Subgroups — C₃²×#5828 #13179204

Order 1728.

2636 conjugacy classes of subgroups.

The subgroup lattice has 456 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	C₂²×C₃²×C₄×D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#946	C₂	1	2	yes	maximal, complemented
4	C₃²×#938	C₂	1	2	yes	maximal, complemented
5	C₃²×#937	C₂	1	2	yes	maximal, complemented
6	C₃²×#935	C₂	1	2	yes	maximal, complemented
7	C₃²×C₄×#67	C₂	1	4	yes	maximal, complemented
8	C₃²×#926	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃²×#525	—	3	1	no	maximal
10	C₃×#5828	C₃	1	4	yes	maximal, direct product factor
11	C₂³×C₃²×D₃	C₂²	1	1	yes	characteristic
12	C₃³×#41	—	2	4	no	—
13	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic, complemented
14	C₂×C₃³×D₄	C₂²	1	2	yes	—
15	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
17	C₂²×C₃³×C₄	C₂²	1	2	yes	complemented
18	C₂×C₃²×#67	C₂²	1	4	yes	—
19	C₂²×C₃²×Dic₃	C₂²	1	1	yes	characteristic
20	C₂×C₃²×C₄×D₃	—	2	4	no	—
21	C₂×C₃²×C₄×D₃	C₂²	1	2	yes	—
22	C₂×C₃²×C₄×D₃	C₂²	1	2	yes	—
23	C₃²×#217	C₂²	1	2	yes	—
24	C₃²×#217	C₂²	1	4	yes	complemented
25	C₃²×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
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	—	2	4	no	—
30	C₂×C₃²×#41	D₃	1	1	yes	characteristic, complemented
31	C₂×C₃²×#41	C₂×C₃	1	4	yes	complemented
32	C₂³×C₃²×C₄	—	3	1	no	—
33	C₂²×C₃×C₄×D₃	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×#946	C₂×C₃	1	8	yes	complemented
41	C₃×#938	C₂×C₃	1	8	yes	complemented
42	C₃×#937	C₂×C₃	1	8	yes	complemented
43	C₃×#935	C₂×C₃	1	8	yes	complemented
44	C₃×C₄×#67	C₂×C₃	1	16	yes	complemented
45	C₃×#926	C₂×C₃	1	4	yes	complemented
46	C₂³×C₃³	C₂³	1	2	yes	—
47	C₂³×C₃³	C₂³	1	1	yes	characteristic
48	C₂²×C₃²×D₃	—	2	2	no	—
49	C₂²×C₃²×D₃	—	2	4	no	—
50	C₂²×C₃²×D₃	C₂³	1	2	yes	—
51	C₃³×Q₈	—	2	2	no	—
52	C₃³×D₄	—	2	4	no	—
53	C₃³×D₄	—	2	2	no	—
54	C₂×C₃³×C₄	—	2	4	no	—
55	C₂×C₃³×C₄	D₄	1	4	yes	complemented
56	C₂×C₃³×C₄	C₂³	1	2	yes	—
57	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
58	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
59	C₃²×#67	—	2	8	no	—
60	C₂×C₃²×Dic₃	—	2	2	no	—
61	C₂×C₃²×Dic₃	C₂³	1	4	yes	—
62	C₂×C₃²×Dic₃	C₂³	1	2	yes	—
63	C₃²×C₄×D₃	—	2	4	no	—
64	C₃²×C₄×D₃	—	2	4	no	—
65	C₃×#525	—	3	4	no	—
66	#5828	C₃²	1	1	yes	characteristic, direct product factor
67	C₂⁴×C₃²	—	3	1	no	—
68	C₂³×C₃×D₃	C₂²×C₃	1	4	yes	—
69	C₃²×#41	—	2	32	no	—
70	C₃²×#41	—	2	4	no	—
71	C₃²×#41	—	2	16	no	—
72	C₂×C₃²×Q₈	—	2	4	no	—
73	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
74	C₂×C₃²×Q₈	C₂²×C₃	1	4	yes	complemented
75	C₂×C₃²×D₄	—	2	8	no	—
76	C₂×C₃²×D₄	—	2	4	no	—
77	C₂×C₃²×D₄	—	3	4	no	—
78	C₂×C₃²×D₄	C₂×D₃	1	2	yes	—
79	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic, complemented
80	C₂×C₃²×D₄	C₂²×C₃	1	8	yes	—
81	C₂×C₃²×D₄	C₂²×C₃	1	4	yes	complemented
82	C₂²×C₃²×C₄	—	2	4	no	—
83	C₂²×C₃²×C₄	—	2	8	no	—
84	C₂²×C₃²×C₄	—	3	1	no	—
85	C₂²×C₃²×C₄	—	3	2	no	—
86	C₂²×C₃²×C₄	—	3	2	no	—
87	C₂²×C₃²×C₄	—	6	4	no	—
88	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
89	C₂²×C₃²×C₄	C₂×D₃	1	2	yes	complemented
90	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
91	C₂²×C₃²×C₄	C₂²×C₃	1	8	yes	complemented
92	C₂×C₃×#67	C₂²×C₃	1	16	yes	—
93	C₂²×C₃×Dic₃	C₂²×C₃	1	4	yes	—
94	C₂×C₃×C₄×D₃	—	2	16	no	—
95	C₂×C₃×C₄×D₃	C₂²×C₃	1	8	yes	—
96	C₂×C₃×C₄×D₃	C₂²×C₃	1	8	yes	—
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	8	yes	—
104	C₃×#217	C₂²×C₃	1	16	yes	complemented
105	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	16	yes	—
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	2	no	—
110	C₂²×C₃³	—	2	2	no	—
111	C₂²×C₃³	—	2	4	no	—
112	C₂²×C₃³	C₂×D₄	1	2	yes	—
113	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
114	C₂×C₃²×D₃	—	2	8	no	—
115	C₂×C₃²×D₃	—	2	2	no	—
116	C₂×C₃²×D₃	—	2	2	no	—
117	C₂×C₃²×D₃	#41	1	4	yes	complemented
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	—	2	4	no	—
124	C₂×C₃×#41	C₃×D₃	1	4	yes	complemented
125	C₂×C₃×#41	C₂×C₃²	1	1	yes	characteristic, complemented
126	C₂³×C₃×C₄	—	3	4	no	—
127	C₂²×C₄×D₃	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	#946	C₂×C₃²	1	2	yes	complemented
135	#938	C₂×C₃²	1	2	yes	complemented
136	#937	C₂×C₃²	1	2	yes	complemented
137	#935	C₂×C₃²	1	2	yes	complemented
138	C₄×#67	C₂×C₃²	1	4	yes	complemented
139	#926	C₂×C₃²	1	1	yes	characteristic, complemented
140	C₂³×C₃²	—	2	8	no	—
141	C₂³×C₃²	—	2	4	no	—
142	C₂³×C₃²	—	3	2	no	—
143	C₂³×C₃²	—	6	4	no	—
144	C₂³×C₃²	—	6	2	no	—
145	C₂³×C₃²	C₂²×D₃	1	2	yes	—
146	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
147	C₂³×C₃²	C₂³×C₃	1	8	yes	—
148	C₂³×C₃²	C₂³×C₃	1	4	yes	—
149	C₂²×C₃×D₃	—	2	8	no	—
150	C₂²×C₃×D₃	—	2	16	no	—
151	C₂²×C₃×D₃	C₂³×C₃	1	8	yes	—
152	C₃²×Q₈	—	2	16	no	—
153	C₃²×Q₈	—	2	2	no	—
154	C₃²×Q₈	—	2	8	no	—
155	C₃²×D₄	—	2	32	no	—
156	C₃²×D₄	—	2	16	no	—
157	C₃²×D₄	—	2	4	no	—
158	C₃²×D₄	—	2	16	no	—
159	C₃²×D₄	—	2	2	no	—
160	C₃²×D₄	—	2	8	no	—
161	C₃²×D₄	—	6	8	no	—
162	C₂×C₃²×C₄	—	2	32	no	—
163	C₂×C₃²×C₄	—	2	4	no	—
164	C₂×C₃²×C₄	—	2	16	no	—
165	C₂×C₃²×C₄	—	2	16	no	—
166	C₂×C₃²×C₄	—	2	4	no	—
167	C₂×C₃²×C₄	—	2	8	no	—
168	C₂×C₃²×C₄	—	2	4	no	—
169	C₂×C₃²×C₄	—	3	4	no	—
170	C₂×C₃²×C₄	—	3	2	no	—
171	C₂×C₃²×C₄	—	6	2	no	—
172	C₂×C₃²×C₄	—	6	4	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	32	no	—
183	C₂×C₃×Dic₃	—	2	8	no	—
184	C₂×C₃×Dic₃	C₂³×C₃	1	16	yes	—
185	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
186	C₃×C₄×D₃	—	2	16	no	—
187	C₃×C₄×D₃	—	2	16	no	—
188	#525	—	3	1	no	Sylow
189	C₂×C₃³	—	2	2	no	—
190	C₂×C₃³	—	4	2	no	—
191	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₃³	C₂×#41	1	2	yes	—
193	C₃²×D₃	—	2	4	no	—
194	C₂⁴×C₃	—	3	4	no	—
195	C₂³×D₃	C₂²×C₃²	1	1	yes	characteristic
196	C₃×#41	—	2	32	no	—
197	C₃×#41	—	2	16	no	—
198	C₃×#41	—	2	4	no	—
199	C₂×C₃×Q₈	—	2	4	no	—
200	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	complemented
201	C₂×C₃×Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
202	C₂×C₃×D₄	—	2	8	no	—
203	C₂×C₃×D₄	—	2	4	no	—
204	C₂×C₃×D₄	—	3	16	no	—
205	C₂×C₃×D₄	C₂×C₃×D₃	1	8	yes	—
206	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	complemented
207	C₂×C₃×D₄	C₂²×C₃²	1	2	yes	—
208	C₂×C₃×D₄	C₂²×C₃²	1	1	yes	characteristic, complemented
209	C₂²×C₃×C₄	—	2	4	no	—
210	C₂²×C₃×C₄	—	2	8	no	—
211	C₂²×C₃×C₄	—	3	4	no	—
212	C₂²×C₃×C₄	—	3	8	no	—
213	C₂²×C₃×C₄	—	3	8	no	—
214	C₂²×C₃×C₄	—	6	16	no	—
215	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
216	C₂²×C₃×C₄	C₂×C₃×D₃	1	8	yes	complemented
217	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
218	C₂²×C₃×C₄	C₂²×C₃²	1	2	yes	complemented
219	C₂×#67	C₂²×C₃²	1	4	yes	—
220	C₂²×Dic₃	C₂²×C₃²	1	1	yes	characteristic
221	C₂×C₄×D₃	—	2	4	no	—
222	C₂×C₄×D₃	C₂²×C₃²	1	2	yes	—
223	C₂×C₄×D₃	C₂²×C₃²	1	2	yes	—
224	C₃×C₄⋊C₄	—	3	16	no	—
225	C₃×C₄⋊C₄	—	3	8	no	—
226	C₃×C₂²⋊C₄	—	3	8	no	—
227	C₃×C₂²⋊C₄	—	3	16	no	—
228	C₃×C₂²⋊C₄	—	3	16	no	—
229	C₃×C₄²	—	3	8	no	—
230	#217	C₂²×C₃²	1	2	yes	—
231	#217	C₂²×C₃²	1	4	yes	complemented
232	(C₂×D₃)⋊C₄	C₂²×C₃²	1	4	yes	—
233	C₄⋊Dic₃	C₂²×C₃²	1	2	yes	complemented
234	Dic₃⋊C₄	C₂²×C₃²	1	4	yes	complemented
235	C₄×Dic₃	C₂²×C₃²	1	2	yes	complemented
236	C₂²×C₃²	—	2	2	no	—
237	C₂²×C₃²	—	2	16	no	—
238	C₂²×C₃²	—	2	4	no	—
239	C₂²×C₃²	—	2	2	no	—
240	C₂²×C₃²	—	2	8	no	—
241	C₂²×C₃²	—	2	4	no	—
242	C₂²×C₃²	—	2	8	no	—
243	C₂²×C₃²	—	2	8	no	—
244	C₂²×C₃²	—	2	16	no	—
245	C₂²×C₃²	—	3	4	no	—
246	C₂²×C₃²	—	4	8	no	—
247	C₂²×C₃²	—	4	16	no	—
248	C₂²×C₃²	—	6	8	no	—
249	C₂²×C₃²	—	6	2	no	—
250	C₂²×C₃²	—	6	2	no	—
251	C₂²×C₃²	C₂×#67	1	2	yes	—
252	C₂²×C₃²	C₂×C₃×D₄	1	8	yes	—
253	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
254	C₂²×C₃²	C₂⁴×C₃	1	4	yes	—
255	C₂×C₃×D₃	—	2	32	no	—
256	C₂×C₃×D₃	—	2	8	no	—
257	C₂×C₃×D₃	—	2	8	no	—
258	C₂×C₃×D₃	C₃×#41	1	16	yes	complemented
259	C₃²×C₄	—	2	16	no	—
260	C₃²×C₄	—	2	2	no	—
261	C₃²×C₄	—	2	8	no	—
262	C₃²×C₄	—	2	8	no	—
263	C₃²×C₄	—	2	8	no	—
264	C₃²×C₄	—	6	4	no	—
265	C₃²×C₄	—	6	2	no	—
266	C₃²×C₄	C₂×#67	1	2	yes	—
267	C₃²×C₄	C₂×#67	1	2	yes	—
268	C₃²×C₄	C₂×C₃×D₄	1	8	yes	—
269	C₃²×C₄	C₂×C₃×D₄	1	8	yes	—
270	C₃×Dic₃	—	2	8	no	—
271	C₃×Dic₃	—	2	16	no	—
272	C₂×#41	C₃²×D₃	1	1	yes	characteristic, complemented
273	C₂³×C₄	—	3	1	no	—
274	#123	—	3	2	no	—
275	C₂²⋊Q₈	—	3	2	no	—
276	#121	—	3	2	no	—
277	#120	—	3	2	no	—
278	C₄×D₄	—	3	4	no	—
279	#117	—	3	1	no	—
280	C₃³	#525	1	1	yes	characteristic, complemented, Sylow
281	C₂³×C₃	—	2	8	no	—
282	C₂³×C₃	—	2	4	no	—
283	C₂³×C₃	—	3	8	no	—
284	C₂³×C₃	—	6	16	no	—
285	C₂³×C₃	—	6	8	no	—
286	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
287	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
288	C₂³×C₃	C₂³×C₃²	1	2	yes	—
289	C₂³×C₃	C₂³×C₃²	1	1	yes	characteristic
290	C₂²×D₃	—	2	2	no	—
291	C₂²×D₃	—	2	4	no	—
292	C₂²×D₃	C₂³×C₃²	1	2	yes	—
293	C₃×Q₈	—	2	16	no	—
294	C₃×Q₈	—	2	8	no	—
295	C₃×Q₈	—	2	2	no	—
296	C₃×D₄	—	2	32	no	—
297	C₃×D₄	—	2	16	no	—
298	C₃×D₄	—	2	16	no	—
299	C₃×D₄	—	2	4	no	—
300	C₃×D₄	—	2	8	no	—
301	C₃×D₄	—	2	2	no	—
302	C₃×D₄	—	6	32	no	—
303	C₂×C₃×C₄	—	2	32	no	—
304	C₂×C₃×C₄	—	2	16	no	—
305	C₂×C₃×C₄	—	2	4	no	—
306	C₂×C₃×C₄	—	2	16	no	—
307	C₂×C₃×C₄	—	2	4	no	—
308	C₂×C₃×C₄	—	2	8	no	—
309	C₂×C₃×C₄	—	2	4	no	—
310	C₂×C₃×C₄	—	3	16	no	—
311	C₂×C₃×C₄	—	3	8	no	—
312	C₂×C₃×C₄	—	6	8	no	—
313	C₂×C₃×C₄	—	6	16	no	—
314	C₂×C₃×C₄	—	6	16	no	—
315	C₂×C₃×C₄	C₃×#67	1	16	yes	complemented
316	C₂×C₃×C₄	C₃²×D₄	1	4	yes	complemented
317	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
318	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
319	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
320	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
321	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
322	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
323	#67	—	2	8	no	—
324	C₂×Dic₃	—	2	2	no	—
325	C₂×Dic₃	C₂³×C₃²	1	4	yes	—
326	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
327	C₄×D₃	—	2	4	no	—
328	C₄×D₃	—	2	4	no	—
329	C₂×C₃²	—	2	2	no	—
330	C₂×C₃²	—	2	8	no	—
331	C₂×C₃²	—	2	4	no	—
332	C₂×C₃²	—	2	8	no	—
333	C₂×C₃²	—	4	8	no	—
334	C₂×C₃²	—	4	16	no	—
335	C₂×C₃²	—	4	2	no	—
336	C₂×C₃²	—	4	8	no	—
337	C₂×C₃²	—	6	4	no	—
338	C₂×C₃²	D₃×#41	1	2	yes	—
339	C₂×C₃²	C₂²×#67	1	1	yes	characteristic
340	C₂×C₃²	C₂²×C₃×D₄	1	4	yes	—
341	C₂×C₃²	C₂×C₃×#41	1	8	yes	—
342	C₃×D₃	—	2	16	no	—
343	C₂⁴	—	3	1	no	—
344	#41	—	2	4	no	—
345	C₂×Q₈	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
346	C₂×D₄	—	3	4	no	—
347	C₂×D₄	C₂×C₃²×D₃	1	2	yes	—
348	C₂×D₄	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
349	C₂²×C₄	—	3	1	no	—
350	C₂²×C₄	—	3	2	no	—
351	C₂²×C₄	—	3	2	no	—
352	C₂²×C₄	—	6	4	no	—
353	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
354	C₂²×C₄	C₂×C₃²×D₃	1	2	yes	complemented
355	C₄⋊C₄	—	3	2	no	—
356	C₄⋊C₄	—	3	4	no	—
357	C₂²⋊C₄	—	3	2	no	—
358	C₂²⋊C₄	—	3	4	no	—
359	C₂²⋊C₄	—	3	4	no	—
360	C₄²	—	3	2	no	—
361	C₂²×C₃	—	2	8	no	—
362	C₂²×C₃	—	2	2	no	—
363	C₂²×C₃	—	2	16	no	—
364	C₂²×C₃	—	2	16	no	—
365	C₂²×C₃	—	2	8	no	—
366	C₂²×C₃	—	2	2	no	—
367	C₂²×C₃	—	2	4	no	—
368	C₂²×C₃	—	2	4	no	—
369	C₂²×C₃	—	2	8	no	—
370	C₂²×C₃	—	3	16	no	—
371	C₂²×C₃	—	4	8	no	—
372	C₂²×C₃	—	4	16	no	—
373	C₂²×C₃	—	6	32	no	—
374	C₂²×C₃	—	6	8	no	—
375	C₂²×C₃	—	6	8	no	—
376	C₂²×C₃	C₂×C₃×#67	1	8	yes	—
377	C₂²×C₃	C₂×C₃²×D₄	1	2	yes	—
378	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
379	C₂²×C₃	C₂⁴×C₃²	1	1	yes	characteristic
380	C₂×D₃	—	2	8	no	—
381	C₂×D₃	—	2	2	no	—
382	C₂×D₃	—	2	2	no	—
383	C₂×D₃	C₃²×#41	1	4	yes	complemented
384	C₃×C₄	—	2	16	no	—
385	C₃×C₄	—	2	8	no	—
386	C₃×C₄	—	2	2	no	—
387	C₃×C₄	—	2	8	no	—
388	C₃×C₄	—	2	8	no	—
389	C₃×C₄	—	6	16	no	—
390	C₃×C₄	—	6	8	no	—
391	C₃×C₄	C₂×C₃×#67	1	8	yes	—
392	C₃×C₄	C₂×C₃×#67	1	8	yes	—
393	C₃×C₄	C₂×C₃²×D₄	1	2	yes	—
394	C₃×C₄	C₂×C₃²×D₄	1	2	yes	—
395	Dic₃	—	2	2	no	—
396	Dic₃	—	2	4	no	—
397	C₃²	—	2	4	no	—
398	C₃²	#5828	1	1	yes	characteristic, direct product factor
399	C₃²	C₃×#525	1	4	yes	complemented
400	C₂³	—	3	2	no	—
401	C₂³	—	6	4	no	—
402	C₂³	—	6	2	no	—
403	C₂³	C₂²×C₃²×D₃	1	2	yes	—
404	C₂³	C₂²×C₃²×D₃	1	1	yes	characteristic
405	Q₈	—	2	2	no	—
406	D₄	—	2	4	no	—
407	D₄	—	2	2	no	—
408	D₄	—	6	8	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	3	4	no	—
411	C₂×C₄	—	3	2	no	—
412	C₂×C₄	—	6	2	no	—
413	C₂×C₄	—	6	4	no	—
414	C₂×C₄	—	6	4	no	—
415	C₂×C₄	C₃²×#67	1	4	yes	complemented
416	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
417	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
418	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
419	C₂×C₃	—	2	8	no	—
420	C₂×C₃	—	2	2	no	—
421	C₂×C₃	—	2	8	no	—
422	C₂×C₃	—	2	4	no	—
423	C₂×C₃	—	4	8	no	—
424	C₂×C₃	—	4	16	no	—
425	C₂×C₃	—	4	8	no	—
426	C₂×C₃	—	4	2	no	—
427	C₂×C₃	—	6	16	no	—
428	C₂×C₃	C₃×D₃×#41	1	8	yes	—
429	C₂×C₃	C₂²×C₃×#67	1	4	yes	—
430	C₂×C₃	C₂²×C₃²×D₄	1	1	yes	characteristic
431	C₂×C₃	C₂×C₃²×#41	1	2	yes	—
432	D₃	—	2	4	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	4	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	3	4	no	—
437	C₂²	—	6	8	no	—
438	C₂²	—	6	2	no	—
439	C₂²	—	6	2	no	—
440	C₂²	C₂×C₃²×#67	1	2	yes	—
441	C₂²	C₂³×C₃²×D₃	1	1	yes	characteristic
442	C₄	—	2	2	no	—
443	C₄	—	6	4	no	—
444	C₄	—	6	2	no	—
445	C₄	C₂×C₃²×#67	1	2	yes	—
446	C₄	C₂×C₃²×#67	1	2	yes	—
447	C₃	—	2	4	no	—
448	C₃	C₃×#5828	1	4	yes	direct product factor
449	C₃	C₃²×#525	1	1	yes	characteristic, complemented
450	C₂	—	2	2	no	—
451	C₂	—	4	2	no	—
452	C₂	—	6	4	no	—
453	C₂	C₃²×D₃×#41	1	2	yes	—
454	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	C₂×C₃³×#41	C₂
socle	C₂²×C₃³	C₂⁴
hypercenter	C₂×C₃²×#41	D₃
hypocenter	C₃	C₃²×#525
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃²×C₄ ◁ 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. C₂²×C₃²×C₄×D₃	C₂	semidirect
3. C₃²×#946	C₂	semidirect
4. C₃²×#938	C₂	semidirect
5. C₃²×#937	C₂	semidirect
6. C₃²×#935	C₂	semidirect
7. C₃²×C₄×#67	C₂	semidirect
8. C₃²×#926	C₂	semidirect
10. C₃×#5828	C₃	direct (N × H)
13. C₂×C₃³×Q₈	C₂²	semidirect
15. C₂×C₃³×D₄	C₂²	semidirect
17. C₂²×C₃³×C₄	C₂²	semidirect
24. C₃²×#217	C₂²	semidirect
26. C₃²×C₄⋊Dic₃	C₂²	semidirect
27. C₃²×Dic₃⋊C₄	C₂²	semidirect
28. C₃²×C₄×Dic₃	C₂²	semidirect
30. C₂×C₃²×#41	D₃	semidirect
31. C₂×C₃²×#41	C₂×C₃	semidirect
33. C₂²×C₃×C₄×D₃	C₂×C₃	semidirect
40. C₃×#946	C₂×C₃	semidirect
41. C₃×#938	C₂×C₃	semidirect
42. C₃×#937	C₂×C₃	semidirect
43. C₃×#935	C₂×C₃	semidirect
44. C₃×C₄×#67	C₂×C₃	semidirect
45. C₃×#926	C₂×C₃	semidirect
55. C₂×C₃³×C₄	D₄	semidirect
66. #5828	C₃²	direct (N × H)
73. C₂×C₃²×Q₈	C₂×D₃	semidirect
74. C₂×C₃²×Q₈	C₂²×C₃	semidirect
79. C₂×C₃²×D₄	C₂×D₃	semidirect
81. C₂×C₃²×D₄	C₂²×C₃	semidirect
89. C₂²×C₃²×C₄	C₂×D₃	semidirect
91. C₂²×C₃²×C₄	C₂²×C₃	semidirect
104. C₃×#217	C₂²×C₃	semidirect
106. C₃×C₄⋊Dic₃	C₂²×C₃	semidirect
107. C₃×Dic₃⋊C₄	C₂²×C₃	semidirect
108. C₃×C₄×Dic₃	C₂²×C₃	semidirect
117. C₂×C₃²×D₃	#41	semidirect
124. C₂×C₃×#41	C₃×D₃	semidirect
125. C₂×C₃×#41	C₂×C₃²	semidirect
127. C₂²×C₄×D₃	C₂×C₃²	semidirect
134. #946	C₂×C₃²	semidirect
135. #938	C₂×C₃²	semidirect
136. #937	C₂×C₃²	semidirect
137. #935	C₂×C₃²	semidirect
138. C₄×#67	C₂×C₃²	semidirect
139. #926	C₂×C₃²	semidirect
174. C₂×C₃²×C₄	#67	semidirect
175. C₂×C₃²×C₄	C₃×D₄	semidirect
200. C₂×C₃×Q₈	C₂×C₃×D₃	semidirect
201. C₂×C₃×Q₈	C₂²×C₃²	semidirect
206. C₂×C₃×D₄	C₂×C₃×D₃	semidirect
208. C₂×C₃×D₄	C₂²×C₃²	semidirect
216. C₂²×C₃×C₄	C₂×C₃×D₃	semidirect
218. C₂²×C₃×C₄	C₂²×C₃²	semidirect
231. #217	C₂²×C₃²	semidirect
233. C₄⋊Dic₃	C₂²×C₃²	semidirect
234. Dic₃⋊C₄	C₂²×C₃²	semidirect
235. C₄×Dic₃	C₂²×C₃²	semidirect
258. C₂×C₃×D₃	C₃×#41	semidirect
272. C₂×#41	C₃²×D₃	semidirect
280. C₃³	#525	semidirect
315. C₂×C₃×C₄	C₃×#67	semidirect
316. C₂×C₃×C₄	C₃²×D₄	semidirect
345. C₂×Q₈	C₂×C₃²×D₃	semidirect
348. C₂×D₄	C₂×C₃²×D₃	semidirect
354. C₂²×C₄	C₂×C₃²×D₃	semidirect
383. C₂×D₃	C₃²×#41	semidirect
398. C₃²	#5828	direct (N × H)
399. C₃²	C₃×#525	semidirect
415. C₂×C₄	C₃²×#67	semidirect
448. C₃	C₃×#5828	direct (N × H)
449. 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
C₂×C₃³×#41	2
C₂²×C₃²×C₄×D₃	2
C₃²×#946	2
C₃²×#938	2
C₃²×#937	2
C₃²×#935	2
C₃²×C₄×#67	2
C₃²×#926	2
C₃²×#525	3
C₃×#5828	3

Subgroups — C32×#5828 #13179204

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#5828 #13179204