Finite Group Databasebeta

← #11889182

Subgroups — #11889182

Order 1152.

1206 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596203C211yesmaximal, characteristic, complemented
2#10596025C211yesmaximal, characteristic
3C32×#476C211yesmaximal, characteristic, complemented
4#10592788C211yesmaximal, characteristic, complemented
5#10592717C211yesmaximal, characteristic, complemented
6#10592567C211yesmaximal, characteristic, complemented
7#10592566C211yesmaximal, characteristic, complemented
8#10592565C211yesmaximal, characteristic, complemented
9#10592563C211yesmaximal, characteristic, complemented
10#10592544C211yesmaximal, characteristic, complemented
11#10592535C211yesmaximal, characteristic, complemented
12#10592482C211yesmaximal, characteristic, complemented
13#10592475C211yesmaximal, characteristic, complemented
14#10592471C211yesmaximal, characteristic, complemented
15#10592469C211yesmaximal, characteristic, complemented
16#81078—34nomaximal
17C2×#3830C2211yescharacteristic
18C2×D4×C3⋊D3C2211yescharacteristic
19C32×C4⋊Q8C2211yescharacteristic, complemented
20C32×C4×D4C2211yescharacteristic
21#64156—21no—
22Q8×C3⋊Dic3—21no—
23C2×#3754C2211yescharacteristic
24#64139—21no—
25C2×#3752—21no—
26C2×#3746C2211yescharacteristic, complemented
27C2×#3744C2211yescharacteristic
28C2×#3743C2211yescharacteristic
29C2×C8×C3⋊D3C2211yescharacteristic, complemented
30#64107—21no—
31#64107—21no—
32#64106C2211yescharacteristic
33#64106C2211yescharacteristic
34#64106C2211yescharacteristic, complemented
35#64104C2211yescharacteristic
36#64101C2211yescharacteristic
37#64101C2211yescharacteristic, complemented
38#64095—21no—
39#64091—21no—
40#64084C2211yescharacteristic
41C4×C4⋊(C3⋊D3)C2211yescharacteristic
42C4×#634C2211yescharacteristic, complemented
43C32×#106C2211yescharacteristic, complemented
44C32×#106C2211yescharacteristic, complemented
45C32×C4⋊C8C2211yescharacteristic, complemented
46C32×#102C2211yescharacteristic
47C32×#102C2211yescharacteristic
48#63659C2211yescharacteristic
49#63648C2211yescharacteristic
50#63647C2211yescharacteristic
51#63647C2211yescharacteristic, complemented
52#63643C2211yescharacteristic, complemented
53#63637C2211yescharacteristic, complemented
54#63637C2211yescharacteristic, complemented
55#63637C2211yescharacteristic, complemented
56#63636C2211yescharacteristic
57#63636C2211yescharacteristic
58#63634C2211yescharacteristic, complemented
59#63630C2211yescharacteristic, complemented
60#5732—34no—
61#5554—34no—
62C3×#476D314yescomplemented
63#5089—34no—
64#5018—34no—
65#4868—34no—
66#4867—34no—
67#4866—34no—
68#4864—34no—
69#4845—34no—
70#4836—34no—
71#4783—34no—
72#4776—34no—
73#4772—34no—
74#4770—34no—
75C23×C3⋊D3—21no—
76C2×C32×Q8—21no—
77C2×C32×D4C2311yescharacteristic
78C22×C32×C4—21no—
79C2×#638—21no—
80C2×#638—21no—
81C22×C3⋊Dic3—21no—
82#3830—22no—
83#3830—41no—
84D4×C3⋊D3—22no—
85D4×C3⋊D3—41no—
86C2×C4⋊(C3⋊D3)—21no—
87C2×C4⋊(C3⋊D3)D411yescharacteristic
88C2×C4⋊(C3⋊D3)C2311yescharacteristic
89C2×C4×C3⋊D3C2311yescharacteristic
90C2×C4×C3⋊D3C2311yescharacteristic
91C2×#634C2311yescharacteristic
92C2×#634C2311yescharacteristic
93C2×C32×C8C2311yescharacteristic
94C2×C32×C8C2311yescharacteristic
95C32×C4⋊C4—21no—
96C32×C4⋊C4C2311yescharacteristic
97C32×C4⋊C4C2311yescharacteristic
98C32×C4⋊C4C2311yescharacteristic
99C32×C22⋊C4—21no—
100C32×C42C2311yescharacteristic
101#3754—22no—
102#3752—21no—
103#3752—21no—
104#3752—21no—
105#3752—21no—
106#3752—21no—
107#3752—21no—
108#3752—21no—
109#3752—21no—
110#3752D411yescharacteristic
111#3752D411yescharacteristic
112C4⋊(C3⋊Dic3)—21no—
113C4⋊(C3⋊Dic3)—21no—
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)D411yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3—21no—
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123#3746—41no—
124#3744—41no—
125#3743—41no—
126C8×C3⋊D3—41no—
127#3311—91noSylow
128C2×#237—34no—
129C2×D3×D4—34no—
130C3×C4⋊Q8C2×D314yescomplemented
131C3×C4×D4C2×D314yes—
132#947—64no—
133Q8×Dic3—64no—
134C2×#214—34no—
135#930—64no—
136C2×(C2×D3)⋊C4—64no—
137C2×Dic12—34no—
138C2×#204—34no—
139C2×ΓL(1,𝔽25)—34no—
140C2×D3×C8—34no—
141#898—64no—
142#898—64no—
143#897—34no—
144#897—34no—
145#897—34no—
146#895—34no—
147#892—34no—
148#892—34no—
149#886—64no—
150#882—64no—
151#875—34no—
152C4×D12—34no—
153C4×Dic6—34no—
154C3×#106C2×D314yescomplemented
155C3×#106C2×D314yescomplemented
156C3×C4⋊C8C2×D314yescomplemented
157C3×#102C2×D314yes—
158C3×#102C2×D314yes—
159#832—34no—
160#821—34no—
161(C2×D3)⋊C8—34no—
162(C2×D3)⋊C8—34no—
163#816—34no—
164#810—34no—
165#810—34no—
166#810—34no—
167#809—34no—
168#809—34no—
169#807—34no—
170#803—34no—
171C23×C32—21no—
172C22×C3⋊D3—21no—
173C22×C3⋊D3—42no—
174C22×C3⋊D3—42no—
175C22×C3⋊D3—81no—
176C22×C3⋊D3C2×D411yescharacteristic
177C22×C3⋊D3C2×D411yescharacteristic
178C32×Q8—42no—
179C32×D4—21no—
180C32×D4#4112yes—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—81no—
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2411yescharacteristic
188#638—42no—
189#638—42no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3—42no—
194C2×C3⋊Dic3C2×D411yescharacteristic
195C2×C3⋊Dic3C2×D411yescharacteristic
196C4⋊(C3⋊D3)—21no—
197C4⋊(C3⋊D3)—21no—
198C4⋊(C3⋊D3)—41no—
199C4⋊(C3⋊D3)—81no—
200C4×C3⋊D3—21no—
201C4×C3⋊D3—21no—
202C4×C3⋊D3—21no—
203C4×C3⋊D3—21no—
204#634—21no—
205#634—21no—
206#634—21no—
207#634—21no—
208C32×C8—21no—
209C32×C8—21no—
210C3⋊(C3⋊C8)—21no—
211C3⋊(C3⋊C8)—21no—
212#556—91no—
213#546—91no—
214#489—91no—
215#485—91no—
216#482—91no—
217#476C3⋊D311yescharacteristic, complemented
218#470—91no—
219#465—91no—
220#464—91no—
221#452—91no—
222#450—91no—
223#440—91no—
224#435—91no—
225#418—91no—
226#416—91no—
227C23×D3—64no—
228C2×C3×Q8—24no—
229C2×C3×D4C22×D314yes—
230C22×C3×C4—24no—
231C2×#67—64no—
232C2×#67—64no—
233C22×Dic3—64no—
234#237—68no—
235#237—124no—
236D3×D4—68no—
237D3×D4—124no—
238C2×D12—34no—
239C2×D12—34no—
240C2×D12—64no—
241C2×C4×D3—34no—
242C2×C4×D3—34no—
243C2×Dic6—34no—
244C2×Dic6—34no—
245C2×C3×C8C22×D314yes—
246C2×C3×C8C22×D314yes—
247C3×C4⋊C4—24no—
248C3×C4⋊C4C22×D314yes—
249C3×C4⋊C4C22×D314yes—
250C3×C4⋊C4C22×D314yes—
251C3×C22⋊C4—24no—
252C3×C42C22×D314yes—
253#214—68no—
254(C2×D3)⋊C4—34no—
255(C2×D3)⋊C4—34no—
256(C2×D3)⋊C4—64no—
257(C2×D3)⋊C4—64no—
258(C2×D3)⋊C4—64no—
259(C2×D3)⋊C4—64no—
260(C2×D3)⋊C4—64no—
261(C2×D3)⋊C4—64no—
262(C2×D3)⋊C4—64no—
263(C2×D3)⋊C4—64no—
264C4⋊Dic3—34no—
265C4⋊Dic3—34no—
266C4⋊Dic3—64no—
267C4⋊Dic3—64no—
268C4⋊Dic3—64no—
269Dic3⋊C4—64no—
270C4×Dic3—64no—
271C4×Dic3—64no—
272C4×Dic3—64no—
273C2×C3⋊C8—34no—
274C2×C3⋊C8—34no—
275Dic12—124no—
276#204—124no—
277ΓL(1,𝔽25)—124no—
278D3×C8—124no—
279C22×C32—22no—
280C22×C32—41no—
281C22×C32—41no—
282C22×C32C22×D411yescharacteristic
283C2×C3⋊D3—21no—
284C2×C3⋊D3—21no—
285C2×C3⋊D3—21no—
286C2×C3⋊D3—21no—
287C2×C3⋊D3—21no—
288C2×C3⋊D3—21no—
289C2×C3⋊D3—41no—
290C2×C3⋊D3—41no—
291C2×C3⋊D3—41no—
292C2×C3⋊D3—84no—
293C32×C4—21no—
294C32×C4—21no—
295C32×C4—41no—
296C32×C4—41no—
297C32×C4—41no—
298C32×C4C2×#4111yescharacteristic
299C32×C4H(5,𝔽2)11yescharacteristic
300C3⋊Dic3—21no—
301C3⋊Dic3—21no—
302C3⋊Dic3—41no—
303C3⋊Dic3—41no—
304C3⋊Dic3—41no—
305C2×#41—91no—
306C22×D4—91no—
307C2×Q16—91no—
308C2×SD16—91no—
309C2×SD16—91no—
310C2×M16—91no—
311C22×C8—91no—
312C4⋊Q8C2×C3⋊D311yescharacteristic, complemented
313#126—181no—
314#126—181no—
315#124—91no—
316#124—181no—
317#123—181no—
318C22⋊Q8—91no—
319C22⋊Q8—91no—
320C22⋊Q8—91no—
321#121—91no—
322#121—181no—
323#120—181no—
324C4×Q8—91no—
325C4×Q8—181no—
326C4×D4—91no—
327C4×D4C2×C3⋊D311yescharacteristic
328#117—91no—
329#117—91no—
330C2×C22⋊C4—181no—
331#107—91no—
332#106C2×C3⋊D311yescharacteristic, complemented
333#106C2×C3⋊D311yescharacteristic, complemented
334C4⋊C8C2×C3⋊D311yescharacteristic, complemented
335#103—91no—
336#103—91no—
337#103—91no—
338#103—91no—
339#102—91no—
340#102—91no—
341#102—91no—
342#102—91no—
343#102C2×C3⋊D311yescharacteristic
344#102C2×C3⋊D311yescharacteristic
345C22⋊C8—91no—
346C22⋊C8—91no—
347#97—91no—
348C23×C3—24no—
349C22×D3—34no—
350C22×D3—34no—
351C22×D3—64no—
352C22×D3—128no—
353C22×D3—128no—
354C22×D3—244no—
355C3×Q8—48no—
356C3×D4—24no—
357C3×D4#23918yes—
358C2×C3×C4—24no—
359C2×C3×C4—24no—
360C2×C3×C4—24no—
361C2×C3×C4—84no—
362C2×C3×C4D3×D414yes—
363C2×C3×C4D3×D414yes—
364C2×C3×C4C23×D314yes—
365#67—128no—
366#67—128no—
367C2×Dic3—34no—
368C2×Dic3—34no—
369C2×Dic3—64no—
370C2×Dic3—64no—
371C2×Dic3—64no—
372C2×Dic3—128no—
373D12—64no—
374D12—64no—
375D12—124no—
376D12—244no—
377C4×D3—64no—
378C4×D3—64no—
379C4×D3—64no—
380C4×D3—64no—
381Dic6—64no—
382Dic6—64no—
383Dic6—64no—
384Dic6—64no—
385C3×C8—24no—
386C3×C8—24no—
387C3⋊C8—64no—
388C3⋊C8—64no—
389C2×C32—42no—
390C2×C32#54611yescharacteristic
391C2×C32#57511yescharacteristic
392C2×C32#57711yescharacteristic
393C3⋊D3—41no—
394C3⋊D3—41no—
395C3⋊D3—81no—
396C24—181no—
397#41—182no—
398#41—361no—
399C2×Q8—21no—
400C2×Q8—91no—
401C2×Q8—91no—
402C2×D4—91no—
403C2×D4—91no—
404C2×D4—181no—
405C2×D4—181no—
406C2×D4—182no—
407C2×D4—181no—
408C2×D4—361no—
409C2×D4C22×C3⋊D311yescharacteristic
410C22×C4—21no—
411C22×C4—91no—
412C22×C4—91no—
413C22×C4—181no—
414Q16—361no—
415SD16—182no—
416SD16—361no—
417M16—361no—
418C2×C8—91no—
419C2×C8—91no—
420C2×C8—361no—
421C2×C8C22×C3⋊D311yescharacteristic
422C2×C8C22×C3⋊D311yescharacteristic
423C4⋊C4—21no—
424C4⋊C4—91no—
425C4⋊C4—91no—
426C4⋊C4—181no—
427C4⋊C4—181no—
428C4⋊C4—181no—
429C4⋊C4—181no—
430C4⋊C4C22×C3⋊D311yescharacteristic
431C4⋊C4C22×C3⋊D311yescharacteristic
432C4⋊C4C22×C3⋊D311yescharacteristic
433C22⋊C4—21no—
434C22⋊C4—91no—
435C22⋊C4—91no—
436C22⋊C4—181no—
437C22⋊C4—181no—
438C22⋊C4—181no—
439C22⋊C4—181no—
440C22⋊C4—181no—
441C22⋊C4—181no—
442C22⋊C4—181no—
443C22⋊C4—181no—
444C42—181no—
445C42—181no—
446C42—181no—
447C42C22×C3⋊D311yescharacteristic
448C22×C3—28no—
449C22×C3—44no—
450C22×C3—44no—
451C22×C3C2×D3×D414yes—
452C2×D3—64no—
453C2×D3—64no—
454C2×D3—64no—
455C2×D3—64no—
456C2×D3—64no—
457C2×D3—64no—
458C2×D3—124no—
459C2×D3—124no—
460C2×D3—124no—
461C2×D3—2416no—
462C3×C4—24no—
463C3×C4—24no—
464C3×C4—44no—
465C3×C4—44no—
466C3×C4—44no—
467C3×C4C2×#23914yes—
468C3×C4#100914yes—
469Dic3—64no—
470Dic3—64no—
471Dic3—124no—
472Dic3—124no—
473Dic3—124no—
474C32#331111yescharacteristic, complemented, Sylow
475C23—21no—
476C23—91no—
477C23—91no—
478C23—181no—
479C23—362no—
480C23—362no—
481C23—721no—
482Q8—42no—
483Q8—181no—
484Q8—181no—
485Q8—181no—
486Q8—181no—
487D4—21no—
488D4—181no—
489D4—181no—
490D4—361no—
491D4—362no—
492D4—362no—
493D4—721no—
494D4#383212yes—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—81no—
499C2×C4—91no—
500C2×C4—91no—
501C2×C4—181no—
502C2×C4—181no—
503C2×C4—181no—
504C2×C4—181no—
505C2×C4—181no—
506C2×C4—181no—
507C2×C4—181no—
508C2×C4—362no—
509C2×C4D4×C3⋊D311yescharacteristic
510C2×C4D4×C3⋊D311yescharacteristic
511C2×C4C23×C3⋊D311yescharacteristic
512C8—21no—
513C8—21no—
514C8—181no—
515C8—181no—
516C2×C3—48no—
517C2×C3#563014yes—
518C2×C3#576214yes—
519C2×C3#577314yes—
520D3—124no—
521D3—124no—
522D3—244no—
523C22—22no—
524C22—41no—
525C22—41no—
526C22—181no—
527C22—181no—
528C22—181no—
529C22—181no—
530C22—181no—
531C22—181no—
532C22—361no—
533C22—361no—
534C22—361no—
535C22—724no—
536C22C2×D4×C3⋊D311yescharacteristic
537C4—21no—
538C4—21no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—181no—
543C4—181no—
544C4—361no—
545C4—361no—
546C4—361no—
547C4C2×#383211yescharacteristic
548C4#6436611yescharacteristic
549C3#8107814yescomplemented
550C2—42no—
551C2—361no—
552C2—361no—
553C2—721no—
554C2#1059610111yescharacteristic
555C2#1059623311yescharacteristic
556C2#1059624411yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#476C2
socleC22×C32C22×D4
prime radical#10596025C2
hypercenter#476C3⋊D3
hypocenterC32#3311
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #10596203C2semidirect
3. C32×#476C2semidirect
4. #10592788C2semidirect
5. #10592717C2semidirect
6. #10592567C2semidirect
7. #10592566C2semidirect
8. #10592565C2semidirect
9. #10592563C2semidirect
10. #10592544C2semidirect
11. #10592535C2semidirect
12. #10592482C2semidirect
13. #10592475C2semidirect
14. #10592471C2semidirect
15. #10592469C2semidirect
19. C32×C4⋊Q8C22semidirect
26. C2×#3746C22semidirect
29. C2×C8×C3⋊D3C22semidirect
34. #64106C22semidirect
37. #64101C22semidirect
42. C4×#634C22semidirect
43. C32×#106C22semidirect
44. C32×#106C22semidirect
45. C32×C4⋊C8C22semidirect
51. #63647C22semidirect
52. #63643C22semidirect
53. #63637C22semidirect
54. #63637C22semidirect
55. #63637C22semidirect
58. #63634C22semidirect
59. #63630C22semidirect
62. C3×#476D3semidirect
130. C3×C4⋊Q8C2×D3semidirect
154. C3×#106C2×D3semidirect
155. C3×#106C2×D3semidirect
156. C3×C4⋊C8C2×D3semidirect
217. #476C3⋊D3semidirect
312. C4⋊Q8C2×C3⋊D3semidirect
332. #106C2×C3⋊D3semidirect
333. #106C2×C3⋊D3semidirect
334. C4⋊C8C2×C3⋊D3semidirect
474. C32#3311semidirect
549. C3#81078semidirect

Maximal subgroups

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

subgroupindex
#105962032
#105960252
C32×#4762
#105927882
#105927172
#105925672
#105925662
#105925652
#105925632
#105925442
#105925352
#105924822
#105924752
#105924712
#105924692
#810783