Subgroups — C₄×#22575459 #46819305

Order 34432.

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×#22575459	C₂	1	2	yes	maximal
2	C₄×#16864402	C₂	1	1	yes	maximal, characteristic
3	#31770560	C₂	1	2	yes	maximal, complemented
4	#31770559	C₂	1	4	yes	maximal, complemented
5	C₄×#16864386	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×#16864385	C₂	1	2	yes	maximal, complemented
7	C₄×C₈×D₂₆₉	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₈×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#16864402	C₂²	1	1	yes	characteristic
10	#22575459	C₄	1	16	yes	direct product factor
11	C₂×#16864386	C₂²	1	2	yes	—
12	C₂×#16864385	C₂²	1	4	yes	—
13	C₂×C₈×D₂₆₉	C₂²	1	4	yes	—
14	C₄×Dic₅₃₈	C₄	1	2	yes	—
15	C₄×D₁₀₇₆	C₄	1	2	yes	—
16	C₄×C₂²⋊D₂₆₉	C₄	1	4	yes	—
17	#22575412	C₂²	1	1	yes	characteristic
18	#22575410	C₂²	1	2	yes	—
19	C₄²×D₂₆₉	C₂²	1	2	yes	—
20	#22575364	C₂²	1	2	yes	—
21	#22575363	C₂²	1	4	yes	—
22	C₄×#14524130	C₂²	1	2	yes	—
23	C₈×Dic₂₆₉	C₂²	1	4	yes	—
24	C₂²×C₈×C₂₆₉	C₂²	1	2	yes	—
25	C₂×C₄²×C₂₆₉	C₂²	1	1	yes	characteristic
26	C₄×C₈×C₂₆₉	C₂²	1	1	yes	characteristic
27	C₄×C₈×C₂₆₉	C₂²	1	2	yes	—
28	C₄×C₈×C₂₆₉	C₂²	1	1	yes	characteristic
29	#16864402	C₂×C₄	1	8	yes	—
30	C₂×Dic₅₃₈	C₂×C₄	1	1	yes	characteristic
31	C₂×D₁₀₇₆	C₂×C₄	1	1	yes	characteristic
32	C₂×C₂²⋊D₂₆₉	C₂×C₄	1	2	yes	—
33	C₂×C₄×D₂₆₉	C₂×C₄	1	4	yes	—
34	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
35	#16864386	C₂×C₄	1	8	yes	complemented
36	#16864385	C₂×C₄	1	16	yes	complemented
37	C₂×#14524130	C₂³	1	4	yes	—
38	C₈×D₂₆₉	C₂×C₄	1	16	yes	complemented
39	C₄⋊Dic₂₆₉	C₂×C₄	1	2	yes	—
40	#16864381	C₂×C₄	1	4	yes	—
41	C₂²⋊Dic₂₆₉	C₂×C₄	1	2	yes	—
42	#16864379	C₂×C₄	1	4	yes	—
43	C₄×Dic₂₆₉	C₂×C₄	1	4	yes	—
44	C₄×Dic₂₆₉	C₂³	1	2	yes	—
45	C₂²×C₄×C₂₆₉	C₂×C₄	1	2	yes	—
46	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
47	C₂×C₈×C₂₆₉	C₂×C₄	1	8	yes	complemented
48	C₂×C₈×C₂₆₉	C₂³	1	2	yes	—
49	C₂×C₈×C₂₆₉	C₂³	1	2	yes	—
50	C₄²×C₂₆₉	C₂×C₄	1	2	yes	—
51	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
52	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
53	C₂²×D₂₆₉	C₂²×C₄	1	2	yes	—
54	Dic₅₃₈	C₄²	1	4	yes	—
55	D₁₀₇₆	C₄²	1	4	yes	—
56	C₂²⋊D₂₆₉	C₄²	1	8	yes	—
57	C₂×Dic₂₆₉	C₂²×C₄	1	4	yes	—
58	C₂×Dic₂₆₉	C₂²×C₄	1	2	yes	—
59	C₄×D₂₆₉	—	2	8	no	—
60	C₄×D₂₆₉	C₂²×C₄	1	8	yes	—
61	#14524130	C₂²×C₄	1	8	yes	—
62	C₂³×C₂₆₉	C₂²×C₄	1	1	yes	characteristic
63	C₂×C₄×C₂₆₉	—	2	4	no	—
64	C₂×C₄×C₂₆₉	C₂²×C₄	1	2	yes	—
65	C₂×C₄×C₂₆₉	C₂²×C₄	1	1	yes	characteristic
66	C₂×C₄×C₂₆₉	C₂²×C₄	1	4	yes	—
67	C₂×C₄×C₂₆₉	C₂²×C₄	1	2	yes	—
68	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
69	C₈×C₂₆₉	C₂²×C₄	1	4	yes	—
70	C₈×C₂₆₉	C₂²×C₄	1	4	yes	—
71	C₂²×C₂₆₉	—	2	2	no	—
72	C₂²×C₂₆₉	C₂×C₄²	1	2	yes	—
73	C₂²×C₂₆₉	C₂³×C₄	1	1	yes	characteristic
74	C₂×D₂₆₉	—	2	4	no	—
75	C₂×D₂₆₉	C₂×C₄²	1	4	yes	—
76	C₄×C₂₆₉	—	2	2	no	—
77	C₄×C₂₆₉	C₂×C₄²	1	2	yes	—
78	C₄×C₂₆₉	#131	1	4	yes	complemented
79	C₄×C₂₆₉	C₂³×C₄	1	2	yes	—
80	Dic₂₆₉	—	2	4	no	—
81	Dic₂₆₉	C₂×C₄²	1	4	yes	—
82	C₂×C₂₆₉	—	2	2	no	—
83	C₂×C₂₆₉	C₂²×C₄²	1	1	yes	characteristic
84	C₂×C₂₆₉	C₂×#131	1	2	yes	—
85	D₂₆₉	—	2	4	no	—
86	C₂₆₉	C₄×#131	1	1	yes	characteristic, complemented, Sylow
87	C₄×#131	—	269	1	no	maximal, Sylow
88	C₂×#131	—	269	2	no	—
89	C₄×#41	—	269	1	no	—
90	#405	—	269	2	no	—
91	#405	—	269	4	no	—
92	C₄×M₁₆	—	269	1	no	—
93	C₄×M₁₆	—	269	2	no	—
94	C₂×C₄×C₈	—	269	2	no	—
95	C₂×C₄×C₈	D₂₆₉	1	1	yes	characteristic, complemented
96	C₂×#41	—	269	1	no	—
97	#131	—	269	16	no	—
98	C₂×M₁₆	—	269	2	no	—
99	C₂×M₁₆	—	269	4	no	—
100	C₂²×C₈	—	269	4	no	—
101	C₂²×C₈	C₂×D₂₆₉	1	2	yes	—
102	C₄×Q₈	—	269	2	no	—
103	C₄×D₄	—	269	4	no	—
104	C₄×D₄	—	269	2	no	—
105	#117	—	269	1	no	—
106	#117	—	269	2	no	—
107	C₂×C₄²	—	269	2	no	—
108	C₂×C₄²	C₂×D₂₆₉	1	1	yes	characteristic
109	#97	—	269	4	no	—
110	#97	—	269	2	no	—
111	C₄×C₈	—	269	4	no	—
112	C₄×C₈	—	269	2	no	—
113	C₄×C₈	C₂×D₂₆₉	1	1	yes	characteristic
114	C₄×C₈	C₂×D₂₆₉	1	2	yes	—
115	C₄×C₈	C₂×D₂₆₉	1	1	yes	characteristic
116	#41	—	269	8	no	—
117	C₂×Q₈	—	269	1	no	—
118	C₂×D₄	—	269	2	no	—
119	C₂×D₄	—	269	1	no	—
120	C₂²×C₄	—	269	2	no	—
121	C₂²×C₄	—	269	4	no	—
122	C₂²×C₄	C₄×D₂₆₉	1	2	yes	—
123	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
124	M₁₆	—	269	8	no	—
125	M₁₆	—	269	16	no	—
126	C₂×C₈	—	269	4	no	—
127	C₂×C₈	—	269	16	no	—
128	C₂×C₈	C₄×D₂₆₉	1	8	yes	complemented
129	C₂×C₈	C₂²×D₂₆₉	1	2	yes	—
130	C₂×C₈	C₂²×D₂₆₉	1	2	yes	—
131	C₄⋊C₄	—	269	4	no	—
132	C₄⋊C₄	—	269	2	no	—
133	C₂²⋊C₄	—	269	2	no	—
134	C₂²⋊C₄	—	269	4	no	—
135	C₄²	—	269	4	no	—
136	C₄²	—	269	2	no	—
137	C₄²	C₄×D₂₆₉	1	2	yes	—
138	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
139	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
140	C₂³	—	269	2	no	—
141	C₂³	C₂×C₄×D₂₆₉	1	1	yes	characteristic
142	Q₈	—	269	4	no	—
143	D₄	—	269	8	no	—
144	D₄	—	269	4	no	—
145	C₂×C₄	—	2	4	no	—
146	C₂×C₄	—	269	2	no	—
147	C₂×C₄	—	269	8	no	—
148	C₂×C₄	—	269	4	no	—
149	C₂×C₄	—	538	8	no	—
150	C₂×C₄	C₂×C₄×D₂₆₉	1	2	yes	—
151	C₂×C₄	C₂×C₄×D₂₆₉	1	1	yes	characteristic
152	C₂×C₄	C₂×C₄×D₂₆₉	1	4	yes	—
153	C₂×C₄	C₂×C₄×D₂₆₉	1	2	yes	—
154	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
155	C₈	—	269	8	no	—
156	C₈	C₂×C₄×D₂₆₉	1	4	yes	—
157	C₈	C₂×C₄×D₂₆₉	1	4	yes	—
158	C₂²	—	2	2	no	—
159	C₂²	—	269	4	no	—
160	C₂²	—	538	4	no	—
161	C₂²	C₄²×D₂₆₉	1	2	yes	—
162	C₂²	C₂²×C₄×D₂₆₉	1	1	yes	characteristic
163	C₄	—	2	2	no	—
164	C₄	—	269	4	no	—
165	C₄	—	538	4	no	—
166	C₄	C₄²×D₂₆₉	1	2	yes	—
167	C₄	#22575459	1	4	yes	direct product factor
168	C₄	C₂²×C₄×D₂₆₉	1	2	yes	—
169	C₂	—	2	2	no	—
170	C₂	—	538	4	no	—
171	C₂	C₂×C₄²×D₂₆₉	1	1	yes	characteristic
172	C₂	C₂×#22575459	1	2	yes	—

	subgroup	G/H
center	C₄×C₈	C₂×D₂₆₉
commutator	C₂×C₂₆₉	C₂²×C₄²
Frattini	C₂×C₄	C₂³×D₂₆₉
Fitting	C₂×C₄×C₈×C₂₆₉	C₂
socle	C₂²×C₂₆₉	C₂³×C₄
prime radical	C₂×#16864402	C₂²
cosocle	C₂×C₄×C₂₆₉	C₂⁴
hypercenter	C₂×C₄×C₈	D₂₆₉
hypocenter	C₂₆₉	C₄×#131
LCS	G ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₄×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
3. #31770560	C₂	semidirect
4. #31770559	C₂	semidirect
5. C₄×#16864386	C₂	semidirect
6. C₄×#16864385	C₂	semidirect
7. C₄×C₈×D₂₆₉	C₂	semidirect
8. C₂×C₄×C₈×C₂₆₉	C₂	semidirect
10. #22575459	C₄	direct (N × H)
35. #16864386	C₂×C₄	semidirect
36. #16864385	C₂×C₄	semidirect
38. C₈×D₂₆₉	C₂×C₄	semidirect
47. C₂×C₈×C₂₆₉	C₂×C₄	semidirect
78. C₄×C₂₆₉	#131	semidirect
86. C₂₆₉	C₄×#131	semidirect
95. C₂×C₄×C₈	D₂₆₉	semidirect
128. C₂×C₈	C₄×D₂₆₉	semidirect
167. C₄	#22575459	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×#22575459	2
C₄×#16864402	2
#31770560	2
#31770559	2
C₄×#16864386	2
C₄×#16864385	2
C₄×C₈×D₂₆₉	2
C₂×C₄×C₈×C₂₆₉	2
C₄×#131	269

Subgroups — C4×#22575459 #46819305

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#22575459 #46819305