Finite Group Databasebeta

← C2×#10591666 #11864784

Subgroups — C2×#10591666 #11864784

Order 1152.

1837 conjugacy classes of subgroups.

The subgroup lattice has 817 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1009C211yesmaximal, characteristic, complemented
2C2×#64158C211yesmaximal, characteristic, complemented
3C2×#63911C211yesmaximal, characteristic, complemented
4C2×#63825C211yesmaximal, characteristic, complemented
5C2×C3×#837C211yesmaximal, characteristic, complemented
6#10591666C218yesmaximal, direct product factor
7C2×#63569C211yesmaximal, characteristic, complemented
8C2×#63558C211yesmaximal, characteristic, complemented
9C2×#5241—31nomaximal
10C2×#4822—31nomaximal
11C2×C32×#41C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
13C3×#1009—22no—
14C3×#1009—22no—
15C3×#1009—22no—
16C3×#1009C2214yescomplemented
17C2×C3×#239—21no—
18C2×C3×D3×D4—21no—
19C2×C3×D3×D4—22no—
20C2×C3×#235—21no—
21C2×C3×#235C2211yescharacteristic
22C22×C3×D12—21no—
23C22×C3×D12C2211yescharacteristic
24C22×#626—22no—
25#64158—22no—
26#64158C2214yescomplemented
27C2×#3755—21no—
28C2×#3753—21no—
29C2×#3748C2211yescharacteristic, complemented
30C2×C3×C4×Dic3C2211yescharacteristic, complemented
31C2×C3×#208C2211yescharacteristic, complemented
32#63911—22no—
33#63911C2214yescomplemented
34C2×#3717—21no—
35#63825—22no—
36#63825C2214yescomplemented
37C2×#3714—21no—
38C3×#837C2214yescomplemented
39#63569C2214yescomplemented
40#63558C2214yescomplemented
41C2×C3×H(5,𝔽2)—31no—
42C2×#1009D311yescharacteristic, complemented
43C2×#949—31no—
44C2×#949—31no—
45C2×#949—31no—
46C2×#949—61no—
47C2×#940—31no—
48C2×#908—31no—
49C2×#874—31no—
50C2×C3×#104—31no—
51#5241—38no—
52C2×#837—31no—
53C2×#837D311yescharacteristic, complemented
54C2×#833—31no—
55C2×#823—31no—
56C2×#805—31no—
57#4822—38no—
58C23×C3⋊D3—21no—
59C23×C3×D3—22no—
60C23×C3×D3D412yes—
61C32×#41—21no—
62C32×#41—21no—
63C32×#41D412yescomplemented
64C32×#41C2312yes—
65C2×C32×Q8D411yescharacteristic, complemented
66C2×C32×D4—21no—
67C2×C32×D4D411yescharacteristic, complemented
68C22×C32×C4—21no—
69C22×C32×C4C2311yescharacteristic
70C2×C4⋊(C3⋊D3)—21no—
71C2×C4⋊(C3⋊D3)—21no—
72C2×C4⋊(C3⋊D3)—21no—
73C2×C4⋊(C3⋊D3)—21no—
74C2×C4⋊(C3⋊D3)—21no—
75C2×C4⋊(C3⋊D3)C2312yescomplemented
76C2×C3×#67—22no—
77C2×C3×#67—21no—
78C22×C3×Dic3—21no—
79C3×#239—24no—
80C3×#239—24no—
81C3×D3×D4—28no—
82C3×D3×D4—24no—
83C3×D3×D4—28no—
84C3×D3×D4—24no—
85C3×#235—24no—
86C3×#235—21no—
87C3×#235—21no—
88C3×#235—24no—
89C3×#235D412yescomplemented
90C3×#235C2312yes—
91C2×C3×D12—22no—
92C2×C3×D12—24no—
93C2×C3×D12—21no—
94C2×C3×D12—21no—
95C2×C3×D12—21no—
96C2×C3×D12—21no—
97C2×C3×D12—24no—
98C2×C3×D12D412yes—
99C2×C3×D12D411yescharacteristic, complemented
100C2×C3×D12C2312yes—
101C2×C3×C4×D3—22no—
102C2×C3×C4×D3—21no—
103C2×C3×Dic6D411yescharacteristic, complemented
104C2×#626—28no—
105C2×#626—48no—
106#3755—24no—
107#3753—24no—
108#3748—21no—
109#3748C2312yescomplemented
110C2×C3⋊(C3⋊C8)—21no—
111C3×C4×Dic3—21no—
112C3×C4×Dic3C2312yescomplemented
113C3×#208—21no—
114C3×#208C2312yescomplemented
115C2×C3×C3⋊C8—21no—
116#3717—24no—
117#3714—24no—
118C2×#453—91noSylow
119C3×H(5,𝔽2)—34no—
120C3×H(5,𝔽2)—62no—
121C3×H(5,𝔽2)—62no—
122C3×H(5,𝔽2)—62no—
123C2×C3×#41—21no—
124C2×C3×#41—31no—
125C2×C3×#41—61no—
126C2×C3×#41—61no—
127C2×C3×#41C2×D311yescharacteristic
128C2×C3×#41C2×D311yescharacteristic
129C22×C3×D4—31no—
130C22×C3×D4—61no—
131C22×C3×D4—62no—
132C22×C3×D4—61no—
133C22×#67—62no—
134#1009—22no—
135#1009—22no—
136#1009—22no—
137#1009C2×D314yescomplemented
138C2×#239—21no—
139C2×D3×D4—22no—
140C2×D3×D4—21no—
141C2×#235—21no—
142C2×#235C2×D311yescharacteristic
143C22×D12—21no—
144C22×D12—31no—
145C22×D12—31no—
146C22×D12—61no—
147C22×D12—62no—
148C22×D12C2×D311yescharacteristic
149C2×C3×M16—31no—
150C2×C3×C42—31no—
151#949—34no—
152#949—34no—
153#949—34no—
154#949—64no—
155#949—62no—
156#949—64no—
157#949—62no—
158#949—62no—
159C2×#215—61no—
160C2×#215—62no—
161C2×#215—61no—
162C2×#215—61no—
163#940—34no—
164#940—62no—
165C2×#213—61no—
166C2×#213—62no—
167C2×#213—61no—
168C2×#213—61no—
169C2×C4×Dic3C2×D311yescharacteristic, complemented
170C2×#208—31no—
171C2×#208—31no—
172C2×#208—61no—
173C2×#208C2×D311yescharacteristic, complemented
174#908—34no—
175#908—62no—
176C2×D24—61no—
177C2×#204—61no—
178#874—34no—
179#874—62no—
180C3×#104—34no—
181#837—34no—
182#837C2×D314yescomplemented
183#833—34no—
184#823—34no—
185#805—34no—
186C23×C32—21no—
187C23×C32C2×D411yescharacteristic
188C22×C3⋊D3—22no—
189C22×C3⋊D3—41no—
190C22×C3⋊D3—41no—
191C22×C3⋊D3—44no—
192C22×C3×D3—21no—
193C22×C3×D3—22no—
194C22×C3×D3—28no—
195C22×C3×D3—22no—
196C22×C3×D3—44no—
197C22×C3×D3—84no—
198C22×C3×D3C2×D414yes—
199C32×Q8—21no—
200C32×Q8C2×D412yescomplemented
201C32×D4—22no—
202C32×D4—22no—
203C32×D4—21no—
204C32×D4C2×D412yescomplemented
205C2×C32×C4—21no—
206C2×C32×C4—22no—
207C2×C32×C4—22no—
208C2×C32×C4C2×D411yescharacteristic
209C2×C32×C4C2×D411yescharacteristic
210C2×C32×C4C2×D411yescharacteristic
211C2×C32×C4C2×D411yescharacteristic
212C2×C32×C4C2×D411yescharacteristic
213C2×C32×C4C2411yescharacteristic
214C4⋊(C3⋊D3)—22no—
215C4⋊(C3⋊D3)—22no—
216C4⋊(C3⋊D3)—41no—
217C4⋊(C3⋊D3)—41no—
218C3×#67—28no—
219C3×#67—22no—
220C3×#67—22no—
221C2×C3×Dic3—24no—
222C2×C3×Dic3—21no—
223C2×C3×Dic3—22no—
224C3×D12—28no—
225C3×D12—22no—
226C3×D12—21no—
227C3×D12—22no—
228C3×D12—22no—
229C3×D12—22no—
230C3×D12C2×D412yescomplemented
231C3×C4×D3—28no—
232C3×C4×D3—22no—
233C3×C4×D3—22no—
234C3×Dic6—21no—
235C3×Dic6C2×D412yescomplemented
236#626—416no—
237C3⋊(C3⋊C8)—22no—
238C3×C3⋊C8—22no—
239C2×H(5,𝔽2)—31no—
240C2×AGL(1,ℤ/8)—91no—
241C2×AGL(1,ℤ/8)—91no—
242C2×#127—91no—
243#453—98no—
244C2×#104—31no—
245C2×#104—91no—
246C2×#100—91no—
247C24×C3—32no—
248C24×C3—62no—
249C23×D3—22no—
250C23×D3—61no—
251C23×D3—61no—
252C23×D3—121no—
253C23×D3#6712yes—
254C3×#41—21no—
255C3×#41—21no—
256C3×#41—21no—
257C3×#41—21no—
258C3×#41—22no—
259C3×#41—22no—
260C3×#41—32no—
261C3×#41—32no—
262C3×#41—41no—
263C3×#41—41no—
264C3×#41—64no—
265C3×#41—64no—
266C3×#41—64no—
267C3×#41—64no—
268C3×#41—61no—
269C3×#41—61no—
270C3×#41D1212yescomplemented
271C3×#41#6712yescomplemented
272C3×#41C22×D312yes—
273C3×#41C22×D312yes—
274C2×C3×Q8—21no—
275C2×C3×Q8—31no—
276C2×C3×Q8D1211yescharacteristic, complemented
277C2×C3×Q8#6711yescharacteristic, complemented
278C2×C3×D4—21no—
279C2×C3×D4—21no—
280C2×C3×D4—21no—
281C2×C3×D4—31no—
282C2×C3×D4—32no—
283C2×C3×D4—32no—
284C2×C3×D4—41no—
285C2×C3×D4—64no—
286C2×C3×D4—62no—
287C2×C3×D4—64no—
288C2×C3×D4—68no—
289C2×C3×D4—68no—
290C2×C3×D4—64no—
291C2×C3×D4—62no—
292C2×C3×D4—61no—
293C2×C3×D4—64no—
294C2×C3×D4—61no—
295C2×C3×D4—61no—
296C2×C3×D4—61no—
297C2×C3×D4—61no—
298C2×C3×D4D1211yescharacteristic, complemented
299C2×C3×D4#6711yescharacteristic, complemented
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—41no—
304C22×C3×C4—62no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C2×#67—22no—
310C2×#67—21no—
311C2×#67—68no—
312C2×#67—128no—
313C22×Dic3—21no—
314#239—24no—
315#239—24no—
316D3×D4—28no—
317D3×D4—24no—
318D3×D4—28no—
319D3×D4—24no—
320#235—24no—
321#235—21no—
322#235—21no—
323#235—24no—
324#235#6712yescomplemented
325#235C22×D312yes—
326C2×D12—22no—
327C2×D12—24no—
328C2×D12—21no—
329C2×D12—21no—
330C2×D12—21no—
331C2×D12—21no—
332C2×D12—24no—
333C2×D12—32no—
334C2×D12—32no—
335C2×D12—62no—
336C2×D12—62no—
337C2×D12—62no—
338C2×D12—61no—
339C2×D12—61no—
340C2×D12—61no—
341C2×D12—61no—
342C2×D12—61no—
343C2×D12—61no—
344C2×D12—61no—
345C2×D12—61no—
346C2×D12—68no—
347C2×D12—61no—
348C2×D12—61no—
349C2×D12—121no—
350C2×D12—121no—
351C2×D12—121no—
352C2×D12—128no—
353C2×D12#6712yes—
354C2×D12#6711yescharacteristic, complemented
355C2×D12C22×D312yes—
356C2×C4×D3—22no—
357C2×C4×D3—21no—
358C2×Dic6#6711yescharacteristic, complemented
359C3×M16—32no—
360C3×M16—61no—
361C2×C3×C8—61no—
362C3×C42—32no—
363C3×C42—61no—
364#215—64no—
365#215—68no—
366#215—64no—
367#215—64no—
368#213—64no—
369#213—68no—
370#213—64no—
371#213—64no—
372C4×Dic3—21no—
373C4×Dic3C22×D312yescomplemented
374#208—21no—
375#208—32no—
376#208—32no—
377#208—62no—
378#208—62no—
379#208—61no—
380#208—61no—
381#208C22×D312yescomplemented
382C2×C3⋊C8—21no—
383C2×C3⋊C8—62no—
384C2×C3⋊C8—61no—
385C2×C3⋊C8—61no—
386D24—64no—
387#204—64no—
388C22×C32—22no—
389C22×C32—22no—
390C22×C32—42no—
391C22×C32#12011yescharacteristic
392C22×C32#12011yescharacteristic
393C22×C32C22×D411yescharacteristic
394C2×C3⋊D3—42no—
395C2×C3⋊D3—44no—
396C2×C3⋊D3—82no—
397C2×C3⋊D3—82no—
398C2×C3×D3—24no—
399C2×C3×D3—22no—
400C2×C3×D3—44no—
401C2×C3×D3—42no—
402C2×C3×D3—44no—
403C2×C3×D3—82no—
404C2×C3×D3—88no—
405C32×C4—22no—
406C32×C4#12011yescharacteristic
407C32×C4#12011yescharacteristic
408C32×C4C22×D411yescharacteristic
409C32×C4C22×D411yescharacteristic
410C3×Dic3—24no—
411C3×Dic3—22no—
412H(5,𝔽2)—34no—
413H(5,𝔽2)—62no—
414H(5,𝔽2)—62no—
415H(5,𝔽2)—62no—
416C2×#41—31no—
417C2×#41—61no—
418C2×#41—61no—
419C2×#41D3211yescharacteristic
420C22×D4—31no—
421C22×D4—61no—
422C22×D4—62no—
423C22×D4—61no—
424C22×D4—91no—
425C22×D4—182no—
426AGL(1,ℤ/8)—94no—
427AGL(1,ℤ/8)—94no—
428AGL(1,ℤ/8)—182no—
429AGL(1,ℤ/8)—182no—
430C2×SD16—181no—
431C2×SD16—181no—
432C2×D8—181no—
433C2×D8—181no—
434C2×M16—31no—
435C2×M16—91no—
436#127—94no—
437#127—182no—
438C2×C42—31no—
439#104—34no—
440#104—94no—
441#100—94no—
442C23×C3—21no—
443C23×C3—21no—
444C23×C3—21no—
445C23×C3—34no—
446C23×C3—41no—
447C23×C3—68no—
448C23×C3—61no—
449C23×C3—62no—
450C23×C3—62no—
451C23×C3—124no—
452C23×C3—244no—
453C23×C3D3×D411yescharacteristic
454C23×C3C2×#6711yescharacteristic
455C22×D3—22no—
456C22×D3—21no—
457C22×D3—28no—
458C22×D3—22no—
459C22×D3—44no—
460C22×D3—62no—
461C22×D3—62no—
462C22×D3—84no—
463C22×D3—122no—
464C22×D3—122no—
465C22×D3—122no—
466C22×D3—124no—
467C22×D3—124no—
468C22×D3—121no—
469C22×D3—121no—
470C22×D3—121no—
471C22×D3—121no—
472C22×D3—244no—
473C22×D3C2×#6714yes—
474C3×Q8—21no—
475C3×Q8—21no—
476C3×Q8—22no—
477C3×Q8—32no—
478C3×Q8—41no—
479C3×Q8—61no—
480C3×Q8C2×D1212yescomplemented
481C3×Q8C2×#6712yescomplemented
482C3×D4—22no—
483C3×D4—22no—
484C3×D4—22no—
485C3×D4—22no—
486C3×D4—21no—
487C3×D4—21no—
488C3×D4—22no—
489C3×D4—32no—
490C3×D4—41no—
491C3×D4—42no—
492C3×D4—42no—
493C3×D4—68no—
494C3×D4—68no—
495C3×D4—62no—
496C3×D4—62no—
497C3×D4—61no—
498C3×D4—62no—
499C3×D4—62no—
500C3×D4—62no—
501C3×D4—62no—
502C3×D4C2×D1212yescomplemented
503C3×D4C2×#6712yescomplemented
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—42no—
517C2×C3×C4—42no—
518C2×C3×C4—41no—
519C2×C3×C4—68no—
520C2×C3×C4—64no—
521C2×C3×C4—61no—
522C2×C3×C4—62no—
523C2×C3×C4—62no—
524C2×C3×C4—62no—
525C2×C3×C4C2×D1211yescharacteristic
526C2×C3×C4C2×D1211yescharacteristic
527C2×C3×C4D3×D411yescharacteristic
528C2×C3×C4D3×D411yescharacteristic
529C2×C3×C4D3×D411yescharacteristic
530C2×C3×C4C2×#6711yescharacteristic
531C2×C3×C4C2×#6711yescharacteristic
532C2×C3×C4C2×#6711yescharacteristic
533C2×C3×C4C2×#6711yescharacteristic
534C2×C3×C4C2×#6711yescharacteristic
535C2×C3×C4C23×D311yescharacteristic
536C2×C3×C4C23×D311yescharacteristic
537#67—28no—
538#67—22no—
539#67—22no—
540#67—1216no—
541C2×Dic3—24no—
542C2×Dic3—21no—
543C2×Dic3—22no—
544D12—28no—
545D12—22no—
546D12—21no—
547D12—22no—
548D12—22no—
549D12—22no—
550D12—64no—
551D12—62no—
552D12—62no—
553D12—62no—
554D12—62no—
555D12—122no—
556D12—122no—
557D12—122no—
558D12—1216no—
559D12—121no—
560D12—121no—
561D12—121no—
562D12—121no—
563D12C2×#6712yescomplemented
564C4×D3—28no—
565C4×D3—22no—
566C4×D3—22no—
567Dic6—21no—
568Dic6C2×#6712yescomplemented
569C3×C8—62no—
570C3⋊C8—22no—
571C3⋊C8—64no—
572C3⋊C8—62no—
573C3⋊C8—62no—
574C2×C32—21no—
575C2×C32—21no—
576C2×C32—42no—
577C2×C32#45312yescomplemented
578C2×C32C2×#12011yescharacteristic
579C3⋊D3—82no—
580C3×D3—44no—
581C3×D3—42no—
582C24—32no—
583C24—62no—
584C24—181no—
585#41—21no—
586#41—21no—
587#41—32no—
588#41—32no—
589#41—64no—
590#41—64no—
591#41—64no—
592#41—64no—
593#41—61no—
594#41—61no—
595#41#62612yescomplemented
596#41C2×D3212yes—
597C2×Q8—31no—
598C2×Q8#62611yescharacteristic, complemented
599C2×D4—21no—
600C2×D4—32no—
601C2×D4—31no—
602C2×D4—32no—
603C2×D4—64no—
604C2×D4—62no—
605C2×D4—64no—
606C2×D4—68no—
607C2×D4—68no—
608C2×D4—64no—
609C2×D4—62no—
610C2×D4—61no—
611C2×D4—64no—
612C2×D4—61no—
613C2×D4—61no—
614C2×D4—61no—
615C2×D4—61no—
616C2×D4—92no—
617C2×D4—188no—
618C2×D4—181no—
619C2×D4—181no—
620C2×D4—181no—
621C2×D4—181no—
622C2×D4—181no—
623C2×D4—368no—
624C2×D4#62611yescharacteristic, complemented
625C22×C4—21no—
626C22×C4—62no—
627C22×C4—61no—
628C22×C4—61no—
629C22×C4C2×D3211yescharacteristic
630SD16—184no—
631SD16—184no—
632D8—184no—
633D8—184no—
634M16—32no—
635M16—61no—
636M16—92no—
637M16—181no—
638C2×C8—61no—
639C2×C8—181no—
640C42—32no—
641C42—61no—
642C22×C3—22no—
643C22×C3—22no—
644C22×C3—22no—
645C22×C3—22no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—42no—
650C22×C3—42no—
651C22×C3—42no—
652C22×C3—42no—
653C22×C3—62no—
654C22×C3—64no—
655C22×C3—82no—
656C22×C3—124no—
657C22×C3—124no—
658C22×C3—122no—
659C22×C3—242no—
660C22×C3—248no—
661C22×C3#88211yescharacteristic
662C22×C3#88211yescharacteristic
663C22×C3#95311yescharacteristic
664C22×C3#95311yescharacteristic
665C22×C3C2×D3×D411yescharacteristic
666C22×C3C22×#6711yescharacteristic
667C2×D3—24no—
668C2×D3—22no—
669C2×D3—44no—
670C2×D3—42no—
671C2×D3—44no—
672C2×D3—82no—
673C2×D3—88no—
674C2×D3—124no—
675C2×D3—124no—
676C2×D3—124no—
677C2×D3—122no—
678C2×D3—122no—
679C2×D3—244no—
680C2×D3—242no—
681C2×D3—242no—
682C2×D3—244no—
683C2×D3—244no—
684C2×D3—242no—
685C2×D3—242no—
686C3×C4—22no—
687C3×C4—22no—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—42no—
693C3×C4—64no—
694C3×C4—62no—
695C3×C4#88211yescharacteristic
696C3×C4#88211yescharacteristic
697C3×C4#95311yescharacteristic
698C3×C4#95311yescharacteristic
699C3×C4C22×D1211yescharacteristic
700C3×C4C2×D3×D411yescharacteristic
701C3×C4C22×#6711yescharacteristic
702C3×C4C22×#6711yescharacteristic
703Dic3—24no—
704Dic3—22no—
705C32C2×#45311yescharacteristic, complemented, Sylow
706C23—21no—
707C23—34no—
708C23—68no—
709C23—61no—
710C23—62no—
711C23—62no—
712C23—124no—
713C23—182no—
714C23—244no—
715C23—364no—
716C23—361no—
717C23—361no—
718C23D3×#6711yescharacteristic
719Q8—21no—
720Q8—32no—
721Q8—61no—
722Q8C2×#62612yescomplemented
723D4—22no—
724D4—22no—
725D4—21no—
726D4—32no—
727D4—68no—
728D4—68no—
729D4—62no—
730D4—62no—
731D4—62no—
732D4—62no—
733D4—61no—
734D4—62no—
735D4—62no—
736D4—182no—
737D4—182no—
738D4—3616no—
739D4—361no—
740D4—361no—
741D4C2×#62612yescomplemented
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—68no—
746C2×C4—64no—
747C2×C4—62no—
748C2×C4—61no—
749C2×C4—62no—
750C2×C4—62no—
751C2×C4C2×#62611yescharacteristic
752C2×C4C2×#62611yescharacteristic
753C2×C4D3×#6711yescharacteristic
754C2×C4D3×#6711yescharacteristic
755C2×C4D3×#6711yescharacteristic
756C2×C4C22×D3211yescharacteristic
757C8—62no—
758C8—182no—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—21no—
763C2×C3—22no—
764C2×C3—21no—
765C2×C3—41no—
766C2×C3—41no—
767C2×C3—42no—
768C2×C3—42no—
769C2×C3—82no—
770C2×C3—124no—
771C2×C3—122no—
772C2×C3#482212yescomplemented
773C2×C3#524112yescomplemented
774C2×C3C2×#88211yescharacteristic
775C2×C3C2×#95311yescharacteristic
776D3—44no—
777D3—42no—
778D3—244no—
779D3—242no—
780D3—242no—
781C22—22no—
782C22—22no—
783C22—42no—
784C22—62no—
785C22—64no—
786C22—124no—
787C22—124no—
788C22—122no—
789C22—242no—
790C22—248no—
791C22—364no—
792C22—362no—
793C22—722no—
794C22—722no—
795C22#6397711yescharacteristic
796C22#6397711yescharacteristic
797C22C2×D3×#6711yescharacteristic
798C4—22no—
799C4—64no—
800C4—62no—
801C4#6397711yescharacteristic
802C4#6397711yescharacteristic
803C4C22×#62611yescharacteristic
804C4C2×D3×#6711yescharacteristic
805C3—21no—
806C3C2×#482211yescharacteristic, complemented
807C3C2×#524111yescharacteristic, complemented
808C2—21no—
809C2—21no—
810C2—42no—
811C2—124no—
812C2—122no—
813C2—722no—
814C2#1059166612yesdirect product factor
815C2C2×#6397711yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32#120
hypercenterC2×#41D32
hypocenterC32C2×#453
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×#64158C2semidirect
3. C2×#63911C2semidirect
4. C2×#63825C2semidirect
5. C2×C3×#837C2semidirect
6. #10591666C2direct (N × H)
7. C2×#63569C2semidirect
8. C2×#63558C2semidirect
12. C22×C4⋊(C3⋊D3)C22semidirect
16. C3×#1009C22semidirect
26. #64158C22semidirect
29. C2×#3748C22semidirect
30. C2×C3×C4×Dic3C22semidirect
31. C2×C3×#208C22semidirect
33. #63911C22semidirect
36. #63825C22semidirect
38. C3×#837C22semidirect
39. #63569C22semidirect
40. #63558C22semidirect
42. C2×#1009D3semidirect
53. C2×#837D3semidirect
63. C32×#41D4semidirect
65. C2×C32×Q8D4semidirect
67. C2×C32×D4D4semidirect
75. C2×C4⋊(C3⋊D3)C23semidirect
89. C3×#235D4semidirect
99. C2×C3×D12D4semidirect
103. C2×C3×Dic6D4semidirect
109. #3748C23semidirect
112. C3×C4×Dic3C23semidirect
114. C3×#208C23semidirect
137. #1009C2×D3semidirect
169. C2×C4×Dic3C2×D3semidirect
173. C2×#208C2×D3semidirect
182. #837C2×D3semidirect
200. C32×Q8C2×D4semidirect
204. C32×D4C2×D4semidirect
230. C3×D12C2×D4semidirect
235. C3×Dic6C2×D4semidirect
270. C3×#41D12semidirect
271. C3×#41#67semidirect
276. C2×C3×Q8D12semidirect
277. C2×C3×Q8#67semidirect
298. C2×C3×D4D12semidirect
299. C2×C3×D4#67semidirect
324. #235#67semidirect
354. C2×D12#67semidirect
358. C2×Dic6#67semidirect
373. C4×Dic3C22×D3semidirect
381. #208C22×D3semidirect
480. C3×Q8C2×D12semidirect
481. C3×Q8C2×#67semidirect
502. C3×D4C2×D12semidirect
503. C3×D4C2×#67semidirect
563. D12C2×#67semidirect
568. Dic6C2×#67semidirect
577. C2×C32#453semidirect
595. #41#626semidirect
598. C2×Q8#626semidirect
624. C2×D4#626semidirect
705. C32C2×#453semidirect
722. Q8C2×#626semidirect
741. D4C2×#626semidirect
772. C2×C3#4822semidirect
773. C2×C3#5241semidirect
806. C3C2×#4822semidirect
807. C3C2×#5241semidirect
814. C2#10591666direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#10092
C2×#641582
C2×#639112
C2×#638252
C2×C3×#8372
#105916662
C2×#635692
C2×#635582
C2×#52413
C2×#48223