Subgroups — C₃²×D₃×#124 #13179051

Order 1728.

2284 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×C₃²×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃²×D₃×D₄	C₂	1	1	yes	maximal, characteristic
3	C₃³×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#947	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×#936	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×#885	C₂	1	4	yes	maximal, complemented
7	C₃²×D₃×C₂²⋊C₄	C₂	1	4	yes	maximal, complemented
8	C₃²×#875	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃²×C₄²×D₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃²×#124	—	3	1	no	maximal
11	C₃×D₃×#124	C₃	1	4	yes	maximal, direct product factor
12	C₂³×C₃²×D₃	C₂²	1	2	yes	—
13	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic, complemented
14	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₃²×#67	C₂²	1	2	yes	—
16	C₃²×D₃×Q₈	—	2	4	no	—
17	C₃²×D₃×D₄	—	2	4	no	—
18	C₂×C₃²×D₁₂	C₂²	1	1	yes	characteristic
19	C₂×C₃²×C₄×D₃	C₂²	1	2	yes	—
20	C₂×C₃²×C₄×D₃	C₂²	1	2	yes	—
21	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
22	C₂×C₃²×Dic₆	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃²×Dic₆	C₂²	1	2	yes	complemented
24	C₃³×C₂²⋊C₄	C₂²	1	4	yes	complemented
25	C₃³×C₄²	C₂²	1	1	yes	characteristic, complemented
26	C₃²×#217	C₂²	1	4	yes	complemented
27	C₃²×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
28	C₃²×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
29	C₃²×C₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
30	C₃²×C₄×Dic₃	C₂²	1	2	yes	complemented
31	C₂²×C₃²×Q₈	—	3	1	no	—
32	C₂²×C₃²×D₄	—	3	1	no	—
33	C₂×C₃×D₃×Q₈	C₂×C₃	1	4	yes	complemented
34	C₂×C₃×D₃×D₄	C₂×C₃	1	4	yes	—
35	C₃²×#124	—	2	4	no	—
36	C₃²×#124	—	3	1	no	—
37	C₃²×#124	—	3	1	no	—
38	C₃²×#124	—	3	4	no	—
39	C₃²×#124	—	3	1	no	—
40	C₃²×#124	D₃	1	1	yes	characteristic, direct product factor
41	C₃²×#124	C₂×C₃	1	4	yes	complemented
42	C₂×C₃²×C₂²⋊C₄	—	3	4	no	—
43	C₂×C₃²×C₄²	—	3	1	no	—
44	C₃×#947	C₂×C₃	1	4	yes	complemented
45	C₃×#936	C₂×C₃	1	4	yes	complemented
46	C₃×#885	C₂×C₃	1	16	yes	complemented
47	C₃×D₃×C₂²⋊C₄	C₂×C₃	1	16	yes	complemented
48	C₃×#875	C₂×C₃	1	4	yes	complemented
49	C₃×C₄²×D₃	C₂×C₃	1	4	yes	complemented
50	C₂³×C₃³	C₂³	1	2	yes	—
51	C₂²×C₃²×D₃	—	2	4	no	—
52	C₂²×C₃²×D₃	—	2	8	no	—
53	C₂²×C₃²×D₃	C₂³	1	2	yes	—
54	C₂²×C₃²×D₃	C₂³	1	1	yes	characteristic
55	C₃³×Q₈	—	2	2	no	—
56	C₃³×D₄	—	2	2	no	—
57	C₂×C₃³×C₄	C₂³	1	2	yes	—
58	C₂×C₃³×C₄	C₂³	1	2	yes	—
59	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
60	C₃²×#67	—	2	4	no	—
61	C₂×C₃²×Dic₃	C₂³	1	2	yes	—
62	C₂×C₃²×Dic₃	C₂³	1	2	yes	—
63	C₂×C₃²×Dic₃	C₂³	1	1	yes	characteristic
64	C₃²×D₁₂	—	2	2	no	—
65	C₃²×C₄×D₃	—	2	4	no	—
66	C₃²×C₄×D₃	—	2	4	no	—
67	C₃²×C₄×D₃	D₄	1	4	yes	—
68	C₃²×Dic₆	—	2	2	no	—
69	C₃²×Dic₆	—	2	4	no	—
70	C₂×C₃×#124	—	3	4	no	—
71	D₃×#124	C₃²	1	1	yes	characteristic, direct product factor
72	C₂⁴×C₃²	—	3	2	no	—
73	C₂³×C₃×D₃	C₂²×C₃	1	8	yes	—
74	C₂×C₃²×Q₈	—	2	4	no	—
75	C₂×C₃²×Q₈	—	3	2	no	—
76	C₂×C₃²×Q₈	—	3	1	no	—
77	C₂×C₃²×Q₈	—	6	4	no	—
78	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
79	C₂×C₃²×Q₈	C₂²×C₃	1	4	yes	complemented
80	C₂×C₃²×D₄	—	2	4	no	—
81	C₂×C₃²×D₄	—	3	2	no	—
82	C₂×C₃²×D₄	—	3	1	no	—
83	C₂×C₃²×D₄	—	6	4	no	—
84	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
85	C₂×C₃²×D₄	C₂²×C₃	1	4	yes	—
86	C₂²×C₃²×C₄	—	3	1	no	—
87	C₂²×C₃²×C₄	—	3	2	no	—
88	C₂²×C₃²×C₄	—	3	2	no	—
89	C₂×C₃×#67	C₂²×C₃	1	8	yes	—
90	C₃×D₃×Q₈	—	2	16	no	—
91	C₃×D₃×D₄	—	2	16	no	—
92	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	—
93	C₂×C₃×C₄×D₃	C₂²×C₃	1	8	yes	—
94	C₂×C₃×C₄×D₃	C₂²×C₃	1	8	yes	—
95	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
96	C₂×C₃×Dic₆	C₂²×C₃	1	8	yes	complemented
97	C₂×C₃×Dic₆	C₂²×C₃	1	4	yes	complemented
98	C₃²×C₂²⋊C₄	—	2	16	no	—
99	C₃²×C₂²⋊C₄	—	3	4	no	—
100	C₃²×C₂²⋊C₄	—	3	4	no	—
101	C₃²×C₂²⋊C₄	—	3	4	no	—
102	C₃²×C₂²⋊C₄	C₂×D₃	1	4	yes	complemented
103	C₃²×C₂²⋊C₄	C₂²×C₃	1	16	yes	complemented
104	C₃²×C₄²	—	2	4	no	—
105	C₃²×C₄²	—	3	2	no	—
106	C₃²×C₄²	—	3	1	no	—
107	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic, complemented
108	C₃²×C₄²	C₂²×C₃	1	4	yes	complemented
109	C₃×#217	C₂²×C₃	1	16	yes	complemented
110	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	16	yes	complemented
111	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	16	yes	complemented
112	C₃×C₄×Dic₃	C₂²×C₃	1	8	yes	complemented
113	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	complemented
114	C₂²×C₃³	—	2	2	no	—
115	C₂²×C₃³	—	2	4	no	—
116	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
117	C₂×C₃²×D₃	—	2	2	no	—
118	C₂×C₃²×D₃	—	2	4	no	—
119	C₂×C₃²×D₃	—	4	8	no	—
120	C₂×C₃²×D₃	C₂×D₄	1	2	yes	—
121	C₂×C₃²×D₃	#41	1	4	yes	—
122	C₃³×C₄	—	2	2	no	—
123	C₃³×C₄	—	2	2	no	—
124	C₃³×C₄	C₂×D₄	1	2	yes	—
125	C₃²×Dic₃	—	2	2	no	—
126	C₃²×Dic₃	—	2	2	no	—
127	C₃²×Dic₃	C₂×D₄	1	2	yes	—
128	C₂²×C₃×Q₈	—	3	4	no	—
129	C₂²×C₃×D₄	—	3	4	no	—
130	C₂×D₃×Q₈	C₂×C₃²	1	1	yes	characteristic, complemented
131	C₂×D₃×D₄	C₂×C₃²	1	1	yes	characteristic
132	C₃×#124	—	2	4	no	—
133	C₃×#124	—	3	4	no	—
134	C₃×#124	—	3	4	no	—
135	C₃×#124	—	3	16	no	—
136	C₃×#124	—	3	4	no	—
137	C₃×#124	C₃×D₃	1	4	yes	direct product factor
138	C₃×#124	C₂×C₃²	1	1	yes	characteristic, complemented
139	C₂×C₃×C₂²⋊C₄	—	3	16	no	—
140	C₂×C₃×C₄²	—	3	4	no	—
141	#947	C₂×C₃²	1	1	yes	characteristic, complemented
142	#936	C₂×C₃²	1	1	yes	characteristic, complemented
143	#885	C₂×C₃²	1	4	yes	complemented
144	D₃×C₂²⋊C₄	C₂×C₃²	1	4	yes	complemented
145	#875	C₂×C₃²	1	1	yes	characteristic, complemented
146	C₄²×D₃	C₂×C₃²	1	1	yes	characteristic, complemented
147	C₂³×C₃²	—	2	8	no	—
148	C₂³×C₃²	—	3	1	no	—
149	C₂³×C₃²	—	3	2	no	—
150	C₂³×C₃²	—	6	8	no	—
151	C₂³×C₃²	—	6	4	no	—
152	C₂³×C₃²	C₂²×D₃	1	2	yes	—
153	C₂³×C₃²	C₂³×C₃	1	8	yes	—
154	C₂²×C₃×D₃	—	2	16	no	—
155	C₂²×C₃×D₃	—	2	32	no	—
156	C₂²×C₃×D₃	C₂³×C₃	1	8	yes	—
157	C₂²×C₃×D₃	C₂³×C₃	1	4	yes	—
158	C₃²×Q₈	—	2	2	no	—
159	C₃²×Q₈	—	2	8	no	—
160	C₃²×Q₈	—	4	8	no	—
161	C₃²×Q₈	—	6	4	no	—
162	C₃²×Q₈	—	6	2	no	—
163	C₃²×D₄	—	2	2	no	—
164	C₃²×D₄	—	2	8	no	—
165	C₃²×D₄	—	4	8	no	—
166	C₃²×D₄	—	6	4	no	—
167	C₃²×D₄	—	6	2	no	—
168	C₂×C₃²×C₄	—	2	4	no	—
169	C₂×C₃²×C₄	—	2	8	no	—
170	C₂×C₃²×C₄	—	2	8	no	—
171	C₂×C₃²×C₄	—	3	1	no	—
172	C₂×C₃²×C₄	—	3	4	no	—
173	C₂×C₃²×C₄	—	3	2	no	—
174	C₂×C₃²×C₄	—	3	2	no	—
175	C₂×C₃²×C₄	—	6	4	no	—
176	C₂×C₃²×C₄	—	6	4	no	—
177	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
178	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
179	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
180	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
181	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
182	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
183	C₃×#67	—	2	16	no	—
184	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
185	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
186	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
187	C₃×D₁₂	—	2	8	no	—
188	C₃×C₄×D₃	—	2	16	no	—
189	C₃×C₄×D₃	—	2	16	no	—
190	C₃×C₄×D₃	C₃×D₄	1	16	yes	—
191	C₃×Dic₆	—	2	8	no	—
192	C₃×Dic₆	—	2	16	no	—
193	C₂×#124	—	3	1	no	Sylow
194	C₂×C₃³	—	4	2	no	—
195	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₃³	C₂×#41	1	2	yes	—
197	C₃²×D₃	—	4	2	no	—
198	C₃²×D₃	#124	1	4	yes	direct product factor
199	C₂⁴×C₃	—	3	8	no	—
200	C₂³×D₃	C₂²×C₃²	1	2	yes	—
201	C₂×C₃×Q₈	—	2	4	no	—
202	C₂×C₃×Q₈	—	3	8	no	—
203	C₂×C₃×Q₈	—	3	4	no	—
204	C₂×C₃×Q₈	—	6	16	no	—
205	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	complemented
206	C₂×C₃×Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
207	C₂×C₃×D₄	—	2	4	no	—
208	C₂×C₃×D₄	—	3	8	no	—
209	C₂×C₃×D₄	—	3	4	no	—
210	C₂×C₃×D₄	—	6	16	no	—
211	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
212	C₂×C₃×D₄	C₂²×C₃²	1	1	yes	characteristic
213	C₂²×C₃×C₄	—	3	4	no	—
214	C₂²×C₃×C₄	—	3	8	no	—
215	C₂²×C₃×C₄	—	3	8	no	—
216	C₂×#67	C₂²×C₃²	1	2	yes	—
217	D₃×Q₈	—	2	4	no	—
218	D₃×D₄	—	2	4	no	—
219	C₂×D₁₂	C₂²×C₃²	1	1	yes	characteristic
220	C₂×C₄×D₃	C₂²×C₃²	1	2	yes	—
221	C₂×C₄×D₃	C₂²×C₃²	1	2	yes	—
222	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
223	C₂×Dic₆	C₂²×C₃²	1	1	yes	characteristic, complemented
224	C₂×Dic₆	C₂²×C₃²	1	2	yes	complemented
225	C₃×C₂²⋊C₄	—	2	16	no	—
226	C₃×C₂²⋊C₄	—	3	16	no	—
227	C₃×C₂²⋊C₄	—	3	16	no	—
228	C₃×C₂²⋊C₄	—	3	16	no	—
229	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	16	yes	complemented
230	C₃×C₂²⋊C₄	C₂²×C₃²	1	4	yes	complemented
231	C₃×C₄²	—	2	4	no	—
232	C₃×C₄²	—	3	8	no	—
233	C₃×C₄²	—	3	4	no	—
234	C₃×C₄²	C₂×C₃×D₃	1	4	yes	complemented
235	C₃×C₄²	C₂²×C₃²	1	1	yes	characteristic, complemented
236	#217	C₂²×C₃²	1	4	yes	complemented
237	(C₂×D₃)⋊C₄	C₂²×C₃²	1	4	yes	complemented
238	(C₂×D₃)⋊C₄	C₂²×C₃²	1	4	yes	complemented
239	C₄×Dic₃	C₂²×C₃²	1	2	yes	complemented
240	C₄×Dic₃	C₂²×C₃²	1	1	yes	characteristic, complemented
241	C₂²×C₃²	—	2	2	no	—
242	C₂²×C₃²	—	2	4	no	—
243	C₂²×C₃²	—	2	4	no	—
244	C₂²×C₃²	—	2	8	no	—
245	C₂²×C₃²	—	2	16	no	—
246	C₂²×C₃²	—	3	2	no	—
247	C₂²×C₃²	—	3	4	no	—
248	C₂²×C₃²	—	4	8	no	—
249	C₂²×C₃²	—	4	16	no	—
250	C₂²×C₃²	—	6	2	no	—
251	C₂²×C₃²	—	6	4	no	—
252	C₂²×C₃²	—	12	8	no	—
253	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
254	C₂²×C₃²	C₂⁴×C₃	1	4	yes	—
255	C₂×C₃×D₃	—	2	8	no	—
256	C₂×C₃×D₃	—	2	16	no	—
257	C₂×C₃×D₃	—	4	32	no	—
258	C₂×C₃×D₃	C₂×C₃×D₄	1	8	yes	—
259	C₂×C₃×D₃	C₃×#41	1	16	yes	—
260	C₃²×C₄	—	2	2	no	—
261	C₃²×C₄	—	2	2	no	—
262	C₃²×C₄	—	2	8	no	—
263	C₃²×C₄	—	2	8	no	—
264	C₃²×C₄	—	2	8	no	—
265	C₃²×C₄	—	3	2	no	—
266	C₃²×C₄	—	4	8	no	—
267	C₃²×C₄	—	4	8	no	—
268	C₃²×C₄	—	6	2	no	—
269	C₃²×C₄	—	6	2	no	—
270	C₃²×C₄	D₃×D₄	1	2	yes	—
271	C₃²×C₄	C₂×C₃×D₄	1	8	yes	—
272	C₃×Dic₃	—	2	8	no	—
273	C₃×Dic₃	—	2	8	no	—
274	C₃×Dic₃	C₂×C₃×D₄	1	8	yes	—
275	C₂²×Q₈	—	3	1	no	—
276	C₂²×D₄	—	3	1	no	—
277	#124	—	3	1	no	—
278	#124	—	3	1	no	—
279	#124	—	3	4	no	—
280	#124	—	3	1	no	—
281	#124	C₃²×D₃	1	1	yes	characteristic, direct product factor
282	C₂×C₂²⋊C₄	—	3	4	no	—
283	C₂×C₄²	—	3	1	no	—
284	C₃³	C₂×#124	1	1	yes	characteristic, complemented, Sylow
285	C₂³×C₃	—	2	8	no	—
286	C₂³×C₃	—	3	4	no	—
287	C₂³×C₃	—	3	8	no	—
288	C₂³×C₃	—	6	16	no	—
289	C₂³×C₃	—	6	32	no	—
290	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
291	C₂³×C₃	C₂³×C₃²	1	2	yes	—
292	C₂²×D₃	—	2	4	no	—
293	C₂²×D₃	—	2	8	no	—
294	C₂²×D₃	C₂³×C₃²	1	2	yes	—
295	C₂²×D₃	C₂³×C₃²	1	1	yes	characteristic
296	C₃×Q₈	—	2	8	no	—
297	C₃×Q₈	—	2	2	no	—
298	C₃×Q₈	—	4	8	no	—
299	C₃×Q₈	—	6	16	no	—
300	C₃×Q₈	—	6	8	no	—
301	C₃×D₄	—	2	8	no	—
302	C₃×D₄	—	2	2	no	—
303	C₃×D₄	—	4	8	no	—
304	C₃×D₄	—	6	16	no	—
305	C₃×D₄	—	6	8	no	—
306	C₂×C₃×C₄	—	2	4	no	—
307	C₂×C₃×C₄	—	2	8	no	—
308	C₂×C₃×C₄	—	2	8	no	—
309	C₂×C₃×C₄	—	3	4	no	—
310	C₂×C₃×C₄	—	3	16	no	—
311	C₂×C₃×C₄	—	3	8	no	—
312	C₂×C₃×C₄	—	3	8	no	—
313	C₂×C₃×C₄	—	6	16	no	—
314	C₂×C₃×C₄	—	6	16	no	—
315	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
316	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
317	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
318	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
319	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
320	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
321	#67	—	2	4	no	—
322	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
323	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
324	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
325	D₁₂	—	2	2	no	—
326	C₄×D₃	—	2	4	no	—
327	C₄×D₃	—	2	4	no	—
328	C₄×D₃	C₃²×D₄	1	4	yes	—
329	Dic₆	—	2	2	no	—
330	Dic₆	—	2	4	no	—
331	C₂×C₃²	—	2	4	no	—
332	C₂×C₃²	—	2	8	no	—
333	C₂×C₃²	—	3	4	no	—
334	C₂×C₃²	—	4	2	no	—
335	C₂×C₃²	—	4	8	no	—
336	C₂×C₃²	—	8	8	no	—
337	C₂×C₃²	—	12	2	no	—
338	C₂×C₃²	C₂×D₃×D₄	1	1	yes	characteristic
339	C₂×C₃²	D₃×#41	1	2	yes	—
340	C₂×C₃²	C₂²×C₃×D₄	1	4	yes	—
341	C₂×C₃²	C₂×C₃×#41	1	8	yes	—
342	C₃×D₃	—	4	8	no	—
343	C₃×D₃	C₃×#124	1	16	yes	direct product factor
344	C₂⁴	—	3	2	no	—
345	C₂×Q₈	—	3	2	no	—
346	C₂×Q₈	—	3	1	no	—
347	C₂×Q₈	—	6	4	no	—
348	C₂×Q₈	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
349	C₂×D₄	—	3	2	no	—
350	C₂×D₄	—	3	1	no	—
351	C₂×D₄	—	6	4	no	—
352	C₂×D₄	C₂×C₃²×D₃	1	1	yes	characteristic
353	C₂²×C₄	—	3	1	no	—
354	C₂²×C₄	—	3	2	no	—
355	C₂²×C₄	—	3	2	no	—
356	C₂²⋊C₄	—	3	4	no	—
357	C₂²⋊C₄	—	3	4	no	—
358	C₂²⋊C₄	—	3	4	no	—
359	C₂²⋊C₄	C₂×C₃²×D₃	1	4	yes	complemented
360	C₄²	—	3	2	no	—
361	C₄²	—	3	1	no	—
362	C₄²	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
363	C₂²×C₃	—	2	8	no	—
364	C₂²×C₃	—	2	16	no	—
365	C₂²×C₃	—	2	2	no	—
366	C₂²×C₃	—	2	4	no	—
367	C₂²×C₃	—	2	4	no	—
368	C₂²×C₃	—	3	8	no	—
369	C₂²×C₃	—	3	16	no	—
370	C₂²×C₃	—	4	8	no	—
371	C₂²×C₃	—	4	16	no	—
372	C₂²×C₃	—	6	8	no	—
373	C₂²×C₃	—	6	16	no	—
374	C₂²×C₃	—	12	32	no	—
375	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
376	C₂²×C₃	C₂⁴×C₃²	1	1	yes	characteristic
377	C₂×D₃	—	2	2	no	—
378	C₂×D₃	—	2	4	no	—
379	C₂×D₃	—	4	8	no	—
380	C₂×D₃	C₂×C₃²×D₄	1	2	yes	—
381	C₂×D₃	C₃²×#41	1	4	yes	—
382	C₃×C₄	—	2	8	no	—
383	C₃×C₄	—	2	8	no	—
384	C₃×C₄	—	2	2	no	—
385	C₃×C₄	—	2	2	no	—
386	C₃×C₄	—	2	8	no	—
387	C₃×C₄	—	3	8	no	—
388	C₃×C₄	—	4	8	no	—
389	C₃×C₄	—	4	8	no	—
390	C₃×C₄	—	6	8	no	—
391	C₃×C₄	—	6	8	no	—
392	C₃×C₄	C₃×D₃×D₄	1	8	yes	—
393	C₃×C₄	C₂×C₃²×D₄	1	2	yes	—
394	Dic₃	—	2	2	no	—
395	Dic₃	—	2	2	no	—
396	Dic₃	C₂×C₃²×D₄	1	2	yes	—
397	C₃²	—	2	4	no	—
398	C₃²	D₃×#124	1	1	yes	characteristic, direct product factor
399	C₃²	C₂×C₃×#124	1	4	yes	complemented
400	C₂³	—	3	1	no	—
401	C₂³	—	3	2	no	—
402	C₂³	—	6	4	no	—
403	C₂³	—	6	8	no	—
404	C₂³	C₂²×C₃²×D₃	1	2	yes	—
405	Q₈	—	2	2	no	—
406	Q₈	—	6	4	no	—
407	Q₈	—	6	2	no	—
408	D₄	—	2	2	no	—
409	D₄	—	6	4	no	—
410	D₄	—	6	2	no	—
411	C₂×C₄	—	3	1	no	—
412	C₂×C₄	—	3	4	no	—
413	C₂×C₄	—	3	2	no	—
414	C₂×C₄	—	3	2	no	—
415	C₂×C₄	—	6	4	no	—
416	C₂×C₄	—	6	4	no	—
417	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
418	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
419	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
420	C₂×C₃	—	2	4	no	—
421	C₂×C₃	—	2	8	no	—
422	C₂×C₃	—	3	16	no	—
423	C₂×C₃	—	4	8	no	—
424	C₂×C₃	—	4	2	no	—
425	C₂×C₃	—	8	8	no	—
426	C₂×C₃	—	12	8	no	—
427	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
428	C₂×C₃	C₃×D₃×#41	1	8	yes	—
429	C₂×C₃	C₂²×C₃²×D₄	1	1	yes	characteristic
430	C₂×C₃	C₂×C₃²×#41	1	2	yes	—
431	D₃	—	4	2	no	—
432	D₃	C₃²×#124	1	4	yes	direct product factor
433	C₂²	—	2	2	no	—
434	C₂²	—	2	4	no	—
435	C₂²	—	3	2	no	—
436	C₂²	—	3	4	no	—
437	C₂²	—	6	2	no	—
438	C₂²	—	6	4	no	—
439	C₂²	—	12	8	no	—
440	C₂²	C₂³×C₃²×D₃	1	1	yes	characteristic
441	C₄	—	2	2	no	—
442	C₄	—	2	2	no	—
443	C₄	—	3	2	no	—
444	C₄	—	6	2	no	—
445	C₄	—	6	2	no	—
446	C₄	C₃²×D₃×D₄	1	2	yes	—
447	C₃	—	2	4	no	—
448	C₃	C₃×D₃×#124	1	4	yes	direct product factor
449	C₃	C₂×C₃²×#124	1	1	yes	characteristic, complemented
450	C₂	—	3	4	no	—
451	C₂	—	4	2	no	—
452	C₂	—	12	2	no	—
453	C₂	C₂×C₃²×D₃×D₄	1	1	yes	characteristic
454	C₂	C₃²×D₃×#41	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃²	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₃²
Frattini	C₂²	C₂³×C₃²×D₃
Fitting	C₃³×#124	C₂
socle	C₂²×C₃³	C₂⁴
prime radical	C₂×C₃²×D₃×D₄	C₂
hypercenter	C₃²×#124	D₃
hypocenter	C₃	C₂×C₃²×#124
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃² ◁ C₃²×#124

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×D₃×Q₈	C₂	semidirect
3. C₃³×#124	C₂	semidirect
4. C₃²×#947	C₂	semidirect
5. C₃²×#936	C₂	semidirect
6. C₃²×#885	C₂	semidirect
7. C₃²×D₃×C₂²⋊C₄	C₂	semidirect
8. C₃²×#875	C₂	semidirect
9. C₃²×C₄²×D₃	C₂	semidirect
11. C₃×D₃×#124	C₃	direct (N × H)
13. C₂×C₃³×Q₈	C₂²	semidirect
22. C₂×C₃²×Dic₆	C₂²	semidirect
23. C₂×C₃²×Dic₆	C₂²	semidirect
24. C₃³×C₂²⋊C₄	C₂²	semidirect
25. C₃³×C₄²	C₂²	semidirect
26. C₃²×#217	C₂²	semidirect
27. C₃²×(C₂×D₃)⋊C₄	C₂²	semidirect
28. C₃²×(C₂×D₃)⋊C₄	C₂²	semidirect
29. C₃²×C₄×Dic₃	C₂²	semidirect
30. C₃²×C₄×Dic₃	C₂²	semidirect
33. C₂×C₃×D₃×Q₈	C₂×C₃	semidirect
40. C₃²×#124	D₃	direct (N × H)
41. C₃²×#124	C₂×C₃	semidirect
44. C₃×#947	C₂×C₃	semidirect
45. C₃×#936	C₂×C₃	semidirect
46. C₃×#885	C₂×C₃	semidirect
47. C₃×D₃×C₂²⋊C₄	C₂×C₃	semidirect
48. C₃×#875	C₂×C₃	semidirect
49. C₃×C₄²×D₃	C₂×C₃	semidirect
71. D₃×#124	C₃²	direct (N × H)
78. C₂×C₃²×Q₈	C₂×D₃	semidirect
79. C₂×C₃²×Q₈	C₂²×C₃	semidirect
96. C₂×C₃×Dic₆	C₂²×C₃	semidirect
97. C₂×C₃×Dic₆	C₂²×C₃	semidirect
102. C₃²×C₂²⋊C₄	C₂×D₃	semidirect
103. C₃²×C₂²⋊C₄	C₂²×C₃	semidirect
107. C₃²×C₄²	C₂×D₃	semidirect
108. C₃²×C₄²	C₂²×C₃	semidirect
109. C₃×#217	C₂²×C₃	semidirect
110. C₃×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
111. C₃×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
112. C₃×C₄×Dic₃	C₂²×C₃	semidirect
113. C₃×C₄×Dic₃	C₂²×C₃	semidirect
130. C₂×D₃×Q₈	C₂×C₃²	semidirect
137. C₃×#124	C₃×D₃	direct (N × H)
138. C₃×#124	C₂×C₃²	semidirect
141. #947	C₂×C₃²	semidirect
142. #936	C₂×C₃²	semidirect
143. #885	C₂×C₃²	semidirect
144. D₃×C₂²⋊C₄	C₂×C₃²	semidirect
145. #875	C₂×C₃²	semidirect
146. C₄²×D₃	C₂×C₃²	semidirect
198. C₃²×D₃	#124	direct (N × H)
205. C₂×C₃×Q₈	C₂×C₃×D₃	semidirect
206. C₂×C₃×Q₈	C₂²×C₃²	semidirect
223. C₂×Dic₆	C₂²×C₃²	semidirect
224. C₂×Dic₆	C₂²×C₃²	semidirect
229. C₃×C₂²⋊C₄	C₂×C₃×D₃	semidirect
230. C₃×C₂²⋊C₄	C₂²×C₃²	semidirect
234. C₃×C₄²	C₂×C₃×D₃	semidirect
235. C₃×C₄²	C₂²×C₃²	semidirect
236. #217	C₂²×C₃²	semidirect
237. (C₂×D₃)⋊C₄	C₂²×C₃²	semidirect
238. (C₂×D₃)⋊C₄	C₂²×C₃²	semidirect
239. C₄×Dic₃	C₂²×C₃²	semidirect
240. C₄×Dic₃	C₂²×C₃²	semidirect
281. #124	C₃²×D₃	direct (N × H)
284. C₃³	C₂×#124	semidirect
343. C₃×D₃	C₃×#124	direct (N × H)
348. C₂×Q₈	C₂×C₃²×D₃	semidirect
359. C₂²⋊C₄	C₂×C₃²×D₃	semidirect
362. C₄²	C₂×C₃²×D₃	semidirect
398. C₃²	D₃×#124	direct (N × H)
399. C₃²	C₂×C₃×#124	semidirect
432. D₃	C₃²×#124	direct (N × H)
448. C₃	C₃×D₃×#124	direct (N × H)
449. C₃	C₂×C₃²×#124	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×D₃×Q₈	2
C₂×C₃²×D₃×D₄	2
C₃³×#124	2
C₃²×#947	2
C₃²×#936	2
C₃²×#885	2
C₃²×D₃×C₂²⋊C₄	2
C₃²×#875	2
C₃²×C₄²×D₃	2
C₂×C₃²×#124	3
C₃×D₃×#124	3

Subgroups — C32×D3×#124 #13179051

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×D₃×#124 #13179051