Finite Group Databasebeta

← C2×#10591533 #11865289

Subgroups — C2×#10591533 #11865289

Order 1152.

1693 conjugacy classes of subgroups.

The subgroup lattice has 647 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1004C211yesmaximal, characteristic
2C2×C3×#935C211yesmaximal, characteristic, complemented
3C2×#63961C212yesmaximal, complemented
4C2×#63661C211yesmaximal, characteristic, complemented
5C2×#63580C212yesmaximal, complemented
6#10591533C218yesmaximal, direct product factor
7C2×#5243—31nomaximal
8C2×#5053—31nomaximal
9C22×C32×D4C2211yescharacteristic
10C22×C3×#67—21no—
11C22×C3×#67C2212yes—
12C23×C3×Dic3C2211yescharacteristic, complemented
13C3×#1004—22no—
14C3×#1004—24no—
15C3×#1004C2214yes—
16C2×C3×#237—22no—
17C2×C3×D3×D4—22no—
18C2×C3×#235—21no—
19C2×#3757C2212yescomplemented
20C2×C3×#217—21no—
21C2×C3×#217C2211yescharacteristic, complemented
22C3×#935—22no—
23C3×#935C2214yescomplemented
24C2×C3×Dic3⋊C4—21no—
25C2×#3724—22no—
26#63961—24no—
27#63961C2218yescomplemented
28C2×(C2×D3)⋊Dic3—22no—
29#63661C2214yescomplemented
30#63580C2218yescomplemented
31C2×C3×H(5,𝔽2)—31no—
32C2×#1004D311yescharacteristic
33C2×C3×#123—31no—
34C2×#935—32no—
35C2×#935D311yescharacteristic, complemented
36C2×#929—32no—
37#5243—38no—
38C2×#834—31no—
39C2×#834—31no—
40C2×#834—32no—
41C2×#834—61no—
42#5053—38no—
43C2×#806—32no—
44C24×C32D411yescharacteristic
45C24×C32C2311yescharacteristic
46C23×C3×D3—21no—
47C23×C3×D3D412yes—
48C2×C32×D4—22no—
49C2×C32×D4—22no—
50C2×C32×D4D412yes—
51C2×C32×D4C2312yes—
52C22×C32×C4D411yescharacteristic
53C22×C3⋊Dic3—22no—
54C2×C3×#67—22no—
55C2×C3×#67—24no—
56C2×C3×#67—22no—
57C2×C3×#67—22no—
58C2×C3×#67—22no—
59C2×C3×#67—22no—
60C2×C3×#67—24no—
61C2×C3×#67D414yes—
62C2×C3×#67C2314yes—
63C22×C3×Dic3—21no—
64C22×C3×Dic3—21no—
65C22×C3×Dic3—21no—
66C22×C3×Dic3—21no—
67C22×C3×Dic3—22no—
68C22×C3×Dic3—22no—
69C22×C3×Dic3D412yes—
70C22×C3×Dic3C2312yescomplemented
71C3×#237—28no—
72C3×#237—28no—
73C3×D3×D4—28no—
74C3×D3×D4—28no—
75C3×#235—24no—
76C3×#235—24no—
77C2×C3×D12—21no—
78C2×C3×C4×D3—22no—
79C2×C3×Dic6—21no—
80#3757—22no—
81#3757C2314yescomplemented
82C3×#217—21no—
83C3×#217—24no—
84C3×#217C2312yescomplemented
85C3×Dic3⋊C4—24no—
86#3724—28no—
87(C2×D3)⋊Dic3—28no—
88C2×#458—91noSylow
89C3×H(5,𝔽2)—34no—
90C3×H(5,𝔽2)—64no—
91C3×H(5,𝔽2)—62no—
92C2×C3×#41—62no—
93C2×C3×#41—61no—
94C22×C3×D4—21no—
95C22×C3×D4—32no—
96C22×C3×D4—62no—
97C22×C3×D4—61no—
98C22×C3×D4C2×D311yescharacteristic
99C22×C3×D4C2×D311yescharacteristic
100C23×C3×C4—31no—
101C22×#67—21no—
102C22×#67C2×D312yes—
103C23×Dic3C2×D311yescharacteristic, complemented
104#1004—22no—
105#1004—24no—
106#1004C2×D314yes—
107C2×#237—22no—
108C2×D3×D4—22no—
109C2×#235—21no—
110C3×#123—34no—
111C3×#123—62no—
112C2×C3×C4⋊C4—61no—
113C2×C3×C22⋊C4—31no—
114C2×C3×C22⋊C4—61no—
115C2×#217—21no—
116C2×#217—32no—
117C2×#217—32no—
118C2×#217—62no—
119C2×#217—62no—
120C2×#217C2×D311yescharacteristic, complemented
121#935—22no—
122#935—38no—
123#935—64no—
124#935C2×D314yescomplemented
125#929—38no—
126#929—64no—
127C2×(C2×D3)⋊C4—62no—
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4—62no—
130C2×Dic3⋊C4—62no—
131#834—34no—
132#834—34no—
133#834—38no—
134#834—64no—
135#806—38no—
136C23×C32—21no—
137C23×C32—21no—
138C23×C32—42no—
139C23×C32—42no—
140C23×C32C2×D412yes—
141C23×C32C2×D412yes—
142C23×C32C2×D411yescharacteristic
143C23×C32C2×D412yes—
144C23×C32C2×D411yescharacteristic
145C23×C32C2411yescharacteristic
146C22×C3×D3—22no—
147C22×C3×D3—24no—
148C22×C3×D3—22no—
149C22×C3×D3—44no—
150C22×C3×D3—82no—
151C22×C3×D3C2×D414yes—
152C32×D4—24no—
153C32×D4—24no—
154C2×C32×C4—21no—
155C2×C32×C4—21no—
156C2×C32×C4C2×D412yes—
157C2×C3⋊Dic3—24no—
158C2×C3⋊Dic3—44no—
159C3×#67—28no—
160C3×#67—24no—
161C3×#67—24no—
162C3×#67—24no—
163C3×#67—24no—
164C2×C3×Dic3—24no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—24no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—42no—
171C2×C3×Dic3—42no—
172C2×C3×Dic3—41no—
173C2×C3×Dic3—41no—
174C2×C3×Dic3C2×D414yes—
175C3×D12—24no—
176C3×C4×D3—28no—
177C3×Dic6—24no—
178C2×H(5,𝔽2)—31no—
179C2×#123—31no—
180C2×#123—92no—
181#458—98no—
182C2×#99—92no—
183C2×#99—91no—
184C24×C3—21no—
185C24×C3—21no—
186C24×C3—32no—
187C24×C3—61no—
188C24×C3#6711yescharacteristic
189C24×C3#6711yescharacteristic
190C24×C3C22×D311yescharacteristic
191C24×C3C22×D311yescharacteristic
192C23×D3—21no—
193C23×D3#6712yes—
194C3×#41—64no—
195C3×#41—68no—
196C3×#41—68no—
197C3×#41—64no—
198C2×C3×Q8—61no—
199C2×C3×D4—22no—
200C2×C3×D4—22no—
201C2×C3×D4—22no—
202C2×C3×D4—22no—
203C2×C3×D4—22no—
204C2×C3×D4—22no—
205C2×C3×D4—34no—
206C2×C3×D4—34no—
207C2×C3×D4—42no—
208C2×C3×D4—42no—
209C2×C3×D4—61no—
210C2×C3×D4—68no—
211C2×C3×D4—68no—
212C2×C3×D4—62no—
213C2×C3×D4—64no—
214C2×C3×D4—62no—
215C2×C3×D4—62no—
216C2×C3×D4—62no—
217C2×C3×D4—62no—
218C2×C3×D4—64no—
219C2×C3×D4#6712yes—
220C2×C3×D4#6712yes—
221C2×C3×D4C22×D312yes—
222C2×C3×D4C22×D312yes—
223C22×C3×C4—21no—
224C22×C3×C4—32no—
225C22×C3×C4—32no—
226C22×C3×C4—62no—
227C22×C3×C4—61no—
228C22×C3×C4—62no—
229C22×C3×C4—62no—
230C22×C3×C4—61no—
231C22×C3×C4—61no—
232C22×C3×C4—61no—
233C22×C3×C4#6711yescharacteristic
234C22×C3×C4#6711yescharacteristic
235C2×#67—22no—
236C2×#67—24no—
237C2×#67—22no—
238C2×#67—22no—
239C2×#67—22no—
240C2×#67—22no—
241C2×#67—24no—
242C2×#67#6714yes—
243C2×#67C22×D314yes—
244C22×Dic3—21no—
245C22×Dic3—22no—
246C22×Dic3—22no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3—62no—
251C22×Dic3—62no—
252C22×Dic3—122no—
253C22×Dic3#6712yes—
254C22×Dic3C22×D312yescomplemented
255#237—28no—
256#237—28no—
257D3×D4—28no—
258D3×D4—28no—
259#235—24no—
260#235—24no—
261C2×D12—21no—
262C2×C4×D3—22no—
263C2×Dic6—21no—
264C3×C4⋊C4—64no—
265C3×C22⋊C4—32no—
266C3×C22⋊C4—61no—
267C3×C22⋊C4—64no—
268#217—21no—
269#217—24no—
270#217—34no—
271#217—34no—
272#217—64no—
273#217—68no—
274#217—62no—
275#217—62no—
276#217—122no—
277#217C22×D312yescomplemented
278(C2×D3)⋊C4—68no—
279Dic3⋊C4—24no—
280Dic3⋊C4—68no—
281Dic3⋊C4—68no—
282C22×C32—22no—
283C22×C32—24no—
284C22×C32—22no—
285C22×C32—42no—
286C22×C32—41no—
287C22×C32—41no—
288C22×C32—42no—
289C22×C32—42no—
290C22×C32—81no—
291C22×C32#12012yes—
292C22×C32#12011yescharacteristic
293C22×C32#12011yescharacteristic
294C22×C32C22×D412yes—
295C22×C32C22×D411yescharacteristic
296C2×C3×D3—24no—
297C2×C3×D3—44no—
298C2×C3×D3—44no—
299C2×C3×D3—82no—
300C2×C3×D3—84no—
301C32×C4—22no—
302C3⋊Dic3—44no—
303C3×Dic3—24no—
304C3×Dic3—42no—
305C3×Dic3—42no—
306H(5,𝔽2)—34no—
307H(5,𝔽2)—64no—
308H(5,𝔽2)—62no—
309C2×#41—62no—
310C2×#41—61no—
311C22×D4—32no—
312C22×D4—62no—
313C22×D4—61no—
314C22×D4D3211yescharacteristic
315C23×C4—31no—
316#123—34no—
317#123—62no—
318#123—98no—
319#123—184no—
320C2×C4⋊C4—61no—
321C2×C4⋊C4—182no—
322C2×C22⋊C4—31no—
323C2×C22⋊C4—61no—
324C2×C22⋊C4—92no—
325C2×C22⋊C4—182no—
326#99—98no—
327#99—94no—
328C23×C3—21no—
329C23×C3—21no—
330C23×C3—21no—
331C23×C3—21no—
332C23×C3—21no—
333C23×C3—21no—
334C23×C3—21no—
335C23×C3—22no—
336C23×C3—22no—
337C23×C3—22no—
338C23×C3—34no—
339C23×C3—41no—
340C23×C3—41no—
341C23×C3—42no—
342C23×C3—42no—
343C23×C3—42no—
344C23×C3—42no—
345C23×C3—64no—
346C23×C3—62no—
347C23×C3—62no—
348C23×C3—82no—
349C23×C3—82no—
350C23×C3—124no—
351C23×C3—242no—
352C23×C3D3×D412yes—
353C23×C3D3×D412yes—
354C23×C3C2×#6711yescharacteristic
355C23×C3C2×#6711yescharacteristic
356C23×C3C2×#6712yes—
357C23×C3C2×#6712yes—
358C23×C3C2×#6711yescharacteristic
359C23×C3C2×#6711yescharacteristic
360C23×C3C2×#6712yes—
361C23×C3C2×#6712yes—
362C23×C3C23×D311yescharacteristic
363C23×C3C23×D311yescharacteristic
364C22×D3—22no—
365C22×D3—24no—
366C22×D3—22no—
367C22×D3—44no—
368C22×D3—82no—
369C22×D3C2×#6714yes—
370C3×Q8—64no—
371C3×D4—24no—
372C3×D4—24no—
373C3×D4—24no—
374C3×D4—24no—
375C3×D4—44no—
376C3×D4—44no—
377C3×D4—64no—
378C3×D4—68no—
379C3×D4—64no—
380C3×D4—64no—
381C3×D4—64no—
382C3×D4—64no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—22no—
388C2×C3×C4—34no—
389C2×C3×C4—41no—
390C2×C3×C4—41no—
391C2×C3×C4—68no—
392C2×C3×C4—64no—
393C2×C3×C4—62no—
394C2×C3×C4—62no—
395C2×C3×C4—64no—
396C2×C3×C4—62no—
397C2×C3×C4—62no—
398C2×C3×C4—122no—
399C2×C3×C4—122no—
400C2×C3×C4—121no—
401C2×C3×C4—121no—
402C2×C3×C4C2×#6712yes—
403C2×C3×C4C2×#6712yes—
404#67—28no—
405#67—24no—
406#67—24no—
407#67—24no—
408#67—24no—
409C2×Dic3—24no—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—24no—
413C2×Dic3—22no—
414C2×Dic3—22no—
415C2×Dic3—42no—
416C2×Dic3—41no—
417C2×Dic3—42no—
418C2×Dic3—41no—
419C2×Dic3—64no—
420C2×Dic3—64no—
421C2×Dic3—124no—
422C2×Dic3—124no—
423C2×Dic3—124no—
424C2×Dic3—244no—
425C2×Dic3C2×#6714yes—
426D12—24no—
427C4×D3—28no—
428Dic6—24no—
429C2×C32—21no—
430C2×C32—22no—
431C2×C32—22no—
432C2×C32—21no—
433C2×C32—42no—
434C2×C32#45812yescomplemented
435C2×C32C2×#12011yescharacteristic
436C3×D3—44no—
437C24—32no—
438C24—61no—
439C24#62511yescharacteristic
440C24C2×D3211yescharacteristic
441#41—64no—
442#41—68no—
443#41—68no—
444#41—64no—
445C2×Q8—61no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—34no—
449C2×D4—34no—
450C2×D4—61no—
451C2×D4—68no—
452C2×D4—68no—
453C2×D4—62no—
454C2×D4—64no—
455C2×D4—62no—
456C2×D4—62no—
457C2×D4—64no—
458C2×D4—62no—
459C2×D4—62no—
460C2×D4#62512yes—
461C2×D4C2×D3212yes—
462C22×C4—32no—
463C22×C4—32no—
464C22×C4—62no—
465C22×C4—61no—
466C22×C4—61no—
467C22×C4—61no—
468C22×C4—61no—
469C22×C4—62no—
470C22×C4—62no—
471C22×C4—182no—
472C22×C4#62511yescharacteristic
473C4⋊C4—64no—
474C4⋊C4—188no—
475C22⋊C4—32no—
476C22⋊C4—61no—
477C22⋊C4—64no—
478C22⋊C4—94no—
479C22⋊C4—188no—
480C22⋊C4—182no—
481C22×C3—24no—
482C22×C3—22no—
483C22×C3—22no—
484C22×C3—24no—
485C22×C3—22no—
486C22×C3—22no—
487C22×C3—21no—
488C22×C3—22no—
489C22×C3—21no—
490C22×C3—22no—
491C22×C3—21no—
492C22×C3—44no—
493C22×C3—42no—
494C22×C3—42no—
495C22×C3—42no—
496C22×C3—41no—
497C22×C3—41no—
498C22×C3—42no—
499C22×C3—41no—
500C22×C3—41no—
501C22×C3—42no—
502C22×C3—42no—
503C22×C3—42no—
504C22×C3—42no—
505C22×C3—64no—
506C22×C3—82no—
507C22×C3—81no—
508C22×C3—81no—
509C22×C3—82no—
510C22×C3—82no—
511C22×C3—81no—
512C22×C3—81no—
513C22×C3—82no—
514C22×C3—124no—
515C22×C3—124no—
516C22×C3—242no—
517C22×C3—244no—
518C22×C3#93711yescharacteristic
519C22×C3#93712yes—
520C22×C3#93711yescharacteristic
521C22×C3#95312yes—
522C22×C3#95311yescharacteristic
523C22×C3#95311yescharacteristic
524C22×C3C2×D3×D412yes—
525C22×C3C22×#6711yescharacteristic
526C22×C3C22×#6711yescharacteristic
527C22×C3C22×#6712yes—
528C2×D3—24no—
529C2×D3—44no—
530C2×D3—44no—
531C2×D3—82no—
532C2×D3—84no—
533C3×C4—22no—
534C3×C4—22no—
535C3×C4—42no—
536C3×C4—64no—
537C3×C4—122no—
538C3×C4—122no—
539Dic3—24no—
540Dic3—42no—
541Dic3—42no—
542Dic3—124no—
543Dic3—124no—
544Dic3—244no—
545C32C2×#45811yescharacteristic, complemented, Sylow
546C23—21no—
547C23—21no—
548C23—34no—
549C23—42no—
550C23—42no—
551C23—64no—
552C23—62no—
553C23—62no—
554C23—124no—
555C23—242no—
556C23C2×#62511yescharacteristic
557C23C2×#62512yes—
558C23C2×#62511yescharacteristic
559C23D3×#6712yes—
560C23D3×#6712yes—
561C23C22×D3211yescharacteristic
562Q8—64no—
563D4—24no—
564D4—24no—
565D4—64no—
566D4—68no—
567D4—64no—
568D4—64no—
569D4—64no—
570D4—64no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—34no—
574C2×C4—68no—
575C2×C4—64no—
576C2×C4—62no—
577C2×C4—62no—
578C2×C4—62no—
579C2×C4—62no—
580C2×C4—64no—
581C2×C4—122no—
582C2×C4—121no—
583C2×C4—122no—
584C2×C4—121no—
585C2×C4—184no—
586C2×C4—364no—
587C2×C4C2×#62512yes—
588C2×C3—22no—
589C2×C3—21no—
590C2×C3—22no—
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—22no—
594C2×C3—21no—
595C2×C3—22no—
596C2×C3—22no—
597C2×C3—21no—
598C2×C3—42no—
599C2×C3—41no—
600C2×C3—41no—
601C2×C3—42no—
602C2×C3—42no—
603C2×C3—42no—
604C2×C3—82no—
605C2×C3—124no—
606C2×C3#505312yescomplemented
607C2×C3#524312yescomplemented
608C2×C3C2×#93711yescharacteristic
609C2×C3C2×#95311yescharacteristic
610D3—44no—
611C22—22no—
612C22—24no—
613C22—22no—
614C22—41no—
615C22—41no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—64no—
620C22—81no—
621C22—124no—
622C22—124no—
623C22—242no—
624C22—244no—
625C22#6397611yescharacteristic
626C22#6397612yes—
627C22#6397611yescharacteristic
628C22C22×#62511yescharacteristic
629C22C2×D3×#6712yes—
630C4—22no—
631C4—64no—
632C4—122no—
633C4—122no—
634C4—364no—
635C3—21no—
636C3C2×#505311yescharacteristic, complemented
637C3C2×#524311yescharacteristic, complemented
638C2—21no—
639C2—22no—
640C2—21no—
641C2—22no—
642C2—42no—
643C2—124no—
644C2#1059153312yesdirect product factor
645C2C2×#6397611yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC22×C32×D4C22
socleC22×C32#120
prime radicalC2×C3×#1004C2
hypercenterC22×D4D32
hypocenterC32C2×#458
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#935C2semidirect
3. C2×#63961C2semidirect
4. C2×#63661C2semidirect
5. C2×#63580C2semidirect
6. #10591533C2direct (N × H)
12. C23×C3×Dic3C22semidirect
19. C2×#3757C22semidirect
21. C2×C3×#217C22semidirect
23. C3×#935C22semidirect
27. #63961C22semidirect
29. #63661C22semidirect
30. #63580C22semidirect
35. C2×#935D3semidirect
70. C22×C3×Dic3C23semidirect
81. #3757C23semidirect
84. C3×#217C23semidirect
103. C23×Dic3C2×D3semidirect
120. C2×#217C2×D3semidirect
124. #935C2×D3semidirect
254. C22×Dic3C22×D3semidirect
277. #217C22×D3semidirect
434. C2×C32#458semidirect
545. C32C2×#458semidirect
606. C2×C3#5053semidirect
607. C2×C3#5243semidirect
636. C3C2×#5053semidirect
637. C3C2×#5243semidirect
644. C2#10591533direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#10042
C2×C3×#9352
C2×#639612
C2×#636612
C2×#635802
#105915332
C2×#52433
C2×#50533