Subgroups — #26018325

Order 11392.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13083549	C₂	1	1	yes	maximal, characteristic
2	#19151351	C₂	1	1	yes	maximal, characteristic
3	#335×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#13083549	C₄	1	1	yes	characteristic
5	C₂×#13083549	C₄	1	1	yes	characteristic
6	C₄⋊#10623494	—	2	1	no	—
7	C₄⋊C₈×C₈₉	—	2	1	no	—
8	C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
9	C₂×#10623494	—	4	1	no	—
10	#13083549	—	2	1	no	—
11	#13083549	C₈	1	2	yes	complemented
12	C₂×C₈×C₈₉	—	4	1	no	—
13	C₂×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₈₉	Q₈	1	1	yes	characteristic
15	C₄²×C₈₉	D₄	1	1	yes	characteristic
16	C₂×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
17	C₂×C₄×C₈₉	D₈	1	1	yes	characteristic
18	C₂×C₄×C₈₉	Q₁₆	1	1	yes	characteristic
19	C₈×C₈₉	—	2	1	no	—
20	C₈×C₈₉	—	8	1	no	—
21	C₈×C₈₉	C₂×C₈	1	1	yes	characteristic
22	C₈×C₈₉	M₁₆	1	1	yes	characteristic
23	#10623494	—	8	1	no	—
24	C₂²×C₈₉	#107	1	1	yes	characteristic
25	C₄×C₈₉	—	2	1	no	—
26	C₄×C₈₉	C₄⋊C₈	1	1	yes	characteristic
27	C₄×C₈₉	#108	1	1	yes	characteristic
28	C₄×C₈₉	SD₃₂	1	1	yes	characteristic
29	C₄×C₈₉	SD₃₂	1	1	yes	characteristic
30	C₂×C₈₉	#335	1	1	yes	characteristic
31	C₂×C₈₉	#367	1	1	yes	characteristic
32	C₂×C₈₉	#368	1	1	yes	characteristic
33	#1372	—	89	1	no	maximal, Sylow
34	C₈₉	#1372	1	1	yes	characteristic, complemented, Sylow
35	C₄×C₁₆	—	89	1	no	—
36	#335	—	89	1	no	—
37	#335	D₈₉	1	1	yes	characteristic
38	C₂×C₁₆	—	89	1	no	—
39	C₂×C₁₆	—	89	1	no	—
40	C₄⋊C₈	—	2	1	no	—
41	C₄⋊C₈	—	178	1	no	—
42	C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
43	C₂×C₈	—	4	1	no	—
44	C₂×C₈	—	356	1	no	—
45	C₂×C₈	Dic₁₇₈	1	1	yes	characteristic
46	C₂×C₈	C₄×D₈₉	1	1	yes	characteristic
47	C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
48	C₁₆	—	89	2	no	—
49	C₁₆	—	178	1	no	—
50	C₂×C₄	#13083553	1	1	yes	characteristic
51	C₂×C₄	#13083559	1	1	yes	characteristic
52	C₂×C₄	#13083564	1	1	yes	characteristic
53	C₈	—	2	1	no	—
54	C₈	—	8	1	no	—
55	C₈	—	712	1	no	—
56	C₈	C₈×D₈₉	1	1	yes	characteristic
57	C₈	#13083557	1	1	yes	characteristic
58	C₂²	#15667945	1	1	yes	characteristic
59	C₄	—	2	1	no	—
60	C₄	#15667941	1	1	yes	characteristic
61	C₄	#15667947	1	1	yes	characteristic
62	C₄	#15667955	1	1	yes	characteristic
63	C₄	#15667956	1	1	yes	characteristic
64	C₂	#19151350	1	1	yes	characteristic
65	C₂	#19151425	1	1	yes	characteristic
66	C₂	#19151427	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13083559
commutator	C₈×C₈₉	C₂×C₈
Frattini	C₄×C₈	C₂×D₈₉
Fitting	#335×C₈₉	C₂
socle, prime radical	C₂²×C₈₉	#107
cosocle	C₄×C₈×C₈₉	C₂²
hypercenter	#335	D₈₉
hypocenter	C₈₉	#1372
LCS	G ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ #335

Complements

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

N	H ≅ G/N	type
11. #13083549	C₈	semidirect
34. C₈₉	#1372	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13083549	2
#19151351	2
#335×C₈₉	2
#1372	89