Subgroups — #18011405

Order 4736.

412 conjugacy classes of subgroups.

The subgroup lattice has 210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558584	C₂	1	2	yes	maximal, complemented
2	#14558568	C₂	1	2	yes	maximal, complemented
3	#14558564	C₂	1	4	yes	maximal, complemented
4	#14558550	C₂	1	2	yes	maximal, complemented
5	#14558549	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×#10596957	C₂	1	2	yes	maximal, complemented
7	C₂×C₄×#64438	C₂	1	1	yes	maximal, characteristic, complemented
8	#41×Dic₃₇	C₂	1	1	yes	maximal, characteristic
9	C₂×#10596957	C₂²	1	4	yes	—
10	C₂²×#64438	C₂²	1	2	yes	—
11	#11924603	C₂²	1	4	yes	—
12	C₄⋊#64438	C₂²	1	2	yes	—
13	C₂²⋊#64438	C₂²	1	2	yes	—
14	C₂²⋊#64438	C₂²	1	4	yes	—
15	#11924591	C₂²	1	4	yes	—
16	C₄×#64438	C₂²	1	1	yes	characteristic
17	C₄×#64438	C₂²	1	1	yes	characteristic
18	C₄×#64438	C₂²	1	2	yes	—
19	C₄×#64438	C₂²	1	2	yes	—
20	Q₈×Dic₃₇	C₄	1	1	yes	characteristic
21	Q₈×Dic₃₇	C₂²	1	1	yes	characteristic
22	D₄×Dic₃₇	C₄	1	2	yes	—
23	D₄×Dic₃₇	C₄	1	1	yes	characteristic
24	D₄×Dic₃₇	C₂²	1	2	yes	—
25	D₄×Dic₃₇	C₂²	1	1	yes	characteristic
26	#11924495	C₄	1	2	yes	—
27	#11924495	C₄	1	1	yes	characteristic
28	C₂×C₄×Dic₃₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×Dic₃₇	C₂²	1	2	yes	—
30	C₂×#41×C₃₇	C₄	1	1	yes	characteristic
31	#41×C₃₇	—	2	4	no	—
32	C₂×Q₈×C₃₇	C₂×C₄	1	1	yes	characteristic
33	C₂×D₄×C₃₇	C₂×C₄	1	2	yes	—
34	C₂×D₄×C₃₇	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₄×C₃₇	C₂×C₄	1	2	yes	—
36	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
37	C₂²×Dic₃₇	C₂×C₄	1	2	yes	—
38	C₂²×Dic₃₇	C₂×C₄	1	1	yes	characteristic
39	C₂²×Dic₃₇	C₂³	1	1	yes	characteristic
40	C₂²×Dic₃₇	C₂³	1	2	yes	—
41	#10596957	—	2	8	no	—
42	C₂×#64438	—	2	4	no	—
43	C₂×#64438	C₂³	1	2	yes	—
44	C₂×#64438	C₂³	1	4	yes	—
45	C₂×#64438	C₂³	1	2	yes	—
46	C₂²⋊Dic₃₇	C₂×C₄	1	2	yes	—
47	C₂²⋊Dic₃₇	C₂×C₄	1	2	yes	—
48	C₂²⋊Dic₃₇	C₂×C₄	1	2	yes	—
49	C₄⋊Dic₃₇	C₂×C₄	1	2	yes	—
50	C₄⋊Dic₃₇	C₂×C₄	1	1	yes	characteristic
51	C₄⋊Dic₃₇	C₂×C₄	1	2	yes	—
52	C₄⋊Dic₃₇	C₂×C₄	1	1	yes	characteristic
53	C₄×Dic₃₇	C₂×C₄	1	1	yes	characteristic
54	C₄×Dic₃₇	C₂×C₄	1	2	yes	—
55	C₄×Dic₃₇	C₂×C₄	1	2	yes	—
56	C₄×Dic₃₇	C₂×C₄	1	1	yes	characteristic
57	C₄×Dic₃₇	C₂³	1	1	yes	characteristic
58	C₄×Dic₃₇	C₂³	1	1	yes	characteristic
59	C₄×Dic₃₇	C₂³	1	2	yes	—
60	C₂³×C₃₇	C₂²×C₄	1	2	yes	—
61	C₂³×C₃₇	C₂²×C₄	1	1	yes	characteristic
62	Q₈×C₃₇	—	2	2	no	—
63	D₄×C₃₇	—	2	4	no	—
64	D₄×C₃₇	—	2	2	no	—
65	C₂×C₄×C₃₇	—	2	4	no	—
66	C₂×C₄×C₃₇	M₁₆	1	4	yes	complemented
67	C₂×C₄×C₃₇	C₂²×C₄	1	2	yes	—
68	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
69	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
70	C₂×Dic₃₇	—	2	2	no	—
71	C₂×Dic₃₇	—	2	4	no	—
72	C₂×Dic₃₇	—	2	2	no	—
73	C₂×Dic₃₇	—	2	4	no	—
74	C₂×Dic₃₇	C₂²×C₄	1	1	yes	characteristic
75	C₂×Dic₃₇	C₂²×C₄	1	2	yes	—
76	C₂×Dic₃₇	C₂²×C₄	1	1	yes	characteristic
77	C₂×Dic₃₇	C₂²×C₄	1	2	yes	—
78	C₂×Dic₃₇	C₂²×C₄	1	1	yes	characteristic
79	C₂×Dic₃₇	C₂⁴	1	1	yes	characteristic
80	#64438	—	2	2	no	—
81	#64438	—	2	4	no	—
82	#64438	#41	1	4	yes	complemented
83	C₂²×C₃₇	—	2	1	no	—
84	C₂²×C₃₇	—	2	1	no	—
85	C₂²×C₃₇	—	2	2	no	—
86	C₂²×C₃₇	—	2	2	no	—
87	C₂²×C₃₇	—	2	2	no	—
88	C₂²×C₃₇	C₂×M₁₆	1	2	yes	—
89	C₂²×C₃₇	C₂³×C₄	1	1	yes	characteristic
90	C₄×C₃₇	—	2	2	no	—
91	C₄×C₃₇	C₂×M₁₆	1	2	yes	—
92	C₄×C₃₇	C₂×M₁₆	1	2	yes	—
93	Dic₃₇	—	2	1	no	—
94	Dic₃₇	—	2	2	no	—
95	Dic₃₇	—	2	1	no	—
96	Dic₃₇	—	2	2	no	—
97	Dic₃₇	#131	1	2	yes	—
98	Dic₃₇	C₂×#41	1	2	yes	—
99	#2965	—	37	1	no	maximal, Sylow
100	C₂×C₃₇	—	2	2	no	—
101	C₂×C₃₇	—	4	2	no	—
102	C₂×C₃₇	C₄×#41	1	1	yes	characteristic
103	C₂×C₃₇	C₂²×M₁₆	1	1	yes	characteristic
104	C₂×C₃₇	C₂×#131	1	1	yes	characteristic
105	C₄×#41	—	37	1	no	—
106	#446	—	37	2	no	—
107	#436	—	37	2	no	—
108	#435	—	37	4	no	—
109	#431	—	37	1	no	—
110	#431	—	37	2	no	—
111	C₄×M₁₆	—	37	2	no	—
112	C₂×C₄×C₈	—	37	1	no	—
113	C₃₇	#2965	1	1	yes	characteristic, complemented, Sylow
114	C₂×#41	#3866	1	1	yes	characteristic
115	C₂×M₁₆	—	37	4	no	—
116	C₂²×C₈	—	37	2	no	—
117	C₄×Q₈	—	37	1	no	—
118	C₄×Q₈	—	37	1	no	—
119	C₄×D₄	—	37	2	no	—
120	C₄×D₄	—	37	1	no	—
121	C₄×D₄	—	37	2	no	—
122	C₄×D₄	—	37	1	no	—
123	#117	—	37	2	no	—
124	#117	—	37	1	no	—
125	C₂×C₄²	—	37	1	no	—
126	C₂×C₄²	—	37	2	no	—
127	C₄⋊C₈	—	37	2	no	—
128	C₄⋊C₈	—	37	4	no	—
129	C₂²⋊C₈	—	37	2	no	—
130	C₂²⋊C₈	—	37	4	no	—
131	#97	—	37	4	no	—
132	C₄×C₈	—	37	1	no	—
133	C₄×C₈	—	37	1	no	—
134	C₄×C₈	—	37	2	no	—
135	C₄×C₈	—	37	2	no	—
136	#41	—	2	4	no	—
137	C₂×Q₈	C₂×#3866	1	1	yes	characteristic
138	C₂×D₄	C₂×#3866	1	2	yes	—
139	C₂×D₄	C₂×#3866	1	1	yes	characteristic
140	C₂²×C₄	—	37	1	no	—
141	C₂²×C₄	—	37	2	no	—
142	C₂²×C₄	—	37	2	no	—
143	C₂²×C₄	—	37	1	no	—
144	C₂²×C₄	C₂×#3866	1	2	yes	—
145	C₂²×C₄	C₂×#3866	1	1	yes	characteristic
146	M₁₆	—	74	8	no	—
147	C₂×C₈	—	37	2	no	—
148	C₂×C₈	—	37	2	no	—
149	C₂×C₈	—	37	4	no	—
150	C₂×C₈	—	74	4	no	—
151	C₄⋊C₄	—	37	2	no	—
152	C₄⋊C₄	—	37	2	no	—
153	C₄⋊C₄	—	37	1	no	—
154	C₄⋊C₄	—	37	1	no	—
155	C₂²⋊C₄	—	37	2	no	—
156	C₂²⋊C₄	—	37	2	no	—
157	C₂²⋊C₄	—	37	2	no	—
158	C₄²	—	37	2	no	—
159	C₄²	—	37	1	no	—
160	C₄²	—	37	1	no	—
161	C₄²	—	37	2	no	—
162	C₄²	—	37	1	no	—
163	C₄²	—	37	2	no	—
164	C₄²	—	37	1	no	—
165	C₂³	C₂²×#3866	1	2	yes	—
166	C₂³	C₂²×#3866	1	1	yes	characteristic
167	Q₈	—	2	2	no	—
168	D₄	—	2	4	no	—
169	D₄	—	2	2	no	—
170	C₂×C₄	—	2	4	no	—
171	C₂×C₄	—	37	1	no	—
172	C₂×C₄	—	37	1	no	—
173	C₂×C₄	—	37	1	no	—
174	C₂×C₄	—	37	2	no	—
175	C₂×C₄	—	37	1	no	—
176	C₂×C₄	—	37	2	no	—
177	C₂×C₄	—	74	2	no	—
178	C₂×C₄	—	74	4	no	—
179	C₂×C₄	—	74	2	no	—
180	C₂×C₄	—	74	4	no	—
181	C₂×C₄	#10596957	1	4	yes	complemented
182	C₂×C₄	C₂²×#3866	1	2	yes	—
183	C₂×C₄	C₂²×#3866	1	1	yes	characteristic
184	C₂×C₄	C₂²×#3866	1	1	yes	characteristic
185	C₈	—	37	4	no	—
186	C₈	—	74	2	no	—
187	C₈	—	74	4	no	—
188	C₂²	—	2	1	no	—
189	C₂²	—	2	1	no	—
190	C₂²	—	2	2	no	—
191	C₂²	—	2	2	no	—
192	C₂²	—	2	2	no	—
193	C₂²	C₂×#10596957	1	2	yes	—
194	C₂²	C₂³×#3866	1	1	yes	characteristic
195	C₄	—	2	2	no	—
196	C₄	—	37	2	no	—
197	C₄	—	37	2	no	—
198	C₄	—	74	1	no	—
199	C₄	—	74	2	no	—
200	C₄	—	74	1	no	—
201	C₄	—	74	2	no	—
202	C₄	C₂×#10596957	1	2	yes	—
203	C₄	C₂×#10596957	1	2	yes	—
204	C₂	—	2	2	no	—
205	C₂	—	4	2	no	—
206	C₂	#41×#3866	1	1	yes	characteristic
207	C₂	C₂²×#10596957	1	1	yes	characteristic
208	C₂	D₃₇⋊#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×#3866
commutator, socle	C₂²×C₃₇	C₂³×C₄
Frattini	C₂²	C₂³×#3866
Fitting, prime radical	C₂×#41×C₃₇	C₄
cosocle	C₂×Dic₃₇	C₂⁴
hypercenter	C₂×#41	#3866
hypocenter	C₃₇	#2965
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
1. #14558584	C₂	semidirect
2. #14558568	C₂	semidirect
3. #14558564	C₂	semidirect
4. #14558550	C₂	semidirect
5. #14558549	C₂	semidirect
6. C₄×#10596957	C₂	semidirect
7. C₂×C₄×#64438	C₂	semidirect
66. C₂×C₄×C₃₇	M₁₆	semidirect
82. #64438	#41	semidirect
113. C₃₇	#2965	semidirect
181. C₂×C₄	#10596957	semidirect

Maximal subgroups

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

subgroup	index
#14558584	2
#14558568	2
#14558564	2
#14558550	2
#14558549	2
C₄×#10596957	2
C₂×C₄×#64438	2
#41×Dic₃₇	2
#2965	37