescomplemented
38#63830—24no—
39C2×#3716C2212yescomplemented
40C2×#3714C2212yescomplemented
41C3×#835C2212yescomplemented
42C3×#832C2212yescomplemented
43#63562C2212yescomplemented
44#63562C2212yescomplemented
45(C2×D3)⋊(C3⋊C8)C2212yescomplemented
46(C2×D3)⋊(C3⋊C8)C2212yescomplemented
47C2×C3×H(5,𝔽2)—31no—
48C2×#1009D311yescharacteristic, complemented
49#5833—31no—
50C2×#950—31no—
51C2×#950—31no—
52C2×#950—61no—
53C2×#932—31no—
54C2×#908—31no—
55#5510—31no—
56C3×#417—31no—
57#5239—32no—
58#5238—32no—
59#5234—31no—
60#5232D311yescharacteristic, complemented
61#5218—32no—
62#5217—32no—
63C2×#832—31no—
64#5129—31no—
65C2×#809—31no—
66#4810—32no—
67#4808—32no—
68#4776—32no—
69#4773—32no—
70C23×C3×D3—21no—
71C23×C3×D3—22no—
72C32×#41—22no—
73C32×#41D414yescomplemented
74C2×C32×Q8C2311yescharacteristic
75C2×C32×D4—21no—
76C2×C32×D4C2311yescharacteristic
77C22×C32×C4—21no—
78C22×C32×C4C2311yescharacteristic
79C2×#638—21no—
80#3828—22no—
81#3828—22no—
82C2×C4⋊(C3⋊D3)C2311yescharacteristic
83C2×C4×C3⋊D3—21no—
84C2×#634C2311yescharacteristic
85C2×C3×#67—22no—
86C2×C3×#67D412yes—
87C22×C3×Dic3—21no—
88C3×#239—24no—
89C3×#239—24no—
90C3×D3×D4—216no—
91C3×D3×D4—24no—
92C3×D3×D4—24no—
93C3×#235—28no—
94C3×#235—22no—
95C3×#235—22no—
96C2×C3×D12—28no—
97C2×C3×D12—22no—
98C2×C3×D12—21no—
99C2×C3×D12—22no—
100C2×C3×D12D411yescharacteristic
101C2×C3×D12D414yescomplemented
102C2×C3×D12C2312yes—
103C2×C3×C4×D3—22no—
104C2×C3×C4×D3C2312yes—
105C2×C3×Dic6D411yescharacteristic
106C2×#626—22no—
107#3756—22no—
108#3755—22no—
109#3754—22no—
110#3753—22no—
111C2×C3⋊(C3⋊C8)—22no—
112C2×C3⋊(C3⋊C8)C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3C2312yes—
116C3×#208—22no—
117C2×C3×C3⋊C8C2312yes—
118Dic3⋊Dic3—22no—
119#3722—22no—
120(C2×D3)⋊Dic3—22no—
121#3716—24no—
122#3714—24no—
123#3012—91noSylow
124C3×H(5,𝔽2)—64no—
125C3×H(5,𝔽2)—64no—
126C2×C3×#41—21no—
127C2×C3×#41—31no—
128C2×C3×#41—32no—
129C2×C3×#41—61no—
130C2×C3×#41C2×D311yescharacteristic
131C2×C3×#41C2×D311yescharacteristic
132C22×C3×D4—32no—
133C22×C3×D4—31no—
134C22×C3×D4—61no—
135C22×C3×D4—62no—
136#1009—24no—
137#1009—24no—
138C2×#239C2×D312yes—
139C2×D3×D4—22no—
140C2×D3×D4C2×D312yes—
141C2×#235—21no—
142C2×#235—31no—
143C2×#235—31no—
144C2×#235—61no—
145C2×#235C2×D311yescharacteristic
146C22×D12—21no—
147C22×D12C2×D311yescharacteristic
148C2×C3×M16—31no—
149C2×C3×C4⋊C4—31no—
150#950—68no—
151#950—64no—
152#950—64no—
153#946—61no—
154C2×#216—31no—
155C2×#216—31no—
156C2×#216—61no—
157C2×#215—31no—
158C2×#215—31no—
159C2×#215—61no—
160#939—62no—
161#938—61no—
162C2×#214—31no—
163C2×#214—31no—
164C2×#214—32no—
165C2×#214—61no—
166#932—64no—
167C2×#213—31no—
168C2×#213—31no—
169C2×#213—32no—
170C2×#213—61no—
171#930—32no—
172#930—62no—
173C2×C4⋊Dic3C2×D311yescharacteristic, complemented
174#924—32no—
175C2×#208C2×D311yescharacteristic, complemented
176C22×C3⋊C8—31no—
177C22×C3⋊C8—31no—
178C22×C3⋊C8—61no—
179#908—64no—
180C2×D24—32no—
181C2×#204—32no—
182#897—32no—
183#897—61no—
184#895—32no—
185#895—61no—
186C3×#103—32no—
187C3×#102—32no—
188#835C2×D312yescomplemented
189#832—32no—
190#832—32no—
191#832C2×D312yescomplemented
192#830—32no—
193#830—32no—
194(C2×D3)⋊C8—32no—
195(C2×D3)⋊C8—32no—
196#809—32no—
197#809—32no—
198C23×C32—21no—
199C23×C32C2×D411yescharacteristic
200C22×C3⋊D3—21no—
201C22×C3×D3—22no—
202C22×C3×D3—28no—
203C22×C3×D3—24no—
204C22×C3×D3—82no—
205C22×C3×D3—82no—
206C22×C3×D3—81no—
207C22×C3×D3—81no—
208C22×C3×D3C2×D412yes—
209C32×Q8—21no—
210C32×Q8C2×D412yes—
211C32×D4—24no—
212C32×D4—21no—
213C32×D4C2×D412yes—
214C2×C32×C4—21no—
215C2×C32×C4—24no—
216C2×C32×C4C2×D412yes—
217C2×C32×C4C2×D411yescharacteristic
218C2×C32×C4C2×D412yes—
219C2×C32×C4C2411yescharacteristic
220#638—42no—
221C2×C3⋊Dic3—21no—
222C4⋊(C3⋊D3)—21no—
223C4⋊(C3⋊D3)—21no—
224C4×C3⋊D3—42no—
225#634—21no—
226#634—21no—
227C3×#67—28no—
228C3×#67—24no—
229C2×C3×Dic3—22no—
230C2×C3×Dic3—81no—
231C2×C3×Dic3C2×D412yes—
232C3×D12—28no—
233C3×D12—22no—
234C3×D12—24no—
235C3×D12—22no—
236C3×D12C2×D414yes—
237C3×C4×D3—28no—
238C3×C4×D3—22no—
239C3×C4×D3—22no—
240C3×Dic6—22no—
241#626—82no—
242C3⋊(C3⋊C8)—21no—
243C3⋊(C3⋊C8)—21no—
244C3×C3⋊C8—22no—
245C2×H(5,𝔽2)—31no—
246C2×AGL(1,ℤ/8)—91no—
247C2×#135—91no—
248#537—91no—
249#452—92no—
250#450—92no—
251#449—92no—
252#447—92no—
253#417—31no—
254C2×#102—91no—
255#408—91no—
256C24×C3—62no—
257C24×C3—61no—
258C23×D3—21no—
259C23×D3—22no—
260C3×#41—22no—
261C3×#41—22no—
262C3×#41—24no—
263C3×#41—42no—
264C3×#41—68no—
265C3×#41—64no—
266C3×#41—64no—
267C3×#41—62no—
268C3×#41—62no—
269C3×#41D1214yescomplemented
270C3×#41#6714yescomplemented
271C2×C3×Q8—21no—
272C2×C3×Q8—31no—
273C2×C3×Q8C22×D311yescharacteristic
274C2×C3×Q8C22×D311yescharacteristic
275C2×C3×D4—21no—
276C2×C3×D4—21no—
277C2×C3×D4—21no—
278C2×C3×D4—32no—
279C2×C3×D4—34no—
280C2×C3×D4—31no—
281C2×C3×D4—32no—
282C2×C3×D4—41no—
283C2×C3×D4—62no—
284C2×C3×D4—68no—
285C2×C3×D4—62no—
286C2×C3×D4—64no—
287C2×C3×D4—616no—
288C2×C3×D4—64no—
289C2×C3×D4—62no—
290C2×C3×D4—61no—
291C2×C3×D4C22×D311yescharacteristic
292C2×C3×D4C22×D311yescharacteristic
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—32no—
297C22×C3×C4—41no—
298C22×C3×C4—62no—
299C22×C3×C4—61no—
300C22×C3×C4C22×D311yescharacteristic
301C22×C3×C4C22×D311yescharacteristic
302C2×#67—22no—
303C2×#67—62no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—121no—
307C2×#67#6712yes—
308C22×Dic3—21no—
309#239—24no—
310#239—24no—
311D3×D4—216no—
312D3×D4—24no—
313D3×D4—24no—
314#235—28no—
315#235—22no—
316#235—22no—
317#235—64no—
318#235—62no—
319#235—62no—
320#235—62no—
321#235—62no—
322#235—122no—
323C2×D12—28no—
324C2×D12—22no—
325C2×D12—21no—
326C2×D12—22no—
327C2×D12—31no—
328C2×D12—31no—
329C2×D12—61no—
330C2×D12—62no—
331C2×D12#6711yescharacteristic
332C2×D12#6714yescomplemented
333C2×D12C22×D312yes—
334C2×C4×D3—22no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—121no—
338C2×C4×D3C22×D312yes—
339C2×Dic6—31no—
340C2×Dic6—31no—
341C2×Dic6—61no—
342C2×Dic6#6711yescharacteristic
343C3×M16—62no—
344C2×C3×C8—32no—
345C3×C4⋊C4—32no—
346C3×C4⋊C4—61no—
347#217—62no—
348#216—64no—
349#216—62no—
350#216—62no—
351#215—64no—
352#215—62no—
353#215—62no—
354#214—64no—
355#214—64no—
356#214—62no—
357#214—62no—
358#213—64no—
359#213—64no—
360#213—62no—
361#213—62no—
362(C2×D3)⋊C4—62no—
363(C2×D3)⋊C4—62no—
364(C2×D3)⋊C4—62no—
365C4⋊Dic3—21no—
366C4⋊Dic3—62no—
367C4⋊Dic3C22×D312yes—
368Dic3⋊C4—62no—
369#208—22no—
370C2×C3⋊C8—31no—
371C2×C3⋊C8—31no—
372C2×C3⋊C8—31no—
373C2×C3⋊C8—31no—
374C2×C3⋊C8—61no—
375C2×C3⋊C8—61no—
376C2×C3⋊C8—64no—
377C2×C3⋊C8—62no—
378C2×C3⋊C8—62no—
379C2×C3⋊C8C22×D312yes—
380D24—64no—
381#204—64no—
382C22×C32—21no—
383C22×C32—21no—
384C22×C32—22no—
385C22×C32—41no—
386C22×C32—41no—
387C22×C32#12012yes—
388C22×C32C22×D411yescharacteristic
389C2×C3⋊D3—41no—
390C2×C3⋊D3—41no—
391C2×C3⋊D3—41no—
392C2×C3×D3—22no—
393C2×C3×D3—24no—
394C2×C3×D3—22no—
395C2×C3×D3—22no—
396C2×C3×D3—42no—
397C2×C3×D3—42no—
398C2×C3×D3—84no—
399C2×C3×D3—88no—
400C32×C4—22no—
401C32×C4#12012yes—
402C32×C4C22×D411yescharacteristic
403C32×C4C22×D411yescharacteristic
404C3⋊Dic3—41no—
405C3×Dic3—22no—
406C3×Dic3—42no—
407H(5,𝔽2)—64no—
408H(5,𝔽2)—64no—
409C2×#41—31no—
410C2×#41—32no—
411C2×#41—61no—
412C2×#41—91no—
413C2×#41D3211yescharacteristic
414C22×D4—32no—
415C22×D4—31no—
416C22×D4—61no—
417C22×D4—62no—
418AGL(1,ℤ/8)—184no—
419#135—184no—
420C2×Q16—91no—
421C2×SD16—92no—
422C2×SD16—91no—
423C2×SD16—91no—
424C2×D8—92no—
425C2×D8—91no—
426C2×M16—31no—
427C22×C8—91no—
428C22⋊Q8—92no—
429C22⋊Q8—181no—
430#121—92no—
431#121—181no—
432#121—182no—
433C2×C4⋊C4—31no—
434#103—32no—
435#102—32no—
436#102—92no—
437#102—92no—
438C22⋊C8—92no—
439C22⋊C8—92no—
440C23×C3—21no—
441C23×C3—21no—
442C23×C3—21no—
443C23×C3—32no—
444C23×C3—41no—
445C23×C3—68no—
446C23×C3—62no—
447C23×C3—64no—
448C23×C3—241no—
449C23×C3—241no—
450C23×C3—242no—
451C23×C3—242no—
452C23×C3D3×D411yescharacteristic
453C23×C3C2×#6711yescharacteristic
454C22×D3—22no—
455C22×D3—28no—
456C22×D3—24no—
457C22×D3—61no—
458C22×D3—61no—
459C22×D3—82no—
460C22×D3—82no—
461C22×D3—81no—
462C22×D3—81no—
463C22×D3—121no—
464C22×D3C2×#6712yes—
465C3×Q8—21no—
466C3×Q8—21no—
467C3×Q8—22no—
468C3×Q8—41no—
469C3×Q8—62no—
470C3×Q8C2×D1212yes—
471C3×Q8C2×#6712yes—
472C3×D4—24no—
473C3×D4—24no—
474C3×D4—21no—
475C3×D4—21no—
476C3×D4—22no—
477C3×D4—34no—
478C3×D4—41no—
479C3×D4—44no—
480C3×D4—68no—
481C3×D4—68no—
482C3×D4—64no—
483C3×D4—64no—
484C3×D4—62no—
485C3×D4—62no—
486C3×D4C2×D1212yes—
487C3×D4C2×#6712yes—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—24no—
491C2×C3×C4—24no—
492C2×C3×C4—21no—
493C2×C3×C4—22no—
494C2×C3×C4—21no—
495C2×C3×C4—22no—
496C2×C3×C4—32no—
497C2×C3×C4—44no—
498C2×C3×C4—41no—
499C2×C3×C4—68no—
500C2×C3×C4—62no—
501C2×C3×C4—62no—
502C2×C3×C4—62no—
503C2×C3×C4—241no—
504C2×C3×C4C2×D1212yes—
505C2×C3×C4D3×D411yescharacteristic
506C2×C3×C4D3×D412yes—
507C2×C3×C4C2×#6712yes—
508C2×C3×C4C2×#6711yescharacteristic
509C2×C3×C4C2×#6712yes—
510C2×C3×C4C23×D311yescharacteristic
511C2×C3×C4C23×D311yescharacteristic
512#67—28no—
513#67—24no—
514#67—124no—
515#67—122no—
516#67—122no—
517#67—242no—
518C2×Dic3—22no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—81no—
522C2×Dic3—121no—
523C2×Dic3C2×#6712yes—
524D12—28no—
525D12—22no—
526D12—24no—
527D12—22no—
528D12—62no—
529D12—61no—
530D12—61no—
531D12—61no—
532D12—61no—
533D12—121no—
534D12—242no—
535D12C2×#6714yes—
536C4×D3—28no—
537C4×D3—22no—
538C4×D3—22no—
539C4×D3—124no—
540C4×D3—122no—
541C4×D3—122no—
542Dic6—22no—
543Dic6—62no—
544Dic6—61no—
545Dic6—61no—
546Dic6—61no—
547Dic6—61no—
548Dic6—121no—
549C3×C8—62no—
550C3⋊C8—22no—
551C3⋊C8—62no—
552C3⋊C8—62no—
553C3⋊C8—61no—
554C3⋊C8—61no—
555C3⋊C8—61no—
556C3⋊C8—61no—
557C2×C32—22no—
558C2×C32—42no—
559C2×C32C2×#12011yescharacteristic
560C2×C32#57611yescharacteristic
561C2×C32#57711yescharacteristic
562C3⋊D3—81no—
563C3×D3—42no—
564C3×D3—44no—
565C24—62no—
566C24—61no—
567#41—22no—
568#41—68no—
569#41—64no—
570#41—64no—
571#41—62no—
572#41—62no—
573#41—182no—
574#41—182no—
575#41#62614yescomplemented
576C2×Q8—31no—
577C2×Q8—91no—
578C2×Q8C2×D3211yescharacteristic
579C2×D4—21no—
580C2×D4—32no—
581C2×D4—32no—
582C2×D4—34no—
583C2×D4—31no—
584C2×D4—62no—
585C2×D4—68no—
586C2×D4—62no—
587C2×D4—64no—
588C2×D4—616no—
589C2×D4—64no—
590C2×D4—62no—
591C2×D4—61no—
592C2×D4—91no—
593C2×D4—182no—
594C2×D4—181no—
595C2×D4C2×D3211yescharacteristic
596C22×C4—21no—
597C22×C4—32no—
598C22×C4—62no—
599C22×C4—61no—
600C22×C4—181no—
601C22×C4C2×D3211yescharacteristic
602Q16—182no—
603SD16—184no—
604SD16—182no—
605SD16—182no—
606D8—184no—
607D8—182no—
608M16—62no—
609C2×C8—32no—
610C2×C8—91no—
611C2×C8—91no—
612C2×C8—182no—
613C4⋊C4—32no—
614C4⋊C4—61no—
615C4⋊C4—182no—
616C22⋊C4—182no—
617C22⋊C4—182no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—22no—
623C22×C3—22no—
624C22×C3—21no—
625C22×C3—22no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—42no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—64no—
634C22×C3—62no—
635C22×C3—62no—
636C22×C3—62no—
637C22×C3—81no—
638C22×C3—81no—
639C22×C3—122no—
640C22×C3—122no—
641C22×C3—244no—
642C22×C3—248no—
643C22×C3#88212yes—
644C22×C3#95312yes—
645C22×C3C2×D3×D411yescharacteristic
646C22×C3C22×#6711yescharacteristic
647C2×D3—22no—
648C2×D3—22no—
649C2×D3—22no—
650C2×D3—24no—
651C2×D3—42no—
652C2×D3—42no—
653C2×D3—84no—
654C2×D3—88no—
655C2×D3—122no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—241no—
663C2×D3—241no—
664C3×C4—22no—
665C3×C4—22no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—22no—
669C3×C4—42no—
670C3×C4—62no—
671C3×C4—122no—
672C3×C4#88212yes—
673C3×C4#95312yes—
674C3×C4C22×D1211yescharacteristic
675C3×C4C2×D3×D411yescharacteristic
676C3×C4C22×#6711yescharacteristic
677C3×C4C22×#6711yescharacteristic
678Dic3—22no—
679Dic3—42no—
680Dic3—122no—
681Dic3—121no—
682Dic3—121no—
683C32#301211yescharacteristic, complemented, Sylow
684C23—21no—
685C23—32no—
686C23—68no—
687C23—62no—
688C23—64no—
689C23—181no—
690C23—241no—
691C23—241no—
692C23—242no—
693C23—242no—
694C23D3×#6711yescharacteristic
695Q8—21no—
696Q8—62no—
697Q8—181no—
698Q8—181no—
699Q8C2×#62612yes—
700D4—24no—
701D4—21no—
702D4—34no—
703D4—68no—
704D4—68no—
705D4—64no—
706D4—62no—
707D4—64no—
708D4—62no—
709D4—181no—
710D4—181no—
711D4—362no—
712D4—722no—
713D4C2×#62612yes—
714C2×C4—21no—
715C2×C4—24no—
716C2×C4—32no—
717C2×C4—68no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—181no—
722C2×C4—241no—
723C2×C4—362no—
724C2×C4C2×#62612yes—
725C2×C4D3×#6712yes—
726C2×C4D3×#6711yescharacteristic
727C2×C4C22×D3211yescharacteristic
728C8—62no—
729C8—181no—
730C8—181no—
731C2×C3—22no—
732C2×C3—22no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—42no—
737C2×C3—42no—
738C2×C3—42no—
739C2×C3—82no—
740C2×C3—122no—
741C2×C3—124no—
742C2×C3C2×#88211yescharacteristic
743C2×C3#577411yescharacteristic
744C2×C3#577811yescharacteristic
745C2×C3#583511yescharacteristic
746C2×C3#583611yescharacteristic
747C2×C3C2×#95311yescharacteristic
748D3—42no—
749D3—44no—
750D3—242no—
751D3—241no—
752D3—241no—
753C22—21no—
754C22—21no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—62no—
759C22—62no—
760C22—64no—
761C22—62no—
762C22—122no—
763C22—122no—
764C22—244no—
765C22—248no—
766C22—361no—
767C22—361no—
768C22—361no—
769C22#6397712yes—
770C22C2×D3×#6711yescharacteristic
771C4—22no—
772C4—62no—
773C4—122no—
774C4—361no—
775C4#6397712yes—
776C4C22×#62611yescharacteristic
777C4C2×D3×#6711yescharacteristic
778C3—21no—
779C3#7888611yescharacteristic, complemented
780C3#8410211yescharacteristic, complemented
781C2—22no—
782C2—42no—
783C2—122no—
784C2—124no—
785C2—721no—
786C2#1059545411yescharacteristic
787C2#1059546411yescharacteristic
788C2C2×#6397711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3012
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1009C2semidirect
2. C2×#64159C2semidirect
3. #10595043C2semidirect
4. C2×#63830C2semidirect
5. C3×#5232C2semidirect
6. #10591599C2semidirect
7. #10591588C2semidirect
8. #10591459C2semidirect
9. #10591448C2semidirect
10. C2×#63562C2semidirect
11. #10591071C2semidirect
15. C2×#3828C22semidirect
26. C2×#3756C22semidirect
27. C2×#3755C22semidirect
28. C2×#3754C22semidirect
29. C2×#3753C22semidirect
30. C22×C3⋊(C3⋊C8)C22semidirect
31. C2×C3×C4⋊Dic3C22semidirect
32. C2×C3×#208C22semidirect
35. #63909C22semidirect
37. #63857C22semidirect
39. C2×#3716C22semidirect
40. C2×#3714C22semidirect
41. C3×#835C22semidirect
42. C3×#832C22semidirect
43. #63562C22semidirect
44. #63562C22semidirect
45. (C2×D3)⋊(C3⋊C8)C22semidirect
46. (C2×D3)⋊(C3⋊C8)C22semidirect
48. C2×#1009D3semidirect
60. #5232D3semidirect
73. C32×#41D4semidirect
101. C2×C3×D12D4semidirect
173. C2×C4⋊Dic3C2×D3semidirect
175. C2×#208C2×D3semidirect
188. #835C2×D3semidirect
191. #832C2×D3semidirect
269. C3×#41D12semidirect
270. C3×#41#67semidirect
332. C2×D12#67semidirect
575. #41#626semidirect
683. C32#3012semidirect
779. C3#78886semidirect
780. C3#84102semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10092
C2×#641592
#105950432
C2×#638302
C3×#52322
#105915992
#105915882
#105914592
#105914482
C2×#635622
#105910712
#841023
#788863