Subgroups — #72266006

Order 2048.

At least 7261 conjugacy classes of subgroups; only the 1792 normal subgroups are shown.

The subgroup lattice has 458 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72266005	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#201687	C₂	1	1	yes	maximal, characteristic, complemented
3	#72241188	C₂	1	8	yes	maximal, complemented
4	#72240568	C₂	1	1	yes	maximal, characteristic, complemented
5	#72238531	C₂	1	2	yes	maximal, complemented
6	C₂×#233541	C₂	1	2	yes	maximal, complemented
7	#72234629	C₂	1	2	yes	maximal, complemented
8	C₂×#6628892	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#35346	C₂	1	1	yes	maximal, characteristic, complemented
10	#72225796	C₂	1	2	yes	maximal, complemented
11	#72225609	C₂	1	8	yes	maximal, complemented
12	#72219254	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#8541	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂⁴×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
15	C₂⁴×#120	C₂²	1	1	yes	characteristic
16	C₂×#35346	C₂²	1	8	yes	—
17	C₂×#34980	C₂²	1	1	yes	characteristic
18	C₂×#34980	C₂²	1	1	yes	characteristic, complemented
19	C₂×#34980	C₂²	1	1	yes	characteristic, complemented
20	C₂×#34980	C₂²	1	2	yes	complemented
21	C₂²×#2403	C₂²	1	2	yes	—
22	C₂²×#2403	C₂²	1	2	yes	—
23	C₂²×#2308	C₂²	1	1	yes	characteristic
24	C₂×#32900	C₂²	1	4	yes	complemented
25	C₂×#32898	C₂²	1	4	yes	complemented
26	C₂×#21746	C₂²	1	2	yes	complemented
27	C₂²×#1781	C₂²	1	1	yes	characteristic
28	C₂²×#1781	C₂²	1	1	yes	characteristic
29	C₂²×#1781	C₂²	1	2	yes	complemented
30	C₂²×#1781	C₂²	1	2	yes	complemented
31	C₂²×#1781	C₂²	1	2	yes	complemented
32	C₂²×#1781	C₂²	1	2	yes	complemented
33	#617161	C₂²	1	4	yes	complemented
34	#616960	C₂²	1	4	yes	complemented
35	#517411	C₂²	1	1	yes	characteristic
36	#517411	C₂²	1	1	yes	characteristic, complemented
37	#517411	C₂²	1	1	yes	characteristic, complemented
38	#517411	C₂²	1	2	yes	complemented
39	#405104	C₂²	1	8	yes	complemented
40	#393929	C₂²	1	8	yes	complemented
41	#392125	C₂²	1	8	yes	complemented
42	#355913	C₂²	1	2	yes	complemented
43	C₂×#10337	C₂²	1	8	yes	complemented
44	C₂×#10336	C₂²	1	8	yes	complemented
45	C₂×#9499	C₂²	1	4	yes	complemented
46	C₂×#9495	C₂²	1	4	yes	complemented
47	C₂×#8541	C₂²	1	8	yes	complemented
48	C₂×#8101	C₂²	1	2	yes	complemented
49	C₂×#8101	C₂²	1	2	yes	complemented
50	#115133	C₂²	1	16	yes	complemented
51	#111458	C₂²	1	16	yes	complemented
52	#106542	C₂²	1	8	yes	complemented
53	C₂⁸	D₄	1	1	yes	characteristic, complemented
54	C₂³×H(5,𝔽₂)	D₄	1	8	yes	complemented
55	C₂³×H(5,𝔽₂)	C₂³	1	4	yes	—
56	C₂⁵×D₄	C₂³	1	2	yes	—
57	C₂⁵×D₄	C₂³	1	1	yes	characteristic
58	C₂⁵×D₄	C₂³	1	1	yes	characteristic
59	C₂⁵×D₄	C₂³	1	1	yes	characteristic
60	C₂²×#534	D₄	1	2	yes	complemented
61	C₂²×#534	C₂³	1	2	yes	complemented
62	C₂³×#120	D₄	1	4	yes	complemented
63	C₂³×#120	D₄	1	4	yes	complemented
64	C₂³×#120	C₂³	1	1	yes	characteristic
65	C₂³×#120	C₂³	1	4	yes	—
66	C₂⁴×C₂²⋊C₄	D₄	1	1	yes	characteristic, complemented
67	C₂⁴×C₂²⋊C₄	D₄	1	1	yes	characteristic, complemented
68	C₂⁴×C₂²⋊C₄	D₄	1	1	yes	characteristic, complemented
69	C₂×#2405	D₄	1	2	yes	complemented
70	C₂×#2405	C₂³	1	2	yes	—
71	C₂×#2405	C₂³	1	2	yes	complemented
72	C₂×#2405	C₂³	1	4	yes	complemented
73	C₂×#2403	D₄	1	8	yes	complemented
74	C₂×#2403	D₄	1	16	yes	complemented
75	C₂×#2403	D₄	1	2	yes	complemented
76	C₂×#2403	C₂³	1	8	yes	—
77	C₂×#2403	C₂³	1	2	yes	—
78	C₂×#2403	C₂³	1	8	yes	—
79	C₂×#2403	C₂³	1	2	yes	complemented
80	C₂×#2403	C₂³	1	4	yes	complemented
81	C₂×#2308	D₄	1	2	yes	complemented
82	C₂×#2308	D₄	1	8	yes	complemented
83	C₂×#2308	D₄	1	4	yes	complemented
84	C₂×#2308	C₂³	1	4	yes	—
85	C₂×#2308	C₂³	1	2	yes	complemented
86	C₂²×#386	D₄	1	4	yes	complemented
87	C₂²×#379	C₂³	1	2	yes	—
88	C₂²×#379	C₂³	1	2	yes	—
89	C₂²×#379	C₂³	1	2	yes	—
90	C₂²×#379	C₂³	1	1	yes	characteristic
91	C₂²×#379	C₂³	1	1	yes	characteristic
92	C₂²×#379	C₂³	1	1	yes	characteristic
93	C₂×#1819	C₂³	1	4	yes	complemented
94	C₂×#1781	D₄	1	8	yes	complemented
95	C₂×#1781	C₂³	1	4	yes	—
96	C₂×#1781	C₂³	1	4	yes	—
97	C₂×#1781	C₂³	1	8	yes	complemented
98	C₂×#1781	C₂³	1	4	yes	complemented
99	C₂×#1781	C₂³	1	8	yes	complemented
100	C₂×#1781	C₂³	1	8	yes	complemented
101	C₂×#1781	C₂³	1	8	yes	complemented
102	#14335	C₂³	1	4	yes	complemented
103	#13867	D₄	1	4	yes	complemented
104	#13867	C₂³	1	4	yes	—
105	#13867	C₂³	1	4	yes	complemented
106	#13867	C₂³	1	8	yes	complemented
107	#10725	C₂³	1	8	yes	complemented
108	C₂×#1304	C₂³	1	8	yes	complemented
109	C₂×#1304	C₂³	1	8	yes	complemented
110	C₂⁷	C₂×D₄	1	1	yes	characteristic
111	C₂⁷	C₂×D₄	1	1	yes	characteristic
112	C₂⁷	C₂×D₄	1	1	yes	characteristic
113	C₂⁷	C₂×D₄	1	2	yes	—
114	C₂⁷	C₂×D₄	1	4	yes	—
115	C₂⁷	C₂⁴	1	1	yes	characteristic
116	C₂²×H(5,𝔽₂)	C₂×D₄	1	16	yes	—
117	C₂⁴×D₄	C₂×D₄	1	2	yes	—
118	C₂⁴×D₄	C₂×D₄	1	2	yes	—
119	C₂⁴×D₄	C₂×D₄	1	4	yes	—
120	C₂⁴×D₄	C₂×D₄	1	4	yes	—
121	C₂⁴×D₄	C₂×D₄	1	8	yes	—
122	C₂⁴×D₄	C₂×D₄	1	2	yes	—
123	C₂⁴×D₄	C₂×D₄	1	4	yes	—
124	C₂⁴×D₄	C₂×D₄	1	2	yes	—
125	C₂⁴×D₄	C₂×D₄	1	4	yes	—
126	C₂⁴×D₄	C₂×D₄	1	8	yes	—
127	C₂⁴×D₄	C₂×D₄	1	8	yes	—
128	C₂⁴×D₄	C₂×D₄	1	4	yes	—
129	C₂⁴×D₄	C₂×D₄	1	4	yes	—
130	C₂⁴×D₄	C₂×D₄	1	2	yes	—
131	C₂⁴×D₄	C₂×D₄	1	2	yes	—
132	C₂⁴×D₄	C₂×D₄	1	2	yes	—
133	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
134	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
135	C₂⁴×D₄	#41	1	4	yes	—
136	C₂⁴×D₄	C₂⁴	1	4	yes	—
137	C₂⁴×D₄	C₂⁴	1	2	yes	—
138	C₂⁴×D₄	C₂⁴	1	2	yes	—
139	C₂⁴×D₄	C₂⁴	1	2	yes	—
140	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
141	C₂⁵×C₄	C₂×D₄	1	2	yes	—
142	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
143	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
144	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
145	C₂²×#123	C₂×D₄	1	4	yes	complemented
146	C₂²×#120	C₂×D₄	1	16	yes	—
147	C₂²×#120	C₂×D₄	1	4	yes	complemented
148	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
149	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
150	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
151	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
152	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
153	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
154	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
155	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
156	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
157	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
158	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
159	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
160	#2403	C₂×D₄	1	32	yes	—
161	#2308	C₂×D₄	1	16	yes	—
162	C₂×#386	C₂×D₄	1	16	yes	—
163	C₂×#386	C₂×D₄	1	4	yes	complemented
164	C₂×#386	C₂×D₄	1	4	yes	complemented
165	C₂×#386	C₂×D₄	1	16	yes	complemented
166	C₂×#379	C₂×D₄	1	8	yes	—
167	C₂×#379	C₂×D₄	1	8	yes	—
168	C₂×#379	C₂×D₄	1	4	yes	—
169	C₂×#379	C₂×D₄	1	8	yes	complemented
170	C₂×#379	C₂×D₄	1	2	yes	complemented
171	C₂×#379	C₂×D₄	1	2	yes	complemented
172	C₂×#379	C₂⁴	1	4	yes	—
173	C₂×#379	C₂⁴	1	4	yes	—
174	C₂×#379	C₂⁴	1	4	yes	—
175	C₂×#379	C₂⁴	1	2	yes	—
176	C₂×#379	C₂⁴	1	2	yes	—
177	#1781	C₂×D₄	1	16	yes	complemented
178	C₂⁶	#120	1	2	yes	—
179	C₂⁶	#120	1	4	yes	—
180	C₂⁶	#120	1	2	yes	—
181	C₂⁶	#120	1	2	yes	—
182	C₂⁶	#120	1	2	yes	—
183	C₂⁶	#120	1	4	yes	—
184	C₂⁶	#120	1	8	yes	complemented
185	C₂⁶	#121	1	4	yes	—
186	C₂⁶	C₂²×D₄	1	2	yes	—
187	C₂⁶	C₂²×D₄	1	2	yes	—
188	C₂⁶	C₂²×D₄	1	1	yes	characteristic
189	C₂⁶	C₂²×D₄	1	1	yes	characteristic
190	C₂⁶	C₂²×D₄	1	1	yes	characteristic
191	C₂⁶	C₂²×D₄	1	2	yes	—
192	C₂⁶	C₂²×D₄	1	4	yes	—
193	C₂⁶	C₂²×D₄	1	2	yes	—
194	C₂⁶	C₂²×D₄	1	1	yes	characteristic
195	C₂⁶	C₂²×D₄	1	2	yes	—
196	C₂⁶	C₂²×D₄	1	1	yes	characteristic
197	C₂⁶	C₂²×D₄	1	1	yes	characteristic
198	C₂⁶	C₂²×D₄	1	2	yes	—
199	C₂⁶	C₂²×D₄	1	2	yes	—
200	C₂⁶	C₂²×D₄	1	4	yes	—
201	C₂⁶	C₂²×D₄	1	2	yes	—
202	C₂⁶	C₂²×D₄	1	1	yes	characteristic, complemented
203	C₂⁶	C₂×#41	1	2	yes	—
204	C₂⁶	H(5,𝔽₂)	1	2	yes	—
205	C₂⁶	H(5,𝔽₂)	1	2	yes	—
206	C₂⁶	H(5,𝔽₂)	1	4	yes	—
207	C₂⁶	C₂⁵	1	1	yes	characteristic
208	C₂³×D₄	#120	1	8	yes	—
209	C₂³×D₄	#120	1	4	yes	—
210	C₂³×D₄	#120	1	4	yes	—
211	C₂³×D₄	#120	1	8	yes	—
212	C₂³×D₄	#120	1	8	yes	—
213	C₂³×D₄	#120	1	8	yes	—
214	C₂³×D₄	#120	1	8	yes	—
215	C₂³×D₄	#120	1	16	yes	complemented
216	C₂³×D₄	#121	1	8	yes	—
217	C₂³×D₄	#121	1	8	yes	—
218	C₂³×D₄	#121	1	8	yes	—
219	C₂³×D₄	#121	1	8	yes	—
220	C₂³×D₄	#121	1	8	yes	—
221	C₂³×D₄	#127	1	8	yes	—
222	C₂³×D₄	#127	1	8	yes	—
223	C₂³×D₄	C₂²×D₄	1	8	yes	—
224	C₂³×D₄	C₂²×D₄	1	4	yes	—
225	C₂³×D₄	C₂²×D₄	1	4	yes	—
226	C₂³×D₄	C₂²×D₄	1	8	yes	—
227	C₂³×D₄	C₂²×D₄	1	8	yes	—
228	C₂³×D₄	C₂²×D₄	1	8	yes	—
229	C₂³×D₄	C₂²×D₄	1	4	yes	—
230	C₂³×D₄	C₂²×D₄	1	4	yes	—
231	C₂³×D₄	C₂²×D₄	1	4	yes	—
232	C₂³×D₄	C₂×#41	1	4	yes	—
233	C₂⁴×C₄	#120	1	2	yes	—
234	C₂⁴×C₄	#120	1	2	yes	—
235	C₂⁴×C₄	#120	1	2	yes	—
236	C₂⁴×C₄	#120	1	4	yes	—
237	C₂⁴×C₄	#120	1	4	yes	—
238	C₂⁴×C₄	#120	1	2	yes	—
239	C₂⁴×C₄	#120	1	8	yes	complemented
240	C₂⁴×C₄	#121	1	4	yes	—
241	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
242	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
243	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
244	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
245	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic, complemented
246	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic, complemented
247	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic, complemented
248	C₂⁴×C₄	C₂²×D₄	1	4	yes	complemented
249	C₂²×C₂²⋊C₄	#120	1	16	yes	complemented
250	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
251	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	complemented
252	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	complemented
253	#379	#120	1	16	yes	complemented
254	#379	C₂²×D₄	1	8	yes	—
255	#379	C₂²×D₄	1	8	yes	—
256	#379	C₂²×D₄	1	8	yes	complemented
257	C₂⁵	#392	1	8	yes	—
258	C₂⁵	#392	1	8	yes	—
259	C₂⁵	B(4,𝔽₂)	1	16	yes	—
260	C₂⁵	C₂×#120	1	1	yes	characteristic
261	C₂⁵	C₂×#120	1	1	yes	characteristic
262	C₂⁵	C₂×#120	1	1	yes	characteristic
263	C₂⁵	C₂×#120	1	4	yes	—
264	C₂⁵	C₂×#120	1	4	yes	—
265	C₂⁵	C₂×#120	1	2	yes	—
266	C₂⁵	C₂×#120	1	2	yes	—
267	C₂⁵	C₂×#120	1	2	yes	—
268	C₂⁵	C₂×#120	1	1	yes	characteristic
269	C₂⁵	C₂×#120	1	1	yes	characteristic
270	C₂⁵	C₂×#120	1	4	yes	—
271	C₂⁵	C₂×#120	1	2	yes	—
272	C₂⁵	C₂×#120	1	4	yes	—
273	C₂⁵	C₂×#120	1	8	yes	—
274	C₂⁵	C₂×#120	1	4	yes	—
275	C₂⁵	C₂×#120	1	4	yes	—
276	C₂⁵	C₂×#120	1	2	yes	—
277	C₂⁵	C₂×#120	1	2	yes	—
278	C₂⁵	C₂×#120	1	4	yes	—
279	C₂⁵	C₂×#120	1	4	yes	—
280	C₂⁵	C₂×#120	1	2	yes	—
281	C₂⁵	C₂×#120	1	1	yes	characteristic
282	C₂⁵	C₂×#121	1	4	yes	—
283	C₂⁵	C₂×#121	1	2	yes	—
284	C₂⁵	C₂×#121	1	2	yes	—
285	C₂⁵	C₂×#121	1	2	yes	—
286	C₂⁵	C₂×#121	1	2	yes	—
287	C₂⁵	C₂×#121	1	2	yes	—
288	C₂⁵	C₂×#121	1	2	yes	—
289	C₂⁵	C₂×#127	1	2	yes	—
290	C₂⁵	C₂×#127	1	2	yes	—
291	C₂⁵	#534	1	1	yes	characteristic
292	C₂⁵	#534	1	2	yes	—
293	C₂⁵	#534	1	1	yes	characteristic
294	C₂⁵	#534	1	2	yes	—
295	C₂⁵	#534	1	4	yes	—
296	C₂⁵	#534	1	2	yes	—
297	C₂⁵	#534	1	4	yes	—
298	C₂⁵	#535	1	4	yes	—
299	C₂⁵	#535	1	4	yes	—
300	C₂⁵	D₄²	1	2	yes	—
301	C₂⁵	D₄²	1	2	yes	—
302	C₂⁵	D₄²	1	2	yes	—
303	C₂⁵	D₄²	1	2	yes	—
304	C₂⁵	D₄²	1	2	yes	—
305	C₂⁵	D₄²	1	2	yes	—
306	C₂⁵	D₄²	1	4	yes	—
307	C₂⁵	D₄²	1	4	yes	—
308	C₂⁵	D₄²	1	2	yes	—
309	C₂⁵	D₄²	1	2	yes	—
310	C₂⁵	D₄²	1	4	yes	—
311	C₂⁵	D₄²	1	4	yes	—
312	C₂⁵	D₄²	1	4	yes	—
313	C₂⁵	D₄²	1	4	yes	—
314	C₂⁵	D₄²	1	4	yes	—
315	C₂⁵	D₄²	1	4	yes	—
316	C₂⁵	#546	1	4	yes	—
317	C₂⁵	#546	1	4	yes	—
318	C₂⁵	#546	1	4	yes	—
319	C₂⁵	#546	1	4	yes	—
320	C₂⁵	C₂³×D₄	1	1	yes	characteristic
321	C₂⁵	C₂³×D₄	1	2	yes	—
322	C₂⁵	C₂³×D₄	1	1	yes	characteristic
323	C₂⁵	C₂³×D₄	1	1	yes	characteristic
324	C₂⁵	C₂³×D₄	1	1	yes	characteristic
325	C₂⁵	C₂³×D₄	1	1	yes	characteristic
326	C₂⁵	C₂³×D₄	1	2	yes	—
327	C₂⁵	C₂³×D₄	1	1	yes	characteristic
328	C₂⁵	C₂²×#41	1	1	yes	characteristic
329	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
330	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
331	C₂²×D₄	#392	1	16	yes	—
332	C₂²×D₄	#392	1	16	yes	—
333	C₂²×D₄	C₂×#120	1	8	yes	—
334	C₂²×D₄	C₂×#121	1	8	yes	—
335	C₂²×D₄	C₂×#121	1	8	yes	—
336	C₂²×D₄	C₂×#127	1	8	yes	—
337	C₂³×C₄	#392	1	8	yes	—
338	C₂³×C₄	#392	1	8	yes	—
339	C₂³×C₄	C₂×#120	1	4	yes	—
340	C₂³×C₄	C₂×#120	1	4	yes	—
341	C₂³×C₄	C₂×#120	1	8	yes	—
342	C₂³×C₄	C₂×#120	1	4	yes	—
343	C₂³×C₄	C₂×#120	1	4	yes	—
344	C₂³×C₄	C₂×#121	1	4	yes	—
345	C₂×C₂²⋊C₄	C₂×#120	1	16	yes	—
346	C₂⁴	#2021	1	32	yes	complemented
347	C₂⁴	C₂×#392	1	2	yes	—
348	C₂⁴	C₂×#392	1	2	yes	—
349	C₂⁴	C₂×#392	1	2	yes	—
350	C₂⁴	C₂×#392	1	8	yes	—
351	C₂⁴	C₂×#392	1	2	yes	—
352	C₂⁴	#2403	1	1	yes	characteristic
353	C₂⁴	#2403	1	2	yes	—
354	C₂⁴	#2403	1	2	yes	—
355	C₂⁴	#2403	1	2	yes	—
356	C₂⁴	#2403	1	1	yes	characteristic
357	C₂⁴	#2403	1	1	yes	characteristic
358	C₂⁴	#2403	1	1	yes	characteristic
359	C₂⁴	#2403	1	4	yes	—
360	C₂⁴	#2403	1	4	yes	—
361	C₂⁴	#2403	1	2	yes	—
362	C₂⁴	#2403	1	4	yes	—
363	C₂⁴	#2403	1	2	yes	—
364	C₂⁴	#2403	1	4	yes	—
365	C₂⁴	#2403	1	2	yes	—
366	C₂⁴	#2408	1	4	yes	—
367	C₂⁴	#2408	1	4	yes	—
368	C₂⁴	#2408	1	4	yes	—
369	C₂⁴	#2408	1	4	yes	—
370	C₂⁴	#2410	1	2	yes	—
371	C₂⁴	#2410	1	2	yes	—
372	C₂⁴	#2410	1	2	yes	—
373	C₂⁴	#2410	1	2	yes	—
374	C₂⁴	#2410	1	4	yes	—
375	C₂⁴	#2410	1	4	yes	—
376	C₂⁴	#2410	1	4	yes	—
377	C₂⁴	#2410	1	4	yes	—
378	C₂⁴	#2410	1	4	yes	—
379	C₂⁴	#2410	1	4	yes	—
380	C₂⁴	#2433	1	4	yes	—
381	C₂⁴	#2433	1	4	yes	—
382	C₂⁴	#2433	1	4	yes	—
383	C₂⁴	#2433	1	4	yes	—
384	C₂⁴	#2613	1	2	yes	—
385	C₂⁴	#2613	1	2	yes	—
386	C₂⁴	#2613	1	4	yes	—
387	C₂⁴	#2846	1	2	yes	—
388	C₂⁴	#2846	1	2	yes	—
389	C₂⁴	#2846	1	4	yes	—
390	C₂⁴	C₂×B(4,𝔽₂)	1	16	yes	—
391	C₂⁴	C₂×B(4,𝔽₂)	1	8	yes	—
392	C₂⁴	#3026	1	8	yes	complemented
393	C₂⁴	C₂²×#120	1	1	yes	characteristic
394	C₂⁴	C₂²×#120	1	1	yes	characteristic
395	C₂⁴	C₂²×#120	1	1	yes	characteristic
396	C₂⁴	C₂²×#120	1	1	yes	characteristic
397	C₂⁴	C₂²×#120	1	2	yes	—
398	C₂⁴	C₂²×#120	1	2	yes	—
399	C₂⁴	C₂²×#120	1	1	yes	characteristic
400	C₂⁴	C₂²×#121	1	1	yes	characteristic
401	C₂⁴	C₂²×#121	1	1	yes	characteristic
402	C₂⁴	C₂²×#121	1	1	yes	characteristic
403	C₂⁴	C₂²×#127	1	1	yes	characteristic
404	C₂⁴	C₂×#534	1	1	yes	characteristic
405	C₂⁴	C₂×#534	1	1	yes	characteristic
406	C₂⁴	C₂×#534	1	2	yes	—
407	C₂⁴	C₂×#535	1	2	yes	—
408	C₂⁴	C₂×D₄²	1	2	yes	—
409	C₂⁴	C₂×D₄²	1	2	yes	—
410	C₂⁴	C₂×D₄²	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×#546	1	2	yes	—
415	C₂⁴	C₂×#546	1	2	yes	—
416	C₂²×C₄	C₂×#392	1	8	yes	—
417	C₂³	#14715	1	2	yes	—
418	C₂³	#14715	1	4	yes	—
419	C₂³	#14715	1	4	yes	—
420	C₂³	#14715	1	2	yes	—
421	C₂³	#14715	1	2	yes	—
422	C₂³	#14715	1	2	yes	—
423	C₂³	C₂×#2021	1	16	yes	—
424	C₂³	C₂×#2021	1	8	yes	—
425	C₂³	#23895	1	4	yes	—
426	C₂³	#23900	1	4	yes	—
427	C₂³	#23900	1	4	yes	—
428	C₂³	#23900	1	8	yes	—
429	C₂³	C₂²×#392	1	1	yes	characteristic
430	C₂³	C₂×#2613	1	1	yes	characteristic
431	C₂³	C₂×#2403	1	2	yes	—
432	C₂³	C₂×#2403	1	1	yes	characteristic
433	C₂³	C₂×#2403	1	1	yes	characteristic
434	C₂³	C₂×#2410	1	1	yes	characteristic
435	C₂³	C₂×#2410	1	2	yes	—
436	C₂³	C₂×#2410	1	1	yes	characteristic
437	C₂³	C₂×#2408	1	2	yes	—
438	C₂³	C₂×#2433	1	2	yes	—
439	C₂³	C₂×#2846	1	1	yes	characteristic
440	C₂³	C₂²×B(4,𝔽₂)	1	4	yes	—
441	C₂³	C₂×#3026	1	4	yes	—
442	C₂²	#394058	1	4	yes	—
443	C₂²	#394058	1	4	yes	—
444	C₂²	#394064	1	4	yes	—
445	C₂²	C₂×#14715	1	1	yes	characteristic
446	C₂²	C₂²×#2021	1	2	yes	—
447	C₂²	C₂×#23900	1	2	yes	—
448	C₂²	C₂×#23900	1	2	yes	—
449	C₂²	#6437621	1	2	yes	—
450	C₂²	C₂×#23895	1	2	yes	—
451	C₂²	#6437995	1	2	yes	—
452	C₂²	#6628892	1	2	yes	—
453	C₂	C₂×#394058	1	1	yes	characteristic
454	C₂	#72233065	1	4	yes	—
455	C₂	C₂×#394064	1	1	yes	characteristic
456	C₂	#72238029	1	1	yes	characteristic

	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. #72266005	C₂	semidirect
2. C₂×#201687	C₂	semidirect
3. #72241188	C₂	semidirect
4. #72240568	C₂	semidirect
5. #72238531	C₂	semidirect
6. C₂×#233541	C₂	semidirect
7. #72234629	C₂	semidirect
8. C₂×#6628892	C₂	semidirect
9. C₂²×#35346	C₂	semidirect
10. #72225796	C₂	semidirect
11. #72225609	C₂	semidirect
12. #72219254	C₂	semidirect
13. C₂²×#8541	C₂	semidirect
18. C₂×#34980	C₂²	semidirect
19. C₂×#34980	C₂²	semidirect
20. C₂×#34980	C₂²	semidirect
24. C₂×#32900	C₂²	semidirect
25. C₂×#32898	C₂²	semidirect
26. C₂×#21746	C₂²	semidirect
29. C₂²×#1781	C₂²	semidirect
30. C₂²×#1781	C₂²	semidirect
31. C₂²×#1781	C₂²	semidirect
32. C₂²×#1781	C₂²	semidirect
33. #617161	C₂²	semidirect
34. #616960	C₂²	semidirect
36. #517411	C₂²	semidirect
37. #517411	C₂²	semidirect
38. #517411	C₂²	semidirect
39. #405104	C₂²	semidirect
40. #393929	C₂²	semidirect
41. #392125	C₂²	semidirect
42. #355913	C₂²	semidirect
43. C₂×#10337	C₂²	semidirect
44. C₂×#10336	C₂²	semidirect
45. C₂×#9499	C₂²	semidirect
46. C₂×#9495	C₂²	semidirect
47. C₂×#8541	C₂²	semidirect
48. C₂×#8101	C₂²	semidirect
49. C₂×#8101	C₂²	semidirect
50. #115133	C₂²	semidirect
51. #111458	C₂²	semidirect
52. #106542	C₂²	semidirect
53. C₂⁸	D₄	semidirect
54. C₂³×H(5,𝔽₂)	D₄	semidirect
60. C₂²×#534	D₄	semidirect
61. C₂²×#534	C₂³	semidirect
62. C₂³×#120	D₄	semidirect
63. C₂³×#120	D₄	semidirect
66. C₂⁴×C₂²⋊C₄	D₄	semidirect
67. C₂⁴×C₂²⋊C₄	D₄	semidirect
68. C₂⁴×C₂²⋊C₄	D₄	semidirect
69. C₂×#2405	D₄	semidirect
71. C₂×#2405	C₂³	semidirect
72. C₂×#2405	C₂³	semidirect
73. C₂×#2403	D₄	semidirect
74. C₂×#2403	D₄	semidirect
75. C₂×#2403	D₄	semidirect
79. C₂×#2403	C₂³	semidirect
80. C₂×#2403	C₂³	semidirect
81. C₂×#2308	D₄	semidirect
82. C₂×#2308	D₄	semidirect
83. C₂×#2308	D₄	semidirect
85. C₂×#2308	C₂³	semidirect
86. C₂²×#386	D₄	semidirect
93. C₂×#1819	C₂³	semidirect
94. C₂×#1781	D₄	semidirect
97. C₂×#1781	C₂³	semidirect
98. C₂×#1781	C₂³	semidirect
99. C₂×#1781	C₂³	semidirect
100. C₂×#1781	C₂³	semidirect
101. C₂×#1781	C₂³	semidirect
102. #14335	C₂³	semidirect
103. #13867	D₄	semidirect
105. #13867	C₂³	semidirect
106. #13867	C₂³	semidirect
107. #10725	C₂³	semidirect
108. C₂×#1304	C₂³	semidirect
109. C₂×#1304	C₂³	semidirect
133. C₂⁴×D₄	C₂×D₄	semidirect
134. C₂⁴×D₄	C₂×D₄	semidirect
145. C₂²×#123	C₂×D₄	semidirect
147. C₂²×#120	C₂×D₄	semidirect
152. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
153. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
154. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
155. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
156. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
157. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
163. C₂×#386	C₂×D₄	semidirect
164. C₂×#386	C₂×D₄	semidirect
165. C₂×#386	C₂×D₄	semidirect
169. C₂×#379	C₂×D₄	semidirect
170. C₂×#379	C₂×D₄	semidirect
171. C₂×#379	C₂×D₄	semidirect
177. #1781	C₂×D₄	semidirect
184. C₂⁶	#120	semidirect
202. C₂⁶	C₂²×D₄	semidirect
215. C₂³×D₄	#120	semidirect
239. C₂⁴×C₄	#120	semidirect
245. C₂⁴×C₄	C₂²×D₄	semidirect
246. C₂⁴×C₄	C₂²×D₄	semidirect
247. C₂⁴×C₄	C₂²×D₄	semidirect
248. C₂⁴×C₄	C₂²×D₄	semidirect
249. C₂²×C₂²⋊C₄	#120	semidirect
251. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
252. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
253. #379	#120	semidirect
256. #379	C₂²×D₄	semidirect
346. C₂⁴	#2021	semidirect
392. C₂⁴	#3026	semidirect

Maximal subgroups

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

subgroup	index
#72266005	2
C₂×#201687	2
#72241188	2
#72240568	2
#72238531	2
C₂×#233541	2
#72234629	2
C₂×#6628892	2
C₂²×#35346	2
#72225796	2
#72225609	2
#72219254	2
C₂²×#8541	2