Subgroups — #34020344

Order 18688.

1078 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22626595	C₂	1	1	yes	maximal, characteristic
2	C₄×#14556670	C₂	1	1	yes	maximal, characteristic
3	#22625725	C₂	1	4	yes	maximal, complemented
4	#22625667	C₂	1	4	yes	maximal
5	#22625644	C₂	1	2	yes	maximal, complemented
6	C₄×#14556645	C₂	1	2	yes	maximal, complemented
7	C₂×C₄×C₈×D₇₃	C₂	1	1	yes	maximal, characteristic
8	C₂×#14556670	C₄	1	2	yes	—
9	#17989606	C₄	1	2	yes	complemented
10	#17989605	C₄	1	2	yes	complemented
11	#17989604	C₄	1	2	yes	complemented
12	#17989603	C₄	1	2	yes	complemented
13	#17989588	C₂²	1	2	yes	—
14	#17989555	C₂²	1	2	yes	—
15	C₂×#14556645	C₂²	1	8	yes	—
16	C₄×#11924036	C₂²	1	2	yes	—
17	C₄×C₄⋊#64408	C₄	1	2	yes	—
18	C₄×C₄⋊#64408	C₂²	1	2	yes	—
19	C₄×C₂²⋊#64408	C₄	1	2	yes	—
20	C₄×C₂²⋊#64408	C₂²	1	2	yes	—
21	#17989523	C₄	1	2	yes	—
22	C₄²×#64408	C₂²	1	2	yes	—
23	#17989452	C₂²	1	8	yes	—
24	C₂²×C₈×D₇₃	C₂²	1	2	yes	—
25	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×#10596831	C₄	1	1	yes	characteristic, complemented
27	C₂×C₈×Dic₇₃	C₄	1	2	yes	complemented
28	C₄×C₈×D₇₃	C₄	1	2	yes	complemented
29	C₄×C₈×D₇₃	C₄	1	1	yes	characteristic, complemented
30	C₄×C₈×D₇₃	C₄	1	1	yes	characteristic, complemented
31	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
32	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
33	C₄×C₈×D₇₃	C₂²	1	2	yes	—
34	C₂×C₄×C₈×C₇₃	C₄	1	1	yes	characteristic, complemented
35	C₂×#11924036	C₂³	1	4	yes	—
36	#14556670	—	2	8	no	—
37	C₂×C₄⋊#64408	C₂×C₄	1	4	yes	—
38	C₂×C₂²⋊#64408	C₂×C₄	1	4	yes	—
39	C₂×C₄×#64408	C₂×C₄	1	4	yes	—
40	C₂×C₄×#64408	C₂×C₄	1	4	yes	—
41	C₂×C₄×#64408	C₂³	1	4	yes	—
42	#14556658	C₂×C₄	1	4	yes	—
43	C₄⋊#10596833	C₂×C₄	1	4	yes	—
44	#14556648	C₂×C₄	1	4	yes	—
45	C₂²⋊#10596833	C₂×C₄	1	4	yes	—
46	#14556645	—	2	16	no	—
47	C₄×#10596833	C₂×C₄	1	4	yes	—
48	C₄×#10596833	C₂×C₄	1	4	yes	—
49	(C₂×#64408)⋊C₄	C₂×C₄	1	4	yes	—
50	(C₂×#64408)⋊C₄	C₂×C₄	1	4	yes	—
51	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
54	C₂²×#10596831	C₂×C₄	1	2	yes	—
55	C₂×C₈×D₇₃	—	2	8	no	—
56	C₂×C₈×D₇₃	C₂×C₄	1	2	yes	—
57	C₂×C₈×D₇₃	C₂×C₄	1	2	yes	—
58	C₂×C₈×D₇₃	C₂³	1	2	yes	—
59	C₂×C₈×D₇₃	C₂³	1	2	yes	—
60	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
63	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
64	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
65	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
66	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
67	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
68	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
69	C₄²×D₇₃	C₂³	1	1	yes	characteristic
70	C₄²×D₇₃	C₂³	1	1	yes	characteristic
71	C₄×#10596831	C₂×C₄	1	2	yes	—
72	C₄×#10596831	C₂×C₄	1	1	yes	characteristic
73	C₄×#10596831	C₂×C₄	1	1	yes	characteristic
74	C₈×Dic₇₃	C₂×C₄	1	2	yes	—
75	C₈×Dic₇₃	C₂×C₄	1	2	yes	—
76	C₈×Dic₇₃	C₂×C₄	1	2	yes	—
77	C₈×Dic₇₃	C₂×C₄	1	2	yes	—
78	C₂²×C₈×C₇₃	C₂×C₄	1	2	yes	—
79	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
80	C₄×C₈×C₇₃	C₂×C₄	1	2	yes	—
81	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
82	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
83	C₂²×#64408	C₂²×C₄	1	8	yes	—
84	#11924036	—	2	8	no	—
85	C₂×#10596833	C₂²×C₄	1	8	yes	—
86	C₄⋊#64408	—	2	8	no	—
87	C₂²⋊#64408	—	2	8	no	—
88	C₄×#64408	—	2	8	no	—
89	C₄×#64408	—	2	8	no	—
90	C₄×#64408	—	2	8	no	—
91	C₂³×D₇₃	C₂²×C₄	1	1	yes	characteristic
92	C₂²×Dic₇₃	C₄²	1	1	yes	characteristic
93	C₂²×Dic₇₃	C₄²	1	1	yes	characteristic
94	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₄×D₇₃	—	2	4	no	—
96	C₂×C₄×D₇₃	—	2	4	no	—
97	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
98	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
99	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
100	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
101	C₂×C₄×D₇₃	M₁₆	1	8	yes	—
102	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
110	C₂×#10596831	—	2	4	no	—
111	C₂×#10596831	C₂²×C₄	1	2	yes	—
112	C₂×#10596831	C₂²×C₄	1	2	yes	—
113	C₈×D₇₃	—	2	4	no	—
114	C₈×D₇₃	—	2	4	no	—
115	C₈×D₇₃	—	2	4	no	—
116	C₈×D₇₃	#41	1	8	yes	—
117	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
118	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
119	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
120	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
121	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
122	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
123	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
124	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
125	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
126	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
127	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
128	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₇₃	C₄²	1	1	yes	characteristic
130	C₂²×C₄×C₇₃	C₄²	1	1	yes	characteristic
131	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₈×C₇₃	—	2	4	no	—
133	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
135	C₄²×C₇₃	C₄²	1	1	yes	characteristic
136	C₄²×C₇₃	C₄²	1	1	yes	characteristic
137	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
138	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
139	C₂³×C₇₃	C₂×C₄²	1	1	yes	characteristic
140	C₂²×D₇₃	—	2	2	no	—
141	C₂²×D₇₃	—	2	2	no	—
142	C₂²×D₇₃	C₂×C₄²	1	1	yes	characteristic
143	C₂²×D₇₃	C₂×M₁₆	1	4	yes	—
144	C₂²×D₇₃	C₂³×C₄	1	1	yes	characteristic
145	C₂×#64408	—	2	8	no	—
146	C₂×#64408	—	2	8	no	—
147	C₂×#64408	—	2	8	no	—
148	C₂×C₄×C₇₃	—	2	2	no	—
149	C₂×C₄×C₇₃	—	2	2	no	—
150	C₂×C₄×C₇₃	#97	1	4	yes	complemented
151	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
152	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
153	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
154	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
155	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
156	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
157	C₂×Dic₇₃	—	2	2	no	—
158	C₂×Dic₇₃	—	2	2	no	—
159	C₂×Dic₇₃	#97	1	4	yes	complemented
160	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
161	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
162	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
163	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
164	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
165	C₂×Dic₇₃	C₂³×C₄	1	1	yes	characteristic
166	C₄×D₇₃	—	2	2	no	—
167	C₄×D₇₃	—	2	2	no	—
168	C₄×D₇₃	—	2	2	no	—
169	C₄×D₇₃	—	2	2	no	—
170	C₄×D₇₃	—	2	2	no	—
171	C₄×D₇₃	—	2	2	no	—
172	C₄×D₇₃	#97	1	4	yes	complemented
173	C₄×D₇₃	#97	1	4	yes	complemented
174	C₄×D₇₃	C₂×M₁₆	1	4	yes	—
175	C₄×D₇₃	C₂×M₁₆	1	4	yes	—
176	C₄×D₇₃	#131	1	4	yes	—
177	C₄×D₇₃	C₂×#41	1	4	yes	—
178	#10596833	—	2	8	no	—
179	C₈×C₇₃	—	2	2	no	—
180	C₈×C₇₃	#117	1	4	yes	complemented
181	#10596831	—	2	2	no	—
182	#10596831	#117	1	4	yes	complemented
183	C₂²×C₇₃	—	2	1	no	—
184	C₂²×C₇₃	—	2	1	no	—
185	C₂²×C₇₃	C₂×#97	1	2	yes	—
186	C₂²×C₇₃	C₂²×C₄²	1	1	yes	characteristic
187	C₂×D₇₃	—	2	1	no	—
188	C₂×D₇₃	—	2	1	no	—
189	C₂×D₇₃	—	2	8	no	—
190	C₂×D₇₃	C₂×#97	1	2	yes	—
191	C₂×D₇₃	C₄×#41	1	2	yes	—
192	C₂×D₇₃	C₂²×M₁₆	1	2	yes	—
193	C₂×D₇₃	C₂×#131	1	2	yes	—
194	#64408	—	4	8	no	—
195	C₄×C₇₃	—	2	1	no	—
196	C₄×C₇₃	—	2	1	no	—
197	C₄×C₇₃	C₂×#97	1	2	yes	—
198	C₄×C₇₃	C₂×#97	1	2	yes	—
199	C₄×C₇₃	#405	1	2	yes	—
200	C₄×C₇₃	C₂×#117	1	2	yes	—
201	Dic₇₃	—	2	1	no	—
202	Dic₇₃	—	2	1	no	—
203	Dic₇₃	C₂×#97	1	2	yes	—
204	Dic₇₃	C₂×#97	1	2	yes	—
205	Dic₇₃	#405	1	2	yes	—
206	Dic₇₃	C₄×#41	1	2	yes	—
207	#20473	—	73	1	no	maximal, Sylow
208	C₂×C₇₃	—	2	2	no	—
209	C₂×C₇₃	C₄×#117	1	1	yes	characteristic
210	C₂×C₇₃	C₂²×#97	1	1	yes	characteristic
211	C₂×C₇₃	C₂×#405	1	1	yes	characteristic
212	D₇₃	—	2	2	no	—
213	D₇₃	#2965	1	4	yes	—
214	C₂×#431	—	73	1	no	—
215	C₂²×C₄×C₈	—	73	1	no	—
216	C₄×#117	—	73	1	no	—
217	#1770	—	73	4	no	—
218	#1752	—	73	4	no	—
219	#1744	—	73	2	no	—
220	C₄×#97	—	73	2	no	—
221	C₇₃	#20473	1	1	yes	characteristic, complemented, Sylow
222	C₂³×C₈	—	73	2	no	—
223	C₂×#117	—	73	2	no	—
224	C₂²×C₄²	—	73	1	no	—
225	#431	—	73	2	no	—
226	#431	—	73	2	no	—
227	#431	—	73	2	no	—
228	#431	—	73	2	no	—
229	C₂×C₄⋊C₈	—	73	2	no	—
230	C₂×C₂²⋊C₈	—	73	2	no	—
231	C₂×#97	—	73	8	no	—
232	C₂×C₄×C₈	—	73	2	no	—
233	C₂×C₄×C₈	—	73	2	no	—
234	C₂×C₄×C₈	—	73	1	no	—
235	C₂×C₄×C₈	—	73	2	no	—
236	C₂×C₄×C₈	—	73	1	no	—
237	C₂×C₄×C₈	—	73	1	no	—
238	C₂×C₄×C₈	—	73	1	no	—
239	C₂×C₄×C₈	—	73	1	no	—
240	C₂×C₄×C₈	—	73	2	no	—
241	C₂×C₄×C₈	#64408	1	1	yes	characteristic, complemented
242	C₄×C₄⋊C₄	—	73	2	no	—
243	C₄×C₄⋊C₄	—	73	2	no	—
244	C₄×C₂²⋊C₄	—	73	2	no	—
245	C₄×C₂²⋊C₄	—	73	2	no	—
246	#376	—	73	2	no	—
247	C₄³	—	73	2	no	—
248	#336	—	73	8	no	—
249	C₂³×C₄	—	73	1	no	—
250	C₂³×C₄	—	73	1	no	—
251	C₂³×C₄	—	73	1	no	—
252	C₂²×C₈	—	73	2	no	—
253	C₂²×C₈	—	73	4	no	—
254	C₂²×C₈	—	73	2	no	—
255	C₂²×C₈	—	73	2	no	—
256	C₂²×C₈	—	73	2	no	—
257	C₂²×C₈	—	73	2	no	—
258	C₂²×C₈	—	146	8	no	—
259	C₂²×C₈	C₂×#64408	1	2	yes	—
260	#117	—	146	8	no	—
261	C₂×C₄⋊C₄	—	73	4	no	—
262	C₂×C₂²⋊C₄	—	73	4	no	—
263	C₂×C₄²	—	73	1	no	—
264	C₂×C₄²	—	73	1	no	—
265	C₂×C₄²	—	73	1	no	—
266	C₂×C₄²	—	73	1	no	—
267	C₂×C₄²	—	73	1	no	—
268	C₂×C₄²	—	73	1	no	—
269	C₂×C₄²	—	73	1	no	—
270	C₂×C₄²	—	73	1	no	—
271	C₂×C₄²	—	73	1	no	—
272	C₂×C₄²	—	73	1	no	—
273	C₂×C₄²	—	73	1	no	—
274	C₂×C₄²	—	73	4	no	—
275	C₂×C₄²	—	73	4	no	—
276	C₂×C₄²	—	73	4	no	—
277	C₂×C₄²	C₂×#64408	1	1	yes	characteristic
278	C₄⋊C₈	—	73	4	no	—
279	C₄⋊C₈	—	73	4	no	—
280	C₂²⋊C₈	—	73	4	no	—
281	C₂²⋊C₈	—	73	4	no	—
282	#97	—	146	16	no	—
283	C₄×C₈	—	73	4	no	—
284	C₄×C₈	—	73	4	no	—
285	C₄×C₈	—	73	2	no	—
286	C₄×C₈	—	73	2	no	—
287	C₄×C₈	—	73	2	no	—
288	C₄×C₈	—	73	2	no	—
289	C₄×C₈	—	73	2	no	—
290	C₄×C₈	—	73	1	no	—
291	C₄×C₈	—	73	1	no	—
292	C₄×C₈	C₂×#64408	1	2	yes	—
293	C₄×C₈	C₂×#64408	1	1	yes	characteristic
294	C₄×C₈	C₂×#64408	1	1	yes	characteristic
295	#95	—	73	4	no	—
296	#95	—	73	4	no	—
297	C₂⁴	—	73	1	no	—
298	C₂²×C₄	—	73	1	no	—
299	C₂²×C₄	—	73	1	no	—
300	C₂²×C₄	—	73	8	no	—
301	C₂²×C₄	—	73	1	no	—
302	C₂²×C₄	—	73	1	no	—
303	C₂²×C₄	—	73	1	no	—
304	C₂²×C₄	—	73	1	no	—
305	C₂²×C₄	—	73	1	no	—
306	C₂²×C₄	—	73	1	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	8	no	—
315	C₂²×C₄	—	146	4	no	—
316	C₂²×C₄	—	146	4	no	—
317	C₂²×C₄	C₄×#64408	1	1	yes	characteristic
318	C₂²×C₄	C₄×#64408	1	1	yes	characteristic
319	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
320	C₂×C₈	—	2	4	no	—
321	C₂×C₈	—	73	2	no	—
322	C₂×C₈	—	73	8	no	—
323	C₂×C₈	—	73	8	no	—
324	C₂×C₈	—	73	2	no	—
325	C₂×C₈	—	146	4	no	—
326	C₂×C₈	—	146	4	no	—
327	C₂×C₈	—	146	4	no	—
328	C₂×C₈	—	146	8	no	—
329	C₂×C₈	—	146	4	no	—
330	C₂×C₈	C₂²×#64408	1	2	yes	—
331	C₂×C₈	C₂²×#64408	1	2	yes	—
332	C₄⋊C₄	—	146	8	no	—
333	C₂²⋊C₄	—	146	8	no	—
334	C₄²	—	73	1	no	—
335	C₄²	—	73	1	no	—
336	C₄²	—	73	1	no	—
337	C₄²	—	73	1	no	—
338	C₄²	—	73	1	no	—
339	C₄²	—	73	1	no	—
340	C₄²	—	73	1	no	—
341	C₄²	—	73	1	no	—
342	C₄²	—	73	1	no	—
343	C₄²	—	73	1	no	—
344	C₄²	—	73	1	no	—
345	C₄²	—	73	1	no	—
346	C₄²	—	146	8	no	—
347	C₄²	—	146	8	no	—
348	C₄²	—	146	8	no	—
349	C₄²	C₄×#64408	1	1	yes	characteristic
350	C₄²	C₄×#64408	1	1	yes	characteristic
351	C₄²	C₂²×#64408	1	1	yes	characteristic
352	C₄²	C₂²×#64408	1	1	yes	characteristic
353	C₂³	—	73	1	no	—
354	C₂³	—	73	1	no	—
355	C₂³	—	73	4	no	—
356	C₂³	—	146	2	no	—
357	C₂³	—	146	2	no	—
358	C₂³	C₂×C₄×#64408	1	1	yes	characteristic
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	73	1	no	—
362	C₂×C₄	—	73	1	no	—
363	C₂×C₄	—	73	1	no	—
364	C₂×C₄	—	73	1	no	—
365	C₂×C₄	—	73	4	no	—
366	C₂×C₄	—	73	4	no	—
367	C₂×C₄	—	73	4	no	—
368	C₂×C₄	—	73	4	no	—
369	C₂×C₄	—	73	4	no	—
370	C₂×C₄	—	73	4	no	—
371	C₂×C₄	—	73	4	no	—
372	C₂×C₄	—	73	1	no	—
373	C₂×C₄	—	73	1	no	—
374	C₂×C₄	—	146	2	no	—
375	C₂×C₄	—	146	2	no	—
376	C₂×C₄	—	146	2	no	—
377	C₂×C₄	—	146	2	no	—
378	C₂×C₄	—	146	8	no	—
379	C₂×C₄	—	146	8	no	—
380	C₂×C₄	—	146	8	no	—
381	C₂×C₄	—	146	2	no	—
382	C₂×C₄	—	146	2	no	—
383	C₂×C₄	—	146	2	no	—
384	C₂×C₄	—	146	2	no	—
385	C₂×C₄	#14556645	1	4	yes	complemented
386	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
387	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
388	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
389	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
390	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
391	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
392	C₈	—	2	2	no	—
393	C₈	—	73	4	no	—
394	C₈	—	146	8	no	—
395	C₈	—	146	2	no	—
396	C₈	#14556670	1	4	yes	complemented
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	73	2	no	—
400	C₂²	—	73	2	no	—
401	C₂²	—	73	2	no	—
402	C₂²	—	73	2	no	—
403	C₂²	—	146	8	no	—
404	C₂²	—	146	1	no	—
405	C₂²	—	146	1	no	—
406	C₂²	C₂×#14556645	1	2	yes	—
407	C₂²	C₂²×C₄×#64408	1	1	yes	characteristic
408	C₄	—	2	1	no	—
409	C₄	—	2	1	no	—
410	C₄	—	292	8	no	—
411	C₄	—	73	2	no	—
412	C₄	—	73	2	no	—
413	C₄	—	73	2	no	—
414	C₄	—	73	2	no	—
415	C₄	—	146	1	no	—
416	C₄	—	146	1	no	—
417	C₄	C₂×#14556645	1	2	yes	—
418	C₄	C₂×#14556645	1	2	yes	—
419	C₄	#17989550	1	2	yes	—
420	C₄	C₂×#14556670	1	2	yes	—
421	C₂	—	2	2	no	—
422	C₂	—	73	4	no	—
423	C₂	—	146	2	no	—
424	C₂	C₄×#14556670	1	1	yes	characteristic
425	C₂	C₂²×#14556645	1	1	yes	characteristic
426	C₂	C₂×#17989550	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂²×#64408
commutator, socle	C₂²×C₇₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#64408
Fitting	C₂×C₄×C₈×C₇₃	C₄
prime radical	C₂³×D₇₃	C₂²×C₄
cosocle	C₂×C₄×D₇₃	C₂⁴
hypercenter	C₂×C₄×C₈	#64408
hypocenter	C₇₃	#20473
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
3. #22625725	C₂	semidirect
5. #22625644	C₂	semidirect
6. C₄×#14556645	C₂	semidirect
9. #17989606	C₄	semidirect
10. #17989605	C₄	semidirect
11. #17989604	C₄	semidirect
12. #17989603	C₄	semidirect
26. C₂×C₄×#10596831	C₄	semidirect
27. C₂×C₈×Dic₇₃	C₄	semidirect
28. C₄×C₈×D₇₃	C₄	semidirect
29. C₄×C₈×D₇₃	C₄	semidirect
30. C₄×C₈×D₇₃	C₄	semidirect
34. C₂×C₄×C₈×C₇₃	C₄	semidirect
150. C₂×C₄×C₇₃	#97	semidirect
159. C₂×Dic₇₃	#97	semidirect
172. C₄×D₇₃	#97	semidirect
173. C₄×D₇₃	#97	semidirect
180. C₈×C₇₃	#117	semidirect
182. #10596831	#117	semidirect
221. C₇₃	#20473	semidirect
241. C₂×C₄×C₈	#64408	semidirect
385. C₂×C₄	#14556645	semidirect
396. C₈	#14556670	semidirect

Maximal subgroups

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

subgroup	index
#22626595	2
C₄×#14556670	2
#22625725	2
#22625667	2
#22625644	2
C₄×#14556645	2
C₂×C₄×C₈×D₇₃	2
#20473	73