Subgroups — C₄×#17988967 #33094421

Order 18688.

1086 conjugacy classes of subgroups.

The subgroup lattice has 244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988967	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₂₉₂	C₂	1	4	yes	maximal
3	C₄×#14556591	C₂	1	2	yes	maximal
4	#22610792	C₂	1	4	yes	maximal
5	#22610733	C₂	1	2	yes	maximal
6	#22610091	C₂	1	1	yes	maximal, characteristic
7	C₄²×C₈×C₇₃	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₂₉₂	C₂²	1	4	yes	—
9	C₂×#14556591	C₂²	1	2	yes	—
10	C₂×C₄×Dic₁₄₆	C₂²	1	4	yes	—
11	#17988967	C₄	1	8	yes	direct product factor
12	C₄×Dic₂₉₂	—	2	16	no	—
13	C₂×#14556525	C₂²	1	4	yes	—
14	C₂×#14556516	C₂²	1	8	yes	—
15	#17988493	C₂²	1	4	yes	—
16	#17988485	—	2	4	no	—
17	#17988457	C₂²	1	2	yes	—
18	C₄×C₄⋊Dic₇₃	—	2	4	no	—
19	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₈×C₇₃	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₇₃	C₂²	1	2	yes	—
23	C₄³×C₇₃	C₂²	1	1	yes	characteristic
24	C₂²×Dic₁₄₆	C₂³	1	4	yes	—
25	C₂×Dic₂₉₂	—	2	8	no	—
26	C₂×Dic₂₉₂	—	2	8	no	—
27	C₂×Dic₂₉₂	C₂×C₄	1	16	yes	—
28	#14556591	—	2	4	no	—
29	#14556591	C₂×C₄	1	8	yes	—
30	C₄×Dic₁₄₆	—	2	16	no	—
31	C₂×C₄⋊Dic₇₃	—	2	4	no	—
32	C₂×C₄⋊Dic₇₃	—	2	4	no	—
33	C₂×C₄⋊Dic₇₃	C₂³	1	4	yes	—
34	C₂×#11924007	—	2	4	no	—
35	C₂×C₄×Dic₇₃	—	2	4	no	—
36	#14556525	—	2	8	no	—
37	#14556516	—	2	16	no	—
38	#14556498	—	2	8	no	—
39	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
40	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
41	C₂×C₄²×C₇₃	D₄	1	2	yes	—
42	C₂×C₄²×C₇₃	D₄	1	2	yes	—
43	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
44	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
45	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
46	C₄×C₈×C₇₃	—	2	4	no	—
47	C₄×C₈×C₇₃	—	2	2	no	—
48	C₄×C₈×C₇₃	C₂×C₄	1	4	yes	—
49	C₄×C₈×C₇₃	D₄	1	8	yes	—
50	C₂×Dic₁₄₆	—	2	8	no	—
51	C₂×Dic₁₄₆	—	2	8	no	—
52	C₂×Dic₁₄₆	—	2	4	no	—
53	C₂×Dic₁₄₆	C₂²×C₄	1	8	yes	—
54	C₂²×Dic₇₃	—	2	4	no	—
55	C₂²×Dic₇₃	—	2	4	no	—
56	Dic₂₉₂	—	2	32	no	—
57	C₄⋊Dic₇₃	—	2	16	no	—
58	C₄⋊Dic₇₃	—	2	8	no	—
59	C₄⋊Dic₇₃	—	4	8	no	—
60	#11924007	—	4	8	no	—
61	C₄×Dic₇₃	—	4	8	no	—
62	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
64	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
65	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
67	C₂×C₈×C₇₃	—	2	2	no	—
68	C₂×C₈×C₇₃	—	2	2	no	—
69	C₂×C₈×C₇₃	C₂²×C₄	1	4	yes	—
70	C₂×C₈×C₇₃	C₂×D₄	1	4	yes	—
71	C₂×C₈×C₇₃	C₂×D₄	1	4	yes	—
72	C₂×C₈×C₇₃	#41	1	4	yes	—
73	C₄²×C₇₃	—	2	4	no	—
74	C₄²×C₇₃	—	2	2	no	—
75	C₄²×C₇₃	Q₁₆	1	8	yes	complemented
76	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
77	C₄²×C₇₃	C₂×D₄	1	4	yes	—
78	C₄²×C₇₃	#41	1	2	yes	—
79	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
80	C₂×C₄×C₇₃	—	2	2	no	—
81	C₂×C₄×C₇₃	—	2	2	no	—
82	C₂×C₄×C₇₃	—	2	2	no	—
83	C₂×C₄×C₇₃	C₄×D₄	1	4	yes	—
84	C₂×C₄×C₇₃	#127	1	2	yes	—
85	C₂×C₄×C₇₃	#127	1	2	yes	—
86	C₂×C₄×C₇₃	C₂×Q₁₆	1	4	yes	—
87	C₂×C₄×C₇₃	C₂×Q₁₆	1	4	yes	—
88	C₂×C₄×C₇₃	C₂×Q₁₆	1	4	yes	—
89	C₂×C₄×C₇₃	#135	1	4	yes	—
90	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
91	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
92	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
93	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
94	C₂×Dic₇₃	—	2	8	no	—
95	C₂×Dic₇₃	—	4	4	no	—
96	C₂×Dic₇₃	—	4	4	no	—
97	C₂×Dic₇₃	—	4	4	no	—
98	C₂×Dic₇₃	—	4	8	no	—
99	Dic₁₄₆	—	2	16	no	—
100	Dic₁₄₆	—	4	8	no	—
101	C₈×C₇₃	—	2	4	no	—
102	C₈×C₇₃	C₄×D₄	1	8	yes	—
103	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
104	C₂²×C₇₃	C₂×#127	1	1	yes	characteristic
105	C₂²×C₇₃	#532	1	1	yes	characteristic
106	C₂²×C₇₃	C₂²×Q₁₆	1	2	yes	—
107	C₂²×C₇₃	C₂×#135	1	2	yes	—
108	C₄×C₇₃	—	2	2	no	—
109	C₄×C₇₃	—	2	4	no	—
110	C₄×C₇₃	C₄×Q₁₆	1	8	yes	complemented
111	C₄×C₇₃	#494	1	4	yes	complemented
112	C₄×C₇₃	C₂×C₄×D₄	1	2	yes	—
113	C₄×C₇₃	#532	1	2	yes	—
114	Dic₇₃	—	4	8	no	—
115	Dic₇₃	—	8	4	no	—
116	C₄×#494	—	73	1	no	maximal, Sylow
117	C₂×C₇₃	C₄×#127	1	1	yes	characteristic
118	C₂×C₇₃	C₂×C₄×Q₁₆	1	2	yes	—
119	C₂×C₇₃	C₂×#494	1	1	yes	characteristic
120	C₂×C₇₃	#3147	1	1	yes	characteristic
121	C₂×C₇₃	#3170	1	2	yes	—
122	C₂×#494	—	73	1	no	—
123	C₂×C₄×Q₁₆	—	73	4	no	—
124	C₄×C₄⋊Q₈	—	73	2	no	—
125	#1969	—	73	4	no	—
126	#1956	—	73	2	no	—
127	#1845	—	73	1	no	—
128	C₄²×C₈	D₇₃	1	1	yes	characteristic
129	C₇₃	C₄×#494	1	1	yes	characteristic, complemented, Sylow
130	C₂²×Q₁₆	—	73	4	no	—
131	C₂×C₄⋊Q₈	—	73	2	no	—
132	C₂×C₄×Q₈	—	73	4	no	—
133	#494	—	73	8	no	—
134	C₄×Q₁₆	—	146	16	no	—
135	C₂×#107	—	73	4	no	—
136	C₂×#103	—	73	8	no	—
137	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
138	C₂×C₄×C₈	C₂×D₇₃	1	2	yes	—
139	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
140	C₂×C₄×C₈	C₂×D₇₃	1	2	yes	—
141	#391	—	73	4	no	—
142	#389	—	146	4	no	—
143	#384	—	73	2	no	—
144	C₄×C₄⋊C₄	—	146	4	no	—
145	C₄³	C₂×D₇₃	1	1	yes	characteristic
146	C₂²×Q₈	—	73	4	no	—
147	C₂×Q₁₆	—	73	16	no	—
148	C₂×Q₁₆	—	146	8	no	—
149	C₂×Q₁₆	—	146	8	no	—
150	C₂²×C₈	C₂²×D₇₃	1	2	yes	—
151	C₂²×C₈	C₂²×D₇₃	1	2	yes	—
152	C₄⋊Q₈	—	73	8	no	—
153	C₄⋊Q₈	—	146	4	no	—
154	C₄×Q₈	—	146	16	no	—
155	C₂×C₄⋊C₄	—	73	4	no	—
156	C₂×C₄⋊C₄	—	146	4	no	—
157	C₂×C₄⋊C₄	—	146	4	no	—
158	C₂×C₄⋊C₄	—	146	4	no	—
159	C₂×C₄²	—	146	4	no	—
160	C₂×C₄²	D₂₉₂	1	2	yes	—
161	C₂×C₄²	D₂₉₂	1	2	yes	—
162	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
163	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
164	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
165	#107	—	146	8	no	—
166	#103	—	146	16	no	—
167	C₄×C₈	—	2	4	no	—
168	C₄×C₈	—	2	2	no	—
169	C₄×C₈	C₄×D₇₃	1	4	yes	—
170	C₄×C₈	D₂₉₂	1	8	yes	—
171	#95	—	146	8	no	—
172	C₂×Q₈	—	73	8	no	—
173	C₂×Q₈	—	146	8	no	—
174	C₂×Q₈	—	146	8	no	—
175	C₂×Q₈	—	146	4	no	—
176	C₂²×C₄	—	146	4	no	—
177	C₂²×C₄	—	146	4	no	—
178	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
179	C₂²×C₄	C₂×D₂₉₂	1	2	yes	—
180	C₂²×C₄	C₂×D₂₉₂	1	2	yes	—
181	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
182	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
183	Q₁₆	—	146	32	no	—
184	C₂×C₈	—	2	2	no	—
185	C₂×C₈	—	2	2	no	—
186	C₂×C₈	C₂×C₄×D₇₃	1	4	yes	—
187	C₂×C₈	C₂×D₂₉₂	1	4	yes	—
188	C₂×C₈	C₂×D₂₉₂	1	4	yes	—
189	C₂×C₈	#11924028	1	4	yes	—
190	C₄⋊C₄	—	292	8	no	—
191	C₄⋊C₄	—	292	8	no	—
192	C₄⋊C₄	—	146	8	no	—
193	C₄⋊C₄	—	146	16	no	—
194	C₄²	—	2	4	no	—
195	C₄²	—	2	2	no	—
196	C₄²	—	292	8	no	—
197	C₄²	Dic₂₉₂	1	8	yes	complemented
198	C₄²	C₂×C₄×D₇₃	1	2	yes	—
199	C₄²	C₂×D₂₉₂	1	4	yes	—
200	C₄²	#11924028	1	2	yes	—
201	C₂³	C₂²×D₂₉₂	1	1	yes	characteristic
202	Q₈	—	292	8	no	—
203	Q₈	—	146	16	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	292	4	no	—
208	C₂×C₄	—	292	4	no	—
209	C₂×C₄	—	292	4	no	—
210	C₂×C₄	—	292	8	no	—
211	C₂×C₄	—	146	8	no	—
212	C₂×C₄	C₄×D₂₉₂	1	4	yes	—
213	C₂×C₄	#14556588	1	2	yes	—
214	C₂×C₄	#14556588	1	2	yes	—
215	C₂×C₄	C₂×Dic₂₉₂	1	4	yes	—
216	C₂×C₄	C₂×Dic₂₉₂	1	4	yes	—
217	C₂×C₄	C₂×Dic₂₉₂	1	4	yes	—
218	C₂×C₄	#14556613	1	4	yes	—
219	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
220	C₂×C₄	C₂²×D₂₉₂	1	2	yes	—
221	C₂×C₄	C₂×#11924028	1	1	yes	characteristic
222	C₂×C₄	C₂×#11924028	1	2	yes	—
223	C₈	—	2	4	no	—
224	C₈	C₄×D₂₉₂	1	8	yes	—
225	C₂²	C₂×C₄×D₂₉₂	1	1	yes	characteristic
226	C₂²	C₂×#14556588	1	1	yes	characteristic
227	C₂²	#17989137	1	1	yes	characteristic
228	C₂²	C₂²×Dic₂₉₂	1	2	yes	—
229	C₂²	C₂×#14556613	1	2	yes	—
230	C₄	—	2	4	no	—
231	C₄	—	2	2	no	—
232	C₄	—	292	8	no	—
233	C₄	—	584	4	no	—
234	C₄	C₄×Dic₂₉₂	1	8	yes	complemented
235	C₄	#17988967	1	4	yes	direct product factor
236	C₄	C₂×C₄×D₂₉₂	1	2	yes	—
237	C₄	#17989137	1	2	yes	—
238	C₂	C₄×#14556588	1	1	yes	characteristic
239	C₂	C₂×C₄×Dic₂₉₂	1	2	yes	—
240	C₂	C₂×#17988967	1	1	yes	characteristic
241	C₂	#22620359	1	1	yes	characteristic
242	C₂	#22620517	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₂₉₂
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₃
Fitting	C₄²×C₈×C₇₃	C₂
socle, prime radical	C₂³×C₇₃	C₂²×D₄
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	C₄²×C₈	D₇₃
hypocenter	C₇₃	C₄×#494
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄²×C₈

Complements

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

N	H ≅ G/N	type
11. #17988967	C₄	direct (N × H)
75. C₄²×C₇₃	Q₁₆	semidirect
110. C₄×C₇₃	C₄×Q₁₆	semidirect
111. C₄×C₇₃	#494	semidirect
129. C₇₃	C₄×#494	semidirect
197. C₄²	Dic₂₉₂	semidirect
234. C₄	C₄×Dic₂₉₂	semidirect
235. C₄	#17988967	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×#17988967	2
C₂×C₄×Dic₂₉₂	2
C₄×#14556591	2
#22610792	2
#22610733	2
#22610091	2
C₄²×C₈×C₇₃	2
C₄×#494	73

Subgroups — C4×#17988967 #33094421

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#17988967 #33094421