Subgroups — C₃²×#5676 #13179055

Order 1728.

2308 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#239	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃²×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃³×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#946	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×#938	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×#884	C₂	1	2	yes	maximal, complemented
7	C₃²×#883	C₂	1	2	yes	maximal, complemented
8	C₃²×#882	C₂	1	2	yes	maximal, complemented
9	C₃²×D₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₃²×C₄×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃²×C₄×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃²×#546	—	3	1	no	maximal
13	C₃×#5676	C₃	1	4	yes	maximal, direct product factor
14	C₂³×C₃²×D₃	C₂²	1	2	yes	—
15	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
17	C₂×C₃²×#67	C₂²	1	2	yes	—
18	C₂×C₃²×#67	C₂²	1	2	yes	complemented
19	C₃²×#239	—	2	4	no	—
20	C₃²×D₃×D₄	—	2	4	no	—
21	C₂×C₃²×D₁₂	C₂²	1	1	yes	characteristic
22	C₂×C₃²×D₁₂	C₂²	1	1	yes	characteristic
23	C₂×C₃²×D₁₂	C₂²	1	2	yes	complemented
24	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
25	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃²×C₄×D₃	C₂²	1	2	yes	complemented
27	C₂×C₃²×C₄×D₃	C₂²	1	2	yes	complemented
28	C₃³×C₂²⋊C₄	C₂²	1	2	yes	complemented
29	C₃³×C₂²⋊C₄	C₂²	1	2	yes	complemented
30	C₃³×C₄²	C₂²	1	1	yes	characteristic, complemented
31	C₃²×#217	C₂²	1	2	yes	complemented
32	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
33	C₃²×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
34	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
35	C₃²×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
36	C₃²×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
37	C₃²×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
38	C₃²×Dic₃⋊C₄	C₂²	1	2	yes	complemented
39	C₂×C₃²×#41	—	3	1	no	—
40	C₂²×C₃²×D₄	—	3	1	no	—
41	C₂×C₃×#239	C₂×C₃	1	4	yes	complemented
42	C₂×C₃×D₃×D₄	C₂×C₃	1	4	yes	complemented
43	C₃²×#124	—	2	4	no	—
44	C₃²×#124	D₃	1	1	yes	characteristic, complemented
45	C₃²×#124	C₂×C₃	1	4	yes	complemented
46	C₃²×#123	—	3	2	no	—
47	C₃²×C₂²⋊Q₈	—	3	1	no	—
48	C₃²×#121	—	3	1	no	—
49	C₃²×#121	—	3	2	no	—
50	C₃²×#120	—	3	2	no	—
51	C₃²×C₄×D₄	—	3	1	no	—
52	C₃²×C₄×D₄	—	3	1	no	—
53	C₂×C₃²×C₂²⋊C₄	—	3	2	no	—
54	C₃×#946	C₂×C₃	1	4	yes	complemented
55	C₃×#938	C₂×C₃	1	4	yes	complemented
56	C₃×#884	C₂×C₃	1	8	yes	complemented
57	C₃×#883	C₂×C₃	1	8	yes	complemented
58	C₃×#882	C₂×C₃	1	8	yes	complemented
59	C₃×D₃×C₂²⋊C₄	C₂×C₃	1	8	yes	complemented
60	C₃×C₄×D₁₂	C₂×C₃	1	4	yes	complemented
61	C₃×C₄×D₁₂	C₂×C₃	1	4	yes	complemented
62	C₂³×C₃³	C₂³	1	2	yes	—
63	C₂²×C₃²×D₃	—	2	4	no	—
64	C₂²×C₃²×D₃	—	2	4	no	—
65	C₂²×C₃²×D₃	—	4	2	no	—
66	C₂²×C₃²×D₃	C₂³	1	1	yes	characteristic
67	C₂²×C₃²×D₃	C₂³	1	2	yes	—
68	C₂²×C₃²×D₃	C₂³	1	1	yes	characteristic
69	C₃³×Q₈	—	2	2	no	—
70	C₃³×D₄	—	2	2	no	—
71	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
72	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
73	C₂×C₃³×C₄	C₂³	1	2	yes	—
74	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
75	C₃²×#67	—	2	4	no	—
76	C₃²×#67	—	4	2	no	—
77	C₂×C₃²×Dic₃	C₂³	1	1	yes	characteristic
78	C₂×C₃²×Dic₃	C₂³	1	2	yes	—
79	C₂×C₃²×Dic₃	C₂³	1	1	yes	characteristic
80	C₃²×D₁₂	—	2	4	no	—
81	C₃²×D₁₂	—	2	2	no	—
82	C₃²×D₁₂	D₄	1	4	yes	complemented
83	C₃²×C₄×D₃	—	2	4	no	—
84	C₃²×C₄×D₃	—	2	2	no	—
85	C₃²×C₄×D₃	—	2	2	no	—
86	C₃²×C₄×D₃	—	4	2	no	—
87	C₃×#546	—	3	4	no	—
88	#5676	C₃²	1	1	yes	characteristic, direct product factor
89	C₂⁴×C₃²	—	3	2	no	—
90	C₂³×C₃×D₃	C₂²×C₃	1	8	yes	—
91	C₃²×#41	—	6	4	no	—
92	C₂×C₃²×Q₈	—	2	4	no	—
93	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
94	C₂×C₃²×Q₈	C₂²×C₃	1	4	yes	complemented
95	C₂×C₃²×D₄	—	2	4	no	—
96	C₂×C₃²×D₄	—	3	2	no	—
97	C₂×C₃²×D₄	—	3	2	no	—
98	C₂×C₃²×D₄	—	3	1	no	—
99	C₂×C₃²×D₄	—	3	2	no	—
100	C₂×C₃²×D₄	—	3	1	no	—
101	C₂×C₃²×D₄	—	6	4	no	—
102	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
103	C₂×C₃²×D₄	C₂²×C₃	1	4	yes	—
104	C₂²×C₃²×C₄	—	3	1	no	—
105	C₂²×C₃²×C₄	—	3	2	no	—
106	C₂²×C₃²×C₄	—	3	1	no	—
107	C₂²×C₃²×C₄	—	3	2	no	—
108	C₂×C₃×#67	C₂²×C₃	1	8	yes	—
109	C₂×C₃×#67	C₂²×C₃	1	8	yes	complemented
110	C₃×#239	—	2	16	no	—
111	C₃×D₃×D₄	—	2	16	no	—
112	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	—
113	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	—
114	C₂×C₃×D₁₂	C₂²×C₃	1	8	yes	complemented
115	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
116	C₂×C₃×C₄×D₃	C₂²×C₃	1	8	yes	complemented
117	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	complemented
118	C₂×C₃×C₄×D₃	C₂²×C₃	1	8	yes	complemented
119	C₃²×C₄⋊C₄	—	3	1	no	—
120	C₃²×C₄⋊C₄	—	3	1	no	—
121	C₃²×C₄⋊C₄	—	3	2	no	—
122	C₃²×C₂²⋊C₄	—	2	8	no	—
123	C₃²×C₂²⋊C₄	—	2	8	no	—
124	C₃²×C₂²⋊C₄	—	3	2	no	—
125	C₃²×C₂²⋊C₄	—	3	1	no	—
126	C₃²×C₂²⋊C₄	—	3	2	no	—
127	C₃²×C₂²⋊C₄	—	3	2	no	—
128	C₃²×C₂²⋊C₄	—	3	1	no	—
129	C₃²×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
130	C₃²×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
131	C₃²×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
132	C₃²×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
133	C₃²×C₄²	—	2	4	no	—
134	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic, complemented
135	C₃²×C₄²	C₂²×C₃	1	4	yes	complemented
136	C₃×#217	C₂²×C₃	1	8	yes	complemented
137	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
138	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
139	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	complemented
140	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	complemented
141	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	complemented
142	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	complemented
143	C₃×Dic₃⋊C₄	C₂²×C₃	1	8	yes	complemented
144	C₂²×C₃³	—	2	2	no	—
145	C₂²×C₃³	—	2	2	no	—
146	C₂²×C₃³	—	2	2	no	—
147	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
148	C₂×C₃²×D₃	—	2	1	no	—
149	C₂×C₃²×D₃	—	2	2	no	—
150	C₂×C₃²×D₃	—	2	2	no	—
151	C₂×C₃²×D₃	—	2	1	no	—
152	C₂×C₃²×D₃	—	2	1	no	—
153	C₂×C₃²×D₃	—	2	1	no	—
154	C₂×C₃²×D₃	—	2	1	no	—
155	C₂×C₃²×D₃	—	4	8	no	—
156	C₂×C₃²×D₃	C₂×D₄	1	4	yes	—
157	C₂×C₃²×D₃	#41	1	2	yes	complemented
158	C₃³×C₄	—	2	2	no	—
159	C₃³×C₄	—	2	1	no	—
160	C₃³×C₄	—	2	1	no	—
161	C₃³×C₄	C₂×D₄	1	2	yes	—
162	C₃²×Dic₃	—	2	1	no	—
163	C₃²×Dic₃	—	2	1	no	—
164	C₃²×Dic₃	—	2	2	no	—
165	C₂×C₃×#41	—	3	4	no	—
166	C₂²×C₃×D₄	—	3	4	no	—
167	C₂×#239	C₂×C₃²	1	1	yes	characteristic, complemented
168	C₂×D₃×D₄	C₂×C₃²	1	1	yes	characteristic, complemented
169	C₃×#124	—	2	4	no	—
170	C₃×#124	C₃×D₃	1	4	yes	complemented
171	C₃×#124	C₂×C₃²	1	1	yes	characteristic, complemented
172	C₃×#123	—	3	8	no	—
173	C₃×C₂²⋊Q₈	—	3	4	no	—
174	C₃×#121	—	3	4	no	—
175	C₃×#121	—	3	8	no	—
176	C₃×#120	—	3	8	no	—
177	C₃×C₄×D₄	—	3	4	no	—
178	C₃×C₄×D₄	—	3	4	no	—
179	C₂×C₃×C₂²⋊C₄	—	3	8	no	—
180	#946	C₂×C₃²	1	1	yes	characteristic, complemented
181	#938	C₂×C₃²	1	1	yes	characteristic, complemented
182	#884	C₂×C₃²	1	2	yes	complemented
183	#883	C₂×C₃²	1	2	yes	complemented
184	#882	C₂×C₃²	1	2	yes	complemented
185	D₃×C₂²⋊C₄	C₂×C₃²	1	2	yes	complemented
186	C₄×D₁₂	C₂×C₃²	1	1	yes	characteristic, complemented
187	C₄×D₁₂	C₂×C₃²	1	1	yes	characteristic, complemented
188	C₂³×C₃²	—	2	8	no	—
189	C₂³×C₃²	—	3	1	no	—
190	C₂³×C₃²	—	3	2	no	—
191	C₂³×C₃²	—	3	1	no	—
192	C₂³×C₃²	—	6	4	no	—
193	C₂³×C₃²	—	6	4	no	—
194	C₂³×C₃²	—	12	2	no	—
195	C₂³×C₃²	C₂²×D₃	1	2	yes	—
196	C₂³×C₃²	C₂³×C₃	1	8	yes	—
197	C₂²×C₃×D₃	—	2	16	no	—
198	C₂²×C₃×D₃	—	2	16	no	—
199	C₂²×C₃×D₃	—	4	8	no	—
200	C₂²×C₃×D₃	C₂³×C₃	1	4	yes	—
201	C₂²×C₃×D₃	C₂³×C₃	1	8	yes	—
202	C₂²×C₃×D₃	C₂³×C₃	1	4	yes	—
203	C₃²×Q₈	—	2	2	no	—
204	C₃²×Q₈	—	2	8	no	—
205	C₃²×Q₈	—	4	8	no	—
206	C₃²×D₄	—	2	2	no	—
207	C₃²×D₄	—	2	8	no	—
208	C₃²×D₄	—	3	4	no	—
209	C₃²×D₄	—	4	8	no	—
210	C₃²×D₄	—	6	2	no	—
211	C₃²×D₄	—	6	4	no	—
212	C₃²×D₄	—	6	4	no	—
213	C₃²×D₄	—	12	2	no	—
214	C₂×C₃²×C₄	—	2	4	no	—
215	C₂×C₃²×C₄	—	2	4	no	—
216	C₂×C₃²×C₄	—	2	4	no	—
217	C₂×C₃²×C₄	—	2	8	no	—
218	C₂×C₃²×C₄	—	3	2	no	—
219	C₂×C₃²×C₄	—	3	1	no	—
220	C₂×C₃²×C₄	—	3	1	no	—
221	C₂×C₃²×C₄	—	6	4	no	—
222	C₂×C₃²×C₄	—	6	2	no	—
223	C₂×C₃²×C₄	—	6	2	no	—
224	C₂×C₃²×C₄	—	12	2	no	—
225	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
226	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
227	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
228	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
229	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
230	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
231	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
232	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
233	C₃×#67	—	2	16	no	—
234	C₃×#67	—	4	8	no	—
235	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
236	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
237	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
238	C₃×D₁₂	—	2	16	no	—
239	C₃×D₁₂	—	2	8	no	—
240	C₃×D₁₂	C₃×D₄	1	16	yes	complemented
241	C₃×C₄×D₃	—	2	16	no	—
242	C₃×C₄×D₃	—	2	8	no	—
243	C₃×C₄×D₃	—	2	8	no	—
244	C₃×C₄×D₃	—	4	8	no	—
245	#546	—	3	1	no	Sylow
246	C₂×C₃³	—	4	2	no	—
247	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₃³	C₂×#41	1	1	yes	characteristic
249	C₂×C₃³	H(5,𝔽₂)	1	1	yes	characteristic
250	C₃²×D₃	—	2	2	no	—
251	C₃²×D₃	—	2	4	no	—
252	C₃²×D₃	—	4	1	no	—
253	C₂⁴×C₃	—	3	8	no	—
254	C₂³×D₃	C₂²×C₃²	1	2	yes	—
255	C₃×#41	—	6	16	no	—
256	C₂×C₃×Q₈	—	2	4	no	—
257	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	complemented
258	C₂×C₃×Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
259	C₂×C₃×D₄	—	2	4	no	—
260	C₂×C₃×D₄	—	3	8	no	—
261	C₂×C₃×D₄	—	3	8	no	—
262	C₂×C₃×D₄	—	3	4	no	—
263	C₂×C₃×D₄	—	3	4	no	—
264	C₂×C₃×D₄	—	3	8	no	—
265	C₂×C₃×D₄	—	6	16	no	—
266	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
267	C₂×C₃×D₄	C₂²×C₃²	1	1	yes	characteristic
268	C₂²×C₃×C₄	—	3	8	no	—
269	C₂²×C₃×C₄	—	3	4	no	—
270	C₂²×C₃×C₄	—	3	4	no	—
271	C₂²×C₃×C₄	—	3	8	no	—
272	C₂×#67	C₂²×C₃²	1	2	yes	—
273	C₂×#67	C₂²×C₃²	1	2	yes	complemented
274	#239	—	2	4	no	—
275	D₃×D₄	—	2	4	no	—
276	C₂×D₁₂	C₂²×C₃²	1	1	yes	characteristic
277	C₂×D₁₂	C₂²×C₃²	1	1	yes	characteristic
278	C₂×D₁₂	C₂²×C₃²	1	2	yes	complemented
279	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
280	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic, complemented
281	C₂×C₄×D₃	C₂²×C₃²	1	2	yes	complemented
282	C₂×C₄×D₃	C₂²×C₃²	1	2	yes	complemented
283	C₃×C₄⋊C₄	—	3	8	no	—
284	C₃×C₄⋊C₄	—	3	4	no	—
285	C₃×C₄⋊C₄	—	3	4	no	—
286	C₃×C₂²⋊C₄	—	2	8	no	—
287	C₃×C₂²⋊C₄	—	2	8	no	—
288	C₃×C₂²⋊C₄	—	3	8	no	—
289	C₃×C₂²⋊C₄	—	3	4	no	—
290	C₃×C₂²⋊C₄	—	3	8	no	—
291	C₃×C₂²⋊C₄	—	3	8	no	—
292	C₃×C₂²⋊C₄	—	3	4	no	—
293	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	8	yes	complemented
294	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	8	yes	complemented
295	C₃×C₂²⋊C₄	C₂²×C₃²	1	2	yes	complemented
296	C₃×C₂²⋊C₄	C₂²×C₃²	1	2	yes	complemented
297	C₃×C₄²	—	2	4	no	—
298	C₃×C₄²	C₂×C₃×D₃	1	4	yes	complemented
299	C₃×C₄²	C₂²×C₃²	1	1	yes	characteristic, complemented
300	#217	C₂²×C₃²	1	2	yes	complemented
301	(C₂×D₃)⋊C₄	C₂²×C₃²	1	1	yes	characteristic
302	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	—
303	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	complemented
304	(C₂×D₃)⋊C₄	C₂²×C₃²	1	1	yes	characteristic, complemented
305	C₄⋊Dic₃	C₂²×C₃²	1	1	yes	characteristic, complemented
306	C₄⋊Dic₃	C₂²×C₃²	1	1	yes	characteristic, complemented
307	Dic₃⋊C₄	C₂²×C₃²	1	2	yes	complemented
308	C₂²×C₃²	—	2	2	no	—
309	C₂²×C₃²	—	2	2	no	—
310	C₂²×C₃²	—	2	2	no	—
311	C₂²×C₃²	—	2	4	no	—
312	C₂²×C₃²	—	2	8	no	—
313	C₂²×C₃²	—	2	8	no	—
314	C₂²×C₃²	—	2	8	no	—
315	C₂²×C₃²	—	3	4	no	—
316	C₂²×C₃²	—	3	2	no	—
317	C₂²×C₃²	—	4	8	no	—
318	C₂²×C₃²	—	4	8	no	—
319	C₂²×C₃²	—	4	8	no	—
320	C₂²×C₃²	—	6	1	no	—
321	C₂²×C₃²	—	6	2	no	—
322	C₂²×C₃²	—	6	2	no	—
323	C₂²×C₃²	—	6	1	no	—
324	C₂²×C₃²	—	6	1	no	—
325	C₂²×C₃²	—	6	1	no	—
326	C₂²×C₃²	—	6	1	no	—
327	C₂²×C₃²	—	12	8	no	—
328	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
329	C₂²×C₃²	C₂⁴×C₃	1	4	yes	—
330	C₂×C₃×D₃	—	2	4	no	—
331	C₂×C₃×D₃	—	2	8	no	—
332	C₂×C₃×D₃	—	2	8	no	—
333	C₂×C₃×D₃	—	2	4	no	—
334	C₂×C₃×D₃	—	2	4	no	—
335	C₂×C₃×D₃	—	2	4	no	—
336	C₂×C₃×D₃	—	2	4	no	—
337	C₂×C₃×D₃	—	4	32	no	—
338	C₂×C₃×D₃	C₂×C₃×D₄	1	16	yes	—
339	C₂×C₃×D₃	C₃×#41	1	8	yes	complemented
340	C₃²×C₄	—	2	2	no	—
341	C₃²×C₄	—	2	1	no	—
342	C₃²×C₄	—	2	1	no	—
343	C₃²×C₄	—	2	8	no	—
344	C₃²×C₄	—	2	8	no	—
345	C₃²×C₄	—	2	4	no	—
346	C₃²×C₄	—	2	4	no	—
347	C₃²×C₄	—	4	4	no	—
348	C₃²×C₄	—	4	4	no	—
349	C₃²×C₄	—	4	8	no	—
350	C₃²×C₄	—	6	1	no	—
351	C₃²×C₄	—	6	1	no	—
352	C₃²×C₄	—	6	2	no	—
353	C₃²×C₄	D₃×D₄	1	2	yes	—
354	C₃²×C₄	C₂×C₃×D₄	1	8	yes	—
355	C₃×Dic₃	—	2	4	no	—
356	C₃×Dic₃	—	2	4	no	—
357	C₃×Dic₃	—	2	8	no	—
358	C₂×#41	—	3	1	no	—
359	C₂²×D₄	—	3	1	no	—
360	#124	C₃²×D₃	1	1	yes	characteristic, complemented
361	#123	—	3	2	no	—
362	C₂²⋊Q₈	—	3	1	no	—
363	#121	—	3	1	no	—
364	#121	—	3	2	no	—
365	#120	—	3	2	no	—
366	C₄×D₄	—	3	1	no	—
367	C₄×D₄	—	3	1	no	—
368	C₂×C₂²⋊C₄	—	3	2	no	—
369	C₃³	#546	1	1	yes	characteristic, complemented, Sylow
370	C₂³×C₃	—	2	8	no	—
371	C₂³×C₃	—	3	4	no	—
372	C₂³×C₃	—	3	8	no	—
373	C₂³×C₃	—	3	4	no	—
374	C₂³×C₃	—	6	16	no	—
375	C₂³×C₃	—	6	16	no	—
376	C₂³×C₃	—	12	8	no	—
377	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
378	C₂³×C₃	C₂³×C₃²	1	2	yes	—
379	C₂²×D₃	—	2	4	no	—
380	C₂²×D₃	—	2	4	no	—
381	C₂²×D₃	—	4	2	no	—
382	C₂²×D₃	C₂³×C₃²	1	1	yes	characteristic
383	C₂²×D₃	C₂³×C₃²	1	2	yes	—
384	C₂²×D₃	C₂³×C₃²	1	1	yes	characteristic
385	C₃×Q₈	—	2	8	no	—
386	C₃×Q₈	—	2	2	no	—
387	C₃×Q₈	—	4	8	no	—
388	C₃×D₄	—	2	8	no	—
389	C₃×D₄	—	2	2	no	—
390	C₃×D₄	—	3	16	no	—
391	C₃×D₄	—	4	8	no	—
392	C₃×D₄	—	6	8	no	—
393	C₃×D₄	—	6	16	no	—
394	C₃×D₄	—	6	16	no	—
395	C₃×D₄	—	12	8	no	—
396	C₂×C₃×C₄	—	2	4	no	—
397	C₂×C₃×C₄	—	2	4	no	—
398	C₂×C₃×C₄	—	2	4	no	—
399	C₂×C₃×C₄	—	2	8	no	—
400	C₂×C₃×C₄	—	3	8	no	—
401	C₂×C₃×C₄	—	3	4	no	—
402	C₂×C₃×C₄	—	3	4	no	—
403	C₂×C₃×C₄	—	6	16	no	—
404	C₂×C₃×C₄	—	6	8	no	—
405	C₂×C₃×C₄	—	6	8	no	—
406	C₂×C₃×C₄	—	12	8	no	—
407	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
408	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
409	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
410	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
411	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
412	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
413	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
414	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
415	#67	—	2	4	no	—
416	#67	—	4	2	no	—
417	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
418	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
419	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
420	D₁₂	—	2	4	no	—
421	D₁₂	—	2	2	no	—
422	D₁₂	C₃²×D₄	1	4	yes	complemented
423	C₄×D₃	—	2	4	no	—
424	C₄×D₃	—	2	2	no	—
425	C₄×D₃	—	2	2	no	—
426	C₄×D₃	—	4	2	no	—
427	C₂×C₃²	—	2	4	no	—
428	C₂×C₃²	—	2	4	no	—
429	C₂×C₃²	—	2	4	no	—
430	C₂×C₃²	—	4	2	no	—
431	C₂×C₃²	—	4	8	no	—
432	C₂×C₃²	—	6	4	no	—
433	C₂×C₃²	—	6	2	no	—
434	C₂×C₃²	—	8	8	no	—
435	C₂×C₃²	—	12	1	no	—
436	C₂×C₃²	C₂×D₃×D₄	1	1	yes	characteristic
437	C₂×C₃²	D₃×#41	1	1	yes	characteristic
438	C₂×C₃²	#1009	1	1	yes	characteristic
439	C₂×C₃²	C₂²×C₃×D₄	1	4	yes	—
440	C₂×C₃²	C₂×C₃×#41	1	4	yes	—
441	C₂×C₃²	C₃×H(5,𝔽₂)	1	4	yes	—
442	C₃×D₃	—	2	8	no	—
443	C₃×D₃	—	2	16	no	—
444	C₃×D₃	—	4	4	no	—
445	C₂⁴	—	3	2	no	—
446	#41	—	6	4	no	—
447	C₂×Q₈	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
448	C₂×D₄	—	3	2	no	—
449	C₂×D₄	—	3	2	no	—
450	C₂×D₄	—	3	1	no	—
451	C₂×D₄	—	3	1	no	—
452	C₂×D₄	—	3	2	no	—
453	C₂×D₄	—	6	4	no	—
454	C₂×D₄	C₂×C₃²×D₃	1	1	yes	characteristic
455	C₂²×C₄	—	3	2	no	—
456	C₂²×C₄	—	3	1	no	—
457	C₂²×C₄	—	3	1	no	—
458	C₂²×C₄	—	3	2	no	—
459	C₄⋊C₄	—	3	1	no	—
460	C₄⋊C₄	—	3	1	no	—
461	C₄⋊C₄	—	3	2	no	—
462	C₂²⋊C₄	—	3	2	no	—
463	C₂²⋊C₄	—	3	1	no	—
464	C₂²⋊C₄	—	3	2	no	—
465	C₂²⋊C₄	—	3	2	no	—
466	C₂²⋊C₄	—	3	1	no	—
467	C₂²⋊C₄	C₂×C₃²×D₃	1	2	yes	complemented
468	C₂²⋊C₄	C₂×C₃²×D₃	1	2	yes	complemented
469	C₄²	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
470	C₂²×C₃	—	2	8	no	—
471	C₂²×C₃	—	2	8	no	—
472	C₂²×C₃	—	2	8	no	—
473	C₂²×C₃	—	2	2	no	—
474	C₂²×C₃	—	2	2	no	—
475	C₂²×C₃	—	2	2	no	—
476	C₂²×C₃	—	2	4	no	—
477	C₂²×C₃	—	3	16	no	—
478	C₂²×C₃	—	3	8	no	—
479	C₂²×C₃	—	4	8	no	—
480	C₂²×C₃	—	4	8	no	—
481	C₂²×C₃	—	4	8	no	—
482	C₂²×C₃	—	6	4	no	—
483	C₂²×C₃	—	6	8	no	—
484	C₂²×C₃	—	6	8	no	—
485	C₂²×C₃	—	6	4	no	—
486	C₂²×C₃	—	6	4	no	—
487	C₂²×C₃	—	6	4	no	—
488	C₂²×C₃	—	6	4	no	—
489	C₂²×C₃	—	12	32	no	—
490	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
491	C₂²×C₃	C₂⁴×C₃²	1	1	yes	characteristic
492	C₂×D₃	—	2	1	no	—
493	C₂×D₃	—	2	2	no	—
494	C₂×D₃	—	2	2	no	—
495	C₂×D₃	—	2	1	no	—
496	C₂×D₃	—	2	1	no	—
497	C₂×D₃	—	2	1	no	—
498	C₂×D₃	—	2	1	no	—
499	C₂×D₃	—	4	8	no	—
500	C₂×D₃	C₂×C₃²×D₄	1	4	yes	—
501	C₂×D₃	C₃²×#41	1	2	yes	complemented
502	C₃×C₄	—	2	8	no	—
503	C₃×C₄	—	2	4	no	—
504	C₃×C₄	—	2	4	no	—
505	C₃×C₄	—	2	2	no	—
506	C₃×C₄	—	2	1	no	—
507	C₃×C₄	—	2	1	no	—
508	C₃×C₄	—	2	8	no	—
509	C₃×C₄	—	4	8	no	—
510	C₃×C₄	—	4	4	no	—
511	C₃×C₄	—	4	4	no	—
512	C₃×C₄	—	6	4	no	—
513	C₃×C₄	—	6	4	no	—
514	C₃×C₄	—	6	8	no	—
515	C₃×C₄	C₃×D₃×D₄	1	8	yes	—
516	C₃×C₄	C₂×C₃²×D₄	1	2	yes	—
517	Dic₃	—	2	1	no	—
518	Dic₃	—	2	1	no	—
519	Dic₃	—	2	2	no	—
520	C₃²	—	2	4	no	—
521	C₃²	#5676	1	1	yes	characteristic, direct product factor
522	C₃²	C₃×#546	1	4	yes	complemented
523	C₂³	—	3	1	no	—
524	C₂³	—	3	2	no	—
525	C₂³	—	3	1	no	—
526	C₂³	—	6	4	no	—
527	C₂³	—	6	4	no	—
528	C₂³	—	12	2	no	—
529	C₂³	C₂²×C₃²×D₃	1	2	yes	—
530	Q₈	—	2	2	no	—
531	D₄	—	2	2	no	—
532	D₄	—	3	4	no	—
533	D₄	—	6	4	no	—
534	D₄	—	6	2	no	—
535	D₄	—	6	4	no	—
536	D₄	—	12	2	no	—
537	C₂×C₄	—	3	2	no	—
538	C₂×C₄	—	3	1	no	—
539	C₂×C₄	—	3	1	no	—
540	C₂×C₄	—	6	4	no	—
541	C₂×C₄	—	6	2	no	—
542	C₂×C₄	—	6	2	no	—
543	C₂×C₄	—	12	2	no	—
544	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
545	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
546	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
547	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
548	C₂×C₃	—	2	4	no	—
549	C₂×C₃	—	2	4	no	—
550	C₂×C₃	—	2	4	no	—
551	C₂×C₃	—	4	8	no	—
552	C₂×C₃	—	4	2	no	—
553	C₂×C₃	—	6	8	no	—
554	C₂×C₃	—	6	16	no	—
555	C₂×C₃	—	8	8	no	—
556	C₂×C₃	—	12	4	no	—
557	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
558	C₂×C₃	C₃×D₃×#41	1	4	yes	—
559	C₂×C₃	C₃×#1009	1	4	yes	—
560	C₂×C₃	C₂²×C₃²×D₄	1	1	yes	characteristic
561	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
562	C₂×C₃	C₃²×H(5,𝔽₂)	1	1	yes	characteristic
563	D₃	—	2	2	no	—
564	D₃	—	2	4	no	—
565	D₃	—	4	1	no	—
566	C₂²	—	2	2	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	3	4	no	—
570	C₂²	—	3	2	no	—
571	C₂²	—	6	1	no	—
572	C₂²	—	6	2	no	—
573	C₂²	—	6	2	no	—
574	C₂²	—	6	1	no	—
575	C₂²	—	6	1	no	—
576	C₂²	—	6	1	no	—
577	C₂²	—	6	1	no	—
578	C₂²	—	12	8	no	—
579	C₂²	C₂³×C₃²×D₃	1	1	yes	characteristic
580	C₄	—	2	2	no	—
581	C₄	—	2	1	no	—
582	C₄	—	2	1	no	—
583	C₄	—	6	1	no	—
584	C₄	—	6	1	no	—
585	C₄	—	6	2	no	—
586	C₄	C₃²×D₃×D₄	1	2	yes	—
587	C₃	—	2	4	no	—
588	C₃	C₃×#5676	1	4	yes	direct product factor
589	C₃	C₃²×#546	1	1	yes	characteristic, complemented
590	C₂	—	4	2	no	—
591	C₂	—	6	2	no	—
592	C₂	—	6	4	no	—
593	C₂	—	12	1	no	—
594	C₂	C₂×C₃²×D₃×D₄	1	1	yes	characteristic
595	C₂	C₃²×D₃×#41	1	1	yes	characteristic
596	C₂	C₃²×#1009	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃²	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₃²
Frattini	C₂²	C₂³×C₃²×D₃
Fitting	C₃³×#124	C₂
socle	C₂²×C₃³	C₂⁴
hypercenter	C₃²×#124	D₃
hypocenter	C₃	C₃²×#546
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃² ◁ C₃²×#124

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×#239	C₂	semidirect
2. C₂×C₃²×D₃×D₄	C₂	semidirect
3. C₃³×#124	C₂	semidirect
4. C₃²×#946	C₂	semidirect
5. C₃²×#938	C₂	semidirect
6. C₃²×#884	C₂	semidirect
7. C₃²×#883	C₂	semidirect
8. C₃²×#882	C₂	semidirect
9. C₃²×D₃×C₂²⋊C₄	C₂	semidirect
10. C₃²×C₄×D₁₂	C₂	semidirect
11. C₃²×C₄×D₁₂	C₂	semidirect
13. C₃×#5676	C₃	direct (N × H)
15. C₂×C₃³×Q₈	C₂²	semidirect
18. C₂×C₃²×#67	C₂²	semidirect
23. C₂×C₃²×D₁₂	C₂²	semidirect
25. C₂×C₃²×C₄×D₃	C₂²	semidirect
26. C₂×C₃²×C₄×D₃	C₂²	semidirect
27. C₂×C₃²×C₄×D₃	C₂²	semidirect
28. C₃³×C₂²⋊C₄	C₂²	semidirect
29. C₃³×C₂²⋊C₄	C₂²	semidirect
30. C₃³×C₄²	C₂²	semidirect
31. C₃²×#217	C₂²	semidirect
34. C₃²×(C₂×D₃)⋊C₄	C₂²	semidirect
35. C₃²×(C₂×D₃)⋊C₄	C₂²	semidirect
36. C₃²×C₄⋊Dic₃	C₂²	semidirect
37. C₃²×C₄⋊Dic₃	C₂²	semidirect
38. C₃²×Dic₃⋊C₄	C₂²	semidirect
41. C₂×C₃×#239	C₂×C₃	semidirect
42. C₂×C₃×D₃×D₄	C₂×C₃	semidirect
44. C₃²×#124	D₃	semidirect
45. C₃²×#124	C₂×C₃	semidirect
54. C₃×#946	C₂×C₃	semidirect
55. C₃×#938	C₂×C₃	semidirect
56. C₃×#884	C₂×C₃	semidirect
57. C₃×#883	C₂×C₃	semidirect
58. C₃×#882	C₂×C₃	semidirect
59. C₃×D₃×C₂²⋊C₄	C₂×C₃	semidirect
60. C₃×C₄×D₁₂	C₂×C₃	semidirect
61. C₃×C₄×D₁₂	C₂×C₃	semidirect
82. C₃²×D₁₂	D₄	semidirect
88. #5676	C₃²	direct (N × H)
93. C₂×C₃²×Q₈	C₂×D₃	semidirect
94. C₂×C₃²×Q₈	C₂²×C₃	semidirect
109. C₂×C₃×#67	C₂²×C₃	semidirect
114. C₂×C₃×D₁₂	C₂²×C₃	semidirect
116. C₂×C₃×C₄×D₃	C₂²×C₃	semidirect
117. C₂×C₃×C₄×D₃	C₂²×C₃	semidirect
118. C₂×C₃×C₄×D₃	C₂²×C₃	semidirect
129. C₃²×C₂²⋊C₄	C₂×D₃	semidirect
130. C₃²×C₂²⋊C₄	C₂×D₃	semidirect
131. C₃²×C₂²⋊C₄	C₂²×C₃	semidirect
132. C₃²×C₂²⋊C₄	C₂²×C₃	semidirect
134. C₃²×C₄²	C₂×D₃	semidirect
135. C₃²×C₄²	C₂²×C₃	semidirect
136. C₃×#217	C₂²×C₃	semidirect
139. C₃×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
140. C₃×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
141. C₃×C₄⋊Dic₃	C₂²×C₃	semidirect
142. C₃×C₄⋊Dic₃	C₂²×C₃	semidirect
143. C₃×Dic₃⋊C₄	C₂²×C₃	semidirect
157. C₂×C₃²×D₃	#41	semidirect
167. C₂×#239	C₂×C₃²	semidirect
168. C₂×D₃×D₄	C₂×C₃²	semidirect
170. C₃×#124	C₃×D₃	semidirect
171. C₃×#124	C₂×C₃²	semidirect
180. #946	C₂×C₃²	semidirect
181. #938	C₂×C₃²	semidirect
182. #884	C₂×C₃²	semidirect
183. #883	C₂×C₃²	semidirect
184. #882	C₂×C₃²	semidirect
185. D₃×C₂²⋊C₄	C₂×C₃²	semidirect
186. C₄×D₁₂	C₂×C₃²	semidirect
187. C₄×D₁₂	C₂×C₃²	semidirect
240. C₃×D₁₂	C₃×D₄	semidirect
257. C₂×C₃×Q₈	C₂×C₃×D₃	semidirect
258. C₂×C₃×Q₈	C₂²×C₃²	semidirect
273. C₂×#67	C₂²×C₃²	semidirect
278. C₂×D₁₂	C₂²×C₃²	semidirect
280. C₂×C₄×D₃	C₂²×C₃²	semidirect
281. C₂×C₄×D₃	C₂²×C₃²	semidirect
282. C₂×C₄×D₃	C₂²×C₃²	semidirect
293. C₃×C₂²⋊C₄	C₂×C₃×D₃	semidirect
294. C₃×C₂²⋊C₄	C₂×C₃×D₃	semidirect
295. C₃×C₂²⋊C₄	C₂²×C₃²	semidirect
296. C₃×C₂²⋊C₄	C₂²×C₃²	semidirect
298. C₃×C₄²	C₂×C₃×D₃	semidirect
299. C₃×C₄²	C₂²×C₃²	semidirect
300. #217	C₂²×C₃²	semidirect
303. (C₂×D₃)⋊C₄	C₂²×C₃²	semidirect
304. (C₂×D₃)⋊C₄	C₂²×C₃²	semidirect
305. C₄⋊Dic₃	C₂²×C₃²	semidirect
306. C₄⋊Dic₃	C₂²×C₃²	semidirect
307. Dic₃⋊C₄	C₂²×C₃²	semidirect
339. C₂×C₃×D₃	C₃×#41	semidirect
360. #124	C₃²×D₃	semidirect
369. C₃³	#546	semidirect
422. D₁₂	C₃²×D₄	semidirect
447. C₂×Q₈	C₂×C₃²×D₃	semidirect
467. C₂²⋊C₄	C₂×C₃²×D₃	semidirect
468. C₂²⋊C₄	C₂×C₃²×D₃	semidirect
469. C₄²	C₂×C₃²×D₃	semidirect
501. C₂×D₃	C₃²×#41	semidirect
521. C₃²	#5676	direct (N × H)
522. C₃²	C₃×#546	semidirect
588. C₃	C₃×#5676	direct (N × H)
589. C₃	C₃²×#546	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×#239	2
C₂×C₃²×D₃×D₄	2
C₃³×#124	2
C₃²×#946	2
C₃²×#938	2
C₃²×#884	2
C₃²×#883	2
C₃²×#882	2
C₃²×D₃×C₂²⋊C₄	2
C₃²×C₄×D₁₂	2
C₃²×#546	3
C₃×#5676	3

Subgroups — C32×#5676 #13179055

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#5676 #13179055