Subgroups — C₂²×#17989384 #33999787

Order 18688.

11294 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#41×D₇₃	C₂	1	2	yes	maximal, complemented
2	C₂×#17989384	C₂	1	48	yes	maximal, direct product factor
3	C₂²×#14556623	C₂	1	2	yes	maximal, complemented
4	C₂²×#14556620	C₂	1	2	yes	maximal, complemented
5	C₂²×#14556618	C₂	1	2	yes	maximal, complemented
6	C₂²×#14556615	C₂	1	2	yes	maximal, complemented
7	C₂²×#14556613	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#14556611	C₂	1	2	yes	maximal, complemented
9	C₂³×#11924011	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#135×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#11924029	C₂²	1	2	yes	—
12	C₂²×#11924028	—	2	2	no	—
13	C₂²×#11924028	C₂²	1	2	yes	complemented
14	C₂²×#11924027	—	2	2	no	—
15	C₂²×#11924027	C₂²	1	2	yes	—
16	C₂×#41×D₇₃	—	2	24	no	—
17	C₂×#41×D₇₃	C₂²	1	48	yes	complemented
18	C₂²×Q₈×D₇₃	C₂²	1	2	yes	complemented
19	C₂²×D₄×D₇₃	—	2	2	no	—
20	C₂²×D₄×D₇₃	C₂²	1	2	yes	complemented
21	C₂³×C₄×D₇₃	—	2	2	no	—
22	C₂³×C₄×D₇₃	C₂²	1	1	yes	characteristic
23	#17989384	C₂²	1	256	yes	direct product factor
24	C₂×#14556623	C₂²	1	48	yes	complemented
25	C₂×#14556620	C₂²	1	48	yes	complemented
26	C₂×#14556618	C₂²	1	48	yes	complemented
27	C₂×#14556615	C₂²	1	48	yes	complemented
28	C₂×#14556613	C₂²	1	24	yes	complemented
29	C₂×#14556611	C₂²	1	48	yes	complemented
30	C₂²×Dic₂₉₂	C₂²	1	1	yes	characteristic, complemented
31	C₂²×#11924018	C₂²	1	2	yes	complemented
32	C₂²×#11924017	C₂²	1	2	yes	complemented
33	C₂²×#11924016	C₂²	1	2	yes	complemented
34	C₂²×#11924015	C₂²	1	2	yes	complemented
35	C₂²×D₅₈₄	C₂²	1	1	yes	characteristic, complemented
36	C₂²×#11924013	C₂²	1	2	yes	complemented
37	C₂²×#11924011	C₂²	1	2	yes	complemented
38	C₂²×#11924011	C₂²	1	2	yes	complemented
39	C₂²×#11924011	C₂²	1	24	yes	complemented
40	C₂³×#10596831	C₂²	1	1	yes	characteristic, complemented
41	C₂²×#41×C₇₃	C₂²	1	2	yes	complemented
42	C₂×#135×C₇₃	C₂²	1	24	yes	complemented
43	C₂²×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
44	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	complemented
45	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
46	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
47	C₂⁴×D₇₃	—	2	2	no	—
48	C₂⁴×D₇₃	D₄	1	1	yes	characteristic
49	C₂×#11924029	—	2	12	no	—
50	C₂×#11924029	C₂³	1	24	yes	—
51	C₂×#11924028	—	2	48	no	—
52	C₂×#11924028	—	2	12	no	—
53	C₂×#11924028	C₂³	1	24	yes	complemented
54	C₂×#11924027	—	2	48	no	—
55	C₂×#11924027	—	2	12	no	—
56	C₂×#11924027	C₂³	1	24	yes	—
57	#41×D₇₃	—	2	192	no	—
58	#41×D₇₃	C₂³	1	128	yes	complemented
59	C₂²×Dic₁₄₆	—	2	2	no	—
60	C₂²×Dic₁₄₆	C₂³	1	2	yes	—
61	C₂×Q₈×D₇₃	—	2	12	no	—
62	C₂×Q₈×D₇₃	C₂³	1	24	yes	complemented
63	C₂²×D₂₉₂	—	2	2	no	—
64	C₂²×D₂₉₂	C₂³	1	2	yes	—
65	C₂²×C₂²⋊D₇₃	—	2	2	no	—
66	C₂²×C₂²⋊D₇₃	—	2	2	no	—
67	C₂²×C₂²⋊D₇₃	—	2	2	no	—
68	C₂×D₄×D₇₃	—	2	48	no	—
69	C₂×D₄×D₇₃	—	2	12	no	—
70	C₂×D₄×D₇₃	C₂³	1	24	yes	complemented
71	C₂³×Dic₇₃	—	2	2	no	—
72	C₂³×Dic₇₃	D₄	1	1	yes	characteristic
73	C₂²×C₄×D₇₃	—	2	2	no	—
74	C₂²×C₄×D₇₃	—	2	2	no	—
75	C₂²×C₄×D₇₃	—	2	48	no	—
76	C₂²×C₄×D₇₃	—	2	2	no	—
77	C₂²×C₄×D₇₃	D₄	1	2	yes	—
78	C₂²×C₄×D₇₃	D₄	1	12	yes	—
79	C₂²×C₄×D₇₃	C₂³	1	2	yes	—
80	C₂²×C₄×D₇₃	C₂³	1	12	yes	—
81	#14556623	C₂³	1	128	yes	complemented
82	#14556620	C₂³	1	128	yes	complemented
83	#14556618	C₂³	1	128	yes	complemented
84	#14556615	C₂³	1	128	yes	complemented
85	#14556613	C₂³	1	64	yes	complemented
86	#14556611	C₂³	1	128	yes	complemented
87	C₂×Dic₂₉₂	C₂³	1	12	yes	complemented
88	C₂×#11924018	C₂³	1	24	yes	complemented
89	C₂×#11924017	C₂³	1	24	yes	complemented
90	C₂×#11924016	C₂³	1	24	yes	complemented
91	C₂×#11924015	C₂³	1	24	yes	complemented
92	C₂×D₅₈₄	C₂³	1	12	yes	complemented
93	C₂×#11924013	C₂³	1	24	yes	complemented
94	C₂×#11924011	C₂³	1	24	yes	complemented
95	C₂×#11924011	C₂³	1	24	yes	complemented
96	C₂×#11924011	C₂³	1	64	yes	complemented
97	C₂²×#10596831	C₂³	1	2	yes	—
98	C₂²×#10596831	C₂³	1	12	yes	complemented
99	C₂×#41×C₇₃	—	2	12	no	—
100	C₂×#41×C₇₃	C₂³	1	24	yes	complemented
101	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
102	C₂²×D₄×C₇₃	—	2	2	no	—
103	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
104	C₂³×C₄×C₇₃	—	2	2	no	—
105	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
106	#135×C₇₃	C₂³	1	64	yes	complemented
107	C₂×Q₁₆×C₇₃	C₂³	1	12	yes	complemented
108	C₂×SD₁₆×C₇₃	C₂³	1	24	yes	complemented
109	C₂×D₈×C₇₃	C₂³	1	12	yes	complemented
110	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₇₃	C₂³	1	12	yes	complemented
113	C₂³×D₇₃	—	2	2	no	—
114	C₂³×D₇₃	—	2	24	no	—
115	C₂³×D₇₃	—	4	4	no	—
116	C₂³×D₇₃	—	4	16	no	—
117	C₂³×D₇₃	C₂×D₄	1	2	yes	—
118	C₂³×D₇₃	C₂×D₄	1	12	yes	—
119	#11924029	—	2	48	no	—
120	#11924029	C₂⁴	1	32	yes	—
121	#11924028	—	2	48	no	—
122	#11924028	—	2	128	no	—
123	#11924028	C₂⁴	1	32	yes	complemented
124	#11924027	—	2	128	no	—
125	#11924027	—	2	48	no	—
126	#11924027	C₂⁴	1	32	yes	—
127	C₂×Dic₁₄₆	—	2	6	no	—
128	C₂×Dic₁₄₆	—	2	24	no	—
129	C₂×Dic₁₄₆	C₂⁴	1	12	yes	—
130	Q₈×D₇₃	—	2	48	no	—
131	Q₈×D₇₃	C₂⁴	1	32	yes	complemented
132	C₂×D₂₉₂	—	2	24	no	—
133	C₂×D₂₉₂	—	2	6	no	—
134	C₂×D₂₉₂	C₂⁴	1	12	yes	—
135	C₂×C₂²⋊D₇₃	—	2	24	no	—
136	C₂×C₂²⋊D₇₃	—	2	24	no	—
137	C₂×C₂²⋊D₇₃	—	2	24	no	—
138	D₄×D₇₃	—	2	128	no	—
139	D₄×D₇₃	—	2	48	no	—
140	D₄×D₇₃	C₂⁴	1	32	yes	complemented
141	C₂²×Dic₇₃	—	2	2	no	—
142	C₂²×Dic₇₃	—	2	24	no	—
143	C₂²×Dic₇₃	C₂×D₄	1	2	yes	—
144	C₂²×Dic₇₃	C₂×D₄	1	12	yes	—
145	C₂×C₄×D₇₃	—	2	24	no	—
146	C₂×C₄×D₇₃	—	2	24	no	—
147	C₂×C₄×D₇₃	—	2	24	no	—
148	C₂×C₄×D₇₃	—	2	128	no	—
149	C₂×C₄×D₇₃	C₂×D₄	1	24	yes	—
150	C₂×C₄×D₇₃	C₂×D₄	1	12	yes	—
151	C₂×C₄×D₇₃	C₂×D₄	1	48	yes	—
152	C₂×C₄×D₇₃	C₂⁴	1	12	yes	—
153	C₂×C₄×D₇₃	C₂⁴	1	16	yes	—
154	Dic₂₉₂	C₂⁴	1	16	yes	complemented
155	#11924018	C₂⁴	1	32	yes	complemented
156	#11924017	C₂⁴	1	32	yes	complemented
157	#11924016	C₂⁴	1	32	yes	complemented
158	#11924015	C₂⁴	1	32	yes	complemented
159	D₅₈₄	C₂⁴	1	16	yes	complemented
160	#11924013	C₂⁴	1	32	yes	complemented
161	#11924011	C₂⁴	1	32	yes	complemented
162	#11924011	C₂⁴	1	32	yes	complemented
163	C₂×#10596831	C₂⁴	1	12	yes	—
164	C₂×#10596831	C₂⁴	1	16	yes	complemented
165	C₂⁴×C₇₃	—	2	2	no	—
166	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
167	#41×C₇₃	—	2	48	no	—
168	#41×C₇₃	C₂⁴	1	32	yes	complemented
169	C₂×Q₈×C₇₃	—	2	6	no	—
170	C₂×Q₈×C₇₃	C₂⁴	1	12	yes	—
171	C₂×D₄×C₇₃	—	2	24	no	—
172	C₂×D₄×C₇₃	—	2	6	no	—
173	C₂×D₄×C₇₃	C₂⁴	1	12	yes	—
174	C₂²×C₄×C₇₃	—	2	2	no	—
175	C₂²×C₄×C₇₃	—	2	24	no	—
176	C₂²×C₄×C₇₃	C₂×D₄	1	6	yes	—
177	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
179	C₂²×C₄×C₇₃	C₂⁴	1	6	yes	—
180	Q₁₆×C₇₃	C₂⁴	1	16	yes	complemented
181	SD₁₆×C₇₃	C₂⁴	1	32	yes	complemented
182	D₈×C₇₃	C₂⁴	1	16	yes	complemented
183	C₂×C₈×C₇₃	C₂⁴	1	6	yes	—
184	C₂×C₈×C₇₃	C₂⁴	1	6	yes	—
185	C₂×C₈×C₇₃	C₂⁴	1	16	yes	complemented
186	C₂³×C₇₃	—	2	4	no	—
187	C₂³×C₇₃	—	2	12	no	—
188	C₂³×C₇₃	—	4	8	no	—
189	C₂³×C₇₃	C₂²×D₄	1	6	yes	—
190	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
191	C₂²×D₇₃	—	2	8	no	—
192	C₂²×D₇₃	—	2	12	no	—
193	C₂²×D₇₃	—	2	32	no	—
194	C₂²×D₇₃	—	4	24	no	—
195	C₂²×D₇₃	—	4	96	no	—
196	C₂²×D₇₃	—	4	8	no	—
197	C₂²×D₇₃	C₂²×D₄	1	12	yes	—
198	C₂²×D₇₃	C₂²×D₄	1	16	yes	—
199	Q₈×C₇₃	—	2	12	no	—
200	Q₈×C₇₃	C₂⁵	1	8	yes	—
201	D₄×C₇₃	—	2	32	no	—
202	D₄×C₇₃	—	2	12	no	—
203	D₄×C₇₃	C₂⁵	1	8	yes	—
204	C₂×C₄×C₇₃	—	2	12	no	—
205	C₂×C₄×C₇₃	—	2	32	no	—
206	C₂×C₄×C₇₃	C₂²×D₄	1	6	yes	—
207	C₂×C₄×C₇₃	C₂²×D₄	1	3	yes	—
208	C₂×C₄×C₇₃	C₂²×D₄	1	12	yes	—
209	C₂×C₄×C₇₃	C₂⁵	1	3	yes	—
210	C₂×C₄×C₇₃	C₂⁵	1	4	yes	—
211	C₂²⋊D₇₃	—	2	32	no	—
212	C₂²⋊D₇₃	—	2	32	no	—
213	C₂²⋊D₇₃	—	2	32	no	—
214	C₂×Dic₇₃	—	2	12	no	—
215	C₂×Dic₇₃	—	2	32	no	—
216	C₂×Dic₇₃	C₂²×D₄	1	12	yes	—
217	C₂×Dic₇₃	C₂²×D₄	1	16	yes	—
218	D₂₉₂	—	2	32	no	—
219	D₂₉₂	—	2	12	no	—
220	D₂₉₂	C₂⁵	1	8	yes	—
221	C₄×D₇₃	—	2	32	no	—
222	C₄×D₇₃	—	2	32	no	—
223	C₄×D₇₃	—	2	32	no	—
224	C₄×D₇₃	C₂²×D₄	1	32	yes	—
225	C₄×D₇₃	C₂²×D₄	1	24	yes	—
226	C₄×D₇₃	C₂⁵	1	8	yes	—
227	Dic₁₄₆	—	2	12	no	—
228	Dic₁₄₆	—	2	32	no	—
229	Dic₁₄₆	C₂⁵	1	8	yes	—
230	C₈×C₇₃	C₂⁵	1	4	yes	—
231	C₈×C₇₃	C₂⁵	1	4	yes	—
232	#10596831	C₂⁵	1	8	yes	—
233	C₂²×C₇₃	—	2	12	no	—
234	C₂²×C₇₃	—	2	8	no	—
235	C₂²×C₇₃	—	4	24	no	—
236	C₂²×C₇₃	#575	1	4	yes	complemented
237	C₂²×C₇₃	C₂³×D₄	1	4	yes	—
238	C₂²×C₇₃	C₂³×D₄	1	3	yes	—
239	C₂×D₇₃	—	2	24	no	—
240	C₂×D₇₃	—	2	8	no	—
241	C₂×D₇₃	—	4	16	no	—
242	C₂×D₇₃	—	4	64	no	—
243	C₂×D₇₃	—	4	24	no	—
244	C₂×D₇₃	C₂³×D₄	1	8	yes	—
245	C₄×C₇₃	—	2	8	no	—
246	C₄×C₇₃	C₂³×D₄	1	3	yes	—
247	C₄×C₇₃	C₂³×D₄	1	4	yes	—
248	C₄×C₇₃	C₂⁶	1	1	yes	characteristic
249	Dic₇₃	—	2	8	no	—
250	Dic₇₃	C₂³×D₄	1	8	yes	—
251	C₂²×#575	—	73	1	no	maximal, Sylow
252	C₂×C₇₃	—	2	4	no	—
253	C₂×C₇₃	—	4	8	no	—
254	C₂×C₇₃	C₂×#575	1	6	yes	complemented
255	C₂×C₇₃	C₂⁴×D₄	1	1	yes	characteristic
256	D₇₃	—	2	8	no	—
257	D₇₃	—	4	8	no	—
258	C₂³×#41	—	73	2	no	—
259	C₂×#575	—	73	48	no	—
260	C₂²×#137	—	73	2	no	—
261	C₂²×#137	—	73	2	no	—
262	C₂²×AGL(1,ℤ/8)	—	73	2	no	—
263	C₂²×AGL(1,ℤ/8)	—	73	2	no	—
264	C₂²×#135	—	73	2	no	—
265	C₂²×#135	—	73	1	no	—
266	C₂²×#135	D₇₃	1	1	yes	characteristic, complemented
267	C₂³×M₁₆	—	73	1	no	—
268	C₇₃	C₂²×#575	1	1	yes	characteristic, complemented, Sylow
269	C₂²×#41	—	73	48	no	—
270	C₂²×#41	—	73	2	no	—
271	C₂²×#41	—	73	2	no	—
272	C₂²×#41	—	73	2	no	—
273	C₂²×#41	—	146	2	no	—
274	C₂²×#41	—	146	2	no	—
275	C₂²×#41	—	146	24	no	—
276	C₂²×#41	C₂×D₇₃	1	2	yes	complemented
277	C₂³×Q₈	—	73	2	no	—
278	C₂³×D₄	—	73	2	no	—
279	C₂³×D₄	—	146	2	no	—
280	C₂⁴×C₄	—	73	1	no	—
281	C₂⁴×C₄	—	146	2	no	—
282	#575	—	73	256	no	—
283	C₂×#137	—	73	48	no	—
284	C₂×#137	—	73	48	no	—
285	C₂×AGL(1,ℤ/8)	—	73	48	no	—
286	C₂×AGL(1,ℤ/8)	—	73	48	no	—
287	C₂×#135	—	73	48	no	—
288	C₂×#135	—	73	24	no	—
289	C₂×#135	C₂×D₇₃	1	24	yes	complemented
290	C₂²×Q₁₆	—	73	2	no	—
291	C₂²×Q₁₆	—	73	1	no	—
292	C₂²×Q₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
293	C₂²×SD₁₆	—	73	2	no	—
294	C₂²×SD₁₆	—	73	2	no	—
295	C₂²×SD₁₆	—	73	2	no	—
296	C₂²×SD₁₆	C₂×D₇₃	1	2	yes	complemented
297	C₂²×D₈	—	73	2	no	—
298	C₂²×D₈	—	73	1	no	—
299	C₂²×D₈	C₂×D₇₃	1	1	yes	characteristic, complemented
300	C₂²×M₁₆	—	73	2	no	—
301	C₂²×M₁₆	—	73	2	no	—
302	C₂²×M₁₆	—	73	24	no	—
303	C₂³×C₈	—	73	1	no	—
304	C₂³×C₈	C₂×D₇₃	1	1	yes	characteristic, complemented
305	C₂⁵	—	73	1	no	—
306	C₂⁵	—	146	2	no	—
307	C₂×#41	—	2	12	no	—
308	C₂×#41	—	73	128	no	—
309	C₂×#41	—	73	24	no	—
310	C₂×#41	—	73	24	no	—
311	C₂×#41	—	73	24	no	—
312	C₂×#41	—	146	48	no	—
313	C₂×#41	—	146	48	no	—
314	C₂×#41	—	146	12	no	—
315	C₂×#41	—	146	12	no	—
316	C₂×#41	—	146	192	no	—
317	C₂×#41	—	146	12	no	—
318	C₂×#41	C₂²×D₇₃	1	24	yes	complemented
319	C₂²×Q₈	—	73	24	no	—
320	C₂²×Q₈	—	73	2	no	—
321	C₂²×Q₈	—	146	2	no	—
322	C₂²×Q₈	—	146	12	no	—
323	C₂²×Q₈	C₂²×D₇₃	1	2	yes	—
324	C₂²×D₄	—	2	2	no	—
325	C₂²×D₄	—	73	24	no	—
326	C₂²×D₄	—	73	2	no	—
327	C₂²×D₄	—	146	2	no	—
328	C₂²×D₄	—	146	12	no	—
329	C₂²×D₄	—	146	2	no	—
330	C₂²×D₄	—	146	48	no	—
331	C₂²×D₄	—	146	2	no	—
332	C₂²×D₄	—	146	2	no	—
333	C₂²×D₄	C₂²×D₇₃	1	2	yes	—
334	C₂³×C₄	—	2	2	no	—
335	C₂³×C₄	—	73	1	no	—
336	C₂³×C₄	—	73	12	no	—
337	C₂³×C₄	—	73	2	no	—
338	C₂³×C₄	—	73	2	no	—
339	C₂³×C₄	—	73	12	no	—
340	C₂³×C₄	—	146	2	no	—
341	C₂³×C₄	—	146	48	no	—
342	C₂³×C₄	—	146	2	no	—
343	C₂³×C₄	—	146	2	no	—
344	C₂³×C₄	—	146	2	no	—
345	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
346	#137	—	73	128	no	—
347	#137	—	73	128	no	—
348	AGL(1,ℤ/8)	—	73	128	no	—
349	AGL(1,ℤ/8)	—	73	128	no	—
350	#135	—	73	128	no	—
351	#135	—	73	64	no	—
352	#135	C₂²×D₇₃	1	64	yes	complemented
353	C₂×Q₁₆	—	73	24	no	—
354	C₂×Q₁₆	—	73	12	no	—
355	C₂×Q₁₆	C₂²×D₇₃	1	12	yes	complemented
356	C₂×SD₁₆	—	73	24	no	—
357	C₂×SD₁₆	—	73	24	no	—
358	C₂×SD₁₆	—	73	24	no	—
359	C₂×SD₁₆	C₂²×D₇₃	1	24	yes	complemented
360	C₂×D₈	—	73	24	no	—
361	C₂×D₈	—	73	12	no	—
362	C₂×D₈	C₂²×D₇₃	1	12	yes	complemented
363	C₂×M₁₆	—	73	24	no	—
364	C₂×M₁₆	—	73	24	no	—
365	C₂×M₁₆	—	73	64	no	—
366	C₂²×C₈	—	73	2	no	—
367	C₂²×C₈	—	73	12	no	—
368	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
369	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
370	C₂²×C₈	C₂²×D₇₃	1	12	yes	complemented
371	C₂⁴	—	2	2	no	—
372	C₂⁴	—	292	4	no	—
373	C₂⁴	—	292	16	no	—
374	C₂⁴	—	73	12	no	—
375	C₂⁴	—	73	2	no	—
376	C₂⁴	—	146	24	no	—
377	C₂⁴	—	146	2	no	—
378	C₂⁴	D₄×D₇₃	1	1	yes	characteristic
379	#41	—	2	48	no	—
380	#41	—	73	32	no	—
381	#41	—	73	32	no	—
382	#41	—	73	32	no	—
383	#41	—	146	128	no	—
384	#41	—	146	128	no	—
385	#41	—	146	48	no	—
386	#41	—	146	48	no	—
387	#41	—	146	48	no	—
388	#41	C₂³×D₇₃	1	32	yes	complemented
389	C₂×Q₈	—	2	6	no	—
390	C₂×Q₈	—	73	32	no	—
391	C₂×Q₈	—	73	12	no	—
392	C₂×Q₈	—	146	24	no	—
393	C₂×Q₈	—	146	48	no	—
394	C₂×Q₈	—	146	6	no	—
395	C₂×Q₈	C₂³×D₇₃	1	12	yes	—
396	C₂×D₄	—	2	24	no	—
397	C₂×D₄	—	2	6	no	—
398	C₂×D₄	—	73	32	no	—
399	C₂×D₄	—	73	12	no	—
400	C₂×D₄	—	146	24	no	—
401	C₂×D₄	—	146	48	no	—
402	C₂×D₄	—	146	24	no	—
403	C₂×D₄	—	146	128	no	—
404	C₂×D₄	—	146	24	no	—
405	C₂×D₄	—	146	24	no	—
406	C₂×D₄	—	146	6	no	—
407	C₂×D₄	C₂³×D₇₃	1	12	yes	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	24	no	—
410	C₂²×C₄	—	73	2	no	—
411	C₂²×C₄	—	73	12	no	—
412	C₂²×C₄	—	73	24	no	—
413	C₂²×C₄	—	73	12	no	—
414	C₂²×C₄	—	73	48	no	—
415	C₂²×C₄	—	73	12	no	—
416	C₂²×C₄	—	73	16	no	—
417	C₂²×C₄	—	146	24	no	—
418	C₂²×C₄	—	146	128	no	—
419	C₂²×C₄	—	146	24	no	—
420	C₂²×C₄	—	146	24	no	—
421	C₂²×C₄	—	146	2	no	—
422	C₂²×C₄	—	146	24	no	—
423	C₂²×C₄	D₄×D₇₃	1	6	yes	—
424	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
425	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
426	C₂²×C₄	C₂³×D₇₃	1	6	yes	—
427	Q₁₆	—	73	32	no	—
428	Q₁₆	—	73	16	no	—
429	Q₁₆	C₂³×D₇₃	1	16	yes	complemented
430	SD₁₆	—	73	32	no	—
431	SD₁₆	—	73	32	no	—
432	SD₁₆	—	73	32	no	—
433	SD₁₆	C₂³×D₇₃	1	32	yes	complemented
434	D₈	—	73	32	no	—
435	D₈	—	73	16	no	—
436	D₈	C₂³×D₇₃	1	16	yes	complemented
437	M₁₆	—	73	32	no	—
438	M₁₆	—	73	32	no	—
439	C₂×C₈	—	73	12	no	—
440	C₂×C₈	—	73	16	no	—
441	C₂×C₈	C₂³×D₇₃	1	6	yes	—
442	C₂×C₈	C₂³×D₇₃	1	6	yes	—
443	C₂×C₈	C₂³×D₇₃	1	16	yes	complemented
444	C₂³	—	2	4	no	—
445	C₂³	—	2	12	no	—
446	C₂³	—	4	8	no	—
447	C₂³	—	292	24	no	—
448	C₂³	—	292	96	no	—
449	C₂³	—	292	8	no	—
450	C₂³	—	73	16	no	—
451	C₂³	—	73	12	no	—
452	C₂³	—	146	32	no	—
453	C₂³	—	146	12	no	—
454	C₂³	—	146	8	no	—
455	C₂³	C₂×D₄×D₇₃	1	6	yes	—
456	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
457	Q₈	—	2	12	no	—
458	Q₈	—	73	8	no	—
459	Q₈	—	146	32	no	—
460	Q₈	—	146	12	no	—
461	Q₈	C₂⁴×D₇₃	1	8	yes	—
462	D₄	—	2	32	no	—
463	D₄	—	2	12	no	—
464	D₄	—	73	8	no	—
465	D₄	—	146	32	no	—
466	D₄	—	146	32	no	—
467	D₄	—	146	32	no	—
468	D₄	—	146	32	no	—
469	D₄	—	146	12	no	—
470	D₄	C₂⁴×D₇₃	1	8	yes	—
471	C₂×C₄	—	2	12	no	—
472	C₂×C₄	—	2	32	no	—
473	C₂×C₄	—	73	12	no	—
474	C₂×C₄	—	73	16	no	—
475	C₂×C₄	—	73	32	no	—
476	C₂×C₄	—	73	24	no	—
477	C₂×C₄	—	73	8	no	—
478	C₂×C₄	—	146	32	no	—
479	C₂×C₄	—	146	32	no	—
480	C₂×C₄	—	146	32	no	—
481	C₂×C₄	—	146	12	no	—
482	C₂×C₄	—	146	32	no	—
483	C₂×C₄	C₂×D₄×D₇₃	1	6	yes	—
484	C₂×C₄	C₂×D₄×D₇₃	1	3	yes	—
485	C₂×C₄	C₂×D₄×D₇₃	1	12	yes	—
486	C₂×C₄	C₂⁴×D₇₃	1	3	yes	—
487	C₂×C₄	C₂⁴×D₇₃	1	4	yes	—
488	C₈	—	73	8	no	—
489	C₈	C₂⁴×D₇₃	1	4	yes	—
490	C₈	C₂⁴×D₇₃	1	4	yes	—
491	C₂²	—	2	12	no	—
492	C₂²	—	2	8	no	—
493	C₂²	—	4	24	no	—
494	C₂²	—	292	16	no	—
495	C₂²	—	292	64	no	—
496	C₂²	—	292	24	no	—
497	C₂²	—	73	8	no	—
498	C₂²	—	146	8	no	—
499	C₂²	—	146	24	no	—
500	C₂²	#17989384	1	4	yes	direct product factor
501	C₂²	C₂²×D₄×D₇₃	1	4	yes	—
502	C₂²	C₂²×D₄×D₇₃	1	3	yes	—
503	C₄	—	2	8	no	—
504	C₄	—	73	8	no	—
505	C₄	—	146	8	no	—
506	C₄	C₂²×D₄×D₇₃	1	4	yes	—
507	C₄	C₂²×D₄×D₇₃	1	3	yes	—
508	C₄	C₂⁵×D₇₃	1	1	yes	characteristic
509	C₂	—	2	4	no	—
510	C₂	—	4	8	no	—
511	C₂	—	292	8	no	—
512	C₂	—	146	8	no	—
513	C₂	C₂×#17989384	1	6	yes	direct product factor
514	C₂	C₂³×D₄×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₇₃
commutator, cosocle	C₄×C₇₃	C₂⁶
Frattini	C₄	C₂⁵×D₇₃
Fitting	C₂²×#135×C₇₃	C₂
socle	C₂³×C₇₃	C₂²×D₄
hypercenter	C₂²×#135	D₇₃
hypocenter	C₇₃	C₂²×#575
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂²×#135

Complements

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

N	H ≅ G/N	type
1. C₂²×#41×D₇₃	C₂	semidirect
2. C₂×#17989384	C₂	direct (N × H)
3. C₂²×#14556623	C₂	semidirect
4. C₂²×#14556620	C₂	semidirect
5. C₂²×#14556618	C₂	semidirect
6. C₂²×#14556615	C₂	semidirect
7. C₂²×#14556613	C₂	semidirect
8. C₂²×#14556611	C₂	semidirect
9. C₂³×#11924011	C₂	semidirect
10. C₂²×#135×C₇₃	C₂	semidirect
13. C₂²×#11924028	C₂²	semidirect
17. C₂×#41×D₇₃	C₂²	semidirect
18. C₂²×Q₈×D₇₃	C₂²	semidirect
20. C₂²×D₄×D₇₃	C₂²	semidirect
23. #17989384	C₂²	direct (N × H)
24. C₂×#14556623	C₂²	semidirect
25. C₂×#14556620	C₂²	semidirect
26. C₂×#14556618	C₂²	semidirect
27. C₂×#14556615	C₂²	semidirect
28. C₂×#14556613	C₂²	semidirect
29. C₂×#14556611	C₂²	semidirect
30. C₂²×Dic₂₉₂	C₂²	semidirect
31. C₂²×#11924018	C₂²	semidirect
32. C₂²×#11924017	C₂²	semidirect
33. C₂²×#11924016	C₂²	semidirect
34. C₂²×#11924015	C₂²	semidirect
35. C₂²×D₅₈₄	C₂²	semidirect
36. C₂²×#11924013	C₂²	semidirect
37. C₂²×#11924011	C₂²	semidirect
38. C₂²×#11924011	C₂²	semidirect
39. C₂²×#11924011	C₂²	semidirect
40. C₂³×#10596831	C₂²	semidirect
41. C₂²×#41×C₇₃	C₂²	semidirect
42. C₂×#135×C₇₃	C₂²	semidirect
43. C₂²×Q₁₆×C₇₃	C₂²	semidirect
44. C₂²×SD₁₆×C₇₃	C₂²	semidirect
45. C₂²×D₈×C₇₃	C₂²	semidirect
46. C₂³×C₈×C₇₃	C₂²	semidirect
53. C₂×#11924028	C₂³	semidirect
58. #41×D₇₃	C₂³	semidirect
62. C₂×Q₈×D₇₃	C₂³	semidirect
70. C₂×D₄×D₇₃	C₂³	semidirect
81. #14556623	C₂³	semidirect
82. #14556620	C₂³	semidirect
83. #14556618	C₂³	semidirect
84. #14556615	C₂³	semidirect
85. #14556613	C₂³	semidirect
86. #14556611	C₂³	semidirect
87. C₂×Dic₂₉₂	C₂³	semidirect
88. C₂×#11924018	C₂³	semidirect
89. C₂×#11924017	C₂³	semidirect
90. C₂×#11924016	C₂³	semidirect
91. C₂×#11924015	C₂³	semidirect
92. C₂×D₅₈₄	C₂³	semidirect
93. C₂×#11924013	C₂³	semidirect
94. C₂×#11924011	C₂³	semidirect
95. C₂×#11924011	C₂³	semidirect
96. C₂×#11924011	C₂³	semidirect
98. C₂²×#10596831	C₂³	semidirect
100. C₂×#41×C₇₃	C₂³	semidirect
106. #135×C₇₃	C₂³	semidirect
107. C₂×Q₁₆×C₇₃	C₂³	semidirect
108. C₂×SD₁₆×C₇₃	C₂³	semidirect
109. C₂×D₈×C₇₃	C₂³	semidirect
112. C₂²×C₈×C₇₃	C₂³	semidirect
123. #11924028	C₂⁴	semidirect
131. Q₈×D₇₃	C₂⁴	semidirect
140. D₄×D₇₃	C₂⁴	semidirect
154. Dic₂₉₂	C₂⁴	semidirect
155. #11924018	C₂⁴	semidirect
156. #11924017	C₂⁴	semidirect
157. #11924016	C₂⁴	semidirect
158. #11924015	C₂⁴	semidirect
159. D₅₈₄	C₂⁴	semidirect
160. #11924013	C₂⁴	semidirect
161. #11924011	C₂⁴	semidirect
162. #11924011	C₂⁴	semidirect
164. C₂×#10596831	C₂⁴	semidirect
168. #41×C₇₃	C₂⁴	semidirect
180. Q₁₆×C₇₃	C₂⁴	semidirect
181. SD₁₆×C₇₃	C₂⁴	semidirect
182. D₈×C₇₃	C₂⁴	semidirect
185. C₂×C₈×C₇₃	C₂⁴	semidirect
236. C₂²×C₇₃	#575	semidirect
254. C₂×C₇₃	C₂×#575	semidirect
266. C₂²×#135	D₇₃	semidirect
268. C₇₃	C₂²×#575	semidirect
276. C₂²×#41	C₂×D₇₃	semidirect
289. C₂×#135	C₂×D₇₃	semidirect
292. C₂²×Q₁₆	C₂×D₇₃	semidirect
296. C₂²×SD₁₆	C₂×D₇₃	semidirect
299. C₂²×D₈	C₂×D₇₃	semidirect
304. C₂³×C₈	C₂×D₇₃	semidirect
318. C₂×#41	C₂²×D₇₃	semidirect
352. #135	C₂²×D₇₃	semidirect
355. C₂×Q₁₆	C₂²×D₇₃	semidirect
359. C₂×SD₁₆	C₂²×D₇₃	semidirect
362. C₂×D₈	C₂²×D₇₃	semidirect
370. C₂²×C₈	C₂²×D₇₃	semidirect
388. #41	C₂³×D₇₃	semidirect
429. Q₁₆	C₂³×D₇₃	semidirect
433. SD₁₆	C₂³×D₇₃	semidirect
436. D₈	C₂³×D₇₃	semidirect
443. C₂×C₈	C₂³×D₇₃	semidirect
500. C₂²	#17989384	direct (N × H)
513. C₂	C₂×#17989384	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×#41×D₇₃	2
C₂×#17989384	2
C₂²×#14556623	2
C₂²×#14556620	2
C₂²×#14556618	2
C₂²×#14556615	2
C₂²×#14556613	2
C₂²×#14556611	2
C₂³×#11924011	2
C₂²×#135×C₇₃	2
C₂²×#575	73

Subgroups — C22×#17989384 #33999787

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#17989384 #33999787