Subgroups — #21462644

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	#16840814	C₂	1	2	yes	maximal, complemented
2	#16840793	C₂	1	2	yes	maximal, complemented
3	#16840793	C₂	1	2	yes	maximal, complemented
4	D₄×#92420	C₂	1	2	yes	maximal, complemented
5	#16840786	C₂	1	2	yes	maximal, complemented
6	#16840779	C₂	1	1	yes	maximal, characteristic, complemented
7	#16840726	C₂	1	2	yes	maximal, complemented
8	C₂×#14519832	C₂	1	1	yes	maximal, characteristic, complemented
9	#16840293	C₂	1	1	yes	maximal, characteristic
10	C₂×#11758217	C₂²	1	2	yes	—
11	C₂²×#92420	C₂²	1	2	yes	—
12	C₂²×#92420	C₂²	1	2	yes	—
13	#14519844	C₂²	1	2	yes	—
14	#14519844	C₂²	1	2	yes	—
15	C₄⋊#92420	C₂²	1	2	yes	—
16	C₂²⋊#92420	C₂²	1	1	yes	characteristic
17	C₂²⋊#92420	C₂²	1	1	yes	characteristic
18	C₂²⋊#92420	C₂²	1	2	yes	—
19	C₂²⋊#92420	C₂²	1	2	yes	—
20	#14519832	C₂²	1	1	yes	characteristic
21	#14519832	C₂²	1	1	yes	characteristic
22	#14519832	C₂²	1	2	yes	—
23	#14519832	C₂²	1	2	yes	—
24	C₄×#92420	C₂²	1	2	yes	—
25	C₄×#92420	C₂²	1	2	yes	—
26	#14519770	C₄	1	2	yes	—
27	#14519768	C₄	1	1	yes	characteristic
28	#14519764	C₄	1	1	yes	characteristic
29	#14519758	C₄	1	2	yes	—
30	#14519756	C₄	1	1	yes	characteristic
31	#14519742	C₂²	1	1	yes	characteristic
32	D₄×Dic₆₁	C₂²	1	2	yes	—
33	D₄×Dic₆₁	C₂²	1	1	yes	characteristic
34	#14519733	C₂²	1	2	yes	—
35	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
36	#121×C₆₁	C₄	1	1	yes	characteristic
37	C₂×D₄×C₆₁	C₂×C₄	1	2	yes	—
38	C₂×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
40	C₂²×Dic₆₁	C₂×C₄	1	1	yes	characteristic
41	C₂²×Dic₆₁	C₂³	1	1	yes	characteristic
42	C₂²×Dic₆₁	C₂³	1	2	yes	—
43	C₂×Dic₁₂₂	C₂×C₄	1	1	yes	characteristic
44	#11758217	—	2	4	no	—
45	C₂×#92420	—	2	4	no	—
46	C₂×#92420	—	2	4	no	—
47	C₂×#92420	C₂³	1	2	yes	—
48	C₂×#92420	C₂³	1	2	yes	—
49	C₂×#92420	C₂³	1	2	yes	—
50	C₂×#92420	C₂³	1	2	yes	—
51	C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
52	C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
53	C₂²⋊Dic₆₁	C₂×C₄	1	2	yes	—
54	C₂²⋊Dic₆₁	C₂×C₄	1	2	yes	—
55	C₂²⋊Dic₆₁	C₂×C₄	1	2	yes	—
56	C₂²⋊Dic₆₁	C₂×C₄	1	2	yes	—
57	C₄⋊Dic₆₁	C₂×C₄	1	1	yes	characteristic
58	C₄⋊Dic₆₁	C₂×C₄	1	2	yes	—
59	#11758196	C₂×C₄	1	2	yes	—
60	#11758196	C₂×C₄	1	2	yes	—
61	#11758196	C₂×C₄	1	2	yes	—
62	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
63	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
64	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
65	C₄×Dic₆₁	C₂³	1	2	yes	—
66	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
67	C₂³×C₆₁	C₂²×C₄	1	2	yes	—
68	C₂³×C₆₁	C₂²×C₄	1	1	yes	characteristic
69	D₄×C₆₁	—	2	4	no	—
70	D₄×C₆₁	—	4	1	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	2	yes	—
75	C₂×Dic₆₁	—	2	2	no	—
76	C₂×Dic₆₁	—	2	2	no	—
77	C₂×Dic₆₁	—	2	2	no	—
78	C₂×Dic₆₁	—	2	2	no	—
79	C₂×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
80	C₂×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
81	C₂×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
82	C₂×Dic₆₁	C₂²×C₄	1	2	yes	—
83	C₂×Dic₆₁	C₂²×C₄	1	2	yes	—
84	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
85	Dic₁₂₂	—	4	1	no	—
86	#92420	—	2	2	no	—
87	#92420	—	2	2	no	—
88	#92420	—	2	2	no	—
89	#92420	#41	1	4	yes	—
90	C₂²×C₆₁	—	2	1	no	—
91	C₂²×C₆₁	—	2	1	no	—
92	C₂²×C₆₁	—	2	2	no	—
93	C₂²×C₆₁	—	2	2	no	—
94	C₂²×C₆₁	—	2	2	no	—
95	C₂²×C₆₁	#131	1	2	yes	—
96	C₂²×C₆₁	C₂³×C₄	1	1	yes	characteristic
97	C₄×C₆₁	—	2	2	no	—
98	C₄×C₆₁	—	2	1	no	—
99	C₄×C₆₁	—	2	1	no	—
100	Dic₆₁	—	2	1	no	—
101	Dic₆₁	—	2	2	no	—
102	Dic₆₁	—	2	1	no	—
103	Dic₆₁	—	2	1	no	—
104	Dic₆₁	—	2	2	no	—
105	Dic₆₁	C₂×#41	1	2	yes	—
106	#2968	—	61	1	no	maximal, Sylow
107	C₂×C₆₁	—	2	2	no	—
108	C₂×C₆₁	—	4	2	no	—
109	C₂×C₆₁	C₄×#41	1	1	yes	characteristic
110	C₂×C₆₁	C₂×#131	1	1	yes	characteristic
111	C₂×C₆₁	#568	1	1	yes	characteristic
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	—	61	1	no	—
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	#6923	1	1	yes	characteristic
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	—	61	1	no	—
136	C₄⋊C₈	—	61	2	no	—
137	C₄⋊C₈	—	61	2	no	—
138	C₄⋊C₈	—	61	2	no	—
139	C₂²⋊C₈	—	61	1	no	—
140	C₂²⋊C₈	—	61	1	no	—
141	C₂²⋊C₈	—	61	2	no	—
142	C₂²⋊C₈	—	61	2	no	—
143	#97	—	61	1	no	—
144	#97	—	61	1	no	—
145	#97	—	61	2	no	—
146	#97	—	61	2	no	—
147	C₄×C₈	—	61	2	no	—
148	C₄×C₈	—	61	2	no	—
149	C₂×Q₈	—	61	1	no	—
150	C₂×D₄	C₂×#6923	1	2	yes	—
151	C₂×D₄	C₂×#6923	1	1	yes	characteristic
152	C₂²×C₄	—	61	1	no	—
153	C₂²×C₄	—	61	2	no	—
154	C₂²×C₄	—	61	1	no	—
155	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
156	M₁₆	—	122	4	no	—
157	C₂×C₈	—	61	2	no	—
158	C₂×C₈	—	61	2	no	—
159	C₂×C₈	—	61	2	no	—
160	C₂×C₈	—	61	2	no	—
161	C₂×C₈	—	122	4	no	—
162	C₂×C₈	—	122	4	no	—
163	C₄⋊C₄	—	61	2	no	—
164	C₄⋊C₄	—	61	2	no	—
165	C₄⋊C₄	—	61	2	no	—
166	C₄⋊C₄	—	61	1	no	—
167	C₄⋊C₄	—	61	2	no	—
168	C₄⋊C₄	C₂×#6923	1	1	yes	characteristic
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	C₂×#6923	1	2	yes	—
174	C₄²	—	61	1	no	—
175	C₄²	—	61	2	no	—
176	C₄²	—	61	1	no	—
177	C₄²	—	61	1	no	—
178	C₄²	—	61	1	no	—
179	C₂³	C₂²×#6923	1	2	yes	—
180	C₂³	C₂²×#6923	1	1	yes	characteristic
181	Q₈	—	244	1	no	—
182	D₄	—	2	4	no	—
183	D₄	—	4	1	no	—
184	C₂×C₄	—	4	1	no	—
185	C₂×C₄	—	61	1	no	—
186	C₂×C₄	—	61	1	no	—
187	C₂×C₄	—	61	1	no	—
188	C₂×C₄	—	61	1	no	—
189	C₂×C₄	—	61	2	no	—
190	C₂×C₄	—	61	2	no	—
191	C₂×C₄	—	122	2	no	—
192	C₂×C₄	—	122	2	no	—
193	C₂×C₄	—	122	2	no	—
194	C₂×C₄	—	122	2	no	—
195	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
196	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
197	C₂×C₄	C₂²×#6923	1	2	yes	—
198	C₈	—	61	4	no	—
199	C₈	—	122	2	no	—
200	C₈	—	122	2	no	—
201	C₈	—	122	2	no	—
202	C₂²	—	2	1	no	—
203	C₂²	—	2	1	no	—
204	C₂²	—	2	2	no	—
205	C₂²	—	2	2	no	—
206	C₂²	—	2	2	no	—
207	C₂²	#14519864	1	2	yes	—
208	C₂²	C₂³×#6923	1	1	yes	characteristic
209	C₄	—	2	2	no	—
210	C₄	—	2	1	no	—
211	C₄	—	2	1	no	—
212	C₄	—	61	2	no	—
213	C₄	—	122	1	no	—
214	C₄	—	122	2	no	—
215	C₄	—	122	1	no	—
216	C₄	—	122	1	no	—
217	C₄	—	122	2	no	—
218	C₂	—	2	2	no	—
219	C₂	—	4	2	no	—
220	C₂	#41×#6923	1	1	yes	characteristic
221	C₂	C₂×#14519864	1	1	yes	characteristic
222	C₂	#16840840	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×#6923
commutator, socle	C₂²×C₆₁	C₂³×C₄
Fitting	#121×C₆₁	C₄
hypercenter	#121	#6923
hypocenter	C₆₁	#2968
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ #121

Complements

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

N	H ≅ G/N	type
1. #16840814	C₂	semidirect
2. #16840793	C₂	semidirect
3. #16840793	C₂	semidirect
4. D₄×#92420	C₂	semidirect
5. #16840786	C₂	semidirect
6. #16840779	C₂	semidirect
7. #16840726	C₂	semidirect
8. C₂×#14519832	C₂	semidirect
121. C₆₁	#2968	semidirect