Subgroups — C₂×#22611393 #33114923

Order 18688.

1006 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988635	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#17988591	C₂	1	1	yes	maximal, characteristic
3	C₂×#17988591	C₂	1	1	yes	maximal, characteristic
4	C₂²×#14556507	C₂	1	1	yes	maximal, characteristic
5	#22611393	C₂	1	8	yes	maximal, direct product factor
6	C₂×#17988357	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#17988357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×H(3,ℤ/4)×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₂₉₂	C₂²	1	1	yes	characteristic
10	C₂²×#11924012	C₂²	1	1	yes	characteristic
11	C₂²×#11924012	C₂²	1	1	yes	characteristic
12	C₂²×#11924012	C₂²	1	1	yes	characteristic
13	#17988635	—	2	2	no	—
14	#17988635	C₂²	1	4	yes	complemented
15	C₂×#14556526	—	2	2	no	—
16	#17988591	—	2	2	no	—
17	#17988591	—	2	2	no	—
18	#17988591	C₂²	1	4	yes	—
19	#17988591	C₂²	1	4	yes	—
20	C₂×#14556511	—	2	2	no	—
21	C₂×#14556511	—	2	2	no	—
22	C₂×#14556507	—	2	2	no	—
23	C₂×#14556507	—	2	2	no	—
24	C₂×#14556507	C₂²	1	4	yes	—
25	#17988357	C₂²	1	4	yes	complemented
26	#17988357	C₂²	1	4	yes	complemented
27	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
28	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
29	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
30	H(3,ℤ/4)×C₇₃	C₂²	1	4	yes	complemented
31	C₂⁴×D₇₃	—	2	1	no	—
32	C₂²×D₂₉₂	—	2	1	no	—
33	C₂²×D₂₉₂	—	2	1	no	—
34	C₂²×D₂₉₂	—	2	1	no	—
35	C₂²×D₂₉₂	—	2	1	no	—
36	C₂²×D₂₉₂	—	2	1	no	—
37	C₂²×D₂₉₂	—	2	1	no	—
38	C₂²×D₂₉₂	—	2	1	no	—
39	C₂²×D₂₉₂	—	2	1	no	—
40	C₂²×D₂₉₂	—	2	1	no	—
41	C₂²×D₂₉₂	—	2	1	no	—
42	C₂²×D₂₉₂	—	2	1	no	—
43	C₂²×D₂₉₂	D₄	1	2	yes	—
44	C₂²×D₂₉₂	D₄	1	2	yes	—
45	C₂²×D₂₉₂	C₂³	1	2	yes	—
46	C₂×#11924012	—	2	1	no	—
47	C₂×#11924012	—	2	1	no	—
48	C₂×#11924012	—	2	1	no	—
49	C₂×#11924012	—	2	1	no	—
50	C₂×#11924012	—	2	1	no	—
51	C₂×#11924012	—	2	1	no	—
52	C₂×#11924012	—	2	1	no	—
53	C₂×#11924012	—	2	1	no	—
54	C₂×#11924012	—	2	1	no	—
55	C₂×#11924012	—	2	1	no	—
56	C₂×#11924012	—	2	1	no	—
57	C₂×#11924012	—	2	1	no	—
58	C₂×#11924012	—	2	1	no	—
59	C₂×#11924012	—	2	1	no	—
60	C₂×#11924012	D₄	1	2	yes	—
61	C₂×#11924012	C₂³	1	2	yes	—
62	C₂×#11924012	C₂³	1	2	yes	—
63	C₂×#11924012	C₂³	1	2	yes	—
64	C₂²×#10596831	—	2	1	no	—
65	C₂²×#10596831	—	2	1	no	—
66	C₂²×#10596831	D₄	1	2	yes	—
67	#14556526	—	2	8	no	—
68	#14556511	—	2	8	no	—
69	#14556511	—	2	8	no	—
70	#14556507	—	2	8	no	—
71	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
72	C₂×M₁₆×C₇₃	—	2	1	no	—
73	C₂×M₁₆×C₇₃	—	2	1	no	—
74	C₂×M₁₆×C₇₃	—	2	1	no	—
75	C₂×M₁₆×C₇₃	—	2	1	no	—
76	C₂×M₁₆×C₇₃	—	2	1	no	—
77	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
78	C₂²×C₈×C₇₃	—	2	1	no	—
79	#117×C₇₃	—	2	1	no	—
80	#117×C₇₃	—	2	1	no	—
81	#117×C₇₃	—	2	1	no	—
82	#117×C₇₃	—	2	1	no	—
83	#117×C₇₃	—	2	1	no	—
84	#117×C₇₃	—	2	1	no	—
85	#117×C₇₃	C₂³	1	2	yes	—
86	#117×C₇₃	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
88	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
91	C₂×C₄²×C₇₃	—	2	1	no	—
92	C₂×C₄²×C₇₃	—	2	1	no	—
93	C₂³×D₇₃	—	2	2	no	—
94	C₂³×D₇₃	—	2	2	no	—
95	C₂³×D₇₃	—	2	2	no	—
96	C₂³×D₇₃	—	4	1	no	—
97	C₂³×D₇₃	—	4	1	no	—
98	C₂³×D₇₃	—	4	1	no	—
99	C₂³×D₇₃	—	4	1	no	—
100	C₂³×D₇₃	—	8	4	no	—
101	C₂×D₂₉₂	—	2	2	no	—
102	C₂×D₂₉₂	—	2	2	no	—
103	C₂×D₂₉₂	—	2	2	no	—
104	C₂×D₂₉₂	—	2	2	no	—
105	C₂×D₂₉₂	—	2	2	no	—
106	C₂×D₂₉₂	—	2	2	no	—
107	C₂×D₂₉₂	—	2	2	no	—
108	C₂×D₂₉₂	—	2	2	no	—
109	C₂×D₂₉₂	—	2	2	no	—
110	C₂×D₂₉₂	—	2	2	no	—
111	C₂×D₂₉₂	—	2	2	no	—
112	C₂×D₂₉₂	—	2	2	no	—
113	C₂×D₂₉₂	—	2	2	no	—
114	C₂×D₂₉₂	—	2	2	no	—
115	C₂×D₂₉₂	—	2	2	no	—
116	C₂×D₂₉₂	—	4	1	no	—
117	C₂×D₂₉₂	—	4	1	no	—
118	C₂×D₂₉₂	—	4	1	no	—
119	C₂×D₂₉₂	—	4	1	no	—
120	C₂×D₂₉₂	—	4	1	no	—
121	C₂×D₂₉₂	—	4	1	no	—
122	C₂×D₂₉₂	—	4	1	no	—
123	C₂×D₂₉₂	—	4	1	no	—
124	C₂×D₂₉₂	—	4	1	no	—
125	C₂×D₂₉₂	—	4	1	no	—
126	C₂×D₂₉₂	—	4	1	no	—
127	C₂×D₂₉₂	—	4	1	no	—
128	C₂×D₂₉₂	C₂×D₄	1	4	yes	—
129	#11924012	—	2	2	no	—
130	#11924012	—	2	2	no	—
131	#11924012	—	2	2	no	—
132	#11924012	—	2	2	no	—
133	#11924012	—	2	2	no	—
134	#11924012	—	2	2	no	—
135	#11924012	—	2	2	no	—
136	#11924012	—	2	2	no	—
137	#11924012	—	4	1	no	—
138	#11924012	—	4	1	no	—
139	#11924012	—	4	1	no	—
140	#11924012	—	4	1	no	—
141	C₂×#10596831	—	2	2	no	—
142	C₂×#10596831	—	2	2	no	—
143	C₂×#10596831	—	2	2	no	—
144	C₂×#10596831	—	2	2	no	—
145	C₂×#10596831	—	4	1	no	—
146	C₂×#10596831	—	4	1	no	—
147	C₂×#10596831	—	4	1	no	—
148	C₂×#10596831	—	4	1	no	—
149	C₂×#10596831	C₂×D₄	1	4	yes	—
150	C₂⁴×C₇₃	#41	1	1	yes	characteristic
151	C₂²×C₄×C₇₃	—	4	1	no	—
152	C₂²×C₄×C₇₃	—	4	1	no	—
153	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
158	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
159	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
160	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
161	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
162	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
163	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
164	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
165	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
166	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
167	M₁₆×C₇₃	—	2	2	no	—
168	M₁₆×C₇₃	—	2	2	no	—
169	M₁₆×C₇₃	—	4	1	no	—
170	M₁₆×C₇₃	—	4	1	no	—
171	C₂×C₈×C₇₃	—	2	2	no	—
172	C₂×C₈×C₇₃	—	4	1	no	—
173	C₂×C₈×C₇₃	—	4	1	no	—
174	C₄⋊C₄×C₇₃	—	2	2	no	—
175	C₄⋊C₄×C₇₃	—	2	2	no	—
176	C₄⋊C₄×C₇₃	—	4	1	no	—
177	C₄⋊C₄×C₇₃	—	4	1	no	—
178	C₂²⋊C₄×C₇₃	—	2	2	no	—
179	C₂²⋊C₄×C₇₃	—	2	2	no	—
180	C₂²⋊C₄×C₇₃	—	4	1	no	—
181	C₂²⋊C₄×C₇₃	—	4	1	no	—
182	C₄²×C₇₃	—	2	2	no	—
183	C₄²×C₇₃	—	2	2	no	—
184	C₄²×C₇₃	—	4	1	no	—
185	C₄²×C₇₃	—	4	1	no	—
186	C₂³×C₇₃	—	4	2	no	—
187	C₂³×C₇₃	#123	1	1	yes	characteristic
188	C₂³×C₇₃	#123	1	1	yes	characteristic
189	C₂³×C₇₃	#124	1	1	yes	characteristic
190	C₂³×C₇₃	#124	1	1	yes	characteristic
191	C₂³×C₇₃	#126	1	1	yes	characteristic
192	C₂³×C₇₃	#126	1	1	yes	characteristic
193	C₂³×C₇₃	C₂×#41	1	1	yes	characteristic
194	C₂²×D₇₃	—	2	4	no	—
195	C₂²×D₇₃	—	4	2	no	—
196	C₂²×D₇₃	—	4	2	no	—
197	C₂²×D₇₃	—	4	2	no	—
198	C₂²×D₇₃	—	4	2	no	—
199	C₂²×D₇₃	—	4	2	no	—
200	C₂²×D₇₃	—	4	2	no	—
201	C₂²×D₇₃	—	8	4	no	—
202	C₂²×D₇₃	—	8	4	no	—
203	C₂²×D₇₃	—	8	4	no	—
204	C₂²×D₇₃	—	8	4	no	—
205	C₂²×D₇₃	—	8	4	no	—
206	C₂²×D₇₃	—	8	4	no	—
207	C₂²×D₇₃	—	8	4	no	—
208	C₂×C₄×C₇₃	—	4	2	no	—
209	C₂×C₄×C₇₃	—	4	2	no	—
210	C₂×C₄×C₇₃	—	8	2	no	—
211	C₂×C₄×C₇₃	—	8	2	no	—
212	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
213	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
214	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
215	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
216	C₂×C₄×C₇₃	#123	1	1	yes	characteristic
217	C₂×C₄×C₇₃	#123	1	1	yes	characteristic
218	C₂×C₄×C₇₃	#123	1	1	yes	characteristic
219	C₂×C₄×C₇₃	#123	1	1	yes	characteristic
220	C₂×C₄×C₇₃	#123	1	1	yes	characteristic
221	C₂×C₄×C₇₃	#123	1	1	yes	characteristic
222	C₂×C₄×C₇₃	#123	1	1	yes	characteristic
223	C₂×C₄×C₇₃	#123	1	1	yes	characteristic
224	C₂×C₄×C₇₃	#123	1	1	yes	characteristic
225	C₂×C₄×C₇₃	#123	1	1	yes	characteristic
226	C₂×C₄×C₇₃	#124	1	1	yes	characteristic
227	C₂×C₄×C₇₃	#124	1	1	yes	characteristic
228	C₂×C₄×C₇₃	#126	1	1	yes	characteristic
229	C₂×C₄×C₇₃	#126	1	1	yes	characteristic
230	C₂×C₄×C₇₃	#126	1	1	yes	characteristic
231	C₂×C₄×C₇₃	#126	1	1	yes	characteristic
232	C₂×C₄×C₇₃	#126	1	1	yes	characteristic
233	C₂×C₄×C₇₃	#126	1	1	yes	characteristic
234	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
238	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
239	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
240	D₂₉₂	—	2	4	no	—
241	D₂₉₂	—	2	4	no	—
242	D₂₉₂	—	4	2	no	—
243	D₂₉₂	—	4	2	no	—
244	D₂₉₂	—	4	2	no	—
245	D₂₉₂	—	4	2	no	—
246	D₂₉₂	—	4	2	no	—
247	D₂₉₂	—	4	2	no	—
248	C₈×C₇₃	—	4	2	no	—
249	#10596831	—	2	4	no	—
250	#10596831	—	4	2	no	—
251	#10596831	—	4	2	no	—
252	C₂²×C₇₃	—	2	2	no	—
253	C₂²×C₇₃	—	2	2	no	—
254	C₂²×C₇₃	—	2	2	no	—
255	C₂²×C₇₃	—	4	1	no	—
256	C₂²×C₇₃	—	4	1	no	—
257	C₂²×C₇₃	—	4	1	no	—
258	C₂²×C₇₃	—	4	1	no	—
259	C₂²×C₇₃	#397	1	1	yes	characteristic
260	C₂²×C₇₃	#397	1	1	yes	characteristic
261	C₂²×C₇₃	#397	1	1	yes	characteristic
262	C₂²×C₇₃	#397	1	1	yes	characteristic
263	C₂²×C₇₃	C₂×#123	1	1	yes	characteristic
264	C₂²×C₇₃	C₂×#124	1	1	yes	characteristic
265	C₂²×C₇₃	C₂×#126	1	1	yes	characteristic
266	C₂×D₇₃	—	4	4	no	—
267	C₂×D₇₃	—	8	4	no	—
268	C₂×D₇₃	—	8	4	no	—
269	C₂×D₇₃	—	8	4	no	—
270	C₂×D₇₃	—	8	4	no	—
271	C₂×D₇₃	—	8	4	no	—
272	C₂×D₇₃	—	8	4	no	—
273	C₂×D₇₃	—	8	4	no	—
274	C₄×C₇₃	—	8	2	no	—
275	C₄×C₇₃	—	8	2	no	—
276	C₄×C₇₃	#397	1	1	yes	characteristic
277	C₄×C₇₃	#397	1	1	yes	characteristic
278	C₄×C₇₃	#397	1	1	yes	characteristic
279	C₄×C₇₃	#397	1	1	yes	characteristic
280	C₄×C₇₃	C₂×#121	1	1	yes	characteristic
281	C₄×C₇₃	C₂×#123	1	1	yes	characteristic
282	C₄×C₇₃	C₂×#123	1	1	yes	characteristic
283	C₄×C₇₃	C₂×#126	1	1	yes	characteristic
284	C₂×#2081	—	73	1	no	maximal, Sylow
285	C₂×C₇₃	—	2	1	no	—
286	C₂×C₇₃	—	2	1	no	—
287	C₂×C₇₃	—	2	1	no	—
288	C₂×C₇₃	—	2	1	no	—
289	C₂×C₇₃	—	2	1	no	—
290	C₂×C₇₃	—	2	1	no	—
291	C₂×C₇₃	#2081	1	2	yes	complemented
292	C₂×C₇₃	C₂×#397	1	1	yes	characteristic
293	D₇₃	—	8	4	no	—
294	C₂×#430	—	73	1	no	—
295	C₂×#418	—	73	1	no	—
296	C₂×#418	—	73	1	no	—
297	C₂²×#100	—	73	1	no	—
298	#2081	—	73	8	no	—
299	C₂×#344	—	73	1	no	—
300	C₂×#344	—	73	1	no	—
301	C₂×H(3,ℤ/4)	D₇₃	1	1	yes	characteristic, complemented
302	C₇₃	C₂×#2081	1	1	yes	characteristic, complemented, Sylow
303	C₂³×D₄	—	73	1	no	—
304	C₂²×M₁₆	—	73	1	no	—
305	C₂²×M₁₆	—	73	1	no	—
306	C₂²×M₁₆	—	73	1	no	—
307	C₂²×M₁₆	C₂×D₇₃	1	1	yes	characteristic
308	C₂×#117	C₂×D₇₃	1	1	yes	characteristic
309	C₂×#117	C₂×D₇₃	1	1	yes	characteristic
310	#430	—	73	4	no	—
311	#430	—	146	2	no	—
312	C₂×#108	—	146	2	no	—
313	#418	—	73	4	no	—
314	#418	—	73	4	no	—
315	#418	—	146	2	no	—
316	#418	—	146	2	no	—
317	C₂×#102	—	146	2	no	—
318	C₂×#102	—	146	2	no	—
319	C₂×#100	—	73	4	no	—
320	C₂×#100	—	146	2	no	—
321	C₂×#100	—	146	2	no	—
322	#344	—	73	4	no	—
323	#344	—	73	4	no	—
324	H(3,ℤ/4)	C₂×D₇₃	1	4	yes	complemented
325	C₂⁵	—	146	1	no	—
326	C₂²×D₄	—	73	2	no	—
327	C₂²×D₄	—	73	2	no	—
328	C₂²×D₄	—	73	2	no	—
329	C₂²×D₄	—	146	1	no	—
330	C₂²×D₄	—	146	1	no	—
331	C₂²×D₄	—	146	1	no	—
332	C₂²×D₄	—	146	1	no	—
333	C₂²×D₄	—	146	1	no	—
334	C₂²×D₄	—	146	1	no	—
335	C₂²×D₄	—	146	1	no	—
336	C₂²×D₄	—	146	1	no	—
337	C₂²×D₄	—	146	1	no	—
338	C₂²×D₄	—	146	1	no	—
339	C₂²×D₄	—	146	1	no	—
340	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
341	C₂×M₁₆	—	2	1	no	—
342	C₂×M₁₆	—	2	1	no	—
343	C₂×M₁₆	—	2	1	no	—
344	C₂×M₁₆	—	2	1	no	—
345	C₂×M₁₆	—	2	1	no	—
346	C₂×M₁₆	—	73	2	no	—
347	C₂×M₁₆	—	73	2	no	—
348	C₂×M₁₆	—	73	2	no	—
349	C₂×M₁₆	—	73	2	no	—
350	C₂×M₁₆	—	146	1	no	—
351	C₂×M₁₆	—	146	1	no	—
352	C₂×M₁₆	—	146	1	no	—
353	C₂×M₁₆	—	146	1	no	—
354	C₂×M₁₆	—	146	1	no	—
355	C₂×M₁₆	—	146	1	no	—
356	C₂×M₁₆	—	146	1	no	—
357	C₂×M₁₆	—	146	1	no	—
358	C₂×M₁₆	—	146	1	no	—
359	C₂×M₁₆	—	146	1	no	—
360	C₂×M₁₆	—	146	1	no	—
361	C₂×M₁₆	—	146	1	no	—
362	C₂×M₁₆	—	146	1	no	—
363	C₂×M₁₆	—	146	1	no	—
364	C₂×M₁₆	C₂²×D₇₃	1	2	yes	—
365	C₂²×C₈	—	2	1	no	—
366	C₂²×C₈	—	73	2	no	—
367	C₂²×C₈	—	146	1	no	—
368	C₂²×C₈	—	146	1	no	—
369	#117	—	2	1	no	—
370	#117	—	2	1	no	—
371	#117	—	2	1	no	—
372	#117	—	2	1	no	—
373	#117	—	2	1	no	—
374	#117	—	2	1	no	—
375	#117	C₂²×D₇₃	1	2	yes	—
376	#117	C₂²×D₇₃	1	2	yes	—
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₂²⋊C₄	—	2	1	no	—
380	C₂×C₂²⋊C₄	—	2	1	no	—
381	C₂×C₄²	—	2	1	no	—
382	C₂×C₄²	—	2	1	no	—
383	#108	—	146	8	no	—
384	#102	—	146	8	no	—
385	#102	—	146	8	no	—
386	#100	—	146	8	no	—
387	C₂⁴	—	292	1	no	—
388	C₂⁴	—	292	1	no	—
389	C₂⁴	—	292	1	no	—
390	C₂⁴	—	292	1	no	—
391	C₂⁴	—	584	4	no	—
392	C₂⁴	—	146	2	no	—
393	C₂⁴	—	146	2	no	—
394	C₂⁴	—	146	2	no	—
395	C₂⁴	#11924027	1	1	yes	characteristic
396	C₂×D₄	—	292	1	no	—
397	C₂×D₄	—	292	1	no	—
398	C₂×D₄	—	292	1	no	—
399	C₂×D₄	—	292	1	no	—
400	C₂×D₄	—	292	1	no	—
401	C₂×D₄	—	292	1	no	—
402	C₂×D₄	—	292	1	no	—
403	C₂×D₄	—	292	1	no	—
404	C₂×D₄	—	292	1	no	—
405	C₂×D₄	—	292	1	no	—
406	C₂×D₄	—	292	1	no	—
407	C₂×D₄	—	292	1	no	—
408	C₂×D₄	—	73	4	no	—
409	C₂×D₄	—	146	2	no	—
410	C₂×D₄	—	146	2	no	—
411	C₂×D₄	—	146	2	no	—
412	C₂×D₄	—	146	2	no	—
413	C₂×D₄	—	146	2	no	—
414	C₂×D₄	—	146	2	no	—
415	C₂×D₄	—	146	2	no	—
416	C₂×D₄	—	146	2	no	—
417	C₂×D₄	—	146	2	no	—
418	C₂×D₄	—	146	2	no	—
419	C₂×D₄	—	146	2	no	—
420	C₂×D₄	—	146	2	no	—
421	C₂×D₄	—	146	2	no	—
422	C₂×D₄	—	146	2	no	—
423	C₂×D₄	—	146	2	no	—
424	C₂²×C₄	—	4	1	no	—
425	C₂²×C₄	—	4	1	no	—
426	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
427	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
428	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
429	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
430	C₂²×C₄	#11924027	1	1	yes	characteristic
431	C₂²×C₄	#11924028	1	1	yes	characteristic
432	C₂²×C₄	#11924028	1	1	yes	characteristic
433	C₂²×C₄	#11924028	1	1	yes	characteristic
434	C₂²×C₄	#11924028	1	1	yes	characteristic
435	C₂²×C₄	#11924028	1	1	yes	characteristic
436	C₂²×C₄	#11924028	1	1	yes	characteristic
437	C₂²×C₄	#11924029	1	1	yes	characteristic
438	C₂²×C₄	#11924029	1	1	yes	characteristic
439	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
440	M₁₆	—	2	2	no	—
441	M₁₆	—	2	2	no	—
442	M₁₆	—	4	1	no	—
443	M₁₆	—	4	1	no	—
444	M₁₆	—	292	1	no	—
445	M₁₆	—	292	1	no	—
446	M₁₆	—	292	1	no	—
447	M₁₆	—	292	1	no	—
448	M₁₆	—	146	2	no	—
449	M₁₆	—	146	2	no	—
450	M₁₆	—	146	2	no	—
451	M₁₆	—	146	2	no	—
452	M₁₆	—	146	2	no	—
453	M₁₆	—	146	2	no	—
454	M₁₆	—	146	2	no	—
455	M₁₆	—	146	2	no	—
456	C₂×C₈	—	2	2	no	—
457	C₂×C₈	—	4	1	no	—
458	C₂×C₈	—	4	1	no	—
459	C₂×C₈	—	292	1	no	—
460	C₂×C₈	—	292	1	no	—
461	C₂×C₈	—	292	1	no	—
462	C₂×C₈	—	292	1	no	—
463	C₂×C₈	—	73	4	no	—
464	C₂×C₈	—	146	2	no	—
465	C₂×C₈	—	146	2	no	—
466	C₂×C₈	—	146	2	no	—
467	C₂×C₈	—	146	2	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	4	1	no	—
471	C₄⋊C₄	—	4	1	no	—
472	C₂²⋊C₄	—	2	2	no	—
473	C₂²⋊C₄	—	2	2	no	—
474	C₂²⋊C₄	—	4	1	no	—
475	C₂²⋊C₄	—	4	1	no	—
476	C₄²	—	2	2	no	—
477	C₄²	—	2	2	no	—
478	C₄²	—	4	1	no	—
479	C₄²	—	4	1	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	292	2	no	—
482	C₂³	—	292	2	no	—
483	C₂³	—	292	2	no	—
484	C₂³	—	292	2	no	—
485	C₂³	—	292	2	no	—
486	C₂³	—	292	2	no	—
487	C₂³	—	584	4	no	—
488	C₂³	—	584	4	no	—
489	C₂³	—	584	4	no	—
490	C₂³	—	584	4	no	—
491	C₂³	—	584	4	no	—
492	C₂³	—	584	4	no	—
493	C₂³	—	584	4	no	—
494	C₂³	—	146	4	no	—
495	C₂³	#14556573	1	1	yes	characteristic
496	C₂³	#14556573	1	1	yes	characteristic
497	C₂³	#14556577	1	1	yes	characteristic
498	C₂³	#14556577	1	1	yes	characteristic
499	C₂³	#14556586	1	1	yes	characteristic
500	C₂³	#14556586	1	1	yes	characteristic
501	C₂³	C₂×#11924027	1	1	yes	characteristic
502	D₄	—	292	2	no	—
503	D₄	—	292	2	no	—
504	D₄	—	292	2	no	—
505	D₄	—	292	2	no	—
506	D₄	—	292	2	no	—
507	D₄	—	292	2	no	—
508	D₄	—	146	4	no	—
509	D₄	—	146	4	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	8	2	no	—
513	C₂×C₄	—	8	2	no	—
514	C₂×C₄	#14556564	1	1	yes	characteristic
515	C₂×C₄	#14556564	1	1	yes	characteristic
516	C₂×C₄	#14556564	1	1	yes	characteristic
517	C₂×C₄	#14556564	1	1	yes	characteristic
518	C₂×C₄	#14556573	1	1	yes	characteristic
519	C₂×C₄	#14556573	1	1	yes	characteristic
520	C₂×C₄	#14556576	1	1	yes	characteristic
521	C₂×C₄	#14556576	1	1	yes	characteristic
522	C₂×C₄	#14556576	1	1	yes	characteristic
523	C₂×C₄	#14556576	1	1	yes	characteristic
524	C₂×C₄	#14556576	1	1	yes	characteristic
525	C₂×C₄	#14556576	1	1	yes	characteristic
526	C₂×C₄	#14556576	1	1	yes	characteristic
527	C₂×C₄	#14556576	1	1	yes	characteristic
528	C₂×C₄	#14556577	1	1	yes	characteristic
529	C₂×C₄	#14556577	1	1	yes	characteristic
530	C₂×C₄	#14556585	1	1	yes	characteristic
531	C₂×C₄	#14556585	1	1	yes	characteristic
532	C₂×C₄	#14556585	1	1	yes	characteristic
533	C₂×C₄	#14556585	1	1	yes	characteristic
534	C₂×C₄	#14556586	1	1	yes	characteristic
535	C₂×C₄	#14556586	1	1	yes	characteristic
536	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
537	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
538	C₂×C₄	C₂×#11924028	1	1	yes	characteristic
539	C₂×C₄	C₂×#11924028	1	1	yes	characteristic
540	C₂×C₄	C₂×#11924028	1	1	yes	characteristic
541	C₂×C₄	C₂×#11924029	1	1	yes	characteristic
542	C₈	—	4	2	no	—
543	C₈	—	292	2	no	—
544	C₈	—	292	2	no	—
545	C₈	—	146	4	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	292	4	no	—
554	C₂²	—	584	4	no	—
555	C₂²	—	584	4	no	—
556	C₂²	—	584	4	no	—
557	C₂²	—	584	4	no	—
558	C₂²	—	584	4	no	—
559	C₂²	—	584	4	no	—
560	C₂²	—	584	4	no	—
561	C₂²	#17988516	1	1	yes	characteristic
562	C₂²	#17988516	1	1	yes	characteristic
563	C₂²	#17988516	1	1	yes	characteristic
564	C₂²	#17988516	1	1	yes	characteristic
565	C₂²	C₂×#14556573	1	1	yes	characteristic
566	C₂²	C₂×#14556577	1	1	yes	characteristic
567	C₂²	C₂×#14556586	1	1	yes	characteristic
568	C₄	—	8	2	no	—
569	C₄	—	8	2	no	—
570	C₄	#17988516	1	1	yes	characteristic
571	C₄	#17988516	1	1	yes	characteristic
572	C₄	#17988516	1	1	yes	characteristic
573	C₄	#17988516	1	1	yes	characteristic
574	C₄	C₂×#14556564	1	1	yes	characteristic
575	C₄	C₂×#14556576	1	1	yes	characteristic
576	C₄	C₂×#14556576	1	1	yes	characteristic
577	C₄	C₂×#14556585	1	1	yes	characteristic
578	C₂	—	2	1	no	—
579	C₂	—	2	1	no	—
580	C₂	—	2	1	no	—
581	C₂	—	2	1	no	—
582	C₂	—	2	1	no	—
583	C₂	—	2	1	no	—
584	C₂	—	584	4	no	—
585	C₂	#22611393	1	2	yes	direct product factor
586	C₂	C₂×#17988516	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#17988516
commutator, cosocle	C₂²×C₄×C₇₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₇₃
Fitting	C₂×H(3,ℤ/4)×C₇₃	C₂
socle	C₂²×C₇₃	#397
prime radical	C₂³×D₂₉₂	C₂²
hypercenter	C₂×H(3,ℤ/4)	D₇₃
hypocenter	C₇₃	C₂×#2081
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×H(3,ℤ/4)

Complements

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

N	H ≅ G/N	type
1. C₂×#17988635	C₂	semidirect
5. #22611393	C₂	direct (N × H)
6. C₂×#17988357	C₂	semidirect
7. C₂×#17988357	C₂	semidirect
8. C₂×H(3,ℤ/4)×C₇₃	C₂	semidirect
14. #17988635	C₂²	semidirect
25. #17988357	C₂²	semidirect
26. #17988357	C₂²	semidirect
30. H(3,ℤ/4)×C₇₃	C₂²	semidirect
291. C₂×C₇₃	#2081	semidirect
301. C₂×H(3,ℤ/4)	D₇₃	semidirect
302. C₇₃	C₂×#2081	semidirect
324. H(3,ℤ/4)	C₂×D₇₃	semidirect
585. C₂	#22611393	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×#17988635	2
C₂×#17988591	2
C₂²×#14556507	2
#22611393	2
C₂×#17988357	2
C₂×H(3,ℤ/4)×C₇₃	2
C₂×#2081	73

Subgroups — C2×#22611393 #33114923

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22611393 #33114923