Subgroups — #72240520

Order 2048.

At least 9362 conjugacy classes of subgroups; only the 1376 normal subgroups are shown.

The subgroup lattice has 576 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#417896	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#417969	C₂	1	2	yes	maximal, complemented
3	C₂×#432839	C₂	1	1	yes	maximal, characteristic, complemented
4	#72240512	C₂	1	2	yes	maximal, complemented
5	#72240511	C₂	1	2	yes	maximal, complemented
6	#72240511	C₂	1	1	yes	maximal, characteristic, complemented
7	#72240510	C₂	1	2	yes	maximal, complemented
8	#72240509	C₂	1	1	yes	maximal, characteristic, complemented
9	#72240508	C₂	1	2	yes	maximal, complemented
10	#72240508	C₂	1	2	yes	maximal, complemented
11	C₂×#392135	C₂	1	2	yes	maximal, complemented
12	#72240406	C₂	1	1	yes	maximal, characteristic, complemented
13	#72240404	C₂	1	2	yes	maximal, complemented
14	#72240400	C₂	1	2	yes	maximal, complemented
15	#72240398	C₂	1	2	yes	maximal, complemented
16	#72240193	C₂	1	2	yes	maximal, complemented
17	#72240192	C₂	1	2	yes	maximal, complemented
18	#72238873	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#6628896	C₂	1	1	yes	maximal, characteristic
20	C₂²×H(7,𝔽₂)	C₂²	1	1	yes	characteristic
21	C₂³×B(4,𝔽₂)	C₂²	1	2	yes	—
22	C₂³×B(4,𝔽₂)	C₂²	1	2	yes	—
23	C₂×#35367	C₂²	1	1	yes	characteristic, complemented
24	C₂×#35346	C₂²	1	1	yes	characteristic
25	C₂×#35346	C₂²	1	1	yes	characteristic
26	C₂×#35346	C₂²	1	1	yes	characteristic
27	C₂²×#2032	C₂²	1	2	yes	complemented
28	C₂²×#2032	C₂²	1	2	yes	complemented
29	C₂×#23468	C₂²	1	1	yes	characteristic, complemented
30	C₂×#23468	C₂²	1	1	yes	characteristic, complemented
31	C₂×#20609	C₂²	1	2	yes	—
32	C₂×#20609	C₂²	1	2	yes	—
33	C₂×#20609	C₂²	1	2	yes	—
34	C₂×#20609	C₂²	1	2	yes	—
35	C₂×#20609	C₂²	1	2	yes	—
36	C₂×#20609	C₂²	1	2	yes	—
37	C₂×#20609	C₂²	1	2	yes	—
38	C₂×#20609	C₂²	1	2	yes	—
39	C₂×#20609	C₂²	1	2	yes	—
40	C₂×#20609	C₂²	1	2	yes	—
41	C₂×#20585	C₂²	1	1	yes	characteristic
42	C₂×#20585	C₂²	1	2	yes	—
43	C₂×#20585	C₂²	1	2	yes	—
44	C₂×#20585	C₂²	1	1	yes	characteristic
45	C₂×#20585	C₂²	1	2	yes	—
46	C₂×#20585	C₂²	1	2	yes	—
47	C₂×#20585	C₂²	1	2	yes	—
48	C₂×#20585	C₂²	1	2	yes	—
49	C₂×#20585	C₂²	1	1	yes	characteristic
50	#5955309	C₂²	1	2	yes	complemented
51	#515326	C₂²	1	1	yes	characteristic, complemented
52	C₂×#11172	C₂²	1	2	yes	complemented
53	C₂×#11172	C₂²	1	2	yes	complemented
54	C₂×#11172	C₂²	1	2	yes	complemented
55	C₂×#11172	C₂²	1	2	yes	complemented
56	C₂×#11172	C₂²	1	2	yes	complemented
57	C₂×#11172	C₂²	1	2	yes	complemented
58	C₂×#11169	C₂²	1	2	yes	complemented
59	C₂×#11169	C₂²	1	2	yes	complemented
60	C₂×#11089	C₂²	1	2	yes	complemented
61	C₂×#11089	C₂²	1	2	yes	complemented
62	C₂×#11089	C₂²	1	2	yes	complemented
63	C₂×#11089	C₂²	1	2	yes	complemented
64	C₂×#11089	C₂²	1	2	yes	complemented
65	C₂×#11089	C₂²	1	2	yes	complemented
66	#357642	C₂²	1	1	yes	characteristic, complemented
67	#357642	C₂²	1	2	yes	complemented
68	#357642	C₂²	1	1	yes	characteristic, complemented
69	#357642	C₂²	1	2	yes	complemented
70	C₂×#10991	C₂²	1	2	yes	complemented
71	C₂×#10991	C₂²	1	2	yes	complemented
72	C₂×#10991	C₂²	1	2	yes	complemented
73	C₂×#10991	C₂²	1	2	yes	complemented
74	C₂×#10991	C₂²	1	2	yes	complemented
75	C₂×#10991	C₂²	1	2	yes	complemented
76	C₂×#10991	C₂²	1	2	yes	complemented
77	C₂×#10991	C₂²	1	2	yes	complemented
78	C₂×#10965	C₂²	1	2	yes	complemented
79	C₂×#10965	C₂²	1	1	yes	characteristic, complemented
80	C₂×#10965	C₂²	1	2	yes	complemented
81	C₂×#10965	C₂²	1	1	yes	characteristic, complemented
82	C₂×#10965	C₂²	1	2	yes	complemented
83	C₂×#10938	C₂²	1	1	yes	characteristic, complemented
84	C₂×#10938	C₂²	1	2	yes	complemented
85	C₂×#10938	C₂²	1	1	yes	characteristic, complemented
86	C₂×#10938	C₂²	1	2	yes	complemented
87	C₂×#10938	C₂²	1	2	yes	complemented
88	C₂×#10938	C₂²	1	1	yes	characteristic, complemented
89	C₂×#10938	C₂²	1	1	yes	characteristic, complemented
90	C₂×#10938	C₂²	1	2	yes	complemented
91	#123581	C₂²	1	2	yes	complemented
92	#123581	C₂²	1	2	yes	complemented
93	#123581	C₂²	1	2	yes	complemented
94	#123581	C₂²	1	2	yes	complemented
95	#123581	C₂²	1	2	yes	complemented
96	#123581	C₂²	1	2	yes	complemented
97	#123539	C₂²	1	2	yes	complemented
98	#123539	C₂²	1	2	yes	complemented
99	#123539	C₂²	1	2	yes	complemented
100	#123539	C₂²	1	2	yes	complemented
101	#123539	C₂²	1	2	yes	complemented
102	#123539	C₂²	1	2	yes	complemented
103	#123527	C₂²	1	2	yes	complemented
104	#123527	C₂²	1	2	yes	complemented
105	#123527	C₂²	1	2	yes	complemented
106	#123527	C₂²	1	2	yes	complemented
107	C₂³×H(5,𝔽₂)	C₂³	1	2	yes	—
108	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
109	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
110	C₂³×H(5,𝔽₂)	C₂³	1	2	yes	—
111	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
112	C₂²×#543	C₂³	1	1	yes	characteristic, complemented
113	C₂³×#120	C₂³	1	2	yes	—
114	C₂³×#120	C₂³	1	2	yes	—
115	C₂³×#120	C₂³	1	1	yes	characteristic
116	C₂³×#120	C₂³	1	1	yes	characteristic
117	C₂³×#120	C₂³	1	1	yes	characteristic
118	C₂³×#99	C₂³	1	2	yes	—
119	C₂³×#99	C₂³	1	2	yes	—
120	C₂³×#99	C₂³	1	2	yes	—
121	C₂³×#99	C₂³	1	2	yes	—
122	C₂³×#99	C₂³	1	2	yes	—
123	C₂³×#99	C₂³	1	2	yes	—
124	C₂³×#99	C₂³	1	2	yes	—
125	C₂³×#99	C₂³	1	2	yes	—
126	C₂³×#99	C₂³	1	2	yes	—
127	C₂³×#99	C₂³	1	2	yes	—
128	C₂³×#99	C₂³	1	2	yes	—
129	C₂³×#99	C₂³	1	2	yes	—
130	C₂³×#99	C₂³	1	2	yes	—
131	C₂³×#99	C₂³	1	2	yes	—
132	C₂³×#99	C₂³	1	2	yes	—
133	C₂³×#99	C₂³	1	2	yes	—
134	C₂³×#99	C₂³	1	2	yes	—
135	C₂³×#99	C₂³	1	2	yes	—
136	C₂³×#99	C₂³	1	2	yes	—
137	C₂³×#99	C₂³	1	2	yes	—
138	C₂³×#99	C₂³	1	2	yes	—
139	C₂³×#99	C₂³	1	2	yes	—
140	#35346	D₄	1	8	yes	—
141	C₂×#2315	C₂³	1	2	yes	complemented
142	C₂×#2315	C₂³	1	1	yes	characteristic, complemented
143	C₂×#2308	C₂³	1	2	yes	—
144	C₂×#2308	C₂³	1	2	yes	—
145	C₂×#2308	C₂³	1	2	yes	—
146	C₂×#2308	C₂³	1	2	yes	—
147	C₂×#2308	C₂³	1	2	yes	—
148	C₂×#2308	C₂³	1	2	yes	—
149	C₂×#2308	C₂³	1	1	yes	characteristic
150	C₂×#2308	C₂³	1	2	yes	—
151	C₂×#2308	C₂³	1	2	yes	—
152	C₂×#2308	C₂³	1	2	yes	—
153	C₂×#2308	C₂³	1	2	yes	—
154	C₂×#2308	C₂³	1	1	yes	characteristic
155	C₂×#2308	C₂³	1	1	yes	characteristic
156	C₂×#2308	C₂³	1	1	yes	characteristic
157	C₂×#2308	C₂³	1	2	yes	—
158	C₂×#2308	C₂³	1	2	yes	—
159	C₂×#2308	C₂³	1	2	yes	—
160	C₂×#2308	C₂³	1	2	yes	—
161	C₂×#2308	C₂³	1	1	yes	characteristic
162	C₂²×#379	C₂³	1	2	yes	complemented
163	C₂²×#379	C₂³	1	2	yes	complemented
164	C₂²×#379	C₂³	1	2	yes	complemented
165	C₂²×#379	C₂³	1	2	yes	complemented
166	C₂×#2273	C₂³	1	1	yes	characteristic, complemented
167	C₂×#2273	C₂³	1	1	yes	characteristic, complemented
168	#20609	D₄	1	16	yes	complemented
169	#20585	D₄	1	8	yes	—
170	C₂×#1782	D₄	1	4	yes	—
171	C₂×#1781	D₄	1	4	yes	—
172	C₂²×#342	C₂³	1	1	yes	characteristic, complemented
173	C₂²×#342	C₂³	1	2	yes	complemented
174	C₂²×#342	C₂³	1	2	yes	complemented
175	C₂²×#342	C₂³	1	2	yes	complemented
176	C₂²×#342	C₂³	1	2	yes	complemented
177	C₂²×#342	C₂³	1	2	yes	complemented
178	C₂²×#342	C₂³	1	2	yes	complemented
179	C₂²×#342	C₂³	1	2	yes	complemented
180	C₂²×#342	C₂³	1	2	yes	complemented
181	C₂²×#342	C₂³	1	2	yes	complemented
182	C₂²×#342	C₂³	1	2	yes	complemented
183	C₂²×#342	C₂³	1	2	yes	complemented
184	C₂²×#342	C₂³	1	2	yes	complemented
185	C₂²×#342	C₂³	1	2	yes	complemented
186	C₂²×#342	C₂³	1	2	yes	complemented
187	C₂²×#342	C₂³	1	2	yes	complemented
188	C₂²×#342	C₂³	1	2	yes	complemented
189	C₂²×#342	C₂³	1	2	yes	complemented
190	C₂²×#342	C₂³	1	1	yes	characteristic, complemented
191	C₂²×#342	C₂³	1	1	yes	characteristic, complemented
192	C₂²×#342	C₂³	1	1	yes	characteristic, complemented
193	C₂²×#342	C₂³	1	2	yes	complemented
194	C₂²×#342	C₂³	1	2	yes	complemented
195	C₂²×#342	C₂³	1	2	yes	complemented
196	C₂²×#342	C₂³	1	2	yes	complemented
197	C₂²×#342	C₂³	1	2	yes	complemented
198	#13794	C₂³	1	2	yes	complemented
199	C₂⁷	C₂⁴	1	1	yes	characteristic
200	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
201	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
202	C₂²×H(5,𝔽₂)	C₂×D₄	1	8	yes	—
203	C₂²×H(5,𝔽₂)	#41	1	8	yes	—
204	C₂³×#41	C₂×D₄	1	2	yes	—
205	C₂³×#41	#41	1	4	yes	—
206	C₂⁴×D₄	C₂×D₄	1	2	yes	—
207	C₂⁴×D₄	#41	1	4	yes	—
208	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
209	C₂⁴×D₄	C₂⁴	1	2	yes	—
210	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
211	C₂⁴×D₄	C₂⁴	1	2	yes	—
212	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
213	C₂²×#120	C₂×D₄	1	4	yes	—
214	C₂²×#120	C₂×D₄	1	4	yes	—
215	C₂²×#120	C₂×D₄	1	4	yes	—
216	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
217	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
218	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
219	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
220	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
221	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
222	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
223	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
224	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
225	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
226	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
227	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
228	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
229	C₂²×#99	C₂×D₄	1	8	yes	—
230	C₂²×#99	C₂×D₄	1	8	yes	—
231	C₂²×#99	C₂×D₄	1	8	yes	—
232	C₂²×#99	C₂×D₄	1	8	yes	—
233	C₂²×#99	C₂×D₄	1	8	yes	—
234	C₂²×#99	C₂×D₄	1	8	yes	—
235	C₂²×#99	C₂×D₄	1	8	yes	—
236	#2308	C₂×D₄	1	4	yes	—
237	#2308	C₂×D₄	1	8	yes	—
238	#2308	C₂×D₄	1	4	yes	—
239	#2308	C₂×D₄	1	4	yes	—
240	#2308	C₂×D₄	1	8	yes	—
241	#2308	C₂×D₄	1	8	yes	—
242	#2308	C₂×D₄	1	4	yes	—
243	#2308	C₂×D₄	1	4	yes	—
244	C₂×#381	C₂×D₄	1	2	yes	—
245	C₂×#381	C₂×D₄	1	2	yes	—
246	C₂×#379	C₂×D₄	1	2	yes	—
247	C₂×#379	C₂×D₄	1	2	yes	—
248	C₂⁶	#124	1	2	yes	complemented
249	C₂⁶	C₂²×D₄	1	2	yes	—
250	C₂⁶	C₂²×D₄	1	1	yes	characteristic
251	C₂⁶	C₂×#41	1	2	yes	—
252	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
253	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
254	C₂⁶	H(5,𝔽₂)	1	2	yes	—
255	C₂⁶	C₂⁵	1	1	yes	characteristic
256	C₂³×Q₈	#124	1	2	yes	complemented
257	C₂³×D₄	#124	1	4	yes	complemented
258	C₂³×D₄	#124	1	2	yes	complemented
259	C₂³×D₄	C₂²×D₄	1	2	yes	—
260	C₂³×D₄	C₂²×D₄	1	2	yes	—
261	C₂³×D₄	C₂²×D₄	1	4	yes	—
262	C₂³×D₄	C₂²×D₄	1	2	yes	—
263	C₂³×D₄	C₂²×D₄	1	2	yes	—
264	C₂³×D₄	C₂²×D₄	1	4	yes	—
265	C₂³×D₄	C₂²×D₄	1	4	yes	—
266	C₂³×D₄	C₂²×D₄	1	4	yes	—
267	C₂³×D₄	C₂²×D₄	1	4	yes	—
268	C₂³×D₄	C₂×#41	1	4	yes	—
269	C₂³×D₄	C₂×#41	1	4	yes	—
270	C₂³×D₄	C₂×#41	1	4	yes	—
271	C₂³×D₄	C₂×#41	1	4	yes	—
272	C₂³×D₄	C₂×#41	1	4	yes	—
273	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
274	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
275	C₂³×D₄	H(5,𝔽₂)	1	4	yes	—
276	C₂³×D₄	H(5,𝔽₂)	1	4	yes	—
277	C₂³×D₄	H(5,𝔽₂)	1	4	yes	—
278	C₂³×D₄	H(5,𝔽₂)	1	4	yes	—
279	C₂³×D₄	H(5,𝔽₂)	1	4	yes	—
280	C₂³×D₄	H(5,𝔽₂)	1	4	yes	—
281	C₂³×D₄	H(5,𝔽₂)	1	4	yes	—
282	C₂³×D₄	H(5,𝔽₂)	1	4	yes	—
283	C₂⁴×C₄	#124	1	2	yes	complemented
284	C₂⁴×C₄	#124	1	4	yes	complemented
285	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
286	C₂⁴×C₄	C₂×#41	1	2	yes	—
287	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
288	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
289	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
290	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
291	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
292	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
293	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
294	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
295	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
296	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
297	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
298	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
299	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
300	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
301	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
302	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
303	#381	#120	1	8	yes	—
304	#379	#120	1	8	yes	—
305	C₂⁵	C₂×#120	1	2	yes	—
306	C₂⁵	C₂×#124	1	2	yes	—
307	C₂⁵	C₂×#124	1	4	yes	—
308	C₂⁵	#534	1	2	yes	—
309	C₂⁵	#534	1	2	yes	—
310	C₂⁵	#535	1	4	yes	—
311	C₂⁵	#535	1	2	yes	—
312	C₂⁵	D₄²	1	2	yes	—
313	C₂⁵	#546	1	4	yes	—
314	C₂⁵	#546	1	4	yes	—
315	C₂⁵	#551	1	2	yes	—
316	C₂⁵	#551	1	4	yes	—
317	C₂⁵	H(3,𝔽₄)	1	4	yes	—
318	C₂⁵	H(3,𝔽₄)	1	2	yes	—
319	C₂⁵	H(3,𝔽₄)	1	2	yes	—
320	C₂⁵	C₂³×D₄	1	1	yes	characteristic
321	C₂⁵	C₂³×D₄	1	1	yes	characteristic
322	C₂⁵	C₂³×D₄	1	1	yes	characteristic
323	C₂⁵	C₂³×D₄	1	2	yes	—
324	C₂⁵	C₂²×#41	1	2	yes	—
325	C₂⁵	C₂²×#41	1	2	yes	—
326	C₂⁵	C₂×H(5,𝔽₂)	1	1	yes	characteristic
327	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
328	C₂⁵	C₂×H(5,𝔽₂)	1	1	yes	characteristic
329	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
330	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
331	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
332	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
333	C₂⁵	C₂×H(5,𝔽₂)	1	1	yes	characteristic
334	C₂⁵	C₂×H(5,𝔽₂)	1	1	yes	characteristic
335	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
336	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
337	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
338	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
339	C₂²×D₄	#525	1	8	yes	—
340	C₂²×D₄	#534	1	8	yes	—
341	C₂²×D₄	#535	1	8	yes	—
342	C₂²×D₄	#538	1	8	yes	—
343	C₂²×D₄	#538	1	8	yes	—
344	C₂²×D₄	#538	1	8	yes	—
345	C₂²×D₄	D₄²	1	8	yes	—
346	C₂²×D₄	D₄²	1	8	yes	—
347	C₂²×D₄	D₄²	1	8	yes	—
348	C₂²×D₄	#546	1	8	yes	—
349	C₂²×D₄	#546	1	8	yes	—
350	C₂²×D₄	#546	1	8	yes	—
351	C₂²×D₄	#546	1	8	yes	—
352	C₂²×D₄	#546	1	8	yes	—
353	C₂³×C₄	C₂×#120	1	2	yes	—
354	C₂³×C₄	C₂×#124	1	2	yes	—
355	C₂³×C₄	C₂×#124	1	4	yes	—
356	C₂³×C₄	#534	1	2	yes	—
357	C₂³×C₄	#534	1	2	yes	—
358	C₂³×C₄	#535	1	4	yes	—
359	C₂³×C₄	#535	1	2	yes	—
360	C₂³×C₄	D₄²	1	2	yes	—
361	C₂³×C₄	#546	1	4	yes	—
362	C₂³×C₄	#546	1	4	yes	—
363	C₂³×C₄	#551	1	2	yes	—
364	C₂³×C₄	#551	1	4	yes	—
365	C₂³×C₄	H(3,𝔽₄)	1	4	yes	—
366	C₂³×C₄	H(3,𝔽₄)	1	2	yes	—
367	C₂³×C₄	H(3,𝔽₄)	1	2	yes	—
368	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
369	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
370	C₂⁴	#2435	1	4	yes	—
371	C₂⁴	#2472	1	8	yes	—
372	C₂⁴	#2670	1	8	yes	—
373	C₂⁴	#2679	1	4	yes	—
374	C₂⁴	#2684	1	4	yes	—
375	C₂⁴	C₂²×#120	1	1	yes	characteristic
376	C₂⁴	C₂×#525	1	2	yes	—
377	C₂⁴	C₂²×#124	1	1	yes	characteristic
378	C₂⁴	C₂×#534	1	2	yes	—
379	C₂⁴	C₂×#534	1	1	yes	characteristic
380	C₂⁴	C₂×#534	1	1	yes	characteristic
381	C₂⁴	C₂×#535	1	2	yes	—
382	C₂⁴	C₂×#535	1	1	yes	characteristic
383	C₂⁴	C₂×#535	1	2	yes	—
384	C₂⁴	C₂×#538	1	2	yes	—
385	C₂⁴	C₂×#538	1	2	yes	—
386	C₂⁴	C₂×#538	1	2	yes	—
387	C₂⁴	C₂×D₄²	1	1	yes	characteristic
388	C₂⁴	C₂×D₄²	1	2	yes	—
389	C₂⁴	C₂×D₄²	1	2	yes	—
390	C₂⁴	C₂×D₄²	1	2	yes	—
391	C₂⁴	C₂×#546	1	2	yes	—
392	C₂⁴	C₂×#546	1	2	yes	—
393	C₂⁴	C₂×#546	1	2	yes	—
394	C₂⁴	C₂×#546	1	2	yes	—
395	C₂⁴	C₂×#546	1	2	yes	—
396	C₂⁴	C₂×#546	1	2	yes	—
397	C₂⁴	C₂×#546	1	2	yes	—
398	C₂⁴	C₂×#551	1	1	yes	characteristic
399	C₂⁴	C₂×#551	1	2	yes	—
400	C₂⁴	#3484	1	2	yes	—
401	C₂⁴	#3484	1	2	yes	—
402	C₂⁴	#3484	1	1	yes	characteristic
403	C₂⁴	#3484	1	1	yes	characteristic
404	C₂⁴	#3484	1	2	yes	—
405	C₂⁴	#3484	1	2	yes	—
406	C₂⁴	#3484	1	2	yes	—
407	C₂⁴	#3484	1	1	yes	characteristic
408	C₂⁴	#3484	1	2	yes	—
409	C₂⁴	#3484	1	2	yes	—
410	C₂⁴	#3484	1	1	yes	characteristic
411	C₂⁴	#3484	1	2	yes	—
412	C₂⁴	#3484	1	2	yes	—
413	C₂⁴	#3484	1	2	yes	—
414	C₂⁴	#3484	1	1	yes	characteristic
415	C₂⁴	#3484	1	2	yes	—
416	C₂⁴	#3484	1	2	yes	—
417	C₂⁴	#3484	1	2	yes	—
418	C₂⁴	#3484	1	1	yes	characteristic
419	C₂⁴	#3490	1	2	yes	—
420	C₂⁴	#3490	1	2	yes	—
421	C₂⁴	#3490	1	2	yes	—
422	C₂⁴	#3490	1	2	yes	—
423	C₂⁴	#3490	1	2	yes	—
424	C₂⁴	#3490	1	2	yes	—
425	C₂⁴	#3490	1	2	yes	—
426	C₂⁴	#3490	1	2	yes	—
427	C₂⁴	#3490	1	2	yes	—
428	C₂⁴	#3490	1	2	yes	—
429	C₂⁴	#3490	1	2	yes	—
430	C₂⁴	#3490	1	2	yes	—
431	C₂⁴	#3490	1	2	yes	—
432	C₂⁴	#3490	1	2	yes	—
433	C₂⁴	C₂×H(3,𝔽₄)	1	2	yes	—
434	C₂⁴	C₂×H(3,𝔽₄)	1	1	yes	characteristic
435	C₂⁴	C₂×H(3,𝔽₄)	1	1	yes	characteristic
436	C₂⁴	#3532	1	2	yes	—
437	C₂⁴	#3532	1	2	yes	—
438	C₂⁴	#3532	1	2	yes	—
439	C₂⁴	#3532	1	2	yes	—
440	C₂⁴	#3532	1	1	yes	characteristic
441	C₂⁴	#3532	1	2	yes	—
442	C₂⁴	#3532	1	1	yes	characteristic
443	C₂⁴	#3532	1	2	yes	—
444	C₂⁴	#3532	1	2	yes	—
445	C₂⁴	#3532	1	2	yes	—
446	C₂⁴	#3532	1	2	yes	—
447	C₂⁴	#3532	1	2	yes	—
448	C₂⁴	#3532	1	2	yes	—
449	C₂⁴	#3532	1	2	yes	—
450	C₂⁴	#3532	1	2	yes	—
451	C₂⁴	#3532	1	2	yes	—
452	C₂⁴	#3532	1	2	yes	—
453	C₂⁴	#3532	1	1	yes	characteristic
454	C₂⁴	#3532	1	2	yes	—
455	C₂⁴	#3532	1	2	yes	—
456	C₂⁴	#3532	1	2	yes	—
457	C₂⁴	#3532	1	2	yes	—
458	C₂⁴	#3532	1	2	yes	—
459	C₂⁴	#3532	1	2	yes	—
460	C₂⁴	#3532	1	2	yes	—
461	C₂⁴	#3532	1	1	yes	characteristic
462	C₂²×C₄	#2435	1	4	yes	—
463	C₂²×C₄	#2472	1	8	yes	—
464	C₂²×C₄	#2670	1	8	yes	—
465	C₂²×C₄	#2679	1	4	yes	—
466	C₂²×C₄	#2684	1	4	yes	—
467	C₂³	C₂×#2472	1	2	yes	—
468	C₂³	C₂×#2435	1	1	yes	characteristic
469	C₂³	#34980	1	1	yes	characteristic
470	C₂³	#34988	1	2	yes	—
471	C₂³	#35050	1	2	yes	—
472	C₂³	#35222	1	1	yes	characteristic
473	C₂³	#35367	1	1	yes	characteristic
474	C₂³	#35367	1	2	yes	—
475	C₂³	#35367	1	1	yes	characteristic
476	C₂³	D₄×#120	1	2	yes	—
477	C₂³	#36098	1	2	yes	—
478	C₂³	#36098	1	2	yes	—
479	C₂³	#36098	1	2	yes	—
480	C₂³	#36152	1	2	yes	—
481	C₂³	#36158	1	2	yes	—
482	C₂³	#36702	1	1	yes	characteristic
483	C₂³	#36702	1	2	yes	—
484	C₂³	#36703	1	1	yes	characteristic
485	C₂³	#36703	1	1	yes	characteristic
486	C₂³	#36703	1	2	yes	—
487	C₂³	#36703	1	2	yes	—
488	C₂³	#36714	1	1	yes	characteristic
489	C₂³	#36725	1	2	yes	—
490	C₂³	#36725	1	2	yes	—
491	C₂³	#36725	1	2	yes	—
492	C₂³	#36725	1	2	yes	—
493	C₂³	#37644	1	2	yes	—
494	C₂³	#37644	1	2	yes	—
495	C₂³	#37644	1	2	yes	—
496	C₂³	#37645	1	2	yes	—
497	C₂³	#37645	1	2	yes	—
498	C₂³	#37645	1	2	yes	—
499	C₂³	#37645	1	2	yes	—
500	C₂³	#37645	1	2	yes	—
501	C₂³	#37660	1	2	yes	—
502	C₂³	#37660	1	2	yes	—
503	C₂³	#37660	1	2	yes	—
504	C₂³	#37660	1	2	yes	—
505	C₂³	#37660	1	2	yes	—
506	C₂³	#37660	1	2	yes	—
507	C₂³	#37660	1	2	yes	—
508	C₂³	#37660	1	2	yes	—
509	C₂³	#37832	1	2	yes	—
510	C₂³	#37832	1	2	yes	—
511	C₂³	#37832	1	2	yes	—
512	C₂³	#37832	1	2	yes	—
513	C₂³	#37832	1	2	yes	—
514	C₂³	#37833	1	2	yes	—
515	C₂³	#37833	1	2	yes	—
516	C₂³	#37833	1	2	yes	—
517	C₂³	#37833	1	2	yes	—
518	C₂³	#37833	1	2	yes	—
519	C₂³	#37848	1	2	yes	—
520	C₂³	#37848	1	2	yes	—
521	C₂³	#37848	1	2	yes	—
522	C₂³	#37848	1	2	yes	—
523	C₂³	#45439	1	1	yes	characteristic
524	C₂³	#45439	1	2	yes	—
525	C₂³	#45439	1	1	yes	characteristic
526	C₂³	#45439	1	1	yes	characteristic
527	C₂³	#45439	1	2	yes	—
528	C₂³	#45439	1	2	yes	—
529	C₂³	#45439	1	2	yes	—
530	C₂³	#45439	1	1	yes	characteristic
531	C₂³	#45458	1	2	yes	—
532	C₂³	#45458	1	2	yes	—
533	C₂³	#45458	1	2	yes	—
534	C₂³	#45458	1	2	yes	—
535	C₂³	#45458	1	2	yes	—
536	C₂³	#45458	1	2	yes	—
537	C₂³	C₂×#2670	1	2	yes	—
538	C₂³	C₂×#2679	1	1	yes	characteristic
539	C₂³	C₂×#2684	1	1	yes	characteristic
540	C₂³	#53158	1	2	yes	—
541	C₂³	#53158	1	2	yes	—
542	C₂³	#53158	1	2	yes	—
543	C₂³	#53158	1	2	yes	—
544	C₂³	#58990	1	1	yes	characteristic
545	C₂³	#58990	1	1	yes	characteristic
546	C₂³	#58991	1	2	yes	—
547	C₂³	#58991	1	2	yes	—
548	C₂³	#58991	1	2	yes	—
549	C₂³	#58991	1	2	yes	—
550	C₂³	#59006	1	1	yes	characteristic
551	C₂³	#59006	1	1	yes	characteristic
552	C₂³	#59006	1	2	yes	—
553	C₂³	#59006	1	2	yes	—
554	C₂²	#617169	1	2	yes	—
555	C₂²	#617534	1	1	yes	characteristic
556	C₂²	#648053	1	1	yes	characteristic
557	C₂²	#648387	1	2	yes	—
558	C₂²	#845297	1	1	yes	characteristic
559	C₂²	#845298	1	2	yes	—
560	C₂²	#845689	1	2	yes	—
561	C₂²	#845690	1	2	yes	—
562	C₂²	#846389	1	1	yes	characteristic
563	C₂²	#850557	1	2	yes	—
564	C₂²	#850883	1	2	yes	—
565	C₂²	#2032000	1	2	yes	—
566	C₂²	#2032000	1	2	yes	—
567	C₂²	#2032000	1	2	yes	—
568	C₂²	#2032088	1	1	yes	characteristic
569	C₂²	#2032505	1	2	yes	—
570	C₂²	#2032565	1	2	yes	—
571	C₂²	#2032565	1	1	yes	characteristic
572	C₂²	#5020751	1	1	yes	characteristic
573	C₂	#72210026	1	2	yes	—
574	C₂	#72210048	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#5020751
commutator, Frattini, cosocle	C₂⁶	C₂⁵
prime radical	C₂×#6628896	C₂
LCS	G ▷ C₂⁶ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁶ ◁ G
LECS	G ▷ C₂⁶ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#417896	C₂	semidirect
2. C₂×#417969	C₂	semidirect
3. C₂×#432839	C₂	semidirect
4. #72240512	C₂	semidirect
5. #72240511	C₂	semidirect
6. #72240511	C₂	semidirect
7. #72240510	C₂	semidirect
8. #72240509	C₂	semidirect
9. #72240508	C₂	semidirect
10. #72240508	C₂	semidirect
11. C₂×#392135	C₂	semidirect
12. #72240406	C₂	semidirect
13. #72240404	C₂	semidirect
14. #72240400	C₂	semidirect
15. #72240398	C₂	semidirect
16. #72240193	C₂	semidirect
17. #72240192	C₂	semidirect
18. #72238873	C₂	semidirect
23. C₂×#35367	C₂²	semidirect
27. C₂²×#2032	C₂²	semidirect
28. C₂²×#2032	C₂²	semidirect
29. C₂×#23468	C₂²	semidirect
30. C₂×#23468	C₂²	semidirect
50. #5955309	C₂²	semidirect
51. #515326	C₂²	semidirect
52. C₂×#11172	C₂²	semidirect
53. C₂×#11172	C₂²	semidirect
54. C₂×#11172	C₂²	semidirect
55. C₂×#11172	C₂²	semidirect
56. C₂×#11172	C₂²	semidirect
57. C₂×#11172	C₂²	semidirect
58. C₂×#11169	C₂²	semidirect
59. C₂×#11169	C₂²	semidirect
60. C₂×#11089	C₂²	semidirect
61. C₂×#11089	C₂²	semidirect
62. C₂×#11089	C₂²	semidirect
63. C₂×#11089	C₂²	semidirect
64. C₂×#11089	C₂²	semidirect
65. C₂×#11089	C₂²	semidirect
66. #357642	C₂²	semidirect
67. #357642	C₂²	semidirect
68. #357642	C₂²	semidirect
69. #357642	C₂²	semidirect
70. C₂×#10991	C₂²	semidirect
71. C₂×#10991	C₂²	semidirect
72. C₂×#10991	C₂²	semidirect
73. C₂×#10991	C₂²	semidirect
74. C₂×#10991	C₂²	semidirect
75. C₂×#10991	C₂²	semidirect
76. C₂×#10991	C₂²	semidirect
77. C₂×#10991	C₂²	semidirect
78. C₂×#10965	C₂²	semidirect
79. C₂×#10965	C₂²	semidirect
80. C₂×#10965	C₂²	semidirect
81. C₂×#10965	C₂²	semidirect
82. C₂×#10965	C₂²	semidirect
83. C₂×#10938	C₂²	semidirect
84. C₂×#10938	C₂²	semidirect
85. C₂×#10938	C₂²	semidirect
86. C₂×#10938	C₂²	semidirect
87. C₂×#10938	C₂²	semidirect
88. C₂×#10938	C₂²	semidirect
89. C₂×#10938	C₂²	semidirect
90. C₂×#10938	C₂²	semidirect
91. #123581	C₂²	semidirect
92. #123581	C₂²	semidirect
93. #123581	C₂²	semidirect
94. #123581	C₂²	semidirect
95. #123581	C₂²	semidirect
96. #123581	C₂²	semidirect
97. #123539	C₂²	semidirect
98. #123539	C₂²	semidirect
99. #123539	C₂²	semidirect
100. #123539	C₂²	semidirect
101. #123539	C₂²	semidirect
102. #123539	C₂²	semidirect
103. #123527	C₂²	semidirect
104. #123527	C₂²	semidirect
105. #123527	C₂²	semidirect
106. #123527	C₂²	semidirect
112. C₂²×#543	C₂³	semidirect
141. C₂×#2315	C₂³	semidirect
142. C₂×#2315	C₂³	semidirect
162. C₂²×#379	C₂³	semidirect
163. C₂²×#379	C₂³	semidirect
164. C₂²×#379	C₂³	semidirect
165. C₂²×#379	C₂³	semidirect
166. C₂×#2273	C₂³	semidirect
167. C₂×#2273	C₂³	semidirect
168. #20609	D₄	semidirect
172. C₂²×#342	C₂³	semidirect
173. C₂²×#342	C₂³	semidirect
174. C₂²×#342	C₂³	semidirect
175. C₂²×#342	C₂³	semidirect
176. C₂²×#342	C₂³	semidirect
177. C₂²×#342	C₂³	semidirect
178. C₂²×#342	C₂³	semidirect
179. C₂²×#342	C₂³	semidirect
180. C₂²×#342	C₂³	semidirect
181. C₂²×#342	C₂³	semidirect
182. C₂²×#342	C₂³	semidirect
183. C₂²×#342	C₂³	semidirect
184. C₂²×#342	C₂³	semidirect
185. C₂²×#342	C₂³	semidirect
186. C₂²×#342	C₂³	semidirect
187. C₂²×#342	C₂³	semidirect
188. C₂²×#342	C₂³	semidirect
189. C₂²×#342	C₂³	semidirect
190. C₂²×#342	C₂³	semidirect
191. C₂²×#342	C₂³	semidirect
192. C₂²×#342	C₂³	semidirect
193. C₂²×#342	C₂³	semidirect
194. C₂²×#342	C₂³	semidirect
195. C₂²×#342	C₂³	semidirect
196. C₂²×#342	C₂³	semidirect
197. C₂²×#342	C₂³	semidirect
198. #13794	C₂³	semidirect
248. C₂⁶	#124	semidirect
256. C₂³×Q₈	#124	semidirect
257. C₂³×D₄	#124	semidirect
258. C₂³×D₄	#124	semidirect
283. C₂⁴×C₄	#124	semidirect
284. C₂⁴×C₄	#124	semidirect

Maximal subgroups

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

subgroup	index
C₂×#417896	2
C₂×#417969	2
C₂×#432839	2
#72240512	2
#72240511	2
#72240510	2
#72240509	2
#72240508	2
C₂×#392135	2
#72240406	2
#72240404	2
#72240400	2
#72240398	2
#72240193	2
#72240192	2
#72238873	2
C₂×#6628896	2