Subgroups — C₂×C₃×#4514 #11796026

Order 1152.

517 conjugacy classes of subgroups.

The subgroup lattice has 381 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×ΓL(1,𝔽₂₅)	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×#4514	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₃×#349	—	3	1	no	maximal
6	C₂×#4514	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₂²×C₃×C₄×D₃	C₄	1	1	yes	characteristic
8	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₃⋊C₈	C₄	1	1	yes	characteristic
10	C₂×C₃×ΓL(1,𝔽₂₅)	—	2	1	no	—
11	C₂×C₃×ΓL(1,𝔽₂₅)	—	2	1	no	—
12	C₂×C₃×ΓL(1,𝔽₂₅)	—	2	1	no	—
13	C₂×C₃×ΓL(1,𝔽₂₅)	—	2	1	no	—
14	C₂×C₃×ΓL(1,𝔽₂₅)	C₄	1	2	yes	—
15	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
16	C₃²×M₃₂	—	2	1	no	—
17	C₃²×M₃₂	C₂²	1	2	yes	complemented
18	C₂×C₃²×C₁₆	—	2	1	no	—
19	C₃×#812	—	2	1	no	—
20	C₃×#812	C₂²	1	2	yes	complemented
21	C₂×C₃×C₃⋊C₁₆	—	2	1	no	—
22	C₂²×C₃×M₁₆	—	3	1	no	—
23	C₂²×ΓL(1,𝔽₂₅)	C₂×C₃	1	1	yes	characteristic
24	C₂×C₃×M₃₂	—	2	1	no	—
25	C₂×C₃×M₃₂	—	3	1	no	—
26	C₂×C₃×M₃₂	D₃	1	1	yes	characteristic, complemented
27	C₂×C₃×M₃₂	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂×#812	C₂×C₃	1	1	yes	characteristic, complemented
29	C₃×#349	—	3	4	no	—
30	#4514	C₂×C₃	1	4	yes	direct product factor
31	C₂³×C₃×D₃	C₈	1	1	yes	characteristic
32	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃×Dic₃	C₈	1	1	yes	characteristic
34	C₂×C₃×C₄×D₃	—	2	1	no	—
35	C₂×C₃×C₄×D₃	—	2	1	no	—
36	C₂×C₃×C₄×D₃	—	2	1	no	—
37	C₂×C₃×C₄×D₃	—	2	1	no	—
38	C₂×C₃×C₄×D₃	C₈	1	2	yes	—
39	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
40	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
42	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
43	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
44	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
45	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
46	C₂×C₃×C₃⋊C₈	—	2	1	no	—
47	C₂×C₃×C₃⋊C₈	—	2	1	no	—
48	C₂×C₃×C₃⋊C₈	C₂×C₄	1	2	yes	—
49	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
50	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
51	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
52	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
53	C₃²×C₁₆	—	2	2	no	—
54	C₃×C₃⋊C₁₆	—	2	2	no	—
55	C₂×#349	—	3	1	no	Sylow
56	C₂³×C₃×C₄	—	3	1	no	—
57	C₂²×C₄×D₃	C₃×C₄	1	1	yes	characteristic
58	C₂×C₃×M₁₆	—	3	2	no	—
59	C₂×C₃×M₁₆	—	3	2	no	—
60	C₂×C₃×M₁₆	—	6	1	no	—
61	C₂×C₃×M₁₆	—	6	1	no	—
62	C₂×C₃×M₁₆	—	6	1	no	—
63	C₂×C₃×M₁₆	—	6	1	no	—
64	C₂²×C₃×C₈	—	2	1	no	—
65	C₂²×C₃×C₈	—	3	1	no	—
66	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
67	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
68	C₂²×C₃⋊C₈	C₃×C₄	1	1	yes	characteristic
69	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
70	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
71	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
72	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
73	C₂×ΓL(1,𝔽₂₅)	C₃×C₄	1	2	yes	—
74	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	2	yes	—
75	C₃×M₃₂	—	2	2	no	—
76	C₃×M₃₂	—	2	1	no	—
77	C₃×M₃₂	—	2	1	no	—
78	C₃×M₃₂	—	2	2	no	—
79	C₃×M₃₂	—	3	2	no	—
80	C₃×M₃₂	—	6	1	no	—
81	C₃×M₃₂	C₂×D₃	1	2	yes	complemented
82	C₃×M₃₂	C₂²×C₃	1	2	yes	complemented
83	C₂×C₃×C₁₆	—	2	2	no	—
84	C₂×C₃×C₁₆	—	2	1	no	—
85	C₂×C₃×C₁₆	—	2	1	no	—
86	C₂×C₃×C₁₆	—	6	1	no	—
87	#812	—	2	1	no	—
88	#812	C₂²×C₃	1	2	yes	complemented
89	C₂×C₃⋊C₁₆	—	2	1	no	—
90	C₂³×C₃²	C₂×C₈	1	1	yes	characteristic
91	C₂²×C₃×D₃	—	2	1	no	—
92	C₂²×C₃×D₃	—	2	1	no	—
93	C₂²×C₃×D₃	—	4	2	no	—
94	C₂²×C₃×D₃	C₂×C₈	1	2	yes	—
95	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₃²×C₄	C₂×C₈	1	1	yes	characteristic
98	C₂×C₃²×C₄	M₁₆	1	1	yes	characteristic
99	C₂×C₃²×C₄	M₁₆	1	1	yes	characteristic
100	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₃×Dic₃	—	2	1	no	—
102	C₂×C₃×Dic₃	—	2	1	no	—
103	C₂×C₃×Dic₃	C₂×C₈	1	2	yes	—
104	C₃×C₄×D₃	—	2	2	no	—
105	C₃×C₄×D₃	—	2	2	no	—
106	C₃×C₄×D₃	—	2	2	no	—
107	C₃×C₄×D₃	—	2	2	no	—
108	C₃²×C₈	C₂²⋊C₄	1	1	yes	characteristic
109	C₃²×C₈	C₂²⋊C₄	1	1	yes	characteristic
110	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
111	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
112	C₃×C₃⋊C₈	—	2	2	no	—
113	C₂²×M₁₆	—	3	1	no	—
114	C₂×M₃₂	—	3	1	no	—
115	C₂×M₃₂	C₃×D₃	1	1	yes	characteristic, complemented
116	#349	—	3	4	no	—
117	C₂⁴×C₃	—	3	1	no	—
118	C₂³×D₃	C₃×C₈	1	1	yes	characteristic
119	C₂²×C₃×C₄	—	2	1	no	—
120	C₂²×C₃×C₄	—	3	1	no	—
121	C₂²×C₃×C₄	—	3	2	no	—
122	C₂²×C₃×C₄	—	3	2	no	—
123	C₂²×C₃×C₄	—	6	1	no	—
124	C₂²×C₃×C₄	—	6	1	no	—
125	C₂²×C₃×C₄	—	6	1	no	—
126	C₂²×C₃×C₄	—	6	1	no	—
127	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
128	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
129	C₂²×Dic₃	C₃×C₈	1	1	yes	characteristic
130	C₂×C₄×D₃	—	2	1	no	—
131	C₂×C₄×D₃	—	2	1	no	—
132	C₂×C₄×D₃	—	2	1	no	—
133	C₂×C₄×D₃	—	2	1	no	—
134	C₂×C₄×D₃	C₃×C₈	1	2	yes	—
135	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
136	C₃×M₁₆	—	6	2	no	—
137	C₃×M₁₆	—	6	2	no	—
138	C₃×M₁₆	—	6	2	no	—
139	C₃×M₁₆	—	6	2	no	—
140	C₂×C₃×C₈	—	2	1	no	—
141	C₂×C₃×C₈	—	2	1	no	—
142	C₂×C₃×C₈	—	2	1	no	—
143	C₂×C₃×C₈	—	2	1	no	—
144	C₂×C₃×C₈	—	2	1	no	—
145	C₂×C₃×C₈	—	2	1	no	—
146	C₂×C₃×C₈	—	3	2	no	—
147	C₂×C₃×C₈	—	6	1	no	—
148	C₂×C₃×C₈	—	6	1	no	—
149	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
150	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
151	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
152	C₂×C₃×C₈	#67	1	1	yes	characteristic
153	C₂×C₃×C₈	#67	1	1	yes	characteristic
154	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
155	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
156	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
157	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
158	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
159	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
160	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
161	C₂×C₃⋊C₈	—	2	1	no	—
162	C₂×C₃⋊C₈	—	2	1	no	—
163	C₂×C₃⋊C₈	C₂×C₃×C₄	1	2	yes	—
164	ΓL(1,𝔽₂₅)	—	2	2	no	—
165	ΓL(1,𝔽₂₅)	—	2	2	no	—
166	ΓL(1,𝔽₂₅)	—	2	2	no	—
167	ΓL(1,𝔽₂₅)	—	2	2	no	—
168	C₃×C₁₆	—	2	4	no	—
169	C₃×C₁₆	—	2	2	no	—
170	C₃×C₁₆	—	2	2	no	—
171	C₃×C₁₆	—	6	2	no	—
172	C₃⋊C₁₆	—	2	2	no	—
173	C₂²×C₃²	—	2	2	no	—
174	C₂²×C₃²	C₂²⋊C₈	1	1	yes	characteristic
175	C₂²×C₃²	C₂²⋊C₈	1	1	yes	characteristic
176	C₂²×C₃²	C₂²×C₈	1	1	yes	characteristic
177	C₂×C₃×D₃	—	2	2	no	—
178	C₂×C₃×D₃	—	4	2	no	—
179	C₂×C₃×D₃	—	4	2	no	—
180	C₂×C₃×D₃	—	4	2	no	—
181	C₃²×C₄	C₂²⋊C₈	1	1	yes	characteristic
182	C₃²×C₄	C₂²⋊C₈	1	1	yes	characteristic
183	C₃²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₃²×C₄	C₂×M₁₆	1	1	yes	characteristic
185	C₃×Dic₃	—	2	2	no	—
186	C₂³×C₄	—	3	1	no	—
187	C₂×M₁₆	—	3	2	no	—
188	C₂×M₁₆	—	3	2	no	—
189	C₂×M₁₆	—	6	1	no	—
190	C₂×M₁₆	—	6	1	no	—
191	C₂×M₁₆	—	6	1	no	—
192	C₂×M₁₆	—	6	1	no	—
193	C₂²×C₈	—	3	1	no	—
194	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
195	M₃₂	—	2	1	no	—
196	M₃₂	—	3	2	no	—
197	M₃₂	—	6	1	no	—
198	M₃₂	C₂×C₃×D₃	1	2	yes	complemented
199	C₂×C₁₆	—	2	1	no	—
200	C₂×C₁₆	—	6	1	no	—
201	C₂³×C₃	—	2	1	no	—
202	C₂³×C₃	—	3	2	no	—
203	C₂³×C₃	—	6	1	no	—
204	C₂³×C₃	—	6	1	no	—
205	C₂³×C₃	—	12	2	no	—
206	C₂³×C₃	D₃×C₈	1	1	yes	characteristic
207	C₂³×C₃	C₂×C₃×C₈	1	1	yes	characteristic
208	C₂²×D₃	—	2	1	no	—
209	C₂²×D₃	—	2	1	no	—
210	C₂²×D₃	—	4	2	no	—
211	C₂²×D₃	C₂×C₃×C₈	1	2	yes	—
212	C₂×C₃×C₄	—	2	1	no	—
213	C₂×C₃×C₄	—	2	1	no	—
214	C₂×C₃×C₄	—	2	1	no	—
215	C₂×C₃×C₄	—	2	1	no	—
216	C₂×C₃×C₄	—	2	1	no	—
217	C₂×C₃×C₄	—	2	1	no	—
218	C₂×C₃×C₄	—	3	2	no	—
219	C₂×C₃×C₄	—	6	1	no	—
220	C₂×C₃×C₄	—	6	1	no	—
221	C₂×C₃×C₄	—	6	2	no	—
222	C₂×C₃×C₄	—	6	2	no	—
223	C₂×C₃×C₄	—	6	2	no	—
224	C₂×C₃×C₄	—	6	2	no	—
225	C₂×C₃×C₄	D₃×C₈	1	1	yes	characteristic
226	C₂×C₃×C₄	ΓL(1,𝔽₂₅)	1	1	yes	characteristic
227	C₂×C₃×C₄	ΓL(1,𝔽₂₅)	1	1	yes	characteristic
228	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
229	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
230	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
231	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
232	C₂×C₃×C₄	C₂×C₃×C₈	1	1	yes	characteristic
233	C₂×C₃×C₄	C₃×M₁₆	1	1	yes	characteristic
234	C₂×C₃×C₄	C₃×M₁₆	1	1	yes	characteristic
235	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
236	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
237	C₂×Dic₃	—	2	1	no	—
238	C₂×Dic₃	—	2	1	no	—
239	C₂×Dic₃	C₂×C₃×C₈	1	2	yes	—
240	C₄×D₃	—	2	2	no	—
241	C₄×D₃	—	2	2	no	—
242	C₄×D₃	—	2	2	no	—
243	C₄×D₃	—	2	2	no	—
244	C₃×C₈	—	2	1	no	—
245	C₃×C₈	—	2	1	no	—
246	C₃×C₈	—	2	1	no	—
247	C₃×C₈	—	2	1	no	—
248	C₃×C₈	—	6	2	no	—
249	C₃×C₈	(C₂×D₃)⋊C₄	1	1	yes	characteristic
250	C₃×C₈	(C₂×D₃)⋊C₄	1	1	yes	characteristic
251	C₃×C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
252	C₃×C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
253	C₃×C₈	C₂×D₁₂	1	1	yes	characteristic
254	C₃×C₈	C₂×#67	1	1	yes	characteristic
255	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
256	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
257	C₃⋊C₈	—	2	2	no	—
258	C₂×C₃²	—	2	1	no	—
259	C₂×C₃²	—	2	1	no	—
260	C₂×C₃²	#349	1	2	yes	complemented
261	C₂×C₃²	C₂×C₂²⋊C₈	1	1	yes	characteristic
262	C₃×D₃	—	4	2	no	—
263	C₂⁴	—	3	1	no	—
264	C₂²×C₄	—	3	1	no	—
265	C₂²×C₄	—	3	2	no	—
266	C₂²×C₄	—	3	2	no	—
267	C₂²×C₄	—	6	1	no	—
268	C₂²×C₄	—	6	1	no	—
269	C₂²×C₄	—	6	1	no	—
270	C₂²×C₄	—	6	1	no	—
271	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
272	M₁₆	—	6	2	no	—
273	M₁₆	—	6	2	no	—
274	M₁₆	—	6	2	no	—
275	M₁₆	—	6	2	no	—
276	C₂×C₈	—	3	2	no	—
277	C₂×C₈	—	6	1	no	—
278	C₂×C₈	—	6	1	no	—
279	C₂×C₈	C₃×C₄×D₃	1	1	yes	characteristic
280	C₂×C₈	C₃×D₁₂	1	1	yes	characteristic
281	C₂×C₈	C₃×D₁₂	1	1	yes	characteristic
282	C₂×C₈	C₃×#67	1	1	yes	characteristic
283	C₂×C₈	C₃×#67	1	1	yes	characteristic
284	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
285	C₁₆	—	2	2	no	—
286	C₁₆	—	6	2	no	—
287	C₂²×C₃	—	2	2	no	—
288	C₂²×C₃	—	2	2	no	—
289	C₂²×C₃	—	2	1	no	—
290	C₂²×C₃	—	2	1	no	—
291	C₂²×C₃	—	2	1	no	—
292	C₂²×C₃	—	4	2	no	—
293	C₂²×C₃	—	6	2	no	—
294	C₂²×C₃	—	12	2	no	—
295	C₂²×C₃	—	12	2	no	—
296	C₂²×C₃	—	12	2	no	—
297	C₂²×C₃	(C₂×D₃)⋊C₈	1	1	yes	characteristic
298	C₂²×C₃	(C₂×D₃)⋊C₈	1	1	yes	characteristic
299	C₂²×C₃	C₃×C₂²⋊C₈	1	1	yes	characteristic
300	C₂²×C₃	C₃×C₂²⋊C₈	1	1	yes	characteristic
301	C₂²×C₃	C₂×D₃×C₈	1	1	yes	characteristic
302	C₂²×C₃	C₂²×C₃×C₈	1	1	yes	characteristic
303	C₂×D₃	—	2	2	no	—
304	C₂×D₃	—	4	2	no	—
305	C₂×D₃	—	4	2	no	—
306	C₂×D₃	—	4	2	no	—
307	C₃×C₄	—	2	1	no	—
308	C₃×C₄	—	2	1	no	—
309	C₃×C₄	—	2	1	no	—
310	C₃×C₄	—	2	1	no	—
311	C₃×C₄	—	6	2	no	—
312	C₃×C₄	(C₂×D₃)⋊C₈	1	1	yes	characteristic
313	C₃×C₄	(C₂×D₃)⋊C₈	1	1	yes	characteristic
314	C₃×C₄	C₃×C₂²⋊C₈	1	1	yes	characteristic
315	C₃×C₄	C₃×C₂²⋊C₈	1	1	yes	characteristic
316	C₃×C₄	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
317	C₃×C₄	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
318	C₃×C₄	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
319	C₃×C₄	C₂×C₃×M₁₆	1	1	yes	characteristic
320	Dic₃	—	2	2	no	—
321	C₃²	C₂×#349	1	1	yes	characteristic, complemented, Sylow
322	C₂³	—	3	2	no	—
323	C₂³	—	6	1	no	—
324	C₂³	—	6	1	no	—
325	C₂³	—	12	2	no	—
326	C₂³	C₃×D₃×C₈	1	1	yes	characteristic
327	C₂×C₄	—	3	2	no	—
328	C₂×C₄	—	6	1	no	—
329	C₂×C₄	—	6	1	no	—
330	C₂×C₄	—	6	2	no	—
331	C₂×C₄	—	6	2	no	—
332	C₂×C₄	—	6	2	no	—
333	C₂×C₄	—	6	2	no	—
334	C₂×C₄	C₃×D₃×C₈	1	1	yes	characteristic
335	C₂×C₄	C₃×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
336	C₂×C₄	C₃×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
337	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
338	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
339	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
340	C₈	—	6	2	no	—
341	C₈	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
342	C₈	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
343	C₈	C₂×C₃×D₁₂	1	1	yes	characteristic
344	C₈	C₂×C₃×#67	1	1	yes	characteristic
345	C₂×C₃	—	2	1	no	—
346	C₂×C₃	—	2	1	no	—
347	C₂×C₃	—	2	1	no	—
348	C₂×C₃	—	2	1	no	—
349	C₂×C₃	—	2	2	no	—
350	C₂×C₃	—	2	1	no	—
351	C₂×C₃	—	4	1	no	—
352	C₂×C₃	—	4	1	no	—
353	C₂×C₃	—	12	2	no	—
354	C₂×C₃	#4514	1	2	yes	direct product factor
355	C₂×C₃	C₃×#349	1	2	yes	complemented
356	C₂×C₃	C₂×(C₂×D₃)⋊C₈	1	1	yes	characteristic
357	C₂×C₃	C₂×C₃×C₂²⋊C₈	1	1	yes	characteristic
358	D₃	—	4	2	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	6	2	no	—
361	C₂²	—	12	2	no	—
362	C₂²	—	12	2	no	—
363	C₂²	—	12	2	no	—
364	C₂²	C₃×(C₂×D₃)⋊C₈	1	1	yes	characteristic
365	C₂²	C₃×(C₂×D₃)⋊C₈	1	1	yes	characteristic
366	C₂²	C₂×C₃×D₃×C₈	1	1	yes	characteristic
367	C₄	—	6	2	no	—
368	C₄	C₃×(C₂×D₃)⋊C₈	1	1	yes	characteristic
369	C₄	C₃×(C₂×D₃)⋊C₈	1	1	yes	characteristic
370	C₄	C₂×C₃×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
371	C₄	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
372	C₃	—	2	1	no	—
373	C₃	C₂×#4514	1	1	yes	characteristic, direct product factor
374	C₃	C₂×C₃×#349	1	1	yes	characteristic, complemented
375	C₂	—	2	1	no	—
376	C₂	—	2	1	no	—
377	C₂	—	12	2	no	—
378	C₂	C₃×#4514	1	2	yes	direct product factor
379	C₂	C₂×C₃×(C₂×D₃)⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	(C₂×D₃)⋊C₄
commutator	C₂²×C₃	C₂²×C₃×C₈
Frattini	C₂×C₈	C₂²×C₃×D₃
Fitting	C₂×C₃²×M₃₂	C₂
socle	C₂²×C₃²	C₂²⋊C₈
prime radical	C₂³×C₃×D₃	C₈
cosocle	C₂×C₃×C₈	C₂³×C₃
hypercenter	C₂×C₃×M₃₂	D₃
hypocenter	C₃	C₂×C₃×#349
LCS	G ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×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×#4514	C₂	direct (N × H)
6. C₂×#4514	C₃	direct (N × H)
17. C₃²×M₃₂	C₂²	semidirect
20. C₃×#812	C₂²	semidirect
26. C₂×C₃×M₃₂	D₃	semidirect
27. C₂×C₃×M₃₂	C₂×C₃	semidirect
28. C₂×#812	C₂×C₃	semidirect
30. #4514	C₂×C₃	direct (N × H)
81. C₃×M₃₂	C₂×D₃	semidirect
82. C₃×M₃₂	C₂²×C₃	semidirect
88. #812	C₂²×C₃	semidirect
115. C₂×M₃₂	C₃×D₃	semidirect
198. M₃₂	C₂×C₃×D₃	semidirect
260. C₂×C₃²	#349	semidirect
321. C₃²	C₂×#349	semidirect
354. C₂×C₃	#4514	direct (N × H)
355. C₂×C₃	C₃×#349	semidirect
373. C₃	C₂×#4514	direct (N × H)
374. C₃	C₂×C₃×#349	semidirect
378. C₂	C₃×#4514	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×ΓL(1,𝔽₂₅)	2
C₂×C₃²×M₃₂	2
C₂×C₃×#812	2
C₃×#4514	2
C₂×C₃×#349	3
C₂×#4514	3

Subgroups — C2×C3×#4514 #11796026

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#4514 #11796026