Subgroups — C₄×D₃₇⋊M₁₆ #18011152

Order 4736.

656 conjugacy classes of subgroups.

The subgroup lattice has 202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₇⋊M₁₆	C₂	1	2	yes	maximal
2	C₄×#10596953	C₂	1	4	yes	maximal, complemented
3	C₄×#10596957	C₂	1	4	yes	maximal, complemented
4	#14558492	C₂	1	2	yes	maximal, complemented
5	C₄×D₃₇⋊C₈	C₂	1	2	yes	maximal, complemented
6	C₂×C₄²×D₃₇	C₂	1	1	yes	maximal, characteristic
7	C₂×#10596953	C₂²	1	4	yes	—
8	D₃₇⋊M₁₆	C₄	1	16	yes	direct product factor
9	C₂×#10596957	C₂²	1	4	yes	—
10	C₂×D₃₇⋊C₈	C₂²	1	4	yes	—
11	#11924591	C₂²	1	8	yes	complemented
12	C₄×#64438	C₂²	1	8	yes	complemented
13	C₂²×C₄×D₃₇	C₄	1	2	yes	—
14	C₂²×C₄×D₃₇	C₂²	1	1	yes	characteristic
15	C₂×C₄×Dic₃₇	C₄	1	1	yes	characteristic
16	C₂×C₄×Dic₃₇	C₂²	1	2	yes	—
17	C₄²×D₃₇	C₄	1	1	yes	characteristic
18	C₄²×D₃₇	C₄	1	2	yes	—
19	C₄²×D₃₇	C₄	1	1	yes	characteristic
20	C₄²×D₃₇	C₂²	1	1	yes	characteristic
21	C₄²×D₃₇	C₂²	1	1	yes	characteristic
22	C₄²×D₃₇	C₂²	1	2	yes	—
23	C₂×C₄²×C₃₇	C₄	1	1	yes	characteristic
24	C₂³×D₃₇	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₄×C₃₇	C₂×C₄	1	2	yes	—
26	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
27	C₂²×Dic₃₇	C₂×C₄	1	2	yes	—
28	C₂²×Dic₃₇	C₂³	1	1	yes	characteristic
29	C₂×C₄×D₃₇	—	2	8	no	—
30	C₂×C₄×D₃₇	C₂×C₄	1	2	yes	—
31	C₂×C₄×D₃₇	C₂×C₄	1	2	yes	—
32	C₂×C₄×D₃₇	C₂×C₄	1	2	yes	—
33	C₂×C₄×D₃₇	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄×D₃₇	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄×D₃₇	C₂×C₄	1	8	yes	—
36	C₂×C₄×D₃₇	C₂×C₄	1	2	yes	—
37	C₂×C₄×D₃₇	C₂³	1	1	yes	characteristic
38	C₂×C₄×D₃₇	C₂³	1	1	yes	characteristic
39	#10596957	C₂×C₄	1	16	yes	complemented
40	C₂×#64438	C₂³	1	8	yes	—
41	#10596953	C₂×C₄	1	16	yes	complemented
42	D₃₇⋊C₈	C₂×C₄	1	16	yes	complemented
43	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
44	C₄²×C₃₇	C₂×C₄	1	2	yes	—
45	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
46	C₄×Dic₃₇	C₂×C₄	1	2	yes	—
47	C₄×Dic₃₇	C₂×C₄	1	2	yes	—
48	C₄×Dic₃₇	C₂×C₄	1	1	yes	characteristic
49	C₄×Dic₃₇	C₂×C₄	1	2	yes	—
50	C₄×Dic₃₇	C₂×C₄	1	1	yes	characteristic
51	C₄×Dic₃₇	C₂³	1	2	yes	—
52	C₄×Dic₃₇	C₂³	1	2	yes	—
53	C₂³×C₃₇	C₂²×C₄	1	1	yes	characteristic
54	C₂²×D₃₇	—	2	4	no	—
55	C₂²×D₃₇	C₄²	1	4	yes	—
56	C₂²×D₃₇	C₂²×C₄	1	1	yes	characteristic
57	C₂²×D₃₇	C₂²×C₄	1	1	yes	characteristic
58	C₂×C₄×C₃₇	—	2	4	no	—
59	C₂×C₄×C₃₇	C₄²	1	4	yes	—
60	C₂×C₄×C₃₇	C₂²×C₄	1	2	yes	—
61	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
62	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
63	C₂×C₄×C₃₇	C₂²×C₄	1	2	yes	—
64	C₂×Dic₃₇	—	2	4	no	—
65	C₂×Dic₃₇	C₂²×C₄	1	2	yes	—
66	C₂×Dic₃₇	C₂²×C₄	1	1	yes	characteristic
67	C₂×Dic₃₇	C₂²×C₄	1	4	yes	—
68	C₂×Dic₃₇	C₂²×C₄	1	2	yes	—
69	C₂×Dic₃₇	C₂⁴	1	1	yes	characteristic
70	C₄×D₃₇	—	2	4	no	—
71	C₄×D₃₇	—	2	4	no	—
72	C₄×D₃₇	—	2	4	no	—
73	C₄×D₃₇	C₄²	1	4	yes	—
74	C₄×D₃₇	C₄²	1	4	yes	—
75	C₄×D₃₇	M₁₆	1	8	yes	complemented
76	C₄×D₃₇	C₂²×C₄	1	4	yes	—
77	C₄×D₃₇	C₂²×C₄	1	4	yes	—
78	#64438	C₂²×C₄	1	16	yes	complemented
79	C₂²×C₃₇	—	2	2	no	—
80	C₂²×C₃₇	C₂×C₄²	1	2	yes	—
81	C₂²×C₃₇	C₂³×C₄	1	1	yes	characteristic
82	C₂×D₃₇	—	2	2	no	—
83	C₂×D₃₇	—	2	8	no	—
84	C₂×D₃₇	C₂×C₄²	1	2	yes	—
85	C₂×D₃₇	C₂×C₄²	1	2	yes	—
86	C₂×D₃₇	C₂×M₁₆	1	4	yes	—
87	C₄×C₃₇	—	2	2	no	—
88	C₄×C₃₇	C₂×C₄²	1	2	yes	—
89	C₄×C₃₇	C₂×C₄²	1	2	yes	—
90	C₄×C₃₇	C₂×M₁₆	1	4	yes	complemented
91	Dic₃₇	—	2	2	no	—
92	Dic₃₇	C₂×C₄²	1	2	yes	—
93	Dic₃₇	C₂×M₁₆	1	4	yes	complemented
94	Dic₃₇	C₂³×C₄	1	2	yes	—
95	C₂×C₄×M₁₆	—	37	1	no	maximal, Sylow
96	C₂×C₃₇	—	2	2	no	—
97	C₂×C₃₇	C₂²×C₄²	1	1	yes	characteristic
98	C₂×C₃₇	C₂²×M₁₆	1	2	yes	—
99	D₃₇	—	2	2	no	—
100	D₃₇	C₄×M₁₆	1	4	yes	complemented
101	C₂²×M₁₆	—	37	2	no	—
102	C₂²×C₄²	—	37	1	no	—
103	C₄×M₁₆	—	37	4	no	—
104	C₄×M₁₆	—	37	4	no	—
105	C₂×#97	—	37	2	no	—
106	C₂×C₄×C₈	—	37	2	no	—
107	C₃₇	C₂×C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
108	C₂³×C₄	—	37	1	no	—
109	C₂³×C₄	—	37	2	no	—
110	C₂×M₁₆	—	37	4	no	—
111	C₂×M₁₆	—	37	16	no	—
112	C₂×M₁₆	—	37	4	no	—
113	C₂²×C₈	—	37	4	no	—
114	C₂×C₄²	—	37	1	no	—
115	C₂×C₄²	—	37	2	no	—
116	C₂×C₄²	—	37	2	no	—
117	C₂×C₄²	—	37	1	no	—
118	C₂×C₄²	—	37	1	no	—
119	C₂×C₄²	—	37	2	no	—
120	C₂×C₄²	—	37	1	no	—
121	C₂×C₄²	—	37	1	no	—
122	C₂×C₄²	#3866	1	1	yes	characteristic
123	#97	—	37	8	no	—
124	C₄×C₈	—	37	8	no	—
125	C₂⁴	—	37	1	no	—
126	C₂²×C₄	—	37	1	no	—
127	C₂²×C₄	—	37	8	no	—
128	C₂²×C₄	—	37	1	no	—
129	C₂²×C₄	—	37	1	no	—
130	C₂²×C₄	—	37	2	no	—
131	C₂²×C₄	—	37	1	no	—
132	C₂²×C₄	—	37	1	no	—
133	C₂²×C₄	—	37	2	no	—
134	C₂²×C₄	—	37	2	no	—
135	C₂²×C₄	—	37	2	no	—
136	C₂²×C₄	—	37	2	no	—
137	C₂²×C₄	—	74	8	no	—
138	C₂²×C₄	C₂×#3866	1	2	yes	—
139	C₂²×C₄	C₂×#3866	1	1	yes	characteristic
140	M₁₆	—	37	16	no	—
141	M₁₆	—	37	16	no	—
142	C₂×C₈	—	37	16	no	—
143	C₂×C₈	—	37	8	no	—
144	C₄²	—	37	2	no	—
145	C₄²	—	37	1	no	—
146	C₄²	—	37	2	no	—
147	C₄²	—	37	2	no	—
148	C₄²	—	37	1	no	—
149	C₄²	—	37	2	no	—
150	C₄²	—	37	2	no	—
151	C₄²	C₂×#3866	1	1	yes	characteristic
152	C₄²	C₂×#3866	1	2	yes	—
153	C₄²	C₂×#3866	1	1	yes	characteristic
154	C₂³	—	37	1	no	—
155	C₂³	—	37	4	no	—
156	C₂³	—	37	1	no	—
157	C₂³	—	74	4	no	—
158	C₂³	C₂²×#3866	1	1	yes	characteristic
159	C₂×C₄	—	2	4	no	—
160	C₂×C₄	—	37	4	no	—
161	C₂×C₄	—	37	1	no	—
162	C₂×C₄	—	37	1	no	—
163	C₂×C₄	—	37	2	no	—
164	C₂×C₄	—	37	4	no	—
165	C₂×C₄	—	37	4	no	—
166	C₂×C₄	—	37	4	no	—
167	C₂×C₄	—	37	4	no	—
168	C₂×C₄	—	37	8	no	—
169	C₂×C₄	—	37	2	no	—
170	C₂×C₄	—	74	4	no	—
171	C₂×C₄	—	74	4	no	—
172	C₂×C₄	—	74	4	no	—
173	C₂×C₄	—	74	4	no	—
174	C₂×C₄	C₄×#3866	1	4	yes	—
175	C₂×C₄	C₂²×#3866	1	2	yes	—
176	C₂×C₄	C₂²×#3866	1	1	yes	characteristic
177	C₂×C₄	C₂²×#3866	1	1	yes	characteristic
178	C₂×C₄	C₂²×#3866	1	2	yes	—
179	C₈	—	37	16	no	—
180	C₂²	—	2	2	no	—
181	C₂²	—	37	2	no	—
182	C₂²	—	37	4	no	—
183	C₂²	—	37	2	no	—
184	C₂²	—	74	8	no	—
185	C₂²	—	74	2	no	—
186	C₂²	C₂×C₄×#3866	1	2	yes	—
187	C₂²	C₂³×#3866	1	1	yes	characteristic
188	C₄	—	2	2	no	—
189	C₄	—	37	2	no	—
190	C₄	—	37	2	no	—
191	C₄	—	37	4	no	—
192	C₄	—	74	2	no	—
193	C₄	C₂×C₄×#3866	1	2	yes	—
194	C₄	C₂×C₄×#3866	1	2	yes	—
195	C₄	D₃₇⋊M₁₆	1	4	yes	direct product factor
196	C₂	—	2	2	no	—
197	C₂	—	37	4	no	—
198	C₂	—	74	2	no	—
199	C₂	C₂²×C₄×#3866	1	1	yes	characteristic
200	C₂	C₂×D₃₇⋊M₁₆	1	2	yes	—

	subgroup	G/H
center	C₄²	C₂×#3866
commutator	C₂×C₃₇	C₂²×C₄²
Frattini	C₂²	C₂³×#3866
Fitting	C₂×C₄²×C₃₇	C₄
socle	C₂²×C₃₇	C₂³×C₄
prime radical	C₂³×D₃₇	C₂×C₄
cosocle	C₂×Dic₃₇	C₂⁴
hypercenter	C₂×C₄²	#3866
hypocenter	C₃₇	C₂×C₄×M₁₆
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄² ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₄×#10596953	C₂	semidirect
3. C₄×#10596957	C₂	semidirect
4. #14558492	C₂	semidirect
5. C₄×D₃₇⋊C₈	C₂	semidirect
8. D₃₇⋊M₁₆	C₄	direct (N × H)
11. #11924591	C₂²	semidirect
12. C₄×#64438	C₂²	semidirect
39. #10596957	C₂×C₄	semidirect
41. #10596953	C₂×C₄	semidirect
42. D₃₇⋊C₈	C₂×C₄	semidirect
75. C₄×D₃₇	M₁₆	semidirect
78. #64438	C₂²×C₄	semidirect
90. C₄×C₃₇	C₂×M₁₆	semidirect
93. Dic₃₇	C₂×M₁₆	semidirect
100. D₃₇	C₄×M₁₆	semidirect
107. C₃₇	C₂×C₄×M₁₆	semidirect
195. C₄	D₃₇⋊M₁₆	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×D₃₇⋊M₁₆	2
C₄×#10596953	2
C₄×#10596957	2
#14558492	2
C₄×D₃₇⋊C₈	2
C₂×C₄²×D₃₇	2
C₂×C₄×M₁₆	37

Subgroups — C4×D37⋊M16 #18011152

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₃₇⋊M₁₆ #18011152