Subgroups — #11861386

Order 1152.

1044 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10595941	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃²×#97	C₂	1	1	yes	maximal, characteristic
3	#10592801	C₂	1	2	yes	maximal
4	#10592800	C₂	1	2	yes	maximal
5	#10592623	C₂	1	1	yes	maximal, characteristic
6	#10592400	C₂	1	8	yes	maximal, complemented
7	#78480	—	3	4	no	maximal
8	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
9	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
10	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
11	#64135	C₂²	1	2	yes	—
12	#64133	C₄	1	4	yes	—
13	C₂×#3748	C₂²	1	2	yes	—
14	#64079	C₄	1	2	yes	—
15	#64078	C₄	1	2	yes	—
16	C₄×#634	C₂²	1	4	yes	—
17	C₃²×#97	C₂²	1	4	yes	—
18	#63642	C₂²	1	4	yes	—
19	#63641	C₂²	1	8	yes	—
20	C₈×C₃⋊Dic₃	C₂²	1	4	yes	—
21	C₄⋊(C₃⋊(C₃⋊C₈))	C₂²	1	4	yes	—
22	#5470	—	3	4	no	—
23	C₂×C₃×#97	D₃	1	4	yes	—
24	#5102	—	3	8	no	—
25	#5101	—	3	8	no	—
26	#4924	—	3	4	no	—
27	#4701	—	3	32	no	—
28	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
29	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
30	C₂×#634	C₂×C₄	1	4	yes	—
31	C₂×C₃²×C₈	—	2	2	no	—
32	C₂×C₃²×C₈	Q₈	1	4	yes	complemented
33	C₂×C₃²×C₈	C₂³	1	2	yes	—
34	C₂×C₃²×C₈	C₂³	1	2	yes	—
35	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
36	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
37	C₃²×C₄²	C₂³	1	2	yes	—
38	#3757	C₂×C₄	1	4	yes	—
39	C₄⋊(C₃⋊Dic₃)	C₂×C₄	1	4	yes	—
40	C₄⋊(C₃⋊Dic₃)	C₂×C₄	1	4	yes	—
41	#3750	C₂×C₄	1	8	yes	—
42	C₄×C₃⋊Dic₃	C₂³	1	4	yes	—
43	#3748	—	2	4	no	—
44	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	4	yes	—
45	#2961	—	9	1	no	Sylow
46	C₂²×C₃×C₈	C₂×D₃	1	4	yes	—
47	C₂²×C₃×C₈	C₂×D₃	1	4	yes	—
48	C₂×C₃×C₄²	C₂×D₃	1	4	yes	—
49	#926	—	3	8	no	—
50	#924	—	3	16	no	—
51	C₂×#208	—	3	8	no	—
52	#870	—	3	8	no	—
53	#869	—	3	8	no	—
54	C₄×Dic₆	—	3	16	no	—
55	C₃×#97	C₂×D₃	1	16	yes	—
56	#815	—	3	16	no	—
57	Dic₃⋊C₈	—	3	32	no	—
58	C₈×Dic₃	—	3	16	no	—
59	C₄⋊(C₃⋊C₈)	—	3	16	no	—
60	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
61	C₂×C₃²×C₄	—	4	2	no	—
62	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
63	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
64	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
65	C₂×C₃²×C₄	C₂×Q₈	1	2	yes	—
66	C₂×C₃²×C₄	#41	1	2	yes	—
67	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
68	C₂×C₃⋊Dic₃	C₂²×C₄	1	8	yes	—
69	#634	—	4	4	no	—
70	C₃²×C₈	—	2	2	no	—
71	C₃²×C₈	C₂×Q₈	1	4	yes	—
72	C₃⋊(C₃⋊C₈)	—	2	4	no	—
73	#533	—	9	1	no	—
74	#446	—	9	8	no	—
75	#424	—	9	2	no	—
76	#423	—	9	1	no	—
77	#405	—	9	2	no	—
78	C₂×#97	C₃⋊D₃	1	1	yes	characteristic
79	C₂²×C₃×C₄	C₄×D₃	1	8	yes	—
80	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
81	C₂×Dic₆	—	3	16	no	—
82	C₂×C₃×C₈	—	2	8	no	—
83	C₂×C₃×C₈	Dic₆	1	16	yes	complemented
84	C₂×C₃×C₈	C₂²×D₃	1	8	yes	—
85	C₂×C₃×C₈	C₂²×D₃	1	8	yes	—
86	C₃×C₄²	C₄×D₃	1	4	yes	—
87	C₃×C₄²	C₄×D₃	1	4	yes	—
88	C₃×C₄²	C₂²×D₃	1	8	yes	—
89	#217	—	3	16	no	—
90	C₄⋊Dic₃	—	3	16	no	—
91	C₄⋊Dic₃	—	3	16	no	—
92	Dic₃⋊C₄	—	3	32	no	—
93	C₄×Dic₃	—	3	16	no	—
94	#208	—	6	16	no	—
95	C₂×C₃⋊C₈	—	3	16	no	—
96	C₂²×C₃²	—	2	2	no	—
97	C₂²×C₃²	C₄×Q₈	1	2	yes	—
98	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
99	C₃²×C₄	—	2	2	no	—
100	C₃²×C₄	—	2	2	no	—
101	C₃²×C₄	C₄×Q₈	1	2	yes	—
102	C₃²×C₄	C₂²×Q₈	1	1	yes	characteristic
103	C₃²×C₄	C₂×#41	1	1	yes	characteristic
104	C₃⋊Dic₃	—	2	8	no	—
105	C₂×M₁₆	—	9	2	no	—
106	C₂²×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
107	C₂²×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
108	C₄⋊Q₈	—	9	2	no	—
109	#125	—	9	2	no	—
110	C₂²⋊Q₈	—	9	4	no	—
111	C₄×Q₈	—	9	4	no	—
112	#117	—	9	2	no	—
113	C₂×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic
114	C₄⋊C₈	—	9	8	no	—
115	C₄⋊C₈	—	9	4	no	—
116	#97	—	9	4	no	—
117	#97	C₂×C₃⋊D₃	1	4	yes	—
118	C₄×C₈	—	9	4	no	—
119	C₂³×C₃	C₂×C₄×D₃	1	4	yes	—
120	C₂×C₃×C₄	—	4	8	no	—
121	C₂×C₃×C₄	C₂×Dic₆	1	8	yes	—
122	C₂×C₃×C₄	C₂×C₄×D₃	1	8	yes	—
123	C₂×C₃×C₄	C₂×C₄×D₃	1	8	yes	—
124	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
125	C₂×C₃×C₄	#235	1	8	yes	—
126	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
127	C₂×Dic₃	—	3	32	no	—
128	Dic₆	—	12	16	no	—
129	C₃×C₈	—	2	8	no	—
130	C₃×C₈	C₂×Dic₆	1	16	yes	—
131	C₃⋊C₈	—	6	16	no	—
132	C₂×C₃²	—	2	2	no	—
133	C₂×C₃²	C₂×C₄×Q₈	1	1	yes	characteristic
134	C₂×C₃²	#568	1	2	yes	—
135	C₂×Q₈	—	9	4	no	—
136	C₂²×C₄	C₄×C₃⋊D₃	1	2	yes	—
137	C₂²×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
138	M₁₆	—	18	4	no	—
139	C₂×C₈	—	2	2	no	—
140	C₂×C₈	—	9	4	no	—
141	C₂×C₈	#634	1	4	yes	complemented
142	C₂×C₈	C₂²×C₃⋊D₃	1	2	yes	—
143	C₂×C₈	C₂²×C₃⋊D₃	1	2	yes	—
144	C₄⋊C₄	—	9	4	no	—
145	C₄⋊C₄	—	9	8	no	—
146	C₄⋊C₄	—	9	4	no	—
147	C₂²⋊C₄	—	9	4	no	—
148	C₄²	—	9	4	no	—
149	C₄²	C₄×C₃⋊D₃	1	1	yes	characteristic
150	C₄²	C₄×C₃⋊D₃	1	1	yes	characteristic
151	C₄²	C₂²×C₃⋊D₃	1	2	yes	—
152	C₂²×C₃	—	2	8	no	—
153	C₂²×C₃	C₄×Dic₆	1	8	yes	—
154	C₂²×C₃	C₂²×C₄×D₃	1	4	yes	—
155	C₃×C₄	—	2	8	no	—
156	C₃×C₄	—	2	8	no	—
157	C₃×C₄	C₄×Dic₆	1	8	yes	—
158	C₃×C₄	C₂²×Dic₆	1	4	yes	—
159	C₃×C₄	C₂×#235	1	4	yes	—
160	Dic₃	—	6	32	no	—
161	C₃²	#2961	1	1	yes	characteristic, complemented, Sylow
162	C₂³	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
163	Q₈	—	36	4	no	—
164	C₂×C₄	—	4	2	no	—
165	C₂×C₄	—	9	8	no	—
166	C₂×C₄	C₂×#634	1	2	yes	—
167	C₂×C₄	C₂×C₄×C₃⋊D₃	1	2	yes	—
168	C₂×C₄	C₂×C₄×C₃⋊D₃	1	2	yes	—
169	C₂×C₄	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
170	C₂×C₄	#3828	1	2	yes	—
171	C₂×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
172	C₈	—	2	2	no	—
173	C₈	—	18	4	no	—
174	C₈	C₂×#634	1	4	yes	—
175	C₂×C₃	—	2	8	no	—
176	C₂×C₃	C₂×C₄×Dic₆	1	4	yes	—
177	C₂×C₃	#5745	1	8	yes	—
178	C₂²	—	2	2	no	—
179	C₂²	C₄×#634	1	2	yes	—
180	C₂²	C₂²×C₄×C₃⋊D₃	1	1	yes	characteristic
181	C₄	—	2	2	no	—
182	C₄	—	2	2	no	—
183	C₄	—	18	8	no	—
184	C₄	C₄×#634	1	2	yes	—
185	C₄	C₂²×#634	1	1	yes	characteristic
186	C₄	C₂×#3828	1	1	yes	characteristic
187	C₃	#78480	1	4	yes	complemented
188	C₂	—	2	2	no	—
189	C₂	C₂×C₄×#634	1	1	yes	characteristic
190	C₂	#10596216	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×C₃⋊D₃
commutator, socle	C₂²×C₃²	C₂³×C₄
Fitting	C₂×C₃²×#97	C₂
prime radical	C₂³×C₃²	C₂²×C₄
cosocle	C₂×C₃²×C₄	C₂⁴
hypercenter	C₂×#97	C₃⋊D₃
hypocenter	C₃²	#2961
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
6. #10592400	C₂	semidirect
32. C₂×C₃²×C₈	Q₈	semidirect
83. C₂×C₃×C₈	Dic₆	semidirect
141. C₂×C₈	#634	semidirect
161. C₃²	#2961	semidirect
187. C₃	#78480	semidirect

Maximal subgroups

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

subgroup	index
#10595941	2
C₂×C₃²×#97	2
#10592801	2
#10592800	2
#10592623	2
#10592400	2
#78480	3