Subgroups — #72234784

Order 2048.

At least 10897 conjugacy classes of subgroups; only the 770 normal subgroups are shown.

The subgroup lattice has 456 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72234783	C₂	1	1	yes	maximal, characteristic, complemented
2	#72234778	C₂	1	1	yes	maximal, characteristic, complemented
3	#72234771	C₂	1	2	yes	maximal, complemented
4	#72234770	C₂	1	2	yes	maximal, complemented
5	#72234757	C₂	1	2	yes	maximal, complemented
6	#72234725	C₂	1	2	yes	maximal, complemented
7	#72234711	C₂	1	2	yes	maximal, complemented
8	#72234701	C₂	1	2	yes	maximal, complemented
9	#72234699	C₂	1	2	yes	maximal, complemented
10	#72233277	C₂	1	1	yes	maximal, characteristic, complemented
11	#72233273	C₂	1	2	yes	maximal, complemented
12	#72233220	C₂	1	1	yes	maximal, characteristic, complemented
13	#72233021	C₂	1	1	yes	maximal, characteristic, complemented
14	#72232960	C₂	1	1	yes	maximal, characteristic, complemented
15	#72232937	C₂	1	1	yes	maximal, characteristic, complemented
16	#72232603	C₂	1	2	yes	maximal, complemented
17	#72231386	C₂	1	2	yes	maximal, complemented
18	#72213827	C₂	1	2	yes	maximal, complemented
19	#72209889	C₂	1	2	yes	maximal, complemented
20	#10586472	C₂²	1	1	yes	characteristic, complemented
21	C₂×#57971	C₂²	1	1	yes	characteristic, complemented
22	C₂×#37644	C₂²	1	1	yes	characteristic
23	#6500011	C₂²	1	2	yes	complemented
24	#6500010	C₂²	1	2	yes	complemented
25	#6499870	C₂²	1	2	yes	complemented
26	#6499867	C₂²	1	2	yes	complemented
27	#6491103	C₂²	1	2	yes	—
28	#6454047	C₂²	1	2	yes	complemented
29	#6385971	C₂²	1	1	yes	characteristic, complemented
30	#6347264	C₂²	1	2	yes	complemented
31	#6346599	C₂²	1	2	yes	complemented
32	#4599081	C₂²	1	1	yes	characteristic, complemented
33	#4466055	C₂²	1	1	yes	characteristic, complemented
34	#4435227	C₂²	1	1	yes	characteristic, complemented
35	#4418479	C₂²	1	1	yes	characteristic
36	#4378714	C₂²	1	1	yes	characteristic, complemented
37	#2805719	C₂²	1	1	yes	characteristic, complemented
38	#2032088	C₂²	1	1	yes	characteristic, complemented
39	#1465620	C₂²	1	1	yes	characteristic, complemented
40	#1460307	C₂²	1	1	yes	characteristic, complemented
41	#649038	C₂²	1	1	yes	characteristic
42	#648360	C₂²	1	1	yes	characteristic, complemented
43	#634305	C₂²	1	1	yes	characteristic, complemented
44	#534229	C₂²	1	1	yes	characteristic, complemented
45	#485388	C₂²	1	4	yes	complemented
46	#485385	C₂²	1	4	yes	complemented
47	#485044	C₂²	1	4	yes	complemented
48	#485039	C₂²	1	4	yes	complemented
49	#482357	C₂²	1	2	yes	complemented
50	#481962	C₂²	1	2	yes	complemented
51	#480710	C₂²	1	2	yes	complemented
52	#480382	C₂²	1	2	yes	complemented
53	#346456	C₂²	1	2	yes	complemented
54	#346456	C₂²	1	2	yes	complemented
55	#346446	C₂²	1	2	yes	—
56	#346446	C₂²	1	2	yes	complemented
57	#346446	C₂²	1	2	yes	complemented
58	#346446	C₂²	1	2	yes	complemented
59	#346446	C₂²	1	2	yes	complemented
60	#346446	C₂²	1	2	yes	complemented
61	#188151	C₂²	1	1	yes	characteristic, complemented
62	#188087	C₂²	1	1	yes	characteristic, complemented
63	#185259	C₂²	1	2	yes	complemented
64	#185246	C₂²	1	2	yes	complemented
65	#142584	C₂²	1	4	yes	complemented
66	#142568	C₂²	1	4	yes	complemented
67	#142553	C₂²	1	4	yes	complemented
68	#142553	C₂²	1	4	yes	complemented
69	#142552	C₂²	1	4	yes	complemented
70	#142536	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	#139644	C₂²	1	4	yes	complemented
75	#139623	C₂²	1	4	yes	complemented
76	#139622	C₂²	1	4	yes	complemented
77	#139504	C₂²	1	2	yes	complemented
78	#139504	C₂²	1	2	yes	complemented
79	#139504	C₂²	1	2	yes	complemented
80	#139504	C₂²	1	2	yes	complemented
81	#139504	C₂²	1	2	yes	complemented
82	#139504	C₂²	1	2	yes	complemented
83	#139486	C₂²	1	2	yes	complemented
84	#139486	C₂²	1	2	yes	complemented
85	#134084	C₂²	1	2	yes	complemented
86	#134083	C₂²	1	2	yes	complemented
87	#134036	C₂²	1	2	yes	complemented
88	#134033	C₂²	1	2	yes	complemented
89	#127232	C₂²	1	2	yes	complemented
90	#127199	C₂²	1	2	yes	complemented
91	#62817	C₂³	1	2	yes	—
92	#62817	C₂³	1	2	yes	—
93	#62773	C₂³	1	2	yes	—
94	C₂²×D₄²	C₂³	1	1	yes	characteristic
95	C₂²×#534	D₄	1	1	yes	characteristic
96	C₂³×#127	D₄	1	1	yes	characteristic, complemented
97	C₂³×#120	D₄	1	1	yes	characteristic
98	C₂³×#120	D₄	1	1	yes	characteristic
99	C₂×#2760	C₂³	1	1	yes	characteristic, complemented
100	C₂×#2670	C₂³	1	1	yes	characteristic, complemented
101	C₂×#2815	C₂³	1	1	yes	characteristic, complemented
102	C₂×#2846	C₂³	1	1	yes	characteristic
103	C₂×#2539	D₄	1	1	yes	characteristic
104	C₂×#2534	C₂³	1	1	yes	characteristic
105	C₂×#2433	D₄	1	1	yes	characteristic, complemented
106	C₂×#2408	C₂³	1	1	yes	characteristic
107	C₂×#2412	C₂³	1	1	yes	characteristic
108	C₂×#2405	D₄	1	1	yes	characteristic
109	C₂×#2410	C₂³	1	1	yes	characteristic
110	C₂×#2403	D₄	1	1	yes	characteristic
111	C₂×#2403	C₂³	1	1	yes	characteristic, complemented
112	C₂×#2657	D₄	1	1	yes	characteristic, complemented
113	C₂×#2631	D₄	1	1	yes	characteristic, complemented
114	C₂×#2631	C₂³	1	1	yes	characteristic
115	C₂×#2617	D₄	1	1	yes	characteristic
116	C₂×#2613	C₂³	1	1	yes	characteristic
117	C₂×D₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
118	C₂×#2321	C₂³	1	1	yes	characteristic
119	#29686	D₄	1	8	yes	complemented
120	#25949	D₄	1	4	yes	complemented
121	#25773	D₄	1	4	yes	complemented
122	#24112	C₂³	1	4	yes	—
123	#23985	C₂³	1	4	yes	—
124	#23984	C₂³	1	4	yes	—
125	#23984	C₂³	1	4	yes	—
126	#21746	C₂³	1	2	yes	—
127	#21746	C₂³	1	2	yes	—
128	#20722	C₂³	1	2	yes	—
129	#18163	C₂³	1	4	yes	—
130	#18162	C₂³	1	4	yes	—
131	#18162	C₂³	1	4	yes	—
132	#18162	C₂³	1	4	yes	—
133	#17364	C₂³	1	2	yes	—
134	#17362	C₂³	1	2	yes	—
135	#15635	C₂³	1	1	yes	characteristic, complemented
136	#15622	C₂³	1	1	yes	characteristic, complemented
137	#15467	C₂³	1	1	yes	characteristic, complemented
138	#15420	C₂³	1	1	yes	characteristic, complemented
139	#15420	C₂³	1	1	yes	characteristic, complemented
140	#15310	D₄	1	1	yes	characteristic, complemented
141	#15310	D₄	1	1	yes	characteristic, complemented
142	#15310	D₄	1	1	yes	characteristic, complemented
143	#15310	D₄	1	1	yes	characteristic, complemented
144	#15267	C₂³	1	1	yes	characteristic, complemented
145	#15267	C₂³	1	1	yes	characteristic, complemented
146	#15267	C₂³	1	1	yes	characteristic, complemented
147	#15259	D₄	1	1	yes	characteristic, complemented
148	#15259	D₄	1	1	yes	characteristic, complemented
149	#15259	C₂³	1	1	yes	characteristic
150	#15259	C₂³	1	1	yes	characteristic
151	#15258	D₄	1	1	yes	characteristic, complemented
152	#15258	D₄	1	1	yes	characteristic, complemented
153	#15258	C₂³	1	1	yes	characteristic
154	#15258	C₂³	1	1	yes	characteristic
155	#15258	C₂³	1	1	yes	characteristic
156	#15258	C₂³	1	1	yes	characteristic
157	#15258	C₂³	1	1	yes	characteristic
158	#15258	C₂³	1	1	yes	characteristic
159	#14698	D₄	1	1	yes	characteristic, complemented
160	#14661	D₄	1	1	yes	characteristic, complemented
161	#14507	C₂³	1	1	yes	characteristic, complemented
162	#14365	C₂³	1	1	yes	characteristic, complemented
163	#13959	D₄	1	1	yes	characteristic, complemented
164	#13959	C₂³	1	1	yes	characteristic
165	#13902	D₄	1	1	yes	characteristic, complemented
166	#13807	C₂³	1	1	yes	characteristic, complemented
167	C₂²⋊C₄²	C₂³	1	1	yes	characteristic, complemented
168	C₄×#386	C₂³	1	1	yes	characteristic
169	#11808	C₂³	1	4	yes	complemented
170	#11796	C₂³	1	4	yes	complemented
171	#11796	C₂³	1	4	yes	complemented
172	#11796	C₂³	1	4	yes	complemented
173	#11517	C₂³	1	4	yes	complemented
174	#11500	C₂³	1	4	yes	complemented
175	#11499	C₂³	1	4	yes	complemented
176	#11499	C₂³	1	4	yes	complemented
177	#8547	C₂³	1	2	yes	—
178	#8547	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	complemented
186	#7213	C₂³	1	4	yes	complemented
187	#7213	C₂³	1	4	yes	complemented
188	#7213	C₂³	1	4	yes	complemented
189	C₂⁷	C₂×D₄	1	1	yes	characteristic
190	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
191	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
192	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
193	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
194	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
195	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
196	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
197	#3501	C₂×D₄	1	2	yes	complemented
198	#3496	C₂×D₄	1	2	yes	complemented
199	#3490	C₂⁴	1	4	yes	—
200	#3459	C₂×D₄	1	4	yes	complemented
201	C₂²×#127	C₂×D₄	1	1	yes	characteristic
202	C₂²×#127	C₂×D₄	1	1	yes	characteristic
203	C₂²×#127	C₂×D₄	1	1	yes	characteristic
204	C₂²×#127	C₂×D₄	1	1	yes	characteristic
205	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
206	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
207	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
208	C₂²×#124	C₂×D₄	1	1	yes	characteristic
209	C₂²×#124	C₂×D₄	1	1	yes	characteristic, complemented
210	C₂²×#124	C₂×D₄	1	1	yes	characteristic, complemented
211	C₂²×#123	C₂×D₄	1	1	yes	characteristic
212	C₂²×#123	C₂×D₄	1	1	yes	characteristic
213	C₂²×#123	C₂×D₄	1	1	yes	characteristic
214	C₂²×#121	C₂×D₄	1	1	yes	characteristic
215	C₂²×#121	C₂×D₄	1	1	yes	characteristic
216	C₂²×#121	C₂×D₄	1	1	yes	characteristic
217	C₂²×#121	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	C₂×D₄	1	1	yes	characteristic
221	C₂²×#120	C₂×D₄	1	1	yes	characteristic
222	C₂²×#120	C₂×D₄	1	1	yes	characteristic
223	C₂²×#120	C₂×D₄	1	1	yes	characteristic
224	C₂²×#120	C₂×D₄	1	1	yes	characteristic
225	C₂²×#120	C₂×D₄	1	1	yes	characteristic
226	C₂²×#120	C₂⁴	1	1	yes	characteristic
227	C₂²×#120	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
230	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
231	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
232	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
233	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
234	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
235	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic, complemented
236	#2534	C₂×D₄	1	4	yes	—
237	#2534	C₂×D₄	1	4	yes	—
238	C₂×#394	C₂×D₄	1	1	yes	characteristic, complemented
239	C₂×#394	C₂×D₄	1	1	yes	characteristic, complemented
240	C₂×#393	C₂×D₄	1	1	yes	characteristic
241	C₂×#393	C₂×D₄	1	1	yes	characteristic, complemented
242	C₂×#393	C₂×D₄	1	1	yes	characteristic, complemented
243	C₂×#393	C₂⁴	1	1	yes	characteristic
244	C₂×#392	C₂×D₄	1	1	yes	characteristic
245	C₂×#392	C₂×D₄	1	1	yes	characteristic
246	C₂×#392	C₂×D₄	1	1	yes	characteristic
247	C₂×#392	C₂×D₄	1	1	yes	characteristic, complemented
248	C₂×#392	C₂×D₄	1	1	yes	characteristic, complemented
249	C₂×#392	C₂×D₄	1	1	yes	characteristic, complemented
250	C₂×#392	C₂×D₄	1	1	yes	characteristic, complemented
251	C₂×#392	C₂⁴	1	1	yes	characteristic
252	C₂×#392	C₂⁴	1	1	yes	characteristic
253	C₂×#392	C₂⁴	1	1	yes	characteristic
254	C₂×#386	C₂×D₄	1	1	yes	characteristic
255	C₂×#386	C₂×D₄	1	1	yes	characteristic
256	C₂×#386	C₂×D₄	1	1	yes	characteristic
257	C₂×#385	C₂⁴	1	1	yes	characteristic
258	C₂×#383	C₂×D₄	1	1	yes	characteristic, complemented
259	C₂×#383	C₂×D₄	1	1	yes	characteristic, complemented
260	C₂×#381	C₂⁴	1	1	yes	characteristic
261	C₂×#380	C₂×D₄	1	1	yes	characteristic
262	C₂×#380	C₂×D₄	1	1	yes	characteristic, complemented
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×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
268	C₂×C₄×C₂²⋊C₄	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	complemented
272	#2022	C₂×D₄	1	8	yes	complemented
273	#2021	C₂×D₄	1	8	yes	complemented
274	#1819	C₂⁴	1	4	yes	—
275	#1799	C₂×D₄	1	4	yes	complemented
276	C₄×#99	C₂×D₄	1	4	yes	complemented
277	#1462	C₂⁴	1	4	yes	—
278	#1462	C₂⁴	1	4	yes	—
279	#1438	C₂×D₄	1	1	yes	characteristic
280	#1438	C₂×D₄	1	1	yes	characteristic
281	#1438	C₂×D₄	1	1	yes	characteristic
282	#1438	C₂×D₄	1	1	yes	characteristic
283	#1438	C₂×D₄	1	1	yes	characteristic, complemented
284	#1438	C₂×D₄	1	1	yes	characteristic, complemented
285	#1438	C₂×D₄	1	1	yes	characteristic, complemented
286	#1438	C₂×D₄	1	1	yes	characteristic, complemented
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	C₂×D₄	1	1	yes	characteristic, complemented
296	#1437	C₂×D₄	1	1	yes	characteristic, complemented
297	#1437	C₂⁴	1	1	yes	characteristic
298	#1437	C₂⁴	1	1	yes	characteristic
299	#1437	C₂⁴	1	1	yes	characteristic
300	#1437	C₂⁴	1	1	yes	characteristic
301	#1436	C₂×D₄	1	1	yes	characteristic, complemented
302	#1436	C₂×D₄	1	1	yes	characteristic, complemented
303	C₂⁶	#120	1	1	yes	characteristic
304	C₂⁶	#120	1	1	yes	characteristic
305	C₂⁶	C₂²×D₄	1	1	yes	characteristic
306	C₂⁶	C₂²×D₄	1	1	yes	characteristic
307	C₂⁶	C₂²×D₄	1	1	yes	characteristic
308	C₂⁶	C₂²×D₄	1	1	yes	characteristic
309	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
310	C₂³×D₄	#120	1	1	yes	characteristic
311	C₂³×D₄	#120	1	1	yes	characteristic
312	C₂³×D₄	#120	1	1	yes	characteristic
313	C₂³×D₄	#120	1	1	yes	characteristic
314	C₂³×D₄	#120	1	1	yes	characteristic
315	C₂³×D₄	#120	1	1	yes	characteristic
316	C₂³×D₄	#120	1	1	yes	characteristic
317	C₂³×D₄	#120	1	1	yes	characteristic
318	C₂³×D₄	#120	1	1	yes	characteristic
319	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
320	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
321	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
322	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
323	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
324	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
325	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
326	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
327	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
328	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
329	C₂⁴×C₄	#120	1	1	yes	characteristic
330	C₂⁴×C₄	#120	1	1	yes	characteristic
331	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
332	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
333	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
334	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
335	#543	C₂²×D₄	1	4	yes	—
336	#534	C₂²×D₄	1	4	yes	—
337	C₂×#123	#120	1	2	yes	—
338	C₂×#123	#120	1	2	yes	—
339	C₂×#120	#120	1	2	yes	—
340	C₂×#120	#120	1	2	yes	—
341	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
342	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
343	C₂×C₄×D₄	H(5,𝔽₂)	1	2	yes	—
344	C₂×C₄×D₄	H(5,𝔽₂)	1	2	yes	—
345	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
346	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
347	C₂²×C₂²⋊C₄	#120	1	4	yes	—
348	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
349	C₂²×C₂²⋊C₄	#120	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	C₂²×D₄	1	1	yes	characteristic
358	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
359	C₂²×C₂²⋊C₄	C₂⁵	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	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
365	#381	C₂²×D₄	1	4	yes	—
366	#380	#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	C₂×#120	1	1	yes	characteristic
383	C₂⁵	C₂×#120	1	1	yes	characteristic
384	C₂⁵	C₂×#120	1	1	yes	characteristic
385	C₂⁵	C₂³×D₄	1	1	yes	characteristic
386	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
387	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
388	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
389	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
390	C₂²×D₄	B(4,𝔽₂)	1	4	yes	—
391	C₂²×D₄	C₂×#120	1	1	yes	characteristic
392	C₂²×D₄	C₂×#120	1	1	yes	characteristic
393	C₂²×D₄	#534	1	1	yes	characteristic
394	C₂²×D₄	#534	1	1	yes	characteristic
395	C₂³×C₄	C₂×#120	1	1	yes	characteristic
396	C₂³×C₄	C₂×#120	1	1	yes	characteristic
397	C₂³×C₄	C₂×#120	1	2	yes	—
398	C₂³×C₄	C₂×#120	1	1	yes	characteristic
399	C₂³×C₄	C₂×#120	1	1	yes	characteristic
400	C₂³×C₄	C₂×#120	1	2	yes	—
401	C₂³×C₄	C₂×#120	1	1	yes	characteristic
402	C₂³×C₄	#534	1	2	yes	—
403	C₂³×C₄	D₄²	1	2	yes	—
404	C₂³×C₄	D₄²	1	2	yes	—
405	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
406	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
407	C₂×C₄⋊C₄	D₄²	1	2	yes	—
408	C₂×C₄⋊C₄	D₄²	1	2	yes	—
409	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
410	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
411	C₂×C₂²⋊C₄	D₄²	1	2	yes	—
412	C₂×C₂²⋊C₄	D₄²	1	2	yes	—
413	C₂×C₂²⋊C₄	C₂³×D₄	1	2	yes	—
414	C₂×C₂²⋊C₄	C₂×H(5,𝔽₂)	1	2	yes	—
415	C₂×C₄²	D₄²	1	2	yes	—
416	C₂×C₄²	D₄²	1	2	yes	—
417	C₂⁴	#2403	1	1	yes	characteristic
418	C₂⁴	#2403	1	1	yes	characteristic
419	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
420	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
421	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
422	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
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	2	yes	—
431	C₂²×C₄	#2403	1	2	yes	—
432	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
433	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
434	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
435	C₂²×C₄	C₂×D₄²	1	2	yes	—
436	C₂²×C₄	C₂×D₄²	1	2	yes	—
437	C₂³	#23897	1	2	yes	—
438	C₂³	#33551	1	2	yes	—
439	C₂³	C₂×#2403	1	1	yes	characteristic
440	C₂³	#60388	1	2	yes	—
441	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
442	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
443	C₂×C₄	#23900	1	2	yes	—
444	C₂×C₄	#23900	1	2	yes	—
445	C₂²	#6437456	1	1	yes	characteristic
446	C₂²	C₂×#23897	1	1	yes	characteristic
447	C₂²	C₂×#23900	1	1	yes	characteristic
448	C₂²	C₂×#33551	1	1	yes	characteristic
449	C₂²	#7622875	1	1	yes	characteristic
450	C₂²	#7622880	1	1	yes	characteristic
451	C₂²	#7622880	1	1	yes	characteristic
452	C₂	#72233116	1	1	yes	characteristic
453	C₂	#72233299	1	1	yes	characteristic
454	C₂	#72234782	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×D₄² ◁ 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. #72234783	C₂	semidirect
2. #72234778	C₂	semidirect
3. #72234771	C₂	semidirect
4. #72234770	C₂	semidirect
5. #72234757	C₂	semidirect
6. #72234725	C₂	semidirect
7. #72234711	C₂	semidirect
8. #72234701	C₂	semidirect
9. #72234699	C₂	semidirect
10. #72233277	C₂	semidirect
11. #72233273	C₂	semidirect
12. #72233220	C₂	semidirect
13. #72233021	C₂	semidirect
14. #72232960	C₂	semidirect
15. #72232937	C₂	semidirect
16. #72232603	C₂	semidirect
17. #72231386	C₂	semidirect
18. #72213827	C₂	semidirect
19. #72209889	C₂	semidirect
20. #10586472	C₂²	semidirect
21. C₂×#57971	C₂²	semidirect
23. #6500011	C₂²	semidirect
24. #6500010	C₂²	semidirect
25. #6499870	C₂²	semidirect
26. #6499867	C₂²	semidirect
28. #6454047	C₂²	semidirect
29. #6385971	C₂²	semidirect
30. #6347264	C₂²	semidirect
31. #6346599	C₂²	semidirect
32. #4599081	C₂²	semidirect
33. #4466055	C₂²	semidirect
34. #4435227	C₂²	semidirect
36. #4378714	C₂²	semidirect
37. #2805719	C₂²	semidirect
38. #2032088	C₂²	semidirect
39. #1465620	C₂²	semidirect
40. #1460307	C₂²	semidirect
42. #648360	C₂²	semidirect
43. #634305	C₂²	semidirect
44. #534229	C₂²	semidirect
45. #485388	C₂²	semidirect
46. #485385	C₂²	semidirect
47. #485044	C₂²	semidirect
48. #485039	C₂²	semidirect
49. #482357	C₂²	semidirect
50. #481962	C₂²	semidirect
51. #480710	C₂²	semidirect
52. #480382	C₂²	semidirect
53. #346456	C₂²	semidirect
54. #346456	C₂²	semidirect
56. #346446	C₂²	semidirect
57. #346446	C₂²	semidirect
58. #346446	C₂²	semidirect
59. #346446	C₂²	semidirect
60. #346446	C₂²	semidirect
61. #188151	C₂²	semidirect
62. #188087	C₂²	semidirect
63. #185259	C₂²	semidirect
64. #185246	C₂²	semidirect
65. #142584	C₂²	semidirect
66. #142568	C₂²	semidirect
67. #142553	C₂²	semidirect
68. #142553	C₂²	semidirect
69. #142552	C₂²	semidirect
70. #142536	C₂²	semidirect
71. #142536	C₂²	semidirect
72. #142536	C₂²	semidirect
73. #139645	C₂²	semidirect
74. #139644	C₂²	semidirect
75. #139623	C₂²	semidirect
76. #139622	C₂²	semidirect
77. #139504	C₂²	semidirect
78. #139504	C₂²	semidirect
79. #139504	C₂²	semidirect
80. #139504	C₂²	semidirect
81. #139504	C₂²	semidirect
82. #139504	C₂²	semidirect
83. #139486	C₂²	semidirect
84. #139486	C₂²	semidirect
85. #134084	C₂²	semidirect
86. #134083	C₂²	semidirect
87. #134036	C₂²	semidirect
88. #134033	C₂²	semidirect
89. #127232	C₂²	semidirect
90. #127199	C₂²	semidirect
96. C₂³×#127	D₄	semidirect
99. C₂×#2760	C₂³	semidirect
100. C₂×#2670	C₂³	semidirect
101. C₂×#2815	C₂³	semidirect
105. C₂×#2433	D₄	semidirect
111. C₂×#2403	C₂³	semidirect
112. C₂×#2657	D₄	semidirect
113. C₂×#2631	D₄	semidirect
119. #29686	D₄	semidirect
120. #25949	D₄	semidirect
121. #25773	D₄	semidirect
135. #15635	C₂³	semidirect
136. #15622	C₂³	semidirect
137. #15467	C₂³	semidirect
138. #15420	C₂³	semidirect
139. #15420	C₂³	semidirect
140. #15310	D₄	semidirect
141. #15310	D₄	semidirect
142. #15310	D₄	semidirect
143. #15310	D₄	semidirect
144. #15267	C₂³	semidirect
145. #15267	C₂³	semidirect
146. #15267	C₂³	semidirect
147. #15259	D₄	semidirect
148. #15259	D₄	semidirect
151. #15258	D₄	semidirect
152. #15258	D₄	semidirect
159. #14698	D₄	semidirect
160. #14661	D₄	semidirect
161. #14507	C₂³	semidirect
162. #14365	C₂³	semidirect
163. #13959	D₄	semidirect
165. #13902	D₄	semidirect
166. #13807	C₂³	semidirect
167. C₂²⋊C₄²	C₂³	semidirect
169. #11808	C₂³	semidirect
170. #11796	C₂³	semidirect
171. #11796	C₂³	semidirect
172. #11796	C₂³	semidirect
173. #11517	C₂³	semidirect
174. #11500	C₂³	semidirect
175. #11499	C₂³	semidirect
176. #11499	C₂³	semidirect
185. #7213	C₂³	semidirect
186. #7213	C₂³	semidirect
187. #7213	C₂³	semidirect
188. #7213	C₂³	semidirect
196. C₂⁴×D₄	C₂×D₄	semidirect
197. #3501	C₂×D₄	semidirect
198. #3496	C₂×D₄	semidirect
200. #3459	C₂×D₄	semidirect
205. C₂²×#127	C₂×D₄	semidirect
206. C₂²×#127	C₂×D₄	semidirect
207. C₂²×#127	C₂×D₄	semidirect
209. C₂²×#124	C₂×D₄	semidirect
210. C₂²×#124	C₂×D₄	semidirect
235. C₂³×C₄²	C₂×D₄	semidirect
238. C₂×#394	C₂×D₄	semidirect
239. C₂×#394	C₂×D₄	semidirect
241. C₂×#393	C₂×D₄	semidirect
242. C₂×#393	C₂×D₄	semidirect
247. C₂×#392	C₂×D₄	semidirect
248. C₂×#392	C₂×D₄	semidirect
249. C₂×#392	C₂×D₄	semidirect
250. C₂×#392	C₂×D₄	semidirect
258. C₂×#383	C₂×D₄	semidirect
259. C₂×#383	C₂×D₄	semidirect
262. C₂×#380	C₂×D₄	semidirect
268. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
269. C₂×#376	C₂×D₄	semidirect
270. #2030	C₂×D₄	semidirect
271. #2029	C₂×D₄	semidirect
272. #2022	C₂×D₄	semidirect
273. #2021	C₂×D₄	semidirect
275. #1799	C₂×D₄	semidirect
276. C₄×#99	C₂×D₄	semidirect
283. #1438	C₂×D₄	semidirect
284. #1438	C₂×D₄	semidirect
285. #1438	C₂×D₄	semidirect
286. #1438	C₂×D₄	semidirect
291. #1437	C₂×D₄	semidirect
292. #1437	C₂×D₄	semidirect
293. #1437	C₂×D₄	semidirect
294. #1437	C₂×D₄	semidirect
295. #1437	C₂×D₄	semidirect
296. #1437	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
#72234783	2
#72234778	2
#72234771	2
#72234770	2
#72234757	2
#72234725	2
#72234711	2
#72234701	2
#72234699	2
#72233277	2
#72233273	2
#72233220	2
#72233021	2
#72232960	2
#72232937	2
#72232603	2
#72231386	2
#72213827	2
#72209889	2