Finite Group Databasebeta

← C2×#10591599 #11863795

Subgroups — C2×#10591599 #11863795

Order 1152.

1649 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#239C211yesmaximal, characteristic
2C22×#3756C211yesmaximal, characteristic, complemented
3C2×#63857C211yesmaximal, characteristic, complemented
4C22×#3716C211yesmaximal, characteristic, complemented
5C2×C3×#835C211yesmaximal, characteristic, complemented
6#10591599C218yesmaximal, direct product factor
7C2×#63562C211yesmaximal, characteristic, complemented
8C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
9C2×#5239—31nomaximal
10C2×#4808—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C2×C3×#239—24no—
14C2×C3×#239—24no—
15C2×C3×#239—22no—
16C2×C3×#239C2214yes—
17C22×C3×D12—21no—
18C22×C3×D12C2211yescharacteristic
19C22×C3×C4×D3—21no—
20C22×C3×C4×D3C2211yescharacteristic
21C2×#3756—24no—
22C2×#3756C2214yescomplemented
23C22×C3⋊(C3⋊C8)C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C2×Dic3⋊Dic3—21no—
27C2×(C2×D3)⋊Dic3—21no—
28#63857—22no—
29#63857C2214yescomplemented
30C2×#3716—24no—
31C2×#3716C2214yescomplemented
32C3×#835C2214yescomplemented
33#63562C2214yescomplemented
34(C2×D3)⋊(C3⋊C8)C2214yescomplemented
35C22×C3×#41—31no—
36C22×#239D311yescharacteristic
37C22×#216—31no—
38C22×#216—31no—
39C22×#216—61no—
40C22×#214—31no—
41C2×#924—31no—
42C22×#204—31no—
43C2×#897—31no—
44C2×C3×#103—31no—
45#5239—38no—
46C2×#835D311yescharacteristic, complemented
47C2×#832—31no—
48C2×#830—31no—
49C2×(C2×D3)⋊C8—31no—
50C2×#809—31no—
51#4808—38no—
52C23×C3×D3—21no—
53C23×C3×D3D411yescharacteristic
54C2×C32×Q8—22no—
55C2×C32×Q8—21no—
56C2×C32×Q8D414yes—
57C2×C32×Q8C2312yes—
58C22×C32×C4—21no—
59C22×C32×C4C2311yescharacteristic
60C22×C3⋊Dic3—21no—
61C2×#634—22no—
62C2×#634—22no—
63C2×#634—21no—
64C2×#634C2312yes—
65C22×C3×Dic3—21no—
66C22×C3×Dic3D411yescharacteristic
67C3×#239—216no—
68C3×#239—28no—
69C3×#239—28no—
70C2×C3×D12—28no—
71C2×C3×D12—24no—
72C2×C3×D12—21no—
73C2×C3×D12—22no—
74C2×C3×D12D414yes—
75C2×C3×D12C2312yes—
76C2×C3×C4×D3—28no—
77C2×C3×C4×D3—22no—
78C2×C3×C4×D3—22no—
79C2×C3×C4×D3—24no—
80C2×C3×C4×D3D412yes—
81C2×C3×C4×D3C2312yes—
82#3756—28no—
83C2×C3⋊(C3⋊C8)—22no—
84C2×C3⋊(C3⋊C8)C2312yes—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3C2312yes—
87C2×C3×C3⋊C8—22no—
88C2×C3×C3⋊C8C2312yes—
89Dic3⋊Dic3—24no—
90(C2×D3)⋊Dic3—24no—
91#3716—28no—
92C2×#452—91noSylow
93C2×C3×#41—34no—
94C2×C3×#41—62no—
95C2×C3×#41—64no—
96C2×C3×#41—64no—
97C22×C3×Q8—21no—
98C22×C3×Q8C2×D311yescharacteristic
99C22×C3×Q8C2×D311yescharacteristic
100C22×C3×D4—31no—
101C22×C3×D4—61no—
102C23×C3×C4—31no—
103C23×C3×C4—61no—
104C2×#239—24no—
105C2×#239—24no—
106C2×#239—22no—
107C2×#239C2×D314yes—
108C22×D12—21no—
109C22×D12C2×D311yescharacteristic
110C22×C4×D3—21no—
111C22×C4×D3C2×D311yescharacteristic
112C22×Dic6—31no—
113C22×Dic6—31no—
114C22×Dic6—61no—
115C22×C3×C8—31no—
116C2×C3×C4⋊C4—31no—
117C2×#217—61no—
118C2×#216—34no—
119C2×#216—34no—
120C2×#216—64no—
121C2×#216—68no—
122C2×#216—64no—
123C2×#216—64no—
124C2×#214—34no—
125C2×#214—64no—
126C2×(C2×D3)⋊C4—61no—
127C2×C4⋊Dic3—61no—
128C2×C4⋊Dic3C2×D311yescharacteristic
129#924—34no—
130#924—62no—
131C2×Dic3⋊C4—61no—
132C22×C3⋊C8—31no—
133C22×C3⋊C8—31no—
134C22×C3⋊C8—61no—
135C22×C3⋊C8C2×D311yescharacteristic
136C2×#204—34no—
137C2×#204—64no—
138#897—34no—
139#897—62no—
140C3×#103—34no—
141#835C2×D314yescomplemented
142#832—34no—
143#830—34no—
144(C2×D3)⋊C8—34no—
145#809—34no—
146C23×C32C2×D411yescharacteristic
147C22×C3×D3—24no—
148C22×C3×D3—22no—
149C22×C3×D3—22no—
150C22×C3×D3—22no—
151C22×C3×D3—22no—
152C22×C3×D3—42no—
153C22×C3×D3—42no—
154C22×C3×D3C2×D412yes—
155C32×Q8—24no—
156C32×Q8—22no—
157C32×Q8C2×D414yes—
158C2×C32×C4—24no—
159C2×C32×C4—22no—
160C2×C32×C4C2×D412yes—
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4C2×D412yes—
163C2×C32×C4C2411yescharacteristic
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—42no—
166#634—22no—
167#634—22no—
168#634—42no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—42no—
172C2×C3×Dic3C2×D412yes—
173C3×D12—216no—
174C3×D12—24no—
175C3×D12—22no—
176C3×D12C2×D414yes—
177C3×C4×D3—216no—
178C3×C4×D3—24no—
179C3×C4×D3—22no—
180C3×C4×D3—22no—
181C3⋊(C3⋊C8)—22no—
182C3×C3⋊C8—22no—
183C22×#41—31no—
184C22×Q16—91no—
185C22×SD16—91no—
186C2×C22⋊Q8—91no—
187#452—98no—
188C2×#103—31no—
189C2×#102—91no—
190C2×C22⋊C8—91no—
191C24×C3—31no—
192C24×C3—61no—
193C23×D3—21no—
194C23×D3#6711yescharacteristic
195C3×#41—68no—
196C3×#41—616no—
197C3×#41—68no—
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—41no—
205C2×C3×Q8—42no—
206C2×C3×Q8D1214yes—
207C2×C3×Q8#6714yes—
208C2×C3×Q8C22×D312yes—
209C2×C3×Q8C22×D312yes—
210C2×C3×D4—34no—
211C2×C3×D4—32no—
212C2×C3×D4—64no—
213C2×C3×D4—68no—
214C2×C3×D4—62no—
215C2×C3×D4—61no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—31no—
220C22×C3×C4—32no—
221C22×C3×C4—32no—
222C22×C3×C4—41no—
223C22×C3×C4—64no—
224C22×C3×C4—68no—
225C22×C3×C4—62no—
226C22×C3×C4—62no—
227C22×C3×C4—61no—
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C22×Dic3—21no—
231C22×Dic3—61no—
232C22×Dic3—61no—
233C22×Dic3—121no—
234C22×Dic3#6711yescharacteristic
235#239—216no—
236#239—28no—
237#239—28no—
238C2×D12—28no—
239C2×D12—24no—
240C2×D12—22no—
241C2×D12—21no—
242C2×D12#6714yes—
243C2×D12C22×D312yes—
244C2×C4×D3—28no—
245C2×C4×D3—22no—
246C2×C4×D3—22no—
247C2×C4×D3—24no—
248C2×C4×D3#6712yes—
249C2×C4×D3C22×D312yes—
250C2×Dic6—32no—
251C2×Dic6—32no—
252C2×Dic6—62no—
253C2×Dic6—64no—
254C2×Dic6—62no—
255C2×Dic6—62no—
256C2×Dic6—62no—
257C2×Dic6—62no—
258C2×Dic6—61no—
259C2×Dic6—61no—
260C2×Dic6—121no—
261C2×Dic6—122no—
262C2×C3×C8—32no—
263C2×C3×C8—62no—
264C3×C4⋊C4—32no—
265C3×C4⋊C4—61no—
266#217—64no—
267#216—616no—
268#216—68no—
269#216—68no—
270#214—68no—
271(C2×D3)⋊C4—64no—
272C4⋊Dic3—21no—
273C4⋊Dic3—64no—
274C4⋊Dic3C22×D312yes—
275Dic3⋊C4—64no—
276C2×C3⋊C8—22no—
277C2×C3⋊C8—32no—
278C2×C3⋊C8—32no—
279C2×C3⋊C8—62no—
280C2×C3⋊C8—64no—
281C2×C3⋊C8—62no—
282C2×C3⋊C8—62no—
283C2×C3⋊C8C22×D312yes—
284#204—68no—
285C22×C32#12012yes—
286C22×C32#13512yes—
287C22×C32#13712yes—
288C22×C32C22×D411yescharacteristic
289C2×C3×D3—22no—
290C2×C3×D3—24no—
291C2×C3×D3—22no—
292C2×C3×D3—22no—
293C2×C3×D3—42no—
294C2×C3×D3—42no—
295C2×C3×D3—44no—
296C2×C3×D3—48no—
297C32×C4—24no—
298C32×C4#12012yes—
299C32×C4C22×D411yescharacteristic
300C32×C4C22×D411yescharacteristic
301C3⋊Dic3—42no—
302C3×Dic3—22no—
303C3×Dic3—42no—
304C2×#41—34no—
305C2×#41—62no—
306C2×#41—64no—
307C2×#41—64no—
308C22×Q8—91no—
309C22×Q8D3211yescharacteristic
310C22×D4—31no—
311C22×D4—61no—
312C23×C4—31no—
313C23×C4—61no—
314C2×Q16—94no—
315C2×Q16—184no—
316C2×SD16—94no—
317C2×SD16—184no—
318C22×C8—31no—
319C22×C8—91no—
320C22⋊Q8—94no—
321C22⋊Q8—182no—
322C2×C4⋊C4—31no—
323C2×C4⋊C4—181no—
324C2×C22⋊C4—181no—
325#103—34no—
326#102—94no—
327C22⋊C8—94no—
328C23×C3—21no—
329C23×C3—32no—
330C23×C3—64no—
331C23×C3—62no—
332C23×C3—62no—
333C23×C3—62no—
334C23×C3—62no—
335C23×C3—122no—
336C23×C3—122no—
337C23×C3D3×D411yescharacteristic
338C23×C3C2×#6711yescharacteristic
339C22×D3—22no—
340C22×D3—22no—
341C22×D3—22no—
342C22×D3—24no—
343C22×D3—22no—
344C22×D3—42no—
345C22×D3—42no—
346C22×D3C2×#6712yes—
347C3×Q8—24no—
348C3×Q8—24no—
349C3×Q8—22no—
350C3×Q8—22no—
351C3×Q8—24no—
352C3×Q8—42no—
353C3×Q8—44no—
354C3×Q8C2×D1214yes—
355C3×Q8C2×#6714yes—
356C3×D4—34no—
357C3×D4—616no—
358C3×D4—64no—
359C3×D4—62no—
360C2×C3×C4—24no—
361C2×C3×C4—24no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—21no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—21no—
368C2×C3×C4—32no—
369C2×C3×C4—42no—
370C2×C3×C4—44no—
371C2×C3×C4—616no—
372C2×C3×C4—62no—
373C2×C3×C4—64no—
374C2×C3×C4—62no—
375C2×C3×C4—62no—
376C2×C3×C4—62no—
377C2×C3×C4—122no—
378C2×C3×C4C2×D1212yes—
379C2×C3×C4D3×D411yescharacteristic
380C2×C3×C4D3×D412yes—
381C2×C3×C4C2×#6712yes—
382C2×C3×C4C2×#6711yescharacteristic
383C2×C3×C4C2×#6712yes—
384C2×C3×C4C23×D311yescharacteristic
385C2×C3×C4C23×D311yescharacteristic
386C2×Dic3—22no—
387C2×Dic3—22no—
388C2×Dic3—42no—
389C2×Dic3—62no—
390C2×Dic3—62no—
391C2×Dic3—122no—
392C2×Dic3—124no—
393C2×Dic3—122no—
394C2×Dic3—122no—
395C2×Dic3C2×#6712yes—
396D12—216no—
397D12—24no—
398D12—22no—
399D12C2×#6714yes—
400C4×D3—216no—
401C4×D3—24no—
402C4×D3—22no—
403C4×D3—22no—
404Dic6—64no—
405Dic6—62no—
406Dic6—62no—
407Dic6—62no—
408Dic6—62no—
409Dic6—122no—
410Dic6—124no—
411Dic6—122no—
412Dic6—122no—
413C3×C8—62no—
414C3⋊C8—22no—
415C3⋊C8—64no—
416C3⋊C8—62no—
417C3⋊C8—62no—
418C2×C32#45214yescomplemented
419C2×C32C2×#12011yescharacteristic
420C2×C32C2×#13511yescharacteristic
421C2×C32C2×#13711yescharacteristic
422C3×D3—42no—
423C3×D3—44no—
424C24—31no—
425C24—61no—
426#41—68no—
427#41—616no—
428#41—68no—
429C2×Q8—21no—
430C2×Q8—22no—
431C2×Q8—92no—
432C2×Q8—181no—
433C2×Q8—182no—
434C2×Q8—182no—
435C2×Q8#62614yes—
436C2×Q8C2×D3212yes—
437C2×D4—32no—
438C2×D4—34no—
439C2×D4—64no—
440C2×D4—68no—
441C2×D4—62no—
442C2×D4—61no—
443C22×C4—21no—
444C22×C4—31no—
445C22×C4—32no—
446C22×C4—32no—
447C22×C4—64no—
448C22×C4—68no—
449C22×C4—62no—
450C22×C4—62no—
451C22×C4—61no—
452C22×C4—181no—
453C22×C4C2×D3211yescharacteristic
454Q16—188no—
455SD16—188no—
456C2×C8—32no—
457C2×C8—62no—
458C2×C8—92no—
459C2×C8—182no—
460C4⋊C4—32no—
461C4⋊C4—61no—
462C4⋊C4—184no—
463C22⋊C4—184no—
464C22×C3—21no—
465C22×C3—22no—
466C22×C3—22no—
467C22×C3—22no—
468C22×C3—64no—
469C22×C3—62no—
470C22×C3—62no—
471C22×C3—62no—
472C22×C3—122no—
473C22×C3—122no—
474C22×C3—124no—
475C22×C3—128no—
476C22×C3#88212yes—
477C22×C3#91612yes—
478C22×C3#91812yes—
479C22×C3#95012yes—
480C22×C3#95112yes—
481C22×C3#95312yes—
482C22×C3C2×D3×D411yescharacteristic
483C22×C3C22×#6711yescharacteristic
484C2×D3—22no—
485C2×D3—22no—
486C2×D3—22no—
487C2×D3—24no—
488C2×D3—44no—
489C2×D3—48no—
490C2×D3—42no—
491C2×D3—42no—
492C3×C4—24no—
493C3×C4—24no—
494C3×C4—21no—
495C3×C4—21no—
496C3×C4—22no—
497C3×C4—44no—
498C3×C4—62no—
499C3×C4—122no—
500C3×C4#88212yes—
501C3×C4#95312yes—
502C3×C4C22×D1211yescharacteristic
503C3×C4C2×D3×D411yescharacteristic
504C3×C4C22×#6711yescharacteristic
505C3×C4C22×#6711yescharacteristic
506Dic3—22no—
507Dic3—42no—
508Dic3—124no—
509Dic3—122no—
510Dic3—122no—
511C32C2×#45211yescharacteristic, complemented, Sylow
512C23—32no—
513C23—62no—
514C23—62no—
515C23—62no—
516C23—64no—
517C23—62no—
518C23—122no—
519C23—122no—
520C23D3×#6711yescharacteristic
521Q8—22no—
522Q8—24no—
523Q8—182no—
524Q8—182no—
525Q8—362no—
526Q8C2×#62614yes—
527D4—34no—
528D4—616no—
529D4—62no—
530D4—64no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—32no—
534C2×C4—616no—
535C2×C4—62no—
536C2×C4—62no—
537C2×C4—62no—
538C2×C4—64no—
539C2×C4—62no—
540C2×C4—122no—
541C2×C4—182no—
542C2×C4—362no—
543C2×C4C2×#62612yes—
544C2×C4D3×#6712yes—
545C2×C4D3×#6711yescharacteristic
546C2×C4C22×D3211yescharacteristic
547C8—62no—
548C8—182no—
549C2×C3—21no—
550C2×C3—24no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—122no—
554C2×C3—124no—
555C2×C3#480814yescomplemented
556C2×C3#523914yescomplemented
557C2×C3C2×#88211yescharacteristic
558C2×C3C2×#91611yescharacteristic
559C2×C3C2×#91811yescharacteristic
560C2×C3C2×#95011yescharacteristic
561C2×C3C2×#95111yescharacteristic
562C2×C3C2×#95311yescharacteristic
563D3—42no—
564D3—44no—
565C22—62no—
566C22—64no—
567C22—62no—
568C22—62no—
569C22—122no—
570C22—124no—
571C22—128no—
572C22—122no—
573C22#6394312yes—
574C22#6394712yes—
575C22#6397712yes—
576C22C2×D3×#6711yescharacteristic
577C4—24no—
578C4—62no—
579C4—122no—
580C4—362no—
581C4#6397712yes—
582C4C22×#62611yescharacteristic
583C4C2×D3×#6711yescharacteristic
584C3—21no—
585C3C2×#480811yescharacteristic, complemented
586C3C2×#523911yescharacteristic, complemented
587C2—122no—
588C2—124no—
589C2#1059159914yesdirect product factor
590C2C2×#6394311yescharacteristic
591C2C2×#6394711yescharacteristic
592C2C2×#6397711yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×C3×#239C2
hypercenterC22×Q8D32
hypocenterC32C2×#452
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
2. C22×#3756C2semidirect
3. C2×#63857C2semidirect
4. C22×#3716C2semidirect
5. C2×C3×#835C2semidirect
6. #10591599C2direct (N × H)
7. C2×#63562C2semidirect
8. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
22. C2×#3756C22semidirect
29. #63857C22semidirect
31. C2×#3716C22semidirect
32. C3×#835C22semidirect
33. #63562C22semidirect
34. (C2×D3)⋊(C3⋊C8)C22semidirect
46. C2×#835D3semidirect
141. #835C2×D3semidirect
418. C2×C32#452semidirect
511. C32C2×#452semidirect
555. C2×C3#4808semidirect
556. C2×C3#5239semidirect
585. C3C2×#4808semidirect
586. C3C2×#5239semidirect
589. C2#10591599direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2392
C22×#37562
C2×#638572
C22×#37162
C2×C3×#8352
#105915992
C2×#635622
C2×(C2×D3)⋊(C3⋊C8)2
C2×#52393
C2×#48083