Finite Group Databasebeta

← #11899740

Subgroups — #11899740

Order 1152.

762 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5769C211yesmaximal, characteristic, complemented
2#10594691C211yesmaximal, characteristic, complemented
3#10592893C211yesmaximal, characteristic, complemented
4C3×#5195C211yesmaximal, characteristic, complemented
5#10591048C212yesmaximal, complemented
6#10591042C212yesmaximal, complemented
7#10591033C212yesmaximal, complemented
8D3×#827C212yesmaximal, complemented
9C2×#63547C211yesmaximal, characteristic, complemented
10#10590633C211yesmaximal, characteristic, complemented
11#10590622C211yesmaximal, characteristic, complemented
12#84008—31nomaximal
13#82040—31nomaximal
14C3×#1009—21no—
15#64297—21no—
16C32×#135C2211yescharacteristic
17#64113C2211yescharacteristic, complemented
18C3×#949—21no—
19C3×#919C2212yes—
20C3×#914—22no—
21C3×D3×D8C2212yes—
22C2×C3×Dic12C2211yescharacteristic, complemented
23C2×C3×D24C2211yescharacteristic
24C3×#901C2211yescharacteristic
25#63833—21no—
26#63808C2212yescomplemented
27#63801—22no—
28D3×Dic12C2212yescomplemented
29#63656C2211yescharacteristic, complemented
30#63655C2211yescharacteristic, complemented
31#63654C2211yescharacteristic, complemented
32#63653C2211yescharacteristic, complemented
33C2×C3⋊(C3⋊C16)C2211yescharacteristic, complemented
34C3×#829C2212yescomplemented
35C3×#827C2212yescomplemented
36C3×#812C2211yescharacteristic, complemented
37#63548C2212yescomplemented
38#63547C2212yescomplemented
39#63547C2212yescomplemented
40#63546C2212yescomplemented
41#63543C2212yescomplemented
42D3×C3⋊C16C2212yescomplemented
43C3×#576—31no—
44#5769D311yescharacteristic, complemented
45#5766—31no—
46#5753—31no—
47C3×#510—31no—
48#5195—32no—
49#5195D311yescharacteristic, complemented
50#5194—31no—
51#5194—31no—
52#5194—32no—
53#5194—61no—
54C2×#828—31no—
55C2×#827—31no—
56C2×#827—32no—
57#5147—32no—
58#5147—31no—
59#5140—31no—
60#4919—32no—
61#4918—32no—
62#4914—32no—
63D3×SD32—32no—
64#4908—31no—
65#4907—31no—
66C32×#41—21no—
67#3828—21no—
68C3×#239—22no—
69C3×D3×D4—22no—
70C3×D3×D4—42no—
71C3×#235—41no—
72C3×#235D411yescharacteristic
73C2×C3×D12—21no—
74C2×C3×D12—41no—
75C2×C3×Dic6—21no—
76#3804—42no—
77#3799—22no—
78#3797—41no—
79#3796—41no—
80D3×Dic6—22no—
81C32×Q16C2311yescharacteristic
82C32×SD16—21no—
83C32×D8C2311yescharacteristic
84C2×C32×C8C2311yescharacteristic
85#3746C2311yescharacteristic
86#3745C2311yescharacteristic
87#3744—21no—
88C3×#215—22no—
89C3×#213—22no—
90C3×#208D411yescharacteristic
91C3×Dic12—21no—
92C3×Dic12C2312yes—
93C3×D24—21no—
94C3×D24C2312yes—
95C3×ΓL(1,𝔽25)D412yes—
96C3×D3×C8C2312yes—
97#3719—22no—
98#3717—22no—
99C3⋊(C3⋊C16)C2311yescharacteristic
100C3⋊(C3⋊C16)C2311yescharacteristic
101C3×C3⋊C16C2312yes—
102#3416—91noSylow
103C3×H(5,𝔽2)—61no—
104#1010—61no—
105#1009—21no—
106#1007—61no—
107C3×AGL(1,ℤ/8)—62no—
108C3×AGL(1,ℤ/8)—61no—
109C3×#135—21no—
110C3×#135—32no—
111C3×#135C2×D311yescharacteristic
112C3×#135C2×D311yescharacteristic
113C2×C3×Q16—31no—
114C2×C3×D8—32no—
115C2×C3×D8—31no—
116C3×#131—31no—
117#949—21no—
118#942—61no—
119#919—32no—
120#919C2×D312yes—
121#918—62no—
122D3×Q16—32no—
123#914—22no—
124D3×D8C2×D312yes—
125#909—62no—
126#909—61no—
127C2×Dic12—32no—
128C2×Dic12C2×D311yescharacteristic, complemented
129#904—31no—
130#904—31no—
131#904—32no—
132#904—61no—
133C2×D24C2×D311yescharacteristic
134#901C2×D311yescharacteristic
135C3×Q32—32no—
136C3×SD32—32no—
137C3×M32—31no—
138#829—31no—
139#829—31no—
140#829—61no—
141#829C2×D312yescomplemented
142#828—31no—
143#828—31no—
144#828—32no—
145#828—32no—
146#828—61no—
147#827—31no—
148#827—31no—
149#827—32no—
150#827—32no—
151#827—32no—
152#827—61no—
153#827C2×D312yescomplemented
154#826—31no—
155#826—31no—
156#826—32no—
157#826—61no—
158#812—32no—
159#812C2×D311yescharacteristic, complemented
160C2×C3⋊C16—31no—
161C2×C3⋊C16—31no—
162C2×C3⋊C16—32no—
163C2×C3⋊C16—61no—
164#800—32no—
165D48—32no—
166#798—32no—
167D3×C16—32no—
168C22×C3×D3—41no—
169C22×C3×D3—42no—
170C32×Q8—21no—
171C32×D4—21no—
172C32×D4—41no—
173C2×C32×C4—41no—
174C2×C32×C4C2×D411yescharacteristic
175#638—41no—
176C4⋊(C3⋊D3)—21no—
177C4×C3⋊D3—41no—
178#634—21no—
179C3×#67—42no—
180C3×#67D812yes—
181C2×C3×Dic3—41no—
182C3×D12—22no—
183C3×D12—42no—
184C3×D12—41no—
185C3×D12D811yescharacteristic
186C3×C4×D3—42no—
187C3×C4×D3C2×D412yes—
188C3×Dic6—22no—
189C3×Dic6—41no—
190C3×Dic6D811yescharacteristic
191#627—42no—
192#626—42no—
193#624—42no—
194D3×Dic3—42no—
195C32×C8C2×D411yescharacteristic
196C32×C8C2411yescharacteristic
197C3×C3⋊C8C2×D412yes—
198#578—91no—
199#576—31no—
200#510—31no—
201#510—92no—
202#509—91no—
203#509—92no—
204#508—92no—
205#508—91no—
206C2×SD32—92no—
207C2×SD32—91no—
208#504—91no—
209C3×#41—21no—
210C3×#41—21no—
211C3×#41—31no—
212C3×#41—41no—
213C3×#41—62no—
214C3×#41—121no—
215C2×C3×Q8—61no—
216C2×C3×D4—62no—
217C2×C3×D4—61no—
218C2×C3×D4—121no—
219C2×C3×D4—122no—
220#239—22no—
221#239—62no—
222#239—121no—
223D3×Q8—62no—
224D3×Q8—121no—
225D3×Q8—121no—
226#237—121no—
227#237—122no—
228D3×D4—22no—
229D3×D4—42no—
230#235—41no—
231#235—62no—
232#235—61no—
233#235—61no—
234#235—121no—
235#235—122no—
236#235#6711yescharacteristic
237C2×D12—21no—
238C2×D12—41no—
239C2×Dic6—21no—
240C2×Dic6—62no—
241C3×Q16—21no—
242C3×Q16—32no—
243C3×Q16—61no—
244C3×Q16C22×D311yescharacteristic
245C3×Q16C22×D311yescharacteristic
246C3×SD16—21no—
247C3×SD16—21no—
248C3×SD16—41no—
249C3×SD16—62no—
250C3×D8—21no—
251C3×D8—32no—
252C3×D8—62no—
253C3×D8—61no—
254C3×D8C22×D311yescharacteristic
255C3×D8C22×D311yescharacteristic
256C3×M16—31no—
257C3×M16—32no—
258C2×C3×C8—21no—
259C2×C3×C8—32no—
260C2×C3×C8C22×D311yescharacteristic
261C2×C3×C8C22×D311yescharacteristic
262#216—62no—
263#215—22no—
264#215—62no—
265#213—22no—
266#208#6711yescharacteristic
267Dic12—21no—
268Dic12—31no—
269Dic12—31no—
270Dic12—61no—
271Dic12—62no—
272Dic12C22×D312yes—
273D24—21no—
274D24—31no—
275D24—31no—
276D24—61no—
277D24C22×D312yes—
278#204—62no—
279#204—61no—
280#204—61no—
281#204—121no—
282ΓL(1,𝔽25)#6712yes—
283D3×C8C22×D312yes—
284C3×C16—32no—
285C3⋊C16—31no—
286C3⋊C16—31no—
287C3⋊C16—31no—
288C3⋊C16—31no—
289C3⋊C16—61no—
290C3⋊C16—61no—
291C3⋊C16C22×D312yes—
292C22×C32—41no—
293C22×C32C2×D811yescharacteristic
294C2×C3⋊D3—41no—
295C2×C3×D3—42no—
296C2×C3×D3—162no—
297C2×C3×D3—161no—
298C2×C3×D3C2×D812yes—
299C32×C4—41no—
300C32×C4C2×D811yescharacteristic
301C32×C4C22×D411yescharacteristic
302C3⋊Dic3—41no—
303C3×Dic3—42no—
304C3×Dic3C2×D812yes—
3052−1+4—181no—
306H(5,𝔽2)—61no—
307#137—182no—
308#137—181no—
309AGL(1,ℤ/8)—62no—
310AGL(1,ℤ/8)—61no—
311#135—32no—
312#135—92no—
313#135—91no—
314#135D3211yescharacteristic
315C2×Q16—31no—
316C2×Q16—92no—
317C2×D8—32no—
318C2×D8—31no—
319#131—31no—
320Q32—32no—
321Q32—91no—
322SD32—32no—
323SD32—92no—
324SD32—92no—
325SD32—92no—
326SD32—91no—
327SD32—91no—
328D16—92no—
329D16—91no—
330M32—31no—
331M32—92no—
332C2×C16—92no—
333C2×C16—91no—
334C23×C3—122no—
335C23×C3—121no—
336C22×D3—41no—
337C22×D3—42no—
338C3×Q8—21no—
339C3×Q8—21no—
340C3×Q8—31no—
341C3×Q8—41no—
342C3×Q8—62no—
343C3×Q8—121no—
344C3×D4—21no—
345C3×D4—21no—
346C3×D4—32no—
347C3×D4—31no—
348C3×D4—41no—
349C3×D4—41no—
350C3×D4—41no—
351C3×D4—62no—
352C3×D4—81no—
353C3×D4—122no—
354C3×D4—122no—
355C3×D4—121no—
356C2×C3×C4—21no—
357C2×C3×C4—32no—
358C2×C3×C4—41no—
359C2×C3×C4—41no—
360C2×C3×C4—81no—
361C2×C3×C4—122no—
362C2×C3×C4—121no—
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4C2×#6711yescharacteristic
365#67—42no—
366#67—122no—
367#67—121no—
368#67—121no—
369#67—241no—
370#67#21312yes—
371C2×Dic3—41no—
372C2×Dic3—122no—
373D12—22no—
374D12—42no—
375D12—41no—
376D12—61no—
377D12—61no—
378D12—121no—
379D12—122no—
380D12#21311yescharacteristic
381C4×D3—42no—
382C4×D3—122no—
383C4×D3—122no—
384C4×D3—121no—
385C4×D3—121no—
386C4×D3—122no—
387C4×D3—241no—
388C4×D3C2×#6712yes—
389Dic6—22no—
390Dic6—41no—
391Dic6—61no—
392Dic6—61no—
393Dic6—121no—
394Dic6—122no—
395Dic6—122no—
396Dic6#21311yescharacteristic
397C3×C8—21no—
398C3×C8—21no—
399C3×C8—32no—
400C3×C8D3×D411yescharacteristic
401C3×C8C2×#6711yescharacteristic
402C3×C8C23×D311yescharacteristic
403C3×C8C23×D311yescharacteristic
404C3⋊C8C2×#6712yes—
405C2×C32—21no—
406C2×C32—81no—
407C2×C32C22×D811yescharacteristic
408C3⋊D3—81no—
409C3×D3—22no—
410C3×D3—82no—
411#41—21no—
412#41—31no—
413#41—62no—
414#41—121no—
415#41—182no—
416#41—181no—
417#41—362no—
418#41—361no—
419C2×Q8—61no—
420C2×Q8—182no—
421C2×Q8—361no—
422C2×D4—62no—
423C2×D4—61no—
424C2×D4—121no—
425C2×D4—122no—
426Q16—32no—
427Q16—61no—
428Q16—91no—
429Q16—182no—
430Q16C2×D3211yescharacteristic
431SD16—21no—
432SD16—62no—
433SD16—182no—
434SD16—181no—
435D8—32no—
436D8—62no—
437D8—61no—
438D8—91no—
439D8C2×D3211yescharacteristic
440M16—31no—
441M16—32no—
442C2×C8—32no—
443C2×C8C2×D3211yescharacteristic
444C16—32no—
445C16—91no—
446C16—91no—
447C22×C3—21no—
448C22×C3—32no—
449C22×C3—41no—
450C22×C3—41no—
451C22×C3—81no—
452C22×C3—122no—
453C22×C3—481no—
454C22×C3—482no—
455C22×C3D3×D811yescharacteristic
456C22×C3C2×#21311yescharacteristic
457C2×D3—42no—
458C2×D3—121no—
459C2×D3—121no—
460C2×D3—162no—
461C2×D3—161no—
462C2×D3—241no—
463C2×D3C2×#21312yes—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—32no—
467C3×C4—41no—
468C3×C4—41no—
469C3×C4—81no—
470C3×C4—122no—
471C3×C4D3×D811yescharacteristic
472C3×C4C2×#21311yescharacteristic
473C3×C4C2×D3×D411yescharacteristic
474C3×C4C22×#6711yescharacteristic
475Dic3—42no—
476Dic3—121no—
477Dic3—121no—
478Dic3—241no—
479Dic3C2×#21312yes—
480C32#341611yescharacteristic, complemented, Sylow
481C23—122no—
482C23—121no—
483Q8—21no—
484Q8—31no—
485Q8—62no—
486Q8—121no—
487Q8—181no—
488Q8—362no—
489D4—21no—
490D4—32no—
491D4—31no—
492D4—41no—
493D4—62no—
494D4—122no—
495D4—122no—
496D4—121no—
497D4—181no—
498D4—362no—
499D4—361no—
500C2×C4—32no—
501C2×C4—41no—
502C2×C4—122no—
503C2×C4—121no—
504C2×C4—362no—
505C2×C4—362no—
506C2×C4—361no—
507C2×C4D3×#6711yescharacteristic
508C8—32no—
509C8D3×#6711yescharacteristic
510C8C22×D3211yescharacteristic
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—41no—
515C2×C3—62no—
516C2×C3—81no—
517C2×C3—81no—
518C2×C3—161no—
519C2×C3—242no—
520C2×C3C2×D3×D811yescharacteristic
521C2×C3C22×#21311yescharacteristic
522D3—22no—
523D3—82no—
524D3—241no—
525D3—241no—
526D3—481no—
527C22—32no—
528C22—41no—
529C22—122no—
530C22—361no—
531C22—481no—
532C22—482no—
533C22D3×#21311yescharacteristic
534C4—32no—
535C4—41no—
536C4—122no—
537C4—361no—
538C4D3×#21311yescharacteristic
539C4C2×D3×#6711yescharacteristic
540C3—21no—
541C3#8204011yescharacteristic, complemented
542C3#8400811yescharacteristic, complemented
543C2—21no—
544C2—62no—
545C2—81no—
546C2—242no—
547C2—721no—
548C2C2×D3×#21311yescharacteristic
subgroupG/H
centerC2C2×D3×#213
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC32×#135C22
socleC2×C32C22×D8
hypercenter#135D32
hypocenterC32#3416
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #135

Complements

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

NH ≅ G/Ntype
1. C3×#5769C2semidirect
2. #10594691C2semidirect
3. #10592893C2semidirect
4. C3×#5195C2semidirect
5. #10591048C2semidirect
6. #10591042C2semidirect
7. #10591033C2semidirect
8. D3×#827C2semidirect
9. C2×#63547C2semidirect
10. #10590633C2semidirect
11. #10590622C2semidirect
17. #64113C22semidirect
22. C2×C3×Dic12C22semidirect
26. #63808C22semidirect
28. D3×Dic12C22semidirect
29. #63656C22semidirect
30. #63655C22semidirect
31. #63654C22semidirect
32. #63653C22semidirect
33. C2×C3⋊(C3⋊C16)C22semidirect
34. C3×#829C22semidirect
35. C3×#827C22semidirect
36. C3×#812C22semidirect
37. #63548C22semidirect
38. #63547C22semidirect
39. #63547C22semidirect
40. #63546C22semidirect
41. #63543C22semidirect
42. D3×C3⋊C16C22semidirect
44. #5769D3semidirect
49. #5195D3semidirect
128. C2×Dic12C2×D3semidirect
141. #829C2×D3semidirect
153. #827C2×D3semidirect
159. #812C2×D3semidirect
480. C32#3416semidirect
541. C3#82040semidirect
542. C3#84008semidirect

Maximal subgroups

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

subgroupindex
C3×#57692
#105946912
#105928932
C3×#51952
#105910482
#105910422
#105910332
D3×#8272
C2×#635472
#105906332
#105906222
#840083
#820403