Finite Group Databasebeta

← #11860634

Subgroups — #11860634

Order 1152.

1019 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5827C211yesmaximal, characteristic
2C2×C3×#951C211yesmaximal, characteristic
3#10594818C211yesmaximal, characteristic, complemented
4#10592932C211yesmaximal, characteristic
5#10591576C212yesmaximal, complemented
6Dic3×#216C212yesmaximal, complemented
7#10591440C212yesmaximal, complemented
8Dic3×#214C212yesmaximal, complemented
9#10591130C211yesmaximal, characteristic, complemented
10C2×#63565C211yesmaximal, characteristic, complemented
11#10591057C211yesmaximal, characteristic, complemented
12#83965—31nomaximal
13#82571—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16#64135C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#951C418yescomplemented
19C3×Q8×Dic3C2212yes—
20C2×C3×#216C2212yes—
21C3×D4×Dic3—22no—
22C3×D4×Dic3C2212yes—
23C2×C3×#214C2212yes—
24C3×#926—21no—
25C3×#926C2211yescharacteristic
26C2×C3×C4⋊Dic3—21no—
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×#208C2211yescharacteristic
29#63955—22no—
30#63843—21no—
31#63843—21no—
32Dic3×Dic6C2212yes—
33Dic3×Dic6C2212yes—
34#63662C2211yescharacteristic
35#63662C2211yescharacteristic
36#63659C2211yescharacteristic
37#63659C2211yescharacteristic
38#63575C2212yes—
39#63573C2212yes—
40#63565C2212yes—
41#63565C2212yes—
42#63554C2212yes—
43Dic3×C3⋊C8C2212yes—
44C2×C3×#137—31no—
45C3×#520—31no—
46#5827D311yescharacteristic
47C2×#951D311yescharacteristic
48#5812—31no—
49#5516—31no—
50#5233—31no—
51#5233—31no—
52#5233—61no—
53C2×#835—31no—
54#5184—32no—
55Dic3×Q16—32no—
56#5164—32no—
57Dic3×SD16—32no—
58#5122—31no—
59#5121—31no—
60#5030—32no—
61C4×#216—32no—
62#5018—32no—
63C4×#214—32no—
64#4997—31no—
65C2×#810—31no—
66#4964—31no—
67C32×#41—22no—
68C32×#41C2×C414yes—
69C2×C32×Q8C2311yescharacteristic
70C2×C32×D4—21no—
71C2×C32×D4C2311yescharacteristic
72C22×C32×C4—21no—
73C22×C32×C4C2311yescharacteristic
74C22×C3×Dic3—21no—
75C22×C3×Dic3—21no—
76C22×C3×Dic3—22no—
77C2×C3×Dic6—21no—
78C2×C3×Dic6—22no—
79C2×C3×Dic6C2×C414yescomplemented
80C2×C3×Dic6C2312yes—
81#3757—21no—
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84C4×C3⋊Dic3—21no—
85C2×C3⋊(C3⋊C8)—22no—
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88C3×#217—22no—
89C3×#217D412yes—
90C3×#216C2×C418yescomplemented
91C3×#214C2×C418yescomplemented
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3—22no—
94C3×C4⋊Dic3D411yescharacteristic
95C3×C4⋊Dic3D411yescharacteristic
96C3×C4⋊Dic3C2312yes—
97C3×C4×Dic3—22no—
98C3×C4×Dic3C2312yes—
99C3×#208C2×C414yescomplemented
100C2×C3×C3⋊C8C2312yes—
101Dic3⋊Dic3—22no—
102Dic3⋊Dic3—22no—
103Dic32—22no—
104Dic32—22no—
105#2947—91noSylow
106C2×C3×#41—21no—
107C2×C3×#41C2×D311yescharacteristic
108C2×C3×#41C2×D311yescharacteristic
109C22×C3×Q8—31no—
110C22×Dic6C2×D311yescharacteristic
111C3×#137—38no—
112C2×C3×Q16—32no—
113C2×C3×SD16—32no—
114C2×C3×M16—31no—
115C3×C4×Q8—32no—
116C3×C4×D4—32no—
117C3×C4×D4—62no—
118C3×#117—31no—
119C3×#117—61no—
120C2×C3×C4⋊C4—31no—
121C2×C3×C4⋊C4—61no—
122#951Dic318yescomplemented
123Q8×Dic3—32no—
124Q8×Dic3—32no—
125Q8×Dic3—61no—
126Q8×Dic3—61no—
127Q8×Dic3C2×D312yes—
128C2×#216C2×D312yes—
129D4×Dic3—22no—
130D4×Dic3C2×D312yes—
131C2×#214C2×D312yes—
132#926—21no—
133#926—31no—
134#926—31no—
135#926—61no—
136#926—62no—
137#926C2×D311yescharacteristic
138C2×C4⋊Dic3—21no—
139C2×C4⋊Dic3C2×D311yescharacteristic
140C2×#208C2×D311yescharacteristic
141C22×C3⋊C8—31no—
142C22×C3⋊C8—31no—
143C22×C3⋊C8—61no—
144#887—61no—
145#887—61no—
146#877—62no—
147C4×Dic6—32no—
148C4×Dic6—32no—
149#835—31no—
150#835—31no—
151#835—31no—
152#835—31no—
153#835—32no—
154#835—32no—
155#835—61no—
156#835—61no—
157#832—31no—
158#832—31no—
159#832—31no—
160#832—31no—
161#832—61no—
162#832—61no—
163#818—32no—
164#817—32no—
165#815—32no—
166C8×Dic3—32no—
167#810—32no—
168#810—32no—
169#808—32no—
170#807—32no—
171#803—32no—
172C4×C3⋊C8—32no—
173C23×C32—21no—
174C23×C32C2×D411yescharacteristic
175C32×Q8—21no—
176C32×Q8C22×C412yes—
177C32×D4—24no—
178C32×D4—21no—
179C32×D4C22×C412yes—
180C2×C32×C4—21no—
181C2×C32×C4—24no—
182C2×C32×C4C22×C412yes—
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4#4112yes—
185C2×C32×C4C2411yescharacteristic
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3×Dic3—24no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—82no—
192C2×C3×Dic3—81no—
193C2×C3×Dic3C2×D412yes—
194C2×C3×Dic3C2×D412yes—
195C3×Dic6—24no—
196C3×Dic6—22no—
197C3×Dic6C22×C414yes—
198C3⋊(C3⋊C8)—21no—
199C3⋊(C3⋊C8)—21no—
200C3×C3⋊C8C22×C414yes—
201C2×#137—31no—
202#520—31no—
203#519—91no—
204#441—92no—
205#440—92no—
206C4×Q16—92no—
207C4×SD16—92no—
208#428—91no—
209#416—91no—
210C2×#103—91no—
211#405—91no—
212C3×#41—22no—
213C3×#41—22no—
214C3×#41—24no—
215C3×#41—42no—
216C3×#41C4×D314yes—
217C3×#41C2×Dic314yes—
218C2×C3×Q8—21no—
219C2×C3×Q8—34no—
220C2×C3×Q8—32no—
221C2×C3×Q8—62no—
222C2×C3×Q8—61no—
223C2×C3×Q8C22×D311yescharacteristic
224C2×C3×Q8C22×D311yescharacteristic
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—41no—
229C2×C3×D4C22×D311yescharacteristic
230C2×C3×D4C22×D311yescharacteristic
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—41no—
235C22×C3×C4—62no—
236C22×C3×C4—61no—
237C22×C3×C4—61no—
238C22×C3×C4C22×D311yescharacteristic
239C22×C3×C4C22×D311yescharacteristic
240C22×Dic3—21no—
241C22×Dic3—21no—
242C22×Dic3—22no—
243C2×Dic6—21no—
244C2×Dic6—22no—
245C2×Dic6C2×Dic314yescomplemented
246C2×Dic6C22×D312yes—
247C3×Q16—38no—
248C3×SD16—38no—
249C3×M16—34no—
250C2×C3×C8—32no—
251C3×C4⋊C4—31no—
252C3×C4⋊C4—31no—
253C3×C4⋊C4—32no—
254C3×C4⋊C4—62no—
255C3×C4⋊C4—61no—
256C3×C22⋊C4—32no—
257C3×C22⋊C4—62no—
258C3×C42—32no—
259C3×C42—62no—
260#217—22no—
261#217—61no—
262#217—61no—
263#217—121no—
264#217#6712yes—
265#216C2×Dic318yescomplemented
266#214C2×Dic318yescomplemented
267C4⋊Dic3—21no—
268C4⋊Dic3—22no—
269C4⋊Dic3—31no—
270C4⋊Dic3—31no—
271C4⋊Dic3—31no—
272C4⋊Dic3—31no—
273C4⋊Dic3—61no—
274C4⋊Dic3—61no—
275C4⋊Dic3—62no—
276C4⋊Dic3—62no—
277C4⋊Dic3#6711yescharacteristic
278C4⋊Dic3#6711yescharacteristic
279C4⋊Dic3C22×D312yes—
280Dic3⋊C4—62no—
281Dic3⋊C4—62no—
282C4×Dic3—22no—
283C4×Dic3—62no—
284C4×Dic3—62no—
285C4×Dic3—61no—
286C4×Dic3—61no—
287C4×Dic3—62no—
288C4×Dic3—62no—
289C4×Dic3—121no—
290C4×Dic3C22×D312yes—
291#208C2×Dic314yescomplemented
292C2×C3⋊C8—31no—
293C2×C3⋊C8—31no—
294C2×C3⋊C8—31no—
295C2×C3⋊C8—31no—
296C2×C3⋊C8—61no—
297C2×C3⋊C8—61no—
298C2×C3⋊C8—62no—
299C2×C3⋊C8—62no—
300C2×C3⋊C8—122no—
301C2×C3⋊C8C22×D312yes—
302C22×C32—21no—
303C22×C32—21no—
304C22×C32—22no—
305C22×C32—41no—
306C22×C32—41no—
307C22×C32C4×D412yes—
308C22×C32C22×D411yescharacteristic
309C32×C4—22no—
310C32×C4C4×D412yes—
311C32×C4C23×C411yescharacteristic
312C32×C4C2×#4111yescharacteristic
313C3⋊Dic3—41no—
314C3⋊Dic3—41no—
315C3×Dic3—24no—
316C3×Dic3—22no—
317C3×Dic3—22no—
318C3×Dic3—42no—
319C2×#41D3211yescharacteristic
320C22×Q8—31no—
321#137—38no—
322C2×Q16—32no—
323C2×SD16—32no—
324C2×M16—31no—
325C22×C8—91no—
326C4×Q8—32no—
327C4×Q8—92no—
328C4×Q8—92no—
329C4×Q8—181no—
330C4×Q8—181no—
331C4×D4—32no—
332C4×D4—62no—
333#117—31no—
334#117—61no—
335#117—91no—
336#117—182no—
337C2×C4⋊C4—31no—
338C2×C4⋊C4—61no—
339#107—92no—
340#106—92no—
341#103—92no—
342#103—92no—
343#103—91no—
344#103—91no—
345#102—91no—
346#102—91no—
347#97—92no—
348C4×C8—92no—
349C23×C3—21no—
350C23×C3—21no—
351C23×C3—21no—
352C23×C3—41no—
353C23×C3D3×D411yescharacteristic
354C23×C3C2×#6711yescharacteristic
355C3×Q8—21no—
356C3×Q8—21no—
357C3×Q8—22no—
358C3×Q8—34no—
359C3×Q8—41no—
360C3×Q8—64no—
361C3×Q8—62no—
362C3×Q8C2×C4×D312yes—
363C3×Q8C22×Dic312yes—
364C3×D4—24no—
365C3×D4—24no—
366C3×D4—21no—
367C3×D4—21no—
368C3×D4—22no—
369C3×D4—41no—
370C3×D4—44no—
371C3×D4C2×C4×D312yes—
372C3×D4C22×Dic312yes—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—24no—
376C2×C3×C4—24no—
377C2×C3×C4—21no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—21no—
381C2×C3×C4—32no—
382C2×C3×C4—32no—
383C2×C3×C4—44no—
384C2×C3×C4—41no—
385C2×C3×C4—64no—
386C2×C3×C4—62no—
387C2×C3×C4—62no—
388C2×C3×C4—242no—
389C2×C3×C4—241no—
390C2×C3×C4C2×C4×D312yes—
391C2×C3×C4#23512yes—
392C2×C3×C4D3×D411yescharacteristic
393C2×C3×C4#23712yes—
394C2×C3×C4C22×Dic312yes—
395C2×C3×C4C2×#6711yescharacteristic
396C2×C3×C4C23×D311yescharacteristic
397C2×C3×C4C23×D311yescharacteristic
398C2×Dic3—24no—
399C2×Dic3—22no—
400C2×Dic3—22no—
401C2×Dic3—61no—
402C2×Dic3—61no—
403C2×Dic3—61no—
404C2×Dic3—61no—
405C2×Dic3—82no—
406C2×Dic3—81no—
407C2×Dic3—121no—
408C2×Dic3—121no—
409C2×Dic3C2×#6712yes—
410C2×Dic3C2×#6712yes—
411Dic6—24no—
412Dic6—22no—
413Dic6C22×Dic314yes—
414C3×C8—34no—
415C3⋊C8—61no—
416C3⋊C8—61no—
417C3⋊C8—61no—
418C3⋊C8—61no—
419C3⋊C8—121no—
420C3⋊C8—121no—
421C3⋊C8C22×Dic314yes—
422C2×C32—22no—
423C2×C32—42no—
424C2×C32C2×C4×D411yescharacteristic
425C2×C32#57711yescharacteristic
426C2×C32#57811yescharacteristic
427#41—22no—
428#41D3×Dic314yes—
429C2×Q8—32no—
430C2×Q8—34no—
431C2×Q8—62no—
432C2×Q8—61no—
433C2×Q8C2×D3211yescharacteristic
434C2×D4—21no—
435C2×D4C2×D3211yescharacteristic
436C22×C4—21no—
437C22×C4—62no—
438C22×C4—61no—
439C22×C4—61no—
440C22×C4C2×D3211yescharacteristic
441Q16—38no—
442SD16—38no—
443M16—34no—
444C2×C8—32no—
445C2×C8—91no—
446C2×C8—91no—
447C2×C8—182no—
448C4⋊C4—31no—
449C4⋊C4—31no—
450C4⋊C4—32no—
451C4⋊C4—62no—
452C4⋊C4—61no—
453C4⋊C4—91no—
454C4⋊C4—91no—
455C4⋊C4—182no—
456C4⋊C4—182no—
457C22⋊C4—32no—
458C22⋊C4—62no—
459C22⋊C4—181no—
460C42—32no—
461C42—62no—
462C42—182no—
463C42—182no—
464C42—181no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—22no—
470C22×C3—22no—
471C22×C3—21no—
472C22×C3—22no—
473C22×C3—41no—
474C22×C3—41no—
475C22×C3—42no—
476C22×C3—41no—
477C22×C3—41no—
478C22×C3—41no—
479C22×C3—41no—
480C22×C3—81no—
481C22×C3—81no—
482C22×C3C4×#6712yes—
483C22×C3D4×Dic312yes—
484C22×C3C2×D3×D411yescharacteristic
485C22×C3C22×#6711yescharacteristic
486C3×C4—22no—
487C3×C4—22no—
488C3×C4—21no—
489C3×C4—21no—
490C3×C4—22no—
491C3×C4—42no—
492C3×C4—62no—
493C3×C4—62no—
494C3×C4—64no—
495C3×C4—122no—
496C3×C4C4×#6712yes—
497C3×C4D4×Dic312yes—
498C3×C4C22×C4×D311yescharacteristic
499C3×C4C2×#23511yescharacteristic
500C3×C4C2×#23711yescharacteristic
501C3×C4C23×Dic311yescharacteristic
502Dic3—24no—
503Dic3—22no—
504Dic3—22no—
505Dic3—42no—
506Dic3—121no—
507Dic3—121no—
508Dic3—121no—
509Dic3—121no—
510Dic3—241no—
511Dic3—241no—
512C32#294711yescharacteristic, complemented, Sylow
513C23—21no—
514C23D3×#6711yescharacteristic
515Q8—21no—
516Q8—34no—
517Q8—62no—
518Q8—64no—
519Q8C2×D3×Dic312yes—
520D4—24no—
521D4—21no—
522D4C2×D3×Dic312yes—
523C2×C4—21no—
524C2×C4—24no—
525C2×C4—32no—
526C2×C4—32no—
527C2×C4—62no—
528C2×C4—64no—
529C2×C4—62no—
530C2×C4—181no—
531C2×C4—181no—
532C2×C4—242no—
533C2×C4—241no—
534C2×C4C2×D3×Dic312yes—
535C2×C4#380412yes—
536C2×C4D3×#6711yescharacteristic
537C2×C4C22×D3211yescharacteristic
538C8—34no—
539C8—181no—
540C8—181no—
541C2×C3—22no—
542C2×C3—22no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—42no—
547C2×C3—42no—
548C2×C3—42no—
549C2×C3—82no—
550C2×C3#577811yescharacteristic
551C2×C3#577911yescharacteristic
552C2×C3C2×C4×#6711yescharacteristic
553C2×C3C2×D4×Dic311yescharacteristic
554C2×C3#583611yescharacteristic
555C2×C3#583811yescharacteristic
556C22—21no—
557C22—21no—
558C22—22no—
559C22—41no—
560C22—41no—
561C22Dic3×#6712yes—
562C22C2×D3×#6711yescharacteristic
563C4—22no—
564C4—62no—
565C4—62no—
566C4—64no—
567C4—122no—
568C4—361no—
569C4—361no—
570C4Dic3×#6712yes—
571C4C22×D3×Dic311yescharacteristic
572C4C2×#380411yescharacteristic
573C3—21no—
574C3#8257111yescharacteristic, complemented
575C3#8396511yescharacteristic, complemented
576C2—22no—
577C2—42no—
578C2#1059546411yescharacteristic
579C2#1059546511yescharacteristic
580C2C2×Dic3×#6711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
Fitting, prime radicalC2×C32×#41C22
socleC22×C32C22×D4
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32#2947
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
3. #10594818C2semidirect
5. #10591576C2semidirect
6. Dic3×#216C2semidirect
7. #10591440C2semidirect
8. Dic3×#214C2semidirect
9. #10591130C2semidirect
10. C2×#63565C2semidirect
11. #10591057C2semidirect
18. C3×#951C4semidirect
79. C2×C3×Dic6C2×C4semidirect
90. C3×#216C2×C4semidirect
91. C3×#214C2×C4semidirect
99. C3×#208C2×C4semidirect
122. #951Dic3semidirect
245. C2×Dic6C2×Dic3semidirect
265. #216C2×Dic3semidirect
266. #214C2×Dic3semidirect
291. #208C2×Dic3semidirect
512. C32#2947semidirect
574. C3#82571semidirect
575. C3#83965semidirect

Maximal subgroups

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

subgroupindex
C3×#58272
C2×C3×#9512
#105948182
#105929322
#105915762
Dic3×#2162
#105914402
Dic3×#2142
#105911302
C2×#635652
#105910572
#839653
#825713