Subgroups — #72264278

Order 2048.

At least 7669 conjugacy classes of subgroups; only the 1514 normal subgroups are shown.

The subgroup lattice has 440 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72264272	C₂	1	2	yes	maximal, complemented
2	#72264269	C₂	1	2	yes	maximal, complemented
3	#72264266	C₂	1	2	yes	maximal, complemented
4	#72264131	C₂	1	4	yes	maximal, complemented
5	#72264097	C₂	1	1	yes	maximal, characteristic, complemented
6	#72264094	C₂	1	1	yes	maximal, characteristic, complemented
7	#72264090	C₂	1	1	yes	maximal, characteristic, complemented
8	#72264086	C₂	1	1	yes	maximal, characteristic, complemented
9	#72264018	C₂	1	4	yes	maximal, complemented
10	C₂²×#61559	C₂	1	1	yes	maximal, characteristic, complemented
11	#72240332	C₂	1	4	yes	maximal, complemented
12	#72237676	C₂	1	1	yes	maximal, characteristic, complemented
13	#72235738	C₂	1	2	yes	maximal, complemented
14	C₂×#248455	C₂	1	4	yes	maximal, complemented
15	D₄×#2403	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#3496	C₂²	1	1	yes	characteristic, complemented
17	C₂³×D₄²	C₂²	1	1	yes	characteristic
18	C₂³×D₄²	C₂²	1	1	yes	characteristic, complemented
19	C₂×#61559	C₂²	1	4	yes	—
20	C₂×#61559	C₂²	1	4	yes	complemented
21	C₂²×#3186	C₂²	1	2	yes	complemented
22	C₂³×#447	C₂²	1	2	yes	—
23	C₂²×#2972	C₂²	1	1	yes	characteristic, complemented
24	C₂×D₄×#120	C₂²	1	2	yes	complemented
25	C₂×#32878	C₂²	1	4	yes	complemented
26	C₂×#24260	C₂²	1	4	yes	complemented
27	C₂×#23918	C₂²	1	2	yes	complemented
28	C₂×#18194	C₂²	1	4	yes	complemented
29	#759292	C₂²	1	1	yes	characteristic, complemented
30	#649038	C₂²	1	2	yes	complemented
31	#647663	C₂²	1	2	yes	complemented
32	#612431	C₂²	1	1	yes	characteristic
33	#612431	C₂²	1	1	yes	characteristic, complemented
34	#612431	C₂²	1	2	yes	complemented
35	D₄×#379	C₂²	1	1	yes	characteristic, complemented
36	D₄×#386	C₂²	1	2	yes	complemented
37	C₄×#2403	C₂²	1	1	yes	characteristic
38	#393946	C₂²	1	4	yes	complemented
39	#393881	C₂²	1	4	yes	complemented
40	#392632	C₂²	1	4	yes	complemented
41	#392147	C₂²	1	1	yes	characteristic, complemented
42	#392118	C₂²	1	2	yes	complemented
43	#361664	C₂²	1	4	yes	complemented
44	#361599	C₂²	1	2	yes	complemented
45	#359519	C₂²	1	2	yes	complemented
46	#359422	C₂²	1	2	yes	complemented
47	C₂×#9946	C₂²	1	8	yes	complemented
48	C₂×#10320	C₂²	1	8	yes	complemented
49	C₂×#9468	C₂²	1	4	yes	complemented
50	C₂×#9259	C₂²	1	8	yes	complemented
51	C₂×#8965	C₂²	1	4	yes	complemented
52	#185958	C₂²	1	4	yes	complemented
53	C₂×#8375	C₂²	1	4	yes	complemented
54	C₂×#8375	C₂²	1	4	yes	complemented
55	#185046	C₂²	1	2	yes	complemented
56	#185046	C₂²	1	2	yes	complemented
57	#184743	C₂²	1	1	yes	characteristic, complemented
58	#114963	C₂²	1	8	yes	complemented
59	#114505	C₂²	1	8	yes	complemented
60	#111444	C₂²	1	8	yes	complemented
61	#108186	C₂²	1	4	yes	complemented
62	#106314	C₂²	1	4	yes	complemented
63	#105542	C₂²	1	2	yes	complemented
64	#105520	C₂²	1	2	yes	complemented
65	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
66	C₂⁵×D₄	C₂³	1	1	yes	characteristic
67	C₂⁵×D₄	C₂³	1	1	yes	characteristic, complemented
68	C₂⁴×D₈	D₄	1	4	yes	complemented
69	C₂×#3496	C₂³	1	4	yes	—
70	C₂²×D₄²	D₄	1	2	yes	complemented
71	C₂²×D₄²	D₄	1	2	yes	complemented
72	C₂²×D₄²	C₂³	1	2	yes	—
73	C₂²×D₄²	C₂³	1	2	yes	—
74	C₂³×#127	D₄	1	1	yes	characteristic, complemented
75	C₂³×#127	C₂³	1	1	yes	characteristic, complemented
76	C₂³×#121	D₄	1	1	yes	characteristic, complemented
77	C₂³×#121	C₂³	1	1	yes	characteristic
78	C₂³×#121	C₂³	1	2	yes	—
79	C₂³×#121	C₂³	1	1	yes	characteristic
80	C₂³×#121	C₂³	1	1	yes	characteristic, complemented
81	C₂³×C₄×D₄	D₄	1	1	yes	characteristic, complemented
82	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
83	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
84	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic, complemented
85	#61559	D₄	1	32	yes	complemented
86	C₂×#3186	C₂³	1	8	yes	—
87	C₂²×#447	D₄	1	8	yes	complemented
88	C₂²×#447	C₂³	1	4	yes	—
89	C₂²×#447	C₂³	1	4	yes	—
90	C₂²×#447	C₂³	1	4	yes	complemented
91	C₂×#2972	C₂³	1	4	yes	—
92	C₂³×#102	D₄	1	4	yes	complemented
93	C₂³×C₂²⋊C₈	C₂³	1	2	yes	—
94	C₂×#2847	C₂³	1	2	yes	complemented
95	C₂×#2847	C₂³	1	4	yes	complemented
96	C₂×#2433	C₂³	1	2	yes	complemented
97	C₂×#2408	C₂³	1	2	yes	—
98	C₂×#2403	D₄	1	1	yes	characteristic
99	C₂×D₄×C₂²⋊C₄	C₂³	1	2	yes	complemented
100	C₂×C₄×#120	C₂³	1	2	yes	—
101	C₂×#1964	C₂³	1	8	yes	complemented
102	C₂×#1874	C₂³	1	4	yes	complemented
103	C₂×#1799	C₂³	1	4	yes	—
104	C₂×#1786	C₂³	1	4	yes	complemented
105	C₂×#1786	C₂³	1	4	yes	complemented
106	C₂×#1786	C₂³	1	4	yes	complemented
107	C₂×#1779	C₂³	1	2	yes	—
108	C₂×#1779	C₂³	1	4	yes	complemented
109	C₂×#1519	C₂³	1	8	yes	complemented
110	C₂×#1519	C₂³	1	8	yes	complemented
111	C₂×#1459	C₂³	1	4	yes	—
112	#14722	D₄	1	4	yes	complemented
113	#14719	D₄	1	2	yes	complemented
114	#14716	D₄	1	2	yes	complemented
115	#14698	C₂³	1	2	yes	complemented
116	#14698	C₂³	1	4	yes	complemented
117	#14680	C₂³	1	2	yes	—
118	#14680	C₂³	1	1	yes	characteristic
119	#14137	C₂³	1	2	yes	complemented
120	#14127	D₄	1	1	yes	characteristic
121	#14015	D₄	1	2	yes	—
122	#13967	D₄	1	2	yes	—
123	#13902	C₂³	1	2	yes	complemented
124	#13872	C₂³	1	2	yes	—
125	#13867	D₄	1	1	yes	characteristic
126	#13867	D₄	1	1	yes	characteristic
127	C₄×#379	C₂³	1	1	yes	characteristic
128	C₄×#386	C₂³	1	2	yes	—
129	#10730	C₂³	1	4	yes	complemented
130	#10712	C₂³	1	4	yes	complemented
131	C₂×#1289	C₂³	1	8	yes	complemented
132	C₂×#1282	C₂³	1	8	yes	complemented
133	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
134	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
135	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
136	C₂⁴×D₄	C₂×D₄	1	4	yes	—
137	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
138	C₂⁴×D₄	C₂×D₄	1	2	yes	—
139	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
140	C₂⁴×D₄	C₂×D₄	1	2	yes	—
141	C₂⁴×D₄	C₂×D₄	1	4	yes	—
142	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
143	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
144	C₂⁴×D₄	C₂×D₄	1	2	yes	complemented
145	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
146	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
147	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
148	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
149	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
150	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
151	C₂³×D₈	C₂×D₄	1	8	yes	—
152	C₂³×D₈	C₂×D₄	1	8	yes	complemented
153	C₂⁴×C₈	C₂×D₄	1	4	yes	complemented
154	#3496	C₂×D₄	1	16	yes	complemented
155	C₂×D₄²	C₂×D₄	1	16	yes	—
156	C₂²×#127	C₂×D₄	1	2	yes	—
157	C₂²×#127	C₂×D₄	1	2	yes	—
158	C₂²×#121	C₂×D₄	1	2	yes	—
159	C₂²×#121	C₂×D₄	1	2	yes	—
160	C₂²×#121	C₂×D₄	1	2	yes	—
161	C₂²×#121	C₂×D₄	1	2	yes	—
162	C₂²×#121	C₂×D₄	1	2	yes	—
163	C₂²×#121	C₂×D₄	1	4	yes	complemented
164	C₂²×#121	C₂⁴	1	4	yes	—
165	C₂²×#121	C₂⁴	1	2	yes	—
166	C₂²×#120	C₂×D₄	1	2	yes	—
167	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
168	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
169	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
170	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
171	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
172	C₂²×C₄×D₄	C₂⁴	1	2	yes	—
173	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
174	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
175	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
176	C₂³×C₄⋊C₄	C₂×D₄	1	2	yes	complemented
177	C₂³×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
178	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
179	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
180	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
181	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
182	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
183	C₂³×C₄²	C₂⁴	1	1	yes	characteristic
184	#3186	C₂×D₄	1	32	yes	complemented
185	C₂×#447	C₂×D₄	1	32	yes	—
186	#2972	C₂×D₄	1	16	yes	complemented
187	C₂²×#102	C₂×D₄	1	8	yes	—
188	C₂²×#102	C₂×D₄	1	8	yes	complemented
189	C₂²×C₂²⋊C₈	C₂×D₄	1	4	yes	complemented
190	C₂²×C₂²⋊C₈	C₂⁴	1	4	yes	—
191	C₂²×C₂²⋊C₈	C₂⁴	1	4	yes	—
192	#2403	D₈	1	8	yes	complemented
193	C₂×#394	C₂×D₄	1	4	yes	—
194	C₂×#392	C₂×D₄	1	4	yes	—
195	C₂×#386	C₂×D₄	1	2	yes	—
196	C₂×#386	C₂×D₄	1	2	yes	—
197	C₂×#386	C₂×D₄	1	2	yes	—
198	C₂×#385	C₂×D₄	1	2	yes	—
199	C₂×#380	C₂⁴	1	4	yes	—
200	C₂×#380	C₂⁴	1	2	yes	—
201	C₂×#379	C₂×D₄	1	2	yes	—
202	C₂×#379	C₂×D₄	1	1	yes	characteristic
203	C₂×#379	C₂×D₄	1	1	yes	characteristic
204	C₂×C₄×C₂²⋊C₄	C₂⁴	1	2	yes	—
205	#1441	C₂×D₄	1	4	yes	—
206	#1439	C₂×D₄	1	4	yes	—
207	C₂²⋊#95	C₂×D₄	1	2	yes	—
208	C₂²⋊#95	C₂×D₄	1	2	yes	—
209	C₂²⋊#95	C₂×D₄	1	2	yes	—
210	C₂²⋊#95	C₂×D₄	1	2	yes	—
211	C₂²⋊#95	C₂×D₄	1	2	yes	—
212	C₂⁶	#120	1	1	yes	characteristic
213	C₂⁶	C₂²×D₄	1	1	yes	characteristic
214	C₂⁶	C₂²×D₄	1	1	yes	characteristic
215	C₂³×D₄	#120	1	2	yes	—
216	C₂³×D₄	#120	1	2	yes	—
217	C₂³×D₄	#120	1	2	yes	—
218	C₂³×D₄	#120	1	4	yes	—
219	C₂³×D₄	#120	1	2	yes	—
220	C₂³×D₄	#120	1	4	yes	—
221	C₂³×D₄	#120	1	2	yes	—
222	C₂³×D₄	#120	1	8	yes	complemented
223	C₂³×D₄	C₂×D₈	1	4	yes	—
224	C₂³×D₄	C₂×D₈	1	4	yes	complemented
225	C₂³×D₄	AGL(1,ℤ/8)	1	4	yes	—
226	C₂³×D₄	C₂²×D₄	1	2	yes	—
227	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
228	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
229	C₂³×D₄	C₂²×D₄	1	4	yes	—
230	C₂³×D₄	C₂²×D₄	1	4	yes	—
231	C₂³×D₄	C₂²×D₄	1	2	yes	—
232	C₂³×D₄	C₂²×D₄	1	2	yes	—
233	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
234	C₂³×D₄	C₂²×D₄	1	4	yes	—
235	C₂³×D₄	C₂²×D₄	1	8	yes	—
236	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
237	C₂⁴×C₄	#120	1	1	yes	characteristic
238	C₂⁴×C₄	#120	1	1	yes	characteristic
239	C₂⁴×C₄	#120	1	2	yes	—
240	C₂⁴×C₄	#120	1	1	yes	characteristic
241	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
242	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
243	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
244	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
245	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
246	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
247	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
248	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
249	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
250	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
251	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
252	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
253	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
254	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
255	C₂²×D₈	#120	1	32	yes	complemented
256	C₂³×C₈	C₂²×D₄	1	8	yes	—
257	C₂×#127	#120	1	8	yes	complemented
258	C₂×#121	#120	1	8	yes	complemented
259	C₂×#121	C₂²×D₄	1	8	yes	—
260	C₂×#121	C₂²×D₄	1	16	yes	—
261	C₂×#120	C₂×D₈	1	8	yes	complemented
262	C₂×C₄×D₄	#120	1	8	yes	complemented
263	C₂×C₄×D₄	C₂²×D₄	1	8	yes	—
264	C₂×C₄×D₄	H(5,𝔽₂)	1	8	yes	—
265	C₂²×C₄⋊C₄	#120	1	2	yes	—
266	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
267	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
268	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
269	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
270	C₂²×C₂²⋊C₄	#120	1	2	yes	—
271	C₂²×C₂²⋊C₄	#120	1	2	yes	—
272	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
273	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
274	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
275	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
276	C₂²×C₄²	#120	1	2	yes	—
277	C₂²×C₄²	C₂²×D₄	1	2	yes	—
278	C₂×#102	#120	1	32	yes	complemented
279	C₂×C₂²⋊C₈	C₂²×D₄	1	16	yes	—
280	#386	C₂×D₈	1	8	yes	complemented
281	#379	C₂×D₈	1	4	yes	complemented
282	C₂×#95	C₂²×D₄	1	4	yes	—
283	C₂⁵	#447	1	4	yes	complemented
284	C₂⁵	C₂×#120	1	1	yes	characteristic
285	C₂⁵	C₂×#120	1	1	yes	characteristic
286	C₂⁵	C₂×#120	1	2	yes	—
287	C₂⁵	D₄²	1	2	yes	—
288	C₂⁵	D₄²	1	2	yes	—
289	C₂⁵	C₂²×D₈	1	2	yes	—
290	C₂⁵	C₂²×D₈	1	2	yes	complemented
291	C₂⁵	C₂×AGL(1,ℤ/8)	1	2	yes	—
292	C₂⁵	#576	1	4	yes	—
293	C₂⁵	C₂³×D₄	1	1	yes	characteristic
294	C₂²×D₄	#447	1	8	yes	complemented
295	C₂²×D₄	B(4,𝔽₂)	1	8	yes	complemented
296	C₂²×D₄	C₂×#120	1	2	yes	—
297	C₂²×D₄	C₂×#120	1	4	yes	—
298	C₂²×D₄	C₂×#120	1	2	yes	—
299	C₂²×D₄	C₂×#120	1	2	yes	—
300	C₂²×D₄	C₂×#120	1	16	yes	—
301	C₂²×D₄	C₂×#120	1	2	yes	—
302	C₂²×D₄	C₂×#120	1	4	yes	—
303	C₂²×D₄	C₂×#120	1	4	yes	—
304	C₂²×D₄	C₂×#120	1	8	yes	complemented
305	C₂²×D₄	D₄²	1	8	yes	—
306	C₂²×D₄	C₂²×D₈	1	4	yes	—
307	C₂²×D₄	C₂×AGL(1,ℤ/8)	1	4	yes	—
308	C₂²×D₄	#576	1	8	yes	—
309	C₂³×C₄	#447	1	4	yes	complemented
310	C₂³×C₄	C₂×#120	1	2	yes	—
311	C₂³×C₄	C₂×#120	1	1	yes	characteristic
312	C₂³×C₄	C₂×#120	1	1	yes	characteristic
313	C₂³×C₄	C₂×#120	1	2	yes	—
314	C₂³×C₄	C₂×#120	1	1	yes	characteristic
315	C₂³×C₄	C₂×#120	1	2	yes	—
316	C₂³×C₄	C₂×#120	1	1	yes	characteristic
317	C₂³×C₄	C₂×#120	1	2	yes	—
318	C₂³×C₄	C₂×#120	1	4	yes	—
319	C₂³×C₄	#534	1	1	yes	characteristic
320	C₂³×C₄	#534	1	1	yes	characteristic
321	C₂³×C₄	#534	1	2	yes	—
322	C₂³×C₄	#534	1	4	yes	—
323	C₂³×C₄	D₄²	1	2	yes	—
324	C₂³×C₄	D₄²	1	2	yes	—
325	C₂³×C₄	D₄²	1	2	yes	—
326	C₂³×C₄	D₄²	1	2	yes	—
327	C₂³×C₄	D₄²	1	2	yes	—
328	C₂³×C₄	D₄²	1	2	yes	—
329	C₂³×C₄	C₂²×D₈	1	2	yes	complemented
330	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
331	C₂³×C₄	C₂³×D₄	1	2	yes	—
332	C₂³×C₄	C₂³×D₄	1	4	yes	—
333	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
334	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
335	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
336	C₂²×C₈	C₂×#120	1	16	yes	complemented
337	C₂×C₄⋊C₄	C₂×#120	1	4	yes	—
338	C₂×C₄⋊C₄	C₂×#120	1	8	yes	complemented
339	C₂×C₄⋊C₄	D₄²	1	8	yes	—
340	C₂×C₂²⋊C₄	D₄²	1	8	yes	—
341	C₂×C₂²⋊C₄	D₄²	1	8	yes	—
342	C₂×C₂²⋊C₄	C₂²×D₈	1	4	yes	complemented
343	C₂×C₄²	C₂×#120	1	4	yes	—
344	C₂×C₄²	#534	1	4	yes	—
345	C₂⁴	#2403	1	2	yes	—
346	C₂⁴	#2403	1	1	yes	characteristic
347	C₂⁴	#2403	1	1	yes	characteristic
348	C₂⁴	#2403	1	4	yes	—
349	C₂⁴	C₂×#447	1	2	yes	—
350	C₂⁴	C₂×#447	1	2	yes	—
351	C₂⁴	C₂×#447	1	4	yes	—
352	C₂⁴	#3008	1	2	yes	—
353	C₂⁴	#3008	1	2	yes	—
354	C₂⁴	#3008	1	4	yes	—
355	C₂⁴	#3264	1	4	yes	—
356	C₂⁴	#3264	1	4	yes	—
357	C₂⁴	D₄×D₈	1	4	yes	—
358	C₂⁴	D₄×D₈	1	4	yes	—
359	C₂⁴	C₂²×#120	1	1	yes	characteristic
360	C₂⁴	C₂×D₄²	1	2	yes	—
361	C₂⁴	C₂×D₄²	1	4	yes	—
362	C₂⁴	C₂³×D₈	1	1	yes	characteristic
363	C₂⁴	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
364	C₂⁴	C₂×#576	1	4	yes	—
365	C₂⁴	C₂×#576	1	2	yes	—
366	C₂×D₄	#2846	1	4	yes	—
367	C₂×D₄	#2846	1	4	yes	—
368	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
369	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
370	C₂×D₄	#3026	1	4	yes	—
371	C₂×D₄	#3264	1	16	yes	—
372	C₂×D₄	D₄×D₈	1	16	yes	—
373	C₂²×C₄	#2403	1	1	yes	characteristic
374	C₂²×C₄	#2403	1	2	yes	—
375	C₂²×C₄	#2403	1	4	yes	—
376	C₂²×C₄	#2403	1	1	yes	characteristic
377	C₂²×C₄	#2403	1	4	yes	—
378	C₂²×C₄	#2403	1	4	yes	—
379	C₂²×C₄	C₂×#447	1	4	yes	—
380	C₂²×C₄	#3008	1	4	yes	—
381	C₂²×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
382	C₂²×C₄	C₂²×#120	1	2	yes	—
383	C₂²×C₄	C₂²×#120	1	4	yes	—
384	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
385	C₂²×C₄	C₂×#534	1	2	yes	—
386	C₂²×C₄	C₂×#534	1	1	yes	characteristic
387	C₂²×C₄	C₂×D₄²	1	2	yes	—
388	C₂²×C₄	C₂×D₄²	1	4	yes	—
389	C₂²×C₄	#3484	1	4	yes	—
390	C₂²×C₄	#3484	1	8	yes	—
391	C₂³	#23848	1	2	yes	—
392	C₂³	#23848	1	4	yes	—
393	C₂³	#23848	1	2	yes	—
394	C₂³	#23848	1	8	yes	complemented
395	C₂³	#23882	1	2	yes	—
396	C₂³	#23900	1	2	yes	—
397	C₂³	C₂×#2403	1	2	yes	—
398	C₂³	C₂×#2403	1	1	yes	characteristic
399	C₂³	D₄×#120	1	4	yes	—
400	C₂³	C₂²×#447	1	1	yes	characteristic
401	C₂³	C₂×#3008	1	1	yes	characteristic
402	C₂³	C₂×#3008	1	2	yes	—
403	C₂³	C₂×#3264	1	2	yes	—
404	C₂³	C₂×#3264	1	4	yes	—
405	C₂³	C₂×D₄×D₈	1	2	yes	—
406	C₂³	C₂×D₄×D₈	1	4	yes	—
407	C₂³	#61049	1	4	yes	—
408	C₂³	#61049	1	8	yes	—
409	D₄	#32898	1	8	yes	complemented
410	C₂×C₄	#23848	1	8	yes	complemented
411	C₂×C₄	#23900	1	2	yes	—
412	C₂×C₄	#34980	1	2	yes	—
413	C₂×C₄	#34980	1	1	yes	characteristic
414	C₂×C₄	D₄×#120	1	4	yes	—
415	C₂×C₄	C₂×#2846	1	1	yes	characteristic
416	C₂×C₄	C₂²×B(4,𝔽₂)	1	2	yes	—
417	C₂×C₄	C₂×#3026	1	2	yes	—
418	C₂²	#248455	1	4	yes	complemented
419	C₂²	#612424	1	1	yes	characteristic
420	C₂²	C₂×#23848	1	2	yes	—
421	C₂²	C₂×#23848	1	1	yes	characteristic
422	C₂²	#6437521	1	2	yes	—
423	C₂²	#6437521	1	1	yes	characteristic
424	C₂²	C₂×#23882	1	1	yes	characteristic
425	C₂²	#6437576	1	1	yes	characteristic
426	C₂²	C₂×#23900	1	1	yes	characteristic
427	C₂²	#6437621	1	1	yes	characteristic
428	C₂²	D₈×#120	1	4	yes	—
429	C₂²	#6573477	1	4	yes	—
430	C₄	#6470225	1	2	yes	—
431	C₄	C₂×#32898	1	2	yes	—
432	C₂	#72214832	1	1	yes	characteristic
433	C₂	#72214896	1	1	yes	characteristic
434	C₂	C₂×#248455	1	1	yes	characteristic
435	C₂	#72237129	1	1	yes	characteristic
436	C₂	#72257452	1	1	yes	characteristic
437	C₂	#72263884	1	1	yes	characteristic
438	C₂	#72263907	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂×#2403
commutator, Frattini, cosocle	C₂⁴×C₄	C₂⁵
LCS	G ▷ C₂⁴×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁵×C₄ ◁ G
LECS	G ▷ C₂⁴×C₄ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72264272	C₂	semidirect
2. #72264269	C₂	semidirect
3. #72264266	C₂	semidirect
4. #72264131	C₂	semidirect
5. #72264097	C₂	semidirect
6. #72264094	C₂	semidirect
7. #72264090	C₂	semidirect
8. #72264086	C₂	semidirect
9. #72264018	C₂	semidirect
10. C₂²×#61559	C₂	semidirect
11. #72240332	C₂	semidirect
12. #72237676	C₂	semidirect
13. #72235738	C₂	semidirect
14. C₂×#248455	C₂	semidirect
15. D₄×#2403	C₂	semidirect
16. C₂²×#3496	C₂²	semidirect
18. C₂³×D₄²	C₂²	semidirect
20. C₂×#61559	C₂²	semidirect
21. C₂²×#3186	C₂²	semidirect
23. C₂²×#2972	C₂²	semidirect
24. C₂×D₄×#120	C₂²	semidirect
25. C₂×#32878	C₂²	semidirect
26. C₂×#24260	C₂²	semidirect
27. C₂×#23918	C₂²	semidirect
28. C₂×#18194	C₂²	semidirect
29. #759292	C₂²	semidirect
30. #649038	C₂²	semidirect
31. #647663	C₂²	semidirect
33. #612431	C₂²	semidirect
34. #612431	C₂²	semidirect
35. D₄×#379	C₂²	semidirect
36. D₄×#386	C₂²	semidirect
38. #393946	C₂²	semidirect
39. #393881	C₂²	semidirect
40. #392632	C₂²	semidirect
41. #392147	C₂²	semidirect
42. #392118	C₂²	semidirect
43. #361664	C₂²	semidirect
44. #361599	C₂²	semidirect
45. #359519	C₂²	semidirect
46. #359422	C₂²	semidirect
47. C₂×#9946	C₂²	semidirect
48. C₂×#10320	C₂²	semidirect
49. C₂×#9468	C₂²	semidirect
50. C₂×#9259	C₂²	semidirect
51. C₂×#8965	C₂²	semidirect
52. #185958	C₂²	semidirect
53. C₂×#8375	C₂²	semidirect
54. C₂×#8375	C₂²	semidirect
55. #185046	C₂²	semidirect
56. #185046	C₂²	semidirect
57. #184743	C₂²	semidirect
58. #114963	C₂²	semidirect
59. #114505	C₂²	semidirect
60. #111444	C₂²	semidirect
61. #108186	C₂²	semidirect
62. #106314	C₂²	semidirect
63. #105542	C₂²	semidirect
64. #105520	C₂²	semidirect
65. C₂⁵×D₄	D₄	semidirect
67. C₂⁵×D₄	C₂³	semidirect
68. C₂⁴×D₈	D₄	semidirect
70. C₂²×D₄²	D₄	semidirect
71. C₂²×D₄²	D₄	semidirect
74. C₂³×#127	D₄	semidirect
75. C₂³×#127	C₂³	semidirect
76. C₂³×#121	D₄	semidirect
80. C₂³×#121	C₂³	semidirect
81. C₂³×C₄×D₄	D₄	semidirect
84. C₂³×C₄×D₄	C₂³	semidirect
85. #61559	D₄	semidirect
87. C₂²×#447	D₄	semidirect
90. C₂²×#447	C₂³	semidirect
92. C₂³×#102	D₄	semidirect
94. C₂×#2847	C₂³	semidirect
95. C₂×#2847	C₂³	semidirect
96. C₂×#2433	C₂³	semidirect
99. C₂×D₄×C₂²⋊C₄	C₂³	semidirect
101. C₂×#1964	C₂³	semidirect
102. C₂×#1874	C₂³	semidirect
104. C₂×#1786	C₂³	semidirect
105. C₂×#1786	C₂³	semidirect
106. C₂×#1786	C₂³	semidirect
108. C₂×#1779	C₂³	semidirect
109. C₂×#1519	C₂³	semidirect
110. C₂×#1519	C₂³	semidirect
112. #14722	D₄	semidirect
113. #14719	D₄	semidirect
114. #14716	D₄	semidirect
115. #14698	C₂³	semidirect
116. #14698	C₂³	semidirect
119. #14137	C₂³	semidirect
123. #13902	C₂³	semidirect
129. #10730	C₂³	semidirect
130. #10712	C₂³	semidirect
131. C₂×#1289	C₂³	semidirect
132. C₂×#1282	C₂³	semidirect
144. C₂⁴×D₄	C₂×D₄	semidirect
152. C₂³×D₈	C₂×D₄	semidirect
153. C₂⁴×C₈	C₂×D₄	semidirect
154. #3496	C₂×D₄	semidirect
163. C₂²×#121	C₂×D₄	semidirect
176. C₂³×C₄⋊C₄	C₂×D₄	semidirect
184. #3186	C₂×D₄	semidirect
186. #2972	C₂×D₄	semidirect
188. C₂²×#102	C₂×D₄	semidirect
189. C₂²×C₂²⋊C₈	C₂×D₄	semidirect
192. #2403	D₈	semidirect
222. C₂³×D₄	#120	semidirect
224. C₂³×D₄	C₂×D₈	semidirect
255. C₂²×D₈	#120	semidirect
257. C₂×#127	#120	semidirect
258. C₂×#121	#120	semidirect
261. C₂×#120	C₂×D₈	semidirect
262. C₂×C₄×D₄	#120	semidirect
278. C₂×#102	#120	semidirect
280. #386	C₂×D₈	semidirect
281. #379	C₂×D₈	semidirect
283. C₂⁵	#447	semidirect
290. C₂⁵	C₂²×D₈	semidirect
294. C₂²×D₄	#447	semidirect
295. C₂²×D₄	B(4,𝔽₂)	semidirect
304. C₂²×D₄	C₂×#120	semidirect
309. C₂³×C₄	#447	semidirect
329. C₂³×C₄	C₂²×D₈	semidirect
336. C₂²×C₈	C₂×#120	semidirect
338. C₂×C₄⋊C₄	C₂×#120	semidirect
342. C₂×C₂²⋊C₄	C₂²×D₈	semidirect
394. C₂³	#23848	semidirect
409. D₄	#32898	semidirect
410. C₂×C₄	#23848	semidirect
418. C₂²	#248455	semidirect

Maximal subgroups

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

subgroup	index
#72264272	2
#72264269	2
#72264266	2
#72264131	2
#72264097	2
#72264094	2
#72264090	2
#72264086	2
#72264018	2
C₂²×#61559	2
#72240332	2
#72237676	2
#72235738	2
C₂×#248455	2
D₄×#2403	2