Subgroups — C₂×#14557581 #18003202

Order 4736.

460 conjugacy classes of subgroups.

The subgroup lattice has 198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10596934	C₂	1	1	yes	maximal, characteristic
2	C₂²×#10596934	C₂	1	1	yes	maximal, characteristic
3	#14557581	C₂	1	8	yes	maximal, direct product factor
4	C₂×#11924471	C₂	1	4	yes	maximal, complemented
5	C₂²×M₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#10596934	—	2	1	no	—
7	C₂×#10596934	—	2	2	no	—
8	C₂×#10596934	C₄	1	2	yes	—
9	C₂×#10596934	C₄	1	2	yes	—
10	C₂×#10596934	C₄	1	4	yes	—
11	C₂×#10596934	C₂²	1	2	yes	—
12	C₂×#10596934	C₂²	1	4	yes	—
13	C₂×#10596934	C₂²	1	4	yes	—
14	C₂²×#64436	—	2	1	no	—
15	C₂²×#64436	C₂²	1	2	yes	—
16	#11924471	C₂²	1	16	yes	complemented
17	C₂³×C₄×C₃₇	C₂²	1	1	yes	characteristic
18	C₂×M₁₆×C₃₇	—	2	1	no	—
19	C₂×M₁₆×C₃₇	—	2	2	no	—
20	C₂×M₁₆×C₃₇	C₂²	1	2	yes	—
21	C₂×M₁₆×C₃₇	C₂²	1	4	yes	—
22	C₂²×C₈×C₃₇	—	2	1	no	—
23	C₂⁴×C₃₇	Q₈	1	1	yes	characteristic
24	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄×C₃₇	C₂×C₄	1	2	yes	—
27	C₂²×C₄×C₃₇	D₄	1	1	yes	characteristic
28	C₂²×C₄×C₃₇	D₄	1	1	yes	characteristic
29	C₂²×C₄×C₃₇	D₄	1	2	yes	—
30	C₂²×C₄×C₃₇	Q₈	1	1	yes	characteristic
31	C₂²×C₄×C₃₇	Q₈	1	2	yes	—
32	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
33	C₂²×C₄×C₃₇	C₂³	1	2	yes	—
34	M₁₆×C₃₇	—	2	4	no	—
35	M₁₆×C₃₇	—	2	2	no	—
36	M₁₆×C₃₇	C₂³	1	4	yes	—
37	C₂×C₈×C₃₇	—	2	4	no	—
38	C₂×C₈×C₃₇	—	2	2	no	—
39	#10596934	—	2	4	no	—
40	#10596934	—	2	2	no	—
41	#10596934	C₂×C₄	1	8	yes	—
42	#10596934	C₂×C₄	1	8	yes	—
43	#10596934	C₂³	1	4	yes	—
44	C₂×#64436	—	2	4	no	—
45	C₂×#64436	—	2	2	no	—
46	C₂×#64436	C₂×C₄	1	4	yes	—
47	C₂×#64436	C₂×C₄	1	4	yes	—
48	C₂×#64436	C₂³	1	4	yes	—
49	C₂³×C₃₇	—	4	2	no	—
50	C₂³×C₃₇	C₄⋊C₄	1	1	yes	characteristic
51	C₂³×C₃₇	C₄⋊C₄	1	1	yes	characteristic
52	C₂³×C₃₇	C₄⋊C₄	1	2	yes	—
53	C₂³×C₃₇	C₂×Q₈	1	1	yes	characteristic
54	C₂³×C₃₇	C₂×Q₈	1	2	yes	—
55	C₂×C₄×C₃₇	C₄⋊C₄	1	2	yes	—
56	C₂×C₄×C₃₇	C₄⋊C₄	1	2	yes	—
57	C₂×C₄×C₃₇	C₄⋊C₄	1	2	yes	—
58	C₂×C₄×C₃₇	C₄⋊C₄	1	2	yes	—
59	C₂×C₄×C₃₇	C₄⋊C₄	1	2	yes	—
60	C₂×C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
61	C₂×C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
62	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
63	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
64	C₂×C₄×C₃₇	C₂²×C₄	1	2	yes	—
65	C₂×C₄×C₃₇	C₂²×C₄	1	2	yes	—
66	C₂×C₄×C₃₇	C₂×D₄	1	2	yes	—
67	C₂×C₄×C₃₇	C₂×D₄	1	2	yes	—
68	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
69	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
70	C₂×C₄×C₃₇	C₂×Q₈	1	1	yes	characteristic
71	C₂×C₄×C₃₇	C₂×Q₈	1	2	yes	—
72	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
73	C₈×C₃₇	—	2	4	no	—
74	#64436	—	2	4	no	—
75	#64436	C₂²×C₄	1	8	yes	—
76	C₂²×C₃₇	—	2	2	no	—
77	C₂²×C₃₇	—	2	2	no	—
78	C₂²×C₃₇	—	2	2	no	—
79	C₂²×C₃₇	—	4	2	no	—
80	C₂²×C₃₇	—	4	2	no	—
81	C₂²×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₃₇	C₂×C₄⋊C₄	1	2	yes	—
83	C₂²×C₃₇	C₂×C₄⋊C₄	1	2	yes	—
84	C₂²×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₃₇	C₂²×Q₈	1	1	yes	characteristic
86	C₄×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
87	C₄×C₃₇	C₂×C₄⋊C₄	1	2	yes	—
88	C₄×C₃₇	C₂×C₄⋊C₄	1	2	yes	—
89	C₄×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
90	C₄×C₃₇	C₂³×C₄	1	1	yes	characteristic
91	C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
92	C₂×#430	—	37	1	no	maximal, Sylow
93	C₂×C₃₇	—	2	2	no	—
94	C₂×C₃₇	—	2	2	no	—
95	C₂×C₃₇	—	2	1	no	—
96	C₂×C₃₇	—	2	1	no	—
97	C₂×C₃₇	#430	1	2	yes	complemented
98	C₂×C₃₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
99	C₂²×M₁₆	—	37	1	no	—
100	C₂²×M₁₆	—	37	1	no	—
101	C₂²×M₁₆	D₃₇	1	1	yes	characteristic
102	#430	—	37	8	no	—
103	C₂×#108	—	37	4	no	—
104	C₃₇	C₂×#430	1	1	yes	characteristic, complemented, Sylow
105	C₂³×C₄	C₂×D₃₇	1	1	yes	characteristic
106	C₂×M₁₆	—	2	2	no	—
107	C₂×M₁₆	—	2	1	no	—
108	C₂×M₁₆	—	37	2	no	—
109	C₂×M₁₆	—	37	2	no	—
110	C₂×M₁₆	—	37	4	no	—
111	C₂×M₁₆	—	37	4	no	—
112	C₂×M₁₆	—	37	2	no	—
113	C₂×M₁₆	—	37	4	no	—
114	C₂×M₁₆	—	74	2	no	—
115	C₂×M₁₆	—	74	1	no	—
116	C₂×M₁₆	C₂×D₃₇	1	2	yes	—
117	C₂×M₁₆	C₂×D₃₇	1	4	yes	—
118	C₂²×C₈	—	2	1	no	—
119	C₂²×C₈	—	37	2	no	—
120	C₂²×C₈	—	74	1	no	—
121	#108	—	37	16	no	—
122	C₂⁴	Dic₇₄	1	1	yes	characteristic
123	C₂²×C₄	Dic₇₄	1	1	yes	characteristic
124	C₂²×C₄	Dic₇₄	1	2	yes	—
125	C₂²×C₄	C₄×D₃₇	1	1	yes	characteristic
126	C₂²×C₄	C₄×D₃₇	1	1	yes	characteristic
127	C₂²×C₄	C₄×D₃₇	1	2	yes	—
128	C₂²×C₄	C₂²⋊D₃₇	1	2	yes	—
129	C₂²×C₄	C₂²⋊D₃₇	1	1	yes	characteristic
130	C₂²×C₄	C₂²⋊D₃₇	1	1	yes	characteristic
131	C₂²×C₄	C₂²×D₃₇	1	2	yes	—
132	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
133	M₁₆	—	2	4	no	—
134	M₁₆	—	2	2	no	—
135	M₁₆	—	37	8	no	—
136	M₁₆	—	37	8	no	—
137	M₁₆	—	37	4	no	—
138	M₁₆	—	74	4	no	—
139	M₁₆	—	74	2	no	—
140	M₁₆	C₂²×D₃₇	1	4	yes	—
141	C₂×C₈	—	2	4	no	—
142	C₂×C₈	—	2	2	no	—
143	C₂×C₈	—	37	4	no	—
144	C₂×C₈	—	37	4	no	—
145	C₂×C₈	—	37	4	no	—
146	C₂×C₈	—	74	4	no	—
147	C₂×C₈	—	74	2	no	—
148	C₂³	—	4	2	no	—
149	C₂³	#10596936	1	1	yes	characteristic
150	C₂³	#10596936	1	1	yes	characteristic
151	C₂³	#10596936	1	2	yes	—
152	C₂³	C₂×Dic₇₄	1	1	yes	characteristic
153	C₂³	C₂×Dic₇₄	1	2	yes	—
154	C₂×C₄	#10596936	1	2	yes	—
155	C₂×C₄	#10596936	1	2	yes	—
156	C₂×C₄	#10596936	1	2	yes	—
157	C₂×C₄	#10596936	1	1	yes	characteristic
158	C₂×C₄	#10596936	1	1	yes	characteristic
159	C₂×C₄	#10596936	1	2	yes	—
160	C₂×C₄	#10596936	1	2	yes	—
161	C₂×C₄	C₂×Dic₇₄	1	2	yes	—
162	C₂×C₄	C₂×Dic₇₄	1	1	yes	characteristic
163	C₂×C₄	C₂×C₄×D₃₇	1	1	yes	characteristic
164	C₂×C₄	C₂×C₄×D₃₇	1	1	yes	characteristic
165	C₂×C₄	C₂×C₄×D₃₇	1	2	yes	—
166	C₂×C₄	C₂×C₄×D₃₇	1	2	yes	—
167	C₂×C₄	C₂×C₂²⋊D₃₇	1	2	yes	—
168	C₂×C₄	C₂×C₂²⋊D₃₇	1	2	yes	—
169	C₂×C₄	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
170	C₂×C₄	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
171	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
172	C₈	—	2	4	no	—
173	C₈	—	37	8	no	—
174	C₈	—	74	4	no	—
175	C₂²	—	2	2	no	—
176	C₂²	—	2	2	no	—
177	C₂²	—	2	2	no	—
178	C₂²	—	4	2	no	—
179	C₂²	—	4	2	no	—
180	C₂²	C₂×#10596936	1	1	yes	characteristic
181	C₂²	C₂×#10596936	1	2	yes	—
182	C₂²	C₂×#10596936	1	2	yes	—
183	C₂²	C₂×#10596936	1	1	yes	characteristic
184	C₂²	C₂²×Dic₇₄	1	1	yes	characteristic
185	C₄	C₂×#10596936	1	1	yes	characteristic
186	C₄	C₂×#10596936	1	2	yes	—
187	C₄	C₂×#10596936	1	2	yes	—
188	C₄	C₂×#10596936	1	1	yes	characteristic
189	C₄	C₂²×C₄×D₃₇	1	1	yes	characteristic
190	C₄	C₂²×C₂²⋊D₃₇	1	1	yes	characteristic
191	C₂	—	2	2	no	—
192	C₂	—	2	2	no	—
193	C₂	—	2	1	no	—
194	C₂	—	2	1	no	—
195	C₂	#14557581	1	2	yes	direct product factor
196	C₂	C₂²×#10596936	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₃₇
commutator	C₄×C₃₇	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₃₇
Fitting	C₂²×M₁₆×C₃₇	C₂
socle	C₂²×C₃₇	C₂×C₄⋊C₄
prime radical	C₂⁴×C₃₇	Q₈
cosocle	C₂×C₄×C₃₇	C₂⁴
hypercenter	C₂²×M₁₆	D₃₇
hypocenter	C₃₇	C₂×#430
LCS	G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×M₁₆

Complements

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

N	H ≅ G/N	type
3. #14557581	C₂	direct (N × H)
4. C₂×#11924471	C₂	semidirect
16. #11924471	C₂²	semidirect
97. C₂×C₃₇	#430	semidirect
104. C₃₇	C₂×#430	semidirect
195. C₂	#14557581	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×#10596934	2
#14557581	2
C₂×#11924471	2
C₂²×M₁₆×C₃₇	2
C₂×#430	37

Subgroups — C2×#14557581 #18003202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14557581 #18003202