Subgroups — C₄×#14556678 #22626499

Order 9344.

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×#14556678	C₂	1	2	yes	maximal
2	#17989552	C₂	1	2	yes	maximal, complemented
3	#17989551	C₂	1	4	yes	maximal, complemented
4	C₄×#11924038	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#11924037	C₂	1	2	yes	maximal, complemented
6	C₄×#11924036	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄×#10596833	C₂	1	2	yes	maximal, complemented
8	C₄×#11924027	C₂	1	1	yes	maximal, characteristic
9	#14556678	C₄	1	16	yes	direct product factor
10	C₂×#11924038	C₂²	1	2	yes	—
11	C₂×#11924037	C₂²	1	4	yes	—
12	C₂×#11924036	C₂²	1	2	yes	—
13	C₂²×#10596833	C₂²	1	4	yes	—
14	#14556646	C₂²	1	4	yes	—
15	#14556646	C₂²	1	2	yes	—
16	C₄×#10596833	C₂²	1	1	yes	characteristic
17	C₄×#10596833	C₂²	1	2	yes	—
18	C₄×#10596833	C₂²	1	4	yes	—
19	C₄×#10596833	C₂²	1	1	yes	characteristic
20	C₄×#10596833	C₂²	1	2	yes	—
21	C₂×#11924027	C₂²	1	1	yes	characteristic
22	C₄×Dic₁₄₆	C₄	1	1	yes	characteristic
23	#14556556	C₄	1	1	yes	characteristic
24	D₄×Dic₇₃	C₄	1	1	yes	characteristic
25	C₄×C₂²⋊D₇₃	C₄	1	2	yes	—
26	#14556551	C₄	1	2	yes	—
27	#14556549	C₂²	1	1	yes	characteristic
28	#14556547	C₂²	1	2	yes	—
29	C₂×C₄×Dic₇₃	C₂²	1	2	yes	—
30	C₄²×D₇₃	C₂²	1	1	yes	characteristic
31	C₄×D₄×C₇₃	C₄	1	1	yes	characteristic
32	#11924038	C₂×C₄	1	8	yes	complemented
33	#11924037	C₂×C₄	1	16	yes	complemented
34	#11924036	C₂×C₄	1	8	yes	complemented
35	C₂×#10596833	C₂×C₄	1	16	yes	complemented
36	C₂×#10596833	C₂³	1	2	yes	—
37	C₂×#10596833	C₂³	1	4	yes	—
38	C₂×#10596833	C₂³	1	2	yes	—
39	#11924027	C₂×C₄	1	8	yes	—
40	C₂×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
41	C₂×C₂²⋊D₇₃	C₂×C₄	1	2	yes	—
42	C₂²×Dic₇₃	C₂×C₄	1	2	yes	—
43	C₂²×Dic₇₃	C₂³	1	2	yes	—
44	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
47	C₄⋊Dic₇₃	C₂×C₄	1	1	yes	characteristic
48	#11924007	C₂×C₄	1	2	yes	—
49	#11924007	C₂×C₄	1	2	yes	—
50	C₂²⋊Dic₇₃	C₂×C₄	1	2	yes	—
51	#11924005	C₂×C₄	1	2	yes	—
52	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
53	C₄×Dic₇₃	C₂×C₄	1	2	yes	—
54	C₄×Dic₇₃	C₂×C₄	1	2	yes	—
55	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
56	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
57	C₄×Dic₇₃	C₂³	1	2	yes	—
58	C₂×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₄×C₇₃	C₂×C₄	1	2	yes	—
60	C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
61	C₂²⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
62	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
63	C₂³×C₇₃	C₂²×C₄	1	2	yes	—
64	C₂²×D₇₃	C₂²×C₄	1	1	yes	characteristic
65	D₄×C₇₃	C₄²	1	4	yes	—
66	C₂×C₄×C₇₃	—	2	4	no	—
67	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
68	C₂×C₄×C₇₃	C₂²×C₄	1	2	yes	—
69	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
70	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
71	C₂²⋊D₇₃	C₄²	1	8	yes	—
72	C₂×Dic₇₃	—	2	4	no	—
73	C₂×Dic₇₃	C₂²×C₄	1	2	yes	—
74	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
75	C₂×Dic₇₃	C₂²×C₄	1	2	yes	—
76	C₂×Dic₇₃	C₂²×C₄	1	8	yes	—
77	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
78	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
79	C₄×D₇₃	—	2	2	no	—
80	C₄×D₇₃	—	2	2	no	—
81	C₄×D₇₃	C₂²×C₄	1	4	yes	—
82	Dic₁₄₆	C₄²	1	4	yes	—
83	#10596833	C₂²×C₄	1	4	yes	—
84	#10596833	C₂²×C₄	1	8	yes	—
85	#10596833	C₂²×C₄	1	4	yes	—
86	C₂²×C₇₃	—	2	2	no	—
87	C₂²×C₇₃	—	2	2	no	—
88	C₂²×C₇₃	C₂×C₄²	1	4	yes	—
89	C₂²×C₇₃	C₂³×C₄	1	1	yes	characteristic
90	C₂×D₇₃	—	2	1	no	—
91	C₂×D₇₃	—	2	1	no	—
92	C₂×D₇₃	C₂×C₄²	1	2	yes	—
93	C₄×C₇₃	—	2	1	no	—
94	C₄×C₇₃	—	2	2	no	—
95	C₄×C₇₃	C₂×C₄²	1	2	yes	—
96	C₄×C₇₃	#131	1	2	yes	complemented
97	Dic₇₃	—	2	1	no	—
98	Dic₇₃	—	2	2	no	—
99	Dic₇₃	C₂×C₄²	1	4	yes	—
100	Dic₇₃	#131	1	2	yes	complemented
101	Dic₇₃	C₂³×C₄	1	2	yes	—
102	C₂×C₇₃	—	2	4	no	—
103	C₂×C₇₃	C₂²×C₄²	1	1	yes	characteristic
104	C₂×C₇₃	C₂×#131	1	1	yes	characteristic
105	C₂×C₇₃	C₂×#131	1	1	yes	characteristic
106	D₇₃	—	2	2	no	—
107	C₄×#131	—	73	1	no	maximal, Sylow
108	C₇₃	C₄×#131	1	1	yes	characteristic, complemented, Sylow
109	C₂×#131	—	73	2	no	—
110	C₄×#41	—	73	1	no	—
111	#405	—	73	4	no	—
112	#405	—	73	2	no	—
113	C₄×M₁₆	—	73	2	no	—
114	C₄×M₁₆	—	73	1	no	—
115	C₂×C₄×C₈	—	73	2	no	—
116	C₂×C₄×C₈	—	73	1	no	—
117	C₂×#41	—	73	1	no	—
118	#131	—	73	16	no	—
119	C₂×M₁₆	—	73	4	no	—
120	C₂×M₁₆	—	73	2	no	—
121	C₂²×C₈	—	73	4	no	—
122	C₂²×C₈	—	73	2	no	—
123	C₄×Q₈	—	73	1	no	—
124	C₄×Q₈	—	73	1	no	—
125	C₄×D₄	—	73	1	no	—
126	C₄×D₄	—	73	2	no	—
127	C₄×D₄	—	73	2	no	—
128	C₄×D₄	#64408	1	1	yes	characteristic
129	#117	—	73	1	no	—
130	#117	—	73	2	no	—
131	C₂×C₄²	—	73	2	no	—
132	C₂×C₄²	—	73	1	no	—
133	#97	—	73	4	no	—
134	#97	—	73	2	no	—
135	C₄×C₈	—	73	1	no	—
136	C₄×C₈	—	73	2	no	—
137	C₄×C₈	—	73	1	no	—
138	C₄×C₈	—	73	4	no	—
139	C₄×C₈	—	73	2	no	—
140	#41	—	73	8	no	—
141	C₂×Q₈	—	73	1	no	—
142	C₂×D₄	—	73	2	no	—
143	C₂×D₄	C₂×#64408	1	1	yes	characteristic
144	C₂²×C₄	—	73	2	no	—
145	C₂²×C₄	—	73	1	no	—
146	C₂²×C₄	—	73	2	no	—
147	C₂²×C₄	—	73	1	no	—
148	C₂²×C₄	—	73	1	no	—
149	C₂²×C₄	C₂×#64408	1	2	yes	—
150	M₁₆	—	73	16	no	—
151	M₁₆	—	73	8	no	—
152	C₂×C₈	—	73	16	no	—
153	C₂×C₈	—	73	2	no	—
154	C₂×C₈	—	73	4	no	—
155	C₂×C₈	—	73	2	no	—
156	C₂×C₈	—	73	8	no	—
157	C₄⋊C₄	—	73	2	no	—
158	C₄⋊C₄	—	73	2	no	—
159	C₄⋊C₄	—	73	1	no	—
160	C₄⋊C₄	C₂×#64408	1	1	yes	characteristic
161	C₂²⋊C₄	—	73	2	no	—
162	C₂²⋊C₄	—	73	2	no	—
163	C₂²⋊C₄	C₂×#64408	1	2	yes	—
164	C₄²	—	73	2	no	—
165	C₄²	—	73	1	no	—
166	C₄²	—	73	2	no	—
167	C₄²	—	73	1	no	—
168	C₄²	—	73	2	no	—
169	C₄²	—	73	1	no	—
170	C₄²	C₂×#64408	1	1	yes	characteristic
171	C₂³	—	73	1	no	—
172	C₂³	C₂²×#64408	1	2	yes	—
173	Q₈	—	73	4	no	—
174	D₄	—	73	8	no	—
175	D₄	C₄×#64408	1	4	yes	—
176	C₂×C₄	—	2	4	no	—
177	C₂×C₄	—	73	1	no	—
178	C₂×C₄	—	73	1	no	—
179	C₂×C₄	—	73	2	no	—
180	C₂×C₄	—	73	8	no	—
181	C₂×C₄	—	73	4	no	—
182	C₂×C₄	—	73	1	no	—
183	C₂×C₄	—	73	2	no	—
184	C₂×C₄	—	146	2	no	—
185	C₂×C₄	—	146	4	no	—
186	C₂×C₄	—	146	2	no	—
187	C₂×C₄	C₂²×#64408	1	2	yes	—
188	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
189	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
190	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
191	C₈	—	73	4	no	—
192	C₈	—	73	8	no	—
193	C₈	—	73	4	no	—
194	C₂²	—	2	2	no	—
195	C₂²	—	2	2	no	—
196	C₂²	—	73	2	no	—
197	C₂²	—	146	1	no	—
198	C₂²	—	146	1	no	—
199	C₂²	C₂×C₄×#64408	1	4	yes	—
200	C₂²	C₂³×#64408	1	1	yes	characteristic
201	C₄	—	2	2	no	—
202	C₄	—	2	1	no	—
203	C₄	—	73	2	no	—
204	C₄	—	73	4	no	—
205	C₄	—	73	2	no	—
206	C₄	—	146	1	no	—
207	C₄	—	146	2	no	—
208	C₄	C₂×C₄×#64408	1	2	yes	—
209	C₄	#14556678	1	2	yes	direct product factor
210	C₂	—	2	4	no	—
211	C₂	—	146	2	no	—
212	C₂	C₂²×C₄×#64408	1	1	yes	characteristic
213	C₂	C₂×#14556678	1	1	yes	characteristic
214	C₂	D₇₃⋊#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×#64408
commutator	C₂×C₇₃	C₂²×C₄²
Frattini	C₂²	C₂³×#64408
Fitting	C₄×D₄×C₇₃	C₄
socle	C₂²×C₇₃	C₂³×C₄
hypercenter	C₄×D₄	#64408
hypocenter	C₇₃	C₄×#131
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
2. #17989552	C₂	semidirect
3. #17989551	C₂	semidirect
4. C₄×#11924038	C₂	semidirect
5. C₄×#11924037	C₂	semidirect
6. C₄×#11924036	C₂	semidirect
7. C₂×C₄×#10596833	C₂	semidirect
9. #14556678	C₄	direct (N × H)
32. #11924038	C₂×C₄	semidirect
33. #11924037	C₂×C₄	semidirect
34. #11924036	C₂×C₄	semidirect
35. C₂×#10596833	C₂×C₄	semidirect
96. C₄×C₇₃	#131	semidirect
100. Dic₇₃	#131	semidirect
108. C₇₃	C₄×#131	semidirect
209. C₄	#14556678	direct (N × H)

Subgroups — C4×#14556678 #22626499

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#14556678 #22626499