Subgroups — #72262700

Order 2048.

At least 9254 conjugacy classes of subgroups; only the 1516 normal subgroups are shown.

The subgroup lattice has 652 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72262699	C₂	1	1	yes	maximal, characteristic, complemented
2	#72256285	C₂	1	2	yes	maximal, complemented
3	#72256212	C₂	1	2	yes	maximal, complemented
4	#72256109	C₂	1	2	yes	maximal, complemented
5	#72256073	C₂	1	2	yes	maximal, complemented
6	#72255629	C₂	1	1	yes	maximal, characteristic, complemented
7	#72252195	C₂	1	2	yes	maximal, complemented
8	C₂×#427241	C₂	1	2	yes	maximal, complemented
9	#72251324	C₂	1	1	yes	maximal, characteristic, complemented
10	#72251207	C₂	1	2	yes	maximal, complemented
11	#72251122	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#10575416	C₂	1	1	yes	maximal, characteristic, complemented
13	#72237713	C₂	1	2	yes	maximal, complemented
14	C₂×#395191	C₂	1	1	yes	maximal, characteristic, complemented
15	#72237668	C₂	1	2	yes	maximal, complemented
16	#72237236	C₂	1	2	yes	maximal, complemented
17	#72237194	C₂	1	2	yes	maximal, complemented
18	#72236780	C₂	1	2	yes	maximal, complemented
19	C₂×#364416	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂³×#525	C₂²	1	2	yes	—
21	C₂×#60511	C₂²	1	2	yes	—
22	C₂×#60511	C₂²	1	2	yes	—
23	#10574916	C₂²	1	1	yes	characteristic, complemented
24	C₂×#60444	C₂²	1	2	yes	—
25	C₂×#60444	C₂²	1	1	yes	characteristic
26	C₂×#60444	C₂²	1	1	yes	characteristic
27	C₂×#60359	C₂²	1	2	yes	—
28	C₂×#60359	C₂²	1	2	yes	—
29	C₂×#60141	C₂²	1	1	yes	characteristic, complemented
30	C₂³×#407	C₂²	1	1	yes	characteristic
31	C₂×#36614	C₂²	1	1	yes	characteristic
32	#7628649	C₂²	1	2	yes	complemented
33	C₂×#23535	C₂²	1	1	yes	characteristic, complemented
34	C₂×#23443	C₂²	1	2	yes	—
35	C₂×#23443	C₂²	1	2	yes	—
36	C₂×#23443	C₂²	1	2	yes	complemented
37	C₂×#23443	C₂²	1	2	yes	complemented
38	C₂×#23414	C₂²	1	1	yes	characteristic, complemented
39	#6431722	C₂²	1	2	yes	complemented
40	C₂×#21244	C₂²	1	1	yes	characteristic, complemented
41	C₂×#21009	C₂²	1	2	yes	complemented
42	C₂×#20989	C₂²	1	1	yes	characteristic, complemented
43	C₂×#20983	C₂²	1	2	yes	complemented
44	C₂²×#1891	C₂²	1	2	yes	complemented
45	C₂×#20671	C₂²	1	1	yes	characteristic, complemented
46	#6370810	C₂²	1	1	yes	characteristic, complemented
47	C₂×#20605	C₂²	1	2	yes	complemented
48	#6370715	C₂²	1	2	yes	complemented
49	C₂×#20584	C₂²	1	2	yes	complemented
50	C₂×#20579	C₂²	1	1	yes	characteristic
51	#607558	C₂²	1	2	yes	—
52	C₂×#11361	C₂²	1	2	yes	complemented
53	C₂×#11277	C₂²	1	2	yes	complemented
54	C₂×#11234	C₂²	1	1	yes	characteristic, complemented
55	#357939	C₂²	1	2	yes	complemented
56	C₂×#11178	C₂²	1	2	yes	complemented
57	C₂×#11138	C₂²	1	2	yes	complemented
58	C₂×#11132	C₂²	1	2	yes	complemented
59	#357818	C₂²	1	2	yes	complemented
60	#357771	C₂²	1	2	yes	complemented
61	C₂×#11102	C₂²	1	1	yes	characteristic, complemented
62	C₂×#11100	C₂²	1	2	yes	complemented
63	C₂×#11100	C₂²	1	2	yes	complemented
64	C₂×#11071	C₂²	1	2	yes	complemented
65	#357593	C₂²	1	2	yes	complemented
66	C₂×#11033	C₂²	1	2	yes	complemented
67	#357586	C₂²	1	2	yes	complemented
68	#357577	C₂²	1	2	yes	complemented
69	#357564	C₂²	1	2	yes	complemented
70	C₂×#11000	C₂²	1	2	yes	complemented
71	#357556	C₂²	1	2	yes	complemented
72	C₂×#10994	C₂²	1	2	yes	—
73	C₂×#10994	C₂²	1	2	yes	—
74	C₂×#10994	C₂²	1	2	yes	—
75	C₂×#10994	C₂²	1	2	yes	—
76	C₂×#10994	C₂²	1	2	yes	complemented
77	C₂×#10994	C₂²	1	2	yes	complemented
78	C₂×#10994	C₂²	1	2	yes	complemented
79	C₂×#10994	C₂²	1	2	yes	complemented
80	C₂×#10993	C₂²	1	2	yes	complemented
81	#357529	C₂²	1	2	yes	—
82	#357529	C₂²	1	2	yes	—
83	#357529	C₂²	1	2	yes	complemented
84	#357529	C₂²	1	2	yes	complemented
85	#357470	C₂²	1	2	yes	complemented
86	C₂×#10951	C₂²	1	2	yes	complemented
87	C₂×#10937	C₂²	1	2	yes	complemented
88	#353711	C₂²	1	1	yes	characteristic, complemented
89	C₂×#10737	C₂²	1	1	yes	characteristic, complemented
90	#353407	C₂²	1	2	yes	complemented
91	#353397	C₂²	1	2	yes	complemented
92	#353386	C₂²	1	2	yes	complemented
93	C₂×#10729	C₂²	1	1	yes	characteristic, complemented
94	C₂×#10717	C₂²	1	1	yes	characteristic, complemented
95	C₂×#10716	C₂²	1	2	yes	complemented
96	#123991	C₂²	1	2	yes	complemented
97	#123983	C₂²	1	2	yes	complemented
98	#123940	C₂²	1	2	yes	complemented
99	#123637	C₂²	1	2	yes	complemented
100	#123627	C₂²	1	2	yes	complemented
101	#123623	C₂²	1	2	yes	complemented
102	#123618	C₂²	1	2	yes	complemented
103	#123610	C₂²	1	2	yes	complemented
104	#123568	C₂²	1	2	yes	complemented
105	#123531	C₂²	1	2	yes	complemented
106	#123531	C₂²	1	2	yes	complemented
107	C₂⁴×#41	C₂³	1	2	yes	—
108	C₂⁶×C₄	C₂³	1	1	yes	characteristic
109	C₂²×#575	C₂³	1	1	yes	characteristic
110	C₂²×#575	C₂³	1	2	yes	—
111	C₂²×#575	C₂³	1	1	yes	characteristic
112	C₂²×#568	C₂³	1	1	yes	characteristic
113	C₂⁴×M₁₆	C₂³	1	1	yes	characteristic
114	C₂⁴×M₁₆	C₂³	1	1	yes	characteristic
115	C₂×#3449	C₂³	1	2	yes	—
116	C₂×#3449	C₂³	1	2	yes	—
117	C₂²×#525	C₂³	1	1	yes	characteristic
118	C₂²×#525	C₂³	1	2	yes	—
119	C₂²×#525	C₂³	1	2	yes	—
120	C₂²×#525	C₂³	1	2	yes	—
121	C₂²×#525	C₂³	1	2	yes	—
122	C₂²×#525	C₂³	1	2	yes	—
123	C₂³×#117	C₂³	1	2	yes	—
124	#60511	D₄	1	16	yes	complemented
125	#60444	D₄	1	8	yes	complemented
126	C₂×#3054	D₄	1	4	yes	complemented
127	C₂×#3050	D₄	1	4	yes	complemented
128	C₂×#3005	D₄	1	4	yes	complemented
129	C₂×#3005	D₄	1	4	yes	complemented
130	C₂×#3004	D₄	1	4	yes	complemented
131	C₂×#3003	D₄	1	4	yes	complemented
132	C₂×#2911	C₂³	1	1	yes	characteristic
133	C₂×#2911	C₂³	1	2	yes	—
134	C₂×#2911	C₂³	1	1	yes	characteristic
135	C₂×#2911	C₂³	1	1	yes	characteristic
136	C₂×#2911	C₂³	1	1	yes	characteristic
137	C₂×#2905	C₂³	1	1	yes	characteristic
138	C₂²×#421	C₂³	1	2	yes	—
139	C₂²×#421	C₂³	1	2	yes	—
140	C₂²×#421	C₂³	1	2	yes	—
141	C₂²×#421	C₂³	1	2	yes	—
142	C₂×#2896	C₂³	1	2	yes	—
143	C₂×#2896	C₂³	1	2	yes	—
144	C₂×#2896	C₂³	1	2	yes	—
145	C₂×#2896	C₂³	1	2	yes	—
146	C₂×#2896	C₂³	1	2	yes	—
147	C₂×#2896	C₂³	1	2	yes	—
148	C₂×#2896	C₂³	1	2	yes	—
149	C₂×#2896	C₂³	1	2	yes	—
150	C₂²×#413	C₂³	1	2	yes	—
151	C₂²×#410	C₂³	1	2	yes	—
152	C₂²×#410	C₂³	1	2	yes	—
153	C₂²×#410	C₂³	1	2	yes	—
154	C₂²×#410	C₂³	1	2	yes	—
155	C₂²×#410	C₂³	1	2	yes	—
156	C₂²×#410	C₂³	1	2	yes	—
157	C₂×#2879	C₂³	1	1	yes	characteristic
158	C₂²×#407	D₄	1	8	yes	complemented
159	C₂²×#407	C₂³	1	2	yes	—
160	C₂²×#407	C₂³	1	1	yes	characteristic
161	C₂²×#407	C₂³	1	2	yes	—
162	C₂²×#407	C₂³	1	2	yes	—
163	C₂²×#407	C₂³	1	2	yes	—
164	C₂²×#407	C₂³	1	1	yes	characteristic
165	C₂×#2873	C₂³	1	1	yes	characteristic
166	C₂×#2849	D₄	1	4	yes	—
167	C₂×#2849	D₄	1	2	yes	—
168	C₂×#2846	D₄	1	2	yes	—
169	#34044	C₂³	1	2	yes	—
170	#34044	C₂³	1	2	yes	—
171	C₂×#2280	C₂³	1	2	yes	—
172	C₂×#2280	C₂³	1	2	yes	—
173	C₂×#2280	C₂³	1	2	yes	—
174	C₂×#2280	C₂³	1	2	yes	—
175	C₂×#2280	C₂³	1	2	yes	—
176	C₂×#2280	C₂³	1	2	yes	—
177	C₂×#2280	C₂³	1	2	yes	—
178	C₂×#2280	C₂³	1	1	yes	characteristic
179	C₂²×#344	C₂³	1	2	yes	—
180	C₂²×#344	C₂³	1	2	yes	—
181	C₂²×#344	C₂³	1	2	yes	—
182	C₂²×#344	C₂³	1	2	yes	—
183	C₂×#1742	C₂³	1	2	yes	—
184	C₂×#1740	C₂³	1	2	yes	—
185	C₂×#1740	C₂³	1	2	yes	—
186	C₂×#1740	C₂³	1	2	yes	—
187	C₂×#1740	C₂³	1	2	yes	—
188	C₂×#1740	C₂³	1	2	yes	—
189	C₂×#1740	C₂³	1	2	yes	—
190	#20347	C₂³	1	2	yes	—
191	C₂×#1733	C₂³	1	2	yes	—
192	C₂×#1733	C₂³	1	2	yes	—
193	C₂×#1733	C₂³	1	2	yes	—
194	C₂×#1733	C₂³	1	2	yes	—
195	C₂×#1733	C₂³	1	2	yes	—
196	C₂×#1733	C₂³	1	2	yes	—
197	C₂×#1733	C₂³	1	2	yes	—
198	C₂×#1733	C₂³	1	2	yes	—
199	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	—
200	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	—
201	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	—
202	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	—
203	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	—
204	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
205	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
206	C₂⁷	C₂×D₄	1	1	yes	characteristic
207	C₂³×#41	C₂×D₄	1	2	yes	—
208	C₂³×#41	C₂×D₄	1	2	yes	—
209	C₂³×#41	C₂⁴	1	2	yes	—
210	C₂³×#41	C₂⁴	1	2	yes	—
211	C₂³×#41	C₂⁴	1	1	yes	characteristic
212	C₂⁴×Q₈	C₂×D₄	1	2	yes	—
213	C₂⁴×D₄	C₂×D₄	1	2	yes	—
214	C₂⁵×C₄	C₂×D₄	1	2	yes	—
215	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
216	C₂⁵×C₄	C₂×D₄	1	4	yes	—
217	C₂⁵×C₄	#41	1	4	yes	—
218	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
219	C₂⁵×C₄	C₂⁴	1	2	yes	—
220	C₂×#575	C₂×D₄	1	4	yes	—
221	C₂²×#137	C₂×D₄	1	4	yes	—
222	C₂²×#137	C₂×D₄	1	4	yes	—
223	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	4	yes	—
224	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	4	yes	—
225	C₂²×#135	C₂×D₄	1	4	yes	—
226	C₂³×M₁₆	C₂×D₄	1	4	yes	—
227	C₂³×M₁₆	C₂×D₄	1	4	yes	—
228	C₂³×M₁₆	C₂×D₄	1	4	yes	—
229	C₂³×M₁₆	C₂×D₄	1	2	yes	—
230	C₂³×M₁₆	C₂⁴	1	2	yes	—
231	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
232	C₂³×M₁₆	C₂⁴	1	2	yes	—
233	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
234	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
235	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
236	C₂⁴×C₈	C₂×D₄	1	2	yes	—
237	C₂×#525	C₂×D₄	1	4	yes	—
238	C₂×#525	C₂×D₄	1	4	yes	—
239	C₂×#525	C₂×D₄	1	8	yes	—
240	C₂×#525	C₂×D₄	1	4	yes	—
241	C₂×#525	C₂×D₄	1	4	yes	—
242	C₂×#525	C₂×D₄	1	8	yes	—
243	C₂²×#123	C₂×D₄	1	2	yes	—
244	C₂²×#123	C₂×D₄	1	4	yes	—
245	C₂²×#120	C₂×D₄	1	2	yes	—
246	C₂²×#120	C₂×D₄	1	4	yes	—
247	C₂²×#117	C₂×D₄	1	8	yes	—
248	C₂²×#117	C₂⁴	1	2	yes	—
249	C₂²×#117	C₂⁴	1	2	yes	—
250	C₂²×#117	C₂⁴	1	2	yes	—
251	C₂²×#117	C₂⁴	1	2	yes	—
252	C₂²×#117	C₂⁴	1	2	yes	—
253	C₂²×#117	C₂⁴	1	2	yes	—
254	C₂²×#117	C₂⁴	1	2	yes	—
255	C₂²×#117	C₂⁴	1	1	yes	characteristic
256	#2911	C₂×D₄	1	8	yes	—
257	#2911	C₂×D₄	1	4	yes	—
258	#2911	C₂×D₄	1	8	yes	—
259	C₂×#427	C₂×D₄	1	4	yes	—
260	#2896	C₂×D₄	1	8	yes	—
261	#2896	C₂×D₄	1	8	yes	—
262	#2896	C₂×D₄	1	8	yes	—
263	C₂×#419	C₂×D₄	1	4	yes	—
264	C₂×#419	C₂×D₄	1	4	yes	—
265	C₂×#418	C₂×D₄	1	4	yes	—
266	C₂×#418	C₂×D₄	1	4	yes	—
267	C₂×#416	C₂×D₄	1	8	yes	—
268	C₂×#407	C₂×D₄	1	8	yes	—
269	C₂×#407	C₂×D₄	1	4	yes	—
270	C₂×#407	C₂×D₄	1	4	yes	—
271	C₂×#407	C₂×D₄	1	8	yes	—
272	C₂×#407	C₂×D₄	1	8	yes	—
273	C₂×#381	C₂×D₄	1	4	yes	—
274	C₂×#381	C₂×D₄	1	2	yes	—
275	C₂×#379	C₂×D₄	1	4	yes	—
276	C₂×#379	C₂×D₄	1	2	yes	—
277	C₂⁶	#121	1	4	yes	—
278	C₂⁶	C₂²×D₄	1	2	yes	—
279	C₂⁶	C₂²×D₄	1	1	yes	characteristic
280	C₂²×#41	C₂²×D₄	1	4	yes	—
281	C₂²×#41	C₂²×D₄	1	4	yes	—
282	C₂²×#41	C₂²×D₄	1	4	yes	—
283	C₂²×#41	C₂²×D₄	1	4	yes	—
284	C₂³×Q₈	C₂²×D₄	1	2	yes	—
285	C₂³×Q₈	C₂²×D₄	1	2	yes	—
286	C₂³×Q₈	H(5,𝔽₂)	1	1	yes	characteristic
287	C₂³×D₄	C₂²×D₄	1	2	yes	—
288	C₂³×D₄	C₂²×D₄	1	2	yes	—
289	C₂³×D₄	C₂²×D₄	1	2	yes	—
290	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
291	C₂⁴×C₄	#121	1	8	yes	—
292	C₂⁴×C₄	#121	1	4	yes	—
293	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
294	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
295	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
296	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
297	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
298	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
299	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
300	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
301	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
302	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
303	C₂⁴×C₄	C₂×#41	1	4	yes	—
304	C₂⁴×C₄	C₂×#41	1	2	yes	—
305	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
306	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
307	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
308	C₂⁴×C₄	H(5,𝔽₂)	1	4	yes	—
309	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
310	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
311	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
312	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
313	C₂²×Q₁₆	#120	1	4	yes	complemented
314	C₂²×SD₁₆	#120	1	8	yes	complemented
315	C₂²×D₈	#120	1	4	yes	complemented
316	C₂²×M₁₆	#120	1	8	yes	complemented
317	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
318	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
319	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
320	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
321	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
322	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
323	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
324	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
325	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
326	C₂²×M₁₆	H(5,𝔽₂)	1	2	yes	—
327	C₂³×C₈	#120	1	8	yes	complemented
328	C₂³×C₈	C₂²×D₄	1	2	yes	—
329	C₂³×C₈	C₂²×D₄	1	2	yes	—
330	C₂³×C₈	H(5,𝔽₂)	1	2	yes	—
331	C₂×#117	C₂²×D₄	1	4	yes	—
332	C₂×#117	C₂²×D₄	1	4	yes	—
333	C₂×#117	C₂²×D₄	1	4	yes	—
334	C₂×#117	C₂²×D₄	1	4	yes	—
335	C₂×#117	C₂²×D₄	1	4	yes	—
336	C₂×#117	C₂²×D₄	1	4	yes	—
337	C₂×#117	H(5,𝔽₂)	1	2	yes	—
338	C₂×#117	H(5,𝔽₂)	1	2	yes	—
339	C₂²×C₄⋊C₄	H(5,𝔽₂)	1	4	yes	—
340	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
341	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
342	C₂²×C₄²	H(5,𝔽₂)	1	4	yes	—
343	#427	#120	1	16	yes	complemented
344	#419	#120	1	16	yes	complemented
345	#418	#120	1	16	yes	complemented
346	#407	#120	1	16	yes	complemented
347	#407	#120	1	16	yes	complemented
348	C₂⁵	C₂×#121	1	4	yes	—
349	C₂⁵	C₂×#121	1	2	yes	—
350	C₂⁵	#534	1	2	yes	—
351	C₂⁵	D₄²	1	1	yes	characteristic
352	C₂⁵	D₄²	1	2	yes	—
353	C₂⁵	D₄²	1	4	yes	—
354	C₂⁵	D₄²	1	2	yes	—
355	C₂⁵	D₄²	1	1	yes	characteristic
356	C₂⁵	D₄²	1	2	yes	—
357	C₂⁵	C₂³×D₄	1	1	yes	characteristic
358	C₂²×Q₈	C₂×#120	1	4	yes	—
359	C₂²×Q₈	C₂×#120	1	4	yes	—
360	C₂²×D₄	C₂×#120	1	4	yes	—
361	C₂²×D₄	C₂×#120	1	4	yes	—
362	C₂³×C₄	C₂×#120	1	4	yes	—
363	C₂³×C₄	C₂×#120	1	4	yes	—
364	C₂³×C₄	C₂×#120	1	2	yes	—
365	C₂³×C₄	C₂×#120	1	2	yes	—
366	C₂³×C₄	C₂×#121	1	4	yes	—
367	C₂³×C₄	C₂×#121	1	2	yes	—
368	C₂³×C₄	#534	1	2	yes	—
369	C₂³×C₄	#535	1	4	yes	—
370	C₂³×C₄	#535	1	2	yes	—
371	C₂³×C₄	#535	1	2	yes	—
372	C₂³×C₄	#535	1	4	yes	—
373	C₂³×C₄	D₄²	1	2	yes	—
374	C₂³×C₄	D₄²	1	4	yes	—
375	C₂³×C₄	D₄²	1	2	yes	—
376	C₂³×C₄	D₄²	1	1	yes	characteristic
377	C₂³×C₄	D₄²	1	1	yes	characteristic
378	C₂³×C₄	D₄²	1	2	yes	—
379	C₂³×C₄	#546	1	4	yes	—
380	C₂³×C₄	#546	1	4	yes	—
381	C₂³×C₄	#546	1	4	yes	—
382	C₂³×C₄	#546	1	2	yes	—
383	C₂³×C₄	#546	1	2	yes	—
384	C₂³×C₄	#546	1	2	yes	—
385	C₂³×C₄	#546	1	2	yes	—
386	C₂³×C₄	#546	1	4	yes	—
387	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
388	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
389	C₂³×C₄	C₂³×D₄	1	2	yes	—
390	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
391	C₂³×C₄	C₂³×D₄	1	2	yes	—
392	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
393	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
394	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
395	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
396	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
397	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
398	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
399	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
400	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
401	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
402	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
403	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
404	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
405	C₂³×C₄	#585	1	1	yes	characteristic
406	C₂³×C₄	#585	1	1	yes	characteristic
407	C₂³×C₄	#585	1	2	yes	—
408	C₂³×C₄	#585	1	2	yes	—
409	C₂×M₁₆	C₂×#120	1	8	yes	—
410	C₂×M₁₆	C₂×#120	1	8	yes	—
411	C₂×M₁₆	C₂×#120	1	8	yes	—
412	C₂²×C₈	C₂×#120	1	4	yes	—
413	C₂²×C₈	C₂×#120	1	4	yes	—
414	C₂²×C₈	C₂×#120	1	4	yes	—
415	C₂²×C₈	C₂×#120	1	4	yes	—
416	#117	C₂×#120	1	8	yes	—
417	#117	C₂×#120	1	8	yes	—
418	C₂×C₂²⋊C₄	#534	1	4	yes	—
419	C₂⁴	#2408	1	2	yes	—
420	C₂⁴	#2408	1	4	yes	—
421	C₂⁴	#2408	1	4	yes	—
422	C₂⁴	#2408	1	2	yes	—
423	C₂⁴	C₂²×#121	1	1	yes	characteristic
424	C₂⁴	C₂×#534	1	1	yes	characteristic
425	C₂⁴	C₂×#534	1	1	yes	characteristic
426	C₂⁴	C₂×D₄²	1	2	yes	—
427	C₂⁴	C₂×D₄²	1	1	yes	characteristic
428	C₂⁴	C₂×D₄²	1	2	yes	—
429	C₂⁴	C₂×D₄²	1	1	yes	characteristic
430	C₂⁴	#3484	1	2	yes	—
431	C₂⁴	#3485	1	2	yes	—
432	C₂⁴	#3496	1	1	yes	characteristic
433	C₂⁴	#3496	1	1	yes	characteristic
434	C₂²×C₄	#2408	1	4	yes	—
435	C₂²×C₄	#2408	1	4	yes	—
436	C₂²×C₄	#2408	1	2	yes	—
437	C₂²×C₄	#2408	1	2	yes	—
438	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
439	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
440	C₂²×C₄	C₂²×#120	1	2	yes	—
441	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
442	C₂²×C₄	C₂²×#120	1	2	yes	—
443	C₂²×C₄	C₂×#535	1	2	yes	—
444	C₂²×C₄	C₂×#535	1	1	yes	characteristic
445	C₂²×C₄	#3459	1	1	yes	characteristic
446	C₂²×C₄	#3459	1	1	yes	characteristic
447	C₂²×C₄	C₂×#546	1	2	yes	—
448	C₂²×C₄	C₂×#546	1	2	yes	—
449	C₂²×C₄	C₂×#546	1	1	yes	characteristic
450	C₂²×C₄	C₂×#546	1	1	yes	characteristic
451	C₂²×C₄	#3484	1	2	yes	—
452	C₂²×C₄	#3484	1	2	yes	—
453	C₂²×C₄	#3484	1	2	yes	—
454	C₂²×C₄	#3484	1	2	yes	—
455	C₂²×C₄	#3484	1	2	yes	—
456	C₂²×C₄	#3484	1	1	yes	characteristic
457	C₂²×C₄	#3484	1	1	yes	characteristic
458	C₂²×C₄	#3484	1	1	yes	characteristic
459	C₂²×C₄	#3484	1	1	yes	characteristic
460	C₂²×C₄	#3484	1	1	yes	characteristic
461	C₂²×C₄	#3484	1	1	yes	characteristic
462	C₂²×C₄	#3484	1	1	yes	characteristic
463	C₂²×C₄	#3484	1	1	yes	characteristic
464	C₂²×C₄	#3484	1	1	yes	characteristic
465	C₂²×C₄	#3484	1	2	yes	—
466	C₂²×C₄	#3484	1	2	yes	—
467	C₂²×C₄	#3484	1	2	yes	—
468	C₂²×C₄	#3484	1	1	yes	characteristic
469	C₂²×C₄	#3485	1	1	yes	characteristic
470	C₂²×C₄	#3485	1	1	yes	characteristic
471	C₂²×C₄	#3485	1	2	yes	—
472	C₂²×C₄	#3488	1	2	yes	—
473	C₂²×C₄	#3488	1	2	yes	—
474	C₂²×C₄	#3488	1	2	yes	—
475	C₂²×C₄	#3488	1	1	yes	characteristic
476	C₂²×C₄	#3488	1	2	yes	—
477	C₂²×C₄	#3488	1	2	yes	—
478	C₂²×C₄	#3488	1	1	yes	characteristic
479	C₂²×C₄	#3488	1	1	yes	characteristic
480	C₂²×C₄	#3488	1	1	yes	characteristic
481	C₂²×C₄	#3490	1	1	yes	characteristic
482	C₂²×C₄	#3490	1	1	yes	characteristic
483	C₂²×C₄	#3496	1	2	yes	—
484	C₂²×C₄	#3496	1	2	yes	—
485	C₂²×C₄	#3496	1	2	yes	—
486	C₂²×C₄	#3496	1	2	yes	—
487	C₂²×C₄	#3496	1	2	yes	—
488	C₂²×C₄	#3496	1	2	yes	—
489	C₂²×C₄	#3496	1	2	yes	—
490	C₂²×C₄	#3498	1	2	yes	—
491	C₂²×C₄	#3498	1	1	yes	characteristic
492	C₂²×C₄	#3498	1	2	yes	—
493	C₂²×C₄	#3498	1	2	yes	—
494	C₂²×C₄	#3500	1	2	yes	—
495	C₂²×C₄	#3500	1	1	yes	characteristic
496	C₂²×C₄	#3505	1	2	yes	—
497	C₂²×C₄	#3505	1	2	yes	—
498	C₂²×C₄	#3532	1	2	yes	—
499	C₂²×C₄	#3532	1	2	yes	—
500	C₂²×C₄	#3532	1	2	yes	—
501	C₂²×C₄	#3533	1	2	yes	—
502	C₂²×C₄	#3534	1	2	yes	—
503	C₂²×C₄	#3534	1	2	yes	—
504	C₂²×C₄	#3534	1	1	yes	characteristic
505	C₂²×C₄	#3534	1	2	yes	—
506	C₂²×C₄	#3534	1	2	yes	—
507	C₂²×C₄	#3534	1	2	yes	—
508	C₂²×C₄	#3534	1	1	yes	characteristic
509	C₂²×C₄	#3534	1	1	yes	characteristic
510	C₂²×C₄	#3534	1	1	yes	characteristic
511	C₂²×C₄	#3537	1	2	yes	—
512	C₂²×C₄	#3537	1	1	yes	characteristic
513	C₂²×C₄	#3537	1	1	yes	characteristic
514	C₂²×C₄	#3537	1	1	yes	characteristic
515	C₂²×C₄	#3537	1	1	yes	characteristic
516	C₂²×C₄	#3542	1	2	yes	—
517	C₂²×C₄	#3542	1	2	yes	—
518	C₂²×C₄	#3542	1	2	yes	—
519	C₂²×C₄	#3542	1	2	yes	—
520	C₂²×C₄	#3543	1	2	yes	—
521	C₂²×C₄	#3543	1	2	yes	—
522	C₂²×C₄	#3543	1	2	yes	—
523	C₂²×C₄	#3545	1	2	yes	—
524	C₂²×C₄	#3558	1	2	yes	—
525	C₂²×C₄	#3560	1	2	yes	—
526	C₂×C₈	#2846	1	8	yes	—
527	C₂³	C₂×#2408	1	2	yes	—
528	C₂³	C₂×#2408	1	1	yes	characteristic
529	C₂³	#34981	1	1	yes	characteristic
530	C₂³	#34984	1	1	yes	characteristic
531	C₂³	#35358	1	2	yes	—
532	C₂³	D₄×#120	1	1	yes	characteristic
533	C₂³	D₄×#120	1	2	yes	—
534	C₂³	D₄×#120	1	1	yes	characteristic
535	C₂³	#37644	1	2	yes	—
536	C₂³	#37646	1	2	yes	—
537	C₂³	#37672	1	1	yes	characteristic
538	C₂³	#37672	1	1	yes	characteristic
539	C₂³	#37672	1	1	yes	characteristic
540	C₂³	#37672	1	1	yes	characteristic
541	C₂³	#39336	1	2	yes	—
542	C₂³	#39338	1	2	yes	—
543	C₂³	#42996	1	2	yes	—
544	C₂³	#43001	1	1	yes	characteristic
545	C₂³	#43017	1	2	yes	—
546	C₂³	#43023	1	2	yes	—
547	C₂³	#43492	1	1	yes	characteristic
548	C₂³	#43886	1	2	yes	—
549	C₂³	#43904	1	2	yes	—
550	C₂×C₄	#35222	1	1	yes	characteristic
551	C₂×C₄	#35222	1	2	yes	—
552	C₂×C₄	#35346	1	1	yes	characteristic
553	C₂×C₄	#35346	1	1	yes	characteristic
554	C₂×C₄	#35347	1	1	yes	characteristic
555	C₂×C₄	#35347	1	1	yes	characteristic
556	C₂×C₄	#35512	1	1	yes	characteristic
557	C₂×C₄	#35512	1	2	yes	—
558	C₂×C₄	#35512	1	1	yes	characteristic
559	C₂×C₄	#35513	1	2	yes	—
560	C₂×C₄	#35513	1	1	yes	characteristic
561	C₂×C₄	#35527	1	1	yes	characteristic
562	C₂×C₄	#35680	1	1	yes	characteristic
563	C₂×C₄	#35680	1	2	yes	—
564	C₂×C₄	#35680	1	2	yes	—
565	C₂×C₄	#35680	1	2	yes	—
566	C₂×C₄	#35680	1	2	yes	—
567	C₂×C₄	#35680	1	2	yes	—
568	C₂×C₄	#35750	1	1	yes	characteristic
569	C₂×C₄	#35750	1	2	yes	—
570	C₂×C₄	#36082	1	1	yes	characteristic
571	C₂×C₄	#36091	1	1	yes	characteristic
572	C₂×C₄	#36152	1	2	yes	—
573	C₂×C₄	#36152	1	1	yes	characteristic
574	C₂×C₄	#36152	1	1	yes	characteristic
575	C₂×C₄	C₂×#2846	1	1	yes	characteristic
576	C₂×C₄	#36717	1	1	yes	characteristic
577	C₂×C₄	#36721	1	1	yes	characteristic
578	C₂×C₄	#36739	1	2	yes	—
579	C₂×C₄	#37744	1	1	yes	characteristic
580	C₂×C₄	#37744	1	1	yes	characteristic
581	C₂×C₄	#37744	1	1	yes	characteristic
582	C₂×C₄	#37744	1	1	yes	characteristic
583	C₂×C₄	#37776	1	2	yes	—
584	C₂×C₄	#37778	1	2	yes	—
585	C₂×C₄	#39428	1	2	yes	—
586	C₂×C₄	#39430	1	2	yes	—
587	C₂×C₄	#40485	1	2	yes	—
588	C₂×C₄	#40485	1	2	yes	—
589	C₂×C₄	#40485	1	2	yes	—
590	C₂×C₄	#40509	1	2	yes	—
591	C₂×C₄	#42997	1	2	yes	—
592	C₂×C₄	#42997	1	2	yes	—
593	C₂×C₄	#43000	1	1	yes	characteristic
594	C₂×C₄	#43022	1	2	yes	—
595	C₂×C₄	#43491	1	1	yes	characteristic
596	C₂×C₄	#43932	1	2	yes	—
597	C₂×C₄	#43932	1	2	yes	—
598	C₂×C₄	#46350	1	2	yes	—
599	C₂×C₄	#46350	1	2	yes	—
600	C₂×C₄	#46351	1	2	yes	—
601	C₂×C₄	#46354	1	1	yes	characteristic
602	C₂×C₄	#46354	1	1	yes	characteristic
603	C₂×C₄	#46355	1	1	yes	characteristic
604	C₂×C₄	#46355	1	1	yes	characteristic
605	C₂×C₄	#46362	1	2	yes	—
606	C₂×C₄	#46364	1	2	yes	—
607	C₂×C₄	#46372	1	2	yes	—
608	C₂×C₄	#46413	1	2	yes	—
609	C₂×C₄	#46419	1	2	yes	—
610	C₂×C₄	#46419	1	2	yes	—
611	C₂×C₄	#46830	1	2	yes	—
612	C₂×C₄	#47826	1	2	yes	—
613	C₂×C₄	#47827	1	2	yes	—
614	C₂×C₄	#47830	1	2	yes	—
615	C₂×C₄	#47830	1	1	yes	characteristic
616	C₂×C₄	#47831	1	1	yes	characteristic
617	C₂×C₄	#47831	1	2	yes	—
618	C₂×C₄	#47846	1	2	yes	—
619	C₂×C₄	#47847	1	2	yes	—
620	C₂×C₄	#48776	1	1	yes	characteristic
621	C₂×C₄	#48777	1	1	yes	characteristic
622	C₂×C₄	#50634	1	2	yes	—
623	C₂×C₄	#50646	1	2	yes	—
624	C₂×C₄	#50647	1	2	yes	—
625	C₂×C₄	#50856	1	2	yes	—
626	C₂²	#612792	1	1	yes	characteristic
627	C₂²	#625760	1	1	yes	characteristic
628	C₂²	#686894	1	2	yes	—
629	C₂²	#687270	1	2	yes	—
630	C₂²	#763807	1	1	yes	characteristic
631	C₂²	#1082737	1	1	yes	characteristic
632	C₂²	#1082739	1	2	yes	—
633	C₂²	#1082741	1	1	yes	characteristic
634	C₂²	#1084729	1	2	yes	—
635	C₂²	#1084731	1	1	yes	characteristic
636	C₂²	#1084733	1	1	yes	characteristic
637	C₄	#1083750	1	1	yes	characteristic
638	C₄	#1083751	1	2	yes	—
639	C₄	#1083754	1	1	yes	characteristic
640	C₄	#1085253	1	2	yes	—
641	C₄	#1085256	1	1	yes	characteristic
642	C₄	#1085258	1	1	yes	characteristic
643	C₄	#4312298	1	2	yes	—
644	C₄	#4312301	1	2	yes	—
645	C₄	#4380236	1	1	yes	characteristic
646	C₄	#4380237	1	1	yes	characteristic
647	C₄	#4928938	1	1	yes	characteristic
648	C₄	#4929082	1	1	yes	characteristic
649	C₂	#72216320	1	2	yes	—
650	C₂	#72251017	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#46355
commutator, Frattini, cosocle	C₂⁴×C₄	C₂⁵
socle	C₂²	#1082737
LCS	G ▷ C₂⁴×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂⁴×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. #72262699	C₂	semidirect
2. #72256285	C₂	semidirect
3. #72256212	C₂	semidirect
4. #72256109	C₂	semidirect
5. #72256073	C₂	semidirect
6. #72255629	C₂	semidirect
7. #72252195	C₂	semidirect
8. C₂×#427241	C₂	semidirect
9. #72251324	C₂	semidirect
10. #72251207	C₂	semidirect
11. #72251122	C₂	semidirect
12. C₂×#10575416	C₂	semidirect
13. #72237713	C₂	semidirect
14. C₂×#395191	C₂	semidirect
15. #72237668	C₂	semidirect
16. #72237236	C₂	semidirect
17. #72237194	C₂	semidirect
18. #72236780	C₂	semidirect
19. C₂×#364416	C₂	semidirect
23. #10574916	C₂²	semidirect
29. C₂×#60141	C₂²	semidirect
32. #7628649	C₂²	semidirect
33. C₂×#23535	C₂²	semidirect
36. C₂×#23443	C₂²	semidirect
37. C₂×#23443	C₂²	semidirect
38. C₂×#23414	C₂²	semidirect
39. #6431722	C₂²	semidirect
40. C₂×#21244	C₂²	semidirect
41. C₂×#21009	C₂²	semidirect
42. C₂×#20989	C₂²	semidirect
43. C₂×#20983	C₂²	semidirect
44. C₂²×#1891	C₂²	semidirect
45. C₂×#20671	C₂²	semidirect
46. #6370810	C₂²	semidirect
47. C₂×#20605	C₂²	semidirect
48. #6370715	C₂²	semidirect
49. C₂×#20584	C₂²	semidirect
52. C₂×#11361	C₂²	semidirect
53. C₂×#11277	C₂²	semidirect
54. C₂×#11234	C₂²	semidirect
55. #357939	C₂²	semidirect
56. C₂×#11178	C₂²	semidirect
57. C₂×#11138	C₂²	semidirect
58. C₂×#11132	C₂²	semidirect
59. #357818	C₂²	semidirect
60. #357771	C₂²	semidirect
61. C₂×#11102	C₂²	semidirect
62. C₂×#11100	C₂²	semidirect
63. C₂×#11100	C₂²	semidirect
64. C₂×#11071	C₂²	semidirect
65. #357593	C₂²	semidirect
66. C₂×#11033	C₂²	semidirect
67. #357586	C₂²	semidirect
68. #357577	C₂²	semidirect
69. #357564	C₂²	semidirect
70. C₂×#11000	C₂²	semidirect
71. #357556	C₂²	semidirect
76. C₂×#10994	C₂²	semidirect
77. C₂×#10994	C₂²	semidirect
78. C₂×#10994	C₂²	semidirect
79. C₂×#10994	C₂²	semidirect
80. C₂×#10993	C₂²	semidirect
83. #357529	C₂²	semidirect
84. #357529	C₂²	semidirect
85. #357470	C₂²	semidirect
86. C₂×#10951	C₂²	semidirect
87. C₂×#10937	C₂²	semidirect
88. #353711	C₂²	semidirect
89. C₂×#10737	C₂²	semidirect
90. #353407	C₂²	semidirect
91. #353397	C₂²	semidirect
92. #353386	C₂²	semidirect
93. C₂×#10729	C₂²	semidirect
94. C₂×#10717	C₂²	semidirect
95. C₂×#10716	C₂²	semidirect
96. #123991	C₂²	semidirect
97. #123983	C₂²	semidirect
98. #123940	C₂²	semidirect
99. #123637	C₂²	semidirect
100. #123627	C₂²	semidirect
101. #123623	C₂²	semidirect
102. #123618	C₂²	semidirect
103. #123610	C₂²	semidirect
104. #123568	C₂²	semidirect
105. #123531	C₂²	semidirect
106. #123531	C₂²	semidirect
124. #60511	D₄	semidirect
125. #60444	D₄	semidirect
126. C₂×#3054	D₄	semidirect
127. C₂×#3050	D₄	semidirect
128. C₂×#3005	D₄	semidirect
129. C₂×#3005	D₄	semidirect
130. C₂×#3004	D₄	semidirect
131. C₂×#3003	D₄	semidirect
158. C₂²×#407	D₄	semidirect
313. C₂²×Q₁₆	#120	semidirect
314. C₂²×SD₁₆	#120	semidirect
315. C₂²×D₈	#120	semidirect
316. C₂²×M₁₆	#120	semidirect
327. C₂³×C₈	#120	semidirect
343. #427	#120	semidirect
344. #419	#120	semidirect
345. #418	#120	semidirect
346. #407	#120	semidirect
347. #407	#120	semidirect

Maximal subgroups

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

subgroup	index
#72262699	2
#72256285	2
#72256212	2
#72256109	2
#72256073	2
#72255629	2
#72252195	2
C₂×#427241	2
#72251324	2
#72251207	2
#72251122	2
C₂×#10575416	2
#72237713	2
C₂×#395191	2
#72237668	2
#72237236	2
#72237194	2
#72236780	2
C₂×#364416	2