Subgroups — D₃×#394058 #72247174

Order 3072.

At least 8860 conjugacy classes of subgroups; only the 2079 normal subgroups are shown.

The subgroup lattice has 615 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72246730	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×#14679	C₂	1	1	yes	maximal, characteristic, complemented
3	#72246193	C₂	1	1	yes	maximal, characteristic, complemented
4	#72246182	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₃×#2846	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#394058	C₂	1	1	yes	maximal, characteristic, complemented
7	#72245687	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₃×#1781	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×D₃×#1898	C₂	1	1	yes	maximal, characteristic, complemented
10	#72245417	C₂	1	1	yes	maximal, characteristic, complemented
11	D₃×#34980	C₂	1	1	yes	maximal, characteristic, complemented
12	#72245238	C₂	1	1	yes	maximal, characteristic, complemented
13	#72245186	C₂	1	1	yes	maximal, characteristic, complemented
14	#72245154	C₂	1	4	yes	maximal, complemented
15	#72245112	C₂	1	4	yes	maximal, complemented
16	D₃×#10735	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×D₃×#2021	C₂	1	4	yes	maximal, complemented
18	D₃×#10991	C₂	1	4	yes	maximal, complemented
19	C₂³×D₃×#120	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁷×D₃	C₂²	1	1	yes	characteristic
21	C₂⁴×D₃×D₄	C₂²	1	1	yes	characteristic
22	C₂×D₃×#534	C₂²	1	2	yes	complemented
23	C₂³×#882	C₂²	1	1	yes	characteristic, complemented
24	C₂³×#953	C₂²	1	1	yes	characteristic, complemented
25	C₂³×#937	C₂²	1	1	yes	characteristic, complemented
26	C₂²×D₃×#120	C₂²	1	4	yes	—
27	C₂²×D₃×#120	C₂²	1	1	yes	characteristic
28	C₂²×D₃×#120	C₂²	1	4	yes	complemented
29	C₂²×D₃×#120	C₂²	1	2	yes	complemented
30	C₂³×D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂²×D₃×#99	C₂²	1	2	yes	complemented
32	C₂²×D₃×#99	C₂²	1	4	yes	complemented
33	C₂×#73861	C₂²	1	1	yes	characteristic, complemented
34	C₂×#73861	C₂²	1	2	yes	complemented
35	C₂×#84128	C₂²	1	1	yes	characteristic, complemented
36	C₂×#82612	C₂²	1	1	yes	characteristic, complemented
37	C₂×#82612	C₂²	1	2	yes	complemented
38	#10967726	C₂²	1	1	yes	characteristic, complemented
39	#10967725	C₂²	1	2	yes	complemented
40	#10967723	C₂²	1	1	yes	characteristic, complemented
41	#10967721	C₂²	1	1	yes	characteristic, complemented
42	#10967719	C₂²	1	2	yes	complemented
43	D₃×#2308	C₂²	1	2	yes	complemented
44	C₂×D₃×#379	C₂²	1	1	yes	characteristic
45	C₂×D₃×#379	C₂²	1	1	yes	characteristic
46	C₂×D₃×#379	C₂²	1	1	yes	characteristic
47	C₂×D₃×#379	C₂²	1	2	yes	complemented
48	C₂×D₃×#379	C₂²	1	4	yes	complemented
49	C₂×#68965	C₂²	1	4	yes	complemented
50	C₂×#69500	C₂²	1	4	yes	complemented
51	C₂×#70037	C₂²	1	4	yes	complemented
52	C₂×#70037	C₂²	1	4	yes	complemented
53	C₂×#71851	C₂²	1	4	yes	complemented
54	C₂×#71671	C₂²	1	4	yes	complemented
55	C₂×#71671	C₂²	1	4	yes	complemented
56	C₂×#71670	C₂²	1	1	yes	characteristic, complemented
57	C₂×#71543	C₂²	1	1	yes	characteristic, complemented
58	C₂×#68970	C₂²	1	2	yes	complemented
59	C₂×#69496	C₂²	1	1	yes	characteristic, complemented
60	C₂×#70036	C₂²	1	2	yes	complemented
61	C₂×#72130	C₂²	1	1	yes	characteristic, complemented
62	C₂×#69498	C₂²	1	1	yes	characteristic, complemented
63	C₂×#69498	C₂²	1	1	yes	characteristic, complemented
64	C₂×#70035	C₂²	1	4	yes	complemented
65	C₂×D₃×#342	C₂²	1	2	yes	complemented
66	C₂×D₃×#342	C₂²	1	4	yes	complemented
67	#10726343	C₂²	1	1	yes	characteristic, complemented
68	#10726342	C₂²	1	1	yes	characteristic, complemented
69	#10726342	C₂²	1	1	yes	characteristic, complemented
70	#10726342	C₂²	1	4	yes	complemented
71	#10701799	C₂²	1	4	yes	complemented
72	#10701798	C₂²	1	4	yes	complemented
73	#10701797	C₂²	1	4	yes	complemented
74	#10701797	C₂²	1	4	yes	complemented
75	#10701796	C₂²	1	4	yes	complemented
76	#10701796	C₂²	1	4	yes	complemented
77	#10701795	C₂²	1	4	yes	complemented
78	#10700486	C₂²	1	1	yes	characteristic, complemented
79	#10700485	C₂²	1	1	yes	characteristic, complemented
80	#10700484	C₂²	1	1	yes	characteristic, complemented
81	#10700483	C₂²	1	4	yes	complemented
82	C₂³×C₃×#120	C₂²	1	1	yes	characteristic, complemented
83	C₂×C₃×#2846	C₂²	1	1	yes	characteristic, complemented
84	C₃×#34980	C₂²	1	1	yes	characteristic, complemented
85	C₂×C₃×#2021	C₂²	1	4	yes	complemented
86	C₂×C₃×#1898	C₂²	1	1	yes	characteristic, complemented
87	C₂×C₃×#1781	C₂²	1	1	yes	characteristic, complemented
88	C₃×#14679	C₂²	1	1	yes	characteristic, complemented
89	C₃×#10991	C₂²	1	4	yes	complemented
90	C₃×#10735	C₂²	1	1	yes	characteristic, complemented
91	#394058	D₃	1	1	yes	characteristic, direct product factor
92	C₂⁷×C₃	C₂³	1	1	yes	characteristic
93	C₂⁶×D₃	D₄	1	8	yes	complemented
94	C₂⁶×D₃	D₄	1	1	yes	characteristic, complemented
95	C₂⁶×D₃	C₂³	1	2	yes	—
96	C₂⁶×D₃	C₂³	1	2	yes	—
97	C₂⁶×D₃	C₂³	1	1	yes	characteristic
98	C₂⁶×D₃	C₂³	1	1	yes	characteristic
99	C₂⁴×C₃×D₄	C₂³	1	1	yes	characteristic
100	C₂⁴×#67	D₄	1	1	yes	characteristic, complemented
101	C₂⁴×#67	C₂³	1	1	yes	characteristic
102	C₂³×D₃×D₄	D₄	1	2	yes	complemented
103	C₂³×D₃×D₄	D₄	1	2	yes	complemented
104	C₂³×D₃×D₄	D₄	1	2	yes	complemented
105	C₂³×D₃×D₄	C₂³	1	2	yes	—
106	C₂³×D₃×D₄	C₂³	1	1	yes	characteristic
107	C₂³×D₃×D₄	C₂³	1	2	yes	—
108	C₂⁴×D₁₂	D₄	1	1	yes	characteristic, complemented
109	C₂⁴×C₄×D₃	D₄	1	1	yes	characteristic, complemented
110	C₂×C₃×#534	C₂³	1	2	yes	complemented
111	C₂²×C₃×#120	C₂³	1	4	yes	—
112	C₂²×C₃×#120	C₂³	1	1	yes	characteristic
113	C₂²×C₃×#120	C₂³	1	2	yes	complemented
114	C₂³×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
115	C₂²×#953	C₂³	1	4	yes	—
116	C₂²×#953	C₂³	1	1	yes	characteristic
117	C₂²×#953	C₂³	1	2	yes	complemented
118	C₂³×#217	C₂³	1	1	yes	characteristic
119	C₂×#5804	C₂³	1	2	yes	complemented
120	C₂×#5804	C₂³	1	2	yes	complemented
121	C₂²×#937	D₄	1	2	yes	complemented
122	C₂²×#937	C₂³	1	4	yes	—
123	C₂²×#937	C₂³	1	1	yes	characteristic
124	C₂²×#937	C₂³	1	2	yes	complemented
125	C₂×D₃×#120	D₄	1	32	yes	complemented
126	C₂×#5493	C₂³	1	2	yes	complemented
127	C₂²×#882	D₄	1	2	yes	complemented
128	C₂²×#882	C₂³	1	4	yes	—
129	C₂²×#882	C₂³	1	1	yes	characteristic
130	C₂²×#882	C₂³	1	2	yes	complemented
131	C₂²×D₃×C₂²⋊C₄	D₄	1	8	yes	complemented
132	C₂²×D₃×C₂²⋊C₄	D₄	1	2	yes	complemented
133	C₂²×D₃×C₂²⋊C₄	D₄	1	4	yes	complemented
134	C₂²×D₃×C₂²⋊C₄	C₂³	1	2	yes	—
135	C₂²×D₃×C₂²⋊C₄	C₂³	1	2	yes	—
136	C₂²×D₃×C₂²⋊C₄	C₂³	1	2	yes	—
137	C₂²×D₃×C₂²⋊C₄	C₂³	1	2	yes	—
138	C₂²×D₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
139	C₂²×D₃×C₂²⋊C₄	C₂³	1	2	yes	—
140	C₂²×C₃×#99	C₂³	1	2	yes	complemented
141	C₂²×C₃×#99	C₂³	1	4	yes	complemented
142	C₃×#2308	C₂³	1	2	yes	complemented
143	C₂×C₃×#379	C₂³	1	1	yes	characteristic
144	C₂×C₃×#379	C₂³	1	1	yes	characteristic
145	C₂×C₃×#379	C₂³	1	1	yes	characteristic
146	C₂×C₃×#379	C₂³	1	2	yes	complemented
147	C₂×C₃×#379	C₂³	1	4	yes	complemented
148	C₂×#5247	C₂³	1	1	yes	characteristic
149	C₂×#5247	C₂³	1	1	yes	characteristic
150	C₂×#5247	C₂³	1	1	yes	characteristic
151	C₂×#5247	C₂³	1	2	yes	complemented
152	C₂×#5247	C₂³	1	4	yes	complemented
153	#84043	C₂³	1	2	yes	complemented
154	C₂²×#834	C₂³	1	2	yes	complemented
155	C₂²×#834	C₂³	1	4	yes	complemented
156	#82121	C₂³	1	2	yes	complemented
157	#82121	C₂³	1	2	yes	complemented
158	C₂×#4955	D₄	1	4	yes	complemented
159	C₂×#4955	C₂³	1	2	yes	—
160	C₂×#4955	C₂³	1	2	yes	—
161	C₂×#4955	C₂³	1	2	yes	—
162	C₂×#4955	C₂³	1	2	yes	complemented
163	C₂×#4955	C₂³	1	2	yes	complemented
164	C₂×#4955	C₂³	1	4	yes	complemented
165	C₂×#4955	C₂³	1	4	yes	complemented
166	C₂²×#806	C₂³	1	2	yes	complemented
167	C₂²×#806	C₂³	1	2	yes	complemented
168	C₂²×#806	C₂³	1	4	yes	complemented
169	C₂²×#806	C₂³	1	4	yes	complemented
170	D₃×#379	D₄	1	8	yes	complemented
171	C₂×C₃×#342	C₂³	1	4	yes	complemented
172	C₂×C₃×#342	C₂³	1	2	yes	complemented
173	C₂×#4527	C₂³	1	4	yes	complemented
174	C₂×#4527	C₂³	1	4	yes	complemented
175	C₂×#4527	C₂³	1	2	yes	complemented
176	C₂×#4527	C₂³	1	2	yes	complemented
177	C₂×#4526	C₂³	1	4	yes	complemented
178	C₂×#4526	C₂³	1	2	yes	complemented
179	C₂³×#120	C₂×D₃	1	1	yes	characteristic, complemented
180	C₂×#2846	C₂×D₃	1	1	yes	characteristic, complemented
181	#34980	C₂×D₃	1	1	yes	characteristic, complemented
182	C₂×#2021	C₂×D₃	1	4	yes	complemented
183	C₂×#1898	C₂×D₃	1	1	yes	characteristic, complemented
184	C₂×#1781	C₂×D₃	1	1	yes	characteristic, complemented
185	#14679	C₂×D₃	1	1	yes	characteristic, complemented
186	#10991	C₂×D₃	1	4	yes	complemented
187	#10735	C₂×D₃	1	1	yes	characteristic, complemented
188	C₂⁶×C₃	C₂×D₄	1	4	yes	complemented
189	C₂⁶×C₃	C₂×D₄	1	1	yes	characteristic, complemented
190	C₂⁶×C₃	C₂⁴	1	2	yes	—
191	C₂⁶×C₃	C₂⁴	1	1	yes	characteristic
192	C₂⁵×D₃	C₂×D₄	1	1	yes	characteristic
193	C₂⁵×D₃	C₂×D₄	1	2	yes	—
194	C₂⁵×D₃	C₂×D₄	1	2	yes	—
195	C₂⁵×D₃	C₂×D₄	1	2	yes	—
196	C₂⁵×D₃	C₂×D₄	1	16	yes	—
197	C₂⁵×D₃	C₂×D₄	1	8	yes	—
198	C₂⁵×D₃	C₂×D₄	1	1	yes	characteristic
199	C₂⁵×D₃	C₂×D₄	1	2	yes	—
200	C₂⁵×D₃	C₂×D₄	1	4	yes	—
201	C₂⁵×D₃	C₂×D₄	1	1	yes	characteristic
202	C₂⁵×D₃	C₂×D₄	1	1	yes	characteristic
203	C₂⁵×D₃	C₂×D₄	1	4	yes	—
204	C₂⁵×D₃	C₂×D₄	1	4	yes	—
205	C₂⁵×D₃	C₂×D₄	1	2	yes	—
206	C₂⁵×D₃	C₂×D₄	1	1	yes	characteristic, complemented
207	C₂⁵×D₃	C₂×D₄	1	2	yes	complemented
208	C₂⁵×D₃	C₂×D₄	1	8	yes	complemented
209	C₂⁵×D₃	C₂×D₄	1	4	yes	complemented
210	C₂⁵×D₃	C₂×D₄	1	1	yes	characteristic, complemented
211	C₂⁵×D₃	#41	1	4	yes	—
212	C₂⁵×D₃	C₂⁴	1	2	yes	—
213	C₂⁵×D₃	C₂⁴	1	1	yes	characteristic
214	C₂⁵×D₃	C₂⁴	1	1	yes	characteristic
215	C₂³×C₃×D₄	C₂×D₄	1	2	yes	complemented
216	C₂³×C₃×D₄	C₂×D₄	1	2	yes	complemented
217	C₂³×C₃×D₄	C₂⁴	1	2	yes	—
218	C₂³×C₃×D₄	C₂⁴	1	1	yes	characteristic
219	C₂⁴×C₃×C₄	C₂×D₄	1	1	yes	characteristic, complemented
220	C₂³×#67	C₂×D₄	1	2	yes	—
221	C₂³×#67	C₂×D₄	1	2	yes	complemented
222	C₂³×#67	C₂×D₄	1	2	yes	complemented
223	C₂³×#67	C₂×D₄	1	2	yes	complemented
224	C₂³×#67	C₂×D₄	1	1	yes	characteristic, complemented
225	C₂³×#67	C₂×D₄	1	2	yes	complemented
226	C₂³×#67	C₂⁴	1	2	yes	—
227	C₂³×#67	C₂⁴	1	1	yes	characteristic
228	C₂⁴×Dic₃	C₂×D₄	1	1	yes	characteristic, complemented
229	C₂²×D₃×D₄	C₂×D₄	1	16	yes	—
230	C₂³×D₁₂	C₂×D₄	1	2	yes	—
231	C₂³×D₁₂	C₂×D₄	1	1	yes	characteristic, complemented
232	C₂³×D₁₂	C₂×D₄	1	2	yes	complemented
233	C₂³×D₁₂	C₂×D₄	1	2	yes	complemented
234	C₂³×C₄×D₃	C₂×D₄	1	2	yes	—
235	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic, complemented
236	C₂³×C₄×D₃	C₂×D₄	1	2	yes	complemented
237	C₂³×C₄×D₃	C₂×D₄	1	2	yes	complemented
238	C₂³×C₄×D₃	C₂×D₄	1	4	yes	complemented
239	C₂×C₃×#120	C₂×D₄	1	16	yes	complemented
240	C₂²×C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
241	C₂²×C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
242	C₂²×C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
243	C₂²×C₃×C₂²⋊C₄	C₂⁴	1	2	yes	—
244	C₂²×C₃×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
245	C₂²×C₃×C₂²⋊C₄	C₂⁴	1	2	yes	—
246	C₂²×C₃×C₂²⋊C₄	C₂⁴	1	2	yes	—
247	C₂²×C₃×C₂²⋊C₄	C₂⁴	1	2	yes	—
248	C₂×#953	C₂×D₄	1	16	yes	complemented
249	C₂²×#217	C₂×D₄	1	2	yes	complemented
250	C₂²×#217	C₂×D₄	1	4	yes	complemented
251	C₂²×#217	C₂×D₄	1	4	yes	complemented
252	C₂²×#217	C₂⁴	1	2	yes	—
253	C₂²×#217	C₂⁴	1	1	yes	characteristic
254	C₂²×#217	C₂⁴	1	2	yes	—
255	C₂²×#217	C₂⁴	1	2	yes	—
256	C₂²×#217	C₂⁴	1	2	yes	—
257	C₂×#937	C₂×D₄	1	16	yes	complemented
258	C₂²×(C₂×D₃)⋊C₄	C₂×D₄	1	2	yes	complemented
259	C₂²×(C₂×D₃)⋊C₄	C₂×D₄	1	4	yes	complemented
260	C₂²×(C₂×D₃)⋊C₄	C₂×D₄	1	2	yes	complemented
261	C₂²×(C₂×D₃)⋊C₄	C₂×D₄	1	2	yes	complemented
262	C₂²×(C₂×D₃)⋊C₄	C₂×D₄	1	8	yes	complemented
263	C₂×#882	C₂×D₄	1	16	yes	complemented
264	C₂×D₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
265	C₂×D₃×C₂²⋊C₄	C₂×D₄	1	16	yes	—
266	C₂×D₃×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
267	C₂×D₃×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
268	C₃×#379	C₂×D₄	1	4	yes	complemented
269	#5247	C₂×D₄	1	4	yes	complemented
270	#4955	C₂×D₄	1	8	yes	complemented
271	C₂⁷	C₂²×D₃	1	1	yes	characteristic
272	C₂⁴×D₄	C₂²×D₃	1	1	yes	characteristic
273	C₂×#534	C₂²×D₃	1	2	yes	complemented
274	C₂²×#120	C₂²×D₃	1	4	yes	—
275	C₂²×#120	C₂²×D₃	1	1	yes	characteristic
276	C₂²×#120	C₂²×D₃	1	2	yes	complemented
277	C₂³×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
278	C₂²×#99	C₂²×D₃	1	2	yes	complemented
279	C₂²×#99	C₂²×D₃	1	4	yes	complemented
280	#2308	C₂²×D₃	1	2	yes	complemented
281	C₂×#379	C₂²×D₃	1	1	yes	characteristic
282	C₂×#379	C₂²×D₃	1	1	yes	characteristic
283	C₂×#379	C₂²×D₃	1	1	yes	characteristic
284	C₂×#379	C₂²×D₃	1	2	yes	complemented
285	C₂×#379	C₂²×D₃	1	4	yes	complemented
286	C₂×#342	C₂²×D₃	1	4	yes	complemented
287	C₂×#342	C₂²×D₃	1	2	yes	complemented
288	C₂⁵×C₃	C₂²×D₄	1	1	yes	characteristic
289	C₂⁵×C₃	C₂²×D₄	1	2	yes	—
290	C₂⁵×C₃	C₂²×D₄	1	2	yes	—
291	C₂⁵×C₃	C₂²×D₄	1	2	yes	—
292	C₂⁵×C₃	C₂²×D₄	1	8	yes	—
293	C₂⁵×C₃	C₂²×D₄	1	4	yes	—
294	C₂⁵×C₃	C₂²×D₄	1	2	yes	—
295	C₂⁵×C₃	C₂²×D₄	1	1	yes	characteristic
296	C₂⁵×C₃	C₂²×D₄	1	2	yes	—
297	C₂⁵×C₃	C₂²×D₄	1	2	yes	—
298	C₂⁵×C₃	C₂²×D₄	1	1	yes	characteristic, complemented
299	C₂⁵×C₃	C₂×#41	1	2	yes	—
300	C₂⁵×C₃	C₂⁵	1	1	yes	characteristic
301	C₂⁴×D₃	#120	1	4	yes	—
302	C₂⁴×D₃	#120	1	2	yes	—
303	C₂⁴×D₃	#120	1	2	yes	—
304	C₂⁴×D₃	#120	1	2	yes	—
305	C₂⁴×D₃	#120	1	2	yes	—
306	C₂⁴×D₃	#120	1	2	yes	—
307	C₂⁴×D₃	#120	1	2	yes	—
308	C₂⁴×D₃	#120	1	8	yes	—
309	C₂⁴×D₃	#120	1	2	yes	—
310	C₂⁴×D₃	#120	1	4	yes	—
311	C₂⁴×D₃	#120	1	2	yes	—
312	C₂⁴×D₃	#120	1	4	yes	—
313	C₂⁴×D₃	#120	1	4	yes	—
314	C₂⁴×D₃	#120	1	8	yes	—
315	C₂⁴×D₃	#120	1	8	yes	complemented
316	C₂⁴×D₃	#120	1	32	yes	complemented
317	C₂⁴×D₃	#121	1	4	yes	—
318	C₂⁴×D₃	#121	1	8	yes	—
319	C₂⁴×D₃	#121	1	8	yes	—
320	C₂⁴×D₃	#121	1	4	yes	—
321	C₂⁴×D₃	#121	1	4	yes	—
322	C₂⁴×D₃	#121	1	4	yes	—
323	C₂⁴×D₃	#121	1	8	yes	—
324	C₂⁴×D₃	#121	1	8	yes	—
325	C₂⁴×D₃	#127	1	8	yes	—
326	C₂⁴×D₃	#127	1	8	yes	—
327	C₂⁴×D₃	C₂²×D₄	1	1	yes	characteristic
328	C₂⁴×D₃	C₂²×D₄	1	2	yes	—
329	C₂⁴×D₃	C₂²×D₄	1	2	yes	—
330	C₂⁴×D₃	C₂²×D₄	1	1	yes	characteristic
331	C₂⁴×D₃	C₂²×D₄	1	1	yes	characteristic
332	C₂⁴×D₃	C₂²×D₄	1	1	yes	characteristic
333	C₂⁴×D₃	C₂²×D₄	1	2	yes	—
334	C₂⁴×D₃	C₂²×D₄	1	8	yes	—
335	C₂⁴×D₃	C₂²×D₄	1	4	yes	—
336	C₂⁴×D₃	C₂²×D₄	1	1	yes	characteristic
337	C₂⁴×D₃	C₂²×D₄	1	2	yes	—
338	C₂⁴×D₃	C₂²×D₄	1	2	yes	—
339	C₂⁴×D₃	C₂²×D₄	1	2	yes	—
340	C₂⁴×D₃	C₂²×D₄	1	1	yes	characteristic
341	C₂⁴×D₃	C₂²×D₄	1	2	yes	—
342	C₂⁴×D₃	C₂²×D₄	1	2	yes	—
343	C₂⁴×D₃	C₂²×D₄	1	8	yes	—
344	C₂⁴×D₃	C₂²×D₄	1	1	yes	characteristic
345	C₂⁴×D₃	C₂²×D₄	1	2	yes	—
346	C₂⁴×D₃	C₂²×D₄	1	1	yes	characteristic
347	C₂⁴×D₃	C₂²×D₄	1	1	yes	characteristic, complemented
348	C₂⁴×D₃	C₂×#41	1	2	yes	—
349	C₂⁴×D₃	C₂×#41	1	2	yes	—
350	C₂⁴×D₃	H(5,𝔽₂)	1	8	yes	—
351	C₂²×C₃×D₄	C₂²×D₄	1	8	yes	—
352	C₂³×C₃×C₄	C₂²×D₄	1	2	yes	—
353	C₂³×C₃×C₄	C₂²×D₄	1	1	yes	characteristic, complemented
354	C₂³×C₃×C₄	C₂²×D₄	1	2	yes	complemented
355	C₂³×C₃×C₄	C₂²×D₄	1	4	yes	complemented
356	C₂²×#67	#120	1	8	yes	complemented
357	C₂²×#67	C₂²×D₄	1	8	yes	—
358	C₂³×Dic₃	C₂²×D₄	1	2	yes	—
359	C₂³×Dic₃	C₂²×D₄	1	1	yes	characteristic, complemented
360	C₂³×Dic₃	C₂²×D₄	1	2	yes	complemented
361	C₂³×Dic₃	C₂²×D₄	1	4	yes	complemented
362	C₂²×D₁₂	#120	1	8	yes	complemented
363	C₂²×C₄×D₃	#120	1	8	yes	complemented
364	C₂×C₃×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
365	C₂×C₃×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
366	C₂×C₃×C₂²⋊C₄	C₂²×D₄	1	4	yes	complemented
367	C₂×#217	C₂²×D₄	1	8	yes	—
368	C₂×#217	C₂²×D₄	1	4	yes	—
369	C₂×#217	C₂²×D₄	1	4	yes	complemented
370	D₃×C₂²⋊C₄	#120	1	32	yes	complemented
371	C₂⁶	D₃×D₄	1	1	yes	characteristic, complemented
372	C₂⁶	D₃×D₄	1	4	yes	complemented
373	C₂⁶	C₂³×D₃	1	2	yes	—
374	C₂⁶	C₂³×D₃	1	1	yes	characteristic
375	C₂³×D₄	D₃×D₄	1	2	yes	complemented
376	C₂³×D₄	D₃×D₄	1	2	yes	complemented
377	C₂³×D₄	C₂³×D₃	1	2	yes	—
378	C₂³×D₄	C₂³×D₃	1	1	yes	characteristic
379	C₂⁴×C₄	D₃×D₄	1	1	yes	characteristic, complemented
380	C₂×#120	D₃×D₄	1	16	yes	complemented
381	C₂²×C₂²⋊C₄	D₃×D₄	1	2	yes	complemented
382	C₂²×C₂²⋊C₄	D₃×D₄	1	4	yes	complemented
383	C₂²×C₂²⋊C₄	D₃×D₄	1	4	yes	complemented
384	C₂²×C₂²⋊C₄	C₂³×D₃	1	2	yes	—
385	C₂²×C₂²⋊C₄	C₂³×D₃	1	1	yes	characteristic
386	C₂²×C₂²⋊C₄	C₂³×D₃	1	2	yes	—
387	C₂²×C₂²⋊C₄	C₂³×D₃	1	2	yes	—
388	C₂²×C₂²⋊C₄	C₂³×D₃	1	2	yes	—
389	#379	D₃×D₄	1	4	yes	complemented
390	C₂⁴×C₃	C₂×#120	1	2	yes	—
391	C₂⁴×C₃	C₂×#120	1	2	yes	—
392	C₂⁴×C₃	C₂×#120	1	4	yes	—
393	C₂⁴×C₃	C₂×#120	1	2	yes	—
394	C₂⁴×C₃	C₂×#120	1	2	yes	—
395	C₂⁴×C₃	C₂×#120	1	8	yes	complemented
396	C₂⁴×C₃	C₂×#120	1	4	yes	complemented
397	C₂⁴×C₃	C₂×#121	1	2	yes	—
398	C₂⁴×C₃	C₂×#121	1	4	yes	—
399	C₂⁴×C₃	C₂×#121	1	4	yes	—
400	C₂⁴×C₃	C₂×#121	1	2	yes	—
401	C₂⁴×C₃	C₂×#127	1	4	yes	—
402	C₂⁴×C₃	C₂³×D₄	1	1	yes	characteristic
403	C₂⁴×C₃	C₂³×D₄	1	1	yes	characteristic
404	C₂⁴×C₃	C₂³×D₄	1	1	yes	characteristic
405	C₂⁴×C₃	C₂³×D₄	1	1	yes	characteristic
406	C₂⁴×C₃	C₂³×D₄	1	1	yes	characteristic
407	C₂⁴×C₃	C₂³×D₄	1	4	yes	—
408	C₂⁴×C₃	C₂³×D₄	1	1	yes	characteristic
409	C₂⁴×C₃	C₂²×#41	1	1	yes	characteristic
410	C₂⁴×C₃	C₂×H(5,𝔽₂)	1	4	yes	—
411	C₂³×D₃	#392	1	8	yes	—
412	C₂³×D₃	#392	1	8	yes	—
413	C₂³×D₃	#392	1	8	yes	—
414	C₂³×D₃	#392	1	8	yes	—
415	C₂³×D₃	#392	1	8	yes	—
416	C₂³×D₃	#392	1	8	yes	—
417	C₂³×D₃	#392	1	8	yes	—
418	C₂³×D₃	#392	1	8	yes	—
419	C₂³×D₃	B(4,𝔽₂)	1	16	yes	—
420	C₂³×D₃	C₂×#120	1	2	yes	—
421	C₂³×D₃	C₂×#120	1	2	yes	—
422	C₂³×D₃	C₂×#120	1	4	yes	—
423	C₂³×D₃	C₂×#120	1	2	yes	—
424	C₂³×D₃	C₂×#120	1	4	yes	—
425	C₂³×D₃	C₂×#120	1	1	yes	characteristic
426	C₂³×D₃	C₂×#120	1	1	yes	characteristic
427	C₂³×D₃	C₂×#120	1	1	yes	characteristic
428	C₂³×D₃	C₂×#120	1	2	yes	—
429	C₂³×D₃	C₂×#120	1	2	yes	—
430	C₂³×D₃	C₂×#120	1	2	yes	—
431	C₂³×D₃	C₂×#120	1	2	yes	—
432	C₂³×D₃	C₂×#120	1	8	yes	—
433	C₂³×D₃	C₂×#120	1	4	yes	—
434	C₂³×D₃	C₂×#120	1	8	yes	—
435	C₂³×D₃	C₂×#120	1	2	yes	—
436	C₂³×D₃	C₂×#120	1	1	yes	characteristic
437	C₂³×D₃	C₂×#120	1	8	yes	complemented
438	C₂³×D₃	C₂×#120	1	4	yes	complemented
439	C₂³×D₃	C₂×#121	1	2	yes	—
440	C₂³×D₃	C₂×#121	1	4	yes	—
441	C₂³×D₃	C₂×#121	1	4	yes	—
442	C₂³×D₃	C₂×#121	1	2	yes	—
443	C₂³×D₃	C₂×#121	1	2	yes	—
444	C₂³×D₃	C₂×#121	1	2	yes	—
445	C₂³×D₃	C₂×#121	1	2	yes	—
446	C₂³×D₃	C₂×#121	1	2	yes	—
447	C₂³×D₃	C₂×#121	1	2	yes	—
448	C₂³×D₃	C₂×#121	1	2	yes	—
449	C₂³×D₃	C₂×#127	1	4	yes	—
450	C₂³×D₃	C₂×#127	1	2	yes	—
451	C₂³×D₃	C₂×#127	1	2	yes	—
452	C₂³×D₃	#534	1	4	yes	—
453	C₂³×D₃	#534	1	4	yes	—
454	C₂³×D₃	#534	1	8	yes	—
455	C₂³×D₃	#535	1	8	yes	—
456	C₂³×D₃	D₄²	1	8	yes	—
457	C₂³×D₃	D₄²	1	8	yes	—
458	C₂³×D₃	D₄²	1	8	yes	—
459	C₂³×D₃	D₄²	1	16	yes	—
460	C₂³×D₃	D₄²	1	8	yes	—
461	C₂³×D₃	#546	1	16	yes	—
462	C₂²×C₃×C₄	C₂×#120	1	4	yes	complemented
463	C₂²×Dic₃	C₂×#120	1	4	yes	complemented
464	C₃×C₂²⋊C₄	C₂×#120	1	8	yes	complemented
465	#217	C₂×#120	1	8	yes	complemented
466	C₂⁵	C₂×D₃×D₄	1	1	yes	characteristic
467	C₂⁵	C₂×D₃×D₄	1	2	yes	—
468	C₂⁵	C₂×D₃×D₄	1	2	yes	—
469	C₂⁵	C₂×D₃×D₄	1	4	yes	—
470	C₂⁵	C₂×D₃×D₄	1	8	yes	—
471	C₂⁵	C₂×D₃×D₄	1	2	yes	—
472	C₂⁵	C₂×D₃×D₄	1	2	yes	—
473	C₂⁵	C₂×D₃×D₄	1	2	yes	—
474	C₂⁵	C₂×D₃×D₄	1	2	yes	—
475	C₂⁵	C₂×D₃×D₄	1	1	yes	characteristic
476	C₂⁵	C₂×D₃×D₄	1	1	yes	characteristic, complemented
477	C₂⁵	D₃×#41	1	2	yes	—
478	C₂⁵	C₂⁴×D₃	1	1	yes	characteristic
479	C₂²×D₄	C₂×D₃×D₄	1	8	yes	—
480	C₂³×C₄	C₂×D₃×D₄	1	2	yes	—
481	C₂³×C₄	C₂×D₃×D₄	1	1	yes	characteristic, complemented
482	C₂³×C₄	C₂×D₃×D₄	1	4	yes	complemented
483	C₂³×C₄	C₂×D₃×D₄	1	2	yes	complemented
484	C₂×C₂²⋊C₄	C₂×D₃×D₄	1	8	yes	—
485	C₂×C₂²⋊C₄	C₂×D₃×D₄	1	4	yes	—
486	C₂×C₂²⋊C₄	C₂×D₃×D₄	1	4	yes	complemented
487	C₂³×C₃	C₂×#392	1	4	yes	—
488	C₂³×C₃	C₂×#392	1	4	yes	—
489	C₂³×C₃	C₂×B(4,𝔽₂)	1	8	yes	—
490	C₂³×C₃	C₂²×#120	1	2	yes	—
491	C₂³×C₃	C₂²×#120	1	1	yes	characteristic
492	C₂³×C₃	C₂²×#120	1	1	yes	characteristic
493	C₂³×C₃	C₂²×#120	1	2	yes	—
494	C₂³×C₃	C₂²×#120	1	2	yes	—
495	C₂³×C₃	C₂²×#120	1	1	yes	characteristic
496	C₂³×C₃	C₂²×#121	1	1	yes	characteristic
497	C₂³×C₃	C₂²×#121	1	1	yes	characteristic
498	C₂³×C₃	C₂²×#121	1	1	yes	characteristic
499	C₂³×C₃	C₂²×#127	1	1	yes	characteristic
500	C₂³×C₃	C₂×#534	1	2	yes	—
501	C₂³×C₃	C₂×#534	1	2	yes	—
502	C₂³×C₃	C₂×#535	1	2	yes	—
503	C₂³×C₃	C₂×D₄²	1	4	yes	—
504	C₂³×C₃	C₂×D₄²	1	4	yes	—
505	C₂³×C₃	C₂×D₄²	1	4	yes	—
506	C₂³×C₃	C₂×#546	1	4	yes	—
507	C₂²×D₃	#2021	1	32	yes	complemented
508	C₂²×D₃	C₂×#392	1	4	yes	—
509	C₂²×D₃	C₂×#392	1	2	yes	—
510	C₂²×D₃	C₂×#392	1	2	yes	—
511	C₂²×D₃	C₂×#392	1	2	yes	—
512	C₂²×D₃	C₂×#392	1	4	yes	—
513	C₂²×D₃	C₂×#392	1	2	yes	—
514	C₂²×D₃	#2403	1	4	yes	—
515	C₂²×D₃	#2403	1	4	yes	—
516	C₂²×D₃	#2403	1	8	yes	—
517	C₂²×D₃	#2403	1	4	yes	—
518	C₂²×D₃	#2403	1	8	yes	—
519	C₂²×D₃	#2403	1	4	yes	—
520	C₂²×D₃	#2408	1	8	yes	—
521	C₂²×D₃	#2408	1	8	yes	—
522	C₂²×D₃	#2410	1	8	yes	—
523	C₂²×D₃	#2410	1	8	yes	—
524	C₂²×D₃	#2410	1	8	yes	—
525	C₂²×D₃	#2410	1	8	yes	—
526	C₂²×D₃	#2433	1	8	yes	—
527	C₂²×D₃	#2433	1	8	yes	—
528	C₂²×D₃	#2613	1	4	yes	—
529	C₂²×D₃	#2613	1	4	yes	—
530	C₂²×D₃	#2846	1	4	yes	—
531	C₂²×D₃	#2846	1	4	yes	—
532	C₂²×D₃	C₂×B(4,𝔽₂)	1	8	yes	—
533	C₂²×D₃	C₂×B(4,𝔽₂)	1	8	yes	—
534	C₂⁴	D₃×#120	1	2	yes	—
535	C₂⁴	D₃×#120	1	2	yes	—
536	C₂⁴	D₃×#120	1	4	yes	—
537	C₂⁴	D₃×#120	1	2	yes	—
538	C₂⁴	D₃×#120	1	2	yes	—
539	C₂⁴	D₃×#120	1	8	yes	complemented
540	C₂⁴	D₃×#120	1	4	yes	complemented
541	C₂⁴	D₃×#121	1	2	yes	—
542	C₂⁴	D₃×#121	1	4	yes	—
543	C₂⁴	D₃×#121	1	4	yes	—
544	C₂⁴	D₃×#121	1	2	yes	—
545	C₂⁴	D₃×#127	1	4	yes	—
546	C₂⁴	C₂²×D₃×D₄	1	1	yes	characteristic
547	C₂⁴	C₂²×D₃×D₄	1	1	yes	characteristic
548	C₂⁴	C₂²×D₃×D₄	1	1	yes	characteristic
549	C₂⁴	C₂²×D₃×D₄	1	1	yes	characteristic
550	C₂⁴	C₂²×D₃×D₄	1	1	yes	characteristic
551	C₂⁴	C₂²×D₃×D₄	1	1	yes	characteristic
552	C₂⁴	C₂²×D₃×D₄	1	4	yes	—
553	C₂⁴	C₂×D₃×#41	1	1	yes	characteristic
554	C₂⁴	D₃×H(5,𝔽₂)	1	4	yes	—
555	C₂²×C₄	D₃×#120	1	4	yes	complemented
556	C₂²⋊C₄	D₃×#120	1	8	yes	complemented
557	C₂²×C₃	C₂×#2021	1	8	yes	complemented
558	C₂²×C₃	C₂²×#392	1	1	yes	characteristic
559	C₂²×C₃	C₂×#2613	1	1	yes	characteristic
560	C₂²×C₃	C₂×#2403	1	2	yes	—
561	C₂²×C₃	C₂×#2403	1	2	yes	—
562	C₂²×C₃	C₂×#2410	1	2	yes	—
563	C₂²×C₃	C₂×#2410	1	2	yes	—
564	C₂²×C₃	C₂×#2408	1	2	yes	—
565	C₂²×C₃	C₂×#2433	1	2	yes	—
566	C₂²×C₃	C₂×#2846	1	1	yes	characteristic
567	C₂²×C₃	C₂²×B(4,𝔽₂)	1	4	yes	—
568	C₂×D₃	#14715	1	4	yes	—
569	C₂×D₃	#14715	1	4	yes	—
570	C₂×D₃	#14715	1	4	yes	—
571	C₂×D₃	#14715	1	4	yes	—
572	C₂×D₃	C₂×#2021	1	8	yes	—
573	C₂×D₃	C₂×#2021	1	8	yes	complemented
574	C₂×D₃	#23900	1	16	yes	—
575	C₂³	D₃×#392	1	4	yes	—
576	C₂³	D₃×#392	1	4	yes	—
577	C₂³	D₃×B(4,𝔽₂)	1	8	yes	—
578	C₂³	C₂×D₃×#120	1	1	yes	characteristic
579	C₂³	C₂×D₃×#120	1	1	yes	characteristic
580	C₂³	C₂×D₃×#120	1	2	yes	—
581	C₂³	C₂×D₃×#120	1	2	yes	—
582	C₂³	C₂×D₃×#120	1	2	yes	—
583	C₂³	C₂×D₃×#120	1	1	yes	characteristic
584	C₂³	C₂×D₃×#121	1	1	yes	characteristic
585	C₂³	C₂×D₃×#121	1	1	yes	characteristic
586	C₂³	C₂×D₃×#121	1	1	yes	characteristic
587	C₂³	C₂×D₃×#127	1	1	yes	characteristic
588	C₂³	D₃×#534	1	2	yes	—
589	C₂³	D₃×#534	1	2	yes	—
590	C₂³	D₃×#535	1	2	yes	—
591	C₂³	D₃×D₄²	1	4	yes	—
592	C₂³	D₃×D₄²	1	4	yes	—
593	C₂³	D₃×D₄²	1	4	yes	—
594	C₂³	D₃×#546	1	4	yes	—
595	C₂×C₃	C₂×#14715	1	1	yes	characteristic
596	C₂×C₃	C₂²×#2021	1	2	yes	—
597	C₂×C₃	C₂×#23900	1	4	yes	—
598	D₃	#394058	1	8	yes	direct product factor
599	C₂²	D₃×#2021	1	8	yes	complemented
600	C₂²	C₂×D₃×#392	1	1	yes	characteristic
601	C₂²	D₃×#2613	1	1	yes	characteristic
602	C₂²	D₃×#2403	1	2	yes	—
603	C₂²	D₃×#2403	1	2	yes	—
604	C₂²	D₃×#2410	1	2	yes	—
605	C₂²	D₃×#2410	1	2	yes	—
606	C₂²	D₃×#2408	1	2	yes	—
607	C₂²	D₃×#2433	1	2	yes	—
608	C₂²	D₃×#2846	1	1	yes	characteristic
609	C₂²	C₂×D₃×B(4,𝔽₂)	1	4	yes	—
610	C₃	C₂×#394058	1	1	yes	characteristic, complemented, Sylow
611	C₂	D₃×#23900	1	4	yes	—
612	C₂	C₂×D₃×#2021	1	2	yes	—
613	C₂	D₃×#14715	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₃×#120
commutator, cosocle	C₂⁵×C₃	C₂⁵
Frattini	C₂⁵	C₂⁴×D₃
Fitting	C₃×#394058	C₂
socle	C₂³×C₃	C₂²×#120
hypercenter	#394058	D₃
hypocenter	C₃	C₂×#394058
LCS	G ▷ C₂⁵×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂⁶ ◁ #394058

Complements

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

N	H ≅ G/N	type
1. #72246730	C₂	semidirect
2. D₃×#14679	C₂	semidirect
3. #72246193	C₂	semidirect
4. #72246182	C₂	semidirect
5. C₂×D₃×#2846	C₂	semidirect
6. C₃×#394058	C₂	semidirect
7. #72245687	C₂	semidirect
8. C₂×D₃×#1781	C₂	semidirect
9. C₂×D₃×#1898	C₂	semidirect
10. #72245417	C₂	semidirect
11. D₃×#34980	C₂	semidirect
12. #72245238	C₂	semidirect
13. #72245186	C₂	semidirect
14. #72245154	C₂	semidirect
15. #72245112	C₂	semidirect
16. D₃×#10735	C₂	semidirect
17. C₂×D₃×#2021	C₂	semidirect
18. D₃×#10991	C₂	semidirect
19. C₂³×D₃×#120	C₂	semidirect
22. C₂×D₃×#534	C₂²	semidirect
23. C₂³×#882	C₂²	semidirect
24. C₂³×#953	C₂²	semidirect
25. C₂³×#937	C₂²	semidirect
28. C₂²×D₃×#120	C₂²	semidirect
29. C₂²×D₃×#120	C₂²	semidirect
31. C₂²×D₃×#99	C₂²	semidirect
32. C₂²×D₃×#99	C₂²	semidirect
33. C₂×#73861	C₂²	semidirect
34. C₂×#73861	C₂²	semidirect
35. C₂×#84128	C₂²	semidirect
36. C₂×#82612	C₂²	semidirect
37. C₂×#82612	C₂²	semidirect
38. #10967726	C₂²	semidirect
39. #10967725	C₂²	semidirect
40. #10967723	C₂²	semidirect
41. #10967721	C₂²	semidirect
42. #10967719	C₂²	semidirect
43. D₃×#2308	C₂²	semidirect
47. C₂×D₃×#379	C₂²	semidirect
48. C₂×D₃×#379	C₂²	semidirect
49. C₂×#68965	C₂²	semidirect
50. C₂×#69500	C₂²	semidirect
51. C₂×#70037	C₂²	semidirect
52. C₂×#70037	C₂²	semidirect
53. C₂×#71851	C₂²	semidirect
54. C₂×#71671	C₂²	semidirect
55. C₂×#71671	C₂²	semidirect
56. C₂×#71670	C₂²	semidirect
57. C₂×#71543	C₂²	semidirect
58. C₂×#68970	C₂²	semidirect
59. C₂×#69496	C₂²	semidirect
60. C₂×#70036	C₂²	semidirect
61. C₂×#72130	C₂²	semidirect
62. C₂×#69498	C₂²	semidirect
63. C₂×#69498	C₂²	semidirect
64. C₂×#70035	C₂²	semidirect
65. C₂×D₃×#342	C₂²	semidirect
66. C₂×D₃×#342	C₂²	semidirect
67. #10726343	C₂²	semidirect
68. #10726342	C₂²	semidirect
69. #10726342	C₂²	semidirect
70. #10726342	C₂²	semidirect
71. #10701799	C₂²	semidirect
72. #10701798	C₂²	semidirect
73. #10701797	C₂²	semidirect
74. #10701797	C₂²	semidirect
75. #10701796	C₂²	semidirect
76. #10701796	C₂²	semidirect
77. #10701795	C₂²	semidirect
78. #10700486	C₂²	semidirect
79. #10700485	C₂²	semidirect
80. #10700484	C₂²	semidirect
81. #10700483	C₂²	semidirect
82. C₂³×C₃×#120	C₂²	semidirect
83. C₂×C₃×#2846	C₂²	semidirect
84. C₃×#34980	C₂²	semidirect
85. C₂×C₃×#2021	C₂²	semidirect
86. C₂×C₃×#1898	C₂²	semidirect
87. C₂×C₃×#1781	C₂²	semidirect
88. C₃×#14679	C₂²	semidirect
89. C₃×#10991	C₂²	semidirect
90. C₃×#10735	C₂²	semidirect
91. #394058	D₃	direct (N × H)
93. C₂⁶×D₃	D₄	semidirect
94. C₂⁶×D₃	D₄	semidirect
100. C₂⁴×#67	D₄	semidirect
102. C₂³×D₃×D₄	D₄	semidirect
103. C₂³×D₃×D₄	D₄	semidirect
104. C₂³×D₃×D₄	D₄	semidirect
108. C₂⁴×D₁₂	D₄	semidirect
109. C₂⁴×C₄×D₃	D₄	semidirect
110. C₂×C₃×#534	C₂³	semidirect
113. C₂²×C₃×#120	C₂³	semidirect
117. C₂²×#953	C₂³	semidirect
119. C₂×#5804	C₂³	semidirect
120. C₂×#5804	C₂³	semidirect
121. C₂²×#937	D₄	semidirect
124. C₂²×#937	C₂³	semidirect
125. C₂×D₃×#120	D₄	semidirect
126. C₂×#5493	C₂³	semidirect
127. C₂²×#882	D₄	semidirect
130. C₂²×#882	C₂³	semidirect
131. C₂²×D₃×C₂²⋊C₄	D₄	semidirect
132. C₂²×D₃×C₂²⋊C₄	D₄	semidirect
133. C₂²×D₃×C₂²⋊C₄	D₄	semidirect
140. C₂²×C₃×#99	C₂³	semidirect
141. C₂²×C₃×#99	C₂³	semidirect
142. C₃×#2308	C₂³	semidirect
146. C₂×C₃×#379	C₂³	semidirect
147. C₂×C₃×#379	C₂³	semidirect
151. C₂×#5247	C₂³	semidirect
152. C₂×#5247	C₂³	semidirect
153. #84043	C₂³	semidirect
154. C₂²×#834	C₂³	semidirect
155. C₂²×#834	C₂³	semidirect
156. #82121	C₂³	semidirect
157. #82121	C₂³	semidirect
158. C₂×#4955	D₄	semidirect
162. C₂×#4955	C₂³	semidirect
163. C₂×#4955	C₂³	semidirect
164. C₂×#4955	C₂³	semidirect
165. C₂×#4955	C₂³	semidirect
166. C₂²×#806	C₂³	semidirect
167. C₂²×#806	C₂³	semidirect
168. C₂²×#806	C₂³	semidirect
169. C₂²×#806	C₂³	semidirect
170. D₃×#379	D₄	semidirect
171. C₂×C₃×#342	C₂³	semidirect
172. C₂×C₃×#342	C₂³	semidirect
173. C₂×#4527	C₂³	semidirect
174. C₂×#4527	C₂³	semidirect
175. C₂×#4527	C₂³	semidirect
176. C₂×#4527	C₂³	semidirect
177. C₂×#4526	C₂³	semidirect
178. C₂×#4526	C₂³	semidirect
179. C₂³×#120	C₂×D₃	semidirect
180. C₂×#2846	C₂×D₃	semidirect
181. #34980	C₂×D₃	semidirect
182. C₂×#2021	C₂×D₃	semidirect
183. C₂×#1898	C₂×D₃	semidirect
184. C₂×#1781	C₂×D₃	semidirect
185. #14679	C₂×D₃	semidirect
186. #10991	C₂×D₃	semidirect
187. #10735	C₂×D₃	semidirect
188. C₂⁶×C₃	C₂×D₄	semidirect
189. C₂⁶×C₃	C₂×D₄	semidirect
206. C₂⁵×D₃	C₂×D₄	semidirect
207. C₂⁵×D₃	C₂×D₄	semidirect
208. C₂⁵×D₃	C₂×D₄	semidirect
209. C₂⁵×D₃	C₂×D₄	semidirect
210. C₂⁵×D₃	C₂×D₄	semidirect
215. C₂³×C₃×D₄	C₂×D₄	semidirect
216. C₂³×C₃×D₄	C₂×D₄	semidirect
219. C₂⁴×C₃×C₄	C₂×D₄	semidirect
221. C₂³×#67	C₂×D₄	semidirect
222. C₂³×#67	C₂×D₄	semidirect
223. C₂³×#67	C₂×D₄	semidirect
224. C₂³×#67	C₂×D₄	semidirect
225. C₂³×#67	C₂×D₄	semidirect
228. C₂⁴×Dic₃	C₂×D₄	semidirect
231. C₂³×D₁₂	C₂×D₄	semidirect
232. C₂³×D₁₂	C₂×D₄	semidirect
233. C₂³×D₁₂	C₂×D₄	semidirect
235. C₂³×C₄×D₃	C₂×D₄	semidirect
236. C₂³×C₄×D₃	C₂×D₄	semidirect
237. C₂³×C₄×D₃	C₂×D₄	semidirect
238. C₂³×C₄×D₃	C₂×D₄	semidirect
239. C₂×C₃×#120	C₂×D₄	semidirect
240. C₂²×C₃×C₂²⋊C₄	C₂×D₄	semidirect
241. C₂²×C₃×C₂²⋊C₄	C₂×D₄	semidirect
242. C₂²×C₃×C₂²⋊C₄	C₂×D₄	semidirect
248. C₂×#953	C₂×D₄	semidirect
249. C₂²×#217	C₂×D₄	semidirect
250. C₂²×#217	C₂×D₄	semidirect
251. C₂²×#217	C₂×D₄	semidirect
257. C₂×#937	C₂×D₄	semidirect
258. C₂²×(C₂×D₃)⋊C₄	C₂×D₄	semidirect
259. C₂²×(C₂×D₃)⋊C₄	C₂×D₄	semidirect
260. C₂²×(C₂×D₃)⋊C₄	C₂×D₄	semidirect
261. C₂²×(C₂×D₃)⋊C₄	C₂×D₄	semidirect
262. C₂²×(C₂×D₃)⋊C₄	C₂×D₄	semidirect
263. C₂×#882	C₂×D₄	semidirect
266. C₂×D₃×C₂²⋊C₄	C₂×D₄	semidirect
267. C₂×D₃×C₂²⋊C₄	C₂×D₄	semidirect
268. C₃×#379	C₂×D₄	semidirect
269. #5247	C₂×D₄	semidirect
270. #4955	C₂×D₄	semidirect
273. C₂×#534	C₂²×D₃	semidirect
276. C₂²×#120	C₂²×D₃	semidirect
278. C₂²×#99	C₂²×D₃	semidirect
279. C₂²×#99	C₂²×D₃	semidirect
280. #2308	C₂²×D₃	semidirect
284. C₂×#379	C₂²×D₃	semidirect
285. C₂×#379	C₂²×D₃	semidirect
286. C₂×#342	C₂²×D₃	semidirect
287. C₂×#342	C₂²×D₃	semidirect
298. C₂⁵×C₃	C₂²×D₄	semidirect
315. C₂⁴×D₃	#120	semidirect
316. C₂⁴×D₃	#120	semidirect
347. C₂⁴×D₃	C₂²×D₄	semidirect
353. C₂³×C₃×C₄	C₂²×D₄	semidirect
354. C₂³×C₃×C₄	C₂²×D₄	semidirect
355. C₂³×C₃×C₄	C₂²×D₄	semidirect
356. C₂²×#67	#120	semidirect
359. C₂³×Dic₃	C₂²×D₄	semidirect
360. C₂³×Dic₃	C₂²×D₄	semidirect
361. C₂³×Dic₃	C₂²×D₄	semidirect
362. C₂²×D₁₂	#120	semidirect
363. C₂²×C₄×D₃	#120	semidirect
366. C₂×C₃×C₂²⋊C₄	C₂²×D₄	semidirect
369. C₂×#217	C₂²×D₄	semidirect
370. D₃×C₂²⋊C₄	#120	semidirect
371. C₂⁶	D₃×D₄	semidirect
372. C₂⁶	D₃×D₄	semidirect
375. C₂³×D₄	D₃×D₄	semidirect
376. C₂³×D₄	D₃×D₄	semidirect
379. C₂⁴×C₄	D₃×D₄	semidirect
380. C₂×#120	D₃×D₄	semidirect
381. C₂²×C₂²⋊C₄	D₃×D₄	semidirect
382. C₂²×C₂²⋊C₄	D₃×D₄	semidirect
383. C₂²×C₂²⋊C₄	D₃×D₄	semidirect
389. #379	D₃×D₄	semidirect
395. C₂⁴×C₃	C₂×#120	semidirect
396. C₂⁴×C₃	C₂×#120	semidirect
437. C₂³×D₃	C₂×#120	semidirect
438. C₂³×D₃	C₂×#120	semidirect
462. C₂²×C₃×C₄	C₂×#120	semidirect
463. C₂²×Dic₃	C₂×#120	semidirect
464. C₃×C₂²⋊C₄	C₂×#120	semidirect
465. #217	C₂×#120	semidirect
476. C₂⁵	C₂×D₃×D₄	semidirect
481. C₂³×C₄	C₂×D₃×D₄	semidirect
482. C₂³×C₄	C₂×D₃×D₄	semidirect
483. C₂³×C₄	C₂×D₃×D₄	semidirect
486. C₂×C₂²⋊C₄	C₂×D₃×D₄	semidirect
507. C₂²×D₃	#2021	semidirect
539. C₂⁴	D₃×#120	semidirect
540. C₂⁴	D₃×#120	semidirect
555. C₂²×C₄	D₃×#120	semidirect
556. C₂²⋊C₄	D₃×#120	semidirect
557. C₂²×C₃	C₂×#2021	semidirect
573. C₂×D₃	C₂×#2021	semidirect
598. D₃	#394058	direct (N × H)
599. C₂²	D₃×#2021	semidirect
610. C₃	C₂×#394058	semidirect

Maximal subgroups

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

subgroup	index
#72246730	2
D₃×#14679	2
#72246193	2
#72246182	2
C₂×D₃×#2846	2
C₃×#394058	2
#72245687	2
C₂×D₃×#1781	2
C₂×D₃×#1898	2
#72245417	2
D₃×#34980	2
#72245238	2
#72245186	2
#72245154	2
#72245112	2
D₃×#10735	2
C₂×D₃×#2021	2
D₃×#10991	2
C₂³×D₃×#120	2
C₂×#394058	3

Subgroups — D3×#394058 #72247174

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#394058 #72247174