Subgroups — C₈×#10596962 #18003553

Order 4736.

456 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	C₄×#10596962	C₂	1	1	yes	maximal, characteristic
2	C₈×Dic₇₄	C₂	1	2	yes	maximal, complemented
3	C₈×D₁₄₈	C₂	1	2	yes	maximal, complemented
4	C₈×C₂²⋊D₃₇	C₂	1	4	yes	maximal, complemented
5	#14557586	C₂	1	1	yes	maximal, characteristic, complemented
6	#14557584	C₂	1	2	yes	maximal, complemented
7	C₄×C₈×D₃₇	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₈×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#10596962	C₄	1	1	yes	characteristic
10	C₂×C₈×D₃₇	C₂²	1	4	yes	—
11	C₄×Dic₇₄	C₄	1	1	yes	characteristic
12	C₄×Dic₇₄	C₂²	1	1	yes	characteristic
13	C₄×D₁₄₈	C₄	1	1	yes	characteristic
14	C₄×D₁₄₈	C₂²	1	1	yes	characteristic
15	C₄×C₂²⋊D₃₇	C₄	1	2	yes	—
16	C₄×C₂²⋊D₃₇	C₂²	1	2	yes	—
17	#11924495	C₄	1	1	yes	characteristic
18	#11924493	C₄	1	2	yes	—
19	C₄²×D₃₇	C₂²	1	2	yes	—
20	C₄⋊#64436	C₂²	1	2	yes	—
21	#11924465	C₂²	1	4	yes	—
22	C₂²⋊#64436	C₂²	1	2	yes	—
23	#11924448	C₂²	1	4	yes	—
24	C₄×#64436	C₂²	1	2	yes	—
25	C₈×Dic₃₇	C₂²	1	4	yes	—
26	C₂²×C₈×C₃₇	C₂²	1	2	yes	—
27	C₂×C₄²×C₃₇	C₂²	1	1	yes	characteristic
28	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
29	C₄×C₈×C₃₇	C₂²	1	2	yes	—
30	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
31	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
34	C₂×C₂²⋊D₃₇	C₂×C₄	1	2	yes	—
35	#10596962	C₈	1	8	yes	direct product factor
36	C₂×D₁₄₈	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄×D₃₇	C₂×C₄	1	2	yes	—
38	C₂×C₄×D₃₇	C₂×C₄	1	2	yes	—
39	C₂×C₄×D₃₇	C₂³	1	2	yes	—
40	C₂×Dic₇₄	C₂×C₄	1	1	yes	characteristic
41	C₂×C₈×C₃₇	—	2	4	no	—
42	C₂×C₈×C₃₇	C₂³	1	2	yes	—
43	C₂×C₈×C₃₇	C₂³	1	2	yes	—
44	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
45	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
46	C₄²×C₃₇	C₂³	1	1	yes	characteristic
47	C₄²×C₃₇	C₂³	1	1	yes	characteristic
48	C₂²⋊Dic₃₇	C₂×C₄	1	2	yes	—
49	#10596938	C₂×C₄	1	2	yes	—
50	#10596938	C₂×C₄	1	2	yes	—
51	C₄⋊Dic₃₇	C₂×C₄	1	1	yes	characteristic
52	C₄⋊Dic₃₇	C₂×C₄	1	1	yes	characteristic
53	#10596936	C₂×C₄	1	2	yes	—
54	#10596936	C₂×C₄	1	2	yes	—
55	C₄×Dic₃₇	C₂×C₄	1	2	yes	—
56	C₄×Dic₃₇	C₂×C₄	1	2	yes	—
57	C₄×Dic₃₇	C₂³	1	2	yes	—
58	C₂×#64436	C₂³	1	4	yes	—
59	C₈×D₃₇	—	2	8	no	—
60	C₂³×C₃₇	C₂²×C₄	1	1	yes	characteristic
61	C₂²×D₃₇	C₂²×C₄	1	2	yes	—
62	C₂×C₄×C₃₇	—	2	2	no	—
63	C₂×C₄×C₃₇	—	2	2	no	—
64	C₂×C₄×C₃₇	C₂×C₈	1	4	yes	complemented
65	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
66	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
67	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
68	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
69	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
70	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
71	C₂²⋊D₃₇	C₂×C₈	1	8	yes	complemented
72	C₂×Dic₃₇	C₂²×C₄	1	2	yes	—
73	C₂×Dic₃₇	C₂²×C₄	1	2	yes	—
74	C₂×Dic₃₇	C₂²×C₄	1	2	yes	—
75	D₁₄₈	C₂×C₈	1	4	yes	complemented
76	C₄×D₃₇	—	2	4	no	—
77	C₄×D₃₇	—	2	4	no	—
78	C₄×D₃₇	C₂×C₈	1	8	yes	complemented
79	Dic₇₄	C₂×C₈	1	4	yes	complemented
80	C₈×C₃₇	—	2	2	no	—
81	C₈×C₃₇	#41	1	4	yes	complemented
82	#64436	—	2	4	no	—
83	C₂²×C₃₇	—	2	1	no	—
84	C₂²×C₃₇	—	2	1	no	—
85	C₂²×C₃₇	C₂²×C₈	1	2	yes	—
86	C₂²×C₃₇	C₂³×C₄	1	1	yes	characteristic
87	C₂×D₃₇	—	2	2	no	—
88	C₂×D₃₇	—	2	2	no	—
89	C₂×D₃₇	C₂²×C₈	1	4	yes	—
90	C₄×C₃₇	—	2	1	no	—
91	C₄×C₃₇	—	2	1	no	—
92	C₄×C₃₇	C₂²×C₈	1	2	yes	—
93	C₄×C₃₇	C₂²×C₈	1	2	yes	—
94	C₄×C₃₇	#131	1	2	yes	—
95	C₄×C₃₇	C₂×#41	1	2	yes	—
96	Dic₃₇	—	2	2	no	—
97	Dic₃₇	—	2	2	no	—
98	Dic₃₇	C₂²×C₈	1	4	yes	—
99	C₈×#41	—	37	1	no	maximal, Sylow
100	C₂×C₃₇	—	2	2	no	—
101	C₂×C₃₇	C₄×#41	1	1	yes	characteristic
102	C₂×C₃₇	C₂³×C₈	1	1	yes	characteristic
103	C₂×C₃₇	C₂×#131	1	1	yes	characteristic
104	D₃₇	—	2	4	no	—
105	C₄×#41	—	37	1	no	—
106	C₈×Q₈	—	37	2	no	—
107	C₈×D₄	—	37	4	no	—
108	C₈×D₄	—	37	2	no	—
109	#431	—	37	1	no	—
110	#431	—	37	2	no	—
111	C₂×C₄×C₈	—	37	2	no	—
112	C₂×C₄×C₈	D₃₇	1	1	yes	characteristic, complemented
113	C₃₇	C₈×#41	1	1	yes	characteristic, complemented, Sylow
114	C₂×#41	—	37	1	no	—
115	C₂²×C₈	—	37	4	no	—
116	C₂²×C₈	C₂×D₃₇	1	2	yes	—
117	C₄×Q₈	—	37	1	no	—
118	C₄×Q₈	—	37	1	no	—
119	C₄×D₄	—	37	2	no	—
120	C₄×D₄	—	37	2	no	—
121	C₄×D₄	—	37	1	no	—
122	C₄×D₄	—	37	1	no	—
123	#117	—	37	1	no	—
124	#117	—	37	2	no	—
125	C₂×C₄²	—	37	2	no	—
126	C₂×C₄²	C₂×D₃₇	1	1	yes	characteristic
127	C₄⋊C₈	—	37	4	no	—
128	C₄⋊C₈	—	37	2	no	—
129	C₂²⋊C₈	—	37	2	no	—
130	C₂²⋊C₈	—	37	4	no	—
131	C₄×C₈	—	37	4	no	—
132	C₄×C₈	—	37	2	no	—
133	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
134	C₄×C₈	C₂×D₃₇	1	2	yes	—
135	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
136	#41	—	37	8	no	—
137	C₂×Q₈	—	37	1	no	—
138	C₂×D₄	—	37	2	no	—
139	C₂×D₄	—	37	1	no	—
140	C₂²×C₄	—	37	2	no	—
141	C₂²×C₄	—	37	2	no	—
142	C₂²×C₄	—	37	2	no	—
143	C₂²×C₄	C₄×D₃₇	1	1	yes	characteristic
144	C₂²×C₄	C₄×D₃₇	1	1	yes	characteristic
145	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
146	C₂×C₈	—	2	4	no	—
147	C₂×C₈	—	37	4	no	—
148	C₂×C₈	—	74	8	no	—
149	C₂×C₈	C₂²×D₃₇	1	2	yes	—
150	C₂×C₈	C₂²×D₃₇	1	2	yes	—
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	2	no	—
160	C₄²	—	37	2	no	—
161	C₄²	C₄×D₃₇	1	1	yes	characteristic
162	C₄²	C₄×D₃₇	1	1	yes	characteristic
163	C₄²	C₂²×D₃₇	1	1	yes	characteristic
164	C₄²	C₂²×D₃₇	1	1	yes	characteristic
165	C₂³	—	37	2	no	—
166	C₂³	C₂×C₄×D₃₇	1	1	yes	characteristic
167	Q₈	—	37	4	no	—
168	D₄	—	37	8	no	—
169	D₄	—	37	4	no	—
170	C₂×C₄	—	2	2	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	37	2	no	—
173	C₂×C₄	—	37	8	no	—
174	C₂×C₄	—	37	2	no	—
175	C₂×C₄	—	37	2	no	—
176	C₂×C₄	—	74	4	no	—
177	C₂×C₄	—	74	4	no	—
178	C₂×C₄	C₈×D₃₇	1	4	yes	complemented
179	C₂×C₄	C₂×C₄×D₃₇	1	1	yes	characteristic
180	C₂×C₄	C₂×C₄×D₃₇	1	1	yes	characteristic
181	C₂×C₄	C₂×C₄×D₃₇	1	1	yes	characteristic
182	C₂×C₄	C₂×C₄×D₃₇	1	1	yes	characteristic
183	C₂×C₄	C₂×C₄×D₃₇	1	1	yes	characteristic
184	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
185	C₈	—	2	2	no	—
186	C₈	—	74	4	no	—
187	C₈	#10596962	1	4	yes	direct product factor
188	C₂²	—	2	1	no	—
189	C₂²	—	2	1	no	—
190	C₂²	—	37	4	no	—
191	C₂²	—	74	2	no	—
192	C₂²	—	74	2	no	—
193	C₂²	C₂×C₈×D₃₇	1	2	yes	—
194	C₂²	C₂²×C₄×D₃₇	1	1	yes	characteristic
195	C₄	—	2	1	no	—
196	C₄	—	2	1	no	—
197	C₄	—	37	4	no	—
198	C₄	—	74	2	no	—
199	C₄	—	74	2	no	—
200	C₄	C₂×C₈×D₃₇	1	2	yes	—
201	C₄	C₂×C₈×D₃₇	1	2	yes	—
202	C₄	#11924542	1	2	yes	—
203	C₄	C₂×#10596962	1	2	yes	—
204	C₂	—	2	2	no	—
205	C₂	—	74	4	no	—
206	C₂	C₄×#10596962	1	1	yes	characteristic
207	C₂	C₂²×C₈×D₃₇	1	1	yes	characteristic
208	C₂	C₂×#11924542	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₈	C₂×D₃₇
commutator	C₂×C₃₇	C₂³×C₈
Frattini	C₂×C₄	C₂³×D₃₇
Fitting	C₂×C₄×C₈×C₃₇	C₂
socle	C₂²×C₃₇	C₂³×C₄
prime radical	C₂×#10596962	C₄
cosocle	C₂×C₄×C₃₇	C₂⁴
hypercenter	C₂×C₄×C₈	D₃₇
hypocenter	C₃₇	C₈×#41
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. C₈×Dic₇₄	C₂	semidirect
3. C₈×D₁₄₈	C₂	semidirect
4. C₈×C₂²⋊D₃₇	C₂	semidirect
5. #14557586	C₂	semidirect
6. #14557584	C₂	semidirect
7. C₄×C₈×D₃₇	C₂	semidirect
8. C₂×C₄×C₈×C₃₇	C₂	semidirect
35. #10596962	C₈	direct (N × H)
64. C₂×C₄×C₃₇	C₂×C₈	semidirect
71. C₂²⋊D₃₇	C₂×C₈	semidirect
75. D₁₄₈	C₂×C₈	semidirect
78. C₄×D₃₇	C₂×C₈	semidirect
79. Dic₇₄	C₂×C₈	semidirect
81. C₈×C₃₇	#41	semidirect
112. C₂×C₄×C₈	D₃₇	semidirect
113. C₃₇	C₈×#41	semidirect
178. C₂×C₄	C₈×D₃₇	semidirect
187. C₈	#10596962	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×#10596962	2
C₈×Dic₇₄	2
C₈×D₁₄₈	2
C₈×C₂²⋊D₃₇	2
#14557586	2
#14557584	2
C₄×C₈×D₃₇	2
C₂×C₄×C₈×C₃₇	2
C₈×#41	37

Subgroups — C8×#10596962 #18003553

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#10596962 #18003553