Subgroups — #34029793

Order 18688.

826 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989643	C₂	1	1	yes	maximal, characteristic
2	C₂×#17989550	C₂	1	1	yes	maximal, characteristic
3	#22626143	C₂	1	4	yes	maximal, complemented
4	#22626139	C₂	1	4	yes	maximal, complemented
5	M₃₂×#64408	C₂	1	4	yes	maximal, complemented
6	C₂×M₃₂×D₇₃	C₂	1	1	yes	maximal, characteristic
7	C₂×D₇₃⋊M₁₆	C₄	1	1	yes	characteristic
8	C₂×#14556670	C₄	1	1	yes	characteristic
9	C₂×#14556666	C₄	1	2	yes	complemented
10	#17989643	C₄	1	2	yes	complemented
11	#17989643	C₄	1	2	yes	complemented
12	#17989643	C₂²	1	2	yes	—
13	#17989643	C₂²	1	2	yes	—
14	C₂×#14556665	C₄	1	2	yes	complemented
15	C₂×#14556664	C₂²	1	2	yes	—
16	#17989550	C₄	1	2	yes	—
17	#17989550	C₄	1	2	yes	—
18	#17989550	C₂²	1	2	yes	—
19	#17989550	C₂²	1	2	yes	—
20	C₂×#14556645	C₄	1	2	yes	—
21	C₂×C₈×#64408	C₂²	1	2	yes	—
22	#17989474	C₂²	1	8	yes	complemented
23	C₁₆×#64408	C₂²	1	8	yes	complemented
24	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
25	C₂×#14556531	C₄	1	1	yes	characteristic, complemented
26	C₂×#14556530	C₄	1	2	yes	complemented
27	M₃₂×D₇₃	C₄	1	2	yes	complemented
28	M₃₂×D₇₃	C₄	1	2	yes	complemented
29	M₃₂×D₇₃	C₂²	1	2	yes	—
30	M₃₂×D₇₃	C₂²	1	2	yes	—
31	C₂×C₁₆×D₇₃	C₂²	1	2	yes	—
32	C₂×M₃₂×C₇₃	C₄	1	1	yes	characteristic, complemented
33	C₂×#11924038	C₈	1	2	yes	—
34	D₇₃⋊M₁₆	C₈	1	2	yes	—
35	D₇₃⋊M₁₆	C₈	1	2	yes	—
36	D₇₃⋊M₁₆	C₂×C₄	1	2	yes	—
37	D₇₃⋊M₁₆	C₂×C₄	1	2	yes	—
38	C₂×#11924037	C₈	1	2	yes	—
39	C₂×#11924036	C₂×C₄	1	2	yes	—
40	#14556670	C₈	1	2	yes	—
41	#14556670	C₈	1	2	yes	—
42	#14556670	C₂×C₄	1	2	yes	—
43	#14556670	C₂×C₄	1	2	yes	—
44	C₂×C₄⋊#64408	C₈	1	2	yes	—
45	C₂×C₂²⋊#64408	C₈	1	2	yes	—
46	C₂×C₄×#64408	C₂×C₄	1	2	yes	—
47	#14556666	C₂×C₄	1	4	yes	—
48	#14556666	C₂×C₄	1	4	yes	complemented
49	#14556665	C₂×C₄	1	4	yes	—
50	#14556665	C₂×C₄	1	4	yes	complemented
51	#14556664	C₂×C₄	1	4	yes	complemented
52	#14556664	C₂³	1	4	yes	—
53	C₂×#11924031	C₂×C₄	1	4	yes	complemented
54	#14556645	C₂×C₄	1	4	yes	—
55	#14556645	C₂×C₄	1	4	yes	—
56	C₈×#64408	C₂×C₄	1	4	yes	—
57	C₈×#64408	C₂³	1	4	yes	—
58	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
59	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
70	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
71	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
72	#14556531	C₂×C₄	1	2	yes	—
73	#14556531	C₂×C₄	1	2	yes	complemented
74	#14556530	C₂×C₄	1	4	yes	—
75	#14556530	C₂×C₄	1	4	yes	complemented
76	C₂×#11924003	C₂×C₄	1	2	yes	complemented
77	C₁₆×D₇₃	C₂×C₄	1	4	yes	complemented
78	C₁₆×D₇₃	C₂³	1	4	yes	—
79	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
80	M₃₂×C₇₃	C₂×C₄	1	2	yes	—
81	M₃₂×C₇₃	C₂×C₄	1	2	yes	complemented
82	C₂×C₁₆×C₇₃	C₂×C₄	1	2	yes	complemented
83	C₂²×#64408	C₂×C₈	1	4	yes	—
84	#11924038	C₂×C₈	1	4	yes	—
85	#11924038	C₂×C₈	1	4	yes	—
86	#11924037	C₂×C₈	1	4	yes	—
87	#11924037	C₂×C₈	1	4	yes	—
88	#11924036	C₂×C₈	1	4	yes	—
89	#11924036	C₂²×C₄	1	4	yes	—
90	C₂×#10596833	C₂×C₈	1	4	yes	—
91	C₄⋊#64408	C₂×C₈	1	4	yes	—
92	C₄⋊#64408	C₂×C₈	1	4	yes	—
93	C₂²⋊#64408	C₂×C₈	1	4	yes	—
94	C₂²⋊#64408	C₂×C₈	1	4	yes	—
95	C₄×#64408	C₂×C₈	1	4	yes	—
96	C₄×#64408	C₂²×C₄	1	4	yes	—
97	#11924031	C₂²×C₄	1	8	yes	—
98	C₂³×D₇₃	C₂×C₈	1	1	yes	characteristic
99	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
100	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
101	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
102	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
103	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
104	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
105	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
106	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
107	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
108	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
109	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×#10596831	C₄²	1	1	yes	characteristic
113	C₂×#10596831	C₄²	1	1	yes	characteristic
114	C₂×#10596831	C₄²	1	1	yes	characteristic
115	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
116	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
117	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
118	C₈×D₇₃	C₄²	1	1	yes	characteristic
119	C₈×D₇₃	C₄²	1	1	yes	characteristic
120	C₈×D₇₃	C₄²	1	1	yes	characteristic
121	C₈×D₇₃	C₄²	1	1	yes	characteristic
122	C₈×D₇₃	C₄²	1	1	yes	characteristic
123	C₈×D₇₃	C₄²	1	1	yes	characteristic
124	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
125	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
126	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
127	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
128	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
129	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
130	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
131	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
132	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
133	C₈×D₇₃	C₂⁴	1	1	yes	characteristic
134	#11924003	C₂²×C₄	1	4	yes	—
135	C₂²×C₄×C₇₃	C₄²	1	1	yes	characteristic
136	C₂×C₈×C₇₃	C₄²	1	1	yes	characteristic
137	C₂×C₈×C₇₃	C₄²	1	1	yes	characteristic
138	C₂×C₈×C₇₃	C₄²	1	1	yes	characteristic
139	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
142	C₁₆×C₇₃	C₂²×C₄	1	4	yes	—
143	C₂³×C₇₃	C₄×C₈	1	1	yes	characteristic
144	C₂²×D₇₃	—	4	2	no	—
145	C₂²×D₇₃	C₄×C₈	1	1	yes	characteristic
146	C₂²×D₇₃	C₄×C₈	1	1	yes	characteristic
147	C₂²×D₇₃	C₄×C₈	1	1	yes	characteristic
148	C₂²×D₇₃	C₂²×C₈	1	1	yes	characteristic
149	C₂²×D₇₃	C₂²×C₈	1	1	yes	characteristic
150	C₂²×D₇₃	C₂²×C₈	1	1	yes	characteristic
151	C₂×#64408	—	4	4	no	—
152	C₂×#64408	C₂²×C₈	1	8	yes	—
153	C₂×C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
154	C₂×C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
155	C₂×C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
156	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
157	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
158	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
159	C₂×Dic₇₃	C₄×C₈	1	1	yes	characteristic
160	C₂×Dic₇₃	C₄×C₈	1	1	yes	characteristic
161	C₂×Dic₇₃	C₄×C₈	1	1	yes	characteristic
162	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
163	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
164	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
165	C₄×D₇₃	C₄×C₈	1	1	yes	characteristic
166	C₄×D₇₃	C₄×C₈	1	1	yes	characteristic
167	C₄×D₇₃	C₄×C₈	1	1	yes	characteristic
168	C₄×D₇₃	C₄×C₈	1	1	yes	characteristic
169	C₄×D₇₃	C₄×C₈	1	1	yes	characteristic
170	C₄×D₇₃	C₄×C₈	1	1	yes	characteristic
171	C₄×D₇₃	C₂×C₄²	1	1	yes	characteristic
172	C₄×D₇₃	C₂×C₄²	1	1	yes	characteristic
173	C₄×D₇₃	C₂×C₄²	1	1	yes	characteristic
174	C₄×D₇₃	C₂²×C₈	1	1	yes	characteristic
175	C₄×D₇₃	C₂²×C₈	1	1	yes	characteristic
176	C₄×D₇₃	C₂²×C₈	1	1	yes	characteristic
177	C₄×D₇₃	C₂²×C₈	1	1	yes	characteristic
178	C₄×D₇₃	C₂²×C₈	1	1	yes	characteristic
179	C₄×D₇₃	C₂²×C₈	1	1	yes	characteristic
180	C₄×D₇₃	C₂³×C₄	1	1	yes	characteristic
181	#10596833	C₂²×C₈	1	8	yes	—
182	C₈×C₇₃	C₂×C₄²	1	1	yes	characteristic
183	C₈×C₇₃	C₂×C₄²	1	1	yes	characteristic
184	C₈×C₇₃	C₂×C₄²	1	1	yes	characteristic
185	C₈×C₇₃	C₂³×C₄	1	1	yes	characteristic
186	#10596831	C₂×C₄²	1	1	yes	characteristic
187	#10596831	C₂×C₄²	1	1	yes	characteristic
188	#10596831	C₂×C₄²	1	1	yes	characteristic
189	#10596831	C₂³×C₄	1	1	yes	characteristic
190	C₂²×C₇₃	—	4	1	no	—
191	C₂²×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
192	C₂²×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
193	C₂²×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
194	C₂×D₇₃	—	2	2	no	—
195	C₂×D₇₃	—	2	2	no	—
196	C₂×D₇₃	—	2	2	no	—
197	C₂×D₇₃	—	4	1	no	—
198	C₂×D₇₃	—	4	1	no	—
199	C₂×D₇₃	—	4	1	no	—
200	C₂×D₇₃	C₂×C₄×C₈	1	1	yes	characteristic
201	C₂×D₇₃	C₂×C₄×C₈	1	1	yes	characteristic
202	C₂×D₇₃	C₂×C₄×C₈	1	1	yes	characteristic
203	C₂×D₇₃	C₂³×C₈	1	1	yes	characteristic
204	#64408	—	2	8	no	—
205	C₄×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
206	C₄×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
207	C₄×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
208	C₄×C₇₃	C₂²×C₄²	1	1	yes	characteristic
209	Dic₇₃	C₂×C₄×C₈	1	1	yes	characteristic
210	Dic₇₃	C₂×C₄×C₈	1	1	yes	characteristic
211	Dic₇₃	C₂×C₄×C₈	1	1	yes	characteristic
212	Dic₇₃	C₂³×C₈	1	1	yes	characteristic
213	#33324	—	73	1	no	maximal, Sylow
214	C₂×C₇₃	—	2	1	no	—
215	C₂×C₇₃	—	2	1	no	—
216	C₂×C₇₃	—	2	1	no	—
217	C₂×C₇₃	C₂²×C₄×C₈	1	1	yes	characteristic
218	D₇₃	—	2	1	no	—
219	D₇₃	—	2	1	no	—
220	D₇₃	—	2	1	no	—
221	D₇₃	#3407	1	2	yes	—
222	C₂²×M₃₂	—	73	1	no	—
223	C₂²×M₃₂	—	73	1	no	—
224	C₂×#405	—	73	1	no	—
225	#2108	—	73	4	no	—
226	#2108	—	73	4	no	—
227	C₄×M₃₂	—	73	4	no	—
228	C₇₃	#33324	1	1	yes	characteristic, complemented, Sylow
229	C₂²×M₁₆	—	73	1	no	—
230	C₂³×C₈	—	73	1	no	—
231	C₂×#117	—	73	1	no	—
232	C₂×M₃₂	—	73	2	no	—
233	C₂×M₃₂	—	73	2	no	—
234	C₂×M₃₂	—	73	2	no	—
235	C₂×M₃₂	—	73	2	no	—
236	C₂×M₃₂	—	73	2	no	—
237	C₂×M₃₂	—	73	2	no	—
238	C₂×M₃₂	—	73	1	no	—
239	C₂×M₃₂	—	73	2	no	—
240	C₂×M₃₂	—	73	2	no	—
241	C₂×M₃₂	—	73	2	no	—
242	C₂×M₃₂	—	73	2	no	—
243	C₂×M₃₂	—	73	2	no	—
244	C₂×M₃₂	#64408	1	1	yes	characteristic, complemented
245	C₂²×C₁₆	—	73	2	no	—
246	C₂²×C₁₆	—	73	2	no	—
247	#405	—	73	2	no	—
248	#405	—	73	2	no	—
249	#405	—	73	2	no	—
250	#405	—	73	2	no	—
251	C₂×#97	—	73	2	no	—
252	C₂×C₄×C₈	—	73	2	no	—
253	#346	—	73	8	no	—
254	C₄×C₁₆	—	73	8	no	—
255	C₂³×C₄	—	73	1	no	—
256	C₂×M₁₆	—	73	2	no	—
257	C₂×M₁₆	—	73	2	no	—
258	C₂×M₁₆	—	73	2	no	—
259	C₂×M₁₆	—	73	2	no	—
260	C₂×M₁₆	—	73	2	no	—
261	C₂×M₁₆	—	73	2	no	—
262	C₂²×C₈	—	73	2	no	—
263	C₂²×C₈	—	73	1	no	—
264	C₂²×C₈	—	73	1	no	—
265	C₂²×C₈	—	73	1	no	—
266	C₂²×C₈	—	73	1	no	—
267	C₂²×C₈	—	73	1	no	—
268	C₂²×C₈	—	73	1	no	—
269	C₂²×C₈	—	73	1	no	—
270	C₂²×C₈	—	73	1	no	—
271	C₂²×C₈	—	73	1	no	—
272	C₂²×C₈	—	73	1	no	—
273	C₂²×C₈	—	73	1	no	—
274	C₂²×C₈	—	73	1	no	—
275	C₂²×C₈	—	73	1	no	—
276	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
277	#117	—	73	2	no	—
278	#117	—	73	2	no	—
279	#117	—	73	2	no	—
280	#117	—	73	2	no	—
281	C₂×C₄⋊C₄	—	73	2	no	—
282	C₂×C₂²⋊C₄	—	73	2	no	—
283	C₂×C₄²	—	73	2	no	—
284	M₃₂	—	73	4	no	—
285	M₃₂	—	73	4	no	—
286	M₃₂	—	73	4	no	—
287	M₃₂	—	73	4	no	—
288	M₃₂	—	73	2	no	—
289	M₃₂	—	73	2	no	—
290	M₃₂	—	73	4	no	—
291	M₃₂	—	73	4	no	—
292	M₃₂	C₂×#64408	1	2	yes	—
293	M₃₂	C₂×#64408	1	2	yes	complemented
294	C₂×C₁₆	—	73	4	no	—
295	C₂×C₁₆	—	73	4	no	—
296	C₂×C₁₆	—	73	4	no	—
297	C₂×C₁₆	—	73	2	no	—
298	C₂×C₁₆	—	73	4	no	—
299	C₂×C₁₆	—	73	4	no	—
300	C₂×C₁₆	C₂×#64408	1	2	yes	complemented
301	#97	—	73	4	no	—
302	#97	—	73	4	no	—
303	C₄×C₈	—	73	4	no	—
304	C₄×C₈	—	73	4	no	—
305	C₂⁴	—	73	1	no	—
306	C₂²×C₄	—	73	4	no	—
307	C₂²×C₄	—	73	1	no	—
308	C₂²×C₄	—	73	1	no	—
309	C₂²×C₄	—	73	1	no	—
310	C₂²×C₄	—	73	1	no	—
311	C₂²×C₄	—	73	1	no	—
312	C₂²×C₄	—	73	1	no	—
313	C₂²×C₄	—	73	1	no	—
314	C₂²×C₄	—	73	1	no	—
315	C₂²×C₄	—	73	1	no	—
316	C₂²×C₄	—	73	1	no	—
317	C₂²×C₄	—	73	1	no	—
318	C₂²×C₄	—	73	1	no	—
319	C₂²×C₄	—	73	1	no	—
320	C₂²×C₄	C₄×#64408	1	1	yes	characteristic
321	M₁₆	—	73	4	no	—
322	M₁₆	—	73	4	no	—
323	M₁₆	—	73	4	no	—
324	M₁₆	—	73	4	no	—
325	C₂×C₈	—	73	4	no	—
326	C₂×C₈	—	73	4	no	—
327	C₂×C₈	—	73	4	no	—
328	C₂×C₈	—	73	1	no	—
329	C₂×C₈	—	73	1	no	—
330	C₂×C₈	—	73	1	no	—
331	C₂×C₈	—	73	1	no	—
332	C₂×C₈	—	73	1	no	—
333	C₂×C₈	—	73	1	no	—
334	C₂×C₈	—	73	1	no	—
335	C₂×C₈	—	73	1	no	—
336	C₂×C₈	—	73	1	no	—
337	C₂×C₈	—	73	1	no	—
338	C₂×C₈	—	73	1	no	—
339	C₂×C₈	—	73	1	no	—
340	C₂×C₈	—	73	1	no	—
341	C₂×C₈	—	73	1	no	—
342	C₂×C₈	—	73	1	no	—
343	C₂×C₈	—	73	1	no	—
344	C₂×C₈	—	73	1	no	—
345	C₂×C₈	—	73	1	no	—
346	C₂×C₈	—	73	1	no	—
347	C₂×C₈	—	73	1	no	—
348	C₂×C₈	—	73	1	no	—
349	C₂×C₈	—	73	1	no	—
350	C₂×C₈	C₄×#64408	1	1	yes	characteristic
351	C₂×C₈	C₄×#64408	1	1	yes	characteristic
352	C₂×C₈	C₄×#64408	1	1	yes	characteristic
353	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
354	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
355	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
356	C₄⋊C₄	—	73	4	no	—
357	C₄⋊C₄	—	73	4	no	—
358	C₂²⋊C₄	—	73	4	no	—
359	C₂²⋊C₄	—	73	4	no	—
360	C₄²	—	73	4	no	—
361	C₄²	—	73	4	no	—
362	C₁₆	—	73	8	no	—
363	C₁₆	—	73	4	no	—
364	C₁₆	C₂²×#64408	1	4	yes	—
365	C₂³	—	292	2	no	—
366	C₂³	—	73	1	no	—
367	C₂³	—	73	1	no	—
368	C₂³	—	73	1	no	—
369	C₂³	—	73	1	no	—
370	C₂³	—	73	1	no	—
371	C₂³	—	73	1	no	—
372	C₂³	C₈×#64408	1	1	yes	characteristic
373	C₂×C₄	—	292	4	no	—
374	C₂×C₄	—	73	1	no	—
375	C₂×C₄	—	73	1	no	—
376	C₂×C₄	—	73	1	no	—
377	C₂×C₄	—	73	1	no	—
378	C₂×C₄	—	73	1	no	—
379	C₂×C₄	—	73	1	no	—
380	C₂×C₄	—	73	1	no	—
381	C₂×C₄	—	73	1	no	—
382	C₂×C₄	—	73	1	no	—
383	C₂×C₄	—	73	1	no	—
384	C₂×C₄	—	73	1	no	—
385	C₂×C₄	—	73	1	no	—
386	C₂×C₄	—	73	1	no	—
387	C₂×C₄	—	73	1	no	—
388	C₂×C₄	—	73	1	no	—
389	C₂×C₄	—	73	1	no	—
390	C₂×C₄	—	73	1	no	—
391	C₂×C₄	—	73	1	no	—
392	C₂×C₄	—	73	1	no	—
393	C₂×C₄	—	73	1	no	—
394	C₂×C₄	—	73	1	no	—
395	C₂×C₄	—	73	1	no	—
396	C₂×C₄	—	73	8	no	—
397	C₂×C₄	C₈×#64408	1	1	yes	characteristic
398	C₂×C₄	C₈×#64408	1	1	yes	characteristic
399	C₂×C₄	C₈×#64408	1	1	yes	characteristic
400	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
401	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
402	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
403	C₈	—	73	8	no	—
404	C₈	—	73	1	no	—
405	C₈	—	73	1	no	—
406	C₈	—	73	1	no	—
407	C₈	—	73	1	no	—
408	C₈	C₂×C₄×#64408	1	1	yes	characteristic
409	C₈	C₂×C₄×#64408	1	1	yes	characteristic
410	C₈	C₂×C₄×#64408	1	1	yes	characteristic
411	C₈	C₂³×#64408	1	1	yes	characteristic
412	C₂²	—	4	1	no	—
413	C₂²	—	292	1	no	—
414	C₂²	—	292	1	no	—
415	C₂²	—	292	1	no	—
416	C₂²	—	73	1	no	—
417	C₂²	—	73	1	no	—
418	C₂²	—	73	1	no	—
419	C₂²	—	73	1	no	—
420	C₂²	—	146	2	no	—
421	C₂²	—	146	2	no	—
422	C₂²	—	146	2	no	—
423	C₂²	C₂×C₈×#64408	1	1	yes	characteristic
424	C₂²	C₂×C₈×#64408	1	1	yes	characteristic
425	C₂²	C₂×C₈×#64408	1	1	yes	characteristic
426	C₄	—	73	1	no	—
427	C₄	—	73	1	no	—
428	C₄	—	73	1	no	—
429	C₄	—	73	1	no	—
430	C₄	—	146	8	no	—
431	C₄	C₂×C₈×#64408	1	1	yes	characteristic
432	C₄	C₂×C₈×#64408	1	1	yes	characteristic
433	C₄	C₂×C₈×#64408	1	1	yes	characteristic
434	C₄	C₂²×C₄×#64408	1	1	yes	characteristic
435	C₂	—	2	1	no	—
436	C₂	—	2	1	no	—
437	C₂	—	2	1	no	—
438	C₂	—	73	2	no	—
439	C₂	—	146	1	no	—
440	C₂	—	146	1	no	—
441	C₂	—	146	1	no	—
442	C₂	C₂²×C₈×#64408	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂³×#64408
commutator, socle	C₂×C₇₃	C₂²×C₄×C₈
Fitting	C₂×M₃₂×C₇₃	C₄
prime radical	C₂³×D₇₃	C₂×C₈
cosocle	C₈×D₇₃	C₂⁴
hypercenter	C₂×M₃₂	#64408
hypocenter	C₇₃	#33324
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
3. #22626143	C₂	semidirect
4. #22626139	C₂	semidirect
5. M₃₂×#64408	C₂	semidirect
9. C₂×#14556666	C₄	semidirect
10. #17989643	C₄	semidirect
11. #17989643	C₄	semidirect
14. C₂×#14556665	C₄	semidirect
22. #17989474	C₂²	semidirect
23. C₁₆×#64408	C₂²	semidirect
25. C₂×#14556531	C₄	semidirect
26. C₂×#14556530	C₄	semidirect
27. M₃₂×D₇₃	C₄	semidirect
28. M₃₂×D₇₃	C₄	semidirect
32. C₂×M₃₂×C₇₃	C₄	semidirect
48. #14556666	C₂×C₄	semidirect
50. #14556665	C₂×C₄	semidirect
51. #14556664	C₂×C₄	semidirect
53. C₂×#11924031	C₂×C₄	semidirect
73. #14556531	C₂×C₄	semidirect
75. #14556530	C₂×C₄	semidirect
76. C₂×#11924003	C₂×C₄	semidirect
77. C₁₆×D₇₃	C₂×C₄	semidirect
81. M₃₂×C₇₃	C₂×C₄	semidirect
82. C₂×C₁₆×C₇₃	C₂×C₄	semidirect
228. C₇₃	#33324	semidirect
244. C₂×M₃₂	#64408	semidirect
293. M₃₂	C₂×#64408	semidirect
300. C₂×C₁₆	C₂×#64408	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17989643	2
C₂×#17989550	2
#22626143	2
#22626139	2
M₃₂×#64408	2
C₂×M₃₂×D₇₃	2
#33324	73