Finite Group Databasebeta

← C2×#10591584 #11863621

Subgroups — C2×#10591584 #11863621

Order 1152.

1733 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×Q8C211yesmaximal, characteristic, complemented
2C22×#3755C211yesmaximal, characteristic, complemented
3C2×#63909C211yesmaximal, characteristic
4C22×#3717C211yesmaximal, characteristic, complemented
5C2×C3×#835C211yesmaximal, characteristic, complemented
6#10591584C218yesmaximal, direct product factor
7C2×#63565C211yesmaximal, characteristic, complemented
8C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
9C2×#5227—31nomaximal
10C2×#4806—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C2×C3×D3×Q8—24no—
14C2×C3×D3×Q8—22no—
15C2×C3×D3×Q8—24no—
16C2×C3×D3×Q8C2214yescomplemented
17C22×C3×C4×D3—21no—
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×Dic6—21no—
20C22×C3×Dic6C2211yescharacteristic
21C22×#626—21no—
22C2×#3755—24no—
23C2×#3755C2214yescomplemented
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27C2×#3722—21no—
28#63909—22no—
29#63909C2214yes—
30C2×#3717—24no—
31C2×#3717C2214yescomplemented
32C3×#835C2214yescomplemented
33#63565C2214yescomplemented
34(C2×D3)⋊(C3⋊C8)C2214yescomplemented
35C23×C3×Q8—31no—
36C22×D3×Q8D311yescharacteristic, complemented
37C22×#215—31no—
38C22×#215—31no—
39C22×#215—31no—
40C22×#215—61no—
41C2×#930—31no—
42C22×#204—31no—
43C2×#895—31no—
44C2×C3×#103—31no—
45#5227—38no—
46C2×#835—31no—
47C2×#835D311yescharacteristic, complemented
48C2×#830—31no—
49C2×(C2×D3)⋊C8—31no—
50C2×#810—31no—
51#4806—38no—
52C23×C3⋊D3—21no—
53C23×C3×D3D411yescharacteristic
54C2×C32×Q8—22no—
55C2×C32×Q8—21no—
56C2×C32×Q8D414yescomplemented
57C2×C32×Q8C2312yes—
58C22×C32×C4—21no—
59C22×C32×C4C2311yescharacteristic
60C2×C4⋊(C3⋊D3)—22no—
61C2×C4⋊(C3⋊D3)—22no—
62C2×C4⋊(C3⋊D3)—21no—
63C2×C4⋊(C3⋊D3)C2312yes—
64C22×C3×Dic3—21no—
65C22×C3×Dic3—21no—
66C22×C3×Dic3D411yescharacteristic
67C3×D3×Q8—216no—
68C3×D3×Q8—28no—
69C3×D3×Q8—28no—
70C2×C3×C4×D3—28no—
71C2×C3×C4×D3—24no—
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3—22no—
74C2×C3×C4×D3D412yes—
75C2×C3×C4×D3C2312yes—
76C2×C3×Dic6—28no—
77C2×C3×Dic6—21no—
78C2×C3×Dic6—22no—
79C2×C3×Dic6—24no—
80C2×C3×Dic6D414yescomplemented
81C2×C3×Dic6C2312yes—
82C2×#626—24no—
83C2×#626—44no—
84#3755—28no—
85C2×C3⋊(C3⋊C8)—22no—
86C2×C3⋊(C3⋊C8)C2312yes—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3C2312yes—
89C2×C3×C3⋊C8—22no—
90C2×C3×C3⋊C8C2312yes—
91#3722—24no—
92#3717—28no—
93C2×#448—91noSylow
94C22×C3×Q8—21no—
95C22×C3×Q8—34no—
96C22×C3×Q8—31no—
97C22×C3×Q8—61no—
98C22×C3×Q8—62no—
99C22×C3×Q8—64no—
100C22×C3×Q8—64no—
101C22×C3×Q8C2×D311yescharacteristic
102C22×C3×Q8C2×D311yescharacteristic
103C23×C3×C4—31no—
104C23×C3×C4—61no—
105C22×#67—61no—
106C2×D3×Q8—24no—
107C2×D3×Q8—22no—
108C2×D3×Q8—24no—
109C2×D3×Q8C2×D314yescomplemented
110C22×D12—31no—
111C22×D12—31no—
112C22×D12—61no—
113C22×D12—61no—
114C22×C4×D3—21no—
115C22×C4×D3C2×D311yescharacteristic
116C22×Dic6—21no—
117C22×Dic6C2×D311yescharacteristic
118C22×C3×C8—31no—
119C2×C3×C4⋊C4—31no—
120C2×#215—34no—
121C2×#215—34no—
122C2×#215—34no—
123C2×#215—64no—
124C2×#215—64no—
125C2×#215—68no—
126C2×#215—64no—
127C2×#215—64no—
128#930—34no—
129#930—62no—
130C2×(C2×D3)⋊C4—61no—
131C2×(C2×D3)⋊C4—61no—
132C2×C4⋊Dic3C2×D311yescharacteristic
133C22×C3⋊C8—31no—
134C22×C3⋊C8—31no—
135C22×C3⋊C8—61no—
136C22×C3⋊C8C2×D311yescharacteristic
137C2×#204—34no—
138C2×#204—64no—
139#895—34no—
140#895—62no—
141C3×#103—34no—
142#835—34no—
143#835C2×D314yescomplemented
144#830—34no—
145(C2×D3)⋊C8—34no—
146#810—34no—
147C23×C32C2×D411yescharacteristic
148C22×C3⋊D3—22no—
149C22×C3⋊D3—42no—
150C22×C3⋊D3—42no—
151C22×C3⋊D3—42no—
152C22×C3×D3—22no—
153C22×C3×D3—22no—
154C22×C3×D3SD1614yescomplemented
155C22×C3×D3C2×D412yes—
156C32×Q8—24no—
157C32×Q8—22no—
158C32×Q8C2×D414yescomplemented
159C2×C32×C4—24no—
160C2×C32×C4—22no—
161C2×C32×C4C2×D412yes—
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2×D412yes—
164C2×C32×C4C2411yescharacteristic
165C4⋊(C3⋊D3)—22no—
166C4⋊(C3⋊D3)—22no—
167C4⋊(C3⋊D3)—42no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—24no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—42no—
173C2×C3×Dic3C2×D412yes—
174C3×C4×D3—216no—
175C3×C4×D3—24no—
176C3×C4×D3—22no—
177C3×C4×D3—22no—
178C3×Dic6—216no—
179C3×Dic6—24no—
180C3×Dic6—22no—
181C3×Dic6C2×D414yescomplemented
182#626—48no—
183C3⋊(C3⋊C8)—22no—
184C3×C3⋊C8—22no—
185C23×Q8—31no—
186C22×SD16—91no—
187C22×SD16—91no—
188C2×#121—91no—
189#448—98no—
190C2×#103—31no—
191C2×#103—91no—
192C2×C22⋊C8—91no—
193C24×C3—31no—
194C23×D3—61no—
195C23×D3—61no—
196C23×D3—121no—
197C23×D3#6711yescharacteristic
198C2×C3×Q8—22no—
199C2×C3×Q8—21no—
200C2×C3×Q8—22no—
201C2×C3×Q8—21no—
202C2×C3×Q8—24no—
203C2×C3×Q8—22no—
204C2×C3×Q8—34no—
205C2×C3×Q8—32no—
206C2×C3×Q8—41no—
207C2×C3×Q8—42no—
208C2×C3×Q8—64no—
209C2×C3×Q8—68no—
210C2×C3×Q8—68no—
211C2×C3×Q8—616no—
212C2×C3×Q8—68no—
213C2×C3×Q8—62no—
214C2×C3×Q8—61no—
215C2×C3×Q8D1214yescomplemented
216C2×C3×Q8#6714yescomplemented
217C2×C3×Q8C22×D312yes—
218C2×C3×Q8C22×D312yes—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—31no—
223C22×C3×C4—32no—
224C22×C3×C4—32no—
225C22×C3×C4—41no—
226C22×C3×C4—64no—
227C22×C3×C4—68no—
228C22×C3×C4—61no—
229C22×C3×C4—62no—
230C22×C3×C4—62no—
231C22×C3×C4—61no—
232C22×C3×C4C22×D311yescharacteristic
233C22×C3×C4C22×D311yescharacteristic
234C2×#67—64no—
235C2×#67—124no—
236C22×Dic3—21no—
237C22×Dic3—21no—
238C22×Dic3#6711yescharacteristic
239D3×Q8—216no—
240D3×Q8—28no—
241D3×Q8—28no—
242C2×D12—32no—
243C2×D12—32no—
244C2×D12—62no—
245C2×D12—64no—
246C2×D12—62no—
247C2×D12—62no—
248C2×D12—62no—
249C2×D12—62no—
250C2×D12—64no—
251C2×D12—61no—
252C2×D12—61no—
253C2×D12—122no—
254C2×D12—121no—
255C2×D12—124no—
256C2×C4×D3—28no—
257C2×C4×D3—24no—
258C2×C4×D3—22no—
259C2×C4×D3—22no—
260C2×C4×D3#6712yes—
261C2×C4×D3C22×D312yes—
262C2×Dic6—28no—
263C2×Dic6—22no—
264C2×Dic6—21no—
265C2×Dic6—24no—
266C2×Dic6#6714yescomplemented
267C2×Dic6C22×D312yes—
268C2×C3×C8—32no—
269C2×C3×C8—62no—
270C3×C4⋊C4—32no—
271C3×C4⋊C4—61no—
272#215—68no—
273#215—616no—
274#215—68no—
275#215—68no—
276(C2×D3)⋊C4—64no—
277(C2×D3)⋊C4—64no—
278C4⋊Dic3—21no—
279C4⋊Dic3C22×D312yes—
280C2×C3⋊C8—22no—
281C2×C3⋊C8—32no—
282C2×C3⋊C8—32no—
283C2×C3⋊C8—62no—
284C2×C3⋊C8—64no—
285C2×C3⋊C8—62no—
286C2×C3⋊C8—62no—
287C2×C3⋊C8C22×D312yes—
288#204—68no—
289C22×C32#12012yes—
290C22×C32C2×SD1612yes—
291C22×C32#13712yes—
292C22×C32C22×D411yescharacteristic
293C2×C3⋊D3—42no—
294C2×C3⋊D3—42no—
295C2×C3⋊D3—42no—
296C2×C3⋊D3—84no—
297C2×C3×D3—22no—
298C2×C3×D3—22no—
299C2×C3×D3—28no—
300C2×C3×D3C2×SD1614yescomplemented
301C32×C4—24no—
302C32×C4#12012yes—
303C32×C4C22×D411yescharacteristic
304C32×C4C22×D411yescharacteristic
305C3×Dic3—22no—
306C3×Dic3—24no—
307C3×Dic3—42no—
308C22×Q8—34no—
309C22×Q8—31no—
310C22×Q8—61no—
311C22×Q8—62no—
312C22×Q8—64no—
313C22×Q8—64no—
314C22×Q8D3211yescharacteristic
315C22×D4—91no—
316C22×D4—181no—
317C23×C4—31no—
318C23×C4—61no—
319C2×SD16—94no—
320C2×SD16—94no—
321C2×SD16—184no—
322C2×SD16—184no—
323C22×C8—31no—
324C22×C8—91no—
325#121—94no—
326#121—182no—
327C2×C4⋊C4—31no—
328C2×C22⋊C4—181no—
329#103—34no—
330#103—94no—
331C22⋊C8—94no—
332C23×C3—21no—
333C23×C3—34no—
334C23×C3—32no—
335C23×C3—62no—
336C23×C3—62no—
337C23×C3D3×D411yescharacteristic
338C23×C3C2×#6711yescharacteristic
339C22×D3—22no—
340C22×D3—22no—
341C22×D3—62no—
342C22×D3—62no—
343C22×D3—122no—
344C22×D3—124no—
345C22×D3—122no—
346C22×D3—122no—
347C22×D3—122no—
348C22×D3—122no—
349C22×D3—122no—
350C22×D3—122no—
351C22×D3—242no—
352C22×D3—242no—
353C22×D3#21514yescomplemented
354C22×D3C2×#6712yes—
355C3×Q8—24no—
356C3×Q8—24no—
357C3×Q8—22no—
358C3×Q8—22no—
359C3×Q8—24no—
360C3×Q8—34no—
361C3×Q8—42no—
362C3×Q8—44no—
363C3×Q8—616no—
364C3×Q8—64no—
365C3×Q8—62no—
366C3×Q8C2×D1214yescomplemented
367C3×Q8C2×#6714yescomplemented
368C2×C3×C4—24no—
369C2×C3×C4—24no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—21no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—21no—
376C2×C3×C4—32no—
377C2×C3×C4—42no—
378C2×C3×C4—44no—
379C2×C3×C4—616no—
380C2×C3×C4—62no—
381C2×C3×C4—64no—
382C2×C3×C4—62no—
383C2×C3×C4—64no—
384C2×C3×C4—62no—
385C2×C3×C4—62no—
386C2×C3×C4—62no—
387C2×C3×C4—122no—
388C2×C3×C4C2×D1212yes—
389C2×C3×C4D3×D411yescharacteristic
390C2×C3×C4D3×D412yes—
391C2×C3×C4C2×#6712yes—
392C2×C3×C4C2×#6711yescharacteristic
393C2×C3×C4C2×#6712yes—
394C2×C3×C4C23×D311yescharacteristic
395C2×C3×C4C23×D311yescharacteristic
396#67—128no—
397C2×Dic3—22no—
398C2×Dic3—24no—
399C2×Dic3—22no—
400C2×Dic3—22no—
401C2×Dic3—42no—
402C2×Dic3C2×#6712yes—
403D12—64no—
404D12—62no—
405D12—62no—
406D12—62no—
407D12—62no—
408D12—122no—
409D12—124no—
410D12—128no—
411D12—122no—
412D12—122no—
413C4×D3—216no—
414C4×D3—24no—
415C4×D3—22no—
416C4×D3—22no—
417Dic6—216no—
418Dic6—24no—
419Dic6—22no—
420Dic6C2×#6714yescomplemented
421C3×C8—62no—
422C3⋊C8—22no—
423C3⋊C8—64no—
424C3⋊C8—62no—
425C3⋊C8—62no—
426C2×C32#44814yescomplemented
427C2×C32C2×#12011yescharacteristic
428C2×C32C22×SD1611yescharacteristic
429C2×C32C2×#13711yescharacteristic
430C3⋊D3—82no—
431C3×D3—24no—
432C24—31no—
433C24—181no—
434C2×Q8—21no—
435C2×Q8—22no—
436C2×Q8—32no—
437C2×Q8—34no—
438C2×Q8—64no—
439C2×Q8—68no—
440C2×Q8—68no—
441C2×Q8—616no—
442C2×Q8—68no—
443C2×Q8—62no—
444C2×Q8—61no—
445C2×Q8#62614yescomplemented
446C2×Q8C2×D3212yes—
447C2×D4—92no—
448C2×D4—184no—
449C2×D4—182no—
450C2×D4—182no—
451C2×D4—181no—
452C2×D4—364no—
453C22×C4—21no—
454C22×C4—31no—
455C22×C4—32no—
456C22×C4—32no—
457C22×C4—64no—
458C22×C4—68no—
459C22×C4—61no—
460C22×C4—62no—
461C22×C4—62no—
462C22×C4—61no—
463C22×C4C2×D3211yescharacteristic
464SD16—188no—
465SD16—188no—
466C2×C8—32no—
467C2×C8—62no—
468C2×C8—92no—
469C2×C8—182no—
470C4⋊C4—32no—
471C4⋊C4—61no—
472C22⋊C4—184no—
473C22×C3—21no—
474C22×C3—22no—
475C22×C3—22no—
476C22×C3—22no—
477C22×C3—34no—
478C22×C3—62no—
479C22×C3—62no—
480C22×C3—68no—
481C22×C3#88212yes—
482C22×C3D3×SD1612yes—
483C22×C3#91812yes—
484C22×C3C2×#21512yes—
485C22×C3#94212yes—
486C22×C3#95312yes—
487C22×C3C2×D3×D411yescharacteristic
488C22×C3C22×#6711yescharacteristic
489C2×D3—28no—
490C2×D3—22no—
491C2×D3—22no—
492C2×D3—124no—
493C2×D3—122no—
494C2×D3—122no—
495C2×D3—122no—
496C2×D3—122no—
497C2×D3—122no—
498C2×D3—122no—
499C2×D3—242no—
500C2×D3—242no—
501C2×D3—248no—
502C2×D3—244no—
503C2×D3—244no—
504C2×D3C2×#21514yescomplemented
505C3×C4—24no—
506C3×C4—24no—
507C3×C4—21no—
508C3×C4—21no—
509C3×C4—22no—
510C3×C4—44no—
511C3×C4—62no—
512C3×C4—64no—
513C3×C4—122no—
514C3×C4#88212yes—
515C3×C4#95312yes—
516C3×C4C22×D1211yescharacteristic
517C3×C4C2×D3×D411yescharacteristic
518C3×C4C22×#6711yescharacteristic
519C3×C4C22×#6711yescharacteristic
520Dic3—22no—
521Dic3—24no—
522Dic3—42no—
523C32C2×#44811yescharacteristic, complemented, Sylow
524C23—32no—
525C23—34no—
526C23—62no—
527C23—62no—
528C23—182no—
529C23—362no—
530C23—362no—
531C23—362no—
532C23D3×#6711yescharacteristic
533Q8—22no—
534Q8—24no—
535Q8—34no—
536Q8—616no—
537Q8—62no—
538Q8—64no—
539Q8C2×#62614yescomplemented
540D4—182no—
541D4—182no—
542D4—368no—
543D4—362no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—32no—
547C2×C4—616no—
548C2×C4—62no—
549C2×C4—62no—
550C2×C4—64no—
551C2×C4—62no—
552C2×C4—62no—
553C2×C4—64no—
554C2×C4—62no—
555C2×C4—122no—
556C2×C4C2×#62612yes—
557C2×C4D3×#6712yes—
558C2×C4D3×#6711yescharacteristic
559C2×C4C22×D3211yescharacteristic
560C8—62no—
561C8—182no—
562C2×C3—21no—
563C2×C3—24no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—64no—
567C2×C3#480614yescomplemented
568C2×C3#522714yescomplemented
569C2×C3C2×#88211yescharacteristic
570C2×C3C2×D3×SD1611yescharacteristic
571C2×C3C2×#91811yescharacteristic
572C2×C3C22×#21511yescharacteristic
573C2×C3C2×#94211yescharacteristic
574C2×C3C2×#95311yescharacteristic
575D3—24no—
576D3—244no—
577D3—242no—
578D3—242no—
579C22—34no—
580C22—62no—
581C22—68no—
582C22—62no—
583C22—362no—
584C22—362no—
585C22—362no—
586C22—724no—
587C22D3×#21512yes—
588C22#6394812yes—
589C22#6397712yes—
590C22C2×D3×#6711yescharacteristic
591C4—24no—
592C4—62no—
593C4—64no—
594C4—122no—
595C4#6397712yes—
596C4C22×#62611yescharacteristic
597C4C2×D3×#6711yescharacteristic
598C3—21no—
599C3C2×#480611yescharacteristic, complemented
600C3C2×#522711yescharacteristic, complemented
601C2—64no—
602C2—722no—
603C2#1059158414yesdirect product factor
604C2C2×D3×#21511yescharacteristic
605C2C2×#6394811yescharacteristic
606C2C2×#6397711yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC2×#63909C2
hypercenterC22×Q8D32
hypocenterC32C2×#448
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
1. C22×C3×D3×Q8C2semidirect
2. C22×#3755C2semidirect
4. C22×#3717C2semidirect
5. C2×C3×#835C2semidirect
6. #10591584C2direct (N × H)
7. C2×#63565C2semidirect
8. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
16. C2×C3×D3×Q8C22semidirect
23. C2×#3755C22semidirect
31. C2×#3717C22semidirect
32. C3×#835C22semidirect
33. #63565C22semidirect
34. (C2×D3)⋊(C3⋊C8)C22semidirect
36. C22×D3×Q8D3semidirect
47. C2×#835D3semidirect
56. C2×C32×Q8D4semidirect
80. C2×C3×Dic6D4semidirect
109. C2×D3×Q8C2×D3semidirect
143. #835C2×D3semidirect
154. C22×C3×D3SD16semidirect
158. C32×Q8C2×D4semidirect
181. C3×Dic6C2×D4semidirect
215. C2×C3×Q8D12semidirect
216. C2×C3×Q8#67semidirect
266. C2×Dic6#67semidirect
300. C2×C3×D3C2×SD16semidirect
353. C22×D3#215semidirect
366. C3×Q8C2×D12semidirect
367. C3×Q8C2×#67semidirect
420. Dic6C2×#67semidirect
426. C2×C32#448semidirect
445. C2×Q8#626semidirect
504. C2×D3C2×#215semidirect
523. C32C2×#448semidirect
539. Q8C2×#626semidirect
567. C2×C3#4806semidirect
568. C2×C3#5227semidirect
599. C3C2×#4806semidirect
600. C3C2×#5227semidirect
603. C2#10591584direct (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×Q82
C22×#37552
C2×#639092
C22×#37172
C2×C3×#8352
#105915842
C2×#635652
C2×(C2×D3)⋊(C3⋊C8)2
C2×#52273
C2×#48063