Subgroups — C₂×#14270918 #16819183

Order 3712.

528 conjugacy classes of subgroups.

The subgroup lattice has 142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#6597	C₂	1	2	yes	maximal
2	#14270918	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₄²×C₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₄×C₂₉	C₄	1	2	yes	—
5	C₂³×C₄×C₂₉	C₂²	1	1	yes	characteristic
6	C₂×C₄²×C₂₉	—	2	4	no	—
7	C₂×C₄²×C₂₉	C₄	1	2	yes	—
8	C₂×C₄²×C₂₉	C₂²	1	2	yes	—
9	C₂²×#6597	—	2	4	no	—
10	C₂²×#6597	—	2	4	no	—
11	C₂²×#6597	C₄	1	8	yes	complemented
12	C₂²×#6597	C₂²	1	4	yes	—
13	C₂⁴×C₂₉	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₄×C₂₉	—	2	4	no	—
15	C₂²×C₄×C₂₉	—	2	4	no	—
16	C₂²×C₄×C₂₉	C₈	1	8	yes	complemented
17	C₂²×C₄×C₂₉	C₂×C₄	1	4	yes	—
18	C₂²×C₄×C₂₉	C₂×C₄	1	4	yes	—
19	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₄×C₂₉	D₄	1	2	yes	—
21	C₂²×C₄×C₂₉	D₄	1	4	yes	—
22	C₂²×C₄×C₂₉	Q₈	1	2	yes	—
23	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
24	C₄²×C₂₉	—	2	4	no	—
25	C₄²×C₂₉	—	2	4	no	—
26	C₂×#6597	—	2	16	no	—
27	C₂×#6597	—	2	4	no	—
28	C₂×#6597	—	2	4	no	—
29	C₂×#6597	C₂×C₄	1	8	yes	complemented
30	C₂³×C₂₉	C₄²	1	2	yes	—
31	C₂³×C₂₉	C₂²⋊C₄	1	2	yes	—
32	C₂³×C₂₉	C₄⋊C₄	1	2	yes	—
33	C₂³×C₂₉	C₂×C₈	1	4	yes	—
34	C₂³×C₂₉	M₁₆	1	4	yes	—
35	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₂₉	—	2	16	no	—
37	C₂×C₄×C₂₉	—	2	4	no	—
38	C₂×C₄×C₂₉	—	2	4	no	—
39	C₂×C₄×C₂₉	C₄²	1	2	yes	—
40	C₂×C₄×C₂₉	C₂²⋊C₄	1	8	yes	—
41	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
42	C₂×C₄×C₂₉	C₄⋊C₄	1	8	yes	—
43	C₂×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
44	C₂×C₄×C₂₉	C₂×C₈	1	8	yes	complemented
45	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
46	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
48	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
49	#6597	—	2	8	no	—
50	C₂×#336	—	29	1	no	maximal, Sylow
51	C₂²×C₂₉	#95	1	4	yes	—
52	C₂²×C₂₉	C₄×C₈	1	4	yes	—
53	C₂²×C₂₉	#97	1	4	yes	—
54	C₂²×C₂₉	C₂²⋊C₈	1	8	yes	—
55	C₂²×C₂₉	C₄⋊C₈	1	8	yes	—
56	C₂²×C₂₉	C₂×C₄²	1	1	yes	characteristic
57	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
58	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
59	C₂²×C₂₉	C₂²×C₈	1	2	yes	—
60	C₂²×C₂₉	C₂×M₁₆	1	2	yes	—
61	C₄×C₂₉	—	2	8	no	—
62	C₄×C₂₉	#95	1	4	yes	—
63	C₄×C₂₉	C₂×C₂²⋊C₄	1	2	yes	—
64	C₄×C₂₉	C₂×C₄⋊C₄	1	2	yes	—
65	C₂³×C₈	—	29	2	no	—
66	C₂²×C₄²	D₂₉	1	1	yes	characteristic
67	#336	—	29	4	no	—
68	C₂×C₂₉	#336	1	8	yes	complemented
69	C₂×C₂₉	C₂×#95	1	1	yes	characteristic
70	C₂×C₂₉	C₂×C₄×C₈	1	1	yes	characteristic
71	C₂×C₂₉	C₂×#97	1	1	yes	characteristic
72	C₂×C₂₉	C₂×C₂²⋊C₈	1	2	yes	—
73	C₂×C₂₉	C₂×C₄⋊C₈	1	2	yes	—
74	C₂³×C₄	Dic₂₉	1	2	yes	—
75	C₂³×C₄	C₂×D₂₉	1	1	yes	characteristic
76	C₂²×C₈	—	29	8	no	—
77	C₂²×C₈	—	29	4	no	—
78	C₂²×C₈	—	58	4	no	—
79	C₂²×C₈	—	58	4	no	—
80	C₂×C₄²	—	2	4	no	—
81	C₂×C₄²	Dic₂₉	1	2	yes	—
82	C₂×C₄²	C₂×D₂₉	1	2	yes	—
83	C₂₉	C₂×#336	1	1	yes	characteristic, complemented, Sylow
84	C₂⁴	C₂×Dic₂₉	1	1	yes	characteristic
85	C₂²×C₄	—	2	4	no	—
86	C₂²×C₄	—	2	4	no	—
87	C₂²×C₄	#6597	1	8	yes	complemented
88	C₂²×C₄	Dic₅₈	1	2	yes	—
89	C₂²×C₄	C₄×D₂₉	1	4	yes	—
90	C₂²×C₄	D₁₁₆	1	2	yes	—
91	C₂²×C₄	C₂×Dic₂₉	1	4	yes	—
92	C₂²×C₄	C₂×Dic₂₉	1	1	yes	characteristic
93	C₂²×C₄	C₂²⋊D₂₉	1	4	yes	—
94	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
95	C₂×C₈	—	29	8	no	—
96	C₂×C₈	—	58	16	no	—
97	C₂×C₈	—	58	4	no	—
98	C₂×C₈	—	58	4	no	—
99	C₄²	—	2	4	no	—
100	C₄²	—	2	4	no	—
101	C₂³	C₂×#6597	1	4	yes	—
102	C₂³	#90777	1	4	yes	—
103	C₂³	C₄×Dic₂₉	1	2	yes	—
104	C₂³	C₄⋊Dic₂₉	1	2	yes	—
105	C₂³	C₂²⋊Dic₂₉	1	2	yes	—
106	C₂³	C₂²×Dic₂₉	1	1	yes	characteristic
107	C₂×C₄	—	2	4	no	—
108	C₂×C₄	—	2	4	no	—
109	C₂×C₄	—	2	16	no	—
110	C₂×C₄	C₂×#6597	1	8	yes	complemented
111	C₂×C₄	C₄×Dic₂₉	1	2	yes	—
112	C₂×C₄	#90779	1	8	yes	—
113	C₂×C₄	C₄⋊Dic₂₉	1	2	yes	—
114	C₂×C₄	#90781	1	8	yes	—
115	C₂×C₄	C₂²⋊Dic₂₉	1	2	yes	—
116	C₂×C₄	C₂×Dic₅₈	1	1	yes	characteristic
117	C₂×C₄	C₂×C₄×D₂₉	1	2	yes	—
118	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
119	C₂×C₄	C₂×C₂²⋊D₂₉	1	2	yes	—
120	C₈	—	58	8	no	—
121	C₂²	C₄×#6597	1	4	yes	—
122	C₂²	#11745151	1	4	yes	—
123	C₂²	C₄⋊#6597	1	8	yes	—
124	C₂²	C₂²⋊#6597	1	8	yes	—
125	C₂²	#11745179	1	4	yes	—
126	C₂²	C₂²×#6597	1	2	yes	—
127	C₂²	C₂×#90777	1	2	yes	—
128	C₂²	C₂×C₄×Dic₂₉	1	1	yes	characteristic
129	C₂²	C₂×C₄⋊Dic₂₉	1	1	yes	characteristic
130	C₂²	C₂×C₂²⋊Dic₂₉	1	1	yes	characteristic
131	C₄	—	2	8	no	—
132	C₄	#11745179	1	4	yes	—
133	C₄	C₂×#90779	1	2	yes	—
134	C₄	C₂×#90781	1	2	yes	—
135	C₂	#14270918	1	8	yes	direct product factor
136	C₂	C₂×#11745179	1	1	yes	characteristic
137	C₂	C₂×C₄×#6597	1	1	yes	characteristic
138	C₂	C₂×#11745151	1	1	yes	characteristic
139	C₂	C₂×C₂²⋊#6597	1	2	yes	—
140	C₂	C₂×C₄⋊#6597	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂×D₂₉
commutator	C₂×C₂₉	C₂×C₄×C₈
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂²×C₄²×C₂₉	C₂
socle, prime radical	C₂⁴×C₂₉	C₂×C₄
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	C₂²×C₄²	D₂₉
hypocenter	C₂₉	C₂×#336
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
2. #14270918	C₂	direct (N × H)
11. C₂²×#6597	C₄	semidirect
16. C₂²×C₄×C₂₉	C₈	semidirect
29. C₂×#6597	C₂×C₄	semidirect
44. C₂×C₄×C₂₉	C₂×C₈	semidirect
68. C₂×C₂₉	#336	semidirect
83. C₂₉	C₂×#336	semidirect
87. C₂²×C₄	#6597	semidirect
110. C₂×C₄	C₂×#6597	semidirect
135. C₂	#14270918	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#6597	2
#14270918	2
C₂²×C₄²×C₂₉	2
C₂×#336	29

Subgroups — C2×#14270918 #16819183

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14270918 #16819183