Subgroups — C₂×C₃×#4926 #11858740

Order 1152.

1225 conjugacy classes of subgroups.

The subgroup lattice has 413 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×C₄²	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#830	C₂	1	2	yes	maximal
3	C₃×#4926	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₃×C₄⋊(C₃⋊C₈)	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#803	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#432	—	3	1	no	maximal
7	C₂×#4926	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂³×C₃²×C₄	C₄	1	1	yes	characteristic
9	C₂³×C₃²×C₄	C₄	1	1	yes	characteristic
10	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
11	C₂×C₃²×C₄²	C₄	1	1	yes	characteristic
12	C₂×C₃²×C₄²	C₄	1	4	yes	—
13	C₂×C₃²×C₄²	C₄	1	1	yes	characteristic
14	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
15	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
16	C₂×C₃²×C₄²	C₂²	1	4	yes	—
17	C₂²×C₃×C₃⋊C₈	C₂²	1	4	yes	—
18	C₃×#830	C₂²	1	8	yes	—
19	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	8	yes	complemented
20	C₃×#803	C₂²	1	8	yes	complemented
21	C₂²×C₃×C₄²	—	2	1	no	—
22	C₂²×C₃×C₄²	D₃	1	1	yes	characteristic
23	C₂²×C₃×C₄²	C₂×C₃	1	1	yes	characteristic
24	C₃×#432	—	3	8	no	—
25	C₂×C₃×C₄⋊C₈	—	3	2	no	—
26	C₂×C₃×C₂²⋊C₈	—	3	2	no	—
27	C₂×C₃×#97	—	3	2	no	—
28	C₂×#830	C₂×C₃	1	2	yes	—
29	#4926	C₂×C₃	1	8	yes	direct product factor
30	C₂×C₄⋊(C₃⋊C₈)	C₂×C₃	1	2	yes	complemented
31	C₂×#803	C₂×C₃	1	2	yes	complemented
32	C₂⁴×C₃²	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃²×C₄	—	2	4	no	—
34	C₂²×C₃²×C₄	—	2	4	no	—
35	C₂²×C₃²×C₄	—	2	4	no	—
36	C₂²×C₃²×C₄	C₂×C₄	1	4	yes	—
37	C₂²×C₃²×C₄	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	C₂×C₄	1	4	yes	—
41	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
43	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₃²×C₄	C₂³	1	2	yes	—
45	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
46	C₃²×C₄²	C₂×C₄	1	4	yes	—
47	C₃²×C₄²	C₂×C₄	1	4	yes	—
48	C₃²×C₄²	C₂×C₄	1	2	yes	—
49	C₃²×C₄²	C₂×C₄	1	2	yes	—
50	C₃²×C₄²	C₂³	1	2	yes	—
51	C₃²×C₄²	C₂³	1	2	yes	—
52	C₂×C₃×C₃⋊C₈	—	2	8	no	—
53	C₂×C₃×C₃⋊C₈	C₂³	1	8	yes	—
54	C₂×#432	—	3	1	no	Sylow
55	C₂³×C₃×C₄	—	2	1	no	—
56	C₂³×C₃×C₄	—	2	1	no	—
57	C₂³×C₃×C₄	—	2	1	no	—
58	C₂³×C₃×C₄	Dic₃	1	1	yes	characteristic
59	C₂³×C₃×C₄	Dic₃	1	1	yes	characteristic
60	C₂³×C₃×C₄	C₃×C₄	1	1	yes	characteristic
61	C₂³×C₃×C₄	C₃×C₄	1	1	yes	characteristic
62	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
63	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
64	C₂²×C₃×C₈	—	3	4	no	—
65	C₂×C₃×C₄²	—	2	1	no	—
66	C₂×C₃×C₄²	—	2	4	no	—
67	C₂×C₃×C₄²	—	2	1	no	—
68	C₂×C₃×C₄²	—	2	1	no	—
69	C₂×C₃×C₄²	—	2	1	no	—
70	C₂×C₃×C₄²	—	2	4	no	—
71	C₂×C₃×C₄²	Dic₃	1	1	yes	characteristic
72	C₂×C₃×C₄²	Dic₃	1	4	yes	—
73	C₂×C₃×C₄²	Dic₃	1	1	yes	characteristic
74	C₂×C₃×C₄²	C₃×C₄	1	1	yes	characteristic
75	C₂×C₃×C₄²	C₃×C₄	1	4	yes	—
76	C₂×C₃×C₄²	C₃×C₄	1	1	yes	characteristic
77	C₂×C₃×C₄²	C₂×D₃	1	4	yes	—
78	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
79	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
80	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
83	C₂²×C₃⋊C₈	C₂²×C₃	1	4	yes	—
84	C₃×C₄⋊C₈	—	3	8	no	—
85	C₃×C₂²⋊C₈	—	3	8	no	—
86	C₃×#97	—	3	8	no	—
87	#830	C₂²×C₃	1	8	yes	—
88	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	8	yes	complemented
89	#803	C₂²×C₃	1	8	yes	complemented
90	C₂³×C₃²	—	2	2	no	—
91	C₂³×C₃²	—	2	2	no	—
92	C₂³×C₃²	M₁₆	1	4	yes	—
93	C₂³×C₃²	C₂²×C₄	1	2	yes	—
94	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₃²×C₄	—	2	2	no	—
96	C₂×C₃²×C₄	—	2	8	no	—
97	C₂×C₃²×C₄	—	2	2	no	—
98	C₂×C₃²×C₄	—	2	2	no	—
99	C₂×C₃²×C₄	—	2	2	no	—
100	C₂×C₃²×C₄	—	2	4	no	—
101	C₂×C₃²×C₄	—	2	8	no	—
102	C₂×C₃²×C₄	—	2	4	no	—
103	C₂×C₃²×C₄	M₁₆	1	4	yes	—
104	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
105	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
106	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
107	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
108	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
110	C₂×C₃²×C₄	#41	1	4	yes	—
111	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
112	C₃×C₃⋊C₈	—	2	8	no	—
113	C₂²×C₄²	C₃×D₃	1	1	yes	characteristic
114	#432	—	3	8	no	—
115	C₂×C₄⋊C₈	—	3	2	no	—
116	C₂×C₂²⋊C₈	—	3	2	no	—
117	C₂×#97	—	3	2	no	—
118	C₂⁴×C₃	—	2	1	no	—
119	C₂⁴×C₃	C₂×Dic₃	1	1	yes	characteristic
120	C₂⁴×C₃	C₂×C₃×C₄	1	1	yes	characteristic
121	C₂²×C₃×C₄	—	2	8	no	—
122	C₂²×C₃×C₄	—	2	8	no	—
123	C₂²×C₃×C₄	—	2	8	no	—
124	C₂²×C₃×C₄	—	2	4	no	—
125	C₂²×C₃×C₄	—	2	4	no	—
126	C₂²×C₃×C₄	—	2	4	no	—
127	C₂²×C₃×C₄	—	2	4	no	—
128	C₂²×C₃×C₄	—	2	4	no	—
129	C₂²×C₃×C₄	—	2	4	no	—
130	C₂²×C₃×C₄	—	2	1	no	—
131	C₂²×C₃×C₄	—	2	2	no	—
132	C₂²×C₃×C₄	—	2	4	no	—
133	C₂²×C₃×C₄	—	2	1	no	—
134	C₂²×C₃×C₄	—	2	1	no	—
135	C₂²×C₃×C₄	—	2	1	no	—
136	C₂²×C₃×C₄	—	2	4	no	—
137	C₂²×C₃×C₄	—	2	1	no	—
138	C₂²×C₃×C₄	—	2	2	no	—
139	C₂²×C₃×C₄	—	2	1	no	—
140	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
141	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
142	C₂²×C₃×C₄	C₂×Dic₃	1	4	yes	—
143	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
144	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
145	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
146	C₂²×C₃×C₄	C₂×Dic₃	1	4	yes	—
147	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
148	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
149	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
150	C₂²×C₃×C₄	C₂×C₃×C₄	1	4	yes	—
151	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
152	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
153	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
154	C₂²×C₃×C₄	C₂×C₃×C₄	1	4	yes	—
155	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
156	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
157	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
158	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
159	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
160	C₂×C₃×C₈	—	3	8	no	—
161	C₂×C₃×C₈	—	6	8	no	—
162	C₃×C₄²	—	2	4	no	—
163	C₃×C₄²	—	2	4	no	—
164	C₃×C₄²	—	2	2	no	—
165	C₃×C₄²	—	2	2	no	—
166	C₃×C₄²	—	2	2	no	—
167	C₃×C₄²	—	2	2	no	—
168	C₃×C₄²	C₂×Dic₃	1	4	yes	—
169	C₃×C₄²	C₂×Dic₃	1	4	yes	—
170	C₃×C₄²	C₂×Dic₃	1	2	yes	—
171	C₃×C₄²	C₂×Dic₃	1	2	yes	—
172	C₃×C₄²	C₂×C₃×C₄	1	4	yes	—
173	C₃×C₄²	C₂×C₃×C₄	1	4	yes	—
174	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
175	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
176	C₃×C₄²	C₂²×D₃	1	2	yes	—
177	C₃×C₄²	C₂²×D₃	1	2	yes	—
178	C₃×C₄²	C₂³×C₃	1	2	yes	—
179	C₃×C₄²	C₂³×C₃	1	2	yes	—
180	C₂×C₃⋊C₈	—	2	8	no	—
181	C₂×C₃⋊C₈	C₂³×C₃	1	8	yes	—
182	C₂²×C₃²	—	2	2	no	—
183	C₂²×C₃²	—	2	2	no	—
184	C₂²×C₃²	—	2	8	no	—
185	C₂²×C₃²	#117	1	2	yes	—
186	C₂²×C₃²	C₂×M₁₆	1	4	yes	—
187	C₂²×C₃²	C₂×M₁₆	1	2	yes	—
188	C₂²×C₃²	C₂×M₁₆	1	2	yes	—
189	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
190	C₃²×C₄	—	2	2	no	—
191	C₃²×C₄	—	2	2	no	—
192	C₃²×C₄	—	2	2	no	—
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	2	yes	—
197	C₂³×C₄	C₃×Dic₃	1	1	yes	characteristic
198	C₂³×C₄	C₃×Dic₃	1	1	yes	characteristic
199	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
200	C₂²×C₈	—	3	4	no	—
201	C₂×C₄²	C₃×Dic₃	1	1	yes	characteristic
202	C₂×C₄²	C₃×Dic₃	1	4	yes	—
203	C₂×C₄²	C₃×Dic₃	1	1	yes	characteristic
204	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
205	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
206	C₂×C₄²	C₂×C₃×D₃	1	4	yes	—
207	C₄⋊C₈	—	3	8	no	—
208	C₂²⋊C₈	—	3	8	no	—
209	#97	—	3	8	no	—
210	C₂³×C₃	—	2	4	no	—
211	C₂³×C₃	—	2	4	no	—
212	C₂³×C₃	—	2	2	no	—
213	C₂³×C₃	—	2	2	no	—
214	C₂³×C₃	—	2	2	no	—
215	C₂³×C₃	—	2	2	no	—
216	C₂³×C₃	—	2	4	no	—
217	C₂³×C₃	—	2	2	no	—
218	C₂³×C₃	—	2	1	no	—
219	C₂³×C₃	#208	1	4	yes	—
220	C₂³×C₃	C₃×M₁₆	1	4	yes	—
221	C₂³×C₃	C₂²×Dic₃	1	2	yes	—
222	C₂³×C₃	C₂²×Dic₃	1	1	yes	characteristic
223	C₂³×C₃	C₂²×C₃×C₄	1	2	yes	—
224	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
225	C₂×C₃×C₄	—	2	16	no	—
226	C₂×C₃×C₄	—	2	4	no	—
227	C₂×C₃×C₄	—	2	4	no	—
228	C₂×C₃×C₄	—	2	4	no	—
229	C₂×C₃×C₄	—	2	4	no	—
230	C₂×C₃×C₄	—	2	16	no	—
231	C₂×C₃×C₄	—	2	8	no	—
232	C₂×C₃×C₄	—	2	8	no	—
233	C₂×C₃×C₄	—	2	8	no	—
234	C₂×C₃×C₄	—	2	2	no	—
235	C₂×C₃×C₄	—	2	2	no	—
236	C₂×C₃×C₄	—	2	2	no	—
237	C₂×C₃×C₄	—	2	2	no	—
238	C₂×C₃×C₄	—	2	2	no	—
239	C₂×C₃×C₄	—	2	8	no	—
240	C₂×C₃×C₄	—	2	2	no	—
241	C₂×C₃×C₄	—	2	2	no	—
242	C₂×C₃×C₄	—	2	2	no	—
243	C₂×C₃×C₄	—	2	8	no	—
244	C₂×C₃×C₄	—	2	4	no	—
245	C₂×C₃×C₄	—	2	4	no	—
246	C₂×C₃×C₄	—	2	8	no	—
247	C₂×C₃×C₄	—	2	4	no	—
248	C₂×C₃×C₄	—	2	4	no	—
249	C₂×C₃×C₄	—	2	1	no	—
250	C₂×C₃×C₄	—	2	4	no	—
251	C₂×C₃×C₄	—	2	4	no	—
252	C₂×C₃×C₄	—	2	2	no	—
253	C₂×C₃×C₄	—	2	2	no	—
254	C₂×C₃×C₄	—	2	2	no	—
255	C₂×C₃×C₄	—	2	2	no	—
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	—	2	1	no	—
258	C₂×C₃×C₄	#208	1	4	yes	—
259	C₂×C₃×C₄	C₃×M₁₆	1	4	yes	—
260	C₂×C₃×C₄	#235	1	4	yes	—
261	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
262	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
263	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
264	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
265	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
266	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
268	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
269	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
270	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
271	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
272	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
273	C₂×C₃×C₄	C₃×#41	1	4	yes	—
274	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
275	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
276	C₃×C₈	—	6	8	no	—
277	C₃⋊C₈	—	2	8	no	—
278	C₂×C₃²	—	2	4	no	—
279	C₂×C₃²	#432	1	4	yes	complemented
280	C₂×C₃²	C₂×#117	1	1	yes	characteristic
281	C₂×C₃²	C₂²×M₁₆	1	1	yes	characteristic
282	C₂×C₃²	C₂²×M₁₆	1	1	yes	characteristic
283	C₂⁴	C₂×C₃×Dic₃	1	1	yes	characteristic
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
288	C₂²×C₄	C₂×C₃×Dic₃	1	2	yes	—
289	C₂²×C₄	C₂×C₃×Dic₃	1	4	yes	—
290	C₂²×C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
291	C₂²×C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
292	C₂²×C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
293	C₂²×C₄	C₂×C₃×Dic₃	1	4	yes	—
294	C₂²×C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
295	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
296	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
297	C₂×C₈	—	3	8	no	—
298	C₂×C₈	—	6	8	no	—
299	C₄²	C₂×C₃×Dic₃	1	4	yes	—
300	C₄²	C₂×C₃×Dic₃	1	4	yes	—
301	C₄²	C₂×C₃×Dic₃	1	2	yes	—
302	C₄²	C₂×C₃×Dic₃	1	2	yes	—
303	C₄²	C₂²×C₃×D₃	1	2	yes	—
304	C₄²	C₂²×C₃×D₃	1	2	yes	—
305	C₂²×C₃	—	2	4	no	—
306	C₂²×C₃	—	2	4	no	—
307	C₂²×C₃	—	2	16	no	—
308	C₂²×C₃	—	2	2	no	—
309	C₂²×C₃	—	2	8	no	—
310	C₂²×C₃	—	2	2	no	—
311	C₂²×C₃	—	2	2	no	—
312	C₂²×C₃	—	2	8	no	—
313	C₂²×C₃	—	2	2	no	—
314	C₂²×C₃	—	2	4	no	—
315	C₂²×C₃	—	2	2	no	—
316	C₂²×C₃	—	2	2	no	—
317	C₂²×C₃	—	2	2	no	—
318	C₂²×C₃	—	2	1	no	—
319	C₂²×C₃	C₂×#208	1	4	yes	—
320	C₂²×C₃	C₂×#208	1	2	yes	—
321	C₂²×C₃	C₂×#208	1	2	yes	—
322	C₂²×C₃	#926	1	2	yes	—
323	C₂²×C₃	C₃×#117	1	2	yes	—
324	C₂²×C₃	C₂×C₃×M₁₆	1	4	yes	—
325	C₂²×C₃	C₂×C₃×M₁₆	1	2	yes	—
326	C₂²×C₃	C₂×C₃×M₁₆	1	2	yes	—
327	C₂²×C₃	C₂³×Dic₃	1	1	yes	characteristic
328	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
329	C₃×C₄	—	2	4	no	—
330	C₃×C₄	—	2	4	no	—
331	C₃×C₄	—	2	4	no	—
332	C₃×C₄	—	2	4	no	—
333	C₃×C₄	—	2	2	no	—
334	C₃×C₄	—	2	2	no	—
335	C₃×C₄	—	2	2	no	—
336	C₃×C₄	—	2	2	no	—
337	C₃×C₄	—	2	2	no	—
338	C₃×C₄	—	2	2	no	—
339	C₃×C₄	—	2	2	no	—
340	C₃×C₄	—	2	2	no	—
341	C₃×C₄	—	2	4	no	—
342	C₃×C₄	—	2	2	no	—
343	C₃×C₄	—	2	2	no	—
344	C₃×C₄	C₂×#208	1	4	yes	—
345	C₃×C₄	#926	1	2	yes	—
346	C₃×C₄	C₃×#117	1	2	yes	—
347	C₃×C₄	C₂×C₃×M₁₆	1	4	yes	—
348	C₃×C₄	C₂×#235	1	2	yes	—
349	C₃×C₄	C₂×C₃×#41	1	2	yes	—
350	C₃²	C₂×#432	1	1	yes	characteristic, complemented, Sylow
351	C₂³	—	2	2	no	—
352	C₂³	—	2	2	no	—
353	C₂³	C₃×#208	1	4	yes	—
354	C₂³	C₂²×C₃×Dic₃	1	2	yes	—
355	C₂³	C₂²×C₃×Dic₃	1	1	yes	characteristic
356	C₂×C₄	—	2	8	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	8	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	C₃×#208	1	4	yes	—
365	C₂×C₄	C₃×#235	1	4	yes	—
366	C₂×C₄	C₂²×C₃×Dic₃	1	2	yes	—
367	C₂×C₄	C₂²×C₃×Dic₃	1	2	yes	—
368	C₂×C₄	C₂²×C₃×Dic₃	1	2	yes	—
369	C₂×C₄	C₂²×C₃×Dic₃	1	2	yes	—
370	C₂×C₄	C₂²×C₃×Dic₃	1	2	yes	—
371	C₂×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
372	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
373	C₈	—	6	8	no	—
374	C₂×C₃	—	2	8	no	—
375	C₂×C₃	—	2	4	no	—
376	C₂×C₃	—	2	4	no	—
377	C₂×C₃	—	2	4	no	—
378	C₂×C₃	—	2	1	no	—
379	C₂×C₃	—	2	1	no	—
380	C₂×C₃	—	2	1	no	—
381	C₂×C₃	#4926	1	4	yes	direct product factor
382	C₂×C₃	C₃×#432	1	4	yes	complemented
383	C₂×C₃	C₂²×#208	1	1	yes	characteristic
384	C₂×C₃	C₂²×#208	1	1	yes	characteristic
385	C₂×C₃	C₂×#926	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	C₂²	—	2	8	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	C₂×C₃×#208	1	4	yes	—
393	C₂²	C₂×C₃×#208	1	2	yes	—
394	C₂²	C₂×C₃×#208	1	2	yes	—
395	C₂²	C₃×#926	1	2	yes	—
396	C₂²	C₂³×C₃×Dic₃	1	1	yes	characteristic
397	C₄	—	2	2	no	—
398	C₄	—	2	2	no	—
399	C₄	—	2	2	no	—
400	C₄	—	2	2	no	—
401	C₄	C₂×C₃×#208	1	4	yes	—
402	C₄	C₃×#926	1	2	yes	—
403	C₄	C₂×C₃×#235	1	2	yes	—
404	C₃	—	2	1	no	—
405	C₃	C₂×#4926	1	1	yes	characteristic, direct product factor
406	C₃	C₂×C₃×#432	1	1	yes	characteristic, complemented
407	C₂	—	2	4	no	—
408	C₂	C₃×#4926	1	4	yes	direct product factor
409	C₂	C₂²×C₃×#208	1	1	yes	characteristic
410	C₂	C₂²×C₃×#208	1	1	yes	characteristic
411	C₂	C₂×C₃×#926	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	C₂²×C₃²×C₄²	C₂
socle	C₂³×C₃²	C₂²×C₄
prime radical	C₂⁴×C₃²	C₂×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂²×C₃×C₄²	D₃
hypocenter	C₃	C₂×C₃×#432
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×C₄²

Complements

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

N	H ≅ G/N	type
3. C₃×#4926	C₂	direct (N × H)
4. C₂×C₃×C₄⋊(C₃⋊C₈)	C₂	semidirect
5. C₂×C₃×#803	C₂	semidirect
7. C₂×#4926	C₃	direct (N × H)
19. C₃×C₄⋊(C₃⋊C₈)	C₂²	semidirect
20. C₃×#803	C₂²	semidirect
29. #4926	C₂×C₃	direct (N × H)
30. C₂×C₄⋊(C₃⋊C₈)	C₂×C₃	semidirect
31. C₂×#803	C₂×C₃	semidirect
88. C₄⋊(C₃⋊C₈)	C₂²×C₃	semidirect
89. #803	C₂²×C₃	semidirect
279. C₂×C₃²	#432	semidirect
350. C₃²	C₂×#432	semidirect
381. C₂×C₃	#4926	direct (N × H)
382. C₂×C₃	C₃×#432	semidirect
405. C₃	C₂×#4926	direct (N × H)
406. C₃	C₂×C₃×#432	semidirect
408. C₂	C₃×#4926	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×C₃²×C₄²	2
C₂×C₃×#830	2
C₃×#4926	2
C₂×C₃×C₄⋊(C₃⋊C₈)	2
C₂×C₃×#803	2
C₂×C₃×#432	3
C₂×#4926	3

Subgroups — C2×C3×#4926 #11858740

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#4926 #11858740