Subgroups — C₃×#79038 #11858821

Order 1152.

1031 conjugacy classes of subgroups.

The subgroup lattice has 420 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×#423	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5126	C₂	1	2	yes	maximal
4	C₃×Dic₃×M₁₆	C₂	1	2	yes	maximal, complemented
5	C₃×#4924	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4835	C₂	1	4	yes	maximal, complemented
7	C₃×#4833	C₂	1	4	yes	maximal, complemented
8	C₃×#2920	—	3	1	no	maximal
9	#79038	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×C₄⋊C₈	C₂²	1	4	yes	complemented
22	C₃×(C₂×D₃)⋊C₈	C₂²	1	8	yes	—
23	C₃×#815	C₂²	1	4	yes	complemented
24	C₃×C₈×Dic₃	C₂²	1	4	yes	complemented
25	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	complemented
26	C₂²×C₃×C₄²	—	3	1	no	—
27	C₂×C₄²×D₃	C₂×C₃	1	1	yes	characteristic
28	C₃×#432	—	3	4	no	—
29	C₃×#431	—	3	4	no	—
30	C₃×#423	—	2	1	no	—
31	C₃×#423	—	3	1	no	—
32	C₃×#423	D₃	1	1	yes	characteristic, complemented
33	C₃×#423	C₂×C₃	1	1	yes	characteristic, complemented
34	C₃×#407	—	3	2	no	—
35	C₃×C₄×M₁₆	—	3	2	no	—
36	#5126	C₂×C₃	1	2	yes	—
37	Dic₃×M₁₆	C₂×C₃	1	2	yes	complemented
38	#4924	C₂×C₃	1	1	yes	characteristic, complemented
39	#4835	C₂×C₃	1	4	yes	complemented
40	#4833	C₂×C₃	1	4	yes	complemented
41	C₂³×C₃×D₃	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
43	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
44	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₃×Dic₃	C₂×C₄	1	2	yes	—
46	C₂×C₃×C₄×D₃	—	2	2	no	—
47	C₂×C₃×C₄×D₃	—	2	2	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	1	yes	characteristic
58	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
59	C₃²×C₄²	C₂³	1	2	yes	—
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	2	yes	—
65	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
66	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
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	—	2	4	no	—
95	C₃×C₄⋊C₈	—	3	4	no	—
96	C₃×C₄⋊C₈	C₂×D₃	1	4	yes	complemented
97	C₃×C₄⋊C₈	C₂²×C₃	1	4	yes	complemented
98	C₃×C₂²⋊C₈	—	3	8	no	—
99	C₃×#97	—	3	4	no	—
100	C₃×C₄×C₈	—	3	4	no	—
101	(C₂×D₃)⋊C₈	C₂²×C₃	1	8	yes	—
102	#815	C₂²×C₃	1	4	yes	complemented
103	C₈×Dic₃	C₂²×C₃	1	4	yes	complemented
104	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	4	yes	complemented
105	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₃×D₃	—	2	2	no	—
107	C₂²×C₃×D₃	—	2	4	no	—
108	C₂²×C₃×D₃	C₂²×C₄	1	2	yes	—
109	C₂×C₃²×C₄	—	2	4	no	—
110	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
111	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
113	C₂×C₃²×C₄	#41	1	2	yes	—
114	C₂×C₃²×C₄	#41	1	2	yes	—
115	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
116	C₂×C₃×Dic₃	—	2	2	no	—
117	C₂×C₃×Dic₃	—	2	4	no	—
118	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
119	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
120	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
121	C₃×C₄×D₃	—	2	4	no	—
122	C₃×C₄×D₃	—	2	4	no	—
123	C₃×C₄×D₃	—	2	4	no	—
124	C₃×C₄×D₃	—	2	2	no	—
125	C₃×C₄×D₃	—	2	2	no	—
126	C₃×C₄×D₃	—	2	4	no	—
127	C₃×C₄×D₃	M₁₆	1	8	yes	complemented
128	C₃²×C₈	—	2	4	no	—
129	C₃×C₃⋊C₈	—	2	4	no	—
130	C₂²×C₄²	—	3	1	no	—
131	#432	—	3	4	no	—
132	#431	—	3	4	no	—
133	#423	—	3	1	no	—
134	#423	C₃×D₃	1	1	yes	characteristic, complemented
135	#407	—	3	2	no	—
136	C₄×M₁₆	—	3	2	no	—
137	C₂⁴×C₃	—	3	1	no	—
138	C₂³×D₃	C₂×C₃×C₄	1	1	yes	characteristic
139	C₂²×C₃×C₄	—	2	2	no	—
140	C₂²×C₃×C₄	—	2	1	no	—
141	C₂²×C₃×C₄	—	3	2	no	—
142	C₂²×C₃×C₄	—	3	2	no	—
143	C₂²×C₃×C₄	—	3	1	no	—
144	C₂²×C₃×C₄	—	3	2	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	—	6	8	no	—
150	C₂²×C₃×C₄	—	6	2	no	—
151	C₂²×C₃×C₄	—	6	2	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	2	no	—
159	C₂×C₄×D₃	—	2	2	no	—
160	C₂×C₄×D₃	—	2	8	no	—
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	C₂×C₃×C₄	1	2	yes	—
166	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
167	C₃×M₁₆	—	2	4	no	—
168	C₃×M₁₆	—	2	4	no	—
169	C₃×M₁₆	—	4	4	no	—
170	C₃×M₁₆	—	6	4	no	—
171	C₂×C₃×C₈	—	2	4	no	—
172	C₂×C₃×C₈	—	3	4	no	—
173	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
174	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
175	C₃×C₄²	—	2	1	no	—
176	C₃×C₄²	—	2	1	no	—
177	C₃×C₄²	—	2	2	no	—
178	C₃×C₄²	—	3	2	no	—
179	C₃×C₄²	—	3	2	no	—
180	C₃×C₄²	—	3	2	no	—
181	C₃×C₄²	—	3	2	no	—
182	C₃×C₄²	—	3	2	no	—
183	C₃×C₄²	—	3	1	no	—
184	C₃×C₄²	—	3	1	no	—
185	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
186	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
187	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
188	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
189	C₃×C₄²	C₂²×D₃	1	2	yes	—
190	C₃×C₄²	C₂³×C₃	1	2	yes	—
191	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
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	1	yes	characteristic
197	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
198	#208	—	2	4	no	—
199	C₂×C₃⋊C₈	C₂³×C₃	1	4	yes	—
200	C₂²×C₃²	—	2	2	no	—
201	C₂²×C₃²	#117	1	2	yes	—
202	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
203	C₂×C₃×D₃	—	2	8	no	—
204	C₂×C₃×D₃	—	2	2	no	—
205	C₂×C₃×D₃	—	2	2	no	—
206	C₂×C₃×D₃	C₂×M₁₆	1	4	yes	—
207	C₃²×C₄	—	2	2	no	—
208	C₃²×C₄	#117	1	2	yes	—
209	C₃²×C₄	C₂×M₁₆	1	4	yes	—
210	C₃²×C₄	C₂×#41	1	1	yes	characteristic
211	C₃²×C₄	C₂×#41	1	1	yes	characteristic
212	C₃×Dic₃	—	2	2	no	—
213	C₃×Dic₃	—	2	2	no	—
214	C₃×Dic₃	C₂×M₁₆	1	4	yes	—
215	C₂³×C₄	—	3	2	no	—
216	C₂³×C₄	—	3	1	no	—
217	C₂×M₁₆	—	3	2	no	—
218	C₂×M₁₆	C₂×C₃×D₃	1	2	yes	—
219	C₂×C₄²	—	3	2	no	—
220	C₂×C₄²	—	3	1	no	—
221	C₂×C₄²	—	3	2	no	—
222	C₂×C₄²	—	3	2	no	—
223	C₂×C₄²	—	3	2	no	—
224	C₂×C₄²	—	3	2	no	—
225	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
226	C₄⋊C₈	—	3	4	no	—
227	C₄⋊C₈	C₂×C₃×D₃	1	4	yes	complemented
228	C₂²⋊C₈	—	3	8	no	—
229	#97	—	3	4	no	—
230	C₄×C₈	—	3	4	no	—
231	C₂³×C₃	—	2	1	no	—
232	C₂³×C₃	—	3	2	no	—
233	C₂³×C₃	—	6	4	no	—
234	C₂³×C₃	—	6	2	no	—
235	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
236	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
237	C₂²×D₃	—	2	2	no	—
238	C₂²×D₃	—	2	4	no	—
239	C₂²×D₃	C₂²×C₃×C₄	1	2	yes	—
240	C₂×C₃×C₄	—	2	4	no	—
241	C₂×C₃×C₄	—	2	4	no	—
242	C₂×C₃×C₄	—	2	1	no	—
243	C₂×C₃×C₄	—	2	1	no	—
244	C₂×C₃×C₄	—	2	2	no	—
245	C₂×C₃×C₄	—	2	2	no	—
246	C₂×C₃×C₄	—	2	2	no	—
247	C₂×C₃×C₄	—	2	2	no	—
248	C₂×C₃×C₄	—	3	2	no	—
249	C₂×C₃×C₄	—	3	8	no	—
250	C₂×C₃×C₄	—	3	2	no	—
251	C₂×C₃×C₄	—	3	2	no	—
252	C₂×C₃×C₄	—	4	4	no	—
253	C₂×C₃×C₄	—	6	4	no	—
254	C₂×C₃×C₄	—	6	4	no	—
255	C₂×C₃×C₄	—	6	4	no	—
256	C₂×C₃×C₄	—	6	2	no	—
257	C₂×C₃×C₄	—	6	4	no	—
258	C₂×C₃×C₄	—	6	4	no	—
259	C₂×C₃×C₄	—	6	2	no	—
260	C₂×C₃×C₄	—	6	2	no	—
261	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
262	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
264	C₂×C₃×C₄	#237	1	2	yes	—
265	C₂×C₃×C₄	#239	1	2	yes	—
266	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
267	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
269	C₂×C₃×C₄	C₃×#41	1	2	yes	—
270	C₂×C₃×C₄	C₃×#41	1	2	yes	—
271	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
272	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
273	C₂×Dic₃	—	2	2	no	—
274	C₂×Dic₃	—	2	4	no	—
275	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
276	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
277	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
278	C₄×D₃	—	2	4	no	—
279	C₄×D₃	—	2	4	no	—
280	C₄×D₃	—	2	4	no	—
281	C₄×D₃	—	2	2	no	—
282	C₄×D₃	—	2	2	no	—
283	C₄×D₃	—	2	4	no	—
284	C₄×D₃	C₃×M₁₆	1	8	yes	complemented
285	C₃×C₈	—	2	4	no	—
286	C₃×C₈	—	2	4	no	—
287	C₃×C₈	—	4	4	no	—
288	C₃×C₈	—	6	4	no	—
289	C₃⋊C₈	—	2	4	no	—
290	C₂×C₃²	—	2	2	no	—
291	C₂×C₃²	C₂×#117	1	1	yes	characteristic
292	C₂×C₃²	C₂²×M₁₆	1	2	yes	—
293	C₃×D₃	—	2	4	no	—
294	C₂⁴	—	3	1	no	—
295	C₂²×C₄	—	3	2	no	—
296	C₂²×C₄	—	3	2	no	—
297	C₂²×C₄	—	3	1	no	—
298	C₂²×C₄	—	3	2	no	—
299	C₂²×C₄	—	3	2	no	—
300	C₂²×C₄	—	3	2	no	—
301	C₂²×C₄	—	3	2	no	—
302	C₂²×C₄	—	3	2	no	—
303	C₂²×C₄	—	6	8	no	—
304	C₂²×C₄	—	6	2	no	—
305	C₂²×C₄	—	6	2	no	—
306	C₂²×C₄	C₃×C₄×D₃	1	2	yes	—
307	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
308	M₁₆	—	2	4	no	—
309	M₁₆	—	6	4	no	—
310	C₂×C₈	—	3	4	no	—
311	C₂×C₈	C₂²×C₃×D₃	1	4	yes	—
312	C₄²	—	3	1	no	—
313	C₄²	—	3	1	no	—
314	C₄²	—	3	2	no	—
315	C₄²	—	3	2	no	—
316	C₄²	—	3	2	no	—
317	C₄²	—	3	2	no	—
318	C₄²	—	3	2	no	—
319	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
320	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
321	C₄²	C₂²×C₃×D₃	1	2	yes	—
322	C₂²×C₃	—	2	2	no	—
323	C₂²×C₃	—	2	2	no	—
324	C₂²×C₃	—	2	2	no	—
325	C₂²×C₃	—	2	1	no	—
326	C₂²×C₃	—	3	4	no	—
327	C₂²×C₃	—	4	2	no	—
328	C₂²×C₃	—	6	8	no	—
329	C₂²×C₃	—	6	2	no	—
330	C₂²×C₃	—	6	2	no	—
331	C₂²×C₃	#892	1	2	yes	—
332	C₂²×C₃	C₃×#117	1	2	yes	—
333	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
334	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
335	C₂×D₃	—	2	8	no	—
336	C₂×D₃	—	2	2	no	—
337	C₂×D₃	—	2	2	no	—
338	C₂×D₃	C₂×C₃×M₁₆	1	4	yes	—
339	C₃×C₄	—	2	2	no	—
340	C₃×C₄	—	2	2	no	—
341	C₃×C₄	—	2	2	no	—
342	C₃×C₄	—	2	4	no	—
343	C₃×C₄	—	2	1	no	—
344	C₃×C₄	—	2	1	no	—
345	C₃×C₄	—	3	4	no	—
346	C₃×C₄	—	4	2	no	—
347	C₃×C₄	—	6	2	no	—
348	C₃×C₄	—	6	2	no	—
349	C₃×C₄	#892	1	2	yes	—
350	C₃×C₄	D₃×M₁₆	1	4	yes	—
351	C₃×C₄	C₃×#117	1	2	yes	—
352	C₃×C₄	C₂×C₃×M₁₆	1	4	yes	—
353	C₃×C₄	C₂×#237	1	1	yes	characteristic
354	C₃×C₄	C₂×#239	1	1	yes	characteristic
355	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
356	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
357	Dic₃	—	2	2	no	—
358	Dic₃	—	2	2	no	—
359	Dic₃	C₂×C₃×M₁₆	1	4	yes	—
360	C₃²	#2920	1	1	yes	characteristic, complemented, Sylow
361	C₂³	—	3	2	no	—
362	C₂³	—	6	4	no	—
363	C₂³	—	6	2	no	—
364	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	3	2	no	—
367	C₂×C₄	—	3	8	no	—
368	C₂×C₄	—	3	2	no	—
369	C₂×C₄	—	3	2	no	—
370	C₂×C₄	—	6	4	no	—
371	C₂×C₄	—	6	4	no	—
372	C₂×C₄	—	6	4	no	—
373	C₂×C₄	—	6	2	no	—
374	C₂×C₄	—	6	4	no	—
375	C₂×C₄	—	6	4	no	—
376	C₂×C₄	—	6	2	no	—
377	C₂×C₄	—	6	2	no	—
378	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
379	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
380	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
381	C₂×C₄	C₃×#237	1	2	yes	—
382	C₂×C₄	C₃×#239	1	2	yes	—
383	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
384	C₈	—	2	4	no	—
385	C₈	—	6	4	no	—
386	C₂×C₃	—	2	2	no	—
387	C₂×C₃	—	2	2	no	—
388	C₂×C₃	—	2	2	no	—
389	C₂×C₃	—	2	1	no	—
390	C₂×C₃	—	4	2	no	—
391	C₂×C₃	—	6	4	no	—
392	C₂×C₃	C₂×#892	1	1	yes	characteristic
393	C₂×C₃	C₂×D₃×M₁₆	1	2	yes	—
394	C₂×C₃	C₂×C₃×#117	1	1	yes	characteristic
395	C₂×C₃	C₂²×C₃×M₁₆	1	2	yes	—
396	D₃	—	2	4	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	3	4	no	—
399	C₂²	—	6	8	no	—
400	C₂²	—	6	2	no	—
401	C₂²	—	6	2	no	—
402	C₂²	C₃×#892	1	2	yes	—
403	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
404	C₄	—	2	2	no	—
405	C₄	—	3	4	no	—
406	C₄	—	6	2	no	—
407	C₄	—	6	2	no	—
408	C₄	C₃×#892	1	2	yes	—
409	C₄	C₃×D₃×M₁₆	1	4	yes	—
410	C₄	C₂×C₃×#237	1	1	yes	characteristic
411	C₄	C₂×C₃×#239	1	1	yes	characteristic
412	C₃	—	2	1	no	—
413	C₃	#79038	1	1	yes	characteristic, direct product factor
414	C₃	C₃×#2920	1	1	yes	characteristic, complemented
415	C₂	—	2	2	no	—
416	C₂	—	6	4	no	—
417	C₂	C₂×C₃×#892	1	1	yes	characteristic
418	C₂	C₂×C₃×D₃×M₁₆	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#423	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₂³×C₃×D₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#423	D₃
hypocenter	C₃	C₃×#2920
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#423

Complements

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

N	H ≅ G/N	type
2. C₃²×#423	C₂	semidirect
4. C₃×Dic₃×M₁₆	C₂	semidirect
5. C₃×#4924	C₂	semidirect
6. C₃×#4835	C₂	semidirect
7. C₃×#4833	C₂	semidirect
9. #79038	C₃	direct (N × H)
21. C₃²×C₄⋊C₈	C₂²	semidirect
23. C₃×#815	C₂²	semidirect
24. C₃×C₈×Dic₃	C₂²	semidirect
25. C₃×C₄⋊(C₃⋊C₈)	C₂²	semidirect
32. C₃×#423	D₃	semidirect
33. C₃×#423	C₂×C₃	semidirect
37. Dic₃×M₁₆	C₂×C₃	semidirect
38. #4924	C₂×C₃	semidirect
39. #4835	C₂×C₃	semidirect
40. #4833	C₂×C₃	semidirect
96. C₃×C₄⋊C₈	C₂×D₃	semidirect
97. C₃×C₄⋊C₈	C₂²×C₃	semidirect
102. #815	C₂²×C₃	semidirect
103. C₈×Dic₃	C₂²×C₃	semidirect
104. C₄⋊(C₃⋊C₈)	C₂²×C₃	semidirect
127. C₃×C₄×D₃	M₁₆	semidirect
134. #423	C₃×D₃	semidirect
227. C₄⋊C₈	C₂×C₃×D₃	semidirect
284. C₄×D₃	C₃×M₁₆	semidirect
360. C₃²	#2920	semidirect
413. C₃	#79038	direct (N × H)
414. 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×#423	2
C₃×#5126	2
C₃×Dic₃×M₁₆	2
C₃×#4924	2
C₃×#4835	2
C₃×#4833	2
C₃×#2920	3
#79038	3

Subgroups — C3×#79038 #11858821

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79038 #11858821