Subgroups — C₂²×C₃×#911 #11918639

Order 1152.

3609 conjugacy classes of subgroups.

The subgroup lattice has 499 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#237	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃²×D₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₃×#214	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₃×#213	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#911	C₂	1	24	yes	maximal, direct product factor
7	C₂²×C₃×#204	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₃×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₃×AGL(1,ℤ/8)	—	3	1	no	maximal
10	C₂²×#911	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂⁴×C₃×D₃	—	2	1	no	—
12	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
13	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic, complemented
14	C₂²×C₃×#67	—	2	1	no	—
15	C₂²×C₃×#67	—	2	1	no	—
16	C₂³×C₃×Dic₃	—	2	1	no	—
17	C₂×C₃×#237	—	2	6	no	—
18	C₂×C₃×#237	C₂²	1	12	yes	complemented
19	C₂×C₃×D₃×D₄	—	2	6	no	—
20	C₂×C₃×D₃×D₄	C₂²	1	12	yes	complemented
21	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic
22	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
23	C₂²×C₃×Dic₆	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃²×D₈	C₂²	1	12	yes	complemented
25	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃×#214	C₂²	1	12	yes	complemented
27	C₂×C₃×#213	C₂²	1	12	yes	complemented
28	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
29	C₃×#911	C₂²	1	64	yes	direct product factor
30	C₂×C₃×#204	C₂²	1	12	yes	complemented
31	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	12	yes	complemented
32	C₂²×C₃×#41	—	3	1	no	—
33	C₂³×C₃×D₄	—	3	1	no	—
34	C₂²×#237	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂²×D₃×D₄	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂×C₃×AGL(1,ℤ/8)	—	3	24	no	—
37	C₂²×C₃×SD₁₆	—	3	1	no	—
38	C₂²×C₃×SD₁₆	—	3	1	no	—
39	C₂²×C₃×D₈	—	2	1	no	—
40	C₂²×C₃×D₈	—	3	1	no	—
41	C₂²×C₃×D₈	D₃	1	1	yes	characteristic, complemented
42	C₂²×C₃×D₈	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂²×C₃×M₁₆	—	3	1	no	—
44	C₂²×#214	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂²×#213	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×#911	C₂×C₃	1	24	yes	direct product factor
47	C₂²×#204	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂²×ΓL(1,𝔽₂₅)	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂⁴×C₃²	—	2	1	no	—
50	C₂⁴×C₃²	—	2	1	no	—
51	C₂³×C₃×D₃	—	2	1	no	—
52	C₂³×C₃×D₃	—	2	12	no	—
53	C₂³×C₃×D₃	—	4	8	no	—
54	C₂³×C₃×D₃	D₄	1	1	yes	characteristic
55	C₂×C₃²×D₄	—	2	3	no	—
56	C₂×C₃²×D₄	—	2	3	no	—
57	C₂×C₃²×D₄	C₂³	1	6	yes	—
58	C₂×C₃²×D₄	C₂³	1	6	yes	complemented
59	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
60	C₂×C₃×#67	—	2	12	no	—
61	C₂×C₃×#67	—	2	12	no	—
62	C₂²×C₃×Dic₃	—	2	1	no	—
63	C₂²×C₃×Dic₃	—	2	12	no	—
64	C₂²×C₃×Dic₃	D₄	1	1	yes	characteristic
65	C₃×#237	—	2	24	no	—
66	C₃×#237	C₂³	1	16	yes	complemented
67	C₃×D₃×D₄	—	2	24	no	—
68	C₃×D₃×D₄	C₂³	1	16	yes	complemented
69	C₂×C₃×D₁₂	—	2	3	no	—
70	C₂×C₃×D₁₂	C₂³	1	6	yes	—
71	C₂×C₃×C₄×D₃	D₄	1	6	yes	—
72	C₂×C₃×C₄×D₃	C₂³	1	6	yes	—
73	C₂×C₃×Dic₆	—	2	3	no	—
74	C₂×C₃×Dic₆	C₂³	1	6	yes	complemented
75	C₃²×D₈	C₂³	1	16	yes	complemented
76	C₂×C₃²×C₈	C₂³	1	6	yes	complemented
77	C₃×#214	C₂³	1	16	yes	complemented
78	C₃×#213	C₂³	1	16	yes	complemented
79	C₂×C₃×C₃⋊C₈	C₂³	1	6	yes	complemented
80	C₃×#204	C₂³	1	16	yes	complemented
81	C₃×ΓL(1,𝔽₂₅)	C₂³	1	16	yes	complemented
82	C₂²×AGL(1,ℤ/8)	—	3	1	no	Sylow
83	C₂⁵×C₃	—	6	1	no	—
84	C₂⁴×D₃	—	2	1	no	—
85	C₂×C₃×#41	—	3	12	no	—
86	C₂×C₃×#41	—	6	6	no	—
87	C₂²×C₃×Q₈	—	3	1	no	—
88	C₂²×C₃×D₄	—	2	1	no	—
89	C₂²×C₃×D₄	—	2	1	no	—
90	C₂²×C₃×D₄	—	3	12	no	—
91	C₂²×C₃×D₄	—	3	1	no	—
92	C₂²×C₃×D₄	—	6	6	no	—
93	C₂²×C₃×D₄	—	6	1	no	—
94	C₂²×C₃×D₄	—	6	1	no	—
95	C₂²×C₃×D₄	C₂×D₃	1	1	yes	characteristic
96	C₂²×C₃×D₄	C₂×D₃	1	1	yes	characteristic, complemented
97	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
98	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
99	C₂³×C₃×C₄	—	3	1	no	—
100	C₂³×C₃×C₄	—	6	1	no	—
101	C₂²×#67	—	2	1	no	—
102	C₂²×#67	—	2	1	no	—
103	C₂³×Dic₃	—	2	1	no	—
104	C₂×#237	—	2	6	no	—
105	C₂×#237	C₂²×C₃	1	12	yes	complemented
106	C₂×D₃×D₄	—	2	6	no	—
107	C₂×D₃×D₄	C₂²×C₃	1	12	yes	complemented
108	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic
109	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
110	C₂²×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
111	C₃×AGL(1,ℤ/8)	—	3	64	no	—
112	C₂×C₃×SD₁₆	—	3	12	no	—
113	C₂×C₃×SD₁₆	—	3	12	no	—
114	C₂×C₃×D₈	—	2	12	no	—
115	C₂×C₃×D₈	—	3	12	no	—
116	C₂×C₃×D₈	C₂×D₃	1	12	yes	complemented
117	C₂×C₃×D₈	C₂²×C₃	1	12	yes	complemented
118	C₂×C₃×M₁₆	—	3	12	no	—
119	C₂²×C₃×C₈	—	2	1	no	—
120	C₂²×C₃×C₈	—	3	1	no	—
121	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic, complemented
122	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
123	C₂×#214	C₂²×C₃	1	12	yes	complemented
124	C₂×#213	C₂²×C₃	1	12	yes	complemented
125	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
126	#911	C₂²×C₃	1	64	yes	direct product factor
127	C₂×#204	C₂²×C₃	1	12	yes	complemented
128	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	12	yes	complemented
129	C₂³×C₃²	—	2	6	no	—
130	C₂³×C₃²	—	2	6	no	—
131	C₂³×C₃²	—	4	4	no	—
132	C₂³×C₃²	—	4	4	no	—
133	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₃×D₃	—	2	4	no	—
135	C₂²×C₃×D₃	—	2	6	no	—
136	C₂²×C₃×D₃	—	2	16	no	—
137	C₂²×C₃×D₃	—	4	48	no	—
138	C₂²×C₃×D₃	—	4	4	no	—
139	C₂²×C₃×D₃	C₂×D₄	1	6	yes	—
140	C₃²×D₄	—	2	6	no	—
141	C₃²×D₄	—	2	6	no	—
142	C₃²×D₄	C₂⁴	1	4	yes	—
143	C₃²×D₄	C₂⁴	1	4	yes	complemented
144	C₂×C₃²×C₄	C₂×D₄	1	3	yes	—
145	C₂×C₃²×C₄	C₂⁴	1	3	yes	—
146	C₃×#67	—	2	16	no	—
147	C₃×#67	—	2	16	no	—
148	C₂×C₃×Dic₃	—	2	6	no	—
149	C₂×C₃×Dic₃	—	2	16	no	—
150	C₂×C₃×Dic₃	C₂×D₄	1	6	yes	—
151	C₃×D₁₂	—	2	6	no	—
152	C₃×D₁₂	C₂⁴	1	4	yes	—
153	C₃×C₄×D₃	C₂×D₄	1	12	yes	—
154	C₃×C₄×D₃	C₂⁴	1	4	yes	—
155	C₃×Dic₆	—	2	6	no	—
156	C₃×Dic₆	C₂⁴	1	4	yes	complemented
157	C₃²×C₈	C₂⁴	1	4	yes	complemented
158	C₃×C₃⋊C₈	C₂⁴	1	4	yes	complemented
159	C₂²×#41	—	3	1	no	—
160	C₂³×D₄	—	3	1	no	—
161	C₂×AGL(1,ℤ/8)	—	3	24	no	—
162	C₂²×SD₁₆	—	3	1	no	—
163	C₂²×SD₁₆	—	3	1	no	—
164	C₂²×D₈	—	3	1	no	—
165	C₂²×D₈	C₃×D₃	1	1	yes	characteristic, complemented
166	C₂²×M₁₆	—	3	1	no	—
167	C₂⁴×C₃	—	2	1	no	—
168	C₂⁴×C₃	—	2	1	no	—
169	C₂⁴×C₃	—	2	1	no	—
170	C₂⁴×C₃	—	2	1	no	—
171	C₂⁴×C₃	—	3	1	no	—
172	C₂⁴×C₃	—	4	1	no	—
173	C₂⁴×C₃	—	4	1	no	—
174	C₂⁴×C₃	—	6	12	no	—
175	C₂⁴×C₃	—	6	1	no	—
176	C₂⁴×C₃	—	12	8	no	—
177	C₂³×D₃	—	2	1	no	—
178	C₂³×D₃	—	2	12	no	—
179	C₂³×D₃	—	4	8	no	—
180	C₂³×D₃	C₃×D₄	1	1	yes	characteristic
181	C₃×#41	—	3	16	no	—
182	C₃×#41	—	6	24	no	—
183	C₂×C₃×Q₈	—	3	6	no	—
184	C₂×C₃×Q₈	—	6	3	no	—
185	C₂×C₃×D₄	—	2	3	no	—
186	C₂×C₃×D₄	—	2	3	no	—
187	C₂×C₃×D₄	—	2	3	no	—
188	C₂×C₃×D₄	—	2	3	no	—
189	C₂×C₃×D₄	—	2	6	no	—
190	C₂×C₃×D₄	—	2	6	no	—
191	C₂×C₃×D₄	—	3	16	no	—
192	C₂×C₃×D₄	—	3	6	no	—
193	C₂×C₃×D₄	—	4	3	no	—
194	C₂×C₃×D₄	—	4	3	no	—
195	C₂×C₃×D₄	—	6	24	no	—
196	C₂×C₃×D₄	—	6	12	no	—
197	C₂×C₃×D₄	—	6	12	no	—
198	C₂×C₃×D₄	—	6	3	no	—
199	C₂×C₃×D₄	C₂²×D₃	1	6	yes	—
200	C₂×C₃×D₄	C₂²×D₃	1	6	yes	complemented
201	C₂×C₃×D₄	C₂³×C₃	1	6	yes	—
202	C₂×C₃×D₄	C₂³×C₃	1	6	yes	complemented
203	C₂²×C₃×C₄	—	2	1	no	—
204	C₂²×C₃×C₄	—	3	1	no	—
205	C₂²×C₃×C₄	—	3	6	no	—
206	C₂²×C₃×C₄	—	3	6	no	—
207	C₂²×C₃×C₄	—	6	12	no	—
208	C₂²×C₃×C₄	—	6	1	no	—
209	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
210	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
211	C₂×#67	—	2	12	no	—
212	C₂×#67	—	2	12	no	—
213	C₂²×Dic₃	—	2	1	no	—
214	C₂²×Dic₃	—	2	12	no	—
215	C₂²×Dic₃	C₃×D₄	1	1	yes	characteristic
216	#237	—	2	24	no	—
217	#237	C₂³×C₃	1	16	yes	complemented
218	D₃×D₄	—	2	24	no	—
219	D₃×D₄	C₂³×C₃	1	16	yes	complemented
220	C₂×D₁₂	—	2	3	no	—
221	C₂×D₁₂	C₂³×C₃	1	6	yes	—
222	C₂×C₄×D₃	C₃×D₄	1	6	yes	—
223	C₂×C₄×D₃	C₂³×C₃	1	6	yes	—
224	C₂×Dic₆	—	2	3	no	—
225	C₂×Dic₆	C₂³×C₃	1	6	yes	complemented
226	C₃×SD₁₆	—	3	16	no	—
227	C₃×SD₁₆	—	3	16	no	—
228	C₃×D₈	—	2	16	no	—
229	C₃×D₈	—	3	16	no	—
230	C₃×D₈	C₂²×D₃	1	16	yes	complemented
231	C₃×D₈	C₂³×C₃	1	16	yes	complemented
232	C₃×M₁₆	—	3	16	no	—
233	C₂×C₃×C₈	—	2	6	no	—
234	C₂×C₃×C₈	—	3	6	no	—
235	C₂×C₃×C₈	C₂²×D₃	1	6	yes	complemented
236	C₂×C₃×C₈	C₂³×C₃	1	6	yes	complemented
237	#214	C₂³×C₃	1	16	yes	complemented
238	#213	C₂³×C₃	1	16	yes	complemented
239	C₂×C₃⋊C₈	C₂³×C₃	1	6	yes	complemented
240	#204	C₂³×C₃	1	16	yes	complemented
241	ΓL(1,𝔽₂₅)	C₂³×C₃	1	16	yes	complemented
242	C₂²×C₃²	—	2	4	no	—
243	C₂²×C₃²	—	2	4	no	—
244	C₂²×C₃²	—	4	12	no	—
245	C₂²×C₃²	—	4	12	no	—
246	C₂²×C₃²	AGL(1,ℤ/8)	1	4	yes	complemented
247	C₂²×C₃²	C₂²×D₄	1	3	yes	—
248	C₂×C₃×D₃	—	2	12	no	—
249	C₂×C₃×D₃	—	2	4	no	—
250	C₂×C₃×D₃	—	4	32	no	—
251	C₂×C₃×D₃	—	4	12	no	—
252	C₂×C₃×D₃	C₂²×D₄	1	4	yes	—
253	C₃²×C₄	C₂²×D₄	1	3	yes	—
254	C₃²×C₄	C₂⁵	1	1	yes	characteristic
255	C₃×Dic₃	—	2	4	no	—
256	C₃×Dic₃	C₂²×D₄	1	4	yes	—
257	C₂⁵	—	6	1	no	—
258	C₂×#41	—	3	12	no	—
259	C₂×#41	—	6	6	no	—
260	C₂²×Q₈	—	3	1	no	—
261	C₂²×D₄	—	3	12	no	—
262	C₂²×D₄	—	3	1	no	—
263	C₂²×D₄	—	6	6	no	—
264	C₂²×D₄	—	6	1	no	—
265	C₂²×D₄	—	6	1	no	—
266	C₂²×D₄	C₂×C₃×D₃	1	1	yes	characteristic
267	C₂²×D₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
268	C₂³×C₄	—	3	1	no	—
269	C₂³×C₄	—	6	1	no	—
270	AGL(1,ℤ/8)	—	3	64	no	—
271	C₂×SD₁₆	—	3	12	no	—
272	C₂×SD₁₆	—	3	12	no	—
273	C₂×D₈	—	3	12	no	—
274	C₂×D₈	C₂×C₃×D₃	1	12	yes	complemented
275	C₂×M₁₆	—	3	12	no	—
276	C₂²×C₈	—	3	1	no	—
277	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
278	C₂³×C₃	—	2	6	no	—
279	C₂³×C₃	—	2	6	no	—
280	C₂³×C₃	—	2	6	no	—
281	C₂³×C₃	—	2	6	no	—
282	C₂³×C₃	—	2	1	no	—
283	C₂³×C₃	—	3	6	no	—
284	C₂³×C₃	—	4	6	no	—
285	C₂³×C₃	—	4	6	no	—
286	C₂³×C₃	—	4	4	no	—
287	C₂³×C₃	—	4	4	no	—
288	C₂³×C₃	—	4	4	no	—
289	C₂³×C₃	—	4	4	no	—
290	C₂³×C₃	—	6	16	no	—
291	C₂³×C₃	—	6	4	no	—
292	C₂³×C₃	—	6	6	no	—
293	C₂³×C₃	—	8	4	no	—
294	C₂³×C₃	—	8	4	no	—
295	C₂³×C₃	—	12	48	no	—
296	C₂³×C₃	—	12	4	no	—
297	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
298	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
299	C₂²×D₃	—	2	4	no	—
300	C₂²×D₃	—	2	6	no	—
301	C₂²×D₃	—	2	16	no	—
302	C₂²×D₃	—	4	48	no	—
303	C₂²×D₃	—	4	4	no	—
304	C₂²×D₃	C₂×C₃×D₄	1	6	yes	—
305	C₃×Q₈	—	3	4	no	—
306	C₃×Q₈	—	6	6	no	—
307	C₃×D₄	—	2	6	no	—
308	C₃×D₄	—	2	6	no	—
309	C₃×D₄	—	2	6	no	—
310	C₃×D₄	—	2	6	no	—
311	C₃×D₄	—	2	4	no	—
312	C₃×D₄	—	2	4	no	—
313	C₃×D₄	—	3	4	no	—
314	C₃×D₄	—	4	6	no	—
315	C₃×D₄	—	4	6	no	—
316	C₃×D₄	—	6	16	no	—
317	C₃×D₄	—	6	16	no	—
318	C₃×D₄	—	6	6	no	—
319	C₃×D₄	C₂³×D₃	1	4	yes	—
320	C₃×D₄	C₂³×D₃	1	4	yes	complemented
321	C₃×D₄	C₂⁴×C₃	1	4	yes	—
322	C₃×D₄	C₂⁴×C₃	1	4	yes	complemented
323	C₂×C₃×C₄	—	2	3	no	—
324	C₂×C₃×C₄	—	2	3	no	—
325	C₂×C₃×C₄	—	3	6	no	—
326	C₂×C₃×C₄	—	3	12	no	—
327	C₂×C₃×C₄	—	3	4	no	—
328	C₂×C₃×C₄	—	6	16	no	—
329	C₂×C₃×C₄	—	6	6	no	—
330	C₂×C₃×C₄	D₃×D₄	1	3	yes	—
331	C₂×C₃×C₄	C₂×C₃×D₄	1	3	yes	—
332	C₂×C₃×C₄	C₂³×D₃	1	3	yes	—
333	C₂×C₃×C₄	C₂⁴×C₃	1	3	yes	—
334	#67	—	2	16	no	—
335	#67	—	2	16	no	—
336	C₂×Dic₃	—	2	6	no	—
337	C₂×Dic₃	—	2	16	no	—
338	C₂×Dic₃	C₂×C₃×D₄	1	6	yes	—
339	D₁₂	—	2	6	no	—
340	D₁₂	C₂⁴×C₃	1	4	yes	—
341	C₄×D₃	C₂×C₃×D₄	1	12	yes	—
342	C₄×D₃	C₂⁴×C₃	1	4	yes	—
343	Dic₆	—	2	6	no	—
344	Dic₆	C₂⁴×C₃	1	4	yes	complemented
345	C₃×C₈	—	2	4	no	—
346	C₃×C₈	—	3	4	no	—
347	C₃×C₈	C₂³×D₃	1	4	yes	complemented
348	C₃×C₈	C₂⁴×C₃	1	4	yes	complemented
349	C₃⋊C₈	C₂⁴×C₃	1	4	yes	complemented
350	C₂×C₃²	—	4	4	no	—
351	C₂×C₃²	—	4	4	no	—
352	C₂×C₃²	C₂×AGL(1,ℤ/8)	1	6	yes	complemented
353	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
354	C₃×D₃	—	2	4	no	—
355	C₃×D₃	—	4	4	no	—
356	C₂⁴	—	2	1	no	—
357	C₂⁴	—	2	1	no	—
358	C₂⁴	—	3	1	no	—
359	C₂⁴	—	6	12	no	—
360	C₂⁴	—	6	1	no	—
361	C₂⁴	—	12	8	no	—
362	#41	—	3	16	no	—
363	#41	—	6	24	no	—
364	C₂×Q₈	—	3	6	no	—
365	C₂×Q₈	—	6	3	no	—
366	C₂×D₄	—	2	3	no	—
367	C₂×D₄	—	2	3	no	—
368	C₂×D₄	—	3	16	no	—
369	C₂×D₄	—	3	6	no	—
370	C₂×D₄	—	6	24	no	—
371	C₂×D₄	—	6	12	no	—
372	C₂×D₄	—	6	12	no	—
373	C₂×D₄	—	6	3	no	—
374	C₂×D₄	C₂²×C₃×D₃	1	6	yes	—
375	C₂×D₄	C₂²×C₃×D₃	1	6	yes	complemented
376	C₂²×C₄	—	3	1	no	—
377	C₂²×C₄	—	3	6	no	—
378	C₂²×C₄	—	3	6	no	—
379	C₂²×C₄	—	6	12	no	—
380	C₂²×C₄	—	6	1	no	—
381	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
382	SD₁₆	—	3	16	no	—
383	SD₁₆	—	3	16	no	—
384	D₈	—	3	16	no	—
385	D₈	C₂²×C₃×D₃	1	16	yes	complemented
386	M₁₆	—	3	16	no	—
387	C₂×C₈	—	3	6	no	—
388	C₂×C₈	C₂²×C₃×D₃	1	6	yes	complemented
389	C₂²×C₃	—	2	4	no	—
390	C₂²×C₃	—	2	4	no	—
391	C₂²×C₃	—	2	4	no	—
392	C₂²×C₃	—	2	4	no	—
393	C₂²×C₃	—	2	4	no	—
394	C₂²×C₃	—	2	3	no	—
395	C₂²×C₃	—	3	4	no	—
396	C₂²×C₃	—	4	4	no	—
397	C₂²×C₃	—	4	4	no	—
398	C₂²×C₃	—	4	12	no	—
399	C₂²×C₃	—	4	12	no	—
400	C₂²×C₃	—	4	12	no	—
401	C₂²×C₃	—	4	12	no	—
402	C₂²×C₃	—	6	12	no	—
403	C₂²×C₃	—	6	4	no	—
404	C₂²×C₃	—	8	12	no	—
405	C₂²×C₃	—	8	12	no	—
406	C₂²×C₃	—	12	32	no	—
407	C₂²×C₃	—	12	12	no	—
408	C₂²×C₃	#911	1	4	yes	direct product factor
409	C₂²×C₃	C₃×AGL(1,ℤ/8)	1	4	yes	complemented
410	C₂²×C₃	C₂×D₃×D₄	1	3	yes	—
411	C₂²×C₃	C₂²×C₃×D₄	1	3	yes	—
412	C₂×D₃	—	2	12	no	—
413	C₂×D₃	—	2	4	no	—
414	C₂×D₃	—	4	32	no	—
415	C₂×D₃	—	4	12	no	—
416	C₂×D₃	C₂²×C₃×D₄	1	4	yes	—
417	C₃×C₄	—	2	3	no	—
418	C₃×C₄	—	2	1	no	—
419	C₃×C₄	—	3	4	no	—
420	C₃×C₄	—	6	4	no	—
421	C₃×C₄	C₂×D₃×D₄	1	3	yes	—
422	C₃×C₄	C₂²×C₃×D₄	1	3	yes	—
423	C₃×C₄	C₂⁴×D₃	1	1	yes	characteristic
424	C₃×C₄	C₂⁵×C₃	1	1	yes	characteristic
425	Dic₃	—	2	4	no	—
426	Dic₃	C₂²×C₃×D₄	1	4	yes	—
427	C₃²	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
428	C₂³	—	2	6	no	—
429	C₂³	—	2	6	no	—
430	C₂³	—	3	6	no	—
431	C₂³	—	4	4	no	—
432	C₂³	—	4	4	no	—
433	C₂³	—	6	16	no	—
434	C₂³	—	6	4	no	—
435	C₂³	—	6	6	no	—
436	C₂³	—	12	48	no	—
437	C₂³	—	12	4	no	—
438	C₂³	C₃×D₃×D₄	1	1	yes	characteristic
439	Q₈	—	3	4	no	—
440	Q₈	—	6	6	no	—
441	D₄	—	2	6	no	—
442	D₄	—	2	6	no	—
443	D₄	—	3	4	no	—
444	D₄	—	6	16	no	—
445	D₄	—	6	16	no	—
446	D₄	—	6	6	no	—
447	D₄	C₂³×C₃×D₃	1	4	yes	—
448	D₄	C₂³×C₃×D₃	1	4	yes	complemented
449	C₂×C₄	—	3	6	no	—
450	C₂×C₄	—	3	12	no	—
451	C₂×C₄	—	3	4	no	—
452	C₂×C₄	—	6	16	no	—
453	C₂×C₄	—	6	6	no	—
454	C₂×C₄	C₃×D₃×D₄	1	3	yes	—
455	C₂×C₄	C₂³×C₃×D₃	1	3	yes	—
456	C₈	—	3	4	no	—
457	C₈	C₂³×C₃×D₃	1	4	yes	complemented
458	C₂×C₃	—	2	6	no	—
459	C₂×C₃	—	2	1	no	—
460	C₂×C₃	—	4	4	no	—
461	C₂×C₃	—	4	4	no	—
462	C₂×C₃	—	4	4	no	—
463	C₂×C₃	—	4	4	no	—
464	C₂×C₃	—	6	4	no	—
465	C₂×C₃	—	8	4	no	—
466	C₂×C₃	—	8	4	no	—
467	C₂×C₃	—	12	4	no	—
468	C₂×C₃	C₂×#911	1	6	yes	direct product factor
469	C₂×C₃	C₂×C₃×AGL(1,ℤ/8)	1	6	yes	complemented
470	C₂×C₃	C₂²×D₃×D₄	1	1	yes	characteristic
471	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
472	D₃	—	2	4	no	—
473	D₃	—	4	4	no	—
474	C₂²	—	2	4	no	—
475	C₂²	—	2	4	no	—
476	C₂²	—	3	4	no	—
477	C₂²	—	4	12	no	—
478	C₂²	—	4	12	no	—
479	C₂²	—	6	12	no	—
480	C₂²	—	6	4	no	—
481	C₂²	—	12	32	no	—
482	C₂²	—	12	12	no	—
483	C₂²	C₃×#911	1	4	yes	direct product factor
484	C₂²	C₂×C₃×D₃×D₄	1	3	yes	—
485	C₄	—	3	4	no	—
486	C₄	—	6	4	no	—
487	C₄	C₂×C₃×D₃×D₄	1	3	yes	—
488	C₄	C₂⁴×C₃×D₃	1	1	yes	characteristic
489	C₃	—	2	1	no	—
490	C₃	C₂²×#911	1	1	yes	characteristic, direct product factor
491	C₃	C₂²×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented
492	C₂	—	4	4	no	—
493	C₂	—	4	4	no	—
494	C₂	—	6	4	no	—
495	C₂	—	12	4	no	—
496	C₂	C₂×C₃×#911	1	6	yes	direct product factor
497	C₂	C₂²×C₃×D₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	D₃×D₄
commutator, cosocle	C₃×C₄	C₂⁵×C₃
Frattini	C₄	C₂⁴×C₃×D₃
Fitting	C₂²×C₃²×D₈	C₂
socle	C₂³×C₃²	C₂×D₄
hypercenter	C₂²×C₃×D₈	D₃
hypocenter	C₃	C₂²×C₃×AGL(1,ℤ/8)
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×D₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×#237	C₂	semidirect
2. C₂²×C₃×D₃×D₄	C₂	semidirect
3. C₂²×C₃²×D₈	C₂	semidirect
4. C₂²×C₃×#214	C₂	semidirect
5. C₂²×C₃×#213	C₂	semidirect
6. C₂×C₃×#911	C₂	direct (N × H)
7. C₂²×C₃×#204	C₂	semidirect
8. C₂²×C₃×ΓL(1,𝔽₂₅)	C₂	semidirect
10. C₂²×#911	C₃	direct (N × H)
13. C₂²×C₃²×D₄	C₂²	semidirect
18. C₂×C₃×#237	C₂²	semidirect
20. C₂×C₃×D₃×D₄	C₂²	semidirect
23. C₂²×C₃×Dic₆	C₂²	semidirect
24. C₂×C₃²×D₈	C₂²	semidirect
25. C₂²×C₃²×C₈	C₂²	semidirect
26. C₂×C₃×#214	C₂²	semidirect
27. C₂×C₃×#213	C₂²	semidirect
28. C₂²×C₃×C₃⋊C₈	C₂²	semidirect
29. C₃×#911	C₂²	direct (N × H)
30. C₂×C₃×#204	C₂²	semidirect
31. C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	semidirect
34. C₂²×#237	C₂×C₃	semidirect
35. C₂²×D₃×D₄	C₂×C₃	semidirect
41. C₂²×C₃×D₈	D₃	semidirect
42. C₂²×C₃×D₈	C₂×C₃	semidirect
44. C₂²×#214	C₂×C₃	semidirect
45. C₂²×#213	C₂×C₃	semidirect
46. C₂×#911	C₂×C₃	direct (N × H)
47. C₂²×#204	C₂×C₃	semidirect
48. C₂²×ΓL(1,𝔽₂₅)	C₂×C₃	semidirect
58. C₂×C₃²×D₄	C₂³	semidirect
66. C₃×#237	C₂³	semidirect
68. C₃×D₃×D₄	C₂³	semidirect
74. C₂×C₃×Dic₆	C₂³	semidirect
75. C₃²×D₈	C₂³	semidirect
76. C₂×C₃²×C₈	C₂³	semidirect
77. C₃×#214	C₂³	semidirect
78. C₃×#213	C₂³	semidirect
79. C₂×C₃×C₃⋊C₈	C₂³	semidirect
80. C₃×#204	C₂³	semidirect
81. C₃×ΓL(1,𝔽₂₅)	C₂³	semidirect
96. C₂²×C₃×D₄	C₂×D₃	semidirect
98. C₂²×C₃×D₄	C₂²×C₃	semidirect
105. C₂×#237	C₂²×C₃	semidirect
107. C₂×D₃×D₄	C₂²×C₃	semidirect
110. C₂²×Dic₆	C₂²×C₃	semidirect
116. C₂×C₃×D₈	C₂×D₃	semidirect
117. C₂×C₃×D₈	C₂²×C₃	semidirect
121. C₂²×C₃×C₈	C₂×D₃	semidirect
122. C₂²×C₃×C₈	C₂²×C₃	semidirect
123. C₂×#214	C₂²×C₃	semidirect
124. C₂×#213	C₂²×C₃	semidirect
125. C₂²×C₃⋊C₈	C₂²×C₃	semidirect
126. #911	C₂²×C₃	direct (N × H)
127. C₂×#204	C₂²×C₃	semidirect
128. C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	semidirect
143. C₃²×D₄	C₂⁴	semidirect
156. C₃×Dic₆	C₂⁴	semidirect
157. C₃²×C₈	C₂⁴	semidirect
158. C₃×C₃⋊C₈	C₂⁴	semidirect
165. C₂²×D₈	C₃×D₃	semidirect
200. C₂×C₃×D₄	C₂²×D₃	semidirect
202. C₂×C₃×D₄	C₂³×C₃	semidirect
217. #237	C₂³×C₃	semidirect
219. D₃×D₄	C₂³×C₃	semidirect
225. C₂×Dic₆	C₂³×C₃	semidirect
230. C₃×D₈	C₂²×D₃	semidirect
231. C₃×D₈	C₂³×C₃	semidirect
235. C₂×C₃×C₈	C₂²×D₃	semidirect
236. C₂×C₃×C₈	C₂³×C₃	semidirect
237. #214	C₂³×C₃	semidirect
238. #213	C₂³×C₃	semidirect
239. C₂×C₃⋊C₈	C₂³×C₃	semidirect
240. #204	C₂³×C₃	semidirect
241. ΓL(1,𝔽₂₅)	C₂³×C₃	semidirect
246. C₂²×C₃²	AGL(1,ℤ/8)	semidirect
267. C₂²×D₄	C₂×C₃×D₃	semidirect
274. C₂×D₈	C₂×C₃×D₃	semidirect
277. C₂²×C₈	C₂×C₃×D₃	semidirect
320. C₃×D₄	C₂³×D₃	semidirect
322. C₃×D₄	C₂⁴×C₃	semidirect
344. Dic₆	C₂⁴×C₃	semidirect
347. C₃×C₈	C₂³×D₃	semidirect
348. C₃×C₈	C₂⁴×C₃	semidirect
349. C₃⋊C₈	C₂⁴×C₃	semidirect
352. C₂×C₃²	C₂×AGL(1,ℤ/8)	semidirect
375. C₂×D₄	C₂²×C₃×D₃	semidirect
385. D₈	C₂²×C₃×D₃	semidirect
388. C₂×C₈	C₂²×C₃×D₃	semidirect
408. C₂²×C₃	#911	direct (N × H)
409. C₂²×C₃	C₃×AGL(1,ℤ/8)	semidirect
427. C₃²	C₂²×AGL(1,ℤ/8)	semidirect
448. D₄	C₂³×C₃×D₃	semidirect
457. C₈	C₂³×C₃×D₃	semidirect
468. C₂×C₃	C₂×#911	direct (N × H)
469. C₂×C₃	C₂×C₃×AGL(1,ℤ/8)	semidirect
483. C₂²	C₃×#911	direct (N × H)
490. C₃	C₂²×#911	direct (N × H)
491. C₃	C₂²×C₃×AGL(1,ℤ/8)	semidirect
496. C₂	C₂×C₃×#911	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×C₃×#237	2
C₂²×C₃×D₃×D₄	2
C₂²×C₃²×D₈	2
C₂²×C₃×#214	2
C₂²×C₃×#213	2
C₂×C₃×#911	2
C₂²×C₃×#204	2
C₂²×C₃×ΓL(1,𝔽₂₅)	2
C₂²×C₃×AGL(1,ℤ/8)	3
C₂²×#911	3

Subgroups — C22×C3×#911 #11918639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#911 #11918639