Finite Group Databasebeta

← C2×#10591459 #11863575

Subgroups — C2×#10591459 #11863575

Order 1152.

2141 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×D4C211yesmaximal, characteristic
2C22×#3754C211yesmaximal, characteristic, complemented
3C2×#63857C211yesmaximal, characteristic, complemented
4C22×#3716C211yesmaximal, characteristic, complemented
5C2×C3×#832C211yesmaximal, characteristic, complemented
6#10591459C218yesmaximal, direct product factor
7C2×#63562C211yesmaximal, characteristic, complemented
8C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
9C2×#5218—31nomaximal
10C2×#4776—31nomaximal
11C24×C3×D3—21no—
12C22×C32×D4C2211yescharacteristic
13C22×#634C2211yescharacteristic, complemented
14C22×C3×#67—21no—
15C2×C3×D3×D4—24no—
16C2×C3×D3×D4—24no—
17C2×C3×D3×D4—22no—
18C2×C3×D3×D4C2214yes—
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C2×#3754—24no—
22C2×#3754C2214yescomplemented
23C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
24C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
25C22×C3×C3⋊C8C2211yescharacteristic, complemented
26C2×Dic3⋊Dic3—21no—
27C2×(C2×D3)⋊Dic3—21no—
28#63857—22no—
29#63857C2214yescomplemented
30C2×#3716—24no—
31C2×#3716C2214yescomplemented
32C3×#832C2214yescomplemented
33#63562C2214yescomplemented
34(C2×D3)⋊(C3⋊C8)C2214yescomplemented
35C23×C3×D4—31no—
36C22×D3×D4D311yescharacteristic
37C22×#214—31no—
38C22×#214—31no—
39C22×#214—31no—
40C22×#214—61no—
41C2×#924—31no—
42C22×#204—31no—
43C2×#897—31no—
44C2×C3×#102—31no—
45#5218—38no—
46C2×#832—31no—
47C2×#832D311yescharacteristic, complemented
48C2×#830—31no—
49C2×(C2×D3)⋊C8—31no—
50C2×#809—31no—
51#4776—38no—
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×#634—22no—
66C2×#634—22no—
67C2×#634—21no—
68C2×#634C2312yescomplemented
69C2×C3×#67—28no—
70C2×C3×#67—24no—
71C22×C3×Dic3—21no—
72C22×C3×Dic3D411yescharacteristic
73C3×D3×D4—216no—
74C3×D3×D4—28no—
75C3×D3×D4—28no—
76C2×C3×D12—21no—
77C2×C3×D12—22no—
78C2×C3×D12D414yes—
79C2×C3×D12C2312yes—
80C2×C3×C4×D3—22no—
81C2×C3×C4×D3—22no—
82C2×C3×C4×D3D412yes—
83C2×C3×C4×D3C2312yes—
84#3754—28no—
85C2×C3⋊(C3⋊C8)—22no—
86C2×C3⋊(C3⋊C8)C2312yescomplemented
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3C2312yescomplemented
89C2×C3×C3⋊C8—22no—
90C2×C3×C3⋊C8C2312yescomplemented
91Dic3⋊Dic3—24no—
92(C2×D3)⋊Dic3—24no—
93#3716—28no—
94C2×#450—91noSylow
95C25×C3—61no—
96C24×D3—21no—
97C22×C3×D4—21no—
98C22×C3×D4—34no—
99C22×C3×D4—31no—
100C22×C3×D4—62no—
101C22×C3×D4—61no—
102C22×C3×D4—64no—
103C22×C3×D4—64no—
104C22×C3×D4C2×D311yescharacteristic
105C22×C3×D4C2×D311yescharacteristic
106C23×C3×C4—31no—
107C22×#67—21no—
108C2×D3×D4—24no—
109C2×D3×D4—24no—
110C2×D3×D4—22no—
111C2×D3×D4C2×D314yes—
112C22×D12C2×D311yescharacteristic
113C22×C4×D3C2×D311yescharacteristic
114C22×Dic6—31no—
115C22×Dic6—31no—
116C22×Dic6—61no—
117C22×C3×C8—31no—
118C2×C3×C4⋊C4—31no—
119C2×#217—61no—
120C2×#214—34no—
121C2×#214—34no—
122C2×#214—34no—
123C2×#214—64no—
124C2×#214—64no—
125C2×#214—68no—
126C2×#214—64no—
127C2×#214—64no—
128C2×(C2×D3)⋊C4—61no—
129C2×C4⋊Dic3—61no—
130C2×C4⋊Dic3C2×D311yescharacteristic, complemented
131#924—34no—
132#924—62no—
133C2×Dic3⋊C4—61no—
134C22×C3⋊C8—31no—
135C22×C3⋊C8—31no—
136C22×C3⋊C8—61no—
137C22×C3⋊C8C2×D311yescharacteristic, complemented
138C2×#204—34no—
139C2×#204—64no—
140#897—34no—
141#897—62no—
142C3×#102—34no—
143#832—34no—
144#832C2×D314yescomplemented
145#830—34no—
146(C2×D3)⋊C8—34no—
147#809—34no—
148C23×C32—24no—
149C23×C32—22no—
150C23×C32—42no—
151C23×C32—42no—
152C23×C32C2×D411yescharacteristic
153C22×C3×D3—22no—
154C22×C3×D3—22no—
155C22×C3×D3—216no—
156C22×C3×D3—24no—
157C22×C3×D3—22no—
158C22×C3×D3—48no—
159C22×C3×D3—432no—
160C22×C3×D3—42no—
161C22×C3×D3—42no—
162C22×C3×D3—48no—
163C22×C3×D3SD1614yescomplemented
164C22×C3×D3C2×D412yes—
165C32×D4—24no—
166C32×D4—22no—
167C32×D4C2×D414yes—
168C2×C32×C4C2×D412yes—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D412yes—
171C2×C32×C4C2411yescharacteristic
172C2×C3⋊Dic3—22no—
173C2×C3⋊Dic3—42no—
174#634—22no—
175#634—22no—
176#634—42no—
177C3×#67—216no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—42no—
181C2×C3×Dic3C2×D412yes—
182C3×D12—24no—
183C3×D12—22no—
184C3×D12C2×D414yes—
185C3×C4×D3—24no—
186C3×C4×D3—22no—
187C3×C4×D3—22no—
188C3⋊(C3⋊C8)—22no—
189C3×C3⋊C8—22no—
190C23×D4—31no—
191C22×SD16—91no—
192C22×SD16—91no—
193C2×C22⋊Q8—91no—
194#450—98no—
195C2×#102—31no—
196C2×#102—91no—
197C2×C22⋊C8—91no—
198C24×C3—21no—
199C24×C3—21no—
200C24×C3—31no—
201C24×C3—41no—
202C24×C3—64no—
203C24×C3—68no—
204C24×C3—61no—
205C24×C3—124no—
206C24×C3—124no—
207C23×D3—28no—
208C23×D3—21no—
209C23×D3—24no—
210C23×D3—44no—
211C23×D3—44no—
212C23×D3#6711yescharacteristic
213C2×C3×D4—21no—
214C2×C3×D4—22no—
215C2×C3×D4—21no—
216C2×C3×D4—22no—
217C2×C3×D4—24no—
218C2×C3×D4—22no—
219C2×C3×D4—34no—
220C2×C3×D4—32no—
221C2×C3×D4—42no—
222C2×C3×D4—41no—
223C2×C3×D4—64no—
224C2×C3×D4—68no—
225C2×C3×D4—616no—
226C2×C3×D4—68no—
227C2×C3×D4—68no—
228C2×C3×D4—62no—
229C2×C3×D4—61no—
230C2×C3×D4D1214yes—
231C2×C3×D4#6714yes—
232C2×C3×D4C22×D312yes—
233C2×C3×D4C22×D312yes—
234C22×C3×C4—21no—
235C22×C3×C4—31no—
236C22×C3×C4—32no—
237C22×C3×C4—32no—
238C22×C3×C4—62no—
239C22×C3×C4—62no—
240C22×C3×C4—61no—
241C22×C3×C4C22×D311yescharacteristic
242C22×C3×C4C22×D311yescharacteristic
243C2×#67—28no—
244C2×#67—24no—
245C22×Dic3—21no—
246C22×Dic3—61no—
247C22×Dic3—61no—
248C22×Dic3—121no—
249C22×Dic3#6711yescharacteristic
250D3×D4—216no—
251D3×D4—28no—
252D3×D4—28no—
253C2×D12—22no—
254C2×D12—21no—
255C2×D12#6714yes—
256C2×D12C22×D312yes—
257C2×C4×D3—22no—
258C2×C4×D3—22no—
259C2×C4×D3#6712yes—
260C2×C4×D3C22×D312yes—
261C2×Dic6—32no—
262C2×Dic6—32no—
263C2×Dic6—62no—
264C2×Dic6—64no—
265C2×Dic6—62no—
266C2×Dic6—62no—
267C2×Dic6—62no—
268C2×Dic6—62no—
269C2×Dic6—61no—
270C2×Dic6—61no—
271C2×Dic6—121no—
272C2×Dic6—122no—
273C2×C3×C8—32no—
274C2×C3×C8—62no—
275C3×C4⋊C4—32no—
276C3×C4⋊C4—61no—
277#217—64no—
278#214—68no—
279#214—616no—
280#214—68no—
281#214—68no—
282(C2×D3)⋊C4—64no—
283C4⋊Dic3—21no—
284C4⋊Dic3—64no—
285C4⋊Dic3C22×D312yescomplemented
286Dic3⋊C4—64no—
287C2×C3⋊C8—22no—
288C2×C3⋊C8—32no—
289C2×C3⋊C8—32no—
290C2×C3⋊C8—62no—
291C2×C3⋊C8—64no—
292C2×C3⋊C8—62no—
293C2×C3⋊C8—62no—
294C2×C3⋊C8C22×D312yescomplemented
295#204—68no—
296C22×C32—24no—
297C22×C32—42no—
298C22×C32—42no—
299C22×C32—48no—
300C22×C32#12012yes—
301C22×C32C2×SD1612yes—
302C22×C32AGL(1,ℤ/8)12yes—
303C22×C32C22×D411yescharacteristic
304C2×C3×D3—22no—
305C2×C3×D3—22no—
306C2×C3×D3—28no—
307C2×C3×D3—24no—
308C2×C3×D3—432no—
309C2×C3×D3—42no—
310C2×C3×D3—42no—
311C2×C3×D3—48no—
312C2×C3×D3C2×SD1614yescomplemented
313C32×C4#12012yes—
314C32×C4C22×D411yescharacteristic
315C32×C4C22×D411yescharacteristic
316C3⋊Dic3—42no—
317C3×Dic3—22no—
318C3×Dic3—42no—
319C25—61no—
320C22×Q8—91no—
321C22×D4—34no—
322C22×D4—31no—
323C22×D4—62no—
324C22×D4—61no—
325C22×D4—64no—
326C22×D4—64no—
327C22×D4D3211yescharacteristic
328C23×C4—31no—
329C2×SD16—94no—
330C2×SD16—94no—
331C2×SD16—184no—
332C2×SD16—184no—
333C22×C8—31no—
334C22×C8—91no—
335C22⋊Q8—94no—
336C22⋊Q8—182no—
337C2×C4⋊C4—31no—
338C2×C4⋊C4—181no—
339C2×C22⋊C4—181no—
340#102—34no—
341#102—94no—
342C22⋊C8—94no—
343C23×C3—24no—
344C23×C3—24no—
345C23×C3—22no—
346C23×C3—22no—
347C23×C3—21no—
348C23×C3—34no—
349C23×C3—32no—
350C23×C3—42no—
351C23×C3—44no—
352C23×C3—42no—
353C23×C3—42no—
354C23×C3—42no—
355C23×C3—42no—
356C23×C3—616no—
357C23×C3—62no—
358C23×C3—62no—
359C23×C3—64no—
360C23×C3—62no—
361C23×C3—82no—
362C23×C3—82no—
363C23×C3—128no—
364C23×C3—128no—
365C23×C3—1232no—
366C23×C3—122no—
367C23×C3—122no—
368C23×C3D3×D411yescharacteristic
369C23×C3C2×#6711yescharacteristic
370C22×D3—22no—
371C22×D3—22no—
372C22×D3—216no—
373C22×D3—24no—
374C22×D3—22no—
375C22×D3—432no—
376C22×D3—48no—
377C22×D3—42no—
378C22×D3—42no—
379C22×D3—48no—
380C22×D3#21414yescomplemented
381C22×D3C2×#6712yes—
382C3×D4—24no—
383C3×D4—24no—
384C3×D4—22no—
385C3×D4—22no—
386C3×D4—24no—
387C3×D4—34no—
388C3×D4—42no—
389C3×D4—44no—
390C3×D4—616no—
391C3×D4—64no—
392C3×D4—62no—
393C3×D4C2×D1214yes—
394C3×D4C2×#6714yes—
395C2×C3×C4—21no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—21no—
399C2×C3×C4—32no—
400C2×C3×C4—62no—
401C2×C3×C4—64no—
402C2×C3×C4—62no—
403C2×C3×C4—62no—
404C2×C3×C4—62no—
405C2×C3×C4—122no—
406C2×C3×C4C2×D1212yes—
407C2×C3×C4D3×D411yescharacteristic
408C2×C3×C4D3×D412yes—
409C2×C3×C4C2×#6712yes—
410C2×C3×C4C2×#6711yescharacteristic
411C2×C3×C4C2×#6712yes—
412C2×C3×C4C23×D311yescharacteristic
413C2×C3×C4C23×D311yescharacteristic
414#67—216no—
415C2×Dic3—22no—
416C2×Dic3—22no—
417C2×Dic3—42no—
418C2×Dic3—62no—
419C2×Dic3—62no—
420C2×Dic3—122no—
421C2×Dic3—124no—
422C2×Dic3—122no—
423C2×Dic3—122no—
424C2×Dic3C2×#6712yes—
425D12—24no—
426D12—22no—
427D12C2×#6714yes—
428C4×D3—24no—
429C4×D3—22no—
430C4×D3—22no—
431Dic6—64no—
432Dic6—62no—
433Dic6—62no—
434Dic6—62no—
435Dic6—62no—
436Dic6—122no—
437Dic6—124no—
438Dic6—122no—
439Dic6—122no—
440C3×C8—62no—
441C3⋊C8—22no—
442C3⋊C8—64no—
443C3⋊C8—62no—
444C3⋊C8—62no—
445C2×C32—44no—
446C2×C32#45014yescomplemented
447C2×C32C2×#12011yescharacteristic
448C2×C32C22×SD1611yescharacteristic
449C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
450C3×D3—24no—
451C3×D3—44no—
452C24—21no—
453C24—31no—
454C24—64no—
455C24—68no—
456C24—61no—
457C24—124no—
458C24—124no—
459C2×Q8—92no—
460C2×Q8—181no—
461C2×Q8—182no—
462C2×Q8—182no—
463C2×D4—22no—
464C2×D4—21no—
465C2×D4—32no—
466C2×D4—34no—
467C2×D4—64no—
468C2×D4—68no—
469C2×D4—616no—
470C2×D4—68no—
471C2×D4—68no—
472C2×D4—62no—
473C2×D4—61no—
474C2×D4#62614yes—
475C2×D4C2×D3212yes—
476C22×C4—31no—
477C22×C4—32no—
478C22×C4—32no—
479C22×C4—62no—
480C22×C4—62no—
481C22×C4—61no—
482C22×C4—181no—
483C22×C4C2×D3211yescharacteristic
484SD16—188no—
485SD16—188no—
486C2×C8—32no—
487C2×C8—62no—
488C2×C8—92no—
489C2×C8—182no—
490C4⋊C4—32no—
491C4⋊C4—61no—
492C4⋊C4—184no—
493C22⋊C4—184no—
494C22×C3—24no—
495C22×C3—24no—
496C22×C3—21no—
497C22×C3—22no—
498C22×C3—22no—
499C22×C3—22no—
500C22×C3—34no—
501C22×C3—44no—
502C22×C3—48no—
503C22×C3—42no—
504C22×C3—42no—
505C22×C3—42no—
506C22×C3—42no—
507C22×C3—48no—
508C22×C3—62no—
509C22×C3—62no—
510C22×C3—68no—
511C22×C3—64no—
512C22×C3—82no—
513C22×C3—82no—
514C22×C3—88no—
515C22×C3—1232no—
516C22×C3—122no—
517C22×C3—122no—
518C22×C3—128no—
519C22×C3#88212yes—
520C22×C3#91112yes—
521C22×C3D3×SD1612yes—
522C22×C3#93212yes—
523C22×C3C2×#21412yes—
524C22×C3#95312yes—
525C22×C3C2×D3×D411yescharacteristic
526C22×C3C22×#6711yescharacteristic
527C2×D3—28no—
528C2×D3—22no—
529C2×D3—22no—
530C2×D3—24no—
531C2×D3—432no—
532C2×D3—48no—
533C2×D3—42no—
534C2×D3—42no—
535C2×D3C2×#21414yescomplemented
536C3×C4—21no—
537C3×C4—21no—
538C3×C4—22no—
539C3×C4—62no—
540C3×C4—122no—
541C3×C4#88212yes—
542C3×C4#95312yes—
543C3×C4C22×D1211yescharacteristic
544C3×C4C2×D3×D411yescharacteristic
545C3×C4C22×#6711yescharacteristic
546C3×C4C22×#6711yescharacteristic
547Dic3—22no—
548Dic3—42no—
549Dic3—124no—
550Dic3—122no—
551Dic3—122no—
552C32C2×#45011yescharacteristic, complemented, Sylow
553C23—22no—
554C23—24no—
555C23—32no—
556C23—34no—
557C23—42no—
558C23—42no—
559C23—616no—
560C23—62no—
561C23—62no—
562C23—62no—
563C23—64no—
564C23—128no—
565C23—128no—
566C23—1232no—
567C23—122no—
568C23—122no—
569C23D3×#6711yescharacteristic
570Q8—182no—
571Q8—182no—
572Q8—362no—
573D4—22no—
574D4—24no—
575D4—34no—
576D4—616no—
577D4—62no—
578D4—64no—
579D4C2×#62614yes—
580C2×C4—32no—
581C2×C4—62no—
582C2×C4—62no—
583C2×C4—62no—
584C2×C4—64no—
585C2×C4—62no—
586C2×C4—122no—
587C2×C4—182no—
588C2×C4—362no—
589C2×C4C2×#62612yes—
590C2×C4D3×#6712yes—
591C2×C4D3×#6711yescharacteristic
592C2×C4C22×D3211yescharacteristic
593C8—62no—
594C8—182no—
595C2×C3—21no—
596C2×C3—21no—
597C2×C3—21no—
598C2×C3—24no—
599C2×C3—44no—
600C2×C3—44no—
601C2×C3—64no—
602C2×C3—84no—
603C2×C3—124no—
604C2×C3#477614yescomplemented
605C2×C3#521814yescomplemented
606C2×C3C2×#88211yescharacteristic
607C2×C3C2×#91111yescharacteristic
608C2×C3C2×D3×SD1611yescharacteristic
609C2×C3C2×#93211yescharacteristic
610C2×C3C22×#21411yescharacteristic
611C2×C3C2×#95311yescharacteristic
612D3—24no—
613D3—44no—
614C22—24no—
615C22—34no—
616C22—42no—
617C22—42no—
618C22—48no—
619C22—62no—
620C22—62no—
621C22—68no—
622C22—64no—
623C22—1232no—
624C22—122no—
625C22—122no—
626C22—128no—
627C22D3×#21412yes—
628C22#6393212yes—
629C22#6397712yes—
630C22C2×D3×#6711yescharacteristic
631C4—62no—
632C4—122no—
633C4—362no—
634C4#6397712yes—
635C4C22×#62611yescharacteristic
636C4C2×D3×#6711yescharacteristic
637C3—21no—
638C3C2×#477611yescharacteristic, complemented
639C3C2×#521811yescharacteristic, complemented
640C2—44no—
641C2—64no—
642C2—124no—
643C2#1059145914yesdirect product factor
644C2C2×D3×#21411yescharacteristic
645C2C2×#6393211yescharacteristic
646C2C2×#6397711yescharacteristic
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×#3754C2semidirect
3. C2×#63857C2semidirect
4. C22×#3716C2semidirect
5. C2×C3×#832C2semidirect
6. #10591459C2direct (N × H)
7. C2×#63562C2semidirect
8. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
13. C22×#634C22semidirect
22. C2×#3754C22semidirect
23. C22×C3⋊(C3⋊C8)C22semidirect
24. C2×C3×C4⋊Dic3C22semidirect
25. C22×C3×C3⋊C8C22semidirect
29. #63857C22semidirect
31. C2×#3716C22semidirect
32. C3×#832C22semidirect
33. #63562C22semidirect
34. (C2×D3)⋊(C3⋊C8)C22semidirect
47. C2×#832D3semidirect
68. C2×#634C23semidirect
86. C2×C3⋊(C3⋊C8)C23semidirect
88. C3×C4⋊Dic3C23semidirect
90. C2×C3×C3⋊C8C23semidirect
130. C2×C4⋊Dic3C2×D3semidirect
137. C22×C3⋊C8C2×D3semidirect
144. #832C2×D3semidirect
163. C22×C3×D3SD16semidirect
285. C4⋊Dic3C22×D3semidirect
294. C2×C3⋊C8C22×D3semidirect
312. C2×C3×D3C2×SD16semidirect
380. C22×D3#214semidirect
446. C2×C32#450semidirect
535. C2×D3C2×#214semidirect
552. C32C2×#450semidirect
604. C2×C3#4776semidirect
605. C2×C3#5218semidirect
638. C3C2×#4776semidirect
639. C3C2×#5218semidirect
643. C2#10591459direct (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×#37542
C2×#638572
C22×#37162
C2×C3×#8322
#105914592
C2×#635622
C2×(C2×D3)⋊(C3⋊C8)2
C2×#52183
C2×#47763