Subgroups — #33055143

Order 18688.

640 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22618563	C₂	1	1	yes	maximal, characteristic
2	C₂×#17988643	C₂	1	1	yes	maximal, characteristic
3	#431×D₇₃	C₂	1	1	yes	maximal, characteristic
4	#22608710	C₂	1	4	yes	maximal, complemented
5	#22608706	C₂	1	1	yes	maximal, characteristic, complemented
6	#22608703	C₂	1	1	yes	maximal, characteristic, complemented
7	#22608701	C₂	1	1	yes	maximal, characteristic, complemented
8	#22608693	C₂	1	4	yes	maximal, complemented
9	C₇₃×#1571	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
11	#17988643	—	2	1	no	—
12	#17988643	—	2	1	no	—
13	#17988643	—	2	1	no	—
14	#17988643	C₂²	1	2	yes	—
15	#17988643	C₂²	1	2	yes	—
16	#17988643	C₂²	1	2	yes	—
17	#17988640	C₂²	1	1	yes	characteristic
18	#17988639	—	2	1	no	—
19	#17988639	C₄	1	2	yes	—
20	#17988639	C₂²	1	2	yes	—
21	#17988638	C₂²	1	2	yes	—
22	#17988637	C₄	1	2	yes	—
23	#17988611	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic
25	C₄⋊C₈×D₇₃	C₄	1	2	yes	—
26	#17988550	—	2	1	no	—
27	C₂×#14556503	—	2	1	no	—
28	C₂²⋊C₈×D₇₃	C₄	1	2	yes	—
29	M₁₆×Dic₇₃	—	2	1	no	—
30	C₂×#14556501	—	2	1	no	—
31	C₄×C₈×D₇₃	C₂²	1	2	yes	—
32	#17988340	C₂²	1	4	yes	complemented
33	#17988337	C₂²	1	4	yes	complemented
34	#17988337	C₂²	1	4	yes	complemented
35	#431×C₇₃	C₂²	1	1	yes	characteristic
36	#423×C₇₃	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
38	#335×C₇₃	C₂²	1	4	yes	complemented
39	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄×D₇₃	D₄	1	1	yes	characteristic
41	C₂²×C₄×D₇₃	Q₈	1	1	yes	characteristic
42	C₂×#11924012	—	2	1	no	—
43	C₂²×#10596831	—	2	1	no	—
44	C₂×C₈×D₇₃	C₂×C₄	1	4	yes	—
45	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₇₃	D₄	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	—	2	1	no	—
57	C₄⋊#10596831	—	2	1	no	—
58	C₄⋊#10596831	C₂×C₄	1	2	yes	—
59	C₄⋊#10596831	C₂³	1	2	yes	—
60	C₄⋊#10596831	C₂³	1	2	yes	—
61	#14556520	C₂×C₄	1	4	yes	—
62	C₂²⋊#10596831	C₂×C₄	1	2	yes	—
63	#14556503	—	2	2	no	—
64	#14556503	—	2	2	no	—
65	#14556503	—	2	2	no	—
66	#14556503	—	2	2	no	—
67	#14556503	C₂×C₄	1	4	yes	—
68	#14556501	—	2	2	no	—
69	#14556501	—	2	2	no	—
70	#14556501	—	2	2	no	—
71	C₄×#10596831	C₂³	1	2	yes	—
72	C₈×Dic₇₃	—	2	2	no	—
73	C₈×Dic₇₃	C₂×C₄	1	4	yes	—
74	C₂×M₁₆×C₇₃	—	2	1	no	—
75	C₂²×C₈×C₇₃	—	2	1	no	—
76	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
77	C₄⋊C₈×C₇₃	—	2	1	no	—
78	C₄⋊C₈×C₇₃	—	2	1	no	—
79	C₄⋊C₈×C₇₃	C₂×C₄	1	2	yes	—
80	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
81	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
82	C₂²⋊C₈×C₇₃	C₂×C₄	1	2	yes	—
83	C₄×C₈×C₇₃	C₂³	1	2	yes	—
84	C₂³×D₇₃	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
88	C₂×C₄×D₇₃	—	2	2	no	—
89	C₂×C₄×D₇₃	—	2	2	no	—
90	C₂×C₄×D₇₃	—	4	2	no	—
91	C₂×C₄×D₇₃	—	4	2	no	—
92	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
93	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
94	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
95	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
96	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
97	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
101	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
102	C₂×C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
103	C₂×C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
104	#11924012	—	4	2	no	—
105	C₂×#10596831	—	2	2	no	—
106	C₂×#10596831	—	2	2	no	—
107	C₂×#10596831	—	4	2	no	—
108	C₂×#10596831	C₂²×C₄	1	4	yes	—
109	C₈×D₇₃	—	4	4	no	—
110	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
111	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
112	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
113	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
114	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
115	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
116	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
117	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
118	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
119	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
120	C₄×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
121	C₄×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
122	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
125	M₁₆×C₇₃	—	4	2	no	—
126	C₂×C₈×C₇₃	—	2	2	no	—
127	C₂×C₈×C₇₃	—	2	2	no	—
128	C₂×C₈×C₇₃	—	4	2	no	—
129	C₂×C₈×C₇₃	C₂²×C₄	1	4	yes	—
130	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₇₃	C₂×Q₈	1	1	yes	characteristic
133	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
134	C₂³×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂²×D₇₃	—	2	2	no	—
136	C₂²×D₇₃	—	2	2	no	—
137	C₂²×D₇₃	—	4	1	no	—
138	C₂²×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂²×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₇₃	—	2	2	no	—
141	C₂×C₄×C₇₃	—	4	1	no	—
142	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₇₃	#135	1	2	yes	—
146	C₂×C₄×C₇₃	#135	1	2	yes	—
147	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
148	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
150	C₂×Dic₇₃	—	2	2	no	—
151	C₂×Dic₇₃	—	4	1	no	—
152	C₂×Dic₇₃	—	4	1	no	—
153	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×Dic₇₃	C₂×C₄⋊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	1	no	—
164	C₄×D₇₃	—	2	1	no	—
165	C₄×D₇₃	—	2	1	no	—
166	C₄×D₇₃	—	2	1	no	—
167	C₄×D₇₃	—	2	2	no	—
168	C₄×D₇₃	—	2	2	no	—
169	C₄×D₇₃	—	4	1	no	—
170	C₄×D₇₃	—	4	1	no	—
171	C₄×D₇₃	—	4	1	no	—
172	C₄×D₇₃	—	4	1	no	—
173	C₈×C₇₃	—	2	4	no	—
174	C₈×C₇₃	—	4	2	no	—
175	C₈×C₇₃	—	4	2	no	—
176	#10596831	—	2	4	no	—
177	#10596831	—	4	2	no	—
178	#10596831	—	4	2	no	—
179	C₂²×C₇₃	—	2	1	no	—
180	C₂²×C₇₃	—	2	1	no	—
181	C₂²×C₇₃	#427	1	2	yes	—
182	C₂²×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
183	C₂×D₇₃	—	2	1	no	—
184	C₂×D₇₃	—	2	1	no	—
185	C₂×D₇₃	—	2	1	no	—
186	C₂×D₇₃	—	2	1	no	—
187	C₂×D₇₃	—	2	1	no	—
188	C₂×D₇₃	—	4	4	no	—
189	C₂×D₇₃	#430	1	2	yes	—
190	C₄×C₇₃	—	2	1	no	—
191	C₄×C₇₃	—	2	1	no	—
192	C₄×C₇₃	—	2	1	no	—
193	C₄×C₇₃	#427	1	2	yes	—
194	C₄×C₇₃	#568	1	2	yes	—
195	C₄×C₇₃	C₂×#135	1	1	yes	characteristic
196	C₄×C₇₃	C₂×#135	1	1	yes	characteristic
197	Dic₇₃	—	2	1	no	—
198	Dic₇₃	—	2	1	no	—
199	Dic₇₃	—	2	1	no	—
200	Dic₇₃	—	2	1	no	—
201	Dic₇₃	—	2	1	no	—
202	Dic₇₃	—	2	1	no	—
203	#17816	—	73	1	no	maximal, Sylow
204	C₂×C₇₃	—	2	2	no	—
205	C₂×C₇₃	#2905	1	1	yes	characteristic
206	C₂×C₇₃	C₂×#427	1	1	yes	characteristic
207	C₂×C₇₃	C₂×#430	1	1	yes	characteristic
208	D₇₃	—	2	2	no	—
209	D₇₃	—	4	1	no	—
210	#2920	—	73	1	no	—
211	C₂×#432	—	73	1	no	—
212	C₂×#431	—	73	1	no	—
213	#1572	—	73	4	no	—
214	#1571	—	73	1	no	—
215	#1571	D₇₃	1	1	yes	characteristic, complemented
216	#1570	—	73	1	no	—
217	#1570	—	73	1	no	—
218	#1568	—	73	4	no	—
219	C₇₃	#17816	1	1	yes	characteristic, complemented, Sylow
220	C₂²×C₄²	—	73	1	no	—
221	#432	—	73	2	no	—
222	#432	—	73	2	no	—
223	#432	—	73	2	no	—
224	#432	—	146	1	no	—
225	#432	—	146	1	no	—
226	#432	—	146	1	no	—
227	#431	—	73	1	no	—
228	#431	—	73	2	no	—
229	#431	—	73	2	no	—
230	#431	—	73	2	no	—
231	#431	—	73	2	no	—
232	#431	—	146	1	no	—
233	#431	C₂×D₇₃	1	1	yes	characteristic
234	#423	—	73	1	no	—
235	#423	C₂×D₇₃	1	1	yes	characteristic
236	C₂×C₄⋊C₈	—	73	2	no	—
237	C₂×C₄⋊C₈	—	73	1	no	—
238	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
239	#407	—	146	1	no	—
240	C₂×C₂²⋊C₈	—	73	2	no	—
241	C₂×C₂²⋊C₈	—	146	1	no	—
242	C₄×M₁₆	—	146	1	no	—
243	C₂×#97	—	146	1	no	—
244	C₂×C₄×C₈	—	73	2	no	—
245	#335	—	73	4	no	—
246	#335	C₂×D₇₃	1	4	yes	complemented
247	#334	—	73	4	no	—
248	#334	—	73	4	no	—
249	C₂³×C₄	—	73	1	no	—
250	C₂³×C₄	—	73	1	no	—
251	C₂³×C₄	—	73	1	no	—
252	C₂×M₁₆	—	2	1	no	—
253	C₂×M₁₆	—	146	1	no	—
254	C₂²×C₈	—	2	1	no	—
255	C₂²×C₈	—	73	4	no	—
256	C₂²×C₈	—	146	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	1	no	—
265	C₂×C₄²	—	73	1	no	—
266	C₂×C₄²	—	73	1	no	—
267	C₂×C₄²	—	73	1	no	—
268	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	2	1	no	—
271	C₄⋊C₈	—	73	4	no	—
272	C₄⋊C₈	—	73	2	no	—
273	C₄⋊C₈	—	73	2	no	—
274	C₄⋊C₈	—	73	2	no	—
275	C₄⋊C₈	—	146	1	no	—
276	C₄⋊C₈	—	146	1	no	—
277	C₄⋊C₈	C₄×D₇₃	1	2	yes	—
278	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
279	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
280	C₂²⋊C₈	—	73	2	no	—
281	C₂²⋊C₈	—	73	4	no	—
282	C₂²⋊C₈	—	146	2	no	—
283	C₂²⋊C₈	—	146	2	no	—
284	C₂²⋊C₈	—	146	2	no	—
285	C₂²⋊C₈	—	146	2	no	—
286	C₂²⋊C₈	C₄×D₇₃	1	2	yes	—
287	#97	—	146	2	no	—
288	#97	—	146	2	no	—
289	#97	—	146	2	no	—
290	C₄×C₈	—	73	4	no	—
291	C₄×C₈	—	73	2	no	—
292	C₄×C₈	—	146	2	no	—
293	C₄×C₈	C₂²×D₇₃	1	2	yes	—
294	C₂⁴	—	73	1	no	—
295	C₂²×C₄	—	292	2	no	—
296	C₂²×C₄	—	292	2	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	—	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	—	146	2	no	—
313	C₂²×C₄	—	146	2	no	—
314	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
315	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
316	C₂²×C₄	Q₈×D₇₃	1	1	yes	characteristic
317	M₁₆	—	4	2	no	—
318	M₁₆	—	292	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	4	2	no	—
322	C₂×C₈	—	292	4	no	—
323	C₂×C₈	—	292	2	no	—
324	C₂×C₈	—	73	4	no	—
325	C₂×C₈	—	146	2	no	—
326	C₂×C₈	—	146	2	no	—
327	C₂×C₈	C₂×C₄×D₇₃	1	4	yes	—
328	C₄²	—	73	1	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	C₂×C₄×D₇₃	1	1	yes	characteristic
341	C₄²	D₄×D₇₃	1	1	yes	characteristic
342	C₄²	Q₈×D₇₃	1	1	yes	characteristic
343	C₄²	C₂³×D₇₃	1	1	yes	characteristic
344	C₂³	—	292	1	no	—
345	C₂³	—	73	1	no	—
346	C₂³	—	73	1	no	—
347	C₂³	—	146	2	no	—
348	C₂³	—	146	2	no	—
349	C₂³	C₄⋊C₄×D₇₃	1	1	yes	characteristic
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	292	1	no	—
353	C₂×C₄	—	292	1	no	—
354	C₂×C₄	—	292	1	no	—
355	C₂×C₄	—	292	1	no	—
356	C₂×C₄	—	292	1	no	—
357	C₂×C₄	—	292	1	no	—
358	C₂×C₄	—	73	1	no	—
359	C₂×C₄	—	73	1	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	—	146	2	no	—
365	C₂×C₄	—	146	2	no	—
366	C₂×C₄	—	146	2	no	—
367	C₂×C₄	—	146	2	no	—
368	C₂×C₄	—	146	2	no	—
369	C₂×C₄	—	146	2	no	—
370	C₂×C₄	—	146	2	no	—
371	C₂×C₄	—	146	1	no	—
372	C₂×C₄	—	146	1	no	—
373	C₂×C₄	—	146	1	no	—
374	C₂×C₄	—	146	1	no	—
375	C₂×C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
376	C₂×C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
377	C₂×C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
378	C₂×C₄	#14556610	1	2	yes	—
379	C₂×C₄	#14556614	1	2	yes	—
380	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
381	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
382	C₂×C₄	C₂×Q₈×D₇₃	1	1	yes	characteristic
383	C₈	—	2	4	no	—
384	C₈	—	4	2	no	—
385	C₈	—	4	2	no	—
386	C₈	—	292	2	no	—
387	C₈	—	292	2	no	—
388	C₈	—	146	4	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	292	4	no	—
392	C₂²	—	73	2	no	—
393	C₂²	—	146	1	no	—
394	C₂²	—	146	1	no	—
395	C₂²	—	146	1	no	—
396	C₂²	—	146	1	no	—
397	C₂²	—	146	1	no	—
398	C₂²	#17988624	1	2	yes	—
399	C₂²	C₂×C₄⋊C₄×D₇₃	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	146	1	no	—
404	C₄	—	146	1	no	—
405	C₄	—	146	1	no	—
406	C₄	—	146	1	no	—
407	C₄	—	146	1	no	—
408	C₄	—	146	1	no	—
409	C₄	#17988624	1	2	yes	—
410	C₄	#17989352	1	2	yes	—
411	C₄	C₂×#14556610	1	1	yes	characteristic
412	C₄	C₂×#14556614	1	1	yes	characteristic
413	C₂	—	2	2	no	—
414	C₂	—	292	1	no	—
415	C₂	—	146	2	no	—
416	C₂	#22618492	1	1	yes	characteristic
417	C₂	C₂×#17988624	1	1	yes	characteristic
418	C₂	#430×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₃
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₄²	C₂³×D₇₃
Fitting	C₇₃×#1571	C₂
socle	C₂²×C₇₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₇₃	C₄⋊C₄
cosocle	C₄²×C₇₃	C₂⁴
hypercenter	#1571	D₇₃
hypocenter	C₇₃	#17816
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1571

Complements

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

N	H ≅ G/N	type
4. #22608710	C₂	semidirect
5. #22608706	C₂	semidirect
6. #22608703	C₂	semidirect
7. #22608701	C₂	semidirect
8. #22608693	C₂	semidirect
9. C₇₃×#1571	C₂	semidirect
32. #17988340	C₂²	semidirect
33. #17988337	C₂²	semidirect
34. #17988337	C₂²	semidirect
38. #335×C₇₃	C₂²	semidirect
215. #1571	D₇₃	semidirect
219. C₇₃	#17816	semidirect
246. #335	C₂×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#22618563	2
C₂×#17988643	2
#431×D₇₃	2
#22608710	2
#22608706	2
#22608703	2
#22608701	2
#22608693	2
C₇₃×#1571	2
#17816	73