Subgroups — C₃×C₄×#440 #10639108

Order 768.

1206 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#440	C₂	1	2	yes	maximal
2	C₂×C₃×C₄×SD₁₆	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄²×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄²×D₄	C₂	1	1	yes	maximal, characteristic
5	C₃×#1776	C₂	1	2	yes	maximal, complemented
6	C₃×C₄×#107	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#1763	C₂	1	2	yes	maximal, complemented
8	C₃×#1762	C₂	1	2	yes	maximal
9	C₃×C₄×#103	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₄×#102	C₂	1	1	yes	maximal, characteristic
11	C₃×C₄×#97	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#440	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂²×C₃×SD₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
16	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
18	C₂²×C₃×C₄²	—	2	1	no	—
19	C₃×#440	C₄	1	16	yes	direct product factor
20	C₃×C₄×SD₁₆	C₄	1	8	yes	complemented
21	C₂×C₃×#107	C₂²	1	2	yes	—
22	C₂×C₃×#106	C₂²	1	1	yes	characteristic
23	C₂×C₃×#103	C₂²	1	2	yes	—
24	C₂×C₃×#103	C₂²	1	1	yes	characteristic
25	C₂×C₃×#102	C₂²	1	2	yes	—
26	C₂×C₃×#102	C₂²	1	1	yes	characteristic
27	C₂×C₃×#97	C₂²	1	2	yes	—
28	C₂×C₃×#97	C₂²	1	2	yes	—
29	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
31	C₃×C₄×C₄⋊C₄	—	2	2	no	—
32	C₃×C₄×C₄⋊C₄	—	2	1	no	—
33	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
36	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
37	C₃×C₄×C₂²⋊C₄	—	2	2	no	—
38	C₃×C₄×C₂²⋊C₄	—	2	1	no	—
39	C₃×C₄³	—	2	1	no	—
40	C₃×C₄³	C₂²	1	1	yes	characteristic
41	C₃×#340	C₂²	1	2	yes	—
42	C₃×#340	C₂²	1	2	yes	—
43	C₃×#340	C₂²	1	2	yes	—
44	C₂×#440	C₂×C₃	1	2	yes	—
45	C₂×C₄×SD₁₆	C₂×C₃	1	1	yes	characteristic
46	C₄²×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
47	C₄²×D₄	C₂×C₃	1	1	yes	characteristic
48	#1776	C₂×C₃	1	2	yes	complemented
49	C₄×#107	C₂×C₃	1	1	yes	characteristic, complemented
50	#1763	C₂×C₃	1	2	yes	complemented
51	#1762	C₂×C₃	1	2	yes	—
52	C₄×#103	C₂×C₃	1	1	yes	characteristic, complemented
53	C₄×#102	C₂×C₃	1	1	yes	characteristic
54	C₄×#97	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
56	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
57	C₂³×C₃×C₄	—	2	2	no	—
58	C₂³×C₃×C₄	—	2	1	no	—
59	C₂×C₃×SD₁₆	C₂×C₄	1	4	yes	—
60	C₂×C₃×SD₁₆	C₂×C₄	1	8	yes	—
61	C₂²×C₃×C₈	C₂³	1	2	yes	—
62	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
64	C₃×C₄×Q₈	—	2	2	no	—
65	C₃×C₄×Q₈	—	2	4	no	—
66	C₃×C₄×Q₈	C₂×C₄	1	4	yes	complemented
67	C₃×C₄×Q₈	C₂×C₄	1	8	yes	complemented
68	C₃×C₄×D₄	—	2	2	no	—
69	C₃×C₄×D₄	—	2	4	no	—
70	C₃×C₄×D₄	C₂×C₄	1	4	yes	—
71	C₃×C₄×D₄	C₂×C₄	1	8	yes	—
72	C₂×C₃×C₄⋊C₄	—	2	1	no	—
73	C₂×C₃×C₄⋊C₄	—	2	2	no	—
74	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
75	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
76	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
78	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
79	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
80	C₂×C₃×C₄²	—	2	2	no	—
81	C₂×C₃×C₄²	—	2	1	no	—
82	C₂×C₃×C₄²	—	2	2	no	—
83	C₂×C₃×C₄²	—	2	2	no	—
84	C₂×C₃×C₄²	—	2	1	no	—
85	C₂×C₃×C₄²	—	2	1	no	—
86	C₂×C₃×C₄²	—	4	4	no	—
87	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
88	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
89	C₂×C₃×C₄²	D₄	1	2	yes	—
90	C₂×C₃×C₄²	C₂³	1	2	yes	—
91	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
92	C₃×#107	C₂×C₄	1	8	yes	complemented
93	C₃×#106	C₂×C₄	1	4	yes	complemented
94	C₃×#103	C₂×C₄	1	4	yes	complemented
95	C₃×#103	C₂×C₄	1	8	yes	complemented
96	C₃×#102	C₂×C₄	1	4	yes	—
97	C₃×#102	C₂×C₄	1	8	yes	—
98	C₃×#97	—	2	4	no	—
99	C₃×#97	C₂×C₄	1	8	yes	complemented
100	C₃×C₄×C₈	—	2	2	no	—
101	C₃×C₄×C₈	C₂×C₄	1	4	yes	complemented
102	C₃×#95	—	2	1	no	—
103	C₃×#95	—	2	2	no	—
104	C₃×#95	—	2	1	no	—
105	C₃×#95	—	2	2	no	—
106	C₂²×SD₁₆	C₂²×C₃	1	1	yes	characteristic
107	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
108	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
109	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
110	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
111	C₂²×C₄²	—	2	1	no	—
112	#440	C₃×C₄	1	16	yes	direct product factor
113	C₄×SD₁₆	C₃×C₄	1	8	yes	complemented
114	C₂×#107	C₂²×C₃	1	2	yes	—
115	C₂×#106	C₂²×C₃	1	1	yes	characteristic
116	C₂×#103	C₂²×C₃	1	1	yes	characteristic
117	C₂×#103	C₂²×C₃	1	2	yes	—
118	C₂×#102	C₂²×C₃	1	1	yes	characteristic
119	C₂×#102	C₂²×C₃	1	2	yes	—
120	C₂×#97	C₂²×C₃	1	2	yes	—
121	C₂×#97	C₂²×C₃	1	2	yes	—
122	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
123	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
124	C₄×C₄⋊C₄	—	2	1	no	—
125	C₄×C₄⋊C₄	—	2	2	no	—
126	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
127	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
128	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
129	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
130	C₄×C₂²⋊C₄	—	2	1	no	—
131	C₄×C₂²⋊C₄	—	2	2	no	—
132	C₄³	—	2	1	no	—
133	C₄³	C₂²×C₃	1	1	yes	characteristic
134	#340	C₂²×C₃	1	2	yes	—
135	#340	C₂²×C₃	1	2	yes	—
136	#340	C₂²×C₃	1	2	yes	—
137	C₂⁴×C₃	—	2	1	no	—
138	C₂×C₃×Q₈	—	2	1	no	—
139	C₂×C₃×Q₈	—	2	2	no	—
140	C₂×C₃×Q₈	C₂²×C₄	1	2	yes	—
141	C₂×C₃×Q₈	C₂²×C₄	1	4	yes	—
142	C₂×C₃×D₄	—	2	1	no	—
143	C₂×C₃×D₄	—	2	2	no	—
144	C₂×C₃×D₄	C₂²×C₄	1	2	yes	—
145	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
146	C₂²×C₃×C₄	—	2	1	no	—
147	C₂²×C₃×C₄	—	2	2	no	—
148	C₂²×C₃×C₄	—	2	1	no	—
149	C₂²×C₃×C₄	—	2	1	no	—
150	C₂²×C₃×C₄	—	2	2	no	—
151	C₂²×C₃×C₄	—	2	8	no	—
152	C₂²×C₃×C₄	—	2	4	no	—
153	C₂²×C₃×C₄	—	4	4	no	—
154	C₂²×C₃×C₄	—	4	4	no	—
155	C₂²×C₃×C₄	—	4	2	no	—
156	C₂²×C₃×C₄	—	4	2	no	—
157	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
159	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
160	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
162	C₃×SD₁₆	C₄²	1	16	yes	complemented
163	C₂×C₃×C₈	—	2	2	no	—
164	C₂×C₃×C₈	—	2	2	no	—
165	C₂×C₃×C₈	—	2	2	no	—
166	C₂×C₃×C₈	C₂²×C₄	1	2	yes	—
167	C₂×C₃×C₈	C₂²×C₄	1	4	yes	—
168	C₂×C₃×C₈	C₂²×C₄	1	2	yes	—
169	C₂×C₃×C₈	C₂²×C₄	1	4	yes	—
170	C₃×C₄⋊C₄	—	2	4	no	—
171	C₃×C₄⋊C₄	—	2	8	no	—
172	C₃×C₄⋊C₄	—	2	1	no	—
173	C₃×C₄⋊C₄	—	2	2	no	—
174	C₃×C₄⋊C₄	—	2	1	no	—
175	C₃×C₄⋊C₄	—	2	2	no	—
176	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
177	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
178	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
179	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
180	C₃×C₂²⋊C₄	—	2	8	no	—
181	C₃×C₂²⋊C₄	—	2	4	no	—
182	C₃×C₄²	—	2	8	no	—
183	C₃×C₄²	—	2	4	no	—
184	C₃×C₄²	—	2	2	no	—
185	C₃×C₄²	—	2	2	no	—
186	C₃×C₄²	—	4	2	no	—
187	C₃×C₄²	—	4	4	no	—
188	C₃×C₄²	—	4	4	no	—
189	C₃×C₄²	—	4	2	no	—
190	C₃×C₄²	—	4	2	no	—
191	C₃×C₄²	C₂²×C₄	1	2	yes	—
192	C₃×C₄²	C₂²×C₄	1	4	yes	—
193	C₃×C₄²	#41	1	2	yes	—
194	C₃×C₄²	#41	1	4	yes	—
195	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
196	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
197	C₂³×C₄	—	2	2	no	—
198	C₂³×C₄	—	2	1	no	—
199	C₂×SD₁₆	C₂×C₃×C₄	1	4	yes	—
200	C₂×SD₁₆	C₂×C₃×C₄	1	8	yes	—
201	C₂²×C₈	C₂³×C₃	1	2	yes	—
202	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
203	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
204	C₄×Q₈	—	2	2	no	—
205	C₄×Q₈	—	2	4	no	—
206	C₄×Q₈	C₂×C₃×C₄	1	4	yes	complemented
207	C₄×Q₈	C₂×C₃×C₄	1	8	yes	complemented
208	C₄×D₄	—	2	2	no	—
209	C₄×D₄	—	2	4	no	—
210	C₄×D₄	C₂×C₃×C₄	1	4	yes	—
211	C₄×D₄	C₂×C₃×C₄	1	8	yes	—
212	C₂×C₄⋊C₄	—	2	1	no	—
213	C₂×C₄⋊C₄	—	2	2	no	—
214	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
215	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
216	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
217	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
218	C₂×C₂²⋊C₄	—	2	1	no	—
219	C₂×C₂²⋊C₄	—	2	2	no	—
220	C₂×C₄²	—	2	2	no	—
221	C₂×C₄²	—	2	1	no	—
222	C₂×C₄²	—	2	2	no	—
223	C₂×C₄²	—	2	1	no	—
224	C₂×C₄²	—	2	2	no	—
225	C₂×C₄²	—	2	1	no	—
226	C₂×C₄²	—	4	4	no	—
227	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
228	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
229	C₂×C₄²	C₃×D₄	1	2	yes	—
230	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
231	C₂×C₄²	C₂³×C₃	1	2	yes	—
232	#107	C₂×C₃×C₄	1	8	yes	complemented
233	#106	C₂×C₃×C₄	1	4	yes	complemented
234	#103	C₂×C₃×C₄	1	4	yes	complemented
235	#103	C₂×C₃×C₄	1	8	yes	complemented
236	#102	C₂×C₃×C₄	1	4	yes	—
237	#102	C₂×C₃×C₄	1	8	yes	—
238	#97	—	2	4	no	—
239	#97	C₂×C₃×C₄	1	8	yes	complemented
240	C₄×C₈	—	2	2	no	—
241	C₄×C₈	C₂×C₃×C₄	1	4	yes	complemented
242	#95	—	2	1	no	—
243	#95	—	2	2	no	—
244	#95	—	2	1	no	—
245	#95	—	2	2	no	—
246	C₂³×C₃	—	2	2	no	—
247	C₂³×C₃	—	2	4	no	—
248	C₂³×C₃	—	4	1	no	—
249	C₂³×C₃	—	4	1	no	—
250	C₂³×C₃	—	4	2	no	—
251	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
252	C₃×Q₈	—	2	2	no	—
253	C₃×Q₈	—	2	4	no	—
254	C₃×Q₈	C₂×C₄²	1	4	yes	complemented
255	C₃×D₄	—	2	2	no	—
256	C₃×D₄	—	2	4	no	—
257	C₃×D₄	C₂×C₄²	1	4	yes	—
258	C₂×C₃×C₄	—	2	2	no	—
259	C₂×C₃×C₄	—	2	4	no	—
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	—	2	2	no	—
262	C₂×C₃×C₄	—	2	2	no	—
263	C₂×C₃×C₄	—	2	2	no	—
264	C₂×C₃×C₄	—	2	2	no	—
265	C₂×C₃×C₄	—	2	2	no	—
266	C₂×C₃×C₄	—	2	4	no	—
267	C₂×C₃×C₄	—	2	2	no	—
268	C₂×C₃×C₄	—	2	4	no	—
269	C₂×C₃×C₄	—	4	16	no	—
270	C₂×C₃×C₄	—	4	1	no	—
271	C₂×C₃×C₄	—	4	2	no	—
272	C₂×C₃×C₄	—	4	2	no	—
273	C₂×C₃×C₄	—	4	1	no	—
274	C₂×C₃×C₄	—	4	2	no	—
275	C₂×C₃×C₄	—	4	2	no	—
276	C₂×C₃×C₄	—	4	2	no	—
277	C₂×C₃×C₄	—	4	8	no	—
278	C₂×C₃×C₄	C₄×D₄	1	4	yes	—
279	C₂×C₃×C₄	C₄×D₄	1	2	yes	—
280	C₂×C₃×C₄	C₄×D₄	1	4	yes	—
281	C₂×C₃×C₄	C₄×D₄	1	2	yes	—
282	C₂×C₃×C₄	AGL(1,ℤ/8)	1	2	yes	—
283	C₂×C₃×C₄	#137	1	2	yes	—
284	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
286	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂×#41	1	2	yes	—
288	C₃×C₈	—	2	4	no	—
289	C₃×C₈	—	2	2	no	—
290	C₃×C₈	C₂×C₄²	1	4	yes	complemented
291	C₂⁴	—	2	1	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	C₂²×C₃×C₄	1	2	yes	—
295	C₂×Q₈	C₂²×C₃×C₄	1	4	yes	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	C₂²×C₃×C₄	1	2	yes	—
299	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	8	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	4	4	no	—
308	C₂²×C₄	—	4	4	no	—
309	C₂²×C₄	—	4	2	no	—
310	C₂²×C₄	—	4	2	no	—
311	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
313	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
314	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
315	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
316	SD₁₆	C₃×C₄²	1	16	yes	complemented
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	C₂²×C₃×C₄	1	2	yes	—
321	C₂×C₈	C₂²×C₃×C₄	1	4	yes	—
322	C₂×C₈	C₂²×C₃×C₄	1	2	yes	—
323	C₂×C₈	C₂²×C₃×C₄	1	4	yes	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	2	8	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	C₂²×C₃×C₄	1	2	yes	—
331	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
332	C₄⋊C₄	C₂²×C₃×C₄	1	2	yes	—
333	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
334	C₂²⋊C₄	—	2	8	no	—
335	C₂²⋊C₄	—	2	4	no	—
336	C₄²	—	2	8	no	—
337	C₄²	—	2	4	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	4	2	no	—
341	C₄²	—	4	4	no	—
342	C₄²	—	4	4	no	—
343	C₄²	—	4	2	no	—
344	C₄²	—	4	2	no	—
345	C₄²	C₂²×C₃×C₄	1	2	yes	—
346	C₄²	C₂²×C₃×C₄	1	4	yes	—
347	C₄²	C₃×#41	1	2	yes	—
348	C₄²	C₃×#41	1	4	yes	—
349	C₂²×C₃	—	2	4	no	—
350	C₂²×C₃	—	4	2	no	—
351	C₂²×C₃	—	4	2	no	—
352	C₂²×C₃	—	4	4	no	—
353	C₂²×C₃	—	4	4	no	—
354	C₂²×C₃	C₂×C₄×D₄	1	1	yes	characteristic
355	C₂²×C₃	C₂×C₄×D₄	1	2	yes	—
356	C₂²×C₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
357	C₂²×C₃	C₂×#137	1	1	yes	characteristic
358	C₂²×C₃	#575	1	2	yes	—
359	C₃×C₄	—	2	2	no	—
360	C₃×C₄	—	2	4	no	—
361	C₃×C₄	—	2	4	no	—
362	C₃×C₄	—	2	4	no	—
363	C₃×C₄	—	4	2	no	—
364	C₃×C₄	—	4	2	no	—
365	C₃×C₄	—	4	4	no	—
366	C₃×C₄	—	4	4	no	—
367	C₃×C₄	#440	1	4	yes	direct product factor
368	C₃×C₄	C₂²×C₄²	1	1	yes	characteristic
369	C₃×C₄	C₄×#41	1	2	yes	—
370	C₃×C₄	C₄×#41	1	1	yes	characteristic
371	C₂³	—	2	2	no	—
372	C₂³	—	2	4	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	2	no	—
376	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
377	Q₈	—	2	2	no	—
378	Q₈	—	2	4	no	—
379	Q₈	C₂×C₃×C₄²	1	4	yes	complemented
380	D₄	—	2	2	no	—
381	D₄	—	2	4	no	—
382	D₄	C₂×C₃×C₄²	1	4	yes	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	4	16	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	8	no	—
403	C₂×C₄	C₃×C₄×D₄	1	4	yes	—
404	C₂×C₄	C₃×C₄×D₄	1	2	yes	—
405	C₂×C₄	C₃×C₄×D₄	1	4	yes	—
406	C₂×C₄	C₃×C₄×D₄	1	2	yes	—
407	C₂×C₄	C₃×AGL(1,ℤ/8)	1	2	yes	—
408	C₂×C₄	C₃×#137	1	2	yes	—
409	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
410	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
411	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
412	C₂×C₄	C₂×C₃×#41	1	2	yes	—
413	C₈	—	2	4	no	—
414	C₈	—	2	2	no	—
415	C₈	C₂×C₃×C₄²	1	4	yes	complemented
416	C₂×C₃	—	4	4	no	—
417	C₂×C₃	C₄²×D₄	1	1	yes	characteristic
418	C₂×C₃	C₂×#440	1	1	yes	characteristic
419	C₂×C₃	#2943	1	1	yes	characteristic
420	C₂×C₃	C₄×AGL(1,ℤ/8)	1	2	yes	—
421	C₂×C₃	C₄×#137	1	2	yes	—
422	C₂²	—	2	4	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	4	4	no	—
426	C₂²	—	4	4	no	—
427	C₂²	C₂×C₃×C₄×D₄	1	1	yes	characteristic
428	C₂²	C₂×C₃×C₄×D₄	1	2	yes	—
429	C₂²	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
430	C₂²	C₂×C₃×#137	1	1	yes	characteristic
431	C₂²	C₃×#575	1	2	yes	—
432	C₄	—	2	2	no	—
433	C₄	—	2	4	no	—
434	C₄	—	2	4	no	—
435	C₄	—	2	4	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	4	no	—
439	C₄	—	4	4	no	—
440	C₄	C₃×#440	1	4	yes	direct product factor
441	C₄	C₂²×C₃×C₄²	1	1	yes	characteristic
442	C₄	C₃×C₄×#41	1	2	yes	—
443	C₄	C₃×C₄×#41	1	1	yes	characteristic
444	C₃	C₄×#440	1	1	yes	characteristic, direct product factor, Sylow
445	C₂	—	4	4	no	—
446	C₂	C₃×C₄²×D₄	1	1	yes	characteristic
447	C₂	C₂×C₃×#440	1	1	yes	characteristic
448	C₂	C₃×#2943	1	1	yes	characteristic
449	C₂	C₃×C₄×AGL(1,ℤ/8)	1	2	yes	—
450	C₂	C₃×C₄×#137	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄	C₂×D₄
commutator	C₄	C₂²×C₃×C₄²
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃
socle	C₂³×C₃	C₂²×D₄
prime radical	C₂²×C₃×D₄	C₂³
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₃×C₄³ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×C₄²×Q₈	C₂	semidirect
5. C₃×#1776	C₂	semidirect
6. C₃×C₄×#107	C₂	semidirect
7. C₃×#1763	C₂	semidirect
9. C₃×C₄×#103	C₂	semidirect
11. C₃×C₄×#97	C₂	semidirect
12. C₄×#440	C₃	direct (N × H)
19. C₃×#440	C₄	direct (N × H)
20. C₃×C₄×SD₁₆	C₄	semidirect
46. C₄²×Q₈	C₂×C₃	semidirect
48. #1776	C₂×C₃	semidirect
49. C₄×#107	C₂×C₃	semidirect
50. #1763	C₂×C₃	semidirect
52. C₄×#103	C₂×C₃	semidirect
54. C₄×#97	C₂×C₃	semidirect
66. C₃×C₄×Q₈	C₂×C₄	semidirect
67. C₃×C₄×Q₈	C₂×C₄	semidirect
92. C₃×#107	C₂×C₄	semidirect
93. C₃×#106	C₂×C₄	semidirect
94. C₃×#103	C₂×C₄	semidirect
95. C₃×#103	C₂×C₄	semidirect
99. C₃×#97	C₂×C₄	semidirect
101. C₃×C₄×C₈	C₂×C₄	semidirect
112. #440	C₃×C₄	direct (N × H)
113. C₄×SD₁₆	C₃×C₄	semidirect
162. C₃×SD₁₆	C₄²	semidirect
206. C₄×Q₈	C₂×C₃×C₄	semidirect
207. C₄×Q₈	C₂×C₃×C₄	semidirect
232. #107	C₂×C₃×C₄	semidirect
233. #106	C₂×C₃×C₄	semidirect
234. #103	C₂×C₃×C₄	semidirect
235. #103	C₂×C₃×C₄	semidirect
239. #97	C₂×C₃×C₄	semidirect
241. C₄×C₈	C₂×C₃×C₄	semidirect
254. C₃×Q₈	C₂×C₄²	semidirect
290. C₃×C₈	C₂×C₄²	semidirect
316. SD₁₆	C₃×C₄²	semidirect
367. C₃×C₄	#440	direct (N × H)
379. Q₈	C₂×C₃×C₄²	semidirect
415. C₈	C₂×C₃×C₄²	semidirect
440. C₄	C₃×#440	direct (N × H)
444. C₃	C₄×#440	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×#440	2
C₂×C₃×C₄×SD₁₆	2
C₃×C₄²×Q₈	2
C₃×C₄²×D₄	2
C₃×#1776	2
C₃×C₄×#107	2
C₃×#1763	2
C₃×#1762	2
C₃×C₄×#103	2
C₃×C₄×#102	2
C₃×C₄×#97	2
C₄×#440	3

Subgroups — C3×C4×#440 #10639108

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×#440 #10639108