Subgroups — C₃×#10596216 #13179496

Order 1728.

1820 conjugacy classes of subgroups.

The subgroup lattice has 412 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	C₂×C₃³×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#3748	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64116	C₂	1	4	yes	maximal, complemented
5	C₃×M₁₆×C₃⋊D₃	C₂	1	4	yes	maximal, complemented
6	C₃×#64110	C₂	1	4	yes	maximal, complemented
7	#10596216	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₃×#5745	—	3	4	no	maximal
9	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
10	C₂×C₃×#638	C₄	1	2	yes	—
11	C₃×#3828	C₄	1	2	yes	—
12	C₃×#3828	C₄	1	2	yes	—
13	C₃×#3828	C₂²	1	2	yes	—
14	C₃×#3828	C₂²	1	2	yes	—
15	C₂×C₃×C₄⋊(C₃⋊D₃)	C₄	1	1	yes	characteristic
16	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	2	yes	—
17	C₂×C₃×#634	C₄	1	1	yes	characteristic
18	C₃³×M₁₆	C₂²	1	2	yes	—
19	C₃³×M₁₆	C₂²	1	2	yes	complemented
20	C₂×C₃³×C₈	C₂²	1	2	yes	complemented
21	C₃×#3748	C₂²	1	2	yes	—
22	C₃×#3748	C₂²	1	2	yes	complemented
23	C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	1	2	yes	complemented
24	C₃×#3743	C₂²	1	8	yes	complemented
25	C₃×C₈×C₃⋊D₃	C₂²	1	8	yes	complemented
26	C₂×#3828	C₂×C₃	1	1	yes	characteristic
27	C₂×C₃×#235	—	3	4	no	—
28	C₂×C₃²×M₁₆	—	2	4	no	—
29	C₂×C₃²×M₁₆	D₃	1	4	yes	complemented
30	C₂×C₃²×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂×#3748	C₂×C₃	1	1	yes	characteristic, complemented
32	#64116	C₂×C₃	1	4	yes	complemented
33	M₁₆×C₃⋊D₃	C₂×C₃	1	4	yes	complemented
34	#64110	C₂×C₃	1	4	yes	complemented
35	C₂×C₃×#208	—	3	4	no	—
36	C₃×#907	—	3	16	no	—
37	C₃×D₃×M₁₆	—	3	16	no	—
38	C₃×#901	—	3	16	no	—
39	C₂³×C₃³	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₃×C₃⋊D₃	C₂×C₄	1	2	yes	—
41	C₂×C₃³×C₄	C₂×C₄	1	1	yes	characteristic
42	C₂×C₃³×C₄	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃³×C₄	C₂×C₄	1	1	yes	characteristic
44	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
45	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
46	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
47	C₃×#638	C₂×C₄	1	4	yes	—
48	C₃×#638	C₂×C₄	1	4	yes	—
49	C₂×C₃×C₃⋊Dic₃	C₂×C₄	1	2	yes	—
50	C₃×C₄⋊(C₃⋊D₃)	C₂×C₄	1	2	yes	—
51	C₃×C₄⋊(C₃⋊D₃)	C₂×C₄	1	2	yes	—
52	C₃×C₄×C₃⋊D₃	C₂×C₄	1	4	yes	—
53	C₃×C₄×C₃⋊D₃	C₂³	1	4	yes	—
54	C₃×#634	C₂×C₄	1	2	yes	—
55	C₃×#634	C₂×C₄	1	2	yes	—
56	C₃³×C₈	C₂³	1	4	yes	—
57	C₃×C₃⋊(C₃⋊C₈)	C₂³	1	4	yes	—
58	C₃×#568	—	9	1	no	—
59	#5745	—	3	4	no	—
60	C₂²×C₃²×C₄	—	2	4	no	—
61	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
62	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
63	C₂×#638	C₃×C₄	1	2	yes	—
64	#3828	C₃×C₄	1	2	yes	—
65	#3828	C₃×C₄	1	2	yes	—
66	#3828	C₂²×C₃	1	2	yes	—
67	#3828	C₂²×C₃	1	2	yes	—
68	C₂×C₄⋊(C₃⋊D₃)	C₃×C₄	1	1	yes	characteristic
69	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	2	yes	—
70	C₂×#634	C₃×C₄	1	1	yes	characteristic
71	C₂×C₃×#67	—	3	8	no	—
72	C₃×#235	—	3	8	no	—
73	C₃×#235	—	3	8	no	—
74	C₃×#235	—	3	8	no	—
75	C₃×#235	—	3	8	no	—
76	C₂×C₃×D₁₂	—	3	4	no	—
77	C₂×C₃×C₄×D₃	—	3	8	no	—
78	C₂×C₃×Dic₆	—	3	4	no	—
79	C₃²×M₁₆	—	2	8	no	—
80	C₃²×M₁₆	—	2	8	no	—
81	C₃²×M₁₆	C₂×D₃	1	8	yes	—
82	C₃²×M₁₆	C₂×D₃	1	8	yes	complemented
83	C₃²×M₁₆	C₂²×C₃	1	2	yes	—
84	C₃²×M₁₆	C₂²×C₃	1	2	yes	complemented
85	C₂×C₃²×C₈	—	2	8	no	—
86	C₂×C₃²×C₈	C₂×D₃	1	8	yes	complemented
87	C₂×C₃²×C₈	C₂²×C₃	1	2	yes	complemented
88	#3748	C₂²×C₃	1	2	yes	—
89	#3748	C₂²×C₃	1	2	yes	complemented
90	C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	1	2	yes	complemented
91	#3743	C₂²×C₃	1	8	yes	complemented
92	C₈×C₃⋊D₃	C₂²×C₃	1	8	yes	complemented
93	C₃×#208	—	3	8	no	—
94	C₃×#208	—	3	8	no	—
95	C₂×C₃×C₃⋊C₈	—	3	8	no	—
96	C₃×ΓL(1,𝔽₂₅)	—	3	32	no	—
97	C₃×D₃×C₈	—	3	32	no	—
98	C₂²×C₃³	—	4	1	no	—
99	C₂²×C₃³	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₃³	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₃³	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₃×C₃⋊D₃	—	4	2	no	—
103	C₂×C₃×C₃⋊D₃	C₂²×C₄	1	4	yes	—
104	C₃³×C₄	C₂²×C₄	1	1	yes	characteristic
105	C₃³×C₄	C₂²×C₄	1	1	yes	characteristic
106	C₃³×C₄	C₂²×C₄	1	1	yes	characteristic
107	C₃³×C₄	C₂⁴	1	1	yes	characteristic
108	C₃×C₃⋊Dic₃	C₂²×C₄	1	4	yes	—
109	C₂×C₃×#41	—	9	1	no	—
110	C₂×#235	—	3	4	no	—
111	C₃×#131	—	9	4	no	—
112	C₃×#131	—	9	4	no	—
113	C₂×C₃×M₁₆	—	2	4	no	—
114	C₂×C₃×M₁₆	—	9	1	no	—
115	C₂×C₃×M₁₆	—	9	4	no	—
116	C₂×C₃×M₁₆	C₃×D₃	1	4	yes	complemented
117	C₂×C₃×M₁₆	C₃⋊D₃	1	1	yes	characteristic, complemented
118	C₂×#208	—	3	4	no	—
119	#907	—	3	16	no	—
120	D₃×M₁₆	—	3	16	no	—
121	#901	—	3	16	no	—
122	C₂³×C₃²	—	2	4	no	—
123	C₂³×C₃²	C₄×D₃	1	4	yes	—
124	C₂³×C₃²	C₂×C₃×C₄	1	1	yes	characteristic
125	C₂²×C₃⋊D₃	C₂×C₃×C₄	1	2	yes	—
126	C₂²×C₃×D₃	—	3	8	no	—
127	C₂×C₃²×C₄	—	2	4	no	—
128	C₂×C₃²×C₄	—	2	4	no	—
129	C₂×C₃²×C₄	—	2	4	no	—
130	C₂×C₃²×C₄	—	2	4	no	—
131	C₂×C₃²×C₄	—	2	4	no	—
132	C₂×C₃²×C₄	—	2	4	no	—
133	C₂×C₃²×C₄	C₄×D₃	1	4	yes	—
134	C₂×C₃²×C₄	C₄×D₃	1	4	yes	—
135	C₂×C₃²×C₄	C₄×D₃	1	4	yes	—
136	C₂×C₃²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
137	C₂×C₃²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
138	C₂×C₃²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
139	C₂×C₃²×C₄	C₂²×D₃	1	4	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	1	yes	characteristic
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	4	yes	—
146	#638	C₂×C₃×C₄	1	4	yes	—
147	C₂×C₃⋊Dic₃	C₂×C₃×C₄	1	2	yes	—
148	C₄⋊(C₃⋊D₃)	C₂×C₃×C₄	1	2	yes	—
149	C₄⋊(C₃⋊D₃)	C₂×C₃×C₄	1	2	yes	—
150	C₄×C₃⋊D₃	C₂×C₃×C₄	1	4	yes	—
151	C₄×C₃⋊D₃	C₂³×C₃	1	4	yes	—
152	#634	C₂×C₃×C₄	1	2	yes	—
153	#634	C₂×C₃×C₄	1	2	yes	—
154	C₃×#67	—	3	16	no	—
155	C₃×#67	—	3	16	no	—
156	C₂×C₃×Dic₃	—	3	8	no	—
157	C₃×D₁₂	—	3	8	no	—
158	C₃×D₁₂	—	3	8	no	—
159	C₃×C₄×D₃	—	3	16	no	—
160	C₃×C₄×D₃	—	3	16	no	—
161	C₃×Dic₆	—	3	8	no	—
162	C₃×Dic₆	—	3	8	no	—
163	C₃²×C₈	—	2	16	no	—
164	C₃²×C₈	C₂²×D₃	1	16	yes	—
165	C₃²×C₈	C₂³×C₃	1	4	yes	—
166	C₃⋊(C₃⋊C₈)	C₂³×C₃	1	4	yes	—
167	C₃×C₃⋊C₈	—	3	16	no	—
168	#568	—	9	1	no	Sylow
169	C₂×C₃³	—	2	1	no	—
170	C₂×C₃³	—	2	1	no	—
171	C₂×C₃³	—	2	1	no	—
172	C₂×C₃³	C₂³×C₄	1	1	yes	characteristic
173	C₃×C₃⋊D₃	—	2	4	no	—
174	C₃×#41	—	9	2	no	—
175	C₃×#41	—	9	2	no	—
176	C₃×#41	—	9	2	no	—
177	C₃×#41	—	9	2	no	—
178	C₂×C₃×Q₈	—	9	1	no	—
179	C₂×C₃×D₄	—	9	2	no	—
180	C₂×C₃×D₄	—	9	1	no	—
181	C₂²×C₃×C₄	—	2	4	no	—
182	C₂²×C₃×C₄	—	9	2	no	—
183	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
184	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
185	C₂×#67	—	3	8	no	—
186	#235	—	3	8	no	—
187	#235	—	3	8	no	—
188	#235	—	3	8	no	—
189	#235	—	3	8	no	—
190	C₂×D₁₂	—	3	4	no	—
191	C₂×C₄×D₃	—	3	8	no	—
192	C₂×Dic₆	—	3	4	no	—
193	C₃×M₁₆	—	2	8	no	—
194	C₃×M₁₆	—	2	8	no	—
195	C₃×M₁₆	—	9	2	no	—
196	C₃×M₁₆	—	9	2	no	—
197	C₃×M₁₆	—	9	8	no	—
198	C₃×M₁₆	C₂×C₃×D₃	1	8	yes	—
199	C₃×M₁₆	C₂×C₃×D₃	1	8	yes	complemented
200	C₃×M₁₆	C₂×C₃⋊D₃	1	2	yes	—
201	C₃×M₁₆	C₂×C₃⋊D₃	1	2	yes	complemented
202	C₂×C₃×C₈	—	2	8	no	—
203	C₂×C₃×C₈	—	9	2	no	—
204	C₂×C₃×C₈	—	9	8	no	—
205	C₂×C₃×C₈	C₂×C₃×D₃	1	8	yes	complemented
206	C₂×C₃×C₈	C₂×C₃⋊D₃	1	2	yes	complemented
207	#208	—	3	8	no	—
208	#208	—	3	8	no	—
209	C₂×C₃⋊C₈	—	3	8	no	—
210	ΓL(1,𝔽₂₅)	—	3	32	no	—
211	D₃×C₈	—	3	32	no	—
212	C₂²×C₃²	—	2	4	no	—
213	C₂²×C₃²	—	2	4	no	—
214	C₂²×C₃²	—	2	4	no	—
215	C₂²×C₃²	—	4	4	no	—
216	C₂²×C₃²	—	4	1	no	—
217	C₂²×C₃²	—	4	8	no	—
218	C₂²×C₃²	C₂×C₄×D₃	1	4	yes	—
219	C₂²×C₃²	C₂×C₄×D₃	1	4	yes	—
220	C₂²×C₃²	C₂×C₄×D₃	1	4	yes	—
221	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
222	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
223	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
224	C₂×C₃⋊D₃	—	4	2	no	—
225	C₂×C₃⋊D₃	C₂²×C₃×C₄	1	4	yes	—
226	C₂×C₃×D₃	—	3	16	no	—
227	C₂×C₃×D₃	—	12	8	no	—
228	C₃²×C₄	—	2	4	no	—
229	C₃²×C₄	—	2	4	no	—
230	C₃²×C₄	—	2	4	no	—
231	C₃²×C₄	—	2	4	no	—
232	C₃²×C₄	C₂×C₄×D₃	1	4	yes	—
233	C₃²×C₄	C₂×C₄×D₃	1	4	yes	—
234	C₃²×C₄	C₂×C₄×D₃	1	4	yes	—
235	C₃²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
236	C₃²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
237	C₃²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
238	C₃²×C₄	C₂³×D₃	1	4	yes	—
239	C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
240	C₃⋊Dic₃	C₂²×C₃×C₄	1	4	yes	—
241	C₃×Dic₃	—	3	16	no	—
242	C₂×#41	—	9	1	no	—
243	#131	—	9	4	no	—
244	#131	—	9	4	no	—
245	C₂×M₁₆	—	9	1	no	—
246	C₂×M₁₆	—	9	4	no	—
247	C₂×M₁₆	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
248	C₃³	#568	1	1	yes	characteristic, complemented, Sylow
249	C₂³×C₃	—	2	4	no	—
250	C₂³×C₃	—	9	2	no	—
251	C₂³×C₃	C₃×C₄×D₃	1	4	yes	—
252	C₂³×C₃	C₄×C₃⋊D₃	1	1	yes	characteristic
253	C₂²×D₃	—	3	8	no	—
254	C₃×Q₈	—	9	2	no	—
255	C₃×Q₈	—	9	2	no	—
256	C₃×D₄	—	9	4	no	—
257	C₃×D₄	—	9	4	no	—
258	C₃×D₄	—	9	2	no	—
259	C₃×D₄	—	9	2	no	—
260	C₂×C₃×C₄	—	2	4	no	—
261	C₂×C₃×C₄	—	2	4	no	—
262	C₂×C₃×C₄	—	2	4	no	—
263	C₂×C₃×C₄	—	2	4	no	—
264	C₂×C₃×C₄	—	2	4	no	—
265	C₂×C₃×C₄	—	2	4	no	—
266	C₂×C₃×C₄	—	9	2	no	—
267	C₂×C₃×C₄	—	9	4	no	—
268	C₂×C₃×C₄	—	9	4	no	—
269	C₂×C₃×C₄	C₃×C₄×D₃	1	4	yes	—
270	C₂×C₃×C₄	C₃×C₄×D₃	1	4	yes	—
271	C₂×C₃×C₄	C₃×C₄×D₃	1	4	yes	—
272	C₂×C₃×C₄	C₄×C₃⋊D₃	1	1	yes	characteristic
273	C₂×C₃×C₄	C₄×C₃⋊D₃	1	1	yes	characteristic
274	C₂×C₃×C₄	C₄×C₃⋊D₃	1	1	yes	characteristic
275	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
276	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
277	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
278	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
279	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
281	#67	—	3	16	no	—
282	#67	—	3	16	no	—
283	C₂×Dic₃	—	3	8	no	—
284	D₁₂	—	3	8	no	—
285	D₁₂	—	3	8	no	—
286	C₄×D₃	—	3	16	no	—
287	C₄×D₃	—	3	16	no	—
288	Dic₆	—	3	8	no	—
289	Dic₆	—	3	8	no	—
290	C₃×C₈	—	2	16	no	—
291	C₃×C₈	—	9	4	no	—
292	C₃×C₈	C₂²×C₃×D₃	1	16	yes	—
293	C₃×C₈	C₂²×C₃⋊D₃	1	4	yes	—
294	C₃⋊C₈	—	3	16	no	—
295	C₂×C₃²	—	2	8	no	—
296	C₂×C₃²	—	2	1	no	—
297	C₂×C₃²	—	2	1	no	—
298	C₂×C₃²	—	2	1	no	—
299	C₂×C₃²	—	2	4	no	—
300	C₂×C₃²	—	2	4	no	—
301	C₂×C₃²	—	2	4	no	—
302	C₂×C₃²	—	2	4	no	—
303	C₂×C₃²	—	4	4	no	—
304	C₂×C₃²	—	4	4	no	—
305	C₂×C₃²	C₂²×C₄×D₃	1	4	yes	—
306	C₂×C₃²	C₂³×C₃×C₄	1	1	yes	characteristic
307	C₃⋊D₃	—	2	4	no	—
308	C₃×D₃	—	6	16	no	—
309	#41	—	9	2	no	—
310	#41	—	9	2	no	—
311	#41	—	9	2	no	—
312	#41	—	9	2	no	—
313	C₂×Q₈	—	9	1	no	—
314	C₂×D₄	—	9	2	no	—
315	C₂×D₄	—	9	1	no	—
316	C₂²×C₄	—	9	2	no	—
317	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
318	M₁₆	—	9	2	no	—
319	M₁₆	—	9	2	no	—
320	M₁₆	—	9	8	no	—
321	M₁₆	C₂×C₃×C₃⋊D₃	1	2	yes	—
322	M₁₆	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
323	C₂×C₈	—	9	2	no	—
324	C₂×C₈	—	9	8	no	—
325	C₂×C₈	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
326	C₂²×C₃	—	2	4	no	—
327	C₂²×C₃	—	2	4	no	—
328	C₂²×C₃	—	2	4	no	—
329	C₂²×C₃	—	4	4	no	—
330	C₂²×C₃	—	4	1	no	—
331	C₂²×C₃	—	4	8	no	—
332	C₂²×C₃	—	9	4	no	—
333	C₂²×C₃	—	36	2	no	—
334	C₂²×C₃	C₂×C₃×C₄×D₃	1	4	yes	—
335	C₂²×C₃	C₂×C₃×C₄×D₃	1	4	yes	—
336	C₂²×C₃	C₂×C₃×C₄×D₃	1	4	yes	—
337	C₂²×C₃	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
338	C₂²×C₃	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
339	C₂²×C₃	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
340	C₂×D₃	—	3	16	no	—
341	C₂×D₃	—	12	8	no	—
342	C₃×C₄	—	2	4	no	—
343	C₃×C₄	—	2	4	no	—
344	C₃×C₄	—	2	4	no	—
345	C₃×C₄	—	2	4	no	—
346	C₃×C₄	—	9	4	no	—
347	C₃×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
348	C₃×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
349	C₃×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
350	C₃×C₄	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
351	C₃×C₄	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
352	C₃×C₄	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
353	C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
354	C₃×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
355	Dic₃	—	3	16	no	—
356	C₃²	—	2	4	no	—
357	C₃²	#5745	1	4	yes	complemented
358	C₃²	C₃×#568	1	1	yes	characteristic, complemented
359	C₂³	—	9	2	no	—
360	C₂³	C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
361	Q₈	—	9	2	no	—
362	Q₈	—	9	2	no	—
363	D₄	—	9	4	no	—
364	D₄	—	9	4	no	—
365	D₄	—	9	2	no	—
366	D₄	—	9	2	no	—
367	C₂×C₄	—	9	2	no	—
368	C₂×C₄	—	9	4	no	—
369	C₂×C₄	—	9	4	no	—
370	C₂×C₄	C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
371	C₂×C₄	C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
372	C₂×C₄	C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
373	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
375	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
376	C₈	—	9	4	no	—
377	C₈	C₂²×C₃×C₃⋊D₃	1	4	yes	—
378	C₂×C₃	—	2	8	no	—
379	C₂×C₃	—	2	4	no	—
380	C₂×C₃	—	2	4	no	—
381	C₂×C₃	—	2	4	no	—
382	C₂×C₃	—	2	1	no	—
383	C₂×C₃	—	2	1	no	—
384	C₂×C₃	—	2	1	no	—
385	C₂×C₃	—	2	4	no	—
386	C₂×C₃	—	4	4	no	—
387	C₂×C₃	—	4	4	no	—
388	C₂×C₃	—	18	4	no	—
389	C₂×C₃	C₂²×C₃×C₄×D₃	1	4	yes	—
390	C₂×C₃	C₂²×C₄×C₃⋊D₃	1	1	yes	characteristic
391	D₃	—	6	16	no	—
392	C₂²	—	4	1	no	—
393	C₂²	—	9	4	no	—
394	C₂²	—	36	2	no	—
395	C₂²	C₂×C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
396	C₂²	C₂×C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
397	C₂²	C₂×C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
398	C₄	—	9	4	no	—
399	C₄	C₂×C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
400	C₄	C₂×C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
401	C₄	C₂×C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
402	C₄	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
403	C₃	—	2	4	no	—
404	C₃	C₃×#5745	1	4	yes	complemented
405	C₃	#10596216	1	1	yes	characteristic, direct product factor
406	C₂	—	2	1	no	—
407	C₂	—	2	1	no	—
408	C₂	—	2	1	no	—
409	C₂	—	18	4	no	—
410	C₂	C₂²×C₃×C₄×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂³×C₃⋊D₃
commutator	C₂×C₃²	C₂³×C₃×C₄
Frattini	C₄	C₂³×C₃×C₃⋊D₃
Fitting	C₂×C₃³×M₁₆	C₂
socle	C₂×C₃³	C₂³×C₄
prime radical	C₂×C₃×#3828	C₂
cosocle	C₃²×C₄	C₂⁴×C₃
hypercenter	C₂×C₃×M₁₆	C₃⋊D₃
hypocenter	C₃²	C₃×#568
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×C₃³×M₁₆	C₂	semidirect
3. C₂×C₃×#3748	C₂	semidirect
4. C₃×#64116	C₂	semidirect
5. C₃×M₁₆×C₃⋊D₃	C₂	semidirect
6. C₃×#64110	C₂	semidirect
7. #10596216	C₃	direct (N × H)
19. C₃³×M₁₆	C₂²	semidirect
20. C₂×C₃³×C₈	C₂²	semidirect
22. C₃×#3748	C₂²	semidirect
23. C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	semidirect
24. C₃×#3743	C₂²	semidirect
25. C₃×C₈×C₃⋊D₃	C₂²	semidirect
29. C₂×C₃²×M₁₆	D₃	semidirect
30. C₂×C₃²×M₁₆	C₂×C₃	semidirect
31. C₂×#3748	C₂×C₃	semidirect
32. #64116	C₂×C₃	semidirect
33. M₁₆×C₃⋊D₃	C₂×C₃	semidirect
34. #64110	C₂×C₃	semidirect
82. C₃²×M₁₆	C₂×D₃	semidirect
84. C₃²×M₁₆	C₂²×C₃	semidirect
86. C₂×C₃²×C₈	C₂×D₃	semidirect
87. C₂×C₃²×C₈	C₂²×C₃	semidirect
89. #3748	C₂²×C₃	semidirect
90. C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	semidirect
91. #3743	C₂²×C₃	semidirect
92. C₈×C₃⋊D₃	C₂²×C₃	semidirect
116. C₂×C₃×M₁₆	C₃×D₃	semidirect
117. C₂×C₃×M₁₆	C₃⋊D₃	semidirect
199. C₃×M₁₆	C₂×C₃×D₃	semidirect
201. C₃×M₁₆	C₂×C₃⋊D₃	semidirect
205. C₂×C₃×C₈	C₂×C₃×D₃	semidirect
206. C₂×C₃×C₈	C₂×C₃⋊D₃	semidirect
247. C₂×M₁₆	C₃×C₃⋊D₃	semidirect
248. C₃³	#568	semidirect
322. M₁₆	C₂×C₃×C₃⋊D₃	semidirect
325. C₂×C₈	C₂×C₃×C₃⋊D₃	semidirect
357. C₃²	#5745	semidirect
358. C₃²	C₃×#568	semidirect
404. C₃	C₃×#5745	semidirect
405. C₃	#10596216	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
C₂×C₃³×M₁₆	2
C₂×C₃×#3748	2
C₃×#64116	2
C₃×M₁₆×C₃⋊D₃	2
C₃×#64110	2
#10596216	3
C₃×#5745	3

Subgroups — C3×#10596216 #13179496

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596216 #13179496