Subgroups — #34020596

Order 18688.

1038 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₃⋊#432	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊#64408	C₂	1	1	yes	maximal, characteristic
3	#22625732	C₂	1	4	yes	maximal, complemented
4	#22625725	C₂	1	2	yes	maximal, complemented
5	C₈×C₄⋊#64408	C₂	1	2	yes	maximal, complemented
6	#22625659	C₂	1	2	yes	maximal
7	C₂²⋊C₈×#64408	C₂	1	2	yes	maximal
8	#431×D₇₃	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₄⋊#64408	C₄	1	2	yes	—
10	C₂²×C₄×#64408	C₂²	1	2	yes	—
11	#17989610	C₄	1	2	yes	complemented
12	#17989609	C₄	1	2	yes	complemented
13	#17989608	C₄	1	2	yes	complemented
14	#17989607	C₄	1	2	yes	complemented
15	#17989588	C₂²	1	2	yes	—
16	#17989555	C₂²	1	2	yes	—
17	#17989546	C₂²	1	2	yes	—
18	C₂×#14556645	C₂²	1	4	yes	—
19	C₂×C₈×#64408	C₂²	1	4	yes	—
20	C₄×C₄⋊#64408	C₄	1	2	yes	—
21	C₄×C₄⋊#64408	C₄	1	2	yes	—
22	C₄×C₄⋊#64408	C₂²	1	1	yes	characteristic
23	C₄×C₄⋊#64408	C₂²	1	1	yes	characteristic
24	C₄×C₄⋊#64408	C₂²	1	2	yes	—
25	C₂×(C₂×#64408)⋊C₄	C₄	1	2	yes	—
26	#17989452	C₂²	1	4	yes	—
27	#17989452	C₂²	1	4	yes	—
28	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
29	#17988640	C₄	1	1	yes	characteristic, complemented
30	#17988639	C₄	1	2	yes	complemented
31	#17988638	C₄	1	2	yes	complemented
32	#17988637	C₄	1	1	yes	characteristic, complemented
33	#17988637	C₄	1	1	yes	characteristic, complemented
34	C₄⋊C₈×D₇₃	C₂²	1	2	yes	—
35	C₂²⋊C₈×D₇₃	C₂²	1	1	yes	characteristic
36	C₂²⋊C₈×D₇₃	C₂²	1	1	yes	characteristic
37	C₄×C₈×D₇₃	C₂²	1	2	yes	—
38	#431×C₇₃	C₄	1	1	yes	characteristic, complemented
39	C₂³×#64408	C₂×C₄	1	4	yes	—
40	C₂×#11924036	C₂³	1	4	yes	—
41	C₂×C₄⋊#64408	—	2	8	no	—
42	C₂×C₄⋊#64408	C₂×C₄	1	4	yes	—
43	C₂×C₄⋊#64408	C₂×C₄	1	2	yes	—
44	C₂×C₄⋊#64408	C₂×C₄	1	2	yes	—
45	C₂×C₄×#64408	—	4	4	no	—
46	C₂×C₄×#64408	C₂×C₄	1	4	yes	—
47	C₂×C₄×#64408	C₂³	1	2	yes	—
48	C₂×C₄×#64408	C₂³	1	2	yes	—
49	#14556658	C₂×C₄	1	4	yes	complemented
50	C₄⋊#10596833	C₂×C₄	1	4	yes	complemented
51	#14556648	C₂×C₄	1	4	yes	—
52	C₂²⋊#10596833	C₂×C₄	1	4	yes	—
53	#14556646	C₂×C₄	1	4	yes	complemented
54	#14556646	C₂×C₄	1	4	yes	complemented
55	#14556645	—	4	4	no	—
56	C₈×#64408	—	4	4	no	—
57	(C₂×#64408)⋊C₄	C₂×C₄	1	2	yes	—
58	(C₂×#64408)⋊C₄	C₂×C₄	1	4	yes	—
59	(C₂×#64408)⋊C₄	C₂×C₄	1	2	yes	—
60	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
63	C₂×C₈×D₇₃	C₂³	1	2	yes	—
64	C₂×C₈×D₇₃	C₂³	1	2	yes	—
65	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
68	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
69	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
70	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
71	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
72	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
73	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
74	C₄²×D₇₃	C₂³	1	1	yes	characteristic
75	C₄²×D₇₃	C₂³	1	1	yes	characteristic
76	C₄⋊#10596831	C₂×C₄	1	2	yes	complemented
77	#14556520	C₂×C₄	1	2	yes	complemented
78	#14556520	C₂×C₄	1	2	yes	complemented
79	C₂²⋊#10596831	C₂×C₄	1	1	yes	characteristic
80	C₂²⋊#10596831	C₂×C₄	1	1	yes	characteristic
81	#14556503	C₂×C₄	1	2	yes	—
82	#14556503	C₂×C₄	1	2	yes	—
83	C₄×#10596831	C₂×C₄	1	2	yes	complemented
84	C₈×Dic₇₃	C₂×C₄	1	2	yes	complemented
85	C₈×Dic₇₃	C₂×C₄	1	2	yes	complemented
86	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
87	C₄⋊C₈×C₇₃	C₂×C₄	1	2	yes	complemented
88	C₂²⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
89	C₂²⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
90	C₄×C₈×C₇₃	C₂×C₄	1	2	yes	complemented
91	C₂²×#64408	—	2	8	no	—
92	C₂²×#64408	—	2	8	no	—
93	C₂²×#64408	—	4	4	no	—
94	C₂²×#64408	C₂²×C₄	1	4	yes	—
95	C₂²×#64408	C₂²×C₄	1	4	yes	—
96	#11924036	—	2	4	no	—
97	#11924036	—	2	4	no	—
98	C₂×#10596833	C₂²×C₄	1	8	yes	—
99	C₄⋊#64408	—	2	8	no	—
100	C₄⋊#64408	—	2	4	no	—
101	C₄⋊#64408	M₁₆	1	8	yes	—
102	C₄×#64408	—	2	4	no	—
103	C₄×#64408	—	2	4	no	—
104	C₄×#64408	—	4	4	no	—
105	C₂³×D₇₃	C₂²×C₄	1	1	yes	characteristic
106	C₂²×Dic₇₃	C₄²	1	1	yes	characteristic
107	C₂²×Dic₇₃	C₄²	1	1	yes	characteristic
108	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₄×D₇₃	—	2	4	no	—
110	C₂×C₄×D₇₃	—	2	4	no	—
111	C₂×C₄×D₇₃	—	2	2	no	—
112	C₂×C₄×D₇₃	—	2	2	no	—
113	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
114	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
115	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
116	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
117	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
125	C₂×#10596831	C₂²×C₄	1	2	yes	—
126	C₂×#10596831	C₂²×C₄	1	2	yes	—
127	C₈×D₇₃	—	2	2	no	—
128	C₈×D₇₃	—	2	2	no	—
129	C₈×D₇₃	—	2	2	no	—
130	C₈×D₇₃	—	2	2	no	—
131	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
132	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
133	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
134	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
135	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
136	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
137	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
138	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
139	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
140	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
141	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
142	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₇₃	C₄²	1	1	yes	characteristic
144	C₂²×C₄×C₇₃	C₄²	1	1	yes	characteristic
145	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
147	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
148	C₄²×C₇₃	C₄²	1	1	yes	characteristic
149	C₄²×C₇₃	C₄²	1	1	yes	characteristic
150	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
151	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
152	C₂³×C₇₃	C₂×C₄²	1	1	yes	characteristic
153	C₂²×D₇₃	—	2	1	no	—
154	C₂²×D₇₃	—	2	1	no	—
155	C₂²×D₇₃	—	2	2	no	—
156	C₂²×D₇₃	C₂×C₄²	1	1	yes	characteristic
157	C₂²×D₇₃	#131	1	4	yes	—
158	C₂²×D₇₃	C₂³×C₄	1	1	yes	characteristic
159	C₂×#64408	—	2	4	no	—
160	C₂×#64408	—	2	4	no	—
161	C₂×#64408	—	2	4	no	—
162	C₂×#64408	—	2	4	no	—
163	C₂×#64408	—	2	4	no	—
164	C₂×#64408	—	4	16	no	—
165	C₂×#64408	C₂×M₁₆	1	8	yes	—
166	C₂×C₄×C₇₃	—	2	2	no	—
167	C₂×C₄×C₇₃	—	2	2	no	—
168	C₂×C₄×C₇₃	—	2	2	no	—
169	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
170	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
171	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
172	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
173	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
174	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
175	C₂×Dic₇₃	—	2	2	no	—
176	C₂×Dic₇₃	—	2	2	no	—
177	C₂×Dic₇₃	—	2	2	no	—
178	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
179	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
180	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
181	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
182	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
183	C₂×Dic₇₃	C₂³×C₄	1	1	yes	characteristic
184	C₄×D₇₃	—	2	1	no	—
185	C₄×D₇₃	—	2	1	no	—
186	C₄×D₇₃	—	2	2	no	—
187	C₄×D₇₃	—	2	2	no	—
188	C₄×D₇₃	—	2	2	no	—
189	C₄×D₇₃	—	2	2	no	—
190	C₄×D₇₃	—	2	2	no	—
191	C₄×D₇₃	—	2	2	no	—
192	C₄×D₇₃	—	2	2	no	—
193	C₄×D₇₃	—	2	2	no	—
194	C₄×D₇₃	—	2	2	no	—
195	C₄×D₇₃	C₂×M₁₆	1	4	yes	—
196	C₄×D₇₃	H(5,𝔽₂)	1	2	yes	—
197	C₄×D₇₃	2₋¹⁺⁴	1	2	yes	—
198	#10596833	—	2	8	no	—
199	C₈×C₇₃	—	2	2	no	—
200	C₈×C₇₃	—	2	2	no	—
201	#10596831	—	2	2	no	—
202	#10596831	—	2	2	no	—
203	C₂²×C₇₃	—	2	1	no	—
204	C₂²×C₇₃	—	2	1	no	—
205	C₂²×C₇₃	#405	1	2	yes	—
206	C₂²×C₇₃	C₂²×C₄²	1	1	yes	characteristic
207	C₂×D₇₃	—	2	1	no	—
208	C₂×D₇₃	—	2	1	no	—
209	C₂×D₇₃	—	2	4	no	—
210	C₂×D₇₃	—	2	4	no	—
211	C₂×D₇₃	#405	1	2	yes	—
212	C₂×D₇₃	#518	1	1	yes	characteristic
213	C₂×D₇₃	#519	1	1	yes	characteristic
214	C₂×D₇₃	C₂²×M₁₆	1	2	yes	—
215	C₂×D₇₃	C₂×#131	1	2	yes	—
216	#64408	—	2	8	no	—
217	#64408	—	4	4	no	—
218	C₄×C₇₃	—	2	1	no	—
219	C₄×C₇₃	—	2	1	no	—
220	C₄×C₇₃	—	2	1	no	—
221	C₄×C₇₃	—	2	1	no	—
222	C₄×C₇₃	C₄×M₁₆	1	2	yes	—
223	C₄×C₇₃	#520	1	2	yes	—
224	Dic₇₃	—	2	1	no	—
225	Dic₇₃	—	2	1	no	—
226	Dic₇₃	—	2	1	no	—
227	Dic₇₃	—	2	1	no	—
228	Dic₇₃	C₄×M₁₆	1	2	yes	—
229	Dic₇₃	#520	1	2	yes	—
230	#20535	—	73	1	no	maximal, Sylow
231	C₂×C₇₃	—	2	2	no	—
232	C₂×C₇₃	#2274	1	1	yes	characteristic
233	C₂×C₇₃	C₂×C₄×M₁₆	1	1	yes	characteristic
234	C₂×C₇₃	C₂×#405	1	1	yes	characteristic
235	D₇₃	—	2	2	no	—
236	D₇₃	#2974	1	2	yes	—
237	D₇₃	#2984	1	2	yes	—
238	C₂×#432	—	73	1	no	—
239	C₂×#431	—	73	1	no	—
240	C₂×C₄×C₄⋊C₄	—	73	1	no	—
241	#1771	—	73	4	no	—
242	#1770	—	73	2	no	—
243	C₈×C₄⋊C₄	—	73	2	no	—
244	#1749	—	73	2	no	—
245	C₄×C₂²⋊C₈	—	73	2	no	—
246	C₇₃	#20535	1	1	yes	characteristic, complemented, Sylow
247	C₂²×C₄⋊C₄	—	73	2	no	—
248	C₂²×C₄²	—	73	2	no	—
249	C₂²×C₄²	—	73	1	no	—
250	#432	—	73	2	no	—
251	#432	—	73	2	no	—
252	#432	—	73	2	no	—
253	#432	—	73	2	no	—
254	#431	—	73	1	no	—
255	#431	—	73	2	no	—
256	#431	—	73	1	no	—
257	#431	—	73	1	no	—
258	#431	—	73	2	no	—
259	#431	#64408	1	1	yes	characteristic, complemented
260	C₂×C₄⋊C₈	—	73	2	no	—
261	C₂×C₄⋊C₈	—	73	2	no	—
262	C₂×C₂²⋊C₈	—	73	2	no	—
263	C₂×C₂²⋊C₈	—	73	1	no	—
264	C₂×C₂²⋊C₈	—	73	1	no	—
265	C₂×#97	—	73	4	no	—
266	C₂×#97	—	73	2	no	—
267	C₂×C₄×C₈	—	73	4	no	—
268	C₂×C₄×C₈	—	73	2	no	—
269	C₄×C₄⋊C₄	—	73	2	no	—
270	C₄×C₄⋊C₄	—	73	2	no	—
271	C₄×C₄⋊C₄	—	73	1	no	—
272	C₄×C₄⋊C₄	—	73	1	no	—
273	C₄×C₄⋊C₄	—	73	2	no	—
274	C₂×#95	—	73	2	no	—
275	#336	—	73	4	no	—
276	#336	—	73	4	no	—
277	C₂³×C₄	—	73	4	no	—
278	C₂³×C₄	—	73	1	no	—
279	C₂³×C₄	—	73	1	no	—
280	C₂³×C₄	—	73	1	no	—
281	C₂²×C₈	—	73	4	no	—
282	C₂²×C₈	—	73	2	no	—
283	C₂²×C₈	—	73	2	no	—
284	C₂×C₄⋊C₄	—	73	2	no	—
285	C₂×C₄⋊C₄	—	73	2	no	—
286	C₂×C₄⋊C₄	—	73	4	no	—
287	C₂×C₄⋊C₄	—	146	8	no	—
288	C₂×C₄²	—	292	4	no	—
289	C₂×C₄²	—	73	4	no	—
290	C₂×C₄²	—	73	1	no	—
291	C₂×C₄²	—	73	1	no	—
292	C₂×C₄²	—	73	1	no	—
293	C₂×C₄²	—	73	1	no	—
294	C₂×C₄²	—	73	1	no	—
295	C₂×C₄²	—	73	1	no	—
296	C₂×C₄²	—	73	1	no	—
297	C₂×C₄²	—	73	1	no	—
298	C₂×C₄²	—	73	1	no	—
299	C₂×C₄²	—	73	1	no	—
300	C₂×C₄²	—	73	1	no	—
301	C₂×C₄²	—	73	2	no	—
302	C₂×C₄²	—	73	2	no	—
303	C₂×C₄²	C₂×#64408	1	1	yes	characteristic
304	C₄⋊C₈	—	73	4	no	—
305	C₄⋊C₈	—	73	4	no	—
306	C₄⋊C₈	—	73	2	no	—
307	C₄⋊C₈	—	73	2	no	—
308	C₄⋊C₈	—	73	2	no	—
309	C₄⋊C₈	C₂×#64408	1	2	yes	complemented
310	C₂²⋊C₈	—	73	4	no	—
311	C₂²⋊C₈	—	73	4	no	—
312	C₂²⋊C₈	—	73	1	no	—
313	C₂²⋊C₈	—	73	1	no	—
314	C₂²⋊C₈	—	73	2	no	—
315	C₂²⋊C₈	—	73	2	no	—
316	C₂²⋊C₈	C₂×#64408	1	1	yes	characteristic
317	C₂²⋊C₈	C₂×#64408	1	1	yes	characteristic
318	#97	—	292	4	no	—
319	#97	—	73	4	no	—
320	#97	—	73	4	no	—
321	C₄×C₈	—	292	4	no	—
322	C₄×C₈	—	73	2	no	—
323	C₄×C₈	—	73	2	no	—
324	C₄×C₈	—	73	2	no	—
325	C₄×C₈	C₂×#64408	1	2	yes	complemented
326	#95	—	73	2	no	—
327	#95	—	73	4	no	—
328	#95	—	73	2	no	—
329	C₂⁴	—	73	1	no	—
330	C₂²×C₄	—	292	4	no	—
331	C₂²×C₄	—	73	1	no	—
332	C₂²×C₄	—	73	1	no	—
333	C₂²×C₄	—	73	4	no	—
334	C₂²×C₄	—	73	1	no	—
335	C₂²×C₄	—	73	1	no	—
336	C₂²×C₄	—	73	1	no	—
337	C₂²×C₄	—	73	1	no	—
338	C₂²×C₄	—	73	1	no	—
339	C₂²×C₄	—	73	1	no	—
340	C₂²×C₄	—	73	1	no	—
341	C₂²×C₄	—	73	1	no	—
342	C₂²×C₄	—	73	1	no	—
343	C₂²×C₄	—	73	1	no	—
344	C₂²×C₄	—	73	1	no	—
345	C₂²×C₄	—	73	1	no	—
346	C₂²×C₄	—	73	1	no	—
347	C₂²×C₄	—	73	4	no	—
348	C₂²×C₄	—	146	2	no	—
349	C₂²×C₄	—	146	4	no	—
350	C₂²×C₄	—	146	2	no	—
351	C₂²×C₄	—	146	4	no	—
352	C₂²×C₄	—	146	8	no	—
353	C₂²×C₄	—	146	8	no	—
354	C₂²×C₄	C₄×#64408	1	1	yes	characteristic
355	C₂²×C₄	C₄×#64408	1	1	yes	characteristic
356	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
357	C₂×C₈	—	73	8	no	—
358	C₂×C₈	—	73	2	no	—
359	C₂×C₈	—	73	2	no	—
360	C₂×C₈	—	146	2	no	—
361	C₂×C₈	—	146	2	no	—
362	C₂×C₈	—	146	2	no	—
363	C₂×C₈	—	146	2	no	—
364	C₂×C₈	—	146	4	no	—
365	C₂×C₈	—	146	4	no	—
366	C₂×C₈	C₂²×#64408	1	2	yes	—
367	C₂×C₈	C₂²×#64408	1	2	yes	—
368	C₄⋊C₄	—	73	8	no	—
369	C₄⋊C₄	—	146	4	no	—
370	C₄⋊C₄	—	146	8	no	—
371	C₄²	—	292	4	no	—
372	C₄²	—	73	1	no	—
373	C₄²	—	73	1	no	—
374	C₄²	—	73	1	no	—
375	C₄²	—	73	1	no	—
376	C₄²	—	73	1	no	—
377	C₄²	—	73	1	no	—
378	C₄²	—	73	1	no	—
379	C₄²	—	73	1	no	—
380	C₄²	—	73	1	no	—
381	C₄²	—	73	1	no	—
382	C₄²	—	73	1	no	—
383	C₄²	—	73	1	no	—
384	C₄²	—	146	4	no	—
385	C₄²	—	146	4	no	—
386	C₄²	C₄×#64408	1	1	yes	characteristic
387	C₄²	C₄×#64408	1	1	yes	characteristic
388	C₄²	C₂²×#64408	1	1	yes	characteristic
389	C₄²	C₂²×#64408	1	1	yes	characteristic
390	C₂³	—	73	1	no	—
391	C₂³	—	73	1	no	—
392	C₂³	—	73	4	no	—
393	C₂³	—	146	1	no	—
394	C₂³	—	146	2	no	—
395	C₂³	—	146	1	no	—
396	C₂³	C₂×C₄×#64408	1	1	yes	characteristic
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	292	16	no	—
401	C₂×C₄	—	73	1	no	—
402	C₂×C₄	—	73	1	no	—
403	C₂×C₄	—	73	2	no	—
404	C₂×C₄	—	73	2	no	—
405	C₂×C₄	—	73	4	no	—
406	C₂×C₄	—	73	8	no	—
407	C₂×C₄	—	73	1	no	—
408	C₂×C₄	—	73	1	no	—
409	C₂×C₄	—	73	1	no	—
410	C₂×C₄	—	73	1	no	—
411	C₂×C₄	—	146	2	no	—
412	C₂×C₄	—	146	2	no	—
413	C₂×C₄	—	146	1	no	—
414	C₂×C₄	—	146	2	no	—
415	C₂×C₄	—	146	1	no	—
416	C₂×C₄	—	146	2	no	—
417	C₂×C₄	—	146	2	no	—
418	C₂×C₄	—	146	2	no	—
419	C₂×C₄	—	146	2	no	—
420	C₂×C₄	—	146	4	no	—
421	C₂×C₄	—	146	4	no	—
422	C₂×C₄	—	146	4	no	—
423	C₂×C₄	—	146	2	no	—
424	C₂×C₄	—	146	2	no	—
425	C₂×C₄	—	146	4	no	—
426	C₂×C₄	—	146	4	no	—
427	C₂×C₄	—	146	2	no	—
428	C₂×C₄	—	146	2	no	—
429	C₂×C₄	—	146	2	no	—
430	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
431	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
432	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
433	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
434	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
435	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
436	C₈	—	2	2	no	—
437	C₈	—	2	2	no	—
438	C₈	—	146	8	no	—
439	C₈	—	146	2	no	—
440	C₈	—	146	2	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	73	1	no	—
444	C₂²	—	73	1	no	—
445	C₂²	—	73	2	no	—
446	C₂²	—	73	2	no	—
447	C₂²	—	73	2	no	—
448	C₂²	—	146	4	no	—
449	C₂²	—	146	4	no	—
450	C₂²	—	146	1	no	—
451	C₂²	—	146	1	no	—
452	C₂²	#17989550	1	2	yes	—
453	C₂²	C₂²×C₄×#64408	1	1	yes	characteristic
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	292	4	no	—
459	C₄	—	73	2	no	—
460	C₄	—	73	2	no	—
461	C₄	—	146	8	no	—
462	C₄	—	146	1	no	—
463	C₄	—	146	1	no	—
464	C₄	—	146	1	no	—
465	C₄	—	146	1	no	—
466	C₄	M₁₆×#64408	1	2	yes	—
467	C₄	#17989656	1	2	yes	—
468	C₂	—	2	2	no	—
469	C₂	—	73	2	no	—
470	C₂	—	73	2	no	—
471	C₂	—	146	2	no	—
472	C₂	#22626368	1	1	yes	characteristic
473	C₂	C₂×M₁₆×#64408	1	1	yes	characteristic
474	C₂	C₂×#17989550	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#64408
commutator, socle	C₂²×C₇₃	C₂²×C₄²
Fitting	#431×C₇₃	C₄
prime radical	C₂³×D₇₃	C₂²×C₄
cosocle	C₂×C₄×D₇₃	C₂⁴
hypercenter	#431	#64408
hypocenter	C₇₃	#20535
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ #431

Complements

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

N	H ≅ G/N	type
3. #22625732	C₂	semidirect
4. #22625725	C₂	semidirect
5. C₈×C₄⋊#64408	C₂	semidirect
11. #17989610	C₄	semidirect
12. #17989609	C₄	semidirect
13. #17989608	C₄	semidirect
14. #17989607	C₄	semidirect
29. #17988640	C₄	semidirect
30. #17988639	C₄	semidirect
31. #17988638	C₄	semidirect
32. #17988637	C₄	semidirect
33. #17988637	C₄	semidirect
38. #431×C₇₃	C₄	semidirect
49. #14556658	C₂×C₄	semidirect
50. C₄⋊#10596833	C₂×C₄	semidirect
53. #14556646	C₂×C₄	semidirect
54. #14556646	C₂×C₄	semidirect
76. C₄⋊#10596831	C₂×C₄	semidirect
77. #14556520	C₂×C₄	semidirect
78. #14556520	C₂×C₄	semidirect
83. C₄×#10596831	C₂×C₄	semidirect
84. C₈×Dic₇₃	C₂×C₄	semidirect
85. C₈×Dic₇₃	C₂×C₄	semidirect
87. C₄⋊C₈×C₇₃	C₂×C₄	semidirect
90. C₄×C₈×C₇₃	C₂×C₄	semidirect
246. C₇₃	#20535	semidirect
259. #431	#64408	semidirect
309. C₄⋊C₈	C₂×#64408	semidirect
325. C₄×C₈	C₂×#64408	semidirect

Maximal subgroups

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

subgroup	index
D₇₃⋊#432	2
C₂×C₄×C₄⋊#64408	2
#22625732	2
#22625725	2
C₈×C₄⋊#64408	2
#22625659	2
C₂²⋊C₈×#64408	2
#431×D₇₃	2
#20535	73