Subgroups — C₂×#22625578 #34018496

Order 18688.

654 conjugacy classes of subgroups.

The subgroup lattice has 246 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989638	C₂	1	2	yes	maximal
2	#22625578	C₂	1	8	yes	maximal, direct product factor
3	C₂×#17989448	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈⋊#10596833	C₂	1	2	yes	maximal
5	C₂×#17989428	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₁₆×Dic₇₃	C₂	1	1	yes	maximal, characteristic
7	#17989638	—	2	4	no	—
8	#17989638	C₂²	1	8	yes	—
9	C₂×#14556658	—	2	2	no	—
10	C₂×C₄⋊#10596833	C₂²	1	2	yes	—
11	C₂×#14556646	—	2	2	no	—
12	C₂×C₄×#10596833	C₂²	1	1	yes	characteristic
13	C₂×C₄×#10596833	C₂²	1	1	yes	characteristic
14	#17989448	C₂²	1	4	yes	—
15	Q₈⋊#10596833	C₂²	1	8	yes	—
16	#17989428	C₂²	1	4	yes	—
17	C₂×Q₈×Dic₇₃	C₂²	1	2	yes	—
18	Q₁₆×Dic₇₃	C₄	1	4	yes	—
19	Q₁₆×Dic₇₃	C₂²	1	4	yes	—
20	C₂×#14556525	C₄	1	1	yes	characteristic
21	C₂×#14556515	C₄	1	2	yes	—
22	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
23	C₂²×Q₁₆×C₇₃	C₄	1	1	yes	characteristic
24	C₂²×#10596833	—	2	2	no	—
25	C₂²×#10596833	—	2	1	no	—
26	C₂²×#10596833	D₄	1	2	yes	—
27	#14556658	—	2	8	no	—
28	C₄⋊#10596833	—	2	2	no	—
29	C₄⋊#10596833	C₂³	1	4	yes	—
30	#14556646	—	2	8	no	—
31	C₄×#10596833	—	2	1	no	—
32	C₄×#10596833	D₄	1	2	yes	—
33	C₄×#10596833	C₂³	1	2	yes	—
34	C₄×#10596833	C₂³	1	2	yes	—
35	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
36	Q₈×Dic₇₃	—	2	2	no	—
37	Q₈×Dic₇₃	—	2	2	no	—
38	Q₈×Dic₇₃	C₂×C₄	1	4	yes	—
39	Q₈×Dic₇₃	C₂³	1	4	yes	—
40	C₂×C₄⋊Dic₇₃	—	2	2	no	—
41	C₂×C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
42	C₂×C₄×Dic₇₃	—	2	2	no	—
43	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
44	#14556525	C₂×C₄	1	4	yes	—
45	#14556515	C₂×C₄	1	8	yes	—
46	C₈×Dic₇₃	C₂×C₄	1	2	yes	—
47	C₈×Dic₇₃	C₂³	1	2	yes	—
48	C₂²×Q₈×C₇₃	C₂×C₄	1	2	yes	—
49	C₂×Q₁₆×C₇₃	—	2	4	no	—
50	C₂×Q₁₆×C₇₃	C₂×C₄	1	4	yes	—
51	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
52	C₂×#10596833	—	2	4	no	—
53	C₂×#10596833	—	2	4	no	—
54	C₂×#10596833	—	2	2	no	—
55	C₂×#10596833	—	4	2	no	—
56	C₂×#10596833	—	4	4	no	—
57	C₂×#10596833	C₂×D₄	1	4	yes	—
58	C₂²×Dic₇₃	—	2	2	no	—
59	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
60	C₂²×Dic₇₃	#41	1	1	yes	characteristic
61	C₂×#10596831	—	2	2	no	—
62	C₂×#10596831	C₂²×C₄	1	2	yes	—
63	C₄⋊Dic₇₃	—	2	2	no	—
64	C₄⋊Dic₇₃	—	2	4	no	—
65	C₄⋊Dic₇₃	—	2	4	no	—
66	C₄⋊Dic₇₃	C₂²×C₄	1	4	yes	—
67	C₄×Dic₇₃	—	2	4	no	—
68	C₄×Dic₇₃	—	2	4	no	—
69	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
70	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
71	C₄×Dic₇₃	#41	1	1	yes	characteristic
72	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
73	C₂×Q₈×C₇₃	—	2	2	no	—
74	C₂×Q₈×C₇₃	—	2	4	no	—
75	C₂×Q₈×C₇₃	—	2	4	no	—
76	C₂×Q₈×C₇₃	C₂²×C₄	1	4	yes	—
77	C₂²×C₄×C₇₃	—	2	2	no	—
78	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
79	Q₁₆×C₇₃	—	2	8	no	—
80	C₂×C₈×C₇₃	M₁₆	1	4	yes	—
81	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
82	C₂³×C₇₃	C₄×D₄	1	1	yes	characteristic
83	Q₈×C₇₃	—	2	4	no	—
84	Q₈×C₇₃	—	2	4	no	—
85	Q₈×C₇₃	—	4	4	no	—
86	C₂×C₄×C₇₃	—	2	4	no	—
87	C₂×C₄×C₇₃	—	4	4	no	—
88	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
89	C₂×C₄×C₇₃	C₂×M₁₆	1	2	yes	—
90	C₂×C₄×C₇₃	#131	1	2	yes	—
91	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
92	C₂×Dic₇₃	—	2	2	no	—
93	C₂×Dic₇₃	—	2	4	no	—
94	C₂×Dic₇₃	—	4	4	no	—
95	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
96	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
97	C₂×Dic₇₃	#137	1	4	yes	—
98	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
99	C₂×Dic₇₃	C₂×#41	1	1	yes	characteristic
100	#10596833	—	2	4	no	—
101	#10596833	—	4	2	no	—
102	#10596833	—	4	4	no	—
103	C₈×C₇₃	C₂×M₁₆	1	4	yes	—
104	#10596831	—	2	2	no	—
105	C₂²×C₇₃	#436	1	2	yes	—
106	C₂²×C₇₃	#441	1	2	yes	—
107	C₂²×C₇₃	#444	1	2	yes	—
108	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
109	C₄×C₇₃	—	4	4	no	—
110	C₄×C₇₃	#436	1	2	yes	—
111	C₄×C₇₃	C₂²×M₁₆	1	1	yes	characteristic
112	C₄×C₇₃	C₂×#131	1	1	yes	characteristic
113	Dic₇₃	—	2	1	no	—
114	Dic₇₃	—	2	1	no	—
115	Dic₇₃	—	4	4	no	—
116	Dic₇₃	#441	1	2	yes	—
117	Dic₇₃	C₂×#137	1	2	yes	—
118	C₂×#1593	—	73	1	no	maximal, Sylow
119	C₂×C₇₃	#1593	1	4	yes	complemented
120	C₂×C₇₃	C₂×#436	1	1	yes	characteristic
121	C₂×C₇₃	C₂×#441	1	1	yes	characteristic
122	C₂×C₇₃	C₂×#444	1	1	yes	characteristic
123	C₂×#446	—	73	2	no	—
124	C₂×C₄×Q₁₆	—	73	1	no	—
125	#1593	—	73	8	no	—
126	C₂×#334	—	73	1	no	—
127	C₂×Q₈⋊C₈	—	73	2	no	—
128	C₂×#322	—	73	1	no	—
129	C₇₃	C₂×#1593	1	1	yes	characteristic, complemented, Sylow
130	C₂²×Q₁₆	#64408	1	1	yes	characteristic
131	C₂×C₄×Q₈	—	73	2	no	—
132	#446	—	73	8	no	—
133	#446	—	146	4	no	—
134	C₄×Q₁₆	—	73	4	no	—
135	C₄×Q₁₆	—	73	4	no	—
136	C₂×#107	—	73	1	no	—
137	C₂×C₄⋊C₈	—	73	2	no	—
138	C₂×C₄⋊C₈	—	146	2	no	—
139	C₂×#103	—	73	2	no	—
140	C₂×#97	—	146	2	no	—
141	C₂×C₄×C₈	—	73	1	no	—
142	C₂×C₄×C₈	—	73	1	no	—
143	C₂×C₄×C₈	—	73	1	no	—
144	#334	—	73	4	no	—
145	Q₈⋊C₈	—	73	8	no	—
146	#322	—	73	4	no	—
147	C₂²×Q₈	C₂×#64408	1	2	yes	—
148	C₂×Q₁₆	—	2	4	no	—
149	C₂×Q₁₆	C₂×#64408	1	4	yes	—
150	C₂²×C₈	—	73	2	no	—
151	C₂²×C₈	—	73	1	no	—
152	C₂²×C₈	—	146	1	no	—
153	C₂²×C₈	—	146	2	no	—
154	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
155	C₄×Q₈	—	73	4	no	—
156	C₄×Q₈	—	73	4	no	—
157	C₄×Q₈	—	146	2	no	—
158	C₄×Q₈	—	146	2	no	—
159	C₂×C₄⋊C₄	—	73	2	no	—
160	C₂×C₄⋊C₄	—	146	2	no	—
161	C₂×C₄²	—	73	1	no	—
162	C₂×C₄²	—	146	2	no	—
163	#107	—	73	4	no	—
164	C₄⋊C₈	—	73	4	no	—
165	C₄⋊C₈	—	146	2	no	—
166	C₄⋊C₈	—	146	8	no	—
167	#103	—	73	8	no	—
168	#97	—	146	8	no	—
169	C₄×C₈	—	73	2	no	—
170	C₄×C₈	—	73	2	no	—
171	C₄×C₈	—	73	2	no	—
172	C₄×C₈	—	73	2	no	—
173	C₄×C₈	—	73	2	no	—
174	C₄×C₈	—	146	1	no	—
175	C₂×Q₈	—	2	2	no	—
176	C₂×Q₈	—	2	4	no	—
177	C₂×Q₈	—	2	4	no	—
178	C₂×Q₈	C₂²×#64408	1	4	yes	—
179	C₂²×C₄	—	2	2	no	—
180	C₂²×C₄	—	73	1	no	—
181	C₂²×C₄	—	73	1	no	—
182	C₂²×C₄	—	146	2	no	—
183	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
184	Q₁₆	—	2	8	no	—
185	C₂×C₈	—	292	4	no	—
186	C₂×C₈	—	292	2	no	—
187	C₂×C₈	—	73	4	no	—
188	C₂×C₈	—	73	2	no	—
189	C₂×C₈	—	146	2	no	—
190	C₂×C₈	—	146	4	no	—
191	C₂×C₈	—	146	4	no	—
192	C₂×C₈	—	146	2	no	—
193	C₂×C₈	#11924037	1	4	yes	—
194	C₂×C₈	C₂²×#64408	1	2	yes	—
195	C₄⋊C₄	—	73	4	no	—
196	C₄⋊C₄	—	146	4	no	—
197	C₄⋊C₄	—	146	4	no	—
198	C₄⋊C₄	—	146	2	no	—
199	C₄²	—	73	1	no	—
200	C₄²	—	73	1	no	—
201	C₄²	—	73	1	no	—
202	C₄²	—	73	1	no	—
203	C₄²	—	146	4	no	—
204	C₄²	—	146	4	no	—
205	C₂³	D₄×#64408	1	1	yes	characteristic
206	Q₈	—	2	4	no	—
207	Q₈	—	2	4	no	—
208	Q₈	—	4	4	no	—
209	C₂×C₄	—	2	4	no	—
210	C₂×C₄	—	4	4	no	—
211	C₂×C₄	—	292	4	no	—
212	C₂×C₄	—	73	1	no	—
213	C₂×C₄	—	73	1	no	—
214	C₂×C₄	—	73	4	no	—
215	C₂×C₄	—	73	1	no	—
216	C₂×C₄	—	73	1	no	—
217	C₂×C₄	—	146	4	no	—
218	C₂×C₄	—	146	2	no	—
219	C₂×C₄	D₄×#64408	1	1	yes	characteristic
220	C₂×C₄	C₂×#11924037	1	2	yes	—
221	C₂×C₄	#14556678	1	2	yes	—
222	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
223	C₈	—	292	4	no	—
224	C₈	—	292	2	no	—
225	C₈	—	146	4	no	—
226	C₈	—	146	2	no	—
227	C₈	C₂×#11924037	1	4	yes	—
228	C₂²	#17989622	1	2	yes	—
229	C₂²	#17989627	1	2	yes	—
230	C₂²	#17989633	1	2	yes	—
231	C₂²	C₂×D₄×#64408	1	1	yes	characteristic
232	C₄	—	4	4	no	—
233	C₄	—	292	4	no	—
234	C₄	—	73	2	no	—
235	C₄	—	73	2	no	—
236	C₄	—	146	1	no	—
237	C₄	—	146	1	no	—
238	C₄	#17989622	1	2	yes	—
239	C₄	C₂²×#11924037	1	1	yes	characteristic
240	C₄	C₂×#14556678	1	1	yes	characteristic
241	C₂	#22625578	1	4	yes	direct product factor
242	C₂	C₂×#17989622	1	1	yes	characteristic
243	C₂	C₂×#17989627	1	1	yes	characteristic
244	C₂	C₂×#17989633	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₄×#64408
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#64408
Fitting	C₂²×Q₁₆×C₇₃	C₄
socle, prime radical	C₂³×C₇₃	C₄×D₄
cosocle	C₄×Dic₇₃	C₂⁴
hypercenter	C₂²×Q₁₆	#64408
hypocenter	C₇₃	C₂×#1593
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×Q₁₆

Complements

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

N	H ≅ G/N	type
2. #22625578	C₂	direct (N × H)
119. C₂×C₇₃	#1593	semidirect
129. C₇₃	C₂×#1593	semidirect
241. C₂	#22625578	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×#17989638	2
#22625578	2
C₂×#17989448	2
C₂×Q₈⋊#10596833	2
C₂×#17989428	2
C₂×Q₁₆×Dic₇₃	2
C₂×#1593	73

Subgroups — C2×#22625578 #34018496

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22625578 #34018496