Finite Group Databasebeta

← #11899690

Subgroups — #11899690

Order 1152.

782 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5769C211yesmaximal, characteristic, complemented
2#10594678C211yesmaximal, characteristic, complemented
3#10592893C211yesmaximal, characteristic, complemented
4C3×#5193C211yesmaximal, characteristic, complemented
5#10591046C212yesmaximal, complemented
6#10591038C212yesmaximal, complemented
7#10591031C212yesmaximal, complemented
8D3×#826C212yesmaximal, complemented
9#10590633C211yesmaximal, characteristic, complemented
10C2×#63545C211yesmaximal, characteristic, complemented
11#10590622C211yesmaximal, characteristic, complemented
12#84007—31nomaximal
13#82036—31nomaximal
14C3×#1009—21no—
15#64307—21no—
16C32×#135C2211yescharacteristic, complemented
17#64113C2211yescharacteristic, complemented
18C3×#949—21no—
19C3×#919C2212yescomplemented
20C3×#914—22no—
21C3×D3×D8C2212yescomplemented
22C2×C3×D24C2211yescharacteristic, complemented
23C2×C3×D24C2211yescharacteristic, complemented
24C3×#901C2211yescharacteristic
25#63830—21no—
26#63807C2212yescomplemented
27#63795—22no—
28D3×D24C2212yescomplemented
29#63656C2211yescharacteristic, complemented
30#63655C2211yescharacteristic, complemented
31#63654C2211yescharacteristic, complemented
32#63653C2211yescharacteristic, complemented
33C2×C3⋊(C3⋊C16)C2211yescharacteristic, complemented
34C3×#828C2212yescomplemented
35C3×#826C2212yescomplemented
36C3×#812C2211yescharacteristic, complemented
37#63548C2212yescomplemented
38#63546C2212yescomplemented
39#63545C2212yescomplemented
40#63545C2212yescomplemented
41#63543C2212yescomplemented
42D3×C3⋊C16C2212yescomplemented
43C3×#576—31no—
44#5769D311yescharacteristic, complemented
45#5757—31no—
46#5752—31no—
47C3×#509—31no—
48#5194—31no—
49#5194—31no—
50#5194—32no—
51#5194—61no—
52#5193—32no—
53#5193D311yescharacteristic, complemented
54#5147—32no—
55#5147—31no—
56C2×#826—31no—
57C2×#826—31no—
58C2×#826—32no—
59#5140—31no—
60#4916—32no—
61#4914—32no—
62#4911—32no—
63D3×D16—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—21no—
75C2×C3×D12—41no—
76D3×#67—42no—
77#3802—41no—
78D3×D12—22no—
79#3796—41no—
80#3795—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×D24—21no—
92C3×D24—21no—
93C3×D24C2312yes—
94C3×D24C2312yes—
95C3×ΓL(1,𝔽25)D412yes—
96C3×D3×C8C2312yes—
97#3716—22no—
98#3714—22no—
99C3⋊(C3⋊C16)C2311yescharacteristic
100C3⋊(C3⋊C16)C2311yescharacteristic
101C3×C3⋊C16C2312yes—
102#3415—91noSylow
103C3×H(5,𝔽2)—61no—
104#1009—21no—
105#1009—61no—
106#1004—61no—
107C3×AGL(1,ℤ/8)—62no—
108C3×AGL(1,ℤ/8)—61no—
109C3×#135—21no—
110C3×#135—32no—
111C3×#135C2×D311yescharacteristic, complemented
112C3×#135C2×D311yescharacteristic, complemented
113C2×C3×D8—32no—
114C2×C3×D8—31no—
115C2×C3×D8—31no—
116C3×#131—31no—
117#949—21no—
118#932—61no—
119#919C2×D312yescomplemented
120#914—22no—
121#912—32no—
122#911—62no—
123D3×D8—32no—
124D3×D8C2×D312yescomplemented
125#908—62no—
126#908—61no—
127#904—31no—
128#904—31no—
129#904—32no—
130#904—61no—
131C2×D24—32no—
132C2×D24C2×D311yescharacteristic, complemented
133C2×D24C2×D311yescharacteristic, complemented
134#901C2×D311yescharacteristic
135C3×SD32—32no—
136C3×D16—32no—
137C3×M32—31no—
138#829—31no—
139#829—31no—
140#829—61no—
141#828—31no—
142#828—31no—
143#828—61no—
144#828C2×D312yescomplemented
145#827—31no—
146#827—31no—
147#827—32no—
148#827—61no—
149#826—31no—
150#826—31no—
151#826—32no—
152#826—32no—
153#826—32no—
154#826—32no—
155#826—32no—
156#826—61no—
157#826C2×D312yescomplemented
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—41no—
170C22×C3×D3—42no—
171C2×D32—42no—
172C32×Q8—21no—
173C32×D4—21no—
174C32×D4—41no—
175C2×C32×C4—41no—
176C2×C32×C4C2×D411yescharacteristic
177#638—41no—
178C4⋊(C3⋊D3)—21no—
179C4×C3⋊D3—41no—
180#634—21no—
181C3×#67—42no—
182C3×#67D812yes—
183C3×D12—22no—
184C3×D12—22no—
185C3×D12—42no—
186C3×D12—41no—
187C3×D12—41no—
188C3×D12D811yescharacteristic
189C3×C4×D3—42no—
190C3×C4×D3C2×D412yes—
191C3×Dic6D811yescharacteristic
192#626—42no—
193#625—42no—
194D3×Dic3—42no—
195C32×C8C2×D411yescharacteristic
196C32×C8C2411yescharacteristic
197C3×C3⋊C8C2×D412yes—
198#576—31no—
199#576—91no—
200#509—31no—
201#509—91no—
202#509—92no—
203#509—92no—
204#508—92no—
205#508—91no—
206C2×D16—92no—
207C2×D16—91no—
208#504—91no—
209C3×#41—21no—
210C3×#41—21no—
211C3×#41—31no—
212C3×#41—41no—
213C3×#41—62no—
214C3×#41—121no—
215C2×C3×D4—62no—
216C2×C3×D4—61no—
217C2×C3×D4—61no—
218C2×C3×D4—121no—
219C2×C3×D4—122no—
220C2×#67—122no—
221#239—22no—
222#239—121no—
223#237—62no—
224#237—121no—
225D3×D4—22no—
226D3×D4—42no—
227D3×D4—62no—
228D3×D4—121no—
229D3×D4—122no—
230D3×D4—121no—
231#235—41no—
232#235—62no—
233#235—61no—
234#235—61no—
235#235—121no—
236#235#6711yescharacteristic
237C2×D12—21no—
238C2×D12—21no—
239C2×D12—41no—
240C2×D12—62no—
241C3×Q16—21no—
242C3×Q16C22×D311yescharacteristic
243C3×Q16C22×D311yescharacteristic
244C3×SD16—21no—
245C3×SD16—21no—
246C3×SD16—41no—
247C3×SD16—62no—
248C3×D8—21no—
249C3×D8—32no—
250C3×D8—32no—
251C3×D8—62no—
252C3×D8—61no—
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#215—22no—
263#214—62no—
264#213—22no—
265#213—62no—
266#208#6711yescharacteristic
267Dic12—31no—
268Dic12—31no—
269Dic12—61no—
270D24—21no—
271D24—21no—
272D24—31no—
273D24—31no—
274D24—61no—
275D24—62no—
276D24C22×D312yes—
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—42no—
297C2×C3×D3—162no—
298C2×C3×D3—161no—
299C2×C3×D3—161no—
300C2×C3×D3C2×D812yes—
301D32—162no—
302C32×C4—41no—
303C32×C4C2×D811yescharacteristic
304C32×C4C22×D411yescharacteristic
305C3⋊Dic3—41no—
306C3×Dic3C2×D812yes—
307H(5,𝔽2)—61no—
308H(5,𝔽2)—181no—
309AGL(1,ℤ/8)—62no—
310AGL(1,ℤ/8)—61no—
311AGL(1,ℤ/8)—182no—
312AGL(1,ℤ/8)—181no—
313#135—32no—
314#135—92no—
315#135—91no—
316#135D3211yescharacteristic, complemented
317C2×D8—32no—
318C2×D8—31no—
319C2×D8—31no—
320C2×D8—92no—
321#131—31no—
322Q32—91no—
323SD32—32no—
324SD32—92no—
325SD32—91no—
326SD32—91no—
327D16—32no—
328D16—92no—
329D16—92no—
330D16—92no—
331D16—91no—
332M32—31no—
333M32—92no—
334C2×C16—92no—
335C2×C16—91no—
336C23×C3—122no—
337C23×C3—121no—
338C23×C3—121no—
339C22×D3—41no—
340C22×D3—41no—
341C22×D3—42no—
342C22×D3—122no—
343C22×D3—122no—
344C3×Q8—21no—
345C3×Q8—21no—
346C3×Q8—31no—
347C3×Q8—41no—
348C3×D4—21no—
349C3×D4—21no—
350C3×D4—32no—
351C3×D4—31no—
352C3×D4—41no—
353C3×D4—41no—
354C3×D4—41no—
355C3×D4—62no—
356C3×D4—62no—
357C3×D4—81no—
358C3×D4—122no—
359C3×D4—122no—
360C3×D4—121no—
361C3×D4—121no—
362C2×C3×C4—21no—
363C2×C3×C4—32no—
364C2×C3×C4—41no—
365C2×C3×C4—41no—
366C2×C3×C4—81no—
367C2×C3×C4—122no—
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4C2×#6711yescharacteristic
370#67—42no—
371#67—122no—
372#67—121no—
373#67—121no—
374#67—122no—
375#67—122no—
376#67—241no—
377#67#21312yes—
378C2×Dic3—122no—
379D12—22no—
380D12—22no—
381D12—42no—
382D12—41no—
383D12—41no—
384D12—61no—
385D12—61no—
386D12—121no—
387D12—122no—
388D12#21311yescharacteristic
389C4×D3—42no—
390C4×D3—122no—
391C4×D3—121no—
392C4×D3—121no—
393C4×D3—241no—
394C4×D3C2×#6712yes—
395Dic6—61no—
396Dic6—61no—
397Dic6—121no—
398Dic6#21311yescharacteristic
399C3×C8—21no—
400C3×C8—21no—
401C3×C8—32no—
402C3×C8D3×D411yescharacteristic
403C3×C8C2×#6711yescharacteristic
404C3×C8C23×D311yescharacteristic
405C3×C8C23×D311yescharacteristic
406C3⋊C8C2×#6712yes—
407C2×C32—21no—
408C2×C32—81no—
409C2×C32C22×D811yescharacteristic
410C3⋊D3—81no—
411C3×D3—22no—
412C3×D3—82no—
413C3×D3—82no—
414#41—21no—
415#41—31no—
416#41—62no—
417#41—121no—
418#41—182no—
419#41—181no—
420#41—361no—
421C2×D4—62no—
422C2×D4—61no—
423C2×D4—61no—
424C2×D4—121no—
425C2×D4—122no—
426C2×D4—182no—
427C2×D4—361no—
428C2×D4—362no—
429Q16—91no—
430Q16C2×D3211yescharacteristic
431SD16—21no—
432SD16—62no—
433SD16—182no—
434SD16—181no—
435D8—32no—
436D8—32no—
437D8—62no—
438D8—61no—
439D8—61no—
440D8—91no—
441D8—182no—
442D8C2×D3211yescharacteristic
443M16—31no—
444M16—32no—
445C2×C8—32no—
446C2×C8C2×D3211yescharacteristic
447C16—32no—
448C16—91no—
449C16—91no—
450C22×C3—21no—
451C22×C3—32no—
452C22×C3—41no—
453C22×C3—41no—
454C22×C3—81no—
455C22×C3—122no—
456C22×C3—122no—
457C22×C3—481no—
458C22×C3—481no—
459C22×C3—482no—
460C22×C3D3×D811yescharacteristic
461C22×C3C2×#21311yescharacteristic
462C2×D3—42no—
463C2×D3—42no—
464C2×D3—121no—
465C2×D3—121no—
466C2×D3—162no—
467C2×D3—161no—
468C2×D3—161no—
469C2×D3—241no—
470C2×D3—482no—
471C2×D3—482no—
472C2×D3C2×#21312yes—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—32no—
476C3×C4—41no—
477C3×C4—41no—
478C3×C4—81no—
479C3×C4D3×D811yescharacteristic
480C3×C4C2×#21311yescharacteristic
481C3×C4C2×D3×D411yescharacteristic
482C3×C4C22×#6711yescharacteristic
483Dic3—121no—
484Dic3—121no—
485Dic3—241no—
486Dic3C2×#21312yes—
487C32#341511yescharacteristic, complemented, Sylow
488C23—122no—
489C23—121no—
490C23—121no—
491C23—362no—
492Q8—21no—
493Q8—31no—
494Q8—181no—
495D4—21no—
496D4—32no—
497D4—31no—
498D4—41no—
499D4—62no—
500D4—62no—
501D4—122no—
502D4—122no—
503D4—121no—
504D4—121no—
505D4—181no—
506D4—362no—
507D4—362no—
508D4—361no—
509C2×C4—32no—
510C2×C4—41no—
511C2×C4—122no—
512C2×C4—362no—
513C2×C4—361no—
514C2×C4D3×#6711yescharacteristic
515C8—32no—
516C8D3×#6711yescharacteristic
517C8C22×D3211yescharacteristic
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—41no—
522C2×C3—62no—
523C2×C3—81no—
524C2×C3—81no—
525C2×C3—161no—
526C2×C3—242no—
527C2×C3—242no—
528C2×C3C2×D3×D811yescharacteristic
529C2×C3C22×#21311yescharacteristic
530D3—22no—
531D3—82no—
532D3—82no—
533D3—241no—
534D3—241no—
535D3—481no—
536C22—32no—
537C22—41no—
538C22—122no—
539C22—122no—
540C22—361no—
541C22—481no—
542C22—481no—
543C22—482no—
544C22—1442no—
545C22D3×#21311yescharacteristic
546C4—32no—
547C4—41no—
548C4—361no—
549C4D3×#21311yescharacteristic
550C4C2×D3×#6711yescharacteristic
551C3—21no—
552C3#8203611yescharacteristic, complemented
553C3#8400711yescharacteristic, complemented
554C2—21no—
555C2—62no—
556C2—81no—
557C2—242no—
558C2—242no—
559C2—721no—
560C2C2×D3×#21311yescharacteristic
subgroupG/H
centerC2C2×D3×#213
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC32×#135C22
socleC2×C32C22×D8
hypercenter#135D32
hypocenterC32#3415
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. #10594678C2semidirect
3. #10592893C2semidirect
4. C3×#5193C2semidirect
5. #10591046C2semidirect
6. #10591038C2semidirect
7. #10591031C2semidirect
8. D3×#826C2semidirect
9. #10590633C2semidirect
10. C2×#63545C2semidirect
11. #10590622C2semidirect
16. C32×#135C22semidirect
17. #64113C22semidirect
19. C3×#919C22semidirect
21. C3×D3×D8C22semidirect
22. C2×C3×D24C22semidirect
23. C2×C3×D24C22semidirect
26. #63807C22semidirect
28. D3×D24C22semidirect
29. #63656C22semidirect
30. #63655C22semidirect
31. #63654C22semidirect
32. #63653C22semidirect
33. C2×C3⋊(C3⋊C16)C22semidirect
34. C3×#828C22semidirect
35. C3×#826C22semidirect
36. C3×#812C22semidirect
37. #63548C22semidirect
38. #63546C22semidirect
39. #63545C22semidirect
40. #63545C22semidirect
41. #63543C22semidirect
42. D3×C3⋊C16C22semidirect
44. #5769D3semidirect
53. #5193D3semidirect
111. C3×#135C2×D3semidirect
112. C3×#135C2×D3semidirect
119. #919C2×D3semidirect
124. D3×D8C2×D3semidirect
132. C2×D24C2×D3semidirect
133. C2×D24C2×D3semidirect
144. #828C2×D3semidirect
157. #826C2×D3semidirect
159. #812C2×D3semidirect
316. #135D32semidirect
487. C32#3415semidirect
552. C3#82036semidirect
553. C3#84007semidirect

Maximal subgroups

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

subgroupindex
C3×#57692
#105946782
#105928932
C3×#51932
#105910462
#105910382
#105910312
D3×#8262
#105906332
C2×#635452
#105906222
#840073
#820363