Subgroups — C₂²×#89039 #13181662

Order 1728.

11164 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₃×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×#638	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₃²×#67	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#89039	C₂	1	24	yes	maximal, direct product factor
6	C₂²×#6292	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#6291	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#6289	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₄×C₃⋊D₃	—	3	1	no	maximal
10	C₂²×#3811	—	3	4	no	maximal
11	C₂⁴×C₃³	C₂²	1	1	yes	characteristic, complemented
12	C₂³×C₃⋊(C₃⋊D₃)	—	2	8	no	—
13	C₂³×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
14	C₂³×C₃⋊(C₃⋊D₃)	C₂²	1	12	yes	complemented
15	C₂³×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic, complemented
16	C₂³×C₃×C₃⋊D₃	C₂²	1	1	yes	characteristic, complemented
17	C₂³×C₃²×D₃	C₂²	1	1	yes	characteristic, complemented
18	C₂²×D₃×C₃⋊D₃	—	2	8	no	—
19	C₂²×D₃×C₃⋊D₃	C₂²	1	12	yes	complemented
20	C₂×C₃×#638	C₂²	1	12	yes	complemented
21	C₂²×C₃×C₃⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃²×#67	C₂²	1	12	yes	complemented
23	C₂²×C₃²×Dic₃	C₂²	1	1	yes	characteristic, complemented
24	#89039	C₂²	1	64	yes	direct product factor
25	C₂×#6292	C₂²	1	12	yes	complemented
26	C₂×#6291	C₂²	1	12	yes	complemented
27	C₂×#6289	C₂²	1	12	yes	complemented
28	C₂⁴×C₃⋊D₃	—	3	1	no	—
29	C₂⁴×C₃⋊D₃	—	3	4	no	—
30	C₂⁴×C₃⋊D₃	—	3	1	no	—
31	C₂⁴×C₃⋊D₃	—	6	4	no	—
32	C₂³×D₃²	—	3	4	no	—
33	C₂²×C₃²×D₄	—	3	1	no	—
34	C₂²×#638	—	3	1	no	—
35	C₂²×#638	D₃	1	1	yes	characteristic, complemented
36	C₂×D₄×C₃⋊D₃	—	3	24	no	—
37	C₂²×C₄⋊(C₃⋊D₃)	—	3	1	no	—
38	C₂²×C₄×C₃⋊D₃	—	3	1	no	—
39	C₂²×C₃×#67	—	3	4	no	—
40	C₂²×C₃×#67	D₃	1	4	yes	complemented
41	C₂×#3811	—	3	96	no	—
42	C₂²×#626	—	3	4	no	—
43	C₂²×#626	—	3	4	no	—
44	C₂²×#624	—	3	4	no	—
45	C₂³×C₃³	—	2	4	no	—
46	C₂³×C₃³	C₂³	1	1	yes	characteristic
47	C₂³×C₃³	C₂³	1	6	yes	complemented
48	C₂²×C₃⋊(C₃⋊D₃)	—	2	4	no	—
49	C₂²×C₃⋊(C₃⋊D₃)	—	2	48	no	—
50	C₂²×C₃⋊(C₃⋊D₃)	D₄	1	8	yes	complemented
51	C₂²×C₃⋊(C₃⋊D₃)	C₂³	1	6	yes	—
52	C₂²×C₃⋊(C₃⋊D₃)	C₂³	1	16	yes	complemented
53	C₂²×C₃⋊(C₃⋊D₃)	C₂³	1	6	yes	complemented
54	C₂²×C₃×C₃⋊D₃	—	2	4	no	—
55	C₂²×C₃×C₃⋊D₃	C₂³	1	6	yes	complemented
56	C₂²×C₃²×D₃	—	2	4	no	—
57	C₂²×C₃²×D₃	C₂³	1	6	yes	complemented
58	C₂×D₃×C₃⋊D₃	—	2	48	no	—
59	C₂×D₃×C₃⋊D₃	C₂³	1	16	yes	complemented
60	C₃×#638	C₂³	1	16	yes	complemented
61	C₂×C₃×C₃⋊Dic₃	C₂³	1	6	yes	complemented
62	C₃²×#67	C₂³	1	16	yes	complemented
63	C₂×C₃²×Dic₃	C₂³	1	6	yes	complemented
64	#6292	C₂³	1	16	yes	complemented
65	#6291	C₂³	1	16	yes	complemented
66	#6289	C₂³	1	16	yes	complemented
67	C₂²×D₃×D₄	—	9	4	no	—
68	C₂²×D₃×D₄	—	9	1	no	—
69	C₂⁴×C₃²	—	2	4	no	—
70	C₂⁴×C₃²	—	3	1	no	—
71	C₂⁴×C₃²	C₂×D₃	1	4	yes	complemented
72	C₂⁴×C₃²	C₂×D₃	1	1	yes	characteristic, complemented
73	C₂³×C₃⋊D₃	—	3	1	no	—
74	C₂³×C₃⋊D₃	—	3	4	no	—
75	C₂³×C₃⋊D₃	—	3	1	no	—
76	C₂³×C₃⋊D₃	—	3	4	no	—
77	C₂³×C₃⋊D₃	—	3	12	no	—
78	C₂³×C₃⋊D₃	—	3	48	no	—
79	C₂³×C₃⋊D₃	—	3	12	no	—
80	C₂³×C₃⋊D₃	—	6	8	no	—
81	C₂³×C₃⋊D₃	—	6	8	no	—
82	C₂³×C₃⋊D₃	—	6	32	no	—
83	C₂³×C₃⋊D₃	—	6	4	no	—
84	C₂³×C₃⋊D₃	—	6	48	no	—
85	C₂³×C₃⋊D₃	—	6	4	no	—
86	C₂³×C₃⋊D₃	—	6	64	no	—
87	C₂³×C₃⋊D₃	C₂×D₃	1	1	yes	characteristic, complemented
88	C₂³×C₃×D₃	—	3	4	no	—
89	C₂³×C₃×D₃	C₂×D₃	1	4	yes	complemented
90	C₂²×D₃²	—	3	48	no	—
91	C₂²×D₃²	—	6	32	no	—
92	C₂×C₃²×D₄	—	3	12	no	—
93	C₂²×C₃²×C₄	—	3	1	no	—
94	C₂×#638	—	3	12	no	—
95	C₂×#638	C₂×D₃	1	12	yes	complemented
96	C₂²×C₃⋊Dic₃	C₂×D₃	1	1	yes	characteristic, complemented
97	D₄×C₃⋊D₃	—	3	64	no	—
98	C₂×C₄⋊(C₃⋊D₃)	—	3	12	no	—
99	C₂×C₄×C₃⋊D₃	—	3	12	no	—
100	C₂×C₃×#67	—	3	48	no	—
101	C₂×C₃×#67	C₂×D₃	1	48	yes	complemented
102	C₂²×C₃×Dic₃	—	3	4	no	—
103	C₂²×C₃×Dic₃	C₂×D₃	1	4	yes	complemented
104	#3811	—	3	256	no	—
105	C₂×#626	—	3	48	no	—
106	C₂×#626	—	3	48	no	—
107	C₂×#624	—	3	48	no	—
108	C₂²×C₃³	—	2	12	no	—
109	C₂²×C₃³	C₂×D₄	1	4	yes	complemented
110	C₂²×C₃³	C₂⁴	1	3	yes	—
111	C₂²×C₃³	C₂⁴	1	4	yes	complemented
112	C₂×C₃⋊(C₃⋊D₃)	—	2	12	no	—
113	C₂×C₃⋊(C₃⋊D₃)	—	2	32	no	—
114	C₂×C₃⋊(C₃⋊D₃)	C₂×D₄	1	24	yes	complemented
115	C₂×C₃⋊(C₃⋊D₃)	C₂⁴	1	4	yes	—
116	C₂×C₃⋊(C₃⋊D₃)	C₂⁴	1	4	yes	complemented
117	C₂×C₃×C₃⋊D₃	—	2	12	no	—
118	C₂×C₃×C₃⋊D₃	C₂⁴	1	4	yes	complemented
119	C₂×C₃²×D₃	—	2	12	no	—
120	C₂×C₃²×D₃	C₂⁴	1	4	yes	complemented
121	D₃×C₃⋊D₃	—	2	32	no	—
122	C₃×C₃⋊Dic₃	C₂⁴	1	4	yes	complemented
123	C₃²×Dic₃	C₂⁴	1	4	yes	complemented
124	C₂⁴×D₃	—	9	4	no	—
125	C₂⁴×D₃	—	9	4	no	—
126	C₂⁴×D₃	—	9	1	no	—
127	C₂⁴×D₃	—	9	1	no	—
128	C₂⁴×D₃	—	18	4	no	—
129	C₂²×C₃×D₄	—	3	4	no	—
130	C₂²×C₃×D₄	—	9	1	no	—
131	C₂²×#67	—	3	4	no	—
132	C₂²×#67	—	9	4	no	—
133	C₂²×#67	—	9	1	no	—
134	C₂²×#67	C₃⋊D₃	1	1	yes	characteristic, complemented
135	C₂×D₃×D₄	—	9	96	no	—
136	C₂×D₃×D₄	—	9	24	no	—
137	C₂²×D₁₂	—	9	4	no	—
138	C₂²×D₁₂	—	9	1	no	—
139	C₂²×C₄×D₃	—	9	4	no	—
140	C₂²×C₄×D₃	—	9	1	no	—
141	C₂³×C₃²	—	2	32	no	—
142	C₂³×C₃²	—	2	16	no	—
143	C₂³×C₃²	—	2	4	no	—
144	C₂³×C₃²	—	2	4	no	—
145	C₂³×C₃²	—	2	24	no	—
146	C₂³×C₃²	—	3	6	no	—
147	C₂³×C₃²	—	6	4	no	—
148	C₂³×C₃²	C₂²×D₃	1	4	yes	—
149	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
150	C₂³×C₃²	C₂²×D₃	1	24	yes	complemented
151	C₂³×C₃²	C₂²×D₃	1	6	yes	complemented
152	C₂²×C₃⋊D₃	—	2	4	no	—
153	C₂²×C₃⋊D₃	—	3	8	no	—
154	C₂²×C₃⋊D₃	—	3	6	no	—
155	C₂²×C₃⋊D₃	—	3	6	no	—
156	C₂²×C₃⋊D₃	—	3	16	no	—
157	C₂²×C₃⋊D₃	—	3	16	no	—
158	C₂²×C₃⋊D₃	—	3	32	no	—
159	C₂²×C₃⋊D₃	—	3	24	no	—
160	C₂²×C₃⋊D₃	—	3	24	no	—
161	C₂²×C₃⋊D₃	—	3	64	no	—
162	C₂²×C₃⋊D₃	—	6	32	no	—
163	C₂²×C₃⋊D₃	—	6	24	no	—
164	C₂²×C₃⋊D₃	—	6	24	no	—
165	C₂²×C₃⋊D₃	—	6	64	no	—
166	C₂²×C₃⋊D₃	—	6	48	no	—
167	C₂²×C₃⋊D₃	—	6	48	no	—
168	C₂²×C₃⋊D₃	—	6	192	no	—
169	C₂²×C₃⋊D₃	—	6	384	no	—
170	C₂²×C₃⋊D₃	—	6	32	no	—
171	C₂²×C₃⋊D₃	—	6	16	no	—
172	C₂²×C₃⋊D₃	—	6	4	no	—
173	C₂²×C₃⋊D₃	C₂²×D₃	1	6	yes	complemented
174	C₂²×C₃×D₃	—	2	16	no	—
175	C₂²×C₃×D₃	—	3	24	no	—
176	C₂²×C₃×D₃	—	6	16	no	—
177	C₂²×C₃×D₃	C₂²×D₃	1	24	yes	complemented
178	C₂×D₃²	—	3	64	no	—
179	C₂×D₃²	—	6	192	no	—
180	C₃²×D₄	—	3	16	no	—
181	C₂×C₃²×C₄	—	3	6	no	—
182	#638	—	3	16	no	—
183	#638	C₂²×D₃	1	16	yes	complemented
184	C₂×C₃⋊Dic₃	C₂²×D₃	1	6	yes	complemented
185	C₄⋊(C₃⋊D₃)	—	3	16	no	—
186	C₄×C₃⋊D₃	—	3	16	no	—
187	C₃×#67	—	3	64	no	—
188	C₃×#67	C₂²×D₃	1	64	yes	complemented
189	C₂×C₃×Dic₃	—	3	24	no	—
190	C₂×C₃×Dic₃	C₂²×D₃	1	24	yes	complemented
191	#626	—	3	64	no	—
192	#626	—	3	64	no	—
193	#624	—	3	64	no	—
194	C₂³×D₄	—	27	1	no	Sylow
195	C₂×C₃³	—	2	4	no	—
196	C₂×C₃³	C₂²×D₄	1	6	yes	complemented
197	C₂×C₃³	C₂⁵	1	1	yes	characteristic
198	C₃⋊(C₃⋊D₃)	—	2	4	no	—
199	C₃⋊(C₃⋊D₃)	C₂²×D₄	1	8	yes	complemented
200	C₃×C₃⋊D₃	—	2	4	no	—
201	C₃²×D₃	—	2	4	no	—
202	C₂⁴×C₃	—	2	4	no	—
203	C₂⁴×C₃	—	3	4	no	—
204	C₂⁴×C₃	—	9	1	no	—
205	C₂⁴×C₃	D₃²	1	4	yes	complemented
206	C₂⁴×C₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
207	C₂³×D₃	—	3	4	no	—
208	C₂³×D₃	—	9	48	no	—
209	C₂³×D₃	—	9	4	no	—
210	C₂³×D₃	—	9	1	no	—
211	C₂³×D₃	—	9	4	no	—
212	C₂³×D₃	—	9	48	no	—
213	C₂³×D₃	—	9	1	no	—
214	C₂³×D₃	—	9	12	no	—
215	C₂³×D₃	—	9	12	no	—
216	C₂³×D₃	—	18	4	no	—
217	C₂³×D₃	—	18	4	no	—
218	C₂³×D₃	—	18	48	no	—
219	C₂³×D₃	—	18	8	no	—
220	C₂³×D₃	—	18	32	no	—
221	C₂³×D₃	—	18	32	no	—
222	C₂³×D₃	—	18	8	no	—
223	C₂³×D₃	—	18	64	no	—
224	C₂³×D₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
225	C₂×C₃×D₄	—	3	48	no	—
226	C₂×C₃×D₄	—	9	12	no	—
227	C₂²×C₃×C₄	—	3	4	no	—
228	C₂²×C₃×C₄	—	9	1	no	—
229	C₂×#67	—	3	48	no	—
230	C₂×#67	—	9	48	no	—
231	C₂×#67	—	9	12	no	—
232	C₂×#67	C₂×C₃⋊D₃	1	12	yes	complemented
233	C₂²×Dic₃	—	3	4	no	—
234	C₂²×Dic₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
235	D₃×D₄	—	9	256	no	—
236	D₃×D₄	—	9	64	no	—
237	C₂×D₁₂	—	9	48	no	—
238	C₂×D₁₂	—	9	12	no	—
239	C₂×C₄×D₃	—	9	48	no	—
240	C₂×C₄×D₃	—	9	12	no	—
241	C₂²×C₃²	—	2	96	no	—
242	C₂²×C₃²	—	2	48	no	—
243	C₂²×C₃²	—	2	12	no	—
244	C₂²×C₃²	—	2	12	no	—
245	C₂²×C₃²	—	2	16	no	—
246	C₂²×C₃²	—	2	16	no	—
247	C₂²×C₃²	—	3	4	no	—
248	C₂²×C₃²	—	6	12	no	—
249	C₂²×C₃²	D₃×D₄	1	16	yes	complemented
250	C₂²×C₃²	D₃×D₄	1	4	yes	complemented
251	C₂²×C₃²	C₂³×D₃	1	12	yes	—
252	C₂²×C₃²	C₂³×D₃	1	3	yes	—
253	C₂²×C₃²	C₂³×D₃	1	16	yes	complemented
254	C₂²×C₃²	C₂³×D₃	1	4	yes	complemented
255	C₂×C₃⋊D₃	—	2	12	no	—
256	C₂×C₃⋊D₃	—	3	24	no	—
257	C₂×C₃⋊D₃	—	3	4	no	—
258	C₂×C₃⋊D₃	—	3	4	no	—
259	C₂×C₃⋊D₃	—	3	96	no	—
260	C₂×C₃⋊D₃	—	3	16	no	—
261	C₂×C₃⋊D₃	—	3	16	no	—
262	C₂×C₃⋊D₃	—	6	96	no	—
263	C₂×C₃⋊D₃	—	6	16	no	—
264	C₂×C₃⋊D₃	—	6	16	no	—
265	C₂×C₃⋊D₃	—	6	32	no	—
266	C₂×C₃⋊D₃	—	6	32	no	—
267	C₂×C₃⋊D₃	—	6	128	no	—
268	C₂×C₃⋊D₃	—	6	256	no	—
269	C₂×C₃⋊D₃	—	6	96	no	—
270	C₂×C₃⋊D₃	—	6	48	no	—
271	C₂×C₃⋊D₃	—	6	12	no	—
272	C₂×C₃⋊D₃	C₂³×D₃	1	4	yes	complemented
273	C₂×C₃×D₃	—	2	48	no	—
274	C₂×C₃×D₃	—	3	16	no	—
275	C₂×C₃×D₃	—	6	48	no	—
276	C₂×C₃×D₃	C₂³×D₃	1	16	yes	complemented
277	D₃²	—	6	128	no	—
278	C₃²×C₄	—	3	4	no	—
279	C₃⋊Dic₃	C₂³×D₃	1	4	yes	complemented
280	C₃×Dic₃	—	3	16	no	—
281	C₃×Dic₃	C₂³×D₃	1	16	yes	complemented
282	C₂⁵	—	27	1	no	—
283	C₂⁵	—	27	1	no	—
284	C₂²×D₄	—	3	1	no	—
285	C₂²×D₄	—	9	1	no	—
286	C₂²×D₄	—	27	1	no	—
287	C₂²×D₄	—	27	1	no	—
288	C₂²×D₄	—	27	24	no	—
289	C₂³×C₄	—	27	1	no	—
290	C₃³	C₂³×D₄	1	1	yes	characteristic, complemented, Sylow
291	C₂³×C₃	—	2	32	no	—
292	C₂³×C₃	—	2	16	no	—
293	C₂³×C₃	—	2	4	no	—
294	C₂³×C₃	—	2	4	no	—
295	C₂³×C₃	—	2	24	no	—
296	C₂³×C₃	—	3	24	no	—
297	C₂³×C₃	—	6	16	no	—
298	C₂³×C₃	—	9	6	no	—
299	C₂³×C₃	—	18	4	no	—
300	C₂³×C₃	C₂×D₃²	1	4	yes	—
301	C₂³×C₃	C₂×D₃²	1	24	yes	complemented
302	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
303	C₂³×C₃	C₂²×C₃⋊D₃	1	6	yes	complemented
304	C₂²×D₃	—	2	4	no	—
305	C₂²×D₃	—	3	24	no	—
306	C₂²×D₃	—	6	16	no	—
307	C₂²×D₃	—	9	64	no	—
308	C₂²×D₃	—	9	24	no	—
309	C₂²×D₃	—	9	6	no	—
310	C₂²×D₃	—	9	32	no	—
311	C₂²×D₃	—	9	8	no	—
312	C₂²×D₃	—	9	24	no	—
313	C₂²×D₃	—	9	64	no	—
314	C₂²×D₃	—	9	6	no	—
315	C₂²×D₃	—	9	16	no	—
316	C₂²×D₃	—	9	16	no	—
317	C₂²×D₃	—	18	24	no	—
318	C₂²×D₃	—	18	32	no	—
319	C₂²×D₃	—	18	24	no	—
320	C₂²×D₃	—	18	64	no	—
321	C₂²×D₃	—	18	48	no	—
322	C₂²×D₃	—	18	192	no	—
323	C₂²×D₃	—	18	192	no	—
324	C₂²×D₃	—	18	48	no	—
325	C₂²×D₃	—	18	384	no	—
326	C₂²×D₃	—	18	32	no	—
327	C₂²×D₃	—	18	16	no	—
328	C₂²×D₃	—	18	4	no	—
329	C₂²×D₃	C₂²×C₃⋊D₃	1	6	yes	complemented
330	C₃×D₄	—	3	64	no	—
331	C₃×D₄	—	9	16	no	—
332	C₂×C₃×C₄	—	3	24	no	—
333	C₂×C₃×C₄	—	9	6	no	—
334	#67	—	3	64	no	—
335	#67	—	9	64	no	—
336	#67	—	9	16	no	—
337	#67	C₂²×C₃⋊D₃	1	16	yes	complemented
338	C₂×Dic₃	—	3	24	no	—
339	C₂×Dic₃	C₂²×C₃⋊D₃	1	6	yes	complemented
340	D₁₂	—	9	64	no	—
341	D₁₂	—	9	16	no	—
342	C₄×D₃	—	9	64	no	—
343	C₄×D₃	—	9	16	no	—
344	C₂×C₃²	—	2	32	no	—
345	C₂×C₃²	—	2	16	no	—
346	C₂×C₃²	—	2	4	no	—
347	C₂×C₃²	—	2	24	no	—
348	C₂×C₃²	—	2	4	no	—
349	C₂×C₃²	—	6	4	no	—
350	C₂×C₃²	C₂×D₃×D₄	1	24	yes	complemented
351	C₂×C₃²	C₂×D₃×D₄	1	6	yes	complemented
352	C₂×C₃²	C₂⁴×D₃	1	4	yes	—
353	C₂×C₃²	C₂⁴×D₃	1	1	yes	characteristic
354	C₃⋊D₃	—	2	4	no	—
355	C₃⋊D₃	—	3	8	no	—
356	C₃⋊D₃	—	3	32	no	—
357	C₃⋊D₃	—	6	32	no	—
358	C₃⋊D₃	—	6	32	no	—
359	C₃⋊D₃	—	6	16	no	—
360	C₃⋊D₃	—	6	4	no	—
361	C₃×D₃	—	2	16	no	—
362	C₃×D₃	—	6	16	no	—
363	C₂⁴	—	3	1	no	—
364	C₂⁴	—	9	1	no	—
365	C₂⁴	—	27	12	no	—
366	C₂⁴	—	27	1	no	—
367	C₂⁴	—	27	1	no	—
368	C₂⁴	—	27	12	no	—
369	C₂⁴	—	54	8	no	—
370	C₂⁴	—	54	8	no	—
371	C₂⁴	D₃×C₃⋊D₃	1	1	yes	characteristic, complemented
372	C₂×D₄	—	3	12	no	—
373	C₂×D₄	—	9	12	no	—
374	C₂×D₄	—	27	12	no	—
375	C₂×D₄	—	27	12	no	—
376	C₂×D₄	—	27	64	no	—
377	C₂²×C₄	—	3	1	no	—
378	C₂²×C₄	—	9	1	no	—
379	C₂²×C₄	—	27	12	no	—
380	C₂²×C₃	—	2	96	no	—
381	C₂²×C₃	—	2	48	no	—
382	C₂²×C₃	—	2	12	no	—
383	C₂²×C₃	—	2	12	no	—
384	C₂²×C₃	—	2	16	no	—
385	C₂²×C₃	—	2	16	no	—
386	C₂²×C₃	—	3	16	no	—
387	C₂²×C₃	—	6	48	no	—
388	C₂²×C₃	—	9	4	no	—
389	C₂²×C₃	—	18	12	no	—
390	C₂²×C₃	#3811	1	16	yes	complemented
391	C₂²×C₃	D₄×C₃⋊D₃	1	4	yes	complemented
392	C₂²×C₃	C₂²×D₃²	1	12	yes	—
393	C₂²×C₃	C₂²×D₃²	1	16	yes	complemented
394	C₂²×C₃	C₂³×C₃⋊D₃	1	3	yes	—
395	C₂²×C₃	C₂³×C₃⋊D₃	1	4	yes	complemented
396	C₂×D₃	—	2	12	no	—
397	C₂×D₃	—	3	16	no	—
398	C₂×D₃	—	6	48	no	—
399	C₂×D₃	—	9	96	no	—
400	C₂×D₃	—	9	24	no	—
401	C₂×D₃	—	9	16	no	—
402	C₂×D₃	—	9	4	no	—
403	C₂×D₃	—	9	16	no	—
404	C₂×D₃	—	9	4	no	—
405	C₂×D₃	—	18	96	no	—
406	C₂×D₃	—	18	16	no	—
407	C₂×D₃	—	18	16	no	—
408	C₂×D₃	—	18	32	no	—
409	C₂×D₃	—	18	128	no	—
410	C₂×D₃	—	18	128	no	—
411	C₂×D₃	—	18	32	no	—
412	C₂×D₃	—	18	256	no	—
413	C₂×D₃	—	18	96	no	—
414	C₂×D₃	—	18	48	no	—
415	C₂×D₃	—	18	12	no	—
416	C₂×D₃	C₂³×C₃⋊D₃	1	4	yes	complemented
417	C₃×C₄	—	3	16	no	—
418	C₃×C₄	—	9	4	no	—
419	Dic₃	—	3	16	no	—
420	Dic₃	C₂³×C₃⋊D₃	1	4	yes	complemented
421	C₃²	—	2	4	no	—
422	C₃²	C₂²×D₃×D₄	1	4	yes	complemented
423	C₃²	C₂²×D₃×D₄	1	1	yes	characteristic, complemented
424	C₂³	—	2	4	no	—
425	C₂³	—	3	6	no	—
426	C₂³	—	6	4	no	—
427	C₂³	—	9	6	no	—
428	C₂³	—	18	4	no	—
429	C₂³	—	27	16	no	—
430	C₂³	—	27	6	no	—
431	C₂³	—	27	8	no	—
432	C₂³	—	27	6	no	—
433	C₂³	—	27	16	no	—
434	C₂³	—	54	48	no	—
435	C₂³	—	54	48	no	—
436	C₂³	—	54	4	no	—
437	C₂³	C₂×D₃×C₃⋊D₃	1	1	yes	characteristic
438	C₂³	C₂×D₃×C₃⋊D₃	1	6	yes	complemented
439	D₄	—	3	16	no	—
440	D₄	—	9	16	no	—
441	D₄	—	27	16	no	—
442	D₄	—	27	16	no	—
443	C₂×C₄	—	3	6	no	—
444	C₂×C₄	—	9	6	no	—
445	C₂×C₄	—	27	16	no	—
446	C₂×C₃	—	2	32	no	—
447	C₂×C₃	—	2	16	no	—
448	C₂×C₃	—	2	4	no	—
449	C₂×C₃	—	2	24	no	—
450	C₂×C₃	—	2	4	no	—
451	C₂×C₃	—	6	16	no	—
452	C₂×C₃	—	18	4	no	—
453	C₂×C₃	C₂×#3811	1	24	yes	complemented
454	C₂×C₃	C₂×D₄×C₃⋊D₃	1	6	yes	complemented
455	C₂×C₃	C₂³×D₃²	1	4	yes	—
456	C₂×C₃	C₂⁴×C₃⋊D₃	1	1	yes	characteristic
457	D₃	—	2	4	no	—
458	D₃	—	6	16	no	—
459	D₃	—	9	32	no	—
460	D₃	—	9	8	no	—
461	D₃	—	18	32	no	—
462	D₃	—	18	32	no	—
463	D₃	—	18	16	no	—
464	D₃	—	18	4	no	—
465	C₂²	—	2	12	no	—
466	C₂²	—	3	4	no	—
467	C₂²	—	6	12	no	—
468	C₂²	—	9	4	no	—
469	C₂²	—	18	12	no	—
470	C₂²	—	27	24	no	—
471	C₂²	—	27	4	no	—
472	C₂²	—	27	4	no	—
473	C₂²	—	54	32	no	—
474	C₂²	—	54	32	no	—
475	C₂²	—	54	12	no	—
476	C₂²	#89039	1	4	yes	direct product factor
477	C₂²	C₂²×D₃×C₃⋊D₃	1	3	yes	—
478	C₂²	C₂²×D₃×C₃⋊D₃	1	4	yes	complemented
479	C₄	—	3	4	no	—
480	C₄	—	9	4	no	—
481	C₃	—	2	4	no	—
482	C₃	C₂²×#3811	1	4	yes	complemented
483	C₃	C₂²×D₄×C₃⋊D₃	1	1	yes	characteristic, complemented
484	C₂	—	2	4	no	—
485	C₂	—	6	4	no	—
486	C₂	—	18	4	no	—
487	C₂	—	27	8	no	—
488	C₂	—	54	4	no	—
489	C₂	C₂×#89039	1	6	yes	direct product factor
490	C₂	C₂³×D₃×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₃×C₃⋊D₃
commutator, cosocle	C₂×C₃³	C₂⁵
Frattini	C₂	C₂³×D₃×C₃⋊D₃
Fitting	C₂⁴×C₃³	C₂²
socle	C₂³×C₃³	C₂³
hypercenter	C₂⁴	D₃×C₃⋊D₃
hypocenter	C₃³	C₂³×D₄
LCS	G ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂³ ◁ C₂⁴

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₃⋊(C₃⋊D₃)	C₂	semidirect
2. C₂³×D₃×C₃⋊D₃	C₂	semidirect
3. C₂²×C₃×#638	C₂	semidirect
4. C₂²×C₃²×#67	C₂	semidirect
5. C₂×#89039	C₂	direct (N × H)
6. C₂²×#6292	C₂	semidirect
7. C₂²×#6291	C₂	semidirect
8. C₂²×#6289	C₂	semidirect
11. C₂⁴×C₃³	C₂²	semidirect
14. C₂³×C₃⋊(C₃⋊D₃)	C₂²	semidirect
15. C₂³×C₃⋊(C₃⋊D₃)	C₂²	semidirect
16. C₂³×C₃×C₃⋊D₃	C₂²	semidirect
17. C₂³×C₃²×D₃	C₂²	semidirect
19. C₂²×D₃×C₃⋊D₃	C₂²	semidirect
20. C₂×C₃×#638	C₂²	semidirect
21. C₂²×C₃×C₃⋊Dic₃	C₂²	semidirect
22. C₂×C₃²×#67	C₂²	semidirect
23. C₂²×C₃²×Dic₃	C₂²	semidirect
24. #89039	C₂²	direct (N × H)
25. C₂×#6292	C₂²	semidirect
26. C₂×#6291	C₂²	semidirect
27. C₂×#6289	C₂²	semidirect
35. C₂²×#638	D₃	semidirect
40. C₂²×C₃×#67	D₃	semidirect
47. C₂³×C₃³	C₂³	semidirect
50. C₂²×C₃⋊(C₃⋊D₃)	D₄	semidirect
52. C₂²×C₃⋊(C₃⋊D₃)	C₂³	semidirect
53. C₂²×C₃⋊(C₃⋊D₃)	C₂³	semidirect
55. C₂²×C₃×C₃⋊D₃	C₂³	semidirect
57. C₂²×C₃²×D₃	C₂³	semidirect
59. C₂×D₃×C₃⋊D₃	C₂³	semidirect
60. C₃×#638	C₂³	semidirect
61. C₂×C₃×C₃⋊Dic₃	C₂³	semidirect
62. C₃²×#67	C₂³	semidirect
63. C₂×C₃²×Dic₃	C₂³	semidirect
64. #6292	C₂³	semidirect
65. #6291	C₂³	semidirect
66. #6289	C₂³	semidirect
71. C₂⁴×C₃²	C₂×D₃	semidirect
72. C₂⁴×C₃²	C₂×D₃	semidirect
87. C₂³×C₃⋊D₃	C₂×D₃	semidirect
89. C₂³×C₃×D₃	C₂×D₃	semidirect
95. C₂×#638	C₂×D₃	semidirect
96. C₂²×C₃⋊Dic₃	C₂×D₃	semidirect
101. C₂×C₃×#67	C₂×D₃	semidirect
103. C₂²×C₃×Dic₃	C₂×D₃	semidirect
109. C₂²×C₃³	C₂×D₄	semidirect
111. C₂²×C₃³	C₂⁴	semidirect
114. C₂×C₃⋊(C₃⋊D₃)	C₂×D₄	semidirect
116. C₂×C₃⋊(C₃⋊D₃)	C₂⁴	semidirect
118. C₂×C₃×C₃⋊D₃	C₂⁴	semidirect
120. C₂×C₃²×D₃	C₂⁴	semidirect
122. C₃×C₃⋊Dic₃	C₂⁴	semidirect
123. C₃²×Dic₃	C₂⁴	semidirect
134. C₂²×#67	C₃⋊D₃	semidirect
150. C₂³×C₃²	C₂²×D₃	semidirect
151. C₂³×C₃²	C₂²×D₃	semidirect
173. C₂²×C₃⋊D₃	C₂²×D₃	semidirect
177. C₂²×C₃×D₃	C₂²×D₃	semidirect
183. #638	C₂²×D₃	semidirect
184. C₂×C₃⋊Dic₃	C₂²×D₃	semidirect
188. C₃×#67	C₂²×D₃	semidirect
190. C₂×C₃×Dic₃	C₂²×D₃	semidirect
196. C₂×C₃³	C₂²×D₄	semidirect
199. C₃⋊(C₃⋊D₃)	C₂²×D₄	semidirect
205. C₂⁴×C₃	D₃²	semidirect
206. C₂⁴×C₃	C₂×C₃⋊D₃	semidirect
224. C₂³×D₃	C₂×C₃⋊D₃	semidirect
232. C₂×#67	C₂×C₃⋊D₃	semidirect
234. C₂²×Dic₃	C₂×C₃⋊D₃	semidirect
249. C₂²×C₃²	D₃×D₄	semidirect
250. C₂²×C₃²	D₃×D₄	semidirect
253. C₂²×C₃²	C₂³×D₃	semidirect
254. C₂²×C₃²	C₂³×D₃	semidirect
272. C₂×C₃⋊D₃	C₂³×D₃	semidirect
276. C₂×C₃×D₃	C₂³×D₃	semidirect
279. C₃⋊Dic₃	C₂³×D₃	semidirect
281. C₃×Dic₃	C₂³×D₃	semidirect
290. C₃³	C₂³×D₄	semidirect
301. C₂³×C₃	C₂×D₃²	semidirect
303. C₂³×C₃	C₂²×C₃⋊D₃	semidirect
329. C₂²×D₃	C₂²×C₃⋊D₃	semidirect
337. #67	C₂²×C₃⋊D₃	semidirect
339. C₂×Dic₃	C₂²×C₃⋊D₃	semidirect
350. C₂×C₃²	C₂×D₃×D₄	semidirect
351. C₂×C₃²	C₂×D₃×D₄	semidirect
371. C₂⁴	D₃×C₃⋊D₃	semidirect
390. C₂²×C₃	#3811	semidirect
391. C₂²×C₃	D₄×C₃⋊D₃	semidirect
393. C₂²×C₃	C₂²×D₃²	semidirect
395. C₂²×C₃	C₂³×C₃⋊D₃	semidirect
416. C₂×D₃	C₂³×C₃⋊D₃	semidirect
420. Dic₃	C₂³×C₃⋊D₃	semidirect
422. C₃²	C₂²×D₃×D₄	semidirect
423. C₃²	C₂²×D₃×D₄	semidirect
438. C₂³	C₂×D₃×C₃⋊D₃	semidirect
453. C₂×C₃	C₂×#3811	semidirect
454. C₂×C₃	C₂×D₄×C₃⋊D₃	semidirect
476. C₂²	#89039	direct (N × H)
478. C₂²	C₂²×D₃×C₃⋊D₃	semidirect
482. C₃	C₂²×#3811	semidirect
483. C₃	C₂²×D₄×C₃⋊D₃	semidirect
489. C₂	C₂×#89039	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₃⋊(C₃⋊D₃)	2
C₂³×D₃×C₃⋊D₃	2
C₂²×C₃×#638	2
C₂²×C₃²×#67	2
C₂×#89039	2
C₂²×#6292	2
C₂²×#6291	2
C₂²×#6289	2
C₂²×D₄×C₃⋊D₃	3
C₂²×#3811	3

Subgroups — C22×#89039 #13181662

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#89039 #13181662