Subgroups — #34021385

Order 18688.

982 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22626380	C₂	1	2	yes	maximal
2	#22625867	C₂	1	2	yes	maximal, complemented
3	#22625852	C₂	1	2	yes	maximal, complemented
4	#22625808	C₂	1	4	yes	maximal
5	C₄×#14556660	C₂	1	4	yes	maximal, complemented
6	C₂×C₄×C₈×D₇₃	C₂	1	1	yes	maximal, characteristic
7	C₂×#14556670	—	2	2	no	—
8	C₂×#14556660	C₂²	1	8	yes	—
9	#17989533	C₂²	1	4	yes	—
10	#17989531	—	2	2	no	—
11	#17989529	—	2	2	no	—
12	#17989529	C₂²	1	4	yes	—
13	C₄×C₄⋊#64408	—	2	2	no	—
14	C₄×C₄⋊#64408	C₂²	1	4	yes	—
15	#17989461	C₂²	1	8	yes	—
16	C₂²×C₈×D₇₃	C₂²	1	2	yes	—
17	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×#10596831	C₄	1	1	yes	characteristic, complemented
19	C₂×C₈×Dic₇₃	C₄	1	2	yes	complemented
20	C₄×C₈×D₇₃	C₄	1	1	yes	characteristic, complemented
21	C₄×C₈×D₇₃	C₄	1	2	yes	complemented
22	C₄×C₈×D₇₃	C₄	1	1	yes	characteristic, complemented
23	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
24	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
25	C₄×C₈×D₇₃	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₇₃	C₄	1	1	yes	characteristic, complemented
27	#14556670	—	4	8	no	—
28	C₂×C₄⋊#64408	—	2	4	no	—
29	C₂×C₄⋊#64408	—	2	4	no	—
30	C₂×C₄⋊#64408	C₂³	1	8	yes	—
31	C₂×C₂²⋊#64408	—	2	4	no	—
32	C₂×C₄×#64408	—	2	4	no	—
33	#14556660	—	2	16	no	—
34	(C₂×#64408)⋊C₄	—	2	4	no	—
35	(C₂×#64408)⋊C₄	—	2	4	no	—
36	C₂²×C₄×D₇₃	D₄	1	1	yes	characteristic
37	C₂²×C₄×D₇₃	D₄	1	1	yes	characteristic
38	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
39	C₂²×#10596831	C₂×C₄	1	2	yes	—
40	C₂×C₈×D₇₃	—	2	8	no	—
41	C₂×C₈×D₇₃	C₂×C₄	1	2	yes	—
42	C₂×C₈×D₇₃	C₂×C₄	1	2	yes	—
43	C₂×C₈×D₇₃	C₂³	1	2	yes	—
44	C₂×C₈×D₇₃	C₂³	1	2	yes	—
45	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₇₃	Q₈	1	1	yes	characteristic
47	C₂×C₄×Dic₇₃	Q₈	1	1	yes	characteristic
48	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
49	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
50	C₄²×D₇₃	D₄	1	1	yes	characteristic
51	C₄²×D₇₃	D₄	1	1	yes	characteristic
52	C₄²×D₇₃	Q₈	1	1	yes	characteristic
53	C₄²×D₇₃	Q₈	1	1	yes	characteristic
54	C₄²×D₇₃	C₂³	1	1	yes	characteristic
55	C₄²×D₇₃	C₂³	1	1	yes	characteristic
56	C₄×#10596831	C₂×C₄	1	1	yes	characteristic
57	C₄×#10596831	C₂×C₄	1	2	yes	—
58	C₄×#10596831	C₂×C₄	1	1	yes	characteristic
59	C₈×Dic₇₃	C₂×C₄	1	2	yes	—
60	C₈×Dic₇₃	C₂×C₄	1	2	yes	—
61	C₈×Dic₇₃	C₂×C₄	1	2	yes	—
62	C₈×Dic₇₃	C₂×C₄	1	2	yes	—
63	C₂²×C₈×C₇₃	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
65	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
66	C₄×C₈×C₇₃	C₂×C₄	1	2	yes	—
67	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
68	C₂²×#64408	—	2	8	no	—
69	C₄⋊#64408	—	2	16	no	—
70	C₄⋊#64408	—	4	8	no	—
71	C₄⋊#64408	—	4	8	no	—
72	C₂²⋊#64408	—	4	8	no	—
73	C₄×#64408	—	4	8	no	—
74	C₂³×D₇₃	C₂×D₄	1	1	yes	characteristic
75	C₂²×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
76	C₂²×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
77	C₂²×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
78	C₂×C₄×D₇₃	—	2	4	no	—
79	C₂×C₄×D₇₃	—	2	4	no	—
80	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
81	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
82	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
83	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×D₇₃	D₈	1	4	yes	—
85	C₂×C₄×D₇₃	Q₁₆	1	4	yes	—
86	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
87	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
88	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
89	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
90	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
91	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
92	C₂×C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
93	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
94	C₂×#10596831	—	2	4	no	—
95	C₂×#10596831	C₂²×C₄	1	2	yes	—
96	C₂×#10596831	C₂²×C₄	1	2	yes	—
97	C₈×D₇₃	—	2	4	no	—
98	C₈×D₇₃	—	2	4	no	—
99	C₈×D₇₃	—	2	4	no	—
100	C₈×D₇₃	#41	1	8	yes	—
101	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
102	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
103	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
104	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
105	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
106	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
107	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
108	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
109	C₄×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
110	C₄×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
111	C₄×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
112	C₄×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
113	C₂²×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
114	C₂²×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
115	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₇₃	—	2	4	no	—
117	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
119	C₄²×C₇₃	C₄⋊C₄	1	1	yes	characteristic
120	C₄²×C₇₃	C₄⋊C₄	1	1	yes	characteristic
121	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
123	C₂³×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
124	C₂²×D₇₃	—	2	2	no	—
125	C₂²×D₇₃	—	2	2	no	—
126	C₂²×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
127	C₂²×D₇₃	C₂×D₈	1	2	yes	—
128	C₂²×D₇₃	C₂×Q₁₆	1	2	yes	—
129	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
130	C₂×#64408	—	4	8	no	—
131	C₂×#64408	—	4	8	no	—
132	C₂×#64408	—	4	8	no	—
133	C₂×C₄×C₇₃	—	2	2	no	—
134	C₂×C₄×C₇₃	—	2	2	no	—
135	C₂×C₄×C₇₃	#107	1	4	yes	complemented
136	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
142	C₂×Dic₇₃	—	2	2	no	—
143	C₂×Dic₇₃	—	2	2	no	—
144	C₂×Dic₇₃	#107	1	4	yes	complemented
145	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×Dic₇₃	C₂²×Q₈	1	1	yes	characteristic
151	C₄×D₇₃	—	2	2	no	—
152	C₄×D₇₃	—	2	2	no	—
153	C₄×D₇₃	—	2	2	no	—
154	C₄×D₇₃	—	2	2	no	—
155	C₄×D₇₃	—	2	2	no	—
156	C₄×D₇₃	—	2	2	no	—
157	C₄×D₇₃	#107	1	4	yes	complemented
158	C₄×D₇₃	#107	1	4	yes	complemented
159	C₄×D₇₃	C₂×D₈	1	2	yes	—
160	C₄×D₇₃	C₂×D₈	1	2	yes	—
161	C₄×D₇₃	C₂×Q₁₆	1	2	yes	—
162	C₄×D₇₃	C₂×Q₁₆	1	2	yes	—
163	C₄×D₇₃	#135	1	4	yes	—
164	C₄×D₇₃	C₂×#41	1	4	yes	—
165	C₈×C₇₃	—	2	2	no	—
166	C₈×C₇₃	#117	1	4	yes	complemented
167	#10596831	—	2	2	no	—
168	#10596831	#117	1	4	yes	complemented
169	C₂²×C₇₃	—	2	1	no	—
170	C₂²×C₇₃	—	2	1	no	—
171	C₂²×C₇₃	C₂×#107	1	2	yes	—
172	C₂²×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
173	C₂×D₇₃	—	2	1	no	—
174	C₂×D₇₃	—	2	1	no	—
175	C₂×D₇₃	—	2	4	no	—
176	C₂×D₇₃	—	2	4	no	—
177	C₂×D₇₃	C₂×#107	1	2	yes	—
178	C₂×D₇₃	#532	1	2	yes	—
179	C₂×D₇₃	C₂²×D₈	1	1	yes	characteristic
180	C₂×D₇₃	C₂²×Q₁₆	1	1	yes	characteristic
181	C₂×D₇₃	C₂×#135	1	2	yes	—
182	#64408	—	8	8	no	—
183	C₄×C₇₃	—	2	1	no	—
184	C₄×C₇₃	—	2	1	no	—
185	C₄×C₇₃	C₂×#107	1	2	yes	—
186	C₄×C₇₃	C₂×#107	1	2	yes	—
187	C₄×C₇₃	#427	1	2	yes	—
188	C₄×C₇₃	C₂×#117	1	2	yes	—
189	Dic₇₃	—	2	1	no	—
190	Dic₇₃	—	2	1	no	—
191	Dic₇₃	C₂×#107	1	2	yes	—
192	Dic₇₃	C₂×#107	1	2	yes	—
193	Dic₇₃	#427	1	2	yes	—
194	Dic₇₃	#533	1	2	yes	—
195	#20817	—	73	1	no	maximal, Sylow
196	C₂×C₇₃	—	2	2	no	—
197	C₂×C₇₃	#2285	1	1	yes	characteristic
198	C₂×C₇₃	C₂²×#107	1	1	yes	characteristic
199	C₂×C₇₃	C₂×#427	1	1	yes	characteristic
200	D₇₃	—	2	2	no	—
201	D₇₃	#3169	1	2	yes	—
202	D₇₃	#3170	1	2	yes	—
203	C₂²×C₄×C₈	—	73	1	no	—
204	#2285	—	73	2	no	—
205	#1845	—	73	2	no	—
206	#1834	—	73	2	no	—
207	#1808	—	73	4	no	—
208	C₄×#107	—	73	4	no	—
209	C₇₃	#20817	1	1	yes	characteristic, complemented, Sylow
210	C₂³×C₈	—	73	2	no	—
211	C₂×#117	—	146	2	no	—
212	C₂²×C₄²	—	73	1	no	—
213	C₂×#107	—	73	8	no	—
214	C₂×C₄×C₈	—	73	2	no	—
215	C₂×C₄×C₈	—	73	1	no	—
216	C₂×C₄×C₈	—	73	1	no	—
217	C₂×C₄×C₈	—	73	1	no	—
218	C₂×C₄×C₈	—	73	1	no	—
219	C₂×C₄×C₈	—	73	2	no	—
220	C₂×C₄×C₈	—	73	1	no	—
221	C₂×C₄×C₈	—	73	2	no	—
222	C₂×C₄×C₈	#64408	1	1	yes	characteristic, complemented
223	#384	—	73	4	no	—
224	#382	—	146	2	no	—
225	#380	—	73	4	no	—
226	#380	—	146	2	no	—
227	C₄×C₄⋊C₄	—	73	4	no	—
228	C₄×C₄⋊C₄	—	146	2	no	—
229	#340	—	73	8	no	—
230	C₂³×C₄	—	73	1	no	—
231	C₂³×C₄	—	73	1	no	—
232	C₂³×C₄	—	73	1	no	—
233	C₂²×C₈	—	73	2	no	—
234	C₂²×C₈	—	73	2	no	—
235	C₂²×C₈	—	73	2	no	—
236	C₂²×C₈	—	73	2	no	—
237	C₂²×C₈	—	73	2	no	—
238	C₂²×C₈	—	146	8	no	—
239	C₂²×C₈	C₂×#64408	1	2	yes	—
240	#117	—	292	8	no	—
241	C₂×C₄⋊C₄	—	73	8	no	—
242	C₂×C₄⋊C₄	—	146	4	no	—
243	C₂×C₄⋊C₄	—	146	4	no	—
244	C₂×C₂²⋊C₄	—	146	4	no	—
245	C₂×C₄²	—	73	1	no	—
246	C₂×C₄²	—	73	1	no	—
247	C₂×C₄²	—	73	1	no	—
248	C₂×C₄²	—	73	1	no	—
249	C₂×C₄²	—	73	1	no	—
250	C₂×C₄²	—	73	1	no	—
251	C₂×C₄²	—	73	1	no	—
252	C₂×C₄²	—	73	1	no	—
253	C₂×C₄²	—	73	1	no	—
254	C₂×C₄²	—	73	1	no	—
255	C₂×C₄²	—	73	1	no	—
256	C₂×C₄²	—	146	4	no	—
257	C₂×C₄²	C₂×#64408	1	1	yes	characteristic
258	#107	—	146	16	no	—
259	C₄×C₈	—	73	2	no	—
260	C₄×C₈	—	73	2	no	—
261	C₄×C₈	—	73	2	no	—
262	C₄×C₈	—	73	2	no	—
263	C₄×C₈	—	73	1	no	—
264	C₄×C₈	—	73	1	no	—
265	C₄×C₈	—	73	2	no	—
266	C₄×C₈	C₂×#64408	1	1	yes	characteristic
267	C₄×C₈	C₂×#64408	1	1	yes	characteristic
268	C₄×C₈	C₂×#64408	1	2	yes	—
269	#95	—	146	4	no	—
270	#95	—	146	4	no	—
271	C₂⁴	—	73	1	no	—
272	C₂²×C₄	—	73	1	no	—
273	C₂²×C₄	—	73	1	no	—
274	C₂²×C₄	—	73	4	no	—
275	C₂²×C₄	—	73	4	no	—
276	C₂²×C₄	—	73	1	no	—
277	C₂²×C₄	—	73	1	no	—
278	C₂²×C₄	—	73	1	no	—
279	C₂²×C₄	—	73	1	no	—
280	C₂²×C₄	—	73	1	no	—
281	C₂²×C₄	—	73	1	no	—
282	C₂²×C₄	—	73	1	no	—
283	C₂²×C₄	—	73	1	no	—
284	C₂²×C₄	—	73	1	no	—
285	C₂²×C₄	—	73	1	no	—
286	C₂²×C₄	—	73	1	no	—
287	C₂²×C₄	—	73	1	no	—
288	C₂²×C₄	—	73	1	no	—
289	C₂²×C₄	—	146	4	no	—
290	C₂²×C₄	—	146	4	no	—
291	C₂²×C₄	—	146	8	no	—
292	C₂²×C₄	C₄⋊#64408	1	1	yes	characteristic
293	C₂²×C₄	C₄⋊#64408	1	1	yes	characteristic
294	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
295	C₂×C₈	—	2	4	no	—
296	C₂×C₈	—	73	2	no	—
297	C₂×C₈	—	73	8	no	—
298	C₂×C₈	—	73	2	no	—
299	C₂×C₈	—	146	4	no	—
300	C₂×C₈	—	146	4	no	—
301	C₂×C₈	—	146	4	no	—
302	C₂×C₈	—	146	4	no	—
303	C₂×C₈	C₂²×#64408	1	2	yes	—
304	C₂×C₈	C₂²×#64408	1	2	yes	—
305	C₄⋊C₄	—	292	8	no	—
306	C₄⋊C₄	—	292	8	no	—
307	C₄⋊C₄	—	146	16	no	—
308	C₂²⋊C₄	—	292	8	no	—
309	C₄²	—	292	8	no	—
310	C₄²	—	73	1	no	—
311	C₄²	—	73	1	no	—
312	C₄²	—	73	1	no	—
313	C₄²	—	73	1	no	—
314	C₄²	—	73	1	no	—
315	C₄²	—	73	1	no	—
316	C₄²	—	73	1	no	—
317	C₄²	—	73	1	no	—
318	C₄²	—	73	1	no	—
319	C₄²	—	73	1	no	—
320	C₄²	—	73	1	no	—
321	C₄²	—	73	1	no	—
322	C₄²	C₄⋊#64408	1	1	yes	characteristic
323	C₄²	C₄⋊#64408	1	1	yes	characteristic
324	C₄²	C₂²×#64408	1	1	yes	characteristic
325	C₄²	C₂²×#64408	1	1	yes	characteristic
326	C₂³	—	73	1	no	—
327	C₂³	—	73	1	no	—
328	C₂³	—	73	2	no	—
329	C₂³	—	73	2	no	—
330	C₂³	—	146	2	no	—
331	C₂³	—	146	2	no	—
332	C₂³	C₂×C₄⋊#64408	1	1	yes	characteristic
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	292	8	no	—
336	C₂×C₄	—	292	8	no	—
337	C₂×C₄	—	292	8	no	—
338	C₂×C₄	—	73	1	no	—
339	C₂×C₄	—	73	1	no	—
340	C₂×C₄	—	73	1	no	—
341	C₂×C₄	—	73	1	no	—
342	C₂×C₄	—	73	4	no	—
343	C₂×C₄	—	73	4	no	—
344	C₂×C₄	—	73	2	no	—
345	C₂×C₄	—	73	2	no	—
346	C₂×C₄	—	73	4	no	—
347	C₂×C₄	—	73	4	no	—
348	C₂×C₄	—	73	2	no	—
349	C₂×C₄	—	73	2	no	—
350	C₂×C₄	—	73	4	no	—
351	C₂×C₄	—	73	1	no	—
352	C₂×C₄	—	73	1	no	—
353	C₂×C₄	—	146	2	no	—
354	C₂×C₄	—	146	2	no	—
355	C₂×C₄	—	146	2	no	—
356	C₂×C₄	—	146	2	no	—
357	C₂×C₄	—	146	2	no	—
358	C₂×C₄	—	146	2	no	—
359	C₂×C₄	—	146	2	no	—
360	C₂×C₄	—	146	2	no	—
361	C₂×C₄	#14556660	1	4	yes	complemented
362	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
363	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
364	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
365	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
366	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
367	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
368	C₈	—	2	2	no	—
369	C₈	—	73	4	no	—
370	C₈	—	146	2	no	—
371	C₈	#14556670	1	4	yes	complemented
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	73	1	no	—
375	C₂²	—	73	1	no	—
376	C₂²	—	73	2	no	—
377	C₂²	—	73	2	no	—
378	C₂²	—	73	2	no	—
379	C₂²	—	146	4	no	—
380	C₂²	—	146	4	no	—
381	C₂²	—	146	1	no	—
382	C₂²	—	146	1	no	—
383	C₂²	C₂×#14556660	1	2	yes	—
384	C₂²	C₂²×C₄⋊#64408	1	1	yes	characteristic
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	584	8	no	—
388	C₄	—	73	2	no	—
389	C₄	—	73	2	no	—
390	C₄	—	73	2	no	—
391	C₄	—	73	2	no	—
392	C₄	—	146	1	no	—
393	C₄	—	146	1	no	—
394	C₄	C₂×#14556660	1	2	yes	—
395	C₄	C₂×#14556660	1	2	yes	—
396	C₄	#17989597	1	2	yes	—
397	C₄	C₂×#14556670	1	2	yes	—
398	C₂	—	2	2	no	—
399	C₂	—	73	2	no	—
400	C₂	—	73	2	no	—
401	C₂	—	146	2	no	—
402	C₂	#22626380	1	1	yes	characteristic
403	C₂	C₂²×#14556660	1	1	yes	characteristic
404	C₂	C₂×#17989597	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₄⋊#64408
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#64408
Fitting	C₂×C₄×C₈×C₇₃	C₄
socle	C₂²×C₇₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₇₃	C₂×D₄
cosocle	C₂×C₄×D₇₃	C₂⁴
hypercenter	C₂×C₄×C₈	#64408
hypocenter	C₇₃	#20817
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #22625867	C₂	semidirect
3. #22625852	C₂	semidirect
5. C₄×#14556660	C₂	semidirect
18. C₂×C₄×#10596831	C₄	semidirect
19. C₂×C₈×Dic₇₃	C₄	semidirect
20. C₄×C₈×D₇₃	C₄	semidirect
21. C₄×C₈×D₇₃	C₄	semidirect
22. C₄×C₈×D₇₃	C₄	semidirect
26. C₂×C₄×C₈×C₇₃	C₄	semidirect
135. C₂×C₄×C₇₃	#107	semidirect
144. C₂×Dic₇₃	#107	semidirect
157. C₄×D₇₃	#107	semidirect
158. C₄×D₇₃	#107	semidirect
166. C₈×C₇₃	#117	semidirect
168. #10596831	#117	semidirect
209. C₇₃	#20817	semidirect
222. C₂×C₄×C₈	#64408	semidirect
361. C₂×C₄	#14556660	semidirect
371. C₈	#14556670	semidirect

Maximal subgroups

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

subgroup	index
#22626380	2
#22625867	2
#22625852	2
#22625808	2
C₄×#14556660	2
C₂×C₄×C₈×D₇₃	2
#20817	73