Finite Group Databasebeta

← #11864300

Subgroups — #11864300

Order 1152.

1647 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1009C211yesmaximal, characteristic, complemented
2C2×C3×#949C211yesmaximal, characteristic, complemented
3#10595040C211yesmaximal, characteristic, complemented
4C22×#3713C211yesmaximal, characteristic, complemented
5#10592932C211yesmaximal, characteristic, complemented
6#10591586C214yesmaximal, complemented
7#10591447C214yesmaximal, complemented
8#10591086C211yesmaximal, characteristic, complemented
9#10591071C211yesmaximal, characteristic, complemented
10#84101—31nomaximal
11#83947—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C3×#1009—24no—
14C3×#1009—24no—
15C2×C3×#239C2212yescomplemented
16C2×C3×D3×D4—22no—
17C2×C3×D3×D4C2212yescomplemented
18C2×C3×#235—21no—
19C2×C3×#235C2211yescharacteristic
20C22×C3×D12—21no—
21C22×C3×D12C2211yescharacteristic
22C22×C3×D12C2211yescharacteristic, complemented
23#64135C2211yescharacteristic, complemented
24C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
25C3×#949—24no—
26C2×C3×#215C2212yescomplemented
27C2×C3×#213C2212yescomplemented
28C2×C3×#208C2211yescharacteristic, complemented
29#63976—22no—
30#63914—21no—
31#63908C2214yescomplemented
32#63863—21no—
33C2×#3713—24no—
34C2×#3713C2214yescomplemented
35#63662C2212yescomplemented
36#63659C2212yescomplemented
37#63563C2214yescomplemented
38(C2×D3)⋊(C3⋊C8)C2214yescomplemented
39C2×C3×H(5,𝔽2)—31no—
40C2×#1009D311yescharacteristic, complemented
41C2×C3×AGL(1,ℤ/8)—31no—
42#5830—31no—
43C2×#949D311yescharacteristic, complemented
44#5805—31no—
45C22×#213—31no—
46C22×#213—31no—
47#5238—34no—
48#5234—31no—
49#5233—31no—
50#5233—31no—
51#5233—61no—
52#5217—34no—
53#5215—31no—
54#5172—34no—
55#5156—34no—
56#5131—31no—
57#5129—31no—
58C23×C3×D3—21no—
59C23×C3×D3—22no—
60C23×C3×D3—21no—
61C32×#41—22no—
62C32×#41D414yescomplemented
63C2×C32×Q8C2311yescharacteristic
64C2×C32×D4—21no—
65C2×C32×D4C2311yescharacteristic
66C22×C32×C4—21no—
67C22×C32×C4C2311yescharacteristic
68C2×C3×#67—22no—
69C2×C3×#67D412yes—
70C3×#239—24no—
71C3×#239—24no—
72C3×D3×D4—216no—
73C3×D3×D4—24no—
74C3×D3×D4—24no—
75C3×#235—28no—
76C3×#235—22no—
77C3×#235—22no—
78C2×C3×D12—28no—
79C2×C3×D12—22no—
80C2×C3×D12—21no—
81C2×C3×D12—22no—
82C2×C3×D12—22no—
83C2×C3×D12—22no—
84C2×C3×D12—21no—
85C2×C3×D12D411yescharacteristic
86C2×C3×D12D414yescomplemented
87C2×C3×D12C2312yes—
88C2×C3×D12C2312yes—
89C2×C3×C4×D3—22no—
90C2×C3×C4×D3C2312yes—
91C2×C3×Dic6D411yescharacteristic
92C2×#625—24no—
93#3757—21no—
94C4⋊(C3⋊Dic3)C2312yes—
95C4×C3⋊Dic3—21no—
96C2×C3⋊(C3⋊C8)—22no—
97C2×C3⋊(C3⋊C8)C2312yes—
98C3×#215—24no—
99C3×#213—24no—
100C3×#208—22no—
101C2×C3×C3⋊C8C2312yes—
102(C2×D3)⋊Dic3—24no—
103#3713—28no—
104#3008—91noSylow
105C3×H(5,𝔽2)—64no—
106C3×H(5,𝔽2)—64no—
107C2×C3×#41—21no—
108C2×C3×#41—31no—
109C2×C3×#41—32no—
110C2×C3×#41—61no—
111C2×C3×#41C2×D311yescharacteristic
112C2×C3×#41C2×D311yescharacteristic
113C22×C3×D4—32no—
114C22×C3×D4—31no—
115C22×C3×D4—31no—
116C22×C3×D4—61no—
117C22×C3×D4—62no—
118#1009—24no—
119#1009—24no—
120C2×#239C2×D312yescomplemented
121C2×D3×D4—22no—
122C2×D3×D4C2×D312yescomplemented
123C2×#235—21no—
124C2×#235C2×D311yescharacteristic
125C22×D12—21no—
126C22×D12C2×D311yescharacteristic
127C22×D12C2×D311yescharacteristic, complemented
128C3×AGL(1,ℤ/8)—64no—
129C2×C3×SD16—32no—
130C2×C3×D8—32no—
131C2×C3×M16—31no—
132#953—62no—
133#949—24no—
134#947—61no—
135C2×#215C2×D312yescomplemented
136#940—61no—
137#940—61no—
138#938—34no—
139#937—62no—
140#936—61no—
141C2×#213—34no—
142C2×#213—34no—
143C2×#213—64no—
144C2×#213—64no—
145C2×#213C2×D312yescomplemented
146#930—34no—
147#926—31no—
148#926—31no—
149#926—61no—
150C2×#208C2×D311yescharacteristic, complemented
151C22×C3⋊C8—31no—
152C22×C3⋊C8—31no—
153C22×C3⋊C8—61no—
154#835—32no—
155#835—32no—
156#835—62no—
157#832—32no—
158#832—32no—
159#832—34no—
160#832—62no—
161#830—34no—
162#821—34no—
163(C2×D3)⋊C8—34no—
164C23×C32—21no—
165C23×C32C2×D411yescharacteristic
166C22×C3×D3—22no—
167C22×C3×D3—28no—
168C22×C3×D3—24no—
169C22×C3×D3—22no—
170C22×C3×D3—42no—
171C22×C3×D3—84no—
172C22×C3×D3—82no—
173C22×C3×D3—82no—
174C22×C3×D3C2×D412yes—
175C32×Q8—21no—
176C32×Q8C2×D412yes—
177C32×D4—24no—
178C32×D4—21no—
179C32×D4C2×D412yes—
180C2×C32×C4—21no—
181C2×C32×C4—24no—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2×D412yes—
184C2×C32×C4C2×D412yes—
185C2×C32×C4C2411yescharacteristic
186C2×C3⋊Dic3—22no—
187C3×#67—28no—
188C3×#67—24no—
189C2×C3×Dic3C2×D412yes—
190C3×D12—28no—
191C3×D12—22no—
192C3×D12—24no—
193C3×D12—22no—
194C3×D12—22no—
195C3×D12—22no—
196C3×D12—42no—
197C3×D12C2×D414yes—
198C3×C4×D3—28no—
199C3×C4×D3—22no—
200C3×C4×D3—22no—
201C3×Dic6—22no—
202#625—84no—
203C3⋊(C3⋊C8)—22no—
204C3×C3⋊C8—22no—
205C2×H(5,𝔽2)—31no—
206C2×AGL(1,ℤ/8)—31no—
207C22×D8—91no—
208#535—91no—
209#449—94no—
210#447—94no—
211#418—91no—
212#416—91no—
213#408—91no—
214C24×C3—62no—
215C24×C3—61no—
216C24×C3—61no—
217C23×D3—21no—
218C23×D3—22no—
219C23×D3—21no—
220C3×#41—22no—
221C3×#41—22no—
222C3×#41—24no—
223C3×#41—42no—
224C3×#41—68no—
225C3×#41—64no—
226C3×#41—64no—
227C3×#41—62no—
228C3×#41—62no—
229C3×#41#6714yescomplemented
230C3×#41#6714yescomplemented
231C2×C3×Q8—21no—
232C2×C3×Q8—31no—
233C2×C3×Q8C22×D311yescharacteristic
234C2×C3×Q8C22×D311yescharacteristic
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—32no—
239C2×C3×D4—34no—
240C2×C3×D4—31no—
241C2×C3×D4—32no—
242C2×C3×D4—32no—
243C2×C3×D4—41no—
244C2×C3×D4—62no—
245C2×C3×D4—68no—
246C2×C3×D4—62no—
247C2×C3×D4—64no—
248C2×C3×D4—616no—
249C2×C3×D4—64no—
250C2×C3×D4—61no—
251C2×C3×D4—62no—
252C2×C3×D4—62no—
253C2×C3×D4—62no—
254C2×C3×D4—61no—
255C2×C3×D4C22×D311yescharacteristic
256C2×C3×D4C22×D311yescharacteristic
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—32no—
261C22×C3×C4—41no—
262C22×C3×C4—62no—
263C22×C3×C4C22×D311yescharacteristic
264C22×C3×C4C22×D311yescharacteristic
265C2×#67—22no—
266C2×#67—64no—
267C2×#67—64no—
268C2×#67#6712yes—
269#239—24no—
270#239—24no—
271D3×D4—216no—
272D3×D4—24no—
273D3×D4—24no—
274#235—28no—
275#235—22no—
276#235—22no—
277C2×D12—28no—
278C2×D12—22no—
279C2×D12—21no—
280C2×D12—22no—
281C2×D12—22no—
282C2×D12—22no—
283C2×D12—21no—
284C2×D12#6711yescharacteristic
285C2×D12#6714yescomplemented
286C2×D12C22×D312yes—
287C2×D12C22×D312yes—
288C2×C4×D3—22no—
289C2×C4×D3C22×D312yes—
290C2×Dic6#6711yescharacteristic
291C3×SD16—64no—
292C3×D8—64no—
293C3×M16—62no—
294C2×C3×C8—32no—
295#217—61no—
296#217—61no—
297#217—64no—
298#217—121no—
299#215—24no—
300#213—24no—
301#213—68no—
302#213—68no—
303(C2×D3)⋊C4—64no—
304C4⋊Dic3—32no—
305C4⋊Dic3—32no—
306C4⋊Dic3—62no—
307C4×Dic3—61no—
308C4×Dic3—61no—
309C4×Dic3—121no—
310#208—22no—
311C2×C3⋊C8—32no—
312C2×C3⋊C8—32no—
313C2×C3⋊C8—62no—
314C2×C3⋊C8—62no—
315C2×C3⋊C8—62no—
316C2×C3⋊C8—122no—
317C2×C3⋊C8C22×D312yes—
318C22×C32—22no—
319C22×C32—22no—
320C22×C32—42no—
321C22×C32#12012yes—
322C22×C32C22×D411yescharacteristic
323C2×C3×D3—22no—
324C2×C3×D3—24no—
325C2×C3×D3—24no—
326C2×C3×D3—44no—
327C2×C3×D3—42no—
328C2×C3×D3—44no—
329C2×C3×D3—84no—
330C2×C3×D3—88no—
331C2×C3×D3—84no—
332C32×C4—22no—
333C32×C4#12012yes—
334C32×C4C22×D411yescharacteristic
335C32×C4C22×D411yescharacteristic
336C3⋊Dic3—42no—
337C3×Dic3—22no—
338H(5,𝔽2)—64no—
339H(5,𝔽2)—64no—
340C2×#41—31no—
341C2×#41—32no—
342C2×#41—61no—
343C2×#41D3211yescharacteristic
344C22×D4—32no—
345C22×D4—31no—
346C22×D4—31no—
347C22×D4—61no—
348C22×D4—62no—
349AGL(1,ℤ/8)—64no—
350C2×SD16—32no—
351C2×D8—32no—
352C2×D8—94no—
353C2×D8—184no—
354C2×M16—31no—
355C22×C8—91no—
356#127—181no—
357#124—181no—
358#121—94no—
359#120—182no—
360#117—91no—
361#103—92no—
362#102—94no—
363#102—92no—
364C22⋊C8—94no—
365C23×C3—21no—
366C23×C3—21no—
367C23×C3—21no—
368C23×C3—32no—
369C23×C3—41no—
370C23×C3—68no—
371C23×C3—62no—
372C23×C3—64no—
373C23×C3—62no—
374C23×C3—122no—
375C23×C3—242no—
376C23×C3—242no—
377C23×C3—244no—
378C23×C3D3×D411yescharacteristic
379C23×C3C2×#6711yescharacteristic
380C22×D3—22no—
381C22×D3—28no—
382C22×D3—24no—
383C22×D3—22no—
384C22×D3—42no—
385C22×D3—84no—
386C22×D3—82no—
387C22×D3—82no—
388C22×D3C2×#6712yes—
389C3×Q8—21no—
390C3×Q8—21no—
391C3×Q8—22no—
392C3×Q8—41no—
393C3×Q8—62no—
394C3×Q8C2×#6712yes—
395C3×Q8C2×#6712yes—
396C3×D4—24no—
397C3×D4—24no—
398C3×D4—21no—
399C3×D4—21no—
400C3×D4—22no—
401C3×D4—34no—
402C3×D4—41no—
403C3×D4—44no—
404C3×D4—68no—
405C3×D4—68no—
406C3×D4—64no—
407C3×D4—64no—
408C3×D4—62no—
409C3×D4—62no—
410C3×D4—62no—
411C3×D4—62no—
412C3×D4—122no—
413C3×D4C2×#6712yes—
414C3×D4C2×#6712yes—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—24no—
418C2×C3×C4—24no—
419C2×C3×C4—21no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—21no—
423C2×C3×C4—32no—
424C2×C3×C4—44no—
425C2×C3×C4—41no—
426C2×C3×C4—68no—
427C2×C3×C4—62no—
428C2×C3×C4—62no—
429C2×C3×C4D3×D411yescharacteristic
430C2×C3×C4D3×D412yes—
431C2×C3×C4C2×#6712yes—
432C2×C3×C4C2×#6712yes—
433C2×C3×C4C2×#6711yescharacteristic
434C2×C3×C4C2×#6712yes—
435C2×C3×C4C23×D311yescharacteristic
436C2×C3×C4C23×D311yescharacteristic
437#67—28no—
438#67—24no—
439#67—244no—
440#67—244no—
441C2×Dic3—62no—
442C2×Dic3—62no—
443C2×Dic3—122no—
444C2×Dic3C2×#6712yes—
445D12—28no—
446D12—22no—
447D12—24no—
448D12—22no—
449D12—22no—
450D12—22no—
451D12—42no—
452D12C2×#6714yes—
453C4×D3—28no—
454C4×D3—22no—
455C4×D3—22no—
456Dic6—22no—
457C3×C8—62no—
458C3⋊C8—22no—
459C3⋊C8—62no—
460C3⋊C8—62no—
461C3⋊C8—122no—
462C2×C32—22no—
463C2×C32—42no—
464C2×C32C2×#12011yescharacteristic
465C2×C32#57612yes—
466C3×D3—42no—
467C3×D3—44no—
468C3×D3—82no—
469C24—62no—
470C24—61no—
471C24—61no—
472#41—22no—
473#41—68no—
474#41—64no—
475#41—64no—
476#41—62no—
477#41—62no—
478#41#62514yescomplemented
479C2×Q8—31no—
480C2×Q8C2×D3211yescharacteristic
481C2×D4—21no—
482C2×D4—32no—
483C2×D4—32no—
484C2×D4—32no—
485C2×D4—34no—
486C2×D4—31no—
487C2×D4—62no—
488C2×D4—68no—
489C2×D4—62no—
490C2×D4—64no—
491C2×D4—616no—
492C2×D4—64no—
493C2×D4—62no—
494C2×D4—62no—
495C2×D4—61no—
496C2×D4—62no—
497C2×D4—61no—
498C2×D4—184no—
499C2×D4C2×D3211yescharacteristic
500C22×C4—21no—
501C22×C4—32no—
502C22×C4—62no—
503C22×C4C2×D3211yescharacteristic
504SD16—64no—
505D8—64no—
506D8—188no—
507M16—62no—
508C2×C8—32no—
509C2×C8—92no—
510C2×C8—182no—
511C4⋊C4—92no—
512C22⋊C4—184no—
513C22⋊C4—181no—
514C42—181no—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—22no—
519C22×C3—21no—
520C22×C3—22no—
521C22×C3—42no—
522C22×C3—42no—
523C22×C3—42no—
524C22×C3—42no—
525C22×C3—64no—
526C22×C3—64no—
527C22×C3—62no—
528C22×C3—82no—
529C22×C3—124no—
530C22×C3—124no—
531C22×C3—122no—
532C22×C3—244no—
533C22×C3—244no—
534C22×C3—248no—
535C22×C3#93712yes—
536C22×C3#95312yes—
537C22×C3C2×D3×D411yescharacteristic
538C22×C3C22×#6711yescharacteristic
539C2×D3—24no—
540C2×D3—22no—
541C2×D3—24no—
542C2×D3—44no—
543C2×D3—44no—
544C2×D3—42no—
545C2×D3—84no—
546C2×D3—88no—
547C2×D3—84no—
548C3×C4—22no—
549C3×C4—22no—
550C3×C4—21no—
551C3×C4—21no—
552C3×C4—22no—
553C3×C4—42no—
554C3×C4—62no—
555C3×C4#93712yes—
556C3×C4#95312yes—
557C3×C4C2×D3×D411yescharacteristic
558C3×C4C22×#6711yescharacteristic
559C3×C4C22×#6711yescharacteristic
560C3×C4C22×#6711yescharacteristic
561Dic3—22no—
562Dic3—122no—
563Dic3—122no—
564Dic3—242no—
565C32#300811yescharacteristic, complemented, Sylow
566C23—21no—
567C23—32no—
568C23—68no—
569C23—62no—
570C23—64no—
571C23—62no—
572C23—122no—
573C23—242no—
574C23—242no—
575C23—244no—
576C23D3×#6711yescharacteristic
577Q8—21no—
578Q8—62no—
579Q8C2×#62512yes—
580D4—24no—
581D4—21no—
582D4—34no—
583D4—68no—
584D4—68no—
585D4—64no—
586D4—62no—
587D4—62no—
588D4—62no—
589D4—64no—
590D4—62no—
591D4—122no—
592D4—724no—
593D4C2×#62512yes—
594C2×C4—21no—
595C2×C4—24no—
596C2×C4—32no—
597C2×C4—68no—
598C2×C4—62no—
599C2×C4—62no—
600C2×C4—182no—
601C2×C4C2×#62512yes—
602C2×C4D3×#6712yes—
603C2×C4D3×#6711yescharacteristic
604C2×C4C22×D3211yescharacteristic
605C8—62no—
606C8—182no—
607C2×C3—22no—
608C2×C3—22no—
609C2×C3—22no—
610C2×C3—21no—
611C2×C3—42no—
612C2×C3—42no—
613C2×C3—42no—
614C2×C3—82no—
615C2×C3—122no—
616C2×C3—124no—
617C2×C3—242no—
618C2×C3#577412yes—
619C2×C3C2×#93711yescharacteristic
620C2×C3#583512yes—
621C2×C3C2×#95311yescharacteristic
622D3—42no—
623D3—44no—
624D3—82no—
625C22—22no—
626C22—22no—
627C22—42no—
628C22—64no—
629C22—64no—
630C22—62no—
631C22—124no—
632C22—124no—
633C22—122no—
634C22—244no—
635C22—244no—
636C22—248no—
637C22#6397612yes—
638C22C2×D3×#6711yescharacteristic
639C4—22no—
640C4—62no—
641C4—362no—
642C4#6397612yes—
643C4C22×#62511yescharacteristic
644C4C2×D3×#6711yescharacteristic
645C3—21no—
646C3#8394711yescharacteristic, complemented
647C3#8410111yescharacteristic, complemented
648C2—22no—
649C2—42no—
650C2—122no—
651C2—124no—
652C2—242no—
653C2#1059545412yes—
654C2C2×#6397611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3008
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×C3×#949C2semidirect
3. #10595040C2semidirect
4. C22×#3713C2semidirect
5. #10592932C2semidirect
6. #10591586C2semidirect
7. #10591447C2semidirect
8. #10591086C2semidirect
9. #10591071C2semidirect
15. C2×C3×#239C22semidirect
17. C2×C3×D3×D4C22semidirect
22. C22×C3×D12C22semidirect
23. #64135C22semidirect
24. C22×C3⋊(C3⋊C8)C22semidirect
26. C2×C3×#215C22semidirect
27. C2×C3×#213C22semidirect
28. C2×C3×#208C22semidirect
31. #63908C22semidirect
34. C2×#3713C22semidirect
35. #63662C22semidirect
36. #63659C22semidirect
37. #63563C22semidirect
38. (C2×D3)⋊(C3⋊C8)C22semidirect
40. C2×#1009D3semidirect
43. C2×#949D3semidirect
62. C32×#41D4semidirect
86. C2×C3×D12D4semidirect
120. C2×#239C2×D3semidirect
122. C2×D3×D4C2×D3semidirect
127. C22×D12C2×D3semidirect
135. C2×#215C2×D3semidirect
145. C2×#213C2×D3semidirect
150. C2×#208C2×D3semidirect
229. C3×#41#67semidirect
230. C3×#41#67semidirect
285. C2×D12#67semidirect
478. #41#625semidirect
565. C32#3008semidirect
646. C3#83947semidirect
647. C3#84101semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10092
C2×C3×#9492
#105950402
C22×#37132
#105929322
#105915862
#105914472
#105910862
#105910712
#841013
#839473