Finite Group Databasebeta

← C2×#10590960 #11863791

Subgroups — C2×#10590960 #11863791

Order 1152.

1601 conjugacy classes of subgroups.

The subgroup lattice has 587 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3795C211yesmaximal, characteristic
2C22×C3×#204C211yesmaximal, characteristic, complemented
3C2×#63856C211yesmaximal, characteristic, complemented
4C22×#3719C211yesmaximal, characteristic, complemented
5C2×#63643C211yesmaximal, characteristic, complemented
6C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
7C2×#63563C211yesmaximal, characteristic, complemented
8#10590960C218yesmaximal, direct product factor
9C2×#5173—31nomaximal
10C2×#4733—31nomaximal
11C22×#634C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×#625—21no—
16C22×D3×Dic3—21no—
17C2×#3795—24no—
18C2×#3795—24no—
19C2×#3795—22no—
20C2×#3795C2214yes—
21C22×C32×C8C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C2×C3×#204—24no—
25C2×C3×#204C2214yescomplemented
26C2×#3724—21no—
27C2×(C2×D3)⋊Dic3—21no—
28#63856—22no—
29#63856C2214yescomplemented
30C2×#3719—24no—
31C2×#3719C2214yescomplemented
32#63643C2214yescomplemented
33C3×(C2×D3)⋊C8C2214yescomplemented
34#63563C2214yescomplemented
35C22×#237—31no—
36C22×#235—31no—
37C22×C3×SD16—31no—
38C2×#946—31no—
39C22×#216—31no—
40C2×#924—31no—
41C22×Dic12—31no—
42C22×#204D311yescharacteristic, complemented
43C2×C3×C22⋊C8—31no—
44C2×#832—31no—
45#5173—38no—
46C2×#821—31no—
47C2×(C2×D3)⋊C8D311yescharacteristic, complemented
48C2×#816—31no—
49C2×#816—31no—
50C2×#816—61no—
51#4733—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×#634D414yes—
60C2×#634C2312yes—
61C22×C3×Dic3—21no—
62C22×C3×Dic3D411yescharacteristic
63C2×C3×D12—21no—
64C2×C3×D12—22no—
65C2×C3×D12D414yes—
66C2×C3×D12C2312yes—
67C2×C3×C4×D3—22no—
68C2×C3×C4×D3—22no—
69C2×C3×C4×D3D412yes—
70C2×C3×C4×D3C2312yes—
71C2×C3×Dic6—22no—
72C2×C3×Dic6—22no—
73C2×C3×Dic6—21no—
74C2×C3×Dic6C2312yes—
75C2×#625—28no—
76C2×#625—24no—
77C2×D3×Dic3—28no—
78C2×D3×Dic3—24no—
79#3795—216no—
80#3795—28no—
81#3795—28no—
82C2×C32×C8—22no—
83C2×C32×C8C2312yes—
84C4⋊(C3⋊Dic3)—21no—
85C4⋊(C3⋊Dic3)C2312yes—
86C2×C3×C3⋊C8—22no—
87C2×C3×C3⋊C8C2312yes—
88C3×#204—28no—
89#3724—24no—
90(C2×D3)⋊Dic3—24no—
91#3719—28no—
92C2×#452—91noSylow
93C22×C3×Q8—31no—
94C22×C3×D4—31no—
95C23×C3×C4—31no—
96C22×#67—61no—
97C22×#67—61no—
98C23×Dic3—61no—
99C2×#237—34no—
100C2×#237—64no—
101C2×#237—64no—
102C2×#237—62no—
103C2×#235—34no—
104C2×#235—64no—
105C2×#235—62no—
106C2×#235—64no—
107C22×D12C2×D311yescharacteristic
108C22×C4×D3—61no—
109C22×C4×D3C2×D311yescharacteristic
110C22×Dic6—31no—
111C22×Dic6—31no—
112C22×Dic6—61no—
113C22×Dic6C2×D311yescharacteristic
114C2×C3×SD16—34no—
115C2×C3×SD16—64no—
116C22×C3×C8—21no—
117C22×C3×C8—31no—
118C22×C3×C8C2×D311yescharacteristic
119C22×C3×C8C2×D311yescharacteristic
120C2×#217—61no—
121#946—34no—
122#946—62no—
123C2×#216—34no—
124C2×#216—64no—
125C2×(C2×D3)⋊C4—61no—
126C2×C4⋊Dic3—31no—
127C2×C4⋊Dic3—31no—
128C2×C4⋊Dic3—61no—
129#924—34no—
130#924—62no—
131C2×Dic3⋊C4—61no—
132C2×Dic3⋊C4—61no—
133C22×C3⋊C8C2×D311yescharacteristic
134C2×Dic12—34no—
135C2×Dic12—64no—
136C2×#204—24no—
137C2×#204C2×D314yescomplemented
138C3×C22⋊C8—34no—
139#832—34no—
140#821—34no—
141(C2×D3)⋊C8C2×D314yescomplemented
142#816—34no—
143#816—34no—
144#816—64no—
145C23×C32C2×D411yescharacteristic
146C22×C3×D3—24no—
147C22×C3×D3—22no—
148C22×C3×D3—22no—
149C22×C3×D3—22no—
150C22×C3×D3—22no—
151C22×C3×D3—42no—
152C22×C3×D3—42no—
153C22×C3×D3C2×D412yes—
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D412yes—
156C2×C32×C4C2×D412yes—
157C2×C32×C4C2411yescharacteristic
158C2×C3⋊Dic3—24no—
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—42no—
162#634—24no—
163#634—22no—
164#634C2×D414yes—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—42no—
168C2×C3×Dic3C2×D412yes—
169C3×D12—24no—
170C3×D12—22no—
171C3×D12C2×D414yes—
172C3×C4×D3—24no—
173C3×C4×D3—22no—
174C3×C4×D3—22no—
175C3×Dic6—22no—
176C3×Dic6—22no—
177C3×Dic6—42no—
178#625—216no—
179D3×Dic3—216no—
180C32×C8—22no—
181C3×C3⋊C8—22no—
182C22×#41—91no—
183C22×Q16—91no—
184C22×SD16—31no—
185C2×C22⋊Q8—91no—
186#452—98no—
187C2×#103—91no—
188C2×#102—91no—
189C2×C22⋊C8—31no—
190C24×C3—31no—
191C24×C3—61no—
192C23×D3—21no—
193C23×D3D1211yescharacteristic
194C2×C3×Q8—32no—
195C2×C3×Q8—61no—
196C2×C3×Q8—62no—
197C2×C3×Q8—62no—
198C2×C3×D4—34no—
199C2×C3×D4—32no—
200C2×C3×D4—61no—
201C2×C3×D4—62no—
202C22×C3×C4—21no—
203C22×C3×C4—31no—
204C22×C3×C4—32no—
205C22×C3×C4—32no—
206C22×C3×C4—62no—
207C22×C3×C4—62no—
208C22×C3×C4—61no—
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C2×#67—64no—
212C2×#67—68no—
213C2×#67—68no—
214C2×#67—64no—
215C22×Dic3—21no—
216C22×Dic3—68no—
217C22×Dic3—61no—
218C22×Dic3—61no—
219C22×Dic3—64no—
220C22×Dic3—61no—
221C22×Dic3—61no—
222C22×Dic3—121no—
223C22×Dic3—121no—
224C22×Dic3D1211yescharacteristic
225#237—68no—
226#237—68no—
227#237—616no—
228#235—68no—
229#235—616no—
230#235—68no—
231C2×D12—21no—
232C2×D12—22no—
233C2×D12#6714yes—
234C2×D12C22×D312yes—
235C2×C4×D3—22no—
236C2×C4×D3—22no—
237C2×C4×D3—64no—
238C2×C4×D3—68no—
239C2×C4×D3D1212yes—
240C2×C4×D3C22×D312yes—
241C2×Dic6—22no—
242C2×Dic6—22no—
243C2×Dic6—21no—
244C2×Dic6—34no—
245C2×Dic6—34no—
246C2×Dic6—32no—
247C2×Dic6—32no—
248C2×Dic6—62no—
249C2×Dic6—64no—
250C2×Dic6—61no—
251C2×Dic6—61no—
252C2×Dic6—62no—
253C2×Dic6—62no—
254C2×Dic6—121no—
255C2×Dic6—122no—
256C2×Dic6C22×D312yes—
257C3×SD16—68no—
258C2×C3×C8—22no—
259C2×C3×C8—22no—
260C2×C3×C8—22no—
261C2×C3×C8—32no—
262C2×C3×C8—42no—
263C2×C3×C8—62no—
264C2×C3×C8C22×D312yes—
265C2×C3×C8C22×D312yes—
266#217—64no—
267#216—68no—
268(C2×D3)⋊C4—64no—
269C4⋊Dic3—32no—
270C4⋊Dic3—32no—
271C4⋊Dic3—62no—
272C4⋊Dic3—61no—
273C4⋊Dic3—61no—
274C4⋊Dic3—121no—
275Dic3⋊C4—64no—
276Dic3⋊C4—64no—
277C2×C3⋊C8—22no—
278C2×C3⋊C8C22×D312yes—
279Dic12—68no—
280#204—28no—
281C22×C32#12012yes—
282C22×C32#13512yes—
283C22×C32#13712yes—
284C22×C32C22×D411yescharacteristic
285C2×C3×D3—24no—
286C2×C3×D3—22no—
287C2×C3×D3—22no—
288C2×C3×D3—22no—
289C2×C3×D3—42no—
290C2×C3×D3—42no—
291C2×C3×D3—44no—
292C2×C3×D3—48no—
293C32×C4#12012yes—
294C32×C4C22×D411yescharacteristic
295C32×C4C22×D411yescharacteristic
296C3⋊Dic3—24no—
297C3⋊Dic3—42no—
298C3×Dic3—22no—
299C3×Dic3—42no—
300C2×#41—94no—
301C2×#41—182no—
302C2×#41—184no—
303C2×#41—184no—
304C22×Q8—31no—
305C22×Q8—91no—
306C22×D4—31no—
307C22×D4—181no—
308C23×C4—31no—
309C23×C4—181no—
310C2×Q16—94no—
311C2×Q16—184no—
312C2×SD16—34no—
313C2×SD16—64no—
314C22×C8—31no—
315C22×C8D3211yescharacteristic
316C22⋊Q8—94no—
317C22⋊Q8—182no—
318C2×C4⋊C4—91no—
319C2×C4⋊C4—181no—
320C2×C22⋊C4—181no—
321#103—94no—
322#102—94no—
323C22⋊C8—34no—
324C23×C3—21no—
325C23×C3—32no—
326C23×C3—64no—
327C23×C3—62no—
328C23×C3—62no—
329C23×C3—62no—
330C23×C3—62no—
331C23×C3—122no—
332C23×C3—122no—
333C23×C3C2×D1211yescharacteristic
334C23×C3D3×D411yescharacteristic
335C22×D3—22no—
336C22×D3—22no—
337C22×D3—22no—
338C22×D3—24no—
339C22×D3—22no—
340C22×D3—42no—
341C22×D3—42no—
342C22×D3C2×D1212yes—
343C3×Q8—62no—
344C3×Q8—62no—
345C3×Q8—122no—
346C3×D4—34no—
347C3×D4—64no—
348C3×D4—62no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—32no—
354C2×C3×C4—62no—
355C2×C3×C4—64no—
356C2×C3×C4—62no—
357C2×C3×C4—62no—
358C2×C3×C4—62no—
359C2×C3×C4—122no—
360C2×C3×C4C2×D1211yescharacteristic
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×D412yes—
363C2×C3×C4D3×D412yes—
364C2×C3×C4D3×D412yes—
365C2×C3×C4C2×#6712yes—
366C2×C3×C4C23×D311yescharacteristic
367C2×C3×C4C23×D311yescharacteristic
368#67—616no—
369#67—616no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—42no—
373C2×Dic3—616no—
374C2×Dic3—64no—
375C2×Dic3—64no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—122no—
381C2×Dic3—124no—
382C2×Dic3—122no—
383C2×Dic3—122no—
384C2×Dic3—122no—
385C2×Dic3—242no—
386C2×Dic3C2×D1212yes—
387D12—24no—
388D12—22no—
389D12C2×#6714yes—
390C4×D3—24no—
391C4×D3—22no—
392C4×D3—22no—
393C4×D3—616no—
394Dic6—22no—
395Dic6—22no—
396Dic6—34no—
397Dic6—34no—
398Dic6—42no—
399Dic6—64no—
400Dic6—64no—
401Dic6—64no—
402Dic6—62no—
403Dic6—62no—
404Dic6—122no—
405Dic6—124no—
406C3×C8—22no—
407C3×C8—22no—
408C3×C8—42no—
409C3×C8—62no—
410C3⋊C8—22no—
411C2×C32#45214yescomplemented
412C2×C32C2×#12011yescharacteristic
413C2×C32C2×#13511yescharacteristic
414C2×C32C2×#13711yescharacteristic
415C3×D3—42no—
416C3×D3—44no—
417C24—31no—
418C24—61no—
419#41—188no—
420#41—188no—
421#41—1816no—
422C2×Q8—32no—
423C2×Q8—61no—
424C2×Q8—62no—
425C2×Q8—62no—
426C2×Q8—92no—
427C2×Q8—94no—
428C2×Q8—181no—
429C2×Q8—182no—
430C2×D4—32no—
431C2×D4—34no—
432C2×D4—61no—
433C2×D4—62no—
434C2×D4—184no—
435C2×D4—188no—
436C22×C4—31no—
437C22×C4—32no—
438C22×C4—32no—
439C22×C4—62no—
440C22×C4—62no—
441C22×C4—61no—
442C22×C4—184no—
443C22×C4—188no—
444C22×C4—181no—
445C22×C4—181no—
446C22×C4C2×D3211yescharacteristic
447Q16—188no—
448SD16—68no—
449C2×C8—22no—
450C2×C8—32no—
451C2×C8—62no—
452C2×C8C2×D3212yes—
453C4⋊C4—92no—
454C4⋊C4—184no—
455C4⋊C4—181no—
456C22⋊C4—184no—
457C22×C3—21no—
458C22×C3—22no—
459C22×C3—22no—
460C22×C3—22no—
461C22×C3—64no—
462C22×C3—62no—
463C22×C3—62no—
464C22×C3—62no—
465C22×C3—124no—
466C22×C3—122no—
467C22×C3—122no—
468C22×C3—128no—
469C22×C3#88212yes—
470C22×C3#90412yes—
471C22×C3#90912yes—
472C22×C3#91512yes—
473C22×C3#91612yes—
474C22×C3#93712yes—
475C22×C3C22×D1211yescharacteristic
476C22×C3C2×D3×D411yescharacteristic
477C2×D3—22no—
478C2×D3—22no—
479C2×D3—22no—
480C2×D3—24no—
481C2×D3—48no—
482C2×D3—44no—
483C2×D3—42no—
484C2×D3—42no—
485C3×C4—21no—
486C3×C4—21no—
487C3×C4—22no—
488C3×C4—62no—
489C3×C4—122no—
490C3×C4#88212yes—
491C3×C4#93712yes—
492C3×C4C2×D3×D411yescharacteristic
493C3×C4C2×D3×D411yescharacteristic
494C3×C4C2×D3×D411yescharacteristic
495C3×C4C22×#6711yescharacteristic
496Dic3—22no—
497Dic3—42no—
498Dic3—64no—
499Dic3—64no—
500Dic3—124no—
501Dic3—122no—
502Dic3—122no—
503Dic3—242no—
504C32C2×#45211yescharacteristic, complemented, Sylow
505C23—32no—
506C23—62no—
507C23—62no—
508C23—62no—
509C23—62no—
510C23—64no—
511C23—122no—
512C23—122no—
513C23D3×D1211yescharacteristic
514Q8—62no—
515Q8—62no—
516Q8—94no—
517Q8—122no—
518Q8—182no—
519Q8—184no—
520D4—34no—
521D4—62no—
522D4—64no—
523D4—1816no—
524C2×C4—32no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—62no—
528C2×C4—64no—
529C2×C4—62no—
530C2×C4—122no—
531C2×C4—1816no—
532C2×C4—182no—
533C2×C4—184no—
534C2×C4—182no—
535C2×C4—362no—
536C2×C4D3×D1211yescharacteristic
537C2×C4#380212yes—
538C2×C4D3×#6712yes—
539C2×C4C22×D3211yescharacteristic
540C8—22no—
541C8—62no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—24no—
545C2×C3—21no—
546C2×C3—124no—
547C2×C3—122no—
548C2×C3#473314yescomplemented
549C2×C3#517314yescomplemented
550C2×C3C2×#88211yescharacteristic
551C2×C3C2×#90411yescharacteristic
552C2×C3C2×#90911yescharacteristic
553C2×C3C2×#91511yescharacteristic
554C2×C3C2×#91611yescharacteristic
555C2×C3C2×#93711yescharacteristic
556D3—42no—
557D3—44no—
558C22—62no—
559C22—62no—
560C22—62no—
561C22—64no—
562C22—122no—
563C22—122no—
564C22—124no—
565C22—128no—
566C22#6380012yes—
567C22#6380612yes—
568C22#6392212yes—
569C22C2×D3×D1211yescharacteristic
570C4—62no—
571C4—122no—
572C4—184no—
573C4—362no—
574C4#6392212yes—
575C4C2×#380211yescharacteristic
576C4C2×D3×#6711yescharacteristic
577C3—21no—
578C3C2×#473311yescharacteristic, complemented
579C3C2×#517311yescharacteristic, complemented
580C2—122no—
581C2—124no—
582C2#1059096014yesdirect product factor
583C2C2×#6380011yescharacteristic
584C2C2×#6380611yescharacteristic
585C2C2×#6392211yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×#3795C2
hypercenterC22×C8D32
hypocenterC32C2×#452
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×C3×#204C2semidirect
3. C2×#63856C2semidirect
4. C22×#3719C2semidirect
5. C2×#63643C2semidirect
6. C2×C3×(C2×D3)⋊C8C2semidirect
7. C2×#63563C2semidirect
8. #10590960C2direct (N × H)
25. C2×C3×#204C22semidirect
29. #63856C22semidirect
31. C2×#3719C22semidirect
32. #63643C22semidirect
33. C3×(C2×D3)⋊C8C22semidirect
34. #63563C22semidirect
42. C22×#204D3semidirect
47. C2×(C2×D3)⋊C8D3semidirect
137. C2×#204C2×D3semidirect
141. (C2×D3)⋊C8C2×D3semidirect
411. C2×C32#452semidirect
504. C32C2×#452semidirect
548. C2×C3#4733semidirect
549. C2×C3#5173semidirect
578. C3C2×#4733semidirect
579. C3C2×#5173semidirect
582. C2#10590960direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37952
C22×C3×#2042
C2×#638562
C22×#37192
C2×#636432
C2×C3×(C2×D3)⋊C82
C2×#635632
#105909602
C2×#51733
C2×#47333