Subgroups — #72313185

Order 2048.

At least 9908 conjugacy classes of subgroups; only the 1568 normal subgroups are shown.

The subgroup lattice has 656 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72313179	C₂	1	8	yes	maximal, complemented
2	#72313178	C₂	1	8	yes	maximal, complemented
3	C₂×#498916	C₂	1	1	yes	maximal, characteristic, complemented
4	#72312755	C₂	1	1	yes	maximal, characteristic, complemented
5	#72312734	C₂	1	1	yes	maximal, characteristic, complemented
6	#72312697	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#6437986	C₂	1	1	yes	maximal, characteristic, complemented
8	#72312254	C₂	1	1	yes	maximal, characteristic, complemented
9	#72310500	C₂	1	1	yes	maximal, characteristic, complemented
10	#72303729	C₂	1	1	yes	maximal, characteristic, complemented
11	#72303727	C₂	1	1	yes	maximal, characteristic, complemented
12	#72280610	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#494758	C₂	1	1	yes	maximal, characteristic, complemented
14	#72256636	C₂	1	1	yes	maximal, characteristic, complemented
15	#72255896	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#33348	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#23882	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#3585	C₂²	1	1	yes	characteristic
19	C₂²×#3484	C₂²	1	1	yes	characteristic
20	C₂×#60753	C₂²	1	1	yes	characteristic
21	C₂²×#3025	C₂²	1	1	yes	characteristic
22	C₂×#60367	C₂²	1	1	yes	characteristic
23	C₂×#60387	C₂²	1	1	yes	characteristic, complemented
24	C₂²×#3021	C₂²	1	1	yes	characteristic
25	C₂²×#2888	C₂²	1	1	yes	characteristic
26	C₂²×#2883	C₂²	1	1	yes	characteristic
27	#7634872	C₂²	1	1	yes	characteristic
28	C₂×#33358	C₂²	1	1	yes	characteristic, complemented
29	C₂×#33348	C₂²	1	8	yes	complemented
30	C₂×#33347	C₂²	1	1	yes	characteristic, complemented
31	C₂²×#2122	C₂²	1	1	yes	characteristic
32	C₂²×#2122	C₂²	1	1	yes	characteristic
33	C₂²×#2120	C₂²	1	1	yes	characteristic
34	C₂²×#2120	C₂²	1	1	yes	characteristic
35	#6470214	C₂²	1	4	yes	complemented
36	#6470213	C₂²	1	4	yes	complemented
37	C₂×#24421	C₂²	1	4	yes	complemented
38	C₂×#24420	C₂²	1	4	yes	complemented
39	C₂×#23882	C₂²	1	8	yes	—
40	#6374164	C₂²	1	1	yes	characteristic
41	#6374112	C₂²	1	1	yes	characteristic
42	C₂×#21017	C₂²	1	1	yes	characteristic, complemented
43	C₂²×#1910	C₂²	1	1	yes	characteristic
44	C₂²×#1891	C₂²	1	1	yes	characteristic
45	C₂×#20860	C₂²	1	1	yes	characteristic, complemented
46	C₂²×#1795	C₂²	1	1	yes	characteristic
47	C₂×#20620	C₂²	1	1	yes	characteristic, complemented
48	C₂×#20612	C₂²	1	1	yes	characteristic, complemented
49	#6370734	C₂²	1	1	yes	characteristic, complemented
50	#6370719	C₂²	1	1	yes	characteristic
51	#498930	C₂²	1	4	yes	complemented
52	#498929	C₂²	1	4	yes	complemented
53	C₂×#13361	C₂²	1	4	yes	complemented
54	C₂×#13360	C₂²	1	4	yes	complemented
55	C₂×#13102	C₂²	1	4	yes	complemented
56	C₂×#13100	C₂²	1	4	yes	complemented
57	C₂×#12589	C₂²	1	1	yes	characteristic, complemented
58	C₂×#12589	C₂²	1	1	yes	characteristic, complemented
59	#492906	C₂²	1	1	yes	characteristic, complemented
60	C₂×#12579	C₂²	1	1	yes	characteristic, complemented
61	C₂×#12577	C₂²	1	1	yes	characteristic, complemented
62	#492886	C₂²	1	1	yes	characteristic, complemented
63	#359546	C₂²	1	8	yes	complemented
64	#353434	C₂²	1	1	yes	characteristic, complemented
65	#353422	C₂²	1	1	yes	characteristic, complemented
66	#148265	C₂²	1	8	yes	complemented
67	#148260	C₂²	1	8	yes	complemented
68	#147856	C₂²	1	4	yes	complemented
69	#147855	C₂²	1	4	yes	complemented
70	#147818	C₂²	1	4	yes	complemented
71	#147817	C₂²	1	4	yes	complemented
72	#147755	C₂²	1	8	yes	complemented
73	#147751	C₂²	1	8	yes	complemented
74	#146591	C₂²	1	8	yes	complemented
75	C₂²×#585	C₂³	1	1	yes	characteristic
76	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
77	C₂⁵×D₄	D₄	1	1	yes	characteristic
78	C₂×#3585	D₄	1	8	yes	complemented
79	C₂×#3585	C₂³	1	4	yes	—
80	C₂²×#575	D₄	1	1	yes	characteristic, complemented
81	C₂³×AGL(1,ℤ/8)	D₄	1	1	yes	characteristic, complemented
82	C₂²×#568	C₂³	1	1	yes	characteristic
83	C₂×#3484	D₄	1	4	yes	—
84	C₂×#3484	C₂³	1	4	yes	—
85	C₂×#3449	C₂³	1	1	yes	characteristic
86	C₂²×#535	D₄	1	1	yes	characteristic
87	C₂²×#535	C₂³	1	1	yes	characteristic
88	C₂²×#525	D₄	1	1	yes	characteristic
89	C₂²×#525	C₂³	1	1	yes	characteristic
90	C₂²×#518	D₄	1	1	yes	characteristic
91	C₂×#3200	C₂³	1	2	yes	—
92	C₂×#3199	C₂³	1	2	yes	—
93	C₂×#3025	C₂³	1	4	yes	—
94	C₂×#3022	C₂³	1	2	yes	complemented
95	C₂×#3021	C₂³	1	4	yes	—
96	C₂×#3021	C₂³	1	2	yes	complemented
97	C₂×#3009	D₄	1	2	yes	complemented
98	C₂×#3009	C₂³	1	2	yes	—
99	C₂×#3008	D₄	1	2	yes	complemented
100	C₂×#3008	C₂³	1	2	yes	—
101	C₂×#2896	D₄	1	1	yes	characteristic, complemented
102	C₂×#2896	D₄	1	1	yes	characteristic, complemented
103	C₂×#2896	D₄	1	1	yes	characteristic, complemented
104	C₂²×#418	D₄	1	1	yes	characteristic, complemented
105	C₂²×#418	D₄	1	1	yes	characteristic, complemented
106	C₂²×#418	D₄	1	1	yes	characteristic, complemented
107	C₂×#2888	D₄	1	8	yes	complemented
108	C₂×#2888	C₂³	1	4	yes	—
109	C₂²×#413	C₂³	1	1	yes	characteristic
110	C₂²×#413	C₂³	1	1	yes	characteristic
111	C₂²×#413	C₂³	1	1	yes	characteristic
112	C₂×#2883	C₂³	1	4	yes	—
113	C₂²×#410	C₂³	1	1	yes	characteristic
114	C₂²×#410	C₂³	1	1	yes	characteristic
115	C₂²×#410	C₂³	1	1	yes	characteristic
116	C₂×#2879	C₂³	1	1	yes	characteristic
117	C₂×#2879	C₂³	1	1	yes	characteristic
118	#37374	C₂³	1	2	yes	—
119	#37269	C₂³	1	2	yes	—
120	#34044	C₂³	1	1	yes	characteristic
121	C₂×#2129	C₂³	1	2	yes	complemented
122	C₂×#2128	C₂³	1	2	yes	complemented
123	C₂×#2123	C₂³	1	2	yes	complemented
124	C₂×#2122	D₄	1	8	yes	complemented
125	C₂×#2122	C₂³	1	4	yes	—
126	C₂×#2122	C₂³	1	4	yes	—
127	C₂×#2122	C₂³	1	2	yes	complemented
128	C₂×#2120	D₄	1	4	yes	—
129	C₂×#2120	C₂³	1	4	yes	—
130	C₂×#2120	C₂³	1	4	yes	—
131	C₂²×#352	D₄	1	2	yes	—
132	C₂²×AΣL(1,𝔽₁₆)	D₄	1	2	yes	—
133	#21770	C₂³	1	4	yes	—
134	#21744	C₂³	1	4	yes	—
135	C₂×#1915	C₂³	1	2	yes	complemented
136	C₂×#1914	C₂³	1	2	yes	complemented
137	C₂×#1910	C₂³	1	4	yes	—
138	C₂×#1891	C₂³	1	4	yes	—
139	C₂×#1858	C₂³	1	4	yes	complemented
140	C₂×#1795	D₄	1	8	yes	complemented
141	C₂×#1795	C₂³	1	4	yes	—
142	C₂×#1794	C₂³	1	4	yes	complemented
143	C₂×#1791	C₂³	1	4	yes	complemented
144	#20610	C₂³	1	4	yes	complemented
145	#20602	D₄	1	4	yes	complemented
146	#20602	C₂³	1	4	yes	—
147	C₂×#1395	C₂³	1	4	yes	complemented
148	C₂×#1395	C₂³	1	4	yes	complemented
149	#12587	C₂³	1	4	yes	complemented
150	C₂×#1392	C₂³	1	4	yes	complemented
151	C₂×#1391	C₂³	1	4	yes	complemented
152	#12575	C₂³	1	4	yes	complemented
153	#10748	C₂³	1	4	yes	complemented
154	#10742	C₂³	1	4	yes	complemented
155	C₂×#585	C₂×D₄	1	4	yes	—
156	C₂×#585	C₂⁴	1	2	yes	—
157	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
158	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
159	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
160	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
161	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
162	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
163	C₂²×H(5,𝔽₂)	#41	1	4	yes	—
164	C₂²×H(5,𝔽₂)	C₂⁴	1	2	yes	—
165	C₂³×#41	C₂×D₄	1	1	yes	characteristic
166	C₂³×#41	C₂×D₄	1	1	yes	characteristic
167	C₂³×#41	C₂×D₄	1	1	yes	characteristic
168	C₂³×#41	C₂×D₄	1	1	yes	characteristic
169	C₂³×#41	C₂⁴	1	1	yes	characteristic
170	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
171	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
172	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
173	C₂⁴×D₄	C₂×D₄	1	4	yes	—
174	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
175	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
176	#3585	C₂×D₄	1	16	yes	—
177	C₂²×#137	C₂×D₄	1	2	yes	complemented
178	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	2	yes	complemented
179	C₂³×SD₁₆	C₂×D₄	1	2	yes	complemented
180	C₂³×D₈	C₂×D₄	1	2	yes	complemented
181	C₂×#568	C₂×D₄	1	4	yes	—
182	C₂×#568	C₂⁴	1	2	yes	—
183	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
184	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
185	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
186	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
187	C₂×#536	C₂×D₄	1	1	yes	characteristic
188	C₂×#536	C₂⁴	1	1	yes	characteristic
189	C₂×#535	C₂×D₄	1	4	yes	—
190	C₂×#535	C₂×D₄	1	1	yes	characteristic
191	C₂×#535	C₂×D₄	1	2	yes	—
192	C₂×#535	C₂×D₄	1	4	yes	—
193	C₂×#535	#41	1	4	yes	—
194	C₂×#535	C₂⁴	1	1	yes	characteristic
195	C₂×#535	C₂⁴	1	2	yes	—
196	C₂×#525	C₂×D₄	1	2	yes	—
197	C₂×#525	C₂×D₄	1	2	yes	—
198	C₂×#525	C₂×D₄	1	4	yes	—
199	C₂×#525	#41	1	2	yes	—
200	C₂×#525	C₂⁴	1	2	yes	—
201	C₂²×#123	C₂×D₄	1	1	yes	characteristic
202	C₂²×#123	#41	1	1	yes	characteristic
203	C₂²×#120	C₂×D₄	1	1	yes	characteristic
204	C₂²×#120	#41	1	1	yes	characteristic
205	C₂×#518	C₂×D₄	1	4	yes	—
206	C₂²×#117	C₂×D₄	1	1	yes	characteristic
207	C₂²×#117	C₂×D₄	1	1	yes	characteristic
208	C₂²×#117	C₂×D₄	1	1	yes	characteristic
209	C₂²×#117	C₂×D₄	1	1	yes	characteristic
210	C₂²×#117	C₂×D₄	1	1	yes	characteristic
211	C₂×#417	C₂×D₄	1	4	yes	complemented
212	C₂×#418	C₂×D₄	1	2	yes	complemented
213	C₂×#418	C₂×D₄	1	2	yes	complemented
214	C₂×#418	C₂×D₄	1	4	yes	complemented
215	C₂×#416	C₂×D₄	1	2	yes	complemented
216	C₂×#416	C₂×D₄	1	2	yes	complemented
217	C₂×#416	C₂×D₄	1	4	yes	complemented
218	C₂²×#102	C₂×D₄	1	4	yes	complemented
219	#2888	C₂×D₄	1	16	yes	complemented
220	C₂×#413	C₂×D₄	1	4	yes	—
221	C₂×#413	C₂×D₄	1	4	yes	—
222	C₂×#413	C₂×D₄	1	4	yes	—
223	C₂×#413	C₂×D₄	1	4	yes	—
224	C₂×#413	C₂×D₄	1	2	yes	—
225	C₂×#413	C₂⁴	1	2	yes	—
226	C₂×#413	C₂⁴	1	2	yes	—
227	C₂×#413	C₂⁴	1	2	yes	—
228	C₂²×#100	C₂×D₄	1	2	yes	—
229	C₂×#410	C₂×D₄	1	4	yes	—
230	C₂×#410	C₂×D₄	1	4	yes	—
231	C₂×#410	C₂×D₄	1	2	yes	—
232	C₂×#410	C₂⁴	1	2	yes	—
233	C₂×#410	C₂⁴	1	2	yes	—
234	C₂×#410	C₂⁴	1	2	yes	—
235	C₂²×#99	C₂×D₄	1	2	yes	—
236	C₂×#408	C₂×D₄	1	2	yes	—
237	C₂×#408	C₂×D₄	1	2	yes	—
238	C₂×#408	C₂⁴	1	2	yes	—
239	C₂×#408	C₂⁴	1	2	yes	—
240	#2311	C₂×D₄	1	2	yes	—
241	#2311	C₂⁴	1	2	yes	—
242	#2122	C₂×D₄	1	16	yes	complemented
243	C₂×#352	C₂×D₄	1	8	yes	—
244	C₂×AΣL(1,𝔽₁₆)	C₂×D₄	1	8	yes	—
245	#1795	C₂×D₄	1	16	yes	—
246	C₂⁶	#121	1	1	yes	characteristic
247	#585	C₂²×D₄	1	4	yes	—
248	C₂×H(5,𝔽₂)	#120	1	8	yes	—
249	C₂×H(5,𝔽₂)	#120	1	8	yes	—
250	C₂×H(5,𝔽₂)	#121	1	8	yes	—
251	C₂×H(5,𝔽₂)	#121	1	8	yes	—
252	C₂×H(5,𝔽₂)	#121	1	8	yes	—
253	C₂×H(5,𝔽₂)	#127	1	8	yes	—
254	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
255	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
256	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
257	C₂×H(5,𝔽₂)	C₂×#41	1	4	yes	—
258	C₂²×#41	#120	1	2	yes	—
259	C₂²×#41	#120	1	2	yes	—
260	C₂²×#41	#120	1	2	yes	—
261	C₂²×#41	#120	1	4	yes	—
262	C₂²×#41	#120	1	4	yes	—
263	C₂²×#41	#121	1	4	yes	—
264	C₂²×#41	#121	1	4	yes	—
265	C₂²×#41	#121	1	4	yes	—
266	C₂²×#41	#127	1	4	yes	—
267	C₂²×#41	C₂²×D₄	1	2	yes	—
268	C₂²×#41	C₂²×D₄	1	2	yes	—
269	C₂²×#41	C₂²×D₄	1	2	yes	—
270	C₂²×#41	C₂²×D₄	1	2	yes	—
271	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
272	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
273	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
274	C₂²×#41	C₂²×D₄	1	2	yes	—
275	C₂²×#41	C₂²×D₄	1	2	yes	—
276	C₂²×#41	C₂²×D₄	1	2	yes	—
277	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
278	C₂²×#41	C₂×#41	1	2	yes	—
279	C₂²×#41	C₂×#41	1	1	yes	characteristic
280	C₂²×#41	C₂×#41	1	2	yes	—
281	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
282	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
283	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
284	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
285	C₂²×#41	C₂⁵	1	1	yes	characteristic
286	C₂³×Q₈	#120	1	1	yes	characteristic
287	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
288	C₂³×Q₈	H(5,𝔽₂)	1	1	yes	characteristic
289	C₂³×D₄	#120	1	4	yes	—
290	C₂³×D₄	#120	1	2	yes	—
291	C₂³×D₄	#120	1	2	yes	—
292	C₂³×D₄	#120	1	4	yes	—
293	C₂³×D₄	#120	1	2	yes	—
294	C₂³×D₄	#120	1	1	yes	characteristic
295	C₂³×D₄	#120	1	1	yes	characteristic
296	C₂³×D₄	#120	1	1	yes	characteristic
297	C₂³×D₄	#121	1	4	yes	—
298	C₂³×D₄	#121	1	4	yes	—
299	C₂³×D₄	#121	1	4	yes	—
300	C₂³×D₄	#121	1	4	yes	—
301	C₂³×D₄	#127	1	4	yes	—
302	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
303	C₂³×D₄	C₂²×D₄	1	2	yes	—
304	C₂³×D₄	C₂²×D₄	1	2	yes	—
305	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
306	C₂³×D₄	C₂²×D₄	1	2	yes	—
307	C₂³×D₄	C₂²×D₄	1	2	yes	—
308	C₂³×D₄	C₂×#41	1	1	yes	characteristic
309	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
310	C₂⁴×C₄	#121	1	1	yes	characteristic
311	C₂⁴×C₄	#121	1	2	yes	—
312	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
313	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
314	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
315	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
316	#568	C₂²×D₄	1	4	yes	—
317	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
318	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
319	C₂³×C₈	C₂²×D₄	1	2	yes	—
320	C₂³×C₈	C₂²×D₄	1	2	yes	—
321	#535	#121	1	8	yes	—
322	#535	C₂²×D₄	1	4	yes	—
323	#535	C₂×#41	1	4	yes	—
324	C₂×#123	#121	1	2	yes	—
325	C₂×#123	#121	1	2	yes	—
326	C₂×#123	C₂²×D₄	1	2	yes	—
327	C₂×#123	C₂×#41	1	2	yes	—
328	C₂×#120	#121	1	2	yes	—
329	C₂×#120	#121	1	2	yes	—
330	C₂×#120	C₂²×D₄	1	2	yes	—
331	C₂×#120	C₂×#41	1	2	yes	—
332	C₂×#117	#121	1	4	yes	—
333	C₂×#117	#121	1	2	yes	—
334	C₂×#117	C₂²×D₄	1	1	yes	characteristic
335	C₂×#117	C₂²×D₄	1	1	yes	characteristic
336	C₂×#117	C₂²×D₄	1	2	yes	—
337	C₂×#117	C₂²×D₄	1	2	yes	—
338	C₂×#117	C₂²×D₄	1	2	yes	—
339	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
340	C₂²×C₂²⋊C₄	#121	1	1	yes	characteristic
341	C₂²×C₂²⋊C₄	#121	1	1	yes	characteristic
342	#413	#120	1	8	yes	—
343	#413	C₂²×D₄	1	4	yes	—
344	#413	C₂²×D₄	1	4	yes	—
345	#413	C₂²×D₄	1	4	yes	—
346	#413	C₂²×D₄	1	4	yes	—
347	C₂×#100	#120	1	8	yes	—
348	C₂×#100	C₂²×D₄	1	4	yes	—
349	#410	C₂²×D₄	1	4	yes	—
350	#410	C₂²×D₄	1	4	yes	—
351	C₂×#99	C₂²×D₄	1	4	yes	—
352	C₂⁵	C₂×#121	1	1	yes	characteristic
353	C₂⁵	C₂×#121	1	2	yes	—
354	C₂⁵	D₄²	1	1	yes	characteristic
355	C₂⁵	#546	1	1	yes	characteristic
356	C₂×#41	#392	1	8	yes	—
357	C₂×#41	#392	1	8	yes	—
358	C₂×#41	#392	1	8	yes	—
359	C₂×#41	C₂×#120	1	4	yes	—
360	C₂×#41	C₂×#120	1	4	yes	—
361	C₂×#41	C₂×#120	1	2	yes	—
362	C₂×#41	C₂×#120	1	2	yes	—
363	C₂×#41	C₂×#120	1	2	yes	—
364	C₂×#41	C₂×#121	1	4	yes	—
365	C₂×#41	C₂×#121	1	4	yes	—
366	C₂×#41	C₂×#121	1	4	yes	—
367	C₂×#41	C₂×#121	1	2	yes	—
368	C₂×#41	C₂×#121	1	2	yes	—
369	C₂×#41	C₂×#121	1	2	yes	—
370	C₂×#41	C₂×#121	1	2	yes	—
371	C₂×#41	#525	1	2	yes	—
372	C₂×#41	#525	1	2	yes	—
373	C₂×#41	#525	1	2	yes	—
374	C₂×#41	C₂×#127	1	4	yes	—
375	C₂×#41	C₂×#127	1	2	yes	—
376	C₂×#41	#534	1	2	yes	—
377	C₂×#41	#534	1	2	yes	—
378	C₂×#41	#535	1	2	yes	—
379	C₂×#41	#538	1	2	yes	—
380	C₂×#41	#538	1	2	yes	—
381	C₂×#41	D₄²	1	2	yes	—
382	C₂×#41	D₄²	1	2	yes	—
383	C₂×#41	D₄²	1	2	yes	—
384	C₂×#41	D₄²	1	2	yes	—
385	C₂×#41	D₄²	1	2	yes	—
386	C₂×#41	D₄²	1	2	yes	—
387	C₂×#41	#546	1	2	yes	—
388	C₂×#41	#546	1	2	yes	—
389	C₂×#41	#546	1	2	yes	—
390	C₂×#41	#546	1	2	yes	—
391	C₂×#41	#546	1	2	yes	—
392	C₂×#41	#546	1	2	yes	—
393	C₂×#41	C₂³×D₄	1	1	yes	characteristic
394	C₂×#41	C₂³×D₄	1	1	yes	characteristic
395	C₂×#41	C₂³×D₄	1	1	yes	characteristic
396	C₂×#41	C₂³×D₄	1	1	yes	characteristic
397	C₂×#41	C₂²×#41	1	1	yes	characteristic
398	C₂×#41	C₂²×#41	1	1	yes	characteristic
399	C₂×#41	C₂×H(5,𝔽₂)	1	1	yes	characteristic
400	C₂×#41	C₂×H(5,𝔽₂)	1	1	yes	characteristic
401	C₂²×Q₈	#392	1	4	yes	—
402	C₂²×Q₈	C₂×#120	1	2	yes	—
403	C₂²×Q₈	#534	1	2	yes	—
404	C₂²×Q₈	#534	1	1	yes	characteristic
405	C₂²×Q₈	#538	1	2	yes	—
406	C₂²×Q₈	D₄²	1	2	yes	—
407	C₂²×Q₈	D₄²	1	1	yes	characteristic
408	C₂²×Q₈	#546	1	1	yes	characteristic
409	C₂²×Q₈	#546	1	2	yes	—
410	C₂²×Q₈	C₂×H(5,𝔽₂)	1	1	yes	characteristic
411	C₂²×D₄	#392	1	4	yes	—
412	C₂²×D₄	#392	1	4	yes	—
413	C₂²×D₄	#392	1	8	yes	—
414	C₂²×D₄	#392	1	8	yes	—
415	C₂²×D₄	#392	1	4	yes	—
416	C₂²×D₄	#392	1	8	yes	—
417	C₂²×D₄	B(4,𝔽₂)	1	2	yes	—
418	C₂²×D₄	B(4,𝔽₂)	1	2	yes	—
419	C₂²×D₄	B(4,𝔽₂)	1	4	yes	—
420	C₂²×D₄	C₂×#120	1	2	yes	—
421	C₂²×D₄	C₂×#120	1	2	yes	—
422	C₂²×D₄	C₂×#120	1	2	yes	—
423	C₂²×D₄	C₂×#120	1	4	yes	—
424	C₂²×D₄	C₂×#120	1	2	yes	—
425	C₂²×D₄	C₂×#120	1	4	yes	—
426	C₂²×D₄	C₂×#121	1	4	yes	—
427	C₂²×D₄	C₂×#121	1	4	yes	—
428	C₂²×D₄	C₂×#121	1	4	yes	—
429	C₂²×D₄	C₂×#121	1	4	yes	—
430	C₂²×D₄	C₂×#121	1	1	yes	characteristic
431	C₂²×D₄	C₂×#121	1	1	yes	characteristic
432	C₂²×D₄	#525	1	2	yes	—
433	C₂²×D₄	#525	1	2	yes	—
434	C₂²×D₄	#525	1	2	yes	—
435	C₂²×D₄	C₂×#127	1	4	yes	—
436	C₂²×D₄	#534	1	1	yes	characteristic
437	C₂²×D₄	#535	1	2	yes	—
438	C₂²×D₄	#538	1	2	yes	—
439	C₂²×D₄	D₄²	1	2	yes	—
440	C₂²×D₄	D₄²	1	2	yes	—
441	C₂²×D₄	D₄²	1	1	yes	characteristic
442	C₂²×D₄	D₄²	1	1	yes	characteristic
443	C₂²×D₄	D₄²	1	2	yes	—
444	C₂²×D₄	D₄²	1	1	yes	characteristic
445	C₂²×D₄	#546	1	1	yes	characteristic
446	C₂²×D₄	#546	1	1	yes	characteristic
447	C₂²×D₄	#546	1	2	yes	—
448	C₂²×D₄	#546	1	2	yes	—
449	C₂²×D₄	#546	1	1	yes	characteristic
450	C₂²×D₄	#546	1	2	yes	—
451	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
452	C₂²×D₄	C₂²×#41	1	1	yes	characteristic
453	C₂²×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
454	C₂³×C₄	C₂×#120	1	2	yes	—
455	C₂³×C₄	C₂×#120	1	1	yes	characteristic
456	C₂³×C₄	C₂×#120	1	1	yes	characteristic
457	C₂³×C₄	C₂×#120	1	2	yes	—
458	C₂³×C₄	C₂×#120	1	1	yes	characteristic
459	C₂³×C₄	C₂×#120	1	1	yes	characteristic
460	C₂³×C₄	C₂×#121	1	1	yes	characteristic
461	C₂³×C₄	C₂×#121	1	2	yes	—
462	C₂³×C₄	C₂×#121	1	2	yes	—
463	C₂³×C₄	C₂×#121	1	2	yes	—
464	C₂³×C₄	C₂×#121	1	2	yes	—
465	C₂³×C₄	C₂×#121	1	2	yes	—
466	C₂³×C₄	C₂×#127	1	2	yes	—
467	C₂³×C₄	#534	1	1	yes	characteristic
468	C₂³×C₄	#534	1	2	yes	—
469	C₂³×C₄	#534	1	1	yes	characteristic
470	C₂³×C₄	D₄²	1	2	yes	—
471	C₂³×C₄	D₄²	1	1	yes	characteristic
472	C₂³×C₄	D₄²	1	1	yes	characteristic
473	C₂³×C₄	D₄²	1	1	yes	characteristic
474	C₂³×C₄	D₄²	1	2	yes	—
475	C₂³×C₄	#546	1	1	yes	characteristic
476	C₂³×C₄	#546	1	2	yes	—
477	C₂³×C₄	#546	1	2	yes	—
478	C₂³×C₄	#546	1	1	yes	characteristic
479	C₂³×C₄	#546	1	1	yes	characteristic
480	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
481	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
482	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
483	#117	C₂×#121	1	4	yes	—
484	C₂×C₂²⋊C₄	C₂×#121	1	2	yes	—
485	C₂×C₂²⋊C₄	C₂×#121	1	2	yes	—
486	#100	C₂×#120	1	8	yes	—
487	C₂⁴	#2404	1	2	yes	—
488	C₂⁴	#2410	1	1	yes	characteristic
489	C₂⁴	#2410	1	1	yes	characteristic
490	C₂⁴	#2410	1	1	yes	characteristic
491	C₂⁴	#2410	1	2	yes	—
492	C₂⁴	#2410	1	1	yes	characteristic
493	C₂⁴	#2424	1	2	yes	—
494	C₂⁴	#2424	1	2	yes	—
495	C₂⁴	#2433	1	2	yes	—
496	C₂⁴	#2847	1	2	yes	—
497	C₂⁴	C₂²×#121	1	1	yes	characteristic
498	C₂⁴	C₂×D₄²	1	1	yes	characteristic
499	C₂⁴	C₂×#546	1	1	yes	characteristic
500	C₂×Q₈	C₂×#392	1	4	yes	—
501	C₂×Q₈	#2403	1	2	yes	—
502	C₂×Q₈	#2410	1	2	yes	—
503	C₂×Q₈	#2424	1	2	yes	—
504	C₂×Q₈	#2424	1	2	yes	—
505	C₂×Q₈	#2539	1	2	yes	—
506	C₂×Q₈	#2617	1	2	yes	—
507	C₂×Q₈	C₂×#534	1	1	yes	characteristic
508	C₂×Q₈	C₂×#538	1	1	yes	characteristic
509	C₂×Q₈	C₂×D₄²	1	1	yes	characteristic
510	C₂×Q₈	C₂×#546	1	1	yes	characteristic
511	C₂×D₄	#2021	1	8	yes	—
512	C₂×D₄	#2021	1	8	yes	—
513	C₂×D₄	C₂×#392	1	4	yes	—
514	C₂×D₄	C₂×#392	1	4	yes	—
515	C₂×D₄	C₂×#392	1	4	yes	—
516	C₂×D₄	#2403	1	2	yes	—
517	C₂×D₄	#2404	1	2	yes	—
518	C₂×D₄	#2404	1	2	yes	—
519	C₂×D₄	#2410	1	2	yes	—
520	C₂×D₄	#2410	1	2	yes	—
521	C₂×D₄	#2410	1	2	yes	—
522	C₂×D₄	#2424	1	2	yes	—
523	C₂×D₄	#2424	1	2	yes	—
524	C₂×D₄	#2424	1	2	yes	—
525	C₂×D₄	#2424	1	2	yes	—
526	C₂×D₄	#2424	1	2	yes	—
527	C₂×D₄	#2424	1	2	yes	—
528	C₂×D₄	#2433	1	2	yes	—
529	C₂×D₄	#2433	1	2	yes	—
530	C₂×D₄	#2539	1	2	yes	—
531	C₂×D₄	#2617	1	2	yes	—
532	C₂×D₄	#2847	1	2	yes	—
533	C₂×D₄	#2847	1	2	yes	—
534	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
535	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
536	C₂×D₄	C₂²×#120	1	1	yes	characteristic
537	C₂×D₄	C₂×#525	1	1	yes	characteristic
538	C₂×D₄	C₂×#525	1	1	yes	characteristic
539	C₂×D₄	C₂×#525	1	1	yes	characteristic
540	C₂×D₄	C₂×#535	1	1	yes	characteristic
541	C₂×D₄	C₂×#538	1	1	yes	characteristic
542	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
543	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
544	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
545	C₂×D₄	C₂×#546	1	1	yes	characteristic
546	C₂×D₄	C₂×#546	1	1	yes	characteristic
547	C₂×D₄	C₂×#546	1	1	yes	characteristic
548	C₂²×C₄	C₂×#392	1	2	yes	—
549	C₂²×C₄	C₂×#392	1	2	yes	—
550	C₂²×C₄	C₂×#392	1	2	yes	—
551	C₂²×C₄	C₂×#392	1	2	yes	—
552	C₂²×C₄	#2403	1	2	yes	—
553	C₂²×C₄	#2403	1	2	yes	—
554	C₂²×C₄	#2404	1	2	yes	—
555	C₂²×C₄	#2410	1	2	yes	—
556	C₂²×C₄	#2410	1	2	yes	—
557	C₂²×C₄	#2410	1	2	yes	—
558	C₂²×C₄	#2410	1	2	yes	—
559	C₂²×C₄	#2410	1	2	yes	—
560	C₂²×C₄	#2410	1	1	yes	characteristic
561	C₂²×C₄	#2410	1	1	yes	characteristic
562	C₂²×C₄	#2410	1	1	yes	characteristic
563	C₂²×C₄	#2410	1	2	yes	—
564	C₂²×C₄	#2410	1	2	yes	—
565	C₂²×C₄	#2410	1	1	yes	characteristic
566	C₂²×C₄	#2424	1	2	yes	—
567	C₂²×C₄	#2424	1	2	yes	—
568	C₂²×C₄	#2424	1	2	yes	—
569	C₂²×C₄	#2424	1	2	yes	—
570	C₂²×C₄	#2424	1	2	yes	—
571	C₂²×C₄	#2424	1	2	yes	—
572	C₂²×C₄	#2433	1	2	yes	—
573	C₂²×C₄	#2539	1	2	yes	—
574	C₂²×C₄	#2539	1	2	yes	—
575	C₂²×C₄	#2617	1	2	yes	—
576	C₂²×C₄	#2617	1	2	yes	—
577	C₂²×C₄	#2847	1	2	yes	—
578	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
579	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
580	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
581	C₂²×C₄	#3026	1	1	yes	characteristic
582	C₂²×C₄	#3026	1	2	yes	—
583	C₂²×C₄	#3026	1	1	yes	characteristic
584	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
585	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
586	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
587	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
588	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
589	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
590	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
591	C₂²×C₄	C₂²×#127	1	1	yes	characteristic
592	C₂²×C₄	C₂×#534	1	1	yes	characteristic
593	C₂²×C₄	C₂×#534	1	1	yes	characteristic
594	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
595	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
596	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
597	C₂²×C₄	C₂×#546	1	1	yes	characteristic
598	C₂²×C₄	C₂×#546	1	1	yes	characteristic
599	C₂²×C₄	C₂×#546	1	1	yes	characteristic
600	C₂³	#14716	1	2	yes	—
601	C₂³	#14716	1	2	yes	—
602	C₂³	#14716	1	2	yes	—
603	C₂³	#14716	1	2	yes	—
604	C₂³	#24404	1	1	yes	characteristic
605	C₂³	#24404	1	1	yes	characteristic
606	C₂³	#24404	1	2	yes	—
607	C₂³	C₂×#2410	1	1	yes	characteristic
608	C₂³	C₂×#2410	1	1	yes	characteristic
609	C₂³	C₂×#2424	1	1	yes	characteristic
610	C₂³	C₂×#2424	1	1	yes	characteristic
611	C₂³	C₂×#2433	1	1	yes	characteristic
612	C₂³	C₂×#2404	1	1	yes	characteristic
613	C₂³	C₂×#2847	1	1	yes	characteristic
614	D₄	C₂×#2021	1	8	yes	—
615	C₂×C₄	#14716	1	2	yes	—
616	C₂×C₄	#14716	1	2	yes	—
617	C₂×C₄	#14716	1	2	yes	—
618	C₂×C₄	#14716	1	2	yes	—
619	C₂×C₄	C₂×#2021	1	2	yes	—
620	C₂×C₄	C₂×#2021	1	2	yes	—
621	C₂×C₄	#23444	1	2	yes	—
622	C₂×C₄	#23444	1	2	yes	—
623	C₂×C₄	#24404	1	2	yes	—
624	C₂×C₄	#24404	1	1	yes	characteristic
625	C₂×C₄	#24404	1	1	yes	characteristic
626	C₂×C₄	#24404	1	2	yes	—
627	C₂×C₄	#24404	1	2	yes	—
628	C₂×C₄	#24404	1	2	yes	—
629	C₂×C₄	#24404	1	2	yes	—
630	C₂×C₄	C₂²×#392	1	1	yes	characteristic
631	C₂×C₄	C₂×#2617	1	1	yes	characteristic
632	C₂×C₄	C₂×#2403	1	1	yes	characteristic
633	C₂×C₄	C₂×#2410	1	1	yes	characteristic
634	C₂×C₄	C₂×#2410	1	1	yes	characteristic
635	C₂×C₄	C₂×#2424	1	1	yes	characteristic
636	C₂×C₄	C₂×#2424	1	1	yes	characteristic
637	C₂×C₄	C₂×#2539	1	1	yes	characteristic
638	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
639	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
640	C₂×C₄	C₂×#3026	1	1	yes	characteristic
641	C₂×C₄	C₂×#3026	1	1	yes	characteristic
642	C₂²	#394267	1	2	yes	—
643	C₂²	#394267	1	2	yes	—
644	C₂²	C₂×#14716	1	1	yes	characteristic
645	C₂²	C₂×#24404	1	1	yes	characteristic
646	C₂²	C₂×#24404	1	1	yes	characteristic
647	C₄	#394267	1	2	yes	—
648	C₄	#394267	1	2	yes	—
649	C₄	C₂²×#2021	1	1	yes	characteristic
650	C₄	C₂×#23444	1	1	yes	characteristic
651	C₄	C₂×#24404	1	1	yes	characteristic
652	C₄	C₂×#24404	1	1	yes	characteristic
653	C₂	#72237544	1	2	yes	—
654	C₂	C₂×#394267	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#24404
commutator, Frattini, cosocle	C₂²×#41	C₂⁵
LCS	G ▷ C₂²×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×H(5,𝔽₂) ◁ G
LECS	G ▷ C₂²×#41 ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72313179	C₂	semidirect
2. #72313178	C₂	semidirect
3. C₂×#498916	C₂	semidirect
4. #72312755	C₂	semidirect
5. #72312734	C₂	semidirect
6. #72312697	C₂	semidirect
7. C₂×#6437986	C₂	semidirect
8. #72312254	C₂	semidirect
9. #72310500	C₂	semidirect
10. #72303729	C₂	semidirect
11. #72303727	C₂	semidirect
12. #72280610	C₂	semidirect
13. C₂×#494758	C₂	semidirect
14. #72256636	C₂	semidirect
15. #72255896	C₂	semidirect
16. C₂²×#33348	C₂	semidirect
17. C₂²×#23882	C₂	semidirect
23. C₂×#60387	C₂²	semidirect
28. C₂×#33358	C₂²	semidirect
29. C₂×#33348	C₂²	semidirect
30. C₂×#33347	C₂²	semidirect
35. #6470214	C₂²	semidirect
36. #6470213	C₂²	semidirect
37. C₂×#24421	C₂²	semidirect
38. C₂×#24420	C₂²	semidirect
42. C₂×#21017	C₂²	semidirect
45. C₂×#20860	C₂²	semidirect
47. C₂×#20620	C₂²	semidirect
48. C₂×#20612	C₂²	semidirect
49. #6370734	C₂²	semidirect
51. #498930	C₂²	semidirect
52. #498929	C₂²	semidirect
53. C₂×#13361	C₂²	semidirect
54. C₂×#13360	C₂²	semidirect
55. C₂×#13102	C₂²	semidirect
56. C₂×#13100	C₂²	semidirect
57. C₂×#12589	C₂²	semidirect
58. C₂×#12589	C₂²	semidirect
59. #492906	C₂²	semidirect
60. C₂×#12579	C₂²	semidirect
61. C₂×#12577	C₂²	semidirect
62. #492886	C₂²	semidirect
63. #359546	C₂²	semidirect
64. #353434	C₂²	semidirect
65. #353422	C₂²	semidirect
66. #148265	C₂²	semidirect
67. #148260	C₂²	semidirect
68. #147856	C₂²	semidirect
69. #147855	C₂²	semidirect
70. #147818	C₂²	semidirect
71. #147817	C₂²	semidirect
72. #147755	C₂²	semidirect
73. #147751	C₂²	semidirect
74. #146591	C₂²	semidirect
78. C₂×#3585	D₄	semidirect
80. C₂²×#575	D₄	semidirect
81. C₂³×AGL(1,ℤ/8)	D₄	semidirect
94. C₂×#3022	C₂³	semidirect
96. C₂×#3021	C₂³	semidirect
97. C₂×#3009	D₄	semidirect
99. C₂×#3008	D₄	semidirect
101. C₂×#2896	D₄	semidirect
102. C₂×#2896	D₄	semidirect
103. C₂×#2896	D₄	semidirect
104. C₂²×#418	D₄	semidirect
105. C₂²×#418	D₄	semidirect
106. C₂²×#418	D₄	semidirect
107. C₂×#2888	D₄	semidirect
121. C₂×#2129	C₂³	semidirect
122. C₂×#2128	C₂³	semidirect
123. C₂×#2123	C₂³	semidirect
124. C₂×#2122	D₄	semidirect
127. C₂×#2122	C₂³	semidirect
135. C₂×#1915	C₂³	semidirect
136. C₂×#1914	C₂³	semidirect
139. C₂×#1858	C₂³	semidirect
140. C₂×#1795	D₄	semidirect
142. C₂×#1794	C₂³	semidirect
143. C₂×#1791	C₂³	semidirect
144. #20610	C₂³	semidirect
145. #20602	D₄	semidirect
147. C₂×#1395	C₂³	semidirect
148. C₂×#1395	C₂³	semidirect
149. #12587	C₂³	semidirect
150. C₂×#1392	C₂³	semidirect
151. C₂×#1391	C₂³	semidirect
152. #12575	C₂³	semidirect
153. #10748	C₂³	semidirect
154. #10742	C₂³	semidirect
177. C₂²×#137	C₂×D₄	semidirect
178. C₂²×AGL(1,ℤ/8)	C₂×D₄	semidirect
179. C₂³×SD₁₆	C₂×D₄	semidirect
180. C₂³×D₈	C₂×D₄	semidirect
211. C₂×#417	C₂×D₄	semidirect
212. C₂×#418	C₂×D₄	semidirect
213. C₂×#418	C₂×D₄	semidirect
214. C₂×#418	C₂×D₄	semidirect
215. C₂×#416	C₂×D₄	semidirect
216. C₂×#416	C₂×D₄	semidirect
217. C₂×#416	C₂×D₄	semidirect
218. C₂²×#102	C₂×D₄	semidirect
219. #2888	C₂×D₄	semidirect
242. #2122	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72313179	2
#72313178	2
C₂×#498916	2
#72312755	2
#72312734	2
#72312697	2
C₂×#6437986	2
#72312254	2
#72310500	2
#72303729	2
#72303727	2
#72280610	2
C₂×#494758	2
#72256636	2
#72255896	2
C₂²×#33348	2
C₂²×#23882	2