Subgroups — #72316604

Order 2048.

At least 7070 conjugacy classes of subgroups; only the 816 normal subgroups are shown.

The subgroup lattice has 444 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72263740	C₂	1	2	yes	maximal, complemented
2	#72263565	C₂	1	2	yes	maximal, complemented
3	#72256710	C₂	1	4	yes	maximal, complemented
4	#72236632	C₂	1	1	yes	maximal, characteristic, complemented
5	#72236615	C₂	1	1	yes	maximal, characteristic, complemented
6	#72235851	C₂	1	1	yes	maximal, characteristic
7	#72213256	C₂	1	4	yes	maximal, complemented
8	C₂³×#525	C₄	1	1	yes	characteristic, complemented
9	C₂⁴×C₄×D₄	C₂²	1	1	yes	characteristic
10	C₂×#34736	C₄	1	1	yes	characteristic, complemented
11	C₂×#34736	C₂²	1	1	yes	characteristic
12	C₂×#20726	C₂²	1	2	yes	—
13	C₂×#20722	C₂²	1	2	yes	—
14	#612428	C₄	1	2	yes	complemented
15	#612428	C₂²	1	2	yes	—
16	#612426	C₄	1	2	yes	complemented
17	#612424	C₂²	1	2	yes	—
18	#607558	C₄	1	1	yes	characteristic, complemented
19	#514052	C₄	1	1	yes	characteristic, complemented
20	#514052	C₂²	1	1	yes	characteristic
21	#496225	C₂²	1	8	yes	—
22	#392249	C₂²	1	2	yes	—
23	#392245	C₂²	1	2	yes	—
24	#392113	C₂²	1	2	yes	—
25	#392109	C₂²	1	2	yes	—
26	#128073	C₂²	1	8	yes	—
27	C₂⁴×#41	C₂×C₄	1	1	yes	characteristic
28	C₂⁵×D₄	C₂³	1	1	yes	characteristic
29	C₂⁶×C₄	C₂×C₄	1	1	yes	characteristic
30	C₂⁶×C₄	D₄	1	1	yes	characteristic
31	C₂³×#123	C₂×C₄	1	2	yes	—
32	C₂³×#120	C₂×C₄	1	2	yes	—
33	C₂³×C₄×D₄	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×D₄	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
36	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
37	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
38	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
39	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
40	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
41	C₂³×#117	C₂×C₄	1	1	yes	characteristic
42	C₂⁴×C₄⋊C₄	D₄	1	1	yes	characteristic
43	C₂⁴×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
44	C₂⁴×C₂²⋊C₄	D₄	1	1	yes	characteristic
45	C₂⁴×C₄²	D₄	1	1	yes	characteristic
46	C₂×#2409	D₄	1	2	yes	—
47	C₂×#2408	D₄	1	2	yes	—
48	C₂×#2405	C₂×C₄	1	2	yes	—
49	C₂×#2405	C₂×C₄	1	2	yes	—
50	C₂×#2403	C₂×C₄	1	2	yes	—
51	C₂×#2403	C₂³	1	2	yes	—
52	C₂×C₄×#120	D₄	1	4	yes	—
53	C₂×#2280	C₂×C₄	1	1	yes	characteristic
54	C₂×#2280	C₂×C₄	1	1	yes	characteristic
55	C₂×#1800	D₄	1	4	yes	complemented
56	C₂×#1799	D₄	1	4	yes	complemented
57	C₂×#1783	C₂³	1	4	yes	—
58	C₂×#1781	C₂³	1	4	yes	—
59	C₂×C₄×#100	D₄	1	4	yes	complemented
60	C₂×C₄×#99	D₄	1	4	yes	complemented
61	#14681	C₂×C₄	1	2	yes	—
62	#14679	C₂×C₄	1	2	yes	—
63	#13871	D₄	1	4	yes	—
64	#13869	C₂×C₄	1	2	yes	—
65	#13869	C₂×C₄	1	2	yes	—
66	#13867	C₂×C₄	1	2	yes	—
67	#13867	C₂³	1	2	yes	—
68	#13839	D₄	1	4	yes	—
69	C₂⁷	C₂²×C₄	1	1	yes	characteristic
70	C₂⁷	C₂×D₄	1	1	yes	characteristic
71	C₂⁴×Q₈	C₂²⋊C₄	1	1	yes	characteristic, complemented
72	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
73	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
74	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
75	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
76	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
77	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
78	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
79	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
80	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
81	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
82	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
83	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
84	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
85	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
86	C₂⁵×C₄	C₂²⋊C₄	1	2	yes	complemented
87	C₂⁵×C₄	C₂²×C₄	1	1	yes	characteristic
88	C₂⁵×C₄	C₂²×C₄	1	1	yes	characteristic
89	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
90	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
91	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
92	C₂²×#120	C₂×D₄	1	4	yes	—
93	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
94	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
95	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
96	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
97	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
98	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
99	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
100	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
101	C₂²×C₄×D₄	#41	1	2	yes	—
102	C₂²×C₄×D₄	#41	1	2	yes	—
103	C₂²×C₄×D₄	#41	1	2	yes	—
104	C₂²×C₄×D₄	#41	1	2	yes	—
105	C₂²×#117	C₂²⋊C₄	1	2	yes	complemented
106	C₂²×#117	C₂²⋊C₄	1	2	yes	complemented
107	C₂³×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
108	C₂³×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
109	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
110	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
111	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
112	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
113	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
114	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
115	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
116	C₂³×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
117	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
118	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
119	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
120	C₂³×C₄²	C₂²⋊C₄	1	1	yes	characteristic
121	C₂³×C₄²	C₂²⋊C₄	1	1	yes	characteristic
122	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
123	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
124	C₂²×#100	C₂×D₄	1	8	yes	—
125	C₂²×#99	C₂×D₄	1	8	yes	—
126	C₂×#386	C₂×D₄	1	4	yes	—
127	C₂×#385	C₂²⋊C₄	1	4	yes	complemented
128	C₂×#380	C₂²⋊C₄	1	2	yes	complemented
129	C₂×#380	C₂²⋊C₄	1	2	yes	complemented
130	C₂×#379	C₂²⋊C₄	1	4	yes	complemented
131	C₂×#379	C₂²×C₄	1	2	yes	—
132	C₂×#379	C₂²×C₄	1	2	yes	—
133	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	complemented
134	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	complemented
135	#1440	C₂²⋊C₄	1	8	yes	complemented
136	#1438	C₂×D₄	1	8	yes	—
137	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
138	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
141	C₂⁶	C₂³×C₄	1	1	yes	characteristic
142	C₂⁶	C₂²×D₄	1	1	yes	characteristic
143	C₂³×D₄	C₂²×D₄	1	2	yes	—
144	C₂³×D₄	C₂²×D₄	1	2	yes	—
145	C₂³×D₄	C₂²×D₄	1	2	yes	—
146	C₂³×D₄	C₂²×D₄	1	2	yes	—
147	C₂³×D₄	C₂×#41	1	2	yes	—
148	C₂³×D₄	C₂×#41	1	2	yes	—
149	C₂⁴×C₄	#99	1	2	yes	—
150	C₂⁴×C₄	#99	1	2	yes	—
151	C₂⁴×C₄	#99	1	2	yes	—
152	C₂⁴×C₄	#99	1	2	yes	—
153	C₂⁴×C₄	#99	1	2	yes	—
154	C₂⁴×C₄	#99	1	2	yes	—
155	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
165	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₂⁴×C₄	C₄×D₄	1	2	yes	—
170	C₂⁴×C₄	C₄×D₄	1	2	yes	—
171	C₂⁴×C₄	C₄×D₄	1	2	yes	—
172	C₂⁴×C₄	C₄×D₄	1	2	yes	—
173	C₂⁴×C₄	#120	1	2	yes	—
174	C₂⁴×C₄	#120	1	2	yes	—
175	C₂⁴×C₄	#120	1	1	yes	characteristic
176	C₂⁴×C₄	#120	1	1	yes	characteristic
177	C₂⁴×C₄	#121	1	2	yes	—
178	C₂⁴×C₄	#121	1	2	yes	—
179	C₂⁴×C₄	#123	1	1	yes	characteristic
180	C₂⁴×C₄	#123	1	1	yes	characteristic
181	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×D₄	#120	1	2	yes	—
183	C₂×C₄×D₄	#120	1	2	yes	—
184	C₂×C₄×D₄	#120	1	2	yes	—
185	C₂×C₄×D₄	#120	1	2	yes	—
186	C₂×C₄×D₄	#121	1	2	yes	—
187	C₂×C₄×D₄	#121	1	2	yes	—
188	C₂×C₄×D₄	#121	1	2	yes	—
189	C₂×C₄×D₄	#121	1	2	yes	—
190	C₂×C₄×D₄	#121	1	2	yes	—
191	C₂×C₄×D₄	#121	1	2	yes	—
192	C₂×C₄×D₄	#121	1	2	yes	—
193	C₂×C₄×D₄	#121	1	2	yes	—
194	C₂×C₄×D₄	#121	1	2	yes	—
195	C₂×C₄×D₄	#121	1	2	yes	—
196	C₂×C₄×D₄	#121	1	2	yes	—
197	C₂×C₄×D₄	#121	1	2	yes	—
198	C₂×C₄×D₄	#121	1	2	yes	—
199	C₂×C₄×D₄	#121	1	2	yes	—
200	C₂×C₄×D₄	#121	1	2	yes	—
201	C₂×C₄×D₄	#121	1	2	yes	—
202	C₂×C₄×D₄	#123	1	2	yes	—
203	C₂×C₄×D₄	#123	1	2	yes	—
204	C₂×C₄×D₄	#123	1	2	yes	—
205	C₂×C₄×D₄	#123	1	2	yes	—
206	C₂×C₄×D₄	#124	1	2	yes	—
207	C₂×C₄×D₄	#124	1	2	yes	—
208	C₂×C₄×D₄	#124	1	2	yes	—
209	C₂×C₄×D₄	#124	1	2	yes	—
210	C₂×C₄×D₄	#127	1	2	yes	—
211	C₂×C₄×D₄	#127	1	2	yes	—
212	C₂×C₄×D₄	#127	1	2	yes	—
213	C₂×C₄×D₄	#127	1	2	yes	—
214	C₂²×C₄⋊C₄	#120	1	2	yes	—
215	C₂²×C₄⋊C₄	#120	1	2	yes	—
216	C₂²×C₄⋊C₄	#120	1	2	yes	—
217	C₂²×C₄⋊C₄	#121	1	2	yes	—
218	C₂²×C₄⋊C₄	#121	1	2	yes	—
219	C₂²×C₄⋊C₄	#123	1	2	yes	—
220	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
221	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
222	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
223	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
224	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
225	C₂²×C₂²⋊C₄	C₄×D₄	1	2	yes	—
226	C₂²×C₂²⋊C₄	C₄×D₄	1	2	yes	—
227	C₂²×C₂²⋊C₄	C₄×D₄	1	2	yes	—
228	C₂²×C₂²⋊C₄	C₄×D₄	1	2	yes	—
229	C₂²×C₂²⋊C₄	#120	1	2	yes	—
230	C₂²×C₂²⋊C₄	#120	1	2	yes	—
231	C₂²×C₂²⋊C₄	#120	1	2	yes	—
232	C₂²×C₂²⋊C₄	#121	1	2	yes	—
233	C₂²×C₂²⋊C₄	#121	1	2	yes	—
234	C₂²×C₂²⋊C₄	#123	1	2	yes	—
235	C₂²×C₄²	#99	1	2	yes	—
236	C₂²×C₄²	#99	1	2	yes	—
237	C₂²×C₄²	#120	1	1	yes	characteristic
238	C₂²×C₄²	#120	1	1	yes	characteristic
239	C₂²×C₄²	#120	1	2	yes	—
240	C₂²×C₄²	#120	1	2	yes	—
241	C₂²×C₄²	#121	1	2	yes	—
242	C₂²×C₄²	#121	1	2	yes	—
243	C₂²×C₄²	#123	1	1	yes	characteristic
244	C₂²×C₄²	#123	1	1	yes	characteristic
245	C₂⁵	C₂×#99	1	2	yes	—
246	C₂⁵	C₂×#99	1	2	yes	—
247	C₂⁵	C₂×#99	1	2	yes	—
248	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
249	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
250	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
251	C₂⁵	C₂×C₄×D₄	1	2	yes	—
252	C₂⁵	C₂×C₄×D₄	1	2	yes	—
253	C₂⁵	C₂×#120	1	1	yes	characteristic
254	C₂⁵	C₂×#120	1	2	yes	—
255	C₂⁵	C₂×#121	1	2	yes	—
256	C₂⁵	C₂×#123	1	1	yes	characteristic
257	C₂²×D₄	C₂×#120	1	2	yes	—
258	C₂²×D₄	C₂×#121	1	2	yes	—
259	C₂²×D₄	C₂×#121	1	2	yes	—
260	C₂²×D₄	C₂×#121	1	2	yes	—
261	C₂²×D₄	C₂×#121	1	2	yes	—
262	C₂²×D₄	C₂×#123	1	2	yes	—
263	C₂²×D₄	C₂×#124	1	2	yes	—
264	C₂²×D₄	C₂×#127	1	2	yes	—
265	C₂³×C₄	AΣL(1,𝔽₁₆)	1	8	yes	complemented
266	C₂³×C₄	#379	1	1	yes	characteristic
267	C₂³×C₄	#379	1	1	yes	characteristic
268	C₂³×C₄	#379	1	2	yes	—
269	C₂³×C₄	#379	1	2	yes	—
270	C₂³×C₄	#379	1	1	yes	characteristic
271	C₂³×C₄	#379	1	1	yes	characteristic
272	C₂³×C₄	#386	1	1	yes	characteristic
273	C₂³×C₄	#386	1	1	yes	characteristic
274	C₂³×C₄	#386	1	1	yes	characteristic
275	C₂³×C₄	#386	1	1	yes	characteristic
276	C₂³×C₄	#386	1	2	yes	—
277	C₂³×C₄	#386	1	1	yes	characteristic
278	C₂³×C₄	#386	1	1	yes	characteristic
279	C₂³×C₄	#386	1	2	yes	—
280	C₂³×C₄	#386	1	2	yes	—
281	C₂³×C₄	#386	1	2	yes	—
282	C₂³×C₄	#386	1	2	yes	—
283	C₂³×C₄	#386	1	2	yes	—
284	C₂³×C₄	#386	1	2	yes	—
285	C₂³×C₄	#386	1	2	yes	—
286	C₂³×C₄	#386	1	1	yes	characteristic
287	C₂³×C₄	#386	1	1	yes	characteristic
288	C₂³×C₄	#390	1	2	yes	—
289	C₂³×C₄	#390	1	2	yes	—
290	C₂³×C₄	#390	1	2	yes	—
291	C₂³×C₄	#390	1	2	yes	—
292	C₂³×C₄	#392	1	2	yes	—
293	C₂³×C₄	#392	1	2	yes	—
294	C₂³×C₄	#392	1	2	yes	—
295	C₂³×C₄	#392	1	2	yes	—
296	C₂³×C₄	#394	1	2	yes	—
297	C₂³×C₄	#394	1	2	yes	—
298	C₂³×C₄	#394	1	2	yes	—
299	C₂³×C₄	#394	1	2	yes	—
300	C₂³×C₄	C₂×#99	1	2	yes	—
301	C₂³×C₄	C₂×#99	1	1	yes	characteristic
302	C₂³×C₄	C₂×#99	1	1	yes	characteristic
303	C₂³×C₄	C₂×#99	1	1	yes	characteristic
304	C₂³×C₄	C₂×#99	1	1	yes	characteristic
305	C₂³×C₄	C₂×#99	1	1	yes	characteristic
306	C₂³×C₄	C₂×#99	1	1	yes	characteristic
307	C₂³×C₄	C₂×#99	1	1	yes	characteristic
308	C₂³×C₄	C₂×#99	1	2	yes	—
309	C₂³×C₄	C₂×#99	1	2	yes	—
310	C₂³×C₄	C₂×#99	1	2	yes	—
311	C₂³×C₄	C₂×#99	1	2	yes	—
312	C₂³×C₄	C₂×#99	1	1	yes	characteristic
313	C₂³×C₄	C₂×#120	1	1	yes	characteristic
314	C₂³×C₄	C₂×#120	1	2	yes	—
315	C₂³×C₄	C₂×#121	1	2	yes	—
316	C₂³×C₄	C₂×#123	1	1	yes	characteristic
317	C₂×C₄⋊C₄	#392	1	2	yes	—
318	C₂×C₄⋊C₄	#392	1	2	yes	—
319	C₂×C₄⋊C₄	#392	1	2	yes	—
320	C₂×C₄⋊C₄	#392	1	2	yes	—
321	C₂×C₄⋊C₄	#394	1	2	yes	—
322	C₂×C₄⋊C₄	#394	1	2	yes	—
323	C₂×C₄⋊C₄	#394	1	2	yes	—
324	C₂×C₄⋊C₄	#394	1	2	yes	—
325	C₂×C₂²⋊C₄	#386	1	2	yes	—
326	C₂×C₂²⋊C₄	#386	1	2	yes	—
327	C₂×C₂²⋊C₄	#386	1	2	yes	—
328	C₂×C₂²⋊C₄	#386	1	2	yes	—
329	C₂×C₂²⋊C₄	#390	1	2	yes	—
330	C₂×C₂²⋊C₄	#390	1	2	yes	—
331	C₂×C₂²⋊C₄	#390	1	2	yes	—
332	C₂×C₂²⋊C₄	#390	1	2	yes	—
333	C₂×C₂²⋊C₄	#392	1	2	yes	—
334	C₂×C₂²⋊C₄	#392	1	2	yes	—
335	C₂×C₂²⋊C₄	#392	1	2	yes	—
336	C₂×C₂²⋊C₄	#392	1	2	yes	—
337	C₂×C₂²⋊C₄	#394	1	2	yes	—
338	C₂×C₂²⋊C₄	#394	1	2	yes	—
339	C₂×C₂²⋊C₄	#394	1	2	yes	—
340	C₂×C₂²⋊C₄	#394	1	2	yes	—
341	C₂×C₄²	#392	1	2	yes	—
342	C₂×C₄²	#392	1	2	yes	—
343	C₂×C₄²	#392	1	2	yes	—
344	C₂×C₄²	#392	1	2	yes	—
345	C₂×C₄²	#394	1	2	yes	—
346	C₂×C₄²	#394	1	2	yes	—
347	C₂×C₄²	#394	1	2	yes	—
348	C₂×C₄²	#394	1	2	yes	—
349	C₂⁴	C₂×AΣL(1,𝔽₁₆)	1	4	yes	—
350	C₂⁴	C₂×#379	1	1	yes	characteristic
351	C₂⁴	C₂×#386	1	1	yes	characteristic
352	C₂⁴	C₂×#386	1	1	yes	characteristic
353	C₂⁴	C₂×#386	1	2	yes	—
354	C₂⁴	C₂×#390	1	2	yes	—
355	C₂⁴	C₂×#392	1	2	yes	—
356	C₂⁴	C₂×#394	1	2	yes	—
357	C₂⁴	C₂²×#99	1	1	yes	characteristic
358	C₂⁴	C₂²×#99	1	1	yes	characteristic
359	C₂⁴	C₂²×#99	1	1	yes	characteristic
360	C₂⁴	C₂²×#99	1	1	yes	characteristic
361	C₂×D₄	#3025	1	8	yes	—
362	C₂²×C₄	#1438	1	1	yes	characteristic
363	C₂²×C₄	#1438	1	1	yes	characteristic
364	C₂²×C₄	#1438	1	1	yes	characteristic
365	C₂²×C₄	#1438	1	1	yes	characteristic
366	C₂²×C₄	#1438	1	2	yes	—
367	C₂²×C₄	#1438	1	2	yes	—
368	C₂²×C₄	#1438	1	2	yes	—
369	C₂²×C₄	#1438	1	2	yes	—
370	C₂²×C₄	#1438	1	2	yes	—
371	C₂²×C₄	#1438	1	2	yes	—
372	C₂²×C₄	#1781	1	1	yes	characteristic
373	C₂²×C₄	#1781	1	1	yes	characteristic
374	C₂²×C₄	#1781	1	1	yes	characteristic
375	C₂²×C₄	#1781	1	1	yes	characteristic
376	C₂²×C₄	#1781	1	1	yes	characteristic
377	C₂²×C₄	#1781	1	1	yes	characteristic
378	C₂²×C₄	#1781	1	1	yes	characteristic
379	C₂²×C₄	#1781	1	1	yes	characteristic
380	C₂²×C₄	#1898	1	1	yes	characteristic
381	C₂²×C₄	#1898	1	1	yes	characteristic
382	C₂²×C₄	#1898	1	1	yes	characteristic
383	C₂²×C₄	#1898	1	1	yes	characteristic
384	C₂²×C₄	#1898	1	1	yes	characteristic
385	C₂²×C₄	#1898	1	1	yes	characteristic
386	C₂²×C₄	#1898	1	1	yes	characteristic
387	C₂²×C₄	#1898	1	1	yes	characteristic
388	C₂²×C₄	#1898	1	1	yes	characteristic
389	C₂²×C₄	#1898	1	1	yes	characteristic
390	C₂²×C₄	#1898	1	1	yes	characteristic
391	C₂²×C₄	#1898	1	1	yes	characteristic
392	C₂²×C₄	#1898	1	1	yes	characteristic
393	C₂²×C₄	#1898	1	1	yes	characteristic
394	C₂²×C₄	#1898	1	1	yes	characteristic
395	C₂²×C₄	#1898	1	1	yes	characteristic
396	C₂²×C₄	C₂×AΣL(1,𝔽₁₆)	1	4	yes	—
397	C₂²×C₄	C₂×AΣL(1,𝔽₁₆)	1	4	yes	—
398	C₂²×C₄	#2121	1	4	yes	—
399	C₂²×C₄	C₂×#392	1	2	yes	—
400	C₂²×C₄	C₂×#394	1	2	yes	—
401	C₂³	C₂×#1438	1	1	yes	characteristic
402	C₂³	C₂×#1781	1	1	yes	characteristic
403	C₂³	C₂×#1781	1	1	yes	characteristic
404	C₂³	#20959	1	4	yes	—
405	C₂³	C₂×#1898	1	1	yes	characteristic
406	C₂³	C₂×#1898	1	1	yes	characteristic
407	C₂³	C₂×#1898	1	1	yes	characteristic
408	C₂³	C₂×#1898	1	1	yes	characteristic
409	C₂³	#23443	1	4	yes	—
410	C₂³	C₂²×AΣL(1,𝔽₁₆)	1	2	yes	—
411	C₂³	C₂×#2121	1	2	yes	—
412	C₂×C₄	#10965	1	1	yes	characteristic
413	C₂×C₄	#10965	1	1	yes	characteristic
414	C₂×C₄	#10965	1	1	yes	characteristic
415	C₂×C₄	#10965	1	1	yes	characteristic
416	C₂×C₄	#10965	1	1	yes	characteristic
417	C₂×C₄	#10965	1	1	yes	characteristic
418	C₂×C₄	#10965	1	1	yes	characteristic
419	C₂×C₄	#10965	1	1	yes	characteristic
420	C₂×C₄	#12687	1	2	yes	—
421	C₂×C₄	#12687	1	2	yes	—
422	C₂×C₄	#12690	1	2	yes	—
423	C₂×C₄	#12690	1	2	yes	—
424	C₂×C₄	#13082	1	4	yes	—
425	C₂×C₄	#13082	1	4	yes	—
426	C₂×C₄	#13086	1	4	yes	—
427	C₂×C₄	#13086	1	4	yes	—
428	C₂×C₄	#23443	1	4	yes	—
429	C₂²	C₂×#10965	1	1	yes	characteristic
430	C₂²	#357529	1	2	yes	—
431	C₂²	C₂×#12687	1	1	yes	characteristic
432	C₂²	C₂×#12690	1	1	yes	characteristic
433	C₂²	#493390	1	2	yes	—
434	C₂²	C₂×#13082	1	2	yes	—
435	C₂²	C₂×#13086	1	2	yes	—
436	C₄	#147555	1	2	yes	—
437	C₄	#147555	1	2	yes	—
438	C₄	#147555	1	2	yes	—
439	C₄	#147555	1	2	yes	—
440	C₂	#72235094	1	1	yes	characteristic
441	C₂	C₂×#147555	1	1	yes	characteristic
442	C₂	#72256657	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10965
commutator	C₂⁶	C₂³×C₄
Frattini, cosocle	C₂⁴×D₄	C₂⁴
socle	C₂²	C₂×#10965
prime radical	#72235851	C₂
LCS	G ▷ C₂⁶ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂⁴×C₄ ◁ C₂⁴×C₄×D₄ ◁ G
LECS	G ▷ C₂⁴×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72263740	C₂	semidirect
2. #72263565	C₂	semidirect
3. #72256710	C₂	semidirect
4. #72236632	C₂	semidirect
5. #72236615	C₂	semidirect
7. #72213256	C₂	semidirect
8. C₂³×#525	C₄	semidirect
10. C₂×#34736	C₄	semidirect
14. #612428	C₄	semidirect
16. #612426	C₄	semidirect
18. #607558	C₄	semidirect
19. #514052	C₄	semidirect
55. C₂×#1800	D₄	semidirect
56. C₂×#1799	D₄	semidirect
59. C₂×C₄×#100	D₄	semidirect
60. C₂×C₄×#99	D₄	semidirect
71. C₂⁴×Q₈	C₂²⋊C₄	semidirect
72. C₂⁴×D₄	C₂²⋊C₄	semidirect
86. C₂⁵×C₄	C₂²⋊C₄	semidirect
105. C₂²×#117	C₂²⋊C₄	semidirect
106. C₂²×#117	C₂²⋊C₄	semidirect
127. C₂×#385	C₂²⋊C₄	semidirect
128. C₂×#380	C₂²⋊C₄	semidirect
129. C₂×#380	C₂²⋊C₄	semidirect
130. C₂×#379	C₂²⋊C₄	semidirect
133. C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	semidirect
134. C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	semidirect
135. #1440	C₂²⋊C₄	semidirect
265. C₂³×C₄	AΣL(1,𝔽₁₆)	semidirect

Maximal subgroups

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

subgroup	index
#72263740	2
#72263565	2
#72256710	2
#72236632	2
#72236615	2
#72235851	2
#72213256	2