Subgroups — C₃²×#5627 #13179008

Order 1728.

2276 conjugacy classes of subgroups.

The subgroup lattice has 604 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	C₂²×C₃²×C₄×D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃³×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#946	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×#930	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×#895	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃²×#894	C₂	1	2	yes	maximal, complemented
8	C₃²×#893	C₂	1	2	yes	maximal, complemented
9	C₃²×#892	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃²×#882	C₂	1	2	yes	maximal, complemented
11	C₃²×#67⋊C₄	C₂	1	2	yes	maximal, complemented
12	C₃²×#525	—	3	1	no	maximal
13	C₃×#5627	C₃	1	4	yes	maximal, direct product factor
14	C₂³×C₃²×D₃	C₂²	1	1	yes	characteristic
15	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃²×#67	C₂²	1	2	yes	—
18	C₂²×C₃²×Dic₃	C₂²	1	1	yes	characteristic
19	C₃²×#239	—	2	4	no	—
20	C₂×C₃²×D₁₂	C₂²	1	2	yes	—
21	C₂×C₃²×D₁₂	C₂²	1	2	yes	—
22	C₂×C₃²×D₁₂	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃²×C₄×D₃	—	2	4	no	—
24	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
25	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
26	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
27	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
28	C₂×C₃²×C₄×D₃	C₂²	1	2	yes	complemented
29	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
30	C₃³×C₄⋊C₄	C₂²	1	2	yes	complemented
31	C₃³×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
33	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
34	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
35	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
36	C₃²×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
37	C₃²×Dic₃⋊C₄	C₂²	1	2	yes	complemented
38	C₃²×C₄×Dic₃	C₂²	1	2	yes	complemented
39	C₂×C₃²×#41	—	3	1	no	—
40	C₂³×C₃²×C₄	—	3	1	no	—
41	C₂×C₃×#239	C₂×C₃	1	4	yes	complemented
42	C₂²×C₃×C₄×D₃	C₂×C₃	1	4	yes	complemented
43	C₃²×#123	—	3	2	no	—
44	C₃²×C₂²⋊Q₈	—	2	4	no	—
45	C₃²×C₂²⋊Q₈	—	3	1	no	—
46	C₃²×C₂²⋊Q₈	D₃	1	1	yes	characteristic, complemented
47	C₃²×C₂²⋊Q₈	C₂×C₃	1	4	yes	complemented
48	C₃²×#121	—	3	1	no	—
49	C₃²×#121	—	3	1	no	—
50	C₃²×#120	—	3	2	no	—
51	C₃²×C₄×D₄	—	3	2	no	—
52	C₃²×C₄×D₄	—	3	2	no	—
53	C₃²×#117	—	3	1	no	—
54	C₃×#946	C₂×C₃	1	4	yes	complemented
55	C₃×#930	C₂×C₃	1	4	yes	complemented
56	C₃×#895	C₂×C₃	1	4	yes	complemented
57	C₃×#894	C₂×C₃	1	8	yes	complemented
58	C₃×#893	C₂×C₃	1	8	yes	complemented
59	C₃×#892	C₂×C₃	1	4	yes	complemented
60	C₃×#882	C₂×C₃	1	8	yes	complemented
61	C₃×#67⋊C₄	C₂×C₃	1	8	yes	complemented
62	C₂³×C₃³	C₂³	1	1	yes	characteristic
63	C₂²×C₃²×D₃	—	2	2	no	—
64	C₂²×C₃²×D₃	—	2	2	no	—
65	C₂²×C₃²×D₃	—	2	2	no	—
66	C₂²×C₃²×D₃	C₂³	1	2	yes	—
67	C₂²×C₃²×D₃	C₂³	1	1	yes	characteristic
68	C₂²×C₃²×D₃	C₂³	1	1	yes	characteristic
69	C₃³×Q₈	—	2	2	no	—
70	C₂×C₃³×C₄	—	2	2	no	—
71	C₂×C₃³×C₄	C₂³	1	2	yes	—
72	C₂×C₃³×C₄	C₂³	1	2	yes	—
73	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
74	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
75	C₃²×#67	—	2	4	no	—
76	C₂×C₃²×Dic₃	—	2	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	4	no	—
82	C₃²×D₁₂	—	2	2	no	—
83	C₃²×C₄×D₃	—	2	2	no	—
84	C₃²×C₄×D₃	—	2	2	no	—
85	C₃²×C₄×D₃	—	2	2	no	—
86	C₃²×C₄×D₃	—	2	4	no	—
87	C₃²×C₄×D₃	D₄	1	4	yes	complemented
88	C₃×#525	—	3	4	no	—
89	#5627	C₃²	1	1	yes	characteristic, direct product factor
90	C₂⁴×C₃²	—	3	1	no	—
91	C₂³×C₃×D₃	C₂²×C₃	1	4	yes	—
92	C₃²×#41	—	6	4	no	—
93	C₂×C₃²×Q₈	—	2	4	no	—
94	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
95	C₂×C₃²×Q₈	C₂²×C₃	1	4	yes	complemented
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	C₂²×C₃²×C₄	—	2	4	no	—
101	C₂²×C₃²×C₄	—	3	1	no	—
102	C₂²×C₃²×C₄	—	3	1	no	—
103	C₂²×C₃²×C₄	—	3	1	no	—
104	C₂²×C₃²×C₄	—	3	1	no	—
105	C₂²×C₃²×C₄	—	3	1	no	—
106	C₂²×C₃²×C₄	—	3	2	no	—
107	C₂²×C₃²×C₄	—	6	4	no	—
108	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
109	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
110	C₂×C₃×#67	C₂²×C₃	1	8	yes	—
111	C₂²×C₃×Dic₃	C₂²×C₃	1	4	yes	—
112	C₃×#239	—	2	16	no	—
113	C₂×C₃×D₁₂	C₂²×C₃	1	8	yes	—
114	C₂×C₃×D₁₂	C₂²×C₃	1	8	yes	—
115	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	complemented
116	C₂×C₃×C₄×D₃	—	2	16	no	—
117	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
118	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
119	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
120	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
121	C₂×C₃×C₄×D₃	C₂²×C₃	1	8	yes	complemented
122	C₃²×C₄⋊C₄	—	2	4	no	—
123	C₃²×C₄⋊C₄	—	2	8	no	—
124	C₃²×C₄⋊C₄	—	3	1	no	—
125	C₃²×C₄⋊C₄	—	3	2	no	—
126	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
127	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
128	C₃²×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
129	C₃²×C₄⋊C₄	C₂²×C₃	1	8	yes	complemented
130	C₃²×C₂²⋊C₄	—	2	8	no	—
131	C₃²×C₂²⋊C₄	—	3	2	no	—
132	C₃²×C₂²⋊C₄	—	3	2	no	—
133	C₃²×C₂²⋊C₄	—	3	2	no	—
134	C₃²×C₂²⋊C₄	—	3	2	no	—
135	C₃²×C₂²⋊C₄	C₂×D₃	1	2	yes	—
136	C₃²×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
137	C₃²×C₄²	—	3	2	no	—
138	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
139	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
140	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	complemented
141	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	complemented
142	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	complemented
143	C₃×Dic₃⋊C₄	C₂²×C₃	1	8	yes	complemented
144	C₃×C₄×Dic₃	C₂²×C₃	1	8	yes	complemented
145	C₂²×C₃³	—	2	1	no	—
146	C₂²×C₃³	—	2	1	no	—
147	C₂²×C₃³	#41	1	2	yes	complemented
148	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
149	C₂×C₃²×D₃	—	2	8	no	—
150	C₂×C₃²×D₃	—	2	1	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	2	no	—
155	C₂×C₃²×D₃	—	2	2	no	—
156	C₂×C₃²×D₃	—	2	2	no	—
157	C₂×C₃²×D₃	C₂×D₄	1	2	yes	—
158	C₂×C₃²×D₃	#41	1	2	yes	complemented
159	C₃³×C₄	—	2	1	no	—
160	C₃³×C₄	—	2	2	no	—
161	C₃³×C₄	—	2	2	no	—
162	C₃³×C₄	C₂×D₄	1	2	yes	—
163	C₃²×Dic₃	—	2	1	no	—
164	C₃²×Dic₃	—	2	2	no	—
165	C₃²×Dic₃	C₂×D₄	1	2	yes	—
166	C₂×C₃×#41	—	3	4	no	—
167	C₂³×C₃×C₄	—	3	4	no	—
168	C₂×#239	C₂×C₃²	1	1	yes	characteristic, complemented
169	C₂²×C₄×D₃	C₂×C₃²	1	1	yes	characteristic, complemented
170	C₃×#123	—	3	8	no	—
171	C₃×C₂²⋊Q₈	—	2	4	no	—
172	C₃×C₂²⋊Q₈	—	3	4	no	—
173	C₃×C₂²⋊Q₈	C₃×D₃	1	4	yes	complemented
174	C₃×C₂²⋊Q₈	C₂×C₃²	1	1	yes	characteristic, complemented
175	C₃×#121	—	3	4	no	—
176	C₃×#121	—	3	4	no	—
177	C₃×#120	—	3	8	no	—
178	C₃×C₄×D₄	—	3	8	no	—
179	C₃×C₄×D₄	—	3	8	no	—
180	C₃×#117	—	3	4	no	—
181	#946	C₂×C₃²	1	1	yes	characteristic, complemented
182	#930	C₂×C₃²	1	1	yes	characteristic, complemented
183	#895	C₂×C₃²	1	1	yes	characteristic, complemented
184	#894	C₂×C₃²	1	2	yes	complemented
185	#893	C₂×C₃²	1	2	yes	complemented
186	#892	C₂×C₃²	1	1	yes	characteristic, complemented
187	#882	C₂×C₃²	1	2	yes	complemented
188	#67⋊C₄	C₂×C₃²	1	2	yes	complemented
189	C₂³×C₃²	—	2	4	no	—
190	C₂³×C₃²	—	3	1	no	—
191	C₂³×C₃²	—	3	1	no	—
192	C₂³×C₃²	—	3	2	no	—
193	C₂³×C₃²	—	6	2	no	—
194	C₂³×C₃²	—	6	2	no	—
195	C₂³×C₃²	—	6	2	no	—
196	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
197	C₂³×C₃²	C₂³×C₃	1	4	yes	—
198	C₂²×C₃×D₃	—	2	8	no	—
199	C₂²×C₃×D₃	—	2	8	no	—
200	C₂²×C₃×D₃	—	2	8	no	—
201	C₂²×C₃×D₃	C₂³×C₃	1	8	yes	—
202	C₂²×C₃×D₃	C₂³×C₃	1	4	yes	—
203	C₂²×C₃×D₃	C₂³×C₃	1	4	yes	—
204	C₃²×Q₈	—	2	2	no	—
205	C₃²×Q₈	—	2	8	no	—
206	C₃²×Q₈	—	4	8	no	—
207	C₃²×D₄	—	6	4	no	—
208	C₃²×D₄	—	6	4	no	—
209	C₃²×D₄	—	6	4	no	—
210	C₃²×D₄	—	6	2	no	—
211	C₂×C₃²×C₄	—	2	2	no	—
212	C₂×C₃²×C₄	—	2	4	no	—
213	C₂×C₃²×C₄	—	2	8	no	—
214	C₂×C₃²×C₄	—	2	8	no	—
215	C₂×C₃²×C₄	—	2	4	no	—
216	C₂×C₃²×C₄	—	2	8	no	—
217	C₂×C₃²×C₄	—	3	1	no	—
218	C₂×C₃²×C₄	—	3	4	no	—
219	C₂×C₃²×C₄	—	3	2	no	—
220	C₂×C₃²×C₄	—	3	1	no	—
221	C₂×C₃²×C₄	—	4	8	no	—
222	C₂×C₃²×C₄	—	6	2	no	—
223	C₂×C₃²×C₄	—	6	4	no	—
224	C₂×C₃²×C₄	—	6	2	no	—
225	C₂×C₃²×C₄	—	6	2	no	—
226	C₂×C₃²×C₄	—	6	2	no	—
227	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
228	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
229	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
230	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
231	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
232	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
233	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
234	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
235	C₃×#67	—	2	16	no	—
236	C₂×C₃×Dic₃	—	2	8	no	—
237	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
238	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
239	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
240	C₃×D₁₂	—	2	16	no	—
241	C₃×D₁₂	—	2	16	no	—
242	C₃×D₁₂	—	2	8	no	—
243	C₃×C₄×D₃	—	2	8	no	—
244	C₃×C₄×D₃	—	2	8	no	—
245	C₃×C₄×D₃	—	2	8	no	—
246	C₃×C₄×D₃	—	2	16	no	—
247	C₃×C₄×D₃	C₃×D₄	1	16	yes	complemented
248	#525	—	3	1	no	Sylow
249	C₂×C₃³	—	2	2	no	—
250	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₃³	C₂×#41	1	1	yes	characteristic
252	C₂×C₃³	C₂×#41	1	1	yes	characteristic
253	C₃²×D₃	—	2	2	no	—
254	C₃²×D₃	—	2	2	no	—
255	C₃²×D₃	—	4	2	no	—
256	C₂⁴×C₃	—	3	4	no	—
257	C₂³×D₃	C₂²×C₃²	1	1	yes	characteristic
258	C₃×#41	—	6	16	no	—
259	C₂×C₃×Q₈	—	2	4	no	—
260	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	complemented
261	C₂×C₃×Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
262	C₂×C₃×D₄	—	3	8	no	—
263	C₂×C₃×D₄	—	3	8	no	—
264	C₂×C₃×D₄	—	3	8	no	—
265	C₂×C₃×D₄	—	3	4	no	—
266	C₂²×C₃×C₄	—	2	4	no	—
267	C₂²×C₃×C₄	—	3	4	no	—
268	C₂²×C₃×C₄	—	3	4	no	—
269	C₂²×C₃×C₄	—	3	4	no	—
270	C₂²×C₃×C₄	—	3	8	no	—
271	C₂²×C₃×C₄	—	3	4	no	—
272	C₂²×C₃×C₄	—	3	4	no	—
273	C₂²×C₃×C₄	—	6	16	no	—
274	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
275	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
276	C₂×#67	C₂²×C₃²	1	2	yes	—
277	C₂²×Dic₃	C₂²×C₃²	1	1	yes	characteristic
278	#239	—	2	4	no	—
279	C₂×D₁₂	C₂²×C₃²	1	2	yes	—
280	C₂×D₁₂	C₂²×C₃²	1	2	yes	—
281	C₂×D₁₂	C₂²×C₃²	1	1	yes	characteristic, complemented
282	C₂×C₄×D₃	—	2	4	no	—
283	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
284	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
285	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
286	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
287	C₂×C₄×D₃	C₂²×C₃²	1	2	yes	complemented
288	C₃×C₄⋊C₄	—	2	4	no	—
289	C₃×C₄⋊C₄	—	2	8	no	—
290	C₃×C₄⋊C₄	—	3	8	no	—
291	C₃×C₄⋊C₄	—	3	4	no	—
292	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	complemented
293	C₃×C₄⋊C₄	C₂×C₃×D₃	1	8	yes	complemented
294	C₃×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic, complemented
295	C₃×C₄⋊C₄	C₂²×C₃²	1	2	yes	complemented
296	C₃×C₂²⋊C₄	—	2	8	no	—
297	C₃×C₂²⋊C₄	—	3	8	no	—
298	C₃×C₂²⋊C₄	—	3	8	no	—
299	C₃×C₂²⋊C₄	—	3	8	no	—
300	C₃×C₂²⋊C₄	—	3	8	no	—
301	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	8	yes	—
302	C₃×C₂²⋊C₄	C₂²×C₃²	1	2	yes	—
303	C₃×C₄²	—	3	8	no	—
304	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	—
305	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	—
306	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	complemented
307	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	complemented
308	C₄⋊Dic₃	C₂²×C₃²	1	1	yes	characteristic, complemented
309	Dic₃⋊C₄	C₂²×C₃²	1	2	yes	complemented
310	C₄×Dic₃	C₂²×C₃²	1	2	yes	complemented
311	C₂²×C₃²	—	2	1	no	—
312	C₂²×C₃²	—	2	1	no	—
313	C₂²×C₃²	—	2	4	no	—
314	C₂²×C₃²	—	2	8	no	—
315	C₂²×C₃²	—	2	4	no	—
316	C₂²×C₃²	—	2	4	no	—
317	C₂²×C₃²	—	3	2	no	—
318	C₂²×C₃²	—	3	2	no	—
319	C₂²×C₃²	—	4	4	no	—
320	C₂²×C₃²	—	4	4	no	—
321	C₂²×C₃²	—	6	8	no	—
322	C₂²×C₃²	—	6	1	no	—
323	C₂²×C₃²	—	6	1	no	—
324	C₂²×C₃²	—	6	1	no	—
325	C₂²×C₃²	—	6	1	no	—
326	C₂²×C₃²	—	6	2	no	—
327	C₂²×C₃²	—	6	2	no	—
328	C₂²×C₃²	—	6	2	no	—
329	C₂²×C₃²	#239	1	2	yes	complemented
330	C₂²×C₃²	C₃×#41	1	8	yes	complemented
331	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
332	C₂²×C₃²	C₂⁴×C₃	1	4	yes	—
333	C₂×C₃×D₃	—	2	32	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	—	2	4	no	—
338	C₂×C₃×D₃	—	2	8	no	—
339	C₂×C₃×D₃	—	2	8	no	—
340	C₂×C₃×D₃	—	2	8	no	—
341	C₂×C₃×D₃	C₂×C₃×D₄	1	8	yes	—
342	C₂×C₃×D₃	C₃×#41	1	8	yes	complemented
343	C₃²×C₄	—	2	1	no	—
344	C₃²×C₄	—	2	2	no	—
345	C₃²×C₄	—	2	2	no	—
346	C₃²×C₄	—	2	8	no	—
347	C₃²×C₄	—	2	4	no	—
348	C₃²×C₄	—	2	8	no	—
349	C₃²×C₄	—	2	8	no	—
350	C₃²×C₄	—	3	2	no	—
351	C₃²×C₄	—	4	8	no	—
352	C₃²×C₄	—	4	4	no	—
353	C₃²×C₄	—	4	8	no	—
354	C₃²×C₄	—	6	1	no	—
355	C₃²×C₄	—	6	2	no	—
356	C₃²×C₄	D₃×D₄	1	2	yes	—
357	C₃²×C₄	C₂×C₃×D₄	1	8	yes	—
358	C₃×Dic₃	—	2	4	no	—
359	C₃×Dic₃	—	2	8	no	—
360	C₃×Dic₃	C₂×C₃×D₄	1	8	yes	—
361	C₂×#41	—	3	1	no	—
362	C₂³×C₄	—	3	1	no	—
363	#123	—	3	2	no	—
364	C₂²⋊Q₈	—	3	1	no	—
365	C₂²⋊Q₈	C₃²×D₃	1	1	yes	characteristic, complemented
366	#121	—	3	1	no	—
367	#121	—	3	1	no	—
368	#120	—	3	2	no	—
369	C₄×D₄	—	3	2	no	—
370	C₄×D₄	—	3	2	no	—
371	#117	—	3	1	no	—
372	C₃³	#525	1	1	yes	characteristic, complemented, Sylow
373	C₂³×C₃	—	2	4	no	—
374	C₂³×C₃	—	3	4	no	—
375	C₂³×C₃	—	3	4	no	—
376	C₂³×C₃	—	3	8	no	—
377	C₂³×C₃	—	6	8	no	—
378	C₂³×C₃	—	6	8	no	—
379	C₂³×C₃	—	6	8	no	—
380	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
381	C₂³×C₃	C₂³×C₃²	1	1	yes	characteristic
382	C₂²×D₃	—	2	2	no	—
383	C₂²×D₃	—	2	2	no	—
384	C₂²×D₃	—	2	2	no	—
385	C₂²×D₃	C₂³×C₃²	1	2	yes	—
386	C₂²×D₃	C₂³×C₃²	1	1	yes	characteristic
387	C₂²×D₃	C₂³×C₃²	1	1	yes	characteristic
388	C₃×Q₈	—	2	8	no	—
389	C₃×Q₈	—	2	2	no	—
390	C₃×Q₈	—	4	8	no	—
391	C₃×D₄	—	6	16	no	—
392	C₃×D₄	—	6	16	no	—
393	C₃×D₄	—	6	16	no	—
394	C₃×D₄	—	6	8	no	—
395	C₂×C₃×C₄	—	2	8	no	—
396	C₂×C₃×C₄	—	2	2	no	—
397	C₂×C₃×C₄	—	2	4	no	—
398	C₂×C₃×C₄	—	2	8	no	—
399	C₂×C₃×C₄	—	2	8	no	—
400	C₂×C₃×C₄	—	2	4	no	—
401	C₂×C₃×C₄	—	3	4	no	—
402	C₂×C₃×C₄	—	3	16	no	—
403	C₂×C₃×C₄	—	3	8	no	—
404	C₂×C₃×C₄	—	3	4	no	—
405	C₂×C₃×C₄	—	4	8	no	—
406	C₂×C₃×C₄	—	6	8	no	—
407	C₂×C₃×C₄	—	6	16	no	—
408	C₂×C₃×C₄	—	6	8	no	—
409	C₂×C₃×C₄	—	6	8	no	—
410	C₂×C₃×C₄	—	6	8	no	—
411	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
412	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
413	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
414	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
415	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
416	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
417	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
418	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
419	#67	—	2	4	no	—
420	C₂×Dic₃	—	2	2	no	—
421	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
422	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
423	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
424	D₁₂	—	2	4	no	—
425	D₁₂	—	2	4	no	—
426	D₁₂	—	2	2	no	—
427	C₄×D₃	—	2	2	no	—
428	C₄×D₃	—	2	2	no	—
429	C₄×D₃	—	2	2	no	—
430	C₄×D₃	—	2	4	no	—
431	C₄×D₃	C₃²×D₄	1	4	yes	complemented
432	C₂×C₃²	—	2	2	no	—
433	C₂×C₃²	—	2	4	no	—
434	C₂×C₃²	—	2	4	no	—
435	C₂×C₃²	—	2	4	no	—
436	C₂×C₃²	—	2	8	no	—
437	C₂×C₃²	—	4	8	no	—
438	C₂×C₃²	—	6	2	no	—
439	C₂×C₃²	—	6	2	no	—
440	C₂×C₃²	—	12	2	no	—
441	C₂×C₃²	C₂×D₃×D₄	1	1	yes	characteristic
442	C₂×C₃²	C₂×#239	1	1	yes	characteristic
443	C₂×C₃²	D₃×#41	1	1	yes	characteristic
444	C₂×C₃²	C₂²×C₃×D₄	1	4	yes	—
445	C₂×C₃²	C₂×C₃×#41	1	4	yes	—
446	C₂×C₃²	C₂×C₃×#41	1	4	yes	—
447	C₃×D₃	—	2	8	no	—
448	C₃×D₃	—	2	8	no	—
449	C₃×D₃	—	4	8	no	—
450	C₂⁴	—	3	1	no	—
451	#41	—	6	4	no	—
452	C₂×Q₈	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
453	C₂×D₄	—	3	2	no	—
454	C₂×D₄	—	3	2	no	—
455	C₂×D₄	—	3	2	no	—
456	C₂×D₄	—	3	1	no	—
457	C₂²×C₄	—	3	1	no	—
458	C₂²×C₄	—	3	1	no	—
459	C₂²×C₄	—	3	1	no	—
460	C₂²×C₄	—	3	2	no	—
461	C₂²×C₄	—	3	1	no	—
462	C₂²×C₄	—	3	1	no	—
463	C₂²×C₄	—	6	4	no	—
464	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
465	C₄⋊C₄	—	3	1	no	—
466	C₄⋊C₄	—	3	2	no	—
467	C₄⋊C₄	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
468	C₄⋊C₄	C₂×C₃²×D₃	1	2	yes	complemented
469	C₂²⋊C₄	—	3	2	no	—
470	C₂²⋊C₄	—	3	2	no	—
471	C₂²⋊C₄	—	3	2	no	—
472	C₂²⋊C₄	—	3	2	no	—
473	C₂²⋊C₄	C₂×C₃²×D₃	1	2	yes	—
474	C₄²	—	3	2	no	—
475	C₂²×C₃	—	2	4	no	—
476	C₂²×C₃	—	2	4	no	—
477	C₂²×C₃	—	2	1	no	—
478	C₂²×C₃	—	2	1	no	—
479	C₂²×C₃	—	2	4	no	—
480	C₂²×C₃	—	2	8	no	—
481	C₂²×C₃	—	3	8	no	—
482	C₂²×C₃	—	3	8	no	—
483	C₂²×C₃	—	4	4	no	—
484	C₂²×C₃	—	4	4	no	—
485	C₂²×C₃	—	6	32	no	—
486	C₂²×C₃	—	6	4	no	—
487	C₂²×C₃	—	6	4	no	—
488	C₂²×C₃	—	6	4	no	—
489	C₂²×C₃	—	6	4	no	—
490	C₂²×C₃	—	6	8	no	—
491	C₂²×C₃	—	6	8	no	—
492	C₂²×C₃	—	6	8	no	—
493	C₂²×C₃	C₃×#239	1	8	yes	complemented
494	C₂²×C₃	C₃²×#41	1	2	yes	complemented
495	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
496	C₂²×C₃	C₂⁴×C₃²	1	1	yes	characteristic
497	C₂×D₃	—	2	8	no	—
498	C₂×D₃	—	2	1	no	—
499	C₂×D₃	—	2	1	no	—
500	C₂×D₃	—	2	1	no	—
501	C₂×D₃	—	2	1	no	—
502	C₂×D₃	—	2	2	no	—
503	C₂×D₃	—	2	2	no	—
504	C₂×D₃	—	2	2	no	—
505	C₂×D₃	C₂×C₃²×D₄	1	2	yes	—
506	C₂×D₃	C₃²×#41	1	2	yes	complemented
507	C₃×C₄	—	2	4	no	—
508	C₃×C₄	—	2	8	no	—
509	C₃×C₄	—	2	8	no	—
510	C₃×C₄	—	2	1	no	—
511	C₃×C₄	—	2	2	no	—
512	C₃×C₄	—	2	2	no	—
513	C₃×C₄	—	2	8	no	—
514	C₃×C₄	—	3	8	no	—
515	C₃×C₄	—	4	4	no	—
516	C₃×C₄	—	4	8	no	—
517	C₃×C₄	—	4	8	no	—
518	C₃×C₄	—	6	4	no	—
519	C₃×C₄	—	6	8	no	—
520	C₃×C₄	C₃×D₃×D₄	1	8	yes	—
521	C₃×C₄	C₂×C₃²×D₄	1	2	yes	—
522	Dic₃	—	2	1	no	—
523	Dic₃	—	2	2	no	—
524	Dic₃	C₂×C₃²×D₄	1	2	yes	—
525	C₃²	—	2	4	no	—
526	C₃²	#5627	1	1	yes	characteristic, direct product factor
527	C₃²	C₃×#525	1	4	yes	complemented
528	C₂³	—	3	1	no	—
529	C₂³	—	3	1	no	—
530	C₂³	—	3	2	no	—
531	C₂³	—	6	2	no	—
532	C₂³	—	6	2	no	—
533	C₂³	—	6	2	no	—
534	C₂³	C₂²×C₃²×D₃	1	1	yes	characteristic
535	Q₈	—	2	2	no	—
536	D₄	—	6	4	no	—
537	D₄	—	6	4	no	—
538	D₄	—	6	4	no	—
539	D₄	—	6	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	3	1	no	—
542	C₂×C₄	—	3	4	no	—
543	C₂×C₄	—	3	2	no	—
544	C₂×C₄	—	3	1	no	—
545	C₂×C₄	—	6	2	no	—
546	C₂×C₄	—	6	4	no	—
547	C₂×C₄	—	6	2	no	—
548	C₂×C₄	—	6	2	no	—
549	C₂×C₄	—	6	2	no	—
550	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
551	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
552	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
553	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
554	C₂×C₃	—	2	8	no	—
555	C₂×C₃	—	2	2	no	—
556	C₂×C₃	—	2	4	no	—
557	C₂×C₃	—	2	4	no	—
558	C₂×C₃	—	2	4	no	—
559	C₂×C₃	—	4	8	no	—
560	C₂×C₃	—	6	8	no	—
561	C₂×C₃	—	6	8	no	—
562	C₂×C₃	—	12	8	no	—
563	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
564	C₂×C₃	C₂×C₃×#239	1	4	yes	—
565	C₂×C₃	C₃×D₃×#41	1	4	yes	—
566	C₂×C₃	C₂²×C₃²×D₄	1	1	yes	characteristic
567	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
568	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
569	D₃	—	2	2	no	—
570	D₃	—	2	2	no	—
571	D₃	—	4	2	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	3	2	no	—
575	C₂²	—	3	2	no	—
576	C₂²	—	6	8	no	—
577	C₂²	—	6	1	no	—
578	C₂²	—	6	1	no	—
579	C₂²	—	6	1	no	—
580	C₂²	—	6	1	no	—
581	C₂²	—	6	2	no	—
582	C₂²	—	6	2	no	—
583	C₂²	—	6	2	no	—
584	C₂²	C₃²×#239	1	2	yes	complemented
585	C₂²	C₂³×C₃²×D₃	1	1	yes	characteristic
586	C₄	—	2	1	no	—
587	C₄	—	2	2	no	—
588	C₄	—	2	2	no	—
589	C₄	—	3	2	no	—
590	C₄	—	6	1	no	—
591	C₄	—	6	2	no	—
592	C₄	C₃²×D₃×D₄	1	2	yes	—
593	C₃	—	2	4	no	—
594	C₃	C₃×#5627	1	4	yes	direct product factor
595	C₃	C₃²×#525	1	1	yes	characteristic, complemented
596	C₂	—	2	2	no	—
597	C₂	—	6	2	no	—
598	C₂	—	6	2	no	—
599	C₂	—	12	2	no	—
600	C₂	C₂×C₃²×D₃×D₄	1	1	yes	characteristic
601	C₂	C₂×C₃²×#239	1	1	yes	characteristic
602	C₂	C₃²×D₃×#41	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×C₂²⋊Q₈	C₂
socle	C₂²×C₃³	C₂⁴
hypercenter	C₃²×C₂²⋊Q₈	D₃
hypocenter	C₃	C₃²×#525
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃² ◁ C₃²×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×#239	C₂	semidirect
2. C₂²×C₃²×C₄×D₃	C₂	semidirect
3. C₃³×C₂²⋊Q₈	C₂	semidirect
4. C₃²×#946	C₂	semidirect
5. C₃²×#930	C₂	semidirect
6. C₃²×#895	C₂	semidirect
7. C₃²×#894	C₂	semidirect
8. C₃²×#893	C₂	semidirect
9. C₃²×#892	C₂	semidirect
10. C₃²×#882	C₂	semidirect
11. C₃²×#67⋊C₄	C₂	semidirect
13. C₃×#5627	C₃	direct (N × H)
15. C₂×C₃³×Q₈	C₂²	semidirect
22. C₂×C₃²×D₁₂	C₂²	semidirect
28. C₂×C₃²×C₄×D₃	C₂²	semidirect
29. C₃³×C₄⋊C₄	C₂²	semidirect
30. C₃³×C₄⋊C₄	C₂²	semidirect
34. C₃²×(C₂×D₃)⋊C₄	C₂²	semidirect
35. C₃²×(C₂×D₃)⋊C₄	C₂²	semidirect
36. C₃²×C₄⋊Dic₃	C₂²	semidirect
37. C₃²×Dic₃⋊C₄	C₂²	semidirect
38. C₃²×C₄×Dic₃	C₂²	semidirect
41. C₂×C₃×#239	C₂×C₃	semidirect
42. C₂²×C₃×C₄×D₃	C₂×C₃	semidirect
46. C₃²×C₂²⋊Q₈	D₃	semidirect
47. C₃²×C₂²⋊Q₈	C₂×C₃	semidirect
54. C₃×#946	C₂×C₃	semidirect
55. C₃×#930	C₂×C₃	semidirect
56. C₃×#895	C₂×C₃	semidirect
57. C₃×#894	C₂×C₃	semidirect
58. C₃×#893	C₂×C₃	semidirect
59. C₃×#892	C₂×C₃	semidirect
60. C₃×#882	C₂×C₃	semidirect
61. C₃×#67⋊C₄	C₂×C₃	semidirect
87. C₃²×C₄×D₃	D₄	semidirect
89. #5627	C₃²	direct (N × H)
94. C₂×C₃²×Q₈	C₂×D₃	semidirect
95. C₂×C₃²×Q₈	C₂²×C₃	semidirect
115. C₂×C₃×D₁₂	C₂²×C₃	semidirect
121. C₂×C₃×C₄×D₃	C₂²×C₃	semidirect
126. C₃²×C₄⋊C₄	C₂×D₃	semidirect
127. C₃²×C₄⋊C₄	C₂×D₃	semidirect
128. C₃²×C₄⋊C₄	C₂²×C₃	semidirect
129. C₃²×C₄⋊C₄	C₂²×C₃	semidirect
140. C₃×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
141. C₃×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
142. C₃×C₄⋊Dic₃	C₂²×C₃	semidirect
143. C₃×Dic₃⋊C₄	C₂²×C₃	semidirect
144. C₃×C₄×Dic₃	C₂²×C₃	semidirect
147. C₂²×C₃³	#41	semidirect
158. C₂×C₃²×D₃	#41	semidirect
168. C₂×#239	C₂×C₃²	semidirect
169. C₂²×C₄×D₃	C₂×C₃²	semidirect
173. C₃×C₂²⋊Q₈	C₃×D₃	semidirect
174. C₃×C₂²⋊Q₈	C₂×C₃²	semidirect
181. #946	C₂×C₃²	semidirect
182. #930	C₂×C₃²	semidirect
183. #895	C₂×C₃²	semidirect
184. #894	C₂×C₃²	semidirect
185. #893	C₂×C₃²	semidirect
186. #892	C₂×C₃²	semidirect
187. #882	C₂×C₃²	semidirect
188. #67⋊C₄	C₂×C₃²	semidirect
247. C₃×C₄×D₃	C₃×D₄	semidirect
260. C₂×C₃×Q₈	C₂×C₃×D₃	semidirect
261. C₂×C₃×Q₈	C₂²×C₃²	semidirect
281. C₂×D₁₂	C₂²×C₃²	semidirect
287. C₂×C₄×D₃	C₂²×C₃²	semidirect
292. C₃×C₄⋊C₄	C₂×C₃×D₃	semidirect
293. C₃×C₄⋊C₄	C₂×C₃×D₃	semidirect
294. C₃×C₄⋊C₄	C₂²×C₃²	semidirect
295. C₃×C₄⋊C₄	C₂²×C₃²	semidirect
306. (C₂×D₃)⋊C₄	C₂²×C₃²	semidirect
307. (C₂×D₃)⋊C₄	C₂²×C₃²	semidirect
308. C₄⋊Dic₃	C₂²×C₃²	semidirect
309. Dic₃⋊C₄	C₂²×C₃²	semidirect
310. C₄×Dic₃	C₂²×C₃²	semidirect
329. C₂²×C₃²	#239	semidirect
330. C₂²×C₃²	C₃×#41	semidirect
342. C₂×C₃×D₃	C₃×#41	semidirect
365. C₂²⋊Q₈	C₃²×D₃	semidirect
372. C₃³	#525	semidirect
431. C₄×D₃	C₃²×D₄	semidirect
452. C₂×Q₈	C₂×C₃²×D₃	semidirect
467. C₄⋊C₄	C₂×C₃²×D₃	semidirect
468. C₄⋊C₄	C₂×C₃²×D₃	semidirect
493. C₂²×C₃	C₃×#239	semidirect
494. C₂²×C₃	C₃²×#41	semidirect
506. C₂×D₃	C₃²×#41	semidirect
526. C₃²	#5627	direct (N × H)
527. C₃²	C₃×#525	semidirect
584. C₂²	C₃²×#239	semidirect
594. C₃	C₃×#5627	direct (N × H)
595. C₃	C₃²×#525	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
C₂²×C₃²×C₄×D₃	2
C₃³×C₂²⋊Q₈	2
C₃²×#946	2
C₃²×#930	2
C₃²×#895	2
C₃²×#894	2
C₃²×#893	2
C₃²×#892	2
C₃²×#882	2
C₃²×#67⋊C₄	2
C₃²×#525	3
C₃×#5627	3

Subgroups — C32×#5627 #13179008

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#5627 #13179008