Subgroups — C₂×#21462786 #30626712

Order 15616.

2074 conjugacy classes of subgroups.

The subgroup lattice has 196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21462786	C₂	1	16	yes	maximal, direct product factor
2	C₂×#16840820	C₂	1	8	yes	maximal, complemented
3	C₂²×#14519851	C₂	1	6	yes	maximal, complemented
4	C₂²×#14519784	C₂	1	1	yes	maximal, characteristic
5	#16840820	C₂²	1	64	yes	complemented
6	C₂×#14519851	C₂²	1	4	yes	—
7	C₂×#14519851	C₂²	1	12	yes	complemented
8	C₂×#14519851	C₂²	1	48	yes	complemented
9	C₂²×#11758187	C₂²	1	12	yes	complemented
10	C₂×#14519784	C₄	1	8	yes	—
11	C₂×#14519784	C₄	1	4	yes	—
12	C₂×#14519784	C₂²	1	8	yes	—
13	C₂×#14519784	C₂²	1	4	yes	—
14	C₂²×#11758194	C₄	1	3	yes	—
15	C₂³×#92418	C₂²	1	3	yes	—
16	C₂²×#41×C₆₁	C₄	1	1	yes	characteristic
17	#14519851	C₂³	1	16	yes	—
18	#14519851	C₂³	1	48	yes	complemented
19	C₂×#11758187	C₂³	1	8	yes	—
20	C₂×#11758187	C₂³	1	48	yes	complemented
21	#14519784	C₂×C₄	1	32	yes	—
22	#14519784	C₂×C₄	1	16	yes	—
23	#14519784	C₂³	1	16	yes	—
24	C₂×#11758194	C₂×C₄	1	24	yes	—
25	C₂×#11758194	C₂×C₄	1	12	yes	—
26	C₂²×#92418	C₂×C₄	1	3	yes	—
27	C₂²×#92418	C₂×C₄	1	12	yes	—
28	C₂²×#92418	C₂×C₄	1	6	yes	—
29	C₂²×#92418	C₂³	1	1	yes	characteristic
30	C₂²×#92418	C₂³	1	6	yes	—
31	C₂²×#92418	C₂³	1	12	yes	—
32	C₂×#41×C₆₁	C₈	1	4	yes	—
33	C₂×#41×C₆₁	C₈	1	8	yes	—
34	C₂×#41×C₆₁	C₂×C₄	1	8	yes	—
35	C₂×#41×C₆₁	C₂×C₄	1	4	yes	—
36	C₂²×Q₈×C₆₁	C₈	1	1	yes	characteristic
37	C₂²×D₄×C₆₁	C₈	1	3	yes	—
38	C₂³×C₄×C₆₁	C₂×C₄	1	3	yes	—
39	C₂⁴×C₆₁	C₂×C₈	1	3	yes	—
40	#41×C₆₁	C₂×C₈	1	32	yes	—
41	#41×C₆₁	C₂×C₈	1	16	yes	—
42	#41×C₆₁	C₂²×C₄	1	16	yes	—
43	C₂×Q₈×C₆₁	C₂×C₈	1	8	yes	—
44	C₂×Q₈×C₆₁	C₂×C₈	1	4	yes	—
45	C₂×D₄×C₆₁	C₂×C₈	1	12	yes	—
46	C₂×D₄×C₆₁	C₂×C₈	1	24	yes	—
47	C₂²×C₄×C₆₁	C₂×C₈	1	3	yes	—
48	C₂²×C₄×C₆₁	C₂×C₈	1	6	yes	—
49	C₂²×C₄×C₆₁	C₂×C₈	1	12	yes	—
50	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
51	C₂²×C₄×C₆₁	C₂²×C₄	1	12	yes	—
52	C₂²×C₄×C₆₁	C₂²×C₄	1	6	yes	—
53	#11758194	C₂²×C₄	1	48	yes	—
54	C₂×#92418	C₂²×C₄	1	2	yes	—
55	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
56	C₂×#92418	C₂²×C₄	1	12	yes	—
57	C₂×#92418	C₂²×C₄	1	6	yes	—
58	C₂×#92418	C₂²×C₄	1	12	yes	—
59	C₂×#92418	C₂²×C₄	1	24	yes	—
60	C₂×#92418	C₂⁴	1	1	yes	characteristic
61	C₂×#92418	C₂⁴	1	12	yes	—
62	C₂×#92418	C₂⁴	1	2	yes	—
63	#11758187	C₂⁴	1	16	yes	—
64	C₂³×C₆₁	—	4	6	no	—
65	C₂³×C₆₁	C₂²×C₈	1	1	yes	characteristic
66	C₂³×C₆₁	C₂²×C₈	1	6	yes	—
67	C₂³×C₆₁	C₂²×C₈	1	12	yes	—
68	Q₈×C₆₁	C₂²×C₈	1	16	yes	—
69	D₄×C₆₁	C₂²×C₈	1	48	yes	—
70	C₂×C₄×C₆₁	C₂²×C₈	1	2	yes	—
71	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
72	C₂×C₄×C₆₁	C₂²×C₈	1	12	yes	—
73	C₂×C₄×C₆₁	C₂²×C₈	1	6	yes	—
74	C₂×C₄×C₆₁	C₂²×C₈	1	24	yes	—
75	C₂×C₄×C₆₁	C₂²×C₈	1	12	yes	—
76	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
77	C₂×C₄×C₆₁	C₂³×C₄	1	12	yes	—
78	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
79	#92418	C₂³×C₄	1	1	yes	characteristic
80	#92418	C₂³×C₄	1	2	yes	—
81	#92418	C₂³×C₄	1	12	yes	—
82	#92418	C₂⁵	1	1	yes	characteristic
83	C₂×#3407	—	61	1	no	maximal, Sylow
84	C₂²×C₆₁	—	2	2	no	—
85	C₂²×C₆₁	—	2	12	no	—
86	C₂²×C₆₁	—	4	12	no	—
87	C₂²×C₆₁	C₂³×C₈	1	2	yes	—
88	C₂²×C₆₁	C₂³×C₈	1	12	yes	—
89	C₂²×C₆₁	C₂³×C₈	1	1	yes	characteristic
90	C₄×C₆₁	C₂³×C₈	1	2	yes	—
91	C₄×C₆₁	C₂³×C₈	1	1	yes	characteristic
92	C₄×C₆₁	C₂³×C₈	1	12	yes	—
93	C₄×C₆₁	C₂⁴×C₄	1	1	yes	characteristic
94	C₂²×#131	—	61	1	no	—
95	#3407	—	61	16	no	—
96	C₂×#504	—	61	8	no	—
97	C₂²×M₃₂	—	61	6	no	—
98	C₂×C₆₁	—	2	2	no	—
99	C₂×C₆₁	—	2	12	no	—
100	C₂×C₆₁	#3407	1	2	yes	complemented
101	C₂×C₆₁	C₂⁴×C₈	1	1	yes	characteristic
102	C₂²×#41	#6923	1	1	yes	characteristic
103	C₂×#131	—	61	8	no	—
104	C₂×#131	—	61	4	no	—
105	C₂×#131	—	61	4	no	—
106	C₂×#131	—	61	8	no	—
107	C₂²×M₁₆	—	61	3	no	—
108	C₂³×C₈	—	61	3	no	—
109	#504	—	61	64	no	—
110	C₂×M₃₂	—	61	4	no	—
111	C₂×M₃₂	—	61	12	no	—
112	C₂×M₃₂	—	61	48	no	—
113	C₂²×C₁₆	—	61	12	no	—
114	C₆₁	C₂×#3407	1	1	yes	characteristic, complemented, Sylow
115	C₂×#41	#92420	1	4	yes	—
116	C₂×#41	#92420	1	8	yes	—
117	C₂×#41	C₂×#6923	1	8	yes	—
118	C₂×#41	C₂×#6923	1	4	yes	—
119	C₂²×Q₈	#92420	1	1	yes	characteristic
120	C₂²×D₄	#92420	1	3	yes	—
121	C₂³×C₄	C₂×#6923	1	3	yes	—
122	#131	—	61	16	no	—
123	#131	—	61	32	no	—
124	#131	—	61	16	no	—
125	C₂×M₁₆	—	61	24	no	—
126	C₂×M₁₆	—	61	12	no	—
127	C₂²×C₈	—	61	1	no	—
128	C₂²×C₈	—	61	3	no	—
129	C₂²×C₈	—	61	12	no	—
130	C₂²×C₈	—	61	6	no	—
131	C₂²×C₈	—	61	6	no	—
132	C₂²×C₈	—	61	12	no	—
133	M₃₂	—	61	16	no	—
134	M₃₂	—	61	48	no	—
135	C₂×C₁₆	—	61	8	no	—
136	C₂×C₁₆	—	61	48	no	—
137	C₂⁴	C₂×#92420	1	3	yes	—
138	#41	C₂×#92420	1	32	yes	—
139	#41	C₂×#92420	1	16	yes	—
140	#41	C₂²×#6923	1	16	yes	—
141	C₂×Q₈	C₂×#92420	1	8	yes	—
142	C₂×Q₈	C₂×#92420	1	4	yes	—
143	C₂×D₄	C₂×#92420	1	12	yes	—
144	C₂×D₄	C₂×#92420	1	24	yes	—
145	C₂²×C₄	C₂×#92420	1	3	yes	—
146	C₂²×C₄	C₂×#92420	1	6	yes	—
147	C₂²×C₄	C₂×#92420	1	12	yes	—
148	C₂²×C₄	C₂²×#6923	1	12	yes	—
149	C₂²×C₄	C₂²×#6923	1	1	yes	characteristic
150	C₂²×C₄	C₂²×#6923	1	6	yes	—
151	M₁₆	—	61	48	no	—
152	C₂×C₈	—	61	12	no	—
153	C₂×C₈	—	61	2	no	—
154	C₂×C₈	—	61	2	no	—
155	C₂×C₈	—	61	12	no	—
156	C₂×C₈	—	61	12	no	—
157	C₂×C₈	—	61	24	no	—
158	C₂×C₈	—	61	1	no	—
159	C₂×C₈	—	61	1	no	—
160	C₂×C₈	—	61	6	no	—
161	C₁₆	—	61	16	no	—
162	C₂³	—	4	6	no	—
163	C₂³	C₂²×#92420	1	1	yes	characteristic
164	C₂³	C₂²×#92420	1	6	yes	—
165	C₂³	C₂²×#92420	1	12	yes	—
166	Q₈	C₂²×#92420	1	16	yes	—
167	D₄	C₂²×#92420	1	48	yes	—
168	C₂×C₄	C₂²×#92420	1	1	yes	characteristic
169	C₂×C₄	C₂²×#92420	1	2	yes	—
170	C₂×C₄	C₂²×#92420	1	12	yes	—
171	C₂×C₄	C₂²×#92420	1	6	yes	—
172	C₂×C₄	C₂²×#92420	1	24	yes	—
173	C₂×C₄	C₂²×#92420	1	12	yes	—
174	C₂×C₄	C₂³×#6923	1	2	yes	—
175	C₂×C₄	C₂³×#6923	1	12	yes	—
176	C₂×C₄	C₂³×#6923	1	1	yes	characteristic
177	C₈	—	61	2	no	—
178	C₈	—	61	1	no	—
179	C₈	—	61	12	no	—
180	C₈	—	61	1	no	—
181	C₂²	—	2	2	no	—
182	C₂²	—	2	12	no	—
183	C₂²	—	4	12	no	—
184	C₂²	C₂³×#92420	1	2	yes	—
185	C₂²	C₂³×#92420	1	12	yes	—
186	C₂²	C₂³×#92420	1	1	yes	characteristic
187	C₄	C₂³×#92420	1	2	yes	—
188	C₄	C₂³×#92420	1	1	yes	characteristic
189	C₄	C₂³×#92420	1	12	yes	—
190	C₄	C₂⁴×#6923	1	1	yes	characteristic
191	C₂	—	2	2	no	—
192	C₂	—	2	12	no	—
193	C₂	#21462786	1	2	yes	direct product factor
194	C₂	C₂⁴×#92420	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×#6923
commutator	C₂×C₆₁	C₂⁴×C₈
Frattini	C₄	C₂⁴×#6923
Fitting, prime radical	C₂²×#41×C₆₁	C₄
socle	C₂²×C₆₁	C₂³×C₈
cosocle	#92418	C₂⁵
hypercenter	C₂²×#41	#6923
hypocenter	C₆₁	C₂×#3407
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×#41

Complements

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

N	H ≅ G/N	type
1. #21462786	C₂	direct (N × H)
2. C₂×#16840820	C₂	semidirect
3. C₂²×#14519851	C₂	semidirect
5. #16840820	C₂²	semidirect
7. C₂×#14519851	C₂²	semidirect
8. C₂×#14519851	C₂²	semidirect
9. C₂²×#11758187	C₂²	semidirect
18. #14519851	C₂³	semidirect
20. C₂×#11758187	C₂³	semidirect
100. C₂×C₆₁	#3407	semidirect
114. C₆₁	C₂×#3407	semidirect
193. C₂	#21462786	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#21462786	2
C₂×#16840820	2
C₂²×#14519851	2
C₂²×#14519784	2
C₂×#3407	61

Subgroups — C2×#21462786 #30626712

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#21462786 #30626712