Subgroups — #34008771

Order 18688.

822 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₇₃⋊#108	C₂	1	1	yes	maximal, characteristic
2	C₂×#17989597	C₂	1	1	yes	maximal, characteristic
3	C₂×#17989458	C₂	1	2	yes	maximal
4	#22625596	C₂	1	2	yes	maximal
5	C₂×C₄×C₈×D₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×D₇₃⋊M₁₆	C₂²	1	2	yes	—
7	C₂×#14556670	C₂²	1	2	yes	—
8	C₂×#14556662	C₄	1	2	yes	complemented
9	D₇₃⋊#108	—	2	2	no	—
10	D₇₃⋊#108	—	2	2	no	—
11	C₂×#14556661	C₄	1	2	yes	complemented
12	#17989597	—	2	2	no	—
13	#17989597	—	2	2	no	—
14	C₂×#14556660	C₄	1	2	yes	complemented
15	C₂×#14556659	C₄	1	2	yes	complemented
16	#17989458	—	2	4	no	—
17	#17989452	—	2	4	no	—
18	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
19	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
20	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×#10596831	C₄	1	1	yes	characteristic, complemented
22	C₂×C₈×Dic₇₃	C₄	1	1	yes	characteristic, complemented
23	C₂×C₈×Dic₇₃	C₄	1	1	yes	characteristic, complemented
24	C₄×C₈×D₇₃	—	2	2	no	—
25	C₄×C₈×D₇₃	—	2	2	no	—
26	C₂×C₄×C₈×C₇₃	C₄	1	1	yes	characteristic, complemented
27	C₂×#11924038	C₂×C₄	1	4	yes	—
28	D₇₃⋊M₁₆	—	2	2	no	—
29	D₇₃⋊M₁₆	—	2	2	no	—
30	D₇₃⋊M₁₆	—	2	2	no	—
31	D₇₃⋊M₁₆	—	2	2	no	—
32	C₂×#11924037	—	2	2	no	—
33	C₂×#11924036	—	2	2	no	—
34	#14556670	—	2	2	no	—
35	#14556670	—	2	2	no	—
36	#14556670	—	2	2	no	—
37	#14556670	—	2	2	no	—
38	C₂×C₄⋊#64408	C₂×C₄	1	4	yes	—
39	C₂×C₂²⋊#64408	—	2	2	no	—
40	C₂×C₄×#64408	—	2	2	no	—
41	#14556662	—	2	4	no	—
42	#14556661	—	2	4	no	—
43	#14556660	—	2	4	no	—
44	#14556659	—	2	4	no	—
45	C₂²×C₄×D₇₃	—	2	1	no	—
46	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
47	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
48	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₇₃	—	2	1	no	—
50	C₂×C₈×D₇₃	—	2	1	no	—
51	C₂×C₈×D₇₃	—	2	1	no	—
52	C₂×C₈×D₇₃	—	2	1	no	—
53	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₇₃	D₄	1	2	yes	—
58	C₂×C₈×D₇₃	D₄	1	2	yes	—
59	C₂×C₈×D₇₃	D₄	1	2	yes	—
60	C₂×C₈×D₇₃	D₄	1	2	yes	—
61	C₂×C₈×D₇₃	Q₈	1	2	yes	—
62	C₂×C₈×D₇₃	Q₈	1	2	yes	—
63	C₂×C₄×Dic₇₃	—	2	1	no	—
64	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
65	C₄²×D₇₃	—	2	1	no	—
66	C₄²×D₇₃	—	2	1	no	—
67	C₄²×D₇₃	D₄	1	2	yes	—
68	C₄²×D₇₃	Q₈	1	2	yes	—
69	C₄×#10596831	—	2	2	no	—
70	C₈×Dic₇₃	—	2	2	no	—
71	C₈×Dic₇₃	—	2	2	no	—
72	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
73	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
75	C₄×C₈×C₇₃	—	2	2	no	—
76	C₂²×#64408	—	2	4	no	—
77	#11924038	—	2	4	no	—
78	#11924038	—	2	4	no	—
79	#11924037	—	4	2	no	—
80	#11924037	—	4	2	no	—
81	#11924036	—	4	2	no	—
82	#11924036	—	4	2	no	—
83	C₂×#10596833	—	2	4	no	—
84	C₄⋊#64408	—	2	4	no	—
85	C₄⋊#64408	—	2	4	no	—
86	C₂²⋊#64408	—	4	2	no	—
87	C₂²⋊#64408	—	4	2	no	—
88	C₄×#64408	—	4	2	no	—
89	C₄×#64408	—	4	2	no	—
90	C₂³×D₇₃	#41	1	1	yes	characteristic
91	C₂²×Dic₇₃	—	2	1	no	—
92	C₂²×Dic₇₃	#41	1	1	yes	characteristic
93	C₂×C₄×D₇₃	—	2	8	no	—
94	C₂×C₄×D₇₃	—	2	2	no	—
95	C₂×C₄×D₇₃	—	2	2	no	—
96	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
99	C₂×C₄×D₇₃	C₂×D₄	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×D₄	1	1	yes	characteristic
103	C₂×C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
104	C₂×C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
105	C₂×C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
106	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
107	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
108	C₂×#10596831	—	2	1	no	—
109	C₂×#10596831	—	2	1	no	—
110	C₂×#10596831	C₄²	1	1	yes	characteristic
111	C₂×#10596831	C₄²	1	1	yes	characteristic
112	C₂×#10596831	C₂²⋊C₄	1	2	yes	—
113	C₂×#10596831	C₄⋊C₄	1	2	yes	—
114	C₂×#10596831	C₄⋊C₄	1	2	yes	—
115	C₈×D₇₃	—	2	2	no	—
116	C₈×D₇₃	—	2	2	no	—
117	C₈×D₇₃	—	2	2	no	—
118	C₈×D₇₃	—	2	2	no	—
119	C₈×D₇₃	C₂²⋊C₄	1	2	yes	—
120	C₈×D₇₃	C₂²⋊C₄	1	2	yes	—
121	C₈×D₇₃	C₂²⋊C₄	1	2	yes	—
122	C₈×D₇₃	C₂²⋊C₄	1	2	yes	—
123	C₈×D₇₃	C₄⋊C₄	1	2	yes	—
124	C₈×D₇₃	C₄⋊C₄	1	2	yes	—
125	C₈×D₇₃	C₄⋊C₄	1	2	yes	—
126	C₈×D₇₃	C₄⋊C₄	1	2	yes	—
127	C₄×Dic₇₃	—	2	1	no	—
128	C₄×Dic₇₃	—	2	2	no	—
129	C₄×Dic₇₃	—	2	2	no	—
130	C₄×Dic₇₃	C₄⋊C₄	1	2	yes	—
131	C₂²×C₄×C₇₃	—	2	1	no	—
132	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₈×C₇₃	—	2	1	no	—
134	C₂×C₈×C₇₃	—	2	1	no	—
135	C₂×C₈×C₇₃	C₄²	1	1	yes	characteristic
136	C₂×C₈×C₇₃	C₄²	1	1	yes	characteristic
137	C₂×C₈×C₇₃	C₂²⋊C₄	1	2	yes	—
138	C₂×C₈×C₇₃	C₄⋊C₄	1	2	yes	—
139	C₂×C₈×C₇₃	C₄⋊C₄	1	2	yes	—
140	C₄²×C₇₃	—	2	1	no	—
141	C₄²×C₇₃	C₄⋊C₄	1	2	yes	—
142	C₂³×C₇₃	#117	1	1	yes	characteristic
143	C₂²×D₇₃	—	2	4	no	—
144	C₂²×D₇₃	C₄×D₄	1	1	yes	characteristic
145	C₂²×D₇₃	C₄×Q₈	1	1	yes	characteristic
146	C₂²×D₇₃	#121	1	1	yes	characteristic
147	C₂²×D₇₃	C₂²⋊Q₈	1	1	yes	characteristic
148	C₂²×D₇₃	#124	1	1	yes	characteristic
149	C₂²×D₇₃	#125	1	1	yes	characteristic
150	C₂×#64408	—	4	4	no	—
151	C₂×#64408	—	4	8	no	—
152	C₂×C₄×C₇₃	—	2	4	no	—
153	C₂×C₄×C₇₃	—	2	2	no	—
154	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
155	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₇₃	#117	1	1	yes	characteristic
160	C₂×Dic₇₃	—	2	4	no	—
161	C₂×Dic₇₃	—	2	2	no	—
162	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
163	C₂×Dic₇₃	C₄×Q₈	1	1	yes	characteristic
164	C₂×Dic₇₃	#121	1	1	yes	characteristic
165	C₂×Dic₇₃	C₂²⋊Q₈	1	1	yes	characteristic
166	C₂×Dic₇₃	#124	1	1	yes	characteristic
167	C₂×Dic₇₃	#125	1	1	yes	characteristic
168	C₄×D₇₃	—	2	8	no	—
169	C₄×D₇₃	—	2	8	no	—
170	C₄×D₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₄×D₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₄×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₄×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
175	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
176	C₄×D₇₃	C₄×Q₈	1	1	yes	characteristic
177	C₄×D₇₃	C₄×Q₈	1	1	yes	characteristic
178	C₄×D₇₃	#121	1	1	yes	characteristic
179	C₄×D₇₃	#121	1	1	yes	characteristic
180	C₄×D₇₃	C₂²⋊Q₈	1	1	yes	characteristic
181	C₄×D₇₃	C₂²⋊Q₈	1	1	yes	characteristic
182	C₄×D₇₃	#127	1	1	yes	characteristic
183	C₄×D₇₃	C₄⋊Q₈	1	1	yes	characteristic
184	C₄×D₇₃	C₄⋊Q₈	1	1	yes	characteristic
185	C₄×D₇₃	C₄⋊Q₈	1	1	yes	characteristic
186	#10596833	—	4	4	no	—
187	C₈×C₇₃	—	2	2	no	—
188	C₈×C₇₃	#95	1	2	yes	—
189	C₈×C₇₃	#95	1	2	yes	—
190	#10596831	—	2	2	no	—
191	#10596831	#95	1	2	yes	—
192	#10596831	#95	1	2	yes	—
193	C₂²×C₇₃	—	2	2	no	—
194	C₂²×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
195	C₂²×C₇₃	#380	1	1	yes	characteristic
196	C₂²×C₇₃	#382	1	1	yes	characteristic
197	C₂×D₇₃	—	2	2	no	—
198	C₂×D₇₃	—	2	2	no	—
199	C₂×D₇₃	—	2	2	no	—
200	C₂×D₇₃	—	2	2	no	—
201	C₂×D₇₃	—	2	2	no	—
202	C₂×D₇₃	#389	1	1	yes	characteristic
203	C₂×D₇₃	#389	1	1	yes	characteristic
204	C₂×D₇₃	#390	1	1	yes	characteristic
205	C₂×D₇₃	#391	1	1	yes	characteristic
206	C₂×D₇₃	#443	1	4	yes	—
207	#64408	—	8	4	no	—
208	C₄×C₇₃	—	2	4	no	—
209	C₄×C₇₃	C₂×#95	1	1	yes	characteristic
210	C₄×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
211	C₄×C₇₃	#380	1	1	yes	characteristic
212	C₄×C₇₃	#384	1	1	yes	characteristic
213	Dic₇₃	—	2	4	no	—
214	Dic₇₃	#389	1	1	yes	characteristic
215	Dic₇₃	#389	1	1	yes	characteristic
216	Dic₇₃	#390	1	1	yes	characteristic
217	Dic₇₃	#391	1	1	yes	characteristic
218	#10859	—	73	1	no	maximal, Sylow
219	C₂×C₇₃	—	2	1	no	—
220	C₂×C₇₃	—	2	1	no	—
221	C₂×C₇₃	C₄⋊#95	1	1	yes	characteristic
222	C₂×C₇₃	#1772	1	2	yes	—
223	D₇₃	—	2	1	no	—
224	D₇₃	—	2	1	no	—
225	D₇₃	#1945	1	2	yes	—
226	D₇₃	#1974	1	2	yes	—
227	C₂²×#108	—	73	1	no	—
228	C₂×#427	—	73	1	no	—
229	C₂²×C₄×C₈	—	73	1	no	—
230	C₂×#339	—	73	2	no	—
231	#1729	—	73	2	no	—
232	C₇₃	#10859	1	1	yes	characteristic, complemented, Sylow
233	C₂²×M₁₆	—	73	2	no	—
234	C₂³×C₈	—	73	1	no	—
235	C₂³×C₈	—	73	1	no	—
236	C₂×#117	—	73	2	no	—
237	C₂²×C₄²	—	73	1	no	—
238	C₂×#108	—	73	2	no	—
239	C₂×#108	—	73	2	no	—
240	C₂×#108	—	146	2	no	—
241	C₂×#108	—	146	2	no	—
242	#427	—	146	2	no	—
243	#427	—	146	2	no	—
244	C₂×#107	—	73	2	no	—
245	C₂×#106	—	73	2	no	—
246	C₂×C₄×C₈	—	73	1	no	—
247	C₂×C₄×C₈	—	73	1	no	—
248	C₂×C₄×C₈	—	73	1	no	—
249	C₂×C₄×C₈	—	146	2	no	—
250	C₂×C₄×C₈	—	146	2	no	—
251	C₂×C₄×C₈	#64408	1	1	yes	characteristic, complemented
252	#339	—	146	4	no	—
253	#336	—	146	4	no	—
254	C₂³×C₄	—	73	1	no	—
255	C₂³×C₄	—	146	1	no	—
256	C₂×M₁₆	—	73	4	no	—
257	C₂×M₁₆	—	146	2	no	—
258	C₂×M₁₆	—	146	2	no	—
259	C₂×M₁₆	—	146	2	no	—
260	C₂×M₁₆	—	146	2	no	—
261	C₂×M₁₆	—	146	2	no	—
262	C₂²×C₈	—	73	1	no	—
263	C₂²×C₈	—	73	1	no	—
264	C₂²×C₈	—	73	1	no	—
265	C₂²×C₈	—	73	1	no	—
266	C₂²×C₈	—	73	1	no	—
267	C₂²×C₈	—	73	2	no	—
268	C₂²×C₈	—	73	2	no	—
269	C₂²×C₈	—	73	2	no	—
270	C₂²×C₈	—	73	2	no	—
271	C₂²×C₈	—	73	1	no	—
272	C₂²×C₈	—	73	2	no	—
273	C₂²×C₈	—	73	2	no	—
274	C₂²×C₈	—	146	1	no	—
275	C₂²×C₈	—	146	1	no	—
276	C₂²×C₈	—	146	1	no	—
277	C₂²×C₈	—	146	1	no	—
278	C₂²×C₈	—	146	2	no	—
279	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
280	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
281	#117	—	146	2	no	—
282	#117	—	146	2	no	—
283	#117	—	146	2	no	—
284	#117	—	146	2	no	—
285	C₂×C₄⋊C₄	—	73	4	no	—
286	C₂×C₂²⋊C₄	—	146	2	no	—
287	C₂×C₄²	—	73	1	no	—
288	C₂×C₄²	—	73	2	no	—
289	C₂×C₄²	—	73	2	no	—
290	C₂×C₄²	—	146	1	no	—
291	C₂×C₄²	—	146	1	no	—
292	C₂×C₄²	—	146	2	no	—
293	C₂×C₄²	—	146	1	no	—
294	C₂×C₄²	C₂×#64408	1	1	yes	characteristic
295	#108	—	146	4	no	—
296	#108	—	146	4	no	—
297	#107	—	146	4	no	—
298	#106	—	146	4	no	—
299	C₄×C₈	—	2	2	no	—
300	C₄×C₈	—	146	2	no	—
301	C₄×C₈	—	146	2	no	—
302	C₄×C₈	—	146	2	no	—
303	C₂⁴	—	73	1	no	—
304	C₂²×C₄	—	2	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	1	no	—
315	C₂²×C₄	—	73	1	no	—
316	C₂²×C₄	—	73	1	no	—
317	C₂²×C₄	—	73	1	no	—
318	C₂²×C₄	—	146	2	no	—
319	C₂²×C₄	—	146	2	no	—
320	C₂²×C₄	—	146	8	no	—
321	C₂²×C₄	—	146	4	no	—
322	C₂²×C₄	—	146	1	no	—
323	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
324	M₁₆	—	292	2	no	—
325	M₁₆	—	292	2	no	—
326	M₁₆	—	146	4	no	—
327	M₁₆	—	146	4	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	292	2	no	—
331	C₂×C₈	—	292	2	no	—
332	C₂×C₈	—	73	1	no	—
333	C₂×C₈	—	73	1	no	—
334	C₂×C₈	—	73	2	no	—
335	C₂×C₈	—	73	2	no	—
336	C₂×C₈	—	73	2	no	—
337	C₂×C₈	—	73	2	no	—
338	C₂×C₈	—	73	2	no	—
339	C₂×C₈	—	73	2	no	—
340	C₂×C₈	—	73	2	no	—
341	C₂×C₈	—	73	2	no	—
342	C₂×C₈	—	73	2	no	—
343	C₂×C₈	—	73	2	no	—
344	C₂×C₈	—	73	2	no	—
345	C₂×C₈	—	146	2	no	—
346	C₂×C₈	—	146	2	no	—
347	C₂×C₈	—	146	2	no	—
348	C₂×C₈	—	146	2	no	—
349	C₂×C₈	—	146	4	no	—
350	C₂×C₈	—	146	1	no	—
351	C₂×C₈	—	146	1	no	—
352	C₂×C₈	C₄×#64408	1	1	yes	characteristic
353	C₂×C₈	C₄×#64408	1	1	yes	characteristic
354	C₂×C₈	C₂²⋊#64408	1	2	yes	—
355	C₂×C₈	C₄⋊#64408	1	2	yes	—
356	C₂×C₈	C₄⋊#64408	1	2	yes	—
357	C₄⋊C₄	—	146	4	no	—
358	C₄⋊C₄	—	146	4	no	—
359	C₂²⋊C₄	—	292	2	no	—
360	C₂²⋊C₄	—	292	2	no	—
361	C₄²	—	2	1	no	—
362	C₄²	—	292	2	no	—
363	C₄²	—	292	2	no	—
364	C₄²	—	73	2	no	—
365	C₄²	—	146	2	no	—
366	C₄²	—	146	2	no	—
367	C₄²	—	146	1	no	—
368	C₄²	C₄⋊#64408	1	2	yes	—
369	C₂³	—	73	1	no	—
370	C₂³	—	73	1	no	—
371	C₂³	—	73	1	no	—
372	C₂³	—	73	1	no	—
373	C₂³	—	73	1	no	—
374	C₂³	—	73	1	no	—
375	C₂³	—	146	4	no	—
376	C₂³	#14556670	1	1	yes	characteristic
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	292	4	no	—
380	C₂×C₄	—	292	8	no	—
381	C₂×C₄	—	73	1	no	—
382	C₂×C₄	—	73	1	no	—
383	C₂×C₄	—	73	1	no	—
384	C₂×C₄	—	73	1	no	—
385	C₂×C₄	—	73	1	no	—
386	C₂×C₄	—	73	1	no	—
387	C₂×C₄	—	73	1	no	—
388	C₂×C₄	—	73	1	no	—
389	C₂×C₄	—	73	1	no	—
390	C₂×C₄	—	73	1	no	—
391	C₂×C₄	—	73	1	no	—
392	C₂×C₄	—	73	1	no	—
393	C₂×C₄	—	73	1	no	—
394	C₂×C₄	—	73	1	no	—
395	C₂×C₄	—	73	1	no	—
396	C₂×C₄	—	73	1	no	—
397	C₂×C₄	—	73	1	no	—
398	C₂×C₄	—	73	1	no	—
399	C₂×C₄	—	73	1	no	—
400	C₂×C₄	—	73	1	no	—
401	C₂×C₄	—	73	1	no	—
402	C₂×C₄	—	73	1	no	—
403	C₂×C₄	—	146	8	no	—
404	C₂×C₄	—	146	8	no	—
405	C₂×C₄	—	146	4	no	—
406	C₂×C₄	—	146	2	no	—
407	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
408	C₂×C₄	C₂×C₂²⋊#64408	1	1	yes	characteristic
409	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
410	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
411	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
412	C₂×C₄	#14556670	1	1	yes	characteristic
413	C₈	—	2	2	no	—
414	C₈	—	292	4	no	—
415	C₈	—	73	2	no	—
416	C₈	—	73	2	no	—
417	C₈	—	146	2	no	—
418	C₈	(C₂×#64408)⋊C₄	1	2	yes	—
419	C₈	(C₂×#64408)⋊C₄	1	2	yes	—
420	C₂²	—	2	2	no	—
421	C₂²	—	73	1	no	—
422	C₂²	—	73	1	no	—
423	C₂²	—	73	4	no	—
424	C₂²	—	73	1	no	—
425	C₂²	—	73	1	no	—
426	C₂²	—	146	2	no	—
427	C₂²	—	146	2	no	—
428	C₂²	—	146	2	no	—
429	C₂²	—	146	2	no	—
430	C₂²	—	146	2	no	—
431	C₂²	C₄×C₄⋊#64408	1	1	yes	characteristic
432	C₂²	#17989529	1	1	yes	characteristic
433	C₂²	#17989531	1	1	yes	characteristic
434	C₄	—	2	4	no	—
435	C₄	—	584	4	no	—
436	C₄	—	73	1	no	—
437	C₄	—	73	1	no	—
438	C₄	—	73	1	no	—
439	C₄	—	73	1	no	—
440	C₄	—	146	4	no	—
441	C₄	C₂×(C₂×#64408)⋊C₄	1	1	yes	characteristic
442	C₄	C₄×C₄⋊#64408	1	1	yes	characteristic
443	C₄	#17989529	1	1	yes	characteristic
444	C₄	#17989533	1	1	yes	characteristic
445	C₂	—	2	1	no	—
446	C₂	—	2	1	no	—
447	C₂	—	73	2	no	—
448	C₂	—	73	2	no	—
449	C₂	—	146	1	no	—
450	C₂	—	146	1	no	—
451	C₂	#22625109	1	1	yes	characteristic
452	C₂	#22625733	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×C₄⋊#64408
commutator	C₂×C₄×C₇₃	C₂×C₄²
Frattini	C₂²×C₄	C₂²×#64408
Fitting	C₂×C₄×C₈×C₇₃	C₄
socle	C₂²×C₇₃	C₄×C₄⋊C₄
prime radical	C₂³×D₇₃	#41
cosocle	C₂²×C₄×D₇₃	C₂³
hypercenter	C₂×C₄×C₈	#64408
hypocenter	C₇₃	#10859
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
8. C₂×#14556662	C₄	semidirect
11. C₂×#14556661	C₄	semidirect
14. C₂×#14556660	C₄	semidirect
15. C₂×#14556659	C₄	semidirect
21. C₂×C₄×#10596831	C₄	semidirect
22. C₂×C₈×Dic₇₃	C₄	semidirect
23. C₂×C₈×Dic₇₃	C₄	semidirect
26. C₂×C₄×C₈×C₇₃	C₄	semidirect
232. C₇₃	#10859	semidirect
251. 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×D₇₃⋊#108	2
C₂×#17989597	2
C₂×#17989458	2
#22625596	2
C₂×C₄×C₈×D₇₃	2
#10859	73