Subgroups — C₂×#22610065 #33086181

Order 18688.

1054 conjugacy classes of subgroups.

The subgroup lattice has 242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988457	C₂	1	1	yes	maximal, characteristic
2	C₂×#17988453	C₂	1	1	yes	maximal, characteristic
3	#22610065	C₂	1	8	yes	maximal, direct product factor
4	C₂×#17988350	C₂	1	4	yes	maximal
5	C₂²×#97×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄⋊Dic₇₃	—	2	2	no	—
7	C₂²×C₄⋊Dic₇₃	C₂²	1	2	yes	—
8	C₂²×C₄⋊Dic₇₃	C₂²	1	2	yes	—
9	#17988457	—	2	2	no	—
10	#17988457	C₂²	1	4	yes	—
11	#17988453	—	2	2	no	—
12	#17988453	C₂²	1	4	yes	—
13	C₂×#14556498	—	2	2	no	—
14	#17988350	C₂²	1	16	yes	—
15	C₂³×C₈×C₇₃	C₂²	1	2	yes	—
16	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×#97×C₇₃	C₄	1	8	yes	complemented
18	C₂×#97×C₇₃	C₂²	1	4	yes	—
19	C₂³×Dic₇₃	—	2	2	no	—
20	C₂³×Dic₇₃	—	2	2	no	—
21	C₂×C₄⋊Dic₇₃	—	2	2	no	—
22	C₂×C₄⋊Dic₇₃	—	2	2	no	—
23	C₂×C₄⋊Dic₇₃	—	2	8	no	—
24	C₂×C₄⋊Dic₇₃	—	2	8	no	—
25	C₂×C₄⋊Dic₇₃	—	2	8	no	—
26	C₂×C₄⋊Dic₇₃	—	4	8	no	—
27	C₂×C₄⋊Dic₇₃	C₂³	1	4	yes	—
28	C₂×C₄⋊Dic₇₃	C₂³	1	4	yes	—
29	#14556498	—	2	8	no	—
30	C₂³×C₄×C₇₃	D₄	1	2	yes	—
31	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
32	C₂²×C₈×C₇₃	—	2	4	no	—
33	C₂²×C₈×C₇₃	—	2	4	no	—
34	C₂²×C₈×C₇₃	C₂×C₄	1	8	yes	—
35	C₂²×C₈×C₇₃	C₂³	1	4	yes	—
36	C₂×C₄²×C₇₃	C₂×C₄	1	4	yes	—
37	C₂×C₄²×C₇₃	D₄	1	2	yes	—
38	C₂×C₄²×C₇₃	Q₈	1	4	yes	—
39	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
40	#97×C₇₃	C₂×C₄	1	16	yes	complemented
41	C₂²×Dic₇₃	—	2	4	no	—
42	C₂²×Dic₇₃	—	2	4	no	—
43	C₂²×Dic₇₃	—	4	4	no	—
44	C₂²×Dic₇₃	—	4	4	no	—
45	C₂²×Dic₇₃	—	4	8	no	—
46	C₂²×Dic₇₃	—	4	4	no	—
47	C₂²×Dic₇₃	—	4	4	no	—
48	C₄⋊Dic₇₃	—	2	8	no	—
49	C₄⋊Dic₇₃	—	2	8	no	—
50	C₄⋊Dic₇₃	—	4	16	no	—
51	C₄⋊Dic₇₃	—	4	4	no	—
52	C₄⋊Dic₇₃	—	4	4	no	—
53	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₇₃	—	2	4	no	—
55	C₂²×C₄×C₇₃	—	2	4	no	—
56	C₂²×C₄×C₇₃	C₄⋊C₄	1	8	yes	—
57	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
58	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
59	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₇₃	C₂×Q₈	1	2	yes	—
61	C₂²×C₄×C₇₃	#41	1	4	yes	—
62	C₂²×C₄×C₇₃	#41	1	4	yes	—
63	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
64	C₂×C₈×C₇₃	—	2	16	no	—
65	C₂×C₈×C₇₃	—	2	4	no	—
66	C₂×C₈×C₇₃	—	2	4	no	—
67	C₂×C₈×C₇₃	C₂²×C₄	1	8	yes	—
68	C₄²×C₇₃	C₄⋊C₄	1	8	yes	—
69	C₄²×C₇₃	C₂²×C₄	1	4	yes	—
70	C₄²×C₇₃	C₂×Q₈	1	4	yes	—
71	C₂³×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
72	C₂³×C₇₃	#124	1	2	yes	—
73	C₂³×C₇₃	#124	1	2	yes	—
74	C₂³×C₇₃	AGL(1,ℤ/8)	1	4	yes	—
75	C₂³×C₇₃	#137	1	4	yes	—
76	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
77	C₂×C₄×C₇₃	—	2	4	no	—
78	C₂×C₄×C₇₃	—	2	4	no	—
79	C₂×C₄×C₇₃	—	2	16	no	—
80	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	8	yes	—
81	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
82	C₂×C₄×C₇₃	#117	1	8	yes	—
83	C₂×C₄×C₇₃	#124	1	2	yes	—
84	C₂×C₄×C₇₃	#124	1	2	yes	—
85	C₂×C₄×C₇₃	#125	1	8	yes	—
86	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
87	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
88	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
89	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
90	C₂×Dic₇₃	—	4	4	no	—
91	C₂×Dic₇₃	—	4	4	no	—
92	C₂×Dic₇₃	—	4	8	no	—
93	C₂×Dic₇₃	—	4	4	no	—
94	C₂×Dic₇₃	—	4	4	no	—
95	C₂×Dic₇₃	—	8	8	no	—
96	C₂×Dic₇₃	—	8	8	no	—
97	C₈×C₇₃	—	2	8	no	—
98	C₂²×C₇₃	#382	1	4	yes	—
99	C₂²×C₇₃	#428	1	8	yes	—
100	C₂²×C₇₃	#489	1	8	yes	—
101	C₂²×C₇₃	#490	1	4	yes	—
102	C₂²×C₇₃	#491	1	4	yes	—
103	C₂²×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
104	C₂²×C₇₃	C₂×#124	1	1	yes	characteristic
105	C₂²×C₇₃	C₂×#124	1	1	yes	characteristic
106	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
107	C₂²×C₇₃	C₂×#137	1	2	yes	—
108	C₄×C₇₃	—	2	8	no	—
109	C₄×C₇₃	#382	1	4	yes	—
110	C₄×C₇₃	C₂×#117	1	2	yes	—
111	C₄×C₇₃	C₂×#125	1	2	yes	—
112	Dic₇₃	—	8	4	no	—
113	Dic₇₃	—	8	4	no	—
114	C₂×#1836	—	73	1	no	maximal, Sylow
115	C₂×C₇₃	#1836	1	8	yes	complemented
116	C₂×C₇₃	C₂×#382	1	1	yes	characteristic
117	C₂×C₇₃	C₂×#428	1	2	yes	—
118	C₂×C₇₃	C₂×#489	1	2	yes	—
119	C₂×C₇₃	C₂×#490	1	1	yes	characteristic
120	C₂×C₇₃	C₂×#491	1	1	yes	characteristic
121	C₂²×#97	D₇₃	1	1	yes	characteristic
122	C₂×#384	—	73	1	no	—
123	C₂×#382	—	73	1	no	—
124	#1836	—	73	8	no	—
125	C₂×#340	—	73	4	no	—
126	C₇₃	C₂×#1836	1	1	yes	characteristic, complemented, Sylow
127	C₂³×C₈	C₂×D₇₃	1	2	yes	—
128	C₂²×C₄⋊C₄	—	73	2	no	—
129	C₂²×C₄⋊C₄	—	73	2	no	—
130	C₂²×C₄⋊C₄	—	146	2	no	—
131	C₂²×C₄²	C₂×D₇₃	1	1	yes	characteristic
132	C₂×#97	Dic₇₃	1	8	yes	complemented
133	C₂×#97	C₂×D₇₃	1	4	yes	—
134	#384	—	73	4	no	—
135	#384	—	146	2	no	—
136	#382	—	73	4	no	—
137	#382	—	146	2	no	—
138	C₂×#95	—	146	2	no	—
139	#340	—	73	16	no	—
140	C₂³×C₄	—	146	2	no	—
141	C₂³×C₄	—	146	2	no	—
142	C₂³×C₄	D₂₉₂	1	2	yes	—
143	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
144	C₂²×C₈	—	2	4	no	—
145	C₂²×C₈	—	2	4	no	—
146	C₂²×C₈	C₂×Dic₇₃	1	8	yes	—
147	C₂²×C₈	C₂²×D₇₃	1	4	yes	—
148	C₂×C₄⋊C₄	—	292	8	no	—
149	C₂×C₄⋊C₄	—	73	4	no	—
150	C₂×C₄⋊C₄	—	73	4	no	—
151	C₂×C₄⋊C₄	—	146	2	no	—
152	C₂×C₄⋊C₄	—	146	2	no	—
153	C₂×C₄⋊C₄	—	146	8	no	—
154	C₂×C₄⋊C₄	—	146	8	no	—
155	C₂×C₄⋊C₄	—	146	8	no	—
156	C₂×C₄²	Dic₁₄₆	1	4	yes	—
157	C₂×C₄²	D₂₉₂	1	2	yes	—
158	C₂×C₄²	C₂×Dic₇₃	1	4	yes	—
159	C₂×C₄²	C₂²×D₇₃	1	2	yes	—
160	#97	C₂×Dic₇₃	1	16	yes	complemented
161	#95	—	146	8	no	—
162	C₂⁴	C₂×D₂₉₂	1	1	yes	characteristic
163	C₂²×C₄	—	2	4	no	—
164	C₂²×C₄	—	2	4	no	—
165	C₂²×C₄	—	292	4	no	—
166	C₂²×C₄	—	292	4	no	—
167	C₂²×C₄	—	292	8	no	—
168	C₂²×C₄	—	292	4	no	—
169	C₂²×C₄	—	292	4	no	—
170	C₂²×C₄	—	146	4	no	—
171	C₂²×C₄	—	146	4	no	—
172	C₂²×C₄	C₄⋊Dic₇₃	1	8	yes	—
173	C₂²×C₄	C₂²×Dic₇₃	1	2	yes	—
174	C₂²×C₄	C₂×D₂₉₂	1	4	yes	—
175	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
176	C₂²×C₄	C₂×Dic₁₄₆	1	2	yes	—
177	C₂²×C₄	#11924028	1	4	yes	—
178	C₂²×C₄	#11924028	1	4	yes	—
179	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
180	C₂×C₈	—	2	16	no	—
181	C₂×C₈	—	2	4	no	—
182	C₂×C₈	—	2	4	no	—
183	C₂×C₈	C₂²×Dic₇₃	1	8	yes	—
184	C₄⋊C₄	—	292	16	no	—
185	C₄⋊C₄	—	292	4	no	—
186	C₄⋊C₄	—	292	4	no	—
187	C₄⋊C₄	—	146	8	no	—
188	C₄⋊C₄	—	146	8	no	—
189	C₄²	C₄⋊Dic₇₃	1	8	yes	—
190	C₄²	C₂²×Dic₇₃	1	4	yes	—
191	C₄²	C₂×Dic₁₄₆	1	4	yes	—
192	C₂³	C₂×C₄⋊Dic₇₃	1	2	yes	—
193	C₂³	#14556579	1	2	yes	—
194	C₂³	#14556579	1	2	yes	—
195	C₂³	#14556619	1	4	yes	—
196	C₂³	#14556624	1	4	yes	—
197	C₂³	C₂²×D₂₉₂	1	1	yes	characteristic
198	C₂×C₄	—	2	4	no	—
199	C₂×C₄	—	2	4	no	—
200	C₂×C₄	—	2	16	no	—
201	C₂×C₄	—	292	8	no	—
202	C₂×C₄	—	292	4	no	—
203	C₂×C₄	—	292	4	no	—
204	C₂×C₄	—	292	4	no	—
205	C₂×C₄	—	292	4	no	—
206	C₂×C₄	—	584	8	no	—
207	C₂×C₄	—	584	8	no	—
208	C₂×C₄	C₂×C₄⋊Dic₇₃	1	8	yes	—
209	C₂×C₄	C₂×C₄⋊Dic₇₃	1	2	yes	—
210	C₂×C₄	#14556550	1	8	yes	—
211	C₂×C₄	#14556579	1	2	yes	—
212	C₂×C₄	#14556579	1	2	yes	—
213	C₂×C₄	#14556583	1	8	yes	—
214	C₂×C₄	C₂³×Dic₇₃	1	1	yes	characteristic
215	C₂×C₄	C₂²×Dic₁₄₆	1	1	yes	characteristic
216	C₂×C₄	C₂×#11924028	1	2	yes	—
217	C₂×C₄	C₂×#11924028	1	2	yes	—
218	C₈	—	2	8	no	—
219	C₂²	#17988453	1	4	yes	—
220	C₂²	#17988629	1	8	yes	—
221	C₂²	#17988947	1	8	yes	—
222	C₂²	#17988952	1	4	yes	—
223	C₂²	#17988956	1	4	yes	—
224	C₂²	C₂²×C₄⋊Dic₇₃	1	1	yes	characteristic
225	C₂²	C₂×#14556579	1	1	yes	characteristic
226	C₂²	C₂×#14556579	1	1	yes	characteristic
227	C₂²	C₂×#14556619	1	2	yes	—
228	C₂²	C₂×#14556624	1	2	yes	—
229	C₄	—	2	8	no	—
230	C₄	—	584	4	no	—
231	C₄	—	584	4	no	—
232	C₄	#17988453	1	4	yes	—
233	C₄	C₂×#14556550	1	2	yes	—
234	C₄	C₂×#14556583	1	2	yes	—
235	C₂	#22610065	1	8	yes	direct product factor
236	C₂	C₂×#17988453	1	1	yes	characteristic
237	C₂	C₂×#17988629	1	2	yes	—
238	C₂	C₂×#17988947	1	2	yes	—
239	C₂	C₂×#17988952	1	1	yes	characteristic
240	C₂	C₂×#17988956	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₂₉₂
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₃
Fitting	C₂²×#97×C₇₃	C₂
socle, prime radical	C₂⁴×C₇₃	C₂×D₄
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	C₂²×#97	D₇₃
hypocenter	C₇₃	C₂×#1836
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂²×#97

Complements

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

N	H ≅ G/N	type
3. #22610065	C₂	direct (N × H)
17. C₂×#97×C₇₃	C₄	semidirect
40. #97×C₇₃	C₂×C₄	semidirect
115. C₂×C₇₃	#1836	semidirect
126. C₇₃	C₂×#1836	semidirect
132. C₂×#97	Dic₇₃	semidirect
160. #97	C₂×Dic₇₃	semidirect
235. C₂	#22610065	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×#17988457	2
C₂×#17988453	2
#22610065	2
C₂×#17988350	2
C₂²×#97×C₇₃	2
C₂×#1836	73

Subgroups — C2×#22610065 #33086181

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22610065 #33086181