Subgroups — C₂×#19139624 #25268351

Order 11008.

3182 conjugacy classes of subgroups.

The subgroup lattice has 252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13063324	C₂	1	4	yes	maximal
2	#19139624	C₂	1	16	yes	maximal, direct product factor
3	C₂×#14582819	C₂	1	4	yes	maximal
4	C₂×#14582795	C₂	1	4	yes	maximal
5	C₂×C₄×C₄⋊Dic₄₃	C₂	1	2	yes	maximal
6	C₂×C₄₃×#384	C₂	1	1	yes	maximal, characteristic
7	C₂³×Dic₈₆	C₂²	1	4	yes	—
8	C₂×#13063324	—	2	32	no	—
9	C₂×#13063324	C₂²	1	32	yes	—
10	C₂²×C₄⋊Dic₄₃	C₂²	1	2	yes	—
11	C₂²×C₄⋊Dic₄₃	C₂²	1	2	yes	—
12	C₂²×Dic₄₃⋊C₄	C₂²	1	8	yes	—
13	C₂²×C₄×Dic₄₃	C₂²	1	4	yes	—
14	#14582819	C₂²	1	32	yes	—
15	#14582795	C₂²	1	32	yes	—
16	C₄×C₄⋊Dic₄₃	C₂²	1	16	yes	—
17	C₂×C₄₃⋊#95	C₂²	1	4	yes	—
18	C₂×C₄₃⋊#95	C₂²	1	4	yes	—
19	C₂²×C₄⋊C₄×C₄₃	C₂²	1	4	yes	—
20	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
21	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
22	C₄₃×#384	C₂²	1	8	yes	—
23	C₂²×Dic₈₆	—	2	32	no	—
24	C₂²×Dic₈₆	—	4	8	no	—
25	C₂²×Dic₈₆	C₂³	1	16	yes	—
26	C₂³×Dic₄₃	C₂³	1	4	yes	—
27	C₂³×Dic₄₃	C₂³	1	4	yes	—
28	#13063324	—	2	128	no	—
29	C₂×C₄⋊Dic₄₃	D₄	1	16	yes	—
30	C₂×C₄⋊Dic₄₃	Q₈	1	16	yes	complemented
31	C₂×C₄⋊Dic₄₃	C₂³	1	8	yes	—
32	C₂×C₄⋊Dic₄₃	C₂³	1	8	yes	—
33	C₂×Dic₄₃⋊C₄	—	2	32	no	—
34	C₂×Dic₄₃⋊C₄	C₂³	1	32	yes	—
35	C₂×C₄×Dic₄₃	—	2	16	no	—
36	C₂×C₄×Dic₄₃	C₂³	1	16	yes	—
37	C₄₃⋊#95	C₂³	1	16	yes	—
38	C₄₃⋊#95	C₂³	1	16	yes	—
39	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
40	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
42	C₂×C₄⋊C₄×C₄₃	—	2	16	no	—
43	C₂×C₄⋊C₄×C₄₃	—	4	4	no	—
44	C₂×C₄⋊C₄×C₄₃	C₂³	1	16	yes	—
45	C₂×C₄⋊C₄×C₄₃	C₂³	1	8	yes	—
46	C₂×C₄²×C₄₃	Q₈	1	8	yes	complemented
47	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
48	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
49	C₂²×C₄×C₄₃	—	2	16	no	—
50	C₂²×C₄×C₄₃	—	2	2	no	—
51	C₂²×C₄×C₄₃	—	2	8	no	—
52	C₂²×C₄×C₄₃	—	2	2	no	—
53	C₂²×C₄×C₄₃	C₂×D₄	1	8	yes	—
54	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
55	C₂²×C₄×C₄₃	C₂×Q₈	1	8	yes	—
56	C₂²×C₄×C₄₃	C₂×Q₈	1	8	yes	—
57	C₂²×C₄×C₄₃	C₂⁴	1	8	yes	—
58	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
59	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
60	C₂²×Dic₄₃	—	2	8	no	—
61	C₂²×Dic₄₃	—	2	8	no	—
62	C₂²×Dic₄₃	—	2	8	no	—
63	C₂²×Dic₄₃	—	2	8	no	—
64	C₂²×Dic₄₃	C₂×D₄	1	16	yes	—
65	C₂²×Dic₄₃	C₂×Q₈	1	16	yes	—
66	C₂²×Dic₄₃	C₂⁴	1	8	yes	—
67	C₂²×Dic₄₃	C₂⁴	1	8	yes	—
68	C₂×Dic₈₆	—	2	64	no	—
69	C₂×Dic₈₆	—	4	16	no	—
70	C₂×Dic₈₆	—	4	64	no	—
71	C₄⋊C₄×C₄₃	—	2	32	no	—
72	C₄⋊C₄×C₄₃	—	4	8	no	—
73	C₄²×C₄₃	C₂×Q₈	1	16	yes	complemented
74	C₄⋊Dic₄₃	C₂×D₄	1	32	yes	—
75	C₄⋊Dic₄₃	C₂×Q₈	1	32	yes	complemented
76	Dic₄₃⋊C₄	—	2	64	no	—
77	C₄×Dic₄₃	—	2	32	no	—
78	C₂³×C₄₃	C₂²×D₄	1	4	yes	—
79	C₂³×C₄₃	C₂²×Q₈	1	4	yes	—
80	C₂³×C₄₃	C₂²×Q₈	1	2	yes	—
81	C₂³×C₄₃	H(5,𝔽₂)	1	2	yes	—
82	C₂³×C₄₃	2₋¹⁺⁴	1	2	yes	—
83	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
84	C₂×C₄×C₄₃	—	2	8	no	—
85	C₂×C₄×C₄₃	—	2	2	no	—
86	C₂×C₄×C₄₃	—	2	2	no	—
87	C₂×C₄×C₄₃	—	2	16	no	—
88	C₂×C₄×C₄₃	—	2	8	no	—
89	C₂×C₄×C₄₃	—	4	16	no	—
90	C₂×C₄×C₄₃	C₄⋊Q₈	1	32	yes	complemented
91	C₂×C₄×C₄₃	C₂²×D₄	1	8	yes	—
92	C₂×C₄×C₄₃	C₂²×Q₈	1	8	yes	—
93	C₂×C₄×C₄₃	C₂²×Q₈	1	4	yes	—
94	C₂×C₄×C₄₃	C₂²×Q₈	1	8	yes	—
95	C₂×Dic₄₃	—	2	32	no	—
96	C₂×Dic₄₃	—	2	32	no	—
97	C₂×Dic₄₃	—	2	8	no	—
98	C₂×Dic₄₃	—	2	8	no	—
99	C₂×Dic₄₃	—	2	8	no	—
100	C₂×Dic₄₃	—	2	8	no	—
101	C₂×Dic₄₃	C₂²×D₄	1	16	yes	—
102	C₂×Dic₄₃	C₂²×Q₈	1	16	yes	—
103	Dic₈₆	—	4	64	no	—
104	C₂×#2551	—	43	1	no	maximal, Sylow
105	C₂²×C₄₃	C₂×C₄⋊Q₈	1	8	yes	—
106	C₂²×C₄₃	#544	1	4	yes	—
107	C₂²×C₄₃	D₄²	1	4	yes	—
108	C₂²×C₄₃	D₄×Q₈	1	8	yes	—
109	C₂²×C₄₃	Q₈²	1	4	yes	—
110	C₂²×C₄₃	C₂³×D₄	1	2	yes	—
111	C₂²×C₄₃	C₂³×Q₈	1	2	yes	—
112	C₂²×C₄₃	C₂³×Q₈	1	1	yes	characteristic
113	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
114	C₂²×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
115	C₄×C₄₃	—	2	4	no	—
116	C₄×C₄₃	—	4	8	no	—
117	C₄×C₄₃	C₂×C₄⋊Q₈	1	16	yes	complemented
118	Dic₄₃	—	2	16	no	—
119	Dic₄₃	—	2	16	no	—
120	C₂²×C₄⋊Q₈	—	43	4	no	—
121	#2551	—	43	16	no	—
122	C₂×#395	—	43	4	no	—
123	C₂×#389	—	43	4	no	—
124	C₂×#384	D₄₃	1	1	yes	characteristic
125	C₂×C₄×C₄⋊C₄	—	43	2	no	—
126	C₂×C₄₃	#2551	1	8	yes	complemented
127	C₂×C₄₃	C₂²×C₄⋊Q₈	1	2	yes	—
128	C₂×C₄₃	C₂×#544	1	1	yes	characteristic
129	C₂×C₄₃	C₂×D₄²	1	1	yes	characteristic
130	C₂×C₄₃	C₂×D₄×Q₈	1	2	yes	—
131	C₂×C₄₃	C₂×Q₈²	1	1	yes	characteristic
132	C₂³×Q₈	—	43	4	no	—
133	C₂×C₄⋊Q₈	—	43	32	no	—
134	C₂×C₄⋊Q₈	—	86	32	no	—
135	C₂²×C₄⋊C₄	—	43	2	no	—
136	C₂²×C₄⋊C₄	—	43	2	no	—
137	C₂²×C₄⋊C₄	—	43	8	no	—
138	C₂²×C₄⋊C₄	C₂×D₄₃	1	4	yes	—
139	C₂²×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
140	C₂²×C₄²	—	43	4	no	—
141	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
142	#395	—	43	32	no	—
143	#389	—	43	32	no	—
144	#384	C₂×D₄₃	1	8	yes	—
145	C₄×C₄⋊C₄	—	43	16	no	—
146	C₂×#95	—	43	4	no	—
147	C₂×#95	—	43	4	no	—
148	C₄₃	C₂×#2551	1	1	yes	characteristic, complemented, Sylow
149	C₂²×Q₈	—	43	16	no	—
150	C₂²×Q₈	—	86	32	no	—
151	C₂²×Q₈	—	172	8	no	—
152	C₂³×C₄	—	43	4	no	—
153	C₂³×C₄	—	43	4	no	—
154	C₂³×C₄	C₂²×D₄₃	1	4	yes	—
155	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
156	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
157	C₄⋊Q₈	—	86	128	no	—
158	C₂×C₄⋊C₄	—	2	16	no	—
159	C₂×C₄⋊C₄	—	4	4	no	—
160	C₂×C₄⋊C₄	—	43	16	no	—
161	C₂×C₄⋊C₄	—	43	16	no	—
162	C₂×C₄⋊C₄	—	43	8	no	—
163	C₂×C₄⋊C₄	—	43	8	no	—
164	C₂×C₄⋊C₄	—	43	32	no	—
165	C₂×C₄⋊C₄	—	86	32	no	—
166	C₂×C₄⋊C₄	C₂²×D₄₃	1	16	yes	—
167	C₂×C₄⋊C₄	C₂²×D₄₃	1	8	yes	—
168	C₂×C₄²	—	43	16	no	—
169	C₂×C₄²	—	86	16	no	—
170	C₂×C₄²	Dic₈₆	1	8	yes	complemented
171	C₂×C₄²	C₂²×D₄₃	1	4	yes	—
172	#95	—	43	16	no	—
173	#95	—	43	16	no	—
174	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
175	C₂×Q₈	—	86	64	no	—
176	C₂×Q₈	—	172	16	no	—
177	C₂×Q₈	—	172	64	no	—
178	C₂²×C₄	—	2	2	no	—
179	C₂²×C₄	—	2	2	no	—
180	C₂²×C₄	—	2	16	no	—
181	C₂²×C₄	—	2	8	no	—
182	C₂²×C₄	—	43	16	no	—
183	C₂²×C₄	—	43	16	no	—
184	C₂²×C₄	—	43	8	no	—
185	C₂²×C₄	—	43	8	no	—
186	C₂²×C₄	—	86	8	no	—
187	C₂²×C₄	—	86	8	no	—
188	C₂²×C₄	—	86	8	no	—
189	C₂²×C₄	—	86	8	no	—
190	C₂²×C₄	C₂×Dic₈₆	1	4	yes	—
191	C₂²×C₄	C₂×Dic₈₆	1	8	yes	—
192	C₂²×C₄	D₄×D₄₃	1	8	yes	—
193	C₂²×C₄	Q₈×D₄₃	1	8	yes	—
194	C₂²×C₄	C₂³×D₄₃	1	8	yes	—
195	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
196	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
197	C₄⋊C₄	—	2	32	no	—
198	C₄⋊C₄	—	4	8	no	—
199	C₄⋊C₄	—	43	32	no	—
200	C₄⋊C₄	—	43	32	no	—
201	C₄⋊C₄	—	86	64	no	—
202	C₄²	—	86	32	no	—
203	C₄²	C₂×Dic₈₆	1	16	yes	complemented
204	C₂³	C₂×D₄×D₄₃	1	4	yes	—
205	C₂³	C₂×Q₈×D₄₃	1	4	yes	—
206	C₂³	C₂²×Dic₈₆	1	2	yes	—
207	C₂³	#13063370	1	2	yes	—
208	C₂³	#13063373	1	2	yes	—
209	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
210	Q₈	—	172	64	no	—
211	C₂×C₄	—	2	2	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	8	no	—
214	C₂×C₄	—	2	16	no	—
215	C₂×C₄	—	2	8	no	—
216	C₂×C₄	—	4	16	no	—
217	C₂×C₄	—	43	16	no	—
218	C₂×C₄	—	43	16	no	—
219	C₂×C₄	—	86	32	no	—
220	C₂×C₄	—	86	8	no	—
221	C₂×C₄	—	86	8	no	—
222	C₂×C₄	—	86	8	no	—
223	C₂×C₄	—	86	8	no	—
224	C₂×C₄	—	86	32	no	—
225	C₂×C₄	#13063324	1	32	yes	complemented
226	C₂×C₄	C₂×D₄×D₄₃	1	8	yes	—
227	C₂×C₄	C₂×Q₈×D₄₃	1	8	yes	—
228	C₂×C₄	C₂²×Dic₈₆	1	4	yes	—
229	C₂×C₄	C₂²×Dic₈₆	1	8	yes	—
230	C₂²	C₂×#13063324	1	8	yes	—
231	C₂²	#14583530	1	4	yes	—
232	C₂²	#14583534	1	4	yes	—
233	C₂²	#14583564	1	8	yes	—
234	C₂²	#14583629	1	4	yes	—
235	C₂²	C₂²×D₄×D₄₃	1	2	yes	—
236	C₂²	C₂²×Q₈×D₄₃	1	2	yes	—
237	C₂²	C₂³×Dic₈₆	1	1	yes	characteristic
238	C₂²	C₂×#13063370	1	1	yes	characteristic
239	C₂²	C₂×#13063373	1	1	yes	characteristic
240	C₄	—	2	4	no	—
241	C₄	—	4	8	no	—
242	C₄	—	86	16	no	—
243	C₄	—	86	16	no	—
244	C₄	C₂×#13063324	1	16	yes	complemented
245	C₂	#19139624	1	8	yes	direct product factor
246	C₂	C₂²×#13063324	1	2	yes	—
247	C₂	C₂×#14583530	1	1	yes	characteristic
248	C₂	C₂×#14583534	1	1	yes	characteristic
249	C₂	C₂×#14583564	1	2	yes	—
250	C₂	C₂×#14583629	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₄₃
commutator, cosocle	C₂³×C₄₃	C₂⁵
Frattini	C₂³	C₂⁴×D₄₃
Fitting	C₂×C₄₃×#384	C₂
socle, prime radical	C₂⁴×C₄₃	C₂⁴
hypercenter	C₂×#384	D₄₃
hypocenter	C₄₃	C₂×#2551
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂⁴ ◁ C₂×#384

Complements

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

N	H ≅ G/N	type
2. #19139624	C₂	direct (N × H)
30. C₂×C₄⋊Dic₄₃	Q₈	semidirect
46. C₂×C₄²×C₄₃	Q₈	semidirect
73. C₄²×C₄₃	C₂×Q₈	semidirect
75. C₄⋊Dic₄₃	C₂×Q₈	semidirect
90. C₂×C₄×C₄₃	C₄⋊Q₈	semidirect
117. C₄×C₄₃	C₂×C₄⋊Q₈	semidirect
126. C₂×C₄₃	#2551	semidirect
148. C₄₃	C₂×#2551	semidirect
170. C₂×C₄²	Dic₈₆	semidirect
203. C₄²	C₂×Dic₈₆	semidirect
225. C₂×C₄	#13063324	semidirect
244. C₄	C₂×#13063324	semidirect
245. C₂	#19139624	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#13063324	2
#19139624	2
C₂×#14582819	2
C₂×#14582795	2
C₂×C₄×C₄⋊Dic₄₃	2
C₂×C₄₃×#384	2
C₂×#2551	43

Subgroups — C2×#19139624 #25268351

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19139624 #25268351