Subgroups — C₄×#14519864 #21462387

Order 7808.

572 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14519864	C₂	1	2	yes	maximal
2	#16840727	C₂	1	2	yes	maximal, complemented
3	#16840726	C₂	1	4	yes	maximal, complemented
4	C₄×#11758213	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#11758217	C₂	1	2	yes	maximal, complemented
6	C₄×D₆₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄×#92420	C₂	1	2	yes	maximal, complemented
8	C₄×#11758224	C₂	1	1	yes	maximal, characteristic
9	#14519864	C₄	1	16	yes	direct product factor
10	C₂×#11758213	C₂²	1	2	yes	—
11	C₂×#11758217	C₂²	1	4	yes	—
12	C₂×D₆₁⋊C₈	C₂²	1	2	yes	—
13	C₂²×#92420	C₂²	1	4	yes	—
14	#14519832	C₂²	1	4	yes	—
15	#14519832	C₂²	1	2	yes	—
16	C₄×#92420	C₂²	1	1	yes	characteristic
17	C₄×#92420	C₂²	1	2	yes	—
18	C₄×#92420	C₂²	1	4	yes	—
19	C₄×#92420	C₂²	1	1	yes	characteristic
20	C₄×#92420	C₂²	1	2	yes	—
21	C₂×#11758224	C₂²	1	1	yes	characteristic
22	C₄×Dic₁₂₂	C₄	1	1	yes	characteristic
23	#14519742	C₄	1	1	yes	characteristic
24	D₄×Dic₆₁	C₄	1	1	yes	characteristic
25	C₄×C₂²⋊D₆₁	C₄	1	2	yes	—
26	#14519737	C₄	1	2	yes	—
27	#14519735	C₂²	1	1	yes	characteristic
28	#14519733	C₂²	1	2	yes	—
29	C₂×C₄×Dic₆₁	C₂²	1	2	yes	—
30	C₄²×D₆₁	C₂²	1	1	yes	characteristic
31	C₄×D₄×C₆₁	C₄	1	1	yes	characteristic
32	C₂×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₄×C₆₁	C₂×C₄	1	2	yes	—
34	C₂×C₂²⋊D₆₁	C₂×C₄	1	2	yes	—
35	C₂²×Dic₆₁	C₂×C₄	1	2	yes	—
36	C₂²×Dic₆₁	C₂³	1	2	yes	—
37	#11758224	C₂×C₄	1	8	yes	—
38	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
41	C₂×Dic₁₂₂	C₂×C₄	1	1	yes	characteristic
42	#11758217	C₂×C₄	1	16	yes	complemented
43	C₂×#92420	C₂×C₄	1	16	yes	complemented
44	C₂×#92420	C₂³	1	2	yes	—
45	C₂×#92420	C₂³	1	4	yes	—
46	C₂×#92420	C₂³	1	2	yes	—
47	#11758213	C₂×C₄	1	8	yes	complemented
48	D₆₁⋊C₈	C₂×C₄	1	8	yes	complemented
49	C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
50	C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
51	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
52	C₂²⋊Dic₆₁	C₂×C₄	1	2	yes	—
53	#11758198	C₂×C₄	1	2	yes	—
54	C₄⋊Dic₆₁	C₂×C₄	1	1	yes	characteristic
55	#11758196	C₂×C₄	1	2	yes	—
56	#11758196	C₂×C₄	1	2	yes	—
57	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
58	C₄×Dic₆₁	C₂×C₄	1	2	yes	—
59	C₄×Dic₆₁	C₂×C₄	1	2	yes	—
60	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
61	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
62	C₄×Dic₆₁	C₂³	1	2	yes	—
63	C₂³×C₆₁	C₂²×C₄	1	2	yes	—
64	C₂²×D₆₁	C₂²×C₄	1	1	yes	characteristic
65	D₄×C₆₁	C₄²	1	4	yes	—
66	C₂×C₄×C₆₁	—	2	4	no	—
67	C₂×C₄×C₆₁	C₂²×C₄	1	2	yes	—
68	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
69	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
70	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
71	C₂²⋊D₆₁	C₄²	1	8	yes	—
72	C₂×Dic₆₁	—	2	4	no	—
73	C₂×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
74	C₂×Dic₆₁	C₂²×C₄	1	2	yes	—
75	C₂×Dic₆₁	C₂²×C₄	1	2	yes	—
76	C₂×Dic₆₁	C₂²×C₄	1	8	yes	—
77	C₂×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
78	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
79	C₄×D₆₁	—	2	2	no	—
80	C₄×D₆₁	—	2	2	no	—
81	C₄×D₆₁	C₂²×C₄	1	4	yes	—
82	Dic₁₂₂	C₄²	1	4	yes	—
83	#92420	C₂²×C₄	1	4	yes	—
84	#92420	C₂²×C₄	1	4	yes	—
85	#92420	C₂²×C₄	1	8	yes	—
86	C₂²×C₆₁	—	2	2	no	—
87	C₂²×C₆₁	—	2	2	no	—
88	C₂²×C₆₁	C₂×C₄²	1	4	yes	—
89	C₂²×C₆₁	C₂³×C₄	1	1	yes	characteristic
90	C₂×D₆₁	—	2	1	no	—
91	C₂×D₆₁	—	2	1	no	—
92	C₂×D₆₁	C₂×C₄²	1	2	yes	—
93	C₄×C₆₁	—	2	1	no	—
94	C₄×C₆₁	—	2	2	no	—
95	C₄×C₆₁	C₂×C₄²	1	2	yes	—
96	C₄×C₆₁	#131	1	2	yes	complemented
97	Dic₆₁	—	2	1	no	—
98	Dic₆₁	—	2	2	no	—
99	Dic₆₁	C₂×C₄²	1	4	yes	—
100	Dic₆₁	#131	1	2	yes	complemented
101	Dic₆₁	C₂³×C₄	1	2	yes	—
102	C₄×#131	—	61	1	no	maximal, Sylow
103	C₂×C₆₁	—	2	4	no	—
104	C₂×C₆₁	C₂²×C₄²	1	1	yes	characteristic
105	C₂×C₆₁	C₂×#131	1	1	yes	characteristic
106	C₂×C₆₁	C₂×#131	1	1	yes	characteristic
107	D₆₁	—	2	2	no	—
108	C₂×#131	—	61	2	no	—
109	C₄×#41	—	61	1	no	—
110	#405	—	61	4	no	—
111	#405	—	61	2	no	—
112	C₄×M₁₆	—	61	2	no	—
113	C₄×M₁₆	—	61	1	no	—
114	C₂×C₄×C₈	—	61	2	no	—
115	C₂×C₄×C₈	—	61	1	no	—
116	C₆₁	C₄×#131	1	1	yes	characteristic, complemented, Sylow
117	C₂×#41	—	61	1	no	—
118	#131	—	61	16	no	—
119	C₂×M₁₆	—	61	4	no	—
120	C₂×M₁₆	—	61	2	no	—
121	C₂²×C₈	—	61	4	no	—
122	C₂²×C₈	—	61	2	no	—
123	C₄×Q₈	—	61	1	no	—
124	C₄×Q₈	—	61	1	no	—
125	C₄×D₄	—	61	1	no	—
126	C₄×D₄	—	61	2	no	—
127	C₄×D₄	—	61	2	no	—
128	C₄×D₄	#6923	1	1	yes	characteristic
129	#117	—	61	1	no	—
130	#117	—	61	2	no	—
131	C₂×C₄²	—	61	2	no	—
132	C₂×C₄²	—	61	1	no	—
133	#97	—	61	4	no	—
134	#97	—	61	2	no	—
135	C₄×C₈	—	61	1	no	—
136	C₄×C₈	—	61	2	no	—
137	C₄×C₈	—	61	1	no	—
138	C₄×C₈	—	61	4	no	—
139	C₄×C₈	—	61	2	no	—
140	#41	—	61	8	no	—
141	C₂×Q₈	—	61	1	no	—
142	C₂×D₄	—	61	2	no	—
143	C₂×D₄	C₂×#6923	1	1	yes	characteristic
144	C₂²×C₄	—	61	2	no	—
145	C₂²×C₄	—	61	1	no	—
146	C₂²×C₄	—	61	2	no	—
147	C₂²×C₄	—	61	1	no	—
148	C₂²×C₄	—	61	1	no	—
149	C₂²×C₄	C₂×#6923	1	2	yes	—
150	M₁₆	—	61	8	no	—
151	M₁₆	—	61	16	no	—
152	C₂×C₈	—	61	2	no	—
153	C₂×C₈	—	61	4	no	—
154	C₂×C₈	—	61	2	no	—
155	C₂×C₈	—	61	8	no	—
156	C₂×C₈	—	61	16	no	—
157	C₄⋊C₄	—	61	2	no	—
158	C₄⋊C₄	—	61	2	no	—
159	C₄⋊C₄	—	61	1	no	—
160	C₄⋊C₄	C₂×#6923	1	1	yes	characteristic
161	C₂²⋊C₄	—	61	2	no	—
162	C₂²⋊C₄	—	61	2	no	—
163	C₂²⋊C₄	C₂×#6923	1	2	yes	—
164	C₄²	—	61	2	no	—
165	C₄²	—	61	1	no	—
166	C₄²	—	61	2	no	—
167	C₄²	—	61	1	no	—
168	C₄²	—	61	1	no	—
169	C₄²	—	61	2	no	—
170	C₄²	C₂×#6923	1	1	yes	characteristic
171	C₂³	—	61	1	no	—
172	C₂³	C₂²×#6923	1	2	yes	—
173	Q₈	—	61	4	no	—
174	D₄	—	61	8	no	—
175	D₄	C₄×#6923	1	4	yes	—
176	C₂×C₄	—	2	4	no	—
177	C₂×C₄	—	61	8	no	—
178	C₂×C₄	—	61	1	no	—
179	C₂×C₄	—	61	2	no	—
180	C₂×C₄	—	61	1	no	—
181	C₂×C₄	—	61	4	no	—
182	C₂×C₄	—	61	1	no	—
183	C₂×C₄	—	61	2	no	—
184	C₂×C₄	—	122	2	no	—
185	C₂×C₄	—	122	4	no	—
186	C₂×C₄	—	122	2	no	—
187	C₂×C₄	C₂²×#6923	1	2	yes	—
188	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
189	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
190	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
191	C₈	—	61	4	no	—
192	C₈	—	61	4	no	—
193	C₈	—	61	8	no	—
194	C₂²	—	2	2	no	—
195	C₂²	—	2	2	no	—
196	C₂²	—	61	2	no	—
197	C₂²	—	122	1	no	—
198	C₂²	—	122	1	no	—
199	C₂²	C₂×C₄×#6923	1	4	yes	—
200	C₂²	C₂³×#6923	1	1	yes	characteristic
201	C₄	—	2	2	no	—
202	C₄	—	2	1	no	—
203	C₄	—	61	4	no	—
204	C₄	—	61	2	no	—
205	C₄	—	61	2	no	—
206	C₄	—	122	1	no	—
207	C₄	—	122	2	no	—
208	C₄	C₂×C₄×#6923	1	2	yes	—
209	C₄	#14519864	1	2	yes	direct product factor
210	C₂	—	2	4	no	—
211	C₂	—	122	2	no	—
212	C₂	C₂²×C₄×#6923	1	1	yes	characteristic
213	C₂	C₂×#14519864	1	1	yes	characteristic
214	C₂	D₆₁⋊#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×#6923
commutator	C₂×C₆₁	C₂²×C₄²
Frattini	C₂²	C₂³×#6923
Fitting	C₄×D₄×C₆₁	C₄
socle	C₂²×C₆₁	C₂³×C₄
hypercenter	C₄×D₄	#6923
hypocenter	C₆₁	C₄×#131
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
2. #16840727	C₂	semidirect
3. #16840726	C₂	semidirect
4. C₄×#11758213	C₂	semidirect
5. C₄×#11758217	C₂	semidirect
6. C₄×D₆₁⋊C₈	C₂	semidirect
7. C₂×C₄×#92420	C₂	semidirect
9. #14519864	C₄	direct (N × H)
42. #11758217	C₂×C₄	semidirect
43. C₂×#92420	C₂×C₄	semidirect
47. #11758213	C₂×C₄	semidirect
48. D₆₁⋊C₈	C₂×C₄	semidirect
96. C₄×C₆₁	#131	semidirect
100. Dic₆₁	#131	semidirect
116. C₆₁	C₄×#131	semidirect
209. C₄	#14519864	direct (N × H)

Subgroups — C4×#14519864 #21462387

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#14519864 #21462387