Subgroups — C₃×#3563 #87447

Order 384.

912 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#564	C₂	1	2	yes	maximal, complemented
2	C₃×#563	C₂	1	2	yes	maximal, complemented
3	C₃×#557	C₂	1	2	yes	maximal, complemented
4	C₃×#554	C₂	1	2	yes	maximal, complemented
5	C₃×#552	C₂	1	4	yes	maximal, complemented
6	C₃×#552	C₂	1	2	yes	maximal, complemented
7	C₃×#552	C₂	1	2	yes	maximal, complemented
8	C₃×#544	C₂	1	2	yes	maximal, complemented
9	C₃×#544	C₂	1	2	yes	maximal, complemented
10	C₃×#541	C₂	1	2	yes	maximal, complemented
11	C₃×#541	C₂	1	4	yes	maximal, complemented
12	C₃×#539	C₂	1	2	yes	maximal
13	C₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#529	C₂	1	1	yes	maximal, characteristic
15	C₂×C₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
16	#3563	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₃×C₄⋊Q₈	C₂²	1	4	yes	—
18	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₃×C₄⋊Q₈	C₂²	1	4	yes	—
21	C₃×C₄⋊Q₈	C₂²	1	2	yes	—
22	C₃×#126	C₂²	1	4	yes	—
23	C₃×#126	C₂²	1	4	yes	—
24	C₃×#126	C₂²	1	2	yes	—
25	C₃×#126	C₂²	1	4	yes	—
26	C₃×#126	C₂²	1	4	yes	—
27	C₃×#125	C₂²	1	2	yes	—
28	C₃×#125	C₂²	1	2	yes	—
29	C₃×#125	C₂²	1	1	yes	characteristic
30	C₃×#125	C₂²	1	4	yes	—
31	C₃×#125	C₂²	1	4	yes	—
32	C₃×#125	C₂²	1	4	yes	—
33	C₃×#125	C₂²	1	4	yes	—
34	C₃×#125	C₂²	1	4	yes	—
35	C₃×#125	C₂²	1	4	yes	—
36	C₃×#125	C₂²	1	2	yes	—
37	C₃×#125	C₂²	1	2	yes	—
38	C₃×#125	C₂²	1	2	yes	—
39	C₃×#125	C₂²	1	4	yes	—
40	C₃×#125	C₂²	1	4	yes	—
41	C₃×#125	C₂²	1	2	yes	—
42	C₃×#124	C₂²	1	1	yes	characteristic
43	C₃×#123	C₂²	1	4	yes	—
44	C₃×#123	C₂²	1	2	yes	—
45	C₃×#123	C₂²	1	4	yes	—
46	C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
47	C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
48	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
49	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
50	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
51	C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
52	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
53	C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
54	C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
55	C₃×#121	C₂²	1	1	yes	characteristic
56	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
57	C₃×C₄×Q₈	C₂²	1	2	yes	—
58	C₃×C₄×Q₈	C₂²	1	2	yes	—
59	C₃×C₄×Q₈	C₂²	1	4	yes	—
60	C₃×C₄×Q₈	C₂²	1	2	yes	—
61	C₃×C₄×Q₈	C₂²	1	2	yes	—
62	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
63	C₃×C₄×D₄	C₂²	1	2	yes	—
64	C₃×C₄×D₄	C₂²	1	4	yes	—
65	C₃×#117	C₂²	1	2	yes	—
66	C₃×#117	C₂²	1	2	yes	—
67	C₃×#117	C₂²	1	4	yes	—
68	C₃×#117	C₂²	1	2	yes	—
69	C₃×#117	C₂²	1	4	yes	—
70	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	—
71	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
72	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	—
73	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
74	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	—
75	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
76	#564	C₂×C₃	1	2	yes	complemented
77	#563	C₂×C₃	1	2	yes	complemented
78	#557	C₂×C₃	1	2	yes	complemented
79	#554	C₂×C₃	1	2	yes	complemented
80	#552	C₂×C₃	1	4	yes	complemented
81	#552	C₂×C₃	1	2	yes	complemented
82	#552	C₂×C₃	1	2	yes	complemented
83	#544	C₂×C₃	1	2	yes	complemented
84	#544	C₂×C₃	1	2	yes	complemented
85	#541	C₂×C₃	1	2	yes	complemented
86	#541	C₂×C₃	1	4	yes	complemented
87	#539	C₂×C₃	1	2	yes	—
88	#533	C₂×C₃	1	1	yes	characteristic, complemented
89	#529	C₂×C₃	1	1	yes	characteristic
90	C₂×#125	C₂×C₃	1	1	yes	characteristic, complemented
91	C₂×C₃×Q₈	C₂³	1	2	yes	—
92	C₂×C₃×Q₈	C₂³	1	4	yes	—
93	C₂×C₃×Q₈	C₂³	1	2	yes	—
94	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
95	C₂×C₃×D₄	C₂³	1	2	yes	—
96	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
97	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
98	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
99	C₂²×C₃×C₄	C₂³	1	2	yes	—
100	C₂²×C₃×C₄	C₂³	1	2	yes	—
101	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
102	C₂²×C₃×C₄	C₂³	1	2	yes	—
103	C₂²×C₃×C₄	C₂³	1	4	yes	—
104	C₃×C₄⋊C₄	C₂³	1	2	yes	—
105	C₃×C₄⋊C₄	C₂³	1	2	yes	—
106	C₃×C₄⋊C₄	C₂³	1	2	yes	—
107	C₃×C₄⋊C₄	C₂³	1	4	yes	—
108	C₃×C₄⋊C₄	C₂³	1	2	yes	—
109	C₃×C₄⋊C₄	C₂³	1	4	yes	—
110	C₃×C₄⋊C₄	C₂³	1	4	yes	—
111	C₃×C₄⋊C₄	C₂³	1	4	yes	—
112	C₃×C₄⋊C₄	C₂³	1	4	yes	—
113	C₃×C₄⋊C₄	C₂³	1	2	yes	—
114	C₃×C₄⋊C₄	C₂³	1	4	yes	—
115	C₃×C₄⋊C₄	C₂³	1	2	yes	—
116	C₃×C₄⋊C₄	C₂³	1	4	yes	—
117	C₃×C₄⋊C₄	C₂³	1	2	yes	—
118	C₃×C₄⋊C₄	C₂³	1	4	yes	—
119	C₃×C₄⋊C₄	C₂³	1	2	yes	—
120	C₃×C₄⋊C₄	C₂³	1	2	yes	—
121	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
122	C₃×C₄⋊C₄	C₂³	1	4	yes	—
123	C₃×C₄⋊C₄	C₂³	1	2	yes	—
124	C₃×C₄⋊C₄	C₂³	1	2	yes	—
125	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
126	C₃×C₄⋊C₄	C₂³	1	4	yes	—
127	C₃×C₄⋊C₄	C₂³	1	4	yes	—
128	C₃×C₄⋊C₄	C₂³	1	4	yes	—
129	C₃×C₄⋊C₄	C₂³	1	4	yes	—
130	C₃×C₄⋊C₄	C₂³	1	2	yes	—
131	C₃×C₄⋊C₄	C₂³	1	4	yes	—
132	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
133	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
134	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
135	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
136	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
137	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
138	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
139	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
141	C₃×C₄²	C₂³	1	1	yes	characteristic
142	C₃×C₄²	C₂³	1	1	yes	characteristic
143	C₃×C₄²	C₂³	1	1	yes	characteristic
144	C₃×C₄²	C₂³	1	1	yes	characteristic
145	C₃×C₄²	C₂³	1	4	yes	—
146	C₃×C₄²	C₂³	1	4	yes	—
147	C₃×C₄²	C₂³	1	2	yes	—
148	C₃×C₄²	C₂³	1	4	yes	—
149	C₃×C₄²	C₂³	1	4	yes	—
150	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
151	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
152	C₄⋊Q₈	C₂²×C₃	1	4	yes	—
153	C₄⋊Q₈	C₂²×C₃	1	2	yes	—
154	C₄⋊Q₈	C₂²×C₃	1	4	yes	—
155	#126	C₂²×C₃	1	2	yes	—
156	#126	C₂²×C₃	1	4	yes	—
157	#126	C₂²×C₃	1	4	yes	—
158	#126	C₂²×C₃	1	4	yes	—
159	#126	C₂²×C₃	1	4	yes	—
160	#125	C₂²×C₃	1	2	yes	—
161	#125	C₂²×C₃	1	2	yes	—
162	#125	C₂²×C₃	1	2	yes	—
163	#125	C₂²×C₃	1	2	yes	—
164	#125	C₂²×C₃	1	1	yes	characteristic
165	#125	C₂²×C₃	1	2	yes	—
166	#125	C₂²×C₃	1	4	yes	—
167	#125	C₂²×C₃	1	4	yes	—
168	#125	C₂²×C₃	1	4	yes	—
169	#125	C₂²×C₃	1	4	yes	—
170	#125	C₂²×C₃	1	4	yes	—
171	#125	C₂²×C₃	1	4	yes	—
172	#125	C₂²×C₃	1	2	yes	—
173	#125	C₂²×C₃	1	4	yes	—
174	#125	C₂²×C₃	1	4	yes	—
175	#124	C₂²×C₃	1	1	yes	characteristic
176	#123	C₂²×C₃	1	2	yes	—
177	#123	C₂²×C₃	1	4	yes	—
178	#123	C₂²×C₃	1	4	yes	—
179	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
180	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
181	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
182	C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
183	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
184	C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
185	C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
186	C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
187	C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
188	#121	C₂²×C₃	1	1	yes	characteristic
189	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
190	C₄×Q₈	C₂²×C₃	1	2	yes	—
191	C₄×Q₈	C₂²×C₃	1	2	yes	—
192	C₄×Q₈	C₂²×C₃	1	4	yes	—
193	C₄×Q₈	C₂²×C₃	1	2	yes	—
194	C₄×Q₈	C₂²×C₃	1	2	yes	—
195	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
196	C₄×D₄	C₂²×C₃	1	2	yes	—
197	C₄×D₄	C₂²×C₃	1	4	yes	—
198	#117	C₂²×C₃	1	2	yes	—
199	#117	C₂²×C₃	1	2	yes	—
200	#117	C₂²×C₃	1	4	yes	—
201	#117	C₂²×C₃	1	2	yes	—
202	#117	C₂²×C₃	1	4	yes	—
203	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	—
204	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
205	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	—
206	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
207	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	—
208	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
209	C₂³×C₃	C₂⁴	1	2	yes	—
210	C₂³×C₃	C₂⁴	1	1	yes	characteristic
211	C₃×Q₈	—	2	4	no	—
212	C₃×Q₈	—	4	4	no	—
213	C₃×Q₈	—	4	1	no	—
214	C₃×Q₈	—	4	2	no	—
215	C₃×D₄	—	2	4	no	—
216	C₃×D₄	—	4	1	no	—
217	C₂×C₃×C₄	—	2	2	no	—
218	C₂×C₃×C₄	—	2	4	no	—
219	C₂×C₃×C₄	—	2	2	no	—
220	C₂×C₃×C₄	—	2	4	no	—
221	C₂×C₃×C₄	—	4	2	no	—
222	C₂×C₃×C₄	—	4	4	no	—
223	C₂×C₃×C₄	—	4	1	no	—
224	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
225	C₂×C₃×C₄	C₂⁴	1	4	yes	—
226	C₂×C₃×C₄	C₂⁴	1	2	yes	—
227	C₂×C₃×C₄	C₂⁴	1	2	yes	—
228	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
229	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
230	C₂×C₃×C₄	C₂⁴	1	2	yes	—
231	C₂×C₃×C₄	C₂⁴	1	4	yes	—
232	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
233	C₂×C₃×C₄	C₂⁴	1	4	yes	—
234	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
235	C₂×C₃×C₄	C₂⁴	1	4	yes	—
236	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
237	C₂×Q₈	C₂³×C₃	1	2	yes	—
238	C₂×Q₈	C₂³×C₃	1	4	yes	—
239	C₂×Q₈	C₂³×C₃	1	2	yes	—
240	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
241	C₂×D₄	C₂³×C₃	1	2	yes	—
242	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
243	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
244	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
245	C₂²×C₄	C₂³×C₃	1	2	yes	—
246	C₂²×C₄	C₂³×C₃	1	2	yes	—
247	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
248	C₂²×C₄	C₂³×C₃	1	2	yes	—
249	C₂²×C₄	C₂³×C₃	1	4	yes	—
250	C₄⋊C₄	C₂³×C₃	1	2	yes	—
251	C₄⋊C₄	C₂³×C₃	1	2	yes	—
252	C₄⋊C₄	C₂³×C₃	1	2	yes	—
253	C₄⋊C₄	C₂³×C₃	1	4	yes	—
254	C₄⋊C₄	C₂³×C₃	1	2	yes	—
255	C₄⋊C₄	C₂³×C₃	1	4	yes	—
256	C₄⋊C₄	C₂³×C₃	1	4	yes	—
257	C₄⋊C₄	C₂³×C₃	1	4	yes	—
258	C₄⋊C₄	C₂³×C₃	1	4	yes	—
259	C₄⋊C₄	C₂³×C₃	1	2	yes	—
260	C₄⋊C₄	C₂³×C₃	1	4	yes	—
261	C₄⋊C₄	C₂³×C₃	1	2	yes	—
262	C₄⋊C₄	C₂³×C₃	1	4	yes	—
263	C₄⋊C₄	C₂³×C₃	1	2	yes	—
264	C₄⋊C₄	C₂³×C₃	1	4	yes	—
265	C₄⋊C₄	C₂³×C₃	1	2	yes	—
266	C₄⋊C₄	C₂³×C₃	1	2	yes	—
267	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
268	C₄⋊C₄	C₂³×C₃	1	4	yes	—
269	C₄⋊C₄	C₂³×C₃	1	2	yes	—
270	C₄⋊C₄	C₂³×C₃	1	2	yes	—
271	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
272	C₄⋊C₄	C₂³×C₃	1	4	yes	—
273	C₄⋊C₄	C₂³×C₃	1	4	yes	—
274	C₄⋊C₄	C₂³×C₃	1	4	yes	—
275	C₄⋊C₄	C₂³×C₃	1	4	yes	—
276	C₄⋊C₄	C₂³×C₃	1	2	yes	—
277	C₄⋊C₄	C₂³×C₃	1	4	yes	—
278	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
279	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
280	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
281	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
282	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
283	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
284	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
285	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
286	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
287	C₄²	C₂³×C₃	1	1	yes	characteristic
288	C₄²	C₂³×C₃	1	1	yes	characteristic
289	C₄²	C₂³×C₃	1	1	yes	characteristic
290	C₄²	C₂³×C₃	1	1	yes	characteristic
291	C₄²	C₂³×C₃	1	4	yes	—
292	C₄²	C₂³×C₃	1	4	yes	—
293	C₄²	C₂³×C₃	1	2	yes	—
294	C₄²	C₂³×C₃	1	4	yes	—
295	C₄²	C₂³×C₃	1	4	yes	—
296	C₂²×C₃	—	2	1	no	—
297	C₂²×C₃	—	2	1	no	—
298	C₂²×C₃	—	2	2	no	—
299	C₂²×C₃	—	2	2	no	—
300	C₂²×C₃	—	2	2	no	—
301	C₂²×C₃	2₋¹⁺⁴	1	2	yes	—
302	C₂²×C₃	C₂⁵	1	1	yes	characteristic
303	C₃×C₄	—	2	1	no	—
304	C₃×C₄	—	2	1	no	—
305	C₃×C₄	—	2	4	no	—
306	C₃×C₄	—	2	1	no	—
307	C₃×C₄	—	2	2	no	—
308	C₃×C₄	—	2	2	no	—
309	C₃×C₄	—	2	4	no	—
310	C₃×C₄	—	2	4	no	—
311	C₃×C₄	—	2	1	no	—
312	C₃×C₄	—	2	4	no	—
313	C₃×C₄	—	2	1	no	—
314	C₃×C₄	—	2	2	no	—
315	C₃×C₄	2₋¹⁺⁴	1	2	yes	—
316	C₂³	C₂⁴×C₃	1	2	yes	—
317	C₂³	C₂⁴×C₃	1	1	yes	characteristic
318	Q₈	—	2	4	no	—
319	Q₈	—	4	4	no	—
320	Q₈	—	4	1	no	—
321	Q₈	—	4	2	no	—
322	D₄	—	2	4	no	—
323	D₄	—	4	1	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
332	C₂×C₄	C₂⁴×C₃	1	4	yes	—
333	C₂×C₄	C₂⁴×C₃	1	2	yes	—
334	C₂×C₄	C₂⁴×C₃	1	2	yes	—
335	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
336	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
337	C₂×C₄	C₂⁴×C₃	1	2	yes	—
338	C₂×C₄	C₂⁴×C₃	1	4	yes	—
339	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
340	C₂×C₄	C₂⁴×C₃	1	4	yes	—
341	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
342	C₂×C₄	C₂⁴×C₃	1	4	yes	—
343	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
344	C₂×C₃	—	2	2	no	—
345	C₂×C₃	—	4	2	no	—
346	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
347	C₂×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
348	C₂×C₃	#585	1	1	yes	characteristic
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	2	no	—
354	C₂²	C₃×2₋¹⁺⁴	1	2	yes	—
355	C₂²	C₂⁵×C₃	1	1	yes	characteristic
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	4	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	2	no	—
361	C₄	—	2	2	no	—
362	C₄	—	2	4	no	—
363	C₄	—	2	4	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	4	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	2	no	—
368	C₄	C₃×2₋¹⁺⁴	1	2	yes	—
369	C₃	#3563	1	1	yes	characteristic, direct product factor, Sylow
370	C₂	—	2	2	no	—
371	C₂	—	4	2	no	—
372	C₂	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
373	C₂	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
374	C₂	C₃×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃
prime radical	C₃×#121	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#564	C₂	semidirect
2. C₃×#563	C₂	semidirect
3. C₃×#557	C₂	semidirect
4. C₃×#554	C₂	semidirect
5. C₃×#552	C₂	semidirect
6. C₃×#552	C₂	semidirect
7. C₃×#552	C₂	semidirect
8. C₃×#544	C₂	semidirect
9. C₃×#544	C₂	semidirect
10. C₃×#541	C₂	semidirect
11. C₃×#541	C₂	semidirect
13. C₃×#533	C₂	semidirect
15. C₂×C₃×#125	C₂	semidirect
16. #3563	C₃	direct (N × H)
76. #564	C₂×C₃	semidirect
77. #563	C₂×C₃	semidirect
78. #557	C₂×C₃	semidirect
79. #554	C₂×C₃	semidirect
80. #552	C₂×C₃	semidirect
81. #552	C₂×C₃	semidirect
82. #552	C₂×C₃	semidirect
83. #544	C₂×C₃	semidirect
84. #544	C₂×C₃	semidirect
85. #541	C₂×C₃	semidirect
86. #541	C₂×C₃	semidirect
88. #533	C₂×C₃	semidirect
90. C₂×#125	C₂×C₃	semidirect
369. C₃	#3563	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#564	2
C₃×#563	2
C₃×#557	2
C₃×#554	2
C₃×#552	2
C₃×#544	2
C₃×#541	2
C₃×#539	2
C₃×#533	2
C₃×#529	2
C₂×C₃×#125	2
#3563	3

Subgroups — C3×#3563 #87447

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3563 #87447