Subgroups — C₃×C₄×#823 #11783777

Order 1152.

791 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#823	C₂	1	2	yes	maximal
4	C₃×C₄×#208	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#4554	C₂	1	2	yes	maximal, complemented
6	C₃×C₄×#100	—	3	1	no	maximal
7	C₄×#823	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₄×D₃	C₄	1	2	yes	—
10	C₂×C₃²×M₁₆	C₂²	1	2	yes	—
11	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
12	C₂×C₃×(C₂×D₃)⋊C₄	C₄	1	2	yes	—
13	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
14	C₂×C₃×#208	C₂²	1	2	yes	—
15	C₃×C₄×D₁₂	—	2	1	no	—
16	C₃×C₄×D₁₂	—	2	1	no	—
17	C₃×C₄×D₁₂	—	2	1	no	—
18	C₃×C₄×D₁₂	—	2	1	no	—
19	C₃²×#97	—	2	1	no	—
20	C₃²×C₄×C₈	—	2	1	no	—
21	C₃×#823	C₄	1	8	yes	direct product factor
22	C₃×#803	—	2	1	no	—
23	C₃×C₄×C₃⋊C₈	—	2	1	no	—
24	C₂×C₃×C₄×D₄	—	3	1	no	—
25	C₂×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic
26	C₂×C₃×#100	—	3	2	no	—
27	C₃×C₄×M₁₆	—	2	1	no	—
28	C₃×C₄×M₁₆	—	3	1	no	—
29	C₃×C₄×M₁₆	D₃	1	1	yes	characteristic, complemented
30	C₃×C₄×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂×#823	C₂×C₃	1	2	yes	—
32	C₄×#208	C₂×C₃	1	1	yes	characteristic, complemented
33	C₃×#343	—	3	2	no	—
34	#4554	C₂×C₃	1	2	yes	complemented
35	C₂³×C₃×D₃	C₂×C₄	1	2	yes	—
36	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
39	C₂²×C₃×Dic₃	C₂×C₄	1	2	yes	—
40	C₂×C₃×D₁₂	—	2	1	no	—
41	C₂×C₃×D₁₂	—	2	1	no	—
42	C₂×C₃×D₁₂	—	2	2	no	—
43	C₂×C₃×D₁₂	C₂×C₄	1	4	yes	—
44	C₂×C₃×C₄×D₃	—	2	2	no	—
45	C₂×C₃×C₄×D₃	—	2	2	no	—
46	C₂×C₃×C₄×D₃	—	4	4	no	—
47	C₃²×M₁₆	—	2	2	no	—
48	C₃²×M₁₆	C₂×C₄	1	4	yes	complemented
49	C₂×C₃²×C₈	—	2	2	no	—
50	C₃²×C₄²	D₄	1	1	yes	characteristic
51	C₃²×C₄²	D₄	1	1	yes	characteristic
52	C₃²×C₄²	D₄	1	1	yes	characteristic
53	C₃²×C₄²	D₄	1	1	yes	characteristic
54	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
55	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
56	C₃×C₄⋊Dic₃	—	2	1	no	—
57	C₃×C₄⋊Dic₃	—	2	1	no	—
58	C₃×#208	—	2	2	no	—
59	C₃×#208	C₂×C₄	1	4	yes	complemented
60	C₂×C₃×C₃⋊C₈	—	2	2	no	—
61	C₄×#100	—	3	1	no	Sylow
62	C₂²×C₃×D₄	—	3	1	no	—
63	C₂³×C₃×C₄	—	3	2	no	—
64	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic
65	C₂²×C₄×D₃	C₃×C₄	1	2	yes	—
66	C₂×C₃×M₁₆	—	2	2	no	—
67	C₂×C₃×M₁₆	—	3	2	no	—
68	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
69	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
70	C₃×C₄×D₄	—	6	1	no	—
71	C₃×C₄×D₄	—	6	1	no	—
72	C₃×C₄×D₄	—	6	1	no	—
73	C₃×C₄×D₄	—	6	1	no	—
74	C₂×C₃×C₄⋊C₄	—	3	1	no	—
75	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
76	C₂×C₃×C₄²	—	2	1	no	—
77	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
78	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
79	C₂×(C₂×D₃)⋊C₄	C₃×C₄	1	2	yes	—
80	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
81	C₂×#208	C₂²×C₃	1	2	yes	—
82	C₄×D₁₂	—	2	1	no	—
83	C₄×D₁₂	—	2	1	no	—
84	C₄×D₁₂	—	2	1	no	—
85	C₄×D₁₂	—	2	1	no	—
86	C₃×#100	—	3	8	no	—
87	C₃×#97	—	2	2	no	—
88	C₃×#97	—	2	1	no	—
89	C₃×#97	—	2	1	no	—
90	C₃×#97	—	6	1	no	—
91	C₃×C₄×C₈	—	2	2	no	—
92	C₃×C₄×C₈	—	2	1	no	—
93	C₃×C₄×C₈	—	2	1	no	—
94	C₃×C₄×C₈	—	6	1	no	—
95	#823	C₃×C₄	1	8	yes	direct product factor
96	#803	—	2	1	no	—
97	C₄×C₃⋊C₈	—	2	1	no	—
98	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₃×D₃	—	2	2	no	—
100	C₂²×C₃×D₃	—	2	2	no	—
101	C₂²×C₃×D₃	—	4	2	no	—
102	C₂²×C₃×D₃	—	4	2	no	—
103	C₂²×C₃×D₃	C₄²	1	4	yes	—
104	C₂×C₃²×C₄	—	2	2	no	—
105	C₂×C₃²×C₄	—	4	1	no	—
106	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
107	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
108	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
109	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
110	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
111	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
112	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃²×C₄	#41	1	2	yes	—
114	C₂×C₃×Dic₃	—	2	2	no	—
115	C₂×C₃×Dic₃	—	4	2	no	—
116	C₃×D₁₂	—	2	4	no	—
117	C₃×D₁₂	—	2	4	no	—
118	C₃×C₄×D₃	—	4	4	no	—
119	C₃×C₄×D₃	—	4	4	no	—
120	C₃²×C₈	—	2	4	no	—
121	C₃×C₃⋊C₈	—	2	4	no	—
122	C₂×C₄×D₄	—	3	1	no	—
123	C₂×#100	—	3	2	no	—
124	C₄×M₁₆	—	3	1	no	—
125	C₄×M₁₆	C₃×D₃	1	1	yes	characteristic, complemented
126	#343	—	3	2	no	—
127	C₂⁴×C₃	—	3	2	no	—
128	C₂³×D₃	C₂×C₃×C₄	1	2	yes	—
129	C₂×C₃×D₄	—	3	4	no	—
130	C₂×C₃×D₄	—	6	1	no	—
131	C₂×C₃×D₄	—	6	2	no	—
132	C₂×C₃×D₄	—	6	1	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	—	3	2	no	—
137	C₂²×C₃×C₄	—	6	2	no	—
138	C₂²×C₃×C₄	—	6	2	no	—
139	C₂²×C₃×C₄	—	12	4	no	—
140	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
141	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
142	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
143	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
144	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
145	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
146	C₂²×Dic₃	C₂×C₃×C₄	1	2	yes	—
147	C₂×D₁₂	—	2	1	no	—
148	C₂×D₁₂	—	2	1	no	—
149	C₂×D₁₂	—	2	2	no	—
150	C₂×D₁₂	C₂×C₃×C₄	1	4	yes	—
151	C₂×C₄×D₃	—	2	2	no	—
152	C₂×C₄×D₃	—	2	2	no	—
153	C₂×C₄×D₃	—	4	4	no	—
154	C₃×M₁₆	—	2	4	no	—
155	C₃×M₁₆	—	2	2	no	—
156	C₃×M₁₆	—	2	2	no	—
157	C₃×M₁₆	—	2	4	no	—
158	C₃×M₁₆	—	3	4	no	—
159	C₃×M₁₆	—	6	2	no	—
160	C₃×M₁₆	C₄×D₃	1	4	yes	complemented
161	C₃×M₁₆	C₂×C₃×C₄	1	4	yes	complemented
162	C₂×C₃×C₈	—	2	4	no	—
163	C₂×C₃×C₈	—	2	2	no	—
164	C₂×C₃×C₈	—	2	2	no	—
165	C₂×C₃×C₈	—	6	2	no	—
166	C₃×C₄⋊C₄	—	6	1	no	—
167	C₃×C₄⋊C₄	—	6	1	no	—
168	C₃×C₂²⋊C₄	—	6	2	no	—
169	C₃×C₂²⋊C₄	—	6	2	no	—
170	C₃×C₄²	—	2	1	no	—
171	C₃×C₄²	—	2	1	no	—
172	C₃×C₄²	—	2	1	no	—
173	C₃×C₄²	—	2	1	no	—
174	C₃×C₄²	D₁₂	1	1	yes	characteristic
175	C₃×C₄²	D₁₂	1	1	yes	characteristic
176	C₃×C₄²	#67	1	1	yes	characteristic
177	C₃×C₄²	#67	1	1	yes	characteristic
178	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
179	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
180	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
181	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
182	(C₂×D₃)⋊C₄	—	2	2	no	—
183	(C₂×D₃)⋊C₄	—	2	2	no	—
184	C₄⋊Dic₃	—	2	1	no	—
185	C₄⋊Dic₃	—	2	1	no	—
186	#208	—	2	2	no	—
187	#208	C₂×C₃×C₄	1	4	yes	complemented
188	C₂×C₃⋊C₈	—	2	2	no	—
189	C₂²×C₃²	—	2	1	no	—
190	C₂²×C₃²	—	2	1	no	—
191	C₂²×C₃²	C₂×C₄²	1	1	yes	characteristic
192	C₂²×C₃²	C₂×C₂²⋊C₄	1	1	yes	characteristic
193	C₂²×C₃²	#117	1	1	yes	characteristic
194	C₂×C₃×D₃	—	2	4	no	—
195	C₂×C₃×D₃	—	4	4	no	—
196	C₂×C₃×D₃	—	4	2	no	—
197	C₂×C₃×D₃	—	4	2	no	—
198	C₂×C₃×D₃	—	4	4	no	—
199	C₃²×C₄	—	2	1	no	—
200	C₃²×C₄	—	2	1	no	—
201	C₃²×C₄	—	2	1	no	—
202	C₃²×C₄	#100	1	2	yes	complemented
203	C₃²×C₄	C₄×D₄	1	2	yes	—
204	C₃²×C₄	C₄×D₄	1	2	yes	—
205	C₃×Dic₃	—	4	2	no	—
206	C₂²×D₄	—	3	1	no	—
207	C₂³×C₄	—	3	2	no	—
208	C₂×M₁₆	—	3	2	no	—
209	C₂×M₁₆	C₂×C₃×D₃	1	2	yes	—
210	C₄×D₄	—	6	1	no	—
211	C₄×D₄	—	6	1	no	—
212	C₄×D₄	—	6	1	no	—
213	C₄×D₄	—	6	1	no	—
214	C₂×C₄⋊C₄	—	3	1	no	—
215	C₂×C₂²⋊C₄	—	3	2	no	—
216	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
217	#100	—	3	8	no	—
218	#97	—	2	1	no	—
219	#97	—	6	1	no	—
220	C₄×C₈	—	2	1	no	—
221	C₄×C₈	—	6	1	no	—
222	C₂³×C₃	—	2	1	no	—
223	C₂³×C₃	—	3	4	no	—
224	C₂³×C₃	—	6	2	no	—
225	C₂³×C₃	—	6	2	no	—
226	C₂³×C₃	—	12	2	no	—
227	C₂³×C₃	—	12	2	no	—
228	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
229	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
230	C₂²×D₃	—	2	2	no	—
231	C₂²×D₃	—	2	2	no	—
232	C₂²×D₃	—	4	2	no	—
233	C₂²×D₃	—	4	2	no	—
234	C₂²×D₃	C₃×C₄²	1	4	yes	—
235	C₃×D₄	—	6	4	no	—
236	C₃×D₄	—	6	4	no	—
237	C₂×C₃×C₄	—	2	2	no	—
238	C₂×C₃×C₄	—	2	2	no	—
239	C₂×C₃×C₄	—	2	1	no	—
240	C₂×C₃×C₄	—	2	1	no	—
241	C₂×C₃×C₄	—	2	1	no	—
242	C₂×C₃×C₄	—	2	1	no	—
243	C₂×C₃×C₄	—	2	2	no	—
244	C₂×C₃×C₄	—	2	1	no	—
245	C₂×C₃×C₄	—	2	2	no	—
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	4	2	no	—
248	C₂×C₃×C₄	—	4	1	no	—
249	C₂×C₃×C₄	—	4	1	no	—
250	C₂×C₃×C₄	—	4	2	no	—
251	C₂×C₃×C₄	—	6	2	no	—
252	C₂×C₃×C₄	—	12	4	no	—
253	C₂×C₃×C₄	—	12	4	no	—
254	C₂×C₃×C₄	—	12	2	no	—
255	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
256	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
257	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
258	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
259	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
260	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
261	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
262	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
264	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
265	C₂×C₃×C₄	#235	1	2	yes	—
266	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
268	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
269	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
270	C₂×C₃×C₄	C₃×#41	1	2	yes	—
271	C₂×Dic₃	—	2	2	no	—
272	C₂×Dic₃	—	4	2	no	—
273	D₁₂	—	2	4	no	—
274	D₁₂	—	2	4	no	—
275	C₄×D₃	—	4	4	no	—
276	C₄×D₃	—	4	4	no	—
277	C₃×C₈	—	2	8	no	—
278	C₃×C₈	—	2	4	no	—
279	C₃×C₈	—	2	4	no	—
280	C₃×C₈	—	6	4	no	—
281	C₃⋊C₈	—	2	4	no	—
282	C₂×C₃²	—	2	1	no	—
283	C₂×C₃²	—	2	1	no	—
284	C₂×C₃²	C₄×C₂²⋊C₄	1	1	yes	characteristic
285	C₂×C₃²	C₂×#100	1	1	yes	characteristic
286	C₂×C₃²	#413	1	1	yes	characteristic
287	C₃×D₃	—	4	4	no	—
288	C₂⁴	—	3	2	no	—
289	C₂×D₄	—	3	4	no	—
290	C₂×D₄	—	6	1	no	—
291	C₂×D₄	—	6	2	no	—
292	C₂×D₄	—	6	1	no	—
293	C₂²×C₄	—	3	2	no	—
294	C₂²×C₄	—	6	2	no	—
295	C₂²×C₄	—	6	2	no	—
296	C₂²×C₄	—	12	4	no	—
297	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
298	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
299	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
300	M₁₆	—	2	2	no	—
301	M₁₆	—	3	4	no	—
302	M₁₆	—	6	2	no	—
303	M₁₆	C₃×C₄×D₃	1	4	yes	complemented
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	6	2	no	—
306	C₄⋊C₄	—	6	1	no	—
307	C₄⋊C₄	—	6	1	no	—
308	C₂²⋊C₄	—	6	2	no	—
309	C₂²⋊C₄	—	6	2	no	—
310	C₄²	C₃×D₁₂	1	1	yes	characteristic
311	C₄²	C₃×D₁₂	1	1	yes	characteristic
312	C₄²	C₃×#67	1	1	yes	characteristic
313	C₄²	C₃×#67	1	1	yes	characteristic
314	C₂²×C₃	—	2	1	no	—
315	C₂²×C₃	—	2	1	no	—
316	C₂²×C₃	—	2	1	no	—
317	C₂²×C₃	—	2	1	no	—
318	C₂²×C₃	—	2	1	no	—
319	C₂²×C₃	—	2	1	no	—
320	C₂²×C₃	—	2	1	no	—
321	C₂²×C₃	—	4	1	no	—
322	C₂²×C₃	—	4	1	no	—
323	C₂²×C₃	—	6	4	no	—
324	C₂²×C₃	—	12	4	no	—
325	C₂²×C₃	—	12	4	no	—
326	C₂²×C₃	—	12	2	no	—
327	C₂²×C₃	—	12	2	no	—
328	C₂²×C₃	C₄²×D₃	1	1	yes	characteristic
329	C₂²×C₃	#872	1	1	yes	characteristic
330	C₂²×C₃	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
331	C₂²×C₃	C₂×C₃×C₄²	1	1	yes	characteristic
332	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
333	C₂²×C₃	C₃×#117	1	1	yes	characteristic
334	C₂×D₃	—	2	4	no	—
335	C₂×D₃	—	4	4	no	—
336	C₂×D₃	—	4	2	no	—
337	C₂×D₃	—	4	2	no	—
338	C₂×D₃	—	4	4	no	—
339	C₃×C₄	—	2	2	no	—
340	C₃×C₄	—	2	1	no	—
341	C₃×C₄	—	2	1	no	—
342	C₃×C₄	—	2	1	no	—
343	C₃×C₄	—	2	1	no	—
344	C₃×C₄	—	2	1	no	—
345	C₃×C₄	—	2	1	no	—
346	C₃×C₄	—	2	2	no	—
347	C₃×C₄	—	2	2	no	—
348	C₃×C₄	—	2	2	no	—
349	C₃×C₄	—	4	1	no	—
350	C₃×C₄	—	4	1	no	—
351	C₃×C₄	—	12	2	no	—
352	C₃×C₄	#823	1	2	yes	direct product factor
353	C₃×C₄	C₃×#100	1	2	yes	complemented
354	C₃×C₄	C₄×D₁₂	1	2	yes	—
355	C₃×C₄	C₄×#67	1	2	yes	—
356	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
357	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
358	Dic₃	—	4	2	no	—
359	C₃²	C₄×#100	1	1	yes	characteristic, complemented, Sylow
360	C₂³	—	3	4	no	—
361	C₂³	—	6	2	no	—
362	C₂³	—	6	2	no	—
363	C₂³	—	12	2	no	—
364	C₂³	—	12	2	no	—
365	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
366	D₄	—	6	4	no	—
367	D₄	—	6	4	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	6	2	no	—
371	C₂×C₄	—	12	4	no	—
372	C₂×C₄	—	12	4	no	—
373	C₂×C₄	—	12	2	no	—
374	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
375	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
376	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
377	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
378	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
379	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
380	C₂×C₄	C₃×#235	1	2	yes	—
381	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
382	C₈	—	2	4	no	—
383	C₈	—	6	4	no	—
384	C₂×C₃	—	2	1	no	—
385	C₂×C₃	—	2	1	no	—
386	C₂×C₃	—	2	1	no	—
387	C₂×C₃	—	2	1	no	—
388	C₂×C₃	—	2	1	no	—
389	C₂×C₃	—	2	1	no	—
390	C₂×C₃	—	2	1	no	—
391	C₂×C₃	—	4	1	no	—
392	C₂×C₃	—	4	1	no	—
393	C₂×C₃	—	12	4	no	—
394	C₂×C₃	C₄×(C₂×D₃)⋊C₄	1	1	yes	characteristic
395	C₂×C₃	C₂×#823	1	1	yes	characteristic
396	C₂×C₃	#5132	1	1	yes	characteristic
397	C₂×C₃	C₃×C₄×C₂²⋊C₄	1	1	yes	characteristic
398	C₂×C₃	C₂×C₃×#100	1	1	yes	characteristic
399	C₂×C₃	C₃×#413	1	1	yes	characteristic
400	D₃	—	4	4	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	6	4	no	—
404	C₂²	—	12	4	no	—
405	C₂²	—	12	4	no	—
406	C₂²	—	12	2	no	—
407	C₂²	—	12	2	no	—
408	C₂²	C₃×C₄²×D₃	1	1	yes	characteristic
409	C₂²	C₃×#872	1	1	yes	characteristic
410	C₂²	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	12	2	no	—
415	C₄	C₃×#823	1	2	yes	direct product factor
416	C₄	C₃×C₄×D₁₂	1	2	yes	—
417	C₄	C₃×C₄×#67	1	2	yes	—
418	C₃	—	2	1	no	—
419	C₃	C₄×#823	1	1	yes	characteristic, direct product factor
420	C₃	C₃×C₄×#100	1	1	yes	characteristic, complemented
421	C₂	—	2	1	no	—
422	C₂	—	2	1	no	—
423	C₂	—	12	4	no	—
424	C₂	C₃×C₄×(C₂×D₃)⋊C₄	1	1	yes	characteristic
425	C₂	C₂×C₃×#823	1	1	yes	characteristic
426	C₂	C₃×#5132	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	(C₂×D₃)⋊C₄
commutator	C₂²×C₃	C₂×C₃×C₄²
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₃²×C₄×M₁₆	C₂
socle	C₂²×C₃²	C₂×C₂²⋊C₄
prime radical	C₂²×C₃×D₁₂	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₃
hypercenter	C₃×C₄×M₁₆	D₃
hypocenter	C₃	C₃×C₄×#100
LCS	G ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₃×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₃²×C₄×M₁₆	C₂	semidirect
4. C₃×C₄×#208	C₂	semidirect
5. C₃×#4554	C₂	semidirect
7. C₄×#823	C₃	direct (N × H)
21. C₃×#823	C₄	direct (N × H)
29. C₃×C₄×M₁₆	D₃	semidirect
30. C₃×C₄×M₁₆	C₂×C₃	semidirect
32. C₄×#208	C₂×C₃	semidirect
34. #4554	C₂×C₃	semidirect
48. C₃²×M₁₆	C₂×C₄	semidirect
59. C₃×#208	C₂×C₄	semidirect
95. #823	C₃×C₄	direct (N × H)
125. C₄×M₁₆	C₃×D₃	semidirect
160. C₃×M₁₆	C₄×D₃	semidirect
161. C₃×M₁₆	C₂×C₃×C₄	semidirect
187. #208	C₂×C₃×C₄	semidirect
202. C₃²×C₄	#100	semidirect
303. M₁₆	C₃×C₄×D₃	semidirect
352. C₃×C₄	#823	direct (N × H)
353. C₃×C₄	C₃×#100	semidirect
359. C₃²	C₄×#100	semidirect
415. C₄	C₃×#823	direct (N × H)
419. C₃	C₄×#823	direct (N × H)
420. C₃	C₃×C₄×#100	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×D₁₂	2
C₃²×C₄×M₁₆	2
C₂×C₃×#823	2
C₃×C₄×#208	2
C₃×#4554	2
C₃×C₄×#100	3
C₄×#823	3

Subgroups — C3×C4×#823 #11783777

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×#823 #11783777