Subgroups — #72266113

Order 2048.

At least 6719 conjugacy classes of subgroups; only the 1316 normal subgroups are shown.

The subgroup lattice has 442 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72266111	C₂	1	1	yes	maximal, characteristic, complemented
2	#72266109	C₂	1	1	yes	maximal, characteristic, complemented
3	#72266100	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#10336	C₂	1	1	yes	maximal, characteristic, complemented
5	#72241143	C₂	1	1	yes	maximal, characteristic, complemented
6	#72240619	C₂	1	2	yes	maximal, complemented
7	C₂×#233541	C₂	1	2	yes	maximal, complemented
8	#72234668	C₂	1	1	yes	maximal, characteristic, complemented
9	#72232805	C₂	1	16	yes	maximal, complemented
10	#72225801	C₂	1	2	yes	maximal, complemented
11	#72225796	C₂	1	1	yes	maximal, characteristic, complemented
12	#72225791	C₂	1	2	yes	maximal, complemented
13	#7652796	C₂²	1	8	yes	complemented
14	#7641846	C₂²	1	1	yes	characteristic
15	C₂×#34980	C₂²	1	1	yes	characteristic
16	C₂×#34980	C₂²	1	2	yes	—
17	C₂²×#2403	C₂²	1	1	yes	characteristic
18	C₂²×#2403	C₂²	1	2	yes	—
19	#7626202	C₂²	1	1	yes	characteristic
20	C₂×#34171	C₂²	1	2	yes	—
21	C₂×#21746	C₂²	1	2	yes	—
22	C₂×#21746	C₂²	1	1	yes	characteristic
23	C₂²×#1781	C₂²	1	1	yes	characteristic
24	C₂²×#1781	C₂²	1	2	yes	—
25	C₂²×#1781	C₂²	1	1	yes	characteristic
26	C₂²×#1781	C₂²	1	2	yes	—
27	C₂²×#1781	C₂²	1	2	yes	—
28	#517411	C₂²	1	2	yes	—
29	#364471	C₂²	1	16	yes	complemented
30	#364440	C₂²	1	8	yes	complemented
31	#355913	C₂²	1	2	yes	—
32	#355913	C₂²	1	2	yes	—
33	#355913	C₂²	1	1	yes	characteristic
34	#355913	C₂²	1	1	yes	characteristic
35	#238082	C₂²	1	8	yes	complemented
36	#233541	C₂²	1	16	yes	complemented
37	C₂×#10336	C₂²	1	8	yes	complemented
38	C₂×#8101	C₂²	1	2	yes	—
39	C₂×#8101	C₂²	1	2	yes	—
40	C₂×#8101	C₂²	1	1	yes	characteristic
41	C₂²×#1304	C₂²	1	1	yes	characteristic
42	#122191	C₂²	1	8	yes	complemented
43	#115204	C₂²	1	16	yes	complemented
44	#111458	C₂²	1	8	yes	complemented
45	#106654	C₂²	1	16	yes	complemented
46	#105752	C₂²	1	8	yes	complemented
47	C₂⁵×D₄	C₂³	1	2	yes	—
48	C₂⁵×D₄	C₂³	1	1	yes	characteristic
49	C₂³×#120	C₂³	1	1	yes	characteristic
50	C₂³×#99	C₂³	1	4	yes	—
51	#37475	D₄	1	8	yes	complemented
52	#37475	C₂³	1	4	yes	—
53	#34980	D₄	1	4	yes	complemented
54	#34980	D₄	1	4	yes	complemented
55	#34980	C₂³	1	4	yes	—
56	#34980	C₂³	1	8	yes	—
57	C₂×#2405	D₄	1	4	yes	complemented
58	C₂×#2403	D₄	1	4	yes	complemented
59	C₂×#2403	D₄	1	4	yes	complemented
60	C₂×#2403	D₄	1	4	yes	complemented
61	C₂×#2403	C₂³	1	4	yes	—
62	C₂×#2403	C₂³	1	8	yes	—
63	#34198	D₄	1	4	yes	complemented
64	#34198	C₂³	1	4	yes	—
65	#34176	D₄	1	2	yes	complemented
66	#34171	D₄	1	2	yes	complemented
67	C₂×D₄×C₂²⋊C₄	D₄	1	8	yes	complemented
68	C₂×D₄×C₂²⋊C₄	C₂³	1	8	yes	—
69	C₂×#2280	D₄	1	4	yes	complemented
70	C₂²×#379	D₄	1	4	yes	complemented
71	C₂²×#379	C₂³	1	2	yes	—
72	C₂²×#379	C₂³	1	1	yes	characteristic
73	C₂²×#379	C₂³	1	1	yes	characteristic
74	C₂²×#379	C₂³	1	1	yes	characteristic
75	C₂²×#379	C₂³	1	2	yes	—
76	C₂²×#379	C₂³	1	2	yes	—
77	C₂²×#379	C₂³	1	1	yes	characteristic
78	C₂²×#379	C₂³	1	1	yes	characteristic
79	#21746	C₂³	1	8	yes	—
80	C₂×#1898	C₂³	1	4	yes	—
81	C₂×#1781	C₂³	1	4	yes	—
82	C₂×#1781	C₂³	1	8	yes	—
83	C₂×#1781	C₂³	1	8	yes	—
84	C₂×#1781	C₂³	1	8	yes	—
85	#13867	C₂³	1	8	yes	—
86	#10735	C₂³	1	8	yes	—
87	#10735	C₂³	1	8	yes	—
88	#10735	C₂³	1	4	yes	—
89	#10725	C₂³	1	4	yes	—
90	#8101	C₂³	1	8	yes	—
91	#8101	C₂³	1	8	yes	—
92	C₂×#1304	C₂³	1	4	yes	—
93	C₂×#1304	C₂³	1	4	yes	—
94	C₂⁷	C₂×D₄	1	2	yes	—
95	C₂⁷	#41	1	1	yes	characteristic, complemented
96	C₂⁷	C₂⁴	1	1	yes	characteristic
97	C₂⁴×D₄	C₂×D₄	1	2	yes	—
98	C₂⁴×D₄	C₂×D₄	1	4	yes	—
99	C₂⁴×D₄	C₂×D₄	1	4	yes	—
100	C₂⁴×D₄	C₂×D₄	1	2	yes	—
101	C₂⁴×D₄	C₂×D₄	1	2	yes	—
102	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
103	C₂⁴×D₄	C₂×D₄	1	2	yes	—
104	C₂⁴×D₄	C₂×D₄	1	2	yes	—
105	C₂⁴×D₄	C₂×D₄	1	4	yes	—
106	C₂⁴×D₄	#41	1	2	yes	complemented
107	C₂⁴×D₄	C₂⁴	1	4	yes	—
108	C₂⁴×D₄	C₂⁴	1	2	yes	—
109	C₂⁵×C₄	C₂×D₄	1	2	yes	—
110	C₂⁵×C₄	#41	1	1	yes	characteristic, complemented
111	C₂²×#120	C₂×D₄	1	4	yes	—
112	C₂²×#120	C₂×D₄	1	2	yes	—
113	C₂²×#120	C₂⁴	1	2	yes	—
114	C₂×#518	C₂×D₄	1	4	yes	complemented
115	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
116	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
117	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
118	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
119	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
120	C₂³×C₂²⋊C₄	#41	1	4	yes	complemented
121	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
122	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
123	#2842	C₂×D₄	1	8	yes	complemented
124	#2842	C₂×D₄	1	4	yes	complemented
125	#2840	C₂×D₄	1	4	yes	complemented
126	#2405	C₂×D₄	1	8	yes	complemented
127	#2405	C₂×D₄	1	8	yes	complemented
128	#2403	C₂×D₄	1	4	yes	complemented
129	#2403	C₂×D₄	1	4	yes	complemented
130	#2403	C₂×D₄	1	8	yes	complemented
131	#2403	C₂×D₄	1	8	yes	complemented
132	#2403	C₂×D₄	1	8	yes	complemented
133	#2315	C₂×D₄	1	4	yes	complemented
134	#2308	C₂×D₄	1	4	yes	complemented
135	C₂×#380	C₂×D₄	1	8	yes	complemented
136	C₂×#379	C₂×D₄	1	4	yes	—
137	C₂×#379	C₂×D₄	1	4	yes	—
138	C₂×#379	C₂×D₄	1	4	yes	—
139	C₂×#379	C₂×D₄	1	4	yes	—
140	C₂×#379	C₂×D₄	1	4	yes	—
141	C₂×#379	C₂×D₄	1	4	yes	—
142	C₂×#379	C₂×D₄	1	4	yes	—
143	C₂×#379	C₂×D₄	1	2	yes	—
144	C₂×#379	C₂×D₄	1	2	yes	—
145	C₂×#379	C₂×D₄	1	2	yes	—
146	C₂×#379	C₂×D₄	1	4	yes	—
147	C₂×#379	C₂×D₄	1	4	yes	—
148	C₂×#379	C₂×D₄	1	8	yes	complemented
149	C₂×#379	#41	1	2	yes	complemented
150	C₂×#379	#41	1	2	yes	complemented
151	C₂×#379	#41	1	4	yes	complemented
152	C₂×#379	C₂⁴	1	4	yes	—
153	C₂×#379	C₂⁴	1	2	yes	—
154	C₂×#379	C₂⁴	1	2	yes	—
155	C₂×#379	C₂⁴	1	4	yes	—
156	C₂×#379	C₂⁴	1	2	yes	—
157	C₂×#379	C₂⁴	1	4	yes	—
158	#2273	C₂×D₄	1	4	yes	complemented
159	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
160	C₂⁶	#120	1	2	yes	—
161	C₂⁶	#120	1	4	yes	—
162	C₂⁶	#120	1	1	yes	characteristic
163	C₂⁶	#120	1	2	yes	—
164	C₂⁶	C₂²×D₄	1	4	yes	—
165	C₂⁶	C₂²×D₄	1	2	yes	—
166	C₂⁶	C₂²×D₄	1	1	yes	characteristic
167	C₂⁶	C₂²×D₄	1	1	yes	characteristic
168	C₂⁶	C₂²×D₄	1	2	yes	—
169	C₂⁶	C₂²×D₄	1	2	yes	—
170	C₂⁶	C₂²×D₄	1	2	yes	—
171	C₂⁶	C₂²×D₄	1	2	yes	—
172	C₂⁶	C₂²×D₄	1	2	yes	—
173	C₂⁶	C₂×#41	1	2	yes	—
174	C₂⁶	C₂×#41	1	1	yes	characteristic
175	C₂⁶	C₂×#41	1	2	yes	—
176	C₂⁶	C₂×#41	1	1	yes	characteristic
177	C₂⁶	C₂×#41	1	1	yes	characteristic
178	C₂⁶	C₂×#41	1	2	yes	—
179	C₂⁶	C₂×#41	1	1	yes	characteristic
180	C₂⁶	H(5,𝔽₂)	1	2	yes	—
181	C₂⁶	H(5,𝔽₂)	1	2	yes	—
182	C₂⁶	H(5,𝔽₂)	1	2	yes	—
183	C₂⁶	2₋¹⁺⁴	1	2	yes	—
184	C₂⁶	C₂⁵	1	1	yes	characteristic
185	C₂³×D₄	#120	1	4	yes	—
186	C₂³×D₄	#120	1	2	yes	—
187	C₂³×D₄	#120	1	4	yes	—
188	C₂³×D₄	#120	1	4	yes	—
189	C₂³×D₄	#120	1	4	yes	—
190	C₂³×D₄	#120	1	4	yes	—
191	C₂³×D₄	C₂²×D₄	1	2	yes	—
192	C₂³×D₄	C₂²×D₄	1	4	yes	—
193	C₂³×D₄	C₂²×D₄	1	4	yes	—
194	C₂³×D₄	C₂²×D₄	1	4	yes	—
195	C₂³×D₄	C₂²×D₄	1	4	yes	—
196	C₂³×D₄	C₂²×D₄	1	4	yes	—
197	C₂⁴×C₄	#120	1	2	yes	—
198	C₂⁴×C₄	#120	1	2	yes	—
199	C₂⁴×C₄	#120	1	4	yes	—
200	C₂⁴×C₄	#120	1	2	yes	—
201	C₂⁴×C₄	#120	1	1	yes	characteristic
202	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
203	C₂⁴×C₄	C₂×#41	1	2	yes	—
204	C₂²×C₂²⋊C₄	#120	1	4	yes	—
205	C₂²×C₂²⋊C₄	#120	1	2	yes	—
206	C₂²×C₂²⋊C₄	#120	1	8	yes	—
207	C₂²×C₂²⋊C₄	#120	1	8	yes	—
208	C₂²×C₂²⋊C₄	#120	1	8	yes	—
209	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
210	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
211	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
212	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
213	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
214	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
215	C₂²×C₂²⋊C₄	C₂×#41	1	8	yes	—
216	#379	#120	1	4	yes	—
217	#379	#120	1	8	yes	—
218	#379	#120	1	8	yes	—
219	#379	#120	1	8	yes	—
220	#379	#120	1	8	yes	—
221	#379	#120	1	4	yes	—
222	#379	C₂²×D₄	1	4	yes	—
223	#379	C₂²×D₄	1	8	yes	—
224	#379	C₂²×D₄	1	8	yes	—
225	#379	C₂²×D₄	1	4	yes	—
226	#379	C₂×#41	1	4	yes	—
227	C₂⁵	C₂×#120	1	1	yes	characteristic
228	C₂⁵	C₂×#120	1	2	yes	—
229	C₂⁵	C₂×#120	1	2	yes	—
230	C₂⁵	C₂×#120	1	1	yes	characteristic
231	C₂⁵	C₂×#120	1	4	yes	—
232	C₂⁵	C₂×#120	1	4	yes	—
233	C₂⁵	C₂×#120	1	2	yes	—
234	C₂⁵	C₂×#120	1	2	yes	—
235	C₂⁵	C₂×#120	1	1	yes	characteristic
236	C₂⁵	C₂×#120	1	2	yes	—
237	C₂⁵	C₂×#120	1	2	yes	—
238	C₂⁵	C₂×#120	1	2	yes	—
239	C₂⁵	C₂×#120	1	2	yes	—
240	C₂⁵	C₂×#120	1	2	yes	—
241	C₂⁵	C₂×#120	1	2	yes	—
242	C₂⁵	C₂×#120	1	2	yes	—
243	C₂⁵	C₂×#120	1	2	yes	—
244	C₂⁵	C₂×#120	1	1	yes	characteristic
245	C₂⁵	C₂×#120	1	2	yes	—
246	C₂⁵	#525	1	2	yes	—
247	C₂⁵	#525	1	1	yes	characteristic
248	C₂⁵	#525	1	2	yes	—
249	C₂⁵	#525	1	1	yes	characteristic
250	C₂⁵	#525	1	2	yes	—
251	C₂⁵	#525	1	2	yes	—
252	C₂⁵	#525	1	1	yes	characteristic
253	C₂⁵	#525	1	1	yes	characteristic
254	C₂⁵	#532	1	1	yes	characteristic
255	C₂⁵	#532	1	2	yes	—
256	C₂⁵	#532	1	2	yes	—
257	C₂⁵	#532	1	2	yes	—
258	C₂⁵	#532	1	2	yes	—
259	C₂⁵	#532	1	1	yes	characteristic
260	C₂⁵	#532	1	2	yes	—
261	C₂⁵	#535	1	2	yes	—
262	C₂⁵	#535	1	1	yes	characteristic
263	C₂⁵	#535	1	2	yes	—
264	C₂⁵	#535	1	2	yes	—
265	C₂⁵	#535	1	2	yes	—
266	C₂⁵	#535	1	2	yes	—
267	C₂⁵	#535	1	1	yes	characteristic
268	C₂⁵	#537	1	2	yes	—
269	C₂⁵	#537	1	2	yes	—
270	C₂⁵	#537	1	2	yes	—
271	C₂⁵	#537	1	2	yes	—
272	C₂⁵	#537	1	2	yes	—
273	C₂⁵	#537	1	2	yes	—
274	C₂⁵	#546	1	2	yes	—
275	C₂⁵	#546	1	2	yes	—
276	C₂⁵	#546	1	2	yes	—
277	C₂⁵	#546	1	2	yes	—
278	C₂⁵	#546	1	2	yes	—
279	C₂⁵	#546	1	2	yes	—
280	C₂⁵	#546	1	2	yes	—
281	C₂⁵	#546	1	2	yes	—
282	C₂⁵	#546	1	2	yes	—
283	C₂⁵	#546	1	2	yes	—
284	C₂⁵	#546	1	2	yes	—
285	C₂⁵	#546	1	2	yes	—
286	C₂⁵	#546	1	2	yes	—
287	C₂⁵	#546	1	2	yes	—
288	C₂⁵	#546	1	2	yes	—
289	C₂⁵	#546	1	2	yes	—
290	C₂⁵	#546	1	2	yes	—
291	C₂⁵	#546	1	2	yes	—
292	C₂⁵	#547	1	2	yes	—
293	C₂⁵	#547	1	2	yes	—
294	C₂⁵	#547	1	2	yes	—
295	C₂⁵	#547	1	2	yes	—
296	C₂⁵	#547	1	2	yes	—
297	C₂⁵	#547	1	2	yes	—
298	C₂⁵	#548	1	2	yes	—
299	C₂⁵	#548	1	2	yes	—
300	C₂⁵	#550	1	2	yes	—
301	C₂⁵	#550	1	2	yes	—
302	C₂⁵	#550	1	2	yes	—
303	C₂⁵	#550	1	2	yes	—
304	C₂⁵	#550	1	2	yes	—
305	C₂⁵	#550	1	2	yes	—
306	C₂⁵	C₂³×D₄	1	2	yes	—
307	C₂⁵	C₂³×D₄	1	1	yes	characteristic
308	C₂⁵	C₂³×D₄	1	1	yes	characteristic
309	C₂⁵	C₂³×D₄	1	2	yes	—
310	C₂⁵	C₂³×D₄	1	1	yes	characteristic
311	C₂⁵	C₂²×#41	1	1	yes	characteristic
312	C₂⁵	C₂²×#41	1	2	yes	—
313	C₂⁵	C₂²×#41	1	1	yes	characteristic
314	C₂⁵	C₂×H(5,𝔽₂)	1	1	yes	characteristic
315	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
316	C₂⁵	C₂×2₋¹⁺⁴	1	1	yes	characteristic
317	C₂³×C₄	C₂×#120	1	2	yes	—
318	C₂³×C₄	C₂×#120	1	4	yes	—
319	C₂³×C₄	C₂×#120	1	4	yes	—
320	C₂³×C₄	C₂×#120	1	4	yes	—
321	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	—
322	C₂×C₂²⋊C₄	C₂×#120	1	16	yes	—
323	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	—
324	C₂⁴	#2388	1	1	yes	characteristic
325	C₂⁴	#2388	1	2	yes	—
326	C₂⁴	#2388	1	2	yes	—
327	C₂⁴	#2388	1	1	yes	characteristic
328	C₂⁴	#2388	1	1	yes	characteristic
329	C₂⁴	#2388	1	1	yes	characteristic
330	C₂⁴	#2404	1	2	yes	—
331	C₂⁴	#2404	1	2	yes	—
332	C₂⁴	#2404	1	1	yes	characteristic
333	C₂⁴	#2404	1	2	yes	—
334	C₂⁴	#2404	1	2	yes	—
335	C₂⁴	#2404	1	2	yes	—
336	C₂⁴	#2404	1	2	yes	—
337	C₂⁴	#2404	1	2	yes	—
338	C₂⁴	#2404	1	2	yes	—
339	C₂⁴	#2404	1	1	yes	characteristic
340	C₂⁴	#2404	1	2	yes	—
341	C₂⁴	#2404	1	1	yes	characteristic
342	C₂⁴	#2404	1	1	yes	characteristic
343	C₂⁴	#2404	1	2	yes	—
344	C₂⁴	#2407	1	2	yes	—
345	C₂⁴	#2407	1	2	yes	—
346	C₂⁴	#2407	1	2	yes	—
347	C₂⁴	#2407	1	2	yes	—
348	C₂⁴	#2407	1	2	yes	—
349	C₂⁴	#2407	1	2	yes	—
350	C₂⁴	#2407	1	2	yes	—
351	C₂⁴	#2407	1	2	yes	—
352	C₂⁴	#2407	1	2	yes	—
353	C₂⁴	#2407	1	2	yes	—
354	C₂⁴	#2407	1	2	yes	—
355	C₂⁴	#2407	1	2	yes	—
356	C₂⁴	#2430	1	2	yes	—
357	C₂⁴	#2430	1	2	yes	—
358	C₂⁴	#2430	1	2	yes	—
359	C₂⁴	#2430	1	2	yes	—
360	C₂⁴	#2430	1	2	yes	—
361	C₂⁴	#2430	1	2	yes	—
362	C₂⁴	#2430	1	2	yes	—
363	C₂⁴	#2430	1	2	yes	—
364	C₂⁴	#2430	1	2	yes	—
365	C₂⁴	#2430	1	2	yes	—
366	C₂⁴	#2430	1	2	yes	—
367	C₂⁴	#2430	1	2	yes	—
368	C₂⁴	#2431	1	2	yes	—
369	C₂⁴	#2431	1	2	yes	—
370	C₂⁴	#2431	1	2	yes	—
371	C₂⁴	#2431	1	2	yes	—
372	C₂⁴	#2431	1	2	yes	—
373	C₂⁴	#2431	1	2	yes	—
374	C₂⁴	#2431	1	2	yes	—
375	C₂⁴	#2431	1	2	yes	—
376	C₂⁴	#2431	1	2	yes	—
377	C₂⁴	#2431	1	2	yes	—
378	C₂⁴	#2431	1	2	yes	—
379	C₂⁴	#2431	1	2	yes	—
380	C₂⁴	#2615	1	2	yes	—
381	C₂⁴	#2615	1	2	yes	—
382	C₂⁴	#2615	1	2	yes	—
383	C₂⁴	#2615	1	2	yes	—
384	C₂⁴	#2846	1	2	yes	—
385	C₂⁴	#2846	1	2	yes	—
386	C₂⁴	#2846	1	2	yes	—
387	C₂⁴	#2846	1	2	yes	—
388	C₂⁴	C₂²×#120	1	2	yes	—
389	C₂⁴	C₂²×#120	1	2	yes	—
390	C₂⁴	C₂²×#120	1	1	yes	characteristic
391	C₂⁴	C₂²×#120	1	1	yes	characteristic
392	C₂⁴	C₂²×#120	1	1	yes	characteristic
393	C₂⁴	C₂×#525	1	2	yes	—
394	C₂⁴	C₂×#525	1	1	yes	characteristic
395	C₂⁴	C₂×#532	1	1	yes	characteristic
396	C₂⁴	C₂×#532	1	2	yes	—
397	C₂⁴	C₂×#535	1	2	yes	—
398	C₂⁴	C₂×#535	1	1	yes	characteristic
399	C₂⁴	C₂×#537	1	1	yes	characteristic
400	C₂⁴	C₂×#537	1	2	yes	—
401	C₂⁴	C₂×#546	1	1	yes	characteristic
402	C₂⁴	C₂×#546	1	2	yes	—
403	C₂⁴	C₂×#546	1	2	yes	—
404	C₂⁴	C₂×#546	1	2	yes	—
405	C₂⁴	C₂×#546	1	2	yes	—
406	C₂⁴	C₂×#547	1	2	yes	—
407	C₂⁴	C₂×#547	1	1	yes	characteristic
408	C₂⁴	C₂×#548	1	1	yes	characteristic
409	C₂⁴	C₂×#550	1	1	yes	characteristic
410	C₂⁴	C₂×#550	1	2	yes	—
411	C₂³	#14885	1	2	yes	—
412	C₂³	#14885	1	2	yes	—
413	C₂³	#14885	1	2	yes	—
414	C₂³	#14885	1	2	yes	—
415	C₂³	#14885	1	2	yes	—
416	C₂³	#14885	1	2	yes	—
417	C₂³	#14885	1	2	yes	—
418	C₂³	#14885	1	2	yes	—
419	C₂³	#23996	1	8	yes	—
420	C₂³	C₂×#2388	1	1	yes	characteristic
421	C₂³	C₂×#2615	1	1	yes	characteristic
422	C₂³	C₂×#2407	1	2	yes	—
423	C₂³	C₂×#2407	1	1	yes	characteristic
424	C₂³	C₂×#2431	1	2	yes	—
425	C₂³	C₂×#2431	1	1	yes	characteristic
426	C₂³	C₂×#2404	1	1	yes	characteristic
427	C₂³	C₂×#2404	1	2	yes	—
428	C₂³	C₂×#2430	1	2	yes	—
429	C₂³	C₂×#2430	1	1	yes	characteristic
430	C₂³	C₂×#2846	1	1	yes	characteristic
431	C₂³	#60399	1	4	yes	—
432	C₂²	#404015	1	4	yes	—
433	C₂²	#404015	1	4	yes	—
434	C₂²	C₂×#14885	1	1	yes	characteristic
435	C₂²	#6432106	1	2	yes	—
436	C₂²	#6435073	1	2	yes	—
437	C₂²	C₂×#23996	1	4	yes	—
438	C₂²	#6628896	1	2	yes	—
439	C₂	C₂×#404015	1	2	yes	—
440	C₂	#72265886	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#14885
commutator, Frattini, cosocle	C₂⁶	C₂⁵
LCS	G ▷ C₂⁶ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁷ ◁ G
LECS	G ▷ C₂⁶ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72266111	C₂	semidirect
2. #72266109	C₂	semidirect
3. #72266100	C₂	semidirect
4. C₂²×#10336	C₂	semidirect
5. #72241143	C₂	semidirect
6. #72240619	C₂	semidirect
7. C₂×#233541	C₂	semidirect
8. #72234668	C₂	semidirect
9. #72232805	C₂	semidirect
10. #72225801	C₂	semidirect
11. #72225796	C₂	semidirect
12. #72225791	C₂	semidirect
13. #7652796	C₂²	semidirect
29. #364471	C₂²	semidirect
30. #364440	C₂²	semidirect
35. #238082	C₂²	semidirect
36. #233541	C₂²	semidirect
37. C₂×#10336	C₂²	semidirect
42. #122191	C₂²	semidirect
43. #115204	C₂²	semidirect
44. #111458	C₂²	semidirect
45. #106654	C₂²	semidirect
46. #105752	C₂²	semidirect
51. #37475	D₄	semidirect
53. #34980	D₄	semidirect
54. #34980	D₄	semidirect
57. C₂×#2405	D₄	semidirect
58. C₂×#2403	D₄	semidirect
59. C₂×#2403	D₄	semidirect
60. C₂×#2403	D₄	semidirect
63. #34198	D₄	semidirect
65. #34176	D₄	semidirect
66. #34171	D₄	semidirect
67. C₂×D₄×C₂²⋊C₄	D₄	semidirect
69. C₂×#2280	D₄	semidirect
70. C₂²×#379	D₄	semidirect
95. C₂⁷	#41	semidirect
106. C₂⁴×D₄	#41	semidirect
110. C₂⁵×C₄	#41	semidirect
114. C₂×#518	C₂×D₄	semidirect
119. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
120. C₂³×C₂²⋊C₄	#41	semidirect
123. #2842	C₂×D₄	semidirect
124. #2842	C₂×D₄	semidirect
125. #2840	C₂×D₄	semidirect
126. #2405	C₂×D₄	semidirect
127. #2405	C₂×D₄	semidirect
128. #2403	C₂×D₄	semidirect
129. #2403	C₂×D₄	semidirect
130. #2403	C₂×D₄	semidirect
131. #2403	C₂×D₄	semidirect
132. #2403	C₂×D₄	semidirect
133. #2315	C₂×D₄	semidirect
134. #2308	C₂×D₄	semidirect
135. C₂×#380	C₂×D₄	semidirect
148. C₂×#379	C₂×D₄	semidirect
149. C₂×#379	#41	semidirect
150. C₂×#379	#41	semidirect
151. C₂×#379	#41	semidirect
158. #2273	C₂×D₄	semidirect
159. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72266111	2
#72266109	2
#72266100	2
C₂²×#10336	2
#72241143	2
#72240619	2
C₂×#233541	2
#72234668	2
#72232805	2
#72225801	2
#72225796	2
#72225791	2