Subgroups — D₆₁⋊#443 #21462585

Order 7808.

472 conjugacy classes of subgroups.

The subgroup lattice has 256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₁⋊#131	C₂	1	2	yes	maximal, complemented
2	#16840806	C₂	1	2	yes	maximal, complemented
3	#16840805	C₂	1	4	yes	maximal, complemented
4	#16840804	C₂	1	2	yes	maximal, complemented
5	D₆₁⋊#108	C₂	1	1	yes	maximal, characteristic, complemented
6	D₆₁⋊#104	C₂	1	2	yes	maximal, complemented
7	C₂×C₈×#6923	C₂	1	1	yes	maximal, characteristic, complemented
8	#135×D₆₁	C₂	1	1	yes	maximal, characteristic
9	#14519865	C₂²	1	4	yes	complemented
10	#14519864	—	2	4	no	—
11	#14519864	C₂²	1	4	yes	complemented
12	D₆₁⋊M₁₆	—	2	2	no	—
13	D₆₁⋊M₁₆	C₂²	1	2	yes	—
14	C₂×D₆₁⋊C₈	—	2	2	no	—
15	C₂×D₆₁⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₄×#6923	C₂²	1	1	yes	characteristic
17	#14519848	C₂²	1	2	yes	complemented
18	#14519847	C₂²	1	2	yes	complemented
19	#14519842	C₂²	1	4	yes	complemented
20	#14519841	C₂²	1	4	yes	complemented
21	C₈×#6923	C₂²	1	2	yes	complemented
22	C₈×#6923	C₂²	1	2	yes	complemented
23	#41×D₆₁	C₂²	1	2	yes	—
24	#14519800	C₂²	1	1	yes	characteristic
25	#14519799	C₄	1	1	yes	characteristic, complemented
26	#14519798	C₂²	1	2	yes	—
27	#14519797	C₄	1	2	yes	complemented
28	#14519796	C₂²	1	1	yes	characteristic
29	Q₁₆×D₆₁	C₄	1	1	yes	characteristic, complemented
30	SD₁₆×D₆₁	C₄	1	2	yes	complemented
31	D₈×D₆₁	C₄	1	1	yes	characteristic, complemented
32	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
33	#135×C₆₁	C₄	1	1	yes	characteristic, complemented
34	C₂²×#6923	—	2	1	no	—
35	#41×C₆₁	C₂×C₄	1	2	yes	—
36	#11758226	C₂³	1	2	yes	—
37	Q₈×D₆₁	C₂×C₄	1	2	yes	—
38	#11758224	—	2	2	no	—
39	#11758224	C₂³	1	2	yes	—
40	D₄×D₆₁	—	2	2	no	—
41	D₄×D₆₁	C₂×C₄	1	2	yes	—
42	#11758222	—	2	2	no	—
43	#11758222	C₂×C₄	1	2	yes	—
44	C₂×C₄×D₆₁	—	2	2	no	—
45	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
46	#11758217	—	2	2	no	—
47	#11758217	—	2	4	no	—
48	C₂×#92420	—	2	4	no	—
49	C₂×#92420	D₄	1	2	yes	—
50	C₄×#6923	—	2	1	no	—
51	C₄×#6923	C₂³	1	2	yes	—
52	#11758213	—	2	4	no	—
53	#11758213	C₂³	1	4	yes	—
54	D₆₁⋊C₈	—	2	2	no	—
55	D₆₁⋊C₈	—	2	4	no	—
56	D₆₁⋊C₈	D₄	1	1	yes	characteristic
57	D₆₁⋊C₈	D₄	1	1	yes	characteristic
58	D₆₁⋊C₈	C₂³	1	2	yes	—
59	Q₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic, complemented
60	SD₁₆×C₆₁	C₂×C₄	1	2	yes	complemented
61	D₈×C₆₁	C₂×C₄	1	1	yes	characteristic, complemented
62	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
63	#11758202	C₂×C₄	1	2	yes	complemented
64	#11758201	C₂×C₄	1	2	yes	complemented
65	#11758200	C₂×C₄	1	2	yes	complemented
66	#11758199	C₂×C₄	1	2	yes	complemented
67	C₂×#92418	C₂×C₄	1	1	yes	characteristic
68	Dic₂₄₄	C₂×C₄	1	1	yes	characteristic, complemented
69	D₄₈₈	C₂×C₄	1	1	yes	characteristic, complemented
70	#11758190	C₂×C₄	1	2	yes	complemented
71	C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
72	C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
73	C₈×D₆₁	C₂³	1	1	yes	characteristic
74	C₈×D₆₁	C₂³	1	1	yes	characteristic
75	C₂²×D₆₁	—	2	2	no	—
76	C₂²×D₆₁	#41	1	1	yes	characteristic
77	C₂×#6923	—	2	4	no	—
78	C₂×#6923	—	2	2	no	—
79	Q₈×C₆₁	C₂²×C₄	1	2	yes	—
80	D₄×C₆₁	—	2	2	no	—
81	D₄×C₆₁	C₂²×C₄	1	2	yes	—
82	C₂×C₄×C₆₁	—	2	2	no	—
83	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
84	C₂²⋊D₆₁	—	2	2	no	—
85	C₂²⋊D₆₁	—	2	2	no	—
86	C₂²⋊D₆₁	—	2	2	no	—
87	C₂×Dic₆₁	—	2	2	no	—
88	C₂×Dic₆₁	C₂×D₄	1	1	yes	characteristic
89	D₂₄₄	—	2	2	no	—
90	D₂₄₄	C₂²×C₄	1	2	yes	—
91	C₄×D₆₁	—	2	2	no	—
92	C₄×D₆₁	—	2	2	no	—
93	C₄×D₆₁	—	2	2	no	—
94	C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
95	C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
96	C₄×D₆₁	#41	1	1	yes	characteristic
97	C₄×D₆₁	C₂⁴	1	1	yes	characteristic
98	Dic₁₂₂	—	2	2	no	—
99	Dic₁₂₂	C₂²×C₄	1	2	yes	—
100	#92420	—	2	4	no	—
101	#92420	C₂×D₄	1	2	yes	—
102	#92420	C₂×D₄	1	2	yes	—
103	C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
104	C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
105	#92418	C₂²×C₄	1	1	yes	characteristic
106	#92418	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₆₁	—	2	2	no	—
108	C₂²×C₆₁	C₄×D₄	1	1	yes	characteristic
109	C₂×D₆₁	—	2	2	no	—
110	C₂×D₆₁	—	2	2	no	—
111	C₂×D₆₁	—	4	4	no	—
112	C₂×D₆₁	C₄×D₄	1	1	yes	characteristic
113	C₂×D₆₁	C₂×#41	1	1	yes	characteristic
114	#6923	—	2	4	no	—
115	C₄×C₆₁	—	2	2	no	—
116	C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
117	C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
118	Dic₆₁	—	2	2	no	—
119	Dic₆₁	C₄×D₄	1	1	yes	characteristic
120	Dic₆₁	C₂²×D₄	1	1	yes	characteristic
121	C₂×#443	—	61	1	no	maximal, Sylow
122	C₂×C₆₁	—	2	1	no	—
123	C₂×C₆₁	—	4	2	no	—
124	C₂×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
125	D₆₁	—	2	1	no	—
126	D₆₁	—	4	2	no	—
127	D₆₁	#443	1	2	yes	complemented
128	C₂×#135	—	61	1	no	—
129	C₂×#131	—	61	2	no	—
130	#443	—	61	2	no	—
131	#443	—	61	4	no	—
132	#443	—	61	2	no	—
133	C₂×#108	—	61	1	no	—
134	C₂×#104	—	61	2	no	—
135	C₂×C₄×C₈	—	61	1	no	—
136	C₆₁	C₂×#443	1	1	yes	characteristic, complemented, Sylow
137	C₂×#41	—	61	2	no	—
138	#135	—	61	2	no	—
139	#135	—	61	1	no	—
140	#135	—	61	2	no	—
141	#135	—	61	1	no	—
142	#135	—	61	1	no	—
143	#135	#6923	1	1	yes	characteristic, complemented
144	C₂×Q₁₆	—	61	1	no	—
145	C₂×SD₁₆	—	61	2	no	—
146	C₂×D₈	—	61	1	no	—
147	#131	—	61	4	no	—
148	#131	—	61	4	no	—
149	#131	—	122	4	no	—
150	C₂×M₁₆	—	61	2	no	—
151	C₂×M₁₆	—	122	2	no	—
152	C₂²×C₈	—	61	1	no	—
153	C₂²×C₈	—	61	1	no	—
154	C₂²×C₈	—	122	2	no	—
155	C₂×C₄²	—	61	1	no	—
156	#108	—	61	2	no	—
157	#108	—	61	2	no	—
158	#104	—	61	4	no	—
159	#104	—	61	4	no	—
160	C₄×C₈	—	61	2	no	—
161	C₄×C₈	—	61	2	no	—
162	#41	—	61	2	no	—
163	#41	—	61	2	no	—
164	#41	—	61	2	no	—
165	#41	—	122	2	no	—
166	#41	—	122	2	no	—
167	#41	C₂×#6923	1	2	yes	—
168	C₂×Q₈	—	61	2	no	—
169	C₂×D₄	—	61	2	no	—
170	C₂×D₄	—	122	2	no	—
171	C₂²×C₄	—	61	1	no	—
172	C₂²×C₄	—	122	2	no	—
173	C₂²×C₄	—	122	1	no	—
174	Q₁₆	—	61	2	no	—
175	Q₁₆	—	61	1	no	—
176	Q₁₆	C₂×#6923	1	1	yes	characteristic, complemented
177	SD₁₆	—	61	2	no	—
178	SD₁₆	—	61	2	no	—
179	SD₁₆	—	61	2	no	—
180	SD₁₆	C₂×#6923	1	2	yes	complemented
181	D₈	—	61	2	no	—
182	D₈	—	61	1	no	—
183	D₈	C₂×#6923	1	1	yes	characteristic, complemented
184	M₁₆	—	61	4	no	—
185	M₁₆	—	122	4	no	—
186	M₁₆	—	122	4	no	—
187	M₁₆	—	122	2	no	—
188	C₂×C₈	—	61	2	no	—
189	C₂×C₈	—	61	1	no	—
190	C₂×C₈	—	61	1	no	—
191	C₂×C₈	—	61	2	no	—
192	C₂×C₈	—	61	1	no	—
193	C₂×C₈	—	61	1	no	—
194	C₂×C₈	—	61	1	no	—
195	C₂×C₈	—	61	1	no	—
196	C₂×C₈	—	61	1	no	—
197	C₂×C₈	—	122	4	no	—
198	C₂×C₈	—	122	4	no	—
199	C₂×C₈	—	122	2	no	—
200	C₂×C₈	C₂×#6923	1	1	yes	characteristic
201	C₄²	—	61	2	no	—
202	C₄²	—	122	1	no	—
203	C₂³	—	61	1	no	—
204	C₂³	—	122	2	no	—
205	Q₈	—	61	2	no	—
206	Q₈	—	122	2	no	—
207	Q₈	C₂²×#6923	1	2	yes	—
208	D₄	—	2	2	no	—
209	D₄	—	61	2	no	—
210	D₄	—	122	2	no	—
211	D₄	—	122	2	no	—
212	D₄	—	122	2	no	—
213	D₄	—	122	2	no	—
214	D₄	C₂²×#6923	1	2	yes	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	61	1	no	—
217	C₂×C₄	—	61	1	no	—
218	C₂×C₄	—	61	1	no	—
219	C₂×C₄	—	61	1	no	—
220	C₂×C₄	—	61	1	no	—
221	C₂×C₄	—	122	2	no	—
222	C₂×C₄	—	122	2	no	—
223	C₂×C₄	—	122	2	no	—
224	C₂×C₄	—	122	2	no	—
225	C₂×C₄	—	122	4	no	—
226	C₂×C₄	—	122	2	no	—
227	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
228	C₈	—	61	2	no	—
229	C₈	—	61	2	no	—
230	C₈	—	61	1	no	—
231	C₈	—	61	1	no	—
232	C₈	—	122	4	no	—
233	C₈	C₂²×#6923	1	1	yes	characteristic
234	C₈	C₂²×#6923	1	1	yes	characteristic
235	C₂²	—	2	2	no	—
236	C₂²	—	61	1	no	—
237	C₂²	—	61	1	no	—
238	C₂²	—	122	2	no	—
239	C₂²	—	122	2	no	—
240	C₂²	—	244	4	no	—
241	C₂²	D₄×#6923	1	1	yes	characteristic
242	C₄	—	2	2	no	—
243	C₄	—	61	1	no	—
244	C₄	—	61	1	no	—
245	C₄	—	122	4	no	—
246	C₄	—	122	2	no	—
247	C₄	D₄×#6923	1	1	yes	characteristic
248	C₄	C₂³×#6923	1	1	yes	characteristic
249	C₂	—	2	1	no	—
250	C₂	—	4	2	no	—
251	C₂	—	61	2	no	—
252	C₂	—	122	1	no	—
253	C₂	—	244	2	no	—
254	C₂	C₂×D₄×#6923	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×#6923
commutator	C₄×C₆₁	C₂³×C₄
Frattini	C₄	C₂³×#6923
Fitting	#135×C₆₁	C₄
socle	C₂×C₆₁	C₂×C₄×D₄
hypercenter	#135	#6923
hypocenter	C₆₁	C₂×#443
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #135

Complements

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

N	H ≅ G/N	type
1. D₆₁⋊#131	C₂	semidirect
2. #16840806	C₂	semidirect
3. #16840805	C₂	semidirect
4. #16840804	C₂	semidirect
5. D₆₁⋊#108	C₂	semidirect
6. D₆₁⋊#104	C₂	semidirect
7. C₂×C₈×#6923	C₂	semidirect
9. #14519865	C₂²	semidirect
11. #14519864	C₂²	semidirect
17. #14519848	C₂²	semidirect
18. #14519847	C₂²	semidirect
19. #14519842	C₂²	semidirect
20. #14519841	C₂²	semidirect
21. C₈×#6923	C₂²	semidirect
22. C₈×#6923	C₂²	semidirect
25. #14519799	C₄	semidirect
27. #14519797	C₄	semidirect
29. Q₁₆×D₆₁	C₄	semidirect
30. SD₁₆×D₆₁	C₄	semidirect
31. D₈×D₆₁	C₄	semidirect
33. #135×C₆₁	C₄	semidirect
59. Q₁₆×C₆₁	C₂×C₄	semidirect
60. SD₁₆×C₆₁	C₂×C₄	semidirect
61. D₈×C₆₁	C₂×C₄	semidirect
63. #11758202	C₂×C₄	semidirect
64. #11758201	C₂×C₄	semidirect
65. #11758200	C₂×C₄	semidirect
66. #11758199	C₂×C₄	semidirect
68. Dic₂₄₄	C₂×C₄	semidirect
69. D₄₈₈	C₂×C₄	semidirect
70. #11758190	C₂×C₄	semidirect
127. D₆₁	#443	semidirect
136. C₆₁	C₂×#443	semidirect
143. #135	#6923	semidirect
176. Q₁₆	C₂×#6923	semidirect
180. SD₁₆	C₂×#6923	semidirect
183. D₈	C₂×#6923	semidirect

Subgroups — D61⋊#443 #21462585

Conjugacy classes of subgroups

Complements

Subgroups — D₆₁⋊#443 #21462585