Subgroups — C₂⁴×#3532 #72295524

Order 2048.

11981096 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×H(3,𝔽₄)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×#560	C₂	1	3	yes	maximal, complemented
3	C₂⁴×#538	C₂	1	6	yes	maximal, complemented
4	C₂⁴×#551	C₂	1	3	yes	maximal, complemented
5	C₂⁴×#535	C₂	1	3	yes	maximal, complemented
6	C₂⁴×#546	C₂	1	6	yes	maximal, complemented
7	C₂⁴×#534	C₂	1	3	yes	maximal, complemented
8	C₂⁵×#120	C₂	1	3	yes	maximal, complemented
9	C₂³×#3532	C₂	1	480	yes	maximal, direct product factor
10	C₂⁴×D₄²	C₂	1	3	yes	maximal, complemented
11	C₂⁹	C₂²	1	1	yes	characteristic, complemented
12	C₂⁵×#41	C₂²	1	3	yes	complemented
13	C₂⁶×D₄	C₂²	1	6	yes	complemented
14	C₂⁶×D₄	C₂²	1	3	yes	complemented
15	C₂⁶×D₄	C₂²	1	3	yes	complemented
16	C₂²×#3532	C₂²	1	35840	yes	direct product factor
17	C₂³×H(3,𝔽₄)	C₂²	1	240	yes	complemented
18	C₂³×#560	C₂²	1	720	yes	complemented
19	C₂³×#551	C₂²	1	720	yes	complemented
20	C₂³×#546	C₂²	1	1440	yes	complemented
21	C₂³×D₄²	C₂²	1	720	yes	complemented
22	C₂³×#535	C₂²	1	720	yes	complemented
23	C₂³×#538	C₂²	1	1440	yes	complemented
24	C₂³×#534	C₂²	1	720	yes	complemented
25	C₂⁴×#127	C₂²	1	3	yes	complemented
26	C₂⁴×#127	C₂²	1	1	yes	characteristic, complemented
27	C₂⁴×#126	C₂²	1	6	yes	complemented
28	C₂⁴×#126	C₂²	1	2	yes	complemented
29	C₂⁴×#124	C₂²	1	3	yes	complemented
30	C₂⁴×#124	C₂²	1	3	yes	complemented
31	C₂⁴×#124	C₂²	1	6	yes	complemented
32	C₂⁴×#123	C₂²	1	6	yes	complemented
33	C₂⁴×#123	C₂²	1	3	yes	complemented
34	C₂⁴×#123	C₂²	1	3	yes	complemented
35	C₂⁴×#123	C₂²	1	6	yes	complemented
36	C₂⁴×C₂²⋊Q₈	C₂²	1	6	yes	complemented
37	C₂⁴×#121	C₂²	1	6	yes	complemented
38	C₂⁴×#121	C₂²	1	6	yes	complemented
39	C₂⁴×#121	C₂²	1	6	yes	complemented
40	C₂⁴×#121	C₂²	1	6	yes	complemented
41	C₂⁴×#121	C₂²	1	6	yes	complemented
42	C₂⁴×#120	C₂²	1	3	yes	—
43	C₂⁴×#120	C₂²	1	6	yes	complemented
44	C₂⁴×#120	C₂²	1	6	yes	complemented
45	C₂⁴×#120	C₂²	1	3	yes	complemented
46	C₂⁴×#120	C₂²	1	3	yes	complemented
47	C₂⁴×#120	C₂²	1	3	yes	complemented
48	C₂⁴×#120	C₂²	1	3	yes	complemented
49	C₂⁴×#120	C₂²	1	1	yes	characteristic, complemented
50	C₂⁴×#120	C₂²	1	6	yes	complemented
51	C₂⁴×#120	C₂²	1	720	yes	complemented
52	C₂⁴×C₄×D₄	C₂²	1	6	yes	complemented
53	C₂⁴×C₄×D₄	C₂²	1	6	yes	complemented
54	C₂⁴×#117	C₂²	1	3	yes	complemented
55	C₂⁵×C₂²⋊C₄	C₂²	1	6	yes	complemented
56	C₂⁵×C₂²⋊C₄	C₂²	1	3	yes	complemented
57	C₂⁵×C₂²⋊C₄	C₂²	1	3	yes	complemented
58	C₂⁸	—	4	96	no	—
59	C₂⁸	C₂³	1	3	yes	—
60	C₂⁸	C₂³	1	3	yes	—
61	C₂⁸	C₂³	1	3	yes	—
62	C₂⁸	C₂³	1	1	yes	characteristic
63	C₂⁸	C₂³	1	120	yes	complemented
64	C₂⁸	C₂³	1	1	yes	characteristic, complemented
65	C₂⁴×#41	—	4	96	no	—
66	C₂⁴×#41	C₂³	1	360	yes	complemented
67	C₂⁵×Q₈	C₂³	1	3	yes	complemented
68	C₂⁵×D₄	—	4	96	no	—
69	C₂⁵×D₄	—	4	192	no	—
70	C₂⁵×D₄	—	4	96	no	—
71	C₂⁵×D₄	C₂³	1	6	yes	—
72	C₂⁵×D₄	C₂³	1	6	yes	—
73	C₂⁵×D₄	C₂³	1	3	yes	—
74	C₂⁵×D₄	C₂³	1	3	yes	—
75	C₂⁵×D₄	C₂³	1	6	yes	—
76	C₂⁵×D₄	C₂³	1	3	yes	—
77	C₂⁵×D₄	C₂³	1	6	yes	—
78	C₂⁵×D₄	C₂³	1	3	yes	—
79	C₂⁵×D₄	C₂³	1	360	yes	complemented
80	C₂⁵×D₄	C₂³	1	720	yes	complemented
81	C₂⁵×D₄	C₂³	1	3	yes	complemented
82	C₂⁵×D₄	C₂³	1	6	yes	complemented
83	C₂⁵×D₄	C₂³	1	360	yes	complemented
84	C₂⁶×C₄	C₂³	1	3	yes	—
85	C₂⁶×C₄	C₂³	1	6	yes	—
86	C₂⁶×C₄	C₂³	1	6	yes	complemented
87	C₂⁶×C₄	C₂³	1	3	yes	complemented
88	C₂×#3532	C₂³	1	491520	yes	direct product factor
89	C₂²×#551	C₂³	1	26880	yes	complemented
90	C₂²×#546	C₂³	1	53760	yes	complemented
91	C₂²×D₄²	C₂³	1	26880	yes	complemented
92	C₂²×H(3,𝔽₄)	C₂³	1	8960	yes	complemented
93	C₂²×#560	C₂³	1	26880	yes	complemented
94	C₂²×#535	C₂³	1	26880	yes	complemented
95	C₂²×#538	C₂³	1	53760	yes	complemented
96	C₂²×#534	C₂³	1	26880	yes	complemented
97	C₂³×#127	C₂³	1	120	yes	complemented
98	C₂³×#127	C₂³	1	360	yes	complemented
99	C₂³×#126	C₂³	1	240	yes	complemented
100	C₂³×#126	C₂³	1	720	yes	complemented
101	C₂³×#124	C₂³	1	360	yes	complemented
102	C₂³×#124	C₂³	1	720	yes	complemented
103	C₂³×#124	C₂³	1	360	yes	complemented
104	C₂³×#123	C₂³	1	720	yes	complemented
105	C₂³×#123	C₂³	1	360	yes	complemented
106	C₂³×#123	C₂³	1	360	yes	complemented
107	C₂³×#123	C₂³	1	720	yes	complemented
108	C₂³×C₂²⋊Q₈	C₂³	1	720	yes	complemented
109	C₂³×#121	C₂³	1	720	yes	complemented
110	C₂³×#121	C₂³	1	720	yes	complemented
111	C₂³×#121	C₂³	1	720	yes	complemented
112	C₂³×#121	C₂³	1	720	yes	complemented
113	C₂³×#121	C₂³	1	720	yes	complemented
114	C₂³×#120	C₂³	1	360	yes	—
115	C₂³×#120	C₂³	1	720	yes	complemented
116	C₂³×#120	C₂³	1	720	yes	complemented
117	C₂³×#120	C₂³	1	360	yes	complemented
118	C₂³×#120	C₂³	1	360	yes	complemented
119	C₂³×#120	C₂³	1	360	yes	complemented
120	C₂³×#120	C₂³	1	120	yes	complemented
121	C₂³×#120	C₂³	1	360	yes	complemented
122	C₂³×#120	C₂³	1	720	yes	complemented
123	C₂³×#120	C₂³	1	26880	yes	complemented
124	C₂³×C₄×D₄	C₂³	1	720	yes	complemented
125	C₂³×C₄×D₄	C₂³	1	720	yes	complemented
126	C₂³×#117	C₂³	1	360	yes	complemented
127	C₂⁴×C₄⋊C₄	C₂³	1	6	yes	complemented
128	C₂⁴×C₄⋊C₄	C₂³	1	6	yes	complemented
129	C₂⁴×C₄⋊C₄	C₂³	1	6	yes	complemented
130	C₂⁴×C₂²⋊C₄	C₂³	1	6	yes	—
131	C₂⁴×C₂²⋊C₄	C₂³	1	6	yes	—
132	C₂⁴×C₂²⋊C₄	C₂³	1	3	yes	—
133	C₂⁴×C₂²⋊C₄	C₂³	1	6	yes	—
134	C₂⁴×C₂²⋊C₄	C₂³	1	6	yes	—
135	C₂⁴×C₂²⋊C₄	C₂³	1	6	yes	—
136	C₂⁴×C₂²⋊C₄	C₂³	1	3	yes	—
137	C₂⁴×C₂²⋊C₄	C₂³	1	360	yes	complemented
138	C₂⁴×C₂²⋊C₄	C₂³	1	720	yes	complemented
139	C₂⁴×C₂²⋊C₄	C₂³	1	3	yes	complemented
140	C₂⁴×C₂²⋊C₄	C₂³	1	3	yes	complemented
141	C₂⁴×C₂²⋊C₄	C₂³	1	6	yes	complemented
142	C₂⁴×C₂²⋊C₄	C₂³	1	6	yes	complemented
143	C₂⁴×C₂²⋊C₄	C₂³	1	360	yes	complemented
144	C₂⁴×C₄²	C₂³	1	1	yes	characteristic, complemented
145	C₂⁴×C₄²	C₂³	1	3	yes	complemented
146	C₂⁴×C₄²	C₂³	1	2	yes	complemented
147	C₂⁷	—	2	192	no	—
148	C₂⁷	—	2	96	no	—
149	C₂⁷	—	2	96	no	—
150	C₂⁷	—	4	48	no	—
151	C₂⁷	—	4	96	no	—
152	C₂⁷	—	4	48	no	—
153	C₂⁷	—	4	5760	no	—
154	C₂⁷	—	4	96	no	—
155	C₂⁷	—	4	48	no	—
156	C₂⁷	—	4	4096	no	—
157	C₂⁷	C₂⁴	1	3	yes	—
158	C₂⁷	C₂⁴	1	3	yes	—
159	C₂⁷	C₂⁴	1	3	yes	—
160	C₂⁷	C₂⁴	1	1	yes	characteristic
161	C₂⁷	C₂⁴	1	180	yes	—
162	C₂⁷	C₂⁴	1	3	yes	—
163	C₂⁷	C₂⁴	1	180	yes	—
164	C₂⁷	C₂⁴	1	180	yes	—
165	C₂⁷	C₂⁴	1	60	yes	—
166	C₂⁷	C₂⁴	1	2240	yes	complemented
167	C₂⁷	C₂⁴	1	60	yes	complemented
168	C₂³×#41	—	4	5760	no	—
169	C₂³×#41	C₂⁴	1	6720	yes	complemented
170	C₂⁴×Q₈	—	4	48	no	—
171	C₂⁴×Q₈	C₂⁴	1	180	yes	complemented
172	C₂⁴×D₄	—	2	192	no	—
173	C₂⁴×D₄	—	2	192	no	—
174	C₂⁴×D₄	—	4	48	no	—
175	C₂⁴×D₄	—	4	48	no	—
176	C₂⁴×D₄	—	4	48	no	—
177	C₂⁴×D₄	—	4	48	no	—
178	C₂⁴×D₄	—	4	96	no	—
179	C₂⁴×D₄	—	4	96	no	—
180	C₂⁴×D₄	—	4	5760	no	—
181	C₂⁴×D₄	—	4	96	no	—
182	C₂⁴×D₄	—	4	48	no	—
183	C₂⁴×D₄	—	4	11520	no	—
184	C₂⁴×D₄	—	4	5760	no	—
185	C₂⁴×D₄	C₂⁴	1	360	yes	—
186	C₂⁴×D₄	C₂⁴	1	360	yes	—
187	C₂⁴×D₄	C₂⁴	1	180	yes	—
188	C₂⁴×D₄	C₂⁴	1	180	yes	—
189	C₂⁴×D₄	C₂⁴	1	360	yes	—
190	C₂⁴×D₄	C₂⁴	1	180	yes	—
191	C₂⁴×D₄	C₂⁴	1	360	yes	—
192	C₂⁴×D₄	C₂⁴	1	180	yes	—
193	C₂⁴×D₄	C₂⁴	1	6720	yes	complemented
194	C₂⁴×D₄	C₂⁴	1	13440	yes	complemented
195	C₂⁴×D₄	C₂⁴	1	360	yes	complemented
196	C₂⁴×D₄	C₂⁴	1	180	yes	complemented
197	C₂⁴×D₄	C₂⁴	1	6720	yes	complemented
198	C₂⁵×C₄	—	2	96	no	—
199	C₂⁵×C₄	—	4	96	no	—
200	C₂⁵×C₄	—	4	48	no	—
201	C₂⁵×C₄	—	4	96	no	—
202	C₂⁵×C₄	C₂⁴	1	180	yes	—
203	C₂⁵×C₄	C₂⁴	1	3	yes	—
204	C₂⁵×C₄	C₂⁴	1	6	yes	—
205	C₂⁵×C₄	C₂⁴	1	6	yes	—
206	C₂⁵×C₄	C₂⁴	1	3	yes	—
207	C₂⁵×C₄	C₂⁴	1	360	yes	—
208	C₂⁵×C₄	C₂⁴	1	180	yes	complemented
209	C₂⁵×C₄	C₂⁴	1	360	yes	complemented
210	#3532	C₂⁴	1	1048576	yes	direct product factor
211	C₂×H(3,𝔽₄)	C₂⁴	1	61440	yes	complemented
212	C₂×#560	C₂⁴	1	184320	yes	complemented
213	C₂×#551	C₂⁴	1	184320	yes	complemented
214	C₂×#546	C₂⁴	1	368640	yes	complemented
215	C₂×D₄²	C₂⁴	1	184320	yes	complemented
216	C₂×#538	C₂⁴	1	368640	yes	complemented
217	C₂×#535	C₂⁴	1	184320	yes	complemented
218	C₂×#534	C₂⁴	1	184320	yes	complemented
219	C₂²×#127	C₂⁴	1	2240	yes	complemented
220	C₂²×#127	C₂⁴	1	6720	yes	complemented
221	C₂²×#126	C₂⁴	1	4480	yes	complemented
222	C₂²×#126	C₂⁴	1	13440	yes	complemented
223	C₂²×#124	C₂⁴	1	6720	yes	complemented
224	C₂²×#124	C₂⁴	1	13440	yes	complemented
225	C₂²×#124	C₂⁴	1	6720	yes	complemented
226	C₂²×#123	C₂⁴	1	6720	yes	complemented
227	C₂²×#123	C₂⁴	1	6720	yes	complemented
228	C₂²×#123	C₂⁴	1	13440	yes	complemented
229	C₂²×#123	C₂⁴	1	13440	yes	complemented
230	C₂²×C₂²⋊Q₈	C₂⁴	1	13440	yes	complemented
231	C₂²×#121	C₂⁴	1	13440	yes	complemented
232	C₂²×#121	C₂⁴	1	13440	yes	complemented
233	C₂²×#121	C₂⁴	1	13440	yes	complemented
234	C₂²×#121	C₂⁴	1	13440	yes	complemented
235	C₂²×#121	C₂⁴	1	13440	yes	complemented
236	C₂²×#120	C₂⁴	1	6720	yes	—
237	C₂²×#120	C₂⁴	1	13440	yes	complemented
238	C₂²×#120	C₂⁴	1	13440	yes	complemented
239	C₂²×#120	C₂⁴	1	6720	yes	complemented
240	C₂²×#120	C₂⁴	1	6720	yes	complemented
241	C₂²×#120	C₂⁴	1	6720	yes	complemented
242	C₂²×#120	C₂⁴	1	13440	yes	complemented
243	C₂²×#120	C₂⁴	1	184320	yes	complemented
244	C₂²×#120	C₂⁴	1	2240	yes	complemented
245	C₂²×#120	C₂⁴	1	6720	yes	complemented
246	C₂²×C₄×D₄	C₂⁴	1	13440	yes	complemented
247	C₂²×C₄×D₄	C₂⁴	1	13440	yes	complemented
248	C₂²×#117	C₂⁴	1	6720	yes	complemented
249	C₂³×C₄⋊C₄	C₂⁴	1	360	yes	complemented
250	C₂³×C₄⋊C₄	C₂⁴	1	360	yes	complemented
251	C₂³×C₄⋊C₄	C₂⁴	1	360	yes	complemented
252	C₂³×C₂²⋊C₄	C₂⁴	1	360	yes	—
253	C₂³×C₂²⋊C₄	C₂⁴	1	360	yes	—
254	C₂³×C₂²⋊C₄	C₂⁴	1	180	yes	—
255	C₂³×C₂²⋊C₄	C₂⁴	1	360	yes	—
256	C₂³×C₂²⋊C₄	C₂⁴	1	360	yes	—
257	C₂³×C₂²⋊C₄	C₂⁴	1	360	yes	—
258	C₂³×C₂²⋊C₄	C₂⁴	1	180	yes	—
259	C₂³×C₂²⋊C₄	C₂⁴	1	6720	yes	complemented
260	C₂³×C₂²⋊C₄	C₂⁴	1	13440	yes	complemented
261	C₂³×C₂²⋊C₄	C₂⁴	1	6720	yes	complemented
262	C₂³×C₂²⋊C₄	C₂⁴	1	180	yes	complemented
263	C₂³×C₂²⋊C₄	C₂⁴	1	180	yes	complemented
264	C₂³×C₂²⋊C₄	C₂⁴	1	360	yes	complemented
265	C₂³×C₂²⋊C₄	C₂⁴	1	360	yes	complemented
266	C₂³×C₄²	C₂⁴	1	60	yes	complemented
267	C₂³×C₄²	C₂⁴	1	180	yes	complemented
268	C₂³×C₄²	C₂⁴	1	120	yes	complemented
269	C₂⁶	—	2	96	no	—
270	C₂⁶	—	2	96	no	—
271	C₂⁶	—	2	48	no	—
272	C₂⁶	—	2	96	no	—
273	C₂⁶	—	2	48	no	—
274	C₂⁶	—	2	5760	no	—
275	C₂⁶	—	2	2880	no	—
276	C₂⁶	—	2	48	no	—
277	C₂⁶	—	2	96	no	—
278	C₂⁶	—	2	48	no	—
279	C₂⁶	—	2	2880	no	—
280	C₂⁶	—	4	1440	no	—
281	C₂⁶	—	4	2880	no	—
282	C₂⁶	—	4	1440	no	—
283	C₂⁶	—	4	53760	no	—
284	C₂⁶	—	4	2880	no	—
285	C₂⁶	—	4	1440	no	—
286	C₂⁶	—	4	3072	no	—
287	C₂⁶	—	4	3072	no	—
288	C₂⁶	—	4	122880	no	—
289	C₂⁶	—	4	1024	no	—
290	C₂⁶	—	8	1536	no	—
291	C₂⁶	—	8	512	no	—
292	C₂⁶	H(5,𝔽₂)	1	96	yes	—
293	C₂⁶	C₂⁵	1	90	yes	—
294	C₂⁶	C₂⁵	1	90	yes	—
295	C₂⁶	C₂⁵	1	90	yes	—
296	C₂⁶	C₂⁵	1	30	yes	—
297	C₂⁶	C₂⁵	1	1680	yes	—
298	C₂⁶	C₂⁵	1	90	yes	—
299	C₂⁶	C₂⁵	1	1680	yes	—
300	C₂⁶	C₂⁵	1	1680	yes	—
301	C₂⁶	C₂⁵	1	560	yes	—
302	C₂⁶	C₂⁵	1	1	yes	characteristic
303	C₂⁶	C₂⁵	1	7680	yes	complemented
304	C₂⁶	C₂⁵	1	560	yes	complemented
305	C₂²×#41	—	4	53760	no	—
306	C₂²×#41	C₂⁵	1	23040	yes	complemented
307	C₂³×Q₈	—	4	1440	no	—
308	C₂³×Q₈	C₂⁵	1	1680	yes	complemented
309	C₂³×D₄	—	2	5760	no	—
310	C₂³×D₄	—	2	5760	no	—
311	C₂³×D₄	—	4	1440	no	—
312	C₂³×D₄	—	4	1440	no	—
313	C₂³×D₄	—	4	1440	no	—
314	C₂³×D₄	—	4	1440	no	—
315	C₂³×D₄	—	4	2880	no	—
316	C₂³×D₄	—	4	2880	no	—
317	C₂³×D₄	—	4	53760	no	—
318	C₂³×D₄	—	4	2880	no	—
319	C₂³×D₄	—	4	1440	no	—
320	C₂³×D₄	—	4	107520	no	—
321	C₂³×D₄	—	4	53760	no	—
322	C₂³×D₄	C₂⁵	1	3360	yes	—
323	C₂³×D₄	C₂⁵	1	3360	yes	—
324	C₂³×D₄	C₂⁵	1	1680	yes	—
325	C₂³×D₄	C₂⁵	1	1680	yes	—
326	C₂³×D₄	C₂⁵	1	3360	yes	—
327	C₂³×D₄	C₂⁵	1	1680	yes	—
328	C₂³×D₄	C₂⁵	1	3360	yes	—
329	C₂³×D₄	C₂⁵	1	1680	yes	—
330	C₂³×D₄	C₂⁵	1	23040	yes	complemented
331	C₂³×D₄	C₂⁵	1	46080	yes	complemented
332	C₂³×D₄	C₂⁵	1	3360	yes	complemented
333	C₂³×D₄	C₂⁵	1	1680	yes	complemented
334	C₂³×D₄	C₂⁵	1	23040	yes	complemented
335	C₂⁴×C₄	—	2	48	no	—
336	C₂⁴×C₄	—	2	48	no	—
337	C₂⁴×C₄	—	2	2880	no	—
338	C₂⁴×C₄	—	2	96	no	—
339	C₂⁴×C₄	—	2	96	no	—
340	C₂⁴×C₄	—	4	2880	no	—
341	C₂⁴×C₄	—	4	1440	no	—
342	C₂⁴×C₄	—	4	2880	no	—
343	C₂⁴×C₄	C₂⁵	1	90	yes	—
344	C₂⁴×C₄	C₂⁵	1	180	yes	—
345	C₂⁴×C₄	C₂⁵	1	180	yes	—
346	C₂⁴×C₄	C₂⁵	1	90	yes	—
347	C₂⁴×C₄	C₂⁵	1	1680	yes	—
348	C₂⁴×C₄	C₂⁵	1	3360	yes	—
349	C₂⁴×C₄	C₂⁵	1	1680	yes	complemented
350	C₂⁴×C₄	C₂⁵	1	3360	yes	complemented
351	H(3,𝔽₄)	C₂⁵	1	65536	yes	complemented
352	#560	C₂⁵	1	196608	yes	complemented
353	#551	C₂⁵	1	196608	yes	complemented
354	#546	C₂⁵	1	393216	yes	complemented
355	D₄²	C₂⁵	1	196608	yes	complemented
356	#538	C₂⁵	1	393216	yes	complemented
357	#535	C₂⁵	1	196608	yes	complemented
358	#534	C₂⁵	1	196608	yes	complemented
359	C₂×#127	C₂⁵	1	7680	yes	complemented
360	C₂×#127	C₂⁵	1	23040	yes	complemented
361	C₂×#126	C₂⁵	1	15360	yes	complemented
362	C₂×#126	C₂⁵	1	46080	yes	complemented
363	C₂×#124	C₂⁵	1	23040	yes	complemented
364	C₂×#124	C₂⁵	1	23040	yes	complemented
365	C₂×#124	C₂⁵	1	46080	yes	complemented
366	C₂×#123	C₂⁵	1	23040	yes	complemented
367	C₂×#123	C₂⁵	1	23040	yes	complemented
368	C₂×#123	C₂⁵	1	46080	yes	complemented
369	C₂×#123	C₂⁵	1	46080	yes	complemented
370	C₂×C₂²⋊Q₈	C₂⁵	1	46080	yes	complemented
371	C₂×#121	C₂⁵	1	46080	yes	complemented
372	C₂×#121	C₂⁵	1	46080	yes	complemented
373	C₂×#121	C₂⁵	1	46080	yes	complemented
374	C₂×#121	C₂⁵	1	46080	yes	complemented
375	C₂×#121	C₂⁵	1	46080	yes	complemented
376	C₂×#120	C₂⁵	1	23040	yes	—
377	C₂×#120	C₂⁵	1	46080	yes	complemented
378	C₂×#120	C₂⁵	1	46080	yes	complemented
379	C₂×#120	C₂⁵	1	23040	yes	complemented
380	C₂×#120	C₂⁵	1	23040	yes	complemented
381	C₂×#120	C₂⁵	1	23040	yes	complemented
382	C₂×#120	C₂⁵	1	46080	yes	complemented
383	C₂×#120	C₂⁵	1	196608	yes	complemented
384	C₂×#120	C₂⁵	1	7680	yes	complemented
385	C₂×#120	C₂⁵	1	23040	yes	complemented
386	C₂×C₄×D₄	C₂⁵	1	46080	yes	complemented
387	C₂×C₄×D₄	C₂⁵	1	46080	yes	complemented
388	C₂×#117	C₂⁵	1	23040	yes	complemented
389	C₂²×C₄⋊C₄	C₂⁵	1	3360	yes	complemented
390	C₂²×C₄⋊C₄	C₂⁵	1	3360	yes	complemented
391	C₂²×C₄⋊C₄	C₂⁵	1	3360	yes	complemented
392	C₂²×C₂²⋊C₄	C₂⁵	1	3360	yes	—
393	C₂²×C₂²⋊C₄	C₂⁵	1	3360	yes	—
394	C₂²×C₂²⋊C₄	C₂⁵	1	1680	yes	—
395	C₂²×C₂²⋊C₄	C₂⁵	1	3360	yes	—
396	C₂²×C₂²⋊C₄	C₂⁵	1	3360	yes	—
397	C₂²×C₂²⋊C₄	C₂⁵	1	3360	yes	—
398	C₂²×C₂²⋊C₄	C₂⁵	1	1680	yes	—
399	C₂²×C₂²⋊C₄	C₂⁵	1	23040	yes	complemented
400	C₂²×C₂²⋊C₄	C₂⁵	1	46080	yes	complemented
401	C₂²×C₂²⋊C₄	C₂⁵	1	23040	yes	complemented
402	C₂²×C₂²⋊C₄	C₂⁵	1	1680	yes	complemented
403	C₂²×C₂²⋊C₄	C₂⁵	1	1680	yes	complemented
404	C₂²×C₂²⋊C₄	C₂⁵	1	3360	yes	complemented
405	C₂²×C₂²⋊C₄	C₂⁵	1	3360	yes	complemented
406	C₂²×C₄²	C₂⁵	1	560	yes	complemented
407	C₂²×C₄²	C₂⁵	1	1680	yes	complemented
408	C₂²×C₄²	C₂⁵	1	1120	yes	complemented
409	C₂⁵	—	2	1440	no	—
410	C₂⁵	—	2	1536	no	—
411	C₂⁵	—	2	1440	no	—
412	C₂⁵	—	2	720	no	—
413	C₂⁵	—	2	1440	no	—
414	C₂⁵	—	2	720	no	—
415	C₂⁵	—	2	26880	no	—
416	C₂⁵	—	2	13440	no	—
417	C₂⁵	—	2	720	no	—
418	C₂⁵	—	2	1440	no	—
419	C₂⁵	—	2	720	no	—
420	C₂⁵	—	2	13440	no	—
421	C₂⁵	—	4	6720	no	—
422	C₂⁵	—	4	13440	no	—
423	C₂⁵	—	4	6720	no	—
424	C₂⁵	—	4	92160	no	—
425	C₂⁵	—	4	13440	no	—
426	C₂⁵	—	4	6720	no	—
427	C₂⁵	—	4	46080	no	—
428	C₂⁵	—	4	46080	no	—
429	C₂⁵	—	4	573440	no	—
430	C₂⁵	—	4	15360	no	—
431	C₂⁵	—	4	768	no	—
432	C₂⁵	—	4	256	no	—
433	C₂⁵	—	4	768	no	—
434	C₂⁵	—	4	768	no	—
435	C₂⁵	—	8	23040	no	—
436	C₂⁵	—	8	7680	no	—
437	C₂⁵	C₂×H(5,𝔽₂)	1	1440	yes	—
438	C₂⁵	C₂×H(5,𝔽₂)	1	48	yes	—
439	C₂⁵	C₂⁶	1	420	yes	—
440	C₂⁵	C₂⁶	1	140	yes	—
441	C₂⁵	C₂⁶	1	420	yes	—
442	C₂⁵	C₂⁶	1	420	yes	—
443	C₂⁵	C₂⁶	1	2880	yes	—
444	C₂⁵	C₂⁶	1	420	yes	—
445	C₂⁵	C₂⁶	1	2880	yes	—
446	C₂⁵	C₂⁶	1	2880	yes	—
447	C₂⁵	C₂⁶	1	960	yes	—
448	C₂⁵	C₂⁶	1	15	yes	—
449	C₂⁵	C₂⁶	1	4096	yes	complemented
450	C₂⁵	C₂⁶	1	960	yes	complemented
451	C₂×#41	—	4	92160	no	—
452	C₂×#41	C₂⁶	1	12288	yes	complemented
453	C₂²×Q₈	—	4	6720	no	—
454	C₂²×Q₈	C₂⁶	1	2880	yes	complemented
455	C₂²×D₄	—	2	26880	no	—
456	C₂²×D₄	—	2	26880	no	—
457	C₂²×D₄	—	4	6720	no	—
458	C₂²×D₄	—	4	6720	no	—
459	C₂²×D₄	—	4	6720	no	—
460	C₂²×D₄	—	4	6720	no	—
461	C₂²×D₄	—	4	13440	no	—
462	C₂²×D₄	—	4	13440	no	—
463	C₂²×D₄	—	4	92160	no	—
464	C₂²×D₄	—	4	13440	no	—
465	C₂²×D₄	—	4	6720	no	—
466	C₂²×D₄	—	4	184320	no	—
467	C₂²×D₄	—	4	92160	no	—
468	C₂²×D₄	C₂⁶	1	5760	yes	—
469	C₂²×D₄	C₂⁶	1	5760	yes	—
470	C₂²×D₄	C₂⁶	1	2880	yes	—
471	C₂²×D₄	C₂⁶	1	2880	yes	—
472	C₂²×D₄	C₂⁶	1	5760	yes	—
473	C₂²×D₄	C₂⁶	1	2880	yes	—
474	C₂²×D₄	C₂⁶	1	5760	yes	—
475	C₂²×D₄	C₂⁶	1	2880	yes	—
476	C₂²×D₄	C₂⁶	1	12288	yes	complemented
477	C₂²×D₄	C₂⁶	1	24576	yes	complemented
478	C₂²×D₄	C₂⁶	1	2880	yes	complemented
479	C₂²×D₄	C₂⁶	1	5760	yes	complemented
480	C₂²×D₄	C₂⁶	1	12288	yes	complemented
481	C₂³×C₄	—	2	720	no	—
482	C₂³×C₄	—	2	720	no	—
483	C₂³×C₄	—	2	13440	no	—
484	C₂³×C₄	—	2	1440	no	—
485	C₂³×C₄	—	2	1440	no	—
486	C₂³×C₄	—	4	13440	no	—
487	C₂³×C₄	—	4	6720	no	—
488	C₂³×C₄	—	4	13440	no	—
489	C₂³×C₄	C₂⁶	1	840	yes	—
490	C₂³×C₄	C₂⁶	1	420	yes	—
491	C₂³×C₄	C₂⁶	1	420	yes	—
492	C₂³×C₄	C₂⁶	1	840	yes	—
493	C₂³×C₄	C₂⁶	1	2880	yes	—
494	C₂³×C₄	C₂⁶	1	5760	yes	—
495	C₂³×C₄	C₂⁶	1	5760	yes	complemented
496	C₂³×C₄	C₂⁶	1	2880	yes	complemented
497	#127	C₂⁶	1	4096	yes	complemented
498	#127	C₂⁶	1	12288	yes	complemented
499	#126	C₂⁶	1	8192	yes	complemented
500	#126	C₂⁶	1	24576	yes	complemented
501	#124	C₂⁶	1	12288	yes	complemented
502	#124	C₂⁶	1	12288	yes	complemented
503	#124	C₂⁶	1	24576	yes	complemented
504	#123	C₂⁶	1	12288	yes	complemented
505	#123	C₂⁶	1	12288	yes	complemented
506	#123	C₂⁶	1	24576	yes	complemented
507	#123	C₂⁶	1	24576	yes	complemented
508	C₂²⋊Q₈	C₂⁶	1	24576	yes	complemented
509	#121	C₂⁶	1	24576	yes	complemented
510	#121	C₂⁶	1	24576	yes	complemented
511	#121	C₂⁶	1	24576	yes	complemented
512	#121	C₂⁶	1	24576	yes	complemented
513	#121	C₂⁶	1	24576	yes	complemented
514	#120	C₂⁶	1	12288	yes	—
515	#120	C₂⁶	1	24576	yes	complemented
516	#120	C₂⁶	1	24576	yes	complemented
517	#120	C₂⁶	1	12288	yes	complemented
518	#120	C₂⁶	1	12288	yes	complemented
519	#120	C₂⁶	1	12288	yes	complemented
520	#120	C₂⁶	1	24576	yes	complemented
521	#120	C₂⁶	1	4096	yes	complemented
522	#120	C₂⁶	1	12288	yes	complemented
523	C₄×D₄	C₂⁶	1	24576	yes	complemented
524	C₄×D₄	C₂⁶	1	24576	yes	complemented
525	#117	C₂⁶	1	12288	yes	complemented
526	C₂×C₄⋊C₄	C₂⁶	1	5760	yes	complemented
527	C₂×C₄⋊C₄	C₂⁶	1	5760	yes	complemented
528	C₂×C₄⋊C₄	C₂⁶	1	5760	yes	complemented
529	C₂×C₂²⋊C₄	C₂⁶	1	5760	yes	—
530	C₂×C₂²⋊C₄	C₂⁶	1	5760	yes	—
531	C₂×C₂²⋊C₄	C₂⁶	1	2880	yes	—
532	C₂×C₂²⋊C₄	C₂⁶	1	5760	yes	—
533	C₂×C₂²⋊C₄	C₂⁶	1	5760	yes	—
534	C₂×C₂²⋊C₄	C₂⁶	1	5760	yes	—
535	C₂×C₂²⋊C₄	C₂⁶	1	2880	yes	—
536	C₂×C₂²⋊C₄	C₂⁶	1	12288	yes	complemented
537	C₂×C₂²⋊C₄	C₂⁶	1	24576	yes	complemented
538	C₂×C₂²⋊C₄	C₂⁶	1	12288	yes	complemented
539	C₂×C₂²⋊C₄	C₂⁶	1	2880	yes	complemented
540	C₂×C₂²⋊C₄	C₂⁶	1	2880	yes	complemented
541	C₂×C₂²⋊C₄	C₂⁶	1	5760	yes	complemented
542	C₂×C₂²⋊C₄	C₂⁶	1	5760	yes	complemented
543	C₂×C₄²	C₂⁶	1	960	yes	complemented
544	C₂×C₄²	C₂⁶	1	2880	yes	complemented
545	C₂×C₄²	C₂⁶	1	1920	yes	complemented
546	C₂⁴	—	2	3360	no	—
547	C₂⁴	—	2	11520	no	—
548	C₂⁴	—	2	3360	no	—
549	C₂⁴	—	2	1680	no	—
550	C₂⁴	—	2	3360	no	—
551	C₂⁴	—	2	1680	no	—
552	C₂⁴	—	2	23040	no	—
553	C₂⁴	—	2	11520	no	—
554	C₂⁴	—	2	1680	no	—
555	C₂⁴	—	2	3360	no	—
556	C₂⁴	—	2	1680	no	—
557	C₂⁴	—	2	11520	no	—
558	C₂⁴	—	4	5760	no	—
559	C₂⁴	—	4	11520	no	—
560	C₂⁴	—	4	5760	no	—
561	C₂⁴	—	4	24576	no	—
562	C₂⁴	—	4	11520	no	—
563	C₂⁴	—	4	5760	no	—
564	C₂⁴	—	4	107520	no	—
565	C₂⁴	—	4	107520	no	—
566	C₂⁴	—	4	491520	no	—
567	C₂⁴	—	4	35840	no	—
568	C₂⁴	—	4	5760	no	—
569	C₂⁴	—	4	1920	no	—
570	C₂⁴	—	4	5760	no	—
571	C₂⁴	—	4	5760	no	—
572	C₂⁴	—	8	53760	no	—
573	C₂⁴	—	8	17920	no	—
574	C₂⁴	#3532	1	256	yes	direct product factor
575	C₂⁴	C₂²×H(5,𝔽₂)	1	3360	yes	—
576	C₂⁴	C₂²×H(5,𝔽₂)	1	360	yes	—
577	C₂⁴	C₂⁷	1	360	yes	—
578	C₂⁴	C₂⁷	1	120	yes	—
579	C₂⁴	C₂⁷	1	360	yes	—
580	C₂⁴	C₂⁷	1	360	yes	—
581	C₂⁴	C₂⁷	1	768	yes	—
582	C₂⁴	C₂⁷	1	360	yes	—
583	C₂⁴	C₂⁷	1	768	yes	—
584	C₂⁴	C₂⁷	1	768	yes	—
585	C₂⁴	C₂⁷	1	256	yes	—
586	C₂⁴	C₂⁷	1	35	yes	—
587	C₂⁴	C₂⁷	1	256	yes	complemented
588	#41	—	4	24576	no	—
589	C₂×Q₈	—	4	5760	no	—
590	C₂×Q₈	C₂⁷	1	768	yes	complemented
591	C₂×D₄	—	2	23040	no	—
592	C₂×D₄	—	2	23040	no	—
593	C₂×D₄	—	4	5760	no	—
594	C₂×D₄	—	4	5760	no	—
595	C₂×D₄	—	4	5760	no	—
596	C₂×D₄	—	4	5760	no	—
597	C₂×D₄	—	4	11520	no	—
598	C₂×D₄	—	4	11520	no	—
599	C₂×D₄	—	4	24576	no	—
600	C₂×D₄	—	4	11520	no	—
601	C₂×D₄	—	4	5760	no	—
602	C₂×D₄	—	4	49152	no	—
603	C₂×D₄	—	4	24576	no	—
604	C₂×D₄	C₂⁷	1	1536	yes	—
605	C₂×D₄	C₂⁷	1	1536	yes	—
606	C₂×D₄	C₂⁷	1	768	yes	—
607	C₂×D₄	C₂⁷	1	768	yes	—
608	C₂×D₄	C₂⁷	1	1536	yes	—
609	C₂×D₄	C₂⁷	1	768	yes	—
610	C₂×D₄	C₂⁷	1	1536	yes	—
611	C₂×D₄	C₂⁷	1	768	yes	—
612	C₂×D₄	C₂⁷	1	768	yes	complemented
613	C₂×D₄	C₂⁷	1	1536	yes	complemented
614	C₂²×C₄	—	2	1680	no	—
615	C₂²×C₄	—	2	1680	no	—
616	C₂²×C₄	—	2	11520	no	—
617	C₂²×C₄	—	2	3360	no	—
618	C₂²×C₄	—	2	3360	no	—
619	C₂²×C₄	—	4	11520	no	—
620	C₂²×C₄	—	4	5760	no	—
621	C₂²×C₄	—	4	11520	no	—
622	C₂²×C₄	C₂⁷	1	360	yes	—
623	C₂²×C₄	C₂⁷	1	720	yes	—
624	C₂²×C₄	C₂⁷	1	720	yes	—
625	C₂²×C₄	C₂⁷	1	360	yes	—
626	C₂²×C₄	C₂⁷	1	768	yes	—
627	C₂²×C₄	C₂⁷	1	1536	yes	—
628	C₂²×C₄	C₂⁷	1	1536	yes	complemented
629	C₂²×C₄	C₂⁷	1	768	yes	complemented
630	C₄⋊C₄	C₂⁷	1	1536	yes	complemented
631	C₄⋊C₄	C₂⁷	1	1536	yes	complemented
632	C₄⋊C₄	C₂⁷	1	1536	yes	complemented
633	C₂²⋊C₄	C₂⁷	1	1536	yes	—
634	C₂²⋊C₄	C₂⁷	1	1536	yes	—
635	C₂²⋊C₄	C₂⁷	1	768	yes	—
636	C₂²⋊C₄	C₂⁷	1	1536	yes	—
637	C₂²⋊C₄	C₂⁷	1	1536	yes	—
638	C₂²⋊C₄	C₂⁷	1	1536	yes	—
639	C₂²⋊C₄	C₂⁷	1	768	yes	—
640	C₂²⋊C₄	C₂⁷	1	768	yes	complemented
641	C₂²⋊C₄	C₂⁷	1	768	yes	complemented
642	C₂²⋊C₄	C₂⁷	1	1536	yes	complemented
643	C₂²⋊C₄	C₂⁷	1	1536	yes	complemented
644	C₄²	C₂⁷	1	256	yes	complemented
645	C₄²	C₂⁷	1	768	yes	complemented
646	C₄²	C₂⁷	1	512	yes	complemented
647	C₂³	—	2	13440	no	—
648	C₂³	—	2	1440	no	—
649	C₂³	—	2	1440	no	—
650	C₂³	—	2	720	no	—
651	C₂³	—	2	1440	no	—
652	C₂³	—	2	720	no	—
653	C₂³	—	2	3072	no	—
654	C₂³	—	2	1536	no	—
655	C₂³	—	2	720	no	—
656	C₂³	—	2	1440	no	—
657	C₂³	—	2	720	no	—
658	C₂³	—	2	1536	no	—
659	C₂³	—	4	768	no	—
660	C₂³	—	4	1536	no	—
661	C₂³	—	4	768	no	—
662	C₂³	—	4	1536	no	—
663	C₂³	—	4	768	no	—
664	C₂³	—	4	46080	no	—
665	C₂³	—	4	46080	no	—
666	C₂³	—	4	65536	no	—
667	C₂³	—	4	15360	no	—
668	C₂³	—	4	6720	no	—
669	C₂³	—	4	2240	no	—
670	C₂³	—	4	6720	no	—
671	C₂³	—	4	6720	no	—
672	C₂³	—	8	23040	no	—
673	C₂³	—	8	7680	no	—
674	C₂³	C₂×#3532	1	960	yes	direct product factor
675	C₂³	C₂³×H(5,𝔽₂)	1	1440	yes	—
676	C₂³	C₂³×H(5,𝔽₂)	1	420	yes	—
677	C₂³	C₂⁸	1	48	yes	—
678	C₂³	C₂⁸	1	16	yes	—
679	C₂³	C₂⁸	1	48	yes	—
680	C₂³	C₂⁸	1	48	yes	—
681	C₂³	C₂⁸	1	48	yes	—
682	C₂³	C₂⁸	1	15	yes	—
683	Q₈	—	4	768	no	—
684	D₄	—	2	3072	no	—
685	D₄	—	2	3072	no	—
686	D₄	—	4	768	no	—
687	D₄	—	4	768	no	—
688	D₄	—	4	768	no	—
689	D₄	—	4	768	no	—
690	D₄	—	4	1536	no	—
691	D₄	—	4	1536	no	—
692	D₄	—	4	1536	no	—
693	D₄	—	4	768	no	—
694	C₂×C₄	—	2	720	no	—
695	C₂×C₄	—	2	720	no	—
696	C₂×C₄	—	2	1536	no	—
697	C₂×C₄	—	2	1440	no	—
698	C₂×C₄	—	2	1440	no	—
699	C₂×C₄	—	4	1536	no	—
700	C₂×C₄	—	4	768	no	—
701	C₂×C₄	—	4	1536	no	—
702	C₂×C₄	C₂⁸	1	48	yes	—
703	C₂×C₄	C₂⁸	1	96	yes	—
704	C₂×C₄	C₂⁸	1	96	yes	—
705	C₂×C₄	C₂⁸	1	48	yes	—
706	C₂²	—	2	96	no	—
707	C₂²	—	2	2880	no	—
708	C₂²	—	2	96	no	—
709	C₂²	—	2	48	no	—
710	C₂²	—	2	96	no	—
711	C₂²	—	2	48	no	—
712	C₂²	—	2	48	no	—
713	C₂²	—	2	96	no	—
714	C₂²	—	2	48	no	—
715	C₂²	—	4	3072	no	—
716	C₂²	—	4	3072	no	—
717	C₂²	—	4	1024	no	—
718	C₂²	—	4	1440	no	—
719	C₂²	—	4	480	no	—
720	C₂²	—	4	1440	no	—
721	C₂²	—	4	1440	no	—
722	C₂²	—	8	1536	no	—
723	C₂²	—	8	512	no	—
724	C₂²	C₂²×#3532	1	560	yes	direct product factor
725	C₂²	C₂⁴×H(5,𝔽₂)	1	96	yes	—
726	C₂²	C₂⁴×H(5,𝔽₂)	1	90	yes	—
727	C₂²	C₂⁹	1	1	yes	characteristic
728	C₄	—	2	48	no	—
729	C₄	—	2	48	no	—
730	C₄	—	2	96	no	—
731	C₄	—	2	96	no	—
732	C₂	—	2	96	no	—
733	C₂	—	4	48	no	—
734	C₂	—	4	16	no	—
735	C₂	—	4	48	no	—
736	C₂	—	4	48	no	—
737	C₂	C₂³×#3532	1	60	yes	direct product factor
738	C₂	C₂⁵×H(5,𝔽₂)	1	3	yes	—

	subgroup	G/H
center, socle	C₂⁶	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁹
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁶ ◁ G
LECS	G ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂⁴×H(3,𝔽₄)	C₂	semidirect
2. C₂⁴×#560	C₂	semidirect
3. C₂⁴×#538	C₂	semidirect
4. C₂⁴×#551	C₂	semidirect
5. C₂⁴×#535	C₂	semidirect
6. C₂⁴×#546	C₂	semidirect
7. C₂⁴×#534	C₂	semidirect
8. C₂⁵×#120	C₂	semidirect
9. C₂³×#3532	C₂	direct (N × H)
10. C₂⁴×D₄²	C₂	semidirect
11. C₂⁹	C₂²	semidirect
12. C₂⁵×#41	C₂²	semidirect
13. C₂⁶×D₄	C₂²	semidirect
14. C₂⁶×D₄	C₂²	semidirect
15. C₂⁶×D₄	C₂²	semidirect
16. C₂²×#3532	C₂²	direct (N × H)
17. C₂³×H(3,𝔽₄)	C₂²	semidirect
18. C₂³×#560	C₂²	semidirect
19. C₂³×#551	C₂²	semidirect
20. C₂³×#546	C₂²	semidirect
21. C₂³×D₄²	C₂²	semidirect
22. C₂³×#535	C₂²	semidirect
23. C₂³×#538	C₂²	semidirect
24. C₂³×#534	C₂²	semidirect
25. C₂⁴×#127	C₂²	semidirect
26. C₂⁴×#127	C₂²	semidirect
27. C₂⁴×#126	C₂²	semidirect
28. C₂⁴×#126	C₂²	semidirect
29. C₂⁴×#124	C₂²	semidirect
30. C₂⁴×#124	C₂²	semidirect
31. C₂⁴×#124	C₂²	semidirect
32. C₂⁴×#123	C₂²	semidirect
33. C₂⁴×#123	C₂²	semidirect
34. C₂⁴×#123	C₂²	semidirect
35. C₂⁴×#123	C₂²	semidirect
36. C₂⁴×C₂²⋊Q₈	C₂²	semidirect
37. C₂⁴×#121	C₂²	semidirect
38. C₂⁴×#121	C₂²	semidirect
39. C₂⁴×#121	C₂²	semidirect
40. C₂⁴×#121	C₂²	semidirect
41. C₂⁴×#121	C₂²	semidirect
43. C₂⁴×#120	C₂²	semidirect
44. C₂⁴×#120	C₂²	semidirect
45. C₂⁴×#120	C₂²	semidirect
46. C₂⁴×#120	C₂²	semidirect
47. C₂⁴×#120	C₂²	semidirect
48. C₂⁴×#120	C₂²	semidirect
49. C₂⁴×#120	C₂²	semidirect
50. C₂⁴×#120	C₂²	semidirect
51. C₂⁴×#120	C₂²	semidirect
52. C₂⁴×C₄×D₄	C₂²	semidirect
53. C₂⁴×C₄×D₄	C₂²	semidirect
54. C₂⁴×#117	C₂²	semidirect
55. C₂⁵×C₂²⋊C₄	C₂²	semidirect
56. C₂⁵×C₂²⋊C₄	C₂²	semidirect
57. C₂⁵×C₂²⋊C₄	C₂²	semidirect
63. C₂⁸	C₂³	semidirect
64. C₂⁸	C₂³	semidirect
66. C₂⁴×#41	C₂³	semidirect
67. C₂⁵×Q₈	C₂³	semidirect
79. C₂⁵×D₄	C₂³	semidirect
80. C₂⁵×D₄	C₂³	semidirect
81. C₂⁵×D₄	C₂³	semidirect
82. C₂⁵×D₄	C₂³	semidirect
83. C₂⁵×D₄	C₂³	semidirect
86. C₂⁶×C₄	C₂³	semidirect
87. C₂⁶×C₄	C₂³	semidirect
88. C₂×#3532	C₂³	direct (N × H)
89. C₂²×#551	C₂³	semidirect
90. C₂²×#546	C₂³	semidirect
91. C₂²×D₄²	C₂³	semidirect
92. C₂²×H(3,𝔽₄)	C₂³	semidirect
93. C₂²×#560	C₂³	semidirect
94. C₂²×#535	C₂³	semidirect
95. C₂²×#538	C₂³	semidirect
96. C₂²×#534	C₂³	semidirect
97. C₂³×#127	C₂³	semidirect
98. C₂³×#127	C₂³	semidirect
99. C₂³×#126	C₂³	semidirect
100. C₂³×#126	C₂³	semidirect
101. C₂³×#124	C₂³	semidirect
102. C₂³×#124	C₂³	semidirect
103. C₂³×#124	C₂³	semidirect
104. C₂³×#123	C₂³	semidirect
105. C₂³×#123	C₂³	semidirect
106. C₂³×#123	C₂³	semidirect
107. C₂³×#123	C₂³	semidirect
108. C₂³×C₂²⋊Q₈	C₂³	semidirect
109. C₂³×#121	C₂³	semidirect
110. C₂³×#121	C₂³	semidirect
111. C₂³×#121	C₂³	semidirect
112. C₂³×#121	C₂³	semidirect
113. C₂³×#121	C₂³	semidirect
115. C₂³×#120	C₂³	semidirect
116. C₂³×#120	C₂³	semidirect
117. C₂³×#120	C₂³	semidirect
118. C₂³×#120	C₂³	semidirect
119. C₂³×#120	C₂³	semidirect
120. C₂³×#120	C₂³	semidirect
121. C₂³×#120	C₂³	semidirect
122. C₂³×#120	C₂³	semidirect
123. C₂³×#120	C₂³	semidirect
124. C₂³×C₄×D₄	C₂³	semidirect
125. C₂³×C₄×D₄	C₂³	semidirect
126. C₂³×#117	C₂³	semidirect
127. C₂⁴×C₄⋊C₄	C₂³	semidirect
128. C₂⁴×C₄⋊C₄	C₂³	semidirect
129. C₂⁴×C₄⋊C₄	C₂³	semidirect
137. C₂⁴×C₂²⋊C₄	C₂³	semidirect
138. C₂⁴×C₂²⋊C₄	C₂³	semidirect
139. C₂⁴×C₂²⋊C₄	C₂³	semidirect
140. C₂⁴×C₂²⋊C₄	C₂³	semidirect
141. C₂⁴×C₂²⋊C₄	C₂³	semidirect
142. C₂⁴×C₂²⋊C₄	C₂³	semidirect
143. C₂⁴×C₂²⋊C₄	C₂³	semidirect
144. C₂⁴×C₄²	C₂³	semidirect
145. C₂⁴×C₄²	C₂³	semidirect
146. C₂⁴×C₄²	C₂³	semidirect
166. C₂⁷	C₂⁴	semidirect
167. C₂⁷	C₂⁴	semidirect
169. C₂³×#41	C₂⁴	semidirect
171. C₂⁴×Q₈	C₂⁴	semidirect
193. C₂⁴×D₄	C₂⁴	semidirect
194. C₂⁴×D₄	C₂⁴	semidirect
195. C₂⁴×D₄	C₂⁴	semidirect
196. C₂⁴×D₄	C₂⁴	semidirect
197. C₂⁴×D₄	C₂⁴	semidirect
208. C₂⁵×C₄	C₂⁴	semidirect
209. C₂⁵×C₄	C₂⁴	semidirect
210. #3532	C₂⁴	direct (N × H)
211. C₂×H(3,𝔽₄)	C₂⁴	semidirect
212. C₂×#560	C₂⁴	semidirect
213. C₂×#551	C₂⁴	semidirect
214. C₂×#546	C₂⁴	semidirect
215. C₂×D₄²	C₂⁴	semidirect
216. C₂×#538	C₂⁴	semidirect
217. C₂×#535	C₂⁴	semidirect
218. C₂×#534	C₂⁴	semidirect
219. C₂²×#127	C₂⁴	semidirect
220. C₂²×#127	C₂⁴	semidirect
221. C₂²×#126	C₂⁴	semidirect
222. C₂²×#126	C₂⁴	semidirect
223. C₂²×#124	C₂⁴	semidirect
224. C₂²×#124	C₂⁴	semidirect
225. C₂²×#124	C₂⁴	semidirect
226. C₂²×#123	C₂⁴	semidirect
227. C₂²×#123	C₂⁴	semidirect
228. C₂²×#123	C₂⁴	semidirect
229. C₂²×#123	C₂⁴	semidirect
230. C₂²×C₂²⋊Q₈	C₂⁴	semidirect
231. C₂²×#121	C₂⁴	semidirect
232. C₂²×#121	C₂⁴	semidirect
233. C₂²×#121	C₂⁴	semidirect
234. C₂²×#121	C₂⁴	semidirect
235. C₂²×#121	C₂⁴	semidirect
237. C₂²×#120	C₂⁴	semidirect
238. C₂²×#120	C₂⁴	semidirect
239. C₂²×#120	C₂⁴	semidirect
240. C₂²×#120	C₂⁴	semidirect
241. C₂²×#120	C₂⁴	semidirect
242. C₂²×#120	C₂⁴	semidirect
243. C₂²×#120	C₂⁴	semidirect
244. C₂²×#120	C₂⁴	semidirect
245. C₂²×#120	C₂⁴	semidirect
246. C₂²×C₄×D₄	C₂⁴	semidirect
247. C₂²×C₄×D₄	C₂⁴	semidirect
248. C₂²×#117	C₂⁴	semidirect
249. C₂³×C₄⋊C₄	C₂⁴	semidirect
250. C₂³×C₄⋊C₄	C₂⁴	semidirect
251. C₂³×C₄⋊C₄	C₂⁴	semidirect
259. C₂³×C₂²⋊C₄	C₂⁴	semidirect
260. C₂³×C₂²⋊C₄	C₂⁴	semidirect
261. C₂³×C₂²⋊C₄	C₂⁴	semidirect
262. C₂³×C₂²⋊C₄	C₂⁴	semidirect
263. C₂³×C₂²⋊C₄	C₂⁴	semidirect
264. C₂³×C₂²⋊C₄	C₂⁴	semidirect
265. C₂³×C₂²⋊C₄	C₂⁴	semidirect
266. C₂³×C₄²	C₂⁴	semidirect
267. C₂³×C₄²	C₂⁴	semidirect
268. C₂³×C₄²	C₂⁴	semidirect
303. C₂⁶	C₂⁵	semidirect
304. C₂⁶	C₂⁵	semidirect
306. C₂²×#41	C₂⁵	semidirect
308. C₂³×Q₈	C₂⁵	semidirect
330. C₂³×D₄	C₂⁵	semidirect
331. C₂³×D₄	C₂⁵	semidirect
332. C₂³×D₄	C₂⁵	semidirect
333. C₂³×D₄	C₂⁵	semidirect
334. C₂³×D₄	C₂⁵	semidirect
349. C₂⁴×C₄	C₂⁵	semidirect
350. C₂⁴×C₄	C₂⁵	semidirect
351. H(3,𝔽₄)	C₂⁵	semidirect
352. #560	C₂⁵	semidirect
353. #551	C₂⁵	semidirect
354. #546	C₂⁵	semidirect
355. D₄²	C₂⁵	semidirect
356. #538	C₂⁵	semidirect
357. #535	C₂⁵	semidirect
358. #534	C₂⁵	semidirect
359. C₂×#127	C₂⁵	semidirect
360. C₂×#127	C₂⁵	semidirect
361. C₂×#126	C₂⁵	semidirect
362. C₂×#126	C₂⁵	semidirect
363. C₂×#124	C₂⁵	semidirect
364. C₂×#124	C₂⁵	semidirect
365. C₂×#124	C₂⁵	semidirect
366. C₂×#123	C₂⁵	semidirect
367. C₂×#123	C₂⁵	semidirect
368. C₂×#123	C₂⁵	semidirect
369. C₂×#123	C₂⁵	semidirect
370. C₂×C₂²⋊Q₈	C₂⁵	semidirect
371. C₂×#121	C₂⁵	semidirect
372. C₂×#121	C₂⁵	semidirect
373. C₂×#121	C₂⁵	semidirect
374. C₂×#121	C₂⁵	semidirect
375. C₂×#121	C₂⁵	semidirect
377. C₂×#120	C₂⁵	semidirect
378. C₂×#120	C₂⁵	semidirect
379. C₂×#120	C₂⁵	semidirect
380. C₂×#120	C₂⁵	semidirect
381. C₂×#120	C₂⁵	semidirect
382. C₂×#120	C₂⁵	semidirect
383. C₂×#120	C₂⁵	semidirect
384. C₂×#120	C₂⁵	semidirect
385. C₂×#120	C₂⁵	semidirect
386. C₂×C₄×D₄	C₂⁵	semidirect
387. C₂×C₄×D₄	C₂⁵	semidirect
388. C₂×#117	C₂⁵	semidirect
389. C₂²×C₄⋊C₄	C₂⁵	semidirect
390. C₂²×C₄⋊C₄	C₂⁵	semidirect
391. C₂²×C₄⋊C₄	C₂⁵	semidirect
399. C₂²×C₂²⋊C₄	C₂⁵	semidirect
400. C₂²×C₂²⋊C₄	C₂⁵	semidirect
401. C₂²×C₂²⋊C₄	C₂⁵	semidirect
402. C₂²×C₂²⋊C₄	C₂⁵	semidirect
403. C₂²×C₂²⋊C₄	C₂⁵	semidirect
404. C₂²×C₂²⋊C₄	C₂⁵	semidirect
405. C₂²×C₂²⋊C₄	C₂⁵	semidirect
406. C₂²×C₄²	C₂⁵	semidirect
407. C₂²×C₄²	C₂⁵	semidirect
408. C₂²×C₄²	C₂⁵	semidirect
449. C₂⁵	C₂⁶	semidirect
450. C₂⁵	C₂⁶	semidirect
452. C₂×#41	C₂⁶	semidirect
454. C₂²×Q₈	C₂⁶	semidirect
476. C₂²×D₄	C₂⁶	semidirect
477. C₂²×D₄	C₂⁶	semidirect
478. C₂²×D₄	C₂⁶	semidirect
479. C₂²×D₄	C₂⁶	semidirect
480. C₂²×D₄	C₂⁶	semidirect
495. C₂³×C₄	C₂⁶	semidirect
496. C₂³×C₄	C₂⁶	semidirect
497. #127	C₂⁶	semidirect
498. #127	C₂⁶	semidirect
499. #126	C₂⁶	semidirect
500. #126	C₂⁶	semidirect
501. #124	C₂⁶	semidirect
502. #124	C₂⁶	semidirect
503. #124	C₂⁶	semidirect
504. #123	C₂⁶	semidirect
505. #123	C₂⁶	semidirect
506. #123	C₂⁶	semidirect
507. #123	C₂⁶	semidirect
508. C₂²⋊Q₈	C₂⁶	semidirect
509. #121	C₂⁶	semidirect
510. #121	C₂⁶	semidirect
511. #121	C₂⁶	semidirect
512. #121	C₂⁶	semidirect
513. #121	C₂⁶	semidirect
515. #120	C₂⁶	semidirect
516. #120	C₂⁶	semidirect
517. #120	C₂⁶	semidirect
518. #120	C₂⁶	semidirect
519. #120	C₂⁶	semidirect
520. #120	C₂⁶	semidirect
521. #120	C₂⁶	semidirect
522. #120	C₂⁶	semidirect
523. C₄×D₄	C₂⁶	semidirect
524. C₄×D₄	C₂⁶	semidirect
525. #117	C₂⁶	semidirect
526. C₂×C₄⋊C₄	C₂⁶	semidirect
527. C₂×C₄⋊C₄	C₂⁶	semidirect
528. C₂×C₄⋊C₄	C₂⁶	semidirect
536. C₂×C₂²⋊C₄	C₂⁶	semidirect
537. C₂×C₂²⋊C₄	C₂⁶	semidirect
538. C₂×C₂²⋊C₄	C₂⁶	semidirect
539. C₂×C₂²⋊C₄	C₂⁶	semidirect
540. C₂×C₂²⋊C₄	C₂⁶	semidirect
541. C₂×C₂²⋊C₄	C₂⁶	semidirect
542. C₂×C₂²⋊C₄	C₂⁶	semidirect
543. C₂×C₄²	C₂⁶	semidirect
544. C₂×C₄²	C₂⁶	semidirect
545. C₂×C₄²	C₂⁶	semidirect
574. C₂⁴	#3532	direct (N × H)
587. C₂⁴	C₂⁷	semidirect
590. C₂×Q₈	C₂⁷	semidirect
612. C₂×D₄	C₂⁷	semidirect
613. C₂×D₄	C₂⁷	semidirect
628. C₂²×C₄	C₂⁷	semidirect
629. C₂²×C₄	C₂⁷	semidirect
630. C₄⋊C₄	C₂⁷	semidirect
631. C₄⋊C₄	C₂⁷	semidirect
632. C₄⋊C₄	C₂⁷	semidirect
640. C₂²⋊C₄	C₂⁷	semidirect
641. C₂²⋊C₄	C₂⁷	semidirect
642. C₂²⋊C₄	C₂⁷	semidirect
643. C₂²⋊C₄	C₂⁷	semidirect
644. C₄²	C₂⁷	semidirect
645. C₄²	C₂⁷	semidirect
646. C₄²	C₂⁷	semidirect
674. C₂³	C₂×#3532	direct (N × H)
724. C₂²	C₂²×#3532	direct (N × H)
737. C₂	C₂³×#3532	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×H(3,𝔽₄)	2
C₂⁴×#560	2
C₂⁴×#538	2
C₂⁴×#551	2
C₂⁴×#535	2
C₂⁴×#546	2
C₂⁴×#534	2
C₂⁵×#120	2
C₂³×#3532	2
C₂⁴×D₄²	2

Subgroups — C24×#3532 #72295524

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×#3532 #72295524