Subgroups — C₂×C₃²×#930 #13179167

Order 1728.

3500 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃³×C₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃²×#67	C₂	1	2	yes	maximal, complemented
3	C₂²×C₃²×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#930	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃²×(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal, complemented
6	C₂×C₃²×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃²×#121	—	3	1	no	maximal
8	C₂×C₃×#930	C₃	1	4	yes	maximal, direct product factor
9	C₂⁴×C₃³	C₂²	1	1	yes	characteristic
10	C₂³×C₃²×D₃	C₂²	1	2	yes	—
11	C₂²×C₃³×C₄	—	2	4	no	—
12	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
13	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
14	C₂²×C₃³×C₄	C₂²	1	4	yes	complemented
15	C₂×C₃²×#67	—	2	8	no	—
16	C₂×C₃²×#67	C₂²	1	8	yes	complemented
17	C₂²×C₃²×Dic₃	C₂²	1	2	yes	—
18	C₂×C₃²×D₁₂	—	2	4	no	—
19	C₂×C₃²×D₁₂	C₂²	1	4	yes	complemented
20	C₃²×(C₂×D₃)⋊C₄	C₂²	1	8	yes	complemented
21	C₃²×C₄⋊Dic₃	C₂²	1	4	yes	complemented
22	C₂²×C₃²×D₄	—	3	1	no	—
23	C₂²×C₃²×D₄	—	3	2	no	—
24	C₂³×C₃²×C₄	—	2	4	no	—
25	C₂³×C₃²×C₄	D₃	1	1	yes	characteristic, complemented
26	C₂³×C₃²×C₄	C₂×C₃	1	4	yes	complemented
27	C₂²×C₃×#67	C₂×C₃	1	8	yes	complemented
28	C₂²×C₃×D₁₂	C₂×C₃	1	4	yes	complemented
29	C₃²×#121	—	3	8	no	—
30	C₂×C₃²×C₄⋊C₄	—	3	1	no	—
31	C₂×C₃²×C₂²⋊C₄	—	3	2	no	—
32	C₃×#930	C₂×C₃	1	32	yes	direct product factor
33	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	8	yes	complemented
34	C₂×C₃×C₄⋊Dic₃	C₂×C₃	1	4	yes	complemented
35	C₂³×C₃³	—	2	2	no	—
36	C₂³×C₃³	—	2	2	no	—
37	C₂³×C₃³	D₄	1	4	yes	complemented
38	C₂³×C₃³	C₂³	1	2	yes	—
39	C₂³×C₃³	C₂³	1	1	yes	characteristic
40	C₂²×C₃²×D₃	—	2	4	no	—
41	C₂²×C₃²×D₃	—	2	4	no	—
42	C₂²×C₃²×D₃	—	2	4	no	—
43	C₂²×C₃²×D₃	C₂³	1	4	yes	—
44	C₂×C₃³×C₄	—	2	2	no	—
45	C₂×C₃³×C₄	—	2	8	no	—
46	C₂×C₃³×C₄	D₄	1	4	yes	complemented
47	C₂×C₃³×C₄	C₂³	1	2	yes	—
48	C₂×C₃³×C₄	C₂³	1	2	yes	—
49	C₃²×#67	—	2	16	no	—
50	C₂×C₃²×Dic₃	—	2	4	no	—
51	C₂×C₃²×Dic₃	C₂³	1	4	yes	—
52	C₃²×D₁₂	—	2	8	no	—
53	C₂×C₃×#121	—	3	4	no	—
54	C₂×#930	C₃²	1	1	yes	characteristic, direct product factor
55	C₂⁴×C₃²	—	2	4	no	—
56	C₂⁴×C₃²	—	3	2	no	—
57	C₂⁴×C₃²	C₂×D₃	1	1	yes	characteristic
58	C₂⁴×C₃²	C₂²×C₃	1	4	yes	—
59	C₂³×C₃×D₃	C₂²×C₃	1	8	yes	—
60	C₂×C₃²×D₄	—	3	8	no	—
61	C₂×C₃²×D₄	—	3	4	no	—
62	C₂×C₃²×D₄	—	6	8	no	—
63	C₂×C₃²×D₄	—	6	4	no	—
64	C₂²×C₃²×C₄	—	2	32	no	—
65	C₂²×C₃²×C₄	—	2	4	no	—
66	C₂²×C₃²×C₄	—	2	4	no	—
67	C₂²×C₃²×C₄	—	2	16	no	—
68	C₂²×C₃²×C₄	—	2	4	no	—
69	C₂²×C₃²×C₄	—	2	16	no	—
70	C₂²×C₃²×C₄	—	3	2	no	—
71	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
72	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
73	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	complemented
74	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
75	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
76	C₂²×C₃²×C₄	C₂²×C₃	1	16	yes	complemented
77	C₂×C₃×#67	—	2	32	no	—
78	C₂×C₃×#67	C₂²×C₃	1	32	yes	complemented
79	C₂²×C₃×Dic₃	C₂²×C₃	1	8	yes	—
80	C₂×C₃×D₁₂	—	2	16	no	—
81	C₂×C₃×D₁₂	C₂²×C₃	1	16	yes	complemented
82	C₃²×C₄⋊C₄	—	3	4	no	—
83	C₃²×C₂²⋊C₄	—	3	8	no	—
84	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	32	yes	complemented
85	C₃×C₄⋊Dic₃	C₂²×C₃	1	16	yes	complemented
86	C₂²×C₃³	—	2	8	no	—
87	C₂²×C₃³	—	2	2	no	—
88	C₂²×C₃³	—	2	2	no	—
89	C₂²×C₃³	C₂×D₄	1	2	yes	—
90	C₂²×C₃³	C₂×D₄	1	2	yes	—
91	C₂²×C₃³	C₂×D₄	1	4	yes	complemented
92	C₂²×C₃³	#41	1	2	yes	—
93	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
94	C₂×C₃²×D₃	—	2	4	no	—
95	C₂×C₃²×D₃	—	2	4	no	—
96	C₂×C₃²×D₃	—	2	4	no	—
97	C₂×C₃²×D₃	—	4	8	no	—
98	C₃³×C₄	—	2	2	no	—
99	C₃³×C₄	C₂×D₄	1	4	yes	complemented
100	C₃²×Dic₃	—	2	4	no	—
101	C₂²×C₃×D₄	—	3	8	no	—
102	C₂²×C₃×D₄	—	3	4	no	—
103	C₂³×C₃×C₄	—	2	4	no	—
104	C₂³×C₃×C₄	C₃×D₃	1	4	yes	complemented
105	C₂³×C₃×C₄	C₂×C₃²	1	1	yes	characteristic, complemented
106	C₂²×#67	C₂×C₃²	1	2	yes	complemented
107	C₂²×D₁₂	C₂×C₃²	1	1	yes	characteristic, complemented
108	C₃×#121	—	3	32	no	—
109	C₂×C₃×C₄⋊C₄	—	3	4	no	—
110	C₂×C₃×C₂²⋊C₄	—	3	8	no	—
111	#930	C₂×C₃²	1	8	yes	direct product factor
112	C₂×(C₂×D₃)⋊C₄	C₂×C₃²	1	2	yes	complemented
113	C₂×C₄⋊Dic₃	C₂×C₃²	1	1	yes	characteristic, complemented
114	C₂³×C₃²	—	2	16	no	—
115	C₂³×C₃²	—	2	16	no	—
116	C₂³×C₃²	—	2	2	no	—
117	C₂³×C₃²	—	2	2	no	—
118	C₂³×C₃²	—	2	8	no	—
119	C₂³×C₃²	—	2	8	no	—
120	C₂³×C₃²	—	2	16	no	—
121	C₂³×C₃²	—	2	8	no	—
122	C₂³×C₃²	—	2	4	no	—
123	C₂³×C₃²	—	3	4	no	—
124	C₂³×C₃²	—	6	4	no	—
125	C₂³×C₃²	—	6	4	no	—
126	C₂³×C₃²	—	6	4	no	—
127	C₂³×C₃²	D₁₂	1	4	yes	complemented
128	C₂³×C₃²	C₃×D₄	1	16	yes	complemented
129	C₂³×C₃²	C₂²×D₃	1	2	yes	—
130	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
131	C₂³×C₃²	C₂³×C₃	1	8	yes	—
132	C₂³×C₃²	C₂³×C₃	1	4	yes	—
133	C₂²×C₃×D₃	—	2	16	no	—
134	C₂²×C₃×D₃	—	2	16	no	—
135	C₂²×C₃×D₃	—	2	16	no	—
136	C₂²×C₃×D₃	C₂³×C₃	1	16	yes	—
137	C₃²×D₄	—	6	16	no	—
138	C₃²×D₄	—	6	8	no	—
139	C₂×C₃²×C₄	—	2	16	no	—
140	C₂×C₃²×C₄	—	2	64	no	—
141	C₂×C₃²×C₄	—	2	2	no	—
142	C₂×C₃²×C₄	—	2	8	no	—
143	C₂×C₃²×C₄	—	2	8	no	—
144	C₂×C₃²×C₄	—	2	32	no	—
145	C₂×C₃²×C₄	—	2	16	no	—
146	C₂×C₃²×C₄	—	2	8	no	—
147	C₂×C₃²×C₄	—	2	8	no	—
148	C₂×C₃²×C₄	—	3	4	no	—
149	C₂×C₃²×C₄	—	6	4	no	—
150	C₂×C₃²×C₄	#67	1	4	yes	complemented
151	C₂×C₃²×C₄	C₃×D₄	1	16	yes	complemented
152	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
153	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
154	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
155	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
156	C₃×#67	—	2	64	no	—
157	C₂×C₃×Dic₃	—	2	16	no	—
158	C₂×C₃×Dic₃	C₂³×C₃	1	16	yes	—
159	C₃×D₁₂	—	2	32	no	—
160	C₂×#121	—	3	1	no	Sylow
161	C₂×C₃³	—	2	4	no	—
162	C₂×C₃³	#121	1	4	yes	complemented
163	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₃³	C₂×#41	1	1	yes	characteristic
166	C₃²×D₃	—	4	4	no	—
167	C₂⁴×C₃	—	2	4	no	—
168	C₂⁴×C₃	—	3	8	no	—
169	C₂⁴×C₃	C₂×C₃×D₃	1	4	yes	—
170	C₂⁴×C₃	C₂²×C₃²	1	1	yes	characteristic
171	C₂³×D₃	C₂²×C₃²	1	2	yes	—
172	C₂×C₃×D₄	—	3	32	no	—
173	C₂×C₃×D₄	—	3	16	no	—
174	C₂×C₃×D₄	—	6	32	no	—
175	C₂×C₃×D₄	—	6	16	no	—
176	C₂²×C₃×C₄	—	2	32	no	—
177	C₂²×C₃×C₄	—	2	16	no	—
178	C₂²×C₃×C₄	—	2	4	no	—
179	C₂²×C₃×C₄	—	2	4	no	—
180	C₂²×C₃×C₄	—	2	4	no	—
181	C₂²×C₃×C₄	—	2	16	no	—
182	C₂²×C₃×C₄	—	3	8	no	—
183	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
184	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
185	C₂²×C₃×C₄	C₂×C₃×D₃	1	16	yes	complemented
186	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
187	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
188	C₂²×C₃×C₄	C₂²×C₃²	1	4	yes	complemented
189	C₂×#67	—	2	8	no	—
190	C₂×#67	C₂²×C₃²	1	8	yes	complemented
191	C₂²×Dic₃	C₂²×C₃²	1	2	yes	—
192	C₂×D₁₂	—	2	4	no	—
193	C₂×D₁₂	C₂²×C₃²	1	4	yes	complemented
194	C₃×C₄⋊C₄	—	3	16	no	—
195	C₃×C₂²⋊C₄	—	3	32	no	—
196	(C₂×D₃)⋊C₄	C₂²×C₃²	1	8	yes	complemented
197	C₄⋊Dic₃	C₂²×C₃²	1	4	yes	complemented
198	C₂²×C₃²	—	2	16	no	—
199	C₂²×C₃²	—	2	64	no	—
200	C₂²×C₃²	—	2	16	no	—
201	C₂²×C₃²	—	2	8	no	—
202	C₂²×C₃²	—	2	32	no	—
203	C₂²×C₃²	—	2	2	no	—
204	C₂²×C₃²	—	2	2	no	—
205	C₂²×C₃²	—	2	8	no	—
206	C₂²×C₃²	—	2	8	no	—
207	C₂²×C₃²	—	2	4	no	—
208	C₂²×C₃²	—	2	8	no	—
209	C₂²×C₃²	—	2	16	no	—
210	C₂²×C₃²	—	2	8	no	—
211	C₂²×C₃²	—	2	8	no	—
212	C₂²×C₃²	—	6	4	no	—
213	C₂²×C₃²	—	6	4	no	—
214	C₂²×C₃²	—	6	4	no	—
215	C₂²×C₃²	—	12	8	no	—
216	C₂²×C₃²	C₂×D₁₂	1	2	yes	—
217	C₂²×C₃²	C₂×D₁₂	1	4	yes	complemented
218	C₂²×C₃²	#235	1	2	yes	—
219	C₂²×C₃²	C₂×#67	1	2	yes	—
220	C₂²×C₃²	C₂×C₃×D₄	1	8	yes	—
221	C₂²×C₃²	C₂×C₃×D₄	1	8	yes	—
222	C₂²×C₃²	C₂×C₃×D₄	1	16	yes	complemented
223	C₂²×C₃²	C₃×#41	1	8	yes	—
224	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
225	C₂²×C₃²	C₂⁴×C₃	1	4	yes	—
226	C₂×C₃×D₃	—	2	16	no	—
227	C₂×C₃×D₃	—	2	16	no	—
228	C₂×C₃×D₃	—	2	16	no	—
229	C₂×C₃×D₃	—	4	32	no	—
230	C₃²×C₄	—	2	16	no	—
231	C₃²×C₄	—	2	2	no	—
232	C₃²×C₄	—	2	8	no	—
233	C₃²×C₄	—	2	16	no	—
234	C₃²×C₄	—	6	4	no	—
235	C₃²×C₄	C₂×#67	1	4	yes	complemented
236	C₃²×C₄	C₂×C₃×D₄	1	16	yes	complemented
237	C₃×Dic₃	—	2	16	no	—
238	C₂²×D₄	—	3	2	no	—
239	C₂²×D₄	—	3	1	no	—
240	C₂³×C₄	C₃²×D₃	1	1	yes	characteristic, complemented
241	#121	—	3	8	no	—
242	C₂×C₄⋊C₄	—	3	1	no	—
243	C₂×C₂²⋊C₄	—	3	2	no	—
244	C₃³	C₂×#121	1	1	yes	characteristic, complemented, Sylow
245	C₂³×C₃	—	2	16	no	—
246	C₂³×C₃	—	2	16	no	—
247	C₂³×C₃	—	2	8	no	—
248	C₂³×C₃	—	2	8	no	—
249	C₂³×C₃	—	2	2	no	—
250	C₂³×C₃	—	2	2	no	—
251	C₂³×C₃	—	2	16	no	—
252	C₂³×C₃	—	2	8	no	—
253	C₂³×C₃	—	2	4	no	—
254	C₂³×C₃	—	3	16	no	—
255	C₂³×C₃	—	6	16	no	—
256	C₂³×C₃	—	6	16	no	—
257	C₂³×C₃	—	6	16	no	—
258	C₂³×C₃	C₃×D₁₂	1	16	yes	complemented
259	C₂³×C₃	C₃²×D₄	1	4	yes	complemented
260	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
261	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
262	C₂³×C₃	C₂³×C₃²	1	2	yes	—
263	C₂³×C₃	C₂³×C₃²	1	1	yes	characteristic
264	C₂²×D₃	—	2	4	no	—
265	C₂²×D₃	—	2	4	no	—
266	C₂²×D₃	—	2	4	no	—
267	C₂²×D₃	C₂³×C₃²	1	4	yes	—
268	C₃×D₄	—	6	64	no	—
269	C₃×D₄	—	6	32	no	—
270	C₂×C₃×C₄	—	2	16	no	—
271	C₂×C₃×C₄	—	2	64	no	—
272	C₂×C₃×C₄	—	2	8	no	—
273	C₂×C₃×C₄	—	2	2	no	—
274	C₂×C₃×C₄	—	2	32	no	—
275	C₂×C₃×C₄	—	2	8	no	—
276	C₂×C₃×C₄	—	2	16	no	—
277	C₂×C₃×C₄	—	2	8	no	—
278	C₂×C₃×C₄	—	2	8	no	—
279	C₂×C₃×C₄	—	3	16	no	—
280	C₂×C₃×C₄	—	6	16	no	—
281	C₂×C₃×C₄	C₃×#67	1	16	yes	complemented
282	C₂×C₃×C₄	C₃²×D₄	1	4	yes	complemented
283	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
284	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
285	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
286	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
287	#67	—	2	16	no	—
288	C₂×Dic₃	—	2	4	no	—
289	C₂×Dic₃	C₂³×C₃²	1	4	yes	—
290	D₁₂	—	2	8	no	—
291	C₂×C₃²	—	2	32	no	—
292	C₂×C₃²	—	2	4	no	—
293	C₂×C₃²	—	2	16	no	—
294	C₂×C₃²	—	2	16	no	—
295	C₂×C₃²	—	2	4	no	—
296	C₂×C₃²	—	2	4	no	—
297	C₂×C₃²	—	2	4	no	—
298	C₂×C₃²	—	12	4	no	—
299	C₂×C₃²	#930	1	4	yes	direct product factor
300	C₂×C₃²	C₃×#121	1	16	yes	complemented
301	C₂×C₃²	C₂²×D₁₂	1	1	yes	characteristic
302	C₂×C₃²	C₂×#235	1	1	yes	characteristic
303	C₂×C₃²	C₂²×#67	1	1	yes	characteristic
304	C₂×C₃²	C₂²×C₃×D₄	1	4	yes	—
305	C₂×C₃²	C₂²×C₃×D₄	1	4	yes	—
306	C₂×C₃²	C₂×C₃×#41	1	4	yes	—
307	C₃×D₃	—	4	16	no	—
308	C₂⁴	—	3	2	no	—
309	C₂⁴	C₂×C₃²×D₃	1	1	yes	characteristic
310	C₂×D₄	—	3	8	no	—
311	C₂×D₄	—	3	4	no	—
312	C₂×D₄	—	6	8	no	—
313	C₂×D₄	—	6	4	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	3	2	no	—
316	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
317	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
318	C₂²×C₄	C₂×C₃²×D₃	1	4	yes	complemented
319	C₄⋊C₄	—	3	4	no	—
320	C₂²⋊C₄	—	3	8	no	—
321	C₂²×C₃	—	2	16	no	—
322	C₂²×C₃	—	2	64	no	—
323	C₂²×C₃	—	2	16	no	—
324	C₂²×C₃	—	2	32	no	—
325	C₂²×C₃	—	2	8	no	—
326	C₂²×C₃	—	2	8	no	—
327	C₂²×C₃	—	2	2	no	—
328	C₂²×C₃	—	2	2	no	—
329	C₂²×C₃	—	2	8	no	—
330	C₂²×C₃	—	2	4	no	—
331	C₂²×C₃	—	2	8	no	—
332	C₂²×C₃	—	2	16	no	—
333	C₂²×C₃	—	2	8	no	—
334	C₂²×C₃	—	2	8	no	—
335	C₂²×C₃	—	6	16	no	—
336	C₂²×C₃	—	6	16	no	—
337	C₂²×C₃	—	6	16	no	—
338	C₂²×C₃	—	12	32	no	—
339	C₂²×C₃	C₂×C₃×D₁₂	1	8	yes	—
340	C₂²×C₃	C₂×C₃×D₁₂	1	16	yes	complemented
341	C₂²×C₃	C₃×#235	1	8	yes	—
342	C₂²×C₃	C₂×C₃×#67	1	8	yes	—
343	C₂²×C₃	C₂×C₃²×D₄	1	2	yes	—
344	C₂²×C₃	C₂×C₃²×D₄	1	2	yes	—
345	C₂²×C₃	C₂×C₃²×D₄	1	4	yes	complemented
346	C₂²×C₃	C₃²×#41	1	2	yes	—
347	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
348	C₂²×C₃	C₂⁴×C₃²	1	1	yes	characteristic
349	C₂×D₃	—	2	4	no	—
350	C₂×D₃	—	2	4	no	—
351	C₂×D₃	—	2	4	no	—
352	C₂×D₃	—	4	8	no	—
353	C₃×C₄	—	2	16	no	—
354	C₃×C₄	—	2	8	no	—
355	C₃×C₄	—	2	2	no	—
356	C₃×C₄	—	2	16	no	—
357	C₃×C₄	—	6	16	no	—
358	C₃×C₄	C₂×C₃×#67	1	16	yes	complemented
359	C₃×C₄	C₂×C₃²×D₄	1	4	yes	complemented
360	Dic₃	—	2	4	no	—
361	C₃²	—	2	4	no	—
362	C₃²	C₂×#930	1	1	yes	characteristic, direct product factor
363	C₃²	C₂×C₃×#121	1	4	yes	complemented
364	C₂³	—	2	2	no	—
365	C₂³	—	2	2	no	—
366	C₂³	—	3	4	no	—
367	C₂³	—	6	4	no	—
368	C₂³	—	6	4	no	—
369	C₂³	—	6	4	no	—
370	C₂³	C₃²×D₁₂	1	4	yes	complemented
371	C₂³	C₂²×C₃²×D₃	1	2	yes	—
372	C₂³	C₂²×C₃²×D₃	1	1	yes	characteristic
373	D₄	—	6	16	no	—
374	D₄	—	6	8	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	8	no	—
377	C₂×C₄	—	3	4	no	—
378	C₂×C₄	—	6	4	no	—
379	C₂×C₄	C₃²×#67	1	4	yes	complemented
380	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
381	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
382	C₂×C₃	—	2	32	no	—
383	C₂×C₃	—	2	16	no	—
384	C₂×C₃	—	2	4	no	—
385	C₂×C₃	—	2	16	no	—
386	C₂×C₃	—	2	4	no	—
387	C₂×C₃	—	2	4	no	—
388	C₂×C₃	—	2	4	no	—
389	C₂×C₃	—	12	16	no	—
390	C₂×C₃	C₃×#930	1	16	yes	direct product factor
391	C₂×C₃	C₃²×#121	1	4	yes	complemented
392	C₂×C₃	C₂²×C₃×D₁₂	1	4	yes	—
393	C₂×C₃	C₂×C₃×#235	1	4	yes	—
394	C₂×C₃	C₂²×C₃×#67	1	4	yes	—
395	C₂×C₃	C₂²×C₃²×D₄	1	1	yes	characteristic
396	C₂×C₃	C₂²×C₃²×D₄	1	1	yes	characteristic
397	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
398	D₃	—	4	4	no	—
399	C₂²	—	2	8	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	6	4	no	—
403	C₂²	—	6	4	no	—
404	C₂²	—	6	4	no	—
405	C₂²	—	12	8	no	—
406	C₂²	C₂×C₃²×D₁₂	1	2	yes	—
407	C₂²	C₂×C₃²×D₁₂	1	4	yes	complemented
408	C₂²	C₃²×#235	1	2	yes	—
409	C₂²	C₂×C₃²×#67	1	2	yes	—
410	C₂²	C₂³×C₃²×D₃	1	1	yes	characteristic
411	C₄	—	2	2	no	—
412	C₄	—	6	4	no	—
413	C₄	C₂×C₃²×#67	1	4	yes	complemented
414	C₃	—	2	4	no	—
415	C₃	C₂×C₃×#930	1	4	yes	direct product factor
416	C₃	C₂×C₃²×#121	1	1	yes	characteristic, complemented
417	C₂	—	2	4	no	—
418	C₂	—	12	4	no	—
419	C₂	C₃²×#930	1	4	yes	direct product factor
420	C₂	C₂²×C₃²×D₁₂	1	1	yes	characteristic
421	C₂	C₂×C₃²×#235	1	1	yes	characteristic
422	C₂	C₂²×C₃²×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃²	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₃²
Frattini	C₂²	C₂³×C₃²×D₃
Fitting	C₂³×C₃³×C₄	C₂
socle	C₂³×C₃³	C₂³
hypercenter	C₂³×C₃²×C₄	D₃
hypocenter	C₃	C₂×C₃²×#121
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃² ◁ C₂³×C₃²×C₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃³×C₄	C₂	semidirect
2. C₂²×C₃²×#67	C₂	semidirect
3. C₂²×C₃²×D₁₂	C₂	semidirect
4. C₃²×#930	C₂	direct (N × H)
5. C₂×C₃²×(C₂×D₃)⋊C₄	C₂	semidirect
6. C₂×C₃²×C₄⋊Dic₃	C₂	semidirect
8. C₂×C₃×#930	C₃	direct (N × H)
14. C₂²×C₃³×C₄	C₂²	semidirect
16. C₂×C₃²×#67	C₂²	semidirect
19. C₂×C₃²×D₁₂	C₂²	semidirect
20. C₃²×(C₂×D₃)⋊C₄	C₂²	semidirect
21. C₃²×C₄⋊Dic₃	C₂²	semidirect
25. C₂³×C₃²×C₄	D₃	semidirect
26. C₂³×C₃²×C₄	C₂×C₃	semidirect
27. C₂²×C₃×#67	C₂×C₃	semidirect
28. C₂²×C₃×D₁₂	C₂×C₃	semidirect
32. C₃×#930	C₂×C₃	direct (N × H)
33. C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	semidirect
34. C₂×C₃×C₄⋊Dic₃	C₂×C₃	semidirect
37. C₂³×C₃³	D₄	semidirect
46. C₂×C₃³×C₄	D₄	semidirect
54. C₂×#930	C₃²	direct (N × H)
73. C₂²×C₃²×C₄	C₂×D₃	semidirect
76. C₂²×C₃²×C₄	C₂²×C₃	semidirect
78. C₂×C₃×#67	C₂²×C₃	semidirect
81. C₂×C₃×D₁₂	C₂²×C₃	semidirect
84. C₃×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
85. C₃×C₄⋊Dic₃	C₂²×C₃	semidirect
91. C₂²×C₃³	C₂×D₄	semidirect
99. C₃³×C₄	C₂×D₄	semidirect
104. C₂³×C₃×C₄	C₃×D₃	semidirect
105. C₂³×C₃×C₄	C₂×C₃²	semidirect
106. C₂²×#67	C₂×C₃²	semidirect
107. C₂²×D₁₂	C₂×C₃²	semidirect
111. #930	C₂×C₃²	direct (N × H)
112. C₂×(C₂×D₃)⋊C₄	C₂×C₃²	semidirect
113. C₂×C₄⋊Dic₃	C₂×C₃²	semidirect
127. C₂³×C₃²	D₁₂	semidirect
128. C₂³×C₃²	C₃×D₄	semidirect
150. C₂×C₃²×C₄	#67	semidirect
151. C₂×C₃²×C₄	C₃×D₄	semidirect
162. C₂×C₃³	#121	semidirect
185. C₂²×C₃×C₄	C₂×C₃×D₃	semidirect
188. C₂²×C₃×C₄	C₂²×C₃²	semidirect
190. C₂×#67	C₂²×C₃²	semidirect
193. C₂×D₁₂	C₂²×C₃²	semidirect
196. (C₂×D₃)⋊C₄	C₂²×C₃²	semidirect
197. C₄⋊Dic₃	C₂²×C₃²	semidirect
217. C₂²×C₃²	C₂×D₁₂	semidirect
222. C₂²×C₃²	C₂×C₃×D₄	semidirect
235. C₃²×C₄	C₂×#67	semidirect
236. C₃²×C₄	C₂×C₃×D₄	semidirect
240. C₂³×C₄	C₃²×D₃	semidirect
244. C₃³	C₂×#121	semidirect
258. C₂³×C₃	C₃×D₁₂	semidirect
259. C₂³×C₃	C₃²×D₄	semidirect
281. C₂×C₃×C₄	C₃×#67	semidirect
282. C₂×C₃×C₄	C₃²×D₄	semidirect
299. C₂×C₃²	#930	direct (N × H)
300. C₂×C₃²	C₃×#121	semidirect
318. C₂²×C₄	C₂×C₃²×D₃	semidirect
340. C₂²×C₃	C₂×C₃×D₁₂	semidirect
345. C₂²×C₃	C₂×C₃²×D₄	semidirect
358. C₃×C₄	C₂×C₃×#67	semidirect
359. C₃×C₄	C₂×C₃²×D₄	semidirect
362. C₃²	C₂×#930	direct (N × H)
363. C₃²	C₂×C₃×#121	semidirect
370. C₂³	C₃²×D₁₂	semidirect
379. C₂×C₄	C₃²×#67	semidirect
390. C₂×C₃	C₃×#930	direct (N × H)
391. C₂×C₃	C₃²×#121	semidirect
407. C₂²	C₂×C₃²×D₁₂	semidirect
413. C₄	C₂×C₃²×#67	semidirect
415. C₃	C₂×C₃×#930	direct (N × H)
416. C₃	C₂×C₃²×#121	semidirect
419. C₂	C₃²×#930	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×C₃³×C₄	2
C₂²×C₃²×#67	2
C₂²×C₃²×D₁₂	2
C₃²×#930	2
C₂×C₃²×(C₂×D₃)⋊C₄	2
C₂×C₃²×C₄⋊Dic₃	2
C₂×C₃²×#121	3
C₂×C₃×#930	3

Subgroups — C2×C32×#930 #13179167

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×#930 #13179167