Subgroups — C₂×#15689794 #20256868

Order 6016.

1736 conjugacy classes of subgroups.

The subgroup lattice has 248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10625350	C₂	1	2	yes	maximal, complemented
2	#15689794	C₂	1	16	yes	maximal, direct product factor
3	C₂×#13094021	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#13094020	C₂	1	2	yes	maximal, complemented
5	C₂×#13093998	C₂	1	2	yes	maximal, complemented
6	C₂×#13093997	C₂	1	4	yes	maximal, complemented
7	C₂×C₄×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#13093986	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#10625350	—	2	16	no	—
11	C₂×#10625350	C₂²	1	16	yes	complemented
12	C₂²×Dic₉₄	C₂²	1	1	yes	characteristic
13	C₂²×D₁₈₈	C₂²	1	2	yes	—
14	C₂²×D₁₈₈	C₂²	1	2	yes	—
15	C₂²×D₁₈₈	C₂²	1	2	yes	—
16	C₂²×C₂²⋊D₄₇	C₂²	1	4	yes	—
17	C₂²×C₂²⋊D₄₇	C₂²	1	4	yes	—
18	C₂²×C₄×D₄₇	C₂²	1	4	yes	—
19	#13094021	C₂²	1	8	yes	complemented
20	#13094020	C₂²	1	16	yes	complemented
21	#13093998	C₂²	1	16	yes	complemented
22	#13093997	C₂²	1	32	yes	complemented
23	C₄×Dic₉₄	C₂²	1	8	yes	complemented
24	#13093986	C₂²	1	16	yes	complemented
25	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
26	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	—
27	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	4	yes	—
28	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
29	C₂²×D₄×C₄₇	C₂²	1	1	yes	characteristic
30	C₂³×C₄×C₄₇	C₂²	1	2	yes	—
31	C₄×D₄×C₄₇	C₂²	1	8	yes	complemented
32	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
34	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
35	C₂⁴×C₄₇	C₂³	1	2	yes	—
36	C₂³×D₄₇	C₂³	1	4	yes	—
37	C₂×D₄×C₄₇	—	2	4	no	—
38	C₂×D₄×C₄₇	C₂³	1	4	yes	—
39	C₂²×C₄×C₄₇	—	2	8	no	—
40	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
41	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
42	C₂²×C₄×C₄₇	C₂³	1	8	yes	—
43	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
44	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
45	C₂×C₂²⋊D₄₇	—	2	16	no	—
46	C₂×C₂²⋊D₄₇	—	4	8	no	—
47	C₂×C₂²⋊D₄₇	C₂³	1	16	yes	—
48	C₂×C₂²⋊D₄₇	C₂³	1	16	yes	—
49	C₂²×Dic₄₇	C₂³	1	2	yes	—
50	C₂²×Dic₄₇	C₂³	1	2	yes	—
51	#10625350	—	2	64	no	—
52	C₂×D₁₈₈	—	2	8	no	—
53	C₂×D₁₈₈	—	2	8	no	—
54	C₂×D₁₈₈	—	4	4	no	—
55	C₂×D₁₈₈	C₂³	1	8	yes	—
56	C₂×D₁₈₈	C₂³	1	8	yes	—
57	C₂×D₁₈₈	C₂³	1	8	yes	—
58	C₂×C₄×D₄₇	—	2	16	no	—
59	C₂×C₄×D₄₇	C₂³	1	16	yes	—
60	C₂×Dic₉₄	D₄	1	8	yes	complemented
61	C₂×Dic₉₄	C₂³	1	4	yes	—
62	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
63	C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
64	C₄²×C₄₇	C₂³	1	4	yes	—
65	(C₂×D₄₇)⋊C₄	C₂³	1	16	yes	—
66	C₄⋊Dic₄₇	C₂³	1	4	yes	—
67	Dic₄₇⋊C₄	C₂³	1	8	yes	—
68	C₄×Dic₄₇	C₂³	1	8	yes	—
69	C₂³×C₄₇	—	2	4	no	—
70	C₂³×C₄₇	—	2	4	no	—
71	C₂³×C₄₇	—	2	4	no	—
72	C₂³×C₄₇	C₂⁴	1	4	yes	—
73	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
74	C₂²×D₄₇	—	2	8	no	—
75	C₂²×D₄₇	—	2	8	no	—
76	C₂²×D₄₇	—	2	8	no	—
77	C₂²×D₄₇	C₂⁴	1	8	yes	—
78	D₄×C₄₇	—	2	8	no	—
79	C₂×C₄×C₄₇	—	2	4	no	—
80	C₂×C₄×C₄₇	—	2	2	no	—
81	C₂×C₄×C₄₇	—	2	16	no	—
82	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
83	C₂×C₄×C₄₇	#41	1	4	yes	complemented
84	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
85	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
86	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
87	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
88	C₂²⋊D₄₇	—	2	32	no	—
89	C₂²⋊D₄₇	—	4	16	no	—
90	C₂×Dic₄₇	—	2	4	no	—
91	C₂×Dic₄₇	C₂×D₄	1	8	yes	—
92	C₂×Dic₄₇	C₂⁴	1	4	yes	—
93	C₂×Dic₄₇	C₂⁴	1	4	yes	—
94	D₁₈₈	—	2	16	no	—
95	D₁₈₈	—	2	16	no	—
96	D₁₈₈	—	4	8	no	—
97	C₄×D₄₇	—	2	32	no	—
98	Dic₉₄	C₂×D₄	1	16	yes	complemented
99	C₂²×C₄₇	—	2	4	no	—
100	C₂²×C₄₇	—	2	4	no	—
101	C₂²×C₄₇	—	2	4	no	—
102	C₂²×C₄₇	—	4	8	no	—
103	C₂²×C₄₇	C₂²×D₄	1	2	yes	—
104	C₂²×C₄₇	C₂×#41	1	2	yes	—
105	C₂²×C₄₇	H(5,𝔽₂)	1	2	yes	—
106	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
107	C₂×D₄₇	—	2	8	no	—
108	C₂×D₄₇	—	2	8	no	—
109	C₂×D₄₇	—	2	8	no	—
110	C₂×D₄₇	—	4	16	no	—
111	C₄×C₄₇	—	2	4	no	—
112	C₄×C₄₇	—	2	2	no	—
113	C₄×C₄₇	C₂²×D₄	1	4	yes	—
114	C₄×C₄₇	C₂×#41	1	4	yes	complemented
115	Dic₄₇	—	2	4	no	—
116	Dic₄₇	C₂²×D₄	1	8	yes	—
117	C₂×#550	—	47	1	no	maximal, Sylow
118	C₂×C₄₇	—	4	4	no	—
119	C₂×C₄₇	#550	1	4	yes	complemented
120	C₂×C₄₇	C₂³×D₄	1	1	yes	characteristic
121	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
122	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
123	D₄₇	—	4	8	no	—
124	C₂²×#41	—	47	2	no	—
125	#550	—	47	16	no	—
126	C₂×#127	—	47	2	no	—
127	C₂×#127	—	47	1	no	—
128	C₂×#121	—	47	2	no	—
129	C₂×#121	—	47	4	no	—
130	C₂×C₄×Q₈	—	47	1	no	—
131	C₂×C₄×D₄	—	47	2	no	—
132	C₂×C₄×D₄	D₄₇	1	1	yes	characteristic, complemented
133	C₄₇	C₂×#550	1	1	yes	characteristic, complemented, Sylow
134	C₂×#41	—	47	16	no	—
135	C₂×#41	—	94	16	no	—
136	C₂²×Q₈	—	47	1	no	—
137	C₂²×D₄	—	47	4	no	—
138	C₂²×D₄	—	47	4	no	—
139	C₂²×D₄	—	47	2	no	—
140	C₂²×D₄	—	47	2	no	—
141	C₂²×D₄	—	47	2	no	—
142	C₂²×D₄	C₂×D₄₇	1	1	yes	characteristic
143	C₂³×C₄	—	47	4	no	—
144	C₂³×C₄	C₂×D₄₇	1	2	yes	—
145	#127	—	47	16	no	—
146	#127	—	47	8	no	—
147	#121	—	47	16	no	—
148	#121	—	47	32	no	—
149	C₄×Q₈	—	47	8	no	—
150	C₄×D₄	—	47	16	no	—
151	C₄×D₄	C₂×D₄₇	1	8	yes	complemented
152	C₂×C₄⋊C₄	—	47	2	no	—
153	C₂×C₄⋊C₄	—	47	1	no	—
154	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
155	C₂×C₂²⋊C₄	—	47	4	no	—
156	C₂×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
157	C₂×C₄²	—	47	2	no	—
158	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
159	C₂⁴	—	47	4	no	—
160	C₂⁴	C₂²×D₄₇	1	2	yes	—
161	#41	—	94	64	no	—
162	C₂×Q₈	—	47	8	no	—
163	C₂×Q₈	—	47	4	no	—
164	C₂×D₄	—	2	4	no	—
165	C₂×D₄	—	47	16	no	—
166	C₂×D₄	—	47	16	no	—
167	C₂×D₄	—	47	8	no	—
168	C₂×D₄	—	47	8	no	—
169	C₂×D₄	—	47	8	no	—
170	C₂×D₄	—	94	16	no	—
171	C₂×D₄	—	94	8	no	—
172	C₂×D₄	—	94	8	no	—
173	C₂×D₄	—	188	4	no	—
174	C₂×D₄	—	188	8	no	—
175	C₂×D₄	C₂²×D₄₇	1	4	yes	—
176	C₂²×C₄	—	2	8	no	—
177	C₂²×C₄	—	47	2	no	—
178	C₂²×C₄	—	47	2	no	—
179	C₂²×C₄	—	47	16	no	—
180	C₂²×C₄	—	94	16	no	—
181	C₂²×C₄	C₂²×D₄₇	1	8	yes	—
182	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
183	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
184	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
185	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
186	C₄⋊C₄	—	47	8	no	—
187	C₄⋊C₄	—	47	4	no	—
188	C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
189	C₂²⋊C₄	—	47	16	no	—
190	C₂²⋊C₄	C₂²×D₄₇	1	8	yes	—
191	C₄²	—	47	8	no	—
192	C₄²	C₂²×D₄₇	1	4	yes	—
193	C₂³	—	2	4	no	—
194	C₂³	—	2	4	no	—
195	C₂³	—	2	4	no	—
196	C₂³	—	47	8	no	—
197	C₂³	—	94	8	no	—
198	C₂³	—	94	8	no	—
199	C₂³	—	94	8	no	—
200	C₂³	C₂³×D₄₇	1	4	yes	—
201	C₂³	C₂³×D₄₇	1	1	yes	characteristic
202	Q₈	—	47	16	no	—
203	D₄	—	2	8	no	—
204	D₄	—	94	32	no	—
205	D₄	—	94	16	no	—
206	D₄	—	94	16	no	—
207	D₄	—	188	8	no	—
208	D₄	—	188	16	no	—
209	C₂×C₄	—	2	4	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	2	16	no	—
212	C₂×C₄	—	47	8	no	—
213	C₂×C₄	—	47	4	no	—
214	C₂×C₄	—	47	4	no	—
215	C₂×C₄	—	94	32	no	—
216	C₂×C₄	—	94	4	no	—
217	C₂×C₄	#10625350	1	4	yes	complemented
218	C₂×C₄	D₄×D₄₇	1	4	yes	—
219	C₂×C₄	C₂³×D₄₇	1	2	yes	—
220	C₂×C₄	C₂³×D₄₇	1	4	yes	—
221	C₂×C₄	C₂³×D₄₇	1	2	yes	—
222	C₂×C₄	C₂³×D₄₇	1	2	yes	—
223	C₂²	—	2	4	no	—
224	C₂²	—	2	4	no	—
225	C₂²	—	2	4	no	—
226	C₂²	—	4	8	no	—
227	C₂²	—	94	8	no	—
228	C₂²	—	94	8	no	—
229	C₂²	—	94	8	no	—
230	C₂²	—	188	16	no	—
231	C₂²	C₂×D₄×D₄₇	1	2	yes	—
232	C₂²	C₂×#10625350	1	2	yes	—
233	C₂²	#13094070	1	2	yes	—
234	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
235	C₄	—	2	4	no	—
236	C₄	—	2	2	no	—
237	C₄	—	47	8	no	—
238	C₄	—	94	4	no	—
239	C₄	C₂×D₄×D₄₇	1	4	yes	—
240	C₄	C₂×#10625350	1	4	yes	complemented
241	C₂	—	4	4	no	—
242	C₂	—	188	8	no	—
243	C₂	#15689794	1	4	yes	direct product factor
244	C₂	C₂²×D₄×D₄₇	1	1	yes	characteristic
245	C₂	C₂²×#10625350	1	1	yes	characteristic
246	C₂	C₂×#13094070	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂⁵
Frattini	C₂²	C₂⁴×D₄₇
Fitting	C₂×C₄×D₄×C₄₇	C₂
socle	C₂³×C₄₇	C₂⁴
hypercenter	C₂×C₄×D₄	D₄₇
hypocenter	C₄₇	C₂×#550
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#10625350	C₂	semidirect
2. #15689794	C₂	direct (N × H)
3. C₂×#13094021	C₂	semidirect
4. C₂×#13094020	C₂	semidirect
5. C₂×#13093998	C₂	semidirect
6. C₂×#13093997	C₂	semidirect
7. C₂×C₄×Dic₉₄	C₂	semidirect
8. C₂×#13093986	C₂	semidirect
9. C₂×C₄×D₄×C₄₇	C₂	semidirect
11. C₂×#10625350	C₂²	semidirect
19. #13094021	C₂²	semidirect
20. #13094020	C₂²	semidirect
21. #13093998	C₂²	semidirect
22. #13093997	C₂²	semidirect
23. C₄×Dic₉₄	C₂²	semidirect
24. #13093986	C₂²	semidirect
31. C₄×D₄×C₄₇	C₂²	semidirect
60. C₂×Dic₉₄	D₄	semidirect
83. C₂×C₄×C₄₇	#41	semidirect
98. Dic₉₄	C₂×D₄	semidirect
114. C₄×C₄₇	C₂×#41	semidirect
119. C₂×C₄₇	#550	semidirect
132. C₂×C₄×D₄	D₄₇	semidirect
133. C₄₇	C₂×#550	semidirect
151. C₄×D₄	C₂×D₄₇	semidirect
217. C₂×C₄	#10625350	semidirect
240. C₄	C₂×#10625350	semidirect
243. C₂	#15689794	direct (N × H)

Subgroups — C2×#15689794 #20256868

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15689794 #20256868