Subgroups — #72262444

Order 2048.

At least 15461 conjugacy classes of subgroups; only the 1240 normal subgroups are shown.

The subgroup lattice has 600 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72262440	C₂	1	1	yes	maximal, characteristic, complemented
2	#72262250	C₂	1	2	yes	maximal, complemented
3	#72262245	C₂	1	4	yes	maximal, complemented
4	#72262203	C₂	1	1	yes	maximal, characteristic, complemented
5	#72262173	C₂	1	1	yes	maximal, characteristic, complemented
6	#72262115	C₂	1	2	yes	maximal, complemented
7	#72249513	C₂	1	2	yes	maximal, complemented
8	C₂×#511853	C₂	1	2	yes	maximal, complemented
9	#72237806	C₂	1	4	yes	maximal, complemented
10	#72234649	C₂	1	2	yes	maximal, complemented
11	#72234170	C₂	1	1	yes	maximal, characteristic, complemented
12	#72234146	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#7622880	C₂	1	1	yes	maximal, characteristic, complemented
14	#72233132	C₂	1	2	yes	maximal, complemented
15	#72233051	C₂	1	2	yes	maximal, complemented
16	#72232863	C₂	1	1	yes	maximal, characteristic, complemented
17	#72232823	C₂	1	2	yes	maximal, complemented
18	C₂×#63012	C₂²	1	1	yes	characteristic, complemented
19	C₂×#63011	C₂²	1	1	yes	characteristic
20	C₂×#60399	C₂²	1	2	yes	complemented
21	C₂×#60388	C₂²	1	1	yes	characteristic, complemented
22	#7819709	C₂²	1	2	yes	complemented
23	#7819605	C₂²	1	2	yes	—
24	#7785082	C₂²	1	2	yes	complemented
25	#7737454	C₂²	1	1	yes	characteristic, complemented
26	#7737411	C₂²	1	1	yes	characteristic
27	#7681966	C₂²	1	2	yes	—
28	#7671593	C₂²	1	1	yes	characteristic
29	C₂×#59816	C₂²	1	1	yes	characteristic, complemented
30	#7626333	C₂²	1	1	yes	characteristic, complemented
31	C₂×#33557	C₂²	1	2	yes	—
32	C₂×#33551	C₂²	1	4	yes	complemented
33	C₂×#33551	C₂²	1	4	yes	complemented
34	C₂²×#2196	C₂²	1	2	yes	complemented
35	C₂²×#2196	C₂²	1	2	yes	complemented
36	C₂×#33359	C₂²	1	1	yes	characteristic, complemented
37	C₂×#33348	C₂²	1	2	yes	complemented
38	#6628896	C₂²	1	2	yes	complemented
39	#6628876	C₂²	1	1	yes	characteristic, complemented
40	C₂×#23996	C₂²	1	4	yes	complemented
41	C₂×#23998	C₂²	1	2	yes	complemented
42	#6370735	C₂²	1	1	yes	characteristic, complemented
43	#498927	C₂²	1	4	yes	complemented
44	#498927	C₂²	1	4	yes	complemented
45	C₂×#13343	C₂²	1	4	yes	complemented
46	#494721	C₂²	1	2	yes	complemented
47	#494700	C₂²	1	2	yes	complemented
48	#494682	C₂²	1	2	yes	complemented
49	#494596	C₂²	1	2	yes	complemented
50	#494582	C₂²	1	4	yes	complemented
51	C₂×#12767	C₂²	1	2	yes	complemented
52	C₂×#12759	C₂²	1	2	yes	complemented
53	C₂×#12759	C₂²	1	2	yes	complemented
54	C₂×#12753	C₂²	1	4	yes	complemented
55	C₂×#12753	C₂²	1	4	yes	complemented
56	C₂×#12727	C₂²	1	2	yes	complemented
57	C₂×#12725	C₂²	1	4	yes	complemented
58	#493430	C₂²	1	1	yes	characteristic, complemented
59	#493424	C₂²	1	2	yes	complemented
60	#405274	C₂²	1	4	yes	complemented
61	#405271	C₂²	1	2	yes	complemented
62	#394174	C₂²	1	4	yes	complemented
63	#394165	C₂²	1	2	yes	complemented
64	#374036	C₂²	1	1	yes	characteristic, complemented
65	#374004	C₂²	1	2	yes	complemented
66	#364547	C₂²	1	2	yes	complemented
67	#364500	C₂²	1	4	yes	complemented
68	#359899	C₂²	1	1	yes	characteristic, complemented
69	#359898	C₂²	1	2	yes	complemented
70	#359601	C₂²	1	1	yes	characteristic, complemented
71	#359591	C₂²	1	2	yes	complemented
72	#147811	C₂²	1	4	yes	complemented
73	#147811	C₂²	1	4	yes	complemented
74	#147779	C₂²	1	4	yes	complemented
75	#147714	C₂²	1	2	yes	complemented
76	#147710	C₂²	1	4	yes	complemented
77	#147610	C₂²	1	2	yes	complemented
78	#147603	C₂²	1	4	yes	complemented
79	#146716	C₂²	1	2	yes	complemented
80	#146678	C₂²	1	4	yes	complemented
81	#146622	C₂²	1	2	yes	complemented
82	#146609	C₂²	1	4	yes	complemented
83	C₂×H(7,𝔽₂)	C₂³	1	1	yes	characteristic
84	C₂×#3508	C₂³	1	1	yes	characteristic
85	C₂×#3498	C₂³	1	1	yes	characteristic
86	C₂×#3490	C₂³	1	2	yes	—
87	C₂×#3484	C₂³	1	2	yes	—
88	C₂×#3549	D₄	1	1	yes	characteristic, complemented
89	C₂×#3543	D₄	1	1	yes	characteristic, complemented
90	C₂×#3543	C₂³	1	1	yes	characteristic
91	C₂×#3537	D₄	1	2	yes	complemented
92	C₂×#3532	D₄	1	2	yes	complemented
93	C₂×#3532	C₂³	1	2	yes	—
94	C₂×#3532	C₂³	1	2	yes	—
95	C₂×#3481	D₄	1	1	yes	characteristic, complemented
96	C₂²×D₄²	D₄	1	1	yes	characteristic, complemented
97	C₂²×D₄²	C₂³	1	1	yes	characteristic
98	C₂²×D₄²	C₂³	1	1	yes	characteristic
99	C₂×#3026	C₂³	1	4	yes	—
100	C₂²×B(4,𝔽₂)	C₂³	1	4	yes	—
101	C₂²×B(4,𝔽₂)	C₂³	1	4	yes	complemented
102	C₂×#3019	C₂³	1	2	yes	—
103	C₂×#3019	C₂³	1	2	yes	complemented
104	C₂²×#453	C₂³	1	2	yes	—
105	C₂×#2888	C₂³	1	1	yes	characteristic
106	C₂×#2883	C₂³	1	1	yes	characteristic
107	C₂×#2883	C₂³	1	2	yes	—
108	C₂×#2883	C₂³	1	2	yes	complemented
109	#59179	D₄	1	2	yes	complemented
110	#59126	D₄	1	1	yes	characteristic, complemented
111	#59126	D₄	1	1	yes	characteristic, complemented
112	#59041	D₄	1	1	yes	characteristic, complemented
113	#59041	D₄	1	1	yes	characteristic, complemented
114	#58990	D₄	1	2	yes	complemented
115	C₂×#2679	C₂³	1	2	yes	—
116	#52004	D₄	1	2	yes	complemented
117	#52004	D₄	1	2	yes	complemented
118	#50856	D₄	1	2	yes	complemented
119	#50646	D₄	1	2	yes	complemented
120	#49562	D₄	1	2	yes	complemented
121	#49545	D₄	1	2	yes	complemented
122	#45452	D₄	1	2	yes	complemented
123	#45439	D₄	1	2	yes	complemented
124	#36702	C₂³	1	2	yes	—
125	#36702	C₂³	1	2	yes	—
126	#36639	D₄	1	1	yes	characteristic, complemented
127	#35541	D₄	1	1	yes	characteristic, complemented
128	#35541	C₂³	1	1	yes	characteristic
129	#35513	D₄	1	1	yes	characteristic, complemented
130	#35513	C₂³	1	1	yes	characteristic
131	#35367	D₄	1	2	yes	complemented
132	#35360	D₄	1	2	yes	complemented
133	#35359	D₄	1	2	yes	complemented
134	#35350	C₂³	1	2	yes	—
135	#35348	D₄	1	2	yes	complemented
136	#35346	C₂³	1	2	yes	—
137	#35280	D₄	1	1	yes	characteristic, complemented
138	#35273	D₄	1	1	yes	characteristic, complemented
139	#35168	D₄	1	1	yes	characteristic, complemented
140	#35168	C₂³	1	1	yes	characteristic
141	C₂×#2408	C₂³	1	2	yes	—
142	C₂×#2410	D₄	1	2	yes	complemented
143	C₂×#2403	D₄	1	2	yes	complemented
144	#34408	C₂³	1	2	yes	—
145	#34364	C₂³	1	1	yes	characteristic
146	#34264	C₂³	1	2	yes	—
147	#34256	D₄	1	1	yes	characteristic, complemented
148	#34256	C₂³	1	1	yes	characteristic
149	#34256	C₂³	1	2	yes	complemented
150	#34198	D₄	1	2	yes	complemented
151	#34171	D₄	1	2	yes	complemented
152	C₄×#532	D₄	1	1	yes	characteristic, complemented
153	C₂×C₄×#127	C₂³	1	1	yes	characteristic
154	#33557	D₄	1	16	yes	complemented
155	C₂×#2127	C₂³	1	2	yes	—
156	C₂×#2127	C₂³	1	2	yes	—
157	C₂×#2127	C₂³	1	4	yes	complemented
158	C₂²×#353	C₂³	1	2	yes	—
159	C₂²×#353	C₂³	1	2	yes	—
160	C₂×#2121	C₂³	1	4	yes	—
161	C₂×#2121	C₂³	1	4	yes	—
162	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	4	yes	—
163	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	4	yes	—
164	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	4	yes	complemented
165	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	4	yes	complemented
166	C₂×#1913	C₂³	1	4	yes	—
167	C₂×#1911	C₂³	1	2	yes	—
168	C₂×#1911	C₂³	1	2	yes	complemented
169	C₂×#1889	C₂³	1	4	yes	—
170	C₂×#1889	C₂³	1	4	yes	complemented
171	C₂×#1887	C₂³	1	2	yes	—
172	C₂×#1829	C₂³	1	2	yes	complemented
173	C₂×#1828	C₂³	1	4	yes	complemented
174	C₂×#1792	C₂³	1	2	yes	complemented
175	#20609	C₂³	1	4	yes	complemented
176	#20592	C₂³	1	1	yes	characteristic
177	#20585	C₂³	1	2	yes	—
178	C₂×#1393	C₂³	1	4	yes	complemented
179	#12574	C₂³	1	4	yes	complemented
180	#12574	C₂³	1	4	yes	complemented
181	#10762	C₂³	1	2	yes	complemented
182	#10761	C₂³	1	4	yes	complemented
183	#10754	C₂³	1	4	yes	complemented
184	#10749	C₂³	1	2	yes	complemented
185	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
186	C₂²×H(5,𝔽₂)	C₂⁴	1	2	yes	—
187	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
188	C₂⁴×D₄	C₂×D₄	1	2	yes	—
189	C₂⁴×D₄	C₂×D₄	1	2	yes	complemented
190	#3543	C₂×D₄	1	8	yes	—
191	C₂×H(3,𝔽₄)	C₂×D₄	1	2	yes	—
192	C₂×H(3,𝔽₄)	C₂×D₄	1	2	yes	complemented
193	C₂×#560	C₂×D₄	1	2	yes	—
194	C₂×#560	C₂×D₄	1	2	yes	—
195	C₂×#560	C₂×D₄	1	2	yes	complemented
196	C₂×#559	C₂×D₄	1	1	yes	characteristic
197	C₂×#551	C₂×D₄	1	2	yes	—
198	C₂×#551	C₂×D₄	1	2	yes	complemented
199	C₂×D₄²	C₂×D₄	1	1	yes	characteristic
200	C₂×D₄²	C₂×D₄	1	2	yes	—
201	C₂×D₄²	C₂×D₄	1	2	yes	—
202	C₂×D₄²	C₂×D₄	1	1	yes	characteristic
203	C₂×D₄²	C₂×D₄	1	1	yes	characteristic
204	C₂×D₄²	C₂×D₄	1	2	yes	complemented
205	C₂×D₄²	C₂×D₄	1	1	yes	characteristic, complemented
206	C₂×D₄²	C₂×D₄	1	2	yes	complemented
207	C₂×D₄²	C₂×D₄	1	1	yes	characteristic, complemented
208	C₂×#543	C₂×D₄	1	2	yes	complemented
209	C₂×#537	C₂×D₄	1	1	yes	characteristic
210	C₂×#537	C₂×D₄	1	1	yes	characteristic, complemented
211	C₂×#535	C₂×D₄	1	1	yes	characteristic
212	C₂×#535	C₂×D₄	1	1	yes	characteristic
213	C₂×#535	C₂×D₄	1	1	yes	characteristic
214	C₂×#535	C₂×D₄	1	1	yes	characteristic
215	C₂×#535	C₂×D₄	1	2	yes	—
216	C₂×#535	C₂×D₄	1	2	yes	—
217	C₂×#535	C₂×D₄	1	1	yes	characteristic
218	C₂×#535	C₂×D₄	1	1	yes	characteristic, complemented
219	C₂×#535	C₂⁴	1	1	yes	characteristic
220	C₂×#535	C₂⁴	1	1	yes	characteristic
221	C₂×#534	C₂×D₄	1	2	yes	—
222	C₂×#534	C₂×D₄	1	2	yes	—
223	C₂×#534	C₂×D₄	1	2	yes	—
224	C₂×#534	C₂⁴	1	2	yes	—
225	C₂×#533	C₂×D₄	1	1	yes	characteristic, complemented
226	C₂×#532	C₂×D₄	1	1	yes	characteristic
227	C₂×#532	C₂×D₄	1	1	yes	characteristic
228	C₂×#532	C₂×D₄	1	1	yes	characteristic
229	C₂×#532	C₂×D₄	1	1	yes	characteristic
230	C₂²×#127	C₂×D₄	1	1	yes	characteristic
231	C₂²×#127	C₂×D₄	1	1	yes	characteristic
232	C₂²×#127	C₂⁴	1	1	yes	characteristic
233	C₂×#525	C₂×D₄	1	2	yes	—
234	C₂×#525	C₂×D₄	1	2	yes	—
235	C₂²×#120	C₂×D₄	1	2	yes	—
236	C₂²×#120	C₂×D₄	1	2	yes	—
237	C₂²×#120	C₂×D₄	1	2	yes	—
238	C₂²×#120	C₂×D₄	1	2	yes	—
239	C₂²×#120	C₂×D₄	1	2	yes	—
240	C₂²×#120	C₂×D₄	1	2	yes	complemented
241	C₂²×#120	C₂⁴	1	2	yes	—
242	C₂²×#120	C₂⁴	1	2	yes	—
243	C₂×#518	C₂×D₄	1	2	yes	—
244	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
245	C₂×#518	C₂×D₄	1	2	yes	complemented
246	C₂×#518	C₂×D₄	1	2	yes	complemented
247	C₂×#518	C₂⁴	1	2	yes	—
248	C₂×#518	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
250	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic, complemented
251	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic, complemented
252	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
253	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
254	#3026	C₂×D₄	1	16	yes	complemented
255	C₂×#453	C₂×D₄	1	8	yes	complemented
256	C₂²×#100	C₂⁴	1	2	yes	—
257	C₂²×#100	C₂⁴	1	2	yes	—
258	C₂²×#99	C₂⁴	1	4	yes	—
259	C₂²×#99	C₂⁴	1	4	yes	—
260	#2684	C₂×D₄	1	2	yes	complemented
261	#2684	C₂×D₄	1	2	yes	complemented
262	#2684	C₂×D₄	1	2	yes	complemented
263	#2684	C₂×D₄	1	2	yes	complemented
264	#2679	C₂×D₄	1	2	yes	complemented
265	#2679	C₂×D₄	1	2	yes	complemented
266	#2679	C₂×D₄	1	2	yes	complemented
267	#2679	C₂×D₄	1	2	yes	complemented
268	#2669	C₂×D₄	1	2	yes	complemented
269	#2669	C₂×D₄	1	2	yes	complemented
270	#2669	C₂×D₄	1	2	yes	complemented
271	#2669	C₂×D₄	1	2	yes	complemented
272	#2435	C₂×D₄	1	2	yes	—
273	#2433	C₂×D₄	1	2	yes	—
274	#2432	C₂×D₄	1	2	yes	—
275	#2431	C₂×D₄	1	2	yes	—
276	#2404	C₂×D₄	1	2	yes	—
277	#2404	C₂×D₄	1	2	yes	—
278	#2404	C₂×D₄	1	2	yes	—
279	#2404	C₂×D₄	1	2	yes	—
280	#2403	C₂×D₄	1	2	yes	—
281	#2403	C₂×D₄	1	2	yes	—
282	#2403	C₂×D₄	1	2	yes	—
283	#2403	C₂×D₄	1	2	yes	—
284	#2380	C₂×D₄	1	2	yes	complemented
285	#2376	C₂×D₄	1	2	yes	complemented
286	#2375	C₂×D₄	1	2	yes	complemented
287	#2374	C₂×D₄	1	2	yes	complemented
288	#2366	C₂×D₄	1	1	yes	characteristic, complemented
289	#2366	C₂×D₄	1	1	yes	characteristic, complemented
290	#2358	C₂×D₄	1	2	yes	complemented
291	#2316	C₂×D₄	1	1	yes	characteristic, complemented
292	#2316	C₂×D₄	1	1	yes	characteristic, complemented
293	#2315	C₂×D₄	1	2	yes	complemented
294	#2315	C₂×D₄	1	2	yes	complemented
295	#2311	C₂×D₄	1	1	yes	characteristic
296	#2311	C₂×D₄	1	1	yes	characteristic
297	#2311	C₂×D₄	1	1	yes	characteristic
298	#2311	C₂×D₄	1	1	yes	characteristic, complemented
299	#2308	C₂×D₄	1	2	yes	—
300	#2308	C₂×D₄	1	2	yes	—
301	#2308	C₂×D₄	1	2	yes	—
302	#2308	C₂×D₄	1	2	yes	—
303	#2308	C₂⁴	1	2	yes	—
304	#2297	C₂×D₄	1	1	yes	characteristic
305	#2297	C₂×D₄	1	1	yes	characteristic
306	#2297	C₂×D₄	1	1	yes	characteristic
307	#2297	C₂×D₄	1	1	yes	characteristic, complemented
308	#2297	C₂×D₄	1	1	yes	characteristic, complemented
309	#2297	C₂×D₄	1	1	yes	characteristic, complemented
310	C₂×#390	C₂×D₄	1	1	yes	characteristic, complemented
311	C₂×#390	C₂⁴	1	1	yes	characteristic
312	C₂×#386	C₂×D₄	1	2	yes	—
313	C₂×#386	C₂×D₄	1	2	yes	—
314	C₂×#386	C₂×D₄	1	2	yes	complemented
315	C₂×#385	C₂×D₄	1	2	yes	complemented
316	#2285	C₂×D₄	1	1	yes	characteristic, complemented
317	C₂×#384	C₂×D₄	1	1	yes	characteristic, complemented
318	C₂×#380	C₂×D₄	1	2	yes	complemented
319	C₂×#379	C₂×D₄	1	2	yes	complemented
320	C₂×#379	C₂×D₄	1	2	yes	complemented
321	C₂×#379	C₂×D₄	1	2	yes	complemented
322	C₂×#379	C₂×D₄	1	2	yes	complemented
323	#2273	C₂×D₄	1	2	yes	complemented
324	C₂×C₄³	C₂×D₄	1	1	yes	characteristic, complemented
325	C₂×#353	C₂×D₄	1	8	yes	complemented
326	#2121	C₂×D₄	1	16	yes	complemented
327	C₂⁶	#120	1	2	yes	—
328	C₂⁶	C₂²×D₄	1	2	yes	—
329	C₂⁶	C₂²×D₄	1	2	yes	—
330	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
331	C₂²×#41	#120	1	1	yes	characteristic
332	C₂²×#41	#120	1	1	yes	characteristic
333	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
334	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
335	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
336	C₂²×#41	C₂²×D₄	1	2	yes	—
337	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
338	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
339	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
340	C₂³×D₄	#120	1	2	yes	—
341	C₂³×D₄	#120	1	2	yes	—
342	C₂³×D₄	#120	1	1	yes	characteristic
343	C₂³×D₄	#120	1	1	yes	characteristic
344	C₂³×D₄	#120	1	2	yes	—
345	C₂³×D₄	#120	1	2	yes	—
346	C₂³×D₄	C₂²×D₄	1	2	yes	—
347	C₂³×D₄	C₂²×D₄	1	2	yes	—
348	C₂³×D₄	C₂²×D₄	1	2	yes	—
349	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
350	C₂³×D₄	C₂²×D₄	1	2	yes	—
351	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
352	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
353	C₂³×D₄	C₂⁵	1	1	yes	characteristic
354	C₂⁴×C₄	#120	1	2	yes	—
355	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
356	#560	#120	1	8	yes	complemented
357	#559	#120	1	4	yes	complemented
358	D₄²	#120	1	4	yes	complemented
359	#534	C₂²×D₄	1	8	yes	—
360	#534	H(5,𝔽₂)	1	8	yes	—
361	C₂×C₄⋊Q₈	#120	1	1	yes	characteristic
362	C₂×C₄⋊Q₈	#120	1	1	yes	characteristic
363	C₂×#127	#120	1	1	yes	characteristic
364	C₂×#127	#120	1	1	yes	characteristic
365	C₂×#127	#120	1	1	yes	characteristic
366	C₂×#127	#120	1	1	yes	characteristic
367	C₂×#127	C₂²×D₄	1	1	yes	characteristic
368	C₂×#127	C₂²×D₄	1	2	yes	—
369	C₂×#127	C₂²×D₄	1	1	yes	characteristic
370	C₂×#127	C₂²×D₄	1	1	yes	characteristic
371	C₂×#127	C₂²×D₄	1	1	yes	characteristic
372	C₂×#127	C₂²×D₄	1	1	yes	characteristic
373	C₂×#127	C₂²×D₄	1	1	yes	characteristic
374	C₂×#127	C₂²×D₄	1	4	yes	—
375	C₂×#127	H(5,𝔽₂)	1	4	yes	—
376	C₂×#124	#120	1	1	yes	characteristic
377	C₂×#124	#120	1	1	yes	characteristic
378	C₂×#124	#120	1	1	yes	characteristic
379	C₂×#124	#120	1	1	yes	characteristic
380	C₂×#124	#120	1	1	yes	characteristic
381	C₂×#124	#120	1	1	yes	characteristic
382	C₂×#124	C₂²×D₄	1	1	yes	characteristic
383	C₂×#124	C₂²×D₄	1	1	yes	characteristic
384	C₂×#124	C₂²×D₄	1	2	yes	—
385	C₂×#123	#120	1	2	yes	—
386	C₂×#123	#120	1	2	yes	—
387	C₂×#123	C₂²×D₄	1	2	yes	—
388	C₂×#123	C₂²×D₄	1	2	yes	—
389	C₂×C₂²⋊Q₈	#120	1	2	yes	—
390	C₂×#121	#120	1	2	yes	—
391	C₂×#120	#120	1	2	yes	—
392	C₂×#120	#120	1	2	yes	—
393	C₂×#120	#120	1	2	yes	—
394	C₂×#120	#120	1	2	yes	—
395	C₂×#120	#120	1	2	yes	—
396	C₂×#120	#120	1	2	yes	—
397	C₂×#120	#120	1	2	yes	—
398	C₂×#120	#120	1	2	yes	—
399	C₂×#120	#120	1	2	yes	—
400	C₂×#120	#120	1	2	yes	—
401	C₂×#120	C₂²×D₄	1	2	yes	—
402	C₂×#120	C₂²×D₄	1	2	yes	—
403	C₂×#120	C₂²×D₄	1	2	yes	—
404	C₂×#120	C₂²×D₄	1	2	yes	—
405	C₂×#120	C₂²×D₄	1	2	yes	—
406	C₂×#120	C₂²×D₄	1	2	yes	—
407	C₂×#120	C₂²×D₄	1	2	yes	—
408	C₂×#120	C₂²×D₄	1	2	yes	—
409	C₂×#120	C₂²×D₄	1	2	yes	—
410	C₂×#120	C₂²×D₄	1	2	yes	—
411	C₂×#117	#120	1	2	yes	—
412	C₂×#117	#120	1	2	yes	—
413	C₂×#117	#120	1	1	yes	characteristic
414	C₂×#117	#120	1	1	yes	characteristic
415	C₂×#117	C₂²×D₄	1	1	yes	characteristic
416	C₂×#117	C₂²×D₄	1	1	yes	characteristic
417	C₂×#117	C₂²×D₄	1	1	yes	characteristic
418	C₂×#117	C₂²×D₄	1	1	yes	characteristic
419	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
420	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
421	C₂²×C₂²⋊C₄	#120	1	2	yes	—
422	C₂²×C₂²⋊C₄	#120	1	2	yes	—
423	C₂²×C₂²⋊C₄	#120	1	2	yes	—
424	C₂²×C₂²⋊C₄	#120	1	2	yes	—
425	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
426	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
427	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
428	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
429	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
430	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
431	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
432	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
433	C₂²×C₄²	#120	1	1	yes	characteristic
434	C₂²×C₄²	#120	1	1	yes	characteristic
435	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
436	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
437	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
438	C₂×#100	C₂²×D₄	1	4	yes	—
439	C₂×#99	C₂²×D₄	1	8	yes	—
440	#391	#120	1	2	yes	—
441	#390	#120	1	2	yes	—
442	#390	C₂²×D₄	1	2	yes	—
443	#390	C₂²×D₄	1	2	yes	—
444	#386	#120	1	1	yes	characteristic
445	#386	#120	1	1	yes	characteristic
446	#386	#120	1	2	yes	—
447	#386	#120	1	2	yes	—
448	#386	#120	1	2	yes	—
449	#386	#120	1	2	yes	—
450	#386	#120	1	2	yes	—
451	#386	#120	1	2	yes	—
452	#386	#120	1	2	yes	—
453	#386	#120	1	2	yes	—
454	#386	#120	1	2	yes	—
455	#386	#120	1	2	yes	—
456	#386	#120	1	1	yes	characteristic
457	#386	#120	1	1	yes	characteristic
458	#386	C₂²×D₄	1	2	yes	—
459	#386	C₂²×D₄	1	2	yes	—
460	#386	C₂²×D₄	1	2	yes	—
461	#386	C₂²×D₄	1	2	yes	—
462	#381	#120	1	2	yes	—
463	#381	#120	1	2	yes	—
464	#379	#120	1	2	yes	—
465	#379	#120	1	2	yes	—
466	C₄×C₂²⋊C₄	#120	1	2	yes	—
467	C₄×C₂²⋊C₄	#120	1	2	yes	—
468	C₂⁵	C₂×#120	1	2	yes	—
469	C₂⁵	C₂×#120	1	2	yes	—
470	C₂⁵	C₂×#120	1	2	yes	—
471	C₂⁵	C₂×#120	1	2	yes	—
472	C₂⁵	C₂×#120	1	2	yes	—
473	C₂⁵	C₂×#120	1	2	yes	—
474	C₂⁵	C₂×#120	1	2	yes	—
475	C₂⁵	C₂³×D₄	1	2	yes	—
476	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
477	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
478	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
479	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
480	C₂²×D₄	C₂×#120	1	2	yes	—
481	C₂²×D₄	C₂×#120	1	1	yes	characteristic
482	C₂²×D₄	C₂×#120	1	2	yes	—
483	C₂²×D₄	C₂×#120	1	2	yes	—
484	C₂²×D₄	C₂×#120	1	1	yes	characteristic
485	C₂²×D₄	C₂×#120	1	2	yes	—
486	C₂²×D₄	C₂×#120	1	2	yes	—
487	C₂²×D₄	C₂×#120	1	1	yes	characteristic
488	C₂²×D₄	C₂×#120	1	1	yes	characteristic
489	C₂²×D₄	C₂×#120	1	1	yes	characteristic
490	C₂²×D₄	C₂×#120	1	1	yes	characteristic
491	C₂²×D₄	C₂×#120	1	1	yes	characteristic
492	C₂²×D₄	C₂×#120	1	1	yes	characteristic
493	C₂²×D₄	D₄²	1	8	yes	—
494	C₂²×D₄	D₄²	1	4	yes	—
495	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
496	C₂²×D₄	C₂³×D₄	1	2	yes	—
497	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
498	C₂²×D₄	C₂³×D₄	1	2	yes	—
499	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
500	C₂²×D₄	C₂×H(5,𝔽₂)	1	4	yes	—
501	C₂³×C₄	C₂×#120	1	2	yes	—
502	C₂³×C₄	C₂×#120	1	1	yes	characteristic
503	C₂³×C₄	C₂×#120	1	1	yes	characteristic
504	C₂³×C₄	C₂×#120	1	1	yes	characteristic
505	C₂³×C₄	C₂×#120	1	1	yes	characteristic
506	C₂³×C₄	C₂×#120	1	2	yes	—
507	C₂³×C₄	C₂×#120	1	2	yes	—
508	C₂³×C₄	C₂×#120	1	2	yes	—
509	C₂³×C₄	C₂×#120	1	2	yes	—
510	C₂³×C₄	C₂×#120	1	2	yes	—
511	C₂³×C₄	C₂×#120	1	2	yes	—
512	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
513	#127	C₂×#120	1	2	yes	—
514	#127	C₂×#120	1	2	yes	—
515	#127	#534	1	2	yes	—
516	#127	#534	1	2	yes	—
517	#127	D₄²	1	4	yes	—
518	#127	D₄²	1	4	yes	—
519	#123	C₂×#120	1	4	yes	—
520	#123	#534	1	4	yes	—
521	#123	D₄²	1	8	yes	—
522	#120	C₂×#120	1	4	yes	—
523	#120	#534	1	4	yes	—
524	#120	D₄²	1	8	yes	—
525	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
526	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
527	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
530	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
531	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
532	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
534	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
537	C₂×C₂²⋊C₄	D₄²	1	8	yes	—
538	C₂×C₄²	C₂×#120	1	1	yes	characteristic
539	C₂×C₄²	C₂×#120	1	2	yes	—
540	C₂×C₄²	C₂×#120	1	1	yes	characteristic
541	C₂×C₄²	C₂×#120	1	1	yes	characteristic
542	C₂×C₄²	C₂×#120	1	1	yes	characteristic
543	C₂×C₄²	C₂×#120	1	1	yes	characteristic
544	C₂×C₄²	C₂×#120	1	1	yes	characteristic
545	C₂×C₄²	D₄²	1	4	yes	—
546	C₂⁴	#2403	1	4	yes	—
547	C₂⁴	#2846	1	2	yes	—
548	C₂⁴	#2846	1	1	yes	characteristic
549	C₂⁴	#2846	1	1	yes	characteristic
550	C₂⁴	C₂²×#120	1	2	yes	—
551	C₂⁴	C₂²×#120	1	2	yes	—
552	C₂⁴	C₂²×#120	1	1	yes	characteristic
553	C₂⁴	C₂×D₄²	1	4	yes	—
554	C₂⁴	#3484	1	4	yes	—
555	C₂×D₄	#2403	1	2	yes	—
556	C₂×D₄	#2403	1	2	yes	—
557	C₂×D₄	#3025	1	2	yes	—
558	C₂×D₄	#3027	1	2	yes	—
559	C₂×D₄	C₂²×#120	1	1	yes	characteristic
560	C₂×D₄	C₂×#534	1	1	yes	characteristic
561	C₂×D₄	C₂×#534	1	2	yes	—
562	C₂×D₄	C₂×D₄²	1	2	yes	—
563	C₂×D₄	C₂×D₄²	1	4	yes	—
564	C₂×D₄	#3484	1	2	yes	—
565	C₂×D₄	#3484	1	4	yes	—
566	C₂²×C₄	#2403	1	4	yes	—
567	C₂²×C₄	#2846	1	2	yes	—
568	C₂²×C₄	#2846	1	1	yes	characteristic
569	C₂²×C₄	#2846	1	1	yes	characteristic
570	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
571	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
572	C₂²×C₄	C₂×D₄²	1	2	yes	—
573	C₂²×C₄	#3484	1	2	yes	—
574	C₂²⋊C₄	#2403	1	4	yes	—
575	C₂²⋊C₄	#2403	1	4	yes	—
576	C₄²	#2403	1	2	yes	—
577	C₄²	#2403	1	2	yes	—
578	C₂³	#32899	1	2	yes	—
579	C₂³	C₂×#2403	1	2	yes	—
580	C₂³	#34980	1	2	yes	—
581	C₂³	D₄×#120	1	4	yes	—
582	C₂³	D₄×#120	1	2	yes	—
583	C₂³	C₂×#2846	1	1	yes	characteristic
584	C₂³	C₂×#3025	1	1	yes	characteristic
585	C₂³	C₂×#3027	1	1	yes	characteristic
586	C₂³	#60399	1	2	yes	—
587	C₂×C₄	#32899	1	2	yes	—
588	C₂×C₄	C₂×#2403	1	1	yes	characteristic
589	C₂×C₄	#34980	1	1	yes	characteristic
590	C₂×C₄	D₄×#120	1	2	yes	—
591	C₂²	#612424	1	1	yes	characteristic
592	C₂²	#6573710	1	2	yes	—
593	C₂²	#6573716	1	2	yes	—
594	C₂²	C₂×#32899	1	1	yes	characteristic
595	C₂²	#6628896	1	1	yes	characteristic
596	C₂	#72216366	1	1	yes	characteristic
597	C₂	#72240574	1	1	yes	characteristic
598	C₂	#72249655	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#6628896
commutator, Frattini, cosocle	C₂³×D₄	C₂⁵
LCS	G ▷ C₂³×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ #34256 ◁ G
LECS	G ▷ C₂³×D₄ ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72262440	C₂	semidirect
2. #72262250	C₂	semidirect
3. #72262245	C₂	semidirect
4. #72262203	C₂	semidirect
5. #72262173	C₂	semidirect
6. #72262115	C₂	semidirect
7. #72249513	C₂	semidirect
8. C₂×#511853	C₂	semidirect
9. #72237806	C₂	semidirect
10. #72234649	C₂	semidirect
11. #72234170	C₂	semidirect
12. #72234146	C₂	semidirect
13. C₂×#7622880	C₂	semidirect
14. #72233132	C₂	semidirect
15. #72233051	C₂	semidirect
16. #72232863	C₂	semidirect
17. #72232823	C₂	semidirect
18. C₂×#63012	C₂²	semidirect
20. C₂×#60399	C₂²	semidirect
21. C₂×#60388	C₂²	semidirect
22. #7819709	C₂²	semidirect
24. #7785082	C₂²	semidirect
25. #7737454	C₂²	semidirect
29. C₂×#59816	C₂²	semidirect
30. #7626333	C₂²	semidirect
32. C₂×#33551	C₂²	semidirect
33. C₂×#33551	C₂²	semidirect
34. C₂²×#2196	C₂²	semidirect
35. C₂²×#2196	C₂²	semidirect
36. C₂×#33359	C₂²	semidirect
37. C₂×#33348	C₂²	semidirect
38. #6628896	C₂²	semidirect
39. #6628876	C₂²	semidirect
40. C₂×#23996	C₂²	semidirect
41. C₂×#23998	C₂²	semidirect
42. #6370735	C₂²	semidirect
43. #498927	C₂²	semidirect
44. #498927	C₂²	semidirect
45. C₂×#13343	C₂²	semidirect
46. #494721	C₂²	semidirect
47. #494700	C₂²	semidirect
48. #494682	C₂²	semidirect
49. #494596	C₂²	semidirect
50. #494582	C₂²	semidirect
51. C₂×#12767	C₂²	semidirect
52. C₂×#12759	C₂²	semidirect
53. C₂×#12759	C₂²	semidirect
54. C₂×#12753	C₂²	semidirect
55. C₂×#12753	C₂²	semidirect
56. C₂×#12727	C₂²	semidirect
57. C₂×#12725	C₂²	semidirect
58. #493430	C₂²	semidirect
59. #493424	C₂²	semidirect
60. #405274	C₂²	semidirect
61. #405271	C₂²	semidirect
62. #394174	C₂²	semidirect
63. #394165	C₂²	semidirect
64. #374036	C₂²	semidirect
65. #374004	C₂²	semidirect
66. #364547	C₂²	semidirect
67. #364500	C₂²	semidirect
68. #359899	C₂²	semidirect
69. #359898	C₂²	semidirect
70. #359601	C₂²	semidirect
71. #359591	C₂²	semidirect
72. #147811	C₂²	semidirect
73. #147811	C₂²	semidirect
74. #147779	C₂²	semidirect
75. #147714	C₂²	semidirect
76. #147710	C₂²	semidirect
77. #147610	C₂²	semidirect
78. #147603	C₂²	semidirect
79. #146716	C₂²	semidirect
80. #146678	C₂²	semidirect
81. #146622	C₂²	semidirect
82. #146609	C₂²	semidirect
88. C₂×#3549	D₄	semidirect
89. C₂×#3543	D₄	semidirect
91. C₂×#3537	D₄	semidirect
92. C₂×#3532	D₄	semidirect
95. C₂×#3481	D₄	semidirect
96. C₂²×D₄²	D₄	semidirect
101. C₂²×B(4,𝔽₂)	C₂³	semidirect
103. C₂×#3019	C₂³	semidirect
108. C₂×#2883	C₂³	semidirect
109. #59179	D₄	semidirect
110. #59126	D₄	semidirect
111. #59126	D₄	semidirect
112. #59041	D₄	semidirect
113. #59041	D₄	semidirect
114. #58990	D₄	semidirect
116. #52004	D₄	semidirect
117. #52004	D₄	semidirect
118. #50856	D₄	semidirect
119. #50646	D₄	semidirect
120. #49562	D₄	semidirect
121. #49545	D₄	semidirect
122. #45452	D₄	semidirect
123. #45439	D₄	semidirect
126. #36639	D₄	semidirect
127. #35541	D₄	semidirect
129. #35513	D₄	semidirect
131. #35367	D₄	semidirect
132. #35360	D₄	semidirect
133. #35359	D₄	semidirect
135. #35348	D₄	semidirect
137. #35280	D₄	semidirect
138. #35273	D₄	semidirect
139. #35168	D₄	semidirect
142. C₂×#2410	D₄	semidirect
143. C₂×#2403	D₄	semidirect
147. #34256	D₄	semidirect
149. #34256	C₂³	semidirect
150. #34198	D₄	semidirect
151. #34171	D₄	semidirect
152. C₄×#532	D₄	semidirect
154. #33557	D₄	semidirect
157. C₂×#2127	C₂³	semidirect
164. C₂²×AΣL(1,𝔽₁₆)	C₂³	semidirect
165. C₂²×AΣL(1,𝔽₁₆)	C₂³	semidirect
168. C₂×#1911	C₂³	semidirect
170. C₂×#1889	C₂³	semidirect
172. C₂×#1829	C₂³	semidirect
173. C₂×#1828	C₂³	semidirect
174. C₂×#1792	C₂³	semidirect
175. #20609	C₂³	semidirect
178. C₂×#1393	C₂³	semidirect
179. #12574	C₂³	semidirect
180. #12574	C₂³	semidirect
181. #10762	C₂³	semidirect
182. #10761	C₂³	semidirect
183. #10754	C₂³	semidirect
184. #10749	C₂³	semidirect
189. C₂⁴×D₄	C₂×D₄	semidirect
192. C₂×H(3,𝔽₄)	C₂×D₄	semidirect
195. C₂×#560	C₂×D₄	semidirect
198. C₂×#551	C₂×D₄	semidirect
204. C₂×D₄²	C₂×D₄	semidirect
205. C₂×D₄²	C₂×D₄	semidirect
206. C₂×D₄²	C₂×D₄	semidirect
207. C₂×D₄²	C₂×D₄	semidirect
208. C₂×#543	C₂×D₄	semidirect
210. C₂×#537	C₂×D₄	semidirect
218. C₂×#535	C₂×D₄	semidirect
225. C₂×#533	C₂×D₄	semidirect
240. C₂²×#120	C₂×D₄	semidirect
244. C₂×#518	C₂×D₄	semidirect
245. C₂×#518	C₂×D₄	semidirect
246. C₂×#518	C₂×D₄	semidirect
250. C₂×C₄×#41	C₂×D₄	semidirect
251. C₂²×C₄×D₄	C₂×D₄	semidirect
253. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
254. #3026	C₂×D₄	semidirect
255. C₂×#453	C₂×D₄	semidirect
260. #2684	C₂×D₄	semidirect
261. #2684	C₂×D₄	semidirect
262. #2684	C₂×D₄	semidirect
263. #2684	C₂×D₄	semidirect
264. #2679	C₂×D₄	semidirect
265. #2679	C₂×D₄	semidirect
266. #2679	C₂×D₄	semidirect
267. #2679	C₂×D₄	semidirect
268. #2669	C₂×D₄	semidirect
269. #2669	C₂×D₄	semidirect
270. #2669	C₂×D₄	semidirect
271. #2669	C₂×D₄	semidirect
284. #2380	C₂×D₄	semidirect
285. #2376	C₂×D₄	semidirect
286. #2375	C₂×D₄	semidirect
287. #2374	C₂×D₄	semidirect
288. #2366	C₂×D₄	semidirect
289. #2366	C₂×D₄	semidirect
290. #2358	C₂×D₄	semidirect
291. #2316	C₂×D₄	semidirect
292. #2316	C₂×D₄	semidirect
293. #2315	C₂×D₄	semidirect
294. #2315	C₂×D₄	semidirect
298. #2311	C₂×D₄	semidirect
307. #2297	C₂×D₄	semidirect
308. #2297	C₂×D₄	semidirect
309. #2297	C₂×D₄	semidirect
310. C₂×#390	C₂×D₄	semidirect
314. C₂×#386	C₂×D₄	semidirect
315. C₂×#385	C₂×D₄	semidirect
316. #2285	C₂×D₄	semidirect
317. C₂×#384	C₂×D₄	semidirect
318. C₂×#380	C₂×D₄	semidirect
319. C₂×#379	C₂×D₄	semidirect
320. C₂×#379	C₂×D₄	semidirect
321. C₂×#379	C₂×D₄	semidirect
322. C₂×#379	C₂×D₄	semidirect
323. #2273	C₂×D₄	semidirect
324. C₂×C₄³	C₂×D₄	semidirect
325. C₂×#353	C₂×D₄	semidirect
326. #2121	C₂×D₄	semidirect
356. #560	#120	semidirect
357. #559	#120	semidirect
358. D₄²	#120	semidirect

Maximal subgroups

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

subgroup	index
#72262440	2
#72262250	2
#72262245	2
#72262203	2
#72262173	2
#72262115	2
#72249513	2
C₂×#511853	2
#72237806	2
#72234649	2
#72234170	2
#72234146	2
C₂×#7622880	2
#72233132	2
#72233051	2
#72232863	2
#72232823	2