Subgroups — C₂×C₃²×#932 #13179176

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×C₃²×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃²×#214	C₂	1	2	yes	maximal, complemented
4	C₃²×#932	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃²×#213	C₂	1	2	yes	maximal, complemented
6	C₂×C₃²×#208	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃²×AGL(1,ℤ/8)	—	3	1	no	maximal
8	C₂×C₃×#932	C₃	1	4	yes	maximal, direct product factor
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×C₃²×#67	—	2	1	no	—
16	C₃²×#235	—	2	2	no	—
17	C₃²×#235	C₂²	1	4	yes	complemented
18	C₂×C₃²×D₁₂	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₃²×C₄×D₃	—	2	1	no	—
20	C₂×C₃²×Dic₆	C₂²	1	1	yes	characteristic, complemented
21	C₃²×#214	C₂²	1	8	yes	complemented
22	C₃²×#213	C₂²	1	8	yes	complemented
23	C₃²×#208	C₂²	1	4	yes	complemented
24	C₂×C₃²×C₃⋊C₈	C₂²	1	2	yes	complemented
25	C₂×C₃²×#41	—	3	1	no	—
26	C₂²×C₃²×D₄	—	2	4	no	—
27	C₂²×C₃²×D₄	D₃	1	1	yes	characteristic, complemented
28	C₂²×C₃²×D₄	C₂×C₃	1	4	yes	complemented
29	C₂×C₃×#235	C₂×C₃	1	4	yes	complemented
30	C₃²×AGL(1,ℤ/8)	—	3	8	no	—
31	C₂×C₃²×SD₁₆	—	3	2	no	—
32	C₂×C₃²×D₈	—	3	2	no	—
33	C₂×C₃²×M₁₆	—	3	1	no	—
34	C₂×C₃×#214	C₂×C₃	1	8	yes	complemented
35	C₃×#932	C₂×C₃	1	32	yes	direct product factor
36	C₂×C₃×#213	C₂×C₃	1	8	yes	complemented
37	C₂×C₃×#208	C₂×C₃	1	4	yes	complemented
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×C₃²×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	C₃²×#67	—	2	4	no	—
51	C₂×C₃²×Dic₃	—	2	1	no	—
52	C₃²×D₁₂	—	2	1	no	—
53	C₃²×D₁₂	C₂³	1	2	yes	complemented
54	C₃²×C₄×D₃	—	2	4	no	—
55	C₃²×Dic₆	—	2	1	no	—
56	C₃²×Dic₆	C₂³	1	2	yes	complemented
57	C₃²×C₃⋊C₈	C₂³	1	4	yes	complemented
58	C₂×C₃×AGL(1,ℤ/8)	—	3	4	no	—
59	C₂×#932	C₃²	1	1	yes	characteristic, direct product factor
60	C₂⁴×C₃²	—	2	8	no	—
61	C₂⁴×C₃²	—	2	1	no	—
62	C₂⁴×C₃²	—	2	4	no	—
63	C₃²×#41	—	3	4	no	—
64	C₃²×#41	—	6	2	no	—
65	C₂×C₃²×Q₈	—	3	1	no	—
66	C₂×C₃²×D₄	—	2	8	no	—
67	C₂×C₃²×D₄	—	2	16	no	—
68	C₂×C₃²×D₄	—	2	8	no	—
69	C₂×C₃²×D₄	—	2	16	no	—
70	C₂×C₃²×D₄	—	2	2	no	—
71	C₂×C₃²×D₄	—	2	1	no	—
72	C₂×C₃²×D₄	—	2	4	no	—
73	C₂×C₃²×D₄	—	2	8	no	—
74	C₂×C₃²×D₄	—	3	1	no	—
75	C₂×C₃²×D₄	—	6	1	no	—
76	C₂×C₃²×D₄	C₂×D₃	1	2	yes	—
77	C₂×C₃²×D₄	C₂×D₃	1	4	yes	complemented
78	C₂×C₃²×D₄	C₂²×C₃	1	8	yes	—
79	C₂×C₃²×D₄	C₂²×C₃	1	16	yes	complemented
80	C₂²×C₃²×C₄	—	2	4	no	—
81	C₂²×C₃²×C₄	—	6	1	no	—
82	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
83	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
84	C₂×C₃×#67	—	2	4	no	—
85	C₃×#235	—	2	8	no	—
86	C₃×#235	C₂²×C₃	1	16	yes	complemented
87	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	complemented
88	C₂×C₃×C₄×D₃	—	2	4	no	—
89	C₂×C₃×Dic₆	C₂²×C₃	1	4	yes	complemented
90	C₃²×SD₁₆	—	3	8	no	—
91	C₃²×D₈	—	3	8	no	—
92	C₃²×M₁₆	—	3	4	no	—
93	C₂×C₃²×C₈	—	3	2	no	—
94	C₃×#214	C₂²×C₃	1	32	yes	complemented
95	C₃×#213	C₂²×C₃	1	32	yes	complemented
96	C₃×#208	C₂²×C₃	1	16	yes	complemented
97	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	8	yes	complemented
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×C₃²×D₃	—	2	2	no	—
105	C₂×C₃²×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	C₃²×Dic₃	—	2	2	no	—
110	C₂×C₃×#41	—	3	4	no	—
111	C₂²×C₃×D₄	—	2	4	no	—
112	C₂²×C₃×D₄	C₃×D₃	1	4	yes	complemented
113	C₂²×C₃×D₄	C₂×C₃²	1	1	yes	characteristic, complemented
114	C₂×#235	C₂×C₃²	1	1	yes	characteristic, complemented
115	C₃×AGL(1,ℤ/8)	—	3	32	no	—
116	C₂×C₃×SD₁₆	—	3	8	no	—
117	C₂×C₃×D₈	—	3	8	no	—
118	C₂×C₃×M₁₆	—	3	4	no	—
119	C₂×#214	C₂×C₃²	1	2	yes	complemented
120	#932	C₂×C₃²	1	8	yes	direct product factor
121	C₂×#213	C₂×C₃²	1	2	yes	complemented
122	C₂×#208	C₂×C₃²	1	1	yes	characteristic, complemented
123	C₂³×C₃²	—	2	16	no	—
124	C₂³×C₃²	—	2	32	no	—
125	C₂³×C₃²	—	2	4	no	—
126	C₂³×C₃²	—	2	2	no	—
127	C₂³×C₃²	—	2	8	no	—
128	C₂³×C₃²	—	2	16	no	—
129	C₂³×C₃²	—	2	4	no	—
130	C₂³×C₃²	—	4	32	no	—
131	C₂³×C₃²	—	4	4	no	—
132	C₂³×C₃²	—	4	16	no	—
133	C₂³×C₃²	—	6	1	no	—
134	C₂³×C₃²	#67	1	1	yes	characteristic
135	C₂³×C₃²	C₃×D₄	1	4	yes	—
136	C₂²×C₃×D₃	—	2	4	no	—
137	C₃²×Q₈	—	3	2	no	—
138	C₃²×Q₈	—	6	1	no	—
139	C₃²×D₄	—	2	16	no	—
140	C₃²×D₄	—	2	32	no	—
141	C₃²×D₄	—	2	2	no	—
142	C₃²×D₄	—	2	4	no	—
143	C₃²×D₄	—	2	8	no	—
144	C₃²×D₄	—	2	16	no	—
145	C₃²×D₄	—	2	16	no	—
146	C₃²×D₄	—	3	2	no	—
147	C₃²×D₄	—	6	4	no	—
148	C₃²×D₄	—	6	1	no	—
149	C₃²×D₄	C₂²×D₃	1	4	yes	—
150	C₃²×D₄	C₂³×C₃	1	16	yes	—
151	C₂×C₃²×C₄	—	2	4	no	—
152	C₂×C₃²×C₄	—	2	8	no	—
153	C₂×C₃²×C₄	—	2	4	no	—
154	C₂×C₃²×C₄	—	2	8	no	—
155	C₂×C₃²×C₄	—	6	1	no	—
156	C₂×C₃²×C₄	—	6	4	no	—
157	C₂×C₃²×C₄	#67	1	2	yes	—
158	C₂×C₃²×C₄	#67	1	1	yes	characteristic
159	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
160	C₂×C₃²×C₄	C₃×D₄	1	8	yes	—
161	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
162	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
163	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
164	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
165	C₃×#67	—	2	16	no	—
166	C₂×C₃×Dic₃	—	2	4	no	—
167	C₃×D₁₂	—	2	4	no	—
168	C₃×D₁₂	C₂³×C₃	1	8	yes	complemented
169	C₃×C₄×D₃	—	2	16	no	—
170	C₃×Dic₆	—	2	4	no	—
171	C₃×Dic₆	C₂³×C₃	1	8	yes	complemented
172	C₃²×C₈	—	3	4	no	—
173	C₃×C₃⋊C₈	C₂³×C₃	1	16	yes	complemented
174	C₂×AGL(1,ℤ/8)	—	3	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	C₃²×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	—	3	16	no	—
184	C₃×#41	—	6	8	no	—
185	C₂×C₃×Q₈	—	3	4	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	1	no	—
191	C₂×C₃×D₄	—	2	2	no	—
192	C₂×C₃×D₄	—	2	8	no	—
193	C₂×C₃×D₄	—	2	16	no	—
194	C₂×C₃×D₄	—	3	4	no	—
195	C₂×C₃×D₄	—	6	4	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	C₂²×C₃²	1	2	yes	—
199	C₂×C₃×D₄	C₂²×C₃²	1	4	yes	complemented
200	C₂²×C₃×C₄	—	2	4	no	—
201	C₂²×C₃×C₄	—	6	4	no	—
202	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
203	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
204	C₂×#67	—	2	1	no	—
205	#235	—	2	2	no	—
206	#235	C₂²×C₃²	1	4	yes	complemented
207	C₂×D₁₂	C₂²×C₃²	1	1	yes	characteristic, complemented
208	C₂×C₄×D₃	—	2	1	no	—
209	C₂×Dic₆	C₂²×C₃²	1	1	yes	characteristic, complemented
210	C₃×SD₁₆	—	3	32	no	—
211	C₃×D₈	—	3	32	no	—
212	C₃×M₁₆	—	3	16	no	—
213	C₂×C₃×C₈	—	3	8	no	—
214	#214	C₂²×C₃²	1	8	yes	complemented
215	#213	C₂²×C₃²	1	8	yes	complemented
216	#208	C₂²×C₃²	1	4	yes	complemented
217	C₂×C₃⋊C₈	C₂²×C₃²	1	2	yes	complemented
218	C₂²×C₃²	—	2	16	no	—
219	C₂²×C₃²	—	2	2	no	—
220	C₂²×C₃²	—	2	8	no	—
221	C₂²×C₃²	—	2	32	no	—
222	C₂²×C₃²	—	2	4	no	—
223	C₂²×C₃²	—	2	16	no	—
224	C₂²×C₃²	—	2	8	no	—
225	C₂²×C₃²	—	2	4	no	—
226	C₂²×C₃²	—	4	64	no	—
227	C₂²×C₃²	—	4	32	no	—
228	C₂²×C₃²	—	4	8	no	—
229	C₂²×C₃²	—	4	32	no	—
230	C₂²×C₃²	—	4	4	no	—
231	C₂²×C₃²	—	4	16	no	—
232	C₂²×C₃²	—	6	2	no	—
233	C₂²×C₃²	—	12	2	no	—
234	C₂²×C₃²	C₂×#67	1	2	yes	—
235	C₂²×C₃²	C₂×#67	1	1	yes	characteristic
236	C₂²×C₃²	C₂×C₃×D₄	1	8	yes	—
237	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
238	C₂×C₃×D₃	—	2	8	no	—
239	C₂×C₃×D₃	—	4	8	no	—
240	C₃²×C₄	—	2	4	no	—
241	C₃²×C₄	—	2	8	no	—
242	C₃²×C₄	—	2	4	no	—
243	C₃²×C₄	—	6	2	no	—
244	C₃²×C₄	C₂×#67	1	2	yes	—
245	C₃²×C₄	C₂×#67	1	1	yes	characteristic
246	C₃²×C₄	C₂×C₃×D₄	1	4	yes	—
247	C₃²×C₄	C₂×C₃×D₄	1	8	yes	—
248	C₃²×C₄	C₂³×D₃	1	1	yes	characteristic
249	C₃²×C₄	C₂⁴×C₃	1	4	yes	—
250	C₃×Dic₃	—	2	8	no	—
251	C₂×#41	—	3	1	no	—
252	C₂²×D₄	C₃²×D₃	1	1	yes	characteristic, complemented
253	AGL(1,ℤ/8)	—	3	8	no	—
254	C₂×SD₁₆	—	3	2	no	—
255	C₂×D₈	—	3	2	no	—
256	C₂×M₁₆	—	3	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	2	no	—
263	C₂³×C₃	—	2	4	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	—	6	4	no	—
269	C₂³×C₃	C₃×#67	1	4	yes	—
270	C₂³×C₃	C₃²×D₄	1	1	yes	characteristic
271	C₂²×D₃	—	2	1	no	—
272	C₃×Q₈	—	3	8	no	—
273	C₃×Q₈	—	6	4	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	—	3	8	no	—
282	C₃×D₄	—	6	16	no	—
283	C₃×D₄	—	6	4	no	—
284	C₃×D₄	C₂²×C₃×D₃	1	16	yes	—
285	C₃×D₄	C₂³×C₃²	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	—	6	4	no	—
291	C₂×C₃×C₄	—	6	16	no	—
292	C₂×C₃×C₄	C₃×#67	1	4	yes	—
293	C₂×C₃×C₄	C₃×#67	1	8	yes	—
294	C₂×C₃×C₄	C₃²×D₄	1	1	yes	characteristic
295	C₂×C₃×C₄	C₃²×D₄	1	2	yes	—
296	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
297	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
298	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
299	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
300	#67	—	2	4	no	—
301	C₂×Dic₃	—	2	1	no	—
302	D₁₂	—	2	1	no	—
303	D₁₂	C₂³×C₃²	1	2	yes	complemented
304	C₄×D₃	—	2	4	no	—
305	Dic₆	—	2	1	no	—
306	Dic₆	C₂³×C₃²	1	2	yes	complemented
307	C₃×C₈	—	3	16	no	—
308	C₃⋊C₈	C₂³×C₃²	1	4	yes	complemented
309	C₂×C₃²	—	2	16	no	—
310	C₂×C₃²	—	2	8	no	—
311	C₂×C₃²	—	2	2	no	—
312	C₂×C₃²	—	2	8	no	—
313	C₂×C₃²	—	2	4	no	—
314	C₂×C₃²	—	4	32	no	—
315	C₂×C₃²	—	4	16	no	—
316	C₂×C₃²	—	4	4	no	—
317	C₂×C₃²	—	12	2	no	—
318	C₂×C₃²	#932	1	2	yes	direct product factor
319	C₂×C₃²	C₃×AGL(1,ℤ/8)	1	8	yes	complemented
320	C₂×C₃²	C₂²×#67	1	1	yes	characteristic
321	C₂×C₃²	C₂²×C₃×D₄	1	4	yes	—
322	C₃×D₃	—	4	8	no	—
323	C₂⁴	—	2	1	no	—
324	#41	—	3	4	no	—
325	#41	—	6	2	no	—
326	C₂×Q₈	—	3	1	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	3	1	no	—
330	C₂×D₄	—	6	1	no	—
331	C₂×D₄	C₂×C₃²×D₃	1	2	yes	—
332	C₂×D₄	C₂×C₃²×D₃	1	4	yes	complemented
333	C₂²×C₄	—	6	1	no	—
334	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
335	SD₁₆	—	3	8	no	—
336	D₈	—	3	8	no	—
337	M₁₆	—	3	4	no	—
338	C₂×C₈	—	3	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	8	no	—
349	C₂²×C₃	—	4	32	no	—
350	C₂²×C₃	—	4	32	no	—
351	C₂²×C₃	—	4	16	no	—
352	C₂²×C₃	—	4	4	no	—
353	C₂²×C₃	—	6	8	no	—
354	C₂²×C₃	—	12	8	no	—
355	C₂²×C₃	C₂×C₃×#67	1	8	yes	—
356	C₂²×C₃	C₂×C₃×#67	1	4	yes	—
357	C₂²×C₃	C₂×C₃²×D₄	1	2	yes	—
358	C₂²×C₃	C₂×C₃²×D₄	1	1	yes	characteristic
359	C₂×D₃	—	2	2	no	—
360	C₂×D₃	—	4	2	no	—
361	C₃×C₄	—	2	4	no	—
362	C₃×C₄	—	2	8	no	—
363	C₃×C₄	—	2	4	no	—
364	C₃×C₄	—	6	8	no	—
365	C₃×C₄	C₂×C₃×#67	1	8	yes	—
366	C₃×C₄	C₂×C₃×#67	1	4	yes	—
367	C₃×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
368	C₃×C₄	C₂×C₃²×D₄	1	2	yes	—
369	C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
370	C₃×C₄	C₂⁴×C₃²	1	1	yes	characteristic
371	Dic₃	—	2	2	no	—
372	C₃²	—	2	4	no	—
373	C₃²	C₂×#932	1	1	yes	characteristic, direct product factor
374	C₃²	C₂×C₃×AGL(1,ℤ/8)	1	4	yes	complemented
375	C₂³	—	2	2	no	—
376	C₂³	—	2	4	no	—
377	C₂³	—	4	4	no	—
378	C₂³	—	6	1	no	—
379	C₂³	C₃²×#67	1	1	yes	characteristic
380	Q₈	—	3	2	no	—
381	Q₈	—	6	1	no	—
382	D₄	—	2	2	no	—
383	D₄	—	2	4	no	—
384	D₄	—	3	2	no	—
385	D₄	—	6	4	no	—
386	D₄	—	6	1	no	—
387	D₄	C₂²×C₃²×D₃	1	4	yes	—
388	C₂×C₄	—	6	1	no	—
389	C₂×C₄	—	6	4	no	—
390	C₂×C₄	C₃²×#67	1	1	yes	characteristic
391	C₂×C₄	C₃²×#67	1	2	yes	—
392	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
393	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
394	C₈	—	3	4	no	—
395	C₂×C₃	—	2	16	no	—
396	C₂×C₃	—	2	2	no	—
397	C₂×C₃	—	2	8	no	—
398	C₂×C₃	—	2	8	no	—
399	C₂×C₃	—	2	4	no	—
400	C₂×C₃	—	4	32	no	—
401	C₂×C₃	—	4	4	no	—
402	C₂×C₃	—	4	16	no	—
403	C₂×C₃	—	12	8	no	—
404	C₂×C₃	C₃×#932	1	8	yes	direct product factor
405	C₂×C₃	C₃²×AGL(1,ℤ/8)	1	2	yes	complemented
406	C₂×C₃	C₂²×C₃×#67	1	4	yes	—
407	C₂×C₃	C₂²×C₃²×D₄	1	1	yes	characteristic
408	D₃	—	4	2	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	2	4	no	—
411	C₂²	—	4	8	no	—
412	C₂²	—	4	4	no	—
413	C₂²	—	6	2	no	—
414	C₂²	—	12	2	no	—
415	C₂²	C₂×C₃²×#67	1	2	yes	—
416	C₂²	C₂×C₃²×#67	1	1	yes	characteristic
417	C₄	—	6	2	no	—
418	C₄	C₂×C₃²×#67	1	2	yes	—
419	C₄	C₂×C₃²×#67	1	1	yes	characteristic
420	C₄	C₂³×C₃²×D₃	1	1	yes	characteristic
421	C₃	—	2	4	no	—
422	C₃	C₂×C₃×#932	1	4	yes	direct product factor
423	C₃	C₂×C₃²×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented
424	C₂	—	2	2	no	—
425	C₂	—	4	4	no	—
426	C₂	—	12	2	no	—
427	C₂	C₃²×#932	1	2	yes	direct product factor
428	C₂	C₂²×C₃²×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃²	C₂×#67
commutator, cosocle	C₃×C₄	C₂⁴×C₃²
Frattini	C₄	C₂³×C₃²×D₃
Fitting	C₂²×C₃³×D₄	C₂
socle	C₂²×C₃³	C₂×D₄
hypercenter	C₂²×C₃²×D₄	D₃
hypocenter	C₃	C₂×C₃²×AGL(1,ℤ/8)
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃² ◁ C₂²×C₃²×C₄ ◁ C₂²×C₃²×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×C₃²×#235	C₂	semidirect
3. C₂×C₃²×#214	C₂	semidirect
4. C₃²×#932	C₂	direct (N × H)
5. C₂×C₃²×#213	C₂	semidirect
6. C₂×C₃²×#208	C₂	semidirect
8. C₂×C₃×#932	C₃	direct (N × H)
13. C₂×C₃³×D₄	C₂²	semidirect
17. C₃²×#235	C₂²	semidirect
18. C₂×C₃²×D₁₂	C₂²	semidirect
20. C₂×C₃²×Dic₆	C₂²	semidirect
21. C₃²×#214	C₂²	semidirect
22. C₃²×#213	C₂²	semidirect
23. C₃²×#208	C₂²	semidirect
24. C₂×C₃²×C₃⋊C₈	C₂²	semidirect
27. C₂²×C₃²×D₄	D₃	semidirect
28. C₂²×C₃²×D₄	C₂×C₃	semidirect
29. C₂×C₃×#235	C₂×C₃	semidirect
34. C₂×C₃×#214	C₂×C₃	semidirect
35. C₃×#932	C₂×C₃	direct (N × H)
36. C₂×C₃×#213	C₂×C₃	semidirect
37. C₂×C₃×#208	C₂×C₃	semidirect
53. C₃²×D₁₂	C₂³	semidirect
56. C₃²×Dic₆	C₂³	semidirect
57. C₃²×C₃⋊C₈	C₂³	semidirect
59. C₂×#932	C₃²	direct (N × H)
77. C₂×C₃²×D₄	C₂×D₃	semidirect
79. C₂×C₃²×D₄	C₂²×C₃	semidirect
86. C₃×#235	C₂²×C₃	semidirect
87. C₂×C₃×D₁₂	C₂²×C₃	semidirect
89. C₂×C₃×Dic₆	C₂²×C₃	semidirect
94. C₃×#214	C₂²×C₃	semidirect
95. C₃×#213	C₂²×C₃	semidirect
96. C₃×#208	C₂²×C₃	semidirect
97. C₂×C₃×C₃⋊C₈	C₂²×C₃	semidirect
112. C₂²×C₃×D₄	C₃×D₃	semidirect
113. C₂²×C₃×D₄	C₂×C₃²	semidirect
114. C₂×#235	C₂×C₃²	semidirect
119. C₂×#214	C₂×C₃²	semidirect
120. #932	C₂×C₃²	direct (N × H)
121. C₂×#213	C₂×C₃²	semidirect
122. C₂×#208	C₂×C₃²	semidirect
168. C₃×D₁₂	C₂³×C₃	semidirect
171. C₃×Dic₆	C₂³×C₃	semidirect
173. 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	C₂²×C₃²	semidirect
206. #235	C₂²×C₃²	semidirect
207. C₂×D₁₂	C₂²×C₃²	semidirect
209. C₂×Dic₆	C₂²×C₃²	semidirect
214. #214	C₂²×C₃²	semidirect
215. #213	C₂²×C₃²	semidirect
216. #208	C₂²×C₃²	semidirect
217. C₂×C₃⋊C₈	C₂²×C₃²	semidirect
252. C₂²×D₄	C₃²×D₃	semidirect
257. C₃³	C₂×AGL(1,ℤ/8)	semidirect
303. D₁₂	C₂³×C₃²	semidirect
306. Dic₆	C₂³×C₃²	semidirect
308. C₃⋊C₈	C₂³×C₃²	semidirect
318. C₂×C₃²	#932	direct (N × H)
319. C₂×C₃²	C₃×AGL(1,ℤ/8)	semidirect
332. C₂×D₄	C₂×C₃²×D₃	semidirect
373. C₃²	C₂×#932	direct (N × H)
374. C₃²	C₂×C₃×AGL(1,ℤ/8)	semidirect
404. C₂×C₃	C₃×#932	direct (N × H)
405. C₂×C₃	C₃²×AGL(1,ℤ/8)	semidirect
422. C₃	C₂×C₃×#932	direct (N × H)
423. C₃	C₂×C₃²×AGL(1,ℤ/8)	semidirect
427. C₂	C₃²×#932	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×C₃²×#235	2
C₂×C₃²×#214	2
C₃²×#932	2
C₂×C₃²×#213	2
C₂×C₃²×#208	2
C₂×C₃²×AGL(1,ℤ/8)	3
C₂×C₃×#932	3

Subgroups — C2×C32×#932 #13179176

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×#932 #13179176