Finite Group Databasebeta

← C2×#10590822 #11863629

Subgroups — C2×#10590822 #11863629

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×D3×Dic6C211yesmaximal, characteristic, complemented
2C22×C3×#204C211yesmaximal, characteristic, complemented
3C2×#63908C211yesmaximal, characteristic
4C22×#3716C211yesmaximal, characteristic, complemented
5C2×#63643C211yesmaximal, characteristic, complemented
6C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
7C2×#63566C211yesmaximal, characteristic, complemented
8#10590822C218yesmaximal, direct product factor
9C2×#5170—31nomaximal
10C2×#4738—31nomaximal
11C22×#634C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×#627—21no—
16C22×#625—21no—
17C22×D3×Dic3—21no—
18C2×D3×Dic6—24no—
19C2×D3×Dic6—22no—
20C2×D3×Dic6—24no—
21C2×D3×Dic6C2214yescomplemented
22C22×C32×C8C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×C3×#204—24no—
26C2×C3×#204C2214yescomplemented
27C2×(C2×D3)⋊Dic3—21no—
28#63908—22no—
29#63908C2214yes—
30C2×#3716—24no—
31C2×#3716C2214yescomplemented
32#63643C2214yescomplemented
33C3×(C2×D3)⋊C8C2214yescomplemented
34#63566C2214yescomplemented
35C22×D3×Q8—31no—
36C23×Dic6—31no—
37C22×C3×SD16—31no—
38C2×#938—31no—
39C22×#214—31no—
40C2×#930—31no—
41C22×#204—31no—
42C22×#204D311yescharacteristic, complemented
43C2×C3×C22⋊C8—31no—
44C2×#835—31no—
45#5170—38no—
46C2×(C2×D3)⋊C8D311yescharacteristic, complemented
47C2×#816—31no—
48C2×#816—31no—
49C2×#816—31no—
50C2×#816—61no—
51#4738—38no—
52C23×C3×D3—21no—
53C23×C3×D3D411yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C22×C3⋊Dic3—21no—
57C2×#634—21no—
58C2×#634—22no—
59C2×#634D414yescomplemented
60C2×#634C2312yes—
61C22×C3×Dic3—21no—
62C22×C3×Dic3D411yescharacteristic
63C2×C3×D12—22no—
64C2×C3×D12—22no—
65C2×C3×D12—21no—
66C2×C3×D12C2312yes—
67C2×C3×C4×D3—22no—
68C2×C3×C4×D3—22no—
69C2×C3×C4×D3D412yes—
70C2×C3×C4×D3C2312yes—
71C2×C3×Dic6—21no—
72C2×C3×Dic6—22no—
73C2×C3×Dic6D414yescomplemented
74C2×C3×Dic6C2312yes—
75C2×#627—28no—
76C2×#627—24no—
77C2×#625—24no—
78C2×#625—44no—
79C2×D3×Dic3—28no—
80C2×D3×Dic3—24no—
81D3×Dic6—216no—
82D3×Dic6—28no—
83D3×Dic6—28no—
84C2×C32×C8—22no—
85C2×C32×C8C2312yes—
86C4⋊(C3⋊Dic3)—21no—
87C4⋊(C3⋊Dic3)C2312yes—
88C2×C3×C3⋊C8—22no—
89C2×C3×C3⋊C8C2312yes—
90C3×#204—28no—
91(C2×D3)⋊Dic3—24no—
92#3716—28no—
93C2×#448—91noSylow
94C22×C3×Q8—31no—
95C22×C3×D4—31no—
96C23×C3×C4—31no—
97C22×#67—61no—
98C22×#67—61no—
99C23×Dic3—61no—
100C2×D3×Q8—34no—
101C2×D3×Q8—64no—
102C2×D3×Q8—64no—
103C2×D3×Q8—62no—
104C22×D12C2×D311yescharacteristic
105C22×C4×D3—61no—
106C22×C4×D3C2×D311yescharacteristic
107C22×Dic6—31no—
108C22×Dic6—31no—
109C22×Dic6—34no—
110C22×Dic6—61no—
111C22×Dic6—64no—
112C22×Dic6—62no—
113C22×Dic6—61no—
114C22×Dic6—61no—
115C22×Dic6—64no—
116C22×Dic6C2×D311yescharacteristic
117C2×C3×SD16—34no—
118C2×C3×SD16—64no—
119C22×C3×C8—21no—
120C22×C3×C8—31no—
121C22×C3×C8C2×D311yescharacteristic
122C22×C3×C8C2×D311yescharacteristic
123C2×#217—61no—
124#938—34no—
125#938—62no—
126C2×#214—34no—
127C2×#214—64no—
128#930—34no—
129#930—62no—
130C2×(C2×D3)⋊C4—61no—
131C2×C4⋊Dic3—31no—
132C2×C4⋊Dic3—31no—
133C2×C4⋊Dic3—61no—
134C22×C3⋊C8C2×D311yescharacteristic
135C2×#204—24no—
136C2×#204—34no—
137C2×#204—64no—
138C2×#204C2×D314yescomplemented
139C3×C22⋊C8—34no—
140#835—34no—
141(C2×D3)⋊C8C2×D314yescomplemented
142#816—34no—
143#816—34no—
144#816—34no—
145#816—64no—
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—
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2×D412yes—
157C2×C32×C4C2×D412yes—
158C2×C32×C4C2411yescharacteristic
159C2×C3⋊Dic3—24no—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—42no—
163#634—24no—
164#634—22no—
165#634C2×D414yescomplemented
166C2×C3×Dic3—24no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3C2×D412yes—
170C3×D12—22no—
171C3×D12—22no—
172C3×D12—42no—
173C3×C4×D3—24no—
174C3×C4×D3—22no—
175C3×C4×D3—22no—
176C3×Dic6—24no—
177C3×Dic6—22no—
178C3×Dic6C2×D414yescomplemented
179#627—216no—
180#625—48no—
181D3×Dic3—216no—
182C32×C8—22no—
183C3×C3⋊C8—22no—
184C23×Q8—91no—
185C22×SD16—31no—
186C22×SD16—91no—
187C2×#121—91no—
188#448—98no—
189C2×#103—91no—
190C2×#103—91no—
191C2×C22⋊C8—31no—
192C24×C3—31no—
193C24×C3—61no—
194C23×D3—21no—
195C23×D3D1211yescharacteristic
196C2×C3×Q8—34no—
197C2×C3×Q8—32no—
198C2×C3×Q8—61no—
199C2×C3×Q8—62no—
200C2×C3×D4—32no—
201C2×C3×D4—61no—
202C2×C3×D4—62no—
203C2×C3×D4—62no—
204C22×C3×C4—21no—
205C22×C3×C4—31no—
206C22×C3×C4—32no—
207C22×C3×C4—32no—
208C22×C3×C4—61no—
209C22×C3×C4—62no—
210C22×C3×C4—62no—
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C2×#67—64no—
214C2×#67—64no—
215C2×#67—124no—
216C2×#67—124no—
217C22×Dic3—21no—
218C22×Dic3—64no—
219C22×Dic3—68no—
220C22×Dic3—61no—
221C22×Dic3—61no—
222C22×Dic3—61no—
223C22×Dic3—61no—
224C22×Dic3—121no—
225C22×Dic3—121no—
226C22×Dic3D1211yescharacteristic
227D3×Q8—68no—
228D3×Q8—68no—
229D3×Q8—616no—
230C2×D12—22no—
231C2×D12—22no—
232C2×D12—21no—
233C2×D12C22×D312yes—
234C2×C4×D3—22no—
235C2×C4×D3—22no—
236C2×C4×D3—68no—
237C2×C4×D3—64no—
238C2×C4×D3D1212yes—
239C2×C4×D3C22×D312yes—
240C2×Dic6—21no—
241C2×Dic6—22no—
242C2×Dic6—34no—
243C2×Dic6—34no—
244C2×Dic6—32no—
245C2×Dic6—32no—
246C2×Dic6—62no—
247C2×Dic6—64no—
248C2×Dic6—68no—
249C2×Dic6—616no—
250C2×Dic6—64no—
251C2×Dic6—68no—
252C2×Dic6—68no—
253C2×Dic6—61no—
254C2×Dic6—61no—
255C2×Dic6—62no—
256C2×Dic6—62no—
257C2×Dic6—64no—
258C2×Dic6—68no—
259C2×Dic6—121no—
260C2×Dic6—122no—
261C2×Dic6#6714yescomplemented
262C2×Dic6C22×D312yes—
263C3×SD16—68no—
264C2×C3×C8—22no—
265C2×C3×C8—22no—
266C2×C3×C8—22no—
267C2×C3×C8—32no—
268C2×C3×C8—42no—
269C2×C3×C8—62no—
270C2×C3×C8C22×D312yes—
271C2×C3×C8C22×D312yes—
272#217—64no—
273#214—68no—
274(C2×D3)⋊C4—64no—
275C4⋊Dic3—32no—
276C4⋊Dic3—32no—
277C4⋊Dic3—62no—
278C4⋊Dic3—61no—
279C4⋊Dic3—61no—
280C4⋊Dic3—121no—
281C2×C3⋊C8—22no—
282C2×C3⋊C8C22×D312yes—
283#204—28no—
284#204—68no—
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#12012yes—
298C32×C4C22×D411yescharacteristic
299C32×C4C22×D411yescharacteristic
300C3⋊Dic3—24no—
301C3⋊Dic3—42no—
302C3×Dic3—24no—
303C3×Dic3—22no—
304C22×Q8—31no—
305C22×Q8—94no—
306C22×Q8—91no—
307C22×Q8—181no—
308C22×Q8—182no—
309C22×Q8—184no—
310C22×Q8—184no—
311C22×D4—31no—
312C22×D4—181no—
313C23×C4—31no—
314C23×C4—181no—
315C2×SD16—34no—
316C2×SD16—64no—
317C2×SD16—94no—
318C2×SD16—184no—
319C22×C8—31no—
320C22×C8D3211yescharacteristic
321#121—94no—
322#121—182no—
323C2×C4⋊C4—91no—
324C2×C22⋊C4—181no—
325#103—94no—
326#103—94no—
327C22⋊C8—34no—
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×C3C2×D1211yescharacteristic
338C23×C3D3×D411yescharacteristic
339C22×D3—22no—
340C22×D3—22no—
341C22×D3—22no—
342C22×D3—42no—
343C22×D3—42no—
344C22×D3—42no—
345C22×D3#20414yescomplemented
346C22×D3C2×D1212yes—
347C3×Q8—34no—
348C3×Q8—64no—
349C3×Q8—62no—
350C3×D4—62no—
351C3×D4—62no—
352C3×D4—122no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—32no—
358C2×C3×C4—64no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—64no—
362C2×C3×C4—62no—
363C2×C3×C4—62no—
364C2×C3×C4C2×D1211yescharacteristic
365C2×C3×C4D3×D411yescharacteristic
366C2×C3×C4D3×D412yes—
367C2×C3×C4D3×D412yes—
368C2×C3×C4D3×D412yes—
369C2×C3×C4C2×#6712yes—
370C2×C3×C4C23×D311yescharacteristic
371C2×C3×C4C23×D311yescharacteristic
372#67—128no—
373#67—128no—
374C2×Dic3—22no—
375C2×Dic3—24no—
376C2×Dic3—22no—
377C2×Dic3—616no—
378C2×Dic3—64no—
379C2×Dic3—64no—
380C2×Dic3—62no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—122no—
385C2×Dic3—124no—
386C2×Dic3—122no—
387C2×Dic3—122no—
388C2×Dic3—122no—
389C2×Dic3—242no—
390C2×Dic3C2×D1212yes—
391D12—22no—
392D12—22no—
393D12—42no—
394C4×D3—24no—
395C4×D3—22no—
396C4×D3—22no—
397C4×D3—616no—
398Dic6—24no—
399Dic6—22no—
400Dic6—34no—
401Dic6—34no—
402Dic6—64no—
403Dic6—616no—
404Dic6—616no—
405Dic6—64no—
406Dic6—64no—
407Dic6—62no—
408Dic6—62no—
409Dic6—122no—
410Dic6—124no—
411Dic6C2×#6714yescomplemented
412C3×C8—22no—
413C3×C8—22no—
414C3×C8—42no—
415C3×C8—62no—
416C3⋊C8—22no—
417C2×C32#44814yescomplemented
418C2×C32C2×#12011yescharacteristic
419C2×C32C22×SD1611yescharacteristic
420C2×C32C2×#13711yescharacteristic
421C3×D3—24no—
422C3×D3—82no—
423C24—31no—
424C24—61no—
425C2×Q8—32no—
426C2×Q8—34no—
427C2×Q8—61no—
428C2×Q8—62no—
429C2×Q8—92no—
430C2×Q8—94no—
431C2×Q8—184no—
432C2×Q8—188no—
433C2×Q8—188no—
434C2×Q8—188no—
435C2×Q8—1816no—
436C2×Q8—181no—
437C2×Q8—182no—
438C2×D4—32no—
439C2×D4—61no—
440C2×D4—62no—
441C2×D4—62no—
442C2×D4—184no—
443C2×D4—364no—
444C22×C4—31no—
445C22×C4—32no—
446C22×C4—32no—
447C22×C4—61no—
448C22×C4—62no—
449C22×C4—62no—
450C22×C4—184no—
451C22×C4—188no—
452C22×C4—181no—
453C22×C4—181no—
454C22×C4C2×D3211yescharacteristic
455SD16—68no—
456SD16—188no—
457C2×C8—22no—
458C2×C8—32no—
459C2×C8—62no—
460C2×C8C2×D3212yes—
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×C3#88212yes—
477C22×C3C2×#20412yes—
478C22×C3#90912yes—
479C22×C3D3×SD1612yes—
480C22×C3#91512yes—
481C22×C3#93712yes—
482C22×C3C22×D1211yescharacteristic
483C22×C3C2×D3×D411yescharacteristic
484C2×D3—22no—
485C2×D3—22no—
486C2×D3—28no—
487C2×D3—42no—
488C2×D3—42no—
489C2×D3—42no—
490C2×D3—84no—
491C2×D3C2×#20414yescomplemented
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—22no—
495C3×C4—64no—
496C3×C4—62no—
497C3×C4#88212yes—
498C3×C4#93712yes—
499C3×C4C2×D3×D411yescharacteristic
500C3×C4C2×D3×D411yescharacteristic
501C3×C4C2×D3×D411yescharacteristic
502C3×C4C22×#6711yescharacteristic
503Dic3—22no—
504Dic3—24no—
505Dic3—64no—
506Dic3—64no—
507Dic3—124no—
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×D1211yescharacteristic
521Q8—34no—
522Q8—62no—
523Q8—64no—
524Q8—94no—
525Q8—1816no—
526Q8—182no—
527Q8—184no—
528D4—62no—
529D4—62no—
530D4—122no—
531D4—368no—
532C2×C4—32no—
533C2×C4—62no—
534C2×C4—62no—
535C2×C4—64no—
536C2×C4—62no—
537C2×C4—62no—
538C2×C4—64no—
539C2×C4—1816no—
540C2×C4—182no—
541C2×C4—184no—
542C2×C4—182no—
543C2×C4—362no—
544C2×C4D3×D1211yescharacteristic
545C2×C4#380212yes—
546C2×C4D3×#6712yes—
547C2×C4C22×D3211yescharacteristic
548C8—22no—
549C8—62no—
550C2×C3—24no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—21no—
554C2×C3—64no—
555C2×C3—242no—
556C2×C3#473814yescomplemented
557C2×C3#517014yescomplemented
558C2×C3C2×#88211yescharacteristic
559C2×C3C22×#20411yescharacteristic
560C2×C3C2×#90911yescharacteristic
561C2×C3C2×D3×SD1611yescharacteristic
562C2×C3C2×#91511yescharacteristic
563C2×C3C2×#93711yescharacteristic
564D3—24no—
565D3—82no—
566C22—34no—
567C22—68no—
568C22—62no—
569C22—62no—
570C22—122no—
571C22—122no—
572C22—122no—
573C22—244no—
574C22D3×#20412yes—
575C22#6380012yes—
576C22#6392212yes—
577C22C2×D3×D1211yescharacteristic
578C4—62no—
579C4—64no—
580C4—184no—
581C4—362no—
582C4#6392212yes—
583C4C2×#380211yescharacteristic
584C4C2×D3×#6711yescharacteristic
585C3—21no—
586C3C2×#473811yescharacteristic, complemented
587C3C2×#517011yescharacteristic, complemented
588C2—64no—
589C2—242no—
590C2#1059082214yesdirect product factor
591C2C2×D3×#20411yescharacteristic
592C2C2×#6380011yescharacteristic
593C2C2×#6392211yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC2×#63908C2
hypercenterC22×C8D32
hypocenterC32C2×#448
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
1. C22×D3×Dic6C2semidirect
2. C22×C3×#204C2semidirect
4. C22×#3716C2semidirect
5. C2×#63643C2semidirect
6. C2×C3×(C2×D3)⋊C8C2semidirect
7. C2×#63566C2semidirect
8. #10590822C2direct (N × H)
21. C2×D3×Dic6C22semidirect
26. C2×C3×#204C22semidirect
31. C2×#3716C22semidirect
32. #63643C22semidirect
33. C3×(C2×D3)⋊C8C22semidirect
34. #63566C22semidirect
42. C22×#204D3semidirect
46. C2×(C2×D3)⋊C8D3semidirect
59. C2×#634D4semidirect
73. C2×C3×Dic6D4semidirect
138. C2×#204C2×D3semidirect
141. (C2×D3)⋊C8C2×D3semidirect
153. C22×C3×D3SD16semidirect
165. #634C2×D4semidirect
178. C3×Dic6C2×D4semidirect
261. C2×Dic6#67semidirect
296. C2×C3×D3C2×SD16semidirect
345. C22×D3#204semidirect
411. Dic6C2×#67semidirect
417. C2×C32#448semidirect
491. C2×D3C2×#204semidirect
511. C32C2×#448semidirect
556. C2×C3#4738semidirect
557. C2×C3#5170semidirect
586. C3C2×#4738semidirect
587. C3C2×#5170semidirect
590. C2#10590822direct (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×C3×#2042
C2×#639082
C22×#37162
C2×#636432
C2×C3×(C2×D3)⋊C82
C2×#635662
#105908222
C2×#51703
C2×#47383