Subgroups — #34020689

Order 18688.

870 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₃⋊#433	C₂	1	1	yes	maximal, characteristic
2	#22626393	C₂	1	1	yes	maximal, characteristic
3	#22625732	C₂	1	1	yes	maximal, characteristic, complemented
4	#22625732	C₂	1	1	yes	maximal, characteristic, complemented
5	#22625728	C₂	1	1	yes	maximal, characteristic, complemented
6	#22625724	C₂	1	1	yes	maximal, characteristic, complemented
7	#22625720	C₂	1	1	yes	maximal, characteristic, complemented
8	#22625720	C₂	1	1	yes	maximal, characteristic, complemented
9	#22625718	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄⋊C₈×#64408	C₂	1	1	yes	maximal, characteristic, complemented
11	#22625671	C₂	1	1	yes	maximal, characteristic
12	#22625671	C₂	1	1	yes	maximal, characteristic
13	#22625667	C₂	1	1	yes	maximal, characteristic
14	C₈×C₂²⋊#64408	C₂	1	1	yes	maximal, characteristic
15	#424×D₇₃	C₂	1	1	yes	maximal, characteristic
16	#17989612	C₄	1	2	yes	complemented
17	#17989612	C₄	1	2	yes	complemented
18	#17989611	C₄	1	2	yes	complemented
19	#17989611	C₄	1	2	yes	complemented
20	#17989588	C₂²	1	1	yes	characteristic
21	#17989588	C₂²	1	1	yes	characteristic
22	#17989555	C₂²	1	1	yes	characteristic
23	#17989555	C₂²	1	1	yes	characteristic
24	#17989546	C₂²	1	1	yes	characteristic
25	C₂×#14556645	C₂²	1	1	yes	characteristic
26	C₂×#14556645	C₂²	1	1	yes	characteristic
27	C₂×#14556645	C₂²	1	1	yes	characteristic
28	C₂×#14556645	C₂²	1	1	yes	characteristic
29	C₄×#11924036	C₂²	1	1	yes	characteristic
30	C₂×C₈×#64408	C₂²	1	1	yes	characteristic
31	C₂×C₈×#64408	C₂²	1	1	yes	characteristic
32	C₂×C₈×#64408	C₂²	1	1	yes	characteristic
33	C₂×C₈×#64408	C₂²	1	1	yes	characteristic
34	#17989537	C₄	1	2	yes	—
35	#17989537	C₄	1	2	yes	—
36	#17989536	C₄	1	2	yes	—
37	#17989536	C₄	1	2	yes	—
38	C₄×C₄⋊#64408	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊#64408	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊#64408	C₂²	1	1	yes	characteristic
41	C₄×C₂²⋊#64408	C₂²	1	1	yes	characteristic
42	#17989523	C₂²	1	1	yes	characteristic
43	C₄²×#64408	C₂²	1	1	yes	characteristic
44	#17989452	C₂²	1	1	yes	characteristic
45	#17989452	C₂²	1	1	yes	characteristic
46	#17989452	C₂²	1	1	yes	characteristic
47	#17989452	C₂²	1	1	yes	characteristic
48	#17989452	C₂²	1	1	yes	characteristic
49	#17989452	C₂²	1	1	yes	characteristic
50	#17989452	C₂²	1	1	yes	characteristic
51	#17989452	C₂²	1	1	yes	characteristic
52	C₂×M₁₆×D₇₃	C₂²	1	1	yes	characteristic
53	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
54	#117×D₇₃	C₂²	1	1	yes	characteristic
55	#17988615	C₄	1	1	yes	characteristic, complemented
56	#17988614	C₄	1	1	yes	characteristic, complemented
57	#17988613	C₄	1	1	yes	characteristic, complemented
58	#17988612	C₄	1	1	yes	characteristic, complemented
59	#17988612	C₄	1	1	yes	characteristic, complemented
60	#17988612	C₄	1	1	yes	characteristic, complemented
61	#17988612	C₄	1	1	yes	characteristic, complemented
62	C₄⋊C₈×D₇₃	C₂²	1	1	yes	characteristic
63	C₄⋊C₈×D₇₃	C₂²	1	1	yes	characteristic
64	C₄⋊C₈×D₇₃	C₂²	1	1	yes	characteristic
65	C₄⋊C₈×D₇₃	C₂²	1	1	yes	characteristic
66	#424×C₇₃	C₄	1	1	yes	characteristic, complemented
67	C₂×#11924036	C₂³	1	1	yes	characteristic
68	C₂×#11924036	C₂³	1	1	yes	characteristic
69	C₂×#11924036	C₂³	1	1	yes	characteristic
70	C₂×#11924036	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊#64408	C₂×C₄	1	2	yes	—
72	C₂×C₄⋊#64408	C₂×C₄	1	2	yes	—
73	C₂×C₂²⋊#64408	C₂×C₄	1	2	yes	—
74	C₂×C₂²⋊#64408	C₂×C₄	1	2	yes	—
75	C₂×C₄×#64408	C₂×C₄	1	2	yes	—
76	C₂×C₄×#64408	C₂×C₄	1	2	yes	—
77	C₂×C₄×#64408	C₂³	1	1	yes	characteristic
78	C₂×C₄×#64408	C₂³	1	1	yes	characteristic
79	C₂×C₄×#64408	C₂³	1	1	yes	characteristic
80	C₂×C₄×#64408	C₂³	1	1	yes	characteristic
81	#14556658	C₂×C₄	1	2	yes	—
82	#14556658	C₂×C₄	1	2	yes	—
83	C₄⋊#10596833	C₂×C₄	1	2	yes	—
84	C₄⋊#10596833	C₂×C₄	1	2	yes	—
85	#14556648	C₂×C₄	1	2	yes	—
86	#14556648	C₂×C₄	1	2	yes	—
87	C₂²⋊#10596833	C₂×C₄	1	2	yes	—
88	C₂²⋊#10596833	C₂×C₄	1	2	yes	—
89	#14556646	C₂×C₄	1	2	yes	—
90	#14556646	C₂×C₄	1	2	yes	—
91	#14556645	—	4	1	no	—
92	#14556645	—	4	1	no	—
93	#14556645	—	4	1	no	—
94	#14556645	—	4	1	no	—
95	C₄×#10596833	C₂×C₄	1	2	yes	—
96	C₄×#10596833	C₂×C₄	1	2	yes	—
97	C₈×#64408	—	4	1	no	—
98	C₈×#64408	—	4	1	no	—
99	C₈×#64408	—	4	1	no	—
100	C₈×#64408	—	4	1	no	—
101	(C₂×#64408)⋊C₄	C₂×C₄	1	2	yes	—
102	(C₂×#64408)⋊C₄	C₂×C₄	1	2	yes	—
103	(C₂×#64408)⋊C₄	C₂×C₄	1	2	yes	—
104	(C₂×#64408)⋊C₄	C₂×C₄	1	2	yes	—
105	(C₂×#64408)⋊C₄	C₂×C₄	1	2	yes	—
106	(C₂×#64408)⋊C₄	C₂×C₄	1	2	yes	—
107	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
108	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
109	C₂×#11924011	C₂×C₄	1	1	yes	characteristic
110	C₂×#11924011	C₂×C₄	1	1	yes	characteristic
111	M₁₆×D₇₃	—	4	1	no	—
112	M₁₆×D₇₃	—	4	1	no	—
113	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
114	C₂×C₈×D₇₃	—	4	1	no	—
115	C₂×C₈×D₇₃	—	4	1	no	—
116	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
117	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
118	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
119	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
120	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
121	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
122	#14556550	C₂×C₄	1	1	yes	characteristic
123	#14556549	C₂×C₄	1	1	yes	characteristic
124	#14556549	C₂×C₄	1	1	yes	characteristic
125	#14556548	C₂×C₄	1	1	yes	characteristic
126	#14556548	C₂×C₄	1	1	yes	characteristic
127	#14556547	C₂×C₄	1	1	yes	characteristic
128	#14556547	C₂×C₄	1	1	yes	characteristic
129	C₄⋊C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
130	C₄⋊C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
131	C₂²⋊C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
132	C₂²⋊C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
133	C₄²×D₇₃	C₂³	1	1	yes	characteristic
134	C₄²×D₇₃	C₂³	1	1	yes	characteristic
135	C₄⋊#10596831	C₂×C₄	1	1	yes	characteristic
136	C₄⋊#10596831	C₂×C₄	1	1	yes	characteristic
137	C₄⋊#10596831	C₂×C₄	1	1	yes	characteristic
138	C₄⋊#10596831	C₂×C₄	1	1	yes	characteristic
139	#14556520	C₂×C₄	1	1	yes	characteristic
140	#14556520	C₂×C₄	1	1	yes	characteristic
141	#14556520	C₂×C₄	1	1	yes	characteristic
142	#14556520	C₂×C₄	1	1	yes	characteristic
143	#14556520	C₂×C₄	1	1	yes	characteristic
144	#14556520	C₂×C₄	1	1	yes	characteristic
145	#14556520	C₂×C₄	1	1	yes	characteristic
146	#14556520	C₂×C₄	1	1	yes	characteristic
147	C₂×M₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
148	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
149	#117×C₇₃	C₂×C₄	1	1	yes	characteristic
150	C₄⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
151	C₄⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
152	C₄⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
153	C₄⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
154	C₂²×#64408	C₂²×C₄	1	2	yes	—
155	C₂²×#64408	C₂²×C₄	1	2	yes	—
156	C₂²×#64408	C₂²×C₄	1	2	yes	—
157	C₂²×#64408	C₂²×C₄	1	2	yes	—
158	#11924036	—	2	1	no	—
159	#11924036	—	2	1	no	—
160	#11924036	—	2	1	no	—
161	#11924036	—	2	1	no	—
162	#11924036	—	2	1	no	—
163	#11924036	—	2	1	no	—
164	#11924036	—	2	1	no	—
165	#11924036	—	2	1	no	—
166	C₂×#10596833	C₂²×C₄	1	2	yes	—
167	C₂×#10596833	C₂²×C₄	1	2	yes	—
168	C₂×#10596833	C₂²×C₄	1	2	yes	—
169	C₂×#10596833	C₂²×C₄	1	2	yes	—
170	C₄⋊#64408	—	2	4	no	—
171	C₄⋊#64408	—	4	2	no	—
172	C₂²⋊#64408	—	2	4	no	—
173	C₂²⋊#64408	—	4	2	no	—
174	C₄×#64408	—	2	4	no	—
175	C₄×#64408	—	2	1	no	—
176	C₄×#64408	—	2	1	no	—
177	C₄×#64408	—	2	1	no	—
178	C₄×#64408	—	2	1	no	—
179	C₄×#64408	—	2	1	no	—
180	C₄×#64408	—	2	1	no	—
181	C₄×#64408	—	2	1	no	—
182	C₄×#64408	—	2	1	no	—
183	C₄×#64408	—	4	2	no	—
184	C₂³×D₇₃	C₂²×C₄	1	1	yes	characteristic
185	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₄×D₇₃	—	2	1	no	—
187	C₂×C₄×D₇₃	—	2	1	no	—
188	C₂×C₄×D₇₃	—	2	1	no	—
189	C₂×C₄×D₇₃	—	2	1	no	—
190	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
194	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
195	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
196	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
198	#11924012	—	4	1	no	—
199	#11924011	—	4	1	no	—
200	#11924011	—	4	1	no	—
201	C₂×#10596831	—	4	1	no	—
202	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
203	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
204	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
205	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
206	C₈×D₇₃	—	2	1	no	—
207	C₈×D₇₃	—	2	1	no	—
208	C₈×D₇₃	—	2	1	no	—
209	C₈×D₇₃	—	2	1	no	—
210	C₈×D₇₃	—	2	1	no	—
211	C₈×D₇₃	—	2	1	no	—
212	C₈×D₇₃	—	2	1	no	—
213	C₈×D₇₃	—	2	1	no	—
214	C₈×D₇₃	—	4	1	no	—
215	C₈×D₇₃	—	4	1	no	—
216	C₄⋊Dic₇₃	C₄²	1	1	yes	characteristic
217	C₄⋊Dic₇₃	C₄²	1	1	yes	characteristic
218	#11924007	C₄²	1	1	yes	characteristic
219	#11924007	C₄²	1	1	yes	characteristic
220	#11924007	C₄²	1	1	yes	characteristic
221	#11924007	C₄²	1	1	yes	characteristic
222	C₂²⋊Dic₇₃	C₄²	1	1	yes	characteristic
223	C₂²⋊Dic₇₃	C₄²	1	1	yes	characteristic
224	#11924005	C₄²	1	1	yes	characteristic
225	#11924005	C₄²	1	1	yes	characteristic
226	#11924005	C₄²	1	1	yes	characteristic
227	#11924005	C₄²	1	1	yes	characteristic
228	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
229	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
230	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
231	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
232	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
233	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
234	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
235	M₁₆×C₇₃	—	4	1	no	—
236	C₂×C₈×C₇₃	—	4	1	no	—
237	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
238	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
239	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
240	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
241	C₄⋊C₄×C₇₃	C₄²	1	1	yes	characteristic
242	C₄⋊C₄×C₇₃	C₄²	1	1	yes	characteristic
243	C₂²⋊C₄×C₇₃	C₄²	1	1	yes	characteristic
244	C₂²⋊C₄×C₇₃	C₄²	1	1	yes	characteristic
245	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
246	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
247	C₂³×C₇₃	C₂×C₄²	1	1	yes	characteristic
248	C₂²×D₇₃	—	2	1	no	—
249	C₂²×D₇₃	—	2	1	no	—
250	C₂²×D₇₃	—	2	2	no	—
251	C₂²×D₇₃	—	2	2	no	—
252	C₂²×D₇₃	C₂×C₄²	1	1	yes	characteristic
253	C₂²×D₇₃	C₂³×C₄	1	1	yes	characteristic
254	C₂×#64408	—	2	2	no	—
255	C₂×#64408	—	2	2	no	—
256	C₂×#64408	—	2	2	no	—
257	C₂×#64408	—	2	2	no	—
258	C₂×#64408	—	2	2	no	—
259	C₂×#64408	—	2	2	no	—
260	C₂×#64408	—	2	2	no	—
261	C₂×#64408	—	2	2	no	—
262	C₂×#64408	—	2	2	no	—
263	C₂×#64408	—	2	2	no	—
264	C₂×#64408	—	2	2	no	—
265	C₂×#64408	#131	1	4	yes	—
266	C₂×C₄×C₇₃	—	2	1	no	—
267	C₂×C₄×C₇₃	—	2	1	no	—
268	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
269	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
270	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
271	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
272	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
273	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
274	C₂×Dic₇₃	—	2	1	no	—
275	C₂×Dic₇₃	—	2	1	no	—
276	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
277	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
278	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
279	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
280	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
281	C₂×Dic₇₃	C₂³×C₄	1	1	yes	characteristic
282	C₄×D₇₃	—	2	1	no	—
283	C₄×D₇₃	—	2	1	no	—
284	C₄×D₇₃	—	2	2	no	—
285	C₄×D₇₃	—	2	2	no	—
286	C₄×D₇₃	—	2	2	no	—
287	C₄×D₇₃	—	2	2	no	—
288	C₄×D₇₃	—	2	1	no	—
289	C₄×D₇₃	—	2	1	no	—
290	C₄×D₇₃	—	2	1	no	—
291	C₄×D₇₃	—	2	1	no	—
292	C₄×D₇₃	H(5,𝔽₂)	1	1	yes	characteristic
293	C₄×D₇₃	H(5,𝔽₂)	1	1	yes	characteristic
294	C₄×D₇₃	2₋¹⁺⁴	1	1	yes	characteristic
295	C₄×D₇₃	2₋¹⁺⁴	1	1	yes	characteristic
296	#10596833	—	2	2	no	—
297	#10596833	—	2	2	no	—
298	#10596833	—	2	2	no	—
299	#10596833	—	2	2	no	—
300	C₈×C₇₃	—	2	1	no	—
301	C₈×C₇₃	—	2	1	no	—
302	C₈×C₇₃	—	2	1	no	—
303	C₈×C₇₃	—	2	1	no	—
304	#10596831	—	2	1	no	—
305	#10596831	—	2	1	no	—
306	#10596831	—	2	1	no	—
307	#10596831	—	2	1	no	—
308	C₂²×C₇₃	—	2	1	no	—
309	C₂²×C₇₃	—	2	1	no	—
310	C₂²×C₇₃	—	2	1	no	—
311	C₂²×C₇₃	C₂²×C₄²	1	1	yes	characteristic
312	C₂×D₇₃	—	2	1	no	—
313	C₂×D₇₃	—	2	1	no	—
314	C₂×D₇₃	—	2	1	no	—
315	C₂×D₇₃	—	4	2	no	—
316	C₂×D₇₃	—	4	2	no	—
317	C₂×D₇₃	#520	1	1	yes	characteristic
318	C₂×D₇₃	#520	1	1	yes	characteristic
319	C₂×D₇₃	C₂×#131	1	2	yes	—
320	C₂×D₇₃	#568	1	2	yes	—
321	#64408	—	2	4	no	—
322	#64408	—	4	2	no	—
323	#64408	—	4	2	no	—
324	#64408	—	4	2	no	—
325	C₄×C₇₃	—	2	1	no	—
326	C₄×C₇₃	—	2	1	no	—
327	C₄×C₇₃	—	2	1	no	—
328	C₄×C₇₃	—	2	1	no	—
329	C₄×C₇₃	—	2	1	no	—
330	C₄×C₇₃	#518	1	1	yes	characteristic
331	C₄×C₇₃	#519	1	1	yes	characteristic
332	Dic₇₃	—	2	1	no	—
333	Dic₇₃	—	2	1	no	—
334	Dic₇₃	—	2	1	no	—
335	Dic₇₃	—	2	1	no	—
336	Dic₇₃	—	2	1	no	—
337	Dic₇₃	#520	1	1	yes	characteristic
338	Dic₇₃	#520	1	1	yes	characteristic
339	#20553	—	73	1	no	maximal, Sylow
340	C₂×C₇₃	—	4	1	no	—
341	C₂×C₇₃	#2274	1	1	yes	characteristic
342	C₂×C₇₃	C₄×#131	1	1	yes	characteristic
343	C₂×C₇₃	#2875	1	1	yes	characteristic
344	D₇₃	—	4	1	no	—
345	D₇₃	#2992	1	2	yes	—
346	D₇₃	#2993	1	2	yes	—
347	C₂×#433	—	73	1	no	—
348	C₂×#424	—	73	1	no	—
349	#2298	—	73	1	no	—
350	#1771	—	73	1	no	—
351	#1771	—	73	1	no	—
352	#1770	—	73	1	no	—
353	C₈×C₄⋊C₄	—	73	1	no	—
354	#1768	—	73	1	no	—
355	#1768	—	73	1	no	—
356	#1767	—	73	1	no	—
357	C₄×C₄⋊C₈	—	73	1	no	—
358	#1753	—	73	1	no	—
359	#1753	—	73	1	no	—
360	#1752	—	73	1	no	—
361	C₈×C₂²⋊C₄	—	73	1	no	—
362	C₇₃	#20553	1	1	yes	characteristic, complemented, Sylow
363	C₂²×M₁₆	—	73	1	no	—
364	C₂³×C₈	—	73	1	no	—
365	C₂×#117	—	73	1	no	—
366	#433	—	73	2	no	—
367	#433	—	73	2	no	—
368	#433	—	73	2	no	—
369	#433	—	73	2	no	—
370	#424	—	73	1	no	—
371	#424	—	73	1	no	—
372	#424	—	73	1	no	—
373	#424	—	73	1	no	—
374	#424	—	73	1	no	—
375	#424	—	73	1	no	—
376	#424	—	73	1	no	—
377	#424	#64408	1	1	yes	characteristic, complemented
378	C₂×C₄⋊C₈	—	73	1	no	—
379	C₂×C₄⋊C₈	—	73	1	no	—
380	C₂×C₄⋊C₈	—	73	1	no	—
381	C₂×C₄⋊C₈	—	73	1	no	—
382	C₂×C₄⋊C₈	—	73	1	no	—
383	C₂×C₄⋊C₈	—	73	1	no	—
384	C₂×C₂²⋊C₈	—	73	1	no	—
385	C₂×C₂²⋊C₈	—	73	1	no	—
386	C₂×#97	—	73	1	no	—
387	C₂×#97	—	73	1	no	—
388	C₂×#97	—	73	1	no	—
389	C₂×#97	—	73	1	no	—
390	C₂×#97	—	73	1	no	—
391	C₂×C₄×C₈	—	73	1	no	—
392	C₂×C₄×C₈	—	73	1	no	—
393	C₂×C₄×C₈	—	73	1	no	—
394	C₂×C₄×C₈	—	73	1	no	—
395	C₂×C₄×C₈	—	73	1	no	—
396	#388	—	73	2	no	—
397	#388	—	73	2	no	—
398	#387	—	73	2	no	—
399	#387	—	73	2	no	—
400	C₄×C₄⋊C₄	—	73	1	no	—
401	C₄×C₄⋊C₄	—	73	1	no	—
402	C₄×C₂²⋊C₄	—	73	1	no	—
403	C₄×C₂²⋊C₄	—	73	1	no	—
404	#376	—	73	1	no	—
405	C₄³	—	73	1	no	—
406	#336	—	73	1	no	—
407	#336	—	73	1	no	—
408	#336	—	73	1	no	—
409	#336	—	73	1	no	—
410	#336	—	73	1	no	—
411	#336	—	73	1	no	—
412	#336	—	73	1	no	—
413	#336	—	73	1	no	—
414	C₂³×C₄	—	73	1	no	—
415	C₂×M₁₆	—	292	1	no	—
416	C₂×M₁₆	—	292	1	no	—
417	C₂×M₁₆	—	73	1	no	—
418	C₂×M₁₆	—	73	1	no	—
419	C₂×M₁₆	—	73	1	no	—
420	C₂×M₁₆	C₂×#64408	1	1	yes	characteristic
421	C₂²×C₈	—	292	1	no	—
422	C₂²×C₈	—	292	1	no	—
423	C₂²×C₈	—	73	1	no	—
424	C₂²×C₈	—	73	1	no	—
425	C₂²×C₈	—	73	1	no	—
426	C₂²×C₈	—	73	1	no	—
427	C₂²×C₈	—	73	1	no	—
428	C₂²×C₈	—	73	1	no	—
429	C₂²×C₈	—	73	1	no	—
430	C₂²×C₈	—	73	1	no	—
431	C₂²×C₈	—	73	1	no	—
432	C₂²×C₈	—	73	1	no	—
433	C₂²×C₈	—	73	1	no	—
434	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
435	#117	—	73	1	no	—
436	#117	—	73	1	no	—
437	#117	—	73	1	no	—
438	#117	—	73	1	no	—
439	#117	—	73	1	no	—
440	#117	—	73	1	no	—
441	#117	—	73	1	no	—
442	#117	C₂×#64408	1	1	yes	characteristic
443	C₂×C₄⋊C₄	—	73	2	no	—
444	C₂×C₄⋊C₄	—	73	1	no	—
445	C₂×C₄⋊C₄	—	73	1	no	—
446	C₂×C₄⋊C₄	—	73	2	no	—
447	C₂×C₂²⋊C₄	—	73	2	no	—
448	C₂×C₂²⋊C₄	—	73	1	no	—
449	C₂×C₂²⋊C₄	—	73	1	no	—
450	C₂×C₂²⋊C₄	—	73	2	no	—
451	C₂×C₄²	—	73	2	no	—
452	C₂×C₄²	—	73	1	no	—
453	C₂×C₄²	—	73	1	no	—
454	C₂×C₄²	—	73	1	no	—
455	C₂×C₄²	—	73	1	no	—
456	C₂×C₄²	—	73	1	no	—
457	C₂×C₄²	—	73	1	no	—
458	C₂×C₄²	—	73	2	no	—
459	C₄⋊C₈	—	73	2	no	—
460	C₄⋊C₈	—	73	2	no	—
461	C₄⋊C₈	—	73	2	no	—
462	C₄⋊C₈	—	73	2	no	—
463	C₄⋊C₈	—	73	1	no	—
464	C₄⋊C₈	—	73	1	no	—
465	C₄⋊C₈	—	73	1	no	—
466	C₄⋊C₈	—	73	1	no	—
467	C₄⋊C₈	—	73	1	no	—
468	C₄⋊C₈	—	73	1	no	—
469	C₄⋊C₈	—	73	1	no	—
470	C₄⋊C₈	—	73	1	no	—
471	C₄⋊C₈	—	73	1	no	—
472	C₄⋊C₈	—	73	1	no	—
473	C₄⋊C₈	—	73	1	no	—
474	C₄⋊C₈	—	73	1	no	—
475	C₄⋊C₈	C₂×#64408	1	1	yes	characteristic
476	C₄⋊C₈	C₂×#64408	1	1	yes	characteristic
477	C₄⋊C₈	C₂×#64408	1	1	yes	characteristic
478	C₄⋊C₈	C₂×#64408	1	1	yes	characteristic
479	C₂²⋊C₈	—	73	2	no	—
480	C₂²⋊C₈	—	73	2	no	—
481	C₂²⋊C₈	—	73	2	no	—
482	C₂²⋊C₈	—	73	2	no	—
483	#97	—	292	1	no	—
484	#97	—	292	1	no	—
485	#97	—	292	1	no	—
486	#97	—	292	1	no	—
487	#97	—	73	2	no	—
488	#97	—	73	2	no	—
489	C₄×C₈	—	292	1	no	—
490	C₄×C₈	—	292	1	no	—
491	C₄×C₈	—	292	1	no	—
492	C₄×C₈	—	292	1	no	—
493	C₄×C₈	—	73	2	no	—
494	C₄×C₈	—	73	2	no	—
495	#95	—	73	2	no	—
496	#95	—	73	2	no	—
497	#95	—	73	2	no	—
498	#95	—	73	2	no	—
499	#95	—	73	2	no	—
500	#95	—	73	2	no	—
501	C₂⁴	—	73	1	no	—
502	C₂²×C₄	—	73	1	no	—
503	C₂²×C₄	—	73	2	no	—
504	C₂²×C₄	—	73	1	no	—
505	C₂²×C₄	—	73	1	no	—
506	C₂²×C₄	—	73	1	no	—
507	C₂²×C₄	—	73	1	no	—
508	C₂²×C₄	—	73	1	no	—
509	C₂²×C₄	—	73	1	no	—
510	C₂²×C₄	—	73	1	no	—
511	C₂²×C₄	—	73	1	no	—
512	C₂²×C₄	—	73	2	no	—
513	C₂²×C₄	—	73	2	no	—
514	C₂²×C₄	—	73	2	no	—
515	C₂²×C₄	—	146	1	no	—
516	C₂²×C₄	—	146	1	no	—
517	C₂²×C₄	—	146	1	no	—
518	C₂²×C₄	—	146	1	no	—
519	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
520	M₁₆	—	4	1	no	—
521	M₁₆	—	292	1	no	—
522	M₁₆	—	292	1	no	—
523	M₁₆	—	292	1	no	—
524	C₂×C₈	—	4	1	no	—
525	C₂×C₈	—	292	1	no	—
526	C₂×C₈	—	292	1	no	—
527	C₂×C₈	—	292	1	no	—
528	C₂×C₈	—	73	2	no	—
529	C₂×C₈	—	73	2	no	—
530	C₂×C₈	—	73	2	no	—
531	C₂×C₈	—	73	2	no	—
532	C₂×C₈	—	73	1	no	—
533	C₂×C₈	—	73	1	no	—
534	C₂×C₈	—	73	1	no	—
535	C₂×C₈	—	73	1	no	—
536	C₂×C₈	—	146	1	no	—
537	C₂×C₈	—	146	1	no	—
538	C₂×C₈	—	146	1	no	—
539	C₂×C₈	—	146	1	no	—
540	C₂×C₈	—	146	1	no	—
541	C₂×C₈	—	146	1	no	—
542	C₂×C₈	—	146	1	no	—
543	C₂×C₈	—	146	1	no	—
544	C₂×C₈	—	146	1	no	—
545	C₂×C₈	—	146	1	no	—
546	C₂×C₈	—	146	1	no	—
547	C₂×C₈	—	146	1	no	—
548	C₂×C₈	—	146	1	no	—
549	C₂×C₈	—	146	1	no	—
550	C₂×C₈	—	146	1	no	—
551	C₂×C₈	—	146	1	no	—
552	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
553	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
554	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
555	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
556	C₄⋊C₄	—	292	2	no	—
557	C₄⋊C₄	—	73	1	no	—
558	C₄⋊C₄	—	73	1	no	—
559	C₄⋊C₄	—	73	1	no	—
560	C₄⋊C₄	—	73	1	no	—
561	C₄⋊C₄	—	73	1	no	—
562	C₄⋊C₄	—	73	1	no	—
563	C₄⋊C₄	—	146	4	no	—
564	C₄⋊C₄	C₄×#64408	1	1	yes	characteristic
565	C₄⋊C₄	C₄×#64408	1	1	yes	characteristic
566	C₂²⋊C₄	—	292	2	no	—
567	C₂²⋊C₄	—	73	1	no	—
568	C₂²⋊C₄	—	73	1	no	—
569	C₂²⋊C₄	—	73	1	no	—
570	C₂²⋊C₄	—	73	1	no	—
571	C₂²⋊C₄	—	73	1	no	—
572	C₂²⋊C₄	—	73	1	no	—
573	C₂²⋊C₄	—	146	4	no	—
574	C₂²⋊C₄	C₄×#64408	1	1	yes	characteristic
575	C₂²⋊C₄	C₄×#64408	1	1	yes	characteristic
576	C₄²	—	292	2	no	—
577	C₄²	—	73	1	no	—
578	C₄²	—	73	1	no	—
579	C₄²	—	73	1	no	—
580	C₄²	—	73	1	no	—
581	C₄²	—	73	1	no	—
582	C₄²	—	73	1	no	—
583	C₄²	—	146	1	no	—
584	C₄²	—	146	1	no	—
585	C₄²	—	146	1	no	—
586	C₄²	—	146	1	no	—
587	C₄²	—	146	1	no	—
588	C₄²	—	146	1	no	—
589	C₄²	—	146	1	no	—
590	C₄²	—	146	1	no	—
591	C₄²	—	146	4	no	—
592	C₄²	C₂²×#64408	1	1	yes	characteristic
593	C₄²	C₂²×#64408	1	1	yes	characteristic
594	C₂³	—	73	1	no	—
595	C₂³	—	73	1	no	—
596	C₂³	—	146	2	no	—
597	C₂³	—	146	2	no	—
598	C₂³	—	146	1	no	—
599	C₂³	—	146	1	no	—
600	C₂³	C₂×C₄×#64408	1	1	yes	characteristic
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	73	1	no	—
604	C₂×C₄	—	73	1	no	—
605	C₂×C₄	—	73	1	no	—
606	C₂×C₄	—	73	1	no	—
607	C₂×C₄	—	73	1	no	—
608	C₂×C₄	—	73	4	no	—
609	C₂×C₄	—	73	1	no	—
610	C₂×C₄	—	73	1	no	—
611	C₂×C₄	—	73	1	no	—
612	C₂×C₄	—	73	1	no	—
613	C₂×C₄	—	73	1	no	—
614	C₂×C₄	—	146	1	no	—
615	C₂×C₄	—	146	1	no	—
616	C₂×C₄	—	146	2	no	—
617	C₂×C₄	—	146	2	no	—
618	C₂×C₄	—	146	2	no	—
619	C₂×C₄	—	146	2	no	—
620	C₂×C₄	—	146	1	no	—
621	C₂×C₄	—	146	1	no	—
622	C₂×C₄	—	146	2	no	—
623	C₂×C₄	—	146	2	no	—
624	C₂×C₄	—	146	2	no	—
625	C₂×C₄	—	146	2	no	—
626	C₂×C₄	—	146	2	no	—
627	C₂×C₄	—	146	2	no	—
628	C₂×C₄	—	146	2	no	—
629	C₂×C₄	—	146	2	no	—
630	C₂×C₄	—	146	2	no	—
631	C₂×C₄	—	146	1	no	—
632	C₂×C₄	—	146	1	no	—
633	C₂×C₄	—	146	2	no	—
634	C₂×C₄	—	146	2	no	—
635	C₂×C₄	—	146	1	no	—
636	C₂×C₄	—	146	1	no	—
637	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
638	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
639	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
640	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
641	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
642	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
643	C₈	—	2	1	no	—
644	C₈	—	2	1	no	—
645	C₈	—	2	1	no	—
646	C₈	—	2	1	no	—
647	C₈	—	146	2	no	—
648	C₈	—	146	2	no	—
649	C₈	—	146	2	no	—
650	C₈	—	146	2	no	—
651	C₈	—	146	1	no	—
652	C₈	—	146	1	no	—
653	C₈	—	146	1	no	—
654	C₈	—	146	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	292	2	no	—
659	C₂²	—	292	2	no	—
660	C₂²	—	73	1	no	—
661	C₂²	—	73	1	no	—
662	C₂²	—	73	2	no	—
663	C₂²	—	73	2	no	—
664	C₂²	—	146	1	no	—
665	C₂²	—	146	1	no	—
666	C₂²	—	146	1	no	—
667	C₂²	C₂²×C₄×#64408	1	1	yes	characteristic
668	C₄	—	2	1	no	—
669	C₄	—	2	1	no	—
670	C₄	—	2	1	no	—
671	C₄	—	2	1	no	—
672	C₄	—	2	1	no	—
673	C₄	—	292	2	no	—
674	C₄	—	292	2	no	—
675	C₄	—	292	2	no	—
676	C₄	—	73	1	no	—
677	C₄	—	73	1	no	—
678	C₄	—	146	4	no	—
679	C₄	—	146	1	no	—
680	C₄	—	146	1	no	—
681	C₄	—	146	1	no	—
682	C₄	—	146	1	no	—
683	C₄	—	146	1	no	—
684	C₄	#17989654	1	1	yes	characteristic
685	C₄	#17989655	1	1	yes	characteristic
686	C₂	—	4	1	no	—
687	C₂	—	292	1	no	—
688	C₂	—	73	2	no	—
689	C₂	—	73	2	no	—
690	C₂	#22626369	1	1	yes	characteristic
691	C₂	#131×#64408	1	1	yes	characteristic
692	C₂	#22626501	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#64408
commutator, socle	C₂²×C₇₃	C₂²×C₄²
Fitting	#424×C₇₃	C₄
prime radical	C₂³×D₇₃	C₂²×C₄
cosocle	C₂×C₄×D₇₃	C₂⁴
hypercenter	#424	#64408
hypocenter	C₇₃	#20553
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ #424

Complements

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

N	H ≅ G/N	type
3. #22625732	C₂	semidirect
4. #22625732	C₂	semidirect
5. #22625728	C₂	semidirect
6. #22625724	C₂	semidirect
7. #22625720	C₂	semidirect
8. #22625720	C₂	semidirect
9. #22625718	C₂	semidirect
10. C₄⋊C₈×#64408	C₂	semidirect
16. #17989612	C₄	semidirect
17. #17989612	C₄	semidirect
18. #17989611	C₄	semidirect
19. #17989611	C₄	semidirect
55. #17988615	C₄	semidirect
56. #17988614	C₄	semidirect
57. #17988613	C₄	semidirect
58. #17988612	C₄	semidirect
59. #17988612	C₄	semidirect
60. #17988612	C₄	semidirect
61. #17988612	C₄	semidirect
66. #424×C₇₃	C₄	semidirect
362. C₇₃	#20553	semidirect
377. #424	#64408	semidirect

Maximal subgroups

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

subgroup	index
D₇₃⋊#433	2
#22626393	2
#22625732	2
#22625728	2
#22625724	2
#22625720	2
#22625718	2
C₄⋊C₈×#64408	2
#22625671	2
#22625667	2
C₈×C₂²⋊#64408	2
#424×D₇₃	2
#20553	73