Subgroups — C₂²×#17989385 #33999788

Order 18688.

11294 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#11924028	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#17989385	C₂	1	48	yes	maximal, direct product factor
3	C₂²×#14556622	C₂	1	2	yes	maximal, complemented
4	C₂²×#14556621	C₂	1	2	yes	maximal, complemented
5	C₂²×#14556617	C₂	1	2	yes	maximal, complemented
6	C₂²×#14556616	C₂	1	2	yes	maximal, complemented
7	C₂²×#14556611	C₂	1	4	yes	maximal, complemented
8	C₂³×#11924012	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×#41×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#11924028	—	2	1	no	—
11	C₂²×#11924028	—	2	1	no	—
12	C₂²×#11924028	—	2	12	no	—
13	C₂²×#11924028	C₂²	1	2	yes	—
14	C₂²×#11924028	C₂²	1	2	yes	complemented
15	C₂²×#11924028	C₂²	1	24	yes	complemented
16	C₂³×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
17	C₂³×D₂₉₂	C₂²	1	1	yes	characteristic, complemented
18	C₂³×C₂²⋊D₇₃	—	2	1	no	—
19	C₂³×C₄×D₇₃	—	2	1	no	—
20	#17989385	C₂²	1	256	yes	direct product factor
21	C₂×#14556622	C₂²	1	48	yes	complemented
22	C₂×#14556621	C₂²	1	48	yes	complemented
23	C₂×#14556617	C₂²	1	48	yes	complemented
24	C₂×#14556616	C₂²	1	48	yes	complemented
25	C₂×#14556611	C₂²	1	96	yes	complemented
26	C₂²×#11924018	C₂²	1	4	yes	complemented
27	C₂²×#11924016	C₂²	1	4	yes	complemented
28	C₂²×#11924015	C₂²	1	4	yes	complemented
29	C₂²×#11924013	C₂²	1	4	yes	complemented
30	C₂²×#11924012	C₂²	1	2	yes	complemented
31	C₂²×#11924012	C₂²	1	2	yes	complemented
32	C₂²×#11924012	C₂²	1	24	yes	complemented
33	C₂³×#10596831	C₂²	1	2	yes	complemented
34	C₂²×#41×C₇₃	—	2	1	no	—
35	C₂²×#41×C₇₃	—	2	1	no	—
36	C₂²×#41×C₇₃	—	2	12	no	—
37	C₂²×#41×C₇₃	C₂²	1	2	yes	—
38	C₂²×#41×C₇₃	C₂²	1	2	yes	complemented
39	C₂²×#41×C₇₃	C₂²	1	24	yes	complemented
40	C₂³×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
41	C₂³×D₄×C₇₃	—	2	1	no	—
42	C₂³×D₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
43	C₂⁴×C₄×C₇₃	—	2	1	no	—
44	C₂⁴×C₄×C₇₃	C₂²	1	1	yes	characteristic
45	C₂⁴×D₇₃	—	2	1	no	—
46	C₂×#11924028	—	2	12	no	—
47	C₂×#11924028	—	2	24	no	—
48	C₂×#11924028	—	2	24	no	—
49	C₂×#11924028	—	2	12	no	—
50	C₂×#11924028	—	2	96	no	—
51	C₂×#11924028	C₂³	1	24	yes	—
52	C₂×#11924028	C₂³	1	24	yes	complemented
53	C₂×#11924028	C₂³	1	64	yes	complemented
54	C₂²×Dic₁₄₆	—	2	1	no	—
55	C₂²×Dic₁₄₆	—	2	6	no	—
56	C₂²×Dic₁₄₆	C₂³	1	2	yes	—
57	C₂²×Dic₁₄₆	C₂³	1	12	yes	complemented
58	C₂²×D₂₉₂	—	2	1	no	—
59	C₂²×D₂₉₂	—	2	6	no	—
60	C₂²×D₂₉₂	C₂³	1	2	yes	—
61	C₂²×D₂₉₂	C₂³	1	12	yes	complemented
62	C₂²×C₂²⋊D₇₃	—	2	2	no	—
63	C₂²×C₂²⋊D₇₃	—	2	2	no	—
64	C₂²×C₂²⋊D₇₃	—	2	24	no	—
65	C₂³×Dic₇₃	—	2	1	no	—
66	C₂²×C₄×D₇₃	—	2	2	no	—
67	C₂²×C₄×D₇₃	—	2	24	no	—
68	C₂²×C₄×D₇₃	—	2	2	no	—
69	#14556622	C₂³	1	128	yes	complemented
70	#14556621	C₂³	1	128	yes	complemented
71	#14556617	C₂³	1	128	yes	complemented
72	#14556616	C₂³	1	128	yes	complemented
73	#14556611	C₂³	1	256	yes	complemented
74	C₂×#11924018	C₂³	1	48	yes	complemented
75	C₂×#11924016	C₂³	1	48	yes	complemented
76	C₂×#11924015	C₂³	1	48	yes	complemented
77	C₂×#11924013	C₂³	1	48	yes	complemented
78	C₂×#11924012	C₂³	1	24	yes	complemented
79	C₂×#11924012	C₂³	1	24	yes	complemented
80	C₂×#11924012	C₂³	1	64	yes	complemented
81	C₂²×#10596831	C₂³	1	4	yes	—
82	C₂²×#10596831	C₂³	1	24	yes	complemented
83	C₂⁵×C₇₃	—	2	1	no	—
84	C₂⁵×C₇₃	D₄	1	1	yes	characteristic
85	C₂×#41×C₇₃	—	2	12	no	—
86	C₂×#41×C₇₃	—	2	24	no	—
87	C₂×#41×C₇₃	—	2	24	no	—
88	C₂×#41×C₇₃	—	2	12	no	—
89	C₂×#41×C₇₃	—	2	96	no	—
90	C₂×#41×C₇₃	C₂³	1	24	yes	—
91	C₂×#41×C₇₃	C₂³	1	24	yes	complemented
92	C₂×#41×C₇₃	C₂³	1	64	yes	complemented
93	C₂²×Q₈×C₇₃	—	2	1	no	—
94	C₂²×Q₈×C₇₃	—	2	6	no	—
95	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
96	C₂²×Q₈×C₇₃	C₂³	1	12	yes	complemented
97	C₂²×D₄×C₇₃	—	2	2	no	—
98	C₂²×D₄×C₇₃	—	2	2	no	—
99	C₂²×D₄×C₇₃	—	2	24	no	—
100	C₂²×D₄×C₇₃	—	2	1	no	—
101	C₂²×D₄×C₇₃	—	2	6	no	—
102	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
103	C₂²×D₄×C₇₃	C₂³	1	12	yes	complemented
104	C₂³×C₄×C₇₃	—	2	1	no	—
105	C₂³×C₄×C₇₃	—	2	2	no	—
106	C₂³×C₄×C₇₃	—	2	2	no	—
107	C₂³×C₄×C₇₃	—	2	24	no	—
108	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
109	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
110	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
111	C₂³×C₄×C₇₃	D₄	1	12	yes	—
112	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₇₃	C₂³	1	12	yes	—
116	C₂³×D₇₃	—	2	2	no	—
117	C₂³×D₇₃	—	2	12	no	—
118	C₂³×D₇₃	—	4	8	no	—
119	#11924028	—	2	48	no	—
120	#11924028	—	2	48	no	—
121	#11924028	—	2	64	no	—
122	#11924028	—	2	64	no	—
123	#11924028	C₂⁴	1	32	yes	—
124	#11924028	C₂⁴	1	32	yes	complemented
125	C₂×Dic₁₄₆	—	2	6	no	—
126	C₂×Dic₁₄₆	—	2	24	no	—
127	C₂×Dic₁₄₆	—	2	12	no	—
128	C₂×Dic₁₄₆	C₂⁴	1	12	yes	—
129	C₂×Dic₁₄₆	C₂⁴	1	16	yes	complemented
130	C₂×D₂₉₂	—	2	6	no	—
131	C₂×D₂₉₂	—	2	24	no	—
132	C₂×D₂₉₂	—	2	12	no	—
133	C₂×D₂₉₂	C₂⁴	1	12	yes	—
134	C₂×D₂₉₂	C₂⁴	1	16	yes	complemented
135	C₂×C₂²⋊D₇₃	—	2	24	no	—
136	C₂×C₂²⋊D₇₃	—	2	24	no	—
137	C₂×C₂²⋊D₇₃	—	2	64	no	—
138	C₂²×Dic₇₃	—	2	2	no	—
139	C₂²×Dic₇₃	—	2	12	no	—
140	C₂×C₄×D₇₃	—	2	24	no	—
141	C₂×C₄×D₇₃	—	2	64	no	—
142	C₂×C₄×D₇₃	—	2	24	no	—
143	#11924018	C₂⁴	1	64	yes	complemented
144	#11924016	C₂⁴	1	64	yes	complemented
145	#11924015	C₂⁴	1	64	yes	complemented
146	#11924013	C₂⁴	1	64	yes	complemented
147	#11924012	C₂⁴	1	32	yes	complemented
148	#11924012	C₂⁴	1	32	yes	complemented
149	C₂×#10596831	C₂⁴	1	24	yes	—
150	C₂×#10596831	C₂⁴	1	32	yes	complemented
151	C₂⁴×C₇₃	—	2	2	no	—
152	C₂⁴×C₇₃	—	2	12	no	—
153	C₂⁴×C₇₃	—	4	4	no	—
154	C₂⁴×C₇₃	—	4	8	no	—
155	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
156	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
157	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
158	C₂⁴×C₇₃	C₂×D₄	1	12	yes	—
159	#41×C₇₃	—	2	48	no	—
160	#41×C₇₃	—	2	64	no	—
161	#41×C₇₃	—	2	64	no	—
162	#41×C₇₃	—	2	48	no	—
163	#41×C₇₃	C₂⁴	1	32	yes	—
164	#41×C₇₃	C₂⁴	1	32	yes	complemented
165	C₂×Q₈×C₇₃	—	2	6	no	—
166	C₂×Q₈×C₇₃	—	2	12	no	—
167	C₂×Q₈×C₇₃	—	2	24	no	—
168	C₂×Q₈×C₇₃	C₂⁴	1	12	yes	—
169	C₂×Q₈×C₇₃	C₂⁴	1	16	yes	complemented
170	C₂×D₄×C₇₃	—	2	24	no	—
171	C₂×D₄×C₇₃	—	2	24	no	—
172	C₂×D₄×C₇₃	—	2	64	no	—
173	C₂×D₄×C₇₃	—	2	6	no	—
174	C₂×D₄×C₇₃	—	2	12	no	—
175	C₂×D₄×C₇₃	—	2	24	no	—
176	C₂×D₄×C₇₃	C₂⁴	1	12	yes	—
177	C₂×D₄×C₇₃	C₂⁴	1	16	yes	complemented
178	C₂²×C₄×C₇₃	—	2	2	no	—
179	C₂²×C₄×C₇₃	—	2	12	no	—
180	C₂²×C₄×C₇₃	—	2	24	no	—
181	C₂²×C₄×C₇₃	—	2	24	no	—
182	C₂²×C₄×C₇₃	—	2	64	no	—
183	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₇₃	C₂×D₄	1	12	yes	—
185	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₇₃	C₂×D₄	1	6	yes	—
187	C₂²×C₄×C₇₃	C₂×D₄	1	12	yes	—
188	C₂²×C₄×C₇₃	C₂×D₄	1	6	yes	—
189	C₂²×C₄×C₇₃	C₂×D₄	1	6	yes	—
190	C₂²×C₄×C₇₃	C₂×D₄	1	12	yes	—
191	C₂²×C₄×C₇₃	C₂×D₄	1	48	yes	—
192	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
194	C₂²×C₄×C₇₃	C₂⁴	1	6	yes	—
195	C₂²×C₄×C₇₃	C₂⁴	1	6	yes	—
196	C₂²×C₄×C₇₃	C₂⁴	1	6	yes	—
197	C₂²×C₄×C₇₃	C₂⁴	1	16	yes	—
198	C₂³×C₇₃	—	2	4	no	—
199	C₂³×C₇₃	—	2	4	no	—
200	C₂³×C₇₃	—	2	4	no	—
201	C₂³×C₇₃	—	2	12	no	—
202	C₂³×C₇₃	—	2	16	no	—
203	C₂³×C₇₃	—	4	24	no	—
204	C₂³×C₇₃	—	4	48	no	—
205	C₂³×C₇₃	—	4	8	no	—
206	C₂³×C₇₃	C₂²×D₄	1	6	yes	—
207	C₂³×C₇₃	C₂²×D₄	1	6	yes	—
208	C₂³×C₇₃	C₂²×D₄	1	6	yes	—
209	C₂³×C₇₃	C₂²×D₄	1	16	yes	—
210	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
211	C₂²×D₇₃	—	2	12	no	—
212	C₂²×D₇₃	—	2	16	no	—
213	C₂²×D₇₃	—	4	48	no	—
214	C₂²×D₇₃	—	4	8	no	—
215	Q₈×C₇₃	—	2	12	no	—
216	Q₈×C₇₃	—	2	16	no	—
217	Q₈×C₇₃	C₂⁵	1	8	yes	—
218	D₄×C₇₃	—	2	32	no	—
219	D₄×C₇₃	—	2	32	no	—
220	D₄×C₇₃	—	2	12	no	—
221	D₄×C₇₃	—	2	16	no	—
222	D₄×C₇₃	C₂⁵	1	8	yes	—
223	C₂×C₄×C₇₃	—	2	12	no	—
224	C₂×C₄×C₇₃	—	2	16	no	—
225	C₂×C₄×C₇₃	—	2	32	no	—
226	C₂×C₄×C₇₃	—	2	32	no	—
227	C₂×C₄×C₇₃	C₂²×D₄	1	6	yes	—
228	C₂×C₄×C₇₃	C₂²×D₄	1	6	yes	—
229	C₂×C₄×C₇₃	C₂²×D₄	1	16	yes	—
230	C₂×C₄×C₇₃	C₂²×D₄	1	6	yes	—
231	C₂×C₄×C₇₃	C₂²×D₄	1	3	yes	—
232	C₂×C₄×C₇₃	C₂²×D₄	1	12	yes	—
233	C₂×C₄×C₇₃	C₂²×D₄	1	16	yes	—
234	C₂×C₄×C₇₃	C₂²×D₄	1	12	yes	—
235	C₂×C₄×C₇₃	C₂²×D₄	1	16	yes	—
236	C₂×C₄×C₇₃	C₂²×D₄	1	12	yes	—
237	C₂×C₄×C₇₃	C₂⁵	1	3	yes	—
238	C₂×C₄×C₇₃	C₂⁵	1	4	yes	—
239	C₂×C₄×C₇₃	C₂⁵	1	4	yes	—
240	C₂×C₄×C₇₃	C₂⁵	1	4	yes	—
241	C₂²⋊D₇₃	—	2	32	no	—
242	C₂²⋊D₇₃	—	2	32	no	—
243	C₂×Dic₇₃	—	2	12	no	—
244	C₂×Dic₇₃	—	2	16	no	—
245	D₂₉₂	—	2	12	no	—
246	D₂₉₂	—	2	16	no	—
247	D₂₉₂	C₂⁵	1	8	yes	—
248	C₄×D₇₃	—	2	32	no	—
249	C₄×D₇₃	—	2	32	no	—
250	Dic₁₄₆	—	2	12	no	—
251	Dic₁₄₆	—	2	16	no	—
252	Dic₁₄₆	C₂⁵	1	8	yes	—
253	#10596831	C₂⁵	1	16	yes	—
254	C₂²×C₇₃	—	2	12	no	—
255	C₂²×C₇₃	—	2	12	no	—
256	C₂²×C₇₃	—	2	12	no	—
257	C₂²×C₇₃	—	2	8	no	—
258	C₂²×C₇₃	—	4	16	no	—
259	C₂²×C₇₃	—	4	32	no	—
260	C₂²×C₇₃	—	4	24	no	—
261	C₂²×C₇₃	#575	1	4	yes	complemented
262	C₂²×C₇₃	C₂³×D₄	1	4	yes	—
263	C₂²×C₇₃	C₂³×D₄	1	4	yes	—
264	C₂²×C₇₃	C₂³×D₄	1	4	yes	—
265	C₂²×C₇₃	C₂³×D₄	1	3	yes	—
266	C₂×D₇₃	—	2	8	no	—
267	C₂×D₇₃	—	4	32	no	—
268	C₂×D₇₃	—	4	24	no	—
269	C₄×C₇₃	—	2	8	no	—
270	C₄×C₇₃	C₂³×D₄	1	4	yes	—
271	C₄×C₇₃	C₂³×D₄	1	3	yes	—
272	C₄×C₇₃	C₂³×D₄	1	4	yes	—
273	C₄×C₇₃	C₂³×D₄	1	4	yes	—
274	C₄×C₇₃	C₂⁶	1	1	yes	characteristic
275	Dic₇₃	—	2	8	no	—
276	C₂²×#575	—	73	1	no	maximal, Sylow
277	C₂×C₇₃	—	2	4	no	—
278	C₂×C₇₃	—	2	4	no	—
279	C₂×C₇₃	—	2	4	no	—
280	C₂×C₇₃	—	4	8	no	—
281	C₂×C₇₃	C₂×#575	1	6	yes	complemented
282	C₂×C₇₃	C₂⁴×D₄	1	1	yes	characteristic
283	D₇₃	—	4	8	no	—
284	C₂³×#41	—	73	1	no	—
285	C₂³×#41	D₇₃	1	1	yes	characteristic, complemented
286	C₂×#575	—	73	48	no	—
287	C₂²×#137	—	73	2	no	—
288	C₂²×#137	—	73	2	no	—
289	C₂²×AGL(1,ℤ/8)	—	73	2	no	—
290	C₂²×AGL(1,ℤ/8)	—	73	2	no	—
291	C₂²×#135	—	73	4	no	—
292	C₂³×M₁₆	—	73	1	no	—
293	C₇₃	C₂²×#575	1	1	yes	characteristic, complemented, Sylow
294	C₂²×#41	—	2	1	no	—
295	C₂²×#41	—	2	12	no	—
296	C₂²×#41	—	2	1	no	—
297	C₂²×#41	—	73	2	no	—
298	C₂²×#41	—	73	2	no	—
299	C₂²×#41	—	73	24	no	—
300	C₂²×#41	—	146	1	no	—
301	C₂²×#41	—	146	12	no	—
302	C₂²×#41	—	146	1	no	—
303	C₂²×#41	C₂×D₇₃	1	2	yes	—
304	C₂²×#41	C₂×D₇₃	1	2	yes	complemented
305	C₂²×#41	C₂×D₇₃	1	24	yes	complemented
306	C₂³×Q₈	—	73	1	no	—
307	C₂³×Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
308	C₂³×D₄	—	2	1	no	—
309	C₂³×D₄	—	73	1	no	—
310	C₂³×D₄	—	146	1	no	—
311	C₂³×D₄	C₂×D₇₃	1	1	yes	characteristic, complemented
312	C₂⁴×C₄	—	2	1	no	—
313	C₂⁴×C₄	—	146	1	no	—
314	C₂⁴×C₄	C₂×D₇₃	1	1	yes	characteristic
315	#575	—	73	256	no	—
316	C₂×#137	—	73	48	no	—
317	C₂×#137	—	73	48	no	—
318	C₂×AGL(1,ℤ/8)	—	73	48	no	—
319	C₂×AGL(1,ℤ/8)	—	73	48	no	—
320	C₂×#135	—	73	96	no	—
321	C₂²×Q₁₆	—	73	4	no	—
322	C₂²×SD₁₆	—	73	4	no	—
323	C₂²×SD₁₆	—	73	4	no	—
324	C₂²×D₈	—	73	4	no	—
325	C₂²×M₁₆	—	73	2	no	—
326	C₂²×M₁₆	—	73	2	no	—
327	C₂²×M₁₆	—	73	24	no	—
328	C₂³×C₈	—	73	2	no	—
329	C₂⁵	—	2	1	no	—
330	C₂⁵	—	146	1	no	—
331	C₂⁵	C₂²⋊D₇₃	1	1	yes	characteristic
332	C₂×#41	—	2	12	no	—
333	C₂×#41	—	2	24	no	—
334	C₂×#41	—	2	24	no	—
335	C₂×#41	—	2	12	no	—
336	C₂×#41	—	2	96	no	—
337	C₂×#41	—	73	24	no	—
338	C₂×#41	—	73	24	no	—
339	C₂×#41	—	73	64	no	—
340	C₂×#41	—	146	24	no	—
341	C₂×#41	—	146	12	no	—
342	C₂×#41	—	146	12	no	—
343	C₂×#41	—	146	24	no	—
344	C₂×#41	—	146	96	no	—
345	C₂×#41	C₂²×D₇₃	1	24	yes	—
346	C₂×#41	C₂²×D₇₃	1	24	yes	complemented
347	C₂×#41	C₂²×D₇₃	1	64	yes	complemented
348	C₂²×Q₈	—	2	1	no	—
349	C₂²×Q₈	—	2	6	no	—
350	C₂²×Q₈	—	73	2	no	—
351	C₂²×Q₈	—	73	12	no	—
352	C₂²×Q₈	—	146	1	no	—
353	C₂²×Q₈	—	146	6	no	—
354	C₂²×Q₈	C₂²×D₇₃	1	2	yes	—
355	C₂²×Q₈	C₂²×D₇₃	1	12	yes	complemented
356	C₂²×D₄	—	2	2	no	—
357	C₂²×D₄	—	2	2	no	—
358	C₂²×D₄	—	2	24	no	—
359	C₂²×D₄	—	2	1	no	—
360	C₂²×D₄	—	2	6	no	—
361	C₂²×D₄	—	73	2	no	—
362	C₂²×D₄	—	73	12	no	—
363	C₂²×D₄	—	146	2	no	—
364	C₂²×D₄	—	146	2	no	—
365	C₂²×D₄	—	146	24	no	—
366	C₂²×D₄	—	146	1	no	—
367	C₂²×D₄	—	146	6	no	—
368	C₂²×D₄	C₂²×D₇₃	1	2	yes	—
369	C₂²×D₄	C₂²×D₇₃	1	12	yes	complemented
370	C₂³×C₄	—	2	1	no	—
371	C₂³×C₄	—	2	2	no	—
372	C₂³×C₄	—	2	24	no	—
373	C₂³×C₄	—	2	2	no	—
374	C₂³×C₄	—	146	1	no	—
375	C₂³×C₄	—	146	2	no	—
376	C₂³×C₄	—	146	24	no	—
377	C₂³×C₄	—	146	2	no	—
378	C₂³×C₄	C₂²⋊D₇₃	1	1	yes	characteristic
379	C₂³×C₄	C₂²⋊D₇₃	1	12	yes	—
380	C₂³×C₄	C₂²⋊D₇₃	1	1	yes	characteristic
381	C₂³×C₄	C₂²⋊D₇₃	1	1	yes	characteristic
382	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
383	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
384	C₂³×C₄	C₂²×D₇₃	1	12	yes	—
385	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
386	#137	—	73	128	no	—
387	#137	—	73	128	no	—
388	AGL(1,ℤ/8)	—	73	128	no	—
389	AGL(1,ℤ/8)	—	73	128	no	—
390	#135	—	73	256	no	—
391	C₂×Q₁₆	—	73	48	no	—
392	C₂×SD₁₆	—	73	48	no	—
393	C₂×SD₁₆	—	73	48	no	—
394	C₂×D₈	—	73	48	no	—
395	C₂×M₁₆	—	73	24	no	—
396	C₂×M₁₆	—	73	24	no	—
397	C₂×M₁₆	—	73	64	no	—
398	C₂²×C₈	—	73	4	no	—
399	C₂²×C₈	—	73	24	no	—
400	C₂⁴	—	2	2	no	—
401	C₂⁴	—	2	12	no	—
402	C₂⁴	—	4	4	no	—
403	C₂⁴	—	4	8	no	—
404	C₂⁴	—	292	8	no	—
405	C₂⁴	—	146	12	no	—
406	C₂⁴	—	146	2	no	—
407	C₂⁴	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
408	C₂⁴	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
409	C₂⁴	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
410	C₂⁴	C₂×C₂²⋊D₇₃	1	12	yes	—
411	#41	—	2	48	no	—
412	#41	—	2	64	no	—
413	#41	—	2	64	no	—
414	#41	—	2	48	no	—
415	#41	—	73	32	no	—
416	#41	—	73	32	no	—
417	#41	—	146	64	no	—
418	#41	—	146	48	no	—
419	#41	—	146	48	no	—
420	#41	—	146	64	no	—
421	#41	C₂³×D₇₃	1	32	yes	—
422	#41	C₂³×D₇₃	1	32	yes	complemented
423	C₂×Q₈	—	2	6	no	—
424	C₂×Q₈	—	2	12	no	—
425	C₂×Q₈	—	2	24	no	—
426	C₂×Q₈	—	73	12	no	—
427	C₂×Q₈	—	73	16	no	—
428	C₂×Q₈	—	146	12	no	—
429	C₂×Q₈	—	146	6	no	—
430	C₂×Q₈	—	146	24	no	—
431	C₂×Q₈	C₂³×D₇₃	1	12	yes	—
432	C₂×Q₈	C₂³×D₇₃	1	16	yes	complemented
433	C₂×D₄	—	2	24	no	—
434	C₂×D₄	—	2	24	no	—
435	C₂×D₄	—	2	64	no	—
436	C₂×D₄	—	2	6	no	—
437	C₂×D₄	—	2	12	no	—
438	C₂×D₄	—	2	24	no	—
439	C₂×D₄	—	73	12	no	—
440	C₂×D₄	—	73	16	no	—
441	C₂×D₄	—	146	24	no	—
442	C₂×D₄	—	146	24	no	—
443	C₂×D₄	—	146	64	no	—
444	C₂×D₄	—	146	12	no	—
445	C₂×D₄	—	146	6	no	—
446	C₂×D₄	—	146	24	no	—
447	C₂×D₄	C₂³×D₇₃	1	12	yes	—
448	C₂×D₄	C₂³×D₇₃	1	16	yes	complemented
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	12	no	—
451	C₂²×C₄	—	2	24	no	—
452	C₂²×C₄	—	2	24	no	—
453	C₂²×C₄	—	2	64	no	—
454	C₂²×C₄	—	146	12	no	—
455	C₂²×C₄	—	146	2	no	—
456	C₂²×C₄	—	146	24	no	—
457	C₂²×C₄	—	146	24	no	—
458	C₂²×C₄	—	146	64	no	—
459	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
460	C₂²×C₄	C₂×C₂²⋊D₇₃	1	12	yes	—
461	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
462	C₂²×C₄	C₂×C₂²⋊D₇₃	1	12	yes	—
463	C₂²×C₄	C₂×C₂²⋊D₇₃	1	6	yes	—
464	C₂²×C₄	C₂×C₂²⋊D₇₃	1	6	yes	—
465	C₂²×C₄	C₂×C₂²⋊D₇₃	1	6	yes	—
466	C₂²×C₄	C₂×C₂²⋊D₇₃	1	12	yes	—
467	C₂²×C₄	C₂×C₂²⋊D₇₃	1	48	yes	—
468	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
469	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
470	C₂²×C₄	C₂³×D₇₃	1	6	yes	—
471	C₂²×C₄	C₂³×D₇₃	1	6	yes	—
472	C₂²×C₄	C₂³×D₇₃	1	6	yes	—
473	C₂²×C₄	C₂³×D₇₃	1	16	yes	—
474	Q₁₆	—	73	64	no	—
475	SD₁₆	—	73	64	no	—
476	SD₁₆	—	73	64	no	—
477	D₈	—	73	64	no	—
478	M₁₆	—	73	32	no	—
479	M₁₆	—	73	32	no	—
480	C₂×C₈	—	73	24	no	—
481	C₂×C₈	—	73	32	no	—
482	C₂³	—	2	4	no	—
483	C₂³	—	2	4	no	—
484	C₂³	—	2	4	no	—
485	C₂³	—	2	12	no	—
486	C₂³	—	2	16	no	—
487	C₂³	—	4	24	no	—
488	C₂³	—	4	48	no	—
489	C₂³	—	4	8	no	—
490	C₂³	—	292	48	no	—
491	C₂³	—	292	8	no	—
492	C₂³	—	146	16	no	—
493	C₂³	—	146	12	no	—
494	C₂³	C₂²×C₂²⋊D₇₃	1	6	yes	—
495	C₂³	C₂²×C₂²⋊D₇₃	1	6	yes	—
496	C₂³	C₂²×C₂²⋊D₇₃	1	6	yes	—
497	C₂³	C₂²×C₂²⋊D₇₃	1	16	yes	—
498	C₂³	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
499	Q₈	—	2	12	no	—
500	Q₈	—	2	16	no	—
501	Q₈	—	73	8	no	—
502	Q₈	—	146	16	no	—
503	Q₈	—	146	12	no	—
504	Q₈	C₂⁴×D₇₃	1	8	yes	—
505	D₄	—	2	32	no	—
506	D₄	—	2	32	no	—
507	D₄	—	2	12	no	—
508	D₄	—	2	16	no	—
509	D₄	—	73	8	no	—
510	D₄	—	146	32	no	—
511	D₄	—	146	32	no	—
512	D₄	—	146	16	no	—
513	D₄	—	146	12	no	—
514	D₄	C₂⁴×D₇₃	1	8	yes	—
515	C₂×C₄	—	2	12	no	—
516	C₂×C₄	—	2	16	no	—
517	C₂×C₄	—	2	32	no	—
518	C₂×C₄	—	2	32	no	—
519	C₂×C₄	—	146	16	no	—
520	C₂×C₄	—	146	12	no	—
521	C₂×C₄	—	146	32	no	—
522	C₂×C₄	—	146	32	no	—
523	C₂×C₄	C₂²×C₂²⋊D₇₃	1	6	yes	—
524	C₂×C₄	C₂²×C₂²⋊D₇₃	1	6	yes	—
525	C₂×C₄	C₂²×C₂²⋊D₇₃	1	16	yes	—
526	C₂×C₄	C₂²×C₂²⋊D₇₃	1	6	yes	—
527	C₂×C₄	C₂²×C₂²⋊D₇₃	1	16	yes	—
528	C₂×C₄	C₂²×C₂²⋊D₇₃	1	3	yes	—
529	C₂×C₄	C₂²×C₂²⋊D₇₃	1	12	yes	—
530	C₂×C₄	C₂²×C₂²⋊D₇₃	1	12	yes	—
531	C₂×C₄	C₂²×C₂²⋊D₇₃	1	12	yes	—
532	C₂×C₄	C₂²×C₂²⋊D₇₃	1	16	yes	—
533	C₂×C₄	C₂⁴×D₇₃	1	3	yes	—
534	C₂×C₄	C₂⁴×D₇₃	1	4	yes	—
535	C₂×C₄	C₂⁴×D₇₃	1	4	yes	—
536	C₂×C₄	C₂⁴×D₇₃	1	4	yes	—
537	C₈	—	73	16	no	—
538	C₂²	—	2	12	no	—
539	C₂²	—	2	12	no	—
540	C₂²	—	2	12	no	—
541	C₂²	—	2	8	no	—
542	C₂²	—	4	16	no	—
543	C₂²	—	4	32	no	—
544	C₂²	—	4	24	no	—
545	C₂²	—	292	32	no	—
546	C₂²	—	292	24	no	—
547	C₂²	—	146	8	no	—
548	C₂²	#17989385	1	4	yes	direct product factor
549	C₂²	C₂³×C₂²⋊D₇₃	1	4	yes	—
550	C₂²	C₂³×C₂²⋊D₇₃	1	4	yes	—
551	C₂²	C₂³×C₂²⋊D₇₃	1	4	yes	—
552	C₂²	C₂³×C₂²⋊D₇₃	1	3	yes	—
553	C₄	—	2	8	no	—
554	C₄	—	146	8	no	—
555	C₄	C₂³×C₂²⋊D₇₃	1	4	yes	—
556	C₄	C₂³×C₂²⋊D₇₃	1	4	yes	—
557	C₄	C₂³×C₂²⋊D₇₃	1	4	yes	—
558	C₄	C₂³×C₂²⋊D₇₃	1	3	yes	—
559	C₄	C₂⁵×D₇₃	1	1	yes	characteristic
560	C₂	—	2	4	no	—
561	C₂	—	2	4	no	—
562	C₂	—	2	4	no	—
563	C₂	—	4	8	no	—
564	C₂	—	292	8	no	—
565	C₂	C₂×#17989385	1	6	yes	direct product factor
566	C₂	C₂⁴×C₂²⋊D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₇₃
commutator, cosocle	C₄×C₇₃	C₂⁶
Frattini	C₄	C₂⁵×D₇₃
Fitting	C₂³×#41×C₇₃	C₂
socle	C₂³×C₇₃	C₂²×D₄
hypercenter	C₂³×#41	D₇₃
hypocenter	C₇₃	C₂²×#575
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂⁴×C₄ ◁ C₂³×#41

Complements

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

N	H ≅ G/N	type
1. C₂³×#11924028	C₂	semidirect
2. C₂×#17989385	C₂	direct (N × H)
3. C₂²×#14556622	C₂	semidirect
4. C₂²×#14556621	C₂	semidirect
5. C₂²×#14556617	C₂	semidirect
6. C₂²×#14556616	C₂	semidirect
7. C₂²×#14556611	C₂	semidirect
8. C₂³×#11924012	C₂	semidirect
9. C₂³×#41×C₇₃	C₂	semidirect
14. C₂²×#11924028	C₂²	semidirect
15. C₂²×#11924028	C₂²	semidirect
16. C₂³×Dic₁₄₆	C₂²	semidirect
17. C₂³×D₂₉₂	C₂²	semidirect
20. #17989385	C₂²	direct (N × H)
21. C₂×#14556622	C₂²	semidirect
22. C₂×#14556621	C₂²	semidirect
23. C₂×#14556617	C₂²	semidirect
24. C₂×#14556616	C₂²	semidirect
25. C₂×#14556611	C₂²	semidirect
26. C₂²×#11924018	C₂²	semidirect
27. C₂²×#11924016	C₂²	semidirect
28. C₂²×#11924015	C₂²	semidirect
29. C₂²×#11924013	C₂²	semidirect
30. C₂²×#11924012	C₂²	semidirect
31. C₂²×#11924012	C₂²	semidirect
32. C₂²×#11924012	C₂²	semidirect
33. C₂³×#10596831	C₂²	semidirect
38. C₂²×#41×C₇₃	C₂²	semidirect
39. C₂²×#41×C₇₃	C₂²	semidirect
40. C₂³×Q₈×C₇₃	C₂²	semidirect
42. C₂³×D₄×C₇₃	C₂²	semidirect
52. C₂×#11924028	C₂³	semidirect
53. C₂×#11924028	C₂³	semidirect
57. C₂²×Dic₁₄₆	C₂³	semidirect
61. C₂²×D₂₉₂	C₂³	semidirect
69. #14556622	C₂³	semidirect
70. #14556621	C₂³	semidirect
71. #14556617	C₂³	semidirect
72. #14556616	C₂³	semidirect
73. #14556611	C₂³	semidirect
74. C₂×#11924018	C₂³	semidirect
75. C₂×#11924016	C₂³	semidirect
76. C₂×#11924015	C₂³	semidirect
77. C₂×#11924013	C₂³	semidirect
78. C₂×#11924012	C₂³	semidirect
79. C₂×#11924012	C₂³	semidirect
80. C₂×#11924012	C₂³	semidirect
82. C₂²×#10596831	C₂³	semidirect
91. C₂×#41×C₇₃	C₂³	semidirect
92. C₂×#41×C₇₃	C₂³	semidirect
96. C₂²×Q₈×C₇₃	C₂³	semidirect
103. C₂²×D₄×C₇₃	C₂³	semidirect
124. #11924028	C₂⁴	semidirect
129. C₂×Dic₁₄₆	C₂⁴	semidirect
134. C₂×D₂₉₂	C₂⁴	semidirect
143. #11924018	C₂⁴	semidirect
144. #11924016	C₂⁴	semidirect
145. #11924015	C₂⁴	semidirect
146. #11924013	C₂⁴	semidirect
147. #11924012	C₂⁴	semidirect
148. #11924012	C₂⁴	semidirect
150. C₂×#10596831	C₂⁴	semidirect
164. #41×C₇₃	C₂⁴	semidirect
169. C₂×Q₈×C₇₃	C₂⁴	semidirect
177. C₂×D₄×C₇₃	C₂⁴	semidirect
261. C₂²×C₇₃	#575	semidirect
281. C₂×C₇₃	C₂×#575	semidirect
285. C₂³×#41	D₇₃	semidirect
293. C₇₃	C₂²×#575	semidirect
304. C₂²×#41	C₂×D₇₃	semidirect
305. C₂²×#41	C₂×D₇₃	semidirect
307. C₂³×Q₈	C₂×D₇₃	semidirect
311. C₂³×D₄	C₂×D₇₃	semidirect
346. C₂×#41	C₂²×D₇₃	semidirect
347. C₂×#41	C₂²×D₇₃	semidirect
355. C₂²×Q₈	C₂²×D₇₃	semidirect
369. C₂²×D₄	C₂²×D₇₃	semidirect
422. #41	C₂³×D₇₃	semidirect
432. C₂×Q₈	C₂³×D₇₃	semidirect
448. C₂×D₄	C₂³×D₇₃	semidirect
548. C₂²	#17989385	direct (N × H)
565. C₂	C₂×#17989385	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#11924028	2
C₂×#17989385	2
C₂²×#14556622	2
C₂²×#14556621	2
C₂²×#14556617	2
C₂²×#14556616	2
C₂²×#14556611	2
C₂³×#11924012	2
C₂³×#41×C₇₃	2
C₂²×#575	73

Subgroups — C22×#17989385 #33999788

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#17989385 #33999788