Finite Group Databasebeta

← C2×#10591523 #11864782

Subgroups — C2×#10591523 #11864782

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×#64307C211yesmaximal, characteristic, complemented
2C2×#64141C211yesmaximal, characteristic, complemented
3C2×C3×#940C211yesmaximal, characteristic, complemented
4C2×C3×#932C211yesmaximal, characteristic, complemented
5#10591523C218yesmaximal, direct product factor
6C2×#63570C211yesmaximal, characteristic, complemented
7C2×#63569C211yesmaximal, characteristic, complemented
8C2×#63558C211yesmaximal, characteristic, complemented
9C2×#5198—31nomaximal
10C2×#5077—31nomaximal
11C22×C32×D4C2211yescharacteristic, complemented
12C2×#3828C2211yescharacteristic
13C22×C3×#67—22no—
14C2×C3×#235C2211yescharacteristic
15C22×C3×D12C2211yescharacteristic
16C2×D3×#67—22no—
17#64307—22no—
18#64307—22no—
19#64307—22no—
20#64307C2214yescomplemented
21C2×#3802—21no—
22C2×D3×D12—21no—
23C2×#3796—21no—
24C2×#3795—21no—
25C2×#3754—21no—
26#64141—22no—
27#64141C2214yescomplemented
28C2×#3753—21no—
29C2×#3748C2211yescharacteristic, complemented
30C3×#940—22no—
31C3×#940C2214yescomplemented
32C2×C3×#214—21no—
33C3×#932—22no—
34C3×#932C2214yescomplemented
35C2×C3×#213—21no—
36C2×C3×C4×Dic3C2211yescharacteristic, complemented
37C2×C3×#208C2211yescharacteristic, complemented
38#63570C2214yescomplemented
39#63569C2214yescomplemented
40#63558C2214yescomplemented
41C2×#1009—31no—
42C2×#1004—31no—
43C2×C3×AGL(1,ℤ/8)—31no—
44C2×C3×#127—31no—
45C2×#940D311yescharacteristic, complemented
46C2×#932—31no—
47C2×#932—31no—
48C2×#932—61no—
49C2×#932D311yescharacteristic, complemented
50C2×#837—31no—
51C2×#833—31no—
52#5198—38no—
53C2×#825—31no—
54C2×#823—31no—
55#5077—38no—
56C2×#805—31no—
57C2×#805—31no—
58C24×C32—21no—
59C23×C3×D3D412yes—
60C22×D32—22no—
61C2×C32×D4—21no—
62C2×C32×D4—21no—
63C2×C32×D4—21no—
64C2×C32×D4—21no—
65C2×C32×D4—21no—
66C2×C32×D4C2312yescomplemented
67C22×C32×C4C2311yescharacteristic
68C2×#638—21no—
69#3828—21no—
70#3828—21no—
71#3828D412yescomplemented
72#3828C2312yes—
73C2×C4⋊(C3⋊D3)D411yescharacteristic, complemented
74C2×C4×C3⋊D3—21no—
75C2×#634D411yescharacteristic, complemented
76C2×C3×#67—21no—
77C2×C3×#67—28no—
78C2×C3×#67—48no—
79C22×C3×Dic3—21no—
80C3×#235—21no—
81C3×#235—21no—
82C3×#235D412yescomplemented
83C3×#235C2312yes—
84C2×C3×D12—21no—
85C2×C3×D12—21no—
86C2×C3×D12—21no—
87C2×C3×D12—21no—
88C2×C3×D12D412yes—
89C2×C3×D12D411yescharacteristic, complemented
90C2×C3×D12C2312yes—
91C2×C3×C4×D3—21no—
92C2×C3×Dic6D411yescharacteristic, complemented
93D3×#67—28no—
94D3×#67—28no—
95C2×#626—22no—
96C2×#625—22no—
97C2×D3×Dic3—22no—
98#3802—24no—
99#3802—24no—
100D3×D12—24no—
101D3×D12—24no—
102#3796—24no—
103#3796—24no—
104#3795—24no—
105#3795—24no—
106#3754—24no—
107#3753—24no—
108#3748—21no—
109#3748C2312yescomplemented
110C2×C3⋊(C3⋊C8)—21no—
111C3×#214—24no—
112C3×#213—24no—
113C3×C4×Dic3—21no—
114C3×C4×Dic3C2312yescomplemented
115C3×#208—21no—
116C3×#208C2312yescomplemented
117C2×C3×C3⋊C8—21no—
118C2×#453—91noSylow
119C2×C3×#41—31no—
120C22×C3×D4—21no—
121C22×C3×D4—31no—
122C22×C3×D4—62no—
123C22×C3×D4C2×D311yescharacteristic, complemented
124C22×C3×D4C2×D311yescharacteristic, complemented
125C22×#67—22no—
126C22×#67—62no—
127#1009—34no—
128#1009—62no—
129#1009—62no—
130#1009—62no—
131C2×#239—61no—
132#1004—34no—
133#1004—62no—
134#1004—62no—
135#1004—62no—
136C2×#237—61no—
137C2×#237—61no—
138C2×D3×D4—61no—
139C2×D3×D4—61no—
140C2×D3×D4—62no—
141C2×D3×D4—61no—
142C2×#235—31no—
143C2×#235—31no—
144C2×#235—61no—
145C2×#235—61no—
146C2×#235C2×D311yescharacteristic
147C22×D12—61no—
148C22×D12C2×D311yescharacteristic
149C3×AGL(1,ℤ/8)—34no—
150C3×AGL(1,ℤ/8)—62no—
151C2×C3×SD16—61no—
152C2×C3×D8—61no—
153C2×C3×M16—31no—
154C3×#127—34no—
155C3×#127—62no—
156C2×C3×C42—31no—
157#940—22no—
158#940C2×D314yescomplemented
159C2×#214—21no—
160C2×#214—61no—
161C2×#214—61no—
162C2×#214—62no—
163#932—22no—
164#932—34no—
165#932—34no—
166#932—64no—
167#932—62no—
168#932—62no—
169#932—64no—
170#932C2×D314yescomplemented
171C2×#213—21no—
172C2×#213—61no—
173C2×#213—61no—
174C2×#213—62no—
175C2×C4×Dic3C2×D311yescharacteristic, complemented
176C2×#208—31no—
177C2×#208—31no—
178C2×#208—61no—
179C2×#208C2×D311yescharacteristic, complemented
180#837—34no—
181#833—34no—
182#825—34no—
183#823—34no—
184#805—34no—
185#805—34no—
186C23×C32—22no—
187C23×C32—41no—
188C23×C32—41no—
189C23×C32—44no—
190C23×C32C2×D411yescharacteristic
191C22×C3⋊D3—21no—
192C22×C3×D3—21no—
193C22×C3×D3—22no—
194C22×C3×D3—22no—
195C22×C3×D3—44no—
196C22×C3×D3C2×D414yes—
197C2×D32—28no—
198C2×D32—84no—
199C32×D4—22no—
200C32×D4—22no—
201C32×D4—41no—
202C32×D4—41no—
203C2×C32×C4C2×D411yescharacteristic
204C2×C32×C4C2×D411yescharacteristic
205C2×C32×C4C2×D411yescharacteristic
206C2×C32×C4C2×D411yescharacteristic
207C2×C32×C4C2×D411yescharacteristic
208C2×C32×C4C2411yescharacteristic
209#638—22no—
210#638—22no—
211C2×C3⋊Dic3—21no—
212C4⋊(C3⋊D3)—21no—
213C4⋊(C3⋊D3)C2×D412yescomplemented
214C4×C3⋊D3—22no—
215C4×C3⋊D3—22no—
216#634—21no—
217#634C2×D412yescomplemented
218C3×#67—22no—
219C3×#67—22no—
220C3×#67—416no—
221C2×C3×Dic3—24no—
222C2×C3×Dic3—21no—
223C2×C3×Dic3—22no—
224C3×D12—22no—
225C3×D12—22no—
226C3×D12—21no—
227C3×D12—22no—
228C3×D12—22no—
229C3×D12C2×D412yescomplemented
230C3×C4×D3—22no—
231C3×C4×D3—22no—
232C3×Dic6—21no—
233C3×Dic6C2×D412yescomplemented
234#626—28no—
235#625—28no—
236D3×Dic3—28no—
237C3⋊(C3⋊C8)—22no—
238C3×C3⋊C8—22no—
239C2×H(5,𝔽2)—91no—
240C2×AGL(1,ℤ/8)—31no—
241C2×AGL(1,ℤ/8)—91no—
242C2×#127—31no—
243#453—98no—
244C2×#104—91no—
245C2×#104—91no—
246C2×#100—91no—
247C24×C3—21no—
248C24×C3—21no—
249C24×C3—32no—
250C24×C3—41no—
251C23×D3—62no—
252C23×D3—62no—
253C23×D3#6712yes—
254C3×#41—32no—
255C3×#41—32no—
256C3×#41—61no—
257C3×#41—61no—
258C2×C3×Q8—31no—
259C2×C3×D4—22no—
260C2×C3×D4—22no—
261C2×C3×D4—21no—
262C2×C3×D4—21no—
263C2×C3×D4—21no—
264C2×C3×D4—21no—
265C2×C3×D4—21no—
266C2×C3×D4—21no—
267C2×C3×D4—21no—
268C2×C3×D4—21no—
269C2×C3×D4—21no—
270C2×C3×D4—21no—
271C2×C3×D4—22no—
272C2×C3×D4—31no—
273C2×C3×D4—32no—
274C2×C3×D4—32no—
275C2×C3×D4—41no—
276C2×C3×D4—41no—
277C2×C3×D4—41no—
278C2×C3×D4—61no—
279C2×C3×D4—68no—
280C2×C3×D4—61no—
281C2×C3×D4—61no—
282C2×C3×D4—61no—
283C2×C3×D4—61no—
284C2×C3×D4—128no—
285C2×C3×D4C22×D312yescomplemented
286C2×C3×D4C22×D312yescomplemented
287C22×C3×C4—21no—
288C22×C3×C4—61no—
289C22×C3×C4—61no—
290C22×C3×C4C22×D311yescharacteristic
291C22×C3×C4C22×D311yescharacteristic
292C2×#67—21no—
293C2×#67—28no—
294C2×#67—48no—
295C2×#67—62no—
296C2×#67—68no—
297C2×#67—68no—
298C2×#67—62no—
299C2×#67—62no—
300C2×#67—61no—
301C2×#67—61no—
302C2×#67—121no—
303C22×Dic3—21no—
304C22×Dic3—62no—
305#239—64no—
306#239—64no—
307#237—64no—
308#237—64no—
309#237—64no—
310#237—64no—
311D3×D4—64no—
312D3×D4—64no—
313D3×D4—64no—
314D3×D4—64no—
315D3×D4—64no—
316D3×D4—68no—
317D3×D4—68no—
318D3×D4—64no—
319#235—21no—
320#235—21no—
321#235—32no—
322#235—32no—
323#235—32no—
324#235—32no—
325#235—62no—
326#235—62no—
327#235—64no—
328#235—64no—
329#235—61no—
330#235—61no—
331#235—61no—
332#235—61no—
333#235—121no—
334#235—121no—
335#235#6712yescomplemented
336#235C22×D312yes—
337C2×D12—21no—
338C2×D12—21no—
339C2×D12—21no—
340C2×D12—21no—
341C2×D12—31no—
342C2×D12—31no—
343C2×D12—61no—
344C2×D12—64no—
345C2×D12—64no—
346C2×D12—62no—
347C2×D12#6712yes—
348C2×D12#6711yescharacteristic, complemented
349C2×D12C22×D312yes—
350C2×C4×D3—21no—
351C2×C4×D3—62no—
352C2×C4×D3—61no—
353C2×C4×D3—61no—
354C2×C4×D3—121no—
355C2×Dic6—31no—
356C2×Dic6—31no—
357C2×Dic6—61no—
358C2×Dic6#6711yescharacteristic, complemented
359C3×SD16—64no—
360C3×D8—64no—
361C3×M16—32no—
362C3×M16—61no—
363C2×C3×C8—61no—
364C3×C42—32no—
365C3×C42—61no—
366#214—24no—
367#214—64no—
368#214—64no—
369#214—68no—
370#213—24no—
371#213—64no—
372#213—64no—
373#213—68no—
374C4×Dic3—21no—
375C4×Dic3C22×D312yescomplemented
376#208—21no—
377#208—32no—
378#208—32no—
379#208—62no—
380#208—62no—
381#208—61no—
382#208—61no—
383#208C22×D312yescomplemented
384C2×C3⋊C8—21no—
385C2×C3⋊C8—62no—
386C2×C3⋊C8—61no—
387C2×C3⋊C8—61no—
388C22×C32—22no—
389C22×C32—42no—
390C22×C32—44no—
391C22×C32—82no—
392C22×C32—82no—
393C22×C32#12011yescharacteristic
394C22×C32#12011yescharacteristic
395C22×C32C22×D411yescharacteristic
396C2×C3⋊D3—22no—
397C2×C3⋊D3—42no—
398C2×C3×D3—24no—
399C2×C3×D3—22no—
400C2×C3×D3—42no—
401C2×C3×D3—44no—
402C2×C3×D3—44no—
403C2×C3×D3—82no—
404D32—88no—
405C32×C4#12011yescharacteristic
406C32×C4#12011yescharacteristic
407C32×C4C22×D411yescharacteristic
408C32×C4C22×D411yescharacteristic
409C3⋊Dic3—22no—
410C3×Dic3—24no—
411C3×Dic3—22no—
412H(5,𝔽2)—94no—
413H(5,𝔽2)—182no—
414H(5,𝔽2)—182no—
415H(5,𝔽2)—182no—
416C2×#41—31no—
417C2×#41—91no—
418C2×#41—181no—
419C2×#41—181no—
420C22×D4—31no—
421C22×D4—62no—
422C22×D4—181no—
423C22×D4—181no—
424C22×D4—182no—
425C22×D4D3211yescharacteristic, complemented
426AGL(1,ℤ/8)—34no—
427AGL(1,ℤ/8)—62no—
428AGL(1,ℤ/8)—94no—
429AGL(1,ℤ/8)—182no—
430C2×SD16—61no—
431C2×SD16—181no—
432C2×D8—61no—
433C2×D8—181no—
434C2×M16—31no—
435C2×M16—91no—
436#127—34no—
437#127—62no—
438C2×C42—31no—
439#104—94no—
440#104—94no—
441#100—94no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—21no—
445C23×C3—34no—
446C23×C3—42no—
447C23×C3—44no—
448C23×C3—42no—
449C23×C3—42no—
450C23×C3—44no—
451C23×C3—41no—
452C23×C3—41no—
453C23×C3—41no—
454C23×C3—41no—
455C23×C3—62no—
456C23×C3—61no—
457C23×C3—62no—
458C23×C3—84no—
459C23×C3—124no—
460C23×C3D3×D411yescharacteristic
461C23×C3C2×#6711yescharacteristic
462C22×D3—21no—
463C22×D3—22no—
464C22×D3—22no—
465C22×D3—44no—
466C22×D3—68no—
467C22×D3—68no—
468C22×D3—61no—
469C22×D3—61no—
470C22×D3—121no—
471C22×D3—244no—
472C22×D3—244no—
473C22×D3C2×#6714yes—
474C3×Q8—32no—
475C3×Q8—61no—
476C3×D4—24no—
477C3×D4—22no—
478C3×D4—22no—
479C3×D4—22no—
480C3×D4—22no—
481C3×D4—32no—
482C3×D4—42no—
483C3×D4—42no—
484C3×D4—42no—
485C3×D4—41no—
486C3×D4—41no—
487C3×D4—41no—
488C3×D4—41no—
489C3×D4—62no—
490C3×D4—62no—
491C3×D4—61no—
492C3×D4—62no—
493C3×D4—62no—
494C3×D4—62no—
495C3×D4—62no—
496C3×D4—1216no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—64no—
504C2×C3×C4—61no—
505C2×C3×C4—62no—
506C2×C3×C4—62no—
507C2×C3×C4—62no—
508C2×C3×C4D3×D411yescharacteristic
509C2×C3×C4D3×D411yescharacteristic
510C2×C3×C4D3×D411yescharacteristic
511C2×C3×C4D3×D411yescharacteristic
512C2×C3×C4D3×D411yescharacteristic
513C2×C3×C4D3×D411yescharacteristic
514C2×C3×C4D3×D411yescharacteristic
515C2×C3×C4C2×#6711yescharacteristic
516C2×C3×C4C2×#6711yescharacteristic
517C2×C3×C4C2×#6711yescharacteristic
518C2×C3×C4C23×D311yescharacteristic
519C2×C3×C4C23×D311yescharacteristic
520#67—22no—
521#67—22no—
522#67—416no—
523#67—68no—
524#67—68no—
525#67—68no—
526#67—62no—
527#67—62no—
528#67—62no—
529#67—62no—
530#67—122no—
531#67—122no—
532C2×Dic3—24no—
533C2×Dic3—21no—
534C2×Dic3—22no—
535C2×Dic3—68no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—121no—
539D12—22no—
540D12—22no—
541D12—21no—
542D12—22no—
543D12—22no—
544D12—32no—
545D12—32no—
546D12—62no—
547D12—68no—
548D12—61no—
549D12—61no—
550D12—121no—
551D12C2×#6712yescomplemented
552C4×D3—22no—
553C4×D3—22no—
554C4×D3—68no—
555C4×D3—62no—
556C4×D3—62no—
557C4×D3—62no—
558C4×D3—62no—
559C4×D3—122no—
560C4×D3—122no—
561Dic6—21no—
562Dic6—32no—
563Dic6—32no—
564Dic6—62no—
565Dic6—61no—
566Dic6—61no—
567Dic6—121no—
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—82no—
577C2×C32#45312yescomplemented
578C2×C32C2×#12011yescharacteristic
579C3⋊D3—42no—
580C3×D3—42no—
581C3×D3—44no—
582C24—21no—
583C24—32no—
584C24—182no—
585#41—32no—
586#41—32no—
587#41—61no—
588#41—61no—
589#41—92no—
590#41—92no—
591#41—184no—
592#41—184no—
593#41—184no—
594#41—184no—
595#41—181no—
596#41—181no—
597C2×Q8—31no—
598C2×Q8—91no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—32no—
605C2×D4—31no—
606C2×D4—32no—
607C2×D4—61no—
608C2×D4—68no—
609C2×D4—61no—
610C2×D4—61no—
611C2×D4—61no—
612C2×D4—61no—
613C2×D4—91no—
614C2×D4—128no—
615C2×D4—184no—
616C2×D4—184no—
617C2×D4—182no—
618C2×D4—184no—
619C2×D4—184no—
620C2×D4—188no—
621C2×D4—188no—
622C2×D4—182no—
623C2×D4—181no—
624C2×D4C2×D3212yescomplemented
625C22×C4—61no—
626C22×C4—61no—
627C22×C4—182no—
628C22×C4—181no—
629C22×C4C2×D3211yescharacteristic
630SD16—64no—
631SD16—184no—
632D8—64no—
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—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—42no—
648C22×C3—44no—
649C22×C3—44no—
650C22×C3—44no—
651C22×C3—42no—
652C22×C3—42no—
653C22×C3—64no—
654C22×C3—62no—
655C22×C3—84no—
656C22×C3—82no—
657C22×C3—82no—
658C22×C3—84no—
659C22×C3—84no—
660C22×C3—82no—
661C22×C3—82no—
662C22×C3—124no—
663C22×C3—124no—
664C22×C3—122no—
665C22×C3—242no—
666C22×C3#93711yescharacteristic
667C22×C3#93711yescharacteristic
668C22×C3#93711yescharacteristic
669C22×C3#93711yescharacteristic
670C22×C3C2×D3×D411yescharacteristic
671C22×C3C22×#6711yescharacteristic
672C2×D3—22no—
673C2×D3—24no—
674C2×D3—42no—
675C2×D3—44no—
676C2×D3—44no—
677C2×D3—62no—
678C2×D3—62no—
679C2×D3—82no—
680C2×D3—122no—
681C2×D3—122no—
682C2×D3—122no—
683C2×D3—242no—
684C2×D3—248no—
685C2×D3—248no—
686C3×C4—21no—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—64no—
691C3×C4—62no—
692C3×C4#93711yescharacteristic
693C3×C4#93711yescharacteristic
694C3×C4#93711yescharacteristic
695C3×C4#93711yescharacteristic
696C3×C4C2×D3×D411yescharacteristic
697C3×C4C2×D3×D411yescharacteristic
698C3×C4C2×D3×D411yescharacteristic
699C3×C4C22×#6711yescharacteristic
700Dic3—24no—
701Dic3—22no—
702Dic3—62no—
703Dic3—62no—
704Dic3—122no—
705C32C2×#45311yescharacteristic, complemented, Sylow
706C23—22no—
707C23—34no—
708C23—44no—
709C23—41no—
710C23—41no—
711C23—61no—
712C23—62no—
713C23—62no—
714C23—124no—
715C23—188no—
716C23—181no—
717C23—724no—
718C23D3×#6711yescharacteristic
719Q8—32no—
720Q8—61no—
721Q8—92no—
722Q8—181no—
723D4—22no—
724D4—22no—
725D4—32no—
726D4—41no—
727D4—41no—
728D4—62no—
729D4—62no—
730D4—62no—
731D4—62no—
732D4—62no—
733D4—62no—
734D4—61no—
735D4—92no—
736D4—1216no—
737D4—188no—
738D4—188no—
739D4—182no—
740D4—182no—
741D4—181no—
742C2×C4—64no—
743C2×C4—62no—
744C2×C4—61no—
745C2×C4—62no—
746C2×C4—62no—
747C2×C4—188no—
748C2×C4—181no—
749C2×C4—182no—
750C2×C4—182no—
751C2×C4D3×#6711yescharacteristic
752C2×C4D3×#6711yescharacteristic
753C2×C4D3×#6711yescharacteristic
754C2×C4#381111yescharacteristic
755C2×C4#381111yescharacteristic
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—84no—
768C2×C3—82no—
769C2×C3—82no—
770C2×C3—122no—
771C2×C3—124no—
772C2×C3#507712yescomplemented
773C2×C3#519812yescomplemented
774C2×C3C2×#93711yescharacteristic
775C2×C3C2×#93711yescharacteristic
776D3—44no—
777D3—42no—
778D3—122no—
779D3—122no—
780D3—242no—
781C22—22no—
782C22—44no—
783C22—42no—
784C22—62no—
785C22—64no—
786C22—82no—
787C22—82no—
788C22—124no—
789C22—124no—
790C22—122no—
791C22—182no—
792C22—242no—
793C22—362no—
794C22—728no—
795C22#6398311yescharacteristic
796C22#6398311yescharacteristic
797C22C2×D3×#6711yescharacteristic
798C4—64no—
799C4—62no—
800C4—182no—
801C4#6398311yescharacteristic
802C4#6398311yescharacteristic
803C4C2×D3×#6711yescharacteristic
804C4C2×#381111yescharacteristic
805C3—21no—
806C3C2×#507711yescharacteristic, complemented
807C3C2×#519811yescharacteristic, complemented
808C2—21no—
809C2—21no—
810C2—82no—
811C2—124no—
812C2—122no—
813C2—362no—
814C2#1059152312yesdirect product factor
815C2C2×#6398311yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32#120
hypercenterC22×D4D32
hypocenterC32C2×#453
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64307C2semidirect
2. C2×#64141C2semidirect
3. C2×C3×#940C2semidirect
4. C2×C3×#932C2semidirect
5. #10591523C2direct (N × H)
6. C2×#63570C2semidirect
7. C2×#63569C2semidirect
8. C2×#63558C2semidirect
11. C22×C32×D4C22semidirect
20. #64307C22semidirect
27. #64141C22semidirect
29. C2×#3748C22semidirect
31. C3×#940C22semidirect
34. C3×#932C22semidirect
36. C2×C3×C4×Dic3C22semidirect
37. C2×C3×#208C22semidirect
38. #63570C22semidirect
39. #63569C22semidirect
40. #63558C22semidirect
45. C2×#940D3semidirect
49. C2×#932D3semidirect
66. C2×C32×D4C23semidirect
71. #3828D4semidirect
73. C2×C4⋊(C3⋊D3)D4semidirect
75. C2×#634D4semidirect
82. C3×#235D4semidirect
89. C2×C3×D12D4semidirect
92. C2×C3×Dic6D4semidirect
109. #3748C23semidirect
114. C3×C4×Dic3C23semidirect
116. C3×#208C23semidirect
123. C22×C3×D4C2×D3semidirect
124. C22×C3×D4C2×D3semidirect
158. #940C2×D3semidirect
170. #932C2×D3semidirect
175. C2×C4×Dic3C2×D3semidirect
179. C2×#208C2×D3semidirect
213. C4⋊(C3⋊D3)C2×D4semidirect
217. #634C2×D4semidirect
229. C3×D12C2×D4semidirect
233. C3×Dic6C2×D4semidirect
285. C2×C3×D4C22×D3semidirect
286. C2×C3×D4C22×D3semidirect
335. #235#67semidirect
348. C2×D12#67semidirect
358. C2×Dic6#67semidirect
375. C4×Dic3C22×D3semidirect
383. #208C22×D3semidirect
425. C22×D4D32semidirect
551. D12C2×#67semidirect
568. Dic6C2×#67semidirect
577. C2×C32#453semidirect
624. C2×D4C2×D32semidirect
705. C32C2×#453semidirect
772. C2×C3#5077semidirect
773. C2×C3#5198semidirect
806. C3C2×#5077semidirect
807. C3C2×#5198semidirect
814. C2#10591523direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643072
C2×#641412
C2×C3×#9402
C2×C3×#9322
#105915232
C2×#635702
C2×#635692
C2×#635582
C2×#51983
C2×#50773