Subgroups — #33088843

Order 18688.

1002 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988644	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#11924012	C₂	1	1	yes	maximal, characteristic, complemented
3	#22610539	C₂	1	2	yes	maximal, complemented
4	#22610490	C₂	1	2	yes	maximal, complemented
5	#22610229	C₂	1	2	yes	maximal
6	#22610116	C₂	1	2	yes	maximal, complemented
7	#22609784	C₂	1	1	yes	maximal, characteristic, complemented
8	#22609693	C₂	1	1	yes	maximal, characteristic, complemented
9	#22609693	C₂	1	1	yes	maximal, characteristic, complemented
10	#22609680	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄²×D₄×C₇₃	C₂	1	1	yes	maximal, characteristic
12	C₂²×#11924012	C₂²	1	2	yes	—
13	#17988644	—	2	4	no	—
14	C₂×C₄⋊#10596831	C₂²	1	2	yes	—
15	C₂×C₄⋊#10596831	C₂²	1	2	yes	—
16	C₂×C₂²⋊#10596831	C₂²	1	2	yes	—
17	C₂×C₂²⋊#10596831	C₂²	1	2	yes	—
18	C₂×C₂²⋊#10596831	C₂²	1	2	yes	—
19	C₄×#11924012	—	2	4	no	—
20	C₂×#14556502	C₂²	1	1	yes	characteristic
21	C₂×#14556502	C₂²	1	1	yes	characteristic
22	C₂×#14556502	C₂²	1	1	yes	characteristic
23	C₂×#14556502	C₂²	1	1	yes	characteristic
24	C₂×C₄×#10596831	C₂²	1	2	yes	—
25	#17988342	C₂²	1	2	yes	—
26	#17988342	C₂²	1	2	yes	—
27	#17988342	C₂²	1	2	yes	—
28	#17988342	C₂²	1	2	yes	—
29	#17988342	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₇₃	C₄	1	1	yes	characteristic
31	C₂×C₄×D₄×C₇₃	C₄	1	1	yes	characteristic
32	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₇₃	C₄	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₇₃	C₄	1	1	yes	characteristic
37	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊C₄×C₇₃	C₄	1	1	yes	characteristic
39	C₄×C₂²⋊C₄×C₇₃	C₄	1	1	yes	characteristic
40	C₄×C₂²⋊C₄×C₇₃	C₄	1	1	yes	characteristic
41	C₄×C₂²⋊C₄×C₇₃	C₄	1	1	yes	characteristic
42	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
43	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
44	C₄³×C₇₃	C₂²	1	1	yes	characteristic
45	C₂×#11924012	—	2	4	no	—
46	C₂×#11924012	—	2	4	no	—
47	C₂×#11924012	—	2	4	no	—
48	C₂²×#10596831	C₂³	1	2	yes	—
49	C₂²×#10596831	C₂³	1	2	yes	—
50	C₂²×#10596831	C₂³	1	2	yes	—
51	C₂²×#10596831	C₂³	1	2	yes	—
52	C₄⋊#10596831	—	2	4	no	—
53	C₄⋊#10596831	—	2	4	no	—
54	C₂²⋊#10596831	—	2	4	no	—
55	C₂²⋊#10596831	—	2	4	no	—
56	C₂²⋊#10596831	—	2	4	no	—
57	#14556502	—	2	2	no	—
58	#14556502	—	2	2	no	—
59	#14556502	—	2	2	no	—
60	#14556502	D₄	1	4	yes	complemented
61	C₄×#10596831	—	2	4	no	—
62	C₂²×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
63	C₂³×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
64	C₂³×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
65	C₂³×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
66	C₂³×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
67	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
69	C₄×D₄×C₇₃	—	2	4	no	—
70	C₄×D₄×C₇₃	—	2	4	no	—
71	C₄×D₄×C₇₃	—	2	4	no	—
72	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
76	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
80	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄²×C₇₃	—	2	2	no	—
82	C₂×C₄²×C₇₃	—	2	2	no	—
83	C₂×C₄²×C₇₃	—	2	2	no	—
84	C₂×C₄²×C₇₃	—	2	2	no	—
85	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
98	#95×C₇₃	C₂×C₄	1	1	yes	characteristic
99	#95×C₇₃	C₂×C₄	1	1	yes	characteristic
100	#95×C₇₃	C₂×C₄	1	1	yes	characteristic
101	#95×C₇₃	C₂×C₄	1	1	yes	characteristic
102	#95×C₇₃	C₂×C₄	1	1	yes	characteristic
103	#95×C₇₃	C₂×C₄	1	1	yes	characteristic
104	#11924012	—	2	16	no	—
105	C₂×#10596831	—	2	2	no	—
106	C₂×#10596831	—	2	2	no	—
107	C₂×#10596831	—	2	2	no	—
108	C₂×#10596831	—	2	2	no	—
109	C₂×#10596831	—	2	2	no	—
110	C₂×#10596831	—	2	2	no	—
111	C₂×#10596831	—	2	2	no	—
112	C₂×#10596831	—	2	2	no	—
113	C₂×#10596831	—	2	2	no	—
114	C₂×#10596831	—	2	2	no	—
115	C₂×#10596831	C₂×D₄	1	4	yes	—
116	C₂×#10596831	#41	1	4	yes	—
117	C₂⁴×C₇₃	C₂²×C₄	1	1	yes	characteristic
118	C₂⁴×C₇₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×D₄×C₇₃	—	2	2	no	—
120	C₂×D₄×C₇₃	—	2	2	no	—
121	C₂×D₄×C₇₃	—	2	2	no	—
122	C₂²×C₄×C₇₃	—	2	1	no	—
123	C₂²×C₄×C₇₃	—	2	1	no	—
124	C₂²×C₄×C₇₃	—	2	2	no	—
125	C₂²×C₄×C₇₃	—	2	2	no	—
126	C₂²×C₄×C₇₃	—	2	2	no	—
127	C₂²×C₄×C₇₃	—	2	2	no	—
128	C₂²×C₄×C₇₃	—	2	2	no	—
129	C₂²×C₄×C₇₃	—	2	2	no	—
130	C₂²×C₄×C₇₃	—	2	2	no	—
131	C₂²×C₄×C₇₃	—	2	2	no	—
132	C₂²×C₄×C₇₃	—	2	2	no	—
133	C₂²×C₄×C₇₃	—	2	1	no	—
134	C₂²×C₄×C₇₃	—	2	1	no	—
135	C₂²×C₄×C₇₃	—	2	2	no	—
136	C₂²×C₄×C₇₃	—	2	2	no	—
137	C₂²×C₄×C₇₃	—	4	1	no	—
138	C₂²×C₄×C₇₃	—	4	1	no	—
139	C₂²×C₄×C₇₃	—	4	1	no	—
140	C₂²×C₄×C₇₃	—	4	1	no	—
141	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₇₃	#41	1	4	yes	—
154	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
155	C₄⋊C₄×C₇₃	—	2	2	no	—
156	C₄⋊C₄×C₇₃	—	2	2	no	—
157	C₄⋊C₄×C₇₃	M₁₆	1	4	yes	complemented
158	C₂²⋊C₄×C₇₃	—	2	2	no	—
159	C₂²⋊C₄×C₇₃	—	2	2	no	—
160	C₂²⋊C₄×C₇₃	—	2	2	no	—
161	C₂²⋊C₄×C₇₃	—	2	2	no	—
162	C₂²⋊C₄×C₇₃	—	2	2	no	—
163	C₂²⋊C₄×C₇₃	M₁₆	1	4	yes	complemented
164	C₄²×C₇₃	—	2	2	no	—
165	C₄²×C₇₃	—	2	2	no	—
166	C₄²×C₇₃	—	2	2	no	—
167	C₄²×C₇₃	—	2	2	no	—
168	C₄²×C₇₃	—	2	2	no	—
169	C₄²×C₇₃	—	2	2	no	—
170	C₄²×C₇₃	—	2	1	no	—
171	C₄²×C₇₃	—	2	1	no	—
172	C₄²×C₇₃	—	2	1	no	—
173	C₄²×C₇₃	—	2	1	no	—
174	C₄²×C₇₃	—	2	2	no	—
175	C₄²×C₇₃	—	2	2	no	—
176	C₄²×C₇₃	—	4	1	no	—
177	C₄²×C₇₃	—	4	1	no	—
178	C₄²×C₇₃	C₂×D₄	1	2	yes	—
179	C₄²×C₇₃	#41	1	2	yes	—
180	C₂³×C₇₃	—	2	1	no	—
181	C₂³×C₇₃	—	2	1	no	—
182	C₂³×C₇₃	—	2	1	no	—
183	C₂³×C₇₃	—	2	1	no	—
184	C₂³×C₇₃	—	2	1	no	—
185	C₂³×C₇₃	—	2	1	no	—
186	C₂³×C₇₃	—	2	1	no	—
187	C₂³×C₇₃	—	2	1	no	—
188	C₂³×C₇₃	—	2	1	no	—
189	C₂³×C₇₃	—	2	1	no	—
190	C₂³×C₇₃	—	2	1	no	—
191	C₂³×C₇₃	—	2	1	no	—
192	C₂³×C₇₃	#117	1	2	yes	—
193	C₂³×C₇₃	C₂×M₁₆	1	2	yes	—
194	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
195	D₄×C₇₃	—	2	8	no	—
196	C₂×C₄×C₇₃	—	2	1	no	—
197	C₂×C₄×C₇₃	—	2	1	no	—
198	C₂×C₄×C₇₃	—	2	1	no	—
199	C₂×C₄×C₇₃	—	2	1	no	—
200	C₂×C₄×C₇₃	—	2	1	no	—
201	C₂×C₄×C₇₃	—	2	1	no	—
202	C₂×C₄×C₇₃	—	2	1	no	—
203	C₂×C₄×C₇₃	—	2	1	no	—
204	C₂×C₄×C₇₃	—	2	1	no	—
205	C₂×C₄×C₇₃	—	2	1	no	—
206	C₂×C₄×C₇₃	—	2	1	no	—
207	C₂×C₄×C₇₃	—	2	1	no	—
208	C₂×C₄×C₇₃	—	2	1	no	—
209	C₂×C₄×C₇₃	—	2	1	no	—
210	C₂×C₄×C₇₃	—	2	1	no	—
211	C₂×C₄×C₇₃	—	2	1	no	—
212	C₂×C₄×C₇₃	—	2	4	no	—
213	C₂×C₄×C₇₃	—	2	4	no	—
214	C₂×C₄×C₇₃	—	2	1	no	—
215	C₂×C₄×C₇₃	—	2	1	no	—
216	C₂×C₄×C₇₃	—	2	1	no	—
217	C₂×C₄×C₇₃	—	2	1	no	—
218	C₂×C₄×C₇₃	—	2	1	no	—
219	C₂×C₄×C₇₃	—	2	1	no	—
220	C₂×C₄×C₇₃	—	2	1	no	—
221	C₂×C₄×C₇₃	—	2	1	no	—
222	C₂×C₄×C₇₃	—	2	1	no	—
223	C₂×C₄×C₇₃	—	2	1	no	—
224	C₂×C₄×C₇₃	—	2	1	no	—
225	C₂×C₄×C₇₃	—	2	1	no	—
226	C₂×C₄×C₇₃	—	4	4	no	—
227	C₂×C₄×C₇₃	—	4	4	no	—
228	C₂×C₄×C₇₃	—	4	4	no	—
229	C₂×C₄×C₇₃	—	4	4	no	—
230	C₂×C₄×C₇₃	—	4	2	no	—
231	C₂×C₄×C₇₃	—	4	2	no	—
232	C₂×C₄×C₇₃	#117	1	2	yes	—
233	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
234	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
235	C₂×C₄×C₇₃	C₂×M₁₆	1	2	yes	—
236	C₂×C₄×C₇₃	C₂×M₁₆	1	2	yes	—
237	C₂×C₄×C₇₃	C₂×M₁₆	1	2	yes	—
238	C₂×C₄×C₇₃	C₂×M₁₆	1	2	yes	—
239	C₂×C₄×C₇₃	C₂×M₁₆	1	2	yes	—
240	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
242	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
243	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
244	#10596831	—	2	4	no	—
245	#10596831	—	2	4	no	—
246	#10596831	—	4	2	no	—
247	#10596831	—	4	2	no	—
248	C₂²×C₇₃	—	2	2	no	—
249	C₂²×C₇₃	—	2	2	no	—
250	C₂²×C₇₃	—	2	2	no	—
251	C₂²×C₇₃	—	2	2	no	—
252	C₂²×C₇₃	—	2	2	no	—
253	C₂²×C₇₃	—	2	2	no	—
254	C₂²×C₇₃	—	4	1	no	—
255	C₂²×C₇₃	—	4	1	no	—
256	C₂²×C₇₃	—	4	1	no	—
257	C₂²×C₇₃	—	4	1	no	—
258	C₂²×C₇₃	—	4	1	no	—
259	C₂²×C₇₃	—	4	1	no	—
260	C₂²×C₇₃	—	4	1	no	—
261	C₂²×C₇₃	—	4	1	no	—
262	C₂²×C₇₃	C₂×#117	1	1	yes	characteristic
263	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
264	C₂²×C₇₃	C₄×#41	1	1	yes	characteristic
265	C₂²×C₇₃	C₂²×M₁₆	1	1	yes	characteristic
266	C₂²×C₇₃	C₂²×M₁₆	1	1	yes	characteristic
267	C₂²×C₇₃	#568	1	1	yes	characteristic
268	C₂²×C₇₃	#568	1	1	yes	characteristic
269	C₄×C₇₃	—	2	2	no	—
270	C₄×C₇₃	—	2	2	no	—
271	C₄×C₇₃	—	2	2	no	—
272	C₄×C₇₃	—	2	2	no	—
273	C₄×C₇₃	—	2	2	no	—
274	C₄×C₇₃	—	2	2	no	—
275	C₄×C₇₃	—	2	2	no	—
276	C₄×C₇₃	—	2	2	no	—
277	C₄×C₇₃	—	4	1	no	—
278	C₄×C₇₃	—	4	1	no	—
279	C₄×C₇₃	—	4	1	no	—
280	C₄×C₇₃	—	4	1	no	—
281	C₄×C₇₃	#525	1	2	yes	—
282	C₄×C₇₃	#529	1	2	yes	—
283	#21108	—	73	1	no	maximal, Sylow
284	C₂×C₇₃	—	4	2	no	—
285	C₂×C₇₃	—	4	2	no	—
286	C₂×C₇₃	#2290	1	1	yes	characteristic
287	C₂×C₇₃	#2920	1	1	yes	characteristic
288	C₂×C₇₃	#2923	1	1	yes	characteristic
289	C₂×C₇₃	D₄×M₁₆	1	1	yes	characteristic
290	C₂×C₇₃	D₄×M₁₆	1	1	yes	characteristic
291	C₂×C₇₃	#2970	1	1	yes	characteristic
292	C₂×C₇₃	#2971	1	1	yes	characteristic
293	C₂×#432	—	73	1	no	—
294	C₂×C₄×M₁₆	—	73	1	no	—
295	C₄²×D₄	D₇₃	1	1	yes	characteristic
296	#1923	—	73	2	no	—
297	#1916	—	73	2	no	—
298	#1870	—	73	2	no	—
299	#1851	—	73	2	no	—
300	#1767	—	73	1	no	—
301	#1749	—	73	1	no	—
302	#1749	—	73	1	no	—
303	#1745	—	73	1	no	—
304	C₇₃	#21108	1	1	yes	characteristic, complemented, Sylow
305	C₂²×M₁₆	—	73	2	no	—
306	C₂×C₄×D₄	Dic₇₃	1	1	yes	characteristic
307	C₂×C₄×D₄	Dic₇₃	1	1	yes	characteristic
308	C₂×C₄×D₄	C₂×D₇₃	1	1	yes	characteristic
309	C₂²×C₄²	C₂×D₇₃	1	1	yes	characteristic
310	C₂²×C₄²	C₂×D₇₃	1	1	yes	characteristic
311	#432	—	146	4	no	—
312	C₂×C₄⋊C₈	—	73	2	no	—
313	C₂×C₄⋊C₈	—	73	2	no	—
314	C₂×C₂²⋊C₈	—	73	2	no	—
315	C₂×C₂²⋊C₈	—	73	2	no	—
316	C₂×C₂²⋊C₈	—	73	2	no	—
317	C₄×M₁₆	—	146	4	no	—
318	C₂×#97	—	73	1	no	—
319	C₂×#97	—	73	1	no	—
320	C₂×#97	—	73	1	no	—
321	C₂×#97	—	73	1	no	—
322	C₂×C₄×C₈	—	73	2	no	—
323	C₄×C₄⋊C₄	Dic₇₃	1	1	yes	characteristic
324	C₄×C₄⋊C₄	Dic₇₃	1	1	yes	characteristic
325	C₄×C₄⋊C₄	C₂×D₇₃	1	1	yes	characteristic
326	C₄×C₂²⋊C₄	Dic₇₃	1	1	yes	characteristic
327	C₄×C₂²⋊C₄	Dic₇₃	1	1	yes	characteristic
328	C₄×C₂²⋊C₄	Dic₇₃	1	1	yes	characteristic
329	C₄×C₂²⋊C₄	Dic₇₃	1	1	yes	characteristic
330	C₄×C₂²⋊C₄	C₂×D₇₃	1	1	yes	characteristic
331	C₄×C₂²⋊C₄	C₂×D₇₃	1	1	yes	characteristic
332	C₄³	C₂×D₇₃	1	1	yes	characteristic
333	#336	—	73	2	no	—
334	#336	—	73	2	no	—
335	#336	—	73	2	no	—
336	#336	—	73	2	no	—
337	#336	—	73	2	no	—
338	C₂²×D₄	C₂×Dic₇₃	1	1	yes	characteristic
339	C₂³×C₄	C₂×Dic₇₃	1	1	yes	characteristic
340	C₂³×C₄	C₂×Dic₇₃	1	1	yes	characteristic
341	C₂³×C₄	C₂×Dic₇₃	1	1	yes	characteristic
342	C₂³×C₄	C₂×Dic₇₃	1	1	yes	characteristic
343	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
344	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
345	C₂×M₁₆	—	146	4	no	—
346	C₂×M₁₆	—	146	4	no	—
347	C₂×M₁₆	—	146	4	no	—
348	C₂²×C₈	—	73	2	no	—
349	C₂²×C₈	—	73	2	no	—
350	C₂²×C₈	—	73	2	no	—
351	C₂²×C₈	—	73	2	no	—
352	C₄×D₄	—	2	4	no	—
353	C₄×D₄	—	2	4	no	—
354	C₄×D₄	—	2	4	no	—
355	C₂×C₄⋊C₄	C₂×Dic₇₃	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂×Dic₇₃	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂×Dic₇₃	1	1	yes	characteristic
358	C₂×C₂²⋊C₄	C₂×Dic₇₃	1	1	yes	characteristic
359	C₂×C₂²⋊C₄	C₂×Dic₇₃	1	1	yes	characteristic
360	C₂×C₂²⋊C₄	C₂×Dic₇₃	1	1	yes	characteristic
361	C₂×C₂²⋊C₄	C₂×Dic₇₃	1	1	yes	characteristic
362	C₂×C₂²⋊C₄	C₂×Dic₇₃	1	1	yes	characteristic
363	C₂×C₂²⋊C₄	C₂×Dic₇₃	1	1	yes	characteristic
364	C₂×C₄²	—	2	2	no	—
365	C₂×C₄²	—	2	2	no	—
366	C₂×C₄²	—	2	2	no	—
367	C₂×C₄²	—	2	2	no	—
368	C₂×C₄²	C₂×Dic₇₃	1	1	yes	characteristic
369	C₂×C₄²	C₂×Dic₇₃	1	1	yes	characteristic
370	C₂×C₄²	C₂×Dic₇₃	1	1	yes	characteristic
371	C₂×C₄²	C₂×Dic₇₃	1	1	yes	characteristic
372	C₂×C₄²	C₂×Dic₇₃	1	1	yes	characteristic
373	C₂×C₄²	C₂×Dic₇₃	1	1	yes	characteristic
374	C₂×C₄²	C₂×Dic₇₃	1	1	yes	characteristic
375	C₂×C₄²	C₂×Dic₇₃	1	1	yes	characteristic
376	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
377	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
378	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
379	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
380	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
381	C₄⋊C₈	—	146	4	no	—
382	C₄⋊C₈	—	146	4	no	—
383	C₂²⋊C₈	—	146	4	no	—
384	C₂²⋊C₈	—	146	4	no	—
385	C₂²⋊C₈	—	146	4	no	—
386	#97	—	73	4	no	—
387	#97	—	146	2	no	—
388	#97	—	146	2	no	—
389	#97	—	146	2	no	—
390	C₄×C₈	—	146	4	no	—
391	#95	C₂×Dic₇₃	1	1	yes	characteristic
392	#95	C₂×Dic₇₃	1	1	yes	characteristic
393	#95	C₂×Dic₇₃	1	1	yes	characteristic
394	#95	C₂×Dic₇₃	1	1	yes	characteristic
395	#95	C₂×Dic₇₃	1	1	yes	characteristic
396	#95	C₂×Dic₇₃	1	1	yes	characteristic
397	C₂⁴	C₂²×Dic₇₃	1	1	yes	characteristic
398	C₂⁴	C₂²×Dic₇₃	1	1	yes	characteristic
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	4	1	no	—
418	C₂²×C₄	—	4	1	no	—
419	C₂²×C₄	—	4	1	no	—
420	C₂²×C₄	—	4	1	no	—
421	C₂²×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
422	C₂²×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
423	C₂²×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
424	C₂²×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
425	C₂²×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
426	C₂²×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
427	C₂²×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
428	C₂²×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
429	C₂²×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
430	C₂²×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
431	C₂²×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
432	C₂²×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
433	C₂²×C₄	#11924028	1	4	yes	—
434	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
435	M₁₆	—	146	16	no	—
436	C₂×C₈	—	73	4	no	—
437	C₂×C₈	—	73	4	no	—
438	C₂×C₈	—	146	2	no	—
439	C₂×C₈	—	146	2	no	—
440	C₂×C₈	—	146	2	no	—
441	C₂×C₈	—	146	2	no	—
442	C₂×C₈	—	146	2	no	—
443	C₂×C₈	—	146	2	no	—
444	C₂×C₈	—	146	2	no	—
445	C₂×C₈	—	146	2	no	—
446	C₂×C₈	—	146	2	no	—
447	C₂×C₈	—	146	2	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	#11924012	1	4	yes	complemented
451	C₂²⋊C₄	—	2	2	no	—
452	C₂²⋊C₄	—	2	2	no	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	—	2	2	no	—
455	C₂²⋊C₄	—	2	2	no	—
456	C₂²⋊C₄	#11924012	1	4	yes	complemented
457	C₄²	—	2	2	no	—
458	C₄²	—	2	2	no	—
459	C₄²	—	2	2	no	—
460	C₄²	—	2	2	no	—
461	C₄²	—	2	2	no	—
462	C₄²	—	2	2	no	—
463	C₄²	—	2	1	no	—
464	C₄²	—	2	1	no	—
465	C₄²	—	2	2	no	—
466	C₄²	—	2	1	no	—
467	C₄²	—	2	1	no	—
468	C₄²	—	2	2	no	—
469	C₄²	—	4	1	no	—
470	C₄²	—	4	1	no	—
471	C₄²	D₄×D₇₃	1	2	yes	—
472	C₄²	#11924027	1	2	yes	—
473	C₂³	—	2	1	no	—
474	C₂³	—	2	1	no	—
475	C₂³	—	2	1	no	—
476	C₂³	—	2	1	no	—
477	C₂³	—	2	1	no	—
478	C₂³	—	2	1	no	—
479	C₂³	—	2	1	no	—
480	C₂³	—	2	1	no	—
481	C₂³	—	2	1	no	—
482	C₂³	—	2	1	no	—
483	C₂³	—	2	1	no	—
484	C₂³	—	2	1	no	—
485	C₂³	#14556550	1	2	yes	—
486	C₂³	C₂×#11924012	1	2	yes	—
487	C₂³	C₂³×Dic₇₃	1	1	yes	characteristic
488	D₄	—	2	8	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	4	4	no	—
520	C₂×C₄	—	4	4	no	—
521	C₂×C₄	—	4	4	no	—
522	C₂×C₄	—	4	4	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	#14556550	1	2	yes	—
526	C₂×C₄	D₄×Dic₇₃	1	2	yes	—
527	C₂×C₄	D₄×Dic₇₃	1	2	yes	—
528	C₂×C₄	C₂×#11924012	1	2	yes	—
529	C₂×C₄	C₂×#11924012	1	2	yes	—
530	C₂×C₄	C₂×#11924012	1	2	yes	—
531	C₂×C₄	C₂×#11924012	1	2	yes	—
532	C₂×C₄	C₂×#11924012	1	2	yes	—
533	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
534	C₂×C₄	#41×D₇₃	1	2	yes	—
535	C₂×C₄	C₂×#11924027	1	1	yes	characteristic
536	C₂×C₄	C₂×#11924028	1	2	yes	—
537	C₈	—	292	2	no	—
538	C₈	—	292	2	no	—
539	C₈	—	146	4	no	—
540	C₈	—	146	4	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	2	2	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	4	1	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	C₂×#14556550	1	1	yes	characteristic
556	C₂²	C₂×D₄×Dic₇₃	1	1	yes	characteristic
557	C₂²	#41×Dic₇₃	1	1	yes	characteristic
558	C₂²	C₂²×#11924012	1	1	yes	characteristic
559	C₂²	C₂²×#11924012	1	1	yes	characteristic
560	C₂²	#17989354	1	1	yes	characteristic
561	C₂²	#17989354	1	1	yes	characteristic
562	C₄	—	2	2	no	—
563	C₄	—	2	2	no	—
564	C₄	—	2	2	no	—
565	C₄	—	2	2	no	—
566	C₄	—	2	2	no	—
567	C₄	—	2	2	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	2	no	—
570	C₄	—	4	1	no	—
571	C₄	—	4	1	no	—
572	C₄	—	4	1	no	—
573	C₄	—	4	1	no	—
574	C₄	#17989096	1	2	yes	—
575	C₄	#17989117	1	2	yes	—
576	C₂	—	4	2	no	—
577	C₂	—	4	2	no	—
578	C₂	#22612376	1	1	yes	characteristic
579	C₂	#22618564	1	1	yes	characteristic
580	C₂	#22618582	1	1	yes	characteristic
581	C₂	D₄×#11924012	1	1	yes	characteristic
582	C₂	D₄×#11924012	1	1	yes	characteristic
583	C₂	#22618945	1	1	yes	characteristic
584	C₂	#22618951	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₃
commutator, socle	C₂³×C₇₃	C₂³×C₄
Fitting	C₄²×D₄×C₇₃	C₂
prime radical	C₂²×D₄×C₇₃	C₂×C₄
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	C₄²×D₄	D₇₃
hypocenter	C₇₃	#21108
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄²×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×#17988644	C₂	semidirect
2. C₂×C₄×#11924012	C₂	semidirect
3. #22610539	C₂	semidirect
4. #22610490	C₂	semidirect
6. #22610116	C₂	semidirect
7. #22609784	C₂	semidirect
8. #22609693	C₂	semidirect
9. #22609693	C₂	semidirect
10. #22609680	C₂	semidirect
60. #14556502	D₄	semidirect
157. C₄⋊C₄×C₇₃	M₁₆	semidirect
163. C₂²⋊C₄×C₇₃	M₁₆	semidirect
304. C₇₃	#21108	semidirect
450. C₄⋊C₄	#11924012	semidirect
456. C₂²⋊C₄	#11924012	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#17988644	2
C₂×C₄×#11924012	2
#22610539	2
#22610490	2
#22610229	2
#22610116	2
#22609784	2
#22609693	2
#22609680	2
C₄²×D₄×C₇₃	2
#21108	73