Subgroups — C₃×#10596293 #13179576

Order 1728.

2228 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#3828	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#64160	C₂	1	2	yes	maximal, complemented
4	C₃×#64159	C₂	1	4	yes	maximal, complemented
5	C₃×#64158	C₂	1	2	yes	maximal, complemented
6	C₃×#64151	C₂	1	2	yes	maximal, complemented
7	C₃×#64141	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×#3748	C₂	1	1	yes	maximal, characteristic, complemented
9	#10596293	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₃×#5822	—	3	4	no	maximal
11	C₃³×#41	—	2	1	no	—
12	C₃³×#41	—	2	1	no	—
13	C₃³×#41	C₂²	1	2	yes	—
14	C₃³×#41	C₂²	1	2	yes	complemented
15	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₃³×D₄	—	2	1	no	—
17	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₃³×C₄	—	2	1	no	—
19	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×#638	—	2	1	no	—
21	C₃×#3828	—	2	1	no	—
22	C₃×#3828	—	2	1	no	—
23	C₃×#3828	C₂²	1	2	yes	—
24	C₃×#3828	C₂²	1	2	yes	complemented
25	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃×C₄×C₃⋊D₃	—	2	1	no	—
27	C₂×C₃×#634	C₂²	1	1	yes	characteristic, complemented
28	C₃×#3756	C₂²	1	4	yes	complemented
29	C₃×#3755	C₂²	1	4	yes	complemented
30	C₃×#3754	C₂²	1	4	yes	complemented
31	C₃×#3753	C₂²	1	4	yes	complemented
32	C₃×#3748	C₂²	1	2	yes	complemented
33	C₃×#3748	C₂²	1	2	yes	complemented
34	C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	1	2	yes	complemented
35	C₂×C₃²×#41	—	2	4	no	—
36	C₂×C₃²×#41	D₃	1	4	yes	complemented
37	C₂×C₃²×#41	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂×#3828	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂×C₃×#235	—	3	4	no	—
40	#64160	C₂×C₃	1	2	yes	complemented
41	#64159	C₂×C₃	1	4	yes	complemented
42	#64158	C₂×C₃	1	2	yes	complemented
43	#64151	C₂×C₃	1	2	yes	complemented
44	#64141	C₂×C₃	1	2	yes	complemented
45	C₂×#3748	C₂×C₃	1	1	yes	characteristic, complemented
46	C₃×#951	—	3	8	no	—
47	C₃×#950	—	3	16	no	—
48	C₃×#949	—	3	8	no	—
49	C₃×#942	—	3	8	no	—
50	C₃×#932	—	3	8	no	—
51	C₂×C₃×#208	—	3	4	no	—
52	C₂³×C₃³	—	2	1	no	—
53	C₂³×C₃³	D₄	1	1	yes	characteristic
54	C₂²×C₃×C₃⋊D₃	—	2	1	no	—
55	C₃³×Q₈	—	2	1	no	—
56	C₃³×Q₈	C₂³	1	2	yes	—
57	C₃³×D₄	—	2	2	no	—
58	C₃³×D₄	—	2	2	no	—
59	C₃³×D₄	—	2	1	no	—
60	C₃³×D₄	C₂³	1	2	yes	—
61	C₂×C₃³×C₄	—	2	1	no	—
62	C₂×C₃³×C₄	—	2	2	no	—
63	C₂×C₃³×C₄	—	2	2	no	—
64	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
65	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
66	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
67	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
68	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
69	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
70	C₃×#638	—	2	2	no	—
71	C₃×#638	—	2	2	no	—
72	C₂×C₃×C₃⋊Dic₃	—	2	1	no	—
73	C₃×C₄⋊(C₃⋊D₃)	—	2	1	no	—
74	C₃×C₄⋊(C₃⋊D₃)	C₂³	1	2	yes	—
75	C₃×C₄×C₃⋊D₃	—	2	2	no	—
76	C₃×C₄×C₃⋊D₃	—	2	2	no	—
77	C₃×#634	—	2	1	no	—
78	C₃×#634	C₂³	1	2	yes	—
79	C₃×C₃⋊(C₃⋊C₈)	C₂³	1	4	yes	—
80	C₃×#575	—	9	1	no	—
81	#5822	—	3	4	no	—
82	C₃²×#41	—	2	8	no	—
83	C₃²×#41	—	2	8	no	—
84	C₃²×#41	—	2	8	no	—
85	C₃²×#41	—	2	8	no	—
86	C₃²×#41	—	2	4	no	—
87	C₃²×#41	—	2	4	no	—
88	C₃²×#41	—	2	1	no	—
89	C₃²×#41	—	2	1	no	—
90	C₃²×#41	C₂×D₃	1	8	yes	—
91	C₃²×#41	C₂×D₃	1	8	yes	complemented
92	C₃²×#41	C₂²×C₃	1	2	yes	—
93	C₃²×#41	C₂²×C₃	1	2	yes	complemented
94	C₂×C₃²×Q₈	—	2	4	no	—
95	C₂×C₃²×Q₈	C₂×D₃	1	4	yes	complemented
96	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
97	C₂×C₃²×D₄	—	2	8	no	—
98	C₂×C₃²×D₄	—	2	4	no	—
99	C₂×C₃²×D₄	—	2	4	no	—
100	C₂×C₃²×D₄	—	2	1	no	—
101	C₂×C₃²×D₄	C₂×D₃	1	4	yes	complemented
102	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
103	C₂²×C₃²×C₄	—	2	8	no	—
104	C₂²×C₃²×C₄	—	2	4	no	—
105	C₂²×C₃²×C₄	—	2	4	no	—
106	C₂²×C₃²×C₄	—	2	1	no	—
107	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
108	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
109	C₂×#638	—	2	1	no	—
110	#3828	—	2	1	no	—
111	#3828	—	2	1	no	—
112	#3828	C₂²×C₃	1	2	yes	—
113	#3828	C₂²×C₃	1	2	yes	complemented
114	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic, complemented
115	C₂×C₄×C₃⋊D₃	—	2	1	no	—
116	C₂×#634	C₂²×C₃	1	1	yes	characteristic, complemented
117	C₂×C₃×#67	—	6	4	no	—
118	C₃×#235	—	3	8	no	—
119	C₃×#235	—	3	8	no	—
120	C₃×#235	—	6	4	no	—
121	C₃×#235	—	6	4	no	—
122	C₂×C₃×D₁₂	—	3	4	no	—
123	C₂×C₃×C₄×D₃	—	6	4	no	—
124	C₂×C₃×Dic₆	—	3	4	no	—
125	#3756	C₂²×C₃	1	4	yes	complemented
126	#3755	C₂²×C₃	1	4	yes	complemented
127	#3754	C₂²×C₃	1	4	yes	complemented
128	#3753	C₂²×C₃	1	4	yes	complemented
129	#3748	C₂²×C₃	1	2	yes	complemented
130	#3748	C₂²×C₃	1	2	yes	complemented
131	C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	1	2	yes	complemented
132	C₃×#216	—	3	16	no	—
133	C₃×#215	—	3	16	no	—
134	C₃×#214	—	3	16	no	—
135	C₃×#213	—	3	16	no	—
136	C₃×#208	—	3	8	no	—
137	C₃×#208	—	3	8	no	—
138	C₂×C₃×C₃⋊C₈	—	3	8	no	—
139	C₂²×C₃³	—	2	2	no	—
140	C₂²×C₃³	—	4	1	no	—
141	C₂²×C₃³	—	4	2	no	—
142	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
145	C₂×C₃×C₃⋊D₃	—	2	2	no	—
146	C₂×C₃×C₃⋊D₃	—	4	2	no	—
147	C₃³×C₄	—	2	2	no	—
148	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
149	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
150	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
151	C₃³×C₄	C₂⁴	1	1	yes	characteristic
152	C₃×C₃⋊Dic₃	—	2	2	no	—
153	C₂×C₃×#41	—	2	4	no	—
154	C₂×C₃×#41	—	9	1	no	—
155	C₂×C₃×#41	C₃×D₃	1	4	yes	complemented
156	C₂×C₃×#41	C₃⋊D₃	1	1	yes	characteristic, complemented
157	C₂×#235	—	3	4	no	—
158	C₃×#137	—	9	2	no	—
159	C₃×#137	—	9	2	no	—
160	C₃×AGL(1,ℤ/8)	—	9	2	no	—
161	C₃×AGL(1,ℤ/8)	—	9	2	no	—
162	C₃×#135	—	9	4	no	—
163	C₂×C₃×M₁₆	—	9	1	no	—
164	#951	—	3	8	no	—
165	#950	—	3	16	no	—
166	#949	—	3	8	no	—
167	#942	—	3	8	no	—
168	#932	—	3	8	no	—
169	C₂×#208	—	3	4	no	—
170	C₂³×C₃²	—	2	8	no	—
171	C₂³×C₃²	—	2	4	no	—
172	C₂³×C₃²	—	2	1	no	—
173	C₂³×C₃²	—	2	4	no	—
174	C₂³×C₃²	#67	1	4	yes	—
175	C₂³×C₃²	C₃×D₄	1	1	yes	characteristic
176	C₂²×C₃⋊D₃	—	2	1	no	—
177	C₂²×C₃×D₃	—	6	4	no	—
178	C₃²×Q₈	—	2	8	no	—
179	C₃²×Q₈	—	2	4	no	—
180	C₃²×Q₈	—	2	1	no	—
181	C₃²×Q₈	—	2	8	no	—
182	C₃²×Q₈	C₂²×D₃	1	8	yes	—
183	C₃²×Q₈	C₂³×C₃	1	2	yes	—
184	C₃²×D₄	—	2	16	no	—
185	C₃²×D₄	—	2	16	no	—
186	C₃²×D₄	—	2	8	no	—
187	C₃²×D₄	—	2	8	no	—
188	C₃²×D₄	—	2	8	no	—
189	C₃²×D₄	—	2	2	no	—
190	C₃²×D₄	—	2	2	no	—
191	C₃²×D₄	—	2	4	no	—
192	C₃²×D₄	—	2	1	no	—
193	C₃²×D₄	—	2	8	no	—
194	C₃²×D₄	C₂²×D₃	1	8	yes	—
195	C₃²×D₄	C₂³×C₃	1	2	yes	—
196	C₂×C₃²×C₄	—	2	8	no	—
197	C₂×C₃²×C₄	—	2	16	no	—
198	C₂×C₃²×C₄	—	2	16	no	—
199	C₂×C₃²×C₄	—	2	4	no	—
200	C₂×C₃²×C₄	—	2	1	no	—
201	C₂×C₃²×C₄	—	2	8	no	—
202	C₂×C₃²×C₄	—	2	8	no	—
203	C₂×C₃²×C₄	—	2	2	no	—
204	C₂×C₃²×C₄	—	2	2	no	—
205	C₂×C₃²×C₄	—	2	4	no	—
206	C₂×C₃²×C₄	—	2	4	no	—
207	C₂×C₃²×C₄	—	2	4	no	—
208	C₂×C₃²×C₄	—	2	4	no	—
209	C₂×C₃²×C₄	—	2	4	no	—
210	C₂×C₃²×C₄	—	2	4	no	—
211	C₂×C₃²×C₄	#67	1	4	yes	—
212	C₂×C₃²×C₄	#67	1	4	yes	—
213	C₂×C₃²×C₄	#67	1	4	yes	—
214	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
215	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
216	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
217	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
218	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
219	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
220	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
221	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
222	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
223	#638	—	2	2	no	—
224	#638	—	2	2	no	—
225	C₂×C₃⋊Dic₃	—	2	1	no	—
226	C₄⋊(C₃⋊D₃)	—	2	1	no	—
227	C₄⋊(C₃⋊D₃)	C₂³×C₃	1	2	yes	—
228	C₄×C₃⋊D₃	—	2	2	no	—
229	C₄×C₃⋊D₃	—	2	2	no	—
230	#634	—	2	1	no	—
231	#634	C₂³×C₃	1	2	yes	—
232	C₃×#67	—	6	8	no	—
233	C₃×#67	—	6	8	no	—
234	C₂×C₃×Dic₃	—	6	4	no	—
235	C₃×D₁₂	—	3	8	no	—
236	C₃×D₁₂	—	6	4	no	—
237	C₃×C₄×D₃	—	6	8	no	—
238	C₃×C₄×D₃	—	6	8	no	—
239	C₃×Dic₆	—	3	8	no	—
240	C₃×Dic₆	—	6	4	no	—
241	C₃⋊(C₃⋊C₈)	C₂³×C₃	1	4	yes	—
242	C₃×C₃⋊C₈	—	3	16	no	—
243	#575	—	9	1	no	Sylow
244	C₂×C₃³	—	2	1	no	—
245	C₂×C₃³	—	2	1	no	—
246	C₂×C₃³	—	2	1	no	—
247	C₂×C₃³	—	4	2	no	—
248	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
249	C₃×C₃⋊D₃	—	4	2	no	—
250	C₃×#41	—	2	8	no	—
251	C₃×#41	—	2	8	no	—
252	C₃×#41	—	2	4	no	—
253	C₃×#41	—	2	4	no	—
254	C₃×#41	—	2	1	no	—
255	C₃×#41	—	2	1	no	—
256	C₃×#41	—	2	8	no	—
257	C₃×#41	—	2	8	no	—
258	C₃×#41	—	9	2	no	—
259	C₃×#41	—	9	2	no	—
260	C₃×#41	—	18	1	no	—
261	C₃×#41	—	18	1	no	—
262	C₃×#41	C₂×C₃×D₃	1	8	yes	—
263	C₃×#41	C₂×C₃×D₃	1	8	yes	complemented
264	C₃×#41	C₂×C₃⋊D₃	1	2	yes	—
265	C₃×#41	C₂×C₃⋊D₃	1	2	yes	complemented
266	C₂×C₃×Q₈	—	2	4	no	—
267	C₂×C₃×Q₈	—	9	1	no	—
268	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	complemented
269	C₂×C₃×Q₈	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
270	C₂×C₃×D₄	—	2	8	no	—
271	C₂×C₃×D₄	—	2	4	no	—
272	C₂×C₃×D₄	—	2	1	no	—
273	C₂×C₃×D₄	—	2	4	no	—
274	C₂×C₃×D₄	—	9	1	no	—
275	C₂×C₃×D₄	—	18	1	no	—
276	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	complemented
277	C₂×C₃×D₄	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
278	C₂²×C₃×C₄	—	2	8	no	—
279	C₂²×C₃×C₄	—	2	4	no	—
280	C₂²×C₃×C₄	—	2	1	no	—
281	C₂²×C₃×C₄	—	2	4	no	—
282	C₂²×C₃×C₄	—	18	1	no	—
283	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
284	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
285	C₂×#67	—	6	4	no	—
286	#235	—	3	8	no	—
287	#235	—	3	8	no	—
288	#235	—	6	4	no	—
289	#235	—	6	4	no	—
290	C₂×D₁₂	—	3	4	no	—
291	C₂×C₄×D₃	—	6	4	no	—
292	C₂×Dic₆	—	3	4	no	—
293	C₃×Q₁₆	—	9	4	no	—
294	C₃×SD₁₆	—	9	4	no	—
295	C₃×SD₁₆	—	9	4	no	—
296	C₃×D₈	—	9	4	no	—
297	C₃×M₁₆	—	9	2	no	—
298	C₃×M₁₆	—	9	2	no	—
299	C₂×C₃×C₈	—	9	2	no	—
300	#216	—	3	16	no	—
301	#215	—	3	16	no	—
302	#214	—	3	16	no	—
303	#213	—	3	16	no	—
304	#208	—	3	8	no	—
305	#208	—	3	8	no	—
306	C₂×C₃⋊C₈	—	3	8	no	—
307	C₂²×C₃²	—	2	16	no	—
308	C₂²×C₃²	—	2	8	no	—
309	C₂²×C₃²	—	2	2	no	—
310	C₂²×C₃²	—	2	4	no	—
311	C₂²×C₃²	—	2	4	no	—
312	C₂²×C₃²	—	2	4	no	—
313	C₂²×C₃²	—	4	4	no	—
314	C₂²×C₃²	—	4	1	no	—
315	C₂²×C₃²	—	4	8	no	—
316	C₂²×C₃²	—	4	16	no	—
317	C₂²×C₃²	—	4	2	no	—
318	C₂²×C₃²	—	4	8	no	—
319	C₂²×C₃²	C₂×#67	1	4	yes	—
320	C₂²×C₃²	C₂×#67	1	4	yes	—
321	C₂²×C₃²	C₂×#67	1	4	yes	—
322	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
323	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
324	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
325	C₂×C₃⋊D₃	—	2	2	no	—
326	C₂×C₃⋊D₃	—	4	2	no	—
327	C₂×C₃×D₃	—	6	8	no	—
328	C₂×C₃×D₃	—	12	8	no	—
329	C₃²×C₄	—	2	16	no	—
330	C₃²×C₄	—	2	8	no	—
331	C₃²×C₄	—	2	2	no	—
332	C₃²×C₄	—	2	4	no	—
333	C₃²×C₄	—	2	4	no	—
334	C₃²×C₄	—	2	4	no	—
335	C₃²×C₄	—	2	4	no	—
336	C₃²×C₄	C₂×#67	1	4	yes	—
337	C₃²×C₄	C₂×#67	1	4	yes	—
338	C₃²×C₄	C₂×#67	1	4	yes	—
339	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
340	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
341	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
342	C₃²×C₄	C₂³×D₃	1	4	yes	—
343	C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
344	C₃⋊Dic₃	—	2	2	no	—
345	C₃×Dic₃	—	6	8	no	—
346	C₂×#41	—	9	1	no	—
347	C₂×#41	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
348	#137	—	9	2	no	—
349	#137	—	9	2	no	—
350	AGL(1,ℤ/8)	—	9	2	no	—
351	AGL(1,ℤ/8)	—	9	2	no	—
352	#135	—	9	4	no	—
353	C₂×M₁₆	—	9	1	no	—
354	C₃³	#575	1	1	yes	characteristic, complemented, Sylow
355	C₂³×C₃	—	2	8	no	—
356	C₂³×C₃	—	2	4	no	—
357	C₂³×C₃	—	2	1	no	—
358	C₂³×C₃	—	2	4	no	—
359	C₂³×C₃	—	18	1	no	—
360	C₂³×C₃	C₃×#67	1	4	yes	—
361	C₂³×C₃	#638	1	1	yes	characteristic
362	C₂²×D₃	—	6	4	no	—
363	C₃×Q₈	—	2	8	no	—
364	C₃×Q₈	—	2	4	no	—
365	C₃×Q₈	—	2	1	no	—
366	C₃×Q₈	—	2	8	no	—
367	C₃×Q₈	—	9	2	no	—
368	C₃×Q₈	—	18	1	no	—
369	C₃×Q₈	C₂²×C₃×D₃	1	8	yes	—
370	C₃×Q₈	C₂²×C₃⋊D₃	1	2	yes	—
371	C₃×D₄	—	2	16	no	—
372	C₃×D₄	—	2	16	no	—
373	C₃×D₄	—	2	8	no	—
374	C₃×D₄	—	2	8	no	—
375	C₃×D₄	—	2	8	no	—
376	C₃×D₄	—	2	2	no	—
377	C₃×D₄	—	2	2	no	—
378	C₃×D₄	—	2	4	no	—
379	C₃×D₄	—	2	1	no	—
380	C₃×D₄	—	2	8	no	—
381	C₃×D₄	—	9	2	no	—
382	C₃×D₄	—	18	2	no	—
383	C₃×D₄	—	18	2	no	—
384	C₃×D₄	—	18	1	no	—
385	C₃×D₄	C₂²×C₃×D₃	1	8	yes	—
386	C₃×D₄	C₂²×C₃⋊D₃	1	2	yes	—
387	C₂×C₃×C₄	—	2	8	no	—
388	C₂×C₃×C₄	—	2	16	no	—
389	C₂×C₃×C₄	—	2	16	no	—
390	C₂×C₃×C₄	—	2	4	no	—
391	C₂×C₃×C₄	—	2	1	no	—
392	C₂×C₃×C₄	—	2	8	no	—
393	C₂×C₃×C₄	—	2	8	no	—
394	C₂×C₃×C₄	—	2	2	no	—
395	C₂×C₃×C₄	—	2	2	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	4	no	—
400	C₂×C₃×C₄	—	2	4	no	—
401	C₂×C₃×C₄	—	2	4	no	—
402	C₂×C₃×C₄	—	18	1	no	—
403	C₂×C₃×C₄	—	18	2	no	—
404	C₂×C₃×C₄	—	18	2	no	—
405	C₂×C₃×C₄	C₃×#67	1	4	yes	—
406	C₂×C₃×C₄	C₃×#67	1	4	yes	—
407	C₂×C₃×C₄	C₃×#67	1	4	yes	—
408	C₂×C₃×C₄	#638	1	1	yes	characteristic
409	C₂×C₃×C₄	#638	1	1	yes	characteristic
410	C₂×C₃×C₄	#638	1	1	yes	characteristic
411	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
412	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
413	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
414	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
415	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
416	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
417	#67	—	6	8	no	—
418	#67	—	6	8	no	—
419	C₂×Dic₃	—	6	4	no	—
420	D₁₂	—	3	8	no	—
421	D₁₂	—	6	4	no	—
422	C₄×D₃	—	6	8	no	—
423	C₄×D₃	—	6	8	no	—
424	Dic₆	—	3	8	no	—
425	Dic₆	—	6	4	no	—
426	C₃×C₈	—	9	4	no	—
427	C₃⋊C₈	—	3	16	no	—
428	C₂×C₃²	—	2	8	no	—
429	C₂×C₃²	—	2	1	no	—
430	C₂×C₃²	—	2	1	no	—
431	C₂×C₃²	—	2	1	no	—
432	C₂×C₃²	—	2	4	no	—
433	C₂×C₃²	—	2	4	no	—
434	C₂×C₃²	—	2	4	no	—
435	C₂×C₃²	—	2	4	no	—
436	C₂×C₃²	—	4	4	no	—
437	C₂×C₃²	—	4	4	no	—
438	C₂×C₃²	—	4	16	no	—
439	C₂×C₃²	—	4	2	no	—
440	C₂×C₃²	—	4	8	no	—
441	C₂×C₃²	C₂²×#67	1	4	yes	—
442	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
443	C₃⋊D₃	—	4	2	no	—
444	C₃×D₃	—	12	8	no	—
445	#41	—	2	1	no	—
446	#41	—	2	1	no	—
447	#41	—	9	2	no	—
448	#41	—	9	2	no	—
449	#41	—	18	1	no	—
450	#41	—	18	1	no	—
451	#41	C₂×C₃×C₃⋊D₃	1	2	yes	—
452	#41	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
453	C₂×Q₈	—	9	1	no	—
454	C₂×Q₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	9	1	no	—
457	C₂×D₄	—	18	1	no	—
458	C₂×D₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	18	1	no	—
461	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
462	Q₁₆	—	9	4	no	—
463	SD₁₆	—	9	4	no	—
464	SD₁₆	—	9	4	no	—
465	D₈	—	9	4	no	—
466	M₁₆	—	9	2	no	—
467	M₁₆	—	9	2	no	—
468	C₂×C₈	—	9	2	no	—
469	C₂²×C₃	—	2	16	no	—
470	C₂²×C₃	—	2	8	no	—
471	C₂²×C₃	—	2	2	no	—
472	C₂²×C₃	—	2	4	no	—
473	C₂²×C₃	—	2	4	no	—
474	C₂²×C₃	—	2	4	no	—
475	C₂²×C₃	—	4	4	no	—
476	C₂²×C₃	—	4	1	no	—
477	C₂²×C₃	—	4	8	no	—
478	C₂²×C₃	—	4	16	no	—
479	C₂²×C₃	—	4	8	no	—
480	C₂²×C₃	—	4	2	no	—
481	C₂²×C₃	—	18	2	no	—
482	C₂²×C₃	—	36	2	no	—
483	C₂²×C₃	C₂×C₃×#67	1	4	yes	—
484	C₂²×C₃	C₂×C₃×#67	1	4	yes	—
485	C₂²×C₃	C₂×C₃×#67	1	4	yes	—
486	C₂²×C₃	C₂×#638	1	1	yes	characteristic
487	C₂²×C₃	C₂×#638	1	1	yes	characteristic
488	C₂²×C₃	C₂×#638	1	1	yes	characteristic
489	C₂×D₃	—	6	8	no	—
490	C₂×D₃	—	12	8	no	—
491	C₃×C₄	—	2	16	no	—
492	C₃×C₄	—	2	8	no	—
493	C₃×C₄	—	2	2	no	—
494	C₃×C₄	—	2	4	no	—
495	C₃×C₄	—	2	4	no	—
496	C₃×C₄	—	2	4	no	—
497	C₃×C₄	—	2	4	no	—
498	C₃×C₄	—	18	2	no	—
499	C₃×C₄	C₂×C₃×#67	1	4	yes	—
500	C₃×C₄	C₂×C₃×#67	1	4	yes	—
501	C₃×C₄	C₂×C₃×#67	1	4	yes	—
502	C₃×C₄	C₂×#638	1	1	yes	characteristic
503	C₃×C₄	C₂×#638	1	1	yes	characteristic
504	C₃×C₄	C₂×#638	1	1	yes	characteristic
505	C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
506	C₃×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
507	Dic₃	—	6	8	no	—
508	C₃²	—	2	4	no	—
509	C₃²	#5822	1	4	yes	complemented
510	C₃²	C₃×#575	1	1	yes	characteristic, complemented
511	C₂³	—	2	1	no	—
512	C₂³	—	18	1	no	—
513	C₂³	C₃×#638	1	1	yes	characteristic
514	Q₈	—	2	1	no	—
515	Q₈	—	9	2	no	—
516	Q₈	—	18	1	no	—
517	Q₈	C₂²×C₃×C₃⋊D₃	1	2	yes	—
518	D₄	—	2	2	no	—
519	D₄	—	2	2	no	—
520	D₄	—	2	1	no	—
521	D₄	—	9	2	no	—
522	D₄	—	18	2	no	—
523	D₄	—	18	2	no	—
524	D₄	—	18	1	no	—
525	D₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	18	1	no	—
530	C₂×C₄	—	18	2	no	—
531	C₂×C₄	—	18	2	no	—
532	C₂×C₄	C₃×#638	1	1	yes	characteristic
533	C₂×C₄	C₃×#638	1	1	yes	characteristic
534	C₂×C₄	C₃×#638	1	1	yes	characteristic
535	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
536	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
537	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
538	C₈	—	9	4	no	—
539	C₂×C₃	—	2	8	no	—
540	C₂×C₃	—	2	4	no	—
541	C₂×C₃	—	2	4	no	—
542	C₂×C₃	—	2	4	no	—
543	C₂×C₃	—	2	1	no	—
544	C₂×C₃	—	2	1	no	—
545	C₂×C₃	—	2	1	no	—
546	C₂×C₃	—	2	4	no	—
547	C₂×C₃	—	4	4	no	—
548	C₂×C₃	—	4	4	no	—
549	C₂×C₃	—	4	16	no	—
550	C₂×C₃	—	4	8	no	—
551	C₂×C₃	—	4	2	no	—
552	C₂×C₃	—	36	2	no	—
553	C₂×C₃	C₂²×C₃×#67	1	4	yes	—
554	C₂×C₃	C₂²×#638	1	1	yes	characteristic
555	D₃	—	12	8	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	18	2	no	—
560	C₂²	—	36	2	no	—
561	C₂²	C₂×C₃×#638	1	1	yes	characteristic
562	C₂²	C₂×C₃×#638	1	1	yes	characteristic
563	C₂²	C₂×C₃×#638	1	1	yes	characteristic
564	C₄	—	2	2	no	—
565	C₄	—	18	2	no	—
566	C₄	C₂×C₃×#638	1	1	yes	characteristic
567	C₄	C₂×C₃×#638	1	1	yes	characteristic
568	C₄	C₂×C₃×#638	1	1	yes	characteristic
569	C₄	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
570	C₃	—	2	4	no	—
571	C₃	C₃×#5822	1	4	yes	complemented
572	C₃	#10596293	1	1	yes	characteristic, direct product factor
573	C₂	—	2	1	no	—
574	C₂	—	2	1	no	—
575	C₂	—	2	1	no	—
576	C₂	—	4	2	no	—
577	C₂	—	36	2	no	—
578	C₂	C₂²×C₃×#638	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂×#638
commutator, cosocle	C₃²×C₄	C₂⁴×C₃
Frattini	C₄	C₂³×C₃×C₃⋊D₃
Fitting	C₂×C₃³×#41	C₂
socle	C₂×C₃³	C₂²×D₄
hypercenter	C₂×C₃×#41	C₃⋊D₃
hypocenter	C₃²	C₃×#575
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#41

Complements

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

N	H ≅ G/N	type
1. C₂×C₃³×#41	C₂	semidirect
2. C₂×C₃×#3828	C₂	semidirect
3. C₃×#64160	C₂	semidirect
4. C₃×#64159	C₂	semidirect
5. C₃×#64158	C₂	semidirect
6. C₃×#64151	C₂	semidirect
7. C₃×#64141	C₂	semidirect
8. C₂×C₃×#3748	C₂	semidirect
9. #10596293	C₃	direct (N × H)
14. C₃³×#41	C₂²	semidirect
15. C₂×C₃³×Q₈	C₂²	semidirect
17. C₂×C₃³×D₄	C₂²	semidirect
24. C₃×#3828	C₂²	semidirect
25. C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	semidirect
27. C₂×C₃×#634	C₂²	semidirect
28. C₃×#3756	C₂²	semidirect
29. C₃×#3755	C₂²	semidirect
30. C₃×#3754	C₂²	semidirect
31. C₃×#3753	C₂²	semidirect
32. C₃×#3748	C₂²	semidirect
33. C₃×#3748	C₂²	semidirect
34. C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	semidirect
36. C₂×C₃²×#41	D₃	semidirect
37. C₂×C₃²×#41	C₂×C₃	semidirect
38. C₂×#3828	C₂×C₃	semidirect
40. #64160	C₂×C₃	semidirect
41. #64159	C₂×C₃	semidirect
42. #64158	C₂×C₃	semidirect
43. #64151	C₂×C₃	semidirect
44. #64141	C₂×C₃	semidirect
45. C₂×#3748	C₂×C₃	semidirect
91. C₃²×#41	C₂×D₃	semidirect
93. C₃²×#41	C₂²×C₃	semidirect
95. C₂×C₃²×Q₈	C₂×D₃	semidirect
96. C₂×C₃²×Q₈	C₂²×C₃	semidirect
101. C₂×C₃²×D₄	C₂×D₃	semidirect
102. C₂×C₃²×D₄	C₂²×C₃	semidirect
113. #3828	C₂²×C₃	semidirect
114. C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	semidirect
116. C₂×#634	C₂²×C₃	semidirect
125. #3756	C₂²×C₃	semidirect
126. #3755	C₂²×C₃	semidirect
127. #3754	C₂²×C₃	semidirect
128. #3753	C₂²×C₃	semidirect
129. #3748	C₂²×C₃	semidirect
130. #3748	C₂²×C₃	semidirect
131. C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	semidirect
155. C₂×C₃×#41	C₃×D₃	semidirect
156. C₂×C₃×#41	C₃⋊D₃	semidirect
263. C₃×#41	C₂×C₃×D₃	semidirect
265. C₃×#41	C₂×C₃⋊D₃	semidirect
268. C₂×C₃×Q₈	C₂×C₃×D₃	semidirect
269. C₂×C₃×Q₈	C₂×C₃⋊D₃	semidirect
276. C₂×C₃×D₄	C₂×C₃×D₃	semidirect
277. C₂×C₃×D₄	C₂×C₃⋊D₃	semidirect
347. C₂×#41	C₃×C₃⋊D₃	semidirect
354. C₃³	#575	semidirect
452. #41	C₂×C₃×C₃⋊D₃	semidirect
454. C₂×Q₈	C₂×C₃×C₃⋊D₃	semidirect
458. C₂×D₄	C₂×C₃×C₃⋊D₃	semidirect
509. C₃²	#5822	semidirect
510. C₃²	C₃×#575	semidirect
571. C₃	C₃×#5822	semidirect
572. C₃	#10596293	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃³×#41	2
C₂×C₃×#3828	2
C₃×#64160	2
C₃×#64159	2
C₃×#64158	2
C₃×#64151	2
C₃×#64141	2
C₂×C₃×#3748	2
#10596293	3
C₃×#5822	3

Subgroups — C3×#10596293 #13179576

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596293 #13179576