Subgroups — C₃×#10873 #10629480

Order 768.

714 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#108	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×#108	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#405	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×#344	C₂	1	2	yes	maximal
5	C₃×#1738	C₂	1	2	yes	maximal
6	#10873	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂²×C₃×M₁₆	C₂²	1	2	yes	—
8	C₂²×C₃×M₁₆	C₂²	1	2	yes	—
9	C₂²×C₃×M₁₆	C₂²	1	1	yes	characteristic
10	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₃×#117	C₂²	1	1	yes	characteristic
12	C₂×C₃×#108	—	2	1	no	—
13	C₂×C₃×#108	—	2	1	no	—
14	C₂×C₃×#108	—	2	2	no	—
15	C₂×C₃×#108	—	2	2	no	—
16	C₂×C₃×#108	—	2	2	no	—
17	C₂×C₃×#108	C₄	1	4	yes	complemented
18	C₂×C₃×#108	C₄	1	4	yes	complemented
19	C₃×#405	—	2	2	no	—
20	C₃×#405	C₄	1	4	yes	—
21	C₂×C₃×#97	—	2	1	no	—
22	C₂×C₃×C₄×C₈	—	2	1	no	—
23	C₃×#344	—	2	4	no	—
24	C₃×#341	—	2	4	no	—
25	C₂²×#108	C₂×C₃	1	1	yes	characteristic
26	C₂²×#108	C₂×C₃	1	1	yes	characteristic
27	C₂×#405	C₂×C₃	1	1	yes	characteristic
28	C₂×#344	C₂×C₃	1	2	yes	—
29	#1738	C₂×C₃	1	2	yes	—
30	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
31	C₂×C₃×M₁₆	—	2	1	no	—
32	C₂×C₃×M₁₆	—	2	1	no	—
33	C₂×C₃×M₁₆	—	2	1	no	—
34	C₂×C₃×M₁₆	—	2	2	no	—
35	C₂×C₃×M₁₆	—	2	2	no	—
36	C₂×C₃×M₁₆	—	2	2	no	—
37	C₂×C₃×M₁₆	—	2	2	no	—
38	C₂×C₃×M₁₆	—	2	2	no	—
39	C₂×C₃×M₁₆	—	2	2	no	—
40	C₂×C₃×M₁₆	—	2	2	no	—
41	C₂×C₃×M₁₆	—	2	2	no	—
42	C₂×C₃×M₁₆	—	2	2	no	—
43	C₂×C₃×M₁₆	—	2	2	no	—
44	C₂×C₃×M₁₆	C₂×C₄	1	4	yes	—
45	C₂×C₃×M₁₆	C₂×C₄	1	4	yes	—
46	C₂×C₃×M₁₆	C₂×C₄	1	2	yes	—
47	C₂×C₃×M₁₆	D₄	1	2	yes	—
48	C₂×C₃×M₁₆	Q₈	1	2	yes	—
49	C₂²×C₃×C₈	—	2	1	no	—
50	C₂²×C₃×C₈	—	2	2	no	—
51	C₂²×C₃×C₈	—	2	2	no	—
52	C₂²×C₃×C₈	C₂×C₄	1	2	yes	—
53	C₂²×C₃×C₈	C₂×C₄	1	2	yes	—
54	C₂²×C₃×C₈	C₂×C₄	1	2	yes	—
55	C₂²×C₃×C₈	D₄	1	1	yes	characteristic
56	C₂²×C₃×C₈	D₄	1	1	yes	characteristic
57	C₂²×C₃×C₈	D₄	1	2	yes	—
58	C₂²×C₃×C₈	D₄	1	2	yes	—
59	C₂²×C₃×C₈	Q₈	1	2	yes	—
60	C₃×#117	—	2	1	no	—
61	C₃×#117	—	2	1	no	—
62	C₃×#117	C₂×C₄	1	2	yes	—
63	C₃×#117	D₄	1	2	yes	—
64	C₂×C₃×C₄⋊C₄	—	2	1	no	—
65	C₂×C₃×C₂²⋊C₄	Q₈	1	2	yes	—
66	C₂×C₃×C₄²	—	2	1	no	—
67	C₃×#108	—	2	4	no	—
68	C₃×#108	—	2	4	no	—
69	C₃×#108	—	2	8	no	—
70	C₃×#97	—	2	4	no	—
71	C₃×C₄×C₈	—	2	4	no	—
72	C₂²×M₁₆	C₂²×C₃	1	2	yes	—
73	C₂²×M₁₆	C₂²×C₃	1	2	yes	—
74	C₂²×M₁₆	C₂²×C₃	1	1	yes	characteristic
75	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
76	C₂×#117	C₂²×C₃	1	1	yes	characteristic
77	C₂×#108	—	2	1	no	—
78	C₂×#108	—	2	1	no	—
79	C₂×#108	—	2	2	no	—
80	C₂×#108	—	2	2	no	—
81	C₂×#108	—	2	2	no	—
82	C₂×#108	C₃×C₄	1	4	yes	complemented
83	C₂×#108	C₃×C₄	1	4	yes	complemented
84	#405	—	2	2	no	—
85	#405	C₃×C₄	1	4	yes	—
86	C₂×#97	—	2	1	no	—
87	C₂×C₄×C₈	—	2	1	no	—
88	#344	—	2	4	no	—
89	#341	—	2	4	no	—
90	C₂⁴×C₃	C₂×Q₈	1	1	yes	characteristic
91	C₂²×C₃×C₄	—	2	2	no	—
92	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₃×C₄	C₂×Q₈	1	1	yes	characteristic
101	C₂²×C₃×C₄	C₂×Q₈	1	1	yes	characteristic
102	C₂²×C₃×C₄	#41	1	1	yes	characteristic
103	C₂²×C₃×C₄	#41	1	1	yes	characteristic
104	C₂²×C₃×C₄	#41	1	1	yes	characteristic
105	C₂²×C₃×C₄	#41	1	1	yes	characteristic
106	C₃×M₁₆	—	2	2	no	—
107	C₃×M₁₆	—	2	2	no	—
108	C₃×M₁₆	—	2	2	no	—
109	C₃×M₁₆	—	2	4	no	—
110	C₃×M₁₆	—	2	4	no	—
111	C₃×M₁₆	—	2	4	no	—
112	C₃×M₁₆	—	2	4	no	—
113	C₃×M₁₆	—	4	2	no	—
114	C₃×M₁₆	—	4	2	no	—
115	C₃×M₁₆	—	4	2	no	—
116	C₃×M₁₆	—	4	2	no	—
117	C₃×M₁₆	C₄⋊C₄	1	4	yes	—
118	C₂×C₃×C₈	—	2	2	no	—
119	C₂×C₃×C₈	—	2	2	no	—
120	C₂×C₃×C₈	—	2	2	no	—
121	C₂×C₃×C₈	—	2	4	no	—
122	C₂×C₃×C₈	—	2	4	no	—
123	C₂×C₃×C₈	—	4	2	no	—
124	C₂×C₃×C₈	—	4	2	no	—
125	C₂×C₃×C₈	—	4	2	no	—
126	C₂×C₃×C₈	—	4	2	no	—
127	C₂×C₃×C₈	C₄²	1	4	yes	—
128	C₂×C₃×C₈	C₂²⋊C₄	1	2	yes	—
129	C₂×C₃×C₈	C₂²⋊C₄	1	2	yes	—
130	C₂×C₃×C₈	C₂²⋊C₄	1	2	yes	—
131	C₂×C₃×C₈	C₂²⋊C₄	1	2	yes	—
132	C₂×C₃×C₈	C₂²⋊C₄	1	4	yes	—
133	C₂×C₃×C₈	C₄⋊C₄	1	4	yes	—
134	C₂×C₃×C₈	C₄⋊C₄	1	2	yes	—
135	C₂×C₃×C₈	C₄⋊C₄	1	2	yes	—
136	C₂×C₃×C₈	C₄⋊C₄	1	4	yes	—
137	C₃×C₄⋊C₄	—	2	2	no	—
138	C₃×C₄⋊C₄	—	2	2	no	—
139	C₃×C₂²⋊C₄	—	2	2	no	—
140	C₃×C₂²⋊C₄	C₄⋊C₄	1	4	yes	—
141	C₃×C₄²	—	2	2	no	—
142	C₃×C₄²	—	2	2	no	—
143	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
144	C₂×M₁₆	—	2	1	no	—
145	C₂×M₁₆	—	2	1	no	—
146	C₂×M₁₆	—	2	1	no	—
147	C₂×M₁₆	—	2	2	no	—
148	C₂×M₁₆	—	2	2	no	—
149	C₂×M₁₆	—	2	2	no	—
150	C₂×M₁₆	—	2	2	no	—
151	C₂×M₁₆	—	2	2	no	—
152	C₂×M₁₆	—	2	2	no	—
153	C₂×M₁₆	—	2	2	no	—
154	C₂×M₁₆	—	2	2	no	—
155	C₂×M₁₆	—	2	2	no	—
156	C₂×M₁₆	—	2	2	no	—
157	C₂×M₁₆	C₂×C₃×C₄	1	4	yes	—
158	C₂×M₁₆	C₂×C₃×C₄	1	4	yes	—
159	C₂×M₁₆	C₂×C₃×C₄	1	2	yes	—
160	C₂×M₁₆	C₃×D₄	1	2	yes	—
161	C₂×M₁₆	C₃×Q₈	1	2	yes	—
162	C₂²×C₈	—	2	1	no	—
163	C₂²×C₈	—	2	2	no	—
164	C₂²×C₈	—	2	2	no	—
165	C₂²×C₈	C₂×C₃×C₄	1	2	yes	—
166	C₂²×C₈	C₂×C₃×C₄	1	2	yes	—
167	C₂²×C₈	C₂×C₃×C₄	1	2	yes	—
168	C₂²×C₈	C₃×D₄	1	1	yes	characteristic
169	C₂²×C₈	C₃×D₄	1	1	yes	characteristic
170	C₂²×C₈	C₃×D₄	1	2	yes	—
171	C₂²×C₈	C₃×D₄	1	2	yes	—
172	C₂²×C₈	C₃×Q₈	1	2	yes	—
173	#117	—	2	1	no	—
174	#117	—	2	1	no	—
175	#117	C₂×C₃×C₄	1	2	yes	—
176	#117	C₃×D₄	1	2	yes	—
177	C₂×C₄⋊C₄	—	2	1	no	—
178	C₂×C₂²⋊C₄	C₃×Q₈	1	2	yes	—
179	C₂×C₄²	—	2	1	no	—
180	#108	—	2	4	no	—
181	#108	—	2	4	no	—
182	#108	—	2	8	no	—
183	#97	—	2	4	no	—
184	C₄×C₈	—	2	4	no	—
185	C₂³×C₃	—	4	2	no	—
186	C₂³×C₃	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂³×C₃	C₄×Q₈	1	1	yes	characteristic
188	C₂³×C₃	C₄×Q₈	1	1	yes	characteristic
189	C₂³×C₃	C₂²⋊Q₈	1	1	yes	characteristic
190	C₂³×C₃	C₂²⋊Q₈	1	1	yes	characteristic
191	C₂³×C₃	C₄⋊Q₈	1	1	yes	characteristic
192	C₂³×C₃	C₄⋊Q₈	1	1	yes	characteristic
193	C₂×C₃×C₄	—	2	4	no	—
194	C₂×C₃×C₄	—	4	4	no	—
195	C₂×C₃×C₄	C₂×C₄²	1	1	yes	characteristic
196	C₂×C₃×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
197	C₂×C₃×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
198	C₂×C₃×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
199	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
200	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
201	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
202	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
203	C₂×C₃×C₄	#117	1	1	yes	characteristic
204	C₂×C₃×C₄	#117	1	1	yes	characteristic
205	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
206	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
207	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
208	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
209	C₂×C₃×C₄	C₄×Q₈	1	1	yes	characteristic
210	C₂×C₃×C₄	C₄×Q₈	1	1	yes	characteristic
211	C₂×C₃×C₄	#121	1	1	yes	characteristic
212	C₂×C₃×C₄	#121	1	1	yes	characteristic
213	C₂×C₃×C₄	#121	1	1	yes	characteristic
214	C₂×C₃×C₄	#121	1	1	yes	characteristic
215	C₂×C₃×C₄	C₂²⋊Q₈	1	1	yes	characteristic
216	C₂×C₃×C₄	C₂²⋊Q₈	1	1	yes	characteristic
217	C₂×C₃×C₄	#124	1	1	yes	characteristic
218	C₂×C₃×C₄	#124	1	1	yes	characteristic
219	C₂×C₃×C₄	#125	1	1	yes	characteristic
220	C₂×C₃×C₄	#125	1	1	yes	characteristic
221	C₂×C₃×C₄	#127	1	1	yes	characteristic
222	C₂×C₃×C₄	C₄⋊Q₈	1	1	yes	characteristic
223	C₃×C₈	—	2	4	no	—
224	C₃×C₈	—	4	4	no	—
225	C₃×C₈	—	4	4	no	—
226	C₃×C₈	#95	1	4	yes	—
227	C₃×C₈	#95	1	4	yes	—
228	C₂⁴	C₂×C₃×Q₈	1	1	yes	characteristic
229	C₂²×C₄	—	2	2	no	—
230	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
231	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
232	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
233	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
234	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
235	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
236	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
237	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
238	C₂²×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
239	C₂²×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
240	C₂²×C₄	C₃×#41	1	1	yes	characteristic
241	C₂²×C₄	C₃×#41	1	1	yes	characteristic
242	C₂²×C₄	C₃×#41	1	1	yes	characteristic
243	C₂²×C₄	C₃×#41	1	1	yes	characteristic
244	M₁₆	—	2	2	no	—
245	M₁₆	—	2	2	no	—
246	M₁₆	—	2	2	no	—
247	M₁₆	—	2	4	no	—
248	M₁₆	—	2	4	no	—
249	M₁₆	—	2	4	no	—
250	M₁₆	—	2	4	no	—
251	M₁₆	—	4	2	no	—
252	M₁₆	—	4	2	no	—
253	M₁₆	—	4	2	no	—
254	M₁₆	—	4	2	no	—
255	M₁₆	C₃×C₄⋊C₄	1	4	yes	—
256	C₂×C₈	—	2	2	no	—
257	C₂×C₈	—	2	2	no	—
258	C₂×C₈	—	2	2	no	—
259	C₂×C₈	—	2	4	no	—
260	C₂×C₈	—	2	4	no	—
261	C₂×C₈	—	4	2	no	—
262	C₂×C₈	—	4	2	no	—
263	C₂×C₈	—	4	2	no	—
264	C₂×C₈	—	4	2	no	—
265	C₂×C₈	C₃×C₄²	1	4	yes	—
266	C₂×C₈	C₃×C₂²⋊C₄	1	2	yes	—
267	C₂×C₈	C₃×C₂²⋊C₄	1	2	yes	—
268	C₂×C₈	C₃×C₂²⋊C₄	1	2	yes	—
269	C₂×C₈	C₃×C₂²⋊C₄	1	2	yes	—
270	C₂×C₈	C₃×C₂²⋊C₄	1	4	yes	—
271	C₂×C₈	C₃×C₄⋊C₄	1	4	yes	—
272	C₂×C₈	C₃×C₄⋊C₄	1	2	yes	—
273	C₂×C₈	C₃×C₄⋊C₄	1	2	yes	—
274	C₂×C₈	C₃×C₄⋊C₄	1	4	yes	—
275	C₄⋊C₄	—	2	2	no	—
276	C₄⋊C₄	—	2	2	no	—
277	C₂²⋊C₄	—	2	2	no	—
278	C₂²⋊C₄	C₃×C₄⋊C₄	1	4	yes	—
279	C₄²	—	2	2	no	—
280	C₄²	—	2	2	no	—
281	C₂²×C₃	—	2	2	no	—
282	C₂²×C₃	—	2	2	no	—
283	C₂²×C₃	—	2	2	no	—
284	C₂²×C₃	—	4	1	no	—
285	C₂²×C₃	—	4	1	no	—
286	C₂²×C₃	—	4	1	no	—
287	C₂²×C₃	—	4	1	no	—
288	C₂²×C₃	C₄×C₄⋊C₄	1	1	yes	characteristic
289	C₂²×C₃	#380	1	1	yes	characteristic
290	C₂²×C₃	#384	1	1	yes	characteristic
291	C₂²×C₃	#389	1	1	yes	characteristic
292	C₂²×C₃	#389	1	1	yes	characteristic
293	C₂²×C₃	#391	1	1	yes	characteristic
294	C₂²×C₃	#391	1	1	yes	characteristic
295	C₃×C₄	—	4	4	no	—
296	C₃×C₄	C₂×#95	1	1	yes	characteristic
297	C₃×C₄	C₄×C₄⋊C₄	1	1	yes	characteristic
298	C₃×C₄	#380	1	1	yes	characteristic
299	C₃×C₄	#382	1	1	yes	characteristic
300	C₃×C₄	#389	1	1	yes	characteristic
301	C₃×C₄	#389	1	1	yes	characteristic
302	C₃×C₄	#390	1	1	yes	characteristic
303	C₃×C₄	#390	1	1	yes	characteristic
304	C₂³	—	4	2	no	—
305	C₂³	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
306	C₂³	C₃×C₄×Q₈	1	1	yes	characteristic
307	C₂³	C₃×C₄×Q₈	1	1	yes	characteristic
308	C₂³	C₃×C₂²⋊Q₈	1	1	yes	characteristic
309	C₂³	C₃×C₂²⋊Q₈	1	1	yes	characteristic
310	C₂³	C₃×C₄⋊Q₈	1	1	yes	characteristic
311	C₂³	C₃×C₄⋊Q₈	1	1	yes	characteristic
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	4	4	no	—
314	C₂×C₄	C₂×C₃×C₄²	1	1	yes	characteristic
315	C₂×C₄	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
316	C₂×C₄	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
317	C₂×C₄	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
318	C₂×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
319	C₂×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
320	C₂×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
321	C₂×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
322	C₂×C₄	C₃×#117	1	1	yes	characteristic
323	C₂×C₄	C₃×#117	1	1	yes	characteristic
324	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
325	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
326	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
327	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
328	C₂×C₄	C₃×C₄×Q₈	1	1	yes	characteristic
329	C₂×C₄	C₃×C₄×Q₈	1	1	yes	characteristic
330	C₂×C₄	C₃×#121	1	1	yes	characteristic
331	C₂×C₄	C₃×#121	1	1	yes	characteristic
332	C₂×C₄	C₃×#121	1	1	yes	characteristic
333	C₂×C₄	C₃×#121	1	1	yes	characteristic
334	C₂×C₄	C₃×C₂²⋊Q₈	1	1	yes	characteristic
335	C₂×C₄	C₃×C₂²⋊Q₈	1	1	yes	characteristic
336	C₂×C₄	C₃×#124	1	1	yes	characteristic
337	C₂×C₄	C₃×#124	1	1	yes	characteristic
338	C₂×C₄	C₃×#125	1	1	yes	characteristic
339	C₂×C₄	C₃×#125	1	1	yes	characteristic
340	C₂×C₄	C₃×#127	1	1	yes	characteristic
341	C₂×C₄	C₃×C₄⋊Q₈	1	1	yes	characteristic
342	C₈	—	2	4	no	—
343	C₈	—	4	4	no	—
344	C₈	—	4	4	no	—
345	C₈	C₃×#95	1	4	yes	—
346	C₈	C₃×#95	1	4	yes	—
347	C₂×C₃	—	2	1	no	—
348	C₂×C₃	—	2	1	no	—
349	C₂×C₃	—	2	1	no	—
350	C₂×C₃	—	2	1	no	—
351	C₂×C₃	—	2	1	no	—
352	C₂×C₃	—	2	1	no	—
353	C₂×C₃	C₄⋊#95	1	1	yes	characteristic
354	C₂×C₃	#1953	1	2	yes	—
355	C₂²	—	2	2	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	4	1	no	—
359	C₂²	—	4	1	no	—
360	C₂²	—	4	1	no	—
361	C₂²	—	4	1	no	—
362	C₂²	C₃×C₄×C₄⋊C₄	1	1	yes	characteristic
363	C₂²	C₃×#380	1	1	yes	characteristic
364	C₂²	C₃×#384	1	1	yes	characteristic
365	C₂²	C₃×#389	1	1	yes	characteristic
366	C₂²	C₃×#389	1	1	yes	characteristic
367	C₂²	C₃×#391	1	1	yes	characteristic
368	C₂²	C₃×#391	1	1	yes	characteristic
369	C₄	—	4	4	no	—
370	C₄	C₂×C₃×#95	1	1	yes	characteristic
371	C₄	C₃×C₄×C₄⋊C₄	1	1	yes	characteristic
372	C₄	C₃×#380	1	1	yes	characteristic
373	C₄	C₃×#382	1	1	yes	characteristic
374	C₄	C₃×#389	1	1	yes	characteristic
375	C₄	C₃×#389	1	1	yes	characteristic
376	C₄	C₃×#390	1	1	yes	characteristic
377	C₄	C₃×#390	1	1	yes	characteristic
378	C₃	#10873	1	1	yes	characteristic, direct product factor, Sylow
379	C₂	—	2	1	no	—
380	C₂	—	2	1	no	—
381	C₂	—	2	1	no	—
382	C₂	—	2	1	no	—
383	C₂	—	2	1	no	—
384	C₂	—	2	1	no	—
385	C₂	C₃×C₄⋊#95	1	1	yes	characteristic
386	C₂	C₃×#1953	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	#121
commutator	C₂×C₄	C₂×C₃×C₄²
Frattini, cosocle	C₂³×C₄	C₂³×C₃
socle	C₂²×C₃	#389
prime radical	C₂⁴×C₃	C₂×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂³×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
6. #10873	C₃	direct (N × H)
17. C₂×C₃×#108	C₄	semidirect
18. C₂×C₃×#108	C₄	semidirect
82. C₂×#108	C₃×C₄	semidirect
83. C₂×#108	C₃×C₄	semidirect
378. C₃	#10873	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×#108	2
C₂×C₃×#405	2
C₂×C₃×#344	2
C₃×#1738	2
#10873	3

Subgroups — C3×#10873 #10629480

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10873 #10629480