Subgroups — #34020337

Order 18688.

1174 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#11924036	C₂	1	1	yes	maximal, characteristic
2	C₄×#14556670	C₂	1	1	yes	maximal, characteristic
3	#22625724	C₂	1	4	yes	maximal, complemented
4	#22625666	C₂	1	4	yes	maximal
5	#22625644	C₂	1	2	yes	maximal, complemented
6	C₄×C₈×#64408	C₂	1	2	yes	maximal, complemented
7	#431×D₇₃	C₂	1	1	yes	maximal, characteristic
8	C₂²×#11924036	C₂²	1	2	yes	—
9	C₂×#14556670	C₄	1	2	yes	—
10	C₄×#11924036	C₄	1	2	yes	complemented
11	C₄×#11924036	C₄	1	2	yes	complemented
12	C₄×#11924036	C₂²	1	1	yes	characteristic
13	C₄×#11924036	C₂²	1	1	yes	characteristic
14	C₄×#11924036	C₂²	1	2	yes	—
15	C₂×C₄×#10596833	C₄	1	2	yes	complemented
16	C₂×C₄×#10596833	C₄	1	2	yes	complemented
17	C₂×C₈×#64408	C₂²	1	8	yes	—
18	C₄×C₄⋊#64408	C₄	1	2	yes	—
19	C₄×C₄⋊#64408	C₂²	1	2	yes	—
20	C₄×C₂²⋊#64408	C₄	1	2	yes	—
21	C₄×C₂²⋊#64408	C₂²	1	2	yes	—
22	#17989523	C₄	1	2	yes	—
23	C₄²×#64408	C₂²	1	2	yes	—
24	#17989452	C₂²	1	8	yes	—
25	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
26	#17988640	C₄	1	1	yes	characteristic, complemented
27	#17988639	C₄	1	2	yes	complemented
28	#17988638	C₄	1	2	yes	complemented
29	#17988637	C₄	1	2	yes	complemented
30	C₄⋊C₈×D₇₃	C₂²	1	2	yes	—
31	C₂²⋊C₈×D₇₃	C₂²	1	2	yes	—
32	C₄×C₈×D₇₃	C₂²	1	2	yes	—
33	#431×C₇₃	C₄	1	1	yes	characteristic, complemented
34	C₂×#11924036	—	2	8	no	—
35	C₂×#11924036	C₂×C₄	1	4	yes	—
36	C₂×#11924036	C₂³	1	2	yes	—
37	C₂×#11924036	C₂³	1	2	yes	—
38	C₂²×#10596833	C₂×C₄	1	4	yes	—
39	#14556670	C₈	1	16	yes	complemented
40	C₂×C₄⋊#64408	C₂×C₄	1	4	yes	—
41	C₂×C₂²⋊#64408	C₂×C₄	1	4	yes	—
42	C₂×C₄×#64408	C₂×C₄	1	4	yes	—
43	C₂×C₄×#64408	C₂×C₄	1	4	yes	—
44	C₂×C₄×#64408	C₂³	1	4	yes	—
45	C₄×#10596833	C₂×C₄	1	2	yes	—
46	C₄×#10596833	C₂×C₄	1	2	yes	—
47	C₄×#10596833	C₂×C₄	1	4	yes	—
48	C₄×#10596833	C₂×C₄	1	4	yes	—
49	C₄×#10596833	C₂×C₄	1	2	yes	—
50	C₄×#10596833	C₂×C₄	1	2	yes	—
51	C₈×#64408	—	2	16	no	—
52	(C₂×#64408)⋊C₄	C₂×C₄	1	4	yes	—
53	(C₂×#64408)⋊C₄	C₂×C₄	1	4	yes	—
54	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
57	C₂×C₈×D₇₃	C₂³	1	4	yes	—
58	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
61	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
62	C₄²×D₇₃	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	C₂³	1	1	yes	characteristic
68	C₄²×D₇₃	C₂³	1	1	yes	characteristic
69	C₄⋊#10596831	C₂×C₄	1	2	yes	—
70	#14556520	C₂×C₄	1	4	yes	—
71	C₂²⋊#10596831	C₂×C₄	1	2	yes	—
72	#14556503	C₂×C₄	1	4	yes	—
73	C₄×#10596831	C₂×C₄	1	2	yes	—
74	C₈×Dic₇₃	C₂×C₄	1	4	yes	—
75	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
76	C₄⋊C₈×C₇₃	C₂×C₄	1	2	yes	—
77	C₂²⋊C₈×C₇₃	C₂×C₄	1	2	yes	—
78	C₄×C₈×C₇₃	C₂×C₄	1	2	yes	—
79	C₂²×#64408	C₂²×C₄	1	8	yes	—
80	#11924036	—	2	4	no	—
81	#11924036	—	2	8	no	—
82	#11924036	#41	1	8	yes	—
83	C₂×#10596833	—	2	8	no	—
84	C₂×#10596833	C₂²×C₄	1	4	yes	—
85	C₂×#10596833	C₂²×C₄	1	4	yes	—
86	C₄⋊#64408	C₂×C₈	1	16	yes	complemented
87	C₂²⋊#64408	C₂×C₈	1	16	yes	—
88	C₄×#64408	—	2	8	no	—
89	C₄×#64408	—	2	8	no	—
90	C₄×#64408	C₂×C₈	1	16	yes	complemented
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	C₂×C₈	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	C₂²×C₄	1	4	yes	—
111	C₈×D₇₃	—	2	8	no	—
112	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
113	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
114	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
115	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
116	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
117	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
118	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
119	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
120	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
121	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
122	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
123	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₇₃	C₄²	1	1	yes	characteristic
125	C₂²×C₄×C₇₃	C₄²	1	1	yes	characteristic
126	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₈×C₇₃	C₂²×C₄	1	4	yes	—
128	C₄²×C₇₃	C₄²	1	1	yes	characteristic
129	C₄²×C₇₃	C₄²	1	1	yes	characteristic
130	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
132	C₂³×C₇₃	C₂×C₄²	1	1	yes	characteristic
133	C₂²×D₇₃	—	2	2	no	—
134	C₂²×D₇₃	—	2	2	no	—
135	C₂²×D₇₃	C₂×C₄²	1	1	yes	characteristic
136	C₂²×D₇₃	C₂²×C₈	1	4	yes	—
137	C₂²×D₇₃	C₂³×C₄	1	1	yes	characteristic
138	C₂×#64408	—	2	8	no	—
139	C₂×#64408	—	2	8	no	—
140	C₂×#64408	C₂²×C₈	1	16	yes	—
141	C₂×C₄×C₇₃	—	2	2	no	—
142	C₂×C₄×C₇₃	—	2	2	no	—
143	C₂×C₄×C₇₃	C₄×C₈	1	4	yes	complemented
144	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
145	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
146	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
147	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
148	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
149	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
150	C₂×Dic₇₃	—	2	2	no	—
151	C₂×Dic₇₃	—	2	2	no	—
152	C₂×Dic₇₃	C₄×C₈	1	4	yes	complemented
153	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
154	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
155	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
156	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
157	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
158	C₂×Dic₇₃	C₂³×C₄	1	1	yes	characteristic
159	C₄×D₇₃	—	2	2	no	—
160	C₄×D₇₃	—	2	2	no	—
161	C₄×D₇₃	—	2	2	no	—
162	C₄×D₇₃	—	2	2	no	—
163	C₄×D₇₃	—	2	2	no	—
164	C₄×D₇₃	—	2	2	no	—
165	C₄×D₇₃	C₄×C₈	1	4	yes	complemented
166	C₄×D₇₃	C₄×C₈	1	4	yes	complemented
167	C₄×D₇₃	C₂²×C₈	1	4	yes	—
168	C₄×D₇₃	C₂²×C₈	1	4	yes	—
169	C₄×D₇₃	#131	1	4	yes	—
170	C₄×D₇₃	C₂×#41	1	4	yes	—
171	#10596833	—	2	4	no	—
172	#10596833	#117	1	8	yes	complemented
173	C₈×C₇₃	—	2	4	no	—
174	#10596831	—	2	4	no	—
175	C₂²×C₇₃	—	2	1	no	—
176	C₂²×C₇₃	—	2	1	no	—
177	C₂²×C₇₃	C₂×C₄×C₈	1	2	yes	—
178	C₂²×C₇₃	C₂²×C₄²	1	1	yes	characteristic
179	C₂×D₇₃	—	2	1	no	—
180	C₂×D₇₃	—	2	1	no	—
181	C₂×D₇₃	—	2	8	no	—
182	C₂×D₇₃	C₂×C₄×C₈	1	2	yes	—
183	C₂×D₇₃	C₄×#41	1	2	yes	—
184	C₂×D₇₃	C₂³×C₈	1	2	yes	—
185	C₂×D₇₃	C₂×#131	1	2	yes	—
186	#64408	—	2	16	no	—
187	C₄×C₇₃	—	2	1	no	—
188	C₄×C₇₃	—	2	1	no	—
189	C₄×C₇₃	C₂×C₄×C₈	1	2	yes	—
190	C₄×C₇₃	C₂×C₄×C₈	1	2	yes	—
191	C₄×C₇₃	#405	1	2	yes	—
192	C₄×C₇₃	C₄×#41	1	2	yes	—
193	Dic₇₃	—	2	1	no	—
194	Dic₇₃	—	2	1	no	—
195	Dic₇₃	C₂×C₄×C₈	1	2	yes	—
196	Dic₇₃	C₂×C₄×C₈	1	2	yes	—
197	Dic₇₃	#405	1	2	yes	—
198	Dic₇₃	C₂×#117	1	2	yes	—
199	C₈×#117	—	73	1	no	maximal, Sylow
200	C₂×C₇₃	—	2	2	no	—
201	C₂×C₇₃	C₄×#117	1	1	yes	characteristic
202	C₂×C₇₃	C₂²×C₄×C₈	1	1	yes	characteristic
203	C₂×C₇₃	C₂×#405	1	1	yes	characteristic
204	D₇₃	—	2	2	no	—
205	D₇₃	C₈×#41	1	4	yes	—
206	C₂×#431	—	73	1	no	—
207	C₂²×C₄×C₈	—	73	1	no	—
208	C₄×#117	—	73	1	no	—
209	C₈×C₄⋊C₄	—	73	4	no	—
210	C₈×C₂²⋊C₄	—	73	4	no	—
211	#1744	—	73	2	no	—
212	C₄²×C₈	—	73	2	no	—
213	C₇₃	C₈×#117	1	1	yes	characteristic, complemented, Sylow
214	C₂³×C₈	—	73	2	no	—
215	C₂×#117	—	73	2	no	—
216	C₂²×C₄²	—	73	1	no	—
217	#431	—	73	1	no	—
218	#431	—	73	2	no	—
219	#431	—	73	2	no	—
220	#431	—	73	2	no	—
221	#431	#64408	1	1	yes	characteristic, complemented
222	C₂×C₄⋊C₈	—	73	2	no	—
223	C₂×C₂²⋊C₈	—	73	2	no	—
224	C₂×C₄×C₈	—	73	2	no	—
225	C₂×C₄×C₈	—	73	2	no	—
226	C₂×C₄×C₈	—	73	2	no	—
227	C₂×C₄×C₈	—	73	2	no	—
228	C₂×C₄×C₈	—	73	1	no	—
229	C₂×C₄×C₈	—	73	1	no	—
230	C₂×C₄×C₈	—	73	2	no	—
231	C₂×C₄×C₈	—	73	2	no	—
232	C₂×C₄×C₈	—	73	8	no	—
233	C₄×C₄⋊C₄	—	73	2	no	—
234	C₄×C₄⋊C₄	—	73	2	no	—
235	C₄×C₂²⋊C₄	—	73	2	no	—
236	C₄×C₂²⋊C₄	—	73	2	no	—
237	#376	—	73	2	no	—
238	C₄³	—	73	2	no	—
239	#336	—	73	8	no	—
240	C₂³×C₄	—	73	1	no	—
241	C₂³×C₄	—	73	1	no	—
242	C₂³×C₄	—	73	1	no	—
243	C₂²×C₈	—	73	2	no	—
244	C₂²×C₈	—	73	4	no	—
245	C₂²×C₈	—	73	4	no	—
246	C₂²×C₈	—	73	2	no	—
247	C₂²×C₈	—	73	4	no	—
248	C₂²×C₈	—	146	8	no	—
249	#117	—	73	16	no	—
250	C₂×C₄⋊C₄	—	73	4	no	—
251	C₂×C₂²⋊C₄	—	73	4	no	—
252	C₂×C₄²	—	73	4	no	—
253	C₂×C₄²	—	73	1	no	—
254	C₂×C₄²	—	73	1	no	—
255	C₂×C₄²	—	73	1	no	—
256	C₂×C₄²	—	73	1	no	—
257	C₂×C₄²	—	73	1	no	—
258	C₂×C₄²	—	73	1	no	—
259	C₂×C₄²	—	73	1	no	—
260	C₂×C₄²	—	73	1	no	—
261	C₂×C₄²	—	73	1	no	—
262	C₂×C₄²	—	73	1	no	—
263	C₂×C₄²	—	73	1	no	—
264	C₂×C₄²	—	73	4	no	—
265	C₂×C₄²	—	73	4	no	—
266	C₂×C₄²	C₂×#64408	1	1	yes	characteristic
267	C₄⋊C₈	—	73	4	no	—
268	C₄⋊C₈	—	73	2	no	—
269	C₄⋊C₈	C₂×#64408	1	2	yes	—
270	C₂²⋊C₈	—	73	2	no	—
271	C₂²⋊C₈	—	73	4	no	—
272	C₂²⋊C₈	C₂×#64408	1	2	yes	—
273	C₄×C₈	—	73	2	no	—
274	C₄×C₈	—	73	2	no	—
275	C₄×C₈	—	73	4	no	—
276	C₄×C₈	—	73	4	no	—
277	C₄×C₈	—	73	2	no	—
278	C₄×C₈	—	73	2	no	—
279	C₄×C₈	—	73	4	no	—
280	C₄×C₈	—	73	2	no	—
281	C₄×C₈	—	146	16	no	—
282	C₄×C₈	C₂×#64408	1	2	yes	—
283	#95	—	73	4	no	—
284	#95	—	73	4	no	—
285	C₂⁴	—	73	1	no	—
286	C₂²×C₄	—	73	1	no	—
287	C₂²×C₄	—	73	1	no	—
288	C₂²×C₄	—	73	8	no	—
289	C₂²×C₄	—	73	1	no	—
290	C₂²×C₄	—	73	1	no	—
291	C₂²×C₄	—	73	1	no	—
292	C₂²×C₄	—	73	1	no	—
293	C₂²×C₄	—	73	1	no	—
294	C₂²×C₄	—	73	8	no	—
295	C₂²×C₄	—	73	1	no	—
296	C₂²×C₄	—	73	1	no	—
297	C₂²×C₄	—	73	1	no	—
298	C₂²×C₄	—	73	1	no	—
299	C₂²×C₄	—	73	1	no	—
300	C₂²×C₄	—	73	1	no	—
301	C₂²×C₄	—	73	1	no	—
302	C₂²×C₄	—	73	1	no	—
303	C₂²×C₄	—	146	4	no	—
304	C₂²×C₄	—	146	4	no	—
305	C₂²×C₄	C₄×#64408	1	1	yes	characteristic
306	C₂²×C₄	C₄×#64408	1	1	yes	characteristic
307	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
308	C₂×C₈	—	73	4	no	—
309	C₂×C₈	—	73	8	no	—
310	C₂×C₈	—	73	4	no	—
311	C₂×C₈	—	73	4	no	—
312	C₂×C₈	—	146	8	no	—
313	C₂×C₈	—	146	8	no	—
314	C₂×C₈	—	146	8	no	—
315	C₂×C₈	—	146	4	no	—
316	C₂×C₈	C₂²×#64408	1	4	yes	—
317	C₄⋊C₄	—	73	16	no	—
318	C₂²⋊C₄	—	73	16	no	—
319	C₄²	—	73	16	no	—
320	C₄²	—	73	1	no	—
321	C₄²	—	73	1	no	—
322	C₄²	—	73	1	no	—
323	C₄²	—	73	1	no	—
324	C₄²	—	73	1	no	—
325	C₄²	—	73	1	no	—
326	C₄²	—	73	1	no	—
327	C₄²	—	73	1	no	—
328	C₄²	—	73	1	no	—
329	C₄²	—	73	1	no	—
330	C₄²	—	73	1	no	—
331	C₄²	—	73	1	no	—
332	C₄²	—	146	8	no	—
333	C₄²	—	146	8	no	—
334	C₄²	C₄×#64408	1	1	yes	characteristic
335	C₄²	C₄×#64408	1	1	yes	characteristic
336	C₄²	C₂²×#64408	1	1	yes	characteristic
337	C₄²	C₂²×#64408	1	1	yes	characteristic
338	C₂³	—	73	1	no	—
339	C₂³	—	73	1	no	—
340	C₂³	—	73	4	no	—
341	C₂³	—	146	2	no	—
342	C₂³	—	146	2	no	—
343	C₂³	C₂×C₄×#64408	1	1	yes	characteristic
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	73	1	no	—
347	C₂×C₄	—	73	1	no	—
348	C₂×C₄	—	73	1	no	—
349	C₂×C₄	—	73	1	no	—
350	C₂×C₄	—	73	4	no	—
351	C₂×C₄	—	73	4	no	—
352	C₂×C₄	—	73	4	no	—
353	C₂×C₄	—	73	4	no	—
354	C₂×C₄	—	73	4	no	—
355	C₂×C₄	—	73	4	no	—
356	C₂×C₄	—	73	4	no	—
357	C₂×C₄	—	73	16	no	—
358	C₂×C₄	—	73	1	no	—
359	C₂×C₄	—	73	1	no	—
360	C₂×C₄	—	146	2	no	—
361	C₂×C₄	—	146	2	no	—
362	C₂×C₄	—	146	2	no	—
363	C₂×C₄	—	146	2	no	—
364	C₂×C₄	—	146	2	no	—
365	C₂×C₄	—	146	2	no	—
366	C₂×C₄	—	146	8	no	—
367	C₂×C₄	—	146	8	no	—
368	C₂×C₄	—	146	2	no	—
369	C₂×C₄	—	146	2	no	—
370	C₂×C₄	C₈×#64408	1	4	yes	complemented
371	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
372	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
373	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
374	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
375	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
376	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
377	C₈	—	2	4	no	—
378	C₈	—	73	8	no	—
379	C₈	—	146	4	no	—
380	C₈	—	146	4	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	73	2	no	—
384	C₂²	—	73	2	no	—
385	C₂²	—	73	2	no	—
386	C₂²	—	73	2	no	—
387	C₂²	—	146	8	no	—
388	C₂²	—	146	1	no	—
389	C₂²	—	146	1	no	—
390	C₂²	C₂×C₈×#64408	1	2	yes	—
391	C₂²	C₂²×C₄×#64408	1	1	yes	characteristic
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	73	2	no	—
395	C₄	—	73	2	no	—
396	C₄	—	73	2	no	—
397	C₄	—	73	2	no	—
398	C₄	—	146	16	no	—
399	C₄	—	146	1	no	—
400	C₄	—	146	1	no	—
401	C₄	C₂×C₈×#64408	1	2	yes	—
402	C₄	C₂×C₈×#64408	1	2	yes	—
403	C₄	#17989553	1	2	yes	—
404	C₄	#41×#64408	1	2	yes	—
405	C₂	—	2	2	no	—
406	C₂	—	73	4	no	—
407	C₂	—	146	2	no	—
408	C₂	#117×#64408	1	1	yes	characteristic
409	C₂	C₂²×C₈×#64408	1	1	yes	characteristic
410	C₂	C₂×#17989553	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂²×#64408
commutator	C₂×C₇₃	C₂²×C₄×C₈
Frattini	C₂×C₄	C₂³×#64408
Fitting	#431×C₇₃	C₄
socle	C₂²×C₇₃	C₂²×C₄²
prime radical	C₂³×D₇₃	C₂²×C₄
cosocle	C₂×C₄×D₇₃	C₂⁴
hypercenter	#431	#64408
hypocenter	C₇₃	C₈×#117
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄² ◁ #431

Complements

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

N	H ≅ G/N	type
3. #22625724	C₂	semidirect
5. #22625644	C₂	semidirect
6. C₄×C₈×#64408	C₂	semidirect
10. C₄×#11924036	C₄	semidirect
11. C₄×#11924036	C₄	semidirect
15. C₂×C₄×#10596833	C₄	semidirect
16. C₂×C₄×#10596833	C₄	semidirect
26. #17988640	C₄	semidirect
27. #17988639	C₄	semidirect
28. #17988638	C₄	semidirect
29. #17988637	C₄	semidirect
33. #431×C₇₃	C₄	semidirect
39. #14556670	C₈	semidirect
86. C₄⋊#64408	C₂×C₈	semidirect
90. C₄×#64408	C₂×C₈	semidirect
143. C₂×C₄×C₇₃	C₄×C₈	semidirect
152. C₂×Dic₇₃	C₄×C₈	semidirect
165. C₄×D₇₃	C₄×C₈	semidirect
166. C₄×D₇₃	C₄×C₈	semidirect
172. #10596833	#117	semidirect
213. C₇₃	C₈×#117	semidirect
221. #431	#64408	semidirect
370. C₂×C₄	C₈×#64408	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#11924036	2
C₄×#14556670	2
#22625724	2
#22625666	2
#22625644	2
C₄×C₈×#64408	2
#431×D₇₃	2
C₈×#117	73