Subgroups — #72252028

Order 2048.

At least 10797 conjugacy classes of subgroups; only the 776 normal subgroups are shown.

The subgroup lattice has 466 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72252027	C₂	1	2	yes	maximal, complemented
2	#72252026	C₂	1	2	yes	maximal, complemented
3	#72252025	C₂	1	2	yes	maximal, complemented
4	#72252024	C₂	1	2	yes	maximal, complemented
5	#72251910	C₂	1	1	yes	maximal, characteristic, complemented
6	#72251903	C₂	1	1	yes	maximal, characteristic, complemented
7	#72251835	C₂	1	2	yes	maximal, complemented
8	#72251770	C₂	1	2	yes	maximal, complemented
9	#72251723	C₂	1	2	yes	maximal, complemented
10	#72238401	C₂	1	2	yes	maximal, complemented
11	#72237556	C₂	1	1	yes	maximal, characteristic, complemented
12	#72235716	C₂	1	2	yes	maximal, complemented
13	#72235079	C₂	1	1	yes	maximal, characteristic, complemented
14	#72234769	C₂	1	2	yes	maximal, complemented
15	#72232713	C₂	1	2	yes	maximal, complemented
16	#72232346	C₂	1	1	yes	maximal, characteristic, complemented
17	#72213843	C₂	1	1	yes	maximal, characteristic, complemented
18	#72213838	C₂	1	1	yes	maximal, characteristic, complemented
19	#72213827	C₂	1	2	yes	maximal, complemented
20	#10586169	C₂²	1	1	yes	characteristic, complemented
21	C₂×#59267	C₂²	1	1	yes	characteristic, complemented
22	C₂×#36614	C₂²	1	1	yes	characteristic
23	#6499869	C₂²	1	2	yes	—
24	#6499869	C₂²	1	2	yes	complemented
25	#6499868	C₂²	1	2	yes	complemented
26	#6499867	C₂²	1	2	yes	—
27	#6451869	C₂²	1	2	yes	—
28	#6451869	C₂²	1	2	yes	complemented
29	#6374123	C₂²	1	1	yes	characteristic, complemented
30	#6347315	C₂²	1	2	yes	complemented
31	#6346626	C₂²	1	2	yes	complemented
32	#2039918	C₂²	1	1	yes	characteristic, complemented
33	#2039819	C₂²	1	1	yes	characteristic, complemented
34	#2039146	C₂²	1	1	yes	characteristic, complemented
35	#2038783	C₂²	1	1	yes	characteristic, complemented
36	#850487	C₂²	1	1	yes	characteristic, complemented
37	#850258	C₂²	1	1	yes	characteristic, complemented
38	#669903	C₂²	1	1	yes	characteristic, complemented
39	#663912	C₂²	1	1	yes	characteristic, complemented
40	#648360	C₂²	1	1	yes	characteristic, complemented
41	#648053	C₂²	1	1	yes	characteristic, complemented
42	#619125	C₂²	1	1	yes	characteristic
43	#619101	C₂²	1	1	yes	characteristic
44	#532104	C₂²	1	1	yes	characteristic, complemented
45	#485390	C₂²	1	4	yes	complemented
46	#485385	C₂²	1	4	yes	complemented
47	#485077	C₂²	1	4	yes	complemented
48	#485039	C₂²	1	4	yes	complemented
49	#482562	C₂²	1	2	yes	complemented
50	#482550	C₂²	1	2	yes	complemented
51	#480245	C₂²	1	2	yes	complemented
52	#480245	C₂²	1	2	yes	complemented
53	#346481	C₂²	1	2	yes	complemented
54	#346466	C₂²	1	2	yes	complemented
55	#346462	C₂²	1	2	yes	complemented
56	#346456	C₂²	1	2	yes	complemented
57	#346452	C₂²	1	2	yes	complemented
58	#346452	C₂²	1	2	yes	complemented
59	#346446	C₂²	1	2	yes	—
60	#346446	C₂²	1	2	yes	—
61	#188081	C₂²	1	1	yes	characteristic, complemented
62	#188081	C₂²	1	1	yes	characteristic, complemented
63	#185263	C₂²	1	2	yes	complemented
64	#185257	C₂²	1	2	yes	complemented
65	#142571	C₂²	1	4	yes	complemented
66	#142570	C₂²	1	4	yes	complemented
67	#142569	C₂²	1	4	yes	complemented
68	#142568	C₂²	1	4	yes	complemented
69	#142537	C₂²	1	4	yes	complemented
70	#142537	C₂²	1	4	yes	complemented
71	#142536	C₂²	1	4	yes	complemented
72	#142536	C₂²	1	4	yes	complemented
73	#139645	C₂²	1	4	yes	complemented
74	#139645	C₂²	1	4	yes	complemented
75	#139622	C₂²	1	4	yes	complemented
76	#139622	C₂²	1	4	yes	complemented
77	#139505	C₂²	1	2	yes	complemented
78	#139505	C₂²	1	2	yes	complemented
79	#139504	C₂²	1	2	yes	complemented
80	#139504	C₂²	1	2	yes	complemented
81	#139487	C₂²	1	2	yes	complemented
82	#139486	C₂²	1	2	yes	complemented
83	#139485	C₂²	1	2	yes	complemented
84	#139484	C₂²	1	2	yes	complemented
85	#134035	C₂²	1	2	yes	complemented
86	#134035	C₂²	1	2	yes	complemented
87	#134034	C₂²	1	2	yes	complemented
88	#134033	C₂²	1	2	yes	complemented
89	#127218	C₂²	1	2	yes	complemented
90	#127216	C₂²	1	2	yes	complemented
91	C₂⁶×C₄	D₄	1	1	yes	characteristic
92	#62820	C₂³	1	2	yes	—
93	#62817	C₂³	1	2	yes	—
94	#62814	C₂³	1	2	yes	—
95	C₂²×#525	D₄	1	1	yes	characteristic
96	C₂²×#525	D₄	1	1	yes	characteristic
97	C₂²×#525	C₂³	1	1	yes	characteristic
98	C₂×#2760	C₂³	1	1	yes	characteristic
99	C₂×#2752	C₂³	1	1	yes	characteristic
100	C₂×#2849	D₄	1	1	yes	characteristic
101	C₂×#2849	D₄	1	1	yes	characteristic
102	C₂×#2849	D₄	1	1	yes	characteristic
103	C₂×#2849	C₂³	1	1	yes	characteristic
104	C₂×#2849	C₂³	1	1	yes	characteristic
105	C₂×#2849	C₂³	1	1	yes	characteristic
106	C₂×#2846	D₄	1	1	yes	characteristic
107	C₂×#2846	C₂³	1	1	yes	characteristic
108	C₂×#2544	D₄	1	1	yes	characteristic, complemented
109	C₂×#2535	D₄	1	1	yes	characteristic, complemented
110	C₂×#2610	C₂³	1	1	yes	characteristic
111	C₂×#2598	C₂³	1	1	yes	characteristic
112	C₂×#2437	C₂³	1	1	yes	characteristic
113	C₂×#2403	C₂³	1	1	yes	characteristic
114	C₂×#2631	D₄	1	1	yes	characteristic, complemented
115	C₂×#2328	D₄	1	1	yes	characteristic, complemented
116	C₂×#2280	D₄	1	1	yes	characteristic
117	C₂×#2280	C₂³	1	1	yes	characteristic
118	C₂×#2280	C₂³	1	1	yes	characteristic
119	#23986	D₄	1	8	yes	complemented
120	#23985	C₂³	1	4	yes	—
121	#23985	C₂³	1	4	yes	—
122	#23984	C₂³	1	4	yes	—
123	#23984	C₂³	1	4	yes	—
124	#23467	D₄	1	4	yes	complemented
125	#23443	D₄	1	4	yes	complemented
126	#21747	C₂³	1	2	yes	—
127	#21746	C₂³	1	2	yes	—
128	#20688	C₂³	1	2	yes	—
129	#18170	C₂³	1	4	yes	—
130	#18163	C₂³	1	4	yes	—
131	#18162	C₂³	1	4	yes	—
132	#18162	C₂³	1	4	yes	—
133	#17357	C₂³	1	2	yes	—
134	#17357	C₂³	1	2	yes	—
135	#15930	C₂³	1	1	yes	characteristic
136	#15916	C₂³	1	1	yes	characteristic
137	#15674	D₄	1	1	yes	characteristic, complemented
138	#15673	D₄	1	1	yes	characteristic, complemented
139	#15671	D₄	1	1	yes	characteristic, complemented
140	#15670	D₄	1	1	yes	characteristic, complemented
141	#15669	C₂³	1	1	yes	characteristic
142	#15668	C₂³	1	1	yes	characteristic
143	#15561	C₂³	1	1	yes	characteristic
144	#15561	C₂³	1	1	yes	characteristic
145	#15467	C₂³	1	1	yes	characteristic
146	#15453	D₄	1	1	yes	characteristic, complemented
147	#15453	D₄	1	1	yes	characteristic, complemented
148	#15412	C₂³	1	1	yes	characteristic
149	#15412	C₂³	1	1	yes	characteristic
150	#15310	D₄	1	1	yes	characteristic, complemented
151	#15310	D₄	1	1	yes	characteristic, complemented
152	#15284	C₂³	1	1	yes	characteristic
153	#15283	C₂³	1	1	yes	characteristic
154	#15267	C₂³	1	1	yes	characteristic
155	#15267	C₂³	1	1	yes	characteristic
156	#15259	C₂³	1	1	yes	characteristic
157	#15258	C₂³	1	1	yes	characteristic
158	#15258	C₂³	1	1	yes	characteristic
159	#14507	C₂³	1	1	yes	characteristic
160	#14507	C₂³	1	1	yes	characteristic
161	#14345	D₄	1	1	yes	characteristic, complemented
162	#13959	D₄	1	1	yes	characteristic, complemented
163	#13959	D₄	1	1	yes	characteristic, complemented
164	#13957	C₂³	1	1	yes	characteristic
165	#13938	C₂³	1	1	yes	characteristic
166	C₂²⋊C₄²	C₂³	1	1	yes	characteristic
167	C₂²⋊C₄²	C₂³	1	1	yes	characteristic
168	#13785	D₄	1	1	yes	characteristic, complemented
169	#11809	C₂³	1	4	yes	—
170	#11808	C₂³	1	4	yes	—
171	#11796	C₂³	1	4	yes	—
172	#11796	C₂³	1	4	yes	—
173	#11500	C₂³	1	4	yes	—
174	#11500	C₂³	1	4	yes	—
175	#11499	C₂³	1	4	yes	—
176	#11499	C₂³	1	4	yes	—
177	#8553	C₂³	1	2	yes	—
178	#8553	C₂³	1	2	yes	—
179	#8547	C₂³	1	2	yes	—
180	#8547	C₂³	1	2	yes	—
181	#8346	C₂³	1	4	yes	—
182	#8346	C₂³	1	4	yes	—
183	#8346	C₂³	1	4	yes	—
184	#8346	C₂³	1	4	yes	—
185	#7213	C₂³	1	4	yes	—
186	#7213	C₂³	1	4	yes	—
187	#7213	C₂³	1	4	yes	—
188	#7213	C₂³	1	4	yes	—
189	C₂⁷	C₂×D₄	1	1	yes	characteristic
190	C₂³×#41	C₂×D₄	1	1	yes	characteristic
191	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
192	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
193	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
194	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
195	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
196	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
197	#3491	C₂×D₄	1	4	yes	complemented
198	#3490	C₂⁴	1	4	yes	—
199	#3458	C₂×D₄	1	2	yes	complemented
200	#3449	C₂×D₄	1	2	yes	complemented
201	C₂²×#127	C₂×D₄	1	1	yes	characteristic
202	C₂²×#127	C₂×D₄	1	1	yes	characteristic
203	C₂²×#124	C₂×D₄	1	1	yes	characteristic
204	C₂²×#124	C₂×D₄	1	1	yes	characteristic, complemented
205	C₂²×#123	C₂×D₄	1	1	yes	characteristic
206	C₂²×#123	C₂×D₄	1	1	yes	characteristic
207	C₂²×#123	C₂×D₄	1	1	yes	characteristic
208	C₂²×#123	C₂×D₄	1	1	yes	characteristic
209	C₂²×#123	C₂×D₄	1	1	yes	characteristic
210	C₂²×#123	C₂⁴	1	1	yes	characteristic
211	C₂²×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
213	C₂²×#121	C₂×D₄	1	1	yes	characteristic
214	C₂²×#121	C₂×D₄	1	1	yes	characteristic
215	C₂²×#120	C₂×D₄	1	1	yes	characteristic
216	C₂²×#120	C₂×D₄	1	1	yes	characteristic
217	C₂²×#120	C₂×D₄	1	1	yes	characteristic
218	C₂²×#120	C₂×D₄	1	1	yes	characteristic
219	C₂²×#120	C₂×D₄	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
224	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic, complemented
226	C₂²×#117	C₂×D₄	1	1	yes	characteristic
227	C₂²×#117	C₂×D₄	1	1	yes	characteristic
228	C₂²×#117	C₂⁴	1	1	yes	characteristic
229	C₂×#400	C₂×D₄	1	1	yes	characteristic, complemented
230	C₂×#399	C₂⁴	1	1	yes	characteristic
231	C₂×#397	C₂×D₄	1	1	yes	characteristic
232	C₂×#397	C₂×D₄	1	1	yes	characteristic, complemented
233	C₂×#395	C₂×D₄	1	1	yes	characteristic, complemented
234	C₂×#394	C₂×D₄	1	1	yes	characteristic, complemented
235	C₂×#394	C₂×D₄	1	1	yes	characteristic, complemented
236	C₂×#393	C₂×D₄	1	1	yes	characteristic
237	C₂×#393	C₂×D₄	1	1	yes	characteristic, complemented
238	C₂×#393	C₂⁴	1	1	yes	characteristic
239	C₂×#392	C₂×D₄	1	1	yes	characteristic
240	C₂×#392	C₂×D₄	1	1	yes	characteristic
241	C₂×#392	C₂×D₄	1	1	yes	characteristic, complemented
242	C₂×#392	C₂×D₄	1	1	yes	characteristic, complemented
243	C₂×#392	C₂⁴	1	1	yes	characteristic
244	C₂×#392	C₂⁴	1	1	yes	characteristic
245	C₂×#391	C₂×D₄	1	1	yes	characteristic, complemented
246	C₂×#390	C₂×D₄	1	1	yes	characteristic
247	C₂×#390	C₂×D₄	1	1	yes	characteristic, complemented
248	C₂×#390	C₂×D₄	1	1	yes	characteristic, complemented
249	C₂×#383	C₂×D₄	1	1	yes	characteristic, complemented
250	C₂×#383	C₂×D₄	1	1	yes	characteristic, complemented
251	C₂×#382	C₂×D₄	1	1	yes	characteristic, complemented
252	C₂×#382	C₂×D₄	1	1	yes	characteristic, complemented
253	#2280	C₂×D₄	1	4	yes	—
254	#2280	C₂×D₄	1	4	yes	—
255	C₂×#381	C₂×D₄	1	1	yes	characteristic
256	C₂×#381	C₂×D₄	1	1	yes	characteristic
257	C₂×#381	C₂×D₄	1	1	yes	characteristic
258	C₂×#381	C₂×D₄	1	1	yes	characteristic
259	C₂×#381	C₂⁴	1	1	yes	characteristic
260	C₂×#381	C₂⁴	1	1	yes	characteristic
261	C₂×#379	C₂×D₄	1	1	yes	characteristic
262	C₂×#379	C₂×D₄	1	1	yes	characteristic
263	C₂×#379	C₂×D₄	1	1	yes	characteristic
264	C₂×#379	C₂×D₄	1	1	yes	characteristic
265	C₂×#379	C₂⁴	1	1	yes	characteristic
266	C₂×#379	C₂⁴	1	1	yes	characteristic
267	C₂×C₄×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
268	C₂×#376	C₂×D₄	1	1	yes	characteristic, complemented
269	C₂×#376	C₂×D₄	1	1	yes	characteristic, complemented
270	#2030	C₂×D₄	1	8	yes	complemented
271	#2029	C₂×D₄	1	8	yes	—
272	#2022	C₂×D₄	1	8	yes	complemented
273	#2021	C₂×D₄	1	8	yes	—
274	#1820	C₂×D₄	1	4	yes	complemented
275	#1819	C₂⁴	1	4	yes	—
276	#1740	C₂×D₄	1	4	yes	complemented
277	#1462	C₂⁴	1	4	yes	—
278	#1462	C₂⁴	1	4	yes	—
279	#1445	C₂×D₄	1	1	yes	characteristic, complemented
280	#1445	C₂×D₄	1	1	yes	characteristic, complemented
281	#1445	C₂×D₄	1	1	yes	characteristic, complemented
282	#1445	C₂×D₄	1	1	yes	characteristic, complemented
283	#1438	C₂×D₄	1	1	yes	characteristic
284	#1438	C₂×D₄	1	1	yes	characteristic
285	#1438	C₂×D₄	1	1	yes	characteristic
286	#1438	C₂×D₄	1	1	yes	characteristic
287	#1437	C₂×D₄	1	1	yes	characteristic
288	#1437	C₂×D₄	1	1	yes	characteristic
289	#1437	C₂×D₄	1	1	yes	characteristic
290	#1437	C₂×D₄	1	1	yes	characteristic
291	#1437	C₂×D₄	1	1	yes	characteristic, complemented
292	#1437	C₂×D₄	1	1	yes	characteristic, complemented
293	#1437	C₂×D₄	1	1	yes	characteristic, complemented
294	#1437	C₂×D₄	1	1	yes	characteristic, complemented
295	#1437	C₂⁴	1	1	yes	characteristic
296	#1437	C₂⁴	1	1	yes	characteristic
297	#1437	C₂⁴	1	1	yes	characteristic
298	#1437	C₂⁴	1	1	yes	characteristic
299	#1436	C₂×D₄	1	1	yes	characteristic, complemented
300	#1436	C₂×D₄	1	1	yes	characteristic, complemented
301	#1436	C₂×D₄	1	1	yes	characteristic, complemented
302	#1436	C₂×D₄	1	1	yes	characteristic, complemented
303	C₂⁶	C₂²×D₄	1	1	yes	characteristic
304	C₂⁶	C₂²×D₄	1	1	yes	characteristic
305	C₂⁶	C₂²×D₄	1	1	yes	characteristic
306	C₂³×Q₈	#120	1	1	yes	characteristic
307	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
308	C₂³×D₄	#120	1	1	yes	characteristic
309	C₂³×D₄	#120	1	1	yes	characteristic
310	C₂³×D₄	#120	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	C₂²×D₄	1	1	yes	characteristic
314	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
315	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
316	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
317	C₂⁴×C₄	#120	1	1	yes	characteristic
318	C₂⁴×C₄	#120	1	1	yes	characteristic
319	C₂⁴×C₄	#120	1	1	yes	characteristic
320	C₂⁴×C₄	#120	1	1	yes	characteristic
321	C₂⁴×C₄	#120	1	2	yes	—
322	C₂⁴×C₄	#120	1	2	yes	—
323	C₂⁴×C₄	#120	1	1	yes	characteristic
324	C₂⁴×C₄	#120	1	1	yes	characteristic
325	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
326	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
327	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
328	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
329	#543	C₂²×D₄	1	4	yes	—
330	#534	C₂²×D₄	1	4	yes	—
331	C₂×#117	#120	1	2	yes	—
332	C₂×#117	#120	1	2	yes	—
333	C₂×#117	C₂²×D₄	1	2	yes	—
334	C₂×#117	C₂²×D₄	1	2	yes	—
335	C₂×#117	H(5,𝔽₂)	1	2	yes	—
336	C₂×#117	H(5,𝔽₂)	1	2	yes	—
337	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
338	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
339	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
340	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
341	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
342	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
343	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
344	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
345	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
346	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
347	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
348	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
349	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
350	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
351	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
352	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
353	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
354	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
355	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
356	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
357	C₂²×C₂²⋊C₄	C₂⁵	1	1	yes	characteristic
358	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
359	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
360	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
361	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
362	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
363	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
364	#381	#120	1	4	yes	—
365	#381	C₂²×D₄	1	4	yes	—
366	#379	#120	1	4	yes	—
367	#379	C₂²×D₄	1	4	yes	—
368	C₂×#95	C₂²×D₄	1	1	yes	characteristic
369	C₂×#95	C₂²×D₄	1	1	yes	characteristic
370	C₂×#95	C₂²×D₄	1	1	yes	characteristic
371	C₂×#95	C₂²×D₄	1	1	yes	characteristic
372	C₂×#95	C₂²×D₄	1	1	yes	characteristic
373	C₂×#95	C₂²×D₄	1	1	yes	characteristic
374	C₂×#95	C₂²×D₄	1	1	yes	characteristic
375	C₂×#95	C₂²×D₄	1	1	yes	characteristic
376	#342	C₂²×D₄	1	8	yes	—
377	C₂⁵	C₂×#120	1	1	yes	characteristic
378	C₂⁵	C₂×#120	1	1	yes	characteristic
379	C₂⁵	C₂×#120	1	1	yes	characteristic
380	C₂⁵	C₂×#120	1	1	yes	characteristic
381	C₂⁵	C₂×#120	1	2	yes	—
382	C₂⁵	C₂³×D₄	1	1	yes	characteristic
383	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
384	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
385	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
386	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
387	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
388	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
389	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
390	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
391	C₂³×C₄	C₂×#120	1	1	yes	characteristic
392	C₂³×C₄	C₂×#120	1	1	yes	characteristic
393	C₂³×C₄	C₂×#120	1	1	yes	characteristic
394	C₂³×C₄	C₂×#120	1	1	yes	characteristic
395	C₂³×C₄	C₂×#120	1	1	yes	characteristic
396	C₂³×C₄	C₂×#120	1	2	yes	—
397	C₂³×C₄	C₂×#120	1	1	yes	characteristic
398	C₂³×C₄	C₂×#120	1	1	yes	characteristic
399	C₂³×C₄	C₂×#120	1	1	yes	characteristic
400	C₂³×C₄	C₂×#120	1	1	yes	characteristic
401	C₂³×C₄	C₂×#120	1	1	yes	characteristic
402	C₂³×C₄	#534	1	1	yes	characteristic
403	C₂³×C₄	#534	1	1	yes	characteristic
404	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
405	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
406	C₂×C₄⋊C₄	D₄²	1	2	yes	—
407	C₂×C₄⋊C₄	D₄²	1	2	yes	—
408	C₂×C₄⋊C₄	D₄²	1	2	yes	—
409	C₂×C₄⋊C₄	D₄²	1	2	yes	—
410	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
411	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
412	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
413	C₂×C₂²⋊C₄	#534	1	2	yes	—
414	C₂×C₂²⋊C₄	C₂³×D₄	1	2	yes	—
415	C₂×C₂²⋊C₄	C₂×H(5,𝔽₂)	1	2	yes	—
416	C₂×C₄²	D₄²	1	2	yes	—
417	C₂×C₄²	D₄²	1	2	yes	—
418	C₂×C₄²	D₄²	1	2	yes	—
419	C₂×C₄²	D₄²	1	2	yes	—
420	C₂⁴	#3019	1	4	yes	—
421	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
422	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
423	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
424	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
425	C₂⁴	C₂²×#120	1	1	yes	characteristic
426	C₂⁴	C₂²×#120	1	1	yes	characteristic
427	C₂⁴	C₂×#534	1	1	yes	characteristic
428	C₂²×C₄	#2403	1	1	yes	characteristic
429	C₂²×C₄	#2403	1	1	yes	characteristic
430	C₂²×C₄	#2403	1	1	yes	characteristic
431	C₂²×C₄	#2403	1	1	yes	characteristic
432	C₂²×C₄	#2403	1	2	yes	—
433	C₂²×C₄	#2403	1	2	yes	—
434	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
435	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
436	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
437	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
438	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
439	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
440	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
441	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄²	1	2	yes	—
443	C₂²×C₄	C₂×D₄²	1	2	yes	—
444	C₂³	#33546	1	2	yes	—
445	C₂³	#33553	1	2	yes	—
446	C₂³	C₂×#2403	1	1	yes	characteristic
447	C₂³	C₂×#3019	1	2	yes	—
448	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
449	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
450	C₂×C₄	#23897	1	2	yes	—
451	C₂×C₄	#23900	1	1	yes	characteristic
452	C₂×C₄	#23900	1	1	yes	characteristic
453	C₂×C₄	#23900	1	1	yes	characteristic
454	C₂×C₄	#23900	1	1	yes	characteristic
455	C₂²	#6437445	1	1	yes	characteristic
456	C₂²	C₂×#23897	1	1	yes	characteristic
457	C₂²	C₂×#23900	1	1	yes	characteristic
458	C₂²	C₂×#33546	1	1	yes	characteristic
459	C₂²	C₂×#33553	1	1	yes	characteristic
460	C₂²	#7622868	1	1	yes	characteristic
461	C₂²	#7622868	1	1	yes	characteristic
462	C₂	#72231810	1	1	yes	characteristic
463	C₂	#72234768	1	1	yes	characteristic
464	C₂	#72234794	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#23900
commutator, Frattini, cosocle	C₂²×C₂²⋊C₄	C₂⁵
LCS	G ▷ C₂²×C₂²⋊C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂²×#525 ◁ G
LECS	G ▷ C₂²×C₂²⋊C₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72252027	C₂	semidirect
2. #72252026	C₂	semidirect
3. #72252025	C₂	semidirect
4. #72252024	C₂	semidirect
5. #72251910	C₂	semidirect
6. #72251903	C₂	semidirect
7. #72251835	C₂	semidirect
8. #72251770	C₂	semidirect
9. #72251723	C₂	semidirect
10. #72238401	C₂	semidirect
11. #72237556	C₂	semidirect
12. #72235716	C₂	semidirect
13. #72235079	C₂	semidirect
14. #72234769	C₂	semidirect
15. #72232713	C₂	semidirect
16. #72232346	C₂	semidirect
17. #72213843	C₂	semidirect
18. #72213838	C₂	semidirect
19. #72213827	C₂	semidirect
20. #10586169	C₂²	semidirect
21. C₂×#59267	C₂²	semidirect
24. #6499869	C₂²	semidirect
25. #6499868	C₂²	semidirect
28. #6451869	C₂²	semidirect
29. #6374123	C₂²	semidirect
30. #6347315	C₂²	semidirect
31. #6346626	C₂²	semidirect
32. #2039918	C₂²	semidirect
33. #2039819	C₂²	semidirect
34. #2039146	C₂²	semidirect
35. #2038783	C₂²	semidirect
36. #850487	C₂²	semidirect
37. #850258	C₂²	semidirect
38. #669903	C₂²	semidirect
39. #663912	C₂²	semidirect
40. #648360	C₂²	semidirect
41. #648053	C₂²	semidirect
44. #532104	C₂²	semidirect
45. #485390	C₂²	semidirect
46. #485385	C₂²	semidirect
47. #485077	C₂²	semidirect
48. #485039	C₂²	semidirect
49. #482562	C₂²	semidirect
50. #482550	C₂²	semidirect
51. #480245	C₂²	semidirect
52. #480245	C₂²	semidirect
53. #346481	C₂²	semidirect
54. #346466	C₂²	semidirect
55. #346462	C₂²	semidirect
56. #346456	C₂²	semidirect
57. #346452	C₂²	semidirect
58. #346452	C₂²	semidirect
61. #188081	C₂²	semidirect
62. #188081	C₂²	semidirect
63. #185263	C₂²	semidirect
64. #185257	C₂²	semidirect
65. #142571	C₂²	semidirect
66. #142570	C₂²	semidirect
67. #142569	C₂²	semidirect
68. #142568	C₂²	semidirect
69. #142537	C₂²	semidirect
70. #142537	C₂²	semidirect
71. #142536	C₂²	semidirect
72. #142536	C₂²	semidirect
73. #139645	C₂²	semidirect
74. #139645	C₂²	semidirect
75. #139622	C₂²	semidirect
76. #139622	C₂²	semidirect
77. #139505	C₂²	semidirect
78. #139505	C₂²	semidirect
79. #139504	C₂²	semidirect
80. #139504	C₂²	semidirect
81. #139487	C₂²	semidirect
82. #139486	C₂²	semidirect
83. #139485	C₂²	semidirect
84. #139484	C₂²	semidirect
85. #134035	C₂²	semidirect
86. #134035	C₂²	semidirect
87. #134034	C₂²	semidirect
88. #134033	C₂²	semidirect
89. #127218	C₂²	semidirect
90. #127216	C₂²	semidirect
108. C₂×#2544	D₄	semidirect
109. C₂×#2535	D₄	semidirect
114. C₂×#2631	D₄	semidirect
115. C₂×#2328	D₄	semidirect
119. #23986	D₄	semidirect
124. #23467	D₄	semidirect
125. #23443	D₄	semidirect
137. #15674	D₄	semidirect
138. #15673	D₄	semidirect
139. #15671	D₄	semidirect
140. #15670	D₄	semidirect
146. #15453	D₄	semidirect
147. #15453	D₄	semidirect
150. #15310	D₄	semidirect
151. #15310	D₄	semidirect
161. #14345	D₄	semidirect
162. #13959	D₄	semidirect
163. #13959	D₄	semidirect
168. #13785	D₄	semidirect
197. #3491	C₂×D₄	semidirect
199. #3458	C₂×D₄	semidirect
200. #3449	C₂×D₄	semidirect
204. C₂²×#124	C₂×D₄	semidirect
225. C₂²×C₄×D₄	C₂×D₄	semidirect
229. C₂×#400	C₂×D₄	semidirect
232. C₂×#397	C₂×D₄	semidirect
233. C₂×#395	C₂×D₄	semidirect
234. C₂×#394	C₂×D₄	semidirect
235. C₂×#394	C₂×D₄	semidirect
237. C₂×#393	C₂×D₄	semidirect
241. C₂×#392	C₂×D₄	semidirect
242. C₂×#392	C₂×D₄	semidirect
245. C₂×#391	C₂×D₄	semidirect
247. C₂×#390	C₂×D₄	semidirect
248. C₂×#390	C₂×D₄	semidirect
249. C₂×#383	C₂×D₄	semidirect
250. C₂×#383	C₂×D₄	semidirect
251. C₂×#382	C₂×D₄	semidirect
252. C₂×#382	C₂×D₄	semidirect
267. C₂×C₄×C₄⋊C₄	C₂×D₄	semidirect
268. C₂×#376	C₂×D₄	semidirect
269. C₂×#376	C₂×D₄	semidirect
270. #2030	C₂×D₄	semidirect
272. #2022	C₂×D₄	semidirect
274. #1820	C₂×D₄	semidirect
276. #1740	C₂×D₄	semidirect
279. #1445	C₂×D₄	semidirect
280. #1445	C₂×D₄	semidirect
281. #1445	C₂×D₄	semidirect
282. #1445	C₂×D₄	semidirect
291. #1437	C₂×D₄	semidirect
292. #1437	C₂×D₄	semidirect
293. #1437	C₂×D₄	semidirect
294. #1437	C₂×D₄	semidirect
299. #1436	C₂×D₄	semidirect
300. #1436	C₂×D₄	semidirect
301. #1436	C₂×D₄	semidirect
302. #1436	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72252027	2
#72252026	2
#72252025	2
#72252024	2
#72251910	2
#72251903	2
#72251835	2
#72251770	2
#72251723	2
#72238401	2
#72237556	2
#72235716	2
#72235079	2
#72234769	2
#72232713	2
#72232346	2
#72213843	2
#72213838	2
#72213827	2