Subgroups — #34020300

Order 18688.

1222 conjugacy classes of subgroups.

The subgroup lattice has 430 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	C₂×C₄²×#64408	C₂	1	1	yes	maximal, characteristic
3	#22625718	C₂	1	4	yes	maximal, complemented
4	#22625659	C₂	1	4	yes	maximal
5	#22625644	C₂	1	2	yes	maximal, complemented
6	C₄×#14556645	C₂	1	2	yes	maximal, complemented
7	#431×D₇₃	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₄×#64408	C₄	1	2	yes	—
9	C₂²×C₄×#64408	C₄	1	2	yes	—
10	C₂²×C₄×#64408	C₂²	1	2	yes	—
11	#17989606	C₄	1	2	yes	complemented
12	#17989605	C₄	1	2	yes	complemented
13	#17989604	C₄	1	2	yes	complemented
14	#17989603	C₄	1	2	yes	complemented
15	#17989588	C₂²	1	2	yes	—
16	#17989555	C₂²	1	2	yes	—
17	C₂×#14556645	C₂²	1	8	yes	—
18	C₄×#11924036	C₂²	1	2	yes	—
19	C₄²×#64408	C₄	1	2	yes	—
20	C₄²×#64408	C₄	1	2	yes	—
21	C₄²×#64408	C₂²	1	1	yes	characteristic
22	C₄²×#64408	C₂²	1	1	yes	characteristic
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	C₂³×#64408	C₂×C₄	1	4	yes	—
35	C₂×#11924036	C₂³	1	4	yes	—
36	C₂×C₄×#64408	—	2	8	no	—
37	C₂×C₄×#64408	—	2	8	no	—
38	C₂×C₄×#64408	—	2	8	no	—
39	C₂×C₄×#64408	C₂×C₄	1	4	yes	—
40	C₂×C₄×#64408	C₂×C₄	1	2	yes	—
41	C₂×C₄×#64408	C₂×C₄	1	2	yes	—
42	C₂×C₄×#64408	C₂×C₄	1	4	yes	—
43	C₂×C₄×#64408	C₂×C₄	1	2	yes	—
44	C₂×C₄×#64408	C₂×C₄	1	4	yes	—
45	C₂×C₄×#64408	C₂×C₄	1	2	yes	—
46	C₂×C₄×#64408	C₂³	1	2	yes	—
47	C₂×C₄×#64408	C₂³	1	2	yes	—
48	#14556658	C₂×C₄	1	4	yes	complemented
49	C₄⋊#10596833	C₂×C₄	1	4	yes	complemented
50	#14556648	C₂×C₄	1	4	yes	—
51	C₂²⋊#10596833	C₂×C₄	1	4	yes	—
52	#14556645	—	2	16	no	—
53	C₄×#10596833	C₂×C₄	1	4	yes	complemented
54	C₄×#10596833	C₂×C₄	1	4	yes	complemented
55	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
58	C₂×C₈×D₇₃	C₂³	1	4	yes	—
59	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×Dic₇₃	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	C₂×C₄	1	1	yes	characteristic
68	C₄²×D₇₃	C₂³	1	1	yes	characteristic
69	C₄²×D₇₃	C₂³	1	1	yes	characteristic
70	C₄⋊#10596831	C₂×C₄	1	2	yes	complemented
71	#14556520	C₂×C₄	1	4	yes	complemented
72	C₂²⋊#10596831	C₂×C₄	1	2	yes	—
73	#14556503	C₂×C₄	1	4	yes	—
74	C₄×#10596831	C₂×C₄	1	2	yes	complemented
75	C₈×Dic₇₃	C₂×C₄	1	4	yes	complemented
76	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
77	C₄⋊C₈×C₇₃	C₂×C₄	1	2	yes	complemented
78	C₂²⋊C₈×C₇₃	C₂×C₄	1	2	yes	—
79	C₄×C₈×C₇₃	C₂×C₄	1	2	yes	complemented
80	C₂²×#64408	—	2	8	no	—
81	C₂²×#64408	—	2	8	no	—
82	C₂²×#64408	—	2	8	no	—
83	C₂²×#64408	C₂²×C₄	1	4	yes	—
84	C₂²×#64408	C₂²×C₄	1	4	yes	—
85	#11924036	—	2	8	no	—
86	C₂×#10596833	C₂²×C₄	1	8	yes	—
87	C₄×#64408	—	2	8	no	—
88	C₄×#64408	—	2	8	no	—
89	C₄×#64408	—	2	4	no	—
90	C₄×#64408	—	2	8	no	—
91	C₄×#64408	—	2	4	no	—
92	C₄×#64408	—	2	4	no	—
93	C₄×#64408	—	2	4	no	—
94	C₄×#64408	M₁₆	1	8	yes	—
95	C₄×#64408	#41	1	8	yes	—
96	C₂³×D₇₃	C₂²×C₄	1	1	yes	characteristic
97	C₂²×Dic₇₃	C₄²	1	1	yes	characteristic
98	C₂²×Dic₇₃	C₄²	1	1	yes	characteristic
99	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₄×D₇₃	—	2	4	no	—
101	C₂×C₄×D₇₃	—	2	4	no	—
102	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
103	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
104	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
105	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
106	C₂×C₄×D₇₃	M₁₆	1	8	yes	—
107	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₇₃	C₂²×C₄	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×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
115	C₂×#10596831	C₂²×C₄	1	4	yes	—
116	C₈×D₇₃	—	2	8	no	—
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	C₂²×C₄	1	4	yes	—
133	C₄²×C₇₃	C₄²	1	1	yes	characteristic
134	C₄²×C₇₃	C₄²	1	1	yes	characteristic
135	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
136	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
137	C₂³×C₇₃	C₂×C₄²	1	1	yes	characteristic
138	C₂²×D₇₃	—	2	2	no	—
139	C₂²×D₇₃	—	2	2	no	—
140	C₂²×D₇₃	C₂×C₄²	1	1	yes	characteristic
141	C₂²×D₇₃	C₂×M₁₆	1	4	yes	—
142	C₂²×D₇₃	C₂³×C₄	1	1	yes	characteristic
143	C₂×#64408	—	2	32	no	—
144	C₂×#64408	—	2	4	no	—
145	C₂×#64408	—	2	4	no	—
146	C₂×#64408	—	2	4	no	—
147	C₂×#64408	—	2	4	no	—
148	C₂×#64408	#117	1	8	yes	—
149	C₂×#64408	C₂×M₁₆	1	8	yes	—
150	C₂×C₄×C₇₃	—	2	2	no	—
151	C₂×C₄×C₇₃	—	2	2	no	—
152	C₂×C₄×C₇₃	#97	1	4	yes	complemented
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	C₂×C₄²	1	1	yes	characteristic
157	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
158	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
159	C₂×Dic₇₃	—	2	2	no	—
160	C₂×Dic₇₃	—	2	2	no	—
161	C₂×Dic₇₃	#97	1	4	yes	complemented
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	C₂×C₄²	1	1	yes	characteristic
166	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
167	C₂×Dic₇₃	C₂³×C₄	1	1	yes	characteristic
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	—	2	2	no	—
173	C₄×D₇₃	—	2	2	no	—
174	C₄×D₇₃	#97	1	4	yes	complemented
175	C₄×D₇₃	#97	1	4	yes	complemented
176	C₄×D₇₃	C₂×M₁₆	1	4	yes	—
177	C₄×D₇₃	C₂×M₁₆	1	4	yes	—
178	C₄×D₇₃	C₂×M₁₆	1	4	yes	—
179	C₄×D₇₃	C₂×#41	1	4	yes	—
180	#10596833	—	2	8	no	—
181	C₈×C₇₃	—	2	4	no	—
182	#10596831	—	2	4	no	—
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	C₂×#117	1	2	yes	—
192	C₂×D₇₃	C₂²×M₁₆	1	2	yes	—
193	C₂×D₇₃	C₂²×M₁₆	1	2	yes	—
194	#64408	—	2	8	no	—
195	#64408	—	2	8	no	—
196	C₄×C₇₃	—	2	1	no	—
197	C₄×C₇₃	—	2	1	no	—
198	C₄×C₇₃	C₂×#97	1	2	yes	—
199	C₄×C₇₃	C₂×#97	1	2	yes	—
200	C₄×C₇₃	C₄×M₁₆	1	2	yes	—
201	C₄×C₇₃	C₄×#41	1	2	yes	—
202	Dic₇₃	—	2	1	no	—
203	Dic₇₃	—	2	1	no	—
204	Dic₇₃	C₂×#97	1	2	yes	—
205	Dic₇₃	C₂×#97	1	2	yes	—
206	Dic₇₃	C₄×M₁₆	1	2	yes	—
207	Dic₇₃	C₄×#41	1	2	yes	—
208	#20463	—	73	1	no	maximal, Sylow
209	C₂×C₇₃	—	2	2	no	—
210	C₂×C₇₃	C₄×#117	1	1	yes	characteristic
211	C₂×C₇₃	C₂²×#97	1	1	yes	characteristic
212	C₂×C₇₃	C₂×C₄×M₁₆	1	1	yes	characteristic
213	D₇₃	—	2	2	no	—
214	D₇₃	#2920	1	4	yes	—
215	C₂×#431	—	73	1	no	—
216	C₂×#431	—	73	1	no	—
217	C₂×C₄³	—	73	1	no	—
218	#1767	—	73	4	no	—
219	#1749	—	73	4	no	—
220	#1744	—	73	2	no	—
221	C₄×#97	—	73	2	no	—
222	C₇₃	#20463	1	1	yes	characteristic, complemented, Sylow
223	C₂²×C₄²	—	73	1	no	—
224	C₂²×C₄²	—	73	2	no	—
225	C₂²×C₄²	—	73	2	no	—
226	C₂²×C₄²	—	73	2	no	—
227	#431	—	73	2	no	—
228	#431	—	73	2	no	—
229	#431	—	73	2	no	—
230	#431	—	73	2	no	—
231	#431	—	73	1	no	—
232	#431	—	73	2	no	—
233	#431	—	73	2	no	—
234	#431	—	73	2	no	—
235	#431	#64408	1	1	yes	characteristic, complemented
236	C₂×C₄⋊C₈	—	73	2	no	—
237	C₂×C₄⋊C₈	—	73	2	no	—
238	C₂×C₂²⋊C₈	—	73	2	no	—
239	C₂×C₂²⋊C₈	—	73	2	no	—
240	C₂×#97	—	73	8	no	—
241	C₂×C₄×C₈	—	73	2	no	—
242	C₂×C₄×C₈	—	73	2	no	—
243	C₄³	—	73	2	no	—
244	C₄³	—	73	2	no	—
245	C₄³	—	73	1	no	—
246	C₄³	—	73	1	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	C₂³×C₄	—	73	4	no	—
253	C₂²×C₈	—	73	4	no	—
254	C₂²×C₈	—	73	4	no	—
255	C₂×C₄²	—	73	2	no	—
256	C₂×C₄²	—	73	2	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	1	no	—
265	C₂×C₄²	—	73	1	no	—
266	C₂×C₄²	—	73	1	no	—
267	C₂×C₄²	—	73	1	no	—
268	C₂×C₄²	—	73	2	no	—
269	C₂×C₄²	—	73	2	no	—
270	C₂×C₄²	—	73	2	no	—
271	C₂×C₄²	—	73	2	no	—
272	C₂×C₄²	—	73	4	no	—
273	C₂×C₄²	—	73	4	no	—
274	C₂×C₄²	—	73	4	no	—
275	C₂×C₄²	—	146	8	no	—
276	C₂×C₄²	—	146	8	no	—
277	C₂×C₄²	—	146	8	no	—
278	C₂×C₄²	C₂×#64408	1	1	yes	characteristic
279	C₄⋊C₈	—	73	4	no	—
280	C₄⋊C₈	—	73	4	no	—
281	C₄⋊C₈	—	73	4	no	—
282	C₄⋊C₈	—	73	2	no	—
283	C₄⋊C₈	C₂×#64408	1	2	yes	complemented
284	C₂²⋊C₈	—	73	4	no	—
285	C₂²⋊C₈	—	73	4	no	—
286	C₂²⋊C₈	—	73	2	no	—
287	C₂²⋊C₈	—	73	4	no	—
288	C₂²⋊C₈	C₂×#64408	1	2	yes	—
289	#97	—	146	16	no	—
290	C₄×C₈	—	73	4	no	—
291	C₄×C₈	—	73	4	no	—
292	C₄×C₈	—	73	4	no	—
293	C₄×C₈	—	73	2	no	—
294	C₄×C₈	C₂×#64408	1	2	yes	complemented
295	C₂⁴	—	73	1	no	—
296	C₂²×C₄	—	73	1	no	—
297	C₂²×C₄	—	73	1	no	—
298	C₂²×C₄	—	73	8	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	—	73	1	no	—
304	C₂²×C₄	—	73	4	no	—
305	C₂²×C₄	—	73	4	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	—	146	4	no	—
315	C₂²×C₄	—	146	4	no	—
316	C₂²×C₄	—	146	8	no	—
317	C₂²×C₄	—	146	8	no	—
318	C₂²×C₄	—	146	8	no	—
319	C₂²×C₄	C₄×#64408	1	1	yes	characteristic
320	C₂²×C₄	C₄×#64408	1	1	yes	characteristic
321	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
322	C₂×C₈	—	73	8	no	—
323	C₂×C₈	—	73	4	no	—
324	C₂×C₈	—	146	8	no	—
325	C₂×C₈	—	146	8	no	—
326	C₂×C₈	C₂²×#64408	1	4	yes	—
327	C₄²	—	73	8	no	—
328	C₄²	—	73	8	no	—
329	C₄²	—	73	1	no	—
330	C₄²	—	73	1	no	—
331	C₄²	—	73	1	no	—
332	C₄²	—	73	1	no	—
333	C₄²	—	73	1	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	—	146	4	no	—
342	C₄²	—	146	4	no	—
343	C₄²	—	146	4	no	—
344	C₄²	—	146	8	no	—
345	C₄²	—	146	4	no	—
346	C₄²	—	146	8	no	—
347	C₄²	—	146	8	no	—
348	C₄²	C₄×#64408	1	1	yes	characteristic
349	C₄²	C₄×#64408	1	1	yes	characteristic
350	C₄²	C₂²×#64408	1	1	yes	characteristic
351	C₄²	C₂²×#64408	1	1	yes	characteristic
352	C₂³	—	73	1	no	—
353	C₂³	—	73	1	no	—
354	C₂³	—	73	4	no	—
355	C₂³	—	146	2	no	—
356	C₂³	—	146	2	no	—
357	C₂³	C₂×C₄×#64408	1	1	yes	characteristic
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	73	1	no	—
361	C₂×C₄	—	73	1	no	—
362	C₂×C₄	—	73	1	no	—
363	C₂×C₄	—	73	1	no	—
364	C₂×C₄	—	73	4	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	8	no	—
372	C₂×C₄	—	73	8	no	—
373	C₂×C₄	—	73	1	no	—
374	C₂×C₄	—	73	1	no	—
375	C₂×C₄	—	146	2	no	—
376	C₂×C₄	—	146	2	no	—
377	C₂×C₄	—	146	2	no	—
378	C₂×C₄	—	146	2	no	—
379	C₂×C₄	—	146	2	no	—
380	C₂×C₄	—	146	2	no	—
381	C₂×C₄	—	146	4	no	—
382	C₂×C₄	—	146	4	no	—
383	C₂×C₄	—	146	4	no	—
384	C₂×C₄	—	146	4	no	—
385	C₂×C₄	—	146	32	no	—
386	C₂×C₄	—	146	2	no	—
387	C₂×C₄	—	146	2	no	—
388	C₂×C₄	#14556645	1	4	yes	complemented
389	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
390	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
391	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
392	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
393	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
394	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
395	C₈	—	2	4	no	—
396	C₈	—	146	8	no	—
397	C₈	—	146	4	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	73	2	no	—
401	C₂²	—	73	2	no	—
402	C₂²	—	73	2	no	—
403	C₂²	—	73	2	no	—
404	C₂²	—	146	8	no	—
405	C₂²	—	146	1	no	—
406	C₂²	—	146	1	no	—
407	C₂²	C₂×#14556645	1	2	yes	—
408	C₂²	C₂²×C₄×#64408	1	1	yes	characteristic
409	C₄	—	2	1	no	—
410	C₄	—	2	1	no	—
411	C₄	—	73	2	no	—
412	C₄	—	73	2	no	—
413	C₄	—	73	2	no	—
414	C₄	—	73	2	no	—
415	C₄	—	146	8	no	—
416	C₄	—	146	8	no	—
417	C₄	—	146	1	no	—
418	C₄	—	146	1	no	—
419	C₄	C₂×#14556645	1	2	yes	—
420	C₄	C₂×#14556645	1	2	yes	—
421	C₄	M₁₆×#64408	1	2	yes	—
422	C₄	#41×#64408	1	2	yes	—
423	C₂	—	2	2	no	—
424	C₂	—	73	4	no	—
425	C₂	—	146	2	no	—
426	C₂	#117×#64408	1	1	yes	characteristic
427	C₂	C₂²×#14556645	1	1	yes	characteristic
428	C₂	C₂×M₁₆×#64408	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂²×#64408
commutator, socle	C₂²×C₇₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#64408
Fitting	#431×C₇₃	C₄
prime radical	C₂³×D₇₃	C₂²×C₄
cosocle	C₂×C₄×D₇₃	C₂⁴
hypercenter	#431	#64408
hypocenter	C₇₃	#20463
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄² ◁ #431

Complements

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

N	H ≅ G/N	type
3. #22625718	C₂	semidirect
5. #22625644	C₂	semidirect
6. C₄×#14556645	C₂	semidirect
11. #17989606	C₄	semidirect
12. #17989605	C₄	semidirect
13. #17989604	C₄	semidirect
14. #17989603	C₄	semidirect
26. #17988640	C₄	semidirect
27. #17988639	C₄	semidirect
28. #17988638	C₄	semidirect
29. #17988637	C₄	semidirect
33. #431×C₇₃	C₄	semidirect
48. #14556658	C₂×C₄	semidirect
49. C₄⋊#10596833	C₂×C₄	semidirect
53. C₄×#10596833	C₂×C₄	semidirect
54. C₄×#10596833	C₂×C₄	semidirect
70. C₄⋊#10596831	C₂×C₄	semidirect
71. #14556520	C₂×C₄	semidirect
74. C₄×#10596831	C₂×C₄	semidirect
75. C₈×Dic₇₃	C₂×C₄	semidirect
77. C₄⋊C₈×C₇₃	C₂×C₄	semidirect
79. C₄×C₈×C₇₃	C₂×C₄	semidirect
152. C₂×C₄×C₇₃	#97	semidirect
161. C₂×Dic₇₃	#97	semidirect
174. C₄×D₇₃	#97	semidirect
175. C₄×D₇₃	#97	semidirect
222. C₇₃	#20463	semidirect
235. #431	#64408	semidirect
283. C₄⋊C₈	C₂×#64408	semidirect
294. C₄×C₈	C₂×#64408	semidirect
388. C₂×C₄	#14556645	semidirect

Maximal subgroups

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

subgroup	index
#22626595	2
C₂×C₄²×#64408	2
#22625718	2
#22625659	2
#22625644	2
C₄×#14556645	2
#431×D₇₃	2
#20463	73