Subgroups — C₂×C₃²×#837 #13162668

Order 1728.

1676 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×#41	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃²×C₄×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃²×#208	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#837	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₃²×#104	—	3	1	no	maximal
6	C₂×C₃×#837	C₃	1	4	yes	maximal, direct product factor
7	C₃³×#41	—	2	1	no	—
8	C₃³×#41	—	2	1	no	—
9	C₃³×#41	C₄	1	2	yes	complemented
10	C₃³×#41	C₂²	1	2	yes	—
11	C₂×C₃³×Q₈	C₄	1	1	yes	characteristic, complemented
12	C₂×C₃³×D₄	—	2	1	no	—
13	C₂×C₃³×D₄	C₄	1	1	yes	characteristic, complemented
14	C₂²×C₃³×C₄	—	2	1	no	—
15	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
16	C₂²×C₃²×Dic₃	—	2	1	no	—
17	C₃²×C₄×Dic₃	—	2	1	no	—
18	C₃²×C₄×Dic₃	C₂²	1	2	yes	complemented
19	C₃²×#208	—	2	1	no	—
20	C₃²×#208	C₂²	1	2	yes	complemented
21	C₂×C₃²×C₃⋊C₈	—	2	1	no	—
22	C₂×C₃²×#41	—	2	4	no	—
23	C₂×C₃²×#41	D₃	1	1	yes	characteristic
24	C₂×C₃²×#41	C₂×C₃	1	4	yes	—
25	C₂×C₃²×M₁₆	—	3	1	no	—
26	C₂×C₃²×C₄²	—	3	1	no	—
27	C₂×C₃×C₄×Dic₃	C₂×C₃	1	4	yes	complemented
28	C₂×C₃×#208	C₂×C₃	1	4	yes	complemented
29	C₃²×#104	—	3	4	no	—
30	C₃×#837	C₂×C₃	1	16	yes	direct product factor
31	C₂³×C₃³	—	2	1	no	—
32	C₂³×C₃³	D₄	1	1	yes	characteristic
33	C₃³×Q₈	—	2	1	no	—
34	C₃³×Q₈	C₂×C₄	1	2	yes	complemented
35	C₃³×D₄	—	2	2	no	—
36	C₃³×D₄	—	2	2	no	—
37	C₃³×D₄	—	2	1	no	—
38	C₃³×D₄	C₂×C₄	1	2	yes	complemented
39	C₂×C₃³×C₄	—	2	1	no	—
40	C₂×C₃³×C₄	—	2	2	no	—
41	C₂×C₃³×C₄	—	2	2	no	—
42	C₂×C₃³×C₄	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃³×C₄	C₂×C₄	1	1	yes	characteristic
44	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
45	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
46	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
47	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
48	C₂×C₃²×Dic₃	—	2	4	no	—
49	C₂×C₃²×Dic₃	—	2	2	no	—
50	C₃²×C₃⋊C₈	—	2	2	no	—
51	C₂×C₃×#104	—	3	4	no	—
52	C₂×#837	C₃²	1	1	yes	characteristic, direct product factor
53	C₃²×#41	—	2	8	no	—
54	C₃²×#41	—	2	8	no	—
55	C₃²×#41	—	2	8	no	—
56	C₃²×#41	—	2	8	no	—
57	C₃²×#41	—	2	1	no	—
58	C₃²×#41	—	2	1	no	—
59	C₃²×#41	—	2	4	no	—
60	C₃²×#41	—	2	4	no	—
61	C₃²×#41	Dic₃	1	2	yes	complemented
62	C₃²×#41	C₃×C₄	1	8	yes	complemented
63	C₃²×#41	C₂×D₃	1	2	yes	—
64	C₃²×#41	C₂²×C₃	1	8	yes	—
65	C₂×C₃²×Q₈	—	2	4	no	—
66	C₂×C₃²×Q₈	Dic₃	1	1	yes	characteristic, complemented
67	C₂×C₃²×Q₈	C₃×C₄	1	4	yes	complemented
68	C₂×C₃²×D₄	—	2	8	no	—
69	C₂×C₃²×D₄	—	2	4	no	—
70	C₂×C₃²×D₄	—	2	1	no	—
71	C₂×C₃²×D₄	—	2	4	no	—
72	C₂×C₃²×D₄	Dic₃	1	1	yes	characteristic, complemented
73	C₂×C₃²×D₄	C₃×C₄	1	4	yes	complemented
74	C₂²×C₃²×C₄	—	2	8	no	—
75	C₂²×C₃²×C₄	—	2	4	no	—
76	C₂²×C₃²×C₄	—	2	1	no	—
77	C₂²×C₃²×C₄	—	2	4	no	—
78	C₂²×C₃²×C₄	—	6	1	no	—
79	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
80	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
81	C₂²×C₃×Dic₃	—	2	4	no	—
82	C₃²×M₁₆	—	3	2	no	—
83	C₃²×M₁₆	—	6	1	no	—
84	C₂×C₃²×C₈	—	6	1	no	—
85	C₃²×C₄²	—	3	2	no	—
86	C₃²×C₄²	—	6	1	no	—
87	C₃×C₄×Dic₃	—	2	4	no	—
88	C₃×C₄×Dic₃	C₂²×C₃	1	8	yes	complemented
89	C₃×#208	—	2	4	no	—
90	C₃×#208	C₂²×C₃	1	8	yes	complemented
91	C₂×C₃×C₃⋊C₈	—	2	4	no	—
92	C₂²×C₃³	—	2	2	no	—
93	C₂²×C₃³	—	2	2	no	—
94	C₂²×C₃³	—	4	2	no	—
95	C₂²×C₃³	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₃³	C₂²⋊C₄	1	1	yes	characteristic
97	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
98	C₃³×C₄	—	2	2	no	—
99	C₃³×C₄	C₂²⋊C₄	1	1	yes	characteristic
100	C₃³×C₄	C₂²⋊C₄	1	1	yes	characteristic
101	C₃³×C₄	C₂²×C₄	1	1	yes	characteristic
102	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
103	C₃²×Dic₃	—	2	4	no	—
104	C₂×C₃×#41	—	2	4	no	—
105	C₂×C₃×#41	C₃×D₃	1	4	yes	—
106	C₂×C₃×#41	C₂×C₃²	1	1	yes	characteristic
107	C₂×C₃×M₁₆	—	3	4	no	—
108	C₂×C₃×C₄²	—	3	4	no	—
109	C₂×C₄×Dic₃	C₂×C₃²	1	1	yes	characteristic, complemented
110	C₂×#208	C₂×C₃²	1	1	yes	characteristic, complemented
111	C₃×#104	—	3	16	no	—
112	#837	C₂×C₃²	1	4	yes	direct product factor
113	C₂³×C₃²	—	2	8	no	—
114	C₂³×C₃²	—	2	1	no	—
115	C₂³×C₃²	—	2	4	no	—
116	C₂³×C₃²	—	2	4	no	—
117	C₂³×C₃²	#67	1	1	yes	characteristic
118	C₂³×C₃²	C₃×D₄	1	4	yes	—
119	C₃²×Q₈	—	2	8	no	—
120	C₃²×Q₈	—	2	1	no	—
121	C₃²×Q₈	—	2	4	no	—
122	C₃²×Q₈	—	2	8	no	—
123	C₃²×Q₈	C₂×Dic₃	1	2	yes	complemented
124	C₃²×Q₈	C₂×C₃×C₄	1	8	yes	complemented
125	C₃²×D₄	—	2	16	no	—
126	C₃²×D₄	—	2	16	no	—
127	C₃²×D₄	—	2	8	no	—
128	C₃²×D₄	—	2	2	no	—
129	C₃²×D₄	—	2	8	no	—
130	C₃²×D₄	—	2	2	no	—
131	C₃²×D₄	—	2	8	no	—
132	C₃²×D₄	—	2	1	no	—
133	C₃²×D₄	—	2	4	no	—
134	C₃²×D₄	—	2	8	no	—
135	C₃²×D₄	C₂×Dic₃	1	2	yes	complemented
136	C₃²×D₄	C₂×C₃×C₄	1	8	yes	complemented
137	C₂×C₃²×C₄	—	2	8	no	—
138	C₂×C₃²×C₄	—	2	16	no	—
139	C₂×C₃²×C₄	—	2	16	no	—
140	C₂×C₃²×C₄	—	2	1	no	—
141	C₂×C₃²×C₄	—	2	4	no	—
142	C₂×C₃²×C₄	—	2	2	no	—
143	C₂×C₃²×C₄	—	2	8	no	—
144	C₂×C₃²×C₄	—	2	2	no	—
145	C₂×C₃²×C₄	—	2	8	no	—
146	C₂×C₃²×C₄	—	2	4	no	—
147	C₂×C₃²×C₄	—	2	4	no	—
148	C₂×C₃²×C₄	—	2	4	no	—
149	C₂×C₃²×C₄	—	2	4	no	—
150	C₂×C₃²×C₄	—	2	4	no	—
151	C₂×C₃²×C₄	—	2	4	no	—
152	C₂×C₃²×C₄	—	6	4	no	—
153	C₂×C₃²×C₄	—	6	2	no	—
154	C₂×C₃²×C₄	C₂×Dic₃	1	1	yes	characteristic
155	C₂×C₃²×C₄	C₂×Dic₃	1	1	yes	characteristic
156	C₂×C₃²×C₄	#67	1	1	yes	characteristic
157	C₂×C₃²×C₄	#67	1	1	yes	characteristic
158	C₂×C₃²×C₄	#67	1	1	yes	characteristic
159	C₂×C₃²×C₄	C₂×C₃×C₄	1	4	yes	—
160	C₂×C₃²×C₄	C₂×C₃×C₄	1	4	yes	—
161	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
162	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
163	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
164	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
165	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
166	C₂×C₃×Dic₃	—	2	16	no	—
167	C₂×C₃×Dic₃	—	2	8	no	—
168	C₃²×C₈	—	6	2	no	—
169	C₃×C₃⋊C₈	—	2	8	no	—
170	C₂×#104	—	3	1	no	Sylow
171	C₂×C₃³	—	2	1	no	—
172	C₂×C₃³	—	2	1	no	—
173	C₂×C₃³	—	4	2	no	—
174	C₂×C₃³	#104	1	2	yes	complemented
175	C₂×C₃³	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₃×#41	—	2	8	no	—
177	C₃×#41	—	2	8	no	—
178	C₃×#41	—	2	4	no	—
179	C₃×#41	—	2	4	no	—
180	C₃×#41	—	2	1	no	—
181	C₃×#41	—	2	1	no	—
182	C₃×#41	—	2	8	no	—
183	C₃×#41	—	2	8	no	—
184	C₃×#41	C₃×Dic₃	1	8	yes	complemented
185	C₃×#41	C₃²×C₄	1	2	yes	complemented
186	C₃×#41	C₂×C₃×D₃	1	8	yes	—
187	C₃×#41	C₂²×C₃²	1	2	yes	—
188	C₂×C₃×Q₈	—	2	4	no	—
189	C₂×C₃×Q₈	C₃×Dic₃	1	4	yes	complemented
190	C₂×C₃×Q₈	C₃²×C₄	1	1	yes	characteristic, complemented
191	C₂×C₃×D₄	—	2	8	no	—
192	C₂×C₃×D₄	—	2	4	no	—
193	C₂×C₃×D₄	—	2	1	no	—
194	C₂×C₃×D₄	—	2	4	no	—
195	C₂×C₃×D₄	C₃×Dic₃	1	4	yes	complemented
196	C₂×C₃×D₄	C₃²×C₄	1	1	yes	characteristic, complemented
197	C₂²×C₃×C₄	—	2	8	no	—
198	C₂²×C₃×C₄	—	2	4	no	—
199	C₂²×C₃×C₄	—	2	1	no	—
200	C₂²×C₃×C₄	—	2	4	no	—
201	C₂²×C₃×C₄	—	6	4	no	—
202	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
203	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
204	C₂²×Dic₃	—	2	1	no	—
205	C₃×M₁₆	—	3	8	no	—
206	C₃×M₁₆	—	6	4	no	—
207	C₂×C₃×C₈	—	6	4	no	—
208	C₃×C₄²	—	3	8	no	—
209	C₃×C₄²	—	6	4	no	—
210	C₄×Dic₃	—	2	1	no	—
211	C₄×Dic₃	C₂²×C₃²	1	2	yes	complemented
212	#208	—	2	1	no	—
213	#208	C₂²×C₃²	1	2	yes	complemented
214	C₂×C₃⋊C₈	—	2	1	no	—
215	C₂²×C₃²	—	2	2	no	—
216	C₂²×C₃²	—	2	16	no	—
217	C₂²×C₃²	—	2	2	no	—
218	C₂²×C₃²	—	2	8	no	—
219	C₂²×C₃²	—	2	4	no	—
220	C₂²×C₃²	—	2	4	no	—
221	C₂²×C₃²	—	2	4	no	—
222	C₂²×C₃²	—	2	8	no	—
223	C₂²×C₃²	—	4	8	no	—
224	C₂²×C₃²	—	4	16	no	—
225	C₂²×C₃²	—	4	2	no	—
226	C₂²×C₃²	—	4	8	no	—
227	C₂²×C₃²	#217	1	1	yes	characteristic
228	C₂²×C₃²	#217	1	1	yes	characteristic
229	C₂²×C₃²	C₃×C₂²⋊C₄	1	4	yes	—
230	C₂²×C₃²	C₃×C₂²⋊C₄	1	4	yes	—
231	C₂²×C₃²	C₂×#67	1	1	yes	characteristic
232	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
233	C₃²×C₄	—	2	16	no	—
234	C₃²×C₄	—	2	2	no	—
235	C₃²×C₄	—	2	8	no	—
236	C₃²×C₄	—	2	4	no	—
237	C₃²×C₄	—	2	4	no	—
238	C₃²×C₄	—	2	4	no	—
239	C₃²×C₄	—	2	4	no	—
240	C₃²×C₄	—	6	4	no	—
241	C₃²×C₄	#217	1	1	yes	characteristic
242	C₃²×C₄	#217	1	1	yes	characteristic
243	C₃²×C₄	C₃×C₂²⋊C₄	1	4	yes	—
244	C₃²×C₄	C₃×C₂²⋊C₄	1	4	yes	—
245	C₃²×C₄	C₂²×Dic₃	1	1	yes	characteristic
246	C₃²×C₄	C₂×#67	1	1	yes	characteristic
247	C₃²×C₄	C₂²×C₃×C₄	1	4	yes	—
248	C₃²×C₄	C₂×C₃×D₄	1	4	yes	—
249	C₃×Dic₃	—	2	16	no	—
250	C₂×#41	C₃²×D₃	1	1	yes	characteristic
251	C₂×M₁₆	—	3	1	no	—
252	C₂×C₄²	—	3	1	no	—
253	#104	—	3	4	no	—
254	C₃³	C₂×#104	1	1	yes	characteristic, complemented, Sylow
255	C₂³×C₃	—	2	8	no	—
256	C₂³×C₃	—	2	4	no	—
257	C₂³×C₃	—	2	1	no	—
258	C₂³×C₃	—	2	4	no	—
259	C₂³×C₃	C₃×#67	1	4	yes	—
260	C₂³×C₃	C₃²×D₄	1	1	yes	characteristic
261	C₃×Q₈	—	2	8	no	—
262	C₃×Q₈	—	2	4	no	—
263	C₃×Q₈	—	2	1	no	—
264	C₃×Q₈	—	2	8	no	—
265	C₃×Q₈	C₂×C₃×Dic₃	1	8	yes	complemented
266	C₃×Q₈	C₂×C₃²×C₄	1	2	yes	complemented
267	C₃×D₄	—	2	16	no	—
268	C₃×D₄	—	2	16	no	—
269	C₃×D₄	—	2	8	no	—
270	C₃×D₄	—	2	8	no	—
271	C₃×D₄	—	2	2	no	—
272	C₃×D₄	—	2	8	no	—
273	C₃×D₄	—	2	2	no	—
274	C₃×D₄	—	2	4	no	—
275	C₃×D₄	—	2	1	no	—
276	C₃×D₄	—	2	8	no	—
277	C₃×D₄	C₂×C₃×Dic₃	1	8	yes	complemented
278	C₃×D₄	C₂×C₃²×C₄	1	2	yes	complemented
279	C₂×C₃×C₄	—	2	8	no	—
280	C₂×C₃×C₄	—	2	16	no	—
281	C₂×C₃×C₄	—	2	16	no	—
282	C₂×C₃×C₄	—	2	4	no	—
283	C₂×C₃×C₄	—	2	1	no	—
284	C₂×C₃×C₄	—	2	8	no	—
285	C₂×C₃×C₄	—	2	2	no	—
286	C₂×C₃×C₄	—	2	8	no	—
287	C₂×C₃×C₄	—	2	2	no	—
288	C₂×C₃×C₄	—	2	4	no	—
289	C₂×C₃×C₄	—	2	4	no	—
290	C₂×C₃×C₄	—	2	4	no	—
291	C₂×C₃×C₄	—	2	4	no	—
292	C₂×C₃×C₄	—	2	4	no	—
293	C₂×C₃×C₄	—	2	4	no	—
294	C₂×C₃×C₄	—	6	16	no	—
295	C₂×C₃×C₄	—	6	8	no	—
296	C₂×C₃×C₄	C₂×C₃×Dic₃	1	4	yes	—
297	C₂×C₃×C₄	C₂×C₃×Dic₃	1	4	yes	—
298	C₂×C₃×C₄	C₃×#67	1	4	yes	—
299	C₂×C₃×C₄	C₃×#67	1	4	yes	—
300	C₂×C₃×C₄	C₃×#67	1	4	yes	—
301	C₂×C₃×C₄	C₂×C₃²×C₄	1	1	yes	characteristic
302	C₂×C₃×C₄	C₂×C₃²×C₄	1	1	yes	characteristic
303	C₂×C₃×C₄	C₃²×D₄	1	1	yes	characteristic
304	C₂×C₃×C₄	C₃²×D₄	1	1	yes	characteristic
305	C₂×C₃×C₄	C₃²×D₄	1	1	yes	characteristic
306	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
307	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
308	C₂×Dic₃	—	2	4	no	—
309	C₂×Dic₃	—	2	2	no	—
310	C₃×C₈	—	6	8	no	—
311	C₃⋊C₈	—	2	2	no	—
312	C₂×C₃²	—	2	1	no	—
313	C₂×C₃²	—	2	1	no	—
314	C₂×C₃²	—	2	4	no	—
315	C₂×C₃²	—	2	8	no	—
316	C₂×C₃²	—	2	4	no	—
317	C₂×C₃²	—	2	4	no	—
318	C₂×C₃²	—	4	4	no	—
319	C₂×C₃²	—	4	4	no	—
320	C₂×C₃²	—	4	16	no	—
321	C₂×C₃²	—	4	2	no	—
322	C₂×C₃²	—	4	8	no	—
323	C₂×C₃²	#837	1	2	yes	direct product factor
324	C₂×C₃²	C₃×#104	1	8	yes	complemented
325	C₂×C₃²	C₂×#217	1	1	yes	characteristic
326	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	4	yes	—
327	#41	—	2	1	no	—
328	#41	—	2	1	no	—
329	#41	C₃²×Dic₃	1	2	yes	complemented
330	#41	C₂×C₃²×D₃	1	2	yes	—
331	C₂×Q₈	C₃²×Dic₃	1	1	yes	characteristic, complemented
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	C₃²×Dic₃	1	1	yes	characteristic, complemented
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	6	1	no	—
336	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
337	M₁₆	—	3	2	no	—
338	M₁₆	—	6	1	no	—
339	C₂×C₈	—	6	1	no	—
340	C₄²	—	3	2	no	—
341	C₄²	—	6	1	no	—
342	C₂²×C₃	—	2	8	no	—
343	C₂²×C₃	—	2	2	no	—
344	C₂²×C₃	—	2	16	no	—
345	C₂²×C₃	—	2	8	no	—
346	C₂²×C₃	—	2	2	no	—
347	C₂²×C₃	—	2	4	no	—
348	C₂²×C₃	—	2	4	no	—
349	C₂²×C₃	—	2	4	no	—
350	C₂²×C₃	—	4	8	no	—
351	C₂²×C₃	—	4	16	no	—
352	C₂²×C₃	—	4	8	no	—
353	C₂²×C₃	—	4	2	no	—
354	C₂²×C₃	C₃×#217	1	4	yes	—
355	C₂²×C₃	C₃×#217	1	4	yes	—
356	C₂²×C₃	C₃²×C₂²⋊C₄	1	1	yes	characteristic
357	C₂²×C₃	C₃²×C₂²⋊C₄	1	1	yes	characteristic
358	C₂²×C₃	C₂×C₃×#67	1	4	yes	—
359	C₂²×C₃	C₂×C₃²×D₄	1	1	yes	characteristic
360	C₃×C₄	—	2	16	no	—
361	C₃×C₄	—	2	8	no	—
362	C₃×C₄	—	2	2	no	—
363	C₃×C₄	—	2	4	no	—
364	C₃×C₄	—	2	4	no	—
365	C₃×C₄	—	2	4	no	—
366	C₃×C₄	—	2	4	no	—
367	C₃×C₄	—	6	16	no	—
368	C₃×C₄	C₃×#217	1	4	yes	—
369	C₃×C₄	C₃×#217	1	4	yes	—
370	C₃×C₄	C₃²×C₂²⋊C₄	1	1	yes	characteristic
371	C₃×C₄	C₃²×C₂²⋊C₄	1	1	yes	characteristic
372	C₃×C₄	C₂²×C₃×Dic₃	1	4	yes	—
373	C₃×C₄	C₂×C₃×#67	1	4	yes	—
374	C₃×C₄	C₂²×C₃²×C₄	1	1	yes	characteristic
375	C₃×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
376	Dic₃	—	2	4	no	—
377	C₃²	—	2	4	no	—
378	C₃²	C₂×#837	1	1	yes	characteristic, direct product factor
379	C₃²	C₂×C₃×#104	1	4	yes	complemented
380	C₂³	—	2	1	no	—
381	C₂³	C₃²×#67	1	1	yes	characteristic
382	Q₈	—	2	1	no	—
383	Q₈	C₂×C₃²×Dic₃	1	2	yes	complemented
384	D₄	—	2	2	no	—
385	D₄	—	2	2	no	—
386	D₄	—	2	1	no	—
387	D₄	C₂×C₃²×Dic₃	1	2	yes	complemented
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	6	4	no	—
392	C₂×C₄	—	6	2	no	—
393	C₂×C₄	C₂×C₃²×Dic₃	1	1	yes	characteristic
394	C₂×C₄	C₂×C₃²×Dic₃	1	1	yes	characteristic
395	C₂×C₄	C₃²×#67	1	1	yes	characteristic
396	C₂×C₄	C₃²×#67	1	1	yes	characteristic
397	C₂×C₄	C₃²×#67	1	1	yes	characteristic
398	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
399	C₈	—	6	2	no	—
400	C₂×C₃	—	2	4	no	—
401	C₂×C₃	—	2	4	no	—
402	C₂×C₃	—	2	1	no	—
403	C₂×C₃	—	2	1	no	—
404	C₂×C₃	—	2	4	no	—
405	C₂×C₃	—	2	8	no	—
406	C₂×C₃	—	4	4	no	—
407	C₂×C₃	—	4	4	no	—
408	C₂×C₃	—	4	16	no	—
409	C₂×C₃	—	4	8	no	—
410	C₂×C₃	—	4	2	no	—
411	C₂×C₃	C₃×#837	1	8	yes	direct product factor
412	C₂×C₃	C₃²×#104	1	2	yes	complemented
413	C₂×C₃	C₂×C₃×#217	1	4	yes	—
414	C₂×C₃	C₂×C₃²×C₂²⋊C₄	1	1	yes	characteristic
415	C₂²	—	2	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	4	2	no	—
418	C₂²	C₃²×#217	1	1	yes	characteristic
419	C₂²	C₃²×#217	1	1	yes	characteristic
420	C₂²	C₂×C₃²×#67	1	1	yes	characteristic
421	C₄	—	2	2	no	—
422	C₄	—	6	4	no	—
423	C₄	C₃²×#217	1	1	yes	characteristic
424	C₄	C₃²×#217	1	1	yes	characteristic
425	C₄	C₂²×C₃²×Dic₃	1	1	yes	characteristic
426	C₄	C₂×C₃²×#67	1	1	yes	characteristic
427	C₃	—	2	4	no	—
428	C₃	C₂×C₃×#837	1	4	yes	direct product factor
429	C₃	C₂×C₃²×#104	1	1	yes	characteristic, complemented
430	C₂	—	2	1	no	—
431	C₂	—	2	1	no	—
432	C₂	—	4	2	no	—
433	C₂	C₃²×#837	1	2	yes	direct product factor
434	C₂	C₂×C₃²×#217	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃²×C₄	#67
commutator	C₃×C₄	C₂²×C₃²×C₄
Frattini	C₂×C₄	C₂²×C₃²×D₃
Fitting, prime radical	C₂×C₃³×#41	C₂
socle	C₂²×C₃³	C₂²⋊C₄
cosocle	C₂×C₃×C₄	C₂³×C₃²
hypercenter	C₂×C₃²×#41	D₃
hypocenter	C₃	C₂×C₃²×#104
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃²×C₄ ◁ C₂²×C₃²×C₄ ◁ C₂×C₃²×#41

Complements

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

N	H ≅ G/N	type
2. C₂×C₃²×C₄×Dic₃	C₂	semidirect
3. C₂×C₃²×#208	C₂	semidirect
4. C₃²×#837	C₂	direct (N × H)
6. C₂×C₃×#837	C₃	direct (N × H)
9. C₃³×#41	C₄	semidirect
11. C₂×C₃³×Q₈	C₄	semidirect
13. C₂×C₃³×D₄	C₄	semidirect
18. C₃²×C₄×Dic₃	C₂²	semidirect
20. C₃²×#208	C₂²	semidirect
27. C₂×C₃×C₄×Dic₃	C₂×C₃	semidirect
28. C₂×C₃×#208	C₂×C₃	semidirect
30. C₃×#837	C₂×C₃	direct (N × H)
34. C₃³×Q₈	C₂×C₄	semidirect
38. C₃³×D₄	C₂×C₄	semidirect
52. C₂×#837	C₃²	direct (N × H)
61. C₃²×#41	Dic₃	semidirect
62. C₃²×#41	C₃×C₄	semidirect
66. C₂×C₃²×Q₈	Dic₃	semidirect
67. C₂×C₃²×Q₈	C₃×C₄	semidirect
72. C₂×C₃²×D₄	Dic₃	semidirect
73. C₂×C₃²×D₄	C₃×C₄	semidirect
88. C₃×C₄×Dic₃	C₂²×C₃	semidirect
90. C₃×#208	C₂²×C₃	semidirect
109. C₂×C₄×Dic₃	C₂×C₃²	semidirect
110. C₂×#208	C₂×C₃²	semidirect
112. #837	C₂×C₃²	direct (N × H)
123. C₃²×Q₈	C₂×Dic₃	semidirect
124. C₃²×Q₈	C₂×C₃×C₄	semidirect
135. C₃²×D₄	C₂×Dic₃	semidirect
136. C₃²×D₄	C₂×C₃×C₄	semidirect
174. C₂×C₃³	#104	semidirect
184. C₃×#41	C₃×Dic₃	semidirect
185. C₃×#41	C₃²×C₄	semidirect
189. C₂×C₃×Q₈	C₃×Dic₃	semidirect
190. C₂×C₃×Q₈	C₃²×C₄	semidirect
195. C₂×C₃×D₄	C₃×Dic₃	semidirect
196. C₂×C₃×D₄	C₃²×C₄	semidirect
211. C₄×Dic₃	C₂²×C₃²	semidirect
213. #208	C₂²×C₃²	semidirect
254. C₃³	C₂×#104	semidirect
265. C₃×Q₈	C₂×C₃×Dic₃	semidirect
266. C₃×Q₈	C₂×C₃²×C₄	semidirect
277. C₃×D₄	C₂×C₃×Dic₃	semidirect
278. C₃×D₄	C₂×C₃²×C₄	semidirect
323. C₂×C₃²	#837	direct (N × H)
324. C₂×C₃²	C₃×#104	semidirect
329. #41	C₃²×Dic₃	semidirect
331. C₂×Q₈	C₃²×Dic₃	semidirect
333. C₂×D₄	C₃²×Dic₃	semidirect
378. C₃²	C₂×#837	direct (N × H)
379. C₃²	C₂×C₃×#104	semidirect
383. Q₈	C₂×C₃²×Dic₃	semidirect
387. D₄	C₂×C₃²×Dic₃	semidirect
411. C₂×C₃	C₃×#837	direct (N × H)
412. C₂×C₃	C₃²×#104	semidirect
428. C₃	C₂×C₃×#837	direct (N × H)
429. C₃	C₂×C₃²×#104	semidirect
433. C₂	C₃²×#837	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×C₃³×#41	2
C₂×C₃²×C₄×Dic₃	2
C₂×C₃²×#208	2
C₃²×#837	2
C₂×C₃²×#104	3
C₂×C₃×#837	3

Subgroups — C2×C32×#837 #13162668

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×#837 #13162668