Finite Group Databasebeta

← C2×#10591583 #11863623

Subgroups — C2×#10591583 #11863623

Order 1152.

1665 conjugacy classes of subgroups.

The subgroup lattice has 595 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×Q8C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic, complemented
3C2×#63908C211yesmaximal, characteristic
4C22×#3715C211yesmaximal, characteristic, complemented
5C2×#63662C211yesmaximal, characteristic, complemented
6#10591583C218yesmaximal, direct product factor
7C2×#63566C211yesmaximal, characteristic, complemented
8C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
9C2×#5227—31nomaximal
10C2×#5170—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C2×C3×D3×Q8—24no—
13C2×C3×D3×Q8—22no—
14C2×C3×D3×Q8—24no—
15C2×C3×D3×Q8C2214yescomplemented
16C22×C3×D12C2211yescharacteristic
17C22×C3×C4×D3—21no—
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×Dic6—21no—
20C22×C3×Dic6C2211yescharacteristic
21C22×#625—21no—
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C22×C3⋊(C3⋊C8)C2211yescharacteristic
24C2×C3×#215—24no—
25C2×C3×#215C2214yescomplemented
26C22×C3×C3⋊C8C2211yescharacteristic
27C2×(C2×D3)⋊Dic3—21no—
28#63908—22no—
29#63908C2214yes—
30C2×#3715—24no—
31C2×#3715C2214yescomplemented
32#63662C2214yescomplemented
33#63566C2214yescomplemented
34(C2×D3)⋊(C3⋊C8)C2214yescomplemented
35C23×C3×Q8—31no—
36C22×D3×Q8D311yescharacteristic, complemented
37C22×C3×SD16—31no—
38C22×#215—31no—
39C22×#215D311yescharacteristic, complemented
40C2×#938—31no—
41C22×#214—31no—
42C2×#930—31no—
43#5227—38no—
44C2×#835—31no—
45C2×#835—31no—
46C2×#835—31no—
47C2×#835—61no—
48C2×#830—31no—
49#5170—38no—
50C2×(C2×D3)⋊C8—31no—
51C2×#816—31no—
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
60C22×C3⋊Dic3—21no—
61C22×C3×Dic3—21no—
62C22×C3×Dic3D411yescharacteristic
63C3×D3×Q8—216no—
64C3×D3×Q8—28no—
65C3×D3×Q8—28no—
66C2×C3×D12—22no—
67C2×C3×D12—22no—
68C2×C3×D12—21no—
69C2×C3×D12C2312yes—
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×#625—24no—
83C2×#625—44no—
84C4⋊(C3⋊Dic3)—21no—
85C4⋊(C3⋊Dic3)C2312yes—
86C2×C3⋊(C3⋊C8)—22no—
87C2×C3⋊(C3⋊C8)C2312yes—
88C3×#215—28no—
89C2×C3×C3⋊C8—22no—
90C2×C3×C3⋊C8C2312yes—
91(C2×D3)⋊Dic3—24no—
92#3715—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
103C22×C3×D4—31no—
104C23×C3×C4—31no—
105C23×C3×C4—61no—
106C22×#67—61no—
107C22×#67—61no—
108C2×D3×Q8—24no—
109C2×D3×Q8—22no—
110C2×D3×Q8—24no—
111C2×D3×Q8C2×D314yescomplemented
112C22×D12C2×D311yescharacteristic
113C22×C4×D3—21no—
114C22×C4×D3C2×D311yescharacteristic
115C22×Dic6—21no—
116C22×Dic6C2×D311yescharacteristic
117C2×C3×SD16—34no—
118C2×C3×SD16—64no—
119C22×C3×C8—31no—
120C2×#217—61no—
121C2×#215—24no—
122C2×#215—34no—
123C2×#215—64no—
124C2×#215C2×D314yescomplemented
125#938—34no—
126#938—62no—
127C2×#214—34no—
128C2×#214—64no—
129#930—34no—
130#930—62no—
131C2×(C2×D3)⋊C4—61no—
132C2×C4⋊Dic3—31no—
133C2×C4⋊Dic3—31no—
134C2×C4⋊Dic3—61no—
135C22×C3⋊C8—31no—
136C22×C3⋊C8—31no—
137C22×C3⋊C8—61no—
138C22×C3⋊C8C2×D311yescharacteristic
139#835—34no—
140#835—34no—
141#835—34no—
142#835—64no—
143#830—34no—
144(C2×D3)⋊C8—34no—
145#816—34no—
146C23×C32C2×D411yescharacteristic
147C22×C3×D3—22no—
148C22×C3×D3—22no—
149C22×C3×D3—22no—
150C22×C3×D3—42no—
151C22×C3×D3—42no—
152C22×C3×D3—42no—
153C22×C3×D3SD1614yescomplemented
154C22×C3×D3C2×D412yes—
155C32×Q8—24no—
156C32×Q8—22no—
157C32×Q8C2×D414yescomplemented
158C2×C32×C4—24no—
159C2×C32×C4—22no—
160C2×C32×C4C2×D411yescharacteristic
161C2×C32×C4C2×D412yes—
162C2×C32×C4C2×D412yes—
163C2×C32×C4C2411yescharacteristic
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—42no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—24no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3C2×D412yes—
170C3×D12—22no—
171C3×D12—22no—
172C3×D12—42no—
173C3×C4×D3—216no—
174C3×C4×D3—24no—
175C3×C4×D3—22no—
176C3×C4×D3—22no—
177C3×Dic6—216no—
178C3×Dic6—24no—
179C3×Dic6—22no—
180C3×Dic6C2×D414yescomplemented
181#625—48no—
182C3⋊(C3⋊C8)—22no—
183C3×C3⋊C8—22no—
184C23×Q8—31no—
185C22×SD16—31no—
186C22×SD16—91no—
187C2×#121—91no—
188#448—98no—
189C2×#103—91no—
190C2×#103—91no—
191C2×C22⋊C8—91no—
192C24×C3—31no—
193C24×C3—61no—
194C23×D3—21no—
195C23×D3#6711yescharacteristic
196C2×C3×Q8—22no—
197C2×C3×Q8—21no—
198C2×C3×Q8—22no—
199C2×C3×Q8—21no—
200C2×C3×Q8—24no—
201C2×C3×Q8—22no—
202C2×C3×Q8—34no—
203C2×C3×Q8—32no—
204C2×C3×Q8—42no—
205C2×C3×Q8—41no—
206C2×C3×Q8—64no—
207C2×C3×Q8—68no—
208C2×C3×Q8—68no—
209C2×C3×Q8—616no—
210C2×C3×Q8—68no—
211C2×C3×Q8—61no—
212C2×C3×Q8—62no—
213C2×C3×Q8#6714yescomplemented
214C2×C3×Q8#6714yescomplemented
215C2×C3×Q8C22×D312yes—
216C2×C3×Q8C22×D312yes—
217C2×C3×D4—32no—
218C2×C3×D4—62no—
219C2×C3×D4—62no—
220C2×C3×D4—61no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—31no—
225C22×C3×C4—32no—
226C22×C3×C4—32no—
227C22×C3×C4—41no—
228C22×C3×C4—64no—
229C22×C3×C4—68no—
230C22×C3×C4—61no—
231C22×C3×C4—62no—
232C22×C3×C4—62no—
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D311yescharacteristic
235C2×#67—64no—
236C2×#67—64no—
237C2×#67—124no—
238C2×#67—124no—
239C22×Dic3—21no—
240C22×Dic3—61no—
241C22×Dic3—61no—
242C22×Dic3—121no—
243C22×Dic3#6711yescharacteristic
244D3×Q8—216no—
245D3×Q8—28no—
246D3×Q8—28no—
247C2×D12—22no—
248C2×D12—22no—
249C2×D12—21no—
250C2×D12C22×D312yes—
251C2×C4×D3—28no—
252C2×C4×D3—24no—
253C2×C4×D3—22no—
254C2×C4×D3—22no—
255C2×C4×D3#6712yes—
256C2×C4×D3C22×D312yes—
257C2×Dic6—28no—
258C2×Dic6—22no—
259C2×Dic6—21no—
260C2×Dic6—24no—
261C2×Dic6#6714yescomplemented
262C2×Dic6C22×D312yes—
263C3×SD16—68no—
264C2×C3×C8—32no—
265C2×C3×C8—62no—
266#217—64no—
267#215—28no—
268#215—68no—
269#214—68no—
270(C2×D3)⋊C4—64no—
271C4⋊Dic3—32no—
272C4⋊Dic3—32no—
273C4⋊Dic3—62no—
274C4⋊Dic3—61no—
275C4⋊Dic3—61no—
276C4⋊Dic3—121no—
277C2×C3⋊C8—22no—
278C2×C3⋊C8—32no—
279C2×C3⋊C8—32no—
280C2×C3⋊C8—62no—
281C2×C3⋊C8—62no—
282C2×C3⋊C8—62no—
283C2×C3⋊C8—122no—
284C2×C3⋊C8C22×D312yes—
285C22×C32#12012yes—
286C22×C32C2×SD1612yes—
287C22×C32#13712yes—
288C22×C32C22×D411yescharacteristic
289C2×C3×D3—22no—
290C2×C3×D3—22no—
291C2×C3×D3—28no—
292C2×C3×D3—42no—
293C2×C3×D3—42no—
294C2×C3×D3—42no—
295C2×C3×D3—84no—
296C2×C3×D3C2×SD1614yescomplemented
297C32×C4—24no—
298C32×C4#12012yes—
299C32×C4C22×D411yescharacteristic
300C32×C4C22×D411yescharacteristic
301C3⋊Dic3—42no—
302C3×Dic3—22no—
303C3×Dic3—24no—
304C22×Q8—34no—
305C22×Q8—31no—
306C22×Q8—61no—
307C22×Q8—62no—
308C22×Q8—64no—
309C22×Q8—64no—
310C22×Q8D3211yescharacteristic
311C22×D4—31no—
312C22×D4—181no—
313C23×C4—31no—
314C23×C4—61no—
315C2×SD16—34no—
316C2×SD16—64no—
317C2×SD16—94no—
318C2×SD16—184no—
319C22×C8—31no—
320C22×C8—91no—
321#121—94no—
322#121—182no—
323C2×C4⋊C4—91no—
324C2×C22⋊C4—181no—
325#103—94no—
326#103—94no—
327C22⋊C8—94no—
328C23×C3—21no—
329C23×C3—34no—
330C23×C3—32no—
331C23×C3—62no—
332C23×C3—62no—
333C23×C3—62no—
334C23×C3—122no—
335C23×C3—122no—
336C23×C3—122no—
337C23×C3D3×D411yescharacteristic
338C23×C3C2×#6711yescharacteristic
339C22×D3—22no—
340C22×D3—22no—
341C22×D3—22no—
342C22×D3—42no—
343C22×D3—42no—
344C22×D3—42no—
345C22×D3#21514yescomplemented
346C22×D3C2×#6712yes—
347C3×Q8—24no—
348C3×Q8—24no—
349C3×Q8—22no—
350C3×Q8—22no—
351C3×Q8—24no—
352C3×Q8—34no—
353C3×Q8—42no—
354C3×Q8—44no—
355C3×Q8—616no—
356C3×Q8—64no—
357C3×Q8—62no—
358C3×Q8C2×#6714yescomplemented
359C3×Q8C2×#6714yescomplemented
360C3×D4—62no—
361C3×D4—62no—
362C3×D4—122no—
363C2×C3×C4—24no—
364C2×C3×C4—24no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—21no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—21no—
371C2×C3×C4—32no—
372C2×C3×C4—42no—
373C2×C3×C4—44no—
374C2×C3×C4—616no—
375C2×C3×C4—62no—
376C2×C3×C4—64no—
377C2×C3×C4—62no—
378C2×C3×C4—64no—
379C2×C3×C4—62no—
380C2×C3×C4—62no—
381C2×C3×C4D3×D411yescharacteristic
382C2×C3×C4D3×D412yes—
383C2×C3×C4C2×#6712yes—
384C2×C3×C4C2×#6712yes—
385C2×C3×C4C2×#6711yescharacteristic
386C2×C3×C4C2×#6712yes—
387C2×C3×C4C23×D311yescharacteristic
388C2×C3×C4C23×D311yescharacteristic
389#67—128no—
390#67—128no—
391C2×Dic3—22no—
392C2×Dic3—24no—
393C2×Dic3—22no—
394C2×Dic3—62no—
395C2×Dic3—62no—
396C2×Dic3—122no—
397C2×Dic3—122no—
398C2×Dic3—122no—
399C2×Dic3—242no—
400C2×Dic3C2×#6712yes—
401D12—22no—
402D12—22no—
403D12—42no—
404C4×D3—216no—
405C4×D3—24no—
406C4×D3—22no—
407C4×D3—22no—
408Dic6—216no—
409Dic6—24no—
410Dic6—22no—
411Dic6C2×#6714yescomplemented
412C3×C8—62no—
413C3⋊C8—22no—
414C3⋊C8—62no—
415C3⋊C8—62no—
416C3⋊C8—122no—
417C2×C32#44814yescomplemented
418C2×C32C2×#12011yescharacteristic
419C2×C32C22×SD1611yescharacteristic
420C2×C32C2×#13711yescharacteristic
421C3×D3—24no—
422C3×D3—82no—
423C24—31no—
424C24—61no—
425C2×Q8—21no—
426C2×Q8—22no—
427C2×Q8—32no—
428C2×Q8—34no—
429C2×Q8—64no—
430C2×Q8—68no—
431C2×Q8—68no—
432C2×Q8—616no—
433C2×Q8—68no—
434C2×Q8—62no—
435C2×Q8—61no—
436C2×Q8#62514yescomplemented
437C2×Q8C2×D3212yes—
438C2×D4—32no—
439C2×D4—62no—
440C2×D4—62no—
441C2×D4—61no—
442C2×D4—184no—
443C2×D4—364no—
444C22×C4—21no—
445C22×C4—31no—
446C22×C4—32no—
447C22×C4—32no—
448C22×C4—64no—
449C22×C4—68no—
450C22×C4—61no—
451C22×C4—62no—
452C22×C4—62no—
453C22×C4—181no—
454C22×C4C2×D3211yescharacteristic
455SD16—68no—
456SD16—188no—
457C2×C8—32no—
458C2×C8—62no—
459C2×C8—92no—
460C2×C8—182no—
461C4⋊C4—92no—
462C4⋊C4—181no—
463C22⋊C4—184no—
464C22×C3—21no—
465C22×C3—22no—
466C22×C3—22no—
467C22×C3—22no—
468C22×C3—34no—
469C22×C3—68no—
470C22×C3—62no—
471C22×C3—62no—
472C22×C3—122no—
473C22×C3—122no—
474C22×C3—122no—
475C22×C3—244no—
476C22×C3D3×SD1612yes—
477C22×C3#91512yes—
478C22×C3#93712yes—
479C22×C3C2×#21512yes—
480C22×C3#94212yes—
481C22×C3#95312yes—
482C22×C3C2×D3×D411yescharacteristic
483C22×C3C22×#6711yescharacteristic
484C2×D3—28no—
485C2×D3—22no—
486C2×D3—22no—
487C2×D3—42no—
488C2×D3—42no—
489C2×D3—42no—
490C2×D3—84no—
491C2×D3C2×#21514yescomplemented
492C3×C4—24no—
493C3×C4—24no—
494C3×C4—21no—
495C3×C4—21no—
496C3×C4—22no—
497C3×C4—44no—
498C3×C4—62no—
499C3×C4—64no—
500C3×C4#93712yes—
501C3×C4#95312yes—
502C3×C4C2×D3×D411yescharacteristic
503C3×C4C22×#6711yescharacteristic
504C3×C4C22×#6711yescharacteristic
505C3×C4C22×#6711yescharacteristic
506Dic3—22no—
507Dic3—24no—
508Dic3—122no—
509Dic3—122no—
510Dic3—242no—
511C32C2×#44811yescharacteristic, complemented, Sylow
512C23—32no—
513C23—34no—
514C23—62no—
515C23—62no—
516C23—62no—
517C23—122no—
518C23—122no—
519C23—122no—
520C23D3×#6711yescharacteristic
521Q8—22no—
522Q8—24no—
523Q8—34no—
524Q8—616no—
525Q8—62no—
526Q8—64no—
527Q8C2×#62514yescomplemented
528D4—62no—
529D4—62no—
530D4—122no—
531D4—368no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—32no—
535C2×C4—616no—
536C2×C4—62no—
537C2×C4—62no—
538C2×C4—64no—
539C2×C4—62no—
540C2×C4—62no—
541C2×C4—64no—
542C2×C4—182no—
543C2×C4—362no—
544C2×C4C2×#62512yes—
545C2×C4D3×#6712yes—
546C2×C4D3×#6711yescharacteristic
547C2×C4C22×D3211yescharacteristic
548C8—62no—
549C8—182no—
550C2×C3—21no—
551C2×C3—24no—
552C2×C3—21no—
553C2×C3—21no—
554C2×C3—64no—
555C2×C3—242no—
556C2×C3#517014yescomplemented
557C2×C3#522714yescomplemented
558C2×C3C2×D3×SD1611yescharacteristic
559C2×C3C2×#91511yescharacteristic
560C2×C3C2×#93711yescharacteristic
561C2×C3C22×#21511yescharacteristic
562C2×C3C2×#94211yescharacteristic
563C2×C3C2×#95311yescharacteristic
564D3—24no—
565D3—82no—
566C22—34no—
567C22—62no—
568C22—68no—
569C22—62no—
570C22—122no—
571C22—122no—
572C22—122no—
573C22—244no—
574C22D3×#21512yes—
575C22#6394612yes—
576C22#6397612yes—
577C22C2×D3×#6711yescharacteristic
578C4—24no—
579C4—62no—
580C4—64no—
581C4—362no—
582C4#6397612yes—
583C4C22×#62511yescharacteristic
584C4C2×D3×#6711yescharacteristic
585C3—21no—
586C3C2×#517011yescharacteristic, complemented
587C3C2×#522711yescharacteristic, complemented
588C2—64no—
589C2—242no—
590C2#1059158314yesdirect product factor
591C2C2×D3×#21511yescharacteristic
592C2C2×#6394611yescharacteristic
593C2C2×#6397611yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC2×#63908C2
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×C3×#215C2semidirect
4. C22×#3715C2semidirect
5. C2×#63662C2semidirect
6. #10591583C2direct (N × H)
7. C2×#63566C2semidirect
8. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
15. C2×C3×D3×Q8C22semidirect
25. C2×C3×#215C22semidirect
31. C2×#3715C22semidirect
32. #63662C22semidirect
33. #63566C22semidirect
34. (C2×D3)⋊(C3⋊C8)C22semidirect
36. C22×D3×Q8D3semidirect
39. C22×#215D3semidirect
56. C2×C32×Q8D4semidirect
80. C2×C3×Dic6D4semidirect
111. C2×D3×Q8C2×D3semidirect
124. C2×#215C2×D3semidirect
153. C22×C3×D3SD16semidirect
157. C32×Q8C2×D4semidirect
180. C3×Dic6C2×D4semidirect
213. C2×C3×Q8#67semidirect
214. C2×C3×Q8#67semidirect
261. C2×Dic6#67semidirect
296. C2×C3×D3C2×SD16semidirect
345. C22×D3#215semidirect
358. C3×Q8C2×#67semidirect
359. C3×Q8C2×#67semidirect
411. Dic6C2×#67semidirect
417. C2×C32#448semidirect
436. C2×Q8#625semidirect
491. C2×D3C2×#215semidirect
511. C32C2×#448semidirect
527. Q8C2×#625semidirect
556. C2×C3#5170semidirect
557. C2×C3#5227semidirect
586. C3C2×#5170semidirect
587. C3C2×#5227semidirect
590. C2#10591583direct (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×C3×#2152
C2×#639082
C22×#37152
C2×#636622
#105915832
C2×#635662
C2×(C2×D3)⋊(C3⋊C8)2
C2×#52273
C2×#51703