Subgroups — C₂×C₇₃×#3176 #32970084

Order 18688.

2098 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#540×C₇₃	C₂	1	2	yes	maximal, complemented
2	C₇₃×#3176	C₂	1	16	yes	maximal, direct product factor
3	C₂×#499×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#493×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#490×C₇₃	C₂	1	2	yes	maximal, complemented
6	C₂×#469×C₇₃	C₂	1	2	yes	maximal, complemented
7	C₂×#466×C₇₃	C₂	1	2	yes	maximal, complemented
8	C₂×#442×C₇₃	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×D₈×C₇₃	C₂	1	2	yes	maximal, complemented
10	C₂×#405×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×D₈×C₇₃	C₂²	1	2	yes	—
12	C₂²×D₈×C₇₃	C₂²	1	2	yes	—
13	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
15	#540×C₇₃	—	2	8	no	—
16	#540×C₇₃	C₂²	1	16	yes	complemented
17	C₂×#127×C₇₃	C₂²	1	2	yes	—
18	C₂×#125×C₇₃	C₂²	1	2	yes	—
19	C₂×#123×C₇₃	—	2	4	no	—
20	C₂×#121×C₇₃	—	2	4	no	—
21	C₂×#121×C₇₃	C₂²	1	4	yes	—
22	C₂×C₄×D₄×C₇₃	C₂²	1	4	yes	—
23	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
24	#499×C₇₃	C₂²	1	8	yes	complemented
25	#493×C₇₃	C₂²	1	8	yes	complemented
26	#490×C₇₃	C₂²	1	16	yes	complemented
27	#469×C₇₃	C₂²	1	16	yes	complemented
28	#466×C₇₃	C₂²	1	16	yes	complemented
29	#442×C₇₃	C₂²	1	16	yes	complemented
30	C₄×D₈×C₇₃	C₂²	1	16	yes	complemented
31	C₂×#107×C₇₃	C₂²	1	2	yes	—
32	C₂×#106×C₇₃	C₂²	1	2	yes	—
33	C₂×#102×C₇₃	C₂²	1	4	yes	—
34	C₂×#102×C₇₃	C₂²	1	4	yes	—
35	#405×C₇₃	C₂²	1	8	yes	complemented
36	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
37	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
40	C₂²×D₄×C₇₃	—	2	4	no	—
41	C₂²×D₄×C₇₃	—	2	4	no	—
42	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
43	C₂³×C₄×C₇₃	—	2	4	no	—
44	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
45	C₂×D₈×C₇₃	—	2	8	no	—
46	C₂×D₈×C₇₃	—	2	8	no	—
47	C₂×D₈×C₇₃	C₂³	1	8	yes	—
48	C₂×D₈×C₇₃	C₂³	1	8	yes	—
49	C₂×M₁₆×C₇₃	—	2	4	no	—
50	C₂×M₁₆×C₇₃	C₂³	1	4	yes	—
51	C₂²×C₈×C₇₃	—	2	4	no	—
52	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₇₃	C₂³	1	4	yes	—
55	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
57	#127×C₇₃	—	2	4	no	—
58	#127×C₇₃	C₂³	1	8	yes	—
59	#125×C₇₃	—	2	4	no	—
60	#125×C₇₃	C₂³	1	8	yes	—
61	#123×C₇₃	—	2	32	no	—
62	#121×C₇₃	—	2	8	no	—
63	#121×C₇₃	—	2	32	no	—
64	#121×C₇₃	C₂³	1	16	yes	—
65	C₄×D₄×C₇₃	—	2	8	no	—
66	C₄×D₄×C₇₃	C₂³	1	16	yes	—
67	#117×C₇₃	D₄	1	4	yes	—
68	#117×C₇₃	C₂³	1	4	yes	—
69	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
70	C₂×C₄⋊C₄×C₇₃	D₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
72	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
74	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
75	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
77	#107×C₇₃	C₂³	1	8	yes	—
78	#106×C₇₃	C₂³	1	8	yes	—
79	#102×C₇₃	C₂³	1	16	yes	—
80	#102×C₇₃	C₂³	1	16	yes	—
81	#97×C₇₃	C₂³	1	4	yes	—
82	#97×C₇₃	C₂³	1	4	yes	—
83	C₄×C₈×C₇₃	C₂³	1	4	yes	—
84	C₄×C₈×C₇₃	C₂³	1	4	yes	—
85	C₂⁴×C₇₃	—	2	4	no	—
86	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
87	C₂×D₄×C₇₃	—	2	16	no	—
88	C₂×D₄×C₇₃	—	2	4	no	—
89	C₂×D₄×C₇₃	—	2	16	no	—
90	C₂×D₄×C₇₃	—	2	8	no	—
91	C₂×D₄×C₇₃	—	2	8	no	—
92	C₂×D₄×C₇₃	—	8	8	no	—
93	C₂×D₄×C₇₃	—	8	8	no	—
94	C₂×D₄×C₇₃	C₂⁴	1	8	yes	—
95	C₂²×C₄×C₇₃	—	2	2	no	—
96	C₂²×C₄×C₇₃	—	2	2	no	—
97	C₂²×C₄×C₇₃	—	2	4	no	—
98	C₂²×C₄×C₇₃	—	2	16	no	—
99	C₂²×C₄×C₇₃	—	8	8	no	—
100	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
105	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
106	D₈×C₇₃	—	2	16	no	—
107	D₈×C₇₃	—	2	16	no	—
108	M₁₆×C₇₃	—	2	8	no	—
109	C₂×C₈×C₇₃	—	2	2	no	—
110	C₂×C₈×C₇₃	—	2	2	no	—
111	C₂×C₈×C₇₃	—	2	8	no	—
112	C₂×C₈×C₇₃	#41	1	4	yes	—
113	C₂×C₈×C₇₃	#41	1	4	yes	—
114	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
115	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
116	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
117	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
118	C₄⋊C₄×C₇₃	—	2	16	no	—
119	C₄⋊C₄×C₇₃	—	2	4	no	—
120	C₄⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
121	C₄⋊C₄×C₇₃	C₂⁴	1	8	yes	—
122	C₂²⋊C₄×C₇₃	—	2	16	no	—
123	C₂²⋊C₄×C₇₃	—	2	16	no	—
124	C₂²⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
125	C₄²×C₇₃	C₂×D₄	1	2	yes	—
126	C₄²×C₇₃	C₂×D₄	1	2	yes	—
127	C₄²×C₇₃	C₂⁴	1	2	yes	—
128	C₄²×C₇₃	C₂⁴	1	2	yes	—
129	C₂³×C₇₃	—	2	2	no	—
130	C₂³×C₇₃	—	2	4	no	—
131	C₂³×C₇₃	—	2	8	no	—
132	C₂³×C₇₃	—	4	8	no	—
133	C₂³×C₇₃	—	4	8	no	—
134	C₂³×C₇₃	—	4	8	no	—
135	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
136	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
137	D₄×C₇₃	—	2	8	no	—
138	D₄×C₇₃	—	2	8	no	—
139	D₄×C₇₃	—	4	8	no	—
140	D₄×C₇₃	—	8	16	no	—
141	D₄×C₇₃	—	8	16	no	—
142	C₂×C₄×C₇₃	—	2	2	no	—
143	C₂×C₄×C₇₃	—	2	4	no	—
144	C₂×C₄×C₇₃	—	2	4	no	—
145	C₂×C₄×C₇₃	—	2	4	no	—
146	C₂×C₄×C₇₃	—	2	2	no	—
147	C₂×C₄×C₇₃	—	2	2	no	—
148	C₂×C₄×C₇₃	—	2	8	no	—
149	C₂×C₄×C₇₃	—	4	8	no	—
150	C₂×C₄×C₇₃	—	8	16	no	—
151	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
152	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
153	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
154	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
156	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
157	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
158	C₈×C₇₃	—	2	2	no	—
159	C₈×C₇₃	—	2	2	no	—
160	C₈×C₇₃	C₂×#41	1	4	yes	—
161	C₈×C₇₃	C₂×#41	1	4	yes	—
162	C₂²×C₇₃	—	2	2	no	—
163	C₂²×C₇₃	—	2	4	no	—
164	C₂²×C₇₃	—	4	4	no	—
165	C₂²×C₇₃	—	4	8	no	—
166	C₂²×C₇₃	—	4	8	no	—
167	C₂²×C₇₃	—	4	8	no	—
168	C₂²×C₇₃	—	8	16	no	—
169	C₂²×C₇₃	#532	1	2	yes	—
170	C₂²×C₇₃	#576	1	4	yes	—
171	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
172	C₄×C₇₃	—	2	2	no	—
173	C₄×C₇₃	—	2	4	no	—
174	C₄×C₇₃	—	2	4	no	—
175	C₄×C₇₃	—	4	8	no	—
176	C₄×C₇₃	#532	1	2	yes	—
177	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
178	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
179	C₂×#3176	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂×C₇₃	—	4	2	no	—
181	C₂×C₇₃	—	8	8	no	—
182	C₂×C₇₃	#3176	1	4	yes	direct product factor
183	C₂×C₇₃	C₂×#532	1	1	yes	characteristic
184	C₂×C₇₃	C₂×#576	1	2	yes	—
185	C₂×#540	C₂×C₇₃	1	2	yes	complemented
186	#3176	C₂×C₇₃	1	16	yes	direct product factor
187	C₂×#499	C₂×C₇₃	1	1	yes	characteristic, complemented
188	C₂×#493	C₂×C₇₃	1	1	yes	characteristic, complemented
189	C₂×#490	C₂×C₇₃	1	2	yes	complemented
190	C₂×#469	C₂×C₇₃	1	2	yes	complemented
191	C₂×#466	C₂×C₇₃	1	2	yes	complemented
192	C₂×#442	C₂×C₇₃	1	2	yes	complemented
193	C₂×C₄×D₈	C₂×C₇₃	1	2	yes	complemented
194	C₂×#405	C₂×C₇₃	1	1	yes	characteristic, complemented
195	C₇₃	C₂×#3176	1	1	yes	characteristic, direct product factor, Sylow
196	C₂²×D₈	C₂²×C₇₃	1	2	yes	—
197	C₂²×D₈	C₂²×C₇₃	1	2	yes	—
198	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
199	C₂³×C₈	C₂²×C₇₃	1	1	yes	characteristic
200	#540	—	2	8	no	—
201	#540	C₂²×C₇₃	1	16	yes	complemented
202	C₂×#127	C₂²×C₇₃	1	2	yes	—
203	C₂×#125	C₂²×C₇₃	1	2	yes	—
204	C₂×#123	—	2	4	no	—
205	C₂×#121	—	2	4	no	—
206	C₂×#121	C₂²×C₇₃	1	4	yes	—
207	C₂×C₄×D₄	C₂²×C₇₃	1	4	yes	—
208	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
209	#499	C₂²×C₇₃	1	8	yes	complemented
210	#493	C₂²×C₇₃	1	8	yes	complemented
211	#490	C₂²×C₇₃	1	16	yes	complemented
212	#469	C₂²×C₇₃	1	16	yes	complemented
213	#466	C₂²×C₇₃	1	16	yes	complemented
214	#442	C₂²×C₇₃	1	16	yes	complemented
215	C₄×D₈	C₂²×C₇₃	1	16	yes	complemented
216	C₂×#107	C₂²×C₇₃	1	2	yes	—
217	C₂×#106	C₂²×C₇₃	1	2	yes	—
218	C₂×#102	C₂²×C₇₃	1	4	yes	—
219	C₂×#102	C₂²×C₇₃	1	4	yes	—
220	#405	C₂²×C₇₃	1	8	yes	complemented
221	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
222	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
223	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
224	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
225	C₂²×D₄	—	2	4	no	—
226	C₂²×D₄	—	2	4	no	—
227	C₂²×D₄	C₂³×C₇₃	1	4	yes	—
228	C₂³×C₄	—	2	4	no	—
229	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
230	C₂×D₈	—	2	8	no	—
231	C₂×D₈	—	2	8	no	—
232	C₂×D₈	C₂³×C₇₃	1	8	yes	—
233	C₂×D₈	C₂³×C₇₃	1	8	yes	—
234	C₂×M₁₆	—	2	4	no	—
235	C₂×M₁₆	C₂³×C₇₃	1	4	yes	—
236	C₂²×C₈	—	2	4	no	—
237	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
238	C₂²×C₈	C₂³×C₇₃	1	4	yes	—
239	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
240	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
241	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
242	#127	—	2	4	no	—
243	#127	C₂³×C₇₃	1	8	yes	—
244	#125	—	2	4	no	—
245	#125	C₂³×C₇₃	1	8	yes	—
246	#123	—	2	32	no	—
247	#121	—	2	8	no	—
248	#121	—	2	32	no	—
249	#121	C₂³×C₇₃	1	16	yes	—
250	C₄×D₄	—	2	8	no	—
251	C₄×D₄	C₂³×C₇₃	1	16	yes	—
252	#117	D₄×C₇₃	1	4	yes	—
253	#117	C₂³×C₇₃	1	4	yes	—
254	C₂×C₄⋊C₄	—	2	4	no	—
255	C₂×C₄⋊C₄	D₄×C₇₃	1	2	yes	—
256	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
257	C₂×C₂²⋊C₄	—	2	4	no	—
258	C₂×C₂²⋊C₄	—	2	4	no	—
259	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
260	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
261	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
262	#107	C₂³×C₇₃	1	8	yes	—
263	#106	C₂³×C₇₃	1	8	yes	—
264	#102	C₂³×C₇₃	1	16	yes	—
265	#102	C₂³×C₇₃	1	16	yes	—
266	#97	C₂³×C₇₃	1	4	yes	—
267	#97	C₂³×C₇₃	1	4	yes	—
268	C₄×C₈	C₂³×C₇₃	1	4	yes	—
269	C₄×C₈	C₂³×C₇₃	1	4	yes	—
270	C₂⁴	—	2	4	no	—
271	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
272	C₂×D₄	—	2	16	no	—
273	C₂×D₄	—	2	4	no	—
274	C₂×D₄	—	2	16	no	—
275	C₂×D₄	—	2	8	no	—
276	C₂×D₄	—	2	8	no	—
277	C₂×D₄	—	8	8	no	—
278	C₂×D₄	—	8	8	no	—
279	C₂×D₄	C₂⁴×C₇₃	1	8	yes	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	16	no	—
284	C₂²×C₄	—	8	8	no	—
285	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
286	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
287	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
288	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
289	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
290	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
291	D₈	—	2	16	no	—
292	D₈	—	2	16	no	—
293	M₁₆	—	2	8	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	8	no	—
297	C₂×C₈	#41×C₇₃	1	4	yes	—
298	C₂×C₈	#41×C₇₃	1	4	yes	—
299	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
300	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
301	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
302	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
303	C₄⋊C₄	—	2	16	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
306	C₄⋊C₄	C₂⁴×C₇₃	1	8	yes	—
307	C₂²⋊C₄	—	2	16	no	—
308	C₂²⋊C₄	—	2	16	no	—
309	C₂²⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
310	C₄²	C₂×D₄×C₇₃	1	2	yes	—
311	C₄²	C₂×D₄×C₇₃	1	2	yes	—
312	C₄²	C₂⁴×C₇₃	1	2	yes	—
313	C₄²	C₂⁴×C₇₃	1	2	yes	—
314	C₂³	—	2	2	no	—
315	C₂³	—	2	4	no	—
316	C₂³	—	2	8	no	—
317	C₂³	—	4	8	no	—
318	C₂³	—	4	8	no	—
319	C₂³	—	4	8	no	—
320	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
321	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
322	D₄	—	2	8	no	—
323	D₄	—	2	8	no	—
324	D₄	—	4	8	no	—
325	D₄	—	8	16	no	—
326	D₄	—	8	16	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	8	no	—
334	C₂×C₄	—	4	8	no	—
335	C₂×C₄	—	8	16	no	—
336	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
337	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
338	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
339	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
340	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
341	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
342	C₂×C₄	C₂⁵×C₇₃	1	1	yes	characteristic
343	C₈	—	2	2	no	—
344	C₈	—	2	2	no	—
345	C₈	C₂×#41×C₇₃	1	4	yes	—
346	C₈	C₂×#41×C₇₃	1	4	yes	—
347	C₂²	—	2	4	no	—
348	C₂²	—	2	2	no	—
349	C₂²	—	4	4	no	—
350	C₂²	—	4	8	no	—
351	C₂²	—	4	8	no	—
352	C₂²	—	4	8	no	—
353	C₂²	—	8	16	no	—
354	C₂²	#532×C₇₃	1	2	yes	—
355	C₂²	#576×C₇₃	1	4	yes	—
356	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
357	C₄	—	2	4	no	—
358	C₄	—	2	4	no	—
359	C₄	—	2	2	no	—
360	C₄	—	4	8	no	—
361	C₄	#532×C₇₃	1	2	yes	—
362	C₄	C₂²×#41×C₇₃	1	1	yes	characteristic
363	C₄	C₂²×#41×C₇₃	1	1	yes	characteristic
364	C₂	—	4	2	no	—
365	C₂	—	8	8	no	—
366	C₂	C₇₃×#3176	1	4	yes	direct product factor
367	C₂	C₂×#532×C₇₃	1	1	yes	characteristic
368	C₂	C₂×#576×C₇₃	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×#117×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#540×C₇₃	C₂	semidirect
2. C₇₃×#3176	C₂	direct (N × H)
3. C₂×#499×C₇₃	C₂	semidirect
4. C₂×#493×C₇₃	C₂	semidirect
5. C₂×#490×C₇₃	C₂	semidirect
6. C₂×#469×C₇₃	C₂	semidirect
7. C₂×#466×C₇₃	C₂	semidirect
8. C₂×#442×C₇₃	C₂	semidirect
9. C₂×C₄×D₈×C₇₃	C₂	semidirect
10. C₂×#405×C₇₃	C₂	semidirect
16. #540×C₇₃	C₂²	semidirect
24. #499×C₇₃	C₂²	semidirect
25. #493×C₇₃	C₂²	semidirect
26. #490×C₇₃	C₂²	semidirect
27. #469×C₇₃	C₂²	semidirect
28. #466×C₇₃	C₂²	semidirect
29. #442×C₇₃	C₂²	semidirect
30. C₄×D₈×C₇₃	C₂²	semidirect
35. #405×C₇₃	C₂²	semidirect
179. C₂×#3176	C₇₃	direct (N × H)
182. C₂×C₇₃	#3176	direct (N × H)
185. C₂×#540	C₂×C₇₃	semidirect
186. #3176	C₂×C₇₃	direct (N × H)
187. C₂×#499	C₂×C₇₃	semidirect
188. C₂×#493	C₂×C₇₃	semidirect
189. C₂×#490	C₂×C₇₃	semidirect
190. C₂×#469	C₂×C₇₃	semidirect
191. C₂×#466	C₂×C₇₃	semidirect
192. C₂×#442	C₂×C₇₃	semidirect
193. C₂×C₄×D₈	C₂×C₇₃	semidirect
194. C₂×#405	C₂×C₇₃	semidirect
195. C₇₃	C₂×#3176	direct (N × H)
201. #540	C₂²×C₇₃	semidirect
209. #499	C₂²×C₇₃	semidirect
210. #493	C₂²×C₇₃	semidirect
211. #490	C₂²×C₇₃	semidirect
212. #469	C₂²×C₇₃	semidirect
213. #466	C₂²×C₇₃	semidirect
214. #442	C₂²×C₇₃	semidirect
215. C₄×D₈	C₂²×C₇₃	semidirect
220. #405	C₂²×C₇₃	semidirect
366. C₂	C₇₃×#3176	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×#540×C₇₃	2
C₇₃×#3176	2
C₂×#499×C₇₃	2
C₂×#493×C₇₃	2
C₂×#490×C₇₃	2
C₂×#469×C₇₃	2
C₂×#466×C₇₃	2
C₂×#442×C₇₃	2
C₂×C₄×D₈×C₇₃	2
C₂×#405×C₇₃	2
C₂×#3176	73

Subgroups — C2×C73×#3176 #32970084

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₃×#3176 #32970084