Subgroups — C₂×D₃×#812 #11899367

Order 1152.

845 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₃×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#63639	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#812	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#63543	C₂	1	2	yes	maximal, complemented
5	D₃×#812	C₂	1	8	yes	maximal, direct product factor
6	C₂×D₃×C₃⋊C₁₆	C₂	1	2	yes	maximal, complemented
7	C₂²×#812	—	3	1	no	maximal
8	C₂×D₃×M₃₂	—	3	1	no	maximal
9	C₂²×C₃×C₄×D₃	C₄	1	1	yes	characteristic
10	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₃⋊C₈	C₄	1	1	yes	characteristic
12	C₂×C₃×D₃×C₈	C₄	1	4	yes	—
13	C₂×C₃×D₃×C₈	C₄	1	1	yes	characteristic
14	C₂×C₃×D₃×C₈	C₄	1	1	yes	characteristic
15	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
16	C₂×C₃×D₃×C₈	C₂²	1	4	yes	—
17	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
18	#63639	C₂²	1	4	yes	complemented
19	C₂×C₃⋊(C₃⋊C₁₆)	C₂²	1	2	yes	complemented
20	C₃×#812	C₂²	1	4	yes	complemented
21	C₂×C₃×C₃⋊C₁₆	C₂²	1	2	yes	complemented
22	#63543	C₂²	1	8	yes	complemented
23	D₃×C₃⋊C₁₆	C₂²	1	8	yes	complemented
24	C₂³×C₃×C₈	—	3	1	no	—
25	C₂²×D₃×C₈	D₃	1	1	yes	characteristic
26	C₂×C₃×M₃₂	—	3	1	no	—
27	C₂×#812	—	3	1	no	—
28	C₂×#812	—	3	1	no	—
29	C₂×#812	—	3	8	no	—
30	C₂×#812	—	3	2	no	—
31	C₂×#812	—	6	1	no	—
32	C₂×#812	D₃	1	1	yes	characteristic, direct product factor
33	C₂²×C₃⋊C₁₆	—	3	2	no	—
34	D₃×M₃₂	—	3	8	no	—
35	C₂×#798	—	3	2	no	—
36	C₂×D₃×C₁₆	—	3	2	no	—
37	C₂³×C₃×D₃	C₈	1	1	yes	characteristic
38	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃×Dic₃	C₈	1	1	yes	characteristic
40	C₂×C₃×C₄×D₃	C₈	1	1	yes	characteristic
41	C₂×C₃×C₄×D₃	C₈	1	4	yes	—
42	C₂×C₃×C₄×D₃	C₈	1	1	yes	characteristic
43	C₂×C₃×C₄×D₃	C₂×C₄	1	4	yes	—
44	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
47	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
48	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
49	C₂×C₃²×C₈	C₂³	1	2	yes	—
50	C₂×C₃×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
51	C₂×C₃×C₃⋊C₈	C₂×C₄	1	4	yes	—
52	C₂×C₃×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
53	C₃×D₃×C₈	C₂×C₄	1	2	yes	—
54	C₃×D₃×C₈	C₂×C₄	1	4	yes	—
55	C₃×D₃×C₈	C₂×C₄	1	4	yes	—
56	C₃×D₃×C₈	C₂×C₄	1	2	yes	—
57	C₃×D₃×C₈	C₂³	1	2	yes	—
58	C₃×D₃×C₈	C₂³	1	2	yes	—
59	C₃⋊(C₃⋊C₁₆)	C₂³	1	4	yes	complemented
60	C₃×C₃⋊C₁₆	C₂³	1	4	yes	complemented
61	C₂²×M₃₂	—	9	1	no	Sylow
62	C₂³×C₃×C₄	—	3	1	no	—
63	C₂²×C₄×D₃	Dic₃	1	1	yes	characteristic
64	C₂²×C₃×C₈	—	2	1	no	—
65	C₂²×C₃×C₈	—	3	1	no	—
66	C₂²×C₃×C₈	—	3	1	no	—
67	C₂²×C₃×C₈	—	3	4	no	—
68	C₂²×C₃×C₈	—	3	1	no	—
69	C₂²×C₃×C₈	—	3	1	no	—
70	C₂²×C₃×C₈	—	3	4	no	—
71	C₂²×C₃×C₈	—	3	1	no	—
72	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
73	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
74	C₂²×C₃⋊C₈	Dic₃	1	1	yes	characteristic
75	C₂×D₃×C₈	Dic₃	1	4	yes	—
76	C₂×D₃×C₈	Dic₃	1	1	yes	characteristic
77	C₂×D₃×C₈	Dic₃	1	1	yes	characteristic
78	C₂×D₃×C₈	C₂×D₃	1	1	yes	characteristic
79	C₂×D₃×C₈	C₂×D₃	1	1	yes	characteristic
80	C₂×D₃×C₈	C₂×D₃	1	4	yes	—
81	C₃×M₃₂	—	3	4	no	—
82	C₂×C₃×C₁₆	—	3	2	no	—
83	#812	—	3	4	no	—
84	#812	—	3	4	no	—
85	#812	—	3	8	no	—
86	#812	—	6	4	no	—
87	#812	C₂×D₃	1	4	yes	direct product factor
88	C₂×C₃⋊C₁₆	—	3	2	no	—
89	C₂×C₃⋊C₁₆	—	3	2	no	—
90	C₂×C₃⋊C₁₆	—	3	8	no	—
91	C₂×C₃⋊C₁₆	—	6	2	no	—
92	C₂×C₃⋊C₁₆	C₂×D₃	1	2	yes	complemented
93	#798	—	3	8	no	—
94	D₃×C₁₆	—	3	8	no	—
95	C₂³×C₃²	C₂×C₈	1	1	yes	characteristic
96	C₂²×C₃×D₃	—	2	4	no	—
97	C₂²×C₃×D₃	C₂×C₈	1	1	yes	characteristic
98	C₂²×C₃×D₃	C₂×C₈	1	4	yes	—
99	C₂²×C₃×D₃	C₂×C₈	1	1	yes	characteristic
100	C₂×C₃²×C₄	C₂×C₈	1	2	yes	—
101	C₂×C₃²×C₄	C₂×C₈	1	1	yes	characteristic
102	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
103	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₃×Dic₃	C₂×C₈	1	4	yes	—
105	C₂×C₃×Dic₃	C₂×C₈	1	1	yes	characteristic
106	C₂×C₃×Dic₃	C₂×C₈	1	1	yes	characteristic
107	C₃×C₄×D₃	C₂×C₈	1	4	yes	—
108	C₃×C₄×D₃	C₂×C₈	1	2	yes	—
109	C₃×C₄×D₃	C₂×C₈	1	2	yes	—
110	C₃×C₄×D₃	C₂×C₈	1	4	yes	—
111	C₃×C₄×D₃	C₂²×C₄	1	2	yes	—
112	C₃×C₄×D₃	C₂²×C₄	1	2	yes	—
113	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
114	C₃²×C₈	C₂²×C₄	1	2	yes	—
115	C₃²×C₈	C₂⁴	1	1	yes	characteristic
116	C₃×C₃⋊C₈	C₂²×C₄	1	2	yes	—
117	C₃×C₃⋊C₈	C₂²×C₄	1	2	yes	—
118	C₂³×C₈	—	3	1	no	—
119	C₂×M₃₂	—	3	1	no	—
120	C₂×M₃₂	—	9	2	no	—
121	C₂×M₃₂	—	9	8	no	—
122	C₂×M₃₂	—	9	1	no	—
123	C₂²×C₁₆	—	9	2	no	—
124	C₂⁴×C₃	—	3	1	no	—
125	C₂³×D₃	C₃⋊C₈	1	1	yes	characteristic
126	C₂²×C₃×C₄	—	2	1	no	—
127	C₂²×C₃×C₄	—	3	1	no	—
128	C₂²×C₃×C₄	—	3	1	no	—
129	C₂²×C₃×C₄	—	3	4	no	—
130	C₂²×C₃×C₄	—	3	1	no	—
131	C₂²×C₃×C₄	—	3	1	no	—
132	C₂²×C₃×C₄	—	3	4	no	—
133	C₂²×C₃×C₄	—	3	1	no	—
134	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
135	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
136	C₂²×Dic₃	C₃⋊C₈	1	1	yes	characteristic
137	C₂×C₄×D₃	C₃⋊C₈	1	1	yes	characteristic
138	C₂×C₄×D₃	C₃⋊C₈	1	4	yes	—
139	C₂×C₄×D₃	C₃⋊C₈	1	1	yes	characteristic
140	C₂×C₄×D₃	C₂×Dic₃	1	1	yes	characteristic
141	C₂×C₄×D₃	C₂×Dic₃	1	4	yes	—
142	C₂×C₄×D₃	C₂×Dic₃	1	1	yes	characteristic
143	C₂×C₃×C₈	—	2	1	no	—
144	C₂×C₃×C₈	—	2	2	no	—
145	C₂×C₃×C₈	—	2	2	no	—
146	C₂×C₃×C₈	—	2	1	no	—
147	C₂×C₃×C₈	—	3	1	no	—
148	C₂×C₃×C₈	—	3	4	no	—
149	C₂×C₃×C₈	—	3	1	no	—
150	C₂×C₃×C₈	—	3	2	no	—
151	C₂×C₃×C₈	—	3	4	no	—
152	C₂×C₃×C₈	—	3	4	no	—
153	C₂×C₃×C₈	—	3	2	no	—
154	C₂×C₃×C₈	—	3	2	no	—
155	C₂×C₃×C₈	—	3	2	no	—
156	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
157	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
158	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
159	C₂×C₃×C₈	C₂×Dic₃	1	2	yes	—
160	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
161	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
162	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
163	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
164	C₂×C₃⋊C₈	C₂×Dic₃	1	1	yes	characteristic
165	C₂×C₃⋊C₈	C₂×Dic₃	1	1	yes	characteristic
166	C₂×C₃⋊C₈	C₂×Dic₃	1	4	yes	—
167	D₃×C₈	C₂×Dic₃	1	2	yes	—
168	D₃×C₈	C₂×Dic₃	1	2	yes	—
169	D₃×C₈	C₂×Dic₃	1	4	yes	—
170	D₃×C₈	C₂×Dic₃	1	4	yes	—
171	D₃×C₈	C₂²×D₃	1	2	yes	—
172	D₃×C₈	C₂²×D₃	1	2	yes	—
173	C₃×C₁₆	—	3	4	no	—
174	C₃⋊C₁₆	—	3	4	no	—
175	C₃⋊C₁₆	—	3	4	no	—
176	C₃⋊C₁₆	—	6	4	no	—
177	C₃⋊C₁₆	C₂²×D₃	1	4	yes	complemented
178	C₂²×C₃²	—	2	2	no	—
179	C₂²×C₃²	C₂²×C₈	1	2	yes	—
180	C₂²×C₃²	C₂²×C₈	1	1	yes	characteristic
181	C₂×C₃×D₃	—	2	2	no	—
182	C₂×C₃×D₃	—	2	8	no	—
183	C₂×C₃×D₃	M₃₂	1	4	yes	complemented
184	C₂×C₃×D₃	C₂²×C₈	1	2	yes	—
185	C₂×C₃×D₃	C₂²×C₈	1	2	yes	—
186	C₃²×C₄	C₂²×C₈	1	1	yes	characteristic
187	C₃²×C₄	C₂²×C₈	1	2	yes	—
188	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
189	C₃×Dic₃	C₂²×C₈	1	2	yes	—
190	C₃×Dic₃	C₂²×C₈	1	2	yes	—
191	C₂³×C₄	—	3	1	no	—
192	C₂²×C₈	—	3	1	no	—
193	C₂²×C₈	—	3	4	no	—
194	C₂²×C₈	—	3	1	no	—
195	C₂²×C₈	—	3	1	no	—
196	C₂²×C₈	—	3	4	no	—
197	C₂²×C₈	—	3	1	no	—
198	C₂²×C₈	—	3	1	no	—
199	C₂²×C₈	D₃²	1	1	yes	characteristic
200	M₃₂	—	3	4	no	—
201	M₃₂	—	9	8	no	—
202	M₃₂	—	9	4	no	—
203	C₂×C₁₆	—	3	2	no	—
204	C₂×C₁₆	—	9	8	no	—
205	C₂×C₁₆	—	9	2	no	—
206	C₂³×C₃	—	2	1	no	—
207	C₂³×C₃	—	3	1	no	—
208	C₂³×C₃	—	3	4	no	—
209	C₂³×C₃	—	3	1	no	—
210	C₂³×C₃	—	6	4	no	—
211	C₂³×C₃	D₃×C₈	1	1	yes	characteristic
212	C₂³×C₃	C₂×C₃⋊C₈	1	1	yes	characteristic
213	C₂²×D₃	—	2	4	no	—
214	C₂²×D₃	C₂×C₃⋊C₈	1	1	yes	characteristic
215	C₂²×D₃	C₂×C₃⋊C₈	1	4	yes	—
216	C₂²×D₃	C₂×C₃⋊C₈	1	1	yes	characteristic
217	C₂×C₃×C₄	—	2	1	no	—
218	C₂×C₃×C₄	—	2	2	no	—
219	C₂×C₃×C₄	—	2	2	no	—
220	C₂×C₃×C₄	—	2	1	no	—
221	C₂×C₃×C₄	—	3	4	no	—
222	C₂×C₃×C₄	—	3	1	no	—
223	C₂×C₃×C₄	—	3	1	no	—
224	C₂×C₃×C₄	—	3	4	no	—
225	C₂×C₃×C₄	—	3	2	no	—
226	C₂×C₃×C₄	—	3	4	no	—
227	C₂×C₃×C₄	—	3	2	no	—
228	C₂×C₃×C₄	—	3	2	no	—
229	C₂×C₃×C₄	—	3	2	no	—
230	C₂×C₃×C₄	D₃×C₈	1	2	yes	—
231	C₂×C₃×C₄	D₃×C₈	1	1	yes	characteristic
232	C₂×C₃×C₄	C₂×C₃⋊C₈	1	2	yes	—
233	C₂×C₃×C₄	C₂×C₃⋊C₈	1	1	yes	characteristic
234	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
235	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
236	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
237	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
238	C₂×Dic₃	C₂×C₃⋊C₈	1	4	yes	—
239	C₂×Dic₃	C₂×C₃⋊C₈	1	1	yes	characteristic
240	C₂×Dic₃	C₂×C₃⋊C₈	1	1	yes	characteristic
241	C₄×D₃	C₂×C₃⋊C₈	1	2	yes	—
242	C₄×D₃	C₂×C₃⋊C₈	1	4	yes	—
243	C₄×D₃	C₂×C₃⋊C₈	1	2	yes	—
244	C₄×D₃	C₂×C₃⋊C₈	1	4	yes	—
245	C₄×D₃	C₂²×Dic₃	1	2	yes	—
246	C₄×D₃	C₂²×Dic₃	1	2	yes	—
247	C₃×C₈	—	2	1	no	—
248	C₃×C₈	—	2	2	no	—
249	C₃×C₈	—	2	1	no	—
250	C₃×C₈	—	3	2	no	—
251	C₃×C₈	—	3	2	no	—
252	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
253	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
254	C₃×C₈	C₂²×Dic₃	1	2	yes	—
255	C₃×C₈	C₂²×Dic₃	1	1	yes	characteristic
256	C₃×C₈	C₂³×D₃	1	1	yes	characteristic
257	C₃×C₈	C₂³×D₃	1	1	yes	characteristic
258	C₃⋊C₈	C₂²×Dic₃	1	2	yes	—
259	C₃⋊C₈	C₂²×Dic₃	1	2	yes	—
260	C₂×C₃²	—	2	2	no	—
261	C₂×C₃²	C₂×M₃₂	1	2	yes	complemented
262	C₂×C₃²	C₂³×C₈	1	1	yes	characteristic
263	C₃×D₃	—	2	2	no	—
264	C₃×D₃	C₂×M₃₂	1	4	yes	complemented
265	C₂⁴	—	3	1	no	—
266	C₂²×C₄	—	3	1	no	—
267	C₂²×C₄	—	3	1	no	—
268	C₂²×C₄	—	3	4	no	—
269	C₂²×C₄	—	3	1	no	—
270	C₂²×C₄	—	3	4	no	—
271	C₂²×C₄	—	3	1	no	—
272	C₂²×C₄	—	3	1	no	—
273	C₂²×C₄	D₃×Dic₃	1	1	yes	characteristic
274	C₂×C₈	—	3	4	no	—
275	C₂×C₈	—	3	1	no	—
276	C₂×C₈	—	3	1	no	—
277	C₂×C₈	—	3	2	no	—
278	C₂×C₈	—	3	2	no	—
279	C₂×C₈	—	3	4	no	—
280	C₂×C₈	—	3	4	no	—
281	C₂×C₈	—	3	2	no	—
282	C₂×C₈	—	3	2	no	—
283	C₂×C₈	D₃×Dic₃	1	1	yes	characteristic
284	C₂×C₈	D₃×Dic₃	1	2	yes	—
285	C₂×C₈	C₂×D₃²	1	2	yes	—
286	C₂×C₈	C₂×D₃²	1	1	yes	characteristic
287	C₁₆	—	3	4	no	—
288	C₁₆	—	9	4	no	—
289	C₂²×C₃	—	2	2	no	—
290	C₂²×C₃	—	2	2	no	—
291	C₂²×C₃	—	2	1	no	—
292	C₂²×C₃	—	2	2	no	—
293	C₂²×C₃	—	3	4	no	—
294	C₂²×C₃	—	3	2	no	—
295	C₂²×C₃	—	3	2	no	—
296	C₂²×C₃	—	4	2	no	—
297	C₂²×C₃	—	6	8	no	—
298	C₂²×C₃	—	6	2	no	—
299	C₂²×C₃	C₂×D₃×C₈	1	2	yes	—
300	C₂²×C₃	C₂×D₃×C₈	1	1	yes	characteristic
301	C₂²×C₃	C₂²×C₃⋊C₈	1	2	yes	—
302	C₂²×C₃	C₂²×C₃⋊C₈	1	1	yes	characteristic
303	C₂×D₃	—	2	2	no	—
304	C₂×D₃	—	2	8	no	—
305	C₂×D₃	#812	1	4	yes	direct product factor
306	C₂×D₃	C₂²×C₃⋊C₈	1	2	yes	—
307	C₂×D₃	C₂²×C₃⋊C₈	1	2	yes	—
308	C₃×C₄	—	2	1	no	—
309	C₃×C₄	—	2	2	no	—
310	C₃×C₄	—	2	1	no	—
311	C₃×C₄	—	3	2	no	—
312	C₃×C₄	—	3	2	no	—
313	C₃×C₄	C₂×D₃×C₈	1	2	yes	—
314	C₃×C₄	C₂×D₃×C₈	1	1	yes	characteristic
315	C₃×C₄	C₂²×C₃⋊C₈	1	2	yes	—
316	C₃×C₄	C₂²×C₃⋊C₈	1	1	yes	characteristic
317	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
318	C₃×C₄	C₂³×Dic₃	1	1	yes	characteristic
319	Dic₃	C₂²×C₃⋊C₈	1	2	yes	—
320	Dic₃	C₂²×C₃⋊C₈	1	2	yes	—
321	C₃²	C₂²×M₃₂	1	1	yes	characteristic, complemented, Sylow
322	C₂³	—	3	1	no	—
323	C₂³	—	3	4	no	—
324	C₂³	—	3	1	no	—
325	C₂³	—	6	4	no	—
326	C₂³	D₃×C₃⋊C₈	1	1	yes	characteristic
327	C₂×C₄	—	3	4	no	—
328	C₂×C₄	—	3	1	no	—
329	C₂×C₄	—	3	1	no	—
330	C₂×C₄	—	3	2	no	—
331	C₂×C₄	—	3	2	no	—
332	C₂×C₄	—	3	4	no	—
333	C₂×C₄	—	3	2	no	—
334	C₂×C₄	—	3	4	no	—
335	C₂×C₄	—	3	2	no	—
336	C₂×C₄	D₃×C₃⋊C₈	1	2	yes	—
337	C₂×C₄	D₃×C₃⋊C₈	1	1	yes	characteristic
338	C₂×C₄	C₂×D₃×Dic₃	1	2	yes	—
339	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
340	C₈	—	3	2	no	—
341	C₈	—	3	2	no	—
342	C₈	C₂×D₃×Dic₃	1	2	yes	—
343	C₈	C₂×D₃×Dic₃	1	1	yes	characteristic
344	C₈	C₂²×D₃²	1	1	yes	characteristic
345	C₂×C₃	—	2	2	no	—
346	C₂×C₃	—	2	2	no	—
347	C₂×C₃	—	2	2	no	—
348	C₂×C₃	—	2	1	no	—
349	C₂×C₃	—	3	4	no	—
350	C₂×C₃	—	4	2	no	—
351	C₂×C₃	—	6	2	no	—
352	C₂×C₃	D₃×M₃₂	1	2	yes	complemented
353	C₂×C₃	C₂×#812	1	2	yes	complemented
354	C₂×C₃	C₂²×D₃×C₈	1	1	yes	characteristic
355	C₂×C₃	C₂³×C₃⋊C₈	1	1	yes	characteristic
356	D₃	—	2	2	no	—
357	D₃	C₂×#812	1	4	yes	direct product factor
358	C₂²	—	2	2	no	—
359	C₂²	—	3	4	no	—
360	C₂²	—	3	2	no	—
361	C₂²	—	3	2	no	—
362	C₂²	—	6	8	no	—
363	C₂²	—	6	2	no	—
364	C₂²	C₂×D₃×C₃⋊C₈	1	2	yes	—
365	C₂²	C₂×D₃×C₃⋊C₈	1	1	yes	characteristic
366	C₄	—	3	2	no	—
367	C₄	—	3	2	no	—
368	C₄	C₂×D₃×C₃⋊C₈	1	2	yes	—
369	C₄	C₂×D₃×C₃⋊C₈	1	1	yes	characteristic
370	C₄	C₂²×D₃×Dic₃	1	1	yes	characteristic
371	C₃	—	2	1	no	—
372	C₃	C₂×D₃×M₃₂	1	1	yes	characteristic, complemented
373	C₃	C₂²×#812	1	1	yes	characteristic, complemented
374	C₂	—	2	2	no	—
375	C₂	—	3	4	no	—
376	C₂	—	6	2	no	—
377	C₂	D₃×#812	1	2	yes	direct product factor
378	C₂	C₂²×D₃×C₃⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₃²
commutator	C₂×C₃²	C₂³×C₈
Frattini	C₈	C₂²×D₃²
Fitting	C₂²×C₃²×C₈	C₂²
socle	C₂²×C₃²	C₂²×C₈
prime radical	C₂³×C₃×D₃	C₈
cosocle	C₃²×C₈	C₂⁴
hypercenter	C₂²×C₈	D₃²
hypocenter	C₃²	C₂²×M₃₂
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×#63639	C₂	semidirect
3. C₂×C₃×#812	C₂	semidirect
4. C₂×#63543	C₂	semidirect
5. D₃×#812	C₂	direct (N × H)
6. C₂×D₃×C₃⋊C₁₆	C₂	semidirect
18. #63639	C₂²	semidirect
19. C₂×C₃⋊(C₃⋊C₁₆)	C₂²	semidirect
20. C₃×#812	C₂²	semidirect
21. C₂×C₃×C₃⋊C₁₆	C₂²	semidirect
22. #63543	C₂²	semidirect
23. D₃×C₃⋊C₁₆	C₂²	semidirect
32. C₂×#812	D₃	direct (N × H)
59. C₃⋊(C₃⋊C₁₆)	C₂³	semidirect
60. C₃×C₃⋊C₁₆	C₂³	semidirect
87. #812	C₂×D₃	direct (N × H)
92. C₂×C₃⋊C₁₆	C₂×D₃	semidirect
177. C₃⋊C₁₆	C₂²×D₃	semidirect
183. C₂×C₃×D₃	M₃₂	semidirect
261. C₂×C₃²	C₂×M₃₂	semidirect
264. C₃×D₃	C₂×M₃₂	semidirect
305. C₂×D₃	#812	direct (N × H)
321. C₃²	C₂²×M₃₂	semidirect
352. C₂×C₃	D₃×M₃₂	semidirect
353. C₂×C₃	C₂×#812	semidirect
357. D₃	C₂×#812	direct (N × H)
372. C₃	C₂×D₃×M₃₂	semidirect
373. C₃	C₂²×#812	semidirect
377. C₂	D₃×#812	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×C₃×D₃×C₈	2
C₂×#63639	2
C₂×C₃×#812	2
C₂×#63543	2
D₃×#812	2
C₂×D₃×C₃⋊C₁₆	2
C₂²×#812	3
C₂×D₃×M₃₂	3

Subgroups — C2×D3×#812 #11899367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×#812 #11899367