Subgroups — #11797203

Order 1152.

361 conjugacy classes of subgroups.

The subgroup lattice has 237 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10592805	C₂	1	1	yes	maximal, characteristic
2	C₃×#5106	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	#10589141	C₂	1	2	yes	maximal, complemented
5	#10589139	C₂	1	2	yes	maximal, complemented
6	#71404	—	3	1	no	maximal
7	#70648	—	3	1	no	maximal
8	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
9	#64135	—	2	1	no	—
10	C₃×#926	—	2	1	no	—
11	#63645	C₂²	1	2	yes	—
12	#63644	—	2	1	no	—
13	C₃×#818	C₂²	1	2	yes	—
14	C₃×#817	—	2	1	no	—
15	C₂×C₃×C₃⋊C₁₆	C₄	1	4	yes	complemented
16	C₂×C₃×C₃⋊C₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₃⋊C₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₁₆	—	3	1	no	—
19	C₃×#427	—	3	1	no	—
20	#5106	—	3	1	no	—
21	#5106	—	3	1	no	—
22	#5106	—	6	1	no	—
23	#5106	D₃	1	1	yes	characteristic
24	C₂²×C₃⋊C₁₆	D₃	1	1	yes	characteristic
25	#4505	—	3	2	no	—
26	#4504	—	3	2	no	—
27	#4490	—	3	2	no	—
28	#4489	—	3	2	no	—
29	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
30	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
31	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
32	C₂×C₃²×C₈	Q₈	1	2	yes	—
33	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
34	#3757	—	4	1	no	—
35	C₄⋊(C₃⋊Dic₃)	—	2	2	no	—
36	C₄×C₃⋊Dic₃	—	4	1	no	—
37	C₃×#217	—	4	1	no	—
38	C₃×C₄⋊Dic₃	—	2	2	no	—
39	C₃×C₄×Dic₃	—	4	1	no	—
40	C₃×C₃⋊C₁₆	C₂×C₄	1	2	yes	—
41	C₃×C₃⋊C₁₆	C₂×C₄	1	2	yes	—
42	#2158	—	9	1	no	Sylow
43	C₂²×C₃×C₈	—	2	1	no	—
44	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
45	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
46	C₃×#117	—	6	1	no	—
47	#926	—	2	1	no	—
48	#926	—	6	2	no	—
49	#926	—	6	1	no	—
50	#926	—	6	1	no	—
51	C₂×C₃×C₁₆	—	3	4	no	—
52	C₂×C₃×C₁₆	—	3	1	no	—
53	C₂×C₃×C₁₆	—	3	1	no	—
54	C₃×#107	—	3	2	no	—
55	C₃×#106	—	6	1	no	—
56	#818	—	3	2	no	—
57	#818	—	3	2	no	—
58	#818	—	6	2	no	—
59	#818	C₂×D₃	1	2	yes	—
60	#817	—	2	1	no	—
61	#817	—	6	2	no	—
62	#817	—	6	1	no	—
63	#817	—	6	1	no	—
64	C₂×C₃⋊C₁₆	Dic₃	1	4	yes	complemented
65	C₂×C₃⋊C₁₆	C₂×D₃	1	1	yes	characteristic
66	C₂×C₃⋊C₁₆	C₂×D₃	1	1	yes	characteristic
67	C₂³×C₃²	D₈	1	1	yes	characteristic
68	C₂×C₃²×C₄	C₄⋊C₄	1	2	yes	—
69	C₂×C₃²×C₄	D₈	1	1	yes	characteristic
70	C₂×C₃²×C₄	Q₁₆	1	2	yes	—
71	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
72	C₂×C₃⋊Dic₃	—	4	2	no	—
73	C₂×C₃×Dic₃	—	4	2	no	—
74	C₃²×C₈	C₄⋊C₄	1	2	yes	—
75	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
76	C₃²×C₈	C₂×Q₈	1	1	yes	characteristic
77	C₂²×C₁₆	—	3	1	no	—
78	#427	—	3	1	no	—
79	#427	—	9	1	no	—
80	#367	—	9	2	no	—
81	#366	—	9	2	no	—
82	C₂²×C₃×C₄	—	2	1	no	—
83	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
84	C₂²×C₃×C₄	#67	1	1	yes	characteristic
85	C₂×C₃×C₈	—	2	2	no	—
86	C₂×C₃×C₈	—	2	1	no	—
87	C₂×C₃×C₈	—	2	2	no	—
88	C₂×C₃×C₈	—	2	1	no	—
89	C₂×C₃×C₈	Dic₆	1	2	yes	—
90	C₂×C₃×C₈	Dic₆	1	2	yes	—
91	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
92	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
93	C₂×C₃×C₈	C₂×Dic₃	1	2	yes	—
94	C₂×C₃×C₈	#67	1	1	yes	characteristic
95	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
96	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
97	C₃×C₄⋊C₄	—	6	2	no	—
98	C₃×C₂²⋊C₄	—	12	1	no	—
99	C₃×C₄²	—	12	1	no	—
100	#217	—	4	1	no	—
101	#217	—	12	2	no	—
102	#217	—	12	1	no	—
103	#217	—	12	1	no	—
104	C₄⋊Dic₃	—	2	2	no	—
105	C₄⋊Dic₃	—	6	4	no	—
106	C₄⋊Dic₃	—	6	2	no	—
107	C₄⋊Dic₃	—	6	2	no	—
108	C₄×Dic₃	—	4	1	no	—
109	C₄×Dic₃	—	12	2	no	—
110	C₄×Dic₃	—	12	1	no	—
111	C₄×Dic₃	—	12	1	no	—
112	C₃×C₁₆	—	3	2	no	—
113	C₃×C₁₆	—	3	2	no	—
114	C₃⋊C₁₆	C₂×Dic₃	1	2	yes	—
115	C₃⋊C₁₆	C₂×Dic₃	1	2	yes	—
116	C₂²×C₃²	—	2	2	no	—
117	C₂²×C₃²	#107	1	2	yes	—
118	C₂²×C₃²	C₂×D₈	1	1	yes	characteristic
119	C₃²×C₄	#107	1	2	yes	—
120	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
121	C₃²×C₄	C₂×Q₁₆	1	1	yes	characteristic
122	C₃⋊Dic₃	—	8	2	no	—
123	C₃×Dic₃	—	8	2	no	—
124	C₂²×C₈	D₃²	1	1	yes	characteristic
125	#117	—	6	1	no	—
126	#117	—	18	1	no	—
127	C₂×C₁₆	—	3	4	no	—
128	C₂×C₁₆	—	3	1	no	—
129	C₂×C₁₆	—	3	1	no	—
130	#107	—	3	2	no	—
131	#107	—	9	2	no	—
132	#106	—	6	1	no	—
133	#106	—	18	1	no	—
134	C₂³×C₃	—	2	1	no	—
135	C₂³×C₃	D₂₄	1	1	yes	characteristic
136	C₂³×C₃	#213	1	1	yes	characteristic
137	C₂×C₃×C₄	—	2	1	no	—
138	C₂×C₃×C₄	—	2	2	no	—
139	C₂×C₃×C₄	—	2	2	no	—
140	C₂×C₃×C₄	—	2	1	no	—
141	C₂×C₃×C₄	—	12	2	no	—
142	C₂×C₃×C₄	D₂₄	1	1	yes	characteristic
143	C₂×C₃×C₄	Dic₁₂	1	2	yes	—
144	C₂×C₃×C₄	Dic₃⋊C₄	1	2	yes	—
145	C₂×C₃×C₄	C₄⋊Dic₃	1	2	yes	—
146	C₂×C₃×C₄	#213	1	1	yes	characteristic
147	C₂×C₃×C₄	#216	1	2	yes	—
148	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
149	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
150	C₂×Dic₃	—	4	2	no	—
151	C₂×Dic₃	—	12	4	no	—
152	C₂×Dic₃	—	12	2	no	—
153	C₂×Dic₃	—	12	2	no	—
154	C₃×C₈	—	2	2	no	—
155	C₃×C₈	—	2	1	no	—
156	C₃×C₈	—	2	1	no	—
157	C₃×C₈	Dic₃⋊C₄	1	2	yes	—
158	C₃×C₈	C₄⋊Dic₃	1	2	yes	—
159	C₃×C₈	C₂×Dic₆	1	1	yes	characteristic
160	C₃×C₈	C₂×Dic₆	1	1	yes	characteristic
161	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
162	C₃×C₈	C₂²×Dic₃	1	1	yes	characteristic
163	C₂×C₃²	—	2	2	no	—
164	C₂×C₃²	C₂×#107	1	1	yes	characteristic
165	C₂×C₃²	#508	1	2	yes	—
166	C₂²×C₄	#626	1	1	yes	characteristic
167	C₂×C₈	D₃×Dic₃	1	2	yes	—
168	C₂×C₈	#626	1	1	yes	characteristic
169	C₂×C₈	#627	1	2	yes	—
170	C₂×C₈	C₂×D₃²	1	1	yes	characteristic
171	C₄⋊C₄	—	6	2	no	—
172	C₄⋊C₄	—	18	2	no	—
173	C₂²⋊C₄	—	12	1	no	—
174	C₂²⋊C₄	—	36	1	no	—
175	C₄²	—	12	1	no	—
176	C₄²	—	36	1	no	—
177	C₁₆	—	3	2	no	—
178	C₁₆	—	3	2	no	—
179	C₂²×C₃	—	2	2	no	—
180	C₂²×C₃	—	2	2	no	—
181	C₂²×C₃	—	2	1	no	—
182	C₂²×C₃	—	2	2	no	—
183	C₂²×C₃	—	4	2	no	—
184	C₂²×C₃	#807	1	2	yes	—
185	C₂²×C₃	#818	1	2	yes	—
186	C₂²×C₃	C₂×D₂₄	1	1	yes	characteristic
187	C₂²×C₃	C₂×#213	1	1	yes	characteristic
188	C₃×C₄	—	2	2	no	—
189	C₃×C₄	—	2	1	no	—
190	C₃×C₄	—	2	1	no	—
191	C₃×C₄	—	24	2	no	—
192	C₃×C₄	#807	1	2	yes	—
193	C₃×C₄	#818	1	2	yes	—
194	C₃×C₄	C₂×Dic₁₂	1	1	yes	characteristic
195	C₃×C₄	C₂×Dic₃⋊C₄	1	1	yes	characteristic
196	C₃×C₄	C₂×C₄⋊Dic₃	1	1	yes	characteristic
197	C₃×C₄	C₂×#216	1	1	yes	characteristic
198	Dic₃	—	8	2	no	—
199	Dic₃	—	24	4	no	—
200	Dic₃	—	24	2	no	—
201	Dic₃	—	24	2	no	—
202	C₃²	#2158	1	1	yes	characteristic, complemented, Sylow
203	C₂³	#3714	1	1	yes	characteristic
204	C₂×C₄	—	12	2	no	—
205	C₂×C₄	—	36	2	no	—
206	C₂×C₄	#3714	1	1	yes	characteristic
207	C₂×C₄	#3719	1	2	yes	—
208	C₂×C₄	Dic₃⋊Dic₃	1	2	yes	—
209	C₂×C₄	C₂×#626	1	1	yes	characteristic
210	C₈	Dic₃⋊Dic₃	1	2	yes	—
211	C₈	C₂×D₃×Dic₃	1	1	yes	characteristic
212	C₈	C₂×#627	1	1	yes	characteristic
213	C₂×C₃	—	2	2	no	—
214	C₂×C₃	—	2	2	no	—
215	C₂×C₃	—	2	1	no	—
216	C₂×C₃	—	2	2	no	—
217	C₂×C₃	—	4	2	no	—
218	C₂×C₃	#4904	1	2	yes	—
219	C₂×C₃	C₂×#807	1	1	yes	characteristic
220	C₂×C₃	C₂×#818	1	1	yes	characteristic
221	C₂×C₃	#5194	1	2	yes	—
222	C₂²	—	2	2	no	—
223	C₂²	#63575	1	2	yes	—
224	C₂²	C₂×#3714	1	1	yes	characteristic
225	C₄	—	24	2	no	—
226	C₄	—	72	2	no	—
227	C₄	#63575	1	2	yes	—
228	C₄	C₂×#3719	1	1	yes	characteristic
229	C₄	C₂×Dic₃⋊Dic₃	1	1	yes	characteristic
230	C₃	—	2	1	no	—
231	C₃	#70648	1	1	yes	characteristic, complemented
232	C₃	#71404	1	1	yes	characteristic, complemented
233	C₂	—	2	2	no	—
234	C₂	#10590632	1	2	yes	—
235	C₂	C₂×#63575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#3714
commutator	C₃²×C₈	C₂²×C₄
Frattini	C₂×C₈	C₂×D₃²
Fitting	C₂²×C₃²×C₈	C₂²
socle	C₂²×C₃²	C₂×D₈
prime radical	C₂³×C₃²	D₈
cosocle	C₂×C₃²×C₈	C₂³
hypercenter	C₂²×C₈	D₃²
hypocenter	C₃²	#2158
LCS	G ▷ C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
4. #10589141	C₂	semidirect
5. #10589139	C₂	semidirect
15. C₂×C₃×C₃⋊C₁₆	C₄	semidirect
64. C₂×C₃⋊C₁₆	Dic₃	semidirect
202. C₃²	#2158	semidirect
231. C₃	#70648	semidirect
232. C₃	#71404	semidirect

Maximal subgroups

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

subgroup	index
#10592805	2
C₃×#5106	2
C₂²×C₃×C₃⋊C₁₆	2
#10589141	2
#10589139	2
#71404	3
#70648	3