Subgroups — C₂×C₃×#4838 #11859264

Order 1152.

1173 conjugacy classes of subgroups.

The subgroup lattice has 379 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	2	yes	maximal, complemented
2	C₂×C₃×C₄×D₁₂	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃²×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×(C₂×D₃)⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×C₄×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4838	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃×#436	—	3	1	no	maximal
8	C₂×#4838	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂²×C₃×D₁₂	C₄	1	1	yes	characteristic
10	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	—
11	C₂²×C₃²×C₈	C₂²	1	2	yes	—
12	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
13	C₂×C₃×(C₂×D₃)⋊C₄	C₄	1	2	yes	—
14	C₂×C₃×C₄⋊Dic₃	C₄	1	1	yes	characteristic
15	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₃×ΓL(1,𝔽₂₅)	—	2	8	no	—
18	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	8	yes	complemented
19	C₃×C₄×D₁₂	C₄	1	4	yes	—
20	C₃×C₄×D₁₂	C₂²	1	4	yes	—
21	C₃²×C₄⋊C₈	C₂²	1	4	yes	complemented
22	C₃×(C₂×D₃)⋊C₈	C₂²	1	8	yes	complemented
23	C₃×C₄×C₃⋊C₈	C₂²	1	4	yes	complemented
24	C₂²×C₃×M₁₆	—	3	2	no	—
25	C₂×C₃×C₄×D₄	—	3	1	no	—
26	C₂²×ΓL(1,𝔽₂₅)	C₂×C₃	1	2	yes	complemented
27	C₂×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic
28	C₃×#436	—	3	8	no	—
29	C₂×C₃×C₄⋊C₈	—	2	1	no	—
30	C₂×C₃×C₄⋊C₈	D₃	1	1	yes	characteristic, complemented
31	C₂×C₃×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂×C₃×C₂²⋊C₈	—	3	2	no	—
33	C₂×C₃×C₄×C₈	—	3	1	no	—
34	C₂×(C₂×D₃)⋊C₈	C₂×C₃	1	2	yes	complemented
35	C₂×C₄×C₃⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
36	#4838	C₂×C₃	1	8	yes	direct product factor
37	C₂³×C₃×D₃	C₂×C₄	1	2	yes	—
38	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
41	C₂²×C₃×Dic₃	C₂×C₄	1	2	yes	—
42	C₂×C₃×D₁₂	—	2	4	no	—
43	C₂×C₃×D₁₂	C₂×C₄	1	4	yes	—
44	C₂×C₃×C₄×D₃	—	2	4	no	—
45	C₂×C₃×C₄×D₃	—	2	4	no	—
46	C₂×C₃×C₄×D₃	C₂×C₄	1	4	yes	—
47	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
48	C₂×C₃²×C₈	—	2	4	no	—
49	C₂×C₃²×C₈	C₂³	1	4	yes	—
50	C₃²×C₄²	C₂×C₄	1	2	yes	—
51	C₃²×C₄²	C₂³	1	2	yes	—
52	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	8	yes	—
53	C₃×C₄⋊Dic₃	C₂×C₄	1	4	yes	—
54	C₂×C₃×C₃⋊C₈	—	2	2	no	—
55	C₂×C₃×C₃⋊C₈	D₄	1	4	yes	complemented
56	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
57	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
58	C₃×ΓL(1,𝔽₂₅)	—	2	16	no	—
59	C₂×#436	—	3	1	no	Sylow
60	C₂²×C₃×D₄	—	3	1	no	—
61	C₂³×C₃×C₄	—	3	2	no	—
62	C₂²×D₁₂	C₃×C₄	1	1	yes	characteristic
63	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	—
64	C₂×C₃×M₁₆	—	3	8	no	—
65	C₂×C₃×M₁₆	—	6	8	no	—
66	C₂²×C₃×C₈	—	2	2	no	—
67	C₂²×C₃×C₈	—	3	1	no	—
68	C₂²×C₃×C₈	—	3	1	no	—
69	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
70	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
71	C₃×C₄×D₄	—	3	4	no	—
72	C₃×C₄×D₄	—	3	4	no	—
73	C₂×C₃×C₄⋊C₄	—	3	1	no	—
74	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
75	C₂×C₃×C₄²	—	2	1	no	—
76	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
77	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
78	C₂×(C₂×D₃)⋊C₄	C₃×C₄	1	2	yes	—
79	C₂×C₄⋊Dic₃	C₃×C₄	1	1	yes	characteristic
80	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
81	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
82	C₂×ΓL(1,𝔽₂₅)	—	2	8	no	—
83	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	8	yes	complemented
84	C₄×D₁₂	C₃×C₄	1	4	yes	—
85	C₄×D₁₂	C₂²×C₃	1	4	yes	—
86	C₃×C₄⋊C₈	—	2	4	no	—
87	C₃×C₄⋊C₈	C₂×D₃	1	4	yes	complemented
88	C₃×C₄⋊C₈	C₂²×C₃	1	4	yes	complemented
89	C₃×C₂²⋊C₈	—	3	8	no	—
90	C₃×C₄×C₈	—	3	4	no	—
91	(C₂×D₃)⋊C₈	C₂²×C₃	1	8	yes	complemented
92	C₄×C₃⋊C₈	C₂²×C₃	1	4	yes	complemented
93	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₃×D₃	—	2	4	no	—
95	C₂²×C₃×D₃	—	2	4	no	—
96	C₂²×C₃×D₃	—	2	4	no	—
97	C₂²×C₃×D₃	C₂²×C₄	1	4	yes	—
98	C₂×C₃²×C₄	—	2	2	no	—
99	C₂×C₃²×C₄	M₁₆	1	4	yes	complemented
100	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
101	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
103	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
104	C₂×C₃²×C₄	#41	1	2	yes	—
105	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
106	C₂×C₃×Dic₃	—	2	4	no	—
107	C₂×C₃×Dic₃	C₂²×C₄	1	4	yes	—
108	C₃×D₁₂	—	2	8	no	—
109	C₃×C₄×D₃	—	2	8	no	—
110	C₃×C₄×D₃	—	2	4	no	—
111	C₃×C₄×D₃	—	2	4	no	—
112	C₃²×C₈	—	2	4	no	—
113	C₃×C₃⋊C₈	—	2	2	no	—
114	C₃×C₃⋊C₈	C₂×D₄	1	4	yes	complemented
115	C₂²×M₁₆	—	3	2	no	—
116	C₂×C₄×D₄	—	3	1	no	—
117	#436	—	3	8	no	—
118	C₂×C₄⋊C₈	C₃×D₃	1	1	yes	characteristic, complemented
119	C₂×C₂²⋊C₈	—	3	2	no	—
120	C₂×C₄×C₈	—	3	1	no	—
121	C₂⁴×C₃	—	3	2	no	—
122	C₂³×D₃	C₂×C₃×C₄	1	2	yes	—
123	C₂×C₃×D₄	—	3	4	no	—
124	C₂×C₃×D₄	—	6	4	no	—
125	C₂²×C₃×C₄	—	2	1	no	—
126	C₂²×C₃×C₄	—	2	1	no	—
127	C₂²×C₃×C₄	—	2	1	no	—
128	C₂²×C₃×C₄	—	3	2	no	—
129	C₂²×C₃×C₄	—	3	4	no	—
130	C₂²×C₃×C₄	—	3	4	no	—
131	C₂²×C₃×C₄	—	6	4	no	—
132	C₂²×C₃×C₄	—	6	4	no	—
133	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
134	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
135	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
136	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
137	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
138	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
139	C₂²×Dic₃	C₂×C₃×C₄	1	2	yes	—
140	C₂×D₁₂	—	2	4	no	—
141	C₂×D₁₂	C₂×C₃×C₄	1	4	yes	—
142	C₂×C₄×D₃	—	2	4	no	—
143	C₂×C₄×D₃	—	2	4	no	—
144	C₂×C₄×D₃	C₂×C₃×C₄	1	4	yes	—
145	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
146	C₃×M₁₆	—	6	16	no	—
147	C₂×C₃×C₈	—	2	4	no	—
148	C₂×C₃×C₈	—	2	4	no	—
149	C₂×C₃×C₈	—	2	4	no	—
150	C₂×C₃×C₈	—	3	4	no	—
151	C₂×C₃×C₈	—	3	2	no	—
152	C₂×C₃×C₈	—	3	2	no	—
153	C₂×C₃×C₈	—	4	4	no	—
154	C₂×C₃×C₈	—	6	2	no	—
155	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
156	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
157	C₃×C₄⋊C₄	—	3	4	no	—
158	C₃×C₂²⋊C₄	—	3	8	no	—
159	C₃×C₄²	—	2	2	no	—
160	C₃×C₄²	—	2	2	no	—
161	C₃×C₄²	C₄×D₃	1	2	yes	—
162	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
163	C₃×C₄²	C₂²×D₃	1	2	yes	—
164	C₃×C₄²	C₂³×C₃	1	2	yes	—
165	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	8	yes	—
166	C₄⋊Dic₃	C₂×C₃×C₄	1	4	yes	—
167	C₂×C₃⋊C₈	—	2	2	no	—
168	C₂×C₃⋊C₈	C₃×D₄	1	4	yes	complemented
169	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
170	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
171	ΓL(1,𝔽₂₅)	—	2	16	no	—
172	C₂²×C₃²	C₄×D₄	1	2	yes	—
173	C₂²×C₃²	C₂×M₁₆	1	2	yes	—
174	C₂²×C₃²	#131	1	2	yes	—
175	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
176	C₂×C₃×D₃	—	2	4	no	—
177	C₂×C₃×D₃	—	2	4	no	—
178	C₂×C₃×D₃	—	2	4	no	—
179	C₂×C₃×D₃	—	4	8	no	—
180	C₃²×C₄	—	2	2	no	—
181	C₃²×C₄	C₄×D₄	1	2	yes	—
182	C₃²×C₄	C₂×M₁₆	1	4	yes	complemented
183	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
184	C₃²×C₄	C₂×#41	1	1	yes	characteristic
185	C₃×Dic₃	—	2	4	no	—
186	C₂²×D₄	—	3	1	no	—
187	C₂³×C₄	—	3	2	no	—
188	C₂×M₁₆	—	3	8	no	—
189	C₂×M₁₆	—	6	8	no	—
190	C₂²×C₈	—	3	1	no	—
191	C₂²×C₈	—	3	1	no	—
192	C₂²×C₈	C₂×C₃×D₃	1	2	yes	—
193	C₄×D₄	—	3	4	no	—
194	C₄×D₄	—	3	4	no	—
195	C₂×C₄⋊C₄	—	3	1	no	—
196	C₂×C₂²⋊C₄	—	3	2	no	—
197	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
198	C₄⋊C₈	C₂×C₃×D₃	1	4	yes	complemented
199	C₂²⋊C₈	—	3	8	no	—
200	C₄×C₈	—	3	4	no	—
201	C₂³×C₃	—	2	1	no	—
202	C₂³×C₃	—	3	4	no	—
203	C₂³×C₃	—	6	4	no	—
204	C₂³×C₃	—	6	4	no	—
205	C₂³×C₃	—	6	4	no	—
206	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
207	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
208	C₂²×D₃	—	2	4	no	—
209	C₂²×D₃	—	2	4	no	—
210	C₂²×D₃	—	2	4	no	—
211	C₂²×D₃	C₂²×C₃×C₄	1	4	yes	—
212	C₃×D₄	—	6	8	no	—
213	C₂×C₃×C₄	—	2	2	no	—
214	C₂×C₃×C₄	—	2	2	no	—
215	C₂×C₃×C₄	—	2	1	no	—
216	C₂×C₃×C₄	—	2	4	no	—
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	2	no	—
221	C₂×C₃×C₄	—	2	2	no	—
222	C₂×C₃×C₄	—	3	4	no	—
223	C₂×C₃×C₄	—	4	2	no	—
224	C₂×C₃×C₄	—	6	4	no	—
225	C₂×C₃×C₄	—	6	8	no	—
226	C₂×C₃×C₄	—	6	4	no	—
227	C₂×C₃×C₄	—	6	4	no	—
228	C₂×C₃×C₄	ΓL(1,𝔽₂₅)	1	4	yes	complemented
229	C₂×C₃×C₄	C₃×M₁₆	1	4	yes	complemented
230	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
231	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
232	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
233	C₂×C₃×C₄	D₃×D₄	1	2	yes	—
234	C₂×C₃×C₄	#239	1	2	yes	—
235	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
236	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
237	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
238	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
239	C₂×C₃×C₄	C₃×#41	1	2	yes	—
240	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
241	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
242	C₂×Dic₃	—	2	4	no	—
243	C₂×Dic₃	C₂²×C₃×C₄	1	4	yes	—
244	D₁₂	—	2	8	no	—
245	C₄×D₃	—	2	8	no	—
246	C₄×D₃	—	2	4	no	—
247	C₄×D₃	—	2	4	no	—
248	C₃×C₈	—	2	4	no	—
249	C₃×C₈	—	2	4	no	—
250	C₃×C₈	—	3	4	no	—
251	C₃×C₈	—	4	4	no	—
252	C₃×C₈	—	6	2	no	—
253	C₃⋊C₈	—	2	2	no	—
254	C₃⋊C₈	C₂×C₃×D₄	1	4	yes	complemented
255	C₂×C₃²	#436	1	4	yes	complemented
256	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
257	C₂×C₃²	C₂²×M₁₆	1	1	yes	characteristic
258	C₂×C₃²	C₂×#131	1	1	yes	characteristic
259	C₃×D₃	—	4	4	no	—
260	C₂⁴	—	3	2	no	—
261	C₂×D₄	—	3	4	no	—
262	C₂×D₄	—	6	4	no	—
263	C₂²×C₄	—	3	2	no	—
264	C₂²×C₄	—	3	4	no	—
265	C₂²×C₄	—	3	4	no	—
266	C₂²×C₄	—	6	4	no	—
267	C₂²×C₄	—	6	4	no	—
268	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
269	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
270	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
271	M₁₆	—	6	16	no	—
272	C₂×C₈	—	2	4	no	—
273	C₂×C₈	—	3	2	no	—
274	C₂×C₈	—	3	4	no	—
275	C₂×C₈	—	3	2	no	—
276	C₂×C₈	—	6	2	no	—
277	C₂×C₈	C₂²×C₃×D₃	1	4	yes	—
278	C₄⋊C₄	—	3	4	no	—
279	C₂²⋊C₄	—	3	8	no	—
280	C₄²	C₃×C₄×D₃	1	2	yes	—
281	C₄²	C₂²×C₃×D₃	1	2	yes	—
282	C₂²×C₃	—	2	2	no	—
283	C₂²×C₃	—	2	2	no	—
284	C₂²×C₃	—	2	2	no	—
285	C₂²×C₃	—	2	1	no	—
286	C₂²×C₃	—	6	4	no	—
287	C₂²×C₃	—	6	4	no	—
288	C₂²×C₃	—	6	4	no	—
289	C₂²×C₃	—	12	8	no	—
290	C₂²×C₃	#893	1	2	yes	—
291	C₂²×C₃	C₂×ΓL(1,𝔽₂₅)	1	2	yes	—
292	C₂²×C₃	#907	1	2	yes	—
293	C₂²×C₃	C₃×C₄×D₄	1	2	yes	—
294	C₂²×C₃	C₂×C₃×M₁₆	1	2	yes	—
295	C₂²×C₃	C₃×#131	1	2	yes	—
296	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
297	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
298	C₂×D₃	—	2	4	no	—
299	C₂×D₃	—	2	4	no	—
300	C₂×D₃	—	2	4	no	—
301	C₂×D₃	—	4	8	no	—
302	C₃×C₄	—	2	2	no	—
303	C₃×C₄	—	2	2	no	—
304	C₃×C₄	—	2	2	no	—
305	C₃×C₄	—	2	4	no	—
306	C₃×C₄	—	2	1	no	—
307	C₃×C₄	—	2	1	no	—
308	C₃×C₄	—	4	2	no	—
309	C₃×C₄	—	6	4	no	—
310	C₃×C₄	#893	1	2	yes	—
311	C₃×C₄	C₂×ΓL(1,𝔽₂₅)	1	4	yes	complemented
312	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
313	C₃×C₄	C₂×C₃×M₁₆	1	4	yes	complemented
314	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
315	C₃×C₄	C₂×#239	1	1	yes	characteristic
316	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
317	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
318	Dic₃	—	2	4	no	—
319	C₃²	C₂×#436	1	1	yes	characteristic, complemented, Sylow
320	C₂³	—	3	4	no	—
321	C₂³	—	6	4	no	—
322	C₂³	—	6	4	no	—
323	C₂³	—	6	4	no	—
324	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
325	D₄	—	6	8	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	3	4	no	—
328	C₂×C₄	—	6	4	no	—
329	C₂×C₄	—	6	8	no	—
330	C₂×C₄	—	6	4	no	—
331	C₂×C₄	—	6	4	no	—
332	C₂×C₄	C₃×ΓL(1,𝔽₂₅)	1	4	yes	complemented
333	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
334	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
335	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
336	C₂×C₄	C₃×D₃×D₄	1	2	yes	—
337	C₂×C₄	C₃×#239	1	2	yes	—
338	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
339	C₈	—	2	4	no	—
340	C₈	—	3	4	no	—
341	C₈	—	6	2	no	—
342	C₂×C₃	—	2	1	no	—
343	C₂×C₃	—	2	1	no	—
344	C₂×C₃	—	2	4	no	—
345	C₂×C₃	—	2	1	no	—
346	C₂×C₃	—	12	4	no	—
347	C₂×C₃	#4838	1	4	yes	direct product factor
348	C₂×C₃	C₃×#436	1	4	yes	complemented
349	C₂×C₃	C₂×#893	1	1	yes	characteristic
350	C₂×C₃	C₂²×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
351	C₂×C₃	C₂×#907	1	1	yes	characteristic
352	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
353	C₂×C₃	C₂²×C₃×M₁₆	1	1	yes	characteristic
354	C₂×C₃	C₂×C₃×#131	1	1	yes	characteristic
355	D₃	—	4	4	no	—
356	C₂²	—	6	4	no	—
357	C₂²	—	6	4	no	—
358	C₂²	—	6	4	no	—
359	C₂²	—	12	8	no	—
360	C₂²	C₃×#893	1	2	yes	—
361	C₂²	C₂×C₃×ΓL(1,𝔽₂₅)	1	2	yes	—
362	C₂²	C₃×#907	1	2	yes	—
363	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
364	C₄	—	2	2	no	—
365	C₄	—	6	4	no	—
366	C₄	C₃×#893	1	2	yes	—
367	C₄	C₂×C₃×ΓL(1,𝔽₂₅)	1	4	yes	complemented
368	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
369	C₄	C₂×C₃×#239	1	1	yes	characteristic
370	C₃	—	2	1	no	—
371	C₃	C₂×#4838	1	1	yes	characteristic, direct product factor
372	C₃	C₂×C₃×#436	1	1	yes	characteristic, complemented
373	C₂	—	12	4	no	—
374	C₂	C₃×#4838	1	4	yes	direct product factor
375	C₂	C₂×C₃×#893	1	1	yes	characteristic
376	C₂	C₂²×C₃×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
377	C₂	C₂×C₃×#907	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×C₄⋊C₈	C₂
socle	C₂³×C₃²	C₂²×C₄
prime radical	C₂²×C₃×D₁₂	C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂×C₃×C₄⋊C₈	D₃
hypocenter	C₃	C₂×C₃×#436
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×ΓL(1,𝔽₂₅)	C₂	semidirect
3. C₂×C₃²×C₄⋊C₈	C₂	semidirect
4. C₂×C₃×(C₂×D₃)⋊C₈	C₂	semidirect
5. C₂×C₃×C₄×C₃⋊C₈	C₂	semidirect
6. C₃×#4838	C₂	direct (N × H)
8. C₂×#4838	C₃	direct (N × H)
18. C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	semidirect
21. C₃²×C₄⋊C₈	C₂²	semidirect
22. C₃×(C₂×D₃)⋊C₈	C₂²	semidirect
23. C₃×C₄×C₃⋊C₈	C₂²	semidirect
26. C₂²×ΓL(1,𝔽₂₅)	C₂×C₃	semidirect
30. C₂×C₃×C₄⋊C₈	D₃	semidirect
31. C₂×C₃×C₄⋊C₈	C₂×C₃	semidirect
34. C₂×(C₂×D₃)⋊C₈	C₂×C₃	semidirect
35. C₂×C₄×C₃⋊C₈	C₂×C₃	semidirect
36. #4838	C₂×C₃	direct (N × H)
55. C₂×C₃×C₃⋊C₈	D₄	semidirect
83. C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	semidirect
87. C₃×C₄⋊C₈	C₂×D₃	semidirect
88. C₃×C₄⋊C₈	C₂²×C₃	semidirect
91. (C₂×D₃)⋊C₈	C₂²×C₃	semidirect
92. C₄×C₃⋊C₈	C₂²×C₃	semidirect
99. C₂×C₃²×C₄	M₁₆	semidirect
114. C₃×C₃⋊C₈	C₂×D₄	semidirect
118. C₂×C₄⋊C₈	C₃×D₃	semidirect
168. C₂×C₃⋊C₈	C₃×D₄	semidirect
182. C₃²×C₄	C₂×M₁₆	semidirect
198. C₄⋊C₈	C₂×C₃×D₃	semidirect
228. C₂×C₃×C₄	ΓL(1,𝔽₂₅)	semidirect
229. C₂×C₃×C₄	C₃×M₁₆	semidirect
254. C₃⋊C₈	C₂×C₃×D₄	semidirect
255. C₂×C₃²	#436	semidirect
311. C₃×C₄	C₂×ΓL(1,𝔽₂₅)	semidirect
313. C₃×C₄	C₂×C₃×M₁₆	semidirect
319. C₃²	C₂×#436	semidirect
332. C₂×C₄	C₃×ΓL(1,𝔽₂₅)	semidirect
347. C₂×C₃	#4838	direct (N × H)
348. C₂×C₃	C₃×#436	semidirect
367. C₄	C₂×C₃×ΓL(1,𝔽₂₅)	semidirect
371. C₃	C₂×#4838	direct (N × H)
372. C₃	C₂×C₃×#436	semidirect
374. C₂	C₃×#4838	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×C₃×C₄×D₁₂	2
C₂×C₃²×C₄⋊C₈	2
C₂×C₃×(C₂×D₃)⋊C₈	2
C₂×C₃×C₄×C₃⋊C₈	2
C₃×#4838	2
C₂×C₃×#436	3
C₂×#4838	3

Subgroups — C2×C3×#4838 #11859264

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#4838 #11859264