Subgroups — C₂²×C₃×#918 #11918693

Order 1152.

3057 conjugacy classes of subgroups.

The subgroup lattice has 457 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#239	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃²×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₃×#216	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₃×#215	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#918	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×#137	—	3	1	no	maximal
10	C₂²×#918	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂²×C₃²×Q₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃²×Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₃×#239	—	2	6	no	—
14	C₂×C₃×#239	C₂²	1	12	yes	—
15	C₂×C₃×D₃×Q₈	—	2	6	no	—
16	C₂×C₃×D₃×Q₈	C₂²	1	12	yes	complemented
17	C₂²×C₃×D₁₂	—	2	1	no	—
18	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₄×D₃	—	2	1	no	—
20	C₂²×C₃×C₄×D₃	—	2	1	no	—
21	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
22	C₂²×C₃×Dic₆	—	2	1	no	—
23	C₂²×C₃×Dic₆	C₂²	1	1	yes	characteristic
24	C₂×C₃²×Q₁₆	C₂²	1	12	yes	complemented
25	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
26	C₂×C₃×#216	C₂²	1	12	yes	complemented
27	C₂×C₃×#215	C₂²	1	12	yes	complemented
28	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
29	C₃×#918	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×Q₈	—	3	1	no	—
34	C₂²×#239	C₂×C₃	1	1	yes	characteristic
35	C₂²×D₃×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂×C₃×#137	—	3	24	no	—
37	C₂²×C₃×Q₁₆	—	2	1	no	—
38	C₂²×C₃×Q₁₆	—	3	1	no	—
39	C₂²×C₃×Q₁₆	D₃	1	1	yes	characteristic, complemented
40	C₂²×C₃×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂²×C₃×SD₁₆	—	3	1	no	—
42	C₂²×C₃×SD₁₆	—	3	1	no	—
43	C₂²×C₃×M₁₆	—	3	1	no	—
44	C₂²×#216	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂²×#215	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×#918	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	C₂³×C₃×D₃	—	2	1	no	—
50	C₂³×C₃×D₃	D₄	1	1	yes	characteristic
51	C₂×C₃²×Q₈	—	2	3	no	—
52	C₂×C₃²×Q₈	—	2	3	no	—
53	C₂×C₃²×Q₈	C₂³	1	6	yes	—
54	C₂×C₃²×Q₈	C₂³	1	6	yes	—
55	C₂²×C₃²×C₄	—	2	1	no	—
56	C₂²×C₃²×C₄	—	2	1	no	—
57	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
58	C₂²×C₃×Dic₃	—	2	1	no	—
59	C₂²×C₃×Dic₃	D₄	1	1	yes	characteristic
60	C₃×#239	—	2	24	no	—
61	C₃×#239	C₂³	1	16	yes	—
62	C₃×D₃×Q₈	—	2	24	no	—
63	C₃×D₃×Q₈	C₂³	1	16	yes	complemented
64	C₂×C₃×D₁₂	—	2	12	no	—
65	C₂×C₃×D₁₂	—	2	3	no	—
66	C₂×C₃×D₁₂	C₂³	1	6	yes	—
67	C₂×C₃×C₄×D₃	—	2	12	no	—
68	C₂×C₃×C₄×D₃	—	2	12	no	—
69	C₂×C₃×C₄×D₃	D₄	1	6	yes	—
70	C₂×C₃×C₄×D₃	C₂³	1	6	yes	—
71	C₂×C₃×Dic₆	—	2	3	no	—
72	C₂×C₃×Dic₆	—	2	12	no	—
73	C₂×C₃×Dic₆	C₂³	1	6	yes	—
74	C₃²×Q₁₆	C₂³	1	16	yes	complemented
75	C₂×C₃²×C₈	C₂³	1	6	yes	—
76	C₃×#216	C₂³	1	16	yes	complemented
77	C₃×#215	C₂³	1	16	yes	complemented
78	C₂×C₃×C₃⋊C₈	C₂³	1	6	yes	—
79	C₃×#204	C₂³	1	16	yes	complemented
80	C₃×ΓL(1,𝔽₂₅)	C₂³	1	16	yes	complemented
81	C₂²×#137	—	3	1	no	Sylow
82	C₂×C₃×#41	—	3	12	no	—
83	C₂×C₃×#41	—	6	6	no	—
84	C₂²×C₃×Q₈	—	2	1	no	—
85	C₂²×C₃×Q₈	—	2	1	no	—
86	C₂²×C₃×Q₈	—	3	12	no	—
87	C₂²×C₃×Q₈	—	3	1	no	—
88	C₂²×C₃×Q₈	—	6	1	no	—
89	C₂²×C₃×Q₈	—	6	6	no	—
90	C₂²×C₃×Q₈	C₂×D₃	1	1	yes	characteristic
91	C₂²×C₃×Q₈	C₂×D₃	1	1	yes	characteristic
92	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
93	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
94	C₂²×C₃×D₄	—	3	1	no	—
95	C₂²×C₃×D₄	—	6	1	no	—
96	C₂³×C₃×C₄	—	3	1	no	—
97	C₂³×C₃×C₄	—	6	1	no	—
98	C₂³×C₃×C₄	—	6	1	no	—
99	C₂×#239	—	2	6	no	—
100	C₂×#239	C₂²×C₃	1	12	yes	—
101	C₂×D₃×Q₈	—	2	6	no	—
102	C₂×D₃×Q₈	C₂²×C₃	1	12	yes	complemented
103	C₂²×D₁₂	—	2	1	no	—
104	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic
105	C₂²×C₄×D₃	—	2	1	no	—
106	C₂²×C₄×D₃	—	2	1	no	—
107	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
108	C₂²×Dic₆	—	2	1	no	—
109	C₂²×Dic₆	C₂²×C₃	1	1	yes	characteristic
110	C₃×#137	—	3	64	no	—
111	C₂×C₃×Q₁₆	—	2	12	no	—
112	C₂×C₃×Q₁₆	—	3	12	no	—
113	C₂×C₃×Q₁₆	C₂×D₃	1	12	yes	complemented
114	C₂×C₃×Q₁₆	C₂²×C₃	1	12	yes	complemented
115	C₂×C₃×SD₁₆	—	3	12	no	—
116	C₂×C₃×SD₁₆	—	3	12	no	—
117	C₂×C₃×M₁₆	—	3	12	no	—
118	C₂²×C₃×C₈	—	2	1	no	—
119	C₂²×C₃×C₈	—	3	1	no	—
120	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
121	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
122	C₂×#216	C₂²×C₃	1	12	yes	complemented
123	C₂×#215	C₂²×C₃	1	12	yes	complemented
124	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
125	#918	C₂²×C₃	1	64	yes	direct product factor
126	C₂×#204	C₂²×C₃	1	12	yes	complemented
127	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	12	yes	complemented
128	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₃×D₃	—	2	4	no	—
130	C₂²×C₃×D₃	—	2	6	no	—
131	C₂²×C₃×D₃	—	4	4	no	—
132	C₂²×C₃×D₃	C₂×D₄	1	6	yes	—
133	C₃²×Q₈	—	2	6	no	—
134	C₃²×Q₈	—	2	6	no	—
135	C₃²×Q₈	C₂⁴	1	4	yes	—
136	C₃²×Q₈	C₂⁴	1	4	yes	—
137	C₂×C₃²×C₄	—	2	6	no	—
138	C₂×C₃²×C₄	—	2	6	no	—
139	C₂×C₃²×C₄	C₂×D₄	1	3	yes	—
140	C₂×C₃²×C₄	C₂⁴	1	3	yes	—
141	C₂×C₃×Dic₃	—	2	6	no	—
142	C₂×C₃×Dic₃	C₂×D₄	1	6	yes	—
143	C₃×D₁₂	—	2	16	no	—
144	C₃×D₁₂	—	2	6	no	—
145	C₃×D₁₂	C₂⁴	1	4	yes	—
146	C₃×C₄×D₃	—	2	16	no	—
147	C₃×C₄×D₃	—	2	16	no	—
148	C₃×C₄×D₃	C₂×D₄	1	12	yes	—
149	C₃×C₄×D₃	C₂⁴	1	4	yes	—
150	C₃×Dic₆	—	2	6	no	—
151	C₃×Dic₆	—	2	16	no	—
152	C₃×Dic₆	C₂⁴	1	4	yes	—
153	C₃²×C₈	C₂⁴	1	4	yes	—
154	C₃×C₃⋊C₈	C₂⁴	1	4	yes	—
155	C₂²×#41	—	3	1	no	—
156	C₂³×Q₈	—	3	1	no	—
157	C₂×#137	—	3	24	no	—
158	C₂²×Q₁₆	—	3	1	no	—
159	C₂²×Q₁₆	C₃×D₃	1	1	yes	characteristic, complemented
160	C₂²×SD₁₆	—	3	1	no	—
161	C₂²×SD₁₆	—	3	1	no	—
162	C₂²×M₁₆	—	3	1	no	—
163	C₂⁴×C₃	—	3	1	no	—
164	C₂⁴×C₃	—	6	1	no	—
165	C₂³×D₃	—	2	1	no	—
166	C₂³×D₃	C₃×D₄	1	1	yes	characteristic
167	C₃×#41	—	3	16	no	—
168	C₃×#41	—	6	24	no	—
169	C₂×C₃×Q₈	—	2	3	no	—
170	C₂×C₃×Q₈	—	2	3	no	—
171	C₂×C₃×Q₈	—	2	3	no	—
172	C₂×C₃×Q₈	—	2	3	no	—
173	C₂×C₃×Q₈	—	2	6	no	—
174	C₂×C₃×Q₈	—	2	6	no	—
175	C₂×C₃×Q₈	—	3	16	no	—
176	C₂×C₃×Q₈	—	3	6	no	—
177	C₂×C₃×Q₈	—	4	3	no	—
178	C₂×C₃×Q₈	—	4	3	no	—
179	C₂×C₃×Q₈	—	6	12	no	—
180	C₂×C₃×Q₈	—	6	24	no	—
181	C₂×C₃×Q₈	—	6	3	no	—
182	C₂×C₃×Q₈	C₂²×D₃	1	6	yes	—
183	C₂×C₃×Q₈	C₂²×D₃	1	6	yes	—
184	C₂×C₃×Q₈	C₂³×C₃	1	6	yes	—
185	C₂×C₃×Q₈	C₂³×C₃	1	6	yes	—
186	C₂×C₃×D₄	—	3	6	no	—
187	C₂×C₃×D₄	—	6	12	no	—
188	C₂×C₃×D₄	—	6	3	no	—
189	C₂²×C₃×C₄	—	2	1	no	—
190	C₂²×C₃×C₄	—	2	1	no	—
191	C₂²×C₃×C₄	—	2	1	no	—
192	C₂²×C₃×C₄	—	2	1	no	—
193	C₂²×C₃×C₄	—	2	1	no	—
194	C₂²×C₃×C₄	—	3	1	no	—
195	C₂²×C₃×C₄	—	3	6	no	—
196	C₂²×C₃×C₄	—	3	6	no	—
197	C₂²×C₃×C₄	—	4	1	no	—
198	C₂²×C₃×C₄	—	4	1	no	—
199	C₂²×C₃×C₄	—	6	12	no	—
200	C₂²×C₃×C₄	—	6	12	no	—
201	C₂²×C₃×C₄	—	6	1	no	—
202	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
203	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
204	C₂²×Dic₃	—	2	1	no	—
205	C₂²×Dic₃	C₃×D₄	1	1	yes	characteristic
206	#239	—	2	24	no	—
207	#239	C₂³×C₃	1	16	yes	—
208	D₃×Q₈	—	2	24	no	—
209	D₃×Q₈	C₂³×C₃	1	16	yes	complemented
210	C₂×D₁₂	—	2	12	no	—
211	C₂×D₁₂	—	2	3	no	—
212	C₂×D₁₂	C₂³×C₃	1	6	yes	—
213	C₂×C₄×D₃	—	2	12	no	—
214	C₂×C₄×D₃	—	2	12	no	—
215	C₂×C₄×D₃	C₃×D₄	1	6	yes	—
216	C₂×C₄×D₃	C₂³×C₃	1	6	yes	—
217	C₂×Dic₆	—	2	3	no	—
218	C₂×Dic₆	—	2	12	no	—
219	C₂×Dic₆	C₂³×C₃	1	6	yes	—
220	C₃×Q₁₆	—	2	16	no	—
221	C₃×Q₁₆	—	3	16	no	—
222	C₃×Q₁₆	C₂²×D₃	1	16	yes	complemented
223	C₃×Q₁₆	C₂³×C₃	1	16	yes	complemented
224	C₃×SD₁₆	—	3	16	no	—
225	C₃×SD₁₆	—	3	16	no	—
226	C₃×M₁₆	—	3	16	no	—
227	C₂×C₃×C₈	—	2	6	no	—
228	C₂×C₃×C₈	—	3	6	no	—
229	C₂×C₃×C₈	C₂²×D₃	1	6	yes	—
230	C₂×C₃×C₈	C₂³×C₃	1	6	yes	—
231	#216	C₂³×C₃	1	16	yes	complemented
232	#215	C₂³×C₃	1	16	yes	complemented
233	C₂×C₃⋊C₈	C₂³×C₃	1	6	yes	—
234	#204	C₂³×C₃	1	16	yes	complemented
235	ΓL(1,𝔽₂₅)	C₂³×C₃	1	16	yes	complemented
236	C₂²×C₃²	#137	1	4	yes	complemented
237	C₂²×C₃²	C₂²×D₄	1	3	yes	—
238	C₂×C₃×D₃	—	2	12	no	—
239	C₂×C₃×D₃	—	2	4	no	—
240	C₂×C₃×D₃	—	4	12	no	—
241	C₂×C₃×D₃	C₂²×D₄	1	4	yes	—
242	C₃²×C₄	—	2	4	no	—
243	C₃²×C₄	—	2	4	no	—
244	C₃²×C₄	C₂²×D₄	1	3	yes	—
245	C₃²×C₄	C₂⁵	1	1	yes	characteristic
246	C₃×Dic₃	—	2	4	no	—
247	C₃×Dic₃	C₂²×D₄	1	4	yes	—
248	C₂×#41	—	3	12	no	—
249	C₂×#41	—	6	6	no	—
250	C₂²×Q₈	—	3	12	no	—
251	C₂²×Q₈	—	3	1	no	—
252	C₂²×Q₈	—	6	1	no	—
253	C₂²×Q₈	—	6	6	no	—
254	C₂²×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
255	C₂²×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
256	C₂²×D₄	—	3	1	no	—
257	C₂²×D₄	—	6	1	no	—
258	C₂³×C₄	—	3	1	no	—
259	C₂³×C₄	—	6	1	no	—
260	C₂³×C₄	—	6	1	no	—
261	#137	—	3	64	no	—
262	C₂×Q₁₆	—	3	12	no	—
263	C₂×Q₁₆	C₂×C₃×D₃	1	12	yes	complemented
264	C₂×SD₁₆	—	3	12	no	—
265	C₂×SD₁₆	—	3	12	no	—
266	C₂×M₁₆	—	3	12	no	—
267	C₂²×C₈	—	3	1	no	—
268	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
269	C₂³×C₃	—	2	1	no	—
270	C₂³×C₃	—	3	6	no	—
271	C₂³×C₃	—	6	4	no	—
272	C₂³×C₃	—	6	6	no	—
273	C₂³×C₃	—	12	4	no	—
274	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
275	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
276	C₂²×D₃	—	2	4	no	—
277	C₂²×D₃	—	2	6	no	—
278	C₂²×D₃	—	4	4	no	—
279	C₂²×D₃	C₂×C₃×D₄	1	6	yes	—
280	C₃×Q₈	—	2	6	no	—
281	C₃×Q₈	—	2	6	no	—
282	C₃×Q₈	—	2	6	no	—
283	C₃×Q₈	—	2	6	no	—
284	C₃×Q₈	—	2	4	no	—
285	C₃×Q₈	—	2	4	no	—
286	C₃×Q₈	—	3	4	no	—
287	C₃×Q₈	—	4	6	no	—
288	C₃×Q₈	—	4	6	no	—
289	C₃×Q₈	—	6	16	no	—
290	C₃×Q₈	—	6	6	no	—
291	C₃×Q₈	C₂³×D₃	1	4	yes	—
292	C₃×Q₈	C₂³×D₃	1	4	yes	—
293	C₃×Q₈	C₂⁴×C₃	1	4	yes	—
294	C₃×Q₈	C₂⁴×C₃	1	4	yes	—
295	C₃×D₄	—	3	4	no	—
296	C₃×D₄	—	6	16	no	—
297	C₃×D₄	—	6	6	no	—
298	C₂×C₃×C₄	—	2	6	no	—
299	C₂×C₃×C₄	—	2	6	no	—
300	C₂×C₃×C₄	—	2	6	no	—
301	C₂×C₃×C₄	—	2	6	no	—
302	C₂×C₃×C₄	—	2	3	no	—
303	C₂×C₃×C₄	—	2	3	no	—
304	C₂×C₃×C₄	—	3	6	no	—
305	C₂×C₃×C₄	—	3	12	no	—
306	C₂×C₃×C₄	—	3	4	no	—
307	C₂×C₃×C₄	—	4	6	no	—
308	C₂×C₃×C₄	—	4	6	no	—
309	C₂×C₃×C₄	—	6	16	no	—
310	C₂×C₃×C₄	—	6	16	no	—
311	C₂×C₃×C₄	—	6	6	no	—
312	C₂×C₃×C₄	D₃×D₄	1	3	yes	—
313	C₂×C₃×C₄	C₂×C₃×D₄	1	3	yes	—
314	C₂×C₃×C₄	C₂³×D₃	1	3	yes	—
315	C₂×C₃×C₄	C₂⁴×C₃	1	3	yes	—
316	C₂×Dic₃	—	2	6	no	—
317	C₂×Dic₃	C₂×C₃×D₄	1	6	yes	—
318	D₁₂	—	2	16	no	—
319	D₁₂	—	2	6	no	—
320	D₁₂	C₂⁴×C₃	1	4	yes	—
321	C₄×D₃	—	2	16	no	—
322	C₄×D₃	—	2	16	no	—
323	C₄×D₃	C₂×C₃×D₄	1	12	yes	—
324	C₄×D₃	C₂⁴×C₃	1	4	yes	—
325	Dic₆	—	2	6	no	—
326	Dic₆	—	2	16	no	—
327	Dic₆	C₂⁴×C₃	1	4	yes	—
328	C₃×C₈	—	2	4	no	—
329	C₃×C₈	—	3	4	no	—
330	C₃×C₈	C₂³×D₃	1	4	yes	—
331	C₃×C₈	C₂⁴×C₃	1	4	yes	—
332	C₃⋊C₈	C₂⁴×C₃	1	4	yes	—
333	C₂×C₃²	C₂×#137	1	6	yes	complemented
334	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
335	C₃×D₃	—	2	4	no	—
336	C₃×D₃	—	4	4	no	—
337	C₂⁴	—	3	1	no	—
338	C₂⁴	—	6	1	no	—
339	#41	—	3	16	no	—
340	#41	—	6	24	no	—
341	C₂×Q₈	—	2	3	no	—
342	C₂×Q₈	—	2	3	no	—
343	C₂×Q₈	—	3	16	no	—
344	C₂×Q₈	—	3	6	no	—
345	C₂×Q₈	—	6	12	no	—
346	C₂×Q₈	—	6	24	no	—
347	C₂×Q₈	—	6	3	no	—
348	C₂×Q₈	C₂²×C₃×D₃	1	6	yes	—
349	C₂×Q₈	C₂²×C₃×D₃	1	6	yes	—
350	C₂×D₄	—	3	6	no	—
351	C₂×D₄	—	6	12	no	—
352	C₂×D₄	—	6	3	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	3	1	no	—
356	C₂²×C₄	—	3	6	no	—
357	C₂²×C₄	—	3	6	no	—
358	C₂²×C₄	—	6	12	no	—
359	C₂²×C₄	—	6	12	no	—
360	C₂²×C₄	—	6	1	no	—
361	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
362	Q₁₆	—	3	16	no	—
363	Q₁₆	C₂²×C₃×D₃	1	16	yes	complemented
364	SD₁₆	—	3	16	no	—
365	SD₁₆	—	3	16	no	—
366	M₁₆	—	3	16	no	—
367	C₂×C₈	—	3	6	no	—
368	C₂×C₈	C₂²×C₃×D₃	1	6	yes	—
369	C₂²×C₃	—	2	4	no	—
370	C₂²×C₃	—	2	3	no	—
371	C₂²×C₃	—	3	4	no	—
372	C₂²×C₃	—	6	12	no	—
373	C₂²×C₃	—	6	4	no	—
374	C₂²×C₃	—	12	12	no	—
375	C₂²×C₃	#918	1	4	yes	direct product factor
376	C₂²×C₃	C₃×#137	1	4	yes	complemented
377	C₂²×C₃	C₂×D₃×D₄	1	3	yes	—
378	C₂²×C₃	C₂²×C₃×D₄	1	3	yes	—
379	C₂×D₃	—	2	12	no	—
380	C₂×D₃	—	2	4	no	—
381	C₂×D₃	—	4	12	no	—
382	C₂×D₃	C₂²×C₃×D₄	1	4	yes	—
383	C₃×C₄	—	2	4	no	—
384	C₃×C₄	—	2	4	no	—
385	C₃×C₄	—	2	4	no	—
386	C₃×C₄	—	2	4	no	—
387	C₃×C₄	—	2	3	no	—
388	C₃×C₄	—	2	1	no	—
389	C₃×C₄	—	3	4	no	—
390	C₃×C₄	—	4	4	no	—
391	C₃×C₄	—	4	4	no	—
392	C₃×C₄	—	6	4	no	—
393	C₃×C₄	C₂×D₃×D₄	1	3	yes	—
394	C₃×C₄	C₂²×C₃×D₄	1	3	yes	—
395	C₃×C₄	C₂⁴×D₃	1	1	yes	characteristic
396	C₃×C₄	C₂⁵×C₃	1	1	yes	characteristic
397	Dic₃	—	2	4	no	—
398	Dic₃	C₂²×C₃×D₄	1	4	yes	—
399	C₃²	C₂²×#137	1	1	yes	characteristic, complemented, Sylow
400	C₂³	—	3	6	no	—
401	C₂³	—	6	4	no	—
402	C₂³	—	6	6	no	—
403	C₂³	—	12	4	no	—
404	C₂³	C₃×D₃×D₄	1	1	yes	characteristic
405	Q₈	—	2	6	no	—
406	Q₈	—	2	6	no	—
407	Q₈	—	3	4	no	—
408	Q₈	—	6	16	no	—
409	Q₈	—	6	6	no	—
410	Q₈	C₂³×C₃×D₃	1	4	yes	—
411	Q₈	C₂³×C₃×D₃	1	4	yes	—
412	D₄	—	3	4	no	—
413	D₄	—	6	16	no	—
414	D₄	—	6	6	no	—
415	C₂×C₄	—	2	6	no	—
416	C₂×C₄	—	2	6	no	—
417	C₂×C₄	—	3	6	no	—
418	C₂×C₄	—	3	12	no	—
419	C₂×C₄	—	3	4	no	—
420	C₂×C₄	—	6	16	no	—
421	C₂×C₄	—	6	16	no	—
422	C₂×C₄	—	6	6	no	—
423	C₂×C₄	C₃×D₃×D₄	1	3	yes	—
424	C₂×C₄	C₂³×C₃×D₃	1	3	yes	—
425	C₈	—	3	4	no	—
426	C₈	C₂³×C₃×D₃	1	4	yes	—
427	C₂×C₃	—	2	6	no	—
428	C₂×C₃	—	2	1	no	—
429	C₂×C₃	—	6	4	no	—
430	C₂×C₃	—	12	4	no	—
431	C₂×C₃	C₂×#918	1	6	yes	direct product factor
432	C₂×C₃	C₂×C₃×#137	1	6	yes	complemented
433	C₂×C₃	C₂²×D₃×D₄	1	1	yes	characteristic
434	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
435	D₃	—	2	4	no	—
436	D₃	—	4	4	no	—
437	C₂²	—	3	4	no	—
438	C₂²	—	6	12	no	—
439	C₂²	—	6	4	no	—
440	C₂²	—	12	12	no	—
441	C₂²	C₃×#918	1	4	yes	direct product factor
442	C₂²	C₂×C₃×D₃×D₄	1	3	yes	—
443	C₄	—	2	4	no	—
444	C₄	—	2	4	no	—
445	C₄	—	3	4	no	—
446	C₄	—	6	4	no	—
447	C₄	C₂×C₃×D₃×D₄	1	3	yes	—
448	C₄	C₂⁴×C₃×D₃	1	1	yes	characteristic
449	C₃	—	2	1	no	—
450	C₃	C₂²×#918	1	1	yes	characteristic, direct product factor
451	C₃	C₂²×C₃×#137	1	1	yes	characteristic, complemented
452	C₂	—	6	4	no	—
453	C₂	—	12	4	no	—
454	C₂	C₂×C₃×#918	1	6	yes	direct product factor
455	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×Q₁₆	C₂
socle	C₂³×C₃²	C₂×D₄
prime radical	C₂²×C₃×#239	C₂
hypercenter	C₂²×C₃×Q₁₆	D₃
hypocenter	C₃	C₂²×C₃×#137
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×Q₁₆

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×D₃×Q₈	C₂	semidirect
3. C₂²×C₃²×Q₁₆	C₂	semidirect
4. C₂²×C₃×#216	C₂	semidirect
5. C₂²×C₃×#215	C₂	semidirect
6. C₂×C₃×#918	C₂	direct (N × H)
7. C₂²×C₃×#204	C₂	semidirect
8. C₂²×C₃×ΓL(1,𝔽₂₅)	C₂	semidirect
10. C₂²×#918	C₃	direct (N × H)
16. C₂×C₃×D₃×Q₈	C₂²	semidirect
24. C₂×C₃²×Q₁₆	C₂²	semidirect
26. C₂×C₃×#216	C₂²	semidirect
27. C₂×C₃×#215	C₂²	semidirect
29. C₃×#918	C₂²	direct (N × H)
30. C₂×C₃×#204	C₂²	semidirect
31. C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	semidirect
35. C₂²×D₃×Q₈	C₂×C₃	semidirect
39. C₂²×C₃×Q₁₆	D₃	semidirect
40. C₂²×C₃×Q₁₆	C₂×C₃	semidirect
44. C₂²×#216	C₂×C₃	semidirect
45. C₂²×#215	C₂×C₃	semidirect
46. C₂×#918	C₂×C₃	direct (N × H)
47. C₂²×#204	C₂×C₃	semidirect
48. C₂²×ΓL(1,𝔽₂₅)	C₂×C₃	semidirect
63. C₃×D₃×Q₈	C₂³	semidirect
74. C₃²×Q₁₆	C₂³	semidirect
76. C₃×#216	C₂³	semidirect
77. C₃×#215	C₂³	semidirect
79. C₃×#204	C₂³	semidirect
80. C₃×ΓL(1,𝔽₂₅)	C₂³	semidirect
102. C₂×D₃×Q₈	C₂²×C₃	semidirect
113. C₂×C₃×Q₁₆	C₂×D₃	semidirect
114. C₂×C₃×Q₁₆	C₂²×C₃	semidirect
122. C₂×#216	C₂²×C₃	semidirect
123. C₂×#215	C₂²×C₃	semidirect
125. #918	C₂²×C₃	direct (N × H)
126. C₂×#204	C₂²×C₃	semidirect
127. C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	semidirect
159. C₂²×Q₁₆	C₃×D₃	semidirect
209. D₃×Q₈	C₂³×C₃	semidirect
222. C₃×Q₁₆	C₂²×D₃	semidirect
223. C₃×Q₁₆	C₂³×C₃	semidirect
231. #216	C₂³×C₃	semidirect
232. #215	C₂³×C₃	semidirect
234. #204	C₂³×C₃	semidirect
235. ΓL(1,𝔽₂₅)	C₂³×C₃	semidirect
236. C₂²×C₃²	#137	semidirect
263. C₂×Q₁₆	C₂×C₃×D₃	semidirect
333. C₂×C₃²	C₂×#137	semidirect
363. Q₁₆	C₂²×C₃×D₃	semidirect
375. C₂²×C₃	#918	direct (N × H)
376. C₂²×C₃	C₃×#137	semidirect
399. C₃²	C₂²×#137	semidirect
431. C₂×C₃	C₂×#918	direct (N × H)
432. C₂×C₃	C₂×C₃×#137	semidirect
441. C₂²	C₃×#918	direct (N × H)
450. C₃	C₂²×#918	direct (N × H)
451. C₃	C₂²×C₃×#137	semidirect
454. C₂	C₂×C₃×#918	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×#239	2
C₂²×C₃×D₃×Q₈	2
C₂²×C₃²×Q₁₆	2
C₂²×C₃×#216	2
C₂²×C₃×#215	2
C₂×C₃×#918	2
C₂²×C₃×#204	2
C₂²×C₃×ΓL(1,𝔽₂₅)	2
C₂²×C₃×#137	3
C₂²×#918	3

Subgroups — C22×C3×#918 #11918693

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#918 #11918693