Subgroups — C₄×#11924615 #18011028

Order 4736.

752 conjugacy classes of subgroups.

The subgroup lattice has 208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11924615	C₂	1	2	yes	maximal
2	C₄×C₄⋊#3866	C₂	1	4	yes	maximal, complemented
3	C₄×C₂²⋊#3866	C₂	1	4	yes	maximal
4	#14558469	C₂	1	2	yes	maximal, complemented
5	C₄²×#3866	C₂	1	2	yes	maximal, complemented
6	C₂×C₄²×D₃₇	C₂	1	1	yes	maximal, characteristic
7	#11924615	C₄	1	16	yes	direct product factor
8	C₂×C₄⋊#3866	C₂²	1	4	yes	—
9	C₂×C₂²⋊#3866	C₂²	1	4	yes	—
10	C₂×C₄×#3866	C₂²	1	8	yes	—
11	C₂×C₄×#3866	C₂²	1	4	yes	—
12	(C₂×#3866)⋊C₄	C₂²	1	8	yes	—
13	C₂²×C₄×D₃₇	C₂²	1	2	yes	—
14	C₂²×C₄×D₃₇	C₂²	1	1	yes	characteristic
15	C₂×C₄×Dic₃₇	C₄	1	1	yes	characteristic, complemented
16	C₂×C₄×Dic₃₇	C₄	1	2	yes	complemented
17	C₄²×D₃₇	C₄	1	2	yes	complemented
18	C₄²×D₃₇	C₄	1	1	yes	characteristic, complemented
19	C₄²×D₃₇	C₄	1	1	yes	characteristic, complemented
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, complemented
24	C₂³×D₃₇	C₂³	1	1	yes	characteristic
25	C₂²×#3866	C₂³	1	8	yes	—
26	C₂²×C₄×C₃₇	C₂×C₄	1	2	yes	—
27	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
28	C₂²×Dic₃₇	C₂×C₄	1	2	yes	—
29	C₂²×Dic₃₇	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄×D₃₇	—	2	8	no	—
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	C₂³	1	2	yes	—
37	C₂×C₄×D₃₇	C₂³	1	1	yes	characteristic
38	C₂×C₄×D₃₇	C₂³	1	1	yes	characteristic
39	C₂×C₄×D₃₇	C₂³	1	2	yes	—
40	C₂²⋊#3866	C₂×C₄	1	16	yes	—
41	C₄⋊#3866	C₂×C₄	1	16	yes	complemented
42	C₄×#3866	—	2	16	no	—
43	C₄×#3866	C₂×C₄	1	16	yes	complemented
44	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
45	C₄²×C₃₇	C₂×C₄	1	2	yes	—
46	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
47	C₄×Dic₃₇	C₂×C₄	1	1	yes	characteristic
48	C₄×Dic₃₇	C₂×C₄	1	2	yes	—
49	C₄×Dic₃₇	C₂×C₄	1	2	yes	—
50	C₄×Dic₃₇	C₂×C₄	1	2	yes	—
51	C₄×Dic₃₇	C₂×C₄	1	2	yes	—
52	C₄×Dic₃₇	C₂×C₄	1	2	yes	—
53	C₄×Dic₃₇	C₂×C₄	1	1	yes	characteristic
54	C₂³×C₃₇	C₂²×C₄	1	1	yes	characteristic
55	C₂²×D₃₇	—	2	4	no	—
56	C₂²×D₃₇	C₂²×C₄	1	1	yes	characteristic
57	C₂²×D₃₇	C₂²×C₄	1	4	yes	—
58	C₂²×D₃₇	C₂⁴	1	1	yes	characteristic
59	C₂×#3866	—	2	16	no	—
60	C₂×#3866	C₂²×C₄	1	16	yes	—
61	C₂×C₄×C₃₇	—	2	4	no	—
62	C₂×C₄×C₃₇	C₄²	1	4	yes	complemented
63	C₂×C₄×C₃₇	C₂²×C₄	1	2	yes	—
64	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
65	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
66	C₂×C₄×C₃₇	C₂²×C₄	1	2	yes	—
67	C₂×Dic₃₇	—	2	4	no	—
68	C₂×Dic₃₇	C₄²	1	4	yes	complemented
69	C₂×Dic₃₇	C₂²×C₄	1	2	yes	—
70	C₂×Dic₃₇	C₂²×C₄	1	1	yes	characteristic
71	C₂×Dic₃₇	C₂²×C₄	1	1	yes	characteristic
72	C₂×Dic₃₇	C₂²×C₄	1	2	yes	—
73	C₄×D₃₇	—	2	4	no	—
74	C₄×D₃₇	—	2	4	no	—
75	C₄×D₃₇	—	2	4	no	—
76	C₄×D₃₇	C₄²	1	4	yes	complemented
77	C₄×D₃₇	C₄²	1	4	yes	complemented
78	C₄×D₃₇	C₂²×C₄	1	4	yes	—
79	C₄×D₃₇	C₂²×C₄	1	4	yes	—
80	C₄×D₃₇	#41	1	8	yes	—
81	C₂²×C₃₇	—	2	2	no	—
82	C₂²×C₃₇	C₂×C₄²	1	2	yes	—
83	C₂²×C₃₇	C₂³×C₄	1	1	yes	characteristic
84	C₂×D₃₇	—	2	2	no	—
85	C₂×D₃₇	—	2	8	no	—
86	C₂×D₃₇	C₂×C₄²	1	2	yes	—
87	C₂×D₃₇	C₂³×C₄	1	2	yes	—
88	C₂×D₃₇	C₂×#41	1	4	yes	—
89	#3866	—	2	16	no	—
90	C₄×C₃₇	—	2	2	no	—
91	C₄×C₃₇	C₂×C₄²	1	2	yes	—
92	C₄×C₃₇	C₂×C₄²	1	2	yes	—
93	C₄×C₃₇	#117	1	4	yes	complemented
94	Dic₃₇	—	2	2	no	—
95	Dic₃₇	C₂×C₄²	1	2	yes	—
96	Dic₃₇	C₂×C₄²	1	2	yes	—
97	Dic₃₇	#117	1	4	yes	complemented
98	C₄×#117	—	37	1	no	maximal, Sylow
99	C₂×C₃₇	—	2	2	no	—
100	C₂×C₃₇	C₂²×C₄²	1	1	yes	characteristic
101	C₂×C₃₇	C₂×#117	1	2	yes	—
102	D₃₇	—	2	2	no	—
103	D₃₇	C₄×#41	1	4	yes	—
104	C₂×#117	—	37	2	no	—
105	C₂²×C₄²	—	37	1	no	—
106	C₄×C₄⋊C₄	—	37	4	no	—
107	C₄×C₂²⋊C₄	—	37	4	no	—
108	#376	—	37	2	no	—
109	C₄³	—	37	2	no	—
110	C₃₇	C₄×#117	1	1	yes	characteristic, complemented, Sylow
111	C₂³×C₄	—	37	1	no	—
112	C₂³×C₄	—	37	2	no	—
113	#117	—	37	16	no	—
114	C₂×C₄⋊C₄	—	37	4	no	—
115	C₂×C₂²⋊C₄	—	37	4	no	—
116	C₂×C₄²	—	37	4	no	—
117	C₂×C₄²	—	37	2	no	—
118	C₂×C₄²	—	37	1	no	—
119	C₂×C₄²	—	37	1	no	—
120	C₂×C₄²	—	37	2	no	—
121	C₂×C₄²	—	37	1	no	—
122	C₂×C₄²	—	37	2	no	—
123	C₂×C₄²	—	37	1	no	—
124	C₂×C₄²	—	37	1	no	—
125	C₂×C₄²	—	37	8	no	—
126	C₂×C₄²	#3866	1	1	yes	characteristic, complemented
127	#95	—	37	8	no	—
128	C₂⁴	—	37	1	no	—
129	C₂²×C₄	—	37	1	no	—
130	C₂²×C₄	—	37	8	no	—
131	C₂²×C₄	—	37	1	no	—
132	C₂²×C₄	—	37	1	no	—
133	C₂²×C₄	—	37	1	no	—
134	C₂²×C₄	—	37	2	no	—
135	C₂²×C₄	—	37	1	no	—
136	C₂²×C₄	—	37	8	no	—
137	C₂²×C₄	—	37	2	no	—
138	C₂²×C₄	—	37	2	no	—
139	C₂²×C₄	—	37	2	no	—
140	C₂²×C₄	—	37	2	no	—
141	C₂²×C₄	—	74	8	no	—
142	C₂²×C₄	C₂×#3866	1	2	yes	—
143	C₂²×C₄	C₂×#3866	1	1	yes	characteristic
144	C₄⋊C₄	—	37	16	no	—
145	C₂²⋊C₄	—	37	16	no	—
146	C₄²	—	37	16	no	—
147	C₄²	—	37	2	no	—
148	C₄²	—	37	1	no	—
149	C₄²	—	37	2	no	—
150	C₄²	—	37	2	no	—
151	C₄²	—	37	2	no	—
152	C₄²	—	37	2	no	—
153	C₄²	—	37	1	no	—
154	C₄²	—	74	16	no	—
155	C₄²	C₂×#3866	1	1	yes	characteristic
156	C₄²	C₂×#3866	1	2	yes	—
157	C₄²	C₂×#3866	1	1	yes	characteristic
158	C₂³	—	37	1	no	—
159	C₂³	—	37	4	no	—
160	C₂³	—	37	1	no	—
161	C₂³	—	74	4	no	—
162	C₂³	C₂²×#3866	1	1	yes	characteristic
163	C₂×C₄	—	2	4	no	—
164	C₂×C₄	—	37	4	no	—
165	C₂×C₄	—	37	1	no	—
166	C₂×C₄	—	37	1	no	—
167	C₂×C₄	—	37	2	no	—
168	C₂×C₄	—	37	4	no	—
169	C₂×C₄	—	37	4	no	—
170	C₂×C₄	—	37	4	no	—
171	C₂×C₄	—	37	4	no	—
172	C₂×C₄	—	37	8	no	—
173	C₂×C₄	—	37	16	no	—
174	C₂×C₄	—	37	2	no	—
175	C₂×C₄	—	74	4	no	—
176	C₂×C₄	—	74	4	no	—
177	C₂×C₄	—	74	4	no	—
178	C₂×C₄	—	74	16	no	—
179	C₂×C₄	—	74	4	no	—
180	C₂×C₄	C₄×#3866	1	4	yes	complemented
181	C₂×C₄	C₂²×#3866	1	2	yes	—
182	C₂×C₄	C₂²×#3866	1	1	yes	characteristic
183	C₂×C₄	C₂²×#3866	1	1	yes	characteristic
184	C₂×C₄	C₂²×#3866	1	2	yes	—
185	C₂²	—	2	2	no	—
186	C₂²	—	37	2	no	—
187	C₂²	—	37	4	no	—
188	C₂²	—	37	2	no	—
189	C₂²	—	74	8	no	—
190	C₂²	—	74	2	no	—
191	C₂²	C₂×C₄×#3866	1	2	yes	—
192	C₂²	C₂³×#3866	1	1	yes	characteristic
193	C₄	—	2	2	no	—
194	C₄	—	37	2	no	—
195	C₄	—	37	2	no	—
196	C₄	—	37	4	no	—
197	C₄	—	74	16	no	—
198	C₄	—	74	2	no	—
199	C₄	C₂×C₄×#3866	1	2	yes	—
200	C₄	C₂×C₄×#3866	1	2	yes	—
201	C₄	#11924615	1	4	yes	direct product factor
202	C₂	—	2	2	no	—
203	C₂	—	37	4	no	—
204	C₂	—	74	2	no	—
205	C₂	C₂²×C₄×#3866	1	1	yes	characteristic
206	C₂	C₂×#11924615	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	C₂³
cosocle	C₂²×D₃₇	C₂⁴
hypercenter	C₂×C₄²	#3866
hypocenter	C₃₇	C₄×#117
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×C₄⋊#3866	C₂	semidirect
4. #14558469	C₂	semidirect
5. C₄²×#3866	C₂	semidirect
7. #11924615	C₄	direct (N × H)
15. C₂×C₄×Dic₃₇	C₄	semidirect
16. C₂×C₄×Dic₃₇	C₄	semidirect
17. C₄²×D₃₇	C₄	semidirect
18. C₄²×D₃₇	C₄	semidirect
19. C₄²×D₃₇	C₄	semidirect
23. C₂×C₄²×C₃₇	C₄	semidirect
41. C₄⋊#3866	C₂×C₄	semidirect
43. C₄×#3866	C₂×C₄	semidirect
62. C₂×C₄×C₃₇	C₄²	semidirect
68. C₂×Dic₃₇	C₄²	semidirect
76. C₄×D₃₇	C₄²	semidirect
77. C₄×D₃₇	C₄²	semidirect
93. C₄×C₃₇	#117	semidirect
97. Dic₃₇	#117	semidirect
110. C₃₇	C₄×#117	semidirect
126. C₂×C₄²	#3866	semidirect
180. C₂×C₄	C₄×#3866	semidirect
201. C₄	#11924615	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×#11924615	2
C₄×C₄⋊#3866	2
C₄×C₂²⋊#3866	2
#14558469	2
C₄²×#3866	2
C₂×C₄²×D₃₇	2
C₄×#117	37

Subgroups — C4×#11924615 #18011028

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11924615 #18011028