Subgroups — C₃×#68236 #11774571

Order 1152.

531 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×D₃×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×#4837	C₂	1	1	yes	maximal, characteristic
3	C₃×#4685	C₂	1	1	yes	maximal, characteristic
4	C₃²×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#4535	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4484	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4456	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#1487	—	3	1	no	maximal
9	#68236	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂×C₃×D₃×Q₈	C₄	1	1	yes	characteristic
11	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
12	C₃×Q₈×Dic₃	C₄	1	1	yes	characteristic
13	C₂×C₃×ΓL(1,𝔽₂₅)	—	2	1	no	—
14	C₃×D₃×C₄⋊C₄	—	2	1	no	—
15	C₃×D₃×C₄⋊C₄	C₄	1	1	yes	characteristic
16	C₃×#887	—	2	1	no	—
17	C₃×#887	C₄	1	1	yes	characteristic
18	C₃×C₄²×D₃	—	2	1	no	—
19	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
20	C₃×C₄×Dic₆	—	2	1	no	—
21	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
22	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
24	C₃×(C₂×D₃)⋊C₈	—	2	1	no	—
25	C₃×Dic₃⋊C₈	—	2	1	no	—
26	C₃×Dic₃⋊C₈	—	2	1	no	—
27	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
28	C₃×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄×Q₈	—	3	1	no	—
30	C₄×D₃×Q₈	C₂×C₃	1	1	yes	characteristic
31	C₃×#431	—	3	1	no	—
32	C₃×#423	—	3	1	no	—
33	#4837	C₂×C₃	1	1	yes	characteristic
34	#4685	C₂×C₃	1	1	yes	characteristic
35	C₃×Q₈⋊C₈	—	2	1	no	—
36	C₃×Q₈⋊C₈	—	3	1	no	—
37	C₃×Q₈⋊C₈	—	3	1	no	—
38	C₃×Q₈⋊C₈	—	3	1	no	—
39	C₃×Q₈⋊C₈	D₃	1	1	yes	characteristic, complemented
40	C₃×Q₈⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
41	#4535	C₂×C₃	1	1	yes	characteristic, complemented
42	#4484	C₂×C₃	1	1	yes	characteristic, complemented
43	#4456	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂×C₃²×Q₈	C₂×C₄	1	1	yes	characteristic
45	C₃×D₃×Q₈	—	2	2	no	—
46	C₃×D₃×Q₈	—	2	2	no	—
47	C₂×C₃×C₄×D₃	—	2	1	no	—
48	C₂×C₃×C₄×D₃	—	2	1	no	—
49	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₃×C₄×D₃	D₄	1	1	yes	characteristic
51	C₂×C₃×C₄×D₃	D₄	1	1	yes	characteristic
52	C₂×C₃×Dic₆	—	2	1	no	—
53	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
54	C₂×C₃²×C₈	—	2	1	no	—
55	C₂×C₃²×C₈	—	2	1	no	—
56	C₃²×C₄⋊C₄	—	2	1	no	—
57	C₃²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₃²×C₄²	—	2	1	no	—
59	C₃²×C₄²	C₂³	1	1	yes	characteristic
60	C₃×C₄⋊Dic₃	—	2	1	no	—
61	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
62	C₃×Dic₃⋊C₄	—	2	1	no	—
63	C₃×Dic₃⋊C₄	—	2	1	no	—
64	C₃×Dic₃⋊C₄	—	2	1	no	—
65	C₃×C₄×Dic₃	—	2	1	no	—
66	C₃×C₄×Dic₃	—	2	1	no	—
67	C₃×C₄×Dic₃	—	2	1	no	—
68	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
69	C₃×C₄×Dic₃	D₄	1	1	yes	characteristic
70	C₃×C₄×Dic₃	D₄	1	1	yes	characteristic
71	C₂×C₃×C₃⋊C₈	—	2	1	no	—
72	C₂×C₃×C₃⋊C₈	—	2	1	no	—
73	C₃×ΓL(1,𝔽₂₅)	—	4	2	no	—
74	#1487	—	3	1	no	Sylow
75	C₂²×C₃×Q₈	—	3	1	no	—
76	C₂×D₃×Q₈	C₃×C₄	1	1	yes	characteristic
77	C₂×C₃×M₁₆	—	6	1	no	—
78	C₃×C₄×Q₈	—	2	1	no	—
79	C₃×C₄×Q₈	—	3	1	no	—
80	C₃×C₄×Q₈	—	3	1	no	—
81	C₃×C₄×Q₈	—	3	1	no	—
82	C₃×C₄×Q₈	—	6	1	no	—
83	C₃×C₄×Q₈	—	6	1	no	—
84	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic
85	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₃×C₄⋊C₄	—	3	1	no	—
87	C₂×C₃×C₄⋊C₄	—	6	1	no	—
88	C₂×C₃×C₄²	—	3	1	no	—
89	C₂×C₃×C₄²	—	6	1	no	—
90	Q₈×Dic₃	C₃×C₄	1	1	yes	characteristic
91	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
92	D₃×C₄⋊C₄	—	2	1	no	—
93	D₃×C₄⋊C₄	C₃×C₄	1	1	yes	characteristic
94	#887	—	2	1	no	—
95	#887	C₃×C₄	1	1	yes	characteristic
96	C₄²×D₃	—	2	1	no	—
97	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
98	C₄×Dic₆	—	2	1	no	—
99	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic
100	C₃×C₄⋊C₈	—	2	1	no	—
101	C₃×C₄⋊C₈	—	3	1	no	—
102	C₃×C₄⋊C₈	—	6	1	no	—
103	C₃×C₄⋊C₈	—	6	1	no	—
104	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
105	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
106	C₃×C₂²⋊C₈	—	6	1	no	—
107	C₃×C₄×C₈	—	2	1	no	—
108	C₃×C₄×C₈	—	3	1	no	—
109	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
110	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
111	(C₂×D₃)⋊C₈	—	2	1	no	—
112	Dic₃⋊C₈	—	2	1	no	—
113	Dic₃⋊C₈	—	2	1	no	—
114	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic
115	C₄×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
116	C₂²×C₃×D₃	C₂²⋊C₄	1	1	yes	characteristic
117	C₃²×Q₈	—	2	1	no	—
118	C₃²×Q₈	M₁₆	1	2	yes	complemented
119	C₂×C₃²×C₄	—	2	1	no	—
120	C₂×C₃²×C₄	—	2	1	no	—
121	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
123	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
124	C₂×C₃×Dic₃	—	2	1	no	—
125	C₂×C₃×Dic₃	—	2	1	no	—
126	C₂×C₃×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
127	C₂×C₃×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
128	C₂×C₃×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
129	C₃×C₄×D₃	—	2	4	no	—
130	C₃×C₄×D₃	—	2	1	no	—
131	C₃×C₄×D₃	—	2	1	no	—
132	C₃×C₄×D₃	—	4	1	no	—
133	C₃×C₄×D₃	—	4	2	no	—
134	C₃×C₄×D₃	SD₁₆	1	2	yes	—
135	C₃×C₄×D₃	Q₁₆	1	2	yes	—
136	C₃×Dic₆	—	2	4	no	—
137	C₃×Dic₆	—	2	1	no	—
138	C₃×Dic₆	M₁₆	1	2	yes	complemented
139	C₃²×C₈	—	4	1	no	—
140	C₃²×C₈	—	4	1	no	—
141	C₃×C₃⋊C₈	—	4	1	no	—
142	C₃×C₃⋊C₈	—	4	1	no	—
143	C₂×C₄×Q₈	—	3	1	no	—
144	#431	—	3	1	no	—
145	#423	—	3	1	no	—
146	Q₈⋊C₈	—	3	1	no	—
147	Q₈⋊C₈	—	3	1	no	—
148	Q₈⋊C₈	—	3	1	no	—
149	Q₈⋊C₈	C₃×D₃	1	1	yes	characteristic, complemented
150	C₂×C₃×Q₈	—	2	1	no	—
151	C₂×C₃×Q₈	—	3	1	no	—
152	C₂×C₃×Q₈	—	6	1	no	—
153	C₂×C₃×Q₈	—	6	2	no	—
154	C₂×C₃×Q₈	—	6	2	no	—
155	C₂×C₃×Q₈	C₄×D₃	1	1	yes	characteristic
156	C₂×C₃×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
157	C₂²×C₃×C₄	—	3	1	no	—
158	C₂²×C₃×C₄	—	3	1	no	—
159	C₂²×C₃×C₄	—	3	1	no	—
160	C₂²×C₃×C₄	—	6	1	no	—
161	C₂²×C₃×C₄	—	6	1	no	—
162	D₃×Q₈	—	2	2	no	—
163	D₃×Q₈	—	2	2	no	—
164	C₂×C₄×D₃	—	2	1	no	—
165	C₂×C₄×D₃	—	2	1	no	—
166	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
167	C₂×C₄×D₃	C₃×D₄	1	1	yes	characteristic
168	C₂×C₄×D₃	C₃×D₄	1	1	yes	characteristic
169	C₂×Dic₆	—	2	1	no	—
170	C₂×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
171	C₃×M₁₆	—	12	2	no	—
172	C₂×C₃×C₈	—	2	1	no	—
173	C₂×C₃×C₈	—	2	1	no	—
174	C₂×C₃×C₈	—	2	1	no	—
175	C₂×C₃×C₈	—	2	1	no	—
176	C₂×C₃×C₈	—	4	1	no	—
177	C₂×C₃×C₈	—	4	1	no	—
178	C₂×C₃×C₈	—	6	1	no	—
179	C₂×C₃×C₈	—	6	1	no	—
180	C₃×C₄⋊C₄	—	2	1	no	—
181	C₃×C₄⋊C₄	—	2	1	no	—
182	C₃×C₄⋊C₄	—	2	1	no	—
183	C₃×C₄⋊C₄	—	3	1	no	—
184	C₃×C₄⋊C₄	—	4	1	no	—
185	C₃×C₄⋊C₄	—	6	1	no	—
186	C₃×C₄⋊C₄	—	6	1	no	—
187	C₃×C₄⋊C₄	—	6	1	no	—
188	C₃×C₄⋊C₄	—	6	1	no	—
189	C₃×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
190	C₃×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
191	C₃×C₄²	—	2	1	no	—
192	C₃×C₄²	—	2	1	no	—
193	C₃×C₄²	—	2	1	no	—
194	C₃×C₄²	—	3	1	no	—
195	C₃×C₄²	—	3	1	no	—
196	C₃×C₄²	—	3	1	no	—
197	C₃×C₄²	—	4	1	no	—
198	C₃×C₄²	—	6	1	no	—
199	C₃×C₄²	—	6	1	no	—
200	C₃×C₄²	—	6	1	no	—
201	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
202	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
203	C₄⋊Dic₃	—	2	1	no	—
204	C₄⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
205	Dic₃⋊C₄	—	2	1	no	—
206	Dic₃⋊C₄	—	2	1	no	—
207	Dic₃⋊C₄	—	2	1	no	—
208	C₄×Dic₃	—	2	1	no	—
209	C₄×Dic₃	—	2	1	no	—
210	C₄×Dic₃	—	2	1	no	—
211	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
212	C₄×Dic₃	C₃×D₄	1	1	yes	characteristic
213	C₄×Dic₃	C₃×D₄	1	1	yes	characteristic
214	C₂×C₃⋊C₈	—	2	1	no	—
215	C₂×C₃⋊C₈	—	2	1	no	—
216	ΓL(1,𝔽₂₅)	—	4	2	no	—
217	C₂²×C₃²	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂×C₃×D₃	—	2	1	no	—
219	C₂×C₃×D₃	—	2	1	no	—
220	C₂×C₃×D₃	#103	1	2	yes	—
221	C₃²×C₄	—	2	2	no	—
222	C₃²×C₄	—	2	1	no	—
223	C₃²×C₄	—	4	1	no	—
224	C₃²×C₄	C₂×M₁₆	1	1	yes	characteristic
225	C₃²×C₄	C₂×M₁₆	1	1	yes	characteristic
226	C₃²×C₄	C₂×SD₁₆	1	1	yes	characteristic
227	C₃²×C₄	C₂×Q₁₆	1	1	yes	characteristic
228	C₃×Dic₃	—	2	1	no	—
229	C₃×Dic₃	—	2	2	no	—
230	C₃×Dic₃	—	2	1	no	—
231	C₃×Dic₃	—	4	1	no	—
232	C₃×Dic₃	#103	1	2	yes	—
233	C₂²×Q₈	—	3	1	no	—
234	C₂×M₁₆	—	6	1	no	—
235	C₄×Q₈	—	3	1	no	—
236	C₄×Q₈	—	3	1	no	—
237	C₄×Q₈	—	3	1	no	—
238	C₄×Q₈	—	6	1	no	—
239	C₄×Q₈	—	6	1	no	—
240	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
241	C₂×C₄⋊C₄	—	3	1	no	—
242	C₂×C₄⋊C₄	—	6	1	no	—
243	C₂×C₄²	—	3	1	no	—
244	C₂×C₄²	—	6	1	no	—
245	C₄⋊C₈	—	3	1	no	—
246	C₄⋊C₈	—	6	1	no	—
247	C₄⋊C₈	—	6	1	no	—
248	C₄⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
249	C₂²⋊C₈	—	6	1	no	—
250	C₄×C₈	—	3	1	no	—
251	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic
252	C₂³×C₃	—	3	1	no	—
253	C₂²×D₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
254	C₃×Q₈	—	2	1	no	—
255	C₃×Q₈	—	2	1	no	—
256	C₃×Q₈	—	2	2	no	—
257	C₃×Q₈	—	3	2	no	—
258	C₃×Q₈	—	4	1	no	—
259	C₃×Q₈	—	6	4	no	—
260	C₃×Q₈	—	6	1	no	—
261	C₃×Q₈	ΓL(1,𝔽₂₅)	1	2	yes	complemented
262	C₃×Q₈	C₃×M₁₆	1	2	yes	complemented
263	C₂×C₃×C₄	—	2	1	no	—
264	C₂×C₃×C₄	—	2	1	no	—
265	C₂×C₃×C₄	—	2	1	no	—
266	C₂×C₃×C₄	—	2	1	no	—
267	C₂×C₃×C₄	—	2	1	no	—
268	C₂×C₃×C₄	—	2	1	no	—
269	C₂×C₃×C₄	—	2	1	no	—
270	C₂×C₃×C₄	—	3	1	no	—
271	C₂×C₃×C₄	—	3	2	no	—
272	C₂×C₃×C₄	—	3	2	no	—
273	C₂×C₃×C₄	—	3	1	no	—
274	C₂×C₃×C₄	—	3	1	no	—
275	C₂×C₃×C₄	—	4	1	no	—
276	C₂×C₃×C₄	—	4	1	no	—
277	C₂×C₃×C₄	—	6	4	no	—
278	C₂×C₃×C₄	—	6	1	no	—
279	C₂×C₃×C₄	—	6	1	no	—
280	C₂×C₃×C₄	—	6	1	no	—
281	C₂×C₃×C₄	—	6	1	no	—
282	C₂×C₃×C₄	—	12	1	no	—
283	C₂×C₃×C₄	—	12	2	no	—
284	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
285	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
286	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
289	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
290	C₂×Dic₃	—	2	1	no	—
291	C₂×Dic₃	—	2	1	no	—
292	C₂×Dic₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
293	C₂×Dic₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
294	C₂×Dic₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
295	C₄×D₃	—	2	4	no	—
296	C₄×D₃	—	2	1	no	—
297	C₄×D₃	—	2	1	no	—
298	C₄×D₃	—	4	1	no	—
299	C₄×D₃	—	4	2	no	—
300	C₄×D₃	C₃×SD₁₆	1	2	yes	—
301	C₄×D₃	C₃×Q₁₆	1	2	yes	—
302	Dic₆	—	2	4	no	—
303	Dic₆	—	2	1	no	—
304	Dic₆	C₃×M₁₆	1	2	yes	complemented
305	C₃×C₈	—	4	1	no	—
306	C₃×C₈	—	4	1	no	—
307	C₃×C₈	—	4	2	no	—
308	C₃×C₈	—	4	1	no	—
309	C₃×C₈	—	4	1	no	—
310	C₃×C₈	—	8	1	no	—
311	C₃×C₈	—	12	1	no	—
312	C₃×C₈	—	12	1	no	—
313	C₃⋊C₈	—	4	1	no	—
314	C₃⋊C₈	—	4	1	no	—
315	C₂×C₃²	#407	1	1	yes	characteristic
316	C₂×C₃²	C₂×#103	1	1	yes	characteristic
317	C₂×C₃²	#421	1	1	yes	characteristic
318	C₃×D₃	—	2	2	no	—
319	C₂×Q₈	—	3	1	no	—
320	C₂×Q₈	—	6	1	no	—
321	C₂×Q₈	—	6	2	no	—
322	C₂×Q₈	—	6	2	no	—
323	C₂×Q₈	C₃×C₄×D₃	1	1	yes	characteristic
324	C₂²×C₄	—	3	1	no	—
325	C₂²×C₄	—	3	1	no	—
326	C₂²×C₄	—	3	1	no	—
327	C₂²×C₄	—	6	1	no	—
328	C₂²×C₄	—	6	1	no	—
329	M₁₆	—	12	2	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	6	1	no	—
333	C₂×C₈	—	6	1	no	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	3	1	no	—
336	C₄⋊C₄	—	6	1	no	—
337	C₄⋊C₄	—	6	1	no	—
338	C₄⋊C₄	—	6	1	no	—
339	C₄⋊C₄	—	6	1	no	—
340	C₄⋊C₄	C₃×C₄×D₃	1	1	yes	characteristic
341	C₄²	—	2	1	no	—
342	C₄²	—	3	1	no	—
343	C₄²	—	3	1	no	—
344	C₄²	—	3	1	no	—
345	C₄²	—	6	1	no	—
346	C₄²	—	6	1	no	—
347	C₄²	—	6	1	no	—
348	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
349	C₂²×C₃	—	2	1	no	—
350	C₂²×C₃	—	3	2	no	—
351	C₂²×C₃	—	6	1	no	—
352	C₂²×C₃	—	6	1	no	—
353	C₂²×C₃	D₃×C₂²⋊C₄	1	1	yes	characteristic
354	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
355	C₂×D₃	—	2	1	no	—
356	C₂×D₃	—	2	1	no	—
357	C₂×D₃	C₃×#103	1	2	yes	—
358	C₃×C₄	—	2	2	no	—
359	C₃×C₄	—	2	2	no	—
360	C₃×C₄	—	2	1	no	—
361	C₃×C₄	—	2	1	no	—
362	C₃×C₄	—	2	1	no	—
363	C₃×C₄	—	2	1	no	—
364	C₃×C₄	—	2	1	no	—
365	C₃×C₄	—	2	1	no	—
366	C₃×C₄	—	3	2	no	—
367	C₃×C₄	—	4	1	no	—
368	C₃×C₄	—	4	2	no	—
369	C₃×C₄	—	4	1	no	—
370	C₃×C₄	—	4	1	no	—
371	C₃×C₄	—	6	1	no	—
372	C₃×C₄	—	6	2	no	—
373	C₃×C₄	—	6	1	no	—
374	C₃×C₄	—	8	1	no	—
375	C₃×C₄	—	12	1	no	—
376	C₃×C₄	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
377	C₃×C₄	D₃×M₁₆	1	1	yes	characteristic
378	C₃×C₄	D₃×SD₁₆	1	1	yes	characteristic
379	C₃×C₄	D₃×Q₁₆	1	1	yes	characteristic
380	C₃×C₄	C₂×C₃×M₁₆	1	1	yes	characteristic
381	C₃×C₄	C₂×C₃×M₁₆	1	1	yes	characteristic
382	C₃×C₄	C₂×C₃×SD₁₆	1	1	yes	characteristic
383	C₃×C₄	C₂×C₃×Q₁₆	1	1	yes	characteristic
384	Dic₃	—	2	1	no	—
385	Dic₃	—	2	2	no	—
386	Dic₃	—	2	1	no	—
387	Dic₃	—	4	1	no	—
388	Dic₃	C₃×#103	1	2	yes	—
389	C₃²	#1487	1	1	yes	characteristic, complemented, Sylow
390	C₂³	—	3	1	no	—
391	Q₈	—	2	1	no	—
392	Q₈	—	3	2	no	—
393	Q₈	—	6	4	no	—
394	Q₈	—	6	1	no	—
395	Q₈	C₃×ΓL(1,𝔽₂₅)	1	2	yes	complemented
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	3	1	no	—
399	C₂×C₄	—	3	2	no	—
400	C₂×C₄	—	3	2	no	—
401	C₂×C₄	—	3	1	no	—
402	C₂×C₄	—	3	1	no	—
403	C₂×C₄	—	6	4	no	—
404	C₂×C₄	—	6	1	no	—
405	C₂×C₄	—	6	1	no	—
406	C₂×C₄	—	6	1	no	—
407	C₂×C₄	—	6	1	no	—
408	C₂×C₄	—	12	1	no	—
409	C₂×C₄	—	12	2	no	—
410	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
411	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
412	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
413	C₈	—	4	1	no	—
414	C₈	—	4	1	no	—
415	C₈	—	12	1	no	—
416	C₈	—	12	1	no	—
417	C₂×C₃	—	2	1	no	—
418	C₂×C₃	—	2	1	no	—
419	C₂×C₃	—	2	1	no	—
420	C₂×C₃	—	6	2	no	—
421	C₂×C₃	#4726	1	1	yes	characteristic
422	C₂×C₃	D₃×#103	1	1	yes	characteristic
423	C₂×C₃	#4821	1	1	yes	characteristic
424	C₂×C₃	C₃×#407	1	1	yes	characteristic
425	C₂×C₃	C₂×C₃×#103	1	1	yes	characteristic
426	C₂×C₃	C₃×#421	1	1	yes	characteristic
427	D₃	—	2	2	no	—
428	C₂²	—	3	2	no	—
429	C₂²	—	6	1	no	—
430	C₂²	—	6	1	no	—
431	C₂²	C₃×D₃×C₂²⋊C₄	1	1	yes	characteristic
432	C₄	—	2	2	no	—
433	C₄	—	2	1	no	—
434	C₄	—	3	2	no	—
435	C₄	—	4	1	no	—
436	C₄	—	6	1	no	—
437	C₄	—	6	2	no	—
438	C₄	—	6	1	no	—
439	C₄	—	12	1	no	—
440	C₄	C₂×C₃×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
441	C₄	C₃×D₃×M₁₆	1	1	yes	characteristic
442	C₄	C₃×D₃×SD₁₆	1	1	yes	characteristic
443	C₄	C₃×D₃×Q₁₆	1	1	yes	characteristic
444	C₃	—	2	1	no	—
445	C₃	#68236	1	1	yes	characteristic, direct product factor
446	C₃	C₃×#1487	1	1	yes	characteristic, complemented
447	C₂	—	6	2	no	—
448	C₂	C₃×#4726	1	1	yes	characteristic
449	C₂	C₃×D₃×#103	1	1	yes	characteristic
450	C₂	C₃×#4821	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	D₃×D₄
commutator	C₂×C₃×C₄	C₂²×C₃×C₄
Frattini	C₄²	C₂²×C₃×D₃
Fitting	C₃²×Q₈⋊C₈	C₂
socle	C₂²×C₃²	C₂×C₂²⋊C₄
prime radical	C₂²×C₃×D₃	C₂²⋊C₄
cosocle	C₃×C₄²	C₂³×C₃
hypercenter	C₃×Q₈⋊C₈	D₃
hypocenter	C₃	C₃×#1487
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄² ◁ C₃×Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
4. C₃²×Q₈⋊C₈	C₂	semidirect
5. C₃×#4535	C₂	semidirect
6. C₃×#4484	C₂	semidirect
7. C₃×#4456	C₂	semidirect
9. #68236	C₃	direct (N × H)
39. C₃×Q₈⋊C₈	D₃	semidirect
40. C₃×Q₈⋊C₈	C₂×C₃	semidirect
41. #4535	C₂×C₃	semidirect
42. #4484	C₂×C₃	semidirect
43. #4456	C₂×C₃	semidirect
118. C₃²×Q₈	M₁₆	semidirect
138. C₃×Dic₆	M₁₆	semidirect
149. Q₈⋊C₈	C₃×D₃	semidirect
261. C₃×Q₈	ΓL(1,𝔽₂₅)	semidirect
262. C₃×Q₈	C₃×M₁₆	semidirect
304. Dic₆	C₃×M₁₆	semidirect
389. C₃²	#1487	semidirect
395. Q₈	C₃×ΓL(1,𝔽₂₅)	semidirect
445. C₃	#68236	direct (N × H)
446. C₃	C₃×#1487	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×D₃×Q₈	2
C₃×#4837	2
C₃×#4685	2
C₃²×Q₈⋊C₈	2
C₃×#4535	2
C₃×#4484	2
C₃×#4456	2
C₃×#1487	3
#68236	3

Subgroups — C3×#68236 #11774571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#68236 #11774571