Subgroups — C₂×C₃×C₄×#235 #11899953

Order 1152.

3705 conjugacy classes of subgroups.

The subgroup lattice has 504 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	1	yes	maximal, characteristic
2	C₂²×C₃²×C₄²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄×#67	C₂	1	4	yes	maximal, complemented
4	C₂×C₃×#926	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×#235	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₃×C₄×D₁₂	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#872	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×C₄²×D₃	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×C₄×Dic₆	C₂	1	2	yes	maximal, complemented
10	C₂×C₃×C₄×#41	—	3	1	no	maximal
11	C₂×C₄×#235	C₃	1	1	yes	maximal, characteristic, direct product factor
12	C₂³×C₃²×C₄	C₂²	1	2	yes	—
13	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
14	C₂²×C₃×#67	C₂²	1	2	yes	—
15	C₂×C₃×#235	C₄	1	16	yes	direct product factor
16	C₂×C₃×#235	C₂²	1	8	yes	—
17	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₄×D₃	C₂²	1	4	yes	—
19	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	—
20	C₂²×C₃×Dic₆	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	1	yes	characteristic
24	C₂×C₃²×C₄²	C₂²	1	8	yes	complemented
25	C₂×C₃×#217	C₂²	1	2	yes	—
26	C₃×C₄×#67	C₂²	1	32	yes	complemented
27	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
28	C₃×#926	C₂²	1	8	yes	complemented
29	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	—
30	C₂×C₃×Dic₃⋊C₄	C₂²	1	4	yes	—
31	C₂×C₃×C₄×Dic₃	C₂²	1	2	yes	—
32	C₂×C₃×C₄×Dic₃	C₂²	1	4	yes	—
33	C₃×C₄×D₁₂	C₂²	1	16	yes	complemented
34	C₃×#872	C₂²	1	16	yes	complemented
35	C₃×C₄²×D₃	C₂²	1	16	yes	complemented
36	C₃×C₄×Dic₆	C₂²	1	16	yes	complemented
37	C₂²×C₃×#41	—	3	1	no	—
38	C₂²×#235	C₂×C₃	1	1	yes	characteristic
39	C₃×C₄×#41	—	3	16	no	—
40	C₂×C₃×C₄×Q₈	—	3	2	no	—
41	C₂×C₃×C₄×D₄	—	3	4	no	—
42	C₂×C₃×C₄×D₄	—	3	2	no	—
43	C₂×C₃×#117	—	3	1	no	—
44	C₂×C₃×#117	—	3	2	no	—
45	C₂²×C₃×C₄²	—	2	1	no	—
46	C₂²×C₃×C₄²	—	3	2	no	—
47	C₂²×C₃×C₄²	D₃	1	1	yes	characteristic, complemented
48	C₂²×C₃×C₄²	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂×C₄×#67	C₂×C₃	1	4	yes	complemented
50	C₂×#926	C₂×C₃	1	1	yes	characteristic, complemented
51	C₄×#235	C₂×C₃	1	16	yes	direct product factor
52	C₂×C₄×D₁₂	C₂×C₃	1	2	yes	complemented
53	C₂×#872	C₂×C₃	1	2	yes	complemented
54	C₂×C₄²×D₃	C₂×C₃	1	2	yes	complemented
55	C₂×C₄×Dic₆	C₂×C₃	1	2	yes	complemented
56	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
57	C₂³×C₃×D₃	C₂³	1	2	yes	—
58	C₂²×C₃²×C₄	—	2	8	no	—
59	C₂²×C₃²×C₄	C₂×C₄	1	8	yes	complemented
60	C₂²×C₃²×C₄	C₂³	1	2	yes	—
61	C₂²×C₃²×C₄	C₂³	1	8	yes	—
62	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
63	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
64	C₂²×C₃²×C₄	C₂³	1	4	yes	—
65	C₂²×C₃²×C₄	C₂³	1	2	yes	—
66	C₂×C₃×#67	C₂×C₄	1	16	yes	complemented
67	C₂×C₃×#67	C₂³	1	8	yes	—
68	C₂²×C₃×Dic₃	C₂³	1	4	yes	—
69	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
70	C₃×#235	C₂×C₄	1	64	yes	direct product factor
71	C₂×C₃×D₁₂	C₂×C₄	1	8	yes	complemented
72	C₂×C₃×D₁₂	C₂³	1	4	yes	—
73	C₂×C₃×C₄×D₃	—	2	16	no	—
74	C₂×C₃×C₄×D₃	C₂×C₄	1	16	yes	complemented
75	C₂×C₃×C₄×D₃	C₂³	1	16	yes	—
76	C₂×C₃×C₄×D₃	C₂³	1	8	yes	—
77	C₂×C₃×Dic₆	C₂×C₄	1	8	yes	complemented
78	C₂×C₃×Dic₆	C₂³	1	4	yes	—
79	C₃²×C₄²	C₂³	1	8	yes	—
80	C₃²×C₄²	C₂³	1	4	yes	—
81	C₃²×C₄²	C₂³	1	4	yes	—
82	C₃×#217	C₂³	1	8	yes	—
83	C₃×(C₂×D₃)⋊C₄	C₂³	1	16	yes	—
84	C₃×C₄⋊Dic₃	C₂³	1	8	yes	—
85	C₃×Dic₃⋊C₄	C₂³	1	16	yes	—
86	C₃×C₄×Dic₃	C₂³	1	8	yes	—
87	C₃×C₄×Dic₃	C₂³	1	16	yes	—
88	C₂×C₄×#41	—	3	1	no	Sylow
89	C₂×C₃×#41	—	3	16	no	—
90	C₂×C₃×#41	—	3	8	no	—
91	C₂²×C₃×Q₈	—	3	1	no	—
92	C₂²×C₃×D₄	—	3	2	no	—
93	C₂²×C₃×D₄	—	3	1	no	—
94	C₂³×C₃×C₄	—	2	2	no	—
95	C₂³×C₃×C₄	—	2	1	no	—
96	C₂³×C₃×C₄	—	3	2	no	—
97	C₂³×C₃×C₄	—	3	4	no	—
98	C₂³×C₃×C₄	C₂×D₃	1	2	yes	—
99	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
100	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
101	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
102	C₂²×#67	C₂²×C₃	1	2	yes	—
103	C₂×#235	C₃×C₄	1	16	yes	direct product factor
104	C₂×#235	C₂²×C₃	1	8	yes	—
105	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic
106	C₂²×C₄×D₃	C₂²×C₃	1	4	yes	—
107	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	—
108	C₂²×Dic₆	C₂²×C₃	1	1	yes	characteristic
109	C₃×C₄×Q₈	—	3	16	no	—
110	C₃×C₄×D₄	—	3	32	no	—
111	C₃×C₄×D₄	—	3	16	no	—
112	C₃×#117	—	3	8	no	—
113	C₃×#117	—	3	16	no	—
114	C₂×C₃×C₄⋊C₄	—	3	4	no	—
115	C₂×C₃×C₄⋊C₄	—	3	2	no	—
116	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
117	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
118	C₂×C₃×C₄²	—	2	1	no	—
119	C₂×C₃×C₄²	—	2	2	no	—
120	C₂×C₃×C₄²	—	2	1	no	—
121	C₂×C₃×C₄²	—	2	8	no	—
122	C₂×C₃×C₄²	—	3	2	no	—
123	C₂×C₃×C₄²	—	3	4	no	—
124	C₂×C₃×C₄²	—	3	16	no	—
125	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
126	C₂×C₃×C₄²	C₂×D₃	1	2	yes	—
127	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
128	C₂×C₃×C₄²	C₂×D₃	1	8	yes	complemented
129	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
130	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
131	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
132	C₂×C₃×C₄²	C₂²×C₃	1	8	yes	complemented
133	C₂×#217	C₂²×C₃	1	2	yes	—
134	C₄×#67	C₂²×C₃	1	32	yes	complemented
135	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
136	#926	C₂²×C₃	1	8	yes	complemented
137	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
138	C₂×Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
139	C₂×C₄×Dic₃	C₂²×C₃	1	4	yes	—
140	C₂×C₄×Dic₃	C₂²×C₃	1	2	yes	—
141	C₄×D₁₂	C₂²×C₃	1	16	yes	complemented
142	#872	C₂²×C₃	1	16	yes	complemented
143	C₄²×D₃	C₂²×C₃	1	16	yes	complemented
144	C₄×Dic₆	C₂²×C₃	1	16	yes	complemented
145	C₂³×C₃²	—	2	4	no	—
146	C₂³×C₃²	C₂²×C₄	1	4	yes	—
147	C₂³×C₃²	C₂⁴	1	2	yes	—
148	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
149	C₂²×C₃×D₃	—	2	8	no	—
150	C₂²×C₃×D₃	C₂²×C₄	1	8	yes	—
151	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
152	C₂×C₃²×C₄	—	2	4	no	—
153	C₂×C₃²×C₄	—	2	16	no	—
154	C₂×C₃²×C₄	C₂²×C₄	1	4	yes	—
155	C₂×C₃²×C₄	C₂²×C₄	1	4	yes	—
156	C₂×C₃²×C₄	C₂²×C₄	1	16	yes	complemented
157	C₂×C₃²×C₄	#41	1	8	yes	complemented
158	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
159	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
160	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
161	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
162	C₃×#67	C₂²×C₄	1	32	yes	complemented
163	C₂×C₃×Dic₃	—	2	8	no	—
164	C₂×C₃×Dic₃	C₂²×C₄	1	8	yes	—
165	C₂×C₃×Dic₃	C₂⁴	1	8	yes	—
166	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
167	C₃×D₁₂	C₂²×C₄	1	16	yes	complemented
168	C₃×C₄×D₃	—	2	32	no	—
169	C₃×C₄×D₃	C₂²×C₄	1	32	yes	complemented
170	C₃×Dic₆	C₂²×C₄	1	16	yes	complemented
171	C₂²×#41	—	3	1	no	—
172	C₄×#41	—	3	16	no	—
173	C₂×C₄×Q₈	—	3	2	no	—
174	C₂×C₄×D₄	—	3	4	no	—
175	C₂×C₄×D₄	—	3	2	no	—
176	C₂×#117	—	3	1	no	—
177	C₂×#117	—	3	2	no	—
178	C₂²×C₄²	—	3	2	no	—
179	C₂²×C₄²	C₃×D₃	1	1	yes	characteristic, complemented
180	C₂⁴×C₃	—	2	1	no	—
181	C₂⁴×C₃	—	3	2	no	—
182	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
183	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
184	C₂³×D₃	C₂³×C₃	1	2	yes	—
185	C₃×#41	—	3	64	no	—
186	C₂×C₃×Q₈	—	3	8	no	—
187	C₂×C₃×Q₈	—	3	4	no	—
188	C₂×C₃×D₄	—	3	16	no	—
189	C₂×C₃×D₄	—	3	8	no	—
190	C₂×C₃×D₄	—	3	8	no	—
191	C₂×C₃×D₄	—	3	4	no	—
192	C₂²×C₃×C₄	—	2	16	no	—
193	C₂²×C₃×C₄	—	2	8	no	—
194	C₂²×C₃×C₄	—	2	8	no	—
195	C₂²×C₃×C₄	—	2	8	no	—
196	C₂²×C₃×C₄	—	2	2	no	—
197	C₂²×C₃×C₄	—	2	8	no	—
198	C₂²×C₃×C₄	—	2	1	no	—
199	C₂²×C₃×C₄	—	2	1	no	—
200	C₂²×C₃×C₄	—	2	4	no	—
201	C₂²×C₃×C₄	—	2	2	no	—
202	C₂²×C₃×C₄	—	3	2	no	—
203	C₂²×C₃×C₄	—	3	16	no	—
204	C₂²×C₃×C₄	—	3	8	no	—
205	C₂²×C₃×C₄	—	3	4	no	—
206	C₂²×C₃×C₄	—	3	16	no	—
207	C₂²×C₃×C₄	—	6	16	no	—
208	C₂²×C₃×C₄	C₄×D₃	1	8	yes	complemented
209	C₂²×C₃×C₄	C₂×C₃×C₄	1	8	yes	complemented
210	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
211	C₂²×C₃×C₄	C₂²×D₃	1	8	yes	—
212	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
213	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
214	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
215	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
216	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
217	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
218	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
219	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
220	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
221	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
222	C₂×#67	C₂×C₃×C₄	1	16	yes	complemented
223	C₂×#67	C₂³×C₃	1	8	yes	—
224	C₂²×Dic₃	C₂³×C₃	1	4	yes	—
225	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
226	#235	C₂×C₃×C₄	1	64	yes	direct product factor
227	C₂×D₁₂	C₂×C₃×C₄	1	8	yes	complemented
228	C₂×D₁₂	C₂³×C₃	1	4	yes	—
229	C₂×C₄×D₃	—	2	16	no	—
230	C₂×C₄×D₃	C₂×C₃×C₄	1	16	yes	complemented
231	C₂×C₄×D₃	C₂³×C₃	1	16	yes	—
232	C₂×C₄×D₃	C₂³×C₃	1	8	yes	—
233	C₂×Dic₆	C₂×C₃×C₄	1	8	yes	complemented
234	C₂×Dic₆	C₂³×C₃	1	4	yes	—
235	C₃×C₄⋊C₄	—	3	16	no	—
236	C₃×C₄⋊C₄	—	3	8	no	—
237	C₃×C₂²⋊C₄	—	3	8	no	—
238	C₃×C₂²⋊C₄	—	3	16	no	—
239	C₃×C₄²	—	2	4	no	—
240	C₃×C₄²	—	2	4	no	—
241	C₃×C₄²	—	2	8	no	—
242	C₃×C₄²	—	3	8	no	—
243	C₃×C₄²	—	3	16	no	—
244	C₃×C₄²	C₂²×D₃	1	4	yes	—
245	C₃×C₄²	C₂²×D₃	1	4	yes	—
246	C₃×C₄²	C₂²×D₃	1	8	yes	—
247	C₃×C₄²	C₂³×C₃	1	8	yes	—
248	C₃×C₄²	C₂³×C₃	1	4	yes	—
249	C₃×C₄²	C₂³×C₃	1	4	yes	—
250	#217	C₂³×C₃	1	8	yes	—
251	(C₂×D₃)⋊C₄	C₂³×C₃	1	16	yes	—
252	C₄⋊Dic₃	C₂³×C₃	1	8	yes	—
253	Dic₃⋊C₄	C₂³×C₃	1	16	yes	—
254	C₄×Dic₃	C₂³×C₃	1	16	yes	—
255	C₄×Dic₃	C₂³×C₃	1	8	yes	—
256	C₂²×C₃²	—	2	8	no	—
257	C₂²×C₃²	—	2	4	no	—
258	C₂²×C₃²	C₂³×C₄	1	4	yes	—
259	C₂²×C₃²	C₂³×C₄	1	2	yes	—
260	C₂²×C₃²	C₂×#41	1	4	yes	—
261	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
262	C₂×C₃×D₃	—	2	16	no	—
263	C₂×C₃×D₃	—	2	8	no	—
264	C₂×C₃×D₃	C₂³×C₄	1	8	yes	—
265	C₃²×C₄	—	2	4	no	—
266	C₃²×C₄	C₂³×C₄	1	4	yes	—
267	C₃²×C₄	C₂³×C₄	1	4	yes	—
268	C₃²×C₄	C₂×#41	1	8	yes	complemented
269	C₃×Dic₃	—	2	8	no	—
270	C₃×Dic₃	C₂³×C₄	1	8	yes	—
271	C₂×#41	—	3	16	no	—
272	C₂×#41	—	3	8	no	—
273	C₂²×Q₈	—	3	1	no	—
274	C₂²×D₄	—	3	2	no	—
275	C₂²×D₄	—	3	1	no	—
276	C₂³×C₄	—	3	2	no	—
277	C₂³×C₄	—	3	4	no	—
278	C₂³×C₄	C₂×C₃×D₃	1	2	yes	—
279	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
280	C₄×Q₈	—	3	16	no	—
281	C₄×D₄	—	3	32	no	—
282	C₄×D₄	—	3	16	no	—
283	#117	—	3	8	no	—
284	#117	—	3	16	no	—
285	C₂×C₄⋊C₄	—	3	4	no	—
286	C₂×C₄⋊C₄	—	3	2	no	—
287	C₂×C₂²⋊C₄	—	3	2	no	—
288	C₂×C₂²⋊C₄	—	3	4	no	—
289	C₂×C₄²	—	3	2	no	—
290	C₂×C₄²	—	3	4	no	—
291	C₂×C₄²	—	3	16	no	—
292	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
293	C₂×C₄²	C₂×C₃×D₃	1	2	yes	—
294	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
295	C₂×C₄²	C₂×C₃×D₃	1	8	yes	complemented
296	C₂³×C₃	—	2	8	no	—
297	C₂³×C₃	—	2	4	no	—
298	C₂³×C₃	—	2	4	no	—
299	C₂³×C₃	—	2	2	no	—
300	C₂³×C₃	—	2	1	no	—
301	C₂³×C₃	—	2	4	no	—
302	C₂³×C₃	—	3	8	no	—
303	C₂³×C₃	—	3	4	no	—
304	C₂³×C₃	—	6	8	no	—
305	C₂³×C₃	C₂×C₄×D₃	1	4	yes	—
306	C₂³×C₃	C₂²×C₃×C₄	1	4	yes	—
307	C₂³×C₃	C₂³×D₃	1	2	yes	—
308	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
309	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
310	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
311	C₂²×D₃	—	2	8	no	—
312	C₂²×D₃	C₂²×C₃×C₄	1	8	yes	—
313	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
314	C₃×Q₈	—	3	16	no	—
315	C₃×D₄	—	3	32	no	—
316	C₃×D₄	—	3	16	no	—
317	C₂×C₃×C₄	—	2	8	no	—
318	C₂×C₃×C₄	—	2	32	no	—
319	C₂×C₃×C₄	—	2	4	no	—
320	C₂×C₃×C₄	—	2	4	no	—
321	C₂×C₃×C₄	—	2	16	no	—
322	C₂×C₃×C₄	—	2	16	no	—
323	C₂×C₃×C₄	—	2	4	no	—
324	C₂×C₃×C₄	—	2	2	no	—
325	C₂×C₃×C₄	—	2	2	no	—
326	C₂×C₃×C₄	—	2	4	no	—
327	C₂×C₃×C₄	—	2	4	no	—
328	C₂×C₃×C₄	—	2	4	no	—
329	C₂×C₃×C₄	—	2	16	no	—
330	C₂×C₃×C₄	—	2	8	no	—
331	C₂×C₃×C₄	—	3	8	no	—
332	C₂×C₃×C₄	—	3	4	no	—
333	C₂×C₃×C₄	—	3	32	no	—
334	C₂×C₃×C₄	—	3	8	no	—
335	C₂×C₃×C₄	—	6	8	no	—
336	C₂×C₃×C₄	—	6	32	no	—
337	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
338	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
339	C₂×C₃×C₄	C₂×C₄×D₃	1	16	yes	complemented
340	C₂×C₃×C₄	#235	1	8	yes	direct product factor
341	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
342	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
343	C₂×C₃×C₄	C₂²×C₃×C₄	1	16	yes	complemented
344	C₂×C₃×C₄	C₃×#41	1	8	yes	complemented
345	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
346	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
347	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
348	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
349	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
350	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
351	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
352	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
353	#67	C₂²×C₃×C₄	1	32	yes	complemented
354	C₂×Dic₃	—	2	8	no	—
355	C₂×Dic₃	C₂²×C₃×C₄	1	8	yes	—
356	C₂×Dic₃	C₂⁴×C₃	1	8	yes	—
357	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
358	D₁₂	C₂²×C₃×C₄	1	16	yes	complemented
359	C₄×D₃	—	2	32	no	—
360	C₄×D₃	C₂²×C₃×C₄	1	32	yes	complemented
361	Dic₆	C₂²×C₃×C₄	1	16	yes	complemented
362	C₂×C₃²	—	2	4	no	—
363	C₂×C₃²	C₄×#41	1	4	yes	complemented
364	C₂×C₃²	C₂⁴×C₄	1	1	yes	characteristic
365	C₂×C₃²	C₂²×#41	1	2	yes	—
366	C₃×D₃	—	2	8	no	—
367	C₂⁴	—	3	2	no	—
368	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
369	#41	—	3	64	no	—
370	C₂×Q₈	—	3	4	no	—
371	C₂×Q₈	—	3	8	no	—
372	C₂×D₄	—	3	8	no	—
373	C₂×D₄	—	3	16	no	—
374	C₂×D₄	—	3	4	no	—
375	C₂×D₄	—	3	8	no	—
376	C₂²×C₄	—	2	8	no	—
377	C₂²×C₄	—	3	2	no	—
378	C₂²×C₄	—	3	8	no	—
379	C₂²×C₄	—	3	16	no	—
380	C₂²×C₄	—	3	4	no	—
381	C₂²×C₄	—	3	16	no	—
382	C₂²×C₄	—	6	16	no	—
383	C₂²×C₄	C₃×C₄×D₃	1	8	yes	complemented
384	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
385	C₂²×C₄	C₂²×C₃×D₃	1	8	yes	—
386	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
387	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
388	C₂²×C₄	C₂²×C₃×D₃	1	4	yes	—
389	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
390	C₄⋊C₄	—	3	16	no	—
391	C₄⋊C₄	—	3	8	no	—
392	C₂²⋊C₄	—	3	8	no	—
393	C₂²⋊C₄	—	3	16	no	—
394	C₄²	—	3	8	no	—
395	C₄²	—	3	16	no	—
396	C₄²	C₂²×C₃×D₃	1	4	yes	—
397	C₄²	C₂²×C₃×D₃	1	4	yes	—
398	C₄²	C₂²×C₃×D₃	1	8	yes	—
399	C₂²×C₃	—	2	8	no	—
400	C₂²×C₃	—	2	16	no	—
401	C₂²×C₃	—	2	4	no	—
402	C₂²×C₃	—	2	4	no	—
403	C₂²×C₃	—	2	8	no	—
404	C₂²×C₃	—	2	8	no	—
405	C₂²×C₃	—	2	4	no	—
406	C₂²×C₃	—	2	2	no	—
407	C₂²×C₃	—	2	4	no	—
408	C₂²×C₃	—	2	1	no	—
409	C₂²×C₃	—	3	8	no	—
410	C₂²×C₃	—	6	8	no	—
411	C₂²×C₃	—	6	16	no	—
412	C₂²×C₃	C₂²×C₄×D₃	1	4	yes	—
413	C₂²×C₃	C₂²×C₄×D₃	1	2	yes	—
414	C₂²×C₃	C₂×#235	1	4	yes	—
415	C₂²×C₃	C₂³×C₃×C₄	1	4	yes	—
416	C₂²×C₃	C₂³×C₃×C₄	1	2	yes	—
417	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
418	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
419	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
420	C₂×D₃	—	2	8	no	—
421	C₂×D₃	—	2	16	no	—
422	C₂×D₃	C₂³×C₃×C₄	1	8	yes	—
423	C₃×C₄	—	2	8	no	—
424	C₃×C₄	—	2	4	no	—
425	C₃×C₄	—	2	4	no	—
426	C₃×C₄	—	2	4	no	—
427	C₃×C₄	—	2	4	no	—
428	C₃×C₄	—	2	8	no	—
429	C₃×C₄	—	3	8	no	—
430	C₃×C₄	—	6	8	no	—
431	C₃×C₄	C₂²×C₄×D₃	1	4	yes	—
432	C₃×C₄	C₂²×C₄×D₃	1	4	yes	—
433	C₃×C₄	C₂×#235	1	8	yes	direct product factor
434	C₃×C₄	C₂³×C₃×C₄	1	4	yes	—
435	C₃×C₄	C₂³×C₃×C₄	1	4	yes	—
436	C₃×C₄	C₂×C₃×#41	1	8	yes	complemented
437	Dic₃	—	2	8	no	—
438	Dic₃	C₂³×C₃×C₄	1	8	yes	—
439	C₃²	C₂×C₄×#41	1	1	yes	characteristic, complemented, Sylow
440	C₂³	—	2	4	no	—
441	C₂³	—	3	8	no	—
442	C₂³	—	3	4	no	—
443	C₂³	—	6	8	no	—
444	C₂³	C₂×C₃×C₄×D₃	1	4	yes	—
445	C₂³	C₂³×C₃×D₃	1	2	yes	—
446	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
447	Q₈	—	3	16	no	—
448	D₄	—	3	32	no	—
449	D₄	—	3	16	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	16	no	—
452	C₂×C₄	—	3	8	no	—
453	C₂×C₄	—	3	4	no	—
454	C₂×C₄	—	3	32	no	—
455	C₂×C₄	—	3	8	no	—
456	C₂×C₄	—	6	8	no	—
457	C₂×C₄	—	6	32	no	—
458	C₂×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
459	C₂×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
460	C₂×C₄	C₂×C₃×C₄×D₃	1	16	yes	complemented
461	C₂×C₄	C₃×#235	1	8	yes	direct product factor
462	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
463	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
464	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
465	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
466	C₂×C₃	—	2	8	no	—
467	C₂×C₃	—	2	4	no	—
468	C₂×C₃	—	2	4	no	—
469	C₂×C₃	—	2	1	no	—
470	C₂×C₃	—	2	2	no	—
471	C₂×C₃	—	2	4	no	—
472	C₂×C₃	—	6	8	no	—
473	C₂×C₃	C₄×#235	1	4	yes	direct product factor
474	C₂×C₃	C₃×C₄×#41	1	4	yes	complemented
475	C₂×C₃	C₂³×C₄×D₃	1	1	yes	characteristic
476	C₂×C₃	C₂²×#235	1	2	yes	—
477	C₂×C₃	C₂⁴×C₃×C₄	1	1	yes	characteristic
478	C₂×C₃	C₂²×C₃×#41	1	2	yes	—
479	D₃	—	2	8	no	—
480	C₂²	—	2	4	no	—
481	C₂²	—	2	8	no	—
482	C₂²	—	3	8	no	—
483	C₂²	—	6	8	no	—
484	C₂²	—	6	16	no	—
485	C₂²	C₂²×C₃×C₄×D₃	1	4	yes	—
486	C₂²	C₂²×C₃×C₄×D₃	1	2	yes	—
487	C₂²	C₂×C₃×#235	1	4	yes	—
488	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
489	C₄	—	2	4	no	—
490	C₄	—	3	8	no	—
491	C₄	—	6	8	no	—
492	C₄	C₂²×C₃×C₄×D₃	1	4	yes	—
493	C₄	C₂²×C₃×C₄×D₃	1	4	yes	—
494	C₄	C₂×C₃×#235	1	8	yes	direct product factor
495	C₃	—	2	1	no	—
496	C₃	C₂×C₄×#235	1	1	yes	characteristic, direct product factor
497	C₃	C₂×C₃×C₄×#41	1	1	yes	characteristic, complemented
498	C₂	—	2	4	no	—
499	C₂	—	6	8	no	—
500	C₂	C₃×C₄×#235	1	4	yes	direct product factor
501	C₂	C₂³×C₃×C₄×D₃	1	1	yes	characteristic
502	C₂	C₂²×C₃×#235	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄²	C₂×D₃
commutator	C₂×C₃	C₂⁴×C₃×C₄
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₂²×C₃²×C₄²	C₂
socle	C₂³×C₃²	C₂⁴
prime radical	C₂²×C₃×#235	C₂
cosocle	C₂²×C₃	C₂⁵×C₃
hypercenter	C₂²×C₃×C₄²	D₃
hypocenter	C₃	C₂×C₃×C₄×#41
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄² ◁ C₂²×C₃×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃²×C₄²	C₂	semidirect
3. C₂×C₃×C₄×#67	C₂	semidirect
4. C₂×C₃×#926	C₂	semidirect
5. C₃×C₄×#235	C₂	direct (N × H)
6. C₂×C₃×C₄×D₁₂	C₂	semidirect
7. C₂×C₃×#872	C₂	semidirect
8. C₂×C₃×C₄²×D₃	C₂	semidirect
9. C₂×C₃×C₄×Dic₆	C₂	semidirect
11. C₂×C₄×#235	C₃	direct (N × H)
15. C₂×C₃×#235	C₄	direct (N × H)
24. C₂×C₃²×C₄²	C₂²	semidirect
26. C₃×C₄×#67	C₂²	semidirect
28. C₃×#926	C₂²	semidirect
33. C₃×C₄×D₁₂	C₂²	semidirect
34. C₃×#872	C₂²	semidirect
35. C₃×C₄²×D₃	C₂²	semidirect
36. C₃×C₄×Dic₆	C₂²	semidirect
47. C₂²×C₃×C₄²	D₃	semidirect
48. C₂²×C₃×C₄²	C₂×C₃	semidirect
49. C₂×C₄×#67	C₂×C₃	semidirect
50. C₂×#926	C₂×C₃	semidirect
51. C₄×#235	C₂×C₃	direct (N × H)
52. C₂×C₄×D₁₂	C₂×C₃	semidirect
53. C₂×#872	C₂×C₃	semidirect
54. C₂×C₄²×D₃	C₂×C₃	semidirect
55. C₂×C₄×Dic₆	C₂×C₃	semidirect
59. C₂²×C₃²×C₄	C₂×C₄	semidirect
66. C₂×C₃×#67	C₂×C₄	semidirect
70. C₃×#235	C₂×C₄	direct (N × H)
71. C₂×C₃×D₁₂	C₂×C₄	semidirect
74. C₂×C₃×C₄×D₃	C₂×C₄	semidirect
77. C₂×C₃×Dic₆	C₂×C₄	semidirect
103. C₂×#235	C₃×C₄	direct (N × H)
128. C₂×C₃×C₄²	C₂×D₃	semidirect
132. C₂×C₃×C₄²	C₂²×C₃	semidirect
134. C₄×#67	C₂²×C₃	semidirect
136. #926	C₂²×C₃	semidirect
141. C₄×D₁₂	C₂²×C₃	semidirect
142. #872	C₂²×C₃	semidirect
143. C₄²×D₃	C₂²×C₃	semidirect
144. C₄×Dic₆	C₂²×C₃	semidirect
156. C₂×C₃²×C₄	C₂²×C₄	semidirect
157. C₂×C₃²×C₄	#41	semidirect
162. C₃×#67	C₂²×C₄	semidirect
167. C₃×D₁₂	C₂²×C₄	semidirect
169. C₃×C₄×D₃	C₂²×C₄	semidirect
170. C₃×Dic₆	C₂²×C₄	semidirect
179. C₂²×C₄²	C₃×D₃	semidirect
208. C₂²×C₃×C₄	C₄×D₃	semidirect
209. C₂²×C₃×C₄	C₂×C₃×C₄	semidirect
222. C₂×#67	C₂×C₃×C₄	semidirect
226. #235	C₂×C₃×C₄	direct (N × H)
227. C₂×D₁₂	C₂×C₃×C₄	semidirect
230. C₂×C₄×D₃	C₂×C₃×C₄	semidirect
233. C₂×Dic₆	C₂×C₃×C₄	semidirect
268. C₃²×C₄	C₂×#41	semidirect
295. C₂×C₄²	C₂×C₃×D₃	semidirect
339. C₂×C₃×C₄	C₂×C₄×D₃	semidirect
340. C₂×C₃×C₄	#235	direct (N × H)
343. C₂×C₃×C₄	C₂²×C₃×C₄	semidirect
344. C₂×C₃×C₄	C₃×#41	semidirect
353. #67	C₂²×C₃×C₄	semidirect
358. D₁₂	C₂²×C₃×C₄	semidirect
360. C₄×D₃	C₂²×C₃×C₄	semidirect
361. Dic₆	C₂²×C₃×C₄	semidirect
363. C₂×C₃²	C₄×#41	semidirect
383. C₂²×C₄	C₃×C₄×D₃	semidirect
433. C₃×C₄	C₂×#235	direct (N × H)
436. C₃×C₄	C₂×C₃×#41	semidirect
439. C₃²	C₂×C₄×#41	semidirect
460. C₂×C₄	C₂×C₃×C₄×D₃	semidirect
461. C₂×C₄	C₃×#235	direct (N × H)
473. C₂×C₃	C₄×#235	direct (N × H)
474. C₂×C₃	C₃×C₄×#41	semidirect
494. C₄	C₂×C₃×#235	direct (N × H)
496. C₃	C₂×C₄×#235	direct (N × H)
497. C₃	C₂×C₃×C₄×#41	semidirect
500. C₂	C₃×C₄×#235	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×C₄×#67	2
C₂×C₃×#926	2
C₃×C₄×#235	2
C₂×C₃×C₄×D₁₂	2
C₂×C₃×#872	2
C₂×C₃×C₄²×D₃	2
C₂×C₃×C₄×Dic₆	2
C₂×C₃×C₄×#41	3
C₂×C₄×#235	3

Subgroups — C2×C3×C4×#235 #11899953

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₄×#235 #11899953