Subgroups — #72256554

Order 2048.

At least 7077 conjugacy classes of subgroups; only the 1912 normal subgroups are shown.

The subgroup lattice has 597 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72256546	C₂	1	1	yes	maximal, characteristic, complemented
2	#72256523	C₂	1	1	yes	maximal, characteristic, complemented
3	#72256513	C₂	1	1	yes	maximal, characteristic, complemented
4	#72256492	C₂	1	4	yes	maximal, complemented
5	#72256490	C₂	1	1	yes	maximal, characteristic, complemented
6	#72256465	C₂	1	1	yes	maximal, characteristic, complemented
7	#72256429	C₂	1	1	yes	maximal, characteristic, complemented
8	#72256273	C₂	1	1	yes	maximal, characteristic, complemented
9	#72255679	C₂	1	1	yes	maximal, characteristic, complemented
10	#72255601	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#395781	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#454694	C₂	1	4	yes	maximal, complemented
13	#72240119	C₂	1	1	yes	maximal, characteristic, complemented
14	#72237236	C₂	1	1	yes	maximal, characteristic, complemented
15	#72237191	C₂	1	4	yes	maximal, complemented
16	#72236779	C₂	1	4	yes	maximal, complemented
17	C₂×#392113	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×#3003	C₂	1	1	yes	maximal, characteristic
19	#72231771	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁶×D₄	C₂²	1	1	yes	characteristic
21	C₂⁴×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
22	C₂⁴×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
23	C₂³×#525	C₂²	1	1	yes	characteristic
24	C₂²×#3003	C₂²	1	4	yes	—
25	C₂²×#3003	C₂²	1	4	yes	—
26	C₂³×#407	C₂²	1	1	yes	characteristic
27	C₂³×#418	C₂²	1	1	yes	characteristic
28	C₂³×#418	C₂²	1	1	yes	characteristic
29	C₂²×#2081	C₂²	1	2	yes	complemented
30	C₂×#23531	C₂²	1	4	yes	complemented
31	C₂×#23521	C₂²	1	2	yes	complemented
32	C₂×#23521	C₂²	1	2	yes	complemented
33	C₂×#20851	C₂²	1	1	yes	characteristic, complemented
34	#6371257	C₂²	1	1	yes	characteristic, complemented
35	C₂×#20605	C₂²	1	1	yes	characteristic, complemented
36	#6370715	C₂²	1	1	yes	characteristic, complemented
37	C₂×#20598	C₂²	1	1	yes	characteristic
38	C₂×#20598	C₂²	1	1	yes	characteristic
39	C₂×#20598	C₂²	1	1	yes	characteristic
40	C₂×#20598	C₂²	1	1	yes	characteristic
41	C₂×#20598	C₂²	1	4	yes	complemented
42	C₂×#20598	C₂²	1	4	yes	complemented
43	C₂×#20591	C₂²	1	1	yes	characteristic, complemented
44	C₂²×#1783	C₂²	1	1	yes	characteristic
45	C₂²×#1783	C₂²	1	1	yes	characteristic
46	C₂²×#1783	C₂²	1	1	yes	characteristic
47	C₂²×#1783	C₂²	1	1	yes	characteristic
48	C₂²×#1783	C₂²	1	2	yes	complemented
49	C₂²×#1783	C₂²	1	2	yes	complemented
50	C₂²×#1783	C₂²	1	2	yes	complemented
51	C₂²×#1783	C₂²	1	2	yes	complemented
52	#6370684	C₂²	1	1	yes	characteristic, complemented
53	C₂×#20579	C₂²	1	1	yes	characteristic
54	C₂×#20579	C₂²	1	1	yes	characteristic
55	C₂×#20579	C₂²	1	1	yes	characteristic
56	#607558	C₂²	1	1	yes	characteristic
57	C₂×#11187	C₂²	1	4	yes	complemented
58	C₂×#11181	C₂²	1	2	yes	complemented
59	C₂×#11157	C₂²	1	4	yes	complemented
60	C₂×#11157	C₂²	1	2	yes	complemented
61	C₂×#11133	C₂²	1	2	yes	complemented
62	C₂×#11058	C₂²	1	4	yes	complemented
63	C₂×#11101	C₂²	1	4	yes	complemented
64	C₂×#11071	C₂²	1	4	yes	complemented
65	C₂×#11034	C₂²	1	4	yes	complemented
66	C₂×#11034	C₂²	1	4	yes	complemented
67	#357581	C₂²	1	4	yes	complemented
68	C₂×#11014	C₂²	1	4	yes	complemented
69	C₂×#11014	C₂²	1	4	yes	complemented
70	C₂×#10994	C₂²	1	4	yes	complemented
71	C₂×#10994	C₂²	1	4	yes	complemented
72	#357541	C₂²	1	2	yes	complemented
73	#357541	C₂²	1	2	yes	complemented
74	C₂×#10993	C₂²	1	4	yes	complemented
75	C₂×#10993	C₂²	1	4	yes	complemented
76	#353416	C₂²	1	1	yes	characteristic, complemented
77	C₂×#10738	C₂²	1	1	yes	characteristic, complemented
78	C₂×#10738	C₂²	1	1	yes	characteristic, complemented
79	C₂×#10737	C₂²	1	1	yes	characteristic, complemented
80	#353403	C₂²	1	1	yes	characteristic, complemented
81	#353388	C₂²	1	1	yes	characteristic, complemented
82	#353386	C₂²	1	1	yes	characteristic, complemented
83	C₂×#10729	C₂²	1	1	yes	characteristic, complemented
84	C₂×C₂²⋊#338	C₂²	1	1	yes	characteristic, complemented
85	C₂×#10716	C₂²	1	1	yes	characteristic, complemented
86	#123644	C₂²	1	4	yes	complemented
87	#123628	C₂²	1	4	yes	complemented
88	#123619	C₂²	1	4	yes	complemented
89	#123535	C₂²	1	4	yes	complemented
90	#123532	C₂²	1	4	yes	complemented
91	C₂⁴×#41	C₂³	1	1	yes	characteristic
92	C₂⁵×D₄	D₄	1	8	yes	—
93	C₂⁵×D₄	C₂³	1	2	yes	—
94	C₂⁵×D₄	C₂³	1	2	yes	—
95	C₂⁵×D₄	C₂³	1	1	yes	characteristic
96	C₂⁵×D₄	C₂³	1	1	yes	characteristic
97	C₂⁶×C₄	C₂³	1	1	yes	characteristic
98	C₂³×AGL(1,ℤ/8)	D₄	1	4	yes	—
99	C₂³×AGL(1,ℤ/8)	C₂³	1	4	yes	—
100	C₂³×AGL(1,ℤ/8)	C₂³	1	2	yes	—
101	C₂³×AGL(1,ℤ/8)	C₂³	1	2	yes	—
102	C₂⁴×SD₁₆	D₄	1	2	yes	—
103	C₂⁴×D₈	D₄	1	2	yes	—
104	C₂⁴×M₁₆	C₂³	1	1	yes	characteristic
105	C₂⁴×M₁₆	C₂³	1	1	yes	characteristic
106	C₂²×#525	C₂³	1	4	yes	—
107	C₂³×#117	C₂³	1	1	yes	characteristic
108	C₂×#3003	D₄	1	32	yes	—
109	C₂²×#430	C₂³	1	2	yes	complemented
110	C₂×#2905	C₂³	1	2	yes	complemented
111	C₂²×#421	C₂³	1	4	yes	complemented
112	C₂×#2896	C₂³	1	2	yes	complemented
113	C₂×#2896	C₂³	1	2	yes	complemented
114	C₂²×#418	D₄	1	8	yes	—
115	C₂²×#418	C₂³	1	4	yes	—
116	C₂²×#418	C₂³	1	2	yes	—
117	C₂²×#418	C₂³	1	2	yes	—
118	C₂²×#418	C₂³	1	2	yes	—
119	C₂²×#418	C₂³	1	2	yes	—
120	C₂²×#418	C₂³	1	2	yes	—
121	C₂²×#418	C₂³	1	2	yes	—
122	C₂²×#418	C₂³	1	4	yes	—
123	C₂²×#418	C₂³	1	4	yes	—
124	C₂²×#413	C₂³	1	2	yes	complemented
125	C₂²×#413	C₂³	1	2	yes	complemented
126	C₂³×#100	C₂³	1	1	yes	characteristic
127	C₂³×#100	C₂³	1	2	yes	—
128	C₂³×#100	C₂³	1	1	yes	characteristic
129	C₂³×#100	C₂³	1	1	yes	characteristic
130	C₂³×#100	C₂³	1	2	yes	—
131	C₂³×#100	C₂³	1	2	yes	—
132	C₂³×#100	C₂³	1	1	yes	characteristic
133	C₂³×#100	C₂³	1	2	yes	—
134	C₂³×#100	C₂³	1	2	yes	—
135	C₂³×#100	C₂³	1	2	yes	—
136	C₂×#2879	C₂³	1	4	yes	complemented
137	C₂²×#407	C₂³	1	4	yes	—
138	C₂²×#407	C₂³	1	4	yes	—
139	C₂²×#407	C₂³	1	2	yes	—
140	C₂²×#407	C₂³	1	2	yes	—
141	C₂²×#407	C₂³	1	2	yes	—
142	C₂²×#407	C₂³	1	2	yes	—
143	C₂²×#407	C₂³	1	1	yes	characteristic
144	C₂²×#407	C₂³	1	1	yes	characteristic
145	C₂²×#407	C₂³	1	1	yes	characteristic
146	C₂²×#407	C₂³	1	1	yes	characteristic
147	C₂²×#407	C₂³	1	1	yes	characteristic
148	C₂²×#407	C₂³	1	1	yes	characteristic
149	C₂×#2280	C₂³	1	4	yes	—
150	C₂×#2280	C₂³	1	1	yes	characteristic
151	C₂×#2280	C₂³	1	1	yes	characteristic
152	C₂×#1786	D₄	1	8	yes	complemented
153	C₂²×#344	C₂³	1	2	yes	complemented
154	C₂²×#344	C₂³	1	2	yes	complemented
155	C₂²×#344	C₂³	1	4	yes	complemented
156	C₂²×#344	C₂³	1	4	yes	complemented
157	C₂²×#344	C₂³	1	2	yes	complemented
158	C₂²×#344	C₂³	1	2	yes	complemented
159	C₂×#1742	C₂³	1	4	yes	complemented
160	C₂×#1738	C₂³	1	2	yes	complemented
161	C₂×#1738	C₂³	1	2	yes	complemented
162	C₂×#1738	C₂³	1	2	yes	complemented
163	C₂×#1738	C₂³	1	4	yes	complemented
164	C₂×#1733	C₂³	1	4	yes	complemented
165	C₂²×#338	C₂³	1	4	yes	complemented
166	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	complemented
167	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	complemented
168	#20335	C₂³	1	2	yes	complemented
169	C₂⁷	#41	1	1	yes	characteristic
170	C₂³×#41	C₂×D₄	1	2	yes	—
171	C₂³×#41	C₂⁴	1	2	yes	—
172	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
173	C₂⁴×D₄	C₂×D₄	1	2	yes	—
174	C₂⁴×D₄	C₂×D₄	1	4	yes	—
175	C₂⁴×D₄	C₂×D₄	1	4	yes	—
176	C₂⁴×D₄	C₂×D₄	1	2	yes	—
177	C₂⁴×D₄	C₂×D₄	1	4	yes	—
178	C₂⁴×D₄	C₂×D₄	1	4	yes	—
179	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
180	C₂⁴×D₄	C₂×D₄	1	8	yes	—
181	C₂⁴×D₄	C₂×D₄	1	8	yes	—
182	C₂⁴×D₄	C₂×D₄	1	16	yes	—
183	C₂⁴×D₄	#41	1	4	yes	—
184	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
185	C₂⁴×D₄	C₂⁴	1	2	yes	—
186	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
187	C₂⁵×C₄	C₂×D₄	1	4	yes	—
188	C₂⁵×C₄	#41	1	1	yes	characteristic
189	C₂⁵×C₄	#41	1	2	yes	—
190	C₂⁵×C₄	#41	1	4	yes	—
191	C₂⁵×C₄	C₂⁴	1	2	yes	—
192	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
193	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	16	yes	—
194	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	16	yes	—
195	C₂³×SD₁₆	C₂×D₄	1	4	yes	—
196	C₂³×SD₁₆	C₂×D₄	1	4	yes	—
197	C₂³×D₈	C₂×D₄	1	4	yes	—
198	C₂³×D₈	C₂×D₄	1	4	yes	—
199	C₂³×M₁₆	C₂×D₄	1	4	yes	—
200	C₂³×M₁₆	C₂×D₄	1	2	yes	—
201	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
202	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
203	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
204	C₂³×M₁₆	C₂⁴	1	2	yes	—
205	C₂³×M₁₆	C₂⁴	1	2	yes	—
206	C₂³×M₁₆	C₂⁴	1	2	yes	—
207	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
208	C₂³×M₁₆	C₂⁴	1	2	yes	—
209	C₂³×M₁₆	C₂⁴	1	2	yes	—
210	C₂³×M₁₆	C₂⁴	1	2	yes	—
211	C₂⁴×C₈	C₂×D₄	1	2	yes	—
212	C₂×#525	C₂×D₄	1	16	yes	—
213	C₂²×#117	C₂×D₄	1	4	yes	—
214	C₂²×#117	C₂⁴	1	2	yes	—
215	C₂²×#117	C₂⁴	1	2	yes	—
216	C₂²×#117	C₂⁴	1	2	yes	—
217	C₂×#418	C₂×D₄	1	16	yes	—
218	C₂×#418	C₂×D₄	1	8	yes	—
219	C₂×#418	C₂×D₄	1	8	yes	—
220	C₂×#418	C₂×D₄	1	16	yes	—
221	C₂²×#102	C₂×D₄	1	16	yes	complemented
222	C₂×#407	C₂×D₄	1	16	yes	—
223	C₂²×C₂²⋊C₈	C₂×D₄	1	4	yes	—
224	C₂×#380	C₂×D₄	1	4	yes	—
225	C₂⁶	#123	1	4	yes	—
226	C₂⁶	C₂×#41	1	2	yes	—
227	C₂⁶	C₂×#41	1	1	yes	characteristic
228	C₂²×#41	C₂²×D₄	1	8	yes	—
229	C₂³×Q₈	C₂²×D₄	1	2	yes	—
230	C₂³×D₄	#120	1	8	yes	—
231	C₂³×D₄	#120	1	8	yes	—
232	C₂³×D₄	#120	1	32	yes	—
233	C₂³×D₄	#121	1	16	yes	—
234	C₂³×D₄	C₂²×D₄	1	2	yes	—
235	C₂³×D₄	C₂²×D₄	1	2	yes	—
236	C₂³×D₄	C₂²×D₄	1	8	yes	—
237	C₂³×D₄	C₂²×D₄	1	2	yes	—
238	C₂³×D₄	C₂²×D₄	1	2	yes	—
239	C₂³×D₄	C₂²×D₄	1	4	yes	—
240	C₂³×D₄	C₂²×D₄	1	2	yes	—
241	C₂³×D₄	C₂²×D₄	1	2	yes	—
242	C₂³×D₄	C₂²×D₄	1	2	yes	—
243	C₂³×D₄	C₂²×D₄	1	8	yes	—
244	C₂³×D₄	C₂²×D₄	1	4	yes	—
245	C₂³×D₄	C₂×#41	1	4	yes	—
246	C₂³×D₄	H(5,𝔽₂)	1	8	yes	—
247	C₂³×D₄	H(5,𝔽₂)	1	8	yes	—
248	C₂⁴×C₄	#123	1	4	yes	—
249	C₂⁴×C₄	#123	1	8	yes	—
250	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
251	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
252	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
253	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
254	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
255	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
256	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
257	C₂⁴×C₄	C₂×#41	1	2	yes	—
258	C₂⁴×C₄	C₂×#41	1	4	yes	—
259	C₂⁴×C₄	C₂×#41	1	2	yes	—
260	C₂⁴×C₄	C₂×#41	1	1	yes	characteristic
261	C₂⁴×C₄	C₂×#41	1	2	yes	—
262	C₂⁴×C₄	H(5,𝔽₂)	1	8	yes	—
263	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
264	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
265	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
266	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
267	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
268	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
269	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
270	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
271	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
272	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
273	C₂²×SD₁₆	#120	1	16	yes	—
274	C₂²×D₈	#120	1	16	yes	—
275	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
276	C₂²×M₁₆	C₂²×D₄	1	8	yes	—
277	C₂²×M₁₆	C₂²×D₄	1	8	yes	—
278	C₂³×C₈	C₂²×D₄	1	4	yes	—
279	C₂³×C₈	C₂²×D₄	1	4	yes	—
280	C₂×#117	C₂²×D₄	1	8	yes	—
281	C₂×#117	C₂²×D₄	1	4	yes	—
282	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
283	#418	#120	1	32	yes	—
284	C₂⁵	C₂×#123	1	4	yes	—
285	C₂⁵	C₂×#123	1	2	yes	—
286	C₂⁵	#538	1	2	yes	—
287	C₂⁵	#538	1	2	yes	—
288	C₂⁵	#546	1	1	yes	characteristic
289	C₂⁵	#546	1	2	yes	—
290	C₂⁵	#546	1	8	yes	—
291	C₂⁵	#546	1	1	yes	characteristic
292	C₂⁵	#546	1	2	yes	—
293	C₂⁵	#551	1	2	yes	—
294	C₂⁵	C₂²×#41	1	1	yes	characteristic
295	C₂²×Q₈	C₂×#120	1	4	yes	—
296	C₂²×D₄	C₂×#120	1	4	yes	—
297	C₂²×D₄	C₂×#120	1	4	yes	—
298	C₂²×D₄	C₂×#120	1	8	yes	—
299	C₂²×D₄	C₂×#120	1	8	yes	—
300	C₂²×D₄	C₂×#120	1	8	yes	—
301	C₂²×D₄	C₂×#120	1	4	yes	—
302	C₂²×D₄	C₂×#120	1	8	yes	—
303	C₂²×D₄	C₂×#121	1	8	yes	—
304	C₂²×D₄	#534	1	8	yes	—
305	C₂²×D₄	#534	1	8	yes	—
306	C₂²×D₄	#534	1	8	yes	—
307	C₂²×D₄	#535	1	8	yes	—
308	C₂²×D₄	D₄²	1	16	yes	—
309	C₂²×D₄	#546	1	16	yes	—
310	C₂³×C₄	C₂×#120	1	8	yes	—
311	C₂³×C₄	C₂×#120	1	2	yes	—
312	C₂³×C₄	C₂×#120	1	2	yes	—
313	C₂³×C₄	C₂×#121	1	4	yes	—
314	C₂³×C₄	C₂×#123	1	4	yes	—
315	C₂³×C₄	C₂×#123	1	2	yes	—
316	C₂³×C₄	#534	1	8	yes	—
317	C₂³×C₄	#534	1	4	yes	—
318	C₂³×C₄	#534	1	4	yes	—
319	C₂³×C₄	#534	1	2	yes	—
320	C₂³×C₄	#534	1	2	yes	—
321	C₂³×C₄	#534	1	2	yes	—
322	C₂³×C₄	#534	1	2	yes	—
323	C₂³×C₄	#534	1	2	yes	—
324	C₂³×C₄	#534	1	2	yes	—
325	C₂³×C₄	#534	1	2	yes	—
326	C₂³×C₄	#534	1	2	yes	—
327	C₂³×C₄	#534	1	4	yes	—
328	C₂³×C₄	#535	1	4	yes	—
329	C₂³×C₄	#535	1	4	yes	—
330	C₂³×C₄	#535	1	4	yes	—
331	C₂³×C₄	#538	1	4	yes	—
332	C₂³×C₄	#538	1	2	yes	—
333	C₂³×C₄	#538	1	2	yes	—
334	C₂³×C₄	#538	1	2	yes	—
335	C₂³×C₄	#538	1	2	yes	—
336	C₂³×C₄	#538	1	4	yes	—
337	C₂³×C₄	#538	1	4	yes	—
338	C₂³×C₄	D₄²	1	2	yes	—
339	C₂³×C₄	D₄²	1	2	yes	—
340	C₂³×C₄	D₄²	1	4	yes	—
341	C₂³×C₄	#546	1	8	yes	—
342	C₂³×C₄	#546	1	16	yes	—
343	C₂³×C₄	#546	1	1	yes	characteristic
344	C₂³×C₄	#546	1	1	yes	characteristic
345	C₂³×C₄	#546	1	2	yes	—
346	C₂³×C₄	#546	1	2	yes	—
347	C₂³×C₄	#546	1	2	yes	—
348	C₂³×C₄	#546	1	2	yes	—
349	C₂³×C₄	#546	1	2	yes	—
350	C₂³×C₄	#546	1	2	yes	—
351	C₂³×C₄	#546	1	2	yes	—
352	C₂³×C₄	#546	1	4	yes	—
353	C₂³×C₄	#546	1	2	yes	—
354	C₂³×C₄	#546	1	4	yes	—
355	C₂³×C₄	#551	1	2	yes	—
356	C₂³×C₄	#551	1	4	yes	—
357	C₂³×C₄	#560	1	2	yes	—
358	C₂³×C₄	#560	1	2	yes	—
359	C₂³×C₄	#560	1	4	yes	—
360	C₂³×C₄	#560	1	2	yes	—
361	C₂³×C₄	#560	1	2	yes	—
362	C₂³×C₄	H(3,𝔽₄)	1	4	yes	—
363	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
364	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
365	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
366	C₂³×C₄	C₂³×D₄	1	4	yes	—
367	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
368	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
369	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
370	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
371	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
372	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
373	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
374	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
375	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
376	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
377	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
378	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
379	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
380	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
381	C₂×M₁₆	C₂×#120	1	8	yes	—
382	C₂²×C₈	C₂×#120	1	8	yes	—
383	#117	C₂×#120	1	8	yes	—
384	C₂⁴	#2405	1	2	yes	—
385	C₂⁴	#2405	1	8	yes	—
386	C₂⁴	#2405	1	2	yes	—
387	C₂⁴	#2412	1	4	yes	—
388	C₂⁴	#2622	1	4	yes	—
389	C₂⁴	#2668	1	2	yes	—
390	C₂⁴	#2668	1	2	yes	—
391	C₂⁴	#2670	1	4	yes	—
392	C₂⁴	#2685	1	4	yes	—
393	C₂⁴	#2697	1	2	yes	—
394	C₂⁴	#2697	1	2	yes	—
395	C₂⁴	C₂²×#123	1	1	yes	characteristic
396	C₂⁴	C₂×#538	1	1	yes	characteristic
397	C₂⁴	C₂×#538	1	1	yes	characteristic
398	C₂⁴	C₂×#546	1	1	yes	characteristic
399	C₂⁴	C₂×#546	1	1	yes	characteristic
400	C₂⁴	C₂×#546	1	4	yes	—
401	C₂⁴	C₂×#546	1	1	yes	characteristic
402	C₂⁴	C₂×#551	1	1	yes	characteristic
403	C₂⁴	#3490	1	4	yes	—
404	C₂×D₄	#2410	1	16	yes	—
405	C₂×D₄	#2613	1	8	yes	—
406	C₂×D₄	#2846	1	8	yes	—
407	C₂²×C₄	#2405	1	8	yes	—
408	C₂²×C₄	#2405	1	2	yes	—
409	C₂²×C₄	#2405	1	2	yes	—
410	C₂²×C₄	#2410	1	4	yes	—
411	C₂²×C₄	#2410	1	4	yes	—
412	C₂²×C₄	#2412	1	4	yes	—
413	C₂²×C₄	#2613	1	4	yes	—
414	C₂²×C₄	#2613	1	4	yes	—
415	C₂²×C₄	#2617	1	4	yes	—
416	C₂²×C₄	#2617	1	4	yes	—
417	C₂²×C₄	#2622	1	4	yes	—
418	C₂²×C₄	#2668	1	2	yes	—
419	C₂²×C₄	#2668	1	2	yes	—
420	C₂²×C₄	#2670	1	4	yes	—
421	C₂²×C₄	#2678	1	4	yes	—
422	C₂²×C₄	#2678	1	4	yes	—
423	C₂²×C₄	#2678	1	4	yes	—
424	C₂²×C₄	#2678	1	4	yes	—
425	C₂²×C₄	#2684	1	4	yes	—
426	C₂²×C₄	#2684	1	4	yes	—
427	C₂²×C₄	#2685	1	4	yes	—
428	C₂²×C₄	#2685	1	4	yes	—
429	C₂²×C₄	#2685	1	4	yes	—
430	C₂²×C₄	#2697	1	2	yes	—
431	C₂²×C₄	#2697	1	2	yes	—
432	C₂²×C₄	#2812	1	4	yes	—
433	C₂²×C₄	#2812	1	4	yes	—
434	C₂²×C₄	C₂²×#120	1	2	yes	—
435	C₂²×C₄	C₂²×#120	1	2	yes	—
436	C₂²×C₄	C₂²×#120	1	2	yes	—
437	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
438	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
439	C₂²×C₄	C₂×#534	1	1	yes	characteristic
440	C₂²×C₄	C₂×#534	1	2	yes	—
441	C₂²×C₄	C₂×#534	1	1	yes	characteristic
442	C₂²×C₄	C₂×#534	1	1	yes	characteristic
443	C₂²×C₄	C₂×#534	1	1	yes	characteristic
444	C₂²×C₄	C₂×#534	1	2	yes	—
445	C₂²×C₄	C₂×#534	1	2	yes	—
446	C₂²×C₄	C₂×#534	1	2	yes	—
447	C₂²×C₄	C₂×#534	1	1	yes	characteristic
448	C₂²×C₄	C₂×#534	1	1	yes	characteristic
449	C₂²×C₄	C₂×#534	1	1	yes	characteristic
450	C₂²×C₄	C₂×#535	1	1	yes	characteristic
451	C₂²×C₄	C₂×#535	1	2	yes	—
452	C₂²×C₄	C₂×#535	1	1	yes	characteristic
453	C₂²×C₄	C₂×#535	1	1	yes	characteristic
454	C₂²×C₄	C₂×#538	1	1	yes	characteristic
455	C₂²×C₄	C₂×#538	1	1	yes	characteristic
456	C₂²×C₄	C₂×#538	1	1	yes	characteristic
457	C₂²×C₄	C₂×#538	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
459	C₂²×C₄	C₂×D₄²	1	4	yes	—
460	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
461	C₂²×C₄	C₂×#546	1	4	yes	—
462	C₂²×C₄	C₂×#546	1	4	yes	—
463	C₂²×C₄	C₂×#546	1	1	yes	characteristic
464	C₂²×C₄	C₂×#546	1	1	yes	characteristic
465	C₂²×C₄	C₂×#546	1	1	yes	characteristic
466	C₂²×C₄	C₂×#546	1	1	yes	characteristic
467	C₂²×C₄	C₂×#546	1	1	yes	characteristic
468	C₂²×C₄	C₂×#551	1	1	yes	characteristic
469	C₂²×C₄	#3484	1	4	yes	—
470	C₂²×C₄	#3484	1	4	yes	—
471	C₂²×C₄	#3484	1	4	yes	—
472	C₂²×C₄	#3484	1	2	yes	—
473	C₂²×C₄	#3484	1	4	yes	—
474	C₂²×C₄	#3484	1	4	yes	—
475	C₂²×C₄	#3484	1	2	yes	—
476	C₂²×C₄	#3484	1	4	yes	—
477	C₂²×C₄	#3484	1	4	yes	—
478	C₂²×C₄	#3484	1	2	yes	—
479	C₂²×C₄	#3484	1	2	yes	—
480	C₂²×C₄	#3484	1	4	yes	—
481	C₂²×C₄	#3484	1	4	yes	—
482	C₂²×C₄	#3490	1	4	yes	—
483	C₂²×C₄	#3490	1	4	yes	—
484	C₂²×C₄	C₂×#560	1	1	yes	characteristic
485	C₂²×C₄	C₂×#560	1	1	yes	characteristic
486	C₂²×C₄	C₂×#560	1	1	yes	characteristic
487	C₂²×C₄	C₂×H(3,𝔽₄)	1	1	yes	characteristic
488	C₂²×C₄	#3532	1	4	yes	—
489	C₂²×C₄	#3532	1	4	yes	—
490	C₂²×C₄	#3532	1	4	yes	—
491	C₂²×C₄	#3532	1	4	yes	—
492	C₂²×C₄	#3532	1	4	yes	—
493	C₂²×C₄	#3532	1	4	yes	—
494	C₂²×C₄	#3532	1	4	yes	—
495	C₂²×C₄	#3532	1	4	yes	—
496	C₂³	#16255	1	4	yes	—
497	C₂³	#16255	1	4	yes	—
498	C₂³	#30434	1	8	yes	—
499	C₂³	C₂×#2622	1	1	yes	characteristic
500	C₂³	C₂×#2405	1	1	yes	characteristic
501	C₂³	C₂×#2405	1	2	yes	—
502	C₂³	C₂×#2412	1	1	yes	characteristic
503	C₂³	#34992	1	2	yes	—
504	C₂³	#36152	1	2	yes	—
505	C₂³	#36152	1	2	yes	—
506	C₂³	#37660	1	4	yes	—
507	C₂³	#37660	1	4	yes	—
508	C₂³	#37832	1	2	yes	—
509	C₂³	#37833	1	2	yes	—
510	C₂³	C₂×#2668	1	1	yes	characteristic
511	C₂³	C₂×#2670	1	1	yes	characteristic
512	C₂³	C₂×#2685	1	1	yes	characteristic
513	C₂³	C₂×#2697	1	1	yes	characteristic
514	C₂³	#58991	1	4	yes	—
515	C₂³	#59006	1	4	yes	—
516	C₂×C₄	#16255	1	4	yes	—
517	C₂×C₄	#16255	1	4	yes	—
518	C₂×C₄	C₂×#2613	1	1	yes	characteristic
519	C₂×C₄	C₂×#2613	1	1	yes	characteristic
520	C₂×C₄	C₂×#2617	1	1	yes	characteristic
521	C₂×C₄	C₂×#2410	1	1	yes	characteristic
522	C₂×C₄	C₂×#2410	1	2	yes	—
523	C₂×C₄	#34980	1	1	yes	characteristic
524	C₂×C₄	#34980	1	1	yes	characteristic
525	C₂×C₄	#34980	1	2	yes	—
526	C₂×C₄	#34980	1	2	yes	—
527	C₂×C₄	#34980	1	2	yes	—
528	C₂×C₄	#34980	1	2	yes	—
529	C₂×C₄	#34980	1	2	yes	—
530	C₂×C₄	#34980	1	2	yes	—
531	C₂×C₄	#34981	1	2	yes	—
532	C₂×C₄	#35222	1	2	yes	—
533	C₂×C₄	#35222	1	2	yes	—
534	C₂×C₄	D₄×#120	1	2	yes	—
535	C₂×C₄	D₄×#120	1	2	yes	—
536	C₂×C₄	#36152	1	2	yes	—
537	C₂×C₄	#36152	1	2	yes	—
538	C₂×C₄	#36152	1	2	yes	—
539	C₂×C₄	#36152	1	2	yes	—
540	C₂×C₄	C₂×#2846	1	1	yes	characteristic
541	C₂×C₄	C₂×#2812	1	1	yes	characteristic
542	C₂×C₄	#36702	1	2	yes	—
543	C₂×C₄	#36703	1	2	yes	—
544	C₂×C₄	#36703	1	2	yes	—
545	C₂×C₄	#36714	1	2	yes	—
546	C₂×C₄	#37436	1	2	yes	—
547	C₂×C₄	#37436	1	2	yes	—
548	C₂×C₄	#37436	1	2	yes	—
549	C₂×C₄	#37436	1	2	yes	—
550	C₂×C₄	#37644	1	4	yes	—
551	C₂×C₄	#37644	1	2	yes	—
552	C₂×C₄	#37645	1	2	yes	—
553	C₂×C₄	#37645	1	4	yes	—
554	C₂×C₄	#37660	1	4	yes	—
555	C₂×C₄	#37660	1	4	yes	—
556	C₂×C₄	#37660	1	4	yes	—
557	C₂×C₄	#37660	1	4	yes	—
558	C₂×C₄	#37832	1	2	yes	—
559	C₂×C₄	#37832	1	2	yes	—
560	C₂×C₄	#37833	1	2	yes	—
561	C₂×C₄	#37833	1	2	yes	—
562	C₂×C₄	#45438	1	4	yes	—
563	C₂×C₄	#45438	1	4	yes	—
564	C₂×C₄	#45438	1	4	yes	—
565	C₂×C₄	#45439	1	4	yes	—
566	C₂×C₄	C₂×#2678	1	1	yes	characteristic
567	C₂×C₄	C₂×#2678	1	1	yes	characteristic
568	C₂×C₄	C₂×#2684	1	1	yes	characteristic
569	C₂×C₄	C₂×#2685	1	1	yes	characteristic
570	C₂×C₄	#58991	1	4	yes	—
571	C₂×C₄	#59006	1	4	yes	—
572	C₂²	#454694	1	8	yes	complemented
573	C₂²	C₂×#16255	1	1	yes	characteristic
574	C₂²	#612617	1	1	yes	characteristic
575	C₂²	#636185	1	1	yes	characteristic
576	C₂²	#639822	1	2	yes	—
577	C₂²	#759297	1	2	yes	—
578	C₂²	#845677	1	2	yes	—
579	C₂²	#845689	1	2	yes	—
580	C₂²	#845705	1	2	yes	—
581	C₂²	#846041	1	2	yes	—
582	C₂²	C₂×#30434	1	4	yes	—
583	C₄	#612433	1	1	yes	characteristic
584	C₄	#635993	1	1	yes	characteristic
585	C₄	#636019	1	2	yes	—
586	C₄	#845309	1	2	yes	—
587	C₄	#845325	1	2	yes	—
588	C₄	#845705	1	2	yes	—
589	C₄	#846389	1	2	yes	—
590	C₄	#4307937	1	1	yes	characteristic
591	C₄	#4308740	1	1	yes	characteristic
592	C₄	#4414082	1	2	yes	—
593	C₂	#72215520	1	4	yes	—
594	C₂	C₂×#454694	1	2	yes	—
595	C₂	#72250304	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂×#2668
commutator, Frattini, cosocle	C₂⁴×C₄	C₂⁵
prime radical	C₂³×#3003	C₂
LCS	G ▷ C₂⁴×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁵×C₄ ◁ G
LECS	G ▷ C₂⁴×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72256546	C₂	semidirect
2. #72256523	C₂	semidirect
3. #72256513	C₂	semidirect
4. #72256492	C₂	semidirect
5. #72256490	C₂	semidirect
6. #72256465	C₂	semidirect
7. #72256429	C₂	semidirect
8. #72256273	C₂	semidirect
9. #72255679	C₂	semidirect
10. #72255601	C₂	semidirect
11. C₂×#395781	C₂	semidirect
12. C₂×#454694	C₂	semidirect
13. #72240119	C₂	semidirect
14. #72237236	C₂	semidirect
15. #72237191	C₂	semidirect
16. #72236779	C₂	semidirect
17. C₂×#392113	C₂	semidirect
19. #72231771	C₂	semidirect
29. C₂²×#2081	C₂²	semidirect
30. C₂×#23531	C₂²	semidirect
31. C₂×#23521	C₂²	semidirect
32. C₂×#23521	C₂²	semidirect
33. C₂×#20851	C₂²	semidirect
34. #6371257	C₂²	semidirect
35. C₂×#20605	C₂²	semidirect
36. #6370715	C₂²	semidirect
41. C₂×#20598	C₂²	semidirect
42. C₂×#20598	C₂²	semidirect
43. C₂×#20591	C₂²	semidirect
48. C₂²×#1783	C₂²	semidirect
49. C₂²×#1783	C₂²	semidirect
50. C₂²×#1783	C₂²	semidirect
51. C₂²×#1783	C₂²	semidirect
52. #6370684	C₂²	semidirect
57. C₂×#11187	C₂²	semidirect
58. C₂×#11181	C₂²	semidirect
59. C₂×#11157	C₂²	semidirect
60. C₂×#11157	C₂²	semidirect
61. C₂×#11133	C₂²	semidirect
62. C₂×#11058	C₂²	semidirect
63. C₂×#11101	C₂²	semidirect
64. C₂×#11071	C₂²	semidirect
65. C₂×#11034	C₂²	semidirect
66. C₂×#11034	C₂²	semidirect
67. #357581	C₂²	semidirect
68. C₂×#11014	C₂²	semidirect
69. C₂×#11014	C₂²	semidirect
70. C₂×#10994	C₂²	semidirect
71. C₂×#10994	C₂²	semidirect
72. #357541	C₂²	semidirect
73. #357541	C₂²	semidirect
74. C₂×#10993	C₂²	semidirect
75. C₂×#10993	C₂²	semidirect
76. #353416	C₂²	semidirect
77. C₂×#10738	C₂²	semidirect
78. C₂×#10738	C₂²	semidirect
79. C₂×#10737	C₂²	semidirect
80. #353403	C₂²	semidirect
81. #353388	C₂²	semidirect
82. #353386	C₂²	semidirect
83. C₂×#10729	C₂²	semidirect
84. C₂×C₂²⋊#338	C₂²	semidirect
85. C₂×#10716	C₂²	semidirect
86. #123644	C₂²	semidirect
87. #123628	C₂²	semidirect
88. #123619	C₂²	semidirect
89. #123535	C₂²	semidirect
90. #123532	C₂²	semidirect
109. C₂²×#430	C₂³	semidirect
110. C₂×#2905	C₂³	semidirect
111. C₂²×#421	C₂³	semidirect
112. C₂×#2896	C₂³	semidirect
113. C₂×#2896	C₂³	semidirect
124. C₂²×#413	C₂³	semidirect
125. C₂²×#413	C₂³	semidirect
136. C₂×#2879	C₂³	semidirect
152. C₂×#1786	D₄	semidirect
153. C₂²×#344	C₂³	semidirect
154. C₂²×#344	C₂³	semidirect
155. C₂²×#344	C₂³	semidirect
156. C₂²×#344	C₂³	semidirect
157. C₂²×#344	C₂³	semidirect
158. C₂²×#344	C₂³	semidirect
159. C₂×#1742	C₂³	semidirect
160. C₂×#1738	C₂³	semidirect
161. C₂×#1738	C₂³	semidirect
162. C₂×#1738	C₂³	semidirect
163. C₂×#1738	C₂³	semidirect
164. C₂×#1733	C₂³	semidirect
165. C₂²×#338	C₂³	semidirect
166. C₂²×H(3,ℤ/4)	C₂³	semidirect
167. C₂²×H(3,ℤ/4)	C₂³	semidirect
168. #20335	C₂³	semidirect
221. C₂²×#102	C₂×D₄	semidirect
572. C₂²	#454694	semidirect

Maximal subgroups

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

subgroup	index
#72256546	2
#72256523	2
#72256513	2
#72256492	2
#72256490	2
#72256465	2
#72256429	2
#72256273	2
#72255679	2
#72255601	2
C₂×#395781	2
C₂×#454694	2
#72240119	2
#72237236	2
#72237191	2
#72236779	2
C₂×#392113	2
C₂³×#3003	2
#72231771	2