Subgroups — #72318544

Order 2048.

At least 12095 conjugacy classes of subgroups; only the 920 normal subgroups are shown.

The subgroup lattice has 550 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72318300	C₂	1	2	yes	maximal, complemented
2	#72318218	C₂	1	2	yes	maximal, complemented
3	#72318203	C₂	1	2	yes	maximal, complemented
4	#72318199	C₂	1	2	yes	maximal, complemented
5	#72318177	C₂	1	2	yes	maximal, complemented
6	#72317976	C₂	1	1	yes	maximal, characteristic, complemented
7	#72317905	C₂	1	1	yes	maximal, characteristic, complemented
8	#72317844	C₂	1	1	yes	maximal, characteristic, complemented
9	#72317805	C₂	1	1	yes	maximal, characteristic, complemented
10	#72317749	C₂	1	1	yes	maximal, characteristic, complemented
11	#72317731	C₂	1	1	yes	maximal, characteristic, complemented
12	#72317716	C₂	1	1	yes	maximal, characteristic, complemented
13	#72317705	C₂	1	1	yes	maximal, characteristic, complemented
14	#72317688	C₂	1	1	yes	maximal, characteristic, complemented
15	#72284398	C₂	1	2	yes	maximal, complemented
16	#72267427	C₂	1	2	yes	maximal, complemented
17	#72264896	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#6595772	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#12759	C₂	1	1	yes	maximal, characteristic, complemented
20	#72232755	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#511771	C₂	1	1	yes	maximal, characteristic, complemented
22	#72231228	C₂	1	2	yes	maximal, complemented
23	#72219693	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#62983	C₂²	1	1	yes	characteristic, complemented
25	C₂³×D₄²	C₂²	1	1	yes	characteristic
26	C₂×#58990	C₂²	1	2	yes	—
27	C₂×D₄×#120	C₂²	1	1	yes	characteristic
28	C₂²×#2196	C₂²	1	2	yes	—
29	C₂²×#2196	C₂²	1	2	yes	complemented
30	C₂³×#353	C₂²	1	1	yes	characteristic, complemented
31	C₂³×AΣL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic
32	C₂³×AΣL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic, complemented
33	C₂×#33020	C₂²	1	1	yes	characteristic, complemented
34	C₂×#33020	C₂²	1	1	yes	characteristic, complemented
35	C₂×#32926	C₂²	1	1	yes	characteristic, complemented
36	C₂×#25947	C₂²	1	1	yes	characteristic, complemented
37	C₂×#24350	C₂²	1	1	yes	characteristic, complemented
38	C₂×#24404	C₂²	1	1	yes	characteristic, complemented
39	C₂×#24404	C₂²	1	1	yes	characteristic, complemented
40	C₂×#23900	C₂²	1	1	yes	characteristic
41	C₂×#23900	C₂²	1	1	yes	characteristic, complemented
42	C₂×#23900	C₂²	1	1	yes	characteristic, complemented
43	C₂×#23906	C₂²	1	1	yes	characteristic, complemented
44	C₂×D₄×#99	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₄×B(4,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
46	C₂²×#1889	C₂²	1	1	yes	characteristic
47	C₂²×#1889	C₂²	1	1	yes	characteristic, complemented
48	C₂²×#1889	C₂²	1	1	yes	characteristic, complemented
49	C₂²×#1887	C₂²	1	1	yes	characteristic, complemented
50	#1418385	C₂²	1	2	yes	—
51	#1418353	C₂²	1	2	yes	—
52	#846785	C₂²	1	1	yes	characteristic
53	#845297	C₂²	1	1	yes	characteristic
54	#649038	C₂²	1	1	yes	characteristic
55	#647656	C₂²	1	1	yes	characteristic
56	#534306	C₂²	1	2	yes	—
57	#531607	C₂²	1	1	yes	characteristic
58	C₂×#13346	C₂²	1	2	yes	complemented
59	C₂×#13343	C₂²	1	2	yes	complemented
60	C₂×#13088	C₂²	1	2	yes	complemented
61	C₂×#13086	C₂²	1	2	yes	complemented
62	C₂×#13086	C₂²	1	1	yes	characteristic, complemented
63	C₂×#13082	C₂²	1	1	yes	characteristic, complemented
64	C₂×#13041	C₂²	1	2	yes	complemented
65	C₂×#12759	C₂²	1	2	yes	—
66	C₂×#12759	C₂²	1	2	yes	—
67	C₂×#12759	C₂²	1	2	yes	—
68	C₂×#12759	C₂²	1	2	yes	complemented
69	C₂×#12759	C₂²	1	2	yes	complemented
70	C₂×#12759	C₂²	1	2	yes	complemented
71	C₂×#12693	C₂²	1	1	yes	characteristic, complemented
72	C₂×#12687	C₂²	1	1	yes	characteristic
73	C₂×#12687	C₂²	1	1	yes	characteristic, complemented
74	C₂×#12687	C₂²	1	2	yes	complemented
75	#403359	C₂²	1	2	yes	complemented
76	#403334	C₂²	1	2	yes	complemented
77	#394066	C₂²	1	2	yes	complemented
78	#393967	C₂²	1	2	yes	complemented
79	#392663	C₂²	1	2	yes	complemented
80	#392658	C₂²	1	2	yes	complemented
81	#392656	C₂²	1	2	yes	complemented
82	#392650	C₂²	1	2	yes	complemented
83	#392225	C₂²	1	1	yes	characteristic, complemented
84	#392222	C₂²	1	1	yes	characteristic, complemented
85	#359583	C₂²	1	1	yes	characteristic, complemented
86	#359579	C₂²	1	1	yes	characteristic, complemented
87	#359539	C₂²	1	1	yes	characteristic, complemented
88	#359531	C₂²	1	1	yes	characteristic, complemented
89	#148463	C₂²	1	2	yes	complemented
90	#148463	C₂²	1	2	yes	complemented
91	#148463	C₂²	1	2	yes	complemented
92	#148237	C₂²	1	2	yes	complemented
93	#148237	C₂²	1	2	yes	complemented
94	#148237	C₂²	1	2	yes	complemented
95	#148234	C₂²	1	2	yes	complemented
96	#148234	C₂²	1	2	yes	complemented
97	#148234	C₂²	1	2	yes	complemented
98	#147999	C₂²	1	2	yes	complemented
99	#147995	C₂²	1	2	yes	complemented
100	#147824	C₂²	1	2	yes	complemented
101	#147824	C₂²	1	2	yes	complemented
102	#147824	C₂²	1	2	yes	complemented
103	#147779	C₂²	1	2	yes	complemented
104	#147779	C₂²	1	2	yes	complemented
105	#147779	C₂²	1	2	yes	complemented
106	#147770	C₂²	1	2	yes	complemented
107	#147749	C₂²	1	2	yes	complemented
108	#147749	C₂²	1	2	yes	complemented
109	#147710	C₂²	1	2	yes	complemented
110	#147559	C₂²	1	2	yes	complemented
111	#147555	C₂²	1	2	yes	complemented
112	#147555	C₂²	1	2	yes	complemented
113	#147507	C₂²	1	2	yes	complemented
114	#147500	C₂²	1	2	yes	complemented
115	#146661	C₂²	1	2	yes	complemented
116	#146599	C₂²	1	2	yes	complemented
117	#146599	C₂²	1	2	yes	complemented
118	#146599	C₂²	1	2	yes	complemented
119	#146569	C₂²	1	1	yes	characteristic, complemented
120	#146569	C₂²	1	1	yes	characteristic, complemented
121	#146566	C₂²	1	1	yes	characteristic, complemented
122	#146564	C₂²	1	1	yes	characteristic, complemented
123	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
124	C₂×#3501	C₂³	1	1	yes	characteristic, complemented
125	C₂×#3484	C₂³	1	1	yes	characteristic
126	C₂×#3484	C₂³	1	1	yes	characteristic, complemented
127	C₂²×D₄²	C₂³	1	2	yes	—
128	C₂²×D₄²	C₂³	1	2	yes	—
129	C₂²×D₄²	C₂³	1	1	yes	characteristic
130	C₂³×#127	C₂³	1	1	yes	characteristic
131	C₂³×#120	D₄	1	1	yes	characteristic, complemented
132	C₂³×#120	C₂³	1	1	yes	characteristic
133	C₂³×#120	C₂³	1	1	yes	characteristic
134	C₂³×#120	C₂³	1	1	yes	characteristic
135	C₂×C₄×H(5,𝔽₂)	C₂³	1	1	yes	characteristic, complemented
136	C₂²×#518	C₂³	1	1	yes	characteristic
137	C₂²×#518	C₂³	1	1	yes	characteristic, complemented
138	C₂²×B(4,𝔽₂)	C₂³	1	1	yes	characteristic
139	C₂²×B(4,𝔽₂)	C₂³	1	2	yes	—
140	C₂²×B(4,𝔽₂)	C₂³	1	1	yes	characteristic
141	C₂²×B(4,𝔽₂)	C₂³	1	1	yes	characteristic, complemented
142	C₂²×#453	C₂³	1	2	yes	—
143	C₂³×#100	C₂³	1	1	yes	characteristic
144	C₂³×#99	C₂³	1	1	yes	characteristic
145	C₂³×#99	C₂³	1	1	yes	characteristic
146	C₂³×#99	C₂³	1	1	yes	characteristic, complemented
147	C₂×#2679	C₂³	1	2	yes	—
148	C₂×#2669	C₂³	1	2	yes	—
149	C₂×#2847	D₄	1	1	yes	characteristic, complemented
150	C₂×#2846	D₄	1	1	yes	characteristic, complemented
151	C₂×#2846	D₄	1	1	yes	characteristic, complemented
152	C₂×#2846	D₄	1	1	yes	characteristic, complemented
153	C₂×#2433	D₄	1	1	yes	characteristic, complemented
154	C₂×#2433	D₄	1	1	yes	characteristic, complemented
155	C₂×#2433	C₂³	1	2	yes	—
156	C₂×#2408	D₄	1	1	yes	characteristic, complemented
157	C₂×#2408	C₂³	1	1	yes	characteristic
158	C₂×#2410	D₄	1	1	yes	characteristic, complemented
159	C₂×#2410	D₄	1	1	yes	characteristic, complemented
160	C₂×#2403	C₂³	1	1	yes	characteristic
161	C₂×#2403	C₂³	1	2	yes	—
162	C₂×#2403	C₂³	1	1	yes	characteristic
163	C₂×#2358	C₂³	1	2	yes	—
164	C₂×D₄×C₂²⋊C₄	D₄	1	1	yes	characteristic, complemented
165	C₂×C₄×#120	C₂³	1	1	yes	characteristic
166	C₂²×#353	C₂³	1	2	yes	—
167	C₂²×#353	C₂³	1	2	yes	—
168	C₂²×#353	C₂³	1	2	yes	—
169	C₂²×#353	C₂³	1	2	yes	—
170	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	—
171	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	—
172	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	—
173	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	—
174	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	—
175	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	—
176	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	—
177	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	—
178	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	complemented
179	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	complemented
180	#23900	D₄	1	8	yes	complemented
181	C₂×#1889	D₄	1	8	yes	complemented
182	C₂×#1889	C₂³	1	2	yes	—
183	C₂×#1889	C₂³	1	2	yes	—
184	C₂×#1889	C₂³	1	2	yes	—
185	C₂×#1889	C₂³	1	1	yes	characteristic
186	C₂×#1889	C₂³	1	1	yes	characteristic
187	C₂×#1889	C₂³	1	1	yes	characteristic
188	C₂×#1889	C₂³	1	1	yes	characteristic
189	C₂×#1889	C₂³	1	1	yes	characteristic
190	C₂×#1889	C₂³	1	1	yes	characteristic
191	C₂×#1889	C₂³	1	1	yes	characteristic, complemented
192	C₂×#1889	C₂³	1	1	yes	characteristic, complemented
193	C₂×#1889	C₂³	1	1	yes	characteristic, complemented
194	C₂×#1887	C₂³	1	2	yes	—
195	C₂×#1887	C₂³	1	2	yes	—
196	C₂×#1887	C₂³	1	2	yes	—
197	C₂×#1867	C₂³	1	1	yes	characteristic, complemented
198	C₂×#1867	C₂³	1	1	yes	characteristic, complemented
199	C₂×#1867	C₂³	1	1	yes	characteristic, complemented
200	C₂×#1799	C₂³	1	1	yes	characteristic, complemented
201	C₂×#1792	C₂³	1	2	yes	complemented
202	C₂×#1790	C₂³	1	1	yes	characteristic, complemented
203	C₂×#1790	C₂³	1	2	yes	complemented
204	C₂×#1783	C₂³	1	1	yes	characteristic
205	C₂×#1783	C₂³	1	2	yes	complemented
206	C₂×#1781	C₂³	1	1	yes	characteristic
207	C₂×#1781	C₂³	1	1	yes	characteristic
208	C₂×#1781	C₂³	1	1	yes	characteristic, complemented
209	C₂×#1781	C₂³	1	2	yes	complemented
210	C₂×C₄×#99	C₂³	1	1	yes	characteristic, complemented
211	#15142	D₄	1	2	yes	complemented
212	#15124	D₄	1	2	yes	complemented
213	#14716	D₄	1	2	yes	complemented
214	#14715	D₄	1	2	yes	complemented
215	#14698	D₄	1	1	yes	characteristic, complemented
216	#14419	C₂³	1	2	yes	—
217	#14357	C₂³	1	2	yes	—
218	#14357	C₂³	1	2	yes	—
219	#14134	D₄	1	1	yes	characteristic, complemented
220	#14025	C₂³	1	2	yes	—
221	#13967	C₂³	1	2	yes	—
222	#13902	C₂³	1	1	yes	characteristic
223	#13867	D₄	1	1	yes	characteristic, complemented
224	#13867	C₂³	1	1	yes	characteristic
225	C₄×#386	D₄	1	1	yes	characteristic, complemented
226	C₂×#1393	C₂³	1	2	yes	complemented
227	C₂×#1393	C₂³	1	2	yes	complemented
228	C₂×#1393	C₂³	1	2	yes	complemented
229	C₂×#1393	C₂³	1	2	yes	complemented
230	C₂×#1390	C₂³	1	2	yes	complemented
231	C₂×#1390	C₂³	1	2	yes	complemented
232	C₂×#1390	C₂³	1	2	yes	complemented
233	C₂×#1390	C₂³	1	2	yes	complemented
234	C₂×#1390	C₂³	1	2	yes	complemented
235	C₂×#1390	C₂³	1	2	yes	complemented
236	#10762	C₂³	1	2	yes	complemented
237	#10761	C₂³	1	2	yes	complemented
238	#10749	C₂³	1	2	yes	complemented
239	#10749	C₂³	1	2	yes	complemented
240	#10749	C₂³	1	2	yes	complemented
241	#10745	C₂³	1	2	yes	complemented
242	#10745	C₂³	1	2	yes	complemented
243	#10745	C₂³	1	2	yes	complemented
244	C₂⁷	C₂×D₄	1	1	yes	characteristic
245	C₂⁷	C₂×D₄	1	1	yes	characteristic
246	C₂⁷	C₂×D₄	1	1	yes	characteristic
247	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
248	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
249	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
250	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
251	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
252	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
253	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
254	C₂⁴×D₄	C₂×D₄	1	2	yes	—
255	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
256	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
257	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
258	#3484	C₂×D₄	1	4	yes	complemented
259	C₂×D₄²	#41	1	8	yes	complemented
260	C₂²×#127	C₂×D₄	1	2	yes	—
261	C₂²×#127	C₂×D₄	1	1	yes	characteristic
262	C₂²×#127	C₂×D₄	1	2	yes	—
263	C₂²×#127	C₂⁴	1	2	yes	—
264	C₂²×#121	C₂×D₄	1	2	yes	—
265	C₂²×#121	C₂×D₄	1	1	yes	characteristic
266	C₂²×#121	C₂×D₄	1	1	yes	characteristic
267	C₂²×#121	C₂×D₄	1	1	yes	characteristic
268	C₂²×#121	C₂×D₄	1	1	yes	characteristic
269	C₂²×#120	C₂×D₄	1	4	yes	—
270	C₂²×#120	C₂×D₄	1	4	yes	—
271	C₂²×#120	C₂×D₄	1	2	yes	—
272	C₂²×#120	C₂×D₄	1	1	yes	characteristic
273	C₂²×#120	C₂×D₄	1	1	yes	characteristic
274	C₂²×#120	C₂×D₄	1	1	yes	characteristic
275	C₂²×#120	C₂×D₄	1	1	yes	characteristic
276	C₂²×#120	C₂×D₄	1	1	yes	characteristic
277	C₂²×#120	C₂×D₄	1	2	yes	—
278	C₂²×#120	C₂×D₄	1	1	yes	characteristic
279	C₂²×#120	C₂×D₄	1	1	yes	characteristic
280	C₂²×#120	C₂×D₄	1	1	yes	characteristic
281	C₂²×#120	C₂×D₄	1	1	yes	characteristic
282	C₂²×#120	C₂×D₄	1	1	yes	characteristic
283	C₂²×#120	C₂⁴	1	1	yes	characteristic
284	C₂²×#120	C₂⁴	1	1	yes	characteristic
285	C₂²×#120	C₂⁴	1	2	yes	—
286	C₂²×#120	C₂⁴	1	1	yes	characteristic
287	C₂×#518	C₂×D₄	1	4	yes	complemented
288	C₂×#518	C₂⁴	1	1	yes	characteristic
289	C₂×#518	C₂⁴	1	1	yes	characteristic
290	C₂×#518	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
292	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
293	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
294	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
295	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
296	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
297	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
298	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
299	C₂×B(4,𝔽₂)	C₂×D₄	1	4	yes	—
300	C₂×B(4,𝔽₂)	C₂×D₄	1	4	yes	complemented
301	C₂²×#100	C₂⁴	1	2	yes	—
302	C₂²×#100	C₂⁴	1	2	yes	—
303	C₂²×#99	C₂×D₄	1	4	yes	complemented
304	C₂²×#99	C₂⁴	1	2	yes	—
305	C₂²×#99	C₂⁴	1	2	yes	—
306	C₂²×#99	C₂⁴	1	1	yes	characteristic
307	C₂²×#99	C₂⁴	1	1	yes	characteristic
308	C₂²×#99	C₂⁴	1	1	yes	characteristic
309	C₂²×#99	C₂⁴	1	1	yes	characteristic
310	C₂×#390	C₂×D₄	1	2	yes	—
311	C₂×#390	C₂×D₄	1	2	yes	—
312	C₂×#390	C₂×D₄	1	2	yes	—
313	C₂×#390	C₂×D₄	1	2	yes	—
314	C₂×#390	C₂⁴	1	2	yes	—
315	C₂×#386	C₂×D₄	1	1	yes	characteristic
316	C₂×#386	C₂×D₄	1	1	yes	characteristic
317	C₂×#386	C₂×D₄	1	2	yes	—
318	C₂×#386	C₂×D₄	1	2	yes	—
319	C₂×#386	C₂⁴	1	1	yes	characteristic
320	C₂×#386	C₂⁴	1	2	yes	—
321	C₂×#385	C₂×D₄	1	1	yes	characteristic
322	C₂×#380	C₂×D₄	1	1	yes	characteristic
323	C₂×#380	C₂×D₄	1	1	yes	characteristic
324	C₂×#379	C₂×D₄	1	1	yes	characteristic
325	C₂×#379	C₂×D₄	1	1	yes	characteristic
326	C₂×#379	C₂×D₄	1	1	yes	characteristic
327	C₂×#379	C₂×D₄	1	1	yes	characteristic
328	C₂×#379	C₂×D₄	1	1	yes	characteristic
329	C₂×#379	C₂×D₄	1	2	yes	—
330	C₂×#379	C₂×D₄	1	1	yes	characteristic
331	C₂×#379	C₂×D₄	1	2	yes	—
332	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	2	yes	—
333	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
334	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
335	#1889	C₂×D₄	1	4	yes	—
336	#1889	C₂×D₄	1	4	yes	—
337	#1889	C₂×D₄	1	4	yes	—
338	#1889	C₂×D₄	1	4	yes	complemented
339	#1889	C₂×D₄	1	4	yes	complemented
340	#1889	C₂×D₄	1	4	yes	complemented
341	#1781	C₂×D₄	1	4	yes	complemented
342	C₄⋊#95	C₂×D₄	1	2	yes	—
343	C₂²⋊#95	C₂×D₄	1	2	yes	—
344	C₂²⋊#95	C₂×D₄	1	2	yes	—
345	C₄×#95	C₂×D₄	1	2	yes	—
346	C₂⁶	#120	1	4	yes	—
347	C₂⁶	C₂²×D₄	1	1	yes	characteristic
348	C₂⁶	C₂²×D₄	1	1	yes	characteristic
349	C₂⁶	C₂²×D₄	1	1	yes	characteristic
350	C₂⁶	C₂²×D₄	1	1	yes	characteristic
351	C₂⁶	C₂²×D₄	1	1	yes	characteristic
352	C₂⁶	C₂²×D₄	1	1	yes	characteristic
353	C₂⁶	C₂²×D₄	1	2	yes	—
354	C₂⁶	C₂²×D₄	1	1	yes	characteristic
355	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
356	C₂³×D₄	#120	1	1	yes	characteristic
357	C₂³×D₄	#120	1	1	yes	characteristic
358	C₂³×D₄	#120	1	1	yes	characteristic
359	C₂³×D₄	#120	1	1	yes	characteristic
360	C₂³×D₄	#120	1	1	yes	characteristic
361	C₂³×D₄	#120	1	1	yes	characteristic
362	C₂³×D₄	#120	1	1	yes	characteristic
363	C₂³×D₄	#120	1	1	yes	characteristic
364	C₂³×D₄	#120	1	1	yes	characteristic
365	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
366	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
367	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
368	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
369	C₂³×D₄	C₂²×D₄	1	2	yes	—
370	C₂³×D₄	C₂²×D₄	1	2	yes	—
371	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
372	C₂³×D₄	C₂²×D₄	1	2	yes	—
373	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
374	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
375	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
376	C₂³×D₄	C₂⁵	1	1	yes	characteristic
377	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
378	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
379	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
380	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
381	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
382	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
383	C₂×#127	C₂×#41	1	4	yes	—
384	C₂×#127	H(5,𝔽₂)	1	4	yes	—
385	C₂×#120	#120	1	4	yes	—
386	C₂×#120	#120	1	4	yes	—
387	C₂×#120	C₂²×D₄	1	2	yes	—
388	C₂×#120	C₂²×D₄	1	2	yes	—
389	C₂×#120	C₂²×D₄	1	2	yes	—
390	C₂×#120	C₂²×D₄	1	2	yes	—
391	C₂×#120	C₂×#41	1	4	yes	—
392	C₂×#120	C₂×#41	1	4	yes	—
393	C₂×#120	H(5,𝔽₂)	1	4	yes	—
394	C₂×#120	H(5,𝔽₂)	1	4	yes	—
395	#518	C₂²×D₄	1	2	yes	—
396	#518	C₂²×D₄	1	2	yes	—
397	#518	C₂²×D₄	1	2	yes	—
398	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
399	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
400	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
401	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
402	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
403	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
404	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
405	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
406	C₂²×C₂²⋊C₄	#120	1	4	yes	—
407	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
408	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
409	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
410	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
411	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
412	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
413	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
414	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
415	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
416	C₂²×C₄²	C₂²×D₄	1	2	yes	—
417	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
418	C₂²×C₄²	C₂²×D₄	1	2	yes	—
419	C₂×#99	C₂²×D₄	1	2	yes	—
420	C₂×#99	C₂²×D₄	1	2	yes	—
421	C₂×#99	C₂²×D₄	1	2	yes	—
422	C₂×#99	C₂²×D₄	1	2	yes	—
423	C₂⁵	C₂×#120	1	1	yes	characteristic
424	C₂⁵	C₂×#120	1	1	yes	characteristic
425	C₂⁵	C₂×#120	1	1	yes	characteristic
426	C₂⁵	C₂×#120	1	1	yes	characteristic
427	C₂⁵	C₂×#120	1	1	yes	characteristic
428	C₂⁵	C₂×#120	1	1	yes	characteristic
429	C₂⁵	C₂×#120	1	2	yes	—
430	C₂⁵	C₂×#120	1	2	yes	—
431	C₂⁵	C₂×#120	1	2	yes	—
432	C₂⁵	#534	1	2	yes	—
433	C₂⁵	D₄²	1	2	yes	—
434	C₂⁵	D₄²	1	2	yes	—
435	C₂⁵	#546	1	4	yes	—
436	C₂⁵	#546	1	4	yes	complemented
437	C₂⁵	C₂³×D₄	1	1	yes	characteristic
438	C₂⁵	C₂³×D₄	1	1	yes	characteristic
439	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
440	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
441	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
442	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
443	C₂²×D₄	B(4,𝔽₂)	1	4	yes	—
444	C₂²×D₄	C₂×#120	1	2	yes	—
445	C₂²×D₄	#534	1	2	yes	—
446	C₂²×D₄	D₄²	1	2	yes	—
447	C₂²×D₄	D₄²	1	2	yes	—
448	C₂²×D₄	D₄²	1	2	yes	—
449	C₂²×D₄	D₄²	1	2	yes	—
450	C₂²×D₄	#546	1	4	yes	complemented
451	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
452	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
453	C₂²×D₄	C₂²×#41	1	2	yes	—
454	C₂²×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
455	C₂²×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
456	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
457	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
458	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
459	C₂³×C₄	C₂×#120	1	1	yes	characteristic
460	C₂³×C₄	C₂×#120	1	1	yes	characteristic
461	C₂³×C₄	C₂×#120	1	1	yes	characteristic
462	C₂³×C₄	C₂×#120	1	1	yes	characteristic
463	C₂³×C₄	C₂×#120	1	1	yes	characteristic
464	C₂³×C₄	C₂×#120	1	1	yes	characteristic
465	C₂³×C₄	D₄²	1	2	yes	—
466	C₂³×C₄	D₄²	1	2	yes	—
467	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
468	#120	#525	1	4	yes	—
469	#120	#535	1	4	yes	—
470	#120	#546	1	8	yes	—
471	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
472	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
473	C₂×C₂²⋊C₄	#546	1	4	yes	—
474	C₂×C₂²⋊C₄	#546	1	4	yes	complemented
475	C₂×C₄²	#546	1	4	yes	complemented
476	C₂⁴	#2403	1	2	yes	—
477	C₂⁴	#2403	1	2	yes	—
478	C₂⁴	#2403	1	2	yes	—
479	C₂⁴	#2404	1	4	yes	complemented
480	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
481	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
482	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
483	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
484	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
485	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
486	C₂⁴	C₂²×#120	1	1	yes	characteristic
487	C₂⁴	C₂²×#120	1	1	yes	characteristic
488	C₂⁴	C₂×#534	1	1	yes	characteristic
489	C₂⁴	C₂×D₄²	1	1	yes	characteristic
490	C₂⁴	C₂×D₄²	1	1	yes	characteristic
491	C₂⁴	C₂×#546	1	2	yes	—
492	C₂⁴	C₂×#546	1	2	yes	—
493	C₂⁴	#3484	1	2	yes	—
494	C₂⁴	#3484	1	2	yes	—
495	C₂×D₄	#2196	1	4	yes	complemented
496	C₂×D₄	C₂×#525	1	1	yes	characteristic
497	C₂×D₄	C₂×#535	1	1	yes	characteristic
498	C₂×D₄	C₂×#546	1	2	yes	—
499	C₂×D₄	#3484	1	1	yes	characteristic
500	C₂×D₄	#3484	1	1	yes	characteristic
501	C₂×D₄	#3484	1	2	yes	—
502	C₂×D₄	#3490	1	2	yes	—
503	C₂×D₄	#3490	1	2	yes	—
504	C₂×D₄	#3532	1	2	yes	—
505	C₂×D₄	#3532	1	2	yes	—
506	C₂²×C₄	#2403	1	2	yes	—
507	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
508	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
509	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
510	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
511	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
512	C₂²×C₄	C₂×#546	1	2	yes	—
513	C₂²×C₄	#3484	1	2	yes	—
514	C₂²⋊C₄	#2404	1	4	yes	complemented
515	C₂³	#23900	1	2	yes	—
516	C₂³	#23900	1	2	yes	—
517	C₂³	C₂×#2196	1	2	yes	—
518	C₂³	C₂×#2196	1	2	yes	—
519	C₂³	#33551	1	2	yes	—
520	C₂³	C₂×#2403	1	1	yes	characteristic
521	C₂³	C₂×#2404	1	1	yes	characteristic
522	C₂³	#35346	1	1	yes	characteristic
523	C₂³	#36098	1	1	yes	characteristic
524	C₂³	#36152	1	2	yes	—
525	C₂³	#37645	1	1	yes	characteristic
526	C₂³	#37832	1	2	yes	—
527	C₂³	#58991	1	2	yes	—
528	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
529	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
530	C₂³	#60401	1	2	yes	—
531	C₂×C₄	C₂×#2196	1	2	yes	—
532	C₂×C₄	#36098	1	1	yes	characteristic
533	C₂×C₄	#37645	1	1	yes	characteristic
534	C₂×C₄	#58991	1	2	yes	—
535	C₂²	#499787	1	4	yes	—
536	C₂²	#647657	1	1	yes	characteristic
537	C₂²	C₂×#23900	1	1	yes	characteristic
538	C₂²	#6437635	1	1	yes	characteristic
539	C₂²	#6591500	1	2	yes	—
540	C₂²	#6591500	1	2	yes	—
541	C₂²	C₂²×#2196	1	1	yes	characteristic
542	C₂²	C₂×#33551	1	1	yes	characteristic
543	C₂²	#7622880	1	2	yes	—
544	C₂	C₂×#499787	1	1	yes	characteristic
545	C₂	#72233119	1	1	yes	characteristic
546	C₂	#72234132	1	2	yes	—
547	C₂	#72234532	1	2	yes	—
548	C₂	#72240616	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂²×B(4,𝔽₂)
commutator, Frattini, cosocle	C₂³×D₄	C₂⁵
LCS	G ▷ C₂³×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂³×D₄ ◁ C₂²×D₄² ◁ 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. #72318300	C₂	semidirect
2. #72318218	C₂	semidirect
3. #72318203	C₂	semidirect
4. #72318199	C₂	semidirect
5. #72318177	C₂	semidirect
6. #72317976	C₂	semidirect
7. #72317905	C₂	semidirect
8. #72317844	C₂	semidirect
9. #72317805	C₂	semidirect
10. #72317749	C₂	semidirect
11. #72317731	C₂	semidirect
12. #72317716	C₂	semidirect
13. #72317705	C₂	semidirect
14. #72317688	C₂	semidirect
15. #72284398	C₂	semidirect
16. #72267427	C₂	semidirect
17. #72264896	C₂	semidirect
18. C₂×#6595772	C₂	semidirect
19. C₂²×#12759	C₂	semidirect
20. #72232755	C₂	semidirect
21. C₂×#511771	C₂	semidirect
22. #72231228	C₂	semidirect
23. #72219693	C₂	semidirect
24. C₂×#62983	C₂²	semidirect
29. C₂²×#2196	C₂²	semidirect
30. C₂³×#353	C₂²	semidirect
32. C₂³×AΣL(1,𝔽₁₆)	C₂²	semidirect
33. C₂×#33020	C₂²	semidirect
34. C₂×#33020	C₂²	semidirect
35. C₂×#32926	C₂²	semidirect
36. C₂×#25947	C₂²	semidirect
37. C₂×#24350	C₂²	semidirect
38. C₂×#24404	C₂²	semidirect
39. C₂×#24404	C₂²	semidirect
41. C₂×#23900	C₂²	semidirect
42. C₂×#23900	C₂²	semidirect
43. C₂×#23906	C₂²	semidirect
44. C₂×D₄×#99	C₂²	semidirect
45. C₂×C₄×B(4,𝔽₂)	C₂²	semidirect
47. C₂²×#1889	C₂²	semidirect
48. C₂²×#1889	C₂²	semidirect
49. C₂²×#1887	C₂²	semidirect
58. C₂×#13346	C₂²	semidirect
59. C₂×#13343	C₂²	semidirect
60. C₂×#13088	C₂²	semidirect
61. C₂×#13086	C₂²	semidirect
62. C₂×#13086	C₂²	semidirect
63. C₂×#13082	C₂²	semidirect
64. C₂×#13041	C₂²	semidirect
68. C₂×#12759	C₂²	semidirect
69. C₂×#12759	C₂²	semidirect
70. C₂×#12759	C₂²	semidirect
71. C₂×#12693	C₂²	semidirect
73. C₂×#12687	C₂²	semidirect
74. C₂×#12687	C₂²	semidirect
75. #403359	C₂²	semidirect
76. #403334	C₂²	semidirect
77. #394066	C₂²	semidirect
78. #393967	C₂²	semidirect
79. #392663	C₂²	semidirect
80. #392658	C₂²	semidirect
81. #392656	C₂²	semidirect
82. #392650	C₂²	semidirect
83. #392225	C₂²	semidirect
84. #392222	C₂²	semidirect
85. #359583	C₂²	semidirect
86. #359579	C₂²	semidirect
87. #359539	C₂²	semidirect
88. #359531	C₂²	semidirect
89. #148463	C₂²	semidirect
90. #148463	C₂²	semidirect
91. #148463	C₂²	semidirect
92. #148237	C₂²	semidirect
93. #148237	C₂²	semidirect
94. #148237	C₂²	semidirect
95. #148234	C₂²	semidirect
96. #148234	C₂²	semidirect
97. #148234	C₂²	semidirect
98. #147999	C₂²	semidirect
99. #147995	C₂²	semidirect
100. #147824	C₂²	semidirect
101. #147824	C₂²	semidirect
102. #147824	C₂²	semidirect
103. #147779	C₂²	semidirect
104. #147779	C₂²	semidirect
105. #147779	C₂²	semidirect
106. #147770	C₂²	semidirect
107. #147749	C₂²	semidirect
108. #147749	C₂²	semidirect
109. #147710	C₂²	semidirect
110. #147559	C₂²	semidirect
111. #147555	C₂²	semidirect
112. #147555	C₂²	semidirect
113. #147507	C₂²	semidirect
114. #147500	C₂²	semidirect
115. #146661	C₂²	semidirect
116. #146599	C₂²	semidirect
117. #146599	C₂²	semidirect
118. #146599	C₂²	semidirect
119. #146569	C₂²	semidirect
120. #146569	C₂²	semidirect
121. #146566	C₂²	semidirect
122. #146564	C₂²	semidirect
123. C₂⁵×D₄	D₄	semidirect
124. C₂×#3501	C₂³	semidirect
126. C₂×#3484	C₂³	semidirect
131. C₂³×#120	D₄	semidirect
135. C₂×C₄×H(5,𝔽₂)	C₂³	semidirect
137. C₂²×#518	C₂³	semidirect
141. C₂²×B(4,𝔽₂)	C₂³	semidirect
146. C₂³×#99	C₂³	semidirect
149. C₂×#2847	D₄	semidirect
150. C₂×#2846	D₄	semidirect
151. C₂×#2846	D₄	semidirect
152. C₂×#2846	D₄	semidirect
153. C₂×#2433	D₄	semidirect
154. C₂×#2433	D₄	semidirect
156. C₂×#2408	D₄	semidirect
158. C₂×#2410	D₄	semidirect
159. C₂×#2410	D₄	semidirect
164. C₂×D₄×C₂²⋊C₄	D₄	semidirect
178. C₂²×AΣL(1,𝔽₁₆)	C₂³	semidirect
179. C₂²×AΣL(1,𝔽₁₆)	C₂³	semidirect
180. #23900	D₄	semidirect
181. C₂×#1889	D₄	semidirect
191. C₂×#1889	C₂³	semidirect
192. C₂×#1889	C₂³	semidirect
193. C₂×#1889	C₂³	semidirect
197. C₂×#1867	C₂³	semidirect
198. C₂×#1867	C₂³	semidirect
199. C₂×#1867	C₂³	semidirect
200. C₂×#1799	C₂³	semidirect
201. C₂×#1792	C₂³	semidirect
202. C₂×#1790	C₂³	semidirect
203. C₂×#1790	C₂³	semidirect
205. C₂×#1783	C₂³	semidirect
208. C₂×#1781	C₂³	semidirect
209. C₂×#1781	C₂³	semidirect
210. C₂×C₄×#99	C₂³	semidirect
211. #15142	D₄	semidirect
212. #15124	D₄	semidirect
213. #14716	D₄	semidirect
214. #14715	D₄	semidirect
215. #14698	D₄	semidirect
219. #14134	D₄	semidirect
223. #13867	D₄	semidirect
225. C₄×#386	D₄	semidirect
226. C₂×#1393	C₂³	semidirect
227. C₂×#1393	C₂³	semidirect
228. C₂×#1393	C₂³	semidirect
229. C₂×#1393	C₂³	semidirect
230. C₂×#1390	C₂³	semidirect
231. C₂×#1390	C₂³	semidirect
232. C₂×#1390	C₂³	semidirect
233. C₂×#1390	C₂³	semidirect
234. C₂×#1390	C₂³	semidirect
235. C₂×#1390	C₂³	semidirect
236. #10762	C₂³	semidirect
237. #10761	C₂³	semidirect
238. #10749	C₂³	semidirect
239. #10749	C₂³	semidirect
240. #10749	C₂³	semidirect
241. #10745	C₂³	semidirect
242. #10745	C₂³	semidirect
243. #10745	C₂³	semidirect
258. #3484	C₂×D₄	semidirect
259. C₂×D₄²	#41	semidirect
287. C₂×#518	C₂×D₄	semidirect
300. C₂×B(4,𝔽₂)	C₂×D₄	semidirect
303. C₂²×#99	C₂×D₄	semidirect
338. #1889	C₂×D₄	semidirect
339. #1889	C₂×D₄	semidirect
340. #1889	C₂×D₄	semidirect
341. #1781	C₂×D₄	semidirect
436. C₂⁵	#546	semidirect
450. C₂²×D₄	#546	semidirect
474. C₂×C₂²⋊C₄	#546	semidirect
475. C₂×C₄²	#546	semidirect
479. C₂⁴	#2404	semidirect
495. C₂×D₄	#2196	semidirect
514. C₂²⋊C₄	#2404	semidirect

Maximal subgroups

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

subgroup	index
#72318300	2
#72318218	2
#72318203	2
#72318199	2
#72318177	2
#72317976	2
#72317905	2
#72317844	2
#72317805	2
#72317749	2
#72317731	2
#72317716	2
#72317705	2
#72317688	2
#72284398	2
#72267427	2
#72264896	2
C₂×#6595772	2
C₂²×#12759	2
#72232755	2
C₂×#511771	2
#72231228	2
#72219693	2