Subgroups — C₃×#10596262 #13179542

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×C₃×#3828	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#64162	C₂	1	2	yes	maximal, complemented
4	C₃×#64139	C₂	1	2	yes	maximal, complemented
5	C₃×#64138	C₂	1	2	yes	maximal, complemented
6	C₃×C₄×#638	C₂	1	4	yes	maximal, complemented
7	C₃×#64135	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#64133	C₂	1	2	yes	maximal, complemented
9	#10596262	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₃×#5791	—	3	4	no	maximal
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×C₃×#638	C₂²	1	4	yes	—
18	C₂×C₃×#638	C₂²	1	2	yes	—
19	C₃×#3828	—	2	4	no	—
20	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	2	yes	complemented
22	C₂×C₃×#634	C₂²	1	1	yes	characteristic, complemented
23	C₃×#3757	C₂²	1	4	yes	—
24	C₃×#3757	C₂²	1	2	yes	—
25	C₃×#3752	C₂²	1	4	yes	complemented
26	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	complemented
27	C₃×#3750	C₂²	1	4	yes	complemented
28	C₃×C₄×C₃⋊Dic₃	C₂²	1	2	yes	complemented
29	C₂³×C₃²×C₄	—	2	4	no	—
30	C₂³×C₃²×C₄	D₃	1	4	yes	complemented
31	C₂³×C₃²×C₄	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂×#3828	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×C₃×#235	—	3	4	no	—
34	#64162	C₂×C₃	1	2	yes	complemented
35	#64139	C₂×C₃	1	2	yes	complemented
36	#64138	C₂×C₃	1	2	yes	complemented
37	C₄×#638	C₂×C₃	1	4	yes	complemented
38	#64135	C₂×C₃	1	1	yes	characteristic, complemented
39	#64133	C₂×C₃	1	2	yes	complemented
40	C₃×#953	—	3	8	no	—
41	C₃×#930	—	3	8	no	—
42	C₃×#929	—	3	8	no	—
43	C₃×C₄×#67	—	3	16	no	—
44	C₃×#926	—	3	4	no	—
45	C₃×#924	—	3	8	no	—
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×C₃×C₃⋊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	C₃×#638	—	2	4	no	—
59	C₃×#638	—	2	8	no	—
60	C₂×C₃×C₃⋊Dic₃	C₂³	1	4	yes	—
61	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
62	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
63	C₃×C₄×C₃⋊D₃	—	2	4	no	—
64	C₃×#634	—	2	2	no	—
65	C₃×#525	—	9	1	no	—
66	#5791	—	3	4	no	—
67	C₂⁴×C₃²	—	2	4	no	—
68	C₂⁴×C₃²	C₂×D₃	1	4	yes	—
69	C₂⁴×C₃²	C₂²×C₃	1	1	yes	characteristic
70	C₂²×C₃²×C₄	—	2	32	no	—
71	C₂²×C₃²×C₄	—	2	8	no	—
72	C₂²×C₃²×C₄	—	2	8	no	—
73	C₂²×C₃²×C₄	—	2	4	no	—
74	C₂²×C₃²×C₄	—	2	4	no	—
75	C₂²×C₃²×C₄	—	2	16	no	—
76	C₂²×C₃²×C₄	—	2	4	no	—
77	C₂²×C₃²×C₄	C₂×D₃	1	8	yes	—
78	C₂²×C₃²×C₄	C₂×D₃	1	8	yes	—
79	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
80	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
81	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
82	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
83	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
84	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
85	C₂×#638	C₂²×C₃	1	2	yes	—
86	C₂×#638	C₂²×C₃	1	4	yes	—
87	#3828	—	2	4	no	—
88	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic, complemented
89	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	2	yes	complemented
90	C₂×#634	C₂²×C₃	1	1	yes	characteristic, complemented
91	C₂×C₃×#67	—	3	16	no	—
92	C₂×C₃×#67	—	3	8	no	—
93	C₃×#235	—	6	16	no	—
94	C₂×C₃×D₁₂	—	3	4	no	—
95	C₂×C₃×C₄×D₃	—	3	8	no	—
96	C₂×C₃×Dic₆	—	3	4	no	—
97	#3757	C₂²×C₃	1	4	yes	—
98	#3757	C₂²×C₃	1	2	yes	—
99	#3752	C₂²×C₃	1	4	yes	complemented
100	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	2	yes	complemented
101	#3750	C₂²×C₃	1	4	yes	complemented
102	C₄×C₃⋊Dic₃	C₂²×C₃	1	2	yes	complemented
103	C₃×#217	—	3	16	no	—
104	C₃×#217	—	3	8	no	—
105	C₃×(C₂×D₃)⋊C₄	—	3	16	no	—
106	C₃×C₄⋊Dic₃	—	3	8	no	—
107	C₃×Dic₃⋊C₄	—	3	16	no	—
108	C₃×C₄×Dic₃	—	3	8	no	—
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×C₃×C₃⋊D₃	—	2	2	no	—
117	C₂×C₃×C₃⋊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	C₃×C₃⋊Dic₃	—	2	2	no	—
122	C₃×C₃⋊Dic₃	—	2	4	no	—
123	C₂×C₃×#41	—	9	1	no	—
124	C₂³×C₃×C₄	—	2	4	no	—
125	C₂³×C₃×C₄	C₃×D₃	1	4	yes	complemented
126	C₂³×C₃×C₄	C₃⋊D₃	1	1	yes	characteristic, complemented
127	C₂×#235	—	3	4	no	—
128	C₃×#123	—	9	2	no	—
129	C₃×C₂²⋊Q₈	—	9	2	no	—
130	C₃×#121	—	9	2	no	—
131	C₃×#120	—	9	2	no	—
132	C₃×C₄×D₄	—	9	4	no	—
133	C₃×#117	—	9	1	no	—
134	#953	—	3	8	no	—
135	#930	—	3	8	no	—
136	#929	—	3	8	no	—
137	C₄×#67	—	3	16	no	—
138	#926	—	3	4	no	—
139	#924	—	3	8	no	—
140	C₂³×C₃²	—	2	32	no	—
141	C₂³×C₃²	—	2	16	no	—
142	C₂³×C₃²	—	2	16	no	—
143	C₂³×C₃²	—	2	8	no	—
144	C₂³×C₃²	—	2	2	no	—
145	C₂³×C₃²	—	2	4	no	—
146	C₂³×C₃²	—	2	8	no	—
147	C₂³×C₃²	—	2	4	no	—
148	C₂³×C₃²	C₂²×D₃	1	8	yes	—
149	C₂³×C₃²	C₂²×D₃	1	4	yes	—
150	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
151	C₂³×C₃²	C₂³×C₃	1	2	yes	—
152	C₂²×C₃⋊D₃	C₂³×C₃	1	2	yes	—
153	C₂²×C₃×D₃	—	3	8	no	—
154	C₂×C₃²×C₄	—	2	16	no	—
155	C₂×C₃²×C₄	—	2	32	no	—
156	C₂×C₃²×C₄	—	2	32	no	—
157	C₂×C₃²×C₄	—	2	8	no	—
158	C₂×C₃²×C₄	—	2	2	no	—
159	C₂×C₃²×C₄	—	2	16	no	—
160	C₂×C₃²×C₄	—	2	16	no	—
161	C₂×C₃²×C₄	—	2	4	no	—
162	C₂×C₃²×C₄	—	2	4	no	—
163	C₂×C₃²×C₄	—	2	16	no	—
164	C₂×C₃²×C₄	—	2	8	no	—
165	C₂×C₃²×C₄	—	2	4	no	—
166	C₂×C₃²×C₄	—	2	4	no	—
167	C₂×C₃²×C₄	#67	1	16	yes	complemented
168	C₂×C₃²×C₄	C₃×D₄	1	4	yes	complemented
169	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
170	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
171	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
172	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
173	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
174	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
175	#638	—	2	4	no	—
176	#638	—	2	8	no	—
177	C₂×C₃⋊Dic₃	C₂³×C₃	1	4	yes	—
178	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
179	C₄⋊(C₃⋊D₃)	—	2	2	no	—
180	C₄×C₃⋊D₃	—	2	4	no	—
181	#634	—	2	2	no	—
182	C₃×#67	—	6	32	no	—
183	C₃×#67	—	6	16	no	—
184	C₂×C₃×Dic₃	—	3	16	no	—
185	C₂×C₃×Dic₃	—	3	8	no	—
186	C₃×D₁₂	—	6	8	no	—
187	C₃×C₄×D₃	—	6	16	no	—
188	C₃×Dic₆	—	6	8	no	—
189	#525	—	9	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	C₃×C₃⋊D₃	—	4	2	no	—
195	C₂⁴×C₃	—	2	4	no	—
196	C₂⁴×C₃	C₂×C₃×D₃	1	4	yes	—
197	C₂⁴×C₃	C₂×C₃⋊D₃	1	1	yes	characteristic
198	C₃×#41	—	18	4	no	—
199	C₂×C₃×Q₈	—	9	1	no	—
200	C₂×C₃×D₄	—	9	4	no	—
201	C₂×C₃×D₄	—	9	2	no	—
202	C₂×C₃×D₄	—	9	1	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	—	9	2	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	C₂×C₃⋊D₃	1	2	yes	—
216	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
217	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	2	yes	—
218	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
219	C₂×#67	—	3	16	no	—
220	C₂×#67	—	3	8	no	—
221	#235	—	6	16	no	—
222	C₂×D₁₂	—	3	4	no	—
223	C₂×C₄×D₃	—	3	8	no	—
224	C₂×Dic₆	—	3	4	no	—
225	C₃×C₄⋊C₄	—	9	4	no	—
226	C₃×C₄⋊C₄	—	9	2	no	—
227	C₃×C₂²⋊C₄	—	9	2	no	—
228	C₃×C₂²⋊C₄	—	9	4	no	—
229	C₃×C₂²⋊C₄	—	9	4	no	—
230	C₃×C₄²	—	9	2	no	—
231	#217	—	3	16	no	—
232	#217	—	3	8	no	—
233	(C₂×D₃)⋊C₄	—	3	16	no	—
234	C₄⋊Dic₃	—	3	8	no	—
235	Dic₃⋊C₄	—	3	16	no	—
236	C₄×Dic₃	—	3	8	no	—
237	C₂²×C₃²	—	2	16	no	—
238	C₂²×C₃²	—	2	64	no	—
239	C₂²×C₃²	—	2	32	no	—
240	C₂²×C₃²	—	2	8	no	—
241	C₂²×C₃²	—	2	16	no	—
242	C₂²×C₃²	—	2	16	no	—
243	C₂²×C₃²	—	2	8	no	—
244	C₂²×C₃²	—	2	8	no	—
245	C₂²×C₃²	—	2	8	no	—
246	C₂²×C₃²	—	2	2	no	—
247	C₂²×C₃²	—	2	2	no	—
248	C₂²×C₃²	—	2	2	no	—
249	C₂²×C₃²	—	2	4	no	—
250	C₂²×C₃²	—	2	16	no	—
251	C₂²×C₃²	—	2	8	no	—
252	C₂²×C₃²	#235	1	16	yes	complemented
253	C₂²×C₃²	C₂×#67	1	8	yes	—
254	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
255	C₂²×C₃²	C₃×#41	1	4	yes	complemented
256	C₂²×C₃²	C₂³×D₃	1	4	yes	—
257	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
258	C₂×C₃⋊D₃	—	2	2	no	—
259	C₂×C₃⋊D₃	—	2	4	no	—
260	C₂×C₃×D₃	—	6	16	no	—
261	C₂×C₃×D₃	—	6	8	no	—
262	C₃²×C₄	—	2	16	no	—
263	C₃²×C₄	—	2	8	no	—
264	C₃²×C₄	—	2	2	no	—
265	C₃²×C₄	—	2	8	no	—
266	C₃²×C₄	—	2	8	no	—
267	C₃²×C₄	C₂×#67	1	8	yes	—
268	C₃²×C₄	C₂×#67	1	8	yes	—
269	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
270	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
271	C₃⋊Dic₃	—	2	2	no	—
272	C₃⋊Dic₃	—	2	4	no	—
273	C₃×Dic₃	—	6	16	no	—
274	C₃×Dic₃	—	6	8	no	—
275	C₂×#41	—	9	1	no	—
276	C₂³×C₄	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
277	#123	—	9	2	no	—
278	C₂²⋊Q₈	—	9	2	no	—
279	#121	—	9	2	no	—
280	#120	—	9	2	no	—
281	C₄×D₄	—	9	4	no	—
282	#117	—	9	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	4	no	—
289	C₂³×C₃	—	2	2	no	—
290	C₂³×C₃	—	2	8	no	—
291	C₂³×C₃	—	2	4	no	—
292	C₂³×C₃	—	9	2	no	—
293	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
294	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
295	C₂³×C₃	C₂²×C₃⋊D₃	1	2	yes	—
296	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
297	C₂²×D₃	—	3	8	no	—
298	C₃×Q₈	—	18	2	no	—
299	C₃×D₄	—	18	8	no	—
300	C₃×D₄	—	18	4	no	—
301	C₃×D₄	—	18	2	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	—	9	4	no	—
316	C₂×C₃×C₄	—	9	2	no	—
317	C₂×C₃×C₄	—	18	4	no	—
318	C₂×C₃×C₄	C₃×#67	1	16	yes	complemented
319	C₂×C₃×C₄	#638	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	C₂²×C₃⋊D₃	1	2	yes	—
324	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
325	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
326	#67	—	6	32	no	—
327	#67	—	6	16	no	—
328	C₂×Dic₃	—	3	16	no	—
329	C₂×Dic₃	—	3	8	no	—
330	D₁₂	—	6	8	no	—
331	C₄×D₃	—	6	16	no	—
332	Dic₆	—	6	8	no	—
333	C₂×C₃²	—	2	32	no	—
334	C₂×C₃²	—	2	16	no	—
335	C₂×C₃²	—	2	16	no	—
336	C₂×C₃²	—	2	8	no	—
337	C₂×C₃²	—	2	2	no	—
338	C₂×C₃²	—	2	4	no	—
339	C₂×C₃²	—	2	8	no	—
340	C₂×C₃²	—	2	4	no	—
341	C₂×C₃²	C₂×#235	1	8	yes	—
342	C₂×C₃²	C₂²×#67	1	4	yes	—
343	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
344	C₂×C₃²	C₂×C₃×#41	1	2	yes	—
345	C₃⋊D₃	—	4	2	no	—
346	C₃×D₃	—	12	8	no	—
347	C₂⁴	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
348	#41	—	18	4	no	—
349	C₂×Q₈	—	9	1	no	—
350	C₂×D₄	—	9	4	no	—
351	C₂×D₄	—	9	2	no	—
352	C₂×D₄	—	9	1	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	9	2	no	—
355	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
356	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
357	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
358	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
359	C₄⋊C₄	—	9	2	no	—
360	C₄⋊C₄	—	9	4	no	—
361	C₂²⋊C₄	—	9	2	no	—
362	C₂²⋊C₄	—	9	4	no	—
363	C₂²⋊C₄	—	9	4	no	—
364	C₄²	—	9	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	—	18	4	no	—
381	C₂²×C₃	—	18	2	no	—
382	C₂²×C₃	C₃×#235	1	16	yes	complemented
383	C₂²×C₃	C₂×C₃×#67	1	8	yes	—
384	C₂²×C₃	#3828	1	4	yes	complemented
385	C₂²×C₃	C₂×#638	1	2	yes	—
386	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
387	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
388	C₂×D₃	—	6	16	no	—
389	C₂×D₃	—	6	8	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	—	18	4	no	—
396	C₃×C₄	—	18	2	no	—
397	C₃×C₄	C₂×C₃×#67	1	8	yes	—
398	C₃×C₄	C₂×C₃×#67	1	8	yes	—
399	C₃×C₄	C₂×#638	1	2	yes	—
400	C₃×C₄	C₂×#638	1	2	yes	—
401	Dic₃	—	6	16	no	—
402	Dic₃	—	6	8	no	—
403	C₃²	—	2	4	no	—
404	C₃²	#5791	1	4	yes	complemented
405	C₃²	C₃×#525	1	1	yes	characteristic, complemented
406	C₂³	—	2	4	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	9	2	no	—
409	C₂³	C₂²×C₃×C₃⋊D₃	1	2	yes	—
410	C₂³	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
411	Q₈	—	18	2	no	—
412	D₄	—	18	8	no	—
413	D₄	—	18	4	no	—
414	D₄	—	18	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	9	4	no	—
419	C₂×C₄	—	9	2	no	—
420	C₂×C₄	—	18	4	no	—
421	C₂×C₄	C₃×#638	1	4	yes	complemented
422	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
423	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
424	C₂×C₄	C₂²×C₃×C₃⋊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	4	no	—
430	C₂×C₃	—	2	2	no	—
431	C₂×C₃	—	2	8	no	—
432	C₂×C₃	—	2	4	no	—
433	C₂×C₃	—	36	2	no	—
434	C₂×C₃	C₂×C₃×#235	1	8	yes	—
435	C₂×C₃	C₂²×C₃×#67	1	4	yes	—
436	C₂×C₃	C₂×#3828	1	2	yes	—
437	C₂×C₃	C₂²×#638	1	1	yes	characteristic
438	D₃	—	12	8	no	—
439	C₂²	—	2	8	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	18	4	no	—
444	C₂²	—	18	2	no	—
445	C₂²	C₃×#3828	1	4	yes	complemented
446	C₂²	C₂×C₃×#638	1	2	yes	—
447	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
448	C₄	—	2	2	no	—
449	C₄	—	18	4	no	—
450	C₄	—	18	2	no	—
451	C₄	C₂×C₃×#638	1	2	yes	—
452	C₄	C₂×C₃×#638	1	2	yes	—
453	C₃	—	2	4	no	—
454	C₃	C₃×#5791	1	4	yes	complemented
455	C₃	#10596262	1	1	yes	characteristic, direct product factor
456	C₂	—	2	4	no	—
457	C₂	—	2	2	no	—
458	C₂	—	36	2	no	—
459	C₂	C₂×C₃×#3828	1	2	yes	—
460	C₂	C₂²×C₃×#638	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×C₃⋊D₃
commutator, cosocle	C₂²×C₃²	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×C₃⋊D₃
Fitting	C₂³×C₃³×C₄	C₂
socle	C₂²×C₃³	C₂⁴
hypercenter	C₂³×C₃×C₄	C₃⋊D₃
hypocenter	C₃²	C₃×#525
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂³×C₃×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×C₃×#3828	C₂	semidirect
3. C₃×#64162	C₂	semidirect
4. C₃×#64139	C₂	semidirect
5. C₃×#64138	C₂	semidirect
6. C₃×C₄×#638	C₂	semidirect
7. C₃×#64135	C₂	semidirect
8. C₃×#64133	C₂	semidirect
9. #10596262	C₃	direct (N × H)
20. C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	semidirect
21. C₂×C₃×C₄×C₃⋊D₃	C₂²	semidirect
22. C₂×C₃×#634	C₂²	semidirect
25. C₃×#3752	C₂²	semidirect
26. C₃×C₄⋊(C₃⋊Dic₃)	C₂²	semidirect
27. C₃×#3750	C₂²	semidirect
28. C₃×C₄×C₃⋊Dic₃	C₂²	semidirect
30. C₂³×C₃²×C₄	D₃	semidirect
31. C₂³×C₃²×C₄	C₂×C₃	semidirect
32. C₂×#3828	C₂×C₃	semidirect
34. #64162	C₂×C₃	semidirect
35. #64139	C₂×C₃	semidirect
36. #64138	C₂×C₃	semidirect
37. C₄×#638	C₂×C₃	semidirect
38. #64135	C₂×C₃	semidirect
39. #64133	C₂×C₃	semidirect
54. C₂×C₃³×C₄	D₄	semidirect
88. C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	semidirect
89. C₂×C₄×C₃⋊D₃	C₂²×C₃	semidirect
90. C₂×#634	C₂²×C₃	semidirect
99. #3752	C₂²×C₃	semidirect
100. C₄⋊(C₃⋊Dic₃)	C₂²×C₃	semidirect
101. #3750	C₂²×C₃	semidirect
102. C₄×C₃⋊Dic₃	C₂²×C₃	semidirect
114. C₂²×C₃³	#41	semidirect
125. C₂³×C₃×C₄	C₃×D₃	semidirect
126. C₂³×C₃×C₄	C₃⋊D₃	semidirect
167. C₂×C₃²×C₄	#67	semidirect
168. C₂×C₃²×C₄	C₃×D₄	semidirect
252. C₂²×C₃²	#235	semidirect
255. C₂²×C₃²	C₃×#41	semidirect
276. C₂³×C₄	C₃×C₃⋊D₃	semidirect
283. C₃³	#525	semidirect
318. C₂×C₃×C₄	C₃×#67	semidirect
319. C₂×C₃×C₄	#638	semidirect
382. C₂²×C₃	C₃×#235	semidirect
384. C₂²×C₃	#3828	semidirect
404. C₃²	#5791	semidirect
405. C₃²	C₃×#525	semidirect
421. C₂×C₄	C₃×#638	semidirect
445. C₂²	C₃×#3828	semidirect
454. C₃	C₃×#5791	semidirect
455. C₃	#10596262	direct (N × H)

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×C₃×#3828	2
C₃×#64162	2
C₃×#64139	2
C₃×#64138	2
C₃×C₄×#638	2
C₃×#64135	2
C₃×#64133	2
#10596262	3
C₃×#5791	3

Subgroups — C3×#10596262 #13179542

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596262 #13179542