Subgroups — C₃×#82007 #11899409

Order 1152.

765 conjugacy classes of subgroups.

The subgroup lattice has 385 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#901	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃²×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#812	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4907	C₂	1	4	yes	maximal, complemented
5	C₃×D₃×M₃₂	C₂	1	4	yes	maximal, complemented
6	C₃×#4901	C₂	1	4	yes	maximal, complemented
7	C₃×#3407	—	3	1	no	maximal
8	#82007	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂×C₃×#235	C₄	1	1	yes	characteristic
10	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₃×#208	C₄	1	1	yes	characteristic
12	C₃×#901	C₄	1	2	yes	—
13	C₃×#901	C₄	1	2	yes	—
14	C₃×#901	C₂²	1	2	yes	—
15	C₃×#901	C₂²	1	2	yes	—
16	C₂×C₃×ΓL(1,𝔽₂₅)	C₄	1	2	yes	—
17	C₂×C₃×D₃×C₈	C₂²	1	2	yes	—
18	C₃²×M₃₂	C₂²	1	2	yes	—
19	C₃²×M₃₂	C₂²	1	2	yes	complemented
20	C₂×C₃²×C₁₆	C₂²	1	2	yes	complemented
21	C₃×#812	C₂²	1	2	yes	—
22	C₃×#812	C₂²	1	2	yes	complemented
23	C₂×C₃×C₃⋊C₁₆	C₂²	1	2	yes	complemented
24	C₃×#798	C₂²	1	8	yes	complemented
25	C₃×D₃×C₁₆	C₂²	1	8	yes	complemented
26	C₂×C₃×#131	—	3	1	no	—
27	C₂×#901	C₂×C₃	1	1	yes	characteristic
28	C₃×#504	—	3	4	no	—
29	C₃×#504	—	3	4	no	—
30	C₂×C₃×M₃₂	—	2	1	no	—
31	C₂×C₃×M₃₂	—	3	1	no	—
32	C₂×C₃×M₃₂	—	3	4	no	—
33	C₂×C₃×M₃₂	D₃	1	1	yes	characteristic, complemented
34	C₂×C₃×M₃₂	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂×#812	C₂×C₃	1	1	yes	characteristic, complemented
36	#4907	C₂×C₃	1	4	yes	complemented
37	D₃×M₃₂	C₂×C₃	1	4	yes	complemented
38	#4901	C₂×C₃	1	4	yes	complemented
39	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
40	C₂×C₃×#67	C₈	1	2	yes	—
41	C₃×#235	C₈	1	2	yes	—
42	C₃×#235	C₈	1	2	yes	—
43	C₃×#235	C₂×C₄	1	2	yes	—
44	C₃×#235	C₂×C₄	1	2	yes	—
45	C₂×C₃×D₁₂	C₈	1	1	yes	characteristic
46	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
47	C₂×C₃×Dic₆	C₈	1	1	yes	characteristic
48	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
49	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
50	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
51	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
52	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
53	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
54	C₃×#208	C₂×C₄	1	2	yes	—
55	C₃×#208	C₂×C₄	1	2	yes	—
56	C₂×C₃×C₃⋊C₈	C₂×C₄	1	2	yes	—
57	C₃×ΓL(1,𝔽₂₅)	C₂×C₄	1	4	yes	—
58	C₃×ΓL(1,𝔽₂₅)	C₂×C₄	1	4	yes	—
59	C₃×D₃×C₈	C₂×C₄	1	4	yes	—
60	C₃×D₃×C₈	C₂³	1	4	yes	—
61	C₃²×C₁₆	C₂³	1	4	yes	—
62	C₃×C₃⋊C₁₆	C₂³	1	4	yes	—
63	#3407	—	3	1	no	Sylow
64	C₂×C₃×#41	—	3	1	no	—
65	C₂×#235	C₃×C₄	1	1	yes	characteristic
66	C₃×#131	—	3	2	no	—
67	C₃×#131	—	3	2	no	—
68	C₃×#131	—	3	2	no	—
69	C₃×#131	—	3	2	no	—
70	C₂×C₃×M₁₆	—	3	1	no	—
71	C₂×C₃×M₁₆	—	3	2	no	—
72	C₂²×C₃×C₈	—	2	1	no	—
73	C₂²×C₃×C₈	—	3	2	no	—
74	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
75	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
76	C₂×#208	C₃×C₄	1	1	yes	characteristic
77	#901	C₃×C₄	1	2	yes	—
78	#901	C₃×C₄	1	2	yes	—
79	#901	C₂²×C₃	1	2	yes	—
80	#901	C₂²×C₃	1	2	yes	—
81	C₂×ΓL(1,𝔽₂₅)	C₃×C₄	1	2	yes	—
82	C₂×D₃×C₈	C₂²×C₃	1	2	yes	—
83	C₃×M₃₂	—	2	2	no	—
84	C₃×M₃₂	—	2	2	no	—
85	C₃×M₃₂	—	3	2	no	—
86	C₃×M₃₂	—	3	2	no	—
87	C₃×M₃₂	—	3	8	no	—
88	C₃×M₃₂	C₂×D₃	1	2	yes	—
89	C₃×M₃₂	C₂×D₃	1	2	yes	complemented
90	C₃×M₃₂	C₂²×C₃	1	2	yes	—
91	C₃×M₃₂	C₂²×C₃	1	2	yes	complemented
92	C₂×C₃×C₁₆	—	2	2	no	—
93	C₂×C₃×C₁₆	—	3	2	no	—
94	C₂×C₃×C₁₆	—	3	8	no	—
95	C₂×C₃×C₁₆	C₂×D₃	1	2	yes	complemented
96	C₂×C₃×C₁₆	C₂²×C₃	1	2	yes	complemented
97	#812	C₂²×C₃	1	2	yes	—
98	#812	C₂²×C₃	1	2	yes	complemented
99	C₂×C₃⋊C₁₆	C₂²×C₃	1	2	yes	complemented
100	#798	C₂²×C₃	1	8	yes	complemented
101	D₃×C₁₆	C₂²×C₃	1	8	yes	complemented
102	C₂³×C₃²	C₂×C₈	1	1	yes	characteristic
103	C₂²×C₃×D₃	C₂×C₈	1	2	yes	—
104	C₂×C₃²×C₄	C₂×C₈	1	1	yes	characteristic
105	C₂×C₃²×C₄	C₂×C₈	1	1	yes	characteristic
106	C₂×C₃²×C₄	C₂×C₈	1	1	yes	characteristic
107	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
110	C₃×#67	C₂×C₈	1	4	yes	—
111	C₃×#67	C₂×C₈	1	4	yes	—
112	C₂×C₃×Dic₃	C₂×C₈	1	2	yes	—
113	C₃×D₁₂	C₂×C₈	1	2	yes	—
114	C₃×D₁₂	C₂×C₈	1	2	yes	—
115	C₃×C₄×D₃	C₂×C₈	1	4	yes	—
116	C₃×C₄×D₃	C₂²×C₄	1	4	yes	—
117	C₃×Dic₆	C₂×C₈	1	2	yes	—
118	C₃×Dic₆	C₂×C₈	1	2	yes	—
119	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
120	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
121	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
122	C₃²×C₈	C₂⁴	1	1	yes	characteristic
123	C₃×C₃⋊C₈	C₂²×C₄	1	4	yes	—
124	C₂×#131	—	3	1	no	—
125	#504	—	3	4	no	—
126	#504	—	3	4	no	—
127	C₂×M₃₂	—	3	1	no	—
128	C₂×M₃₂	—	3	4	no	—
129	C₂×M₃₂	C₃×D₃	1	1	yes	characteristic, complemented
130	C₃×#41	—	3	2	no	—
131	C₃×#41	—	3	2	no	—
132	C₃×#41	—	3	2	no	—
133	C₃×#41	—	3	2	no	—
134	C₂×C₃×Q₈	—	3	1	no	—
135	C₂×C₃×D₄	—	3	2	no	—
136	C₂×C₃×D₄	—	3	1	no	—
137	C₂²×C₃×C₄	—	2	1	no	—
138	C₂²×C₃×C₄	—	3	2	no	—
139	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
140	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
141	C₂×#67	C₃×C₈	1	2	yes	—
142	#235	C₃×C₈	1	2	yes	—
143	#235	C₃×C₈	1	2	yes	—
144	#235	C₂×C₃×C₄	1	2	yes	—
145	#235	C₂×C₃×C₄	1	2	yes	—
146	C₂×D₁₂	C₃×C₈	1	1	yes	characteristic
147	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
148	C₂×Dic₆	C₃×C₈	1	1	yes	characteristic
149	C₃×M₁₆	—	3	2	no	—
150	C₃×M₁₆	—	3	2	no	—
151	C₃×M₁₆	—	3	4	no	—
152	C₃×M₁₆	—	3	4	no	—
153	C₂×C₃×C₈	—	2	1	no	—
154	C₂×C₃×C₈	—	2	1	no	—
155	C₂×C₃×C₈	—	2	1	no	—
156	C₂×C₃×C₈	—	2	1	no	—
157	C₂×C₃×C₈	—	2	1	no	—
158	C₂×C₃×C₈	—	2	1	no	—
159	C₂×C₃×C₈	—	3	2	no	—
160	C₂×C₃×C₈	—	3	4	no	—
161	C₂×C₃×C₈	—	3	4	no	—
162	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
163	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
164	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
165	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
166	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
167	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
168	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
169	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
170	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
171	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
172	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
173	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
174	#208	C₂×C₃×C₄	1	2	yes	—
175	#208	C₂×C₃×C₄	1	2	yes	—
176	C₂×C₃⋊C₈	C₂×C₃×C₄	1	2	yes	—
177	ΓL(1,𝔽₂₅)	C₂×C₃×C₄	1	4	yes	—
178	ΓL(1,𝔽₂₅)	C₂×C₃×C₄	1	4	yes	—
179	D₃×C₈	C₂×C₃×C₄	1	4	yes	—
180	D₃×C₈	C₂³×C₃	1	4	yes	—
181	C₃×C₁₆	—	2	4	no	—
182	C₃×C₁₆	—	3	4	no	—
183	C₃×C₁₆	C₂²×D₃	1	4	yes	—
184	C₃×C₁₆	C₂³×C₃	1	4	yes	—
185	C₃⋊C₁₆	C₂³×C₃	1	4	yes	—
186	C₂²×C₃²	—	4	1	no	—
187	C₂²×C₃²	C₂²×C₈	1	1	yes	characteristic
188	C₂²×C₃²	C₂²×C₈	1	1	yes	characteristic
189	C₂²×C₃²	C₂²×C₈	1	1	yes	characteristic
190	C₂×C₃×D₃	—	4	2	no	—
191	C₂×C₃×D₃	C₂²×C₈	1	4	yes	—
192	C₃²×C₄	C₂²×C₈	1	1	yes	characteristic
193	C₃²×C₄	C₂²×C₈	1	1	yes	characteristic
194	C₃²×C₄	C₂²×C₈	1	1	yes	characteristic
195	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
196	C₃×Dic₃	C₂²×C₈	1	4	yes	—
197	C₂×#41	—	3	1	no	—
198	#131	—	3	2	no	—
199	#131	—	3	2	no	—
200	#131	—	3	2	no	—
201	#131	—	3	2	no	—
202	C₂×M₁₆	—	3	1	no	—
203	C₂×M₁₆	—	3	2	no	—
204	C₂²×C₈	—	3	2	no	—
205	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
206	M₃₂	—	3	2	no	—
207	M₃₂	—	3	2	no	—
208	M₃₂	—	3	8	no	—
209	M₃₂	C₂×C₃×D₃	1	2	yes	—
210	M₃₂	C₂×C₃×D₃	1	2	yes	complemented
211	C₂×C₁₆	—	3	2	no	—
212	C₂×C₁₆	—	3	8	no	—
213	C₂×C₁₆	C₂×C₃×D₃	1	2	yes	complemented
214	C₂³×C₃	—	2	1	no	—
215	C₂³×C₃	—	3	2	no	—
216	C₂³×C₃	D₃×C₈	1	1	yes	characteristic
217	C₂³×C₃	C₂×C₃×C₈	1	1	yes	characteristic
218	C₂²×D₃	C₂×C₃×C₈	1	2	yes	—
219	C₃×Q₈	—	3	2	no	—
220	C₃×Q₈	—	3	2	no	—
221	C₃×D₄	—	3	4	no	—
222	C₃×D₄	—	3	4	no	—
223	C₃×D₄	—	3	2	no	—
224	C₃×D₄	—	3	2	no	—
225	C₂×C₃×C₄	—	2	1	no	—
226	C₂×C₃×C₄	—	2	1	no	—
227	C₂×C₃×C₄	—	2	1	no	—
228	C₂×C₃×C₄	—	2	1	no	—
229	C₂×C₃×C₄	—	2	1	no	—
230	C₂×C₃×C₄	—	2	1	no	—
231	C₂×C₃×C₄	—	3	2	no	—
232	C₂×C₃×C₄	—	3	4	no	—
233	C₂×C₃×C₄	—	3	4	no	—
234	C₂×C₃×C₄	D₃×C₈	1	1	yes	characteristic
235	C₂×C₃×C₄	D₃×C₈	1	1	yes	characteristic
236	C₂×C₃×C₄	D₃×C₈	1	1	yes	characteristic
237	C₂×C₃×C₄	C₂×C₃×C₈	1	1	yes	characteristic
238	C₂×C₃×C₄	C₂×C₃×C₈	1	1	yes	characteristic
239	C₂×C₃×C₄	C₂×C₃×C₈	1	1	yes	characteristic
240	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
241	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
242	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
243	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
244	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
245	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
246	#67	C₂×C₃×C₈	1	4	yes	—
247	#67	C₂×C₃×C₈	1	4	yes	—
248	C₂×Dic₃	C₂×C₃×C₈	1	2	yes	—
249	D₁₂	C₂×C₃×C₈	1	2	yes	—
250	D₁₂	C₂×C₃×C₈	1	2	yes	—
251	C₄×D₃	C₂×C₃×C₈	1	4	yes	—
252	C₄×D₃	C₂²×C₃×C₄	1	4	yes	—
253	Dic₆	C₂×C₃×C₈	1	2	yes	—
254	Dic₆	C₂×C₃×C₈	1	2	yes	—
255	C₃×C₈	—	2	1	no	—
256	C₃×C₈	—	2	1	no	—
257	C₃×C₈	—	2	1	no	—
258	C₃×C₈	—	2	1	no	—
259	C₃×C₈	—	3	4	no	—
260	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
261	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
262	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
263	C₃×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
264	C₃×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
265	C₃×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
266	C₃×C₈	C₂³×D₃	1	1	yes	characteristic
267	C₃×C₈	C₂⁴×C₃	1	1	yes	characteristic
268	C₃⋊C₈	C₂²×C₃×C₄	1	4	yes	—
269	C₂×C₃²	—	2	1	no	—
270	C₂×C₃²	—	2	1	no	—
271	C₂×C₃²	—	2	1	no	—
272	C₂×C₃²	C₂³×C₈	1	1	yes	characteristic
273	C₃×D₃	—	2	4	no	—
274	#41	—	3	2	no	—
275	#41	—	3	2	no	—
276	#41	—	3	2	no	—
277	#41	—	3	2	no	—
278	C₂×Q₈	—	3	1	no	—
279	C₂×D₄	—	3	2	no	—
280	C₂×D₄	—	3	1	no	—
281	C₂²×C₄	—	3	2	no	—
282	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
283	M₁₆	—	3	2	no	—
284	M₁₆	—	3	2	no	—
285	M₁₆	—	3	4	no	—
286	M₁₆	—	3	4	no	—
287	C₂×C₈	—	3	2	no	—
288	C₂×C₈	—	3	4	no	—
289	C₂×C₈	—	3	4	no	—
290	C₂×C₈	C₃×C₄×D₃	1	1	yes	characteristic
291	C₂×C₈	C₃×C₄×D₃	1	1	yes	characteristic
292	C₂×C₈	C₃×C₄×D₃	1	1	yes	characteristic
293	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
294	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
295	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
296	C₁₆	—	3	4	no	—
297	C₁₆	C₂²×C₃×D₃	1	4	yes	—
298	C₂²×C₃	—	2	1	no	—
299	C₂²×C₃	—	2	1	no	—
300	C₂²×C₃	—	2	1	no	—
301	C₂²×C₃	—	3	4	no	—
302	C₂²×C₃	—	4	1	no	—
303	C₂²×C₃	—	4	1	no	—
304	C₂²×C₃	—	4	2	no	—
305	C₂²×C₃	—	12	2	no	—
306	C₂²×C₃	C₂×D₃×C₈	1	1	yes	characteristic
307	C₂²×C₃	C₂×D₃×C₈	1	1	yes	characteristic
308	C₂²×C₃	C₂×D₃×C₈	1	1	yes	characteristic
309	C₂²×C₃	C₂²×C₃×C₈	1	1	yes	characteristic
310	C₂²×C₃	C₂²×C₃×C₈	1	1	yes	characteristic
311	C₂²×C₃	C₂²×C₃×C₈	1	1	yes	characteristic
312	C₂×D₃	—	4	2	no	—
313	C₂×D₃	C₂²×C₃×C₈	1	4	yes	—
314	C₃×C₄	—	2	1	no	—
315	C₃×C₄	—	2	1	no	—
316	C₃×C₄	—	2	1	no	—
317	C₃×C₄	—	2	1	no	—
318	C₃×C₄	—	3	4	no	—
319	C₃×C₄	C₂×D₃×C₈	1	1	yes	characteristic
320	C₃×C₄	C₂×D₃×C₈	1	1	yes	characteristic
321	C₃×C₄	C₂×D₃×C₈	1	1	yes	characteristic
322	C₃×C₄	C₂²×C₃×C₈	1	1	yes	characteristic
323	C₃×C₄	C₂²×C₃×C₈	1	1	yes	characteristic
324	C₃×C₄	C₂²×C₃×C₈	1	1	yes	characteristic
325	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
326	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
327	Dic₃	C₂²×C₃×C₈	1	4	yes	—
328	C₃²	#3407	1	1	yes	characteristic, complemented, Sylow
329	C₂³	—	3	2	no	—
330	C₂³	C₃×D₃×C₈	1	1	yes	characteristic
331	Q₈	—	3	2	no	—
332	Q₈	—	3	2	no	—
333	D₄	—	3	4	no	—
334	D₄	—	3	4	no	—
335	D₄	—	3	2	no	—
336	D₄	—	3	2	no	—
337	C₂×C₄	—	3	2	no	—
338	C₂×C₄	—	3	4	no	—
339	C₂×C₄	—	3	4	no	—
340	C₂×C₄	C₃×D₃×C₈	1	1	yes	characteristic
341	C₂×C₄	C₃×D₃×C₈	1	1	yes	characteristic
342	C₂×C₄	C₃×D₃×C₈	1	1	yes	characteristic
343	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
344	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
345	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
346	C₈	—	3	4	no	—
347	C₈	C₂×C₃×C₄×D₃	1	1	yes	characteristic
348	C₈	C₂×C₃×C₄×D₃	1	1	yes	characteristic
349	C₈	C₂×C₃×C₄×D₃	1	1	yes	characteristic
350	C₈	C₂³×C₃×D₃	1	1	yes	characteristic
351	C₂×C₃	—	2	2	no	—
352	C₂×C₃	—	2	1	no	—
353	C₂×C₃	—	2	1	no	—
354	C₂×C₃	—	2	1	no	—
355	C₂×C₃	—	2	1	no	—
356	C₂×C₃	—	2	1	no	—
357	C₂×C₃	—	2	1	no	—
358	C₂×C₃	—	2	1	no	—
359	C₂×C₃	—	4	1	no	—
360	C₂×C₃	—	4	1	no	—
361	C₂×C₃	—	6	4	no	—
362	C₂×C₃	C₂²×D₃×C₈	1	1	yes	characteristic
363	C₂×C₃	C₂³×C₃×C₈	1	1	yes	characteristic
364	D₃	—	2	4	no	—
365	C₂²	—	3	4	no	—
366	C₂²	—	4	1	no	—
367	C₂²	—	12	2	no	—
368	C₂²	C₂×C₃×D₃×C₈	1	1	yes	characteristic
369	C₂²	C₂×C₃×D₃×C₈	1	1	yes	characteristic
370	C₂²	C₂×C₃×D₃×C₈	1	1	yes	characteristic
371	C₄	—	3	4	no	—
372	C₄	C₂×C₃×D₃×C₈	1	1	yes	characteristic
373	C₄	C₂×C₃×D₃×C₈	1	1	yes	characteristic
374	C₄	C₂×C₃×D₃×C₈	1	1	yes	characteristic
375	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
376	C₃	—	2	1	no	—
377	C₃	#82007	1	1	yes	characteristic, direct product factor
378	C₃	C₃×#3407	1	1	yes	characteristic, complemented
379	C₂	—	2	1	no	—
380	C₂	—	2	1	no	—
381	C₂	—	2	1	no	—
382	C₂	—	6	4	no	—
383	C₂	C₂²×C₃×D₃×C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₈	C₂³×D₃
commutator	C₂×C₃	C₂³×C₃×C₈
Frattini	C₈	C₂³×C₃×D₃
Fitting	C₂×C₃²×M₃₂	C₂
socle	C₂×C₃²	C₂³×C₈
prime radical	C₂×C₃×#235	C₄
cosocle	C₃×C₈	C₂⁴×C₃
hypercenter	C₂×C₃×M₃₂	D₃
hypocenter	C₃	C₃×#3407
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₃×C₈ ◁ C₂×C₃×M₃₂

Complements

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

N	H ≅ G/N	type
2. C₂×C₃²×M₃₂	C₂	semidirect
3. C₂×C₃×#812	C₂	semidirect
4. C₃×#4907	C₂	semidirect
5. C₃×D₃×M₃₂	C₂	semidirect
6. C₃×#4901	C₂	semidirect
8. #82007	C₃	direct (N × H)
19. C₃²×M₃₂	C₂²	semidirect
20. C₂×C₃²×C₁₆	C₂²	semidirect
22. C₃×#812	C₂²	semidirect
23. C₂×C₃×C₃⋊C₁₆	C₂²	semidirect
24. C₃×#798	C₂²	semidirect
25. C₃×D₃×C₁₆	C₂²	semidirect
33. C₂×C₃×M₃₂	D₃	semidirect
34. C₂×C₃×M₃₂	C₂×C₃	semidirect
35. C₂×#812	C₂×C₃	semidirect
36. #4907	C₂×C₃	semidirect
37. D₃×M₃₂	C₂×C₃	semidirect
38. #4901	C₂×C₃	semidirect
89. C₃×M₃₂	C₂×D₃	semidirect
91. C₃×M₃₂	C₂²×C₃	semidirect
95. C₂×C₃×C₁₆	C₂×D₃	semidirect
96. C₂×C₃×C₁₆	C₂²×C₃	semidirect
98. #812	C₂²×C₃	semidirect
99. C₂×C₃⋊C₁₆	C₂²×C₃	semidirect
100. #798	C₂²×C₃	semidirect
101. D₃×C₁₆	C₂²×C₃	semidirect
129. C₂×M₃₂	C₃×D₃	semidirect
210. M₃₂	C₂×C₃×D₃	semidirect
213. C₂×C₁₆	C₂×C₃×D₃	semidirect
328. C₃²	#3407	semidirect
377. C₃	#82007	direct (N × H)
378. C₃	C₃×#3407	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#901	2
C₂×C₃²×M₃₂	2
C₂×C₃×#812	2
C₃×#4907	2
C₃×D₃×M₃₂	2
C₃×#4901	2
C₃×#3407	3
#82007	3

Subgroups — C3×#82007 #11899409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#82007 #11899409