Subgroups — C₃×#78517 #11858818

Order 1152.

1039 conjugacy classes of subgroups.

The subgroup lattice has 407 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄²×D₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5126	C₂	1	2	yes	maximal
4	C₃×#5118	C₂	1	2	yes	maximal, complemented
5	C₃×C₄×#208	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4705	C₂	1	4	yes	maximal, complemented
7	C₃×#4685	C₂	1	4	yes	maximal, complemented
8	C₃×#2920	—	3	1	no	maximal
9	#78517	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂²×C₃×C₄×D₃	C₄	1	2	yes	—
11	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
12	C₂×C₃²×M₁₆	C₂²	1	2	yes	—
13	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄×Dic₃	C₄	1	2	yes	—
15	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
16	C₂×C₃×#208	C₂²	1	2	yes	—
17	C₃×C₄²×D₃	C₄	1	2	yes	—
18	C₃×C₄²×D₃	C₄	1	2	yes	—
19	C₃×C₄²×D₃	C₂²	1	2	yes	—
20	C₃×C₄²×D₃	C₂²	1	2	yes	—
21	C₃²×#97	C₂²	1	2	yes	complemented
22	C₃²×C₄×C₈	C₂²	1	2	yes	complemented
23	C₃×(C₂×D₃)⋊C₈	C₂²	1	8	yes	—
24	C₃×Dic₃⋊C₈	C₂²	1	8	yes	complemented
25	C₃×#803	C₂²	1	2	yes	complemented
26	C₃×C₄×C₃⋊C₈	C₂²	1	2	yes	complemented
27	C₂²×C₃×C₄²	—	3	1	no	—
28	C₂×C₄²×D₃	C₂×C₃	1	1	yes	characteristic
29	C₃×#432	—	3	4	no	—
30	C₃×#431	—	3	4	no	—
31	C₃×#423	—	3	2	no	—
32	C₃×#407	—	3	2	no	—
33	C₃×C₄×M₁₆	—	2	1	no	—
34	C₃×C₄×M₁₆	—	3	1	no	—
35	C₃×C₄×M₁₆	D₃	1	1	yes	characteristic, complemented
36	C₃×C₄×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
37	#5126	C₂×C₃	1	2	yes	—
38	#5118	C₂×C₃	1	2	yes	complemented
39	C₄×#208	C₂×C₃	1	1	yes	characteristic, complemented
40	#4705	C₂×C₃	1	4	yes	complemented
41	#4685	C₂×C₃	1	4	yes	complemented
42	C₂³×C₃×D₃	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
44	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
45	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₃×Dic₃	C₂×C₄	1	2	yes	—
47	C₂×C₃×C₄×D₃	—	2	4	no	—
48	C₂×C₃×C₄×D₃	—	2	8	no	—
49	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
50	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
51	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
52	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
53	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
54	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
55	C₃²×M₁₆	—	2	4	no	—
56	C₂×C₃²×C₈	C₂³	1	4	yes	—
57	C₃²×C₄²	C₂×C₄	1	2	yes	—
58	C₃²×C₄²	C₂³	1	1	yes	characteristic
59	C₃²×C₄²	C₂³	1	1	yes	characteristic
60	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
61	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
62	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
63	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
64	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
65	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
66	C₃×C₄×Dic₃	C₂³	1	2	yes	—
67	C₃×#208	—	2	4	no	—
68	C₂×C₃×C₃⋊C₈	C₂³	1	4	yes	—
69	#2920	—	3	1	no	Sylow
70	C₂³×C₃×C₄	—	3	2	no	—
71	C₂³×C₃×C₄	—	3	1	no	—
72	C₂²×C₄×D₃	C₃×C₄	1	2	yes	—
73	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₃×M₁₆	—	2	2	no	—
75	C₂×C₃×M₁₆	—	3	2	no	—
76	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
77	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
78	C₂×C₃×C₄²	—	2	1	no	—
79	C₂×C₃×C₄²	—	3	2	no	—
80	C₂×C₃×C₄²	—	3	1	no	—
81	C₂×C₃×C₄²	—	3	2	no	—
82	C₂×C₃×C₄²	—	3	2	no	—
83	C₂×C₃×C₄²	—	3	2	no	—
84	C₂×C₃×C₄²	—	3	2	no	—
85	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
86	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₄×Dic₃	C₃×C₄	1	2	yes	—
88	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
89	C₂×#208	C₂²×C₃	1	2	yes	—
90	C₄²×D₃	C₃×C₄	1	2	yes	—
91	C₄²×D₃	C₃×C₄	1	2	yes	—
92	C₄²×D₃	C₂²×C₃	1	2	yes	—
93	C₄²×D₃	C₂²×C₃	1	2	yes	—
94	C₃×C₄⋊C₈	—	3	8	no	—
95	C₃×C₂²⋊C₈	—	3	8	no	—
96	C₃×#97	—	2	2	no	—
97	C₃×#97	—	3	2	no	—
98	C₃×#97	C₂×D₃	1	2	yes	complemented
99	C₃×#97	C₂²×C₃	1	2	yes	complemented
100	C₃×C₄×C₈	—	2	2	no	—
101	C₃×C₄×C₈	—	3	2	no	—
102	C₃×C₄×C₈	C₂×D₃	1	2	yes	complemented
103	C₃×C₄×C₈	C₂²×C₃	1	2	yes	complemented
104	(C₂×D₃)⋊C₈	C₂²×C₃	1	8	yes	—
105	Dic₃⋊C₈	C₂²×C₃	1	8	yes	complemented
106	#803	C₂²×C₃	1	2	yes	complemented
107	C₄×C₃⋊C₈	C₂²×C₃	1	2	yes	complemented
108	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₃×D₃	—	2	2	no	—
110	C₂²×C₃×D₃	—	2	4	no	—
111	C₂²×C₃×D₃	C₂²×C₄	1	2	yes	—
112	C₂×C₃²×C₄	—	2	4	no	—
113	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
114	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
116	C₂×C₃²×C₄	#41	1	4	yes	—
117	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
118	C₂×C₃×Dic₃	—	2	2	no	—
119	C₂×C₃×Dic₃	—	2	4	no	—
120	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
121	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
122	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
123	C₃×C₄×D₃	—	2	4	no	—
124	C₃×C₄×D₃	—	2	4	no	—
125	C₃×C₄×D₃	—	2	4	no	—
126	C₃×C₄×D₃	—	2	4	no	—
127	C₃×C₄×D₃	—	2	4	no	—
128	C₃×C₄×D₃	M₁₆	1	8	yes	complemented
129	C₃²×C₈	—	2	4	no	—
130	C₃×C₃⋊C₈	—	2	4	no	—
131	C₂²×C₄²	—	3	1	no	—
132	#432	—	3	4	no	—
133	#431	—	3	4	no	—
134	#423	—	3	2	no	—
135	#407	—	3	2	no	—
136	C₄×M₁₆	—	3	1	no	—
137	C₄×M₁₆	C₃×D₃	1	1	yes	characteristic, complemented
138	C₂⁴×C₃	—	3	1	no	—
139	C₂³×D₃	C₂×C₃×C₄	1	1	yes	characteristic
140	C₂²×C₃×C₄	—	2	2	no	—
141	C₂²×C₃×C₄	—	2	1	no	—
142	C₂²×C₃×C₄	—	3	2	no	—
143	C₂²×C₃×C₄	—	3	2	no	—
144	C₂²×C₃×C₄	—	3	1	no	—
145	C₂²×C₃×C₄	—	3	2	no	—
146	C₂²×C₃×C₄	—	3	2	no	—
147	C₂²×C₃×C₄	—	3	2	no	—
148	C₂²×C₃×C₄	—	3	2	no	—
149	C₂²×C₃×C₄	—	3	2	no	—
150	C₂²×C₃×C₄	—	6	8	no	—
151	C₂²×C₃×C₄	—	6	4	no	—
152	C₂²×C₃×C₄	C₄×D₃	1	2	yes	—
153	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
154	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
155	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
156	C₂²×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
157	C₂²×Dic₃	C₂×C₃×C₄	1	2	yes	—
158	C₂×C₄×D₃	—	2	4	no	—
159	C₂×C₄×D₃	—	2	8	no	—
160	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
161	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
162	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
163	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
164	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
165	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
166	C₃×M₁₆	—	2	8	no	—
167	C₃×M₁₆	—	2	4	no	—
168	C₃×M₁₆	—	2	4	no	—
169	C₃×M₁₆	—	6	4	no	—
170	C₂×C₃×C₈	—	2	4	no	—
171	C₂×C₃×C₈	—	3	4	no	—
172	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
173	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
174	C₃×C₄²	—	2	2	no	—
175	C₃×C₄²	—	2	1	no	—
176	C₃×C₄²	—	2	1	no	—
177	C₃×C₄²	—	3	1	no	—
178	C₃×C₄²	—	3	2	no	—
179	C₃×C₄²	—	3	2	no	—
180	C₃×C₄²	—	3	2	no	—
181	C₃×C₄²	—	3	1	no	—
182	C₃×C₄²	—	3	2	no	—
183	C₃×C₄²	—	3	2	no	—
184	C₃×C₄²	C₄×D₃	1	2	yes	—
185	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
186	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
187	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
188	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
189	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
190	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
191	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
192	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
193	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
194	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
195	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
196	C₄×Dic₃	C₂³×C₃	1	2	yes	—
197	#208	—	2	4	no	—
198	C₂×C₃⋊C₈	C₂³×C₃	1	4	yes	—
199	C₂²×C₃²	—	2	2	no	—
200	C₂²×C₃²	#117	1	2	yes	—
201	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
202	C₂×C₃×D₃	—	2	8	no	—
203	C₂×C₃×D₃	—	2	2	no	—
204	C₂×C₃×D₃	—	2	2	no	—
205	C₂×C₃×D₃	C₂×M₁₆	1	4	yes	—
206	C₃²×C₄	—	2	2	no	—
207	C₃²×C₄	#117	1	2	yes	—
208	C₃²×C₄	C₂×M₁₆	1	4	yes	—
209	C₃²×C₄	C₂×#41	1	2	yes	—
210	C₃×Dic₃	—	2	2	no	—
211	C₃×Dic₃	—	2	2	no	—
212	C₃×Dic₃	C₂×M₁₆	1	4	yes	—
213	C₂³×C₄	—	3	2	no	—
214	C₂³×C₄	—	3	1	no	—
215	C₂×M₁₆	—	3	2	no	—
216	C₂×M₁₆	C₂×C₃×D₃	1	2	yes	—
217	C₂×C₄²	—	3	2	no	—
218	C₂×C₄²	—	3	1	no	—
219	C₂×C₄²	—	3	2	no	—
220	C₂×C₄²	—	3	2	no	—
221	C₂×C₄²	—	3	2	no	—
222	C₂×C₄²	—	3	2	no	—
223	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
224	C₄⋊C₈	—	3	8	no	—
225	C₂²⋊C₈	—	3	8	no	—
226	#97	—	3	2	no	—
227	#97	C₂×C₃×D₃	1	2	yes	complemented
228	C₄×C₈	—	3	2	no	—
229	C₄×C₈	C₂×C₃×D₃	1	2	yes	complemented
230	C₂³×C₃	—	2	1	no	—
231	C₂³×C₃	—	3	2	no	—
232	C₂³×C₃	—	6	4	no	—
233	C₂³×C₃	—	6	2	no	—
234	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
235	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
236	C₂²×D₃	—	2	2	no	—
237	C₂²×D₃	—	2	4	no	—
238	C₂²×D₃	C₂²×C₃×C₄	1	2	yes	—
239	C₂×C₃×C₄	—	2	4	no	—
240	C₂×C₃×C₄	—	2	4	no	—
241	C₂×C₃×C₄	—	2	1	no	—
242	C₂×C₃×C₄	—	2	2	no	—
243	C₂×C₃×C₄	—	2	1	no	—
244	C₂×C₃×C₄	—	2	2	no	—
245	C₂×C₃×C₄	—	2	4	no	—
246	C₂×C₃×C₄	—	3	2	no	—
247	C₂×C₃×C₄	—	3	8	no	—
248	C₂×C₃×C₄	—	3	2	no	—
249	C₂×C₃×C₄	—	3	2	no	—
250	C₂×C₃×C₄	—	4	4	no	—
251	C₂×C₃×C₄	—	6	4	no	—
252	C₂×C₃×C₄	—	6	4	no	—
253	C₂×C₃×C₄	—	6	4	no	—
254	C₂×C₃×C₄	—	6	2	no	—
255	C₂×C₃×C₄	—	6	4	no	—
256	C₂×C₃×C₄	—	6	4	no	—
257	C₂×C₃×C₄	—	6	4	no	—
258	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
259	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
261	C₂×C₃×C₄	#235	1	4	yes	—
262	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
263	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
265	C₂×C₃×C₄	C₃×#41	1	4	yes	—
266	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
268	C₂×Dic₃	—	2	2	no	—
269	C₂×Dic₃	—	2	4	no	—
270	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
271	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
272	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
273	C₄×D₃	—	2	4	no	—
274	C₄×D₃	—	2	4	no	—
275	C₄×D₃	—	2	4	no	—
276	C₄×D₃	—	2	4	no	—
277	C₄×D₃	—	2	4	no	—
278	C₄×D₃	C₃×M₁₆	1	8	yes	complemented
279	C₃×C₈	—	2	8	no	—
280	C₃×C₈	—	2	4	no	—
281	C₃×C₈	—	2	4	no	—
282	C₃×C₈	—	6	4	no	—
283	C₃⋊C₈	—	2	4	no	—
284	C₂×C₃²	—	2	2	no	—
285	C₂×C₃²	C₂×#117	1	1	yes	characteristic
286	C₂×C₃²	C₂²×M₁₆	1	2	yes	—
287	C₃×D₃	—	2	4	no	—
288	C₂⁴	—	3	1	no	—
289	C₂²×C₄	—	3	2	no	—
290	C₂²×C₄	—	3	2	no	—
291	C₂²×C₄	—	3	1	no	—
292	C₂²×C₄	—	3	2	no	—
293	C₂²×C₄	—	3	2	no	—
294	C₂²×C₄	—	3	2	no	—
295	C₂²×C₄	—	3	2	no	—
296	C₂²×C₄	—	3	2	no	—
297	C₂²×C₄	—	6	8	no	—
298	C₂²×C₄	—	6	4	no	—
299	C₂²×C₄	C₃×C₄×D₃	1	2	yes	—
300	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
301	M₁₆	—	2	4	no	—
302	M₁₆	—	6	4	no	—
303	C₂×C₈	—	3	4	no	—
304	C₂×C₈	C₂²×C₃×D₃	1	4	yes	—
305	C₄²	—	3	2	no	—
306	C₄²	—	3	1	no	—
307	C₄²	—	3	2	no	—
308	C₄²	—	3	2	no	—
309	C₄²	—	3	2	no	—
310	C₄²	—	3	2	no	—
311	C₄²	—	3	1	no	—
312	C₄²	C₃×C₄×D₃	1	2	yes	—
313	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
314	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
315	C₂²×C₃	—	2	2	no	—
316	C₂²×C₃	—	2	2	no	—
317	C₂²×C₃	—	2	1	no	—
318	C₂²×C₃	—	2	2	no	—
319	C₂²×C₃	—	3	4	no	—
320	C₂²×C₃	—	4	2	no	—
321	C₂²×C₃	—	6	8	no	—
322	C₂²×C₃	—	6	2	no	—
323	C₂²×C₃	—	6	2	no	—
324	C₂²×C₃	#872	1	2	yes	—
325	C₂²×C₃	C₃×#117	1	2	yes	—
326	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
327	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
328	C₂×D₃	—	2	8	no	—
329	C₂×D₃	—	2	2	no	—
330	C₂×D₃	—	2	2	no	—
331	C₂×D₃	C₂×C₃×M₁₆	1	4	yes	—
332	C₃×C₄	—	2	2	no	—
333	C₃×C₄	—	2	2	no	—
334	C₃×C₄	—	2	4	no	—
335	C₃×C₄	—	2	2	no	—
336	C₃×C₄	—	2	2	no	—
337	C₃×C₄	—	3	4	no	—
338	C₃×C₄	—	4	2	no	—
339	C₃×C₄	—	6	2	no	—
340	C₃×C₄	—	6	2	no	—
341	C₃×C₄	#872	1	2	yes	—
342	C₃×C₄	D₃×M₁₆	1	4	yes	—
343	C₃×C₄	C₃×#117	1	2	yes	—
344	C₃×C₄	C₂×C₃×M₁₆	1	4	yes	—
345	C₃×C₄	C₂×#235	1	2	yes	—
346	C₃×C₄	C₂×C₃×#41	1	2	yes	—
347	Dic₃	—	2	2	no	—
348	Dic₃	—	2	2	no	—
349	Dic₃	C₂×C₃×M₁₆	1	4	yes	—
350	C₃²	#2920	1	1	yes	characteristic, complemented, Sylow
351	C₂³	—	3	2	no	—
352	C₂³	—	6	4	no	—
353	C₂³	—	6	2	no	—
354	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	3	2	no	—
357	C₂×C₄	—	3	8	no	—
358	C₂×C₄	—	3	2	no	—
359	C₂×C₄	—	3	2	no	—
360	C₂×C₄	—	6	4	no	—
361	C₂×C₄	—	6	4	no	—
362	C₂×C₄	—	6	4	no	—
363	C₂×C₄	—	6	2	no	—
364	C₂×C₄	—	6	4	no	—
365	C₂×C₄	—	6	4	no	—
366	C₂×C₄	—	6	4	no	—
367	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
368	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
369	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
370	C₂×C₄	C₃×#235	1	4	yes	—
371	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
372	C₈	—	2	4	no	—
373	C₈	—	6	4	no	—
374	C₂×C₃	—	2	2	no	—
375	C₂×C₃	—	2	2	no	—
376	C₂×C₃	—	2	2	no	—
377	C₂×C₃	—	2	1	no	—
378	C₂×C₃	—	4	2	no	—
379	C₂×C₃	—	6	4	no	—
380	C₂×C₃	C₂×#872	1	1	yes	characteristic
381	C₂×C₃	C₂×D₃×M₁₆	1	2	yes	—
382	C₂×C₃	C₂×C₃×#117	1	1	yes	characteristic
383	C₂×C₃	C₂²×C₃×M₁₆	1	2	yes	—
384	D₃	—	2	4	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	3	4	no	—
387	C₂²	—	6	8	no	—
388	C₂²	—	6	2	no	—
389	C₂²	—	6	2	no	—
390	C₂²	C₃×#872	1	2	yes	—
391	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
392	C₄	—	2	2	no	—
393	C₄	—	3	4	no	—
394	C₄	—	6	2	no	—
395	C₄	—	6	2	no	—
396	C₄	C₃×#872	1	2	yes	—
397	C₄	C₃×D₃×M₁₆	1	4	yes	—
398	C₄	C₂×C₃×#235	1	2	yes	—
399	C₃	—	2	1	no	—
400	C₃	#78517	1	1	yes	characteristic, direct product factor
401	C₃	C₃×#2920	1	1	yes	characteristic, complemented
402	C₂	—	2	2	no	—
403	C₂	—	6	4	no	—
404	C₂	C₂×C₃×#872	1	1	yes	characteristic
405	C₂	C₂×C₃×D₃×M₁₆	1	2	yes	—

	subgroup	G/H
center	C₃×C₄²	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×C₄×M₁₆	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₂³×C₃×D₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×C₄×M₁₆	D₃
hypocenter	C₃	C₃×#2920
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₃×C₄² ◁ C₃×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₃²×C₄×M₁₆	C₂	semidirect
4. C₃×#5118	C₂	semidirect
5. C₃×C₄×#208	C₂	semidirect
6. C₃×#4705	C₂	semidirect
7. C₃×#4685	C₂	semidirect
9. #78517	C₃	direct (N × H)
21. C₃²×#97	C₂²	semidirect
22. C₃²×C₄×C₈	C₂²	semidirect
24. C₃×Dic₃⋊C₈	C₂²	semidirect
25. C₃×#803	C₂²	semidirect
26. C₃×C₄×C₃⋊C₈	C₂²	semidirect
35. C₃×C₄×M₁₆	D₃	semidirect
36. C₃×C₄×M₁₆	C₂×C₃	semidirect
38. #5118	C₂×C₃	semidirect
39. C₄×#208	C₂×C₃	semidirect
40. #4705	C₂×C₃	semidirect
41. #4685	C₂×C₃	semidirect
98. C₃×#97	C₂×D₃	semidirect
99. C₃×#97	C₂²×C₃	semidirect
102. C₃×C₄×C₈	C₂×D₃	semidirect
103. C₃×C₄×C₈	C₂²×C₃	semidirect
105. Dic₃⋊C₈	C₂²×C₃	semidirect
106. #803	C₂²×C₃	semidirect
107. C₄×C₃⋊C₈	C₂²×C₃	semidirect
128. C₃×C₄×D₃	M₁₆	semidirect
137. C₄×M₁₆	C₃×D₃	semidirect
227. #97	C₂×C₃×D₃	semidirect
229. C₄×C₈	C₂×C₃×D₃	semidirect
278. C₄×D₃	C₃×M₁₆	semidirect
350. C₃²	#2920	semidirect
400. C₃	#78517	direct (N × H)
401. C₃	C₃×#2920	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄²×D₃	2
C₃²×C₄×M₁₆	2
C₃×#5126	2
C₃×#5118	2
C₃×C₄×#208	2
C₃×#4705	2
C₃×#4685	2
C₃×#2920	3
#78517	3

Subgroups — C3×#78517 #11858818

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#78517 #11858818