Subgroups — #72312727

Order 1024.

At least 6288 conjugacy classes of subgroups; only the 965 normal subgroups are shown.

The subgroup lattice has 577 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×#63017	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#33558	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#33552	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#33551	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#2197	C₂	1	1	yes	maximal, characteristic, complemented
6	#6437635	C₂	1	1	yes	maximal, characteristic, complemented
7	#6437632	C₂	1	1	yes	maximal, characteristic, complemented
8	#6437457	C₂	1	1	yes	maximal, characteristic, complemented
9	#511788	C₂	1	2	yes	maximal, complemented
10	#511786	C₂	1	2	yes	maximal, complemented
11	#511783	C₂	1	2	yes	maximal, complemented
12	#511782	C₂	1	2	yes	maximal, complemented
13	#511780	C₂	1	2	yes	maximal, complemented
14	#511779	C₂	1	2	yes	maximal, complemented
15	#511774	C₂	1	2	yes	maximal, complemented
16	#511772	C₂	1	2	yes	maximal, complemented
17	#493632	C₂	1	1	yes	maximal, characteristic, complemented
18	#493583	C₂	1	1	yes	maximal, characteristic, complemented
19	#493582	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#12761	C₂	1	1	yes	maximal, characteristic, complemented
21	#493433	C₂	1	1	yes	maximal, characteristic, complemented
22	#493427	C₂	1	1	yes	maximal, characteristic, complemented
23	#493424	C₂	1	1	yes	maximal, characteristic, complemented
24	#62842	C₂²	1	1	yes	characteristic, complemented
25	C₂×#3500	C₂²	1	1	yes	characteristic
26	C₂×#3485	C₂²	1	1	yes	characteristic
27	C₂×#3484	C₂²	1	1	yes	characteristic
28	C₂×#3545	C₂²	1	1	yes	characteristic
29	C₂×#3545	C₂²	1	1	yes	characteristic, complemented
30	C₂×#3551	C₂²	1	1	yes	characteristic, complemented
31	C₂×#3540	C₂²	1	1	yes	characteristic, complemented
32	C₂×#3533	C₂²	1	1	yes	characteristic
33	C₂×#3533	C₂²	1	1	yes	characteristic, complemented
34	C₂×#3538	C₂²	1	1	yes	characteristic, complemented
35	C₂×#3532	C₂²	1	1	yes	characteristic
36	C₂×#3532	C₂²	1	1	yes	characteristic, complemented
37	C₂×#3481	C₂²	1	1	yes	characteristic, complemented
38	C₂²×#551	C₂²	1	1	yes	characteristic
39	C₂²×#551	C₂²	1	1	yes	characteristic, complemented
40	C₂×#3026	C₂²	1	1	yes	characteristic, complemented
41	C₂×#3026	C₂²	1	1	yes	characteristic, complemented
42	C₂²×#458	C₂²	1	1	yes	characteristic, complemented
43	C₂²×B(4,𝔽₂)	C₂²	1	1	yes	characteristic
44	C₂×#3019	C₂²	1	1	yes	characteristic, complemented
45	C₂²×#455	C₂²	1	1	yes	characteristic, complemented
46	C₂×#2201	C₂²	1	2	yes	complemented
47	C₂×#2201	C₂²	1	2	yes	complemented
48	C₂×#2200	C₂²	1	2	yes	complemented
49	C₂×#2200	C₂²	1	2	yes	complemented
50	C₂×#2199	C₂²	1	2	yes	complemented
51	C₂×#2199	C₂²	1	2	yes	complemented
52	C₂×#2198	C₂²	1	2	yes	complemented
53	C₂×#2197	C₂²	1	2	yes	complemented
54	C₂×#2197	C₂²	1	2	yes	complemented
55	C₂×#2197	C₂²	1	2	yes	complemented
56	C₂×#2197	C₂²	1	2	yes	complemented
57	C₂×#2197	C₂²	1	2	yes	complemented
58	C₂×#2197	C₂²	1	2	yes	complemented
59	C₂×#2197	C₂²	1	2	yes	complemented
60	C₂×#2197	C₂²	1	2	yes	complemented
61	C₂×#2196	C₂²	1	2	yes	complemented
62	C₂×#2127	C₂²	1	1	yes	characteristic, complemented
63	C₂×#2127	C₂²	1	1	yes	characteristic, complemented
64	C₂²×#354	C₂²	1	1	yes	characteristic, complemented
65	C₂²×#354	C₂²	1	1	yes	characteristic, complemented
66	C₂×#2121	C₂²	1	1	yes	characteristic, complemented
67	C₂×#2121	C₂²	1	1	yes	characteristic, complemented
68	C₂×#2121	C₂²	1	1	yes	characteristic, complemented
69	C₂×#2121	C₂²	1	1	yes	characteristic, complemented
70	C₂²×#352	C₂²	1	1	yes	characteristic, complemented
71	C₂²×#352	C₂²	1	1	yes	characteristic, complemented
72	C₂²×AΣL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic
73	C₂²×AΣL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic
74	#23914	C₂²	1	2	yes	complemented
75	#23912	C₂²	1	2	yes	complemented
76	#23908	C₂²	1	2	yes	complemented
77	#23907	C₂²	1	2	yes	complemented
78	#23905	C₂²	1	2	yes	complemented
79	#23904	C₂²	1	2	yes	complemented
80	#23903	C₂²	1	2	yes	complemented
81	#23903	C₂²	1	2	yes	complemented
82	#23902	C₂²	1	2	yes	—
83	#23902	C₂²	1	2	yes	complemented
84	#23901	C₂²	1	2	yes	complemented
85	#23900	C₂²	1	2	yes	—
86	#20960	C₂²	1	1	yes	characteristic, complemented
87	#20960	C₂²	1	1	yes	characteristic, complemented
88	C₂×#1890	C₂²	1	1	yes	characteristic, complemented
89	C₂×#1889	C₂²	1	1	yes	characteristic
90	#20953	C₂²	1	1	yes	characteristic, complemented
91	C₂×#1885	C₂²	1	1	yes	characteristic, complemented
92	#20592	C₂²	1	1	yes	characteristic, complemented
93	#20585	C₂²	1	1	yes	characteristic, complemented
94	#20585	C₂²	1	1	yes	characteristic, complemented
95	#12764	C₂²	1	2	yes	complemented
96	#12764	C₂²	1	2	yes	complemented
97	#12763	C₂²	1	2	yes	complemented
98	#12763	C₂²	1	2	yes	complemented
99	#12762	C₂²	1	2	yes	complemented
100	#12762	C₂²	1	2	yes	complemented
101	#12761	C₂²	1	2	yes	complemented
102	#12761	C₂²	1	2	yes	complemented
103	#12761	C₂²	1	2	yes	complemented
104	#12761	C₂²	1	2	yes	complemented
105	#12761	C₂²	1	2	yes	complemented
106	#12761	C₂²	1	2	yes	complemented
107	#12761	C₂²	1	2	yes	complemented
108	#12761	C₂²	1	2	yes	complemented
109	#12760	C₂²	1	2	yes	complemented
110	#12759	C₂²	1	2	yes	complemented
111	#12698	C₂²	1	2	yes	complemented
112	#12696	C₂²	1	2	yes	complemented
113	#12695	C₂²	1	2	yes	complemented
114	#12694	C₂²	1	2	yes	complemented
115	#12692	C₂²	1	2	yes	complemented
116	#12691	C₂²	1	2	yes	complemented
117	#12690	C₂²	1	2	yes	complemented
118	#12690	C₂²	1	2	yes	complemented
119	#12689	C₂²	1	2	yes	complemented
120	#12689	C₂²	1	2	yes	complemented
121	#12688	C₂²	1	2	yes	complemented
122	#12687	C₂²	1	2	yes	complemented
123	C₂²×2₋¹⁺⁴	D₄	1	1	yes	characteristic, complemented
124	C₂²×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
125	C₂²×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
126	C₂³×#41	D₄	1	1	yes	characteristic, complemented
127	C₂⁴×D₄	D₄	1	1	yes	characteristic, complemented
128	#3545	D₄	1	8	yes	complemented
129	#3533	D₄	1	8	yes	complemented
130	#3532	D₄	1	8	yes	complemented
131	C₂×#563	C₂³	1	1	yes	characteristic
132	C₂×#563	C₂³	1	1	yes	characteristic
133	C₂×H(3,𝔽₄)	C₂³	1	1	yes	characteristic
134	C₂×H(3,𝔽₄)	C₂³	1	1	yes	characteristic
135	C₂×#560	C₂³	1	1	yes	characteristic
136	C₂×#560	C₂³	1	1	yes	characteristic
137	#3485	C₂³	1	2	yes	—
138	#3484	C₂³	1	2	yes	—
139	C₂×#559	C₂³	1	1	yes	characteristic
140	C₂×#551	D₄	1	8	yes	complemented
141	C₂×#551	C₂³	1	1	yes	characteristic
142	C₂×#551	C₂³	1	1	yes	characteristic
143	C₂×#551	C₂³	1	1	yes	characteristic
144	C₂×#551	C₂³	1	1	yes	characteristic
145	C₂×#551	C₂³	1	1	yes	characteristic
146	C₂×#551	C₂³	1	1	yes	characteristic
147	C₂×#551	C₂³	1	1	yes	characteristic
148	C₂×#551	C₂³	1	1	yes	characteristic
149	C₂×D₄²	C₂³	1	1	yes	characteristic
150	C₂×#536	D₄	1	1	yes	characteristic, complemented
151	C₂×#536	D₄	1	1	yes	characteristic, complemented
152	C₂×#536	D₄	1	1	yes	characteristic, complemented
153	C₂×#536	C₂³	1	1	yes	characteristic
154	C₂×#536	C₂³	1	1	yes	characteristic
155	C₂×#535	D₄	1	1	yes	characteristic, complemented
156	C₂×#535	D₄	1	1	yes	characteristic, complemented
157	C₂×#535	C₂³	1	1	yes	characteristic
158	C₂×#535	C₂³	1	1	yes	characteristic
159	C₂×#535	C₂³	1	1	yes	characteristic
160	C₂×#534	D₄	1	1	yes	characteristic, complemented
161	C₂×#534	D₄	1	1	yes	characteristic, complemented
162	C₂×#534	D₄	1	1	yes	characteristic, complemented
163	C₂×#534	D₄	1	1	yes	characteristic, complemented
164	C₂×#534	C₂³	1	1	yes	characteristic
165	C₂×#534	C₂³	1	1	yes	characteristic
166	C₂×#534	C₂³	1	1	yes	characteristic
167	C₂×#534	C₂³	1	1	yes	characteristic
168	C₂×#532	D₄	1	1	yes	characteristic, complemented
169	C₂×#532	D₄	1	1	yes	characteristic, complemented
170	C₂×#532	C₂³	1	1	yes	characteristic
171	C₂²×#124	D₄	1	1	yes	characteristic, complemented
172	C₂²×#124	C₂³	1	1	yes	characteristic
173	C₂²×#124	C₂³	1	1	yes	characteristic
174	C₂×#525	D₄	1	1	yes	characteristic, complemented
175	C₂×#525	D₄	1	1	yes	characteristic, complemented
176	C₂×#525	C₂³	1	1	yes	characteristic
177	C₂×#525	C₂³	1	1	yes	characteristic
178	C₂²×#123	D₄	1	1	yes	characteristic, complemented
179	C₂²×#123	D₄	1	1	yes	characteristic, complemented
180	C₂²×#123	C₂³	1	1	yes	characteristic
181	C₂²×#123	C₂³	1	1	yes	characteristic
182	C₂²×#120	D₄	1	1	yes	characteristic, complemented
183	C₂²×#120	D₄	1	1	yes	characteristic, complemented
184	C₂²×#120	C₂³	1	1	yes	characteristic
185	C₂²×#120	C₂³	1	1	yes	characteristic
186	C₂×#518	D₄	1	1	yes	characteristic, complemented
187	C₂×#518	D₄	1	1	yes	characteristic, complemented
188	C₂×#518	C₂³	1	1	yes	characteristic
189	C₂×C₄×#41	D₄	1	1	yes	characteristic, complemented
190	C₂×#458	C₂³	1	2	yes	—
191	C₂×#458	C₂³	1	2	yes	—
192	C₂×#458	C₂³	1	2	yes	—
193	C₂×#458	C₂³	1	2	yes	—
194	C₂×B(4,𝔽₂)	C₂³	1	2	yes	—
195	C₂×B(4,𝔽₂)	C₂³	1	2	yes	—
196	C₂×B(4,𝔽₂)	C₂³	1	2	yes	—
197	C₂×B(4,𝔽₂)	C₂³	1	2	yes	—
198	C₂×#455	C₂³	1	2	yes	—
199	C₂×#455	C₂³	1	2	yes	—
200	C₂×#455	C₂³	1	2	yes	—
201	C₂×#453	C₂³	1	2	yes	—
202	C₂²×#100	C₂³	1	1	yes	characteristic
203	C₂²×#100	C₂³	1	1	yes	characteristic
204	C₂²×#99	C₂³	1	1	yes	characteristic
205	C₂²×#99	C₂³	1	1	yes	characteristic
206	C₂²×#99	C₂³	1	1	yes	characteristic
207	C₂²×#99	C₂³	1	1	yes	characteristic
208	C₂×#354	C₂³	1	2	yes	—
209	C₂×#354	C₂³	1	2	yes	—
210	C₂×#354	C₂³	1	2	yes	—
211	C₂×#354	C₂³	1	2	yes	—
212	C₂×#354	C₂³	1	2	yes	—
213	C₂×#354	C₂³	1	2	yes	—
214	C₂×#353	C₂³	1	2	yes	—
215	C₂×#353	C₂³	1	2	yes	—
216	C₂×#352	C₂³	1	2	yes	—
217	C₂×#352	C₂³	1	2	yes	—
218	C₂×#352	C₂³	1	2	yes	—
219	C₂×#352	C₂³	1	2	yes	—
220	C₂×#352	C₂³	1	2	yes	—
221	C₂×#352	C₂³	1	2	yes	—
222	C₂×#352	C₂³	1	2	yes	—
223	C₂×#352	C₂³	1	2	yes	—
224	C₂×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	—
225	C₂×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	—
226	C₂×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	—
227	C₂×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	—
228	C₂×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	—
229	C₂×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	—
230	C₂×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	—
231	C₂×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	—
232	#1890	C₂³	1	2	yes	—
233	#1890	C₂³	1	2	yes	—
234	#1890	C₂³	1	2	yes	—
235	#1890	C₂³	1	2	yes	—
236	#1889	C₂³	1	2	yes	—
237	#1889	C₂³	1	2	yes	—
238	#1889	C₂³	1	2	yes	—
239	#1889	C₂³	1	2	yes	—
240	#1887	C₂³	1	2	yes	—
241	#1885	C₂³	1	2	yes	—
242	#1885	C₂³	1	2	yes	—
243	#1885	C₂³	1	2	yes	—
244	#1785	C₂³	1	2	yes	—
245	#1783	C₂³	1	2	yes	—
246	#1782	C₂³	1	2	yes	—
247	#1782	C₂³	1	2	yes	—
248	#1781	C₂³	1	2	yes	—
249	#1781	C₂³	1	2	yes	—
250	C₂⁶	C₂×D₄	1	1	yes	characteristic
251	C₂⁶	C₂×D₄	1	1	yes	characteristic
252	C₂×H(5,𝔽₂)	C₂⁴	1	2	yes	—
253	C₂²×#41	C₂×D₄	1	1	yes	characteristic
254	C₂²×#41	C₂×D₄	1	1	yes	characteristic
255	C₂²×#41	C₂×D₄	1	1	yes	characteristic
256	C₂²×#41	C₂×D₄	1	1	yes	characteristic
257	C₂²×#41	C₂×D₄	1	1	yes	characteristic
258	C₂²×#41	C₂×D₄	1	1	yes	characteristic
259	C₂²×#41	C₂×D₄	1	1	yes	characteristic, complemented
260	C₂²×#41	C₂×D₄	1	1	yes	characteristic, complemented
261	C₂²×#41	C₂⁴	1	1	yes	characteristic
262	C₂³×Q₈	C₂×D₄	1	1	yes	characteristic
263	C₂³×Q₈	C₂×D₄	1	1	yes	characteristic, complemented
264	C₂³×Q₈	C₂×D₄	1	1	yes	characteristic, complemented
265	C₂³×Q₈	C₂×D₄	1	1	yes	characteristic, complemented
266	C₂³×D₄	C₂×D₄	1	1	yes	characteristic
267	C₂³×D₄	C₂×D₄	1	1	yes	characteristic
268	C₂³×D₄	C₂×D₄	1	1	yes	characteristic
269	C₂³×D₄	C₂×D₄	1	1	yes	characteristic
270	C₂³×D₄	C₂×D₄	1	1	yes	characteristic
271	C₂³×D₄	C₂×D₄	1	1	yes	characteristic
272	C₂³×D₄	C₂×D₄	1	1	yes	characteristic
273	C₂³×D₄	C₂×D₄	1	1	yes	characteristic
274	C₂³×D₄	C₂×D₄	1	1	yes	characteristic
275	C₂³×D₄	C₂×D₄	1	1	yes	characteristic
276	C₂³×D₄	C₂×D₄	1	1	yes	characteristic
277	C₂³×D₄	C₂×D₄	1	1	yes	characteristic, complemented
278	C₂³×D₄	C₂⁴	1	1	yes	characteristic
279	C₂³×D₄	C₂⁴	1	1	yes	characteristic
280	C₂⁴×C₄	C₂×D₄	1	1	yes	characteristic
281	C₂⁴×C₄	C₂×D₄	1	1	yes	characteristic
282	C₂⁴×C₄	C₂×D₄	1	1	yes	characteristic, complemented
283	C₂⁴×C₄	C₂×D₄	1	1	yes	characteristic, complemented
284	#563	C₂×D₄	1	4	yes	complemented
285	#563	C₂×D₄	1	4	yes	complemented
286	H(3,𝔽₄)	C₂×D₄	1	4	yes	complemented
287	H(3,𝔽₄)	C₂×D₄	1	4	yes	complemented
288	#560	C₂×D₄	1	4	yes	complemented
289	#560	C₂×D₄	1	4	yes	complemented
290	#559	C₂×D₄	1	4	yes	complemented
291	#551	C₂×D₄	1	4	yes	complemented
292	#551	C₂×D₄	1	4	yes	complemented
293	#551	C₂×D₄	1	4	yes	complemented
294	#551	C₂×D₄	1	4	yes	complemented
295	#551	C₂×D₄	1	4	yes	complemented
296	#551	C₂×D₄	1	4	yes	complemented
297	#551	C₂×D₄	1	4	yes	complemented
298	#551	C₂×D₄	1	4	yes	complemented
299	D₄²	C₂×D₄	1	4	yes	complemented
300	#535	C₂×D₄	1	4	yes	—
301	#535	C₂×D₄	1	4	yes	—
302	#534	C₂×D₄	1	4	yes	—
303	#534	C₂×D₄	1	4	yes	—
304	#534	C₂×D₄	1	4	yes	—
305	#534	C₂×D₄	1	4	yes	—
306	C₂×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic, complemented
307	C₂×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic, complemented
308	C₂×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic, complemented
309	C₂×#127	C₂×D₄	1	1	yes	characteristic
310	C₂×#127	C₂×D₄	1	1	yes	characteristic, complemented
311	C₂×#127	C₂⁴	1	1	yes	characteristic
312	C₂×#124	C₂×D₄	1	4	yes	—
313	C₂×#124	C₂×D₄	1	4	yes	—
314	C₂×#124	C₂×D₄	1	1	yes	characteristic
315	C₂×#124	C₂×D₄	1	1	yes	characteristic
316	C₂×#124	C₂×D₄	1	1	yes	characteristic
317	C₂×#124	C₂×D₄	1	1	yes	characteristic, complemented
318	C₂×#124	C₂×D₄	1	1	yes	characteristic, complemented
319	C₂×#124	C₂×D₄	1	1	yes	characteristic, complemented
320	C₂×#124	C₂×D₄	1	1	yes	characteristic, complemented
321	C₂×#124	C₂⁴	1	1	yes	characteristic
322	C₂×#124	C₂⁴	1	1	yes	characteristic
323	C₂×#124	C₂⁴	1	1	yes	characteristic
324	C₂×#123	C₂×D₄	1	4	yes	—
325	C₂×#123	C₂×D₄	1	4	yes	—
326	C₂×#123	C₂×D₄	1	1	yes	characteristic
327	C₂×#123	C₂×D₄	1	1	yes	characteristic
328	C₂×#123	C₂×D₄	1	1	yes	characteristic
329	C₂×#123	C₂×D₄	1	1	yes	characteristic
330	C₂×#123	C₂×D₄	1	1	yes	characteristic
331	C₂×#123	C₂×D₄	1	1	yes	characteristic
332	C₂×#123	C₂×D₄	1	1	yes	characteristic, complemented
333	C₂×#123	C₂×D₄	1	1	yes	characteristic, complemented
334	C₂×#123	C₂×D₄	1	1	yes	characteristic, complemented
335	C₂×#123	C₂×D₄	1	1	yes	characteristic, complemented
336	C₂×#123	C₂×D₄	1	1	yes	characteristic, complemented
337	C₂×#123	C₂×D₄	1	1	yes	characteristic, complemented
338	C₂×#123	C₂⁴	1	1	yes	characteristic
339	C₂×#123	C₂⁴	1	1	yes	characteristic
340	C₂×#123	C₂⁴	1	1	yes	characteristic
341	C₂×#123	C₂⁴	1	1	yes	characteristic
342	C₂×#120	C₂×D₄	1	4	yes	—
343	C₂×#120	C₂×D₄	1	4	yes	—
344	C₂×#120	C₂×D₄	1	1	yes	characteristic
345	C₂×#120	C₂×D₄	1	1	yes	characteristic
346	C₂×#120	C₂×D₄	1	1	yes	characteristic
347	C₂×#120	C₂×D₄	1	1	yes	characteristic
348	C₂×#120	C₂×D₄	1	1	yes	characteristic
349	C₂×#120	C₂×D₄	1	1	yes	characteristic
350	C₂×#120	C₂×D₄	1	1	yes	characteristic
351	C₂×#120	C₂×D₄	1	1	yes	characteristic
352	C₂×#120	C₂×D₄	1	1	yes	characteristic
353	C₂×#120	C₂×D₄	1	1	yes	characteristic
354	C₂×#120	C₂×D₄	1	1	yes	characteristic, complemented
355	C₂×#120	C₂×D₄	1	1	yes	characteristic, complemented
356	C₂×#120	C₂⁴	1	1	yes	characteristic
357	C₂×#120	C₂⁴	1	1	yes	characteristic
358	C₂×#120	C₂⁴	1	1	yes	characteristic
359	C₂×#120	C₂⁴	1	1	yes	characteristic
360	#518	C₂⁴	1	2	yes	—
361	C₂×#117	C₂×D₄	1	1	yes	characteristic
362	C₂×#117	C₂×D₄	1	1	yes	characteristic
363	C₂×#117	C₂×D₄	1	1	yes	characteristic
364	C₂×#117	C₂×D₄	1	1	yes	characteristic, complemented
365	C₂×#117	C₂×D₄	1	1	yes	characteristic, complemented
366	C₂×#117	C₂×D₄	1	1	yes	characteristic, complemented
367	C₂×#117	C₂×D₄	1	1	yes	characteristic, complemented
368	C₂²×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
370	C₂²×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
371	C₂²×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
372	C₂²×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
373	C₂²×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
374	C₂²×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
375	C₂²×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
376	C₂²×C₄²	C₂×D₄	1	1	yes	characteristic
377	C₂²×C₄²	C₂×D₄	1	1	yes	characteristic, complemented
378	C₂²×C₄²	C₂×D₄	1	1	yes	characteristic, complemented
379	C₂×#100	C₂⁴	1	2	yes	—
380	C₂×#100	C₂⁴	1	2	yes	—
381	C₂×#99	C₂⁴	1	2	yes	—
382	C₂×#99	C₂⁴	1	2	yes	—
383	C₂×#99	C₂⁴	1	2	yes	—
384	C₂×#99	C₂⁴	1	2	yes	—
385	C₂⁵	#120	1	4	yes	—
386	C₂⁵	#120	1	1	yes	characteristic
387	C₂⁵	#120	1	1	yes	characteristic
388	C₂⁵	C₂²×D₄	1	1	yes	characteristic
389	C₂⁵	C₂²×D₄	1	1	yes	characteristic
390	C₂⁵	C₂²×D₄	1	1	yes	characteristic
391	C₂⁵	C₂²×D₄	1	1	yes	characteristic
392	C₂⁵	C₂²×D₄	1	1	yes	characteristic
393	C₂⁵	C₂²×D₄	1	1	yes	characteristic
394	C₂⁵	C₂²×D₄	1	1	yes	characteristic
395	C₂⁵	C₂²×D₄	1	1	yes	characteristic
396	C₂×#41	#120	1	4	yes	complemented
397	C₂²×Q₈	#120	1	1	yes	characteristic
398	C₂²×Q₈	#120	1	4	yes	complemented
399	C₂²×Q₈	C₂²×D₄	1	1	yes	characteristic
400	C₂²×Q₈	C₂²×D₄	1	1	yes	characteristic
401	C₂²×Q₈	C₂²×D₄	1	1	yes	characteristic
402	C₂²×Q₈	C₂²×D₄	1	1	yes	characteristic
403	C₂²×D₄	#120	1	1	yes	characteristic
404	C₂²×D₄	#120	1	1	yes	characteristic
405	C₂²×D₄	#120	1	1	yes	characteristic
406	C₂²×D₄	#120	1	1	yes	characteristic
407	C₂²×D₄	#120	1	1	yes	characteristic
408	C₂²×D₄	#120	1	1	yes	characteristic
409	C₂²×D₄	#120	1	1	yes	characteristic
410	C₂²×D₄	#120	1	1	yes	characteristic
411	C₂²×D₄	#120	1	4	yes	—
412	C₂²×D₄	#120	1	1	yes	characteristic
413	C₂²×D₄	#120	1	4	yes	complemented
414	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
415	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
416	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
417	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
418	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
419	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
420	C₂²×D₄	C₂²×D₄	1	2	yes	—
421	C₂²×D₄	C₂²×D₄	1	2	yes	—
422	C₂²×D₄	C₂²×D₄	1	2	yes	—
423	C₂²×D₄	C₂²×D₄	1	2	yes	—
424	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
425	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
426	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
427	C₂²×D₄	C₂⁵	1	1	yes	characteristic
428	C₂³×C₄	#120	1	1	yes	characteristic
429	C₂³×C₄	#120	1	1	yes	characteristic
430	C₂³×C₄	#120	1	1	yes	characteristic
431	C₂³×C₄	#120	1	1	yes	characteristic
432	C₂³×C₄	#120	1	4	yes	complemented
433	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
434	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
435	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
436	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
437	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
438	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
439	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
440	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
441	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
442	#127	#120	1	4	yes	complemented
443	#127	C₂²×D₄	1	2	yes	—
444	#127	C₂²×D₄	1	2	yes	—
445	#124	#120	1	4	yes	complemented
446	#124	#120	1	4	yes	complemented
447	#124	#120	1	4	yes	complemented
448	#124	C₂²×D₄	1	2	yes	—
449	#124	C₂²×D₄	1	2	yes	—
450	#124	C₂²×D₄	1	2	yes	—
451	#124	C₂²×D₄	1	2	yes	—
452	#124	C₂²×D₄	1	2	yes	—
453	#124	C₂²×D₄	1	2	yes	—
454	#123	#120	1	4	yes	—
455	#123	#120	1	4	yes	complemented
456	#123	#120	1	4	yes	complemented
457	#123	#120	1	4	yes	complemented
458	#123	C₂²×D₄	1	2	yes	—
459	#123	C₂²×D₄	1	2	yes	—
460	#123	C₂²×D₄	1	2	yes	—
461	#123	C₂²×D₄	1	2	yes	—
462	#123	C₂²×D₄	1	2	yes	—
463	#123	C₂²×D₄	1	2	yes	—
464	#123	C₂²×D₄	1	2	yes	—
465	#123	C₂²×D₄	1	2	yes	—
466	#120	#120	1	4	yes	—
467	#120	#120	1	4	yes	—
468	#120	#120	1	4	yes	—
469	#120	#120	1	4	yes	complemented
470	#120	C₂²×D₄	1	2	yes	—
471	#120	C₂²×D₄	1	2	yes	—
472	#120	C₂²×D₄	1	2	yes	—
473	#120	C₂²×D₄	1	2	yes	—
474	#120	C₂²×D₄	1	2	yes	—
475	#120	C₂²×D₄	1	2	yes	—
476	#120	C₂²×D₄	1	2	yes	—
477	#120	C₂²×D₄	1	2	yes	—
478	#117	#120	1	4	yes	complemented
479	C₂×C₂²⋊C₄	#120	1	4	yes	—
480	C₂×C₂²⋊C₄	#120	1	4	yes	—
481	C₂×C₂²⋊C₄	#120	1	4	yes	complemented
482	C₂×C₂²⋊C₄	#120	1	4	yes	complemented
483	C₂×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
488	C₂×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄²	#120	1	4	yes	complemented
492	C₂×C₄²	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄²	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄²	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄²	C₂²×D₄	1	1	yes	characteristic
496	C₂⁴	C₂×#120	1	1	yes	characteristic
497	C₂⁴	C₂×#120	1	1	yes	characteristic
498	C₂⁴	C₂×#120	1	1	yes	characteristic
499	C₂⁴	C₂×#120	1	1	yes	characteristic
500	C₂⁴	C₂×#120	1	1	yes	characteristic
501	C₂⁴	C₂×#120	1	1	yes	characteristic
502	C₂⁴	C₂×#120	1	2	yes	—
503	C₂⁴	C₂×#120	1	2	yes	—
504	C₂⁴	C₂×#120	1	2	yes	—
505	C₂⁴	C₂×#120	1	2	yes	—
506	C₂⁴	C₂×#120	1	2	yes	—
507	C₂⁴	C₂×#120	1	2	yes	—
508	C₂⁴	C₂×#120	1	2	yes	—
509	C₂⁴	C₂×#120	1	2	yes	—
510	C₂⁴	C₂×#120	1	1	yes	characteristic
511	C₂⁴	C₂³×D₄	1	1	yes	characteristic
512	C₂⁴	C₂³×D₄	1	1	yes	characteristic
513	C₂×Q₈	C₂×#120	1	2	yes	—
514	C₂×Q₈	C₂×#120	1	2	yes	—
515	C₂×Q₈	C₂×#120	1	2	yes	—
516	C₂×D₄	B(4,𝔽₂)	1	2	yes	—
517	C₂×D₄	B(4,𝔽₂)	1	2	yes	—
518	C₂×D₄	C₂×#120	1	2	yes	—
519	C₂×D₄	C₂×#120	1	2	yes	—
520	C₂×D₄	C₂×#120	1	2	yes	—
521	C₂×D₄	C₂×#120	1	2	yes	—
522	C₂×D₄	C₂×#120	1	2	yes	—
523	C₂×D₄	C₂×#120	1	2	yes	—
524	C₂×D₄	C₂×#120	1	2	yes	—
525	C₂×D₄	C₂³×D₄	1	1	yes	characteristic
526	C₂×D₄	C₂³×D₄	1	1	yes	characteristic
527	C₂×D₄	C₂³×D₄	1	1	yes	characteristic
528	C₂×D₄	C₂³×D₄	1	1	yes	characteristic
529	C₂²×C₄	C₂×#120	1	1	yes	characteristic
530	C₂²×C₄	C₂×#120	1	1	yes	characteristic
531	C₂²×C₄	C₂×#120	1	1	yes	characteristic
532	C₂²×C₄	C₂×#120	1	1	yes	characteristic
533	C₂²×C₄	C₂×#120	1	2	yes	—
534	C₂²×C₄	C₂×#120	1	2	yes	—
535	C₂²×C₄	C₂×#120	1	1	yes	characteristic
536	C₂²×C₄	C₂×#120	1	2	yes	—
537	C₂²×C₄	C₂×#120	1	2	yes	—
538	C₂²×C₄	C₂×#120	1	2	yes	—
539	C₂²×C₄	C₂×#120	1	2	yes	—
540	C₂²×C₄	C₂³×D₄	1	1	yes	characteristic
541	C₂²⋊C₄	C₂×#120	1	2	yes	—
542	C₂²⋊C₄	C₂×#120	1	2	yes	—
543	C₂²⋊C₄	C₂×#120	1	2	yes	—
544	C₂²⋊C₄	C₂×#120	1	2	yes	—
545	C₂²⋊C₄	C₂×#120	1	2	yes	—
546	C₂²⋊C₄	C₂×#120	1	2	yes	—
547	C₂²⋊C₄	C₂×#120	1	2	yes	—
548	C₂²⋊C₄	C₂×#120	1	2	yes	—
549	C₄²	C₂×#120	1	2	yes	—
550	C₄²	C₂×#120	1	2	yes	—
551	C₄²	C₂×#120	1	2	yes	—
552	C₄²	C₂×#120	1	2	yes	—
553	C₂³	#2846	1	2	yes	—
554	C₂³	#2846	1	2	yes	—
555	C₂³	#2846	1	2	yes	—
556	C₂³	C₂×B(4,𝔽₂)	1	2	yes	—
557	C₂³	C₂×B(4,𝔽₂)	1	1	yes	characteristic
558	C₂³	C₂×B(4,𝔽₂)	1	1	yes	characteristic
559	C₂³	#3026	1	2	yes	—
560	C₂³	C₂²×#120	1	1	yes	characteristic
561	C₂³	C₂²×#120	1	1	yes	characteristic
562	C₂³	C₂²×#120	1	1	yes	characteristic
563	C₂³	C₂²×#120	1	1	yes	characteristic
564	C₂³	C₂²×#120	1	1	yes	characteristic
565	C₂×C₄	#2846	1	2	yes	—
566	C₂×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
567	C₂×C₄	C₂²×#120	1	1	yes	characteristic
568	C₂×C₄	C₂²×#120	1	1	yes	characteristic
569	C₂²	#32898	1	2	yes	—
570	C₂²	#32898	1	2	yes	—
571	C₂²	C₂×#2846	1	1	yes	characteristic
572	C₂²	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
573	C₂²	C₂×#3026	1	1	yes	characteristic
574	C₂	C₂×#32898	1	1	yes	characteristic
575	C₂	#7622881	1	2	yes	—

	subgroup	G/H
center, socle	C₂²	C₂²×B(4,𝔽₂)
commutator, Frattini, cosocle	C₂²×D₄	C₂⁵
LCS	G ▷ C₂²×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂²×D₄ ◁ C₂²×H(5,𝔽₂) ◁ G
LECS	G ▷ C₂²×D₄ ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#63017	C₂	semidirect
2. C₂×#33558	C₂	semidirect
3. C₂×#33552	C₂	semidirect
4. C₂×#33551	C₂	semidirect
5. C₂²×#2197	C₂	semidirect
6. #6437635	C₂	semidirect
7. #6437632	C₂	semidirect
8. #6437457	C₂	semidirect
9. #511788	C₂	semidirect
10. #511786	C₂	semidirect
11. #511783	C₂	semidirect
12. #511782	C₂	semidirect
13. #511780	C₂	semidirect
14. #511779	C₂	semidirect
15. #511774	C₂	semidirect
16. #511772	C₂	semidirect
17. #493632	C₂	semidirect
18. #493583	C₂	semidirect
19. #493582	C₂	semidirect
20. C₂×#12761	C₂	semidirect
21. #493433	C₂	semidirect
22. #493427	C₂	semidirect
23. #493424	C₂	semidirect
24. #62842	C₂²	semidirect
29. C₂×#3545	C₂²	semidirect
30. C₂×#3551	C₂²	semidirect
31. C₂×#3540	C₂²	semidirect
33. C₂×#3533	C₂²	semidirect
34. C₂×#3538	C₂²	semidirect
36. C₂×#3532	C₂²	semidirect
37. C₂×#3481	C₂²	semidirect
39. C₂²×#551	C₂²	semidirect
40. C₂×#3026	C₂²	semidirect
41. C₂×#3026	C₂²	semidirect
42. C₂²×#458	C₂²	semidirect
44. C₂×#3019	C₂²	semidirect
45. C₂²×#455	C₂²	semidirect
46. C₂×#2201	C₂²	semidirect
47. C₂×#2201	C₂²	semidirect
48. C₂×#2200	C₂²	semidirect
49. C₂×#2200	C₂²	semidirect
50. C₂×#2199	C₂²	semidirect
51. C₂×#2199	C₂²	semidirect
52. C₂×#2198	C₂²	semidirect
53. C₂×#2197	C₂²	semidirect
54. C₂×#2197	C₂²	semidirect
55. C₂×#2197	C₂²	semidirect
56. C₂×#2197	C₂²	semidirect
57. C₂×#2197	C₂²	semidirect
58. C₂×#2197	C₂²	semidirect
59. C₂×#2197	C₂²	semidirect
60. C₂×#2197	C₂²	semidirect
61. C₂×#2196	C₂²	semidirect
62. C₂×#2127	C₂²	semidirect
63. C₂×#2127	C₂²	semidirect
64. C₂²×#354	C₂²	semidirect
65. C₂²×#354	C₂²	semidirect
66. C₂×#2121	C₂²	semidirect
67. C₂×#2121	C₂²	semidirect
68. C₂×#2121	C₂²	semidirect
69. C₂×#2121	C₂²	semidirect
70. C₂²×#352	C₂²	semidirect
71. C₂²×#352	C₂²	semidirect
74. #23914	C₂²	semidirect
75. #23912	C₂²	semidirect
76. #23908	C₂²	semidirect
77. #23907	C₂²	semidirect
78. #23905	C₂²	semidirect
79. #23904	C₂²	semidirect
80. #23903	C₂²	semidirect
81. #23903	C₂²	semidirect
83. #23902	C₂²	semidirect
84. #23901	C₂²	semidirect
86. #20960	C₂²	semidirect
87. #20960	C₂²	semidirect
88. C₂×#1890	C₂²	semidirect
90. #20953	C₂²	semidirect
91. C₂×#1885	C₂²	semidirect
92. #20592	C₂²	semidirect
93. #20585	C₂²	semidirect
94. #20585	C₂²	semidirect
95. #12764	C₂²	semidirect
96. #12764	C₂²	semidirect
97. #12763	C₂²	semidirect
98. #12763	C₂²	semidirect
99. #12762	C₂²	semidirect
100. #12762	C₂²	semidirect
101. #12761	C₂²	semidirect
102. #12761	C₂²	semidirect
103. #12761	C₂²	semidirect
104. #12761	C₂²	semidirect
105. #12761	C₂²	semidirect
106. #12761	C₂²	semidirect
107. #12761	C₂²	semidirect
108. #12761	C₂²	semidirect
109. #12760	C₂²	semidirect
110. #12759	C₂²	semidirect
111. #12698	C₂²	semidirect
112. #12696	C₂²	semidirect
113. #12695	C₂²	semidirect
114. #12694	C₂²	semidirect
115. #12692	C₂²	semidirect
116. #12691	C₂²	semidirect
117. #12690	C₂²	semidirect
118. #12690	C₂²	semidirect
119. #12689	C₂²	semidirect
120. #12689	C₂²	semidirect
121. #12688	C₂²	semidirect
122. #12687	C₂²	semidirect
123. C₂²×2₋¹⁺⁴	D₄	semidirect
126. C₂³×#41	D₄	semidirect
127. C₂⁴×D₄	D₄	semidirect
128. #3545	D₄	semidirect
129. #3533	D₄	semidirect
130. #3532	D₄	semidirect
140. C₂×#551	D₄	semidirect
150. C₂×#536	D₄	semidirect
151. C₂×#536	D₄	semidirect
152. C₂×#536	D₄	semidirect
155. C₂×#535	D₄	semidirect
156. C₂×#535	D₄	semidirect
160. C₂×#534	D₄	semidirect
161. C₂×#534	D₄	semidirect
162. C₂×#534	D₄	semidirect
163. C₂×#534	D₄	semidirect
168. C₂×#532	D₄	semidirect
169. C₂×#532	D₄	semidirect
171. C₂²×#124	D₄	semidirect
174. C₂×#525	D₄	semidirect
175. C₂×#525	D₄	semidirect
178. C₂²×#123	D₄	semidirect
179. C₂²×#123	D₄	semidirect
182. C₂²×#120	D₄	semidirect
183. C₂²×#120	D₄	semidirect
186. C₂×#518	D₄	semidirect
187. C₂×#518	D₄	semidirect
189. C₂×C₄×#41	D₄	semidirect
259. C₂²×#41	C₂×D₄	semidirect
260. C₂²×#41	C₂×D₄	semidirect
263. C₂³×Q₈	C₂×D₄	semidirect
264. C₂³×Q₈	C₂×D₄	semidirect
265. C₂³×Q₈	C₂×D₄	semidirect
277. C₂³×D₄	C₂×D₄	semidirect
282. C₂⁴×C₄	C₂×D₄	semidirect
283. C₂⁴×C₄	C₂×D₄	semidirect
284. #563	C₂×D₄	semidirect
285. #563	C₂×D₄	semidirect
286. H(3,𝔽₄)	C₂×D₄	semidirect
287. H(3,𝔽₄)	C₂×D₄	semidirect
288. #560	C₂×D₄	semidirect
289. #560	C₂×D₄	semidirect
290. #559	C₂×D₄	semidirect
291. #551	C₂×D₄	semidirect
292. #551	C₂×D₄	semidirect
293. #551	C₂×D₄	semidirect
294. #551	C₂×D₄	semidirect
295. #551	C₂×D₄	semidirect
296. #551	C₂×D₄	semidirect
297. #551	C₂×D₄	semidirect
298. #551	C₂×D₄	semidirect
299. D₄²	C₂×D₄	semidirect
306. C₂×C₄⋊Q₈	C₂×D₄	semidirect
307. C₂×C₄⋊Q₈	C₂×D₄	semidirect
308. C₂×C₄⋊Q₈	C₂×D₄	semidirect
310. C₂×#127	C₂×D₄	semidirect
317. C₂×#124	C₂×D₄	semidirect
318. C₂×#124	C₂×D₄	semidirect
319. C₂×#124	C₂×D₄	semidirect
320. C₂×#124	C₂×D₄	semidirect
332. C₂×#123	C₂×D₄	semidirect
333. C₂×#123	C₂×D₄	semidirect
334. C₂×#123	C₂×D₄	semidirect
335. C₂×#123	C₂×D₄	semidirect
336. C₂×#123	C₂×D₄	semidirect
337. C₂×#123	C₂×D₄	semidirect
354. C₂×#120	C₂×D₄	semidirect
355. C₂×#120	C₂×D₄	semidirect
364. C₂×#117	C₂×D₄	semidirect
365. C₂×#117	C₂×D₄	semidirect
366. C₂×#117	C₂×D₄	semidirect
367. C₂×#117	C₂×D₄	semidirect
374. C₂²×C₂²⋊C₄	C₂×D₄	semidirect
375. C₂²×C₂²⋊C₄	C₂×D₄	semidirect
377. C₂²×C₄²	C₂×D₄	semidirect
378. C₂²×C₄²	C₂×D₄	semidirect
396. C₂×#41	#120	semidirect
398. C₂²×Q₈	#120	semidirect
413. C₂²×D₄	#120	semidirect
432. C₂³×C₄	#120	semidirect
442. #127	#120	semidirect
445. #124	#120	semidirect
446. #124	#120	semidirect
447. #124	#120	semidirect
455. #123	#120	semidirect
456. #123	#120	semidirect
457. #123	#120	semidirect
469. #120	#120	semidirect
478. #117	#120	semidirect
481. C₂×C₂²⋊C₄	#120	semidirect
482. C₂×C₂²⋊C₄	#120	semidirect
491. C₂×C₄²	#120	semidirect

Maximal subgroups

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

subgroup	index
C₂×#63017	2
C₂×#33558	2
C₂×#33552	2
C₂×#33551	2
C₂²×#2197	2
#6437635	2
#6437632	2
#6437457	2
#511788	2
#511786	2
#511783	2
#511782	2
#511780	2
#511779	2
#511774	2
#511772	2
#493632	2
#493583	2
#493582	2
C₂×#12761	2
#493433	2
#493427	2
#493424	2