Subgroups — C₂×#19134312 #25093997

Order 11008.

2398 conjugacy classes of subgroups.

The subgroup lattice has 264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13063284	C₂	1	2	yes	maximal
2	#19134312	C₂	1	8	yes	maximal, direct product factor
3	C₂×#14582662	C₂	1	4	yes	maximal, complemented
4	C₂⁴×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#13063284	—	2	4	no	—
6	C₂×#13063284	—	2	8	no	—
7	C₂×#13063284	C₄	1	16	yes	complemented
8	C₂×#13063284	C₂²	1	8	yes	—
9	C₂²×C₄⋊Dic₄₃	C₂²	1	4	yes	—
10	C₂²×C₂²⋊Dic₄₃	—	2	2	no	—
11	C₂²×C₄×Dic₄₃	—	2	2	no	—
12	#14582662	C₂²	1	16	yes	complemented
13	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₄₃	—	2	8	no	—
15	C₂³×C₈×C₄₃	C₄	1	8	yes	complemented
16	C₂³×C₈×C₄₃	C₂²	1	2	yes	—
17	C₂³×C₈×C₄₃	C₂²	1	4	yes	—
18	C₂³×Dic₄₃	—	2	4	no	—
19	#13063284	—	2	32	no	—
20	#13063284	—	2	16	no	—
21	#13063284	C₂×C₄	1	32	yes	complemented
22	C₂×C₄⋊Dic₄₃	—	2	4	no	—
23	C₂×C₄⋊Dic₄₃	—	2	8	no	—
24	C₂×C₄⋊Dic₄₃	C₂×C₄	1	16	yes	—
25	C₂×C₄⋊Dic₄₃	C₂³	1	8	yes	—
26	C₂×C₂²⋊Dic₄₃	—	2	16	no	—
27	C₂×C₂²⋊Dic₄₃	—	2	8	no	—
28	C₂×C₄×Dic₄₃	—	2	16	no	—
29	C₂×C₄×Dic₄₃	—	2	8	no	—
30	C₂⁵×C₄₃	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₄₃	C₂×C₄	1	8	yes	—
32	C₂³×C₄×C₄₃	C₂×C₄	1	4	yes	—
33	C₂³×C₄×C₄₃	D₄	1	2	yes	—
34	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₄₃	D₄	1	8	yes	—
36	C₂³×C₄×C₄₃	Q₈	1	4	yes	—
37	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
39	C₂²×C₈×C₄₃	—	2	32	no	—
40	C₂²×C₈×C₄₃	—	2	8	no	—
41	C₂²×C₈×C₄₃	—	2	16	no	—
42	C₂²×C₈×C₄₃	C₂×C₄	1	8	yes	—
43	C₂²×C₈×C₄₃	C₂×C₄	1	16	yes	complemented
44	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
45	C₂⁴×C₄₃	—	2	8	no	—
46	C₂⁴×C₄₃	C₂²⋊C₄	1	8	yes	—
47	C₂⁴×C₄₃	C₄⋊C₄	1	4	yes	—
48	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
49	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
50	C₂²×C₄×C₄₃	C₄²	1	16	yes	—
51	C₂²×C₄×C₄₃	C₂²⋊C₄	1	16	yes	—
52	C₂²×C₄×C₄₃	C₂²⋊C₄	1	8	yes	—
53	C₂²×C₄×C₄₃	C₂²⋊C₄	1	16	yes	—
54	C₂²×C₄×C₄₃	C₄⋊C₄	1	32	yes	—
55	C₂²×C₄×C₄₃	C₄⋊C₄	1	8	yes	—
56	C₂²×C₄×C₄₃	C₄⋊C₄	1	4	yes	—
57	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
58	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
59	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
60	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
61	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
62	C₂²×C₄×C₄₃	C₂×D₄	1	8	yes	—
63	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
64	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
66	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
67	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
68	C₂²×Dic₄₃	—	2	16	no	—
69	C₂²×Dic₄₃	—	2	8	no	—
70	C₂²×Dic₄₃	—	4	16	no	—
71	C₂×C₈×C₄₃	—	2	16	no	—
72	C₂×C₈×C₄₃	—	2	32	no	—
73	C₂×C₈×C₄₃	—	2	8	no	—
74	C₂×C₈×C₄₃	C₂²×C₄	1	8	yes	—
75	C₂²⋊Dic₄₃	—	2	32	no	—
76	C₄⋊Dic₄₃	—	2	16	no	—
77	C₄⋊Dic₄₃	—	2	8	no	—
78	C₄⋊Dic₄₃	C₂²×C₄	1	16	yes	—
79	C₄×Dic₄₃	—	2	32	no	—
80	C₂³×C₄₃	—	2	8	no	—
81	C₂³×C₄₃	—	2	32	no	—
82	C₂³×C₄₃	—	2	16	no	—
83	C₂³×C₄₃	#95	1	16	yes	—
84	C₂³×C₄₃	C₂×C₂²⋊C₄	1	8	yes	—
85	C₂³×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
86	C₂³×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
87	C₂³×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
88	C₂³×C₄₃	#135	1	8	yes	—
89	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
90	C₂×C₄×C₄₃	#95	1	32	yes	—
91	C₂×C₄×C₄₃	#95	1	16	yes	—
92	C₂×C₄×C₄₃	C₂×C₄²	1	8	yes	—
93	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
94	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	8	yes	—
95	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
96	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	8	yes	—
97	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
98	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	16	yes	—
99	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	8	yes	—
100	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
101	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
102	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
103	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
104	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
105	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
106	C₂×Dic₄₃	—	2	16	no	—
107	C₂×Dic₄₃	—	4	16	no	—
108	C₂×Dic₄₃	—	4	32	no	—
109	C₈×C₄₃	—	2	8	no	—
110	C₂×#1735	—	43	1	no	maximal, Sylow
111	C₂²×C₄₃	—	2	16	no	—
112	C₂²×C₄₃	—	2	8	no	—
113	C₂²×C₄₃	—	2	32	no	—
114	C₂²×C₄₃	C₂×#95	1	8	yes	—
115	C₂²×C₄₃	C₂×#95	1	4	yes	—
116	C₂²×C₄₃	#416	1	16	yes	—
117	C₂²×C₄₃	#427	1	8	yes	—
118	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	2	yes	—
119	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
120	C₂²×C₄₃	C₂×#135	1	4	yes	—
121	C₄×C₄₃	C₂×#95	1	8	yes	—
122	C₄×C₄₃	C₂×#95	1	4	yes	—
123	C₄×C₄₃	C₂²×C₄²	1	1	yes	characteristic
124	C₄×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
125	C₄×C₄₃	C₂²×C₄⋊C₄	1	2	yes	—
126	Dic₄₃	—	4	16	no	—
127	C₂⁴×C₈	D₄₃	1	1	yes	characteristic
128	C₂²×#117	—	43	2	no	—
129	#1735	—	43	8	no	—
130	C₂×#340	—	43	4	no	—
131	C₂×C₄₃	—	2	8	no	—
132	C₂×C₄₃	#1735	1	8	yes	complemented
133	C₂×C₄₃	C₂²×#95	1	1	yes	characteristic
134	C₂×C₄₃	C₂×#416	1	4	yes	—
135	C₂×C₄₃	C₂×#427	1	2	yes	—
136	C₂⁴×C₄	C₂×D₄₃	1	1	yes	characteristic
137	C₂³×C₈	—	2	8	no	—
138	C₂³×C₈	Dic₄₃	1	8	yes	complemented
139	C₂³×C₈	C₂×D₄₃	1	2	yes	—
140	C₂³×C₈	C₂×D₄₃	1	4	yes	—
141	C₂×#117	—	43	8	no	—
142	C₂×#117	—	43	16	no	—
143	C₂×#117	—	86	4	no	—
144	C₂×#117	—	86	8	no	—
145	C₂²×C₄⋊C₄	—	43	4	no	—
146	C₂²×C₂²⋊C₄	—	86	2	no	—
147	C₂²×C₄²	—	86	2	no	—
148	#340	—	43	16	no	—
149	C₄₃	C₂×#1735	1	1	yes	characteristic, complemented, Sylow
150	C₂⁵	D₁₇₂	1	1	yes	characteristic
151	C₂³×C₄	—	86	4	no	—
152	C₂³×C₄	Dic₈₆	1	4	yes	—
153	C₂³×C₄	C₄×D₄₃	1	8	yes	—
154	C₂³×C₄	D₁₇₂	1	2	yes	—
155	C₂³×C₄	D₁₇₂	1	1	yes	characteristic
156	C₂³×C₄	C₂×Dic₄₃	1	4	yes	—
157	C₂³×C₄	C₂²⋊D₄₃	1	8	yes	—
158	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
159	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
160	C₂²×C₈	—	2	32	no	—
161	C₂²×C₈	—	2	8	no	—
162	C₂²×C₈	—	2	16	no	—
163	C₂²×C₈	C₂×Dic₄₃	1	8	yes	—
164	C₂²×C₈	C₂×Dic₄₃	1	16	yes	complemented
165	C₂²×C₈	C₂²×D₄₃	1	4	yes	—
166	#117	—	43	32	no	—
167	#117	—	86	32	no	—
168	#117	—	86	16	no	—
169	C₂×C₄⋊C₄	—	43	16	no	—
170	C₂×C₄⋊C₄	—	43	8	no	—
171	C₂×C₄⋊C₄	—	86	4	no	—
172	C₂×C₄⋊C₄	—	86	8	no	—
173	C₂×C₂²⋊C₄	—	86	16	no	—
174	C₂×C₂²⋊C₄	—	86	8	no	—
175	C₂×C₄²	—	86	16	no	—
176	C₂×C₄²	—	86	8	no	—
177	C₂⁴	—	2	8	no	—
178	C₂⁴	C₄⋊Dic₄₃	1	4	yes	—
179	C₂⁴	(C₂×D₄₃)⋊C₄	1	8	yes	—
180	C₂⁴	C₂×D₁₇₂	1	2	yes	—
181	C₂⁴	C₂×D₁₇₂	1	1	yes	characteristic
182	C₂²×C₄	—	86	16	no	—
183	C₂²×C₄	—	86	8	no	—
184	C₂²×C₄	—	172	16	no	—
185	C₂²×C₄	C₄×Dic₄₃	1	16	yes	—
186	C₂²×C₄	Dic₄₃⋊C₄	1	32	yes	—
187	C₂²×C₄	C₄⋊Dic₄₃	1	8	yes	—
188	C₂²×C₄	C₄⋊Dic₄₃	1	4	yes	—
189	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	8	yes	—
190	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	16	yes	—
191	C₂²×C₄	C₂²⋊Dic₄₃	1	16	yes	—
192	C₂²×C₄	C₂×Dic₈₆	1	4	yes	—
193	C₂²×C₄	C₂×Dic₈₆	1	2	yes	—
194	C₂²×C₄	C₂×C₄×D₄₃	1	4	yes	—
195	C₂²×C₄	C₂×C₄×D₄₃	1	8	yes	—
196	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
197	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
198	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
199	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
200	C₂²×C₄	C₂×C₂²⋊D₄₃	1	4	yes	—
201	C₂²×C₄	C₂×C₂²⋊D₄₃	1	8	yes	—
202	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
203	C₂×C₈	—	2	16	no	—
204	C₂×C₈	—	2	32	no	—
205	C₂×C₈	—	2	8	no	—
206	C₂×C₈	C₂²×Dic₄₃	1	8	yes	—
207	C₄⋊C₄	—	43	16	no	—
208	C₄⋊C₄	—	86	16	no	—
209	C₄⋊C₄	—	86	8	no	—
210	C₂²⋊C₄	—	86	32	no	—
211	C₄²	—	86	32	no	—
212	C₂³	—	2	32	no	—
213	C₂³	—	2	8	no	—
214	C₂³	—	2	16	no	—
215	C₂³	C₄₃⋊#95	1	16	yes	—
216	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	8	yes	—
217	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	4	yes	—
218	C₂³	C₂×C₄⋊Dic₄₃	1	4	yes	—
219	C₂³	C₂×C₄⋊Dic₄₃	1	2	yes	—
220	C₂³	#13063347	1	8	yes	—
221	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
222	C₂×C₄	—	86	16	no	—
223	C₂×C₄	—	172	32	no	—
224	C₂×C₄	—	172	16	no	—
225	C₂×C₄	C₄₃⋊#95	1	32	yes	—
226	C₂×C₄	C₄₃⋊#95	1	16	yes	—
227	C₂×C₄	C₂×C₄×Dic₄₃	1	8	yes	—
228	C₂×C₄	C₂×C₄×Dic₄₃	1	4	yes	—
229	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	8	yes	—
230	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	4	yes	—
231	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	8	yes	—
232	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	4	yes	—
233	C₂×C₄	C₂×Dic₄₃⋊C₄	1	16	yes	—
234	C₂×C₄	C₂×Dic₄₃⋊C₄	1	8	yes	—
235	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
236	C₂×C₄	C₂×C₄⋊Dic₄₃	1	4	yes	—
237	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
238	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
239	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
240	C₂×C₄	C₂²×Dic₈₆	1	1	yes	characteristic
241	C₈	—	2	8	no	—
242	C₂²	—	2	8	no	—
243	C₂²	—	2	32	no	—
244	C₂²	—	2	16	no	—
245	C₂²	C₂×C₄₃⋊#95	1	8	yes	—
246	C₂²	C₂×C₄₃⋊#95	1	4	yes	—
247	C₂²	#14582896	1	16	yes	—
248	C₂²	#14582937	1	8	yes	—
249	C₂²	C₂²×(C₂×D₄₃)⋊C₄	1	2	yes	—
250	C₂²	C₂²×C₄⋊Dic₄₃	1	1	yes	characteristic
251	C₂²	C₂×#13063347	1	4	yes	—
252	C₄	—	172	16	no	—
253	C₄	C₂×C₄₃⋊#95	1	8	yes	—
254	C₄	C₂×C₄₃⋊#95	1	4	yes	—
255	C₄	C₂²×C₄×Dic₄₃	1	1	yes	characteristic
256	C₄	C₂²×C₂²⋊Dic₄₃	1	1	yes	characteristic
257	C₄	C₂²×Dic₄₃⋊C₄	1	2	yes	—
258	C₂	—	2	8	no	—
259	C₂	#19134312	1	8	yes	direct product factor
260	C₂	C₂²×C₄₃⋊#95	1	1	yes	characteristic
261	C₂	C₂×#14582896	1	4	yes	—
262	C₂	C₂×#14582937	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄	D₁₇₂
commutator	C₄×C₄₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂⁴×C₈×C₄₃	C₂
socle	C₂⁴×C₄₃	C₂×D₄
prime radical	C₂⁵×C₄₃	D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂⁴×C₈	D₄₃
hypocenter	C₄₃	C₂×#1735
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂⁴×C₄ ◁ C₂⁴×C₈

Complements

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

N	H ≅ G/N	type
2. #19134312	C₂	direct (N × H)
3. C₂×#14582662	C₂	semidirect
7. C₂×#13063284	C₄	semidirect
12. #14582662	C₂²	semidirect
15. C₂³×C₈×C₄₃	C₄	semidirect
21. #13063284	C₂×C₄	semidirect
43. C₂²×C₈×C₄₃	C₂×C₄	semidirect
132. C₂×C₄₃	#1735	semidirect
138. C₂³×C₈	Dic₄₃	semidirect
149. C₄₃	C₂×#1735	semidirect
164. C₂²×C₈	C₂×Dic₄₃	semidirect
259. C₂	#19134312	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×#13063284	2
#19134312	2
C₂×#14582662	2
C₂⁴×C₈×C₄₃	2
C₂×#1735	43

Subgroups — C2×#19134312 #25093997

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19134312 #25093997