Subgroups — C₃×#70577 #11785338

Order 1152.

737 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₃×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃²×#106	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#817	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4987	C₂	1	2	yes	maximal
5	C₃×#4529	C₂	1	2	yes	maximal, complemented
6	C₃×#1807	—	3	1	no	maximal
7	#70577	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
9	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
10	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	—
11	C₂×C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
12	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	—
13	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×D₃×C₈	—	2	2	no	—
15	C₂×C₃×D₃×C₈	—	2	2	no	—
16	C₂×C₃×D₃×C₈	C₄	1	4	yes	complemented
17	C₃²×#106	—	2	2	no	—
18	C₃×C₃⋊#95	—	2	2	no	—
19	C₃×#817	—	2	2	no	—
20	C₂³×C₃×C₈	—	3	1	no	—
21	C₂²×D₃×C₈	C₂×C₃	1	1	yes	characteristic
22	C₂×C₃×#106	—	2	1	no	—
23	C₂×C₃×#106	—	3	1	no	—
24	C₂×C₃×#106	D₃	1	1	yes	characteristic, complemented
25	C₂×C₃×#106	C₂×C₃	1	1	yes	characteristic, complemented
26	C₃×#380	—	3	2	no	—
27	C₂×#817	C₂×C₃	1	1	yes	characteristic, complemented
28	#4987	C₂×C₃	1	2	yes	—
29	C₃×#340	—	3	2	no	—
30	#4529	C₂×C₃	1	2	yes	complemented
31	C₂³×C₃×D₃	D₄	1	1	yes	characteristic
32	C₂²×C₃²×C₄	—	2	2	no	—
33	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
34	C₂²×C₃×Dic₃	—	2	2	no	—
35	C₂²×C₃×Dic₃	D₄	1	1	yes	characteristic
36	C₂×C₃×C₄×D₃	—	2	1	no	—
37	C₂×C₃×C₄×D₃	—	2	1	no	—
38	C₂×C₃×C₄×D₃	—	2	1	no	—
39	C₂×C₃×C₄×D₃	—	2	1	no	—
40	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
41	C₂×C₃×C₄×D₃	Q₈	1	2	yes	—
42	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
43	C₂×C₃²×C₈	D₄	1	2	yes	—
44	C₂×C₃²×C₈	D₄	1	2	yes	—
45	C₃²×C₄⋊C₄	—	2	2	no	—
46	C₃²×C₄⋊C₄	—	2	2	no	—
47	C₃×(C₂×D₃)⋊C₄	—	4	4	no	—
48	C₃×C₄⋊Dic₃	—	2	2	no	—
49	C₃×C₄⋊Dic₃	—	2	2	no	—
50	C₂×C₃×C₃⋊C₈	—	2	1	no	—
51	C₂×C₃×C₃⋊C₈	—	2	1	no	—
52	C₂×C₃×C₃⋊C₈	C₂×C₄	1	2	yes	—
53	C₃×D₃×C₈	—	2	8	no	—
54	#1807	—	3	1	no	Sylow
55	C₂³×C₃×C₄	—	3	1	no	—
56	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
57	C₂²×C₃×C₈	—	2	1	no	—
58	C₂²×C₃×C₈	—	3	1	no	—
59	C₂²×C₃×C₈	—	3	4	no	—
60	C₂²×C₃×C₈	—	6	2	no	—
61	C₂²×C₃×C₈	—	6	2	no	—
62	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
63	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
64	C₂×C₃×C₄⋊C₄	—	2	2	no	—
65	C₂×C₃×C₄⋊C₄	—	3	2	no	—
66	C₂×C₃×C₄⋊C₄	C₂×D₃	1	2	yes	—
67	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
68	C₂×C₃×C₂²⋊C₄	—	6	2	no	—
69	C₂×(C₂×D₃)⋊C₄	—	2	2	no	—
70	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
71	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
72	C₂×D₃×C₈	—	2	2	no	—
73	C₂×D₃×C₈	—	2	2	no	—
74	C₂×D₃×C₈	C₃×C₄	1	4	yes	complemented
75	C₃×#106	—	2	4	no	—
76	C₃×#106	—	2	2	no	—
77	C₃×#106	—	2	2	no	—
78	C₃×#106	—	6	2	no	—
79	C₃×#95	—	6	2	no	—
80	C₃⋊#95	—	2	2	no	—
81	#817	—	2	2	no	—
82	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₃×D₃	—	2	1	no	—
84	C₂²×C₃×D₃	—	2	1	no	—
85	C₂²×C₃×D₃	—	2	2	no	—
86	C₂²×C₃×D₃	C₄⋊C₄	1	2	yes	—
87	C₂²×C₃×D₃	SD₁₆	1	4	yes	—
88	C₂×C₃²×C₄	—	4	2	no	—
89	C₂×C₃²×C₄	—	4	2	no	—
90	C₂×C₃²×C₄	—	4	2	no	—
91	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
93	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
94	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
95	C₂×C₃²×C₄	#41	1	1	yes	characteristic
96	C₂×C₃²×C₄	#41	1	1	yes	characteristic
97	C₂×C₃×Dic₃	—	2	1	no	—
98	C₂×C₃×Dic₃	—	2	1	no	—
99	C₂×C₃×Dic₃	—	4	2	no	—
100	C₂×C₃×Dic₃	—	4	2	no	—
101	C₂×C₃×Dic₃	—	4	2	no	—
102	C₂×C₃×Dic₃	C₄⋊C₄	1	2	yes	—
103	C₃×C₄×D₃	—	2	2	no	—
104	C₃×C₄×D₃	—	2	2	no	—
105	C₃×C₄×D₃	—	2	2	no	—
106	C₃×C₄×D₃	—	2	2	no	—
107	C₃²×C₈	C₂²⋊C₄	1	4	yes	complemented
108	C₃×C₃⋊C₈	—	2	2	no	—
109	C₂³×C₈	—	3	1	no	—
110	C₂×#106	—	3	1	no	—
111	C₂×#106	C₃×D₃	1	1	yes	characteristic, complemented
112	#380	—	3	2	no	—
113	#340	—	3	2	no	—
114	C₂⁴×C₃	—	3	1	no	—
115	C₂³×D₃	C₃×D₄	1	1	yes	characteristic
116	C₂²×C₃×C₄	—	2	2	no	—
117	C₂²×C₃×C₄	—	2	2	no	—
118	C₂²×C₃×C₄	—	2	1	no	—
119	C₂²×C₃×C₄	—	3	1	no	—
120	C₂²×C₃×C₄	—	3	2	no	—
121	C₂²×C₃×C₄	—	3	2	no	—
122	C₂²×C₃×C₄	—	4	2	no	—
123	C₂²×C₃×C₄	—	6	1	no	—
124	C₂²×C₃×C₄	—	6	1	no	—
125	C₂²×C₃×C₄	—	6	1	no	—
126	C₂²×C₃×C₄	—	6	1	no	—
127	C₂²×C₃×C₄	—	6	2	no	—
128	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
129	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
130	C₂²×Dic₃	—	2	2	no	—
131	C₂²×Dic₃	C₃×D₄	1	1	yes	characteristic
132	C₂×C₄×D₃	—	2	1	no	—
133	C₂×C₄×D₃	—	2	1	no	—
134	C₂×C₄×D₃	—	2	1	no	—
135	C₂×C₄×D₃	—	2	1	no	—
136	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
137	C₂×C₄×D₃	C₃×Q₈	1	2	yes	—
138	C₂×C₃×C₈	—	2	2	no	—
139	C₂×C₃×C₈	—	2	2	no	—
140	C₂×C₃×C₈	—	2	2	no	—
141	C₂×C₃×C₈	—	3	2	no	—
142	C₂×C₃×C₈	—	6	1	no	—
143	C₂×C₃×C₈	—	6	1	no	—
144	C₂×C₃×C₈	—	6	8	no	—
145	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
146	C₂×C₃×C₈	D₁₂	1	2	yes	—
147	C₂×C₃×C₈	#67	1	2	yes	—
148	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
149	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
150	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
151	C₃×C₄⋊C₄	—	2	4	no	—
152	C₃×C₄⋊C₄	—	2	2	no	—
153	C₃×C₄⋊C₄	—	2	2	no	—
154	C₃×C₄⋊C₄	—	2	2	no	—
155	C₃×C₄⋊C₄	—	2	2	no	—
156	C₃×C₄⋊C₄	—	4	2	no	—
157	C₃×C₄⋊C₄	—	6	2	no	—
158	C₃×C₄⋊C₄	—	6	2	no	—
159	C₃×C₂²⋊C₄	—	12	4	no	—
160	(C₂×D₃)⋊C₄	—	4	4	no	—
161	C₄⋊Dic₃	—	2	2	no	—
162	C₄⋊Dic₃	—	2	2	no	—
163	C₂×C₃⋊C₈	—	2	1	no	—
164	C₂×C₃⋊C₈	—	2	1	no	—
165	C₂×C₃⋊C₈	C₂×C₃×C₄	1	2	yes	—
166	D₃×C₈	—	2	8	no	—
167	C₂²×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂²×C₃²	#121	1	1	yes	characteristic
169	C₂²×C₃²	#121	1	1	yes	characteristic
170	C₂²×C₃²	C₂×SD₁₆	1	2	yes	—
171	C₂²×C₃²	#135	1	2	yes	—
172	C₂×C₃×D₃	—	2	2	no	—
173	C₂×C₃×D₃	—	2	2	no	—
174	C₂×C₃×D₃	—	2	4	no	—
175	C₂×C₃×D₃	—	2	4	no	—
176	C₂×C₃×D₃	#106	1	4	yes	complemented
177	C₃²×C₄	—	8	2	no	—
178	C₃²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₃²×C₄	#117	1	1	yes	characteristic
180	C₃²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
181	C₃²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
182	C₃×Dic₃	—	2	2	no	—
183	C₃×Dic₃	—	8	2	no	—
184	C₂³×C₄	—	3	1	no	—
185	C₂²×C₈	—	3	1	no	—
186	C₂²×C₈	—	3	4	no	—
187	C₂²×C₈	—	6	2	no	—
188	C₂²×C₈	—	6	2	no	—
189	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
190	C₂×C₄⋊C₄	—	3	2	no	—
191	C₂×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
192	C₂×C₂²⋊C₄	—	6	2	no	—
193	#106	—	2	2	no	—
194	#106	—	6	2	no	—
195	#95	—	6	2	no	—
196	C₂³×C₃	—	2	1	no	—
197	C₂³×C₃	—	3	2	no	—
198	C₂³×C₃	—	3	4	no	—
199	C₂³×C₃	—	6	1	no	—
200	C₂³×C₃	—	6	2	no	—
201	C₂³×C₃	—	6	1	no	—
202	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
203	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
204	C₂²×D₃	—	2	1	no	—
205	C₂²×D₃	—	2	1	no	—
206	C₂²×D₃	—	2	2	no	—
207	C₂²×D₃	C₃×C₄⋊C₄	1	2	yes	—
208	C₂²×D₃	C₃×SD₁₆	1	4	yes	—
209	C₂×C₃×C₄	—	2	1	no	—
210	C₂×C₃×C₄	—	2	1	no	—
211	C₂×C₃×C₄	—	2	1	no	—
212	C₂×C₃×C₄	—	2	1	no	—
213	C₂×C₃×C₄	—	2	1	no	—
214	C₂×C₃×C₄	—	2	1	no	—
215	C₂×C₃×C₄	—	3	2	no	—
216	C₂×C₃×C₄	—	4	4	no	—
217	C₂×C₃×C₄	—	4	2	no	—
218	C₂×C₃×C₄	—	4	2	no	—
219	C₂×C₃×C₄	—	4	2	no	—
220	C₂×C₃×C₄	—	4	2	no	—
221	C₂×C₃×C₄	—	4	2	no	—
222	C₂×C₃×C₄	—	4	2	no	—
223	C₂×C₃×C₄	—	6	1	no	—
224	C₂×C₃×C₄	—	6	1	no	—
225	C₂×C₃×C₄	—	6	2	no	—
226	C₂×C₃×C₄	—	6	2	no	—
227	C₂×C₃×C₄	—	6	2	no	—
228	C₂×C₃×C₄	—	6	2	no	—
229	C₂×C₃×C₄	—	8	2	no	—
230	C₂×C₃×C₄	—	8	2	no	—
231	C₂×C₃×C₄	—	12	2	no	—
232	C₂×C₃×C₄	—	12	2	no	—
233	C₂×C₃×C₄	—	12	2	no	—
234	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
235	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
236	C₂×C₃×C₄	#237	1	1	yes	characteristic
237	C₂×C₃×C₄	D₃×Q₈	1	1	yes	characteristic
238	C₂×C₃×C₄	#239	1	1	yes	characteristic
239	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
240	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
241	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
242	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
243	C₂×C₃×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
244	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
245	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
246	C₂×Dic₃	—	2	1	no	—
247	C₂×Dic₃	—	2	1	no	—
248	C₂×Dic₃	—	4	2	no	—
249	C₂×Dic₃	—	4	2	no	—
250	C₂×Dic₃	—	4	2	no	—
251	C₂×Dic₃	C₃×C₄⋊C₄	1	2	yes	—
252	C₄×D₃	—	2	2	no	—
253	C₄×D₃	—	2	2	no	—
254	C₄×D₃	—	2	2	no	—
255	C₄×D₃	—	2	2	no	—
256	C₃×C₈	—	2	4	no	—
257	C₃×C₈	—	6	2	no	—
258	C₃×C₈	(C₂×D₃)⋊C₄	1	4	yes	complemented
259	C₃×C₈	C₃×C₂²⋊C₄	1	4	yes	complemented
260	C₃⋊C₈	—	2	2	no	—
261	C₂×C₃²	#380	1	1	yes	characteristic
262	C₂×C₃²	C₂×#106	1	1	yes	characteristic
263	C₂×C₃²	#427	1	1	yes	characteristic
264	C₂×C₃²	#465	1	2	yes	—
265	C₂×C₃²	#465	1	2	yes	—
266	C₃×D₃	—	2	4	no	—
267	C₂⁴	—	3	1	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	3	1	no	—
270	C₂²×C₄	—	3	2	no	—
271	C₂²×C₄	—	3	2	no	—
272	C₂²×C₄	—	6	1	no	—
273	C₂²×C₄	—	6	1	no	—
274	C₂²×C₄	—	6	1	no	—
275	C₂²×C₄	—	6	1	no	—
276	C₂²×C₄	—	6	2	no	—
277	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
278	C₂×C₈	—	3	2	no	—
279	C₂×C₈	—	6	1	no	—
280	C₂×C₈	—	6	1	no	—
281	C₂×C₈	—	6	8	no	—
282	C₂×C₈	C₃×C₄×D₃	1	2	yes	—
283	C₂×C₈	C₃×D₁₂	1	2	yes	—
284	C₂×C₈	C₃×#67	1	2	yes	—
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	6	2	no	—
288	C₄⋊C₄	—	6	2	no	—
289	C₂²⋊C₄	—	12	4	no	—
290	C₂²×C₃	—	2	1	no	—
291	C₂²×C₃	—	2	1	no	—
292	C₂²×C₃	—	2	2	no	—
293	C₂²×C₃	—	2	2	no	—
294	C₂²×C₃	—	2	1	no	—
295	C₂²×C₃	—	3	4	no	—
296	C₂²×C₃	—	6	4	no	—
297	C₂²×C₃	—	6	4	no	—
298	C₂²×C₃	—	6	2	no	—
299	C₂²×C₃	—	6	2	no	—
300	C₂²×C₃	D₃×C₄⋊C₄	1	1	yes	characteristic
301	C₂²×C₃	#895	1	1	yes	characteristic
302	C₂²×C₃	D₃×SD₁₆	1	2	yes	—
303	C₂²×C₃	#916	1	2	yes	—
304	C₂²×C₃	#938	1	1	yes	characteristic
305	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
306	C₂²×C₃	C₃×#121	1	1	yes	characteristic
307	C₂²×C₃	C₃×#121	1	1	yes	characteristic
308	C₂²×C₃	C₂×C₃×SD₁₆	1	2	yes	—
309	C₂²×C₃	C₃×#135	1	2	yes	—
310	C₂×D₃	—	2	2	no	—
311	C₂×D₃	—	2	2	no	—
312	C₂×D₃	—	2	4	no	—
313	C₂×D₃	—	2	4	no	—
314	C₂×D₃	C₃×#106	1	4	yes	complemented
315	C₃×C₄	—	2	1	no	—
316	C₃×C₄	—	2	1	no	—
317	C₃×C₄	—	2	1	no	—
318	C₃×C₄	—	2	1	no	—
319	C₃×C₄	—	6	2	no	—
320	C₃×C₄	—	8	4	no	—
321	C₃×C₄	—	8	2	no	—
322	C₃×C₄	—	8	2	no	—
323	C₃×C₄	—	24	2	no	—
324	C₃×C₄	#892	1	1	yes	characteristic
325	C₃×C₄	#897	1	1	yes	characteristic
326	C₃×C₄	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
327	C₃×C₄	#946	1	1	yes	characteristic
328	C₃×C₄	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
329	C₃×C₄	C₃×#117	1	1	yes	characteristic
330	C₃×C₄	C₃×C₂²⋊Q₈	1	1	yes	characteristic
331	C₃×C₄	C₃×C₂²⋊Q₈	1	1	yes	characteristic
332	Dic₃	—	2	2	no	—
333	Dic₃	—	8	2	no	—
334	C₃²	#1807	1	1	yes	characteristic, complemented, Sylow
335	C₂³	—	3	2	no	—
336	C₂³	—	3	4	no	—
337	C₂³	—	6	1	no	—
338	C₂³	—	6	2	no	—
339	C₂³	—	6	1	no	—
340	C₂³	C₃×D₃×D₄	1	1	yes	characteristic
341	C₂×C₄	—	3	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	6	1	no	—
346	C₂×C₄	—	6	1	no	—
347	C₂×C₄	—	6	2	no	—
348	C₂×C₄	—	6	2	no	—
349	C₂×C₄	—	6	2	no	—
350	C₂×C₄	—	6	2	no	—
351	C₂×C₄	—	12	2	no	—
352	C₂×C₄	—	12	2	no	—
353	C₂×C₄	—	12	2	no	—
354	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
355	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
356	C₂×C₄	C₃×#237	1	1	yes	characteristic
357	C₂×C₄	C₃×D₃×Q₈	1	1	yes	characteristic
358	C₂×C₄	C₃×#239	1	1	yes	characteristic
359	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
360	C₈	—	6	2	no	—
361	C₈	C₃×(C₂×D₃)⋊C₄	1	4	yes	complemented
362	C₂×C₃	—	2	2	no	—
363	C₂×C₃	—	2	1	no	—
364	C₂×C₃	—	2	1	no	—
365	C₂×C₃	—	2	1	no	—
366	C₂×C₃	—	2	2	no	—
367	C₂×C₃	—	6	4	no	—
368	C₂×C₃	D₃×#106	1	1	yes	characteristic
369	C₂×C₃	#4860	1	1	yes	characteristic
370	C₂×C₃	#4864	1	2	yes	—
371	C₂×C₃	#4987	1	1	yes	characteristic
372	C₂×C₃	#5171	1	2	yes	—
373	C₂×C₃	C₃×#380	1	1	yes	characteristic
374	C₂×C₃	C₂×C₃×#106	1	1	yes	characteristic
375	C₂×C₃	C₃×#427	1	1	yes	characteristic
376	C₂×C₃	C₃×#465	1	2	yes	—
377	C₂×C₃	C₃×#465	1	2	yes	—
378	D₃	—	2	4	no	—
379	C₂²	—	3	4	no	—
380	C₂²	—	6	4	no	—
381	C₂²	—	6	2	no	—
382	C₂²	—	6	2	no	—
383	C₂²	—	6	4	no	—
384	C₂²	C₃×D₃×C₄⋊C₄	1	1	yes	characteristic
385	C₂²	C₃×#895	1	1	yes	characteristic
386	C₂²	C₃×D₃×SD₁₆	1	2	yes	—
387	C₂²	C₃×#916	1	2	yes	—
388	C₂²	C₃×#938	1	1	yes	characteristic
389	C₄	—	6	2	no	—
390	C₄	—	8	2	no	—
391	C₄	—	24	2	no	—
392	C₄	C₃×#892	1	1	yes	characteristic
393	C₄	C₃×#897	1	1	yes	characteristic
394	C₄	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
395	C₄	C₃×#946	1	1	yes	characteristic
396	C₃	—	2	1	no	—
397	C₃	#70577	1	1	yes	characteristic, direct product factor
398	C₃	C₃×#1807	1	1	yes	characteristic, complemented
399	C₂	—	6	4	no	—
400	C₂	C₃×D₃×#106	1	1	yes	characteristic
401	C₂	C₃×#4860	1	1	yes	characteristic
402	C₂	C₃×#4864	1	2	yes	—
403	C₂	C₃×#4987	1	1	yes	characteristic
404	C₂	C₃×#5171	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	D₃×D₄
commutator	C₂×C₃×C₄	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₂×C₃²×#106	C₂
socle	C₂³×C₃²	C₂×D₄
prime radical	C₂³×C₃×D₃	D₄
cosocle	C₂²×C₃×C₄	C₂³×C₃
hypercenter	C₂×C₃×#106	D₃
hypocenter	C₃	C₃×#1807
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#106

Complements

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

N	H ≅ G/N	type
2. C₂×C₃²×#106	C₂	semidirect
3. C₂×C₃×#817	C₂	semidirect
5. C₃×#4529	C₂	semidirect
7. #70577	C₃	direct (N × H)
16. C₂×C₃×D₃×C₈	C₄	semidirect
24. C₂×C₃×#106	D₃	semidirect
25. C₂×C₃×#106	C₂×C₃	semidirect
27. C₂×#817	C₂×C₃	semidirect
30. #4529	C₂×C₃	semidirect
74. C₂×D₃×C₈	C₃×C₄	semidirect
107. C₃²×C₈	C₂²⋊C₄	semidirect
111. C₂×#106	C₃×D₃	semidirect
176. C₂×C₃×D₃	#106	semidirect
258. C₃×C₈	(C₂×D₃)⋊C₄	semidirect
259. C₃×C₈	C₃×C₂²⋊C₄	semidirect
314. C₂×D₃	C₃×#106	semidirect
334. C₃²	#1807	semidirect
361. C₈	C₃×(C₂×D₃)⋊C₄	semidirect
397. C₃	#70577	direct (N × H)
398. C₃	C₃×#1807	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×D₃×C₈	2
C₂×C₃²×#106	2
C₂×C₃×#817	2
C₃×#4987	2
C₃×#4529	2
C₃×#1807	3
#70577	3

Subgroups — C3×#70577 #11785338

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#70577 #11785338