Finite Group Databasebeta

← #11860226

Subgroups — #11860226

Order 1152.

1063 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Dic3×#41C211yesmaximal, characteristic, complemented
2C2×C3×#950C211yesmaximal, characteristic
3Dic3×#235C211yesmaximal, characteristic, complemented
4#10592932C211yesmaximal, characteristic, complemented
5#10591576C212yesmaximal, complemented
6#10591566C212yesmaximal, complemented
7#10591440C212yesmaximal, complemented
8#10591430C212yesmaximal, complemented
9#10591122C211yesmaximal, characteristic, complemented
10#10591083C211yesmaximal, characteristic, complemented
11C2×#63554C211yesmaximal, characteristic, complemented
12#83897—31nomaximal
13#82506—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16#64135C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#950C418yescomplemented
19C3×Q8×Dic3C2212yes—
20C2×C3×#216C2211yescharacteristic
21C2×C3×#215C2211yescharacteristic
22C3×D4×Dic3—22no—
23C3×D4×Dic3C2212yes—
24C2×C3×#214C2211yescharacteristic
25C2×C3×#213C2211yescharacteristic
26C3×#926—21no—
27C3×#926C2211yescharacteristic
28C2×C3×C4×Dic3—21no—
29C2×C3×C4×Dic3C2211yescharacteristic
30C22×C3×C3⋊C8C2211yescharacteristic
31Dic3×#67—22no—
32Dic3×D12C2212yes—
33C4×D3×Dic3—21no—
34#63855—21no—
35Dic3×Dic6C2212yes—
36#63662C2212yes—
37#63659C2212yes—
38#63575C2212yes—
39#63573C2212yes—
40#63565C2212yes—
41#63562C2212yes—
42#63554C2212yes—
43#63554C2212yes—
44C2×C3×#135—31no—
45C3×C4×#41—31no—
46Dic3×#41—31no—
47Dic3×#41D311yescharacteristic, complemented
48C2×#950D311yescharacteristic
49C4×#235—31no—
50#5233—31no—
51#5233—31no—
52#5233—31no—
53#5233—61no—
54#5184—32no—
55#5164—32no—
56#5164—32no—
57#5152—32no—
58#5106—31no—
59C2×#815—31no—
60#5030—32no—
61#5026—32no—
62#5018—32no—
63#5014—32no—
64#5002—31no—
65#4998—31no—
66C2×#803—31no—
67C32×#41—22no—
68C32×#41C2×C414yescomplemented
69C2×C32×Q8C2311yescharacteristic
70C2×C32×D4—21no—
71C2×C32×D4C2311yescharacteristic
72C22×C32×C4—21no—
73C22×C32×C4C2311yescharacteristic
74C2×C3×#67—21no—
75C22×C3×Dic3—22no—
76C22×C3×Dic3D412yes—
77C3×#235—22no—
78C3×#235C2×C414yescomplemented
79C2×C3×D12C2311yescharacteristic
80C2×C3×C4×D3—21no—
81C2×C3×Dic6C2311yescharacteristic
82C2×D3×Dic3—22no—
83#3757—21no—
84C4⋊(C3⋊Dic3)C2312yes—
85C4×C3⋊Dic3—21no—
86C2×C3⋊(C3⋊C8)—22no—
87C2×C3⋊(C3⋊C8)C2312yes—
88C3×#217—21no—
89C3×#217—22no—
90C3×#216C2×C414yescomplemented
91C3×#215C2×C414yescomplemented
92C3×#214C2×C414yescomplemented
93C3×#213C2×C414yescomplemented
94C3×C4⋊Dic3—22no—
95C3×C4⋊Dic3C2312yes—
96C3×C4×Dic3—21no—
97C3×C4×Dic3—22no—
98C3×C4×Dic3D411yescharacteristic
99C3×C4×Dic3D411yescharacteristic
100C3×C4×Dic3C2312yes—
101C2×C3×C3⋊C8C2×C414yescomplemented
102C2×C3×C3⋊C8C2311yescharacteristic
103C2×C3×C3⋊C8C2311yescharacteristic
104Dic3⋊Dic3—22no—
105(C2×D3)⋊Dic3—22no—
106Dic32—22no—
107#2943—91noSylow
108C2×C3×#41—21no—
109C2×C3×#41—31no—
110C2×C3×#41C2×D311yescharacteristic
111C2×C3×#41C2×D311yescharacteristic
112C2×#235C2×D311yescharacteristic
113C3×#135—38no—
114C2×C3×Q16—31no—
115C2×C3×SD16—31no—
116C2×C3×SD16—31no—
117C2×C3×D8—31no—
118C22×C3×C8—31no—
119C3×C4×Q8—32no—
120C3×C4×D4—32no—
121C3×C4×D4—62no—
122C3×#117—31no—
123C3×#117—61no—
124C2×C3×C42—31no—
125C2×C3×C42—61no—
126#950Dic318yescomplemented
127Q8×Dic3—32no—
128Q8×Dic3C2×D312yes—
129C2×#216C2×D311yescharacteristic
130C2×#215C2×D311yescharacteristic
131D4×Dic3—22no—
132D4×Dic3—32no—
133D4×Dic3—62no—
134D4×Dic3C2×D312yes—
135C2×#214C2×D311yescharacteristic
136C2×#213C2×D311yescharacteristic
137C4×#67—62no—
138#926—21no—
139#926—31no—
140#926—31no—
141#926—61no—
142#926—61no—
143#926C2×D311yescharacteristic
144C2×C4×Dic3—21no—
145C2×C4×Dic3—61no—
146C2×C4×Dic3C2×D311yescharacteristic
147C22×C3⋊C8—31no—
148C22×C3⋊C8—31no—
149C22×C3⋊C8—61no—
150C22×C3⋊C8C2×D311yescharacteristic
151C4×D12—32no—
152#872—61no—
153C42×D3—61no—
154C4×Dic6—32no—
155#835—32no—
156#835—32no—
157#835—32no—
158#835—62no—
159#832—32no—
160#832—32no—
161#832—32no—
162#832—62no—
163#818—32no—
164#817—32no—
165#815—32no—
166#815—32no—
167#810—32no—
168#809—32no—
169#808—32no—
170#807—32no—
171#803—32no—
172#803—32no—
173C23×C32—21no—
174C23×C32C2×D411yescharacteristic
175C22×C3×D3—21no—
176C32×Q8—21no—
177C32×Q8C22×C412yes—
178C32×D4—24no—
179C32×D4—21no—
180C32×D4C22×C412yes—
181C2×C32×C4—21no—
182C2×C32×C4—24no—
183C2×C32×C4C22×C412yes—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4#4112yes—
186C2×C32×C4C2411yescharacteristic
187C2×C3⋊Dic3—22no—
188C3×#67—24no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—42no—
192C2×C3×Dic3—44no—
193C2×C3×Dic3C2×D412yes—
194C2×C3×Dic3C2×D412yes—
195C3×D12—21no—
196C3×D12C22×C412yes—
197C3×C4×D3—24no—
198C3×Dic6—21no—
199C3×Dic6C22×C412yes—
200D3×Dic3—44no—
201C3⋊(C3⋊C8)—22no—
202C3×C3⋊C8C22×C412yes—
203C3×C3⋊C8C22×C412yes—
204C2×#135—31no—
205C4×#41—31no—
206C4×#41—91no—
207#442—92no—
208#441—92no—
209#440—92no—
210#440—92no—
211#427—91no—
212#416—91no—
213#416—91no—
214C2×#97—91no—
215C3×#41—22no—
216C3×#41—22no—
217C3×#41—24no—
218C3×#41—34no—
219C3×#41—42no—
220C3×#41—62no—
221C3×#41C4×D314yescomplemented
222C3×#41C2×Dic314yescomplemented
223C2×C3×Q8—21no—
224C2×C3×Q8—31no—
225C2×C3×Q8C22×D311yescharacteristic
226C2×C3×Q8C22×D311yescharacteristic
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—31no—
231C2×C3×D4—41no—
232C2×C3×D4—61no—
233C2×C3×D4C22×D311yescharacteristic
234C2×C3×D4C22×D311yescharacteristic
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—32no—
239C22×C3×C4—41no—
240C22×C3×C4—62no—
241C22×C3×C4—61no—
242C22×C3×C4C22×D311yescharacteristic
243C22×C3×C4C22×D311yescharacteristic
244C2×#67—21no—
245C22×Dic3—22no—
246C22×Dic3—62no—
247C22×Dic3#6712yes—
248#235—22no—
249#235C2×Dic314yescomplemented
250C2×D12C22×D311yescharacteristic
251C2×C4×D3—21no—
252C2×C4×D3—62no—
253C2×Dic6C22×D311yescharacteristic
254C3×Q16—34no—
255C3×SD16—34no—
256C3×SD16—34no—
257C3×D8—34no—
258C2×C3×C8—34no—
259C2×C3×C8—31no—
260C2×C3×C8—31no—
261C3×C4⋊C4—32no—
262C3×C4⋊C4—62no—
263C3×C22⋊C4—62no—
264C3×C22⋊C4—61no—
265C3×C42—31no—
266C3×C42—31no—
267C3×C42—32no—
268C3×C42—62no—
269C3×C42—61no—
270#217—21no—
271#217—22no—
272#217—61no—
273#217—61no—
274#217—62no—
275#217—121no—
276#216C2×Dic314yescomplemented
277#215C2×Dic314yescomplemented
278#214C2×Dic314yescomplemented
279#213C2×Dic314yescomplemented
280(C2×D3)⋊C4—62no—
281C4⋊Dic3—22no—
282C4⋊Dic3—32no—
283C4⋊Dic3—32no—
284C4⋊Dic3—62no—
285C4⋊Dic3—62no—
286C4⋊Dic3C22×D312yes—
287Dic3⋊C4—62no—
288C4×Dic3—21no—
289C4×Dic3—22no—
290C4×Dic3—62no—
291C4×Dic3—61no—
292C4×Dic3—61no—
293C4×Dic3—62no—
294C4×Dic3—121no—
295C4×Dic3#6711yescharacteristic
296C4×Dic3#6711yescharacteristic
297C4×Dic3C22×D312yes—
298C2×C3⋊C8—32no—
299C2×C3⋊C8—32no—
300C2×C3⋊C8—62no—
301C2×C3⋊C8—62no—
302C2×C3⋊C8—62no—
303C2×C3⋊C8—122no—
304C2×C3⋊C8C2×Dic314yescomplemented
305C2×C3⋊C8C22×D311yescharacteristic
306C2×C3⋊C8C22×D311yescharacteristic
307C22×C32—22no—
308C22×C32—22no—
309C22×C32—42no—
310C22×C32C4×D412yes—
311C22×C32C22×D411yescharacteristic
312C2×C3×D3—22no—
313C2×C3×D3—42no—
314C32×C4—22no—
315C32×C4C4×D412yes—
316C32×C4C23×C411yescharacteristic
317C32×C4C2×#4111yescharacteristic
318C3⋊Dic3—42no—
319C3×Dic3—22no—
320C3×Dic3—22no—
321C3×Dic3—22no—
322C3×Dic3—42no—
323C2×#41—31no—
324C2×#41D3211yescharacteristic
325#135—38no—
326C2×Q16—31no—
327C2×SD16—31no—
328C2×SD16—31no—
329C2×D8—31no—
330C22×C8—31no—
331C22×C8—91no—
332C4×Q8—32no—
333C4×Q8—92no—
334C4×D4—32no—
335C4×D4—62no—
336C4×D4—92no—
337C4×D4—182no—
338#117—31no—
339#117—61no—
340#117—91no—
341#117—181no—
342C2×C42—31no—
343C2×C42—61no—
344C2×C42—181no—
345#107—92no—
346#106—92no—
347#103—92no—
348#103—92no—
349#102—92no—
350#102—92no—
351#97—92no—
352#97—92no—
353C23×C3—21no—
354C23×C3—21no—
355C23×C3—21no—
356C23×C3—41no—
357C23×C3—61no—
358C23×C3D3×D411yescharacteristic
359C23×C3C2×#6711yescharacteristic
360C22×D3—21no—
361C3×Q8—21no—
362C3×Q8—21no—
363C3×Q8—22no—
364C3×Q8—32no—
365C3×Q8—41no—
366C3×Q8—61no—
367C3×Q8C2×C4×D312yes—
368C3×Q8C22×Dic312yes—
369C3×D4—24no—
370C3×D4—24no—
371C3×D4—21no—
372C3×D4—21no—
373C3×D4—22no—
374C3×D4—32no—
375C3×D4—41no—
376C3×D4—44no—
377C3×D4—64no—
378C3×D4—61no—
379C3×D4C2×C4×D312yes—
380C3×D4C22×Dic312yes—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—24no—
384C2×C3×C4—24no—
385C2×C3×C4—21no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—21no—
389C2×C3×C4—32no—
390C2×C3×C4—32no—
391C2×C3×C4—44no—
392C2×C3×C4—41no—
393C2×C3×C4—61no—
394C2×C3×C4—64no—
395C2×C3×C4—62no—
396C2×C3×C4—122no—
397C2×C3×C4—124no—
398C2×C3×C4C2×C4×D312yes—
399C2×C3×C4#23512yes—
400C2×C3×C4D3×D411yescharacteristic
401C2×C3×C4#23712yes—
402C2×C3×C4C22×Dic312yes—
403C2×C3×C4C2×#6711yescharacteristic
404C2×C3×C4C23×D311yescharacteristic
405C2×C3×C4C23×D311yescharacteristic
406#67—24no—
407C2×Dic3—21no—
408C2×Dic3—22no—
409C2×Dic3—42no—
410C2×Dic3—44no—
411C2×Dic3—62no—
412C2×Dic3—62no—
413C2×Dic3—122no—
414C2×Dic3—124no—
415C2×Dic3C2×#6712yes—
416C2×Dic3C2×#6712yes—
417D12—21no—
418D12C22×Dic312yes—
419C4×D3—24no—
420C4×D3—124no—
421Dic6—21no—
422Dic6C22×Dic312yes—
423C3×C8—32no—
424C3×C8—32no—
425C3⋊C8—62no—
426C3⋊C8—62no—
427C3⋊C8—122no—
428C3⋊C8C22×Dic312yes—
429C3⋊C8C22×Dic312yes—
430C2×C32—22no—
431C2×C32—42no—
432C2×C32C2×C4×D411yescharacteristic
433C2×C32#57512yes—
434C3×D3—42no—
435#41—22no—
436#41—34no—
437#41—62no—
438#41D3×Dic314yescomplemented
439C2×Q8—31no—
440C2×Q8C2×D3211yescharacteristic
441C2×D4—21no—
442C2×D4—31no—
443C2×D4—61no—
444C2×D4C2×D3211yescharacteristic
445C22×C4—21no—
446C22×C4—32no—
447C22×C4—62no—
448C22×C4—61no—
449C22×C4—182no—
450C22×C4C2×D3211yescharacteristic
451Q16—34no—
452SD16—34no—
453SD16—34no—
454D8—34no—
455C2×C8—31no—
456C2×C8—31no—
457C2×C8—34no—
458C2×C8—92no—
459C2×C8—182no—
460C4⋊C4—32no—
461C4⋊C4—62no—
462C4⋊C4—92no—
463C4⋊C4—182no—
464C22⋊C4—62no—
465C22⋊C4—61no—
466C22⋊C4—182no—
467C22⋊C4—181no—
468C42—32no—
469C42—31no—
470C42—31no—
471C42—62no—
472C42—61no—
473C42—182no—
474C42—181no—
475C22×C3—22no—
476C22×C3—22no—
477C22×C3—22no—
478C22×C3—22no—
479C22×C3—21no—
480C22×C3—22no—
481C22×C3—42no—
482C22×C3—42no—
483C22×C3—42no—
484C22×C3—42no—
485C22×C3—62no—
486C22×C3—82no—
487C22×C3—122no—
488C22×C3C4×#6712yes—
489C22×C3D4×Dic312yes—
490C22×C3C2×D3×D411yescharacteristic
491C22×C3C22×#6711yescharacteristic
492C2×D3—22no—
493C2×D3—42no—
494C3×C4—22no—
495C3×C4—22no—
496C3×C4—21no—
497C3×C4—21no—
498C3×C4—22no—
499C3×C4—42no—
500C3×C4—62no—
501C3×C4—62no—
502C3×C4—62no—
503C3×C4—122no—
504C3×C4C4×#6712yes—
505C3×C4D4×Dic312yes—
506C3×C4C22×C4×D311yescharacteristic
507C3×C4C2×#23511yescharacteristic
508C3×C4C2×#23711yescharacteristic
509C3×C4C23×Dic311yescharacteristic
510Dic3—22no—
511Dic3—22no—
512Dic3—22no—
513Dic3—42no—
514Dic3—122no—
515Dic3—122no—
516Dic3—242no—
517C32#294311yescharacteristic, complemented, Sylow
518C23—21no—
519C23—61no—
520C23D3×#6711yescharacteristic
521Q8—21no—
522Q8—32no—
523Q8—61no—
524Q8C2×D3×Dic312yes—
525D4—24no—
526D4—21no—
527D4—32no—
528D4—64no—
529D4—61no—
530D4C2×D3×Dic312yes—
531C2×C4—21no—
532C2×C4—24no—
533C2×C4—32no—
534C2×C4—32no—
535C2×C4—61no—
536C2×C4—64no—
537C2×C4—62no—
538C2×C4—122no—
539C2×C4—124no—
540C2×C4—182no—
541C2×C4—364no—
542C2×C4C2×D3×Dic312yes—
543C2×C4#380412yes—
544C2×C4D3×#6711yescharacteristic
545C2×C4C22×D3211yescharacteristic
546C8—32no—
547C8—32no—
548C8—182no—
549C2×C3—22no—
550C2×C3—22no—
551C2×C3—22no—
552C2×C3—21no—
553C2×C3—42no—
554C2×C3—42no—
555C2×C3—42no—
556C2×C3—82no—
557C2×C3—122no—
558C2×C3#576812yes—
559C2×C3C2×C4×#6711yescharacteristic
560C2×C3C2×D4×Dic311yescharacteristic
561C2×C3#582212yes—
562D3—42no—
563C22—22no—
564C22—22no—
565C22—42no—
566C22—62no—
567C22—122no—
568C22Dic3×#6712yes—
569C22C2×D3×#6711yescharacteristic
570C4—22no—
571C4—62no—
572C4—62no—
573C4—62no—
574C4—122no—
575C4—362no—
576C4Dic3×#6712yes—
577C4C22×D3×Dic311yescharacteristic
578C4C2×#380411yescharacteristic
579C3—21no—
580C3#8250611yescharacteristic, complemented
581C3#8389711yescharacteristic, complemented
582C2—22no—
583C2—42no—
584C2—122no—
585C2#1059545312yes—
586C2C2×Dic3×#6711yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC2×C3×#950C2
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32#2943
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×Dic3×#41C2semidirect
3. Dic3×#235C2semidirect
4. #10592932C2semidirect
5. #10591576C2semidirect
6. #10591566C2semidirect
7. #10591440C2semidirect
8. #10591430C2semidirect
9. #10591122C2semidirect
10. #10591083C2semidirect
11. C2×#63554C2semidirect
18. C3×#950C4semidirect
47. Dic3×#41D3semidirect
68. C32×#41C2×C4semidirect
78. C3×#235C2×C4semidirect
90. C3×#216C2×C4semidirect
91. C3×#215C2×C4semidirect
92. C3×#214C2×C4semidirect
93. C3×#213C2×C4semidirect
101. C2×C3×C3⋊C8C2×C4semidirect
126. #950Dic3semidirect
221. C3×#41C4×D3semidirect
222. C3×#41C2×Dic3semidirect
249. #235C2×Dic3semidirect
276. #216C2×Dic3semidirect
277. #215C2×Dic3semidirect
278. #214C2×Dic3semidirect
279. #213C2×Dic3semidirect
304. C2×C3⋊C8C2×Dic3semidirect
438. #41D3×Dic3semidirect
517. C32#2943semidirect
580. C3#82506semidirect
581. C3#83897semidirect

Maximal subgroups

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

subgroupindex
C3×Dic3×#412
C2×C3×#9502
Dic3×#2352
#105929322
#105915762
#105915662
#105914402
#105914302
#105911222
#105910832
C2×#635542
#838973
#825063