Subgroups — C₂×C₇₃×#2191 #32942933

Order 18688.

1128 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#575×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#510×C₇₃	C₂	1	2	yes	maximal, complemented
3	C₂×#470×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2191	C₂	1	8	yes	maximal, direct product factor
5	C₂×#360×C₇₃	C₂	1	2	yes	maximal, complemented
6	C₂×#349×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#41×C₇₃	—	2	1	no	—
8	#575×C₇₃	—	2	4	no	—
9	#575×C₇₃	—	2	2	no	—
10	#575×C₇₃	C₂²	1	4	yes	—
11	C₂×#137×C₇₃	—	2	2	no	—
12	C₂×AGL(1,ℤ/8)×C₇₃	—	2	2	no	—
13	C₂×#135×C₇₃	—	2	1	no	—
14	C₂×#135×C₇₃	C₂²	1	2	yes	—
15	C₂²×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
16	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊Q₈×C₇₃	—	2	1	no	—
18	#510×C₇₃	—	2	4	no	—
19	#510×C₇₃	C₂²	1	8	yes	complemented
20	C₂×Q₃₂×C₇₃	—	2	2	no	—
21	C₂×SD₃₂×C₇₃	—	2	2	no	—
22	C₂×M₃₂×C₇₃	C₂²	1	2	yes	complemented
23	#470×C₇₃	—	2	2	no	—
24	#470×C₇₃	C₂²	1	4	yes	complemented
25	C₂×#106×C₇₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×#103×C₇₃	—	2	1	no	—
27	#360×C₇₃	C₂²	1	8	yes	complemented
28	#349×C₇₃	C₂²	1	4	yes	complemented
29	C₂×#41×C₇₃	—	2	2	no	—
30	C₂×#41×C₇₃	—	2	4	no	—
31	C₂×#41×C₇₃	—	2	4	no	—
32	C₂×#41×C₇₃	—	2	2	no	—
33	C₂×#41×C₇₃	—	4	1	no	—
34	C₂×#41×C₇₃	—	4	2	no	—
35	C₂×#41×C₇₃	—	4	1	no	—
36	C₂×#41×C₇₃	—	4	2	no	—
37	C₂²×Q₈×C₇₃	—	2	1	no	—
38	C₂²×Q₈×C₇₃	—	2	1	no	—
39	C₂²×D₄×C₇₃	—	2	1	no	—
40	C₂²×D₄×C₇₃	—	4	1	no	—
41	C₂³×C₄×C₇₃	—	4	1	no	—
42	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
43	#137×C₇₃	—	2	8	no	—
44	#137×C₇₃	—	2	8	no	—
45	AGL(1,ℤ/8)×C₇₃	—	2	8	no	—
46	AGL(1,ℤ/8)×C₇₃	—	2	8	no	—
47	#135×C₇₃	—	2	4	no	—
48	#135×C₇₃	—	2	4	no	—
49	#135×C₇₃	—	2	2	no	—
50	#135×C₇₃	—	2	2	no	—
51	#135×C₇₃	D₄	1	4	yes	—
52	#135×C₇₃	C₂³	1	4	yes	—
53	C₂×Q₁₆×C₇₃	—	2	1	no	—
54	C₂×Q₁₆×C₇₃	—	2	2	no	—
55	C₂×Q₁₆×C₇₃	—	2	2	no	—
56	C₂×Q₁₆×C₇₃	—	2	1	no	—
57	C₂×Q₁₆×C₇₃	D₄	1	2	yes	—
58	C₂×Q₁₆×C₇₃	C₂³	1	2	yes	complemented
59	C₂×SD₁₆×C₇₃	—	2	2	no	—
60	C₂×SD₁₆×C₇₃	—	2	2	no	—
61	C₂×D₈×C₇₃	—	2	1	no	—
62	C₂×D₈×C₇₃	D₄	1	2	yes	—
63	C₂×M₁₆×C₇₃	—	2	2	no	—
64	C₂×M₁₆×C₇₃	—	2	2	no	—
65	C₂×M₁₆×C₇₃	D₄	1	2	yes	—
66	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
67	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
68	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
69	C₂²⋊Q₈×C₇₃	—	2	4	no	—
70	C₂²⋊Q₈×C₇₃	—	4	2	no	—
71	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
72	C₂×C₄⋊C₄×C₇₃	—	4	1	no	—
73	C₂×C₂²⋊C₄×C₇₃	—	4	1	no	—
74	Q₃₂×C₇₃	—	2	8	no	—
75	SD₃₂×C₇₃	—	2	8	no	—
76	M₃₂×C₇₃	—	2	2	no	—
77	M₃₂×C₇₃	C₂³	1	4	yes	complemented
78	C₂×C₁₆×C₇₃	—	2	2	no	—
79	#106×C₇₃	—	2	1	no	—
80	#106×C₇₃	C₂³	1	2	yes	complemented
81	#103×C₇₃	—	2	4	no	—
82	C₂⁴×C₇₃	—	4	1	no	—
83	C₂⁴×C₇₃	D₈	1	1	yes	characteristic
84	#41×C₇₃	—	2	8	no	—
85	#41×C₇₃	—	2	4	no	—
86	#41×C₇₃	—	2	4	no	—
87	#41×C₇₃	—	4	4	no	—
88	#41×C₇₃	—	4	4	no	—
89	#41×C₇₃	—	4	4	no	—
90	#41×C₇₃	—	4	4	no	—
91	#41×C₇₃	—	4	4	no	—
92	#41×C₇₃	—	4	2	no	—
93	#41×C₇₃	—	4	2	no	—
94	C₂×Q₈×C₇₃	—	2	4	no	—
95	C₂×Q₈×C₇₃	—	2	2	no	—
96	C₂×Q₈×C₇₃	—	2	2	no	—
97	C₂×Q₈×C₇₃	—	4	1	no	—
98	C₂×Q₈×C₇₃	—	4	2	no	—
99	C₂×Q₈×C₇₃	—	4	1	no	—
100	C₂×Q₈×C₇₃	—	4	1	no	—
101	C₂×Q₈×C₇₃	—	4	1	no	—
102	C₂×Q₈×C₇₃	—	4	1	no	—
103	C₂×Q₈×C₇₃	—	4	1	no	—
104	C₂×D₄×C₇₃	—	2	4	no	—
105	C₂×D₄×C₇₃	—	2	2	no	—
106	C₂×D₄×C₇₃	—	4	1	no	—
107	C₂×D₄×C₇₃	—	4	2	no	—
108	C₂×D₄×C₇₃	—	4	4	no	—
109	C₂×D₄×C₇₃	—	4	2	no	—
110	C₂×D₄×C₇₃	—	4	4	no	—
111	C₂×D₄×C₇₃	—	4	2	no	—
112	C₂²×C₄×C₇₃	—	2	1	no	—
113	C₂²×C₄×C₇₃	—	2	1	no	—
114	C₂²×C₄×C₇₃	—	2	1	no	—
115	C₂²×C₄×C₇₃	—	2	1	no	—
116	C₂²×C₄×C₇₃	—	4	2	no	—
117	C₂²×C₄×C₇₃	—	4	4	no	—
118	C₂²×C₄×C₇₃	—	4	4	no	—
119	C₂²×C₄×C₇₃	—	4	1	no	—
120	C₂²×C₄×C₇₃	—	4	2	no	—
121	C₂²×C₄×C₇₃	—	4	1	no	—
122	C₂²×C₄×C₇₃	—	4	1	no	—
123	C₂²×C₄×C₇₃	D₈	1	1	yes	characteristic
124	C₂²×C₄×C₇₃	D₈	1	2	yes	—
125	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
127	Q₁₆×C₇₃	—	2	4	no	—
128	Q₁₆×C₇₃	—	2	2	no	—
129	Q₁₆×C₇₃	—	2	4	no	—
130	Q₁₆×C₇₃	—	4	2	no	—
131	Q₁₆×C₇₃	C₂×D₄	1	4	yes	—
132	SD₁₆×C₇₃	—	2	8	no	—
133	SD₁₆×C₇₃	—	2	4	no	—
134	SD₁₆×C₇₃	—	2	4	no	—
135	D₈×C₇₃	—	2	4	no	—
136	D₈×C₇₃	—	2	2	no	—
137	D₈×C₇₃	C₂×D₄	1	4	yes	—
138	M₁₆×C₇₃	—	2	4	no	—
139	M₁₆×C₇₃	—	2	4	no	—
140	C₂×C₈×C₇₃	—	2	1	no	—
141	C₂×C₈×C₇₃	—	2	1	no	—
142	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
145	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
146	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
147	C₄⋊C₄×C₇₃	—	2	2	no	—
148	C₄⋊C₄×C₇₃	—	4	1	no	—
149	C₄⋊C₄×C₇₃	—	4	4	no	—
150	C₂²⋊C₄×C₇₃	—	4	4	no	—
151	C₁₆×C₇₃	—	2	4	no	—
152	C₂³×C₇₃	—	2	1	no	—
153	C₂³×C₇₃	—	2	1	no	—
154	C₂³×C₇₃	—	4	2	no	—
155	C₂³×C₇₃	—	4	4	no	—
156	C₂³×C₇₃	—	4	2	no	—
157	C₂³×C₇₃	—	8	4	no	—
158	C₂³×C₇₃	C₂×D₈	1	1	yes	characteristic
159	C₂³×C₇₃	C₂×D₈	1	2	yes	—
160	Q₈×C₇₃	—	2	4	no	—
161	Q₈×C₇₃	—	4	4	no	—
162	Q₈×C₇₃	—	4	2	no	—
163	Q₈×C₇₃	—	4	2	no	—
164	Q₈×C₇₃	—	4	2	no	—
165	Q₈×C₇₃	—	8	1	no	—
166	Q₈×C₇₃	—	8	1	no	—
167	D₄×C₇₃	—	2	4	no	—
168	D₄×C₇₃	—	4	4	no	—
169	D₄×C₇₃	—	4	8	no	—
170	D₄×C₇₃	—	4	4	no	—
171	D₄×C₇₃	—	4	4	no	—
172	D₄×C₇₃	—	4	2	no	—
173	C₂×C₄×C₇₃	—	2	1	no	—
174	C₂×C₄×C₇₃	—	2	1	no	—
175	C₂×C₄×C₇₃	—	2	2	no	—
176	C₂×C₄×C₇₃	—	2	2	no	—
177	C₂×C₄×C₇₃	—	2	2	no	—
178	C₂×C₄×C₇₃	—	2	2	no	—
179	C₂×C₄×C₇₃	—	4	8	no	—
180	C₂×C₄×C₇₃	—	4	4	no	—
181	C₂×C₄×C₇₃	—	4	2	no	—
182	C₂×C₄×C₇₃	—	4	4	no	—
183	C₂×C₄×C₇₃	—	4	4	no	—
184	C₂×C₄×C₇₃	—	4	2	no	—
185	C₂×C₄×C₇₃	—	4	2	no	—
186	C₂×C₄×C₇₃	—	8	2	no	—
187	C₂×C₄×C₇₃	—	8	1	no	—
188	C₂×C₄×C₇₃	—	8	1	no	—
189	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
190	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
191	C₂×C₄×C₇₃	C₂×D₈	1	2	yes	—
192	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
193	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
194	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
195	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
196	C₈×C₇₃	—	2	2	no	—
197	C₈×C₇₃	#120	1	2	yes	—
198	C₈×C₇₃	C₂²×D₄	1	2	yes	—
199	C₂²×C₇₃	—	2	2	no	—
200	C₂²×C₇₃	—	2	2	no	—
201	C₂²×C₇₃	—	4	2	no	—
202	C₂²×C₇₃	—	4	2	no	—
203	C₂²×C₇₃	—	4	4	no	—
204	C₂²×C₇₃	—	8	1	no	—
205	C₂²×C₇₃	—	8	8	no	—
206	C₂²×C₇₃	—	8	4	no	—
207	C₂²×C₇₃	#447	1	1	yes	characteristic
208	C₂²×C₇₃	#447	1	1	yes	characteristic
209	C₂²×C₇₃	C₂²×D₈	1	1	yes	characteristic
210	C₄×C₇₃	—	2	2	no	—
211	C₄×C₇₃	—	4	4	no	—
212	C₄×C₇₃	—	8	2	no	—
213	C₄×C₇₃	—	8	2	no	—
214	C₄×C₇₃	#447	1	1	yes	characteristic
215	C₄×C₇₃	#447	1	1	yes	characteristic
216	C₄×C₇₃	C₂×#120	1	1	yes	characteristic
217	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
218	C₂×#2191	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂×C₇₃	—	2	1	no	—
220	C₂×C₇₃	—	2	1	no	—
221	C₂×C₇₃	—	4	2	no	—
222	C₂×C₇₃	—	8	4	no	—
223	C₂×C₇₃	#2191	1	2	yes	direct product factor
224	C₂×C₇₃	C₂×#447	1	1	yes	characteristic
225	C₂×#575	C₂×C₇₃	1	1	yes	characteristic
226	C₂×#510	C₂×C₇₃	1	2	yes	complemented
227	C₂×#470	C₂×C₇₃	1	1	yes	characteristic, complemented
228	#2191	C₂×C₇₃	1	8	yes	direct product factor
229	C₂×#360	C₂×C₇₃	1	2	yes	complemented
230	C₂×#349	C₂×C₇₃	1	1	yes	characteristic, complemented
231	C₇₃	C₂×#2191	1	1	yes	characteristic, direct product factor, Sylow
232	C₂²×#41	—	2	1	no	—
233	#575	—	2	4	no	—
234	#575	—	2	2	no	—
235	#575	C₂²×C₇₃	1	4	yes	—
236	C₂×#137	—	2	2	no	—
237	C₂×AGL(1,ℤ/8)	—	2	2	no	—
238	C₂×#135	—	2	1	no	—
239	C₂×#135	C₂²×C₇₃	1	2	yes	—
240	C₂²×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
241	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
242	C₂×C₂²⋊Q₈	—	2	1	no	—
243	#510	—	2	4	no	—
244	#510	C₂²×C₇₃	1	8	yes	complemented
245	C₂×Q₃₂	—	2	2	no	—
246	C₂×SD₃₂	—	2	2	no	—
247	C₂×M₃₂	C₂²×C₇₃	1	2	yes	complemented
248	#470	—	2	2	no	—
249	#470	C₂²×C₇₃	1	4	yes	complemented
250	C₂×#106	C₂²×C₇₃	1	1	yes	characteristic, complemented
251	C₂×#103	—	2	1	no	—
252	#360	C₂²×C₇₃	1	8	yes	complemented
253	#349	C₂²×C₇₃	1	4	yes	complemented
254	C₂×#41	—	2	2	no	—
255	C₂×#41	—	2	4	no	—
256	C₂×#41	—	2	2	no	—
257	C₂×#41	—	2	4	no	—
258	C₂×#41	—	4	1	no	—
259	C₂×#41	—	4	2	no	—
260	C₂×#41	—	4	1	no	—
261	C₂×#41	—	4	2	no	—
262	C₂²×Q₈	—	2	1	no	—
263	C₂²×Q₈	—	2	1	no	—
264	C₂²×D₄	—	2	1	no	—
265	C₂²×D₄	—	4	1	no	—
266	C₂³×C₄	—	4	1	no	—
267	C₂³×C₄	D₄×C₇₃	1	1	yes	characteristic
268	#137	—	2	8	no	—
269	#137	—	2	8	no	—
270	AGL(1,ℤ/8)	—	2	8	no	—
271	AGL(1,ℤ/8)	—	2	8	no	—
272	#135	—	2	4	no	—
273	#135	—	2	4	no	—
274	#135	—	2	2	no	—
275	#135	—	2	2	no	—
276	#135	D₄×C₇₃	1	4	yes	—
277	#135	C₂³×C₇₃	1	4	yes	—
278	C₂×Q₁₆	—	2	1	no	—
279	C₂×Q₁₆	—	2	2	no	—
280	C₂×Q₁₆	—	2	2	no	—
281	C₂×Q₁₆	—	2	1	no	—
282	C₂×Q₁₆	D₄×C₇₃	1	2	yes	—
283	C₂×Q₁₆	C₂³×C₇₃	1	2	yes	complemented
284	C₂×SD₁₆	—	2	2	no	—
285	C₂×SD₁₆	—	2	2	no	—
286	C₂×D₈	—	2	1	no	—
287	C₂×D₈	D₄×C₇₃	1	2	yes	—
288	C₂×M₁₆	—	2	2	no	—
289	C₂×M₁₆	—	2	2	no	—
290	C₂×M₁₆	D₄×C₇₃	1	2	yes	—
291	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
292	C₂²×C₈	D₄×C₇₃	1	1	yes	characteristic
293	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
294	C₂²⋊Q₈	—	2	4	no	—
295	C₂²⋊Q₈	—	4	2	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	4	1	no	—
298	C₂×C₂²⋊C₄	—	4	1	no	—
299	Q₃₂	—	2	8	no	—
300	SD₃₂	—	2	8	no	—
301	M₃₂	—	2	2	no	—
302	M₃₂	C₂³×C₇₃	1	4	yes	complemented
303	C₂×C₁₆	—	2	2	no	—
304	#106	—	2	1	no	—
305	#106	C₂³×C₇₃	1	2	yes	complemented
306	#103	—	2	4	no	—
307	C₂⁴	—	4	1	no	—
308	C₂⁴	D₈×C₇₃	1	1	yes	characteristic
309	#41	—	2	8	no	—
310	#41	—	2	4	no	—
311	#41	—	2	4	no	—
312	#41	—	4	4	no	—
313	#41	—	4	4	no	—
314	#41	—	4	4	no	—
315	#41	—	4	4	no	—
316	#41	—	4	4	no	—
317	#41	—	4	2	no	—
318	#41	—	4	2	no	—
319	C₂×Q₈	—	2	4	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	4	1	no	—
323	C₂×Q₈	—	4	2	no	—
324	C₂×Q₈	—	4	1	no	—
325	C₂×Q₈	—	4	1	no	—
326	C₂×Q₈	—	4	1	no	—
327	C₂×Q₈	—	4	1	no	—
328	C₂×Q₈	—	4	1	no	—
329	C₂×D₄	—	2	4	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	4	1	no	—
332	C₂×D₄	—	4	2	no	—
333	C₂×D₄	—	4	4	no	—
334	C₂×D₄	—	4	2	no	—
335	C₂×D₄	—	4	4	no	—
336	C₂×D₄	—	4	2	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	—	4	4	no	—
343	C₂²×C₄	—	4	4	no	—
344	C₂²×C₄	—	4	1	no	—
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	—	4	1	no	—
347	C₂²×C₄	—	4	1	no	—
348	C₂²×C₄	D₈×C₇₃	1	1	yes	characteristic
349	C₂²×C₄	D₈×C₇₃	1	2	yes	—
350	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
351	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
352	Q₁₆	—	2	4	no	—
353	Q₁₆	—	2	2	no	—
354	Q₁₆	—	2	4	no	—
355	Q₁₆	—	4	2	no	—
356	Q₁₆	C₂×D₄×C₇₃	1	4	yes	—
357	SD₁₆	—	2	8	no	—
358	SD₁₆	—	2	4	no	—
359	SD₁₆	—	2	4	no	—
360	D₈	—	2	4	no	—
361	D₈	—	2	2	no	—
362	D₈	C₂×D₄×C₇₃	1	4	yes	—
363	M₁₆	—	2	4	no	—
364	M₁₆	—	2	4	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
368	C₂×C₈	C₂×D₄×C₇₃	1	1	yes	characteristic
369	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
370	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
371	C₂×C₈	C₂⁴×C₇₃	1	1	yes	characteristic
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	4	1	no	—
374	C₄⋊C₄	—	4	4	no	—
375	C₂²⋊C₄	—	4	4	no	—
376	C₁₆	—	2	4	no	—
377	C₂³	—	2	1	no	—
378	C₂³	—	2	1	no	—
379	C₂³	—	4	2	no	—
380	C₂³	—	4	4	no	—
381	C₂³	—	4	2	no	—
382	C₂³	—	8	4	no	—
383	C₂³	C₂×D₈×C₇₃	1	1	yes	characteristic
384	C₂³	C₂×D₈×C₇₃	1	2	yes	—
385	Q₈	—	2	4	no	—
386	Q₈	—	4	4	no	—
387	Q₈	—	4	2	no	—
388	Q₈	—	4	2	no	—
389	Q₈	—	4	2	no	—
390	Q₈	—	8	1	no	—
391	Q₈	—	8	1	no	—
392	D₄	—	2	4	no	—
393	D₄	—	4	4	no	—
394	D₄	—	4	8	no	—
395	D₄	—	4	4	no	—
396	D₄	—	4	4	no	—
397	D₄	—	4	2	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	8	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	4	no	—
408	C₂×C₄	—	4	4	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	8	2	no	—
412	C₂×C₄	—	8	1	no	—
413	C₂×C₄	—	8	1	no	—
414	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
415	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
416	C₂×C₄	C₂×D₈×C₇₃	1	2	yes	—
417	C₂×C₄	C₂×D₈×C₇₃	1	1	yes	characteristic
418	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
419	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
420	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
421	C₈	—	2	2	no	—
422	C₈	#120×C₇₃	1	2	yes	—
423	C₈	C₂²×D₄×C₇₃	1	2	yes	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	4	no	—
429	C₂²	—	8	1	no	—
430	C₂²	—	8	8	no	—
431	C₂²	—	8	4	no	—
432	C₂²	#447×C₇₃	1	1	yes	characteristic
433	C₂²	#447×C₇₃	1	1	yes	characteristic
434	C₂²	C₂²×D₈×C₇₃	1	1	yes	characteristic
435	C₄	—	2	2	no	—
436	C₄	—	4	4	no	—
437	C₄	—	8	2	no	—
438	C₄	—	8	2	no	—
439	C₄	#447×C₇₃	1	1	yes	characteristic
440	C₄	#447×C₇₃	1	1	yes	characteristic
441	C₄	C₂×#120×C₇₃	1	1	yes	characteristic
442	C₄	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	—	4	2	no	—
446	C₂	—	8	4	no	—
447	C₂	C₇₃×#2191	1	2	yes	direct product factor
448	C₂	C₂×#447×C₇₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	#447
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₇₃
prime radical	C₂×#575×C₇₃	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂²×C₄×C₇₃ ◁ C₂²×M₁₆×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#510×C₇₃	C₂	semidirect
3. C₂×#470×C₇₃	C₂	semidirect
4. C₇₃×#2191	C₂	direct (N × H)
5. C₂×#360×C₇₃	C₂	semidirect
6. C₂×#349×C₇₃	C₂	semidirect
15. C₂²×Q₁₆×C₇₃	C₂²	semidirect
19. #510×C₇₃	C₂²	semidirect
22. C₂×M₃₂×C₇₃	C₂²	semidirect
24. #470×C₇₃	C₂²	semidirect
25. C₂×#106×C₇₃	C₂²	semidirect
27. #360×C₇₃	C₂²	semidirect
28. #349×C₇₃	C₂²	semidirect
58. C₂×Q₁₆×C₇₃	C₂³	semidirect
77. M₃₂×C₇₃	C₂³	semidirect
80. #106×C₇₃	C₂³	semidirect
218. C₂×#2191	C₇₃	direct (N × H)
223. C₂×C₇₃	#2191	direct (N × H)
226. C₂×#510	C₂×C₇₃	semidirect
227. C₂×#470	C₂×C₇₃	semidirect
228. #2191	C₂×C₇₃	direct (N × H)
229. C₂×#360	C₂×C₇₃	semidirect
230. C₂×#349	C₂×C₇₃	semidirect
231. C₇₃	C₂×#2191	direct (N × H)
240. C₂²×Q₁₆	C₂²×C₇₃	semidirect
244. #510	C₂²×C₇₃	semidirect
247. C₂×M₃₂	C₂²×C₇₃	semidirect
249. #470	C₂²×C₇₃	semidirect
250. C₂×#106	C₂²×C₇₃	semidirect
252. #360	C₂²×C₇₃	semidirect
253. #349	C₂²×C₇₃	semidirect
283. C₂×Q₁₆	C₂³×C₇₃	semidirect
302. M₃₂	C₂³×C₇₃	semidirect
305. #106	C₂³×C₇₃	semidirect
447. C₂	C₇₃×#2191	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×#575×C₇₃	2
C₂×#510×C₇₃	2
C₂×#470×C₇₃	2
C₇₃×#2191	2
C₂×#360×C₇₃	2
C₂×#349×C₇₃	2
C₂×#2191	73

Subgroups — C2×C73×#2191 #32942933

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₃×#2191 #32942933