Finite Group Databasebeta

← C2×#10591517 #11863619

Subgroups — C2×#10591517 #11863619

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×D3×Dic6C211yesmaximal, characteristic, complemented
2C22×#3754C211yesmaximal, characteristic, complemented
3C2×C3×#938C211yesmaximal, characteristic
4C22×C3×#214C211yesmaximal, characteristic, complemented
5#10591517C218yesmaximal, direct product factor
6C2×#63567C211yesmaximal, characteristic, complemented
7C2×#63565C211yesmaximal, characteristic, complemented
8C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
9C2×#5170—31nomaximal
10C2×#5040—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×#67—21no—
14C22×C3×C4×D3C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C22×#627—21no—
17C22×D3×Dic3—21no—
18C2×D3×Dic6—24no—
19C2×D3×Dic6—22no—
20C2×D3×Dic6—24no—
21C2×D3×Dic6C2214yescomplemented
22C2×#3754—24no—
23C2×#3754C2214yescomplemented
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25C2×C3×#217—21no—
26C3×#938—22no—
27C3×#938C2214yes—
28C2×C3×#214—24no—
29C2×C3×#214C2214yescomplemented
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C22×C3×C3⋊C8C2211yescharacteristic
32#63567C2214yescomplemented
33#63565C2214yescomplemented
34(C2×D3)⋊(C3⋊C8)C2214yescomplemented
35C22×D3×Q8—31no—
36C23×Dic6—31no—
37C22×C3×SD16—31no—
38C2×C3×#121—31no—
39C2×#938D311yescharacteristic
40C22×#214—31no—
41C22×#214—31no—
42C22×#214—61no—
43C22×#214D311yescharacteristic, complemented
44C2×#835—31no—
45C2×#830—31no—
46#5170—38no—
47C2×(C2×D3)⋊C8—31no—
48C2×#816—31no—
49#5040—38no—
50C2×#810—31no—
51C2×#810—31no—
52C24×C32—21no—
53C23×C3×D3D411yescharacteristic
54C2×C32×D4—22no—
55C2×C32×D4—22no—
56C2×C32×D4—21no—
57C2×C32×D4C2312yes—
58C22×C32×C4C2311yescharacteristic
59C22×C3⋊Dic3—21no—
60C2×#634—21no—
61C2×#634—22no—
62C2×#634D414yescomplemented
63C2×#634C2312yes—
64C2×C3×#67—24no—
65C2×C3×#67—44no—
66C22×C3×Dic3—21no—
67C22×C3×Dic3—21no—
68C22×C3×Dic3D411yescharacteristic
69C2×C3×C4×D3—22no—
70C2×C3×C4×D3—22no—
71C2×C3×C4×D3D412yes—
72C2×C3×C4×D3C2312yes—
73C2×C3×Dic6—21no—
74C2×C3×Dic6—22no—
75C2×C3×Dic6D414yescomplemented
76C2×C3×Dic6C2312yes—
77C2×#627—28no—
78C2×#627—24no—
79C2×D3×Dic3—28no—
80C2×D3×Dic3—24no—
81D3×Dic6—216no—
82D3×Dic6—28no—
83D3×Dic6—28no—
84#3754—28no—
85C2×C3⋊(C3⋊C8)—22no—
86C2×C3⋊(C3⋊C8)C2312yes—
87C3×#217—24no—
88C3×#214—28no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3C2312yes—
91C2×C3×C3⋊C8—22no—
92C2×C3×C3⋊C8C2312yes—
93C2×#448—91noSylow
94C22×C3×Q8—31no—
95C22×C3×D4—21no—
96C22×C3×D4—61no—
97C22×C3×D4C2×D311yescharacteristic
98C22×C3×D4C2×D311yescharacteristic
99C23×C3×C4—31no—
100C22×#67—21no—
101C23×Dic3—61no—
102C2×D3×Q8—34no—
103C2×D3×Q8—64no—
104C2×D3×Q8—64no—
105C2×D3×Q8—62no—
106C22×C4×D3—61no—
107C22×C4×D3C2×D311yescharacteristic
108C22×Dic6—31no—
109C22×Dic6—31no—
110C22×Dic6—34no—
111C22×Dic6—61no—
112C22×Dic6—64no—
113C22×Dic6—62no—
114C22×Dic6—61no—
115C22×Dic6—61no—
116C22×Dic6—64no—
117C22×Dic6C2×D311yescharacteristic
118C2×C3×SD16—34no—
119C2×C3×SD16—64no—
120C22×C3×C8—31no—
121C3×#121—34no—
122C3×#121—62no—
123C2×C3×C4⋊C4—31no—
124C2×C3×C22⋊C4—61no—
125C2×#217—21no—
126#938—22no—
127#938C2×D314yes—
128C2×#214—24no—
129C2×#214—34no—
130C2×#214—34no—
131C2×#214—64no—
132C2×#214—64no—
133C2×#214—64no—
134C2×#214—68no—
135C2×#214C2×D314yescomplemented
136C2×C4⋊Dic3C2×D311yescharacteristic
137C22×C3⋊C8—31no—
138C22×C3⋊C8—31no—
139C22×C3⋊C8—61no—
140C22×C3⋊C8C2×D311yescharacteristic
141#835—34no—
142#830—34no—
143(C2×D3)⋊C8—34no—
144#816—34no—
145#810—34no—
146#810—34no—
147C23×C32—22no—
148C23×C32—42no—
149C23×C32—42no—
150C23×C32—42no—
151C23×C32C2×D411yescharacteristic
152C22×C3×D3—22no—
153C22×C3×D3—22no—
154C22×C3×D3SD1614yescomplemented
155C22×C3×D3C2×D412yes—
156C32×D4—22no—
157C32×D4—22no—
158C32×D4—42no—
159C2×C32×C4C2×D412yes—
160C2×C32×C4C2×D411yescharacteristic
161C2×C32×C4C2×D412yes—
162C2×C32×C4C2411yescharacteristic
163C2×C3⋊Dic3—24no—
164C2×C3⋊Dic3—22no—
165#634—24no—
166#634—22no—
167#634C2×D414yescomplemented
168C3×#67—48no—
169C2×C3×Dic3—24no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—42no—
174C2×C3×Dic3C2×D412yes—
175C3×C4×D3—24no—
176C3×C4×D3—22no—
177C3×C4×D3—22no—
178C3×Dic6—24no—
179C3×Dic6—22no—
180C3×Dic6C2×D414yescomplemented
181#627—216no—
182D3×Dic3—216no—
183C3⋊(C3⋊C8)—22no—
184C3×C3⋊C8—22no—
185C23×Q8—91no—
186C22×SD16—31no—
187C22×SD16—91no—
188C2×#121—31no—
189#448—98no—
190C2×#103—91no—
191C2×#103—91no—
192C2×C22⋊C8—91no—
193C24×C3—21no—
194C24×C3—21no—
195C24×C3—31no—
196C24×C3—41no—
197C23×D3#6711yescharacteristic
198C2×C3×Q8—34no—
199C2×C3×Q8—32no—
200C2×C3×Q8—62no—
201C2×C3×Q8—61no—
202C2×C3×D4—24no—
203C2×C3×D4—22no—
204C2×C3×D4—22no—
205C2×C3×D4—22no—
206C2×C3×D4—21no—
207C2×C3×D4—22no—
208C2×C3×D4—21no—
209C2×C3×D4—22no—
210C2×C3×D4—42no—
211C2×C3×D4—41no—
212C2×C3×D4—64no—
213C2×C3×D4—124no—
214C2×C3×D4C22×D312yes—
215C2×C3×D4C22×D312yes—
216C22×C3×C4—21no—
217C22×C3×C4—31no—
218C22×C3×C4—32no—
219C22×C3×C4—32no—
220C22×C3×C4—61no—
221C22×C3×C4—62no—
222C22×C3×C4—62no—
223C22×C3×C4—61no—
224C22×C3×C4C22×D311yescharacteristic
225C22×C3×C4C22×D311yescharacteristic
226C2×#67—24no—
227C2×#67—44no—
228C22×Dic3—21no—
229C22×Dic3—21no—
230C22×Dic3—64no—
231C22×Dic3—68no—
232C22×Dic3—61no—
233C22×Dic3—61no—
234C22×Dic3—121no—
235C22×Dic3#6711yescharacteristic
236D3×Q8—68no—
237D3×Q8—68no—
238D3×Q8—616no—
239C2×C4×D3—22no—
240C2×C4×D3—22no—
241C2×C4×D3—68no—
242C2×C4×D3—64no—
243C2×C4×D3#6712yes—
244C2×C4×D3C22×D312yes—
245C2×Dic6—21no—
246C2×Dic6—22no—
247C2×Dic6—34no—
248C2×Dic6—34no—
249C2×Dic6—32no—
250C2×Dic6—32no—
251C2×Dic6—64no—
252C2×Dic6—62no—
253C2×Dic6—68no—
254C2×Dic6—616no—
255C2×Dic6—64no—
256C2×Dic6—68no—
257C2×Dic6—68no—
258C2×Dic6—61no—
259C2×Dic6—62no—
260C2×Dic6—62no—
261C2×Dic6—61no—
262C2×Dic6—64no—
263C2×Dic6—68no—
264C2×Dic6—121no—
265C2×Dic6—122no—
266C2×Dic6#6714yescomplemented
267C2×Dic6C22×D312yes—
268C3×SD16—68no—
269C2×C3×C8—32no—
270C2×C3×C8—62no—
271C3×C4⋊C4—32no—
272C3×C4⋊C4—61no—
273C3×C22⋊C4—64no—
274#217—24no—
275#214—28no—
276#214—68no—
277#214—68no—
278#214—616no—
279C4⋊Dic3—21no—
280C4⋊Dic3C22×D312yes—
281C2×C3⋊C8—22no—
282C2×C3⋊C8—32no—
283C2×C3⋊C8—32no—
284C2×C3⋊C8—62no—
285C2×C3⋊C8—64no—
286C2×C3⋊C8—62no—
287C2×C3⋊C8—62no—
288C2×C3⋊C8C22×D312yes—
289C22×C32—42no—
290C22×C32—42no—
291C22×C32—42no—
292C22×C32—84no—
293C22×C32#12012yes—
294C22×C32C2×SD1612yes—
295C22×C32#13712yes—
296C22×C32C22×D411yescharacteristic
297C2×C3×D3—22no—
298C2×C3×D3—22no—
299C2×C3×D3—28no—
300C2×C3×D3C2×SD1614yescomplemented
301C32×C4#12012yes—
302C32×C4C22×D411yescharacteristic
303C32×C4C22×D411yescharacteristic
304C3⋊Dic3—24no—
305C3×Dic3—24no—
306C3×Dic3—22no—
307C3×Dic3—42no—
308C22×Q8—31no—
309C22×Q8—94no—
310C22×Q8—91no—
311C22×Q8—181no—
312C22×Q8—182no—
313C22×Q8—184no—
314C22×Q8—184no—
315C22×D4—61no—
316C22×D4D3211yescharacteristic
317C23×C4—31no—
318C23×C4—181no—
319C2×SD16—34no—
320C2×SD16—64no—
321C2×SD16—94no—
322C2×SD16—184no—
323C22×C8—31no—
324C22×C8—91no—
325#121—34no—
326#121—62no—
327C2×C4⋊C4—31no—
328C2×C22⋊C4—61no—
329#103—94no—
330#103—94no—
331C22⋊C8—94no—
332C23×C3—22no—
333C23×C3—22no—
334C23×C3—21no—
335C23×C3—34no—
336C23×C3—32no—
337C23×C3—42no—
338C23×C3—44no—
339C23×C3—42no—
340C23×C3—42no—
341C23×C3—42no—
342C23×C3—42no—
343C23×C3—42no—
344C23×C3—42no—
345C23×C3—62no—
346C23×C3—62no—
347C23×C3—82no—
348C23×C3—82no—
349C23×C3D3×D411yescharacteristic
350C23×C3C2×#6711yescharacteristic
351C22×D3—22no—
352C22×D3—22no—
353C22×D3#21414yescomplemented
354C22×D3C2×#6712yes—
355C3×Q8—34no—
356C3×Q8—64no—
357C3×Q8—62no—
358C3×D4—24no—
359C3×D4—22no—
360C3×D4—22no—
361C3×D4—22no—
362C3×D4—22no—
363C3×D4—42no—
364C3×D4—44no—
365C3×D4—42no—
366C3×D4—42no—
367C3×D4—128no—
368C2×C3×C4—21no—
369C2×C3×C4—22no—
370C2×C3×C4—21no—
371C2×C3×C4—22no—
372C2×C3×C4—32no—
373C2×C3×C4—62no—
374C2×C3×C4—64no—
375C2×C3×C4—62no—
376C2×C3×C4—64no—
377C2×C3×C4—62no—
378C2×C3×C4—62no—
379C2×C3×C4—62no—
380C2×C3×C4—122no—
381C2×C3×C4D3×D411yescharacteristic
382C2×C3×C4D3×D412yes—
383C2×C3×C4D3×D412yes—
384C2×C3×C4D3×D412yes—
385C2×C3×C4C2×#6711yescharacteristic
386C2×C3×C4C2×#6712yes—
387C2×C3×C4C23×D311yescharacteristic
388C2×C3×C4C23×D311yescharacteristic
389#67—48no—
390C2×Dic3—24no—
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—42no—
395C2×Dic3—616no—
396C2×Dic3—64no—
397C2×Dic3—64no—
398C2×Dic3—62no—
399C2×Dic3—62no—
400C2×Dic3—122no—
401C2×Dic3—124no—
402C2×Dic3C2×#6712yes—
403C4×D3—24no—
404C4×D3—22no—
405C4×D3—22no—
406C4×D3—616no—
407Dic6—24no—
408Dic6—22no—
409Dic6—34no—
410Dic6—34no—
411Dic6—64no—
412Dic6—616no—
413Dic6—616no—
414Dic6—64no—
415Dic6—64no—
416Dic6—62no—
417Dic6—62no—
418Dic6—122no—
419Dic6—124no—
420Dic6C2×#6714yescomplemented
421C3×C8—62no—
422C3⋊C8—22no—
423C3⋊C8—64no—
424C3⋊C8—62no—
425C3⋊C8—62no—
426C2×C32—82no—
427C2×C32#44814yescomplemented
428C2×C32C2×#12011yescharacteristic
429C2×C32C22×SD1611yescharacteristic
430C2×C32C2×#13711yescharacteristic
431C3×D3—24no—
432C24—21no—
433C24—31no—
434C2×Q8—32no—
435C2×Q8—34no—
436C2×Q8—61no—
437C2×Q8—62no—
438C2×Q8—92no—
439C2×Q8—94no—
440C2×Q8—184no—
441C2×Q8—188no—
442C2×Q8—188no—
443C2×Q8—188no—
444C2×Q8—1816no—
445C2×Q8—181no—
446C2×Q8—182no—
447C2×D4—22no—
448C2×D4—21no—
449C2×D4—22no—
450C2×D4—64no—
451C2×D4—124no—
452C2×D4C2×D3212yes—
453C22×C4—31no—
454C22×C4—32no—
455C22×C4—32no—
456C22×C4—61no—
457C22×C4—62no—
458C22×C4—62no—
459C22×C4—61no—
460C22×C4—184no—
461C22×C4—188no—
462C22×C4—181no—
463C22×C4C2×D3211yescharacteristic
464SD16—68no—
465SD16—188no—
466C2×C8—32no—
467C2×C8—62no—
468C2×C8—92no—
469C2×C8—182no—
470C4⋊C4—32no—
471C4⋊C4—61no—
472C22⋊C4—64no—
473C22×C3—21no—
474C22×C3—22no—
475C22×C3—22no—
476C22×C3—22no—
477C22×C3—34no—
478C22×C3—44no—
479C22×C3—42no—
480C22×C3—42no—
481C22×C3—42no—
482C22×C3—42no—
483C22×C3—42no—
484C22×C3—42no—
485C22×C3—68no—
486C22×C3—62no—
487C22×C3—62no—
488C22×C3—82no—
489C22×C3—82no—
490C22×C3—88no—
491C22×C3—84no—
492C22×C3—84no—
493C22×C3D3×SD1612yes—
494C22×C3#91512yes—
495C22×C3C2×#21412yes—
496C22×C3#93712yes—
497C22×C3#93712yes—
498C22×C3#95112yes—
499C22×C3C2×D3×D411yescharacteristic
500C22×C3C22×#6711yescharacteristic
501C2×D3—22no—
502C2×D3—28no—
503C2×D3—22no—
504C2×D3C2×#21414yescomplemented
505C3×C4—21no—
506C3×C4—21no—
507C3×C4—22no—
508C3×C4—62no—
509C3×C4—64no—
510C3×C4—122no—
511C3×C4#93712yes—
512C3×C4#93712yes—
513C3×C4C2×D3×D411yescharacteristic
514C3×C4C2×D3×D411yescharacteristic
515C3×C4C2×D3×D411yescharacteristic
516C3×C4C22×#6711yescharacteristic
517Dic3—24no—
518Dic3—22no—
519Dic3—42no—
520Dic3—64no—
521Dic3—64no—
522Dic3—124no—
523C32C2×#44811yescharacteristic, complemented, Sylow
524C23—22no—
525C23—32no—
526C23—34no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—62no—
531C23—62no—
532C23D3×#6711yescharacteristic
533Q8—34no—
534Q8—62no—
535Q8—64no—
536Q8—94no—
537Q8—1816no—
538Q8—182no—
539Q8—184no—
540D4—22no—
541D4—22no—
542D4—42no—
543D4—128no—
544C2×C4—32no—
545C2×C4—62no—
546C2×C4—62no—
547C2×C4—64no—
548C2×C4—62no—
549C2×C4—62no—
550C2×C4—64no—
551C2×C4—62no—
552C2×C4—122no—
553C2×C4—1816no—
554C2×C4—182no—
555C2×C4—184no—
556C2×C4D3×#6712yes—
557C2×C4D3×#6711yescharacteristic
558C2×C4#381112yes—
559C2×C4C22×D3211yescharacteristic
560C8—62no—
561C8—182no—
562C2×C3—24no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—64no—
567C2×C3—84no—
568C2×C3—82no—
569C2×C3—82no—
570C2×C3#504014yescomplemented
571C2×C3#517014yescomplemented
572C2×C3C2×D3×SD1611yescharacteristic
573C2×C3C2×#91511yescharacteristic
574C2×C3C22×#21411yescharacteristic
575C2×C3C2×#93711yescharacteristic
576C2×C3C2×#93711yescharacteristic
577C2×C3C2×#95111yescharacteristic
578D3—24no—
579C22—34no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—68no—
584C22—62no—
585C22—62no—
586C22—84no—
587C22D3×#21412yes—
588C22#6392912yes—
589C22#6398312yes—
590C22C2×D3×#6711yescharacteristic
591C4—62no—
592C4—64no—
593C4—122no—
594C4—184no—
595C4#6398312yes—
596C4C2×D3×#6711yescharacteristic
597C4C2×#381111yescharacteristic
598C3—21no—
599C3C2×#504011yescharacteristic, complemented
600C3C2×#517011yescharacteristic, complemented
601C2—64no—
602C2—82no—
603C2#1059151714yesdirect product factor
604C2C2×D3×#21411yescharacteristic
605C2C2×#6392911yescharacteristic
606C2C2×#6398311yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC2×C3×#938C2
hypercenterC22×D4D32
hypocenterC32C2×#448
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
1. C22×D3×Dic6C2semidirect
2. C22×#3754C2semidirect
4. C22×C3×#214C2semidirect
5. #10591517C2direct (N × H)
6. C2×#63567C2semidirect
7. C2×#63565C2semidirect
8. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
21. C2×D3×Dic6C22semidirect
23. C2×#3754C22semidirect
29. C2×C3×#214C22semidirect
32. #63567C22semidirect
33. #63565C22semidirect
34. (C2×D3)⋊(C3⋊C8)C22semidirect
43. C22×#214D3semidirect
62. C2×#634D4semidirect
75. C2×C3×Dic6D4semidirect
135. C2×#214C2×D3semidirect
154. C22×C3×D3SD16semidirect
167. #634C2×D4semidirect
180. C3×Dic6C2×D4semidirect
266. C2×Dic6#67semidirect
300. C2×C3×D3C2×SD16semidirect
353. C22×D3#214semidirect
420. Dic6C2×#67semidirect
427. C2×C32#448semidirect
504. C2×D3C2×#214semidirect
523. C32C2×#448semidirect
570. C2×C3#5040semidirect
571. C2×C3#5170semidirect
599. C3C2×#5040semidirect
600. C3C2×#5170semidirect
603. C2#10591517direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×Dic62
C22×#37542
C2×C3×#9382
C22×C3×#2142
#105915172
C2×#635672
C2×#635652
C2×(C2×D3)⋊(C3⋊C8)2
C2×#51703
C2×#50403