Subgroups — #368×Dic₇₃ #33001398

Order 18688.

314 conjugacy classes of subgroups.

The subgroup lattice has 178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988417	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₆×Dic₇₃	C₂	1	1	yes	maximal, characteristic
3	#108×Dic₇₃	C₂	1	2	yes	maximal
4	#22608024	C₂	1	2	yes	maximal
5	C₂×#368×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×#11924003	C₂²	1	1	yes	characteristic
7	C₂×#14556527	C₂²	1	2	yes	—
8	M₁₆×Dic₇₃	—	2	2	no	—
9	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
10	#17988417	C₄	1	4	yes	complemented
11	C₁₆×Dic₇₃	C₄	1	4	yes	—
12	#17988351	—	2	2	no	—
13	C₂²×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×#108×C₇₃	C₂²	1	2	yes	—
15	#368×C₇₃	C₄	1	4	yes	complemented
16	C₂×#11924012	—	2	2	no	—
17	C₂²×#10596831	D₄	1	1	yes	characteristic
18	C₂×C₄×Dic₇₃	D₄	1	1	yes	characteristic
19	C₂×#11924003	—	2	1	no	—
20	C₂×#11924003	—	2	1	no	—
21	C₂×#11924003	C₂×C₄	1	2	yes	—
22	#14556527	—	2	2	no	—
23	#14556527	C₂×C₄	1	4	yes	—
24	#14556501	—	4	2	no	—
25	C₈×Dic₇₃	—	4	2	no	—
26	C₈×Dic₇₃	C₂×C₄	1	2	yes	—
27	C₈×Dic₇₃	Q₈	1	2	yes	—
28	C₂×M₁₆×C₇₃	—	2	2	no	—
29	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
30	C₂×C₁₆×C₇₃	C₂×C₄	1	2	yes	—
31	C₂×C₁₆×C₇₃	C₂×C₄	1	2	yes	—
32	C₂×C₁₆×C₇₃	C₂×C₄	1	2	yes	—
33	#108×C₇₃	—	2	2	no	—
34	#108×C₇₃	C₂×C₄	1	4	yes	—
35	C₂²×Dic₇₃	Q₁₆	1	2	yes	—
36	#11924012	—	2	4	no	—
37	#11924012	—	4	2	no	—
38	C₂×#10596831	—	2	1	no	—
39	C₂×#10596831	—	2	1	no	—
40	C₂×#10596831	—	4	2	no	—
41	C₂×#10596831	C₄⋊C₄	1	2	yes	—
42	C₄×Dic₇₃	C₄⋊C₄	1	2	yes	—
43	C₄×Dic₇₃	D₈	1	1	yes	characteristic
44	C₄×Dic₇₃	D₈	1	1	yes	characteristic
45	#11924003	—	2	2	no	—
46	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
47	M₁₆×C₇₃	—	2	4	no	—
48	M₁₆×C₇₃	—	4	2	no	—
49	C₂×C₈×C₇₃	—	4	2	no	—
50	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
52	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
53	C₂×C₈×C₇₃	C₂×Q₈	1	1	yes	characteristic
54	C₂×C₈×C₇₃	#41	1	1	yes	characteristic
55	C₂×C₈×C₇₃	#41	1	1	yes	characteristic
56	C₁₆×C₇₃	C₄²	1	4	yes	—
57	C₂³×C₇₃	C₂×Q₁₆	1	1	yes	characteristic
58	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
59	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
60	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
61	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
62	C₂×C₄×C₇₃	#135	1	1	yes	characteristic
63	C₂×C₄×C₇₃	#135	1	1	yes	characteristic
64	C₂×Dic₇₃	—	2	4	no	—
65	C₂×Dic₇₃	#107	1	2	yes	—
66	C₂×Dic₇₃	#107	1	2	yes	—
67	C₈×C₇₃	—	4	4	no	—
68	C₈×C₇₃	C₂×C₄²	1	1	yes	characteristic
69	C₈×C₇₃	#117	1	1	yes	characteristic
70	C₈×C₇₃	C₄×Q₈	1	1	yes	characteristic
71	C₈×C₇₃	C₄×Q₈	1	1	yes	characteristic
72	#10596831	—	2	2	no	—
73	#10596831	—	4	4	no	—
74	C₂²×C₇₃	—	2	2	no	—
75	C₂²×C₇₃	C₂×#107	1	1	yes	characteristic
76	C₂²×C₇₃	C₄×Q₁₆	1	1	yes	characteristic
77	C₂²×C₇₃	C₄×Q₁₆	1	1	yes	characteristic
78	C₄×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
79	C₄×C₇₃	#427	1	1	yes	characteristic
80	C₄×C₇₃	C₄×D₈	1	1	yes	characteristic
81	C₄×C₇₃	C₄×D₈	1	1	yes	characteristic
82	Dic₇₃	—	2	2	no	—
83	Dic₇₃	#368	1	4	yes	direct product factor
84	C₄×#368	—	73	1	no	maximal, Sylow
85	C₂×C₇₃	—	2	1	no	—
86	C₂×C₇₃	—	2	1	no	—
87	C₂×C₇₃	C₄×#107	1	1	yes	characteristic
88	C₂×C₇₃	C₂×#368	1	2	yes	—
89	C₂×#368	—	73	1	no	—
90	C₂×#368	D₇₃	1	1	yes	characteristic
91	C₂×C₄×C₁₆	—	73	1	no	—
92	C₄×#108	—	73	2	no	—
93	#1381	—	73	2	no	—
94	C₇₃	C₄×#368	1	1	yes	characteristic, complemented, Sylow
95	C₂²×C₁₆	—	73	1	no	—
96	C₂²×C₁₆	C₂×D₇₃	1	1	yes	characteristic
97	C₂×#108	—	73	2	no	—
98	C₂×#108	C₂×D₇₃	1	2	yes	—
99	C₄×M₁₆	—	146	2	no	—
100	C₂×C₄×C₈	—	73	1	no	—
101	#368	—	73	4	no	—
102	#368	Dic₇₃	1	4	yes	direct product factor
103	C₄×C₁₆	—	73	4	no	—
104	#341	—	146	2	no	—
105	C₂×M₁₆	—	2	2	no	—
106	C₂×M₁₆	—	146	2	no	—
107	C₂²×C₈	—	73	1	no	—
108	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
109	C₂×C₄²	—	73	1	no	—
110	C₂×C₁₆	—	73	2	no	—
111	C₂×C₁₆	—	146	1	no	—
112	C₂×C₁₆	—	146	1	no	—
113	C₂×C₁₆	C₄×D₇₃	1	2	yes	—
114	C₂×C₁₆	C₄×D₇₃	1	2	yes	—
115	C₂×C₁₆	C₂×Dic₇₃	1	2	yes	—
116	#108	—	2	2	no	—
117	#108	—	73	4	no	—
118	#108	—	146	2	no	—
119	#108	C₂×Dic₇₃	1	4	yes	—
120	#97	—	292	2	no	—
121	C₄×C₈	—	292	2	no	—
122	C₄×C₈	—	73	2	no	—
123	C₄×C₈	—	73	2	no	—
124	C₂²×C₄	—	73	2	no	—
125	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
126	M₁₆	—	2	4	no	—
127	M₁₆	—	4	2	no	—
128	M₁₆	—	292	2	no	—
129	M₁₆	—	146	4	no	—
130	C₂×C₈	—	4	2	no	—
131	C₂×C₈	—	292	2	no	—
132	C₂×C₈	—	73	2	no	—
133	C₂×C₈	—	146	1	no	—
134	C₂×C₈	—	146	1	no	—
135	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
136	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
137	C₂×C₈	C₂²×Dic₇₃	1	1	yes	characteristic
138	C₂×C₈	Q₈×D₇₃	1	1	yes	characteristic
139	C₂×C₈	#11924027	1	1	yes	characteristic
140	C₂×C₈	#11924029	1	1	yes	characteristic
141	C₄²	—	73	2	no	—
142	C₄²	—	73	1	no	—
143	C₄²	—	73	1	no	—
144	C₁₆	—	146	2	no	—
145	C₁₆	C₄×Dic₇₃	1	4	yes	—
146	C₂³	Q₁₆×D₇₃	1	1	yes	characteristic
147	C₂×C₄	—	73	2	no	—
148	C₂×C₄	—	73	2	no	—
149	C₂×C₄	—	146	4	no	—
150	C₂×C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
151	C₂×C₄	#14556553	1	1	yes	characteristic
152	C₂×C₄	D₄×Dic₇₃	1	1	yes	characteristic
153	C₂×C₄	D₈×D₇₃	1	1	yes	characteristic
154	C₂×C₄	#14556610	1	1	yes	characteristic
155	C₂×C₄	#14556614	1	1	yes	characteristic
156	C₈	—	4	4	no	—
157	C₈	—	292	4	no	—
158	C₈	—	146	2	no	—
159	C₈	C₂×C₄×Dic₇₃	1	1	yes	characteristic
160	C₈	#14556549	1	1	yes	characteristic
161	C₈	#14556556	1	1	yes	characteristic
162	C₈	Q₈×Dic₇₃	1	1	yes	characteristic
163	C₂²	—	2	2	no	—
164	C₂²	#107×D₇₃	1	1	yes	characteristic
165	C₂²	#17988681	1	1	yes	characteristic
166	C₂²	Q₁₆×Dic₇₃	1	1	yes	characteristic
167	C₄	—	73	4	no	—
168	C₄	—	146	2	no	—
169	C₄	C₄⋊C₄×Dic₇₃	1	1	yes	characteristic
170	C₄	#17988624	1	1	yes	characteristic
171	C₄	#17988669	1	1	yes	characteristic
172	C₄	D₈×Dic₇₃	1	1	yes	characteristic
173	C₂	—	2	1	no	—
174	C₂	—	2	1	no	—
175	C₂	#107×Dic₇₃	1	1	yes	characteristic
176	C₂	#368×D₇₃	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₈×D₇₃
commutator	C₈×C₇₃	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₇₃
Fitting	C₂×#368×C₇₃	C₂
socle	C₂²×C₇₃	C₂×#107
prime radical	C₂³×C₇₃	C₂×Q₁₆
cosocle	C₂²×C₈×C₇₃	C₂³
hypercenter	C₂×#368	D₇₃
hypocenter	C₇₃	C₄×#368
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#368

Complements

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

N	H ≅ G/N	type
10. #17988417	C₄	semidirect
15. #368×C₇₃	C₄	semidirect
83. Dic₇₃	#368	direct (N × H)
94. C₇₃	C₄×#368	semidirect
102. #368	Dic₇₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#17988417	2
C₂×C₁₆×Dic₇₃	2
#108×Dic₇₃	2
#22608024	2
C₂×#368×C₇₃	2
C₄×#368	73

Subgroups — #368×Dic73 #33001398

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #368×Dic₇₃ #33001398