Subgroups — #72261851

Order 2048.

At least 8592 conjugacy classes of subgroups; only the 1424 normal subgroups are shown.

The subgroup lattice has 462 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72261821	C₂	1	2	yes	maximal, complemented
2	#72261812	C₂	1	1	yes	maximal, characteristic, complemented
3	#72261803	C₂	1	1	yes	maximal, characteristic, complemented
4	#72261788	C₂	1	1	yes	maximal, characteristic, complemented
5	#72261782	C₂	1	1	yes	maximal, characteristic, complemented
6	#72261779	C₂	1	4	yes	maximal, complemented
7	#72261770	C₂	1	4	yes	maximal, complemented
8	#72261767	C₂	1	4	yes	maximal, complemented
9	#72258626	C₂	1	2	yes	maximal, complemented
10	C₂×#115133	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#6470225	C₂	1	2	yes	maximal, complemented
12	C₂×#6628892	C₂	1	1	yes	maximal, characteristic, complemented
13	#72225796	C₂	1	2	yes	maximal, complemented
14	C₂²×#32898	C₂	1	1	yes	maximal, characteristic, complemented
15	#72219165	C₂	1	4	yes	maximal, complemented
16	C₂⁴×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
17	C₂²×#3484	C₂²	1	1	yes	characteristic, complemented
18	C₂×#34980	C₂²	1	2	yes	—
19	C₂×#34980	C₂²	1	1	yes	characteristic
20	C₂×#34980	C₂²	1	2	yes	—
21	C₂²×#2403	C₂²	1	1	yes	characteristic
22	C₂²×#2403	C₂²	1	2	yes	—
23	C₂²×#2613	C₂²	1	1	yes	characteristic
24	C₂×#33020	C₂²	1	4	yes	complemented
25	C₂×#32900	C₂²	1	4	yes	complemented
26	C₂×#32898	C₂²	1	4	yes	—
27	C₂×#32898	C₂²	1	4	yes	complemented
28	C₂×#32898	C₂²	1	4	yes	complemented
29	C₂×#32898	C₂²	1	4	yes	complemented
30	C₂×#29634	C₂²	1	4	yes	complemented
31	C₂×#29634	C₂²	1	4	yes	complemented
32	C₂×#21746	C₂²	1	2	yes	complemented
33	C₂×#21746	C₂²	1	2	yes	complemented
34	C₂²×#1781	C₂²	1	2	yes	complemented
35	C₂²×#1781	C₂²	1	2	yes	complemented
36	C₂²×#1781	C₂²	1	1	yes	characteristic, complemented
37	C₂²×#1781	C₂²	1	1	yes	characteristic, complemented
38	C₂²×#1781	C₂²	1	2	yes	complemented
39	#4928993	C₂²	1	4	yes	complemented
40	#4928941	C₂²	1	2	yes	complemented
41	#4928938	C₂²	1	4	yes	complemented
42	#4928938	C₂²	1	2	yes	complemented
43	#4453283	C₂²	1	2	yes	complemented
44	#4453257	C₂²	1	2	yes	complemented
45	#556752	C₂²	1	1	yes	characteristic, complemented
46	#556752	C₂²	1	1	yes	characteristic, complemented
47	#517411	C₂²	1	2	yes	complemented
48	#517411	C₂²	1	1	yes	characteristic, complemented
49	C₂×#14335	C₂²	1	1	yes	characteristic, complemented
50	#355913	C₂²	1	2	yes	complemented
51	C₂×#8101	C₂²	1	2	yes	complemented
52	C₂²×#1304	C₂²	1	2	yes	complemented
53	#115135	C₂²	1	4	yes	complemented
54	#115134	C₂²	1	8	yes	complemented
55	#115133	C₂²	1	8	yes	complemented
56	#115133	C₂²	1	4	yes	complemented
57	#115133	C₂²	1	4	yes	complemented
58	#115133	C₂²	1	4	yes	complemented
59	#111517	C₂²	1	4	yes	complemented
60	#111516	C₂²	1	4	yes	complemented
61	#111459	C₂²	1	8	yes	complemented
62	#111458	C₂²	1	8	yes	complemented
63	#111458	C₂²	1	8	yes	complemented
64	#111458	C₂²	1	8	yes	complemented
65	C₂³×H(5,𝔽₂)	C₂³	1	4	yes	—
66	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic, complemented
67	C₂⁵×D₄	C₂³	1	2	yes	—
68	C₂⁵×D₄	C₂³	1	1	yes	characteristic
69	C₂⁵×D₄	C₂³	1	1	yes	characteristic
70	C₂²×#534	D₄	1	2	yes	complemented
71	C₂²×#534	C₂³	1	1	yes	characteristic, complemented
72	C₂²×#534	C₂³	1	1	yes	characteristic, complemented
73	C₂³×#123	D₄	1	1	yes	characteristic, complemented
74	C₂³×#120	D₄	1	2	yes	complemented
75	C₂³×#120	D₄	1	1	yes	characteristic, complemented
76	C₂³×#120	C₂³	1	1	yes	characteristic
77	C₂³×#120	C₂³	1	1	yes	characteristic
78	C₂²×#518	C₂³	1	1	yes	characteristic, complemented
79	C₂×#2849	D₄	1	4	yes	complemented
80	C₂×#2846	D₄	1	4	yes	complemented
81	#34980	D₄	1	16	yes	complemented
82	C₂×#2405	D₄	1	2	yes	complemented
83	C₂×#2405	C₂³	1	4	yes	—
84	C₂×#2405	C₂³	1	2	yes	—
85	C₂×#2405	C₂³	1	4	yes	—
86	C₂×#2410	D₄	1	8	yes	complemented
87	C₂×#2403	D₄	1	2	yes	complemented
88	C₂×#2403	D₄	1	2	yes	complemented
89	C₂×#2403	D₄	1	2	yes	complemented
90	C₂×#2403	D₄	1	16	yes	complemented
91	C₂×#2403	C₂³	1	2	yes	—
92	C₂×#2403	C₂³	1	2	yes	—
93	C₂×#2403	C₂³	1	2	yes	—
94	C₂×#2403	C₂³	1	4	yes	—
95	C₂×#2403	C₂³	1	4	yes	—
96	C₂×#2403	C₂³	1	4	yes	—
97	C₂×#2403	C₂³	1	4	yes	—
98	C₂²×#394	D₄	1	2	yes	complemented
99	C₂²×#394	C₂³	1	2	yes	—
100	C₂²×#392	D₄	1	2	yes	complemented
101	C₂²×#392	C₂³	1	2	yes	—
102	C₂×#2308	D₄	1	2	yes	complemented
103	C₂²×#386	D₄	1	2	yes	complemented
104	C₂²×#381	D₄	1	1	yes	characteristic, complemented
105	C₂²×#379	D₄	1	1	yes	characteristic, complemented
106	C₂²×#379	C₂³	1	2	yes	—
107	C₂²×#379	C₂³	1	2	yes	—
108	C₂²×#379	C₂³	1	1	yes	characteristic
109	C₂²×#379	C₂³	1	2	yes	—
110	C₂²×#379	C₂³	1	1	yes	characteristic
111	C₂²×#379	C₂³	1	1	yes	characteristic
112	C₂×#1819	C₂³	1	4	yes	complemented
113	C₂×#1819	C₂³	1	4	yes	complemented
114	C₂×#1781	C₂³	1	8	yes	—
115	C₂×#1781	C₂³	1	4	yes	—
116	C₂×#1781	C₂³	1	8	yes	—
117	C₂×#1781	C₂³	1	4	yes	—
118	C₂×#1781	C₂³	1	4	yes	complemented
119	C₂×#1781	C₂³	1	4	yes	complemented
120	C₂×#1781	C₂³	1	4	yes	complemented
121	C₂×#1781	C₂³	1	4	yes	complemented
122	#14341	C₂³	1	2	yes	complemented
123	#14335	C₂³	1	4	yes	—
124	#14335	C₂³	1	2	yes	complemented
125	#13869	C₂³	1	2	yes	complemented
126	#13867	C₂³	1	8	yes	—
127	#13867	C₂³	1	2	yes	complemented
128	#13867	C₂³	1	2	yes	complemented
129	#13867	C₂³	1	2	yes	complemented
130	#10725	C₂³	1	8	yes	complemented
131	C₂×#1304	C₂³	1	8	yes	complemented
132	C₂×#1304	C₂³	1	8	yes	complemented
133	C₂⁷	C₂×D₄	1	1	yes	characteristic
134	C₂⁷	C₂×D₄	1	2	yes	—
135	C₂⁷	C₂×D₄	1	1	yes	characteristic
136	C₂⁷	C₂⁴	1	1	yes	characteristic
137	C₂⁴×D₄	C₂×D₄	1	2	yes	—
138	C₂⁴×D₄	C₂×D₄	1	2	yes	—
139	C₂⁴×D₄	C₂×D₄	1	2	yes	—
140	C₂⁴×D₄	C₂×D₄	1	2	yes	—
141	C₂⁴×D₄	C₂×D₄	1	8	yes	—
142	C₂⁴×D₄	C₂×D₄	1	8	yes	—
143	C₂⁴×D₄	C₂×D₄	1	8	yes	—
144	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
145	C₂⁴×D₄	C₂×D₄	1	2	yes	—
146	C₂⁴×D₄	C₂×D₄	1	4	yes	—
147	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
148	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
149	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
150	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
151	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
152	C₂⁴×D₄	C₂×D₄	1	2	yes	complemented
153	C₂⁴×D₄	C₂⁴	1	4	yes	—
154	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
155	C₂⁴×D₄	C₂⁴	1	2	yes	—
156	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
157	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
158	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
159	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
160	C₂⁵×C₄	C₂×D₄	1	2	yes	—
161	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
162	C₂²×#123	C₂×D₄	1	4	yes	complemented
163	C₂²×#120	C₂×D₄	1	4	yes	—
164	C₂²×#120	C₂×D₄	1	4	yes	—
165	C₂²×#120	C₂×D₄	1	4	yes	—
166	C₂²×#120	C₂×D₄	1	4	yes	—
167	C₂²×#120	C₂×D₄	1	8	yes	—
168	C₂²×#120	C₂×D₄	1	4	yes	complemented
169	C₂²×#120	C₂×D₄	1	8	yes	complemented
170	C₂³×C₄⋊C₄	C₂×D₄	1	2	yes	complemented
171	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
172	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
173	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
174	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
175	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
176	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
177	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
178	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
179	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
180	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
181	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
182	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
183	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
184	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
185	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
186	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
187	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
188	#2405	C₂×D₄	1	16	yes	complemented
189	#2403	C₂×D₄	1	16	yes	—
190	#2403	C₂×D₄	1	16	yes	—
191	#2403	C₂×D₄	1	16	yes	complemented
192	C₂×#386	C₂×D₄	1	4	yes	—
193	C₂×#386	C₂×D₄	1	4	yes	—
194	C₂×#386	C₂×D₄	1	8	yes	complemented
195	C₂×#386	C₂×D₄	1	4	yes	complemented
196	C₂×#386	C₂×D₄	1	4	yes	complemented
197	C₂×#385	C₂×D₄	1	8	yes	complemented
198	C₂×#379	C₂×D₄	1	8	yes	—
199	C₂×#379	C₂×D₄	1	8	yes	—
200	C₂×#379	C₂×D₄	1	4	yes	—
201	C₂×#379	C₂×D₄	1	2	yes	—
202	C₂×#379	C₂×D₄	1	2	yes	—
203	C₂×#379	C₂×D₄	1	8	yes	complemented
204	C₂×#379	C₂⁴	1	4	yes	—
205	C₂×#379	C₂⁴	1	4	yes	—
206	C₂×#379	C₂⁴	1	2	yes	—
207	C₂×#379	C₂⁴	1	2	yes	—
208	C₂×#379	C₂⁴	1	4	yes	—
209	C₂²×#95	C₂×D₄	1	2	yes	complemented
210	C₂²×#95	C₂×D₄	1	2	yes	complemented
211	C₂⁶	#120	1	2	yes	—
212	C₂⁶	#120	1	2	yes	—
213	C₂⁶	#120	1	8	yes	complemented
214	C₂⁶	#120	1	4	yes	complemented
215	C₂⁶	C₂²×D₄	1	2	yes	—
216	C₂⁶	C₂²×D₄	1	1	yes	characteristic
217	C₂⁶	C₂²×D₄	1	1	yes	characteristic
218	C₂⁶	C₂²×D₄	1	1	yes	characteristic
219	C₂⁶	C₂²×D₄	1	4	yes	—
220	C₂⁶	C₂²×D₄	1	1	yes	characteristic
221	C₂⁶	C₂²×D₄	1	1	yes	characteristic
222	C₂⁶	C₂²×D₄	1	1	yes	characteristic
223	C₂⁶	C₂²×D₄	1	1	yes	characteristic
224	C₂⁶	C₂²×D₄	1	2	yes	—
225	C₂⁶	C₂²×D₄	1	1	yes	characteristic
226	C₂⁶	C₂²×D₄	1	2	yes	—
227	C₂⁶	C₂²×D₄	1	1	yes	characteristic
228	C₂⁶	C₂²×D₄	1	1	yes	characteristic
229	C₂⁶	C₂²×D₄	1	4	yes	—
230	C₂⁶	C₂²×D₄	1	4	yes	—
231	C₂⁶	H(5,𝔽₂)	1	2	yes	—
232	C₂⁶	H(5,𝔽₂)	1	2	yes	—
233	C₂⁶	H(5,𝔽₂)	1	4	yes	—
234	C₂⁶	H(5,𝔽₂)	1	4	yes	—
235	C₂⁶	C₂⁵	1	1	yes	characteristic
236	C₂³×D₄	#120	1	4	yes	—
237	C₂³×D₄	#120	1	4	yes	—
238	C₂³×D₄	#120	1	2	yes	—
239	C₂³×D₄	#120	1	2	yes	—
240	C₂³×D₄	#120	1	4	yes	—
241	C₂³×D₄	#120	1	16	yes	complemented
242	C₂³×D₄	#120	1	4	yes	complemented
243	C₂³×D₄	#120	1	4	yes	complemented
244	C₂³×D₄	#120	1	4	yes	complemented
245	C₂³×D₄	#120	1	4	yes	complemented
246	C₂³×D₄	C₂²×D₄	1	4	yes	—
247	C₂³×D₄	C₂²×D₄	1	4	yes	—
248	C₂³×D₄	C₂²×D₄	1	8	yes	—
249	C₂³×D₄	C₂²×D₄	1	8	yes	—
250	C₂³×D₄	C₂²×D₄	1	4	yes	—
251	C₂³×D₄	C₂²×D₄	1	4	yes	—
252	C₂³×D₄	C₂²×D₄	1	4	yes	—
253	C₂³×D₄	C₂²×D₄	1	4	yes	—
254	C₂⁴×C₄	#120	1	2	yes	—
255	C₂⁴×C₄	#120	1	2	yes	—
256	C₂⁴×C₄	#120	1	8	yes	complemented
257	C₂⁴×C₄	#120	1	4	yes	complemented
258	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
259	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
260	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
261	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
262	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
263	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
264	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
265	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
266	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
267	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
268	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
269	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
270	C₂²×C₂²⋊C₄	#120	1	4	yes	—
271	C₂²×C₂²⋊C₄	#120	1	2	yes	—
272	C₂²×C₂²⋊C₄	#120	1	2	yes	—
273	C₂²×C₂²⋊C₄	#120	1	4	yes	complemented
274	C₂²×C₂²⋊C₄	#120	1	4	yes	complemented
275	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
276	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
277	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
278	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
279	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
280	#379	C₂²×D₄	1	8	yes	—
281	#379	C₂²×D₄	1	8	yes	—
282	C₂⁵	B(4,𝔽₂)	1	8	yes	complemented
283	C₂⁵	C₂×#120	1	1	yes	characteristic
284	C₂⁵	C₂×#120	1	1	yes	characteristic
285	C₂⁵	C₂×#120	1	2	yes	—
286	C₂⁵	C₂×#120	1	4	yes	—
287	C₂⁵	C₂×#120	1	1	yes	characteristic
288	C₂⁵	C₂×#120	1	1	yes	characteristic
289	C₂⁵	C₂×#120	1	2	yes	—
290	C₂⁵	C₂×#120	1	1	yes	characteristic
291	C₂⁵	C₂×#120	1	2	yes	—
292	C₂⁵	C₂×#120	1	2	yes	—
293	C₂⁵	C₂×#120	1	2	yes	—
294	C₂⁵	C₂×#120	1	8	yes	—
295	C₂⁵	C₂×#120	1	2	yes	—
296	C₂⁵	C₂×#120	1	2	yes	—
297	C₂⁵	C₂×#120	1	4	yes	—
298	C₂⁵	C₂×#120	1	4	yes	—
299	C₂⁵	C₂×#120	1	1	yes	characteristic
300	C₂⁵	C₂×#120	1	2	yes	—
301	C₂⁵	C₂×#120	1	2	yes	—
302	C₂⁵	#534	1	1	yes	characteristic
303	C₂⁵	#534	1	1	yes	characteristic
304	C₂⁵	#534	1	2	yes	—
305	C₂⁵	#534	1	2	yes	—
306	C₂⁵	#534	1	2	yes	—
307	C₂⁵	#534	1	4	yes	—
308	C₂⁵	#534	1	4	yes	—
309	C₂⁵	#534	1	4	yes	—
310	C₂⁵	#534	1	4	yes	—
311	C₂⁵	#534	1	2	yes	—
312	C₂⁵	#534	1	4	yes	—
313	C₂⁵	#534	1	2	yes	—
314	C₂⁵	#534	1	4	yes	—
315	C₂⁵	D₄²	1	2	yes	—
316	C₂⁵	D₄²	1	2	yes	—
317	C₂⁵	D₄²	1	2	yes	—
318	C₂⁵	D₄²	1	2	yes	—
319	C₂⁵	D₄²	1	4	yes	—
320	C₂⁵	D₄²	1	4	yes	—
321	C₂⁵	D₄²	1	4	yes	—
322	C₂⁵	D₄²	1	4	yes	—
323	C₂⁵	D₄²	1	2	yes	—
324	C₂⁵	D₄²	1	2	yes	—
325	C₂⁵	D₄²	1	2	yes	—
326	C₂⁵	D₄²	1	2	yes	—
327	C₂⁵	D₄²	1	4	yes	—
328	C₂⁵	D₄²	1	4	yes	—
329	C₂⁵	D₄²	1	4	yes	—
330	C₂⁵	D₄²	1	4	yes	—
331	C₂⁵	D₄²	1	4	yes	—
332	C₂⁵	D₄²	1	4	yes	—
333	C₂⁵	D₄²	1	4	yes	—
334	C₂⁵	D₄²	1	4	yes	—
335	C₂⁵	D₄²	1	4	yes	—
336	C₂⁵	D₄²	1	4	yes	—
337	C₂⁵	H(3,𝔽₄)	1	4	yes	—
338	C₂⁵	H(3,𝔽₄)	1	4	yes	—
339	C₂⁵	C₂³×D₄	1	1	yes	characteristic
340	C₂⁵	C₂³×D₄	1	1	yes	characteristic
341	C₂⁵	C₂³×D₄	1	2	yes	—
342	C₂⁵	C₂³×D₄	1	1	yes	characteristic
343	C₂⁵	C₂³×D₄	1	2	yes	—
344	C₂⁵	C₂³×D₄	1	2	yes	—
345	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
346	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
347	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
348	C₂³×C₄	B(4,𝔽₂)	1	8	yes	complemented
349	C₂³×C₄	C₂×#120	1	2	yes	—
350	C₂³×C₄	C₂×#120	1	4	yes	—
351	C₂³×C₄	C₂×#120	1	2	yes	—
352	C₂³×C₄	C₂×#120	1	2	yes	—
353	C₂³×C₄	C₂×#120	1	2	yes	—
354	C₂³×C₄	C₂×#120	1	2	yes	—
355	C₂³×C₄	C₂×#120	1	8	yes	—
356	C₂³×C₄	C₂×#120	1	2	yes	—
357	C₂³×C₄	C₂×#120	1	2	yes	—
358	C₂³×C₄	C₂×#120	1	2	yes	—
359	C₂⁴	#2403	1	1	yes	characteristic
360	C₂⁴	#2403	1	1	yes	characteristic
361	C₂⁴	#2403	1	2	yes	—
362	C₂⁴	#2403	1	2	yes	—
363	C₂⁴	#2403	1	4	yes	—
364	C₂⁴	#2403	1	4	yes	—
365	C₂⁴	#2403	1	1	yes	characteristic
366	C₂⁴	#2403	1	1	yes	characteristic
367	C₂⁴	#2403	1	2	yes	—
368	C₂⁴	#2403	1	2	yes	—
369	C₂⁴	#2403	1	4	yes	—
370	C₂⁴	#2403	1	4	yes	—
371	C₂⁴	#2403	1	4	yes	—
372	C₂⁴	#2403	1	2	yes	—
373	C₂⁴	#2403	1	4	yes	—
374	C₂⁴	#2403	1	2	yes	—
375	C₂⁴	#2403	1	2	yes	—
376	C₂⁴	#2403	1	2	yes	—
377	C₂⁴	#2403	1	4	yes	—
378	C₂⁴	#2403	1	4	yes	—
379	C₂⁴	#2403	1	4	yes	—
380	C₂⁴	#2403	1	4	yes	—
381	C₂⁴	#2403	1	4	yes	—
382	C₂⁴	#2403	1	4	yes	—
383	C₂⁴	#2403	1	2	yes	—
384	C₂⁴	#2403	1	2	yes	—
385	C₂⁴	#2679	1	4	yes	—
386	C₂⁴	#2679	1	4	yes	—
387	C₂⁴	#2679	1	4	yes	—
388	C₂⁴	#2679	1	4	yes	—
389	C₂⁴	#2679	1	4	yes	—
390	C₂⁴	#2679	1	4	yes	—
391	C₂⁴	#2679	1	4	yes	—
392	C₂⁴	#2679	1	4	yes	—
393	C₂⁴	#2679	1	4	yes	—
394	C₂⁴	#2679	1	4	yes	—
395	C₂⁴	#2679	1	4	yes	—
396	C₂⁴	#2679	1	4	yes	—
397	C₂⁴	C₂×B(4,𝔽₂)	1	8	yes	—
398	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
399	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
400	C₂⁴	C₂²×#120	1	1	yes	characteristic
401	C₂⁴	C₂²×#120	1	1	yes	characteristic
402	C₂⁴	C₂²×#120	1	2	yes	—
403	C₂⁴	C₂²×#120	1	1	yes	characteristic
404	C₂⁴	C₂²×#120	1	1	yes	characteristic
405	C₂⁴	C₂×#534	1	1	yes	characteristic
406	C₂⁴	C₂×#534	1	2	yes	—
407	C₂⁴	C₂×#534	1	1	yes	characteristic
408	C₂⁴	C₂×#534	1	1	yes	characteristic
409	C₂⁴	C₂×#534	1	2	yes	—
410	C₂⁴	C₂×#534	1	2	yes	—
411	C₂⁴	C₂×D₄²	1	2	yes	—
412	C₂⁴	C₂×D₄²	1	2	yes	—
413	C₂⁴	C₂×D₄²	1	2	yes	—
414	C₂⁴	C₂×D₄²	1	2	yes	—
415	C₂⁴	C₂×D₄²	1	2	yes	—
416	C₂⁴	C₂×D₄²	1	2	yes	—
417	C₂⁴	C₂×D₄²	1	2	yes	—
418	C₂⁴	C₂×D₄²	1	2	yes	—
419	C₂⁴	C₂×D₄²	1	2	yes	—
420	C₂⁴	C₂×H(3,𝔽₄)	1	2	yes	—
421	C₂²×C₄	C₂×B(4,𝔽₂)	1	8	yes	—
422	C₂³	#15947	1	2	yes	—
423	C₂³	#15947	1	4	yes	—
424	C₂³	#15947	1	2	yes	—
425	C₂³	#15947	1	4	yes	—
426	C₂³	#15947	1	2	yes	—
427	C₂³	#15947	1	2	yes	—
428	C₂³	#23900	1	2	yes	—
429	C₂³	#23900	1	2	yes	—
430	C₂³	#23900	1	2	yes	—
431	C₂³	#23900	1	2	yes	—
432	C₂³	#23900	1	8	yes	—
433	C₂³	#23900	1	8	yes	—
434	C₂³	C₂×#2403	1	2	yes	—
435	C₂³	C₂×#2403	1	2	yes	—
436	C₂³	C₂×#2403	1	2	yes	—
437	C₂³	C₂×#2403	1	1	yes	characteristic
438	C₂³	C₂×#2403	1	1	yes	characteristic
439	C₂³	C₂×#2403	1	1	yes	characteristic
440	C₂³	C₂×#2679	1	2	yes	—
441	C₂³	C₂×#2679	1	2	yes	—
442	C₂³	C₂×#2679	1	2	yes	—
443	C₂³	C₂²×B(4,𝔽₂)	1	2	yes	—
444	C₂³	C₂²×B(4,𝔽₂)	1	2	yes	—
445	C₂³	#60399	1	4	yes	—
446	C₂²	#449475	1	4	yes	—
447	C₂²	#449475	1	4	yes	—
448	C₂²	C₂×#15947	1	1	yes	characteristic
449	C₂²	C₂×#23900	1	2	yes	—
450	C₂²	C₂×#23900	1	2	yes	—
451	C₂²	C₂×#23900	1	1	yes	characteristic
452	C₂²	C₂×#23900	1	1	yes	characteristic
453	C₂²	#6437629	1	2	yes	—
454	C₂²	#6437632	1	4	yes	—
455	C₂²	#6437632	1	2	yes	—
456	C₂	C₂×#449475	1	1	yes	characteristic
457	C₂	#72237496	1	2	yes	—
458	C₂	#72240604	1	1	yes	characteristic
459	C₂	#72261085	1	1	yes	characteristic
460	C₂	#72261209	1	2	yes	—

	subgroup	G/H
center, socle	C₂³	C₂×#2403
commutator, Frattini, cosocle	C₂⁶	C₂⁵
LCS	G ▷ C₂⁶ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁷ ◁ G
LECS	G ▷ C₂⁶ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72261821	C₂	semidirect
2. #72261812	C₂	semidirect
3. #72261803	C₂	semidirect
4. #72261788	C₂	semidirect
5. #72261782	C₂	semidirect
6. #72261779	C₂	semidirect
7. #72261770	C₂	semidirect
8. #72261767	C₂	semidirect
9. #72258626	C₂	semidirect
10. C₂×#115133	C₂	semidirect
11. C₂×#6470225	C₂	semidirect
12. C₂×#6628892	C₂	semidirect
13. #72225796	C₂	semidirect
14. C₂²×#32898	C₂	semidirect
15. #72219165	C₂	semidirect
16. C₂⁴×H(5,𝔽₂)	C₂²	semidirect
17. C₂²×#3484	C₂²	semidirect
24. C₂×#33020	C₂²	semidirect
25. C₂×#32900	C₂²	semidirect
27. C₂×#32898	C₂²	semidirect
28. C₂×#32898	C₂²	semidirect
29. C₂×#32898	C₂²	semidirect
30. C₂×#29634	C₂²	semidirect
31. C₂×#29634	C₂²	semidirect
32. C₂×#21746	C₂²	semidirect
33. C₂×#21746	C₂²	semidirect
34. C₂²×#1781	C₂²	semidirect
35. C₂²×#1781	C₂²	semidirect
36. C₂²×#1781	C₂²	semidirect
37. C₂²×#1781	C₂²	semidirect
38. C₂²×#1781	C₂²	semidirect
39. #4928993	C₂²	semidirect
40. #4928941	C₂²	semidirect
41. #4928938	C₂²	semidirect
42. #4928938	C₂²	semidirect
43. #4453283	C₂²	semidirect
44. #4453257	C₂²	semidirect
45. #556752	C₂²	semidirect
46. #556752	C₂²	semidirect
47. #517411	C₂²	semidirect
48. #517411	C₂²	semidirect
49. C₂×#14335	C₂²	semidirect
50. #355913	C₂²	semidirect
51. C₂×#8101	C₂²	semidirect
52. C₂²×#1304	C₂²	semidirect
53. #115135	C₂²	semidirect
54. #115134	C₂²	semidirect
55. #115133	C₂²	semidirect
56. #115133	C₂²	semidirect
57. #115133	C₂²	semidirect
58. #115133	C₂²	semidirect
59. #111517	C₂²	semidirect
60. #111516	C₂²	semidirect
61. #111459	C₂²	semidirect
62. #111458	C₂²	semidirect
63. #111458	C₂²	semidirect
64. #111458	C₂²	semidirect
66. C₂³×H(5,𝔽₂)	C₂³	semidirect
70. C₂²×#534	D₄	semidirect
71. C₂²×#534	C₂³	semidirect
72. C₂²×#534	C₂³	semidirect
73. C₂³×#123	D₄	semidirect
74. C₂³×#120	D₄	semidirect
75. C₂³×#120	D₄	semidirect
78. C₂²×#518	C₂³	semidirect
79. C₂×#2849	D₄	semidirect
80. C₂×#2846	D₄	semidirect
81. #34980	D₄	semidirect
82. C₂×#2405	D₄	semidirect
86. C₂×#2410	D₄	semidirect
87. C₂×#2403	D₄	semidirect
88. C₂×#2403	D₄	semidirect
89. C₂×#2403	D₄	semidirect
90. C₂×#2403	D₄	semidirect
98. C₂²×#394	D₄	semidirect
100. C₂²×#392	D₄	semidirect
102. C₂×#2308	D₄	semidirect
103. C₂²×#386	D₄	semidirect
104. C₂²×#381	D₄	semidirect
105. C₂²×#379	D₄	semidirect
112. C₂×#1819	C₂³	semidirect
113. C₂×#1819	C₂³	semidirect
118. C₂×#1781	C₂³	semidirect
119. C₂×#1781	C₂³	semidirect
120. C₂×#1781	C₂³	semidirect
121. C₂×#1781	C₂³	semidirect
122. #14341	C₂³	semidirect
124. #14335	C₂³	semidirect
125. #13869	C₂³	semidirect
127. #13867	C₂³	semidirect
128. #13867	C₂³	semidirect
129. #13867	C₂³	semidirect
130. #10725	C₂³	semidirect
131. C₂×#1304	C₂³	semidirect
132. C₂×#1304	C₂³	semidirect
152. C₂⁴×D₄	C₂×D₄	semidirect
162. C₂²×#123	C₂×D₄	semidirect
168. C₂²×#120	C₂×D₄	semidirect
169. C₂²×#120	C₂×D₄	semidirect
170. C₂³×C₄⋊C₄	C₂×D₄	semidirect
181. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
182. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
183. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
184. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
188. #2405	C₂×D₄	semidirect
191. #2403	C₂×D₄	semidirect
194. C₂×#386	C₂×D₄	semidirect
195. C₂×#386	C₂×D₄	semidirect
196. C₂×#386	C₂×D₄	semidirect
197. C₂×#385	C₂×D₄	semidirect
203. C₂×#379	C₂×D₄	semidirect
209. C₂²×#95	C₂×D₄	semidirect
210. C₂²×#95	C₂×D₄	semidirect
213. C₂⁶	#120	semidirect
214. C₂⁶	#120	semidirect
241. C₂³×D₄	#120	semidirect
242. C₂³×D₄	#120	semidirect
243. C₂³×D₄	#120	semidirect
244. C₂³×D₄	#120	semidirect
245. C₂³×D₄	#120	semidirect
256. C₂⁴×C₄	#120	semidirect
257. C₂⁴×C₄	#120	semidirect
273. C₂²×C₂²⋊C₄	#120	semidirect
274. C₂²×C₂²⋊C₄	#120	semidirect
282. C₂⁵	B(4,𝔽₂)	semidirect
348. C₂³×C₄	B(4,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
#72261821	2
#72261812	2
#72261803	2
#72261788	2
#72261782	2
#72261779	2
#72261770	2
#72261767	2
#72258626	2
C₂×#115133	2
C₂×#6470225	2
C₂×#6628892	2
#72225796	2
C₂²×#32898	2
#72219165	2