Subgroups — C₂×#22624702 #33999815

Order 18688.

10858 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	C₂×#17989423	C₂	1	1	yes	maximal, characteristic, complemented
2	#22624702	C₂	1	32	yes	maximal, direct product factor
3	C₂×#17989402	C₂	1	4	yes	maximal, complemented
4	C₂×#17989398	C₂	1	4	yes	maximal, complemented
5	C₂×#17989395	C₂	1	4	yes	maximal, complemented
6	C₂×#17989390	C₂	1	4	yes	maximal, complemented
7	C₂×#17989385	C₂	1	6	yes	maximal, complemented
8	C₂²×#14556611	C₂	1	6	yes	maximal, complemented
9	C₂²×#14556598	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#585×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#17989423	—	2	8	no	—
12	#17989423	C₂²	1	16	yes	complemented
13	C₂×#14556639	—	2	1	no	—
14	C₂×#14556638	C₂²	1	4	yes	complemented
15	C₂×#14556637	C₂²	1	4	yes	complemented
16	C₂×#14556636	—	2	3	no	—
17	C₂²×#11924028	C₂²	1	6	yes	complemented
18	C₂×#41×D₇₃	—	2	4	no	—
19	#17989402	C₂²	1	64	yes	complemented
20	#17989398	C₂²	1	64	yes	complemented
21	#17989395	C₂²	1	64	yes	complemented
22	#17989390	C₂²	1	64	yes	complemented
23	#17989385	C₂²	1	96	yes	complemented
24	C₂×#14556622	C₂²	1	12	yes	complemented
25	C₂×#14556621	C₂²	1	12	yes	complemented
26	C₂×#14556617	C₂²	1	12	yes	complemented
27	C₂×#14556616	C₂²	1	12	yes	complemented
28	C₂×#14556611	C₂²	1	4	yes	complemented
29	C₂×#14556611	C₂²	1	12	yes	complemented
30	C₂×#14556611	C₂²	1	12	yes	complemented
31	C₂×#14556611	C₂²	1	12	yes	complemented
32	C₂×#14556611	C₂²	1	96	yes	complemented
33	C₂²×#11924018	C₂²	1	6	yes	complemented
34	C₂²×#11924016	C₂²	1	6	yes	complemented
35	C₂²×#11924015	C₂²	1	6	yes	complemented
36	C₂²×#11924013	C₂²	1	6	yes	complemented
37	C₂×#14556598	C₂²	1	4	yes	complemented
38	C₂×#14556598	C₂²	1	4	yes	complemented
39	C₂×#14556598	C₂²	1	16	yes	complemented
40	C₂²×#11924012	C₂²	1	3	yes	complemented
41	C₂³×#10596831	C₂²	1	3	yes	complemented
42	#585×C₇₃	—	2	8	no	—
43	#585×C₇₃	C₂²	1	16	yes	complemented
44	C₂×2₋¹⁺⁴×C₇₃	—	2	1	no	—
45	C₂×2₋¹⁺⁴×C₇₃	C₂²	1	4	yes	complemented
46	C₂×H(5,𝔽₂)×C₇₃	—	2	3	no	—
47	C₂×H(5,𝔽₂)×C₇₃	C₂²	1	4	yes	complemented
48	C₂²×#41×C₇₃	—	2	4	no	—
49	C₂²×#41×C₇₃	C₂²	1	1	yes	characteristic
50	C₂²×#41×C₇₃	C₂²	1	6	yes	complemented
51	#14556639	—	2	16	no	—
52	#14556638	—	2	16	no	—
53	#14556638	C₂³	1	32	yes	complemented
54	#14556637	—	2	16	no	—
55	#14556637	C₂³	1	32	yes	complemented
56	#14556636	—	2	48	no	—
57	C₂×#11924029	—	2	4	no	—
58	C₂×#11924028	—	2	6	no	—
59	C₂×#11924028	—	2	6	no	—
60	C₂×#11924028	—	2	24	no	—
61	C₂×#11924028	C₂³	1	12	yes	—
62	C₂×#11924028	C₂³	1	4	yes	—
63	C₂×#11924028	C₂³	1	48	yes	complemented
64	C₂×#11924027	—	2	12	no	—
65	#41×D₇₃	—	2	64	no	—
66	C₂²×Dic₁₄₆	C₂³	1	6	yes	—
67	C₂×Q₈×D₇₃	—	2	4	no	—
68	C₂²×D₂₉₂	C₂³	1	6	yes	—
69	C₂²×C₂²⋊D₇₃	—	2	6	no	—
70	C₂×D₄×D₇₃	—	2	12	no	—
71	C₂²×C₄×D₇₃	—	2	6	no	—
72	#14556622	C₂³	1	96	yes	complemented
73	#14556621	C₂³	1	96	yes	complemented
74	#14556617	C₂³	1	96	yes	complemented
75	#14556616	C₂³	1	96	yes	complemented
76	#14556611	C₂³	1	96	yes	complemented
77	#14556611	C₂³	1	96	yes	complemented
78	#14556611	C₂³	1	96	yes	complemented
79	#14556611	C₂³	1	32	yes	complemented
80	C₂×#11924018	C₂³	1	12	yes	—
81	C₂×#11924018	C₂³	1	4	yes	—
82	C₂×#11924018	C₂³	1	48	yes	complemented
83	C₂×#11924016	C₂³	1	12	yes	—
84	C₂×#11924016	C₂³	1	4	yes	—
85	C₂×#11924016	C₂³	1	48	yes	complemented
86	C₂×#11924015	C₂³	1	12	yes	—
87	C₂×#11924015	C₂³	1	4	yes	—
88	C₂×#11924015	C₂³	1	48	yes	complemented
89	C₂×#11924013	C₂³	1	4	yes	—
90	C₂×#11924013	C₂³	1	12	yes	—
91	C₂×#11924013	C₂³	1	48	yes	complemented
92	#14556598	C₂³	1	32	yes	complemented
93	#14556598	C₂³	1	32	yes	complemented
94	C₂×#11924012	C₂³	1	12	yes	—
95	C₂×#11924012	C₂³	1	24	yes	complemented
96	C₂²×#10596831	C₂³	1	1	yes	characteristic
97	C₂²×#10596831	C₂³	1	3	yes	—
98	C₂²×#10596831	C₂³	1	6	yes	—
99	C₂²×#10596831	C₂³	1	6	yes	—
100	C₂²×#10596831	C₂³	1	24	yes	complemented
101	2₋¹⁺⁴×C₇₃	—	2	16	no	—
102	2₋¹⁺⁴×C₇₃	—	2	16	no	—
103	2₋¹⁺⁴×C₇₃	C₂³	1	32	yes	complemented
104	H(5,𝔽₂)×C₇₃	—	2	16	no	—
105	H(5,𝔽₂)×C₇₃	—	2	48	no	—
106	H(5,𝔽₂)×C₇₃	C₂³	1	32	yes	complemented
107	C₂×#41×C₇₃	—	2	64	no	—
108	C₂×#41×C₇₃	—	2	4	no	—
109	C₂×#41×C₇₃	—	2	12	no	—
110	C₂×#41×C₇₃	—	2	6	no	—
111	C₂×#41×C₇₃	—	2	6	no	—
112	C₂×#41×C₇₃	—	2	24	no	—
113	C₂×#41×C₇₃	D₄	1	4	yes	—
114	C₂×#41×C₇₃	D₄	1	8	yes	—
115	C₂×#41×C₇₃	C₂³	1	12	yes	—
116	C₂×#41×C₇₃	C₂³	1	4	yes	—
117	C₂×#41×C₇₃	C₂³	1	4	yes	—
118	C₂×#41×C₇₃	C₂³	1	8	yes	—
119	C₂×#41×C₇₃	C₂³	1	48	yes	complemented
120	C₂²×Q₈×C₇₃	—	2	4	no	—
121	C₂²×Q₈×C₇₃	D₄	1	1	yes	characteristic
122	C₂²×Q₈×C₇₃	C₂³	1	6	yes	—
123	C₂²×D₄×C₇₃	—	2	6	no	—
124	C₂²×D₄×C₇₃	—	2	12	no	—
125	C₂²×D₄×C₇₃	D₄	1	3	yes	—
126	C₂²×D₄×C₇₃	C₂³	1	6	yes	—
127	C₂³×C₄×C₇₃	—	2	6	no	—
128	C₂³×C₄×C₇₃	C₂³	1	3	yes	—
129	C₂³×D₇₃	—	2	6	no	—
130	#11924029	—	2	32	no	—
131	#11924028	—	2	48	no	—
132	#11924028	—	2	8	no	—
133	#11924028	—	2	24	no	—
134	#11924028	—	2	48	no	—
135	#11924028	C₂⁴	1	16	yes	—
136	#11924028	C₂⁴	1	48	yes	—
137	#11924027	—	2	96	no	—
138	C₂×Dic₁₄₆	—	2	6	no	—
139	C₂×Dic₁₄₆	—	2	12	no	—
140	C₂×Dic₁₄₆	C₂⁴	1	4	yes	—
141	C₂×Dic₁₄₆	C₂⁴	1	24	yes	—
142	Q₈×D₇₃	—	2	32	no	—
143	C₂×D₂₉₂	—	2	6	no	—
144	C₂×D₂₉₂	—	2	12	no	—
145	C₂×D₂₉₂	C₂⁴	1	4	yes	—
146	C₂×D₂₉₂	C₂⁴	1	24	yes	—
147	C₂×C₂²⋊D₇₃	—	2	12	no	—
148	C₂×C₂²⋊D₇₃	—	2	4	no	—
149	C₂×C₂²⋊D₇₃	—	2	48	no	—
150	D₄×D₇₃	—	2	96	no	—
151	C₂²×Dic₇₃	—	2	6	no	—
152	C₂×C₄×D₇₃	—	2	4	no	—
153	C₂×C₄×D₇₃	—	2	12	no	—
154	C₂×C₄×D₇₃	—	2	48	no	—
155	#11924018	C₂⁴	1	16	yes	—
156	#11924018	C₂⁴	1	48	yes	—
157	#11924016	C₂⁴	1	16	yes	—
158	#11924016	C₂⁴	1	48	yes	—
159	#11924015	C₂⁴	1	16	yes	—
160	#11924015	C₂⁴	1	48	yes	—
161	#11924013	C₂⁴	1	16	yes	—
162	#11924013	C₂⁴	1	48	yes	—
163	#11924012	C₂⁴	1	48	yes	—
164	C₂×#10596831	C₂⁴	1	1	yes	characteristic
165	C₂×#10596831	C₂⁴	1	1	yes	characteristic
166	C₂×#10596831	C₂⁴	1	6	yes	—
167	C₂×#10596831	C₂⁴	1	4	yes	—
168	C₂×#10596831	C₂⁴	1	12	yes	—
169	C₂×#10596831	C₂⁴	1	24	yes	—
170	C₂×#10596831	C₂⁴	1	24	yes	—
171	C₂⁴×C₇₃	—	2	6	no	—
172	C₂⁴×C₇₃	C₂×D₄	1	3	yes	—
173	#41×C₇₃	—	2	32	no	—
174	#41×C₇₃	—	2	96	no	—
175	#41×C₇₃	—	2	8	no	—
176	#41×C₇₃	—	2	48	no	—
177	#41×C₇₃	—	2	24	no	—
178	#41×C₇₃	—	2	48	no	—
179	#41×C₇₃	C₂×D₄	1	32	yes	—
180	#41×C₇₃	C₂×D₄	1	16	yes	—
181	#41×C₇₃	C₂⁴	1	16	yes	—
182	#41×C₇₃	C₂⁴	1	48	yes	—
183	#41×C₇₃	C₂⁴	1	16	yes	—
184	C₂×Q₈×C₇₃	—	2	32	no	—
185	C₂×Q₈×C₇₃	—	2	6	no	—
186	C₂×Q₈×C₇₃	—	2	12	no	—
187	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
188	C₂×Q₈×C₇₃	C₂×D₄	1	8	yes	—
189	C₂×Q₈×C₇₃	C₂⁴	1	4	yes	—
190	C₂×Q₈×C₇₃	C₂⁴	1	24	yes	—
191	C₂×D₄×C₇₃	—	2	12	no	—
192	C₂×D₄×C₇₃	—	2	4	no	—
193	C₂×D₄×C₇₃	—	2	48	no	—
194	C₂×D₄×C₇₃	—	2	96	no	—
195	C₂×D₄×C₇₃	—	2	6	no	—
196	C₂×D₄×C₇₃	—	2	12	no	—
197	C₂×D₄×C₇₃	C₂×D₄	1	12	yes	—
198	C₂×D₄×C₇₃	C₂×D₄	1	24	yes	—
199	C₂×D₄×C₇₃	C₂⁴	1	4	yes	—
200	C₂×D₄×C₇₃	C₂⁴	1	24	yes	—
201	C₂²×C₄×C₇₃	—	2	6	no	—
202	C₂²×C₄×C₇₃	—	2	4	no	—
203	C₂²×C₄×C₇₃	—	2	12	no	—
204	C₂²×C₄×C₇₃	—	2	48	no	—
205	C₂²×C₄×C₇₃	C₂×D₄	1	6	yes	—
206	C₂²×C₄×C₇₃	C₂×D₄	1	3	yes	—
207	C₂²×C₄×C₇₃	C₂×D₄	1	12	yes	—
208	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₇₃	C₂⁴	1	6	yes	—
210	C₂²×C₄×C₇₃	C₂⁴	1	12	yes	—
211	C₂³×C₇₃	—	2	4	no	—
212	C₂³×C₇₃	—	2	24	no	—
213	C₂³×C₇₃	—	4	6	no	—
214	C₂³×C₇₃	—	8	12	no	—
215	C₂³×C₇₃	C₂²×D₄	1	6	yes	—
216	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
217	C₂³×C₇₃	C₂²×D₄	1	12	yes	—
218	C₂²×D₇₃	—	2	4	no	—
219	C₂²×D₇₃	—	2	24	no	—
220	C₂²×D₇₃	—	8	12	no	—
221	Q₈×C₇₃	—	2	4	no	—
222	Q₈×C₇₃	—	2	24	no	—
223	Q₈×C₇₃	C₂²×D₄	1	16	yes	—
224	Q₈×C₇₃	C₂⁵	1	8	yes	—
225	D₄×C₇₃	—	2	48	no	—
226	D₄×C₇₃	—	2	16	no	—
227	D₄×C₇₃	—	2	4	no	—
228	D₄×C₇₃	—	2	24	no	—
229	D₄×C₇₃	C₂²×D₄	1	48	yes	—
230	D₄×C₇₃	C₂⁵	1	8	yes	—
231	C₂×C₄×C₇₃	—	2	4	no	—
232	C₂×C₄×C₇₃	—	2	24	no	—
233	C₂×C₄×C₇₃	—	2	16	no	—
234	C₂×C₄×C₇₃	—	2	48	no	—
235	C₂×C₄×C₇₃	C₂²×D₄	1	6	yes	—
236	C₂×C₄×C₇₃	C₂²×D₄	1	24	yes	—
237	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
238	C₂×C₄×C₇₃	C₂²×D₄	1	12	yes	—
239	C₂×C₄×C₇₃	C₂²×D₄	1	12	yes	—
240	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
242	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
243	C₂×C₄×C₇₃	C₂⁵	1	12	yes	—
244	C₂²⋊D₇₃	—	2	48	no	—
245	C₂²⋊D₇₃	—	2	16	no	—
246	C₂×Dic₇₃	—	2	4	no	—
247	C₂×Dic₇₃	—	2	24	no	—
248	D₂₉₂	—	2	24	no	—
249	D₂₉₂	—	2	4	no	—
250	D₂₉₂	C₂⁵	1	8	yes	—
251	C₄×D₇₃	—	2	16	no	—
252	C₄×D₇₃	—	2	48	no	—
253	Dic₁₄₆	—	2	24	no	—
254	Dic₁₄₆	—	2	4	no	—
255	Dic₁₄₆	C₂⁵	1	8	yes	—
256	#10596831	C₂⁵	1	2	yes	—
257	#10596831	C₂⁵	1	2	yes	—
258	#10596831	C₂⁵	1	12	yes	—
259	C₂²×C₇₃	—	2	12	no	—
260	C₂²×C₇₃	—	2	2	no	—
261	C₂²×C₇₃	—	2	8	no	—
262	C₂²×C₇₃	—	4	12	no	—
263	C₂²×C₇₃	—	4	8	no	—
264	C₂²×C₇₃	—	8	24	no	—
265	C₂²×C₇₃	C₂³×D₄	1	12	yes	—
266	C₂²×C₇₃	C₂³×D₄	1	2	yes	—
267	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
268	C₂×D₇₃	—	2	8	no	—
269	C₂×D₇₃	—	4	8	no	—
270	C₂×D₇₃	—	8	24	no	—
271	C₄×C₇₃	—	2	8	no	—
272	C₄×C₇₃	C₂³×D₄	1	1	yes	characteristic
273	C₄×C₇₃	C₂³×D₄	1	12	yes	—
274	C₄×C₇₃	C₂³×D₄	1	2	yes	—
275	C₄×C₇₃	C₂⁶	1	1	yes	characteristic
276	Dic₇₃	—	2	8	no	—
277	C₂×#3584	—	73	1	no	maximal, Sylow
278	C₂×C₇₃	—	2	12	no	—
279	C₂×C₇₃	—	2	2	no	—
280	C₂×C₇₃	—	4	8	no	—
281	C₂×C₇₃	#3584	1	2	yes	complemented
282	C₂×C₇₃	C₂⁴×D₄	1	1	yes	characteristic
283	D₇₃	—	4	8	no	—
284	C₂×#585	—	73	1	no	—
285	C₂×#585	D₇₃	1	1	yes	characteristic, complemented
286	#3584	—	73	32	no	—
287	C₂×#578	—	73	4	no	—
288	C₂×#577	—	73	4	no	—
289	C₂×#577	—	73	4	no	—
290	C₂×#576	—	73	4	no	—
291	C₂×#575	—	73	6	no	—
292	C₂²×#135	—	73	6	no	—
293	C₂²×#131	—	73	1	no	—
294	C₇₃	C₂×#3584	1	1	yes	characteristic, complemented, Sylow
295	#585	—	2	8	no	—
296	#585	—	73	16	no	—
297	#585	—	146	8	no	—
298	#585	C₂×D₇₃	1	16	yes	complemented
299	C₂×2₋¹⁺⁴	—	2	1	no	—
300	C₂×2₋¹⁺⁴	—	73	4	no	—
301	C₂×2₋¹⁺⁴	—	146	1	no	—
302	C₂×2₋¹⁺⁴	C₂×D₇₃	1	4	yes	complemented
303	C₂×H(5,𝔽₂)	—	2	3	no	—
304	C₂×H(5,𝔽₂)	—	73	4	no	—
305	C₂×H(5,𝔽₂)	—	146	3	no	—
306	C₂×H(5,𝔽₂)	C₂×D₇₃	1	4	yes	complemented
307	C₂²×#41	—	2	4	no	—
308	C₂²×#41	—	73	6	no	—
309	C₂²×#41	—	146	4	no	—
310	C₂²×#41	C₂×D₇₃	1	1	yes	characteristic
311	C₂²×#41	C₂×D₇₃	1	6	yes	complemented
312	#578	—	73	64	no	—
313	#577	—	73	64	no	—
314	#577	—	73	64	no	—
315	#576	—	73	64	no	—
316	#575	—	73	96	no	—
317	C₂×#137	—	73	12	no	—
318	C₂×#137	—	73	12	no	—
319	C₂×AGL(1,ℤ/8)	—	73	12	no	—
320	C₂×AGL(1,ℤ/8)	—	73	12	no	—
321	C₂×#135	—	73	4	no	—
322	C₂×#135	—	73	12	no	—
323	C₂×#135	—	73	12	no	—
324	C₂×#135	—	73	12	no	—
325	C₂×#135	—	73	96	no	—
326	C₂²×Q₁₆	—	73	6	no	—
327	C₂²×SD₁₆	—	73	6	no	—
328	C₂²×SD₁₆	—	73	6	no	—
329	C₂²×D₈	—	73	6	no	—
330	C₂×#131	—	73	16	no	—
331	C₂×#131	—	73	4	no	—
332	C₂×#131	—	73	4	no	—
333	C₂²×M₁₆	—	73	3	no	—
334	C₂³×C₈	—	73	3	no	—
335	2₋¹⁺⁴	—	2	16	no	—
336	2₋¹⁺⁴	—	2	16	no	—
337	2₋¹⁺⁴	—	73	32	no	—
338	2₋¹⁺⁴	—	146	16	no	—
339	2₋¹⁺⁴	—	146	16	no	—
340	2₋¹⁺⁴	C₂²×D₇₃	1	32	yes	complemented
341	H(5,𝔽₂)	—	2	16	no	—
342	H(5,𝔽₂)	—	2	48	no	—
343	H(5,𝔽₂)	—	73	32	no	—
344	H(5,𝔽₂)	—	146	16	no	—
345	H(5,𝔽₂)	—	146	48	no	—
346	H(5,𝔽₂)	C₂²×D₇₃	1	32	yes	complemented
347	C₂×#41	—	2	64	no	—
348	C₂×#41	—	2	4	no	—
349	C₂×#41	—	2	12	no	—
350	C₂×#41	—	2	6	no	—
351	C₂×#41	—	2	6	no	—
352	C₂×#41	—	2	24	no	—
353	C₂×#41	—	73	4	no	—
354	C₂×#41	—	73	12	no	—
355	C₂×#41	—	73	48	no	—
356	C₂×#41	—	146	64	no	—
357	C₂×#41	—	146	4	no	—
358	C₂×#41	—	146	12	no	—
359	C₂×#41	—	146	6	no	—
360	C₂×#41	—	146	6	no	—
361	C₂×#41	—	146	24	no	—
362	C₂×#41	C₂²⋊D₇₃	1	4	yes	—
363	C₂×#41	C₂²⋊D₇₃	1	8	yes	—
364	C₂×#41	C₂²×D₇₃	1	4	yes	—
365	C₂×#41	C₂²×D₇₃	1	12	yes	—
366	C₂×#41	C₂²×D₇₃	1	4	yes	—
367	C₂×#41	C₂²×D₇₃	1	8	yes	—
368	C₂×#41	C₂²×D₇₃	1	48	yes	complemented
369	C₂²×Q₈	—	2	4	no	—
370	C₂²×Q₈	—	73	6	no	—
371	C₂²×Q₈	—	146	4	no	—
372	C₂²×Q₈	C₂²⋊D₇₃	1	1	yes	characteristic
373	C₂²×Q₈	C₂²×D₇₃	1	6	yes	—
374	C₂²×D₄	—	2	6	no	—
375	C₂²×D₄	—	2	12	no	—
376	C₂²×D₄	—	73	6	no	—
377	C₂²×D₄	—	146	6	no	—
378	C₂²×D₄	—	146	12	no	—
379	C₂²×D₄	C₂²⋊D₇₃	1	3	yes	—
380	C₂²×D₄	C₂²×D₇₃	1	6	yes	—
381	C₂³×C₄	—	2	6	no	—
382	C₂³×C₄	—	146	6	no	—
383	C₂³×C₄	C₂²×D₇₃	1	3	yes	—
384	#137	—	73	96	no	—
385	#137	—	73	96	no	—
386	AGL(1,ℤ/8)	—	73	96	no	—
387	AGL(1,ℤ/8)	—	73	96	no	—
388	#135	—	73	32	no	—
389	#135	—	73	96	no	—
390	#135	—	73	96	no	—
391	#135	—	73	96	no	—
392	C₂×Q₁₆	—	73	4	no	—
393	C₂×Q₁₆	—	73	12	no	—
394	C₂×Q₁₆	—	73	48	no	—
395	C₂×SD₁₆	—	73	4	no	—
396	C₂×SD₁₆	—	73	12	no	—
397	C₂×SD₁₆	—	73	48	no	—
398	C₂×SD₁₆	—	73	4	no	—
399	C₂×SD₁₆	—	73	12	no	—
400	C₂×SD₁₆	—	73	48	no	—
401	C₂×D₈	—	73	4	no	—
402	C₂×D₈	—	73	12	no	—
403	C₂×D₈	—	73	48	no	—
404	#131	—	73	32	no	—
405	#131	—	73	32	no	—
406	C₂×M₁₆	—	73	12	no	—
407	C₂×M₁₆	—	73	24	no	—
408	C₂²×C₈	—	73	1	no	—
409	C₂²×C₈	—	73	3	no	—
410	C₂²×C₈	—	73	6	no	—
411	C₂²×C₈	—	73	6	no	—
412	C₂²×C₈	—	73	24	no	—
413	C₂⁴	—	2	6	no	—
414	C₂⁴	—	146	6	no	—
415	C₂⁴	C₂×C₂²⋊D₇₃	1	3	yes	—
416	#41	—	2	32	no	—
417	#41	—	2	96	no	—
418	#41	—	2	8	no	—
419	#41	—	2	48	no	—
420	#41	—	2	24	no	—
421	#41	—	2	48	no	—
422	#41	—	73	16	no	—
423	#41	—	73	48	no	—
424	#41	—	146	32	no	—
425	#41	—	146	96	no	—
426	#41	—	146	48	no	—
427	#41	—	146	8	no	—
428	#41	—	146	24	no	—
429	#41	—	146	48	no	—
430	#41	C₂×C₂²⋊D₇₃	1	32	yes	—
431	#41	C₂×C₂²⋊D₇₃	1	16	yes	—
432	#41	C₂³×D₇₃	1	16	yes	—
433	#41	C₂³×D₇₃	1	48	yes	—
434	#41	C₂³×D₇₃	1	16	yes	—
435	C₂×Q₈	—	2	32	no	—
436	C₂×Q₈	—	2	6	no	—
437	C₂×Q₈	—	2	12	no	—
438	C₂×Q₈	—	73	4	no	—
439	C₂×Q₈	—	73	24	no	—
440	C₂×Q₈	—	146	32	no	—
441	C₂×Q₈	—	146	6	no	—
442	C₂×Q₈	—	146	12	no	—
443	C₂×Q₈	C₂×C₂²⋊D₇₃	1	4	yes	—
444	C₂×Q₈	C₂×C₂²⋊D₇₃	1	8	yes	—
445	C₂×Q₈	C₂³×D₇₃	1	4	yes	—
446	C₂×Q₈	C₂³×D₇₃	1	24	yes	—
447	C₂×D₄	—	2	12	no	—
448	C₂×D₄	—	2	4	no	—
449	C₂×D₄	—	2	48	no	—
450	C₂×D₄	—	2	96	no	—
451	C₂×D₄	—	2	6	no	—
452	C₂×D₄	—	2	12	no	—
453	C₂×D₄	—	73	4	no	—
454	C₂×D₄	—	73	24	no	—
455	C₂×D₄	—	146	12	no	—
456	C₂×D₄	—	146	4	no	—
457	C₂×D₄	—	146	48	no	—
458	C₂×D₄	—	146	96	no	—
459	C₂×D₄	—	146	6	no	—
460	C₂×D₄	—	146	12	no	—
461	C₂×D₄	C₂×C₂²⋊D₇₃	1	12	yes	—
462	C₂×D₄	C₂×C₂²⋊D₇₃	1	24	yes	—
463	C₂×D₄	C₂³×D₇₃	1	4	yes	—
464	C₂×D₄	C₂³×D₇₃	1	24	yes	—
465	C₂²×C₄	—	2	6	no	—
466	C₂²×C₄	—	2	12	no	—
467	C₂²×C₄	—	2	48	no	—
468	C₂²×C₄	—	2	4	no	—
469	C₂²×C₄	—	146	6	no	—
470	C₂²×C₄	—	146	12	no	—
471	C₂²×C₄	—	146	48	no	—
472	C₂²×C₄	—	146	4	no	—
473	C₂²×C₄	C₂×C₂²⋊D₇₃	1	3	yes	—
474	C₂²×C₄	C₂×C₂²⋊D₇₃	1	12	yes	—
475	C₂²×C₄	C₂×C₂²⋊D₇₃	1	6	yes	—
476	C₂²×C₄	C₂³×D₇₃	1	6	yes	—
477	C₂²×C₄	C₂³×D₇₃	1	12	yes	—
478	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
479	Q₁₆	—	73	16	no	—
480	Q₁₆	—	73	48	no	—
481	SD₁₆	—	73	16	no	—
482	SD₁₆	—	73	48	no	—
483	SD₁₆	—	73	16	no	—
484	SD₁₆	—	73	48	no	—
485	D₈	—	73	16	no	—
486	D₈	—	73	48	no	—
487	M₁₆	—	73	48	no	—
488	C₂×C₈	—	73	1	no	—
489	C₂×C₈	—	73	1	no	—
490	C₂×C₈	—	73	4	no	—
491	C₂×C₈	—	73	6	no	—
492	C₂×C₈	—	73	12	no	—
493	C₂×C₈	—	73	24	no	—
494	C₂×C₈	—	73	24	no	—
495	C₂³	—	2	4	no	—
496	C₂³	—	2	24	no	—
497	C₂³	—	4	6	no	—
498	C₂³	—	8	12	no	—
499	C₂³	—	584	12	no	—
500	C₂³	—	146	4	no	—
501	C₂³	—	146	24	no	—
502	C₂³	C₂²×C₂²⋊D₇₃	1	6	yes	—
503	C₂³	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
504	C₂³	C₂²×C₂²⋊D₇₃	1	12	yes	—
505	Q₈	—	2	24	no	—
506	Q₈	—	2	4	no	—
507	Q₈	—	73	8	no	—
508	Q₈	—	146	24	no	—
509	Q₈	—	146	4	no	—
510	Q₈	C₂²×C₂²⋊D₇₃	1	16	yes	—
511	Q₈	C₂⁴×D₇₃	1	8	yes	—
512	D₄	—	2	48	no	—
513	D₄	—	2	16	no	—
514	D₄	—	2	24	no	—
515	D₄	—	2	4	no	—
516	D₄	—	73	8	no	—
517	D₄	—	146	48	no	—
518	D₄	—	146	16	no	—
519	D₄	—	146	24	no	—
520	D₄	—	146	4	no	—
521	D₄	C₂²×C₂²⋊D₇₃	1	48	yes	—
522	D₄	C₂⁴×D₇₃	1	8	yes	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	24	no	—
525	C₂×C₄	—	2	16	no	—
526	C₂×C₄	—	2	48	no	—
527	C₂×C₄	—	146	4	no	—
528	C₂×C₄	—	146	24	no	—
529	C₂×C₄	—	146	16	no	—
530	C₂×C₄	—	146	48	no	—
531	C₂×C₄	C₂²×C₂²⋊D₇₃	1	6	yes	—
532	C₂×C₄	C₂²×C₂²⋊D₇₃	1	24	yes	—
533	C₂×C₄	C₂²×C₂²⋊D₇₃	1	2	yes	—
534	C₂×C₄	C₂²×C₂²⋊D₇₃	1	12	yes	—
535	C₂×C₄	C₂²×C₂²⋊D₇₃	1	12	yes	—
536	C₂×C₄	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
537	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
538	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
539	C₂×C₄	C₂⁴×D₇₃	1	12	yes	—
540	C₈	—	73	2	no	—
541	C₈	—	73	2	no	—
542	C₈	—	73	12	no	—
543	C₂²	—	2	2	no	—
544	C₂²	—	2	12	no	—
545	C₂²	—	2	8	no	—
546	C₂²	—	4	12	no	—
547	C₂²	—	4	8	no	—
548	C₂²	—	8	24	no	—
549	C₂²	—	292	8	no	—
550	C₂²	—	584	24	no	—
551	C₂²	—	146	8	no	—
552	C₂²	C₂³×C₂²⋊D₇₃	1	12	yes	—
553	C₂²	C₂³×C₂²⋊D₇₃	1	2	yes	—
554	C₂²	C₂³×C₂²⋊D₇₃	1	1	yes	characteristic
555	C₄	—	2	8	no	—
556	C₄	—	146	8	no	—
557	C₄	C₂³×C₂²⋊D₇₃	1	2	yes	—
558	C₄	C₂³×C₂²⋊D₇₃	1	12	yes	—
559	C₄	C₂³×C₂²⋊D₇₃	1	1	yes	characteristic
560	C₄	C₂⁵×D₇₃	1	1	yes	characteristic
561	C₂	—	2	2	no	—
562	C₂	—	2	12	no	—
563	C₂	—	4	8	no	—
564	C₂	—	292	8	no	—
565	C₂	#22624702	1	2	yes	direct product factor
566	C₂	C₂⁴×C₂²⋊D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₇₃
commutator, cosocle	C₄×C₇₃	C₂⁶
Frattini	C₄	C₂⁵×D₇₃
Fitting	C₂×#585×C₇₃	C₂
socle	C₂²×C₇₃	C₂³×D₄
hypercenter	C₂×#585	D₇₃
hypocenter	C₇₃	C₂×#3584
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×#41 ◁ C₂×#585

Complements

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

N	H ≅ G/N	type
1. C₂×#17989423	C₂	semidirect
2. #22624702	C₂	direct (N × H)
3. C₂×#17989402	C₂	semidirect
4. C₂×#17989398	C₂	semidirect
5. C₂×#17989395	C₂	semidirect
6. C₂×#17989390	C₂	semidirect
7. C₂×#17989385	C₂	semidirect
8. C₂²×#14556611	C₂	semidirect
9. C₂²×#14556598	C₂	semidirect
10. C₂×#585×C₇₃	C₂	semidirect
12. #17989423	C₂²	semidirect
14. C₂×#14556638	C₂²	semidirect
15. C₂×#14556637	C₂²	semidirect
17. C₂²×#11924028	C₂²	semidirect
19. #17989402	C₂²	semidirect
20. #17989398	C₂²	semidirect
21. #17989395	C₂²	semidirect
22. #17989390	C₂²	semidirect
23. #17989385	C₂²	semidirect
24. C₂×#14556622	C₂²	semidirect
25. C₂×#14556621	C₂²	semidirect
26. C₂×#14556617	C₂²	semidirect
27. C₂×#14556616	C₂²	semidirect
28. C₂×#14556611	C₂²	semidirect
29. C₂×#14556611	C₂²	semidirect
30. C₂×#14556611	C₂²	semidirect
31. C₂×#14556611	C₂²	semidirect
32. C₂×#14556611	C₂²	semidirect
33. C₂²×#11924018	C₂²	semidirect
34. C₂²×#11924016	C₂²	semidirect
35. C₂²×#11924015	C₂²	semidirect
36. C₂²×#11924013	C₂²	semidirect
37. C₂×#14556598	C₂²	semidirect
38. C₂×#14556598	C₂²	semidirect
39. C₂×#14556598	C₂²	semidirect
40. C₂²×#11924012	C₂²	semidirect
41. C₂³×#10596831	C₂²	semidirect
43. #585×C₇₃	C₂²	semidirect
45. C₂×2₋¹⁺⁴×C₇₃	C₂²	semidirect
47. C₂×H(5,𝔽₂)×C₇₃	C₂²	semidirect
50. C₂²×#41×C₇₃	C₂²	semidirect
53. #14556638	C₂³	semidirect
55. #14556637	C₂³	semidirect
63. C₂×#11924028	C₂³	semidirect
72. #14556622	C₂³	semidirect
73. #14556621	C₂³	semidirect
74. #14556617	C₂³	semidirect
75. #14556616	C₂³	semidirect
76. #14556611	C₂³	semidirect
77. #14556611	C₂³	semidirect
78. #14556611	C₂³	semidirect
79. #14556611	C₂³	semidirect
82. C₂×#11924018	C₂³	semidirect
85. C₂×#11924016	C₂³	semidirect
88. C₂×#11924015	C₂³	semidirect
91. C₂×#11924013	C₂³	semidirect
92. #14556598	C₂³	semidirect
93. #14556598	C₂³	semidirect
95. C₂×#11924012	C₂³	semidirect
100. C₂²×#10596831	C₂³	semidirect
103. 2₋¹⁺⁴×C₇₃	C₂³	semidirect
106. H(5,𝔽₂)×C₇₃	C₂³	semidirect
119. C₂×#41×C₇₃	C₂³	semidirect
281. C₂×C₇₃	#3584	semidirect
285. C₂×#585	D₇₃	semidirect
294. C₇₃	C₂×#3584	semidirect
298. #585	C₂×D₇₃	semidirect
302. C₂×2₋¹⁺⁴	C₂×D₇₃	semidirect
306. C₂×H(5,𝔽₂)	C₂×D₇₃	semidirect
311. C₂²×#41	C₂×D₇₃	semidirect
340. 2₋¹⁺⁴	C₂²×D₇₃	semidirect
346. H(5,𝔽₂)	C₂²×D₇₃	semidirect
368. C₂×#41	C₂²×D₇₃	semidirect
565. C₂	#22624702	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×#17989423	2
#22624702	2
C₂×#17989402	2
C₂×#17989398	2
C₂×#17989395	2
C₂×#17989390	2
C₂×#17989385	2
C₂²×#14556611	2
C₂²×#14556598	2
C₂×#585×C₇₃	2
C₂×#3584	73

Subgroups — C2×#22624702 #33999815

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22624702 #33999815