Subgroups — C₂×C₃×#4835 #11858737

Order 1152.

1045 conjugacy classes of subgroups.

The subgroup lattice has 415 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄²×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃²×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×(C₂×D₃)⋊C₈	C₂	1	2	yes	maximal
4	C₂×C₃×#815	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4835	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃×#432	—	3	1	no	maximal
8	C₂×#4835	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂²×C₃×C₄×D₃	C₄	1	1	yes	characteristic
10	C₂²×C₃×C₄×D₃	C₄	1	1	yes	characteristic
11	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
12	C₂²×C₃²×C₈	C₂²	1	2	yes	—
13	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄×Dic₃	C₄	1	1	yes	characteristic
15	C₂×C₃×C₄×Dic₃	C₄	1	1	yes	characteristic
16	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₃⋊C₈	C₂²	1	2	yes	—
18	C₃×C₄²×D₃	C₄	1	4	yes	—
19	C₃×C₄²×D₃	C₂²	1	4	yes	—
20	C₃²×C₄⋊C₈	C₂²	1	4	yes	complemented
21	C₃×(C₂×D₃)⋊C₈	C₂²	1	8	yes	—
22	C₃×#815	C₂²	1	8	yes	complemented
23	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	complemented
24	C₂²×C₃×C₄²	—	3	1	no	—
25	C₂×C₄²×D₃	C₂×C₃	1	1	yes	characteristic
26	C₃×#432	—	3	8	no	—
27	C₂×C₃×C₄⋊C₈	—	2	1	no	—
28	C₂×C₃×C₄⋊C₈	—	3	1	no	—
29	C₂×C₃×C₄⋊C₈	D₃	1	1	yes	characteristic, complemented
30	C₂×C₃×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂×C₃×C₂²⋊C₈	—	3	2	no	—
32	C₂×C₃×#97	—	3	2	no	—
33	C₂×(C₂×D₃)⋊C₈	C₂×C₃	1	2	yes	—
34	C₂×#815	C₂×C₃	1	2	yes	complemented
35	C₂×C₄⋊(C₃⋊C₈)	C₂×C₃	1	1	yes	characteristic, complemented
36	#4835	C₂×C₃	1	8	yes	direct product factor
37	C₂³×C₃×D₃	C₂×C₄	1	1	yes	characteristic
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	1	yes	characteristic
42	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₃×C₄×D₃	—	2	4	no	—
45	C₂×C₃×C₄×D₃	—	2	4	no	—
46	C₂×C₃×C₄×D₃	—	2	2	no	—
47	C₂×C₃×C₄×D₃	—	2	2	no	—
48	C₂×C₃×C₄×D₃	C₂×C₄	1	4	yes	—
49	C₂×C₃×C₄×D₃	C₂×C₄	1	4	yes	—
50	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
51	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
52	C₂×C₃²×C₈	—	2	4	no	—
53	C₂×C₃²×C₈	C₂³	1	4	yes	—
54	C₃²×C₄²	C₂×C₄	1	2	yes	—
55	C₃²×C₄²	C₂³	1	2	yes	—
56	C₃×C₄×Dic₃	C₂×C₄	1	4	yes	—
57	C₃×C₄×Dic₃	C₂×C₄	1	4	yes	—
58	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
59	C₃×C₄×Dic₃	C₂³	1	2	yes	—
60	C₂×C₃×C₃⋊C₈	—	2	4	no	—
61	C₂×C₃×C₃⋊C₈	C₂³	1	4	yes	—
62	C₂×#432	—	3	1	no	Sylow
63	C₂³×C₃×C₄	—	3	1	no	—
64	C₂³×C₃×C₄	—	3	1	no	—
65	C₂³×C₃×C₄	—	3	1	no	—
66	C₂²×C₄×D₃	C₃×C₄	1	1	yes	characteristic
67	C₂²×C₄×D₃	C₃×C₄	1	1	yes	characteristic
68	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
69	C₂²×C₃×C₈	—	2	2	no	—
70	C₂²×C₃×C₈	—	3	2	no	—
71	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
72	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
73	C₂×C₃×C₄²	—	2	1	no	—
74	C₂×C₃×C₄²	—	3	1	no	—
75	C₂×C₃×C₄²	—	3	1	no	—
76	C₂×C₃×C₄²	—	3	1	no	—
77	C₂×C₃×C₄²	—	3	4	no	—
78	C₂×C₃×C₄²	—	3	4	no	—
79	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
80	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₄×Dic₃	C₃×C₄	1	1	yes	characteristic
82	C₂×C₄×Dic₃	C₃×C₄	1	1	yes	characteristic
83	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
84	C₂²×C₃⋊C₈	C₂²×C₃	1	2	yes	—
85	C₄²×D₃	C₃×C₄	1	4	yes	—
86	C₄²×D₃	C₂²×C₃	1	4	yes	—
87	C₃×C₄⋊C₈	—	2	4	no	—
88	C₃×C₄⋊C₈	—	3	4	no	—
89	C₃×C₄⋊C₈	C₂×D₃	1	4	yes	complemented
90	C₃×C₄⋊C₈	C₂²×C₃	1	4	yes	complemented
91	C₃×C₂²⋊C₈	—	3	8	no	—
92	C₃×#97	—	3	8	no	—
93	(C₂×D₃)⋊C₈	C₂²×C₃	1	8	yes	—
94	#815	C₂²×C₃	1	8	yes	complemented
95	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	4	yes	complemented
96	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₃×D₃	—	2	2	no	—
98	C₂²×C₃×D₃	—	2	2	no	—
99	C₂²×C₃×D₃	M₁₆	1	4	yes	—
100	C₂²×C₃×D₃	C₂²×C₄	1	2	yes	—
101	C₂×C₃²×C₄	—	2	2	no	—
102	C₂×C₃²×C₄	M₁₆	1	4	yes	—
103	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
104	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
106	C₂×C₃²×C₄	#41	1	2	yes	—
107	C₂×C₃²×C₄	#41	1	2	yes	—
108	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
109	C₂×C₃×Dic₃	—	2	2	no	—
110	C₂×C₃×Dic₃	—	2	2	no	—
111	C₂×C₃×Dic₃	—	2	2	no	—
112	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
113	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
114	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
115	C₃×C₄×D₃	—	2	8	no	—
116	C₃×C₄×D₃	—	2	4	no	—
117	C₃×C₄×D₃	—	2	8	no	—
118	C₃×C₄×D₃	—	2	2	no	—
119	C₃×C₄×D₃	—	2	2	no	—
120	C₃²×C₈	—	2	4	no	—
121	C₃×C₃⋊C₈	—	2	4	no	—
122	C₂²×C₄²	—	3	1	no	—
123	#432	—	3	8	no	—
124	C₂×C₄⋊C₈	—	3	1	no	—
125	C₂×C₄⋊C₈	C₃×D₃	1	1	yes	characteristic, complemented
126	C₂×C₂²⋊C₈	—	3	2	no	—
127	C₂×#97	—	3	2	no	—
128	C₂⁴×C₃	—	3	1	no	—
129	C₂³×D₃	C₂×C₃×C₄	1	1	yes	characteristic
130	C₂²×C₃×C₄	—	2	1	no	—
131	C₂²×C₃×C₄	—	2	1	no	—
132	C₂²×C₃×C₄	—	2	1	no	—
133	C₂²×C₃×C₄	—	3	1	no	—
134	C₂²×C₃×C₄	—	3	1	no	—
135	C₂²×C₃×C₄	—	3	1	no	—
136	C₂²×C₃×C₄	—	3	4	no	—
137	C₂²×C₃×C₄	—	3	2	no	—
138	C₂²×C₃×C₄	—	3	4	no	—
139	C₂²×C₃×C₄	—	3	2	no	—
140	C₂²×C₃×C₄	—	6	4	no	—
141	C₂²×C₃×C₄	—	6	4	no	—
142	C₂²×C₃×C₄	—	6	2	no	—
143	C₂²×C₃×C₄	—	6	2	no	—
144	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
145	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
146	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
147	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
148	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
149	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
150	C₂²×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
151	C₂²×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
152	C₂²×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
153	C₂×C₄×D₃	—	2	4	no	—
154	C₂×C₄×D₃	—	2	4	no	—
155	C₂×C₄×D₃	—	2	2	no	—
156	C₂×C₄×D₃	—	2	2	no	—
157	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
158	C₂×C₄×D₃	C₂×C₃×C₄	1	4	yes	—
159	C₂×C₄×D₃	C₂×C₃×C₄	1	4	yes	—
160	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
161	C₂×C₃×C₈	—	2	4	no	—
162	C₂×C₃×C₈	—	2	4	no	—
163	C₂×C₃×C₈	—	2	4	no	—
164	C₂×C₃×C₈	—	3	4	no	—
165	C₂×C₃×C₈	—	4	4	no	—
166	C₂×C₃×C₈	—	6	4	no	—
167	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
168	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
169	C₃×C₄²	—	2	2	no	—
170	C₃×C₄²	—	2	2	no	—
171	C₃×C₄²	—	3	4	no	—
172	C₃×C₄²	—	3	2	no	—
173	C₃×C₄²	—	3	4	no	—
174	C₃×C₄²	—	3	2	no	—
175	C₃×C₄²	C₄×D₃	1	2	yes	—
176	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
177	C₃×C₄²	C₂²×D₃	1	2	yes	—
178	C₃×C₄²	C₂³×C₃	1	2	yes	—
179	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
180	C₄×Dic₃	C₂×C₃×C₄	1	4	yes	—
181	C₄×Dic₃	C₂×C₃×C₄	1	4	yes	—
182	C₄×Dic₃	C₂³×C₃	1	2	yes	—
183	C₂×C₃⋊C₈	—	2	4	no	—
184	C₂×C₃⋊C₈	C₂³×C₃	1	4	yes	—
185	C₂²×C₃²	#117	1	2	yes	—
186	C₂²×C₃²	C₂×M₁₆	1	2	yes	—
187	C₂²×C₃²	C₂×M₁₆	1	2	yes	—
188	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₃×D₃	—	2	2	no	—
190	C₂×C₃×D₃	—	2	2	no	—
191	C₂×C₃×D₃	—	2	8	no	—
192	C₂×C₃×D₃	C₂×M₁₆	1	4	yes	—
193	C₃²×C₄	—	2	2	no	—
194	C₃²×C₄	#117	1	2	yes	—
195	C₃²×C₄	C₂×M₁₆	1	4	yes	—
196	C₃²×C₄	C₂×#41	1	1	yes	characteristic
197	C₃²×C₄	C₂×#41	1	1	yes	characteristic
198	C₃×Dic₃	—	2	2	no	—
199	C₃×Dic₃	—	2	2	no	—
200	C₃×Dic₃	—	2	2	no	—
201	C₂³×C₄	—	3	1	no	—
202	C₂³×C₄	—	3	1	no	—
203	C₂³×C₄	—	3	1	no	—
204	C₂²×C₈	—	3	2	no	—
205	C₂²×C₈	C₂×C₃×D₃	1	2	yes	—
206	C₂×C₄²	—	3	1	no	—
207	C₂×C₄²	—	3	1	no	—
208	C₂×C₄²	—	3	1	no	—
209	C₂×C₄²	—	3	4	no	—
210	C₂×C₄²	—	3	4	no	—
211	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
212	C₄⋊C₈	—	3	4	no	—
213	C₄⋊C₈	C₂×C₃×D₃	1	4	yes	complemented
214	C₂²⋊C₈	—	3	8	no	—
215	#97	—	3	8	no	—
216	C₂³×C₃	—	2	1	no	—
217	C₂³×C₃	—	3	4	no	—
218	C₂³×C₃	—	3	2	no	—
219	C₂³×C₃	—	6	2	no	—
220	C₂³×C₃	—	6	2	no	—
221	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
222	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
223	C₂²×D₃	—	2	2	no	—
224	C₂²×D₃	—	2	2	no	—
225	C₂²×D₃	C₃×M₁₆	1	4	yes	—
226	C₂²×D₃	C₂²×C₃×C₄	1	2	yes	—
227	C₂×C₃×C₄	—	2	2	no	—
228	C₂×C₃×C₄	—	2	2	no	—
229	C₂×C₃×C₄	—	2	1	no	—
230	C₂×C₃×C₄	—	2	4	no	—
231	C₂×C₃×C₄	—	2	1	no	—
232	C₂×C₃×C₄	—	2	2	no	—
233	C₂×C₃×C₄	—	2	2	no	—
234	C₂×C₃×C₄	—	2	2	no	—
235	C₂×C₃×C₄	—	2	2	no	—
236	C₂×C₃×C₄	—	3	2	no	—
237	C₂×C₃×C₄	—	3	2	no	—
238	C₂×C₃×C₄	—	3	2	no	—
239	C₂×C₃×C₄	—	4	2	no	—
240	C₂×C₃×C₄	—	6	8	no	—
241	C₂×C₃×C₄	—	6	2	no	—
242	C₂×C₃×C₄	—	6	2	no	—
243	C₂×C₃×C₄	—	6	2	no	—
244	C₂×C₃×C₄	—	6	4	no	—
245	C₂×C₃×C₄	—	6	8	no	—
246	C₂×C₃×C₄	—	6	2	no	—
247	C₂×C₃×C₄	—	6	2	no	—
248	C₂×C₃×C₄	ΓL(1,𝔽₂₅)	1	4	yes	—
249	C₂×C₃×C₄	C₃×M₁₆	1	4	yes	—
250	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
251	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
253	C₂×C₃×C₄	#237	1	2	yes	—
254	C₂×C₃×C₄	#239	1	2	yes	—
255	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
256	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
257	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
258	C₂×C₃×C₄	C₃×#41	1	2	yes	—
259	C₂×C₃×C₄	C₃×#41	1	2	yes	—
260	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
262	C₂×Dic₃	—	2	2	no	—
263	C₂×Dic₃	—	2	2	no	—
264	C₂×Dic₃	—	2	2	no	—
265	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
266	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
267	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
268	C₄×D₃	—	2	8	no	—
269	C₄×D₃	—	2	4	no	—
270	C₄×D₃	—	2	8	no	—
271	C₄×D₃	—	2	2	no	—
272	C₄×D₃	—	2	2	no	—
273	C₃×C₈	—	2	4	no	—
274	C₃×C₈	—	2	4	no	—
275	C₃×C₈	—	4	4	no	—
276	C₃×C₈	—	6	4	no	—
277	C₃⋊C₈	—	2	4	no	—
278	C₂×C₃²	#432	1	4	yes	complemented
279	C₂×C₃²	C₂×#117	1	1	yes	characteristic
280	C₂×C₃²	C₂²×M₁₆	1	1	yes	characteristic
281	C₂×C₃²	C₂²×M₁₆	1	1	yes	characteristic
282	C₃×D₃	—	2	4	no	—
283	C₂⁴	—	3	1	no	—
284	C₂²×C₄	—	3	1	no	—
285	C₂²×C₄	—	3	1	no	—
286	C₂²×C₄	—	3	1	no	—
287	C₂²×C₄	—	3	2	no	—
288	C₂²×C₄	—	3	4	no	—
289	C₂²×C₄	—	3	2	no	—
290	C₂²×C₄	—	3	4	no	—
291	C₂²×C₄	—	6	4	no	—
292	C₂²×C₄	—	6	4	no	—
293	C₂²×C₄	—	6	2	no	—
294	C₂²×C₄	—	6	2	no	—
295	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
296	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
297	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
298	C₂×C₈	—	2	4	no	—
299	C₂×C₈	—	3	4	no	—
300	C₂×C₈	—	6	4	no	—
301	C₂×C₈	C₂²×C₃×D₃	1	4	yes	—
302	C₄²	—	3	2	no	—
303	C₄²	—	3	4	no	—
304	C₄²	—	3	2	no	—
305	C₄²	—	3	4	no	—
306	C₄²	C₃×C₄×D₃	1	2	yes	—
307	C₄²	C₂²×C₃×D₃	1	2	yes	—
308	C₂²×C₃	—	2	2	no	—
309	C₂²×C₃	—	2	2	no	—
310	C₂²×C₃	—	2	2	no	—
311	C₂²×C₃	—	2	1	no	—
312	C₂²×C₃	—	3	4	no	—
313	C₂²×C₃	—	6	2	no	—
314	C₂²×C₃	—	6	2	no	—
315	C₂²×C₃	—	6	8	no	—
316	C₂²×C₃	#892	1	2	yes	—
317	C₂²×C₃	C₂×ΓL(1,𝔽₂₅)	1	2	yes	—
318	C₂²×C₃	D₃×M₁₆	1	2	yes	—
319	C₂²×C₃	C₃×#117	1	2	yes	—
320	C₂²×C₃	C₂×C₃×M₁₆	1	2	yes	—
321	C₂²×C₃	C₂×C₃×M₁₆	1	2	yes	—
322	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
323	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
324	C₂×D₃	—	2	2	no	—
325	C₂×D₃	—	2	8	no	—
326	C₂×D₃	—	2	2	no	—
327	C₂×D₃	C₂×C₃×M₁₆	1	4	yes	—
328	C₃×C₄	—	2	2	no	—
329	C₃×C₄	—	2	2	no	—
330	C₃×C₄	—	2	2	no	—
331	C₃×C₄	—	2	4	no	—
332	C₃×C₄	—	2	1	no	—
333	C₃×C₄	—	2	1	no	—
334	C₃×C₄	—	4	2	no	—
335	C₃×C₄	—	6	2	no	—
336	C₃×C₄	—	6	2	no	—
337	C₃×C₄	—	6	2	no	—
338	C₃×C₄	#892	1	2	yes	—
339	C₃×C₄	C₂×ΓL(1,𝔽₂₅)	1	4	yes	—
340	C₃×C₄	C₃×#117	1	2	yes	—
341	C₃×C₄	C₂×C₃×M₁₆	1	4	yes	—
342	C₃×C₄	C₂×#237	1	1	yes	characteristic
343	C₃×C₄	C₂×#239	1	1	yes	characteristic
344	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
345	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
346	Dic₃	—	2	2	no	—
347	Dic₃	—	2	2	no	—
348	Dic₃	—	2	2	no	—
349	C₃²	C₂×#432	1	1	yes	characteristic, complemented, Sylow
350	C₂³	—	3	4	no	—
351	C₂³	—	3	2	no	—
352	C₂³	—	6	2	no	—
353	C₂³	—	6	2	no	—
354	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	3	2	no	—
357	C₂×C₄	—	3	2	no	—
358	C₂×C₄	—	3	2	no	—
359	C₂×C₄	—	6	8	no	—
360	C₂×C₄	—	6	2	no	—
361	C₂×C₄	—	6	2	no	—
362	C₂×C₄	—	6	2	no	—
363	C₂×C₄	—	6	4	no	—
364	C₂×C₄	—	6	8	no	—
365	C₂×C₄	—	6	2	no	—
366	C₂×C₄	—	6	2	no	—
367	C₂×C₄	C₃×ΓL(1,𝔽₂₅)	1	4	yes	—
368	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
369	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
370	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
371	C₂×C₄	C₃×#237	1	2	yes	—
372	C₂×C₄	C₃×#239	1	2	yes	—
373	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
374	C₈	—	2	4	no	—
375	C₈	—	6	4	no	—
376	C₂×C₃	—	2	1	no	—
377	C₂×C₃	—	2	1	no	—
378	C₂×C₃	—	2	4	no	—
379	C₂×C₃	—	2	1	no	—
380	C₂×C₃	—	6	4	no	—
381	C₂×C₃	#4835	1	4	yes	direct product factor
382	C₂×C₃	C₃×#432	1	4	yes	complemented
383	C₂×C₃	C₂×#892	1	1	yes	characteristic
384	C₂×C₃	C₂²×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
385	C₂×C₃	C₂×D₃×M₁₆	1	1	yes	characteristic
386	C₂×C₃	C₂×C₃×#117	1	1	yes	characteristic
387	C₂×C₃	C₂²×C₃×M₁₆	1	1	yes	characteristic
388	C₂×C₃	C₂²×C₃×M₁₆	1	1	yes	characteristic
389	D₃	—	2	4	no	—
390	C₂²	—	3	4	no	—
391	C₂²	—	6	2	no	—
392	C₂²	—	6	8	no	—
393	C₂²	—	6	2	no	—
394	C₂²	C₃×#892	1	2	yes	—
395	C₂²	C₂×C₃×ΓL(1,𝔽₂₅)	1	2	yes	—
396	C₂²	C₃×D₃×M₁₆	1	2	yes	—
397	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
398	C₄	—	2	2	no	—
399	C₄	—	6	2	no	—
400	C₄	—	6	2	no	—
401	C₄	—	6	2	no	—
402	C₄	C₃×#892	1	2	yes	—
403	C₄	C₂×C₃×ΓL(1,𝔽₂₅)	1	4	yes	—
404	C₄	C₂×C₃×#237	1	1	yes	characteristic
405	C₄	C₂×C₃×#239	1	1	yes	characteristic
406	C₃	—	2	1	no	—
407	C₃	C₂×#4835	1	1	yes	characteristic, direct product factor
408	C₃	C₂×C₃×#432	1	1	yes	characteristic, complemented
409	C₂	—	6	4	no	—
410	C₂	C₃×#4835	1	4	yes	direct product factor
411	C₂	C₂×C₃×#892	1	1	yes	characteristic
412	C₂	C₂²×C₃×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
413	C₂	C₂×C₃×D₃×M₁₆	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	C₂³×C₃×D₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂×C₃×C₄⋊C₈	D₃
hypocenter	C₃	C₂×C₃×#432
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
2. C₂×C₃²×C₄⋊C₈	C₂	semidirect
4. C₂×C₃×#815	C₂	semidirect
5. C₂×C₃×C₄⋊(C₃⋊C₈)	C₂	semidirect
6. C₃×#4835	C₂	direct (N × H)
8. C₂×#4835	C₃	direct (N × H)
20. C₃²×C₄⋊C₈	C₂²	semidirect
22. C₃×#815	C₂²	semidirect
23. C₃×C₄⋊(C₃⋊C₈)	C₂²	semidirect
29. C₂×C₃×C₄⋊C₈	D₃	semidirect
30. C₂×C₃×C₄⋊C₈	C₂×C₃	semidirect
34. C₂×#815	C₂×C₃	semidirect
35. C₂×C₄⋊(C₃⋊C₈)	C₂×C₃	semidirect
36. #4835	C₂×C₃	direct (N × H)
89. C₃×C₄⋊C₈	C₂×D₃	semidirect
90. C₃×C₄⋊C₈	C₂²×C₃	semidirect
94. #815	C₂²×C₃	semidirect
95. C₄⋊(C₃⋊C₈)	C₂²×C₃	semidirect
125. C₂×C₄⋊C₈	C₃×D₃	semidirect
213. C₄⋊C₈	C₂×C₃×D₃	semidirect
278. C₂×C₃²	#432	semidirect
349. C₃²	C₂×#432	semidirect
381. C₂×C₃	#4835	direct (N × H)
382. C₂×C₃	C₃×#432	semidirect
407. C₃	C₂×#4835	direct (N × H)
408. C₃	C₂×C₃×#432	semidirect
410. C₂	C₃×#4835	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄²×D₃	2
C₂×C₃²×C₄⋊C₈	2
C₂×C₃×(C₂×D₃)⋊C₈	2
C₂×C₃×#815	2
C₂×C₃×C₄⋊(C₃⋊C₈)	2
C₃×#4835	2
C₂×C₃×#432	3
C₂×#4835	3

Subgroups — C2×C3×#4835 #11858737

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#4835 #11858737