Subgroups — #72312668

Order 2048.

At least 6105 conjugacy classes of subgroups; only the 1288 normal subgroups are shown.

The subgroup lattice has 662 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72312647	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#500801	C₂	1	1	yes	maximal, characteristic
3	#72312593	C₂	1	2	yes	maximal, complemented
4	#72312577	C₂	1	1	yes	maximal, characteristic, complemented
5	#72312568	C₂	1	1	yes	maximal, characteristic, complemented
6	#72312542	C₂	1	1	yes	maximal, characteristic, complemented
7	#72312518	C₂	1	1	yes	maximal, characteristic, complemented
8	#72312487	C₂	1	1	yes	maximal, characteristic, complemented
9	#72312467	C₂	1	1	yes	maximal, characteristic, complemented
10	#72312428	C₂	1	2	yes	maximal, complemented
11	#72312398	C₂	1	2	yes	maximal, complemented
12	#72312358	C₂	1	2	yes	maximal, complemented
13	#72312265	C₂	1	1	yes	maximal, characteristic, complemented
14	#72312172	C₂	1	1	yes	maximal, characteristic, complemented
15	#72312136	C₂	1	1	yes	maximal, characteristic, complemented
16	#72312079	C₂	1	2	yes	maximal, complemented
17	#72311949	C₂	1	2	yes	maximal, complemented
18	#72311871	C₂	1	1	yes	maximal, characteristic, complemented
19	#72311811	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#33553	C₂	1	2	yes	maximal, complemented
21	C₄×#12755	C₂	1	2	yes	maximal, complemented
22	#72281292	C₂	1	1	yes	maximal, characteristic, complemented
23	#72281182	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#62270	C₂²	1	1	yes	characteristic
25	#10574037	C₂²	1	1	yes	characteristic, complemented
26	C₄×#3537	C₂²	1	2	yes	—
27	C₂×#33553	C₂²	1	2	yes	—
28	C₂×#32951	C₂²	1	1	yes	characteristic
29	C₂×#32948	C₂²	1	1	yes	characteristic
30	#6396141	C₂²	1	2	yes	—
31	#6393473	C₂²	1	2	yes	—
32	#6389172	C₂²	1	1	yes	characteristic
33	#6389172	C₂²	1	1	yes	characteristic
34	#6386748	C₂²	1	1	yes	characteristic
35	#6377534	C₂²	1	2	yes	—
36	#6372955	C₂²	1	1	yes	characteristic
37	#6372955	C₂²	1	1	yes	characteristic
38	C₂×#21483	C₂²	1	1	yes	characteristic
39	C₂×#21483	C₂²	1	1	yes	characteristic
40	C₄×#3027	C₂²	1	2	yes	complemented
41	C₄×#3025	C₂²	1	1	yes	characteristic
42	C₄×#3021	C₂²	1	2	yes	complemented
43	#6370031	C₂²	1	1	yes	characteristic
44	#500801	C₄	1	16	yes	complemented
45	C₂×#13432	C₂²	1	2	yes	—
46	C₂×#13353	C₂²	1	2	yes	—
47	C₂×#13234	C₂²	1	1	yes	characteristic
48	C₂×#13234	C₂²	1	1	yes	characteristic
49	C₂×#13231	C₂²	1	1	yes	characteristic
50	C₂×#13231	C₂²	1	1	yes	characteristic
51	#494601	C₂²	1	2	yes	complemented
52	#494580	C₂²	1	2	yes	complemented
53	#494577	C₂²	1	2	yes	—
54	#494375	C₂²	1	2	yes	complemented
55	#494354	C₂²	1	2	yes	complemented
56	#494351	C₂²	1	2	yes	—
57	C₂×#12805	C₂²	1	1	yes	characteristic
58	C₂×#12805	C₂²	1	1	yes	characteristic
59	#493584	C₂²	1	2	yes	—
60	C₂×#12755	C₂²	1	2	yes	—
61	C₂×#12755	C₂²	1	2	yes	—
62	C₄×#2134	C₂²	1	2	yes	complemented
63	C₄×#2128	C₂²	1	2	yes	complemented
64	C₄×#2122	C₂²	1	2	yes	complemented
65	C₄×#2122	C₂²	1	2	yes	complemented
66	C₄×#2120	C₂²	1	2	yes	—
67	#393035	C₂²	1	1	yes	characteristic
68	#393031	C₂²	1	1	yes	characteristic
69	#392903	C₂²	1	1	yes	characteristic, complemented
70	#392897	C₂²	1	1	yes	characteristic, complemented
71	#392828	C₂²	1	2	yes	complemented
72	#392825	C₂²	1	2	yes	complemented
73	#392717	C₂²	1	2	yes	complemented
74	#392710	C₂²	1	2	yes	complemented
75	#392198	C₂²	1	1	yes	characteristic, complemented
76	#392195	C₂²	1	1	yes	characteristic, complemented
77	#354938	C₂²	1	1	yes	characteristic, complemented
78	#354936	C₂²	1	1	yes	characteristic, complemented
79	#354788	C₂²	1	1	yes	characteristic, complemented
80	#354788	C₂²	1	1	yes	characteristic, complemented
81	#354786	C₂²	1	1	yes	characteristic, complemented
82	#354478	C₂²	1	1	yes	characteristic, complemented
83	#354478	C₂²	1	1	yes	characteristic, complemented
84	#354459	C₂²	1	1	yes	characteristic, complemented
85	#354316	C₂²	1	1	yes	characteristic
86	#354316	C₂²	1	1	yes	characteristic
87	C₄×#1891	C₂²	1	1	yes	characteristic
88	C₄×#1914	C₂²	1	2	yes	complemented
89	C₄×#1910	C₂²	1	2	yes	complemented
90	#353208	C₂²	1	1	yes	characteristic, complemented
91	#149288	C₂²	1	2	yes	complemented
92	#149033	C₂²	1	2	yes	complemented
93	#148824	C₂²	1	2	yes	complemented
94	#148474	C₂²	1	2	yes	complemented
95	#148471	C₂²	1	2	yes	complemented
96	#148279	C₂²	1	2	yes	complemented
97	#148252	C₂²	1	2	yes	complemented
98	#148244	C₂²	1	2	yes	complemented
99	#148241	C₂²	1	2	yes	complemented
100	#148175	C₂²	1	2	yes	complemented
101	#147855	C₂²	1	2	yes	—
102	#147837	C₂²	1	2	yes	—
103	#147762	C₂²	1	2	yes	complemented
104	#147755	C₂²	1	2	yes	complemented
105	#147521	C₂²	1	2	yes	complemented
106	#147521	C₂²	1	2	yes	complemented
107	#147517	C₂²	1	2	yes	complemented
108	#147517	C₂²	1	2	yes	complemented
109	#147079	C₂²	1	1	yes	characteristic, complemented
110	#147079	C₂²	1	1	yes	characteristic, complemented
111	#147077	C₂²	1	1	yes	characteristic, complemented
112	#147077	C₂²	1	1	yes	characteristic, complemented
113	#147021	C₂²	1	1	yes	characteristic, complemented
114	#147021	C₂²	1	1	yes	characteristic, complemented
115	#146872	C₂²	1	2	yes	complemented
116	#146669	C₂²	1	2	yes	—
117	#146651	C₂²	1	2	yes	complemented
118	#146651	C₂²	1	2	yes	complemented
119	#146616	C₂²	1	2	yes	complemented
120	#146616	C₂²	1	2	yes	complemented
121	#146596	C₂²	1	2	yes	—
122	#146596	C₂²	1	2	yes	—
123	#146363	C₂²	1	2	yes	complemented
124	C₂×#3573	C₂³	1	1	yes	characteristic
125	C₂×#3573	C₂³	1	1	yes	characteristic
126	C₂×#3537	C₂³	1	2	yes	—
127	C₄×#585	C₂³	1	1	yes	characteristic
128	#62270	C₂×C₄	1	8	yes	complemented
129	C₂×#3199	C₂³	1	2	yes	—
130	C₂×#3058	C₂³	1	1	yes	characteristic
131	C₂×#3058	C₂³	1	1	yes	characteristic
132	C₂×#3027	C₂³	1	2	yes	—
133	C₂×#3025	C₂³	1	1	yes	characteristic
134	C₂×#3021	C₂³	1	2	yes	—
135	C₂²×#442	D₄	1	1	yes	characteristic, complemented
136	C₂²×#442	D₄	1	1	yes	characteristic, complemented
137	C₂×#2929	C₂³	1	1	yes	characteristic
138	C₂×#2929	C₂³	1	1	yes	characteristic
139	#60058	C₂³	1	1	yes	characteristic
140	#60058	C₂³	1	1	yes	characteristic
141	C₄×#568	C₂³	1	1	yes	characteristic
142	C₂×#2875	C₂³	1	1	yes	characteristic
143	C₂³×#97	D₄	1	1	yes	characteristic, complemented
144	#34411	C₂³	1	2	yes	—
145	#34411	C₂³	1	2	yes	—
146	#34360	C₂³	1	2	yes	—
147	C₄×#535	C₂³	1	2	yes	—
148	C₄×#535	C₂³	1	2	yes	—
149	C₄×#525	C₂³	1	1	yes	characteristic
150	#33553	C₂×C₄	1	16	yes	complemented
151	C₂×#2134	C₂³	1	2	yes	—
152	C₂×#2134	C₂³	1	2	yes	—
153	C₂×#2128	C₂³	1	2	yes	—
154	C₂×#2128	C₂³	1	2	yes	—
155	C₂×#2122	C₂³	1	2	yes	—
156	C₂×#2122	C₂³	1	2	yes	—
157	C₂×#2122	C₂³	1	2	yes	—
158	C₂×#2122	C₂³	1	2	yes	—
159	C₂×#2120	C₂³	1	2	yes	—
160	C₂×#2120	C₂³	1	2	yes	—
161	#32951	C₂×C₄	1	8	yes	complemented
162	#32948	C₂×C₄	1	8	yes	complemented
163	#21946	C₂³	1	2	yes	—
164	#21770	C₂³	1	2	yes	—
165	#21770	C₂³	1	2	yes	—
166	#21483	C₂×C₄	1	8	yes	complemented
167	C₄×#458	D₄	1	4	yes	—
168	C₄×B(4,𝔽₂)	D₄	1	4	yes	—
169	#21233	D₄	1	1	yes	characteristic, complemented
170	#21233	D₄	1	1	yes	characteristic, complemented
171	#21155	D₄	1	1	yes	characteristic, complemented
172	#21155	D₄	1	1	yes	characteristic, complemented
173	#21091	D₄	1	2	yes	complemented
174	#21091	D₄	1	2	yes	complemented
175	C₂×#1914	C₂³	1	2	yes	—
176	C₂×#1914	C₂³	1	2	yes	—
177	C₂×#1910	C₂³	1	2	yes	—
178	C₂×#1910	C₂³	1	2	yes	—
179	#20975	C₂³	1	2	yes	—
180	#20975	C₂³	1	2	yes	—
181	C₂×#1891	C₂³	1	1	yes	characteristic
182	C₂×#1891	C₂³	1	1	yes	characteristic
183	#20961	C₂³	1	2	yes	—
184	#20959	C₂³	1	1	yes	characteristic
185	#20956	C₂³	1	2	yes	—
186	C₂×#1868	C₂³	1	1	yes	characteristic
187	C₂×#1868	C₂³	1	1	yes	characteristic
188	#20890	C₂³	1	2	yes	—
189	#20888	C₂³	1	1	yes	characteristic
190	#20858	C₂³	1	2	yes	—
191	C₂×#1813	C₂³	1	1	yes	characteristic
192	C₂×#1813	C₂³	1	1	yes	characteristic
193	C₂×#1812	C₂³	1	1	yes	characteristic
194	C₂×#1812	C₂³	1	1	yes	characteristic
195	#20662	C₂³	1	1	yes	characteristic
196	#20662	C₂³	1	1	yes	characteristic
197	#20618	C₂³	1	2	yes	—
198	C₂×#1791	C₂³	1	1	yes	characteristic
199	C₂×#1791	C₂³	1	1	yes	characteristic
200	#20610	C₂³	1	2	yes	—
201	#20608	C₂³	1	1	yes	characteristic
202	#20451	D₄	1	1	yes	characteristic, complemented
203	#20451	D₄	1	1	yes	characteristic, complemented
204	#20436	D₄	1	1	yes	characteristic, complemented
205	#20436	D₄	1	1	yes	characteristic, complemented
206	#20427	D₄	1	1	yes	characteristic, complemented
207	C₄×#418	D₄	1	2	yes	complemented
208	C₄×#418	D₄	1	2	yes	complemented
209	C₂×#1757	C₂³	1	1	yes	characteristic
210	C₂×#1757	C₂³	1	1	yes	characteristic
211	C₂×#1757	C₂³	1	1	yes	characteristic
212	C₂×#1757	C₂³	1	1	yes	characteristic
213	C₄×#413	C₂³	1	2	yes	—
214	C₄×#413	C₂³	1	1	yes	characteristic
215	C₄×#410	C₂³	1	2	yes	—
216	C₄×#410	C₂³	1	1	yes	characteristic
217	#20385	D₄	1	1	yes	characteristic, complemented
218	#20385	D₄	1	1	yes	characteristic, complemented
219	#20384	C₂³	1	1	yes	characteristic
220	#20384	C₂³	1	1	yes	characteristic
221	C₄×#407	D₄	1	1	yes	characteristic, complemented
222	#20375	C₂³	1	1	yes	characteristic
223	#20331	D₄	1	1	yes	characteristic, complemented
224	#13432	C₂×C₄	1	16	yes	complemented
225	#13353	C₂×C₄	1	16	yes	complemented
226	#13234	C₂×C₄	1	8	yes	complemented
227	#13231	C₂×C₄	1	8	yes	complemented
228	#12805	C₂×C₄	1	8	yes	complemented
229	#12755	C₂×C₄	1	16	yes	complemented
230	C₂×#1395	C₂³	1	2	yes	—
231	C₂×#1395	C₂³	1	2	yes	—
232	C₂×#1395	C₂³	1	2	yes	—
233	C₂×#1395	C₂³	1	2	yes	—
234	#12587	C₂³	1	2	yes	—
235	#12587	C₂³	1	2	yes	—
236	#12583	C₂³	1	2	yes	—
237	#12583	C₂³	1	2	yes	—
238	#12575	C₂³	1	2	yes	—
239	#12575	C₂³	1	2	yes	—
240	#12575	C₂³	1	2	yes	—
241	#12575	C₂³	1	2	yes	—
242	#12573	C₂³	1	2	yes	—
243	#12573	C₂³	1	2	yes	—
244	#10760	C₂³	1	2	yes	—
245	#10759	C₂³	1	2	yes	—
246	#10755	C₂³	1	2	yes	—
247	#10755	C₂³	1	2	yes	—
248	#10748	C₂³	1	1	yes	characteristic
249	#10748	C₂³	1	1	yes	characteristic
250	#10747	C₂³	1	1	yes	characteristic
251	#10747	C₂³	1	1	yes	characteristic
252	#10746	C₂³	1	1	yes	characteristic
253	#10746	C₂³	1	1	yes	characteristic
254	#10742	C₂³	1	2	yes	—
255	#10742	C₂³	1	2	yes	—
256	C₂×#585	C₂⁴	1	1	yes	characteristic
257	C₂³×D₈	C₂×D₄	1	1	yes	characteristic
258	C₂³×D₈	C₂×D₄	1	1	yes	characteristic
259	#3573	C₂²×C₄	1	4	yes	complemented
260	C₂×#568	C₂⁴	1	1	yes	characteristic
261	C₂×#568	C₂⁴	1	1	yes	characteristic
262	C₂²×#131	C₂⁴	1	1	yes	characteristic
263	C₂²×#131	C₂⁴	1	1	yes	characteristic
264	C₂⁴×C₈	C₂×D₄	1	1	yes	characteristic
265	C₂⁴×C₈	C₂×D₄	1	1	yes	characteristic
266	#3537	C₂²×C₄	1	8	yes	—
267	C₂×#535	C₂⁴	1	2	yes	—
268	C₂×#535	C₂⁴	1	2	yes	—
269	C₂×#525	C₂⁴	1	1	yes	characteristic
270	C₄×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
271	#3428	C₂⁴	1	1	yes	characteristic
272	C₂×C₄×#41	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
274	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
275	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
276	#3199	C₂²×C₄	1	8	yes	—
277	#3058	C₂²×C₄	1	4	yes	—
278	#3058	C₂²×C₄	1	4	yes	—
279	#3058	#41	1	4	yes	—
280	#3058	#41	1	4	yes	—
281	#3027	C₂²×C₄	1	8	yes	complemented
282	#3025	C₂²×C₄	1	4	yes	—
283	#3025	#41	1	4	yes	—
284	C₂×#458	C₂×D₄	1	2	yes	—
285	C₂×B(4,𝔽₂)	C₂×D₄	1	2	yes	—
286	#3021	C₂²×C₄	1	8	yes	complemented
287	#2929	C₂²×C₄	1	4	yes	—
288	#2929	#41	1	4	yes	—
289	C₂×#427	C₂×D₄	1	1	yes	characteristic
290	C₂×#427	C₂×D₄	1	1	yes	characteristic
291	C₂×#427	C₂×D₄	1	1	yes	characteristic
292	C₂×#427	C₂×D₄	1	1	yes	characteristic
293	C₂²×#106	C₂×D₄	1	1	yes	characteristic
294	C₂²×#106	C₂×D₄	1	1	yes	characteristic
295	C₂×#424	C₂×D₄	1	1	yes	characteristic
296	C₂×#424	C₂×D₄	1	1	yes	characteristic
297	C₂×#418	C₂×D₄	1	2	yes	—
298	C₂×#418	C₂×D₄	1	2	yes	—
299	C₂×#418	C₂×D₄	1	2	yes	—
300	C₂×#418	C₂×D₄	1	2	yes	—
301	C₂²×#102	C₂×D₄	1	2	yes	—
302	C₂²×#102	C₂×D₄	1	2	yes	—
303	C₂×#413	C₂⁴	1	2	yes	—
304	C₂×#413	C₂⁴	1	2	yes	—
305	C₂×#413	C₂⁴	1	1	yes	characteristic
306	C₂×#413	C₂⁴	1	1	yes	characteristic
307	C₂×#410	C₂⁴	1	2	yes	—
308	C₂×#410	C₂⁴	1	2	yes	—
309	C₂×#410	C₂⁴	1	1	yes	characteristic
310	C₂×#410	C₂⁴	1	1	yes	characteristic
311	C₂×#408	C₂⁴	1	1	yes	characteristic
312	C₂×#408	C₂⁴	1	1	yes	characteristic
313	C₂×#407	C₂×D₄	1	1	yes	characteristic
314	C₂×#407	C₂×D₄	1	1	yes	characteristic
315	C₂×#405	C₂×D₄	1	1	yes	characteristic
316	C₂×#405	C₂×D₄	1	1	yes	characteristic
317	C₂×#405	C₂×D₄	1	1	yes	characteristic
318	C₂×#405	C₂×D₄	1	1	yes	characteristic
319	C₂×#405	C₂×D₄	1	1	yes	characteristic
320	C₂×#405	C₂×D₄	1	1	yes	characteristic
321	C₂×#405	C₂×D₄	1	1	yes	characteristic
322	C₂×#405	C₂×D₄	1	1	yes	characteristic
323	C₂×#405	C₂×D₄	1	1	yes	characteristic
324	C₂×#405	C₂×D₄	1	1	yes	characteristic
325	C₂×C₄×M₁₆	C₂×D₄	1	1	yes	characteristic
326	C₂×C₄×M₁₆	C₂×D₄	1	1	yes	characteristic
327	C₂×C₄×M₁₆	C₂×D₄	1	1	yes	characteristic
328	C₂×C₄×M₁₆	C₂×D₄	1	1	yes	characteristic
329	C₂²×#97	C₂×D₄	1	1	yes	characteristic
330	C₂²×#97	C₂×D₄	1	1	yes	characteristic
331	C₂²×#97	C₂×D₄	1	1	yes	characteristic
332	C₂²×#97	C₂×D₄	1	1	yes	characteristic
333	C₂²×#97	C₂×D₄	1	1	yes	characteristic
334	C₂²×#97	C₂×D₄	1	1	yes	characteristic
335	#2317	C₂×D₄	1	2	yes	—
336	#2317	C₂×D₄	1	2	yes	—
337	#2311	C₂⁴	1	2	yes	—
338	#2311	C₂⁴	1	2	yes	—
339	#2309	C₂×D₄	1	2	yes	—
340	#2309	C₂×D₄	1	2	yes	—
341	C₄×#123	C₂×D₄	1	2	yes	—
342	C₄×#123	#41	1	2	yes	—
343	C₄×#120	C₂×D₄	1	2	yes	—
344	C₄×#120	#41	1	2	yes	—
345	#2297	C₂⁴	1	1	yes	characteristic
346	#2296	C₂×D₄	1	1	yes	characteristic
347	#2280	C₂×D₄	1	1	yes	characteristic
348	C₄×#117	C₂×D₄	1	2	yes	—
349	C₄×#117	C₂×D₄	1	2	yes	—
350	C₄×#117	C₂×D₄	1	1	yes	characteristic
351	#2134	C₂²×C₄	1	8	yes	complemented
352	#2128	C₂²×C₄	1	8	yes	complemented
353	#2122	C₂²×C₄	1	8	yes	complemented
354	#2122	C₂²×C₄	1	8	yes	complemented
355	#2120	C₂²×C₄	1	8	yes	—
356	#1914	C₂²×C₄	1	8	yes	complemented
357	#1910	C₂²×C₄	1	8	yes	complemented
358	#1891	C₂²×C₄	1	4	yes	—
359	#1891	#41	1	4	yes	—
360	#1890	C₂×D₄	1	2	yes	—
361	#1889	C₂×D₄	1	2	yes	—
362	#1868	C₂²×C₄	1	4	yes	complemented
363	#1867	C₂×D₄	1	4	yes	—
364	#1813	C₂²×C₄	1	4	yes	complemented
365	#1812	C₂²×C₄	1	4	yes	complemented
366	#1791	C₂²×C₄	1	4	yes	complemented
367	#1790	C₂×D₄	1	4	yes	—
368	#1757	C₂²×C₄	1	4	yes	complemented
369	C₄×#99	C₂×D₄	1	4	yes	—
370	#1736	C₂×D₄	1	2	yes	—
371	#1736	C₂×D₄	1	2	yes	—
372	#1736	C₂×D₄	1	2	yes	—
373	#1736	C₂×D₄	1	2	yes	—
374	#1735	C₂×D₄	1	2	yes	—
375	#1735	C₂×D₄	1	2	yes	—
376	#1729	C₂×D₄	1	1	yes	characteristic
377	#1729	C₂×D₄	1	1	yes	characteristic
378	#1729	C₂×D₄	1	1	yes	characteristic
379	#1729	C₂×D₄	1	1	yes	characteristic
380	#1728	C₂×D₄	1	1	yes	characteristic
381	#1728	C₂×D₄	1	1	yes	characteristic
382	#1395	C₂²×C₄	1	8	yes	complemented
383	#585	C₂³×C₄	1	2	yes	—
384	#585	C₂×#41	1	2	yes	—
385	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
386	C₂²×#41	C₂⁵	1	1	yes	characteristic
387	C₂³×D₄	C₂²×D₄	1	2	yes	—
388	C₂³×D₄	C₂²×D₄	1	2	yes	—
389	C₂⁴×C₄	#121	1	2	yes	—
390	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
391	C₂²×D₈	C₄×D₄	1	4	yes	complemented
392	C₂²×D₈	C₄×D₄	1	4	yes	complemented
393	#568	C₂³×C₄	1	2	yes	—
394	#568	C₂×#41	1	2	yes	—
395	C₂×#131	C₂³×C₄	1	2	yes	—
396	C₂×#131	C₂×#41	1	2	yes	—
397	C₂×#131	C₂×#41	1	2	yes	—
398	C₂×#131	C₂×#41	1	2	yes	—
399	C₂²×M₁₆	C₂²×D₄	1	1	yes	characteristic
400	C₂²×M₁₆	C₂²×D₄	1	1	yes	characteristic
401	C₂²×M₁₆	C₂²×D₄	1	1	yes	characteristic
402	C₂²×M₁₆	C₂²×D₄	1	1	yes	characteristic
403	C₂²×M₁₆	C₂²×D₄	1	1	yes	characteristic
404	C₂²×M₁₆	C₂²×D₄	1	1	yes	characteristic
405	C₂²×M₁₆	C₂²×D₄	1	1	yes	characteristic
406	C₂²×M₁₆	C₂²×D₄	1	1	yes	characteristic
407	C₂³×C₈	C₄×D₄	1	4	yes	complemented
408	C₂³×C₈	C₂²×D₄	1	1	yes	characteristic
409	C₂³×C₈	C₂²×D₄	1	1	yes	characteristic
410	C₂³×C₈	C₂²×D₄	1	1	yes	characteristic
411	C₂³×C₈	C₂²×D₄	1	1	yes	characteristic
412	C₂³×C₈	C₂²×D₄	1	1	yes	characteristic
413	C₂³×C₈	C₂²×D₄	1	1	yes	characteristic
414	C₂³×C₈	C₂²×D₄	1	1	yes	characteristic
415	C₂³×C₈	C₂²×D₄	1	1	yes	characteristic
416	#535	C₂³×C₄	1	4	yes	—
417	#535	C₂³×C₄	1	4	yes	—
418	#535	C₂×#41	1	4	yes	—
419	#535	C₂×#41	1	4	yes	—
420	#525	C₂³×C₄	1	2	yes	—
421	#525	C₂×#41	1	2	yes	—
422	#525	C₂×#41	1	2	yes	—
423	#525	C₂×#41	1	2	yes	—
424	C₂×#123	C₂²×D₄	1	1	yes	characteristic
425	C₂×#123	C₂×#41	1	1	yes	characteristic
426	C₂×#120	C₂²×D₄	1	1	yes	characteristic
427	C₂×#120	C₂×#41	1	1	yes	characteristic
428	#518	C₂²×D₄	1	2	yes	—
429	C₂×C₄×Q₈	H(5,𝔽₂)	1	2	yes	—
430	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
431	C₂×C₄×D₄	C₂×#41	1	2	yes	—
432	C₂×C₄×D₄	H(5,𝔽₂)	1	2	yes	—
433	C₂×#117	C₂²×D₄	1	2	yes	—
434	C₂×#117	C₂²×D₄	1	2	yes	—
435	C₂×#117	C₂²×D₄	1	2	yes	—
436	C₂×#117	C₂²×D₄	1	2	yes	—
437	C₂×#117	C₂²×D₄	1	1	yes	characteristic
438	C₂×#117	C₂²×D₄	1	1	yes	characteristic
439	C₂×#117	C₂²×D₄	1	1	yes	characteristic
440	C₂×#117	C₂²×D₄	1	1	yes	characteristic
441	C₂×#117	C₂²×D₄	1	1	yes	characteristic
442	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
443	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
444	C₂²×C₄²	#121	1	2	yes	—
445	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
446	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
447	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
448	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
449	#458	C₄×D₄	1	8	yes	—
450	B(4,𝔽₂)	C₄×D₄	1	8	yes	—
451	#427	C₄×D₄	1	4	yes	complemented
452	#427	C₄×D₄	1	4	yes	complemented
453	#424	C₄×D₄	1	4	yes	complemented
454	#418	C₄×D₄	1	8	yes	complemented
455	#418	C₄×D₄	1	8	yes	complemented
456	#413	C₂³×C₄	1	4	yes	—
457	#413	C₂³×C₄	1	2	yes	—
458	#413	C₂×#41	1	2	yes	—
459	#410	C₂³×C₄	1	4	yes	—
460	#410	C₂³×C₄	1	2	yes	—
461	#410	C₂×#41	1	2	yes	—
462	C₂×#99	C₂²×D₄	1	2	yes	—
463	C₂×#99	C₂²×D₄	1	2	yes	—
464	#408	C₂³×C₄	1	2	yes	—
465	#408	C₂×#41	1	2	yes	—
466	#407	C₄×D₄	1	4	yes	complemented
467	#405	C₄×D₄	1	4	yes	complemented
468	C₂×#97	#120	1	1	yes	characteristic
469	C₂×#97	#120	1	1	yes	characteristic
470	C₂×#97	#120	1	1	yes	characteristic
471	C₂×#97	#120	1	1	yes	characteristic
472	C₂×#97	#120	1	1	yes	characteristic
473	C₂×#97	#120	1	1	yes	characteristic
474	C₂×#97	#120	1	1	yes	characteristic
475	C₂×#97	#120	1	1	yes	characteristic
476	C₂×#97	#120	1	1	yes	characteristic
477	C₂×#97	#120	1	1	yes	characteristic
478	C₂×C₄×C₈	#120	1	1	yes	characteristic
479	C₂×C₄×C₈	#120	1	1	yes	characteristic
480	C₂×C₄×C₈	#120	1	1	yes	characteristic
481	C₂×C₄×C₈	#120	1	1	yes	characteristic
482	C₂×C₄×C₈	#120	1	1	yes	characteristic
483	C₂×C₄×C₈	#120	1	1	yes	characteristic
484	#386	C₂²×D₄	1	2	yes	—
485	#386	C₂×#41	1	2	yes	—
486	#385	#121	1	2	yes	—
487	#385	#121	1	2	yes	—
488	#381	#121	1	2	yes	—
489	#379	#121	1	2	yes	—
490	C₄×C₂²⋊C₄	#121	1	2	yes	—
491	C₄×C₂²⋊C₄	#121	1	2	yes	—
492	C₂⁵	C₂×#121	1	1	yes	characteristic
493	H(5,𝔽₂)	C₂×C₄×D₄	1	4	yes	—
494	C₂×#41	C₂⁴×C₄	1	1	yes	characteristic
495	C₂×#41	C₂²×#41	1	1	yes	characteristic
496	C₂×#41	C₂²×#41	1	1	yes	characteristic
497	C₂×#41	C₂²×#41	1	1	yes	characteristic
498	C₂×#41	C₂²×#41	1	1	yes	characteristic
499	C₂×#41	C₂²×#41	1	1	yes	characteristic
500	C₂×#41	#585	1	1	yes	characteristic
501	C₂×#41	#585	1	1	yes	characteristic
502	C₂²×Q₈	C₂×H(5,𝔽₂)	1	1	yes	characteristic
503	C₂²×D₄	C₂×C₄×D₄	1	4	yes	—
504	C₂²×D₄	C₂×C₄×D₄	1	4	yes	—
505	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
506	C₂²×D₄	C₂²×#41	1	1	yes	characteristic
507	C₂²×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
508	C₂³×C₄	C₂×C₄×D₄	1	2	yes	—
509	C₂³×C₄	C₂×#121	1	1	yes	characteristic
510	C₂³×C₄	C₂×#121	1	2	yes	—
511	C₂³×C₄	C₂×#121	1	2	yes	—
512	C₂³×C₄	#525	1	2	yes	—
513	C₂³×C₄	D₄²	1	2	yes	—
514	C₂³×C₄	#546	1	2	yes	—
515	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
516	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
517	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
518	C₂×M₁₆	C₂×C₄×D₄	1	2	yes	—
519	C₂×M₁₆	C₂×C₄×D₄	1	2	yes	—
520	C₂×M₁₆	C₂×C₄×D₄	1	2	yes	—
521	C₂×M₁₆	C₂×C₄×D₄	1	2	yes	—
522	C₂×M₁₆	#525	1	2	yes	—
523	C₂×M₁₆	#525	1	2	yes	—
524	C₂×M₁₆	#525	1	2	yes	—
525	C₂²×C₈	C₂×C₄×D₄	1	2	yes	—
526	C₂²×C₈	C₂×C₄×D₄	1	2	yes	—
527	C₂²×C₈	C₂×C₄×D₄	1	2	yes	—
528	C₂²×C₈	C₂×C₄×D₄	1	2	yes	—
529	C₂²×C₈	C₂×#120	1	1	yes	characteristic
530	C₂²×C₈	C₂×#120	1	1	yes	characteristic
531	C₂²×C₈	C₂×#120	1	1	yes	characteristic
532	C₂²×C₈	C₂×#120	1	1	yes	characteristic
533	C₂²×C₈	C₂×#120	1	1	yes	characteristic
534	C₂²×C₈	C₂×#120	1	1	yes	characteristic
535	C₂²×C₈	C₂×#120	1	1	yes	characteristic
536	C₂²×C₈	C₂×#120	1	1	yes	characteristic
537	C₂²×C₈	#525	1	2	yes	—
538	C₂²×C₈	#525	1	2	yes	—
539	C₂²×C₈	#525	1	2	yes	—
540	#123	C₂×C₄×D₄	1	2	yes	—
541	#123	C₄×#41	1	2	yes	—
542	#123	#529	1	2	yes	—
543	#123	#532	1	2	yes	—
544	#120	C₂×C₄×D₄	1	2	yes	—
545	#120	C₄×#41	1	2	yes	—
546	#120	#529	1	2	yes	—
547	#120	#532	1	2	yes	—
548	#117	C₂×C₄×D₄	1	4	yes	—
549	#117	C₂×C₄×D₄	1	4	yes	—
550	#117	C₂×C₄×D₄	1	2	yes	—
551	#117	#525	1	2	yes	—
552	C₂×C₄⋊C₄	#535	1	2	yes	—
553	C₂×C₄⋊C₄	D₄²	1	2	yes	—
554	C₂×C₄⋊C₄	#546	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
556	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
557	C₂×C₂²⋊C₄	C₂×#121	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂×#121	1	2	yes	—
559	C₂×C₂²⋊C₄	D₄²	1	2	yes	—
560	C₂×C₂²⋊C₄	#546	1	2	yes	—
561	C₂×C₄²	C₂×#120	1	1	yes	characteristic
562	C₂×C₄²	C₂×#120	1	1	yes	characteristic
563	C₂×C₄²	C₂×#120	1	1	yes	characteristic
564	C₂×C₄²	C₂×#120	1	1	yes	characteristic
565	C₂×C₄²	#535	1	2	yes	—
566	C₂×C₄²	D₄²	1	2	yes	—
567	C₂×C₄²	#546	1	2	yes	—
568	#99	C₂×C₄×D₄	1	4	yes	—
569	#97	B(4,𝔽₂)	1	1	yes	characteristic
570	#97	B(4,𝔽₂)	1	1	yes	characteristic
571	#97	B(4,𝔽₂)	1	1	yes	characteristic
572	#97	B(4,𝔽₂)	1	1	yes	characteristic
573	C₂⁴	C₄×#121	1	2	yes	—
574	C₂⁴	C₂²×#121	1	1	yes	characteristic
575	C₂⁴	C₂×D₄²	1	1	yes	characteristic
576	C₂⁴	C₂×#546	1	1	yes	characteristic
577	C₂×Q₈	C₄×H(5,𝔽₂)	1	1	yes	characteristic
578	C₂×Q₈	#3460	1	1	yes	characteristic
579	C₂×Q₈	#3481	1	1	yes	characteristic
580	C₂×Q₈	#3481	1	1	yes	characteristic
581	C₂×D₄	C₂²×C₄×D₄	1	1	yes	characteristic
582	C₂×D₄	C₂×C₄×#41	1	1	yes	characteristic
583	C₂×D₄	C₄×H(5,𝔽₂)	1	1	yes	characteristic
584	C₂×D₄	C₂×#529	1	1	yes	characteristic
585	C₂×D₄	C₂×#532	1	1	yes	characteristic
586	C₂×D₄	#3460	1	1	yes	characteristic
587	C₂×D₄	D₄×#41	1	1	yes	characteristic
588	C₂×D₄	D₄×#41	1	1	yes	characteristic
589	C₂×D₄	#3475	1	1	yes	characteristic
590	C₂×D₄	#3475	1	1	yes	characteristic
591	C₂×D₄	#3481	1	1	yes	characteristic
592	C₂×D₄	#3481	1	1	yes	characteristic
593	C₂²×C₄	C₄×#121	1	2	yes	—
594	C₂²×C₄	#2408	1	2	yes	—
595	C₂²×C₄	#2408	1	2	yes	—
596	C₂²×C₄	#2408	1	2	yes	—
597	C₂²×C₄	#2408	1	2	yes	—
598	C₂²×C₄	C₂²×C₄×D₄	1	1	yes	characteristic
599	C₂²×C₄	C₂²×C₄×D₄	1	1	yes	characteristic
600	C₂²×C₄	C₂²×C₄×D₄	1	1	yes	characteristic
601	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
602	C₂²×C₄	C₂×#525	1	1	yes	characteristic
603	C₂²×C₄	C₂×#525	1	1	yes	characteristic
604	C₂²×C₄	C₂×#525	1	1	yes	characteristic
605	C₂²×C₄	C₂×#525	1	1	yes	characteristic
606	C₂²×C₄	C₂×#535	1	1	yes	characteristic
607	C₂²×C₄	#3449	1	1	yes	characteristic
608	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
609	C₂²×C₄	C₂×#546	1	1	yes	characteristic
610	C₂²×C₄	D₄×#41	1	1	yes	characteristic
611	C₂²×C₄	D₄×#41	1	1	yes	characteristic
612	C₂²×C₄	D₄×#41	1	1	yes	characteristic
613	C₂²×C₄	D₄×#41	1	1	yes	characteristic
614	C₂×C₈	C₄×#120	1	2	yes	—
615	C₂×C₈	C₄×#120	1	2	yes	—
616	C₂×C₈	C₄×#120	1	2	yes	—
617	C₂×C₈	C₄×#120	1	2	yes	—
618	C₂×C₈	C₂×B(4,𝔽₂)	1	1	yes	characteristic
619	C₂×C₈	C₂×B(4,𝔽₂)	1	1	yes	characteristic
620	C₂×C₈	C₂×B(4,𝔽₂)	1	1	yes	characteristic
621	C₂×C₈	C₂×B(4,𝔽₂)	1	1	yes	characteristic
622	C₂×C₈	#3025	1	2	yes	—
623	C₂×C₈	#3025	1	2	yes	—
624	C₂²⋊C₄	C₄×#121	1	2	yes	—
625	C₂²⋊C₄	C₄×#121	1	2	yes	—
626	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
627	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
628	C₄²	#3025	1	2	yes	—
629	C₂³	C₂×C₄×#121	1	1	yes	characteristic
630	C₂³	C₄×D₄²	1	1	yes	characteristic
631	C₂³	C₄×#546	1	1	yes	characteristic
632	C₂³	C₂×#2408	1	1	yes	characteristic
633	C₂³	#34681	1	1	yes	characteristic
634	C₂³	#34700	1	1	yes	characteristic
635	C₂³	#34935	1	1	yes	characteristic
636	C₂×C₄	#24260	1	2	yes	—
637	C₂×C₄	#24260	1	2	yes	—
638	C₂×C₄	C₂×C₄×#120	1	1	yes	characteristic
639	C₂×C₄	C₄×#535	1	1	yes	characteristic
640	C₂×C₄	C₄×D₄²	1	1	yes	characteristic
641	C₂×C₄	C₄×#546	1	1	yes	characteristic
642	C₂×C₄	#34681	1	1	yes	characteristic
643	C₂×C₄	#34700	1	1	yes	characteristic
644	C₂×C₄	#34736	1	1	yes	characteristic
645	C₂×C₄	#34963	1	1	yes	characteristic
646	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
647	C₂×C₄	C₂×#3025	1	1	yes	characteristic
648	C₂×C₄	C₂×#3025	1	1	yes	characteristic
649	C₂×C₄	C₂×#3025	1	1	yes	characteristic
650	C₈	C₄×B(4,𝔽₂)	1	2	yes	—
651	C₈	C₄×B(4,𝔽₂)	1	2	yes	—
652	C₂²	C₄×#2408	1	1	yes	characteristic
653	C₂²	C₂×#24260	1	1	yes	characteristic
654	C₂²	#6442721	1	1	yes	characteristic
655	C₄	C₂×C₄×B(4,𝔽₂)	1	1	yes	characteristic
656	C₄	C₄×#3025	1	1	yes	characteristic
657	C₄	#6454041	1	1	yes	characteristic
658	C₄	#6454043	1	1	yes	characteristic
659	C₂	#72236890	1	2	yes	—
660	C₂	C₄×#24260	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#24260
commutator	C₂×#41	C₂⁴×C₄
Frattini, cosocle	C₂²×#41	C₂⁵
prime radical	C₂×#500801	C₂
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#2875 ◁ 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. #72312647	C₂	semidirect
3. #72312593	C₂	semidirect
4. #72312577	C₂	semidirect
5. #72312568	C₂	semidirect
6. #72312542	C₂	semidirect
7. #72312518	C₂	semidirect
8. #72312487	C₂	semidirect
9. #72312467	C₂	semidirect
10. #72312428	C₂	semidirect
11. #72312398	C₂	semidirect
12. #72312358	C₂	semidirect
13. #72312265	C₂	semidirect
14. #72312172	C₂	semidirect
15. #72312136	C₂	semidirect
16. #72312079	C₂	semidirect
17. #72311949	C₂	semidirect
18. #72311871	C₂	semidirect
19. #72311811	C₂	semidirect
20. C₄×#33553	C₂	semidirect
21. C₄×#12755	C₂	semidirect
22. #72281292	C₂	semidirect
23. #72281182	C₂	semidirect
25. #10574037	C₂²	semidirect
40. C₄×#3027	C₂²	semidirect
42. C₄×#3021	C₂²	semidirect
44. #500801	C₄	semidirect
51. #494601	C₂²	semidirect
52. #494580	C₂²	semidirect
54. #494375	C₂²	semidirect
55. #494354	C₂²	semidirect
62. C₄×#2134	C₂²	semidirect
63. C₄×#2128	C₂²	semidirect
64. C₄×#2122	C₂²	semidirect
65. C₄×#2122	C₂²	semidirect
69. #392903	C₂²	semidirect
70. #392897	C₂²	semidirect
71. #392828	C₂²	semidirect
72. #392825	C₂²	semidirect
73. #392717	C₂²	semidirect
74. #392710	C₂²	semidirect
75. #392198	C₂²	semidirect
76. #392195	C₂²	semidirect
77. #354938	C₂²	semidirect
78. #354936	C₂²	semidirect
79. #354788	C₂²	semidirect
80. #354788	C₂²	semidirect
81. #354786	C₂²	semidirect
82. #354478	C₂²	semidirect
83. #354478	C₂²	semidirect
84. #354459	C₂²	semidirect
88. C₄×#1914	C₂²	semidirect
89. C₄×#1910	C₂²	semidirect
90. #353208	C₂²	semidirect
91. #149288	C₂²	semidirect
92. #149033	C₂²	semidirect
93. #148824	C₂²	semidirect
94. #148474	C₂²	semidirect
95. #148471	C₂²	semidirect
96. #148279	C₂²	semidirect
97. #148252	C₂²	semidirect
98. #148244	C₂²	semidirect
99. #148241	C₂²	semidirect
100. #148175	C₂²	semidirect
103. #147762	C₂²	semidirect
104. #147755	C₂²	semidirect
105. #147521	C₂²	semidirect
106. #147521	C₂²	semidirect
107. #147517	C₂²	semidirect
108. #147517	C₂²	semidirect
109. #147079	C₂²	semidirect
110. #147079	C₂²	semidirect
111. #147077	C₂²	semidirect
112. #147077	C₂²	semidirect
113. #147021	C₂²	semidirect
114. #147021	C₂²	semidirect
115. #146872	C₂²	semidirect
117. #146651	C₂²	semidirect
118. #146651	C₂²	semidirect
119. #146616	C₂²	semidirect
120. #146616	C₂²	semidirect
123. #146363	C₂²	semidirect
128. #62270	C₂×C₄	semidirect
135. C₂²×#442	D₄	semidirect
136. C₂²×#442	D₄	semidirect
143. C₂³×#97	D₄	semidirect
150. #33553	C₂×C₄	semidirect
161. #32951	C₂×C₄	semidirect
162. #32948	C₂×C₄	semidirect
166. #21483	C₂×C₄	semidirect
169. #21233	D₄	semidirect
170. #21233	D₄	semidirect
171. #21155	D₄	semidirect
172. #21155	D₄	semidirect
173. #21091	D₄	semidirect
174. #21091	D₄	semidirect
202. #20451	D₄	semidirect
203. #20451	D₄	semidirect
204. #20436	D₄	semidirect
205. #20436	D₄	semidirect
206. #20427	D₄	semidirect
207. C₄×#418	D₄	semidirect
208. C₄×#418	D₄	semidirect
217. #20385	D₄	semidirect
218. #20385	D₄	semidirect
221. C₄×#407	D₄	semidirect
223. #20331	D₄	semidirect
224. #13432	C₂×C₄	semidirect
225. #13353	C₂×C₄	semidirect
226. #13234	C₂×C₄	semidirect
227. #13231	C₂×C₄	semidirect
228. #12805	C₂×C₄	semidirect
229. #12755	C₂×C₄	semidirect
259. #3573	C₂²×C₄	semidirect
281. #3027	C₂²×C₄	semidirect
286. #3021	C₂²×C₄	semidirect
351. #2134	C₂²×C₄	semidirect
352. #2128	C₂²×C₄	semidirect
353. #2122	C₂²×C₄	semidirect
354. #2122	C₂²×C₄	semidirect
356. #1914	C₂²×C₄	semidirect
357. #1910	C₂²×C₄	semidirect
362. #1868	C₂²×C₄	semidirect
364. #1813	C₂²×C₄	semidirect
365. #1812	C₂²×C₄	semidirect
366. #1791	C₂²×C₄	semidirect
368. #1757	C₂²×C₄	semidirect
382. #1395	C₂²×C₄	semidirect
391. C₂²×D₈	C₄×D₄	semidirect
392. C₂²×D₈	C₄×D₄	semidirect
407. C₂³×C₈	C₄×D₄	semidirect
451. #427	C₄×D₄	semidirect
452. #427	C₄×D₄	semidirect
453. #424	C₄×D₄	semidirect
454. #418	C₄×D₄	semidirect
455. #418	C₄×D₄	semidirect
466. #407	C₄×D₄	semidirect
467. #405	C₄×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72312647	2
C₂×#500801	2
#72312593	2
#72312577	2
#72312568	2
#72312542	2
#72312518	2
#72312487	2
#72312467	2
#72312428	2
#72312398	2
#72312358	2
#72312265	2
#72312172	2
#72312136	2
#72312079	2
#72311949	2
#72311871	2
#72311811	2
C₄×#33553	2
C₄×#12755	2
#72281292	2
#72281182	2