Subgroups — #72341670

Order 2048.

At least 9682 conjugacy classes of subgroups; only the 2832 normal subgroups are shown.

The subgroup lattice has 581 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72341644	C₂	1	2	yes	maximal, complemented
2	#72293567	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#359552	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#359501	C₂	1	1	yes	maximal, characteristic, complemented
5	#72240113	C₂	1	2	yes	maximal, complemented
6	C₂×#394066	C₂	1	4	yes	maximal, complemented
7	C₂×#392109	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×#2403	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#7630939	C₂	1	1	yes	maximal, characteristic, complemented
10	#72225643	C₂	1	8	yes	maximal, complemented
11	#72219232	C₂	1	4	yes	maximal, complemented
12	C₂×#394058	C₂	1	2	yes	maximal, complemented
13	#72218744	C₂	1	2	yes	maximal, complemented
14	C₂²×#23900	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂⁶×D₄	C₂²	1	1	yes	characteristic
16	C₂⁶×D₄	C₂²	1	1	yes	characteristic, complemented
17	C₂²×#3484	C₂²	1	1	yes	characteristic
18	C₂²×#3484	C₂²	1	2	yes	complemented
19	C₂⁴×#120	C₂²	1	1	yes	characteristic
20	C₂⁴×#120	C₂²	1	1	yes	characteristic, complemented
21	C₂³×B(4,𝔽₂)	C₂²	1	2	yes	complemented
22	C₂²×#2846	C₂²	1	2	yes	—
23	C₂²×#2846	C₂²	1	2	yes	complemented
24	C₂×#34980	C₂²	1	2	yes	—
25	C₂×#34980	C₂²	1	4	yes	complemented
26	C₂²×#2403	C₂²	1	4	yes	—
27	C₂²×#2403	C₂²	1	4	yes	complemented
28	C₂×#34171	C₂²	1	1	yes	characteristic
29	C₂×#34171	C₂²	1	2	yes	complemented
30	C₂³×#386	C₂²	1	1	yes	characteristic
31	C₂³×#386	C₂²	1	1	yes	characteristic, complemented
32	C₂³×#379	C₂²	1	1	yes	characteristic, complemented
33	C₂²×#2021	C₂²	1	4	yes	complemented
34	C₂²×#2021	C₂²	1	8	yes	complemented
35	C₂²×#1898	C₂²	1	2	yes	complemented
36	C₂²×#1898	C₂²	1	2	yes	complemented
37	C₂²×#1889	C₂²	1	2	yes	complemented
38	C₂²×#1889	C₂²	1	4	yes	complemented
39	C₂²×#1790	C₂²	1	2	yes	complemented
40	C₂²×#1781	C₂²	1	1	yes	characteristic
41	C₂²×#1781	C₂²	1	1	yes	characteristic
42	C₂²×#1781	C₂²	1	2	yes	complemented
43	C₂²×#1781	C₂²	1	4	yes	complemented
44	C₂²×#1781	C₂²	1	4	yes	complemented
45	C₂×#14715	C₂²	1	8	yes	complemented
46	C₂×#14694	C₂²	1	2	yes	complemented
47	C₂×#14679	C₂²	1	2	yes	complemented
48	C₂×#14679	C₂²	1	2	yes	complemented
49	C₂×#10991	C₂²	1	8	yes	complemented
50	C₂×#10991	C₂²	1	4	yes	complemented
51	C₂×#10995	C₂²	1	4	yes	complemented
52	C₂×#10995	C₂²	1	8	yes	complemented
53	C₂×#10965	C₂²	1	8	yes	complemented
54	C₂×#10745	C₂²	1	2	yes	complemented
55	C₂×#10745	C₂²	1	4	yes	complemented
56	C₂×#10735	C₂²	1	2	yes	complemented
57	C₂×#10735	C₂²	1	2	yes	complemented
58	#154094	C₂²	1	8	yes	complemented
59	#154077	C₂²	1	2	yes	complemented
60	#123590	C₂²	1	8	yes	complemented
61	#123590	C₂²	1	4	yes	complemented
62	#123513	C₂²	1	8	yes	complemented
63	C₂⁸	D₄	1	1	yes	characteristic, complemented
64	C₂⁸	C₂³	1	1	yes	characteristic
65	C₂⁸	C₂³	1	1	yes	characteristic
66	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
67	C₂⁵×D₄	D₄	1	2	yes	complemented
68	C₂⁵×D₄	D₄	1	2	yes	complemented
69	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
70	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
71	C₂⁵×D₄	C₂³	1	1	yes	characteristic
72	C₂⁵×D₄	C₂³	1	2	yes	—
73	C₂⁵×D₄	C₂³	1	2	yes	—
74	C₂⁵×D₄	C₂³	1	1	yes	characteristic
75	C₂⁵×D₄	C₂³	1	4	yes	—
76	C₂⁶×C₄	D₄	1	1	yes	characteristic, complemented
77	C₂⁶×C₄	C₂³	1	1	yes	characteristic
78	C₂×#3484	D₄	1	8	yes	complemented
79	C₂²×#534	C₂³	1	2	yes	—
80	C₂²×#534	C₂³	1	4	yes	—
81	C₂³×#120	D₄	1	8	yes	complemented
82	C₂³×#120	D₄	1	8	yes	complemented
83	C₂³×#120	C₂³	1	2	yes	—
84	C₂³×#120	C₂³	1	2	yes	—
85	C₂³×#120	C₂³	1	4	yes	—
86	C₂³×#120	C₂³	1	2	yes	—
87	C₂³×#120	C₂³	1	4	yes	—
88	C₂³×#120	C₂³	1	4	yes	complemented
89	C₂²×#518	C₂³	1	1	yes	characteristic
90	C₂²×#518	C₂³	1	2	yes	—
91	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
92	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
93	C₂³×#99	C₂³	1	2	yes	—
94	C₂³×#99	C₂³	1	2	yes	—
95	C₂³×#99	C₂³	1	8	yes	—
96	C₂³×#99	C₂³	1	2	yes	—
97	C₂³×#99	C₂³	1	2	yes	—
98	C₂³×#99	C₂³	1	4	yes	complemented
99	C₂³×#99	C₂³	1	4	yes	complemented
100	#34980	D₄	1	16	yes	complemented
101	C₂×#2403	D₄	1	32	yes	complemented
102	#34171	D₄	1	8	yes	complemented
103	C₂×#2308	C₂³	1	4	yes	—
104	C₂×#2308	C₂³	1	2	yes	—
105	C₂²×#386	D₄	1	8	yes	complemented
106	C₂²×#386	C₂³	1	2	yes	—
107	C₂²×#386	C₂³	1	4	yes	—
108	C₂²×#386	C₂³	1	2	yes	—
109	C₂²×#386	C₂³	1	4	yes	complemented
110	C₂²×#379	D₄	1	8	yes	complemented
111	C₂²×#379	C₂³	1	2	yes	—
112	C₂²×#379	C₂³	1	4	yes	—
113	C₂²×#379	C₂³	1	2	yes	—
114	C₂²×#379	C₂³	1	8	yes	—
115	C₂²×#379	C₂³	1	2	yes	—
116	C₂²×#379	C₂³	1	4	yes	—
117	C₂²×#379	C₂³	1	4	yes	complemented
118	C₂²×#379	C₂³	1	8	yes	complemented
119	C₂×#1781	D₄	1	8	yes	complemented
120	C₂²×#342	C₂³	1	4	yes	complemented
121	C₂²×#342	C₂³	1	8	yes	complemented
122	C₂²×#342	C₂³	1	8	yes	complemented
123	C₂²×#342	C₂³	1	4	yes	complemented
124	C₂×C₂²⋊#95	C₂³	1	4	yes	complemented
125	C₂×C₂²⋊#95	C₂³	1	8	yes	complemented
126	C₂⁷	C₂×D₄	1	1	yes	characteristic
127	C₂⁷	C₂×D₄	1	8	yes	—
128	C₂⁷	C₂×D₄	1	1	yes	characteristic
129	C₂⁷	C₂×D₄	1	1	yes	characteristic
130	C₂⁷	C₂×D₄	1	2	yes	—
131	C₂⁷	C₂×D₄	1	2	yes	—
132	C₂⁷	C₂×D₄	1	2	yes	—
133	C₂⁷	C₂×D₄	1	1	yes	characteristic
134	C₂⁷	C₂×D₄	1	4	yes	complemented
135	C₂⁷	C₂⁴	1	2	yes	—
136	C₂⁷	C₂⁴	1	2	yes	—
137	C₂⁷	C₂⁴	1	1	yes	characteristic
138	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	complemented
139	C₂⁴×D₄	C₂×D₄	1	8	yes	—
140	C₂⁴×D₄	C₂×D₄	1	4	yes	—
141	C₂⁴×D₄	C₂×D₄	1	4	yes	—
142	C₂⁴×D₄	C₂×D₄	1	4	yes	—
143	C₂⁴×D₄	C₂×D₄	1	4	yes	—
144	C₂⁴×D₄	C₂×D₄	1	16	yes	—
145	C₂⁴×D₄	C₂×D₄	1	4	yes	—
146	C₂⁴×D₄	C₂×D₄	1	2	yes	—
147	C₂⁴×D₄	C₂×D₄	1	2	yes	—
148	C₂⁴×D₄	C₂×D₄	1	2	yes	—
149	C₂⁴×D₄	C₂×D₄	1	2	yes	—
150	C₂⁴×D₄	C₂×D₄	1	2	yes	—
151	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
152	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
153	C₂⁴×D₄	C₂×D₄	1	4	yes	—
154	C₂⁴×D₄	C₂×D₄	1	16	yes	complemented
155	C₂⁴×D₄	C₂×D₄	1	8	yes	complemented
156	C₂⁴×D₄	#41	1	4	yes	—
157	C₂⁴×D₄	C₂⁴	1	2	yes	—
158	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
159	C₂⁴×D₄	C₂⁴	1	2	yes	—
160	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
161	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
162	C₂⁵×C₄	C₂×D₄	1	2	yes	—
163	C₂⁵×C₄	C₂×D₄	1	2	yes	—
164	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
165	C₂⁵×C₄	C₂×D₄	1	4	yes	complemented
166	C₂⁵×C₄	C₂⁴	1	2	yes	—
167	C₂×#534	C₂×D₄	1	16	yes	complemented
168	C₂×#534	C₂×D₄	1	8	yes	complemented
169	C₂²×#120	C₂×D₄	1	8	yes	—
170	C₂²×#120	C₂×D₄	1	16	yes	—
171	C₂²×#120	C₂×D₄	1	8	yes	—
172	C₂²×#120	C₂×D₄	1	8	yes	—
173	C₂²×#120	C₂×D₄	1	8	yes	complemented
174	C₂²×#120	C₂×D₄	1	16	yes	complemented
175	C₂×#518	C₂×D₄	1	8	yes	complemented
176	C₂×#518	C₂×D₄	1	4	yes	complemented
177	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
178	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	—
179	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
180	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
181	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
182	C₂³×C₂²⋊C₄	C₂×D₄	1	16	yes	complemented
183	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
184	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
185	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
186	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
187	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
188	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
189	C₂²×#99	C₂×D₄	1	8	yes	complemented
190	C₂²×#99	C₂×D₄	1	8	yes	complemented
191	#2308	C₂×D₄	1	16	yes	complemented
192	#2308	C₂×D₄	1	8	yes	complemented
193	C₂×#386	C₂×D₄	1	8	yes	—
194	C₂×#386	C₂×D₄	1	16	yes	—
195	C₂×#386	C₂×D₄	1	8	yes	complemented
196	C₂×#386	C₂×D₄	1	16	yes	complemented
197	C₂×#379	C₂×D₄	1	8	yes	—
198	C₂×#379	C₂×D₄	1	8	yes	—
199	C₂×#379	C₂×D₄	1	8	yes	complemented
200	C₂×#379	C₂×D₄	1	16	yes	complemented
201	C₂⁶	#120	1	4	yes	—
202	C₂⁶	#120	1	4	yes	—
203	C₂⁶	#120	1	8	yes	—
204	C₂⁶	#120	1	4	yes	—
205	C₂⁶	#120	1	4	yes	—
206	C₂⁶	#120	1	4	yes	—
207	C₂⁶	#120	1	8	yes	complemented
208	C₂⁶	#121	1	4	yes	—
209	C₂⁶	C₂²×D₄	1	1	yes	characteristic
210	C₂⁶	C₂²×D₄	1	2	yes	—
211	C₂⁶	C₂²×D₄	1	8	yes	—
212	C₂⁶	C₂²×D₄	1	4	yes	—
213	C₂⁶	C₂²×D₄	1	2	yes	—
214	C₂⁶	C₂²×D₄	1	4	yes	—
215	C₂⁶	C₂²×D₄	1	8	yes	—
216	C₂⁶	C₂²×D₄	1	1	yes	characteristic
217	C₂⁶	C₂²×D₄	1	2	yes	—
218	C₂⁶	C₂²×D₄	1	2	yes	—
219	C₂⁶	C₂²×D₄	1	8	yes	—
220	C₂⁶	C₂²×D₄	1	1	yes	characteristic
221	C₂⁶	C₂²×D₄	1	1	yes	characteristic
222	C₂⁶	C₂²×D₄	1	2	yes	—
223	C₂⁶	C₂²×D₄	1	2	yes	—
224	C₂⁶	C₂²×D₄	1	4	yes	—
225	C₂⁶	C₂²×D₄	1	2	yes	—
226	C₂⁶	C₂²×D₄	1	2	yes	—
227	C₂⁶	C₂²×D₄	1	2	yes	—
228	C₂⁶	C₂×#41	1	2	yes	—
229	C₂⁶	H(5,𝔽₂)	1	8	yes	—
230	C₂⁶	H(5,𝔽₂)	1	4	yes	—
231	C₂⁶	H(5,𝔽₂)	1	4	yes	—
232	C₂⁶	C₂⁵	1	1	yes	characteristic
233	C₂³×D₄	#120	1	8	yes	—
234	C₂³×D₄	#120	1	4	yes	—
235	C₂³×D₄	#120	1	4	yes	—
236	C₂³×D₄	#120	1	4	yes	—
237	C₂³×D₄	#120	1	4	yes	—
238	C₂³×D₄	#120	1	16	yes	—
239	C₂³×D₄	#120	1	8	yes	complemented
240	C₂³×D₄	#120	1	8	yes	complemented
241	C₂³×D₄	#120	1	16	yes	complemented
242	C₂³×D₄	#121	1	4	yes	—
243	C₂³×D₄	#121	1	4	yes	—
244	C₂³×D₄	#121	1	16	yes	—
245	C₂³×D₄	#121	1	16	yes	—
246	C₂³×D₄	#127	1	16	yes	—
247	C₂³×D₄	C₂²×D₄	1	2	yes	—
248	C₂³×D₄	C₂²×D₄	1	2	yes	—
249	C₂³×D₄	C₂²×D₄	1	2	yes	—
250	C₂³×D₄	C₂²×D₄	1	2	yes	—
251	C₂³×D₄	C₂²×D₄	1	8	yes	—
252	C₂³×D₄	C₂²×D₄	1	8	yes	—
253	C₂³×D₄	C₂²×D₄	1	2	yes	—
254	C₂³×D₄	C₂²×D₄	1	2	yes	—
255	C₂³×D₄	C₂²×D₄	1	8	yes	—
256	C₂³×D₄	C₂²×D₄	1	2	yes	—
257	C₂³×D₄	C₂²×D₄	1	2	yes	—
258	C₂³×D₄	C₂²×D₄	1	4	yes	—
259	C₂³×D₄	C₂²×D₄	1	4	yes	—
260	C₂³×D₄	C₂²×D₄	1	2	yes	—
261	C₂³×D₄	C₂²×D₄	1	2	yes	—
262	C₂³×D₄	C₂×#41	1	2	yes	—
263	C₂³×D₄	C₂×#41	1	2	yes	—
264	C₂³×D₄	H(5,𝔽₂)	1	8	yes	—
265	C₂³×D₄	H(5,𝔽₂)	1	8	yes	—
266	C₂⁴×C₄	#120	1	4	yes	—
267	C₂⁴×C₄	#120	1	4	yes	—
268	C₂⁴×C₄	#120	1	4	yes	—
269	C₂⁴×C₄	#120	1	8	yes	complemented
270	C₂⁴×C₄	#121	1	4	yes	—
271	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
272	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
273	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
274	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
275	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
276	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
277	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
278	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
279	C₂×#120	#120	1	32	yes	complemented
280	C₂²×C₂²⋊C₄	#120	1	16	yes	complemented
281	C₂²×C₂²⋊C₄	#120	1	32	yes	complemented
282	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
283	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
284	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
285	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
286	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
287	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
288	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
289	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
290	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
291	#386	#120	1	32	yes	complemented
292	C₂⁵	#392	1	16	yes	complemented
293	C₂⁵	B(4,𝔽₂)	1	16	yes	complemented
294	C₂⁵	C₂×#120	1	4	yes	—
295	C₂⁵	C₂×#120	1	2	yes	—
296	C₂⁵	C₂×#120	1	2	yes	—
297	C₂⁵	C₂×#120	1	2	yes	—
298	C₂⁵	C₂×#120	1	2	yes	—
299	C₂⁵	C₂×#120	1	4	yes	—
300	C₂⁵	C₂×#120	1	4	yes	—
301	C₂⁵	C₂×#120	1	8	yes	—
302	C₂⁵	C₂×#120	1	8	yes	—
303	C₂⁵	C₂×#120	1	2	yes	—
304	C₂⁵	C₂×#120	1	2	yes	—
305	C₂⁵	C₂×#120	1	2	yes	—
306	C₂⁵	C₂×#120	1	4	yes	—
307	C₂⁵	C₂×#120	1	4	yes	—
308	C₂⁵	C₂×#120	1	4	yes	—
309	C₂⁵	C₂×#120	1	2	yes	—
310	C₂⁵	C₂×#120	1	2	yes	—
311	C₂⁵	C₂×#120	1	4	yes	—
312	C₂⁵	C₂×#120	1	2	yes	—
313	C₂⁵	C₂×#120	1	2	yes	—
314	C₂⁵	C₂×#120	1	2	yes	—
315	C₂⁵	C₂×#120	1	4	yes	—
316	C₂⁵	C₂×#120	1	4	yes	complemented
317	C₂⁵	C₂×#120	1	8	yes	complemented
318	C₂⁵	C₂×#121	1	2	yes	—
319	C₂⁵	C₂×#121	1	2	yes	—
320	C₂⁵	C₂×#121	1	4	yes	—
321	C₂⁵	C₂×#121	1	4	yes	—
322	C₂⁵	C₂×#121	1	2	yes	—
323	C₂⁵	C₂×#121	1	2	yes	—
324	C₂⁵	C₂×#127	1	4	yes	—
325	C₂⁵	#534	1	2	yes	—
326	C₂⁵	#534	1	2	yes	—
327	C₂⁵	#534	1	4	yes	—
328	C₂⁵	#534	1	4	yes	—
329	C₂⁵	#534	1	4	yes	—
330	C₂⁵	#534	1	2	yes	—
331	C₂⁵	#534	1	4	yes	—
332	C₂⁵	#534	1	8	yes	—
333	C₂⁵	#534	1	2	yes	—
334	C₂⁵	#535	1	8	yes	—
335	C₂⁵	D₄²	1	32	yes	—
336	C₂⁵	D₄²	1	8	yes	—
337	C₂⁵	D₄²	1	8	yes	—
338	C₂⁵	D₄²	1	8	yes	—
339	C₂⁵	D₄²	1	8	yes	—
340	C₂⁵	D₄²	1	8	yes	—
341	C₂⁵	D₄²	1	8	yes	—
342	C₂⁵	#546	1	8	yes	—
343	C₂⁵	#546	1	8	yes	—
344	C₂⁵	C₂³×D₄	1	1	yes	characteristic
345	C₂⁵	C₂³×D₄	1	2	yes	—
346	C₂⁵	C₂³×D₄	1	1	yes	characteristic
347	C₂⁵	C₂³×D₄	1	1	yes	characteristic
348	C₂⁵	C₂³×D₄	1	1	yes	characteristic
349	C₂⁵	C₂³×D₄	1	1	yes	characteristic
350	C₂⁵	C₂³×D₄	1	2	yes	—
351	C₂⁵	C₂³×D₄	1	4	yes	—
352	C₂⁵	C₂³×D₄	1	1	yes	characteristic
353	C₂⁵	C₂²×#41	1	1	yes	characteristic
354	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
355	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
356	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
357	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
358	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
359	C₂²×D₄	#392	1	16	yes	complemented
360	C₂²×D₄	#392	1	16	yes	complemented
361	C₂²×D₄	C₂×#120	1	8	yes	—
362	C₂²×D₄	C₂×#120	1	8	yes	—
363	C₂²×D₄	C₂×#120	1	4	yes	—
364	C₂²×D₄	C₂×#120	1	4	yes	—
365	C₂²×D₄	C₂×#121	1	4	yes	—
366	C₂²×D₄	C₂×#121	1	4	yes	—
367	C₂²×D₄	C₂×#121	1	4	yes	—
368	C₂²×D₄	C₂×#121	1	4	yes	—
369	C₂²×D₄	C₂×#127	1	4	yes	—
370	C₂²×D₄	C₂×#127	1	4	yes	—
371	C₂²×D₄	#534	1	8	yes	—
372	C₂²×D₄	#535	1	8	yes	—
373	C₂²×D₄	D₄²	1	32	yes	—
374	C₂²×D₄	D₄²	1	16	yes	—
375	C₂²×D₄	D₄²	1	16	yes	—
376	C₂²×D₄	D₄²	1	16	yes	—
377	C₂²×D₄	#546	1	16	yes	—
378	C₂³×C₄	#392	1	16	yes	complemented
379	C₂³×C₄	C₂×#120	1	2	yes	—
380	C₂³×C₄	C₂×#120	1	2	yes	—
381	C₂³×C₄	C₂×#120	1	4	yes	—
382	C₂³×C₄	C₂×#120	1	4	yes	—
383	C₂³×C₄	C₂×#120	1	2	yes	—
384	C₂³×C₄	C₂×#120	1	4	yes	—
385	C₂³×C₄	C₂×#120	1	2	yes	—
386	C₂³×C₄	C₂×#120	1	4	yes	complemented
387	C₂³×C₄	C₂×#120	1	8	yes	complemented
388	C₂³×C₄	C₂×#120	1	16	yes	complemented
389	C₂³×C₄	C₂×#120	1	8	yes	complemented
390	C₂³×C₄	C₂×#121	1	2	yes	—
391	C₂³×C₄	C₂×#121	1	2	yes	—
392	C₂³×C₄	#534	1	4	yes	—
393	C₂³×C₄	#534	1	4	yes	—
394	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	complemented
395	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	complemented
396	C₂⁴	C₂×#392	1	4	yes	—
397	C₂⁴	C₂×#392	1	4	yes	—
398	C₂⁴	C₂×#392	1	4	yes	—
399	C₂⁴	C₂×#392	1	4	yes	—
400	C₂⁴	#2403	1	8	yes	—
401	C₂⁴	#2403	1	8	yes	—
402	C₂⁴	#2403	1	4	yes	—
403	C₂⁴	#2403	1	4	yes	—
404	C₂⁴	#2403	1	16	yes	—
405	C₂⁴	#2403	1	4	yes	—
406	C₂⁴	#2403	1	8	yes	—
407	C₂⁴	#2403	1	4	yes	—
408	C₂⁴	#2403	1	8	yes	—
409	C₂⁴	#2408	1	16	yes	—
410	C₂⁴	#2410	1	4	yes	—
411	C₂⁴	#2410	1	4	yes	—
412	C₂⁴	#2410	1	16	yes	—
413	C₂⁴	#2410	1	4	yes	—
414	C₂⁴	#2410	1	4	yes	—
415	C₂⁴	#2410	1	8	yes	—
416	C₂⁴	#2433	1	16	yes	—
417	C₂⁴	#2613	1	4	yes	—
418	C₂⁴	#2613	1	4	yes	—
419	C₂⁴	#2613	1	4	yes	—
420	C₂⁴	#2846	1	4	yes	—
421	C₂⁴	#2846	1	4	yes	—
422	C₂⁴	#2846	1	4	yes	—
423	C₂⁴	C₂×B(4,𝔽₂)	1	16	yes	—
424	C₂⁴	C₂×B(4,𝔽₂)	1	8	yes	—
425	C₂⁴	#3026	1	8	yes	—
426	C₂⁴	C₂²×#120	1	1	yes	characteristic
427	C₂⁴	C₂²×#120	1	2	yes	—
428	C₂⁴	C₂²×#120	1	1	yes	characteristic
429	C₂⁴	C₂²×#120	1	1	yes	characteristic
430	C₂⁴	C₂²×#120	1	2	yes	—
431	C₂⁴	C₂²×#120	1	2	yes	—
432	C₂⁴	C₂²×#120	1	2	yes	—
433	C₂⁴	C₂²×#120	1	2	yes	—
434	C₂⁴	C₂²×#120	1	1	yes	characteristic
435	C₂⁴	C₂²×#120	1	1	yes	characteristic
436	C₂⁴	C₂²×#121	1	1	yes	characteristic
437	C₂⁴	C₂²×#121	1	1	yes	characteristic
438	C₂⁴	C₂²×#121	1	1	yes	characteristic
439	C₂⁴	C₂²×#127	1	1	yes	characteristic
440	C₂⁴	C₂×#534	1	1	yes	characteristic
441	C₂⁴	C₂×#534	1	1	yes	characteristic
442	C₂⁴	C₂×#534	1	2	yes	—
443	C₂⁴	C₂×#534	1	2	yes	—
444	C₂⁴	C₂×#534	1	2	yes	—
445	C₂⁴	C₂×#534	1	2	yes	—
446	C₂⁴	C₂×#534	1	2	yes	—
447	C₂⁴	C₂×#535	1	2	yes	—
448	C₂⁴	C₂×#535	1	2	yes	—
449	C₂⁴	C₂×D₄²	1	2	yes	—
450	C₂⁴	C₂×D₄²	1	2	yes	—
451	C₂⁴	C₂×D₄²	1	2	yes	—
452	C₂⁴	C₂×D₄²	1	8	yes	—
453	C₂⁴	C₂×D₄²	1	2	yes	—
454	C₂⁴	C₂×D₄²	1	4	yes	—
455	C₂⁴	C₂×D₄²	1	2	yes	—
456	C₂⁴	C₂×D₄²	1	4	yes	—
457	C₂⁴	C₂×D₄²	1	2	yes	—
458	C₂⁴	C₂×D₄²	1	4	yes	—
459	C₂⁴	C₂×D₄²	1	8	yes	—
460	C₂⁴	C₂×#546	1	2	yes	—
461	C₂⁴	C₂×#546	1	2	yes	—
462	C₂⁴	C₂×#546	1	4	yes	—
463	C₂⁴	#3484	1	8	yes	—
464	C₂⁴	#3484	1	4	yes	—
465	C₂⁴	#3484	1	2	yes	—
466	C₂⁴	#3484	1	2	yes	—
467	C₂⁴	#3484	1	8	yes	—
468	C₂⁴	#3484	1	8	yes	—
469	C₂⁴	#3484	1	8	yes	—
470	C₂⁴	#3484	1	2	yes	—
471	C₂⁴	#3484	1	4	yes	—
472	C₂⁴	#3484	1	2	yes	—
473	C₂⁴	#3484	1	4	yes	—
474	C₂⁴	#3490	1	4	yes	—
475	C₂⁴	#3532	1	8	yes	—
476	C₂⁴	#3532	1	8	yes	—
477	C₂×D₄	#2403	1	16	yes	—
478	C₂×D₄	#2408	1	16	yes	—
479	C₂×D₄	#2410	1	16	yes	—
480	C₂×D₄	#2433	1	16	yes	—
481	C₂²×C₄	C₂×#392	1	4	yes	—
482	C₂²×C₄	C₂×#392	1	4	yes	—
483	C₂²×C₄	#2403	1	8	yes	—
484	C₂²×C₄	#2403	1	8	yes	—
485	C₂²×C₄	#2410	1	8	yes	—
486	C₂²×C₄	#2613	1	4	yes	—
487	C₂²×C₄	#2846	1	4	yes	—
488	C₂³	#14715	1	8	yes	—
489	C₂³	#14715	1	8	yes	—
490	C₂³	#14715	1	8	yes	complemented
491	C₂³	#23900	1	8	yes	—
492	C₂³	#23900	1	16	yes	complemented
493	C₂³	#23903	1	8	yes	—
494	C₂³	#24404	1	16	yes	—
495	C₂³	#32898	1	16	yes	—
496	C₂³	C₂²×#392	1	1	yes	characteristic
497	C₂³	C₂×#2613	1	1	yes	characteristic
498	C₂³	C₂×#2613	1	1	yes	characteristic
499	C₂³	C₂×#2403	1	2	yes	—
500	C₂³	C₂×#2403	1	1	yes	characteristic
501	C₂³	C₂×#2403	1	2	yes	—
502	C₂³	C₂×#2403	1	2	yes	—
503	C₂³	C₂×#2403	1	2	yes	—
504	C₂³	C₂×#2403	1	2	yes	—
505	C₂³	C₂×#2403	1	1	yes	characteristic
506	C₂³	C₂×#2410	1	2	yes	—
507	C₂³	C₂×#2410	1	1	yes	characteristic
508	C₂³	C₂×#2410	1	2	yes	—
509	C₂³	C₂×#2410	1	2	yes	—
510	C₂³	C₂×#2410	1	1	yes	characteristic
511	C₂³	C₂×#2408	1	2	yes	—
512	C₂³	C₂×#2408	1	2	yes	—
513	C₂³	C₂×#2433	1	2	yes	—
514	C₂³	C₂×#2433	1	2	yes	—
515	C₂³	#34980	1	2	yes	—
516	C₂³	#34980	1	1	yes	characteristic
517	C₂³	#34980	1	1	yes	characteristic
518	C₂³	#34980	1	2	yes	—
519	C₂³	#34980	1	2	yes	—
520	C₂³	#34980	1	2	yes	—
521	C₂³	#34980	1	2	yes	—
522	C₂³	#34981	1	2	yes	—
523	C₂³	#35346	1	2	yes	—
524	C₂³	#35348	1	2	yes	—
525	C₂³	#35348	1	2	yes	—
526	C₂³	#35390	1	2	yes	—
527	C₂³	D₄×#120	1	8	yes	—
528	C₂³	D₄×#120	1	4	yes	—
529	C₂³	D₄×#120	1	8	yes	—
530	C₂³	D₄×#120	1	4	yes	—
531	C₂³	D₄×#120	1	4	yes	—
532	C₂³	D₄×#120	1	4	yes	—
533	C₂³	C₂×#2846	1	1	yes	characteristic
534	C₂³	C₂×#2846	1	1	yes	characteristic
535	C₂³	#37436	1	2	yes	—
536	C₂³	#37436	1	2	yes	—
537	C₂³	#37644	1	4	yes	—
538	C₂³	#37644	1	8	yes	—
539	C₂³	#37644	1	4	yes	—
540	C₂³	#37645	1	4	yes	—
541	C₂³	#37645	1	4	yes	—
542	C₂³	#37645	1	8	yes	—
543	C₂³	#58990	1	8	yes	—
544	C₂³	#58990	1	8	yes	—
545	C₂³	#58991	1	8	yes	—
546	C₂³	#58991	1	8	yes	—
547	C₂³	C₂²×B(4,𝔽₂)	1	4	yes	—
548	C₂³	C₂×#3026	1	4	yes	—
549	C₂×C₄	#14715	1	8	yes	complemented
550	C₂²	#394066	1	16	yes	complemented
551	C₂²	C₂×#14715	1	1	yes	characteristic
552	C₂²	C₂×#14715	1	1	yes	characteristic
553	C₂²	#612424	1	1	yes	characteristic
554	C₂²	#612424	1	2	yes	—
555	C₂²	#612424	1	1	yes	characteristic
556	C₂²	#635984	1	1	yes	characteristic
557	C₂²	#635984	1	2	yes	—
558	C₂²	#635984	1	1	yes	characteristic
559	C₂²	#647656	1	4	yes	—
560	C₂²	#647670	1	4	yes	—
561	C₂²	#647670	1	4	yes	—
562	C₂²	#648360	1	4	yes	—
563	C₂²	#759288	1	2	yes	—
564	C₂²	#759288	1	2	yes	—
565	C₂²	#5955303	1	1	yes	characteristic
566	C₂²	C₂×#23900	1	4	yes	—
567	C₂²	C₂×#23900	1	2	yes	—
568	C₂²	C₂×#23903	1	2	yes	—
569	C₂²	#6437621	1	4	yes	—
570	C₂²	C₂×#24404	1	4	yes	—
571	C₂²	#6470225	1	8	yes	—
572	C₂²	C₂×#32898	1	4	yes	—
573	C₂	#72214832	1	4	yes	—
574	C₂	#72215858	1	1	yes	characteristic
575	C₂	C₂×#394066	1	2	yes	—
576	C₂	#72236727	1	1	yes	characteristic
577	C₂	#72251131	1	4	yes	—
578	C₂	#72294303	1	2	yes	—
579	C₂	#72341629	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴	C₂²×#120
commutator, Frattini, cosocle	C₂⁶	C₂⁵
LCS	G ▷ C₂⁶ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴ ◁ C₂⁸ ◁ G
LECS	G ▷ C₂⁶ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72341644	C₂	semidirect
2. #72293567	C₂	semidirect
3. C₂×#359552	C₂	semidirect
4. C₂×#359501	C₂	semidirect
5. #72240113	C₂	semidirect
6. C₂×#394066	C₂	semidirect
7. C₂×#392109	C₂	semidirect
8. C₂³×#2403	C₂	semidirect
9. C₂×#7630939	C₂	semidirect
10. #72225643	C₂	semidirect
11. #72219232	C₂	semidirect
12. C₂×#394058	C₂	semidirect
13. #72218744	C₂	semidirect
14. C₂²×#23900	C₂	semidirect
16. C₂⁶×D₄	C₂²	semidirect
18. C₂²×#3484	C₂²	semidirect
20. C₂⁴×#120	C₂²	semidirect
21. C₂³×B(4,𝔽₂)	C₂²	semidirect
23. C₂²×#2846	C₂²	semidirect
25. C₂×#34980	C₂²	semidirect
27. C₂²×#2403	C₂²	semidirect
29. C₂×#34171	C₂²	semidirect
31. C₂³×#386	C₂²	semidirect
32. C₂³×#379	C₂²	semidirect
33. C₂²×#2021	C₂²	semidirect
34. C₂²×#2021	C₂²	semidirect
35. C₂²×#1898	C₂²	semidirect
36. C₂²×#1898	C₂²	semidirect
37. C₂²×#1889	C₂²	semidirect
38. C₂²×#1889	C₂²	semidirect
39. C₂²×#1790	C₂²	semidirect
42. C₂²×#1781	C₂²	semidirect
43. C₂²×#1781	C₂²	semidirect
44. C₂²×#1781	C₂²	semidirect
45. C₂×#14715	C₂²	semidirect
46. C₂×#14694	C₂²	semidirect
47. C₂×#14679	C₂²	semidirect
48. C₂×#14679	C₂²	semidirect
49. C₂×#10991	C₂²	semidirect
50. C₂×#10991	C₂²	semidirect
51. C₂×#10995	C₂²	semidirect
52. C₂×#10995	C₂²	semidirect
53. C₂×#10965	C₂²	semidirect
54. C₂×#10745	C₂²	semidirect
55. C₂×#10745	C₂²	semidirect
56. C₂×#10735	C₂²	semidirect
57. C₂×#10735	C₂²	semidirect
58. #154094	C₂²	semidirect
59. #154077	C₂²	semidirect
60. #123590	C₂²	semidirect
61. #123590	C₂²	semidirect
62. #123513	C₂²	semidirect
63. C₂⁸	D₄	semidirect
67. C₂⁵×D₄	D₄	semidirect
68. C₂⁵×D₄	D₄	semidirect
69. C₂⁵×D₄	D₄	semidirect
70. C₂⁵×D₄	D₄	semidirect
76. C₂⁶×C₄	D₄	semidirect
78. C₂×#3484	D₄	semidirect
81. C₂³×#120	D₄	semidirect
82. C₂³×#120	D₄	semidirect
88. C₂³×#120	C₂³	semidirect
98. C₂³×#99	C₂³	semidirect
99. C₂³×#99	C₂³	semidirect
100. #34980	D₄	semidirect
101. C₂×#2403	D₄	semidirect
102. #34171	D₄	semidirect
105. C₂²×#386	D₄	semidirect
109. C₂²×#386	C₂³	semidirect
110. C₂²×#379	D₄	semidirect
117. C₂²×#379	C₂³	semidirect
118. C₂²×#379	C₂³	semidirect
119. C₂×#1781	D₄	semidirect
120. C₂²×#342	C₂³	semidirect
121. C₂²×#342	C₂³	semidirect
122. C₂²×#342	C₂³	semidirect
123. C₂²×#342	C₂³	semidirect
124. C₂×C₂²⋊#95	C₂³	semidirect
125. C₂×C₂²⋊#95	C₂³	semidirect
134. C₂⁷	C₂×D₄	semidirect
138. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
154. C₂⁴×D₄	C₂×D₄	semidirect
155. C₂⁴×D₄	C₂×D₄	semidirect
165. C₂⁵×C₄	C₂×D₄	semidirect
167. C₂×#534	C₂×D₄	semidirect
168. C₂×#534	C₂×D₄	semidirect
173. C₂²×#120	C₂×D₄	semidirect
174. C₂²×#120	C₂×D₄	semidirect
175. C₂×#518	C₂×D₄	semidirect
176. C₂×#518	C₂×D₄	semidirect
179. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
180. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
181. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
182. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
189. C₂²×#99	C₂×D₄	semidirect
190. C₂²×#99	C₂×D₄	semidirect
191. #2308	C₂×D₄	semidirect
192. #2308	C₂×D₄	semidirect
195. C₂×#386	C₂×D₄	semidirect
196. C₂×#386	C₂×D₄	semidirect
199. C₂×#379	C₂×D₄	semidirect
200. C₂×#379	C₂×D₄	semidirect
207. C₂⁶	#120	semidirect
239. C₂³×D₄	#120	semidirect
240. C₂³×D₄	#120	semidirect
241. C₂³×D₄	#120	semidirect
269. C₂⁴×C₄	#120	semidirect
279. C₂×#120	#120	semidirect
280. C₂²×C₂²⋊C₄	#120	semidirect
281. C₂²×C₂²⋊C₄	#120	semidirect
291. #386	#120	semidirect
292. C₂⁵	#392	semidirect
293. C₂⁵	B(4,𝔽₂)	semidirect
316. C₂⁵	C₂×#120	semidirect
317. C₂⁵	C₂×#120	semidirect
359. C₂²×D₄	#392	semidirect
360. C₂²×D₄	#392	semidirect
378. C₂³×C₄	#392	semidirect
386. C₂³×C₄	C₂×#120	semidirect
387. C₂³×C₄	C₂×#120	semidirect
388. C₂³×C₄	C₂×#120	semidirect
389. C₂³×C₄	C₂×#120	semidirect
394. C₂×C₂²⋊C₄	C₂×#120	semidirect
395. C₂×C₂²⋊C₄	C₂×#120	semidirect
490. C₂³	#14715	semidirect
492. C₂³	#23900	semidirect
549. C₂×C₄	#14715	semidirect
550. C₂²	#394066	semidirect

Maximal subgroups

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

subgroup	index
#72341644	2
#72293567	2
C₂×#359552	2
C₂×#359501	2
#72240113	2
C₂×#394066	2
C₂×#392109	2
C₂³×#2403	2
C₂×#7630939	2
#72225643	2
#72219232	2
C₂×#394058	2
#72218744	2
C₂²×#23900	2