Subgroups — C₂×C₃×#64141 #13179550

Order 1728.

2732 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃³×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#3828	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#3754	C₂	1	2	yes	maximal, complemented
4	C₃×#64141	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×#3753	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#3748	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#64141	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₃×#932	—	3	4	no	maximal
9	C₂⁴×C₃³	—	2	1	no	—
10	C₂×C₃³×D₄	—	2	1	no	—
11	C₂×C₃³×D₄	—	2	2	no	—
12	C₂×C₃³×D₄	C₂²	1	2	yes	—
13	C₂×C₃³×D₄	C₂²	1	4	yes	complemented
14	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×#638	—	2	1	no	—
16	C₃×#3828	—	2	2	no	—
17	C₃×#3828	C₂²	1	4	yes	complemented
18	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₃×C₄×C₃⋊D₃	—	2	1	no	—
20	C₂×C₃×#634	C₂²	1	1	yes	characteristic, complemented
21	C₃×#3754	C₂²	1	8	yes	complemented
22	C₃×#3753	C₂²	1	8	yes	complemented
23	C₃×#3748	C₂²	1	4	yes	complemented
24	C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	1	2	yes	complemented
25	C₂²×C₃²×D₄	—	2	4	no	—
26	C₂²×C₃²×D₄	D₃	1	4	yes	complemented
27	C₂²×C₃²×D₄	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂×#3828	C₂×C₃	1	1	yes	characteristic, complemented
29	C₂×C₃×#235	—	3	4	no	—
30	C₂×#3754	C₂×C₃	1	2	yes	complemented
31	#64141	C₂×C₃	1	8	yes	direct product factor
32	C₂×#3753	C₂×C₃	1	2	yes	complemented
33	C₂×#3748	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×C₃×#214	—	3	8	no	—
35	C₃×#932	—	3	32	no	—
36	C₂×C₃×#213	—	3	8	no	—
37	C₂×C₃×#208	—	3	4	no	—
38	C₂³×C₃³	—	2	2	no	—
39	C₂³×C₃³	—	2	4	no	—
40	C₂³×C₃³	—	4	4	no	—
41	C₂³×C₃³	D₄	1	1	yes	characteristic
42	C₂²×C₃×C₃⋊D₃	—	2	1	no	—
43	C₃³×D₄	—	2	2	no	—
44	C₃³×D₄	—	2	4	no	—
45	C₃³×D₄	C₂³	1	4	yes	—
46	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
47	C₂×C₃³×C₄	D₄	1	2	yes	—
48	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
49	C₂×C₃³×C₄	C₂³	1	2	yes	—
50	C₃×#638	—	2	4	no	—
51	C₂×C₃×C₃⋊Dic₃	—	2	1	no	—
52	C₃×C₄⋊(C₃⋊D₃)	—	2	1	no	—
53	C₃×C₄⋊(C₃⋊D₃)	C₂³	1	2	yes	complemented
54	C₃×C₄×C₃⋊D₃	—	2	4	no	—
55	C₃×#634	—	2	1	no	—
56	C₃×#634	C₂³	1	2	yes	complemented
57	C₃×C₃⋊(C₃⋊C₈)	C₂³	1	4	yes	complemented
58	C₂×C₃×AGL(1,ℤ/8)	—	9	1	no	—
59	C₂×#932	—	3	4	no	—
60	C₂⁴×C₃²	—	2	8	no	—
61	C₂⁴×C₃²	—	2	4	no	—
62	C₂⁴×C₃²	—	2	1	no	—
63	C₂×C₃²×D₄	—	2	8	no	—
64	C₂×C₃²×D₄	—	2	16	no	—
65	C₂×C₃²×D₄	—	2	8	no	—
66	C₂×C₃²×D₄	—	2	16	no	—
67	C₂×C₃²×D₄	—	2	4	no	—
68	C₂×C₃²×D₄	—	2	8	no	—
69	C₂×C₃²×D₄	—	2	1	no	—
70	C₂×C₃²×D₄	—	2	2	no	—
71	C₂×C₃²×D₄	C₂×D₃	1	8	yes	—
72	C₂×C₃²×D₄	C₂×D₃	1	16	yes	complemented
73	C₂×C₃²×D₄	C₂²×C₃	1	2	yes	—
74	C₂×C₃²×D₄	C₂²×C₃	1	4	yes	complemented
75	C₂²×C₃²×C₄	—	2	4	no	—
76	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
77	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
78	C₂×#638	—	2	1	no	—
79	#3828	—	2	2	no	—
80	#3828	C₂²×C₃	1	4	yes	complemented
81	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic, complemented
82	C₂×C₄×C₃⋊D₃	—	2	1	no	—
83	C₂×#634	C₂²×C₃	1	1	yes	characteristic, complemented
84	C₂×C₃×#67	—	6	4	no	—
85	C₃×#235	—	3	16	no	—
86	C₃×#235	—	6	8	no	—
87	C₂×C₃×D₁₂	—	3	4	no	—
88	C₂×C₃×C₄×D₃	—	6	4	no	—
89	C₂×C₃×Dic₆	—	3	4	no	—
90	#3754	C₂²×C₃	1	8	yes	complemented
91	#3753	C₂²×C₃	1	8	yes	complemented
92	#3748	C₂²×C₃	1	4	yes	complemented
93	C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	1	2	yes	complemented
94	C₃×#214	—	3	32	no	—
95	C₃×#213	—	3	32	no	—
96	C₃×#208	—	3	16	no	—
97	C₂×C₃×C₃⋊C₈	—	3	8	no	—
98	C₂²×C₃³	—	2	2	no	—
99	C₂²×C₃³	—	2	4	no	—
100	C₂²×C₃³	—	4	8	no	—
101	C₂²×C₃³	—	4	4	no	—
102	C₂²×C₃³	C₂×D₄	1	2	yes	—
103	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
104	C₂×C₃×C₃⋊D₃	—	2	2	no	—
105	C₂×C₃×C₃⋊D₃	—	4	2	no	—
106	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
107	C₃³×C₄	C₂×D₄	1	2	yes	—
108	C₃³×C₄	C₂⁴	1	1	yes	characteristic
109	C₃×C₃⋊Dic₃	—	2	2	no	—
110	C₂×C₃×#41	—	9	1	no	—
111	C₂²×C₃×D₄	—	2	4	no	—
112	C₂²×C₃×D₄	C₃×D₃	1	4	yes	complemented
113	C₂²×C₃×D₄	C₃⋊D₃	1	1	yes	characteristic, complemented
114	C₂×#235	—	3	4	no	—
115	C₃×AGL(1,ℤ/8)	—	9	8	no	—
116	C₂×C₃×SD₁₆	—	9	2	no	—
117	C₂×C₃×D₈	—	9	2	no	—
118	C₂×C₃×M₁₆	—	9	1	no	—
119	C₂×#214	—	3	8	no	—
120	#932	—	3	32	no	—
121	C₂×#213	—	3	8	no	—
122	C₂×#208	—	3	4	no	—
123	C₂³×C₃²	—	2	16	no	—
124	C₂³×C₃²	—	2	32	no	—
125	C₂³×C₃²	—	2	8	no	—
126	C₂³×C₃²	—	2	16	no	—
127	C₂³×C₃²	—	2	2	no	—
128	C₂³×C₃²	—	2	4	no	—
129	C₂³×C₃²	—	2	4	no	—
130	C₂³×C₃²	—	4	32	no	—
131	C₂³×C₃²	—	4	16	no	—
132	C₂³×C₃²	—	4	4	no	—
133	C₂³×C₃²	#67	1	4	yes	—
134	C₂³×C₃²	C₃×D₄	1	1	yes	characteristic
135	C₂²×C₃⋊D₃	—	2	1	no	—
136	C₂²×C₃×D₃	—	6	4	no	—
137	C₃²×D₄	—	2	16	no	—
138	C₃²×D₄	—	2	32	no	—
139	C₃²×D₄	—	2	8	no	—
140	C₃²×D₄	—	2	16	no	—
141	C₃²×D₄	—	2	2	no	—
142	C₃²×D₄	—	2	4	no	—
143	C₃²×D₄	—	2	16	no	—
144	C₃²×D₄	C₂²×D₃	1	16	yes	—
145	C₃²×D₄	C₂³×C₃	1	4	yes	—
146	C₂×C₃²×C₄	—	2	4	no	—
147	C₂×C₃²×C₄	—	2	8	no	—
148	C₂×C₃²×C₄	—	2	4	no	—
149	C₂×C₃²×C₄	—	2	8	no	—
150	C₂×C₃²×C₄	#67	1	4	yes	—
151	C₂×C₃²×C₄	#67	1	8	yes	—
152	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
153	C₂×C₃²×C₄	C₃×D₄	1	2	yes	—
154	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
155	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
156	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
157	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
158	#638	—	2	4	no	—
159	C₂×C₃⋊Dic₃	—	2	1	no	—
160	C₄⋊(C₃⋊D₃)	—	2	1	no	—
161	C₄⋊(C₃⋊D₃)	C₂³×C₃	1	2	yes	complemented
162	C₄×C₃⋊D₃	—	2	4	no	—
163	#634	—	2	1	no	—
164	#634	C₂³×C₃	1	2	yes	complemented
165	C₃×#67	—	6	16	no	—
166	C₂×C₃×Dic₃	—	6	4	no	—
167	C₃×D₁₂	—	3	8	no	—
168	C₃×D₁₂	—	6	4	no	—
169	C₃×C₄×D₃	—	6	16	no	—
170	C₃×Dic₆	—	3	8	no	—
171	C₃×Dic₆	—	6	4	no	—
172	C₃⋊(C₃⋊C₈)	C₂³×C₃	1	4	yes	complemented
173	C₃×C₃⋊C₈	—	3	16	no	—
174	C₂×AGL(1,ℤ/8)	—	9	1	no	Sylow
175	C₂×C₃³	—	2	2	no	—
176	C₂×C₃³	—	4	4	no	—
177	C₂×C₃³	AGL(1,ℤ/8)	1	2	yes	complemented
178	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
179	C₃×C₃⋊D₃	—	4	2	no	—
180	C₂⁴×C₃	—	2	8	no	—
181	C₂⁴×C₃	—	2	4	no	—
182	C₂⁴×C₃	—	2	1	no	—
183	C₃×#41	—	9	4	no	—
184	C₃×#41	—	18	2	no	—
185	C₂×C₃×Q₈	—	9	1	no	—
186	C₂×C₃×D₄	—	2	8	no	—
187	C₂×C₃×D₄	—	2	16	no	—
188	C₂×C₃×D₄	—	2	4	no	—
189	C₂×C₃×D₄	—	2	8	no	—
190	C₂×C₃×D₄	—	2	2	no	—
191	C₂×C₃×D₄	—	2	1	no	—
192	C₂×C₃×D₄	—	2	8	no	—
193	C₂×C₃×D₄	—	2	16	no	—
194	C₂×C₃×D₄	—	9	1	no	—
195	C₂×C₃×D₄	—	18	1	no	—
196	C₂×C₃×D₄	C₂×C₃×D₃	1	8	yes	—
197	C₂×C₃×D₄	C₂×C₃×D₃	1	16	yes	complemented
198	C₂×C₃×D₄	C₂×C₃⋊D₃	1	2	yes	—
199	C₂×C₃×D₄	C₂×C₃⋊D₃	1	4	yes	complemented
200	C₂²×C₃×C₄	—	2	4	no	—
201	C₂²×C₃×C₄	—	18	1	no	—
202	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
203	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
204	C₂×#67	—	6	4	no	—
205	#235	—	3	16	no	—
206	#235	—	6	8	no	—
207	C₂×D₁₂	—	3	4	no	—
208	C₂×C₄×D₃	—	6	4	no	—
209	C₂×Dic₆	—	3	4	no	—
210	C₃×SD₁₆	—	9	8	no	—
211	C₃×D₈	—	9	8	no	—
212	C₃×M₁₆	—	9	4	no	—
213	C₂×C₃×C₈	—	9	2	no	—
214	#214	—	3	32	no	—
215	#213	—	3	32	no	—
216	#208	—	3	16	no	—
217	C₂×C₃⋊C₈	—	3	8	no	—
218	C₂²×C₃²	—	2	16	no	—
219	C₂²×C₃²	—	2	8	no	—
220	C₂²×C₃²	—	2	2	no	—
221	C₂²×C₃²	—	2	32	no	—
222	C₂²×C₃²	—	2	16	no	—
223	C₂²×C₃²	—	2	4	no	—
224	C₂²×C₃²	—	2	8	no	—
225	C₂²×C₃²	—	2	4	no	—
226	C₂²×C₃²	—	4	64	no	—
227	C₂²×C₃²	—	4	8	no	—
228	C₂²×C₃²	—	4	32	no	—
229	C₂²×C₃²	—	4	32	no	—
230	C₂²×C₃²	—	4	16	no	—
231	C₂²×C₃²	—	4	4	no	—
232	C₂²×C₃²	C₂×#67	1	8	yes	—
233	C₂²×C₃²	C₂×#67	1	4	yes	—
234	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
235	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
236	C₂×C₃⋊D₃	—	2	2	no	—
237	C₂×C₃⋊D₃	—	4	2	no	—
238	C₂×C₃×D₃	—	6	8	no	—
239	C₂×C₃×D₃	—	12	8	no	—
240	C₃²×C₄	—	2	4	no	—
241	C₃²×C₄	—	2	4	no	—
242	C₃²×C₄	—	2	8	no	—
243	C₃²×C₄	C₂×#67	1	4	yes	—
244	C₃²×C₄	C₂×#67	1	8	yes	—
245	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
246	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
247	C₃²×C₄	C₂³×D₃	1	4	yes	—
248	C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
249	C₃⋊Dic₃	—	2	2	no	—
250	C₃×Dic₃	—	6	8	no	—
251	C₂×#41	—	9	1	no	—
252	C₂²×D₄	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
253	AGL(1,ℤ/8)	—	9	8	no	—
254	C₂×SD₁₆	—	9	2	no	—
255	C₂×D₈	—	9	2	no	—
256	C₂×M₁₆	—	9	1	no	—
257	C₃³	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
258	C₂³×C₃	—	2	16	no	—
259	C₂³×C₃	—	2	32	no	—
260	C₂³×C₃	—	2	8	no	—
261	C₂³×C₃	—	2	16	no	—
262	C₂³×C₃	—	2	4	no	—
263	C₂³×C₃	—	2	2	no	—
264	C₂³×C₃	—	2	4	no	—
265	C₂³×C₃	—	4	32	no	—
266	C₂³×C₃	—	4	16	no	—
267	C₂³×C₃	—	4	4	no	—
268	C₂³×C₃	—	18	1	no	—
269	C₂³×C₃	C₃×#67	1	4	yes	—
270	C₂³×C₃	#638	1	1	yes	characteristic
271	C₂²×D₃	—	6	4	no	—
272	C₃×Q₈	—	9	2	no	—
273	C₃×Q₈	—	18	1	no	—
274	C₃×D₄	—	2	16	no	—
275	C₃×D₄	—	2	32	no	—
276	C₃×D₄	—	2	8	no	—
277	C₃×D₄	—	2	16	no	—
278	C₃×D₄	—	2	2	no	—
279	C₃×D₄	—	2	4	no	—
280	C₃×D₄	—	2	16	no	—
281	C₃×D₄	—	9	2	no	—
282	C₃×D₄	—	18	4	no	—
283	C₃×D₄	—	18	1	no	—
284	C₃×D₄	C₂²×C₃×D₃	1	16	yes	—
285	C₃×D₄	C₂²×C₃⋊D₃	1	4	yes	—
286	C₂×C₃×C₄	—	2	4	no	—
287	C₂×C₃×C₄	—	2	8	no	—
288	C₂×C₃×C₄	—	2	4	no	—
289	C₂×C₃×C₄	—	2	8	no	—
290	C₂×C₃×C₄	—	18	1	no	—
291	C₂×C₃×C₄	—	18	4	no	—
292	C₂×C₃×C₄	C₃×#67	1	4	yes	—
293	C₂×C₃×C₄	C₃×#67	1	8	yes	—
294	C₂×C₃×C₄	#638	1	2	yes	—
295	C₂×C₃×C₄	#638	1	1	yes	characteristic
296	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
297	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
298	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
299	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
300	#67	—	6	16	no	—
301	C₂×Dic₃	—	6	4	no	—
302	D₁₂	—	3	8	no	—
303	D₁₂	—	6	4	no	—
304	C₄×D₃	—	6	16	no	—
305	Dic₆	—	3	8	no	—
306	Dic₆	—	6	4	no	—
307	C₃×C₈	—	9	4	no	—
308	C₃⋊C₈	—	3	16	no	—
309	C₂×C₃²	—	2	16	no	—
310	C₂×C₃²	—	2	2	no	—
311	C₂×C₃²	—	2	8	no	—
312	C₂×C₃²	—	2	8	no	—
313	C₂×C₃²	—	2	4	no	—
314	C₂×C₃²	—	4	32	no	—
315	C₂×C₃²	—	4	4	no	—
316	C₂×C₃²	—	4	16	no	—
317	C₂×C₃²	#932	1	8	yes	complemented
318	C₂×C₃²	C₃×AGL(1,ℤ/8)	1	2	yes	complemented
319	C₂×C₃²	C₂²×#67	1	4	yes	—
320	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
321	C₃⋊D₃	—	4	2	no	—
322	C₃×D₃	—	12	8	no	—
323	C₂⁴	—	2	1	no	—
324	#41	—	9	4	no	—
325	#41	—	18	2	no	—
326	C₂×Q₈	—	9	1	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	9	1	no	—
330	C₂×D₄	—	18	1	no	—
331	C₂×D₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
332	C₂×D₄	C₂×C₃×C₃⋊D₃	1	4	yes	complemented
333	C₂²×C₄	—	18	1	no	—
334	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
335	SD₁₆	—	9	8	no	—
336	D₈	—	9	8	no	—
337	M₁₆	—	9	4	no	—
338	C₂×C₈	—	9	2	no	—
339	C₂²×C₃	—	2	16	no	—
340	C₂²×C₃	—	2	8	no	—
341	C₂²×C₃	—	2	2	no	—
342	C₂²×C₃	—	2	32	no	—
343	C₂²×C₃	—	2	16	no	—
344	C₂²×C₃	—	2	4	no	—
345	C₂²×C₃	—	2	8	no	—
346	C₂²×C₃	—	2	4	no	—
347	C₂²×C₃	—	4	64	no	—
348	C₂²×C₃	—	4	32	no	—
349	C₂²×C₃	—	4	8	no	—
350	C₂²×C₃	—	4	32	no	—
351	C₂²×C₃	—	4	16	no	—
352	C₂²×C₃	—	4	4	no	—
353	C₂²×C₃	—	18	2	no	—
354	C₂²×C₃	—	36	2	no	—
355	C₂²×C₃	C₂×C₃×#67	1	8	yes	—
356	C₂²×C₃	C₂×C₃×#67	1	4	yes	—
357	C₂²×C₃	C₂×#638	1	2	yes	—
358	C₂²×C₃	C₂×#638	1	1	yes	characteristic
359	C₂×D₃	—	6	8	no	—
360	C₂×D₃	—	12	8	no	—
361	C₃×C₄	—	2	4	no	—
362	C₃×C₄	—	2	8	no	—
363	C₃×C₄	—	2	4	no	—
364	C₃×C₄	—	18	2	no	—
365	C₃×C₄	C₂×C₃×#67	1	4	yes	—
366	C₃×C₄	C₂×C₃×#67	1	8	yes	—
367	C₃×C₄	C₂×#638	1	2	yes	—
368	C₃×C₄	C₂×#638	1	1	yes	characteristic
369	C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
370	C₃×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
371	Dic₃	—	6	8	no	—
372	C₃²	—	2	4	no	—
373	C₃²	C₂×#932	1	4	yes	complemented
374	C₃²	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented
375	C₂³	—	2	2	no	—
376	C₂³	—	2	4	no	—
377	C₂³	—	4	4	no	—
378	C₂³	—	18	1	no	—
379	C₂³	C₃×#638	1	1	yes	characteristic
380	Q₈	—	9	2	no	—
381	Q₈	—	18	1	no	—
382	D₄	—	2	2	no	—
383	D₄	—	2	4	no	—
384	D₄	—	9	2	no	—
385	D₄	—	18	4	no	—
386	D₄	—	18	1	no	—
387	D₄	C₂²×C₃×C₃⋊D₃	1	4	yes	—
388	C₂×C₄	—	18	1	no	—
389	C₂×C₄	—	18	4	no	—
390	C₂×C₄	C₃×#638	1	1	yes	characteristic
391	C₂×C₄	C₃×#638	1	2	yes	—
392	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
393	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
394	C₈	—	9	4	no	—
395	C₂×C₃	—	2	16	no	—
396	C₂×C₃	—	2	8	no	—
397	C₂×C₃	—	2	2	no	—
398	C₂×C₃	—	2	8	no	—
399	C₂×C₃	—	2	4	no	—
400	C₂×C₃	—	4	32	no	—
401	C₂×C₃	—	4	16	no	—
402	C₂×C₃	—	4	4	no	—
403	C₂×C₃	—	36	2	no	—
404	C₂×C₃	C₃×#932	1	8	yes	complemented
405	C₂×C₃	#64141	1	2	yes	direct product factor
406	C₂×C₃	C₂²×C₃×#67	1	4	yes	—
407	C₂×C₃	C₂²×#638	1	1	yes	characteristic
408	D₃	—	12	8	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	2	4	no	—
411	C₂²	—	4	8	no	—
412	C₂²	—	4	4	no	—
413	C₂²	—	18	2	no	—
414	C₂²	—	36	2	no	—
415	C₂²	C₂×C₃×#638	1	2	yes	—
416	C₂²	C₂×C₃×#638	1	1	yes	characteristic
417	C₄	—	18	2	no	—
418	C₄	C₂×C₃×#638	1	2	yes	—
419	C₄	C₂×C₃×#638	1	1	yes	characteristic
420	C₄	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
421	C₃	—	2	4	no	—
422	C₃	C₂×C₃×#932	1	4	yes	complemented
423	C₃	C₂×#64141	1	1	yes	characteristic, direct product factor
424	C₂	—	2	2	no	—
425	C₂	—	4	4	no	—
426	C₂	—	36	2	no	—
427	C₂	C₃×#64141	1	2	yes	direct product factor
428	C₂	C₂²×C₃×#638	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×#638
commutator, cosocle	C₃²×C₄	C₂⁴×C₃
Frattini	C₄	C₂³×C₃×C₃⋊D₃
Fitting	C₂²×C₃³×D₄	C₂
socle	C₂²×C₃³	C₂×D₄
hypercenter	C₂²×C₃×D₄	C₃⋊D₃
hypocenter	C₃²	C₂×C₃×AGL(1,ℤ/8)
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃³×D₄	C₂	semidirect
2. C₂×C₃×#3828	C₂	semidirect
3. C₂×C₃×#3754	C₂	semidirect
4. C₃×#64141	C₂	direct (N × H)
5. C₂×C₃×#3753	C₂	semidirect
6. C₂×C₃×#3748	C₂	semidirect
7. C₂×#64141	C₃	direct (N × H)
13. C₂×C₃³×D₄	C₂²	semidirect
17. C₃×#3828	C₂²	semidirect
18. C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	semidirect
20. C₂×C₃×#634	C₂²	semidirect
21. C₃×#3754	C₂²	semidirect
22. C₃×#3753	C₂²	semidirect
23. C₃×#3748	C₂²	semidirect
24. C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	semidirect
26. C₂²×C₃²×D₄	D₃	semidirect
27. C₂²×C₃²×D₄	C₂×C₃	semidirect
28. C₂×#3828	C₂×C₃	semidirect
30. C₂×#3754	C₂×C₃	semidirect
31. #64141	C₂×C₃	direct (N × H)
32. C₂×#3753	C₂×C₃	semidirect
33. C₂×#3748	C₂×C₃	semidirect
53. C₃×C₄⋊(C₃⋊D₃)	C₂³	semidirect
56. C₃×#634	C₂³	semidirect
57. C₃×C₃⋊(C₃⋊C₈)	C₂³	semidirect
72. C₂×C₃²×D₄	C₂×D₃	semidirect
74. C₂×C₃²×D₄	C₂²×C₃	semidirect
80. #3828	C₂²×C₃	semidirect
81. C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	semidirect
83. C₂×#634	C₂²×C₃	semidirect
90. #3754	C₂²×C₃	semidirect
91. #3753	C₂²×C₃	semidirect
92. #3748	C₂²×C₃	semidirect
93. C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	semidirect
112. C₂²×C₃×D₄	C₃×D₃	semidirect
113. C₂²×C₃×D₄	C₃⋊D₃	semidirect
161. C₄⋊(C₃⋊D₃)	C₂³×C₃	semidirect
164. #634	C₂³×C₃	semidirect
172. C₃⋊(C₃⋊C₈)	C₂³×C₃	semidirect
177. C₂×C₃³	AGL(1,ℤ/8)	semidirect
197. C₂×C₃×D₄	C₂×C₃×D₃	semidirect
199. C₂×C₃×D₄	C₂×C₃⋊D₃	semidirect
252. C₂²×D₄	C₃×C₃⋊D₃	semidirect
257. C₃³	C₂×AGL(1,ℤ/8)	semidirect
317. C₂×C₃²	#932	semidirect
318. C₂×C₃²	C₃×AGL(1,ℤ/8)	semidirect
332. C₂×D₄	C₂×C₃×C₃⋊D₃	semidirect
373. C₃²	C₂×#932	semidirect
374. C₃²	C₂×C₃×AGL(1,ℤ/8)	semidirect
404. C₂×C₃	C₃×#932	semidirect
405. C₂×C₃	#64141	direct (N × H)
422. C₃	C₂×C₃×#932	semidirect
423. C₃	C₂×#64141	direct (N × H)
427. C₂	C₃×#64141	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃³×D₄	2
C₂×C₃×#3828	2
C₂×C₃×#3754	2
C₃×#64141	2
C₂×C₃×#3753	2
C₂×C₃×#3748	2
C₂×#64141	3
C₂×C₃×#932	3

Subgroups — C2×C3×#64141 #13179550

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#64141 #13179550