Subgroups — C₂×#10592401 #11875021

Order 1152.

1152 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#64079	C₂	1	1	yes	maximal, characteristic
2	C₂×#64078	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃²×#97	C₂	1	1	yes	maximal, characteristic
4	C₂×#63645	C₂	1	2	yes	maximal
5	C₂×#63644	C₂	1	2	yes	maximal
6	#10592401	C₂	1	8	yes	maximal, direct product factor
7	C₂×#4702	—	3	4	no	maximal
8	C₂²×#634	—	2	1	no	—
9	C₂²×C₃²×C₈	C₂²	1	2	yes	—
10	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₃⋊Dic₃)	—	2	1	no	—
12	C₂×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
14	C₂×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
15	C₂×#3750	—	2	1	no	—
16	C₂×#3750	—	2	1	no	—
17	#64079	—	2	2	no	—
18	#64079	C₂²	1	4	yes	—
19	#64078	—	2	2	no	—
20	#64078	C₂²	1	4	yes	—
21	C₃²×#97	C₂²	1	4	yes	—
22	#63645	C₂²	1	8	yes	—
23	#63644	C₂²	1	8	yes	—
24	C₂×#870	—	3	4	no	—
25	C₂×#869	—	3	4	no	—
26	C₂×C₃×#97	D₃	1	4	yes	—
27	C₂×#818	—	3	8	no	—
28	C₂×#817	—	3	8	no	—
29	#4702	—	3	32	no	—
30	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
31	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
32	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
33	C₂²×C₃⋊Dic₃	—	2	2	no	—
34	C₂²×C₃⋊Dic₃	—	2	1	no	—
35	C₂²×C₃⋊Dic₃	—	2	1	no	—
36	C₂×#634	—	2	4	no	—
37	C₂×#634	—	4	4	no	—
38	C₂×C₃²×C₈	Q₈	1	8	yes	complemented
39	C₂×C₃²×C₈	C₂³	1	4	yes	—
40	C₃²×C₄²	D₄	1	2	yes	—
41	C₃²×C₄²	C₂³	1	2	yes	—
42	C₄⋊(C₃⋊Dic₃)	—	2	2	no	—
43	C₄⋊(C₃⋊Dic₃)	—	2	4	no	—
44	C₄⋊(C₃⋊Dic₃)	—	2	1	no	—
45	C₄⋊(C₃⋊Dic₃)	—	2	1	no	—
46	C₄⋊(C₃⋊Dic₃)	C₂³	1	4	yes	—
47	C₄⋊(C₃⋊Dic₃)	C₂³	1	2	yes	—
48	C₄⋊(C₃⋊Dic₃)	C₂³	1	2	yes	—
49	#3750	—	2	4	no	—
50	#3750	—	2	4	no	—
51	C₂×#501	—	9	1	no	Sylow
52	C₂²×Dic₆	—	6	4	no	—
53	C₂²×C₃×C₈	C₂×D₃	1	8	yes	—
54	C₂×C₃×C₄²	C₂×D₃	1	4	yes	—
55	C₂×C₄⋊Dic₃	—	3	8	no	—
56	C₂×C₄⋊Dic₃	—	3	4	no	—
57	C₂×C₄⋊Dic₃	—	3	4	no	—
58	C₂×C₄⋊Dic₃	—	6	4	no	—
59	C₂×Dic₃⋊C₄	—	6	4	no	—
60	C₂×Dic₃⋊C₄	—	6	4	no	—
61	#870	—	3	16	no	—
62	#870	—	6	8	no	—
63	#869	—	3	16	no	—
64	#869	—	6	8	no	—
65	C₃×#97	C₂×D₃	1	16	yes	—
66	#818	—	3	32	no	—
67	#817	—	3	32	no	—
68	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
69	C₂×C₃²×C₄	—	2	2	no	—
70	C₂×C₃²×C₄	—	2	2	no	—
71	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
72	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
73	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
74	C₂×C₃²×C₄	C₂×Q₈	1	4	yes	—
75	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
76	C₂×C₃⋊Dic₃	—	2	2	no	—
77	C₂×C₃⋊Dic₃	—	2	2	no	—
78	C₂×C₃⋊Dic₃	—	2	4	no	—
79	C₂×C₃⋊Dic₃	—	4	4	no	—
80	C₂×C₃⋊Dic₃	—	4	2	no	—
81	C₂×C₃⋊Dic₃	—	4	2	no	—
82	#634	—	4	8	no	—
83	C₃²×C₈	C₂×Q₈	1	8	yes	complemented
84	C₂×C₄⋊Q₈	—	9	1	no	—
85	C₂×#125	—	9	1	no	—
86	#501	—	9	8	no	—
87	C₂×#107	—	9	2	no	—
88	C₂×#106	—	9	2	no	—
89	C₂×#97	C₃⋊D₃	1	1	yes	characteristic
90	C₂²×C₃×C₄	D₁₂	1	4	yes	—
91	C₂²×C₃×C₄	D₁₂	1	4	yes	—
92	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
93	C₂²×Dic₃	—	6	4	no	—
94	C₂²×Dic₃	—	6	4	no	—
95	C₂²×Dic₃	—	6	8	no	—
96	C₂×Dic₆	—	6	16	no	—
97	C₂×Dic₆	—	12	16	no	—
98	C₂×C₃×C₈	Dic₆	1	32	yes	complemented
99	C₂×C₃×C₈	C₂²×D₃	1	16	yes	—
100	C₃×C₄²	D₁₂	1	8	yes	—
101	C₃×C₄²	C₂²×D₃	1	8	yes	—
102	C₄⋊Dic₃	—	3	8	no	—
103	C₄⋊Dic₃	—	3	16	no	—
104	C₄⋊Dic₃	—	3	8	no	—
105	C₄⋊Dic₃	—	6	16	no	—
106	C₄⋊Dic₃	—	6	8	no	—
107	C₄⋊Dic₃	—	6	4	no	—
108	C₄⋊Dic₃	—	6	4	no	—
109	Dic₃⋊C₄	—	6	16	no	—
110	Dic₃⋊C₄	—	6	16	no	—
111	C₂²×C₃²	C₄⋊Q₈	1	2	yes	—
112	C₂²×C₃²	AGL(1,ℤ/8)	1	2	yes	—
113	C₂²×C₃²	#137	1	2	yes	—
114	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
115	C₃²×C₄	—	2	2	no	—
116	C₃²×C₄	—	2	2	no	—
117	C₃²×C₄	C₄⋊Q₈	1	2	yes	—
118	C₃²×C₄	C₂²×Q₈	1	2	yes	—
119	C₃⋊Dic₃	—	4	4	no	—
120	C₃⋊Dic₃	—	4	2	no	—
121	C₃⋊Dic₃	—	4	2	no	—
122	C₂²×Q₈	—	18	1	no	—
123	C₂²×C₈	C₂×C₃⋊D₃	1	2	yes	—
124	C₄⋊Q₈	—	9	4	no	—
125	C₄⋊Q₈	—	18	2	no	—
126	#125	—	9	4	no	—
127	#125	—	18	2	no	—
128	C₂×C₄⋊C₄	—	9	1	no	—
129	C₂×C₄⋊C₄	—	9	1	no	—
130	C₂×C₄⋊C₄	—	9	2	no	—
131	C₂×C₄⋊C₄	—	18	1	no	—
132	C₂×C₄⋊C₄	—	18	1	no	—
133	C₂×C₄⋊C₄	—	18	1	no	—
134	C₂×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic
135	#107	—	9	8	no	—
136	#106	—	9	8	no	—
137	#97	C₂×C₃⋊D₃	1	4	yes	—
138	C₂³×C₃	C₂×D₁₂	1	4	yes	—
139	C₂×C₃×C₄	—	2	8	no	—
140	C₂×C₃×C₄	—	2	8	no	—
141	C₂×C₃×C₄	C₂×Dic₆	1	16	yes	—
142	C₂×C₃×C₄	C₂×D₁₂	1	8	yes	—
143	C₂×C₃×C₄	C₂×D₁₂	1	8	yes	—
144	C₂×C₃×C₄	C₂×D₁₂	1	4	yes	—
145	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
146	C₂×Dic₃	—	6	8	no	—
147	C₂×Dic₃	—	6	8	no	—
148	C₂×Dic₃	—	6	16	no	—
149	C₂×Dic₃	—	12	16	no	—
150	C₂×Dic₃	—	12	8	no	—
151	C₂×Dic₃	—	12	8	no	—
152	Dic₆	—	12	32	no	—
153	C₃×C₈	C₂×Dic₆	1	32	yes	complemented
154	C₂×C₃²	#501	1	4	yes	complemented
155	C₂×C₃²	C₂×C₄⋊Q₈	1	1	yes	characteristic
156	C₂×C₃²	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
157	C₂×C₃²	C₂×#137	1	1	yes	characteristic
158	C₂×Q₈	—	18	4	no	—
159	C₂×Q₈	—	36	4	no	—
160	C₂²×C₄	—	18	1	no	—
161	C₂²×C₄	—	18	1	no	—
162	C₂²×C₄	—	18	2	no	—
163	C₂²×C₄	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
164	C₂²×C₄	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
165	C₂²×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
166	C₂×C₈	#634	1	8	yes	complemented
167	C₂×C₈	C₂²×C₃⋊D₃	1	4	yes	—
168	C₄⋊C₄	—	9	2	no	—
169	C₄⋊C₄	—	9	4	no	—
170	C₄⋊C₄	—	9	2	no	—
171	C₄⋊C₄	—	18	1	no	—
172	C₄⋊C₄	—	18	1	no	—
173	C₄⋊C₄	—	18	2	no	—
174	C₄⋊C₄	—	18	4	no	—
175	C₄⋊C₄	—	18	4	no	—
176	C₄⋊C₄	—	18	4	no	—
177	C₄²	C₄⋊(C₃⋊D₃)	1	2	yes	—
178	C₄²	C₂²×C₃⋊D₃	1	2	yes	—
179	C₂²×C₃	#869	1	8	yes	—
180	C₂²×C₃	#908	1	8	yes	—
181	C₂²×C₃	#909	1	8	yes	—
182	C₂²×C₃	C₂²×D₁₂	1	4	yes	—
183	C₃×C₄	—	2	8	no	—
184	C₃×C₄	—	2	8	no	—
185	C₃×C₄	#869	1	8	yes	—
186	C₃×C₄	C₂²×Dic₆	1	8	yes	—
187	Dic₃	—	12	16	no	—
188	Dic₃	—	12	8	no	—
189	Dic₃	—	12	8	no	—
190	C₃²	C₂×#501	1	1	yes	characteristic, complemented, Sylow
191	C₂³	C₂×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
192	Q₈	—	36	8	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	18	2	no	—
196	C₂×C₄	—	18	2	no	—
197	C₂×C₄	—	18	4	no	—
198	C₂×C₄	—	36	4	no	—
199	C₂×C₄	—	36	2	no	—
200	C₂×C₄	—	36	2	no	—
201	C₂×C₄	C₂×#634	1	4	yes	—
202	C₂×C₄	C₂×C₄⋊(C₃⋊D₃)	1	2	yes	—
203	C₂×C₄	C₂×C₄⋊(C₃⋊D₃)	1	2	yes	—
204	C₂×C₄	C₂×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
205	C₂×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
206	C₈	C₂×#634	1	8	yes	complemented
207	C₂×C₃	#4702	1	16	yes	complemented
208	C₂×C₃	C₂×#869	1	4	yes	—
209	C₂×C₃	C₂×#908	1	4	yes	—
210	C₂×C₃	C₂×#909	1	4	yes	—
211	C₂²	#64078	1	2	yes	—
212	C₂²	#64117	1	2	yes	—
213	C₂²	#64118	1	2	yes	—
214	C₂²	C₂²×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
215	C₄	—	2	2	no	—
216	C₄	—	2	2	no	—
217	C₄	—	36	4	no	—
218	C₄	—	36	2	no	—
219	C₄	—	36	2	no	—
220	C₄	#64078	1	2	yes	—
221	C₄	C₂²×#634	1	2	yes	—
222	C₃	C₂×#4702	1	4	yes	complemented
223	C₂	#10592401	1	4	yes	direct product factor
224	C₂	C₂×#64078	1	1	yes	characteristic
225	C₂	C₂×#64117	1	1	yes	characteristic
226	C₂	C₂×#64118	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₄⋊(C₃⋊D₃)
commutator, cosocle	C₂×C₃²×C₄	C₂⁴
Frattini	C₂×C₄	C₂³×C₃⋊D₃
Fitting	C₂×C₃²×#97	C₂
socle, prime radical	C₂³×C₃²	C₂×D₄
hypercenter	C₂×#97	C₃⋊D₃
hypocenter	C₃²	C₂×#501
LCS	G ▷ C₂×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
6. #10592401	C₂	direct (N × H)
38. C₂×C₃²×C₈	Q₈	semidirect
83. C₃²×C₈	C₂×Q₈	semidirect
98. C₂×C₃×C₈	Dic₆	semidirect
153. C₃×C₈	C₂×Dic₆	semidirect
154. C₂×C₃²	#501	semidirect
166. C₂×C₈	#634	semidirect
190. C₃²	C₂×#501	semidirect
206. C₈	C₂×#634	semidirect
207. C₂×C₃	#4702	semidirect
222. C₃	C₂×#4702	semidirect
223. C₂	#10592401	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×#64079	2
C₂×#64078	2
C₂×C₃²×#97	2
C₂×#63645	2
C₂×#63644	2
#10592401	2
C₂×#4702	3

Subgroups — C2×#10592401 #11875021

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10592401 #11875021