Subgroups — #34030223

Order 18688.

734 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14556666	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#17989643	C₂	1	1	yes	maximal, characteristic, complemented
3	#22626316	C₂	1	2	yes	maximal, complemented
4	#22626314	C₂	1	2	yes	maximal, complemented
5	#22626311	C₂	1	2	yes	maximal, complemented
6	#22626309	C₂	1	2	yes	maximal, complemented
7	#22626264	C₂	1	1	yes	maximal, characteristic, complemented
8	#22626159	C₂	1	1	yes	maximal, characteristic, complemented
9	#22626159	C₂	1	1	yes	maximal, characteristic, complemented
10	#22626138	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₄×D₇₃	C₂	1	1	yes	maximal, characteristic
12	C₂×#14556666	—	2	4	no	—
13	C₂×#14556666	C₂²	1	1	yes	characteristic
14	C₂×#14556666	C₂²	1	1	yes	characteristic
15	C₂×#14556666	C₂²	1	1	yes	characteristic
16	C₂×#14556666	C₂²	1	1	yes	characteristic
17	C₂×#14556666	C₂²	1	2	yes	complemented
18	#17989643	—	2	4	no	—
19	C₂×#14556665	C₂²	1	2	yes	complemented
20	C₂×#14556664	C₂²	1	2	yes	complemented
21	C₂²×#11924031	C₂²	1	2	yes	complemented
22	#17989508	C₂²	1	2	yes	complemented
23	C₄⋊#11924031	C₂²	1	2	yes	complemented
24	#17989482	C₂²	1	2	yes	complemented
25	#17989482	C₂²	1	2	yes	complemented
26	C₂²⋊#11924031	C₂²	1	2	yes	complemented
27	C₂²⋊#11924031	C₂²	1	2	yes	complemented
28	#17989475	C₂²	1	2	yes	complemented
29	#17989473	C₂²	1	2	yes	complemented
30	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
31	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
32	C₄×D₄×D₇₃	C₄	1	1	yes	characteristic
33	C₈×D₂₉₂	C₄	1	1	yes	characteristic
34	D₄×#10596831	C₂²	1	1	yes	characteristic
35	#17988652	C₂²	1	1	yes	characteristic
36	C₈×C₂²⋊D₇₃	C₄	1	1	yes	characteristic
37	C₈×C₂²⋊D₇₃	C₄	1	1	yes	characteristic
38	#17988650	C₂²	1	1	yes	characteristic
39	#17988650	C₂²	1	1	yes	characteristic
40	C₄⋊C₈×D₇₃	C₄	1	1	yes	characteristic
41	C₂²⋊C₈×D₇₃	C₄	1	1	yes	characteristic
42	C₂²⋊C₈×D₇₃	C₄	1	1	yes	characteristic
43	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
44	C₈×D₄×C₇₃	C₄	1	1	yes	characteristic
45	#14556666	—	2	4	no	—
46	#14556666	—	2	2	no	—
47	#14556666	—	2	2	no	—
48	#14556666	—	2	2	no	—
49	#14556666	D₄	1	4	yes	complemented
50	#14556665	—	2	4	no	—
51	#14556664	—	2	4	no	—
52	C₂×#11924031	—	2	4	no	—
53	C₂×#11924031	C₂³	1	2	yes	—
54	C₂×#11924031	C₂³	1	2	yes	—
55	C₂×#11924031	C₂³	1	2	yes	—
56	C₂×#11924031	C₂³	1	2	yes	—
57	C₂×D₄×D₇₃	C₈	1	1	yes	characteristic
58	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
60	C₂²×#10596831	C₂³	1	1	yes	characteristic
61	C₂²×#10596831	C₂³	1	1	yes	characteristic
62	C₂×C₈×D₇₃	—	2	2	no	—
63	C₂×C₈×D₇₃	—	2	2	no	—
64	C₂×C₈×D₇₃	—	2	2	no	—
65	C₂×C₈×D₇₃	—	2	2	no	—
66	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
71	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
72	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
73	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
74	C₄×D₂₉₂	C₂×C₄	1	1	yes	characteristic
75	D₄×Dic₇₃	C₈	1	1	yes	characteristic
76	#14556553	C₈	1	1	yes	characteristic
77	C₄×C₂²⋊D₇₃	C₂×C₄	1	1	yes	characteristic
78	C₄×C₂²⋊D₇₃	C₂×C₄	1	1	yes	characteristic
79	#14556551	C₈	1	1	yes	characteristic
80	#14556551	C₈	1	1	yes	characteristic
81	C₄⋊C₄×D₇₃	C₈	1	1	yes	characteristic
82	C₂²⋊C₄×D₇₃	C₈	1	1	yes	characteristic
83	C₂²⋊C₄×D₇₃	C₈	1	1	yes	characteristic
84	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
85	C₄⋊#10596831	C₂×C₄	1	1	yes	characteristic
86	#14556520	C₂×C₄	1	1	yes	characteristic
87	#14556520	C₂×C₄	1	1	yes	characteristic
88	C₂²⋊#10596831	C₂×C₄	1	1	yes	characteristic
89	C₂²⋊#10596831	C₂×C₄	1	1	yes	characteristic
90	#14556503	C₂×C₄	1	1	yes	characteristic
91	#14556503	C₂×C₄	1	1	yes	characteristic
92	#14556503	C₂×C₄	1	1	yes	characteristic
93	#14556503	C₂×C₄	1	1	yes	characteristic
94	C₄×#10596831	C₂³	1	1	yes	characteristic
95	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
96	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
98	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
99	C₄×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
100	C₄⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
101	C₂²⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
102	C₂²⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
103	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
104	#11924031	—	2	2	no	—
105	#11924031	—	2	2	no	—
106	#11924031	—	2	2	no	—
107	#11924031	C₂×D₄	1	4	yes	complemented
108	C₂³×D₇₃	C₂×C₈	1	1	yes	characteristic
109	C₂³×D₇₃	C₂×C₈	1	1	yes	characteristic
110	C₂×D₂₉₂	C₂×C₈	1	1	yes	characteristic
111	C₂×C₂²⋊D₇₃	C₂×C₈	1	1	yes	characteristic
112	C₂×C₂²⋊D₇₃	C₂×C₈	1	1	yes	characteristic
113	D₄×D₇₃	—	2	4	no	—
114	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
115	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
116	C₂×C₄×D₇₃	—	2	2	no	—
117	C₂×C₄×D₇₃	—	2	2	no	—
118	C₂×C₄×D₇₃	—	2	2	no	—
119	C₂×C₄×D₇₃	—	2	2	no	—
120	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
121	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
122	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
123	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
124	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
125	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
126	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
129	C₂×#10596831	—	2	1	no	—
130	C₂×#10596831	—	2	1	no	—
131	C₂×#10596831	—	2	1	no	—
132	C₂×#10596831	—	2	1	no	—
133	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
134	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
135	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
136	C₂×#10596831	C₂⁴	1	1	yes	characteristic
137	C₈×D₇₃	—	2	2	no	—
138	C₈×D₇₃	—	2	2	no	—
139	C₈×D₇₃	—	2	2	no	—
140	C₈×D₇₃	—	2	2	no	—
141	C₈×D₇₃	—	2	2	no	—
142	C₈×D₇₃	—	2	1	no	—
143	C₈×D₇₃	—	2	1	no	—
144	C₈×D₇₃	—	2	1	no	—
145	C₈×D₇₃	—	2	1	no	—
146	C₈×D₇₃	C₂×D₄	1	2	yes	—
147	C₈×D₇₃	#41	1	2	yes	—
148	C₄⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
149	#11924007	C₂×C₈	1	1	yes	characteristic
150	#11924007	C₂×C₈	1	1	yes	characteristic
151	C₂²⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
152	C₂²⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
153	#11924005	C₂×C₈	1	1	yes	characteristic
154	#11924005	C₂×C₈	1	1	yes	characteristic
155	#11924005	C₂×C₈	1	1	yes	characteristic
156	#11924005	C₂×C₈	1	1	yes	characteristic
157	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
158	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
159	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
160	C₂×D₄×C₇₃	C₂×C₈	1	1	yes	characteristic
161	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₈×C₇₃	—	2	2	no	—
164	C₂×C₈×C₇₃	—	2	2	no	—
165	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
169	C₄⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
170	C₂²⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
171	C₂²⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
172	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
173	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
174	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
175	C₂²×D₇₃	—	2	2	no	—
176	C₂²×D₇₃	—	2	2	no	—
177	C₂²×D₇₃	—	2	2	no	—
178	C₂²×D₇₃	—	2	2	no	—
179	C₂²×D₇₃	—	4	1	no	—
180	C₂²×D₇₃	—	4	1	no	—
181	C₂²×D₇₃	C₂²×C₈	1	1	yes	characteristic
182	C₂²×D₇₃	C₂²×C₈	1	1	yes	characteristic
183	C₂²×D₇₃	C₂²×C₈	1	1	yes	characteristic
184	D₄×C₇₃	—	2	2	no	—
185	C₂×C₄×C₇₃	—	2	1	no	—
186	C₂×C₄×C₇₃	—	2	1	no	—
187	C₂×C₄×C₇₃	—	2	1	no	—
188	C₂×C₄×C₇₃	—	2	1	no	—
189	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
190	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
191	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
192	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
193	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
194	C₂²⋊D₇₃	—	2	2	no	—
195	C₂²⋊D₇₃	M₃₂	1	4	yes	complemented
196	C₂×Dic₇₃	—	2	2	no	—
197	C₂×Dic₇₃	—	2	2	no	—
198	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
199	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
200	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
201	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
202	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
203	D₂₉₂	—	2	2	no	—
204	C₄×D₇₃	—	2	2	no	—
205	C₄×D₇₃	—	2	2	no	—
206	C₄×D₇₃	—	2	1	no	—
207	C₄×D₇₃	—	2	1	no	—
208	C₄×D₇₃	—	2	1	no	—
209	C₄×D₇₃	—	2	1	no	—
210	C₄×D₇₃	—	2	2	no	—
211	C₄×D₇₃	—	2	2	no	—
212	C₄×D₇₃	—	2	2	no	—
213	C₄×D₇₃	—	4	1	no	—
214	C₄×D₇₃	C₄×D₄	1	2	yes	—
215	C₄×D₇₃	#131	1	2	yes	—
216	C₈×C₇₃	—	2	1	no	—
217	C₈×C₇₃	—	2	1	no	—
218	C₈×C₇₃	—	2	1	no	—
219	C₈×C₇₃	C₄×D₄	1	2	yes	—
220	#10596831	—	2	1	no	—
221	#10596831	—	2	1	no	—
222	#10596831	—	2	1	no	—
223	#10596831	C₂²×D₄	1	1	yes	characteristic
224	#10596831	C₂×#41	1	1	yes	characteristic
225	C₂²×C₇₃	—	2	1	no	—
226	C₂²×C₇₃	—	2	1	no	—
227	C₂²×C₇₃	—	2	1	no	—
228	C₂²×C₇₃	—	2	1	no	—
229	C₂²×C₇₃	—	2	1	no	—
230	C₂²×C₇₃	C₂×M₃₂	1	2	yes	complemented
231	C₂²×C₇₃	C₂³×C₈	1	1	yes	characteristic
232	C₂×D₇₃	—	2	1	no	—
233	C₂×D₇₃	—	2	1	no	—
234	C₂×D₇₃	—	2	1	no	—
235	C₂×D₇₃	—	2	1	no	—
236	C₂×D₇₃	—	2	1	no	—
237	C₂×D₇₃	—	2	1	no	—
238	C₂×D₇₃	—	2	1	no	—
239	C₂×D₇₃	—	4	4	no	—
240	C₂×D₇₃	—	4	4	no	—
241	C₂×D₇₃	C₈×D₄	1	2	yes	—
242	C₂×D₇₃	C₂×M₃₂	1	2	yes	complemented
243	C₄×C₇₃	—	2	1	no	—
244	C₄×C₇₃	—	2	1	no	—
245	C₄×C₇₃	—	2	1	no	—
246	C₄×C₇₃	—	2	1	no	—
247	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
248	C₄×C₇₃	C₂×#131	1	1	yes	characteristic
249	Dic₇₃	—	2	1	no	—
250	Dic₇₃	—	2	1	no	—
251	Dic₇₃	—	2	1	no	—
252	Dic₇₃	C₈×D₄	1	2	yes	—
253	Dic₇₃	C₂×M₃₂	1	2	yes	complemented
254	D₄×M₃₂	—	73	1	no	maximal, Sylow
255	C₂×C₇₃	—	2	2	no	—
256	C₂×C₇₃	—	4	1	no	—
257	C₂×C₇₃	C₂×C₈×D₄	1	1	yes	characteristic
258	C₂×C₇₃	C₂²×M₃₂	1	1	yes	characteristic
259	C₂×C₇₃	#3407	1	1	yes	characteristic
260	D₇₃	—	2	2	no	—
261	D₇₃	—	2	2	no	—
262	D₇₃	—	4	1	no	—
263	C₂²×M₃₂	—	73	1	no	—
264	C₂²×M₃₂	—	73	1	no	—
265	C₂×C₈×D₄	—	73	1	no	—
266	#2169	—	73	2	no	—
267	#2168	—	73	2	no	—
268	#2168	—	73	2	no	—
269	D₄×C₁₆	—	73	2	no	—
270	#2150	—	73	1	no	—
271	#2112	—	73	1	no	—
272	#2112	—	73	1	no	—
273	C₄×M₃₂	—	73	1	no	—
274	C₇₃	D₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
275	C₂³×C₈	—	73	1	no	—
276	C₂³×C₈	—	73	1	no	—
277	C₂×C₄×D₄	—	73	1	no	—
278	C₂×M₃₂	—	73	1	no	—
279	C₂×M₃₂	—	73	2	no	—
280	C₂×M₃₂	—	73	1	no	—
281	C₂×M₃₂	—	73	1	no	—
282	C₂×M₃₂	—	73	1	no	—
283	C₂×M₃₂	—	73	2	no	—
284	C₂×M₃₂	—	146	4	no	—
285	C₂×M₃₂	—	146	4	no	—
286	C₂²×C₁₆	—	73	2	no	—
287	C₂²×C₁₆	—	73	2	no	—
288	C₈×D₄	—	73	1	no	—
289	C₈×D₄	—	73	1	no	—
290	C₈×D₄	—	73	1	no	—
291	C₈×D₄	—	73	1	no	—
292	C₈×D₄	—	73	1	no	—
293	C₈×D₄	—	73	1	no	—
294	C₈×D₄	—	73	1	no	—
295	C₈×D₄	#64408	1	1	yes	characteristic
296	C₂×C₄⋊C₈	—	73	1	no	—
297	C₂×C₂²⋊C₈	—	73	1	no	—
298	C₂×C₂²⋊C₈	—	73	1	no	—
299	C₂×C₄×C₈	—	73	1	no	—
300	C₄⋊C₁₆	—	73	2	no	—
301	C₄⋊C₁₆	—	73	2	no	—
302	C₂²⋊C₁₆	—	73	2	no	—
303	C₂²⋊C₁₆	—	73	2	no	—
304	C₂²⋊C₁₆	—	73	2	no	—
305	C₂²⋊C₁₆	—	73	2	no	—
306	#346	—	73	2	no	—
307	C₄×C₁₆	—	73	2	no	—
308	C₂²×D₄	—	73	1	no	—
309	C₂³×C₄	—	73	1	no	—
310	C₂³×C₄	—	73	1	no	—
311	C₂²×C₈	—	73	1	no	—
312	C₂²×C₈	—	73	1	no	—
313	C₂²×C₈	—	73	1	no	—
314	C₂²×C₈	—	73	1	no	—
315	C₂²×C₈	—	73	1	no	—
316	C₂²×C₈	—	73	1	no	—
317	C₂²×C₈	—	73	1	no	—
318	C₂²×C₈	—	73	1	no	—
319	C₂²×C₈	—	73	1	no	—
320	C₂²×C₈	—	73	1	no	—
321	C₂²×C₈	—	146	2	no	—
322	C₂²×C₈	—	146	2	no	—
323	C₂²×C₈	—	146	2	no	—
324	C₂²×C₈	—	146	2	no	—
325	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
326	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
327	C₄×D₄	—	73	1	no	—
328	C₄×D₄	—	73	1	no	—
329	C₄×D₄	—	73	1	no	—
330	C₄×D₄	—	73	1	no	—
331	C₄×D₄	—	73	1	no	—
332	C₄×D₄	—	73	1	no	—
333	C₄×D₄	—	73	1	no	—
334	C₄×D₄	C₂×#64408	1	1	yes	characteristic
335	C₂×C₄⋊C₄	—	73	1	no	—
336	C₂×C₂²⋊C₄	—	73	1	no	—
337	C₂×C₂²⋊C₄	—	73	1	no	—
338	C₂×C₄²	—	73	1	no	—
339	M₃₂	—	73	4	no	—
340	M₃₂	—	146	4	no	—
341	M₃₂	—	146	4	no	—
342	M₃₂	—	146	2	no	—
343	M₃₂	—	146	2	no	—
344	M₃₂	—	146	2	no	—
345	C₂×C₁₆	—	73	2	no	—
346	C₂×C₁₆	—	73	2	no	—
347	C₂×C₁₆	—	73	2	no	—
348	C₂×C₁₆	—	73	2	no	—
349	C₂×C₁₆	—	146	4	no	—
350	C₂×C₁₆	—	146	4	no	—
351	C₄⋊C₈	—	73	1	no	—
352	C₄⋊C₈	—	73	1	no	—
353	C₄⋊C₈	—	73	1	no	—
354	C₄⋊C₈	C₂×#64408	1	1	yes	characteristic
355	C₂²⋊C₈	—	73	1	no	—
356	C₂²⋊C₈	—	73	1	no	—
357	C₂²⋊C₈	—	73	1	no	—
358	C₂²⋊C₈	—	73	1	no	—
359	C₂²⋊C₈	—	73	1	no	—
360	C₂²⋊C₈	—	73	1	no	—
361	C₂²⋊C₈	C₂×#64408	1	1	yes	characteristic
362	C₂²⋊C₈	C₂×#64408	1	1	yes	characteristic
363	C₄×C₈	—	73	1	no	—
364	C₄×C₈	—	73	1	no	—
365	C₄×C₈	—	73	1	no	—
366	C₄×C₈	C₂×#64408	1	1	yes	characteristic
367	C₂⁴	—	73	1	no	—
368	C₂⁴	—	73	1	no	—
369	C₂×D₄	—	73	1	no	—
370	C₂×D₄	—	73	1	no	—
371	C₂×D₄	—	73	1	no	—
372	C₂×D₄	—	146	4	no	—
373	C₂×D₄	#11924036	1	1	yes	characteristic
374	C₂²×C₄	—	73	1	no	—
375	C₂²×C₄	—	73	1	no	—
376	C₂²×C₄	—	73	1	no	—
377	C₂²×C₄	—	73	1	no	—
378	C₂²×C₄	—	73	1	no	—
379	C₂²×C₄	—	73	1	no	—
380	C₂²×C₄	—	73	1	no	—
381	C₂²×C₄	—	73	1	no	—
382	C₂²×C₄	—	73	1	no	—
383	C₂²×C₄	—	73	1	no	—
384	C₂²×C₄	—	73	1	no	—
385	C₂²×C₄	—	146	2	no	—
386	C₂²×C₄	—	146	2	no	—
387	C₂²×C₄	—	146	2	no	—
388	C₂²×C₄	—	146	2	no	—
389	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
390	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	73	1	no	—
394	C₂×C₈	—	73	2	no	—
395	C₂×C₈	—	73	2	no	—
396	C₂×C₈	—	73	1	no	—
397	C₂×C₈	—	73	1	no	—
398	C₂×C₈	—	73	1	no	—
399	C₂×C₈	—	146	1	no	—
400	C₂×C₈	—	146	1	no	—
401	C₂×C₈	—	146	1	no	—
402	C₂×C₈	—	146	1	no	—
403	C₂×C₈	—	146	2	no	—
404	C₂×C₈	—	146	2	no	—
405	C₂×C₈	—	146	2	no	—
406	C₂×C₈	—	146	1	no	—
407	C₂×C₈	—	146	1	no	—
408	C₂×C₈	—	146	1	no	—
409	C₂×C₈	—	146	1	no	—
410	C₂×C₈	—	146	2	no	—
411	C₂×C₈	—	146	2	no	—
412	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
413	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
414	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
415	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
416	C₄⋊C₄	—	73	1	no	—
417	C₄⋊C₄	—	73	1	no	—
418	C₄⋊C₄	—	73	1	no	—
419	C₄⋊C₄	#11924036	1	1	yes	characteristic
420	C₂²⋊C₄	—	73	1	no	—
421	C₂²⋊C₄	—	73	1	no	—
422	C₂²⋊C₄	—	73	1	no	—
423	C₂²⋊C₄	—	73	1	no	—
424	C₂²⋊C₄	—	73	1	no	—
425	C₂²⋊C₄	—	73	1	no	—
426	C₂²⋊C₄	#11924036	1	1	yes	characteristic
427	C₂²⋊C₄	#11924036	1	1	yes	characteristic
428	C₄²	—	73	1	no	—
429	C₄²	—	73	1	no	—
430	C₄²	—	73	1	no	—
431	C₄²	C₂²×#64408	1	1	yes	characteristic
432	C₁₆	—	73	4	no	—
433	C₁₆	—	146	2	no	—
434	C₁₆	—	146	2	no	—
435	C₁₆	—	146	2	no	—
436	C₂³	—	292	1	no	—
437	C₂³	—	292	1	no	—
438	C₂³	—	73	1	no	—
439	C₂³	—	73	1	no	—
440	C₂³	—	73	1	no	—
441	C₂³	—	146	2	no	—
442	C₂³	—	146	2	no	—
443	C₂³	—	146	2	no	—
444	C₂³	—	146	2	no	—
445	C₂³	C₂×#11924036	1	1	yes	characteristic
446	C₂³	C₂×#11924036	1	1	yes	characteristic
447	D₄	—	2	2	no	—
448	D₄	—	73	4	no	—
449	D₄	—	146	2	no	—
450	D₄	—	146	2	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	292	1	no	—
456	C₂×C₄	—	73	1	no	—
457	C₂×C₄	—	73	1	no	—
458	C₂×C₄	—	73	2	no	—
459	C₂×C₄	—	73	2	no	—
460	C₂×C₄	—	73	1	no	—
461	C₂×C₄	—	73	1	no	—
462	C₂×C₄	—	73	1	no	—
463	C₂×C₄	—	146	2	no	—
464	C₂×C₄	—	146	2	no	—
465	C₂×C₄	—	146	2	no	—
466	C₂×C₄	—	146	2	no	—
467	C₂×C₄	—	146	2	no	—
468	C₂×C₄	—	146	2	no	—
469	C₂×C₄	—	146	2	no	—
470	C₂×C₄	—	146	1	no	—
471	C₂×C₄	—	146	1	no	—
472	C₂×C₄	—	146	1	no	—
473	C₂×C₄	—	146	1	no	—
474	C₂×C₄	C₂×#11924036	1	1	yes	characteristic
475	C₂×C₄	C₂×#11924036	1	1	yes	characteristic
476	C₂×C₄	C₂×#11924036	1	1	yes	characteristic
477	C₂×C₄	C₂×#11924036	1	1	yes	characteristic
478	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
479	C₈	—	2	1	no	—
480	C₈	—	2	1	no	—
481	C₈	—	2	1	no	—
482	C₈	—	73	1	no	—
483	C₈	—	73	1	no	—
484	C₈	—	146	1	no	—
485	C₈	—	146	1	no	—
486	C₈	—	146	1	no	—
487	C₈	D₄×#64408	1	2	yes	—
488	C₂²	—	2	1	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	292	4	no	—
494	C₂²	—	292	4	no	—
495	C₂²	—	73	2	no	—
496	C₂²	—	73	2	no	—
497	C₂²	—	146	1	no	—
498	C₂²	—	146	1	no	—
499	C₂²	—	146	1	no	—
500	C₂²	—	146	1	no	—
501	C₂²	—	146	1	no	—
502	C₂²	—	146	1	no	—
503	C₂²	—	146	1	no	—
504	C₂²	#17989643	1	2	yes	complemented
505	C₂²	C₂²×#11924036	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	2	1	no	—
510	C₄	—	73	2	no	—
511	C₄	—	73	2	no	—
512	C₄	—	146	1	no	—
513	C₄	—	146	1	no	—
514	C₄	—	146	1	no	—
515	C₄	C₂×D₄×#64408	1	1	yes	characteristic
516	C₄	D₇₃⋊#131	1	1	yes	characteristic
517	C₂	—	2	2	no	—
518	C₂	—	4	1	no	—
519	C₂	—	292	1	no	—
520	C₂	—	146	2	no	—
521	C₂	—	146	2	no	—
522	C₂	D₄×#11924036	1	1	yes	characteristic
523	C₂	C₂×#17989643	1	1	yes	characteristic
524	C₂	#22626899	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#64408
commutator, socle	C₂²×C₇₃	C₂³×C₈
Fitting	C₈×D₄×C₇₃	C₄
prime radical	C₂×D₄×D₇₃	C₈
cosocle	C₂×#10596831	C₂⁴
hypercenter	C₈×D₄	#64408
hypocenter	C₇₃	D₄×M₃₂
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₈×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#14556666	C₂	semidirect
2. C₂×#17989643	C₂	semidirect
3. #22626316	C₂	semidirect
4. #22626314	C₂	semidirect
5. #22626311	C₂	semidirect
6. #22626309	C₂	semidirect
7. #22626264	C₂	semidirect
8. #22626159	C₂	semidirect
9. #22626159	C₂	semidirect
10. #22626138	C₂	semidirect
17. C₂×#14556666	C₂²	semidirect
19. C₂×#14556665	C₂²	semidirect
20. C₂×#14556664	C₂²	semidirect
21. C₂²×#11924031	C₂²	semidirect
22. #17989508	C₂²	semidirect
23. C₄⋊#11924031	C₂²	semidirect
24. #17989482	C₂²	semidirect
25. #17989482	C₂²	semidirect
26. C₂²⋊#11924031	C₂²	semidirect
27. C₂²⋊#11924031	C₂²	semidirect
28. #17989475	C₂²	semidirect
29. #17989473	C₂²	semidirect
49. #14556666	D₄	semidirect
107. #11924031	C₂×D₄	semidirect
195. C₂²⋊D₇₃	M₃₂	semidirect
230. C₂²×C₇₃	C₂×M₃₂	semidirect
242. C₂×D₇₃	C₂×M₃₂	semidirect
253. Dic₇₃	C₂×M₃₂	semidirect
274. C₇₃	D₄×M₃₂	semidirect
504. C₂²	#17989643	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14556666	2
C₂×#17989643	2
#22626316	2
#22626314	2
#22626311	2
#22626309	2
#22626264	2
#22626159	2
#22626138	2
C₈×D₄×D₇₃	2
D₄×M₃₂	73