Subgroups — C₂³×#90779 #16832652

Order 3712.

2488 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×Dic₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×Dic₂₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×#90779	C₂	1	28	yes	maximal, direct product factor
4	C₂⁴×C₄×C₂₉	C₂	1	1	yes	maximal, characteristic
5	C₂⁵×C₂₉	C₂²	1	1	yes	characteristic
6	C₂³×C₄×C₂₉	—	2	8	no	—
7	C₂³×C₄×C₂₉	C₂²	1	14	yes	—
8	C₂³×Dic₂₉	—	2	8	no	—
9	C₂³×Dic₂₉	C₄	1	16	yes	complemented
10	C₂³×Dic₂₉	C₂²	1	14	yes	—
11	C₂³×Dic₂₉	C₂²	1	14	yes	—
12	C₂×#90779	C₂²	1	112	yes	direct product factor
13	C₂⁴×C₂₉	C₂×C₄	1	8	yes	—
14	C₂⁴×C₂₉	D₄	1	8	yes	—
15	C₂⁴×C₂₉	Q₈	1	8	yes	—
16	C₂⁴×C₂₉	C₂³	1	7	yes	—
17	C₂²×C₄×C₂₉	—	2	56	no	—
18	C₂²×C₄×C₂₉	C₂³	1	28	yes	—
19	C₂²×Dic₂₉	—	2	56	no	—
20	C₂²×Dic₂₉	C₂×C₄	1	112	yes	complemented
21	C₂²×Dic₂₉	C₂³	1	28	yes	—
22	C₂²×Dic₂₉	C₂³	1	28	yes	—
23	#90779	C₂³	1	64	yes	direct product factor
24	C₂³×C₂₉	C₄⋊C₄	1	64	yes	complemented
25	C₂³×C₂₉	C₂²×C₄	1	28	yes	—
26	C₂³×C₂₉	C₂×D₄	1	28	yes	—
27	C₂³×C₂₉	C₂×Q₈	1	28	yes	—
28	C₂³×C₂₉	C₂⁴	1	7	yes	—
29	C₂×C₄×C₂₉	—	2	56	no	—
30	C₂×C₄×C₂₉	C₂⁴	1	8	yes	—
31	C₂×Dic₂₉	—	2	56	no	—
32	C₂×Dic₂₉	C₂²×C₄	1	112	yes	complemented
33	C₂×Dic₂₉	C₂⁴	1	8	yes	—
34	C₂×Dic₂₉	C₂⁴	1	8	yes	—
35	C₂³×C₄⋊C₄	—	29	1	no	maximal, Sylow
36	C₂²×C₂₉	C₂×C₄⋊C₄	1	112	yes	complemented
37	C₂²×C₂₉	C₂³×C₄	1	14	yes	—
38	C₂²×C₂₉	C₂²×D₄	1	14	yes	—
39	C₂²×C₂₉	C₂²×Q₈	1	14	yes	—
40	C₂²×C₂₉	C₂⁵	1	1	yes	characteristic
41	C₄×C₂₉	—	2	8	no	—
42	Dic₂₉	—	2	8	no	—
43	Dic₂₉	C₂³×C₄	1	16	yes	complemented
44	C₂⁴×C₄	—	29	1	no	—
45	C₂⁴×C₄	—	29	1	no	—
46	C₂⁴×C₄	D₂₉	1	1	yes	characteristic
47	C₂²×C₄⋊C₄	—	29	28	no	—
48	C₂×C₂₉	C₂²×C₄⋊C₄	1	28	yes	complemented
49	C₂×C₂₉	C₂⁴×C₄	1	1	yes	characteristic
50	C₂×C₂₉	C₂³×D₄	1	1	yes	characteristic
51	C₂×C₂₉	C₂³×Q₈	1	1	yes	characteristic
52	C₂⁵	C₂×D₂₉	1	1	yes	characteristic
53	C₂³×C₄	—	2	8	no	—
54	C₂³×C₄	—	29	16	no	—
55	C₂³×C₄	—	29	14	no	—
56	C₂³×C₄	—	29	14	no	—
57	C₂³×C₄	—	58	8	no	—
58	C₂³×C₄	C₂×D₂₉	1	14	yes	—
59	C₂×C₄⋊C₄	—	29	112	no	—
60	C₂₉	C₂³×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
61	C₂⁴	Dic₅₈	1	8	yes	—
62	C₂⁴	C₄×D₂₉	1	8	yes	—
63	C₂⁴	C₂²⋊D₂₉	1	8	yes	—
64	C₂⁴	C₂²×D₂₉	1	7	yes	—
65	C₂²×C₄	—	2	56	no	—
66	C₂²×C₄	—	29	112	no	—
67	C₂²×C₄	—	29	28	no	—
68	C₂²×C₄	—	29	28	no	—
69	C₂²×C₄	—	58	56	no	—
70	C₂²×C₄	C₂²×D₂₉	1	28	yes	—
71	C₄⋊C₄	—	29	64	no	—
72	C₂³	#90779	1	64	yes	direct product factor
73	C₂³	C₂×Dic₅₈	1	28	yes	—
74	C₂³	C₂×C₄×D₂₉	1	28	yes	—
75	C₂³	C₂×C₂²⋊D₂₉	1	28	yes	—
76	C₂³	C₂³×D₂₉	1	7	yes	—
77	C₂×C₄	—	2	56	no	—
78	C₂×C₄	—	29	112	no	—
79	C₂×C₄	—	29	8	no	—
80	C₂×C₄	—	29	8	no	—
81	C₂×C₄	—	58	56	no	—
82	C₂×C₄	C₂³×D₂₉	1	8	yes	—
83	C₂²	C₂×#90779	1	112	yes	direct product factor
84	C₂²	C₂²×Dic₅₈	1	14	yes	—
85	C₂²	C₂²×C₄×D₂₉	1	14	yes	—
86	C₂²	C₂²×C₂²⋊D₂₉	1	14	yes	—
87	C₂²	C₂⁴×D₂₉	1	1	yes	characteristic
88	C₄	—	2	8	no	—
89	C₄	—	29	16	no	—
90	C₄	—	58	8	no	—
91	C₂	C₂²×#90779	1	28	yes	direct product factor
92	C₂	C₂³×C₄×D₂₉	1	1	yes	characteristic
93	C₂	C₂³×C₂²⋊D₂₉	1	1	yes	characteristic
94	C₂	C₂³×Dic₅₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁵	C₂×D₂₉
commutator	C₂×C₂₉	C₂⁴×C₄
Frattini	C₂²	C₂⁴×D₂₉
Fitting	C₂⁴×C₄×C₂₉	C₂
socle, prime radical	C₂⁵×C₂₉	C₂²
cosocle	C₂²×C₂₉	C₂⁵
hypercenter	C₂⁴×C₄	D₂₉
hypocenter	C₂₉	C₂³×C₄⋊C₄
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂⁵ ◁ C₂⁴×C₄

Complements

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

N	H ≅ G/N	type
3. C₂²×#90779	C₂	direct (N × H)
9. C₂³×Dic₂₉	C₄	semidirect
12. C₂×#90779	C₂²	direct (N × H)
20. C₂²×Dic₂₉	C₂×C₄	semidirect
23. #90779	C₂³	direct (N × H)
24. C₂³×C₂₉	C₄⋊C₄	semidirect
32. C₂×Dic₂₉	C₂²×C₄	semidirect
36. C₂²×C₂₉	C₂×C₄⋊C₄	semidirect
43. Dic₂₉	C₂³×C₄	semidirect
48. C₂×C₂₉	C₂²×C₄⋊C₄	semidirect
60. C₂₉	C₂³×C₄⋊C₄	semidirect
72. C₂³	#90779	direct (N × H)
83. C₂²	C₂×#90779	direct (N × H)
91. C₂	C₂²×#90779	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×Dic₂₉	2
C₂²×#90779	2
C₂⁴×C₄×C₂₉	2
C₂³×C₄⋊C₄	29

Subgroups — C23×#90779 #16832652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#90779 #16832652