Finite Group Databasebeta

← C2×#10591651 #11863573

Subgroups — C2×#10591651 #11863573

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×D3×D12C211yesmaximal, characteristic
2C22×#3755C211yesmaximal, characteristic, complemented
3C2×C3×#946C211yesmaximal, characteristic, complemented
4C22×C3×#215C211yesmaximal, characteristic, complemented
5#10591651C218yesmaximal, direct product factor
6C2×#63564C211yesmaximal, characteristic, complemented
7C2×#63562C211yesmaximal, characteristic, complemented
8C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
9C2×#5169—31nomaximal
10C2×#5046—31nomaximal
11C23×D32—21no—
12C22×C32×Q8C2211yescharacteristic, complemented
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C22×#626—21no—
17C2×D3×D12—24no—
18C2×D3×D12—24no—
19C2×D3×D12—22no—
20C2×D3×D12C2214yes—
21C2×#3755—24no—
22C2×#3755C2214yescomplemented
23C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
24C3×#946—22no—
25C3×#946C2214yescomplemented
26C2×C3×#215—24no—
27C2×C3×#215C2214yescomplemented
28C2×C3×(C2×D3)⋊C4—21no—
29C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
30C2×C3×Dic3⋊C4—21no—
31C22×C3×C3⋊C8C2211yescharacteristic, complemented
32#63564C2214yescomplemented
33#63562C2214yescomplemented
34(C2×D3)⋊(C3⋊C8)C2214yescomplemented
35C22×D3×D4—31no—
36C23×D12—31no—
37C22×C3×SD16—31no—
38C2×C3×C22⋊Q8—31no—
39C2×#946D311yescharacteristic, complemented
40C22×#215—31no—
41C22×#215—31no—
42C22×#215—61no—
43C22×#215D311yescharacteristic, complemented
44C2×#832—31no—
45C2×#830—31no—
46#5169—38no—
47C2×#821—31no—
48C2×(C2×D3)⋊C8—31no—
49#5046—38no—
50C2×#809—31no—
51C2×#809—31no—
52C23×C3⋊D3—21no—
53C23×C3×D3—21no—
54C23×C3×D3D411yescharacteristic
55C22×D32—28no—
56C22×D32—24no—
57C22×D32—44no—
58C22×D32—44no—
59C2×C32×Q8—21no—
60C2×C32×Q8—22no—
61C2×C32×Q8—22no—
62C2×C32×Q8C2312yescomplemented
63C22×C32×C4—21no—
64C22×C32×C4C2311yescharacteristic
65C2×C4⋊(C3⋊D3)—21no—
66C2×C4⋊(C3⋊D3)—22no—
67C2×C4⋊(C3⋊D3)D414yes—
68C2×C4⋊(C3⋊D3)C2312yes—
69C22×C3×Dic3—21no—
70C22×C3×Dic3D411yescharacteristic
71C2×C3×D12—21no—
72C2×C3×D12—22no—
73C2×C3×D12D414yes—
74C2×C3×D12C2312yes—
75C2×C3×C4×D3—22no—
76C2×C3×C4×D3—22no—
77C2×C3×C4×D3D412yes—
78C2×C3×C4×D3C2312yes—
79C2×#626—28no—
80C2×#626—24no—
81D3×D12—216no—
82D3×D12—28no—
83D3×D12—28no—
84#3755—28no—
85C2×C3⋊(C3⋊C8)—22no—
86C2×C3⋊(C3⋊C8)C2312yescomplemented
87C3×#215—28no—
88C3×(C2×D3)⋊C4—24no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3C2312yescomplemented
91C3×Dic3⋊C4—24no—
92C2×C3×C3⋊C8—22no—
93C2×C3×C3⋊C8C2312yescomplemented
94C2×#450—91noSylow
95C24×D3—61no—
96C24×D3—61no—
97C22×C3×Q8—21no—
98C22×C3×Q8C2×D311yescharacteristic, complemented
99C22×C3×Q8C2×D311yescharacteristic, complemented
100C22×C3×D4—31no—
101C23×C3×C4—31no—
102C22×#67—61no—
103C2×D3×D4—34no—
104C2×D3×D4—64no—
105C2×D3×D4—64no—
106C2×D3×D4—62no—
107C22×D12—31no—
108C22×D12—31no—
109C22×D12—34no—
110C22×D12—61no—
111C22×D12—64no—
112C22×D12—62no—
113C22×D12—61no—
114C22×D12—64no—
115C22×D12C2×D311yescharacteristic
116C22×C4×D3C2×D311yescharacteristic
117C2×C3×SD16—34no—
118C2×C3×SD16—64no—
119C22×C3×C8—31no—
120C3×C22⋊Q8—34no—
121C3×C22⋊Q8—62no—
122C2×C3×C4⋊C4—31no—
123C2×C3×C4⋊C4—61no—
124C2×C3×C22⋊C4—61no—
125#946—22no—
126#946C2×D314yescomplemented
127C2×#215—24no—
128C2×#215—34no—
129C2×#215—34no—
130C2×#215—64no—
131C2×#215—64no—
132C2×#215—64no—
133C2×#215—68no—
134C2×#215C2×D314yescomplemented
135C2×(C2×D3)⋊C4—21no—
136C2×C4⋊Dic3C2×D311yescharacteristic, complemented
137C2×Dic3⋊C4—21no—
138C22×C3⋊C8—31no—
139C22×C3⋊C8—31no—
140C22×C3⋊C8—61no—
141C22×C3⋊C8C2×D311yescharacteristic, complemented
142#832—34no—
143#830—34no—
144#821—34no—
145(C2×D3)⋊C8—34no—
146#809—34no—
147#809—34no—
148C23×C32C2×D411yescharacteristic
149C22×C3⋊D3—24no—
150C22×C3⋊D3—22no—
151C22×C3⋊D3—42no—
152C22×C3⋊D3—42no—
153C22×C3×D3—22no—
154C22×C3×D3—22no—
155C22×C3×D3—24no—
156C22×C3×D3—22no—
157C22×C3×D3—42no—
158C22×C3×D3—42no—
159C22×C3×D3SD1614yescomplemented
160C22×C3×D3C2×D412yes—
161C2×D32—216no—
162C2×D32—48no—
163C2×D32—432no—
164C2×D32—48no—
165C32×Q8—22no—
166C32×Q8—22no—
167C32×Q8—42no—
168C2×C32×C4—22no—
169C2×C32×C4—42no—
170C2×C32×C4C2×D412yes—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D412yes—
173C2×C32×C4C2411yescharacteristic
174C4⋊(C3⋊D3)—24no—
175C4⋊(C3⋊D3)—22no—
176C4⋊(C3⋊D3)C2×D414yes—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—42no—
180C2×C3×Dic3C2×D412yes—
181C3×D12—24no—
182C3×D12—22no—
183C3×D12C2×D414yes—
184C3×C4×D3—24no—
185C3×C4×D3—22no—
186C3×C4×D3—22no—
187#626—216no—
188C3⋊(C3⋊C8)—22no—
189C3×C3⋊C8—22no—
190C23×D4—91no—
191C22×SD16—31no—
192C22×SD16—91no—
193C2×C22⋊Q8—31no—
194#450—98no—
195C2×#102—91no—
196C2×#102—91no—
197C2×C22⋊C8—91no—
198C24×C3—31no—
199C24×C3—61no—
200C23×D3—21no—
201C23×D3—64no—
202C23×D3—68no—
203C23×D3—68no—
204C23×D3—61no—
205C23×D3—61no—
206C23×D3—64no—
207C23×D3—121no—
208C23×D3—124no—
209C23×D3—124no—
210C23×D3—124no—
211C23×D3—124no—
212C23×D3#6711yescharacteristic
213C2×C3×Q8—21no—
214C2×C3×Q8—21no—
215C2×C3×Q8—24no—
216C2×C3×Q8—22no—
217C2×C3×Q8—22no—
218C2×C3×Q8—22no—
219C2×C3×Q8—22no—
220C2×C3×Q8—22no—
221C2×C3×Q8—41no—
222C2×C3×Q8—42no—
223C2×C3×Q8C22×D312yescomplemented
224C2×C3×Q8C22×D312yescomplemented
225C2×C3×D4—34no—
226C2×C3×D4—32no—
227C2×C3×D4—62no—
228C2×C3×D4—61no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—31no—
233C22×C3×C4—32no—
234C22×C3×C4—32no—
235C22×C3×C4—41no—
236C22×C3×C4—62no—
237C22×C3×C4—62no—
238C22×C3×C4—61no—
239C22×C3×C4C22×D311yescharacteristic
240C22×C3×C4C22×D311yescharacteristic
241C2×#67—68no—
242C2×#67—64no—
243C22×Dic3—21no—
244C22×Dic3#6711yescharacteristic
245D3×D4—68no—
246D3×D4—68no—
247D3×D4—616no—
248C2×D12—21no—
249C2×D12—22no—
250C2×D12—34no—
251C2×D12—34no—
252C2×D12—32no—
253C2×D12—32no—
254C2×D12—64no—
255C2×D12—62no—
256C2×D12—68no—
257C2×D12—616no—
258C2×D12—64no—
259C2×D12—68no—
260C2×D12—61no—
261C2×D12—62no—
262C2×D12—62no—
263C2×D12—61no—
264C2×D12—68no—
265C2×D12—122no—
266C2×D12—121no—
267C2×D12#6714yes—
268C2×D12C22×D312yes—
269C2×C4×D3—22no—
270C2×C4×D3—22no—
271C2×C4×D3#6712yes—
272C2×C4×D3C22×D312yes—
273C3×SD16—68no—
274C2×C3×C8—32no—
275C2×C3×C8—62no—
276C3×C4⋊C4—32no—
277C3×C4⋊C4—64no—
278C3×C4⋊C4—61no—
279C3×C22⋊C4—64no—
280#215—28no—
281#215—68no—
282#215—68no—
283#215—616no—
284(C2×D3)⋊C4—24no—
285C4⋊Dic3—21no—
286C4⋊Dic3C22×D312yescomplemented
287Dic3⋊C4—24no—
288C2×C3⋊C8—22no—
289C2×C3⋊C8—32no—
290C2×C3⋊C8—32no—
291C2×C3⋊C8—62no—
292C2×C3⋊C8—64no—
293C2×C3⋊C8—62no—
294C2×C3⋊C8—62no—
295C2×C3⋊C8C22×D312yescomplemented
296C22×C32#12012yes—
297C22×C32C2×SD1612yes—
298C22×C32AGL(1,ℤ/8)12yes—
299C22×C32C22×D411yescharacteristic
300C2×C3⋊D3—24no—
301C2×C3⋊D3—42no—
302C2×C3⋊D3—42no—
303C2×C3⋊D3—48no—
304C2×C3×D3—22no—
305C2×C3×D3—22no—
306C2×C3×D3—28no—
307C2×C3×D3—24no—
308C2×C3×D3—42no—
309C2×C3×D3—42no—
310C2×C3×D3—48no—
311C2×C3×D3C2×SD1614yescomplemented
312D32—432no—
313C32×C4—42no—
314C32×C4#12012yes—
315C32×C4C22×D411yescharacteristic
316C32×C4C22×D411yescharacteristic
317C3×Dic3—22no—
318C3×Dic3—42no—
319C25—181no—
320C22×Q8D3211yescharacteristic, complemented
321C22×D4—31no—
322C22×D4—94no—
323C22×D4—91no—
324C22×D4—182no—
325C22×D4—181no—
326C22×D4—184no—
327C22×D4—184no—
328C23×C4—31no—
329C2×SD16—34no—
330C2×SD16—64no—
331C2×SD16—94no—
332C2×SD16—184no—
333C22×C8—31no—
334C22×C8—91no—
335C22⋊Q8—34no—
336C22⋊Q8—62no—
337C2×C4⋊C4—31no—
338C2×C4⋊C4—61no—
339C2×C22⋊C4—61no—
340#102—94no—
341#102—94no—
342C22⋊C8—94no—
343C23×C3—21no—
344C23×C3—34no—
345C23×C3—32no—
346C23×C3—62no—
347C23×C3—62no—
348C23×C3—64no—
349C23×C3—62no—
350C23×C3—122no—
351C23×C3—122no—
352C23×C3D3×D411yescharacteristic
353C23×C3C2×#6711yescharacteristic
354C22×D3—22no—
355C22×D3—22no—
356C22×D3—24no—
357C22×D3—22no—
358C22×D3—42no—
359C22×D3—42no—
360C22×D3—616no—
361C22×D3—616no—
362C22×D3—64no—
363C22×D3—64no—
364C22×D3—62no—
365C22×D3—62no—
366C22×D3—122no—
367C22×D3—124no—
368C22×D3—1232no—
369C22×D3—128no—
370C22×D3—128no—
371C22×D3—1232no—
372C22×D3—128no—
373C22×D3—122no—
374C22×D3—122no—
375C22×D3—122no—
376C22×D3—122no—
377C22×D3—128no—
378C22×D3—242no—
379C22×D3—242no—
380C22×D3#21514yescomplemented
381C22×D3C2×#6712yes—
382C3×Q8—24no—
383C3×Q8—22no—
384C3×Q8—22no—
385C3×Q8—22no—
386C3×Q8—22no—
387C3×Q8—42no—
388C3×Q8—44no—
389C3×Q8—42no—
390C3×Q8—42no—
391C3×D4—34no—
392C3×D4—64no—
393C3×D4—62no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—21no—
397C2×C3×C4—22no—
398C2×C3×C4—21no—
399C2×C3×C4—22no—
400C2×C3×C4—32no—
401C2×C3×C4—42no—
402C2×C3×C4—44no—
403C2×C3×C4—42no—
404C2×C3×C4—42no—
405C2×C3×C4—62no—
406C2×C3×C4—64no—
407C2×C3×C4—62no—
408C2×C3×C4—62no—
409C2×C3×C4—62no—
410C2×C3×C4—122no—
411C2×C3×C4D3×D411yescharacteristic
412C2×C3×C4D3×D412yes—
413C2×C3×C4D3×D412yes—
414C2×C3×C4D3×D412yes—
415C2×C3×C4C2×#6711yescharacteristic
416C2×C3×C4C2×#6712yes—
417C2×C3×C4C23×D311yescharacteristic
418C2×C3×C4C23×D311yescharacteristic
419#67—616no—
420C2×Dic3—22no—
421C2×Dic3—22no—
422C2×Dic3—42no—
423C2×Dic3C2×#6712yes—
424D12—24no—
425D12—22no—
426D12—34no—
427D12—34no—
428D12—64no—
429D12—616no—
430D12—64no—
431D12—64no—
432D12—62no—
433D12—62no—
434D12—122no—
435D12—124no—
436D12C2×#6714yes—
437C4×D3—24no—
438C4×D3—22no—
439C4×D3—22no—
440C3×C8—62no—
441C3⋊C8—22no—
442C3⋊C8—64no—
443C3⋊C8—62no—
444C3⋊C8—62no—
445C2×C32#45014yescomplemented
446C2×C32C2×#12011yescharacteristic
447C2×C32C22×SD1611yescharacteristic
448C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
449C3⋊D3—44no—
450C3×D3—24no—
451C3×D3—44no—
452C24—31no—
453C24—61no—
454C24—184no—
455C24—188no—
456C24—181no—
457C24—364no—
458C24—364no—
459C2×Q8—21no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8C2×D3212yescomplemented
463C2×D4—32no—
464C2×D4—34no—
465C2×D4—61no—
466C2×D4—62no—
467C2×D4—92no—
468C2×D4—94no—
469C2×D4—184no—
470C2×D4—188no—
471C2×D4—188no—
472C2×D4—1816no—
473C2×D4—188no—
474C2×D4—182no—
475C2×D4—181no—
476C22×C4—21no—
477C22×C4—31no—
478C22×C4—32no—
479C22×C4—32no—
480C22×C4—62no—
481C22×C4—62no—
482C22×C4—61no—
483C22×C4C2×D3211yescharacteristic
484SD16—68no—
485SD16—188no—
486C2×C8—32no—
487C2×C8—62no—
488C2×C8—92no—
489C2×C8—182no—
490C4⋊C4—32no—
491C4⋊C4—64no—
492C4⋊C4—61no—
493C22⋊C4—64no—
494C22×C3—21no—
495C22×C3—22no—
496C22×C3—22no—
497C22×C3—22no—
498C22×C3—34no—
499C22×C3—68no—
500C22×C3—62no—
501C22×C3—62no—
502C22×C3—64no—
503C22×C3—122no—
504C22×C3—128no—
505C22×C3—122no—
506C22×C3D3×SD1612yes—
507C22×C3#91412yes—
508C22×C3#93712yes—
509C22×C3#93712yes—
510C22×C3C2×#21512yes—
511C22×C3#94912yes—
512C22×C3C2×D3×D411yescharacteristic
513C22×C3C22×#6711yescharacteristic
514C2×D3—22no—
515C2×D3—28no—
516C2×D3—22no—
517C2×D3—24no—
518C2×D3—48no—
519C2×D3—42no—
520C2×D3—42no—
521C2×D3—64no—
522C2×D3—64no—
523C2×D3—124no—
524C2×D3—1232no—
525C2×D3—1232no—
526C2×D3—128no—
527C2×D3—122no—
528C2×D3—122no—
529C2×D3—122no—
530C2×D3—128no—
531C2×D3—122no—
532C2×D3—248no—
533C2×D3—242no—
534C2×D3—242no—
535C2×D3C2×#21514yescomplemented
536C3×C4—21no—
537C3×C4—21no—
538C3×C4—22no—
539C3×C4—44no—
540C3×C4—42no—
541C3×C4—42no—
542C3×C4—62no—
543C3×C4—122no—
544C3×C4#93712yes—
545C3×C4#93712yes—
546C3×C4C2×D3×D411yescharacteristic
547C3×C4C2×D3×D411yescharacteristic
548C3×C4C2×D3×D411yescharacteristic
549C3×C4C22×#6711yescharacteristic
550Dic3—22no—
551Dic3—42no—
552C32C2×#45011yescharacteristic, complemented, Sylow
553C23—32no—
554C23—34no—
555C23—62no—
556C23—62no—
557C23—62no—
558C23—64no—
559C23—122no—
560C23—122no—
561C23—1816no—
562C23—182no—
563C23—184no—
564C23—368no—
565C23—3632no—
566C23—368no—
567C23—362no—
568C23—362no—
569C23D3×#6711yescharacteristic
570Q8—22no—
571Q8—22no—
572Q8—42no—
573D4—34no—
574D4—62no—
575D4—64no—
576D4—94no—
577D4—1816no—
578D4—182no—
579D4—184no—
580C2×C4—22no—
581C2×C4—32no—
582C2×C4—42no—
583C2×C4—62no—
584C2×C4—62no—
585C2×C4—62no—
586C2×C4—64no—
587C2×C4—62no—
588C2×C4—122no—
589C2×C4D3×#6712yes—
590C2×C4D3×#6711yescharacteristic
591C2×C4#381112yes—
592C2×C4C22×D3211yescharacteristic
593C8—62no—
594C8—182no—
595C2×C3—24no—
596C2×C3—21no—
597C2×C3—21no—
598C2×C3—21no—
599C2×C3—64no—
600C2×C3—124no—
601C2×C3#504614yescomplemented
602C2×C3#516914yescomplemented
603C2×C3C2×D3×SD1611yescharacteristic
604C2×C3C2×#91411yescharacteristic
605C2×C3C2×#93711yescharacteristic
606C2×C3C2×#93711yescharacteristic
607C2×C3C22×#21511yescharacteristic
608C2×C3C2×#94911yescharacteristic
609D3—24no—
610D3—44no—
611D3—124no—
612D3—124no—
613D3—244no—
614C22—34no—
615C22—68no—
616C22—62no—
617C22—62no—
618C22—64no—
619C22—128no—
620C22—122no—
621C22—122no—
622C22—184no—
623C22—3632no—
624C22—368no—
625C22—362no—
626C22—362no—
627C22D3×#21512yes—
628C22#6393912yes—
629C22#6398312yes—
630C22C2×D3×#6711yescharacteristic
631C4—42no—
632C4—62no—
633C4—122no—
634C4#6398312yes—
635C4C2×D3×#6711yescharacteristic
636C4C2×#381111yescharacteristic
637C3—21no—
638C3C2×#504611yescharacteristic, complemented
639C3C2×#516911yescharacteristic, complemented
640C2—64no—
641C2—124no—
642C2—364no—
643C2#1059165114yesdirect product factor
644C2C2×D3×#21511yescharacteristic
645C2C2×#6393911yescharacteristic
646C2C2×#6398311yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×D3×D12C2
hypercenterC22×Q8D32
hypocenterC32C2×#450
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C22×#3755C2semidirect
3. C2×C3×#946C2semidirect
4. C22×C3×#215C2semidirect
5. #10591651C2direct (N × H)
6. C2×#63564C2semidirect
7. C2×#63562C2semidirect
8. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
12. C22×C32×Q8C22semidirect
22. C2×#3755C22semidirect
23. C22×C3⋊(C3⋊C8)C22semidirect
25. C3×#946C22semidirect
27. C2×C3×#215C22semidirect
29. C2×C3×C4⋊Dic3C22semidirect
31. C22×C3×C3⋊C8C22semidirect
32. #63564C22semidirect
33. #63562C22semidirect
34. (C2×D3)⋊(C3⋊C8)C22semidirect
39. C2×#946D3semidirect
43. C22×#215D3semidirect
62. C2×C32×Q8C23semidirect
86. C2×C3⋊(C3⋊C8)C23semidirect
90. C3×C4⋊Dic3C23semidirect
93. C2×C3×C3⋊C8C23semidirect
98. C22×C3×Q8C2×D3semidirect
99. C22×C3×Q8C2×D3semidirect
126. #946C2×D3semidirect
134. C2×#215C2×D3semidirect
136. C2×C4⋊Dic3C2×D3semidirect
141. C22×C3⋊C8C2×D3semidirect
159. C22×C3×D3SD16semidirect
223. C2×C3×Q8C22×D3semidirect
224. C2×C3×Q8C22×D3semidirect
286. C4⋊Dic3C22×D3semidirect
295. C2×C3⋊C8C22×D3semidirect
311. C2×C3×D3C2×SD16semidirect
320. C22×Q8D32semidirect
380. C22×D3#215semidirect
445. C2×C32#450semidirect
462. C2×Q8C2×D32semidirect
535. C2×D3C2×#215semidirect
552. C32C2×#450semidirect
601. C2×C3#5046semidirect
602. C2×C3#5169semidirect
638. C3C2×#5046semidirect
639. C3C2×#5169semidirect
643. C2#10591651direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×D122
C22×#37552
C2×C3×#9462
C22×C3×#2152
#105916512
C2×#635642
C2×#635622
C2×(C2×D3)⋊(C3⋊C8)2
C2×#51693
C2×#50463