Finite Group Databasebeta

← #11886820

Subgroups — #11886820

Order 1152.

973 conjugacy classes of subgroups.

The subgroup lattice has 641 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594692C211yesmaximal, characteristic, complemented
2#10594680C211yesmaximal, characteristic, complemented
3#10594679C212yesmaximal, complemented
4#10592395C211yesmaximal, characteristic, complemented
5C3×#4700C211yesmaximal, characteristic, complemented
6C3×#4700C211yesmaximal, characteristic, complemented
7#10590932C211yesmaximal, characteristic, complemented
8#10590931C212yesmaximal, complemented
9#10590927C211yesmaximal, characteristic, complemented
10#10590402C212yesmaximal, complemented
11#10590398C212yesmaximal, complemented
12#79892—31nomaximal
13#79891—31nomaximal
14#64308C2212yes—
15#64298C2212yescomplemented
16C2×#3746C2211yescharacteristic, complemented
17C2×#3745C2211yescharacteristic
18C2×#3744C2212yescomplemented
19#64084C2212yescomplemented
20C3×#904C2211yescharacteristic
21C3×#904C2211yescharacteristic
22C3×#901C2211yescharacteristic
23C3×#901C2212yescomplemented
24C3×#901C2211yescharacteristic, complemented
25#63831C2212yes—
26#63831C2212yescomplemented
27#63825C2212yes—
28#63825C2212yescomplemented
29#63808—21no—
30#63807—21no—
31#63806—22no—
32#63801—22no—
33#63800—22no—
34D3×Dic12—21no—
35#63795—22no—
36#63794—22no—
37D3×D24—21no—
38D3×#204—22no—
39C32×C4×C8C2211yescharacteristic, complemented
40C3×#819C2211yescharacteristic, complemented
41C3×#819C2211yescharacteristic, complemented
42C3×#805C2211yescharacteristic
43C3×#805C2212yescomplemented
44C3×#805C2211yescharacteristic, complemented
45#63561C2212yescomplemented
46#63559C2212yescomplemented
47#5771—31no—
48#5770—32no—
49#5769—31no—
50#5753—31no—
51#5752—31no—
52#5751—32no—
53C3×#443—31no—
54C3×#443—31no—
55#5143—31no—
56#5142—31no—
57#5141—32no—
58#4898—32no—
59#4897—31no—
60#4896—31no—
61#4827—32no—
62#4827—32no—
63#4825—32no—
64#4825—32no—
65#4700D311yescharacteristic, complemented
66#4700D311yescharacteristic, complemented
67#4696—31no—
68#4696—31no—
69#4696—61no—
70C2×C4⋊(C3⋊D3)C2312yes—
71C2×#634C2312yes—
72C3×#235C2311yescharacteristic
73C3×#235C2311yescharacteristic
74C3×#235C2312yes—
75#3811—42no—
76#3805—42no—
77D3×D12—22no—
78D3×D12—22no—
79#3799—22no—
80#3799—22no—
81#3795—22no—
82#3795—22no—
83D3×Dic6—22no—
84D3×Dic6—22no—
85C2×C32×C8C2311yescharacteristic
86C2×C32×C8C2311yescharacteristic
87C32×C42C2311yescharacteristic
88#3752—42no—
89#3746—21no—
90#3746—21no—
91#3745—21no—
92#3745—21no—
93#3744—22no—
94#3744—22no—
95C3×#208C2311yescharacteristic
96C3×#208C2311yescharacteristic
97C3×#208C2312yes—
98C3×Dic12D411yescharacteristic
99C3×Dic12D411yescharacteristic
100C3×D24D411yescharacteristic
101C3×D24D411yescharacteristic
102C3×#204D411yescharacteristic
103C3×#204D412yes—
104C3×#204D411yescharacteristic
105C3×ΓL(1,𝔽25)—21no—
106C3×ΓL(1,𝔽25)—22no—
107C3×ΓL(1,𝔽25)—21no—
108C3×D3×C8—21no—
109C3×D3×C8—22no—
110C3×D3×C8—21no—
111#3719—22no—
112#3719—22no—
113#3717—22no—
114#3717—22no—
115#3716—22no—
116#3716—22no—
117#3714—22no—
118#3714—22no—
119#3290—91noSylow
120#1010—32no—
121#1010—32no—
122#1009—32no—
123#1009—32no—
124C3×#135—31no—
125C3×#135—31no—
126C3×#131—32no—
127C3×#131—31no—
128C3×#131—31no—
129#951—32no—
130#951—32no—
131#949—32no—
132#949—32no—
133#919—61no—
134#918—62no—
135D3×Q16—61no—
136#916—62no—
137#915—62no—
138#914—62no—
139D3×SD16—62no—
140#912—61no—
141#911—62no—
142D3×D8—61no—
143#909—32no—
144#909—32no—
145#909—62no—
146#909—62no—
147#908—32no—
148#908—32no—
149#908—62no—
150#908—62no—
151C2×Dic12—31no—
152C2×Dic12—31no—
153C2×Dic12—61no—
154C2×Dic12—61no—
155#904—61no—
156#904—61no—
157#904—62no—
158#904C2×D311yescharacteristic
159#904C2×D311yescharacteristic
160C2×D24—31no—
161C2×D24—31no—
162C2×D24—61no—
163C2×D24—61no—
164C2×#204—32no—
165C2×#204—32no—
166C2×#204—62no—
167C2×#204—62no—
168#901C2×D311yescharacteristic
169#901C2×D311yescharacteristic, complemented
170#901C2×D312yescomplemented
171#875—32no—
172#875—32no—
173#875—62no—
174C3×#108—31no—
175C3×#108—31no—
176C3×#104—31no—
177C3×#104—32no—
178C3×#104—31no—
179C3×C4×C8—21no—
180C3×C4×C8C2×D311yescharacteristic, complemented
181C3×C4×C8C2×D311yescharacteristic, complemented
182#824—32no—
183#824—32no—
184#823—32no—
185#823—32no—
186#819C2×D311yescharacteristic, complemented
187#819C2×D311yescharacteristic, complemented
188#805C2×D311yescharacteristic
189#805C2×D312yescomplemented
190#805C2×D311yescharacteristic, complemented
191C22×C3⋊D3—22no—
192C2×D32—42no—
193C2×C32×C4—21no—
194C2×C32×C4C2411yescharacteristic
195C2×C3⋊Dic3—22no—
196C4⋊(C3⋊D3)—22no—
197C4⋊(C3⋊D3)—22no—
198#634—22no—
199#634—22no—
200C3×#67—21no—
201C3×#67—22no—
202C3×#67—21no—
203C3×D12C2×D411yescharacteristic
204C3×D12C2×D412yes—
205C3×D12C2×D411yescharacteristic
206C3×C4×D3—21no—
207C3×C4×D3—22no—
208C3×C4×D3—21no—
209C3×Dic6C2×D411yescharacteristic
210C3×Dic6C2×D412yes—
211C3×Dic6C2×D411yescharacteristic
212#627—42no—
213#626—42no—
214#626—42no—
215#625—42no—
216#624—42no—
217D3×Dic3—42no—
218D3×Dic3—42no—
219C32×C8C2×D411yescharacteristic
220C32×C8C2×D411yescharacteristic
221C32×C8C2×D411yescharacteristic
222C32×C8C2×D411yescharacteristic
223C3×C3⋊C8—21no—
224C3×C3⋊C8—22no—
225C3×C3⋊C8—21no—
226#578—91no—
227#577—92no—
228#576—91no—
229#495—91no—
230#473—91no—
231#472—91no—
232#471—92no—
233#455—92no—
234#454—92no—
235#443—31no—
236#443—31no—
237C3×#41—31no—
238C3×#41—32no—
239C3×#41—31no—
240#239—62no—
241#239—62no—
242D3×Q8—62no—
243D3×Q8—62no—
244#237—62no—
245#237—62no—
246#237—122no—
247#237—122no—
248D3×D4—62no—
249D3×D4—62no—
250D3×D4—122no—
251D3×D4—122no—
252#235—62no—
253#235—62no—
254#235—62no—
255#235—62no—
256#235C22×D311yescharacteristic
257#235C22×D311yescharacteristic
258#235C22×D312yes—
259C2×D12—32no—
260C2×D12—32no—
261C2×D12—62no—
262C2×D12—62no—
263C2×D12—62no—
264C2×Dic6—32no—
265C2×Dic6—32no—
266C2×Dic6—62no—
267C2×Dic6—62no—
268C2×Dic6—62no—
269C3×Q16—31no—
270C3×Q16—31no—
271C3×SD16—31no—
272C3×SD16—32no—
273C3×SD16—31no—
274C3×D8—31no—
275C3×D8—31no—
276C3×M16—31no—
277C3×M16—32no—
278C3×M16—31no—
279C3×M16—61no—
280C3×M16—62no—
281C3×M16—61no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—62no—
285C2×C3×C8—61no—
286C2×C3×C8—61no—
287C2×C3×C8C22×D311yescharacteristic
288C2×C3×C8C22×D311yescharacteristic
289C2×C3×C8C22×D311yescharacteristic
290C2×C3×C8C22×D311yescharacteristic
291C3×C42—21no—
292C3×C42C22×D311yescharacteristic
293C3×C42C22×D311yescharacteristic
294#216—62no—
295#216—62no—
296#215—62no—
297#215—62no—
298#214—62no—
299#214—62no—
300#213—62no—
301#213—62no—
302(C2×D3)⋊C4—122no—
303(C2×D3)⋊C4—122no—
304(C2×D3)⋊C4—124no—
305#208C22×D311yescharacteristic
306#208C22×D312yes—
307#208C22×D311yescharacteristic
308Dic12—62no—
309Dic12—62no—
310Dic12—61no—
311Dic12—61no—
312Dic12—61no—
313Dic12—61no—
314Dic12—121no—
315Dic12—121no—
316Dic12D1211yescharacteristic
317Dic12D1211yescharacteristic
318D24—62no—
319D24—62no—
320D24—61no—
321D24—61no—
322D24—61no—
323D24—61no—
324D24—121no—
325D24—121no—
326D24D1211yescharacteristic
327D24D1211yescharacteristic
328#204—62no—
329#204—62no—
330#204—62no—
331#204—62no—
332#204—62no—
333#204—62no—
334#204—62no—
335#204—62no—
336#204—122no—
337#204—122no—
338#204D1211yescharacteristic
339#204D1211yescharacteristic
340#204D1212yes—
341ΓL(1,𝔽25)—21no—
342ΓL(1,𝔽25)—22no—
343ΓL(1,𝔽25)—21no—
344D3×C8—21no—
345D3×C8—21no—
346D3×C8—22no—
347C22×C32H(5,𝔽2)11yescharacteristic
348C2×C3⋊D3—42no—
349C2×C3⋊D3—82no—
350C2×C3×D3—21no—
351C2×C3×D3—22no—
352C2×C3×D3—21no—
353D32—162no—
354C32×C4—41no—
355C32×C4C22×D411yescharacteristic
356C32×C4C22×D411yescharacteristic
357C3⋊Dic3—42no—
358C3×Dic3—21no—
359C3×Dic3—22no—
360C3×Dic3—21no—
3612−1+4—92no—
362H(5,𝔽2)—92no—
363#137—92no—
364#137—92no—
365#137—182no—
366#137—182no—
367AGL(1,ℤ/8)—92no—
368AGL(1,ℤ/8)—92no—
369AGL(1,ℤ/8)—182no—
370AGL(1,ℤ/8)—182no—
371#135—31no—
372#135—31no—
373#135—181no—
374#135—182no—
375#135—181no—
376C2×Q16—91no—
377C2×Q16—181no—
378C2×SD16—92no—
379C2×SD16—182no—
380C2×D8—91no—
381C2×D8—181no—
382#131—31no—
383#131—32no—
384#131—31no—
385#124—92no—
386#108—31no—
387#108—31no—
388#104—31no—
389#104—31no—
390#104—32no—
391#101—92no—
392#100—92no—
393C4×C8D3211yescharacteristic, complemented
394C22×D3—62no—
395C22×D3—62no—
396C22×D3—122no—
397C22×D3—122no—
398C22×D3—122no—
399C3×Q8—31no—
400C3×Q8—32no—
401C3×Q8—31no—
402C3×D4—31no—
403C3×D4—32no—
404C3×D4—31no—
405C3×D4—61no—
406C3×D4—62no—
407C3×D4—61no—
408C2×C3×C4—22no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—61no—
413C2×C3×C4—62no—
414C2×C3×C4—61no—
415C2×C3×C4C23×D311yescharacteristic
416C2×C3×C4C23×D311yescharacteristic
417#67—21no—
418#67—22no—
419#67—21no—
420#67—122no—
421#67—122no—
422#67—122no—
423#67—122no—
424C2×Dic3—62no—
425C2×Dic3—62no—
426C2×Dic3—122no—
427C2×Dic3—122no—
428C2×Dic3—122no—
429D12—62no—
430D12—62no—
431D12—62no—
432D12—62no—
433D12—122no—
434D12—122no—
435D12—122no—
436D12—122no—
437D12C2×D1211yescharacteristic
438D12C2×D1212yes—
439D12C2×D1211yescharacteristic
440C4×D3—21no—
441C4×D3—22no—
442C4×D3—21no—
443C4×D3—122no—
444C4×D3—122no—
445C4×D3—122no—
446C4×D3—122no—
447Dic6—62no—
448Dic6—62no—
449Dic6—62no—
450Dic6—62no—
451Dic6—122no—
452Dic6—122no—
453Dic6—122no—
454Dic6—122no—
455Dic6C2×D1211yescharacteristic
456Dic6C2×D1212yes—
457Dic6C2×D1211yescharacteristic
458C3×C8—21no—
459C3×C8—21no—
460C3×C8—21no—
461C3×C8—21no—
462C3×C8—61no—
463C3×C8—62no—
464C3×C8—61no—
465C3×C8C2×D1211yescharacteristic
466C3×C8C2×D1211yescharacteristic
467C3×C8C2×D1211yescharacteristic
468C3×C8C2×D1211yescharacteristic
469C3×C8D3×D411yescharacteristic
470C3×C8D3×D411yescharacteristic
471C3×C8D3×D411yescharacteristic
472C3×C8D3×D411yescharacteristic
473C3⋊C8—21no—
474C3⋊C8—22no—
475C3⋊C8—21no—
476C2×C32—21no—
477C2×C32D4211yescharacteristic
478C3⋊D3—82no—
479C3×D3—41no—
480C3×D3—42no—
481C3×D3—41no—
482#41—31no—
483#41—32no—
484#41—31no—
485#41—182no—
486#41—182no—
487#41—182no—
488#41—182no—
489#41—362no—
490C2×Q8—92no—
491C2×Q8—182no—
492C2×Q8—182no—
493C2×D4—92no—
494C2×D4—182no—
495C2×D4—182no—
496C2×D4—362no—
497Q16—31no—
498Q16—31no—
499Q16—182no—
500Q16—182no—
501Q16—181no—
502Q16—181no—
503SD16—31no—
504SD16—31no—
505SD16—32no—
506SD16—182no—
507SD16—182no—
508SD16—182no—
509SD16—182no—
510SD16—182no—
511SD16—182no—
512D8—31no—
513D8—31no—
514D8—182no—
515D8—182no—
516D8—181no—
517D8—181no—
518M16—31no—
519M16—32no—
520M16—31no—
521M16—61no—
522M16—62no—
523M16—61no—
524C2×C8—61no—
525C2×C8—62no—
526C2×C8—61no—
527C2×C8C2×D3211yescharacteristic
528C2×C8C2×D3211yescharacteristic
529C22⋊C4—362no—
530C42C2×D3211yescharacteristic
531C22×C3—21no—
532C22×C3—61no—
533C22×C3—62no—
534C22×C3—61no—
535C22×C3#100911yescharacteristic
536C22×C3#100911yescharacteristic
537C2×D3—21no—
538C2×D3—22no—
539C2×D3—21no—
540C2×D3—122no—
541C2×D3—122no—
542C2×D3—242no—
543C2×D3—242no—
544C2×D3—242no—
545C2×D3—244no—
546C2×D3—482no—
547C2×D3—482no—
548C3×C4—21no—
549C3×C4—21no—
550C3×C4—42no—
551C3×C4—41no—
552C3×C4—41no—
553C3×C4—61no—
554C3×C4—62no—
555C3×C4—61no—
556C3×C4C22×D1211yescharacteristic
557C3×C4C22×D1211yescharacteristic
558C3×C4C2×D3×D411yescharacteristic
559C3×C4C2×D3×D411yescharacteristic
560Dic3—21no—
561Dic3—22no—
562Dic3—21no—
563Dic3—122no—
564Dic3—122no—
565Dic3—242no—
566C32#329011yescharacteristic, complemented, Sylow
567C23—182no—
568C23—362no—
569Q8—31no—
570Q8—32no—
571Q8—31no—
572Q8—182no—
573Q8—182no—
574Q8—362no—
575D4—31no—
576D4—32no—
577D4—31no—
578D4—61no—
579D4—62no—
580D4—61no—
581D4—182no—
582D4—182no—
583D4—362no—
584D4—362no—
585D4—362no—
586C2×C4—21no—
587C2×C4—61no—
588C2×C4—62no—
589C2×C4—61no—
590C2×C4—182no—
591C2×C4—362no—
592C2×C4—362no—
593C2×C4—362no—
594C2×C4C22×D3211yescharacteristic
595C8—61no—
596C8—62no—
597C8—61no—
598C8D3×D1211yescharacteristic
599C8D3×D1211yescharacteristic
600C8D3×D1211yescharacteristic
601C8D3×D1211yescharacteristic
602C2×C3—22no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—122no—
607C2×C3—121no—
608C2×C3—121no—
609C2×C3D4×D1211yescharacteristic
610C2×C3D4×D1211yescharacteristic
611D3—41no—
612D3—41no—
613D3—42no—
614D3—242no—
615D3—242no—
616D3—482no—
617C22—61no—
618C22—62no—
619C22—61no—
620C22—362no—
621C22—722no—
622C22—1442no—
623C22#6430811yescharacteristic
624C4—41no—
625C4—61no—
626C4—62no—
627C4—61no—
628C4—362no—
629C4C2×D3×D1211yescharacteristic
630C4C2×D3×D1211yescharacteristic
631C3—21no—
632C3#7989111yescharacteristic, complemented
633C3#7989211yescharacteristic, complemented
634C2—21no—
635C2—121no—
636C2—122no—
637C2—121no—
638C2—722no—
639C2D12211yescharacteristic
subgroupG/H
centerC2D122
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC2×C32D42
hypercenterC4×C8D32
hypocenterC32#3290
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #10594692C2semidirect
2. #10594680C2semidirect
3. #10594679C2semidirect
4. #10592395C2semidirect
5. C3×#4700C2semidirect
6. C3×#4700C2semidirect
7. #10590932C2semidirect
8. #10590931C2semidirect
9. #10590927C2semidirect
10. #10590402C2semidirect
11. #10590398C2semidirect
15. #64298C22semidirect
16. C2×#3746C22semidirect
18. C2×#3744C22semidirect
19. #64084C22semidirect
23. C3×#901C22semidirect
24. C3×#901C22semidirect
26. #63831C22semidirect
28. #63825C22semidirect
39. C32×C4×C8C22semidirect
40. C3×#819C22semidirect
41. C3×#819C22semidirect
43. C3×#805C22semidirect
44. C3×#805C22semidirect
45. #63561C22semidirect
46. #63559C22semidirect
65. #4700D3semidirect
66. #4700D3semidirect
169. #901C2×D3semidirect
170. #901C2×D3semidirect
180. C3×C4×C8C2×D3semidirect
181. C3×C4×C8C2×D3semidirect
186. #819C2×D3semidirect
187. #819C2×D3semidirect
189. #805C2×D3semidirect
190. #805C2×D3semidirect
393. C4×C8D32semidirect
566. C32#3290semidirect
632. C3#79891semidirect
633. C3#79892semidirect

Maximal subgroups

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

subgroupindex
#105946922
#105946802
#105946792
#105923952
C3×#47002
#105909322
#105909312
#105909272
#105904022
#105903982
#798923
#798913