Subgroups — D₇₃⋊#2161 #34030102

Order 18688.

642 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₇₃⋊#108	C₂	1	2	yes	maximal
2	#22626287	C₂	1	8	yes	maximal, complemented
3	D₇₃⋊#368	C₂	1	4	yes	maximal, complemented
4	C₂×M₃₂×D₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂×D₇₃⋊M₁₆	—	2	2	no	—
6	C₂×#14556662	C₂²	1	4	yes	—
7	D₇₃⋊#108	—	2	2	no	—
8	D₇₃⋊#108	—	2	2	no	—
9	D₇₃⋊#108	C₂²	1	4	yes	—
10	D₇₃⋊#108	C₂²	1	4	yes	—
11	C₂×#14556661	—	2	2	no	—
12	#17989516	C₂²	1	8	yes	complemented
13	#17989515	C₂²	1	8	yes	complemented
14	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
15	C₂×#14556531	C₄	1	1	yes	characteristic
16	C₂×#14556530	C₄	1	2	yes	—
17	M₃₂×D₇₃	C₄	1	4	yes	—
18	M₃₂×D₇₃	C₂²	1	4	yes	—
19	C₂×C₁₆×D₇₃	C₂²	1	2	yes	—
20	C₂×M₃₂×C₇₃	C₄	1	1	yes	characteristic
21	C₂×#11924038	—	2	4	no	—
22	D₇₃⋊M₁₆	—	2	4	no	—
23	D₇₃⋊M₁₆	—	2	4	no	—
24	D₇₃⋊M₁₆	—	4	2	no	—
25	D₇₃⋊M₁₆	—	4	2	no	—
26	C₂×#11924037	—	4	2	no	—
27	C₂×#11924036	—	4	2	no	—
28	#14556662	—	2	4	no	—
29	#14556662	C₂³	1	8	yes	—
30	#14556661	—	2	4	no	—
31	#14556661	—	2	4	no	—
32	C₂²×C₄×D₇₃	D₄	1	1	yes	characteristic
33	C₂²×#10596831	Q₈	1	1	yes	characteristic
34	C₂×C₈×D₇₃	C₂×C₄	1	2	yes	—
35	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
36	C₂×C₈×D₇₃	D₄	1	2	yes	—
37	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
38	C₂×C₈×D₇₃	Q₈	1	2	yes	—
39	C₂×C₈×D₇₃	Q₈	1	1	yes	characteristic
40	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
41	C₂×C₈×D₇₃	C₂³	1	2	yes	—
42	#14556531	C₂×C₄	1	4	yes	—
43	#14556530	C₂×C₄	1	8	yes	—
44	C₂×#11924003	C₂×C₄	1	2	yes	—
45	C₁₆×D₇₃	C₂×C₄	1	4	yes	—
46	C₁₆×D₇₃	C₂³	1	4	yes	—
47	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
48	M₃₂×C₇₃	C₂×C₄	1	4	yes	—
49	C₂×C₁₆×C₇₃	C₂×C₄	1	2	yes	—
50	#11924038	—	2	8	no	—
51	#11924038	—	4	4	no	—
52	#11924037	—	4	4	no	—
53	#11924037	—	4	4	no	—
54	#11924036	—	4	4	no	—
55	#11924036	—	4	4	no	—
56	C₂×#10596833	—	4	4	no	—
57	C₂³×D₇₃	Q₁₆	1	1	yes	characteristic
58	C₂²×Dic₇₃	D₈	1	1	yes	characteristic
59	C₂×C₄×D₇₃	C₄⋊C₄	1	2	yes	—
60	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
61	C₂×C₄×D₇₃	D₈	1	2	yes	—
62	C₂×C₄×D₇₃	D₈	1	1	yes	characteristic
63	C₂×C₄×D₇₃	Q₁₆	1	1	yes	characteristic
64	C₂×C₄×D₇₃	Q₁₆	1	2	yes	—
65	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
66	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
67	C₂×#10596831	C₄⋊C₄	1	2	yes	—
68	C₂×#10596831	C₄⋊C₄	1	1	yes	characteristic
69	C₂×#10596831	C₂×Q₈	1	1	yes	characteristic
70	C₂×#10596831	C₂×Q₈	1	2	yes	—
71	C₈×D₇₃	C₄⋊C₄	1	2	yes	—
72	C₈×D₇₃	C₄⋊C₄	1	2	yes	—
73	C₈×D₇₃	C₄⋊C₄	1	2	yes	—
74	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
75	C₈×D₇₃	C₂²×C₄	1	2	yes	—
76	C₈×D₇₃	C₂×D₄	1	1	yes	characteristic
77	C₈×D₇₃	C₂×D₄	1	2	yes	—
78	C₈×D₇₃	C₂×Q₈	1	1	yes	characteristic
79	C₈×D₇₃	C₂×Q₈	1	2	yes	—
80	C₈×D₇₃	C₂⁴	1	1	yes	characteristic
81	#11924003	C₂²×C₄	1	4	yes	—
82	C₂²×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
83	C₂×C₈×C₇₃	C₄⋊C₄	1	2	yes	—
84	C₂×C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
85	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
86	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
87	C₁₆×C₇₃	C₂²×C₄	1	4	yes	—
88	C₂³×C₇₃	#107	1	1	yes	characteristic
89	C₂²×D₇₃	—	4	2	no	—
90	C₂²×D₇₃	#107	1	2	yes	—
91	C₂²×D₇₃	#107	1	1	yes	characteristic
92	C₂²×D₇₃	C₂×Q₁₆	1	1	yes	characteristic
93	C₂²×D₇₃	C₂×Q₁₆	1	2	yes	—
94	C₂×C₄×C₇₃	#107	1	1	yes	characteristic
95	C₂×C₄×C₇₃	#107	1	2	yes	—
96	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
97	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
98	C₂×Dic₇₃	#107	1	1	yes	characteristic
99	C₂×Dic₇₃	#107	1	2	yes	—
100	C₂×Dic₇₃	C₂×D₈	1	2	yes	—
101	C₂×Dic₇₃	C₂×D₈	1	1	yes	characteristic
102	C₄×D₇₃	#107	1	2	yes	—
103	C₄×D₇₃	#107	1	2	yes	—
104	C₄×D₇₃	#107	1	2	yes	—
105	C₄×D₇₃	C₂×C₄⋊C₄	1	2	yes	—
106	C₄×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
107	C₄×D₇₃	C₂×D₈	1	1	yes	characteristic
108	C₄×D₇₃	C₂×D₈	1	2	yes	—
109	C₄×D₇₃	C₂×Q₁₆	1	2	yes	—
110	C₄×D₇₃	C₂×Q₁₆	1	1	yes	characteristic
111	C₄×D₇₃	C₂²×D₄	1	1	yes	characteristic
112	#10596833	—	4	8	no	—
113	C₈×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
114	C₈×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
115	C₈×C₇₃	C₂³×C₄	1	1	yes	characteristic
116	#10596831	C₂×C₄⋊C₄	1	1	yes	characteristic
117	#10596831	C₂×C₄⋊C₄	1	2	yes	—
118	#10596831	C₂²×Q₈	1	1	yes	characteristic
119	C₂²×C₇₃	—	4	1	no	—
120	C₂²×C₇₃	C₂×#107	1	2	yes	—
121	C₂²×C₇₃	C₂×#107	1	1	yes	characteristic
122	C₂×D₇₃	—	2	4	no	—
123	C₂×D₇₃	—	2	2	no	—
124	C₂×D₇₃	—	4	1	no	—
125	C₂×D₇₃	—	4	2	no	—
126	C₂×D₇₃	C₂×#107	1	2	yes	—
127	C₂×D₇₃	C₂×#107	1	1	yes	characteristic
128	C₂×D₇₃	C₂²×Q₁₆	1	1	yes	characteristic
129	C₄×C₇₃	C₂×#107	1	2	yes	—
130	C₄×C₇₃	C₂×#107	1	1	yes	characteristic
131	C₄×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
132	Dic₇₃	C₂×#107	1	2	yes	—
133	Dic₇₃	C₂×#107	1	1	yes	characteristic
134	Dic₇₃	C₂²×D₈	1	1	yes	characteristic
135	C₂×#2161	—	73	1	no	maximal, Sylow
136	C₂×C₇₃	—	2	2	no	—
137	C₂×C₇₃	—	2	1	no	—
138	C₂×C₇₃	C₂²×#107	1	1	yes	characteristic
139	D₇₃	—	2	1	no	—
140	D₇₃	—	2	2	no	—
141	D₇₃	#2161	1	2	yes	complemented
142	C₂²×M₃₂	—	73	1	no	—
143	C₂²×#108	—	73	2	no	—
144	#2161	—	73	8	no	—
145	C₂×#368	—	73	4	no	—
146	C₇₃	C₂×#2161	1	1	yes	characteristic, complemented, Sylow
147	C₂²×M₁₆	—	146	2	no	—
148	C₂³×C₈	—	73	1	no	—
149	C₂×M₃₂	—	73	1	no	—
150	C₂×M₃₂	—	73	4	no	—
151	C₂×M₃₂	—	73	4	no	—
152	C₂×M₃₂	—	73	2	no	—
153	C₂×M₃₂	#64408	1	1	yes	characteristic
154	C₂²×C₁₆	—	73	2	no	—
155	C₂×#108	—	73	4	no	—
156	C₂×#108	—	73	4	no	—
157	C₂×#108	—	73	4	no	—
158	C₂×#108	—	146	2	no	—
159	C₂×#108	—	146	2	no	—
160	C₂×#108	—	146	2	no	—
161	#368	—	73	8	no	—
162	#368	—	73	8	no	—
163	C₂³×C₄	—	73	1	no	—
164	C₂×M₁₆	—	292	2	no	—
165	C₂×M₁₆	—	292	2	no	—
166	C₂×M₁₆	—	292	2	no	—
167	C₂×M₁₆	—	146	4	no	—
168	C₂×M₁₆	—	146	4	no	—
169	C₂×M₁₆	—	146	4	no	—
170	C₂²×C₈	—	292	2	no	—
171	C₂²×C₈	—	73	1	no	—
172	C₂²×C₈	—	73	2	no	—
173	C₂²×C₈	—	73	1	no	—
174	C₂²×C₈	—	73	2	no	—
175	C₂²×C₈	—	73	1	no	—
176	C₂²×C₈	—	73	1	no	—
177	C₂²×C₈	—	73	2	no	—
178	C₂²×C₈	—	73	2	no	—
179	C₂²×C₈	—	73	1	no	—
180	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
181	M₃₂	—	73	4	no	—
182	M₃₂	—	73	8	no	—
183	M₃₂	C₂×#64408	1	4	yes	—
184	C₂×C₁₆	—	73	2	no	—
185	C₂×C₁₆	—	73	4	no	—
186	C₂×C₁₆	—	73	4	no	—
187	C₂×C₁₆	C₂×#64408	1	2	yes	—
188	#108	—	73	8	no	—
189	#108	—	146	4	no	—
190	#108	—	146	4	no	—
191	#108	—	146	4	no	—
192	C₂⁴	—	73	1	no	—
193	C₂²×C₄	—	73	1	no	—
194	C₂²×C₄	—	73	2	no	—
195	C₂²×C₄	—	73	1	no	—
196	C₂²×C₄	—	73	1	no	—
197	C₂²×C₄	—	73	2	no	—
198	C₂²×C₄	—	73	2	no	—
199	C₂²×C₄	—	73	1	no	—
200	C₂²×C₄	—	73	2	no	—
201	C₂²×C₄	—	73	1	no	—
202	C₂²×C₄	C₄⋊#64408	1	1	yes	characteristic
203	M₁₆	—	292	4	no	—
204	M₁₆	—	292	4	no	—
205	M₁₆	—	292	4	no	—
206	M₁₆	—	146	8	no	—
207	C₂×C₈	—	292	4	no	—
208	C₂×C₈	—	292	4	no	—
209	C₂×C₈	—	292	4	no	—
210	C₂×C₈	—	73	2	no	—
211	C₂×C₈	—	73	1	no	—
212	C₂×C₈	—	73	2	no	—
213	C₂×C₈	—	73	1	no	—
214	C₂×C₈	—	73	1	no	—
215	C₂×C₈	—	73	2	no	—
216	C₂×C₈	—	73	1	no	—
217	C₂×C₈	—	73	2	no	—
218	C₂×C₈	—	73	2	no	—
219	C₂×C₈	—	73	2	no	—
220	C₂×C₈	—	73	1	no	—
221	C₂×C₈	—	73	2	no	—
222	C₂×C₈	—	73	1	no	—
223	C₂×C₈	—	73	2	no	—
224	C₂×C₈	C₄⋊#64408	1	2	yes	—
225	C₂×C₈	C₄⋊#64408	1	1	yes	characteristic
226	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
227	C₂×C₈	C₂²×#64408	1	2	yes	—
228	C₁₆	—	73	4	no	—
229	C₁₆	C₂²×#64408	1	4	yes	—
230	C₂³	—	292	2	no	—
231	C₂³	—	73	1	no	—
232	C₂³	—	73	2	no	—
233	C₂³	—	73	2	no	—
234	C₂³	—	73	1	no	—
235	C₂³	#14556660	1	1	yes	characteristic
236	C₂×C₄	—	73	2	no	—
237	C₂×C₄	—	73	1	no	—
238	C₂×C₄	—	73	1	no	—
239	C₂×C₄	—	73	2	no	—
240	C₂×C₄	—	73	1	no	—
241	C₂×C₄	—	73	1	no	—
242	C₂×C₄	—	73	2	no	—
243	C₂×C₄	—	73	2	no	—
244	C₂×C₄	—	73	2	no	—
245	C₂×C₄	—	73	2	no	—
246	C₂×C₄	—	73	2	no	—
247	C₂×C₄	—	73	1	no	—
248	C₂×C₄	—	73	2	no	—
249	C₂×C₄	—	73	1	no	—
250	C₂×C₄	#14556660	1	1	yes	characteristic
251	C₂×C₄	#14556660	1	2	yes	—
252	C₂×C₄	C₂×C₄⋊#64408	1	2	yes	—
253	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
254	C₈	—	292	8	no	—
255	C₈	—	73	1	no	—
256	C₈	—	73	2	no	—
257	C₈	—	73	1	no	—
258	C₈	C₂×C₄⋊#64408	1	1	yes	characteristic
259	C₈	C₂×C₄⋊#64408	1	2	yes	—
260	C₈	C₂³×#64408	1	1	yes	characteristic
261	C₂²	—	4	1	no	—
262	C₂²	—	292	1	no	—
263	C₂²	—	292	2	no	—
264	C₂²	—	73	1	no	—
265	C₂²	—	73	1	no	—
266	C₂²	—	73	2	no	—
267	C₂²	—	146	4	no	—
268	C₂²	—	146	2	no	—
269	C₂²	C₂×#14556660	1	2	yes	—
270	C₂²	C₂×#14556660	1	1	yes	characteristic
271	C₄	—	73	1	no	—
272	C₄	—	73	2	no	—
273	C₄	—	73	1	no	—
274	C₄	C₂×#14556660	1	2	yes	—
275	C₄	C₂×#14556660	1	1	yes	characteristic
276	C₄	C₂²×C₄⋊#64408	1	1	yes	characteristic
277	C₂	—	2	1	no	—
278	C₂	—	2	2	no	—
279	C₂	—	73	2	no	—
280	C₂	—	146	1	no	—
281	C₂	—	146	2	no	—
282	C₂	C₂²×#14556660	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#14556660
commutator	C₈×C₇₃	C₂³×C₄
Frattini	C₈	C₂³×#64408
Fitting	C₂×M₃₂×C₇₃	C₄
socle	C₂×C₇₃	C₂²×#107
prime radical	C₂³×D₇₃	Q₁₆
cosocle	C₈×D₇₃	C₂⁴
hypercenter	C₂×M₃₂	#64408
hypocenter	C₇₃	C₂×#2161
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
2. #22626287	C₂	semidirect
3. D₇₃⋊#368	C₂	semidirect
12. #17989516	C₂²	semidirect
13. #17989515	C₂²	semidirect
141. D₇₃	#2161	semidirect
146. C₇₃	C₂×#2161	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₇₃⋊#108	2
#22626287	2
D₇₃⋊#368	2
C₂×M₃₂×D₇₃	2
C₂×#2161	73

Subgroups — D73⋊#2161 #34030102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇₃⋊#2161 #34030102