Finite Group Databasebeta

← #11860225

Subgroups — #11860225

Order 1152.

1041 conjugacy classes of subgroups.

The subgroup lattice has 577 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5522C211yesmaximal, characteristic, complemented
2Dic3×#235C211yesmaximal, characteristic, complemented
3C2×#63822C211yesmaximal, characteristic
4#10592697C211yesmaximal, characteristic, complemented
5C3×#5002C211yesmaximal, characteristic, complemented
6#10591084C211yesmaximal, characteristic, complemented
7C2×#63554C211yesmaximal, characteristic, complemented
8#10590478C212yesmaximal, complemented
9#10590477C212yesmaximal, complemented
10#10590455C212yesmaximal, complemented
11#10590454C212yesmaximal, complemented
12#82506—31nomaximal
13#78819—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C32×#117C2211yescharacteristic
17#64135C2211yescharacteristic
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#893C2212yes—
22C3×#887C2212yes—
23C3×#67⋊C4—22no—
24C3×#872—21no—
25C3×C42×D3—21no—
26Dic3×#67—22no—
27Dic3×D12C2212yes—
28C4×D3×Dic3—21no—
29#63855—21no—
30Dic3×Dic6C2212yes—
31C2×#3718C2211yescharacteristic
32C2×#3715C2211yescharacteristic
33C2×#3715C2211yescharacteristic
34#63822C418yescomplemented
35C2×#3713C2211yescharacteristic
36#63635C2212yes—
37#63634C2212yes—
38C3×#810C2212yes—
39C3×#809C2212yes—
40#63566C2212yes—
41#63563C2212yes—
42#63554C2212yes—
43#63554C2212yes—
44C3×C4×#41—31no—
45Dic3×#41—31no—
46C2×#950—31no—
47C2×#950—31no—
48#5522D311yescharacteristic, complemented
49C4×#235—31no—
50C3×#416—31no—
51#5233—31no—
52#5113—31no—
53C2×#815—31no—
54#5030—32no—
55#5026—32no—
56#5018—32no—
57#5014—32no—
58#5002D311yescharacteristic, complemented
59#4998—31no—
60#4998—31no—
61#4998—61no—
62C2×#803—31no—
63#4817—32no—
64#4789—32no—
65#4785—32no—
66#4757—32no—
67C22×C32×C4C2311yescharacteristic
68C2×C3×#67—21no—
69C2×C3×#67—21no—
70C22×C3×Dic3D412yes—
71C3×#235—22no—
72C3×#235—22no—
73C3×#235C2×C414yescomplemented
74C3×#235C2×C414yescomplemented
75C2×C3×D12C2311yescharacteristic
76C2×C3×D12C2311yescharacteristic
77C2×C3×C4×D3—21no—
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3—22no—
80C2×C3×Dic6C2311yescharacteristic
81C2×C3×Dic6C2311yescharacteristic
82C2×D3×Dic3—22no—
83C32×C4⋊C4C2312yes—
84C32×C22⋊C4—21no—
85C32×C42—21no—
86#3757—21no—
87C4⋊(C3⋊Dic3)C2312yes—
88C4×C3⋊Dic3—21no—
89C2×C3⋊(C3⋊C8)C2×C414yescomplemented
90C2×C3⋊(C3⋊C8)C2311yescharacteristic
91C2×C3⋊(C3⋊C8)C2311yescharacteristic
92C3×(C2×D3)⋊C4—22no—
93C3×Dic3⋊C4—22no—
94C3×C4×Dic3—22no—
95C3×C4×Dic3D411yescharacteristic
96C3×C4×Dic3D411yescharacteristic
97C3×C4×Dic3C2312yes—
98C2×C3×C3⋊C8—22no—
99C2×C3×C3⋊C8C2312yes—
100Dic3⋊Dic3—22no—
101(C2×D3)⋊Dic3—22no—
102Dic32—22no—
103#3718C2×C414yescomplemented
104#3715C2×C414yescomplemented
105#3715C2×C414yescomplemented
106#3713C2×C414yescomplemented
107#2943—91noSylow
108C2×C3×#41—31no—
109C2×C3×#41—31no—
110C2×#235C2×D311yescharacteristic
111C2×#235C2×D311yescharacteristic
112C22×C3×C8—31no—
113C3×C4×Q8—32no—
114C3×C4×D4—32no—
115C3×C4×D4—62no—
116C3×#117—21no—
117C3×#117—61no—
118C3×#117C2×D311yescharacteristic
119C3×#117C2×D311yescharacteristic
120C2×C3×C42—31no—
121C2×C3×C42—61no—
122#950—38no—
123#950—38no—
124Q8×Dic3—32no—
125C2×#216—31no—
126C2×#216—31no—
127C2×#215—31no—
128C2×#215—31no—
129D4×Dic3—32no—
130D4×Dic3—62no—
131C2×#214—31no—
132C2×#214—31no—
133C2×#213—31no—
134C2×#213—31no—
135C4×#67—62no—
136#926—31no—
137#926—31no—
138#926—61no—
139#926—61no—
140C2×C4×Dic3—61no—
141C2×C4×Dic3C2×D311yescharacteristic
142C22×C3⋊C8—31no—
143C22×C3⋊C8—31no—
144C22×C3⋊C8—61no—
145C22×C3⋊C8C2×D311yescharacteristic
146#893C2×D312yes—
147#887C2×D312yes—
148#67⋊C4—22no—
149C4×D12—32no—
150#872—21no—
151#872—61no—
152C42×D3—21no—
153C42×D3—61no—
154C4×Dic6—32no—
155C3×#103—32no—
156C3×#102—32no—
157#835—32no—
158#832—32no—
159#821—32no—
160#816—32no—
161#815—32no—
162#815—32no—
163#810C2×D312yes—
164#809C2×D312yes—
165#808—32no—
166#808—32no—
167#808—62no—
168#807—32no—
169#807—32no—
170#807—62no—
171#803—32no—
172#803—32no—
173C23×C32C2×D411yescharacteristic
174C22×C3×D3—21no—
175C22×C3×D3—21no—
176C2×C32×C4—22no—
177C2×C32×C4C22×C412yes—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4#4112yes—
180C2×C32×C4C2411yescharacteristic
181C2×C3⋊Dic3—22no—
182C3×#67—24no—
183C3×#67—24no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—42no—
187C2×C3×Dic3C2×D412yes—
188C2×C3×Dic3C2×D412yes—
189C3×D12—21no—
190C3×D12—21no—
191C3×D12C22×C412yes—
192C3×D12C22×C412yes—
193C3×C4×D3—24no—
194C3×C4×D3—24no—
195C3×C4×D3—44no—
196C3×Dic6—21no—
197C3×Dic6—21no—
198C3×Dic6C22×C412yes—
199C3×Dic6C22×C412yes—
200D3×Dic3—44no—
201C3⋊(C3⋊C8)C22×C412yes—
202C3⋊(C3⋊C8)C22×C412yes—
203C3×C3⋊C8—22no—
204C2×#135—91no—
205C4×#41—31no—
206C4×#41—91no—
207#442—92no—
208#441—92no—
209#440—92no—
210#440—92no—
211#427—91no—
212#416—31no—
213#416—91no—
214C2×#97—91no—
215C3×#41—34no—
216C3×#41—34no—
217C3×#41—62no—
218C3×#41—62no—
219C2×C3×Q8—31no—
220C2×C3×Q8—31no—
221C2×C3×D4—31no—
222C2×C3×D4—31no—
223C2×C3×D4—61no—
224C2×C3×D4—61no—
225C22×C3×C4—21no—
226C22×C3×C4—32no—
227C22×C3×C4—62no—
228C22×C3×C4—61no—
229C22×C3×C4—61no—
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C22×D311yescharacteristic
232C2×#67—21no—
233C2×#67—21no—
234C22×Dic3—62no—
235C22×Dic3#6712yes—
236#235—22no—
237#235—22no—
238#235C4×D314yescomplemented
239#235C4×D314yescomplemented
240C2×D12C22×D311yescharacteristic
241C2×D12C22×D311yescharacteristic
242C2×C4×D3—21no—
243C2×C4×D3—21no—
244C2×C4×D3—22no—
245C2×C4×D3—62no—
246C2×Dic6C22×D311yescharacteristic
247C2×Dic6C22×D311yescharacteristic
248C2×C3×C8—32no—
249C2×C3×C8—62no—
250C3×C4⋊C4—22no—
251C3×C4⋊C4—62no—
252C3×C4⋊C4C22×D312yes—
253C3×C4⋊C4C22×D312yes—
254C3×C22⋊C4—21no—
255C3×C22⋊C4—21no—
256C3×C22⋊C4—41no—
257C3×C22⋊C4—62no—
258C3×C42—21no—
259C3×C42—21no—
260C3×C42—31no—
261C3×C42—31no—
262C3×C42—32no—
263C3×C42—41no—
264C3×C42—62no—
265#217—61no—
266#217—61no—
267#217—62no—
268#217—121no—
269#216—34no—
270#216—34no—
271#215—34no—
272#215—34no—
273#214—34no—
274#214—34no—
275#213—34no—
276#213—34no—
277(C2×D3)⋊C4—22no—
278(C2×D3)⋊C4—62no—
279C4⋊Dic3—32no—
280C4⋊Dic3—32no—
281C4⋊Dic3—62no—
282C4⋊Dic3—62no—
283Dic3⋊C4—22no—
284Dic3⋊C4—62no—
285C4×Dic3—22no—
286C4×Dic3—62no—
287C4×Dic3—61no—
288C4×Dic3—61no—
289C4×Dic3—62no—
290C4×Dic3—121no—
291C4×Dic3#6711yescharacteristic
292C4×Dic3#6711yescharacteristic
293C4×Dic3C22×D312yes—
294C2×C3⋊C8—22no—
295C2×C3⋊C8—34no—
296C2×C3⋊C8—34no—
297C2×C3⋊C8—31no—
298C2×C3⋊C8—31no—
299C2×C3⋊C8—31no—
300C2×C3⋊C8—31no—
301C2×C3⋊C8—61no—
302C2×C3⋊C8—61no—
303C2×C3⋊C8—64no—
304C2×C3⋊C8C22×D312yes—
305C22×C32—22no—
306C22×C32C4×D412yes—
307C22×C32C22×D411yescharacteristic
308C2×C3×D3—22no—
309C2×C3×D3—22no—
310C2×C3×D3—42no—
311C2×C3×D3—42no—
312C32×C4—42no—
313C32×C4C4×D412yes—
314C32×C4C23×C411yescharacteristic
315C32×C4C2×#4111yescharacteristic
316C3⋊Dic3—42no—
317C3×Dic3—22no—
318C3×Dic3—22no—
319C3×Dic3—22no—
320C3×Dic3—22no—
321C2×#41—31no—
322C2×#41—31no—
323#135—98no—
324C2×Q16—91no—
325C2×SD16—91no—
326C2×SD16—91no—
327C2×D8—91no—
328C22×C8—31no—
329C22×C8—91no—
330C4×Q8—32no—
331C4×Q8—92no—
332C4×D4—32no—
333C4×D4—62no—
334C4×D4—92no—
335C4×D4—182no—
336#117—61no—
337#117—91no—
338#117—181no—
339#117D3211yescharacteristic
340C2×C42—31no—
341C2×C42—61no—
342C2×C42—181no—
343#107—92no—
344#106—92no—
345#103—32no—
346#103—92no—
347#102—32no—
348#102—92no—
349#97—92no—
350#97—92no—
351C23×C3—21no—
352C23×C3—61no—
353C23×C3—61no—
354C23×C3D3×D411yescharacteristic
355C23×C3C2×#6711yescharacteristic
356C22×D3—21no—
357C22×D3—21no—
358C3×Q8—32no—
359C3×Q8—32no—
360C3×Q8—61no—
361C3×Q8—61no—
362C3×D4—32no—
363C3×D4—32no—
364C3×D4—64no—
365C3×D4—64no—
366C3×D4—61no—
367C3×D4—61no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—21no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—21no—
374C2×C3×C4—32no—
375C2×C3×C4—32no—
376C2×C3×C4—42no—
377C2×C3×C4—61no—
378C2×C3×C4—61no—
379C2×C3×C4—64no—
380C2×C3×C4—64no—
381C2×C3×C4—124no—
382C2×C3×C4—122no—
383C2×C3×C4C2×C4×D312yes—
384C2×C3×C4C2×C4×D312yes—
385C2×C3×C4#23512yes—
386C2×C3×C4D3×D411yescharacteristic
387C2×C3×C4#23712yes—
388C2×C3×C4C2×#6711yescharacteristic
389C2×C3×C4C23×D311yescharacteristic
390C2×C3×C4C23×D311yescharacteristic
391#67—24no—
392#67—24no—
393C2×Dic3—21no—
394C2×Dic3—21no—
395C2×Dic3—42no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398C2×Dic3—122no—
399C2×Dic3—124no—
400C2×Dic3C2×#6712yes—
401C2×Dic3C2×#6712yes—
402D12—21no—
403D12—21no—
404D12C2×C4×D312yes—
405D12C2×C4×D312yes—
406C4×D3—24no—
407C4×D3—24no—
408C4×D3—44no—
409C4×D3—124no—
410Dic6—21no—
411Dic6—21no—
412Dic6C2×C4×D312yes—
413Dic6C2×C4×D312yes—
414C3×C8—62no—
415C3⋊C8—22no—
416C3⋊C8—32no—
417C3⋊C8—32no—
418C3⋊C8—32no—
419C3⋊C8—32no—
420C3⋊C8—62no—
421C3⋊C8—62no—
422C2×C32—22no—
423C2×C32C2×C4×D411yescharacteristic
424C2×C32#57512yes—
425C3×D3—42no—
426C3×D3—42no—
427#41—34no—
428#41—34no—
429#41—62no—
430#41—62no—
431C2×Q8—31no—
432C2×Q8—31no—
433C2×D4—31no—
434C2×D4—31no—
435C2×D4—61no—
436C2×D4—61no—
437C22×C4—32no—
438C22×C4—62no—
439C22×C4—61no—
440C22×C4—61no—
441C22×C4—182no—
442C22×C4C2×D3211yescharacteristic
443Q16—94no—
444SD16—94no—
445SD16—94no—
446D8—94no—
447C2×C8—32no—
448C2×C8—62no—
449C2×C8—91no—
450C2×C8—91no—
451C2×C8—94no—
452C4⋊C4—62no—
453C4⋊C4—92no—
454C4⋊C4—182no—
455C4⋊C4C2×D3212yes—
456C22⋊C4—21no—
457C22⋊C4—62no—
458C22⋊C4—182no—
459C22⋊C4—181no—
460C42—21no—
461C42—32no—
462C42—31no—
463C42—31no—
464C42—62no—
465C42—182no—
466C42—181no—
467C22×C3—22no—
468C22×C3—22no—
469C22×C3—21no—
470C22×C3—22no—
471C22×C3—42no—
472C22×C3—62no—
473C22×C3—62no—
474C22×C3—122no—
475C22×C3—122no—
476C22×C3#67⋊C412yes—
477C22×C3C4×#6712yes—
478C22×C3C2×D3×D411yescharacteristic
479C22×C3C22×#6711yescharacteristic
480C2×D3—22no—
481C2×D3—22no—
482C2×D3—42no—
483C2×D3—42no—
484C3×C4—21no—
485C3×C4—21no—
486C3×C4—22no—
487C3×C4—42no—
488C3×C4—42no—
489C3×C4—62no—
490C3×C4—62no—
491C3×C4—62no—
492C3×C4—62no—
493C3×C4—82no—
494C3×C4#67⋊C412yes—
495C3×C4C4×#6712yes—
496C3×C4C22×C4×D311yescharacteristic
497C3×C4C22×C4×D311yescharacteristic
498C3×C4C2×#23511yescharacteristic
499C3×C4C2×#23711yescharacteristic
500Dic3—22no—
501Dic3—22no—
502Dic3—22no—
503Dic3—22no—
504Dic3—122no—
505Dic3—122no—
506Dic3—242no—
507C32#294311yescharacteristic, complemented, Sylow
508C23—61no—
509C23—61no—
510C23D3×#6711yescharacteristic
511Q8—32no—
512Q8—32no—
513Q8—61no—
514Q8—61no—
515D4—32no—
516D4—32no—
517D4—64no—
518D4—64no—
519D4—61no—
520D4—61no—
521C2×C4—22no—
522C2×C4—32no—
523C2×C4—32no—
524C2×C4—61no—
525C2×C4—61no—
526C2×C4—64no—
527C2×C4—64no—
528C2×C4—124no—
529C2×C4—122no—
530C2×C4—182no—
531C2×C4—364no—
532C2×C4#379512yes—
533C2×C4C4×D3212yes—
534C2×C4D3×#6711yescharacteristic
535C2×C4C22×D3211yescharacteristic
536C8—62no—
537C8—92no—
538C8—92no—
539C2×C3—22no—
540C2×C3—22no—
541C2×C3—21no—
542C2×C3—22no—
543C2×C3—42no—
544C2×C3—122no—
545C2×C3—122no—
546C2×C3C2×#67⋊C411yescharacteristic
547C2×C3#576812yes—
548C2×C3C2×C4×#6711yescharacteristic
549C2×C3#582212yes—
550D3—42no—
551D3—42no—
552C22—22no—
553C22—62no—
554C22—62no—
555C22—122no—
556C22—122no—
557C22#6387912yes—
558C22C2×D3×#6711yescharacteristic
559C4—42no—
560C4—62no—
561C4—62no—
562C4—62no—
563C4—62no—
564C4—362no—
565C4#6387912yes—
566C4C2×#379511yescharacteristic
567C4C2×C4×D3211yescharacteristic
568C3—21no—
569C3#7881911yescharacteristic, complemented
570C3#8250611yescharacteristic, complemented
571C2—22no—
572C2—122no—
573C2—122no—
574C2C2×#6387911yescharacteristic
575C2#1059545312yes—
subgroupG/H
centerC2×C4D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC2×#63822C2
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32#2943
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×#5522C2semidirect
2. Dic3×#235C2semidirect
4. #10592697C2semidirect
5. C3×#5002C2semidirect
6. #10591084C2semidirect
7. C2×#63554C2semidirect
8. #10590478C2semidirect
9. #10590477C2semidirect
10. #10590455C2semidirect
11. #10590454C2semidirect
34. #63822C4semidirect
48. #5522D3semidirect
58. #5002D3semidirect
73. C3×#235C2×C4semidirect
74. C3×#235C2×C4semidirect
89. C2×C3⋊(C3⋊C8)C2×C4semidirect
103. #3718C2×C4semidirect
104. #3715C2×C4semidirect
105. #3715C2×C4semidirect
106. #3713C2×C4semidirect
238. #235C4×D3semidirect
239. #235C4×D3semidirect
507. C32#2943semidirect
569. C3#78819semidirect
570. C3#82506semidirect

Maximal subgroups

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

subgroupindex
C3×#55222
Dic3×#2352
C2×#638222
#105926972
C3×#50022
#105910842
C2×#635542
#105904782
#105904772
#105904552
#105904542
#825063
#788193