Subgroups — C₂×#22623719 #33994453

Order 18688.

11534 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14556638	C₂	1	1	yes	maximal, characteristic, complemented
2	#22623719	C₂	1	32	yes	maximal, direct product factor
3	C₂×#17989244	C₂	1	4	yes	maximal, complemented
4	C₂×#17989231	C₂	1	12	yes	maximal, complemented
5	C₂×#17989158	C₂	1	3	yes	maximal, complemented
6	C₂×#17989154	C₂	1	3	yes	maximal, complemented
7	C₂×#17989133	C₂	1	3	yes	maximal, complemented
8	C₂²×#14556578	C₂	1	3	yes	maximal, complemented
9	C₂×#41×Dic₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×H(5,𝔽₂)×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#14556638	—	2	16	no	—
12	C₂×#14556638	C₂²	1	16	yes	complemented
13	C₂²×#11924028	C₂²	1	3	yes	complemented
14	C₂²×#11924027	C₂²	1	6	yes	complemented
15	C₂³×Dic₁₄₆	C₂²	1	3	yes	complemented
16	C₂²×Q₈×D₇₃	C₂²	1	2	yes	complemented
17	#17989244	C₂²	1	64	yes	complemented
18	#17989231	C₂²	1	192	yes	complemented
19	#17989158	C₂²	1	48	yes	complemented
20	#17989154	C₂²	1	48	yes	complemented
21	#17989133	C₂²	1	48	yes	complemented
22	C₂×#14556589	C₂²	1	3	yes	complemented
23	C₂×#14556587	C₂²	1	3	yes	complemented
24	C₂×#14556580	C₂²	1	1	yes	characteristic, complemented
25	C₂×#14556578	C₂²	1	6	yes	complemented
26	C₂×#14556578	C₂²	1	12	yes	complemented
27	C₂×#14556578	C₂²	1	3	yes	complemented
28	C₂×#14556578	C₂²	1	48	yes	complemented
29	C₂×#14556572	C₂²	1	12	yes	complemented
30	C₂×#14556570	C₂²	1	12	yes	complemented
31	C₂×#14556563	C₂²	1	12	yes	complemented
32	C₂×#14556562	C₂²	1	12	yes	complemented
33	C₂×#14556560	C₂²	1	12	yes	complemented
34	#41×Dic₇₃	C₂²	1	16	yes	complemented
35	C₂×Q₈×Dic₇₃	C₂²	1	2	yes	complemented
36	C₂×D₄×Dic₇₃	C₂²	1	6	yes	complemented
37	C₂×C₄×C₂²⋊D₇₃	C₂²	1	12	yes	complemented
38	C₂×#14556550	C₂²	1	3	yes	complemented
39	C₂²×C₂²⋊Dic₇₃	C₂²	1	12	yes	complemented
40	C₂²×C₄×Dic₇₃	C₂²	1	3	yes	complemented
41	C₂×H(5,𝔽₂)×C₇₃	—	2	16	no	—
42	C₂×H(5,𝔽₂)×C₇₃	C₂²	1	16	yes	complemented
43	C₂²×#41×C₇₃	C₂²	1	3	yes	—
44	C₂²×#41×C₇₃	C₂²	1	2	yes	—
45	C₂²×#41×C₇₃	C₂²	1	1	yes	characteristic
46	C₂³×D₄×C₇₃	C₂²	1	3	yes	—
47	C₂³×D₄×C₇₃	C₂²	1	6	yes	—
48	#14556638	—	2	128	no	—
49	C₂×#11924028	—	2	24	no	—
50	C₂×#11924028	C₂³	1	24	yes	complemented
51	C₂×#11924027	—	2	48	no	—
52	C₂×#11924027	C₂³	1	48	yes	complemented
53	C₂²×Dic₁₄₆	—	2	24	no	—
54	C₂²×Dic₁₄₆	C₂³	1	3	yes	—
55	C₂²×Dic₁₄₆	C₂³	1	6	yes	—
56	C₂²×Dic₁₄₆	C₂³	1	24	yes	complemented
57	C₂×Q₈×D₇₃	—	2	16	no	—
58	C₂×Q₈×D₇₃	C₂³	1	16	yes	complemented
59	C₂²×D₂₉₂	C₂³	1	1	yes	characteristic
60	C₂²×C₂²⋊D₇₃	C₂³	1	6	yes	—
61	C₂²×C₂²⋊D₇₃	C₂³	1	12	yes	—
62	C₂³×Dic₇₃	C₂³	1	6	yes	—
63	C₂³×Dic₇₃	C₂³	1	6	yes	—
64	C₂²×C₄×D₇₃	C₂³	1	6	yes	—
65	#14556589	C₂³	1	24	yes	complemented
66	#14556587	C₂³	1	24	yes	complemented
67	#14556580	C₂³	1	8	yes	complemented
68	#14556578	C₂³	1	24	yes	complemented
69	#14556578	C₂³	1	48	yes	complemented
70	#14556578	C₂³	1	96	yes	complemented
71	#14556572	C₂³	1	96	yes	complemented
72	#14556570	C₂³	1	96	yes	complemented
73	#14556563	C₂³	1	96	yes	complemented
74	#14556562	C₂³	1	96	yes	complemented
75	#14556560	C₂³	1	96	yes	complemented
76	Q₈×Dic₇₃	C₂³	1	16	yes	complemented
77	D₄×Dic₇₃	C₂³	1	48	yes	complemented
78	C₄×C₂²⋊D₇₃	C₂³	1	96	yes	complemented
79	#14556550	C₂³	1	24	yes	complemented
80	C₂×C₄⋊Dic₇₃	C₂³	1	6	yes	—
81	C₂×#11924007	C₂³	1	12	yes	—
82	C₂×C₂²⋊Dic₇₃	C₂³	1	12	yes	—
83	C₂×C₂²⋊Dic₇₃	C₂³	1	24	yes	—
84	C₂×C₂²⋊Dic₇₃	C₂³	1	6	yes	—
85	C₂×C₂²⋊Dic₇₃	C₂³	1	96	yes	complemented
86	C₂×#11924005	C₂³	1	4	yes	—
87	C₂×C₄×Dic₇₃	C₂³	1	3	yes	—
88	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
89	C₂×C₄×Dic₇₃	C₂³	1	6	yes	—
90	C₂×C₄×Dic₇₃	C₂³	1	24	yes	complemented
91	C₂⁵×C₇₃	C₂³	1	6	yes	—
92	H(5,𝔽₂)×C₇₃	—	2	128	no	—
93	C₂×#41×C₇₃	—	2	16	no	—
94	C₂×#41×C₇₃	—	2	24	no	—
95	C₂×#41×C₇₃	D₄	1	16	yes	complemented
96	C₂×#41×C₇₃	C₂³	1	24	yes	—
97	C₂×#41×C₇₃	C₂³	1	16	yes	—
98	C₂×#41×C₇₃	C₂³	1	8	yes	—
99	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
100	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
101	C₂²×D₄×C₇₃	—	2	48	no	—
102	C₂²×D₄×C₇₃	—	2	24	no	—
103	C₂²×D₄×C₇₃	C₂³	1	3	yes	—
104	C₂²×D₄×C₇₃	C₂³	1	24	yes	—
105	C₂²×D₄×C₇₃	C₂³	1	48	yes	—
106	C₂²×D₄×C₇₃	C₂³	1	6	yes	—
107	C₂²×D₄×C₇₃	C₂³	1	6	yes	—
108	C₂²×D₄×C₇₃	C₂³	1	3	yes	—
109	C₂³×C₄×C₇₃	C₂³	1	6	yes	—
110	C₂³×C₄×C₇₃	C₂³	1	3	yes	—
111	C₂³×D₇₃	C₂⁴	1	2	yes	—
112	#11924028	—	2	96	no	—
113	#11924027	—	2	192	no	—
114	C₂×Dic₁₄₆	—	2	24	no	—
115	C₂×Dic₁₄₆	—	2	12	no	—
116	C₂×Dic₁₄₆	—	2	96	no	—
117	C₂×Dic₁₄₆	C₂⁴	1	24	yes	—
118	C₂×Dic₁₄₆	C₂⁴	1	12	yes	—
119	Q₈×D₇₃	—	2	64	no	—
120	C₂×D₂₉₂	—	2	4	no	—
121	C₂×D₂₉₂	C₂⁴	1	4	yes	—
122	C₂×C₂²⋊D₇₃	—	2	24	no	—
123	C₂×C₂²⋊D₇₃	—	4	24	no	—
124	C₂×C₂²⋊D₇₃	C₂⁴	1	24	yes	—
125	C₂×C₂²⋊D₇₃	C₂⁴	1	48	yes	—
126	C₂²×Dic₇₃	—	2	24	no	—
127	C₂²×Dic₇₃	—	4	12	no	—
128	C₂²×Dic₇₃	C₂⁴	1	2	yes	—
129	C₂²×Dic₇₃	C₂⁴	1	6	yes	—
130	C₂²×Dic₇₃	C₂⁴	1	6	yes	—
131	C₂²×Dic₇₃	C₂⁴	1	24	yes	—
132	C₂²×Dic₇₃	C₂⁴	1	24	yes	—
133	C₂×C₄×D₇₃	—	2	24	no	—
134	C₂×C₄×D₇₃	C₂⁴	1	24	yes	—
135	C₄⋊Dic₇₃	C₂⁴	1	24	yes	—
136	#11924007	C₂⁴	1	48	yes	—
137	C₂²⋊Dic₇₃	C₂⁴	1	48	yes	—
138	C₂²⋊Dic₇₃	C₂⁴	1	96	yes	—
139	C₂²⋊Dic₇₃	C₂⁴	1	24	yes	—
140	#11924005	C₂⁴	1	16	yes	—
141	C₄×Dic₇₃	C₂⁴	1	4	yes	—
142	C₄×Dic₇₃	C₂⁴	1	12	yes	—
143	C₄×Dic₇₃	C₂⁴	1	24	yes	—
144	C₂⁴×C₇₃	—	2	24	no	—
145	C₂⁴×C₇₃	—	4	24	no	—
146	C₂⁴×C₇₃	C₂⁴	1	6	yes	—
147	C₂⁴×C₇₃	C₂⁴	1	3	yes	—
148	C₂⁴×C₇₃	C₂⁴	1	24	yes	—
149	#41×C₇₃	—	2	64	no	—
150	#41×C₇₃	—	2	96	no	—
151	#41×C₇₃	C₂×D₄	1	64	yes	complemented
152	C₂×Q₈×C₇₃	—	2	4	no	—
153	C₂×Q₈×C₇₃	C₂×D₄	1	8	yes	—
154	C₂×Q₈×C₇₃	C₂⁴	1	4	yes	—
155	C₂×Q₈×C₇₃	C₂⁴	1	4	yes	—
156	C₂×D₄×C₇₃	—	2	24	no	—
157	C₂×D₄×C₇₃	—	2	192	no	—
158	C₂×D₄×C₇₃	—	2	24	no	—
159	C₂×D₄×C₇₃	—	2	12	no	—
160	C₂×D₄×C₇₃	—	2	96	no	—
161	C₂×D₄×C₇₃	C₂×D₄	1	24	yes	—
162	C₂×D₄×C₇₃	C₂⁴	1	24	yes	—
163	C₂×D₄×C₇₃	C₂⁴	1	24	yes	—
164	C₂×D₄×C₇₃	C₂⁴	1	12	yes	—
165	C₂×D₄×C₇₃	C₂⁴	1	12	yes	—
166	C₂²×C₄×C₇₃	—	2	24	no	—
167	C₂²×C₄×C₇₃	C₂×D₄	1	24	yes	—
168	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
169	C₂²×C₄×C₇₃	C₂⁴	1	24	yes	—
170	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
171	C₂²×C₄×C₇₃	C₂⁴	1	3	yes	—
172	C₂²×C₄×C₇₃	C₂⁴	1	12	yes	—
173	C₂³×C₇₃	—	2	12	no	—
174	C₂³×C₇₃	—	2	12	no	—
175	C₂³×C₇₃	—	2	24	no	—
176	C₂³×C₇₃	—	2	48	no	—
177	C₂³×C₇₃	—	4	48	no	—
178	C₂³×C₇₃	—	8	48	no	—
179	C₂³×C₇₃	C₂²×D₄	1	12	yes	—
180	C₂³×C₇₃	C₂⁵	1	12	yes	—
181	C₂³×C₇₃	C₂⁵	1	6	yes	—
182	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
183	C₂²×D₇₃	—	2	4	no	—
184	C₂²×D₇₃	—	2	8	no	—
185	C₂²×D₇₃	C₂⁵	1	4	yes	—
186	Q₈×C₇₃	—	2	8	no	—
187	Q₈×C₇₃	C₂²×D₄	1	16	yes	—
188	D₄×C₇₃	—	2	48	no	—
189	D₄×C₇₃	—	2	24	no	—
190	D₄×C₇₃	—	2	48	no	—
191	D₄×C₇₃	C₂²×D₄	1	48	yes	—
192	C₂×C₄×C₇₃	—	2	4	no	—
193	C₂×C₄×C₇₃	—	2	48	no	—
194	C₂×C₄×C₇₃	C₂²×D₄	1	12	yes	—
195	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
196	C₂×C₄×C₇₃	C₂²×D₄	1	48	yes	—
197	C₂×C₄×C₇₃	C₂⁵	1	4	yes	—
198	C₂×C₄×C₇₃	C₂⁵	1	2	yes	—
199	C₂×C₄×C₇₃	C₂⁵	1	6	yes	—
200	C₂²⋊D₇₃	—	2	48	no	—
201	C₂²⋊D₇₃	—	4	48	no	—
202	C₂×Dic₇₃	—	2	12	no	—
203	C₂×Dic₇₃	—	2	48	no	—
204	C₂×Dic₇₃	—	2	4	no	—
205	C₂×Dic₇₃	—	2	12	no	—
206	C₂×Dic₇₃	—	4	24	no	—
207	C₂×Dic₇₃	C₂⁵	1	4	yes	—
208	C₂×Dic₇₃	C₂⁵	1	12	yes	—
209	C₂×Dic₇₃	C₂⁵	1	12	yes	—
210	D₂₉₂	—	2	8	no	—
211	C₄×D₇₃	—	2	48	no	—
212	Dic₁₄₆	—	2	48	no	—
213	Dic₁₄₆	—	2	24	no	—
214	C₂²×C₇₃	—	2	12	no	—
215	C₂²×C₇₃	—	2	24	no	—
216	C₂²×C₇₃	—	2	12	no	—
217	C₂²×C₇₃	—	2	24	no	—
218	C₂²×C₇₃	—	4	24	no	—
219	C₂²×C₇₃	—	8	48	no	—
220	C₂²×C₇₃	C₂³×D₄	1	12	yes	—
221	C₂²×C₇₃	C₂³×D₄	1	2	yes	—
222	C₂²×C₇₃	#585	1	4	yes	—
223	C₂²×C₇₃	C₂⁶	1	1	yes	characteristic
224	C₂×D₇₃	—	2	4	no	—
225	C₂×D₇₃	—	2	8	no	—
226	C₂×D₇₃	—	4	8	no	—
227	C₄×C₇₃	—	2	4	no	—
228	C₄×C₇₃	C₂³×D₄	1	4	yes	—
229	C₄×C₇₃	C₂³×D₄	1	12	yes	—
230	Dic₇₃	—	2	12	no	—
231	Dic₇₃	—	2	4	no	—
232	Dic₇₃	—	2	12	no	—
233	C₂×#3500	—	73	1	no	maximal, Sylow
234	C₂×C₇₃	—	2	12	no	—
235	C₂×C₇₃	—	4	12	no	—
236	C₂×C₇₃	#3500	1	4	yes	complemented
237	C₂×C₇₃	C₂⁴×D₄	1	1	yes	characteristic
238	C₂×C₇₃	C₂×#585	1	2	yes	—
239	D₇₃	—	4	4	no	—
240	C₂²×2₋¹⁺⁴	—	73	1	no	—
241	C₂²×H(5,𝔽₂)	D₇₃	1	1	yes	characteristic, complemented
242	#3500	—	73	32	no	—
243	C₂×#548	—	73	4	no	—
244	C₂×#546	—	73	12	no	—
245	C₂×#536	—	73	3	no	—
246	C₂×#535	—	73	3	no	—
247	C₂×#532	—	73	3	no	—
248	C₂²×#124	—	73	3	no	—
249	C₂×C₄×#41	—	73	1	no	—
250	C₇₃	C₂×#3500	1	1	yes	characteristic, complemented, Sylow
251	C₂×2₋¹⁺⁴	—	73	16	no	—
252	C₂×2₋¹⁺⁴	—	146	16	no	—
253	C₂×H(5,𝔽₂)	—	2	16	no	—
254	C₂×H(5,𝔽₂)	C₂×D₇₃	1	16	yes	complemented
255	C₂²×#41	—	73	6	no	—
256	C₂²×#41	—	73	3	no	—
257	C₂²×#41	C₂×D₇₃	1	3	yes	—
258	C₂²×#41	C₂×D₇₃	1	2	yes	—
259	C₂²×#41	C₂×D₇₃	1	1	yes	characteristic
260	C₂³×Q₈	—	73	2	no	—
261	C₂³×Q₈	—	73	3	no	—
262	C₂³×D₄	C₂×D₇₃	1	3	yes	—
263	C₂³×D₄	C₂×D₇₃	1	6	yes	—
264	#548	—	73	64	no	—
265	#546	—	73	192	no	—
266	#536	—	73	48	no	—
267	#535	—	73	48	no	—
268	#532	—	73	48	no	—
269	C₂×C₄⋊Q₈	—	73	3	no	—
270	C₂×#127	—	73	3	no	—
271	C₂×#124	—	73	1	no	—
272	C₂×#124	—	73	3	no	—
273	C₂×#124	—	73	6	no	—
274	C₂×#124	—	73	12	no	—
275	C₂×#124	—	73	48	no	—
276	C₂×#123	—	73	12	no	—
277	C₂×C₂²⋊Q₈	—	73	12	no	—
278	C₂×#121	—	73	12	no	—
279	C₂×#121	—	73	12	no	—
280	C₂×#120	—	73	12	no	—
281	C₄×#41	—	73	16	no	—
282	C₂×C₄×Q₈	—	73	2	no	—
283	C₂×C₄×D₄	—	73	6	no	—
284	C₂×C₄×D₄	—	73	12	no	—
285	C₂×#117	—	73	3	no	—
286	C₂²×C₂²⋊C₄	—	73	12	no	—
287	C₂²×C₄²	—	73	3	no	—
288	C₂⁵	C₂²×D₇₃	1	6	yes	—
289	2₋¹⁺⁴	—	146	128	no	—
290	H(5,𝔽₂)	—	2	128	no	—
291	C₂×#41	—	2	16	no	—
292	C₂×#41	—	2	24	no	—
293	C₂×#41	—	73	48	no	—
294	C₂×#41	—	73	24	no	—
295	C₂×#41	—	146	48	no	—
296	C₂×#41	—	146	24	no	—
297	C₂×#41	C₂²⋊D₇₃	1	16	yes	complemented
298	C₂×#41	C₂²×D₇₃	1	24	yes	—
299	C₂×#41	C₂²×D₇₃	1	16	yes	—
300	C₂×#41	C₂²×D₇₃	1	8	yes	—
301	C₂²×Q₈	—	73	16	no	—
302	C₂²×Q₈	—	73	6	no	—
303	C₂²×Q₈	—	73	3	no	—
304	C₂²×Q₈	—	73	24	no	—
305	C₂²×Q₈	—	146	16	no	—
306	C₂²×Q₈	—	146	24	no	—
307	C₂²×Q₈	C₂²×D₇₃	1	1	yes	characteristic
308	C₂²×Q₈	C₂²×D₇₃	1	1	yes	characteristic
309	C₂²×D₄	—	2	48	no	—
310	C₂²×D₄	—	2	24	no	—
311	C₂²×D₄	—	73	12	no	—
312	C₂²×D₄	—	73	6	no	—
313	C₂²×D₄	—	73	1	no	—
314	C₂²×D₄	C₂²×D₇₃	1	6	yes	—
315	C₂²×D₄	C₂²×D₇₃	1	6	yes	—
316	C₂²×D₄	C₂²×D₇₃	1	3	yes	—
317	C₂²×D₄	C₂²×D₇₃	1	24	yes	—
318	C₂²×D₄	C₂²×D₇₃	1	48	yes	—
319	C₂²×D₄	C₂²×D₇₃	1	3	yes	—
320	C₂³×C₄	—	73	6	no	—
321	C₂³×C₄	—	73	6	no	—
322	C₂³×C₄	—	73	6	no	—
323	C₂³×C₄	C₂²×D₇₃	1	6	yes	—
324	C₂³×C₄	C₂²×D₇₃	1	3	yes	—
325	C₄⋊Q₈	—	73	24	no	—
326	#127	—	73	24	no	—
327	#124	—	73	8	no	—
328	#124	—	73	24	no	—
329	#124	—	73	48	no	—
330	#124	—	73	96	no	—
331	#123	—	73	96	no	—
332	C₂²⋊Q₈	—	73	96	no	—
333	#121	—	73	96	no	—
334	#121	—	73	96	no	—
335	#120	—	73	96	no	—
336	C₄×Q₈	—	73	16	no	—
337	C₄×D₄	—	73	48	no	—
338	C₄×D₄	—	73	96	no	—
339	#117	—	73	24	no	—
340	C₂×C₄⋊C₄	—	73	6	no	—
341	C₂×C₄⋊C₄	—	73	12	no	—
342	C₂×C₂²⋊C₄	—	73	12	no	—
343	C₂×C₂²⋊C₄	—	73	24	no	—
344	C₂×C₂²⋊C₄	—	73	96	no	—
345	C₂×C₂²⋊C₄	—	73	6	no	—
346	C₂×C₂²⋊C₄	—	73	4	no	—
347	C₂×C₄²	—	73	3	no	—
348	C₂×C₄²	—	73	6	no	—
349	C₂×C₄²	—	73	24	no	—
350	C₂×C₄²	—	73	1	no	—
351	C₂⁴	—	2	24	no	—
352	C₂⁴	—	4	24	no	—
353	C₂⁴	—	73	2	no	—
354	C₂⁴	C₂³×D₇₃	1	6	yes	—
355	C₂⁴	C₂³×D₇₃	1	3	yes	—
356	C₂⁴	C₂³×D₇₃	1	24	yes	—
357	#41	—	2	64	no	—
358	#41	—	2	96	no	—
359	#41	—	146	192	no	—
360	#41	—	146	96	no	—
361	#41	C₂×C₂²⋊D₇₃	1	64	yes	complemented
362	C₂×Q₈	—	2	4	no	—
363	C₂×Q₈	—	73	24	no	—
364	C₂×Q₈	—	73	12	no	—
365	C₂×Q₈	—	146	64	no	—
366	C₂×Q₈	—	146	24	no	—
367	C₂×Q₈	—	146	12	no	—
368	C₂×Q₈	—	146	96	no	—
369	C₂×Q₈	C₂×C₂²⋊D₇₃	1	8	yes	—
370	C₂×Q₈	C₂³×D₇₃	1	4	yes	—
371	C₂×Q₈	C₂³×D₇₃	1	4	yes	—
372	C₂×D₄	—	2	24	no	—
373	C₂×D₄	—	2	192	no	—
374	C₂×D₄	—	2	24	no	—
375	C₂×D₄	—	2	12	no	—
376	C₂×D₄	—	2	96	no	—
377	C₂×D₄	—	292	24	no	—
378	C₂×D₄	—	73	48	no	—
379	C₂×D₄	—	73	24	no	—
380	C₂×D₄	—	73	4	no	—
381	C₂×D₄	—	146	24	no	—
382	C₂×D₄	—	146	4	no	—
383	C₂×D₄	C₂×C₂²⋊D₇₃	1	24	yes	—
384	C₂×D₄	C₂³×D₇₃	1	24	yes	—
385	C₂×D₄	C₂³×D₇₃	1	24	yes	—
386	C₂×D₄	C₂³×D₇₃	1	12	yes	—
387	C₂×D₄	C₂³×D₇₃	1	12	yes	—
388	C₂²×C₄	—	2	24	no	—
389	C₂²×C₄	—	292	12	no	—
390	C₂²×C₄	—	73	24	no	—
391	C₂²×C₄	—	73	24	no	—
392	C₂²×C₄	—	73	2	no	—
393	C₂²×C₄	—	73	6	no	—
394	C₂²×C₄	—	73	6	no	—
395	C₂²×C₄	—	73	24	no	—
396	C₂²×C₄	—	146	24	no	—
397	C₂²×C₄	—	146	24	no	—
398	C₂²×C₄	C₂×C₂²⋊D₇₃	1	24	yes	—
399	C₂²×C₄	C₂³×D₇₃	1	24	yes	—
400	C₂²×C₄	C₂³×D₇₃	1	2	yes	—
401	C₂²×C₄	C₂³×D₇₃	1	12	yes	—
402	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
403	C₂²×C₄	C₂³×D₇₃	1	3	yes	—
404	C₄⋊C₄	—	73	48	no	—
405	C₄⋊C₄	—	73	24	no	—
406	C₂²⋊C₄	—	73	48	no	—
407	C₂²⋊C₄	—	73	96	no	—
408	C₂²⋊C₄	—	73	24	no	—
409	C₂²⋊C₄	—	73	16	no	—
410	C₄²	—	73	4	no	—
411	C₄²	—	73	12	no	—
412	C₄²	—	73	24	no	—
413	C₂³	—	2	12	no	—
414	C₂³	—	2	12	no	—
415	C₂³	—	2	24	no	—
416	C₂³	—	2	48	no	—
417	C₂³	—	4	48	no	—
418	C₂³	—	8	48	no	—
419	C₂³	—	73	4	no	—
420	C₂³	—	146	4	no	—
421	C₂³	—	146	8	no	—
422	C₂³	C₂²×C₂²⋊D₇₃	1	12	yes	—
423	C₂³	C₂⁴×D₇₃	1	12	yes	—
424	C₂³	C₂⁴×D₇₃	1	6	yes	—
425	C₂³	C₂⁴×D₇₃	1	1	yes	characteristic
426	Q₈	—	2	8	no	—
427	Q₈	—	146	48	no	—
428	Q₈	—	146	24	no	—
429	Q₈	C₂²×C₂²⋊D₇₃	1	16	yes	—
430	D₄	—	2	48	no	—
431	D₄	—	2	48	no	—
432	D₄	—	2	24	no	—
433	D₄	—	292	48	no	—
434	D₄	—	146	48	no	—
435	D₄	—	146	8	no	—
436	D₄	C₂²×C₂²⋊D₇₃	1	48	yes	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	48	no	—
439	C₂×C₄	—	292	24	no	—
440	C₂×C₄	—	73	4	no	—
441	C₂×C₄	—	73	12	no	—
442	C₂×C₄	—	73	12	no	—
443	C₂×C₄	—	146	12	no	—
444	C₂×C₄	—	146	48	no	—
445	C₂×C₄	—	146	4	no	—
446	C₂×C₄	—	146	12	no	—
447	C₂×C₄	—	146	48	no	—
448	C₂×C₄	C₂²×C₂²⋊D₇₃	1	12	yes	—
449	C₂×C₄	C₂²×C₂²⋊D₇₃	1	4	yes	—
450	C₂×C₄	C₂²×C₂²⋊D₇₃	1	48	yes	—
451	C₂×C₄	C₂⁴×D₇₃	1	4	yes	—
452	C₂×C₄	C₂⁴×D₇₃	1	2	yes	—
453	C₂×C₄	C₂⁴×D₇₃	1	6	yes	—
454	C₂²	—	2	12	no	—
455	C₂²	—	2	24	no	—
456	C₂²	—	2	12	no	—
457	C₂²	—	2	24	no	—
458	C₂²	—	4	24	no	—
459	C₂²	—	8	48	no	—
460	C₂²	—	292	8	no	—
461	C₂²	—	146	4	no	—
462	C₂²	—	146	8	no	—
463	C₂²	C₂³×C₂²⋊D₇₃	1	12	yes	—
464	C₂²	C₂³×C₂²⋊D₇₃	1	2	yes	—
465	C₂²	#17989422	1	4	yes	—
466	C₂²	C₂⁵×D₇₃	1	1	yes	characteristic
467	C₄	—	2	4	no	—
468	C₄	—	146	12	no	—
469	C₄	—	146	4	no	—
470	C₄	—	146	12	no	—
471	C₄	C₂³×C₂²⋊D₇₃	1	12	yes	—
472	C₄	C₂³×C₂²⋊D₇₃	1	4	yes	—
473	C₂	—	2	12	no	—
474	C₂	—	4	12	no	—
475	C₂	—	292	4	no	—
476	C₂	#22623719	1	4	yes	direct product factor
477	C₂	C₂⁴×C₂²⋊D₇₃	1	1	yes	characteristic
478	C₂	C₂×#17989422	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₇₃
commutator, cosocle	C₂²×C₇₃	C₂⁶
Frattini	C₂²	C₂⁵×D₇₃
Fitting	C₂²×H(5,𝔽₂)×C₇₃	C₂
socle	C₂³×C₇₃	C₂⁵
hypercenter	C₂²×H(5,𝔽₂)	D₇₃
hypocenter	C₇₃	C₂×#3500
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂²×H(5,𝔽₂)

Complements

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

N	H ≅ G/N	type
1. C₂²×#14556638	C₂	semidirect
2. #22623719	C₂	direct (N × H)
3. C₂×#17989244	C₂	semidirect
4. C₂×#17989231	C₂	semidirect
5. C₂×#17989158	C₂	semidirect
6. C₂×#17989154	C₂	semidirect
7. C₂×#17989133	C₂	semidirect
8. C₂²×#14556578	C₂	semidirect
9. C₂×#41×Dic₇₃	C₂	semidirect
10. C₂²×H(5,𝔽₂)×C₇₃	C₂	semidirect
12. C₂×#14556638	C₂²	semidirect
13. C₂²×#11924028	C₂²	semidirect
14. C₂²×#11924027	C₂²	semidirect
15. C₂³×Dic₁₄₆	C₂²	semidirect
16. C₂²×Q₈×D₇₃	C₂²	semidirect
17. #17989244	C₂²	semidirect
18. #17989231	C₂²	semidirect
19. #17989158	C₂²	semidirect
20. #17989154	C₂²	semidirect
21. #17989133	C₂²	semidirect
22. C₂×#14556589	C₂²	semidirect
23. C₂×#14556587	C₂²	semidirect
24. C₂×#14556580	C₂²	semidirect
25. C₂×#14556578	C₂²	semidirect
26. C₂×#14556578	C₂²	semidirect
27. C₂×#14556578	C₂²	semidirect
28. C₂×#14556578	C₂²	semidirect
29. C₂×#14556572	C₂²	semidirect
30. C₂×#14556570	C₂²	semidirect
31. C₂×#14556563	C₂²	semidirect
32. C₂×#14556562	C₂²	semidirect
33. C₂×#14556560	C₂²	semidirect
34. #41×Dic₇₃	C₂²	semidirect
35. C₂×Q₈×Dic₇₃	C₂²	semidirect
36. C₂×D₄×Dic₇₃	C₂²	semidirect
37. C₂×C₄×C₂²⋊D₇₃	C₂²	semidirect
38. C₂×#14556550	C₂²	semidirect
39. C₂²×C₂²⋊Dic₇₃	C₂²	semidirect
40. C₂²×C₄×Dic₇₃	C₂²	semidirect
42. C₂×H(5,𝔽₂)×C₇₃	C₂²	semidirect
50. C₂×#11924028	C₂³	semidirect
52. C₂×#11924027	C₂³	semidirect
56. C₂²×Dic₁₄₆	C₂³	semidirect
58. C₂×Q₈×D₇₃	C₂³	semidirect
65. #14556589	C₂³	semidirect
66. #14556587	C₂³	semidirect
67. #14556580	C₂³	semidirect
68. #14556578	C₂³	semidirect
69. #14556578	C₂³	semidirect
70. #14556578	C₂³	semidirect
71. #14556572	C₂³	semidirect
72. #14556570	C₂³	semidirect
73. #14556563	C₂³	semidirect
74. #14556562	C₂³	semidirect
75. #14556560	C₂³	semidirect
76. Q₈×Dic₇₃	C₂³	semidirect
77. D₄×Dic₇₃	C₂³	semidirect
78. C₄×C₂²⋊D₇₃	C₂³	semidirect
79. #14556550	C₂³	semidirect
85. C₂×C₂²⋊Dic₇₃	C₂³	semidirect
90. C₂×C₄×Dic₇₃	C₂³	semidirect
95. C₂×#41×C₇₃	D₄	semidirect
151. #41×C₇₃	C₂×D₄	semidirect
236. C₂×C₇₃	#3500	semidirect
241. C₂²×H(5,𝔽₂)	D₇₃	semidirect
250. C₇₃	C₂×#3500	semidirect
254. C₂×H(5,𝔽₂)	C₂×D₇₃	semidirect
297. C₂×#41	C₂²⋊D₇₃	semidirect
361. #41	C₂×C₂²⋊D₇₃	semidirect
476. C₂	#22623719	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#14556638	2
#22623719	2
C₂×#17989244	2
C₂×#17989231	2
C₂×#17989158	2
C₂×#17989154	2
C₂×#17989133	2
C₂²×#14556578	2
C₂×#41×Dic₇₃	2
C₂²×H(5,𝔽₂)×C₇₃	2
C₂×#3500	73

Subgroups — C2×#22623719 #33994453

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22623719 #33994453