Subgroups — C₂×C₃×#5477 #11900755

Order 1152.

3705 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#235	C₂	1	2	yes	maximal, complemented
2	C₂²×C₃²×C₄²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#930	C₂	1	4	yes	maximal, complemented
4	C₃×#5477	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃×#875	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#874	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×C₄×D₁₂	C₂	1	4	yes	maximal, complemented
8	C₂×C₃×#869	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#532	—	3	1	no	maximal
10	C₂×#5477	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂³×C₃²×C₄	C₂²	1	2	yes	—
12	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
13	C₂²×C₃×#67	C₂²	1	4	yes	—
14	C₂×C₃×#235	—	2	16	no	—
15	C₂×C₃×#235	C₂²	1	16	yes	complemented
16	C₂²×C₃×D₁₂	C₂²	1	4	yes	—
17	C₂²×C₃×D₁₂	C₂²	1	2	yes	—
18	C₂²×C₃×C₄×D₃	C₂²	1	4	yes	—
19	C₂²×C₃×Dic₆	C₂²	1	2	yes	—
20	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
21	C₂×C₃²×C₄²	C₂²	1	2	yes	—
22	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
23	C₂×C₃²×C₄²	C₂²	1	8	yes	complemented
24	C₃×#930	C₂²	1	32	yes	complemented
25	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	8	yes	—
26	C₂×C₃×C₄⋊Dic₃	C₂²	1	4	yes	—
27	C₃×#875	C₂²	1	16	yes	complemented
28	C₃×#874	C₂²	1	8	yes	complemented
29	C₃×C₄×D₁₂	C₂²	1	32	yes	complemented
30	C₃×#869	C₂²	1	8	yes	complemented
31	C₂²×C₃×#41	—	3	2	no	—
32	C₂²×#235	C₂×C₃	1	2	yes	complemented
33	C₃×#532	—	3	16	no	—
34	C₂×C₃×C₄⋊Q₈	—	3	1	no	—
35	C₂×C₃×#127	—	3	1	no	—
36	C₂×C₃×#124	—	3	2	no	—
37	C₂×C₃×#121	—	3	4	no	—
38	C₂×C₃×C₄×D₄	—	3	4	no	—
39	C₂²×C₃×C₄²	—	2	1	no	—
40	C₂²×C₃×C₄²	D₃	1	1	yes	characteristic, complemented
41	C₂²×C₃×C₄²	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂×#930	C₂×C₃	1	4	yes	complemented
43	#5477	C₂×C₃	1	16	yes	direct product factor
44	C₂×#875	C₂×C₃	1	2	yes	complemented
45	C₂×#874	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×C₄×D₁₂	C₂×C₃	1	4	yes	complemented
47	C₂×#869	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
49	C₂³×C₃×D₃	C₂³	1	4	yes	—
50	C₂²×C₃²×C₄	—	2	8	no	—
51	C₂²×C₃²×C₄	D₄	1	8	yes	complemented
52	C₂²×C₃²×C₄	C₂³	1	2	yes	—
53	C₂²×C₃²×C₄	C₂³	1	8	yes	—
54	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
55	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
56	C₂²×C₃²×C₄	C₂³	1	4	yes	—
57	C₂²×C₃²×C₄	C₂³	1	2	yes	—
58	C₂×C₃×#67	—	2	16	no	—
59	C₂×C₃×#67	C₂³	1	16	yes	—
60	C₂²×C₃×Dic₃	C₂³	1	4	yes	—
61	C₃×#235	—	2	64	no	—
62	C₂×C₃×D₁₂	—	2	8	no	—
63	C₂×C₃×D₁₂	—	2	16	no	—
64	C₂×C₃×D₁₂	C₂³	1	16	yes	—
65	C₂×C₃×D₁₂	C₂³	1	8	yes	—
66	C₂×C₃×C₄×D₃	—	2	16	no	—
67	C₂×C₃×C₄×D₃	C₂³	1	16	yes	—
68	C₂×C₃×Dic₆	—	2	8	no	—
69	C₂×C₃×Dic₆	C₂³	1	8	yes	—
70	C₃²×C₄²	C₂³	1	4	yes	—
71	C₃²×C₄²	C₂³	1	8	yes	—
72	C₃²×C₄²	C₂³	1	4	yes	—
73	C₃×(C₂×D₃)⋊C₄	C₂³	1	32	yes	—
74	C₃×C₄⋊Dic₃	C₂³	1	16	yes	—
75	C₂×#532	—	3	1	no	Sylow
76	C₂×C₃×#41	—	3	16	no	—
77	C₂×C₃×#41	—	6	16	no	—
78	C₂²×C₃×Q₈	—	3	2	no	—
79	C₂²×C₃×D₄	—	3	4	no	—
80	C₂²×C₃×D₄	—	3	2	no	—
81	C₂²×C₃×D₄	—	3	4	no	—
82	C₂³×C₃×C₄	—	2	2	no	—
83	C₂³×C₃×C₄	—	2	1	no	—
84	C₂³×C₃×C₄	—	3	4	no	—
85	C₂³×C₃×C₄	C₂×D₃	1	2	yes	—
86	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
87	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
88	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
89	C₂²×#67	C₂²×C₃	1	4	yes	—
90	C₂×#235	—	2	16	no	—
91	C₂×#235	C₂²×C₃	1	16	yes	complemented
92	C₂²×D₁₂	C₂²×C₃	1	2	yes	—
93	C₂²×D₁₂	C₂²×C₃	1	4	yes	—
94	C₂²×C₄×D₃	C₂²×C₃	1	4	yes	—
95	C₂²×Dic₆	C₂²×C₃	1	2	yes	—
96	C₃×C₄⋊Q₈	—	3	8	no	—
97	C₃×#127	—	3	8	no	—
98	C₃×#124	—	3	16	no	—
99	C₃×#121	—	3	32	no	—
100	C₃×C₄×D₄	—	3	32	no	—
101	C₂×C₃×C₄⋊C₄	—	3	4	no	—
102	C₂×C₃×C₂²⋊C₄	—	3	8	no	—
103	C₂×C₃×C₄²	—	2	2	no	—
104	C₂×C₃×C₄²	—	2	1	no	—
105	C₂×C₃×C₄²	—	2	1	no	—
106	C₂×C₃×C₄²	—	2	8	no	—
107	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
108	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
109	C₂×C₃×C₄²	C₂×D₃	1	2	yes	—
110	C₂×C₃×C₄²	C₂×D₃	1	8	yes	complemented
111	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
112	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
113	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
114	C₂×C₃×C₄²	C₂²×C₃	1	8	yes	complemented
115	#930	C₂²×C₃	1	32	yes	complemented
116	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
117	C₂×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
118	#875	C₂²×C₃	1	16	yes	complemented
119	#874	C₂²×C₃	1	8	yes	complemented
120	C₄×D₁₂	C₂²×C₃	1	32	yes	complemented
121	#869	C₂²×C₃	1	8	yes	complemented
122	C₂³×C₃²	—	2	4	no	—
123	C₂³×C₃²	C₂×D₄	1	4	yes	—
124	C₂³×C₃²	C₂⁴	1	2	yes	—
125	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
126	C₂²×C₃×D₃	—	2	8	no	—
127	C₂²×C₃×D₃	—	2	16	no	—
128	C₂²×C₃×D₃	C₂⁴	1	8	yes	—
129	C₂×C₃²×C₄	—	2	4	no	—
130	C₂×C₃²×C₄	—	2	16	no	—
131	C₂×C₃²×C₄	C₂×D₄	1	4	yes	—
132	C₂×C₃²×C₄	C₂×D₄	1	4	yes	—
133	C₂×C₃²×C₄	C₂×D₄	1	16	yes	complemented
134	C₂×C₃²×C₄	#41	1	8	yes	complemented
135	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
136	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
137	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
138	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
139	C₃×#67	—	2	32	no	—
140	C₂×C₃×Dic₃	—	2	8	no	—
141	C₂×C₃×Dic₃	C₂⁴	1	8	yes	—
142	C₃×D₁₂	—	2	16	no	—
143	C₃×D₁₂	—	2	32	no	—
144	C₃×C₄×D₃	—	2	32	no	—
145	C₃×Dic₆	—	2	16	no	—
146	C₂²×#41	—	3	2	no	—
147	#532	—	3	16	no	—
148	C₂×C₄⋊Q₈	—	3	1	no	—
149	C₂×#127	—	3	1	no	—
150	C₂×#124	—	3	2	no	—
151	C₂×#121	—	3	4	no	—
152	C₂×C₄×D₄	—	3	4	no	—
153	C₂²×C₄²	C₃×D₃	1	1	yes	characteristic, complemented
154	C₂⁴×C₃	—	2	1	no	—
155	C₂⁴×C₃	—	3	4	no	—
156	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
157	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
158	C₂³×D₃	C₂³×C₃	1	4	yes	—
159	C₃×#41	—	6	64	no	—
160	C₂×C₃×Q₈	—	3	8	no	—
161	C₂×C₃×Q₈	—	6	8	no	—
162	C₂×C₃×D₄	—	3	16	no	—
163	C₂×C₃×D₄	—	3	16	no	—
164	C₂×C₃×D₄	—	3	8	no	—
165	C₂×C₃×D₄	—	6	16	no	—
166	C₂×C₃×D₄	—	6	8	no	—
167	C₂×C₃×D₄	—	6	16	no	—
168	C₂²×C₃×C₄	—	2	16	no	—
169	C₂²×C₃×C₄	—	2	8	no	—
170	C₂²×C₃×C₄	—	2	8	no	—
171	C₂²×C₃×C₄	—	2	8	no	—
172	C₂²×C₃×C₄	—	2	2	no	—
173	C₂²×C₃×C₄	—	2	8	no	—
174	C₂²×C₃×C₄	—	2	1	no	—
175	C₂²×C₃×C₄	—	2	1	no	—
176	C₂²×C₃×C₄	—	2	4	no	—
177	C₂²×C₃×C₄	—	2	2	no	—
178	C₂²×C₃×C₄	—	3	4	no	—
179	C₂²×C₃×C₄	—	3	16	no	—
180	C₂²×C₃×C₄	—	6	16	no	—
181	C₂²×C₃×C₄	D₁₂	1	8	yes	complemented
182	C₂²×C₃×C₄	C₃×D₄	1	8	yes	complemented
183	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
184	C₂²×C₃×C₄	C₂²×D₃	1	8	yes	—
185	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
186	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
187	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
188	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
189	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
190	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
191	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
192	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
193	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
194	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
195	C₂×#67	—	2	16	no	—
196	C₂×#67	C₂³×C₃	1	16	yes	—
197	C₂²×Dic₃	C₂³×C₃	1	4	yes	—
198	#235	—	2	64	no	—
199	C₂×D₁₂	—	2	8	no	—
200	C₂×D₁₂	—	2	16	no	—
201	C₂×D₁₂	C₂³×C₃	1	16	yes	—
202	C₂×D₁₂	C₂³×C₃	1	8	yes	—
203	C₂×C₄×D₃	—	2	16	no	—
204	C₂×C₄×D₃	C₂³×C₃	1	16	yes	—
205	C₂×Dic₆	—	2	8	no	—
206	C₂×Dic₆	C₂³×C₃	1	8	yes	—
207	C₃×C₄⋊C₄	—	3	16	no	—
208	C₃×C₂²⋊C₄	—	3	32	no	—
209	C₃×C₄²	—	2	8	no	—
210	C₃×C₄²	—	2	4	no	—
211	C₃×C₄²	—	2	4	no	—
212	C₃×C₄²	C₂²×D₃	1	8	yes	—
213	C₃×C₄²	C₂²×D₃	1	4	yes	—
214	C₃×C₄²	C₂²×D₃	1	4	yes	—
215	C₃×C₄²	C₂³×C₃	1	4	yes	—
216	C₃×C₄²	C₂³×C₃	1	8	yes	—
217	C₃×C₄²	C₂³×C₃	1	4	yes	—
218	(C₂×D₃)⋊C₄	C₂³×C₃	1	32	yes	—
219	C₄⋊Dic₃	C₂³×C₃	1	16	yes	—
220	C₂²×C₃²	—	2	8	no	—
221	C₂²×C₃²	—	2	4	no	—
222	C₂²×C₃²	C₂²×D₄	1	4	yes	—
223	C₂²×C₃²	C₂²×D₄	1	2	yes	—
224	C₂²×C₃²	C₂×#41	1	4	yes	—
225	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
226	C₂×C₃×D₃	—	2	8	no	—
227	C₂×C₃×D₃	—	2	16	no	—
228	C₂×C₃×D₃	—	4	16	no	—
229	C₃²×C₄	—	2	4	no	—
230	C₃²×C₄	C₂²×D₄	1	4	yes	—
231	C₃²×C₄	C₂²×D₄	1	4	yes	—
232	C₃²×C₄	C₂×#41	1	8	yes	complemented
233	C₃×Dic₃	—	2	8	no	—
234	C₂×#41	—	3	16	no	—
235	C₂×#41	—	6	16	no	—
236	C₂²×Q₈	—	3	2	no	—
237	C₂²×D₄	—	3	4	no	—
238	C₂²×D₄	—	3	4	no	—
239	C₂²×D₄	—	3	2	no	—
240	C₂³×C₄	—	3	4	no	—
241	C₂³×C₄	C₂×C₃×D₃	1	2	yes	—
242	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
243	C₄⋊Q₈	—	3	8	no	—
244	#127	—	3	8	no	—
245	#124	—	3	16	no	—
246	#121	—	3	32	no	—
247	C₄×D₄	—	3	32	no	—
248	C₂×C₄⋊C₄	—	3	4	no	—
249	C₂×C₂²⋊C₄	—	3	8	no	—
250	C₂×C₄²	C₂×C₃×D₃	1	2	yes	—
251	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
252	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
253	C₂×C₄²	C₂×C₃×D₃	1	8	yes	complemented
254	C₂³×C₃	—	2	8	no	—
255	C₂³×C₃	—	2	4	no	—
256	C₂³×C₃	—	2	4	no	—
257	C₂³×C₃	—	2	2	no	—
258	C₂³×C₃	—	2	1	no	—
259	C₂³×C₃	—	2	4	no	—
260	C₂³×C₃	—	3	8	no	—
261	C₂³×C₃	—	6	8	no	—
262	C₂³×C₃	—	6	16	no	—
263	C₂³×C₃	C₂×D₁₂	1	4	yes	—
264	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
265	C₂³×C₃	C₂³×D₃	1	2	yes	—
266	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
267	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
268	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
269	C₂²×D₃	—	2	8	no	—
270	C₂²×D₃	—	2	16	no	—
271	C₂²×D₃	C₂⁴×C₃	1	8	yes	—
272	C₃×Q₈	—	6	16	no	—
273	C₃×D₄	—	6	32	no	—
274	C₃×D₄	—	6	16	no	—
275	C₃×D₄	—	6	32	no	—
276	C₂×C₃×C₄	—	2	8	no	—
277	C₂×C₃×C₄	—	2	32	no	—
278	C₂×C₃×C₄	—	2	4	no	—
279	C₂×C₃×C₄	—	2	4	no	—
280	C₂×C₃×C₄	—	2	16	no	—
281	C₂×C₃×C₄	—	2	16	no	—
282	C₂×C₃×C₄	—	2	4	no	—
283	C₂×C₃×C₄	—	2	2	no	—
284	C₂×C₃×C₄	—	2	2	no	—
285	C₂×C₃×C₄	—	2	4	no	—
286	C₂×C₃×C₄	—	2	4	no	—
287	C₂×C₃×C₄	—	2	4	no	—
288	C₂×C₃×C₄	—	2	16	no	—
289	C₂×C₃×C₄	—	2	8	no	—
290	C₂×C₃×C₄	—	3	8	no	—
291	C₂×C₃×C₄	—	6	8	no	—
292	C₂×C₃×C₄	—	6	32	no	—
293	C₂×C₃×C₄	C₂×D₁₂	1	4	yes	—
294	C₂×C₃×C₄	C₂×D₁₂	1	4	yes	—
295	C₂×C₃×C₄	C₂×D₁₂	1	16	yes	complemented
296	C₂×C₃×C₄	#235	1	8	yes	complemented
297	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
298	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
299	C₂×C₃×C₄	C₂×C₃×D₄	1	16	yes	complemented
300	C₂×C₃×C₄	C₃×#41	1	8	yes	complemented
301	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
302	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
303	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
304	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
305	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
306	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
307	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
308	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
309	#67	—	2	32	no	—
310	C₂×Dic₃	—	2	8	no	—
311	C₂×Dic₃	C₂⁴×C₃	1	8	yes	—
312	D₁₂	—	2	16	no	—
313	D₁₂	—	2	32	no	—
314	C₄×D₃	—	2	32	no	—
315	Dic₆	—	2	16	no	—
316	C₂×C₃²	—	2	4	no	—
317	C₂×C₃²	#532	1	4	yes	complemented
318	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
319	C₂×C₃²	C₂²×#41	1	2	yes	—
320	C₃×D₃	—	4	8	no	—
321	C₂⁴	—	3	4	no	—
322	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
323	#41	—	6	64	no	—
324	C₂×Q₈	—	3	8	no	—
325	C₂×Q₈	—	6	8	no	—
326	C₂×D₄	—	3	16	no	—
327	C₂×D₄	—	3	16	no	—
328	C₂×D₄	—	3	8	no	—
329	C₂×D₄	—	6	16	no	—
330	C₂×D₄	—	6	8	no	—
331	C₂×D₄	—	6	16	no	—
332	C₂²×C₄	—	2	8	no	—
333	C₂²×C₄	—	3	4	no	—
334	C₂²×C₄	—	3	16	no	—
335	C₂²×C₄	—	6	16	no	—
336	C₂²×C₄	C₃×D₁₂	1	8	yes	complemented
337	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
338	C₂²×C₄	C₂²×C₃×D₃	1	8	yes	—
339	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
340	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
341	C₂²×C₄	C₂²×C₃×D₃	1	4	yes	—
342	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
343	C₄⋊C₄	—	3	16	no	—
344	C₂²⋊C₄	—	3	32	no	—
345	C₄²	C₂²×C₃×D₃	1	8	yes	—
346	C₄²	C₂²×C₃×D₃	1	4	yes	—
347	C₄²	C₂²×C₃×D₃	1	4	yes	—
348	C₂²×C₃	—	2	8	no	—
349	C₂²×C₃	—	2	16	no	—
350	C₂²×C₃	—	2	4	no	—
351	C₂²×C₃	—	2	4	no	—
352	C₂²×C₃	—	2	8	no	—
353	C₂²×C₃	—	2	8	no	—
354	C₂²×C₃	—	2	4	no	—
355	C₂²×C₃	—	2	2	no	—
356	C₂²×C₃	—	2	4	no	—
357	C₂²×C₃	—	2	1	no	—
358	C₂²×C₃	—	6	8	no	—
359	C₂²×C₃	—	6	16	no	—
360	C₂²×C₃	—	12	16	no	—
361	C₂²×C₃	C₂²×D₁₂	1	4	yes	—
362	C₂²×C₃	C₂²×D₁₂	1	2	yes	—
363	C₂²×C₃	C₂×#235	1	4	yes	—
364	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
365	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
366	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
367	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
368	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
369	C₂×D₃	—	2	8	no	—
370	C₂×D₃	—	2	16	no	—
371	C₂×D₃	—	4	16	no	—
372	C₃×C₄	—	2	8	no	—
373	C₃×C₄	—	2	4	no	—
374	C₃×C₄	—	2	4	no	—
375	C₃×C₄	—	2	4	no	—
376	C₃×C₄	—	2	4	no	—
377	C₃×C₄	—	2	8	no	—
378	C₃×C₄	—	6	8	no	—
379	C₃×C₄	C₂²×D₁₂	1	4	yes	—
380	C₃×C₄	C₂²×D₁₂	1	4	yes	—
381	C₃×C₄	C₂×#235	1	8	yes	complemented
382	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
383	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
384	C₃×C₄	C₂×C₃×#41	1	8	yes	complemented
385	Dic₃	—	2	8	no	—
386	C₃²	C₂×#532	1	1	yes	characteristic, complemented, Sylow
387	C₂³	—	2	4	no	—
388	C₂³	—	3	8	no	—
389	C₂³	—	6	8	no	—
390	C₂³	—	6	16	no	—
391	C₂³	C₂×C₃×D₁₂	1	4	yes	—
392	C₂³	C₂³×C₃×D₃	1	2	yes	—
393	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
394	Q₈	—	6	16	no	—
395	D₄	—	6	32	no	—
396	D₄	—	6	16	no	—
397	D₄	—	6	32	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	16	no	—
400	C₂×C₄	—	3	8	no	—
401	C₂×C₄	—	6	8	no	—
402	C₂×C₄	—	6	32	no	—
403	C₂×C₄	C₂×C₃×D₁₂	1	4	yes	—
404	C₂×C₄	C₂×C₃×D₁₂	1	4	yes	—
405	C₂×C₄	C₂×C₃×D₁₂	1	16	yes	complemented
406	C₂×C₄	C₃×#235	1	8	yes	complemented
407	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
408	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
409	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
410	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
411	C₂×C₃	—	2	8	no	—
412	C₂×C₃	—	2	4	no	—
413	C₂×C₃	—	2	4	no	—
414	C₂×C₃	—	2	1	no	—
415	C₂×C₃	—	2	2	no	—
416	C₂×C₃	—	2	4	no	—
417	C₂×C₃	—	12	8	no	—
418	C₂×C₃	#5477	1	4	yes	direct product factor
419	C₂×C₃	C₃×#532	1	4	yes	complemented
420	C₂×C₃	C₂³×D₁₂	1	1	yes	characteristic
421	C₂×C₃	C₂²×#235	1	2	yes	—
422	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
423	C₂×C₃	C₂²×C₃×#41	1	2	yes	—
424	D₃	—	4	8	no	—
425	C₂²	—	2	4	no	—
426	C₂²	—	2	8	no	—
427	C₂²	—	6	8	no	—
428	C₂²	—	6	16	no	—
429	C₂²	—	12	16	no	—
430	C₂²	C₂²×C₃×D₁₂	1	4	yes	—
431	C₂²	C₂²×C₃×D₁₂	1	2	yes	—
432	C₂²	C₂×C₃×#235	1	4	yes	—
433	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
434	C₄	—	2	4	no	—
435	C₄	—	6	8	no	—
436	C₄	C₂²×C₃×D₁₂	1	4	yes	—
437	C₄	C₂²×C₃×D₁₂	1	4	yes	—
438	C₄	C₂×C₃×#235	1	8	yes	complemented
439	C₃	—	2	1	no	—
440	C₃	C₂×#5477	1	1	yes	characteristic, direct product factor
441	C₃	C₂×C₃×#532	1	1	yes	characteristic, complemented
442	C₂	—	2	4	no	—
443	C₂	—	12	8	no	—
444	C₂	C₃×#5477	1	4	yes	direct product factor
445	C₂	C₂³×C₃×D₁₂	1	1	yes	characteristic
446	C₂	C₂²×C₃×#235	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₂²×C₃²×C₄²	C₂
socle	C₂³×C₃²	C₂⁴
hypercenter	C₂²×C₃×C₄²	D₃
hypocenter	C₃	C₂×C₃×#532
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
1. C₂²×C₃×#235	C₂	semidirect
2. C₂²×C₃²×C₄²	C₂	semidirect
3. C₂×C₃×#930	C₂	semidirect
4. C₃×#5477	C₂	direct (N × H)
5. C₂×C₃×#875	C₂	semidirect
6. C₂×C₃×#874	C₂	semidirect
7. C₂×C₃×C₄×D₁₂	C₂	semidirect
8. C₂×C₃×#869	C₂	semidirect
10. C₂×#5477	C₃	direct (N × H)
15. C₂×C₃×#235	C₂²	semidirect
23. C₂×C₃²×C₄²	C₂²	semidirect
24. C₃×#930	C₂²	semidirect
27. C₃×#875	C₂²	semidirect
28. C₃×#874	C₂²	semidirect
29. C₃×C₄×D₁₂	C₂²	semidirect
30. C₃×#869	C₂²	semidirect
32. C₂²×#235	C₂×C₃	semidirect
40. C₂²×C₃×C₄²	D₃	semidirect
41. C₂²×C₃×C₄²	C₂×C₃	semidirect
42. C₂×#930	C₂×C₃	semidirect
43. #5477	C₂×C₃	direct (N × H)
44. C₂×#875	C₂×C₃	semidirect
45. C₂×#874	C₂×C₃	semidirect
46. C₂×C₄×D₁₂	C₂×C₃	semidirect
47. C₂×#869	C₂×C₃	semidirect
51. C₂²×C₃²×C₄	D₄	semidirect
91. C₂×#235	C₂²×C₃	semidirect
110. C₂×C₃×C₄²	C₂×D₃	semidirect
114. C₂×C₃×C₄²	C₂²×C₃	semidirect
115. #930	C₂²×C₃	semidirect
118. #875	C₂²×C₃	semidirect
119. #874	C₂²×C₃	semidirect
120. C₄×D₁₂	C₂²×C₃	semidirect
121. #869	C₂²×C₃	semidirect
133. C₂×C₃²×C₄	C₂×D₄	semidirect
134. C₂×C₃²×C₄	#41	semidirect
153. C₂²×C₄²	C₃×D₃	semidirect
181. C₂²×C₃×C₄	D₁₂	semidirect
182. C₂²×C₃×C₄	C₃×D₄	semidirect
232. C₃²×C₄	C₂×#41	semidirect
253. C₂×C₄²	C₂×C₃×D₃	semidirect
295. C₂×C₃×C₄	C₂×D₁₂	semidirect
296. C₂×C₃×C₄	#235	semidirect
299. C₂×C₃×C₄	C₂×C₃×D₄	semidirect
300. C₂×C₃×C₄	C₃×#41	semidirect
317. C₂×C₃²	#532	semidirect
336. C₂²×C₄	C₃×D₁₂	semidirect
381. C₃×C₄	C₂×#235	semidirect
384. C₃×C₄	C₂×C₃×#41	semidirect
386. C₃²	C₂×#532	semidirect
405. C₂×C₄	C₂×C₃×D₁₂	semidirect
406. C₂×C₄	C₃×#235	semidirect
418. C₂×C₃	#5477	direct (N × H)
419. C₂×C₃	C₃×#532	semidirect
438. C₄	C₂×C₃×#235	semidirect
440. C₃	C₂×#5477	direct (N × H)
441. C₃	C₂×C₃×#532	semidirect
444. C₂	C₃×#5477	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×#235	2
C₂²×C₃²×C₄²	2
C₂×C₃×#930	2
C₃×#5477	2
C₂×C₃×#875	2
C₂×C₃×#874	2
C₂×C₃×C₄×D₁₂	2
C₂×C₃×#869	2
C₂×C₃×#532	3
C₂×#5477	3

Subgroups — C2×C3×#5477 #11900755

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5477 #11900755