Subgroups — D₃×#498929 #72253975

Order 3072.

At least 10332 conjugacy classes of subgroups; only the 1239 normal subgroups are shown.

The subgroup lattice has 618 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72253973	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×#37269	C₂	1	1	yes	maximal, characteristic, complemented
3	#72253970	C₂	1	4	yes	maximal, complemented
4	C₃×#498929	C₂	1	1	yes	maximal, characteristic, complemented
5	#72253966	C₂	1	1	yes	maximal, characteristic, complemented
6	D₃×#12575	C₂	1	1	yes	maximal, characteristic, complemented
7	#72253963	C₂	1	1	yes	maximal, characteristic, complemented
8	D₃×#20610	C₂	1	1	yes	maximal, characteristic, complemented
9	#72253954	C₂	1	4	yes	maximal, complemented
10	#72253942	C₂	1	1	yes	maximal, characteristic, complemented
11	#72253934	C₂	1	1	yes	maximal, characteristic, complemented
12	#72253927	C₂	1	1	yes	maximal, characteristic, complemented
13	#72253913	C₂	1	1	yes	maximal, characteristic, complemented
14	D₃×#13346	C₂	1	4	yes	maximal, complemented
15	D₃×#13347	C₂	1	4	yes	maximal, complemented
16	C₂×D₃×#3025	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×D₃×#3021	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×D₃×#2120	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×D₃×#2128	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×D₃×#585	C₂²	1	1	yes	characteristic
21	C₂×D₃×#535	C₂²	1	1	yes	characteristic
22	C₂×D₃×#525	C₂²	1	1	yes	characteristic
23	C₂×#78690	C₂²	1	1	yes	characteristic, complemented
24	C₂×#80308	C₂²	1	2	yes	complemented
25	C₂×#84125	C₂²	1	1	yes	characteristic, complemented
26	C₂×#82936	C₂²	1	1	yes	characteristic, complemented
27	C₂×#80304	C₂²	1	2	yes	complemented
28	C₂×D₃×#458	C₂²	1	2	yes	complemented
29	C₂×D₃×B(4,𝔽₂)	C₂²	1	2	yes	complemented
30	C₂×#78717	C₂²	1	1	yes	characteristic, complemented
31	C₂×#84122	C₂²	1	1	yes	characteristic, complemented
32	C₂×#83395	C₂²	1	1	yes	characteristic, complemented
33	C₂×#80279	C₂²	1	4	yes	complemented
34	C₂×D₃×#453	C₂²	1	4	yes	—
35	C₂×D₃×#413	C₂²	1	1	yes	characteristic
36	C₂×D₃×#410	C₂²	1	1	yes	characteristic
37	C₂×D₃×#410	C₂²	1	1	yes	characteristic
38	D₃×#2709	C₂²	1	2	yes	complemented
39	D₃×#2669	C₂²	1	2	yes	complemented
40	#11016711	C₂²	1	1	yes	characteristic, complemented
41	#11016710	C₂²	1	1	yes	characteristic, complemented
42	#11016702	C₂²	1	2	yes	complemented
43	#11016701	C₂²	1	1	yes	characteristic, complemented
44	#11016698	C₂²	1	2	yes	complemented
45	D₃×#2311	C₂²	1	1	yes	characteristic
46	C₂×#71861	C₂²	1	1	yes	characteristic, complemented
47	C₂×#70061	C₂²	1	1	yes	characteristic, complemented
48	C₂×#70061	C₂²	1	1	yes	characteristic, complemented
49	C₂×#69152	C₂²	1	4	yes	complemented
50	C₂×D₃×#353	C₂²	1	4	yes	complemented
51	C₂×#70145	C₂²	1	1	yes	characteristic, complemented
52	C₂×#71716	C₂²	1	1	yes	characteristic, complemented
53	C₂×#69144	C₂²	1	2	yes	complemented
54	C₂×#70056	C₂²	1	1	yes	characteristic, complemented
55	C₂×#69136	C₂²	1	2	yes	complemented
56	C₂×D₃×#352	C₂²	1	2	yes	complemented
57	C₂×D₃×AΣL(1,𝔽₁₆)	C₂²	1	2	yes	complemented
58	#10794459	C₂²	1	1	yes	characteristic, complemented
59	#10794458	C₂²	1	1	yes	characteristic, complemented
60	#10794457	C₂²	1	1	yes	characteristic, complemented
61	#10794456	C₂²	1	4	yes	complemented
62	D₃×#1790	C₂²	1	4	yes	complemented
63	#10714154	C₂²	1	4	yes	complemented
64	#10714153	C₂²	1	4	yes	complemented
65	#10714152	C₂²	1	4	yes	complemented
66	#10714151	C₂²	1	4	yes	complemented
67	#10714150	C₂²	1	4	yes	complemented
68	#10714149	C₂²	1	4	yes	complemented
69	#10714148	C₂²	1	4	yes	complemented
70	#10714147	C₂²	1	4	yes	complemented
71	#10714146	C₂²	1	4	yes	complemented
72	#10714145	C₂²	1	4	yes	complemented
73	#10714144	C₂²	1	4	yes	complemented
74	#10714143	C₂²	1	4	yes	complemented
75	#10714142	C₂²	1	4	yes	complemented
76	#10714141	C₂²	1	4	yes	complemented
77	#10710139	C₂²	1	1	yes	characteristic, complemented
78	#10710138	C₂²	1	1	yes	characteristic, complemented
79	#10710137	C₂²	1	1	yes	characteristic, complemented
80	#10710136	C₂²	1	4	yes	complemented
81	D₃×#1390	C₂²	1	4	yes	complemented
82	C₂×C₃×#3025	C₂²	1	1	yes	characteristic, complemented
83	C₂×C₃×#3021	C₂²	1	1	yes	characteristic, complemented
84	C₃×#37269	C₂²	1	1	yes	characteristic, complemented
85	C₂×C₃×#2128	C₂²	1	1	yes	characteristic, complemented
86	C₂×C₃×#2120	C₂²	1	1	yes	characteristic, complemented
87	C₃×#20610	C₂²	1	1	yes	characteristic, complemented
88	C₃×#13347	C₂²	1	4	yes	complemented
89	C₃×#13346	C₂²	1	4	yes	complemented
90	C₃×#12575	C₂²	1	1	yes	characteristic, complemented
91	#498929	D₃	1	1	yes	characteristic, direct product factor
92	C₂×C₃×#585	C₂³	1	1	yes	characteristic
93	D₃×#585	D₄	1	8	yes	complemented
94	C₂×D₃×H(5,𝔽₂)	C₂³	1	2	yes	—
95	C₂×#5966	C₂³	1	2	yes	—
96	C₂×#5964	C₂³	1	1	yes	characteristic
97	C₂²×D₃×#41	C₂³	1	1	yes	characteristic
98	C₂³×D₃×D₄	D₄	1	1	yes	characteristic, complemented
99	C₂⁴×C₄×D₃	D₄	1	1	yes	characteristic
100	C₂×C₃×#535	C₂³	1	1	yes	characteristic
101	C₂×C₃×#525	C₂³	1	1	yes	characteristic
102	C₂×#5830	C₂³	1	1	yes	characteristic
103	C₂×#5828	C₂³	1	1	yes	characteristic
104	C₂×#5805	D₄	1	1	yes	characteristic, complemented
105	C₂×#5791	D₄	1	1	yes	characteristic
106	C₂×#5715	C₂³	1	2	yes	—
107	C₂×D₃×#127	C₂³	1	2	yes	—
108	C₂×#5674	D₄	1	2	yes	complemented
109	C₂×D₃×#124	D₄	1	2	yes	complemented
110	C₂×D₃×#123	D₄	1	1	yes	characteristic
111	C₂×D₃×#123	C₂³	1	1	yes	characteristic
112	C₂×#5656	D₄	1	1	yes	characteristic
113	C₂×#5656	C₂³	1	1	yes	characteristic
114	C₂×D₃×#120	D₄	1	1	yes	characteristic
115	C₂×D₃×#120	C₂³	1	1	yes	characteristic
116	C₂×#5586	D₄	1	1	yes	characteristic
117	C₂×#5586	C₂³	1	1	yes	characteristic
118	C₂×#5525	D₄	1	1	yes	characteristic, complemented
119	C₂×#5524	D₄	1	1	yes	characteristic
120	C₂×D₃×#117	D₄	1	1	yes	characteristic
121	C₂×D₃×#117	D₄	1	1	yes	characteristic, complemented
122	C₂×D₃×#117	D₄	1	1	yes	characteristic, complemented
123	C₂²×D₃×C₄⋊C₄	D₄	1	1	yes	characteristic, complemented
124	C₂×C₃×#458	C₂³	1	2	yes	complemented
125	C₂×C₃×B(4,𝔽₂)	C₂³	1	2	yes	complemented
126	C₂×C₃×#453	C₂³	1	4	yes	—
127	C₂×C₃×#413	C₂³	1	1	yes	characteristic
128	C₂×C₃×#410	C₂³	1	1	yes	characteristic
129	C₂×C₃×#410	C₂³	1	1	yes	characteristic
130	C₃×#2709	C₂³	1	2	yes	complemented
131	C₃×#2669	C₂³	1	2	yes	complemented
132	C₃×#2311	C₂³	1	1	yes	characteristic
133	C₂×#5244	C₂³	1	2	yes	complemented
134	C₂×#5243	C₂³	1	2	yes	complemented
135	C₂×#5241	C₂³	1	4	yes	—
136	#84087	C₂³	1	1	yes	characteristic
137	C₂×#5240	C₂³	1	1	yes	characteristic
138	C₂×#5240	C₂³	1	1	yes	characteristic
139	C₂×#5237	C₂³	1	1	yes	characteristic
140	#83190	C₂³	1	2	yes	complemented
141	#83183	C₂³	1	2	yes	complemented
142	C₂×#5077	C₂³	1	4	yes	—
143	C₂×#5053	C₂³	1	2	yes	complemented
144	#82884	C₂³	1	2	yes	complemented
145	C₂×#5032	C₂³	1	2	yes	complemented
146	#82594	C₂³	1	2	yes	complemented
147	#82270	D₄	1	1	yes	characteristic, complemented
148	#82186	D₄	1	1	yes	characteristic, complemented
149	D₃×#413	D₄	1	8	yes	complemented
150	C₂×#4747	C₂³	1	4	yes	—
151	C₂×#4745	C₂³	1	2	yes	—
152	C₂×D₃×#100	C₂³	1	2	yes	—
153	D₃×#410	D₄	1	8	yes	complemented
154	C₂×D₃×#99	C₂³	1	2	yes	—
155	C₂×D₃×#99	C₂³	1	2	yes	—
156	C₂×#4742	C₂³	1	2	yes	complemented
157	C₂×#4741	C₂³	1	2	yes	complemented
158	C₂×#4740	C₂³	1	2	yes	—
159	C₂×#4740	C₂³	1	2	yes	—
160	#74912	C₂³	1	2	yes	complemented
161	D₃×#386	D₄	1	2	yes	complemented
162	D₃×#386	C₂³	1	2	yes	—
163	#74820	C₂³	1	2	yes	complemented
164	#74662	D₄	1	2	yes	complemented
165	#74662	C₂³	1	2	yes	—
166	C₂×C₃×#353	C₂³	1	4	yes	complemented
167	C₂×C₃×#352	C₂³	1	2	yes	complemented
168	C₂×C₃×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	complemented
169	C₃×#1790	C₂³	1	4	yes	complemented
170	#72142	C₂³	1	4	yes	complemented
171	C₂×#4545	C₂³	1	4	yes	complemented
172	C₂×#4539	C₂³	1	2	yes	complemented
173	C₂×#4536	C₂³	1	2	yes	complemented
174	C₂×#4476	C₂³	1	2	yes	complemented
175	C₂×#4475	C₂³	1	2	yes	complemented
176	#70033	C₂³	1	4	yes	complemented
177	C₂×#4474	C₂³	1	4	yes	complemented
178	C₂×#4474	C₂³	1	4	yes	complemented
179	C₂×#4472	C₂³	1	2	yes	complemented
180	C₂×#4471	C₂³	1	2	yes	complemented
181	#69598	C₂³	1	4	yes	complemented
182	C₃×#1390	C₂³	1	4	yes	complemented
183	#67698	C₂³	1	4	yes	complemented
184	#67694	C₂³	1	4	yes	complemented
185	#67637	C₂³	1	4	yes	complemented
186	C₂×#3025	C₂×D₃	1	1	yes	characteristic, complemented
187	C₂×#3021	C₂×D₃	1	1	yes	characteristic, complemented
188	#37269	C₂×D₃	1	1	yes	characteristic, complemented
189	C₂×#2128	C₂×D₃	1	1	yes	characteristic, complemented
190	C₂×#2120	C₂×D₃	1	1	yes	characteristic, complemented
191	#20610	C₂×D₃	1	1	yes	characteristic, complemented
192	#13347	C₂×D₃	1	4	yes	complemented
193	#13346	C₂×D₃	1	4	yes	complemented
194	#12575	C₂×D₃	1	1	yes	characteristic, complemented
195	C₂⁵×D₃	C₂×D₄	1	1	yes	characteristic
196	C₃×#585	C₂×D₄	1	4	yes	complemented
197	C₂×C₃×H(5,𝔽₂)	C₂⁴	1	2	yes	—
198	C₂²×C₃×#41	C₂⁴	1	1	yes	characteristic
199	C₂³×C₃×D₄	C₂×D₄	1	1	yes	characteristic, complemented
200	C₂⁴×C₃×C₄	C₂×D₄	1	1	yes	characteristic
201	C₂⁴×Dic₃	C₂×D₄	1	1	yes	characteristic
202	#5966	C₂×D₄	1	8	yes	complemented
203	D₃×H(5,𝔽₂)	C₂×D₄	1	8	yes	—
204	#5964	C₂×D₄	1	4	yes	complemented
205	C₂×D₃×#41	C₂×D₄	1	4	yes	—
206	C₂×D₃×#41	C₂×D₄	1	4	yes	—
207	C₂×D₃×#41	C₂×D₄	1	4	yes	—
208	C₂×D₃×#41	#41	1	4	yes	—
209	C₂²×#239	C₂×D₄	1	1	yes	characteristic
210	C₂²×D₃×Q₈	C₂×D₄	1	1	yes	characteristic
211	C₂×#1004	C₂⁴	1	2	yes	—
212	C₂²×#237	C₂×D₄	1	1	yes	characteristic
213	C₂²×#237	C₂×D₄	1	1	yes	characteristic
214	C₂²×#237	C₂⁴	1	1	yes	characteristic
215	C₂²×D₃×D₄	C₂×D₄	1	1	yes	characteristic
216	C₂²×D₃×D₄	C₂×D₄	1	1	yes	characteristic
217	C₂²×D₃×D₄	C₂×D₄	1	2	yes	—
218	C₂²×D₃×D₄	C₂×D₄	1	2	yes	complemented
219	C₂²×D₃×D₄	C₂⁴	1	1	yes	characteristic
220	C₂²×#235	C₂×D₄	1	1	yes	characteristic
221	C₂²×#235	C₂×D₄	1	1	yes	characteristic
222	C₂²×#235	C₂×D₄	1	1	yes	characteristic
223	C₂³×D₁₂	C₂×D₄	1	1	yes	characteristic, complemented
224	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
225	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
226	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
227	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
228	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
229	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
230	C₂³×C₄×D₃	C₂×D₄	1	2	yes	—
231	C₂×C₃×#127	C₂⁴	1	2	yes	—
232	C₂×C₃×#124	C₂×D₄	1	2	yes	complemented
233	C₂×C₃×#123	C₂×D₄	1	1	yes	characteristic
234	C₂×C₃×#123	C₂⁴	1	1	yes	characteristic
235	C₂×C₃×#120	C₂×D₄	1	1	yes	characteristic
236	C₂×C₃×#120	C₂⁴	1	1	yes	characteristic
237	C₂×C₃×#117	C₂×D₄	1	1	yes	characteristic
238	C₂×C₃×#117	C₂×D₄	1	1	yes	characteristic, complemented
239	C₂×C₃×#117	C₂×D₄	1	1	yes	characteristic, complemented
240	C₂²×C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
241	C₂×#953	C₂×D₄	1	1	yes	characteristic
242	C₂×#953	C₂×D₄	1	1	yes	characteristic
243	C₂×#947	C₂×D₄	1	2	yes	complemented
244	C₂×#940	C₂×D₄	1	2	yes	—
245	C₂×#940	C₂⁴	1	2	yes	—
246	C₂×#937	C₂×D₄	1	1	yes	characteristic
247	C₂×#937	C₂⁴	1	1	yes	characteristic
248	C₂×#936	C₂×D₄	1	2	yes	complemented
249	C₂×#935	C₂×D₄	1	1	yes	characteristic
250	C₂×#935	C₂⁴	1	1	yes	characteristic
251	C₂×#929	C₂×D₄	1	1	yes	characteristic
252	C₂×#929	C₂×D₄	1	1	yes	characteristic
253	C₂×#926	C₂×D₄	1	1	yes	characteristic
254	C₂×#926	C₂×D₄	1	1	yes	characteristic, complemented
255	C₂×#926	C₂×D₄	1	1	yes	characteristic, complemented
256	C₂²×C₄⋊Dic₃	C₂×D₄	1	1	yes	characteristic, complemented
257	C₂²×Dic₃⋊C₄	C₂×D₄	1	2	yes	complemented
258	C₂×#886	C₂×D₄	1	1	yes	characteristic
259	C₂×#886	C₂×D₄	1	1	yes	characteristic
260	C₂×#882	C₂×D₄	1	1	yes	characteristic
261	C₂×#882	C₂×D₄	1	1	yes	characteristic
262	C₂×D₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
263	C₂×D₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
264	C₂×D₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
265	C₂×#877	C₂×D₄	1	1	yes	characteristic
266	C₂×#877	C₂×D₄	1	1	yes	characteristic
267	C₂×#877	C₂×D₄	1	2	yes	complemented
268	C₂×#875	C₂×D₄	1	2	yes	complemented
269	C₂×#874	C₂×D₄	1	2	yes	—
270	C₂×#872	C₂×D₄	1	2	yes	complemented
271	C₂×C₄²×D₃	C₂×D₄	1	2	yes	—
272	C₃×#413	C₂×D₄	1	4	yes	complemented
273	C₂×C₃×#100	C₂⁴	1	2	yes	—
274	C₃×#410	C₂×D₄	1	4	yes	complemented
275	C₂×C₃×#99	C₂⁴	1	2	yes	—
276	C₂×C₃×#99	C₂⁴	1	2	yes	—
277	C₃×#386	C₂×D₄	1	2	yes	complemented
278	C₃×#386	C₂⁴	1	2	yes	—
279	#5240	C₂×D₄	1	4	yes	complemented
280	#5237	C₂×D₄	1	4	yes	complemented
281	#5220	C₂×D₄	1	2	yes	complemented
282	#5220	C₂⁴	1	2	yes	—
283	C₂×#834	C₂⁴	1	2	yes	—
284	C₂×#834	C₂⁴	1	2	yes	—
285	C₂×#833	C₂⁴	1	2	yes	—
286	#5213	C₂×D₄	1	2	yes	—
287	#5213	C₂×D₄	1	2	yes	complemented
288	#4958	C₂×D₄	1	2	yes	—
289	#4958	C₂×D₄	1	2	yes	complemented
290	#4745	C₂×D₄	1	8	yes	complemented
291	D₃×#100	C₂×D₄	1	8	yes	—
292	D₃×#99	C₂×D₄	1	8	yes	—
293	#4740	C₂×D₄	1	8	yes	complemented
294	C₂×#585	C₂²×D₃	1	1	yes	characteristic
295	C₂×#535	C₂²×D₃	1	1	yes	characteristic
296	C₂×#525	C₂²×D₃	1	1	yes	characteristic
297	C₂×#458	C₂²×D₃	1	2	yes	complemented
298	C₂×B(4,𝔽₂)	C₂²×D₃	1	2	yes	complemented
299	C₂×#453	C₂²×D₃	1	4	yes	—
300	C₂×#413	C₂²×D₃	1	1	yes	characteristic
301	C₂×#410	C₂²×D₃	1	1	yes	characteristic
302	C₂×#410	C₂²×D₃	1	1	yes	characteristic
303	#2709	C₂²×D₃	1	2	yes	complemented
304	#2669	C₂²×D₃	1	2	yes	complemented
305	#2311	C₂²×D₃	1	1	yes	characteristic
306	C₂×#353	C₂²×D₃	1	4	yes	complemented
307	C₂×#352	C₂²×D₃	1	2	yes	complemented
308	C₂×AΣL(1,𝔽₁₆)	C₂²×D₃	1	2	yes	complemented
309	#1790	C₂²×D₃	1	4	yes	complemented
310	#1390	C₂²×D₃	1	4	yes	complemented
311	C₂⁵×C₃	C₂²×D₄	1	1	yes	characteristic
312	C₂⁴×D₃	#120	1	1	yes	characteristic
313	C₂⁴×D₃	C₂²×D₄	1	1	yes	characteristic
314	C₂⁴×D₃	C₂²×D₄	1	1	yes	characteristic
315	C₂⁴×D₃	C₂²×D₄	1	1	yes	characteristic
316	C₃×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
317	C₂×C₃×#41	C₂²×D₄	1	2	yes	—
318	C₂×C₃×#41	C₂²×D₄	1	2	yes	—
319	C₂×C₃×#41	C₂²×D₄	1	2	yes	—
320	C₂×C₃×#41	C₂×#41	1	2	yes	—
321	C₂²×C₃×Q₈	C₂²×D₄	1	1	yes	characteristic
322	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
323	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
324	C₂²×C₃×D₄	C₂²×D₄	1	2	yes	—
325	C₂²×C₃×D₄	C₂⁵	1	1	yes	characteristic
326	C₂³×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
327	C₂³×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
328	C₂³×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
329	C₂³×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
330	C₂³×C₃×C₄	C₂²×D₄	1	2	yes	—
331	C₂²×#67	#120	1	1	yes	characteristic
332	C₂²×#67	#120	1	1	yes	characteristic
333	C₂²×#67	C₂²×D₄	1	1	yes	characteristic
334	C₂²×#67	C₂²×D₄	1	1	yes	characteristic
335	C₂²×#67	C₂²×D₄	1	1	yes	characteristic
336	C₂²×#67	C₂²×D₄	1	1	yes	characteristic
337	C₂³×Dic₃	#120	1	1	yes	characteristic
338	C₂³×Dic₃	C₂²×D₄	1	1	yes	characteristic
339	C₂³×Dic₃	C₂²×D₄	1	1	yes	characteristic
340	C₂³×Dic₃	C₂²×D₄	1	1	yes	characteristic
341	C₂³×Dic₃	C₂²×D₄	1	2	yes	—
342	C₂×#239	#120	1	4	yes	—
343	C₂×#239	#121	1	4	yes	—
344	C₂×D₃×Q₈	#120	1	4	yes	—
345	C₂×D₃×Q₈	#121	1	4	yes	—
346	#1004	C₂²×D₄	1	4	yes	—
347	C₂×#237	#120	1	4	yes	—
348	C₂×#237	#121	1	4	yes	—
349	C₂×#237	#121	1	4	yes	—
350	C₂×#237	#127	1	4	yes	—
351	C₂×#237	C₂²×D₄	1	2	yes	—
352	C₂×#237	C₂²×D₄	1	2	yes	—
353	C₂×#237	C₂²×D₄	1	2	yes	—
354	C₂×#237	C₂×#41	1	2	yes	—
355	C₂×D₃×D₄	#120	1	4	yes	—
356	C₂×D₃×D₄	#121	1	4	yes	—
357	C₂×D₃×D₄	#121	1	4	yes	—
358	C₂×D₃×D₄	#127	1	4	yes	—
359	C₂×D₃×D₄	C₂²×D₄	1	2	yes	—
360	C₂×D₃×D₄	C₂²×D₄	1	2	yes	—
361	C₂×D₃×D₄	C₂²×D₄	1	2	yes	—
362	C₂×D₃×D₄	C₂×#41	1	2	yes	—
363	C₂×#235	#120	1	4	yes	—
364	C₂×#235	#120	1	4	yes	—
365	C₂×#235	#121	1	4	yes	—
366	C₂×#235	#121	1	4	yes	—
367	C₂×#235	#121	1	4	yes	—
368	C₂×#235	#127	1	4	yes	—
369	C₂²×D₁₂	#120	1	1	yes	characteristic
370	C₂²×D₁₂	#120	1	1	yes	characteristic
371	C₂²×D₁₂	C₂²×D₄	1	2	yes	—
372	C₂²×D₁₂	C₂²×D₄	1	1	yes	characteristic
373	C₂²×C₄×D₃	#120	1	4	yes	—
374	C₂²×C₄×D₃	#120	1	1	yes	characteristic
375	C₂²×C₄×D₃	#120	1	1	yes	characteristic
376	C₂²×C₄×D₃	#120	1	1	yes	characteristic
377	C₂²×C₄×D₃	#120	1	4	yes	—
378	C₂²×C₄×D₃	#120	1	1	yes	characteristic
379	C₂²×C₄×D₃	#120	1	1	yes	characteristic
380	C₂²×C₄×D₃	#120	1	1	yes	characteristic
381	C₂²×C₄×D₃	#120	1	1	yes	characteristic
382	C₂²×C₄×D₃	#120	1	1	yes	characteristic
383	C₂²×C₄×D₃	#121	1	4	yes	—
384	C₂²×C₄×D₃	#121	1	4	yes	—
385	C₂²×C₄×D₃	#121	1	4	yes	—
386	C₂²×C₄×D₃	#127	1	4	yes	—
387	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
388	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
389	C₂²×Dic₆	#120	1	1	yes	characteristic
390	C₂²×Dic₆	#120	1	1	yes	characteristic
391	C₂²×Dic₆	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₃×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₃×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₃×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
395	C₂×C₃×C₄²	C₂²×D₄	1	2	yes	—
396	C₂×#217	C₂²×D₄	1	1	yes	characteristic
397	C₂×#217	C₂²×D₄	1	1	yes	characteristic
398	C₂×#217	C₂²×D₄	1	2	yes	—
399	C₂×C₄×Dic₃	C₂²×D₄	1	2	yes	—
400	C₃×#100	C₂²×D₄	1	4	yes	—
401	C₃×#99	C₂²×D₄	1	4	yes	—
402	#834	C₂²×D₄	1	4	yes	—
403	#833	C₂²×D₄	1	4	yes	—
404	#585	D₃×D₄	1	4	yes	complemented
405	C₂×H(5,𝔽₂)	C₂³×D₃	1	2	yes	—
406	C₂²×#41	C₂³×D₃	1	1	yes	characteristic
407	C₂³×D₄	D₃×D₄	1	1	yes	characteristic, complemented
408	C₂⁴×C₄	D₃×D₄	1	1	yes	characteristic
409	C₂×#127	C₂³×D₃	1	2	yes	—
410	C₂×#124	D₃×D₄	1	2	yes	complemented
411	C₂×#123	D₃×D₄	1	1	yes	characteristic
412	C₂×#123	C₂³×D₃	1	1	yes	characteristic
413	C₂×#120	D₃×D₄	1	1	yes	characteristic
414	C₂×#120	C₂³×D₃	1	1	yes	characteristic
415	C₂×#117	D₃×D₄	1	1	yes	characteristic
416	C₂×#117	D₃×D₄	1	1	yes	characteristic, complemented
417	C₂×#117	D₃×D₄	1	1	yes	characteristic, complemented
418	C₂²×C₄⋊C₄	D₃×D₄	1	1	yes	characteristic, complemented
419	#413	D₃×D₄	1	4	yes	complemented
420	C₂×#100	C₂³×D₃	1	2	yes	—
421	#410	D₃×D₄	1	4	yes	complemented
422	C₂×#99	C₂³×D₃	1	2	yes	—
423	C₂×#99	C₂³×D₃	1	2	yes	—
424	#386	D₃×D₄	1	2	yes	complemented
425	#386	C₂³×D₃	1	2	yes	—
426	C₂⁴×C₃	C₂×#120	1	1	yes	characteristic
427	C₂⁴×C₃	C₂³×D₄	1	1	yes	characteristic
428	C₂⁴×C₃	C₂³×D₄	1	1	yes	characteristic
429	C₂³×D₃	#392	1	4	yes	—
430	C₂³×D₃	C₂×#120	1	1	yes	characteristic
431	C₂³×D₃	C₂×#120	1	2	yes	—
432	C₂³×D₃	C₂×#120	1	1	yes	characteristic
433	C₂³×D₃	C₂×#120	1	1	yes	characteristic
434	C₂³×D₃	C₂×#120	1	1	yes	characteristic
435	C₂³×D₃	C₂×#121	1	2	yes	—
436	C₂³×D₃	C₂×#121	1	2	yes	—
437	C₂³×D₃	C₂×#127	1	2	yes	—
438	C₂×C₃×Q₈	C₂×#120	1	2	yes	—
439	C₂×C₃×Q₈	C₂×#121	1	2	yes	—
440	C₂×C₃×D₄	C₂×#120	1	2	yes	—
441	C₂×C₃×D₄	C₂×#121	1	2	yes	—
442	C₂×C₃×D₄	C₂×#121	1	2	yes	—
443	C₂×C₃×D₄	C₂×#127	1	2	yes	—
444	C₂×C₃×D₄	C₂³×D₄	1	1	yes	characteristic
445	C₂×C₃×D₄	C₂³×D₄	1	1	yes	characteristic
446	C₂×C₃×D₄	C₂³×D₄	1	1	yes	characteristic
447	C₂×C₃×D₄	C₂²×#41	1	1	yes	characteristic
448	C₂²×C₃×C₄	C₂×#120	1	1	yes	characteristic
449	C₂²×C₃×C₄	C₂×#120	1	1	yes	characteristic
450	C₂²×C₃×C₄	C₂×#120	1	2	yes	—
451	C₂²×C₃×C₄	C₂×#120	1	2	yes	—
452	C₂²×C₃×C₄	C₂×#120	1	1	yes	characteristic
453	C₂²×C₃×C₄	C₂×#121	1	2	yes	—
454	C₂²×C₃×C₄	C₂×#121	1	2	yes	—
455	C₂²×C₃×C₄	C₂×#121	1	2	yes	—
456	C₂²×C₃×C₄	C₂×#127	1	2	yes	—
457	C₂²×C₃×C₄	C₂³×D₄	1	1	yes	characteristic
458	C₂×#67	#392	1	4	yes	—
459	C₂×#67	#392	1	4	yes	—
460	C₂×#67	C₂×#120	1	2	yes	—
461	C₂×#67	C₂×#120	1	2	yes	—
462	C₂×#67	C₂×#121	1	2	yes	—
463	C₂×#67	C₂×#121	1	2	yes	—
464	C₂×#67	C₂×#121	1	2	yes	—
465	C₂×#67	C₂×#121	1	2	yes	—
466	C₂×#67	C₂×#127	1	2	yes	—
467	C₂×#67	C₂×#127	1	2	yes	—
468	C₂²×Dic₃	#392	1	4	yes	—
469	C₂²×Dic₃	C₂×#120	1	1	yes	characteristic
470	C₂²×Dic₃	C₂×#120	1	1	yes	characteristic
471	C₂²×Dic₃	C₂×#120	1	2	yes	—
472	C₂²×Dic₃	C₂×#120	1	1	yes	characteristic
473	C₂²×Dic₃	C₂×#120	1	1	yes	characteristic
474	C₂²×Dic₃	C₂×#121	1	2	yes	—
475	C₂²×Dic₃	C₂×#121	1	2	yes	—
476	C₂²×Dic₃	C₂×#127	1	2	yes	—
477	C₂×D₁₂	#392	1	4	yes	—
478	C₂×D₁₂	#392	1	4	yes	—
479	C₂×D₁₂	C₂×#120	1	2	yes	—
480	C₂×D₁₂	C₂×#121	1	2	yes	—
481	C₂×C₄×D₃	#392	1	4	yes	—
482	C₂×C₄×D₃	#392	1	4	yes	—
483	C₂×C₄×D₃	#392	1	4	yes	—
484	C₂×C₄×D₃	#392	1	4	yes	—
485	C₂×C₄×D₃	#392	1	4	yes	—
486	C₂×C₄×D₃	#392	1	4	yes	—
487	C₂×C₄×D₃	#392	1	4	yes	—
488	C₂×C₄×D₃	#392	1	4	yes	—
489	C₂×C₄×D₃	B(4,𝔽₂)	1	1	yes	characteristic
490	C₂×C₄×D₃	B(4,𝔽₂)	1	1	yes	characteristic
491	C₂×C₄×D₃	B(4,𝔽₂)	1	1	yes	characteristic
492	C₂×C₄×D₃	B(4,𝔽₂)	1	1	yes	characteristic
493	C₂×C₄×D₃	B(4,𝔽₂)	1	4	yes	—
494	C₂×C₄×D₃	C₂×#120	1	2	yes	—
495	C₂×C₄×D₃	C₂×#120	1	2	yes	—
496	C₂×C₄×D₃	C₂×#121	1	2	yes	—
497	C₂×C₄×D₃	C₂×#121	1	2	yes	—
498	C₂×Dic₆	#392	1	4	yes	—
499	C₂×Dic₆	#392	1	4	yes	—
500	C₂×Dic₆	C₂×#120	1	2	yes	—
501	C₂×Dic₆	C₂×#121	1	2	yes	—
502	C₂⁵	C₂×D₃×D₄	1	1	yes	characteristic
503	H(5,𝔽₂)	C₂×D₃×D₄	1	4	yes	—
504	C₂×#41	C₂×D₃×D₄	1	2	yes	—
505	C₂×#41	C₂×D₃×D₄	1	2	yes	—
506	C₂×#41	C₂×D₃×D₄	1	2	yes	—
507	C₂×#41	D₃×#41	1	2	yes	—
508	C₂²×Q₈	C₂×D₃×D₄	1	1	yes	characteristic
509	C₂²×D₄	C₂×D₃×D₄	1	2	yes	—
510	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
511	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
512	C₂²×D₄	C₂⁴×D₃	1	1	yes	characteristic
513	C₂³×C₄	C₂×D₃×D₄	1	1	yes	characteristic
514	C₂³×C₄	C₂×D₃×D₄	1	1	yes	characteristic
515	C₂³×C₄	C₂×D₃×D₄	1	1	yes	characteristic
516	C₂³×C₄	C₂×D₃×D₄	1	1	yes	characteristic
517	C₂³×C₄	C₂×D₃×D₄	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂×D₃×D₄	1	1	yes	characteristic
519	C₂×C₂²⋊C₄	C₂×D₃×D₄	1	1	yes	characteristic
520	C₂×C₂²⋊C₄	C₂×D₃×D₄	1	2	yes	—
521	C₂×C₄²	C₂×D₃×D₄	1	2	yes	—
522	#100	C₂×D₃×D₄	1	4	yes	—
523	#99	C₂×D₃×D₄	1	4	yes	—
524	C₂³×C₃	C₂×#392	1	2	yes	—
525	C₂³×C₃	C₂²×#120	1	1	yes	characteristic
526	C₂³×C₃	C₂²×#120	1	1	yes	characteristic
527	C₂³×C₃	C₂²×#121	1	1	yes	characteristic
528	C₂³×C₃	C₂²×#121	1	1	yes	characteristic
529	C₂³×C₃	C₂²×#127	1	1	yes	characteristic
530	C₂²×D₃	C₂×#392	1	2	yes	—
531	C₂²×D₃	C₂×#392	1	2	yes	—
532	C₂²×D₃	C₂×#392	1	2	yes	—
533	C₂²×D₃	C₂×#392	1	2	yes	—
534	C₂²×D₃	C₂×B(4,𝔽₂)	1	1	yes	characteristic
535	C₂²×D₃	C₂×B(4,𝔽₂)	1	2	yes	—
536	C₂²×D₃	C₂×B(4,𝔽₂)	1	1	yes	characteristic
537	C₂×C₃×C₄	C₂×#392	1	2	yes	—
538	C₂×C₃×C₄	C₂×#392	1	2	yes	—
539	C₂×C₃×C₄	C₂×#392	1	2	yes	—
540	C₂×C₃×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
541	C₂×C₃×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
542	C₂×C₃×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
543	C₂×C₃×C₄	C₂²×#120	1	1	yes	characteristic
544	C₂×C₃×C₄	C₂²×#121	1	1	yes	characteristic
545	C₂×Dic₃	C₂×#392	1	2	yes	—
546	C₂×Dic₃	C₂×#392	1	2	yes	—
547	C₂×Dic₃	C₂×#392	1	2	yes	—
548	C₂×Dic₃	C₂×#392	1	2	yes	—
549	C₂×Dic₃	C₂×B(4,𝔽₂)	1	1	yes	characteristic
550	C₂×Dic₃	C₂×B(4,𝔽₂)	1	1	yes	characteristic
551	C₂×Dic₃	C₂×B(4,𝔽₂)	1	2	yes	—
552	C₄×D₃	#2021	1	4	yes	—
553	C₄×D₃	#2021	1	4	yes	—
554	C₄×D₃	#2021	1	4	yes	—
555	C₄×D₃	#2021	1	4	yes	—
556	C₂⁴	D₃×#120	1	1	yes	characteristic
557	C₂⁴	C₂²×D₃×D₄	1	1	yes	characteristic
558	C₂⁴	C₂²×D₃×D₄	1	1	yes	characteristic
559	C₂×Q₈	D₃×#120	1	2	yes	—
560	C₂×Q₈	D₃×#121	1	2	yes	—
561	C₂×D₄	D₃×#120	1	2	yes	—
562	C₂×D₄	D₃×#121	1	2	yes	—
563	C₂×D₄	D₃×#121	1	2	yes	—
564	C₂×D₄	D₃×#127	1	2	yes	—
565	C₂×D₄	C₂²×D₃×D₄	1	1	yes	characteristic
566	C₂×D₄	C₂²×D₃×D₄	1	1	yes	characteristic
567	C₂×D₄	C₂²×D₃×D₄	1	1	yes	characteristic
568	C₂×D₄	C₂×D₃×#41	1	1	yes	characteristic
569	C₂²×C₄	D₃×#120	1	2	yes	—
570	C₂²×C₄	D₃×#120	1	1	yes	characteristic
571	C₂²×C₄	D₃×#120	1	1	yes	characteristic
572	C₂²×C₄	D₃×#120	1	2	yes	—
573	C₂²×C₄	D₃×#120	1	1	yes	characteristic
574	C₂²×C₄	D₃×#121	1	2	yes	—
575	C₂²×C₄	D₃×#121	1	2	yes	—
576	C₂²×C₄	D₃×#121	1	2	yes	—
577	C₂²×C₄	D₃×#127	1	2	yes	—
578	C₂²×C₄	C₂²×D₃×D₄	1	1	yes	characteristic
579	C₂²×C₃	C₂²×#392	1	1	yes	characteristic
580	C₂²×C₃	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
581	C₂²×C₃	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
582	C₂×D₃	C₂×#2021	1	2	yes	—
583	C₂×D₃	C₂×#2021	1	2	yes	—
584	C₂×D₃	#33553	1	2	yes	—
585	C₂×D₃	#33556	1	2	yes	—
586	C₃×C₄	C₂×#2021	1	2	yes	—
587	C₃×C₄	C₂×#2021	1	2	yes	—
588	Dic₃	C₂×#2021	1	2	yes	—
589	Dic₃	C₂×#2021	1	2	yes	—
590	C₂³	D₃×#392	1	2	yes	—
591	C₂³	C₂×D₃×#120	1	1	yes	characteristic
592	C₂³	C₂×D₃×#120	1	1	yes	characteristic
593	C₂³	C₂×D₃×#121	1	1	yes	characteristic
594	C₂³	C₂×D₃×#121	1	1	yes	characteristic
595	C₂³	C₂×D₃×#127	1	1	yes	characteristic
596	C₂×C₄	D₃×#392	1	2	yes	—
597	C₂×C₄	D₃×#392	1	2	yes	—
598	C₂×C₄	D₃×#392	1	2	yes	—
599	C₂×C₄	D₃×B(4,𝔽₂)	1	2	yes	—
600	C₂×C₄	D₃×B(4,𝔽₂)	1	1	yes	characteristic
601	C₂×C₄	D₃×B(4,𝔽₂)	1	1	yes	characteristic
602	C₂×C₄	C₂×D₃×#120	1	1	yes	characteristic
603	C₂×C₄	C₂×D₃×#121	1	1	yes	characteristic
604	C₂×C₃	C₂²×#2021	1	1	yes	characteristic
605	C₂×C₃	C₂×#33553	1	1	yes	characteristic
606	C₂×C₃	C₂×#33556	1	1	yes	characteristic
607	D₃	#498929	1	4	yes	direct product factor
608	C₂²	C₂×D₃×#392	1	1	yes	characteristic
609	C₂²	C₂×D₃×B(4,𝔽₂)	1	1	yes	characteristic
610	C₂²	C₂×D₃×B(4,𝔽₂)	1	1	yes	characteristic
611	C₄	D₃×#2021	1	2	yes	—
612	C₄	D₃×#2021	1	2	yes	—
613	C₃	C₂×#498929	1	1	yes	characteristic, complemented, Sylow
614	C₂	C₂×D₃×#2021	1	1	yes	characteristic
615	C₂	D₃×#33553	1	1	yes	characteristic
616	C₂	D₃×#33556	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₃×B(4,𝔽₂)
commutator, cosocle	C₂²×C₃×D₄	C₂⁵
Frattini	C₂²×D₄	C₂⁴×D₃
Fitting	C₃×#498929	C₂
socle	C₂²×C₃	C₂²×B(4,𝔽₂)
hypercenter	#498929	D₃
hypocenter	C₃	C₂×#498929
LCS	G ▷ C₂²×C₃×D₄ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×#41 ◁ #498929

Complements

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

N	H ≅ G/N	type
1. #72253973	C₂	semidirect
2. D₃×#37269	C₂	semidirect
3. #72253970	C₂	semidirect
4. C₃×#498929	C₂	semidirect
5. #72253966	C₂	semidirect
6. D₃×#12575	C₂	semidirect
7. #72253963	C₂	semidirect
8. D₃×#20610	C₂	semidirect
9. #72253954	C₂	semidirect
10. #72253942	C₂	semidirect
11. #72253934	C₂	semidirect
12. #72253927	C₂	semidirect
13. #72253913	C₂	semidirect
14. D₃×#13346	C₂	semidirect
15. D₃×#13347	C₂	semidirect
16. C₂×D₃×#3025	C₂	semidirect
17. C₂×D₃×#3021	C₂	semidirect
18. C₂×D₃×#2120	C₂	semidirect
19. C₂×D₃×#2128	C₂	semidirect
23. C₂×#78690	C₂²	semidirect
24. C₂×#80308	C₂²	semidirect
25. C₂×#84125	C₂²	semidirect
26. C₂×#82936	C₂²	semidirect
27. C₂×#80304	C₂²	semidirect
28. C₂×D₃×#458	C₂²	semidirect
29. C₂×D₃×B(4,𝔽₂)	C₂²	semidirect
30. C₂×#78717	C₂²	semidirect
31. C₂×#84122	C₂²	semidirect
32. C₂×#83395	C₂²	semidirect
33. C₂×#80279	C₂²	semidirect
38. D₃×#2709	C₂²	semidirect
39. D₃×#2669	C₂²	semidirect
40. #11016711	C₂²	semidirect
41. #11016710	C₂²	semidirect
42. #11016702	C₂²	semidirect
43. #11016701	C₂²	semidirect
44. #11016698	C₂²	semidirect
46. C₂×#71861	C₂²	semidirect
47. C₂×#70061	C₂²	semidirect
48. C₂×#70061	C₂²	semidirect
49. C₂×#69152	C₂²	semidirect
50. C₂×D₃×#353	C₂²	semidirect
51. C₂×#70145	C₂²	semidirect
52. C₂×#71716	C₂²	semidirect
53. C₂×#69144	C₂²	semidirect
54. C₂×#70056	C₂²	semidirect
55. C₂×#69136	C₂²	semidirect
56. C₂×D₃×#352	C₂²	semidirect
57. C₂×D₃×AΣL(1,𝔽₁₆)	C₂²	semidirect
58. #10794459	C₂²	semidirect
59. #10794458	C₂²	semidirect
60. #10794457	C₂²	semidirect
61. #10794456	C₂²	semidirect
62. D₃×#1790	C₂²	semidirect
63. #10714154	C₂²	semidirect
64. #10714153	C₂²	semidirect
65. #10714152	C₂²	semidirect
66. #10714151	C₂²	semidirect
67. #10714150	C₂²	semidirect
68. #10714149	C₂²	semidirect
69. #10714148	C₂²	semidirect
70. #10714147	C₂²	semidirect
71. #10714146	C₂²	semidirect
72. #10714145	C₂²	semidirect
73. #10714144	C₂²	semidirect
74. #10714143	C₂²	semidirect
75. #10714142	C₂²	semidirect
76. #10714141	C₂²	semidirect
77. #10710139	C₂²	semidirect
78. #10710138	C₂²	semidirect
79. #10710137	C₂²	semidirect
80. #10710136	C₂²	semidirect
81. D₃×#1390	C₂²	semidirect
82. C₂×C₃×#3025	C₂²	semidirect
83. C₂×C₃×#3021	C₂²	semidirect
84. C₃×#37269	C₂²	semidirect
85. C₂×C₃×#2128	C₂²	semidirect
86. C₂×C₃×#2120	C₂²	semidirect
87. C₃×#20610	C₂²	semidirect
88. C₃×#13347	C₂²	semidirect
89. C₃×#13346	C₂²	semidirect
90. C₃×#12575	C₂²	semidirect
91. #498929	D₃	direct (N × H)
93. D₃×#585	D₄	semidirect
98. C₂³×D₃×D₄	D₄	semidirect
104. C₂×#5805	D₄	semidirect
108. C₂×#5674	D₄	semidirect
109. C₂×D₃×#124	D₄	semidirect
118. C₂×#5525	D₄	semidirect
121. C₂×D₃×#117	D₄	semidirect
122. C₂×D₃×#117	D₄	semidirect
123. C₂²×D₃×C₄⋊C₄	D₄	semidirect
124. C₂×C₃×#458	C₂³	semidirect
125. C₂×C₃×B(4,𝔽₂)	C₂³	semidirect
130. C₃×#2709	C₂³	semidirect
131. C₃×#2669	C₂³	semidirect
133. C₂×#5244	C₂³	semidirect
134. C₂×#5243	C₂³	semidirect
140. #83190	C₂³	semidirect
141. #83183	C₂³	semidirect
143. C₂×#5053	C₂³	semidirect
144. #82884	C₂³	semidirect
145. C₂×#5032	C₂³	semidirect
146. #82594	C₂³	semidirect
147. #82270	D₄	semidirect
148. #82186	D₄	semidirect
149. D₃×#413	D₄	semidirect
153. D₃×#410	D₄	semidirect
156. C₂×#4742	C₂³	semidirect
157. C₂×#4741	C₂³	semidirect
160. #74912	C₂³	semidirect
161. D₃×#386	D₄	semidirect
163. #74820	C₂³	semidirect
164. #74662	D₄	semidirect
166. C₂×C₃×#353	C₂³	semidirect
167. C₂×C₃×#352	C₂³	semidirect
168. C₂×C₃×AΣL(1,𝔽₁₆)	C₂³	semidirect
169. C₃×#1790	C₂³	semidirect
170. #72142	C₂³	semidirect
171. C₂×#4545	C₂³	semidirect
172. C₂×#4539	C₂³	semidirect
173. C₂×#4536	C₂³	semidirect
174. C₂×#4476	C₂³	semidirect
175. C₂×#4475	C₂³	semidirect
176. #70033	C₂³	semidirect
177. C₂×#4474	C₂³	semidirect
178. C₂×#4474	C₂³	semidirect
179. C₂×#4472	C₂³	semidirect
180. C₂×#4471	C₂³	semidirect
181. #69598	C₂³	semidirect
182. C₃×#1390	C₂³	semidirect
183. #67698	C₂³	semidirect
184. #67694	C₂³	semidirect
185. #67637	C₂³	semidirect
186. C₂×#3025	C₂×D₃	semidirect
187. C₂×#3021	C₂×D₃	semidirect
188. #37269	C₂×D₃	semidirect
189. C₂×#2128	C₂×D₃	semidirect
190. C₂×#2120	C₂×D₃	semidirect
191. #20610	C₂×D₃	semidirect
192. #13347	C₂×D₃	semidirect
193. #13346	C₂×D₃	semidirect
194. #12575	C₂×D₃	semidirect
196. C₃×#585	C₂×D₄	semidirect
199. C₂³×C₃×D₄	C₂×D₄	semidirect
202. #5966	C₂×D₄	semidirect
204. #5964	C₂×D₄	semidirect
218. C₂²×D₃×D₄	C₂×D₄	semidirect
223. C₂³×D₁₂	C₂×D₄	semidirect
232. C₂×C₃×#124	C₂×D₄	semidirect
238. C₂×C₃×#117	C₂×D₄	semidirect
239. C₂×C₃×#117	C₂×D₄	semidirect
240. C₂²×C₃×C₄⋊C₄	C₂×D₄	semidirect
243. C₂×#947	C₂×D₄	semidirect
248. C₂×#936	C₂×D₄	semidirect
254. C₂×#926	C₂×D₄	semidirect
255. C₂×#926	C₂×D₄	semidirect
256. C₂²×C₄⋊Dic₃	C₂×D₄	semidirect
257. C₂²×Dic₃⋊C₄	C₂×D₄	semidirect
267. C₂×#877	C₂×D₄	semidirect
268. C₂×#875	C₂×D₄	semidirect
270. C₂×#872	C₂×D₄	semidirect
272. C₃×#413	C₂×D₄	semidirect
274. C₃×#410	C₂×D₄	semidirect
277. C₃×#386	C₂×D₄	semidirect
279. #5240	C₂×D₄	semidirect
280. #5237	C₂×D₄	semidirect
281. #5220	C₂×D₄	semidirect
287. #5213	C₂×D₄	semidirect
289. #4958	C₂×D₄	semidirect
290. #4745	C₂×D₄	semidirect
293. #4740	C₂×D₄	semidirect
297. C₂×#458	C₂²×D₃	semidirect
298. C₂×B(4,𝔽₂)	C₂²×D₃	semidirect
303. #2709	C₂²×D₃	semidirect
304. #2669	C₂²×D₃	semidirect
306. C₂×#353	C₂²×D₃	semidirect
307. C₂×#352	C₂²×D₃	semidirect
308. C₂×AΣL(1,𝔽₁₆)	C₂²×D₃	semidirect
309. #1790	C₂²×D₃	semidirect
310. #1390	C₂²×D₃	semidirect
404. #585	D₃×D₄	semidirect
407. C₂³×D₄	D₃×D₄	semidirect
410. C₂×#124	D₃×D₄	semidirect
416. C₂×#117	D₃×D₄	semidirect
417. C₂×#117	D₃×D₄	semidirect
418. C₂²×C₄⋊C₄	D₃×D₄	semidirect
419. #413	D₃×D₄	semidirect
421. #410	D₃×D₄	semidirect
424. #386	D₃×D₄	semidirect
607. D₃	#498929	direct (N × H)
613. C₃	C₂×#498929	semidirect

Maximal subgroups

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

subgroup	index
#72253973	2
D₃×#37269	2
#72253970	2
C₃×#498929	2
#72253966	2
D₃×#12575	2
#72253963	2
D₃×#20610	2
#72253954	2
C₂×#498929	3
#72253942	2
#72253934	2
#72253927	2
#72253913	2
D₃×#13346	2
D₃×#13347	2
C₂×D₃×#3025	2
C₂×D₃×#3021	2
C₂×D₃×#2120	2
C₂×D₃×#2128	2

Subgroups — D3×#498929 #72253975

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#498929 #72253975