Finite Group Databasebeta

← C2×#10590946 #11863581

Subgroups — C2×#10590946 #11863581

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×#3744C211yesmaximal, characteristic, complemented
3C2×#63857C211yesmaximal, characteristic, complemented
4C22×#3716C211yesmaximal, characteristic, complemented
5C2×C3×#821C211yesmaximal, characteristic, complemented
6C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic, complemented
8#10590946C218yesmaximal, direct product factor
9C2×#4776—31nomaximal
10C2×#4731—31nomaximal
11C23×D32—21no—
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×#634C2211yescharacteristic, complemented
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—
21C22×C32×C8C2211yescharacteristic, complemented
22C2×#3744—24no—
23C2×#3744C2214yescomplemented
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×#821C2214yescomplemented
33C3×(C2×D3)⋊C8C2214yescomplemented
34#63564C2214yescomplemented
35C22×D3×D4—31no—
36C23×D12—31no—
37C22×#214—31no—
38C2×#924—31no—
39C22×#204—31no—
40C22×#204—31no—
41C22×#204—31no—
42C22×#204—61no—
43C2×#897—31no—
44C2×C3×#102—31no—
45C2×C3×C22⋊C8—31no—
46C2×#821—31no—
47C2×#821D311yescharacteristic, complemented
48C2×(C2×D3)⋊C8D311yescharacteristic, complemented
49C2×#809—31no—
50#4776—38no—
51#4731—38no—
52C23×C3⋊D3—21no—
53C23×C3×D3—21no—
54C23×C3×D3D411yescharacteristic
55C22×D32—28no—
56C22×D32—24no—
57C22×D32—44no—
58C22×D32—44no—
59C22×C32×C4C2311yescharacteristic
60C22×C3⋊Dic3—21no—
61C2×C4⋊(C3⋊D3)—21no—
62C2×C4⋊(C3⋊D3)—22no—
63C2×C4⋊(C3⋊D3)D414yes—
64C2×C4⋊(C3⋊D3)C2312yes—
65C2×#634—22no—
66C2×#634—22no—
67C2×#634—21no—
68C2×#634C2312yescomplemented
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—
84C2×C32×C8—22no—
85C2×C32×C8C2312yescomplemented
86#3744—28no—
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
95C24×D3—61no—
96C24×D3—61no—
97C22×C3×D4—31no—
98C23×C3×C4—31no—
99C22×#67—61no—
100C2×D3×D4—34no—
101C2×D3×D4—64no—
102C2×D3×D4—64no—
103C2×D3×D4—62no—
104C22×D12—31no—
105C22×D12—31no—
106C22×D12—34no—
107C22×D12—61no—
108C22×D12—64no—
109C22×D12—62no—
110C22×D12—61no—
111C22×D12—64no—
112C22×D12C2×D311yescharacteristic
113C22×C4×D3C2×D311yescharacteristic
114C22×Dic6—31no—
115C22×Dic6—31no—
116C22×Dic6—61no—
117C22×C3×C8—21no—
118C22×C3×C8—31no—
119C22×C3×C8C2×D311yescharacteristic, complemented
120C22×C3×C8C2×D311yescharacteristic, complemented
121C2×C3×C4⋊C4—31no—
122C2×#217—61no—
123C2×#214—34no—
124C2×#214—64no—
125C2×(C2×D3)⋊C4—61no—
126C2×C4⋊Dic3—61no—
127C2×C4⋊Dic3C2×D311yescharacteristic, complemented
128#924—34no—
129#924—62no—
130C2×Dic3⋊C4—61no—
131C22×C3⋊C8C2×D311yescharacteristic, complemented
132C2×#204—34no—
133C2×#204—34no—
134C2×#204—34no—
135C2×#204—64no—
136C2×#204—64no—
137C2×#204—64no—
138C2×#204—68no—
139C2×#204—64no—
140#897—34no—
141#897—62no—
142C3×#102—34no—
143C3×C22⋊C8—34no—
144#821—34no—
145#821C2×D314yescomplemented
146(C2×D3)⋊C8C2×D314yescomplemented
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—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D412yes—
167C2×C32×C4C2×D412yes—
168C2×C32×C4C2411yescharacteristic
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—42no—
171C4⋊(C3⋊D3)—24no—
172C4⋊(C3⋊D3)—22no—
173C4⋊(C3⋊D3)C2×D414yes—
174#634—22no—
175#634—22no—
176#634—42no—
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—
188C32×C8—22no—
189C3×C3⋊C8—22no—
190C23×D4—91no—
191C22×SD16—91no—
192C22×SD16—91no—
193C2×C22⋊Q8—91no—
194#450—98no—
195C2×#102—31no—
196C2×#102—91no—
197C2×C22⋊C8—31no—
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×D3D1211yescharacteristic
213C2×C3×D4—34no—
214C2×C3×D4—32no—
215C2×C3×D4—61no—
216C2×C3×D4—62no—
217C22×C3×C4—21no—
218C22×C3×C4—31no—
219C22×C3×C4—32no—
220C22×C3×C4—32no—
221C22×C3×C4—62no—
222C22×C3×C4—62no—
223C22×C3×C4—61no—
224C22×C3×C4C22×D311yescharacteristic
225C22×C3×C4C22×D311yescharacteristic
226C2×#67—68no—
227C2×#67—64no—
228C22×Dic3—21no—
229C22×Dic3—61no—
230C22×Dic3—61no—
231C22×Dic3—121no—
232C22×Dic3D1211yescharacteristic
233D3×D4—68no—
234D3×D4—68no—
235D3×D4—616no—
236C2×D12—21no—
237C2×D12—22no—
238C2×D12—34no—
239C2×D12—34no—
240C2×D12—32no—
241C2×D12—32no—
242C2×D12—64no—
243C2×D12—62no—
244C2×D12—68no—
245C2×D12—616no—
246C2×D12—64no—
247C2×D12—68no—
248C2×D12—62no—
249C2×D12—61no—
250C2×D12—61no—
251C2×D12—62no—
252C2×D12—68no—
253C2×D12—122no—
254C2×D12—121no—
255C2×D12D1214yes—
256C2×D12C22×D312yes—
257C2×C4×D3—22no—
258C2×C4×D3—22no—
259C2×C4×D3D1212yes—
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—24no—
274C2×C3×C8—22no—
275C2×C3×C8—22no—
276C2×C3×C8—22no—
277C2×C3×C8—32no—
278C2×C3×C8—62no—
279C2×C3×C8C22×D312yescomplemented
280C2×C3×C8C22×D312yescomplemented
281C3×C4⋊C4—32no—
282C3×C4⋊C4—61no—
283#217—64no—
284#214—68no—
285(C2×D3)⋊C4—64no—
286C4⋊Dic3—21no—
287C4⋊Dic3—64no—
288C4⋊Dic3C22×D312yescomplemented
289Dic3⋊C4—64no—
290C2×C3⋊C8—22no—
291C2×C3⋊C8C22×D312yescomplemented
292#204—68no—
293#204—68no—
294#204—616no—
295#204—68no—
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#12012yes—
314C32×C4C22×D411yescharacteristic
315C32×C4C22×D411yescharacteristic
316C3⋊Dic3—42no—
317C3×Dic3—22no—
318C3×Dic3—42no—
319C25—181no—
320C22×Q8—91no—
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—94no—
330C2×SD16—94no—
331C2×SD16—184no—
332C2×SD16—184no—
333C22×C8—31no—
334C22×C8D3211yescharacteristic, complemented
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—34no—
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×C3C2×D1211yescharacteristic
353C23×C3D3×D411yescharacteristic
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—128no—
369C22×D3—1232no—
370C22×D3—128no—
371C22×D3—128no—
372C22×D3—1232no—
373C22×D3—122no—
374C22×D3—122no—
375C22×D3—122no—
376C22×D3—122no—
377C22×D3—128no—
378C22×D3—242no—
379C22×D3—242no—
380C22×D3#20414yescomplemented
381C22×D3C2×D1212yes—
382C3×D4—34no—
383C3×D4—64no—
384C3×D4—62no—
385C2×C3×C4—21no—
386C2×C3×C4—22no—
387C2×C3×C4—21no—
388C2×C3×C4—22no—
389C2×C3×C4—32no—
390C2×C3×C4—62no—
391C2×C3×C4—64no—
392C2×C3×C4—62no—
393C2×C3×C4—62no—
394C2×C3×C4—62no—
395C2×C3×C4—122no—
396C2×C3×C4C2×D1211yescharacteristic
397C2×C3×C4C2×D1212yes—
398C2×C3×C4D3×D411yescharacteristic
399C2×C3×C4D3×D412yes—
400C2×C3×C4D3×D412yes—
401C2×C3×C4D3×D412yes—
402C2×C3×C4C23×D311yescharacteristic
403C2×C3×C4C23×D311yescharacteristic
404#67—616no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—42no—
408C2×Dic3—62no—
409C2×Dic3—62no—
410C2×Dic3—122no—
411C2×Dic3—124no—
412C2×Dic3—122no—
413C2×Dic3—122no—
414C2×Dic3C2×D1212yes—
415D12—24no—
416D12—22no—
417D12—34no—
418D12—34no—
419D12—64no—
420D12—616no—
421D12—64no—
422D12—64no—
423D12—62no—
424D12—62no—
425D12—122no—
426D12—124no—
427D12C2×D1214yes—
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—24no—
441C3×C8—22no—
442C3×C8—22no—
443C3×C8—62no—
444C3⋊C8—22no—
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—92no—
460C2×Q8—181no—
461C2×Q8—182no—
462C2×Q8—182no—
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—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—22no—
487C2×C8—32no—
488C2×C8—62no—
489C2×C8C2×D3212yescomplemented
490C4⋊C4—32no—
491C4⋊C4—61no—
492C4⋊C4—184no—
493C22⋊C4—184no—
494C22×C3—21no—
495C22×C3—22no—
496C22×C3—22no—
497C22×C3—22no—
498C22×C3—34no—
499C22×C3—62no—
500C22×C3—62no—
501C22×C3—68no—
502C22×C3—64no—
503C22×C3—122no—
504C22×C3—122no—
505C22×C3—128no—
506C22×C3#88212yes—
507C22×C3#88212yes—
508C22×C3C2×#20412yes—
509C22×C3#90812yes—
510C22×C3#91112yes—
511C22×C3D3×SD1612yes—
512C22×C3C22×D1211yescharacteristic
513C22×C3C2×D3×D411yescharacteristic
514C2×D3—22no—
515C2×D3—22no—
516C2×D3—28no—
517C2×D3—24no—
518C2×D3—42no—
519C2×D3—42no—
520C2×D3—48no—
521C2×D3—64no—
522C2×D3—64no—
523C2×D3—124no—
524C2×D3—1232no—
525C2×D3—1232no—
526C2×D3—122no—
527C2×D3—122no—
528C2×D3—128no—
529C2×D3—122no—
530C2×D3—122no—
531C2×D3—128no—
532C2×D3—242no—
533C2×D3—242no—
534C2×D3—248no—
535C2×D3C2×#20414yescomplemented
536C3×C4—21no—
537C3×C4—21no—
538C3×C4—22no—
539C3×C4—62no—
540C3×C4—122no—
541C3×C4#88212yes—
542C3×C4#88212yes—
543C3×C4C22×D1211yescharacteristic
544C3×C4C2×D3×D411yescharacteristic
545C3×C4C2×D3×D411yescharacteristic
546C3×C4C2×D3×D411yescharacteristic
547Dic3—22no—
548Dic3—42no—
549Dic3—124no—
550Dic3—122no—
551Dic3—122no—
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—368no—
566C23—3632no—
567C23—362no—
568C23—362no—
569C23D3×D1211yescharacteristic
570Q8—182no—
571Q8—182no—
572Q8—362no—
573D4—34no—
574D4—62no—
575D4—64no—
576D4—94no—
577D4—1816no—
578D4—182no—
579D4—184no—
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×C4D3×D1212yes—
590C2×C4D3×D1211yescharacteristic
591C2×C4#381112yes—
592C2×C4C22×D3211yescharacteristic
593C8—22no—
594C8—62no—
595C2×C3—21no—
596C2×C3—21no—
597C2×C3—24no—
598C2×C3—21no—
599C2×C3—64no—
600C2×C3—124no—
601C2×C3#473114yescomplemented
602C2×C3#477614yescomplemented
603C2×C3C2×#88211yescharacteristic
604C2×C3C2×#88211yescharacteristic
605C2×C3C22×#20411yescharacteristic
606C2×C3C2×#90811yescharacteristic
607C2×C3C2×#91111yescharacteristic
608C2×C3C2×D3×SD1611yescharacteristic
609D3—24no—
610D3—44no—
611D3—124no—
612D3—124no—
613D3—244no—
614C22—34no—
615C22—62no—
616C22—68no—
617C22—62no—
618C22—64no—
619C22—122no—
620C22—122no—
621C22—128no—
622C22—184no—
623C22—3632no—
624C22—362no—
625C22—362no—
626C22—368no—
627C22D3×#20412yes—
628C22#6379512yes—
629C22#6392312yes—
630C22C2×D3×D1211yescharacteristic
631C4—62no—
632C4—122no—
633C4—362no—
634C4#6392312yes—
635C4C2×D3×D1211yescharacteristic
636C4C2×#381111yescharacteristic
637C3—21no—
638C3C2×#473111yescharacteristic, complemented
639C3C2×#477611yescharacteristic, complemented
640C2—64no—
641C2—124no—
642C2—364no—
643C2#1059094614yesdirect product factor
644C2C2×D3×#20411yescharacteristic
645C2C2×#6379511yescharacteristic
646C2C2×#6392311yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×D3×D12C2
hypercenterC22×C8D32
hypocenterC32C2×#450
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C22×#3744C2semidirect
3. C2×#63857C2semidirect
4. C22×#3716C2semidirect
5. C2×C3×#821C2semidirect
6. C2×C3×(C2×D3)⋊C8C2semidirect
7. C2×#63564C2semidirect
8. #10590946C2direct (N × H)
13. C22×#634C22semidirect
21. C22×C32×C8C22semidirect
23. C2×#3744C22semidirect
24. C2×C3×C4⋊Dic3C22semidirect
25. C22×C3×C3⋊C8C22semidirect
29. #63857C22semidirect
31. C2×#3716C22semidirect
32. C3×#821C22semidirect
33. C3×(C2×D3)⋊C8C22semidirect
34. #63564C22semidirect
47. C2×#821D3semidirect
48. C2×(C2×D3)⋊C8D3semidirect
68. C2×#634C23semidirect
85. C2×C32×C8C23semidirect
88. C3×C4⋊Dic3C23semidirect
90. C2×C3×C3⋊C8C23semidirect
119. C22×C3×C8C2×D3semidirect
120. C22×C3×C8C2×D3semidirect
127. C2×C4⋊Dic3C2×D3semidirect
131. C22×C3⋊C8C2×D3semidirect
145. #821C2×D3semidirect
146. (C2×D3)⋊C8C2×D3semidirect
159. C22×C3×D3SD16semidirect
279. C2×C3×C8C22×D3semidirect
280. C2×C3×C8C22×D3semidirect
288. C4⋊Dic3C22×D3semidirect
291. C2×C3⋊C8C22×D3semidirect
311. C2×C3×D3C2×SD16semidirect
334. C22×C8D32semidirect
380. C22×D3#204semidirect
445. C2×C32#450semidirect
489. C2×C8C2×D32semidirect
535. C2×D3C2×#204semidirect
552. C32C2×#450semidirect
601. C2×C3#4731semidirect
602. C2×C3#4776semidirect
638. C3C2×#4731semidirect
639. C3C2×#4776semidirect
643. C2#10590946direct (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×#37442
C2×#638572
C22×#37162
C2×C3×#8212
C2×C3×(C2×D3)⋊C82
C2×#635642
#105909462
C2×#47763
C2×#47313