Subgroups — C₃×#10596300 #13179579

Order 1728.

2660 conjugacy classes of subgroups.

The subgroup lattice has 612 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×D₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#64156	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64155	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#64148	C₂	1	2	yes	maximal, complemented
6	C₃×#64146	C₂	1	2	yes	maximal, complemented
7	C₃×D₄×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#64139	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#64138	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×#638	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×#3752	C₂	1	2	yes	maximal, complemented
12	#10596300	C₃	1	1	yes	maximal, characteristic, direct product factor
13	C₃×#5829	—	3	4	no	maximal
14	C₂³×C₃×C₃⋊D₃	C₂²	1	2	yes	—
15	C₃³×#41	—	2	4	no	—
16	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
18	C₂×C₃³×D₄	C₂²	1	2	yes	complemented
19	C₂²×C₃³×C₄	C₂²	1	2	yes	complemented
20	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₃×#638	C₂²	1	1	yes	characteristic
22	C₂×C₃×#638	C₂²	1	2	yes	—
23	C₂×C₃×#638	C₂²	1	2	yes	complemented
24	C₂²×C₃×C₃⋊Dic₃	C₂²	1	2	yes	complemented
25	C₃×D₄×C₃⋊D₃	—	2	4	no	—
26	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
28	C₃×#3757	C₂²	1	1	yes	characteristic, complemented
29	C₃×#3757	C₂²	1	2	yes	complemented
30	C₃×#3752	C₂²	1	1	yes	characteristic
31	C₃×#3752	C₂²	1	2	yes	—
32	C₃×#3752	C₂²	1	2	yes	complemented
33	C₃×#3752	C₂²	1	2	yes	complemented
34	C₃×#3752	C₂²	1	2	yes	complemented
35	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic, complemented
36	C₃×#3750	C₂²	1	1	yes	characteristic, complemented
37	C₃×#3750	C₂²	1	2	yes	complemented
38	C₃×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃²×#41	—	2	4	no	—
40	C₂×C₃²×#41	D₃	1	4	yes	complemented
41	C₂×C₃²×#41	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂×D₄×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂×C₃×D₃×D₄	—	3	4	no	—
44	#64156	C₂×C₃	1	1	yes	characteristic, complemented
45	#64155	C₂×C₃	1	1	yes	characteristic, complemented
46	#64148	C₂×C₃	1	2	yes	complemented
47	#64146	C₂×C₃	1	2	yes	complemented
48	D₄×C₃⋊Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
49	#64139	C₂×C₃	1	1	yes	characteristic, complemented
50	#64138	C₂×C₃	1	2	yes	complemented
51	C₄×#638	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂×#3752	C₂×C₃	1	2	yes	complemented
53	C₃×#947	—	3	4	no	—
54	C₃×#946	—	3	4	no	—
55	C₃×#939	—	3	8	no	—
56	C₃×#937	—	3	8	no	—
57	C₃×D₄×Dic₃	—	3	4	no	—
58	C₃×#930	—	3	4	no	—
59	C₃×#929	—	3	8	no	—
60	C₃×C₄×#67	—	3	4	no	—
61	C₂×C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
62	C₂³×C₃³	C₂³	1	1	yes	characteristic
63	C₂³×C₃³	C₂³	1	2	yes	—
64	C₂²×C₃×C₃⋊D₃	—	2	4	no	—
65	C₂²×C₃×C₃⋊D₃	—	2	4	no	—
66	C₂²×C₃×C₃⋊D₃	—	4	2	no	—
67	C₂²×C₃×C₃⋊D₃	C₂³	1	2	yes	—
68	C₂²×C₃×C₃⋊D₃	C₂³	1	1	yes	characteristic
69	C₃³×Q₈	—	2	2	no	—
70	C₃³×D₄	—	2	4	no	—
71	C₃³×D₄	D₄	1	4	yes	complemented
72	C₂×C₃³×C₄	—	2	4	no	—
73	C₂×C₃³×C₄	—	2	2	no	—
74	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
75	C₂×C₃³×C₄	C₂³	1	2	yes	—
76	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
77	C₃×#638	—	2	4	no	—
78	C₃×#638	—	2	2	no	—
79	C₃×#638	—	4	2	no	—
80	C₂×C₃×C₃⋊Dic₃	—	4	2	no	—
81	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
83	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
84	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
85	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
86	C₃×C₄×C₃⋊D₃	—	2	2	no	—
87	C₃×#546	—	9	1	no	—
88	#5829	—	3	4	no	—
89	C₂³×C₃⋊D₃	C₂²×C₃	1	2	yes	—
90	C₂³×C₃×D₃	—	3	8	no	—
91	C₃²×#41	—	2	32	no	—
92	C₃²×#41	—	2	16	no	—
93	C₃²×#41	—	2	4	no	—
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	4	no	—
98	C₂×C₃²×D₄	—	2	8	no	—
99	C₂×C₃²×D₄	C₂×D₃	1	4	yes	—
100	C₂×C₃²×D₄	C₂×D₃	1	8	yes	complemented
101	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
102	C₂×C₃²×D₄	C₂²×C₃	1	2	yes	complemented
103	C₂²×C₃²×C₄	—	2	8	no	—
104	C₂²×C₃²×C₄	—	2	4	no	—
105	C₂²×C₃²×C₄	C₂×D₃	1	8	yes	complemented
106	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	complemented
107	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	complemented
108	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic, complemented
109	C₂×#638	C₂²×C₃	1	2	yes	—
110	C₂×#638	C₂²×C₃	1	1	yes	characteristic
111	C₂×#638	C₂²×C₃	1	2	yes	complemented
112	C₂²×C₃⋊Dic₃	C₂²×C₃	1	2	yes	complemented
113	D₄×C₃⋊D₃	—	2	4	no	—
114	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic
115	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
116	C₂×C₃×#67	—	3	4	no	—
117	C₂×C₃×#67	—	3	8	no	—
118	C₂×C₃×#67	—	3	8	no	—
119	C₂²×C₃×Dic₃	—	3	8	no	—
120	C₃×D₃×D₄	—	6	16	no	—
121	C₂×C₃×D₁₂	—	3	4	no	—
122	C₂×C₃×C₄×D₃	—	3	4	no	—
123	#3757	C₂²×C₃	1	1	yes	characteristic, complemented
124	#3757	C₂²×C₃	1	2	yes	complemented
125	#3752	C₂²×C₃	1	1	yes	characteristic
126	#3752	C₂²×C₃	1	2	yes	—
127	#3752	C₂²×C₃	1	2	yes	complemented
128	#3752	C₂²×C₃	1	2	yes	complemented
129	#3752	C₂²×C₃	1	2	yes	complemented
130	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	1	yes	characteristic, complemented
131	#3750	C₂²×C₃	1	1	yes	characteristic, complemented
132	#3750	C₂²×C₃	1	2	yes	complemented
133	C₄×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
134	C₃×#217	—	3	4	no	—
135	C₃×#217	—	3	8	no	—
136	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
137	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
138	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
139	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
140	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
141	C₃×C₄⋊Dic₃	—	3	4	no	—
142	C₃×Dic₃⋊C₄	—	3	4	no	—
143	C₃×Dic₃⋊C₄	—	3	8	no	—
144	C₃×C₄×Dic₃	—	3	4	no	—
145	C₂²×C₃³	—	2	2	no	—
146	C₂²×C₃³	—	2	2	no	—
147	C₂²×C₃³	—	2	1	no	—
148	C₂²×C₃³	—	2	1	no	—
149	C₂²×C₃³	—	2	1	no	—
150	C₂²×C₃³	C₂×D₄	1	4	yes	—
151	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
152	C₂×C₃×C₃⋊D₃	—	2	1	no	—
153	C₂×C₃×C₃⋊D₃	—	2	1	no	—
154	C₂×C₃×C₃⋊D₃	—	2	2	no	—
155	C₂×C₃×C₃⋊D₃	—	2	2	no	—
156	C₂×C₃×C₃⋊D₃	—	2	2	no	—
157	C₂×C₃×C₃⋊D₃	—	4	8	no	—
158	C₂×C₃×C₃⋊D₃	#41	1	2	yes	complemented
159	C₃³×C₄	—	2	1	no	—
160	C₃³×C₄	—	2	2	no	—
161	C₃³×C₄	C₂×D₄	1	2	yes	—
162	C₃×C₃⋊Dic₃	—	2	1	no	—
163	C₃×C₃⋊Dic₃	—	2	1	no	—
164	C₃×C₃⋊Dic₃	—	2	1	no	—
165	C₃×C₃⋊Dic₃	—	2	2	no	—
166	C₂×C₃×#41	—	2	4	no	—
167	C₂×C₃×#41	C₃×D₃	1	4	yes	complemented
168	C₂×C₃×#41	C₃⋊D₃	1	1	yes	characteristic, complemented
169	C₂²×C₃×D₄	—	9	1	no	—
170	C₂×D₃×D₄	—	3	4	no	—
171	C₃×#124	—	9	1	no	—
172	C₃×#123	—	9	2	no	—
173	C₃×C₂²⋊Q₈	—	9	1	no	—
174	C₃×#121	—	9	2	no	—
175	C₃×#121	—	9	1	no	—
176	C₃×#120	—	9	2	no	—
177	C₃×C₄×D₄	—	9	1	no	—
178	C₃×C₄×D₄	—	9	1	no	—
179	C₂×C₃×C₂²⋊C₄	—	9	2	no	—
180	#947	—	3	4	no	—
181	#946	—	3	4	no	—
182	#939	—	3	8	no	—
183	#937	—	3	8	no	—
184	D₄×Dic₃	—	3	4	no	—
185	#930	—	3	4	no	—
186	#929	—	3	8	no	—
187	C₄×#67	—	3	4	no	—
188	C₂×(C₂×D₃)⋊C₄	—	3	8	no	—
189	C₂³×C₃²	—	2	4	no	—
190	C₂³×C₃²	—	2	8	no	—
191	C₂³×C₃²	C₂²×D₃	1	4	yes	—
192	C₂³×C₃²	C₂²×D₃	1	8	yes	—
193	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
194	C₂³×C₃²	C₂³×C₃	1	2	yes	—
195	C₂²×C₃⋊D₃	—	2	4	no	—
196	C₂²×C₃⋊D₃	—	2	4	no	—
197	C₂²×C₃⋊D₃	—	4	2	no	—
198	C₂²×C₃⋊D₃	C₂³×C₃	1	2	yes	—
199	C₂²×C₃⋊D₃	C₂³×C₃	1	1	yes	characteristic
200	C₂²×C₃×D₃	—	3	4	no	—
201	C₂²×C₃×D₃	—	3	8	no	—
202	C₂²×C₃×D₃	—	6	16	no	—
203	C₂²×C₃×D₃	—	6	16	no	—
204	C₂²×C₃×D₃	—	12	8	no	—
205	C₃²×Q₈	—	2	16	no	—
206	C₃²×Q₈	—	2	8	no	—
207	C₃²×Q₈	—	2	2	no	—
208	C₃²×D₄	—	2	32	no	—
209	C₃²×D₄	—	2	16	no	—
210	C₃²×D₄	—	2	4	no	—
211	C₃²×D₄	—	2	16	no	—
212	C₃²×D₄	#67	1	16	yes	complemented
213	C₃²×D₄	C₃×D₄	1	4	yes	complemented
214	C₂×C₃²×C₄	—	2	32	no	—
215	C₂×C₃²×C₄	—	2	16	no	—
216	C₂×C₃²×C₄	—	2	16	no	—
217	C₂×C₃²×C₄	—	2	4	no	—
218	C₂×C₃²×C₄	—	2	8	no	—
219	C₂×C₃²×C₄	—	2	2	no	—
220	C₂×C₃²×C₄	—	2	4	no	—
221	C₂×C₃²×C₄	—	2	8	no	—
222	C₂×C₃²×C₄	—	2	4	no	—
223	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
224	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
225	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
226	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
227	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
228	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
229	#638	—	2	4	no	—
230	#638	—	2	2	no	—
231	#638	—	4	2	no	—
232	C₂×C₃⋊Dic₃	—	4	2	no	—
233	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
234	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
235	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
236	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
237	C₄⋊(C₃⋊D₃)	—	2	2	no	—
238	C₄×C₃⋊D₃	—	2	2	no	—
239	C₃×#67	—	6	8	no	—
240	C₃×#67	—	6	16	no	—
241	C₃×#67	—	12	8	no	—
242	C₂×C₃×Dic₃	—	3	4	no	—
243	C₂×C₃×Dic₃	—	3	4	no	—
244	C₂×C₃×Dic₃	—	3	4	no	—
245	C₂×C₃×Dic₃	—	3	8	no	—
246	C₂×C₃×Dic₃	—	12	8	no	—
247	C₃×D₁₂	—	6	8	no	—
248	C₃×C₄×D₃	—	6	8	no	—
249	#546	—	9	1	no	Sylow
250	C₂×C₃³	—	2	4	no	—
251	C₂×C₃³	—	4	1	no	—
252	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₃³	C₂×#41	1	1	yes	characteristic
254	C₂×C₃³	H(5,𝔽₂)	1	1	yes	characteristic
255	C₃×C₃⋊D₃	—	2	2	no	—
256	C₃×C₃⋊D₃	—	4	2	no	—
257	C₂⁴×C₃	—	9	2	no	—
258	C₂³×D₃	—	3	8	no	—
259	C₃×#41	—	2	32	no	—
260	C₃×#41	—	2	16	no	—
261	C₃×#41	—	2	4	no	—
262	C₂×C₃×Q₈	—	2	4	no	—
263	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	complemented
264	C₂×C₃×Q₈	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
265	C₂×C₃×D₄	—	2	4	no	—
266	C₂×C₃×D₄	—	2	8	no	—
267	C₂×C₃×D₄	—	9	1	no	—
268	C₂×C₃×D₄	—	9	2	no	—
269	C₂×C₃×D₄	—	9	2	no	—
270	C₂×C₃×D₄	—	9	1	no	—
271	C₂×C₃×D₄	—	18	4	no	—
272	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
273	C₂×C₃×D₄	C₂×C₃×D₃	1	8	yes	complemented
274	C₂×C₃×D₄	C₂×C₃⋊D₃	1	1	yes	characteristic
275	C₂×C₃×D₄	C₂×C₃⋊D₃	1	2	yes	complemented
276	C₂²×C₃×C₄	—	2	8	no	—
277	C₂²×C₃×C₄	—	2	4	no	—
278	C₂²×C₃×C₄	—	9	2	no	—
279	C₂²×C₃×C₄	—	9	1	no	—
280	C₂²×C₃×C₄	C₂×C₃×D₃	1	8	yes	complemented
281	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	complemented
282	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	2	yes	complemented
283	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
284	C₂×#67	—	3	4	no	—
285	C₂×#67	—	3	8	no	—
286	C₂×#67	—	3	8	no	—
287	C₂²×Dic₃	—	3	8	no	—
288	D₃×D₄	—	6	16	no	—
289	C₂×D₁₂	—	3	4	no	—
290	C₂×C₄×D₃	—	3	4	no	—
291	C₃×C₄⋊C₄	—	9	1	no	—
292	C₃×C₄⋊C₄	—	9	2	no	—
293	C₃×C₄⋊C₄	—	9	1	no	—
294	C₃×C₂²⋊C₄	—	9	2	no	—
295	C₃×C₂²⋊C₄	—	9	1	no	—
296	C₃×C₂²⋊C₄	—	9	1	no	—
297	C₃×C₂²⋊C₄	—	9	2	no	—
298	C₃×C₂²⋊C₄	—	9	2	no	—
299	C₃×C₂²⋊C₄	—	9	2	no	—
300	C₃×C₂²⋊C₄	—	9	2	no	—
301	C₃×C₄²	—	9	1	no	—
302	#217	—	3	4	no	—
303	#217	—	3	8	no	—
304	(C₂×D₃)⋊C₄	—	3	4	no	—
305	(C₂×D₃)⋊C₄	—	3	8	no	—
306	(C₂×D₃)⋊C₄	—	3	8	no	—
307	(C₂×D₃)⋊C₄	—	3	8	no	—
308	(C₂×D₃)⋊C₄	—	3	8	no	—
309	C₄⋊Dic₃	—	3	4	no	—
310	Dic₃⋊C₄	—	3	4	no	—
311	Dic₃⋊C₄	—	3	8	no	—
312	C₄×Dic₃	—	3	4	no	—
313	C₂²×C₃²	—	2	2	no	—
314	C₂²×C₃²	—	2	2	no	—
315	C₂²×C₃²	—	2	8	no	—
316	C₂²×C₃²	—	2	4	no	—
317	C₂²×C₃²	—	2	1	no	—
318	C₂²×C₃²	—	2	1	no	—
319	C₂²×C₃²	—	2	1	no	—
320	C₂²×C₃²	—	2	4	no	—
321	C₂²×C₃²	—	2	16	no	—
322	C₂²×C₃²	—	2	8	no	—
323	C₂²×C₃²	—	2	8	no	—
324	C₂²×C₃²	—	2	4	no	—
325	C₂²×C₃²	—	2	4	no	—
326	C₂²×C₃²	—	4	8	no	—
327	C₂²×C₃²	—	4	8	no	—
328	C₂²×C₃²	—	4	4	no	—
329	C₂²×C₃²	—	4	4	no	—
330	C₂²×C₃²	C₂×#67	1	16	yes	—
331	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
332	C₂²×C₃²	C₂³×D₃	1	4	yes	—
333	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
334	C₂×C₃⋊D₃	—	2	1	no	—
335	C₂×C₃⋊D₃	—	2	1	no	—
336	C₂×C₃⋊D₃	—	2	2	no	—
337	C₂×C₃⋊D₃	—	2	2	no	—
338	C₂×C₃⋊D₃	—	2	2	no	—
339	C₂×C₃⋊D₃	—	4	8	no	—
340	C₂×C₃⋊D₃	C₃×#41	1	2	yes	complemented
341	C₂×C₃×D₃	—	3	8	no	—
342	C₂×C₃×D₃	—	6	4	no	—
343	C₂×C₃×D₃	—	6	4	no	—
344	C₂×C₃×D₃	—	6	8	no	—
345	C₂×C₃×D₃	—	6	8	no	—
346	C₂×C₃×D₃	—	6	8	no	—
347	C₂×C₃×D₃	—	12	32	no	—
348	C₃²×C₄	—	2	8	no	—
349	C₃²×C₄	—	2	16	no	—
350	C₃²×C₄	—	2	4	no	—
351	C₃²×C₄	—	2	8	no	—
352	C₃²×C₄	—	2	1	no	—
353	C₃²×C₄	—	2	2	no	—
354	C₃²×C₄	—	2	8	no	—
355	C₃²×C₄	C₂×#67	1	8	yes	—
356	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
357	C₃⋊Dic₃	—	2	1	no	—
358	C₃⋊Dic₃	—	2	1	no	—
359	C₃⋊Dic₃	—	2	1	no	—
360	C₃⋊Dic₃	—	2	2	no	—
361	C₃×Dic₃	—	6	4	no	—
362	C₃×Dic₃	—	6	4	no	—
363	C₃×Dic₃	—	6	8	no	—
364	C₃×Dic₃	—	6	4	no	—
365	C₂×#41	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
366	C₂²×D₄	—	9	1	no	—
367	#124	—	9	1	no	—
368	#123	—	9	2	no	—
369	C₂²⋊Q₈	—	9	1	no	—
370	#121	—	9	2	no	—
371	#121	—	9	1	no	—
372	#120	—	9	2	no	—
373	C₄×D₄	—	9	1	no	—
374	C₄×D₄	—	9	1	no	—
375	C₂×C₂²⋊C₄	—	9	2	no	—
376	C₃³	#546	1	1	yes	characteristic, complemented, Sylow
377	C₂³×C₃	—	2	4	no	—
378	C₂³×C₃	—	2	8	no	—
379	C₂³×C₃	—	9	1	no	—
380	C₂³×C₃	—	9	2	no	—
381	C₂³×C₃	—	18	4	no	—
382	C₂³×C₃	—	18	4	no	—
383	C₂³×C₃	—	36	2	no	—
384	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
385	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
386	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
387	C₂³×C₃	C₂²×C₃⋊D₃	1	2	yes	—
388	C₂²×D₃	—	3	4	no	—
389	C₂²×D₃	—	3	8	no	—
390	C₂²×D₃	—	6	16	no	—
391	C₂²×D₃	—	6	16	no	—
392	C₂²×D₃	—	12	8	no	—
393	C₃×Q₈	—	2	16	no	—
394	C₃×Q₈	—	2	8	no	—
395	C₃×Q₈	—	2	2	no	—
396	C₃×D₄	—	2	32	no	—
397	C₃×D₄	—	2	16	no	—
398	C₃×D₄	—	2	4	no	—
399	C₃×D₄	—	2	16	no	—
400	C₃×D₄	—	18	2	no	—
401	C₃×D₄	—	18	4	no	—
402	C₃×D₄	—	18	2	no	—
403	C₃×D₄	—	36	2	no	—
404	C₃×D₄	C₃×#67	1	16	yes	complemented
405	C₃×D₄	#638	1	4	yes	complemented
406	C₂×C₃×C₄	—	2	32	no	—
407	C₂×C₃×C₄	—	2	16	no	—
408	C₂×C₃×C₄	—	2	16	no	—
409	C₂×C₃×C₄	—	2	4	no	—
410	C₂×C₃×C₄	—	2	8	no	—
411	C₂×C₃×C₄	—	2	2	no	—
412	C₂×C₃×C₄	—	2	4	no	—
413	C₂×C₃×C₄	—	2	8	no	—
414	C₂×C₃×C₄	—	2	4	no	—
415	C₂×C₃×C₄	—	9	1	no	—
416	C₂×C₃×C₄	—	9	1	no	—
417	C₂×C₃×C₄	—	9	2	no	—
418	C₂×C₃×C₄	—	9	1	no	—
419	C₂×C₃×C₄	—	18	2	no	—
420	C₂×C₃×C₄	—	36	2	no	—
421	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
422	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
423	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
424	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
425	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
426	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
427	#67	—	6	8	no	—
428	#67	—	6	16	no	—
429	#67	—	12	8	no	—
430	C₂×Dic₃	—	3	4	no	—
431	C₂×Dic₃	—	3	4	no	—
432	C₂×Dic₃	—	3	4	no	—
433	C₂×Dic₃	—	3	8	no	—
434	C₂×Dic₃	—	12	8	no	—
435	D₁₂	—	6	8	no	—
436	C₄×D₃	—	6	8	no	—
437	C₂×C₃²	—	2	4	no	—
438	C₂×C₃²	—	2	4	no	—
439	C₂×C₃²	—	2	4	no	—
440	C₂×C₃²	—	2	4	no	—
441	C₂×C₃²	—	2	16	no	—
442	C₂×C₃²	—	4	16	no	—
443	C₂×C₃²	—	4	8	no	—
444	C₂×C₃²	—	4	4	no	—
445	C₂×C₃²	—	4	1	no	—
446	C₂×C₃²	D₃×#41	1	4	yes	—
447	C₂×C₃²	#1009	1	4	yes	—
448	C₂×C₃²	C₂²×#67	1	4	yes	—
449	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
450	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
451	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
452	C₃⋊D₃	—	2	2	no	—
453	C₃⋊D₃	—	4	2	no	—
454	C₃×D₃	—	6	8	no	—
455	C₃×D₃	—	12	8	no	—
456	C₂⁴	—	9	2	no	—
457	#41	—	2	4	no	—
458	C₂×Q₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
459	C₂×D₄	—	9	1	no	—
460	C₂×D₄	—	9	2	no	—
461	C₂×D₄	—	9	2	no	—
462	C₂×D₄	—	9	1	no	—
463	C₂×D₄	—	18	4	no	—
464	C₂×D₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
465	C₂×D₄	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
466	C₂²×C₄	—	9	2	no	—
467	C₂²×C₄	—	9	1	no	—
468	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
469	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
470	C₄⋊C₄	—	9	1	no	—
471	C₄⋊C₄	—	9	1	no	—
472	C₄⋊C₄	—	9	2	no	—
473	C₂²⋊C₄	—	9	2	no	—
474	C₂²⋊C₄	—	9	1	no	—
475	C₂²⋊C₄	—	9	1	no	—
476	C₂²⋊C₄	—	9	2	no	—
477	C₂²⋊C₄	—	9	2	no	—
478	C₂²⋊C₄	—	9	2	no	—
479	C₂²⋊C₄	—	9	2	no	—
480	C₄²	—	9	1	no	—
481	C₂²×C₃	—	2	8	no	—
482	C₂²×C₃	—	2	8	no	—
483	C₂²×C₃	—	2	2	no	—
484	C₂²×C₃	—	2	2	no	—
485	C₂²×C₃	—	2	8	no	—
486	C₂²×C₃	—	2	4	no	—
487	C₂²×C₃	—	2	4	no	—
488	C₂²×C₃	—	2	4	no	—
489	C₂²×C₃	—	2	1	no	—
490	C₂²×C₃	—	2	1	no	—
491	C₂²×C₃	—	2	1	no	—
492	C₂²×C₃	—	2	4	no	—
493	C₂²×C₃	—	2	16	no	—
494	C₂²×C₃	—	4	8	no	—
495	C₂²×C₃	—	4	8	no	—
496	C₂²×C₃	—	4	4	no	—
497	C₂²×C₃	—	4	4	no	—
498	C₂²×C₃	—	9	2	no	—
499	C₂²×C₃	—	18	1	no	—
500	C₂²×C₃	—	18	1	no	—
501	C₂²×C₃	—	18	2	no	—
502	C₂²×C₃	—	18	2	no	—
503	C₂²×C₃	—	18	2	no	—
504	C₂²×C₃	—	36	8	no	—
505	C₂²×C₃	C₂×C₃×#67	1	16	yes	—
506	C₂²×C₃	C₂×#638	1	4	yes	—
507	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
508	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
509	C₂×D₃	—	3	8	no	—
510	C₂×D₃	—	6	4	no	—
511	C₂×D₃	—	6	4	no	—
512	C₂×D₃	—	6	8	no	—
513	C₂×D₃	—	6	8	no	—
514	C₂×D₃	—	6	8	no	—
515	C₂×D₃	—	12	32	no	—
516	C₃×C₄	—	2	8	no	—
517	C₃×C₄	—	2	16	no	—
518	C₃×C₄	—	2	4	no	—
519	C₃×C₄	—	2	8	no	—
520	C₃×C₄	—	2	1	no	—
521	C₃×C₄	—	2	2	no	—
522	C₃×C₄	—	2	8	no	—
523	C₃×C₄	—	18	1	no	—
524	C₃×C₄	—	18	1	no	—
525	C₃×C₄	—	18	2	no	—
526	C₃×C₄	—	18	1	no	—
527	C₃×C₄	C₂×C₃×#67	1	8	yes	—
528	C₃×C₄	C₂×#638	1	2	yes	—
529	Dic₃	—	6	4	no	—
530	Dic₃	—	6	4	no	—
531	Dic₃	—	6	8	no	—
532	Dic₃	—	6	4	no	—
533	C₃²	—	2	4	no	—
534	C₃²	#5829	1	4	yes	complemented
535	C₃²	C₃×#546	1	1	yes	characteristic, complemented
536	C₂³	—	9	1	no	—
537	C₂³	—	9	2	no	—
538	C₂³	—	18	4	no	—
539	C₂³	—	18	4	no	—
540	C₂³	—	36	2	no	—
541	C₂³	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
542	C₂³	C₂²×C₃×C₃⋊D₃	1	2	yes	—
543	Q₈	—	2	2	no	—
544	D₄	—	2	4	no	—
545	D₄	—	18	2	no	—
546	D₄	—	18	4	no	—
547	D₄	—	18	2	no	—
548	D₄	—	36	2	no	—
549	D₄	C₃×#638	1	4	yes	complemented
550	C₂×C₄	—	2	4	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	9	1	no	—
553	C₂×C₄	—	9	1	no	—
554	C₂×C₄	—	9	2	no	—
555	C₂×C₄	—	9	1	no	—
556	C₂×C₄	—	18	2	no	—
557	C₂×C₄	—	36	2	no	—
558	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
559	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
560	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
561	C₂×C₃	—	2	16	no	—
562	C₂×C₃	—	2	4	no	—
563	C₂×C₃	—	2	4	no	—
564	C₂×C₃	—	2	4	no	—
565	C₂×C₃	—	2	4	no	—
566	C₂×C₃	—	4	16	no	—
567	C₂×C₃	—	4	8	no	—
568	C₂×C₃	—	4	4	no	—
569	C₂×C₃	—	4	1	no	—
570	C₂×C₃	—	18	2	no	—
571	C₂×C₃	—	36	2	no	—
572	C₂×C₃	C₃×D₃×#41	1	4	yes	—
573	C₂×C₃	C₃×#1009	1	4	yes	—
574	C₂×C₃	C₂²×C₃×#67	1	4	yes	—
575	C₂×C₃	#41×C₃⋊D₃	1	1	yes	characteristic
576	C₂×C₃	#64366	1	1	yes	characteristic
577	C₂×C₃	C₂²×#638	1	1	yes	characteristic
578	D₃	—	6	8	no	—
579	D₃	—	12	8	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	1	no	—
585	C₂²	—	9	2	no	—
586	C₂²	—	18	1	no	—
587	C₂²	—	18	1	no	—
588	C₂²	—	18	2	no	—
589	C₂²	—	18	2	no	—
590	C₂²	—	18	2	no	—
591	C₂²	—	36	8	no	—
592	C₂²	C₂×C₃×#638	1	4	yes	—
593	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
594	C₄	—	2	1	no	—
595	C₄	—	2	2	no	—
596	C₄	—	18	1	no	—
597	C₄	—	18	1	no	—
598	C₄	—	18	2	no	—
599	C₄	—	18	1	no	—
600	C₄	C₂×C₃×#638	1	2	yes	—
601	C₃	—	2	4	no	—
602	C₃	C₃×#5829	1	4	yes	complemented
603	C₃	#10596300	1	1	yes	characteristic, direct product factor
604	C₂	—	2	4	no	—
605	C₂	—	4	1	no	—
606	C₂	—	18	2	no	—
607	C₂	—	36	2	no	—
608	C₂	C₃×#41×C₃⋊D₃	1	1	yes	characteristic
609	C₂	C₃×#64366	1	1	yes	characteristic
610	C₂	C₂²×C₃×#638	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×C₃⋊D₃
commutator, cosocle	C₂²×C₃²	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×C₃⋊D₃
Fitting	C₂×C₃³×#41	C₂
socle	C₂²×C₃³	C₂⁴
hypercenter	C₂×C₃×#41	C₃⋊D₃
hypocenter	C₃²	C₃×#546
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ 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×D₄×C₃⋊D₃	C₂	semidirect
3. C₃×#64156	C₂	semidirect
4. C₃×#64155	C₂	semidirect
5. C₃×#64148	C₂	semidirect
6. C₃×#64146	C₂	semidirect
7. C₃×D₄×C₃⋊Dic₃	C₂	semidirect
8. C₃×#64139	C₂	semidirect
9. C₃×#64138	C₂	semidirect
10. C₃×C₄×#638	C₂	semidirect
11. C₂×C₃×#3752	C₂	semidirect
12. #10596300	C₃	direct (N × H)
16. C₂×C₃³×Q₈	C₂²	semidirect
18. C₂×C₃³×D₄	C₂²	semidirect
19. C₂²×C₃³×C₄	C₂²	semidirect
20. C₂²×C₃³×C₄	C₂²	semidirect
23. C₂×C₃×#638	C₂²	semidirect
24. C₂²×C₃×C₃⋊Dic₃	C₂²	semidirect
28. C₃×#3757	C₂²	semidirect
29. C₃×#3757	C₂²	semidirect
32. C₃×#3752	C₂²	semidirect
33. C₃×#3752	C₂²	semidirect
34. C₃×#3752	C₂²	semidirect
35. C₃×C₄⋊(C₃⋊Dic₃)	C₂²	semidirect
36. C₃×#3750	C₂²	semidirect
37. C₃×#3750	C₂²	semidirect
38. C₃×C₄×C₃⋊Dic₃	C₂²	semidirect
40. C₂×C₃²×#41	D₃	semidirect
41. C₂×C₃²×#41	C₂×C₃	semidirect
42. C₂×D₄×C₃⋊D₃	C₂×C₃	semidirect
44. #64156	C₂×C₃	semidirect
45. #64155	C₂×C₃	semidirect
46. #64148	C₂×C₃	semidirect
47. #64146	C₂×C₃	semidirect
48. D₄×C₃⋊Dic₃	C₂×C₃	semidirect
49. #64139	C₂×C₃	semidirect
50. #64138	C₂×C₃	semidirect
51. C₄×#638	C₂×C₃	semidirect
52. C₂×#3752	C₂×C₃	semidirect
71. C₃³×D₄	D₄	semidirect
95. C₂×C₃²×Q₈	C₂×D₃	semidirect
96. C₂×C₃²×Q₈	C₂²×C₃	semidirect
100. C₂×C₃²×D₄	C₂×D₃	semidirect
102. C₂×C₃²×D₄	C₂²×C₃	semidirect
105. C₂²×C₃²×C₄	C₂×D₃	semidirect
106. C₂²×C₃²×C₄	C₂×D₃	semidirect
107. C₂²×C₃²×C₄	C₂²×C₃	semidirect
108. C₂²×C₃²×C₄	C₂²×C₃	semidirect
111. C₂×#638	C₂²×C₃	semidirect
112. C₂²×C₃⋊Dic₃	C₂²×C₃	semidirect
123. #3757	C₂²×C₃	semidirect
124. #3757	C₂²×C₃	semidirect
127. #3752	C₂²×C₃	semidirect
128. #3752	C₂²×C₃	semidirect
129. #3752	C₂²×C₃	semidirect
130. C₄⋊(C₃⋊Dic₃)	C₂²×C₃	semidirect
131. #3750	C₂²×C₃	semidirect
132. #3750	C₂²×C₃	semidirect
133. C₄×C₃⋊Dic₃	C₂²×C₃	semidirect
158. C₂×C₃×C₃⋊D₃	#41	semidirect
167. C₂×C₃×#41	C₃×D₃	semidirect
168. C₂×C₃×#41	C₃⋊D₃	semidirect
212. C₃²×D₄	#67	semidirect
213. C₃²×D₄	C₃×D₄	semidirect
263. C₂×C₃×Q₈	C₂×C₃×D₃	semidirect
264. C₂×C₃×Q₈	C₂×C₃⋊D₃	semidirect
273. C₂×C₃×D₄	C₂×C₃×D₃	semidirect
275. C₂×C₃×D₄	C₂×C₃⋊D₃	semidirect
280. C₂²×C₃×C₄	C₂×C₃×D₃	semidirect
281. C₂²×C₃×C₄	C₂×C₃×D₃	semidirect
282. C₂²×C₃×C₄	C₂×C₃⋊D₃	semidirect
283. C₂²×C₃×C₄	C₂×C₃⋊D₃	semidirect
340. C₂×C₃⋊D₃	C₃×#41	semidirect
365. C₂×#41	C₃×C₃⋊D₃	semidirect
376. C₃³	#546	semidirect
404. C₃×D₄	C₃×#67	semidirect
405. C₃×D₄	#638	semidirect
458. C₂×Q₈	C₂×C₃×C₃⋊D₃	semidirect
465. C₂×D₄	C₂×C₃×C₃⋊D₃	semidirect
468. C₂²×C₄	C₂×C₃×C₃⋊D₃	semidirect
469. C₂²×C₄	C₂×C₃×C₃⋊D₃	semidirect
534. C₃²	#5829	semidirect
535. C₃²	C₃×#546	semidirect
549. D₄	C₃×#638	semidirect
602. C₃	C₃×#5829	semidirect
603. C₃	#10596300	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×D₄×C₃⋊D₃	2
C₃×#64156	2
C₃×#64155	2
C₃×#64148	2
C₃×#64146	2
C₃×D₄×C₃⋊Dic₃	2
C₃×#64139	2
C₃×#64138	2
C₃×C₄×#638	2
C₂×C₃×#3752	2
#10596300	3
C₃×#5829	3

Subgroups — C3×#10596300 #13179579

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596300 #13179579