Subgroups — C₂×#379×D₇₃ #33244237

Order 18688.

33214 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×D₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂²⋊C₄×D₇₃	C₂	1	6	yes	maximal, complemented
3	C₂×#17988443	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#17988442	C₂	1	6	yes	maximal, complemented
5	#379×D₇₃	C₂	1	16	yes	maximal, direct product factor
6	C₂×#379×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂⁵×D₇₃	—	2	48	no	—
8	C₂⁵×D₇₃	C₄	1	16	yes	complemented
9	C₂⁵×D₇₃	C₂²	1	8	yes	—
10	C₂⁵×D₇₃	C₂²	1	3	yes	—
11	C₂⁵×D₇₃	C₂²	1	3	yes	—
12	C₂³×C₄×D₇₃	C₂²	1	4	yes	complemented
13	C₂²×C₂²⋊Dic₇₃	C₂²	1	6	yes	complemented
14	C₂²×#11924005	C₂²	1	12	yes	complemented
15	C₂×C₂²⋊C₄×D₇₃	—	2	48	no	—
16	C₂×C₂²⋊C₄×D₇₃	C₂²	1	48	yes	complemented
17	#17988443	C₂²	1	8	yes	complemented
18	#17988442	C₂²	1	48	yes	complemented
19	C₂⁶×C₇₃	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	6	yes	complemented
21	#379×C₇₃	C₂²	1	8	yes	complemented
22	C₂⁴×D₇₃	—	2	512	no	—
23	C₂⁴×D₇₃	—	2	384	no	—
24	C₂⁴×D₇₃	—	2	192	no	—
25	C₂⁴×D₇₃	—	2	48	no	—
26	C₂⁴×D₇₃	—	2	48	no	—
27	C₂⁴×D₇₃	—	2	24	no	—
28	C₂⁴×D₇₃	C₂×C₄	1	24	yes	—
29	C₂⁴×D₇₃	C₂×C₄	1	24	yes	complemented
30	C₂⁴×D₇₃	C₂×C₄	1	64	yes	complemented
31	C₂⁴×D₇₃	D₄	1	48	yes	—
32	C₂⁴×D₇₃	C₂³	1	12	yes	—
33	C₂⁴×D₇₃	C₂³	1	12	yes	—
34	C₂⁴×D₇₃	C₂³	1	3	yes	—
35	C₂⁴×D₇₃	C₂³	1	1	yes	characteristic
36	C₂³×Dic₇₃	C₂³	1	4	yes	complemented
37	C₂²×C₄×D₇₃	—	2	48	no	—
38	C₂²×C₄×D₇₃	C₂³	1	16	yes	complemented
39	C₂×C₂²⋊Dic₇₃	—	2	24	no	—
40	C₂×C₂²⋊Dic₇₃	C₂³	1	24	yes	complemented
41	C₂×#11924005	—	2	48	no	—
42	C₂×#11924005	C₂³	1	48	yes	complemented
43	C₂²⋊C₄×D₇₃	—	2	192	no	—
44	C₂⁵×C₇₃	—	2	24	no	—
45	C₂⁵×C₇₃	C₂×C₄	1	8	yes	complemented
46	C₂⁵×C₇₃	C₂³	1	4	yes	—
47	C₂⁵×C₇₃	C₂³	1	3	yes	—
48	C₂³×C₄×C₇₃	C₂³	1	4	yes	complemented
49	C₂×C₂²⋊C₄×C₇₃	—	2	24	no	—
50	C₂×C₂²⋊C₄×C₇₃	C₂³	1	24	yes	complemented
51	C₂³×D₇₃	—	2	384	no	—
52	C₂³×D₇₃	—	2	1024	no	—
53	C₂³×D₇₃	—	2	2048	no	—
54	C₂³×D₇₃	—	2	96	no	—
55	C₂³×D₇₃	—	2	48	no	—
56	C₂³×D₇₃	—	2	24	no	—
57	C₂³×D₇₃	—	2	192	no	—
58	C₂³×D₇₃	—	2	192	no	—
59	C₂³×D₇₃	—	2	768	no	—
60	C₂³×D₇₃	—	2	384	no	—
61	C₂³×D₇₃	—	2	96	no	—
62	C₂³×D₇₃	—	2	96	no	—
63	C₂³×D₇₃	C₂²⋊C₄	1	192	yes	complemented
64	C₂³×D₇₃	C₂²×C₄	1	12	yes	—
65	C₂³×D₇₃	C₂²×C₄	1	48	yes	—
66	C₂³×D₇₃	C₂²×C₄	1	4	yes	—
67	C₂³×D₇₃	C₂²×C₄	1	48	yes	complemented
68	C₂³×D₇₃	C₂×D₄	1	96	yes	—
69	C₂³×D₇₃	C₂×D₄	1	24	yes	—
70	C₂³×D₇₃	C₂×D₄	1	24	yes	—
71	C₂³×D₇₃	C₂⁴	1	6	yes	—
72	C₂³×D₇₃	C₂⁴	1	2	yes	—
73	C₂²×Dic₇₃	—	2	24	no	—
74	C₂²×Dic₇₃	C₂⁴	1	8	yes	complemented
75	C₂×C₄×D₇₃	—	2	96	no	—
76	C₂×C₄×D₇₃	—	4	64	no	—
77	C₂²⋊Dic₇₃	—	2	48	no	—
78	#11924005	—	2	96	no	—
79	C₂⁴×C₇₃	—	2	128	no	—
80	C₂⁴×C₇₃	—	2	96	no	—
81	C₂⁴×C₇₃	—	2	48	no	—
82	C₂⁴×C₇₃	—	2	24	no	—
83	C₂⁴×C₇₃	C₂²×C₄	1	12	yes	—
84	C₂⁴×C₇₃	C₂²×C₄	1	16	yes	complemented
85	C₂⁴×C₇₃	C₂×D₄	1	24	yes	—
86	C₂⁴×C₇₃	C₂⁴	1	6	yes	—
87	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
88	C₂²×C₄×C₇₃	—	2	24	no	—
89	C₂²×C₄×C₇₃	C₂⁴	1	8	yes	complemented
90	C₂²⋊C₄×C₇₃	—	2	48	no	—
91	C₂³×C₇₃	—	2	128	no	—
92	C₂³×C₇₃	—	2	256	no	—
93	C₂³×C₇₃	—	2	48	no	—
94	C₂³×C₇₃	—	2	96	no	—
95	C₂³×C₇₃	—	2	96	no	—
96	C₂³×C₇₃	—	2	24	no	—
97	C₂³×C₇₃	C₂×C₂²⋊C₄	1	48	yes	complemented
98	C₂³×C₇₃	C₂³×C₄	1	12	yes	—
99	C₂³×C₇₃	C₂³×C₄	1	2	yes	—
100	C₂³×C₇₃	C₂²×D₄	1	24	yes	—
101	C₂³×C₇₃	C₂²×D₄	1	12	yes	—
102	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
103	C₂²×D₇₃	—	2	384	no	—
104	C₂²×D₇₃	—	2	768	no	—
105	C₂²×D₇₃	—	2	2048	no	—
106	C₂²×D₇₃	—	2	48	no	—
107	C₂²×D₇₃	—	2	96	no	—
108	C₂²×D₇₃	—	2	96	no	—
109	C₂²×D₇₃	—	2	24	no	—
110	C₂²×D₇₃	—	2	192	no	—
111	C₂²×D₇₃	—	2	192	no	—
112	C₂²×D₇₃	—	2	384	no	—
113	C₂²×D₇₃	—	2	768	no	—
114	C₂²×D₇₃	C₂×C₂²⋊C₄	1	48	yes	—
115	C₂²×D₇₃	C₂×C₂²⋊C₄	1	192	yes	complemented
116	C₂²×D₇₃	C₂×C₂²⋊C₄	1	48	yes	complemented
117	C₂²×D₇₃	#120	1	64	yes	—
118	C₂²×D₇₃	C₂³×C₄	1	12	yes	—
119	C₂²×D₇₃	C₂³×C₄	1	4	yes	—
120	C₂²×D₇₃	C₂²×D₄	1	24	yes	—
121	C₂²×D₇₃	C₂²×D₄	1	24	yes	—
122	C₂×C₄×C₇₃	—	2	24	no	—
123	C₂×C₄×C₇₃	—	4	16	no	—
124	C₂×Dic₇₃	—	2	24	no	—
125	C₂×Dic₇₃	—	4	16	no	—
126	C₄×D₇₃	—	4	64	no	—
127	C₂²×C₇₃	—	2	128	no	—
128	C₂²×C₇₃	—	2	24	no	—
129	C₂²×C₇₃	—	2	48	no	—
130	C₂²×C₇₃	—	2	96	no	—
131	C₂²×C₇₃	C₂²×C₂²⋊C₄	1	12	yes	—
132	C₂²×C₇₃	C₂²×C₂²⋊C₄	1	24	yes	complemented
133	C₂²×C₇₃	C₂×#120	1	16	yes	—
134	C₂²×C₇₃	C₂⁴×C₄	1	1	yes	characteristic
135	C₂²×C₇₃	C₂³×D₄	1	6	yes	—
136	C₂×D₇₃	—	2	384	no	—
137	C₂×D₇₃	—	2	24	no	—
138	C₂×D₇₃	—	2	48	no	—
139	C₂×D₇₃	—	2	96	no	—
140	C₂×D₇₃	—	2	384	no	—
141	C₂×D₇₃	#379	1	64	yes	direct product factor
142	C₂×D₇₃	C₂²×C₂²⋊C₄	1	24	yes	—
143	C₂×D₇₃	C₂²×C₂²⋊C₄	1	24	yes	complemented
144	C₂×D₇₃	C₂×#120	1	32	yes	—
145	C₄×C₇₃	—	4	8	no	—
146	Dic₇₃	—	4	8	no	—
147	C₂²×#379	—	73	1	no	maximal, Sylow
148	C₂×C₇₃	—	2	24	no	—
149	C₂×C₇₃	C₂×#379	1	8	yes	complemented
150	C₂×C₇₃	C₂³×C₂²⋊C₄	1	3	yes	—
151	C₂×C₇₃	C₂²×#120	1	4	yes	—
152	D₇₃	—	2	24	no	—
153	D₇₃	C₂×#379	1	16	yes	direct product factor
154	C₂⁷	—	73	1	no	—
155	C₂³×C₂²⋊C₄	—	73	6	no	—
156	C₂×#379	—	73	16	no	—
157	C₂×#379	—	73	1	no	—
158	C₂×#379	—	73	6	no	—
159	C₂×#379	D₇₃	1	1	yes	characteristic, direct product factor
160	C₇₃	C₂²×#379	1	1	yes	characteristic, complemented, Sylow
161	C₂⁶	—	73	3	no	—
162	C₂⁶	—	73	16	no	—
163	C₂⁶	—	73	8	no	—
164	C₂⁶	—	73	3	no	—
165	C₂⁶	—	146	48	no	—
166	C₂⁶	C₂×D₇₃	1	1	yes	characteristic
167	C₂⁴×C₄	—	73	4	no	—
168	C₂²×C₂²⋊C₄	—	73	6	no	—
169	C₂²×C₂²⋊C₄	—	73	12	no	—
170	C₂²×C₂²⋊C₄	—	73	48	no	—
171	C₂²×C₂²⋊C₄	—	146	48	no	—
172	C₂²×C₂²⋊C₄	C₂×D₇₃	1	6	yes	complemented
173	#379	—	73	8	no	—
174	#379	—	73	48	no	—
175	#379	C₂×D₇₃	1	8	yes	direct product factor
176	C₂⁵	—	2	24	no	—
177	C₂⁵	—	73	1	no	—
178	C₂⁵	—	73	24	no	—
179	C₂⁵	—	73	48	no	—
180	C₂⁵	—	73	12	no	—
181	C₂⁵	—	73	3	no	—
182	C₂⁵	—	73	24	no	—
183	C₂⁵	—	73	64	no	—
184	C₂⁵	—	73	12	no	—
185	C₂⁵	—	146	384	no	—
186	C₂⁵	—	146	48	no	—
187	C₂⁵	—	146	192	no	—
188	C₂⁵	—	146	48	no	—
189	C₂⁵	—	146	512	no	—
190	C₂⁵	—	146	24	no	—
191	C₂⁵	C₄×D₇₃	1	8	yes	complemented
192	C₂⁵	C₂²×D₇₃	1	4	yes	—
193	C₂⁵	C₂²×D₇₃	1	3	yes	—
194	C₂³×C₄	—	73	4	no	—
195	C₂³×C₄	—	73	16	no	—
196	C₂³×C₄	—	146	48	no	—
197	C₂³×C₄	C₂²×D₇₃	1	4	yes	complemented
198	C₂×C₂²⋊C₄	—	2	24	no	—
199	C₂×C₂²⋊C₄	—	73	24	no	—
200	C₂×C₂²⋊C₄	—	73	48	no	—
201	C₂×C₂²⋊C₄	—	146	192	no	—
202	C₂×C₂²⋊C₄	—	146	48	no	—
203	C₂×C₂²⋊C₄	—	146	24	no	—
204	C₂×C₂²⋊C₄	C₂²×D₇₃	1	24	yes	complemented
205	C₂⁴	—	2	128	no	—
206	C₂⁴	—	2	96	no	—
207	C₂⁴	—	2	48	no	—
208	C₂⁴	—	2	24	no	—
209	C₂⁴	—	73	4	no	—
210	C₂⁴	—	73	24	no	—
211	C₂⁴	—	73	2	no	—
212	C₂⁴	—	73	192	no	—
213	C₂⁴	—	73	48	no	—
214	C₂⁴	—	73	12	no	—
215	C₂⁴	—	73	96	no	—
216	C₂⁴	—	73	24	no	—
217	C₂⁴	—	73	6	no	—
218	C₂⁴	—	73	48	no	—
219	C₂⁴	—	146	96	no	—
220	C₂⁴	—	146	96	no	—
221	C₂⁴	—	146	192	no	—
222	C₂⁴	—	146	192	no	—
223	C₂⁴	—	146	768	no	—
224	C₂⁴	—	146	384	no	—
225	C₂⁴	—	146	2048	no	—
226	C₂⁴	—	146	1024	no	—
227	C₂⁴	—	146	384	no	—
228	C₂⁴	—	146	96	no	—
229	C₂⁴	—	146	48	no	—
230	C₂⁴	—	146	24	no	—
231	C₂⁴	C₂×C₄×D₇₃	1	12	yes	—
232	C₂⁴	C₂×C₄×D₇₃	1	16	yes	complemented
233	C₂⁴	D₄×D₇₃	1	24	yes	—
234	C₂⁴	C₂³×D₇₃	1	6	yes	—
235	C₂⁴	C₂³×D₇₃	1	1	yes	characteristic
236	C₂²×C₄	—	2	24	no	—
237	C₂²×C₄	—	292	64	no	—
238	C₂²×C₄	—	73	8	no	—
239	C₂²×C₄	—	146	96	no	—
240	C₂²×C₄	—	146	24	no	—
241	C₂²×C₄	C₂³×D₇₃	1	8	yes	complemented
242	C₂²⋊C₄	—	2	48	no	—
243	C₂²⋊C₄	—	146	96	no	—
244	C₂²⋊C₄	—	146	48	no	—
245	C₂³	—	2	256	no	—
246	C₂³	—	2	128	no	—
247	C₂³	—	2	24	no	—
248	C₂³	—	2	48	no	—
249	C₂³	—	2	96	no	—
250	C₂³	—	2	96	no	—
251	C₂³	—	73	4	no	—
252	C₂³	—	73	24	no	—
253	C₂³	—	73	48	no	—
254	C₂³	—	73	64	no	—
255	C₂³	—	73	12	no	—
256	C₂³	—	73	24	no	—
257	C₂³	—	73	48	no	—
258	C₂³	—	73	192	no	—
259	C₂³	—	146	768	no	—
260	C₂³	—	146	192	no	—
261	C₂³	—	146	192	no	—
262	C₂³	—	146	384	no	—
263	C₂³	—	146	2048	no	—
264	C₂³	—	146	768	no	—
265	C₂³	—	146	384	no	—
266	C₂³	—	146	24	no	—
267	C₂³	—	146	48	no	—
268	C₂³	—	146	96	no	—
269	C₂³	—	146	96	no	—
270	C₂³	C₂²⋊C₄×D₇₃	1	48	yes	complemented
271	C₂³	C₂²×C₄×D₇₃	1	12	yes	—
272	C₂³	C₂²×C₄×D₇₃	1	2	yes	—
273	C₂³	C₂×D₄×D₇₃	1	24	yes	—
274	C₂³	C₂×D₄×D₇₃	1	12	yes	—
275	C₂³	C₂⁴×D₇₃	1	1	yes	characteristic
276	C₂×C₄	—	2	24	no	—
277	C₂×C₄	—	4	16	no	—
278	C₂×C₄	—	292	64	no	—
279	C₂×C₄	—	292	16	no	—
280	C₂×C₄	—	146	24	no	—
281	C₂²	—	2	128	no	—
282	C₂²	—	2	96	no	—
283	C₂²	—	2	24	no	—
284	C₂²	—	2	48	no	—
285	C₂²	—	73	64	no	—
286	C₂²	—	73	24	no	—
287	C₂²	—	73	32	no	—
288	C₂²	—	73	24	no	—
289	C₂²	—	146	384	no	—
290	C₂²	—	146	384	no	—
291	C₂²	—	146	96	no	—
292	C₂²	—	146	24	no	—
293	C₂²	—	146	48	no	—
294	C₂²	C₂×C₂²⋊C₄×D₇₃	1	12	yes	—
295	C₂²	C₂×C₂²⋊C₄×D₇₃	1	24	yes	complemented
296	C₂²	#120×D₇₃	1	16	yes	—
297	C₂²	C₂³×C₄×D₇₃	1	1	yes	characteristic
298	C₂²	C₂²×D₄×D₇₃	1	6	yes	—
299	C₄	—	4	8	no	—
300	C₄	—	292	8	no	—
301	C₂	—	2	24	no	—
302	C₂	—	73	16	no	—
303	C₂	—	146	24	no	—
304	C₂	#379×D₇₃	1	8	yes	direct product factor
305	C₂	C₂²×C₂²⋊C₄×D₇₃	1	3	yes	—
306	C₂	C₂×#120×D₇₃	1	4	yes	—

	subgroup	G/H
center	C₂⁴	C₂³×D₇₃
commutator	C₂²×C₇₃	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₇₃
Fitting	C₂×#379×C₇₃	C₂
socle	C₂⁴×C₇₃	C₂⁴
prime radical	C₂⁶×D₇₃	C₂
cosocle	C₂³×C₇₃	C₂⁵
hypercenter	C₂×#379	D₇₃
hypocenter	C₇₃	C₂²×#379
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂⁴ ◁ C₂×#379

Complements

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

N	H ≅ G/N	type
2. C₂²×C₂²⋊C₄×D₇₃	C₂	semidirect
3. C₂×#17988443	C₂	semidirect
4. C₂×#17988442	C₂	semidirect
5. #379×D₇₃	C₂	direct (N × H)
6. C₂×#379×C₇₃	C₂	semidirect
8. C₂⁵×D₇₃	C₄	semidirect
12. C₂³×C₄×D₇₃	C₂²	semidirect
13. C₂²×C₂²⋊Dic₇₃	C₂²	semidirect
14. C₂²×#11924005	C₂²	semidirect
16. C₂×C₂²⋊C₄×D₇₃	C₂²	semidirect
17. #17988443	C₂²	semidirect
18. #17988442	C₂²	semidirect
20. C₂²×C₂²⋊C₄×C₇₃	C₂²	semidirect
21. #379×C₇₃	C₂²	semidirect
29. C₂⁴×D₇₃	C₂×C₄	semidirect
30. C₂⁴×D₇₃	C₂×C₄	semidirect
36. C₂³×Dic₇₃	C₂³	semidirect
38. C₂²×C₄×D₇₃	C₂³	semidirect
40. C₂×C₂²⋊Dic₇₃	C₂³	semidirect
42. C₂×#11924005	C₂³	semidirect
45. C₂⁵×C₇₃	C₂×C₄	semidirect
48. C₂³×C₄×C₇₃	C₂³	semidirect
50. C₂×C₂²⋊C₄×C₇₃	C₂³	semidirect
63. C₂³×D₇₃	C₂²⋊C₄	semidirect
67. C₂³×D₇₃	C₂²×C₄	semidirect
74. C₂²×Dic₇₃	C₂⁴	semidirect
84. C₂⁴×C₇₃	C₂²×C₄	semidirect
89. C₂²×C₄×C₇₃	C₂⁴	semidirect
97. C₂³×C₇₃	C₂×C₂²⋊C₄	semidirect
115. C₂²×D₇₃	C₂×C₂²⋊C₄	semidirect
116. C₂²×D₇₃	C₂×C₂²⋊C₄	semidirect
132. C₂²×C₇₃	C₂²×C₂²⋊C₄	semidirect
141. C₂×D₇₃	#379	direct (N × H)
143. C₂×D₇₃	C₂²×C₂²⋊C₄	semidirect
149. C₂×C₇₃	C₂×#379	semidirect
153. D₇₃	C₂×#379	direct (N × H)
159. C₂×#379	D₇₃	direct (N × H)
160. C₇₃	C₂²×#379	semidirect
172. C₂²×C₂²⋊C₄	C₂×D₇₃	semidirect
175. #379	C₂×D₇₃	direct (N × H)
191. C₂⁵	C₄×D₇₃	semidirect
197. C₂³×C₄	C₂²×D₇₃	semidirect
204. C₂×C₂²⋊C₄	C₂²×D₇₃	semidirect
232. C₂⁴	C₂×C₄×D₇₃	semidirect
241. C₂²×C₄	C₂³×D₇₃	semidirect
270. C₂³	C₂²⋊C₄×D₇₃	semidirect
295. C₂²	C₂×C₂²⋊C₄×D₇₃	semidirect
304. C₂	#379×D₇₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁶×D₇₃	2
C₂²×C₂²⋊C₄×D₇₃	2
C₂×#17988443	2
C₂×#17988442	2
#379×D₇₃	2
C₂×#379×C₇₃	2
C₂²×#379	73

Subgroups — C2×#379×D73 #33244237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#379×D₇₃ #33244237