Subgroups — C₂×C₄×H(5,𝔽₂)×C₇₃ #32972053

Order 18688.

12378 conjugacy classes of subgroups.

The subgroup lattice has 248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×H(5,𝔽₂)×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₄×H(5,𝔽₂)×C₇₃	C₂	1	32	yes	maximal, direct product factor
3	C₂×#520×C₇₃	C₂	1	6	yes	maximal, complemented
4	C₂×#518×C₇₃	C₂	1	9	yes	maximal, complemented
5	C₂×C₄×#41×C₇₃	C₂	1	6	yes	maximal, complemented
6	C₂²×C₄×D₄×C₇₃	C₂	1	9	yes	maximal, complemented
7	C₂×H(5,𝔽₂)×C₇₃	C₄	1	32	yes	direct product factor
8	C₂×H(5,𝔽₂)×C₇₃	C₂²	1	16	yes	—
9	C₂²×#41×C₇₃	C₂²	1	6	yes	—
10	C₂³×D₄×C₇₃	C₂²	1	9	yes	—
11	C₂⁴×C₄×C₇₃	C₂²	1	6	yes	complemented
12	#520×C₇₃	C₂²	1	96	yes	complemented
13	#518×C₇₃	C₂²	1	144	yes	complemented
14	C₄×#41×C₇₃	C₂²	1	96	yes	complemented
15	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	complemented
16	C₂×C₄×Q₈×C₇₃	C₂²	1	6	yes	complemented
17	C₂×C₄×D₄×C₇₃	C₂²	1	18	yes	complemented
18	C₂×C₄×D₄×C₇₃	C₂²	1	36	yes	complemented
19	C₂×C₄×D₄×C₇₃	C₂²	1	18	yes	complemented
20	C₂×C₄×D₄×C₇₃	C₂²	1	144	yes	complemented
21	C₂×#117×C₇₃	C₂²	1	18	yes	complemented
22	C₂²×C₄⋊C₄×C₇₃	C₂²	1	9	yes	complemented
23	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	18	yes	complemented
24	C₂²×C₄²×C₇₃	C₂²	1	9	yes	complemented
25	C₂⁵×C₇₃	C₂³	1	6	yes	—
26	H(5,𝔽₂)×C₇₃	C₂×C₄	1	256	yes	direct product factor
27	C₂×#41×C₇₃	C₂×C₄	1	96	yes	complemented
28	C₂×#41×C₇₃	C₂³	1	48	yes	—
29	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
30	C₂²×D₄×C₇₃	C₂×C₄	1	144	yes	complemented
31	C₂²×D₄×C₇₃	C₂³	1	18	yes	—
32	C₂²×D₄×C₇₃	C₂³	1	72	yes	—
33	C₂³×C₄×C₇₃	—	4	24	no	—
34	C₂³×C₄×C₇₃	C₂³	1	9	yes	—
35	C₂³×C₄×C₇₃	C₂³	1	9	yes	—
36	C₂³×C₄×C₇₃	C₂³	1	18	yes	—
37	C₂³×C₄×C₇₃	C₂³	1	9	yes	—
38	C₂³×C₄×C₇₃	C₂³	1	48	yes	complemented
39	C₄×Q₈×C₇₃	C₂³	1	16	yes	complemented
40	C₄×Q₈×C₇₃	C₂³	1	48	yes	complemented
41	C₄×D₄×C₇₃	C₂³	1	144	yes	complemented
42	C₄×D₄×C₇₃	C₂³	1	288	yes	complemented
43	C₄×D₄×C₇₃	C₂³	1	144	yes	complemented
44	#117×C₇₃	C₂³	1	144	yes	complemented
45	C₂×C₄⋊C₄×C₇₃	C₂³	1	18	yes	—
46	C₂×C₄⋊C₄×C₇₃	C₂³	1	6	yes	—
47	C₂×C₄⋊C₄×C₇₃	C₂³	1	72	yes	complemented
48	C₂×C₂²⋊C₄×C₇₃	C₂³	1	36	yes	—
49	C₂×C₂²⋊C₄×C₇₃	C₂³	1	144	yes	complemented
50	C₂×C₄²×C₇₃	C₂³	1	18	yes	—
51	C₂×C₄²×C₇₃	C₂³	1	6	yes	—
52	C₂×C₄²×C₇₃	C₂³	1	72	yes	complemented
53	C₂⁴×C₇₃	—	4	12	no	—
54	C₂⁴×C₇₃	—	4	12	no	—
55	C₂⁴×C₇₃	C₂²×C₄	1	48	yes	complemented
56	C₂⁴×C₇₃	C₂⁴	1	9	yes	—
57	C₂⁴×C₇₃	C₂⁴	1	24	yes	—
58	#41×C₇₃	C₂²×C₄	1	384	yes	complemented
59	C₂×Q₈×C₇₃	C₂²×C₄	1	16	yes	complemented
60	C₂×Q₈×C₇₃	C₂⁴	1	8	yes	—
61	C₂×D₄×C₇₃	C₂²×C₄	1	144	yes	complemented
62	C₂×D₄×C₇₃	C₂²×C₄	1	576	yes	complemented
63	C₂×D₄×C₇₃	C₂⁴	1	72	yes	—
64	C₂²×C₄×C₇₃	—	2	36	no	—
65	C₂²×C₄×C₇₃	—	4	96	no	—
66	C₂²×C₄×C₇₃	—	4	36	no	—
67	C₂²×C₄×C₇₃	—	4	18	no	—
68	C₂²×C₄×C₇₃	C₂²×C₄	1	72	yes	complemented
69	C₂²×C₄×C₇₃	C₂⁴	1	6	yes	—
70	C₂²×C₄×C₇₃	C₂⁴	1	9	yes	—
71	C₂²×C₄×C₇₃	C₂⁴	1	36	yes	—
72	C₂²×C₄×C₇₃	C₂⁴	1	36	yes	—
73	C₂²×C₄×C₇₃	C₂⁴	1	72	yes	—
74	C₂²×C₄×C₇₃	C₂⁴	1	6	yes	—
75	C₂²×C₄×C₇₃	C₂⁴	1	36	yes	—
76	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
77	C₄⋊C₄×C₇₃	C₂⁴	1	72	yes	—
78	C₄⋊C₄×C₇₃	C₂⁴	1	24	yes	—
79	C₂²⋊C₄×C₇₃	C₂⁴	1	144	yes	—
80	C₄²×C₇₃	C₂⁴	1	24	yes	—
81	C₄²×C₇₃	C₂⁴	1	72	yes	—
82	C₂³×C₇₃	—	2	18	no	—
83	C₂³×C₇₃	—	2	18	no	—
84	C₂³×C₇₃	—	4	24	no	—
85	C₂³×C₇₃	—	4	96	no	—
86	C₂³×C₇₃	—	4	24	no	—
87	C₂³×C₇₃	C₂³×C₄	1	36	yes	—
88	C₂³×C₇₃	C₂³×C₄	1	96	yes	complemented
89	C₂³×C₇₃	C₂⁵	1	18	yes	—
90	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
91	Q₈×C₇₃	C₂³×C₄	1	32	yes	complemented
92	D₄×C₇₃	C₂³×C₄	1	288	yes	complemented
93	C₂×C₄×C₇₃	—	2	18	no	—
94	C₂×C₄×C₇₃	—	2	12	no	—
95	C₂×C₄×C₇₃	—	2	72	no	—
96	C₂×C₄×C₇₃	—	4	72	no	—
97	C₂×C₄×C₇₃	—	4	36	no	—
98	C₂×C₄×C₇₃	C₂³×C₄	1	24	yes	—
99	C₂×C₄×C₇₃	C₂³×C₄	1	144	yes	complemented
100	C₂×C₄×C₇₃	H(5,𝔽₂)	1	4	yes	direct product factor
101	C₂×C₄×C₇₃	C₂⁵	1	12	yes	—
102	C₂×C₄×C₇₃	C₂⁵	1	18	yes	—
103	C₂×C₄×C₇₃	C₂⁵	1	12	yes	—
104	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
105	C₂²×C₇₃	—	2	18	no	—
106	C₂²×C₇₃	—	2	18	no	—
107	C₂²×C₇₃	—	2	72	no	—
108	C₂²×C₇₃	—	4	96	no	—
109	C₂²×C₇₃	C₂⁴×C₄	1	36	yes	—
110	C₂²×C₇₃	C₂⁴×C₄	1	2	yes	—
111	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	2	yes	—
112	C₂²×C₇₃	#585	1	2	yes	—
113	C₂²×C₇₃	C₂⁶	1	1	yes	characteristic
114	C₄×C₇₃	—	2	18	no	—
115	C₄×C₇₃	—	2	12	no	—
116	C₄×C₇₃	C₂⁴×C₄	1	24	yes	—
117	C₄×C₇₃	C₂×H(5,𝔽₂)	1	4	yes	direct product factor
118	C₂×C₄×H(5,𝔽₂)	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₂×C₇₃	—	2	36	no	—
120	C₂×C₇₃	C₄×H(5,𝔽₂)	1	4	yes	direct product factor
121	C₂×C₇₃	C₂⁵×C₄	1	1	yes	characteristic
122	C₂×C₇₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
123	C₂×C₇₃	C₂×#585	1	1	yes	characteristic
124	C₂²×H(5,𝔽₂)	C₂×C₇₃	1	1	yes	characteristic
125	C₄×H(5,𝔽₂)	C₂×C₇₃	1	32	yes	direct product factor
126	C₂×#520	C₂×C₇₃	1	6	yes	complemented
127	C₂×#518	C₂×C₇₃	1	9	yes	complemented
128	C₂×C₄×#41	C₂×C₇₃	1	6	yes	complemented
129	C₂²×C₄×D₄	C₂×C₇₃	1	9	yes	complemented
130	C₇₃	C₂×C₄×H(5,𝔽₂)	1	1	yes	characteristic, direct product factor, Sylow
131	C₂×H(5,𝔽₂)	C₄×C₇₃	1	32	yes	direct product factor
132	C₂×H(5,𝔽₂)	C₂²×C₇₃	1	16	yes	—
133	C₂²×#41	C₂²×C₇₃	1	6	yes	—
134	C₂³×D₄	C₂²×C₇₃	1	9	yes	—
135	C₂⁴×C₄	C₂²×C₇₃	1	6	yes	complemented
136	#520	C₂²×C₇₃	1	96	yes	complemented
137	#518	C₂²×C₇₃	1	144	yes	complemented
138	C₄×#41	C₂²×C₇₃	1	96	yes	complemented
139	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	complemented
140	C₂×C₄×Q₈	C₂²×C₇₃	1	6	yes	complemented
141	C₂×C₄×D₄	C₂²×C₇₃	1	18	yes	complemented
142	C₂×C₄×D₄	C₂²×C₇₃	1	36	yes	complemented
143	C₂×C₄×D₄	C₂²×C₇₃	1	18	yes	complemented
144	C₂×C₄×D₄	C₂²×C₇₃	1	144	yes	complemented
145	C₂×#117	C₂²×C₇₃	1	18	yes	complemented
146	C₂²×C₄⋊C₄	C₂²×C₇₃	1	9	yes	complemented
147	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	18	yes	complemented
148	C₂²×C₄²	C₂²×C₇₃	1	9	yes	complemented
149	C₂⁵	C₂³×C₇₃	1	6	yes	—
150	H(5,𝔽₂)	C₂×C₄×C₇₃	1	256	yes	direct product factor
151	C₂×#41	C₂×C₄×C₇₃	1	96	yes	complemented
152	C₂×#41	C₂³×C₇₃	1	48	yes	—
153	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
154	C₂²×D₄	C₂×C₄×C₇₃	1	144	yes	complemented
155	C₂²×D₄	C₂³×C₇₃	1	18	yes	—
156	C₂²×D₄	C₂³×C₇₃	1	72	yes	—
157	C₂³×C₄	—	4	24	no	—
158	C₂³×C₄	C₂³×C₇₃	1	9	yes	—
159	C₂³×C₄	C₂³×C₇₃	1	9	yes	—
160	C₂³×C₄	C₂³×C₇₃	1	18	yes	—
161	C₂³×C₄	C₂³×C₇₃	1	9	yes	—
162	C₂³×C₄	C₂³×C₇₃	1	48	yes	complemented
163	C₄×Q₈	C₂³×C₇₃	1	16	yes	complemented
164	C₄×Q₈	C₂³×C₇₃	1	48	yes	complemented
165	C₄×D₄	C₂³×C₇₃	1	144	yes	complemented
166	C₄×D₄	C₂³×C₇₃	1	288	yes	complemented
167	C₄×D₄	C₂³×C₇₃	1	144	yes	complemented
168	#117	C₂³×C₇₃	1	144	yes	complemented
169	C₂×C₄⋊C₄	C₂³×C₇₃	1	18	yes	—
170	C₂×C₄⋊C₄	C₂³×C₇₃	1	6	yes	—
171	C₂×C₄⋊C₄	C₂³×C₇₃	1	72	yes	complemented
172	C₂×C₂²⋊C₄	C₂³×C₇₃	1	36	yes	—
173	C₂×C₂²⋊C₄	C₂³×C₇₃	1	144	yes	complemented
174	C₂×C₄²	C₂³×C₇₃	1	18	yes	—
175	C₂×C₄²	C₂³×C₇₃	1	6	yes	—
176	C₂×C₄²	C₂³×C₇₃	1	72	yes	complemented
177	C₂⁴	—	4	12	no	—
178	C₂⁴	—	4	12	no	—
179	C₂⁴	C₂²×C₄×C₇₃	1	48	yes	complemented
180	C₂⁴	C₂⁴×C₇₃	1	9	yes	—
181	C₂⁴	C₂⁴×C₇₃	1	24	yes	—
182	#41	C₂²×C₄×C₇₃	1	384	yes	complemented
183	C₂×Q₈	C₂²×C₄×C₇₃	1	16	yes	complemented
184	C₂×Q₈	C₂⁴×C₇₃	1	8	yes	—
185	C₂×D₄	C₂²×C₄×C₇₃	1	144	yes	complemented
186	C₂×D₄	C₂²×C₄×C₇₃	1	576	yes	complemented
187	C₂×D₄	C₂⁴×C₇₃	1	72	yes	—
188	C₂²×C₄	—	2	36	no	—
189	C₂²×C₄	—	4	96	no	—
190	C₂²×C₄	—	4	36	no	—
191	C₂²×C₄	—	4	18	no	—
192	C₂²×C₄	C₂²×C₄×C₇₃	1	72	yes	complemented
193	C₂²×C₄	C₂⁴×C₇₃	1	6	yes	—
194	C₂²×C₄	C₂⁴×C₇₃	1	9	yes	—
195	C₂²×C₄	C₂⁴×C₇₃	1	36	yes	—
196	C₂²×C₄	C₂⁴×C₇₃	1	36	yes	—
197	C₂²×C₄	C₂⁴×C₇₃	1	72	yes	—
198	C₂²×C₄	C₂⁴×C₇₃	1	6	yes	—
199	C₂²×C₄	C₂⁴×C₇₃	1	36	yes	—
200	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
201	C₄⋊C₄	C₂⁴×C₇₃	1	72	yes	—
202	C₄⋊C₄	C₂⁴×C₇₃	1	24	yes	—
203	C₂²⋊C₄	C₂⁴×C₇₃	1	144	yes	—
204	C₄²	C₂⁴×C₇₃	1	24	yes	—
205	C₄²	C₂⁴×C₇₃	1	72	yes	—
206	C₂³	—	2	18	no	—
207	C₂³	—	2	18	no	—
208	C₂³	—	4	24	no	—
209	C₂³	—	4	96	no	—
210	C₂³	—	4	24	no	—
211	C₂³	C₂³×C₄×C₇₃	1	36	yes	—
212	C₂³	C₂³×C₄×C₇₃	1	96	yes	complemented
213	C₂³	C₂⁵×C₇₃	1	18	yes	—
214	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
215	Q₈	C₂³×C₄×C₇₃	1	32	yes	complemented
216	D₄	C₂³×C₄×C₇₃	1	288	yes	complemented
217	C₂×C₄	—	2	18	no	—
218	C₂×C₄	—	2	12	no	—
219	C₂×C₄	—	2	72	no	—
220	C₂×C₄	—	4	72	no	—
221	C₂×C₄	—	4	36	no	—
222	C₂×C₄	C₂³×C₄×C₇₃	1	24	yes	—
223	C₂×C₄	C₂³×C₄×C₇₃	1	144	yes	complemented
224	C₂×C₄	H(5,𝔽₂)×C₇₃	1	4	yes	direct product factor
225	C₂×C₄	C₂⁵×C₇₃	1	12	yes	—
226	C₂×C₄	C₂⁵×C₇₃	1	18	yes	—
227	C₂×C₄	C₂⁵×C₇₃	1	12	yes	—
228	C₂×C₄	C₂⁵×C₇₃	1	2	yes	—
229	C₂²	—	2	18	no	—
230	C₂²	—	2	18	no	—
231	C₂²	—	2	72	no	—
232	C₂²	—	4	96	no	—
233	C₂²	C₂⁴×C₄×C₇₃	1	36	yes	—
234	C₂²	C₂⁴×C₄×C₇₃	1	2	yes	—
235	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	2	yes	—
236	C₂²	#585×C₇₃	1	2	yes	—
237	C₂²	C₂⁶×C₇₃	1	1	yes	characteristic
238	C₄	—	2	18	no	—
239	C₄	—	2	12	no	—
240	C₄	C₂⁴×C₄×C₇₃	1	24	yes	—
241	C₄	C₂×H(5,𝔽₂)×C₇₃	1	4	yes	direct product factor
242	C₂	—	2	36	no	—
243	C₂	C₄×H(5,𝔽₂)×C₇₃	1	4	yes	direct product factor
244	C₂	C₂⁵×C₄×C₇₃	1	1	yes	characteristic
245	C₂	C₂²×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
246	C₂	C₂×#585×C₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇₃	C₂⁴
commutator	C₂	C₂⁵×C₄×C₇₃
Frattini, cosocle	C₂²	C₂⁶×C₇₃
socle	C₂³×C₇₃	C₂⁵
prime radical	C₂²×H(5,𝔽₂)×C₇₃	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×H(5,𝔽₂)×C₇₃	C₂	direct (N × H)
3. C₂×#520×C₇₃	C₂	semidirect
4. C₂×#518×C₇₃	C₂	semidirect
5. C₂×C₄×#41×C₇₃	C₂	semidirect
6. C₂²×C₄×D₄×C₇₃	C₂	semidirect
7. C₂×H(5,𝔽₂)×C₇₃	C₄	direct (N × H)
11. C₂⁴×C₄×C₇₃	C₂²	semidirect
12. #520×C₇₃	C₂²	semidirect
13. #518×C₇₃	C₂²	semidirect
14. C₄×#41×C₇₃	C₂²	semidirect
15. C₂×C₄×Q₈×C₇₃	C₂²	semidirect
16. C₂×C₄×Q₈×C₇₃	C₂²	semidirect
17. C₂×C₄×D₄×C₇₃	C₂²	semidirect
18. C₂×C₄×D₄×C₇₃	C₂²	semidirect
19. C₂×C₄×D₄×C₇₃	C₂²	semidirect
20. C₂×C₄×D₄×C₇₃	C₂²	semidirect
21. C₂×#117×C₇₃	C₂²	semidirect
22. C₂²×C₄⋊C₄×C₇₃	C₂²	semidirect
23. C₂²×C₂²⋊C₄×C₇₃	C₂²	semidirect
24. C₂²×C₄²×C₇₃	C₂²	semidirect
26. H(5,𝔽₂)×C₇₃	C₂×C₄	direct (N × H)
27. C₂×#41×C₇₃	C₂×C₄	semidirect
30. C₂²×D₄×C₇₃	C₂×C₄	semidirect
38. C₂³×C₄×C₇₃	C₂³	semidirect
39. C₄×Q₈×C₇₃	C₂³	semidirect
40. C₄×Q₈×C₇₃	C₂³	semidirect
41. C₄×D₄×C₇₃	C₂³	semidirect
42. C₄×D₄×C₇₃	C₂³	semidirect
43. C₄×D₄×C₇₃	C₂³	semidirect
44. #117×C₇₃	C₂³	semidirect
47. C₂×C₄⋊C₄×C₇₃	C₂³	semidirect
49. C₂×C₂²⋊C₄×C₇₃	C₂³	semidirect
52. C₂×C₄²×C₇₃	C₂³	semidirect
55. C₂⁴×C₇₃	C₂²×C₄	semidirect
58. #41×C₇₃	C₂²×C₄	semidirect
59. C₂×Q₈×C₇₃	C₂²×C₄	semidirect
61. C₂×D₄×C₇₃	C₂²×C₄	semidirect
62. C₂×D₄×C₇₃	C₂²×C₄	semidirect
68. C₂²×C₄×C₇₃	C₂²×C₄	semidirect
88. C₂³×C₇₃	C₂³×C₄	semidirect
91. Q₈×C₇₃	C₂³×C₄	semidirect
92. D₄×C₇₃	C₂³×C₄	semidirect
99. C₂×C₄×C₇₃	C₂³×C₄	semidirect
100. C₂×C₄×C₇₃	H(5,𝔽₂)	direct (N × H)
117. C₄×C₇₃	C₂×H(5,𝔽₂)	direct (N × H)
118. C₂×C₄×H(5,𝔽₂)	C₇₃	direct (N × H)
120. C₂×C₇₃	C₄×H(5,𝔽₂)	direct (N × H)
125. C₄×H(5,𝔽₂)	C₂×C₇₃	direct (N × H)
126. C₂×#520	C₂×C₇₃	semidirect
127. C₂×#518	C₂×C₇₃	semidirect
128. C₂×C₄×#41	C₂×C₇₃	semidirect
129. C₂²×C₄×D₄	C₂×C₇₃	semidirect
130. C₇₃	C₂×C₄×H(5,𝔽₂)	direct (N × H)
131. C₂×H(5,𝔽₂)	C₄×C₇₃	direct (N × H)
135. C₂⁴×C₄	C₂²×C₇₃	semidirect
136. #520	C₂²×C₇₃	semidirect
137. #518	C₂²×C₇₃	semidirect
138. C₄×#41	C₂²×C₇₃	semidirect
139. C₂×C₄×Q₈	C₂²×C₇₃	semidirect
140. C₂×C₄×Q₈	C₂²×C₇₃	semidirect
141. C₂×C₄×D₄	C₂²×C₇₃	semidirect
142. C₂×C₄×D₄	C₂²×C₇₃	semidirect
143. C₂×C₄×D₄	C₂²×C₇₃	semidirect
144. C₂×C₄×D₄	C₂²×C₇₃	semidirect
145. C₂×#117	C₂²×C₇₃	semidirect
146. C₂²×C₄⋊C₄	C₂²×C₇₃	semidirect
147. C₂²×C₂²⋊C₄	C₂²×C₇₃	semidirect
148. C₂²×C₄²	C₂²×C₇₃	semidirect
150. H(5,𝔽₂)	C₂×C₄×C₇₃	direct (N × H)
151. C₂×#41	C₂×C₄×C₇₃	semidirect
154. C₂²×D₄	C₂×C₄×C₇₃	semidirect
162. C₂³×C₄	C₂³×C₇₃	semidirect
163. C₄×Q₈	C₂³×C₇₃	semidirect
164. C₄×Q₈	C₂³×C₇₃	semidirect
165. C₄×D₄	C₂³×C₇₃	semidirect
166. C₄×D₄	C₂³×C₇₃	semidirect
167. C₄×D₄	C₂³×C₇₃	semidirect
168. #117	C₂³×C₇₃	semidirect
171. C₂×C₄⋊C₄	C₂³×C₇₃	semidirect
173. C₂×C₂²⋊C₄	C₂³×C₇₃	semidirect
176. C₂×C₄²	C₂³×C₇₃	semidirect
179. C₂⁴	C₂²×C₄×C₇₃	semidirect
182. #41	C₂²×C₄×C₇₃	semidirect
183. C₂×Q₈	C₂²×C₄×C₇₃	semidirect
185. C₂×D₄	C₂²×C₄×C₇₃	semidirect
186. C₂×D₄	C₂²×C₄×C₇₃	semidirect
192. C₂²×C₄	C₂²×C₄×C₇₃	semidirect
212. C₂³	C₂³×C₄×C₇₃	semidirect
215. Q₈	C₂³×C₄×C₇₃	semidirect
216. D₄	C₂³×C₄×C₇₃	semidirect
223. C₂×C₄	C₂³×C₄×C₇₃	semidirect
224. C₂×C₄	H(5,𝔽₂)×C₇₃	direct (N × H)
241. C₄	C₂×H(5,𝔽₂)×C₇₃	direct (N × H)
243. C₂	C₄×H(5,𝔽₂)×C₇₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×H(5,𝔽₂)×C₇₃	2
C₄×H(5,𝔽₂)×C₇₃	2
C₂×#520×C₇₃	2
C₂×#518×C₇₃	2
C₂×C₄×#41×C₇₃	2
C₂²×C₄×D₄×C₇₃	2
C₂×C₄×H(5,𝔽₂)	73

Subgroups — C2×C4×H(5,𝔽2)×C73 #32972053

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×H(5,𝔽₂)×C₇₃ #32972053