Finite Group Databasebeta

← C2×#10591535 #11865288

Subgroups — C2×#10591535 #11865288

Order 1152.

2037 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64361C211yesmaximal, characteristic
2C2×C3×#935C211yesmaximal, characteristic, complemented
3C2×#63966C212yesmaximal, complemented
4C2×C3×#834C211yesmaximal, characteristic, complemented
5C2×#63581C212yesmaximal, complemented
6#10591535C218yesmaximal, direct product factor
7C2×#5053—31nomaximal
8C2×#4742—31nomaximal
9C22×C32×D4C2211yescharacteristic
10C22×#638—21no—
11C22×#638C2212yes—
12#64361—22no—
13#64361—24no—
14#64361C2214yes—
15C2×#3830—22no—
16C2×D4×C3⋊D3—22no—
17C2×#3828—21no—
18C23×C3×Dic3C2211yescharacteristic, complemented
19C2×C3×#217—21no—
20C2×C3×#217C2211yescharacteristic, complemented
21C2×C3×#217C2212yescomplemented
22C3×#935—22no—
23C3×#935C2214yescomplemented
24C2×C3×Dic3⋊C4—21no—
25#63966—24no—
26#63966C2218yescomplemented
27C2×Dic3⋊Dic3—22no—
28C2×#3722—22no—
29C3×#834C2214yescomplemented
30#63581C2218yescomplemented
31C2×#1004—31no—
32C2×#1004—31no—
33C2×#1004—61no—
34C2×C3×#123—31no—
35C2×#935D311yescharacteristic, complemented
36C2×#929—32no—
37C2×#886—32no—
38C2×C3×#99—31no—
39C2×#834D311yescharacteristic, complemented
40#5053—38no—
41C2×#806—32no—
42C2×#806—32no—
43#4742—38no—
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
53C2×#638—22no—
54C2×#638—24no—
55C2×#638—22no—
56C2×#638—22no—
57C2×#638—22no—
58C2×#638—22no—
59C2×#638—24no—
60C2×#638D414yes—
61C2×#638C2314yes—
62C22×C3⋊Dic3—21no—
63C22×C3⋊Dic3D412yes—
64#3830—28no—
65#3830—28no—
66D4×C3⋊D3—28no—
67D4×C3⋊D3—28no—
68#3828—24no—
69#3828—24no—
70C2×C4⋊(C3⋊D3)—21no—
71C2×C4×C3⋊D3—22no—
72C2×#634—21no—
73C22×C3×Dic3—21no—
74C22×C3×Dic3—21no—
75C22×C3×Dic3—21no—
76C22×C3×Dic3—22no—
77C22×C3×Dic3—22no—
78C22×C3×Dic3—22no—
79C22×C3×Dic3C2312yescomplemented
80C3×#217—21no—
81C3×#217—24no—
82C3×#217—22no—
83C3×#217C2312yescomplemented
84C3×#217C2314yescomplemented
85C3×Dic3⋊C4—24no—
86Dic3⋊Dic3—28no—
87#3722—28no—
88C2×#458—91noSylow
89C22×C3×D4—21no—
90C22×C3×D4C2×D311yescharacteristic
91C22×C3×D4C2×D311yescharacteristic
92C23×C3×C4—31no—
93C22×#67—32no—
94C22×#67—32no—
95C22×#67—62no—
96C22×#67—62no—
97C22×#67—61no—
98C22×#67—61no—
99C23×Dic3C2×D311yescharacteristic, complemented
100#1004—34no—
101#1004—34no—
102#1004—64no—
103#1004—64no—
104#1004—64no—
105#1004—68no—
106#1004—64no—
107#1004—62no—
108#1004—62no—
109C2×#237—62no—
110C2×#237—62no—
111C2×#237—64no—
112C2×D3×D4—62no—
113C2×D3×D4—62no—
114C2×D3×D4—64no—
115C2×#235—62no—
116C2×#235—61no—
117C2×#235—61no—
118C3×#123—34no—
119C3×#123—62no—
120C2×C3×C4⋊C4—61no—
121C2×C3×C22⋊C4—31no—
122C2×C3×C22⋊C4—32no—
123C2×C3×C22⋊C4—61no—
124C2×#217—21no—
125C2×#217C2×D311yescharacteristic, complemented
126C2×#217C2×D312yescomplemented
127#935—22no—
128#935C2×D314yescomplemented
129#929—38no—
130#929—64no—
131C2×(C2×D3)⋊C4—62no—
132C2×(C2×D3)⋊C4—62no—
133C2×C4⋊Dic3—62no—
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—62no—
136#886—38no—
137#886—64no—
138C3×#99—34no—
139#834C2×D314yescomplemented
140#806—38no—
141#806—38no—
142C23×C32—21no—
143C23×C32—21no—
144C23×C32—42no—
145C23×C32—42no—
146C23×C32C2×D411yescharacteristic
147C23×C32C2×D412yes—
148C23×C32C2×D411yescharacteristic
149C23×C32C2×D412yes—
150C23×C32C2×D412yes—
151C23×C32C2411yescharacteristic
152C22×C3⋊D3—22no—
153C22×C3⋊D3—24no—
154C22×C3⋊D3—22no—
155C22×C3⋊D3—44no—
156C22×C3⋊D3—82no—
157C22×C3⋊D3C2×D414yes—
158C32×D4—24no—
159C32×D4—24no—
160C2×C32×C4—21no—
161C2×C32×C4—21no—
162C2×C32×C4C2×D412yes—
163#638—28no—
164#638—24no—
165#638—24no—
166#638—24no—
167#638—24no—
168C2×C3⋊Dic3—24no—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3C2×D414yes—
172C4⋊(C3⋊D3)—24no—
173C4×C3⋊D3—28no—
174#634—24no—
175C2×C3×Dic3—24no—
176C2×C3×Dic3—24no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—44no—
180C2×C3×Dic3—42no—
181C2×C3×Dic3—42no—
182C2×C3×Dic3—41no—
183C2×C3×Dic3—41no—
184C2×H(5,𝔽2)—91no—
185C2×#123—31no—
186C2×#123—92no—
187#458—98no—
188C2×#99—31no—
189C2×#99—92no—
190C24×C3—21no—
191C24×C3—21no—
192C24×C3D1211yescharacteristic
193C24×C3#6711yescharacteristic
194C24×C3C22×D311yescharacteristic
195C24×C3C22×D311yescharacteristic
196C23×D3—32no—
197C23×D3—32no—
198C23×D3—62no—
199C23×D3—62no—
200C23×D3—61no—
201C23×D3—61no—
202C2×C3×D4—24no—
203C2×C3×D4—24no—
204C2×C3×D4—22no—
205C2×C3×D4—22no—
206C2×C3×D4—22no—
207C2×C3×D4—22no—
208C2×C3×D4—22no—
209C2×C3×D4—22no—
210C2×C3×D4D1212yes—
211C2×C3×D4#6712yes—
212C2×C3×D4C22×D312yes—
213C2×C3×D4C22×D312yes—
214C22×C3×C4—21no—
215C22×C3×C4—32no—
216C22×C3×C4—61no—
217C22×C3×C4—61no—
218C22×C3×C4—61no—
219C22×C3×C4—62no—
220C22×C3×C4—62no—
221C22×C3×C4—62no—
222C22×C3×C4D1211yescharacteristic
223C22×C3×C4#6711yescharacteristic
224C2×#67—34no—
225C2×#67—34no—
226C2×#67—34no—
227C2×#67—34no—
228C2×#67—64no—
229C2×#67—64no—
230C2×#67—64no—
231C2×#67—64no—
232C2×#67—62no—
233C2×#67—62no—
234C2×#67—64no—
235C2×#67—68no—
236C2×#67—64no—
237C2×#67—64no—
238C2×#67—64no—
239C2×#67—68no—
240C2×#67—64no—
241C2×#67—62no—
242C2×#67—64no—
243C2×#67—62no—
244C2×#67—62no—
245C2×#67—62no—
246C2×#67—62no—
247C2×#67—62no—
248C2×#67—62no—
249C2×#67—64no—
250C2×#67—62no—
251C22×Dic3—22no—
252C22×Dic3—22no—
253C22×Dic3—22no—
254C22×Dic3—21no—
255C22×Dic3—21no—
256C22×Dic3—21no—
257C22×Dic3—32no—
258C22×Dic3—32no—
259C22×Dic3—62no—
260C22×Dic3—62no—
261C22×Dic3—61no—
262C22×Dic3—61no—
263C22×Dic3C22×D312yescomplemented
264#237—68no—
265#237—68no—
266#237—616no—
267#237—616no—
268#237—68no—
269#237—68no—
270D3×D4—68no—
271D3×D4—68no—
272D3×D4—616no—
273D3×D4—616no—
274D3×D4—68no—
275D3×D4—68no—
276#235—68no—
277#235—64no—
278#235—64no—
279#235—68no—
280#235—64no—
281#235—64no—
282C2×D12—62no—
283C2×D12—61no—
284C2×D12—61no—
285C2×C4×D3—64no—
286C2×C4×D3—62no—
287C2×C4×D3—62no—
288C2×Dic6—62no—
289C2×Dic6—61no—
290C2×Dic6—61no—
291C3×C4⋊C4—64no—
292C3×C22⋊C4—32no—
293C3×C22⋊C4—34no—
294C3×C22⋊C4—61no—
295C3×C22⋊C4—64no—
296C3×C22⋊C4—62no—
297#217—22no—
298#217—21no—
299#217—24no—
300#217C22×D312yescomplemented
301#217C22×D314yescomplemented
302(C2×D3)⋊C4—68no—
303(C2×D3)⋊C4—68no—
304C4⋊Dic3—68no—
305Dic3⋊C4—24no—
306Dic3⋊C4—68no—
307C22×C32—22no—
308C22×C32—24no—
309C22×C32—22no—
310C22×C32—42no—
311C22×C32—41no—
312C22×C32—42no—
313C22×C32—41no—
314C22×C32—42no—
315C22×C32—81no—
316C22×C32#12012yes—
317C22×C32#12011yescharacteristic
318C22×C32#12011yescharacteristic
319C22×C32C22×D411yescharacteristic
320C22×C32C22×D412yes—
321C2×C3⋊D3—24no—
322C2×C3⋊D3—44no—
323C2×C3⋊D3—44no—
324C2×C3⋊D3—82no—
325C2×C3⋊D3—84no—
326C32×C4—22no—
327C3⋊Dic3—24no—
328C3×Dic3—44no—
329C3×Dic3—42no—
330C3×Dic3—42no—
331H(5,𝔽2)—94no—
332H(5,𝔽2)—184no—
333H(5,𝔽2)—182no—
334C2×#41—182no—
335C2×#41—181no—
336C22×D4—92no—
337C22×D4—182no—
338C22×D4—181no—
339C22×D4D3211yescharacteristic
340C23×C4—31no—
341#123—34no—
342#123—62no—
343#123—98no—
344#123—184no—
345C2×C4⋊C4—61no—
346C2×C4⋊C4—182no—
347C2×C22⋊C4—31no—
348C2×C22⋊C4—32no—
349C2×C22⋊C4—61no—
350C2×C22⋊C4—182no—
351#99—34no—
352#99—98no—
353C23×C3—22no—
354C23×C3—22no—
355C23×C3—21no—
356C23×C3—21no—
357C23×C3—21no—
358C23×C3—21no—
359C23×C3—21no—
360C23×C3—21no—
361C23×C3—22no—
362C23×C3—21no—
363C23×C3—22no—
364C23×C3—22no—
365C23×C3—42no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3—82no—
370C23×C3—82no—
371C23×C3C2×D1211yescharacteristic
372C23×C3C2×D1212yes—
373C23×C3C2×D1211yescharacteristic
374C23×C3D3×D412yes—
375C23×C3D3×D412yes—
376C23×C3D3×D412yes—
377C23×C3D3×D412yes—
378C23×C3C2×#6711yescharacteristic
379C23×C3C2×#6712yes—
380C23×C3C2×#6711yescharacteristic
381C23×C3C23×D311yescharacteristic
382C23×C3C23×D311yescharacteristic
383C22×D3—34no—
384C22×D3—34no—
385C22×D3—64no—
386C22×D3—64no—
387C22×D3—62no—
388C22×D3—62no—
389C22×D3—68no—
390C22×D3—64no—
391C22×D3—64no—
392C22×D3—64no—
393C22×D3—62no—
394C22×D3—62no—
395C22×D3—124no—
396C22×D3—124no—
397C22×D3—244no—
398C22×D3—244no—
399C22×D3—242no—
400C22×D3—242no—
401C3×D4—28no—
402C3×D4—28no—
403C3×D4—24no—
404C3×D4—24no—
405C3×D4—24no—
406C3×D4—24no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—22no—
414C2×C3×C4—62no—
415C2×C3×C4—62no—
416C2×C3×C4—64no—
417C2×C3×C4—64no—
418C2×C3×C4—122no—
419C2×C3×C4—124no—
420C2×C3×C4—122no—
421C2×C3×C4—121no—
422C2×C3×C4—121no—
423C2×C3×C4C2×D1212yes—
424C2×C3×C4C2×#6712yes—
425#67—68no—
426#67—68no—
427#67—616no—
428#67—68no—
429#67—68no—
430#67—68no—
431#67—68no—
432#67—64no—
433#67—64no—
434#67—64no—
435#67—64no—
436#67—64no—
437#67—64no—
438#67—64no—
439#67—64no—
440C2×Dic3—24no—
441C2×Dic3—24no—
442C2×Dic3—22no—
443C2×Dic3—22no—
444C2×Dic3—34no—
445C2×Dic3—34no—
446C2×Dic3—44no—
447C2×Dic3—42no—
448C2×Dic3—42no—
449C2×Dic3—41no—
450C2×Dic3—41no—
451C2×Dic3—64no—
452C2×Dic3—64no—
453C2×Dic3—68no—
454C2×Dic3—64no—
455C2×Dic3—64no—
456C2×Dic3—64no—
457C2×Dic3—62no—
458C2×Dic3—62no—
459C2×Dic3—62no—
460C2×Dic3—62no—
461D12—68no—
462D12—64no—
463D12—64no—
464C4×D3—616no—
465C4×D3—68no—
466C4×D3—68no—
467Dic6—68no—
468Dic6—64no—
469Dic6—64no—
470C2×C32—22no—
471C2×C32—21no—
472C2×C32—22no—
473C2×C32—21no—
474C2×C32—42no—
475C2×C32#45812yescomplemented
476C2×C32C2×#12011yescharacteristic
477C3⋊D3—44no—
478C24—92no—
479C24—181no—
480C24#62611yescharacteristic
481C24C2×D3211yescharacteristic
482#41—184no—
483#41—188no—
484#41—188no—
485#41—184no—
486C2×Q8—181no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—94no—
490C2×D4—94no—
491C2×D4—181no—
492C2×D4—188no—
493C2×D4—188no—
494C2×D4—182no—
495C2×D4—184no—
496C2×D4—182no—
497C2×D4—182no—
498C2×D4—184no—
499C2×D4—182no—
500C2×D4—182no—
501C2×D4#62612yes—
502C2×D4C2×D3212yes—
503C22×C4—32no—
504C22×C4—61no—
505C22×C4—61no—
506C22×C4—61no—
507C22×C4—62no—
508C22×C4—62no—
509C22×C4—62no—
510C22×C4—92no—
511C22×C4—182no—
512C22×C4—181no—
513C22×C4#62611yescharacteristic
514C4⋊C4—64no—
515C4⋊C4—188no—
516C22⋊C4—34no—
517C22⋊C4—32no—
518C22⋊C4—61no—
519C22⋊C4—64no—
520C22⋊C4—62no—
521C22⋊C4—188no—
522C22×C3—24no—
523C22×C3—22no—
524C22×C3—22no—
525C22×C3—24no—
526C22×C3—24no—
527C22×C3—22no—
528C22×C3—22no—
529C22×C3—21no—
530C22×C3—22no—
531C22×C3—22no—
532C22×C3—21no—
533C22×C3—21no—
534C22×C3—44no—
535C22×C3—42no—
536C22×C3—41no—
537C22×C3—42no—
538C22×C3—42no—
539C22×C3—41no—
540C22×C3—41no—
541C22×C3—41no—
542C22×C3—42no—
543C22×C3—42no—
544C22×C3—44no—
545C22×C3—42no—
546C22×C3—42no—
547C22×C3—81no—
548C22×C3—81no—
549C22×C3—82no—
550C22×C3—82no—
551C22×C3—81no—
552C22×C3—81no—
553C22×C3—82no—
554C22×C3#88212yes—
555C22×C3#88211yescharacteristic
556C22×C3#88211yescharacteristic
557C22×C3#93712yes—
558C22×C3#93711yescharacteristic
559C22×C3#93711yescharacteristic
560C22×C3C22×D1211yescharacteristic
561C22×C3C2×D3×D412yes—
562C22×C3C2×D3×D412yes—
563C22×C3C22×#6711yescharacteristic
564C2×D3—68no—
565C2×D3—64no—
566C2×D3—64no—
567C2×D3—128no—
568C2×D3—124no—
569C2×D3—124no—
570C2×D3—124no—
571C2×D3—124no—
572C2×D3—244no—
573C2×D3—242no—
574C2×D3—242no—
575C2×D3—244no—
576C2×D3—248no—
577C2×D3—244no—
578C2×D3—244no—
579C3×C4—24no—
580C3×C4—22no—
581C3×C4—22no—
582C3×C4—122no—
583C3×C4—124no—
584C3×C4—122no—
585Dic3—44no—
586Dic3—42no—
587Dic3—42no—
588Dic3—68no—
589Dic3—64no—
590Dic3—64no—
591C32C2×#45811yescharacteristic, complemented, Sylow
592C23—21no—
593C23—21no—
594C23—42no—
595C23—42no—
596C23—94no—
597C23—184no—
598C23—182no—
599C23—182no—
600C23—364no—
601C23—722no—
602C23C2×#62611yescharacteristic
603C23C2×#62612yes—
604C23C2×#62611yescharacteristic
605C23#381112yes—
606C23#381112yes—
607C23C22×D3211yescharacteristic
608Q8—184no—
609D4—24no—
610D4—24no—
611D4—184no—
612D4—188no—
613D4—184no—
614D4—184no—
615D4—184no—
616D4—184no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—62no—
620C2×C4—62no—
621C2×C4—64no—
622C2×C4—64no—
623C2×C4—94no—
624C2×C4—122no—
625C2×C4—124no—
626C2×C4—121no—
627C2×C4—122no—
628C2×C4—121no—
629C2×C4—188no—
630C2×C4—184no—
631C2×C4—182no—
632C2×C4—182no—
633C2×C4C2×#62612yes—
634C2×C3—22no—
635C2×C3—21no—
636C2×C3—22no—
637C2×C3—21no—
638C2×C3—21no—
639C2×C3—22no—
640C2×C3—22no—
641C2×C3—21no—
642C2×C3—22no—
643C2×C3—21no—
644C2×C3—42no—
645C2×C3—42no—
646C2×C3—41no—
647C2×C3—41no—
648C2×C3—44no—
649C2×C3—42no—
650C2×C3—42no—
651C2×C3#474212yescomplemented
652C2×C3#505312yescomplemented
653C2×C3C2×#88211yescharacteristic
654C2×C3C2×#93711yescharacteristic
655D3—128no—
656D3—124no—
657D3—124no—
658C22—22no—
659C22—24no—
660C22—22no—
661C22—41no—
662C22—41no—
663C22—42no—
664C22—42no—
665C22—42no—
666C22—81no—
667C22—184no—
668C22—364no—
669C22—364no—
670C22—722no—
671C22—724no—
672C22#6398111yescharacteristic
673C22#6398112yes—
674C22#6398111yescharacteristic
675C22C22×#62611yescharacteristic
676C22C2×#381112yes—
677C4—22no—
678C4—122no—
679C4—124no—
680C4—122no—
681C4—184no—
682C3—21no—
683C3C2×#474211yescharacteristic, complemented
684C3C2×#505311yescharacteristic, complemented
685C2—21no—
686C2—22no—
687C2—21no—
688C2—22no—
689C2—42no—
690C2—364no—
691C2#1059153512yesdirect product factor
692C2C2×#6398111yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC22×C32×D4C22
socleC22×C32#120
prime radicalC2×#64361C2
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×#63966C2semidirect
4. C2×C3×#834C2semidirect
5. C2×#63581C2semidirect
6. #10591535C2direct (N × H)
18. C23×C3×Dic3C22semidirect
20. C2×C3×#217C22semidirect
21. C2×C3×#217C22semidirect
23. C3×#935C22semidirect
26. #63966C22semidirect
29. C3×#834C22semidirect
30. #63581C22semidirect
35. C2×#935D3semidirect
39. C2×#834D3semidirect
79. C22×C3×Dic3C23semidirect
83. C3×#217C23semidirect
84. C3×#217C23semidirect
99. C23×Dic3C2×D3semidirect
125. C2×#217C2×D3semidirect
126. C2×#217C2×D3semidirect
128. #935C2×D3semidirect
139. #834C2×D3semidirect
263. C22×Dic3C22×D3semidirect
300. #217C22×D3semidirect
301. #217C22×D3semidirect
475. C2×C32#458semidirect
591. C32C2×#458semidirect
651. C2×C3#4742semidirect
652. C2×C3#5053semidirect
683. C3C2×#4742semidirect
684. C3C2×#5053semidirect
691. C2#10591535direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643612
C2×C3×#9352
C2×#639662
C2×C3×#8342
C2×#635812
#105915352
C2×#50533
C2×#47423