Finite Group Databasebeta

← C2×#10591017 #11864929

Subgroups — C2×#10591017 #11864929

Order 1152.

1489 conjugacy classes of subgroups.

The subgroup lattice has 733 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64298C211yesmaximal, characteristic
2C2×C3×#909C211yesmaximal, characteristic, complemented
3C2×#63866C211yesmaximal, characteristic, complemented
4C2×#63827C211yesmaximal, characteristic, complemented
5C2×#63651C211yesmaximal, characteristic, complemented
6C2×C3×#825C211yesmaximal, characteristic, complemented
7C2×#63569C211yesmaximal, characteristic, complemented
8#10591017C218yesmaximal, direct product factor
9C2×#5205—31nomaximal
10C2×#4826—31nomaximal
11C22×#634C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C2×#3805—22no—
16#64298—22no—
17#64298—22no—
18#64298—22no—
19#64298C2214yes—
20C2×#3795—21no—
21C2×#3795—21no—
22C2×D3×Dic6—21no—
23C2×D3×Dic6—21no—
24C2×C32×M16C2211yescharacteristic
25C2×#3748C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27C3×#909—22no—
28C3×#909C2214yescomplemented
29C2×C3×Dic12—21no—
30C2×C3×#204—21no—
31C2×Dic3⋊Dic3—22no—
32#63866—22no—
33#63866C2214yescomplemented
34C2×#3718—21no—
35#63827—22no—
36#63827C2214yescomplemented
37C2×#3715—21no—
38#63651C2214yescomplemented
39C3×#825C2214yescomplemented
40#63569C2214yescomplemented
41C2×#1010—31no—
42C2×#1010—31no—
43C2×C3×#137—31no—
44C2×#951—31no—
45C2×#944—31no—
46C2×#942—31no—
47C2×#909D311yescharacteristic, complemented
48C2×#869—31no—
49C2×C3×#104—31no—
50C2×#837—31no—
51#5205—38no—
52C2×#825D311yescharacteristic, complemented
53C2×#824—31no—
54C2×#824—31no—
55C2×#824—61no—
56C2×#805—31no—
57#4826—38no—
58C22×C32×C4C2311yescharacteristic
59C22×C3⋊Dic3D412yes—
60C2×#634—21no—
61C2×#634—21no—
62C2×#634—21no—
63C2×#634—21no—
64C2×#634D412yes—
65C2×#634C2312yes—
66C2×C3×#67—21no—
67C2×C3×#67—21no—
68C22×C3×Dic3—21no—
69C22×C3×Dic3—21no—
70C3×#235—21no—
71C3×#235—21no—
72C3×#235—21no—
73C3×#235—21no—
74C3×#235D412yes—
75C3×#235D412yes—
76C3×#235C2312yes—
77C3×#235C2312yes—
78C2×C3×D12D411yescharacteristic
79C2×C3×D12D411yescharacteristic
80C2×C3×C4×D3—21no—
81C2×C3×C4×D3—21no—
82C2×C3×Dic6—21no—
83C2×C3×Dic6—21no—
84C2×C3×Dic6—21no—
85C2×C3×Dic6—21no—
86C2×C3×Dic6—21no—
87C2×C3×Dic6D411yescharacteristic
88C2×C3×Dic6D411yescharacteristic
89C2×C3×Dic6C2312yes—
90C2×#627—22no—
91C2×#625—22no—
92#3805—28no—
93#3805—28no—
94C2×D3×Dic3—22no—
95C2×D3×Dic3—22no—
96#3795—24no—
97#3795—24no—
98#3795—24no—
99#3795—24no—
100D3×Dic6—24no—
101D3×Dic6—24no—
102D3×Dic6—24no—
103D3×Dic6—24no—
104C32×M16—21no—
105C32×M16C2312yes—
106C2×C32×C8—21no—
107#3748—21no—
108#3748C2312yes—
109C2×C3⋊(C3⋊C8)—21no—
110C3×C4×Dic3—21no—
111C3×C4×Dic3C2312yes—
112C3×Dic12—24no—
113C3×#204—24no—
114Dic3⋊Dic3—28no—
115#3718—24no—
116#3715—24no—
117C2×#456—91noSylow
118C2×C3×#41—31no—
119C2×C3×#41—31no—
120C22×C3×Q8—31no—
121#1010—34no—
122#1010—34no—
123#1010—62no—
124#1010—62no—
125#1010—62no—
126#1010—62no—
127#1010—62no—
128#1010—62no—
129C2×D3×Q8—61no—
130C2×D3×Q8—61no—
131C2×#237—61no—
132C2×#237—61no—
133C2×#237—62no—
134C2×#237—62no—
135C2×#235—61no—
136C2×#235—61no—
137C2×#235C2×D311yescharacteristic
138C2×#235C2×D311yescharacteristic
139C22×Dic6—31no—
140C22×Dic6—31no—
141C22×Dic6—61no—
142C22×Dic6—61no—
143C22×Dic6—61no—
144C22×Dic6C2×D311yescharacteristic
145C3×#137—34no—
146C3×#137—62no—
147C2×C3×Q16—61no—
148C2×C3×SD16—61no—
149C2×C3×M16—21no—
150C2×C3×M16C2×D311yescharacteristic
151C2×C3×M16C2×D311yescharacteristic
152C2×C3×C42—31no—
153#951—34no—
154#951—62no—
155#944—34no—
156#944—62no—
157C2×#216—61no—
158C2×#216—61no—
159#942—34no—
160#942—62no—
161C2×#215—61no—
162C2×#214—61no—
163C2×C4⋊Dic3—62no—
164C2×Dic3⋊C4—62no—
165C2×C4×Dic3C2×D311yescharacteristic
166C2×#208—31no—
167C2×#208—31no—
168C2×#208—61no—
169#909—22no—
170#909C2×D314yescomplemented
171C2×Dic12—21no—
172C2×#204—21no—
173#869—34no—
174#869—62no—
175C3×#104—34no—
176#837—34no—
177#825C2×D314yescomplemented
178#824—34no—
179#824—34no—
180#824—64no—
181#805—34no—
182C23×C32C2×D411yescharacteristic
183C22×C3×D3—21no—
184C22×C3×D3—21no—
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4C2411yescharacteristic
191C2×C3⋊Dic3—22no—
192C2×C3⋊Dic3—22no—
193C2×C3⋊Dic3C2×D414yes—
194#634—22no—
195#634—22no—
196#634—22no—
197#634—22no—
198C3×#67—22no—
199C3×#67—22no—
200C3×#67—22no—
201C3×#67—22no—
202C2×C3×Dic3—24no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3—21no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—41no—
208C2×C3×Dic3—41no—
209C3×D12—21no—
210C3×D12—21no—
211C3×D12C2×D412yes—
212C3×D12C2×D412yes—
213C3×C4×D3—22no—
214C3×C4×D3—22no—
215C3×C4×D3—22no—
216C3×C4×D3—22no—
217C3×Dic6—21no—
218C3×Dic6—21no—
219C3×Dic6—22no—
220C3×Dic6—22no—
221C3×Dic6—41no—
222C3×Dic6—41no—
223C3×Dic6C2×D412yes—
224C3×Dic6C2×D412yes—
225#627—28no—
226#625—28no—
227D3×Dic3—28no—
228D3×Dic3—28no—
229C32×C8—22no—
230C3⋊(C3⋊C8)—22no—
231C2×2−1+4—91no—
232C2×#137—31no—
233C2×#137—91no—
234C2×C4⋊Q8—91no—
235#456—98no—
236C2×#104—31no—
237C2×#104—91no—
238C2×#101—91no—
239C3×#41—32no—
240C3×#41—32no—
241C3×#41—32no—
242C3×#41—32no—
243C3×#41—61no—
244C3×#41—61no—
245C3×#41—61no—
246C3×#41—61no—
247C2×C3×Q8—31no—
248C2×C3×Q8—31no—
249C2×C3×Q8—32no—
250C2×C3×Q8—61no—
251C2×C3×Q8—61no—
252C2×C3×Q8—61no—
253C2×C3×Q8—61no—
254C2×C3×Q8—61no—
255C2×C3×D4—31no—
256C2×C3×D4—31no—
257C2×C3×D4—61no—
258C2×C3×D4—61no—
259C22×C3×C4—21no—
260C22×C3×C4—61no—
261C22×C3×C4—61no—
262C22×C3×C4—61no—
263C22×C3×C4—61no—
264C22×C3×C4C22×D311yescharacteristic
265C22×C3×C4C22×D311yescharacteristic
266C2×#67—21no—
267C2×#67—21no—
268C2×#67—62no—
269C2×#67—62no—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3—32no—
273C22×Dic3—32no—
274C22×Dic3—62no—
275C22×Dic3—62no—
276C22×Dic3—62no—
277D3×Q8—64no—
278D3×Q8—64no—
279D3×Q8—64no—
280D3×Q8—64no—
281#237—64no—
282#237—64no—
283#237—64no—
284#237—64no—
285#237—68no—
286#237—68no—
287#237—68no—
288#237—68no—
289#235—21no—
290#235—21no—
291#235—21no—
292#235—21no—
293#235—64no—
294#235—64no—
295#235—64no—
296#235—64no—
297#235D1212yes—
298#235#6712yes—
299#235C22×D312yes—
300#235C22×D312yes—
301C2×D12D1211yescharacteristic
302C2×D12#6711yescharacteristic
303C2×C4×D3—21no—
304C2×C4×D3—21no—
305C2×C4×D3—62no—
306C2×C4×D3—62no—
307C2×Dic6—21no—
308C2×Dic6—21no—
309C2×Dic6—21no—
310C2×Dic6—21no—
311C2×Dic6—21no—
312C2×Dic6—32no—
313C2×Dic6—32no—
314C2×Dic6—32no—
315C2×Dic6—32no—
316C2×Dic6—62no—
317C2×Dic6—62no—
318C2×Dic6—64no—
319C2×Dic6—64no—
320C2×Dic6—62no—
321C2×Dic6—62no—
322C2×Dic6—61no—
323C2×Dic6—61no—
324C2×Dic6—61no—
325C2×Dic6—61no—
326C2×Dic6—61no—
327C2×Dic6—61no—
328C2×Dic6—61no—
329C2×Dic6—61no—
330C2×Dic6—64no—
331C2×Dic6—64no—
332C2×Dic6—121no—
333C2×Dic6—121no—
334C2×Dic6—121no—
335C2×Dic6—121no—
336C2×Dic6D1211yescharacteristic
337C2×Dic6#6711yescharacteristic
338C2×Dic6C22×D312yes—
339C3×Q16—64no—
340C3×SD16—64no—
341C3×M16—21no—
342C3×M16—21no—
343C3×M16—22no—
344C3×M16—41no—
345C3×M16C22×D312yes—
346C3×M16C22×D312yes—
347C2×C3×C8—21no—
348C2×C3×C8—21no—
349C2×C3×C8—41no—
350C3×C42—32no—
351C3×C42—61no—
352#216—64no—
353#216—64no—
354#215—64no—
355#214—64no—
356C4⋊Dic3—68no—
357Dic3⋊C4—68no—
358C4×Dic3—21no—
359C4×Dic3C22×D312yes—
360#208—32no—
361#208—32no—
362#208—62no—
363#208—61no—
364#208—61no—
365#208—121no—
366C2×C3⋊C8—61no—
367C2×C3⋊C8—61no—
368C2×C3⋊C8—121no—
369Dic12—24no—
370#204—24no—
371C22×C32—22no—
372C22×C32#12011yescharacteristic
373C22×C32#12011yescharacteristic
374C22×C32C22×D411yescharacteristic
375C2×C3×D3—22no—
376C2×C3×D3—22no—
377C2×C3×D3—42no—
378C2×C3×D3—42no—
379C32×C4#12011yescharacteristic
380C32×C4#12011yescharacteristic
381C32×C4C22×D411yescharacteristic
382C32×C4C22×D411yescharacteristic
383C3⋊Dic3—24no—
384C3×Dic3—24no—
385C3×Dic3—22no—
386C3×Dic3—22no—
387C3×Dic3—42no—
3882−1+4—94no—
3892−1+4—182no—
3902−1+4—182no—
3912−1+4—182no—
392C2×#41—31no—
393C2×#41—31no—
394C2×#41—181no—
395C2×#41—181no—
396C2×#41—182no—
397C22×Q8—31no—
398C22×Q8—91no—
399C22×Q8—181no—
400C22×Q8—181no—
401#137—34no—
402#137—62no—
403#137—94no—
404#137—182no—
405C2×Q16—61no—
406C2×Q16—181no—
407C2×SD16—61no—
408C2×SD16—181no—
409C2×M16—91no—
410C2×M16D3211yescharacteristic
411C4⋊Q8—94no—
412C4⋊Q8—182no—
413C2×C4⋊C4—182no—
414C2×C42—31no—
415#104—34no—
416#104—94no—
417#101—94no—
418C23×C3—21no—
419C23×C3—61no—
420C23×C3—61no—
421C23×C3D3×D411yescharacteristic
422C23×C3D3×D411yescharacteristic
423C22×D3—21no—
424C22×D3—21no—
425C3×Q8—32no—
426C3×Q8—32no—
427C3×Q8—61no—
428C3×Q8—61no—
429C3×Q8—62no—
430C3×Q8—62no—
431C3×Q8—121no—
432C3×Q8—121no—
433C3×D4—32no—
434C3×D4—32no—
435C3×D4—62no—
436C3×D4—62no—
437C3×D4—62no—
438C3×D4—62no—
439C3×D4—61no—
440C3×D4—61no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—64no—
448C2×C3×C4—61no—
449C2×C3×C4—61no—
450C2×C3×C4—62no—
451C2×C3×C4—62no—
452C2×C3×C4—62no—
453C2×C3×C4—62no—
454C2×C3×C4—62no—
455C2×C3×C4—62no—
456C2×C3×C4—121no—
457C2×C3×C4—121no—
458C2×C3×C4C2×D1211yescharacteristic
459C2×C3×C4C2×D1211yescharacteristic
460C2×C3×C4D3×D411yescharacteristic
461C2×C3×C4D3×D411yescharacteristic
462C2×C3×C4D3×D411yescharacteristic
463C2×C3×C4D3×D411yescharacteristic
464C2×C3×C4D3×D411yescharacteristic
465C2×C3×C4D3×D411yescharacteristic
466C2×C3×C4C2×#6711yescharacteristic
467C2×C3×C4C2×#6711yescharacteristic
468C2×C3×C4C23×D311yescharacteristic
469C2×C3×C4C23×D311yescharacteristic
470#67—22no—
471#67—22no—
472#67—22no—
473#67—22no—
474#67—68no—
475#67—68no—
476C2×Dic3—24no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—34no—
482C2×Dic3—34no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—64no—
486C2×Dic3—68no—
487C2×Dic3—68no—
488C2×Dic3—62no—
489C2×Dic3—62no—
490C2×Dic3—62no—
491C2×Dic3—62no—
492C2×Dic3—122no—
493C2×Dic3—122no—
494D12—21no—
495D12—21no—
496D12C2×D1212yes—
497D12C2×#6712yes—
498C4×D3—22no—
499C4×D3—22no—
500C4×D3—22no—
501C4×D3—22no—
502C4×D3—68no—
503C4×D3—68no—
504Dic6—21no—
505Dic6—21no—
506Dic6—22no—
507Dic6—22no—
508Dic6—41no—
509Dic6—41no—
510Dic6—68no—
511Dic6—68no—
512Dic6—62no—
513Dic6—62no—
514Dic6—62no—
515Dic6—62no—
516Dic6—62no—
517Dic6—62no—
518Dic6—62no—
519Dic6—62no—
520Dic6—122no—
521Dic6—122no—
522Dic6—122no—
523Dic6—122no—
524Dic6C2×D1212yes—
525Dic6C2×#6712yes—
526C3×C8—22no—
527C3×C8—22no—
528C3×C8—42no—
529C3⋊C8—62no—
530C3⋊C8—62no—
531C3⋊C8—122no—
532C2×C32—21no—
533C2×C32—21no—
534C2×C32#45612yescomplemented
535C2×C32C2×#12011yescharacteristic
536C3×D3—42no—
537C3×D3—42no—
538#41—32no—
539#41—32no—
540#41—32no—
541#41—32no—
542#41—61no—
543#41—61no—
544#41—61no—
545#41—61no—
546#41—184no—
547#41—184no—
548#41—184no—
549#41—184no—
550#41—188no—
551#41—188no—
552C2×Q8—32no—
553C2×Q8—31no—
554C2×Q8—31no—
555C2×Q8—61no—
556C2×Q8—61no—
557C2×Q8—61no—
558C2×Q8—61no—
559C2×Q8—61no—
560C2×Q8—92no—
561C2×Q8—92no—
562C2×Q8—182no—
563C2×Q8—184no—
564C2×Q8—184no—
565C2×Q8—184no—
566C2×Q8—184no—
567C2×Q8—181no—
568C2×Q8—181no—
569C2×Q8—181no—
570C2×Q8—181no—
571C2×D4—31no—
572C2×D4—31no—
573C2×D4—61no—
574C2×D4—61no—
575C2×D4—182no—
576C22×C4—61no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—92no—
581C22×C4—182no—
582C22×C4—182no—
583C22×C4C2×D3211yescharacteristic
584Q16—64no—
585Q16—184no—
586SD16—64no—
587SD16—184no—
588M16—21no—
589M16—92no—
590M16—181no—
591M16C2×D3212yes—
592C2×C8—21no—
593C2×C8—181no—
594C4⋊C4—188no—
595C42—32no—
596C42—61no—
597C22×C3—22no—
598C22×C3—22no—
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—42no—
603C22×C3—62no—
604C22×C3—62no—
605C22×C3—122no—
606C22×C3—122no—
607C22×C3#88211yescharacteristic
608C22×C3#88211yescharacteristic
609C22×C3#93711yescharacteristic
610C22×C3#93711yescharacteristic
611C22×C3C2×D3×D411yescharacteristic
612C22×C3C2×D3×D411yescharacteristic
613C2×D3—22no—
614C2×D3—22no—
615C2×D3—42no—
616C2×D3—42no—
617C3×C4—21no—
618C3×C4—21no—
619C3×C4—21no—
620C3×C4—21no—
621C3×C4—64no—
622C3×C4—62no—
623C3×C4—62no—
624C3×C4—122no—
625C3×C4#88211yescharacteristic
626C3×C4#88211yescharacteristic
627C3×C4#93711yescharacteristic
628C3×C4#93711yescharacteristic
629C3×C4C22×D1211yescharacteristic
630C3×C4C2×D3×D411yescharacteristic
631C3×C4C2×D3×D411yescharacteristic
632C3×C4C22×#6711yescharacteristic
633Dic3—24no—
634Dic3—22no—
635Dic3—22no—
636Dic3—42no—
637Dic3—64no—
638Dic3—64no—
639Dic3—124no—
640C32C2×#45611yescharacteristic, complemented, Sylow
641C23—61no—
642C23—61no—
643C23#380211yescharacteristic
644Q8—32no—
645Q8—32no—
646Q8—61no—
647Q8—61no—
648Q8—62no—
649Q8—62no—
650Q8—121no—
651Q8—121no—
652Q8—188no—
653Q8—182no—
654Q8—182no—
655Q8—182no—
656Q8—182no—
657D4—32no—
658D4—32no—
659D4—62no—
660D4—62no—
661D4—62no—
662D4—62no—
663D4—61no—
664D4—61no—
665D4—188no—
666C2×C4—64no—
667C2×C4—62no—
668C2×C4—61no—
669C2×C4—61no—
670C2×C4—62no—
671C2×C4—62no—
672C2×C4—62no—
673C2×C4—62no—
674C2×C4—62no—
675C2×C4—94no—
676C2×C4—121no—
677C2×C4—121no—
678C2×C4—188no—
679C2×C4—188no—
680C2×C4—182no—
681C2×C4—182no—
682C2×C4D3×D1211yescharacteristic
683C2×C4D3×D1211yescharacteristic
684C2×C4#380211yescharacteristic
685C2×C4D3×#6711yescharacteristic
686C2×C4D3×#6711yescharacteristic
687C2×C4C22×D3211yescharacteristic
688C8—22no—
689C8—182no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—21no—
694C2×C3—22no—
695C2×C3—21no—
696C2×C3—41no—
697C2×C3—41no—
698C2×C3—122no—
699C2×C3—122no—
700C2×C3#482612yescomplemented
701C2×C3#520512yescomplemented
702C2×C3C2×#88211yescharacteristic
703C2×C3C2×#93711yescharacteristic
704D3—42no—
705D3—42no—
706C22—22no—
707C22—62no—
708C22—62no—
709C22—122no—
710C22—122no—
711C22#6392211yescharacteristic
712C22#6392211yescharacteristic
713C22C2×#380211yescharacteristic
714C4—64no—
715C4—62no—
716C4—62no—
717C4—122no—
718C4—184no—
719C4#6392211yescharacteristic
720C4#6392211yescharacteristic
721C4C2×D3×D1211yescharacteristic
722C4C2×D3×#6711yescharacteristic
723C3—21no—
724C3C2×#482611yescharacteristic, complemented
725C3C2×#520511yescharacteristic, complemented
726C2—21no—
727C2—21no—
728C2—122no—
729C2—122no—
730C2#1059101712yesdirect product factor
731C2C2×#6392211yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32#120
prime radicalC2×#64298C2
hypercenterC2×M16D32
hypocenterC32C2×#456
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×C3×#909C2semidirect
3. C2×#63866C2semidirect
4. C2×#63827C2semidirect
5. C2×#63651C2semidirect
6. C2×C3×#825C2semidirect
7. C2×#63569C2semidirect
8. #10591017C2direct (N × H)
28. C3×#909C22semidirect
33. #63866C22semidirect
36. #63827C22semidirect
38. #63651C22semidirect
39. C3×#825C22semidirect
40. #63569C22semidirect
47. C2×#909D3semidirect
52. C2×#825D3semidirect
170. #909C2×D3semidirect
177. #825C2×D3semidirect
534. C2×C32#456semidirect
640. C32C2×#456semidirect
700. C2×C3#4826semidirect
701. C2×C3#5205semidirect
724. C3C2×#4826semidirect
725. C3C2×#5205semidirect
730. C2#10591017direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#642982
C2×C3×#9092
C2×#638662
C2×#638272
C2×#636512
C2×C3×#8252
C2×#635692
#105910172
C2×#52053
C2×#48263