Subgroups — #72263065

Order 2048.

At least 10259 conjugacy classes of subgroups; only the 620 normal subgroups are shown.

The subgroup lattice has 409 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72263063	C₂	1	2	yes	maximal, complemented
2	#72263062	C₂	1	2	yes	maximal, complemented
3	#72262570	C₂	1	2	yes	maximal, complemented
4	#72236963	C₂	1	2	yes	maximal, complemented
5	#72234143	C₂	1	2	yes	maximal, complemented
6	#72233429	C₂	1	2	yes	maximal, complemented
7	#72233426	C₂	1	2	yes	maximal, complemented
8	#72233378	C₂	1	2	yes	maximal, complemented
9	#72233244	C₂	1	1	yes	maximal, characteristic, complemented
10	#72233150	C₂	1	2	yes	maximal, complemented
11	#72233058	C₂	1	1	yes	maximal, characteristic, complemented
12	#72233027	C₂	1	2	yes	maximal, complemented
13	#72232967	C₂	1	1	yes	maximal, characteristic, complemented
14	#72232866	C₂	1	1	yes	maximal, characteristic, complemented
15	#72232757	C₂	1	1	yes	maximal, characteristic, complemented
16	#72226358	C₂	1	1	yes	maximal, characteristic, complemented
17	#72216323	C₂	1	1	yes	maximal, characteristic, complemented
18	#72213719	C₂	1	2	yes	maximal, complemented
19	#72210587	C₂	1	2	yes	maximal, complemented
20	#10586472	C₂²	1	1	yes	characteristic, complemented
21	#6512701	C₂²	1	2	yes	complemented
22	#6500010	C₂²	1	2	yes	complemented
23	#6499867	C₂²	1	2	yes	—
24	#4035541	C₂²	1	1	yes	characteristic, complemented
25	#4035539	C₂²	1	1	yes	characteristic, complemented
26	#2306524	C₂²	1	1	yes	characteristic, complemented
27	#2306453	C₂²	1	1	yes	characteristic, complemented
28	#2109018	C₂²	1	1	yes	characteristic, complemented
29	#2108839	C₂²	1	1	yes	characteristic, complemented
30	#1420706	C₂²	1	1	yes	characteristic, complemented
31	#1420272	C₂²	1	1	yes	characteristic, complemented
32	#1419288	C₂²	1	1	yes	characteristic, complemented
33	#1418393	C₂²	1	1	yes	characteristic, complemented
34	#719145	C₂²	1	1	yes	characteristic
35	#687584	C₂²	1	1	yes	characteristic
36	#648750	C₂²	1	1	yes	characteristic, complemented
37	#647656	C₂²	1	1	yes	characteristic
38	#647656	C₂²	1	1	yes	characteristic, complemented
39	#512142	C₂²	1	4	yes	complemented
40	#511771	C₂²	1	4	yes	complemented
41	#347056	C₂²	1	2	yes	complemented
42	#347048	C₂²	1	2	yes	complemented
43	#347047	C₂²	1	2	yes	—
44	#347047	C₂²	1	2	yes	complemented
45	#347047	C₂²	1	2	yes	complemented
46	#347042	C₂²	1	2	yes	—
47	#347042	C₂²	1	2	yes	—
48	#347042	C₂²	1	2	yes	complemented
49	#346466	C₂²	1	2	yes	complemented
50	#346466	C₂²	1	2	yes	complemented
51	#346446	C₂²	1	2	yes	—
52	#346446	C₂²	1	2	yes	complemented
53	#188151	C₂²	1	1	yes	characteristic, complemented
54	#188035	C₂²	1	1	yes	characteristic, complemented
55	#188035	C₂²	1	1	yes	characteristic, complemented
56	#187940	C₂²	1	2	yes	complemented
57	#187934	C₂²	1	2	yes	complemented
58	#186819	C₂²	1	2	yes	complemented
59	#144654	C₂²	1	4	yes	complemented
60	#144627	C₂²	1	4	yes	complemented
61	#144414	C₂²	1	4	yes	complemented
62	#144412	C₂²	1	4	yes	complemented
63	#144404	C₂²	1	4	yes	complemented
64	#144404	C₂²	1	4	yes	complemented
65	#144386	C₂²	1	4	yes	complemented
66	#144366	C₂²	1	4	yes	complemented
67	#139846	C₂²	1	2	yes	complemented
68	#139830	C₂²	1	2	yes	complemented
69	#139830	C₂²	1	2	yes	complemented
70	#139828	C₂²	1	2	yes	complemented
71	#139815	C₂²	1	4	yes	complemented
72	#139790	C₂²	1	2	yes	complemented
73	#139790	C₂²	1	2	yes	complemented
74	#139790	C₂²	1	2	yes	complemented
75	#139773	C₂²	1	4	yes	complemented
76	#139767	C₂²	1	4	yes	complemented
77	#139718	C₂²	1	2	yes	complemented
78	#139718	C₂²	1	2	yes	complemented
79	#139716	C₂²	1	2	yes	complemented
80	#139716	C₂²	1	2	yes	complemented
81	#139716	C₂²	1	2	yes	complemented
82	#139706	C₂²	1	4	yes	complemented
83	#139700	C₂²	1	4	yes	complemented
84	#139700	C₂²	1	4	yes	complemented
85	#135548	C₂²	1	2	yes	complemented
86	#135522	C₂²	1	2	yes	complemented
87	#135507	C₂²	1	2	yes	complemented
88	#133893	C₂²	1	2	yes	complemented
89	#133853	C₂²	1	2	yes	complemented
90	#133822	C₂²	1	2	yes	complemented
91	#62832	C₂³	1	2	yes	—
92	#62817	C₂³	1	2	yes	—
93	#62817	C₂³	1	2	yes	—
94	C₂²×D₄²	C₂³	1	1	yes	characteristic
95	C₂²×D₄²	C₂³	1	1	yes	characteristic, complemented
96	C₂²×#534	D₄	1	1	yes	characteristic, complemented
97	C₂³×#120	D₄	1	1	yes	characteristic, complemented
98	C₂³×#120	D₄	1	1	yes	characteristic, complemented
99	C₂×#2846	C₂³	1	1	yes	characteristic
100	C₂×#2541	C₂³	1	1	yes	characteristic
101	C₂×#2535	D₄	1	1	yes	characteristic, complemented
102	C₂×#2410	C₂³	1	1	yes	characteristic
103	C₂×#2403	D₄	1	1	yes	characteristic, complemented
104	C₂×#2397	D₄	1	1	yes	characteristic, complemented
105	C₂×#2358	C₂³	1	1	yes	characteristic, complemented
106	#24056	C₂³	1	4	yes	—
107	#24018	C₂³	1	4	yes	—
108	#23906	C₂³	1	4	yes	—
109	#23900	C₂³	1	4	yes	—
110	#23900	C₂³	1	4	yes	—
111	#23900	C₂³	1	4	yes	—
112	#21797	C₂³	1	2	yes	—
113	#21746	C₂³	1	2	yes	—
114	#21746	C₂³	1	2	yes	—
115	#17137	C₂³	1	1	yes	characteristic, complemented
116	#17136	C₂³	1	1	yes	characteristic, complemented
117	#15950	D₄	1	1	yes	characteristic, complemented
118	#15948	C₂³	1	1	yes	characteristic
119	#15947	C₂³	1	1	yes	characteristic
120	#15947	C₂³	1	1	yes	characteristic
121	#15947	C₂³	1	1	yes	characteristic
122	#15947	C₂³	1	1	yes	characteristic, complemented
123	#15313	C₂³	1	1	yes	characteristic, complemented
124	#15283	D₄	1	1	yes	characteristic, complemented
125	#15283	D₄	1	1	yes	characteristic, complemented
126	#15283	C₂³	1	1	yes	characteristic
127	#15283	C₂³	1	1	yes	characteristic
128	#15281	C₂³	1	1	yes	characteristic, complemented
129	#15281	C₂³	1	1	yes	characteristic, complemented
130	#15266	C₂³	1	1	yes	characteristic, complemented
131	#15261	C₂³	1	1	yes	characteristic
132	#15260	D₄	1	1	yes	characteristic, complemented
133	#15258	D₄	1	1	yes	characteristic, complemented
134	#15258	D₄	1	1	yes	characteristic, complemented
135	#15258	C₂³	1	1	yes	characteristic
136	#15258	C₂³	1	1	yes	characteristic
137	#15258	C₂³	1	1	yes	characteristic
138	#15258	C₂³	1	1	yes	characteristic
139	#15258	C₂³	1	1	yes	characteristic
140	#15258	C₂³	1	1	yes	characteristic, complemented
141	#15257	D₄	1	1	yes	characteristic, complemented
142	#15257	D₄	1	1	yes	characteristic, complemented
143	#15257	D₄	1	1	yes	characteristic, complemented
144	#15257	D₄	1	1	yes	characteristic, complemented
145	#15257	D₄	1	1	yes	characteristic, complemented
146	#15257	D₄	1	1	yes	characteristic, complemented
147	#14445	C₂³	1	1	yes	characteristic, complemented
148	#14419	C₂³	1	1	yes	characteristic, complemented
149	#14410	C₂³	1	1	yes	characteristic, complemented
150	#14358	C₂³	1	1	yes	characteristic, complemented
151	#14272	C₂³	1	1	yes	characteristic
152	#14255	C₂³	1	1	yes	characteristic
153	#14134	C₂³	1	1	yes	characteristic
154	#14134	C₂³	1	1	yes	characteristic, complemented
155	#14134	C₂³	1	1	yes	characteristic, complemented
156	#13905	D₄	1	1	yes	characteristic, complemented
157	#13867	D₄	1	1	yes	characteristic, complemented
158	#13867	D₄	1	1	yes	characteristic, complemented
159	#13867	D₄	1	1	yes	characteristic, complemented
160	C₂×#1438	D₄	1	1	yes	characteristic, complemented
161	#13785	D₄	1	1	yes	characteristic, complemented
162	#12856	C₂³	1	4	yes	complemented
163	#12852	C₂³	1	4	yes	complemented
164	#12693	C₂³	1	4	yes	complemented
165	#12687	C₂³	1	4	yes	complemented
166	#12687	C₂³	1	4	yes	complemented
167	#12687	C₂³	1	4	yes	complemented
168	#8547	C₂³	1	2	yes	—
169	#8547	C₂³	1	2	yes	—
170	#8546	C₂³	1	2	yes	—
171	#8546	C₂³	1	2	yes	—
172	#8541	C₂³	1	2	yes	—
173	#8541	C₂³	1	2	yes	—
174	#8534	C₂³	1	4	yes	—
175	#8534	C₂³	1	4	yes	—
176	#8534	C₂³	1	4	yes	—
177	#8534	C₂³	1	4	yes	—
178	#8453	C₂³	1	4	yes	—
179	#8453	C₂³	1	4	yes	—
180	#7307	C₂³	1	4	yes	complemented
181	#7307	C₂³	1	4	yes	complemented
182	#7304	C₂³	1	4	yes	complemented
183	#7304	C₂³	1	4	yes	complemented
184	#7304	C₂³	1	4	yes	complemented
185	#7304	C₂³	1	4	yes	complemented
186	C₂⁷	C₂×D₄	1	1	yes	characteristic
187	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
188	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
189	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
190	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
191	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
192	#3484	C₂⁴	1	4	yes	—
193	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
194	C₂²×#127	C₂⁴	1	1	yes	characteristic
195	C₂²×#127	C₂⁴	1	1	yes	characteristic
196	C₂²×#123	C₂×D₄	1	1	yes	characteristic
197	C₂²×#123	C₂×D₄	1	1	yes	characteristic, complemented
198	C₂²×#121	C₂×D₄	1	1	yes	characteristic
199	C₂²×#121	C₂×D₄	1	1	yes	characteristic
200	C₂²×#121	C₂×D₄	1	1	yes	characteristic
201	C₂²×#121	C₂×D₄	1	1	yes	characteristic
202	C₂²×#120	C₂×D₄	1	1	yes	characteristic
203	C₂²×#120	C₂×D₄	1	1	yes	characteristic
204	C₂²×#120	C₂×D₄	1	1	yes	characteristic
205	C₂²×#120	C₂×D₄	1	1	yes	characteristic
206	C₂²×#120	C₂×D₄	1	1	yes	characteristic
207	C₂²×#120	C₂×D₄	1	1	yes	characteristic
208	C₂²×#120	C₂×D₄	1	1	yes	characteristic
209	C₂²×#120	C₂×D₄	1	1	yes	characteristic
210	C₂²×#120	C₂×D₄	1	1	yes	characteristic
211	C₂²×#120	C₂×D₄	1	1	yes	characteristic
212	C₂²×#120	C₂×D₄	1	1	yes	characteristic
213	C₂²×#120	C₂×D₄	1	1	yes	characteristic
214	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
215	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
216	C₂²×#120	C₂⁴	1	1	yes	characteristic
217	C₂²×#120	C₂⁴	1	1	yes	characteristic
218	C₂²×#120	C₂⁴	1	1	yes	characteristic
219	C₂²×#120	C₂⁴	1	1	yes	characteristic
220	C₂²×#120	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic, complemented
224	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
225	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
226	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
227	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
228	C₂×#399	C₂×D₄	1	1	yes	characteristic
229	C₂×#399	C₂×D₄	1	1	yes	characteristic, complemented
230	C₂×#397	C₂×D₄	1	1	yes	characteristic
231	C₂×#397	C₂×D₄	1	1	yes	characteristic, complemented
232	C₂×#392	C₂×D₄	1	1	yes	characteristic
233	C₂×#392	C₂×D₄	1	1	yes	characteristic
234	C₂×#392	C₂×D₄	1	1	yes	characteristic, complemented
235	C₂×#392	C₂×D₄	1	1	yes	characteristic, complemented
236	C₂×#390	C₂×D₄	1	1	yes	characteristic, complemented
237	C₂×#390	C₂⁴	1	1	yes	characteristic
238	C₂×#386	C₂×D₄	1	1	yes	characteristic
239	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
240	C₂×#386	C₂⁴	1	1	yes	characteristic
241	C₂×#385	C₂×D₄	1	1	yes	characteristic, complemented
242	C₂×#382	C₂×D₄	1	1	yes	characteristic, complemented
243	C₂×#379	C₂×D₄	1	1	yes	characteristic
244	C₂×#379	C₂×D₄	1	1	yes	characteristic
245	C₂×#379	C₂×D₄	1	1	yes	characteristic
246	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
247	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
248	C₂×C₄×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
249	C₂×#376	C₂×D₄	1	1	yes	characteristic, complemented
250	#1783	C₂⁴	1	4	yes	—
251	#1781	C₂⁴	1	4	yes	—
252	#1781	C₂⁴	1	4	yes	—
253	#1440	C₂×D₄	1	1	yes	characteristic
254	#1440	C₂×D₄	1	1	yes	characteristic
255	#1440	C₂×D₄	1	1	yes	characteristic, complemented
256	#1440	C₂×D₄	1	1	yes	characteristic, complemented
257	#1438	C₂×D₄	1	1	yes	characteristic
258	#1438	C₂×D₄	1	1	yes	characteristic
259	#1438	C₂×D₄	1	1	yes	characteristic
260	#1438	C₂×D₄	1	1	yes	characteristic
261	#1438	C₂×D₄	1	1	yes	characteristic
262	#1438	C₂×D₄	1	1	yes	characteristic
263	#1438	C₂×D₄	1	1	yes	characteristic
264	#1438	C₂×D₄	1	1	yes	characteristic
265	#1438	C₂×D₄	1	1	yes	characteristic
266	#1438	C₂×D₄	1	1	yes	characteristic
267	#1438	C₂×D₄	1	1	yes	characteristic
268	#1438	C₂×D₄	1	1	yes	characteristic
269	#1438	C₂×D₄	1	1	yes	characteristic, complemented
270	#1438	C₂×D₄	1	1	yes	characteristic, complemented
271	#1438	C₂×D₄	1	1	yes	characteristic, complemented
272	#1438	C₂×D₄	1	1	yes	characteristic, complemented
273	#1438	C₂×D₄	1	1	yes	characteristic, complemented
274	#1438	C₂×D₄	1	1	yes	characteristic, complemented
275	#1438	C₂⁴	1	1	yes	characteristic
276	#1438	C₂⁴	1	1	yes	characteristic
277	#1438	C₂⁴	1	1	yes	characteristic
278	#1438	C₂⁴	1	1	yes	characteristic
279	#1438	C₂⁴	1	1	yes	characteristic
280	#1438	C₂⁴	1	1	yes	characteristic
281	#1437	C₂×D₄	1	1	yes	characteristic
282	#1437	C₂×D₄	1	1	yes	characteristic
283	#1437	C₂×D₄	1	1	yes	characteristic
284	#1437	C₂×D₄	1	1	yes	characteristic
285	#1437	C₂×D₄	1	1	yes	characteristic, complemented
286	#1437	C₂×D₄	1	1	yes	characteristic, complemented
287	#1437	C₂×D₄	1	1	yes	characteristic, complemented
288	#1437	C₂×D₄	1	1	yes	characteristic, complemented
289	C₂⁶	#120	1	1	yes	characteristic
290	C₂⁶	#120	1	1	yes	characteristic
291	C₂⁶	C₂²×D₄	1	1	yes	characteristic
292	C₂⁶	C₂²×D₄	1	1	yes	characteristic
293	C₂⁶	C₂²×D₄	1	1	yes	characteristic
294	C₂⁶	C₂²×D₄	1	1	yes	characteristic
295	C₂⁶	C₂²×D₄	1	1	yes	characteristic
296	C₂×H(5,𝔽₂)	H(5,𝔽₂)	1	4	yes	—
297	C₂³×D₄	#120	1	1	yes	characteristic
298	C₂³×D₄	#120	1	1	yes	characteristic
299	C₂³×D₄	#120	1	1	yes	characteristic
300	C₂³×D₄	#120	1	1	yes	characteristic
301	C₂³×D₄	#120	1	1	yes	characteristic
302	C₂³×D₄	#120	1	1	yes	characteristic
303	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
304	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
305	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
306	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
307	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
308	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
309	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
310	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
311	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
312	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
313	C₂³×D₄	C₂⁵	1	1	yes	characteristic
314	C₂⁴×C₄	#120	1	1	yes	characteristic
315	C₂⁴×C₄	#120	1	1	yes	characteristic
316	C₂⁴×C₄	#120	1	1	yes	characteristic
317	C₂⁴×C₄	#120	1	1	yes	characteristic
318	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
319	#518	H(5,𝔽₂)	1	4	yes	—
320	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
321	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
322	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
323	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
324	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
325	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
326	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
327	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
328	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
329	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
330	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
331	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
332	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
333	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
334	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
335	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
336	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
337	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
338	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
339	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
340	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
341	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
342	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
343	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
344	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
345	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
346	C₂×#95	C₂²×D₄	1	1	yes	characteristic
347	C₂×#95	C₂²×D₄	1	1	yes	characteristic
348	C₂×#95	C₂²×D₄	1	1	yes	characteristic
349	C₂×#95	C₂²×D₄	1	1	yes	characteristic
350	C₂⁵	C₂×#120	1	1	yes	characteristic
351	C₂⁵	C₂×#120	1	1	yes	characteristic
352	C₂⁵	C₂×#120	1	1	yes	characteristic
353	C₂⁵	C₂×#120	1	1	yes	characteristic
354	C₂⁵	C₂×#120	1	1	yes	characteristic
355	C₂⁵	C₂×#120	1	1	yes	characteristic
356	C₂⁵	C₂³×D₄	1	1	yes	characteristic
357	C₂⁵	C₂³×D₄	1	1	yes	characteristic
358	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
359	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
360	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
361	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
362	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
363	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
364	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
365	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
366	C₂²×D₄	C₂×H(5,𝔽₂)	1	4	yes	—
367	C₂³×C₄	C₂×#120	1	1	yes	characteristic
368	C₂³×C₄	C₂×#120	1	1	yes	characteristic
369	C₂³×C₄	C₂×#120	1	1	yes	characteristic
370	C₂³×C₄	C₂×#120	1	1	yes	characteristic
371	C₂³×C₄	C₂×#120	1	1	yes	characteristic
372	C₂³×C₄	C₂×#120	1	1	yes	characteristic
373	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
374	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
375	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
376	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
377	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
378	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
379	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
380	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
381	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
382	C₂⁴	C₂²×#120	1	1	yes	characteristic
383	C₂⁴	#3484	1	2	yes	—
384	C₂⁴	#3484	1	2	yes	—
385	C₂×D₄	#2196	1	4	yes	complemented
386	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
387	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
388	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
389	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
390	C₂²×C₄	#3484	1	2	yes	—
391	C₂³	C₂×#2196	1	2	yes	—
392	C₂³	C₂×#2196	1	2	yes	—
393	C₂³	#33551	1	2	yes	—
394	C₂³	#35346	1	1	yes	characteristic
395	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
396	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
397	C₂×C₄	C₂×#2196	1	2	yes	—
398	C₂²	#6499867	1	1	yes	characteristic
399	C₂²	#6499874	1	1	yes	characteristic
400	C₂²	#6499875	1	1	yes	characteristic
401	C₂²	C₂²×#2196	1	1	yes	characteristic
402	C₂²	C₂×#33551	1	1	yes	characteristic
403	C₂²	#7622875	1	1	yes	characteristic
404	C₂²	#7622875	1	1	yes	characteristic
405	C₂	#72233421	1	1	yes	characteristic
406	C₂	#72233435	1	1	yes	characteristic
407	C₂	#72238471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#6499867
commutator, Frattini, cosocle	C₂³×D₄	C₂⁵
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂²×D₄² ◁ G
LECS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72263063	C₂	semidirect
2. #72263062	C₂	semidirect
3. #72262570	C₂	semidirect
4. #72236963	C₂	semidirect
5. #72234143	C₂	semidirect
6. #72233429	C₂	semidirect
7. #72233426	C₂	semidirect
8. #72233378	C₂	semidirect
9. #72233244	C₂	semidirect
10. #72233150	C₂	semidirect
11. #72233058	C₂	semidirect
12. #72233027	C₂	semidirect
13. #72232967	C₂	semidirect
14. #72232866	C₂	semidirect
15. #72232757	C₂	semidirect
16. #72226358	C₂	semidirect
17. #72216323	C₂	semidirect
18. #72213719	C₂	semidirect
19. #72210587	C₂	semidirect
20. #10586472	C₂²	semidirect
21. #6512701	C₂²	semidirect
22. #6500010	C₂²	semidirect
24. #4035541	C₂²	semidirect
25. #4035539	C₂²	semidirect
26. #2306524	C₂²	semidirect
27. #2306453	C₂²	semidirect
28. #2109018	C₂²	semidirect
29. #2108839	C₂²	semidirect
30. #1420706	C₂²	semidirect
31. #1420272	C₂²	semidirect
32. #1419288	C₂²	semidirect
33. #1418393	C₂²	semidirect
36. #648750	C₂²	semidirect
38. #647656	C₂²	semidirect
39. #512142	C₂²	semidirect
40. #511771	C₂²	semidirect
41. #347056	C₂²	semidirect
42. #347048	C₂²	semidirect
44. #347047	C₂²	semidirect
45. #347047	C₂²	semidirect
48. #347042	C₂²	semidirect
49. #346466	C₂²	semidirect
50. #346466	C₂²	semidirect
52. #346446	C₂²	semidirect
53. #188151	C₂²	semidirect
54. #188035	C₂²	semidirect
55. #188035	C₂²	semidirect
56. #187940	C₂²	semidirect
57. #187934	C₂²	semidirect
58. #186819	C₂²	semidirect
59. #144654	C₂²	semidirect
60. #144627	C₂²	semidirect
61. #144414	C₂²	semidirect
62. #144412	C₂²	semidirect
63. #144404	C₂²	semidirect
64. #144404	C₂²	semidirect
65. #144386	C₂²	semidirect
66. #144366	C₂²	semidirect
67. #139846	C₂²	semidirect
68. #139830	C₂²	semidirect
69. #139830	C₂²	semidirect
70. #139828	C₂²	semidirect
71. #139815	C₂²	semidirect
72. #139790	C₂²	semidirect
73. #139790	C₂²	semidirect
74. #139790	C₂²	semidirect
75. #139773	C₂²	semidirect
76. #139767	C₂²	semidirect
77. #139718	C₂²	semidirect
78. #139718	C₂²	semidirect
79. #139716	C₂²	semidirect
80. #139716	C₂²	semidirect
81. #139716	C₂²	semidirect
82. #139706	C₂²	semidirect
83. #139700	C₂²	semidirect
84. #139700	C₂²	semidirect
85. #135548	C₂²	semidirect
86. #135522	C₂²	semidirect
87. #135507	C₂²	semidirect
88. #133893	C₂²	semidirect
89. #133853	C₂²	semidirect
90. #133822	C₂²	semidirect
95. C₂²×D₄²	C₂³	semidirect
96. C₂²×#534	D₄	semidirect
97. C₂³×#120	D₄	semidirect
98. C₂³×#120	D₄	semidirect
101. C₂×#2535	D₄	semidirect
103. C₂×#2403	D₄	semidirect
104. C₂×#2397	D₄	semidirect
105. C₂×#2358	C₂³	semidirect
115. #17137	C₂³	semidirect
116. #17136	C₂³	semidirect
117. #15950	D₄	semidirect
122. #15947	C₂³	semidirect
123. #15313	C₂³	semidirect
124. #15283	D₄	semidirect
125. #15283	D₄	semidirect
128. #15281	C₂³	semidirect
129. #15281	C₂³	semidirect
130. #15266	C₂³	semidirect
132. #15260	D₄	semidirect
133. #15258	D₄	semidirect
134. #15258	D₄	semidirect
140. #15258	C₂³	semidirect
141. #15257	D₄	semidirect
142. #15257	D₄	semidirect
143. #15257	D₄	semidirect
144. #15257	D₄	semidirect
145. #15257	D₄	semidirect
146. #15257	D₄	semidirect
147. #14445	C₂³	semidirect
148. #14419	C₂³	semidirect
149. #14410	C₂³	semidirect
150. #14358	C₂³	semidirect
154. #14134	C₂³	semidirect
155. #14134	C₂³	semidirect
156. #13905	D₄	semidirect
157. #13867	D₄	semidirect
158. #13867	D₄	semidirect
159. #13867	D₄	semidirect
160. C₂×#1438	D₄	semidirect
161. #13785	D₄	semidirect
162. #12856	C₂³	semidirect
163. #12852	C₂³	semidirect
164. #12693	C₂³	semidirect
165. #12687	C₂³	semidirect
166. #12687	C₂³	semidirect
167. #12687	C₂³	semidirect
180. #7307	C₂³	semidirect
181. #7307	C₂³	semidirect
182. #7304	C₂³	semidirect
183. #7304	C₂³	semidirect
184. #7304	C₂³	semidirect
185. #7304	C₂³	semidirect
191. C₂⁴×D₄	C₂×D₄	semidirect
193. C₂²×#127	C₂×D₄	semidirect
197. C₂²×#123	C₂×D₄	semidirect
214. C₂²×#120	C₂×D₄	semidirect
215. C₂²×#120	C₂×D₄	semidirect
223. C₂²×C₄×D₄	C₂×D₄	semidirect
226. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
227. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
229. C₂×#399	C₂×D₄	semidirect
231. C₂×#397	C₂×D₄	semidirect
234. C₂×#392	C₂×D₄	semidirect
235. C₂×#392	C₂×D₄	semidirect
236. C₂×#390	C₂×D₄	semidirect
239. C₂×#386	C₂×D₄	semidirect
241. C₂×#385	C₂×D₄	semidirect
242. C₂×#382	C₂×D₄	semidirect
246. C₂×#379	C₂×D₄	semidirect
247. C₂×#379	C₂×D₄	semidirect
248. C₂×C₄×C₄⋊C₄	C₂×D₄	semidirect
249. C₂×#376	C₂×D₄	semidirect
255. #1440	C₂×D₄	semidirect
256. #1440	C₂×D₄	semidirect
269. #1438	C₂×D₄	semidirect
270. #1438	C₂×D₄	semidirect
271. #1438	C₂×D₄	semidirect
272. #1438	C₂×D₄	semidirect
273. #1438	C₂×D₄	semidirect
274. #1438	C₂×D₄	semidirect
285. #1437	C₂×D₄	semidirect
286. #1437	C₂×D₄	semidirect
287. #1437	C₂×D₄	semidirect
288. #1437	C₂×D₄	semidirect
385. C₂×D₄	#2196	semidirect

Maximal subgroups

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

subgroup	index
#72263063	2
#72263062	2
#72262570	2
#72236963	2
#72234143	2
#72233429	2
#72233426	2
#72233378	2
#72233244	2
#72233150	2
#72233058	2
#72233027	2
#72232967	2
#72232866	2
#72232757	2
#72226358	2
#72216323	2
#72213719	2
#72210587	2