Subgroups — C₂×#30632328 #44563811

Order 32128.

1900 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#16860811	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₁₀₀₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#30632328	C₂	1	16	yes	maximal, direct product factor
4	C₂×#22548704	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#22548700	C₂	1	2	yes	maximal, complemented
6	C₂×#22548690	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#22548690	C₂	1	2	yes	maximal, complemented
8	C₂×#22548685	C₂	1	2	yes	maximal, complemented
9	C₂×#22548677	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄×C₂²⋊D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂²⋊C₄×D₂₅₁	C₂	1	2	yes	maximal, complemented
12	C₂×C₂²⋊Q₈×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁴×D₂₅₁	C₂²	1	2	yes	—
14	C₂×#16860811	—	2	8	no	—
15	C₂×#16860811	C₂²	1	8	yes	complemented
16	C₂²×D₁₀₀₄	—	2	8	no	—
17	C₂²×D₁₀₀₄	C₂²	1	2	yes	—
18	C₂²×D₁₀₀₄	C₂²	1	1	yes	characteristic
19	C₂²×D₁₀₀₄	C₂²	1	1	yes	characteristic
20	C₂²×D₁₀₀₄	C₂²	1	8	yes	complemented
21	C₂²×D₁₀₀₄	C₂²	1	2	yes	complemented
22	C₂²×D₁₀₀₄	C₂²	1	2	yes	complemented
23	C₂²×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
24	C₂²×C₄×D₂₅₁	C₂²	1	2	yes	complemented
25	C₂²×C₄×D₂₅₁	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₄×D₂₅₁	C₂²	1	2	yes	complemented
27	#22548704	C₂²	1	8	yes	complemented
28	#22548700	C₂²	1	16	yes	complemented
29	#22548690	C₂²	1	8	yes	complemented
30	#22548690	C₂²	1	16	yes	complemented
31	#22548685	C₂²	1	16	yes	complemented
32	#22548677	C₂²	1	8	yes	complemented
33	C₄×C₂²⋊D₂₅₁	C₂²	1	8	yes	complemented
34	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₂²⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
36	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	2	yes	complemented
37	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	2	yes	complemented
38	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	2	yes	complemented
39	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	2	yes	complemented
40	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
41	C₂²⋊C₄×D₂₅₁	C₂²	1	16	yes	complemented
42	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
43	C₂²×Q₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
44	C₂³×C₄×C₂₅₁	C₂²	1	1	yes	characteristic
45	C₂²⋊Q₈×C₂₅₁	C₂²	1	8	yes	complemented
46	C₂×C₄⋊C₄×C₂₅₁	C₂²	1	2	yes	complemented
47	C₂×C₄⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₂²⋊C₄×C₂₅₁	C₂²	1	2	yes	—
49	C₂³×D₂₅₁	—	2	8	no	—
50	C₂³×D₂₅₁	—	2	8	no	—
51	C₂³×D₂₅₁	—	4	4	no	—
52	C₂³×D₂₅₁	C₂³	1	1	yes	characteristic
53	C₂³×D₂₅₁	C₂³	1	2	yes	—
54	C₂³×D₂₅₁	C₂³	1	8	yes	—
55	C₂³×D₂₅₁	C₂³	1	2	yes	—
56	#16860811	—	2	32	no	—
57	C₂×D₁₀₀₄	—	2	8	no	—
58	C₂×D₁₀₀₄	—	2	8	no	—
59	C₂×D₁₀₀₄	—	2	32	no	—
60	C₂×D₁₀₀₄	—	2	4	no	—
61	C₂×D₁₀₀₄	—	4	4	no	—
62	C₂×D₁₀₀₄	D₄	1	8	yes	complemented
63	C₂×D₁₀₀₄	C₂³	1	8	yes	—
64	C₂×D₁₀₀₄	C₂³	1	4	yes	—
65	C₂×D₁₀₀₄	C₂³	1	4	yes	—
66	C₂×D₁₀₀₄	C₂³	1	8	yes	complemented
67	C₂×D₁₀₀₄	C₂³	1	8	yes	complemented
68	C₂×C₂²⋊D₂₅₁	—	2	4	no	—
69	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
70	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
71	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
72	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
73	C₂×C₄×D₂₅₁	—	2	8	no	—
74	C₂×C₄×D₂₅₁	—	2	4	no	—
75	C₂×C₄×D₂₅₁	—	4	4	no	—
76	C₂×C₄×D₂₅₁	C₂³	1	8	yes	complemented
77	C₂×C₄×D₂₅₁	C₂³	1	4	yes	complemented
78	C₂×C₄×D₂₅₁	C₂³	1	8	yes	complemented
79	Dic₂₅₁⋊C₄	C₂³	1	4	yes	complemented
80	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
81	(C₂×D₂₅₁)⋊C₄	C₂³	1	8	yes	complemented
82	(C₂×D₂₅₁)⋊C₄	C₂³	1	8	yes	complemented
83	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	complemented
84	(C₂×D₂₅₁)⋊C₄	C₂³	1	8	yes	complemented
85	(C₂×D₂₅₁)⋊C₄	C₂³	1	8	yes	complemented
86	C₄×Dic₂₅₁	C₂³	1	4	yes	complemented
87	C₂⁴×C₂₅₁	C₂³	1	1	yes	characteristic
88	C₂×Q₈×C₂₅₁	—	2	4	no	—
89	C₂×Q₈×C₂₅₁	C₂³	1	4	yes	complemented
90	C₂²×C₄×C₂₅₁	—	2	4	no	—
91	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
92	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
93	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
94	C₂²×C₄×C₂₅₁	C₂³	1	4	yes	—
95	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
96	C₄⋊C₄×C₂₅₁	C₂³	1	4	yes	complemented
97	C₄⋊C₄×C₂₅₁	C₂³	1	8	yes	complemented
98	C₂²⋊C₄×C₂₅₁	C₂³	1	8	yes	—
99	C₂²×D₂₅₁	—	2	4	no	—
100	C₂²×D₂₅₁	—	2	4	no	—
101	C₂²×D₂₅₁	—	2	2	no	—
102	C₂²×D₂₅₁	—	2	4	no	—
103	C₂²×D₂₅₁	—	2	2	no	—
104	C₂²×D₂₅₁	—	2	4	no	—
105	C₂²×D₂₅₁	—	2	16	no	—
106	C₂²×D₂₅₁	—	2	2	no	—
107	C₂²×D₂₅₁	—	2	4	no	—
108	C₂²×D₂₅₁	—	2	16	no	—
109	C₂²×D₂₅₁	—	4	8	no	—
110	C₂²×D₂₅₁	—	4	32	no	—
111	C₂²×D₂₅₁	C₂×D₄	1	8	yes	—
112	C₂²×D₂₅₁	C₂⁴	1	4	yes	—
113	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
114	C₂²×D₂₅₁	C₂⁴	1	4	yes	—
115	D₁₀₀₄	—	2	16	no	—
116	D₁₀₀₄	—	2	16	no	—
117	D₁₀₀₄	—	2	8	no	—
118	D₁₀₀₄	—	4	8	no	—
119	D₁₀₀₄	C₂×D₄	1	16	yes	complemented
120	C₂²⋊D₂₅₁	—	2	8	no	—
121	C₂×Dic₂₅₁	—	2	2	no	—
122	C₂×Dic₂₅₁	—	2	2	no	—
123	C₂×Dic₂₅₁	—	2	2	no	—
124	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
125	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
126	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
127	C₄×D₂₅₁	—	2	16	no	—
128	C₄×D₂₅₁	—	2	8	no	—
129	C₄×D₂₅₁	—	4	8	no	—
130	C₂³×C₂₅₁	—	2	2	no	—
131	C₂³×C₂₅₁	—	2	2	no	—
132	C₂³×C₂₅₁	#41	1	4	yes	complemented
133	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
134	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
135	Q₈×C₂₅₁	—	2	8	no	—
136	C₂×C₄×C₂₅₁	—	2	2	no	—
137	C₂×C₄×C₂₅₁	—	2	4	no	—
138	C₂×C₄×C₂₅₁	—	2	4	no	—
139	C₂×C₄×C₂₅₁	—	2	8	no	—
140	C₂×C₄×C₂₅₁	C₂×D₄	1	4	yes	—
141	C₂×C₄×C₂₅₁	C₂⁴	1	4	yes	—
142	C₂×C₄×C₂₅₁	C₂⁴	1	4	yes	—
143	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
144	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
145	C₂²×C₂₅₁	—	2	8	no	—
146	C₂²×C₂₅₁	—	2	2	no	—
147	C₂²×C₂₅₁	—	2	2	no	—
148	C₂²×C₂₅₁	C₂²×D₄	1	2	yes	—
149	C₂²×C₂₅₁	C₂×#41	1	2	yes	—
150	C₂²×C₂₅₁	C₂×#41	1	4	yes	complemented
151	C₂²×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
152	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
153	C₂×D₂₅₁	—	2	16	no	—
154	C₂×D₂₅₁	—	2	4	no	—
155	C₂×D₂₅₁	—	2	4	no	—
156	C₂×D₂₅₁	—	2	2	no	—
157	C₂×D₂₅₁	—	2	4	no	—
158	C₂×D₂₅₁	—	2	2	no	—
159	C₂×D₂₅₁	—	2	4	no	—
160	C₂×D₂₅₁	—	2	2	no	—
161	C₂×D₂₅₁	—	2	4	no	—
162	C₂×D₂₅₁	—	4	32	no	—
163	C₂×D₂₅₁	—	4	4	no	—
164	C₂×D₂₅₁	—	4	8	no	—
165	C₂×D₂₅₁	C₂²×D₄	1	8	yes	—
166	C₄×C₂₅₁	—	2	2	no	—
167	C₄×C₂₅₁	—	2	4	no	—
168	C₄×C₂₅₁	—	2	4	no	—
169	C₄×C₂₅₁	C₂²×D₄	1	4	yes	—
170	Dic₂₅₁	—	2	2	no	—
171	Dic₂₅₁	—	2	2	no	—
172	Dic₂₅₁	—	2	2	no	—
173	C₂×C₂₅₁	—	2	4	no	—
174	C₂×C₂₅₁	#546	1	4	yes	complemented
175	C₂×C₂₅₁	C₂³×D₄	1	1	yes	characteristic
176	C₂×C₂₅₁	C₂²×#41	1	1	yes	characteristic
177	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
178	D₂₅₁	—	2	8	no	—
179	D₂₅₁	—	4	2	no	—
180	D₂₅₁	—	4	4	no	—
181	C₂₅₁	C₂×#546	1	1	yes	characteristic, complemented, Sylow
182	C₂×#546	—	251	1	no	maximal, Sylow
183	C₂²×#41	—	251	1	no	—
184	C₂³×D₄	—	251	1	no	—
185	#546	—	251	16	no	—
186	C₂×#124	—	251	1	no	—
187	C₂×#123	—	251	2	no	—
188	C₂×C₂²⋊Q₈	D₂₅₁	1	1	yes	characteristic, complemented
189	C₂×#121	—	251	1	no	—
190	C₂×#121	—	251	2	no	—
191	C₂×#120	—	251	2	no	—
192	C₂×C₄×D₄	—	251	1	no	—
193	C₂×C₄×D₄	—	251	1	no	—
194	C₂²×C₂²⋊C₄	—	251	2	no	—
195	C₂⁵	—	251	2	no	—
196	C₂×#41	—	502	8	no	—
197	C₂×#41	—	251	8	no	—
198	C₂²×Q₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
199	C₂²×D₄	—	502	8	no	—
200	C₂²×D₄	—	251	1	no	—
201	C₂²×D₄	—	251	2	no	—
202	C₂²×D₄	—	251	2	no	—
203	C₂²×D₄	—	251	2	no	—
204	C₂²×D₄	—	251	1	no	—
205	C₂²×D₄	—	251	8	no	—
206	C₂²×D₄	—	251	1	no	—
207	C₂³×C₄	—	251	2	no	—
208	C₂³×C₄	—	251	2	no	—
209	C₂³×C₄	—	251	1	no	—
210	C₂³×C₄	C₂×D₂₅₁	1	1	yes	characteristic
211	#124	—	251	8	no	—
212	#123	—	251	16	no	—
213	C₂²⋊Q₈	C₂×D₂₅₁	1	8	yes	complemented
214	#121	—	251	8	no	—
215	#121	—	251	16	no	—
216	#120	—	251	16	no	—
217	C₄×D₄	—	251	8	no	—
218	C₄×D₄	—	251	8	no	—
219	C₂×C₄⋊C₄	—	251	1	no	—
220	C₂×C₄⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic, complemented
221	C₂×C₄⋊C₄	C₂×D₂₅₁	1	2	yes	complemented
222	C₂×C₂²⋊C₄	—	251	1	no	—
223	C₂×C₂²⋊C₄	—	251	2	no	—
224	C₂×C₂²⋊C₄	—	251	2	no	—
225	C₂×C₂²⋊C₄	—	251	2	no	—
226	C₂×C₂²⋊C₄	—	251	1	no	—
227	C₂×C₂²⋊C₄	—	251	2	no	—
228	C₂×C₂²⋊C₄	—	251	16	no	—
229	C₂×C₂²⋊C₄	C₂×D₂₅₁	1	2	yes	—
230	C₂×C₄²	—	251	1	no	—
231	C₂⁴	—	1004	4	no	—
232	C₂⁴	—	502	8	no	—
233	C₂⁴	—	502	8	no	—
234	C₂⁴	—	251	8	no	—
235	C₂⁴	—	251	2	no	—
236	C₂⁴	—	251	1	no	—
237	C₂⁴	—	251	2	no	—
238	C₂⁴	C₂²×D₂₅₁	1	1	yes	characteristic
239	#41	—	502	32	no	—
240	C₂×Q₈	—	2	4	no	—
241	C₂×Q₈	C₂²×D₂₅₁	1	4	yes	complemented
242	C₂×D₄	—	1004	4	no	—
243	C₂×D₄	—	502	8	no	—
244	C₂×D₄	—	502	8	no	—
245	C₂×D₄	—	502	32	no	—
246	C₂×D₄	—	502	4	no	—
247	C₂×D₄	—	502	4	no	—
248	C₂×D₄	—	251	4	no	—
249	C₂×D₄	—	251	8	no	—
250	C₂×D₄	—	251	8	no	—
251	C₂×D₄	—	251	8	no	—
252	C₂×D₄	—	251	8	no	—
253	C₂×D₄	—	251	4	no	—
254	C₂×D₄	—	251	4	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	1004	4	no	—
257	C₂²×C₄	—	502	8	no	—
258	C₂²×C₄	—	502	4	no	—
259	C₂²×C₄	—	251	8	no	—
260	C₂²×C₄	—	251	1	no	—
261	C₂²×C₄	—	251	1	no	—
262	C₂²×C₄	—	251	1	no	—
263	C₂²×C₄	—	251	8	no	—
264	C₂²×C₄	—	251	4	no	—
265	C₂²×C₄	C₂²×D₂₅₁	1	4	yes	—
266	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
267	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
268	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
269	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
270	C₄⋊C₄	—	251	4	no	—
271	C₄⋊C₄	C₂²×D₂₅₁	1	4	yes	complemented
272	C₄⋊C₄	C₂²×D₂₅₁	1	8	yes	complemented
273	C₂²⋊C₄	—	251	4	no	—
274	C₂²⋊C₄	—	251	8	no	—
275	C₂²⋊C₄	—	251	8	no	—
276	C₂²⋊C₄	—	251	8	no	—
277	C₂²⋊C₄	—	251	4	no	—
278	C₂²⋊C₄	—	251	8	no	—
279	C₂²⋊C₄	C₂²×D₂₅₁	1	8	yes	—
280	C₄²	—	251	4	no	—
281	C₂³	—	2	2	no	—
282	C₂³	—	2	2	no	—
283	C₂³	—	1004	32	no	—
284	C₂³	—	1004	8	no	—
285	C₂³	—	502	16	no	—
286	C₂³	—	502	2	no	—
287	C₂³	—	502	4	no	—
288	C₂³	—	502	2	no	—
289	C₂³	—	502	4	no	—
290	C₂³	—	502	16	no	—
291	C₂³	—	502	2	no	—
292	C₂³	—	502	4	no	—
293	C₂³	—	502	4	no	—
294	C₂³	—	502	4	no	—
295	C₂³	—	251	4	no	—
296	C₂³	—	251	2	no	—
297	C₂³	—	251	8	no	—
298	C₂³	—	251	4	no	—
299	C₂³	#16860811	1	4	yes	complemented
300	C₂³	C₂³×D₂₅₁	1	2	yes	—
301	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
302	Q₈	—	2	8	no	—
303	D₄	—	1004	8	no	—
304	D₄	—	502	16	no	—
305	D₄	—	502	16	no	—
306	D₄	—	502	8	no	—
307	D₄	—	502	8	no	—
308	D₄	—	251	16	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	8	no	—
313	C₂×C₄	—	1004	8	no	—
314	C₂×C₄	—	502	16	no	—
315	C₂×C₄	—	502	2	no	—
316	C₂×C₄	—	502	2	no	—
317	C₂×C₄	—	502	2	no	—
318	C₂×C₄	—	502	8	no	—
319	C₂×C₄	—	251	2	no	—
320	C₂×C₄	—	251	2	no	—
321	C₂×C₄	—	251	2	no	—
322	C₂×C₄	D₄×D₂₅₁	1	4	yes	—
323	C₂×C₄	C₂³×D₂₅₁	1	4	yes	—
324	C₂×C₄	C₂³×D₂₅₁	1	4	yes	—
325	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
326	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
327	C₂²	—	2	2	no	—
328	C₂²	—	2	2	no	—
329	C₂²	—	2	8	no	—
330	C₂²	—	1004	32	no	—
331	C₂²	—	1004	8	no	—
332	C₂²	—	1004	4	no	—
333	C₂²	—	502	2	no	—
334	C₂²	—	502	4	no	—
335	C₂²	—	502	2	no	—
336	C₂²	—	502	4	no	—
337	C₂²	—	502	2	no	—
338	C₂²	—	502	4	no	—
339	C₂²	—	502	4	no	—
340	C₂²	—	502	4	no	—
341	C₂²	—	502	16	no	—
342	C₂²	—	251	8	no	—
343	C₂²	C₂×D₄×D₂₅₁	1	2	yes	—
344	C₂²	C₂×#16860811	1	2	yes	—
345	C₂²	C₂×#16860811	1	4	yes	complemented
346	C₂²	#22548761	1	2	yes	—
347	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
348	C₄	—	2	2	no	—
349	C₄	—	2	4	no	—
350	C₄	—	2	4	no	—
351	C₄	—	502	2	no	—
352	C₄	—	502	2	no	—
353	C₄	—	502	2	no	—
354	C₄	C₂×D₄×D₂₅₁	1	4	yes	—
355	C₂	—	2	4	no	—
356	C₂	—	1004	4	no	—
357	C₂	—	1004	2	no	—
358	C₂	—	502	8	no	—
359	C₂	#30632328	1	4	yes	direct product factor
360	C₂	C₂²×D₄×D₂₅₁	1	1	yes	characteristic
361	C₂	C₂²×#16860811	1	1	yes	characteristic
362	C₂	C₂×#22548761	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₂₅₁
commutator, cosocle	C₂²×C₂₅₁	C₂⁵
Frattini	C₂²	C₂⁴×D₂₅₁
Fitting	C₂×C₂²⋊Q₈×C₂₅₁	C₂
socle	C₂³×C₂₅₁	C₂⁴
hypercenter	C₂×C₂²⋊Q₈	D₂₅₁
hypocenter	C₂₅₁	C₂×#546
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂²×#16860811	C₂	semidirect
2. C₂³×D₁₀₀₄	C₂	semidirect
3. #30632328	C₂	direct (N × H)
4. C₂×#22548704	C₂	semidirect
5. C₂×#22548700	C₂	semidirect
6. C₂×#22548690	C₂	semidirect
7. C₂×#22548690	C₂	semidirect
8. C₂×#22548685	C₂	semidirect
9. C₂×#22548677	C₂	semidirect
10. C₂×C₄×C₂²⋊D₂₅₁	C₂	semidirect
11. C₂×C₂²⋊C₄×D₂₅₁	C₂	semidirect
12. C₂×C₂²⋊Q₈×C₂₅₁	C₂	semidirect
15. C₂×#16860811	C₂²	semidirect
20. C₂²×D₁₀₀₄	C₂²	semidirect
21. C₂²×D₁₀₀₄	C₂²	semidirect
22. C₂²×D₁₀₀₄	C₂²	semidirect
24. C₂²×C₄×D₂₅₁	C₂²	semidirect
25. C₂²×C₄×D₂₅₁	C₂²	semidirect
26. C₂²×C₄×D₂₅₁	C₂²	semidirect
27. #22548704	C₂²	semidirect
28. #22548700	C₂²	semidirect
29. #22548690	C₂²	semidirect
30. #22548690	C₂²	semidirect
31. #22548685	C₂²	semidirect
32. #22548677	C₂²	semidirect
33. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
34. C₂×Dic₂₅₁⋊C₄	C₂²	semidirect
36. C₂×(C₂×D₂₅₁)⋊C₄	C₂²	semidirect
37. C₂×(C₂×D₂₅₁)⋊C₄	C₂²	semidirect
38. C₂×(C₂×D₂₅₁)⋊C₄	C₂²	semidirect
39. C₂×(C₂×D₂₅₁)⋊C₄	C₂²	semidirect
40. C₂×(C₂×D₂₅₁)⋊C₄	C₂²	semidirect
41. C₂²⋊C₄×D₂₅₁	C₂²	semidirect
42. C₂×C₄×Dic₂₅₁	C₂²	semidirect
43. C₂²×Q₈×C₂₅₁	C₂²	semidirect
45. C₂²⋊Q₈×C₂₅₁	C₂²	semidirect
46. C₂×C₄⋊C₄×C₂₅₁	C₂²	semidirect
47. C₂×C₄⋊C₄×C₂₅₁	C₂²	semidirect
62. C₂×D₁₀₀₄	D₄	semidirect
66. C₂×D₁₀₀₄	C₂³	semidirect
67. C₂×D₁₀₀₄	C₂³	semidirect
76. C₂×C₄×D₂₅₁	C₂³	semidirect
77. C₂×C₄×D₂₅₁	C₂³	semidirect
78. C₂×C₄×D₂₅₁	C₂³	semidirect
79. Dic₂₅₁⋊C₄	C₂³	semidirect
81. (C₂×D₂₅₁)⋊C₄	C₂³	semidirect
82. (C₂×D₂₅₁)⋊C₄	C₂³	semidirect
83. (C₂×D₂₅₁)⋊C₄	C₂³	semidirect
84. (C₂×D₂₅₁)⋊C₄	C₂³	semidirect
85. (C₂×D₂₅₁)⋊C₄	C₂³	semidirect
86. C₄×Dic₂₅₁	C₂³	semidirect
89. C₂×Q₈×C₂₅₁	C₂³	semidirect
96. C₄⋊C₄×C₂₅₁	C₂³	semidirect
97. C₄⋊C₄×C₂₅₁	C₂³	semidirect
119. D₁₀₀₄	C₂×D₄	semidirect
132. C₂³×C₂₅₁	#41	semidirect
150. C₂²×C₂₅₁	C₂×#41	semidirect
174. C₂×C₂₅₁	#546	semidirect
181. C₂₅₁	C₂×#546	semidirect
188. C₂×C₂²⋊Q₈	D₂₅₁	semidirect
198. C₂²×Q₈	C₂×D₂₅₁	semidirect
213. C₂²⋊Q₈	C₂×D₂₅₁	semidirect
220. C₂×C₄⋊C₄	C₂×D₂₅₁	semidirect
221. C₂×C₄⋊C₄	C₂×D₂₅₁	semidirect
241. C₂×Q₈	C₂²×D₂₅₁	semidirect
271. C₄⋊C₄	C₂²×D₂₅₁	semidirect
272. C₄⋊C₄	C₂²×D₂₅₁	semidirect
299. C₂³	#16860811	semidirect
345. C₂²	C₂×#16860811	semidirect
359. C₂	#30632328	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#16860811	2
C₂³×D₁₀₀₄	2
#30632328	2
C₂×#22548704	2
C₂×#22548700	2
C₂×#22548690	2
C₂×#22548685	2
C₂×#22548677	2
C₂×C₄×C₂²⋊D₂₅₁	2
C₂×C₂²⋊C₄×D₂₅₁	2
C₂×C₂²⋊Q₈×C₂₅₁	2
C₂×#546	251

Subgroups — C2×#30632328 #44563811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#30632328 #44563811