Subgroups — C₃×#10592627 #13162971

Order 1728.

1452 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×C₄²	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄⋊(C₃⋊Dic₃)	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄⋊(C₃⋊Dic₃)	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×#3750	C₂	1	2	yes	maximal
5	C₃×#63658	C₂	1	2	yes	maximal
6	#10592627	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₃×#4928	—	3	4	no	maximal
8	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
9	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
10	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₃⋊Dic₃	C₂²	1	2	yes	—
12	C₂²×C₃×C₃⋊Dic₃	C₂²	1	2	yes	—
13	C₃³×C₄²	—	2	2	no	—
14	C₃×C₄⋊(C₃⋊Dic₃)	—	2	2	no	—
15	C₃×C₄⋊(C₃⋊Dic₃)	C₄	1	4	yes	complemented
16	C₃×#3750	—	2	4	no	—
17	C₂×C₃²×C₄²	—	2	4	no	—
18	C₂×C₃²×C₄²	D₃	1	4	yes	—
19	C₂×C₃²×C₄²	C₂×C₃	1	1	yes	characteristic
20	C₂×C₄⋊(C₃⋊Dic₃)	C₂×C₃	1	1	yes	characteristic
21	C₂×C₄⋊(C₃⋊Dic₃)	C₂×C₃	1	1	yes	characteristic
22	C₂×#3750	C₂×C₃	1	2	yes	—
23	C₂×C₃×C₄⋊Dic₃	—	3	4	no	—
24	C₂×C₃×C₄⋊Dic₃	—	3	4	no	—
25	C₂×C₃×Dic₃⋊C₄	—	3	8	no	—
26	#63658	C₂×C₃	1	2	yes	—
27	C₃×C₃⋊#95	—	3	8	no	—
28	C₂³×C₃³	C₂³	1	1	yes	characteristic
29	C₂×C₃³×C₄	—	2	1	no	—
30	C₂×C₃³×C₄	—	2	1	no	—
31	C₂×C₃³×C₄	—	2	1	no	—
32	C₂×C₃³×C₄	—	2	1	no	—
33	C₂×C₃³×C₄	C₂×C₄	1	2	yes	—
34	C₂×C₃³×C₄	D₄	1	2	yes	—
35	C₂×C₃³×C₄	D₄	1	2	yes	—
36	C₂×C₃³×C₄	Q₈	1	2	yes	—
37	C₂×C₃³×C₄	Q₈	1	2	yes	—
38	C₂×C₃×C₃⋊Dic₃	—	2	2	no	—
39	C₂×C₃×C₃⋊Dic₃	—	2	2	no	—
40	C₂×C₃×C₃⋊Dic₃	—	2	2	no	—
41	C₂×C₃×C₃⋊Dic₃	—	2	2	no	—
42	C₂×C₃×C₃⋊Dic₃	—	2	2	no	—
43	C₂×C₃×C₃⋊Dic₃	C₂×C₄	1	4	yes	—
44	C₃×#389	—	9	1	no	—
45	#4928	—	3	4	no	—
46	C₂²×C₃²×C₄	—	2	4	no	—
47	C₂²×C₃²×C₄	—	2	4	no	—
48	C₂²×C₃²×C₄	—	2	4	no	—
49	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
50	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
51	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
52	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
53	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
54	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
55	C₂²×C₃⋊Dic₃	C₂²×C₃	1	2	yes	—
56	C₂²×C₃⋊Dic₃	C₂²×C₃	1	2	yes	—
57	C₂²×C₃×Dic₃	—	3	8	no	—
58	C₂²×C₃×Dic₃	—	3	8	no	—
59	C₃²×C₄²	—	2	16	no	—
60	C₃²×C₄²	—	2	8	no	—
61	C₃²×C₄²	—	2	2	no	—
62	C₄⋊(C₃⋊Dic₃)	—	2	2	no	—
63	C₄⋊(C₃⋊Dic₃)	C₃×C₄	1	4	yes	complemented
64	#3750	—	2	4	no	—
65	C₃×C₄⋊Dic₃	—	3	16	no	—
66	C₃×C₄⋊Dic₃	—	6	8	no	—
67	C₃×Dic₃⋊C₄	—	6	16	no	—
68	C₂²×C₃³	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₃³	C₂×Q₈	1	1	yes	characteristic
72	C₂²×C₃³	C₂×Q₈	1	1	yes	characteristic
73	C₂²×C₃³	#41	1	1	yes	characteristic
74	C₂²×C₃³	#41	1	1	yes	characteristic
75	C₃³×C₄	—	2	2	no	—
76	C₃³×C₄	—	2	2	no	—
77	C₃³×C₄	C₄⋊C₄	1	4	yes	complemented
78	C₃×C₃⋊Dic₃	—	2	4	no	—
79	C₃×C₃⋊Dic₃	—	4	2	no	—
80	C₂×C₃×C₄⋊C₄	—	9	1	no	—
81	C₂×C₃×C₄⋊C₄	—	9	2	no	—
82	C₂×C₃×C₄⋊C₄	—	9	1	no	—
83	C₂×C₃×C₄²	—	2	4	no	—
84	C₂×C₃×C₄²	C₃×D₃	1	4	yes	—
85	C₂×C₃×C₄²	C₃⋊D₃	1	1	yes	characteristic
86	C₂×C₄⋊Dic₃	—	3	4	no	—
87	C₂×C₄⋊Dic₃	—	3	4	no	—
88	C₂×Dic₃⋊C₄	—	3	8	no	—
89	C₃×#95	—	9	2	no	—
90	C₃⋊#95	—	3	8	no	—
91	C₂³×C₃²	—	2	4	no	—
92	C₂³×C₃²	C₂²×D₃	1	4	yes	—
93	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
94	C₂×C₃²×C₄	—	2	8	no	—
95	C₂×C₃²×C₄	—	2	8	no	—
96	C₂×C₃²×C₄	—	2	8	no	—
97	C₂×C₃²×C₄	—	2	8	no	—
98	C₂×C₃²×C₄	—	2	4	no	—
99	C₂×C₃²×C₄	—	2	4	no	—
100	C₂×C₃²×C₄	—	2	4	no	—
101	C₂×C₃²×C₄	—	2	4	no	—
102	C₂×C₃²×C₄	—	2	1	no	—
103	C₂×C₃²×C₄	—	2	1	no	—
104	C₂×C₃²×C₄	—	2	1	no	—
105	C₂×C₃²×C₄	—	2	1	no	—
106	C₂×C₃²×C₄	—	2	8	no	—
107	C₂×C₃²×C₄	—	2	8	no	—
108	C₂×C₃²×C₄	—	2	8	no	—
109	C₂×C₃²×C₄	—	2	8	no	—
110	C₂×C₃²×C₄	—	2	8	no	—
111	C₂×C₃²×C₄	Dic₆	1	8	yes	—
112	C₂×C₃²×C₄	Dic₆	1	8	yes	—
113	C₂×C₃²×C₄	C₄×D₃	1	8	yes	—
114	C₂×C₃²×C₄	D₁₂	1	8	yes	—
115	C₂×C₃²×C₄	#67	1	8	yes	—
116	C₂×C₃²×C₄	C₂×C₃×C₄	1	2	yes	—
117	C₂×C₃²×C₄	C₃×D₄	1	2	yes	—
118	C₂×C₃²×C₄	C₃×D₄	1	2	yes	—
119	C₂×C₃²×C₄	C₃×Q₈	1	2	yes	—
120	C₂×C₃²×C₄	C₃×Q₈	1	2	yes	—
121	C₂×C₃⋊Dic₃	—	2	2	no	—
122	C₂×C₃⋊Dic₃	—	2	2	no	—
123	C₂×C₃⋊Dic₃	—	2	2	no	—
124	C₂×C₃⋊Dic₃	—	2	2	no	—
125	C₂×C₃⋊Dic₃	—	2	2	no	—
126	C₂×C₃⋊Dic₃	C₂×C₃×C₄	1	4	yes	—
127	C₂×C₃×Dic₃	—	3	16	no	—
128	C₂×C₃×Dic₃	—	6	8	no	—
129	C₂×C₃×Dic₃	—	6	8	no	—
130	C₂×C₃×Dic₃	—	6	8	no	—
131	C₂×C₃×Dic₃	—	6	8	no	—
132	C₂×C₃×Dic₃	—	6	8	no	—
133	#389	—	9	1	no	Sylow
134	C₂×C₃³	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂×C₃³	C₄×D₄	1	1	yes	characteristic
136	C₂×C₃³	C₄×Q₈	1	1	yes	characteristic
137	C₂×C₃³	#121	1	1	yes	characteristic
138	C₂×C₃³	C₂²⋊Q₈	1	1	yes	characteristic
139	C₂×C₃³	#125	1	1	yes	characteristic
140	C₂×C₃³	C₄⋊Q₈	1	1	yes	characteristic
141	C₂²×C₃×C₄	—	2	4	no	—
142	C₂²×C₃×C₄	—	2	4	no	—
143	C₂²×C₃×C₄	—	2	4	no	—
144	C₂²×C₃×C₄	—	9	2	no	—
145	C₂²×C₃×C₄	—	9	2	no	—
146	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
147	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
148	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
149	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
150	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
151	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
152	C₂²×Dic₃	—	3	8	no	—
153	C₂²×Dic₃	—	3	8	no	—
154	C₃×C₄⋊C₄	—	9	4	no	—
155	C₃×C₄⋊C₄	—	18	4	no	—
156	C₃×C₄⋊C₄	—	18	2	no	—
157	C₃×C₄²	—	2	16	no	—
158	C₃×C₄²	—	2	8	no	—
159	C₃×C₄²	—	2	2	no	—
160	C₄⋊Dic₃	—	3	16	no	—
161	C₄⋊Dic₃	—	6	8	no	—
162	Dic₃⋊C₄	—	6	16	no	—
163	C₂²×C₃²	—	2	4	no	—
164	C₂²×C₃²	—	2	4	no	—
165	C₂²×C₃²	—	2	4	no	—
166	C₂²×C₃²	—	2	4	no	—
167	C₂²×C₃²	—	2	4	no	—
168	C₂²×C₃²	—	2	4	no	—
169	C₂²×C₃²	—	2	4	no	—
170	C₂²×C₃²	C₂×Dic₆	1	4	yes	—
171	C₂²×C₃²	C₂×Dic₆	1	4	yes	—
172	C₂²×C₃²	C₂×C₄×D₃	1	4	yes	—
173	C₂²×C₃²	C₂×D₁₂	1	4	yes	—
174	C₂²×C₃²	#235	1	4	yes	—
175	C₂²×C₃²	#235	1	4	yes	—
176	C₂²×C₃²	C₂×#67	1	4	yes	—
177	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
178	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
179	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
180	C₂²×C₃²	C₂×C₃×Q₈	1	1	yes	characteristic
181	C₂²×C₃²	C₂×C₃×Q₈	1	1	yes	characteristic
182	C₂²×C₃²	C₃×#41	1	1	yes	characteristic
183	C₂²×C₃²	C₃×#41	1	1	yes	characteristic
184	C₃²×C₄	—	2	16	no	—
185	C₃²×C₄	—	2	16	no	—
186	C₃²×C₄	—	2	8	no	—
187	C₃²×C₄	—	2	8	no	—
188	C₃²×C₄	—	2	2	no	—
189	C₃²×C₄	—	2	2	no	—
190	C₃²×C₄	—	2	16	no	—
191	C₃²×C₄	Dic₃⋊C₄	1	16	yes	complemented
192	C₃²×C₄	C₃×C₄⋊C₄	1	4	yes	complemented
193	C₃⋊Dic₃	—	2	4	no	—
194	C₃⋊Dic₃	—	4	2	no	—
195	C₃×Dic₃	—	6	16	no	—
196	C₃×Dic₃	—	12	8	no	—
197	C₂×C₄⋊C₄	—	9	1	no	—
198	C₂×C₄⋊C₄	—	9	2	no	—
199	C₂×C₄⋊C₄	—	9	1	no	—
200	C₂×C₄²	C₃×C₃⋊D₃	1	1	yes	characteristic
201	#95	—	9	2	no	—
202	C₃³	#389	1	1	yes	characteristic, complemented, Sylow
203	C₂³×C₃	—	2	4	no	—
204	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
205	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
206	C₂×C₃×C₄	—	2	8	no	—
207	C₂×C₃×C₄	—	2	8	no	—
208	C₂×C₃×C₄	—	2	8	no	—
209	C₂×C₃×C₄	—	2	8	no	—
210	C₂×C₃×C₄	—	2	4	no	—
211	C₂×C₃×C₄	—	2	4	no	—
212	C₂×C₃×C₄	—	2	4	no	—
213	C₂×C₃×C₄	—	2	4	no	—
214	C₂×C₃×C₄	—	2	1	no	—
215	C₂×C₃×C₄	—	2	1	no	—
216	C₂×C₃×C₄	—	2	1	no	—
217	C₂×C₃×C₄	—	2	1	no	—
218	C₂×C₃×C₄	—	2	8	no	—
219	C₂×C₃×C₄	—	2	8	no	—
220	C₂×C₃×C₄	—	2	8	no	—
221	C₂×C₃×C₄	—	2	8	no	—
222	C₂×C₃×C₄	—	2	8	no	—
223	C₂×C₃×C₄	—	9	4	no	—
224	C₂×C₃×C₄	—	18	2	no	—
225	C₂×C₃×C₄	—	18	2	no	—
226	C₂×C₃×C₄	—	18	2	no	—
227	C₂×C₃×C₄	—	18	2	no	—
228	C₂×C₃×C₄	—	18	2	no	—
229	C₂×C₃×C₄	C₃×Dic₆	1	8	yes	—
230	C₂×C₃×C₄	C₃×Dic₆	1	8	yes	—
231	C₂×C₃×C₄	C₃×C₄×D₃	1	8	yes	—
232	C₂×C₃×C₄	C₃×D₁₂	1	8	yes	—
233	C₂×C₃×C₄	C₃×#67	1	8	yes	—
234	C₂×C₃×C₄	#634	1	2	yes	—
235	C₂×C₃×C₄	#634	1	2	yes	—
236	C₂×C₃×C₄	C₄×C₃⋊D₃	1	2	yes	—
237	C₂×C₃×C₄	C₄⋊(C₃⋊D₃)	1	2	yes	—
238	C₂×C₃×C₄	#638	1	2	yes	—
239	C₂×Dic₃	—	3	16	no	—
240	C₂×Dic₃	—	6	8	no	—
241	C₂×Dic₃	—	6	8	no	—
242	C₂×Dic₃	—	6	8	no	—
243	C₂×Dic₃	—	6	8	no	—
244	C₂×Dic₃	—	6	8	no	—
245	C₂×C₃²	—	2	4	no	—
246	C₂×C₃²	—	2	4	no	—
247	C₂×C₃²	—	2	4	no	—
248	C₂×C₃²	—	2	4	no	—
249	C₂×C₃²	—	2	4	no	—
250	C₂×C₃²	—	2	4	no	—
251	C₂×C₃²	—	2	4	no	—
252	C₂×C₃²	C₄×Dic₆	1	4	yes	—
253	C₂×C₃²	#869	1	4	yes	—
254	C₂×C₃²	#870	1	4	yes	—
255	C₂×C₃²	C₄×D₁₂	1	4	yes	—
256	C₂×C₃²	C₂×Dic₃⋊C₄	1	4	yes	—
257	C₂×C₃²	#924	1	4	yes	—
258	C₂×C₃²	#930	1	4	yes	—
259	C₂×C₃²	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
260	C₂×C₃²	C₃×C₄×D₄	1	1	yes	characteristic
261	C₂×C₃²	C₃×C₄×Q₈	1	1	yes	characteristic
262	C₂×C₃²	C₃×#121	1	1	yes	characteristic
263	C₂×C₃²	C₃×C₂²⋊Q₈	1	1	yes	characteristic
264	C₂×C₃²	C₃×#125	1	1	yes	characteristic
265	C₂×C₃²	C₃×C₄⋊Q₈	1	1	yes	characteristic
266	C₂²×C₄	—	9	2	no	—
267	C₂²×C₄	—	9	2	no	—
268	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
269	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
270	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
271	C₄⋊C₄	—	9	4	no	—
272	C₄⋊C₄	—	18	4	no	—
273	C₄⋊C₄	—	18	2	no	—
274	C₄²	—	2	2	no	—
275	C₂²×C₃	—	2	4	no	—
276	C₂²×C₃	—	2	4	no	—
277	C₂²×C₃	—	2	4	no	—
278	C₂²×C₃	—	2	4	no	—
279	C₂²×C₃	—	2	4	no	—
280	C₂²×C₃	—	2	4	no	—
281	C₂²×C₃	—	2	4	no	—
282	C₂²×C₃	C₂×C₃×Dic₆	1	4	yes	—
283	C₂²×C₃	C₂×C₃×Dic₆	1	4	yes	—
284	C₂²×C₃	C₂×C₃×C₄×D₃	1	4	yes	—
285	C₂²×C₃	C₂×C₃×D₁₂	1	4	yes	—
286	C₂²×C₃	C₃×#235	1	4	yes	—
287	C₂²×C₃	C₃×#235	1	4	yes	—
288	C₂²×C₃	C₂×C₃×#67	1	4	yes	—
289	C₂²×C₃	C₂×#634	1	1	yes	characteristic
290	C₂²×C₃	C₂×#634	1	1	yes	characteristic
291	C₂²×C₃	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
292	C₂²×C₃	C₂×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
293	C₂²×C₃	#3828	1	1	yes	characteristic
294	C₂²×C₃	#3828	1	1	yes	characteristic
295	C₂²×C₃	C₂×#638	1	1	yes	characteristic
296	C₃×C₄	—	2	16	no	—
297	C₃×C₄	—	2	16	no	—
298	C₃×C₄	—	2	8	no	—
299	C₃×C₄	—	2	8	no	—
300	C₃×C₄	—	2	2	no	—
301	C₃×C₄	—	2	2	no	—
302	C₃×C₄	—	2	16	no	—
303	C₃×C₄	—	18	4	no	—
304	C₃×C₄	—	36	2	no	—
305	C₃×C₄	C₃×Dic₃⋊C₄	1	16	yes	complemented
306	C₃×C₄	#3750	1	4	yes	complemented
307	Dic₃	—	6	16	no	—
308	Dic₃	—	12	8	no	—
309	C₃²	—	2	4	no	—
310	C₃²	#4928	1	4	yes	complemented
311	C₃²	C₃×#389	1	1	yes	characteristic, complemented
312	C₂³	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	9	4	no	—
318	C₂×C₄	—	18	2	no	—
319	C₂×C₄	—	18	2	no	—
320	C₂×C₄	—	18	2	no	—
321	C₂×C₄	—	18	2	no	—
322	C₂×C₄	—	18	2	no	—
323	C₂×C₄	C₃×#634	1	2	yes	—
324	C₂×C₄	C₃×#634	1	2	yes	—
325	C₂×C₄	C₃×C₄×C₃⋊D₃	1	2	yes	—
326	C₂×C₄	C₃×C₄⋊(C₃⋊D₃)	1	2	yes	—
327	C₂×C₄	C₃×#638	1	2	yes	—
328	C₂×C₃	—	2	4	no	—
329	C₂×C₃	—	2	4	no	—
330	C₂×C₃	—	2	4	no	—
331	C₂×C₃	—	2	4	no	—
332	C₂×C₃	—	2	4	no	—
333	C₂×C₃	—	2	4	no	—
334	C₂×C₃	—	2	4	no	—
335	C₂×C₃	C₃×C₄×Dic₆	1	4	yes	—
336	C₂×C₃	C₃×#869	1	4	yes	—
337	C₂×C₃	C₃×#870	1	4	yes	—
338	C₂×C₃	C₃×C₄×D₁₂	1	4	yes	—
339	C₂×C₃	C₂×C₃×Dic₃⋊C₄	1	4	yes	—
340	C₂×C₃	C₃×#924	1	4	yes	—
341	C₂×C₃	C₃×#930	1	4	yes	—
342	C₂×C₃	C₄×#634	1	1	yes	characteristic
343	C₂×C₃	#64078	1	1	yes	characteristic
344	C₂×C₃	#64079	1	1	yes	characteristic
345	C₂×C₃	C₄×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
346	C₂×C₃	C₂×#3750	1	1	yes	characteristic
347	C₂×C₃	#64133	1	1	yes	characteristic
348	C₂×C₃	#64139	1	1	yes	characteristic
349	C₂²	C₂×C₃×#634	1	1	yes	characteristic
350	C₂²	C₂×C₃×#634	1	1	yes	characteristic
351	C₂²	C₂×C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
352	C₂²	C₂×C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
353	C₂²	C₃×#3828	1	1	yes	characteristic
354	C₂²	C₃×#3828	1	1	yes	characteristic
355	C₂²	C₂×C₃×#638	1	1	yes	characteristic
356	C₄	—	2	2	no	—
357	C₄	—	2	2	no	—
358	C₄	—	18	4	no	—
359	C₄	—	36	2	no	—
360	C₄	C₃×#3750	1	4	yes	complemented
361	C₃	—	2	4	no	—
362	C₃	C₃×#4928	1	4	yes	complemented
363	C₃	#10592627	1	1	yes	characteristic, direct product factor
364	C₂	C₃×C₄×#634	1	1	yes	characteristic
365	C₂	C₃×#64078	1	1	yes	characteristic
366	C₂	C₃×#64079	1	1	yes	characteristic
367	C₂	C₃×C₄×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
368	C₂	C₂×C₃×#3750	1	1	yes	characteristic
369	C₂	C₃×#64133	1	1	yes	characteristic
370	C₂	C₃×#64139	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂²×C₃⋊D₃
commutator	C₂²×C₃²	C₂²×C₃×C₄
Frattini	C₂³	C₂²×C₃×C₃⋊D₃
Fitting	C₂×C₃³×C₄²	C₂
socle, prime radical	C₂³×C₃³	C₂³
cosocle	C₂³×C₃²	C₂³×C₃
hypercenter	C₂×C₃×C₄²	C₃⋊D₃
hypocenter	C₃²	C₃×#389
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄²

Complements

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

N	H ≅ G/N	type
6. #10592627	C₃	direct (N × H)
15. C₃×C₄⋊(C₃⋊Dic₃)	C₄	semidirect
63. C₄⋊(C₃⋊Dic₃)	C₃×C₄	semidirect
77. C₃³×C₄	C₄⋊C₄	semidirect
191. C₃²×C₄	Dic₃⋊C₄	semidirect
192. C₃²×C₄	C₃×C₄⋊C₄	semidirect
202. C₃³	#389	semidirect
305. C₃×C₄	C₃×Dic₃⋊C₄	semidirect
306. C₃×C₄	#3750	semidirect
310. C₃²	#4928	semidirect
311. C₃²	C₃×#389	semidirect
360. C₄	C₃×#3750	semidirect
362. C₃	C₃×#4928	semidirect
363. C₃	#10592627	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×C₃³×C₄²	2
C₂×C₃×C₄⋊(C₃⋊Dic₃)	2
C₂×C₃×#3750	2
C₃×#63658	2
#10592627	3
C₃×#4928	3

Subgroups — C3×#10592627 #13162971

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10592627 #13162971