Subgroups — C₄×#16813628 #28398994

Order 14464.

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×#16813628	C₂	1	2	yes	maximal
2	C₄×#14268647	C₂	1	1	yes	maximal, characteristic
3	#20298553	C₂	1	2	yes	maximal, complemented
4	#20298552	C₂	1	4	yes	maximal, complemented
5	C₄×#14268631	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×#14268630	C₂	1	2	yes	maximal, complemented
7	C₄×C₈×D₁₁₃	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#14268647	C₂²	1	1	yes	characteristic
10	#16813628	C₄	1	16	yes	direct product factor
11	C₂×#14268631	C₂²	1	2	yes	—
12	C₂×#14268630	C₂²	1	4	yes	—
13	C₂×C₈×D₁₁₃	C₂²	1	4	yes	—
14	C₄×Dic₂₂₆	C₄	1	2	yes	—
15	C₄×D₄₅₂	C₄	1	2	yes	—
16	C₄×C₂²⋊D₁₁₃	C₄	1	4	yes	—
17	#16813581	C₂²	1	1	yes	characteristic
18	#16813579	C₂²	1	2	yes	—
19	C₄²×D₁₁₃	C₂²	1	2	yes	—
20	#16813533	C₂²	1	2	yes	—
21	#16813532	C₂²	1	4	yes	—
22	C₄×#11744751	C₂²	1	2	yes	—
23	C₈×Dic₁₁₃	C₂²	1	4	yes	—
24	C₂²×C₈×C₁₁₃	C₂²	1	2	yes	—
25	C₂×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
26	C₄×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
27	C₄×C₈×C₁₁₃	C₂²	1	2	yes	—
28	C₄×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
29	#14268647	C₂×C₄	1	8	yes	—
30	C₂×Dic₂₂₆	C₂×C₄	1	1	yes	characteristic
31	C₂×D₄₅₂	C₂×C₄	1	1	yes	characteristic
32	C₂×C₂²⋊D₁₁₃	C₂×C₄	1	2	yes	—
33	C₂×C₄×D₁₁₃	C₂×C₄	1	4	yes	—
34	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
35	#14268631	C₂×C₄	1	8	yes	complemented
36	#14268630	C₂×C₄	1	16	yes	complemented
37	C₂×#11744751	C₂³	1	4	yes	—
38	C₈×D₁₁₃	C₂×C₄	1	16	yes	complemented
39	C₄⋊Dic₁₁₃	C₂×C₄	1	2	yes	—
40	#14268626	C₂×C₄	1	4	yes	—
41	C₂²⋊Dic₁₁₃	C₂×C₄	1	2	yes	—
42	#14268624	C₂×C₄	1	4	yes	—
43	C₄×Dic₁₁₃	C₂×C₄	1	4	yes	—
44	C₄×Dic₁₁₃	C₂³	1	2	yes	—
45	C₂²×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
46	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
47	C₂×C₈×C₁₁₃	C₂×C₄	1	8	yes	complemented
48	C₂×C₈×C₁₁₃	C₂³	1	2	yes	—
49	C₂×C₈×C₁₁₃	C₂³	1	2	yes	—
50	C₄²×C₁₁₃	C₂×C₄	1	2	yes	—
51	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
52	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
53	C₂³×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
54	C₂²×D₁₁₃	C₂²×C₄	1	2	yes	—
55	C₂×C₄×C₁₁₃	—	2	4	no	—
56	C₂×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
57	C₂×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
58	C₂×C₄×C₁₁₃	C₂²×C₄	1	4	yes	—
59	C₂×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
60	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
61	C₂²⋊D₁₁₃	C₄²	1	8	yes	—
62	C₂×Dic₁₁₃	C₂²×C₄	1	4	yes	—
63	C₂×Dic₁₁₃	C₂²×C₄	1	2	yes	—
64	D₄₅₂	C₄²	1	4	yes	—
65	C₄×D₁₁₃	—	2	8	no	—
66	C₄×D₁₁₃	C₂²×C₄	1	8	yes	—
67	Dic₂₂₆	C₄²	1	4	yes	—
68	C₈×C₁₁₃	C₂²×C₄	1	4	yes	—
69	C₈×C₁₁₃	C₂²×C₄	1	4	yes	—
70	#11744751	C₂²×C₄	1	8	yes	—
71	C₂²×C₁₁₃	—	2	2	no	—
72	C₂²×C₁₁₃	C₂×C₄²	1	2	yes	—
73	C₂²×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
74	C₂×D₁₁₃	—	2	4	no	—
75	C₂×D₁₁₃	C₂×C₄²	1	4	yes	—
76	C₄×C₁₁₃	—	2	2	no	—
77	C₄×C₁₁₃	C₂×C₄²	1	2	yes	—
78	C₄×C₁₁₃	#131	1	4	yes	complemented
79	C₄×C₁₁₃	C₂³×C₄	1	2	yes	—
80	Dic₁₁₃	—	2	4	no	—
81	Dic₁₁₃	C₂×C₄²	1	4	yes	—
82	C₂×C₁₁₃	—	2	2	no	—
83	C₂×C₁₁₃	C₂²×C₄²	1	1	yes	characteristic
84	C₂×C₁₁₃	C₂×#131	1	2	yes	—
85	D₁₁₃	—	2	4	no	—
86	C₄×#131	—	113	1	no	maximal, Sylow
87	C₁₁₃	C₄×#131	1	1	yes	characteristic, complemented, Sylow
88	C₂×#131	—	113	2	no	—
89	C₄×#41	—	113	1	no	—
90	#405	—	113	2	no	—
91	#405	—	113	4	no	—
92	C₄×M₁₆	—	113	1	no	—
93	C₄×M₁₆	—	113	2	no	—
94	C₂×C₄×C₈	—	113	2	no	—
95	C₂×C₄×C₈	D₁₁₃	1	1	yes	characteristic, complemented
96	C₂×#41	—	113	1	no	—
97	#131	—	113	16	no	—
98	C₂×M₁₆	—	113	2	no	—
99	C₂×M₁₆	—	113	4	no	—
100	C₂²×C₈	—	113	4	no	—
101	C₂²×C₈	C₂×D₁₁₃	1	2	yes	—
102	C₄×Q₈	—	113	2	no	—
103	C₄×D₄	—	113	4	no	—
104	C₄×D₄	—	113	2	no	—
105	#117	—	113	1	no	—
106	#117	—	113	2	no	—
107	C₂×C₄²	—	113	2	no	—
108	C₂×C₄²	C₂×D₁₁₃	1	1	yes	characteristic
109	#97	—	113	4	no	—
110	#97	—	113	2	no	—
111	C₄×C₈	—	113	4	no	—
112	C₄×C₈	—	113	2	no	—
113	C₄×C₈	C₂×D₁₁₃	1	1	yes	characteristic
114	C₄×C₈	C₂×D₁₁₃	1	2	yes	—
115	C₄×C₈	C₂×D₁₁₃	1	1	yes	characteristic
116	#41	—	113	8	no	—
117	C₂×Q₈	—	113	1	no	—
118	C₂×D₄	—	113	2	no	—
119	C₂×D₄	—	113	1	no	—
120	C₂²×C₄	—	113	2	no	—
121	C₂²×C₄	—	113	4	no	—
122	C₂²×C₄	C₄×D₁₁₃	1	2	yes	—
123	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
124	M₁₆	—	113	8	no	—
125	M₁₆	—	113	16	no	—
126	C₂×C₈	—	113	4	no	—
127	C₂×C₈	—	113	16	no	—
128	C₂×C₈	C₄×D₁₁₃	1	8	yes	complemented
129	C₂×C₈	C₂²×D₁₁₃	1	2	yes	—
130	C₂×C₈	C₂²×D₁₁₃	1	2	yes	—
131	C₄⋊C₄	—	113	4	no	—
132	C₄⋊C₄	—	113	2	no	—
133	C₂²⋊C₄	—	113	2	no	—
134	C₂²⋊C₄	—	113	4	no	—
135	C₄²	—	113	4	no	—
136	C₄²	—	113	2	no	—
137	C₄²	C₄×D₁₁₃	1	2	yes	—
138	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
139	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
140	C₂³	—	113	2	no	—
141	C₂³	C₂×C₄×D₁₁₃	1	1	yes	characteristic
142	Q₈	—	113	4	no	—
143	D₄	—	113	8	no	—
144	D₄	—	113	4	no	—
145	C₂×C₄	—	2	4	no	—
146	C₂×C₄	—	113	2	no	—
147	C₂×C₄	—	113	8	no	—
148	C₂×C₄	—	113	4	no	—
149	C₂×C₄	—	226	8	no	—
150	C₂×C₄	C₂×C₄×D₁₁₃	1	2	yes	—
151	C₂×C₄	C₂×C₄×D₁₁₃	1	1	yes	characteristic
152	C₂×C₄	C₂×C₄×D₁₁₃	1	4	yes	—
153	C₂×C₄	C₂×C₄×D₁₁₃	1	2	yes	—
154	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
155	C₈	—	113	8	no	—
156	C₈	C₂×C₄×D₁₁₃	1	4	yes	—
157	C₈	C₂×C₄×D₁₁₃	1	4	yes	—
158	C₂²	—	2	2	no	—
159	C₂²	—	113	4	no	—
160	C₂²	—	226	4	no	—
161	C₂²	C₄²×D₁₁₃	1	2	yes	—
162	C₂²	C₂²×C₄×D₁₁₃	1	1	yes	characteristic
163	C₄	—	2	2	no	—
164	C₄	—	113	4	no	—
165	C₄	—	226	4	no	—
166	C₄	C₄²×D₁₁₃	1	2	yes	—
167	C₄	#16813628	1	4	yes	direct product factor
168	C₄	C₂²×C₄×D₁₁₃	1	2	yes	—
169	C₂	—	2	2	no	—
170	C₂	—	226	4	no	—
171	C₂	C₂×C₄²×D₁₁₃	1	1	yes	characteristic
172	C₂	C₂×#16813628	1	2	yes	—

	subgroup	G/H
center	C₄×C₈	C₂×D₁₁₃
commutator	C₂×C₁₁₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×D₁₁₃
Fitting	C₂×C₄×C₈×C₁₁₃	C₂
socle	C₂²×C₁₁₃	C₂³×C₄
prime radical	C₂×#14268647	C₂²
cosocle	C₂×C₄×C₁₁₃	C₂⁴
hypercenter	C₂×C₄×C₈	D₁₁₃
hypocenter	C₁₁₃	C₄×#131
LCS	G ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₄×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
3. #20298553	C₂	semidirect
4. #20298552	C₂	semidirect
5. C₄×#14268631	C₂	semidirect
6. C₄×#14268630	C₂	semidirect
7. C₄×C₈×D₁₁₃	C₂	semidirect
8. C₂×C₄×C₈×C₁₁₃	C₂	semidirect
10. #16813628	C₄	direct (N × H)
35. #14268631	C₂×C₄	semidirect
36. #14268630	C₂×C₄	semidirect
38. C₈×D₁₁₃	C₂×C₄	semidirect
47. C₂×C₈×C₁₁₃	C₂×C₄	semidirect
78. C₄×C₁₁₃	#131	semidirect
87. C₁₁₃	C₄×#131	semidirect
95. C₂×C₄×C₈	D₁₁₃	semidirect
128. C₂×C₈	C₄×D₁₁₃	semidirect
167. C₄	#16813628	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×#16813628	2
C₄×#14268647	2
#20298553	2
#20298552	2
C₄×#14268631	2
C₄×#14268630	2
C₄×C₈×D₁₁₃	2
C₂×C₄×C₈×C₁₁₃	2
C₄×#131	113

Subgroups — C4×#16813628 #28398994

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#16813628 #28398994