Subgroups — C₂×#22625733 #34020231

Order 18688.

1102 conjugacy classes of subgroups.

The subgroup lattice has 486 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×#17989550	C₂	1	2	yes	maximal
4	#22625733	C₂	1	8	yes	maximal, direct product factor
5	C₂×#17989458	C₂	1	2	yes	maximal
6	C₂×C₄×C₈×D₇₃	C₂	1	1	yes	maximal, characteristic
7	C₂×D₇₃⋊M₁₆	C₂²	1	2	yes	—
8	C₂×#14556670	C₂²	1	2	yes	—
9	C₂×#14556662	C₄	1	2	yes	complemented
10	D₇₃⋊#108	C₄	1	4	yes	complemented
11	D₇₃⋊#108	C₂²	1	4	yes	—
12	C₂×#14556661	C₄	1	2	yes	complemented
13	#17989597	C₄	1	4	yes	complemented
14	#17989597	C₂²	1	4	yes	—
15	C₂×#14556660	C₄	1	2	yes	complemented
16	C₂×#14556659	C₄	1	2	yes	complemented
17	#17989550	—	2	4	no	—
18	#17989550	C₂²	1	8	yes	—
19	C₂×#14556645	—	2	2	no	—
20	C₂×C₈×#64408	—	2	2	no	—
21	#17989458	C₂²	1	8	yes	—
22	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
23	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
24	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×#10596831	C₄	1	1	yes	characteristic, complemented
26	C₂×C₈×Dic₇₃	C₄	1	1	yes	characteristic, complemented
27	C₂×C₈×Dic₇₃	C₄	1	1	yes	characteristic, complemented
28	C₄×C₈×D₇₃	C₄	1	4	yes	complemented
29	C₄×C₈×D₇₃	C₂²	1	4	yes	—
30	C₂×C₄×C₈×C₇₃	C₄	1	1	yes	characteristic, complemented
31	C₂×#11924038	C₂×C₄	1	4	yes	—
32	D₇₃⋊M₁₆	—	2	2	no	—
33	D₇₃⋊M₁₆	—	2	2	no	—
34	D₇₃⋊M₁₆	C₂×C₄	1	4	yes	—
35	D₇₃⋊M₁₆	C₂³	1	4	yes	—
36	C₂×#11924037	—	2	2	no	—
37	C₂×#11924036	—	2	2	no	—
38	#14556670	—	2	2	no	—
39	#14556670	—	2	2	no	—
40	#14556670	C₂×C₄	1	4	yes	—
41	#14556670	C₂³	1	4	yes	—
42	C₂×C₄⋊#64408	C₂×C₄	1	4	yes	—
43	C₂×C₂²⋊#64408	—	2	2	no	—
44	C₂×C₄×#64408	—	2	2	no	—
45	#14556662	C₂×C₄	1	8	yes	complemented
46	#14556661	C₂×C₄	1	8	yes	complemented
47	#14556660	C₂×C₄	1	8	yes	complemented
48	#14556659	C₂×C₄	1	8	yes	complemented
49	#14556645	—	2	8	no	—
50	C₈×#64408	—	2	8	no	—
51	C₂²×C₄×D₇₃	—	2	1	no	—
52	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
53	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
54	C₂²×#10596831	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	C₂×C₄	1	2	yes	—
58	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₈×D₇₃	C₂×C₄	1	2	yes	—
60	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₇₃	C₂×C₄	1	2	yes	—
62	C₂×C₈×D₇₃	C₂×C₄	1	2	yes	—
63	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
64	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
65	C₂×C₈×D₇₃	D₄	1	2	yes	—
66	C₂×C₈×D₇₃	Q₈	1	1	yes	characteristic
67	C₂×C₈×D₇₃	Q₈	1	2	yes	—
68	C₂×C₈×D₇₃	Q₈	1	1	yes	characteristic
69	C₂×C₈×D₇₃	C₂³	1	2	yes	—
70	C₂×C₈×D₇₃	C₂³	1	2	yes	—
71	C₂×C₄×Dic₇₃	—	2	1	no	—
72	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
73	C₄²×D₇₃	—	2	1	no	—
74	C₄²×D₇₃	—	2	1	no	—
75	C₄²×D₇₃	C₂×C₄	1	2	yes	—
76	C₄²×D₇₃	C₂³	1	2	yes	—
77	C₄×#10596831	C₂×C₄	1	4	yes	complemented
78	C₈×Dic₇₃	C₂×C₄	1	4	yes	complemented
79	C₈×Dic₇₃	C₂×C₄	1	4	yes	complemented
80	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
81	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
83	C₄×C₈×C₇₃	C₂×C₄	1	4	yes	complemented
84	C₂²×#64408	—	2	4	no	—
85	#11924038	—	2	4	no	—
86	#11924038	C₂²×C₄	1	8	yes	—
87	#11924037	—	2	4	no	—
88	#11924037	—	2	4	no	—
89	#11924036	—	2	4	no	—
90	#11924036	—	2	4	no	—
91	C₂×#10596833	—	2	4	no	—
92	C₄⋊#64408	—	2	4	no	—
93	C₄⋊#64408	C₂²×C₄	1	8	yes	—
94	C₂²⋊#64408	—	2	4	no	—
95	C₂²⋊#64408	—	2	4	no	—
96	C₄×#64408	—	2	4	no	—
97	C₄×#64408	—	2	4	no	—
98	C₂³×D₇₃	#41	1	1	yes	characteristic
99	C₂²×Dic₇₃	—	2	1	no	—
100	C₂²×Dic₇₃	#41	1	1	yes	characteristic
101	C₂×C₄×D₇₃	—	2	8	no	—
102	C₂×C₄×D₇₃	—	2	2	no	—
103	C₂×C₄×D₇₃	—	2	2	no	—
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	C₂×D₄	1	1	yes	characteristic
110	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
111	C₂×C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
112	C₂×C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
113	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
114	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
115	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
116	C₂×#10596831	C₄²	1	1	yes	characteristic
117	C₂×#10596831	C₄²	1	1	yes	characteristic
118	C₂×#10596831	C₄²	1	2	yes	—
119	C₂×#10596831	C₄⋊C₄	1	1	yes	characteristic
120	C₂×#10596831	C₄⋊C₄	1	1	yes	characteristic
121	C₂×#10596831	C₄⋊C₄	1	2	yes	—
122	C₂×#10596831	C₂²×C₄	1	2	yes	—
123	C₂×#10596831	C₂²×C₄	1	2	yes	—
124	C₈×D₇₃	C₄²	1	2	yes	—
125	C₈×D₇₃	C₄²	1	2	yes	—
126	C₈×D₇₃	C₄²	1	2	yes	—
127	C₈×D₇₃	C₄²	1	2	yes	—
128	C₈×D₇₃	C₄⋊C₄	1	2	yes	—
129	C₈×D₇₃	C₄⋊C₄	1	2	yes	—
130	C₈×D₇₃	C₄⋊C₄	1	2	yes	—
131	C₈×D₇₃	C₄⋊C₄	1	2	yes	—
132	C₈×D₇₃	C₂²×C₄	1	2	yes	—
133	C₈×D₇₃	C₂²×C₄	1	2	yes	—
134	C₈×D₇₃	C₂²×C₄	1	2	yes	—
135	C₈×D₇₃	C₂²×C₄	1	2	yes	—
136	C₈×D₇₃	C₂×D₄	1	2	yes	—
137	C₈×D₇₃	C₂×D₄	1	2	yes	—
138	C₈×D₇₃	C₂×Q₈	1	2	yes	—
139	C₈×D₇₃	C₂×Q₈	1	2	yes	—
140	C₄×Dic₇₃	—	2	1	no	—
141	C₄×Dic₇₃	—	2	2	no	—
142	C₄×Dic₇₃	—	2	2	no	—
143	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
144	C₂²×C₄×C₇₃	—	2	1	no	—
145	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₈×C₇₃	C₄²	1	1	yes	characteristic
147	C₂×C₈×C₇₃	C₄²	1	1	yes	characteristic
148	C₂×C₈×C₇₃	C₄²	1	2	yes	—
149	C₂×C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₈×C₇₃	C₄⋊C₄	1	2	yes	—
151	C₂×C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
153	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
154	C₄²×C₇₃	—	2	1	no	—
155	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
156	C₂³×C₇₃	#117	1	1	yes	characteristic
157	C₂²×D₇₃	—	2	4	no	—
158	C₂²×D₇₃	#117	1	1	yes	characteristic
159	C₂²×D₇₃	C₄×D₄	1	1	yes	characteristic
160	C₂²×D₇₃	C₄×D₄	1	1	yes	characteristic
161	C₂²×D₇₃	C₄×Q₈	1	1	yes	characteristic
162	C₂²×D₇₃	C₄×Q₈	1	1	yes	characteristic
163	C₂²×D₇₃	C₂×#41	1	1	yes	characteristic
164	C₂×#64408	—	2	8	no	—
165	C₂×#64408	—	4	8	no	—
166	C₂×C₄×C₇₃	—	2	4	no	—
167	C₂×C₄×C₇₃	—	2	2	no	—
168	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
169	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
170	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₇₃	#117	1	1	yes	characteristic
173	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
174	C₂×Dic₇₃	—	2	4	no	—
175	C₂×Dic₇₃	—	2	2	no	—
176	C₂×Dic₇₃	#117	1	1	yes	characteristic
177	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
178	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
179	C₂×Dic₇₃	C₄×Q₈	1	1	yes	characteristic
180	C₂×Dic₇₃	C₄×Q₈	1	1	yes	characteristic
181	C₂×Dic₇₃	C₂×#41	1	1	yes	characteristic
182	C₄×D₇₃	—	2	8	no	—
183	C₄×D₇₃	—	2	8	no	—
184	C₄×D₇₃	C₂×C₄²	1	1	yes	characteristic
185	C₄×D₇₃	C₂×C₄²	1	1	yes	characteristic
186	C₄×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₄×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
189	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
190	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
191	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
192	C₄×D₇₃	C₄×Q₈	1	1	yes	characteristic
193	C₄×D₇₃	C₄×Q₈	1	1	yes	characteristic
194	C₄×D₇₃	C₄×Q₈	1	1	yes	characteristic
195	C₄×D₇₃	C₄×Q₈	1	1	yes	characteristic
196	C₄×D₇₃	C₂³×C₄	1	1	yes	characteristic
197	C₄×D₇₃	C₂³×C₄	1	1	yes	characteristic
198	C₄×D₇₃	C₂²×D₄	1	1	yes	characteristic
199	C₄×D₇₃	C₂²×Q₈	1	1	yes	characteristic
200	#10596833	—	2	8	no	—
201	C₈×C₇₃	C₂×C₄²	1	2	yes	—
202	C₈×C₇₃	C₂×C₄²	1	2	yes	—
203	C₈×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
204	C₈×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
205	#10596831	C₂×C₄²	1	2	yes	—
206	#10596831	C₂×C₄²	1	2	yes	—
207	#10596831	C₂×C₄⋊C₄	1	2	yes	—
208	#10596831	C₂×C₄⋊C₄	1	2	yes	—
209	C₂²×C₇₃	—	2	2	no	—
210	C₂²×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
211	C₂²×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
212	C₂²×C₇₃	C₂×#117	1	1	yes	characteristic
213	C₂×D₇₃	—	2	2	no	—
214	C₂×D₇₃	—	2	2	no	—
215	C₂×D₇₃	—	2	2	no	—
216	C₂×D₇₃	—	2	2	no	—
217	C₂×D₇₃	—	2	2	no	—
218	C₂×D₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
219	C₂×D₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
220	C₂×D₇₃	#443	1	4	yes	—
221	C₂×D₇₃	C₂×C₄×D₄	1	1	yes	characteristic
222	C₂×D₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
223	#64408	—	4	8	no	—
224	C₄×C₇₃	—	2	4	no	—
225	C₄×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
226	C₄×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
227	C₄×C₇₃	C₂²×C₄²	1	1	yes	characteristic
228	C₄×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
229	Dic₇₃	—	2	4	no	—
230	Dic₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
231	Dic₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
232	Dic₇₃	C₂×C₄×D₄	1	1	yes	characteristic
233	Dic₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
234	C₂×#1772	—	73	1	no	maximal, Sylow
235	C₂×C₇₃	—	2	1	no	—
236	C₂×C₇₃	—	2	1	no	—
237	C₂×C₇₃	#1772	1	2	yes	complemented
238	C₂×C₇₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
239	D₇₃	—	2	1	no	—
240	D₇₃	—	2	1	no	—
241	D₇₃	#1772	1	2	yes	complemented
242	D₇₃	C₂×#443	1	2	yes	—
243	C₂²×#108	—	73	1	no	—
244	C₂×#427	—	73	1	no	—
245	C₂×#405	—	73	2	no	—
246	C₂²×C₄×C₈	—	73	1	no	—
247	#1772	—	73	8	no	—
248	C₂×#339	—	73	2	no	—
249	C₇₃	C₂×#1772	1	1	yes	characteristic, complemented, Sylow
250	C₂²×M₁₆	—	73	2	no	—
251	C₂³×C₈	—	73	1	no	—
252	C₂³×C₈	—	73	1	no	—
253	C₂×#117	—	73	2	no	—
254	C₂²×C₄²	—	73	1	no	—
255	C₂×#108	—	73	2	no	—
256	C₂×#108	—	73	4	no	—
257	C₂×#108	—	73	4	no	—
258	C₂×#108	—	73	2	no	—
259	#427	—	73	4	no	—
260	#427	—	73	4	no	—
261	C₂×#107	—	73	2	no	—
262	C₂×#106	—	73	2	no	—
263	#405	—	73	8	no	—
264	#405	—	146	4	no	—
265	C₂×#97	—	146	2	no	—
266	C₂×C₄×C₈	—	73	1	no	—
267	C₂×C₄×C₈	—	73	1	no	—
268	C₂×C₄×C₈	—	73	1	no	—
269	C₂×C₄×C₈	—	73	4	no	—
270	C₂×C₄×C₈	—	73	4	no	—
271	C₂×C₄×C₈	—	146	2	no	—
272	C₂×C₄×C₈	#64408	1	1	yes	characteristic, complemented
273	#339	—	73	8	no	—
274	C₂³×C₄	—	73	1	no	—
275	C₂³×C₄	—	146	1	no	—
276	C₂×M₁₆	—	73	4	no	—
277	C₂×M₁₆	—	73	4	no	—
278	C₂×M₁₆	—	73	4	no	—
279	C₂×M₁₆	—	146	2	no	—
280	C₂×M₁₆	—	146	2	no	—
281	C₂×M₁₆	—	146	2	no	—
282	C₂²×C₈	—	73	1	no	—
283	C₂²×C₈	—	73	1	no	—
284	C₂²×C₈	—	73	1	no	—
285	C₂²×C₈	—	73	1	no	—
286	C₂²×C₈	—	73	2	no	—
287	C₂²×C₈	—	73	1	no	—
288	C₂²×C₈	—	73	2	no	—
289	C₂²×C₈	—	73	1	no	—
290	C₂²×C₈	—	73	1	no	—
291	C₂²×C₈	—	73	2	no	—
292	C₂²×C₈	—	73	2	no	—
293	C₂²×C₈	—	73	1	no	—
294	C₂²×C₈	—	73	1	no	—
295	C₂²×C₈	—	73	1	no	—
296	C₂²×C₈	—	73	2	no	—
297	C₂²×C₈	—	73	2	no	—
298	C₂²×C₈	—	73	2	no	—
299	C₂²×C₈	—	73	2	no	—
300	C₂²×C₈	—	146	2	no	—
301	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
302	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
303	#117	—	73	4	no	—
304	#117	—	73	4	no	—
305	#117	—	146	2	no	—
306	#117	—	146	2	no	—
307	C₂×C₄⋊C₄	—	73	4	no	—
308	C₂×C₂²⋊C₄	—	146	2	no	—
309	C₂×C₄²	—	73	1	no	—
310	C₂×C₄²	—	73	2	no	—
311	C₂×C₄²	—	73	2	no	—
312	C₂×C₄²	—	146	1	no	—
313	C₂×C₄²	—	146	1	no	—
314	C₂×C₄²	—	146	1	no	—
315	C₂×C₄²	—	146	2	no	—
316	C₂×C₄²	C₂×#64408	1	1	yes	characteristic
317	#108	—	73	8	no	—
318	#108	—	73	8	no	—
319	#107	—	73	8	no	—
320	#106	—	73	8	no	—
321	#97	—	146	8	no	—
322	C₄×C₈	—	73	4	no	—
323	C₄×C₈	—	73	4	no	—
324	C₄×C₈	—	73	4	no	—
325	C₄×C₈	—	146	8	no	—
326	C₄×C₈	C₂×#64408	1	4	yes	complemented
327	C₂⁴	—	73	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	73	1	no	—
330	C₂²×C₄	—	73	1	no	—
331	C₂²×C₄	—	73	1	no	—
332	C₂²×C₄	—	73	1	no	—
333	C₂²×C₄	—	73	1	no	—
334	C₂²×C₄	—	73	1	no	—
335	C₂²×C₄	—	73	1	no	—
336	C₂²×C₄	—	73	1	no	—
337	C₂²×C₄	—	73	1	no	—
338	C₂²×C₄	—	73	1	no	—
339	C₂²×C₄	—	73	1	no	—
340	C₂²×C₄	—	73	1	no	—
341	C₂²×C₄	—	73	1	no	—
342	C₂²×C₄	—	146	2	no	—
343	C₂²×C₄	—	146	2	no	—
344	C₂²×C₄	—	146	8	no	—
345	C₂²×C₄	—	146	4	no	—
346	C₂²×C₄	—	146	1	no	—
347	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
348	M₁₆	—	73	8	no	—
349	M₁₆	—	146	4	no	—
350	M₁₆	—	146	4	no	—
351	M₁₆	—	146	4	no	—
352	C₂×C₈	—	73	2	no	—
353	C₂×C₈	—	73	2	no	—
354	C₂×C₈	—	73	1	no	—
355	C₂×C₈	—	73	1	no	—
356	C₂×C₈	—	73	2	no	—
357	C₂×C₈	—	73	2	no	—
358	C₂×C₈	—	73	1	no	—
359	C₂×C₈	—	73	1	no	—
360	C₂×C₈	—	73	2	no	—
361	C₂×C₈	—	73	2	no	—
362	C₂×C₈	—	73	2	no	—
363	C₂×C₈	—	73	2	no	—
364	C₂×C₈	—	73	2	no	—
365	C₂×C₈	—	73	2	no	—
366	C₂×C₈	—	73	2	no	—
367	C₂×C₈	—	73	2	no	—
368	C₂×C₈	—	73	2	no	—
369	C₂×C₈	—	73	2	no	—
370	C₂×C₈	—	73	2	no	—
371	C₂×C₈	—	73	2	no	—
372	C₂×C₈	—	73	2	no	—
373	C₂×C₈	—	73	2	no	—
374	C₂×C₈	—	73	2	no	—
375	C₂×C₈	—	73	2	no	—
376	C₂×C₈	—	146	4	no	—
377	C₂×C₈	—	146	4	no	—
378	C₂×C₈	—	146	4	no	—
379	C₂×C₈	C₄×#64408	1	1	yes	characteristic
380	C₂×C₈	C₄×#64408	1	1	yes	characteristic
381	C₂×C₈	C₄×#64408	1	2	yes	—
382	C₂×C₈	C₄⋊#64408	1	1	yes	characteristic
383	C₂×C₈	C₄⋊#64408	1	2	yes	—
384	C₂×C₈	C₄⋊#64408	1	1	yes	characteristic
385	C₂×C₈	C₂²×#64408	1	2	yes	—
386	C₂×C₈	C₂²×#64408	1	2	yes	—
387	C₄⋊C₄	—	73	8	no	—
388	C₄⋊C₄	—	146	4	no	—
389	C₂²⋊C₄	—	146	4	no	—
390	C₂²⋊C₄	—	146	4	no	—
391	C₄²	—	2	1	no	—
392	C₄²	—	73	2	no	—
393	C₄²	—	146	2	no	—
394	C₄²	—	146	2	no	—
395	C₄²	—	146	4	no	—
396	C₄²	—	146	4	no	—
397	C₄²	—	146	1	no	—
398	C₄²	C₂²×#64408	1	2	yes	—
399	C₂³	—	73	1	no	—
400	C₂³	—	73	1	no	—
401	C₂³	—	73	1	no	—
402	C₂³	—	73	1	no	—
403	C₂³	—	73	1	no	—
404	C₂³	—	73	1	no	—
405	C₂³	—	146	4	no	—
406	C₂³	#14556670	1	1	yes	characteristic
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	292	8	no	—
410	C₂×C₄	—	73	1	no	—
411	C₂×C₄	—	73	1	no	—
412	C₂×C₄	—	73	1	no	—
413	C₂×C₄	—	73	1	no	—
414	C₂×C₄	—	73	1	no	—
415	C₂×C₄	—	73	1	no	—
416	C₂×C₄	—	73	1	no	—
417	C₂×C₄	—	73	1	no	—
418	C₂×C₄	—	73	1	no	—
419	C₂×C₄	—	73	1	no	—
420	C₂×C₄	—	73	1	no	—
421	C₂×C₄	—	73	1	no	—
422	C₂×C₄	—	73	1	no	—
423	C₂×C₄	—	73	1	no	—
424	C₂×C₄	—	73	1	no	—
425	C₂×C₄	—	73	1	no	—
426	C₂×C₄	—	73	1	no	—
427	C₂×C₄	—	73	1	no	—
428	C₂×C₄	—	73	1	no	—
429	C₂×C₄	—	73	1	no	—
430	C₂×C₄	—	73	1	no	—
431	C₂×C₄	—	73	1	no	—
432	C₂×C₄	—	146	8	no	—
433	C₂×C₄	—	146	8	no	—
434	C₂×C₄	—	146	8	no	—
435	C₂×C₄	—	146	4	no	—
436	C₂×C₄	—	146	2	no	—
437	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
438	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
439	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
440	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
441	C₂×C₄	#14556670	1	1	yes	characteristic
442	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
443	C₈	—	73	2	no	—
444	C₈	—	73	2	no	—
445	C₈	—	73	2	no	—
446	C₈	—	73	2	no	—
447	C₈	—	146	8	no	—
448	C₈	C₂×C₄×#64408	1	2	yes	—
449	C₈	C₂×C₄×#64408	1	2	yes	—
450	C₈	C₂×C₄⋊#64408	1	2	yes	—
451	C₈	C₂×C₄⋊#64408	1	2	yes	—
452	C₂²	—	2	2	no	—
453	C₂²	—	73	1	no	—
454	C₂²	—	73	1	no	—
455	C₂²	—	73	4	no	—
456	C₂²	—	73	1	no	—
457	C₂²	—	73	1	no	—
458	C₂²	—	146	2	no	—
459	C₂²	—	146	2	no	—
460	C₂²	—	146	2	no	—
461	C₂²	—	146	2	no	—
462	C₂²	—	146	2	no	—
463	C₂²	C₄×C₄⋊#64408	1	1	yes	characteristic
464	C₂²	C₄×C₄⋊#64408	1	1	yes	characteristic
465	C₂²	C₂×#14556670	1	1	yes	characteristic
466	C₄	—	2	4	no	—
467	C₄	—	292	8	no	—
468	C₄	—	73	1	no	—
469	C₄	—	73	1	no	—
470	C₄	—	73	1	no	—
471	C₄	—	73	1	no	—
472	C₄	—	146	4	no	—
473	C₄	C₄×C₄⋊#64408	1	1	yes	characteristic
474	C₄	C₄×C₄⋊#64408	1	1	yes	characteristic
475	C₄	C₂²×C₄×#64408	1	1	yes	characteristic
476	C₄	C₂²×C₄⋊#64408	1	1	yes	characteristic
477	C₂	—	2	1	no	—
478	C₂	—	2	1	no	—
479	C₂	—	73	2	no	—
480	C₂	—	73	2	no	—
481	C₂	—	146	1	no	—
482	C₂	—	146	1	no	—
483	C₂	#22625733	1	2	yes	direct product factor
484	C₂	C₂×C₄×C₄⋊#64408	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₄⋊#64408
commutator	C₄×C₇₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#64408
Fitting	C₂×C₄×C₈×C₇₃	C₄
socle	C₂²×C₇₃	C₄×C₄⋊C₄
prime radical	C₂³×D₇₃	#41
cosocle	C₂×C₄×D₇₃	C₂⁴
hypercenter	C₂×C₄×C₈	#64408
hypocenter	C₇₃	C₂×#1772
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
4. #22625733	C₂	direct (N × H)
9. C₂×#14556662	C₄	semidirect
10. D₇₃⋊#108	C₄	semidirect
12. C₂×#14556661	C₄	semidirect
13. #17989597	C₄	semidirect
15. C₂×#14556660	C₄	semidirect
16. C₂×#14556659	C₄	semidirect
25. C₂×C₄×#10596831	C₄	semidirect
26. C₂×C₈×Dic₇₃	C₄	semidirect
27. C₂×C₈×Dic₇₃	C₄	semidirect
28. C₄×C₈×D₇₃	C₄	semidirect
30. C₂×C₄×C₈×C₇₃	C₄	semidirect
45. #14556662	C₂×C₄	semidirect
46. #14556661	C₂×C₄	semidirect
47. #14556660	C₂×C₄	semidirect
48. #14556659	C₂×C₄	semidirect
77. C₄×#10596831	C₂×C₄	semidirect
78. C₈×Dic₇₃	C₂×C₄	semidirect
79. C₈×Dic₇₃	C₂×C₄	semidirect
83. C₄×C₈×C₇₃	C₂×C₄	semidirect
237. C₂×C₇₃	#1772	semidirect
241. D₇₃	#1772	semidirect
249. C₇₃	C₂×#1772	semidirect
272. C₂×C₄×C₈	#64408	semidirect
326. C₄×C₈	C₂×#64408	semidirect
483. C₂	#22625733	direct (N × H)

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×#17989550	2
#22625733	2
C₂×#17989458	2
C₂×C₄×C₈×D₇₃	2
C₂×#1772	73

Subgroups — C2×#22625733 #34020231

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22625733 #34020231