Subgroups — C₂×#19099286 #23776949

Order 10112.

1112 conjugacy classes of subgroups.

The subgroup lattice has 212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19099286	C₂	1	16	yes	maximal, direct product factor
2	C₂×#14579161	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#14579156	C₂	1	4	yes	maximal, complemented
4	C₂×#14579149	C₂	1	2	yes	maximal
5	C₂×#14579137	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×Dic₁₅₈	C₂	1	2	yes	maximal, complemented
7	C₂×C₄×D₃₁₆	C₂	1	1	yes	maximal, characteristic
8	C₂×#14579119	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×Q₈×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×Dic₁₅₈	C₂²	1	2	yes	—
11	C₂²×D₃₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₄×D₇₉	C₂²	1	2	yes	—
13	#14579161	C₂²	1	8	yes	complemented
14	#14579156	C₂²	1	32	yes	complemented
15	#14579149	C₂²	1	16	yes	—
16	#14579137	C₂²	1	16	yes	complemented
17	C₄×Dic₁₅₈	C₂²	1	16	yes	complemented
18	C₄×D₃₁₆	C₂²	1	8	yes	—
19	#14579119	C₂²	1	16	yes	complemented
20	C₂×C₄⋊Dic₇₉	C₂²	1	2	yes	—
21	C₂×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊Dic₇₉	C₂²	1	2	yes	—
23	C₂×Dic₇₉⋊C₄	C₂²	1	4	yes	—
24	C₂×(C₂×D₇₉)⋊C₄	C₂²	1	4	yes	—
25	C₂×(C₂×D₇₉)⋊C₄	C₂²	1	2	yes	—
26	C₂×(C₂×D₇₉)⋊C₄	C₂²	1	4	yes	—
27	C₂×C₄×Dic₇₉	C₂²	1	4	yes	—
28	C₂²×Q₈×C₇₉	C₂²	1	1	yes	characteristic
29	C₄×Q₈×C₇₉	C₂²	1	8	yes	complemented
30	C₂×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
32	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
33	C₂×C₄²×C₇₉	C₂²	1	2	yes	—
34	C₂³×D₇₉	C₂³	1	2	yes	—
35	C₂×Dic₁₅₈	—	2	8	no	—
36	C₂×Dic₁₅₈	C₂³	1	8	yes	—
37	C₂×D₃₁₆	—	2	4	no	—
38	C₂×D₃₁₆	C₂³	1	4	yes	—
39	C₂²×Dic₇₉	C₂³	1	4	yes	—
40	C₂²×Dic₇₉	C₂³	1	2	yes	—
41	C₂×C₄×D₇₉	—	2	8	no	—
42	C₂×C₄×D₇₉	C₂³	1	8	yes	—
43	C₄⋊Dic₇₉	C₂³	1	8	yes	—
44	C₄⋊Dic₇₉	C₂³	1	4	yes	—
45	C₄⋊Dic₇₉	C₂³	1	8	yes	—
46	Dic₇₉⋊C₄	C₂³	1	16	yes	—
47	(C₂×D₇₉)⋊C₄	C₂³	1	16	yes	—
48	(C₂×D₇₉)⋊C₄	C₂³	1	8	yes	—
49	(C₂×D₇₉)⋊C₄	C₂³	1	16	yes	—
50	C₄×Dic₇₉	C₂³	1	16	yes	—
51	C₂×Q₈×C₇₉	—	2	4	no	—
52	C₂×Q₈×C₇₉	C₂³	1	4	yes	—
53	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
54	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
55	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
56	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
57	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
58	C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
59	C₄⋊C₄×C₇₉	C₂³	1	8	yes	—
60	C₄²×C₇₉	C₂³	1	4	yes	—
61	C₄²×C₇₉	C₂³	1	8	yes	—
62	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
63	C₂²×D₇₉	—	2	4	no	—
64	C₂²×D₇₉	—	2	4	no	—
65	C₂²×D₇₉	—	2	4	no	—
66	C₂²×D₇₉	C₂⁴	1	4	yes	—
67	Q₈×C₇₉	—	2	8	no	—
68	C₂×C₄×C₇₉	—	2	4	no	—
69	C₂×C₄×C₇₉	—	2	4	no	—
70	C₂×C₄×C₇₉	—	2	2	no	—
71	C₂×C₄×C₇₉	#41	1	4	yes	—
72	C₂×C₄×C₇₉	#41	1	4	yes	—
73	C₂×C₄×C₇₉	C₂⁴	1	4	yes	—
74	C₂×C₄×C₇₉	C₂⁴	1	4	yes	—
75	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
76	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
77	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
78	C₂×Dic₇₉	—	2	4	no	—
79	C₂×Dic₇₉	—	2	8	no	—
80	C₂×Dic₇₉	C₂⁴	1	4	yes	—
81	C₂×Dic₇₉	C₂⁴	1	8	yes	—
82	D₃₁₆	—	2	8	no	—
83	C₄×D₇₉	—	2	16	no	—
84	Dic₁₅₈	—	2	16	no	—
85	C₂²×C₇₉	C₂×#41	1	2	yes	—
86	C₂²×C₇₉	C₂×#41	1	2	yes	—
87	C₂²×C₇₉	2₋¹⁺⁴	1	2	yes	—
88	C₂²×C₇₉	C₂⁵	1	1	yes	characteristic
89	C₂×D₇₉	—	2	4	no	—
90	C₂×D₇₉	—	2	4	no	—
91	C₂×D₇₉	—	2	4	no	—
92	C₂×D₇₉	—	4	8	no	—
93	C₄×C₇₉	—	2	4	no	—
94	C₄×C₇₉	—	2	4	no	—
95	C₄×C₇₉	—	2	2	no	—
96	C₄×C₇₉	C₂×#41	1	4	yes	—
97	C₄×C₇₉	C₂×#41	1	4	yes	—
98	Dic₇₉	—	2	8	no	—
99	Dic₇₉	—	2	4	no	—
100	C₂×C₇₉	#556	1	4	yes	complemented
101	C₂×C₇₉	C₂²×#41	1	1	yes	characteristic
102	C₂×C₇₉	C₂²×#41	1	1	yes	characteristic
103	C₂×C₇₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
104	D₇₉	—	4	4	no	—
105	C₂×#556	—	79	1	no	maximal, Sylow
106	C₇₉	C₂×#556	1	1	yes	characteristic, complemented, Sylow
107	#556	—	79	16	no	—
108	C₂×C₄⋊Q₈	—	79	1	no	—
109	C₂×#126	—	79	4	no	—
110	C₂×#124	—	79	2	no	—
111	C₂×C₂²⋊Q₈	—	79	2	no	—
112	C₂×C₄×Q₈	—	79	2	no	—
113	C₂×C₄×Q₈	D₇₉	1	1	yes	characteristic, complemented
114	C₂×C₄×D₄	—	79	1	no	—
115	C₂×#117	—	79	2	no	—
116	C₂²×Q₈	—	79	2	no	—
117	C₂²×Q₈	C₂×D₇₉	1	1	yes	characteristic
118	C₂²×D₄	—	79	1	no	—
119	C₂³×C₄	—	79	2	no	—
120	C₄⋊Q₈	—	79	8	no	—
121	#126	—	79	32	no	—
122	#124	—	79	16	no	—
123	C₂²⋊Q₈	—	79	16	no	—
124	C₄×Q₈	—	79	16	no	—
125	C₄×Q₈	C₂×D₇₉	1	8	yes	complemented
126	C₄×D₄	—	79	8	no	—
127	#117	—	79	16	no	—
128	C₂×C₄⋊C₄	—	79	2	no	—
129	C₂×C₄⋊C₄	—	79	1	no	—
130	C₂×C₄⋊C₄	—	79	4	no	—
131	C₂×C₄⋊C₄	—	79	2	no	—
132	C₂×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
133	C₂×C₄⋊C₄	C₂×D₇₉	1	2	yes	—
134	C₂×C₂²⋊C₄	—	79	4	no	—
135	C₂×C₂²⋊C₄	—	79	2	no	—
136	C₂×C₂²⋊C₄	—	79	4	no	—
137	C₂×C₄²	—	79	4	no	—
138	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
139	C₂×C₄²	C₂×D₇₉	1	2	yes	—
140	C₂⁴	—	79	2	no	—
141	C₂×Q₈	—	2	4	no	—
142	C₂×Q₈	—	79	8	no	—
143	C₂×Q₈	—	158	8	no	—
144	C₂×Q₈	C₂²×D₇₉	1	4	yes	—
145	C₂×D₄	—	79	4	no	—
146	C₂×D₄	—	158	4	no	—
147	C₂²×C₄	—	79	2	no	—
148	C₂²×C₄	—	79	4	no	—
149	C₂²×C₄	—	79	8	no	—
150	C₂²×C₄	—	158	8	no	—
151	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
152	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
153	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
154	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
155	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
156	C₄⋊C₄	—	79	16	no	—
157	C₄⋊C₄	—	79	8	no	—
158	C₄⋊C₄	—	79	4	no	—
159	C₄⋊C₄	—	79	8	no	—
160	C₄⋊C₄	C₂²×D₇₉	1	4	yes	—
161	C₄⋊C₄	C₂²×D₇₉	1	8	yes	—
162	C₂²⋊C₄	—	79	16	no	—
163	C₂²⋊C₄	—	79	8	no	—
164	C₂²⋊C₄	—	79	16	no	—
165	C₄²	—	79	16	no	—
166	C₄²	C₂²×D₇₉	1	4	yes	—
167	C₄²	C₂²×D₇₉	1	8	yes	—
168	C₂³	—	79	4	no	—
169	C₂³	—	158	4	no	—
170	C₂³	—	158	4	no	—
171	C₂³	—	158	4	no	—
172	C₂³	C₂³×D₇₉	1	1	yes	characteristic
173	Q₈	—	2	8	no	—
174	Q₈	—	158	16	no	—
175	D₄	—	158	8	no	—
176	C₂×C₄	—	2	4	no	—
177	C₂×C₄	—	2	4	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	79	4	no	—
180	C₂×C₄	—	79	8	no	—
181	C₂×C₄	—	158	4	no	—
182	C₂×C₄	—	158	8	no	—
183	C₂×C₄	—	158	16	no	—
184	C₂×C₄	#11929624	1	4	yes	—
185	C₂×C₄	#11929625	1	4	yes	—
186	C₂×C₄	C₂³×D₇₉	1	4	yes	—
187	C₂×C₄	C₂³×D₇₉	1	2	yes	—
188	C₂×C₄	C₂³×D₇₉	1	4	yes	—
189	C₂×C₄	C₂³×D₇₉	1	2	yes	—
190	C₂×C₄	C₂³×D₇₉	1	2	yes	—
191	C₂²	—	316	8	no	—
192	C₂²	—	158	4	no	—
193	C₂²	—	158	4	no	—
194	C₂²	—	158	4	no	—
195	C₂²	C₂×#11929624	1	2	yes	—
196	C₂²	C₂×#11929625	1	2	yes	—
197	C₂²	#14579208	1	2	yes	—
198	C₂²	C₂⁴×D₇₉	1	1	yes	characteristic
199	C₄	—	2	4	no	—
200	C₄	—	2	2	no	—
201	C₄	—	2	4	no	—
202	C₄	—	158	4	no	—
203	C₄	—	158	8	no	—
204	C₄	C₂×#11929624	1	4	yes	—
205	C₄	C₂×#11929625	1	4	yes	—
206	C₂	—	316	4	no	—
207	C₂	#19099286	1	4	yes	direct product factor
208	C₂	C₂²×#11929624	1	1	yes	characteristic
209	C₂	C₂²×#11929625	1	1	yes	characteristic
210	C₂	C₂×#14579208	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₇₉
commutator, cosocle	C₂²×C₇₉	C₂⁵
Frattini	C₂²	C₂⁴×D₇₉
Fitting	C₂×C₄×Q₈×C₇₉	C₂
socle	C₂³×C₇₉	C₂⁴
prime radical	C₂²×D₃₁₆	C₂²
hypercenter	C₂×C₄×Q₈	D₇₉
hypocenter	C₇₉	C₂×#556
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×Q₈

Complements

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

N	H ≅ G/N	type
1. #19099286	C₂	direct (N × H)
2. C₂×#14579161	C₂	semidirect
3. C₂×#14579156	C₂	semidirect
5. C₂×#14579137	C₂	semidirect
6. C₂×C₄×Dic₁₅₈	C₂	semidirect
8. C₂×#14579119	C₂	semidirect
9. C₂×C₄×Q₈×C₇₉	C₂	semidirect
13. #14579161	C₂²	semidirect
14. #14579156	C₂²	semidirect
16. #14579137	C₂²	semidirect
17. C₄×Dic₁₅₈	C₂²	semidirect
19. #14579119	C₂²	semidirect
29. C₄×Q₈×C₇₉	C₂²	semidirect
100. C₂×C₇₉	#556	semidirect
106. C₇₉	C₂×#556	semidirect
113. C₂×C₄×Q₈	D₇₉	semidirect
125. C₄×Q₈	C₂×D₇₉	semidirect
207. C₂	#19099286	direct (N × H)

Subgroups — C2×#19099286 #23776949

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#19099286 #23776949