Subgroups — C₂²×C₃×#884 #11900275

Order 1152.

5393 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×#67	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₃×#67	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₃×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×C₃×C₄×D₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₃²×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₃×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₃×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#884	C₂	1	24	yes	maximal, direct product factor
9	C₂²×C₃×#121	—	3	1	no	maximal
10	C₂²×#884	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂⁵×C₃²	C₂²	1	1	yes	characteristic
12	C₂⁴×C₃×D₃	C₂²	1	1	yes	characteristic
13	C₂⁴×C₃×D₃	C₂²	1	1	yes	characteristic
14	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
15	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
16	C₂²×C₃×#67	—	2	8	no	—
17	C₂²×C₃×#67	—	2	8	no	—
18	C₂²×C₃×#67	C₂²	1	12	yes	complemented
19	C₂²×C₃×#67	C₂²	1	12	yes	complemented
20	C₂³×C₃×Dic₃	C₂²	1	1	yes	characteristic
21	C₂³×C₃×Dic₃	C₂²	1	1	yes	characteristic
22	C₂²×C₃×D₁₂	—	2	8	no	—
23	C₂²×C₃×D₁₂	C₂²	1	12	yes	complemented
24	C₂²×C₃×C₄×D₃	—	2	8	no	—
25	C₂²×C₃×C₄×D₃	C₂²	1	12	yes	complemented
26	C₂×C₃²×C₂²⋊C₄	C₂²	1	12	yes	complemented
27	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	12	yes	complemented
28	C₂×C₃×Dic₃⋊C₄	C₂²	1	12	yes	complemented
29	C₃×#884	C₂²	1	64	yes	direct product factor
30	C₂³×C₃×D₄	—	3	1	no	—
31	C₂³×C₃×D₄	—	3	1	no	—
32	C₂³×C₃×D₄	—	3	1	no	—
33	C₂⁴×C₃×C₄	—	3	1	no	—
34	C₂³×#67	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂³×#67	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂³×D₁₂	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂³×C₄×D₃	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂×C₃×#121	—	3	24	no	—
39	C₂²×C₃×C₄⋊C₄	—	3	1	no	—
40	C₂²×C₃×C₂²⋊C₄	—	2	1	no	—
41	C₂²×C₃×C₂²⋊C₄	—	3	1	no	—
42	C₂²×C₃×C₂²⋊C₄	D₃	1	1	yes	characteristic, complemented
43	C₂²×C₃×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂²×(C₂×D₃)⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂²×Dic₃⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×#884	C₂×C₃	1	24	yes	direct product factor
47	C₂⁴×C₃²	—	2	4	no	—
48	C₂⁴×C₃²	—	2	4	no	—
49	C₂⁴×C₃²	—	2	4	no	—
50	C₂⁴×C₃²	C₂³	1	6	yes	—
51	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
52	C₂³×C₃×D₃	—	2	4	no	—
53	C₂³×C₃×D₃	—	2	4	no	—
54	C₂³×C₃×D₃	—	2	4	no	—
55	C₂³×C₃×D₃	—	2	4	no	—
56	C₂³×C₃×D₃	—	2	4	no	—
57	C₂³×C₃×D₃	D₄	1	8	yes	complemented
58	C₂³×C₃×D₃	C₂³	1	6	yes	—
59	C₂³×C₃×D₃	C₂³	1	6	yes	—
60	C₂²×C₃²×C₄	—	2	4	no	—
61	C₂²×C₃²×C₄	—	2	4	no	—
62	C₂²×C₃²×C₄	C₂³	1	6	yes	—
63	C₂²×C₃²×C₄	C₂³	1	6	yes	—
64	C₂×C₃×#67	—	2	48	no	—
65	C₂×C₃×#67	—	2	48	no	—
66	C₂×C₃×#67	C₂³	1	16	yes	complemented
67	C₂×C₃×#67	C₂³	1	16	yes	complemented
68	C₂²×C₃×Dic₃	—	2	4	no	—
69	C₂²×C₃×Dic₃	D₄	1	8	yes	complemented
70	C₂²×C₃×Dic₃	C₂³	1	6	yes	—
71	C₂²×C₃×Dic₃	C₂³	1	6	yes	—
72	C₂×C₃×D₁₂	—	2	48	no	—
73	C₂×C₃×D₁₂	C₂³	1	16	yes	complemented
74	C₂×C₃×C₄×D₃	—	2	48	no	—
75	C₂×C₃×C₄×D₃	C₂³	1	16	yes	complemented
76	C₃²×C₂²⋊C₄	C₂³	1	16	yes	complemented
77	C₃×(C₂×D₃)⋊C₄	C₂³	1	16	yes	complemented
78	C₃×Dic₃⋊C₄	C₂³	1	16	yes	complemented
79	C₂²×#121	—	3	1	no	Sylow
80	C₂⁵×C₃	—	2	1	no	—
81	C₂⁵×C₃	—	3	1	no	—
82	C₂⁵×C₃	—	3	1	no	—
83	C₂⁵×C₃	C₂×D₃	1	1	yes	characteristic
84	C₂⁵×C₃	C₂²×C₃	1	1	yes	characteristic
85	C₂⁴×D₃	C₂²×C₃	1	1	yes	characteristic
86	C₂⁴×D₃	C₂²×C₃	1	1	yes	characteristic
87	C₂²×C₃×D₄	—	3	12	no	—
88	C₂²×C₃×D₄	—	3	12	no	—
89	C₂²×C₃×D₄	—	3	12	no	—
90	C₂²×C₃×D₄	—	6	8	no	—
91	C₂²×C₃×D₄	—	6	8	no	—
92	C₂²×C₃×D₄	—	6	8	no	—
93	C₂³×C₃×C₄	—	2	1	no	—
94	C₂³×C₃×C₄	—	2	1	no	—
95	C₂³×C₃×C₄	—	3	1	no	—
96	C₂³×C₃×C₄	—	3	1	no	—
97	C₂³×C₃×C₄	—	3	12	no	—
98	C₂³×C₃×C₄	—	6	8	no	—
99	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
100	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
101	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
102	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
103	C₂²×#67	—	2	8	no	—
104	C₂²×#67	—	2	8	no	—
105	C₂²×#67	C₂²×C₃	1	12	yes	complemented
106	C₂²×#67	C₂²×C₃	1	12	yes	complemented
107	C₂³×Dic₃	C₂²×C₃	1	1	yes	characteristic
108	C₂³×Dic₃	C₂²×C₃	1	1	yes	characteristic
109	C₂²×D₁₂	—	2	8	no	—
110	C₂²×D₁₂	C₂²×C₃	1	12	yes	complemented
111	C₂²×C₄×D₃	—	2	8	no	—
112	C₂²×C₄×D₃	C₂²×C₃	1	12	yes	complemented
113	C₃×#121	—	3	64	no	—
114	C₂×C₃×C₄⋊C₄	—	3	12	no	—
115	C₂×C₃×C₂²⋊C₄	—	2	12	no	—
116	C₂×C₃×C₂²⋊C₄	—	3	12	no	—
117	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	12	yes	complemented
118	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	12	yes	complemented
119	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	12	yes	complemented
120	C₂×Dic₃⋊C₄	C₂²×C₃	1	12	yes	complemented
121	#884	C₂²×C₃	1	64	yes	direct product factor
122	C₂³×C₃²	—	2	12	no	—
123	C₂³×C₃²	—	2	12	no	—
124	C₂³×C₃²	—	2	12	no	—
125	C₂³×C₃²	—	4	16	no	—
126	C₂³×C₃²	C₂×D₄	1	4	yes	—
127	C₂³×C₃²	C₂×D₄	1	4	yes	—
128	C₂³×C₃²	#41	1	4	yes	—
129	C₂³×C₃²	C₂⁴	1	4	yes	—
130	C₂³×C₃²	C₂⁴	1	3	yes	—
131	C₂²×C₃×D₃	—	2	32	no	—
132	C₂²×C₃×D₃	—	2	12	no	—
133	C₂²×C₃×D₃	—	2	12	no	—
134	C₂²×C₃×D₃	—	2	12	no	—
135	C₂²×C₃×D₃	—	2	12	no	—
136	C₂²×C₃×D₃	—	2	12	no	—
137	C₂²×C₃×D₃	—	4	16	no	—
138	C₂²×C₃×D₃	C₂×D₄	1	24	yes	complemented
139	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
140	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
141	C₂×C₃²×C₄	—	2	12	no	—
142	C₂×C₃²×C₄	—	2	12	no	—
143	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
144	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
145	C₃×#67	—	2	32	no	—
146	C₃×#67	—	2	32	no	—
147	C₂×C₃×Dic₃	—	2	12	no	—
148	C₂×C₃×Dic₃	C₂×D₄	1	24	yes	complemented
149	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
150	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
151	C₃×D₁₂	—	2	32	no	—
152	C₃×C₄×D₃	—	2	32	no	—
153	C₂³×D₄	—	3	1	no	—
154	C₂³×D₄	—	3	1	no	—
155	C₂³×D₄	—	3	1	no	—
156	C₂⁴×C₄	—	3	1	no	—
157	C₂×#121	—	3	24	no	—
158	C₂²×C₄⋊C₄	—	3	1	no	—
159	C₂²×C₂²⋊C₄	—	3	1	no	—
160	C₂²×C₂²⋊C₄	C₃×D₃	1	1	yes	characteristic, complemented
161	C₂⁴×C₃	—	2	8	no	—
162	C₂⁴×C₃	—	2	4	no	—
163	C₂⁴×C₃	—	2	4	no	—
164	C₂⁴×C₃	—	2	4	no	—
165	C₂⁴×C₃	—	2	4	no	—
166	C₂⁴×C₃	—	2	4	no	—
167	C₂⁴×C₃	—	2	4	no	—
168	C₂⁴×C₃	—	2	1	no	—
169	C₂⁴×C₃	—	2	6	no	—
170	C₂⁴×C₃	—	3	8	no	—
171	C₂⁴×C₃	—	3	6	no	—
172	C₂⁴×C₃	—	3	6	no	—
173	C₂⁴×C₃	—	4	4	no	—
174	C₂⁴×C₃	—	4	4	no	—
175	C₂⁴×C₃	—	6	4	no	—
176	C₂⁴×C₃	—	6	4	no	—
177	C₂⁴×C₃	—	6	4	no	—
178	C₂⁴×C₃	—	6	4	no	—
179	C₂⁴×C₃	—	6	4	no	—
180	C₂⁴×C₃	C₂²×D₃	1	6	yes	—
181	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
182	C₂⁴×C₃	C₂³×C₃	1	6	yes	—
183	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
184	C₂³×D₃	—	2	4	no	—
185	C₂³×D₃	—	2	4	no	—
186	C₂³×D₃	—	2	4	no	—
187	C₂³×D₃	—	2	4	no	—
188	C₂³×D₃	—	2	4	no	—
189	C₂³×D₃	C₃×D₄	1	8	yes	complemented
190	C₂³×D₃	C₂³×C₃	1	6	yes	—
191	C₂³×D₃	C₂³×C₃	1	6	yes	—
192	C₂×C₃×D₄	—	3	16	no	—
193	C₂×C₃×D₄	—	3	16	no	—
194	C₂×C₃×D₄	—	3	16	no	—
195	C₂×C₃×D₄	—	6	48	no	—
196	C₂×C₃×D₄	—	6	48	no	—
197	C₂×C₃×D₄	—	6	48	no	—
198	C₂²×C₃×C₄	—	2	4	no	—
199	C₂²×C₃×C₄	—	2	4	no	—
200	C₂²×C₃×C₄	—	2	4	no	—
201	C₂²×C₃×C₄	—	2	4	no	—
202	C₂²×C₃×C₄	—	2	6	no	—
203	C₂²×C₃×C₄	—	2	6	no	—
204	C₂²×C₃×C₄	—	3	8	no	—
205	C₂²×C₃×C₄	—	3	6	no	—
206	C₂²×C₃×C₄	—	3	6	no	—
207	C₂²×C₃×C₄	—	3	16	no	—
208	C₂²×C₃×C₄	—	4	4	no	—
209	C₂²×C₃×C₄	—	4	4	no	—
210	C₂²×C₃×C₄	—	6	48	no	—
211	C₂²×C₃×C₄	—	6	4	no	—
212	C₂²×C₃×C₄	C₂²×D₃	1	6	yes	—
213	C₂²×C₃×C₄	C₂²×D₃	1	6	yes	—
214	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	—
215	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	—
216	C₂×#67	—	2	48	no	—
217	C₂×#67	—	2	48	no	—
218	C₂×#67	C₂³×C₃	1	16	yes	complemented
219	C₂×#67	C₂³×C₃	1	16	yes	complemented
220	C₂²×Dic₃	—	2	4	no	—
221	C₂²×Dic₃	C₃×D₄	1	8	yes	complemented
222	C₂²×Dic₃	C₂³×C₃	1	6	yes	—
223	C₂²×Dic₃	C₂³×C₃	1	6	yes	—
224	C₂×D₁₂	—	2	48	no	—
225	C₂×D₁₂	C₂³×C₃	1	16	yes	complemented
226	C₂×C₄×D₃	—	2	48	no	—
227	C₂×C₄×D₃	C₂³×C₃	1	16	yes	complemented
228	C₃×C₄⋊C₄	—	3	16	no	—
229	C₃×C₂²⋊C₄	—	2	16	no	—
230	C₃×C₂²⋊C₄	—	3	16	no	—
231	C₃×C₂²⋊C₄	C₂²×D₃	1	16	yes	complemented
232	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	complemented
233	(C₂×D₃)⋊C₄	C₂³×C₃	1	16	yes	complemented
234	Dic₃⋊C₄	C₂³×C₃	1	16	yes	complemented
235	C₂²×C₃²	—	2	4	no	—
236	C₂²×C₃²	—	2	4	no	—
237	C₂²×C₃²	—	2	4	no	—
238	C₂²×C₃²	—	4	24	no	—
239	C₂²×C₃²	#121	1	16	yes	complemented
240	C₂²×C₃²	C₂²×D₄	1	6	yes	—
241	C₂²×C₃²	C₂²×D₄	1	6	yes	—
242	C₂²×C₃²	C₂×#41	1	6	yes	—
243	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
244	C₂×C₃×D₃	—	2	48	no	—
245	C₂×C₃×D₃	—	2	4	no	—
246	C₂×C₃×D₃	—	2	4	no	—
247	C₂×C₃×D₃	—	2	4	no	—
248	C₂×C₃×D₃	—	2	4	no	—
249	C₂×C₃×D₃	—	2	4	no	—
250	C₂×C₃×D₃	—	4	24	no	—
251	C₂×C₃×D₃	C₂²×D₄	1	8	yes	complemented
252	C₃²×C₄	—	2	4	no	—
253	C₃²×C₄	—	2	4	no	—
254	C₃×Dic₃	—	2	4	no	—
255	C₃×Dic₃	C₂²×D₄	1	8	yes	complemented
256	C₂⁵	—	3	1	no	—
257	C₂⁵	—	3	1	no	—
258	C₂⁵	C₂×C₃×D₃	1	1	yes	characteristic
259	C₂²×D₄	—	3	12	no	—
260	C₂²×D₄	—	3	12	no	—
261	C₂²×D₄	—	3	12	no	—
262	C₂²×D₄	—	6	8	no	—
263	C₂²×D₄	—	6	8	no	—
264	C₂²×D₄	—	6	8	no	—
265	C₂³×C₄	—	3	1	no	—
266	C₂³×C₄	—	3	1	no	—
267	C₂³×C₄	—	3	12	no	—
268	C₂³×C₄	—	6	8	no	—
269	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
270	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
271	#121	—	3	64	no	—
272	C₂×C₄⋊C₄	—	3	12	no	—
273	C₂×C₂²⋊C₄	—	3	12	no	—
274	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	12	yes	complemented
275	C₂³×C₃	—	2	24	no	—
276	C₂³×C₃	—	2	12	no	—
277	C₂³×C₃	—	2	12	no	—
278	C₂³×C₃	—	2	12	no	—
279	C₂³×C₃	—	2	12	no	—
280	C₂³×C₃	—	2	12	no	—
281	C₂³×C₃	—	2	12	no	—
282	C₂³×C₃	—	2	3	no	—
283	C₂³×C₃	—	2	4	no	—
284	C₂³×C₃	—	2	4	no	—
285	C₂³×C₃	—	2	4	no	—
286	C₂³×C₃	—	2	4	no	—
287	C₂³×C₃	—	3	24	no	—
288	C₂³×C₃	—	3	4	no	—
289	C₂³×C₃	—	3	4	no	—
290	C₂³×C₃	—	4	12	no	—
291	C₂³×C₃	—	4	12	no	—
292	C₂³×C₃	—	4	32	no	—
293	C₂³×C₃	—	4	16	no	—
294	C₂³×C₃	—	4	16	no	—
295	C₂³×C₃	—	6	32	no	—
296	C₂³×C₃	—	6	12	no	—
297	C₂³×C₃	—	6	12	no	—
298	C₂³×C₃	—	6	12	no	—
299	C₂³×C₃	—	6	12	no	—
300	C₂³×C₃	—	6	12	no	—
301	C₂³×C₃	—	12	16	no	—
302	C₂³×C₃	#235	1	4	yes	—
303	C₂³×C₃	D₃×D₄	1	4	yes	—
304	C₂³×C₃	D₃×D₄	1	4	yes	—
305	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
306	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
307	C₂³×C₃	C₃×#41	1	4	yes	—
308	C₂³×C₃	C₂³×D₃	1	4	yes	—
309	C₂³×C₃	C₂³×D₃	1	3	yes	—
310	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
311	C₂³×C₃	C₂⁴×C₃	1	3	yes	—
312	C₂²×D₃	—	2	32	no	—
313	C₂²×D₃	—	2	12	no	—
314	C₂²×D₃	—	2	12	no	—
315	C₂²×D₃	—	2	12	no	—
316	C₂²×D₃	—	2	12	no	—
317	C₂²×D₃	—	2	12	no	—
318	C₂²×D₃	—	4	16	no	—
319	C₂²×D₃	C₂×C₃×D₄	1	24	yes	complemented
320	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
321	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
322	C₃×D₄	—	6	32	no	—
323	C₃×D₄	—	6	32	no	—
324	C₃×D₄	—	6	32	no	—
325	C₂×C₃×C₄	—	2	12	no	—
326	C₂×C₃×C₄	—	2	12	no	—
327	C₂×C₃×C₄	—	2	12	no	—
328	C₂×C₃×C₄	—	2	12	no	—
329	C₂×C₃×C₄	—	2	4	no	—
330	C₂×C₃×C₄	—	2	4	no	—
331	C₂×C₃×C₄	—	3	24	no	—
332	C₂×C₃×C₄	—	3	4	no	—
333	C₂×C₃×C₄	—	3	4	no	—
334	C₂×C₃×C₄	—	4	12	no	—
335	C₂×C₃×C₄	—	4	12	no	—
336	C₂×C₃×C₄	—	6	32	no	—
337	C₂×C₃×C₄	—	6	12	no	—
338	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
339	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
340	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
341	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
342	#67	—	2	32	no	—
343	#67	—	2	32	no	—
344	C₂×Dic₃	—	2	12	no	—
345	C₂×Dic₃	C₂×C₃×D₄	1	24	yes	complemented
346	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
347	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
348	D₁₂	—	2	32	no	—
349	C₄×D₃	—	2	32	no	—
350	C₂×C₃²	—	4	4	no	—
351	C₂×C₃²	C₂×#121	1	12	yes	complemented
352	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
353	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
354	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
355	C₃×D₃	—	2	8	no	—
356	C₃×D₃	—	4	4	no	—
357	C₂⁴	—	2	4	no	—
358	C₂⁴	—	2	4	no	—
359	C₂⁴	—	2	4	no	—
360	C₂⁴	—	3	6	no	—
361	C₂⁴	—	3	8	no	—
362	C₂⁴	—	3	6	no	—
363	C₂⁴	—	6	4	no	—
364	C₂⁴	—	6	4	no	—
365	C₂⁴	—	6	4	no	—
366	C₂⁴	—	6	4	no	—
367	C₂⁴	—	6	4	no	—
368	C₂⁴	C₂²×C₃×D₃	1	6	yes	—
369	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
370	C₂×D₄	—	3	16	no	—
371	C₂×D₄	—	3	16	no	—
372	C₂×D₄	—	3	16	no	—
373	C₂×D₄	—	6	48	no	—
374	C₂×D₄	—	6	48	no	—
375	C₂×D₄	—	6	48	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	3	6	no	—
379	C₂²×C₄	—	3	8	no	—
380	C₂²×C₄	—	3	6	no	—
381	C₂²×C₄	—	3	16	no	—
382	C₂²×C₄	—	6	48	no	—
383	C₂²×C₄	—	6	4	no	—
384	C₂²×C₄	C₂²×C₃×D₃	1	6	yes	—
385	C₂²×C₄	C₂²×C₃×D₃	1	6	yes	—
386	C₄⋊C₄	—	3	16	no	—
387	C₂²⋊C₄	—	3	16	no	—
388	C₂²⋊C₄	C₂²×C₃×D₃	1	16	yes	complemented
389	C₂²×C₃	—	2	8	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	4	no	—
395	C₂²×C₃	—	2	4	no	—
396	C₂²×C₃	—	2	16	no	—
397	C₂²×C₃	—	2	6	no	—
398	C₂²×C₃	—	2	6	no	—
399	C₂²×C₃	—	2	6	no	—
400	C₂²×C₃	—	2	1	no	—
401	C₂²×C₃	—	3	8	no	—
402	C₂²×C₃	—	4	4	no	—
403	C₂²×C₃	—	4	4	no	—
404	C₂²×C₃	—	4	48	no	—
405	C₂²×C₃	—	4	24	no	—
406	C₂²×C₃	—	4	24	no	—
407	C₂²×C₃	—	6	4	no	—
408	C₂²×C₃	—	6	4	no	—
409	C₂²×C₃	—	6	48	no	—
410	C₂²×C₃	—	6	4	no	—
411	C₂²×C₃	—	6	4	no	—
412	C₂²×C₃	—	6	4	no	—
413	C₂²×C₃	—	12	24	no	—
414	C₂²×C₃	#884	1	16	yes	direct product factor
415	C₂²×C₃	C₃×#121	1	16	yes	complemented
416	C₂²×C₃	C₂×#235	1	6	yes	—
417	C₂²×C₃	C₂×D₃×D₄	1	6	yes	—
418	C₂²×C₃	C₂×D₃×D₄	1	6	yes	—
419	C₂²×C₃	C₂²×C₃×D₄	1	6	yes	—
420	C₂²×C₃	C₂²×C₃×D₄	1	6	yes	—
421	C₂²×C₃	C₂×C₃×#41	1	6	yes	—
422	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
423	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
424	C₂×D₃	—	2	4	no	—
425	C₂×D₃	—	2	4	no	—
426	C₂×D₃	—	2	48	no	—
427	C₂×D₃	—	2	4	no	—
428	C₂×D₃	—	2	4	no	—
429	C₂×D₃	—	2	4	no	—
430	C₂×D₃	—	4	24	no	—
431	C₂×D₃	C₂²×C₃×D₄	1	8	yes	complemented
432	C₃×C₄	—	2	4	no	—
433	C₃×C₄	—	2	4	no	—
434	C₃×C₄	—	2	4	no	—
435	C₃×C₄	—	2	4	no	—
436	C₃×C₄	—	3	8	no	—
437	C₃×C₄	—	4	4	no	—
438	C₃×C₄	—	4	4	no	—
439	C₃×C₄	—	6	4	no	—
440	Dic₃	—	2	4	no	—
441	Dic₃	C₂²×C₃×D₄	1	8	yes	complemented
442	C₃²	C₂²×#121	1	1	yes	characteristic, complemented, Sylow
443	C₂³	—	2	12	no	—
444	C₂³	—	2	12	no	—
445	C₂³	—	2	12	no	—
446	C₂³	—	3	24	no	—
447	C₂³	—	3	4	no	—
448	C₂³	—	3	4	no	—
449	C₂³	—	4	16	no	—
450	C₂³	—	6	32	no	—
451	C₂³	—	6	12	no	—
452	C₂³	—	6	12	no	—
453	C₂³	—	6	12	no	—
454	C₂³	—	6	12	no	—
455	C₂³	—	6	12	no	—
456	C₂³	—	12	16	no	—
457	C₂³	C₃×#235	1	4	yes	—
458	C₂³	C₃×D₃×D₄	1	4	yes	—
459	C₂³	C₃×D₃×D₄	1	4	yes	—
460	C₂³	C₂³×C₃×D₃	1	4	yes	—
461	C₂³	C₂³×C₃×D₃	1	3	yes	—
462	D₄	—	6	32	no	—
463	D₄	—	6	32	no	—
464	D₄	—	6	32	no	—
465	C₂×C₄	—	2	12	no	—
466	C₂×C₄	—	2	12	no	—
467	C₂×C₄	—	3	24	no	—
468	C₂×C₄	—	3	4	no	—
469	C₂×C₄	—	3	4	no	—
470	C₂×C₄	—	6	32	no	—
471	C₂×C₄	—	6	12	no	—
472	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
473	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
474	C₂×C₃	—	2	12	no	—
475	C₂×C₃	—	2	1	no	—
476	C₂×C₃	—	2	1	no	—
477	C₂×C₃	—	2	1	no	—
478	C₂×C₃	—	4	8	no	—
479	C₂×C₃	—	4	4	no	—
480	C₂×C₃	—	4	4	no	—
481	C₂×C₃	—	6	8	no	—
482	C₂×C₃	—	12	4	no	—
483	C₂×C₃	C₂×#884	1	12	yes	direct product factor
484	C₂×C₃	C₂×C₃×#121	1	12	yes	complemented
485	C₂×C₃	C₂²×#235	1	1	yes	characteristic
486	C₂×C₃	C₂²×D₃×D₄	1	1	yes	characteristic
487	C₂×C₃	C₂²×D₃×D₄	1	1	yes	characteristic
488	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
489	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
490	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
491	D₃	—	2	8	no	—
492	D₃	—	4	4	no	—
493	C₂²	—	2	4	no	—
494	C₂²	—	2	4	no	—
495	C₂²	—	2	4	no	—
496	C₂²	—	3	8	no	—
497	C₂²	—	4	24	no	—
498	C₂²	—	6	48	no	—
499	C₂²	—	6	4	no	—
500	C₂²	—	6	4	no	—
501	C₂²	—	6	4	no	—
502	C₂²	—	6	4	no	—
503	C₂²	—	6	4	no	—
504	C₂²	—	12	24	no	—
505	C₂²	C₃×#884	1	16	yes	direct product factor
506	C₂²	C₂×C₃×#235	1	6	yes	—
507	C₂²	C₂×C₃×D₃×D₄	1	6	yes	—
508	C₂²	C₂×C₃×D₃×D₄	1	6	yes	—
509	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
510	C₄	—	2	4	no	—
511	C₄	—	2	4	no	—
512	C₄	—	3	8	no	—
513	C₄	—	6	4	no	—
514	C₃	—	2	1	no	—
515	C₃	C₂²×#884	1	1	yes	characteristic, direct product factor
516	C₃	C₂²×C₃×#121	1	1	yes	characteristic, complemented
517	C₂	—	4	4	no	—
518	C₂	—	6	8	no	—
519	C₂	—	12	4	no	—
520	C₂	C₂×C₃×#884	1	12	yes	direct product factor
521	C₂	C₂²×C₃×#235	1	1	yes	characteristic
522	C₂	C₂²×C₃×D₃×D₄	1	1	yes	characteristic
523	C₂	C₂²×C₃×D₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴×C₃	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₂²×C₃²×C₂²⋊C₄	C₂
socle	C₂⁴×C₃²	C₂³
hypercenter	C₂²×C₃×C₂²⋊C₄	D₃
hypocenter	C₃	C₂²×C₃×#121
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴×C₃ ◁ C₂²×C₃×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×#67	C₂	semidirect
2. C₂³×C₃×#67	C₂	semidirect
3. C₂³×C₃×D₁₂	C₂	semidirect
4. C₂³×C₃×C₄×D₃	C₂	semidirect
5. C₂²×C₃²×C₂²⋊C₄	C₂	semidirect
6. C₂²×C₃×(C₂×D₃)⋊C₄	C₂	semidirect
7. C₂²×C₃×Dic₃⋊C₄	C₂	semidirect
8. C₂×C₃×#884	C₂	direct (N × H)
10. C₂²×#884	C₃	direct (N × H)
18. C₂²×C₃×#67	C₂²	semidirect
19. C₂²×C₃×#67	C₂²	semidirect
23. C₂²×C₃×D₁₂	C₂²	semidirect
25. C₂²×C₃×C₄×D₃	C₂²	semidirect
26. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
27. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
28. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
29. C₃×#884	C₂²	direct (N × H)
34. C₂³×#67	C₂×C₃	semidirect
35. C₂³×#67	C₂×C₃	semidirect
36. C₂³×D₁₂	C₂×C₃	semidirect
37. C₂³×C₄×D₃	C₂×C₃	semidirect
42. C₂²×C₃×C₂²⋊C₄	D₃	semidirect
43. C₂²×C₃×C₂²⋊C₄	C₂×C₃	semidirect
44. C₂²×(C₂×D₃)⋊C₄	C₂×C₃	semidirect
45. C₂²×Dic₃⋊C₄	C₂×C₃	semidirect
46. C₂×#884	C₂×C₃	direct (N × H)
57. C₂³×C₃×D₃	D₄	semidirect
66. C₂×C₃×#67	C₂³	semidirect
67. C₂×C₃×#67	C₂³	semidirect
69. C₂²×C₃×Dic₃	D₄	semidirect
73. C₂×C₃×D₁₂	C₂³	semidirect
75. C₂×C₃×C₄×D₃	C₂³	semidirect
76. C₃²×C₂²⋊C₄	C₂³	semidirect
77. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
78. C₃×Dic₃⋊C₄	C₂³	semidirect
105. C₂²×#67	C₂²×C₃	semidirect
106. C₂²×#67	C₂²×C₃	semidirect
110. C₂²×D₁₂	C₂²×C₃	semidirect
112. C₂²×C₄×D₃	C₂²×C₃	semidirect
117. C₂×C₃×C₂²⋊C₄	C₂×D₃	semidirect
118. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
119. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
120. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
121. #884	C₂²×C₃	direct (N × H)
138. C₂²×C₃×D₃	C₂×D₄	semidirect
148. C₂×C₃×Dic₃	C₂×D₄	semidirect
160. C₂²×C₂²⋊C₄	C₃×D₃	semidirect
189. C₂³×D₃	C₃×D₄	semidirect
218. C₂×#67	C₂³×C₃	semidirect
219. C₂×#67	C₂³×C₃	semidirect
221. C₂²×Dic₃	C₃×D₄	semidirect
225. C₂×D₁₂	C₂³×C₃	semidirect
227. C₂×C₄×D₃	C₂³×C₃	semidirect
231. C₃×C₂²⋊C₄	C₂²×D₃	semidirect
232. C₃×C₂²⋊C₄	C₂³×C₃	semidirect
233. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
234. Dic₃⋊C₄	C₂³×C₃	semidirect
239. C₂²×C₃²	#121	semidirect
251. C₂×C₃×D₃	C₂²×D₄	semidirect
255. C₃×Dic₃	C₂²×D₄	semidirect
274. C₂×C₂²⋊C₄	C₂×C₃×D₃	semidirect
319. C₂²×D₃	C₂×C₃×D₄	semidirect
345. C₂×Dic₃	C₂×C₃×D₄	semidirect
351. C₂×C₃²	C₂×#121	semidirect
388. C₂²⋊C₄	C₂²×C₃×D₃	semidirect
414. C₂²×C₃	#884	direct (N × H)
415. C₂²×C₃	C₃×#121	semidirect
431. C₂×D₃	C₂²×C₃×D₄	semidirect
441. Dic₃	C₂²×C₃×D₄	semidirect
442. C₃²	C₂²×#121	semidirect
483. C₂×C₃	C₂×#884	direct (N × H)
484. C₂×C₃	C₂×C₃×#121	semidirect
505. C₂²	C₃×#884	direct (N × H)
515. C₃	C₂²×#884	direct (N × H)
516. C₃	C₂²×C₃×#121	semidirect
520. C₂	C₂×C₃×#884	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×#67	2
C₂³×C₃×D₁₂	2
C₂³×C₃×C₄×D₃	2
C₂²×C₃²×C₂²⋊C₄	2
C₂²×C₃×(C₂×D₃)⋊C₄	2
C₂²×C₃×Dic₃⋊C₄	2
C₂×C₃×#884	2
C₂²×C₃×#121	3
C₂²×#884	3

Subgroups — C22×C3×#884 #11900275

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#884 #11900275