Subgroups — C₄×#14581798 #24915883

Order 10624.

572 conjugacy classes of subgroups.

The subgroup lattice has 174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14581798	C₂	1	2	yes	maximal
2	C₄×#13050590	C₂	1	1	yes	maximal, characteristic
3	#19127656	C₂	1	2	yes	maximal, complemented
4	#19127655	C₂	1	4	yes	maximal, complemented
5	C₄×#13050574	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×#13050573	C₂	1	2	yes	maximal, complemented
7	C₄×C₈×D₈₃	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₈×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#13050590	C₂²	1	1	yes	characteristic
10	#14581798	C₄	1	16	yes	direct product factor
11	C₂×#13050574	C₂²	1	2	yes	—
12	C₂×#13050573	C₂²	1	4	yes	—
13	C₂×C₈×D₈₃	C₂²	1	4	yes	—
14	C₄×Dic₁₆₆	C₄	1	2	yes	—
15	C₄×D₃₃₂	C₄	1	2	yes	—
16	C₄×C₂²⋊D₈₃	C₄	1	4	yes	—
17	#14581751	C₂²	1	1	yes	characteristic
18	#14581749	C₂²	1	2	yes	—
19	C₄²×D₈₃	C₂²	1	2	yes	—
20	#14581703	C₂²	1	2	yes	—
21	#14581702	C₂²	1	4	yes	—
22	C₄×C₈₃⋊C₈	C₂²	1	2	yes	—
23	C₈×Dic₈₃	C₂²	1	4	yes	—
24	C₂²×C₈×C₈₃	C₂²	1	2	yes	—
25	C₂×C₄²×C₈₃	C₂²	1	1	yes	characteristic
26	C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
27	C₄×C₈×C₈₃	C₂²	1	2	yes	—
28	C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
29	#13050590	C₂×C₄	1	8	yes	—
30	C₂×Dic₁₆₆	C₂×C₄	1	1	yes	characteristic
31	C₂×D₃₃₂	C₂×C₄	1	1	yes	characteristic
32	C₂×C₂²⋊D₈₃	C₂×C₄	1	2	yes	—
33	C₂×C₄×D₈₃	C₂×C₄	1	4	yes	—
34	C₂×C₄×D₈₃	C₂³	1	2	yes	—
35	#13050574	C₂×C₄	1	8	yes	complemented
36	#13050573	C₂×C₄	1	16	yes	complemented
37	C₂×C₈₃⋊C₈	C₂³	1	4	yes	—
38	C₈×D₈₃	C₂×C₄	1	16	yes	complemented
39	C₄⋊Dic₈₃	C₂×C₄	1	2	yes	—
40	Dic₈₃⋊C₄	C₂×C₄	1	4	yes	—
41	C₂²⋊Dic₈₃	C₂×C₄	1	2	yes	—
42	(C₂×D₈₃)⋊C₄	C₂×C₄	1	4	yes	—
43	C₄×Dic₈₃	C₂×C₄	1	4	yes	—
44	C₄×Dic₈₃	C₂³	1	2	yes	—
45	C₂²×C₄×C₈₃	C₂×C₄	1	2	yes	—
46	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
47	C₂×C₈×C₈₃	C₂×C₄	1	8	yes	complemented
48	C₂×C₈×C₈₃	C₂³	1	2	yes	—
49	C₂×C₈×C₈₃	C₂³	1	2	yes	—
50	C₄²×C₈₃	C₂×C₄	1	2	yes	—
51	C₄²×C₈₃	C₂³	1	1	yes	characteristic
52	C₄²×C₈₃	C₂³	1	1	yes	characteristic
53	C₂³×C₈₃	C₂²×C₄	1	1	yes	characteristic
54	C₂²×D₈₃	C₂²×C₄	1	2	yes	—
55	C₂×C₄×C₈₃	—	2	4	no	—
56	C₂×C₄×C₈₃	C₂²×C₄	1	2	yes	—
57	C₂×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
58	C₂×C₄×C₈₃	C₂²×C₄	1	4	yes	—
59	C₂×C₄×C₈₃	C₂²×C₄	1	2	yes	—
60	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
61	C₂²⋊D₈₃	C₄²	1	8	yes	—
62	C₂×Dic₈₃	C₂²×C₄	1	4	yes	—
63	C₂×Dic₈₃	C₂²×C₄	1	2	yes	—
64	D₃₃₂	C₄²	1	4	yes	—
65	C₄×D₈₃	—	2	8	no	—
66	C₄×D₈₃	C₂²×C₄	1	8	yes	—
67	Dic₁₆₆	C₄²	1	4	yes	—
68	C₈×C₈₃	C₂²×C₄	1	4	yes	—
69	C₈×C₈₃	C₂²×C₄	1	4	yes	—
70	C₈₃⋊C₈	C₂²×C₄	1	8	yes	—
71	C₂²×C₈₃	—	2	2	no	—
72	C₂²×C₈₃	C₂×C₄²	1	2	yes	—
73	C₂²×C₈₃	C₂³×C₄	1	1	yes	characteristic
74	C₂×D₈₃	—	2	4	no	—
75	C₂×D₈₃	C₂×C₄²	1	4	yes	—
76	C₄×C₈₃	—	2	2	no	—
77	C₄×C₈₃	C₂×C₄²	1	2	yes	—
78	C₄×C₈₃	#131	1	4	yes	complemented
79	C₄×C₈₃	C₂³×C₄	1	2	yes	—
80	Dic₈₃	—	2	4	no	—
81	Dic₈₃	C₂×C₄²	1	4	yes	—
82	C₂×C₈₃	—	2	2	no	—
83	C₂×C₈₃	C₂²×C₄²	1	1	yes	characteristic
84	C₂×C₈₃	C₂×#131	1	2	yes	—
85	D₈₃	—	2	4	no	—
86	C₄×#131	—	83	1	no	maximal, Sylow
87	C₈₃	C₄×#131	1	1	yes	characteristic, complemented, Sylow
88	C₂×#131	—	83	2	no	—
89	C₄×#41	—	83	1	no	—
90	#405	—	83	2	no	—
91	#405	—	83	4	no	—
92	C₄×M₁₆	—	83	1	no	—
93	C₄×M₁₆	—	83	2	no	—
94	C₂×C₄×C₈	—	83	2	no	—
95	C₂×C₄×C₈	D₈₃	1	1	yes	characteristic, complemented
96	C₂×#41	—	83	1	no	—
97	#131	—	83	16	no	—
98	C₂×M₁₆	—	83	2	no	—
99	C₂×M₁₆	—	83	4	no	—
100	C₂²×C₈	—	83	4	no	—
101	C₂²×C₈	C₂×D₈₃	1	2	yes	—
102	C₄×Q₈	—	83	2	no	—
103	C₄×D₄	—	83	4	no	—
104	C₄×D₄	—	83	2	no	—
105	#117	—	83	1	no	—
106	#117	—	83	2	no	—
107	C₂×C₄²	—	83	2	no	—
108	C₂×C₄²	C₂×D₈₃	1	1	yes	characteristic
109	#97	—	83	4	no	—
110	#97	—	83	2	no	—
111	C₄×C₈	—	83	4	no	—
112	C₄×C₈	—	83	2	no	—
113	C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
114	C₄×C₈	C₂×D₈₃	1	2	yes	—
115	C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
116	#41	—	83	8	no	—
117	C₂×Q₈	—	83	1	no	—
118	C₂×D₄	—	83	2	no	—
119	C₂×D₄	—	83	1	no	—
120	C₂²×C₄	—	83	2	no	—
121	C₂²×C₄	—	83	4	no	—
122	C₂²×C₄	C₄×D₈₃	1	2	yes	—
123	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
124	M₁₆	—	83	8	no	—
125	M₁₆	—	83	16	no	—
126	C₂×C₈	—	83	4	no	—
127	C₂×C₈	—	83	16	no	—
128	C₂×C₈	C₄×D₈₃	1	8	yes	complemented
129	C₂×C₈	C₂²×D₈₃	1	2	yes	—
130	C₂×C₈	C₂²×D₈₃	1	2	yes	—
131	C₄⋊C₄	—	83	4	no	—
132	C₄⋊C₄	—	83	2	no	—
133	C₂²⋊C₄	—	83	2	no	—
134	C₂²⋊C₄	—	83	4	no	—
135	C₄²	—	83	4	no	—
136	C₄²	—	83	2	no	—
137	C₄²	C₄×D₈₃	1	2	yes	—
138	C₄²	C₂²×D₈₃	1	1	yes	characteristic
139	C₄²	C₂²×D₈₃	1	1	yes	characteristic
140	C₂³	—	83	2	no	—
141	C₂³	C₂×C₄×D₈₃	1	1	yes	characteristic
142	Q₈	—	83	4	no	—
143	D₄	—	83	8	no	—
144	D₄	—	83	4	no	—
145	C₂×C₄	—	2	4	no	—
146	C₂×C₄	—	83	2	no	—
147	C₂×C₄	—	83	8	no	—
148	C₂×C₄	—	83	4	no	—
149	C₂×C₄	—	166	8	no	—
150	C₂×C₄	C₂×C₄×D₈₃	1	2	yes	—
151	C₂×C₄	C₂×C₄×D₈₃	1	2	yes	—
152	C₂×C₄	C₂×C₄×D₈₃	1	4	yes	—
153	C₂×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
154	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
155	C₈	—	83	8	no	—
156	C₈	C₂×C₄×D₈₃	1	4	yes	—
157	C₈	C₂×C₄×D₈₃	1	4	yes	—
158	C₂²	—	2	2	no	—
159	C₂²	—	83	4	no	—
160	C₂²	—	166	4	no	—
161	C₂²	C₄²×D₈₃	1	2	yes	—
162	C₂²	C₂²×C₄×D₈₃	1	1	yes	characteristic
163	C₄	—	2	2	no	—
164	C₄	—	83	4	no	—
165	C₄	—	166	4	no	—
166	C₄	C₄²×D₈₃	1	2	yes	—
167	C₄	#14581798	1	4	yes	direct product factor
168	C₄	C₂²×C₄×D₈₃	1	2	yes	—
169	C₂	—	2	2	no	—
170	C₂	—	166	4	no	—
171	C₂	C₂×C₄²×D₈₃	1	1	yes	characteristic
172	C₂	C₂×#14581798	1	2	yes	—

	subgroup	G/H
center	C₄×C₈	C₂×D₈₃
commutator	C₂×C₈₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×D₈₃
Fitting	C₂×C₄×C₈×C₈₃	C₂
socle	C₂²×C₈₃	C₂³×C₄
prime radical	C₂×#13050590	C₂²
cosocle	C₂×C₄×C₈₃	C₂⁴
hypercenter	C₂×C₄×C₈	D₈₃
hypocenter	C₈₃	C₄×#131
LCS	G ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₄×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
3. #19127656	C₂	semidirect
4. #19127655	C₂	semidirect
5. C₄×#13050574	C₂	semidirect
6. C₄×#13050573	C₂	semidirect
7. C₄×C₈×D₈₃	C₂	semidirect
8. C₂×C₄×C₈×C₈₃	C₂	semidirect
10. #14581798	C₄	direct (N × H)
35. #13050574	C₂×C₄	semidirect
36. #13050573	C₂×C₄	semidirect
38. C₈×D₈₃	C₂×C₄	semidirect
47. C₂×C₈×C₈₃	C₂×C₄	semidirect
78. C₄×C₈₃	#131	semidirect
87. C₈₃	C₄×#131	semidirect
95. C₂×C₄×C₈	D₈₃	semidirect
128. C₂×C₈	C₄×D₈₃	semidirect
167. C₄	#14581798	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×#14581798	2
C₄×#13050590	2
#19127656	2
#19127655	2
C₄×#13050574	2
C₄×#13050573	2
C₄×C₈×D₈₃	2
C₂×C₄×C₈×C₈₃	2
C₄×#131	83

Subgroups — C4×#14581798 #24915883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#14581798 #24915883