Finite Group Databasebeta

← #11866716

Subgroups — #11866716

Order 1152.

1209 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595429C211yesmaximal, characteristic, complemented
2C2×#63940C211yesmaximal, characteristic, complemented
3C2×D32×C8C211yesmaximal, characteristic, complemented
4#10594612C211yesmaximal, characteristic
5C3⋊D3×#103C211yesmaximal, characteristic, complemented
6C3×#4807C212yesmaximal, complemented
7#10591634C212yesmaximal, complemented
8#10590940C211yesmaximal, characteristic, complemented
9#10590825C212yesmaximal, complemented
10#10590578C212yesmaximal, complemented
11#10590575C211yesmaximal, characteristic, complemented
12D3×#465—32nomaximal
13C2×Q8×C3⋊D3C2211yescharacteristic
14C2×#3802—21no—
15C2×#3802C2211yescharacteristic
16C2×C4×D32C2211yescharacteristic
17C2×C8×C3⋊D3C2211yescharacteristic
18C4⋊C4×C3⋊D3C2211yescharacteristic
19C3×#946C2212yescomplemented
20C2×C3×#215C2212yescomplemented
21C2×C3×D3×C8C2212yescomplemented
22C3×#895C2212yes—
23#63940—24no—
24#63921—21no—
25#63921—21no—
26#63908C2212yes—
27#63900C2211yescharacteristic
28#63896—22no—
29#63885—22no—
30#63883—21no—
31#63857C2212yescomplemented
32C2×#3716C2212yescomplemented
33C2×#3710C2211yescharacteristic
34C2×D3×C3⋊C8C2212yescomplemented
35D32×C8—24no—
36C32×#103C2211yescharacteristic, complemented
37#63662C2211yescharacteristic, complemented
38#63643C2211yescharacteristic, complemented
39#63637C2211yescharacteristic, complemented
40C3×#821C2212yescomplemented
41C3×#808C2212yescomplemented
42#63573C2212yescomplemented
43#63562C2212yescomplemented
44C2×D3×SD16—32no—
45C22×D3×C8—32no—
46D3×C22⋊Q8—32no—
47D3×#121—32no—
48C3×#465—32no—
49#5171—32no—
50#5114—32no—
51#5048—32no—
52#5041—32no—
53#4864—32no—
54D3×#106—32no—
55#4807D312yescomplemented
56D3×#103—32no—
57D3×#103—61no—
58#4778—32no—
59D3×#102—32no—
60C22×D32—21no—
61C22×D32D411yescharacteristic
62C2×C32×Q8C2311yescharacteristic
63Q8×C3⋊D3—22no—
64Q8×C3⋊D3—22no—
65C2×C4×C3⋊D3—21no—
66C2×C4×C3⋊D3—21no—
67C2×C4×C3⋊D3C2311yescharacteristic
68C2×#634—21no—
69C2×#634C2311yescharacteristic
70C2×C3×D12—22no—
71C2×C3×D12C2312yes—
72C2×C3×C4×D3C2312yes—
73C2×#625—22no—
74C2×#625—21no—
75C2×#624—21no—
76C2×#624D411yescharacteristic
77C2×D3×Dic3D412yes—
78#3802—22no—
79#3802—22no—
80#3802—44no—
81C4×D32—22no—
82C4×D32—22no—
83C2×C32×C8C2311yescharacteristic
84C32×C4⋊C4C2311yescharacteristic
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86#3750—21no—
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88C8×C3⋊D3—22no—
89C3×#215—24no—
90C3×(C2×D3)⋊C4—22no—
91C3×(C2×D3)⋊C4—22no—
92C3×C4⋊Dic3C2312yes—
93C3×Dic3⋊C4—22no—
94C2×C3×C3⋊C8C2312yes—
95C3×D3×C8—24no—
96#3724—21no—
97Dic3⋊Dic3—22no—
98(C2×D3)⋊Dic3—22no—
99(C2×D3)⋊Dic3—22no—
100#3716—24no—
101#3710D414yescomplemented
102D3×C3⋊C8—24no—
103C2×#465—91noSylow
104C2×D3×Q8—32no—
105C2×D3×Q8—61no—
106C2×D3×D4—32no—
107C2×D3×D4—62no—
108C22×C4×D3—32no—
109C2×C3×SD16—32no—
110C22×C3×C8—32no—
111C3×C22⋊Q8—32no—
112C3×#121—32no—
113#946C2×D312yescomplemented
114C2×#215C2×D312yescomplemented
115#939—62no—
116#938—32no—
117C2×#214—32no—
118#930—32no—
119#924—32no—
120C22×C3⋊C8—32no—
121D3×SD16—68no—
122C2×#204—32no—
123C2×D3×C8—32no—
124C2×D3×C8—32no—
125C2×D3×C8—32no—
126C2×D3×C8—61no—
127C2×D3×C8—68no—
128C2×D3×C8C2×D312yescomplemented
129#897—32no—
130#896—62no—
131#895C2×D312yes—
132D3×C4⋊C4—32no—
133D3×C4⋊C4—32no—
134D3×C4⋊C4—61no—
135D3×C4⋊C4—62no—
136#884—62no—
137D3×C22⋊C4—62no—
138D3×C22⋊C4—62no—
139#878—62no—
140C3×#106—32no—
141C3×#103—21no—
142C3×#103C2×D312yescomplemented
143C3×#102—32no—
144#835—32no—
145#835—61no—
146#832—32no—
147#821C2×D312yescomplemented
148#817—32no—
149#816—32no—
150#816—61no—
151#810—32no—
152#810—61no—
153#809—32no—
154#808—32no—
155#808C2×D312yescomplemented
156C22×C3⋊D3C2×D411yescharacteristic
157C22×C3×D3—22no—
158C22×C3×D3C2×D412yes—
159C2×D32—22no—
160C2×D32—22no—
161C2×D32—42no—
162C2×D32—42no—
163C2×D32—42no—
164C2×D32SD1614yescomplemented
165C32×Q8—21no—
166C32×Q8—21no—
167C2×C32×C4—21no—
168C2×C32×C4—21no—
169C2×C32×C4C2411yescharacteristic
170C2×C3⋊Dic3—21no—
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3C2×D411yescharacteristic
173C4×C3⋊D3—42no—
174C4×C3⋊D3—42no—
175C4×C3⋊D3C2×D412yes—
176C4×C3⋊D3#4112yes—
177#634—21no—
178#634—21no—
179#634—42no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3C2×D412yes—
182C3×D12—22no—
183C3×D12—22no—
184C3×D12—44no—
185C3×C4×D3—22no—
186C3×C4×D3—22no—
187#625—44no—
188#625—42no—
189#624—22no—
190#624—42no—
191D3×Dic3—24no—
192C32×C8—21no—
193C3⋊(C3⋊C8)—21no—
194C3×C3⋊C8C2×D414yescomplemented
195C22×SD16—91no—
196C23×C8—91no—
197C2×C22⋊Q8—91no—
198C2×#121—91no—
199#465—32no—
200#465—92no—
201#465—92no—
202#465—92no—
203C2×#106—91no—
204C2×#103—91no—
205C2×#102—91no—
206C23×D3—32no—
207C23×D3—62no—
208C2×C3×Q8—21no—
209C2×C3×Q8C22×D312yes—
210C2×C3×D4—32no—
211C2×C3×D4—62no—
212C22×C3×C4—32no—
213C2×#67—62no—
214C2×#67—62no—
215C2×#67—62no—
216C22×Dic3—32no—
217D3×Q8—64no—
218D3×Q8—64no—
219D3×Q8—64no—
220D3×Q8—122no—
221D3×D4—64no—
222D3×D4—64no—
223D3×D4—128no—
224C2×D12—22no—
225C2×D12C22×D312yes—
226C2×C4×D3—32no—
227C2×C4×D3—32no—
228C2×C4×D3—32no—
229C2×C4×D3—61no—
230C2×C4×D3—64no—
231C2×C4×D3—64no—
232C2×C4×D3—62no—
233C2×C4×D3—62no—
234C2×C4×D3—62no—
235C2×C4×D3—121no—
236C2×C4×D3—121no—
237C2×C4×D3C22×D312yes—
238C2×Dic6—32no—
239C2×Dic6—61no—
240C2×Dic6—62no—
241C2×Dic6—121no—
242C3×SD16—64no—
243C2×C3×C8—21no—
244C2×C3×C8—32no—
245C2×C3×C8—64no—
246C2×C3×C8C22×D312yes—
247C3×C4⋊C4—21no—
248C3×C4⋊C4—32no—
249C3×C4⋊C4—62no—
250C3×C4⋊C4C22×D312yes—
251C3×C22⋊C4—62no—
252C3×C22⋊C4—62no—
253#217—62no—
254#217—62no—
255#215—24no—
256#214—64no—
257(C2×D3)⋊C4—22no—
258(C2×D3)⋊C4—22no—
259(C2×D3)⋊C4—62no—
260(C2×D3)⋊C4—62no—
261C4⋊Dic3—32no—
262C4⋊Dic3—61no—
263C4⋊Dic3—62no—
264C4⋊Dic3C22×D312yes—
265Dic3⋊C4—22no—
266Dic3⋊C4—62no—
267Dic3⋊C4—62no—
268Dic3⋊C4—62no—
269Dic3⋊C4—121no—
270C2×C3⋊C8—32no—
271C2×C3⋊C8—61no—
272C2×C3⋊C8—64no—
273C2×C3⋊C8C22×D312yes—
274#204—64no—
275D3×C8—24no—
276D3×C8—38no—
277D3×C8—64no—
278D3×C8—64no—
279D3×C8—122no—
280C22×C32C22×D411yescharacteristic
281C2×C3⋊D3#12112yes—
282C2×C3⋊D3C2×SD1612yes—
283C2×C3⋊D3#13512yes—
284C2×C3×D3—22no—
285C2×C3×D3—22no—
286C2×C3×D3—42no—
287C2×C3×D3—42no—
288C2×C3×D3—42no—
289C2×C3×D3C2×SD1614yescomplemented
290D32—28no—
291D32—84no—
292C32×C4—41no—
293C32×C4—41no—
294C32×C4C22×D411yescharacteristic
295C32×C4C2×#4111yescharacteristic
296C3⋊Dic3—41no—
297C3⋊Dic3—41no—
298C3⋊Dic3#12112yes—
299C3×Dic3—22no—
300C3×Dic3—42no—
301C22×Q8—91no—
302C22×D4—91no—
303C22×D4—181no—
304C23×C4—91no—
305C2×SD16—32no—
306C2×SD16—92no—
307C2×SD16—184no—
308C22×C8—32no—
309C22×C8—91no—
310C22×C8—92no—
311C22×C8—91no—
312C22×C8—184no—
313C22⋊Q8—32no—
314C22⋊Q8—92no—
315C22⋊Q8—182no—
316#121—32no—
317#121—92no—
318#121—182no—
319C2×C4⋊C4—91no—
320C2×C4⋊C4—91no—
321C2×C4⋊C4—181no—
322C2×C22⋊C4—181no—
323C2×C22⋊C4—181no—
324#106—32no—
325#106—92no—
326#103—91no—
327#103—91no—
328#103—91no—
329#103D3211yescharacteristic, complemented
330#102—32no—
331#102—92no—
332C23×C3—32no—
333C23×C3—62no—
334C22×D3—22no—
335C22×D3—32no—
336C22×D3—38no—
337C22×D3—61no—
338C22×D3—64no—
339C22×D3—64no—
340C22×D3—124no—
341C22×D3—124no—
342C22×D3—124no—
343C22×D3D3×D412yes—
344C3×Q8—22no—
345C3×Q8—22no—
346C3×Q8—22no—
347C3×Q8—41no—
348C3×D4—62no—
349C3×D4—62no—
350C3×D4—124no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—21no—
354C2×C3×C4—32no—
355C2×C3×C4—41no—
356C2×C3×C4—41no—
357C2×C3×C4—62no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4C23×D312yes—
361#67—124no—
362#67—124no—
363#67—124no—
364C2×Dic3—22no—
365C2×Dic3—32no—
366C2×Dic3—61no—
367C2×Dic3—64no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—121no—
371C2×Dic3—121no—
372C2×Dic3D3×D412yes—
373D12—22no—
374D12—22no—
375D12—44no—
376C4×D3—22no—
377C4×D3—22no—
378C4×D3—34no—
379C4×D3—34no—
380C4×D3—62no—
381C4×D3—62no—
382C4×D3—64no—
383C4×D3—64no—
384C4×D3—124no—
385C4×D3—124no—
386C4×D3—124no—
387C4×D3—124no—
388C4×D3—242no—
389Dic6—62no—
390Dic6—62no—
391Dic6—62no—
392Dic6—121no—
393Dic6—124no—
394Dic6—124no—
395C3×C8—22no—
396C3×C8—34no—
397C3×C8—41no—
398C3⋊C8—62no—
399C3⋊C8—121no—
400C3⋊C8D3×D414yescomplemented
401C2×C32C2×#12111yescharacteristic
402C2×C32C22×SD1611yescharacteristic
403C2×C32C2×#13511yescharacteristic
404C3⋊D3#46514yescomplemented
405C3×D3—24no—
406C3×D3—82no—
407C24—91no—
408C24—181no—
409C2×Q8—91no—
410C2×Q8—181no—
411C2×Q8—182no—
412C2×Q8—182no—
413C2×Q8C2×D3211yescharacteristic
414C2×D4—32no—
415C2×D4—62no—
416C2×D4—182no—
417C2×D4—182no—
418C2×D4—181no—
419C2×D4—182no—
420C2×D4—364no—
421C22×C4—32no—
422C22×C4—91no—
423C22×C4—92no—
424C22×C4—91no—
425C22×C4—181no—
426C22×C4—181no—
427C22×C4—182no—
428C22×C4—182no—
429C22×C4—181no—
430SD16—64no—
431SD16—184no—
432C2×C8—32no—
433C2×C8—64no—
434C2×C8—94no—
435C2×C8—91no—
436C2×C8—182no—
437C2×C8—184no—
438C2×C8C2×D3211yescharacteristic
439C4⋊C4—32no—
440C4⋊C4—62no—
441C4⋊C4—91no—
442C4⋊C4—181no—
443C4⋊C4—182no—
444C4⋊C4—181no—
445C4⋊C4C2×D3211yescharacteristic
446C22⋊C4—62no—
447C22⋊C4—62no—
448C22⋊C4—182no—
449C22⋊C4—182no—
450C22×C3—21no—
451C22×C3—34no—
452C22×C3—62no—
453C22×C3—62no—
454C22×C3—122no—
455C22×C3—122no—
456C22×C3—122no—
457C22×C3C2×D3×D412yes—
458C2×D3—22no—
459C2×D3—22no—
460C2×D3—34no—
461C2×D3—34no—
462C2×D3—34no—
463C2×D3—42no—
464C2×D3—42no—
465C2×D3—42no—
466C2×D3—62no—
467C2×D3—62no—
468C2×D3—62no—
469C2×D3—616no—
470C2×D3—248no—
471C2×D3D3×SD1614yescomplemented
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—42no—
475C3×C4—42no—
476C3×C4—42no—
477C3×C4—62no—
478C3×C4—81no—
479C3×C4—122no—
480C3×C4C2×D3×D412yes—
481C3×C4D3×#4112yes—
482Dic3—22no—
483Dic3—34no—
484Dic3—42no—
485Dic3—62no—
486Dic3—122no—
487Dic3—122no—
488Dic3—122no—
489Dic3—241no—
490C32C2×#46511yescharacteristic, complemented, Sylow
491C23—32no—
492C23—62no—
493C23—94no—
494C23—91no—
495C23—182no—
496C23—182no—
497C23—362no—
498C23—362no—
499C23—362no—
500Q8—21no—
501Q8—21no—
502Q8—181no—
503Q8—181no—
504Q8—362no—
505D4—62no—
506D4—62no—
507D4—124no—
508D4—362no—
509D4—364no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—32no—
513C2×C4—62no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—91no—
517C2×C4—92no—
518C2×C4—92no—
519C2×C4—182no—
520C2×C4—184no—
521C2×C4—181no—
522C2×C4—181no—
523C2×C4—362no—
524C2×C4—362no—
525C2×C4—362no—
526C2×C4C22×D3211yescharacteristic
527C8—21no—
528C8—34no—
529C8—181no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—64no—
534C2×C3—242no—
535C2×C3D3×#12112yes—
536C2×C3C2×D3×SD1612yes—
537C2×C3D3×#13512yes—
538D3—24no—
539D3—38no—
540D3—64no—
541D3—82no—
542C22—34no—
543C22—62no—
544C22—62no—
545C22—92no—
546C22—92no—
547C22—92no—
548C22—122no—
549C22—122no—
550C22—122no—
551C22—188no—
552C22—724no—
553C22D32×D411yescharacteristic
554C4—41no—
555C4—41no—
556C4—62no—
557C4—92no—
558C4—122no—
559C4—361no—
560C4—361no—
561C4#6430611yescharacteristic
562C4D32×D411yescharacteristic
563C3—21no—
564C3D3×#46512yescomplemented
565C2—64no—
566C2—94no—
567C2—242no—
568C2#1059426511yescharacteristic
569C2D32×SD1611yescharacteristic
570C2#1059476411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10594612C2
hypercenter#103D32
hypocenterC32C2×#465
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10595429C2semidirect
2. C2×#63940C2semidirect
3. C2×D32×C8C2semidirect
5. C3⋊D3×#103C2semidirect
6. C3×#4807C2semidirect
7. #10591634C2semidirect
8. #10590940C2semidirect
9. #10590825C2semidirect
10. #10590578C2semidirect
11. #10590575C2semidirect
19. C3×#946C22semidirect
20. C2×C3×#215C22semidirect
21. C2×C3×D3×C8C22semidirect
31. #63857C22semidirect
32. C2×#3716C22semidirect
34. C2×D3×C3⋊C8C22semidirect
36. C32×#103C22semidirect
37. #63662C22semidirect
38. #63643C22semidirect
39. #63637C22semidirect
40. C3×#821C22semidirect
41. C3×#808C22semidirect
42. #63573C22semidirect
43. #63562C22semidirect
55. #4807D3semidirect
101. #3710D4semidirect
113. #946C2×D3semidirect
114. C2×#215C2×D3semidirect
128. C2×D3×C8C2×D3semidirect
142. C3×#103C2×D3semidirect
147. #821C2×D3semidirect
155. #808C2×D3semidirect
164. C2×D32SD16semidirect
194. C3×C3⋊C8C2×D4semidirect
289. C2×C3×D3C2×SD16semidirect
329. #103D32semidirect
400. C3⋊C8D3×D4semidirect
404. C3⋊D3#465semidirect
471. C2×D3D3×SD16semidirect
490. C32C2×#465semidirect
564. C3D3×#465semidirect

Maximal subgroups

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

subgroupindex
#105954292
C2×#639402
C2×D32×C82
#105946122
C3⋊D3×#1032
C3×#48072
#105916342
#105909402
#105908252
#105905782
#105905752
D3×#4653