Subgroups — #26018299

Order 11392.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19151975	C₂	1	1	yes	maximal, characteristic
2	#19151351	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊C₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₇₁₂	—	2	1	no	—
5	C₂×D₇₁₂	C₄	1	2	yes	—
6	#15668009	—	2	1	no	—
7	C₄⋊#10623494	—	2	1	no	—
8	C₂×C₁₆×C₈₉	—	2	1	no	—
9	C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
10	C₂×D₃₅₆	—	2	2	no	—
11	C₂×D₃₅₆	—	4	1	no	—
12	C₂×D₃₅₆	—	4	1	no	—
13	D₇₁₂	—	4	2	no	—
14	D₇₁₂	—	4	1	no	—
15	D₇₁₂	—	4	1	no	—
16	C₂×#10623494	—	4	1	no	—
17	C₂×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₈₉	D₄	1	1	yes	characteristic
19	C₄²×C₈₉	D₄	1	1	yes	characteristic
20	C₁₆×C₈₉	—	4	1	no	—
21	C₂²×D₈₉	—	4	2	no	—
22	C₂×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₈₉	D₈	1	1	yes	characteristic
24	C₂×C₄×C₈₉	SD₁₆	1	1	yes	characteristic
25	D₃₅₆	—	4	2	no	—
26	D₃₅₆	—	4	2	no	—
27	D₃₅₆	—	8	2	no	—
28	D₃₅₆	—	8	1	no	—
29	D₃₅₆	—	8	1	no	—
30	C₈×C₈₉	—	2	1	no	—
31	C₈×C₈₉	D₈	1	1	yes	characteristic
32	C₈×C₈₉	SD₁₆	1	1	yes	characteristic
33	#10623494	—	8	1	no	—
34	C₂²×C₈₉	#102	1	1	yes	characteristic
35	C₂×D₈₉	—	8	2	no	—
36	C₂×D₈₉	—	8	2	no	—
37	C₂×D₈₉	—	8	2	no	—
38	C₄×C₈₉	—	2	1	no	—
39	C₄×C₈₉	#100	1	1	yes	characteristic
40	C₄×C₈₉	#102	1	1	yes	characteristic
41	C₄×C₈₉	D₁₆	1	1	yes	characteristic
42	C₄×C₈₉	SD₃₂	1	1	yes	characteristic
43	C₂×C₈₉	#331	1	1	yes	characteristic
44	C₂×C₈₉	#357	1	1	yes	characteristic
45	C₂×C₈₉	#361	1	1	yes	characteristic
46	D₈₉	—	16	2	no	—
47	#1361	—	89	1	no	maximal, Sylow
48	C₈₉	#1361	1	1	yes	characteristic, complemented, Sylow
49	#493	—	89	1	no	—
50	C₄⋊C₁₆	D₈₉	1	1	yes	characteristic, complemented
51	#335	—	89	1	no	—
52	C₂×D₈	—	89	2	no	—
53	C₂×D₈	—	178	1	no	—
54	#127	—	178	1	no	—
55	C₂×C₁₆	—	2	1	no	—
56	C₄⋊C₈	—	178	1	no	—
57	C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
58	C₂×D₄	—	356	1	no	—
59	C₂×D₄	—	356	1	no	—
60	C₂×D₄	—	178	2	no	—
61	D₈	—	356	2	no	—
62	D₈	—	356	1	no	—
63	D₈	—	356	1	no	—
64	C₂×C₈	—	356	1	no	—
65	C₂×C₈	C₄×D₈₉	1	1	yes	characteristic
66	C₂×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
67	C₄²	D₃₅₆	1	1	yes	characteristic
68	C₁₆	—	4	1	no	—
69	C₂³	—	356	2	no	—
70	D₄	—	356	2	no	—
71	D₄	—	356	2	no	—
72	D₄	—	712	2	no	—
73	D₄	—	712	1	no	—
74	D₄	—	712	1	no	—
75	C₂×C₄	#13083551	1	1	yes	characteristic
76	C₂×C₄	D₇₁₂	1	1	yes	characteristic
77	C₂×C₄	#13083563	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	712	1	no	—
80	C₈	#13083559	1	1	yes	characteristic
81	C₈	#13083561	1	1	yes	characteristic
82	C₂²	—	712	2	no	—
83	C₂²	—	712	2	no	—
84	C₂²	—	712	2	no	—
85	C₂²	#15667934	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	#15667928	1	1	yes	characteristic
88	C₄	#15667932	1	1	yes	characteristic
89	C₄	D₁₄₂₄	1	1	yes	characteristic
90	C₄	#15667957	1	1	yes	characteristic
91	C₂	—	1424	2	no	—
92	C₂	#19151341	1	1	yes	characteristic
93	C₂	#19151400	1	1	yes	characteristic
94	C₂	#19151412	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#15667934
commutator	C₂×C₈×C₈₉	C₂×C₄
Frattini	C₄×C₈	C₂×D₈₉
Fitting	C₄⋊C₁₆×C₈₉	C₂
socle	C₂²×C₈₉	#102
prime radical	#19151975	C₂
cosocle	C₄×C₈×C₈₉	C₂²
hypercenter	C₄⋊C₁₆	D₈₉
hypocenter	C₈₉	#1361
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
2. #19151351	C₂	semidirect
3. C₄⋊C₁₆×C₈₉	C₂	semidirect
48. C₈₉	#1361	semidirect
50. C₄⋊C₁₆	D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19151975	2
#19151351	2
C₄⋊C₁₆×C₈₉	2
#1361	89