Subgroups — #72282619

Order 2048.

At least 9772 conjugacy classes of subgroups; only the 838 normal subgroups are shown.

The subgroup lattice has 499 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72282602	C₂	1	1	yes	maximal, characteristic, complemented
2	#72282586	C₂	1	1	yes	maximal, characteristic, complemented
3	#72282575	C₂	1	1	yes	maximal, characteristic, complemented
4	#72282552	C₂	1	4	yes	maximal, complemented
5	#72282485	C₂	1	4	yes	maximal, complemented
6	#72282465	C₂	1	1	yes	maximal, characteristic, complemented
7	#72282461	C₂	1	1	yes	maximal, characteristic, complemented
8	#72282452	C₂	1	1	yes	maximal, characteristic, complemented
9	#72282441	C₂	1	1	yes	maximal, characteristic, complemented
10	#72282307	C₂	1	1	yes	maximal, characteristic, complemented
11	#72282289	C₂	1	1	yes	maximal, characteristic, complemented
12	#72282264	C₂	1	1	yes	maximal, characteristic, complemented
13	#72282253	C₂	1	1	yes	maximal, characteristic, complemented
14	#72281732	C₂	1	4	yes	maximal, complemented
15	#72281272	C₂	1	4	yes	maximal, complemented
16	C₂×#130740	C₂	1	1	yes	maximal, characteristic, complemented
17	#72278640	C₂	1	1	yes	maximal, characteristic, complemented
18	#72278550	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×D₄×B(4,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×D₄×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
21	#7708460	C₂²	1	1	yes	characteristic, complemented
22	C₂×D₄×#120	C₂²	1	1	yes	characteristic
23	#7523380	C₂²	1	2	yes	complemented
24	#7514000	C₂²	1	2	yes	complemented
25	#7200303	C₂²	1	2	yes	complemented
26	#7200004	C₂²	1	2	yes	complemented
27	#6634504	C₂²	1	1	yes	characteristic, complemented
28	#6632009	C₂²	1	1	yes	characteristic, complemented
29	#6629108	C₂²	1	1	yes	characteristic, complemented
30	#6628983	C₂²	1	1	yes	characteristic, complemented
31	C₂×#32926	C₂²	1	1	yes	characteristic
32	D₄×B(4,𝔽₂)	C₂²	1	4	yes	—
33	D₄×B(4,𝔽₂)	C₂²	1	4	yes	—
34	#6487535	C₂²	1	1	yes	characteristic
35	#6470077	C₂²	1	1	yes	characteristic
36	C₂×#25771	C₂²	1	1	yes	characteristic
37	C₂×#24260	C₂²	1	1	yes	characteristic
38	#6408084	C₂²	1	1	yes	characteristic, complemented
39	C₂×D₄×#99	C₂²	1	1	yes	characteristic
40	C₂×C₄×B(4,𝔽₂)	C₂²	1	1	yes	characteristic
41	#6347464	C₂²	1	1	yes	characteristic, complemented
42	#6347432	C₂²	1	1	yes	characteristic, complemented
43	#500484	C₂²	1	2	yes	complemented
44	#500483	C₂²	1	2	yes	complemented
45	#500476	C₂²	1	2	yes	complemented
46	#500475	C₂²	1	2	yes	complemented
47	#495417	C₂²	1	1	yes	characteristic, complemented
48	#495161	C₂²	1	1	yes	characteristic, complemented
49	C₂×#12793	C₂²	1	1	yes	characteristic, complemented
50	#486498	C₂²	1	2	yes	complemented
51	#486497	C₂²	1	2	yes	complemented
52	#486492	C₂²	1	2	yes	complemented
53	#486491	C₂²	1	2	yes	complemented
54	#482118	C₂²	1	1	yes	characteristic, complemented
55	C₂×#11880	C₂²	1	1	yes	characteristic, complemented
56	#482049	C₂²	1	1	yes	characteristic, complemented
57	C₂×#11873	C₂²	1	1	yes	characteristic, complemented
58	C₂×#11471	C₂²	1	1	yes	characteristic, complemented
59	#347298	C₂²	1	4	yes	complemented
60	#347250	C₂²	1	4	yes	complemented
61	#346534	C₂²	1	4	yes	complemented
62	#346518	C₂²	1	4	yes	complemented
63	C₂×#8383	C₂²	1	1	yes	characteristic
64	C₂×#8375	C₂²	1	1	yes	characteristic
65	#185384	C₂²	1	1	yes	characteristic, complemented
66	#185331	C₂²	1	1	yes	characteristic, complemented
67	#184930	C₂²	1	1	yes	characteristic, complemented
68	#184905	C₂²	1	1	yes	characteristic, complemented
69	#144274	C₂²	1	4	yes	complemented
70	#144272	C₂²	1	4	yes	complemented
71	#144205	C₂²	1	4	yes	complemented
72	#144204	C₂²	1	4	yes	complemented
73	#142738	C₂²	1	4	yes	complemented
74	#142736	C₂²	1	4	yes	complemented
75	#142602	C₂²	1	4	yes	complemented
76	#142600	C₂²	1	4	yes	complemented
77	#139612	C₂²	1	4	yes	complemented
78	#139610	C₂²	1	4	yes	complemented
79	#138962	C₂²	1	4	yes	complemented
80	#138960	C₂²	1	4	yes	complemented
81	#138894	C₂²	1	4	yes	complemented
82	#138892	C₂²	1	4	yes	complemented
83	#136847	C₂²	1	4	yes	complemented
84	#136845	C₂²	1	4	yes	complemented
85	#130740	C₂²	1	4	yes	complemented
86	#130740	C₂²	1	4	yes	complemented
87	#127353	C₂²	1	1	yes	characteristic, complemented
88	#127335	C₂²	1	1	yes	characteristic, complemented
89	#127075	C₂²	1	1	yes	characteristic, complemented
90	#127071	C₂²	1	1	yes	characteristic, complemented
91	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
92	D₄×H(5,𝔽₂)	C₂³	1	4	yes	—
93	C₂×#3496	C₂³	1	1	yes	characteristic
94	C₂²×D₄²	C₂³	1	1	yes	characteristic
95	C₂×C₄×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
96	C₂×#3208	D₄	1	1	yes	characteristic, complemented
97	C₂×#3186	D₄	1	1	yes	characteristic, complemented
98	C₂×#3101	D₄	1	1	yes	characteristic, complemented
99	C₂²×B(4,𝔽₂)	D₄	1	1	yes	characteristic
100	C₂²×#447	D₄	1	1	yes	characteristic, complemented
101	#59201	C₂³	1	1	yes	characteristic, complemented
102	#59000	C₂³	1	1	yes	characteristic, complemented
103	#45645	C₂³	1	1	yes	characteristic, complemented
104	#45622	C₂³	1	1	yes	characteristic, complemented
105	C₂×#2847	D₄	1	1	yes	characteristic, complemented
106	D₄×#120	D₄	1	2	yes	complemented
107	D₄×#120	D₄	1	2	yes	complemented
108	D₄×#120	C₂³	1	2	yes	—
109	D₄×#120	C₂³	1	2	yes	—
110	#35172	C₂³	1	1	yes	characteristic
111	#35000	C₂³	1	1	yes	characteristic
112	C₂×#2433	D₄	1	1	yes	characteristic, complemented
113	C₂×#2408	C₂³	1	1	yes	characteristic
114	C₂×D₄×C₂²⋊C₄	D₄	1	1	yes	characteristic, complemented
115	C₂×C₄×#120	C₂³	1	1	yes	characteristic
116	#32971	C₂³	1	2	yes	complemented
117	#32969	C₂³	1	2	yes	complemented
118	#32927	C₂³	1	2	yes	complemented
119	#32926	C₂³	1	4	yes	—
120	#32926	C₂³	1	2	yes	complemented
121	#31666	C₂³	1	2	yes	complemented
122	#31261	C₂³	1	2	yes	complemented
123	#31056	C₂³	1	2	yes	complemented
124	#30500	C₂³	1	2	yes	complemented
125	#25881	D₄	1	2	yes	complemented
126	#25881	C₂³	1	2	yes	—
127	#25771	C₂³	1	4	yes	—
128	#25753	D₄	1	2	yes	complemented
129	#25753	C₂³	1	2	yes	—
130	#24260	D₄	1	2	yes	complemented
131	#24260	D₄	1	2	yes	complemented
132	#24260	C₂³	1	2	yes	—
133	#24260	C₂³	1	2	yes	—
134	#24032	D₄	1	2	yes	complemented
135	#24032	C₂³	1	2	yes	—
136	#23848	D₄	1	2	yes	complemented
137	#23848	C₂³	1	2	yes	—
138	C₂×#2044	D₄	1	2	yes	complemented
139	C₂×#2021	D₄	1	2	yes	complemented
140	#23307	C₂³	1	2	yes	complemented
141	#22850	C₂³	1	2	yes	complemented
142	D₄×#99	C₂³	1	4	yes	—
143	#21803	D₄	1	1	yes	characteristic, complemented
144	#21786	C₂³	1	1	yes	characteristic
145	#21758	D₄	1	1	yes	characteristic, complemented
146	#21738	C₂³	1	1	yes	characteristic
147	C₄×B(4,𝔽₂)	D₄	1	2	yes	—
148	C₄×B(4,𝔽₂)	D₄	1	2	yes	—
149	C₄×B(4,𝔽₂)	C₂³	1	2	yes	—
150	C₄×B(4,𝔽₂)	C₂³	1	2	yes	—
151	C₂×#1889	D₄	1	1	yes	characteristic
152	C₂×#1867	D₄	1	1	yes	characteristic
153	#20732	D₄	1	1	yes	characteristic, complemented
154	C₂×#1800	C₂³	1	1	yes	characteristic
155	C₂×#1799	C₂³	1	1	yes	characteristic
156	C₂×#1799	C₂³	1	1	yes	characteristic
157	C₂×#1790	D₄	1	1	yes	characteristic
158	C₂×#1786	D₄	1	1	yes	characteristic, complemented
159	C₂×C₄×#99	C₂³	1	1	yes	characteristic
160	#18395	C₂³	1	2	yes	complemented
161	#18388	C₂³	1	2	yes	complemented
162	#18202	C₂³	1	2	yes	complemented
163	#18194	C₂³	1	2	yes	complemented
164	C₂×#1460	C₂³	1	1	yes	characteristic
165	C₂×#1459	C₂³	1	1	yes	characteristic
166	#13299	C₂³	1	2	yes	complemented
167	#13298	C₂³	1	2	yes	complemented
168	#13221	C₂³	1	2	yes	complemented
169	#13220	C₂³	1	2	yes	complemented
170	#12793	C₂³	1	2	yes	complemented
171	#12793	C₂³	1	2	yes	complemented
172	#11901	C₂³	1	2	yes	complemented
173	#11900	C₂³	1	2	yes	complemented
174	#11880	C₂³	1	4	yes	complemented
175	#11874	C₂³	1	2	yes	complemented
176	#11873	C₂³	1	2	yes	complemented
177	#11873	C₂³	1	4	yes	complemented
178	#11471	C₂³	1	2	yes	complemented
179	#11471	C₂³	1	2	yes	complemented
180	#8383	C₂³	1	4	yes	—
181	#8375	C₂³	1	4	yes	—
182	#8353	C₂³	1	4	yes	complemented
183	#8350	C₂³	1	4	yes	complemented
184	#8318	C₂³	1	4	yes	complemented
185	#8316	C₂³	1	4	yes	complemented
186	#7237	C₂³	1	4	yes	complemented
187	#7236	C₂³	1	4	yes	complemented
188	#7205	C₂³	1	4	yes	complemented
189	#7204	C₂³	1	4	yes	complemented
190	C₂²×H(5,𝔽₂)	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	2	yes	—
195	C₂⁴×D₄	C₂×D₄	1	2	yes	—
196	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
197	C₂³×D₈	C₂×D₄	1	2	yes	complemented
198	#3496	C₂×D₄	1	2	yes	—
199	#3496	C₂⁴	1	2	yes	—
200	C₂×D₄²	C₂×D₄	1	2	yes	—
201	C₂×D₄²	C₂×D₄	1	2	yes	—
202	C₂×D₄²	C₂×D₄	1	2	yes	—
203	C₂×D₄²	C₂⁴	1	2	yes	—
204	C₂×#534	C₂×D₄	1	2	yes	—
205	C₂×#533	C₂×D₄	1	1	yes	characteristic, complemented
206	C₂²×#127	C₂×D₄	1	1	yes	characteristic
207	C₂²×#121	C₂×D₄	1	1	yes	characteristic
208	C₂²×#121	C₂×D₄	1	1	yes	characteristic
209	C₂²×#121	C₂×D₄	1	1	yes	characteristic, complemented
210	C₂²×#120	C₂×D₄	1	1	yes	characteristic
211	C₄×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
212	C₄×H(5,𝔽₂)	C₂⁴	1	2	yes	—
213	C₂×#518	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
216	C₂×#492	C₂×D₄	1	2	yes	complemented
217	C₂×#486	C₂×D₄	1	2	yes	complemented
218	C₂×#480	C₂×D₄	1	2	yes	complemented
219	C₂×#476	C₂×D₄	1	2	yes	complemented
220	C₂×#461	C₂×D₄	1	2	yes	complemented
221	C₂×B(4,𝔽₂)	C₂×D₄	1	2	yes	—
222	C₂×B(4,𝔽₂)	C₂×D₄	1	2	yes	—
223	C₂×#447	C₂×D₄	1	2	yes	complemented
224	C₂×#431	C₂×D₄	1	1	yes	characteristic, complemented
225	C₂×#431	C₂×D₄	1	1	yes	characteristic, complemented
226	C₂²×#102	C₂×D₄	1	2	yes	complemented
227	C₂²×#99	C₂×D₄	1	1	yes	characteristic
228	C₂²×#99	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic, complemented
230	C₂²×C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic, complemented
231	#2847	C₂×D₄	1	2	yes	—
232	#2847	C₂×D₄	1	2	yes	—
233	#2563	C₂×D₄	1	1	yes	characteristic, complemented
234	#2563	C₂⁴	1	1	yes	characteristic
235	#2542	C₂×D₄	1	1	yes	characteristic, complemented
236	#2542	C₂⁴	1	1	yes	characteristic
237	#2486	C₂×D₄	1	1	yes	characteristic, complemented
238	#2486	C₂⁴	1	1	yes	characteristic
239	#2433	C₂×D₄	1	2	yes	—
240	#2433	C₂×D₄	1	2	yes	—
241	#2408	C₂×D₄	1	2	yes	—
242	#2408	C₂×D₄	1	1	yes	characteristic, complemented
243	#2408	C₂⁴	1	2	yes	—
244	#2408	C₂⁴	1	1	yes	characteristic
245	D₄×C₂²⋊C₄	C₂×D₄	1	2	yes	—
246	D₄×C₂²⋊C₄	C₂×D₄	1	2	yes	—
247	C₄×#120	C₂×D₄	1	1	yes	characteristic
248	C₄×#120	C₂×D₄	1	1	yes	characteristic
249	C₄×#120	C₂×D₄	1	1	yes	characteristic
250	C₄×#120	C₂×D₄	1	1	yes	characteristic
251	C₄×#120	C₂×D₄	1	1	yes	characteristic
252	C₄×#120	C₂×D₄	1	1	yes	characteristic
253	C₄×#120	C₂⁴	1	1	yes	characteristic
254	C₄×#120	C₂⁴	1	1	yes	characteristic
255	C₂×#386	C₂×D₄	1	1	yes	characteristic
256	C₂×#385	C₂×D₄	1	1	yes	characteristic
257	#2285	C₂×D₄	1	1	yes	characteristic, complemented
258	C₂×#380	C₂×D₄	1	1	yes	characteristic
259	C₂×#380	C₂×D₄	1	1	yes	characteristic, complemented
260	C₂×#379	C₂×D₄	1	1	yes	characteristic
261	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
262	#2044	C₂×D₄	1	4	yes	—
263	#2044	C₂×D₄	1	4	yes	—
264	#2021	C₂×D₄	1	4	yes	—
265	#2021	C₂×D₄	1	4	yes	—
266	#1982	C₂×D₄	1	2	yes	complemented
267	#1982	C₂×D₄	1	2	yes	complemented
268	#1954	C₂×D₄	1	2	yes	complemented
269	#1954	C₂⁴	1	2	yes	—
270	#1893	C₂×D₄	1	2	yes	complemented
271	#1893	C₂×D₄	1	2	yes	complemented
272	#1889	C₂×D₄	1	2	yes	—
273	#1889	C₂×D₄	1	2	yes	—
274	#1869	C₂×D₄	1	2	yes	complemented
275	#1869	C₂⁴	1	2	yes	—
276	#1867	C₂×D₄	1	2	yes	—
277	#1867	C₂×D₄	1	2	yes	—
278	#1800	C₂⁴	1	2	yes	—
279	#1799	C₂×D₄	1	2	yes	—
280	#1799	C₂⁴	1	2	yes	—
281	#1799	C₂⁴	1	2	yes	—
282	#1790	C₂×D₄	1	2	yes	—
283	#1790	C₂×D₄	1	2	yes	—
284	#1786	C₂×D₄	1	2	yes	complemented
285	#1786	C₂×D₄	1	2	yes	complemented
286	C₄×#102	C₂×D₄	1	2	yes	complemented
287	C₄×#102	C₂×D₄	1	2	yes	complemented
288	C₄×#99	C₂×D₄	1	2	yes	—
289	C₄×#99	C₂⁴	1	2	yes	—
290	C₂×#342	C₂×D₄	1	2	yes	—
291	#1460	C₂⁴	1	2	yes	—
292	#1459	C₂⁴	1	2	yes	—
293	C₂⁶	#120	1	1	yes	characteristic
294	C₂×H(5,𝔽₂)	AGL(1,ℤ/8)	1	4	yes	complemented
295	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
296	C₂³×D₄	#120	1	2	yes	—
297	C₂³×D₄	#120	1	2	yes	—
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	C₂²×D₄	1	1	yes	characteristic
302	C₂³×D₄	C₂²×D₄	1	2	yes	—
303	C₂³×D₄	C₂²×D₄	1	2	yes	—
304	C₂³×D₄	C₂²×D₄	1	2	yes	—
305	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic, complemented
306	C₂⁴×C₄	#120	1	1	yes	characteristic
307	C₂⁴×C₄	#120	1	1	yes	characteristic
308	C₂⁴×C₄	#120	1	1	yes	characteristic
309	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
310	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
311	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
312	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
313	C₂³×C₈	C₂²×D₄	1	2	yes	complemented
314	#534	C₂²×D₄	1	4	yes	—
315	C₂×C₄⋊Q₈	C₂²×D₄	1	1	yes	characteristic, complemented
316	C₂×C₄⋊Q₈	C₂²×D₄	1	1	yes	characteristic, complemented
317	C₂×#127	#120	1	2	yes	—
318	C₂×#127	C₂²×D₄	1	2	yes	—
319	C₂×#121	#120	1	2	yes	—
320	C₂×#121	#120	1	2	yes	—
321	C₂×#121	C₂²×D₄	1	2	yes	—
322	C₂×#121	C₂²×D₄	1	2	yes	—
323	C₂×#120	#120	1	1	yes	characteristic
324	C₂×#120	#120	1	1	yes	characteristic
325	C₂×#120	C₂²×D₄	1	1	yes	characteristic
326	C₂×#120	C₂²×D₄	1	1	yes	characteristic
327	#518	C₂²×D₄	1	2	yes	—
328	C₂×C₄×D₄	#120	1	2	yes	—
329	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
334	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×D₄	H(5,𝔽₂)	1	1	yes	characteristic
336	C₂×C₄×D₄	H(5,𝔽₂)	1	1	yes	characteristic
337	C₂×C₄×D₄	C₂⁵	1	1	yes	characteristic
338	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
339	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic, complemented
340	C₂²×C₄⋊C₄	H(5,𝔽₂)	1	1	yes	characteristic
341	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
342	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
343	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
344	C₂²×C₂²⋊C₄	H(5,𝔽₂)	1	1	yes	characteristic
345	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄⋊C₈	C₂²×D₄	1	2	yes	complemented
347	C₂×#99	AGL(1,ℤ/8)	1	4	yes	complemented
348	C₂×#99	C₂²×D₄	1	2	yes	—
349	C₂×#99	C₂²×D₄	1	2	yes	—
350	C₂×C₂²⋊C₈	C₂²×D₄	1	2	yes	complemented
351	C₂×C₄×C₈	C₂²×D₄	1	2	yes	complemented
352	#386	#120	1	1	yes	characteristic
353	#386	#120	1	1	yes	characteristic
354	#386	C₂²×D₄	1	1	yes	characteristic
355	#386	C₂²×D₄	1	1	yes	characteristic
356	#385	#120	1	1	yes	characteristic
357	#385	#120	1	1	yes	characteristic
358	#385	C₂²×D₄	1	1	yes	characteristic
359	#385	C₂²×D₄	1	1	yes	characteristic
360	#380	C₂²×D₄	1	2	yes	—
361	#380	C₂²×D₄	1	1	yes	characteristic, complemented
362	#380	C₂²×D₄	1	1	yes	characteristic, complemented
363	#379	#120	1	1	yes	characteristic
364	#379	#120	1	1	yes	characteristic
365	#379	C₂²×D₄	1	1	yes	characteristic
366	#379	C₂²×D₄	1	1	yes	characteristic
367	C₄×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic, complemented
368	C₄×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic, complemented
369	C₄×C₂²⋊C₄	#120	1	1	yes	characteristic
370	C₄×C₂²⋊C₄	#120	1	1	yes	characteristic
371	C₄×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
372	C₄×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
373	#342	C₂²×D₄	1	4	yes	—
374	C₂⁵	C₂×#120	1	1	yes	characteristic
375	C₂⁵	C₂×#120	1	1	yes	characteristic
376	C₂⁵	C₂×#120	1	1	yes	characteristic
377	C₂⁵	D₄²	1	1	yes	characteristic
378	H(5,𝔽₂)	C₂×AGL(1,ℤ/8)	1	4	yes	—
379	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
380	C₂²×D₄	B(4,𝔽₂)	1	2	yes	—
381	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
382	C₂²×D₄	B(4,𝔽₂)	1	2	yes	—
383	C₂²×D₄	B(4,𝔽₂)	1	2	yes	—
384	C₂²×D₄	C₂×#120	1	1	yes	characteristic
385	C₂²×D₄	C₂×#120	1	2	yes	—
386	C₂²×D₄	C₂×#120	1	2	yes	—
387	C₂²×D₄	C₂×#120	1	2	yes	—
388	C₂²×D₄	D₄²	1	1	yes	characteristic
389	C₂²×D₄	D₄²	1	1	yes	characteristic
390	C₂²×D₄	C₂×AGL(1,ℤ/8)	1	2	yes	—
391	C₂²×D₄	C₂×AGL(1,ℤ/8)	1	2	yes	—
392	C₂²×D₄	#576	1	2	yes	—
393	C₂²×D₄	#577	1	2	yes	—
394	C₂²×D₄	C₂³×D₄	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	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	#534	1	1	yes	characteristic
402	C₂³×C₄	#534	1	1	yes	characteristic
403	C₂³×C₄	D₄²	1	1	yes	characteristic
404	C₂³×C₄	D₄²	1	1	yes	characteristic
405	C₂³×C₄	D₄²	1	1	yes	characteristic
406	C₂³×C₄	D₄²	1	1	yes	characteristic
407	C₂³×C₄	D₄²	1	1	yes	characteristic
408	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
409	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
411	C₂×C₄⋊C₄	#534	1	1	yes	characteristic
412	C₂×C₄⋊C₄	D₄²	1	1	yes	characteristic
413	C₂×C₄⋊C₄	D₄²	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
415	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
416	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
417	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
418	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
419	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
420	C₂×C₂²⋊C₄	#534	1	1	yes	characteristic
421	C₂×C₂²⋊C₄	D₄²	1	1	yes	characteristic
422	C₂×C₂²⋊C₄	D₄²	1	1	yes	characteristic
423	C₂×C₂²⋊C₄	D₄²	1	1	yes	characteristic
424	C₂×C₂²⋊C₄	D₄²	1	1	yes	characteristic
425	C₂×C₂²⋊C₄	C₂³×D₄	1	1	yes	characteristic
426	C₂×C₂²⋊C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
427	C₂×C₄²	C₂×#120	1	1	yes	characteristic
428	C₂×C₄²	D₄²	1	1	yes	characteristic
429	C₂×C₄²	D₄²	1	1	yes	characteristic
430	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
431	#99	C₂×AGL(1,ℤ/8)	1	4	yes	—
432	C₂⁴	#2403	1	1	yes	characteristic
433	C₂⁴	#2403	1	1	yes	characteristic
434	C₂⁴	#2403	1	1	yes	characteristic
435	C₂⁴	#3003	1	2	yes	—
436	C₂⁴	#3012	1	2	yes	—
437	C₂⁴	#3264	1	2	yes	—
438	C₂⁴	#3272	1	2	yes	—
439	C₂⁴	C₂²×#120	1	1	yes	characteristic
440	C₂⁴	C₂×D₄²	1	1	yes	characteristic
441	C₂×D₄	#3003	1	2	yes	—
442	C₂×D₄	#3012	1	2	yes	—
443	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
444	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
445	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
446	C₂×D₄	#3264	1	2	yes	—
447	C₂×D₄	#3265	1	2	yes	—
448	C₂×D₄	#3272	1	2	yes	—
449	C₂×D₄	#3274	1	2	yes	—
450	C₂×D₄	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
451	C₂×D₄	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
452	C₂×D₄	C₂×#576	1	1	yes	characteristic
453	C₂×D₄	C₂×#577	1	1	yes	characteristic
454	C₂²×C₄	#2403	1	1	yes	characteristic
455	C₂²×C₄	#2403	1	1	yes	characteristic
456	C₂²×C₄	#2403	1	1	yes	characteristic
457	C₂²×C₄	#2403	1	1	yes	characteristic
458	C₂²×C₄	#2403	1	1	yes	characteristic
459	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
460	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
461	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
462	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
463	C₂²×C₄	#3265	1	2	yes	—
464	C₂²×C₄	#3274	1	2	yes	—
465	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
466	C₂²×C₄	C₂×#534	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
468	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
470	C₂³	#23860	1	2	yes	—
471	C₂³	#23860	1	2	yes	—
472	C₂³	#23860	1	2	yes	—
473	C₂³	#23882	1	2	yes	—
474	C₂³	#23900	1	1	yes	characteristic
475	C₂³	#23900	1	1	yes	characteristic
476	C₂³	C₂×#2403	1	1	yes	characteristic
477	C₂³	C₂×#3003	1	1	yes	characteristic
478	C₂³	C₂×#3012	1	1	yes	characteristic
479	C₂³	C₂×#3264	1	1	yes	characteristic
480	C₂³	C₂×#3272	1	1	yes	characteristic
481	D₄	#33551	1	4	yes	—
482	C₂×C₄	#23860	1	2	yes	—
483	C₂×C₄	#23900	1	1	yes	characteristic
484	C₂×C₄	#23900	1	1	yes	characteristic
485	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
486	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
487	C₂×C₄	C₂×#3265	1	1	yes	characteristic
488	C₂×C₄	C₂×#3274	1	1	yes	characteristic
489	C₂²	#248551	1	2	yes	—
490	C₂²	#248551	1	2	yes	—
491	C₂²	C₂×#23860	1	1	yes	characteristic
492	C₂²	C₂×#23882	1	1	yes	characteristic
493	C₂²	C₂×#23900	1	1	yes	characteristic
494	C₄	C₂×#33551	1	2	yes	—
495	C₂	#72218077	1	1	yes	characteristic
496	C₂	#72231746	1	1	yes	characteristic
497	C₂	C₂×#248551	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#23900
commutator, Frattini, cosocle	C₂×C₄×D₄	C₂⁵
LCS	G ▷ C₂×C₄×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂²×D₄² ◁ G
LECS	G ▷ C₂×C₄×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72282602	C₂	semidirect
2. #72282586	C₂	semidirect
3. #72282575	C₂	semidirect
4. #72282552	C₂	semidirect
5. #72282485	C₂	semidirect
6. #72282465	C₂	semidirect
7. #72282461	C₂	semidirect
8. #72282452	C₂	semidirect
9. #72282441	C₂	semidirect
10. #72282307	C₂	semidirect
11. #72282289	C₂	semidirect
12. #72282264	C₂	semidirect
13. #72282253	C₂	semidirect
14. #72281732	C₂	semidirect
15. #72281272	C₂	semidirect
16. C₂×#130740	C₂	semidirect
17. #72278640	C₂	semidirect
18. #72278550	C₂	semidirect
19. C₂×D₄×B(4,𝔽₂)	C₂	semidirect
21. #7708460	C₂²	semidirect
23. #7523380	C₂²	semidirect
24. #7514000	C₂²	semidirect
25. #7200303	C₂²	semidirect
26. #7200004	C₂²	semidirect
27. #6634504	C₂²	semidirect
28. #6632009	C₂²	semidirect
29. #6629108	C₂²	semidirect
30. #6628983	C₂²	semidirect
38. #6408084	C₂²	semidirect
41. #6347464	C₂²	semidirect
42. #6347432	C₂²	semidirect
43. #500484	C₂²	semidirect
44. #500483	C₂²	semidirect
45. #500476	C₂²	semidirect
46. #500475	C₂²	semidirect
47. #495417	C₂²	semidirect
48. #495161	C₂²	semidirect
49. C₂×#12793	C₂²	semidirect
50. #486498	C₂²	semidirect
51. #486497	C₂²	semidirect
52. #486492	C₂²	semidirect
53. #486491	C₂²	semidirect
54. #482118	C₂²	semidirect
55. C₂×#11880	C₂²	semidirect
56. #482049	C₂²	semidirect
57. C₂×#11873	C₂²	semidirect
58. C₂×#11471	C₂²	semidirect
59. #347298	C₂²	semidirect
60. #347250	C₂²	semidirect
61. #346534	C₂²	semidirect
62. #346518	C₂²	semidirect
65. #185384	C₂²	semidirect
66. #185331	C₂²	semidirect
67. #184930	C₂²	semidirect
68. #184905	C₂²	semidirect
69. #144274	C₂²	semidirect
70. #144272	C₂²	semidirect
71. #144205	C₂²	semidirect
72. #144204	C₂²	semidirect
73. #142738	C₂²	semidirect
74. #142736	C₂²	semidirect
75. #142602	C₂²	semidirect
76. #142600	C₂²	semidirect
77. #139612	C₂²	semidirect
78. #139610	C₂²	semidirect
79. #138962	C₂²	semidirect
80. #138960	C₂²	semidirect
81. #138894	C₂²	semidirect
82. #138892	C₂²	semidirect
83. #136847	C₂²	semidirect
84. #136845	C₂²	semidirect
85. #130740	C₂²	semidirect
86. #130740	C₂²	semidirect
87. #127353	C₂²	semidirect
88. #127335	C₂²	semidirect
89. #127075	C₂²	semidirect
90. #127071	C₂²	semidirect
91. C₂⁵×D₄	D₄	semidirect
96. C₂×#3208	D₄	semidirect
97. C₂×#3186	D₄	semidirect
98. C₂×#3101	D₄	semidirect
100. C₂²×#447	D₄	semidirect
101. #59201	C₂³	semidirect
102. #59000	C₂³	semidirect
103. #45645	C₂³	semidirect
104. #45622	C₂³	semidirect
105. C₂×#2847	D₄	semidirect
106. D₄×#120	D₄	semidirect
107. D₄×#120	D₄	semidirect
112. C₂×#2433	D₄	semidirect
114. C₂×D₄×C₂²⋊C₄	D₄	semidirect
116. #32971	C₂³	semidirect
117. #32969	C₂³	semidirect
118. #32927	C₂³	semidirect
120. #32926	C₂³	semidirect
121. #31666	C₂³	semidirect
122. #31261	C₂³	semidirect
123. #31056	C₂³	semidirect
124. #30500	C₂³	semidirect
125. #25881	D₄	semidirect
128. #25753	D₄	semidirect
130. #24260	D₄	semidirect
131. #24260	D₄	semidirect
134. #24032	D₄	semidirect
136. #23848	D₄	semidirect
138. C₂×#2044	D₄	semidirect
139. C₂×#2021	D₄	semidirect
140. #23307	C₂³	semidirect
141. #22850	C₂³	semidirect
143. #21803	D₄	semidirect
145. #21758	D₄	semidirect
153. #20732	D₄	semidirect
158. C₂×#1786	D₄	semidirect
160. #18395	C₂³	semidirect
161. #18388	C₂³	semidirect
162. #18202	C₂³	semidirect
163. #18194	C₂³	semidirect
166. #13299	C₂³	semidirect
167. #13298	C₂³	semidirect
168. #13221	C₂³	semidirect
169. #13220	C₂³	semidirect
170. #12793	C₂³	semidirect
171. #12793	C₂³	semidirect
172. #11901	C₂³	semidirect
173. #11900	C₂³	semidirect
174. #11880	C₂³	semidirect
175. #11874	C₂³	semidirect
176. #11873	C₂³	semidirect
177. #11873	C₂³	semidirect
178. #11471	C₂³	semidirect
179. #11471	C₂³	semidirect
182. #8353	C₂³	semidirect
183. #8350	C₂³	semidirect
184. #8318	C₂³	semidirect
185. #8316	C₂³	semidirect
186. #7237	C₂³	semidirect
187. #7236	C₂³	semidirect
188. #7205	C₂³	semidirect
189. #7204	C₂³	semidirect
197. C₂³×D₈	C₂×D₄	semidirect
205. C₂×#533	C₂×D₄	semidirect
209. C₂²×#121	C₂×D₄	semidirect
216. C₂×#492	C₂×D₄	semidirect
217. C₂×#486	C₂×D₄	semidirect
218. C₂×#480	C₂×D₄	semidirect
219. C₂×#476	C₂×D₄	semidirect
220. C₂×#461	C₂×D₄	semidirect
223. C₂×#447	C₂×D₄	semidirect
224. C₂×#431	C₂×D₄	semidirect
225. C₂×#431	C₂×D₄	semidirect
226. C₂²×#102	C₂×D₄	semidirect
229. C₂²×C₂²⋊C₈	C₂×D₄	semidirect
230. C₂²×C₂²⋊C₈	C₂×D₄	semidirect
233. #2563	C₂×D₄	semidirect
235. #2542	C₂×D₄	semidirect
237. #2486	C₂×D₄	semidirect
242. #2408	C₂×D₄	semidirect
257. #2285	C₂×D₄	semidirect
259. C₂×#380	C₂×D₄	semidirect
266. #1982	C₂×D₄	semidirect
267. #1982	C₂×D₄	semidirect
268. #1954	C₂×D₄	semidirect
270. #1893	C₂×D₄	semidirect
271. #1893	C₂×D₄	semidirect
274. #1869	C₂×D₄	semidirect
284. #1786	C₂×D₄	semidirect
285. #1786	C₂×D₄	semidirect
286. C₄×#102	C₂×D₄	semidirect
287. C₄×#102	C₂×D₄	semidirect
294. C₂×H(5,𝔽₂)	AGL(1,ℤ/8)	semidirect
305. C₂³×D₄	C₂²×D₄	semidirect
313. C₂³×C₈	C₂²×D₄	semidirect
315. C₂×C₄⋊Q₈	C₂²×D₄	semidirect
316. C₂×C₄⋊Q₈	C₂²×D₄	semidirect
339. C₂²×C₄⋊C₄	C₂²×D₄	semidirect
346. C₂×C₄⋊C₈	C₂²×D₄	semidirect
347. C₂×#99	AGL(1,ℤ/8)	semidirect
350. C₂×C₂²⋊C₈	C₂²×D₄	semidirect
351. C₂×C₄×C₈	C₂²×D₄	semidirect
361. #380	C₂²×D₄	semidirect
362. #380	C₂²×D₄	semidirect
367. C₄×C₄⋊C₄	C₂²×D₄	semidirect
368. C₄×C₄⋊C₄	C₂²×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72282602	2
#72282586	2
#72282575	2
#72282552	2
#72282485	2
#72282465	2
#72282461	2
#72282452	2
#72282441	2
#72282307	2
#72282289	2
#72282264	2
#72282253	2
#72281732	2
#72281272	2
C₂×#130740	2
#72278640	2
#72278550	2
C₂×D₄×B(4,𝔽₂)	2