Subgroups — C₂×C₃²×#938 #13179179

Order 1728.

3500 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃³×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃²×#67	C₂	1	2	yes	maximal, complemented
3	C₂²×C₃²×C₄×D₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃²×#217	C₂	1	2	yes	maximal, complemented
5	C₃²×#938	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃²×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃²×#121	—	3	1	no	maximal
8	C₂×C₃×#938	C₃	1	4	yes	maximal, direct product factor
9	C₂⁴×C₃³	C₂²	1	2	yes	—
10	C₂³×C₃²×D₃	C₂²	1	1	yes	characteristic
11	C₂×C₃³×D₄	—	2	4	no	—
12	C₂×C₃³×D₄	C₂²	1	4	yes	complemented
13	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
14	C₂×C₃²×#67	—	2	8	no	—
15	C₂×C₃²×#67	C₂²	1	8	yes	complemented
16	C₂²×C₃²×Dic₃	C₂²	1	2	yes	—
17	C₂²×C₃²×Dic₃	C₂²	1	1	yes	characteristic
18	C₂×C₃²×C₄×D₃	—	2	4	no	—
19	C₂×C₃²×C₄×D₃	C₂²	1	4	yes	complemented
20	C₃²×#217	C₂²	1	8	yes	complemented
21	C₃²×C₄⋊Dic₃	C₂²	1	4	yes	complemented
22	C₂²×C₃²×D₄	—	2	4	no	—
23	C₂²×C₃²×D₄	—	3	2	no	—
24	C₂²×C₃²×D₄	D₃	1	1	yes	characteristic, complemented
25	C₂²×C₃²×D₄	C₂×C₃	1	4	yes	complemented
26	C₂³×C₃²×C₄	—	3	1	no	—
27	C₂²×C₃×#67	C₂×C₃	1	8	yes	complemented
28	C₂²×C₃×C₄×D₃	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	C₂×C₃×#217	C₂×C₃	1	8	yes	complemented
33	C₃×#938	C₂×C₃	1	32	yes	direct product factor
34	C₂×C₃×C₄⋊Dic₃	C₂×C₃	1	4	yes	complemented
35	C₂³×C₃³	—	2	4	no	—
36	C₂³×C₃³	—	2	4	no	—
37	C₂³×C₃³	—	2	4	no	—
38	C₂³×C₃³	C₂³	1	4	yes	—
39	C₂³×C₃³	C₂³	1	1	yes	characteristic
40	C₂²×C₃²×D₃	—	2	2	no	—
41	C₂²×C₃²×D₃	—	2	2	no	—
42	C₂²×C₃²×D₃	D₄	1	4	yes	complemented
43	C₂²×C₃²×D₃	C₂³	1	2	yes	—
44	C₃³×D₄	—	2	8	no	—
45	C₂×C₃³×C₄	D₄	1	4	yes	complemented
46	C₂×C₃³×C₄	C₂³	1	2	yes	—
47	C₃²×#67	—	2	16	no	—
48	C₂×C₃²×Dic₃	—	2	2	no	—
49	C₂×C₃²×Dic₃	—	2	4	no	—
50	C₂×C₃²×Dic₃	C₂³	1	2	yes	—
51	C₂×C₃²×Dic₃	C₂³	1	4	yes	—
52	C₃²×C₄×D₃	—	2	8	no	—
53	C₂×C₃×#121	—	3	4	no	—
54	C₂×#938	C₃²	1	1	yes	characteristic, direct product factor
55	C₂⁴×C₃²	—	2	8	no	—
56	C₂⁴×C₃²	—	3	1	no	—
57	C₂⁴×C₃²	C₂×D₃	1	2	yes	—
58	C₂⁴×C₃²	C₂²×C₃	1	8	yes	—
59	C₂³×C₃×D₃	C₂²×C₃	1	4	yes	—
60	C₂×C₃²×D₄	—	2	32	no	—
61	C₂×C₃²×D₄	—	2	16	no	—
62	C₂×C₃²×D₄	—	2	4	no	—
63	C₂×C₃²×D₄	—	2	16	no	—
64	C₂×C₃²×D₄	—	3	8	no	—
65	C₂×C₃²×D₄	—	6	8	no	—
66	C₂×C₃²×D₄	C₂×D₃	1	4	yes	complemented
67	C₂×C₃²×D₄	C₂²×C₃	1	16	yes	complemented
68	C₂²×C₃²×C₄	—	2	4	no	—
69	C₂²×C₃²×C₄	—	3	1	no	—
70	C₂²×C₃²×C₄	—	3	2	no	—
71	C₂²×C₃²×C₄	—	3	4	no	—
72	C₂²×C₃²×C₄	—	6	4	no	—
73	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
74	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
75	C₂×C₃×#67	—	2	32	no	—
76	C₂×C₃×#67	C₂²×C₃	1	32	yes	complemented
77	C₂²×C₃×Dic₃	C₂²×C₃	1	8	yes	—
78	C₂²×C₃×Dic₃	C₂²×C₃	1	4	yes	—
79	C₂×C₃×C₄×D₃	—	2	16	no	—
80	C₂×C₃×C₄×D₃	C₂²×C₃	1	16	yes	complemented
81	C₃²×C₄⋊C₄	—	3	4	no	—
82	C₃²×C₂²⋊C₄	—	3	8	no	—
83	C₃×#217	C₂²×C₃	1	32	yes	complemented
84	C₃×C₄⋊Dic₃	C₂²×C₃	1	16	yes	complemented
85	C₂²×C₃³	—	2	4	no	—
86	C₂²×C₃³	—	2	4	no	—
87	C₂²×C₃³	—	2	4	no	—
88	C₂²×C₃³	—	4	8	no	—
89	C₂²×C₃³	C₂×D₄	1	2	yes	—
90	C₂²×C₃³	C₂×D₄	1	2	yes	—
91	C₂²×C₃³	#41	1	2	yes	—
92	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
93	C₂×C₃²×D₃	—	2	8	no	—
94	C₂×C₃²×D₃	—	2	2	no	—
95	C₂×C₃²×D₃	—	2	2	no	—
96	C₂×C₃²×D₃	C₂×D₄	1	4	yes	complemented
97	C₃³×C₄	C₂×D₄	1	4	yes	complemented
98	C₃²×Dic₃	—	2	2	no	—
99	C₃²×Dic₃	—	2	4	no	—
100	C₂²×C₃×D₄	—	2	4	no	—
101	C₂²×C₃×D₄	—	3	8	no	—
102	C₂²×C₃×D₄	C₃×D₃	1	4	yes	complemented
103	C₂²×C₃×D₄	C₂×C₃²	1	1	yes	characteristic, complemented
104	C₂³×C₃×C₄	—	3	4	no	—
105	C₂²×#67	C₂×C₃²	1	2	yes	complemented
106	C₂²×C₄×D₃	C₂×C₃²	1	1	yes	characteristic, complemented
107	C₃×#121	—	3	32	no	—
108	C₂×C₃×C₄⋊C₄	—	3	4	no	—
109	C₂×C₃×C₂²⋊C₄	—	3	8	no	—
110	C₂×#217	C₂×C₃²	1	2	yes	complemented
111	#938	C₂×C₃²	1	8	yes	direct product factor
112	C₂×C₄⋊Dic₃	C₂×C₃²	1	1	yes	characteristic, complemented
113	C₂³×C₃²	—	2	32	no	—
114	C₂³×C₃²	—	2	4	no	—
115	C₂³×C₃²	—	2	4	no	—
116	C₂³×C₃²	—	2	4	no	—
117	C₂³×C₃²	—	2	16	no	—
118	C₂³×C₃²	—	2	4	no	—
119	C₂³×C₃²	—	2	16	no	—
120	C₂³×C₃²	—	2	16	no	—
121	C₂³×C₃²	—	2	16	no	—
122	C₂³×C₃²	—	3	4	no	—
123	C₂³×C₃²	—	3	2	no	—
124	C₂³×C₃²	—	4	16	no	—
125	C₂³×C₃²	—	4	16	no	—
126	C₂³×C₃²	—	6	2	no	—
127	C₂³×C₃²	—	6	2	no	—
128	C₂³×C₃²	C₂²×D₃	1	4	yes	—
129	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
130	C₂³×C₃²	C₂³×C₃	1	16	yes	—
131	C₂³×C₃²	C₂³×C₃	1	4	yes	—
132	C₂²×C₃×D₃	—	2	8	no	—
133	C₂²×C₃×D₃	—	2	8	no	—
134	C₂²×C₃×D₃	C₃×D₄	1	16	yes	complemented
135	C₂²×C₃×D₃	C₂³×C₃	1	8	yes	—
136	C₃²×D₄	—	2	64	no	—
137	C₃²×D₄	—	2	8	no	—
138	C₃²×D₄	—	2	32	no	—
139	C₃²×D₄	—	6	16	no	—
140	C₂×C₃²×C₄	—	2	16	no	—
141	C₂×C₃²×C₄	—	2	8	no	—
142	C₂×C₃²×C₄	—	3	2	no	—
143	C₂×C₃²×C₄	—	3	4	no	—
144	C₂×C₃²×C₄	—	6	4	no	—
145	C₂×C₃²×C₄	—	6	2	no	—
146	C₂×C₃²×C₄	—	6	8	no	—
147	C₂×C₃²×C₄	#67	1	4	yes	complemented
148	C₂×C₃²×C₄	C₃×D₄	1	16	yes	complemented
149	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
150	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
151	C₃×#67	—	2	64	no	—
152	C₂×C₃×Dic₃	—	2	8	no	—
153	C₂×C₃×Dic₃	—	2	16	no	—
154	C₂×C₃×Dic₃	C₂³×C₃	1	16	yes	—
155	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
156	C₃×C₄×D₃	—	2	32	no	—
157	C₂×#121	—	3	1	no	Sylow
158	C₂×C₃³	—	4	4	no	—
159	C₂×C₃³	#121	1	4	yes	complemented
160	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₃³	C₂×#41	1	1	yes	characteristic
163	C₃²×D₃	—	2	4	no	—
164	C₂⁴×C₃	—	2	8	no	—
165	C₂⁴×C₃	—	3	4	no	—
166	C₂⁴×C₃	C₂×C₃×D₃	1	8	yes	—
167	C₂⁴×C₃	C₂²×C₃²	1	2	yes	—
168	C₂³×D₃	C₂²×C₃²	1	1	yes	characteristic
169	C₂×C₃×D₄	—	2	32	no	—
170	C₂×C₃×D₄	—	2	16	no	—
171	C₂×C₃×D₄	—	2	4	no	—
172	C₂×C₃×D₄	—	2	16	no	—
173	C₂×C₃×D₄	—	3	32	no	—
174	C₂×C₃×D₄	—	6	32	no	—
175	C₂×C₃×D₄	C₂×C₃×D₃	1	16	yes	complemented
176	C₂×C₃×D₄	C₂²×C₃²	1	4	yes	complemented
177	C₂²×C₃×C₄	—	2	4	no	—
178	C₂²×C₃×C₄	—	3	4	no	—
179	C₂²×C₃×C₄	—	3	8	no	—
180	C₂²×C₃×C₄	—	3	16	no	—
181	C₂²×C₃×C₄	—	6	16	no	—
182	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
183	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
184	C₂×#67	—	2	8	no	—
185	C₂×#67	C₂²×C₃²	1	8	yes	complemented
186	C₂²×Dic₃	C₂²×C₃²	1	2	yes	—
187	C₂²×Dic₃	C₂²×C₃²	1	1	yes	characteristic
188	C₂×C₄×D₃	—	2	4	no	—
189	C₂×C₄×D₃	C₂²×C₃²	1	4	yes	complemented
190	C₃×C₄⋊C₄	—	3	16	no	—
191	C₃×C₂²⋊C₄	—	3	32	no	—
192	#217	C₂²×C₃²	1	8	yes	complemented
193	C₄⋊Dic₃	C₂²×C₃²	1	4	yes	complemented
194	C₂²×C₃²	—	2	32	no	—
195	C₂²×C₃²	—	2	4	no	—
196	C₂²×C₃²	—	2	4	no	—
197	C₂²×C₃²	—	2	4	no	—
198	C₂²×C₃²	—	2	16	no	—
199	C₂²×C₃²	—	2	4	no	—
200	C₂²×C₃²	—	2	8	no	—
201	C₂²×C₃²	—	2	8	no	—
202	C₂²×C₃²	—	2	8	no	—
203	C₂²×C₃²	—	2	16	no	—
204	C₂²×C₃²	—	2	16	no	—
205	C₂²×C₃²	—	3	4	no	—
206	C₂²×C₃²	—	4	16	no	—
207	C₂²×C₃²	—	4	16	no	—
208	C₂²×C₃²	—	4	64	no	—
209	C₂²×C₃²	—	4	8	no	—
210	C₂²×C₃²	—	4	32	no	—
211	C₂²×C₃²	—	6	8	no	—
212	C₂²×C₃²	—	6	2	no	—
213	C₂²×C₃²	—	6	2	no	—
214	C₂²×C₃²	D₃×D₄	1	2	yes	—
215	C₂²×C₃²	#237	1	2	yes	—
216	C₂²×C₃²	C₂×#67	1	2	yes	—
217	C₂²×C₃²	C₂×C₃×D₄	1	8	yes	—
218	C₂²×C₃²	C₂×C₃×D₄	1	8	yes	—
219	C₂²×C₃²	C₃×#41	1	8	yes	—
220	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
221	C₂²×C₃²	C₂⁴×C₃	1	4	yes	—
222	C₂×C₃×D₃	—	2	32	no	—
223	C₂×C₃×D₃	—	2	8	no	—
224	C₂×C₃×D₃	—	2	8	no	—
225	C₂×C₃×D₃	C₂×C₃×D₄	1	16	yes	complemented
226	C₃²×C₄	—	2	16	no	—
227	C₃²×C₄	—	6	4	no	—
228	C₃²×C₄	—	6	2	no	—
229	C₃²×C₄	C₂×#67	1	4	yes	complemented
230	C₃²×C₄	C₂×C₃×D₄	1	16	yes	complemented
231	C₃×Dic₃	—	2	8	no	—
232	C₃×Dic₃	—	2	16	no	—
233	C₂²×D₄	—	3	2	no	—
234	C₂²×D₄	C₃²×D₃	1	1	yes	characteristic, complemented
235	C₂³×C₄	—	3	1	no	—
236	#121	—	3	8	no	—
237	C₂×C₄⋊C₄	—	3	1	no	—
238	C₂×C₂²⋊C₄	—	3	2	no	—
239	C₃³	C₂×#121	1	1	yes	characteristic, complemented, Sylow
240	C₂³×C₃	—	2	32	no	—
241	C₂³×C₃	—	2	16	no	—
242	C₂³×C₃	—	2	16	no	—
243	C₂³×C₃	—	2	16	no	—
244	C₂³×C₃	—	2	4	no	—
245	C₂³×C₃	—	2	4	no	—
246	C₂³×C₃	—	2	4	no	—
247	C₂³×C₃	—	2	4	no	—
248	C₂³×C₃	—	2	16	no	—
249	C₂³×C₃	—	3	8	no	—
250	C₂³×C₃	—	3	16	no	—
251	C₂³×C₃	—	4	16	no	—
252	C₂³×C₃	—	4	16	no	—
253	C₂³×C₃	—	6	8	no	—
254	C₂³×C₃	—	6	8	no	—
255	C₂³×C₃	C₂²×C₃×D₃	1	16	yes	—
256	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
257	C₂³×C₃	C₂³×C₃²	1	4	yes	—
258	C₂³×C₃	C₂³×C₃²	1	1	yes	characteristic
259	C₂²×D₃	—	2	2	no	—
260	C₂²×D₃	—	2	2	no	—
261	C₂²×D₃	C₃²×D₄	1	4	yes	complemented
262	C₂²×D₃	C₂³×C₃²	1	2	yes	—
263	C₃×D₄	—	2	64	no	—
264	C₃×D₄	—	2	32	no	—
265	C₃×D₄	—	2	8	no	—
266	C₃×D₄	—	6	64	no	—
267	C₂×C₃×C₄	—	2	16	no	—
268	C₂×C₃×C₄	—	2	8	no	—
269	C₂×C₃×C₄	—	3	8	no	—
270	C₂×C₃×C₄	—	3	16	no	—
271	C₂×C₃×C₄	—	6	16	no	—
272	C₂×C₃×C₄	—	6	8	no	—
273	C₂×C₃×C₄	—	6	32	no	—
274	C₂×C₃×C₄	C₃×#67	1	16	yes	complemented
275	C₂×C₃×C₄	C₃²×D₄	1	4	yes	complemented
276	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
277	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
278	#67	—	2	16	no	—
279	C₂×Dic₃	—	2	2	no	—
280	C₂×Dic₃	—	2	4	no	—
281	C₂×Dic₃	C₂³×C₃²	1	4	yes	—
282	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
283	C₄×D₃	—	2	8	no	—
284	C₂×C₃²	—	2	16	no	—
285	C₂×C₃²	—	2	4	no	—
286	C₂×C₃²	—	2	4	no	—
287	C₂×C₃²	—	2	4	no	—
288	C₂×C₃²	—	4	32	no	—
289	C₂×C₃²	—	4	4	no	—
290	C₂×C₃²	—	4	16	no	—
291	C₂×C₃²	—	6	4	no	—
292	C₂×C₃²	#938	1	4	yes	direct product factor
293	C₂×C₃²	C₃×#121	1	16	yes	complemented
294	C₂×C₃²	C₂×D₃×D₄	1	1	yes	characteristic
295	C₂×C₃²	C₂×#237	1	1	yes	characteristic
296	C₂×C₃²	C₂²×#67	1	1	yes	characteristic
297	C₂×C₃²	C₂²×C₃×D₄	1	4	yes	—
298	C₂×C₃²	C₂²×C₃×D₄	1	4	yes	—
299	C₂×C₃²	C₂×C₃×#41	1	4	yes	—
300	C₃×D₃	—	2	16	no	—
301	C₂⁴	—	3	1	no	—
302	C₂⁴	C₂×C₃²×D₃	1	2	yes	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	3	8	no	—
305	C₂×D₄	—	6	8	no	—
306	C₂×D₄	C₂×C₃²×D₃	1	4	yes	complemented
307	C₂²×C₄	—	3	1	no	—
308	C₂²×C₄	—	3	2	no	—
309	C₂²×C₄	—	3	4	no	—
310	C₂²×C₄	—	6	4	no	—
311	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
312	C₄⋊C₄	—	3	4	no	—
313	C₂²⋊C₄	—	3	8	no	—
314	C₂²×C₃	—	2	32	no	—
315	C₂²×C₃	—	2	16	no	—
316	C₂²×C₃	—	2	16	no	—
317	C₂²×C₃	—	2	16	no	—
318	C₂²×C₃	—	2	4	no	—
319	C₂²×C₃	—	2	4	no	—
320	C₂²×C₃	—	2	4	no	—
321	C₂²×C₃	—	2	4	no	—
322	C₂²×C₃	—	2	8	no	—
323	C₂²×C₃	—	2	8	no	—
324	C₂²×C₃	—	2	8	no	—
325	C₂²×C₃	—	3	16	no	—
326	C₂²×C₃	—	4	16	no	—
327	C₂²×C₃	—	4	16	no	—
328	C₂²×C₃	—	4	64	no	—
329	C₂²×C₃	—	4	32	no	—
330	C₂²×C₃	—	4	8	no	—
331	C₂²×C₃	—	6	32	no	—
332	C₂²×C₃	—	6	8	no	—
333	C₂²×C₃	—	6	8	no	—
334	C₂²×C₃	C₃×D₃×D₄	1	8	yes	—
335	C₂²×C₃	C₃×#237	1	8	yes	—
336	C₂²×C₃	C₂×C₃×#67	1	8	yes	—
337	C₂²×C₃	C₂×C₃²×D₄	1	2	yes	—
338	C₂²×C₃	C₂×C₃²×D₄	1	2	yes	—
339	C₂²×C₃	C₃²×#41	1	2	yes	—
340	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
341	C₂²×C₃	C₂⁴×C₃²	1	1	yes	characteristic
342	C₂×D₃	—	2	2	no	—
343	C₂×D₃	—	2	2	no	—
344	C₂×D₃	—	2	8	no	—
345	C₂×D₃	C₂×C₃²×D₄	1	4	yes	complemented
346	C₃×C₄	—	2	16	no	—
347	C₃×C₄	—	6	16	no	—
348	C₃×C₄	—	6	8	no	—
349	C₃×C₄	C₂×C₃×#67	1	16	yes	complemented
350	C₃×C₄	C₂×C₃²×D₄	1	4	yes	complemented
351	Dic₃	—	2	2	no	—
352	Dic₃	—	2	4	no	—
353	C₃²	—	2	4	no	—
354	C₃²	C₂×#938	1	1	yes	characteristic, direct product factor
355	C₃²	C₂×C₃×#121	1	4	yes	complemented
356	C₂³	—	2	4	no	—
357	C₂³	—	2	4	no	—
358	C₂³	—	2	4	no	—
359	C₂³	—	3	2	no	—
360	C₂³	—	3	4	no	—
361	C₂³	—	6	2	no	—
362	C₂³	—	6	2	no	—
363	C₂³	C₂²×C₃²×D₃	1	4	yes	—
364	C₂³	C₂²×C₃²×D₃	1	1	yes	characteristic
365	D₄	—	2	8	no	—
366	D₄	—	6	16	no	—
367	C₂×C₄	—	3	2	no	—
368	C₂×C₄	—	3	4	no	—
369	C₂×C₄	—	6	4	no	—
370	C₂×C₄	—	6	2	no	—
371	C₂×C₄	—	6	8	no	—
372	C₂×C₄	C₃²×#67	1	4	yes	complemented
373	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
374	C₂×C₃	—	2	16	no	—
375	C₂×C₃	—	2	4	no	—
376	C₂×C₃	—	2	4	no	—
377	C₂×C₃	—	2	4	no	—
378	C₂×C₃	—	4	32	no	—
379	C₂×C₃	—	4	16	no	—
380	C₂×C₃	—	4	4	no	—
381	C₂×C₃	—	6	16	no	—
382	C₂×C₃	C₃×#938	1	16	yes	direct product factor
383	C₂×C₃	C₃²×#121	1	4	yes	complemented
384	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
385	C₂×C₃	C₂×C₃×#237	1	4	yes	—
386	C₂×C₃	C₂²×C₃×#67	1	4	yes	—
387	C₂×C₃	C₂²×C₃²×D₄	1	1	yes	characteristic
388	C₂×C₃	C₂²×C₃²×D₄	1	1	yes	characteristic
389	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
390	D₃	—	2	4	no	—
391	C₂²	—	2	4	no	—
392	C₂²	—	2	4	no	—
393	C₂²	—	2	4	no	—
394	C₂²	—	3	4	no	—
395	C₂²	—	4	8	no	—
396	C₂²	—	6	8	no	—
397	C₂²	—	6	2	no	—
398	C₂²	—	6	2	no	—
399	C₂²	C₃²×D₃×D₄	1	2	yes	—
400	C₂²	C₃²×#237	1	2	yes	—
401	C₂²	C₂×C₃²×#67	1	2	yes	—
402	C₂²	C₂³×C₃²×D₃	1	1	yes	characteristic
403	C₄	—	6	4	no	—
404	C₄	—	6	2	no	—
405	C₄	C₂×C₃²×#67	1	4	yes	complemented
406	C₃	—	2	4	no	—
407	C₃	C₂×C₃×#938	1	4	yes	direct product factor
408	C₃	C₂×C₃²×#121	1	1	yes	characteristic, complemented
409	C₂	—	4	4	no	—
410	C₂	—	6	4	no	—
411	C₂	C₃²×#938	1	4	yes	direct product factor
412	C₂	C₂×C₃²×D₃×D₄	1	1	yes	characteristic
413	C₂	C₂×C₃²×#237	1	1	yes	characteristic
414	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	C₂²×C₃³×D₄	C₂
socle	C₂³×C₃³	C₂³
hypercenter	C₂²×C₃²×D₄	D₃
hypocenter	C₃	C₂×C₃²×#121
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃² ◁ C₂²×C₃²×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃³×D₄	C₂	semidirect
2. C₂²×C₃²×#67	C₂	semidirect
3. C₂²×C₃²×C₄×D₃	C₂	semidirect
4. C₂×C₃²×#217	C₂	semidirect
5. C₃²×#938	C₂	direct (N × H)
6. C₂×C₃²×C₄⋊Dic₃	C₂	semidirect
8. C₂×C₃×#938	C₃	direct (N × H)
12. C₂×C₃³×D₄	C₂²	semidirect
15. C₂×C₃²×#67	C₂²	semidirect
19. C₂×C₃²×C₄×D₃	C₂²	semidirect
20. C₃²×#217	C₂²	semidirect
21. C₃²×C₄⋊Dic₃	C₂²	semidirect
24. C₂²×C₃²×D₄	D₃	semidirect
25. C₂²×C₃²×D₄	C₂×C₃	semidirect
27. C₂²×C₃×#67	C₂×C₃	semidirect
28. C₂²×C₃×C₄×D₃	C₂×C₃	semidirect
32. C₂×C₃×#217	C₂×C₃	semidirect
33. C₃×#938	C₂×C₃	direct (N × H)
34. C₂×C₃×C₄⋊Dic₃	C₂×C₃	semidirect
42. C₂²×C₃²×D₃	D₄	semidirect
45. C₂×C₃³×C₄	D₄	semidirect
54. C₂×#938	C₃²	direct (N × H)
66. C₂×C₃²×D₄	C₂×D₃	semidirect
67. C₂×C₃²×D₄	C₂²×C₃	semidirect
76. C₂×C₃×#67	C₂²×C₃	semidirect
80. C₂×C₃×C₄×D₃	C₂²×C₃	semidirect
83. C₃×#217	C₂²×C₃	semidirect
84. C₃×C₄⋊Dic₃	C₂²×C₃	semidirect
96. C₂×C₃²×D₃	C₂×D₄	semidirect
97. C₃³×C₄	C₂×D₄	semidirect
102. C₂²×C₃×D₄	C₃×D₃	semidirect
103. C₂²×C₃×D₄	C₂×C₃²	semidirect
105. C₂²×#67	C₂×C₃²	semidirect
106. C₂²×C₄×D₃	C₂×C₃²	semidirect
110. C₂×#217	C₂×C₃²	semidirect
111. #938	C₂×C₃²	direct (N × H)
112. C₂×C₄⋊Dic₃	C₂×C₃²	semidirect
134. C₂²×C₃×D₃	C₃×D₄	semidirect
147. C₂×C₃²×C₄	#67	semidirect
148. C₂×C₃²×C₄	C₃×D₄	semidirect
159. C₂×C₃³	#121	semidirect
175. C₂×C₃×D₄	C₂×C₃×D₃	semidirect
176. C₂×C₃×D₄	C₂²×C₃²	semidirect
185. C₂×#67	C₂²×C₃²	semidirect
189. C₂×C₄×D₃	C₂²×C₃²	semidirect
192. #217	C₂²×C₃²	semidirect
193. C₄⋊Dic₃	C₂²×C₃²	semidirect
225. C₂×C₃×D₃	C₂×C₃×D₄	semidirect
229. C₃²×C₄	C₂×#67	semidirect
230. C₃²×C₄	C₂×C₃×D₄	semidirect
234. C₂²×D₄	C₃²×D₃	semidirect
239. C₃³	C₂×#121	semidirect
261. C₂²×D₃	C₃²×D₄	semidirect
274. C₂×C₃×C₄	C₃×#67	semidirect
275. C₂×C₃×C₄	C₃²×D₄	semidirect
292. C₂×C₃²	#938	direct (N × H)
293. C₂×C₃²	C₃×#121	semidirect
306. C₂×D₄	C₂×C₃²×D₃	semidirect
345. C₂×D₃	C₂×C₃²×D₄	semidirect
349. C₃×C₄	C₂×C₃×#67	semidirect
350. C₃×C₄	C₂×C₃²×D₄	semidirect
354. C₃²	C₂×#938	direct (N × H)
355. C₃²	C₂×C₃×#121	semidirect
372. C₂×C₄	C₃²×#67	semidirect
382. C₂×C₃	C₃×#938	direct (N × H)
383. C₂×C₃	C₃²×#121	semidirect
405. C₄	C₂×C₃²×#67	semidirect
407. C₃	C₂×C₃×#938	direct (N × H)
408. C₃	C₂×C₃²×#121	semidirect
411. C₂	C₃²×#938	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃³×D₄	2
C₂²×C₃²×#67	2
C₂²×C₃²×C₄×D₃	2
C₂×C₃²×#217	2
C₃²×#938	2
C₂×C₃²×C₄⋊Dic₃	2
C₂×C₃²×#121	3
C₂×C₃×#938	3

Subgroups — C2×C32×#938 #13179179

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×#938 #13179179