Subgroups — C₃×#10596197 #13179478

Order 1728.

2024 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#3832	C₂	1	2	yes	maximal, complemented
2	C₃³×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#64155	C₂	1	2	yes	maximal, complemented
4	C₃×#64104	C₂	1	2	yes	maximal, complemented
5	C₃×#64103	C₂	1	4	yes	maximal, complemented
6	C₃×C₄⋊C₄×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₄×C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
9	#10596197	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₃×#5726	—	3	4	no	maximal
11	C₂×C₃³×Q₈	C₂²	1	2	yes	—
12	C₃×#3832	—	2	8	no	—
13	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	4	yes	—
15	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	2	yes	—
17	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	2	yes	—
18	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	4	yes	—
19	C₃³×C₄⋊C₄	C₂²	1	2	yes	—
20	C₃³×C₄⋊C₄	C₂²	1	2	yes	—
21	C₃³×C₄²	C₂²	1	1	yes	characteristic
22	C₃×#3752	C₂²	1	2	yes	—
23	C₃×#3752	C₂²	1	2	yes	—
24	C₃×#3752	C₂²	1	4	yes	—
25	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
26	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
27	C₃×#3750	C₂²	1	4	yes	—
28	C₂×#3832	C₂×C₃	1	2	yes	complemented
29	C₂×C₃×#239	—	3	8	no	—
30	C₃²×C₄⋊Q₈	—	2	4	no	—
31	C₃²×C₄⋊Q₈	D₃	1	4	yes	complemented
32	C₃²×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
33	#64155	C₂×C₃	1	2	yes	complemented
34	#64104	C₂×C₃	1	2	yes	complemented
35	#64103	C₂×C₃	1	4	yes	complemented
36	C₄⋊C₄×C₃⋊D₃	C₂×C₃	1	2	yes	complemented
37	C₄×C₄⋊(C₃⋊D₃)	C₂×C₃	1	1	yes	characteristic, complemented
38	C₄×C₄⋊(C₃⋊D₃)	C₂×C₃	1	1	yes	characteristic, complemented
39	C₃×#946	—	3	8	no	—
40	C₃×#895	—	3	8	no	—
41	C₃×#894	—	3	16	no	—
42	C₃×D₃×C₄⋊C₄	—	3	8	no	—
43	C₃×C₄×D₁₂	—	3	4	no	—
44	C₃×C₄×D₁₂	—	3	4	no	—
45	C₂²×C₃×C₃⋊D₃	C₂³	1	2	yes	—
46	C₂²×C₃×C₃⋊D₃	C₂³	1	2	yes	—
47	C₃³×Q₈	—	2	4	no	—
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	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
52	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
53	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
54	C₃×C₄⋊(C₃⋊D₃)	—	2	8	no	—
55	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
56	C₃×C₄⋊(C₃⋊D₃)	D₄	1	4	yes	complemented
57	C₃×C₄×C₃⋊D₃	—	2	8	no	—
58	C₃×C₄×C₃⋊D₃	—	2	4	no	—
59	C₃×C₄×C₃⋊D₃	—	2	4	no	—
60	C₃×#547	—	9	1	no	—
61	#5726	—	3	4	no	—
62	C₂×C₃²×Q₈	—	2	8	no	—
63	C₂×C₃²×Q₈	C₂×D₃	1	8	yes	—
64	C₂×C₃²×Q₈	C₂²×C₃	1	2	yes	—
65	#3832	—	2	8	no	—
66	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic
67	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	4	yes	—
68	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic
69	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	2	yes	—
70	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	2	yes	—
71	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	4	yes	—
72	C₃×#239	—	6	32	no	—
73	C₂×C₃×D₁₂	—	3	4	no	—
74	C₂×C₃×D₁₂	—	3	16	no	—
75	C₂×C₃×D₁₂	—	3	4	no	—
76	C₂×C₃×C₄×D₃	—	3	16	no	—
77	C₂×C₃×C₄×D₃	—	3	8	no	—
78	C₂×C₃×C₄×D₃	—	3	8	no	—
79	C₃²×C₄⋊C₄	—	2	8	no	—
80	C₃²×C₄⋊C₄	—	2	8	no	—
81	C₃²×C₄⋊C₄	C₂×D₃	1	8	yes	—
82	C₃²×C₄⋊C₄	C₂×D₃	1	8	yes	—
83	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
84	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
85	C₃²×C₄²	—	2	4	no	—
86	C₃²×C₄²	C₂×D₃	1	4	yes	—
87	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
88	#3752	C₂²×C₃	1	2	yes	—
89	#3752	C₂²×C₃	1	2	yes	—
90	#3752	C₂²×C₃	1	4	yes	—
91	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	1	yes	characteristic
92	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	1	yes	characteristic
93	#3750	C₂²×C₃	1	4	yes	—
94	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
95	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
96	C₃×(C₂×D₃)⋊C₄	—	3	16	no	—
97	C₃×C₄⋊Dic₃	—	3	4	no	—
98	C₃×C₄⋊Dic₃	—	3	4	no	—
99	C₃×Dic₃⋊C₄	—	3	16	no	—
100	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
101	C₂×C₃×C₃⋊D₃	—	2	2	no	—
102	C₂×C₃×C₃⋊D₃	—	2	2	no	—
103	C₂×C₃×C₃⋊D₃	—	2	2	no	—
104	C₂×C₃×C₃⋊D₃	—	2	2	no	—
105	C₂×C₃×C₃⋊D₃	—	2	2	no	—
106	C₂×C₃×C₃⋊D₃	C₂×D₄	1	4	yes	—
107	C₃³×C₄	—	2	4	no	—
108	C₃³×C₄	—	2	1	no	—
109	C₃³×C₄	C₂×D₄	1	2	yes	—
110	C₃³×C₄	#41	1	2	yes	complemented
111	C₃×C₃⋊Dic₃	—	2	2	no	—
112	C₃×C₃⋊Dic₃	—	2	2	no	—
113	C₂×C₃×#41	—	9	2	no	—
114	C₂×#239	—	3	8	no	—
115	C₃×C₄⋊Q₈	—	2	4	no	—
116	C₃×C₄⋊Q₈	C₃×D₃	1	4	yes	complemented
117	C₃×C₄⋊Q₈	C₃⋊D₃	1	1	yes	characteristic, complemented
118	C₃×#123	—	9	4	no	—
119	C₃×C₂²⋊Q₈	—	9	2	no	—
120	C₃×#121	—	9	2	no	—
121	C₃×C₄×D₄	—	9	1	no	—
122	C₃×C₄×D₄	—	9	1	no	—
123	C₂×C₃×C₄⋊C₄	—	9	2	no	—
124	#946	—	3	8	no	—
125	#895	—	3	8	no	—
126	#894	—	3	16	no	—
127	D₃×C₄⋊C₄	—	3	8	no	—
128	C₄×D₁₂	—	3	4	no	—
129	C₄×D₁₂	—	3	4	no	—
130	C₂²×C₃⋊D₃	C₂³×C₃	1	2	yes	—
131	C₂²×C₃⋊D₃	C₂³×C₃	1	2	yes	—
132	C₂²×C₃×D₃	—	3	8	no	—
133	C₂²×C₃×D₃	—	3	8	no	—
134	C₃²×Q₈	—	2	4	no	—
135	C₃²×Q₈	—	2	16	no	—
136	C₃²×Q₈	—	4	16	no	—
137	C₂×C₃²×C₄	—	2	4	no	—
138	C₂×C₃²×C₄	—	2	4	no	—
139	C₂×C₃²×C₄	—	2	4	no	—
140	C₂×C₃²×C₄	—	2	16	no	—
141	C₂×C₃²×C₄	C₂²×D₃	1	16	yes	—
142	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
143	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
144	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
145	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
146	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
147	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
148	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
149	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
150	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
151	C₄⋊(C₃⋊D₃)	—	2	8	no	—
152	C₄⋊(C₃⋊D₃)	—	2	2	no	—
153	C₄⋊(C₃⋊D₃)	C₃×D₄	1	4	yes	complemented
154	C₄×C₃⋊D₃	—	2	8	no	—
155	C₄×C₃⋊D₃	—	2	4	no	—
156	C₄×C₃⋊D₃	—	2	4	no	—
157	C₂×C₃×Dic₃	—	3	8	no	—
158	C₂×C₃×Dic₃	—	3	8	no	—
159	C₃×D₁₂	—	3	16	no	—
160	C₃×D₁₂	—	6	32	no	—
161	C₃×D₁₂	—	6	8	no	—
162	C₃×C₄×D₃	—	6	32	no	—
163	C₃×C₄×D₃	—	6	16	no	—
164	C₃×C₄×D₃	—	6	16	no	—
165	#547	—	9	1	no	Sylow
166	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₃³	C₂×#41	1	1	yes	characteristic
168	C₂×C₃³	2₋¹⁺⁴	1	1	yes	characteristic
169	C₃×C₃⋊D₃	—	2	4	no	—
170	C₃×C₃⋊D₃	—	4	2	no	—
171	C₃×#41	—	18	8	no	—
172	C₂×C₃×Q₈	—	2	8	no	—
173	C₂×C₃×Q₈	C₂×C₃×D₃	1	8	yes	—
174	C₂×C₃×Q₈	C₂×C₃⋊D₃	1	2	yes	—
175	C₂×C₃×D₄	—	9	1	no	—
176	C₂×C₃×D₄	—	9	1	no	—
177	C₂×C₃×D₄	—	9	4	no	—
178	C₂²×C₃×C₄	—	9	2	no	—
179	C₂²×C₃×C₄	—	9	4	no	—
180	C₂²×C₃×C₄	—	9	2	no	—
181	#239	—	6	32	no	—
182	C₂×D₁₂	—	3	4	no	—
183	C₂×D₁₂	—	3	4	no	—
184	C₂×D₁₂	—	3	16	no	—
185	C₂×C₄×D₃	—	3	8	no	—
186	C₂×C₄×D₃	—	3	8	no	—
187	C₂×C₄×D₃	—	3	16	no	—
188	C₃×C₄⋊C₄	—	2	8	no	—
189	C₃×C₄⋊C₄	—	2	8	no	—
190	C₃×C₄⋊C₄	—	9	4	no	—
191	C₃×C₄⋊C₄	—	9	1	no	—
192	C₃×C₄⋊C₄	—	9	1	no	—
193	C₃×C₄⋊C₄	C₂×C₃×D₃	1	8	yes	—
194	C₃×C₄⋊C₄	C₂×C₃×D₃	1	8	yes	—
195	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	2	yes	—
196	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	2	yes	—
197	C₃×C₂²⋊C₄	—	9	2	no	—
198	C₃×C₂²⋊C₄	—	9	2	no	—
199	C₃×C₂²⋊C₄	—	9	4	no	—
200	C₃×C₄²	—	2	4	no	—
201	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
202	C₃×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic
203	(C₂×D₃)⋊C₄	—	3	8	no	—
204	(C₂×D₃)⋊C₄	—	3	8	no	—
205	(C₂×D₃)⋊C₄	—	3	16	no	—
206	C₄⋊Dic₃	—	3	4	no	—
207	C₄⋊Dic₃	—	3	4	no	—
208	Dic₃⋊C₄	—	3	16	no	—
209	C₂²×C₃²	—	2	4	no	—
210	C₂²×C₃²	C₂³×D₃	1	4	yes	—
211	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
212	C₂×C₃⋊D₃	—	2	2	no	—
213	C₂×C₃⋊D₃	—	2	2	no	—
214	C₂×C₃⋊D₃	—	2	2	no	—
215	C₂×C₃⋊D₃	—	2	2	no	—
216	C₂×C₃⋊D₃	—	2	2	no	—
217	C₂×C₃⋊D₃	C₂×C₃×D₄	1	4	yes	—
218	C₂×C₃×D₃	—	3	16	no	—
219	C₂×C₃×D₃	—	6	8	no	—
220	C₂×C₃×D₃	—	6	8	no	—
221	C₂×C₃×D₃	—	6	8	no	—
222	C₂×C₃×D₃	—	6	8	no	—
223	C₂×C₃×D₃	—	6	8	no	—
224	C₃²×C₄	—	2	8	no	—
225	C₃²×C₄	—	2	4	no	—
226	C₃²×C₄	—	2	4	no	—
227	C₃²×C₄	—	2	1	no	—
228	C₃²×C₄	—	2	8	no	—
229	C₃²×C₄	—	2	8	no	—
230	C₃²×C₄	—	2	16	no	—
231	C₃²×C₄	—	4	16	no	—
232	C₃²×C₄	D₃×D₄	1	8	yes	—
233	C₃²×C₄	#239	1	8	yes	complemented
234	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
235	C₃²×C₄	C₃×#41	1	2	yes	complemented
236	C₃⋊Dic₃	—	2	2	no	—
237	C₃⋊Dic₃	—	2	2	no	—
238	C₃×Dic₃	—	6	8	no	—
239	C₃×Dic₃	—	6	8	no	—
240	C₂×#41	—	9	2	no	—
241	C₄⋊Q₈	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
242	#123	—	9	4	no	—
243	C₂²⋊Q₈	—	9	2	no	—
244	#121	—	9	2	no	—
245	C₄×D₄	—	9	1	no	—
246	C₄×D₄	—	9	1	no	—
247	C₂×C₄⋊C₄	—	9	2	no	—
248	C₃³	#547	1	1	yes	characteristic, complemented, Sylow
249	C₂³×C₃	—	9	2	no	—
250	C₂³×C₃	—	9	2	no	—
251	C₂²×D₃	—	3	8	no	—
252	C₂²×D₃	—	3	8	no	—
253	C₃×Q₈	—	2	16	no	—
254	C₃×Q₈	—	2	4	no	—
255	C₃×Q₈	—	4	16	no	—
256	C₃×D₄	—	9	4	no	—
257	C₃×D₄	—	18	8	no	—
258	C₃×D₄	—	18	2	no	—
259	C₂×C₃×C₄	—	2	4	no	—
260	C₂×C₃×C₄	—	2	4	no	—
261	C₂×C₃×C₄	—	2	4	no	—
262	C₂×C₃×C₄	—	2	16	no	—
263	C₂×C₃×C₄	—	9	2	no	—
264	C₂×C₃×C₄	—	9	2	no	—
265	C₂×C₃×C₄	—	18	8	no	—
266	C₂×C₃×C₄	—	18	4	no	—
267	C₂×C₃×C₄	—	18	4	no	—
268	C₂×C₃×C₄	C₂²×C₃×D₃	1	16	yes	—
269	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
270	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
271	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
272	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
273	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	4	yes	—
274	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
275	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
276	C₂×Dic₃	—	3	8	no	—
277	C₂×Dic₃	—	3	8	no	—
278	D₁₂	—	3	16	no	—
279	D₁₂	—	6	32	no	—
280	D₁₂	—	6	8	no	—
281	C₄×D₃	—	6	32	no	—
282	C₄×D₃	—	6	16	no	—
283	C₄×D₃	—	6	16	no	—
284	C₂×C₃²	—	2	4	no	—
285	C₂×C₃²	—	2	4	no	—
286	C₂×C₃²	—	2	4	no	—
287	C₂×C₃²	C₂×D₃×D₄	1	4	yes	—
288	C₂×C₃²	C₂×#239	1	4	yes	—
289	C₂×C₃²	#1007	1	4	yes	—
290	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
291	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
292	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
293	C₃⋊D₃	—	2	4	no	—
294	C₃⋊D₃	—	4	2	no	—
295	C₃×D₃	—	6	16	no	—
296	C₃×D₃	—	12	8	no	—
297	#41	—	18	8	no	—
298	C₂×Q₈	C₂×C₃×C₃⋊D₃	1	2	yes	—
299	C₂×D₄	—	9	1	no	—
300	C₂×D₄	—	9	1	no	—
301	C₂×D₄	—	9	4	no	—
302	C₂²×C₄	—	9	2	no	—
303	C₂²×C₄	—	9	4	no	—
304	C₂²×C₄	—	9	2	no	—
305	C₄⋊C₄	—	9	1	no	—
306	C₄⋊C₄	—	9	4	no	—
307	C₄⋊C₄	—	9	1	no	—
308	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
309	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
310	C₂²⋊C₄	—	9	2	no	—
311	C₂²⋊C₄	—	9	2	no	—
312	C₂²⋊C₄	—	9	4	no	—
313	C₄²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
314	C₂²×C₃	—	2	4	no	—
315	C₂²×C₃	—	9	4	no	—
316	C₂²×C₃	—	18	2	no	—
317	C₂²×C₃	—	18	2	no	—
318	C₂²×C₃	—	18	2	no	—
319	C₂²×C₃	—	18	2	no	—
320	C₂²×C₃	—	18	2	no	—
321	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
322	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
323	C₂×D₃	—	3	16	no	—
324	C₂×D₃	—	6	8	no	—
325	C₂×D₃	—	6	8	no	—
326	C₂×D₃	—	6	8	no	—
327	C₂×D₃	—	6	8	no	—
328	C₂×D₃	—	6	8	no	—
329	C₃×C₄	—	2	8	no	—
330	C₃×C₄	—	2	16	no	—
331	C₃×C₄	—	2	4	no	—
332	C₃×C₄	—	2	4	no	—
333	C₃×C₄	—	2	1	no	—
334	C₃×C₄	—	2	8	no	—
335	C₃×C₄	—	2	8	no	—
336	C₃×C₄	—	4	16	no	—
337	C₃×C₄	—	18	2	no	—
338	C₃×C₄	—	18	2	no	—
339	C₃×C₄	C₃×D₃×D₄	1	8	yes	—
340	C₃×C₄	C₃×#239	1	8	yes	complemented
341	C₃×C₄	D₄×C₃⋊D₃	1	2	yes	—
342	C₃×C₄	#3832	1	2	yes	complemented
343	Dic₃	—	6	8	no	—
344	Dic₃	—	6	8	no	—
345	C₃²	—	2	4	no	—
346	C₃²	#5726	1	4	yes	complemented
347	C₃²	C₃×#547	1	1	yes	characteristic, complemented
348	C₂³	—	9	2	no	—
349	C₂³	—	9	2	no	—
350	Q₈	—	2	4	no	—
351	D₄	—	9	4	no	—
352	D₄	—	18	8	no	—
353	D₄	—	18	2	no	—
354	C₂×C₄	—	9	2	no	—
355	C₂×C₄	—	9	2	no	—
356	C₂×C₄	—	18	8	no	—
357	C₂×C₄	—	18	4	no	—
358	C₂×C₄	—	18	4	no	—
359	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
360	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	4	yes	—
361	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
362	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
363	C₂×C₃	—	2	4	no	—
364	C₂×C₃	—	2	4	no	—
365	C₂×C₃	—	2	4	no	—
366	C₂×C₃	—	18	4	no	—
367	C₂×C₃	—	36	2	no	—
368	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
369	C₂×C₃	C₂×C₃×#239	1	4	yes	—
370	C₂×C₃	C₃×#1007	1	4	yes	—
371	C₂×C₃	C₂×D₄×C₃⋊D₃	1	1	yes	characteristic
372	C₂×C₃	C₂×#3832	1	1	yes	characteristic
373	C₂×C₃	#64364	1	1	yes	characteristic
374	D₃	—	6	16	no	—
375	D₃	—	12	8	no	—
376	C₂²	—	9	4	no	—
377	C₂²	—	18	2	no	—
378	C₂²	—	18	2	no	—
379	C₂²	—	18	2	no	—
380	C₂²	—	18	2	no	—
381	C₂²	—	18	2	no	—
382	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
383	C₄	—	2	4	no	—
384	C₄	—	2	1	no	—
385	C₄	—	18	2	no	—
386	C₄	—	18	2	no	—
387	C₄	C₃×D₄×C₃⋊D₃	1	2	yes	—
388	C₄	C₃×#3832	1	2	yes	complemented
389	C₃	—	2	4	no	—
390	C₃	C₃×#5726	1	4	yes	complemented
391	C₃	#10596197	1	1	yes	characteristic, direct product factor
392	C₂	—	18	4	no	—
393	C₂	—	36	2	no	—
394	C₂	C₂×C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
395	C₂	C₂×C₃×#3832	1	1	yes	characteristic
396	C₂	C₃×#64364	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×C₃⋊D₃
commutator, cosocle	C₂²×C₃²	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×C₃⋊D₃
Fitting	C₃³×C₄⋊Q₈	C₂
socle	C₂²×C₃³	C₂⁴
hypercenter	C₃×C₄⋊Q₈	C₃⋊D₃
hypocenter	C₃²	C₃×#547
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#3832	C₂	semidirect
2. C₃³×C₄⋊Q₈	C₂	semidirect
3. C₃×#64155	C₂	semidirect
4. C₃×#64104	C₂	semidirect
5. C₃×#64103	C₂	semidirect
6. C₃×C₄⋊C₄×C₃⋊D₃	C₂	semidirect
7. C₃×C₄×C₄⋊(C₃⋊D₃)	C₂	semidirect
8. C₃×C₄×C₄⋊(C₃⋊D₃)	C₂	semidirect
9. #10596197	C₃	direct (N × H)
28. C₂×#3832	C₂×C₃	semidirect
31. C₃²×C₄⋊Q₈	D₃	semidirect
32. C₃²×C₄⋊Q₈	C₂×C₃	semidirect
33. #64155	C₂×C₃	semidirect
34. #64104	C₂×C₃	semidirect
35. #64103	C₂×C₃	semidirect
36. C₄⋊C₄×C₃⋊D₃	C₂×C₃	semidirect
37. C₄×C₄⋊(C₃⋊D₃)	C₂×C₃	semidirect
38. C₄×C₄⋊(C₃⋊D₃)	C₂×C₃	semidirect
56. C₃×C₄⋊(C₃⋊D₃)	D₄	semidirect
110. C₃³×C₄	#41	semidirect
116. C₃×C₄⋊Q₈	C₃×D₃	semidirect
117. C₃×C₄⋊Q₈	C₃⋊D₃	semidirect
153. C₄⋊(C₃⋊D₃)	C₃×D₄	semidirect
233. C₃²×C₄	#239	semidirect
235. C₃²×C₄	C₃×#41	semidirect
241. C₄⋊Q₈	C₃×C₃⋊D₃	semidirect
248. C₃³	#547	semidirect
340. C₃×C₄	C₃×#239	semidirect
342. C₃×C₄	#3832	semidirect
346. C₃²	#5726	semidirect
347. C₃²	C₃×#547	semidirect
388. C₄	C₃×#3832	semidirect
390. C₃	C₃×#5726	semidirect
391. C₃	#10596197	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×#3832	2
C₃³×C₄⋊Q₈	2
C₃×#64155	2
C₃×#64104	2
C₃×#64103	2
C₃×C₄⋊C₄×C₃⋊D₃	2
C₃×C₄×C₄⋊(C₃⋊D₃)	2
#10596197	3
C₃×#5726	3

Subgroups — C3×#10596197 #13179478

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596197 #13179478