Subgroups — C₂×#14558086 #18007883

Order 4736.

1168 conjugacy classes of subgroups.

The subgroup lattice has 184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558086	C₂	1	16	yes	maximal, direct product factor
2	C₂×#11924535	C₂	1	2	yes	maximal, complemented
3	C₂×#11924527	C₂	1	2	yes	maximal, complemented
4	C₂×#11924513	C₂	1	4	yes	maximal
5	C₂×C₄×Dic₇₄	C₂	1	4	yes	maximal, complemented
6	C₂×#11924495	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₄×Dic₃₇	C₂	1	1	yes	maximal, characteristic
8	C₂×#117×C₃₇	C₂	1	1	yes	maximal, characteristic
9	C₂²×Dic₇₄	C₂²	1	4	yes	—
10	C₂³×Dic₃₇	C₂²	1	2	yes	—
11	#11924535	C₂²	1	16	yes	complemented
12	#11924527	C₂²	1	16	yes	complemented
13	#11924513	C₂²	1	32	yes	—
14	C₄×Dic₇₄	C₂²	1	32	yes	complemented
15	#11924495	C₂²	1	8	yes	—
16	C₂×C₄⋊Dic₃₇	C₂²	1	2	yes	—
17	C₂×C₄⋊Dic₃₇	C₂²	1	4	yes	—
18	C₂×#10596936	C₂²	1	4	yes	—
19	C₂×#10596936	C₂²	1	4	yes	—
20	C₂×C₂²⋊Dic₃₇	C₂²	1	2	yes	—
21	C₂×C₄×Dic₃₇	C₂²	1	2	yes	—
22	C₂×C₄×Dic₃₇	C₂²	1	1	yes	characteristic
23	C₂×C₄×Dic₃₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×Dic₃₇	C₂²	1	8	yes	—
25	C₂×C₄×Dic₃₇	C₂²	1	2	yes	—
26	C₂³×C₄×C₃₇	C₂²	1	1	yes	characteristic
27	#117×C₃₇	C₂²	1	8	yes	—
28	C₂×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
29	C₂×C₂²⋊C₄×C₃₇	C₂²	1	2	yes	—
30	C₂×C₄²×C₃₇	C₂²	1	2	yes	—
31	C₂⁴×C₃₇	C₂³	1	1	yes	characteristic
32	C₂²×C₄×C₃₇	Q₈	1	8	yes	complemented
33	C₂²×C₄×C₃₇	C₂³	1	4	yes	—
34	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
35	C₂²×C₄×C₃₇	C₂³	1	4	yes	—
36	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
37	C₂²×Dic₃₇	—	2	8	no	—
38	C₂²×Dic₃₇	C₂³	1	2	yes	—
39	C₂²×Dic₃₇	C₂³	1	8	yes	—
40	C₂²×Dic₃₇	C₂³	1	4	yes	—
41	C₂²×Dic₃₇	C₂³	1	2	yes	—
42	C₂×Dic₇₄	—	2	16	no	—
43	C₂×Dic₇₄	C₂³	1	16	yes	—
44	C₄⋊C₄×C₃₇	C₂³	1	8	yes	—
45	C₂²⋊C₄×C₃₇	C₂³	1	8	yes	—
46	C₄²×C₃₇	C₂³	1	8	yes	—
47	C₂²⋊Dic₃₇	C₂³	1	8	yes	—
48	C₄⋊Dic₃₇	C₂³	1	8	yes	—
49	C₄⋊Dic₃₇	C₂³	1	16	yes	—
50	#10596936	C₂³	1	16	yes	—
51	#10596936	C₂³	1	16	yes	—
52	C₄×Dic₃₇	C₂³	1	8	yes	—
53	C₄×Dic₃₇	C₂³	1	4	yes	—
54	C₄×Dic₃₇	C₂³	1	4	yes	—
55	C₄×Dic₃₇	C₂³	1	8	yes	—
56	C₂³×C₃₇	—	2	4	no	—
57	C₂³×C₃₇	C₂×Q₈	1	4	yes	—
58	C₂³×C₃₇	C₂⁴	1	2	yes	—
59	C₂³×C₃₇	C₂⁴	1	1	yes	characteristic
60	C₂×C₄×C₃₇	—	2	8	no	—
61	C₂×C₄×C₃₇	C₂×Q₈	1	4	yes	—
62	C₂×C₄×C₃₇	C₂×Q₈	1	4	yes	—
63	C₂×C₄×C₃₇	C₂×Q₈	1	16	yes	complemented
64	C₂×C₄×C₃₇	C₂⁴	1	8	yes	—
65	C₂×C₄×C₃₇	C₂⁴	1	2	yes	—
66	C₂×C₄×C₃₇	C₂⁴	1	2	yes	—
67	C₂×Dic₃₇	—	2	8	no	—
68	C₂×Dic₃₇	—	2	4	no	—
69	C₂×Dic₃₇	—	2	16	no	—
70	C₂×Dic₃₇	#41	1	8	yes	—
71	C₂×Dic₃₇	C₂⁴	1	4	yes	—
72	C₂×Dic₃₇	C₂⁴	1	8	yes	—
73	C₂×Dic₃₇	C₂⁴	1	4	yes	—
74	Dic₇₄	—	2	32	no	—
75	C₂²×C₃₇	—	2	8	no	—
76	C₂²×C₃₇	—	2	4	no	—
77	C₂²×C₃₇	C₂²×Q₈	1	4	yes	—
78	C₂²×C₃₇	C₂²×Q₈	1	2	yes	—
79	C₂²×C₃₇	C₂×#41	1	4	yes	—
80	C₂²×C₃₇	C₂⁵	1	1	yes	characteristic
81	C₄×C₃₇	—	2	8	no	—
82	C₄×C₃₇	C₂²×Q₈	1	4	yes	—
83	C₄×C₃₇	C₂²×Q₈	1	4	yes	—
84	Dic₃₇	—	2	8	no	—
85	Dic₃₇	—	2	4	no	—
86	Dic₃₇	C₂×#41	1	8	yes	—
87	C₂×#533	—	37	1	no	maximal, Sylow
88	C₂×C₃₇	—	2	4	no	—
89	C₂×C₃₇	#533	1	4	yes	complemented
90	C₂×C₃₇	C₂³×Q₈	1	1	yes	characteristic
91	C₂×C₃₇	C₂²×#41	1	2	yes	—
92	#533	—	37	16	no	—
93	C₂×C₄⋊Q₈	—	37	2	no	—
94	C₂×#125	—	37	2	no	—
95	C₂×C₂²⋊Q₈	—	37	4	no	—
96	C₂×C₄×Q₈	—	37	4	no	—
97	C₂×#117	—	37	1	no	—
98	C₂×#117	D₃₇	1	1	yes	characteristic
99	C₂²×C₄²	—	37	1	no	—
100	C₃₇	C₂×#533	1	1	yes	characteristic, complemented, Sylow
101	C₂²×Q₈	—	37	4	no	—
102	C₂³×C₄	—	37	2	no	—
103	C₂³×C₄	C₂×D₃₇	1	1	yes	characteristic
104	C₄⋊Q₈	—	37	16	no	—
105	#125	—	37	16	no	—
106	C₂²⋊Q₈	—	37	32	no	—
107	C₄×Q₈	—	37	32	no	—
108	#117	—	37	8	no	—
109	#117	C₂×D₃₇	1	8	yes	—
110	C₂×C₄⋊C₄	—	37	2	no	—
111	C₂×C₄⋊C₄	—	37	4	no	—
112	C₂×C₄⋊C₄	—	37	4	no	—
113	C₂×C₄⋊C₄	—	37	4	no	—
114	C₂×C₄⋊C₄	C₂×D₃₇	1	2	yes	—
115	C₂×C₂²⋊C₄	—	37	2	no	—
116	C₂×C₂²⋊C₄	C₂×D₃₇	1	2	yes	—
117	C₂×C₄²	—	37	1	no	—
118	C₂×C₄²	—	37	1	no	—
119	C₂×C₄²	—	37	8	no	—
120	C₂×C₄²	—	37	2	no	—
121	C₂×C₄²	—	37	2	no	—
122	C₂×C₄²	C₂×D₃₇	1	2	yes	—
123	C₂⁴	C₂²×D₃₇	1	1	yes	characteristic
124	C₂×Q₈	—	37	16	no	—
125	C₂×Q₈	—	74	16	no	—
126	C₂²×C₄	—	37	2	no	—
127	C₂²×C₄	—	37	2	no	—
128	C₂²×C₄	—	37	8	no	—
129	C₂²×C₄	—	37	4	no	—
130	C₂²×C₄	—	74	8	no	—
131	C₂²×C₄	Dic₇₄	1	8	yes	complemented
132	C₂²×C₄	C₂²×D₃₇	1	4	yes	—
133	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
134	C₂²×C₄	C₂²×D₃₇	1	4	yes	—
135	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
136	C₄⋊C₄	—	37	16	no	—
137	C₄⋊C₄	—	37	16	no	—
138	C₄⋊C₄	—	37	8	no	—
139	C₄⋊C₄	—	37	16	no	—
140	C₄⋊C₄	C₂²×D₃₇	1	8	yes	—
141	C₂²⋊C₄	—	37	8	no	—
142	C₂²⋊C₄	C₂²×D₃₇	1	8	yes	—
143	C₄²	—	37	8	no	—
144	C₄²	—	37	4	no	—
145	C₄²	—	37	4	no	—
146	C₄²	—	37	8	no	—
147	C₄²	C₂²×D₃₇	1	8	yes	—
148	C₂³	—	2	4	no	—
149	C₂³	C₂×Dic₇₄	1	4	yes	—
150	C₂³	C₂³×D₃₇	1	2	yes	—
151	C₂³	C₂³×D₃₇	1	1	yes	characteristic
152	Q₈	—	74	32	no	—
153	C₂×C₄	—	2	8	no	—
154	C₂×C₄	—	37	8	no	—
155	C₂×C₄	—	37	4	no	—
156	C₂×C₄	—	37	4	no	—
157	C₂×C₄	—	37	8	no	—
158	C₂×C₄	—	74	16	no	—
159	C₂×C₄	—	74	4	no	—
160	C₂×C₄	—	74	8	no	—
161	C₂×C₄	C₂×Dic₇₄	1	4	yes	—
162	C₂×C₄	C₂×Dic₇₄	1	4	yes	—
163	C₂×C₄	C₂×Dic₇₄	1	16	yes	complemented
164	C₂×C₄	C₂³×D₃₇	1	8	yes	—
165	C₂×C₄	C₂³×D₃₇	1	2	yes	—
166	C₂×C₄	C₂³×D₃₇	1	2	yes	—
167	C₂²	—	2	8	no	—
168	C₂²	—	2	4	no	—
169	C₂²	C₂²×Dic₇₄	1	4	yes	—
170	C₂²	C₂²×Dic₇₄	1	2	yes	—
171	C₂²	#41×D₃₇	1	4	yes	—
172	C₂²	C₂⁴×D₃₇	1	1	yes	characteristic
173	C₄	—	2	8	no	—
174	C₄	—	37	8	no	—
175	C₄	—	74	4	no	—
176	C₄	—	74	8	no	—
177	C₄	C₂²×Dic₇₄	1	4	yes	—
178	C₄	C₂²×Dic₇₄	1	4	yes	—
179	C₂	—	2	4	no	—
180	C₂	#14558086	1	4	yes	direct product factor
181	C₂	C₂³×Dic₇₄	1	1	yes	characteristic
182	C₂	C₂×#41×D₃₇	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₃₇
commutator, cosocle	C₂²×C₃₇	C₂⁵
Frattini	C₂²	C₂⁴×D₃₇
Fitting	C₂×#117×C₃₇	C₂
socle	C₂³×C₃₇	C₂⁴
prime radical	C₂⁴×C₃₇	C₂³
hypercenter	C₂×#117	D₃₇
hypocenter	C₃₇	C₂×#533
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#117

Complements

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

N	H ≅ G/N	type
1. #14558086	C₂	direct (N × H)
2. C₂×#11924535	C₂	semidirect
3. C₂×#11924527	C₂	semidirect
5. C₂×C₄×Dic₇₄	C₂	semidirect
11. #11924535	C₂²	semidirect
12. #11924527	C₂²	semidirect
14. C₄×Dic₇₄	C₂²	semidirect
32. C₂²×C₄×C₃₇	Q₈	semidirect
63. C₂×C₄×C₃₇	C₂×Q₈	semidirect
89. C₂×C₃₇	#533	semidirect
100. C₃₇	C₂×#533	semidirect
131. C₂²×C₄	Dic₇₄	semidirect
163. C₂×C₄	C₂×Dic₇₄	semidirect
180. C₂	#14558086	direct (N × H)

Maximal subgroups

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

subgroup	index
#14558086	2
C₂×#11924535	2
C₂×#11924527	2
C₂×#11924513	2
C₂×C₄×Dic₇₄	2
C₂×#11924495	2
C₂²×C₄×Dic₃₇	2
C₂×#117×C₃₇	2
C₂×#533	37

Subgroups — C2×#14558086 #18007883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14558086 #18007883