Subgroups — #11858681

Order 1152.

1009 conjugacy classes of subgroups.

The subgroup lattice has 238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10596290	C₂	1	1	yes	maximal, characteristic
2	C₃×#5819	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#948	C₂	1	1	yes	maximal, characteristic
4	#10591141	C₂	1	6	yes	maximal, complemented
5	C₂×#63577	C₂	1	6	yes	maximal, complemented
6	#83810	—	3	1	no	maximal
7	#83789	—	3	1	no	maximal
8	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
9	#64157	—	2	4	no	—
10	C₂×#3748	C₂²	1	6	yes	—
11	C₃×#948	—	2	4	no	—
12	C₃×#948	C₄	1	8	yes	—
13	C₂×C₃×#208	C₂²	1	6	yes	—
14	C₂×C₃×#208	C₂²	1	3	yes	—
15	C₂²×C₃×C₃⋊C₈	C₂²	1	3	yes	—
16	#63577	C₂²	1	4	yes	—
17	#63577	C₂²	1	12	yes	—
18	C₃×#568	—	3	1	no	—
19	C₂×C₃×#131	—	3	1	no	—
20	#5819	—	3	1	no	—
21	#5819	—	3	1	no	—
22	#5819	—	6	1	no	—
23	#5819	D₃	1	1	yes	characteristic
24	C₂×#948	D₃	1	1	yes	characteristic
25	#5125	—	3	6	no	—
26	#5124	—	3	6	no	—
27	C₂×#822	—	3	6	no	—
28	C₂×#819	—	3	6	no	—
29	C₃²×#41	C₂×C₄	1	4	yes	—
30	C₃²×#41	D₄	1	4	yes	—
31	C₂×C₃²×Q₈	Q₈	1	1	yes	characteristic
32	C₂×C₃²×D₄	Q₈	1	3	yes	—
33	C₂²×C₃²×C₄	C₂³	1	3	yes	—
34	#3748	—	2	6	no	—
35	#3748	C₂³	1	4	yes	—
36	C₂×C₃⋊(C₃⋊C₈)	—	2	6	no	—
37	C₃×#208	—	2	6	no	—
38	C₃×#208	C₂×C₄	1	12	yes	—
39	C₃×#208	C₂³	1	4	yes	—
40	C₂×C₃×C₃⋊C₈	—	2	6	no	—
41	C₂×C₃×C₃⋊C₈	C₂×C₄	1	12	yes	—
42	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
43	C₂×C₃×C₃⋊C₈	C₂³	1	3	yes	—
44	#2916	—	9	1	no	Sylow
45	C₂×C₃×#41	—	2	1	no	—
46	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic
47	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic
48	C₃×#131	—	3	8	no	—
49	C₃×#131	—	6	4	no	—
50	C₂×C₃×M₁₆	—	3	3	no	—
51	C₂×C₃×M₁₆	—	3	6	no	—
52	C₂²×C₃×C₈	—	3	3	no	—
53	#948	—	2	4	no	—
54	#948	—	6	8	no	—
55	#948	—	6	4	no	—
56	#948	—	6	4	no	—
57	#948	Dic₃	1	8	yes	—
58	C₂×#208	—	3	6	no	—
59	C₂×#208	—	3	6	no	—
60	C₂×#208	—	6	6	no	—
61	C₂×#208	C₂×D₃	1	6	yes	—
62	C₂×#208	C₂×D₃	1	3	yes	—
63	C₂²×C₃⋊C₈	C₂×D₃	1	3	yes	—
64	#822	—	3	4	no	—
65	#822	—	3	12	no	—
66	#819	—	3	12	no	—
67	#819	—	3	4	no	—
68	C₂³×C₃²	C₂×Q₈	1	3	yes	—
69	C₃²×Q₈	C₄⋊C₄	1	4	yes	—
70	C₃²×D₄	C₄⋊C₄	1	12	yes	—
71	C₂×C₃²×C₄	C₂²×C₄	1	6	yes	—
72	C₂×C₃²×C₄	C₂×D₄	1	6	yes	—
73	C₂×C₃²×C₄	C₂×Q₈	1	3	yes	—
74	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
75	C₃⋊(C₃⋊C₈)	—	2	4	no	—
76	C₃×C₃⋊C₈	—	2	4	no	—
77	C₃×C₃⋊C₈	C₂²×C₄	1	2	yes	—
78	C₃×C₃⋊C₈	C₂²×C₄	1	6	yes	—
79	#568	—	3	1	no	—
80	#568	—	9	1	no	—
81	C₂×#131	—	3	1	no	—
82	#430	—	9	6	no	—
83	C₂×#108	—	9	6	no	—
84	C₃×#41	—	2	4	no	—
85	C₃×#41	—	2	4	no	—
86	C₃×#41	C₄×D₃	1	4	yes	—
87	C₃×#41	D₁₂	1	4	yes	—
88	C₃×#41	C₂×Dic₃	1	4	yes	—
89	C₃×#41	#67	1	4	yes	—
90	C₂×C₃×Q₈	—	2	1	no	—
91	C₂×C₃×Q₈	Dic₆	1	1	yes	characteristic
92	C₂×C₃×Q₈	Dic₆	1	1	yes	characteristic
93	C₂×C₃×D₄	—	2	3	no	—
94	C₂×C₃×D₄	Dic₆	1	3	yes	—
95	C₂×C₃×D₄	Dic₆	1	3	yes	—
96	C₂²×C₃×C₄	—	2	3	no	—
97	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
98	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
99	C₃×M₁₆	—	3	12	no	—
100	C₃×M₁₆	—	3	4	no	—
101	C₃×M₁₆	—	6	6	no	—
102	C₂×C₃×C₈	—	3	12	no	—
103	C₂×C₃×C₈	—	3	1	no	—
104	C₂×C₃×C₈	—	3	3	no	—
105	C₂×C₃×C₈	—	6	6	no	—
106	#208	—	2	6	no	—
107	#208	—	3	4	no	—
108	#208	—	3	4	no	—
109	#208	—	6	4	no	—
110	#208	—	6	12	no	—
111	#208	—	6	6	no	—
112	#208	—	6	6	no	—
113	#208	C₂×Dic₃	1	12	yes	—
114	#208	C₂²×D₃	1	4	yes	—
115	C₂×C₃⋊C₈	—	2	6	no	—
116	C₂×C₃⋊C₈	—	6	12	no	—
117	C₂×C₃⋊C₈	—	6	6	no	—
118	C₂×C₃⋊C₈	—	6	6	no	—
119	C₂×C₃⋊C₈	C₂×Dic₃	1	12	yes	—
120	C₂×C₃⋊C₈	C₂²×D₃	1	1	yes	characteristic
121	C₂×C₃⋊C₈	C₂²×D₃	1	3	yes	—
122	C₂²×C₃²	—	4	3	no	—
123	C₂²×C₃²	C₂×C₄⋊C₄	1	6	yes	—
124	C₂²×C₃²	C₂²×Q₈	1	1	yes	characteristic
125	C₃²×C₄	C₂×C₄⋊C₄	1	6	yes	—
126	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
127	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
128	C₂×#41	D₃²	1	1	yes	characteristic
129	#131	—	3	8	no	—
130	#131	—	6	4	no	—
131	#131	—	18	4	no	—
132	C₂×M₁₆	—	3	3	no	—
133	C₂×M₁₆	—	3	6	no	—
134	C₂×M₁₆	—	9	6	no	—
135	C₂²×C₈	—	3	3	no	—
136	#108	—	9	4	no	—
137	#108	—	9	12	no	—
138	C₂³×C₃	—	2	3	no	—
139	C₂³×C₃	C₂×Dic₆	1	3	yes	—
140	C₂³×C₃	C₂×Dic₆	1	3	yes	—
141	C₃×Q₈	—	2	4	no	—
142	C₃×Q₈	Dic₃⋊C₄	1	4	yes	—
143	C₃×Q₈	C₄⋊Dic₃	1	4	yes	—
144	C₃×D₄	—	2	12	no	—
145	C₃×D₄	Dic₃⋊C₄	1	12	yes	—
146	C₃×D₄	C₄⋊Dic₃	1	12	yes	—
147	C₂×C₃×C₄	—	2	1	no	—
148	C₂×C₃×C₄	—	2	6	no	—
149	C₂×C₃×C₄	—	2	6	no	—
150	C₂×C₃×C₄	—	2	3	no	—
151	C₂×C₃×C₄	C₂×Dic₆	1	3	yes	—
152	C₂×C₃×C₄	C₂×Dic₆	1	3	yes	—
153	C₂×C₃×C₄	C₂×C₄×D₃	1	6	yes	—
154	C₂×C₃×C₄	C₂×D₁₂	1	6	yes	—
155	C₂×C₃×C₄	C₂²×Dic₃	1	6	yes	—
156	C₂×C₃×C₄	C₂×#67	1	6	yes	—
157	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
158	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
159	C₃×C₈	—	3	2	no	—
160	C₃×C₈	—	3	6	no	—
161	C₃×C₈	—	6	4	no	—
162	C₃⋊C₈	—	2	4	no	—
163	C₃⋊C₈	—	6	8	no	—
164	C₃⋊C₈	—	6	4	no	—
165	C₃⋊C₈	—	6	4	no	—
166	C₃⋊C₈	C₂²×Dic₃	1	2	yes	—
167	C₃⋊C₈	C₂²×Dic₃	1	6	yes	—
168	C₂×C₃²	—	2	1	no	—
169	C₂×C₃²	—	2	6	no	—
170	C₂×C₃²	C₂²×C₄⋊C₄	1	1	yes	characteristic
171	#41	D₃×Dic₃	1	4	yes	—
172	#41	#626	1	4	yes	—
173	C₂×Q₈	#627	1	1	yes	characteristic
174	C₂×D₄	#627	1	3	yes	—
175	C₂²×C₄	C₂×D₃²	1	3	yes	—
176	M₁₆	—	3	12	no	—
177	M₁₆	—	3	4	no	—
178	M₁₆	—	6	6	no	—
179	M₁₆	—	9	4	no	—
180	M₁₆	—	18	6	no	—
181	C₂×C₈	—	3	1	no	—
182	C₂×C₈	—	3	3	no	—
183	C₂×C₈	—	3	12	no	—
184	C₂×C₈	—	6	6	no	—
185	C₂×C₈	—	18	6	no	—
186	C₂²×C₃	—	2	1	no	—
187	C₂²×C₃	—	2	6	no	—
188	C₂²×C₃	—	4	3	no	—
189	C₂²×C₃	—	4	3	no	—
190	C₂²×C₃	—	8	3	no	—
191	C₂²×C₃	C₂×Dic₃⋊C₄	1	6	yes	—
192	C₂²×C₃	C₂×C₄⋊Dic₃	1	6	yes	—
193	C₂²×C₃	C₂²×Dic₆	1	1	yes	characteristic
194	C₂²×C₃	C₂²×Dic₆	1	1	yes	characteristic
195	C₃×C₄	—	2	1	no	—
196	C₃×C₄	—	2	1	no	—
197	C₃×C₄	—	2	6	no	—
198	C₃×C₄	C₂×Dic₃⋊C₄	1	6	yes	—
199	C₃×C₄	C₂×C₄⋊Dic₃	1	6	yes	—
200	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
201	C₃×C₄	C₂²×D₁₂	1	1	yes	characteristic
202	C₃×C₄	C₂³×Dic₃	1	1	yes	characteristic
203	C₃×C₄	C₂²×#67	1	1	yes	characteristic
204	C₃²	#2916	1	1	yes	characteristic, complemented, Sylow
205	C₂³	C₂×#627	1	3	yes	—
206	Q₈	Dic₃⋊Dic₃	1	4	yes	—
207	D₄	Dic₃⋊Dic₃	1	12	yes	—
208	C₂×C₄	C₂×D₃×Dic₃	1	6	yes	—
209	C₂×C₄	C₂×#626	1	6	yes	—
210	C₂×C₄	C₂×#627	1	3	yes	—
211	C₂×C₄	C₂²×D₃²	1	1	yes	characteristic
212	C₈	—	3	2	no	—
213	C₈	—	3	6	no	—
214	C₈	—	6	4	no	—
215	C₈	—	18	4	no	—
216	C₂×C₃	—	2	1	no	—
217	C₂×C₃	—	2	6	no	—
218	C₂×C₃	—	2	1	no	—
219	C₂×C₃	—	2	6	no	—
220	C₂×C₃	—	2	1	no	—
221	C₂×C₃	—	4	1	no	—
222	C₂×C₃	—	4	6	no	—
223	C₂×C₃	C₂²×Dic₃⋊C₄	1	1	yes	characteristic
224	C₂×C₃	C₂²×C₄⋊Dic₃	1	1	yes	characteristic
225	C₂²	—	4	3	no	—
226	C₂²	C₂×Dic₃⋊Dic₃	1	6	yes	—
227	C₂²	C₂²×#627	1	1	yes	characteristic
228	C₄	C₂×Dic₃⋊Dic₃	1	6	yes	—
229	C₄	C₂²×D₃×Dic₃	1	1	yes	characteristic
230	C₄	C₂²×#626	1	1	yes	characteristic
231	C₃	—	2	1	no	—
232	C₃	#83789	1	1	yes	characteristic, complemented
233	C₃	#83810	1	1	yes	characteristic, complemented
234	C₂	—	2	1	no	—
235	C₂	—	2	6	no	—
236	C₂	C₂²×Dic₃⋊Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×#626
commutator	C₃²×C₄	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃²
Fitting, prime radical	C₂×C₃²×#41	C₂²
socle	C₂×C₃²	C₂²×C₄⋊C₄
cosocle	C₂×C₃²×C₄	C₂⁴
hypercenter	C₂×#41	D₃²
hypocenter	C₃²	#2916
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
4. #10591141	C₂	semidirect
5. C₂×#63577	C₂	semidirect
204. C₃²	#2916	semidirect
232. C₃	#83789	semidirect
233. C₃	#83810	semidirect

Maximal subgroups

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

subgroup	index
#10596290	2
C₃×#5819	2
C₂×C₃×#948	2
#10591141	2
C₂×#63577	2
#83810	3
#83789	3