Subgroups — C₄×#19151423 #36469828

Order 22784.

366 conjugacy classes of subgroups.

The subgroup lattice has 190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151423	C₂	1	2	yes	maximal
2	C₂×C₄×#13083549	C₂	1	1	yes	maximal, characteristic
3	C₄×#15667946	C₂	1	1	yes	maximal, characteristic
4	#26018343	C₂	1	2	yes	maximal
5	C₄×#107×C₈₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×#13083549	C₂²	1	1	yes	characteristic
7	C₂²×#13083549	C₂²	1	1	yes	characteristic
8	C₂×#15667946	C₂²	1	2	yes	—
9	C₄×C₄⋊Dic₈₉	—	2	1	no	—
10	#19151423	C₄	1	8	yes	direct product factor
11	C₄×#13083549	C₄	1	4	yes	complemented
12	#19151361	—	2	1	no	—
13	C₂×#107×C₈₉	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
15	C₄×C₄⋊C₄×C₈₉	—	2	1	no	—
16	#340×C₈₉	—	2	1	no	—
17	C₂×C₄⋊Dic₈₉	—	2	2	no	—
18	C₂×C₄×Dic₈₉	—	4	1	no	—
19	C₂×#13083549	—	2	2	no	—
20	C₂×#13083549	C₂×C₄	1	2	yes	—
21	C₂×#13083549	C₂×C₄	1	2	yes	—
22	C₂×#13083549	C₂×C₄	1	4	yes	—
23	#15667946	—	2	2	no	—
24	#15667946	C₂×C₄	1	4	yes	—
25	#15667919	—	4	1	no	—
26	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
27	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
28	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
29	C₂×C₄²×C₈₉	—	4	1	no	—
30	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
31	#107×C₈₉	—	2	2	no	—
32	#107×C₈₉	C₂×C₄	1	4	yes	—
33	C₄×C₈×C₈₉	C₂×C₄	1	2	yes	—
34	C₄×C₈×C₈₉	Q₈	1	2	yes	—
35	#95×C₈₉	—	4	1	no	—
36	C₂²×Dic₈₉	—	4	2	no	—
37	C₄⋊Dic₈₉	—	2	4	no	—
38	C₄⋊Dic₈₉	—	4	2	no	—
39	C₄×Dic₈₉	—	8	2	no	—
40	#13083549	—	2	2	no	—
41	#13083549	C₄²	1	4	yes	complemented
42	C₂²×C₄×C₈₉	—	4	2	no	—
43	C₂²×C₄×C₈₉	D₈	1	1	yes	characteristic
44	C₂²×C₄×C₈₉	D₈	1	1	yes	characteristic
45	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
46	C₂×C₈×C₈₉	—	2	2	no	—
47	C₂×C₈×C₈₉	C₄⋊C₄	1	2	yes	—
48	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
49	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
50	C₂×C₈×C₈₉	C₂×Q₈	1	1	yes	characteristic
51	C₂×C₈×C₈₉	#41	1	2	yes	—
52	C₄⋊C₄×C₈₉	—	2	4	no	—
53	C₄⋊C₄×C₈₉	—	4	2	no	—
54	C₄²×C₈₉	—	8	2	no	—
55	C₄²×C₈₉	C₄⋊C₄	1	2	yes	—
56	C₄²×C₈₉	Q₁₆	1	2	yes	—
57	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
58	C₂×C₄×C₈₉	—	2	2	no	—
59	C₂×C₄×C₈₉	—	4	4	no	—
60	C₂×C₄×C₈₉	—	8	2	no	—
61	C₂×C₄×C₈₉	—	8	2	no	—
62	C₂×C₄×C₈₉	#107	1	2	yes	—
63	C₂×C₄×C₈₉	#107	1	2	yes	—
64	C₂×C₄×C₈₉	D₁₆	1	2	yes	—
65	C₂×C₄×C₈₉	Q₃₂	1	2	yes	—
66	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
67	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
68	C₂×C₄×C₈₉	C₂×Q₁₆	1	1	yes	characteristic
69	C₂×C₄×C₈₉	#135	1	2	yes	—
70	C₂×Dic₈₉	—	4	4	no	—
71	C₂×Dic₈₉	—	8	2	no	—
72	C₂×Dic₈₉	—	8	2	no	—
73	C₈×C₈₉	—	2	2	no	—
74	C₈×C₈₉	C₂×C₄²	1	1	yes	characteristic
75	C₈×C₈₉	#117	1	1	yes	characteristic
76	C₈×C₈₉	C₄×Q₈	1	2	yes	—
77	C₂²×C₈₉	C₂×#107	1	1	yes	characteristic
78	C₂²×C₈₉	C₄×D₈	1	2	yes	—
79	C₂²×C₈₉	C₂×D₁₆	1	1	yes	characteristic
80	C₂²×C₈₉	C₂×Q₃₂	1	1	yes	characteristic
81	C₂²×C₈₉	#508	1	2	yes	—
82	C₄×C₈₉	—	2	2	no	—
83	C₄×C₈₉	—	8	4	no	—
84	C₄×C₈₉	#366	1	4	yes	complemented
85	C₄×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
86	C₄×C₈₉	#427	1	1	yes	characteristic
87	C₄×C₈₉	C₄×Q₁₆	1	2	yes	—
88	Dic₈₉	—	8	4	no	—
89	C₄×#366	—	89	1	no	maximal, Sylow
90	C₂×C₈₉	C₄×#107	1	1	yes	characteristic
91	C₂×C₈₉	C₂×#366	1	1	yes	characteristic
92	C₂×C₈₉	#2158	1	1	yes	characteristic
93	C₂×C₈₉	C₄×D₁₆	1	2	yes	—
94	C₂×C₈₉	C₄×Q₃₂	1	2	yes	—
95	C₂×#366	—	89	2	no	—
96	C₂×C₄×C₁₆	—	89	1	no	—
97	C₄×#107	—	89	1	no	—
98	C₄×#107	D₈₉	1	1	yes	characteristic
99	#1380	—	89	2	no	—
100	C₈₉	C₄×#366	1	1	yes	characteristic, complemented, Sylow
101	C₂²×C₁₆	—	89	1	no	—
102	C₂²×C₁₆	—	89	1	no	—
103	C₂×#107	—	89	2	no	—
104	C₂×#107	C₂×D₈₉	1	2	yes	—
105	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
106	C₄×C₄⋊C₄	—	2	1	no	—
107	C₄×C₄⋊C₄	—	178	1	no	—
108	#366	—	89	8	no	—
109	C₄×C₁₆	—	89	4	no	—
110	#340	—	2	1	no	—
111	#340	—	178	1	no	—
112	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
113	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
114	C₂×C₄⋊C₄	—	2	2	no	—
115	C₂×C₄⋊C₄	—	178	2	no	—
116	C₂×C₄²	—	4	1	no	—
117	C₂×C₄²	—	356	1	no	—
118	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
119	C₂×C₁₆	—	89	2	no	—
120	C₂×C₁₆	—	89	4	no	—
121	C₂×C₁₆	—	89	2	no	—
122	C₂×C₁₆	—	178	2	no	—
123	#107	—	2	2	no	—
124	#107	—	89	4	no	—
125	#107	—	178	2	no	—
126	#107	C₄×D₈₉	1	4	yes	—
127	C₄×C₈	Dic₁₇₈	1	2	yes	—
128	C₄×C₈	C₄×D₈₉	1	2	yes	—
129	#95	—	4	1	no	—
130	#95	—	356	1	no	—
131	C₂²×C₄	—	4	2	no	—
132	C₂²×C₄	—	356	2	no	—
133	C₂²×C₄	#13083559	1	1	yes	characteristic
134	C₂²×C₄	#13083559	1	1	yes	characteristic
135	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
136	C₂×C₈	—	2	2	no	—
137	C₂×C₈	#13083553	1	2	yes	—
138	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
139	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
140	C₂×C₈	C₂×Dic₁₇₈	1	1	yes	characteristic
141	C₂×C₈	#13083574	1	2	yes	—
142	C₄⋊C₄	—	2	4	no	—
143	C₄⋊C₄	—	4	2	no	—
144	C₄⋊C₄	—	356	2	no	—
145	C₄⋊C₄	—	178	4	no	—
146	C₄²	—	8	2	no	—
147	C₄²	—	712	2	no	—
148	C₄²	#13083553	1	2	yes	—
149	C₄²	#13083564	1	2	yes	—
150	C₁₆	—	89	4	no	—
151	C₁₆	—	178	2	no	—
152	C₂³	C₂×#13083559	1	1	yes	characteristic
153	C₂×C₄	—	2	2	no	—
154	C₂×C₄	—	4	4	no	—
155	C₂×C₄	—	8	2	no	—
156	C₂×C₄	—	8	2	no	—
157	C₂×C₄	—	356	4	no	—
158	C₂×C₄	—	712	2	no	—
159	C₂×C₄	—	712	2	no	—
160	C₂×C₄	#15667945	1	2	yes	—
161	C₂×C₄	#15667945	1	2	yes	—
162	C₂×C₄	#15667953	1	2	yes	—
163	C₂×C₄	#15667958	1	2	yes	—
164	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
165	C₂×C₄	C₄×C₂²⋊D₈₉	1	2	yes	—
166	C₂×C₄	C₂×#13083564	1	1	yes	characteristic
167	C₂×C₄	#15668032	1	2	yes	—
168	C₈	—	2	2	no	—
169	C₈	C₄²×D₈₉	1	1	yes	characteristic
170	C₈	#15667969	1	1	yes	characteristic
171	C₈	C₄×Dic₁₇₈	1	2	yes	—
172	C₂²	C₂×#15667945	1	1	yes	characteristic
173	C₂²	C₄×#13083559	1	2	yes	—
174	C₂²	C₂×#15667953	1	1	yes	characteristic
175	C₂²	C₂×#15667958	1	1	yes	characteristic
176	C₂²	#19152028	1	2	yes	—
177	C₄	—	2	2	no	—
178	C₄	—	8	4	no	—
179	C₄	—	712	4	no	—
180	C₄	#19151423	1	4	yes	direct product factor
181	C₄	C₄×#13083553	1	1	yes	characteristic
182	C₄	#19151634	1	1	yes	characteristic
183	C₄	C₄×#13083564	1	2	yes	—
184	C₂	C₄×#15667945	1	1	yes	characteristic
185	C₂	C₂×#19151423	1	1	yes	characteristic
186	C₂	#26022034	1	1	yes	characteristic
187	C₂	C₄×#15667953	1	2	yes	—
188	C₂	C₄×#15667958	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	#13083559
commutator	C₈×C₈₉	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₈₉
Fitting	C₄×#107×C₈₉	C₂
socle, prime radical	C₂³×C₈₉	C₂×D₈
cosocle	C₂²×C₈×C₈₉	C₂³
hypercenter	C₄×#107	D₈₉
hypocenter	C₈₉	C₄×#366
LCS	G ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₄×#107

Complements

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

N	H ≅ G/N	type
10. #19151423	C₄	direct (N × H)
11. C₄×#13083549	C₄	semidirect
41. #13083549	C₄²	semidirect
84. C₄×C₈₉	#366	semidirect
100. C₈₉	C₄×#366	semidirect
180. C₄	#19151423	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×#19151423	2
C₂×C₄×#13083549	2
C₄×#15667946	2
#26018343	2
C₄×#107×C₈₉	2
C₄×#366	89

Subgroups — C4×#19151423 #36469828

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#19151423 #36469828