Subgroups — C₂×#10589081 #11774181

Order 1152.

757 conjugacy classes of subgroups.

The subgroup lattice has 420 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	C₂×C₄⋊(C₃⋊(C₃⋊C₈))	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#10589081	C₂	1	4	yes	maximal, direct product factor
5	C₂×D₄⋊(C₃⋊C₈)	—	3	1	no	maximal
6	C₂×#4459	—	3	1	no	maximal
7	C₂²×C₃×D₁₂	C₄	1	1	yes	characteristic
8	C₂²×C₃×C₄×D₃	—	2	1	no	—
9	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
10	C₂²×C₃⋊(C₃⋊C₈)	—	2	1	no	—
11	C₂×C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
12	C₂×C₃×C₄⋊Dic₃	C₄	1	1	yes	characteristic
13	C₂²×C₃×C₃⋊C₈	—	2	1	no	—
14	C₃×C₄×D₁₂	—	2	1	no	—
15	C₃×C₄×D₁₂	—	2	1	no	—
16	C₃×C₄×D₁₂	C₄	1	2	yes	—
17	C₃×C₄×D₁₂	C₂²	1	2	yes	—
18	C₄⋊(C₃⋊(C₃⋊C₈))	—	2	1	no	—
19	C₄⋊(C₃⋊(C₃⋊C₈))	C₂²	1	2	yes	complemented
20	C₃×C₄×C₃⋊C₈	—	2	1	no	—
21	C₃×C₄×C₃⋊C₈	C₂²	1	2	yes	complemented
22	C₂×C₃×C₄×D₄	—	3	1	no	—
23	C₂×C₄×D₁₂	D₃	1	1	yes	characteristic
24	C₂×C₃×C₄×C₈	—	3	1	no	—
25	C₂×C₄⋊(C₃⋊C₈)	—	3	1	no	—
26	C₂×C₄⋊(C₃⋊C₈)	—	3	1	no	—
27	C₂×C₄⋊(C₃⋊C₈)	—	6	1	no	—
28	C₂×C₄×C₃⋊C₈	D₃	1	1	yes	characteristic, complemented
29	D₄⋊(C₃⋊C₈)	—	3	4	no	—
30	#4459	—	3	4	no	—
31	C₂³×C₃×D₃	—	2	1	no	—
32	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
34	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
35	C₂²×C₃×Dic₃	—	2	1	no	—
36	C₂×C₃×D₁₂	—	2	1	no	—
37	C₂×C₃×D₁₂	—	2	2	no	—
38	C₂×C₃×D₁₂	C₈	1	4	yes	complemented
39	C₂×C₃×D₁₂	C₂×C₄	1	2	yes	—
40	C₂×C₃×C₄×D₃	—	2	2	no	—
41	C₂×C₃×C₄×D₃	—	2	2	no	—
42	C₂×C₃×C₄×D₃	—	4	2	no	—
43	C₂×C₃×C₄×D₃	—	4	2	no	—
44	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
45	C₃²×C₄²	D₄	1	1	yes	characteristic
46	C₃²×C₄²	D₄	1	1	yes	characteristic
47	C₃²×C₄²	C₂³	1	1	yes	characteristic
48	C₂×C₃⋊(C₃⋊C₈)	—	2	2	no	—
49	C₂×C₃⋊(C₃⋊C₈)	—	4	2	no	—
50	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
51	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
52	C₃×C₄⋊Dic₃	—	2	1	no	—
53	C₃×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
54	C₂×C₃×C₃⋊C₈	—	2	4	no	—
55	C₂×C₃×C₃⋊C₈	—	2	2	no	—
56	C₂×D₄⋊C₈	—	9	1	no	Sylow
57	C₂²×C₃×D₄	—	3	1	no	—
58	C₂³×C₃×C₄	—	6	1	no	—
59	C₂²×D₁₂	Dic₃	1	1	yes	characteristic
60	C₂²×C₄×D₃	—	2	1	no	—
61	C₂²×C₃×C₈	—	6	1	no	—
62	C₃×C₄×D₄	—	3	2	no	—
63	C₃×C₄×D₄	—	3	2	no	—
64	C₃×C₄×D₄	—	6	1	no	—
65	C₃×C₄×D₄	—	6	1	no	—
66	C₂×C₃×C₄⋊C₄	—	3	1	no	—
67	C₂×C₃×C₂²⋊C₄	—	6	1	no	—
68	C₂×C₃×C₄²	—	2	1	no	—
69	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
70	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
71	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
72	C₂×C₄⋊Dic₃	Dic₃	1	1	yes	characteristic
73	C₂²×C₃⋊C₈	—	2	1	no	—
74	C₂²×C₃⋊C₈	—	6	2	no	—
75	C₂²×C₃⋊C₈	—	6	1	no	—
76	C₂²×C₃⋊C₈	—	6	1	no	—
77	C₄×D₁₂	—	2	1	no	—
78	C₄×D₁₂	—	2	1	no	—
79	C₄×D₁₂	Dic₃	1	2	yes	—
80	C₄×D₁₂	C₂×D₃	1	2	yes	—
81	C₃×C₄×C₈	—	3	2	no	—
82	C₃×C₄×C₈	—	6	1	no	—
83	C₄⋊(C₃⋊C₈)	—	3	2	no	—
84	C₄⋊(C₃⋊C₈)	—	3	2	no	—
85	C₄⋊(C₃⋊C₈)	—	6	2	no	—
86	C₄⋊(C₃⋊C₈)	—	6	2	no	—
87	C₄⋊(C₃⋊C₈)	—	6	1	no	—
88	C₄⋊(C₃⋊C₈)	—	6	1	no	—
89	C₄×C₃⋊C₈	—	2	1	no	—
90	C₄×C₃⋊C₈	C₂×D₃	1	2	yes	complemented
91	C₂³×C₃²	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₃×D₃	—	2	4	no	—
93	C₂²×C₃×D₃	—	2	2	no	—
94	C₂²×C₃×D₃	—	4	2	no	—
95	C₂²×C₃×D₃	—	4	2	no	—
96	C₂×C₃²×C₄	—	2	2	no	—
97	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₃²×C₄	C₂×C₈	1	2	yes	—
101	C₂×C₃²×C₄	M₁₆	1	2	yes	—
102	C₂×C₃²×C₄	D₈	1	2	yes	—
103	C₂×C₃²×C₄	SD₁₆	1	2	yes	—
104	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
106	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃×Dic₃	—	2	2	no	—
108	C₂×C₃×Dic₃	—	4	2	no	—
109	C₃×D₁₂	—	2	4	no	—
110	C₃×D₁₂	—	2	2	no	—
111	C₃×D₁₂	C₂×C₈	1	4	yes	complemented
112	C₃×C₄×D₃	—	4	4	no	—
113	C₃×C₄×D₃	—	4	2	no	—
114	C₃×C₄×D₃	—	4	2	no	—
115	C₃⋊(C₃⋊C₈)	—	4	2	no	—
116	C₃×C₃⋊C₈	—	2	4	no	—
117	C₂×C₄×D₄	—	3	1	no	—
118	C₂×C₄⋊C₈	—	9	1	no	—
119	C₂×C₄×C₈	—	3	1	no	—
120	D₄⋊C₈	—	9	4	no	—
121	C₂⁴×C₃	—	6	1	no	—
122	C₂³×D₃	—	2	1	no	—
123	C₂×C₃×D₄	—	3	4	no	—
124	C₂×C₃×D₄	—	3	2	no	—
125	C₂×C₃×D₄	—	6	2	no	—
126	C₂×C₃×D₄	—	6	1	no	—
127	C₂²×C₃×C₄	—	2	1	no	—
128	C₂²×C₃×C₄	—	2	1	no	—
129	C₂²×C₃×C₄	—	2	1	no	—
130	C₂²×C₃×C₄	—	6	1	no	—
131	C₂²×C₃×C₄	—	6	2	no	—
132	C₂²×C₃×C₄	—	6	2	no	—
133	C₂²×C₃×C₄	—	12	2	no	—
134	C₂²×C₃×C₄	—	12	2	no	—
135	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
136	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
137	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
138	C₂²×C₃×C₄	#67	1	1	yes	characteristic
139	C₂²×C₃×C₄	#67	1	1	yes	characteristic
140	C₂²×C₃×C₄	#67	1	1	yes	characteristic
141	C₂²×Dic₃	—	2	1	no	—
142	C₂×D₁₂	—	2	2	no	—
143	C₂×D₁₂	—	2	1	no	—
144	C₂×D₁₂	C₃⋊C₈	1	4	yes	complemented
145	C₂×D₁₂	C₂×Dic₃	1	2	yes	—
146	C₂×C₄×D₃	—	2	2	no	—
147	C₂×C₄×D₃	—	2	2	no	—
148	C₂×C₄×D₃	—	4	2	no	—
149	C₂×C₄×D₃	—	4	2	no	—
150	C₂×C₃×C₈	—	6	4	no	—
151	C₂×C₃×C₈	—	6	2	no	—
152	C₃×C₄⋊C₄	—	3	2	no	—
153	C₃×C₄⋊C₄	—	6	1	no	—
154	C₃×C₂²⋊C₄	—	6	2	no	—
155	C₃×C₂²⋊C₄	—	6	2	no	—
156	C₃×C₄²	—	2	1	no	—
157	C₃×C₄²	—	2	1	no	—
158	C₃×C₄²	—	2	1	no	—
159	C₃×C₄²	—	2	1	no	—
160	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
161	C₃×C₄²	D₁₂	1	1	yes	characteristic
162	C₃×C₄²	C₂×Dic₃	1	1	yes	characteristic
163	C₃×C₄²	#67	1	1	yes	characteristic
164	C₃×C₄²	#67	1	1	yes	characteristic
165	C₃×C₄²	#67	1	1	yes	characteristic
166	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
167	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
168	(C₂×D₃)⋊C₄	—	2	2	no	—
169	(C₂×D₃)⋊C₄	—	2	2	no	—
170	C₄⋊Dic₃	—	2	1	no	—
171	C₄⋊Dic₃	C₂×Dic₃	1	2	yes	—
172	C₂×C₃⋊C₈	—	2	4	no	—
173	C₂×C₃⋊C₈	—	2	2	no	—
174	C₂×C₃⋊C₈	—	6	4	no	—
175	C₂×C₃⋊C₈	—	6	2	no	—
176	C₂×C₃⋊C₈	—	6	2	no	—
177	C₂×C₃⋊C₈	—	12	4	no	—
178	C₂×C₃⋊C₈	—	12	2	no	—
179	C₂×C₃⋊C₈	—	12	2	no	—
180	C₂²×C₃²	C₂²⋊C₈	1	2	yes	—
181	C₂²×C₃²	#102	1	2	yes	—
182	C₂²×C₃²	#104	1	2	yes	—
183	C₂²×C₃²	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₃×D₃	—	2	4	no	—
185	C₂×C₃×D₃	—	4	8	no	—
186	C₂×C₃×D₃	—	4	2	no	—
187	C₂×C₃×D₃	—	4	2	no	—
188	C₃²×C₄	—	2	1	no	—
189	C₃²×C₄	—	2	1	no	—
190	C₃²×C₄	C₂²⋊C₈	1	2	yes	—
191	C₃²×C₄	#102	1	2	yes	—
192	C₃²×C₄	C₂²×C₈	1	1	yes	characteristic
193	C₃²×C₄	C₂×M₁₆	1	1	yes	characteristic
194	C₃²×C₄	C₂×D₈	1	1	yes	characteristic
195	C₃²×C₄	C₂×SD₁₆	1	1	yes	characteristic
196	C₃×Dic₃	—	4	2	no	—
197	C₂²×D₄	—	3	1	no	—
198	C₂³×C₄	—	6	1	no	—
199	C₂²×C₈	—	6	1	no	—
200	C₂²×C₈	—	18	1	no	—
201	C₄×D₄	—	3	2	no	—
202	C₄×D₄	—	3	2	no	—
203	C₄×D₄	—	6	1	no	—
204	C₄×D₄	—	6	1	no	—
205	C₂×C₄⋊C₄	—	3	1	no	—
206	C₂×C₂²⋊C₄	—	6	1	no	—
207	C₂×C₄²	D₃²	1	1	yes	characteristic
208	C₄⋊C₈	—	9	2	no	—
209	C₄⋊C₈	—	18	1	no	—
210	C₄×C₈	—	3	2	no	—
211	C₄×C₈	—	6	1	no	—
212	C₂³×C₃	—	2	1	no	—
213	C₂³×C₃	—	6	4	no	—
214	C₂³×C₃	—	6	2	no	—
215	C₂³×C₃	—	12	2	no	—
216	C₂³×C₃	—	12	2	no	—
217	C₂³×C₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
218	C₂³×C₃	#217	1	1	yes	characteristic
219	C₂²×D₃	—	2	4	no	—
220	C₂²×D₃	—	2	2	no	—
221	C₂²×D₃	—	4	2	no	—
222	C₂²×D₃	—	4	2	no	—
223	C₃×D₄	—	3	4	no	—
224	C₃×D₄	—	6	4	no	—
225	C₃×D₄	—	6	2	no	—
226	C₂×C₃×C₄	—	2	2	no	—
227	C₂×C₃×C₄	—	2	2	no	—
228	C₂×C₃×C₄	—	2	2	no	—
229	C₂×C₃×C₄	—	2	2	no	—
230	C₂×C₃×C₄	—	2	2	no	—
231	C₂×C₃×C₄	—	2	2	no	—
232	C₂×C₃×C₄	—	2	1	no	—
233	C₂×C₃×C₄	—	2	1	no	—
234	C₂×C₃×C₄	—	2	1	no	—
235	C₂×C₃×C₄	—	2	1	no	—
236	C₂×C₃×C₄	—	2	1	no	—
237	C₂×C₃×C₄	—	2	1	no	—
238	C₂×C₃×C₄	—	4	2	no	—
239	C₂×C₃×C₄	—	6	2	no	—
240	C₂×C₃×C₄	—	12	2	no	—
241	C₂×C₃×C₄	—	12	4	no	—
242	C₂×C₃×C₄	—	12	2	no	—
243	C₂×C₃×C₄	—	12	2	no	—
244	C₂×C₃×C₄	D₃×C₈	1	2	yes	—
245	C₂×C₃×C₄	ΓL(1,𝔽₂₅)	1	2	yes	—
246	C₂×C₃×C₄	#204	1	2	yes	—
247	C₂×C₃×C₄	D₂₄	1	2	yes	—
248	C₂×C₃×C₄	C₂×C₃⋊C₈	1	2	yes	—
249	C₂×C₃×C₄	#208	1	2	yes	—
250	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
251	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
252	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
253	C₂×C₃×C₄	#213	1	2	yes	—
254	C₂×C₃×C₄	#214	1	2	yes	—
255	C₂×C₃×C₄	#217	1	1	yes	characteristic
256	C₂×C₃×C₄	#217	1	1	yes	characteristic
257	C₂×C₃×C₄	#217	1	1	yes	characteristic
258	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
259	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
262	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
264	C₂×Dic₃	—	2	2	no	—
265	C₂×Dic₃	—	4	2	no	—
266	D₁₂	—	2	4	no	—
267	D₁₂	—	2	2	no	—
268	D₁₂	C₂×C₃⋊C₈	1	4	yes	complemented
269	C₄×D₃	—	4	4	no	—
270	C₄×D₃	—	4	2	no	—
271	C₄×D₃	—	4	2	no	—
272	C₃×C₈	—	6	4	no	—
273	C₃⋊C₈	—	2	4	no	—
274	C₃⋊C₈	—	12	4	no	—
275	C₃⋊C₈	—	12	2	no	—
276	C₃⋊C₈	—	12	2	no	—
277	C₂×C₃²	D₄⋊C₈	1	4	yes	complemented
278	C₂×C₃²	C₂×C₂²⋊C₈	1	1	yes	characteristic
279	C₂×C₃²	C₂×#102	1	1	yes	characteristic
280	C₂×C₃²	C₂×#104	1	1	yes	characteristic
281	C₃×D₃	—	4	4	no	—
282	C₂⁴	—	6	1	no	—
283	C₂×D₄	—	3	4	no	—
284	C₂×D₄	—	3	2	no	—
285	C₂×D₄	—	6	2	no	—
286	C₂×D₄	—	6	1	no	—
287	C₂²×C₄	—	6	1	no	—
288	C₂²×C₄	—	6	2	no	—
289	C₂²×C₄	—	6	2	no	—
290	C₂²×C₄	—	12	2	no	—
291	C₂²×C₄	—	12	2	no	—
292	C₂²×C₄	D₃×Dic₃	1	1	yes	characteristic
293	C₂²×C₄	#625	1	1	yes	characteristic
294	C₂²×C₄	#626	1	1	yes	characteristic
295	C₂×C₈	—	6	4	no	—
296	C₂×C₈	—	6	2	no	—
297	C₂×C₈	—	18	2	no	—
298	C₂×C₈	—	36	2	no	—
299	C₄⋊C₄	—	3	2	no	—
300	C₄⋊C₄	—	6	1	no	—
301	C₂²⋊C₄	—	6	2	no	—
302	C₂²⋊C₄	—	6	2	no	—
303	C₄²	D₃×Dic₃	1	1	yes	characteristic
304	C₄²	#625	1	1	yes	characteristic
305	C₄²	#626	1	1	yes	characteristic
306	C₄²	C₂×D₃²	1	1	yes	characteristic
307	C₂²×C₃	—	2	2	no	—
308	C₂²×C₃	—	2	2	no	—
309	C₂²×C₃	—	2	2	no	—
310	C₂²×C₃	—	2	1	no	—
311	C₂²×C₃	—	6	4	no	—
312	C₂²×C₃	—	12	2	no	—
313	C₂²×C₃	—	12	8	no	—
314	C₂²×C₃	—	12	2	no	—
315	C₂²×C₃	#805	1	2	yes	—
316	C₂²×C₃	(C₂×D₃)⋊C₈	1	2	yes	—
317	C₂²×C₃	#821	1	2	yes	—
318	C₂²×C₃	#830	1	2	yes	—
319	C₂²×C₃	#832	1	2	yes	—
320	C₂²×C₃	#837	1	2	yes	—
321	C₂²×C₃	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
322	C₂²×C₃	C₂×#217	1	1	yes	characteristic
323	C₂×D₃	—	2	4	no	—
324	C₂×D₃	—	4	2	no	—
325	C₂×D₃	—	4	2	no	—
326	C₂×D₃	—	4	8	no	—
327	C₃×C₄	—	2	1	no	—
328	C₃×C₄	—	2	1	no	—
329	C₃×C₄	—	2	1	no	—
330	C₃×C₄	—	2	1	no	—
331	C₃×C₄	—	2	2	no	—
332	C₃×C₄	—	2	1	no	—
333	C₃×C₄	—	2	2	no	—
334	C₃×C₄	—	2	1	no	—
335	C₃×C₄	—	2	1	no	—
336	C₃×C₄	—	2	1	no	—
337	C₃×C₄	—	4	1	no	—
338	C₃×C₄	—	4	1	no	—
339	C₃×C₄	—	12	2	no	—
340	C₃×C₄	(C₂×D₃)⋊C₈	1	2	yes	—
341	C₃×C₄	#821	1	2	yes	—
342	C₃×C₄	#830	1	2	yes	—
343	C₃×C₄	#832	1	2	yes	—
344	C₃×C₄	C₂×D₃×C₈	1	1	yes	characteristic
345	C₃×C₄	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
346	C₃×C₄	C₂×#204	1	1	yes	characteristic
347	C₃×C₄	C₂×D₂₄	1	1	yes	characteristic
348	C₃×C₄	C₂²×C₃⋊C₈	1	1	yes	characteristic
349	C₃×C₄	C₂×#208	1	1	yes	characteristic
350	C₃×C₄	C₂×#213	1	1	yes	characteristic
351	C₃×C₄	C₂×#214	1	1	yes	characteristic
352	Dic₃	—	4	2	no	—
353	C₃²	C₂×D₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
354	C₂³	—	6	4	no	—
355	C₂³	—	6	2	no	—
356	C₂³	—	12	2	no	—
357	C₂³	—	12	2	no	—
358	C₂³	(C₂×D₃)⋊Dic₃	1	1	yes	characteristic
359	D₄	—	3	4	no	—
360	D₄	—	6	4	no	—
361	D₄	—	6	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	6	2	no	—
364	C₂×C₄	—	12	2	no	—
365	C₂×C₄	—	12	4	no	—
366	C₂×C₄	—	12	2	no	—
367	C₂×C₄	—	12	2	no	—
368	C₂×C₄	D₃×C₃⋊C₈	1	2	yes	—
369	C₂×C₄	#3711	1	2	yes	—
370	C₂×C₄	#3714	1	2	yes	—
371	C₂×C₄	#3716	1	2	yes	—
372	C₂×C₄	(C₂×D₃)⋊Dic₃	1	1	yes	characteristic
373	C₂×C₄	(C₂×D₃)⋊Dic₃	1	1	yes	characteristic
374	C₂×C₄	(C₂×D₃)⋊Dic₃	1	1	yes	characteristic
375	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
376	C₂×C₄	C₂×#625	1	1	yes	characteristic
377	C₂×C₄	C₂×#626	1	1	yes	characteristic
378	C₈	—	6	4	no	—
379	C₈	—	36	2	no	—
380	C₂×C₃	—	2	1	no	—
381	C₂×C₃	—	2	1	no	—
382	C₂×C₃	—	2	1	no	—
383	C₂×C₃	—	2	4	no	—
384	C₂×C₃	—	12	4	no	—
385	C₂×C₃	#4459	1	4	yes	complemented
386	C₂×C₃	D₄⋊(C₃⋊C₈)	1	4	yes	complemented
387	C₂×C₃	C₂×#805	1	1	yes	characteristic
388	C₂×C₃	C₂×(C₂×D₃)⋊C₈	1	1	yes	characteristic
389	C₂×C₃	C₂×#821	1	1	yes	characteristic
390	C₂×C₃	C₂×#830	1	1	yes	characteristic
391	C₂×C₃	C₂×#832	1	1	yes	characteristic
392	C₂×C₃	C₂×#837	1	1	yes	characteristic
393	D₃	—	4	4	no	—
394	C₂²	—	6	4	no	—
395	C₂²	—	12	2	no	—
396	C₂²	—	12	2	no	—
397	C₂²	—	12	8	no	—
398	C₂²	(C₂×D₃)⋊(C₃⋊C₈)	1	2	yes	—
399	C₂²	#63563	1	2	yes	—
400	C₂²	#63569	1	2	yes	—
401	C₂²	C₂×(C₂×D₃)⋊Dic₃	1	1	yes	characteristic
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	12	2	no	—
405	C₄	(C₂×D₃)⋊(C₃⋊C₈)	1	2	yes	—
406	C₄	#63563	1	2	yes	—
407	C₄	C₂×D₃×C₃⋊C₈	1	1	yes	characteristic
408	C₄	C₂×#3711	1	1	yes	characteristic
409	C₄	C₂×#3714	1	1	yes	characteristic
410	C₄	C₂×#3716	1	1	yes	characteristic
411	C₃	—	2	1	no	—
412	C₃	C₂×#4459	1	1	yes	characteristic, complemented
413	C₃	C₂×D₄⋊(C₃⋊C₈)	1	1	yes	characteristic, complemented
414	C₂	—	12	4	no	—
415	C₂	#10589081	1	4	yes	direct product factor
416	C₂	C₂×(C₂×D₃)⋊(C₃⋊C₈)	1	1	yes	characteristic
417	C₂	C₂×#63563	1	1	yes	characteristic
418	C₂	C₂×#63569	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	#626
commutator	C₃²×C₄	C₂²×C₈
Frattini	C₄²	C₂×D₃²
Fitting	C₂×C₃²×C₄²	C₂²
socle	C₂³×C₃²	C₂²⋊C₄
prime radical	C₂²×C₃×D₁₂	C₄
cosocle	C₃²×C₄²	C₂³
hypercenter	C₂×C₄²	D₃²
hypocenter	C₃²	C₂×D₄⋊C₈
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂×C₄⋊(C₃⋊(C₃⋊C₈))	C₂	semidirect
3. C₂×C₃×C₄×C₃⋊C₈	C₂	semidirect
4. #10589081	C₂	direct (N × H)
19. C₄⋊(C₃⋊(C₃⋊C₈))	C₂²	semidirect
21. C₃×C₄×C₃⋊C₈	C₂²	semidirect
28. C₂×C₄×C₃⋊C₈	D₃	semidirect
38. C₂×C₃×D₁₂	C₈	semidirect
90. C₄×C₃⋊C₈	C₂×D₃	semidirect
111. C₃×D₁₂	C₂×C₈	semidirect
144. C₂×D₁₂	C₃⋊C₈	semidirect
268. D₁₂	C₂×C₃⋊C₈	semidirect
277. C₂×C₃²	D₄⋊C₈	semidirect
353. C₃²	C₂×D₄⋊C₈	semidirect
385. C₂×C₃	#4459	semidirect
386. C₂×C₃	D₄⋊(C₃⋊C₈)	semidirect
412. C₃	C₂×#4459	semidirect
413. C₃	C₂×D₄⋊(C₃⋊C₈)	semidirect
415. C₂	#10589081	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×C₄×D₁₂	2
C₂×C₄⋊(C₃⋊(C₃⋊C₈))	2
C₂×C₃×C₄×C₃⋊C₈	2
#10589081	2
C₂×D₄⋊(C₃⋊C₈)	3
C₂×#4459	3

Subgroups — C2×#10589081 #11774181

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10589081 #11774181