Subgroups — #34020712

Order 18688.

1030 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#11924036	C₂	1	1	yes	maximal, characteristic
2	#22626385	C₂	1	1	yes	maximal, characteristic
3	#22625729	C₂	1	1	yes	maximal, characteristic, complemented
4	#22625724	C₂	1	1	yes	maximal, characteristic, complemented
5	#22625720	C₂	1	1	yes	maximal, characteristic, complemented
6	#22625671	C₂	1	1	yes	maximal, characteristic, complemented
7	#22625670	C₂	1	1	yes	maximal, characteristic, complemented
8	#22625666	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×C₂²⋊#64408	C₂	1	1	yes	maximal, characteristic, complemented
10	#22625662	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²⋊C₈×#64408	C₂	1	1	yes	maximal, characteristic, complemented
12	#22625651	C₂	1	1	yes	maximal, characteristic, complemented
13	#22625599	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#17989452	C₂	1	1	yes	maximal, characteristic, complemented
15	#435×D₇₃	C₂	1	1	yes	maximal, characteristic
16	C₂²×#11924036	C₂²	1	1	yes	characteristic
17	C₂²×#11924036	C₂²	1	1	yes	characteristic
18	C₂×#14556670	C₂²	1	1	yes	characteristic
19	C₂²×C₄×#64408	C₂²	1	1	yes	characteristic
20	#17989615	C₄	1	2	yes	complemented
21	#17989614	C₄	1	2	yes	complemented
22	#17989614	C₄	1	2	yes	complemented
23	D₄×#10596833	C₄	1	2	yes	complemented
24	#17989588	C₂²	1	1	yes	characteristic
25	#17989555	C₂²	1	1	yes	characteristic
26	#17989555	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	#17989536	C₄	1	2	yes	—
36	#17989535	C₄	1	2	yes	—
37	#17989534	C₄	1	2	yes	—
38	C₄×C₄⋊#64408	C₂²	1	1	yes	characteristic
39	C₄×C₂²⋊#64408	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊#64408	C₂²	1	1	yes	characteristic
41	#17989523	C₂²	1	1	yes	characteristic
42	#17989452	C₂²	1	1	yes	characteristic
43	#17989452	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	C₄×D₄×D₇₃	C₂²	1	1	yes	characteristic
55	#17988661	C₄	1	1	yes	characteristic, complemented
56	#17988660	C₄	1	1	yes	characteristic, complemented
57	#17988659	C₄	1	1	yes	characteristic, complemented
58	#17988658	C₄	1	1	yes	characteristic, complemented
59	#17988657	C₄	1	1	yes	characteristic, complemented
60	#17988656	C₄	1	1	yes	characteristic, complemented
61	#17988655	C₄	1	1	yes	characteristic, complemented
62	C₄⋊C₈×D₇₃	C₂²	1	1	yes	characteristic
63	C₂²⋊C₈×D₇₃	C₂²	1	1	yes	characteristic
64	C₂²⋊C₈×D₇₃	C₂²	1	1	yes	characteristic
65	#97×D₇₃	C₂²	1	1	yes	characteristic
66	#435×C₇₃	C₄	1	1	yes	characteristic, complemented
67	C₂³×#64408	C₂×C₄	1	2	yes	—
68	C₂×#11924036	—	4	1	no	—
69	C₂×#11924036	—	4	1	no	—
70	C₂×#11924036	—	4	1	no	—
71	C₂×#11924036	—	4	1	no	—
72	C₂×#11924036	C₂×C₄	1	2	yes	—
73	C₂×#11924036	C₂×C₄	1	2	yes	complemented
74	C₂×#11924036	C₂³	1	1	yes	characteristic
75	C₂×#11924036	C₂³	1	1	yes	characteristic
76	C₂×#11924036	C₂³	1	1	yes	characteristic
77	C₂×#11924036	C₂³	1	1	yes	characteristic
78	C₂²×#10596833	C₂×C₄	1	2	yes	—
79	C₂²×#10596833	C₂×C₄	1	2	yes	complemented
80	#14556670	—	4	1	no	—
81	#14556670	—	4	1	no	—
82	C₂×C₄⋊#64408	C₂×C₄	1	2	yes	—
83	C₂×C₄⋊#64408	C₂×C₄	1	2	yes	—
84	C₂×C₂²⋊#64408	C₂×C₄	1	2	yes	—
85	C₂×C₂²⋊#64408	C₂×C₄	1	2	yes	—
86	C₂×C₂²⋊#64408	C₂×C₄	1	2	yes	—
87	C₂×C₄×#64408	—	4	1	no	—
88	C₂×C₄×#64408	—	4	1	no	—
89	C₂×C₄×#64408	C₂×C₄	1	2	yes	—
90	C₂×C₄×#64408	C₂³	1	1	yes	characteristic
91	C₂×C₄×#64408	C₂³	1	1	yes	characteristic
92	C₂×C₄×#64408	C₂³	1	1	yes	characteristic
93	C₂×C₄×#64408	C₂³	1	1	yes	characteristic
94	#14556658	C₂×C₄	1	2	yes	complemented
95	C₄⋊#10596833	C₂×C₄	1	2	yes	complemented
96	#14556648	C₂×C₄	1	2	yes	—
97	#14556648	C₂×C₄	1	2	yes	complemented
98	C₂²⋊#10596833	C₂×C₄	1	2	yes	—
99	C₂²⋊#10596833	C₂×C₄	1	2	yes	complemented
100	#14556645	—	4	1	no	—
101	#14556645	—	4	1	no	—
102	C₄×#10596833	C₂×C₄	1	2	yes	complemented
103	C₄×#10596833	C₂×C₄	1	2	yes	complemented
104	C₈×#64408	—	4	1	no	—
105	C₈×#64408	—	4	1	no	—
106	C₈×#64408	—	4	1	no	—
107	C₈×#64408	—	4	1	no	—
108	(C₂×#64408)⋊C₄	C₂×C₄	1	2	yes	—
109	(C₂×#64408)⋊C₄	C₂×C₄	1	2	yes	—
110	(C₂×#64408)⋊C₄	C₂×C₄	1	2	yes	—
111	(C₂×#64408)⋊C₄	C₂×C₄	1	2	yes	—
112	(C₂×#64408)⋊C₄	C₂×C₄	1	2	yes	—
113	C₂×D₄×D₇₃	C₂×C₄	1	1	yes	characteristic
114	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
115	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
116	C₂×#11924012	C₂×C₄	1	1	yes	characteristic, complemented
117	C₂×#11924011	C₂×C₄	1	1	yes	characteristic, complemented
118	C₂×#11924011	C₂×C₄	1	1	yes	characteristic, complemented
119	M₁₆×D₇₃	—	4	1	no	—
120	M₁₆×D₇₃	—	4	1	no	—
121	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
122	C₂×C₈×D₇₃	—	4	1	no	—
123	C₂×C₈×D₇₃	—	4	1	no	—
124	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
125	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
126	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
127	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
128	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
129	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
130	C₄×D₂₉₂	C₂×C₄	1	1	yes	characteristic
131	D₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
132	#14556553	C₂×C₄	1	1	yes	characteristic
133	C₄×C₂²⋊D₇₃	C₂×C₄	1	1	yes	characteristic
134	C₄×C₂²⋊D₇₃	C₂×C₄	1	1	yes	characteristic
135	#14556551	C₂×C₄	1	1	yes	characteristic
136	#14556551	C₂×C₄	1	1	yes	characteristic
137	C₄⋊C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
138	C₂²⋊C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
139	C₂²⋊C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
140	C₄²×D₇₃	C₂³	1	1	yes	characteristic
141	C₄⋊#10596831	C₂×C₄	1	1	yes	characteristic, complemented
142	#14556520	C₂×C₄	1	1	yes	characteristic, complemented
143	#14556520	C₂×C₄	1	1	yes	characteristic, complemented
144	C₂²⋊#10596831	C₂×C₄	1	1	yes	characteristic
145	C₂²⋊#10596831	C₂×C₄	1	1	yes	characteristic, complemented
146	#14556503	C₂×C₄	1	1	yes	characteristic
147	#14556503	C₂×C₄	1	1	yes	characteristic
148	#14556503	C₂×C₄	1	1	yes	characteristic, complemented
149	#14556503	C₂×C₄	1	1	yes	characteristic, complemented
150	#14556502	C₂×C₄	1	1	yes	characteristic, complemented
151	#14556501	C₂×C₄	1	1	yes	characteristic, complemented
152	#14556501	C₂×C₄	1	1	yes	characteristic, complemented
153	C₂×M₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
154	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
155	C₄×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
156	C₄⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
157	C₂²⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
158	C₂²⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
159	#97×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
160	C₂²×#64408	—	2	4	no	—
161	C₂²×#64408	—	2	4	no	—
162	C₂²×#64408	—	4	2	no	—
163	C₂²×#64408	C₂²×C₄	1	2	yes	—
164	C₂²×#64408	C₂²×C₄	1	2	yes	—
165	C₂²×#64408	C₂²×C₄	1	2	yes	—
166	C₂²×#64408	C₂²×C₄	1	2	yes	—
167	#11924036	—	2	1	no	—
168	#11924036	—	2	1	no	—
169	#11924036	—	2	1	no	—
170	#11924036	—	2	1	no	—
171	#11924036	—	2	1	no	—
172	#11924036	—	2	1	no	—
173	#11924036	—	2	1	no	—
174	#11924036	—	2	1	no	—
175	#11924036	—	4	2	no	—
176	#11924036	—	4	2	no	—
177	C₂×#10596833	—	4	2	no	—
178	C₂×#10596833	—	4	2	no	—
179	C₂×#10596833	C₂²×C₄	1	2	yes	—
180	C₂×#10596833	C₂²×C₄	1	2	yes	—
181	C₂×#10596833	C₂²×C₄	1	2	yes	—
182	C₂×#10596833	C₂²×C₄	1	2	yes	—
183	C₄⋊#64408	—	2	4	no	—
184	C₄⋊#64408	—	4	2	no	—
185	C₂²⋊#64408	—	2	4	no	—
186	C₂²⋊#64408	—	2	4	no	—
187	C₂²⋊#64408	—	4	2	no	—
188	C₄×#64408	—	2	1	no	—
189	C₄×#64408	—	2	1	no	—
190	C₄×#64408	—	2	1	no	—
191	C₄×#64408	—	2	1	no	—
192	C₄×#64408	—	2	1	no	—
193	C₄×#64408	—	2	1	no	—
194	C₄×#64408	—	2	1	no	—
195	C₄×#64408	—	2	1	no	—
196	C₄×#64408	—	4	2	no	—
197	C₂³×D₇₃	C₂²×C₄	1	1	yes	characteristic
198	C₂³×D₇₃	C₂²×C₄	1	1	yes	characteristic
199	C₂×D₂₉₂	C₄²	1	1	yes	characteristic
200	C₂×C₂²⋊D₇₃	C₄²	1	1	yes	characteristic
201	C₂×C₂²⋊D₇₃	C₄²	1	1	yes	characteristic
202	D₄×D₇₃	—	2	4	no	—
203	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
204	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
205	C₂×C₄×D₇₃	—	2	1	no	—
206	C₂×C₄×D₇₃	—	2	1	no	—
207	C₂×C₄×D₇₃	—	2	1	no	—
208	C₂×C₄×D₇₃	—	2	1	no	—
209	C₂×C₄×D₇₃	—	2	1	no	—
210	C₂×C₄×D₇₃	—	2	1	no	—
211	C₂×C₄×D₇₃	—	2	1	no	—
212	C₂×C₄×D₇₃	—	2	1	no	—
213	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
214	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
215	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
216	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
217	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
218	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
219	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
220	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
221	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
222	#11924012	—	4	1	no	—
223	#11924011	—	4	1	no	—
224	#11924011	—	4	1	no	—
225	C₂×#10596831	—	4	1	no	—
226	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
227	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
228	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
229	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
230	C₈×D₇₃	—	2	1	no	—
231	C₈×D₇₃	—	2	1	no	—
232	C₈×D₇₃	—	2	1	no	—
233	C₈×D₇₃	—	2	1	no	—
234	C₈×D₇₃	—	2	1	no	—
235	C₈×D₇₃	—	2	1	no	—
236	C₈×D₇₃	—	2	1	no	—
237	C₈×D₇₃	—	2	1	no	—
238	C₈×D₇₃	—	4	1	no	—
239	C₈×D₇₃	—	4	1	no	—
240	C₄⋊Dic₇₃	C₄²	1	1	yes	characteristic
241	#11924007	C₄²	1	1	yes	characteristic
242	#11924007	C₄²	1	1	yes	characteristic
243	C₂²⋊Dic₇₃	C₄²	1	1	yes	characteristic
244	C₂²⋊Dic₇₃	C₄²	1	1	yes	characteristic
245	#11924005	C₄²	1	1	yes	characteristic
246	#11924005	C₄²	1	1	yes	characteristic
247	#11924005	C₄²	1	1	yes	characteristic
248	#11924005	C₄²	1	1	yes	characteristic
249	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
250	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
251	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
252	C₂×D₄×C₇₃	C₄²	1	1	yes	characteristic
253	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
254	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
255	M₁₆×C₇₃	—	4	1	no	—
256	C₂×C₈×C₇₃	—	4	1	no	—
257	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
258	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
259	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
260	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
261	C₄⋊C₄×C₇₃	C₄²	1	1	yes	characteristic
262	C₂²⋊C₄×C₇₃	C₄²	1	1	yes	characteristic
263	C₂²⋊C₄×C₇₃	C₄²	1	1	yes	characteristic
264	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
265	C₂³×C₇₃	C₂×C₄²	1	1	yes	characteristic
266	C₂³×C₇₃	C₂×C₄²	1	1	yes	characteristic
267	C₂²×D₇₃	—	2	1	no	—
268	C₂²×D₇₃	—	2	1	no	—
269	C₂²×D₇₃	—	2	2	no	—
270	C₂²×D₇₃	—	2	1	no	—
271	C₂²×D₇₃	—	2	1	no	—
272	C₂²×D₇₃	—	2	2	no	—
273	C₂²×D₇₃	—	2	2	no	—
274	C₂²×D₇₃	C₂×C₄²	1	1	yes	characteristic
275	C₂²×D₇₃	C₂×C₄²	1	1	yes	characteristic
276	C₂²×D₇₃	#131	1	4	yes	—
277	C₂²×D₇₃	C₂³×C₄	1	1	yes	characteristic
278	C₂×#64408	—	2	2	no	—
279	C₂×#64408	—	2	2	no	—
280	C₂×#64408	—	2	2	no	—
281	C₂×#64408	—	2	2	no	—
282	C₂×#64408	—	2	2	no	—
283	C₂×#64408	—	2	2	no	—
284	C₂×#64408	—	2	2	no	—
285	C₂×#64408	—	2	2	no	—
286	C₂×#64408	—	2	2	no	—
287	C₂×#64408	—	2	2	no	—
288	C₂×#64408	—	2	2	no	—
289	C₂×#64408	—	4	8	no	—
290	C₂×#64408	#131	1	4	yes	—
291	D₄×C₇₃	—	2	2	no	—
292	C₂×C₄×C₇₃	—	2	1	no	—
293	C₂×C₄×C₇₃	—	2	1	no	—
294	C₂×C₄×C₇₃	—	2	1	no	—
295	C₂×C₄×C₇₃	—	2	1	no	—
296	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
297	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
298	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
299	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
300	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
301	C₂²⋊D₇₃	—	2	2	no	—
302	C₂²⋊D₇₃	—	2	2	no	—
303	C₂×Dic₇₃	—	2	1	no	—
304	C₂×Dic₇₃	—	2	1	no	—
305	C₂×Dic₇₃	—	2	1	no	—
306	C₂×Dic₇₃	—	2	1	no	—
307	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
308	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
309	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
310	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
311	C₂×Dic₇₃	C₂³×C₄	1	1	yes	characteristic
312	D₂₉₂	—	2	2	no	—
313	C₄×D₇₃	—	2	1	no	—
314	C₄×D₇₃	—	2	1	no	—
315	C₄×D₇₃	—	2	1	no	—
316	C₄×D₇₃	—	2	1	no	—
317	C₄×D₇₃	—	2	2	no	—
318	C₄×D₇₃	—	2	2	no	—
319	C₄×D₇₃	—	2	1	no	—
320	C₄×D₇₃	—	2	1	no	—
321	C₄×D₇₃	—	2	1	no	—
322	C₄×D₇₃	—	2	1	no	—
323	C₄×D₇₃	—	2	1	no	—
324	C₄×D₇₃	—	2	1	no	—
325	C₄×D₇₃	—	2	1	no	—
326	C₄×D₇₃	—	2	1	no	—
327	C₄×D₇₃	H(5,𝔽₂)	1	1	yes	characteristic
328	C₄×D₇₃	H(5,𝔽₂)	1	1	yes	characteristic
329	C₄×D₇₃	H(5,𝔽₂)	1	1	yes	characteristic
330	C₄×D₇₃	2₋¹⁺⁴	1	1	yes	characteristic
331	#10596833	—	2	2	no	—
332	#10596833	—	2	2	no	—
333	#10596833	—	2	2	no	—
334	#10596833	—	2	2	no	—
335	C₈×C₇₃	—	2	1	no	—
336	C₈×C₇₃	—	2	1	no	—
337	C₈×C₇₃	—	2	1	no	—
338	C₈×C₇₃	—	2	1	no	—
339	#10596831	—	2	1	no	—
340	#10596831	—	2	1	no	—
341	#10596831	—	2	1	no	—
342	#10596831	—	2	1	no	—
343	C₂²×C₇₃	—	2	1	no	—
344	C₂²×C₇₃	—	2	1	no	—
345	C₂²×C₇₃	—	2	1	no	—
346	C₂²×C₇₃	—	2	1	no	—
347	C₂²×C₇₃	—	2	1	no	—
348	C₂²×C₇₃	#405	1	2	yes	—
349	C₂²×C₇₃	C₂²×C₄²	1	1	yes	characteristic
350	C₂×D₇₃	—	2	1	no	—
351	C₂×D₇₃	—	2	1	no	—
352	C₂×D₇₃	—	2	4	no	—
353	C₂×D₇₃	—	2	4	no	—
354	C₂×D₇₃	—	2	1	no	—
355	C₂×D₇₃	—	2	1	no	—
356	C₂×D₇₃	—	2	1	no	—
357	C₂×D₇₃	—	4	2	no	—
358	C₂×D₇₃	—	4	2	no	—
359	C₂×D₇₃	#405	1	2	yes	—
360	C₂×D₇₃	#518	1	1	yes	characteristic
361	C₂×D₇₃	#520	1	1	yes	characteristic
362	C₂×D₇₃	C₂×#131	1	2	yes	—
363	C₂×D₇₃	C₂×#131	1	2	yes	—
364	#64408	—	2	4	no	—
365	#64408	—	4	2	no	—
366	#64408	—	4	2	no	—
367	#64408	—	4	2	no	—
368	C₄×C₇₃	—	2	1	no	—
369	C₄×C₇₃	—	2	1	no	—
370	C₄×C₇₃	—	2	1	no	—
371	C₄×C₇₃	—	2	1	no	—
372	C₄×C₇₃	#518	1	1	yes	characteristic
373	C₄×C₇₃	#520	1	1	yes	characteristic
374	Dic₇₃	—	2	1	no	—
375	Dic₇₃	—	2	1	no	—
376	Dic₇₃	—	2	1	no	—
377	Dic₇₃	—	2	1	no	—
378	Dic₇₃	#518	1	1	yes	characteristic
379	Dic₇₃	#520	1	1	yes	characteristic
380	#20557	—	73	1	no	maximal, Sylow
381	C₂×C₇₃	—	2	2	no	—
382	C₂×C₇₃	—	4	1	no	—
383	C₂×C₇₃	#2275	1	1	yes	characteristic
384	C₂×C₇₃	C₂×#405	1	1	yes	characteristic
385	C₂×C₇₃	C₄×#131	1	1	yes	characteristic
386	D₇₃	—	2	2	no	—
387	D₇₃	—	4	1	no	—
388	D₇₃	#2977	1	2	yes	—
389	D₇₃	#2994	1	2	yes	—
390	C₂×#435	—	73	1	no	—
391	C₂×C₈×D₄	—	73	1	no	—
392	#2290	—	73	1	no	—
393	#1771	—	73	1	no	—
394	C₈×C₄⋊C₄	—	73	1	no	—
395	#1768	—	73	1	no	—
396	#1753	—	73	1	no	—
397	#1752	—	73	1	no	—
398	C₈×C₂²⋊C₄	—	73	1	no	—
399	C₈×C₂²⋊C₄	—	73	1	no	—
400	#1750	—	73	1	no	—
401	C₄×C₂²⋊C₈	—	73	1	no	—
402	#1746	—	73	1	no	—
403	#1729	—	73	1	no	—
404	C₂×#336	—	73	1	no	—
405	C₇₃	#20557	1	1	yes	characteristic, complemented, Sylow
406	C₂²×M₁₆	—	73	1	no	—
407	C₂³×C₈	—	73	1	no	—
408	C₂³×C₈	—	73	1	no	—
409	C₂³×C₈	—	73	1	no	—
410	C₂×C₄×D₄	—	73	1	no	—
411	C₂×#117	—	73	1	no	—
412	C₂²×C₄²	—	73	1	no	—
413	#435	—	73	1	no	—
414	#435	—	73	1	no	—
415	#435	—	73	1	no	—
416	#435	—	73	1	no	—
417	#435	—	73	1	no	—
418	#435	—	73	1	no	—
419	#435	—	73	1	no	—
420	#435	#64408	1	1	yes	characteristic, complemented
421	C₈×D₄	—	73	2	no	—
422	C₈×D₄	—	73	2	no	—
423	C₈×D₄	—	73	2	no	—
424	C₈×D₄	—	73	2	no	—
425	C₂×C₄⋊C₈	—	73	1	no	—
426	C₂×C₄⋊C₈	—	73	1	no	—
427	C₂×C₂²⋊C₈	—	73	1	no	—
428	C₂×C₂²⋊C₈	—	73	1	no	—
429	C₂×C₂²⋊C₈	—	73	1	no	—
430	C₂×C₂²⋊C₈	—	73	1	no	—
431	C₂×#97	—	73	1	no	—
432	C₂×#97	—	73	1	no	—
433	C₂×#97	—	73	1	no	—
434	C₂×C₄×C₈	—	73	1	no	—
435	C₂×C₄×C₈	—	73	1	no	—
436	C₂×C₄×C₈	—	73	1	no	—
437	C₂×C₄×C₈	—	73	1	no	—
438	C₂×C₄×C₈	—	73	1	no	—
439	#388	—	73	2	no	—
440	#387	—	73	2	no	—
441	#386	—	73	2	no	—
442	#385	—	73	2	no	—
443	C₄×C₄⋊C₄	—	73	1	no	—
444	C₄×C₂²⋊C₄	—	73	1	no	—
445	C₄×C₂²⋊C₄	—	73	1	no	—
446	#376	—	73	1	no	—
447	#336	—	73	1	no	—
448	#336	—	73	1	no	—
449	#336	—	73	1	no	—
450	#336	—	73	1	no	—
451	#336	—	73	1	no	—
452	#336	—	73	1	no	—
453	#336	—	73	1	no	—
454	#336	—	73	1	no	—
455	#336	—	73	1	no	—
456	#336	—	73	1	no	—
457	C₂²×D₄	—	73	1	no	—
458	C₂³×C₄	—	73	2	no	—
459	C₂³×C₄	—	73	1	no	—
460	C₂³×C₄	—	73	1	no	—
461	C₂×M₁₆	—	292	1	no	—
462	C₂×M₁₆	—	292	1	no	—
463	C₂×M₁₆	—	73	1	no	—
464	C₂×M₁₆	—	73	1	no	—
465	C₂×M₁₆	—	73	1	no	—
466	C₂×M₁₆	C₂×#64408	1	1	yes	characteristic, complemented
467	C₂²×C₈	—	292	1	no	—
468	C₂²×C₈	—	292	1	no	—
469	C₂²×C₈	—	292	1	no	—
470	C₂²×C₈	—	292	1	no	—
471	C₂²×C₈	—	292	1	no	—
472	C₂²×C₈	—	292	1	no	—
473	C₂²×C₈	—	73	2	no	—
474	C₂²×C₈	—	73	2	no	—
475	C₂²×C₈	—	73	2	no	—
476	C₂²×C₈	—	73	2	no	—
477	C₂²×C₈	—	73	1	no	—
478	C₂²×C₈	—	73	1	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	1	no	—
486	C₂²×C₈	—	73	1	no	—
487	C₂²×C₈	—	73	1	no	—
488	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
489	C₄×D₄	—	73	1	no	—
490	C₄×D₄	—	73	1	no	—
491	C₄×D₄	—	73	1	no	—
492	C₄×D₄	—	73	1	no	—
493	C₄×D₄	—	73	1	no	—
494	C₄×D₄	—	73	1	no	—
495	C₄×D₄	—	73	1	no	—
496	C₄×D₄	C₂×#64408	1	1	yes	characteristic
497	#117	—	292	1	no	—
498	#117	—	292	1	no	—
499	C₂×C₄⋊C₄	—	73	2	no	—
500	C₂×C₄⋊C₄	—	73	1	no	—
501	C₂×C₄⋊C₄	—	73	2	no	—
502	C₂×C₂²⋊C₄	—	73	2	no	—
503	C₂×C₂²⋊C₄	—	73	1	no	—
504	C₂×C₂²⋊C₄	—	73	1	no	—
505	C₂×C₂²⋊C₄	—	73	2	no	—
506	C₂×C₂²⋊C₄	—	73	2	no	—
507	C₂×C₄²	—	292	1	no	—
508	C₂×C₄²	—	292	1	no	—
509	C₂×C₄²	—	73	2	no	—
510	C₂×C₄²	—	73	1	no	—
511	C₂×C₄²	—	73	1	no	—
512	C₂×C₄²	—	73	1	no	—
513	C₂×C₄²	—	73	1	no	—
514	C₂×C₄²	—	73	1	no	—
515	C₄⋊C₈	—	73	2	no	—
516	C₄⋊C₈	—	73	2	no	—
517	C₄⋊C₈	—	73	1	no	—
518	C₄⋊C₈	—	73	1	no	—
519	C₄⋊C₈	—	73	1	no	—
520	C₄⋊C₈	C₂×#64408	1	1	yes	characteristic, complemented
521	C₂²⋊C₈	—	73	2	no	—
522	C₂²⋊C₈	—	73	2	no	—
523	C₂²⋊C₈	—	73	2	no	—
524	C₂²⋊C₈	—	73	2	no	—
525	C₂²⋊C₈	—	73	1	no	—
526	C₂²⋊C₈	—	73	1	no	—
527	C₂²⋊C₈	—	73	1	no	—
528	C₂²⋊C₈	—	73	1	no	—
529	C₂²⋊C₈	—	73	1	no	—
530	C₂²⋊C₈	—	73	1	no	—
531	C₂²⋊C₈	C₂×#64408	1	1	yes	characteristic
532	C₂²⋊C₈	C₂×#64408	1	1	yes	characteristic, complemented
533	#97	—	292	1	no	—
534	#97	—	292	1	no	—
535	#97	—	73	1	no	—
536	#97	—	73	1	no	—
537	#97	—	73	1	no	—
538	#97	C₂×#64408	1	1	yes	characteristic, complemented
539	C₄×C₈	—	292	1	no	—
540	C₄×C₈	—	292	1	no	—
541	C₄×C₈	—	292	1	no	—
542	C₄×C₈	—	292	1	no	—
543	C₄×C₈	—	73	2	no	—
544	C₄×C₈	—	73	2	no	—
545	#95	—	73	2	no	—
546	#95	—	73	2	no	—
547	#95	—	73	2	no	—
548	#95	—	73	2	no	—
549	#95	—	73	2	no	—
550	C₂⁴	—	73	1	no	—
551	C₂⁴	—	73	1	no	—
552	C₂×D₄	—	73	1	no	—
553	C₂×D₄	—	73	1	no	—
554	C₂×D₄	—	73	1	no	—
555	C₂×D₄	—	146	4	no	—
556	C₂×D₄	C₄×#64408	1	1	yes	characteristic
557	C₂²×C₄	—	292	2	no	—
558	C₂²×C₄	—	73	1	no	—
559	C₂²×C₄	—	73	2	no	—
560	C₂²×C₄	—	73	1	no	—
561	C₂²×C₄	—	73	1	no	—
562	C₂²×C₄	—	73	1	no	—
563	C₂²×C₄	—	73	1	no	—
564	C₂²×C₄	—	73	1	no	—
565	C₂²×C₄	—	73	1	no	—
566	C₂²×C₄	—	73	1	no	—
567	C₂²×C₄	—	73	1	no	—
568	C₂²×C₄	—	73	1	no	—
569	C₂²×C₄	—	73	1	no	—
570	C₂²×C₄	—	73	2	no	—
571	C₂²×C₄	—	73	2	no	—
572	C₂²×C₄	—	73	2	no	—
573	C₂²×C₄	—	146	1	no	—
574	C₂²×C₄	—	146	1	no	—
575	C₂²×C₄	—	146	1	no	—
576	C₂²×C₄	—	146	1	no	—
577	C₂²×C₄	—	146	1	no	—
578	C₂²×C₄	—	146	1	no	—
579	C₂²×C₄	—	146	1	no	—
580	C₂²×C₄	—	146	1	no	—
581	C₂²×C₄	—	146	4	no	—
582	C₂²×C₄	—	146	4	no	—
583	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
584	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
585	M₁₆	—	4	1	no	—
586	M₁₆	—	292	1	no	—
587	M₁₆	—	292	1	no	—
588	M₁₆	—	292	1	no	—
589	C₂×C₈	—	4	1	no	—
590	C₂×C₈	—	292	1	no	—
591	C₂×C₈	—	292	1	no	—
592	C₂×C₈	—	292	1	no	—
593	C₂×C₈	—	292	2	no	—
594	C₂×C₈	—	292	2	no	—
595	C₂×C₈	—	292	2	no	—
596	C₂×C₈	—	292	2	no	—
597	C₂×C₈	—	73	2	no	—
598	C₂×C₈	—	73	2	no	—
599	C₂×C₈	—	73	2	no	—
600	C₂×C₈	—	73	2	no	—
601	C₂×C₈	—	73	1	no	—
602	C₂×C₈	—	73	1	no	—
603	C₂×C₈	—	73	1	no	—
604	C₂×C₈	—	73	1	no	—
605	C₂×C₈	—	146	1	no	—
606	C₂×C₈	—	146	1	no	—
607	C₂×C₈	—	146	1	no	—
608	C₂×C₈	—	146	1	no	—
609	C₂×C₈	—	146	1	no	—
610	C₂×C₈	—	146	1	no	—
611	C₂×C₈	—	146	1	no	—
612	C₂×C₈	—	146	1	no	—
613	C₂×C₈	—	146	1	no	—
614	C₂×C₈	—	146	1	no	—
615	C₂×C₈	—	146	1	no	—
616	C₂×C₈	—	146	1	no	—
617	C₂×C₈	—	146	1	no	—
618	C₂×C₈	—	146	1	no	—
619	C₂×C₈	—	146	1	no	—
620	C₂×C₈	—	146	1	no	—
621	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
622	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
623	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
624	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
625	C₄⋊C₄	—	292	2	no	—
626	C₄⋊C₄	—	73	1	no	—
627	C₄⋊C₄	—	73	1	no	—
628	C₄⋊C₄	—	73	1	no	—
629	C₄⋊C₄	—	146	4	no	—
630	C₄⋊C₄	C₄×#64408	1	1	yes	characteristic
631	C₂²⋊C₄	—	292	2	no	—
632	C₂²⋊C₄	—	73	1	no	—
633	C₂²⋊C₄	—	73	1	no	—
634	C₂²⋊C₄	—	73	1	no	—
635	C₂²⋊C₄	—	73	1	no	—
636	C₂²⋊C₄	—	73	1	no	—
637	C₂²⋊C₄	—	73	1	no	—
638	C₂²⋊C₄	—	146	4	no	—
639	C₂²⋊C₄	—	146	4	no	—
640	C₂²⋊C₄	C₄×#64408	1	1	yes	characteristic
641	C₂²⋊C₄	C₄×#64408	1	1	yes	characteristic
642	C₄²	—	292	2	no	—
643	C₄²	—	73	1	no	—
644	C₄²	—	73	1	no	—
645	C₄²	—	73	1	no	—
646	C₄²	—	146	1	no	—
647	C₄²	—	146	1	no	—
648	C₄²	—	146	1	no	—
649	C₄²	—	146	1	no	—
650	C₄²	—	146	1	no	—
651	C₄²	—	146	1	no	—
652	C₄²	—	146	1	no	—
653	C₄²	—	146	1	no	—
654	C₄²	C₂²×#64408	1	1	yes	characteristic
655	C₂³	—	73	1	no	—
656	C₂³	—	73	1	no	—
657	C₂³	—	73	4	no	—
658	C₂³	—	73	1	no	—
659	C₂³	—	146	1	no	—
660	C₂³	—	146	2	no	—
661	C₂³	—	146	1	no	—
662	C₂³	—	146	2	no	—
663	C₂³	—	146	1	no	—
664	C₂³	—	146	1	no	—
665	C₂³	—	146	2	no	—
666	C₂³	C₂×C₄×#64408	1	1	yes	characteristic
667	C₂³	C₂×C₄×#64408	1	1	yes	characteristic
668	D₄	—	2	2	no	—
669	D₄	—	146	2	no	—
670	D₄	—	146	2	no	—
671	D₄	—	146	2	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	292	8	no	—
677	C₂×C₄	—	73	1	no	—
678	C₂×C₄	—	73	1	no	—
679	C₂×C₄	—	73	1	no	—
680	C₂×C₄	—	73	1	no	—
681	C₂×C₄	—	73	1	no	—
682	C₂×C₄	—	73	4	no	—
683	C₂×C₄	—	73	1	no	—
684	C₂×C₄	—	73	1	no	—
685	C₂×C₄	—	73	1	no	—
686	C₂×C₄	—	73	1	no	—
687	C₂×C₄	—	146	1	no	—
688	C₂×C₄	—	146	1	no	—
689	C₂×C₄	—	146	1	no	—
690	C₂×C₄	—	146	1	no	—
691	C₂×C₄	—	146	1	no	—
692	C₂×C₄	—	146	1	no	—
693	C₂×C₄	—	146	2	no	—
694	C₂×C₄	—	146	1	no	—
695	C₂×C₄	—	146	1	no	—
696	C₂×C₄	—	146	2	no	—
697	C₂×C₄	—	146	2	no	—
698	C₂×C₄	—	146	2	no	—
699	C₂×C₄	—	146	2	no	—
700	C₂×C₄	—	146	2	no	—
701	C₂×C₄	—	146	2	no	—
702	C₂×C₄	—	146	2	no	—
703	C₂×C₄	—	146	2	no	—
704	C₂×C₄	—	146	2	no	—
705	C₂×C₄	—	146	2	no	—
706	C₂×C₄	—	146	1	no	—
707	C₂×C₄	—	146	1	no	—
708	C₂×C₄	—	146	1	no	—
709	C₂×C₄	—	146	1	no	—
710	C₂×C₄	—	146	2	no	—
711	C₂×C₄	—	146	2	no	—
712	C₂×C₄	—	146	1	no	—
713	C₂×C₄	—	146	1	no	—
714	C₂×C₄	—	146	1	no	—
715	C₂×C₄	—	146	1	no	—
716	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
717	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
718	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
719	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
720	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
721	C₈	—	2	1	no	—
722	C₈	—	2	1	no	—
723	C₈	—	2	1	no	—
724	C₈	—	2	1	no	—
725	C₈	—	146	2	no	—
726	C₈	—	146	2	no	—
727	C₈	—	146	2	no	—
728	C₈	—	146	2	no	—
729	C₈	—	146	1	no	—
730	C₈	—	146	1	no	—
731	C₈	—	146	1	no	—
732	C₈	—	146	1	no	—
733	C₂²	—	2	1	no	—
734	C₂²	—	2	1	no	—
735	C₂²	—	2	1	no	—
736	C₂²	—	2	1	no	—
737	C₂²	—	2	1	no	—
738	C₂²	—	292	2	no	—
739	C₂²	—	292	2	no	—
740	C₂²	—	73	1	no	—
741	C₂²	—	73	1	no	—
742	C₂²	—	73	2	no	—
743	C₂²	—	73	2	no	—
744	C₂²	—	73	2	no	—
745	C₂²	—	146	4	no	—
746	C₂²	—	146	4	no	—
747	C₂²	—	146	1	no	—
748	C₂²	—	146	1	no	—
749	C₂²	—	146	1	no	—
750	C₂²	—	146	1	no	—
751	C₂²	—	146	1	no	—
752	C₂²	#17989553	1	2	yes	—
753	C₂²	C₂²×C₄×#64408	1	1	yes	characteristic
754	C₄	—	2	1	no	—
755	C₄	—	2	1	no	—
756	C₄	—	2	1	no	—
757	C₄	—	2	1	no	—
758	C₄	—	292	2	no	—
759	C₄	—	292	2	no	—
760	C₄	—	292	2	no	—
761	C₄	—	73	1	no	—
762	C₄	—	73	1	no	—
763	C₄	—	146	4	no	—
764	C₄	—	146	1	no	—
765	C₄	—	146	1	no	—
766	C₄	—	146	1	no	—
767	C₄	—	146	1	no	—
768	C₄	#17989654	1	1	yes	characteristic
769	C₄	#17989656	1	1	yes	characteristic
770	C₂	—	2	2	no	—
771	C₂	—	4	1	no	—
772	C₂	—	292	1	no	—
773	C₂	—	73	2	no	—
774	C₂	—	73	2	no	—
775	C₂	—	146	2	no	—
776	C₂	#22626370	1	1	yes	characteristic
777	C₂	C₂×#17989553	1	1	yes	characteristic
778	C₂	#131×#64408	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#64408
commutator, socle	C₂²×C₇₃	C₂²×C₄²
Fitting	#435×C₇₃	C₄
prime radical	C₂×D₄×D₇₃	C₂×C₄
cosocle	C₂×C₄×D₇₃	C₂⁴
hypercenter	#435	#64408
hypocenter	C₇₃	#20557
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
3. #22625729	C₂	semidirect
4. #22625724	C₂	semidirect
5. #22625720	C₂	semidirect
6. #22625671	C₂	semidirect
7. #22625670	C₂	semidirect
8. #22625666	C₂	semidirect
9. C₈×C₂²⋊#64408	C₂	semidirect
10. #22625662	C₂	semidirect
11. C₂²⋊C₈×#64408	C₂	semidirect
12. #22625651	C₂	semidirect
13. #22625599	C₂	semidirect
14. C₂×#17989452	C₂	semidirect
20. #17989615	C₄	semidirect
21. #17989614	C₄	semidirect
22. #17989614	C₄	semidirect
23. D₄×#10596833	C₄	semidirect
55. #17988661	C₄	semidirect
56. #17988660	C₄	semidirect
57. #17988659	C₄	semidirect
58. #17988658	C₄	semidirect
59. #17988657	C₄	semidirect
60. #17988656	C₄	semidirect
61. #17988655	C₄	semidirect
66. #435×C₇₃	C₄	semidirect
73. C₂×#11924036	C₂×C₄	semidirect
79. C₂²×#10596833	C₂×C₄	semidirect
94. #14556658	C₂×C₄	semidirect
95. C₄⋊#10596833	C₂×C₄	semidirect
97. #14556648	C₂×C₄	semidirect
99. C₂²⋊#10596833	C₂×C₄	semidirect
102. C₄×#10596833	C₂×C₄	semidirect
103. C₄×#10596833	C₂×C₄	semidirect
116. C₂×#11924012	C₂×C₄	semidirect
117. C₂×#11924011	C₂×C₄	semidirect
118. C₂×#11924011	C₂×C₄	semidirect
141. C₄⋊#10596831	C₂×C₄	semidirect
142. #14556520	C₂×C₄	semidirect
143. #14556520	C₂×C₄	semidirect
145. C₂²⋊#10596831	C₂×C₄	semidirect
148. #14556503	C₂×C₄	semidirect
149. #14556503	C₂×C₄	semidirect
150. #14556502	C₂×C₄	semidirect
151. #14556501	C₂×C₄	semidirect
152. #14556501	C₂×C₄	semidirect
153. C₂×M₁₆×C₇₃	C₂×C₄	semidirect
156. C₄⋊C₈×C₇₃	C₂×C₄	semidirect
158. C₂²⋊C₈×C₇₃	C₂×C₄	semidirect
159. #97×C₇₃	C₂×C₄	semidirect
405. C₇₃	#20557	semidirect
420. #435	#64408	semidirect
466. C₂×M₁₆	C₂×#64408	semidirect
520. C₄⋊C₈	C₂×#64408	semidirect
532. C₂²⋊C₈	C₂×#64408	semidirect
538. #97	C₂×#64408	semidirect

Maximal subgroups

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

subgroup	index
D₄×#11924036	2
#22626385	2
#22625729	2
#22625724	2
#22625720	2
#22625671	2
#22625670	2
#22625666	2
C₈×C₂²⋊#64408	2
#22625662	2
C₂²⋊C₈×#64408	2
#22625651	2
#22625599	2
C₂×#17989452	2
#435×D₇₃	2
#20557	73