Subgroups — #11795072

Order 1152.

345 conjugacy classes of subgroups.

The subgroup lattice has 231 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63378	C₂	1	2	yes	maximal
2	#10588615	C₂	1	1	yes	maximal, characteristic
3	#10588608	C₂	1	1	yes	maximal, characteristic
4	C₉×#336	C₂	1	1	yes	maximal, characteristic
5	#10588229	C₂	1	2	yes	maximal
6	#68639	—	3	1	no	maximal
7	C₂²×C₈×C₉	C₂²	1	2	yes	—
8	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₉	—	2	1	no	—
10	C₂×C₄⋊Dic₉	—	2	1	no	—
11	C₂×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Dic₉	C₂²	1	2	yes	—
13	C₂×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
14	C₂×Dic₉⋊C₄	—	2	1	no	—
15	C₉⋊#95	—	2	1	no	—
16	#63378	—	2	4	no	—
17	C₂×#818	—	3	2	no	—
18	#4935	—	3	1	no	—
19	#4928	—	3	1	no	—
20	C₃×#336	D₃	1	1	yes	characteristic
21	#4551	—	3	2	no	—
22	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
23	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
24	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
25	C₂²×Dic₉	—	2	1	no	—
26	C₂²×Dic₉	—	2	1	no	—
27	C₂²×Dic₉	—	2	2	no	—
28	C₂×C₈×C₉	—	2	2	no	—
29	C₂×C₈×C₉	—	2	2	no	—
30	C₂×C₈×C₉	Q₈	1	4	yes	—
31	C₄²×C₉	—	2	2	no	—
32	C₄⋊Dic₉	—	2	1	no	—
33	C₄⋊Dic₉	—	2	2	no	—
34	C₄⋊Dic₉	—	2	2	no	—
35	C₄⋊Dic₉	—	2	2	no	—
36	C₄⋊Dic₉	—	4	2	no	—
37	C₄⋊Dic₉	—	4	2	no	—
38	C₄⋊Dic₉	D₄	1	2	yes	—
39	Dic₉⋊C₄	—	4	2	no	—
40	#2083	—	9	1	no	Sylow
41	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
42	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
43	C₂×C₄⋊Dic₃	—	3	1	no	—
44	C₂×C₄⋊Dic₃	—	3	1	no	—
45	C₂×C₄⋊Dic₃	—	3	2	no	—
46	C₂×C₄⋊Dic₃	—	6	1	no	—
47	C₂×C₄⋊Dic₃	—	6	1	no	—
48	C₂×Dic₃⋊C₄	—	6	1	no	—
49	C₃⋊#95	—	6	1	no	—
50	#818	—	6	4	no	—
51	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄×C₉	—	2	1	no	—
53	C₂×C₄×C₉	—	2	1	no	—
54	C₂×C₄×C₉	—	2	1	no	—
55	C₂×C₄×C₉	—	2	1	no	—
56	C₂×C₄×C₉	D₈	1	2	yes	—
57	C₂×C₄×C₉	Q₁₆	1	2	yes	—
58	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
59	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
60	C₂×C₄×C₉	#41	1	2	yes	—
61	C₂×C₄×C₉	#41	1	1	yes	characteristic
62	C₂×Dic₉	—	2	2	no	—
63	C₂×Dic₉	—	4	1	no	—
64	C₂×Dic₉	—	4	1	no	—
65	C₂×Dic₉	—	4	2	no	—
66	C₂×Dic₉	—	4	1	no	—
67	C₂×Dic₉	—	4	1	no	—
68	C₂×Dic₉	—	4	2	no	—
69	C₂×Dic₉	—	4	2	no	—
70	C₂×Dic₉	—	4	1	no	—
71	C₈×C₉	—	2	4	no	—
72	C₂×#107	—	9	2	no	—
73	#389	—	9	1	no	—
74	#384	—	9	1	no	—
75	#340	—	9	2	no	—
76	#336	D₉	1	1	yes	characteristic
77	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
78	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
79	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
80	C₂²×Dic₃	—	6	1	no	—
81	C₂²×Dic₃	—	6	1	no	—
82	C₂²×Dic₃	—	6	2	no	—
83	C₂×C₃×C₈	—	2	2	no	—
84	C₂×C₃×C₈	—	2	2	no	—
85	C₂×C₃×C₈	Dic₆	1	4	yes	—
86	C₃×C₄²	—	2	2	no	—
87	C₄⋊Dic₃	—	3	2	no	—
88	C₄⋊Dic₃	—	6	1	no	—
89	C₄⋊Dic₃	—	6	2	no	—
90	C₄⋊Dic₃	—	6	2	no	—
91	C₄⋊Dic₃	—	6	2	no	—
92	C₄⋊Dic₃	—	12	2	no	—
93	C₄⋊Dic₃	—	12	2	no	—
94	Dic₃⋊C₄	—	12	2	no	—
95	C₂²×C₉	#121	1	1	yes	characteristic
96	C₂²×C₉	#123	1	1	yes	characteristic
97	C₂²×C₉	C₄⋊Q₈	1	1	yes	characteristic
98	C₂²×C₉	C₂×D₈	1	1	yes	characteristic
99	C₂²×C₉	C₂×Q₁₆	1	1	yes	characteristic
100	C₂²×C₉	AGL(1,ℤ/8)	1	1	yes	characteristic
101	C₂²×C₉	#137	1	1	yes	characteristic
102	C₄×C₉	—	2	2	no	—
103	C₄×C₉	—	2	2	no	—
104	C₄×C₉	C₂²⋊Q₈	1	2	yes	—
105	C₄×C₉	#125	1	2	yes	—
106	Dic₉	—	4	2	no	—
107	Dic₉	—	8	2	no	—
108	Dic₉	—	8	1	no	—
109	C₂²×C₈	C₂×D₉	1	2	yes	—
110	C₂×C₄⋊C₄	—	9	1	no	—
111	C₂×C₄⋊C₄	—	9	1	no	—
112	C₂×C₄⋊C₄	—	9	2	no	—
113	C₂×C₄⋊C₄	—	18	1	no	—
114	C₂×C₄⋊C₄	—	18	1	no	—
115	C₂×C₄⋊C₄	—	18	1	no	—
116	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
117	#107	—	18	4	no	—
118	#95	—	18	1	no	—
119	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
120	C₂×C₃×C₄	—	2	1	no	—
121	C₂×C₃×C₄	—	2	1	no	—
122	C₂×C₃×C₄	—	2	1	no	—
123	C₂×C₃×C₄	—	2	1	no	—
124	C₂×C₃×C₄	D₂₄	1	2	yes	—
125	C₂×C₃×C₄	Dic₁₂	1	2	yes	—
126	C₂×C₃×C₄	C₂×Dic₆	1	2	yes	—
127	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
128	C₂×C₃×C₄	#237	1	2	yes	—
129	C₂×C₃×C₄	#239	1	1	yes	characteristic
130	C₂×Dic₃	—	6	2	no	—
131	C₂×Dic₃	—	12	1	no	—
132	C₂×Dic₃	—	12	1	no	—
133	C₂×Dic₃	—	12	1	no	—
134	C₂×Dic₃	—	12	2	no	—
135	C₂×Dic₃	—	12	1	no	—
136	C₂×Dic₃	—	12	2	no	—
137	C₂×Dic₃	—	12	2	no	—
138	C₂×Dic₃	—	12	1	no	—
139	C₃×C₈	—	2	4	no	—
140	C₂×C₉	#398	1	1	yes	characteristic
141	C₂×C₉	#459	1	1	yes	characteristic
142	C₂×C₉	#462	1	1	yes	characteristic
143	C₂×C₉	#480	1	1	yes	characteristic
144	C₂×C₉	#484	1	1	yes	characteristic
145	C₂×C₉	#500	1	1	yes	characteristic
146	C₂×C₉	#501	1	1	yes	characteristic
147	C₂²×C₄	—	18	1	no	—
148	C₂²×C₄	—	18	1	no	—
149	C₂²×C₄	—	18	2	no	—
150	C₂²×C₄	D₃₆	1	1	yes	characteristic
151	C₂²×C₄	D₃₆	1	1	yes	characteristic
152	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
153	C₂×C₈	—	2	2	no	—
154	C₂×C₈	—	2	2	no	—
155	C₂×C₈	Dic₁₈	1	4	yes	—
156	C₄⋊C₄	—	9	2	no	—
157	C₄⋊C₄	—	18	1	no	—
158	C₄⋊C₄	—	18	2	no	—
159	C₄⋊C₄	—	18	2	no	—
160	C₄⋊C₄	—	18	2	no	—
161	C₄⋊C₄	—	36	2	no	—
162	C₄⋊C₄	—	36	2	no	—
163	C₄⋊C₄	—	36	2	no	—
164	C₄²	—	2	2	no	—
165	C₂²×C₃	#869	1	1	yes	characteristic
166	C₂²×C₃	#886	1	1	yes	characteristic
167	C₂²×C₃	#895	1	1	yes	characteristic
168	C₂²×C₃	C₂×D₂₄	1	1	yes	characteristic
169	C₂²×C₃	C₂×Dic₁₂	1	1	yes	characteristic
170	C₂²×C₃	#908	1	1	yes	characteristic
171	C₂²×C₃	#909	1	1	yes	characteristic
172	C₃×C₄	—	2	2	no	—
173	C₃×C₄	—	2	2	no	—
174	C₃×C₄	#878	1	2	yes	—
175	C₃×C₄	#890	1	2	yes	—
176	Dic₃	—	12	2	no	—
177	Dic₃	—	24	1	no	—
178	Dic₃	—	24	2	no	—
179	C₉	#2083	1	1	yes	characteristic, complemented, Sylow
180	C₂³	C₂×D₃₆	1	1	yes	characteristic
181	C₂×C₄	—	2	1	no	—
182	C₂×C₄	—	2	1	no	—
183	C₂×C₄	—	2	1	no	—
184	C₂×C₄	—	2	1	no	—
185	C₂×C₄	—	18	2	no	—
186	C₂×C₄	—	36	1	no	—
187	C₂×C₄	—	36	1	no	—
188	C₂×C₄	—	36	1	no	—
189	C₂×C₄	—	36	2	no	—
190	C₂×C₄	—	36	1	no	—
191	C₂×C₄	—	36	2	no	—
192	C₂×C₄	—	36	2	no	—
193	C₂×C₄	—	36	1	no	—
194	C₂×C₄	Dic₃₆	1	2	yes	—
195	C₂×C₄	D₇₂	1	2	yes	—
196	C₂×C₄	C₂×Dic₁₈	1	2	yes	—
197	C₂×C₄	D₄×D₉	1	1	yes	characteristic
198	C₂×C₄	#3699	1	2	yes	—
199	C₂×C₄	#3701	1	1	yes	characteristic
200	C₈	—	2	4	no	—
201	C₂×C₃	#4661	1	1	yes	characteristic
202	C₂×C₃	#4682	1	1	yes	characteristic
203	C₂×C₃	#4702	1	1	yes	characteristic
204	C₂×C₃	#4722	1	1	yes	characteristic
205	C₂×C₃	#4736	1	1	yes	characteristic
206	C₂×C₃	#4843	1	1	yes	characteristic
207	C₂×C₃	#4849	1	1	yes	characteristic
208	C₂²	#63431	1	1	yes	characteristic
209	C₂²	#63448	1	1	yes	characteristic
210	C₂²	#63457	1	1	yes	characteristic
211	C₂²	C₂×Dic₃₆	1	1	yes	characteristic
212	C₂²	C₂×D₇₂	1	1	yes	characteristic
213	C₂²	#63470	1	1	yes	characteristic
214	C₂²	#63471	1	1	yes	characteristic
215	C₄	—	2	2	no	—
216	C₄	—	2	2	no	—
217	C₄	—	36	2	no	—
218	C₄	—	72	1	no	—
219	C₄	—	72	2	no	—
220	C₄	#63440	1	2	yes	—
221	C₄	#63452	1	2	yes	—
222	C₃	#68639	1	1	yes	characteristic
223	C₂	#10588341	1	1	yes	characteristic
224	C₂	#10588362	1	1	yes	characteristic
225	C₂	#10588382	1	1	yes	characteristic
226	C₂	#10588402	1	1	yes	characteristic
227	C₂	#10588418	1	1	yes	characteristic
228	C₂	#10588513	1	1	yes	characteristic
229	C₂	#10588527	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₃₆
commutator, cosocle	C₂²×C₄×C₉	C₂³
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₉×#336	C₂
socle, prime radical	C₂³×C₃	C₂×D₁₂
hypercenter	#336	D₉
hypocenter	C₉	#2083
LCS	G ▷ C₂²×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

Complements

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

N	H ≅ G/N	type
179. C₉	#2083	semidirect

Maximal subgroups

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

subgroup	index
C₂×#63378	2
#10588615	2
#10588608	2
C₉×#336	2
#10588229	2
#68639	3