Finite Group Databasebeta

← #11860231

Subgroups — #11860231

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
1#10594954C211yesmaximal, characteristic, complemented
2Dic3×#235C211yesmaximal, characteristic, complemented
3C2×#63829C211yesmaximal, characteristic
4#10592812C211yesmaximal, characteristic, complemented
5C3×#5113C211yesmaximal, characteristic, complemented
6C2×C3×#815C211yesmaximal, characteristic, complemented
7#10591122C211yesmaximal, characteristic, complemented
8#10590795C212yesmaximal, complemented
9#10590794C212yesmaximal, complemented
10#10590747C212yesmaximal, complemented
11#10590746C212yesmaximal, complemented
12#78819—31nomaximal
13#78494—31nomaximal
14C2×#3828C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C22×C32×C8C2211yescharacteristic
17#64135C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21Dic3×#67—22no—
22#63952—22no—
23#63894C2212yes—
24Dic3×D12C2212yes—
25C4×#624—21no—
26C4×D3×Dic3—21no—
27#63874—21no—
28#63855—21no—
29#63844C2212yes—
30Dic3×Dic6C2212yes—
31C2×#3719C2211yescharacteristic
32C2×#3717C2211yescharacteristic
33#63829C418yescomplemented
34C2×#3716C2211yescharacteristic
35C2×#3714C2211yescharacteristic
36#63648C2212yes—
37#63643C2212yes—
38C3×#821C2212yes—
39C3×#816C2212yes—
40C3×#815C2212yes—
41C3×#815C2212yes—
42#63575C2212yes—
43#63573C2212yes—
44Dic3×#41—31no—
45C2×#950—31no—
46C2×#904—31no—
47#5522—31no—
48C4×#235—31no—
49C4×#235—31no—
50C3×#416—31no—
51C2×C3×#97—31no—
52#5113—31no—
53#5113—31no—
54#5113—61no—
55#5113D311yescharacteristic, complemented
56#5106—31no—
57C2×#815D311yescharacteristic, complemented
58#4998—31no—
59#4817—32no—
60#4789—32no—
61#4785—32no—
62#4757—32no—
63#4716—32no—
64#4711—32no—
65#4710—32no—
66#4710—32no—
67C22×C32×C4C2311yescharacteristic
68C2×#638—21no—
69#3828—22no—
70#3828C2×C414yescomplemented
71C2×C4⋊(C3⋊D3)C2311yescharacteristic
72C2×C4×C3⋊D3—21no—
73C2×#634C2311yescharacteristic
74C2×C3×#67—21no—
75C22×C3×Dic3D412yes—
76C3×#235—22no—
77C3×#235C2×C414yescomplemented
78C2×C3×D12C2311yescharacteristic
79C2×C3×C4×D3—21no—
80C2×C3×Dic6C2311yescharacteristic
81C2×#624—22no—
82C2×D3×Dic3—22no—
83C2×C32×C8—22no—
84C2×C32×C8C2312yes—
85#3757—21no—
86C4⋊(C3⋊Dic3)C2312yes—
87C4×C3⋊Dic3—21no—
88C3×#217—21no—
89C3×C4⋊Dic3C2312yes—
90C3×C4×Dic3—21no—
91C3×C4×Dic3D411yescharacteristic
92C3×C4×Dic3D411yescharacteristic
93C3×C4×Dic3C2312yes—
94C2×C3×C3⋊C8C2×C414yescomplemented
95C2×C3×C3⋊C8C2311yescharacteristic
96C2×C3×C3⋊C8C2311yescharacteristic
97#3724—22no—
98Dic3⋊Dic3—22no—
99#3722—22no—
100(C2×D3)⋊Dic3—22no—
101Dic32—22no—
102Dic32—22no—
103#3719C2×C414yescomplemented
104#3717C2×C414yescomplemented
105#3716C2×C414yescomplemented
106#3714C2×C414yescomplemented
107#2943—91noSylow
108C2×C3×#41—31no—
109C2×#235—31no—
110C2×#235—31no—
111C2×#235—61no—
112C2×#235C2×D311yescharacteristic
113C22×C3×C8—21no—
114C22×C3×C8—31no—
115C22×C3×C8C2×D311yescharacteristic
116C22×C3×C8C2×D311yescharacteristic
117C3×#117—31no—
118C2×C3×C42—31no—
119#950—38no—
120Q8×Dic3—32no—
121C2×#216—31no—
122C2×#215—31no—
123D4×Dic3—32no—
124D4×Dic3—62no—
125C2×#214—31no—
126C2×#213—31no—
127C4×#67—62no—
128C4×#67—62no—
129#926—31no—
130#926—31no—
131#926—61no—
132#926—61no—
133#926C2×D311yescharacteristic
134C2×C4×Dic3—61no—
135C2×C4×Dic3C2×D311yescharacteristic
136C22×C3⋊C8C2×D311yescharacteristic
137C2×Dic12—31no—
138#904—38no—
139C2×D24—31no—
140C2×#204—31no—
141C2×#204—31no—
142#893—32no—
143#887—32no—
144#67⋊C4—62no—
145C4×D12—32no—
146C4×D12—32no—
147#872—61no—
148#872—61no—
149#872—61no—
150C42×D3—61no—
151C42×D3—61no—
152C42×D3—61no—
153C4×Dic6—32no—
154C4×Dic6—32no—
155C3×#103—32no—
156C3×#102—32no—
157C3×#97—32no—
158C3×#97—32no—
159#821—32no—
160#821—32no—
161#821—62no—
162#821C2×D312yes—
163#818—32no—
164#817—32no—
165#816—32no—
166#816—32no—
167#816—62no—
168#816C2×D312yes—
169#815C2×D312yes—
170#815C2×D312yes—
171#808—32no—
172#807—32no—
173C23×C32C2×D411yescharacteristic
174C22×C3⋊D3—21no—
175C22×C3×D3—21no—
176C2×C32×C4C22×C412yes—
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4#4112yes—
179C2×C32×C4C2411yescharacteristic
180#638—24no—
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3—22no—
183C4⋊(C3⋊D3)—21no—
184C4⋊(C3⋊D3)C22×C412yes—
185C4×C3⋊D3—24no—
186#634—21no—
187#634C22×C412yes—
188C3×#67—24no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—42no—
192C2×C3×Dic3C2×D412yes—
193C2×C3×Dic3C2×D412yes—
194C3×D12—21no—
195C3×D12C22×C412yes—
196C3×C4×D3—24no—
197C3×Dic6—21no—
198C3×Dic6C22×C412yes—
199#624—44no—
200D3×Dic3—44no—
201C32×C8—22no—
202C3×C3⋊C8C22×C412yes—
203C3×C3⋊C8C22×C412yes—
204C2×#135—91no—
205C4×#41—91no—
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—31no—
215C3×#41—34no—
216C3×#41—62no—
217C2×C3×Q8—31no—
218C2×C3×D4—31no—
219C2×C3×D4—61no—
220C22×C3×C4—21no—
221C22×C3×C4—32no—
222C22×C3×C4—61no—
223C22×C3×C4C22×D311yescharacteristic
224C22×C3×C4C22×D311yescharacteristic
225C2×#67—21no—
226C2×#67—61no—
227C2×#67—61no—
228C2×#67—121no—
229C22×Dic3—62no—
230C22×Dic3D1212yes—
231#235—22no—
232#235—34no—
233#235—34no—
234#235—64no—
235#235—62no—
236#235—62no—
237#235—122no—
238#235C4×D314yescomplemented
239C2×D12—31no—
240C2×D12—31no—
241C2×D12—61no—
242C2×D12C22×D311yescharacteristic
243C2×C4×D3—21no—
244C2×C4×D3—61no—
245C2×C4×D3—61no—
246C2×C4×D3—62no—
247C2×C4×D3—62no—
248C2×C4×D3—62no—
249C2×C4×D3—121no—
250C2×Dic6—31no—
251C2×Dic6—31no—
252C2×Dic6—61no—
253C2×Dic6C22×D311yescharacteristic
254C2×C3×C8—22no—
255C2×C3×C8—22no—
256C2×C3×C8—22no—
257C2×C3×C8—34no—
258C2×C3×C8—31no—
259C2×C3×C8—31no—
260C2×C3×C8—42no—
261C2×C3×C8C22×D312yes—
262C2×C3×C8C22×D312yes—
263C3×C4⋊C4—32no—
264C3×C22⋊C4—61no—
265C3×C42—31no—
266C3×C42—31no—
267C3×C42—32no—
268C3×C42—61no—
269#217—21no—
270#217—61no—
271#217—61no—
272#217—62no—
273#217—121no—
274#216—34no—
275#215—34no—
276#214—34no—
277#213—34no—
278(C2×D3)⋊C4—62no—
279(C2×D3)⋊C4—62no—
280(C2×D3)⋊C4—62no—
281C4⋊Dic3—32no—
282C4⋊Dic3—32no—
283C4⋊Dic3—62no—
284C4⋊Dic3—62no—
285C4⋊Dic3C22×D312yes—
286Dic3⋊C4—62no—
287Dic3⋊C4—62no—
288Dic3⋊C4—62no—
289C4×Dic3—21no—
290C4×Dic3—62no—
291C4×Dic3—62no—
292C4×Dic3—61no—
293C4×Dic3—61no—
294C4×Dic3—62no—
295C4×Dic3—62no—
296C4×Dic3—121no—
297C4×Dic3D1211yescharacteristic
298C4×Dic3D1211yescharacteristic
299C4×Dic3C22×D312yes—
300C2×C3⋊C8C4×D314yescomplemented
301C2×C3⋊C8C22×D311yescharacteristic
302C2×C3⋊C8C22×D311yescharacteristic
303Dic12—34no—
304D24—34no—
305#204—34no—
306#204—34no—
307C22×C32—22no—
308C22×C32C4×D412yes—
309C22×C32C22×D411yescharacteristic
310C2×C3⋊D3—22no—
311C2×C3⋊D3—42no—
312C2×C3×D3—22no—
313C2×C3×D3—42no—
314C32×C4C4×D412yes—
315C32×C4C23×C411yescharacteristic
316C32×C4C2×#4111yescharacteristic
317C3⋊Dic3—22no—
318C3⋊Dic3—42no—
319C3×Dic3—22no—
320C3×Dic3—22no—
321C3×Dic3—22no—
322C3×Dic3—42no—
323C2×#41—31no—
324C2×#41—91no—
325#135—98no—
326C2×Q16—91no—
327C2×SD16—91no—
328C2×SD16—91no—
329C2×D8—91no—
330C22×C8—31no—
331C22×C8D3211yescharacteristic
332C4×Q8—92no—
333C4×Q8—92no—
334C4×D4—92no—
335C4×D4—92no—
336C4×D4—182no—
337C4×D4—182no—
338#117—31no—
339#117—91no—
340#117—181no—
341#117—181no—
342C2×C42—31no—
343C2×C42—181no—
344C2×C42—181no—
345#107—92no—
346#106—92no—
347#103—32no—
348#103—92no—
349#102—32no—
350#102—92no—
351#97—32no—
352#97—32no—
353C23×C3—21no—
354C23×C3—61no—
355C23×C3C2×D1211yescharacteristic
356C23×C3D3×D411yescharacteristic
357C22×D3—21no—
358C22×D3—61no—
359C22×D3—61no—
360C22×D3—121no—
361C3×Q8—32no—
362C3×Q8—61no—
363C3×D4—32no—
364C3×D4—64no—
365C3×D4—61no—
366C2×C3×C4—21no—
367C2×C3×C4—22no—
368C2×C3×C4—21no—
369C2×C3×C4—22no—
370C2×C3×C4—32no—
371C2×C3×C4—32no—
372C2×C3×C4—61no—
373C2×C3×C4—64no—
374C2×C3×C4—62no—
375C2×C3×C4—122no—
376C2×C3×C4C2×C4×D312yes—
377C2×C3×C4C2×C4×D312yes—
378C2×C3×C4C2×D1211yescharacteristic
379C2×C3×C4#23512yes—
380C2×C3×C4D3×D411yescharacteristic
381C2×C3×C4#23712yes—
382C2×C3×C4C23×D311yescharacteristic
383C2×C3×C4C23×D311yescharacteristic
384#67—24no—
385#67—64no—
386#67—64no—
387#67—124no—
388C2×Dic3—21no—
389C2×Dic3—22no—
390C2×Dic3—42no—
391C2×Dic3—61no—
392C2×Dic3—61no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—121no—
396C2×Dic3—122no—
397C2×Dic3—124no—
398C2×Dic3C2×D1212yes—
399C2×Dic3C2×D1212yes—
400D12—21no—
401D12—32no—
402D12—32no—
403D12—62no—
404D12—61no—
405D12—61no—
406D12—121no—
407D12C2×C4×D312yes—
408C4×D3—24no—
409C4×D3—64no—
410C4×D3—64no—
411C4×D3—124no—
412C4×D3—124no—
413C4×D3—124no—
414C4×D3—124no—
415Dic6—21no—
416Dic6—32no—
417Dic6—32no—
418Dic6—62no—
419Dic6—61no—
420Dic6—61no—
421Dic6—121no—
422Dic6C2×C4×D312yes—
423C3×C8—22no—
424C3×C8—22no—
425C3×C8—32no—
426C3×C8—32no—
427C3×C8—42no—
428C3⋊C8C2×C4×D312yes—
429C3⋊C8C2×C4×D312yes—
430C2×C32—22no—
431C2×C32C2×C4×D411yescharacteristic
432C2×C32#57512yes—
433C3⋊D3—42no—
434C3×D3—42no—
435#41—34no—
436#41—62no—
437#41—94no—
438#41—182no—
439C2×Q8—31no—
440C2×Q8—91no—
441C2×D4—31no—
442C2×D4—61no—
443C2×D4—91no—
444C2×D4—181no—
445C22×C4—32no—
446C22×C4—61no—
447C22×C4—182no—
448C22×C4—182no—
449C22×C4—181no—
450C22×C4C2×D3211yescharacteristic
451Q16—94no—
452SD16—94no—
453SD16—94no—
454D8—94no—
455C2×C8—22no—
456C2×C8—31no—
457C2×C8—31no—
458C2×C8—34no—
459C2×C8C2×D3212yes—
460C4⋊C4—32no—
461C4⋊C4—92no—
462C4⋊C4—182no—
463C4⋊C4—182no—
464C22⋊C4—61no—
465C22⋊C4—182no—
466C22⋊C4—182no—
467C22⋊C4—181no—
468C42—32no—
469C42—31no—
470C42—31no—
471C42—61no—
472C42—182no—
473C42—182no—
474C42—181no—
475C22×C3—22no—
476C22×C3—22no—
477C22×C3—21no—
478C22×C3—22no—
479C22×C3—42no—
480C22×C3—62no—
481C22×C3—122no—
482C22×C3C4×D1212yes—
483C22×C3#67⋊C412yes—
484C22×C3C22×D1211yescharacteristic
485C22×C3C2×D3×D411yescharacteristic
486C2×D3—22no—
487C2×D3—42no—
488C2×D3—62no—
489C2×D3—62no—
490C2×D3—122no—
491C2×D3—122no—
492C2×D3—122no—
493C2×D3—242no—
494C3×C4—21no—
495C3×C4—21no—
496C3×C4—22no—
497C3×C4—62no—
498C3×C4—62no—
499C3×C4—62no—
500C3×C4—122no—
501C3×C4C4×D1212yes—
502C3×C4#67⋊C412yes—
503C3×C4C22×C4×D311yescharacteristic
504C3×C4C22×C4×D311yescharacteristic
505C3×C4C2×#23511yescharacteristic
506C3×C4C2×#23711yescharacteristic
507Dic3—22no—
508Dic3—22no—
509Dic3—22no—
510Dic3—42no—
511Dic3—62no—
512Dic3—62no—
513Dic3—122no—
514Dic3—122no—
515Dic3—122no—
516Dic3—242no—
517C32#294311yescharacteristic, complemented, Sylow
518C23—61no—
519C23—181no—
520C23D3×D1211yescharacteristic
521Q8—32no—
522Q8—61no—
523Q8—92no—
524Q8—181no—
525D4—32no—
526D4—64no—
527D4—61no—
528D4—92no—
529D4—184no—
530D4—181no—
531C2×C4—32no—
532C2×C4—32no—
533C2×C4—61no—
534C2×C4—64no—
535C2×C4—62no—
536C2×C4—122no—
537C2×C4—181no—
538C2×C4—184no—
539C2×C4—182no—
540C2×C4—364no—
541C2×C4—364no—
542C2×C4C4×D3212yes—
543C2×C4D3×D1211yescharacteristic
544C2×C4#380412yes—
545C2×C4C22×D3211yescharacteristic
546C8—22no—
547C8—32no—
548C8—32no—
549C2×C3—22no—
550C2×C3—22no—
551C2×C3—21no—
552C2×C3—22no—
553C2×C3—42no—
554C2×C3—122no—
555C2×C3C2×C4×D1211yescharacteristic
556C2×C3C2×#67⋊C411yescharacteristic
557C2×C3#574812yes—
558C2×C3#576812yes—
559D3—42no—
560D3—122no—
561D3—122no—
562D3—242no—
563C22—22no—
564C22—62no—
565C22—122no—
566C22—182no—
567C22—362no—
568C22#6388012yes—
569C22C2×D3×D1211yescharacteristic
570C4—62no—
571C4—62no—
572C4—62no—
573C4—122no—
574C4—182no—
575C4—362no—
576C4#6388012yes—
577C4C2×C4×D3211yescharacteristic
578C4C2×#380411yescharacteristic
579C3—21no—
580C3#7849411yescharacteristic, complemented
581C3#7881911yescharacteristic, complemented
582C2—22no—
583C2—122no—
584C2—362no—
585C2#1059467612yes—
586C2C2×#6388011yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radicalC2×#63829C2
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32#2943
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. #10594954C2semidirect
2. Dic3×#235C2semidirect
4. #10592812C2semidirect
5. C3×#5113C2semidirect
6. C2×C3×#815C2semidirect
7. #10591122C2semidirect
8. #10590795C2semidirect
9. #10590794C2semidirect
10. #10590747C2semidirect
11. #10590746C2semidirect
33. #63829C4semidirect
55. #5113D3semidirect
57. C2×#815D3semidirect
70. #3828C2×C4semidirect
77. C3×#235C2×C4semidirect
94. C2×C3×C3⋊C8C2×C4semidirect
103. #3719C2×C4semidirect
104. #3717C2×C4semidirect
105. #3716C2×C4semidirect
106. #3714C2×C4semidirect
238. #235C4×D3semidirect
300. C2×C3⋊C8C4×D3semidirect
517. C32#2943semidirect
580. C3#78494semidirect
581. C3#78819semidirect

Maximal subgroups

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

subgroupindex
#105949542
Dic3×#2352
C2×#638292
#105928122
C3×#51132
C2×C3×#8152
#105911222
#105907952
#105907942
#105907472
#105907462
#788193
#784943