Subgroups — C₂×C₃×#64124 #13179511

Order 1728.

1820 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₈×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#3830	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃³×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#3756	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3754	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64124	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃×#3746	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#3743	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#64124	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂×C₃×#915	—	3	4	no	maximal
11	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
13	C₂×C₃×#638	—	2	1	no	—
14	C₂²×C₃×C₃⋊Dic₃	—	2	1	no	—
15	C₃×Q₈×C₃⋊D₃	—	2	2	no	—
16	C₃×Q₈×C₃⋊D₃	C₂²	1	4	yes	complemented
17	C₃×#3830	—	2	2	no	—
18	C₃×#3830	C₂²	1	4	yes	—
19	C₂×C₃×C₄×C₃⋊D₃	—	2	1	no	—
20	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
21	C₂×C₃×#634	—	2	1	no	—
22	C₂×C₃×#634	C₂²	1	1	yes	characteristic
23	C₂×C₃×#634	C₂²	1	1	yes	characteristic
24	C₃³×SD₁₆	C₂²	1	4	yes	complemented
25	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
26	C₃×#3756	C₂²	1	4	yes	complemented
27	C₃×#3754	C₂²	1	4	yes	complemented
28	C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
29	C₃×#3746	C₂²	1	4	yes	complemented
30	C₃×#3743	C₂²	1	4	yes	complemented
31	C₂×Q₈×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂×#3830	C₂×C₃	1	1	yes	characteristic
33	C₂×C₃×D₃×Q₈	—	3	4	no	—
34	C₂×C₃×#237	—	3	4	no	—
35	C₂×C₃²×SD₁₆	—	2	4	no	—
36	C₂×C₃²×SD₁₆	D₃	1	4	yes	complemented
37	C₂×C₃²×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂×#3756	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂×#3754	C₂×C₃	1	1	yes	characteristic, complemented
40	#64124	C₂×C₃	1	8	yes	direct product factor
41	C₂×#3746	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂×#3743	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂×C₃×#216	—	3	4	no	—
44	C₂×C₃×#214	—	3	4	no	—
45	C₃×#915	—	3	32	no	—
46	C₂×C₃×Dic₁₂	—	3	4	no	—
47	C₂×C₃×ΓL(1,𝔽₂₅)	—	3	4	no	—
48	C₂³×C₃³	—	2	1	no	—
49	C₂²×C₃×C₃⋊D₃	D₄	1	1	yes	characteristic
50	C₃³×Q₈	—	2	1	no	—
51	C₃³×Q₈	C₂³	1	2	yes	—
52	C₃³×D₄	—	2	1	no	—
53	C₃³×D₄	C₂³	1	2	yes	—
54	C₂×C₃³×C₄	—	2	1	no	—
55	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
56	C₃×#638	—	2	4	no	—
57	C₂×C₃×C₃⋊Dic₃	—	2	1	no	—
58	C₂×C₃×C₃⋊Dic₃	—	2	1	no	—
59	C₂×C₃×C₃⋊Dic₃	—	2	4	no	—
60	C₂×C₃×C₃⋊Dic₃	D₄	1	1	yes	characteristic
61	C₃×C₄×C₃⋊D₃	—	2	4	no	—
62	C₃×C₄×C₃⋊D₃	D₄	1	2	yes	—
63	C₃×C₄×C₃⋊D₃	C₂³	1	2	yes	—
64	C₃×#634	—	2	1	no	—
65	C₃×#634	—	2	1	no	—
66	C₃×#634	—	2	4	no	—
67	C₃×#634	C₂³	1	2	yes	—
68	C₃×#634	C₂³	1	2	yes	—
69	C₃³×C₈	C₂³	1	2	yes	—
70	C₃×C₃⋊(C₃⋊C₈)	C₂³	1	2	yes	—
71	C₂×C₃×#137	—	9	1	no	—
72	C₂×#915	—	3	4	no	—
73	C₂×C₃²×Q₈	—	2	4	no	—
74	C₂×C₃²×Q₈	C₂×D₃	1	4	yes	—
75	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₃²×D₄	—	2	4	no	—
77	C₂×C₃²×D₄	C₂×D₃	1	4	yes	—
78	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
79	C₂×#638	—	2	1	no	—
80	C₂²×C₃⋊Dic₃	—	2	1	no	—
81	Q₈×C₃⋊D₃	—	2	2	no	—
82	Q₈×C₃⋊D₃	C₂²×C₃	1	4	yes	complemented
83	#3830	—	2	2	no	—
84	#3830	C₂²×C₃	1	4	yes	—
85	C₂×C₄×C₃⋊D₃	—	2	1	no	—
86	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
87	C₂×#634	—	2	1	no	—
88	C₂×#634	C₂²×C₃	1	1	yes	characteristic
89	C₂×#634	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₃×#67	—	6	4	no	—
91	C₂²×C₃×Dic₃	—	6	4	no	—
92	C₃×D₃×Q₈	—	3	16	no	—
93	C₃×D₃×Q₈	—	6	8	no	—
94	C₃×#237	—	3	16	no	—
95	C₃×#237	—	6	8	no	—
96	C₂×C₃×C₄×D₃	—	3	4	no	—
97	C₂×C₃×C₄×D₃	—	6	4	no	—
98	C₂×C₃×Dic₆	—	3	4	no	—
99	C₂×C₃×Dic₆	—	3	4	no	—
100	C₂×C₃×Dic₆	—	6	4	no	—
101	C₃²×SD₁₆	—	2	16	no	—
102	C₃²×SD₁₆	C₂×D₃	1	16	yes	complemented
103	C₃²×SD₁₆	C₂²×C₃	1	4	yes	complemented
104	C₂×C₃²×C₈	—	2	4	no	—
105	C₂×C₃²×C₈	C₂×D₃	1	4	yes	—
106	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
107	#3756	C₂²×C₃	1	4	yes	complemented
108	#3754	C₂²×C₃	1	4	yes	complemented
109	C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic
110	#3746	C₂²×C₃	1	4	yes	complemented
111	#3743	C₂²×C₃	1	4	yes	complemented
112	C₃×#216	—	3	16	no	—
113	C₃×#214	—	3	16	no	—
114	C₂×C₃×C₃⋊C₈	—	3	4	no	—
115	C₃×Dic₁₂	—	3	16	no	—
116	C₃×ΓL(1,𝔽₂₅)	—	3	16	no	—
117	C₂²×C₃³	—	2	2	no	—
118	C₂²×C₃³	—	4	2	no	—
119	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
120	C₂×C₃×C₃⋊D₃	—	2	2	no	—
121	C₂×C₃×C₃⋊D₃	C₂×D₄	1	2	yes	—
122	C₃³×C₄	—	2	2	no	—
123	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
124	C₃³×C₄	C₂⁴	1	1	yes	characteristic
125	C₃×C₃⋊Dic₃	—	2	2	no	—
126	C₃×C₃⋊Dic₃	—	2	2	no	—
127	C₃×C₃⋊Dic₃	C₂×D₄	1	2	yes	—
128	C₂×C₃×#41	—	9	1	no	—
129	C₂²×C₃×Q₈	—	9	1	no	—
130	C₂×D₃×Q₈	—	3	4	no	—
131	C₂×#237	—	3	4	no	—
132	C₃×#137	—	9	8	no	—
133	C₂×C₃×Q₁₆	—	9	1	no	—
134	C₂×C₃×Q₁₆	—	9	1	no	—
135	C₂×C₃×SD₁₆	—	2	4	no	—
136	C₂×C₃×SD₁₆	—	9	1	no	—
137	C₂×C₃×SD₁₆	C₃×D₃	1	4	yes	complemented
138	C₂×C₃×SD₁₆	C₃⋊D₃	1	1	yes	characteristic, complemented
139	C₂×C₃×M₁₆	—	9	1	no	—
140	C₂×#216	—	3	4	no	—
141	C₂×#214	—	3	4	no	—
142	#915	—	3	32	no	—
143	C₂×Dic₁₂	—	3	4	no	—
144	C₂×ΓL(1,𝔽₂₅)	—	3	4	no	—
145	C₂³×C₃²	—	2	1	no	—
146	C₂³×C₃²	—	2	4	no	—
147	C₂³×C₃²	—	4	4	no	—
148	C₂²×C₃⋊D₃	C₃×D₄	1	1	yes	characteristic
149	C₂²×C₃×D₃	—	3	4	no	—
150	C₃²×Q₈	—	2	1	no	—
151	C₃²×Q₈	—	2	8	no	—
152	C₃²×Q₈	—	2	4	no	—
153	C₃²×Q₈	—	4	4	no	—
154	C₃²×Q₈	C₂²×D₃	1	8	yes	—
155	C₃²×Q₈	C₂³×C₃	1	2	yes	—
156	C₃²×D₄	—	2	1	no	—
157	C₃²×D₄	—	2	8	no	—
158	C₃²×D₄	—	2	4	no	—
159	C₃²×D₄	—	4	4	no	—
160	C₃²×D₄	C₂²×D₃	1	8	yes	—
161	C₃²×D₄	C₂³×C₃	1	2	yes	—
162	C₂×C₃²×C₄	—	2	1	no	—
163	C₂×C₃²×C₄	—	2	4	no	—
164	C₂×C₃²×C₄	—	2	4	no	—
165	C₂×C₃²×C₄	—	4	4	no	—
166	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
167	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
168	#638	—	2	4	no	—
169	C₂×C₃⋊Dic₃	—	2	1	no	—
170	C₂×C₃⋊Dic₃	—	2	1	no	—
171	C₂×C₃⋊Dic₃	—	2	4	no	—
172	C₂×C₃⋊Dic₃	C₃×D₄	1	1	yes	characteristic
173	C₄×C₃⋊D₃	—	2	4	no	—
174	C₄×C₃⋊D₃	C₃×D₄	1	2	yes	—
175	C₄×C₃⋊D₃	C₂³×C₃	1	2	yes	—
176	#634	—	2	1	no	—
177	#634	—	2	1	no	—
178	#634	—	2	4	no	—
179	#634	C₂³×C₃	1	2	yes	—
180	#634	C₂³×C₃	1	2	yes	—
181	C₃×#67	—	6	16	no	—
182	C₂×C₃×Dic₃	—	3	4	no	—
183	C₂×C₃×Dic₃	—	6	16	no	—
184	C₂×C₃×Dic₃	—	6	4	no	—
185	C₂×C₃×Dic₃	—	6	4	no	—
186	C₃×C₄×D₃	—	3	8	no	—
187	C₃×C₄×D₃	—	3	8	no	—
188	C₃×C₄×D₃	—	6	16	no	—
189	C₃×Dic₆	—	3	8	no	—
190	C₃×Dic₆	—	3	8	no	—
191	C₃×Dic₆	—	6	16	no	—
192	C₃×Dic₆	—	6	4	no	—
193	C₃×Dic₆	—	6	4	no	—
194	C₃²×C₈	—	2	8	no	—
195	C₃²×C₈	C₂²×D₃	1	8	yes	—
196	C₃²×C₈	C₂³×C₃	1	2	yes	—
197	C₃⋊(C₃⋊C₈)	C₂³×C₃	1	2	yes	—
198	C₃×C₃⋊C₈	—	3	8	no	—
199	C₂×#137	—	9	1	no	Sylow
200	C₂×C₃³	—	4	2	no	—
201	C₂×C₃³	#137	1	2	yes	complemented
202	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
203	C₃×C₃⋊D₃	—	2	2	no	—
204	C₃×#41	—	9	4	no	—
205	C₃×#41	—	18	2	no	—
206	C₂×C₃×Q₈	—	2	4	no	—
207	C₂×C₃×Q₈	—	9	4	no	—
208	C₂×C₃×Q₈	—	9	1	no	—
209	C₂×C₃×Q₈	—	9	1	no	—
210	C₂×C₃×Q₈	—	18	1	no	—
211	C₂×C₃×Q₈	—	18	2	no	—
212	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	—
213	C₂×C₃×Q₈	C₂×C₃⋊D₃	1	1	yes	characteristic
214	C₂×C₃×D₄	—	2	4	no	—
215	C₂×C₃×D₄	—	18	1	no	—
216	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
217	C₂×C₃×D₄	C₂×C₃⋊D₃	1	1	yes	characteristic
218	C₂²×C₃×C₄	—	9	1	no	—
219	C₂²×C₃×C₄	—	18	1	no	—
220	C₂²×C₃×C₄	—	18	1	no	—
221	C₂×#67	—	6	4	no	—
222	C₂²×Dic₃	—	6	4	no	—
223	D₃×Q₈	—	3	16	no	—
224	D₃×Q₈	—	6	8	no	—
225	#237	—	3	16	no	—
226	#237	—	6	8	no	—
227	C₂×C₄×D₃	—	3	4	no	—
228	C₂×C₄×D₃	—	6	4	no	—
229	C₂×Dic₆	—	3	4	no	—
230	C₂×Dic₆	—	3	4	no	—
231	C₂×Dic₆	—	6	4	no	—
232	C₃×Q₁₆	—	9	4	no	—
233	C₃×Q₁₆	—	9	4	no	—
234	C₃×SD₁₆	—	2	16	no	—
235	C₃×SD₁₆	—	9	4	no	—
236	C₃×SD₁₆	C₂×C₃×D₃	1	16	yes	complemented
237	C₃×SD₁₆	C₂×C₃⋊D₃	1	4	yes	complemented
238	C₃×M₁₆	—	9	4	no	—
239	C₂×C₃×C₈	—	2	4	no	—
240	C₂×C₃×C₈	—	9	1	no	—
241	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	—
242	C₂×C₃×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
243	#216	—	3	16	no	—
244	#214	—	3	16	no	—
245	C₂×C₃⋊C₈	—	3	4	no	—
246	Dic₁₂	—	3	16	no	—
247	ΓL(1,𝔽₂₅)	—	3	16	no	—
248	C₂²×C₃²	—	2	2	no	—
249	C₂²×C₃²	—	2	4	no	—
250	C₂²×C₃²	—	2	8	no	—
251	C₂²×C₃²	—	4	8	no	—
252	C₂²×C₃²	—	4	2	no	—
253	C₂²×C₃²	—	4	8	no	—
254	C₂²×C₃²	—	8	8	no	—
255	C₂²×C₃²	D₃×D₄	1	4	yes	—
256	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
257	C₂×C₃⋊D₃	—	2	2	no	—
258	C₂×C₃⋊D₃	C₂×C₃×D₄	1	2	yes	—
259	C₂×C₃×D₃	—	3	8	no	—
260	C₂×C₃×D₃	—	6	8	no	—
261	C₃²×C₄	—	2	2	no	—
262	C₃²×C₄	—	2	4	no	—
263	C₃²×C₄	—	2	4	no	—
264	C₃²×C₄	—	2	8	no	—
265	C₃²×C₄	—	4	8	no	—
266	C₃²×C₄	D₃×D₄	1	4	yes	—
267	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
268	C₃²×C₄	C₂³×D₃	1	4	yes	—
269	C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
270	C₃⋊Dic₃	—	2	2	no	—
271	C₃⋊Dic₃	—	2	2	no	—
272	C₃⋊Dic₃	C₂×C₃×D₄	1	2	yes	—
273	C₃×Dic₃	—	3	8	no	—
274	C₃×Dic₃	—	6	8	no	—
275	C₃×Dic₃	—	6	8	no	—
276	C₂×#41	—	9	1	no	—
277	C₂²×Q₈	—	9	1	no	—
278	#137	—	9	8	no	—
279	C₂×Q₁₆	—	9	1	no	—
280	C₂×Q₁₆	—	9	1	no	—
281	C₂×SD₁₆	—	9	1	no	—
282	C₂×SD₁₆	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
283	C₂×M₁₆	—	9	1	no	—
284	C₃³	C₂×#137	1	1	yes	characteristic, complemented, Sylow
285	C₂³×C₃	—	2	4	no	—
286	C₂³×C₃	—	2	1	no	—
287	C₂³×C₃	—	4	4	no	—
288	C₂³×C₃	—	9	1	no	—
289	C₂²×D₃	—	3	4	no	—
290	C₃×Q₈	—	2	4	no	—
291	C₃×Q₈	—	2	1	no	—
292	C₃×Q₈	—	2	8	no	—
293	C₃×Q₈	—	4	4	no	—
294	C₃×Q₈	—	9	2	no	—
295	C₃×Q₈	—	9	2	no	—
296	C₃×Q₈	—	18	4	no	—
297	C₃×Q₈	—	18	1	no	—
298	C₃×Q₈	—	18	1	no	—
299	C₃×Q₈	C₂²×C₃×D₃	1	8	yes	—
300	C₃×Q₈	C₂²×C₃⋊D₃	1	2	yes	—
301	C₃×D₄	—	2	4	no	—
302	C₃×D₄	—	2	1	no	—
303	C₃×D₄	—	2	8	no	—
304	C₃×D₄	—	4	4	no	—
305	C₃×D₄	—	18	4	no	—
306	C₃×D₄	C₂²×C₃×D₃	1	8	yes	—
307	C₃×D₄	C₂²×C₃⋊D₃	1	2	yes	—
308	C₂×C₃×C₄	—	2	4	no	—
309	C₂×C₃×C₄	—	2	1	no	—
310	C₂×C₃×C₄	—	2	4	no	—
311	C₂×C₃×C₄	—	4	4	no	—
312	C₂×C₃×C₄	—	9	1	no	—
313	C₂×C₃×C₄	—	9	2	no	—
314	C₂×C₃×C₄	—	9	2	no	—
315	C₂×C₃×C₄	—	18	4	no	—
316	C₂×C₃×C₄	—	18	4	no	—
317	C₂×C₃×C₄	—	18	1	no	—
318	C₂×C₃×C₄	—	18	1	no	—
319	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
320	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
321	#67	—	6	16	no	—
322	C₂×Dic₃	—	3	4	no	—
323	C₂×Dic₃	—	6	16	no	—
324	C₂×Dic₃	—	6	4	no	—
325	C₂×Dic₃	—	6	4	no	—
326	C₄×D₃	—	3	8	no	—
327	C₄×D₃	—	3	8	no	—
328	C₄×D₃	—	6	16	no	—
329	Dic₆	—	3	8	no	—
330	Dic₆	—	3	8	no	—
331	Dic₆	—	6	16	no	—
332	Dic₆	—	6	4	no	—
333	Dic₆	—	6	4	no	—
334	C₃×C₈	—	2	8	no	—
335	C₃×C₈	—	9	2	no	—
336	C₃×C₈	C₂²×C₃×D₃	1	8	yes	—
337	C₃×C₈	C₂²×C₃⋊D₃	1	2	yes	—
338	C₃⋊C₈	—	3	8	no	—
339	C₂×C₃²	—	2	8	no	—
340	C₂×C₃²	—	2	4	no	—
341	C₂×C₃²	—	4	2	no	—
342	C₂×C₃²	—	4	8	no	—
343	C₂×C₃²	—	8	8	no	—
344	C₂×C₃²	#915	1	8	yes	complemented
345	C₂×C₃²	C₃×#137	1	2	yes	complemented
346	C₂×C₃²	C₂×D₃×D₄	1	4	yes	—
347	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
348	C₃⋊D₃	—	2	2	no	—
349	C₃×D₃	—	6	8	no	—
350	#41	—	9	4	no	—
351	#41	—	18	2	no	—
352	C₂×Q₈	—	9	4	no	—
353	C₂×Q₈	—	9	1	no	—
354	C₂×Q₈	—	9	1	no	—
355	C₂×Q₈	—	18	1	no	—
356	C₂×Q₈	—	18	2	no	—
357	C₂×Q₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
358	C₂×D₄	—	18	1	no	—
359	C₂×D₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
360	C₂²×C₄	—	9	1	no	—
361	C₂²×C₄	—	18	1	no	—
362	C₂²×C₄	—	18	1	no	—
363	Q₁₆	—	9	4	no	—
364	Q₁₆	—	9	4	no	—
365	SD₁₆	—	9	4	no	—
366	SD₁₆	C₂×C₃×C₃⋊D₃	1	4	yes	complemented
367	M₁₆	—	9	4	no	—
368	C₂×C₈	—	9	1	no	—
369	C₂×C₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
370	C₂²×C₃	—	2	8	no	—
371	C₂²×C₃	—	2	2	no	—
372	C₂²×C₃	—	2	4	no	—
373	C₂²×C₃	—	4	8	no	—
374	C₂²×C₃	—	4	8	no	—
375	C₂²×C₃	—	4	2	no	—
376	C₂²×C₃	—	8	8	no	—
377	C₂²×C₃	—	9	2	no	—
378	C₂²×C₃	—	18	2	no	—
379	C₂²×C₃	C₃×D₃×D₄	1	4	yes	—
380	C₂²×C₃	D₄×C₃⋊D₃	1	1	yes	characteristic
381	C₂×D₃	—	3	8	no	—
382	C₂×D₃	—	6	8	no	—
383	C₃×C₄	—	2	8	no	—
384	C₃×C₄	—	2	2	no	—
385	C₃×C₄	—	2	4	no	—
386	C₃×C₄	—	2	4	no	—
387	C₃×C₄	—	4	8	no	—
388	C₃×C₄	—	9	2	no	—
389	C₃×C₄	—	18	2	no	—
390	C₃×C₄	—	18	2	no	—
391	C₃×C₄	C₃×D₃×D₄	1	4	yes	—
392	C₃×C₄	D₄×C₃⋊D₃	1	1	yes	characteristic
393	C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
394	C₃×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
395	Dic₃	—	3	8	no	—
396	Dic₃	—	6	8	no	—
397	Dic₃	—	6	8	no	—
398	C₃²	—	2	4	no	—
399	C₃²	C₂×#915	1	4	yes	complemented
400	C₃²	C₂×C₃×#137	1	1	yes	characteristic, complemented
401	C₂³	—	2	1	no	—
402	C₂³	—	9	1	no	—
403	Q₈	—	2	1	no	—
404	Q₈	—	9	2	no	—
405	Q₈	—	9	2	no	—
406	Q₈	—	18	4	no	—
407	Q₈	—	18	1	no	—
408	Q₈	—	18	1	no	—
409	Q₈	C₂²×C₃×C₃⋊D₃	1	2	yes	—
410	D₄	—	2	1	no	—
411	D₄	—	18	4	no	—
412	D₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	9	1	no	—
415	C₂×C₄	—	9	2	no	—
416	C₂×C₄	—	9	2	no	—
417	C₂×C₄	—	18	4	no	—
418	C₂×C₄	—	18	4	no	—
419	C₂×C₄	—	18	1	no	—
420	C₂×C₄	—	18	1	no	—
421	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
422	C₈	—	9	2	no	—
423	C₈	C₂²×C₃×C₃⋊D₃	1	2	yes	—
424	C₂×C₃	—	2	8	no	—
425	C₂×C₃	—	2	4	no	—
426	C₂×C₃	—	4	8	no	—
427	C₂×C₃	—	4	2	no	—
428	C₂×C₃	—	8	8	no	—
429	C₂×C₃	—	18	2	no	—
430	C₂×C₃	C₃×#915	1	8	yes	complemented
431	C₂×C₃	#64124	1	2	yes	direct product factor
432	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
433	C₂×C₃	C₂×D₄×C₃⋊D₃	1	1	yes	characteristic
434	D₃	—	6	8	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	4	2	no	—
437	C₂²	—	9	2	no	—
438	C₂²	—	18	2	no	—
439	C₂²	C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
440	C₄	—	2	2	no	—
441	C₄	—	9	2	no	—
442	C₄	—	18	2	no	—
443	C₄	—	18	2	no	—
444	C₄	C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
445	C₄	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
446	C₃	—	2	4	no	—
447	C₃	C₂×C₃×#915	1	4	yes	complemented
448	C₃	C₂×#64124	1	1	yes	characteristic, direct product factor
449	C₂	—	4	2	no	—
450	C₂	—	18	2	no	—
451	C₂	C₃×#64124	1	2	yes	direct product factor
452	C₂	C₂×C₃×D₄×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	D₄×C₃⋊D₃
commutator, cosocle	C₃²×C₄	C₂⁴×C₃
Frattini	C₄	C₂³×C₃×C₃⋊D₃
Fitting	C₂×C₃³×SD₁₆	C₂
socle	C₂²×C₃³	C₂×D₄
prime radical	C₂×C₃×#3830	C₂
hypercenter	C₂×C₃×SD₁₆	C₃⋊D₃
hypocenter	C₃²	C₂×C₃×#137
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×SD₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×Q₈×C₃⋊D₃	C₂	semidirect
3. C₂×C₃³×SD₁₆	C₂	semidirect
4. C₂×C₃×#3756	C₂	semidirect
5. C₂×C₃×#3754	C₂	semidirect
6. C₃×#64124	C₂	direct (N × H)
7. C₂×C₃×#3746	C₂	semidirect
8. C₂×C₃×#3743	C₂	semidirect
9. C₂×#64124	C₃	direct (N × H)
16. C₃×Q₈×C₃⋊D₃	C₂²	semidirect
24. C₃³×SD₁₆	C₂²	semidirect
26. C₃×#3756	C₂²	semidirect
27. C₃×#3754	C₂²	semidirect
29. C₃×#3746	C₂²	semidirect
30. C₃×#3743	C₂²	semidirect
31. C₂×Q₈×C₃⋊D₃	C₂×C₃	semidirect
36. C₂×C₃²×SD₁₆	D₃	semidirect
37. C₂×C₃²×SD₁₆	C₂×C₃	semidirect
38. C₂×#3756	C₂×C₃	semidirect
39. C₂×#3754	C₂×C₃	semidirect
40. #64124	C₂×C₃	direct (N × H)
41. C₂×#3746	C₂×C₃	semidirect
42. C₂×#3743	C₂×C₃	semidirect
82. Q₈×C₃⋊D₃	C₂²×C₃	semidirect
102. C₃²×SD₁₆	C₂×D₃	semidirect
103. C₃²×SD₁₆	C₂²×C₃	semidirect
107. #3756	C₂²×C₃	semidirect
108. #3754	C₂²×C₃	semidirect
110. #3746	C₂²×C₃	semidirect
111. #3743	C₂²×C₃	semidirect
137. C₂×C₃×SD₁₆	C₃×D₃	semidirect
138. C₂×C₃×SD₁₆	C₃⋊D₃	semidirect
201. C₂×C₃³	#137	semidirect
236. C₃×SD₁₆	C₂×C₃×D₃	semidirect
237. C₃×SD₁₆	C₂×C₃⋊D₃	semidirect
282. C₂×SD₁₆	C₃×C₃⋊D₃	semidirect
284. C₃³	C₂×#137	semidirect
344. C₂×C₃²	#915	semidirect
345. C₂×C₃²	C₃×#137	semidirect
366. SD₁₆	C₂×C₃×C₃⋊D₃	semidirect
399. C₃²	C₂×#915	semidirect
400. C₃²	C₂×C₃×#137	semidirect
430. C₂×C₃	C₃×#915	semidirect
431. C₂×C₃	#64124	direct (N × H)
447. C₃	C₂×C₃×#915	semidirect
448. C₃	C₂×#64124	direct (N × H)
451. C₂	C₃×#64124	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×Q₈×C₃⋊D₃	2
C₂×C₃×#3830	2
C₂×C₃³×SD₁₆	2
C₂×C₃×#3756	2
C₂×C₃×#3754	2
C₃×#64124	2
C₂×C₃×#3746	2
C₂×C₃×#3743	2
C₂×#64124	3
C₂×C₃×#915	3

Subgroups — C2×C3×#64124 #13179511

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#64124 #13179511