Subgroups — C₃²×#5829 #13179205

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×C₃²×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#947	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#946	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×#939	C₂	1	2	yes	maximal, complemented
6	C₃²×#937	C₂	1	2	yes	maximal, complemented
7	C₃²×D₄×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#930	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃²×#929	C₂	1	2	yes	maximal, complemented
10	C₃²×C₄×#67	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃²×(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal, complemented
12	C₃²×#546	—	3	1	no	maximal
13	C₃×#5829	C₃	1	4	yes	maximal, direct product factor
14	C₂³×C₃²×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×C₃²×#67	C₂²	1	1	yes	characteristic
22	C₂×C₃²×#67	C₂²	1	2	yes	—
23	C₂×C₃²×#67	C₂²	1	2	yes	complemented
24	C₂²×C₃²×Dic₃	C₂²	1	2	yes	complemented
25	C₃²×D₃×D₄	—	2	4	no	—
26	C₂×C₃²×D₁₂	C₂²	1	1	yes	characteristic
27	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
28	C₃²×#217	C₂²	1	1	yes	characteristic, complemented
29	C₃²×#217	C₂²	1	2	yes	complemented
30	C₃²×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
31	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
32	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
33	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
34	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
35	C₃²×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
36	C₃²×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
37	C₃²×Dic₃⋊C₄	C₂²	1	2	yes	complemented
38	C₃²×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃²×#41	—	2	4	no	—
40	C₂×C₃²×#41	D₃	1	1	yes	characteristic, complemented
41	C₂×C₃²×#41	C₂×C₃	1	4	yes	complemented
42	C₂²×C₃²×D₄	—	3	1	no	—
43	C₂×C₃×D₃×D₄	C₂×C₃	1	4	yes	complemented
44	C₃²×#124	—	3	1	no	—
45	C₃²×#123	—	3	2	no	—
46	C₃²×C₂²⋊Q₈	—	3	1	no	—
47	C₃²×#121	—	3	2	no	—
48	C₃²×#121	—	3	1	no	—
49	C₃²×#120	—	3	2	no	—
50	C₃²×C₄×D₄	—	3	1	no	—
51	C₃²×C₄×D₄	—	3	1	no	—
52	C₂×C₃²×C₂²⋊C₄	—	3	2	no	—
53	C₃×#947	C₂×C₃	1	4	yes	complemented
54	C₃×#946	C₂×C₃	1	4	yes	complemented
55	C₃×#939	C₂×C₃	1	8	yes	complemented
56	C₃×#937	C₂×C₃	1	8	yes	complemented
57	C₃×D₄×Dic₃	C₂×C₃	1	4	yes	complemented
58	C₃×#930	C₂×C₃	1	4	yes	complemented
59	C₃×#929	C₂×C₃	1	8	yes	complemented
60	C₃×C₄×#67	C₂×C₃	1	4	yes	complemented
61	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	8	yes	complemented
62	C₂³×C₃³	C₂³	1	1	yes	characteristic
63	C₂³×C₃³	C₂³	1	2	yes	—
64	C₂²×C₃²×D₃	—	2	4	no	—
65	C₂²×C₃²×D₃	—	2	4	no	—
66	C₂²×C₃²×D₃	—	4	2	no	—
67	C₂²×C₃²×D₃	C₂³	1	2	yes	—
68	C₂²×C₃²×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	C₃²×#67	—	2	4	no	—
78	C₃²×#67	—	2	2	no	—
79	C₃²×#67	—	4	2	no	—
80	C₂×C₃²×Dic₃	—	4	2	no	—
81	C₂×C₃²×Dic₃	C₂³	1	1	yes	characteristic
82	C₂×C₃²×Dic₃	C₂³	1	1	yes	characteristic
83	C₂×C₃²×Dic₃	C₂³	1	1	yes	characteristic
84	C₂×C₃²×Dic₃	C₂³	1	2	yes	—
85	C₃²×D₁₂	—	2	2	no	—
86	C₃²×C₄×D₃	—	2	2	no	—
87	C₃×#546	—	3	4	no	—
88	#5829	C₃²	1	1	yes	characteristic, direct product factor
89	C₂⁴×C₃²	—	3	2	no	—
90	C₂³×C₃×D₃	C₂²×C₃	1	8	yes	—
91	C₃²×#41	—	2	32	no	—
92	C₃²×#41	—	2	4	no	—
93	C₃²×#41	—	2	16	no	—
94	C₂×C₃²×Q₈	—	2	4	no	—
95	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
96	C₂×C₃²×Q₈	C₂²×C₃	1	4	yes	complemented
97	C₂×C₃²×D₄	—	2	4	no	—
98	C₂×C₃²×D₄	—	2	8	no	—
99	C₂×C₃²×D₄	—	3	2	no	—
100	C₂×C₃²×D₄	—	3	1	no	—
101	C₂×C₃²×D₄	—	3	2	no	—
102	C₂×C₃²×D₄	—	3	1	no	—
103	C₂×C₃²×D₄	—	6	4	no	—
104	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
105	C₂×C₃²×D₄	C₂×D₃	1	2	yes	complemented
106	C₂×C₃²×D₄	C₂²×C₃	1	4	yes	—
107	C₂×C₃²×D₄	C₂²×C₃	1	8	yes	complemented
108	C₂²×C₃²×C₄	—	2	8	no	—
109	C₂²×C₃²×C₄	—	2	4	no	—
110	C₂²×C₃²×C₄	—	3	2	no	—
111	C₂²×C₃²×C₄	—	3	1	no	—
112	C₂²×C₃²×C₄	C₂×D₃	1	2	yes	complemented
113	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic, complemented
114	C₂²×C₃²×C₄	C₂²×C₃	1	8	yes	complemented
115	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	complemented
116	C₂×C₃×#67	C₂²×C₃	1	4	yes	—
117	C₂×C₃×#67	C₂²×C₃	1	8	yes	—
118	C₂×C₃×#67	C₂²×C₃	1	8	yes	complemented
119	C₂²×C₃×Dic₃	C₂²×C₃	1	8	yes	complemented
120	C₃×D₃×D₄	—	2	16	no	—
121	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	—
122	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
123	C₃²×C₄⋊C₄	—	3	1	no	—
124	C₃²×C₄⋊C₄	—	3	1	no	—
125	C₃²×C₄⋊C₄	—	3	2	no	—
126	C₃²×C₂²⋊C₄	—	3	2	no	—
127	C₃²×C₂²⋊C₄	—	3	1	no	—
128	C₃²×C₂²⋊C₄	—	3	1	no	—
129	C₃²×C₂²⋊C₄	—	3	2	no	—
130	C₃²×C₂²⋊C₄	—	3	2	no	—
131	C₃²×C₂²⋊C₄	—	3	2	no	—
132	C₃²×C₂²⋊C₄	—	3	2	no	—
133	C₃²×C₄²	—	3	1	no	—
134	C₃×#217	C₂²×C₃	1	4	yes	complemented
135	C₃×#217	C₂²×C₃	1	8	yes	complemented
136	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
137	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
138	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	complemented
139	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	complemented
140	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	complemented
141	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	complemented
142	C₃×Dic₃⋊C₄	C₂²×C₃	1	4	yes	complemented
143	C₃×Dic₃⋊C₄	C₂²×C₃	1	8	yes	complemented
144	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	complemented
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×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	—	4	8	no	—
158	C₂×C₃²×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	C₃²×Dic₃	—	2	1	no	—
163	C₃²×Dic₃	—	2	1	no	—
164	C₃²×Dic₃	—	2	1	no	—
165	C₃²×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	C₂×C₃²	1	1	yes	characteristic, complemented
169	C₂²×C₃×D₄	—	3	4	no	—
170	C₂×D₃×D₄	C₂×C₃²	1	1	yes	characteristic, complemented
171	C₃×#124	—	3	4	no	—
172	C₃×#123	—	3	8	no	—
173	C₃×C₂²⋊Q₈	—	3	4	no	—
174	C₃×#121	—	3	8	no	—
175	C₃×#121	—	3	4	no	—
176	C₃×#120	—	3	8	no	—
177	C₃×C₄×D₄	—	3	4	no	—
178	C₃×C₄×D₄	—	3	4	no	—
179	C₂×C₃×C₂²⋊C₄	—	3	8	no	—
180	#947	C₂×C₃²	1	1	yes	characteristic, complemented
181	#946	C₂×C₃²	1	1	yes	characteristic, complemented
182	#939	C₂×C₃²	1	2	yes	complemented
183	#937	C₂×C₃²	1	2	yes	complemented
184	D₄×Dic₃	C₂×C₃²	1	1	yes	characteristic, complemented
185	#930	C₂×C₃²	1	1	yes	characteristic, complemented
186	#929	C₂×C₃²	1	2	yes	complemented
187	C₄×#67	C₂×C₃²	1	1	yes	characteristic, complemented
188	C₂×(C₂×D₃)⋊C₄	C₂×C₃²	1	2	yes	complemented
189	C₂³×C₃²	—	2	4	no	—
190	C₂³×C₃²	—	2	8	no	—
191	C₂³×C₃²	—	3	1	no	—
192	C₂³×C₃²	—	3	2	no	—
193	C₂³×C₃²	—	6	4	no	—
194	C₂³×C₃²	—	6	4	no	—
195	C₂³×C₃²	—	12	2	no	—
196	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
197	C₂³×C₃²	C₂²×D₃	1	2	yes	—
198	C₂³×C₃²	C₂³×C₃	1	4	yes	—
199	C₂³×C₃²	C₂³×C₃	1	8	yes	—
200	C₂²×C₃×D₃	—	2	16	no	—
201	C₂²×C₃×D₃	—	2	16	no	—
202	C₂²×C₃×D₃	—	4	8	no	—
203	C₂²×C₃×D₃	C₂³×C₃	1	8	yes	—
204	C₂²×C₃×D₃	C₂³×C₃	1	4	yes	—
205	C₃²×Q₈	—	2	16	no	—
206	C₃²×Q₈	—	2	2	no	—
207	C₃²×Q₈	—	2	8	no	—
208	C₃²×D₄	—	2	32	no	—
209	C₃²×D₄	—	2	4	no	—
210	C₃²×D₄	—	2	16	no	—
211	C₃²×D₄	—	2	16	no	—
212	C₃²×D₄	—	6	2	no	—
213	C₃²×D₄	—	6	4	no	—
214	C₃²×D₄	—	6	2	no	—
215	C₃²×D₄	—	12	2	no	—
216	C₃²×D₄	#67	1	4	yes	complemented
217	C₃²×D₄	C₃×D₄	1	16	yes	complemented
218	C₂×C₃²×C₄	—	2	32	no	—
219	C₂×C₃²×C₄	—	2	16	no	—
220	C₂×C₃²×C₄	—	2	4	no	—
221	C₂×C₃²×C₄	—	2	16	no	—
222	C₂×C₃²×C₄	—	2	2	no	—
223	C₂×C₃²×C₄	—	2	8	no	—
224	C₂×C₃²×C₄	—	2	4	no	—
225	C₂×C₃²×C₄	—	2	8	no	—
226	C₂×C₃²×C₄	—	2	4	no	—
227	C₂×C₃²×C₄	—	3	1	no	—
228	C₂×C₃²×C₄	—	3	1	no	—
229	C₂×C₃²×C₄	—	3	2	no	—
230	C₂×C₃²×C₄	—	3	1	no	—
231	C₂×C₃²×C₄	—	6	2	no	—
232	C₂×C₃²×C₄	—	12	2	no	—
233	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
234	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
235	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
236	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
237	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
238	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
239	C₃×#67	—	2	16	no	—
240	C₃×#67	—	2	8	no	—
241	C₃×#67	—	4	8	no	—
242	C₂×C₃×Dic₃	—	4	8	no	—
243	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
244	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
245	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
246	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
247	C₃×D₁₂	—	2	8	no	—
248	C₃×C₄×D₃	—	2	8	no	—
249	#546	—	3	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	C₃²×D₃	—	2	2	no	—
256	C₃²×D₃	—	4	2	no	—
257	C₂⁴×C₃	—	3	8	no	—
258	C₂³×D₃	C₂²×C₃²	1	2	yes	—
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	C₂²×C₃²	1	1	yes	characteristic, complemented
265	C₂×C₃×D₄	—	2	4	no	—
266	C₂×C₃×D₄	—	2	8	no	—
267	C₂×C₃×D₄	—	3	4	no	—
268	C₂×C₃×D₄	—	3	8	no	—
269	C₂×C₃×D₄	—	3	8	no	—
270	C₂×C₃×D₄	—	3	4	no	—
271	C₂×C₃×D₄	—	6	16	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	C₂²×C₃²	1	1	yes	characteristic
275	C₂×C₃×D₄	C₂²×C₃²	1	2	yes	complemented
276	C₂²×C₃×C₄	—	2	8	no	—
277	C₂²×C₃×C₄	—	2	4	no	—
278	C₂²×C₃×C₄	—	3	8	no	—
279	C₂²×C₃×C₄	—	3	4	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	C₂²×C₃²	1	2	yes	complemented
283	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic, complemented
284	C₂×#67	C₂²×C₃²	1	1	yes	characteristic
285	C₂×#67	C₂²×C₃²	1	2	yes	—
286	C₂×#67	C₂²×C₃²	1	2	yes	complemented
287	C₂²×Dic₃	C₂²×C₃²	1	2	yes	complemented
288	D₃×D₄	—	2	4	no	—
289	C₂×D₁₂	C₂²×C₃²	1	1	yes	characteristic
290	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
291	C₃×C₄⋊C₄	—	3	4	no	—
292	C₃×C₄⋊C₄	—	3	8	no	—
293	C₃×C₄⋊C₄	—	3	4	no	—
294	C₃×C₂²⋊C₄	—	3	8	no	—
295	C₃×C₂²⋊C₄	—	3	4	no	—
296	C₃×C₂²⋊C₄	—	3	4	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×C₄²	—	3	4	no	—
302	#217	C₂²×C₃²	1	1	yes	characteristic, complemented
303	#217	C₂²×C₃²	1	2	yes	complemented
304	(C₂×D₃)⋊C₄	C₂²×C₃²	1	1	yes	characteristic
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	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	complemented
309	C₄⋊Dic₃	C₂²×C₃²	1	1	yes	characteristic, complemented
310	Dic₃⋊C₄	C₂²×C₃²	1	1	yes	characteristic, complemented
311	Dic₃⋊C₄	C₂²×C₃²	1	2	yes	complemented
312	C₄×Dic₃	C₂²×C₃²	1	1	yes	characteristic, complemented
313	C₂²×C₃²	—	2	2	no	—
314	C₂²×C₃²	—	2	2	no	—
315	C₂²×C₃²	—	2	8	no	—
316	C₂²×C₃²	—	2	1	no	—
317	C₂²×C₃²	—	2	1	no	—
318	C₂²×C₃²	—	2	1	no	—
319	C₂²×C₃²	—	2	4	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	—	3	2	no	—
327	C₂²×C₃²	—	4	8	no	—
328	C₂²×C₃²	—	4	8	no	—
329	C₂²×C₃²	—	4	4	no	—
330	C₂²×C₃²	—	4	4	no	—
331	C₂²×C₃²	—	6	1	no	—
332	C₂²×C₃²	—	6	1	no	—
333	C₂²×C₃²	—	6	2	no	—
334	C₂²×C₃²	—	6	2	no	—
335	C₂²×C₃²	—	6	2	no	—
336	C₂²×C₃²	—	12	8	no	—
337	C₂²×C₃²	C₂×#67	1	4	yes	—
338	C₂²×C₃²	C₂×C₃×D₄	1	16	yes	—
339	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
340	C₂²×C₃²	C₂⁴×C₃	1	4	yes	—
341	C₂×C₃×D₃	—	2	4	no	—
342	C₂×C₃×D₃	—	2	4	no	—
343	C₂×C₃×D₃	—	2	8	no	—
344	C₂×C₃×D₃	—	2	8	no	—
345	C₂×C₃×D₃	—	2	8	no	—
346	C₂×C₃×D₃	—	4	32	no	—
347	C₂×C₃×D₃	C₃×#41	1	8	yes	complemented
348	C₃²×C₄	—	2	8	no	—
349	C₃²×C₄	—	2	16	no	—
350	C₃²×C₄	—	2	1	no	—
351	C₃²×C₄	—	2	2	no	—
352	C₃²×C₄	—	2	4	no	—
353	C₃²×C₄	—	2	8	no	—
354	C₃²×C₄	—	2	8	no	—
355	C₃²×C₄	—	6	1	no	—
356	C₃²×C₄	—	6	1	no	—
357	C₃²×C₄	—	6	2	no	—
358	C₃²×C₄	—	6	1	no	—
359	C₃²×C₄	C₂×#67	1	2	yes	—
360	C₃²×C₄	C₂×C₃×D₄	1	8	yes	—
361	C₃×Dic₃	—	2	4	no	—
362	C₃×Dic₃	—	2	4	no	—
363	C₃×Dic₃	—	2	4	no	—
364	C₃×Dic₃	—	2	8	no	—
365	C₂×#41	C₃²×D₃	1	1	yes	characteristic, complemented
366	C₂²×D₄	—	3	1	no	—
367	#124	—	3	1	no	—
368	#123	—	3	2	no	—
369	C₂²⋊Q₈	—	3	1	no	—
370	#121	—	3	2	no	—
371	#121	—	3	1	no	—
372	#120	—	3	2	no	—
373	C₄×D₄	—	3	1	no	—
374	C₄×D₄	—	3	1	no	—
375	C₂×C₂²⋊C₄	—	3	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	—	3	4	no	—
380	C₂³×C₃	—	3	8	no	—
381	C₂³×C₃	—	6	16	no	—
382	C₂³×C₃	—	6	16	no	—
383	C₂³×C₃	—	12	8	no	—
384	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
385	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
386	C₂³×C₃	C₂³×C₃²	1	1	yes	characteristic
387	C₂³×C₃	C₂³×C₃²	1	2	yes	—
388	C₂²×D₃	—	2	4	no	—
389	C₂²×D₃	—	2	4	no	—
390	C₂²×D₃	—	4	2	no	—
391	C₂²×D₃	C₂³×C₃²	1	2	yes	—
392	C₂²×D₃	C₂³×C₃²	1	1	yes	characteristic
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	—	6	8	no	—
401	C₃×D₄	—	6	16	no	—
402	C₃×D₄	—	6	8	no	—
403	C₃×D₄	—	12	8	no	—
404	C₃×D₄	C₃×#67	1	16	yes	complemented
405	C₃×D₄	C₃²×D₄	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	—	3	4	no	—
416	C₂×C₃×C₄	—	3	4	no	—
417	C₂×C₃×C₄	—	3	8	no	—
418	C₂×C₃×C₄	—	3	4	no	—
419	C₂×C₃×C₄	—	6	8	no	—
420	C₂×C₃×C₄	—	12	8	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	C₂³×C₃²	1	1	yes	characteristic
425	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
426	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
427	#67	—	2	4	no	—
428	#67	—	2	2	no	—
429	#67	—	4	2	no	—
430	C₂×Dic₃	—	4	2	no	—
431	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
432	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
433	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
434	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
435	D₁₂	—	2	2	no	—
436	C₄×D₃	—	2	2	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	1	no	—
445	C₂×C₃²	—	4	4	no	—
446	C₂×C₃²	—	6	2	no	—
447	C₂×C₃²	—	12	2	no	—
448	C₂×C₃²	D₃×#41	1	1	yes	characteristic
449	C₂×C₃²	#1009	1	1	yes	characteristic
450	C₂×C₃²	C₂²×#67	1	1	yes	characteristic
451	C₂×C₃²	C₂²×C₃×D₄	1	4	yes	—
452	C₂×C₃²	C₂×C₃×#41	1	4	yes	—
453	C₂×C₃²	C₃×H(5,𝔽₂)	1	4	yes	—
454	C₃×D₃	—	2	8	no	—
455	C₃×D₃	—	4	8	no	—
456	C₂⁴	—	3	2	no	—
457	#41	—	2	4	no	—
458	C₂×Q₈	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
459	C₂×D₄	—	3	1	no	—
460	C₂×D₄	—	3	2	no	—
461	C₂×D₄	—	3	2	no	—
462	C₂×D₄	—	3	1	no	—
463	C₂×D₄	—	6	4	no	—
464	C₂×D₄	C₂×C₃²×D₃	1	1	yes	characteristic
465	C₂×D₄	C₂×C₃²×D₃	1	2	yes	complemented
466	C₂²×C₄	—	3	2	no	—
467	C₂²×C₄	—	3	1	no	—
468	C₂²×C₄	C₂×C₃²×D₃	1	2	yes	complemented
469	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
470	C₄⋊C₄	—	3	1	no	—
471	C₄⋊C₄	—	3	1	no	—
472	C₄⋊C₄	—	3	2	no	—
473	C₂²⋊C₄	—	3	2	no	—
474	C₂²⋊C₄	—	3	1	no	—
475	C₂²⋊C₄	—	3	1	no	—
476	C₂²⋊C₄	—	3	2	no	—
477	C₂²⋊C₄	—	3	2	no	—
478	C₂²⋊C₄	—	3	2	no	—
479	C₂²⋊C₄	—	3	2	no	—
480	C₄²	—	3	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	—	3	8	no	—
495	C₂²×C₃	—	4	8	no	—
496	C₂²×C₃	—	4	8	no	—
497	C₂²×C₃	—	4	4	no	—
498	C₂²×C₃	—	4	4	no	—
499	C₂²×C₃	—	6	4	no	—
500	C₂²×C₃	—	6	4	no	—
501	C₂²×C₃	—	6	8	no	—
502	C₂²×C₃	—	6	8	no	—
503	C₂²×C₃	—	6	8	no	—
504	C₂²×C₃	—	12	32	no	—
505	C₂²×C₃	C₂×C₃×#67	1	16	yes	—
506	C₂²×C₃	C₂×C₃²×D₄	1	4	yes	—
507	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
508	C₂²×C₃	C₂⁴×C₃²	1	1	yes	characteristic
509	C₂×D₃	—	2	1	no	—
510	C₂×D₃	—	2	1	no	—
511	C₂×D₃	—	2	2	no	—
512	C₂×D₃	—	2	2	no	—
513	C₂×D₃	—	2	2	no	—
514	C₂×D₃	—	4	8	no	—
515	C₂×D₃	C₃²×#41	1	2	yes	complemented
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	—	6	4	no	—
524	C₃×C₄	—	6	4	no	—
525	C₃×C₄	—	6	8	no	—
526	C₃×C₄	—	6	4	no	—
527	C₃×C₄	C₂×C₃×#67	1	8	yes	—
528	C₃×C₄	C₂×C₃²×D₄	1	2	yes	—
529	Dic₃	—	2	1	no	—
530	Dic₃	—	2	1	no	—
531	Dic₃	—	2	1	no	—
532	Dic₃	—	2	2	no	—
533	C₃²	—	2	4	no	—
534	C₃²	#5829	1	1	yes	characteristic, direct product factor
535	C₃²	C₃×#546	1	4	yes	complemented
536	C₂³	—	3	1	no	—
537	C₂³	—	3	2	no	—
538	C₂³	—	6	4	no	—
539	C₂³	—	6	4	no	—
540	C₂³	—	12	2	no	—
541	C₂³	C₂²×C₃²×D₃	1	1	yes	characteristic
542	C₂³	C₂²×C₃²×D₃	1	2	yes	—
543	Q₈	—	2	2	no	—
544	D₄	—	2	4	no	—
545	D₄	—	6	2	no	—
546	D₄	—	6	4	no	—
547	D₄	—	6	2	no	—
548	D₄	—	12	2	no	—
549	D₄	C₃²×#67	1	4	yes	complemented
550	C₂×C₄	—	2	4	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	3	1	no	—
553	C₂×C₄	—	3	1	no	—
554	C₂×C₄	—	3	2	no	—
555	C₂×C₄	—	3	1	no	—
556	C₂×C₄	—	6	2	no	—
557	C₂×C₄	—	12	2	no	—
558	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
559	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
560	C₂×C₄	C₂²×C₃²×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	—	6	8	no	—
571	C₂×C₃	—	12	8	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	C₂²×C₃²×D₄	1	1	yes	characteristic
576	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
577	C₂×C₃	C₃²×H(5,𝔽₂)	1	1	yes	characteristic
578	D₃	—	2	2	no	—
579	D₃	—	4	2	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	—	3	2	no	—
586	C₂²	—	6	1	no	—
587	C₂²	—	6	1	no	—
588	C₂²	—	6	2	no	—
589	C₂²	—	6	2	no	—
590	C₂²	—	6	2	no	—
591	C₂²	—	12	8	no	—
592	C₂²	C₂×C₃²×#67	1	4	yes	—
593	C₂²	C₂³×C₃²×D₃	1	1	yes	characteristic
594	C₄	—	2	1	no	—
595	C₄	—	2	2	no	—
596	C₄	—	6	1	no	—
597	C₄	—	6	1	no	—
598	C₄	—	6	2	no	—
599	C₄	—	6	1	no	—
600	C₄	C₂×C₃²×#67	1	2	yes	—
601	C₃	—	2	4	no	—
602	C₃	C₃×#5829	1	4	yes	direct product factor
603	C₃	C₃²×#546	1	1	yes	characteristic, complemented
604	C₂	—	2	4	no	—
605	C₂	—	4	1	no	—
606	C₂	—	6	2	no	—
607	C₂	—	12	2	no	—
608	C₂	C₃²×D₃×#41	1	1	yes	characteristic
609	C₂	C₃²×#1009	1	1	yes	characteristic
610	C₂	C₂²×C₃²×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃²	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₃²
Frattini	C₂²	C₂³×C₃²×D₃
Fitting	C₂×C₃³×#41	C₂
socle	C₂²×C₃³	C₂⁴
hypercenter	C₂×C₃²×#41	D₃
hypocenter	C₃	C₃²×#546
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃² ◁ C₂×C₃²×#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×C₃²×D₃×D₄	C₂	semidirect
3. C₃²×#947	C₂	semidirect
4. C₃²×#946	C₂	semidirect
5. C₃²×#939	C₂	semidirect
6. C₃²×#937	C₂	semidirect
7. C₃²×D₄×Dic₃	C₂	semidirect
8. C₃²×#930	C₂	semidirect
9. C₃²×#929	C₂	semidirect
10. C₃²×C₄×#67	C₂	semidirect
11. C₂×C₃²×(C₂×D₃)⋊C₄	C₂	semidirect
13. C₃×#5829	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×C₃²×#67	C₂²	semidirect
24. C₂²×C₃²×Dic₃	C₂²	semidirect
28. C₃²×#217	C₂²	semidirect
29. C₃²×#217	C₂²	semidirect
32. C₃²×(C₂×D₃)⋊C₄	C₂²	semidirect
33. C₃²×(C₂×D₃)⋊C₄	C₂²	semidirect
34. C₃²×(C₂×D₃)⋊C₄	C₂²	semidirect
35. C₃²×C₄⋊Dic₃	C₂²	semidirect
36. C₃²×Dic₃⋊C₄	C₂²	semidirect
37. C₃²×Dic₃⋊C₄	C₂²	semidirect
38. C₃²×C₄×Dic₃	C₂²	semidirect
40. C₂×C₃²×#41	D₃	semidirect
41. C₂×C₃²×#41	C₂×C₃	semidirect
43. C₂×C₃×D₃×D₄	C₂×C₃	semidirect
53. C₃×#947	C₂×C₃	semidirect
54. C₃×#946	C₂×C₃	semidirect
55. C₃×#939	C₂×C₃	semidirect
56. C₃×#937	C₂×C₃	semidirect
57. C₃×D₄×Dic₃	C₂×C₃	semidirect
58. C₃×#930	C₂×C₃	semidirect
59. C₃×#929	C₂×C₃	semidirect
60. C₃×C₄×#67	C₂×C₃	semidirect
61. C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	semidirect
71. C₃³×D₄	D₄	semidirect
88. #5829	C₃²	direct (N × H)
95. C₂×C₃²×Q₈	C₂×D₃	semidirect
96. C₂×C₃²×Q₈	C₂²×C₃	semidirect
105. C₂×C₃²×D₄	C₂×D₃	semidirect
107. C₂×C₃²×D₄	C₂²×C₃	semidirect
112. C₂²×C₃²×C₄	C₂×D₃	semidirect
113. C₂²×C₃²×C₄	C₂×D₃	semidirect
114. C₂²×C₃²×C₄	C₂²×C₃	semidirect
115. C₂²×C₃²×C₄	C₂²×C₃	semidirect
118. C₂×C₃×#67	C₂²×C₃	semidirect
119. C₂²×C₃×Dic₃	C₂²×C₃	semidirect
134. C₃×#217	C₂²×C₃	semidirect
135. C₃×#217	C₂²×C₃	semidirect
138. C₃×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
139. C₃×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
140. C₃×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
141. C₃×C₄⋊Dic₃	C₂²×C₃	semidirect
142. C₃×Dic₃⋊C₄	C₂²×C₃	semidirect
143. C₃×Dic₃⋊C₄	C₂²×C₃	semidirect
144. C₃×C₄×Dic₃	C₂²×C₃	semidirect
158. C₂×C₃²×D₃	#41	semidirect
167. C₂×C₃×#41	C₃×D₃	semidirect
168. C₂×C₃×#41	C₂×C₃²	semidirect
170. C₂×D₃×D₄	C₂×C₃²	semidirect
180. #947	C₂×C₃²	semidirect
181. #946	C₂×C₃²	semidirect
182. #939	C₂×C₃²	semidirect
183. #937	C₂×C₃²	semidirect
184. D₄×Dic₃	C₂×C₃²	semidirect
185. #930	C₂×C₃²	semidirect
186. #929	C₂×C₃²	semidirect
187. C₄×#67	C₂×C₃²	semidirect
188. C₂×(C₂×D₃)⋊C₄	C₂×C₃²	semidirect
216. C₃²×D₄	#67	semidirect
217. C₃²×D₄	C₃×D₄	semidirect
263. C₂×C₃×Q₈	C₂×C₃×D₃	semidirect
264. C₂×C₃×Q₈	C₂²×C₃²	semidirect
273. C₂×C₃×D₄	C₂×C₃×D₃	semidirect
275. C₂×C₃×D₄	C₂²×C₃²	semidirect
280. C₂²×C₃×C₄	C₂×C₃×D₃	semidirect
281. C₂²×C₃×C₄	C₂×C₃×D₃	semidirect
282. C₂²×C₃×C₄	C₂²×C₃²	semidirect
283. C₂²×C₃×C₄	C₂²×C₃²	semidirect
286. C₂×#67	C₂²×C₃²	semidirect
287. C₂²×Dic₃	C₂²×C₃²	semidirect
302. #217	C₂²×C₃²	semidirect
303. #217	C₂²×C₃²	semidirect
306. (C₂×D₃)⋊C₄	C₂²×C₃²	semidirect
307. (C₂×D₃)⋊C₄	C₂²×C₃²	semidirect
308. (C₂×D₃)⋊C₄	C₂²×C₃²	semidirect
309. C₄⋊Dic₃	C₂²×C₃²	semidirect
310. Dic₃⋊C₄	C₂²×C₃²	semidirect
311. Dic₃⋊C₄	C₂²×C₃²	semidirect
312. C₄×Dic₃	C₂²×C₃²	semidirect
347. C₂×C₃×D₃	C₃×#41	semidirect
365. C₂×#41	C₃²×D₃	semidirect
376. C₃³	#546	semidirect
404. C₃×D₄	C₃×#67	semidirect
405. C₃×D₄	C₃²×D₄	semidirect
458. C₂×Q₈	C₂×C₃²×D₃	semidirect
465. C₂×D₄	C₂×C₃²×D₃	semidirect
468. C₂²×C₄	C₂×C₃²×D₃	semidirect
469. C₂²×C₄	C₂×C₃²×D₃	semidirect
515. C₂×D₃	C₃²×#41	semidirect
534. C₃²	#5829	direct (N × H)
535. C₃²	C₃×#546	semidirect
549. D₄	C₃²×#67	semidirect
602. C₃	C₃×#5829	direct (N × H)
603. C₃	C₃²×#546	semidirect

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×C₃²×D₃×D₄	2
C₃²×#947	2
C₃²×#946	2
C₃²×#939	2
C₃²×#937	2
C₃²×D₄×Dic₃	2
C₃²×#930	2
C₃²×#929	2
C₃²×C₄×#67	2
C₂×C₃²×(C₂×D₃)⋊C₄	2
C₃²×#546	3
C₃×#5829	3

Subgroups — C32×#5829 #13179205

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#5829 #13179205