Subgroups — C₃²×#5791 #13179168

Order 1728.

2924 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃³×C₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃²×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#953	C₂	1	2	yes	maximal, complemented
4	C₃²×#930	C₂	1	2	yes	maximal, complemented
5	C₃²×#929	C₂	1	2	yes	maximal, complemented
6	C₃²×C₄×#67	C₂	1	4	yes	maximal, complemented
7	C₃²×#926	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#924	C₂	1	2	yes	maximal, complemented
9	C₃²×#525	—	3	1	no	maximal
10	C₃×#5791	C₃	1	4	yes	maximal, direct product factor
11	C₂⁴×C₃³	C₂²	1	1	yes	characteristic
12	C₂²×C₃³×C₄	—	2	4	no	—
13	C₂²×C₃³×C₄	C₂²	1	2	yes	—
14	C₂²×C₃³×C₄	C₂²	1	2	yes	—
15	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
16	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃²×#67	C₂²	1	4	yes	—
18	C₂×C₃²×#67	C₂²	1	2	yes	—
19	C₃²×#235	—	2	4	no	—
20	C₂×C₃²×D₁₂	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₃²×C₄×D₃	C₂²	1	2	yes	complemented
22	C₂×C₃²×Dic₆	C₂²	1	1	yes	characteristic, complemented
23	C₃²×#217	C₂²	1	4	yes	—
24	C₃²×#217	C₂²	1	2	yes	—
25	C₃²×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
26	C₃²×C₄⋊Dic₃	C₂²	1	2	yes	complemented
27	C₃²×Dic₃⋊C₄	C₂²	1	4	yes	complemented
28	C₃²×C₄×Dic₃	C₂²	1	2	yes	complemented
29	C₂×C₃²×#41	—	3	1	no	—
30	C₂³×C₃²×C₄	—	2	4	no	—
31	C₂³×C₃²×C₄	D₃	1	1	yes	characteristic, complemented
32	C₂³×C₃²×C₄	C₂×C₃	1	4	yes	complemented
33	C₂×C₃×#235	C₂×C₃	1	4	yes	complemented
34	C₃²×#123	—	3	2	no	—
35	C₃²×C₂²⋊Q₈	—	3	2	no	—
36	C₃²×#121	—	3	2	no	—
37	C₃²×#120	—	3	2	no	—
38	C₃²×C₄×D₄	—	3	4	no	—
39	C₃²×#117	—	3	1	no	—
40	C₃×#953	C₂×C₃	1	8	yes	complemented
41	C₃×#930	C₂×C₃	1	8	yes	complemented
42	C₃×#929	C₂×C₃	1	8	yes	complemented
43	C₃×C₄×#67	C₂×C₃	1	16	yes	complemented
44	C₃×#926	C₂×C₃	1	4	yes	complemented
45	C₃×#924	C₂×C₃	1	8	yes	complemented
46	C₂³×C₃³	—	2	2	no	—
47	C₂³×C₃³	—	2	4	no	—
48	C₂³×C₃³	C₂³	1	1	yes	characteristic
49	C₂³×C₃³	C₂³	1	2	yes	—
50	C₂²×C₃²×D₃	C₂³	1	2	yes	—
51	C₂×C₃³×C₄	—	2	2	no	—
52	C₂×C₃³×C₄	—	2	4	no	—
53	C₂×C₃³×C₄	—	2	4	no	—
54	C₂×C₃³×C₄	D₄	1	4	yes	complemented
55	C₂×C₃³×C₄	C₂³	1	2	yes	—
56	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
57	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
58	C₃²×#67	—	2	4	no	—
59	C₃²×#67	—	2	8	no	—
60	C₂×C₃²×Dic₃	C₂³	1	2	yes	—
61	C₂×C₃²×Dic₃	C₂³	1	4	yes	—
62	C₃²×D₁₂	—	2	2	no	—
63	C₃²×C₄×D₃	—	2	4	no	—
64	C₃²×Dic₆	—	2	2	no	—
65	C₃×#525	—	3	4	no	—
66	#5791	C₃²	1	1	yes	characteristic, direct product factor
67	C₂⁴×C₃²	—	2	4	no	—
68	C₂⁴×C₃²	C₂×D₃	1	1	yes	characteristic
69	C₂⁴×C₃²	C₂²×C₃	1	4	yes	—
70	C₃²×#41	—	6	4	no	—
71	C₂×C₃²×Q₈	—	3	1	no	—
72	C₂×C₃²×D₄	—	3	2	no	—
73	C₂×C₃²×D₄	—	3	4	no	—
74	C₂×C₃²×D₄	—	3	1	no	—
75	C₂²×C₃²×C₄	—	2	32	no	—
76	C₂²×C₃²×C₄	—	2	8	no	—
77	C₂²×C₃²×C₄	—	2	8	no	—
78	C₂²×C₃²×C₄	—	2	4	no	—
79	C₂²×C₃²×C₄	—	2	4	no	—
80	C₂²×C₃²×C₄	—	2	4	no	—
81	C₂²×C₃²×C₄	—	2	16	no	—
82	C₂²×C₃²×C₄	—	3	2	no	—
83	C₂²×C₃²×C₄	C₂×D₃	1	2	yes	—
84	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
85	C₂²×C₃²×C₄	C₂×D₃	1	2	yes	—
86	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
87	C₂²×C₃²×C₄	C₂²×C₃	1	8	yes	—
88	C₂²×C₃²×C₄	C₂²×C₃	1	8	yes	—
89	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
90	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
91	C₂×C₃×#67	C₂²×C₃	1	16	yes	—
92	C₂×C₃×#67	C₂²×C₃	1	8	yes	—
93	C₃×#235	—	2	16	no	—
94	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	complemented
95	C₂×C₃×C₄×D₃	C₂²×C₃	1	8	yes	complemented
96	C₂×C₃×Dic₆	C₂²×C₃	1	4	yes	complemented
97	C₃²×C₄⋊C₄	—	3	2	no	—
98	C₃²×C₄⋊C₄	—	3	4	no	—
99	C₃²×C₂²⋊C₄	—	3	2	no	—
100	C₃²×C₂²⋊C₄	—	3	4	no	—
101	C₃²×C₂²⋊C₄	—	3	4	no	—
102	C₃²×C₄²	—	3	2	no	—
103	C₃×#217	C₂²×C₃	1	16	yes	—
104	C₃×#217	C₂²×C₃	1	8	yes	—
105	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	16	yes	complemented
106	C₃×C₄⋊Dic₃	C₂²×C₃	1	8	yes	complemented
107	C₃×Dic₃⋊C₄	C₂²×C₃	1	16	yes	complemented
108	C₃×C₄×Dic₃	C₂²×C₃	1	8	yes	complemented
109	C₂²×C₃³	—	2	8	no	—
110	C₂²×C₃³	—	2	2	no	—
111	C₂²×C₃³	—	2	2	no	—
112	C₂²×C₃³	—	2	2	no	—
113	C₂²×C₃³	C₂×D₄	1	2	yes	—
114	C₂²×C₃³	#41	1	4	yes	complemented
115	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
116	C₂×C₃²×D₃	—	2	2	no	—
117	C₂×C₃²×D₃	—	2	4	no	—
118	C₃³×C₄	—	2	2	no	—
119	C₃³×C₄	C₂×D₄	1	2	yes	—
120	C₃³×C₄	C₂×D₄	1	2	yes	—
121	C₃²×Dic₃	—	2	2	no	—
122	C₃²×Dic₃	—	2	4	no	—
123	C₂×C₃×#41	—	3	4	no	—
124	C₂³×C₃×C₄	—	2	4	no	—
125	C₂³×C₃×C₄	C₃×D₃	1	4	yes	complemented
126	C₂³×C₃×C₄	C₂×C₃²	1	1	yes	characteristic, complemented
127	C₂×#235	C₂×C₃²	1	1	yes	characteristic, complemented
128	C₃×#123	—	3	8	no	—
129	C₃×C₂²⋊Q₈	—	3	8	no	—
130	C₃×#121	—	3	8	no	—
131	C₃×#120	—	3	8	no	—
132	C₃×C₄×D₄	—	3	16	no	—
133	C₃×#117	—	3	4	no	—
134	#953	C₂×C₃²	1	2	yes	complemented
135	#930	C₂×C₃²	1	2	yes	complemented
136	#929	C₂×C₃²	1	2	yes	complemented
137	C₄×#67	C₂×C₃²	1	4	yes	complemented
138	#926	C₂×C₃²	1	1	yes	characteristic, complemented
139	#924	C₂×C₃²	1	2	yes	complemented
140	C₂³×C₃²	—	2	32	no	—
141	C₂³×C₃²	—	2	16	no	—
142	C₂³×C₃²	—	2	4	no	—
143	C₂³×C₃²	—	2	2	no	—
144	C₂³×C₃²	—	2	8	no	—
145	C₂³×C₃²	—	2	16	no	—
146	C₂³×C₃²	—	2	8	no	—
147	C₂³×C₃²	—	2	4	no	—
148	C₂³×C₃²	—	3	2	no	—
149	C₂³×C₃²	C₂²×D₃	1	2	yes	—
150	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
151	C₂³×C₃²	C₂³×C₃	1	4	yes	—
152	C₂³×C₃²	C₂³×C₃	1	8	yes	—
153	C₂²×C₃×D₃	C₂³×C₃	1	8	yes	—
154	C₃²×Q₈	—	6	2	no	—
155	C₃²×D₄	—	6	8	no	—
156	C₃²×D₄	—	6	4	no	—
157	C₃²×D₄	—	6	2	no	—
158	C₂×C₃²×C₄	—	2	16	no	—
159	C₂×C₃²×C₄	—	2	32	no	—
160	C₂×C₃²×C₄	—	2	32	no	—
161	C₂×C₃²×C₄	—	2	2	no	—
162	C₂×C₃²×C₄	—	2	8	no	—
163	C₂×C₃²×C₄	—	2	4	no	—
164	C₂×C₃²×C₄	—	2	4	no	—
165	C₂×C₃²×C₄	—	2	16	no	—
166	C₂×C₃²×C₄	—	2	16	no	—
167	C₂×C₃²×C₄	—	2	16	no	—
168	C₂×C₃²×C₄	—	2	8	no	—
169	C₂×C₃²×C₄	—	2	4	no	—
170	C₂×C₃²×C₄	—	2	4	no	—
171	C₂×C₃²×C₄	—	3	4	no	—
172	C₂×C₃²×C₄	—	3	2	no	—
173	C₂×C₃²×C₄	—	6	4	no	—
174	C₂×C₃²×C₄	#67	1	4	yes	complemented
175	C₂×C₃²×C₄	C₃×D₄	1	16	yes	complemented
176	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
177	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
178	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
179	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
180	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
181	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
182	C₃×#67	—	2	16	no	—
183	C₃×#67	—	2	32	no	—
184	C₂×C₃×Dic₃	C₂³×C₃	1	16	yes	—
185	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
186	C₃×D₁₂	—	2	8	no	—
187	C₃×C₄×D₃	—	2	16	no	—
188	C₃×Dic₆	—	2	8	no	—
189	#525	—	3	1	no	Sylow
190	C₂×C₃³	—	2	2	no	—
191	C₂×C₃³	—	2	4	no	—
192	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₃³	C₂×#41	1	2	yes	—
194	C₃²×D₃	—	4	2	no	—
195	C₂⁴×C₃	—	2	4	no	—
196	C₂⁴×C₃	C₂×C₃×D₃	1	4	yes	—
197	C₂⁴×C₃	C₂²×C₃²	1	1	yes	characteristic
198	C₃×#41	—	6	16	no	—
199	C₂×C₃×Q₈	—	3	4	no	—
200	C₂×C₃×D₄	—	3	16	no	—
201	C₂×C₃×D₄	—	3	8	no	—
202	C₂×C₃×D₄	—	3	4	no	—
203	C₂²×C₃×C₄	—	2	32	no	—
204	C₂²×C₃×C₄	—	2	16	no	—
205	C₂²×C₃×C₄	—	2	4	no	—
206	C₂²×C₃×C₄	—	2	8	no	—
207	C₂²×C₃×C₄	—	2	8	no	—
208	C₂²×C₃×C₄	—	2	4	no	—
209	C₂²×C₃×C₄	—	2	4	no	—
210	C₂²×C₃×C₄	—	3	8	no	—
211	C₂²×C₃×C₄	C₂×C₃×D₃	1	8	yes	—
212	C₂²×C₃×C₄	C₂×C₃×D₃	1	8	yes	—
213	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
214	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
215	C₂²×C₃×C₄	C₂²×C₃²	1	2	yes	—
216	C₂²×C₃×C₄	C₂²×C₃²	1	2	yes	—
217	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
218	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
219	C₂×#67	C₂²×C₃²	1	4	yes	—
220	C₂×#67	C₂²×C₃²	1	2	yes	—
221	#235	—	2	4	no	—
222	C₂×D₁₂	C₂²×C₃²	1	1	yes	characteristic, complemented
223	C₂×C₄×D₃	C₂²×C₃²	1	2	yes	complemented
224	C₂×Dic₆	C₂²×C₃²	1	1	yes	characteristic, complemented
225	C₃×C₄⋊C₄	—	3	16	no	—
226	C₃×C₄⋊C₄	—	3	8	no	—
227	C₃×C₂²⋊C₄	—	3	8	no	—
228	C₃×C₂²⋊C₄	—	3	16	no	—
229	C₃×C₂²⋊C₄	—	3	16	no	—
230	C₃×C₄²	—	3	8	no	—
231	#217	C₂²×C₃²	1	4	yes	—
232	#217	C₂²×C₃²	1	2	yes	—
233	(C₂×D₃)⋊C₄	C₂²×C₃²	1	4	yes	complemented
234	C₄⋊Dic₃	C₂²×C₃²	1	2	yes	complemented
235	Dic₃⋊C₄	C₂²×C₃²	1	4	yes	complemented
236	C₄×Dic₃	C₂²×C₃²	1	2	yes	complemented
237	C₂²×C₃²	—	2	16	no	—
238	C₂²×C₃²	—	2	64	no	—
239	C₂²×C₃²	—	2	8	no	—
240	C₂²×C₃²	—	2	32	no	—
241	C₂²×C₃²	—	2	16	no	—
242	C₂²×C₃²	—	2	16	no	—
243	C₂²×C₃²	—	2	2	no	—
244	C₂²×C₃²	—	2	2	no	—
245	C₂²×C₃²	—	2	2	no	—
246	C₂²×C₃²	—	2	8	no	—
247	C₂²×C₃²	—	2	8	no	—
248	C₂²×C₃²	—	2	8	no	—
249	C₂²×C₃²	—	2	4	no	—
250	C₂²×C₃²	—	2	16	no	—
251	C₂²×C₃²	—	2	8	no	—
252	C₂²×C₃²	—	6	4	no	—
253	C₂²×C₃²	—	6	2	no	—
254	C₂²×C₃²	#235	1	4	yes	complemented
255	C₂²×C₃²	C₂×#67	1	2	yes	—
256	C₂²×C₃²	C₂×C₃×D₄	1	8	yes	—
257	C₂²×C₃²	C₃×#41	1	16	yes	complemented
258	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
259	C₂²×C₃²	C₂⁴×C₃	1	4	yes	—
260	C₂×C₃×D₃	—	2	8	no	—
261	C₂×C₃×D₃	—	2	16	no	—
262	C₃²×C₄	—	2	16	no	—
263	C₃²×C₄	—	2	2	no	—
264	C₃²×C₄	—	2	8	no	—
265	C₃²×C₄	—	2	8	no	—
266	C₃²×C₄	—	2	8	no	—
267	C₃²×C₄	—	6	4	no	—
268	C₃²×C₄	—	6	2	no	—
269	C₃²×C₄	C₂×#67	1	2	yes	—
270	C₃²×C₄	C₂×#67	1	2	yes	—
271	C₃²×C₄	C₂×C₃×D₄	1	8	yes	—
272	C₃²×C₄	C₂×C₃×D₄	1	8	yes	—
273	C₃×Dic₃	—	2	8	no	—
274	C₃×Dic₃	—	2	16	no	—
275	C₂×#41	—	3	1	no	—
276	C₂³×C₄	C₃²×D₃	1	1	yes	characteristic, complemented
277	#123	—	3	2	no	—
278	C₂²⋊Q₈	—	3	2	no	—
279	#121	—	3	2	no	—
280	#120	—	3	2	no	—
281	C₄×D₄	—	3	4	no	—
282	#117	—	3	1	no	—
283	C₃³	#525	1	1	yes	characteristic, complemented, Sylow
284	C₂³×C₃	—	2	16	no	—
285	C₂³×C₃	—	2	32	no	—
286	C₂³×C₃	—	2	16	no	—
287	C₂³×C₃	—	2	8	no	—
288	C₂³×C₃	—	2	2	no	—
289	C₂³×C₃	—	2	4	no	—
290	C₂³×C₃	—	2	8	no	—
291	C₂³×C₃	—	2	4	no	—
292	C₂³×C₃	—	3	8	no	—
293	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
294	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
295	C₂³×C₃	C₂³×C₃²	1	1	yes	characteristic
296	C₂³×C₃	C₂³×C₃²	1	2	yes	—
297	C₂²×D₃	C₂³×C₃²	1	2	yes	—
298	C₃×Q₈	—	6	8	no	—
299	C₃×D₄	—	6	32	no	—
300	C₃×D₄	—	6	16	no	—
301	C₃×D₄	—	6	8	no	—
302	C₂×C₃×C₄	—	2	16	no	—
303	C₂×C₃×C₄	—	2	32	no	—
304	C₂×C₃×C₄	—	2	32	no	—
305	C₂×C₃×C₄	—	2	8	no	—
306	C₂×C₃×C₄	—	2	2	no	—
307	C₂×C₃×C₄	—	2	16	no	—
308	C₂×C₃×C₄	—	2	16	no	—
309	C₂×C₃×C₄	—	2	4	no	—
310	C₂×C₃×C₄	—	2	4	no	—
311	C₂×C₃×C₄	—	2	16	no	—
312	C₂×C₃×C₄	—	2	8	no	—
313	C₂×C₃×C₄	—	2	4	no	—
314	C₂×C₃×C₄	—	2	4	no	—
315	C₂×C₃×C₄	—	3	16	no	—
316	C₂×C₃×C₄	—	3	8	no	—
317	C₂×C₃×C₄	—	6	16	no	—
318	C₂×C₃×C₄	C₃×#67	1	16	yes	complemented
319	C₂×C₃×C₄	C₃²×D₄	1	4	yes	complemented
320	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
321	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
322	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
323	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
324	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
325	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
326	#67	—	2	4	no	—
327	#67	—	2	8	no	—
328	C₂×Dic₃	C₂³×C₃²	1	4	yes	—
329	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
330	D₁₂	—	2	2	no	—
331	C₄×D₃	—	2	4	no	—
332	Dic₆	—	2	2	no	—
333	C₂×C₃²	—	2	32	no	—
334	C₂×C₃²	—	2	16	no	—
335	C₂×C₃²	—	2	4	no	—
336	C₂×C₃²	—	2	2	no	—
337	C₂×C₃²	—	2	8	no	—
338	C₂×C₃²	—	2	16	no	—
339	C₂×C₃²	—	2	8	no	—
340	C₂×C₃²	—	2	4	no	—
341	C₂×C₃²	—	12	2	no	—
342	C₂×C₃²	C₂×#235	1	2	yes	—
343	C₂×C₃²	C₂²×#67	1	1	yes	characteristic
344	C₂×C₃²	C₂²×C₃×D₄	1	4	yes	—
345	C₂×C₃²	C₂×C₃×#41	1	8	yes	—
346	C₃×D₃	—	4	8	no	—
347	C₂⁴	C₂×C₃²×D₃	1	1	yes	characteristic
348	#41	—	6	4	no	—
349	C₂×Q₈	—	3	1	no	—
350	C₂×D₄	—	3	4	no	—
351	C₂×D₄	—	3	2	no	—
352	C₂×D₄	—	3	1	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	3	2	no	—
355	C₂²×C₄	C₂×C₃²×D₃	1	2	yes	—
356	C₂²×C₄	C₂×C₃²×D₃	1	2	yes	—
357	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
358	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
359	C₄⋊C₄	—	3	2	no	—
360	C₄⋊C₄	—	3	4	no	—
361	C₂²⋊C₄	—	3	2	no	—
362	C₂²⋊C₄	—	3	4	no	—
363	C₂²⋊C₄	—	3	4	no	—
364	C₄²	—	3	2	no	—
365	C₂²×C₃	—	2	16	no	—
366	C₂²×C₃	—	2	64	no	—
367	C₂²×C₃	—	2	32	no	—
368	C₂²×C₃	—	2	8	no	—
369	C₂²×C₃	—	2	16	no	—
370	C₂²×C₃	—	2	16	no	—
371	C₂²×C₃	—	2	8	no	—
372	C₂²×C₃	—	2	8	no	—
373	C₂²×C₃	—	2	8	no	—
374	C₂²×C₃	—	2	2	no	—
375	C₂²×C₃	—	2	2	no	—
376	C₂²×C₃	—	2	2	no	—
377	C₂²×C₃	—	2	4	no	—
378	C₂²×C₃	—	2	16	no	—
379	C₂²×C₃	—	2	8	no	—
380	C₂²×C₃	—	6	16	no	—
381	C₂²×C₃	—	6	8	no	—
382	C₂²×C₃	C₃×#235	1	16	yes	complemented
383	C₂²×C₃	C₂×C₃×#67	1	8	yes	—
384	C₂²×C₃	C₂×C₃²×D₄	1	2	yes	—
385	C₂²×C₃	C₃²×#41	1	4	yes	complemented
386	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
387	C₂²×C₃	C₂⁴×C₃²	1	1	yes	characteristic
388	C₂×D₃	—	2	2	no	—
389	C₂×D₃	—	2	4	no	—
390	C₃×C₄	—	2	16	no	—
391	C₃×C₄	—	2	8	no	—
392	C₃×C₄	—	2	2	no	—
393	C₃×C₄	—	2	8	no	—
394	C₃×C₄	—	2	8	no	—
395	C₃×C₄	—	6	16	no	—
396	C₃×C₄	—	6	8	no	—
397	C₃×C₄	C₂×C₃×#67	1	8	yes	—
398	C₃×C₄	C₂×C₃×#67	1	8	yes	—
399	C₃×C₄	C₂×C₃²×D₄	1	2	yes	—
400	C₃×C₄	C₂×C₃²×D₄	1	2	yes	—
401	Dic₃	—	2	2	no	—
402	Dic₃	—	2	4	no	—
403	C₃²	—	2	4	no	—
404	C₃²	#5791	1	1	yes	characteristic, direct product factor
405	C₃²	C₃×#525	1	4	yes	complemented
406	C₂³	—	2	4	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	3	2	no	—
409	C₂³	C₂²×C₃²×D₃	1	2	yes	—
410	C₂³	C₂²×C₃²×D₃	1	1	yes	characteristic
411	Q₈	—	6	2	no	—
412	D₄	—	6	8	no	—
413	D₄	—	6	4	no	—
414	D₄	—	6	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	3	4	no	—
419	C₂×C₄	—	3	2	no	—
420	C₂×C₄	—	6	4	no	—
421	C₂×C₄	C₃²×#67	1	4	yes	complemented
422	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
423	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
424	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
425	C₂×C₃	—	2	32	no	—
426	C₂×C₃	—	2	16	no	—
427	C₂×C₃	—	2	16	no	—
428	C₂×C₃	—	2	8	no	—
429	C₂×C₃	—	2	2	no	—
430	C₂×C₃	—	2	4	no	—
431	C₂×C₃	—	2	8	no	—
432	C₂×C₃	—	2	4	no	—
433	C₂×C₃	—	12	8	no	—
434	C₂×C₃	C₂×C₃×#235	1	8	yes	—
435	C₂×C₃	C₂²×C₃×#67	1	4	yes	—
436	C₂×C₃	C₂²×C₃²×D₄	1	1	yes	characteristic
437	C₂×C₃	C₂×C₃²×#41	1	2	yes	—
438	D₃	—	4	2	no	—
439	C₂²	—	2	8	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	6	4	no	—
444	C₂²	—	6	2	no	—
445	C₂²	C₃²×#235	1	4	yes	complemented
446	C₂²	C₂×C₃²×#67	1	2	yes	—
447	C₂²	C₂³×C₃²×D₃	1	1	yes	characteristic
448	C₄	—	2	2	no	—
449	C₄	—	6	4	no	—
450	C₄	—	6	2	no	—
451	C₄	C₂×C₃²×#67	1	2	yes	—
452	C₄	C₂×C₃²×#67	1	2	yes	—
453	C₃	—	2	4	no	—
454	C₃	C₃×#5791	1	4	yes	direct product factor
455	C₃	C₃²×#525	1	1	yes	characteristic, complemented
456	C₂	—	2	4	no	—
457	C₂	—	2	2	no	—
458	C₂	—	12	2	no	—
459	C₂	C₂×C₃²×#235	1	2	yes	—
460	C₂	C₂²×C₃²×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃²×C₄	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₃²
Frattini	C₂²	C₂³×C₃²×D₃
Fitting	C₂³×C₃³×C₄	C₂
socle	C₂²×C₃³	C₂⁴
hypercenter	C₂³×C₃²×C₄	D₃
hypocenter	C₃	C₃²×#525
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃²×C₄ ◁ C₂³×C₃²×C₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃³×C₄	C₂	semidirect
2. C₂×C₃²×#235	C₂	semidirect
3. C₃²×#953	C₂	semidirect
4. C₃²×#930	C₂	semidirect
5. C₃²×#929	C₂	semidirect
6. C₃²×C₄×#67	C₂	semidirect
7. C₃²×#926	C₂	semidirect
8. C₃²×#924	C₂	semidirect
10. C₃×#5791	C₃	direct (N × H)
20. C₂×C₃²×D₁₂	C₂²	semidirect
21. C₂×C₃²×C₄×D₃	C₂²	semidirect
22. C₂×C₃²×Dic₆	C₂²	semidirect
25. C₃²×(C₂×D₃)⋊C₄	C₂²	semidirect
26. C₃²×C₄⋊Dic₃	C₂²	semidirect
27. C₃²×Dic₃⋊C₄	C₂²	semidirect
28. C₃²×C₄×Dic₃	C₂²	semidirect
31. C₂³×C₃²×C₄	D₃	semidirect
32. C₂³×C₃²×C₄	C₂×C₃	semidirect
33. C₂×C₃×#235	C₂×C₃	semidirect
40. C₃×#953	C₂×C₃	semidirect
41. C₃×#930	C₂×C₃	semidirect
42. C₃×#929	C₂×C₃	semidirect
43. C₃×C₄×#67	C₂×C₃	semidirect
44. C₃×#926	C₂×C₃	semidirect
45. C₃×#924	C₂×C₃	semidirect
54. C₂×C₃³×C₄	D₄	semidirect
66. #5791	C₃²	direct (N × H)
94. C₂×C₃×D₁₂	C₂²×C₃	semidirect
95. C₂×C₃×C₄×D₃	C₂²×C₃	semidirect
96. C₂×C₃×Dic₆	C₂²×C₃	semidirect
105. C₃×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
106. C₃×C₄⋊Dic₃	C₂²×C₃	semidirect
107. C₃×Dic₃⋊C₄	C₂²×C₃	semidirect
108. C₃×C₄×Dic₃	C₂²×C₃	semidirect
114. C₂²×C₃³	#41	semidirect
125. C₂³×C₃×C₄	C₃×D₃	semidirect
126. C₂³×C₃×C₄	C₂×C₃²	semidirect
127. C₂×#235	C₂×C₃²	semidirect
134. #953	C₂×C₃²	semidirect
135. #930	C₂×C₃²	semidirect
136. #929	C₂×C₃²	semidirect
137. C₄×#67	C₂×C₃²	semidirect
138. #926	C₂×C₃²	semidirect
139. #924	C₂×C₃²	semidirect
174. C₂×C₃²×C₄	#67	semidirect
175. C₂×C₃²×C₄	C₃×D₄	semidirect
222. C₂×D₁₂	C₂²×C₃²	semidirect
223. C₂×C₄×D₃	C₂²×C₃²	semidirect
224. C₂×Dic₆	C₂²×C₃²	semidirect
233. (C₂×D₃)⋊C₄	C₂²×C₃²	semidirect
234. C₄⋊Dic₃	C₂²×C₃²	semidirect
235. Dic₃⋊C₄	C₂²×C₃²	semidirect
236. C₄×Dic₃	C₂²×C₃²	semidirect
254. C₂²×C₃²	#235	semidirect
257. C₂²×C₃²	C₃×#41	semidirect
276. C₂³×C₄	C₃²×D₃	semidirect
283. C₃³	#525	semidirect
318. C₂×C₃×C₄	C₃×#67	semidirect
319. C₂×C₃×C₄	C₃²×D₄	semidirect
382. C₂²×C₃	C₃×#235	semidirect
385. C₂²×C₃	C₃²×#41	semidirect
404. C₃²	#5791	direct (N × H)
405. C₃²	C₃×#525	semidirect
421. C₂×C₄	C₃²×#67	semidirect
445. C₂²	C₃²×#235	semidirect
454. C₃	C₃×#5791	direct (N × H)
455. 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
C₂³×C₃³×C₄	2
C₂×C₃²×#235	2
C₃²×#953	2
C₃²×#930	2
C₃²×#929	2
C₃²×C₄×#67	2
C₃²×#926	2
C₃²×#924	2
C₃²×#525	3
C₃×#5791	3

Subgroups — C32×#5791 #13179168

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#5791 #13179168