Subgroups — C₂×#11724579 #13181605

Order 1728.

6044 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#89076	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#3828	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃²×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₃×#638	C₂	1	4	yes	maximal, complemented
5	#11724579	C₂	1	16	yes	maximal, direct product factor
6	C₂×#89026	C₂	1	2	yes	maximal, complemented
7	C₂×C₃⋊D₃×D₁₂	C₂	1	2	yes	maximal, complemented
8	C₂×#89015	C₂	1	2	yes	maximal, complemented
9	C₂×#89014	C₂	1	2	yes	maximal, complemented
10	C₂×#64361	—	3	1	no	maximal
11	C₂×#64307	—	3	4	no	maximal
12	C₂³×C₃²×D₃	C₂²	1	2	yes	complemented
13	C₂²×D₃×C₃⋊D₃	C₂²	1	4	yes	complemented
14	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic, complemented
15	C₂×#6312	C₂²	1	2	yes	complemented
16	#89076	C₂²	1	8	yes	complemented
17	C₂×C₄⋊(C₃⋊(C₃⋊D₃))	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	2	yes	complemented
19	C₂×#6308	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₃×#638	C₂²	1	2	yes	complemented
21	C₃×#3828	C₂²	1	8	yes	complemented
22	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	2	yes	complemented
24	C₂×C₃×#634	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃²×D₁₂	C₂²	1	2	yes	complemented
26	C₂×C₃²×D₁₂	C₂²	1	2	yes	complemented
27	C₂×C₃²×D₁₂	C₂²	1	8	yes	complemented
28	D₃×#638	C₂²	1	32	yes	complemented
29	C₂×#6291	C₂²	1	4	yes	complemented
30	C₂×#6290	C₂²	1	4	yes	complemented
31	C₂×D₃×C₃⋊Dic₃	C₂²	1	4	yes	complemented
32	#89026	C₂²	1	16	yes	complemented
33	C₃⋊D₃×D₁₂	C₂²	1	16	yes	complemented
34	#89015	C₂²	1	16	yes	complemented
35	#89014	C₂²	1	16	yes	complemented
36	C₂²×C₃²×D₄	—	3	1	no	—
37	C₂²×#638	—	3	4	no	—
38	#64361	—	3	16	no	—
39	C₂×#3830	—	3	2	no	—
40	C₂×#3830	—	3	2	no	—
41	C₂×D₄×C₃⋊D₃	—	3	2	no	—
42	C₂×D₄×C₃⋊D₃	—	3	2	no	—
43	C₂×#3828	—	3	1	no	—
44	C₂×#3828	—	3	4	no	—
45	C₂×#3828	—	6	4	no	—
46	C₂×#3828	D₃	1	1	yes	characteristic, complemented
47	C₂×C₃×#235	—	3	4	no	—
48	C₂²×C₃×D₁₂	D₃	1	4	yes	complemented
49	C₂×D₃×#67	—	3	16	no	—
50	#64307	—	3	64	no	—
51	C₂×#3802	—	3	8	no	—
52	C₂×D₃×D₁₂	—	3	8	no	—
53	C₂×#3796	—	3	8	no	—
54	C₂×#3795	—	3	8	no	—
55	C₂³×C₃³	C₂³	1	1	yes	characteristic
56	C₂²×C₃⋊(C₃⋊D₃)	C₂³	1	2	yes	—
57	C₂²×C₃×C₃⋊D₃	C₂³	1	2	yes	—
58	C₂²×C₃²×D₃	—	4	4	no	—
59	C₂²×C₃²×D₃	C₂³	1	4	yes	—
60	C₂²×C₃²×D₃	C₂³	1	8	yes	complemented
61	C₂×D₃×C₃⋊D₃	—	4	8	no	—
62	C₂×D₃×C₃⋊D₃	C₂³	1	16	yes	complemented
63	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
64	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
65	C₂×C₃³×C₄	C₂³	1	4	yes	complemented
66	#6312	C₂³	1	8	yes	complemented
67	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	2	yes	—
68	C₄⋊(C₃⋊(C₃⋊D₃))	C₂³	1	4	yes	complemented
69	C₄×C₃⋊(C₃⋊D₃)	C₂³	1	8	yes	complemented
70	#6308	C₂³	1	4	yes	complemented
71	C₃×#638	C₂³	1	8	yes	complemented
72	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
73	C₃×C₄⋊(C₃⋊D₃)	C₂³	1	4	yes	complemented
74	C₃×C₄×C₃⋊D₃	C₂³	1	8	yes	complemented
75	C₃×#634	C₂³	1	4	yes	complemented
76	C₃²×D₁₂	C₂³	1	8	yes	complemented
77	C₃²×D₁₂	C₂³	1	8	yes	complemented
78	#6291	C₂³	1	16	yes	complemented
79	#6290	C₂³	1	16	yes	complemented
80	D₃×C₃⋊Dic₃	C₂³	1	16	yes	complemented
81	C₂×#1009	—	9	1	no	—
82	C₂×#1004	—	9	4	no	—
83	C₂⁴×C₃²	—	3	2	no	—
84	C₂³×C₃⋊D₃	—	3	4	no	—
85	C₂³×C₃×D₃	C₂×D₃	1	8	yes	complemented
86	C₂²×D₃²	—	3	16	no	—
87	C₂×C₃²×D₄	—	3	2	no	—
88	C₂×C₃²×D₄	—	3	2	no	—
89	C₂×C₃²×D₄	—	3	8	no	—
90	C₂²×C₃²×C₄	—	2	4	no	—
91	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	complemented
92	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic, complemented
93	C₂×#638	—	3	2	no	—
94	C₂×#638	—	3	8	no	—
95	C₂×#638	—	3	4	no	—
96	C₂×#638	—	3	32	no	—
97	C₂×#638	—	3	4	no	—
98	C₂×#638	—	6	8	no	—
99	C₂×#638	C₂×D₃	1	2	yes	complemented
100	C₂²×C₃⋊Dic₃	—	3	4	no	—
101	#3830	—	3	16	no	—
102	#3830	—	3	16	no	—
103	D₄×C₃⋊D₃	—	3	16	no	—
104	D₄×C₃⋊D₃	—	3	16	no	—
105	#3828	—	3	8	no	—
106	#3828	—	3	32	no	—
107	#3828	—	6	32	no	—
108	#3828	C₂×D₃	1	8	yes	complemented
109	C₂×C₄⋊(C₃⋊D₃)	—	3	1	no	—
110	C₂×C₄⋊(C₃⋊D₃)	—	3	4	no	—
111	C₂×C₄⋊(C₃⋊D₃)	—	6	4	no	—
112	C₂×C₄⋊(C₃⋊D₃)	C₂×D₃	1	1	yes	characteristic, complemented
113	C₂×C₄×C₃⋊D₃	—	3	2	no	—
114	C₂×C₄×C₃⋊D₃	—	3	8	no	—
115	C₂×C₄×C₃⋊D₃	—	6	8	no	—
116	C₂×C₄×C₃⋊D₃	C₂×D₃	1	2	yes	complemented
117	C₂×#634	—	3	1	no	—
118	C₂×#634	—	3	4	no	—
119	C₂×#634	—	6	4	no	—
120	C₂×#634	C₂×D₃	1	1	yes	characteristic, complemented
121	C₂×C₃×#67	—	3	8	no	—
122	C₃×#235	—	3	32	no	—
123	C₂×C₃×D₁₂	—	3	4	no	—
124	C₂×C₃×D₁₂	C₂×D₃	1	8	yes	complemented
125	C₂×C₃×D₁₂	C₂×D₃	1	8	yes	complemented
126	C₂×C₃×D₁₂	C₂×D₃	1	32	yes	complemented
127	C₂×C₃×C₄×D₃	—	3	8	no	—
128	C₂×C₃×Dic₆	—	3	4	no	—
129	D₃×#67	—	3	128	no	—
130	C₂×#626	—	3	16	no	—
131	C₂×#625	—	3	16	no	—
132	C₂×D₃×Dic₃	—	3	16	no	—
133	#3802	—	3	64	no	—
134	D₃×D₁₂	—	3	64	no	—
135	#3796	—	3	64	no	—
136	#3795	—	3	64	no	—
137	C₂²×C₃³	—	2	2	no	—
138	C₂²×C₃³	C₂⁴	1	2	yes	—
139	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
140	C₂×C₃⋊(C₃⋊D₃)	—	2	4	no	—
141	C₂×C₃⋊(C₃⋊D₃)	C₂⁴	1	4	yes	—
142	C₂×C₃×C₃⋊D₃	—	2	4	no	—
143	C₂×C₃×C₃⋊D₃	C₂⁴	1	4	yes	—
144	C₂×C₃²×D₃	—	2	8	no	—
145	C₂×C₃²×D₃	—	4	8	no	—
146	C₂×C₃²×D₃	C₂⁴	1	8	yes	—
147	D₃×C₃⋊D₃	—	4	16	no	—
148	C₃³×C₄	C₂⁴	1	2	yes	—
149	C₃³×C₄	C₂⁴	1	2	yes	—
150	C₃⋊(C₃⋊Dic₃)	C₂⁴	1	4	yes	—
151	C₃×C₃⋊Dic₃	C₂⁴	1	4	yes	—
152	C₂×C₃×#41	—	9	1	no	—
153	C₂²×C₃×D₄	—	3	4	no	—
154	C₂²×#67	—	9	16	no	—
155	#1009	—	9	16	no	—
156	C₂×#239	—	9	2	no	—
157	#1004	—	9	64	no	—
158	C₂×#237	—	9	8	no	—
159	C₂×#237	—	9	8	no	—
160	C₂×D₃×D₄	—	9	8	no	—
161	C₂×D₃×D₄	—	9	8	no	—
162	C₂×D₃×D₄	—	9	4	no	—
163	C₂×D₃×D₄	—	9	2	no	—
164	C₂×#235	—	3	4	no	—
165	C₂×#235	—	9	4	no	—
166	C₂×#235	—	9	1	no	—
167	C₂×#235	—	9	2	no	—
168	C₂×#235	—	18	4	no	—
169	C₂²×D₁₂	—	9	2	no	—
170	C₂²×D₁₂	C₃⋊D₃	1	1	yes	characteristic, complemented
171	C₂³×C₃²	—	2	4	no	—
172	C₂³×C₃²	—	3	4	no	—
173	C₂³×C₃²	—	3	8	no	—
174	C₂³×C₃²	—	12	4	no	—
175	C₂³×C₃²	C₂²×D₃	1	4	yes	—
176	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
177	C₂²×C₃⋊D₃	—	3	2	no	—
178	C₂²×C₃⋊D₃	—	3	16	no	—
179	C₂²×C₃⋊D₃	—	3	8	no	—
180	C₂²×C₃⋊D₃	—	6	8	no	—
181	C₂²×C₃⋊D₃	—	12	8	no	—
182	C₂²×C₃⋊D₃	C₂²×D₃	1	2	yes	—
183	C₂²×C₃×D₃	—	3	8	no	—
184	C₂²×C₃×D₃	—	4	16	no	—
185	C₂²×C₃×D₃	C₂²×D₃	1	16	yes	—
186	C₂²×C₃×D₃	C₂²×D₃	1	32	yes	complemented
187	C₂×D₃²	—	3	64	no	—
188	C₂×D₃²	—	12	32	no	—
189	C₃²×D₄	—	3	8	no	—
190	C₃²×D₄	—	3	8	no	—
191	C₂×C₃²×C₄	—	2	4	no	—
192	C₂×C₃²×C₄	—	2	4	no	—
193	C₂×C₃²×C₄	—	2	16	no	—
194	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
195	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
196	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
197	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
198	C₂×C₃²×C₄	C₂²×D₃	1	16	yes	complemented
199	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	complemented
200	#638	—	3	8	no	—
201	#638	—	3	16	no	—
202	#638	—	3	16	no	—
203	#638	—	3	32	no	—
204	#638	—	6	32	no	—
205	#638	C₂²×D₃	1	8	yes	complemented
206	C₂×C₃⋊Dic₃	—	3	2	no	—
207	C₂×C₃⋊Dic₃	—	3	16	no	—
208	C₂×C₃⋊Dic₃	—	3	8	no	—
209	C₂×C₃⋊Dic₃	—	6	8	no	—
210	C₂×C₃⋊Dic₃	C₂²×D₃	1	2	yes	—
211	C₄⋊(C₃⋊D₃)	—	3	4	no	—
212	C₄⋊(C₃⋊D₃)	—	3	16	no	—
213	C₄⋊(C₃⋊D₃)	—	6	16	no	—
214	C₄⋊(C₃⋊D₃)	C₂²×D₃	1	4	yes	complemented
215	C₄×C₃⋊D₃	—	3	8	no	—
216	C₄×C₃⋊D₃	—	3	32	no	—
217	C₄×C₃⋊D₃	—	6	32	no	—
218	C₄×C₃⋊D₃	C₂²×D₃	1	8	yes	complemented
219	#634	—	3	4	no	—
220	#634	—	3	16	no	—
221	#634	—	6	16	no	—
222	#634	C₂²×D₃	1	4	yes	complemented
223	C₃×#67	—	3	32	no	—
224	C₂×C₃×Dic₃	—	3	8	no	—
225	C₃×D₁₂	—	3	16	no	—
226	C₃×D₁₂	C₂²×D₃	1	32	yes	complemented
227	C₃×D₁₂	C₂²×D₃	1	32	yes	complemented
228	C₃×C₄×D₃	—	3	32	no	—
229	C₃×Dic₆	—	3	16	no	—
230	#626	—	3	64	no	—
231	#625	—	3	64	no	—
232	D₃×Dic₃	—	3	64	no	—
233	C₂×H(5,𝔽₂)	—	27	1	no	Sylow
234	C₂×C₃³	—	2	2	no	—
235	C₂×C₃³	H(5,𝔽₂)	1	2	yes	complemented
236	C₂×C₃³	C₂⁵	1	1	yes	characteristic
237	C₃⋊(C₃⋊D₃)	—	2	4	no	—
238	C₃×C₃⋊D₃	—	2	4	no	—
239	C₃²×D₃	—	2	8	no	—
240	C₂⁴×C₃	—	3	8	no	—
241	C₂³×D₃	—	9	16	no	—
242	C₂³×D₃	—	9	4	no	—
243	C₂³×D₃	C₂×C₃⋊D₃	1	2	yes	complemented
244	C₃×#41	—	9	8	no	—
245	C₂×C₃×Q₈	—	9	1	no	—
246	C₂×C₃×D₄	—	3	8	no	—
247	C₂×C₃×D₄	—	3	8	no	—
248	C₂×C₃×D₄	—	3	32	no	—
249	C₂×C₃×D₄	—	9	2	no	—
250	C₂×C₃×D₄	—	9	1	no	—
251	C₂²×C₃×C₄	—	2	4	no	—
252	C₂²×C₃×C₄	—	9	2	no	—
253	C₂²×C₃×C₄	D₃²	1	4	yes	complemented
254	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
255	C₂×#67	—	3	8	no	—
256	C₂×#67	—	9	16	no	—
257	C₂×#67	—	9	128	no	—
258	C₂×#67	—	9	16	no	—
259	C₂×#67	—	9	8	no	—
260	C₂×#67	—	9	2	no	—
261	C₂×#67	—	9	4	no	—
262	C₂×#67	—	18	8	no	—
263	C₂²×Dic₃	—	9	16	no	—
264	#239	—	9	16	no	—
265	#237	—	9	64	no	—
266	#237	—	9	64	no	—
267	D₃×D₄	—	9	64	no	—
268	D₃×D₄	—	9	64	no	—
269	D₃×D₄	—	9	32	no	—
270	D₃×D₄	—	9	16	no	—
271	#235	—	3	32	no	—
272	#235	—	9	32	no	—
273	#235	—	9	8	no	—
274	#235	—	9	16	no	—
275	#235	—	18	32	no	—
276	C₂×D₁₂	—	3	4	no	—
277	C₂×D₁₂	—	9	4	no	—
278	C₂×D₁₂	—	9	4	no	—
279	C₂×D₁₂	—	9	1	no	—
280	C₂×D₁₂	—	9	16	no	—
281	C₂×D₁₂	—	18	4	no	—
282	C₂×D₁₂	C₂×C₃⋊D₃	1	2	yes	complemented
283	C₂×D₁₂	C₂×C₃⋊D₃	1	2	yes	complemented
284	C₂×D₁₂	C₂×C₃⋊D₃	1	8	yes	complemented
285	C₂×C₄×D₃	—	3	8	no	—
286	C₂×C₄×D₃	—	9	4	no	—
287	C₂×C₄×D₃	—	9	8	no	—
288	C₂×C₄×D₃	—	9	2	no	—
289	C₂×C₄×D₃	—	18	8	no	—
290	C₂×Dic₆	—	3	4	no	—
291	C₂×Dic₆	—	9	4	no	—
292	C₂×Dic₆	—	9	1	no	—
293	C₂×Dic₆	—	18	4	no	—
294	C₂²×C₃²	—	2	2	no	—
295	C₂²×C₃²	—	2	4	no	—
296	C₂²×C₃²	—	2	8	no	—
297	C₂²×C₃²	—	2	8	no	—
298	C₂²×C₃²	—	3	8	no	—
299	C₂²×C₃²	—	4	8	no	—
300	C₂²×C₃²	—	6	8	no	—
301	C₂²×C₃²	—	12	8	no	—
302	C₂²×C₃²	C₂³×D₃	1	8	yes	—
303	C₂²×C₃²	C₂³×D₃	1	4	yes	—
304	C₂²×C₃²	C₂³×D₃	1	2	yes	—
305	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
306	C₂×C₃⋊D₃	—	2	4	no	—
307	C₂×C₃⋊D₃	—	3	4	no	—
308	C₂×C₃⋊D₃	—	3	16	no	—
309	C₂×C₃⋊D₃	—	6	16	no	—
310	C₂×C₃⋊D₃	—	6	4	no	—
311	C₂×C₃⋊D₃	—	6	16	no	—
312	C₂×C₃⋊D₃	—	12	16	no	—
313	C₂×C₃⋊D₃	—	12	16	no	—
314	C₂×C₃⋊D₃	C₂³×D₃	1	4	yes	—
315	C₂×C₃×D₃	—	2	32	no	—
316	C₂×C₃×D₃	—	3	16	no	—
317	C₂×C₃×D₃	—	4	32	no	—
318	C₂×C₃×D₃	—	6	16	no	—
319	C₂×C₃×D₃	C₂³×D₃	1	32	yes	—
320	D₃²	—	12	64	no	—
321	C₃²×C₄	—	2	8	no	—
322	C₃²×C₄	—	2	8	no	—
323	C₃²×C₄	C₂³×D₃	1	8	yes	—
324	C₃²×C₄	C₂³×D₃	1	8	yes	—
325	C₃²×C₄	C₂³×D₃	1	2	yes	—
326	C₃²×C₄	C₂³×D₃	1	2	yes	—
327	C₃⋊Dic₃	—	3	4	no	—
328	C₃⋊Dic₃	—	3	16	no	—
329	C₃⋊Dic₃	—	6	16	no	—
330	C₃⋊Dic₃	C₂³×D₃	1	4	yes	—
331	C₃×Dic₃	—	3	16	no	—
332	H(5,𝔽₂)	—	27	16	no	—
333	C₂×#41	—	9	1	no	—
334	C₂×#41	—	27	2	no	—
335	C₂×#41	—	27	2	no	—
336	C₂×#41	—	27	1	no	—
337	C₂²×D₄	—	3	1	no	—
338	C₂²×D₄	—	27	2	no	—
339	C₂²×D₄	—	27	2	no	—
340	C₂²×D₄	—	27	4	no	—
341	C₃³	C₂×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
342	C₂³×C₃	—	2	4	no	—
343	C₂³×C₃	—	3	16	no	—
344	C₂³×C₃	—	3	32	no	—
345	C₂³×C₃	—	9	2	no	—
346	C₂³×C₃	—	12	16	no	—
347	C₂³×C₃	C₂×D₃²	1	4	yes	—
348	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
349	C₂²×D₃	—	3	8	no	—
350	C₂²×D₃	—	4	4	no	—
351	C₂²×D₃	—	9	64	no	—
352	C₂²×D₃	—	9	8	no	—
353	C₂²×D₃	—	9	2	no	—
354	C₂²×D₃	—	9	16	no	—
355	C₂²×D₃	—	18	8	no	—
356	C₂²×D₃	—	36	8	no	—
357	C₂²×D₃	—	36	32	no	—
358	C₂²×D₃	C₂²×C₃⋊D₃	1	4	yes	—
359	C₂²×D₃	C₂²×C₃⋊D₃	1	8	yes	complemented
360	C₃×Q₈	—	9	4	no	—
361	C₃×D₄	—	3	32	no	—
362	C₃×D₄	—	3	32	no	—
363	C₃×D₄	—	9	8	no	—
364	C₃×D₄	—	9	4	no	—
365	C₂×C₃×C₄	—	2	4	no	—
366	C₂×C₃×C₄	—	2	4	no	—
367	C₂×C₃×C₄	—	2	16	no	—
368	C₂×C₃×C₄	—	9	2	no	—
369	C₂×C₃×C₄	—	9	8	no	—
370	C₂×C₃×C₄	C₂×D₃²	1	4	yes	—
371	C₂×C₃×C₄	C₂×D₃²	1	4	yes	—
372	C₂×C₃×C₄	C₂×D₃²	1	16	yes	complemented
373	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
374	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
375	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	4	yes	complemented
376	#67	—	3	32	no	—
377	#67	—	9	64	no	—
378	#67	—	9	64	no	—
379	#67	—	9	32	no	—
380	#67	—	9	8	no	—
381	#67	—	9	16	no	—
382	#67	—	18	32	no	—
383	C₂×Dic₃	—	3	8	no	—
384	C₂×Dic₃	—	9	64	no	—
385	C₂×Dic₃	—	9	8	no	—
386	C₂×Dic₃	—	9	2	no	—
387	C₂×Dic₃	—	18	8	no	—
388	D₁₂	—	3	16	no	—
389	D₁₂	—	9	16	no	—
390	D₁₂	—	9	16	no	—
391	D₁₂	—	9	4	no	—
392	D₁₂	—	18	16	no	—
393	D₁₂	C₂²×C₃⋊D₃	1	8	yes	complemented
394	D₁₂	C₂²×C₃⋊D₃	1	8	yes	complemented
395	C₄×D₃	—	3	32	no	—
396	C₄×D₃	—	9	16	no	—
397	C₄×D₃	—	9	32	no	—
398	C₄×D₃	—	9	8	no	—
399	C₄×D₃	—	18	32	no	—
400	Dic₆	—	3	16	no	—
401	Dic₆	—	9	16	no	—
402	Dic₆	—	9	4	no	—
403	Dic₆	—	18	16	no	—
404	C₂×C₃²	—	2	2	no	—
405	C₂×C₃²	—	2	8	no	—
406	C₂×C₃²	—	2	4	no	—
407	C₂×C₃²	—	2	8	no	—
408	C₂×C₃²	—	4	8	no	—
409	C₂×C₃²	—	6	8	no	—
410	C₂×C₃²	#1004	1	8	yes	complemented
411	C₂×C₃²	#1009	1	2	yes	complemented
412	C₂×C₃²	C₂⁴×D₃	1	4	yes	—
413	C₂×C₃²	C₂⁴×D₃	1	1	yes	characteristic
414	C₃⋊D₃	—	2	4	no	—
415	C₃⋊D₃	—	6	4	no	—
416	C₃⋊D₃	—	6	16	no	—
417	C₃⋊D₃	—	12	16	no	—
418	C₃×D₃	—	2	32	no	—
419	C₃×D₃	—	6	16	no	—
420	C₂⁴	—	3	2	no	—
421	C₂⁴	—	27	4	no	—
422	#41	—	9	8	no	—
423	#41	—	27	16	no	—
424	#41	—	27	16	no	—
425	#41	—	27	8	no	—
426	C₂×Q₈	—	9	1	no	—
427	C₂×Q₈	—	27	1	no	—
428	C₂×D₄	—	3	2	no	—
429	C₂×D₄	—	3	2	no	—
430	C₂×D₄	—	3	8	no	—
431	C₂×D₄	—	9	2	no	—
432	C₂×D₄	—	9	1	no	—
433	C₂×D₄	—	27	16	no	—
434	C₂×D₄	—	27	4	no	—
435	C₂×D₄	—	27	16	no	—
436	C₂×D₄	—	27	32	no	—
437	C₂×D₄	—	27	4	no	—
438	C₂×D₄	—	27	2	no	—
439	C₂×D₄	—	27	1	no	—
440	C₂²×C₄	—	9	2	no	—
441	C₂²×C₄	—	27	4	no	—
442	C₂²×C₄	—	27	2	no	—
443	C₂²×C₄	D₃×C₃⋊D₃	1	1	yes	characteristic, complemented
444	C₂²×C₃	—	2	8	no	—
445	C₂²×C₃	—	2	2	no	—
446	C₂²×C₃	—	2	8	no	—
447	C₂²×C₃	—	2	4	no	—
448	C₂²×C₃	—	3	32	no	—
449	C₂²×C₃	—	4	8	no	—
450	C₂²×C₃	—	6	32	no	—
451	C₂²×C₃	—	9	4	no	—
452	C₂²×C₃	—	12	32	no	—
453	C₂²×C₃	—	18	4	no	—
454	C₂²×C₃	C₂²×D₃²	1	8	yes	—
455	C₂²×C₃	C₂²×D₃²	1	4	yes	—
456	C₂²×C₃	C₂³×C₃⋊D₃	1	2	yes	—
457	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
458	C₂×D₃	—	2	8	no	—
459	C₂×D₃	—	3	16	no	—
460	C₂×D₃	—	4	8	no	—
461	C₂×D₃	—	6	16	no	—
462	C₂×D₃	—	9	16	no	—
463	C₂×D₃	—	9	4	no	—
464	C₂×D₃	—	18	16	no	—
465	C₂×D₃	—	18	16	no	—
466	C₂×D₃	—	18	4	no	—
467	C₂×D₃	—	36	16	no	—
468	C₂×D₃	—	36	16	no	—
469	C₂×D₃	—	36	64	no	—
470	C₂×D₃	C₂³×C₃⋊D₃	1	8	yes	—
471	C₃×C₄	—	2	8	no	—
472	C₃×C₄	—	2	8	no	—
473	C₃×C₄	—	9	4	no	—
474	C₃×C₄	C₂²×D₃²	1	8	yes	—
475	C₃×C₄	C₂²×D₃²	1	8	yes	—
476	C₃×C₄	C₂³×C₃⋊D₃	1	2	yes	—
477	C₃×C₄	C₂³×C₃⋊D₃	1	2	yes	—
478	Dic₃	—	3	16	no	—
479	Dic₃	—	9	16	no	—
480	Dic₃	—	9	4	no	—
481	Dic₃	—	18	16	no	—
482	C₃²	—	2	4	no	—
483	C₃²	C₂×#1004	1	4	yes	complemented
484	C₃²	C₂×#1009	1	1	yes	characteristic, complemented
485	C₂³	—	3	4	no	—
486	C₂³	—	3	8	no	—
487	C₂³	—	9	2	no	—
488	C₂³	—	12	4	no	—
489	C₂³	—	27	16	no	—
490	C₂³	—	27	2	no	—
491	C₂³	—	108	8	no	—
492	C₂³	C₂×D₃×C₃⋊D₃	1	1	yes	characteristic
493	Q₈	—	9	4	no	—
494	Q₈	—	27	4	no	—
495	D₄	—	3	8	no	—
496	D₄	—	3	8	no	—
497	D₄	—	9	8	no	—
498	D₄	—	9	4	no	—
499	D₄	—	27	16	no	—
500	D₄	—	27	16	no	—
501	D₄	—	27	8	no	—
502	D₄	—	27	4	no	—
503	C₂×C₄	—	9	2	no	—
504	C₂×C₄	—	9	8	no	—
505	C₂×C₄	—	27	16	no	—
506	C₂×C₄	—	27	2	no	—
507	C₂×C₄	—	27	8	no	—
508	C₂×C₄	C₂×D₃×C₃⋊D₃	1	1	yes	characteristic
509	C₂×C₄	C₂×D₃×C₃⋊D₃	1	1	yes	characteristic
510	C₂×C₄	C₂×D₃×C₃⋊D₃	1	4	yes	complemented
511	C₂×C₃	—	2	8	no	—
512	C₂×C₃	—	2	2	no	—
513	C₂×C₃	—	2	8	no	—
514	C₂×C₃	—	2	4	no	—
515	C₂×C₃	—	4	8	no	—
516	C₂×C₃	—	6	32	no	—
517	C₂×C₃	—	18	4	no	—
518	C₂×C₃	#64307	1	8	yes	complemented
519	C₂×C₃	#64361	1	2	yes	complemented
520	C₂×C₃	C₂³×D₃²	1	4	yes	—
521	C₂×C₃	C₂⁴×C₃⋊D₃	1	1	yes	characteristic
522	D₃	—	2	8	no	—
523	D₃	—	6	16	no	—
524	D₃	—	18	16	no	—
525	D₃	—	18	4	no	—
526	D₃	—	36	16	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	3	8	no	—
529	C₂²	—	6	8	no	—
530	C₂²	—	9	4	no	—
531	C₂²	—	12	8	no	—
532	C₂²	—	18	4	no	—
533	C₂²	—	27	4	no	—
534	C₂²	—	54	4	no	—
535	C₂²	—	108	16	no	—
536	C₂²	C₂²×D₃×C₃⋊D₃	1	2	yes	—
537	C₂²	C₂²×D₃×C₃⋊D₃	1	1	yes	characteristic
538	C₄	—	9	4	no	—
539	C₄	—	27	4	no	—
540	C₄	C₂²×D₃×C₃⋊D₃	1	2	yes	—
541	C₄	C₂²×D₃×C₃⋊D₃	1	2	yes	—
542	C₃	—	2	4	no	—
543	C₃	C₂×#64307	1	4	yes	complemented
544	C₃	C₂×#64361	1	1	yes	characteristic, complemented
545	C₂	—	2	2	no	—
546	C₂	—	6	8	no	—
547	C₂	—	18	4	no	—
548	C₂	—	54	4	no	—
549	C₂	#11724579	1	2	yes	direct product factor
550	C₂	C₂³×D₃×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₃×C₃⋊D₃
commutator, cosocle	C₂×C₃³	C₂⁵
Frattini	C₂	C₂³×D₃×C₃⋊D₃
Fitting	C₂²×C₃³×C₄	C₂²
socle	C₂²×C₃³	C₂⁴
hypercenter	C₂²×C₄	D₃×C₃⋊D₃
hypocenter	C₃³	C₂×H(5,𝔽₂)
LCS	G ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂² ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. C₂×#89076	C₂	semidirect
2. C₂×C₃×#3828	C₂	semidirect
3. C₂²×C₃²×D₁₂	C₂	semidirect
4. C₂×D₃×#638	C₂	semidirect
5. #11724579	C₂	direct (N × H)
6. C₂×#89026	C₂	semidirect
7. C₂×C₃⋊D₃×D₁₂	C₂	semidirect
8. C₂×#89015	C₂	semidirect
9. C₂×#89014	C₂	semidirect
12. C₂³×C₃²×D₃	C₂²	semidirect
13. C₂²×D₃×C₃⋊D₃	C₂²	semidirect
14. C₂²×C₃³×C₄	C₂²	semidirect
15. C₂×#6312	C₂²	semidirect
16. #89076	C₂²	semidirect
17. C₂×C₄⋊(C₃⋊(C₃⋊D₃))	C₂²	semidirect
18. C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	semidirect
19. C₂×#6308	C₂²	semidirect
20. C₂×C₃×#638	C₂²	semidirect
21. C₃×#3828	C₂²	semidirect
22. C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	semidirect
23. C₂×C₃×C₄×C₃⋊D₃	C₂²	semidirect
24. C₂×C₃×#634	C₂²	semidirect
25. C₂×C₃²×D₁₂	C₂²	semidirect
26. C₂×C₃²×D₁₂	C₂²	semidirect
27. C₂×C₃²×D₁₂	C₂²	semidirect
28. D₃×#638	C₂²	semidirect
29. C₂×#6291	C₂²	semidirect
30. C₂×#6290	C₂²	semidirect
31. C₂×D₃×C₃⋊Dic₃	C₂²	semidirect
32. #89026	C₂²	semidirect
33. C₃⋊D₃×D₁₂	C₂²	semidirect
34. #89015	C₂²	semidirect
35. #89014	C₂²	semidirect
46. C₂×#3828	D₃	semidirect
48. C₂²×C₃×D₁₂	D₃	semidirect
60. C₂²×C₃²×D₃	C₂³	semidirect
62. C₂×D₃×C₃⋊D₃	C₂³	semidirect
65. C₂×C₃³×C₄	C₂³	semidirect
66. #6312	C₂³	semidirect
68. C₄⋊(C₃⋊(C₃⋊D₃))	C₂³	semidirect
69. C₄×C₃⋊(C₃⋊D₃)	C₂³	semidirect
70. #6308	C₂³	semidirect
71. C₃×#638	C₂³	semidirect
73. C₃×C₄⋊(C₃⋊D₃)	C₂³	semidirect
74. C₃×C₄×C₃⋊D₃	C₂³	semidirect
75. C₃×#634	C₂³	semidirect
76. C₃²×D₁₂	C₂³	semidirect
77. C₃²×D₁₂	C₂³	semidirect
78. #6291	C₂³	semidirect
79. #6290	C₂³	semidirect
80. D₃×C₃⋊Dic₃	C₂³	semidirect
85. C₂³×C₃×D₃	C₂×D₃	semidirect
91. C₂²×C₃²×C₄	C₂×D₃	semidirect
92. C₂²×C₃²×C₄	C₂×D₃	semidirect
99. C₂×#638	C₂×D₃	semidirect
108. #3828	C₂×D₃	semidirect
112. C₂×C₄⋊(C₃⋊D₃)	C₂×D₃	semidirect
116. C₂×C₄×C₃⋊D₃	C₂×D₃	semidirect
120. C₂×#634	C₂×D₃	semidirect
124. C₂×C₃×D₁₂	C₂×D₃	semidirect
125. C₂×C₃×D₁₂	C₂×D₃	semidirect
126. C₂×C₃×D₁₂	C₂×D₃	semidirect
170. C₂²×D₁₂	C₃⋊D₃	semidirect
186. C₂²×C₃×D₃	C₂²×D₃	semidirect
198. C₂×C₃²×C₄	C₂²×D₃	semidirect
199. C₂×C₃²×C₄	C₂²×D₃	semidirect
205. #638	C₂²×D₃	semidirect
214. C₄⋊(C₃⋊D₃)	C₂²×D₃	semidirect
218. C₄×C₃⋊D₃	C₂²×D₃	semidirect
222. #634	C₂²×D₃	semidirect
226. C₃×D₁₂	C₂²×D₃	semidirect
227. C₃×D₁₂	C₂²×D₃	semidirect
235. C₂×C₃³	H(5,𝔽₂)	semidirect
243. C₂³×D₃	C₂×C₃⋊D₃	semidirect
253. C₂²×C₃×C₄	D₃²	semidirect
254. C₂²×C₃×C₄	C₂×C₃⋊D₃	semidirect
282. C₂×D₁₂	C₂×C₃⋊D₃	semidirect
283. C₂×D₁₂	C₂×C₃⋊D₃	semidirect
284. C₂×D₁₂	C₂×C₃⋊D₃	semidirect
341. C₃³	C₂×H(5,𝔽₂)	semidirect
359. C₂²×D₃	C₂²×C₃⋊D₃	semidirect
372. C₂×C₃×C₄	C₂×D₃²	semidirect
375. C₂×C₃×C₄	C₂²×C₃⋊D₃	semidirect
393. D₁₂	C₂²×C₃⋊D₃	semidirect
394. D₁₂	C₂²×C₃⋊D₃	semidirect
410. C₂×C₃²	#1004	semidirect
411. C₂×C₃²	#1009	semidirect
443. C₂²×C₄	D₃×C₃⋊D₃	semidirect
483. C₃²	C₂×#1004	semidirect
484. C₃²	C₂×#1009	semidirect
510. C₂×C₄	C₂×D₃×C₃⋊D₃	semidirect
518. C₂×C₃	#64307	semidirect
519. C₂×C₃	#64361	semidirect
543. C₃	C₂×#64307	semidirect
544. C₃	C₂×#64361	semidirect
549. C₂	#11724579	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#89076	2
C₂×C₃×#3828	2
C₂²×C₃²×D₁₂	2
C₂×D₃×#638	2
#11724579	2
C₂×#89026	2
C₂×C₃⋊D₃×D₁₂	2
C₂×#89015	2
C₂×#89014	2
C₂×#64361	3
C₂×#64307	3

Subgroups — C2×#11724579 #13181605

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11724579 #13181605