Subgroups — C₂×#22618845 #33950302

Order 18688.

2642 conjugacy classes of subgroups.

The subgroup lattice has 714 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	#22618845	C₂	1	16	yes	maximal, direct product factor
4	C₂×#17988710	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#17988709	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#17988708	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#17988702	C₂	1	2	yes	maximal, complemented
8	C₂×#17988701	C₂	1	2	yes	maximal, complemented
9	C₂×#108×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#17988602	C₂	1	2	yes	maximal, complemented
11	C₂×#17988544	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#444×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	#17988710	C₂²	1	8	yes	complemented
38	#17988709	C₂²	1	8	yes	complemented
39	#17988708	C₂²	1	8	yes	complemented
40	#17988702	C₂²	1	16	yes	complemented
41	#17988701	C₂²	1	16	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	#17988544	C₂²	1	8	yes	complemented
50	C₂×#14556501	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₄×#10596831	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	#444×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×#97×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	2	yes	—
105	C₂×#11924011	D₄	1	2	yes	—
106	C₂×#11924011	D₄	1	4	yes	—
107	C₂×#11924011	C₂³	1	4	yes	—
108	M₁₆×D₇₃	—	2	4	no	—
109	M₁₆×D₇₃	—	2	16	no	—
110	M₁₆×D₇₃	C₂³	1	8	yes	—
111	C₂²×#10596831	—	2	2	no	—
112	C₂²×#10596831	C₂³	1	1	yes	characteristic
113	C₂²×#10596831	C₂³	1	1	yes	characteristic
114	C₂×C₈×D₇₃	—	2	2	no	—
115	C₂×C₈×D₇₃	—	2	2	no	—
116	C₂×C₈×D₇₃	—	2	2	no	—
117	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
118	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
119	C₂×C₈×D₇₃	C₂×C₄	1	4	yes	—
120	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
121	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
122	C₂×C₈×D₇₃	C₂³	1	4	yes	—
123	#14556548	—	2	2	no	—
124	#14556548	C₂³	1	4	yes	—
125	C₂×#11924007	—	2	1	no	—
126	C₂×#11924005	—	2	1	no	—
127	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
128	#14556527	C₂³	1	4	yes	complemented
129	#14556526	C₂³	1	8	yes	complemented
130	#14556519	C₂³	1	8	yes	complemented
131	#14556518	C₂³	1	8	yes	complemented
132	#14556517	C₂³	1	8	yes	complemented
133	#14556501	C₂³	1	4	yes	complemented
134	C₄×#10596831	C₂³	1	4	yes	complemented
135	C₈×Dic₇₃	C₂³	1	4	yes	complemented
136	C₂×#41×C₇₃	C₂³	1	2	yes	—
137	#135×C₇₃	C₂×C₄	1	4	yes	—
138	#135×C₇₃	C₂³	1	4	yes	—
139	C₂×Q₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
140	C₂×SD₁₆×C₇₃	C₂×C₄	1	2	yes	—
141	C₂×D₈×C₇₃	C₂×C₄	1	1	yes	characteristic
142	#131×C₇₃	—	2	4	no	—
143	#131×C₇₃	C₂³	1	8	yes	complemented
144	C₂×M₁₆×C₇₃	—	2	2	no	—
145	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
146	C₂²×C₈×C₇₃	—	2	2	no	—
147	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
148	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
149	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
150	#108×C₇₃	C₂³	1	4	yes	complemented
151	#104×C₇₃	C₂³	1	8	yes	complemented
152	#97×C₇₃	C₂³	1	4	yes	complemented
153	C₂³×D₇₃	—	2	2	no	—
154	C₂³×D₇₃	#41	1	1	yes	characteristic
155	#11924029	—	2	4	no	—
156	#11924029	C₂²×C₄	1	8	yes	—
157	#11924028	—	2	2	no	—
158	#11924028	—	2	2	no	—
159	#11924028	—	2	8	no	—
160	#11924028	—	2	8	no	—
161	#11924028	C₂²×C₄	1	4	yes	—
162	#11924028	C₂⁴	1	4	yes	—
163	#11924027	—	2	8	no	—
164	#11924027	—	2	8	no	—
165	#11924027	—	2	4	no	—
166	#11924027	C₂²×C₄	1	8	yes	—
167	C₂×Dic₁₄₆	—	2	2	no	—
168	C₂×Dic₁₄₆	C₂²×C₄	1	2	yes	—
169	Q₈×D₇₃	—	2	4	no	—
170	Q₈×D₇₃	C₂²×C₄	1	8	yes	—
171	C₂×D₂₉₂	—	2	2	no	—
172	C₂×D₂₉₂	C₂²×C₄	1	2	yes	—
173	C₂×C₂²⋊D₇₃	—	2	2	no	—
174	C₂×C₂²⋊D₇₃	—	2	2	no	—
175	C₂×C₂²⋊D₇₃	—	2	2	no	—
176	D₄×D₇₃	—	2	8	no	—
177	D₄×D₇₃	—	2	8	no	—
178	D₄×D₇₃	—	2	4	no	—
179	D₄×D₇₃	C₂²×C₄	1	8	yes	—
180	C₂²×Dic₇₃	—	2	2	no	—
181	C₂²×Dic₇₃	—	2	1	no	—
182	C₂²×Dic₇₃	#41	1	1	yes	characteristic
183	C₂×C₄×D₇₃	—	2	2	no	—
184	C₂×C₄×D₇₃	—	2	2	no	—
185	C₂×C₄×D₇₃	—	2	2	no	—
186	C₂×C₄×D₇₃	—	2	8	no	—
187	C₂×C₄×D₇₃	—	2	8	no	—
188	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
190	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
192	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
193	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
194	C₂×C₄×D₇₃	#41	1	2	yes	—
195	C₂×C₄×D₇₃	C₂⁴	1	2	yes	—
196	Dic₂₉₂	C₂²×C₄	1	4	yes	—
197	#11924018	C₂²×C₄	1	8	yes	—
198	#11924017	C₂²×C₄	1	8	yes	—
199	#11924016	C₂²×C₄	1	8	yes	—
200	#11924015	C₂²×C₄	1	8	yes	—
201	D₅₈₄	C₂²×C₄	1	4	yes	—
202	#11924013	C₂²×C₄	1	8	yes	—
203	#11924012	—	2	2	no	—
204	#11924012	—	2	8	no	—
205	#11924012	C₂⁴	1	4	yes	—
206	#11924011	—	2	8	no	—
207	#11924011	—	2	8	no	—
208	#11924011	—	2	8	no	—
209	#11924011	C₂×D₄	1	8	yes	—
210	#11924011	C₂×D₄	1	8	yes	—
211	C₂×#10596831	—	2	2	no	—
212	C₂×#10596831	—	2	8	no	—
213	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
214	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
215	C₂×#10596831	C₂²×C₄	1	2	yes	—
216	C₂×#10596831	C₂×D₄	1	2	yes	—
217	C₂×#10596831	C₂×D₄	1	2	yes	—
218	C₂×#10596831	C₂⁴	1	2	yes	—
219	C₂×#10596831	C₂⁴	1	2	yes	—
220	C₈×D₇₃	—	2	8	no	—
221	C₈×D₇₃	—	2	8	no	—
222	C₈×D₇₃	—	2	8	no	—
223	C₈×D₇₃	C₂²×C₄	1	4	yes	—
224	C₈×D₇₃	C₂²×C₄	1	4	yes	—
225	C₈×D₇₃	C₂²×C₄	1	4	yes	—
226	C₈×D₇₃	C₂²×C₄	1	4	yes	—
227	#11924007	—	2	4	no	—
228	#11924005	—	2	4	no	—
229	C₄×Dic₇₃	—	2	1	no	—
230	C₄×Dic₇₃	C₂⁴	1	2	yes	—
231	#41×C₇₃	—	2	2	no	—
232	#41×C₇₃	—	2	2	no	—
233	#41×C₇₃	C₂²×C₄	1	4	yes	—
234	#41×C₇₃	C₂⁴	1	4	yes	—
235	C₂×Q₈×C₇₃	C₂²×C₄	1	2	yes	—
236	C₂×D₄×C₇₃	—	2	2	no	—
237	C₂×D₄×C₇₃	C₂²×C₄	1	2	yes	—
238	C₂²×C₄×C₇₃	—	2	2	no	—
239	C₂²×C₄×C₇₃	—	2	1	no	—
240	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
241	Q₁₆×C₇₃	C₂²×C₄	1	4	yes	—
242	SD₁₆×C₇₃	C₂²×C₄	1	8	yes	—
243	D₈×C₇₃	C₂²×C₄	1	4	yes	—
244	M₁₆×C₇₃	—	2	2	no	—
245	M₁₆×C₇₃	—	2	8	no	—
246	M₁₆×C₇₃	C₂⁴	1	4	yes	—
247	C₂×C₈×C₇₃	—	2	2	no	—
248	C₂×C₈×C₇₃	—	2	8	no	—
249	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
250	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
251	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
252	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
253	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
254	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
255	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
256	C₄²×C₇₃	—	2	1	no	—
257	C₄²×C₇₃	C₂⁴	1	2	yes	—
258	C₂³×C₇₃	—	2	2	no	—
259	C₂³×C₇₃	C₂×#41	1	1	yes	characteristic
260	C₂²×D₇₃	—	2	2	no	—
261	C₂²×D₇₃	—	2	8	no	—
262	C₂²×D₇₃	—	4	2	no	—
263	C₂²×D₇₃	—	8	4	no	—
264	C₂²×D₇₃	C₄×D₄	1	1	yes	characteristic
265	C₂²×D₇₃	C₄×D₄	1	1	yes	characteristic
266	C₂²×D₇₃	C₄×D₄	1	2	yes	—
267	C₂²×D₇₃	C₂×#41	1	2	yes	—
268	Q₈×C₇₃	—	2	2	no	—
269	Q₈×C₇₃	C₂³×C₄	1	4	yes	—
270	D₄×C₇₃	—	2	4	no	—
271	D₄×C₇₃	—	2	4	no	—
272	D₄×C₇₃	—	2	2	no	—
273	D₄×C₇₃	C₂³×C₄	1	4	yes	—
274	C₂×C₄×C₇₃	—	2	2	no	—
275	C₂×C₄×C₇₃	—	2	4	no	—
276	C₂×C₄×C₇₃	—	2	4	no	—
277	C₂×C₄×C₇₃	—	2	2	no	—
278	C₂×C₄×C₇₃	—	4	2	no	—
279	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
280	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
281	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
283	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
284	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
285	C₂²⋊D₇₃	—	2	4	no	—
286	C₂²⋊D₇₃	—	2	4	no	—
287	C₂²⋊D₇₃	—	2	8	no	—
288	C₂²⋊D₇₃	—	2	8	no	—
289	C₂×Dic₇₃	—	2	2	no	—
290	C₂×Dic₇₃	—	2	8	no	—
291	C₂×Dic₇₃	—	2	2	no	—
292	C₂×Dic₇₃	—	4	2	no	—
293	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
294	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
295	C₂×Dic₇₃	C₄×D₄	1	2	yes	—
296	C₂×Dic₇₃	C₂×#41	1	2	yes	—
297	D₂₉₂	—	2	8	no	—
298	D₂₉₂	—	2	2	no	—
299	D₂₉₂	C₂³×C₄	1	4	yes	—
300	C₄×D₇₃	—	2	8	no	—
301	C₄×D₇₃	—	2	4	no	—
302	C₄×D₇₃	—	2	4	no	—
303	C₄×D₇₃	—	2	8	no	—
304	C₄×D₇₃	C₄×D₄	1	2	yes	—
305	C₄×D₇₃	C₄×D₄	1	2	yes	—
306	C₄×D₇₃	C₄×D₄	1	2	yes	—
307	C₄×D₇₃	C₄×D₄	1	2	yes	—
308	C₄×D₇₃	C₂³×C₄	1	2	yes	—
309	C₄×D₇₃	C₂³×C₄	1	2	yes	—
310	C₄×D₇₃	C₂²×D₄	1	2	yes	—
311	C₄×D₇₃	C₂²×D₄	1	2	yes	—
312	Dic₁₄₆	—	2	2	no	—
313	Dic₁₄₆	—	2	8	no	—
314	Dic₁₄₆	C₂³×C₄	1	4	yes	—
315	C₈×C₇₃	—	2	4	no	—
316	C₈×C₇₃	C₂³×C₄	1	2	yes	—
317	C₈×C₇₃	C₂³×C₄	1	2	yes	—
318	C₈×C₇₃	C₂²×D₄	1	4	yes	—
319	#10596831	—	2	4	no	—
320	#10596831	C₂³×C₄	1	2	yes	—
321	#10596831	C₂³×C₄	1	2	yes	—
322	#10596831	C₂²×D₄	1	4	yes	—
323	C₂²×C₇₃	—	2	2	no	—
324	C₂²×C₇₃	—	2	4	no	—
325	C₂²×C₇₃	—	4	4	no	—
326	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
327	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
328	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
329	C₂×D₇₃	—	2	2	no	—
330	C₂×D₇₃	—	2	2	no	—
331	C₂×D₇₃	—	2	4	no	—
332	C₂×D₇₃	—	4	2	no	—
333	C₂×D₇₃	—	4	2	no	—
334	C₂×D₇₃	—	4	4	no	—
335	C₂×D₇₃	—	8	8	no	—
336	C₂×D₇₃	C₂×C₄×D₄	1	2	yes	—
337	C₂×D₇₃	C₂×C₄×D₄	1	2	yes	—
338	C₄×C₇₃	—	2	4	no	—
339	C₄×C₇₃	—	4	2	no	—
340	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
341	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
342	C₄×C₇₃	C₂⁴×C₄	1	1	yes	characteristic
343	C₄×C₇₃	C₂³×D₄	1	1	yes	characteristic
344	Dic₇₃	—	2	4	no	—
345	Dic₇₃	—	4	2	no	—
346	Dic₇₃	C₂×C₄×D₄	1	2	yes	—
347	Dic₇₃	C₂×C₄×D₄	1	2	yes	—
348	C₂×#2957	—	73	1	no	maximal, Sylow
349	C₂×C₇₃	—	2	1	no	—
350	C₂×C₇₃	—	2	1	no	—
351	C₂×C₇₃	—	4	4	no	—
352	C₂×C₇₃	#2957	1	2	yes	complemented
353	C₂×C₇₃	C₂²×C₄×D₄	1	1	yes	characteristic
354	D₇₃	—	2	2	no	—
355	D₇₃	—	2	2	no	—
356	D₇₃	—	4	4	no	—
357	C₂²×#135	—	73	1	no	—
358	C₂×#568	—	73	2	no	—
359	#2957	—	73	16	no	—
360	C₂×#444	—	73	1	no	—
361	C₂×#444	—	73	1	no	—
362	C₂×#444	—	73	1	no	—
363	C₂×#444	D₇₃	1	1	yes	characteristic, complemented
364	C₂×#443	—	73	2	no	—
365	C₂×#443	—	73	2	no	—
366	C₂²×#108	—	73	1	no	—
367	C₂×#421	—	73	2	no	—
368	C₂×#405	—	73	1	no	—
369	C₇₃	C₂×#2957	1	1	yes	characteristic, complemented, Sylow
370	C₂²×#41	—	73	2	no	—
371	C₂×#135	—	73	2	no	—
372	C₂×#135	—	73	8	no	—
373	C₂×#135	—	73	8	no	—
374	C₂×#135	—	73	1	no	—
375	C₂×#135	—	73	2	no	—
376	C₂×#135	—	73	1	no	—
377	C₂×#135	—	73	1	no	—
378	C₂×#135	C₂×D₇₃	1	1	yes	characteristic
379	C₂²×Q₁₆	—	73	1	no	—
380	C₂²×SD₁₆	—	73	2	no	—
381	C₂²×D₈	—	73	1	no	—
382	#568	—	73	16	no	—
383	#568	—	146	8	no	—
384	C₂×#131	—	73	2	no	—
385	C₂×#131	—	73	2	no	—
386	C₂×#131	—	73	2	no	—
387	C₂×#131	—	146	2	no	—
388	C₂×#131	—	146	2	no	—
389	C₂×#131	C₂×D₇₃	1	2	yes	complemented
390	C₂²×M₁₆	—	73	1	no	—
391	C₂²×M₁₆	—	73	2	no	—
392	C₂²×M₁₆	—	146	2	no	—
393	C₂²×M₁₆	—	146	2	no	—
394	C₂³×C₈	—	73	1	no	—
395	C₂×#117	—	73	1	no	—
396	#444	—	73	8	no	—
397	#444	—	73	8	no	—
398	#444	—	73	8	no	—
399	#444	C₂×D₇₃	1	8	yes	complemented
400	#443	—	73	16	no	—
401	#443	—	73	16	no	—
402	C₂×#108	—	73	2	no	—
403	C₂×#108	—	73	1	no	—
404	C₂×#108	—	73	8	no	—
405	C₂×#108	C₂×D₇₃	1	1	yes	characteristic, complemented
406	#421	—	73	16	no	—
407	C₂×#104	—	73	2	no	—
408	C₂×#104	—	73	2	no	—
409	C₂×#104	—	73	2	no	—
410	C₂×#104	C₂×D₇₃	1	2	yes	complemented
411	#405	—	73	8	no	—
412	C₂×#97	—	73	1	no	—
413	C₂×#97	C₂×D₇₃	1	1	yes	characteristic, complemented
414	C₂×C₄×C₈	—	73	1	no	—
415	C₂×C₄×C₈	—	73	1	no	—
416	C₂×#41	—	73	8	no	—
417	C₂×#41	—	73	8	no	—
418	C₂×#41	—	73	2	no	—
419	C₂×#41	—	73	2	no	—
420	C₂×#41	—	73	2	no	—
421	C₂×#41	—	146	2	no	—
422	C₂×#41	—	146	2	no	—
423	C₂×#41	—	146	4	no	—
424	C₂×#41	—	146	4	no	—
425	C₂×#41	C₂²×D₇₃	1	2	yes	—
426	C₂²×Q₈	—	73	2	no	—
427	C₂²×D₄	—	73	2	no	—
428	C₂²×D₄	—	146	2	no	—
429	C₂³×C₄	—	73	1	no	—
430	C₂³×C₄	—	146	2	no	—
431	#135	—	73	8	no	—
432	#135	—	73	8	no	—
433	#135	—	73	8	no	—
434	#135	—	73	16	no	—
435	#135	—	73	8	no	—
436	#135	—	73	4	no	—
437	#135	—	73	4	no	—
438	#135	C₄×D₇₃	1	4	yes	—
439	#135	C₂²×D₇₃	1	4	yes	—
440	C₂×Q₁₆	—	73	2	no	—
441	C₂×Q₁₆	—	73	8	no	—
442	C₂×Q₁₆	—	73	1	no	—
443	C₂×Q₁₆	C₄×D₇₃	1	1	yes	characteristic
444	C₂×SD₁₆	—	73	2	no	—
445	C₂×SD₁₆	—	73	2	no	—
446	C₂×SD₁₆	—	73	16	no	—
447	C₂×SD₁₆	—	73	2	no	—
448	C₂×SD₁₆	C₄×D₇₃	1	2	yes	—
449	C₂×D₈	—	73	2	no	—
450	C₂×D₈	—	73	8	no	—
451	C₂×D₈	—	73	1	no	—
452	C₂×D₈	C₄×D₇₃	1	1	yes	characteristic
453	#131	—	2	4	no	—
454	#131	—	73	8	no	—
455	#131	—	73	8	no	—
456	#131	—	73	8	no	—
457	#131	—	146	16	no	—
458	#131	—	146	4	no	—
459	#131	—	146	4	no	—
460	#131	—	146	16	no	—
461	#131	—	146	4	no	—
462	#131	C₂²×D₇₃	1	8	yes	complemented
463	C₂×M₁₆	—	2	2	no	—
464	C₂×M₁₆	—	73	2	no	—
465	C₂×M₁₆	—	73	2	no	—
466	C₂×M₁₆	—	73	4	no	—
467	C₂×M₁₆	—	73	4	no	—
468	C₂×M₁₆	—	73	2	no	—
469	C₂×M₁₆	—	73	8	no	—
470	C₂×M₁₆	—	146	2	no	—
471	C₂×M₁₆	—	146	16	no	—
472	C₂×M₁₆	—	146	2	no	—
473	C₂×M₁₆	—	146	2	no	—
474	C₂×M₁₆	—	146	16	no	—
475	C₂×M₁₆	—	146	4	no	—
476	C₂×M₁₆	—	146	2	no	—
477	C₂×M₁₆	C₂²×D₇₃	1	2	yes	—
478	C₂²×C₈	—	2	2	no	—
479	C₂²×C₈	—	73	1	no	—
480	C₂²×C₈	—	73	1	no	—
481	C₂²×C₈	—	73	1	no	—
482	C₂²×C₈	—	73	1	no	—
483	C₂²×C₈	—	73	1	no	—
484	C₂²×C₈	—	73	1	no	—
485	C₂²×C₈	—	73	4	no	—
486	C₂²×C₈	—	73	4	no	—
487	C₂²×C₈	—	146	2	no	—
488	C₂²×C₈	—	146	2	no	—
489	C₂²×C₈	—	146	2	no	—
490	C₂²×C₈	—	146	2	no	—
491	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
492	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
493	#117	—	73	4	no	—
494	#117	—	146	2	no	—
495	C₂×C₄⋊C₄	—	146	1	no	—
496	C₂×C₂²⋊C₄	—	146	1	no	—
497	C₂×C₄²	—	73	1	no	—
498	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
499	#108	—	73	8	no	—
500	#108	—	73	4	no	—
501	#108	C₂²×D₇₃	1	4	yes	complemented
502	#104	—	73	8	no	—
503	#104	—	73	8	no	—
504	#104	—	73	8	no	—
505	#104	C₂²×D₇₃	1	8	yes	complemented
506	#97	—	73	4	no	—
507	#97	C₂²×D₇₃	1	4	yes	complemented
508	C₄×C₈	—	73	4	no	—
509	C₄×C₈	—	73	4	no	—
510	C₂⁴	—	73	1	no	—
511	C₂⁴	—	146	2	no	—
512	#41	—	2	2	no	—
513	#41	—	2	2	no	—
514	#41	—	73	8	no	—
515	#41	—	73	8	no	—
516	#41	—	73	4	no	—
517	#41	—	73	4	no	—
518	#41	—	146	8	no	—
519	#41	—	146	8	no	—
520	#41	—	146	8	no	—
521	#41	—	146	8	no	—
522	#41	—	146	4	no	—
523	#41	—	146	4	no	—
524	#41	—	146	2	no	—
525	#41	—	146	2	no	—
526	#41	C₂×C₄×D₇₃	1	4	yes	—
527	#41	C₂³×D₇₃	1	4	yes	—
528	C₂×Q₈	—	73	8	no	—
529	C₂×Q₈	—	73	2	no	—
530	C₂×Q₈	—	146	2	no	—
531	C₂×Q₈	—	146	4	no	—
532	C₂×Q₈	C₂×C₄×D₇₃	1	2	yes	—
533	C₂×D₄	—	2	2	no	—
534	C₂×D₄	—	73	8	no	—
535	C₂×D₄	—	73	2	no	—
536	C₂×D₄	—	146	2	no	—
537	C₂×D₄	—	146	4	no	—
538	C₂×D₄	—	146	2	no	—
539	C₂×D₄	—	146	8	no	—
540	C₂×D₄	—	146	8	no	—
541	C₂×D₄	—	146	2	no	—
542	C₂×D₄	—	146	2	no	—
543	C₂×D₄	C₂×C₄×D₇₃	1	2	yes	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	73	1	no	—
547	C₂²×C₄	—	73	1	no	—
548	C₂²×C₄	—	73	1	no	—
549	C₂²×C₄	—	73	2	no	—
550	C₂²×C₄	—	73	2	no	—
551	C₂²×C₄	—	73	1	no	—
552	C₂²×C₄	—	73	1	no	—
553	C₂²×C₄	—	73	2	no	—
554	C₂²×C₄	—	73	2	no	—
555	C₂²×C₄	—	146	8	no	—
556	C₂²×C₄	—	146	2	no	—
557	C₂²×C₄	—	146	8	no	—
558	C₂²×C₄	—	146	2	no	—
559	C₂²×C₄	—	146	1	no	—
560	C₂²×C₄	—	146	2	no	—
561	C₂²×C₄	—	146	2	no	—
562	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
563	Q₁₆	—	73	8	no	—
564	Q₁₆	—	73	4	no	—
565	Q₁₆	C₂×C₄×D₇₃	1	4	yes	—
566	SD₁₆	—	73	8	no	—
567	SD₁₆	—	73	8	no	—
568	SD₁₆	—	73	8	no	—
569	SD₁₆	C₂×C₄×D₇₃	1	8	yes	—
570	D₈	—	73	8	no	—
571	D₈	—	73	4	no	—
572	D₈	C₂×C₄×D₇₃	1	4	yes	—
573	M₁₆	—	2	2	no	—
574	M₁₆	—	2	8	no	—
575	M₁₆	—	73	8	no	—
576	M₁₆	—	73	8	no	—
577	M₁₆	—	73	4	no	—
578	M₁₆	—	146	8	no	—
579	M₁₆	—	146	8	no	—
580	M₁₆	—	146	8	no	—
581	M₁₆	—	146	2	no	—
582	M₁₆	—	146	8	no	—
583	M₁₆	C₂³×D₇₃	1	4	yes	—
584	C₂×C₈	—	2	2	no	—
585	C₂×C₈	—	2	8	no	—
586	C₂×C₈	—	73	1	no	—
587	C₂×C₈	—	73	1	no	—
588	C₂×C₈	—	73	2	no	—
589	C₂×C₈	—	73	2	no	—
590	C₂×C₈	—	73	2	no	—
591	C₂×C₈	—	73	2	no	—
592	C₂×C₈	—	73	2	no	—
593	C₂×C₈	—	73	4	no	—
594	C₂×C₈	—	73	4	no	—
595	C₂×C₈	—	73	4	no	—
596	C₂×C₈	—	73	4	no	—
597	C₂×C₈	—	146	8	no	—
598	C₂×C₈	—	146	8	no	—
599	C₂×C₈	—	146	8	no	—
600	C₂×C₈	—	146	2	no	—
601	C₂×C₈	—	146	8	no	—
602	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
603	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
604	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
605	C₂×C₈	D₄×D₇₃	1	2	yes	—
606	C₂×C₈	D₄×D₇₃	1	2	yes	—
607	C₂×C₈	C₂³×D₇₃	1	2	yes	—
608	C₂×C₈	C₂³×D₇₃	1	2	yes	—
609	C₄⋊C₄	—	146	4	no	—
610	C₂²⋊C₄	—	146	4	no	—
611	C₄²	—	2	1	no	—
612	C₄²	—	73	2	no	—
613	C₄²	—	146	1	no	—
614	C₄²	C₂³×D₇₃	1	2	yes	—
615	C₂³	—	2	2	no	—
616	C₂³	—	292	2	no	—
617	C₂³	—	584	4	no	—
618	C₂³	—	73	2	no	—
619	C₂³	—	73	2	no	—
620	C₂³	—	73	1	no	—
621	C₂³	—	73	1	no	—
622	C₂³	—	146	8	no	—
623	C₂³	—	146	2	no	—
624	C₂³	#41×D₇₃	1	1	yes	characteristic
625	Q₈	—	2	2	no	—
626	Q₈	—	73	4	no	—
627	Q₈	—	146	8	no	—
628	Q₈	—	146	2	no	—
629	Q₈	C₂²×C₄×D₇₃	1	4	yes	—
630	D₄	—	2	4	no	—
631	D₄	—	2	4	no	—
632	D₄	—	2	2	no	—
633	D₄	—	73	4	no	—
634	D₄	—	146	8	no	—
635	D₄	—	146	8	no	—
636	D₄	—	146	8	no	—
637	D₄	—	146	4	no	—
638	D₄	—	146	4	no	—
639	D₄	—	146	2	no	—
640	D₄	C₂²×C₄×D₇₃	1	4	yes	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	4	2	no	—
646	C₂×C₄	—	292	2	no	—
647	C₂×C₄	—	73	2	no	—
648	C₂×C₄	—	73	1	no	—
649	C₂×C₄	—	73	1	no	—
650	C₂×C₄	—	73	2	no	—
651	C₂×C₄	—	73	2	no	—
652	C₂×C₄	—	73	2	no	—
653	C₂×C₄	—	73	2	no	—
654	C₂×C₄	—	73	2	no	—
655	C₂×C₄	—	73	2	no	—
656	C₂×C₄	—	73	2	no	—
657	C₂×C₄	—	73	2	no	—
658	C₂×C₄	—	73	2	no	—
659	C₂×C₄	—	146	8	no	—
660	C₂×C₄	—	146	8	no	—
661	C₂×C₄	—	146	2	no	—
662	C₂×C₄	—	146	8	no	—
663	C₂×C₄	—	146	2	no	—
664	C₂×C₄	—	146	4	no	—
665	C₂×C₄	—	146	4	no	—
666	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
667	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
668	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
669	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
670	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
671	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
672	C₈	—	2	4	no	—
673	C₈	—	73	2	no	—
674	C₈	—	73	2	no	—
675	C₈	—	73	4	no	—
676	C₈	—	146	4	no	—
677	C₈	C₂²×C₄×D₇₃	1	2	yes	—
678	C₈	C₂²×C₄×D₇₃	1	2	yes	—
679	C₈	C₂×D₄×D₇₃	1	4	yes	—
680	C₂²	—	2	2	no	—
681	C₂²	—	2	4	no	—
682	C₂²	—	4	4	no	—
683	C₂²	—	292	2	no	—
684	C₂²	—	292	2	no	—
685	C₂²	—	292	4	no	—
686	C₂²	—	584	8	no	—
687	C₂²	—	73	2	no	—
688	C₂²	—	73	2	no	—
689	C₂²	—	146	4	no	—
690	C₂²	—	146	2	no	—
691	C₂²	—	146	2	no	—
692	C₂²	C₄×D₄×D₇₃	1	1	yes	characteristic
693	C₂²	C₄×D₄×D₇₃	1	1	yes	characteristic
694	C₂²	C₂×#41×D₇₃	1	1	yes	characteristic
695	C₄	—	2	4	no	—
696	C₄	—	4	2	no	—
697	C₄	—	292	2	no	—
698	C₄	—	73	2	no	—
699	C₄	—	73	2	no	—
700	C₄	—	146	4	no	—
701	C₄	C₄×D₄×D₇₃	1	1	yes	characteristic
702	C₄	C₄×D₄×D₇₃	1	1	yes	characteristic
703	C₄	C₂³×C₄×D₇₃	1	1	yes	characteristic
704	C₄	C₂²×D₄×D₇₃	1	1	yes	characteristic
705	C₂	—	2	1	no	—
706	C₂	—	2	1	no	—
707	C₂	—	4	4	no	—
708	C₂	—	292	4	no	—
709	C₂	—	146	2	no	—
710	C₂	—	146	2	no	—
711	C₂	#22618845	1	2	yes	direct product factor
712	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×#444×C₇₃	C₂
socle	C₂²×C₇₃	C₂×C₄×D₄
prime radical	C₂×#135×D₇₃	C₂
cosocle	C₂×C₄×C₇₃	C₂⁵
hypercenter	C₂×#444	D₇₃
hypocenter	C₇₃	C₂×#2957
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×#444

Complements

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

N	H ≅ G/N	type
2. C₂×#17989352	C₂	semidirect
3. #22618845	C₂	direct (N × H)
4. C₂×#17988710	C₂	semidirect
5. C₂×#17988709	C₂	semidirect
6. C₂×#17988708	C₂	semidirect
7. C₂×#17988702	C₂	semidirect
8. C₂×#17988701	C₂	semidirect
9. C₂×#108×D₇₃	C₂	semidirect
10. C₂×#17988602	C₂	semidirect
11. C₂×#17988544	C₂	semidirect
12. C₂×#444×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. #17988710	C₂²	semidirect
38. #17988709	C₂²	semidirect
39. #17988708	C₂²	semidirect
40. #17988702	C₂²	semidirect
41. #17988701	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. #17988544	C₂²	semidirect
50. C₂×#14556501	C₂²	semidirect
51. C₂×C₄×#10596831	C₂²	semidirect
52. C₂×C₈×Dic₇₃	C₂²	semidirect
54. C₂×#131×C₇₃	C₂²	semidirect
55. #444×C₇₃	C₂²	semidirect
56. C₂×#108×C₇₃	C₂²	semidirect
57. C₂×#104×C₇₃	C₂²	semidirect
58. C₂×#97×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
128. #14556527	C₂³	semidirect
129. #14556526	C₂³	semidirect
130. #14556519	C₂³	semidirect
131. #14556518	C₂³	semidirect
132. #14556517	C₂³	semidirect
133. #14556501	C₂³	semidirect
134. C₄×#10596831	C₂³	semidirect
135. C₈×Dic₇₃	C₂³	semidirect
143. #131×C₇₃	C₂³	semidirect
150. #108×C₇₃	C₂³	semidirect
151. #104×C₇₃	C₂³	semidirect
152. #97×C₇₃	C₂³	semidirect
352. C₂×C₇₃	#2957	semidirect
363. C₂×#444	D₇₃	semidirect
369. C₇₃	C₂×#2957	semidirect
389. C₂×#131	C₂×D₇₃	semidirect
399. #444	C₂×D₇₃	semidirect
405. C₂×#108	C₂×D₇₃	semidirect
410. C₂×#104	C₂×D₇₃	semidirect
413. C₂×#97	C₂×D₇₃	semidirect
462. #131	C₂²×D₇₃	semidirect
501. #108	C₂²×D₇₃	semidirect
505. #104	C₂²×D₇₃	semidirect
507. #97	C₂²×D₇₃	semidirect
711. C₂	#22618845	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
#22618845	2
C₂×#17988710	2
C₂×#17988709	2
C₂×#17988708	2
C₂×#17988702	2
C₂×#17988701	2
C₂×#108×D₇₃	2
C₂×#17988602	2
C₂×#17988544	2
C₂×#444×C₇₃	2
C₂×#2957	73

Subgroups — C2×#22618845 #33950302

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22618845 #33950302