Subgroups — C₂×D₄×C₄⋊Dic₇₃ #33245271

Order 18688.

4718 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄×Dic₇₃	C₂	1	2	yes	maximal
2	C₂³×C₄⋊Dic₇₃	C₂	1	2	yes	maximal, complemented
3	D₄×C₄⋊Dic₇₃	C₂	1	16	yes	maximal, direct product factor
4	C₂×#17988486	C₂	1	2	yes	maximal, complemented
5	C₂×#17988462	C₂	1	4	yes	maximal, complemented
6	C₂×#17988457	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#17988447	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₄⋊Dic₇₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₄×D₄×C₇₃	C₂	1	1	yes	maximal, characteristic
10	C₂⁴×Dic₇₃	C₂²	1	4	yes	—
11	C₂×D₄×Dic₇₃	—	2	16	no	—
12	C₂×D₄×Dic₇₃	C₂²	1	16	yes	—
13	C₂²×C₄⋊Dic₇₃	—	2	16	no	—
14	C₂²×C₄⋊Dic₇₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊Dic₇₃	C₂²	1	2	yes	—
16	C₂²×C₄⋊Dic₇₃	C₂²	1	2	yes	—
17	C₂²×C₄⋊Dic₇₃	C₂²	1	4	yes	—
18	C₂²×C₄⋊Dic₇₃	C₂²	1	2	yes	—
19	C₂²×C₄⋊Dic₇₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊Dic₇₃	C₂²	1	16	yes	complemented
21	C₂²×C₂²⋊Dic₇₃	C₂²	1	4	yes	—
22	C₂²×C₄×Dic₇₃	C₂²	1	2	yes	—
23	#17988486	C₂²	1	16	yes	complemented
24	#17988462	C₂²	1	32	yes	complemented
25	#17988457	C₂²	1	8	yes	complemented
26	#17988447	C₂²	1	16	yes	complemented
27	C₄×C₄⋊Dic₇₃	C₂²	1	8	yes	complemented
28	C₂×#14556498	C₂²	1	2	yes	—
29	C₂×#14556498	C₂²	1	4	yes	—
30	C₂³×D₄×C₇₃	C₂²	1	1	yes	characteristic
31	C₂⁴×C₄×C₇₃	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₇₃	C₄	1	16	yes	complemented
33	C₂×C₄×D₄×C₇₃	C₂²	1	8	yes	—
34	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
35	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
36	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
37	C₂³×Dic₇₃	—	2	16	no	—
38	C₂³×Dic₇₃	—	2	16	no	—
39	C₂³×Dic₇₃	—	4	8	no	—
40	C₂³×Dic₇₃	C₂³	1	4	yes	—
41	C₂³×Dic₇₃	C₂³	1	2	yes	—
42	C₂³×Dic₇₃	C₂³	1	16	yes	—
43	C₂³×Dic₇₃	C₂³	1	2	yes	—
44	D₄×Dic₇₃	—	2	64	no	—
45	C₂×C₄⋊Dic₇₃	—	2	16	no	—
46	C₂×C₄⋊Dic₇₃	—	2	64	no	—
47	C₂×C₄⋊Dic₇₃	—	2	8	no	—
48	C₂×C₄⋊Dic₇₃	—	2	8	no	—
49	C₂×C₄⋊Dic₇₃	—	2	4	no	—
50	C₂×C₄⋊Dic₇₃	—	4	4	no	—
51	C₂×C₄⋊Dic₇₃	D₄	1	8	yes	direct product factor
52	C₂×C₄⋊Dic₇₃	C₂³	1	4	yes	—
53	C₂×C₄⋊Dic₇₃	C₂³	1	8	yes	—
54	C₂×C₄⋊Dic₇₃	C₂³	1	8	yes	—
55	C₂×C₄⋊Dic₇₃	C₂³	1	16	yes	—
56	C₂×C₄⋊Dic₇₃	C₂³	1	8	yes	—
57	C₂×C₄⋊Dic₇₃	C₂³	1	4	yes	—
58	C₂×C₂²⋊Dic₇₃	—	2	16	no	—
59	C₂×C₂²⋊Dic₇₃	C₂³	1	16	yes	—
60	C₂×C₄×Dic₇₃	—	2	8	no	—
61	C₂×C₄×Dic₇₃	C₂³	1	8	yes	—
62	#14556498	C₂³	1	8	yes	—
63	#14556498	C₂³	1	16	yes	—
64	C₂⁵×C₇₃	C₂³	1	2	yes	—
65	C₂²×D₄×C₇₃	C₂×C₄	1	8	yes	—
66	C₂²×D₄×C₇₃	D₄	1	8	yes	—
67	C₂²×D₄×C₇₃	Q₈	1	8	yes	—
68	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
69	C₂³×C₄×C₇₃	—	2	8	no	—
70	C₂³×C₄×C₇₃	—	2	8	no	—
71	C₂³×C₄×C₇₃	C₂×C₄	1	16	yes	complemented
72	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
74	C₂³×C₄×C₇₃	C₂³	1	8	yes	—
75	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
77	C₄×D₄×C₇₃	C₂×C₄	1	64	yes	complemented
78	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	8	yes	complemented
79	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
80	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	16	yes	complemented
81	C₂×C₂²⋊C₄×C₇₃	C₂³	1	8	yes	—
82	C₂×C₄²×C₇₃	C₂×C₄	1	8	yes	complemented
83	C₂×C₄²×C₇₃	C₂³	1	4	yes	—
84	C₂²×Dic₇₃	—	2	4	no	—
85	C₂²×Dic₇₃	—	2	4	no	—
86	C₂²×Dic₇₃	—	2	4	no	—
87	C₂²×Dic₇₃	—	2	8	no	—
88	C₂²×Dic₇₃	—	2	8	no	—
89	C₂²×Dic₇₃	—	2	32	no	—
90	C₂²×Dic₇₃	—	2	4	no	—
91	C₂²×Dic₇₃	—	2	8	no	—
92	C₂²×Dic₇₃	—	2	4	no	—
93	C₂²×Dic₇₃	—	2	32	no	—
94	C₂²×Dic₇₃	—	4	16	no	—
95	C₂²×Dic₇₃	—	4	64	no	—
96	C₂²×Dic₇₃	C₂×D₄	1	8	yes	—
97	C₂²×Dic₇₃	C₂⁴	1	4	yes	—
98	C₂²×Dic₇₃	C₂⁴	1	8	yes	—
99	C₂²×Dic₇₃	C₂⁴	1	4	yes	—
100	C₄⋊Dic₇₃	—	2	16	no	—
101	C₄⋊Dic₇₃	—	2	16	no	—
102	C₄⋊Dic₇₃	—	2	8	no	—
103	C₄⋊Dic₇₃	—	2	32	no	—
104	C₄⋊Dic₇₃	—	4	8	no	—
105	C₄⋊Dic₇₃	C₂×D₄	1	16	yes	direct product factor
106	C₂²⋊Dic₇₃	—	2	32	no	—
107	C₄×Dic₇₃	—	2	16	no	—
108	C₂⁴×C₇₃	—	2	4	no	—
109	C₂⁴×C₇₃	—	2	4	no	—
110	C₂⁴×C₇₃	—	2	4	no	—
111	C₂⁴×C₇₃	—	2	4	no	—
112	C₂⁴×C₇₃	C₂²×C₄	1	8	yes	—
113	C₂⁴×C₇₃	C₂×D₄	1	8	yes	—
114	C₂⁴×C₇₃	C₂×Q₈	1	8	yes	—
115	C₂⁴×C₇₃	C₂⁴	1	4	yes	—
116	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
117	C₂×D₄×C₇₃	C₄⋊C₄	1	64	yes	complemented
118	C₂×D₄×C₇₃	C₂²×C₄	1	16	yes	—
119	C₂×D₄×C₇₃	C₂×D₄	1	16	yes	—
120	C₂×D₄×C₇₃	C₂×Q₈	1	16	yes	—
121	C₂²×C₄×C₇₃	—	2	4	no	—
122	C₂²×C₄×C₇₃	—	2	4	no	—
123	C₂²×C₄×C₇₃	—	2	2	no	—
124	C₂²×C₄×C₇₃	—	2	2	no	—
125	C₂²×C₄×C₇₃	—	2	64	no	—
126	C₂²×C₄×C₇₃	—	2	16	no	—
127	C₂²×C₄×C₇₃	—	2	16	no	—
128	C₂²×C₄×C₇₃	C₂²×C₄	1	4	yes	—
129	C₂²×C₄×C₇₃	C₂²×C₄	1	8	yes	—
130	C₂²×C₄×C₇₃	C₂²×C₄	1	4	yes	—
131	C₂²×C₄×C₇₃	C₂²×C₄	1	4	yes	—
132	C₂²×C₄×C₇₃	C₂²×C₄	1	32	yes	complemented
133	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
134	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
135	C₂²×C₄×C₇₃	C₂×Q₈	1	4	yes	—
136	C₂²×C₄×C₇₃	#41	1	4	yes	—
137	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
139	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
140	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
141	C₄⋊C₄×C₇₃	C₂²×C₄	1	16	yes	complemented
142	C₂²⋊C₄×C₇₃	C₂²×C₄	1	32	yes	complemented
143	C₄²×C₇₃	C₂²×C₄	1	16	yes	complemented
144	C₂³×C₇₃	—	2	16	no	—
145	C₂³×C₇₃	—	2	16	no	—
146	C₂³×C₇₃	—	2	16	no	—
147	C₂³×C₇₃	—	2	16	no	—
148	C₂³×C₇₃	—	2	16	no	—
149	C₂³×C₇₃	—	2	16	no	—
150	C₂³×C₇₃	—	2	4	no	—
151	C₂³×C₇₃	—	2	4	no	—
152	C₂³×C₇₃	—	2	4	no	—
153	C₂³×C₇₃	—	2	4	no	—
154	C₂³×C₇₃	C₂×C₄⋊C₄	1	32	yes	complemented
155	C₂³×C₇₃	C₂³×C₄	1	8	yes	—
156	C₂³×C₇₃	C₂³×C₄	1	2	yes	—
157	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
158	C₂³×C₇₃	C₂²×D₄	1	8	yes	—
159	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
160	C₂³×C₇₃	C₂²×Q₈	1	8	yes	—
161	C₂³×C₇₃	C₂²×Q₈	1	2	yes	—
162	C₂³×C₇₃	C₂×#41	1	2	yes	—
163	C₂³×C₇₃	H(5,𝔽₂)	1	2	yes	—
164	C₂³×C₇₃	2₋¹⁺⁴	1	2	yes	—
165	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
166	D₄×C₇₃	C₂×C₄⋊C₄	1	64	yes	complemented
167	C₂×C₄×C₇₃	—	2	16	no	—
168	C₂×C₄×C₇₃	—	2	8	no	—
169	C₂×C₄×C₇₃	—	2	4	no	—
170	C₂×C₄×C₇₃	—	2	4	no	—
171	C₂×C₄×C₇₃	—	2	2	no	—
172	C₂×C₄×C₇₃	—	2	2	no	—
173	C₂×C₄×C₇₃	—	2	64	no	—
174	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	16	yes	complemented
175	C₂×C₄×C₇₃	C₄×D₄	1	16	yes	complemented
176	C₂×C₄×C₇₃	C₂³×C₄	1	4	yes	—
177	C₂×C₄×C₇₃	C₂³×C₄	1	8	yes	—
178	C₂×C₄×C₇₃	C₂³×C₄	1	4	yes	—
179	C₂×C₄×C₇₃	C₂³×C₄	1	4	yes	—
180	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
181	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
182	C₂×C₄×C₇₃	C₂²×Q₈	1	4	yes	—
183	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
184	C₂×Dic₇₃	—	2	16	no	—
185	C₂×Dic₇₃	—	2	4	no	—
186	C₂×Dic₇₃	—	2	4	no	—
187	C₂×Dic₇₃	—	2	4	no	—
188	C₂×Dic₇₃	—	2	8	no	—
189	C₂×Dic₇₃	—	2	8	no	—
190	C₂×Dic₇₃	—	2	4	no	—
191	C₂×Dic₇₃	—	2	8	no	—
192	C₂×Dic₇₃	—	2	4	no	—
193	C₂×Dic₇₃	—	4	64	no	—
194	C₂×Dic₇₃	—	4	16	no	—
195	C₂×Dic₇₃	—	4	8	no	—
196	C₂×Dic₇₃	C₂²×D₄	1	8	yes	—
197	C₂²×C₇₃	—	2	64	no	—
198	C₂²×C₇₃	—	2	8	no	—
199	C₂²×C₇₃	—	2	8	no	—
200	C₂²×C₇₃	—	2	8	no	—
201	C₂²×C₇₃	—	2	8	no	—
202	C₂²×C₇₃	—	2	8	no	—
203	C₂²×C₇₃	—	2	8	no	—
204	C₂²×C₇₃	C₂²×C₄⋊C₄	1	4	yes	—
205	C₂²×C₇₃	C₂²×C₄⋊C₄	1	16	yes	complemented
206	C₂²×C₇₃	C₂×C₄×D₄	1	4	yes	—
207	C₂²×C₇₃	#520	1	4	yes	—
208	C₂²×C₇₃	D₄²	1	4	yes	—
209	C₂²×C₇₃	#547	1	4	yes	—
210	C₂²×C₇₃	D₄×Q₈	1	4	yes	—
211	C₂²×C₇₃	#554	1	4	yes	—
212	C₂²×C₇₃	C₂⁴×C₄	1	1	yes	characteristic
213	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
214	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
215	C₂²×C₇₃	C₂³×Q₈	1	1	yes	characteristic
216	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
217	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
218	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
219	C₄×C₇₃	—	2	8	no	—
220	C₄×C₇₃	—	2	4	no	—
221	C₄×C₇₃	C₂²×C₄⋊C₄	1	8	yes	complemented
222	C₄×C₇₃	C₂×C₄×D₄	1	8	yes	complemented
223	Dic₇₃	—	2	8	no	—
224	Dic₇₃	—	4	8	no	—
225	Dic₇₃	—	4	4	no	—
226	C₂×D₄×C₄⋊C₄	—	73	1	no	maximal, Sylow
227	C₂×C₇₃	—	2	16	no	—
228	C₂×C₇₃	D₄×C₄⋊C₄	1	8	yes	complemented
229	C₂×C₇₃	C₂³×C₄⋊C₄	1	1	yes	characteristic
230	C₂×C₇₃	C₂²×C₄×D₄	1	1	yes	characteristic
231	C₂×C₇₃	C₂×#520	1	1	yes	characteristic
232	C₂×C₇₃	C₂×D₄²	1	1	yes	characteristic
233	C₂×C₇₃	C₂×#547	1	1	yes	characteristic
234	C₂×C₇₃	C₂×D₄×Q₈	1	1	yes	characteristic
235	C₂×C₇₃	C₂×#554	1	1	yes	characteristic
236	C₂²×C₄×D₄	—	73	2	no	—
237	C₂²×C₄×D₄	D₇₃	1	1	yes	characteristic
238	C₂³×C₄⋊C₄	—	73	2	no	—
239	D₄×C₄⋊C₄	—	73	16	no	—
240	C₂×#389	—	73	2	no	—
241	C₂×#385	—	73	4	no	—
242	C₂×#384	—	73	1	no	—
243	C₂×#380	—	73	2	no	—
244	C₂×C₄×C₄⋊C₄	—	73	1	no	—
245	C₇₃	C₂×D₄×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
246	C₂³×D₄	C₂×D₇₃	1	1	yes	characteristic
247	C₂⁴×C₄	—	73	4	no	—
248	C₂⁴×C₄	C₂×D₇₃	1	2	yes	—
249	C₂×C₄×D₄	—	73	16	no	—
250	C₂×C₄×D₄	—	146	16	no	—
251	C₂×C₄×D₄	Dic₇₃	1	16	yes	complemented
252	C₂×C₄×D₄	C₂×D₇₃	1	8	yes	—
253	C₂²×C₄⋊C₄	—	73	2	no	—
254	C₂²×C₄⋊C₄	—	73	1	no	—
255	C₂²×C₄⋊C₄	—	73	16	no	—
256	C₂²×C₄⋊C₄	—	73	2	no	—
257	C₂²×C₄⋊C₄	—	73	4	no	—
258	C₂²×C₄⋊C₄	—	73	2	no	—
259	C₂²×C₄⋊C₄	—	73	1	no	—
260	C₂²×C₄⋊C₄	—	146	16	no	—
261	C₂²×C₄⋊C₄	C₂×D₇₃	1	1	yes	characteristic
262	C₂²×C₂²⋊C₄	—	73	4	no	—
263	C₂²×C₂²⋊C₄	C₂×D₇₃	1	2	yes	—
264	C₂²×C₄²	—	73	2	no	—
265	C₂²×C₄²	C₂×D₇₃	1	1	yes	characteristic
266	#389	—	73	16	no	—
267	#385	—	73	32	no	—
268	#384	—	73	8	no	—
269	#380	—	73	16	no	—
270	C₄×C₄⋊C₄	—	73	8	no	—
271	C₂×#95	—	73	2	no	—
272	C₂×#95	—	73	4	no	—
273	C₂⁵	C₂²×D₇₃	1	2	yes	—
274	C₂²×D₄	Dic₁₄₆	1	8	yes	—
275	C₂²×D₄	D₂₉₂	1	8	yes	—
276	C₂²×D₄	C₂×Dic₇₃	1	8	yes	—
277	C₂²×D₄	C₂²×D₇₃	1	4	yes	—
278	C₂³×C₄	—	2	8	no	—
279	C₂³×C₄	—	2	8	no	—
280	C₂³×C₄	—	292	8	no	—
281	C₂³×C₄	—	73	16	no	—
282	C₂³×C₄	—	73	2	no	—
283	C₂³×C₄	—	73	2	no	—
284	C₂³×C₄	—	73	4	no	—
285	C₂³×C₄	—	146	16	no	—
286	C₂³×C₄	—	146	16	no	—
287	C₂³×C₄	C₂×Dic₇₃	1	16	yes	complemented
288	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
289	C₂³×C₄	C₂²×D₇₃	1	2	yes	—
290	C₂³×C₄	C₂²×D₇₃	1	8	yes	—
291	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
292	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
293	C₄×D₄	—	146	64	no	—
294	C₄×D₄	C₂×Dic₇₃	1	64	yes	complemented
295	C₂×C₄⋊C₄	—	292	4	no	—
296	C₂×C₄⋊C₄	—	73	8	no	—
297	C₂×C₄⋊C₄	—	73	8	no	—
298	C₂×C₄⋊C₄	—	73	4	no	—
299	C₂×C₄⋊C₄	—	73	8	no	—
300	C₂×C₄⋊C₄	—	73	16	no	—
301	C₂×C₄⋊C₄	—	73	8	no	—
302	C₂×C₄⋊C₄	—	73	4	no	—
303	C₂×C₄⋊C₄	—	146	64	no	—
304	C₂×C₄⋊C₄	—	146	16	no	—
305	C₂×C₄⋊C₄	—	146	8	no	—
306	C₂×C₄⋊C₄	—	146	8	no	—
307	C₂×C₄⋊C₄	—	146	4	no	—
308	C₂×C₄⋊C₄	C₂×Dic₇₃	1	8	yes	complemented
309	C₂×C₄⋊C₄	C₂²×D₇₃	1	4	yes	—
310	C₂×C₂²⋊C₄	—	73	16	no	—
311	C₂×C₂²⋊C₄	—	146	16	no	—
312	C₂×C₂²⋊C₄	C₂×Dic₇₃	1	16	yes	complemented
313	C₂×C₂²⋊C₄	C₂²×D₇₃	1	8	yes	—
314	C₂×C₄²	—	73	8	no	—
315	C₂×C₄²	—	146	8	no	—
316	C₂×C₄²	C₂×Dic₇₃	1	8	yes	complemented
317	C₂×C₄²	C₂²×D₇₃	1	4	yes	—
318	#95	—	73	8	no	—
319	#95	—	73	16	no	—
320	C₂⁴	—	2	4	no	—
321	C₂⁴	—	2	4	no	—
322	C₂⁴	—	2	4	no	—
323	C₂⁴	—	2	4	no	—
324	C₂⁴	C₂²×Dic₇₃	1	8	yes	—
325	C₂⁴	C₂×D₂₉₂	1	8	yes	—
326	C₂⁴	C₂×Dic₁₄₆	1	8	yes	—
327	C₂⁴	C₂³×D₇₃	1	4	yes	—
328	C₂⁴	C₂³×D₇₃	1	1	yes	characteristic
329	C₂×D₄	C₄⋊Dic₇₃	1	64	yes	direct product factor
330	C₂×D₄	C₂²×Dic₇₃	1	16	yes	—
331	C₂×D₄	C₂×D₂₉₂	1	16	yes	—
332	C₂×D₄	C₂×Dic₁₄₆	1	16	yes	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	64	no	—
338	C₂²×C₄	—	2	16	no	—
339	C₂²×C₄	—	2	16	no	—
340	C₂²×C₄	—	292	64	no	—
341	C₂²×C₄	—	292	16	no	—
342	C₂²×C₄	—	73	8	no	—
343	C₂²×C₄	—	73	4	no	—
344	C₂²×C₄	—	73	4	no	—
345	C₂²×C₄	—	73	8	no	—
346	C₂²×C₄	—	146	32	no	—
347	C₂²×C₄	—	146	8	no	—
348	C₂²×C₄	—	146	4	no	—
349	C₂²×C₄	—	146	8	no	—
350	C₂²×C₄	—	146	32	no	—
351	C₂²×C₄	—	146	4	no	—
352	C₂²×C₄	—	146	8	no	—
353	C₂²×C₄	—	146	4	no	—
354	C₂²×C₄	—	146	4	no	—
355	C₂²×C₄	—	146	4	no	—
356	C₂²×C₄	C₂²×Dic₇₃	1	4	yes	—
357	C₂²×C₄	C₂²×Dic₇₃	1	8	yes	—
358	C₂²×C₄	C₂²×Dic₇₃	1	4	yes	—
359	C₂²×C₄	C₂²×Dic₇₃	1	4	yes	—
360	C₂²×C₄	C₂²×Dic₇₃	1	32	yes	complemented
361	C₂²×C₄	D₄×D₇₃	1	4	yes	—
362	C₂²×C₄	C₂×D₂₉₂	1	4	yes	—
363	C₂²×C₄	C₂×Dic₁₄₆	1	4	yes	—
364	C₂²×C₄	#11924027	1	4	yes	—
365	C₂²×C₄	C₂³×D₇₃	1	2	yes	—
366	C₂²×C₄	C₂³×D₇₃	1	4	yes	—
367	C₂²×C₄	C₂³×D₇₃	1	2	yes	—
368	C₂²×C₄	C₂³×D₇₃	1	2	yes	—
369	C₄⋊C₄	—	292	8	no	—
370	C₄⋊C₄	—	73	16	no	—
371	C₄⋊C₄	—	146	32	no	—
372	C₄⋊C₄	—	146	16	no	—
373	C₄⋊C₄	—	146	16	no	—
374	C₄⋊C₄	—	146	8	no	—
375	C₄⋊C₄	C₂²×Dic₇₃	1	16	yes	complemented
376	C₂²⋊C₄	—	146	32	no	—
377	C₂²⋊C₄	C₂²×Dic₇₃	1	32	yes	complemented
378	C₄²	—	146	16	no	—
379	C₄²	C₂²×Dic₇₃	1	16	yes	complemented
380	C₂³	—	2	4	no	—
381	C₂³	—	2	4	no	—
382	C₂³	—	2	4	no	—
383	C₂³	—	2	4	no	—
384	C₂³	—	2	16	no	—
385	C₂³	—	2	16	no	—
386	C₂³	—	2	16	no	—
387	C₂³	—	2	16	no	—
388	C₂³	—	2	16	no	—
389	C₂³	—	2	16	no	—
390	C₂³	C₂×C₄⋊Dic₇₃	1	32	yes	complemented
391	C₂³	C₂³×Dic₇₃	1	8	yes	—
392	C₂³	C₂³×Dic₇₃	1	2	yes	—
393	C₂³	C₂×D₄×D₇₃	1	2	yes	—
394	C₂³	C₂²×D₂₉₂	1	8	yes	—
395	C₂³	C₂²×D₂₉₂	1	2	yes	—
396	C₂³	C₂²×Dic₁₄₆	1	8	yes	—
397	C₂³	C₂²×Dic₁₄₆	1	2	yes	—
398	C₂³	C₂×#11924027	1	2	yes	—
399	C₂³	#14556637	1	2	yes	—
400	C₂³	#14556638	1	2	yes	—
401	C₂³	C₂⁴×D₇₃	1	1	yes	characteristic
402	D₄	C₂×C₄⋊Dic₇₃	1	64	yes	direct product factor
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	16	no	—
408	C₂×C₄	—	2	8	no	—
409	C₂×C₄	—	2	64	no	—
410	C₂×C₄	—	292	16	no	—
411	C₂×C₄	—	292	8	no	—
412	C₂×C₄	—	292	64	no	—
413	C₂×C₄	—	73	8	no	—
414	C₂×C₄	—	146	8	no	—
415	C₂×C₄	—	146	4	no	—
416	C₂×C₄	—	146	8	no	—
417	C₂×C₄	—	146	4	no	—
418	C₂×C₄	—	146	8	no	—
419	C₂×C₄	—	146	4	no	—
420	C₂×C₄	—	146	4	no	—
421	C₂×C₄	—	146	4	no	—
422	C₂×C₄	—	146	16	no	—
423	C₂×C₄	C₂×C₄⋊Dic₇₃	1	16	yes	complemented
424	C₂×C₄	D₄×Dic₇₃	1	16	yes	complemented
425	C₂×C₄	C₂³×Dic₇₃	1	4	yes	—
426	C₂×C₄	C₂³×Dic₇₃	1	8	yes	—
427	C₂×C₄	C₂³×Dic₇₃	1	4	yes	—
428	C₂×C₄	C₂³×Dic₇₃	1	4	yes	—
429	C₂×C₄	C₂×D₄×D₇₃	1	4	yes	—
430	C₂×C₄	C₂²×D₂₉₂	1	4	yes	—
431	C₂×C₄	C₂²×Dic₁₄₆	1	4	yes	—
432	C₂×C₄	C₂×#11924027	1	4	yes	—
433	C₂²	—	2	64	no	—
434	C₂²	—	2	8	no	—
435	C₂²	—	2	8	no	—
436	C₂²	—	2	8	no	—
437	C₂²	—	2	8	no	—
438	C₂²	—	2	8	no	—
439	C₂²	—	2	8	no	—
440	C₂²	C₂²×C₄⋊Dic₇₃	1	4	yes	—
441	C₂²	C₂²×C₄⋊Dic₇₃	1	16	yes	complemented
442	C₂²	C₂×D₄×Dic₇₃	1	4	yes	—
443	C₂²	#17989070	1	4	yes	—
444	C₂²	D₄×D₂₉₂	1	4	yes	—
445	C₂²	#17989241	1	4	yes	—
446	C₂²	D₄×Dic₁₄₆	1	4	yes	—
447	C₂²	#17989294	1	4	yes	—
448	C₂²	C₂⁴×Dic₇₃	1	1	yes	characteristic
449	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
450	C₂²	C₂³×D₂₉₂	1	1	yes	characteristic
451	C₂²	C₂³×Dic₁₄₆	1	1	yes	characteristic
452	C₂²	C₂²×#11924027	1	1	yes	characteristic
453	C₂²	C₂×#14556637	1	1	yes	characteristic
454	C₂²	C₂×#14556638	1	1	yes	characteristic
455	C₄	—	2	8	no	—
456	C₄	—	2	4	no	—
457	C₄	—	292	8	no	—
458	C₄	—	292	4	no	—
459	C₄	—	146	8	no	—
460	C₄	C₂²×C₄⋊Dic₇₃	1	8	yes	complemented
461	C₄	C₂×D₄×Dic₇₃	1	8	yes	complemented
462	C₂	—	2	16	no	—
463	C₂	D₄×C₄⋊Dic₇₃	1	8	yes	direct product factor
464	C₂	C₂³×C₄⋊Dic₇₃	1	1	yes	characteristic
465	C₂	C₂²×D₄×Dic₇₃	1	1	yes	characteristic
466	C₂	C₂×#17989070	1	1	yes	characteristic
467	C₂	C₂×D₄×D₂₉₂	1	1	yes	characteristic
468	C₂	C₂×#17989241	1	1	yes	characteristic
469	C₂	C₂×D₄×Dic₁₄₆	1	1	yes	characteristic
470	C₂	C₂×#17989294	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₇₃
commutator	C₂²×C₇₃	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₇₃
Fitting	C₂²×C₄×D₄×C₇₃	C₂
socle	C₂⁴×C₇₃	C₂⁴
prime radical	C₂³×D₄×C₇₃	C₂²
cosocle	C₂³×C₇₃	C₂⁵
hypercenter	C₂²×C₄×D₄	D₇₃
hypocenter	C₇₃	C₂×D₄×C₄⋊C₄
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₂³×C₄⋊Dic₇₃	C₂	semidirect
3. D₄×C₄⋊Dic₇₃	C₂	direct (N × H)
4. C₂×#17988486	C₂	semidirect
5. C₂×#17988462	C₂	semidirect
6. C₂×#17988457	C₂	semidirect
7. C₂×#17988447	C₂	semidirect
8. C₂×C₄×C₄⋊Dic₇₃	C₂	semidirect
20. C₂²×C₄⋊Dic₇₃	C₂²	semidirect
23. #17988486	C₂²	semidirect
24. #17988462	C₂²	semidirect
25. #17988457	C₂²	semidirect
26. #17988447	C₂²	semidirect
27. C₄×C₄⋊Dic₇₃	C₂²	semidirect
32. C₂×C₄×D₄×C₇₃	C₄	semidirect
51. C₂×C₄⋊Dic₇₃	D₄	direct (N × H)
71. C₂³×C₄×C₇₃	C₂×C₄	semidirect
77. C₄×D₄×C₇₃	C₂×C₄	semidirect
78. C₂×C₄⋊C₄×C₇₃	C₂×C₄	semidirect
80. C₂×C₂²⋊C₄×C₇₃	C₂×C₄	semidirect
82. C₂×C₄²×C₇₃	C₂×C₄	semidirect
105. C₄⋊Dic₇₃	C₂×D₄	direct (N × H)
117. C₂×D₄×C₇₃	C₄⋊C₄	semidirect
132. C₂²×C₄×C₇₃	C₂²×C₄	semidirect
141. C₄⋊C₄×C₇₃	C₂²×C₄	semidirect
142. C₂²⋊C₄×C₇₃	C₂²×C₄	semidirect
143. C₄²×C₇₃	C₂²×C₄	semidirect
154. C₂³×C₇₃	C₂×C₄⋊C₄	semidirect
166. D₄×C₇₃	C₂×C₄⋊C₄	semidirect
174. C₂×C₄×C₇₃	C₂×C₄⋊C₄	semidirect
175. C₂×C₄×C₇₃	C₄×D₄	semidirect
205. C₂²×C₇₃	C₂²×C₄⋊C₄	semidirect
221. C₄×C₇₃	C₂²×C₄⋊C₄	semidirect
222. C₄×C₇₃	C₂×C₄×D₄	semidirect
228. C₂×C₇₃	D₄×C₄⋊C₄	semidirect
245. C₇₃	C₂×D₄×C₄⋊C₄	semidirect
251. C₂×C₄×D₄	Dic₇₃	semidirect
287. C₂³×C₄	C₂×Dic₇₃	semidirect
294. C₄×D₄	C₂×Dic₇₃	semidirect
308. C₂×C₄⋊C₄	C₂×Dic₇₃	semidirect
312. C₂×C₂²⋊C₄	C₂×Dic₇₃	semidirect
316. C₂×C₄²	C₂×Dic₇₃	semidirect
329. C₂×D₄	C₄⋊Dic₇₃	direct (N × H)
360. C₂²×C₄	C₂²×Dic₇₃	semidirect
375. C₄⋊C₄	C₂²×Dic₇₃	semidirect
377. C₂²⋊C₄	C₂²×Dic₇₃	semidirect
379. C₄²	C₂²×Dic₇₃	semidirect
390. C₂³	C₂×C₄⋊Dic₇₃	semidirect
402. D₄	C₂×C₄⋊Dic₇₃	direct (N × H)
423. C₂×C₄	C₂×C₄⋊Dic₇₃	semidirect
424. C₂×C₄	D₄×Dic₇₃	semidirect
441. C₂²	C₂²×C₄⋊Dic₇₃	semidirect
460. C₄	C₂²×C₄⋊Dic₇₃	semidirect
461. C₄	C₂×D₄×Dic₇₃	semidirect
463. C₂	D₄×C₄⋊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
C₂²×D₄×Dic₇₃	2
C₂³×C₄⋊Dic₇₃	2
D₄×C₄⋊Dic₇₃	2
C₂×#17988486	2
C₂×#17988462	2
C₂×#17988457	2
C₂×#17988447	2
C₂×C₄×C₄⋊Dic₇₃	2
C₂²×C₄×D₄×C₇₃	2
C₂×D₄×C₄⋊C₄	73

Subgroups — C2×D4×C4⋊Dic73 #33245271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄×C₄⋊Dic₇₃ #33245271