Subgroups — C₂×#72219819 #72269977

Order 3072.

At least 15468 conjugacy classes of subgroups; only the 1279 normal subgroups are shown.

The subgroup lattice has 687 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10710645	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10826738	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10710711	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11703802	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10949250	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10949248	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#10826767	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10710944	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#12753	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#10949251	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#10949249	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#10710947	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#10710719	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#10710949	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#10826748	C₂	1	1	yes	maximal, characteristic, complemented
16	#72219819	C₂	1	16	yes	maximal, direct product factor
17	#11703802	C₂²	1	8	yes	complemented
18	C₂×#85867	C₂²	1	1	yes	characteristic, complemented
19	C₂×#86330	C₂²	1	1	yes	characteristic
20	C₂×#86308	C₂²	1	1	yes	characteristic
21	C₂×#85921	C₂²	1	1	yes	characteristic
22	C₂×#86310	C₂²	1	1	yes	characteristic
23	C₂×#86333	C₂²	1	1	yes	characteristic
24	C₂²×D₃×#120	C₂²	1	1	yes	characteristic
25	C₂×#78686	C₂²	1	1	yes	characteristic, complemented
26	C₂×#83375	C₂²	1	1	yes	characteristic, complemented
27	C₂²×#4741	C₂²	1	1	yes	characteristic, complemented
28	C₂²×#5032	C₂²	1	1	yes	characteristic, complemented
29	C₂×#78700	C₂²	1	1	yes	characteristic, complemented
30	C₂×#83394	C₂²	1	1	yes	characteristic, complemented
31	#10949251	C₂²	1	8	yes	complemented
32	#10949250	C₂²	1	8	yes	complemented
33	#10949249	C₂²	1	8	yes	complemented
34	#10949248	C₂²	1	8	yes	complemented
35	C₂×#71860	C₂²	1	1	yes	characteristic, complemented
36	C₂×#70019	C₂²	1	1	yes	characteristic, complemented
37	C₂×#70019	C₂²	1	1	yes	characteristic, complemented
38	C₂×#70094	C₂²	1	1	yes	characteristic, complemented
39	C₂×#71847	C₂²	1	1	yes	characteristic, complemented
40	C₂×#70015	C₂²	1	1	yes	characteristic, complemented
41	C₂²×#4475	C₂²	1	1	yes	characteristic, complemented
42	C₂²×#4536	C₂²	1	1	yes	characteristic, complemented
43	C₂²×#4471	C₂²	1	1	yes	characteristic, complemented
44	#10826767	C₂²	1	8	yes	complemented
45	#10826748	C₂²	1	8	yes	complemented
46	#10826738	C₂²	1	8	yes	complemented
47	C₂×#71656	C₂²	1	1	yes	characteristic, complemented
48	C₂×#71652	C₂²	1	1	yes	characteristic, complemented
49	C₂×#71654	C₂²	1	1	yes	characteristic, complemented
50	C₂×#70079	C₂²	1	1	yes	characteristic, complemented
51	C₂×#70035	C₂²	1	1	yes	characteristic, complemented
52	C₂×#70035	C₂²	1	1	yes	characteristic, complemented
53	#10710949	C₂²	1	8	yes	complemented
54	#10710947	C₂²	1	8	yes	complemented
55	#10710944	C₂²	1	8	yes	complemented
56	#10710719	C₂²	1	8	yes	complemented
57	#10710711	C₂²	1	8	yes	complemented
58	#10710645	C₂²	1	8	yes	complemented
59	C₂×C₃×#3532	C₂²	1	1	yes	characteristic
60	C₂×C₃×#2127	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₃×#2121	C₂²	1	1	yes	characteristic, complemented
62	C₂²×C₃×AΣL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₃×#1913	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₃×#1911	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₃×#1889	C₂²	1	1	yes	characteristic, complemented
66	C₃×#12753	C₂²	1	8	yes	complemented
67	C₂×#12753	D₃	1	1	yes	characteristic, complemented
68	C₂⁶×D₃	D₄	1	1	yes	characteristic, complemented
69	C₂²×#1009	D₄	1	1	yes	characteristic, complemented
70	C₂²×#1004	D₄	1	1	yes	characteristic, complemented
71	C₂²×#1004	C₂³	1	1	yes	characteristic, complemented
72	C₂³×D₃×D₄	C₂³	1	1	yes	characteristic
73	C₃×#3532	D₄	1	4	yes	complemented
74	C₃×#3532	C₂³	1	4	yes	—
75	C₂×C₃×H(3,𝔽₄)	D₄	1	1	yes	characteristic, complemented
76	C₂×C₃×#560	D₄	1	1	yes	characteristic, complemented
77	C₂×C₃×#551	D₄	1	1	yes	characteristic, complemented
78	C₂×C₃×D₄²	D₄	1	1	yes	characteristic, complemented
79	C₂×C₃×#535	C₂³	1	1	yes	characteristic
80	C₂×C₃×#534	C₂³	1	1	yes	characteristic
81	C₂²×C₃×#120	C₂³	1	1	yes	characteristic
82	C₂×C₃×#518	C₂³	1	1	yes	characteristic, complemented
83	C₂²×#953	D₄	1	1	yes	characteristic, complemented
84	C₂×#5828	D₄	1	1	yes	characteristic, complemented
85	C₂×#5805	C₂³	1	1	yes	characteristic
86	C₂×#5804	C₂³	1	1	yes	characteristic
87	C₂²×#937	D₄	1	1	yes	characteristic, complemented
88	C₂²×#937	C₂³	1	1	yes	characteristic
89	#86333	D₄	1	4	yes	complemented
90	#86333	C₂³	1	4	yes	—
91	#86330	D₄	1	4	yes	complemented
92	#86330	C₂³	1	4	yes	—
93	#86310	D₄	1	4	yes	complemented
94	#86310	C₂³	1	4	yes	—
95	#86308	D₄	1	4	yes	complemented
96	#86308	C₂³	1	4	yes	—
97	C₂×#5720	D₄	1	1	yes	characteristic, complemented
98	C₂×#5717	D₄	1	1	yes	characteristic, complemented
99	C₂×#5683	D₄	1	1	yes	characteristic, complemented
100	C₂×#5679	D₄	1	1	yes	characteristic, complemented
101	C₂×#5666	D₄	1	1	yes	characteristic, complemented
102	C₂×#5659	D₄	1	1	yes	characteristic, complemented
103	#85921	D₄	1	4	yes	complemented
104	#85921	C₂³	1	4	yes	—
105	C₂×#5595	D₄	1	1	yes	characteristic, complemented
106	C₂×#5590	D₄	1	1	yes	characteristic, complemented
107	C₂×#5590	D₄	1	1	yes	characteristic, complemented
108	C₂×D₃×#120	D₄	1	4	yes	complemented
109	C₂×D₃×#120	C₂³	1	4	yes	—
110	C₂×#5594	D₄	1	1	yes	characteristic, complemented
111	C₂×#5594	D₄	1	1	yes	characteristic, complemented
112	C₂×#5587	D₄	1	1	yes	characteristic, complemented
113	#85867	C₂³	1	4	yes	complemented
114	C₂×#5524	D₄	1	1	yes	characteristic, complemented
115	C₂×#5521	D₄	1	1	yes	characteristic, complemented
116	C₂²×#882	D₄	1	1	yes	characteristic, complemented
117	C₂²×#882	D₄	1	1	yes	characteristic, complemented
118	C₂×#5486	D₄	1	1	yes	characteristic, complemented
119	C₂²×D₃×C₂²⋊C₄	D₄	1	1	yes	characteristic, complemented
120	C₂²×C₃×#100	C₂³	1	1	yes	characteristic, complemented
121	C₂²×C₃×#99	C₂³	1	1	yes	characteristic, complemented
122	C₂²×C₃×#99	C₂³	1	1	yes	characteristic, complemented
123	C₂²×#834	C₂³	1	1	yes	characteristic, complemented
124	C₂²×#834	C₂³	1	1	yes	characteristic, complemented
125	C₂²×#833	C₂³	1	1	yes	characteristic, complemented
126	#83394	C₂³	1	4	yes	complemented
127	#83375	C₂³	1	4	yes	complemented
128	C₂×#5032	C₂³	1	4	yes	complemented
129	#78700	C₂³	1	4	yes	complemented
130	#78686	C₂³	1	4	yes	complemented
131	C₂×#4741	C₂³	1	4	yes	complemented
132	C₃×#2127	C₂³	1	4	yes	complemented
133	C₃×#2121	C₂³	1	4	yes	complemented
134	C₂×C₃×AΣL(1,𝔽₁₆)	C₂³	1	4	yes	complemented
135	C₃×#1913	C₂³	1	4	yes	complemented
136	C₃×#1911	C₂³	1	4	yes	complemented
137	C₃×#1889	C₂³	1	4	yes	complemented
138	#71860	C₂³	1	4	yes	complemented
139	#71847	C₂³	1	4	yes	complemented
140	C₂×#4536	C₂³	1	4	yes	complemented
141	#71656	C₂³	1	4	yes	complemented
142	#71654	C₂³	1	4	yes	complemented
143	#71652	C₂³	1	4	yes	complemented
144	#70094	C₂³	1	4	yes	complemented
145	C₂×#4475	C₂³	1	4	yes	complemented
146	#70079	C₂³	1	4	yes	complemented
147	#70035	C₂³	1	4	yes	complemented
148	#70035	C₂³	1	4	yes	complemented
149	#70019	C₂³	1	4	yes	complemented
150	#70019	C₂³	1	4	yes	complemented
151	#70015	C₂³	1	4	yes	complemented
152	C₂×#4471	C₂³	1	4	yes	complemented
153	C₂×#3532	C₂×D₃	1	1	yes	characteristic
154	C₂×#2127	C₂×D₃	1	1	yes	characteristic, complemented
155	C₂×#2121	C₂×D₃	1	1	yes	characteristic, complemented
156	C₂²×AΣL(1,𝔽₁₆)	C₂×D₃	1	1	yes	characteristic, complemented
157	C₂×#1913	C₂×D₃	1	1	yes	characteristic, complemented
158	C₂×#1911	C₂×D₃	1	1	yes	characteristic, complemented
159	C₂×#1889	C₂×D₃	1	1	yes	characteristic, complemented
160	#12753	C₂×D₃	1	8	yes	complemented
161	C₂⁶×C₃	C₂×D₄	1	1	yes	characteristic
162	C₂⁵×D₃	C₂×D₄	1	1	yes	characteristic
163	C₂⁵×D₃	C₂×D₄	1	1	yes	characteristic
164	C₂⁵×D₃	C₂×D₄	1	1	yes	characteristic
165	C₂⁵×D₃	C₂×D₄	1	4	yes	complemented
166	C₂²×C₃×#41	C₂×D₄	1	1	yes	characteristic
167	C₂³×C₃×D₄	C₂×D₄	1	1	yes	characteristic
168	C₂³×C₃×D₄	C₂⁴	1	1	yes	characteristic
169	C₂³×#67	C₂×D₄	1	1	yes	characteristic
170	C₂³×#67	C₂×D₄	1	1	yes	characteristic
171	C₂³×#67	C₂×D₄	1	1	yes	characteristic
172	C₂×#1009	C₂×D₄	1	4	yes	complemented
173	C₂×#1004	C₂×D₄	1	4	yes	complemented
174	C₂×#1004	C₂⁴	1	2	yes	complemented
175	C₂²×D₃×D₄	C₂×D₄	1	2	yes	—
176	C₂²×D₃×D₄	C₂×D₄	1	2	yes	—
177	C₂²×D₃×D₄	C₂×D₄	1	2	yes	—
178	C₂²×D₃×D₄	C₂⁴	1	2	yes	—
179	C₂²×#235	C₂×D₄	1	1	yes	characteristic
180	C₂³×D₁₂	C₂×D₄	1	1	yes	characteristic
181	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
182	C₃×H(3,𝔽₄)	C₂×D₄	1	4	yes	complemented
183	C₃×#560	C₂×D₄	1	4	yes	complemented
184	C₃×#551	C₂×D₄	1	4	yes	complemented
185	C₃×D₄²	C₂×D₄	1	4	yes	complemented
186	C₃×#535	C₂×D₄	1	2	yes	—
187	C₃×#535	C₂×D₄	1	2	yes	—
188	C₃×#535	C₂×D₄	1	2	yes	—
189	C₃×#535	C₂⁴	1	2	yes	—
190	C₃×#534	C₂×D₄	1	2	yes	—
191	C₃×#534	C₂×D₄	1	2	yes	—
192	C₃×#534	C₂×D₄	1	2	yes	—
193	C₃×#534	C₂⁴	1	2	yes	—
194	C₂×C₃×#127	C₂×D₄	1	1	yes	characteristic
195	C₂×C₃×#127	C₂×D₄	1	1	yes	characteristic
196	C₂×C₃×#124	C₂×D₄	1	1	yes	characteristic
197	C₂×C₃×#124	C₂×D₄	1	1	yes	characteristic
198	C₂×C₃×#123	C₂×D₄	1	1	yes	characteristic
199	C₂×C₃×#123	C₂×D₄	1	1	yes	characteristic
200	C₂×C₃×#120	C₂×D₄	1	1	yes	characteristic
201	C₂×C₃×#120	C₂×D₄	1	1	yes	characteristic
202	C₂×C₃×#120	C₂×D₄	1	2	yes	—
203	C₂×C₃×#120	C₂×D₄	1	1	yes	characteristic
204	C₂×C₃×#120	C₂×D₄	1	1	yes	characteristic
205	C₂×C₃×#120	C₂×D₄	1	2	yes	—
206	C₂×C₃×#120	C₂×D₄	1	1	yes	characteristic
207	C₂×C₃×#120	C₂×D₄	1	1	yes	characteristic
208	C₂×C₃×#120	C₂×D₄	1	2	yes	—
209	C₂×C₃×#120	C₂⁴	1	2	yes	—
210	C₃×#518	C₂⁴	1	2	yes	complemented
211	C₂×C₃×#117	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
214	C₂×#953	C₂×D₄	1	4	yes	complemented
215	C₂²×#217	C₂×D₄	1	1	yes	characteristic
216	C₂²×#217	C₂×D₄	1	1	yes	characteristic
217	#5828	C₂×D₄	1	4	yes	complemented
218	#5805	C₂×D₄	1	2	yes	—
219	#5805	C₂×D₄	1	2	yes	—
220	#5805	C₂×D₄	1	2	yes	—
221	#5805	C₂⁴	1	2	yes	—
222	#5804	C₂×D₄	1	2	yes	—
223	#5804	C₂×D₄	1	2	yes	—
224	#5804	C₂×D₄	1	2	yes	—
225	#5804	C₂⁴	1	2	yes	—
226	C₂×#940	C₂×D₄	1	1	yes	characteristic
227	C₂×#940	C₂×D₄	1	1	yes	characteristic
228	C₂×#937	C₂×D₄	1	2	yes	—
229	C₂×#937	C₂×D₄	1	2	yes	—
230	C₂×#937	C₂×D₄	1	2	yes	—
231	C₂×#937	C₂×D₄	1	1	yes	characteristic
232	C₂×#937	C₂×D₄	1	1	yes	characteristic
233	C₂×#937	C₂×D₄	1	1	yes	characteristic
234	C₂×#937	C₂×D₄	1	1	yes	characteristic
235	C₂×#937	C₂×D₄	1	1	yes	characteristic
236	C₂×#937	C₂×D₄	1	1	yes	characteristic
237	C₂×#937	C₂×D₄	1	4	yes	complemented
238	C₂×#937	C₂⁴	1	2	yes	—
239	C₂×#936	C₂×D₄	1	1	yes	characteristic
240	C₂×#936	C₂×D₄	1	1	yes	characteristic
241	C₂×#935	C₂×D₄	1	1	yes	characteristic
242	C₂×#935	C₂×D₄	1	1	yes	characteristic
243	C₂×#926	C₂×D₄	1	1	yes	characteristic
244	#5720	C₂×D₄	1	4	yes	complemented
245	#5717	C₂×D₄	1	4	yes	complemented
246	#5683	C₂×D₄	1	4	yes	complemented
247	#5679	C₂×D₄	1	4	yes	complemented
248	#5666	C₂×D₄	1	4	yes	complemented
249	#5659	C₂×D₄	1	4	yes	complemented
250	#5595	C₂×D₄	1	4	yes	complemented
251	#5594	C₂×D₄	1	4	yes	complemented
252	#5594	C₂×D₄	1	4	yes	complemented
253	#5590	C₂×D₄	1	4	yes	complemented
254	#5590	C₂×D₄	1	4	yes	complemented
255	#5587	C₂×D₄	1	4	yes	complemented
256	#5524	C₂×D₄	1	4	yes	complemented
257	#5521	C₂×D₄	1	4	yes	complemented
258	C₂×#882	C₂×D₄	1	4	yes	complemented
259	C₂×#882	C₂×D₄	1	4	yes	complemented
260	#5486	C₂×D₄	1	4	yes	complemented
261	C₂×D₃×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
262	C₂×C₃×#100	C₂⁴	1	2	yes	complemented
263	C₂×C₃×#99	C₂⁴	1	2	yes	complemented
264	C₂×C₃×#99	C₂⁴	1	2	yes	complemented
265	C₂×#834	C₂⁴	1	2	yes	complemented
266	C₂×#834	C₂⁴	1	2	yes	complemented
267	C₂×#833	C₂⁴	1	2	yes	complemented
268	#3532	D₁₂	1	4	yes	complemented
269	#3532	C₂²×D₃	1	4	yes	—
270	C₂×H(3,𝔽₄)	D₁₂	1	1	yes	characteristic, complemented
271	C₂×#560	D₁₂	1	1	yes	characteristic, complemented
272	C₂×#551	D₁₂	1	1	yes	characteristic, complemented
273	C₂×D₄²	D₁₂	1	1	yes	characteristic, complemented
274	C₂×#535	C₂²×D₃	1	1	yes	characteristic
275	C₂×#534	C₂²×D₃	1	1	yes	characteristic
276	C₂²×#120	C₂²×D₃	1	1	yes	characteristic
277	C₂×#518	C₂²×D₃	1	1	yes	characteristic, complemented
278	C₂²×#100	C₂²×D₃	1	1	yes	characteristic, complemented
279	C₂²×#99	C₂²×D₃	1	1	yes	characteristic, complemented
280	C₂²×#99	C₂²×D₃	1	1	yes	characteristic, complemented
281	#2127	C₂²×D₃	1	4	yes	complemented
282	#2121	C₂²×D₃	1	4	yes	complemented
283	C₂×AΣL(1,𝔽₁₆)	C₂²×D₃	1	4	yes	complemented
284	#1913	C₂²×D₃	1	4	yes	complemented
285	#1911	C₂²×D₃	1	4	yes	complemented
286	#1889	C₂²×D₃	1	4	yes	complemented
287	C₂⁵×C₃	#120	1	1	yes	characteristic
288	C₂⁵×C₃	#120	1	1	yes	characteristic
289	C₂⁵×C₃	#120	1	2	yes	—
290	C₂⁵×C₃	#120	1	1	yes	characteristic, complemented
291	C₂⁵×C₃	C₂²×D₄	1	1	yes	characteristic
292	C₂⁵×C₃	C₂²×D₄	1	1	yes	characteristic
293	C₂⁵×C₃	C₂²×D₄	1	2	yes	—
294	C₂⁴×D₃	#120	1	1	yes	characteristic
295	C₂⁴×D₃	#120	1	1	yes	characteristic
296	C₂⁴×D₃	#120	1	2	yes	—
297	C₂⁴×D₃	#120	1	1	yes	characteristic
298	C₂⁴×D₃	#120	1	1	yes	characteristic
299	C₂⁴×D₃	#120	1	2	yes	—
300	C₂⁴×D₃	#120	1	1	yes	characteristic
301	C₂⁴×D₃	#120	1	2	yes	—
302	C₂⁴×D₃	#120	1	1	yes	characteristic, complemented
303	C₂⁴×D₃	C₂²×D₄	1	2	yes	—
304	C₂⁴×D₃	C₂²×D₄	1	2	yes	—
305	C₂⁴×D₃	C₂²×D₄	1	2	yes	—
306	C₂×C₃×#41	#120	1	2	yes	complemented
307	C₂×C₃×#41	C₂²×D₄	1	2	yes	—
308	C₂²×C₃×Q₈	#120	1	1	yes	characteristic, complemented
309	C₂²×C₃×D₄	#120	1	1	yes	characteristic, complemented
310	C₂²×C₃×D₄	#120	1	2	yes	complemented
311	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
312	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
313	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
314	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
315	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
316	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
317	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
318	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
319	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
320	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
321	C₂²×C₃×D₄	C₂²×D₄	1	2	yes	—
322	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
323	C₂²×C₃×D₄	C₂⁵	1	1	yes	characteristic
324	C₂³×C₃×C₄	#120	1	1	yes	characteristic, complemented
325	C₂³×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
326	C₂²×#67	#120	1	2	yes	—
327	C₂²×#67	#120	1	2	yes	—
328	C₂²×#67	#120	1	2	yes	complemented
329	C₂²×#67	C₂²×D₄	1	2	yes	—
330	C₂²×#67	C₂²×D₄	1	2	yes	—
331	C₂²×#67	C₂²×D₄	1	2	yes	—
332	C₂³×Dic₃	#120	1	1	yes	characteristic
333	C₂³×Dic₃	#120	1	1	yes	characteristic, complemented
334	C₂×#235	#120	1	2	yes	complemented
335	C₂×#235	C₂²×D₄	1	2	yes	—
336	C₂²×D₁₂	#120	1	2	yes	—
337	C₂²×D₁₂	#120	1	1	yes	characteristic, complemented
338	C₂²×D₁₂	C₂²×D₄	1	2	yes	—
339	C₂²×C₄×D₃	#120	1	2	yes	—
340	C₂²×C₄×D₃	C₂²×D₄	1	2	yes	—
341	C₂²×Dic₆	#120	1	1	yes	characteristic, complemented
342	C₃×#127	#120	1	2	yes	complemented
343	C₃×#127	#120	1	2	yes	complemented
344	C₃×#127	C₂²×D₄	1	2	yes	—
345	C₃×#127	C₂²×D₄	1	2	yes	—
346	C₃×#124	#120	1	2	yes	complemented
347	C₃×#124	#120	1	2	yes	complemented
348	C₃×#124	C₂²×D₄	1	2	yes	—
349	C₃×#124	C₂²×D₄	1	2	yes	—
350	C₃×#123	#120	1	2	yes	complemented
351	C₃×#123	#120	1	2	yes	complemented
352	C₃×#123	C₂²×D₄	1	2	yes	—
353	C₃×#123	C₂²×D₄	1	2	yes	—
354	C₃×#120	#120	1	2	yes	—
355	C₃×#120	#120	1	2	yes	—
356	C₃×#120	#120	1	2	yes	—
357	C₃×#120	#120	1	2	yes	—
358	C₃×#120	#120	1	2	yes	complemented
359	C₃×#120	#120	1	2	yes	complemented
360	C₃×#120	C₂²×D₄	1	2	yes	—
361	C₃×#120	C₂²×D₄	1	2	yes	—
362	C₃×#120	C₂²×D₄	1	2	yes	—
363	C₃×#120	C₂²×D₄	1	2	yes	—
364	C₃×#120	C₂²×D₄	1	2	yes	—
365	C₃×#120	C₂²×D₄	1	2	yes	—
366	C₃×#117	#120	1	2	yes	complemented
367	C₃×#117	C₂²×D₄	1	2	yes	—
368	C₂×C₃×C₂²⋊C₄	#120	1	1	yes	characteristic
369	C₂×C₃×C₂²⋊C₄	#120	1	1	yes	characteristic
370	C₂×C₃×C₂²⋊C₄	#120	1	2	yes	—
371	C₂×C₃×C₂²⋊C₄	#120	1	1	yes	characteristic, complemented
372	C₂×C₃×C₂²⋊C₄	#120	1	1	yes	characteristic, complemented
373	C₂×C₃×C₂²⋊C₄	#120	1	2	yes	complemented
374	C₂×C₃×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
375	C₂×C₃×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
376	C₂×C₃×C₄²	#120	1	1	yes	characteristic, complemented
377	C₂×C₃×C₄²	#120	1	1	yes	characteristic, complemented
378	C₂×#217	#120	1	1	yes	characteristic
379	C₂×#217	#120	1	1	yes	characteristic
380	C₂×#217	#120	1	2	yes	—
381	C₂×#217	#120	1	2	yes	complemented
382	C₂×#217	#120	1	1	yes	characteristic, complemented
383	C₂×#217	#120	1	1	yes	characteristic, complemented
384	C₂×#217	C₂²×D₄	1	2	yes	—
385	C₂×#217	C₂²×D₄	1	2	yes	—
386	#940	#120	1	2	yes	complemented
387	#940	#120	1	2	yes	complemented
388	#940	C₂²×D₄	1	2	yes	—
389	#940	C₂²×D₄	1	2	yes	—
390	#937	#120	1	2	yes	—
391	#937	#120	1	2	yes	—
392	#937	#120	1	2	yes	—
393	#937	#120	1	2	yes	—
394	#937	#120	1	2	yes	complemented
395	#937	#120	1	2	yes	complemented
396	#937	C₂²×D₄	1	2	yes	—
397	#937	C₂²×D₄	1	2	yes	—
398	#937	C₂²×D₄	1	2	yes	—
399	#937	C₂²×D₄	1	2	yes	—
400	#937	C₂²×D₄	1	2	yes	—
401	#937	C₂²×D₄	1	2	yes	—
402	#936	#120	1	2	yes	complemented
403	#936	#120	1	2	yes	complemented
404	#936	C₂²×D₄	1	2	yes	—
405	#936	C₂²×D₄	1	2	yes	—
406	#935	#120	1	2	yes	complemented
407	#935	#120	1	2	yes	complemented
408	#935	C₂²×D₄	1	2	yes	—
409	#935	C₂²×D₄	1	2	yes	—
410	#926	#120	1	2	yes	complemented
411	#926	C₂²×D₄	1	2	yes	—
412	C₂×C₄×Dic₃	#120	1	1	yes	characteristic, complemented
413	C₂×C₄×Dic₃	#120	1	1	yes	characteristic, complemented
414	C₂⁶	D₃×D₄	1	1	yes	characteristic
415	C₂²×#41	D₃×D₄	1	1	yes	characteristic
416	C₂³×D₄	D₃×D₄	1	1	yes	characteristic
417	C₂³×D₄	C₂³×D₃	1	1	yes	characteristic
418	H(3,𝔽₄)	C₂×D₁₂	1	4	yes	complemented
419	#560	C₂×D₁₂	1	4	yes	complemented
420	#551	C₂×D₁₂	1	4	yes	complemented
421	D₄²	C₂×D₁₂	1	4	yes	complemented
422	#535	C₂×D₁₂	1	2	yes	—
423	#535	D₃×D₄	1	2	yes	—
424	#535	D₃×D₄	1	2	yes	—
425	#535	C₂³×D₃	1	2	yes	—
426	#534	C₂×D₁₂	1	2	yes	—
427	#534	D₃×D₄	1	2	yes	—
428	#534	D₃×D₄	1	2	yes	—
429	#534	C₂³×D₃	1	2	yes	—
430	C₂×#127	C₂×D₁₂	1	1	yes	characteristic
431	C₂×#127	D₃×D₄	1	1	yes	characteristic
432	C₂×#124	C₂×D₁₂	1	1	yes	characteristic
433	C₂×#124	D₃×D₄	1	1	yes	characteristic
434	C₂×#123	C₂×D₁₂	1	1	yes	characteristic
435	C₂×#123	D₃×D₄	1	1	yes	characteristic
436	C₂×#120	C₂×D₁₂	1	1	yes	characteristic
437	C₂×#120	C₂×D₁₂	1	1	yes	characteristic
438	C₂×#120	C₂×D₁₂	1	2	yes	—
439	C₂×#120	C₂×D₁₂	1	1	yes	characteristic
440	C₂×#120	D₃×D₄	1	1	yes	characteristic
441	C₂×#120	D₃×D₄	1	1	yes	characteristic
442	C₂×#120	D₃×D₄	1	2	yes	—
443	C₂×#120	D₃×D₄	1	1	yes	characteristic
444	C₂×#120	D₃×D₄	1	2	yes	—
445	C₂×#120	C₂³×D₃	1	2	yes	—
446	#518	C₂³×D₃	1	2	yes	complemented
447	C₂×#117	D₃×D₄	1	1	yes	characteristic
448	C₂²×C₂²⋊C₄	D₃×D₄	1	1	yes	characteristic
449	C₂²×C₂²⋊C₄	D₃×D₄	1	1	yes	characteristic
450	C₂×#100	C₂³×D₃	1	2	yes	complemented
451	C₂×#99	C₂³×D₃	1	2	yes	complemented
452	C₂×#99	C₂³×D₃	1	2	yes	complemented
453	C₂⁴×C₃	C₂×#120	1	1	yes	characteristic
454	C₂⁴×C₃	C₂×#120	1	1	yes	characteristic
455	C₂⁴×C₃	C₂×#120	1	1	yes	characteristic
456	C₂⁴×C₃	C₂×#120	1	1	yes	characteristic
457	C₂⁴×C₃	C₂×#120	1	2	yes	—
458	C₂⁴×C₃	C₂×#120	1	2	yes	—
459	C₂⁴×C₃	C₂×#120	1	1	yes	characteristic
460	C₂⁴×C₃	C₂×#120	1	1	yes	characteristic
461	C₂⁴×C₃	C₂×#120	1	1	yes	characteristic
462	C₂⁴×C₃	C₂×#120	1	1	yes	characteristic
463	C₂⁴×C₃	C₂×#120	1	1	yes	characteristic
464	C₂⁴×C₃	C₂×#120	1	1	yes	characteristic
465	C₂⁴×C₃	C₂×#120	1	1	yes	characteristic
466	C₂⁴×C₃	C₂×#120	1	2	yes	complemented
467	C₂⁴×C₃	C₂³×D₄	1	1	yes	characteristic
468	C₂⁴×C₃	C₂³×D₄	1	1	yes	characteristic
469	C₂³×D₃	B(4,𝔽₂)	1	2	yes	—
470	C₂³×D₃	B(4,𝔽₂)	1	2	yes	—
471	C₂³×D₃	C₂×#120	1	2	yes	—
472	C₂³×D₃	C₂×#120	1	2	yes	—
473	C₂³×D₃	C₂×#120	1	2	yes	—
474	C₂³×D₃	C₂×#120	1	2	yes	—
475	C₂³×D₃	C₂×#120	1	2	yes	—
476	C₂³×D₃	C₂×#120	1	2	yes	complemented
477	C₂×C₃×Q₈	C₂×#120	1	2	yes	complemented
478	C₂×C₃×D₄	C₂×#120	1	1	yes	characteristic
479	C₂×C₃×D₄	C₂×#120	1	1	yes	characteristic
480	C₂×C₃×D₄	C₂×#120	1	1	yes	characteristic
481	C₂×C₃×D₄	C₂×#120	1	1	yes	characteristic
482	C₂×C₃×D₄	C₂×#120	1	1	yes	characteristic
483	C₂×C₃×D₄	C₂×#120	1	1	yes	characteristic
484	C₂×C₃×D₄	C₂×#120	1	1	yes	characteristic
485	C₂×C₃×D₄	C₂×#120	1	1	yes	characteristic
486	C₂×C₃×D₄	C₂×#120	1	1	yes	characteristic
487	C₂×C₃×D₄	C₂×#120	1	1	yes	characteristic
488	C₂×C₃×D₄	C₂×#120	1	1	yes	characteristic
489	C₂×C₃×D₄	C₂×#120	1	1	yes	characteristic
490	C₂×C₃×D₄	C₂×#120	1	2	yes	complemented
491	C₂×C₃×D₄	C₂³×D₄	1	1	yes	characteristic
492	C₂×C₃×D₄	C₂³×D₄	1	1	yes	characteristic
493	C₂×C₃×D₄	C₂³×D₄	1	1	yes	characteristic
494	C₂×C₃×D₄	C₂³×D₄	1	1	yes	characteristic
495	C₂²×C₃×C₄	C₂×#120	1	1	yes	characteristic
496	C₂²×C₃×C₄	C₂×#120	1	1	yes	characteristic
497	C₂²×C₃×C₄	C₂×#120	1	1	yes	characteristic
498	C₂²×C₃×C₄	C₂×#120	1	1	yes	characteristic
499	C₂²×C₃×C₄	C₂×#120	1	1	yes	characteristic
500	C₂²×C₃×C₄	C₂×#120	1	2	yes	complemented
501	C₂²×C₃×C₄	C₂³×D₄	1	1	yes	characteristic
502	C₂²×Dic₃	C₂×#120	1	2	yes	—
503	C₂²×Dic₃	C₂×#120	1	2	yes	complemented
504	C₂×D₁₂	C₂×#120	1	2	yes	complemented
505	C₂×Dic₆	C₂×#120	1	2	yes	complemented
506	C₃×C₂²⋊C₄	C₂×#120	1	2	yes	—
507	C₃×C₂²⋊C₄	C₂×#120	1	2	yes	—
508	C₃×C₂²⋊C₄	C₂×#120	1	2	yes	complemented
509	C₃×C₂²⋊C₄	C₂×#120	1	2	yes	complemented
510	C₃×C₄²	C₂×#120	1	2	yes	complemented
511	C₃×C₄²	C₂×#120	1	2	yes	complemented
512	#217	C₂×#120	1	2	yes	—
513	#217	C₂×#120	1	2	yes	—
514	#217	C₂×#120	1	2	yes	complemented
515	#217	C₂×#120	1	2	yes	complemented
516	C₄×Dic₃	C₂×#120	1	2	yes	complemented
517	C₄×Dic₃	C₂×#120	1	2	yes	complemented
518	C₂⁵	#882	1	1	yes	characteristic
519	C₂⁵	#882	1	1	yes	characteristic
520	C₂⁵	#882	1	2	yes	—
521	C₂⁵	#882	1	1	yes	characteristic, complemented
522	C₂⁵	C₂×D₃×D₄	1	1	yes	characteristic
523	C₂⁵	C₂×D₃×D₄	1	1	yes	characteristic
524	C₂⁵	C₂×D₃×D₄	1	2	yes	—
525	C₂×#41	#882	1	2	yes	complemented
526	C₂×#41	C₂×D₃×D₄	1	2	yes	—
527	C₂²×Q₈	#882	1	1	yes	characteristic, complemented
528	C₂²×D₄	#882	1	1	yes	characteristic, complemented
529	C₂²×D₄	#882	1	2	yes	complemented
530	C₂²×D₄	C₂²×D₁₂	1	1	yes	characteristic
531	C₂²×D₄	C₂²×D₁₂	1	1	yes	characteristic
532	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
533	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
534	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
535	C₂²×D₄	C₂×D₃×D₄	1	2	yes	—
536	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
537	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
538	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
539	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
540	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
541	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic
542	C₂²×D₄	C₂⁴×D₃	1	1	yes	characteristic
543	C₂³×C₄	#882	1	1	yes	characteristic, complemented
544	C₂³×C₄	C₂×D₃×D₄	1	1	yes	characteristic
545	#127	#882	1	2	yes	complemented
546	#127	#882	1	2	yes	complemented
547	#127	C₂²×D₁₂	1	2	yes	—
548	#127	C₂×D₃×D₄	1	2	yes	—
549	#124	#882	1	2	yes	complemented
550	#124	#882	1	2	yes	complemented
551	#124	C₂²×D₁₂	1	2	yes	—
552	#124	C₂×D₃×D₄	1	2	yes	—
553	#123	#882	1	2	yes	complemented
554	#123	#882	1	2	yes	complemented
555	#123	C₂²×D₁₂	1	2	yes	—
556	#123	C₂×D₃×D₄	1	2	yes	—
557	#120	#882	1	2	yes	—
558	#120	#882	1	2	yes	—
559	#120	#882	1	2	yes	—
560	#120	#882	1	2	yes	—
561	#120	#882	1	2	yes	complemented
562	#120	#882	1	2	yes	complemented
563	#120	C₂²×D₁₂	1	2	yes	—
564	#120	C₂²×D₁₂	1	2	yes	—
565	#120	C₂²×D₁₂	1	2	yes	—
566	#120	C₂×D₃×D₄	1	2	yes	—
567	#120	C₂×D₃×D₄	1	2	yes	—
568	#120	C₂×D₃×D₄	1	2	yes	—
569	#117	#882	1	2	yes	complemented
570	#117	C₂×D₃×D₄	1	2	yes	—
571	C₂×C₂²⋊C₄	#882	1	1	yes	characteristic
572	C₂×C₂²⋊C₄	#882	1	1	yes	characteristic
573	C₂×C₂²⋊C₄	#882	1	2	yes	—
574	C₂×C₂²⋊C₄	#882	1	1	yes	characteristic, complemented
575	C₂×C₂²⋊C₄	#882	1	1	yes	characteristic, complemented
576	C₂×C₂²⋊C₄	#882	1	2	yes	complemented
577	C₂×C₂²⋊C₄	C₂×D₃×D₄	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂×D₃×D₄	1	2	yes	—
579	C₂×C₄²	#882	1	1	yes	characteristic, complemented
580	C₂×C₄²	#882	1	1	yes	characteristic, complemented
581	C₂³×C₃	#2846	1	1	yes	characteristic
582	C₂³×C₃	#2846	1	1	yes	characteristic
583	C₂³×C₃	#2846	1	1	yes	characteristic
584	C₂³×C₃	#2846	1	1	yes	characteristic
585	C₂³×C₃	#2846	1	1	yes	characteristic
586	C₂³×C₃	#2846	1	1	yes	characteristic
587	C₂³×C₃	C₂×B(4,𝔽₂)	1	1	yes	characteristic
588	C₂³×C₃	C₂×B(4,𝔽₂)	1	1	yes	characteristic
589	C₂³×C₃	#3026	1	1	yes	characteristic
590	C₂³×C₃	#3026	1	1	yes	characteristic
591	C₂³×C₃	C₂²×#120	1	1	yes	characteristic
592	C₂³×C₃	C₂²×#120	1	1	yes	characteristic
593	C₂³×C₃	C₂²×#120	1	1	yes	characteristic
594	C₂³×C₃	C₂²×#120	1	1	yes	characteristic
595	C₂³×C₃	C₂²×#120	1	1	yes	characteristic
596	C₂²×D₃	C₂×B(4,𝔽₂)	1	4	yes	—
597	C₂×C₃×C₄	#2846	1	1	yes	characteristic
598	C₂×C₃×C₄	#2846	1	1	yes	characteristic
599	C₂×C₃×C₄	C₂²×#120	1	1	yes	characteristic
600	C₂×C₃×C₄	C₂²×#120	1	1	yes	characteristic
601	C₂⁴	C₂×#882	1	1	yes	characteristic
602	C₂⁴	C₂×#882	1	1	yes	characteristic
603	C₂⁴	C₂×#882	1	1	yes	characteristic
604	C₂⁴	C₂×#882	1	1	yes	characteristic
605	C₂⁴	C₂×#882	1	2	yes	—
606	C₂⁴	C₂×#882	1	2	yes	—
607	C₂⁴	C₂×#882	1	2	yes	complemented
608	C₂⁴	D₃×#120	1	1	yes	characteristic
609	C₂⁴	D₃×#120	1	1	yes	characteristic
610	C₂⁴	D₃×#120	1	1	yes	characteristic
611	C₂⁴	D₃×#120	1	1	yes	characteristic
612	C₂⁴	D₃×#120	1	1	yes	characteristic
613	C₂⁴	D₃×#120	1	1	yes	characteristic
614	C₂⁴	D₃×#120	1	1	yes	characteristic
615	C₂⁴	C₂²×D₃×D₄	1	1	yes	characteristic
616	C₂⁴	C₂²×D₃×D₄	1	1	yes	characteristic
617	C₂×Q₈	C₂×#882	1	2	yes	complemented
618	C₂×D₄	C₂×#882	1	1	yes	characteristic
619	C₂×D₄	C₂×#882	1	1	yes	characteristic
620	C₂×D₄	C₂×#882	1	1	yes	characteristic
621	C₂×D₄	C₂×#882	1	1	yes	characteristic
622	C₂×D₄	C₂×#882	1	1	yes	characteristic
623	C₂×D₄	C₂×#882	1	1	yes	characteristic
624	C₂×D₄	C₂×#882	1	2	yes	complemented
625	C₂×D₄	D₃×#120	1	1	yes	characteristic
626	C₂×D₄	D₃×#120	1	1	yes	characteristic
627	C₂×D₄	D₃×#120	1	1	yes	characteristic
628	C₂×D₄	D₃×#120	1	1	yes	characteristic
629	C₂×D₄	D₃×#120	1	1	yes	characteristic
630	C₂×D₄	D₃×#120	1	1	yes	characteristic
631	C₂×D₄	C₂³×D₁₂	1	1	yes	characteristic
632	C₂×D₄	C₂²×D₃×D₄	1	1	yes	characteristic
633	C₂×D₄	C₂²×D₃×D₄	1	1	yes	characteristic
634	C₂×D₄	C₂²×D₃×D₄	1	1	yes	characteristic
635	C₂²×C₄	C₂×#882	1	1	yes	characteristic
636	C₂²×C₄	C₂×#882	1	1	yes	characteristic
637	C₂²×C₄	C₂×#882	1	2	yes	complemented
638	C₂²×C₄	D₃×#120	1	1	yes	characteristic
639	C₂²×C₄	D₃×#120	1	1	yes	characteristic
640	C₂²×C₄	D₃×#120	1	1	yes	characteristic
641	C₂²×C₄	C₂²×D₃×D₄	1	1	yes	characteristic
642	C₂²⋊C₄	C₂×#882	1	2	yes	—
643	C₂²⋊C₄	C₂×#882	1	2	yes	—
644	C₂²⋊C₄	C₂×#882	1	2	yes	complemented
645	C₂²⋊C₄	C₂×#882	1	2	yes	complemented
646	C₄²	C₂×#882	1	2	yes	complemented
647	C₄²	C₂×#882	1	2	yes	complemented
648	C₂²×C₃	#32898	1	1	yes	characteristic
649	C₂²×C₃	#32898	1	1	yes	characteristic
650	C₂²×C₃	#32898	1	1	yes	characteristic
651	C₂²×C₃	#32898	1	1	yes	characteristic
652	C₂²×C₃	C₂×#2846	1	1	yes	characteristic
653	C₂²×C₃	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
654	C₂²×C₃	C₂×#3026	1	1	yes	characteristic
655	C₂³	#73861	1	1	yes	characteristic
656	C₂³	#73861	1	1	yes	characteristic
657	C₂³	#73861	1	1	yes	characteristic
658	C₂³	#73861	1	1	yes	characteristic
659	C₂³	#73861	1	1	yes	characteristic
660	C₂³	#73861	1	1	yes	characteristic
661	C₂³	D₃×B(4,𝔽₂)	1	1	yes	characteristic
662	C₂³	D₃×B(4,𝔽₂)	1	1	yes	characteristic
663	C₂³	#80311	1	1	yes	characteristic
664	C₂³	#80311	1	1	yes	characteristic
665	C₂³	C₂²×#882	1	1	yes	characteristic
666	C₂³	C₂²×#882	1	1	yes	characteristic
667	C₂³	C₂×D₃×#120	1	1	yes	characteristic
668	C₂³	C₂×D₃×#120	1	1	yes	characteristic
669	C₂³	C₂×D₃×#120	1	1	yes	characteristic
670	C₂×C₄	#73861	1	1	yes	characteristic
671	C₂×C₄	#73861	1	1	yes	characteristic
672	C₂×C₄	C₂²×#882	1	1	yes	characteristic
673	C₂×C₄	C₂×D₃×#120	1	1	yes	characteristic
674	C₂×C₃	#511790	1	2	yes	complemented
675	C₂×C₃	C₂×#32898	1	1	yes	characteristic
676	C₂²	#10943959	1	1	yes	characteristic
677	C₂²	#10943959	1	1	yes	characteristic
678	C₂²	#10943959	1	1	yes	characteristic
679	C₂²	#10943959	1	1	yes	characteristic
680	C₂²	C₂×#73861	1	1	yes	characteristic
681	C₂²	C₂×D₃×B(4,𝔽₂)	1	1	yes	characteristic
682	C₂²	C₂×#80311	1	1	yes	characteristic
683	C₃	C₂×#511790	1	1	yes	characteristic, complemented, Sylow
684	C₂	#72219819	1	2	yes	direct product factor
685	C₂	C₂×#10943959	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10943959
commutator, cosocle	C₂²×C₃×D₄	C₂⁵
Frattini	C₂²×D₄	C₂⁴×D₃
Fitting	C₂×C₃×#12753	C₂
socle	C₂²×C₃	#32898
hypercenter	C₂×#12753	D₃
hypocenter	C₃	C₂×#511790
LCS	G ▷ C₂²×C₃×D₄ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂³×D₄ ◁ C₂×#12753

Complements

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

N	H ≅ G/N	type
1. C₂×#10710645	C₂	semidirect
2. C₂×#10826738	C₂	semidirect
3. C₂×#10710711	C₂	semidirect
4. C₂×#11703802	C₂	semidirect
5. C₂×#10949250	C₂	semidirect
6. C₂×#10949248	C₂	semidirect
7. C₂×#10826767	C₂	semidirect
8. C₂×#10710944	C₂	semidirect
9. C₂×C₃×#12753	C₂	semidirect
10. C₂×#10949251	C₂	semidirect
11. C₂×#10949249	C₂	semidirect
12. C₂×#10710947	C₂	semidirect
13. C₂×#10710719	C₂	semidirect
14. C₂×#10710949	C₂	semidirect
15. C₂×#10826748	C₂	semidirect
16. #72219819	C₂	direct (N × H)
17. #11703802	C₂²	semidirect
18. C₂×#85867	C₂²	semidirect
25. C₂×#78686	C₂²	semidirect
26. C₂×#83375	C₂²	semidirect
27. C₂²×#4741	C₂²	semidirect
28. C₂²×#5032	C₂²	semidirect
29. C₂×#78700	C₂²	semidirect
30. C₂×#83394	C₂²	semidirect
31. #10949251	C₂²	semidirect
32. #10949250	C₂²	semidirect
33. #10949249	C₂²	semidirect
34. #10949248	C₂²	semidirect
35. C₂×#71860	C₂²	semidirect
36. C₂×#70019	C₂²	semidirect
37. C₂×#70019	C₂²	semidirect
38. C₂×#70094	C₂²	semidirect
39. C₂×#71847	C₂²	semidirect
40. C₂×#70015	C₂²	semidirect
41. C₂²×#4475	C₂²	semidirect
42. C₂²×#4536	C₂²	semidirect
43. C₂²×#4471	C₂²	semidirect
44. #10826767	C₂²	semidirect
45. #10826748	C₂²	semidirect
46. #10826738	C₂²	semidirect
47. C₂×#71656	C₂²	semidirect
48. C₂×#71652	C₂²	semidirect
49. C₂×#71654	C₂²	semidirect
50. C₂×#70079	C₂²	semidirect
51. C₂×#70035	C₂²	semidirect
52. C₂×#70035	C₂²	semidirect
53. #10710949	C₂²	semidirect
54. #10710947	C₂²	semidirect
55. #10710944	C₂²	semidirect
56. #10710719	C₂²	semidirect
57. #10710711	C₂²	semidirect
58. #10710645	C₂²	semidirect
60. C₂×C₃×#2127	C₂²	semidirect
61. C₂×C₃×#2121	C₂²	semidirect
62. C₂²×C₃×AΣL(1,𝔽₁₆)	C₂²	semidirect
63. C₂×C₃×#1913	C₂²	semidirect
64. C₂×C₃×#1911	C₂²	semidirect
65. C₂×C₃×#1889	C₂²	semidirect
66. C₃×#12753	C₂²	semidirect
67. C₂×#12753	D₃	semidirect
68. C₂⁶×D₃	D₄	semidirect
69. C₂²×#1009	D₄	semidirect
70. C₂²×#1004	D₄	semidirect
71. C₂²×#1004	C₂³	semidirect
73. C₃×#3532	D₄	semidirect
75. C₂×C₃×H(3,𝔽₄)	D₄	semidirect
76. C₂×C₃×#560	D₄	semidirect
77. C₂×C₃×#551	D₄	semidirect
78. C₂×C₃×D₄²	D₄	semidirect
82. C₂×C₃×#518	C₂³	semidirect
83. C₂²×#953	D₄	semidirect
84. C₂×#5828	D₄	semidirect
87. C₂²×#937	D₄	semidirect
89. #86333	D₄	semidirect
91. #86330	D₄	semidirect
93. #86310	D₄	semidirect
95. #86308	D₄	semidirect
97. C₂×#5720	D₄	semidirect
98. C₂×#5717	D₄	semidirect
99. C₂×#5683	D₄	semidirect
100. C₂×#5679	D₄	semidirect
101. C₂×#5666	D₄	semidirect
102. C₂×#5659	D₄	semidirect
103. #85921	D₄	semidirect
105. C₂×#5595	D₄	semidirect
106. C₂×#5590	D₄	semidirect
107. C₂×#5590	D₄	semidirect
108. C₂×D₃×#120	D₄	semidirect
110. C₂×#5594	D₄	semidirect
111. C₂×#5594	D₄	semidirect
112. C₂×#5587	D₄	semidirect
113. #85867	C₂³	semidirect
114. C₂×#5524	D₄	semidirect
115. C₂×#5521	D₄	semidirect
116. C₂²×#882	D₄	semidirect
117. C₂²×#882	D₄	semidirect
118. C₂×#5486	D₄	semidirect
119. C₂²×D₃×C₂²⋊C₄	D₄	semidirect
120. C₂²×C₃×#100	C₂³	semidirect
121. C₂²×C₃×#99	C₂³	semidirect
122. C₂²×C₃×#99	C₂³	semidirect
123. C₂²×#834	C₂³	semidirect
124. C₂²×#834	C₂³	semidirect
125. C₂²×#833	C₂³	semidirect
126. #83394	C₂³	semidirect
127. #83375	C₂³	semidirect
128. C₂×#5032	C₂³	semidirect
129. #78700	C₂³	semidirect
130. #78686	C₂³	semidirect
131. C₂×#4741	C₂³	semidirect
132. C₃×#2127	C₂³	semidirect
133. C₃×#2121	C₂³	semidirect
134. C₂×C₃×AΣL(1,𝔽₁₆)	C₂³	semidirect
135. C₃×#1913	C₂³	semidirect
136. C₃×#1911	C₂³	semidirect
137. C₃×#1889	C₂³	semidirect
138. #71860	C₂³	semidirect
139. #71847	C₂³	semidirect
140. C₂×#4536	C₂³	semidirect
141. #71656	C₂³	semidirect
142. #71654	C₂³	semidirect
143. #71652	C₂³	semidirect
144. #70094	C₂³	semidirect
145. C₂×#4475	C₂³	semidirect
146. #70079	C₂³	semidirect
147. #70035	C₂³	semidirect
148. #70035	C₂³	semidirect
149. #70019	C₂³	semidirect
150. #70019	C₂³	semidirect
151. #70015	C₂³	semidirect
152. C₂×#4471	C₂³	semidirect
154. C₂×#2127	C₂×D₃	semidirect
155. C₂×#2121	C₂×D₃	semidirect
156. C₂²×AΣL(1,𝔽₁₆)	C₂×D₃	semidirect
157. C₂×#1913	C₂×D₃	semidirect
158. C₂×#1911	C₂×D₃	semidirect
159. C₂×#1889	C₂×D₃	semidirect
160. #12753	C₂×D₃	semidirect
165. C₂⁵×D₃	C₂×D₄	semidirect
172. C₂×#1009	C₂×D₄	semidirect
173. C₂×#1004	C₂×D₄	semidirect
174. C₂×#1004	C₂⁴	semidirect
182. C₃×H(3,𝔽₄)	C₂×D₄	semidirect
183. C₃×#560	C₂×D₄	semidirect
184. C₃×#551	C₂×D₄	semidirect
185. C₃×D₄²	C₂×D₄	semidirect
210. C₃×#518	C₂⁴	semidirect
214. C₂×#953	C₂×D₄	semidirect
217. #5828	C₂×D₄	semidirect
237. C₂×#937	C₂×D₄	semidirect
244. #5720	C₂×D₄	semidirect
245. #5717	C₂×D₄	semidirect
246. #5683	C₂×D₄	semidirect
247. #5679	C₂×D₄	semidirect
248. #5666	C₂×D₄	semidirect
249. #5659	C₂×D₄	semidirect
250. #5595	C₂×D₄	semidirect
251. #5594	C₂×D₄	semidirect
252. #5594	C₂×D₄	semidirect
253. #5590	C₂×D₄	semidirect
254. #5590	C₂×D₄	semidirect
255. #5587	C₂×D₄	semidirect
256. #5524	C₂×D₄	semidirect
257. #5521	C₂×D₄	semidirect
258. C₂×#882	C₂×D₄	semidirect
259. C₂×#882	C₂×D₄	semidirect
260. #5486	C₂×D₄	semidirect
261. C₂×D₃×C₂²⋊C₄	C₂×D₄	semidirect
262. C₂×C₃×#100	C₂⁴	semidirect
263. C₂×C₃×#99	C₂⁴	semidirect
264. C₂×C₃×#99	C₂⁴	semidirect
265. C₂×#834	C₂⁴	semidirect
266. C₂×#834	C₂⁴	semidirect
267. C₂×#833	C₂⁴	semidirect
268. #3532	D₁₂	semidirect
270. C₂×H(3,𝔽₄)	D₁₂	semidirect
271. C₂×#560	D₁₂	semidirect
272. C₂×#551	D₁₂	semidirect
273. C₂×D₄²	D₁₂	semidirect
277. C₂×#518	C₂²×D₃	semidirect
278. C₂²×#100	C₂²×D₃	semidirect
279. C₂²×#99	C₂²×D₃	semidirect
280. C₂²×#99	C₂²×D₃	semidirect
281. #2127	C₂²×D₃	semidirect
282. #2121	C₂²×D₃	semidirect
283. C₂×AΣL(1,𝔽₁₆)	C₂²×D₃	semidirect
284. #1913	C₂²×D₃	semidirect
285. #1911	C₂²×D₃	semidirect
286. #1889	C₂²×D₃	semidirect
290. C₂⁵×C₃	#120	semidirect
302. C₂⁴×D₃	#120	semidirect
306. C₂×C₃×#41	#120	semidirect
308. C₂²×C₃×Q₈	#120	semidirect
309. C₂²×C₃×D₄	#120	semidirect
310. C₂²×C₃×D₄	#120	semidirect
324. C₂³×C₃×C₄	#120	semidirect
328. C₂²×#67	#120	semidirect
333. C₂³×Dic₃	#120	semidirect
334. C₂×#235	#120	semidirect
337. C₂²×D₁₂	#120	semidirect
341. C₂²×Dic₆	#120	semidirect
342. C₃×#127	#120	semidirect
343. C₃×#127	#120	semidirect
346. C₃×#124	#120	semidirect
347. C₃×#124	#120	semidirect
350. C₃×#123	#120	semidirect
351. C₃×#123	#120	semidirect
358. C₃×#120	#120	semidirect
359. C₃×#120	#120	semidirect
366. C₃×#117	#120	semidirect
371. C₂×C₃×C₂²⋊C₄	#120	semidirect
372. C₂×C₃×C₂²⋊C₄	#120	semidirect
373. C₂×C₃×C₂²⋊C₄	#120	semidirect
376. C₂×C₃×C₄²	#120	semidirect
377. C₂×C₃×C₄²	#120	semidirect
381. C₂×#217	#120	semidirect
382. C₂×#217	#120	semidirect
383. C₂×#217	#120	semidirect
386. #940	#120	semidirect
387. #940	#120	semidirect
394. #937	#120	semidirect
395. #937	#120	semidirect
402. #936	#120	semidirect
403. #936	#120	semidirect
406. #935	#120	semidirect
407. #935	#120	semidirect
410. #926	#120	semidirect
412. C₂×C₄×Dic₃	#120	semidirect
413. C₂×C₄×Dic₃	#120	semidirect
418. H(3,𝔽₄)	C₂×D₁₂	semidirect
419. #560	C₂×D₁₂	semidirect
420. #551	C₂×D₁₂	semidirect
421. D₄²	C₂×D₁₂	semidirect
446. #518	C₂³×D₃	semidirect
450. C₂×#100	C₂³×D₃	semidirect
451. C₂×#99	C₂³×D₃	semidirect
452. C₂×#99	C₂³×D₃	semidirect
466. C₂⁴×C₃	C₂×#120	semidirect
476. C₂³×D₃	C₂×#120	semidirect
477. C₂×C₃×Q₈	C₂×#120	semidirect
490. C₂×C₃×D₄	C₂×#120	semidirect
500. C₂²×C₃×C₄	C₂×#120	semidirect
503. C₂²×Dic₃	C₂×#120	semidirect
504. C₂×D₁₂	C₂×#120	semidirect
505. C₂×Dic₆	C₂×#120	semidirect
508. C₃×C₂²⋊C₄	C₂×#120	semidirect
509. C₃×C₂²⋊C₄	C₂×#120	semidirect
510. C₃×C₄²	C₂×#120	semidirect
511. C₃×C₄²	C₂×#120	semidirect
514. #217	C₂×#120	semidirect
515. #217	C₂×#120	semidirect
516. C₄×Dic₃	C₂×#120	semidirect
517. C₄×Dic₃	C₂×#120	semidirect
521. C₂⁵	#882	semidirect
525. C₂×#41	#882	semidirect
527. C₂²×Q₈	#882	semidirect
528. C₂²×D₄	#882	semidirect
529. C₂²×D₄	#882	semidirect
543. C₂³×C₄	#882	semidirect
545. #127	#882	semidirect
546. #127	#882	semidirect
549. #124	#882	semidirect
550. #124	#882	semidirect
553. #123	#882	semidirect
554. #123	#882	semidirect
561. #120	#882	semidirect
562. #120	#882	semidirect
569. #117	#882	semidirect
574. C₂×C₂²⋊C₄	#882	semidirect
575. C₂×C₂²⋊C₄	#882	semidirect
576. C₂×C₂²⋊C₄	#882	semidirect
579. C₂×C₄²	#882	semidirect
580. C₂×C₄²	#882	semidirect
607. C₂⁴	C₂×#882	semidirect
617. C₂×Q₈	C₂×#882	semidirect
624. C₂×D₄	C₂×#882	semidirect
637. C₂²×C₄	C₂×#882	semidirect
644. C₂²⋊C₄	C₂×#882	semidirect
645. C₂²⋊C₄	C₂×#882	semidirect
646. C₄²	C₂×#882	semidirect
647. C₄²	C₂×#882	semidirect
674. C₂×C₃	#511790	semidirect
683. C₃	C₂×#511790	semidirect
684. C₂	#72219819	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×#10710645	2
C₂×#10826738	2
C₂×#10710711	2
C₂×#11703802	2
C₂×#10949250	2
C₂×#10949248	2
C₂×#10826767	2
C₂×#10710944	2
C₂×C₃×#12753	2
C₂×#10949251	2
C₂×#10949249	2
C₂×#10710947	2
C₂×#10710719	2
C₂×#10710949	2
C₂×#10826748	2
#72219819	2
C₂×#511790	3

Subgroups — C2×#72219819 #72269977

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72219819 #72269977