Subgroups — #72236968

Order 2048.

At least 9110 conjugacy classes of subgroups; only the 670 normal subgroups are shown.

The subgroup lattice has 433 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72236966	C₂	1	2	yes	maximal, complemented
2	#72236965	C₂	1	2	yes	maximal, complemented
3	#72236963	C₂	1	2	yes	maximal, complemented
4	#72236962	C₂	1	2	yes	maximal, complemented
5	#72236961	C₂	1	2	yes	maximal, complemented
6	#72236960	C₂	1	2	yes	maximal, complemented
7	#72236959	C₂	1	2	yes	maximal, complemented
8	#72236958	C₂	1	2	yes	maximal, complemented
9	#72236957	C₂	1	2	yes	maximal, complemented
10	#72236953	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#139700	C₂	1	2	yes	maximal, complemented
12	#72233597	C₂	1	1	yes	maximal, characteristic, complemented
13	#72233423	C₂	1	1	yes	maximal, characteristic, complemented
14	#72233265	C₂	1	1	yes	maximal, characteristic, complemented
15	#72233177	C₂	1	2	yes	maximal, complemented
16	#72233043	C₂	1	2	yes	maximal, complemented
17	#72233035	C₂	1	1	yes	maximal, characteristic, complemented
18	#72232736	C₂	1	1	yes	maximal, characteristic, complemented
19	#72216323	C₂	1	1	yes	maximal, characteristic
20	#10586472	C₂²	1	1	yes	characteristic
21	#6470226	C₂²	1	2	yes	—
22	C₂×#23900	C₂²	1	2	yes	—
23	#6385983	C₂²	1	1	yes	characteristic
24	#5486624	C₂²	1	1	yes	characteristic, complemented
25	#5486602	C₂²	1	1	yes	characteristic, complemented
26	#5486439	C₂²	1	1	yes	characteristic, complemented
27	#5486276	C₂²	1	1	yes	characteristic, complemented
28	#2600505	C₂²	1	1	yes	characteristic, complemented
29	#2549486	C₂²	1	1	yes	characteristic, complemented
30	#2306524	C₂²	1	1	yes	characteristic, complemented
31	#2177857	C₂²	1	1	yes	characteristic, complemented
32	#949904	C₂²	1	1	yes	characteristic, complemented
33	#845677	C₂²	1	1	yes	characteristic, complemented
34	#705152	C₂²	1	1	yes	characteristic
35	#647656	C₂²	1	1	yes	characteristic
36	#582871	C₂²	1	1	yes	characteristic, complemented
37	#553180	C₂²	1	1	yes	characteristic
38	C₂×#14134	C₂²	1	1	yes	characteristic, complemented
39	#496226	C₂²	1	2	yes	complemented
40	C₂×#12687	C₂²	1	2	yes	complemented
41	#347056	C₂²	1	2	yes	complemented
42	#347056	C₂²	1	2	yes	complemented
43	#347052	C₂²	1	2	yes	complemented
44	#347049	C₂²	1	2	yes	complemented
45	#347047	C₂²	1	2	yes	—
46	#347047	C₂²	1	2	yes	—
47	#347043	C₂²	1	2	yes	—
48	#347043	C₂²	1	2	yes	—
49	#188035	C₂²	1	1	yes	characteristic
50	#188035	C₂²	1	1	yes	characteristic
51	#187928	C₂²	1	2	yes	—
52	C₂×#8534	C₂²	1	2	yes	—
53	#186843	C₂²	1	2	yes	complemented
54	#186842	C₂²	1	2	yes	complemented
55	#186824	C₂²	1	2	yes	complemented
56	#186819	C₂²	1	2	yes	complemented
57	#186808	C₂²	1	2	yes	—
58	C₂×#8453	C₂²	1	2	yes	—
59	#144655	C₂²	1	4	yes	complemented
60	#144655	C₂²	1	4	yes	complemented
61	#144644	C₂²	1	4	yes	complemented
62	#144627	C₂²	1	4	yes	complemented
63	#144412	C₂²	1	4	yes	complemented
64	#144412	C₂²	1	4	yes	complemented
65	#144367	C₂²	1	4	yes	complemented
66	#144367	C₂²	1	4	yes	complemented
67	#139846	C₂²	1	2	yes	complemented
68	#139826	C₂²	1	2	yes	complemented
69	#139815	C₂²	1	4	yes	complemented
70	#139790	C₂²	1	2	yes	complemented
71	#139790	C₂²	1	2	yes	complemented
72	#139788	C₂²	1	2	yes	complemented
73	#139774	C₂²	1	4	yes	complemented
74	#139764	C₂²	1	4	yes	complemented
75	#139713	C₂²	1	2	yes	complemented
76	#139713	C₂²	1	2	yes	complemented
77	#139712	C₂²	1	2	yes	complemented
78	#139703	C₂²	1	4	yes	complemented
79	#139700	C₂²	1	4	yes	complemented
80	#139700	C₂²	1	4	yes	complemented
81	#139700	C₂²	1	4	yes	complemented
82	#139700	C₂²	1	4	yes	complemented
83	#135548	C₂²	1	2	yes	complemented
84	#135537	C₂²	1	2	yes	complemented
85	#135519	C₂²	1	2	yes	complemented
86	#135510	C₂²	1	2	yes	complemented
87	#128073	C₂²	1	2	yes	complemented
88	#128058	C₂²	1	2	yes	complemented
89	C₂×#7304	C₂²	1	2	yes	complemented
90	C₂×#7307	C₂²	1	2	yes	complemented
91	#62832	C₂³	1	2	yes	—
92	#62818	C₂³	1	2	yes	—
93	C₂×#3484	C₂³	1	2	yes	—
94	C₂²×D₄²	C₂³	1	1	yes	characteristic
95	C₂³×#120	D₄	1	1	yes	characteristic
96	C₂³×#120	C₂³	1	1	yes	characteristic
97	C₂×#2846	D₄	1	1	yes	characteristic
98	C₂×#2412	D₄	1	1	yes	characteristic, complemented
99	C₂×#2405	C₂³	1	1	yes	characteristic
100	C₂×#2353	D₄	1	1	yes	characteristic, complemented
101	C₂×#2318	D₄	1	1	yes	characteristic, complemented
102	C₂×#2308	D₄	1	1	yes	characteristic, complemented
103	#24056	C₂³	1	4	yes	—
104	#23901	C₂³	1	4	yes	—
105	#23900	C₂³	1	4	yes	—
106	#23900	C₂³	1	4	yes	—
107	#21797	C₂³	1	2	yes	—
108	#21752	C₂³	1	2	yes	—
109	C₂×#1783	C₂³	1	2	yes	—
110	C₂×#1781	C₂³	1	2	yes	—
111	C₂×#1781	C₂³	1	2	yes	—
112	#17273	C₂³	1	1	yes	characteristic, complemented
113	#17272	C₂³	1	1	yes	characteristic, complemented
114	#17272	C₂³	1	1	yes	characteristic, complemented
115	#17137	C₂³	1	1	yes	characteristic, complemented
116	#15984	D₄	1	1	yes	characteristic, complemented
117	#15984	C₂³	1	1	yes	characteristic
118	#15950	C₂³	1	1	yes	characteristic
119	#15948	D₄	1	1	yes	characteristic, complemented
120	#15948	D₄	1	1	yes	characteristic, complemented
121	#15948	C₂³	1	1	yes	characteristic, complemented
122	#15948	C₂³	1	1	yes	characteristic, complemented
123	#15947	D₄	1	1	yes	characteristic
124	#15947	D₄	1	1	yes	characteristic
125	#15266	C₂³	1	1	yes	characteristic, complemented
126	#15266	C₂³	1	1	yes	characteristic, complemented
127	#15261	C₂³	1	1	yes	characteristic
128	#15261	C₂³	1	1	yes	characteristic
129	#15260	D₄	1	1	yes	characteristic, complemented
130	#15258	C₂³	1	1	yes	characteristic
131	#15258	C₂³	1	1	yes	characteristic
132	#15257	D₄	1	1	yes	characteristic
133	#15257	D₄	1	1	yes	characteristic
134	#15257	C₂³	1	1	yes	characteristic
135	#15257	C₂³	1	1	yes	characteristic
136	#14666	C₂³	1	1	yes	characteristic, complemented
137	#14661	C₂³	1	1	yes	characteristic
138	#14659	C₂³	1	1	yes	characteristic
139	#14658	C₂³	1	1	yes	characteristic, complemented
140	#14506	C₂³	1	1	yes	characteristic, complemented
141	#14410	C₂³	1	1	yes	characteristic, complemented
142	#14345	D₄	1	1	yes	characteristic, complemented
143	#14335	D₄	1	1	yes	characteristic, complemented
144	#14290	C₂³	1	1	yes	characteristic
145	#14272	C₂³	1	1	yes	characteristic
146	#14271	D₄	1	1	yes	characteristic, complemented
147	#14255	D₄	1	1	yes	characteristic, complemented
148	#14152	D₄	1	1	yes	characteristic, complemented
149	#14134	D₄	1	1	yes	characteristic
150	#14134	C₂³	1	1	yes	characteristic, complemented
151	#14134	C₂³	1	1	yes	characteristic, complemented
152	#14134	C₂³	1	1	yes	characteristic, complemented
153	#14134	C₂³	1	1	yes	characteristic, complemented
154	#13959	D₄	1	1	yes	characteristic, complemented
155	#13902	D₄	1	1	yes	characteristic, complemented
156	#13902	C₂³	1	1	yes	characteristic
157	#13867	D₄	1	1	yes	characteristic
158	#13867	D₄	1	1	yes	characteristic, complemented
159	#13867	C₂³	1	1	yes	characteristic
160	C₂×#1438	C₂³	1	1	yes	characteristic
161	C₂×#1438	C₂³	1	1	yes	characteristic
162	#12852	C₂³	1	4	yes	complemented
163	#12688	C₂³	1	4	yes	complemented
164	#12687	C₂³	1	4	yes	complemented
165	#12687	C₂³	1	4	yes	complemented
166	#8546	C₂³	1	2	yes	—
167	#8546	C₂³	1	2	yes	—
168	#8542	C₂³	1	2	yes	—
169	#8542	C₂³	1	2	yes	—
170	#8534	C₂³	1	4	yes	—
171	#8534	C₂³	1	4	yes	—
172	#8534	C₂³	1	4	yes	—
173	#8534	C₂³	1	4	yes	—
174	#8453	C₂³	1	4	yes	—
175	#8453	C₂³	1	4	yes	—
176	#8453	C₂³	1	4	yes	—
177	#8453	C₂³	1	4	yes	—
178	#7307	C₂³	1	4	yes	complemented
179	#7307	C₂³	1	4	yes	complemented
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	C₂²×H(5,𝔽₂)	#41	1	2	yes	—
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	C₂⁴	1	1	yes	characteristic
192	#3484	#41	1	4	yes	—
193	#3484	C₂⁴	1	4	yes	—
194	C₂²×#127	C₂⁴	1	1	yes	characteristic
195	C₂²×#123	C₂×D₄	1	1	yes	characteristic
196	C₂²×#123	C₂×D₄	1	1	yes	characteristic, complemented
197	C₂²×#123	C₂⁴	1	1	yes	characteristic
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	C₂⁴	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	C₂⁴	1	1	yes	characteristic
215	C₂²×#120	C₂⁴	1	1	yes	characteristic
216	C₂×#518	#41	1	2	yes	—
217	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
219	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
220	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
221	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
222	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
223	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
224	C₂×#386	C₂×D₄	1	1	yes	characteristic
225	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
226	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
227	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
228	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
229	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
230	C₂×#386	C₂⁴	1	1	yes	characteristic
231	C₂×#385	C₂×D₄	1	1	yes	characteristic, complemented
232	C₂×#383	C₂×D₄	1	1	yes	characteristic, complemented
233	C₂×#383	C₂×D₄	1	1	yes	characteristic, complemented
234	C₂×#382	C₂×D₄	1	1	yes	characteristic, complemented
235	C₂×#381	C₂×D₄	1	1	yes	characteristic, complemented
236	C₂×#381	C₂×D₄	1	1	yes	characteristic, complemented
237	C₂×#381	C₂×D₄	1	1	yes	characteristic, complemented
238	C₂×#380	C₂×D₄	1	1	yes	characteristic
239	C₂×#380	C₂×D₄	1	1	yes	characteristic, complemented
240	C₂×#379	C₂×D₄	1	1	yes	characteristic
241	C₂×#379	C₂×D₄	1	1	yes	characteristic
242	C₂×#379	C₂×D₄	1	1	yes	characteristic
243	C₂×#379	C₂×D₄	1	1	yes	characteristic
244	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
245	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
246	C₂×#376	C₂×D₄	1	1	yes	characteristic, complemented
247	C₂²×#95	C₂×D₄	1	1	yes	characteristic
248	C₂²×#95	C₂×D₄	1	1	yes	characteristic
249	#1783	C₂⁴	1	4	yes	—
250	#1781	C₂⁴	1	4	yes	—
251	#1781	C₂⁴	1	4	yes	—
252	#1445	C₂×D₄	1	1	yes	characteristic, complemented
253	#1445	C₂×D₄	1	1	yes	characteristic, complemented
254	#1445	C₂×D₄	1	1	yes	characteristic, complemented
255	#1445	C₂×D₄	1	1	yes	characteristic, complemented
256	#1440	C₂×D₄	1	1	yes	characteristic
257	#1440	C₂×D₄	1	1	yes	characteristic
258	#1440	C₂×D₄	1	1	yes	characteristic, complemented
259	#1440	C₂×D₄	1	1	yes	characteristic, complemented
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
270	#1438	C₂×D₄	1	1	yes	characteristic
271	#1438	C₂×D₄	1	1	yes	characteristic
272	#1438	C₂×D₄	1	1	yes	characteristic
273	#1438	C₂×D₄	1	1	yes	characteristic
274	#1438	C₂×D₄	1	1	yes	characteristic, complemented
275	#1438	C₂×D₄	1	1	yes	characteristic, complemented
276	#1438	C₂×D₄	1	1	yes	characteristic, complemented
277	#1438	C₂×D₄	1	1	yes	characteristic, complemented
278	#1438	C₂×D₄	1	1	yes	characteristic, complemented
279	#1438	C₂×D₄	1	1	yes	characteristic, complemented
280	#1438	C₂×D₄	1	1	yes	characteristic, complemented
281	#1438	C₂×D₄	1	1	yes	characteristic, complemented
282	#1438	C₂×D₄	1	1	yes	characteristic, complemented
283	#1438	C₂×D₄	1	1	yes	characteristic, complemented
284	#1438	C₂⁴	1	1	yes	characteristic
285	#1438	C₂⁴	1	1	yes	characteristic
286	#1438	C₂⁴	1	1	yes	characteristic
287	#1438	C₂⁴	1	1	yes	characteristic
288	#1438	C₂⁴	1	1	yes	characteristic
289	#1438	C₂⁴	1	1	yes	characteristic
290	#1438	C₂⁴	1	1	yes	characteristic
291	#1438	C₂⁴	1	1	yes	characteristic
292	C₂⁶	#120	1	1	yes	characteristic
293	C₂⁶	#120	1	1	yes	characteristic
294	C₂⁶	C₂²×D₄	1	1	yes	characteristic
295	C₂⁶	C₂²×D₄	1	1	yes	characteristic
296	C₂⁶	C₂²×D₄	1	1	yes	characteristic
297	C₂⁶	C₂²×D₄	1	1	yes	characteristic
298	C₂×H(5,𝔽₂)	C₂×#41	1	4	yes	—
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	#120	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	C₂²×D₄	1	1	yes	characteristic
314	C₂³×D₄	C₂×#41	1	2	yes	—
315	C₂³×D₄	C₂×#41	1	2	yes	—
316	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
317	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
318	C₂³×D₄	C₂⁵	1	1	yes	characteristic
319	C₂⁴×C₄	#120	1	1	yes	characteristic
320	C₂⁴×C₄	#120	1	1	yes	characteristic
321	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
322	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
323	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
324	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
325	#518	C₂×#41	1	4	yes	—
326	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
327	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
328	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
329	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
330	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
331	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
332	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
333	C₂²×C₂²⋊C₄	#120	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×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
344	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
345	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
346	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
347	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
348	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
349	C₂×#95	C₂²×D₄	1	1	yes	characteristic
350	C₂×#95	C₂²×D₄	1	1	yes	characteristic
351	C₂×#95	C₂²×D₄	1	1	yes	characteristic
352	C₂×#95	C₂²×D₄	1	1	yes	characteristic
353	C₂×#95	C₂²×D₄	1	1	yes	characteristic
354	C₂×#95	C₂²×D₄	1	1	yes	characteristic
355	C₂×#95	C₂²×D₄	1	1	yes	characteristic
356	C₂×#95	C₂²×D₄	1	1	yes	characteristic
357	C₂⁵	C₂×#120	1	1	yes	characteristic
358	C₂⁵	C₂×#120	1	1	yes	characteristic
359	C₂⁵	C₂×#120	1	1	yes	characteristic
360	C₂⁵	C₂×#120	1	1	yes	characteristic
361	C₂⁵	C₂×#120	1	1	yes	characteristic
362	C₂⁵	C₂×#120	1	1	yes	characteristic
363	C₂⁵	#546	1	2	yes	—
364	C₂⁵	#546	1	2	yes	—
365	C₂⁵	#546	1	2	yes	—
366	C₂⁵	#546	1	2	yes	—
367	C₂⁵	C₂³×D₄	1	1	yes	characteristic
368	C₂⁵	C₂³×D₄	1	1	yes	characteristic
369	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
370	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
371	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
372	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
373	C₂²×D₄	#525	1	1	yes	characteristic
374	C₂²×D₄	#525	1	1	yes	characteristic
375	C₂²×D₄	#535	1	1	yes	characteristic
376	C₂²×D₄	#535	1	1	yes	characteristic
377	C₂²×D₄	#546	1	2	yes	—
378	C₂²×D₄	#546	1	2	yes	—
379	C₂²×D₄	#546	1	2	yes	—
380	C₂²×D₄	#546	1	2	yes	—
381	C₂²×D₄	C₂²×#41	1	2	yes	—
382	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
383	C₂³×C₄	C₂×#120	1	1	yes	characteristic
384	C₂³×C₄	C₂×#120	1	1	yes	characteristic
385	C₂³×C₄	C₂×#120	1	1	yes	characteristic
386	C₂³×C₄	C₂×#120	1	1	yes	characteristic
387	C₂³×C₄	C₂×#120	1	1	yes	characteristic
388	C₂³×C₄	C₂×#120	1	1	yes	characteristic
389	C₂³×C₄	#525	1	2	yes	—
390	C₂³×C₄	#535	1	2	yes	—
391	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
392	C₂×C₂²⋊C₄	B(4,𝔽₂)	1	4	yes	—
393	C₂⁴	#2404	1	2	yes	—
394	C₂⁴	#2404	1	1	yes	characteristic
395	C₂⁴	#2404	1	1	yes	characteristic
396	C₂⁴	#2404	1	1	yes	characteristic
397	C₂⁴	#2404	1	1	yes	characteristic
398	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
399	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
400	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
401	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
402	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
403	C₂⁴	C₂²×#120	1	1	yes	characteristic
404	C₂⁴	C₂×#546	1	2	yes	—
405	C₂⁴	C₂×#546	1	2	yes	—
406	C₂²×C₄	#2404	1	2	yes	—
407	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
408	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
409	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
410	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
411	C₂²×C₄	C₂×#525	1	1	yes	characteristic
412	C₂²×C₄	C₂×#535	1	1	yes	characteristic
413	C₂³	#23984	1	2	yes	—
414	C₂³	#23984	1	2	yes	—
415	C₂³	#23996	1	2	yes	—
416	C₂³	#33551	1	2	yes	—
417	C₂³	#33552	1	2	yes	—
418	C₂³	C₂×#2404	1	1	yes	characteristic
419	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
420	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
421	C₂²	#500035	1	4	yes	—
422	C₂²	C₂×#23996	1	1	yes	characteristic
423	C₂²	#6451863	1	1	yes	characteristic
424	C₂²	C₂×#23984	1	1	yes	characteristic
425	C₂²	C₂×#33551	1	1	yes	characteristic
426	C₂²	C₂×#33552	1	1	yes	characteristic
427	C₂²	#7622880	1	1	yes	characteristic
428	C₂²	#7622881	1	1	yes	characteristic
429	C₂	#72233179	1	1	yes	characteristic
430	C₂	#72234955	1	1	yes	characteristic
431	C₂	C₂×#500035	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#23984
commutator, Frattini, cosocle	C₂³×D₄	C₂⁵
prime radical	#72216323	C₂
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ 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. #72236966	C₂	semidirect
2. #72236965	C₂	semidirect
3. #72236963	C₂	semidirect
4. #72236962	C₂	semidirect
5. #72236961	C₂	semidirect
6. #72236960	C₂	semidirect
7. #72236959	C₂	semidirect
8. #72236958	C₂	semidirect
9. #72236957	C₂	semidirect
10. #72236953	C₂	semidirect
11. C₂×#139700	C₂	semidirect
12. #72233597	C₂	semidirect
13. #72233423	C₂	semidirect
14. #72233265	C₂	semidirect
15. #72233177	C₂	semidirect
16. #72233043	C₂	semidirect
17. #72233035	C₂	semidirect
18. #72232736	C₂	semidirect
24. #5486624	C₂²	semidirect
25. #5486602	C₂²	semidirect
26. #5486439	C₂²	semidirect
27. #5486276	C₂²	semidirect
28. #2600505	C₂²	semidirect
29. #2549486	C₂²	semidirect
30. #2306524	C₂²	semidirect
31. #2177857	C₂²	semidirect
32. #949904	C₂²	semidirect
33. #845677	C₂²	semidirect
36. #582871	C₂²	semidirect
38. C₂×#14134	C₂²	semidirect
39. #496226	C₂²	semidirect
40. C₂×#12687	C₂²	semidirect
41. #347056	C₂²	semidirect
42. #347056	C₂²	semidirect
43. #347052	C₂²	semidirect
44. #347049	C₂²	semidirect
53. #186843	C₂²	semidirect
54. #186842	C₂²	semidirect
55. #186824	C₂²	semidirect
56. #186819	C₂²	semidirect
59. #144655	C₂²	semidirect
60. #144655	C₂²	semidirect
61. #144644	C₂²	semidirect
62. #144627	C₂²	semidirect
63. #144412	C₂²	semidirect
64. #144412	C₂²	semidirect
65. #144367	C₂²	semidirect
66. #144367	C₂²	semidirect
67. #139846	C₂²	semidirect
68. #139826	C₂²	semidirect
69. #139815	C₂²	semidirect
70. #139790	C₂²	semidirect
71. #139790	C₂²	semidirect
72. #139788	C₂²	semidirect
73. #139774	C₂²	semidirect
74. #139764	C₂²	semidirect
75. #139713	C₂²	semidirect
76. #139713	C₂²	semidirect
77. #139712	C₂²	semidirect
78. #139703	C₂²	semidirect
79. #139700	C₂²	semidirect
80. #139700	C₂²	semidirect
81. #139700	C₂²	semidirect
82. #139700	C₂²	semidirect
83. #135548	C₂²	semidirect
84. #135537	C₂²	semidirect
85. #135519	C₂²	semidirect
86. #135510	C₂²	semidirect
87. #128073	C₂²	semidirect
88. #128058	C₂²	semidirect
89. C₂×#7304	C₂²	semidirect
90. C₂×#7307	C₂²	semidirect
98. C₂×#2412	D₄	semidirect
100. C₂×#2353	D₄	semidirect
101. C₂×#2318	D₄	semidirect
102. C₂×#2308	D₄	semidirect
112. #17273	C₂³	semidirect
113. #17272	C₂³	semidirect
114. #17272	C₂³	semidirect
115. #17137	C₂³	semidirect
116. #15984	D₄	semidirect
119. #15948	D₄	semidirect
120. #15948	D₄	semidirect
121. #15948	C₂³	semidirect
122. #15948	C₂³	semidirect
125. #15266	C₂³	semidirect
126. #15266	C₂³	semidirect
129. #15260	D₄	semidirect
136. #14666	C₂³	semidirect
139. #14658	C₂³	semidirect
140. #14506	C₂³	semidirect
141. #14410	C₂³	semidirect
142. #14345	D₄	semidirect
143. #14335	D₄	semidirect
146. #14271	D₄	semidirect
147. #14255	D₄	semidirect
148. #14152	D₄	semidirect
150. #14134	C₂³	semidirect
151. #14134	C₂³	semidirect
152. #14134	C₂³	semidirect
153. #14134	C₂³	semidirect
154. #13959	D₄	semidirect
155. #13902	D₄	semidirect
158. #13867	D₄	semidirect
162. #12852	C₂³	semidirect
163. #12688	C₂³	semidirect
164. #12687	C₂³	semidirect
165. #12687	C₂³	semidirect
178. #7307	C₂³	semidirect
179. #7307	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
196. C₂²×#123	C₂×D₄	semidirect
225. C₂×#386	C₂×D₄	semidirect
226. C₂×#386	C₂×D₄	semidirect
227. C₂×#386	C₂×D₄	semidirect
228. C₂×#386	C₂×D₄	semidirect
229. C₂×#386	C₂×D₄	semidirect
231. C₂×#385	C₂×D₄	semidirect
232. C₂×#383	C₂×D₄	semidirect
233. C₂×#383	C₂×D₄	semidirect
234. C₂×#382	C₂×D₄	semidirect
235. C₂×#381	C₂×D₄	semidirect
236. C₂×#381	C₂×D₄	semidirect
237. C₂×#381	C₂×D₄	semidirect
239. C₂×#380	C₂×D₄	semidirect
245. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
246. C₂×#376	C₂×D₄	semidirect
252. #1445	C₂×D₄	semidirect
253. #1445	C₂×D₄	semidirect
254. #1445	C₂×D₄	semidirect
255. #1445	C₂×D₄	semidirect
258. #1440	C₂×D₄	semidirect
259. #1440	C₂×D₄	semidirect
274. #1438	C₂×D₄	semidirect
275. #1438	C₂×D₄	semidirect
276. #1438	C₂×D₄	semidirect
277. #1438	C₂×D₄	semidirect
278. #1438	C₂×D₄	semidirect
279. #1438	C₂×D₄	semidirect
280. #1438	C₂×D₄	semidirect
281. #1438	C₂×D₄	semidirect
282. #1438	C₂×D₄	semidirect
283. #1438	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72236966	2
#72236965	2
#72236963	2
#72236962	2
#72236961	2
#72236960	2
#72236959	2
#72236958	2
#72236957	2
#72236953	2
C₂×#139700	2
#72233597	2
#72233423	2
#72233265	2
#72233177	2
#72233043	2
#72233035	2
#72232736	2
#72216323	2