Subgroups — C₂×#22618843 #33950300

Order 18688.

2642 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#135×D₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#17989352	C₂	1	2	yes	maximal, complemented
3	#22618843	C₂	1	16	yes	maximal, direct product factor
4	C₂×#17988707	C₂	1	2	yes	maximal, complemented
5	C₂×#17988706	C₂	1	2	yes	maximal, complemented
6	C₂×#17988705	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#17988704	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#17988703	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#108×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#17988602	C₂	1	2	yes	maximal, complemented
11	C₂×#17988541	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#443×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#41×D₇₃	C₂²	1	2	yes	—
14	C₂×#14556614	C₄	1	1	yes	characteristic, complemented
15	C₂×#14556613	C₂²	1	1	yes	characteristic
16	C₂×#14556612	C₄	1	2	yes	complemented
17	C₂×#14556611	C₂²	1	2	yes	—
18	C₂×#14556610	C₄	1	1	yes	characteristic, complemented
19	#135×D₇₃	C₄	1	8	yes	complemented
20	#135×D₇₃	C₂²	1	8	yes	—
21	C₂×Q₁₆×D₇₃	C₄	1	1	yes	characteristic, complemented
22	C₂×SD₁₆×D₇₃	C₄	1	2	yes	complemented
23	C₂×D₈×D₇₃	C₄	1	1	yes	characteristic, complemented
24	#17989352	—	2	8	no	—
25	#17989352	C₂²	1	16	yes	complemented
26	C₂×#14556599	—	2	2	no	—
27	C₂×#14556599	C₂²	1	2	yes	complemented
28	C₂×#14556598	C₂²	1	2	yes	complemented
29	C₂×#14556597	—	2	2	no	—
30	C₂×#14556597	C₂²	1	2	yes	complemented
31	C₂²×#11924011	—	2	2	no	—
32	C₂²×#11924011	C₂²	1	1	yes	characteristic
33	C₂×M₁₆×D₇₃	—	2	2	no	—
34	C₂×M₁₆×D₇₃	C₂²	1	2	yes	—
35	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
36	C₂×#14556548	C₂²	1	1	yes	characteristic
37	#17988707	C₂²	1	16	yes	complemented
38	#17988706	C₂²	1	16	yes	complemented
39	#17988705	C₂²	1	8	yes	complemented
40	#17988704	C₂²	1	8	yes	complemented
41	#17988703	C₂²	1	8	yes	complemented
42	C₂×#14556527	C₂²	1	1	yes	characteristic, complemented
43	C₂×#14556526	C₂²	1	2	yes	complemented
44	#108×D₇₃	C₂²	1	8	yes	complemented
45	#17988602	C₂²	1	16	yes	complemented
46	C₂×#14556519	C₂²	1	2	yes	complemented
47	C₂×#14556518	C₂²	1	2	yes	complemented
48	C₂×#14556517	C₂²	1	2	yes	complemented
49	#17988541	C₂²	1	8	yes	complemented
50	C₂×#14556502	C₂²	1	1	yes	characteristic, complemented
51	C₂×#14556501	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
53	C₂×#135×C₇₃	C₂²	1	1	yes	characteristic
54	C₂×#131×C₇₃	C₂²	1	2	yes	complemented
55	#443×C₇₃	C₂²	1	8	yes	complemented
56	C₂×#108×C₇₃	C₂²	1	1	yes	characteristic, complemented
57	C₂×#104×C₇₃	C₂²	1	2	yes	complemented
58	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
59	C₂×#11924029	C₂×C₄	1	2	yes	—
60	C₂×#11924028	—	2	2	no	—
61	C₂×#11924028	C₂³	1	2	yes	—
62	C₂×#11924027	—	2	2	no	—
63	C₂×#11924027	C₂×C₄	1	2	yes	—
64	#41×D₇₃	—	2	4	no	—
65	#41×D₇₃	—	2	4	no	—
66	#41×D₇₃	C₂×C₄	1	8	yes	—
67	#41×D₇₃	C₂³	1	8	yes	—
68	C₂×Q₈×D₇₃	C₂×C₄	1	2	yes	—
69	C₂×D₄×D₇₃	—	2	2	no	—
70	C₂×D₄×D₇₃	C₂×C₄	1	2	yes	—
71	C₂²×C₄×D₇₃	—	2	2	no	—
72	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
73	#14556614	C₂×C₄	1	8	yes	complemented
74	#14556613	C₂×C₄	1	4	yes	—
75	#14556613	C₂³	1	4	yes	—
76	#14556612	C₂×C₄	1	16	yes	complemented
77	#14556611	C₂×C₄	1	8	yes	—
78	#14556611	C₂³	1	8	yes	—
79	#14556610	C₂×C₄	1	8	yes	complemented
80	C₂×Dic₂₉₂	C₂×C₄	1	1	yes	characteristic
81	C₂×#11924018	C₂×C₄	1	2	yes	—
82	Q₁₆×D₇₃	C₂×C₄	1	8	yes	complemented
83	C₂×#11924017	C₂×C₄	1	2	yes	—
84	C₂×#11924016	C₂×C₄	1	2	yes	—
85	C₂×#11924015	C₂×C₄	1	2	yes	—
86	SD₁₆×D₇₃	C₂×C₄	1	16	yes	complemented
87	C₂×D₅₈₄	C₂×C₄	1	1	yes	characteristic
88	C₂×#11924013	C₂×C₄	1	2	yes	—
89	D₈×D₇₃	C₂×C₄	1	8	yes	complemented
90	#14556599	—	2	16	no	—
91	#14556599	—	2	4	no	—
92	#14556599	C₂³	1	8	yes	complemented
93	#14556598	—	2	4	no	—
94	#14556598	C₂³	1	8	yes	complemented
95	#14556597	—	2	16	no	—
96	#14556597	—	2	4	no	—
97	#14556597	C₂³	1	8	yes	complemented
98	C₂×#11924012	—	2	2	no	—
99	C₂×#11924012	C₂³	1	2	yes	—
100	C₂×#11924011	—	2	2	no	—
101	C₂×#11924011	—	2	16	no	—
102	C₂×#11924011	—	2	2	no	—
103	C₂×#11924011	—	2	2	no	—
104	C₂×#11924011	D₄	1	1	yes	characteristic
105	C₂×#11924011	D₄	1	1	yes	characteristic
106	C₂×#11924011	D₄	1	1	yes	characteristic
107	C₂×#11924011	D₄	1	1	yes	characteristic
108	C₂×#11924011	D₄	1	4	yes	—
109	C₂×#11924011	C₂³	1	4	yes	—
110	M₁₆×D₇₃	—	2	4	no	—
111	M₁₆×D₇₃	—	2	16	no	—
112	M₁₆×D₇₃	C₂³	1	8	yes	—
113	C₂²×#10596831	—	2	2	no	—
114	C₂²×#10596831	C₂³	1	1	yes	characteristic
115	C₂²×#10596831	C₂³	1	1	yes	characteristic
116	C₂×C₈×D₇₃	—	2	2	no	—
117	C₂×C₈×D₇₃	—	2	2	no	—
118	C₂×C₈×D₇₃	—	2	2	no	—
119	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
120	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
121	C₂×C₈×D₇₃	C₂×C₄	1	4	yes	—
122	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
123	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
124	C₂×C₈×D₇₃	C₂³	1	4	yes	—
125	#14556548	—	2	2	no	—
126	#14556548	C₂³	1	4	yes	—
127	C₂×#11924007	—	2	1	no	—
128	C₂×#11924005	—	2	1	no	—
129	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
130	#14556527	C₂³	1	4	yes	complemented
131	#14556526	C₂³	1	8	yes	complemented
132	#14556519	C₂³	1	8	yes	complemented
133	#14556518	C₂³	1	8	yes	complemented
134	#14556517	C₂³	1	8	yes	complemented
135	#14556502	C₂³	1	4	yes	complemented
136	#14556501	C₂³	1	4	yes	complemented
137	C₈×Dic₇₃	C₂³	1	4	yes	complemented
138	C₂×#41×C₇₃	C₂³	1	2	yes	—
139	#135×C₇₃	C₂×C₄	1	4	yes	—
140	#135×C₇₃	C₂³	1	4	yes	—
141	C₂×Q₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
142	C₂×SD₁₆×C₇₃	C₂×C₄	1	2	yes	—
143	C₂×D₈×C₇₃	C₂×C₄	1	1	yes	characteristic
144	#131×C₇₃	—	2	4	no	—
145	#131×C₇₃	C₂³	1	8	yes	complemented
146	C₂×M₁₆×C₇₃	—	2	2	no	—
147	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
148	C₂²×C₈×C₇₃	—	2	2	no	—
149	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
152	#108×C₇₃	C₂³	1	4	yes	complemented
153	#104×C₇₃	C₂³	1	8	yes	complemented
154	C₄×C₈×C₇₃	C₂³	1	4	yes	complemented
155	C₂³×D₇₃	—	2	2	no	—
156	C₂³×D₇₃	#41	1	1	yes	characteristic
157	#11924029	—	2	4	no	—
158	#11924029	C₂²×C₄	1	8	yes	—
159	#11924028	—	2	2	no	—
160	#11924028	—	2	2	no	—
161	#11924028	—	2	8	no	—
162	#11924028	—	2	8	no	—
163	#11924028	C₂²×C₄	1	4	yes	—
164	#11924028	C₂⁴	1	4	yes	—
165	#11924027	—	2	8	no	—
166	#11924027	—	2	8	no	—
167	#11924027	—	2	4	no	—
168	#11924027	C₂²×C₄	1	8	yes	—
169	C₂×Dic₁₄₆	—	2	2	no	—
170	C₂×Dic₁₄₆	C₂²×C₄	1	2	yes	—
171	Q₈×D₇₃	—	2	4	no	—
172	Q₈×D₇₃	C₂²×C₄	1	8	yes	—
173	C₂×D₂₉₂	—	2	2	no	—
174	C₂×D₂₉₂	C₂²×C₄	1	2	yes	—
175	C₂×C₂²⋊D₇₃	—	2	2	no	—
176	C₂×C₂²⋊D₇₃	—	2	2	no	—
177	C₂×C₂²⋊D₇₃	—	2	2	no	—
178	D₄×D₇₃	—	2	8	no	—
179	D₄×D₇₃	—	2	8	no	—
180	D₄×D₇₃	—	2	4	no	—
181	D₄×D₇₃	C₂²×C₄	1	8	yes	—
182	C₂²×Dic₇₃	—	2	2	no	—
183	C₂²×Dic₇₃	—	2	1	no	—
184	C₂²×Dic₇₃	#41	1	1	yes	characteristic
185	C₂×C₄×D₇₃	—	2	2	no	—
186	C₂×C₄×D₇₃	—	2	2	no	—
187	C₂×C₄×D₇₃	—	2	2	no	—
188	C₂×C₄×D₇₃	—	2	8	no	—
189	C₂×C₄×D₇₃	—	2	8	no	—
190	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
192	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
194	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
195	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
196	C₂×C₄×D₇₃	#41	1	2	yes	—
197	C₂×C₄×D₇₃	C₂⁴	1	2	yes	—
198	Dic₂₉₂	C₂²×C₄	1	4	yes	—
199	#11924018	C₂²×C₄	1	8	yes	—
200	#11924017	C₂²×C₄	1	8	yes	—
201	#11924016	C₂²×C₄	1	8	yes	—
202	#11924015	C₂²×C₄	1	8	yes	—
203	D₅₈₄	C₂²×C₄	1	4	yes	—
204	#11924013	C₂²×C₄	1	8	yes	—
205	#11924012	—	2	2	no	—
206	#11924012	—	2	8	no	—
207	#11924012	C₂⁴	1	4	yes	—
208	#11924011	—	2	8	no	—
209	#11924011	—	2	8	no	—
210	#11924011	—	2	8	no	—
211	#11924011	C₂×D₄	1	4	yes	—
212	#11924011	C₂×D₄	1	4	yes	—
213	#11924011	C₂×D₄	1	4	yes	—
214	#11924011	C₂×D₄	1	4	yes	—
215	C₂×#10596831	—	2	2	no	—
216	C₂×#10596831	—	2	8	no	—
217	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
218	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
219	C₂×#10596831	C₂²×C₄	1	2	yes	—
220	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
221	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
222	C₂×#10596831	C₂×D₄	1	2	yes	—
223	C₂×#10596831	C₂⁴	1	2	yes	—
224	C₂×#10596831	C₂⁴	1	2	yes	—
225	C₈×D₇₃	—	2	8	no	—
226	C₈×D₇₃	—	2	8	no	—
227	C₈×D₇₃	—	2	8	no	—
228	C₈×D₇₃	C₂²×C₄	1	4	yes	—
229	C₈×D₇₃	C₂²×C₄	1	4	yes	—
230	C₈×D₇₃	C₂²×C₄	1	4	yes	—
231	C₈×D₇₃	C₂²×C₄	1	4	yes	—
232	#11924007	—	2	4	no	—
233	#11924005	—	2	4	no	—
234	C₄×Dic₇₃	—	2	1	no	—
235	C₄×Dic₇₃	C₂⁴	1	2	yes	—
236	#41×C₇₃	—	2	2	no	—
237	#41×C₇₃	—	2	2	no	—
238	#41×C₇₃	C₂²×C₄	1	4	yes	—
239	#41×C₇₃	C₂⁴	1	4	yes	—
240	C₂×Q₈×C₇₃	C₂²×C₄	1	2	yes	—
241	C₂×D₄×C₇₃	—	2	2	no	—
242	C₂×D₄×C₇₃	C₂²×C₄	1	2	yes	—
243	C₂²×C₄×C₇₃	—	2	2	no	—
244	C₂²×C₄×C₇₃	—	2	1	no	—
245	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
246	Q₁₆×C₇₃	C₂²×C₄	1	4	yes	—
247	SD₁₆×C₇₃	C₂²×C₄	1	8	yes	—
248	D₈×C₇₃	C₂²×C₄	1	4	yes	—
249	M₁₆×C₇₃	—	2	2	no	—
250	M₁₆×C₇₃	—	2	8	no	—
251	M₁₆×C₇₃	C₂⁴	1	4	yes	—
252	C₂×C₈×C₇₃	—	2	2	no	—
253	C₂×C₈×C₇₃	—	2	8	no	—
254	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
255	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
256	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
257	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
258	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
259	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
260	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
261	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
262	C₄²×C₇₃	—	2	1	no	—
263	C₄²×C₇₃	C₂⁴	1	2	yes	—
264	C₂³×C₇₃	—	2	2	no	—
265	C₂³×C₇₃	C₂×#41	1	1	yes	characteristic
266	C₂²×D₇₃	—	2	2	no	—
267	C₂²×D₇₃	—	2	8	no	—
268	C₂²×D₇₃	—	4	2	no	—
269	C₂²×D₇₃	—	8	4	no	—
270	C₂²×D₇₃	C₄×D₄	1	1	yes	characteristic
271	C₂²×D₇₃	C₄×D₄	1	1	yes	characteristic
272	C₂²×D₇₃	C₄×D₄	1	2	yes	—
273	C₂²×D₇₃	C₂×#41	1	2	yes	—
274	Q₈×C₇₃	—	2	2	no	—
275	Q₈×C₇₃	C₂³×C₄	1	4	yes	—
276	D₄×C₇₃	—	2	4	no	—
277	D₄×C₇₃	—	2	4	no	—
278	D₄×C₇₃	—	2	2	no	—
279	D₄×C₇₃	C₂³×C₄	1	4	yes	—
280	C₂×C₄×C₇₃	—	2	2	no	—
281	C₂×C₄×C₇₃	—	2	4	no	—
282	C₂×C₄×C₇₃	—	2	4	no	—
283	C₂×C₄×C₇₃	—	2	2	no	—
284	C₂×C₄×C₇₃	—	4	2	no	—
285	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
286	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
287	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
288	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
289	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
290	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
291	C₂²⋊D₇₃	—	2	4	no	—
292	C₂²⋊D₇₃	—	2	4	no	—
293	C₂²⋊D₇₃	—	2	8	no	—
294	C₂²⋊D₇₃	—	2	8	no	—
295	C₂×Dic₇₃	—	2	2	no	—
296	C₂×Dic₇₃	—	2	8	no	—
297	C₂×Dic₇₃	—	2	2	no	—
298	C₂×Dic₇₃	—	4	2	no	—
299	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
300	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
301	C₂×Dic₇₃	C₄×D₄	1	2	yes	—
302	C₂×Dic₇₃	C₂×#41	1	2	yes	—
303	D₂₉₂	—	2	8	no	—
304	D₂₉₂	—	2	2	no	—
305	D₂₉₂	C₂³×C₄	1	4	yes	—
306	C₄×D₇₃	—	2	8	no	—
307	C₄×D₇₃	—	2	4	no	—
308	C₄×D₇₃	—	2	4	no	—
309	C₄×D₇₃	—	2	8	no	—
310	C₄×D₇₃	C₄×D₄	1	2	yes	—
311	C₄×D₇₃	C₄×D₄	1	2	yes	—
312	C₄×D₇₃	C₄×D₄	1	2	yes	—
313	C₄×D₇₃	C₄×D₄	1	2	yes	—
314	C₄×D₇₃	C₂³×C₄	1	2	yes	—
315	C₄×D₇₃	C₂³×C₄	1	2	yes	—
316	C₄×D₇₃	C₂²×D₄	1	2	yes	—
317	C₄×D₇₃	C₂²×D₄	1	2	yes	—
318	Dic₁₄₆	—	2	2	no	—
319	Dic₁₄₆	—	2	8	no	—
320	Dic₁₄₆	C₂³×C₄	1	4	yes	—
321	C₈×C₇₃	—	2	4	no	—
322	C₈×C₇₃	C₂³×C₄	1	2	yes	—
323	C₈×C₇₃	C₂³×C₄	1	2	yes	—
324	C₈×C₇₃	C₂²×D₄	1	2	yes	—
325	C₈×C₇₃	C₂²×D₄	1	2	yes	—
326	#10596831	—	2	4	no	—
327	#10596831	C₂³×C₄	1	2	yes	—
328	#10596831	C₂³×C₄	1	2	yes	—
329	#10596831	C₂²×D₄	1	2	yes	—
330	#10596831	C₂²×D₄	1	2	yes	—
331	C₂²×C₇₃	—	2	2	no	—
332	C₂²×C₇₃	—	2	4	no	—
333	C₂²×C₇₃	—	4	4	no	—
334	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
335	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
336	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
337	C₂×D₇₃	—	2	2	no	—
338	C₂×D₇₃	—	2	2	no	—
339	C₂×D₇₃	—	2	4	no	—
340	C₂×D₇₃	—	4	2	no	—
341	C₂×D₇₃	—	4	2	no	—
342	C₂×D₇₃	—	4	4	no	—
343	C₂×D₇₃	—	8	8	no	—
344	C₂×D₇₃	C₂×C₄×D₄	1	2	yes	—
345	C₂×D₇₃	C₂×C₄×D₄	1	2	yes	—
346	C₄×C₇₃	—	2	4	no	—
347	C₄×C₇₃	—	4	2	no	—
348	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
349	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
350	C₄×C₇₃	C₂⁴×C₄	1	1	yes	characteristic
351	C₄×C₇₃	C₂³×D₄	1	1	yes	characteristic
352	Dic₇₃	—	2	4	no	—
353	Dic₇₃	—	4	2	no	—
354	Dic₇₃	C₂×C₄×D₄	1	2	yes	—
355	Dic₇₃	C₂×C₄×D₄	1	2	yes	—
356	C₂×#2957	—	73	1	no	maximal, Sylow
357	C₂×C₇₃	—	2	1	no	—
358	C₂×C₇₃	—	2	1	no	—
359	C₂×C₇₃	—	4	4	no	—
360	C₂×C₇₃	#2957	1	2	yes	complemented
361	C₂×C₇₃	C₂²×C₄×D₄	1	1	yes	characteristic
362	D₇₃	—	2	2	no	—
363	D₇₃	—	2	2	no	—
364	D₇₃	—	4	4	no	—
365	C₂²×#135	—	73	1	no	—
366	C₂×#568	—	73	2	no	—
367	#2957	—	73	16	no	—
368	C₂×#444	—	73	2	no	—
369	C₂×#444	—	73	2	no	—
370	C₂×#443	—	73	1	no	—
371	C₂×#443	—	73	1	no	—
372	C₂×#443	—	73	1	no	—
373	C₂×#443	D₇₃	1	1	yes	characteristic, complemented
374	C₂²×#108	—	73	1	no	—
375	C₂×#421	—	73	2	no	—
376	C₂×#405	—	73	1	no	—
377	C₇₃	C₂×#2957	1	1	yes	characteristic, complemented, Sylow
378	C₂²×#41	—	73	2	no	—
379	C₂×#135	—	73	2	no	—
380	C₂×#135	—	73	8	no	—
381	C₂×#135	—	73	8	no	—
382	C₂×#135	—	73	1	no	—
383	C₂×#135	—	73	2	no	—
384	C₂×#135	—	73	1	no	—
385	C₂×#135	—	73	1	no	—
386	C₂×#135	C₂×D₇₃	1	1	yes	characteristic
387	C₂²×Q₁₆	—	73	1	no	—
388	C₂²×SD₁₆	—	73	2	no	—
389	C₂²×D₈	—	73	1	no	—
390	#568	—	73	16	no	—
391	#568	—	146	8	no	—
392	C₂×#131	—	73	2	no	—
393	C₂×#131	—	73	2	no	—
394	C₂×#131	—	73	2	no	—
395	C₂×#131	—	146	2	no	—
396	C₂×#131	—	146	2	no	—
397	C₂×#131	C₂×D₇₃	1	2	yes	complemented
398	C₂²×M₁₆	—	73	1	no	—
399	C₂²×M₁₆	—	73	2	no	—
400	C₂²×M₁₆	—	146	2	no	—
401	C₂²×M₁₆	—	146	2	no	—
402	C₂³×C₈	—	73	1	no	—
403	C₂×#117	—	73	1	no	—
404	#444	—	73	16	no	—
405	#444	—	73	16	no	—
406	#443	—	73	8	no	—
407	#443	—	73	8	no	—
408	#443	—	73	8	no	—
409	#443	C₂×D₇₃	1	8	yes	complemented
410	C₂×#108	—	73	2	no	—
411	C₂×#108	—	73	1	no	—
412	C₂×#108	—	73	8	no	—
413	C₂×#108	C₂×D₇₃	1	1	yes	characteristic, complemented
414	#421	—	73	16	no	—
415	C₂×#104	—	73	2	no	—
416	C₂×#104	—	73	2	no	—
417	C₂×#104	—	73	2	no	—
418	C₂×#104	C₂×D₇₃	1	2	yes	complemented
419	#405	—	73	8	no	—
420	C₂×#97	—	73	1	no	—
421	C₂×#97	—	73	1	no	—
422	C₂×C₄×C₈	—	73	1	no	—
423	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic, complemented
424	C₂×#41	—	73	8	no	—
425	C₂×#41	—	73	8	no	—
426	C₂×#41	—	73	2	no	—
427	C₂×#41	—	73	2	no	—
428	C₂×#41	—	73	2	no	—
429	C₂×#41	—	146	2	no	—
430	C₂×#41	—	146	2	no	—
431	C₂×#41	—	146	4	no	—
432	C₂×#41	—	146	4	no	—
433	C₂×#41	C₂²×D₇₃	1	2	yes	—
434	C₂²×Q₈	—	73	2	no	—
435	C₂²×D₄	—	73	2	no	—
436	C₂²×D₄	—	146	2	no	—
437	C₂³×C₄	—	73	1	no	—
438	C₂³×C₄	—	146	2	no	—
439	#135	—	73	8	no	—
440	#135	—	73	8	no	—
441	#135	—	73	8	no	—
442	#135	—	73	16	no	—
443	#135	—	73	8	no	—
444	#135	—	73	4	no	—
445	#135	—	73	4	no	—
446	#135	C₄×D₇₃	1	4	yes	—
447	#135	C₂²×D₇₃	1	4	yes	—
448	C₂×Q₁₆	—	73	2	no	—
449	C₂×Q₁₆	—	73	8	no	—
450	C₂×Q₁₆	—	73	1	no	—
451	C₂×Q₁₆	C₄×D₇₃	1	1	yes	characteristic
452	C₂×SD₁₆	—	73	2	no	—
453	C₂×SD₁₆	—	73	2	no	—
454	C₂×SD₁₆	—	73	16	no	—
455	C₂×SD₁₆	—	73	2	no	—
456	C₂×SD₁₆	C₄×D₇₃	1	2	yes	—
457	C₂×D₈	—	73	2	no	—
458	C₂×D₈	—	73	8	no	—
459	C₂×D₈	—	73	1	no	—
460	C₂×D₈	C₄×D₇₃	1	1	yes	characteristic
461	#131	—	2	4	no	—
462	#131	—	73	8	no	—
463	#131	—	73	8	no	—
464	#131	—	73	8	no	—
465	#131	—	146	16	no	—
466	#131	—	146	4	no	—
467	#131	—	146	4	no	—
468	#131	—	146	16	no	—
469	#131	—	146	4	no	—
470	#131	C₂²×D₇₃	1	8	yes	complemented
471	C₂×M₁₆	—	2	2	no	—
472	C₂×M₁₆	—	73	1	no	—
473	C₂×M₁₆	—	73	1	no	—
474	C₂×M₁₆	—	73	1	no	—
475	C₂×M₁₆	—	73	1	no	—
476	C₂×M₁₆	—	73	4	no	—
477	C₂×M₁₆	—	73	4	no	—
478	C₂×M₁₆	—	73	2	no	—
479	C₂×M₁₆	—	73	8	no	—
480	C₂×M₁₆	—	146	2	no	—
481	C₂×M₁₆	—	146	16	no	—
482	C₂×M₁₆	—	146	2	no	—
483	C₂×M₁₆	—	146	2	no	—
484	C₂×M₁₆	—	146	16	no	—
485	C₂×M₁₆	—	146	4	no	—
486	C₂×M₁₆	—	146	2	no	—
487	C₂×M₁₆	C₂²×D₇₃	1	2	yes	—
488	C₂²×C₈	—	2	2	no	—
489	C₂²×C₈	—	73	1	no	—
490	C₂²×C₈	—	73	1	no	—
491	C₂²×C₈	—	73	1	no	—
492	C₂²×C₈	—	73	1	no	—
493	C₂²×C₈	—	73	1	no	—
494	C₂²×C₈	—	73	1	no	—
495	C₂²×C₈	—	73	4	no	—
496	C₂²×C₈	—	73	4	no	—
497	C₂²×C₈	—	146	2	no	—
498	C₂²×C₈	—	146	2	no	—
499	C₂²×C₈	—	146	2	no	—
500	C₂²×C₈	—	146	2	no	—
501	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
502	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
503	#117	—	73	4	no	—
504	#117	—	146	2	no	—
505	C₂×C₄⋊C₄	—	146	1	no	—
506	C₂×C₂²⋊C₄	—	146	1	no	—
507	C₂×C₄²	—	73	1	no	—
508	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
509	#108	—	73	8	no	—
510	#108	—	73	4	no	—
511	#108	C₂²×D₇₃	1	4	yes	complemented
512	#104	—	73	8	no	—
513	#104	—	73	8	no	—
514	#104	—	73	8	no	—
515	#104	C₂²×D₇₃	1	8	yes	complemented
516	#97	—	73	4	no	—
517	#97	—	73	4	no	—
518	C₄×C₈	—	73	4	no	—
519	C₄×C₈	C₂²×D₇₃	1	4	yes	complemented
520	C₂⁴	—	73	1	no	—
521	C₂⁴	—	146	2	no	—
522	#41	—	2	2	no	—
523	#41	—	2	2	no	—
524	#41	—	73	8	no	—
525	#41	—	73	8	no	—
526	#41	—	73	4	no	—
527	#41	—	73	4	no	—
528	#41	—	146	8	no	—
529	#41	—	146	8	no	—
530	#41	—	146	8	no	—
531	#41	—	146	8	no	—
532	#41	—	146	4	no	—
533	#41	—	146	4	no	—
534	#41	—	146	2	no	—
535	#41	—	146	2	no	—
536	#41	C₂×C₄×D₇₃	1	4	yes	—
537	#41	C₂³×D₇₃	1	4	yes	—
538	C₂×Q₈	—	73	8	no	—
539	C₂×Q₈	—	73	2	no	—
540	C₂×Q₈	—	146	2	no	—
541	C₂×Q₈	—	146	4	no	—
542	C₂×Q₈	C₂×C₄×D₇₃	1	2	yes	—
543	C₂×D₄	—	2	2	no	—
544	C₂×D₄	—	73	8	no	—
545	C₂×D₄	—	73	2	no	—
546	C₂×D₄	—	146	2	no	—
547	C₂×D₄	—	146	4	no	—
548	C₂×D₄	—	146	2	no	—
549	C₂×D₄	—	146	8	no	—
550	C₂×D₄	—	146	8	no	—
551	C₂×D₄	—	146	2	no	—
552	C₂×D₄	—	146	2	no	—
553	C₂×D₄	C₂×C₄×D₇₃	1	2	yes	—
554	C₂²×C₄	—	2	2	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	73	1	no	—
557	C₂²×C₄	—	73	1	no	—
558	C₂²×C₄	—	73	1	no	—
559	C₂²×C₄	—	73	2	no	—
560	C₂²×C₄	—	73	2	no	—
561	C₂²×C₄	—	73	1	no	—
562	C₂²×C₄	—	73	1	no	—
563	C₂²×C₄	—	73	2	no	—
564	C₂²×C₄	—	73	2	no	—
565	C₂²×C₄	—	146	8	no	—
566	C₂²×C₄	—	146	2	no	—
567	C₂²×C₄	—	146	8	no	—
568	C₂²×C₄	—	146	2	no	—
569	C₂²×C₄	—	146	1	no	—
570	C₂²×C₄	—	146	2	no	—
571	C₂²×C₄	—	146	2	no	—
572	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
573	Q₁₆	—	73	8	no	—
574	Q₁₆	—	73	4	no	—
575	Q₁₆	C₂×C₄×D₇₃	1	4	yes	—
576	SD₁₆	—	73	8	no	—
577	SD₁₆	—	73	8	no	—
578	SD₁₆	—	73	8	no	—
579	SD₁₆	C₂×C₄×D₇₃	1	8	yes	—
580	D₈	—	73	8	no	—
581	D₈	—	73	4	no	—
582	D₈	C₂×C₄×D₇₃	1	4	yes	—
583	M₁₆	—	2	2	no	—
584	M₁₆	—	2	8	no	—
585	M₁₆	—	73	4	no	—
586	M₁₆	—	73	4	no	—
587	M₁₆	—	73	4	no	—
588	M₁₆	—	73	4	no	—
589	M₁₆	—	73	4	no	—
590	M₁₆	—	146	8	no	—
591	M₁₆	—	146	8	no	—
592	M₁₆	—	146	8	no	—
593	M₁₆	—	146	2	no	—
594	M₁₆	—	146	8	no	—
595	M₁₆	C₂³×D₇₃	1	4	yes	—
596	C₂×C₈	—	2	2	no	—
597	C₂×C₈	—	2	8	no	—
598	C₂×C₈	—	73	1	no	—
599	C₂×C₈	—	73	1	no	—
600	C₂×C₈	—	73	2	no	—
601	C₂×C₈	—	73	2	no	—
602	C₂×C₈	—	73	1	no	—
603	C₂×C₈	—	73	1	no	—
604	C₂×C₈	—	73	2	no	—
605	C₂×C₈	—	73	2	no	—
606	C₂×C₈	—	73	4	no	—
607	C₂×C₈	—	73	4	no	—
608	C₂×C₈	—	73	4	no	—
609	C₂×C₈	—	73	4	no	—
610	C₂×C₈	—	146	8	no	—
611	C₂×C₈	—	146	8	no	—
612	C₂×C₈	—	146	8	no	—
613	C₂×C₈	—	146	2	no	—
614	C₂×C₈	—	146	8	no	—
615	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
616	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
617	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
618	C₂×C₈	D₄×D₇₃	1	2	yes	—
619	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
620	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
621	C₂×C₈	C₂³×D₇₃	1	2	yes	—
622	C₂×C₈	C₂³×D₇₃	1	2	yes	—
623	C₄⋊C₄	—	146	4	no	—
624	C₂²⋊C₄	—	146	4	no	—
625	C₄²	—	2	1	no	—
626	C₄²	—	73	2	no	—
627	C₄²	—	146	1	no	—
628	C₄²	C₂³×D₇₃	1	2	yes	—
629	C₂³	—	2	2	no	—
630	C₂³	—	292	2	no	—
631	C₂³	—	584	4	no	—
632	C₂³	—	73	2	no	—
633	C₂³	—	73	2	no	—
634	C₂³	—	73	1	no	—
635	C₂³	—	73	1	no	—
636	C₂³	—	146	8	no	—
637	C₂³	—	146	2	no	—
638	C₂³	#41×D₇₃	1	1	yes	characteristic
639	Q₈	—	2	2	no	—
640	Q₈	—	73	4	no	—
641	Q₈	—	146	8	no	—
642	Q₈	—	146	2	no	—
643	Q₈	C₂²×C₄×D₇₃	1	4	yes	—
644	D₄	—	2	4	no	—
645	D₄	—	2	4	no	—
646	D₄	—	2	2	no	—
647	D₄	—	73	4	no	—
648	D₄	—	146	8	no	—
649	D₄	—	146	8	no	—
650	D₄	—	146	8	no	—
651	D₄	—	146	4	no	—
652	D₄	—	146	4	no	—
653	D₄	—	146	2	no	—
654	D₄	C₂²×C₄×D₇₃	1	4	yes	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	4	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	4	2	no	—
660	C₂×C₄	—	292	2	no	—
661	C₂×C₄	—	73	2	no	—
662	C₂×C₄	—	73	1	no	—
663	C₂×C₄	—	73	1	no	—
664	C₂×C₄	—	73	2	no	—
665	C₂×C₄	—	73	2	no	—
666	C₂×C₄	—	73	2	no	—
667	C₂×C₄	—	73	2	no	—
668	C₂×C₄	—	73	2	no	—
669	C₂×C₄	—	73	2	no	—
670	C₂×C₄	—	73	2	no	—
671	C₂×C₄	—	73	2	no	—
672	C₂×C₄	—	73	2	no	—
673	C₂×C₄	—	146	8	no	—
674	C₂×C₄	—	146	8	no	—
675	C₂×C₄	—	146	2	no	—
676	C₂×C₄	—	146	8	no	—
677	C₂×C₄	—	146	2	no	—
678	C₂×C₄	—	146	4	no	—
679	C₂×C₄	—	146	4	no	—
680	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
681	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
682	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
683	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
684	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
685	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
686	C₈	—	2	4	no	—
687	C₈	—	73	2	no	—
688	C₈	—	73	2	no	—
689	C₈	—	73	2	no	—
690	C₈	—	73	2	no	—
691	C₈	—	146	4	no	—
692	C₈	C₂²×C₄×D₇₃	1	2	yes	—
693	C₈	C₂²×C₄×D₇₃	1	2	yes	—
694	C₈	C₂×D₄×D₇₃	1	2	yes	—
695	C₈	C₂×D₄×D₇₃	1	2	yes	—
696	C₂²	—	2	2	no	—
697	C₂²	—	2	4	no	—
698	C₂²	—	4	4	no	—
699	C₂²	—	292	2	no	—
700	C₂²	—	292	2	no	—
701	C₂²	—	292	4	no	—
702	C₂²	—	584	8	no	—
703	C₂²	—	73	2	no	—
704	C₂²	—	73	2	no	—
705	C₂²	—	146	4	no	—
706	C₂²	—	146	2	no	—
707	C₂²	—	146	2	no	—
708	C₂²	C₄×D₄×D₇₃	1	1	yes	characteristic
709	C₂²	C₄×D₄×D₇₃	1	1	yes	characteristic
710	C₂²	C₂×#41×D₇₃	1	1	yes	characteristic
711	C₄	—	2	4	no	—
712	C₄	—	4	2	no	—
713	C₄	—	292	2	no	—
714	C₄	—	73	2	no	—
715	C₄	—	73	2	no	—
716	C₄	—	146	4	no	—
717	C₄	C₄×D₄×D₇₃	1	1	yes	characteristic
718	C₄	C₄×D₄×D₇₃	1	1	yes	characteristic
719	C₄	C₂³×C₄×D₇₃	1	1	yes	characteristic
720	C₄	C₂²×D₄×D₇₃	1	1	yes	characteristic
721	C₂	—	2	1	no	—
722	C₂	—	2	1	no	—
723	C₂	—	4	4	no	—
724	C₂	—	292	4	no	—
725	C₂	—	146	2	no	—
726	C₂	—	146	2	no	—
727	C₂	#22618843	1	2	yes	direct product factor
728	C₂	C₂×C₄×D₄×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₃
commutator	C₄×C₇₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₂×#443×C₇₃	C₂
socle	C₂²×C₇₃	C₂×C₄×D₄
prime radical	C₂×#135×D₇₃	C₂
cosocle	C₂×C₄×C₇₃	C₂⁵
hypercenter	C₂×#443	D₇₃
hypocenter	C₇₃	C₂×#2957
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×#443

Complements

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

N	H ≅ G/N	type
2. C₂×#17989352	C₂	semidirect
3. #22618843	C₂	direct (N × H)
4. C₂×#17988707	C₂	semidirect
5. C₂×#17988706	C₂	semidirect
6. C₂×#17988705	C₂	semidirect
7. C₂×#17988704	C₂	semidirect
8. C₂×#17988703	C₂	semidirect
9. C₂×#108×D₇₃	C₂	semidirect
10. C₂×#17988602	C₂	semidirect
11. C₂×#17988541	C₂	semidirect
12. C₂×#443×C₇₃	C₂	semidirect
14. C₂×#14556614	C₄	semidirect
16. C₂×#14556612	C₄	semidirect
18. C₂×#14556610	C₄	semidirect
19. #135×D₇₃	C₄	semidirect
21. C₂×Q₁₆×D₇₃	C₄	semidirect
22. C₂×SD₁₆×D₇₃	C₄	semidirect
23. C₂×D₈×D₇₃	C₄	semidirect
25. #17989352	C₂²	semidirect
27. C₂×#14556599	C₂²	semidirect
28. C₂×#14556598	C₂²	semidirect
30. C₂×#14556597	C₂²	semidirect
37. #17988707	C₂²	semidirect
38. #17988706	C₂²	semidirect
39. #17988705	C₂²	semidirect
40. #17988704	C₂²	semidirect
41. #17988703	C₂²	semidirect
42. C₂×#14556527	C₂²	semidirect
43. C₂×#14556526	C₂²	semidirect
44. #108×D₇₃	C₂²	semidirect
45. #17988602	C₂²	semidirect
46. C₂×#14556519	C₂²	semidirect
47. C₂×#14556518	C₂²	semidirect
48. C₂×#14556517	C₂²	semidirect
49. #17988541	C₂²	semidirect
50. C₂×#14556502	C₂²	semidirect
51. C₂×#14556501	C₂²	semidirect
52. C₂×C₈×Dic₇₃	C₂²	semidirect
54. C₂×#131×C₇₃	C₂²	semidirect
55. #443×C₇₃	C₂²	semidirect
56. C₂×#108×C₇₃	C₂²	semidirect
57. C₂×#104×C₇₃	C₂²	semidirect
58. C₂×C₄×C₈×C₇₃	C₂²	semidirect
73. #14556614	C₂×C₄	semidirect
76. #14556612	C₂×C₄	semidirect
79. #14556610	C₂×C₄	semidirect
82. Q₁₆×D₇₃	C₂×C₄	semidirect
86. SD₁₆×D₇₃	C₂×C₄	semidirect
89. D₈×D₇₃	C₂×C₄	semidirect
92. #14556599	C₂³	semidirect
94. #14556598	C₂³	semidirect
97. #14556597	C₂³	semidirect
130. #14556527	C₂³	semidirect
131. #14556526	C₂³	semidirect
132. #14556519	C₂³	semidirect
133. #14556518	C₂³	semidirect
134. #14556517	C₂³	semidirect
135. #14556502	C₂³	semidirect
136. #14556501	C₂³	semidirect
137. C₈×Dic₇₃	C₂³	semidirect
145. #131×C₇₃	C₂³	semidirect
152. #108×C₇₃	C₂³	semidirect
153. #104×C₇₃	C₂³	semidirect
154. C₄×C₈×C₇₃	C₂³	semidirect
360. C₂×C₇₃	#2957	semidirect
373. C₂×#443	D₇₃	semidirect
377. C₇₃	C₂×#2957	semidirect
397. C₂×#131	C₂×D₇₃	semidirect
409. #443	C₂×D₇₃	semidirect
413. C₂×#108	C₂×D₇₃	semidirect
418. C₂×#104	C₂×D₇₃	semidirect
423. C₂×C₄×C₈	C₂×D₇₃	semidirect
470. #131	C₂²×D₇₃	semidirect
511. #108	C₂²×D₇₃	semidirect
515. #104	C₂²×D₇₃	semidirect
519. C₄×C₈	C₂²×D₇₃	semidirect
727. C₂	#22618843	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×#135×D₇₃	2
C₂×#17989352	2
#22618843	2
C₂×#17988707	2
C₂×#17988706	2
C₂×#17988705	2
C₂×#17988704	2
C₂×#17988703	2
C₂×#108×D₇₃	2
C₂×#17988602	2
C₂×#17988541	2
C₂×#443×C₇₃	2
C₂×#2957	73

Subgroups — C2×#22618843 #33950300

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22618843 #33950300