Subgroups — #22618673

Order 9344.

492 conjugacy classes of subgroups.

The subgroup lattice has 286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14556599	C₂	1	1	yes	maximal, characteristic, complemented
2	#17989133	C₂	1	1	yes	maximal, characteristic
3	#17988663	C₂	1	2	yes	maximal, complemented
4	#17988658	C₂	1	2	yes	maximal, complemented
5	#17988656	C₂	1	2	yes	maximal, complemented
6	C₈×C₂²⋊D₇₃	C₂	1	2	yes	maximal, complemented
7	C₂×#14556520	C₂	1	1	yes	maximal, characteristic, complemented
8	#17988554	C₂	1	1	yes	maximal, characteristic, complemented
9	#17988553	C₂	1	1	yes	maximal, characteristic, complemented
10	M₁₆×Dic₇₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#131×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#11924028	C₂²	1	1	yes	characteristic
13	#14556599	—	2	4	no	—
14	C₂×#11924012	C₂²	1	1	yes	characteristic
15	C₂×#11924011	C₂²	1	2	yes	—
16	C₂²×#10596831	C₂²	1	1	yes	characteristic
17	C₂×C₈×D₇₃	C₂²	1	2	yes	—
18	#14556589	C₄	1	1	yes	characteristic
19	#14556587	C₄	1	1	yes	characteristic
20	#14556580	C₄	1	1	yes	characteristic
21	#14556578	C₄	1	1	yes	characteristic
22	#14556563	C₄	1	2	yes	—
23	#14556563	C₄	1	2	yes	—
24	C₄×C₂²⋊D₇₃	C₂²	1	2	yes	—
25	C₄×C₂²⋊D₇₃	C₂²	1	2	yes	—
26	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
27	#14556520	C₂²	1	1	yes	characteristic
28	#14556520	C₂²	1	1	yes	characteristic
29	#14556520	C₂²	1	1	yes	characteristic
30	#14556520	C₂²	1	1	yes	characteristic
31	C₂²⋊#10596831	C₂²	1	2	yes	—
32	C₂²⋊#10596831	C₂²	1	2	yes	—
33	#14556503	C₂²	1	2	yes	—
34	#14556503	C₂²	1	2	yes	—
35	#14556501	C₂²	1	2	yes	—
36	C₈×Dic₇₃	C₂²	1	2	yes	—
37	C₂×#41×C₇₃	C₂²	1	1	yes	characteristic
38	#131×C₇₃	—	2	4	no	—
39	C₂×M₁₆×C₇₃	C₂²	1	2	yes	—
40	C₂×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
41	C₂²×C₈×C₇₃	C₂²	1	2	yes	—
42	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
43	#11924028	—	2	2	no	—
44	#11924028	—	2	2	no	—
45	C₂×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
46	C₂×D₂₉₂	C₂×C₄	1	1	yes	characteristic
47	C₂×C₂²⋊D₇₃	C₂×C₄	1	2	yes	—
48	C₂×C₂²⋊D₇₃	C₂×C₄	1	2	yes	—
49	C₂×C₂²⋊D₇₃	C₂×C₄	1	2	yes	—
50	C₂²×Dic₇₃	C₂×C₄	1	1	yes	characteristic
51	C₂²×Dic₇₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄×D₇₃	C₂³	1	2	yes	—
53	#11924012	—	2	2	no	—
54	#11924011	—	2	4	no	—
55	C₂×#10596831	—	2	2	no	—
56	C₂×#10596831	C₂³	1	2	yes	—
57	C₂×#10596831	C₂³	1	1	yes	characteristic
58	C₂×#10596831	C₂³	1	1	yes	characteristic
59	C₈×D₇₃	—	2	4	no	—
60	#11924007	C₂×C₄	1	2	yes	—
61	#11924007	C₂×C₄	1	2	yes	—
62	C₂²⋊Dic₇₃	C₂×C₄	1	2	yes	—
63	C₂²⋊Dic₇₃	C₂×C₄	1	2	yes	—
64	#11924005	C₂×C₄	1	2	yes	—
65	#11924005	C₂×C₄	1	2	yes	—
66	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
67	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
68	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
69	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
70	#41×C₇₃	—	2	2	no	—
71	#41×C₇₃	—	2	2	no	—
72	C₂×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
73	C₂×D₄×C₇₃	C₂×C₄	1	2	yes	—
74	C₂×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₇₃	C₂³	1	2	yes	—
76	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
77	M₁₆×C₇₃	—	2	4	no	—
78	M₁₆×C₇₃	D₄	1	4	yes	complemented
79	C₂×C₈×C₇₃	—	2	2	no	—
80	C₂×C₈×C₇₃	—	2	4	no	—
81	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
82	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
83	C₂×C₈×C₇₃	C₂³	1	2	yes	—
84	C₂³×C₇₃	C₂²×C₄	1	2	yes	—
85	C₂³×C₇₃	C₂²×C₄	1	1	yes	characteristic
86	C₂²×D₇₃	C₂²×C₄	1	2	yes	—
87	Q₈×C₇₃	—	2	2	no	—
88	D₄×C₇₃	—	2	4	no	—
89	D₄×C₇₃	—	2	2	no	—
90	C₂×C₄×C₇₃	—	2	2	no	—
91	C₂×C₄×C₇₃	—	2	2	no	—
92	C₂×C₄×C₇₃	C₂²×C₄	1	2	yes	—
93	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
95	C₂×C₄×C₇₃	#41	1	2	yes	—
96	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
97	C₂²⋊D₇₃	—	2	4	no	—
98	C₂²⋊D₇₃	—	2	4	no	—
99	C₂²⋊D₇₃	—	4	2	no	—
100	C₂×Dic₇₃	—	2	2	no	—
101	C₂×Dic₇₃	—	4	1	no	—
102	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
103	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
104	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
105	C₂×Dic₇₃	C₂²×C₄	1	2	yes	—
106	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
107	D₂₉₂	—	2	2	no	—
108	C₄×D₇₃	—	2	2	no	—
109	C₄×D₇₃	—	2	2	no	—
110	Dic₁₄₆	—	2	2	no	—
111	C₈×C₇₃	—	2	1	no	—
112	C₈×C₇₃	—	2	1	no	—
113	C₈×C₇₃	C₂×D₄	1	4	yes	—
114	#10596831	—	2	1	no	—
115	#10596831	—	2	1	no	—
116	#10596831	—	2	2	no	—
117	C₂²×C₇₃	—	2	1	no	—
118	C₂²×C₇₃	—	2	1	no	—
119	C₂²×C₇₃	—	2	2	no	—
120	C₂²×C₇₃	—	2	2	no	—
121	C₂²×C₇₃	—	2	2	no	—
122	C₂²×C₇₃	C₄×D₄	1	2	yes	—
123	C₂²×C₇₃	C₂³×C₄	1	1	yes	characteristic
124	C₂×D₇₃	—	2	2	no	—
125	C₂×D₇₃	—	2	2	no	—
126	C₂×D₇₃	—	2	2	no	—
127	C₄×C₇₃	—	2	2	no	—
128	C₄×C₇₃	C₄×D₄	1	2	yes	—
129	C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
130	C₄×C₇₃	C₂×#41	1	1	yes	characteristic
131	Dic₇₃	—	2	2	no	—
132	Dic₇₃	—	2	1	no	—
133	Dic₇₃	—	2	1	no	—
134	Dic₇₃	—	2	1	no	—
135	Dic₇₃	#131	1	2	yes	complemented
136	C₂×C₇₃	—	2	2	no	—
137	C₂×C₇₃	—	4	2	no	—
138	C₂×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
139	C₂×C₇₃	C₂×#131	1	1	yes	characteristic
140	C₂×C₇₃	#568	1	1	yes	characteristic
141	D₇₃	—	4	2	no	—
142	#2935	—	73	1	no	maximal, Sylow
143	C₇₃	#2935	1	1	yes	characteristic, complemented, Sylow
144	C₂×#131	—	73	1	no	—
145	C₂×#131	D₇₃	1	1	yes	characteristic, complemented
146	#532	—	73	1	no	—
147	#436	—	73	2	no	—
148	#435	—	73	2	no	—
149	#435	—	73	2	no	—
150	C₈×D₄	—	73	2	no	—
151	C₂×C₄⋊C₈	—	73	1	no	—
152	#408	—	73	1	no	—
153	#408	—	73	1	no	—
154	C₄×M₁₆	—	73	1	no	—
155	C₂×#41	—	73	1	no	—
156	C₂×#41	C₂×D₇₃	1	1	yes	characteristic
157	#131	—	2	4	no	—
158	#131	—	146	4	no	—
159	C₂×M₁₆	—	73	1	no	—
160	C₂×M₁₆	—	73	2	no	—
161	C₂×M₁₆	C₂×D₇₃	1	2	yes	—
162	C₂×M₁₆	C₂×D₇₃	1	1	yes	characteristic
163	C₂²×C₈	—	73	1	no	—
164	C₂²×C₈	—	73	2	no	—
165	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
166	C₂²×C₈	C₂×D₇₃	1	2	yes	—
167	C₄⋊Q₈	—	73	1	no	—
168	#127	—	73	1	no	—
169	#124	—	73	1	no	—
170	#124	—	73	1	no	—
171	#121	—	73	2	no	—
172	#121	—	73	2	no	—
173	C₄×D₄	—	73	2	no	—
174	C₄×D₄	—	73	2	no	—
175	C₂×C₄²	—	73	1	no	—
176	C₄⋊C₈	—	73	1	no	—
177	C₄⋊C₈	—	73	1	no	—
178	C₄⋊C₈	—	73	1	no	—
179	C₄⋊C₈	—	73	1	no	—
180	C₂²⋊C₈	—	73	2	no	—
181	C₂²⋊C₈	—	73	2	no	—
182	C₂²⋊C₈	—	73	2	no	—
183	C₂²⋊C₈	—	73	2	no	—
184	#97	—	73	2	no	—
185	C₄×C₈	—	73	2	no	—
186	#41	—	2	2	no	—
187	#41	—	2	2	no	—
188	#41	—	146	2	no	—
189	#41	—	146	2	no	—
190	C₂×Q₈	—	73	1	no	—
191	C₂×Q₈	C₄×D₇₃	1	1	yes	characteristic
192	C₂×D₄	—	73	2	no	—
193	C₂×D₄	—	73	2	no	—
194	C₂×D₄	—	73	2	no	—
195	C₂×D₄	—	73	1	no	—
196	C₂×D₄	C₄×D₇₃	1	2	yes	—
197	C₂×D₄	C₄×D₇₃	1	1	yes	characteristic
198	C₂²×C₄	—	73	1	no	—
199	C₂²×C₄	—	73	1	no	—
200	C₂²×C₄	—	73	2	no	—
201	C₂²×C₄	C₂²×D₇₃	1	2	yes	—
202	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
203	M₁₆	—	2	4	no	—
204	M₁₆	—	146	2	no	—
205	M₁₆	—	146	4	no	—
206	M₁₆	C₂²⋊D₇₃	1	4	yes	complemented
207	C₂×C₈	—	2	2	no	—
208	C₂×C₈	—	2	4	no	—
209	C₂×C₈	—	73	2	no	—
210	C₂×C₈	—	73	1	no	—
211	C₂×C₈	—	73	1	no	—
212	C₂×C₈	—	146	2	no	—
213	C₂×C₈	—	146	4	no	—
214	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
215	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
216	C₂×C₈	C₂²×D₇₃	1	2	yes	—
217	C₄⋊C₄	—	73	2	no	—
218	C₄⋊C₄	—	73	2	no	—
219	C₂²⋊C₄	—	73	2	no	—
220	C₂²⋊C₄	—	73	2	no	—
221	C₂²⋊C₄	—	73	2	no	—
222	C₂²⋊C₄	—	73	2	no	—
223	C₄²	—	73	1	no	—
224	C₄²	—	73	1	no	—
225	C₄²	—	73	1	no	—
226	C₄²	—	73	1	no	—
227	C₂³	—	73	2	no	—
228	C₂³	C₂×C₄×D₇₃	1	2	yes	—
229	C₂³	C₂×C₄×D₇₃	1	1	yes	characteristic
230	Q₈	—	2	2	no	—
231	Q₈	—	146	2	no	—
232	D₄	—	2	4	no	—
233	D₄	—	2	2	no	—
234	D₄	—	292	2	no	—
235	D₄	—	146	4	no	—
236	D₄	—	146	4	no	—
237	D₄	—	146	2	no	—
238	C₂×C₄	—	2	2	no	—
239	C₂×C₄	—	2	2	no	—
240	C₂×C₄	—	292	1	no	—
241	C₂×C₄	—	73	1	no	—
242	C₂×C₄	—	73	1	no	—
243	C₂×C₄	—	73	1	no	—
244	C₂×C₄	—	73	1	no	—
245	C₂×C₄	—	73	2	no	—
246	C₂×C₄	—	146	2	no	—
247	C₂×C₄	—	146	2	no	—
248	C₂×C₄	—	146	2	no	—
249	C₂×C₄	C₂×C₄×D₇₃	1	2	yes	—
250	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
251	C₂×C₄	C₂×C₂²⋊D₇₃	1	2	yes	—
252	C₂×C₄	#11924028	1	2	yes	—
253	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
254	C₈	—	2	1	no	—
255	C₈	—	2	1	no	—
256	C₈	—	146	1	no	—
257	C₈	—	146	1	no	—
258	C₈	—	146	2	no	—
259	C₈	C₂×C₂²⋊D₇₃	1	4	yes	—
260	C₂²	—	2	1	no	—
261	C₂²	—	2	1	no	—
262	C₂²	—	2	2	no	—
263	C₂²	—	2	2	no	—
264	C₂²	—	2	2	no	—
265	C₂²	—	146	2	no	—
266	C₂²	—	146	2	no	—
267	C₂²	—	146	2	no	—
268	C₂²	C₄×C₂²⋊D₇₃	1	2	yes	—
269	C₂²	C₂²×C₄×D₇₃	1	1	yes	characteristic
270	C₄	—	2	2	no	—
271	C₄	—	73	2	no	—
272	C₄	—	146	2	no	—
273	C₄	—	146	1	no	—
274	C₄	—	146	1	no	—
275	C₄	—	146	1	no	—
276	C₄	C₄×C₂²⋊D₇₃	1	2	yes	—
277	C₄	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
278	C₄	C₂×#11924028	1	1	yes	characteristic
279	C₂	—	2	2	no	—
280	C₂	—	4	2	no	—
281	C₂	—	292	2	no	—
282	C₂	C₂×C₄×C₂²⋊D₇₃	1	1	yes	characteristic
283	C₂	#131×D₇₃	1	1	yes	characteristic
284	C₂	#17989352	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₇₃
commutator, socle	C₂²×C₇₃	C₂³×C₄
Fitting	C₂×#131×C₇₃	C₂
hypercenter	C₂×#131	D₇₃
hypocenter	C₇₃	#2935
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#131

Complements

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

N	H ≅ G/N	type
1. C₂×#14556599	C₂	semidirect
3. #17988663	C₂	semidirect
4. #17988658	C₂	semidirect
5. #17988656	C₂	semidirect
6. C₈×C₂²⋊D₇₃	C₂	semidirect
7. C₂×#14556520	C₂	semidirect
8. #17988554	C₂	semidirect
9. #17988553	C₂	semidirect
10. M₁₆×Dic₇₃	C₂	semidirect
11. C₂×#131×C₇₃	C₂	semidirect
78. M₁₆×C₇₃	D₄	semidirect
135. Dic₇₃	#131	semidirect
143. C₇₃	#2935	semidirect
145. C₂×#131	D₇₃	semidirect
206. M₁₆	C₂²⋊D₇₃	semidirect