Subgroups — C₂²×C₃×#939 #11900272

Order 1152.

5737 conjugacy classes of subgroups.

The subgroup lattice has 537 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃²×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₃×#67	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₃×#67	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂⁴×C₃×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₃×#217	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#939	C₂	1	24	yes	maximal, direct product factor
7	C₂²×C₃×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₃×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₃×#121	—	3	1	no	maximal
10	C₂²×#939	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂⁵×C₃²	C₂²	1	1	yes	characteristic
12	C₂⁵×C₃²	C₂²	1	1	yes	characteristic
13	C₂⁴×C₃×D₃	C₂²	1	1	yes	characteristic
14	C₂²×C₃²×D₄	—	2	8	no	—
15	C₂²×C₃²×D₄	C₂²	1	12	yes	complemented
16	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
17	C₂²×C₃×#67	—	2	8	no	—
18	C₂²×C₃×#67	—	2	8	no	—
19	C₂²×C₃×#67	C₂²	1	12	yes	complemented
20	C₂²×C₃×#67	C₂²	1	12	yes	complemented
21	C₂³×C₃×Dic₃	—	2	8	no	—
22	C₂³×C₃×Dic₃	C₂²	1	1	yes	characteristic
23	C₂³×C₃×Dic₃	C₂²	1	1	yes	characteristic
24	C₂³×C₃×Dic₃	C₂²	1	1	yes	characteristic
25	C₂³×C₃×Dic₃	C₂²	1	12	yes	complemented
26	C₂×C₃×#217	C₂²	1	12	yes	complemented
27	C₃×#939	C₂²	1	64	yes	direct product factor
28	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	12	yes	complemented
29	C₂×C₃×Dic₃⋊C₄	C₂²	1	12	yes	complemented
30	C₂³×C₃×D₄	—	2	1	no	—
31	C₂³×C₃×D₄	—	3	1	no	—
32	C₂³×C₃×D₄	—	3	1	no	—
33	C₂³×C₃×D₄	D₃	1	1	yes	characteristic, complemented
34	C₂³×C₃×D₄	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂⁴×C₃×C₄	—	3	1	no	—
36	C₂³×#67	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂³×#67	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂⁴×Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂×C₃×#121	—	3	24	no	—
40	C₂²×C₃×C₄⋊C₄	—	3	1	no	—
41	C₂²×C₃×C₂²⋊C₄	—	3	1	no	—
42	C₂²×C₃×C₂²⋊C₄	—	3	1	no	—
43	C₂²×#217	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂×#939	C₂×C₃	1	24	yes	direct product factor
45	C₂²×(C₂×D₃)⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂²×Dic₃⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂⁴×C₃²	—	2	4	no	—
48	C₂⁴×C₃²	—	2	4	no	—
49	C₂⁴×C₃²	—	2	4	no	—
50	C₂⁴×C₃²	—	2	4	no	—
51	C₂⁴×C₃²	—	2	4	no	—
52	C₂⁴×C₃²	D₄	1	8	yes	complemented
53	C₂⁴×C₃²	C₂³	1	6	yes	—
54	C₂⁴×C₃²	C₂³	1	6	yes	—
55	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
56	C₂³×C₃×D₃	—	2	4	no	—
57	C₂³×C₃×D₃	—	2	4	no	—
58	C₂³×C₃×D₃	—	2	4	no	—
59	C₂³×C₃×D₃	C₂³	1	6	yes	—
60	C₂×C₃²×D₄	—	2	48	no	—
61	C₂×C₃²×D₄	C₂³	1	16	yes	complemented
62	C₂²×C₃²×C₄	—	2	4	no	—
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	—	2	4	no	—
70	C₂²×C₃×Dic₃	—	2	48	no	—
71	C₂²×C₃×Dic₃	D₄	1	8	yes	complemented
72	C₂²×C₃×Dic₃	C₂³	1	6	yes	—
73	C₂²×C₃×Dic₃	C₂³	1	6	yes	—
74	C₂²×C₃×Dic₃	C₂³	1	6	yes	—
75	C₂²×C₃×Dic₃	C₂³	1	16	yes	complemented
76	C₃×#217	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	—	2	1	no	—
82	C₂⁵×C₃	—	3	1	no	—
83	C₂⁵×C₃	C₂×D₃	1	1	yes	characteristic
84	C₂⁵×C₃	C₂×D₃	1	1	yes	characteristic
85	C₂⁵×C₃	C₂²×C₃	1	1	yes	characteristic
86	C₂⁵×C₃	C₂²×C₃	1	1	yes	characteristic
87	C₂⁴×D₃	C₂²×C₃	1	1	yes	characteristic
88	C₂²×C₃×D₄	—	2	16	no	—
89	C₂²×C₃×D₄	—	2	8	no	—
90	C₂²×C₃×D₄	—	2	8	no	—
91	C₂²×C₃×D₄	—	2	12	no	—
92	C₂²×C₃×D₄	—	3	12	no	—
93	C₂²×C₃×D₄	—	3	12	no	—
94	C₂²×C₃×D₄	—	6	8	no	—
95	C₂²×C₃×D₄	—	6	8	no	—
96	C₂²×C₃×D₄	C₂×D₃	1	12	yes	complemented
97	C₂²×C₃×D₄	C₂²×C₃	1	12	yes	complemented
98	C₂³×C₃×C₄	—	2	1	no	—
99	C₂³×C₃×C₄	—	3	1	no	—
100	C₂³×C₃×C₄	—	3	12	no	—
101	C₂³×C₃×C₄	—	3	1	no	—
102	C₂³×C₃×C₄	—	3	1	no	—
103	C₂³×C₃×C₄	—	6	8	no	—
104	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
105	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
106	C₂²×#67	—	2	8	no	—
107	C₂²×#67	—	2	8	no	—
108	C₂²×#67	C₂²×C₃	1	12	yes	complemented
109	C₂²×#67	C₂²×C₃	1	12	yes	complemented
110	C₂³×Dic₃	—	2	8	no	—
111	C₂³×Dic₃	C₂²×C₃	1	1	yes	characteristic
112	C₂³×Dic₃	C₂²×C₃	1	1	yes	characteristic
113	C₂³×Dic₃	C₂²×C₃	1	1	yes	characteristic
114	C₂³×Dic₃	C₂²×C₃	1	12	yes	complemented
115	C₃×#121	—	3	64	no	—
116	C₂×C₃×C₄⋊C₄	—	3	12	no	—
117	C₂×C₃×C₂²⋊C₄	—	3	12	no	—
118	C₂×C₃×C₂²⋊C₄	—	3	12	no	—
119	C₂×#217	C₂²×C₃	1	12	yes	complemented
120	#939	C₂²×C₃	1	64	yes	direct product factor
121	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	12	yes	complemented
122	C₂×Dic₃⋊C₄	C₂²×C₃	1	12	yes	complemented
123	C₂³×C₃²	—	2	12	no	—
124	C₂³×C₃²	—	2	32	no	—
125	C₂³×C₃²	—	2	12	no	—
126	C₂³×C₃²	—	2	12	no	—
127	C₂³×C₃²	—	2	12	no	—
128	C₂³×C₃²	—	2	12	no	—
129	C₂³×C₃²	—	4	16	no	—
130	C₂³×C₃²	C₂×D₄	1	4	yes	—
131	C₂³×C₃²	C₂×D₄	1	4	yes	—
132	C₂³×C₃²	C₂×D₄	1	24	yes	complemented
133	C₂³×C₃²	#41	1	4	yes	—
134	C₂³×C₃²	C₂⁴	1	4	yes	—
135	C₂³×C₃²	C₂⁴	1	4	yes	—
136	C₂³×C₃²	C₂⁴	1	3	yes	—
137	C₂²×C₃×D₃	—	2	12	no	—
138	C₂²×C₃×D₃	—	2	12	no	—
139	C₂²×C₃×D₃	—	2	12	no	—
140	C₂²×C₃×D₃	—	4	16	no	—
141	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
142	C₃²×D₄	—	2	32	no	—
143	C₂×C₃²×C₄	—	2	12	no	—
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	—	2	12	no	—
149	C₂×C₃×Dic₃	—	2	32	no	—
150	C₂×C₃×Dic₃	C₂×D₄	1	24	yes	complemented
151	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
152	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
153	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
154	C₂³×D₄	—	3	1	no	—
155	C₂³×D₄	—	3	1	no	—
156	C₂³×D₄	C₃×D₃	1	1	yes	characteristic, complemented
157	C₂⁴×C₄	—	3	1	no	—
158	C₂×#121	—	3	24	no	—
159	C₂²×C₄⋊C₄	—	3	1	no	—
160	C₂²×C₂²⋊C₄	—	3	1	no	—
161	C₂²×C₂²⋊C₄	—	3	1	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	8	no	—
167	C₂⁴×C₃	—	2	4	no	—
168	C₂⁴×C₃	—	2	4	no	—
169	C₂⁴×C₃	—	2	4	no	—
170	C₂⁴×C₃	—	2	4	no	—
171	C₂⁴×C₃	—	2	4	no	—
172	C₂⁴×C₃	—	2	4	no	—
173	C₂⁴×C₃	—	2	8	no	—
174	C₂⁴×C₃	—	2	1	no	—
175	C₂⁴×C₃	—	2	6	no	—
176	C₂⁴×C₃	—	2	6	no	—
177	C₂⁴×C₃	—	3	6	no	—
178	C₂⁴×C₃	—	4	4	no	—
179	C₂⁴×C₃	—	4	4	no	—
180	C₂⁴×C₃	—	4	4	no	—
181	C₂⁴×C₃	—	4	4	no	—
182	C₂⁴×C₃	—	6	4	no	—
183	C₂⁴×C₃	—	6	4	no	—
184	C₂⁴×C₃	—	6	4	no	—
185	C₂⁴×C₃	#67	1	8	yes	complemented
186	C₂⁴×C₃	C₃×D₄	1	8	yes	complemented
187	C₂⁴×C₃	C₂²×D₃	1	6	yes	—
188	C₂⁴×C₃	C₂²×D₃	1	6	yes	—
189	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
190	C₂⁴×C₃	C₂³×C₃	1	6	yes	—
191	C₂⁴×C₃	C₂³×C₃	1	6	yes	—
192	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
193	C₂³×D₃	—	2	4	no	—
194	C₂³×D₃	—	2	4	no	—
195	C₂³×D₃	—	2	4	no	—
196	C₂³×D₃	C₂³×C₃	1	6	yes	—
197	C₂×C₃×D₄	—	2	96	no	—
198	C₂×C₃×D₄	—	2	48	no	—
199	C₂×C₃×D₄	—	2	48	no	—
200	C₂×C₃×D₄	—	2	16	no	—
201	C₂×C₃×D₄	—	3	16	no	—
202	C₂×C₃×D₄	—	3	16	no	—
203	C₂×C₃×D₄	—	6	48	no	—
204	C₂×C₃×D₄	—	6	48	no	—
205	C₂×C₃×D₄	C₂²×D₃	1	16	yes	complemented
206	C₂×C₃×D₄	C₂³×C₃	1	16	yes	complemented
207	C₂²×C₃×C₄	—	2	8	no	—
208	C₂²×C₃×C₄	—	2	4	no	—
209	C₂²×C₃×C₄	—	2	4	no	—
210	C₂²×C₃×C₄	—	2	6	no	—
211	C₂²×C₃×C₄	—	3	8	no	—
212	C₂²×C₃×C₄	—	3	6	no	—
213	C₂²×C₃×C₄	—	3	6	no	—
214	C₂²×C₃×C₄	—	3	6	no	—
215	C₂²×C₃×C₄	—	3	16	no	—
216	C₂²×C₃×C₄	—	6	48	no	—
217	C₂²×C₃×C₄	—	6	4	no	—
218	C₂²×C₃×C₄	—	6	4	no	—
219	C₂²×C₃×C₄	C₂²×D₃	1	6	yes	—
220	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	—
221	C₂×#67	—	2	48	no	—
222	C₂×#67	—	2	48	no	—
223	C₂×#67	C₂³×C₃	1	16	yes	complemented
224	C₂×#67	C₂³×C₃	1	16	yes	complemented
225	C₂²×Dic₃	—	2	4	no	—
226	C₂²×Dic₃	—	2	4	no	—
227	C₂²×Dic₃	—	2	48	no	—
228	C₂²×Dic₃	C₃×D₄	1	8	yes	complemented
229	C₂²×Dic₃	C₂³×C₃	1	6	yes	—
230	C₂²×Dic₃	C₂³×C₃	1	6	yes	—
231	C₂²×Dic₃	C₂³×C₃	1	6	yes	—
232	C₂²×Dic₃	C₂³×C₃	1	16	yes	complemented
233	C₃×C₄⋊C₄	—	3	16	no	—
234	C₃×C₂²⋊C₄	—	3	16	no	—
235	C₃×C₂²⋊C₄	—	3	16	no	—
236	#217	C₂³×C₃	1	16	yes	complemented
237	(C₂×D₃)⋊C₄	C₂³×C₃	1	16	yes	complemented
238	Dic₃⋊C₄	C₂³×C₃	1	16	yes	complemented
239	C₂²×C₃²	—	2	4	no	—
240	C₂²×C₃²	—	2	48	no	—
241	C₂²×C₃²	—	2	4	no	—
242	C₂²×C₃²	—	2	4	no	—
243	C₂²×C₃²	—	2	4	no	—
244	C₂²×C₃²	—	2	4	no	—
245	C₂²×C₃²	—	4	24	no	—
246	C₂²×C₃²	#121	1	16	yes	complemented
247	C₂²×C₃²	C₂²×D₄	1	6	yes	—
248	C₂²×C₃²	C₂²×D₄	1	6	yes	—
249	C₂²×C₃²	C₂²×D₄	1	8	yes	complemented
250	C₂²×C₃²	C₂×#41	1	6	yes	—
251	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
252	C₂×C₃×D₃	—	2	4	no	—
253	C₂×C₃×D₃	—	2	4	no	—
254	C₂×C₃×D₃	—	2	4	no	—
255	C₂×C₃×D₃	—	4	24	no	—
256	C₃²×C₄	—	2	4	no	—
257	C₃×Dic₃	—	2	4	no	—
258	C₃×Dic₃	—	2	4	no	—
259	C₃×Dic₃	C₂²×D₄	1	8	yes	complemented
260	C₂⁵	—	3	1	no	—
261	C₂⁵	C₂×C₃×D₃	1	1	yes	characteristic
262	C₂⁵	C₂×C₃×D₃	1	1	yes	characteristic
263	C₂²×D₄	—	2	8	no	—
264	C₂²×D₄	—	3	12	no	—
265	C₂²×D₄	—	3	12	no	—
266	C₂²×D₄	—	6	8	no	—
267	C₂²×D₄	—	6	8	no	—
268	C₂²×D₄	C₂×C₃×D₃	1	12	yes	complemented
269	C₂³×C₄	—	3	1	no	—
270	C₂³×C₄	—	3	1	no	—
271	C₂³×C₄	—	3	1	no	—
272	C₂³×C₄	—	3	12	no	—
273	C₂³×C₄	—	6	8	no	—
274	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
275	#121	—	3	64	no	—
276	C₂×C₄⋊C₄	—	3	12	no	—
277	C₂×C₂²⋊C₄	—	3	12	no	—
278	C₂×C₂²⋊C₄	—	3	12	no	—
279	C₂³×C₃	—	2	32	no	—
280	C₂³×C₃	—	2	32	no	—
281	C₂³×C₃	—	2	12	no	—
282	C₂³×C₃	—	2	12	no	—
283	C₂³×C₃	—	2	12	no	—
284	C₂³×C₃	—	2	12	no	—
285	C₂³×C₃	—	2	24	no	—
286	C₂³×C₃	—	2	12	no	—
287	C₂³×C₃	—	2	12	no	—
288	C₂³×C₃	—	2	12	no	—
289	C₂³×C₃	—	2	12	no	—
290	C₂³×C₃	—	2	12	no	—
291	C₂³×C₃	—	2	12	no	—
292	C₂³×C₃	—	2	3	no	—
293	C₂³×C₃	—	2	4	no	—
294	C₂³×C₃	—	2	4	no	—
295	C₂³×C₃	—	2	4	no	—
296	C₂³×C₃	—	2	4	no	—
297	C₂³×C₃	—	2	4	no	—
298	C₂³×C₃	—	2	24	no	—
299	C₂³×C₃	—	3	4	no	—
300	C₂³×C₃	—	4	32	no	—
301	C₂³×C₃	—	4	12	no	—
302	C₂³×C₃	—	4	12	no	—
303	C₂³×C₃	—	4	12	no	—
304	C₂³×C₃	—	4	12	no	—
305	C₂³×C₃	—	4	32	no	—
306	C₂³×C₃	—	4	16	no	—
307	C₂³×C₃	—	4	16	no	—
308	C₂³×C₃	—	6	12	no	—
309	C₂³×C₃	—	6	12	no	—
310	C₂³×C₃	—	6	12	no	—
311	C₂³×C₃	—	12	16	no	—
312	C₂³×C₃	D₃×D₄	1	4	yes	—
313	C₂³×C₃	#237	1	4	yes	—
314	C₂³×C₃	C₂×#67	1	4	yes	—
315	C₂³×C₃	C₂×#67	1	24	yes	complemented
316	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
317	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
318	C₂³×C₃	C₂×C₃×D₄	1	24	yes	complemented
319	C₂³×C₃	C₃×#41	1	4	yes	—
320	C₂³×C₃	C₂³×D₃	1	4	yes	—
321	C₂³×C₃	C₂³×D₃	1	4	yes	—
322	C₂³×C₃	C₂³×D₃	1	3	yes	—
323	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
324	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
325	C₂³×C₃	C₂⁴×C₃	1	3	yes	—
326	C₂²×D₃	—	2	12	no	—
327	C₂²×D₃	—	2	12	no	—
328	C₂²×D₃	—	2	12	no	—
329	C₂²×D₃	—	4	16	no	—
330	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
331	C₃×D₄	—	2	64	no	—
332	C₃×D₄	—	2	32	no	—
333	C₃×D₄	—	2	32	no	—
334	C₃×D₄	—	6	32	no	—
335	C₃×D₄	—	6	32	no	—
336	C₂×C₃×C₄	—	2	24	no	—
337	C₂×C₃×C₄	—	2	12	no	—
338	C₂×C₃×C₄	—	2	12	no	—
339	C₂×C₃×C₄	—	2	4	no	—
340	C₂×C₃×C₄	—	3	24	no	—
341	C₂×C₃×C₄	—	3	4	no	—
342	C₂×C₃×C₄	—	3	4	no	—
343	C₂×C₃×C₄	—	3	4	no	—
344	C₂×C₃×C₄	—	6	32	no	—
345	C₂×C₃×C₄	—	6	12	no	—
346	C₂×C₃×C₄	—	6	12	no	—
347	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
348	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
349	#67	—	2	32	no	—
350	#67	—	2	32	no	—
351	C₂×Dic₃	—	2	12	no	—
352	C₂×Dic₃	—	2	12	no	—
353	C₂×Dic₃	—	2	32	no	—
354	C₂×Dic₃	C₂×C₃×D₄	1	24	yes	complemented
355	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
356	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
357	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
358	C₂×C₃²	—	2	8	no	—
359	C₂×C₃²	—	4	4	no	—
360	C₂×C₃²	C₂×#121	1	12	yes	complemented
361	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
362	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
363	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
364	C₃×D₃	—	4	4	no	—
365	C₂⁴	—	2	4	no	—
366	C₂⁴	—	2	4	no	—
367	C₂⁴	—	2	4	no	—
368	C₂⁴	—	2	4	no	—
369	C₂⁴	—	2	4	no	—
370	C₂⁴	—	3	6	no	—
371	C₂⁴	—	6	4	no	—
372	C₂⁴	—	6	4	no	—
373	C₂⁴	—	6	4	no	—
374	C₂⁴	C₃×#67	1	8	yes	complemented
375	C₂⁴	C₂²×C₃×D₃	1	6	yes	—
376	C₂⁴	C₂²×C₃×D₃	1	6	yes	—
377	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
378	C₂×D₄	—	2	48	no	—
379	C₂×D₄	—	3	16	no	—
380	C₂×D₄	—	3	16	no	—
381	C₂×D₄	—	6	48	no	—
382	C₂×D₄	—	6	48	no	—
383	C₂×D₄	C₂²×C₃×D₃	1	16	yes	complemented
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	3	6	no	—
386	C₂²×C₄	—	3	8	no	—
387	C₂²×C₄	—	3	6	no	—
388	C₂²×C₄	—	3	6	no	—
389	C₂²×C₄	—	3	16	no	—
390	C₂²×C₄	—	6	48	no	—
391	C₂²×C₄	—	6	4	no	—
392	C₂²×C₄	—	6	4	no	—
393	C₂²×C₄	C₂²×C₃×D₃	1	6	yes	—
394	C₄⋊C₄	—	3	16	no	—
395	C₂²⋊C₄	—	3	16	no	—
396	C₂²⋊C₄	—	3	16	no	—
397	C₂²×C₃	—	2	4	no	—
398	C₂²×C₃	—	2	4	no	—
399	C₂²×C₃	—	2	4	no	—
400	C₂²×C₃	—	2	4	no	—
401	C₂²×C₃	—	2	48	no	—
402	C₂²×C₃	—	2	48	no	—
403	C₂²×C₃	—	2	8	no	—
404	C₂²×C₃	—	2	4	no	—
405	C₂²×C₃	—	2	4	no	—
406	C₂²×C₃	—	2	4	no	—
407	C₂²×C₃	—	2	4	no	—
408	C₂²×C₃	—	2	4	no	—
409	C₂²×C₃	—	2	4	no	—
410	C₂²×C₃	—	2	16	no	—
411	C₂²×C₃	—	2	6	no	—
412	C₂²×C₃	—	2	6	no	—
413	C₂²×C₃	—	2	6	no	—
414	C₂²×C₃	—	2	8	no	—
415	C₂²×C₃	—	2	1	no	—
416	C₂²×C₃	—	4	48	no	—
417	C₂²×C₃	—	4	4	no	—
418	C₂²×C₃	—	4	4	no	—
419	C₂²×C₃	—	4	4	no	—
420	C₂²×C₃	—	4	4	no	—
421	C₂²×C₃	—	4	48	no	—
422	C₂²×C₃	—	4	24	no	—
423	C₂²×C₃	—	4	24	no	—
424	C₂²×C₃	—	6	4	no	—
425	C₂²×C₃	—	6	4	no	—
426	C₂²×C₃	—	6	4	no	—
427	C₂²×C₃	—	12	24	no	—
428	C₂²×C₃	#939	1	16	yes	direct product factor
429	C₂²×C₃	C₃×#121	1	16	yes	complemented
430	C₂²×C₃	C₂×D₃×D₄	1	6	yes	—
431	C₂²×C₃	C₂×#237	1	6	yes	—
432	C₂²×C₃	C₂²×#67	1	6	yes	—
433	C₂²×C₃	C₂²×#67	1	8	yes	complemented
434	C₂²×C₃	C₂²×C₃×D₄	1	6	yes	—
435	C₂²×C₃	C₂²×C₃×D₄	1	6	yes	—
436	C₂²×C₃	C₂²×C₃×D₄	1	8	yes	complemented
437	C₂²×C₃	C₂×C₃×#41	1	6	yes	—
438	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
439	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
440	C₂×D₃	—	2	4	no	—
441	C₂×D₃	—	2	4	no	—
442	C₂×D₃	—	2	4	no	—
443	C₂×D₃	—	4	24	no	—
444	C₃×C₄	—	2	8	no	—
445	C₃×C₄	—	2	4	no	—
446	C₃×C₄	—	2	4	no	—
447	C₃×C₄	—	3	8	no	—
448	C₃×C₄	—	6	4	no	—
449	C₃×C₄	—	6	4	no	—
450	Dic₃	—	2	4	no	—
451	Dic₃	—	2	4	no	—
452	Dic₃	C₂²×C₃×D₄	1	8	yes	complemented
453	C₃²	C₂²×#121	1	1	yes	characteristic, complemented, Sylow
454	C₂³	—	2	32	no	—
455	C₂³	—	2	12	no	—
456	C₂³	—	2	12	no	—
457	C₂³	—	2	12	no	—
458	C₂³	—	2	12	no	—
459	C₂³	—	2	12	no	—
460	C₂³	—	3	4	no	—
461	C₂³	—	4	16	no	—
462	C₂³	—	6	12	no	—
463	C₂³	—	6	12	no	—
464	C₂³	—	6	12	no	—
465	C₂³	—	12	16	no	—
466	C₂³	C₃×D₃×D₄	1	4	yes	—
467	C₂³	C₃×#237	1	4	yes	—
468	C₂³	C₂×C₃×#67	1	4	yes	—
469	C₂³	C₂×C₃×#67	1	24	yes	complemented
470	C₂³	C₂³×C₃×D₃	1	4	yes	—
471	C₂³	C₂³×C₃×D₃	1	4	yes	—
472	C₂³	C₂³×C₃×D₃	1	3	yes	—
473	D₄	—	2	32	no	—
474	D₄	—	6	32	no	—
475	D₄	—	6	32	no	—
476	C₂×C₄	—	2	12	no	—
477	C₂×C₄	—	3	24	no	—
478	C₂×C₄	—	3	4	no	—
479	C₂×C₄	—	3	4	no	—
480	C₂×C₄	—	3	4	no	—
481	C₂×C₄	—	6	32	no	—
482	C₂×C₄	—	6	12	no	—
483	C₂×C₄	—	6	12	no	—
484	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
485	C₂×C₃	—	2	8	no	—
486	C₂×C₃	—	2	8	no	—
487	C₂×C₃	—	2	12	no	—
488	C₂×C₃	—	2	1	no	—
489	C₂×C₃	—	2	1	no	—
490	C₂×C₃	—	2	1	no	—
491	C₂×C₃	—	4	8	no	—
492	C₂×C₃	—	4	8	no	—
493	C₂×C₃	—	4	4	no	—
494	C₂×C₃	—	4	4	no	—
495	C₂×C₃	—	12	4	no	—
496	C₂×C₃	C₂×#939	1	12	yes	direct product factor
497	C₂×C₃	C₂×C₃×#121	1	12	yes	complemented
498	C₂×C₃	C₂²×D₃×D₄	1	1	yes	characteristic
499	C₂×C₃	C₂²×#237	1	1	yes	characteristic
500	C₂×C₃	C₂³×#67	1	1	yes	characteristic
501	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
502	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
503	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
504	D₃	—	4	4	no	—
505	C₂²	—	2	48	no	—
506	C₂²	—	2	4	no	—
507	C₂²	—	2	4	no	—
508	C₂²	—	2	4	no	—
509	C₂²	—	2	4	no	—
510	C₂²	—	2	4	no	—
511	C₂²	—	4	24	no	—
512	C₂²	—	6	4	no	—
513	C₂²	—	6	4	no	—
514	C₂²	—	6	4	no	—
515	C₂²	—	12	24	no	—
516	C₂²	C₃×#939	1	16	yes	direct product factor
517	C₂²	C₂×C₃×D₃×D₄	1	6	yes	—
518	C₂²	C₂×C₃×#237	1	6	yes	—
519	C₂²	C₂²×C₃×#67	1	6	yes	—
520	C₂²	C₂²×C₃×#67	1	8	yes	complemented
521	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
522	C₄	—	2	4	no	—
523	C₄	—	3	8	no	—
524	C₄	—	6	4	no	—
525	C₄	—	6	4	no	—
526	C₃	—	2	1	no	—
527	C₃	C₂²×#939	1	1	yes	characteristic, direct product factor
528	C₃	C₂²×C₃×#121	1	1	yes	characteristic, complemented
529	C₂	—	2	8	no	—
530	C₂	—	4	4	no	—
531	C₂	—	12	4	no	—
532	C₂	C₂×C₃×#939	1	12	yes	direct product factor
533	C₂	C₂²×C₃×D₃×D₄	1	1	yes	characteristic
534	C₂	C₂²×C₃×#237	1	1	yes	characteristic
535	C₂	C₂³×C₃×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴×C₃	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₂³×C₃²×D₄	C₂
socle	C₂⁴×C₃²	C₂³
hypercenter	C₂³×C₃×D₄	D₃
hypocenter	C₃	C₂²×C₃×#121
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴×C₃ ◁ C₂³×C₃×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃²×D₄	C₂	semidirect
2. C₂³×C₃×#67	C₂	semidirect
3. C₂³×C₃×#67	C₂	semidirect
4. C₂⁴×C₃×Dic₃	C₂	semidirect
5. C₂²×C₃×#217	C₂	semidirect
6. C₂×C₃×#939	C₂	direct (N × H)
7. C₂²×C₃×(C₂×D₃)⋊C₄	C₂	semidirect
8. C₂²×C₃×Dic₃⋊C₄	C₂	semidirect
10. C₂²×#939	C₃	direct (N × H)
15. C₂²×C₃²×D₄	C₂²	semidirect
19. C₂²×C₃×#67	C₂²	semidirect
20. C₂²×C₃×#67	C₂²	semidirect
25. C₂³×C₃×Dic₃	C₂²	semidirect
26. C₂×C₃×#217	C₂²	semidirect
27. C₃×#939	C₂²	direct (N × H)
28. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
29. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
33. C₂³×C₃×D₄	D₃	semidirect
34. C₂³×C₃×D₄	C₂×C₃	semidirect
36. C₂³×#67	C₂×C₃	semidirect
37. C₂³×#67	C₂×C₃	semidirect
38. C₂⁴×Dic₃	C₂×C₃	semidirect
43. C₂²×#217	C₂×C₃	semidirect
44. C₂×#939	C₂×C₃	direct (N × H)
45. C₂²×(C₂×D₃)⋊C₄	C₂×C₃	semidirect
46. C₂²×Dic₃⋊C₄	C₂×C₃	semidirect
52. C₂⁴×C₃²	D₄	semidirect
61. C₂×C₃²×D₄	C₂³	semidirect
66. C₂×C₃×#67	C₂³	semidirect
67. C₂×C₃×#67	C₂³	semidirect
71. C₂²×C₃×Dic₃	D₄	semidirect
75. C₂²×C₃×Dic₃	C₂³	semidirect
76. C₃×#217	C₂³	semidirect
77. C₃×(C₂×D₃)⋊C₄	C₂³	semidirect
78. C₃×Dic₃⋊C₄	C₂³	semidirect
96. C₂²×C₃×D₄	C₂×D₃	semidirect
97. C₂²×C₃×D₄	C₂²×C₃	semidirect
108. C₂²×#67	C₂²×C₃	semidirect
109. C₂²×#67	C₂²×C₃	semidirect
114. C₂³×Dic₃	C₂²×C₃	semidirect
119. C₂×#217	C₂²×C₃	semidirect
120. #939	C₂²×C₃	direct (N × H)
121. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
122. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
132. C₂³×C₃²	C₂×D₄	semidirect
150. C₂×C₃×Dic₃	C₂×D₄	semidirect
156. C₂³×D₄	C₃×D₃	semidirect
185. C₂⁴×C₃	#67	semidirect
186. C₂⁴×C₃	C₃×D₄	semidirect
205. C₂×C₃×D₄	C₂²×D₃	semidirect
206. C₂×C₃×D₄	C₂³×C₃	semidirect
223. C₂×#67	C₂³×C₃	semidirect
224. C₂×#67	C₂³×C₃	semidirect
228. C₂²×Dic₃	C₃×D₄	semidirect
232. C₂²×Dic₃	C₂³×C₃	semidirect
236. #217	C₂³×C₃	semidirect
237. (C₂×D₃)⋊C₄	C₂³×C₃	semidirect
238. Dic₃⋊C₄	C₂³×C₃	semidirect
246. C₂²×C₃²	#121	semidirect
249. C₂²×C₃²	C₂²×D₄	semidirect
259. C₃×Dic₃	C₂²×D₄	semidirect
268. C₂²×D₄	C₂×C₃×D₃	semidirect
315. C₂³×C₃	C₂×#67	semidirect
318. C₂³×C₃	C₂×C₃×D₄	semidirect
354. C₂×Dic₃	C₂×C₃×D₄	semidirect
360. C₂×C₃²	C₂×#121	semidirect
374. C₂⁴	C₃×#67	semidirect
383. C₂×D₄	C₂²×C₃×D₃	semidirect
428. C₂²×C₃	#939	direct (N × H)
429. C₂²×C₃	C₃×#121	semidirect
433. C₂²×C₃	C₂²×#67	semidirect
436. C₂²×C₃	C₂²×C₃×D₄	semidirect
452. Dic₃	C₂²×C₃×D₄	semidirect
453. C₃²	C₂²×#121	semidirect
469. C₂³	C₂×C₃×#67	semidirect
496. C₂×C₃	C₂×#939	direct (N × H)
497. C₂×C₃	C₂×C₃×#121	semidirect
516. C₂²	C₃×#939	direct (N × H)
520. C₂²	C₂²×C₃×#67	semidirect
527. C₃	C₂²×#939	direct (N × H)
528. C₃	C₂²×C₃×#121	semidirect
532. C₂	C₂×C₃×#939	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×C₃²×D₄	2
C₂³×C₃×#67	2
C₂⁴×C₃×Dic₃	2
C₂²×C₃×#217	2
C₂×C₃×#939	2
C₂²×C₃×(C₂×D₃)⋊C₄	2
C₂²×C₃×Dic₃⋊C₄	2
C₂²×C₃×#121	3
C₂²×#939	3

Subgroups — C22×C3×#939 #11900272

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#939 #11900272