Subgroups — C₃×#10595993 #13179276

Order 1728.

2164 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#3828	C₂	1	1	yes	maximal, characteristic
2	C₃³×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64102	C₂	1	2	yes	maximal, complemented
5	C₃×#64096	C₂	1	2	yes	maximal, complemented
6	C₃×#64090	C₂	1	4	yes	maximal, complemented
7	C₃×#64081	C₂	1	2	yes	maximal, complemented
8	C₃×C₄²×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
9	#10595993	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₃×#5522	—	3	4	no	maximal
11	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
12	C₂×C₃×#638	C₂²	1	2	yes	—
13	C₂²×C₃×C₃⋊Dic₃	C₂²	1	2	yes	—
14	C₃×#3828	C₄	1	8	yes	complemented
15	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	4	yes	—
17	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	2	yes	—
18	C₂×C₃×#634	C₂²	1	1	yes	characteristic
19	C₃³×C₄⋊C₄	C₂²	1	2	yes	—
20	C₃³×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₃³×C₄²	C₂²	1	2	yes	—
22	C₃×#3752	C₂²	1	4	yes	—
23	C₃×#3750	C₂²	1	4	yes	—
24	C₃×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
25	C₃×C₄×C₃⋊Dic₃	C₂²	1	4	yes	—
26	C₃×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
27	C₃×C₄×C₃⋊Dic₃	C₂²	1	2	yes	—
28	C₂×#3828	C₂×C₃	1	1	yes	characteristic
29	C₂×C₃×#235	—	3	4	no	—
30	C₃²×#117	—	2	4	no	—
31	C₃²×#117	D₃	1	4	yes	complemented
32	C₃²×#117	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×C₄×C₃⋊Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
34	#64102	C₂×C₃	1	2	yes	complemented
35	#64096	C₂×C₃	1	2	yes	complemented
36	#64090	C₂×C₃	1	4	yes	complemented
37	#64081	C₂×C₃	1	2	yes	complemented
38	C₄²×C₃⋊D₃	C₂×C₃	1	2	yes	complemented
39	C₂×C₃×C₄×Dic₃	—	3	4	no	—
40	C₃×#893	—	3	8	no	—
41	C₃×#887	—	3	8	no	—
42	C₃×#67⋊C₄	—	3	16	no	—
43	C₃×#872	—	3	8	no	—
44	C₃×C₄²×D₃	—	3	8	no	—
45	C₂³×C₃³	C₂³	1	1	yes	characteristic
46	C₂²×C₃×C₃⋊D₃	C₂³	1	2	yes	—
47	C₂×C₃³×C₄	C₂×C₄	1	4	yes	complemented
48	C₂×C₃³×C₄	C₂³	1	4	yes	—
49	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
50	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
51	C₃×#638	C₂×C₄	1	8	yes	complemented
52	C₂×C₃×C₃⋊Dic₃	—	2	4	no	—
53	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
54	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
55	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
56	C₃×C₄⋊(C₃⋊D₃)	C₂×C₄	1	4	yes	complemented
57	C₃×C₄×C₃⋊D₃	—	2	8	no	—
58	C₃×C₄×C₃⋊D₃	C₂×C₄	1	8	yes	complemented
59	C₃×#634	C₂×C₄	1	4	yes	complemented
60	C₃×C₄×#41	—	9	1	no	—
61	#5522	—	3	4	no	—
62	C₂²×C₃²×C₄	—	2	4	no	—
63	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
64	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
65	C₂×#638	C₂²×C₃	1	2	yes	—
66	C₂²×C₃⋊Dic₃	C₂²×C₃	1	2	yes	—
67	#3828	C₃×C₄	1	8	yes	complemented
68	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic
69	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	4	yes	—
70	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	2	yes	—
71	C₂×#634	C₂²×C₃	1	1	yes	characteristic
72	C₂×C₃×#67	—	3	8	no	—
73	C₂²×C₃×Dic₃	—	3	8	no	—
74	C₃×#235	—	3	32	no	—
75	C₂×C₃×D₁₂	—	3	4	no	—
76	C₂×C₃×C₄×D₃	—	3	8	no	—
77	C₂×C₃×C₄×D₃	—	3	16	no	—
78	C₂×C₃×Dic₆	—	3	4	no	—
79	C₃²×C₄⋊C₄	—	2	8	no	—
80	C₃²×C₄⋊C₄	C₂×D₃	1	8	yes	—
81	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
82	C₃²×C₂²⋊C₄	—	2	8	no	—
83	C₃²×C₂²⋊C₄	C₂×D₃	1	8	yes	—
84	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
85	C₃²×C₄²	—	2	8	no	—
86	C₃²×C₄²	C₂×D₃	1	8	yes	—
87	C₃²×C₄²	C₂²×C₃	1	2	yes	—
88	#3752	C₂²×C₃	1	4	yes	—
89	#3750	C₂²×C₃	1	4	yes	—
90	C₄×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
91	C₄×C₃⋊Dic₃	C₂²×C₃	1	4	yes	—
92	C₄×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
93	C₄×C₃⋊Dic₃	C₂²×C₃	1	2	yes	—
94	C₃×(C₂×D₃)⋊C₄	—	3	16	no	—
95	C₃×Dic₃⋊C₄	—	3	16	no	—
96	C₃×C₄×Dic₃	—	3	16	no	—
97	C₃×C₄×Dic₃	—	3	8	no	—
98	C₃×C₄×Dic₃	—	3	4	no	—
99	C₃×C₄×Dic₃	—	3	4	no	—
100	C₂²×C₃³	—	2	2	no	—
101	C₂²×C₃³	C₂²×C₄	1	2	yes	—
102	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
103	C₂×C₃×C₃⋊D₃	—	2	4	no	—
104	C₂×C₃×C₃⋊D₃	C₂²×C₄	1	4	yes	—
105	C₃³×C₄	—	2	4	no	—
106	C₃³×C₄	C₂²×C₄	1	2	yes	—
107	C₃³×C₄	C₂²×C₄	1	2	yes	—
108	C₃×C₃⋊Dic₃	—	2	2	no	—
109	C₃×C₃⋊Dic₃	C₂²×C₄	1	4	yes	—
110	C₃×C₃⋊Dic₃	#41	1	4	yes	complemented
111	C₂×C₃×#41	—	9	1	no	—
112	C₂×#235	—	3	4	no	—
113	C₃×C₄×Q₈	—	9	2	no	—
114	C₃×C₄×D₄	—	9	2	no	—
115	C₃×C₄×D₄	—	9	4	no	—
116	C₃×#117	—	2	4	no	—
117	C₃×#117	—	9	2	no	—
118	C₃×#117	C₃×D₃	1	4	yes	complemented
119	C₃×#117	C₃⋊D₃	1	1	yes	characteristic, complemented
120	C₂×C₃×C₄²	—	9	1	no	—
121	C₂×C₃×C₄²	—	9	2	no	—
122	C₂×C₄×Dic₃	—	3	4	no	—
123	#893	—	3	8	no	—
124	#887	—	3	8	no	—
125	#67⋊C₄	—	3	16	no	—
126	#872	—	3	8	no	—
127	C₄²×D₃	—	3	8	no	—
128	C₂³×C₃²	—	2	4	no	—
129	C₂³×C₃²	C₂²×D₃	1	4	yes	—
130	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
131	C₂²×C₃⋊D₃	C₂³×C₃	1	2	yes	—
132	C₂²×C₃×D₃	—	3	8	no	—
133	C₂×C₃²×C₄	—	2	16	no	—
134	C₂×C₃²×C₄	—	2	4	no	—
135	C₂×C₃²×C₄	—	2	4	no	—
136	C₂×C₃²×C₄	—	2	16	no	—
137	C₂×C₃²×C₄	C₄×D₃	1	16	yes	complemented
138	C₂×C₃²×C₄	C₂×C₃×C₄	1	4	yes	complemented
139	C₂×C₃²×C₄	C₂²×D₃	1	16	yes	—
140	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
141	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
142	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
143	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
144	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
145	#638	C₂×C₃×C₄	1	8	yes	complemented
146	C₂×C₃⋊Dic₃	—	2	4	no	—
147	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
148	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
149	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
150	C₄⋊(C₃⋊D₃)	C₂×C₃×C₄	1	4	yes	complemented
151	C₄×C₃⋊D₃	—	2	8	no	—
152	C₄×C₃⋊D₃	C₂×C₃×C₄	1	8	yes	complemented
153	#634	C₂×C₃×C₄	1	4	yes	complemented
154	C₃×#67	—	3	32	no	—
155	C₂×C₃×Dic₃	—	3	8	no	—
156	C₂×C₃×Dic₃	—	3	8	no	—
157	C₂×C₃×Dic₃	—	3	8	no	—
158	C₂×C₃×Dic₃	—	6	16	no	—
159	C₃×D₁₂	—	3	16	no	—
160	C₃×C₄×D₃	—	3	32	no	—
161	C₃×C₄×D₃	—	6	32	no	—
162	C₃×Dic₆	—	3	16	no	—
163	C₄×#41	—	9	1	no	Sylow
164	C₂×C₃³	—	2	2	no	—
165	C₂×C₃³	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₃³	C₂×#41	1	2	yes	—
167	C₃×C₃⋊D₃	—	2	4	no	—
168	C₃×#41	—	9	8	no	—
169	C₂×C₃×Q₈	—	9	1	no	—
170	C₂×C₃×D₄	—	9	2	no	—
171	C₂×C₃×D₄	—	9	1	no	—
172	C₂²×C₃×C₄	—	2	4	no	—
173	C₂²×C₃×C₄	—	9	2	no	—
174	C₂²×C₃×C₄	—	9	2	no	—
175	C₂²×C₃×C₄	—	9	4	no	—
176	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
177	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
178	C₂×#67	—	3	8	no	—
179	C₂²×Dic₃	—	3	8	no	—
180	#235	—	3	32	no	—
181	C₂×D₁₂	—	3	4	no	—
182	C₂×C₄×D₃	—	3	8	no	—
183	C₂×C₄×D₃	—	3	16	no	—
184	C₂×Dic₆	—	3	4	no	—
185	C₃×C₄⋊C₄	—	2	8	no	—
186	C₃×C₄⋊C₄	—	9	4	no	—
187	C₃×C₄⋊C₄	C₂×C₃×D₃	1	8	yes	—
188	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	2	yes	—
189	C₃×C₂²⋊C₄	—	2	8	no	—
190	C₃×C₂²⋊C₄	—	9	4	no	—
191	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	8	yes	—
192	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	2	yes	—
193	C₃×C₄²	—	2	8	no	—
194	C₃×C₄²	—	9	4	no	—
195	C₃×C₄²	—	9	2	no	—
196	C₃×C₄²	—	9	1	no	—
197	C₃×C₄²	—	9	1	no	—
198	C₃×C₄²	C₂×C₃×D₃	1	8	yes	—
199	C₃×C₄²	C₂×C₃⋊D₃	1	2	yes	—
200	(C₂×D₃)⋊C₄	—	3	16	no	—
201	Dic₃⋊C₄	—	3	16	no	—
202	C₄×Dic₃	—	3	4	no	—
203	C₄×Dic₃	—	3	16	no	—
204	C₄×Dic₃	—	3	4	no	—
205	C₄×Dic₃	—	3	8	no	—
206	C₂²×C₃²	—	2	2	no	—
207	C₂²×C₃²	—	2	4	no	—
208	C₂²×C₃²	—	2	8	no	—
209	C₂²×C₃²	—	2	8	no	—
210	C₂²×C₃²	—	4	8	no	—
211	C₂²×C₃²	C₂×C₄×D₃	1	8	yes	—
212	C₂²×C₃²	C₂²×C₃×C₄	1	2	yes	—
213	C₂²×C₃²	C₂³×D₃	1	4	yes	—
214	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
215	C₂×C₃⋊D₃	—	2	4	no	—
216	C₂×C₃⋊D₃	C₂²×C₃×C₄	1	4	yes	—
217	C₂×C₃×D₃	—	3	16	no	—
218	C₂×C₃×D₃	—	6	16	no	—
219	C₃²×C₄	—	2	4	no	—
220	C₃²×C₄	—	2	8	no	—
221	C₃²×C₄	—	2	8	no	—
222	C₃²×C₄	—	2	16	no	—
223	C₃²×C₄	—	4	16	no	—
224	C₃²×C₄	C₂×C₄×D₃	1	8	yes	—
225	C₃²×C₄	C₂×C₄×D₃	1	8	yes	—
226	C₃²×C₄	C₂²×C₃×C₄	1	2	yes	—
227	C₃²×C₄	C₂²×C₃×C₄	1	2	yes	—
228	C₃⋊Dic₃	—	2	2	no	—
229	C₃⋊Dic₃	C₂²×C₃×C₄	1	4	yes	—
230	C₃⋊Dic₃	C₃×#41	1	4	yes	complemented
231	C₃×Dic₃	—	3	16	no	—
232	C₃×Dic₃	—	3	16	no	—
233	C₃×Dic₃	—	6	8	no	—
234	C₂×#41	—	9	1	no	—
235	C₄×Q₈	—	9	2	no	—
236	C₄×D₄	—	9	2	no	—
237	C₄×D₄	—	9	4	no	—
238	#117	—	9	2	no	—
239	#117	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
240	C₂×C₄²	—	9	1	no	—
241	C₂×C₄²	—	9	2	no	—
242	C₃³	C₄×#41	1	1	yes	characteristic, complemented, Sylow
243	C₂³×C₃	—	2	4	no	—
244	C₂³×C₃	—	9	2	no	—
245	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
246	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
247	C₂²×D₃	—	3	8	no	—
248	C₃×Q₈	—	9	4	no	—
249	C₃×D₄	—	9	8	no	—
250	C₃×D₄	—	9	4	no	—
251	C₂×C₃×C₄	—	2	16	no	—
252	C₂×C₃×C₄	—	2	4	no	—
253	C₂×C₃×C₄	—	2	4	no	—
254	C₂×C₃×C₄	—	2	16	no	—
255	C₂×C₃×C₄	—	9	2	no	—
256	C₂×C₃×C₄	—	9	2	no	—
257	C₂×C₃×C₄	—	9	8	no	—
258	C₂×C₃×C₄	—	9	2	no	—
259	C₂×C₃×C₄	—	18	8	no	—
260	C₂×C₃×C₄	—	18	4	no	—
261	C₂×C₃×C₄	C₃×C₄×D₃	1	16	yes	complemented
262	C₂×C₃×C₄	C₄×C₃⋊D₃	1	4	yes	complemented
263	C₂×C₃×C₄	C₂²×C₃×D₃	1	16	yes	—
264	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
265	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
266	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	4	yes	—
267	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
269	#67	—	3	32	no	—
270	C₂×Dic₃	—	3	8	no	—
271	C₂×Dic₃	—	3	8	no	—
272	C₂×Dic₃	—	3	8	no	—
273	C₂×Dic₃	—	6	16	no	—
274	D₁₂	—	3	16	no	—
275	C₄×D₃	—	3	32	no	—
276	C₄×D₃	—	6	32	no	—
277	Dic₆	—	3	16	no	—
278	C₂×C₃²	—	2	2	no	—
279	C₂×C₃²	—	2	4	no	—
280	C₂×C₃²	—	2	8	no	—
281	C₂×C₃²	—	2	8	no	—
282	C₂×C₃²	—	4	8	no	—
283	C₂×C₃²	C₂²×C₄×D₃	1	4	yes	—
284	C₂×C₃²	D₃×#41	1	8	yes	—
285	C₂×C₃²	C₂³×C₃×C₄	1	1	yes	characteristic
286	C₂×C₃²	C₂×C₃×#41	1	2	yes	—
287	C₃⋊D₃	—	2	4	no	—
288	C₃×D₃	—	6	16	no	—
289	#41	—	9	8	no	—
290	C₂×Q₈	—	9	1	no	—
291	C₂×D₄	—	9	2	no	—
292	C₂×D₄	—	9	1	no	—
293	C₂²×C₄	—	9	2	no	—
294	C₂²×C₄	—	9	2	no	—
295	C₂²×C₄	—	9	4	no	—
296	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
297	C₄⋊C₄	—	9	4	no	—
298	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
299	C₂²⋊C₄	—	9	4	no	—
300	C₂²⋊C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
301	C₄²	—	9	1	no	—
302	C₄²	—	9	1	no	—
303	C₄²	—	9	4	no	—
304	C₄²	—	9	2	no	—
305	C₄²	C₂×C₃×C₃⋊D₃	1	2	yes	—
306	C₂²×C₃	—	2	8	no	—
307	C₂²×C₃	—	2	2	no	—
308	C₂²×C₃	—	2	4	no	—
309	C₂²×C₃	—	2	8	no	—
310	C₂²×C₃	—	4	8	no	—
311	C₂²×C₃	—	9	4	no	—
312	C₂²×C₃	—	18	4	no	—
313	C₂²×C₃	C₂×C₃×C₄×D₃	1	8	yes	—
314	C₂²×C₃	C₂×C₄×C₃⋊D₃	1	2	yes	—
315	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
316	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
317	C₂×D₃	—	3	16	no	—
318	C₂×D₃	—	6	16	no	—
319	C₃×C₄	—	2	16	no	—
320	C₃×C₄	—	2	4	no	—
321	C₃×C₄	—	2	8	no	—
322	C₃×C₄	—	2	8	no	—
323	C₃×C₄	—	4	16	no	—
324	C₃×C₄	—	9	4	no	—
325	C₃×C₄	—	9	4	no	—
326	C₃×C₄	—	18	2	no	—
327	C₃×C₄	C₂×C₃×C₄×D₃	1	8	yes	—
328	C₃×C₄	C₂×C₃×C₄×D₃	1	8	yes	—
329	C₃×C₄	C₂×C₄×C₃⋊D₃	1	2	yes	—
330	C₃×C₄	C₂×C₄×C₃⋊D₃	1	2	yes	—
331	Dic₃	—	3	16	no	—
332	Dic₃	—	3	16	no	—
333	Dic₃	—	6	8	no	—
334	C₃²	—	2	4	no	—
335	C₃²	#5522	1	4	yes	complemented
336	C₃²	C₃×C₄×#41	1	1	yes	characteristic, complemented
337	C₂³	—	9	2	no	—
338	C₂³	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
339	Q₈	—	9	4	no	—
340	D₄	—	9	8	no	—
341	D₄	—	9	4	no	—
342	C₂×C₄	—	9	2	no	—
343	C₂×C₄	—	9	2	no	—
344	C₂×C₄	—	9	8	no	—
345	C₂×C₄	—	9	2	no	—
346	C₂×C₄	—	18	8	no	—
347	C₂×C₄	—	18	4	no	—
348	C₂×C₄	C₃×C₄×C₃⋊D₃	1	4	yes	complemented
349	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	4	yes	—
350	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
351	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
352	C₂×C₃	—	2	8	no	—
353	C₂×C₃	—	2	2	no	—
354	C₂×C₃	—	2	4	no	—
355	C₂×C₃	—	2	8	no	—
356	C₂×C₃	—	4	8	no	—
357	C₂×C₃	—	18	4	no	—
358	C₂×C₃	C₂²×C₃×C₄×D₃	1	4	yes	—
359	C₂×C₃	C₃×D₃×#41	1	8	yes	—
360	C₂×C₃	C₂²×C₄×C₃⋊D₃	1	1	yes	characteristic
361	C₂×C₃	#41×C₃⋊D₃	1	2	yes	—
362	D₃	—	6	16	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	9	4	no	—
365	C₂²	—	18	4	no	—
366	C₂²	C₂×C₃×C₄×C₃⋊D₃	1	2	yes	—
367	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
368	C₄	—	2	4	no	—
369	C₄	—	9	4	no	—
370	C₄	—	9	4	no	—
371	C₄	—	18	2	no	—
372	C₄	C₂×C₃×C₄×C₃⋊D₃	1	2	yes	—
373	C₄	C₂×C₃×C₄×C₃⋊D₃	1	2	yes	—
374	C₃	—	2	4	no	—
375	C₃	C₃×#5522	1	4	yes	complemented
376	C₃	#10595993	1	1	yes	characteristic, direct product factor
377	C₂	—	2	2	no	—
378	C₂	—	18	4	no	—
379	C₂	C₂²×C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
380	C₂	C₃×#41×C₃⋊D₃	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×C₃⋊D₃
commutator	C₂×C₃²	C₂³×C₃×C₄
Frattini	C₂²	C₂³×C₃×C₃⋊D₃
Fitting	C₃³×#117	C₂
socle	C₂²×C₃³	C₂⁴
prime radical	C₂×C₃×#3828	C₂
cosocle	C₂²×C₃²	C₂⁴×C₃
hypercenter	C₃×#117	C₃⋊D₃
hypocenter	C₃²	C₃×C₄×#41
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#117

Complements

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

N	H ≅ G/N	type
2. C₃³×#117	C₂	semidirect
3. C₂×C₃×C₄×C₃⋊Dic₃	C₂	semidirect
4. C₃×#64102	C₂	semidirect
5. C₃×#64096	C₂	semidirect
6. C₃×#64090	C₂	semidirect
7. C₃×#64081	C₂	semidirect
8. C₃×C₄²×C₃⋊D₃	C₂	semidirect
9. #10595993	C₃	direct (N × H)
14. C₃×#3828	C₄	semidirect
31. C₃²×#117	D₃	semidirect
32. C₃²×#117	C₂×C₃	semidirect
33. C₂×C₄×C₃⋊Dic₃	C₂×C₃	semidirect
34. #64102	C₂×C₃	semidirect
35. #64096	C₂×C₃	semidirect
36. #64090	C₂×C₃	semidirect
37. #64081	C₂×C₃	semidirect
38. C₄²×C₃⋊D₃	C₂×C₃	semidirect
47. C₂×C₃³×C₄	C₂×C₄	semidirect
51. C₃×#638	C₂×C₄	semidirect
56. C₃×C₄⋊(C₃⋊D₃)	C₂×C₄	semidirect
58. C₃×C₄×C₃⋊D₃	C₂×C₄	semidirect
59. C₃×#634	C₂×C₄	semidirect
67. #3828	C₃×C₄	semidirect
110. C₃×C₃⋊Dic₃	#41	semidirect
118. C₃×#117	C₃×D₃	semidirect
119. C₃×#117	C₃⋊D₃	semidirect
137. C₂×C₃²×C₄	C₄×D₃	semidirect
138. C₂×C₃²×C₄	C₂×C₃×C₄	semidirect
145. #638	C₂×C₃×C₄	semidirect
150. C₄⋊(C₃⋊D₃)	C₂×C₃×C₄	semidirect
152. C₄×C₃⋊D₃	C₂×C₃×C₄	semidirect
153. #634	C₂×C₃×C₄	semidirect
230. C₃⋊Dic₃	C₃×#41	semidirect
239. #117	C₃×C₃⋊D₃	semidirect
242. C₃³	C₄×#41	semidirect
261. C₂×C₃×C₄	C₃×C₄×D₃	semidirect
262. C₂×C₃×C₄	C₄×C₃⋊D₃	semidirect
335. C₃²	#5522	semidirect
336. C₃²	C₃×C₄×#41	semidirect
348. C₂×C₄	C₃×C₄×C₃⋊D₃	semidirect
375. C₃	C₃×#5522	semidirect
376. C₃	#10595993	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#3828	2
C₃³×#117	2
C₂×C₃×C₄×C₃⋊Dic₃	2
C₃×#64102	2
C₃×#64096	2
C₃×#64090	2
C₃×#64081	2
C₃×C₄²×C₃⋊D₃	2
#10595993	3
C₃×#5522	3

Subgroups — C3×#10595993 #13179276

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10595993 #13179276