Subgroups — C₂×#14271120 #16827906

Order 3712.

592 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	C₂²×#90772	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×D₂₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#11745234	C₂	1	1	yes	maximal, characteristic
4	#14271120	C₂	1	8	yes	maximal, direct product factor
5	C₂×#11745163	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×#6597	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₈×Dic₂₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₉×#97	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₄×D₂₉	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
11	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
12	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
13	C₂×#90781	C₄	1	2	yes	—
14	C₂×#90779	C₄	1	2	yes	—
15	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
16	C₂²×#6597	C₂²	1	1	yes	characteristic
17	C₂²×#6597	C₂²	1	1	yes	characteristic
18	C₂×#90772	C₄	1	8	yes	complemented
19	C₂×#90772	C₂²	1	4	yes	—
20	C₂×C₈×D₂₉	C₄	1	8	yes	complemented
21	C₂×C₈×D₂₉	C₂²	1	4	yes	—
22	#11745234	C₄	1	4	yes	—
23	#11745234	C₂²	1	4	yes	—
24	C₂₉×#97	C₂²	1	4	yes	complemented
25	#11745163	C₂²	1	4	yes	complemented
26	C₈×Dic₂₉	C₂²	1	4	yes	complemented
27	C₄×#6597	C₂²	1	4	yes	complemented
28	C₂³×D₂₉	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
30	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
31	C₂²×Dic₂₉	C₂×C₄	1	2	yes	—
32	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄×D₂₉	C₂×C₄	1	2	yes	—
34	C₂×C₄×D₂₉	C₂×C₄	1	4	yes	—
35	C₂×C₄×D₂₉	C₂×C₄	1	4	yes	—
36	C₂×C₄×D₂₉	C₂³	1	2	yes	—
37	C₂×C₈×C₂₉	C₂×C₄	1	4	yes	—
38	C₂×C₈×C₂₉	C₂×C₄	1	4	yes	—
39	C₂×C₈×C₂₉	C₂³	1	2	yes	—
40	C₂×C₈×C₂₉	C₂³	1	2	yes	—
41	C₄²×C₂₉	C₂×C₄	1	2	yes	—
42	C₄²×C₂₉	C₂³	1	2	yes	—
43	#90781	C₂×C₄	1	8	yes	—
44	#90779	C₂×C₄	1	8	yes	—
45	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
46	C₄×Dic₂₉	C₂³	1	2	yes	—
47	C₂×#6597	C₂×C₄	1	4	yes	—
48	C₂×#6597	C₂×C₄	1	4	yes	—
49	C₂×#6597	C₂³	1	2	yes	—
50	C₂×#6597	C₂³	1	2	yes	—
51	#90772	C₂×C₄	1	16	yes	complemented
52	C₈×D₂₉	C₂×C₄	1	16	yes	complemented
53	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
54	C₂²×D₂₉	—	2	4	no	—
55	C₂²×D₂₉	C₄²	1	4	yes	—
56	C₂²×D₂₉	C₂²×C₄	1	2	yes	—
57	C₂×C₄×C₂₉	—	2	4	no	—
58	C₂×C₄×C₂₉	C₂²×C₄	1	4	yes	—
59	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
60	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
61	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
62	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
63	C₂×Dic₂₉	—	2	4	no	—
64	C₂×Dic₂₉	C₄²	1	4	yes	—
65	C₂×Dic₂₉	C₂²×C₄	1	4	yes	—
66	C₂×Dic₂₉	C₂²×C₄	1	2	yes	—
67	C₄×D₂₉	C₄²	1	8	yes	—
68	C₄×D₂₉	C₂²×C₄	1	4	yes	—
69	C₄×D₂₉	C₂²×C₄	1	4	yes	—
70	C₈×C₂₉	C₂²×C₄	1	4	yes	—
71	C₈×C₂₉	C₂²×C₄	1	4	yes	—
72	#6597	C₂²×C₄	1	4	yes	—
73	#6597	C₂²×C₄	1	4	yes	—
74	C₂×#405	—	29	1	no	maximal, Sylow
75	C₂²×C₂₉	C₂×C₄²	1	2	yes	—
76	C₂²×C₂₉	#131	1	4	yes	—
77	C₂²×C₂₉	C₂³×C₄	1	1	yes	characteristic
78	C₂×D₂₉	—	2	4	no	—
79	C₂×D₂₉	—	2	8	no	—
80	C₂×D₂₉	C₂×C₄²	1	4	yes	—
81	C₄×C₂₉	—	2	4	no	—
82	C₄×C₂₉	C₂×C₄²	1	2	yes	—
83	C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
84	C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
85	Dic₂₉	—	2	4	no	—
86	Dic₂₉	C₂×C₄²	1	4	yes	—
87	C₂²×M₁₆	—	29	1	no	—
88	C₂³×C₈	—	29	1	no	—
89	C₂×#117	—	29	1	no	—
90	#405	—	29	8	no	—
91	C₂×#97	—	29	1	no	—
92	C₂×#97	D₂₉	1	1	yes	characteristic, complemented
93	C₂×C₄×C₈	—	29	1	no	—
94	C₂×C₄×C₈	—	29	1	no	—
95	C₂×C₂₉	#405	1	4	yes	complemented
96	C₂×C₂₉	C₂²×C₄²	1	1	yes	characteristic
97	C₂×C₂₉	C₂×#131	1	2	yes	—
98	D₂₉	—	2	4	no	—
99	C₂³×C₄	—	29	1	no	—
100	C₂×M₁₆	—	29	8	no	—
101	C₂×M₁₆	—	29	4	no	—
102	C₂²×C₈	—	29	1	no	—
103	C₂²×C₈	—	29	1	no	—
104	C₂²×C₈	—	29	8	no	—
105	C₂²×C₈	—	29	4	no	—
106	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
107	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
108	#117	—	29	4	no	—
109	#117	—	29	4	no	—
110	C₂×C₄⋊C₄	—	29	2	no	—
111	C₂×C₂²⋊C₄	—	29	2	no	—
112	C₂×C₄²	—	29	1	no	—
113	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
114	#97	—	29	4	no	—
115	#97	C₂×D₂₉	1	4	yes	complemented
116	C₄×C₈	—	29	4	no	—
117	C₄×C₈	—	29	4	no	—
118	C₂₉	C₂×#405	1	1	yes	characteristic, complemented, Sylow
119	C₂⁴	—	29	1	no	—
120	C₂²×C₄	—	29	1	no	—
121	C₂²×C₄	—	29	2	no	—
122	C₂²×C₄	—	29	4	no	—
123	C₂²×C₄	—	29	4	no	—
124	C₂²×C₄	—	29	2	no	—
125	C₂²×C₄	—	29	2	no	—
126	C₂²×C₄	C₄×D₂₉	1	2	yes	—
127	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
128	M₁₆	—	29	16	no	—
129	C₂×C₈	—	29	4	no	—
130	C₂×C₈	—	29	4	no	—
131	C₂×C₈	—	29	2	no	—
132	C₂×C₈	—	29	2	no	—
133	C₂×C₈	—	29	16	no	—
134	C₂×C₈	C₄×D₂₉	1	4	yes	—
135	C₂×C₈	C₄×D₂₉	1	4	yes	—
136	C₂×C₈	C₂²×D₂₉	1	2	yes	—
137	C₂×C₈	C₂²×D₂₉	1	2	yes	—
138	C₄⋊C₄	—	29	8	no	—
139	C₂²⋊C₄	—	29	8	no	—
140	C₄²	—	29	2	no	—
141	C₄²	—	29	2	no	—
142	C₄²	C₄×D₂₉	1	2	yes	—
143	C₄²	C₂²×D₂₉	1	2	yes	—
144	C₂³	—	29	2	no	—
145	C₂³	—	29	4	no	—
146	C₂³	—	58	4	no	—
147	C₂³	C₂×C₄×D₂₉	1	1	yes	characteristic
148	C₂×C₄	—	2	4	no	—
149	C₂×C₄	—	29	2	no	—
150	C₂×C₄	—	29	4	no	—
151	C₂×C₄	—	29	4	no	—
152	C₂×C₄	—	29	4	no	—
153	C₂×C₄	—	29	8	no	—
154	C₂×C₄	—	29	4	no	—
155	C₂×C₄	—	58	4	no	—
156	C₂×C₄	C₂×C₄×D₂₉	1	4	yes	—
157	C₂×C₄	C₂×C₄×D₂₉	1	2	yes	—
158	C₂×C₄	C₂×C₄×D₂₉	1	2	yes	—
159	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
160	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
161	C₈	—	29	4	no	—
162	C₈	—	29	4	no	—
163	C₈	C₂×C₄×D₂₉	1	4	yes	—
164	C₈	C₂×C₄×D₂₉	1	4	yes	—
165	C₂²	—	29	4	no	—
166	C₂²	—	58	8	no	—
167	C₂²	—	58	4	no	—
168	C₂²	C₄²×D₂₉	1	2	yes	—
169	C₂²	#11745269	1	4	yes	—
170	C₂²	C₂²×C₄×D₂₉	1	1	yes	characteristic
171	C₄	—	2	4	no	—
172	C₄	—	29	4	no	—
173	C₄	—	58	4	no	—
174	C₄	C₄²×D₂₉	1	2	yes	—
175	C₄	C₂²×C₄×D₂₉	1	1	yes	characteristic
176	C₄	C₂²×C₄×D₂₉	1	1	yes	characteristic
177	C₂	—	58	4	no	—
178	C₂	#14271120	1	4	yes	direct product factor
179	C₂	C₂×C₄²×D₂₉	1	1	yes	characteristic
180	C₂	C₂×#11745269	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₂₉
commutator	C₂×C₂₉	C₂²×C₄²
Frattini	C₂×C₄	C₂³×D₂₉
Fitting	C₂×C₂₉×#97	C₂
socle	C₂³×C₂₉	C₂²×C₄
prime radical	C₂³×D₂₉	C₂×C₄
cosocle	C₂×C₄×C₂₉	C₂⁴
hypercenter	C₂×#97	D₂₉
hypocenter	C₂₉	C₂×#405
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
4. #14271120	C₂	direct (N × H)
5. C₂×#11745163	C₂	semidirect
6. C₂×C₄×#6597	C₂	semidirect
7. C₂×C₈×Dic₂₉	C₂	semidirect
8. C₂×C₂₉×#97	C₂	semidirect
18. C₂×#90772	C₄	semidirect
20. C₂×C₈×D₂₉	C₄	semidirect
24. C₂₉×#97	C₂²	semidirect
25. #11745163	C₂²	semidirect
26. C₈×Dic₂₉	C₂²	semidirect
27. C₄×#6597	C₂²	semidirect
51. #90772	C₂×C₄	semidirect
52. C₈×D₂₉	C₂×C₄	semidirect
92. C₂×#97	D₂₉	semidirect
95. C₂×C₂₉	#405	semidirect
115. #97	C₂×D₂₉	semidirect
118. C₂₉	C₂×#405	semidirect
178. C₂	#14271120	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#90772	2
C₂²×C₈×D₂₉	2
C₂×#11745234	2
#14271120	2
C₂×#11745163	2
C₂×C₄×#6597	2
C₂×C₈×Dic₂₉	2
C₂×C₂₉×#97	2
C₂×#405	29

Subgroups — C2×#14271120 #16827906

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14271120 #16827906