Subgroups — D₆₁⋊#446 #21462605

Order 7808.

400 conjugacy classes of subgroups.

The subgroup lattice has 208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840814	C₂	1	4	yes	maximal, complemented
2	#16840813	C₂	1	2	yes	maximal, complemented
3	#16840812	C₂	1	2	yes	maximal, complemented
4	D₆₁⋊(C₄⋊C₈)	C₂	1	1	yes	maximal, characteristic
5	D₆₁⋊(C₄⋊C₈)	C₂	1	2	yes	maximal
6	#16840721	C₂	1	2	yes	maximal
7	C₄×D₆₁⋊C₈	C₂	1	1	yes	maximal, characteristic
8	C₄×Q₈×D₆₁	C₂	1	1	yes	maximal, characteristic
9	C₂×D₆₁⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×D₆₁⋊C₈	C₂²	1	2	yes	—
11	C₂×D₆₁⋊C₈	C₂²	1	1	yes	characteristic
12	#14519844	C₂²	1	4	yes	—
13	#14519844	C₂²	1	2	yes	—
14	C₄⋊#92420	C₂²	1	2	yes	—
15	C₄⋊#92420	C₂²	1	4	yes	—
16	#14519832	C₂²	1	4	yes	—
17	#14519832	C₂²	1	4	yes	—
18	C₄×#92420	C₂²	1	2	yes	—
19	C₄×#92420	C₂²	1	2	yes	—
20	C₂×Q₈×D₆₁	C₄	1	1	yes	characteristic
21	Q₈×Dic₆₁	C₂²	1	1	yes	characteristic
22	C₄×Dic₁₂₂	C₄	1	1	yes	characteristic
23	C₄×Dic₁₂₂	C₄	1	2	yes	—
24	#14519742	C₂²	1	1	yes	characteristic
25	#14519742	C₂²	1	2	yes	—
26	C₄⋊C₄×D₆₁	C₄	1	2	yes	—
27	C₄⋊C₄×D₆₁	C₄	1	1	yes	characteristic
28	C₄²×D₆₁	C₂²	1	1	yes	characteristic
29	C₄²×D₆₁	C₂²	1	2	yes	—
30	C₄×Q₈×C₆₁	C₄	1	1	yes	characteristic
31	C₂×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
32	Q₈×D₆₁	—	2	4	no	—
33	C₂×C₄×D₆₁	C₂×C₄	1	2	yes	—
34	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄×D₆₁	C₂×C₄	1	2	yes	—
36	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
38	C₂×Dic₁₂₂	C₂×C₄	1	1	yes	characteristic
39	C₂×Dic₁₂₂	C₂×C₄	1	2	yes	—
40	C₂×#92420	C₂³	1	2	yes	—
41	C₂×#92420	C₂³	1	4	yes	—
42	C₂×#92420	C₂³	1	2	yes	—
43	D₆₁⋊C₈	—	2	2	no	—
44	D₆₁⋊C₈	—	2	4	no	—
45	D₆₁⋊C₈	Q₈	1	4	yes	complemented
46	C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
47	C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
48	C₄²×C₆₁	C₂×C₄	1	2	yes	—
49	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
50	C₄⋊Dic₆₁	C₂×C₄	1	2	yes	—
51	C₄⋊Dic₆₁	C₂×C₄	1	1	yes	characteristic
52	#11758196	C₂×C₄	1	2	yes	—
53	#11758196	C₂×C₄	1	2	yes	—
54	#11758196	C₂×C₄	1	2	yes	—
55	C₄×Dic₆₁	C₂×C₄	1	2	yes	—
56	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
57	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
58	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
59	C₄×Dic₆₁	C₂³	1	2	yes	—
60	C₄×Dic₆₁	C₂³	1	2	yes	—
61	C₂²×D₆₁	C₂²×C₄	1	1	yes	characteristic
62	Q₈×C₆₁	—	2	2	no	—
63	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
64	C₂×C₄×C₆₁	C₂²×C₄	1	2	yes	—
65	C₂×C₄×C₆₁	C₂²×C₄	1	2	yes	—
66	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
67	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
68	C₂×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
69	C₂×Dic₆₁	C₂²×C₄	1	2	yes	—
70	C₂×Dic₆₁	C₂²×C₄	1	2	yes	—
71	C₂×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
72	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
73	C₄×D₆₁	—	2	4	no	—
74	C₄×D₆₁	—	2	2	no	—
75	C₄×D₆₁	—	2	4	no	—
76	C₄×D₆₁	M₁₆	1	4	yes	—
77	C₄×D₆₁	C₂×Q₈	1	2	yes	—
78	C₄×D₆₁	#41	1	2	yes	—
79	Dic₁₂₂	—	2	2	no	—
80	Dic₁₂₂	—	2	4	no	—
81	#92420	—	2	2	no	—
82	#92420	—	2	4	no	—
83	#92420	C₂×Q₈	1	4	yes	complemented
84	C₂²×C₆₁	C₂³×C₄	1	1	yes	characteristic
85	C₂×D₆₁	C₄×Q₈	1	2	yes	—
86	C₂×D₆₁	C₂×M₁₆	1	2	yes	—
87	C₂×D₆₁	#131	1	2	yes	—
88	C₄×C₆₁	—	2	2	no	—
89	C₄×C₆₁	—	2	1	no	—
90	C₄×C₆₁	—	2	2	no	—
91	C₄×C₆₁	C₄×Q₈	1	2	yes	—
92	C₄×C₆₁	C₂×M₁₆	1	2	yes	—
93	Dic₆₁	—	2	2	no	—
94	Dic₆₁	—	2	1	no	—
95	Dic₆₁	—	2	2	no	—
96	Dic₆₁	C₂×M₁₆	1	2	yes	—
97	Dic₆₁	C₂²×Q₈	1	1	yes	characteristic
98	Dic₆₁	C₂×#41	1	1	yes	characteristic
99	C₂×#446	—	61	1	no	maximal, Sylow
100	C₂×C₆₁	C₂×C₄×Q₈	1	1	yes	characteristic
101	C₂×C₆₁	C₂²×M₁₆	1	1	yes	characteristic
102	C₂×C₆₁	C₂×#131	1	1	yes	characteristic
103	D₆₁	#446	1	4	yes	complemented
104	C₂×C₄×Q₈	—	61	1	no	—
105	#446	—	61	2	no	—
106	#446	—	61	2	no	—
107	#446	—	61	4	no	—
108	C₂×C₄⋊C₈	—	61	1	no	—
109	C₂×C₄⋊C₈	—	61	2	no	—
110	C₂×#97	—	61	2	no	—
111	C₂×C₄×C₈	—	61	1	no	—
112	C₆₁	C₂×#446	1	1	yes	characteristic, complemented, Sylow
113	C₂²×Q₈	—	61	1	no	—
114	C₂²×C₈	—	61	1	no	—
115	C₂²×C₈	—	61	1	no	—
116	C₂²×C₈	—	61	2	no	—
117	C₄×Q₈	—	61	1	no	—
118	C₄×Q₈	—	61	1	no	—
119	C₄×Q₈	—	61	2	no	—
120	C₄×Q₈	—	61	2	no	—
121	C₄×Q₈	—	61	1	no	—
122	C₄×Q₈	#6923	1	1	yes	characteristic
123	C₂×C₄⋊C₄	—	61	1	no	—
124	C₂×C₄⋊C₄	—	61	2	no	—
125	C₂×C₄²	—	61	1	no	—
126	C₂×C₄²	—	61	2	no	—
127	C₄⋊C₈	—	61	2	no	—
128	C₄⋊C₈	—	61	4	no	—
129	C₄⋊C₈	—	61	2	no	—
130	C₄⋊C₈	—	61	4	no	—
131	#97	—	61	4	no	—
132	#97	—	61	4	no	—
133	C₄×C₈	—	61	2	no	—
134	C₄×C₈	—	61	2	no	—
135	C₂×Q₈	—	61	2	no	—
136	C₂×Q₈	—	61	1	no	—
137	C₂×Q₈	—	122	4	no	—
138	C₂×Q₈	C₂×#6923	1	1	yes	characteristic
139	C₂²×C₄	—	61	1	no	—
140	C₂²×C₄	—	61	1	no	—
141	C₂²×C₄	—	61	1	no	—
142	C₂²×C₄	—	61	2	no	—
143	C₂²×C₄	—	61	2	no	—
144	C₂×C₈	—	61	2	no	—
145	C₂×C₈	—	61	4	no	—
146	C₂×C₈	—	61	2	no	—
147	C₂×C₈	—	61	4	no	—
148	C₂×C₈	—	122	2	no	—
149	C₂×C₈	—	122	4	no	—
150	C₄⋊C₄	—	61	2	no	—
151	C₄⋊C₄	—	61	2	no	—
152	C₄⋊C₄	—	61	2	no	—
153	C₄⋊C₄	—	61	2	no	—
154	C₄⋊C₄	—	61	1	no	—
155	C₄⋊C₄	C₂×#6923	1	2	yes	—
156	C₄⋊C₄	C₂×#6923	1	1	yes	characteristic
157	C₄²	—	61	1	no	—
158	C₄²	—	61	1	no	—
159	C₄²	—	61	2	no	—
160	C₄²	—	61	2	no	—
161	C₄²	—	61	1	no	—
162	C₄²	—	61	2	no	—
163	C₄²	C₂×#6923	1	2	yes	—
164	C₄²	C₂×#6923	1	1	yes	characteristic
165	C₂³	—	61	1	no	—
166	Q₈	—	2	2	no	—
167	Q₈	—	122	4	no	—
168	Q₈	—	122	2	no	—
169	C₂×C₄	—	61	1	no	—
170	C₂×C₄	—	61	1	no	—
171	C₂×C₄	—	61	2	no	—
172	C₂×C₄	—	61	2	no	—
173	C₂×C₄	—	61	4	no	—
174	C₂×C₄	—	61	1	no	—
175	C₂×C₄	—	61	2	no	—
176	C₂×C₄	—	61	2	no	—
177	C₂×C₄	—	122	2	no	—
178	C₂×C₄	—	122	4	no	—
179	C₂×C₄	—	122	4	no	—
180	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
181	C₂×C₄	C₂²×#6923	1	2	yes	—
182	C₂×C₄	C₂²×#6923	1	2	yes	—
183	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
184	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
185	C₈	—	61	4	no	—
186	C₈	—	122	2	no	—
187	C₈	—	122	4	no	—
188	C₂²	—	61	2	no	—
189	C₂²	—	61	2	no	—
190	C₂²	—	61	2	no	—
191	C₂²	C₂³×#6923	1	1	yes	characteristic
192	C₄	—	2	2	no	—
193	C₄	—	2	1	no	—
194	C₄	—	2	2	no	—
195	C₄	—	61	1	no	—
196	C₄	—	61	1	no	—
197	C₄	—	61	2	no	—
198	C₄	—	122	2	no	—
199	C₄	—	122	1	no	—
200	C₄	—	122	2	no	—
201	C₄	Q₈×#6923	1	2	yes	—
202	C₄	D₆₁⋊M₁₆	1	2	yes	—
203	C₂	—	61	4	no	—
204	C₂	C₂×Q₈×#6923	1	1	yes	characteristic
205	C₂	C₂×D₆₁⋊M₁₆	1	1	yes	characteristic
206	C₂	D₆₁⋊#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×#6923
commutator, socle	C₂²×C₆₁	C₂³×C₄
Frattini	C₂²	C₂³×#6923
Fitting	C₄×Q₈×C₆₁	C₄
hypercenter	C₄×Q₈	#6923
hypocenter	C₆₁	C₂×#446
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
1. #16840814	C₂	semidirect
2. #16840813	C₂	semidirect
3. #16840812	C₂	semidirect
45. D₆₁⋊C₈	Q₈	semidirect
83. #92420	C₂×Q₈	semidirect
103. D₆₁	#446	semidirect
112. C₆₁	C₂×#446	semidirect

Subgroups — D61⋊#446 #21462605

Conjugacy classes of subgroups

Complements

Subgroups — D₆₁⋊#446 #21462605