Subgroups — #21454836

Order 7808.

402 conjugacy classes of subgroups.

The subgroup lattice has 210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#11758222	C₂	1	1	yes	maximal, characteristic
2	#16839886	C₂	1	2	yes	maximal, complemented
3	#16839839	C₂	1	2	yes	maximal, complemented
4	#16839837	C₂	1	4	yes	maximal, complemented
5	#16839817	C₂	1	2	yes	maximal, complemented
6	C₄×#11758194	C₂	1	1	yes	maximal, characteristic, complemented
7	#16839714	C₂	1	2	yes	maximal, complemented
8	C₆₁×#432	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#11758222	C₄	1	1	yes	characteristic
10	C₂×#11758194	C₂²	1	2	yes	—
11	C₂×#11758189	C₂²	1	4	yes	—
12	C₄×Dic₁₂₂	C₄	1	1	yes	characteristic
13	C₄×Dic₁₂₂	C₂²	1	1	yes	characteristic
14	C₄×D₂₄₄	C₄	1	1	yes	characteristic
15	C₄×D₂₄₄	C₂²	1	1	yes	characteristic
16	C₄×C₂²⋊D₆₁	C₄	1	2	yes	—
17	C₄×C₂²⋊D₆₁	C₂²	1	2	yes	—
18	#14519736	C₄	1	1	yes	characteristic
19	#14519734	C₄	1	2	yes	—
20	C₄²×D₆₁	C₂²	1	2	yes	—
21	#14519706	C₂²	1	4	yes	—
22	#14519689	C₂²	1	4	yes	—
23	#14519688	C₂²	1	1	yes	characteristic
24	#14519688	C₂²	1	1	yes	characteristic
25	C₄×#92418	C₂²	1	2	yes	—
26	C₈×Dic₆₁	C₂²	1	4	yes	—
27	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
28	C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
29	C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
30	#97×C₆₁	C₂²	1	2	yes	—
31	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
34	C₂×C₂²⋊D₆₁	C₂×C₄	1	2	yes	—
35	#11758222	—	2	4	no	—
36	C₂×D₂₄₄	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄×D₆₁	C₂×C₄	1	2	yes	—
38	C₂×C₄×D₆₁	C₂×C₄	1	2	yes	—
39	C₂×C₄×D₆₁	C₂³	1	2	yes	—
40	C₂×Dic₁₂₂	C₂×C₄	1	1	yes	characteristic
41	C₂×C₈×C₆₁	C₂³	1	4	yes	—
42	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
43	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
44	C₄²×C₆₁	C₂³	1	1	yes	characteristic
45	C₄²×C₆₁	C₂³	1	1	yes	characteristic
46	C₂²⋊Dic₆₁	C₂×C₄	1	2	yes	—
47	#11758198	C₂×C₄	1	2	yes	—
48	#11758198	C₂×C₄	1	2	yes	—
49	C₄⋊Dic₆₁	C₂×C₄	1	1	yes	characteristic
50	C₄⋊Dic₆₁	C₂×C₄	1	1	yes	characteristic
51	#11758196	C₂×C₄	1	2	yes	—
52	#11758196	C₂×C₄	1	2	yes	—
53	C₄×Dic₆₁	C₂×C₄	1	2	yes	—
54	C₄×Dic₆₁	C₂×C₄	1	2	yes	—
55	C₄×Dic₆₁	C₂³	1	2	yes	—
56	#11758194	—	2	4	no	—
57	C₂×#92418	C₂³	1	2	yes	—
58	C₂×#92418	C₂³	1	2	yes	—
59	#11758189	—	2	8	no	—
60	C₂³×C₆₁	C₂²×C₄	1	1	yes	characteristic
61	C₂²×D₆₁	C₂²×C₄	1	2	yes	—
62	C₂×C₄×C₆₁	—	2	2	no	—
63	C₂×C₄×C₆₁	—	2	2	no	—
64	C₂×C₄×C₆₁	—	4	1	no	—
65	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
66	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
67	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
68	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
69	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
70	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
71	C₂²⋊D₆₁	—	2	4	no	—
72	C₂×Dic₆₁	C₂²×C₄	1	2	yes	—
73	C₂×Dic₆₁	C₂²×C₄	1	2	yes	—
74	C₂×Dic₆₁	C₂²×C₄	1	2	yes	—
75	D₂₄₄	—	2	2	no	—
76	C₄×D₆₁	—	2	4	no	—
77	C₄×D₆₁	—	2	4	no	—
78	C₄×D₆₁	—	4	2	no	—
79	Dic₁₂₂	M₁₆	1	4	yes	complemented
80	C₈×C₆₁	—	2	4	no	—
81	#92418	—	2	2	no	—
82	#92418	#41	1	4	yes	complemented
83	C₂²×C₆₁	—	2	1	no	—
84	C₂²×C₆₁	—	2	1	no	—
85	C₂²×C₆₁	—	2	1	no	—
86	C₂²×C₆₁	C₂³×C₄	1	1	yes	characteristic
87	C₂×D₆₁	—	2	2	no	—
88	C₂×D₆₁	—	2	2	no	—
89	C₂×D₆₁	—	2	2	no	—
90	C₄×C₆₁	—	2	1	no	—
91	C₄×C₆₁	—	2	1	no	—
92	C₄×C₆₁	—	2	1	no	—
93	C₄×C₆₁	—	2	1	no	—
94	C₄×C₆₁	C₂×M₁₆	1	2	yes	—
95	C₄×C₆₁	C₂×#41	1	2	yes	—
96	Dic₆₁	—	2	2	no	—
97	Dic₆₁	—	2	2	no	—
98	Dic₆₁	C₂×M₁₆	1	4	yes	—
99	#2971	—	61	1	no	maximal, Sylow
100	C₂×C₆₁	—	4	1	no	—
101	C₂×C₆₁	C₄×#41	1	1	yes	characteristic
102	C₂×C₆₁	C₂²×M₁₆	1	1	yes	characteristic
103	C₂×C₆₁	#568	1	1	yes	characteristic
104	D₆₁	—	4	2	no	—
105	C₄×#41	—	61	1	no	—
106	C₈×Q₈	—	61	2	no	—
107	#436	—	61	2	no	—
108	#436	—	61	4	no	—
109	#432	—	61	2	no	—
110	#432	D₆₁	1	1	yes	characteristic, complemented
111	C₄×M₁₆	—	61	1	no	—
112	C₄×M₁₆	—	61	2	no	—
113	C₆₁	#2971	1	1	yes	characteristic, complemented, Sylow
114	C₂×#41	—	61	1	no	—
115	C₂×M₁₆	—	61	2	no	—
116	C₂×M₁₆	—	61	4	no	—
117	C₄×Q₈	—	61	1	no	—
118	C₄×Q₈	—	61	1	no	—
119	C₄×D₄	—	61	2	no	—
120	C₄×D₄	—	61	2	no	—
121	C₄×D₄	—	61	1	no	—
122	C₄×D₄	—	61	1	no	—
123	#117	—	61	1	no	—
124	#117	—	61	2	no	—
125	C₂×C₄²	—	61	2	no	—
126	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
127	C₄⋊C₈	—	61	4	no	—
128	C₄⋊C₈	C₂×D₆₁	1	2	yes	—
129	C₂²⋊C₈	—	61	4	no	—
130	C₂²⋊C₈	C₂×D₆₁	1	2	yes	—
131	#97	—	61	1	no	—
132	#97	—	61	1	no	—
133	#97	C₂×D₆₁	1	2	yes	—
134	C₄×C₈	—	61	4	no	—
135	C₄×C₈	—	61	2	no	—
136	#41	—	122	4	no	—
137	C₂×Q₈	—	61	1	no	—
138	C₂×D₄	—	61	2	no	—
139	C₂×D₄	—	61	1	no	—
140	C₂²×C₄	—	61	2	no	—
141	C₂²×C₄	—	61	2	no	—
142	C₂²×C₄	—	61	2	no	—
143	C₂²×C₄	C₄×D₆₁	1	1	yes	characteristic
144	C₂²×C₄	C₄×D₆₁	1	1	yes	characteristic
145	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
146	M₁₆	—	122	8	no	—
147	M₁₆	—	122	4	no	—
148	C₂×C₈	—	61	2	no	—
149	C₂×C₈	—	61	2	no	—
150	C₂×C₈	C₂²×D₆₁	1	4	yes	—
151	C₄⋊C₄	—	61	2	no	—
152	C₄⋊C₄	—	61	2	no	—
153	C₄⋊C₄	—	61	1	no	—
154	C₄⋊C₄	—	61	1	no	—
155	C₂²⋊C₄	—	61	2	no	—
156	C₂²⋊C₄	—	61	2	no	—
157	C₂²⋊C₄	—	61	2	no	—
158	C₄²	—	61	2	no	—
159	C₄²	—	61	2	no	—
160	C₄²	—	61	2	no	—
161	C₄²	C₄×D₆₁	1	1	yes	characteristic
162	C₄²	C₄×D₆₁	1	1	yes	characteristic
163	C₄²	C₂²×D₆₁	1	1	yes	characteristic
164	C₄²	C₂²×D₆₁	1	1	yes	characteristic
165	C₂³	—	61	2	no	—
166	C₂³	C₂×C₄×D₆₁	1	1	yes	characteristic
167	Q₈	—	61	4	no	—
168	D₄	—	122	4	no	—
169	D₄	—	122	2	no	—
170	C₂×C₄	—	2	2	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	4	1	no	—
173	C₂×C₄	—	61	2	no	—
174	C₂×C₄	—	61	2	no	—
175	C₂×C₄	—	61	2	no	—
176	C₂×C₄	—	122	4	no	—
177	C₂×C₄	—	122	4	no	—
178	C₂×C₄	—	244	2	no	—
179	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
180	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
181	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
182	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
183	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
184	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
185	C₈	—	2	4	no	—
186	C₈	—	61	4	no	—
187	C₈	—	122	2	no	—
188	C₂²	—	2	1	no	—
189	C₂²	—	2	1	no	—
190	C₂²	—	2	1	no	—
191	C₂²	—	122	2	no	—
192	C₂²	—	122	2	no	—
193	C₂²	—	122	2	no	—
194	C₂²	C₂²×C₄×D₆₁	1	1	yes	characteristic
195	C₄	—	2	1	no	—
196	C₄	—	2	1	no	—
197	C₄	—	2	1	no	—
198	C₄	—	2	1	no	—
199	C₄	—	61	4	no	—
200	C₄	—	122	2	no	—
201	C₄	—	122	2	no	—
202	C₄	M₁₆×D₆₁	1	2	yes	—
203	C₄	#41×D₆₁	1	2	yes	—
204	C₂	—	4	1	no	—
205	C₂	—	244	2	no	—
206	C₂	#16840230	1	1	yes	characteristic
207	C₂	C₂×M₁₆×D₆₁	1	1	yes	characteristic
208	C₂	#16840528	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₆₁
commutator, socle	C₂²×C₆₁	C₂³×C₄
Fitting	C₆₁×#432	C₂
hypercenter	#432	D₆₁
hypocenter	C₆₁	#2971
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ #432

Complements

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

N	H ≅ G/N	type
2. #16839886	C₂	semidirect
3. #16839839	C₂	semidirect
4. #16839837	C₂	semidirect
5. #16839817	C₂	semidirect
6. C₄×#11758194	C₂	semidirect
7. #16839714	C₂	semidirect
8. C₆₁×#432	C₂	semidirect
79. Dic₁₂₂	M₁₆	semidirect
82. #92418	#41	semidirect
110. #432	D₆₁	semidirect
113. C₆₁	#2971	semidirect