Subgroups — C₂×C₂₉×#418 #16816607

Order 3712.

1008 conjugacy classes of subgroups.

The subgroup lattice has 196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₄×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×M₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#418	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₂₉×#102	C₂	1	4	yes	maximal, complemented
6	C₂⁵×C₂₉	—	2	1	no	—
7	C₂²×D₄×C₂₉	—	2	2	no	—
8	C₂²×D₄×C₂₉	—	2	1	no	—
9	C₂²×D₄×C₂₉	—	2	4	no	—
10	C₂²×D₄×C₂₉	C₄	1	8	yes	complemented
11	C₂²×D₄×C₂₉	C₂²	1	2	yes	—
12	C₂²×D₄×C₂₉	C₂²	1	4	yes	—
13	C₂³×C₄×C₂₉	C₂²	1	1	yes	characteristic
14	C₂×M₁₆×C₂₉	—	2	4	no	—
15	C₂×M₁₆×C₂₉	C₂²	1	4	yes	complemented
16	C₂²×C₈×C₂₉	C₂²	1	2	yes	complemented
17	C₂₉×#117	—	2	2	no	—
18	C₂₉×#117	C₂²	1	4	yes	complemented
19	C₂×C₄⋊C₄×C₂₉	C₂²	1	2	yes	complemented
20	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
21	C₂×C₄²×C₂₉	—	2	1	no	—
22	C₂₉×#102	C₂²	1	16	yes	complemented
23	C₂⁴×C₂₉	—	2	8	no	—
24	C₂⁴×C₂₉	—	2	4	no	—
25	C₂⁴×C₂₉	—	2	2	no	—
26	C₂⁴×C₂₉	—	4	8	no	—
27	C₂⁴×C₂₉	D₄	1	1	yes	characteristic
28	C₂×D₄×C₂₉	—	2	16	no	—
29	C₂×D₄×C₂₉	—	2	8	no	—
30	C₂×D₄×C₂₉	—	2	4	no	—
31	C₂×D₄×C₂₉	—	2	2	no	—
32	C₂×D₄×C₂₉	—	2	4	no	—
33	C₂×D₄×C₂₉	—	2	8	no	—
34	C₂×D₄×C₂₉	C₂×C₄	1	8	yes	—
35	C₂×D₄×C₂₉	C₂×C₄	1	16	yes	complemented
36	C₂×D₄×C₂₉	C₂³	1	4	yes	—
37	C₂²×C₄×C₂₉	—	2	2	no	—
38	C₂²×C₄×C₂₉	C₂×C₄	1	4	yes	—
39	C₂²×C₄×C₂₉	D₄	1	2	yes	—
40	C₂²×C₄×C₂₉	D₄	1	1	yes	characteristic
41	C₂²×C₄×C₂₉	D₄	1	4	yes	—
42	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
43	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
44	M₁₆×C₂₉	—	2	8	no	—
45	C₂×C₈×C₂₉	—	2	4	no	—
46	C₂×C₈×C₂₉	C₂³	1	4	yes	complemented
47	C₄⋊C₄×C₂₉	—	2	2	no	—
48	C₄⋊C₄×C₂₉	C₂³	1	4	yes	complemented
49	C₂²⋊C₄×C₂₉	—	2	4	no	—
50	C₄²×C₂₉	—	2	4	no	—
51	C₂³×C₂₉	—	2	4	no	—
52	C₂³×C₂₉	—	2	8	no	—
53	C₂³×C₂₉	—	2	16	no	—
54	C₂³×C₂₉	—	2	4	no	—
55	C₂³×C₂₉	—	4	16	no	—
56	C₂³×C₂₉	—	4	32	no	—
57	C₂³×C₂₉	—	4	8	no	—
58	C₂³×C₂₉	C₂²⋊C₄	1	4	yes	—
59	C₂³×C₂₉	C₂×D₄	1	2	yes	—
60	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
61	D₄×C₂₉	—	2	8	no	—
62	D₄×C₂₉	—	2	16	no	—
63	D₄×C₂₉	—	2	4	no	—
64	D₄×C₂₉	C₂²×C₄	1	8	yes	—
65	C₂×C₄×C₂₉	—	2	4	no	—
66	C₂×C₄×C₂₉	—	4	4	no	—
67	C₂×C₄×C₂₉	C₂²⋊C₄	1	8	yes	—
68	C₂×C₄×C₂₉	C₂²⋊C₄	1	4	yes	—
69	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
70	C₂×C₄×C₂₉	C₂²×C₄	1	4	yes	—
71	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
72	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
73	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
74	C₂×C₄×C₂₉	C₂×D₄	1	4	yes	—
75	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
76	C₈×C₂₉	—	2	4	no	—
77	C₂×#418	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
78	C₂²×C₂₉	—	2	4	no	—
79	C₂²×C₂₉	—	2	8	no	—
80	C₂²×C₂₉	—	2	8	no	—
81	C₂²×C₂₉	—	4	32	no	—
82	C₂²×C₂₉	—	4	8	no	—
83	C₂²×C₂₉	—	4	16	no	—
84	C₂²×C₂₉	C₂×C₂²⋊C₄	1	4	yes	—
85	C₂²×C₂₉	C₂×C₂²⋊C₄	1	2	yes	—
86	C₂²×C₂₉	AGL(1,ℤ/8)	1	4	yes	—
87	C₂²×C₂₉	C₂²×D₄	1	1	yes	characteristic
88	C₄×C₂₉	—	4	4	no	—
89	C₄×C₂₉	C₂×C₂²⋊C₄	1	2	yes	—
90	C₄×C₂₉	C₂×C₂²⋊C₄	1	4	yes	—
91	C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
92	C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
93	C₂³×D₄	C₂×C₂₉	1	1	yes	characteristic
94	C₂²×M₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
95	C₂×#117	C₂×C₂₉	1	1	yes	characteristic, complemented
96	#418	C₂×C₂₉	1	8	yes	direct product factor
97	C₂×#102	C₂×C₂₉	1	4	yes	complemented
98	C₂×C₂₉	—	2	4	no	—
99	C₂×C₂₉	—	4	8	no	—
100	C₂×C₂₉	#418	1	4	yes	direct product factor
101	C₂×C₂₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₂₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
103	C₂⁵	—	2	1	no	—
104	C₂²×D₄	—	2	1	no	—
105	C₂²×D₄	—	2	2	no	—
106	C₂²×D₄	—	2	4	no	—
107	C₂²×D₄	C₄×C₂₉	1	8	yes	complemented
108	C₂²×D₄	C₂²×C₂₉	1	2	yes	—
109	C₂²×D₄	C₂²×C₂₉	1	4	yes	—
110	C₂³×C₄	C₂²×C₂₉	1	1	yes	characteristic
111	C₂×M₁₆	—	2	4	no	—
112	C₂×M₁₆	C₂²×C₂₉	1	4	yes	complemented
113	C₂²×C₈	C₂²×C₂₉	1	2	yes	complemented
114	#117	—	2	2	no	—
115	#117	C₂²×C₂₉	1	4	yes	complemented
116	C₂×C₄⋊C₄	C₂²×C₂₉	1	2	yes	complemented
117	C₂×C₂²⋊C₄	—	2	1	no	—
118	C₂×C₄²	—	2	1	no	—
119	#102	C₂²×C₂₉	1	16	yes	complemented
120	C₂₉	C₂×#418	1	1	yes	characteristic, direct product factor, Sylow
121	C₂⁴	—	2	8	no	—
122	C₂⁴	—	2	2	no	—
123	C₂⁴	—	2	4	no	—
124	C₂⁴	—	4	8	no	—
125	C₂⁴	D₄×C₂₉	1	1	yes	characteristic
126	C₂×D₄	—	2	16	no	—
127	C₂×D₄	—	2	8	no	—
128	C₂×D₄	—	2	4	no	—
129	C₂×D₄	—	2	2	no	—
130	C₂×D₄	—	2	4	no	—
131	C₂×D₄	—	2	8	no	—
132	C₂×D₄	C₂×C₄×C₂₉	1	8	yes	—
133	C₂×D₄	C₂×C₄×C₂₉	1	16	yes	complemented
134	C₂×D₄	C₂³×C₂₉	1	4	yes	—
135	C₂²×C₄	—	2	2	no	—
136	C₂²×C₄	C₂×C₄×C₂₉	1	4	yes	—
137	C₂²×C₄	D₄×C₂₉	1	1	yes	characteristic
138	C₂²×C₄	D₄×C₂₉	1	2	yes	—
139	C₂²×C₄	D₄×C₂₉	1	4	yes	—
140	C₂²×C₄	C₂³×C₂₉	1	1	yes	characteristic
141	C₂²×C₄	C₂³×C₂₉	1	2	yes	—
142	M₁₆	—	2	8	no	—
143	C₂×C₈	—	2	4	no	—
144	C₂×C₈	C₂³×C₂₉	1	4	yes	complemented
145	C₄⋊C₄	—	2	2	no	—
146	C₄⋊C₄	C₂³×C₂₉	1	4	yes	complemented
147	C₂²⋊C₄	—	2	4	no	—
148	C₄²	—	2	4	no	—
149	C₂³	—	2	4	no	—
150	C₂³	—	2	8	no	—
151	C₂³	—	2	16	no	—
152	C₂³	—	2	4	no	—
153	C₂³	—	4	16	no	—
154	C₂³	—	4	32	no	—
155	C₂³	—	4	8	no	—
156	C₂³	C₂²⋊C₄×C₂₉	1	4	yes	—
157	C₂³	C₂×D₄×C₂₉	1	2	yes	—
158	C₂³	C₂×D₄×C₂₉	1	1	yes	characteristic
159	D₄	—	2	8	no	—
160	D₄	—	2	16	no	—
161	D₄	—	2	4	no	—
162	D₄	C₂²×C₄×C₂₉	1	8	yes	—
163	C₂×C₄	—	2	4	no	—
164	C₂×C₄	—	4	4	no	—
165	C₂×C₄	C₂²⋊C₄×C₂₉	1	8	yes	—
166	C₂×C₄	C₂²⋊C₄×C₂₉	1	4	yes	—
167	C₂×C₄	C₂²×C₄×C₂₉	1	2	yes	—
168	C₂×C₄	C₂²×C₄×C₂₉	1	4	yes	—
169	C₂×C₄	C₂×D₄×C₂₉	1	2	yes	—
170	C₂×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
171	C₂×C₄	C₂×D₄×C₂₉	1	2	yes	—
172	C₂×C₄	C₂×D₄×C₂₉	1	4	yes	—
173	C₂×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
174	C₈	—	2	4	no	—
175	C₂²	—	2	4	no	—
176	C₂²	—	2	8	no	—
177	C₂²	—	2	8	no	—
178	C₂²	—	4	32	no	—
179	C₂²	—	4	8	no	—
180	C₂²	—	4	16	no	—
181	C₂²	C₂×C₂²⋊C₄×C₂₉	1	4	yes	—
182	C₂²	C₂×C₂²⋊C₄×C₂₉	1	2	yes	—
183	C₂²	C₂₉×AGL(1,ℤ/8)	1	4	yes	—
184	C₂²	C₂²×D₄×C₂₉	1	1	yes	characteristic
185	C₄	—	4	4	no	—
186	C₄	C₂×C₂²⋊C₄×C₂₉	1	2	yes	—
187	C₄	C₂×C₂²⋊C₄×C₂₉	1	4	yes	—
188	C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
189	C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
190	C₂	—	2	4	no	—
191	C₂	—	4	8	no	—
192	C₂	C₂₉×#418	1	4	yes	direct product factor
193	C₂	C₂²×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
194	C₂	C₂×C₂₉×AGL(1,ℤ/8)	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂×D₄
commutator	C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
prime radical	C₂³×D₄×C₂₉	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂³×C₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×M₁₆×C₂₉	C₂	semidirect
3. C₂×C₂₉×#117	C₂	semidirect
4. C₂₉×#418	C₂	direct (N × H)
5. C₂×C₂₉×#102	C₂	semidirect
10. C₂²×D₄×C₂₉	C₄	semidirect
15. C₂×M₁₆×C₂₉	C₂²	semidirect
16. C₂²×C₈×C₂₉	C₂²	semidirect
18. C₂₉×#117	C₂²	semidirect
19. C₂×C₄⋊C₄×C₂₉	C₂²	semidirect
22. C₂₉×#102	C₂²	semidirect
35. C₂×D₄×C₂₉	C₂×C₄	semidirect
46. C₂×C₈×C₂₉	C₂³	semidirect
48. C₄⋊C₄×C₂₉	C₂³	semidirect
77. C₂×#418	C₂₉	direct (N × H)
94. C₂²×M₁₆	C₂×C₂₉	semidirect
95. C₂×#117	C₂×C₂₉	semidirect
96. #418	C₂×C₂₉	direct (N × H)
97. C₂×#102	C₂×C₂₉	semidirect
100. C₂×C₂₉	#418	direct (N × H)
107. C₂²×D₄	C₄×C₂₉	semidirect
112. C₂×M₁₆	C₂²×C₂₉	semidirect
113. C₂²×C₈	C₂²×C₂₉	semidirect
115. #117	C₂²×C₂₉	semidirect
116. C₂×C₄⋊C₄	C₂²×C₂₉	semidirect
119. #102	C₂²×C₂₉	semidirect
120. C₂₉	C₂×#418	direct (N × H)
133. C₂×D₄	C₂×C₄×C₂₉	semidirect
144. C₂×C₈	C₂³×C₂₉	semidirect
146. C₄⋊C₄	C₂³×C₂₉	semidirect
192. C₂	C₂₉×#418	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×D₄×C₂₉	2
C₂²×M₁₆×C₂₉	2
C₂×C₂₉×#117	2
C₂₉×#418	2
C₂×C₂₉×#102	2
C₂×#418	29

Subgroups — C2×C29×#418 #16816607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉×#418 #16816607