Subgroups — C₂×D₆₁⋊#108 #21462476

Order 7808.

480 conjugacy classes of subgroups.

The subgroup lattice has 204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₆₁⋊M₁₆	C₂	1	2	yes	maximal
2	C₂×#14519848	C₂	1	2	yes	maximal, complemented
3	D₆₁⋊#108	C₂	1	8	yes	maximal, direct product factor
4	C₂×#14519847	C₂	1	2	yes	maximal, complemented
5	C₂²×C₈×D₆₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#11758213	C₂²	1	4	yes	—
7	D₆₁⋊M₁₆	—	2	4	no	—
8	D₆₁⋊M₁₆	C₂²	1	8	yes	—
9	C₂×#11758217	—	2	2	no	—
10	C₂×D₆₁⋊C₈	—	2	2	no	—
11	#14519848	C₂²	1	8	yes	complemented
12	#14519847	C₂²	1	8	yes	complemented
13	C₂²×C₄×D₆₁	C₂²	1	1	yes	characteristic
14	C₂²×#92418	C₄	1	1	yes	characteristic
15	C₂×C₈×D₆₁	C₄	1	4	yes	—
16	C₂×C₈×D₆₁	C₄	1	1	yes	characteristic
17	C₂×C₈×D₆₁	C₄	1	1	yes	characteristic
18	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
19	C₂×C₈×D₆₁	C₂²	1	4	yes	—
20	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
21	C₂²×C₈×C₆₁	C₄	1	1	yes	characteristic
22	C₂³×D₆₁	Q₈	1	1	yes	characteristic
23	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
24	C₂²×Dic₆₁	D₄	1	1	yes	characteristic
25	C₂×C₄×D₆₁	C₂×C₄	1	2	yes	—
26	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄×D₆₁	D₄	1	1	yes	characteristic
28	C₂×C₄×D₆₁	D₄	1	2	yes	—
29	C₂×C₄×D₆₁	Q₈	1	2	yes	—
30	C₂×C₄×D₆₁	Q₈	1	1	yes	characteristic
31	C₂×C₄×D₆₁	C₂³	1	2	yes	—
32	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
33	#11758217	—	2	8	no	—
34	C₂×#92420	—	2	4	no	—
35	#11758213	—	2	4	no	—
36	#11758213	C₂³	1	8	yes	—
37	D₆₁⋊C₈	—	2	8	no	—
38	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
39	C₂×C₈×C₆₁	C₂×C₄	1	4	yes	—
40	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
41	C₂×#92418	C₂×C₄	1	1	yes	characteristic
42	C₂×#92418	C₂×C₄	1	4	yes	—
43	C₂×#92418	C₂×C₄	1	1	yes	characteristic
44	C₈×D₆₁	C₂×C₄	1	2	yes	—
45	C₈×D₆₁	C₂×C₄	1	4	yes	—
46	C₈×D₆₁	C₂×C₄	1	4	yes	—
47	C₈×D₆₁	C₂×C₄	1	2	yes	—
48	C₈×D₆₁	C₂³	1	2	yes	—
49	C₈×D₆₁	C₂³	1	2	yes	—
50	C₂³×C₆₁	C₄⋊C₄	1	1	yes	characteristic
51	C₂²×D₆₁	—	2	4	no	—
52	C₂²×D₆₁	C₄⋊C₄	1	2	yes	—
53	C₂²×D₆₁	C₄⋊C₄	1	1	yes	characteristic
54	C₂²×D₆₁	C₂×Q₈	1	1	yes	characteristic
55	C₂²×D₆₁	C₂×Q₈	1	2	yes	—
56	C₂×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
57	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
58	C₂×C₄×C₆₁	C₂²×C₄	1	2	yes	—
59	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
60	C₂×Dic₆₁	C₄⋊C₄	1	2	yes	—
61	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
62	C₂×Dic₆₁	C₂×D₄	1	1	yes	characteristic
63	C₂×Dic₆₁	C₂×D₄	1	2	yes	—
64	C₄×D₆₁	C₄⋊C₄	1	2	yes	—
65	C₄×D₆₁	C₄⋊C₄	1	2	yes	—
66	C₄×D₆₁	C₄⋊C₄	1	2	yes	—
67	C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
68	C₄×D₆₁	C₂²×C₄	1	2	yes	—
69	C₄×D₆₁	C₂×D₄	1	2	yes	—
70	C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
71	C₄×D₆₁	C₂×Q₈	1	2	yes	—
72	C₄×D₆₁	C₂×Q₈	1	1	yes	characteristic
73	C₄×D₆₁	C₂⁴	1	1	yes	characteristic
74	#92420	—	2	8	no	—
75	C₈×C₆₁	C₂²×C₄	1	2	yes	—
76	C₈×C₆₁	C₂²×C₄	1	2	yes	—
77	#92418	C₂²×C₄	1	2	yes	—
78	#92418	C₂²×C₄	1	2	yes	—
79	C₂²×C₆₁	—	2	2	no	—
80	C₂²×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
81	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
82	C₂×D₆₁	—	2	2	no	—
83	C₂×D₆₁	—	2	4	no	—
84	C₂×D₆₁	—	2	4	no	—
85	C₂×D₆₁	#108	1	4	yes	complemented
86	C₂×D₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
87	C₂×D₆₁	C₂×C₄⋊C₄	1	2	yes	—
88	C₂×D₆₁	C₂²×Q₈	1	1	yes	characteristic
89	C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
90	C₄×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
91	C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
92	Dic₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
93	Dic₆₁	C₂×C₄⋊C₄	1	2	yes	—
94	Dic₆₁	C₂²×D₄	1	1	yes	characteristic
95	C₂²×#108	—	61	1	no	maximal, Sylow
96	C₂×C₆₁	—	2	2	no	—
97	C₂×C₆₁	C₂×#108	1	2	yes	complemented
98	C₂×C₆₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
99	D₆₁	—	2	1	no	—
100	D₆₁	—	2	1	no	—
101	D₆₁	C₂×#108	1	4	yes	complemented
102	C₂²×M₁₆	—	61	2	no	—
103	C₂³×C₈	—	61	1	no	—
104	C₂×#108	—	61	2	no	—
105	C₂×#108	—	61	8	no	—
106	C₂×#108	—	61	2	no	—
107	C₆₁	C₂²×#108	1	1	yes	characteristic, complemented, Sylow
108	C₂³×C₄	—	61	1	no	—
109	C₂×M₁₆	—	61	8	no	—
110	C₂×M₁₆	—	61	4	no	—
111	C₂×M₁₆	—	122	2	no	—
112	C₂×M₁₆	—	122	4	no	—
113	C₂²×C₈	—	61	1	no	—
114	C₂²×C₈	—	61	1	no	—
115	C₂²×C₈	—	61	4	no	—
116	C₂²×C₈	—	61	1	no	—
117	C₂²×C₈	—	61	1	no	—
118	C₂²×C₈	—	61	1	no	—
119	C₂²×C₈	—	61	4	no	—
120	C₂²×C₈	—	122	2	no	—
121	C₂²×C₈	#6923	1	1	yes	characteristic
122	#108	—	61	8	no	—
123	#108	—	61	8	no	—
124	C₂⁴	—	61	1	no	—
125	C₂²×C₄	—	61	1	no	—
126	C₂²×C₄	—	61	2	no	—
127	C₂²×C₄	—	61	2	no	—
128	C₂²×C₄	—	61	1	no	—
129	C₂²×C₄	—	61	1	no	—
130	C₂²×C₄	—	61	1	no	—
131	C₂²×C₄	—	61	2	no	—
132	C₂²×C₄	—	61	1	no	—
133	C₂²×C₄	—	61	2	no	—
134	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
135	M₁₆	—	61	8	no	—
136	M₁₆	—	122	4	no	—
137	M₁₆	—	122	8	no	—
138	C₂×C₈	—	61	1	no	—
139	C₂×C₈	—	61	1	no	—
140	C₂×C₈	—	61	4	no	—
141	C₂×C₈	—	61	2	no	—
142	C₂×C₈	—	61	2	no	—
143	C₂×C₈	—	61	4	no	—
144	C₂×C₈	—	61	4	no	—
145	C₂×C₈	—	61	2	no	—
146	C₂×C₈	—	61	2	no	—
147	C₂×C₈	—	122	8	no	—
148	C₂×C₈	—	122	4	no	—
149	C₂×C₈	C₂×#6923	1	1	yes	characteristic
150	C₂×C₈	C₂×#6923	1	1	yes	characteristic
151	C₂×C₈	C₂×#6923	1	4	yes	—
152	C₂³	—	61	1	no	—
153	C₂³	—	61	2	no	—
154	C₂³	—	61	2	no	—
155	C₂³	—	61	1	no	—
156	C₂³	—	122	4	no	—
157	C₂³	C₄⋊#6923	1	1	yes	characteristic
158	C₂×C₄	—	61	2	no	—
159	C₂×C₄	—	61	1	no	—
160	C₂×C₄	—	61	1	no	—
161	C₂×C₄	—	61	2	no	—
162	C₂×C₄	—	61	2	no	—
163	C₂×C₄	—	61	2	no	—
164	C₂×C₄	—	61	2	no	—
165	C₂×C₄	—	61	2	no	—
166	C₂×C₄	—	61	1	no	—
167	C₂×C₄	—	61	1	no	—
168	C₂×C₄	—	61	2	no	—
169	C₂×C₄	—	61	2	no	—
170	C₂×C₄	—	61	1	no	—
171	C₂×C₄	—	61	1	no	—
172	C₂×C₄	C₄⋊#6923	1	2	yes	—
173	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
174	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
175	C₂×C₄	C₂²×#6923	1	2	yes	—
176	C₈	—	61	2	no	—
177	C₈	—	61	2	no	—
178	C₈	—	122	8	no	—
179	C₈	C₂²×#6923	1	2	yes	—
180	C₈	C₂²×#6923	1	2	yes	—
181	C₂²	—	2	2	no	—
182	C₂²	—	61	4	no	—
183	C₂²	—	61	2	no	—
184	C₂²	—	61	1	no	—
185	C₂²	—	61	1	no	—
186	C₂²	—	122	4	no	—
187	C₂²	—	122	4	no	—
188	C₂²	—	122	2	no	—
189	C₂²	C₂×C₄⋊#6923	1	2	yes	—
190	C₂²	C₂×C₄⋊#6923	1	1	yes	characteristic
191	C₄	—	61	1	no	—
192	C₄	—	61	2	no	—
193	C₄	—	61	1	no	—
194	C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
195	C₄	C₂×C₄⋊#6923	1	2	yes	—
196	C₄	C₂³×#6923	1	1	yes	characteristic
197	C₂	—	2	2	no	—
198	C₂	—	61	4	no	—
199	C₂	—	122	1	no	—
200	C₂	—	122	1	no	—
201	C₂	D₆₁⋊#108	1	2	yes	direct product factor
202	C₂	C₂²×C₄⋊#6923	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄⋊#6923
commutator	C₄×C₆₁	C₂³×C₄
Frattini	C₄	C₂³×#6923
Fitting	C₂²×C₈×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₄⋊C₄
hypercenter	C₂²×C₈	#6923
hypocenter	C₆₁	C₂²×#108
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×#14519848	C₂	semidirect
3. D₆₁⋊#108	C₂	direct (N × H)
4. C₂×#14519847	C₂	semidirect
11. #14519848	C₂²	semidirect
12. #14519847	C₂²	semidirect
85. C₂×D₆₁	#108	semidirect
97. C₂×C₆₁	C₂×#108	semidirect
101. D₆₁	C₂×#108	semidirect
107. C₆₁	C₂²×#108	semidirect
201. C₂	D₆₁⋊#108	direct (N × H)

Subgroups — C2×D61⋊#108 #21462476

Conjugacy classes of subgroups

Complements

Subgroups — C₂×D₆₁⋊#108 #21462476