Subgroups — C₂×#14557662 #18003522

Order 4736.

400 conjugacy classes of subgroups.

The subgroup lattice has 188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Dic₇₄	C₂	1	1	yes	maximal, characteristic
2	#14557662	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11924465	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924465	C₂	1	1	yes	maximal, characteristic
5	C₂×#11924447	C₂	1	1	yes	maximal, characteristic
6	C₂×#11924446	C₂	1	1	yes	maximal, characteristic
7	C₂×C₈×Dic₃₇	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄⋊C₈×C₃₇	C₂	1	1	yes	maximal, characteristic
9	C₂²×Dic₇₄	C₄	1	1	yes	characteristic
10	C₂²×#64436	C₂²	1	1	yes	characteristic
11	C₂²×#64436	C₂²	1	1	yes	characteristic
12	C₄×Dic₇₄	C₄	1	4	yes	—
13	C₄×Dic₇₄	C₂²	1	4	yes	—
14	C₂×C₄⋊Dic₃₇	C₄	1	1	yes	characteristic
15	C₂×#10596936	C₄	1	1	yes	characteristic
16	C₂×#10596936	C₄	1	1	yes	characteristic
17	C₂×C₄×Dic₃₇	C₂²	1	1	yes	characteristic
18	C₂×C₄×Dic₃₇	C₂²	1	1	yes	characteristic
19	#11924465	C₂²	1	4	yes	—
20	#11924465	C₂²	1	4	yes	—
21	#11924447	C₂²	1	4	yes	—
22	#11924446	C₂²	1	4	yes	—
23	C₈×Dic₃₇	C₂²	1	4	yes	—
24	C₂²×C₈×C₃₇	C₂²	1	1	yes	characteristic
25	C₂²×C₈×C₃₇	C₂²	1	1	yes	characteristic
26	C₂×C₄²×C₃₇	C₂²	1	1	yes	characteristic
27	C₄⋊C₈×C₃₇	C₂²	1	4	yes	—
28	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
31	C₂²×Dic₃₇	C₂×C₄	1	1	yes	characteristic
32	C₂²×Dic₃₇	C₂×C₄	1	1	yes	characteristic
33	C₂²×Dic₃₇	C₂×C₄	1	1	yes	characteristic
34	C₂²×Dic₃₇	C₂×C₄	1	1	yes	characteristic
35	C₂×Dic₇₄	—	2	4	no	—
36	C₂×Dic₇₄	C₂×C₄	1	4	yes	—
37	C₂×C₈×C₃₇	—	2	2	no	—
38	C₂×C₈×C₃₇	—	2	2	no	—
39	C₂×C₈×C₃₇	C₂³	1	2	yes	—
40	C₂×C₈×C₃₇	C₂³	1	2	yes	—
41	C₄²×C₃₇	C₂×C₄	1	2	yes	—
42	C₄²×C₃₇	C₂³	1	2	yes	—
43	C₄⋊Dic₃₇	C₂×C₄	1	4	yes	—
44	#10596936	C₂×C₄	1	4	yes	—
45	#10596936	C₂×C₄	1	4	yes	—
46	C₄×Dic₃₇	C₂×C₄	1	2	yes	—
47	C₄×Dic₃₇	C₂×C₄	1	2	yes	—
48	C₄×Dic₃₇	C₂³	1	2	yes	—
49	C₄×Dic₃₇	C₂³	1	2	yes	—
50	C₂×#64436	—	2	2	no	—
51	C₂×#64436	Q₈	1	4	yes	complemented
52	C₂×#64436	C₂³	1	2	yes	—
53	C₂×#64436	C₂³	1	2	yes	—
54	C₂³×C₃₇	C₂²×C₄	1	1	yes	characteristic
55	C₂×C₄×C₃₇	—	2	2	no	—
56	C₂×C₄×C₃₇	—	2	2	no	—
57	C₂×C₄×C₃₇	C₂²×C₄	1	2	yes	—
58	C₂×C₄×C₃₇	C₂²×C₄	1	2	yes	—
59	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
60	C₂×C₄×C₃₇	C₂×Q₈	1	2	yes	—
61	C₂×C₄×C₃₇	#41	1	2	yes	—
62	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
63	C₂×Dic₃₇	—	2	2	no	—
64	C₂×Dic₃₇	—	2	2	no	—
65	C₂×Dic₃₇	—	2	2	no	—
66	C₂×Dic₃₇	M₁₆	1	4	yes	—
67	C₂×Dic₃₇	C₂²×C₄	1	2	yes	—
68	C₂×Dic₃₇	C₂²×C₄	1	2	yes	—
69	C₂×Dic₃₇	C₂²×C₄	1	2	yes	—
70	C₂×Dic₃₇	C₂²×C₄	1	2	yes	—
71	Dic₇₄	—	2	8	no	—
72	C₈×C₃₇	—	2	2	no	—
73	C₈×C₃₇	—	2	2	no	—
74	#64436	—	2	2	no	—
75	#64436	C₂×Q₈	1	4	yes	complemented
76	C₂²×C₃₇	C₄×Q₈	1	2	yes	—
77	C₂²×C₃₇	C₂×M₁₆	1	2	yes	—
78	C₂²×C₃₇	#131	1	2	yes	—
79	C₂²×C₃₇	C₂³×C₄	1	1	yes	characteristic
80	C₄×C₃₇	—	2	2	no	—
81	C₄×C₃₇	—	2	2	no	—
82	C₄×C₃₇	C₄×Q₈	1	2	yes	—
83	C₄×C₃₇	C₂²×Q₈	1	1	yes	characteristic
84	C₄×C₃₇	C₂×#41	1	1	yes	characteristic
85	Dic₃₇	—	2	2	no	—
86	Dic₃₇	—	2	2	no	—
87	Dic₃₇	—	2	2	no	—
88	Dic₃₇	C₂×M₁₆	1	4	yes	—
89	C₂×#446	—	37	1	no	maximal, Sylow
90	C₂×C₃₇	#446	1	4	yes	complemented
91	C₂×C₃₇	C₂×C₄×Q₈	1	1	yes	characteristic
92	C₂×C₃₇	C₂²×M₁₆	1	1	yes	characteristic
93	C₂×C₃₇	C₂×#131	1	1	yes	characteristic
94	C₂×C₄×Q₈	—	37	1	no	—
95	#446	—	37	8	no	—
96	C₂×C₄⋊C₈	—	37	1	no	—
97	C₂×C₄⋊C₈	—	37	1	no	—
98	C₂×C₄⋊C₈	D₃₇	1	1	yes	characteristic
99	C₂×#97	—	37	1	no	—
100	C₂×#97	—	37	1	no	—
101	C₂×C₄×C₈	—	37	1	no	—
102	C₃₇	C₂×#446	1	1	yes	characteristic, complemented, Sylow
103	C₂²×Q₈	—	37	1	no	—
104	C₂²×C₈	—	37	1	no	—
105	C₂²×C₈	—	37	1	no	—
106	C₂²×C₈	C₂×D₃₇	1	1	yes	characteristic
107	C₂²×C₈	C₂×D₃₇	1	1	yes	characteristic
108	C₄×Q₈	—	37	4	no	—
109	C₄×Q₈	—	37	4	no	—
110	C₂×C₄⋊C₄	—	37	1	no	—
111	C₂×C₄⋊C₄	—	37	1	no	—
112	C₂×C₄⋊C₄	—	37	1	no	—
113	C₂×C₄²	—	37	1	no	—
114	C₂×C₄²	—	37	1	no	—
115	C₂×C₄²	C₂×D₃₇	1	1	yes	characteristic
116	C₄⋊C₈	—	37	4	no	—
117	C₄⋊C₈	—	37	4	no	—
118	C₄⋊C₈	C₂×D₃₇	1	4	yes	—
119	#97	—	37	4	no	—
120	#97	—	37	4	no	—
121	C₄×C₈	—	37	4	no	—
122	C₂×Q₈	—	37	4	no	—
123	C₂×Q₈	—	74	4	no	—
124	C₂²×C₄	—	37	1	no	—
125	C₂²×C₄	—	37	1	no	—
126	C₂²×C₄	—	37	1	no	—
127	C₂²×C₄	—	37	1	no	—
128	C₂²×C₄	C₄×D₃₇	1	1	yes	characteristic
129	C₂²×C₄	C₄×D₃₇	1	1	yes	characteristic
130	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
131	C₂×C₈	—	2	2	no	—
132	C₂×C₈	—	2	2	no	—
133	C₂×C₈	—	37	4	no	—
134	C₂×C₈	—	37	2	no	—
135	C₂×C₈	—	37	2	no	—
136	C₂×C₈	—	74	2	no	—
137	C₂×C₈	C₂²×D₃₇	1	2	yes	—
138	C₂×C₈	C₂²×D₃₇	1	2	yes	—
139	C₄⋊C₄	—	37	4	no	—
140	C₄⋊C₄	—	37	4	no	—
141	C₄⋊C₄	—	37	4	no	—
142	C₄²	—	37	2	no	—
143	C₄²	—	37	2	no	—
144	C₄²	—	37	2	no	—
145	C₄²	—	37	2	no	—
146	C₄²	C₄×D₃₇	1	2	yes	—
147	C₄²	C₂²×D₃₇	1	2	yes	—
148	C₂³	C₂×C₄×D₃₇	1	1	yes	characteristic
149	Q₈	—	74	8	no	—
150	C₂×C₄	—	2	2	no	—
151	C₂×C₄	—	2	2	no	—
152	C₂×C₄	—	37	4	no	—
153	C₂×C₄	—	37	2	no	—
154	C₂×C₄	—	37	2	no	—
155	C₂×C₄	—	37	2	no	—
156	C₂×C₄	—	37	2	no	—
157	C₂×C₄	—	74	2	no	—
158	C₂×C₄	—	74	2	no	—
159	C₂×C₄	—	74	2	no	—
160	C₂×C₄	C₂×C₄×D₃₇	1	2	yes	—
161	C₂×C₄	C₂×C₄×D₃₇	1	2	yes	—
162	C₂×C₄	C₂×C₄×D₃₇	1	1	yes	characteristic
163	C₂×C₄	#10596964	1	2	yes	—
164	C₂×C₄	Q₈×D₃₇	1	2	yes	—
165	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
166	C₈	—	2	2	no	—
167	C₈	—	2	2	no	—
168	C₈	—	37	4	no	—
169	C₈	—	74	2	no	—
170	C₂²	#11924501	1	2	yes	—
171	C₂²	M₁₆×D₃₇	1	2	yes	—
172	C₂²	#11924542	1	2	yes	—
173	C₂²	C₂²×C₄×D₃₇	1	1	yes	characteristic
174	C₄	—	2	2	no	—
175	C₄	—	2	2	no	—
176	C₄	—	37	4	no	—
177	C₄	—	74	2	no	—
178	C₄	—	74	2	no	—
179	C₄	—	74	2	no	—
180	C₄	#11924501	1	2	yes	—
181	C₄	C₂×Q₈×D₃₇	1	1	yes	characteristic
182	C₄	C₂×#10596964	1	1	yes	characteristic
183	C₂	#14557662	1	4	yes	direct product factor
184	C₂	C₂×#11924501	1	1	yes	characteristic
185	C₂	C₂×M₁₆×D₃₇	1	1	yes	characteristic
186	C₂	C₂×#11924542	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₃₇
commutator	C₂²×C₃₇	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₃₇
Fitting	C₂×C₄⋊C₈×C₃₇	C₂
socle, prime radical	C₂³×C₃₇	C₂²×C₄
cosocle	C₂×C₄×C₃₇	C₂⁴
hypercenter	C₂×C₄⋊C₈	D₃₇
hypocenter	C₃₇	C₂×#446
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. #14557662	C₂	direct (N × H)
51. C₂×#64436	Q₈	semidirect
75. #64436	C₂×Q₈	semidirect
90. C₂×C₃₇	#446	semidirect
102. C₃₇	C₂×#446	semidirect
183. C₂	#14557662	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×Dic₇₄	2
#14557662	2
C₂×#11924465	2
C₂×#11924447	2
C₂×#11924446	2
C₂×C₈×Dic₃₇	2
C₂×C₄⋊C₈×C₃₇	2
C₂×#446	37

Subgroups — C2×#14557662 #18003522

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14557662 #18003522