Finite Group Databasebeta

← #11860631

Subgroups — #11860631

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
1#10594990C211yesmaximal, characteristic
2#10594818C211yesmaximal, characteristic, complemented
3C2×#63833C211yesmaximal, characteristic
4#10592812C211yesmaximal, characteristic
5C2×C3×#816C211yesmaximal, characteristic, complemented
6C3×#5101C211yesmaximal, characteristic, complemented
7#10591130C211yesmaximal, characteristic, complemented
8#10590795C212yesmaximal, complemented
9#10590794C212yesmaximal, complemented
10#10590793C212yesmaximal, complemented
11#10590792C212yesmaximal, complemented
12#78774—31nomaximal
13#78571—31nomaximal
14C2×#3828C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C22×C32×C8C2211yescharacteristic
17#64135C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21#63955—22no—
22#63952—22no—
23#63900—21no—
24#63894C2212yes—
25#63849—21no—
26#63844C2212yes—
27#63843—21no—
28#63843—21no—
29Dic3×Dic6C2212yes—
30Dic3×Dic6C2212yes—
31C2×#3719C2212yes—
32#63833C418yescomplemented
33C2×#3717C2212yes—
34#63648C2211yescharacteristic
35#63648C2211yescharacteristic
36#63643C2211yescharacteristic
37#63643C2211yescharacteristic
38C3×#816C2212yes—
39C3×#816C2212yes—
40C3×#815C2212yes—
41C3×C8×Dic3C2212yes—
42#63575C2212yes—
43#63573C2212yes—
44#5812—31no—
45C2×#942—31no—
46C2×#909—31no—
47#5523—31no—
48#5516—31no—
49#5504—31no—
50C2×C3×#103—31no—
51C3×#405—31no—
52#5121—31no—
53#5113—31no—
54#5113—31no—
55#5113—61no—
56C2×#816D311yescharacteristic, complemented
57#5101D311yescharacteristic, complemented
58#4964—31no—
59#4817—32no—
60#4790—32no—
61#4789—32no—
62#4788—32no—
63#4716—32no—
64#4710—32no—
65C4×Dic12—32no—
66C4×#204—32no—
67C22×C32×C4C2311yescharacteristic
68C2×#638—21no—
69#3828—22no—
70#3828C2×C414yes—
71C2×C4⋊(C3⋊D3)C2311yescharacteristic
72C2×C4×C3⋊D3—21no—
73C2×#634C2311yescharacteristic
74C22×C3×Dic3—21no—
75C22×C3×Dic3—21no—
76C2×C3×Dic6—21no—
77C2×C3×Dic6—22no—
78C2×C3×Dic6C2×C414yescomplemented
79C2×C3×Dic6C2312yes—
80C2×#624—22no—
81C2×C32×C8—22no—
82C2×C32×C8C2311yescharacteristic
83C2×C32×C8C2311yescharacteristic
84#3757—21no—
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86C4⋊(C3⋊Dic3)C2311yescharacteristic
87C4×C3⋊Dic3—21no—
88C3×#217D412yes—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3D411yescharacteristic
91C3×C4⋊Dic3D411yescharacteristic
92C3×C4⋊Dic3C2312yes—
93C3×C4×Dic3C2312yes—
94C3×#208C2×C414yescomplemented
95C2×C3×C3⋊C8C2312yes—
96#3724—22no—
97Dic3⋊Dic3—22no—
98Dic3⋊Dic3—22no—
99#3722—22no—
100Dic32—22no—
101Dic32—22no—
102Dic32—22no—
103#3719C2×C418yescomplemented
104#3717C2×C418yescomplemented
105#2947—91noSylow
106C22×C3×Q8—31no—
107C2×#235—31no—
108C2×#235—31no—
109C2×#235—61no—
110C22×Dic6C2×D311yescharacteristic
111C2×C3×M16—31no—
112C22×C3×C8—21no—
113C22×C3×C8C2×D311yescharacteristic
114C22×C3×C8C2×D311yescharacteristic
115C3×#117—31no—
116C2×C3×C4⋊C4—31no—
117Q8×Dic3—32no—
118Q8×Dic3—32no—
119Q8×Dic3—61no—
120Q8×Dic3—61no—
121C2×#216—32no—
122#942—38no—
123C2×#215—32no—
124C4×#67—62no—
125#926—31no—
126#926—31no—
127#926—61no—
128#926—62no—
129#926C2×D311yescharacteristic
130C2×C4⋊Dic3C2×D311yescharacteristic
131C2×#208C2×D311yescharacteristic
132#909—38no—
133C2×Dic12—32no—
134C2×#204—32no—
135#893—32no—
136#892—61no—
137#892—61no—
138D3×C4⋊C4—61no—
139D3×C4⋊C4—61no—
140#887—32no—
141#887—61no—
142#887—61no—
143#67⋊C4—62no—
144#877—62no—
145C4×D12—32no—
146C4×Dic6—32no—
147C4×Dic6—32no—
148C4×Dic6—32no—
149C3×#103—32no—
150C3×#103—32no—
151C3×#97—32no—
152C3×C4×C8—32no—
153#821—31no—
154#821—31no—
155#821—31no—
156#821—31no—
157#821—61no—
158#821—61no—
159#818—32no—
160#817—32no—
161#816—31no—
162#816—31no—
163#816—31no—
164#816—31no—
165#816—61no—
166#816—61no—
167#816C2×D312yes—
168#816C2×D312yes—
169#815C2×D312yes—
170C8×Dic3C2×D312yes—
171#808—32no—
172#807—32no—
173C23×C32C2×D411yescharacteristic
174C22×C3⋊D3—21no—
175C2×C32×C4C22×C412yes—
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4#4112yes—
178C2×C32×C4C2411yescharacteristic
179#638—24no—
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3—21no—
183C4⋊(C3⋊D3)—21no—
184C4⋊(C3⋊D3)C22×C412yes—
185C4×C3⋊D3—24no—
186#634—21no—
187#634C22×C412yes—
188C2×C3×Dic3—24no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—81no—
192C2×C3×Dic3C2×D412yes—
193C2×C3×Dic3C2×D412yes—
194C3×Dic6—24no—
195C3×Dic6—22no—
196C3×Dic6C22×C414yes—
197#624—82no—
198C32×C8—21no—
199C32×C8—21no—
200C3×C3⋊C8C22×C414yes—
201C2×#137—91no—
202#520—91no—
203#519—91no—
204#441—92no—
205#440—92no—
206C4×Q16—92no—
207C4×SD16—92no—
208#428—91no—
209#416—91no—
210C2×#103—31no—
211#405—31no—
212C2×C3×Q8—34no—
213C2×C3×Q8—32no—
214C2×C3×Q8—61no—
215C2×C3×Q8—62no—
216C22×C3×C4—21no—
217C22×C3×C4—61no—
218C22×C3×C4—61no—
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C22×D311yescharacteristic
221C2×#67—61no—
222C2×#67—61no—
223C2×#67—121no—
224C22×Dic3—21no—
225C22×Dic3—21no—
226#235—34no—
227#235—34no—
228#235—64no—
229#235—62no—
230#235—62no—
231#235—122no—
232C2×D12—31no—
233C2×D12—31no—
234C2×D12—61no—
235C2×C4×D3—61no—
236C2×C4×D3—61no—
237C2×C4×D3—62no—
238C2×C4×D3—62no—
239C2×C4×D3—121no—
240C2×Dic6—21no—
241C2×Dic6—22no—
242C2×Dic6—31no—
243C2×Dic6—31no—
244C2×Dic6—61no—
245C2×Dic6C4×D314yescomplemented
246C2×Dic6C22×D312yes—
247C3×M16—34no—
248C2×C3×C8—22no—
249C2×C3×C8—22no—
250C2×C3×C8—21no—
251C2×C3×C8—21no—
252C2×C3×C8—32no—
253C2×C3×C8—42no—
254C2×C3×C8C22×D311yescharacteristic
255C2×C3×C8C22×D311yescharacteristic
256C2×C3×C8C22×D311yescharacteristic
257C2×C3×C8C22×D311yescharacteristic
258C3×C4⋊C4—31no—
259C3×C4⋊C4—31no—
260C3×C4⋊C4—32no—
261C3×C4⋊C4—61no—
262C3×C22⋊C4—32no—
263C3×C42—32no—
264#217—61no—
265#217—61no—
266#217—121no—
267#217D1212yes—
268#216—38no—
269#215—38no—
270(C2×D3)⋊C4—62no—
271(C2×D3)⋊C4—62no—
272C4⋊Dic3—21no—
273C4⋊Dic3—31no—
274C4⋊Dic3—31no—
275C4⋊Dic3—31no—
276C4⋊Dic3—31no—
277C4⋊Dic3—61no—
278C4⋊Dic3—61no—
279C4⋊Dic3—62no—
280C4⋊Dic3—62no—
281C4⋊Dic3D1211yescharacteristic
282C4⋊Dic3D1211yescharacteristic
283C4⋊Dic3C22×D312yes—
284Dic3⋊C4—62no—
285Dic3⋊C4—62no—
286Dic3⋊C4—62no—
287Dic3⋊C4—62no—
288C4×Dic3—62no—
289C4×Dic3—62no—
290C4×Dic3—62no—
291C4×Dic3—61no—
292C4×Dic3—61no—
293C4×Dic3—62no—
294C4×Dic3—62no—
295C4×Dic3—62no—
296C4×Dic3—121no—
297C4×Dic3C22×D312yes—
298#208C4×D314yescomplemented
299C2×C3⋊C8C22×D312yes—
300Dic12—38no—
301#204—38no—
302C22×C32—21no—
303C22×C32—21no—
304C22×C32C4×D412yes—
305C22×C32C22×D411yescharacteristic
306C2×C3⋊D3—22no—
307C2×C3⋊D3—41no—
308C2×C3⋊D3—41no—
309C32×C4C4×D412yes—
310C32×C4C23×C411yescharacteristic
311C32×C4C2×#4111yescharacteristic
312C3⋊Dic3—22no—
313C3⋊Dic3—41no—
314C3⋊Dic3—41no—
315C3×Dic3—24no—
316C3×Dic3—22no—
317C3×Dic3—22no—
318C3×Dic3—42no—
319C2×#41—91no—
320C22×Q8—31no—
321#137—98no—
322C2×Q16—92no—
323C2×SD16—92no—
324C2×M16—31no—
325C22×C8D3211yescharacteristic
326C4×Q8—92no—
327C4×Q8—92no—
328C4×Q8—92no—
329C4×Q8—181no—
330C4×Q8—181no—
331C4×D4—92no—
332C4×D4—182no—
333#117—31no—
334#117—91no—
335#117—182no—
336#117—181no—
337C2×C4⋊C4—31no—
338C2×C4⋊C4—181no—
339#107—92no—
340#106—92no—
341#103—32no—
342#103—32no—
343#103—91no—
344#103—91no—
345#102—91no—
346#102—91no—
347#97—32no—
348C4×C8—32no—
349C23×C3—21no—
350C23×C3C2×D1211yescharacteristic
351C23×C3D3×D411yescharacteristic
352C22×D3—61no—
353C22×D3—61no—
354C22×D3—121no—
355C3×Q8—34no—
356C3×Q8—64no—
357C3×Q8—62no—
358C2×C3×C4—21no—
359C2×C3×C4—22no—
360C2×C3×C4—21no—
361C2×C3×C4—22no—
362C2×C3×C4—32no—
363C2×C3×C4—32no—
364C2×C3×C4—64no—
365C2×C3×C4—62no—
366C2×C3×C4—62no—
367C2×C3×C4—241no—
368C2×C3×C4C2×C4×D312yes—
369C2×C3×C4C2×C4×D312yes—
370C2×C3×C4C2×D1211yescharacteristic
371C2×C3×C4#23512yes—
372C2×C3×C4D3×D411yescharacteristic
373C2×C3×C4#23712yes—
374C2×C3×C4C23×D311yescharacteristic
375C2×C3×C4C23×D311yescharacteristic
376#67—64no—
377#67—64no—
378#67—124no—
379C2×Dic3—24no—
380C2×Dic3—22no—
381C2×Dic3—22no—
382C2×Dic3—61no—
383C2×Dic3—61no—
384C2×Dic3—61no—
385C2×Dic3—61no—
386C2×Dic3—61no—
387C2×Dic3—61no—
388C2×Dic3—81no—
389C2×Dic3—121no—
390C2×Dic3—121no—
391C2×Dic3—121no—
392C2×Dic3C2×D1212yes—
393C2×Dic3C2×D1212yes—
394D12—32no—
395D12—32no—
396D12—62no—
397D12—61no—
398D12—61no—
399D12—121no—
400C4×D3—64no—
401C4×D3—64no—
402C4×D3—124no—
403C4×D3—242no—
404C4×D3—242no—
405Dic6—24no—
406Dic6—22no—
407Dic6—32no—
408Dic6—32no—
409Dic6—62no—
410Dic6—61no—
411Dic6—61no—
412Dic6—121no—
413Dic6C2×C4×D314yes—
414C3×C8—21no—
415C3×C8—21no—
416C3×C8—21no—
417C3×C8—21no—
418C3×C8—34no—
419C3×C8—41no—
420C3×C8—41no—
421C3⋊C8C2×C4×D314yes—
422C2×C32—22no—
423C2×C32C2×C4×D411yescharacteristic
424C2×C32#57711yescharacteristic
425C2×C32#57811yescharacteristic
426C3⋊D3—42no—
427#41—94no—
428#41—182no—
429C2×Q8—32no—
430C2×Q8—34no—
431C2×Q8—61no—
432C2×Q8—62no—
433C2×Q8—91no—
434C2×D4—91no—
435C2×D4—181no—
436C22×C4—61no—
437C22×C4—61no—
438C22×C4—182no—
439C22×C4—181no—
440C22×C4C2×D3211yescharacteristic
441Q16—98no—
442SD16—98no—
443M16—34no—
444C2×C8—22no—
445C2×C8—32no—
446C2×C8C2×D3211yescharacteristic
447C2×C8C2×D3211yescharacteristic
448C4⋊C4—31no—
449C4⋊C4—31no—
450C4⋊C4—32no—
451C4⋊C4—61no—
452C4⋊C4—91no—
453C4⋊C4—91no—
454C4⋊C4—182no—
455C4⋊C4—182no—
456C4⋊C4—182no—
457C22⋊C4—32no—
458C22⋊C4—182no—
459C22⋊C4—181no—
460C42—32no—
461C42—182no—
462C42—182no—
463C42—182no—
464C42—181no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—22no—
471C22×C3—41no—
472C22×C3—41no—
473C22×C3C4×D1212yes—
474C22×C3#67⋊C412yes—
475C22×C3C22×D1211yescharacteristic
476C22×C3C2×D3×D411yescharacteristic
477C2×D3—62no—
478C2×D3—62no—
479C2×D3—122no—
480C2×D3—121no—
481C2×D3—121no—
482C2×D3—121no—
483C2×D3—121no—
484C2×D3—241no—
485C2×D3—241no—
486C3×C4—21no—
487C3×C4—21no—
488C3×C4—22no—
489C3×C4—64no—
490C3×C4—62no—
491C3×C4—62no—
492C3×C4—122no—
493C3×C4C4×D1212yes—
494C3×C4#67⋊C412yes—
495C3×C4C22×C4×D311yescharacteristic
496C3×C4C22×C4×D311yescharacteristic
497C3×C4C2×#23511yescharacteristic
498C3×C4C2×#23711yescharacteristic
499Dic3—24no—
500Dic3—22no—
501Dic3—22no—
502Dic3—42no—
503Dic3—62no—
504Dic3—62no—
505Dic3—122no—
506Dic3—121no—
507Dic3—121no—
508Dic3—121no—
509Dic3—121no—
510Dic3—241no—
511Dic3—241no—
512C32#294711yescharacteristic, complemented, Sylow
513C23—181no—
514C23D3×D1211yescharacteristic
515Q8—34no—
516Q8—62no—
517Q8—64no—
518Q8—92no—
519Q8—181no—
520D4—92no—
521D4—184no—
522D4—181no—
523C2×C4—32no—
524C2×C4—32no—
525C2×C4—62no—
526C2×C4—64no—
527C2×C4—62no—
528C2×C4—181no—
529C2×C4—184no—
530C2×C4—181no—
531C2×C4—181no—
532C2×C4—241no—
533C2×C4—722no—
534C2×C4C4×D3212yes—
535C2×C4D3×D1211yescharacteristic
536C2×C4#380412yes—
537C2×C4C22×D3211yescharacteristic
538C8—21no—
539C8—21no—
540C8—34no—
541C2×C3—22no—
542C2×C3—22no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—42no—
547C2×C3C2×C4×D1211yescharacteristic
548C2×C3C2×#67⋊C411yescharacteristic
549C2×C3#575111yescharacteristic
550C2×C3#575311yescharacteristic
551C2×C3#576211yescharacteristic
552C2×C3#576611yescharacteristic
553D3—122no—
554D3—122no—
555D3—242no—
556C22—21no—
557C22—21no—
558C22—182no—
559C22—361no—
560C22—361no—
561C22#6388012yes—
562C22C2×D3×D1211yescharacteristic
563C4—64no—
564C4—62no—
565C4—62no—
566C4—122no—
567C4—182no—
568C4—361no—
569C4—361no—
570C4#6388012yes—
571C4C2×C4×D3211yescharacteristic
572C4C2×#380411yescharacteristic
573C3—21no—
574C3#7857111yescharacteristic, complemented
575C3#7877411yescharacteristic, complemented
576C2—22no—
577C2—362no—
578C2#1059467711yescharacteristic
579C2#1059469111yescharacteristic
580C2C2×#6388011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radicalC2×#3828C22
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32#2947
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #10594818C2semidirect
5. C2×C3×#816C2semidirect
6. C3×#5101C2semidirect
7. #10591130C2semidirect
8. #10590795C2semidirect
9. #10590794C2semidirect
10. #10590793C2semidirect
11. #10590792C2semidirect
32. #63833C4semidirect
56. C2×#816D3semidirect
57. #5101D3semidirect
78. C2×C3×Dic6C2×C4semidirect
94. C3×#208C2×C4semidirect
103. #3719C2×C4semidirect
104. #3717C2×C4semidirect
245. C2×Dic6C4×D3semidirect
298. #208C4×D3semidirect
512. C32#2947semidirect
574. C3#78571semidirect
575. C3#78774semidirect

Maximal subgroups

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

subgroupindex
#105949902
#105948182
C2×#638332
#105928122
C2×C3×#8162
C3×#51012
#105911302
#105907952
#105907942
#105907932
#105907922
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