Subgroups — #11791651

Order 1152.

390 conjugacy classes of subgroups.

The subgroup lattice has 225 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63432	C₂	1	1	yes	maximal, characteristic
2	C₄×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊(C₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
4	#10588206	C₂	1	2	yes	maximal
5	#10588206	C₂	1	2	yes	maximal
6	#69491	—	3	1	no	maximal
7	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
8	C₂×C₄²×C₉	—	2	1	no	—
9	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
12	C₂×Dic₉⋊C₄	—	2	1	no	—
13	C₂×Dic₉⋊C₄	—	2	1	no	—
14	C₂²×C₉⋊C₈	C₂²	1	2	yes	—
15	#63432	—	2	2	no	—
16	#63432	C₄	1	4	yes	complemented
17	C₉×#95	—	2	1	no	—
18	C₄⋊(C₉⋊C₈)	—	2	2	no	—
19	C₂×#870	—	3	1	no	—
20	C₃×C₄×C₄⋊C₄	D₃	1	1	yes	characteristic
21	C₂×C₄⋊(C₃⋊C₈)	—	3	1	no	—
22	#4529	—	3	2	no	—
23	#4529	—	3	2	no	—
24	C₂²×C₄×C₉	—	2	2	no	—
25	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
26	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
27	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
28	C₂²×Dic₉	—	2	1	no	—
29	C₂²×Dic₉	—	2	1	no	—
30	C₉×C₄⋊C₄	—	2	2	no	—
31	C₉×C₄⋊C₄	Q₈	1	4	yes	—
32	C₄²×C₉	—	4	2	no	—
33	C₄²×C₉	C₂×C₄	1	2	yes	—
34	C₄²×C₉	D₄	1	2	yes	—
35	C₄⋊Dic₉	—	2	1	no	—
36	C₄⋊Dic₉	—	2	1	no	—
37	C₄⋊Dic₉	C₂×C₄	1	2	yes	—
38	C₄⋊Dic₉	C₂×C₄	1	2	yes	—
39	Dic₉⋊C₄	—	2	4	no	—
40	Dic₉⋊C₄	—	2	4	no	—
41	C₂×C₉⋊C₈	—	2	2	no	—
42	C₂×C₉⋊C₈	—	2	4	no	—
43	#1989	—	9	1	no	Sylow
44	C₂×C₃×C₄⋊C₄	C₂×D₃	1	2	yes	—
45	C₂×C₃×C₄²	—	2	1	no	—
46	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
47	C₂×C₄⋊Dic₃	—	3	1	no	—
48	C₂×C₄⋊Dic₃	—	3	1	no	—
49	C₂×Dic₃⋊C₄	—	6	1	no	—
50	C₂×Dic₃⋊C₄	—	6	1	no	—
51	C₂²×C₃⋊C₈	—	3	2	no	—
52	#870	—	3	4	no	—
53	#870	—	6	2	no	—
54	C₃×#95	—	2	1	no	—
55	C₄⋊(C₃⋊C₈)	—	6	2	no	—
56	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
57	C₂×C₄×C₉	—	2	2	no	—
58	C₂×C₄×C₉	—	2	1	no	—
59	C₂×C₄×C₉	—	2	1	no	—
60	C₂×C₄×C₉	—	2	4	no	—
61	C₂×C₄×C₉	—	4	2	no	—
62	C₂×C₄×C₉	—	4	2	no	—
63	C₂×C₄×C₉	C₂²⋊C₄	1	2	yes	—
64	C₂×C₄×C₉	C₂²⋊C₄	1	2	yes	—
65	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
66	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
67	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
68	C₂×C₄×C₉	#41	1	2	yes	—
69	C₂×Dic₉	—	2	2	no	—
70	C₂×Dic₉	—	2	2	no	—
71	C₂×Dic₉	—	4	2	no	—
72	C₂×Dic₉	—	4	1	no	—
73	C₂×Dic₉	—	4	1	no	—
74	C₉⋊C₈	—	4	2	no	—
75	C₂×#125	—	9	1	no	—
76	C₂×C₄⋊C₈	—	9	1	no	—
77	C₄×C₄⋊C₄	D₉	1	1	yes	characteristic
78	#340	—	9	2	no	—
79	#340	—	9	2	no	—
80	C₂²×C₃×C₄	—	2	2	no	—
81	C₂²×C₃×C₄	#67	1	1	yes	characteristic
82	C₂²×C₃×C₄	#67	1	1	yes	characteristic
83	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
84	C₂²×Dic₃	—	6	1	no	—
85	C₂²×Dic₃	—	6	1	no	—
86	C₃×C₄⋊C₄	—	2	2	no	—
87	C₃×C₄⋊C₄	Dic₆	1	4	yes	—
88	C₃×C₄²	—	4	2	no	—
89	C₃×C₄²	C₄×D₃	1	2	yes	—
90	C₃×C₄²	D₁₂	1	2	yes	—
91	C₄⋊Dic₃	—	3	2	no	—
92	C₄⋊Dic₃	—	3	2	no	—
93	C₄⋊Dic₃	—	6	1	no	—
94	C₄⋊Dic₃	—	6	1	no	—
95	Dic₃⋊C₄	—	6	4	no	—
96	Dic₃⋊C₄	—	6	4	no	—
97	C₂×C₃⋊C₈	—	6	2	no	—
98	C₂×C₃⋊C₈	—	6	4	no	—
99	C₂²×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
100	C₂²×C₉	C₂²⋊Q₈	1	2	yes	—
101	C₂²×C₉	#135	1	2	yes	—
102	C₂²×C₉	AGL(1,ℤ/8)	1	1	yes	characteristic
103	C₂²×C₉	#137	1	1	yes	characteristic
104	C₄×C₉	—	2	2	no	—
105	C₄×C₉	—	2	2	no	—
106	C₄×C₉	—	4	4	no	—
107	C₄×C₉	C₄×Q₈	1	2	yes	—
108	C₄×C₉	#124	1	1	yes	characteristic
109	C₄×C₉	C₄⋊Q₈	1	1	yes	characteristic
110	Dic₉	—	4	2	no	—
111	Dic₉	—	4	2	no	—
112	C₂²×C₈	—	9	2	no	—
113	#125	—	9	4	no	—
114	#125	—	18	2	no	—
115	C₂×C₄⋊C₄	—	9	1	no	—
116	C₂×C₄⋊C₄	—	9	1	no	—
117	C₂×C₄⋊C₄	—	18	1	no	—
118	C₂×C₄⋊C₄	—	18	1	no	—
119	C₂×C₄⋊C₄	C₂×D₉	1	2	yes	—
120	C₂×C₄²	—	2	1	no	—
121	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
122	C₄⋊C₈	—	18	2	no	—
123	#95	—	2	1	no	—
124	C₂³×C₃	C₂×#67	1	1	yes	characteristic
125	C₂×C₃×C₄	—	2	1	no	—
126	C₂×C₃×C₄	—	2	1	no	—
127	C₂×C₃×C₄	—	2	2	no	—
128	C₂×C₃×C₄	—	2	4	no	—
129	C₂×C₃×C₄	—	4	2	no	—
130	C₂×C₃×C₄	—	4	2	no	—
131	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	2	yes	—
132	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	2	yes	—
133	C₂×C₃×C₄	C₂×Dic₆	1	2	yes	—
134	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
135	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
136	C₂×C₃×C₄	#235	1	2	yes	—
137	C₂×Dic₃	—	6	2	no	—
138	C₂×Dic₃	—	6	2	no	—
139	C₂×Dic₃	—	12	1	no	—
140	C₂×Dic₃	—	12	1	no	—
141	C₂×Dic₃	—	12	2	no	—
142	C₃⋊C₈	—	12	2	no	—
143	C₂×C₉	#391	1	1	yes	characteristic
144	C₂×C₉	#416	1	1	yes	characteristic
145	C₂×C₉	#417	1	1	yes	characteristic
146	C₂×C₉	#478	1	2	yes	—
147	C₂×C₉	#479	1	2	yes	—
148	C₂²×C₄	—	2	2	no	—
149	C₂²×C₄	—	18	1	no	—
150	C₂²×C₄	—	18	1	no	—
151	C₂²×C₄	#611	1	1	yes	characteristic
152	C₂²×C₄	#611	1	1	yes	characteristic
153	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
154	C₂×C₈	—	18	2	no	—
155	C₂×C₈	—	18	4	no	—
156	C₄⋊C₄	—	2	2	no	—
157	C₄⋊C₄	—	9	2	no	—
158	C₄⋊C₄	—	9	2	no	—
159	C₄⋊C₄	—	18	4	no	—
160	C₄⋊C₄	—	18	4	no	—
161	C₄⋊C₄	—	18	1	no	—
162	C₄⋊C₄	—	18	1	no	—
163	C₄⋊C₄	Dic₁₈	1	4	yes	—
164	C₄²	—	4	2	no	—
165	C₄²	C₄×D₉	1	2	yes	—
166	C₄²	D₃₆	1	2	yes	—
167	C₂²×C₃	#924	1	2	yes	—
168	C₂²×C₃	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
169	C₂²×C₃	#932	1	1	yes	characteristic
170	C₂²×C₃	#942	1	1	yes	characteristic
171	C₂²×C₃	#950	1	2	yes	—
172	C₃×C₄	—	2	2	no	—
173	C₃×C₄	—	2	2	no	—
174	C₃×C₄	—	4	4	no	—
175	C₃×C₄	C₄×Dic₆	1	2	yes	—
176	C₃×C₄	#869	1	1	yes	characteristic
177	C₃×C₄	#875	1	1	yes	characteristic
178	Dic₃	—	12	2	no	—
179	Dic₃	—	12	2	no	—
180	C₉	#1989	1	1	yes	characteristic, complemented, Sylow
181	C₂³	C₂×#611	1	1	yes	characteristic
182	C₂×C₄	—	2	1	no	—
183	C₂×C₄	—	2	1	no	—
184	C₂×C₄	—	2	2	no	—
185	C₂×C₄	—	2	4	no	—
186	C₂×C₄	—	4	2	no	—
187	C₂×C₄	—	4	2	no	—
188	C₂×C₄	—	18	2	no	—
189	C₂×C₄	—	18	2	no	—
190	C₂×C₄	—	36	1	no	—
191	C₂×C₄	—	36	1	no	—
192	C₂×C₄	—	36	2	no	—
193	C₂×C₄	(C₂×D₉)⋊C₄	1	2	yes	—
194	C₂×C₄	(C₂×D₉)⋊C₄	1	2	yes	—
195	C₂×C₄	C₂×Dic₁₈	1	2	yes	—
196	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
197	C₂×C₄	C₂×D₃₆	1	1	yes	characteristic
198	C₂×C₄	#3697	1	2	yes	—
199	C₈	—	36	2	no	—
200	C₂×C₃	#4929	1	1	yes	characteristic
201	C₂×C₃	#4966	1	1	yes	characteristic
202	C₂×C₃	#5002	1	1	yes	characteristic
203	C₂×C₃	#5009	1	2	yes	—
204	C₂×C₃	#5022	1	2	yes	—
205	C₂²	#63486	1	2	yes	—
206	C₂²	C₂×(C₂×D₉)⋊C₄	1	1	yes	characteristic
207	C₂²	#63495	1	1	yes	characteristic
208	C₂²	#63505	1	1	yes	characteristic
209	C₂²	#63513	1	2	yes	—
210	C₄	—	2	2	no	—
211	C₄	—	2	2	no	—
212	C₄	—	4	4	no	—
213	C₄	—	36	2	no	—
214	C₄	—	36	2	no	—
215	C₄	C₄×Dic₁₈	1	2	yes	—
216	C₄	#63431	1	1	yes	characteristic
217	C₄	#63437	1	1	yes	characteristic
218	C₃	#69491	1	1	yes	characteristic
219	C₂	#10588609	1	1	yes	characteristic
220	C₂	#10588649	1	1	yes	characteristic
221	C₂	#10588683	1	1	yes	characteristic
222	C₂	#10588692	1	2	yes	—
223	C₂	#10588704	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×#611
commutator	C₂×C₄×C₉	C₂²×C₄
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₄×C₉×C₄⋊C₄	C₂
socle, prime radical	C₂³×C₃	C₂×#67
cosocle	C₂²×C₄×C₉	C₂³
hypercenter	C₄×C₄⋊C₄	D₉
hypocenter	C₉	#1989
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
16. #63432	C₄	semidirect
180. C₉	#1989	semidirect

Maximal subgroups

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

subgroup	index
C₂×#63432	2
C₄×C₉×C₄⋊C₄	2
C₂×C₄⋊(C₉⋊C₈)	2
#10588206	2
#69491	3