Subgroups — C₄×#17988407 #33001303

Order 18688.

398 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988407	C₂	1	2	yes	maximal
2	C₄×#14556531	C₂	1	1	yes	maximal, characteristic
3	C₄×C₈×Dic₇₃	C₂	1	1	yes	maximal, characteristic
4	#22608012	C₂	1	2	yes	maximal
5	C₄×M₃₂×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#14556531	C₂²	1	2	yes	—
7	C₂×C₄×#10596831	C₄	1	1	yes	characteristic
8	C₂×C₈×Dic₇₃	C₄	1	1	yes	characteristic
9	C₂×C₈×Dic₇₃	C₄	1	1	yes	characteristic
10	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
11	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
12	C₄²×Dic₇₃	C₄	1	1	yes	characteristic
13	#17988407	C₄	1	8	yes	direct product factor
14	#17988363	—	2	1	no	—
15	C₄×#11924003	—	2	1	no	—
16	C₂×M₃₂×C₇₃	C₂²	1	2	yes	—
17	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
18	#346×C₇₃	—	2	1	no	—
19	C₄×C₁₆×C₇₃	—	2	1	no	—
20	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
21	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×Dic₇₃	—	2	2	no	—
23	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
25	#14556531	—	2	2	no	—
26	#14556531	C₂×C₄	1	4	yes	—
27	C₂×#11924003	—	2	2	no	—
28	C₄×#10596831	C₈	1	4	yes	—
29	C₈×Dic₇₃	—	2	2	no	—
30	C₈×Dic₇₃	—	2	2	no	—
31	C₈×Dic₇₃	C₈	1	4	yes	—
32	C₈×Dic₇₃	C₂×C₄	1	4	yes	—
33	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
35	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
36	M₃₂×C₇₃	—	2	2	no	—
37	M₃₂×C₇₃	C₂×C₄	1	4	yes	—
38	C₂×C₁₆×C₇₃	—	2	2	no	—
39	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
40	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
41	C₄×C₈×C₇₃	Q₈	1	1	yes	characteristic
42	C₄×C₈×C₇₃	Q₈	1	1	yes	characteristic
43	C₂²×Dic₇₃	—	2	1	no	—
44	C₂²×Dic₇₃	—	2	1	no	—
45	C₂×#10596831	—	2	1	no	—
46	C₂×#10596831	—	2	1	no	—
47	C₂×#10596831	C₄²	1	2	yes	—
48	C₂×#10596831	C₂×C₈	1	2	yes	—
49	C₂×#10596831	C₂×C₈	1	2	yes	—
50	C₂×#10596831	C₂×C₈	1	2	yes	—
51	C₄×Dic₇₃	—	2	8	no	—
52	C₄×Dic₇₃	—	2	1	no	—
53	C₄×Dic₇₃	—	2	1	no	—
54	C₄×Dic₇₃	C₄²	1	2	yes	—
55	C₄×Dic₇₃	C₂×C₈	1	2	yes	—
56	#11924003	—	2	4	no	—
57	C₂²×C₄×C₇₃	M₁₆	1	2	yes	—
58	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
59	C₂×C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
60	C₂×C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
61	C₂×C₈×C₇₃	C₂×C₈	1	2	yes	—
62	C₂×C₈×C₇₃	M₁₆	1	2	yes	—
63	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
64	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
65	C₂×C₈×C₇₃	C₂×Q₈	1	1	yes	characteristic
66	C₂×C₈×C₇₃	#41	1	2	yes	—
67	C₄²×C₇₃	C₄⋊C₄	1	1	yes	characteristic
68	C₄²×C₇₃	C₄⋊C₄	1	1	yes	characteristic
69	C₄²×C₇₃	C₂×C₈	1	2	yes	—
70	C₁₆×C₇₃	—	2	4	no	—
71	C₂³×C₇₃	C₂×M₁₆	1	1	yes	characteristic
72	C₂×C₄×C₇₃	—	2	4	no	—
73	C₂×C₄×C₇₃	C₄⋊C₈	1	2	yes	—
74	C₂×C₄×C₇₃	C₄⋊C₈	1	2	yes	—
75	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
76	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
77	C₂×C₄×C₇₃	#117	1	1	yes	characteristic
78	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
79	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
80	C₂×C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
81	C₂×Dic₇₃	—	2	4	no	—
82	C₂×Dic₇₃	—	2	4	no	—
83	C₂×Dic₇₃	—	2	2	no	—
84	C₂×Dic₇₃	—	2	2	no	—
85	C₈×C₇₃	C₄⋊C₈	1	2	yes	—
86	C₈×C₇₃	C₄⋊C₈	1	2	yes	—
87	C₈×C₇₃	C₄×D₄	1	2	yes	—
88	C₈×C₇₃	C₄×Q₈	1	2	yes	—
89	#10596831	—	2	2	no	—
90	#10596831	C₄×C₈	1	4	yes	—
91	C₂²×C₇₃	—	2	2	no	—
92	C₂²×C₇₃	C₄×M₁₆	1	1	yes	characteristic
93	C₂²×C₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
94	C₂²×C₇₃	#431	1	1	yes	characteristic
95	C₄×C₇₃	—	2	2	no	—
96	C₄×C₇₃	#364	1	4	yes	complemented
97	C₄×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
98	C₄×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
99	C₄×C₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
100	C₄×C₇₃	#431	1	1	yes	characteristic
101	Dic₇₃	—	2	4	no	—
102	Dic₇₃	—	2	4	no	—
103	C₄×#364	—	73	1	no	maximal, Sylow
104	C₂×C₇₃	—	2	1	no	—
105	C₂×C₇₃	—	2	1	no	—
106	C₂×C₇₃	C₄×C₄⋊C₈	1	1	yes	characteristic
107	C₂×C₇₃	C₂×#364	1	2	yes	—
108	C₂×#364	—	73	2	no	—
109	C₄×M₃₂	—	73	1	no	—
110	C₄×M₃₂	D₇₃	1	1	yes	characteristic
111	C₄²×C₈	—	73	1	no	—
112	#1376	—	73	2	no	—
113	C₇₃	C₄×#364	1	1	yes	characteristic, complemented, Sylow
114	C₂×M₃₂	—	73	2	no	—
115	C₂×M₃₂	C₂×D₇₃	1	2	yes	—
116	C₂×C₄×C₈	—	73	1	no	—
117	C₂×C₄×C₈	—	73	1	no	—
118	C₂×C₄×C₈	—	73	1	no	—
119	C₂×C₄×C₈	—	73	1	no	—
120	C₂×C₄×C₈	—	73	1	no	—
121	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
122	C₄³	—	73	1	no	—
123	#364	—	73	8	no	—
124	#346	—	2	1	no	—
125	#346	—	146	1	no	—
126	C₄×C₁₆	—	2	1	no	—
127	C₄×C₁₆	—	146	1	no	—
128	C₂²×C₈	—	73	1	no	—
129	C₂²×C₈	—	73	1	no	—
130	C₂²×C₈	C₄×D₇₃	1	1	yes	characteristic
131	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
132	C₂×C₄²	—	73	1	no	—
133	C₂×C₄²	—	73	1	no	—
134	C₂×C₄²	—	146	2	no	—
135	C₂×C₄²	C₄×D₇₃	1	1	yes	characteristic
136	M₃₂	—	2	2	no	—
137	M₃₂	—	73	4	no	—
138	M₃₂	—	146	2	no	—
139	M₃₂	C₄×D₇₃	1	4	yes	—
140	C₂×C₁₆	—	2	2	no	—
141	C₂×C₁₆	—	146	2	no	—
142	C₄×C₈	—	73	4	no	—
143	C₄×C₈	—	73	4	no	—
144	C₄×C₈	—	73	4	no	—
145	C₄×C₈	—	146	2	no	—
146	C₄×C₈	—	146	2	no	—
147	C₄×C₈	Dic₁₄₆	1	1	yes	characteristic
148	C₄×C₈	Dic₁₄₆	1	1	yes	characteristic
149	C₄×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
150	C₄×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
151	C₂²×C₄	—	146	1	no	—
152	C₂²×C₄	—	146	1	no	—
153	C₂²×C₄	#11924011	1	2	yes	—
154	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
155	C₂×C₈	—	73	2	no	—
156	C₂×C₈	—	73	2	no	—
157	C₂×C₈	—	73	2	no	—
158	C₂×C₈	—	73	2	no	—
159	C₂×C₈	—	146	1	no	—
160	C₂×C₈	—	146	1	no	—
161	C₂×C₈	#11924007	1	1	yes	characteristic
162	C₂×C₈	#11924007	1	1	yes	characteristic
163	C₂×C₈	C₈×D₇₃	1	2	yes	—
164	C₂×C₈	#11924011	1	2	yes	—
165	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
166	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
167	C₂×C₈	C₂×Dic₁₄₆	1	1	yes	characteristic
168	C₂×C₈	#11924028	1	2	yes	—
169	C₄²	—	73	2	no	—
170	C₄²	—	73	2	no	—
171	C₄²	—	146	8	no	—
172	C₄²	—	146	1	no	—
173	C₄²	—	146	1	no	—
174	C₄²	#11924007	1	1	yes	characteristic
175	C₄²	#11924007	1	1	yes	characteristic
176	C₄²	C₈×D₇₃	1	2	yes	—
177	C₁₆	—	2	4	no	—
178	C₁₆	—	146	4	no	—
179	C₂³	C₂×#11924011	1	1	yes	characteristic
180	C₂×C₄	—	2	4	no	—
181	C₂×C₄	—	146	4	no	—
182	C₂×C₄	—	146	4	no	—
183	C₂×C₄	—	146	2	no	—
184	C₂×C₄	—	146	2	no	—
185	C₂×C₄	#14556520	1	2	yes	—
186	C₂×C₄	#14556520	1	2	yes	—
187	C₂×C₄	C₄²×D₇₃	1	1	yes	characteristic
188	C₂×C₄	C₂×#11924007	1	1	yes	characteristic
189	C₂×C₄	#14556548	1	1	yes	characteristic
190	C₂×C₄	C₂×C₈×D₇₃	1	1	yes	characteristic
191	C₂×C₄	C₂×C₈×D₇₃	1	1	yes	characteristic
192	C₂×C₄	C₂×#11924011	1	1	yes	characteristic
193	C₈	—	73	4	no	—
194	C₈	—	146	2	no	—
195	C₈	#14556520	1	2	yes	—
196	C₈	#14556520	1	2	yes	—
197	C₈	C₄×C₂²⋊D₇₃	1	2	yes	—
198	C₈	C₄×Dic₁₄₆	1	2	yes	—
199	C₂²	—	2	2	no	—
200	C₂²	C₄×#11924011	1	1	yes	characteristic
201	C₂²	C₂×#14556520	1	1	yes	characteristic
202	C₂²	#17988638	1	1	yes	characteristic
203	C₄	—	2	2	no	—
204	C₄	—	146	4	no	—
205	C₄	—	146	4	no	—
206	C₄	#17988407	1	4	yes	direct product factor
207	C₄	C₄×#11924007	1	1	yes	characteristic
208	C₄	C₄×C₈×D₇₃	1	1	yes	characteristic
209	C₄	C₂×#14556520	1	1	yes	characteristic
210	C₄	#17988638	1	1	yes	characteristic
211	C₂	—	2	1	no	—
212	C₂	—	2	1	no	—
213	C₂	C₄×#14556520	1	1	yes	characteristic
214	C₂	C₂×#17988407	1	2	yes	—

	subgroup	G/H
center	C₄×C₈	C₂²⋊D₇₃
commutator	C₄×C₇₃	C₂×C₄×C₈
Frattini	C₂²×C₈	C₂²×D₇₃
Fitting	C₄×M₃₂×C₇₃	C₂
socle	C₂²×C₇₃	C₂×C₄⋊C₈
prime radical	C₂³×C₇₃	C₂×M₁₆
cosocle	C₂²×C₈×C₇₃	C₂³
hypercenter	C₄×M₃₂	D₇₃
hypocenter	C₇₃	C₄×#364
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄×C₈ ◁ C₂×C₄×C₈ ◁ C₄×M₃₂

Complements

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

N	H ≅ G/N	type
13. #17988407	C₄	direct (N × H)
96. C₄×C₇₃	#364	semidirect
113. C₇₃	C₄×#364	semidirect
206. C₄	#17988407	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×#17988407	2
C₄×#14556531	2
C₄×C₈×Dic₇₃	2
#22608012	2
C₄×M₃₂×C₇₃	2
C₄×#364	73

Subgroups — C4×#17988407 #33001303

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#17988407 #33001303