Subgroups — C₂×C₃²×#805 #13162373

Order 1728.

1452 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#235	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃³×C₄²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃²×#208	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#805	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₃²×#104	—	3	1	no	maximal
6	C₂×C₃×#805	C₃	1	4	yes	maximal, direct product factor
7	C₂²×C₃³×C₄	—	2	1	no	—
8	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
9	C₂×C₃²×#67	—	2	1	no	—
10	C₃²×#235	—	2	1	no	—
11	C₃²×#235	—	2	1	no	—
12	C₃²×#235	C₄	1	2	yes	complemented
13	C₃²×#235	C₂²	1	2	yes	—
14	C₂×C₃²×D₁₂	C₄	1	1	yes	characteristic, complemented
15	C₂×C₃²×C₄×D₃	—	2	1	no	—
16	C₂×C₃²×Dic₆	C₄	1	1	yes	characteristic, complemented
17	C₃³×C₄²	—	2	1	no	—
18	C₃³×C₄²	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	—	3	1	no	—
23	C₂×C₃×#235	C₂×C₃	1	4	yes	—
24	C₂×C₃²×M₁₆	—	3	1	no	—
25	C₂×C₃²×C₄²	—	2	4	no	—
26	C₂×C₃²×C₄²	D₃	1	1	yes	characteristic, complemented
27	C₂×C₃²×C₄²	C₂×C₃	1	4	yes	complemented
28	C₂×C₃×#208	C₂×C₃	1	4	yes	complemented
29	C₃²×#104	—	3	4	no	—
30	C₃×#805	C₂×C₃	1	16	yes	direct product factor
31	C₂³×C₃³	D₄	1	1	yes	characteristic
32	C₂²×C₃²×D₃	—	2	1	no	—
33	C₂×C₃³×C₄	—	2	4	no	—
34	C₂×C₃³×C₄	—	2	2	no	—
35	C₂×C₃³×C₄	C₂×C₄	1	1	yes	characteristic
36	C₂×C₃³×C₄	C₂×C₄	1	1	yes	characteristic
37	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
38	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
39	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
40	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
41	C₃²×#67	—	2	2	no	—
42	C₃²×#67	—	2	2	no	—
43	C₂×C₃²×Dic₃	—	2	1	no	—
44	C₃²×D₁₂	—	2	1	no	—
45	C₃²×D₁₂	C₂×C₄	1	2	yes	complemented
46	C₃²×C₄×D₃	—	2	2	no	—
47	C₃²×C₄×D₃	—	2	2	no	—
48	C₃²×Dic₆	—	2	1	no	—
49	C₃²×Dic₆	C₂×C₄	1	2	yes	complemented
50	C₃²×C₃⋊C₈	—	2	2	no	—
51	C₂×C₃×#104	—	3	4	no	—
52	C₂×#805	C₃²	1	1	yes	characteristic, direct product factor
53	C₃²×#41	—	3	2	no	—
54	C₃²×#41	—	3	2	no	—
55	C₃²×#41	—	6	1	no	—
56	C₃²×#41	—	6	1	no	—
57	C₂×C₃²×Q₈	—	3	1	no	—
58	C₂×C₃²×D₄	—	3	1	no	—
59	C₂×C₃²×D₄	—	6	1	no	—
60	C₂²×C₃²×C₄	—	2	8	no	—
61	C₂²×C₃²×C₄	—	2	4	no	—
62	C₂²×C₃²×C₄	—	2	1	no	—
63	C₂²×C₃²×C₄	—	2	4	no	—
64	C₂²×C₃²×C₄	—	6	1	no	—
65	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
66	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
67	C₂×C₃×#67	—	2	4	no	—
68	C₃×#235	—	2	4	no	—
69	C₃×#235	—	2	4	no	—
70	C₃×#235	C₃×C₄	1	8	yes	complemented
71	C₃×#235	C₂²×C₃	1	8	yes	—
72	C₂×C₃×D₁₂	C₃×C₄	1	4	yes	complemented
73	C₂×C₃×C₄×D₃	—	2	4	no	—
74	C₂×C₃×Dic₆	C₃×C₄	1	4	yes	complemented
75	C₃²×M₁₆	—	3	2	no	—
76	C₃²×M₁₆	—	6	1	no	—
77	C₂×C₃²×C₈	—	6	1	no	—
78	C₃²×C₄²	—	2	8	no	—
79	C₃²×C₄²	—	2	8	no	—
80	C₃²×C₄²	—	2	1	no	—
81	C₃²×C₄²	—	2	4	no	—
82	C₃²×C₄²	C₂×D₃	1	2	yes	complemented
83	C₃²×C₄²	C₂²×C₃	1	8	yes	complemented
84	C₃×#208	—	2	4	no	—
85	C₃×#208	C₂²×C₃	1	8	yes	complemented
86	C₂×C₃×C₃⋊C₈	—	2	4	no	—
87	C₂²×C₃³	—	2	2	no	—
88	C₂²×C₃³	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×C₃³	C₂²⋊C₄	1	1	yes	characteristic
90	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
91	C₂×C₃²×D₃	—	2	2	no	—
92	C₂×C₃²×D₃	—	4	2	no	—
93	C₃³×C₄	—	2	4	no	—
94	C₃³×C₄	C₂²⋊C₄	1	1	yes	characteristic
95	C₃³×C₄	C₂²⋊C₄	1	1	yes	characteristic
96	C₃³×C₄	C₂²×C₄	1	1	yes	characteristic
97	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
98	C₃²×Dic₃	—	2	2	no	—
99	C₂×C₃×#41	—	3	4	no	—
100	C₂×#235	C₂×C₃²	1	1	yes	characteristic
101	C₂×C₃×M₁₆	—	3	4	no	—
102	C₂×C₃×C₄²	—	2	4	no	—
103	C₂×C₃×C₄²	C₃×D₃	1	4	yes	complemented
104	C₂×C₃×C₄²	C₂×C₃²	1	1	yes	characteristic, complemented
105	C₂×#208	C₂×C₃²	1	1	yes	characteristic, complemented
106	C₃×#104	—	3	16	no	—
107	#805	C₂×C₃²	1	4	yes	direct product factor
108	C₂³×C₃²	—	2	4	no	—
109	C₂³×C₃²	—	6	1	no	—
110	C₂³×C₃²	#67	1	1	yes	characteristic
111	C₂³×C₃²	C₃×D₄	1	4	yes	—
112	C₂²×C₃×D₃	—	2	4	no	—
113	C₃²×Q₈	—	3	2	no	—
114	C₃²×Q₈	—	6	1	no	—
115	C₃²×D₄	—	3	2	no	—
116	C₃²×D₄	—	6	2	no	—
117	C₃²×D₄	—	6	2	no	—
118	C₃²×D₄	—	6	1	no	—
119	C₂×C₃²×C₄	—	2	16	no	—
120	C₂×C₃²×C₄	—	2	32	no	—
121	C₂×C₃²×C₄	—	2	4	no	—
122	C₂×C₃²×C₄	—	2	16	no	—
123	C₂×C₃²×C₄	—	2	2	no	—
124	C₂×C₃²×C₄	—	2	8	no	—
125	C₂×C₃²×C₄	—	2	4	no	—
126	C₂×C₃²×C₄	—	2	4	no	—
127	C₂×C₃²×C₄	—	2	4	no	—
128	C₂×C₃²×C₄	—	2	4	no	—
129	C₂×C₃²×C₄	—	2	4	no	—
130	C₂×C₃²×C₄	—	2	4	no	—
131	C₂×C₃²×C₄	—	6	1	no	—
132	C₂×C₃²×C₄	—	6	2	no	—
133	C₂×C₃²×C₄	—	6	2	no	—
134	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
135	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
136	C₂×C₃²×C₄	D₁₂	1	1	yes	characteristic
137	C₂×C₃²×C₄	D₁₂	1	1	yes	characteristic
138	C₂×C₃²×C₄	#67	1	1	yes	characteristic
139	C₂×C₃²×C₄	C₂×C₃×C₄	1	4	yes	—
140	C₂×C₃²×C₄	C₂×C₃×C₄	1	4	yes	—
141	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
142	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
143	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
144	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
145	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
146	C₃×#67	—	2	8	no	—
147	C₃×#67	—	2	8	no	—
148	C₂×C₃×Dic₃	—	2	4	no	—
149	C₃×D₁₂	—	2	4	no	—
150	C₃×D₁₂	C₂×C₃×C₄	1	8	yes	complemented
151	C₃×C₄×D₃	—	2	8	no	—
152	C₃×C₄×D₃	—	2	8	no	—
153	C₃×Dic₆	—	2	4	no	—
154	C₃×Dic₆	C₂×C₃×C₄	1	8	yes	complemented
155	C₃²×C₈	—	6	2	no	—
156	C₃×C₃⋊C₈	—	2	8	no	—
157	C₂×#104	—	3	1	no	Sylow
158	C₂×C₃³	—	2	1	no	—
159	C₂×C₃³	—	2	1	no	—
160	C₂×C₃³	#104	1	2	yes	complemented
161	C₂×C₃³	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₃²×D₃	—	4	2	no	—
163	C₃×#41	—	3	8	no	—
164	C₃×#41	—	3	8	no	—
165	C₃×#41	—	6	4	no	—
166	C₃×#41	—	6	4	no	—
167	C₂×C₃×Q₈	—	3	4	no	—
168	C₂×C₃×D₄	—	3	4	no	—
169	C₂×C₃×D₄	—	6	4	no	—
170	C₂²×C₃×C₄	—	2	8	no	—
171	C₂²×C₃×C₄	—	2	4	no	—
172	C₂²×C₃×C₄	—	2	1	no	—
173	C₂²×C₃×C₄	—	2	4	no	—
174	C₂²×C₃×C₄	—	6	4	no	—
175	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
176	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
177	C₂×#67	—	2	1	no	—
178	#235	—	2	1	no	—
179	#235	—	2	1	no	—
180	#235	C₃²×C₄	1	2	yes	complemented
181	#235	C₂²×C₃²	1	2	yes	—
182	C₂×D₁₂	C₃²×C₄	1	1	yes	characteristic, complemented
183	C₂×C₄×D₃	—	2	1	no	—
184	C₂×Dic₆	C₃²×C₄	1	1	yes	characteristic, complemented
185	C₃×M₁₆	—	3	8	no	—
186	C₃×M₁₆	—	6	4	no	—
187	C₂×C₃×C₈	—	6	4	no	—
188	C₃×C₄²	—	2	8	no	—
189	C₃×C₄²	—	2	4	no	—
190	C₃×C₄²	—	2	1	no	—
191	C₃×C₄²	—	2	8	no	—
192	C₃×C₄²	C₂×C₃×D₃	1	8	yes	complemented
193	C₃×C₄²	C₂²×C₃²	1	2	yes	complemented
194	#208	—	2	1	no	—
195	#208	C₂²×C₃²	1	2	yes	complemented
196	C₂×C₃⋊C₈	—	2	1	no	—
197	C₂²×C₃²	—	2	16	no	—
198	C₂²×C₃²	—	2	2	no	—
199	C₂²×C₃²	—	2	8	no	—
200	C₂²×C₃²	—	2	4	no	—
201	C₂²×C₃²	—	2	4	no	—
202	C₂²×C₃²	—	2	4	no	—
203	C₂²×C₃²	—	6	2	no	—
204	C₂²×C₃²	—	12	2	no	—
205	C₂²×C₃²	(C₂×D₃)⋊C₄	1	1	yes	characteristic
206	C₂²×C₃²	(C₂×D₃)⋊C₄	1	1	yes	characteristic
207	C₂²×C₃²	C₃×C₂²⋊C₄	1	4	yes	—
208	C₂²×C₃²	C₃×C₂²⋊C₄	1	4	yes	—
209	C₂²×C₃²	C₂×#67	1	1	yes	characteristic
210	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
211	C₂×C₃×D₃	—	2	8	no	—
212	C₂×C₃×D₃	—	4	8	no	—
213	C₃²×C₄	—	2	32	no	—
214	C₃²×C₄	—	2	4	no	—
215	C₃²×C₄	—	2	16	no	—
216	C₃²×C₄	—	2	4	no	—
217	C₃²×C₄	—	2	4	no	—
218	C₃²×C₄	—	2	4	no	—
219	C₃²×C₄	—	2	4	no	—
220	C₃²×C₄	—	6	2	no	—
221	C₃²×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
222	C₃²×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
223	C₃²×C₄	C₃×C₂²⋊C₄	1	4	yes	—
224	C₃²×C₄	C₃×C₂²⋊C₄	1	4	yes	—
225	C₃²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
226	C₃²×C₄	C₂×D₁₂	1	1	yes	characteristic
227	C₃²×C₄	C₂²×C₃×C₄	1	4	yes	—
228	C₃²×C₄	C₂×C₃×D₄	1	4	yes	—
229	C₃×Dic₃	—	2	8	no	—
230	C₂×#41	—	3	1	no	—
231	C₂×M₁₆	—	3	1	no	—
232	C₂×C₄²	C₃²×D₃	1	1	yes	characteristic, complemented
233	#104	—	3	4	no	—
234	C₃³	C₂×#104	1	1	yes	characteristic, complemented, Sylow
235	C₂³×C₃	—	2	4	no	—
236	C₂³×C₃	—	6	4	no	—
237	C₂³×C₃	C₃×#67	1	4	yes	—
238	C₂³×C₃	C₃²×D₄	1	1	yes	characteristic
239	C₂²×D₃	—	2	1	no	—
240	C₃×Q₈	—	3	8	no	—
241	C₃×Q₈	—	6	4	no	—
242	C₃×D₄	—	3	8	no	—
243	C₃×D₄	—	6	8	no	—
244	C₃×D₄	—	6	8	no	—
245	C₃×D₄	—	6	4	no	—
246	C₂×C₃×C₄	—	2	16	no	—
247	C₂×C₃×C₄	—	2	32	no	—
248	C₂×C₃×C₄	—	2	16	no	—
249	C₂×C₃×C₄	—	2	4	no	—
250	C₂×C₃×C₄	—	2	8	no	—
251	C₂×C₃×C₄	—	2	2	no	—
252	C₂×C₃×C₄	—	2	4	no	—
253	C₂×C₃×C₄	—	2	4	no	—
254	C₂×C₃×C₄	—	2	4	no	—
255	C₂×C₃×C₄	—	2	4	no	—
256	C₂×C₃×C₄	—	2	4	no	—
257	C₂×C₃×C₄	—	2	4	no	—
258	C₂×C₃×C₄	—	6	4	no	—
259	C₂×C₃×C₄	—	6	8	no	—
260	C₂×C₃×C₄	—	6	8	no	—
261	C₂×C₃×C₄	C₃×C₄×D₃	1	4	yes	—
262	C₂×C₃×C₄	C₃×C₄×D₃	1	4	yes	—
263	C₂×C₃×C₄	C₃×D₁₂	1	4	yes	—
264	C₂×C₃×C₄	C₃×D₁₂	1	4	yes	—
265	C₂×C₃×C₄	C₃×#67	1	4	yes	—
266	C₂×C₃×C₄	C₂×C₃²×C₄	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂×C₃²×C₄	1	1	yes	characteristic
268	C₂×C₃×C₄	C₃²×D₄	1	1	yes	characteristic
269	C₂×C₃×C₄	C₃²×D₄	1	1	yes	characteristic
270	C₂×C₃×C₄	C₃²×D₄	1	1	yes	characteristic
271	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
272	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
273	#67	—	2	2	no	—
274	#67	—	2	2	no	—
275	C₂×Dic₃	—	2	1	no	—
276	D₁₂	—	2	1	no	—
277	D₁₂	C₂×C₃²×C₄	1	2	yes	complemented
278	C₄×D₃	—	2	2	no	—
279	C₄×D₃	—	2	2	no	—
280	Dic₆	—	2	1	no	—
281	Dic₆	C₂×C₃²×C₄	1	2	yes	complemented
282	C₃×C₈	—	6	8	no	—
283	C₃⋊C₈	—	2	2	no	—
284	C₂×C₃²	—	2	8	no	—
285	C₂×C₃²	—	2	8	no	—
286	C₂×C₃²	—	2	1	no	—
287	C₂×C₃²	—	2	1	no	—
288	C₂×C₃²	—	2	4	no	—
289	C₂×C₃²	—	2	4	no	—
290	C₂×C₃²	—	2	4	no	—
291	C₂×C₃²	—	2	8	no	—
292	C₂×C₃²	—	12	2	no	—
293	C₂×C₃²	#805	1	2	yes	direct product factor
294	C₂×C₃²	C₃×#104	1	8	yes	complemented
295	C₂×C₃²	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
296	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	4	yes	—
297	C₃×D₃	—	4	8	no	—
298	#41	—	3	2	no	—
299	#41	—	3	2	no	—
300	#41	—	6	1	no	—
301	#41	—	6	1	no	—
302	C₂×Q₈	—	3	1	no	—
303	C₂×D₄	—	3	1	no	—
304	C₂×D₄	—	6	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	6	1	no	—
307	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
308	M₁₆	—	3	2	no	—
309	M₁₆	—	6	1	no	—
310	C₂×C₈	—	6	1	no	—
311	C₄²	—	2	1	no	—
312	C₄²	C₂×C₃²×D₃	1	2	yes	complemented
313	C₂²×C₃	—	2	16	no	—
314	C₂²×C₃	—	2	8	no	—
315	C₂²×C₃	—	2	2	no	—
316	C₂²×C₃	—	2	4	no	—
317	C₂²×C₃	—	2	4	no	—
318	C₂²×C₃	—	2	4	no	—
319	C₂²×C₃	—	6	8	no	—
320	C₂²×C₃	—	12	8	no	—
321	C₂²×C₃	C₃×(C₂×D₃)⋊C₄	1	4	yes	—
322	C₂²×C₃	C₃×(C₂×D₃)⋊C₄	1	4	yes	—
323	C₂²×C₃	C₃²×C₂²⋊C₄	1	1	yes	characteristic
324	C₂²×C₃	C₃²×C₂²⋊C₄	1	1	yes	characteristic
325	C₂²×C₃	C₂×C₃×#67	1	4	yes	—
326	C₂²×C₃	C₂×C₃²×D₄	1	1	yes	characteristic
327	C₂×D₃	—	2	2	no	—
328	C₂×D₃	—	4	2	no	—
329	C₃×C₄	—	2	32	no	—
330	C₃×C₄	—	2	16	no	—
331	C₃×C₄	—	2	4	no	—
332	C₃×C₄	—	2	4	no	—
333	C₃×C₄	—	2	4	no	—
334	C₃×C₄	—	2	4	no	—
335	C₃×C₄	—	2	4	no	—
336	C₃×C₄	—	6	8	no	—
337	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	4	yes	—
338	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	4	yes	—
339	C₃×C₄	C₃²×C₂²⋊C₄	1	1	yes	characteristic
340	C₃×C₄	C₃²×C₂²⋊C₄	1	1	yes	characteristic
341	C₃×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
342	C₃×C₄	C₂×C₃×D₁₂	1	4	yes	—
343	C₃×C₄	C₂²×C₃²×C₄	1	1	yes	characteristic
344	C₃×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
345	Dic₃	—	2	2	no	—
346	C₃²	—	2	4	no	—
347	C₃²	C₂×#805	1	1	yes	characteristic, direct product factor
348	C₃²	C₂×C₃×#104	1	4	yes	complemented
349	C₂³	—	6	1	no	—
350	C₂³	C₃²×#67	1	1	yes	characteristic
351	Q₈	—	3	2	no	—
352	Q₈	—	6	1	no	—
353	D₄	—	3	2	no	—
354	D₄	—	6	2	no	—
355	D₄	—	6	2	no	—
356	D₄	—	6	1	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	6	1	no	—
360	C₂×C₄	—	6	2	no	—
361	C₂×C₄	—	6	2	no	—
362	C₂×C₄	C₃²×C₄×D₃	1	1	yes	characteristic
363	C₂×C₄	C₃²×C₄×D₃	1	1	yes	characteristic
364	C₂×C₄	C₃²×D₁₂	1	1	yes	characteristic
365	C₂×C₄	C₃²×D₁₂	1	1	yes	characteristic
366	C₂×C₄	C₃²×#67	1	1	yes	characteristic
367	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
368	C₈	—	6	2	no	—
369	C₂×C₃	—	2	8	no	—
370	C₂×C₃	—	2	8	no	—
371	C₂×C₃	—	2	4	no	—
372	C₂×C₃	—	2	4	no	—
373	C₂×C₃	—	2	1	no	—
374	C₂×C₃	—	2	1	no	—
375	C₂×C₃	—	2	4	no	—
376	C₂×C₃	—	2	8	no	—
377	C₂×C₃	—	12	8	no	—
378	C₂×C₃	C₃×#805	1	8	yes	direct product factor
379	C₂×C₃	C₃²×#104	1	2	yes	complemented
380	C₂×C₃	C₂×C₃×(C₂×D₃)⋊C₄	1	4	yes	—
381	C₂×C₃	C₂×C₃²×C₂²⋊C₄	1	1	yes	characteristic
382	D₃	—	4	2	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	6	2	no	—
385	C₂²	—	12	2	no	—
386	C₂²	C₃²×(C₂×D₃)⋊C₄	1	1	yes	characteristic
387	C₂²	C₃²×(C₂×D₃)⋊C₄	1	1	yes	characteristic
388	C₂²	C₂×C₃²×#67	1	1	yes	characteristic
389	C₄	—	2	4	no	—
390	C₄	—	6	2	no	—
391	C₄	C₃²×(C₂×D₃)⋊C₄	1	1	yes	characteristic
392	C₄	C₃²×(C₂×D₃)⋊C₄	1	1	yes	characteristic
393	C₄	C₂×C₃²×C₄×D₃	1	1	yes	characteristic
394	C₄	C₂×C₃²×D₁₂	1	1	yes	characteristic
395	C₃	—	2	4	no	—
396	C₃	C₂×C₃×#805	1	4	yes	direct product factor
397	C₃	C₂×C₃²×#104	1	1	yes	characteristic, complemented
398	C₂	—	2	1	no	—
399	C₂	—	2	1	no	—
400	C₂	—	12	2	no	—
401	C₂	C₃²×#805	1	2	yes	direct product factor
402	C₂	C₂×C₃²×(C₂×D₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃²×C₄	D₁₂
commutator	C₃×C₄	C₂²×C₃²×C₄
Frattini	C₂×C₄	C₂²×C₃²×D₃
Fitting	C₂×C₃³×C₄²	C₂
socle	C₂²×C₃³	C₂²⋊C₄
prime radical	C₂×C₃²×#235	C₂
cosocle	C₂×C₃×C₄	C₂³×C₃²
hypercenter	C₂×C₃²×C₄²	D₃
hypocenter	C₃	C₂×C₃²×#104
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃²×C₄ ◁ C₂²×C₃²×C₄ ◁ C₂×C₃²×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂×C₃³×C₄²	C₂	semidirect
3. C₂×C₃²×#208	C₂	semidirect
4. C₃²×#805	C₂	direct (N × H)
6. C₂×C₃×#805	C₃	direct (N × H)
12. C₃²×#235	C₄	semidirect
14. C₂×C₃²×D₁₂	C₄	semidirect
16. C₂×C₃²×Dic₆	C₄	semidirect
18. C₃³×C₄²	C₂²	semidirect
20. C₃²×#208	C₂²	semidirect
26. C₂×C₃²×C₄²	D₃	semidirect
27. C₂×C₃²×C₄²	C₂×C₃	semidirect
28. C₂×C₃×#208	C₂×C₃	semidirect
30. C₃×#805	C₂×C₃	direct (N × H)
45. C₃²×D₁₂	C₂×C₄	semidirect
49. C₃²×Dic₆	C₂×C₄	semidirect
52. C₂×#805	C₃²	direct (N × H)
70. C₃×#235	C₃×C₄	semidirect
72. C₂×C₃×D₁₂	C₃×C₄	semidirect
74. C₂×C₃×Dic₆	C₃×C₄	semidirect
82. C₃²×C₄²	C₂×D₃	semidirect
83. C₃²×C₄²	C₂²×C₃	semidirect
85. C₃×#208	C₂²×C₃	semidirect
103. C₂×C₃×C₄²	C₃×D₃	semidirect
104. C₂×C₃×C₄²	C₂×C₃²	semidirect
105. C₂×#208	C₂×C₃²	semidirect
107. #805	C₂×C₃²	direct (N × H)
150. C₃×D₁₂	C₂×C₃×C₄	semidirect
154. C₃×Dic₆	C₂×C₃×C₄	semidirect
160. C₂×C₃³	#104	semidirect
180. #235	C₃²×C₄	semidirect
182. C₂×D₁₂	C₃²×C₄	semidirect
184. C₂×Dic₆	C₃²×C₄	semidirect
192. C₃×C₄²	C₂×C₃×D₃	semidirect
193. C₃×C₄²	C₂²×C₃²	semidirect
195. #208	C₂²×C₃²	semidirect
232. C₂×C₄²	C₃²×D₃	semidirect
234. C₃³	C₂×#104	semidirect
277. D₁₂	C₂×C₃²×C₄	semidirect
281. Dic₆	C₂×C₃²×C₄	semidirect
293. C₂×C₃²	#805	direct (N × H)
294. C₂×C₃²	C₃×#104	semidirect
312. C₄²	C₂×C₃²×D₃	semidirect
347. C₃²	C₂×#805	direct (N × H)
348. C₃²	C₂×C₃×#104	semidirect
378. C₂×C₃	C₃×#805	direct (N × H)
379. C₂×C₃	C₃²×#104	semidirect
396. C₃	C₂×C₃×#805	direct (N × H)
397. C₃	C₂×C₃²×#104	semidirect
401. C₂	C₃²×#805	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×C₃²×#235	2
C₂×C₃³×C₄²	2
C₂×C₃²×#208	2
C₃²×#805	2
C₂×C₃²×#104	3
C₂×C₃×#805	3

Subgroups — C2×C32×#805 #13162373

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×#805 #13162373