Finite Group Databasebeta

← C2×#10591458 #11863577

Subgroups — C2×#10591458 #11863577

Order 1152.

2093 conjugacy classes of subgroups.

The subgroup lattice has 641 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×D4C211yesmaximal, characteristic
2C22×C3×#214C211yesmaximal, characteristic, complemented
3C2×#63856C211yesmaximal, characteristic, complemented
4C22×#3715C211yesmaximal, characteristic, complemented
5C2×#63659C211yesmaximal, characteristic, complemented
6#10591458C218yesmaximal, direct product factor
7C2×#63563C211yesmaximal, characteristic, complemented
8C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
9C2×#5218—31nomaximal
10C2×#5169—31nomaximal
11C24×C3×D3—21no—
12C22×C32×D4C2211yescharacteristic
13C22×C3×#67—21no—
14C2×C3×D3×D4—24no—
15C2×C3×D3×D4—24no—
16C2×C3×D3×D4—22no—
17C2×C3×D3×D4C2214yes—
18C22×C3×D12C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic, complemented
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
22C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
23C2×C3×#214—24no—
24C2×C3×#214C2214yescomplemented
25C22×C3×C3⋊C8C2211yescharacteristic, complemented
26C2×#3724—21no—
27C2×(C2×D3)⋊Dic3—21no—
28#63856—22no—
29#63856C2214yescomplemented
30C2×#3715—24no—
31C2×#3715C2214yescomplemented
32#63659C2214yescomplemented
33#63563C2214yescomplemented
34(C2×D3)⋊(C3⋊C8)C2214yescomplemented
35C23×C3×D4—31no—
36C22×D3×D4D311yescharacteristic
37C22×C3×SD16—31no—
38C2×#946—31no—
39C22×#215—31no—
40C22×#214—31no—
41C22×#214D311yescharacteristic, complemented
42C2×#924—31no—
43#5218—38no—
44C2×#832—31no—
45C2×#832—31no—
46C2×#832—31no—
47C2×#832—61no—
48C2×#830—31no—
49#5169—38no—
50C2×#821—31no—
51C2×(C2×D3)⋊C8—31no—
52C24×C32—21no—
53C23×C3×D3—28no—
54C23×C3×D3—21no—
55C23×C3×D3—24no—
56C23×C3×D3—44no—
57C23×C3×D3—44no—
58C23×C3×D3D411yescharacteristic
59C2×C32×D4—21no—
60C2×C32×D4—22no—
61C2×C32×D4D414yes—
62C2×C32×D4C2312yes—
63C22×C32×C4C2311yescharacteristic
64C22×C3⋊Dic3—21no—
65C2×C3×#67—28no—
66C2×C3×#67—24no—
67C22×C3×Dic3—21no—
68C22×C3×Dic3D411yescharacteristic
69C3×D3×D4—216no—
70C3×D3×D4—28no—
71C3×D3×D4—28no—
72C2×C3×D12—21no—
73C2×C3×D12—22no—
74C2×C3×D12D414yes—
75C2×C3×D12C2312yes—
76C2×C3×C4×D3—22no—
77C2×C3×C4×D3—22no—
78C2×C3×C4×D3D412yes—
79C2×C3×C4×D3C2312yes—
80C2×C3×Dic6—22no—
81C2×C3×Dic6—22no—
82C2×C3×Dic6—21no—
83C2×C3×Dic6C2312yescomplemented
84C4⋊(C3⋊Dic3)—21no—
85C4⋊(C3⋊Dic3)C2312yescomplemented
86C2×C3⋊(C3⋊C8)—22no—
87C2×C3⋊(C3⋊C8)C2312yescomplemented
88C3×#214—28no—
89C2×C3×C3⋊C8—22no—
90C2×C3×C3⋊C8C2312yescomplemented
91#3724—24no—
92(C2×D3)⋊Dic3—24no—
93#3715—28no—
94C2×#450—91noSylow
95C25×C3—61no—
96C24×D3—21no—
97C22×C3×Q8—31no—
98C22×C3×D4—21no—
99C22×C3×D4—34no—
100C22×C3×D4—31no—
101C22×C3×D4—62no—
102C22×C3×D4—61no—
103C22×C3×D4—64no—
104C22×C3×D4—64no—
105C22×C3×D4C2×D311yescharacteristic
106C22×C3×D4C2×D311yescharacteristic
107C23×C3×C4—31no—
108C22×#67—21no—
109C2×D3×D4—24no—
110C2×D3×D4—24no—
111C2×D3×D4—22no—
112C2×D3×D4C2×D314yes—
113C22×D12C2×D311yescharacteristic
114C22×C4×D3C2×D311yescharacteristic
115C22×Dic6C2×D311yescharacteristic, complemented
116C2×C3×SD16—34no—
117C2×C3×SD16—64no—
118C22×C3×C8—31no—
119C2×#217—61no—
120#946—34no—
121#946—62no—
122C2×#215—34no—
123C2×#215—64no—
124C2×#214—24no—
125C2×#214—34no—
126C2×#214—64no—
127C2×#214C2×D314yescomplemented
128C2×(C2×D3)⋊C4—61no—
129C2×C4⋊Dic3—31no—
130C2×C4⋊Dic3—31no—
131C2×C4⋊Dic3—61no—
132#924—34no—
133#924—62no—
134C2×Dic3⋊C4—61no—
135C2×Dic3⋊C4—61no—
136C22×C3⋊C8—31no—
137C22×C3⋊C8—31no—
138C22×C3⋊C8—61no—
139C22×C3⋊C8C2×D311yescharacteristic, complemented
140#832—34no—
141#832—34no—
142#832—34no—
143#832—64no—
144#830—34no—
145#821—34no—
146(C2×D3)⋊C8—34no—
147C23×C32—24no—
148C23×C32—22no—
149C23×C32—42no—
150C23×C32—42no—
151C23×C32C2×D411yescharacteristic
152C22×C3×D3—22no—
153C22×C3×D3—22no—
154C22×C3×D3—216no—
155C22×C3×D3—24no—
156C22×C3×D3—22no—
157C22×C3×D3—48no—
158C22×C3×D3—432no—
159C22×C3×D3—42no—
160C22×C3×D3—42no—
161C22×C3×D3—48no—
162C22×C3×D3SD1614yescomplemented
163C22×C3×D3C2×D412yes—
164C32×D4—24no—
165C32×D4—22no—
166C32×D4C2×D414yes—
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D412yes—
169C2×C32×C4C2×D412yes—
170C2×C32×C4C2411yescharacteristic
171C2×C3⋊Dic3—22no—
172C2×C3⋊Dic3—42no—
173C3×#67—216no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—42no—
177C2×C3×Dic3C2×D412yes—
178C3×D12—24no—
179C3×D12—22no—
180C3×D12C2×D414yes—
181C3×C4×D3—24no—
182C3×C4×D3—22no—
183C3×C4×D3—22no—
184C3×Dic6—22no—
185C3×Dic6—22no—
186C3×Dic6—42no—
187C3⋊(C3⋊C8)—22no—
188C3×C3⋊C8—22no—
189C23×D4—31no—
190C22×SD16—31no—
191C22×SD16—91no—
192C2×C22⋊Q8—91no—
193#450—98no—
194C2×#102—91no—
195C2×#102—91no—
196C2×C22⋊C8—91no—
197C24×C3—21no—
198C24×C3—21no—
199C24×C3—31no—
200C24×C3—41no—
201C24×C3—64no—
202C24×C3—68no—
203C24×C3—61no—
204C24×C3—124no—
205C24×C3—124no—
206C23×D3—28no—
207C23×D3—21no—
208C23×D3—24no—
209C23×D3—44no—
210C23×D3—44no—
211C23×D3#6711yescharacteristic
212C2×C3×Q8—32no—
213C2×C3×Q8—61no—
214C2×C3×Q8—62no—
215C2×C3×Q8—62no—
216C2×C3×D4—21no—
217C2×C3×D4—22no—
218C2×C3×D4—21no—
219C2×C3×D4—22no—
220C2×C3×D4—24no—
221C2×C3×D4—22no—
222C2×C3×D4—34no—
223C2×C3×D4—32no—
224C2×C3×D4—42no—
225C2×C3×D4—41no—
226C2×C3×D4—64no—
227C2×C3×D4—68no—
228C2×C3×D4—616no—
229C2×C3×D4—68no—
230C2×C3×D4—68no—
231C2×C3×D4—61no—
232C2×C3×D4—62no—
233C2×C3×D4#6714yes—
234C2×C3×D4#6714yes—
235C2×C3×D4C22×D312yes—
236C2×C3×D4C22×D312yes—
237C22×C3×C4—21no—
238C22×C3×C4—31no—
239C22×C3×C4—32no—
240C22×C3×C4—32no—
241C22×C3×C4—62no—
242C22×C3×C4—62no—
243C22×C3×C4—61no—
244C22×C3×C4C22×D311yescharacteristic
245C22×C3×C4C22×D311yescharacteristic
246C2×#67—28no—
247C2×#67—24no—
248C22×Dic3—21no—
249C22×Dic3—61no—
250C22×Dic3—61no—
251C22×Dic3—121no—
252C22×Dic3#6711yescharacteristic
253D3×D4—216no—
254D3×D4—28no—
255D3×D4—28no—
256C2×D12—22no—
257C2×D12—21no—
258C2×D12#6714yes—
259C2×D12C22×D312yes—
260C2×C4×D3—22no—
261C2×C4×D3—22no—
262C2×C4×D3#6712yes—
263C2×C4×D3C22×D312yes—
264C2×Dic6—22no—
265C2×Dic6—22no—
266C2×Dic6—21no—
267C2×Dic6C22×D312yescomplemented
268C3×SD16—68no—
269C2×C3×C8—32no—
270C2×C3×C8—62no—
271#217—64no—
272#215—68no—
273#214—28no—
274#214—68no—
275(C2×D3)⋊C4—64no—
276C4⋊Dic3—32no—
277C4⋊Dic3—32no—
278C4⋊Dic3—62no—
279C4⋊Dic3—61no—
280C4⋊Dic3—61no—
281C4⋊Dic3—121no—
282Dic3⋊C4—64no—
283Dic3⋊C4—64no—
284C2×C3⋊C8—22no—
285C2×C3⋊C8—32no—
286C2×C3⋊C8—32no—
287C2×C3⋊C8—62no—
288C2×C3⋊C8—62no—
289C2×C3⋊C8—62no—
290C2×C3⋊C8—122no—
291C2×C3⋊C8C22×D312yescomplemented
292C22×C32—24no—
293C22×C32—42no—
294C22×C32—42no—
295C22×C32—48no—
296C22×C32#12012yes—
297C22×C32C2×SD1612yes—
298C22×C32AGL(1,ℤ/8)12yes—
299C22×C32C22×D411yescharacteristic
300C2×C3×D3—22no—
301C2×C3×D3—22no—
302C2×C3×D3—28no—
303C2×C3×D3—24no—
304C2×C3×D3—432no—
305C2×C3×D3—42no—
306C2×C3×D3—42no—
307C2×C3×D3—48no—
308C2×C3×D3C2×SD1614yescomplemented
309C32×C4#12012yes—
310C32×C4C22×D411yescharacteristic
311C32×C4C22×D411yescharacteristic
312C3⋊Dic3—42no—
313C3×Dic3—22no—
314C3×Dic3—42no—
315C25—61no—
316C22×Q8—31no—
317C22×D4—34no—
318C22×D4—31no—
319C22×D4—62no—
320C22×D4—61no—
321C22×D4—64no—
322C22×D4—64no—
323C22×D4D3211yescharacteristic
324C23×C4—31no—
325C2×SD16—34no—
326C2×SD16—64no—
327C2×SD16—94no—
328C2×SD16—184no—
329C22×C8—31no—
330C22×C8—91no—
331C22⋊Q8—94no—
332C22⋊Q8—182no—
333C2×C4⋊C4—91no—
334C2×C4⋊C4—181no—
335C2×C22⋊C4—181no—
336#102—94no—
337#102—94no—
338C22⋊C8—94no—
339C23×C3—24no—
340C23×C3—24no—
341C23×C3—22no—
342C23×C3—22no—
343C23×C3—21no—
344C23×C3—34no—
345C23×C3—32no—
346C23×C3—42no—
347C23×C3—44no—
348C23×C3—42no—
349C23×C3—42no—
350C23×C3—42no—
351C23×C3—42no—
352C23×C3—616no—
353C23×C3—62no—
354C23×C3—62no—
355C23×C3—64no—
356C23×C3—62no—
357C23×C3—82no—
358C23×C3—82no—
359C23×C3—128no—
360C23×C3—1232no—
361C23×C3—128no—
362C23×C3—122no—
363C23×C3—122no—
364C23×C3D3×D411yescharacteristic
365C23×C3C2×#6711yescharacteristic
366C22×D3—22no—
367C22×D3—22no—
368C22×D3—216no—
369C22×D3—24no—
370C22×D3—22no—
371C22×D3—432no—
372C22×D3—48no—
373C22×D3—42no—
374C22×D3—42no—
375C22×D3—48no—
376C22×D3#21414yescomplemented
377C22×D3C2×#6712yes—
378C3×Q8—62no—
379C3×Q8—62no—
380C3×Q8—122no—
381C3×D4—24no—
382C3×D4—24no—
383C3×D4—22no—
384C3×D4—22no—
385C3×D4—24no—
386C3×D4—34no—
387C3×D4—42no—
388C3×D4—44no—
389C3×D4—616no—
390C3×D4—64no—
391C3×D4—62no—
392C3×D4C2×#6714yes—
393C3×D4C2×#6714yes—
394C2×C3×C4—21no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—21no—
398C2×C3×C4—32no—
399C2×C3×C4—62no—
400C2×C3×C4—64no—
401C2×C3×C4—62no—
402C2×C3×C4—62no—
403C2×C3×C4—62no—
404C2×C3×C4—122no—
405C2×C3×C4D3×D411yescharacteristic
406C2×C3×C4D3×D412yes—
407C2×C3×C4C2×#6712yes—
408C2×C3×C4C2×#6712yes—
409C2×C3×C4C2×#6711yescharacteristic
410C2×C3×C4C2×#6712yes—
411C2×C3×C4C23×D311yescharacteristic
412C2×C3×C4C23×D311yescharacteristic
413#67—216no—
414C2×Dic3—22no—
415C2×Dic3—22no—
416C2×Dic3—42no—
417C2×Dic3—62no—
418C2×Dic3—62no—
419C2×Dic3—122no—
420C2×Dic3—122no—
421C2×Dic3—122no—
422C2×Dic3—242no—
423C2×Dic3C2×#6712yes—
424D12—24no—
425D12—22no—
426D12C2×#6714yes—
427C4×D3—24no—
428C4×D3—22no—
429C4×D3—22no—
430Dic6—22no—
431Dic6—22no—
432Dic6—42no—
433C3×C8—62no—
434C3⋊C8—22no—
435C3⋊C8—62no—
436C3⋊C8—62no—
437C3⋊C8—122no—
438C2×C32—44no—
439C2×C32#45014yescomplemented
440C2×C32C2×#12011yescharacteristic
441C2×C32C22×SD1611yescharacteristic
442C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
443C3×D3—24no—
444C3×D3—44no—
445C24—21no—
446C24—31no—
447C24—64no—
448C24—68no—
449C24—61no—
450C24—124no—
451C24—124no—
452C2×Q8—32no—
453C2×Q8—61no—
454C2×Q8—62no—
455C2×Q8—62no—
456C2×D4—22no—
457C2×D4—21no—
458C2×D4—32no—
459C2×D4—34no—
460C2×D4—64no—
461C2×D4—68no—
462C2×D4—616no—
463C2×D4—68no—
464C2×D4—68no—
465C2×D4—62no—
466C2×D4—61no—
467C2×D4#62514yes—
468C2×D4C2×D3212yes—
469C22×C4—31no—
470C22×C4—32no—
471C22×C4—32no—
472C22×C4—62no—
473C22×C4—62no—
474C22×C4—61no—
475C22×C4—181no—
476C22×C4C2×D3211yescharacteristic
477SD16—68no—
478SD16—188no—
479C2×C8—32no—
480C2×C8—62no—
481C2×C8—92no—
482C2×C8—182no—
483C4⋊C4—92no—
484C4⋊C4—184no—
485C4⋊C4—181no—
486C22⋊C4—184no—
487C22×C3—24no—
488C22×C3—24no—
489C22×C3—21no—
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—22no—
493C22×C3—34no—
494C22×C3—44no—
495C22×C3—48no—
496C22×C3—48no—
497C22×C3—42no—
498C22×C3—42no—
499C22×C3—42no—
500C22×C3—42no—
501C22×C3—68no—
502C22×C3—62no—
503C22×C3—62no—
504C22×C3—64no—
505C22×C3—82no—
506C22×C3—82no—
507C22×C3—88no—
508C22×C3—1232no—
509C22×C3—128no—
510C22×C3—122no—
511C22×C3—122no—
512C22×C3D3×SD1612yes—
513C22×C3#91412yes—
514C22×C3#93212yes—
515C22×C3C2×#21412yes—
516C22×C3#93712yes—
517C22×C3#95312yes—
518C22×C3C2×D3×D411yescharacteristic
519C22×C3C22×#6711yescharacteristic
520C2×D3—28no—
521C2×D3—22no—
522C2×D3—22no—
523C2×D3—24no—
524C2×D3—432no—
525C2×D3—48no—
526C2×D3—42no—
527C2×D3—42no—
528C2×D3C2×#21414yescomplemented
529C3×C4—21no—
530C3×C4—21no—
531C3×C4—22no—
532C3×C4—62no—
533C3×C4—122no—
534C3×C4#93712yes—
535C3×C4#95312yes—
536C3×C4C2×D3×D411yescharacteristic
537C3×C4C22×#6711yescharacteristic
538C3×C4C22×#6711yescharacteristic
539C3×C4C22×#6711yescharacteristic
540Dic3—22no—
541Dic3—42no—
542Dic3—122no—
543Dic3—122no—
544Dic3—242no—
545C32C2×#45011yescharacteristic, complemented, Sylow
546C23—22no—
547C23—24no—
548C23—32no—
549C23—34no—
550C23—42no—
551C23—42no—
552C23—616no—
553C23—62no—
554C23—62no—
555C23—62no—
556C23—64no—
557C23—128no—
558C23—128no—
559C23—1232no—
560C23—122no—
561C23—122no—
562C23D3×#6711yescharacteristic
563Q8—62no—
564Q8—62no—
565Q8—122no—
566D4—22no—
567D4—24no—
568D4—34no—
569D4—616no—
570D4—62no—
571D4—64no—
572D4C2×#62514yes—
573C2×C4—32no—
574C2×C4—62no—
575C2×C4—62no—
576C2×C4—62no—
577C2×C4—64no—
578C2×C4—62no—
579C2×C4—122no—
580C2×C4—182no—
581C2×C4—362no—
582C2×C4C2×#62512yes—
583C2×C4D3×#6712yes—
584C2×C4D3×#6711yescharacteristic
585C2×C4C22×D3211yescharacteristic
586C8—62no—
587C8—182no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—24no—
592C2×C3—44no—
593C2×C3—44no—
594C2×C3—64no—
595C2×C3—84no—
596C2×C3—124no—
597C2×C3#516914yescomplemented
598C2×C3#521814yescomplemented
599C2×C3C2×D3×SD1611yescharacteristic
600C2×C3C2×#91411yescharacteristic
601C2×C3C2×#93211yescharacteristic
602C2×C3C22×#21411yescharacteristic
603C2×C3C2×#93711yescharacteristic
604C2×C3C2×#95311yescharacteristic
605D3—24no—
606D3—44no—
607C22—24no—
608C22—34no—
609C22—42no—
610C22—42no—
611C22—48no—
612C22—62no—
613C22—62no—
614C22—68no—
615C22—64no—
616C22—1232no—
617C22—122no—
618C22—122no—
619C22—128no—
620C22D3×#21412yes—
621C22#6393412yes—
622C22#6397612yes—
623C22C2×D3×#6711yescharacteristic
624C4—62no—
625C4—122no—
626C4—362no—
627C4#6397612yes—
628C4C22×#62511yescharacteristic
629C4C2×D3×#6711yescharacteristic
630C3—21no—
631C3C2×#516911yescharacteristic, complemented
632C3C2×#521811yescharacteristic, complemented
633C2—44no—
634C2—64no—
635C2—124no—
636C2#1059145814yesdirect product factor
637C2C2×D3×#21411yescharacteristic
638C2C2×#6393411yescharacteristic
639C2C2×#6397611yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC22×C3×D3×D4C2
hypercenterC22×D4D32
hypocenterC32C2×#450
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C22×C3×#214C2semidirect
3. C2×#63856C2semidirect
4. C22×#3715C2semidirect
5. C2×#63659C2semidirect
6. #10591458C2direct (N × H)
7. C2×#63563C2semidirect
8. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
20. C22×C3×Dic6C22semidirect
21. C2×C4⋊(C3⋊Dic3)C22semidirect
22. C22×C3⋊(C3⋊C8)C22semidirect
24. C2×C3×#214C22semidirect
25. C22×C3×C3⋊C8C22semidirect
29. #63856C22semidirect
31. C2×#3715C22semidirect
32. #63659C22semidirect
33. #63563C22semidirect
34. (C2×D3)⋊(C3⋊C8)C22semidirect
41. C22×#214D3semidirect
83. C2×C3×Dic6C23semidirect
85. C4⋊(C3⋊Dic3)C23semidirect
87. C2×C3⋊(C3⋊C8)C23semidirect
90. C2×C3×C3⋊C8C23semidirect
115. C22×Dic6C2×D3semidirect
127. C2×#214C2×D3semidirect
139. C22×C3⋊C8C2×D3semidirect
162. C22×C3×D3SD16semidirect
267. C2×Dic6C22×D3semidirect
291. C2×C3⋊C8C22×D3semidirect
308. C2×C3×D3C2×SD16semidirect
376. C22×D3#214semidirect
439. C2×C32#450semidirect
528. C2×D3C2×#214semidirect
545. C32C2×#450semidirect
597. C2×C3#5169semidirect
598. C2×C3#5218semidirect
631. C3C2×#5169semidirect
632. C3C2×#5218semidirect
636. C2#10591458direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×D42
C22×C3×#2142
C2×#638562
C22×#37152
C2×#636592
#105914582
C2×#635632
C2×(C2×D3)⋊(C3⋊C8)2
C2×#52183
C2×#51693