Subgroups — C₂×#14270917 #16819182

Order 3712.

528 conjugacy classes of subgroups.

The subgroup lattice has 182 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	1	yes	maximal, characteristic
2	C₂²×C₄×Dic₂₉	C₂	1	1	yes	maximal, characteristic
3	#14270917	C₂	1	4	yes	maximal, direct product factor
4	C₂³×C₈×C₂₉	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₄×C₂₉	C₂²	1	1	yes	characteristic
6	C₂³×Dic₂₉	C₄	1	2	yes	—
7	C₂²×C₈×C₂₉	—	2	2	no	—
8	C₂²×C₈×C₂₉	—	2	2	no	—
9	C₂²×C₈×C₂₉	C₄	1	4	yes	complemented
10	C₂²×C₈×C₂₉	C₂²	1	2	yes	—
11	C₂×C₄×Dic₂₉	—	2	2	no	—
12	C₂×C₄×Dic₂₉	—	2	2	no	—
13	C₂×C₄×Dic₂₉	C₄	1	2	yes	—
14	C₂×C₄×Dic₂₉	C₂²	1	2	yes	—
15	C₂²×#6597	—	2	2	no	—
16	C₂²×#6597	—	2	2	no	—
17	C₂²×#6597	C₄	1	4	yes	complemented
18	C₂²×#6597	C₂²	1	2	yes	—
19	C₂⁴×C₂₉	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
22	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
23	C₂²×C₄×C₂₉	D₄	1	2	yes	—
24	C₂²×C₄×C₂₉	D₄	1	2	yes	—
25	C₂²×C₄×C₂₉	D₄	1	2	yes	—
26	C₂²×C₄×C₂₉	Q₈	1	2	yes	—
27	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
28	C₂²×Dic₂₉	—	2	4	no	—
29	C₂²×Dic₂₉	—	2	4	no	—
30	C₂²×Dic₂₉	C₈	1	8	yes	complemented
31	C₂²×Dic₂₉	C₂×C₄	1	4	yes	—
32	C₂×C₈×C₂₉	—	2	8	no	—
33	C₂×C₈×C₂₉	—	2	2	no	—
34	C₂×C₈×C₂₉	—	2	2	no	—
35	C₂×C₈×C₂₉	C₂×C₄	1	4	yes	complemented
36	C₄×Dic₂₉	—	2	4	no	—
37	C₄×Dic₂₉	—	2	2	no	—
38	C₄×Dic₂₉	—	2	2	no	—
39	C₂×#6597	—	2	8	no	—
40	C₂×#6597	—	2	2	no	—
41	C₂×#6597	—	2	2	no	—
42	C₂×#6597	C₂×C₄	1	4	yes	complemented
43	C₂³×C₂₉	C₄²	1	2	yes	—
44	C₂³×C₂₉	C₂²⋊C₄	1	2	yes	—
45	C₂³×C₂₉	C₄⋊C₄	1	2	yes	—
46	C₂³×C₂₉	C₂×C₈	1	4	yes	—
47	C₂³×C₂₉	M₁₆	1	4	yes	—
48	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
49	C₂×C₄×C₂₉	C₄²	1	2	yes	—
50	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
51	C₂×C₄×C₂₉	C₂²⋊C₄	1	4	yes	—
52	C₂×C₄×C₂₉	C₂²⋊C₄	1	4	yes	—
53	C₂×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
54	C₂×C₄×C₂₉	C₄⋊C₄	1	4	yes	—
55	C₂×C₄×C₂₉	C₄⋊C₄	1	4	yes	—
56	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
57	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
58	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
59	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
60	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
61	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
62	C₂×Dic₂₉	—	2	16	no	—
63	C₂×Dic₂₉	—	2	4	no	—
64	C₂×Dic₂₉	—	2	4	no	—
65	C₂×Dic₂₉	C₂×C₈	1	8	yes	complemented
66	C₈×C₂₉	—	2	4	no	—
67	#6597	—	2	4	no	—
68	C₂×#336	—	29	1	no	maximal, Sylow
69	C₂²×C₂₉	#95	1	4	yes	—
70	C₂²×C₂₉	C₄×C₈	1	4	yes	—
71	C₂²×C₂₉	#97	1	4	yes	—
72	C₂²×C₂₉	C₂²⋊C₈	1	8	yes	—
73	C₂²×C₂₉	C₄⋊C₈	1	8	yes	—
74	C₂²×C₂₉	C₂×C₄²	1	1	yes	characteristic
75	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
77	C₂²×C₂₉	C₂²×C₈	1	2	yes	—
78	C₂²×C₂₉	C₂×M₁₆	1	2	yes	—
79	C₄×C₂₉	#95	1	4	yes	—
80	C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
81	C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
83	C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
84	Dic₂₉	—	2	8	no	—
85	C₂³×C₈	—	29	1	no	—
86	C₂³×C₈	D₂₉	1	1	yes	characteristic
87	C₂²×C₄²	—	29	1	no	—
88	#336	—	29	4	no	—
89	C₂×C₂₉	#336	1	8	yes	complemented
90	C₂×C₂₉	C₂×#95	1	1	yes	characteristic
91	C₂×C₂₉	C₂×C₄×C₈	1	1	yes	characteristic
92	C₂×C₂₉	C₂×#97	1	1	yes	characteristic
93	C₂×C₂₉	C₂×C₂²⋊C₈	1	2	yes	—
94	C₂×C₂₉	C₂×C₄⋊C₈	1	2	yes	—
95	C₂³×C₄	—	29	2	no	—
96	C₂³×C₄	C₂×D₂₉	1	1	yes	characteristic
97	C₂²×C₈	—	2	2	no	—
98	C₂²×C₈	—	2	2	no	—
99	C₂²×C₈	—	29	4	no	—
100	C₂²×C₈	—	29	2	no	—
101	C₂²×C₈	—	58	2	no	—
102	C₂²×C₈	—	58	2	no	—
103	C₂²×C₈	Dic₂₉	1	4	yes	complemented
104	C₂²×C₈	C₂×D₂₉	1	2	yes	—
105	C₂×C₄²	—	29	2	no	—
106	C₂×C₄²	—	29	2	no	—
107	C₂×C₄²	—	58	2	no	—
108	C₂×C₄²	—	58	2	no	—
109	C₂₉	C₂×#336	1	1	yes	characteristic, complemented, Sylow
110	C₂⁴	C₄×D₂₉	1	1	yes	characteristic
111	C₂²×C₄	—	29	8	no	—
112	C₂²×C₄	—	29	4	no	—
113	C₂²×C₄	—	58	4	no	—
114	C₂²×C₄	—	58	4	no	—
115	C₂²×C₄	Dic₅₈	1	2	yes	—
116	C₂²×C₄	C₄×D₂₉	1	1	yes	characteristic
117	C₂²×C₄	C₄×D₂₉	1	2	yes	—
118	C₂²×C₄	D₁₁₆	1	2	yes	—
119	C₂²×C₄	C₂×Dic₂₉	1	2	yes	—
120	C₂²×C₄	C₂²⋊D₂₉	1	2	yes	—
121	C₂²×C₄	C₂²⋊D₂₉	1	2	yes	—
122	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
123	C₂×C₈	—	2	8	no	—
124	C₂×C₈	—	2	2	no	—
125	C₂×C₈	—	2	2	no	—
126	C₂×C₈	—	29	4	no	—
127	C₂×C₈	—	58	8	no	—
128	C₂×C₈	—	58	2	no	—
129	C₂×C₈	—	58	2	no	—
130	C₂×C₈	C₂×Dic₂₉	1	4	yes	complemented
131	C₄²	—	58	4	no	—
132	C₄²	—	58	2	no	—
133	C₄²	—	58	2	no	—
134	C₂³	C₈×D₂₉	1	4	yes	—
135	C₂³	#90772	1	4	yes	—
136	C₂³	C₄×Dic₂₉	1	2	yes	—
137	C₂³	#90779	1	2	yes	—
138	C₂³	#90781	1	2	yes	—
139	C₂³	C₂×C₄×D₂₉	1	1	yes	characteristic
140	C₂×C₄	—	29	8	no	—
141	C₂×C₄	—	58	4	no	—
142	C₂×C₄	—	58	16	no	—
143	C₂×C₄	—	58	4	no	—
144	C₂×C₄	C₄×Dic₂₉	1	2	yes	—
145	C₂×C₄	#90779	1	4	yes	—
146	C₂×C₄	#90779	1	2	yes	—
147	C₂×C₄	C₄⋊Dic₂₉	1	4	yes	—
148	C₂×C₄	#90781	1	4	yes	—
149	C₂×C₄	#90781	1	2	yes	—
150	C₂×C₄	C₂²⋊Dic₂₉	1	4	yes	—
151	C₂×C₄	C₂×Dic₅₈	1	1	yes	characteristic
152	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
153	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
154	C₂×C₄	C₂²×Dic₂₉	1	1	yes	characteristic
155	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
156	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
157	C₈	—	2	4	no	—
158	C₈	—	58	4	no	—
159	C₂²	C₈×Dic₂₉	1	4	yes	—
160	C₂²	#11745162	1	8	yes	—
161	C₂²	#11745163	1	4	yes	—
162	C₂²	#11745168	1	8	yes	—
163	C₂²	#11745179	1	4	yes	—
164	C₂²	C₂×C₈×D₂₉	1	2	yes	—
165	C₂²	C₂×#90772	1	2	yes	—
166	C₂²	C₂×C₄×Dic₂₉	1	1	yes	characteristic
167	C₂²	C₂×#90779	1	1	yes	characteristic
168	C₂²	C₂×#90781	1	1	yes	characteristic
169	C₄	—	58	8	no	—
170	C₄	#11745179	1	4	yes	—
171	C₄	C₂×#90779	1	1	yes	characteristic
172	C₄	C₂×C₄⋊Dic₂₉	1	1	yes	characteristic
173	C₄	C₂×#90781	1	1	yes	characteristic
174	C₄	C₂×C₂²⋊Dic₂₉	1	1	yes	characteristic
175	C₂	#14270917	1	8	yes	direct product factor
176	C₂	C₂×#11745179	1	1	yes	characteristic
177	C₂	C₂×C₈×Dic₂₉	1	1	yes	characteristic
178	C₂	C₂×#11745163	1	1	yes	characteristic
179	C₂	C₂×#11745168	1	2	yes	—
180	C₂	C₂×#11745162	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. #14270917	C₂	direct (N × H)
9. C₂²×C₈×C₂₉	C₄	semidirect
17. C₂²×#6597	C₄	semidirect
30. C₂²×Dic₂₉	C₈	semidirect
35. C₂×C₈×C₂₉	C₂×C₄	semidirect
42. C₂×#6597	C₂×C₄	semidirect
65. C₂×Dic₂₉	C₂×C₈	semidirect
89. C₂×C₂₉	#336	semidirect
103. C₂²×C₈	Dic₂₉	semidirect
109. C₂₉	C₂×#336	semidirect
130. C₂×C₈	C₂×Dic₂₉	semidirect
175. C₂	#14270917	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
C₂²×C₄×Dic₂₉	2
#14270917	2
C₂³×C₈×C₂₉	2
C₂×#336	29

Subgroups — C2×#14270917 #16819182

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14270917 #16819182