Subgroups — C₃×#10595996 #13179279

Order 1728.

2308 conjugacy classes of subgroups.

The subgroup lattice has 388 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, complemented
2	C₂²×C₃×C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃³×#117	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64104	C₂	1	4	yes	maximal, complemented
5	C₃×#64091	C₂	1	4	yes	maximal, complemented
6	C₃×#64084	C₂	1	2	yes	maximal, complemented
7	C₃×#64083	C₂	1	2	yes	maximal, complemented
8	#10595996	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₃×#5525	—	3	4	no	maximal
10	C₂³×C₃×C₃⋊D₃	C₂²	1	2	yes	—
11	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
12	C₂×C₃×#638	C₂²	1	2	yes	—
13	C₃×#3828	—	2	4	no	—
14	C₂×C₃×C₄⋊(C₃⋊D₃)	—	2	4	no	—
15	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	2	yes	—
16	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	2	yes	—
17	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	8	yes	complemented
19	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	2	yes	complemented
20	C₂×C₃×#634	C₂²	1	1	yes	characteristic, complemented
21	C₃³×C₄⋊C₄	C₂²	1	2	yes	complemented
22	C₃³×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₃³×C₄²	C₂²	1	2	yes	complemented
24	C₃×#3752	C₂²	1	8	yes	complemented
25	C₂×#3828	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂²×C₄⋊(C₃⋊D₃)	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂×C₃×#235	—	3	4	no	—
28	C₂²×C₃×D₁₂	—	3	4	no	—
29	C₃²×#117	—	2	4	no	—
30	C₃²×#117	D₃	1	4	yes	complemented
31	C₃²×#117	C₂×C₃	1	1	yes	characteristic, complemented
32	#64104	C₂×C₃	1	4	yes	complemented
33	#64091	C₂×C₃	1	4	yes	complemented
34	#64084	C₂×C₃	1	2	yes	complemented
35	#64083	C₂×C₃	1	2	yes	complemented
36	C₃×#895	—	3	16	no	—
37	C₃×#882	—	3	16	no	—
38	C₃×#875	—	3	8	no	—
39	C₃×#874	—	3	8	no	—
40	C₂³×C₃³	C₂³	1	1	yes	characteristic
41	C₂²×C₃×C₃⋊D₃	—	2	4	no	—
42	C₂²×C₃×C₃⋊D₃	—	4	4	no	—
43	C₂²×C₃×C₃⋊D₃	C₂³	1	4	yes	—
44	C₂²×C₃×C₃⋊D₃	C₂³	1	2	yes	—
45	C₂×C₃³×C₄	D₄	1	4	yes	complemented
46	C₂×C₃³×C₄	C₂³	1	4	yes	—
47	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
48	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
49	C₃×#638	—	2	4	no	—
50	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
51	C₃×C₄⋊(C₃⋊D₃)	—	2	4	no	—
52	C₃×C₄⋊(C₃⋊D₃)	—	2	4	no	—
53	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
54	C₃×C₄⋊(C₃⋊D₃)	—	4	8	no	—
55	C₃×C₄×C₃⋊D₃	—	2	4	no	—
56	C₃×#634	—	2	2	no	—
57	C₃×#535	—	9	1	no	—
58	#5525	—	3	4	no	—
59	C₂³×C₃⋊D₃	C₂²×C₃	1	2	yes	—
60	C₂³×C₃×D₃	—	3	8	no	—
61	C₂²×C₃²×C₄	—	2	4	no	—
62	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
63	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
64	C₂×#638	C₂²×C₃	1	2	yes	—
65	#3828	—	2	4	no	—
66	C₂×C₄⋊(C₃⋊D₃)	—	2	4	no	—
67	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	2	yes	—
68	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	2	yes	—
69	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic, complemented
70	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	8	yes	complemented
71	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	2	yes	complemented
72	C₂×#634	C₂²×C₃	1	1	yes	characteristic, complemented
73	C₂×C₃×#67	—	3	8	no	—
74	C₃×#235	—	6	16	no	—
75	C₂×C₃×D₁₂	—	3	8	no	—
76	C₂×C₃×D₁₂	—	3	8	no	—
77	C₂×C₃×D₁₂	—	3	4	no	—
78	C₂×C₃×D₁₂	—	3	32	no	—
79	C₂×C₃×D₁₂	—	6	16	no	—
80	C₂×C₃×C₄×D₃	—	3	8	no	—
81	C₂×C₃×Dic₆	—	3	4	no	—
82	C₃²×C₄⋊C₄	—	2	8	no	—
83	C₃²×C₄⋊C₄	C₂×D₃	1	8	yes	complemented
84	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
85	C₃²×C₂²⋊C₄	—	2	8	no	—
86	C₃²×C₂²⋊C₄	C₂×D₃	1	8	yes	—
87	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
88	C₃²×C₄²	—	2	8	no	—
89	C₃²×C₄²	C₂×D₃	1	8	yes	complemented
90	C₃²×C₄²	C₂²×C₃	1	2	yes	complemented
91	#3752	C₂²×C₃	1	8	yes	complemented
92	C₃×(C₂×D₃)⋊C₄	—	3	32	no	—
93	C₂²×C₃³	—	2	2	no	—
94	C₂²×C₃³	C₂×D₄	1	2	yes	—
95	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
96	C₂×C₃×C₃⋊D₃	—	2	2	no	—
97	C₂×C₃×C₃⋊D₃	—	2	4	no	—
98	C₂×C₃×C₃⋊D₃	—	2	4	no	—
99	C₂×C₃×C₃⋊D₃	—	2	8	no	—
100	C₂×C₃×C₃⋊D₃	—	4	8	no	—
101	C₃³×C₄	—	2	4	no	—
102	C₃³×C₄	C₂×D₄	1	2	yes	—
103	C₃³×C₄	C₂×D₄	1	2	yes	—
104	C₃×C₃⋊Dic₃	—	2	2	no	—
105	C₂×C₃×#41	—	9	1	no	—
106	C₂²×C₃×D₄	—	9	1	no	—
107	C₂×#235	—	3	4	no	—
108	C₂²×D₁₂	—	3	4	no	—
109	C₃×#127	—	9	2	no	—
110	C₃×#124	—	9	2	no	—
111	C₃×#121	—	9	4	no	—
112	C₃×#120	—	9	4	no	—
113	C₃×#117	—	2	4	no	—
114	C₃×#117	C₃×D₃	1	4	yes	complemented
115	C₃×#117	C₃⋊D₃	1	1	yes	characteristic, complemented
116	#895	—	3	16	no	—
117	#882	—	3	16	no	—
118	#875	—	3	8	no	—
119	#874	—	3	8	no	—
120	C₂³×C₃²	—	2	4	no	—
121	C₂³×C₃²	C₂²×D₃	1	4	yes	—
122	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
123	C₂²×C₃⋊D₃	—	2	4	no	—
124	C₂²×C₃⋊D₃	—	4	4	no	—
125	C₂²×C₃⋊D₃	C₂³×C₃	1	4	yes	—
126	C₂²×C₃⋊D₃	C₂³×C₃	1	2	yes	—
127	C₂²×C₃×D₃	—	3	16	no	—
128	C₂²×C₃×D₃	—	3	8	no	—
129	C₂²×C₃×D₃	—	6	16	no	—
130	C₂²×C₃×D₃	—	12	16	no	—
131	C₂×C₃²×C₄	—	2	16	no	—
132	C₂×C₃²×C₄	—	2	4	no	—
133	C₂×C₃²×C₄	—	2	4	no	—
134	C₂×C₃²×C₄	—	2	16	no	—
135	C₂×C₃²×C₄	D₁₂	1	16	yes	complemented
136	C₂×C₃²×C₄	C₃×D₄	1	4	yes	complemented
137	C₂×C₃²×C₄	C₂²×D₃	1	16	yes	—
138	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
139	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
140	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
141	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
142	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
143	#638	—	2	4	no	—
144	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
145	C₄⋊(C₃⋊D₃)	—	2	4	no	—
146	C₄⋊(C₃⋊D₃)	—	2	4	no	—
147	C₄⋊(C₃⋊D₃)	—	2	2	no	—
148	C₄⋊(C₃⋊D₃)	—	4	8	no	—
149	C₄×C₃⋊D₃	—	2	4	no	—
150	#634	—	2	2	no	—
151	C₃×#67	—	6	16	no	—
152	C₂×C₃×Dic₃	—	3	8	no	—
153	C₃×D₁₂	—	6	16	no	—
154	C₃×D₁₂	—	6	16	no	—
155	C₃×D₁₂	—	6	8	no	—
156	C₃×D₁₂	—	12	32	no	—
157	C₃×C₄×D₃	—	6	16	no	—
158	C₃×Dic₆	—	6	8	no	—
159	#535	—	9	1	no	Sylow
160	C₂×C₃³	—	2	2	no	—
161	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₃³	H(5,𝔽₂)	1	2	yes	—
163	C₃×C₃⋊D₃	—	4	2	no	—
164	C₃×C₃⋊D₃	—	4	4	no	—
165	C₂⁴×C₃	—	9	2	no	—
166	C₂³×D₃	—	3	8	no	—
167	C₃×#41	—	18	4	no	—
168	C₂×C₃×Q₈	—	9	1	no	—
169	C₂×C₃×D₄	—	9	2	no	—
170	C₂×C₃×D₄	—	9	2	no	—
171	C₂×C₃×D₄	—	9	2	no	—
172	C₂×C₃×D₄	—	9	1	no	—
173	C₂×C₃×D₄	—	9	8	no	—
174	C₂×C₃×D₄	—	18	4	no	—
175	C₂²×C₃×C₄	—	2	4	no	—
176	C₂²×C₃×C₄	—	9	2	no	—
177	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
178	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
179	C₂×#67	—	3	8	no	—
180	#235	—	6	16	no	—
181	C₂×D₁₂	—	3	4	no	—
182	C₂×D₁₂	—	3	8	no	—
183	C₂×D₁₂	—	3	8	no	—
184	C₂×D₁₂	—	3	32	no	—
185	C₂×D₁₂	—	6	16	no	—
186	C₂×C₄×D₃	—	3	8	no	—
187	C₂×Dic₆	—	3	4	no	—
188	C₃×C₄⋊C₄	—	2	8	no	—
189	C₃×C₄⋊C₄	C₂×C₃×D₃	1	8	yes	complemented
190	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	2	yes	complemented
191	C₃×C₂²⋊C₄	—	2	8	no	—
192	C₃×C₂²⋊C₄	—	9	8	no	—
193	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	8	yes	—
194	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	2	yes	—
195	C₃×C₄²	—	2	8	no	—
196	C₃×C₄²	C₂×C₃×D₃	1	8	yes	complemented
197	C₃×C₄²	C₂×C₃⋊D₃	1	2	yes	complemented
198	(C₂×D₃)⋊C₄	—	3	32	no	—
199	C₂²×C₃²	—	2	2	no	—
200	C₂²×C₃²	—	2	4	no	—
201	C₂²×C₃²	—	2	8	no	—
202	C₂²×C₃²	—	2	8	no	—
203	C₂²×C₃²	—	4	8	no	—
204	C₂²×C₃²	C₂×D₁₂	1	8	yes	—
205	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
206	C₂²×C₃²	C₂³×D₃	1	4	yes	—
207	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
208	C₂×C₃⋊D₃	—	2	2	no	—
209	C₂×C₃⋊D₃	—	2	4	no	—
210	C₂×C₃⋊D₃	—	2	4	no	—
211	C₂×C₃⋊D₃	—	2	8	no	—
212	C₂×C₃⋊D₃	—	4	8	no	—
213	C₂×C₃×D₃	—	6	8	no	—
214	C₂×C₃×D₃	—	6	16	no	—
215	C₂×C₃×D₃	—	6	16	no	—
216	C₂×C₃×D₃	—	6	32	no	—
217	C₂×C₃×D₃	—	12	32	no	—
218	C₃²×C₄	—	2	4	no	—
219	C₃²×C₄	—	2	8	no	—
220	C₃²×C₄	—	2	8	no	—
221	C₃²×C₄	—	2	16	no	—
222	C₃²×C₄	—	4	16	no	—
223	C₃²×C₄	C₂×D₁₂	1	8	yes	—
224	C₃²×C₄	C₂×D₁₂	1	8	yes	—
225	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
226	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
227	C₃⋊Dic₃	—	2	2	no	—
228	C₃×Dic₃	—	6	8	no	—
229	C₂×#41	—	9	1	no	—
230	C₂²×D₄	—	9	1	no	—
231	#127	—	9	2	no	—
232	#124	—	9	2	no	—
233	#121	—	9	4	no	—
234	#120	—	9	4	no	—
235	#117	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
236	C₃³	#535	1	1	yes	characteristic, complemented, Sylow
237	C₂³×C₃	—	2	4	no	—
238	C₂³×C₃	—	9	4	no	—
239	C₂³×C₃	—	9	2	no	—
240	C₂³×C₃	—	18	4	no	—
241	C₂³×C₃	—	36	4	no	—
242	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
243	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
244	C₂²×D₃	—	3	16	no	—
245	C₂²×D₃	—	3	8	no	—
246	C₂²×D₃	—	6	16	no	—
247	C₂²×D₃	—	12	16	no	—
248	C₃×Q₈	—	18	2	no	—
249	C₃×D₄	—	18	4	no	—
250	C₃×D₄	—	18	4	no	—
251	C₃×D₄	—	18	4	no	—
252	C₃×D₄	—	18	2	no	—
253	C₃×D₄	—	36	8	no	—
254	C₂×C₃×C₄	—	2	16	no	—
255	C₂×C₃×C₄	—	2	4	no	—
256	C₂×C₃×C₄	—	2	4	no	—
257	C₂×C₃×C₄	—	2	16	no	—
258	C₂×C₃×C₄	—	9	2	no	—
259	C₂×C₃×C₄	—	18	4	no	—
260	C₂×C₃×C₄	C₃×D₁₂	1	16	yes	complemented
261	C₂×C₃×C₄	C₄⋊(C₃⋊D₃)	1	4	yes	complemented
262	C₂×C₃×C₄	C₂²×C₃×D₃	1	16	yes	—
263	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	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	1	yes	characteristic
267	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
268	#67	—	6	16	no	—
269	C₂×Dic₃	—	3	8	no	—
270	D₁₂	—	6	16	no	—
271	D₁₂	—	6	16	no	—
272	D₁₂	—	6	8	no	—
273	D₁₂	—	12	32	no	—
274	C₄×D₃	—	6	16	no	—
275	Dic₆	—	6	8	no	—
276	C₂×C₃²	—	2	2	no	—
277	C₂×C₃²	—	2	4	no	—
278	C₂×C₃²	—	2	8	no	—
279	C₂×C₃²	—	2	8	no	—
280	C₂×C₃²	—	4	8	no	—
281	C₂×C₃²	C₂²×D₁₂	1	4	yes	—
282	C₂×C₃²	#1009	1	8	yes	—
283	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
284	C₂×C₃²	C₃×H(5,𝔽₂)	1	2	yes	—
285	C₃⋊D₃	—	4	2	no	—
286	C₃⋊D₃	—	4	4	no	—
287	C₃×D₃	—	12	8	no	—
288	C₃×D₃	—	12	16	no	—
289	C₂⁴	—	9	2	no	—
290	#41	—	18	4	no	—
291	C₂×Q₈	—	9	1	no	—
292	C₂×D₄	—	9	2	no	—
293	C₂×D₄	—	9	2	no	—
294	C₂×D₄	—	9	2	no	—
295	C₂×D₄	—	9	1	no	—
296	C₂×D₄	—	9	8	no	—
297	C₂×D₄	—	18	4	no	—
298	C₂²×C₄	—	9	2	no	—
299	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
300	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
301	C₂²⋊C₄	—	9	8	no	—
302	C₂²⋊C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
303	C₄²	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
304	C₂²×C₃	—	2	8	no	—
305	C₂²×C₃	—	2	2	no	—
306	C₂²×C₃	—	2	4	no	—
307	C₂²×C₃	—	2	8	no	—
308	C₂²×C₃	—	4	8	no	—
309	C₂²×C₃	—	18	2	no	—
310	C₂²×C₃	—	18	4	no	—
311	C₂²×C₃	—	18	4	no	—
312	C₂²×C₃	—	18	8	no	—
313	C₂²×C₃	—	36	8	no	—
314	C₂²×C₃	C₂×C₃×D₁₂	1	8	yes	—
315	C₂²×C₃	C₂×C₄⋊(C₃⋊D₃)	1	2	yes	—
316	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
317	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
318	C₂×D₃	—	6	8	no	—
319	C₂×D₃	—	6	16	no	—
320	C₂×D₃	—	6	16	no	—
321	C₂×D₃	—	6	32	no	—
322	C₂×D₃	—	12	32	no	—
323	C₃×C₄	—	2	16	no	—
324	C₃×C₄	—	2	4	no	—
325	C₃×C₄	—	2	8	no	—
326	C₃×C₄	—	2	8	no	—
327	C₃×C₄	—	4	16	no	—
328	C₃×C₄	—	18	2	no	—
329	C₃×C₄	C₂×C₃×D₁₂	1	8	yes	—
330	C₃×C₄	C₂×C₃×D₁₂	1	8	yes	—
331	C₃×C₄	C₂×C₄⋊(C₃⋊D₃)	1	2	yes	—
332	C₃×C₄	C₂×C₄⋊(C₃⋊D₃)	1	2	yes	—
333	Dic₃	—	6	8	no	—
334	C₃²	—	2	4	no	—
335	C₃²	#5525	1	4	yes	complemented
336	C₃²	C₃×#535	1	1	yes	characteristic, complemented
337	C₂³	—	9	4	no	—
338	C₂³	—	9	2	no	—
339	C₂³	—	18	4	no	—
340	C₂³	—	36	4	no	—
341	C₂³	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
342	Q₈	—	18	2	no	—
343	D₄	—	18	4	no	—
344	D₄	—	18	4	no	—
345	D₄	—	18	4	no	—
346	D₄	—	18	2	no	—
347	D₄	—	36	8	no	—
348	C₂×C₄	—	9	2	no	—
349	C₂×C₄	—	18	4	no	—
350	C₂×C₄	C₃×C₄⋊(C₃⋊D₃)	1	4	yes	complemented
351	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	4	yes	—
352	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
353	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
354	C₂×C₃	—	2	8	no	—
355	C₂×C₃	—	2	2	no	—
356	C₂×C₃	—	2	4	no	—
357	C₂×C₃	—	2	8	no	—
358	C₂×C₃	—	4	8	no	—
359	C₂×C₃	—	36	4	no	—
360	C₂×C₃	—	36	2	no	—
361	C₂×C₃	C₂²×C₃×D₁₂	1	4	yes	—
362	C₂×C₃	C₃×#1009	1	8	yes	—
363	C₂×C₃	C₂²×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
364	C₂×C₃	#64366	1	2	yes	—
365	D₃	—	12	16	no	—
366	D₃	—	12	8	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	18	2	no	—
369	C₂²	—	18	4	no	—
370	C₂²	—	18	4	no	—
371	C₂²	—	18	8	no	—
372	C₂²	—	36	8	no	—
373	C₂²	C₂×C₃×C₄⋊(C₃⋊D₃)	1	2	yes	—
374	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
375	C₄	—	2	4	no	—
376	C₄	—	18	2	no	—
377	C₄	C₂×C₃×C₄⋊(C₃⋊D₃)	1	2	yes	—
378	C₄	C₂×C₃×C₄⋊(C₃⋊D₃)	1	2	yes	—
379	C₃	—	2	4	no	—
380	C₃	C₃×#5525	1	4	yes	complemented
381	C₃	#10595996	1	1	yes	characteristic, direct product factor
382	C₂	—	2	2	no	—
383	C₂	—	36	4	no	—
384	C₂	—	36	2	no	—
385	C₂	C₂²×C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
386	C₂	C₃×#64366	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂³×C₃⋊D₃
commutator, cosocle	C₂²×C₃²	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×C₃⋊D₃
Fitting	C₃³×#117	C₂
socle	C₂²×C₃³	C₂⁴
hypercenter	C₃×#117	C₃⋊D₃
hypocenter	C₃²	C₃×#535
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#117

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#3828	C₂	semidirect
2. C₂²×C₃×C₄⋊(C₃⋊D₃)	C₂	semidirect
3. C₃³×#117	C₂	semidirect
4. C₃×#64104	C₂	semidirect
5. C₃×#64091	C₂	semidirect
6. C₃×#64084	C₂	semidirect
7. C₃×#64083	C₂	semidirect
8. #10595996	C₃	direct (N × H)
17. C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	semidirect
18. C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	semidirect
19. C₂×C₃×C₄×C₃⋊D₃	C₂²	semidirect
20. C₂×C₃×#634	C₂²	semidirect
21. C₃³×C₄⋊C₄	C₂²	semidirect
23. C₃³×C₄²	C₂²	semidirect
24. C₃×#3752	C₂²	semidirect
25. C₂×#3828	C₂×C₃	semidirect
26. C₂²×C₄⋊(C₃⋊D₃)	C₂×C₃	semidirect
30. C₃²×#117	D₃	semidirect
31. C₃²×#117	C₂×C₃	semidirect
32. #64104	C₂×C₃	semidirect
33. #64091	C₂×C₃	semidirect
34. #64084	C₂×C₃	semidirect
35. #64083	C₂×C₃	semidirect
45. C₂×C₃³×C₄	D₄	semidirect
69. C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	semidirect
70. C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	semidirect
71. C₂×C₄×C₃⋊D₃	C₂²×C₃	semidirect
72. C₂×#634	C₂²×C₃	semidirect
83. C₃²×C₄⋊C₄	C₂×D₃	semidirect
84. C₃²×C₄⋊C₄	C₂²×C₃	semidirect
89. C₃²×C₄²	C₂×D₃	semidirect
90. C₃²×C₄²	C₂²×C₃	semidirect
91. #3752	C₂²×C₃	semidirect
114. C₃×#117	C₃×D₃	semidirect
115. C₃×#117	C₃⋊D₃	semidirect
135. C₂×C₃²×C₄	D₁₂	semidirect
136. C₂×C₃²×C₄	C₃×D₄	semidirect
189. C₃×C₄⋊C₄	C₂×C₃×D₃	semidirect
190. C₃×C₄⋊C₄	C₂×C₃⋊D₃	semidirect
196. C₃×C₄²	C₂×C₃×D₃	semidirect
197. C₃×C₄²	C₂×C₃⋊D₃	semidirect
235. #117	C₃×C₃⋊D₃	semidirect
236. C₃³	#535	semidirect
260. C₂×C₃×C₄	C₃×D₁₂	semidirect
261. C₂×C₃×C₄	C₄⋊(C₃⋊D₃)	semidirect
300. C₄⋊C₄	C₂×C₃×C₃⋊D₃	semidirect
303. C₄²	C₂×C₃×C₃⋊D₃	semidirect
335. C₃²	#5525	semidirect
336. C₃²	C₃×#535	semidirect
350. C₂×C₄	C₃×C₄⋊(C₃⋊D₃)	semidirect
380. C₃	C₃×#5525	semidirect
381. C₃	#10595996	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
C₂²×C₃×C₄⋊(C₃⋊D₃)	2
C₃³×#117	2
C₃×#64104	2
C₃×#64091	2
C₃×#64084	2
C₃×#64083	2
#10595996	3
C₃×#5525	3

Subgroups — C3×#10595996 #13179279

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10595996 #13179279