Subgroups — C₂×C₃×#2925 #10678729

Order 768.

2178 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×#41	C₂	1	1	yes	maximal, characteristic
2	C₃×#2925	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₃×#433	C₂	1	4	yes	maximal, complemented
4	C₂×C₃×#432	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#431	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#423	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#408	C₂	1	2	yes	maximal
9	C₂×C₃×#405	C₂	1	2	yes	maximal, complemented
10	C₂×#2925	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
12	C₂²×C₃×M₁₆	C₂²	1	2	yes	—
13	C₂³×C₃×C₈	C₂²	1	2	yes	—
14	C₃×C₄×#41	C₄	1	8	yes	—
15	C₃×C₄×#41	C₂²	1	8	yes	—
16	C₂×C₃×C₄×Q₈	C₄	1	1	yes	characteristic
17	C₂×C₃×C₄×Q₈	C₄	1	1	yes	characteristic
18	C₂×C₃×C₄×D₄	C₄	1	2	yes	—
19	C₂×C₃×C₄×D₄	C₄	1	1	yes	characteristic
20	C₂×C₃×C₄×D₄	C₄	1	2	yes	—
21	C₂×C₃×C₄×D₄	C₄	1	1	yes	characteristic
22	C₂×C₃×#117	C₂²	1	1	yes	characteristic
23	C₂×C₃×#117	C₂²	1	2	yes	—
24	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
25	C₂²×C₃×C₄²	C₂²	1	2	yes	—
26	C₃×#433	C₂²	1	32	yes	complemented
27	C₃×#432	C₂²	1	16	yes	complemented
28	C₃×#431	C₂²	1	16	yes	complemented
29	C₃×#423	C₂²	1	8	yes	complemented
30	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄⋊C₈	C₂²	1	2	yes	—
33	C₂×C₃×C₄⋊C₈	C₂²	1	2	yes	—
34	C₂×C₃×C₄⋊C₈	C₂²	1	2	yes	—
35	C₂×C₃×C₄⋊C₈	C₂²	1	8	yes	complemented
36	C₃×#408	C₂²	1	16	yes	—
37	C₂×C₃×C₂²⋊C₈	C₂²	1	4	yes	—
38	C₂×C₃×C₂²⋊C₈	C₂²	1	4	yes	—
39	C₃×#405	C₂²	1	16	yes	complemented
40	C₂×C₃×#97	C₂²	1	4	yes	—
41	C₂×C₃×C₄×C₈	C₂²	1	4	yes	—
42	C₂×C₄×#41	C₂×C₃	1	1	yes	characteristic
43	#2925	C₂×C₃	1	16	yes	direct product factor
44	C₂×#433	C₂×C₃	1	4	yes	complemented
45	C₂×#432	C₂×C₃	1	2	yes	complemented
46	C₂×#431	C₂×C₃	1	2	yes	complemented
47	C₂×#423	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂²×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂×#408	C₂×C₃	1	2	yes	—
50	C₂×#405	C₂×C₃	1	2	yes	complemented
51	C₂×C₃×#41	—	2	4	no	—
52	C₂×C₃×#41	—	2	4	no	—
53	C₂×C₃×#41	C₂×C₄	1	4	yes	—
54	C₂×C₃×#41	C₂³	1	4	yes	—
55	C₂²×C₃×Q₈	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₃×D₄	C₂×C₄	1	2	yes	—
57	C₂²×C₃×D₄	C₂×C₄	1	1	yes	characteristic
58	C₂³×C₃×C₄	C₂×C₄	1	2	yes	—
59	C₂³×C₃×C₄	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₃×C₄	C₂×C₄	1	2	yes	—
61	C₂³×C₃×C₄	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₃×C₄	C₂³	1	2	yes	—
63	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
64	C₂×C₃×M₁₆	—	2	8	no	—
65	C₂×C₃×M₁₆	C₂³	1	8	yes	—
66	C₂²×C₃×C₈	—	2	8	no	—
67	C₂²×C₃×C₈	C₂³	1	8	yes	—
68	C₂²×C₃×C₈	C₂³	1	2	yes	—
69	C₂²×C₃×C₈	C₂³	1	2	yes	—
70	C₂²×C₃×C₈	C₂³	1	4	yes	—
71	C₃×C₄×Q₈	C₂×C₄	1	8	yes	—
72	C₃×C₄×Q₈	C₂×C₄	1	8	yes	—
73	C₃×C₄×D₄	C₂×C₄	1	16	yes	—
74	C₃×C₄×D₄	C₂×C₄	1	8	yes	—
75	C₃×C₄×D₄	C₂×C₄	1	16	yes	—
76	C₃×C₄×D₄	C₂×C₄	1	8	yes	—
77	C₃×#117	C₂×C₄	1	8	yes	—
78	C₃×#117	C₂×C₄	1	4	yes	—
79	C₃×#117	C₂³	1	4	yes	—
80	C₃×#117	C₂³	1	8	yes	—
81	C₂×C₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
82	C₂×C₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
83	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
84	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
85	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
86	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
87	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
88	C₂×C₃×C₄²	C₂×C₄	1	2	yes	—
89	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
90	C₂×C₃×C₄²	C₂×C₄	1	2	yes	—
91	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
92	C₂×C₃×C₄²	C₂×C₄	1	8	yes	—
93	C₂×C₃×C₄²	C₂×C₄	1	4	yes	—
94	C₂×C₃×C₄²	C₂³	1	4	yes	—
95	C₂×C₃×C₄²	C₂³	1	8	yes	—
96	C₂×C₃×C₄²	C₂³	1	2	yes	—
97	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
98	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
99	C₃×C₄⋊C₈	C₂³	1	4	yes	—
100	C₃×C₄⋊C₈	C₂³	1	4	yes	—
101	C₃×C₄⋊C₈	C₂³	1	8	yes	—
102	C₃×C₄⋊C₈	C₂³	1	8	yes	—
103	C₃×C₄⋊C₈	C₂³	1	8	yes	—
104	C₃×C₂²⋊C₈	C₂³	1	16	yes	—
105	C₃×C₂²⋊C₈	C₂³	1	16	yes	—
106	C₃×#97	C₂³	1	16	yes	—
107	C₃×C₄×C₈	C₂³	1	16	yes	—
108	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
109	C₂²×M₁₆	C₂²×C₃	1	2	yes	—
110	C₂³×C₈	C₂²×C₃	1	2	yes	—
111	C₄×#41	C₃×C₄	1	8	yes	—
112	C₄×#41	C₂²×C₃	1	8	yes	—
113	C₂×C₄×Q₈	C₃×C₄	1	1	yes	characteristic
114	C₂×C₄×Q₈	C₃×C₄	1	1	yes	characteristic
115	C₂×C₄×D₄	C₃×C₄	1	2	yes	—
116	C₂×C₄×D₄	C₃×C₄	1	1	yes	characteristic
117	C₂×C₄×D₄	C₃×C₄	1	2	yes	—
118	C₂×C₄×D₄	C₃×C₄	1	1	yes	characteristic
119	C₂×#117	C₂²×C₃	1	1	yes	characteristic
120	C₂×#117	C₂²×C₃	1	2	yes	—
121	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
122	C₂²×C₄²	C₂²×C₃	1	2	yes	—
123	#433	C₂²×C₃	1	32	yes	complemented
124	#432	C₂²×C₃	1	16	yes	complemented
125	#431	C₂²×C₃	1	16	yes	complemented
126	#423	C₂²×C₃	1	8	yes	complemented
127	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
128	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
129	C₂×C₄⋊C₈	C₂²×C₃	1	2	yes	—
130	C₂×C₄⋊C₈	C₂²×C₃	1	2	yes	—
131	C₂×C₄⋊C₈	C₂²×C₃	1	2	yes	—
132	C₂×C₄⋊C₈	C₂²×C₃	1	8	yes	complemented
133	#408	C₂²×C₃	1	16	yes	—
134	C₂×C₂²⋊C₈	C₂²×C₃	1	4	yes	—
135	C₂×C₂²⋊C₈	C₂²×C₃	1	4	yes	—
136	#405	C₂²×C₃	1	16	yes	complemented
137	C₂×#97	C₂²×C₃	1	4	yes	—
138	C₂×C₄×C₈	C₂²×C₃	1	4	yes	—
139	C₂⁴×C₃	C₂²×C₄	1	2	yes	—
140	C₂⁴×C₃	C₂²×C₄	1	1	yes	characteristic
141	C₃×#41	—	2	16	no	—
142	C₃×#41	—	2	8	no	—
143	C₃×#41	—	2	8	no	—
144	C₂×C₃×Q₈	—	2	4	no	—
145	C₂×C₃×Q₈	C₂²×C₄	1	4	yes	—
146	C₂×C₃×D₄	—	2	8	no	—
147	C₂×C₃×D₄	—	2	4	no	—
148	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
149	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
150	C₂²×C₃×C₄	—	2	4	no	—
151	C₂²×C₃×C₄	—	2	8	no	—
152	C₂²×C₃×C₄	—	2	4	no	—
153	C₂²×C₃×C₄	—	2	4	no	—
154	C₂²×C₃×C₄	—	4	2	no	—
155	C₂²×C₃×C₄	—	4	4	no	—
156	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
158	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
159	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
160	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
162	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
164	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
165	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
166	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
167	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₃×C₄	C₂²×C₄	1	2	yes	—
169	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₃×C₄	#41	1	4	yes	—
171	C₂²×C₃×C₄	#41	1	4	yes	—
172	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
173	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
174	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
175	C₃×M₁₆	—	2	16	no	—
176	C₂×C₃×C₈	—	2	4	no	—
177	C₂×C₃×C₈	—	2	4	no	—
178	C₂×C₃×C₈	—	2	16	no	—
179	C₂×C₃×C₈	—	2	8	no	—
180	C₂×C₃×C₈	C₂⁴	1	4	yes	—
181	C₂×C₃×C₈	C₂⁴	1	8	yes	—
182	C₂×C₃×C₈	C₂⁴	1	4	yes	—
183	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
184	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
185	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
186	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
187	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
188	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
189	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
190	C₃×C₄²	C₂²×C₄	1	2	yes	—
191	C₃×C₄²	C₂²×C₄	1	4	yes	—
192	C₃×C₄²	C₂²×C₄	1	2	yes	—
193	C₃×C₄²	C₂²×C₄	1	8	yes	—
194	C₃×C₄²	C₂²×C₄	1	4	yes	—
195	C₃×C₄²	C₂²×C₄	1	8	yes	—
196	C₃×C₄²	C₂²×C₄	1	4	yes	—
197	C₃×C₄²	C₂⁴	1	4	yes	—
198	C₃×C₄²	C₂⁴	1	2	yes	—
199	C₃×C₄²	C₂⁴	1	2	yes	—
200	C₂×#41	—	2	4	no	—
201	C₂×#41	—	2	4	no	—
202	C₂×#41	C₂×C₃×C₄	1	4	yes	—
203	C₂×#41	C₂³×C₃	1	4	yes	—
204	C₂²×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
205	C₂²×D₄	C₂×C₃×C₄	1	2	yes	—
206	C₂²×D₄	C₂×C₃×C₄	1	1	yes	characteristic
207	C₂³×C₄	C₂×C₃×C₄	1	2	yes	—
208	C₂³×C₄	C₂×C₃×C₄	1	1	yes	characteristic
209	C₂³×C₄	C₂×C₃×C₄	1	2	yes	—
210	C₂³×C₄	C₂×C₃×C₄	1	1	yes	characteristic
211	C₂³×C₄	C₂³×C₃	1	2	yes	—
212	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
213	C₂×M₁₆	—	2	8	no	—
214	C₂×M₁₆	C₂³×C₃	1	8	yes	—
215	C₂²×C₈	—	2	8	no	—
216	C₂²×C₈	C₂³×C₃	1	2	yes	—
217	C₂²×C₈	C₂³×C₃	1	2	yes	—
218	C₂²×C₈	C₂³×C₃	1	8	yes	—
219	C₂²×C₈	C₂³×C₃	1	4	yes	—
220	C₄×Q₈	C₂×C₃×C₄	1	8	yes	—
221	C₄×Q₈	C₂×C₃×C₄	1	8	yes	—
222	C₄×D₄	C₂×C₃×C₄	1	16	yes	—
223	C₄×D₄	C₂×C₃×C₄	1	8	yes	—
224	C₄×D₄	C₂×C₃×C₄	1	16	yes	—
225	C₄×D₄	C₂×C₃×C₄	1	8	yes	—
226	#117	C₂×C₃×C₄	1	8	yes	—
227	#117	C₂×C₃×C₄	1	4	yes	—
228	#117	C₂³×C₃	1	4	yes	—
229	#117	C₂³×C₃	1	8	yes	—
230	C₂×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
231	C₂×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
232	C₂×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
233	C₂×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
234	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
235	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
236	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
237	C₂×C₄²	C₂×C₃×C₄	1	2	yes	—
238	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
239	C₂×C₄²	C₂×C₃×C₄	1	2	yes	—
240	C₂×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
241	C₂×C₄²	C₂×C₃×C₄	1	8	yes	—
242	C₂×C₄²	C₂×C₃×C₄	1	4	yes	—
243	C₂×C₄²	C₂³×C₃	1	2	yes	—
244	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
245	C₂×C₄²	C₂³×C₃	1	4	yes	—
246	C₂×C₄²	C₂³×C₃	1	8	yes	—
247	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
248	C₄⋊C₈	C₂³×C₃	1	4	yes	—
249	C₄⋊C₈	C₂³×C₃	1	4	yes	—
250	C₄⋊C₈	C₂³×C₃	1	8	yes	—
251	C₄⋊C₈	C₂³×C₃	1	8	yes	—
252	C₄⋊C₈	C₂³×C₃	1	8	yes	—
253	C₂²⋊C₈	C₂³×C₃	1	16	yes	—
254	C₂²⋊C₈	C₂³×C₃	1	16	yes	—
255	#97	C₂³×C₃	1	16	yes	—
256	C₄×C₈	C₂³×C₃	1	16	yes	—
257	C₂³×C₃	—	2	2	no	—
258	C₂³×C₃	—	2	2	no	—
259	C₂³×C₃	—	2	4	no	—
260	C₂³×C₃	—	2	4	no	—
261	C₂³×C₃	—	2	4	no	—
262	C₂³×C₃	#117	1	4	yes	—
263	C₂³×C₃	C₂³×C₄	1	4	yes	—
264	C₂³×C₃	C₂³×C₄	1	2	yes	—
265	C₂³×C₃	C₂³×C₄	1	1	yes	characteristic
266	C₃×Q₈	—	2	8	no	—
267	C₃×D₄	—	2	16	no	—
268	C₃×D₄	—	2	8	no	—
269	C₂×C₃×C₄	—	2	4	no	—
270	C₂×C₃×C₄	—	2	2	no	—
271	C₂×C₃×C₄	—	2	4	no	—
272	C₂×C₃×C₄	—	2	2	no	—
273	C₂×C₃×C₄	—	2	2	no	—
274	C₂×C₃×C₄	—	2	4	no	—
275	C₂×C₃×C₄	—	2	8	no	—
276	C₂×C₃×C₄	—	2	8	no	—
277	C₂×C₃×C₄	—	2	16	no	—
278	C₂×C₃×C₄	—	2	4	no	—
279	C₂×C₃×C₄	—	2	4	no	—
280	C₂×C₃×C₄	—	4	4	no	—
281	C₂×C₃×C₄	—	4	8	no	—
282	C₂×C₃×C₄	#117	1	4	yes	—
283	C₂×C₃×C₄	#117	1	8	yes	—
284	C₂×C₃×C₄	#131	1	4	yes	—
285	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
286	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
287	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
288	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
289	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
290	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
291	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
292	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
293	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
294	C₂×C₃×C₄	C₂×#41	1	2	yes	—
295	C₂×C₃×C₄	C₂×#41	1	2	yes	—
296	C₂×C₃×C₄	C₂×#41	1	4	yes	—
297	C₂×C₃×C₄	C₂×#41	1	4	yes	—
298	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
299	C₃×C₈	—	2	4	no	—
300	C₃×C₈	—	2	4	no	—
301	C₃×C₈	—	2	8	no	—
302	C₂⁴	C₂²×C₃×C₄	1	2	yes	—
303	C₂⁴	C₂²×C₃×C₄	1	1	yes	characteristic
304	#41	—	2	16	no	—
305	#41	—	2	8	no	—
306	#41	—	2	8	no	—
307	C₂×Q₈	—	2	4	no	—
308	C₂×Q₈	C₂²×C₃×C₄	1	4	yes	—
309	C₂×D₄	—	2	8	no	—
310	C₂×D₄	—	2	4	no	—
311	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
312	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	8	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	4	2	no	—
318	C₂²×C₄	—	4	4	no	—
319	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
320	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
321	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
322	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
323	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
324	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
325	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
326	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
327	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
328	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
329	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
330	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
331	C₂²×C₄	C₂²×C₃×C₄	1	2	yes	—
332	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
333	C₂²×C₄	C₃×#41	1	4	yes	—
334	C₂²×C₄	C₃×#41	1	4	yes	—
335	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
336	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
337	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
338	M₁₆	—	2	16	no	—
339	C₂×C₈	—	2	4	no	—
340	C₂×C₈	—	2	4	no	—
341	C₂×C₈	—	2	16	no	—
342	C₂×C₈	—	2	8	no	—
343	C₂×C₈	C₂⁴×C₃	1	4	yes	—
344	C₂×C₈	C₂⁴×C₃	1	8	yes	—
345	C₂×C₈	C₂⁴×C₃	1	4	yes	—
346	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
347	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
348	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
349	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
350	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
351	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
352	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
353	C₄²	C₂²×C₃×C₄	1	2	yes	—
354	C₄²	C₂²×C₃×C₄	1	4	yes	—
355	C₄²	C₂²×C₃×C₄	1	2	yes	—
356	C₄²	C₂²×C₃×C₄	1	8	yes	—
357	C₄²	C₂²×C₃×C₄	1	4	yes	—
358	C₄²	C₂²×C₃×C₄	1	8	yes	—
359	C₄²	C₂²×C₃×C₄	1	4	yes	—
360	C₄²	C₂⁴×C₃	1	4	yes	—
361	C₄²	C₂⁴×C₃	1	2	yes	—
362	C₄²	C₂⁴×C₃	1	2	yes	—
363	C₂²×C₃	—	2	8	no	—
364	C₂²×C₃	—	2	2	no	—
365	C₂²×C₃	—	2	2	no	—
366	C₂²×C₃	—	2	4	no	—
367	C₂²×C₃	—	2	4	no	—
368	C₂²×C₃	—	2	4	no	—
369	C₂²×C₃	—	4	8	no	—
370	C₂²×C₃	C₂×#117	1	4	yes	—
371	C₂²×C₃	C₂×#117	1	2	yes	—
372	C₂²×C₃	C₂×#131	1	2	yes	—
373	C₂²×C₃	#568	1	2	yes	—
374	C₂²×C₃	C₂⁴×C₄	1	1	yes	characteristic
375	C₃×C₄	—	2	4	no	—
376	C₃×C₄	—	2	2	no	—
377	C₃×C₄	—	2	4	no	—
378	C₃×C₄	—	2	2	no	—
379	C₃×C₄	—	2	2	no	—
380	C₃×C₄	—	2	4	no	—
381	C₃×C₄	C₂×#117	1	2	yes	—
382	C₃×C₄	C₂×#117	1	4	yes	—
383	C₃×C₄	C₂×#131	1	4	yes	—
384	C₃×C₄	C₂²×#41	1	1	yes	characteristic
385	C₃×C₄	C₂²×#41	1	1	yes	characteristic
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	4	no	—
389	C₂³	—	2	4	no	—
390	C₂³	—	2	4	no	—
391	C₂³	C₃×#117	1	4	yes	—
392	C₂³	C₂³×C₃×C₄	1	4	yes	—
393	C₂³	C₂³×C₃×C₄	1	2	yes	—
394	C₂³	C₂³×C₃×C₄	1	1	yes	characteristic
395	Q₈	—	2	8	no	—
396	D₄	—	2	16	no	—
397	D₄	—	2	8	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	8	no	—
405	C₂×C₄	—	2	16	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	8	no	—
409	C₂×C₄	—	4	4	no	—
410	C₂×C₄	—	4	8	no	—
411	C₂×C₄	C₃×#117	1	4	yes	—
412	C₂×C₄	C₃×#117	1	8	yes	—
413	C₂×C₄	C₃×#131	1	4	yes	—
414	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
415	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
416	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
417	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
418	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
419	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
420	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
421	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
422	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
423	C₂×C₄	C₂×C₃×#41	1	2	yes	—
424	C₂×C₄	C₂×C₃×#41	1	2	yes	—
425	C₂×C₄	C₂×C₃×#41	1	4	yes	—
426	C₂×C₄	C₂×C₃×#41	1	4	yes	—
427	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
428	C₈	—	2	4	no	—
429	C₈	—	2	4	no	—
430	C₈	—	2	8	no	—
431	C₂×C₃	—	2	4	no	—
432	C₂×C₃	—	4	4	no	—
433	C₂×C₃	#2925	1	4	yes	direct product factor
434	C₂×C₃	C₂²×#117	1	1	yes	characteristic
435	C₂×C₃	C₂²×#131	1	1	yes	characteristic
436	C₂×C₃	C₂×#568	1	1	yes	characteristic
437	C₂²	—	2	8	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	4	no	—
441	C₂²	—	2	4	no	—
442	C₂²	—	2	4	no	—
443	C₂²	—	4	8	no	—
444	C₂²	C₂×C₃×#117	1	4	yes	—
445	C₂²	C₂×C₃×#117	1	2	yes	—
446	C₂²	C₂×C₃×#131	1	2	yes	—
447	C₂²	C₃×#568	1	2	yes	—
448	C₂²	C₂⁴×C₃×C₄	1	1	yes	characteristic
449	C₄	—	2	4	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	4	no	—
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	2	4	no	—
455	C₄	C₂×C₃×#117	1	2	yes	—
456	C₄	C₂×C₃×#117	1	4	yes	—
457	C₄	C₂×C₃×#131	1	4	yes	—
458	C₄	C₂²×C₃×#41	1	1	yes	characteristic
459	C₄	C₂²×C₃×#41	1	1	yes	characteristic
460	C₃	C₂×#2925	1	1	yes	characteristic, direct product factor, Sylow
461	C₂	—	2	4	no	—
462	C₂	—	4	4	no	—
463	C₂	C₃×#2925	1	4	yes	direct product factor
464	C₂	C₂²×C₃×#117	1	1	yes	characteristic
465	C₂	C₂²×C₃×#131	1	1	yes	characteristic
466	C₂	C₂×C₃×#568	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	C₂⁴
commutator	C₂²	C₂⁴×C₃×C₄
Frattini, cosocle	C₂×C₄	C₂⁵×C₃
socle	C₂³×C₃	C₂³×C₄
prime radical	C₂²×C₃×#41	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#2925	C₂	direct (N × H)
3. C₂×C₃×#433	C₂	semidirect
4. C₂×C₃×#432	C₂	semidirect
5. C₂×C₃×#431	C₂	semidirect
6. C₂×C₃×#423	C₂	semidirect
7. C₂²×C₃×C₄⋊C₈	C₂	semidirect
9. C₂×C₃×#405	C₂	semidirect
10. C₂×#2925	C₃	direct (N × H)
26. C₃×#433	C₂²	semidirect
27. C₃×#432	C₂²	semidirect
28. C₃×#431	C₂²	semidirect
29. C₃×#423	C₂²	semidirect
35. C₂×C₃×C₄⋊C₈	C₂²	semidirect
39. C₃×#405	C₂²	semidirect
43. #2925	C₂×C₃	direct (N × H)
44. C₂×#433	C₂×C₃	semidirect
45. C₂×#432	C₂×C₃	semidirect
46. C₂×#431	C₂×C₃	semidirect
47. C₂×#423	C₂×C₃	semidirect
48. C₂²×C₄⋊C₈	C₂×C₃	semidirect
50. C₂×#405	C₂×C₃	semidirect
123. #433	C₂²×C₃	semidirect
124. #432	C₂²×C₃	semidirect
125. #431	C₂²×C₃	semidirect
126. #423	C₂²×C₃	semidirect
132. C₂×C₄⋊C₈	C₂²×C₃	semidirect
136. #405	C₂²×C₃	semidirect
433. C₂×C₃	#2925	direct (N × H)
460. C₃	C₂×#2925	direct (N × H)
463. C₂	C₃×#2925	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×#41	2
C₃×#2925	2
C₂×C₃×#433	2
C₂×C₃×#432	2
C₂×C₃×#431	2
C₂×C₃×#423	2
C₂²×C₃×C₄⋊C₈	2
C₂×C₃×#408	2
C₂×C₃×#405	2
C₂×#2925	3

Subgroups — C2×C3×#2925 #10678729

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#2925 #10678729