Subgroups — #21454808

Order 7808.

372 conjugacy classes of subgroups.

The subgroup lattice has 224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840296	C₂	1	1	yes	maximal, characteristic
2	#16839891	C₂	1	2	yes	maximal, complemented
3	#16839832	C₂	1	2	yes	maximal, complemented
4	#16839830	C₂	1	2	yes	maximal, complemented
5	#16839825	C₂	1	2	yes	maximal, complemented
6	#16839821	C₂	1	2	yes	maximal, complemented
7	#16839716	C₂	1	2	yes	maximal, complemented
8	C₂×#14519688	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#431	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#11758189	C₂²	1	2	yes	—
11	C₂²×#92418	C₂²	1	2	yes	—
12	C₂×C₈×D₆₁	C₂²	1	2	yes	—
13	#14519771	C₄	1	2	yes	—
14	#14519769	C₄	1	1	yes	characteristic
15	#14519765	C₄	1	1	yes	characteristic
16	#14519760	C₄	1	2	yes	—
17	#14519756	C₄	1	1	yes	characteristic
18	#14519751	C₄	1	1	yes	characteristic
19	C₄×Dic₁₂₂	C₂²	1	1	yes	characteristic
20	C₄×D₂₄₄	C₂²	1	1	yes	characteristic
21	C₄×C₂²⋊D₆₁	C₂²	1	2	yes	—
22	#14519734	C₂²	1	2	yes	—
23	#14519706	C₂²	1	2	yes	—
24	#14519706	C₂²	1	2	yes	—
25	#14519689	C₂²	1	2	yes	—
26	#14519689	C₂²	1	2	yes	—
27	#14519688	C₂²	1	1	yes	characteristic
28	#14519688	C₂²	1	1	yes	characteristic
29	#14519688	C₂²	1	2	yes	—
30	#14519687	C₂²	1	2	yes	—
31	C₈×Dic₆₁	C₂²	1	2	yes	—
32	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
33	C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
34	C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
35	C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
36	C₄×C₈×C₆₁	C₂²	1	2	yes	—
37	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
40	C₂×C₂²⋊D₆₁	C₂×C₄	1	2	yes	—
41	C₂×D₂₄₄	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄×D₆₁	C₂³	1	2	yes	—
43	C₂×Dic₁₂₂	C₂×C₄	1	1	yes	characteristic
44	C₂×C₈×C₆₁	C₂³	1	2	yes	—
45	C₂×C₈×C₆₁	C₂³	1	2	yes	—
46	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
47	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
48	C₄²×C₆₁	C₂³	1	1	yes	characteristic
49	C₄²×C₆₁	C₂³	1	1	yes	characteristic
50	C₂²⋊Dic₆₁	C₂×C₄	1	2	yes	—
51	#11758198	C₂×C₄	1	2	yes	—
52	#11758198	C₂×C₄	1	2	yes	—
53	#11758198	C₂×C₄	1	2	yes	—
54	#11758198	C₂×C₄	1	2	yes	—
55	C₄⋊Dic₆₁	C₂×C₄	1	1	yes	characteristic
56	C₄⋊Dic₆₁	C₂×C₄	1	1	yes	characteristic
57	#11758196	C₂×C₄	1	2	yes	—
58	#11758196	C₂×C₄	1	2	yes	—
59	#11758196	C₂×C₄	1	2	yes	—
60	#11758196	C₂×C₄	1	2	yes	—
61	C₄×Dic₆₁	C₂³	1	2	yes	—
62	C₂×#92418	—	2	4	no	—
63	C₂×#92418	C₂³	1	2	yes	—
64	C₂×#92418	C₂³	1	2	yes	—
65	#11758189	—	2	4	no	—
66	C₈×D₆₁	—	2	4	no	—
67	C₂³×C₆₁	C₂²×C₄	1	1	yes	characteristic
68	C₂²×D₆₁	C₂²×C₄	1	2	yes	—
69	C₂×C₄×C₆₁	—	2	2	no	—
70	C₂×C₄×C₆₁	—	2	2	no	—
71	C₂×C₄×C₆₁	—	4	1	no	—
72	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
73	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
74	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
75	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
76	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
77	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
78	C₂²⋊D₆₁	—	2	4	no	—
79	C₂×Dic₆₁	C₂²×C₄	1	2	yes	—
80	C₂×Dic₆₁	C₂²×C₄	1	2	yes	—
81	C₂×Dic₆₁	C₂²×C₄	1	2	yes	—
82	D₂₄₄	—	4	1	no	—
83	C₄×D₆₁	—	2	2	no	—
84	C₄×D₆₁	—	2	2	no	—
85	Dic₁₂₂	—	4	1	no	—
86	C₈×C₆₁	—	2	2	no	—
87	C₈×C₆₁	—	2	2	no	—
88	#92418	—	2	2	no	—
89	#92418	#41	1	4	yes	—
90	C₂²×C₆₁	—	2	1	no	—
91	C₂²×C₆₁	—	2	1	no	—
92	C₂²×C₆₁	#131	1	2	yes	—
93	C₂²×C₆₁	C₂³×C₄	1	1	yes	characteristic
94	C₂×D₆₁	—	2	2	no	—
95	C₂×D₆₁	—	2	2	no	—
96	C₂×D₆₁	—	2	2	no	—
97	C₄×C₆₁	—	2	1	no	—
98	C₄×C₆₁	—	2	1	no	—
99	C₄×C₆₁	—	2	1	no	—
100	C₄×C₆₁	—	2	1	no	—
101	C₄×C₆₁	—	2	1	no	—
102	C₄×C₆₁	C₂×#41	1	2	yes	—
103	Dic₆₁	—	2	2	no	—
104	Dic₆₁	—	2	2	no	—
105	Dic₆₁	—	2	2	no	—
106	#2968	—	61	1	no	maximal, Sylow
107	C₂×C₆₁	—	2	2	no	—
108	C₂×C₆₁	C₄×#41	1	1	yes	characteristic
109	C₂×C₆₁	C₂×#131	1	1	yes	characteristic
110	C₂×C₆₁	#568	1	1	yes	characteristic
111	D₆₁	—	4	2	no	—
112	#529	—	61	1	no	—
113	#446	—	61	2	no	—
114	#435	—	61	2	no	—
115	#435	—	61	2	no	—
116	C₈×D₄	—	61	2	no	—
117	#433	—	61	2	no	—
118	#431	D₆₁	1	1	yes	characteristic, complemented
119	#405	—	61	2	no	—
120	C₂×#97	—	61	1	no	—
121	C₆₁	#2968	1	1	yes	characteristic, complemented, Sylow
122	C₂×M₁₆	—	61	2	no	—
123	C₂²×C₈	—	61	2	no	—
124	C₂²×C₈	—	61	2	no	—
125	#126	—	61	2	no	—
126	#125	—	61	1	no	—
127	#124	—	61	1	no	—
128	#123	—	61	2	no	—
129	C₂²⋊Q₈	—	61	1	no	—
130	#121	—	61	1	no	—
131	C₄×Q₈	—	61	1	no	—
132	C₄×D₄	—	61	2	no	—
133	C₄×D₄	—	61	1	no	—
134	#117	—	61	2	no	—
135	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
136	C₄⋊C₈	—	61	2	no	—
137	C₄⋊C₈	—	61	2	no	—
138	C₄⋊C₈	C₂×D₆₁	1	2	yes	—
139	C₂²⋊C₈	—	61	2	no	—
140	C₂²⋊C₈	—	61	2	no	—
141	C₂²⋊C₈	C₂×D₆₁	1	1	yes	characteristic
142	C₂²⋊C₈	C₂×D₆₁	1	1	yes	characteristic
143	#97	—	61	2	no	—
144	#97	—	61	1	no	—
145	#97	—	61	1	no	—
146	#97	—	61	2	no	—
147	C₄×C₈	—	61	2	no	—
148	C₄×C₈	C₂×D₆₁	1	2	yes	—
149	C₂×Q₈	—	61	1	no	—
150	C₂×D₄	—	61	2	no	—
151	C₂×D₄	—	61	1	no	—
152	C₂²×C₄	—	61	2	no	—
153	C₂²×C₄	C₄×D₆₁	1	1	yes	characteristic
154	C₂²×C₄	C₄×D₆₁	1	1	yes	characteristic
155	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
156	M₁₆	—	122	4	no	—
157	C₂×C₈	—	61	2	no	—
158	C₂×C₈	—	61	2	no	—
159	C₂×C₈	—	122	4	no	—
160	C₂×C₈	—	122	4	no	—
161	C₂×C₈	C₂²×D₆₁	1	2	yes	—
162	C₂×C₈	C₂²×D₆₁	1	2	yes	—
163	C₄⋊C₄	—	61	2	no	—
164	C₄⋊C₄	—	61	2	no	—
165	C₄⋊C₄	—	61	2	no	—
166	C₄⋊C₄	—	61	2	no	—
167	C₄⋊C₄	—	61	1	no	—
168	C₄⋊C₄	—	61	1	no	—
169	C₂²⋊C₄	—	61	2	no	—
170	C₂²⋊C₄	—	61	2	no	—
171	C₂²⋊C₄	—	61	2	no	—
172	C₂²⋊C₄	—	61	2	no	—
173	C₂²⋊C₄	—	61	2	no	—
174	C₄²	—	61	2	no	—
175	C₄²	C₄×D₆₁	1	1	yes	characteristic
176	C₄²	C₄×D₆₁	1	1	yes	characteristic
177	C₄²	C₂²×D₆₁	1	1	yes	characteristic
178	C₄²	C₂²×D₆₁	1	1	yes	characteristic
179	C₂³	—	61	2	no	—
180	C₂³	C₂×C₄×D₆₁	1	1	yes	characteristic
181	Q₈	—	244	1	no	—
182	D₄	—	122	4	no	—
183	D₄	—	244	1	no	—
184	C₂×C₄	—	2	2	no	—
185	C₂×C₄	—	2	2	no	—
186	C₂×C₄	—	4	1	no	—
187	C₂×C₄	—	61	2	no	—
188	C₂×C₄	—	61	2	no	—
189	C₂×C₄	—	61	2	no	—
190	C₂×C₄	—	122	2	no	—
191	C₂×C₄	—	122	2	no	—
192	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
193	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
194	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
195	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
196	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
197	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
198	C₈	—	2	2	no	—
199	C₈	—	2	2	no	—
200	C₈	—	61	4	no	—
201	C₈	—	122	2	no	—
202	C₂²	—	2	1	no	—
203	C₂²	—	2	1	no	—
204	C₂²	—	122	2	no	—
205	C₂²	—	122	2	no	—
206	C₂²	—	122	2	no	—
207	C₂²	#14519783	1	2	yes	—
208	C₂²	C₂²×C₄×D₆₁	1	1	yes	characteristic
209	C₄	—	2	1	no	—
210	C₄	—	2	1	no	—
211	C₄	—	2	1	no	—
212	C₄	—	2	1	no	—
213	C₄	—	2	1	no	—
214	C₄	—	122	2	no	—
215	C₄	—	122	2	no	—
216	C₄	—	122	2	no	—
217	C₄	#41×D₆₁	1	2	yes	—
218	C₂	—	2	2	no	—
219	C₂	—	244	2	no	—
220	C₂	#16840230	1	1	yes	characteristic
221	C₂	C₂×#14519783	1	1	yes	characteristic
222	C₂	#16840528	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₆₁
commutator, socle	C₂²×C₆₁	C₂³×C₄
Fitting	C₆₁×#431	C₂
hypercenter	#431	D₆₁
hypocenter	C₆₁	#2968
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ #431

Complements

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

N	H ≅ G/N	type
2. #16839891	C₂	semidirect
3. #16839832	C₂	semidirect
4. #16839830	C₂	semidirect
5. #16839825	C₂	semidirect
6. #16839821	C₂	semidirect
7. #16839716	C₂	semidirect
8. C₂×#14519688	C₂	semidirect
9. C₆₁×#431	C₂	semidirect
118. #431	D₆₁	semidirect
121. C₆₁	#2968	semidirect