Subgroups — C₂×#16840569 #21460575

Order 7808.

1460 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14519824	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14519823	C₂	1	1	yes	maximal, characteristic, complemented
3	#16840569	C₂	1	16	yes	maximal, direct product factor
4	C₂×#14519809	C₂	1	2	yes	maximal, complemented
5	C₂×#14519807	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14519802	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#14519801	C₂	1	2	yes	maximal, complemented
8	C₂×#14519798	C₂	1	2	yes	maximal, complemented
9	C₂²×#11758190	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×SD₁₆×D₆₁	C₂	1	2	yes	maximal, complemented
11	C₂×#14519783	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
13	#14519824	—	2	4	no	—
14	#14519824	C₂²	1	8	yes	complemented
15	#14519823	—	2	4	no	—
16	#14519823	C₂²	1	8	yes	complemented
17	C₂×#11758226	C₂²	1	2	yes	—
18	C₂×#11758222	—	2	1	no	—
19	C₂×#11758222	—	2	1	no	—
20	C₂×#11758222	C₂²	1	1	yes	characteristic
21	C₂×#11758224	—	2	2	no	—
22	C₂×#11758224	C₂²	1	2	yes	complemented
23	C₂²×Dic₁₂₂	—	2	1	no	—
24	C₂²×Dic₁₂₂	C₂²	1	1	yes	characteristic, complemented
25	C₂×Q₈×D₆₁	C₂²	1	2	yes	complemented
26	C₂²×D₂₄₄	—	2	1	no	—
27	C₂²×D₂₄₄	C₂²	1	1	yes	characteristic
28	C₂×D₄×D₆₁	—	2	2	no	—
29	C₂×D₄×D₆₁	C₂²	1	2	yes	—
30	#14519809	C₂²	1	16	yes	complemented
31	#14519807	C₂²	1	8	yes	complemented
32	#14519802	C₂²	1	8	yes	complemented
33	#14519801	C₂²	1	16	yes	complemented
34	#14519798	C₂²	1	16	yes	complemented
35	C₂×#11758202	C₂²	1	2	yes	complemented
36	C₂×#11758190	C₂²	1	2	yes	complemented
37	C₂×#11758190	C₂²	1	2	yes	complemented
38	C₂×#11758190	C₂²	1	8	yes	complemented
39	C₂×#11758200	C₂²	1	2	yes	complemented
40	C₂×#11758201	C₂²	1	2	yes	complemented
41	SD₁₆×D₆₁	C₂²	1	16	yes	complemented
42	C₂×#11758199	C₂²	1	2	yes	complemented
43	#14519783	C₂²	1	8	yes	complemented
44	C₂×#11758194	C₂²	1	1	yes	characteristic, complemented
45	C₂×#11758189	C₂²	1	2	yes	complemented
46	C₂×C₈×D₆₁	C₂²	1	2	yes	complemented
47	C₂×#41×C₆₁	C₂²	1	1	yes	characteristic
48	C₂×#41×C₆₁	C₂²	1	1	yes	characteristic, complemented
49	#135×C₆₁	C₂²	1	8	yes	complemented
50	C₂×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
51	C₂×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
52	C₂×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
53	C₂×D₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
54	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
55	C₂³×D₆₁	—	2	1	no	—
56	C₂³×D₆₁	—	2	2	no	—
57	#41×C₆₁	—	2	2	no	—
58	#41×C₆₁	—	2	2	no	—
59	#41×C₆₁	C₂³	1	4	yes	—
60	#41×C₆₁	C₂³	1	4	yes	complemented
61	C₂×Q₈×C₆₁	C₂³	1	1	yes	characteristic
62	C₂×Q₈×C₆₁	C₂³	1	1	yes	characteristic
63	C₂×D₄×C₆₁	—	2	1	no	—
64	C₂×D₄×C₆₁	—	2	1	no	—
65	C₂×D₄×C₆₁	C₂³	1	1	yes	characteristic
66	C₂×D₄×C₆₁	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₆₁	—	2	1	no	—
68	C₂²×C₄×C₆₁	—	2	1	no	—
69	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊D₆₁	—	2	2	no	—
71	C₂×C₂²⋊D₆₁	—	2	2	no	—
72	C₂×C₂²⋊D₆₁	D₄	1	2	yes	—
73	C₂²×Dic₆₁	—	2	1	no	—
74	C₂²×Dic₆₁	—	2	2	no	—
75	#11758226	—	2	4	no	—
76	#11758226	C₂³	1	8	yes	—
77	Q₈×D₆₁	—	2	4	no	—
78	Q₈×D₆₁	C₂³	1	8	yes	complemented
79	#11758224	—	2	16	no	—
80	#11758224	—	2	4	no	—
81	#11758224	C₂³	1	8	yes	complemented
82	D₄×D₆₁	—	2	16	no	—
83	D₄×D₆₁	—	2	4	no	—
84	D₄×D₆₁	C₂³	1	8	yes	—
85	#11758222	—	2	8	no	—
86	#11758222	—	2	8	no	—
87	#11758222	D₄	1	4	yes	—
88	#11758222	C₂³	1	4	yes	—
89	C₂×D₂₄₄	—	2	2	no	—
90	C₂×D₂₄₄	—	2	1	no	—
91	C₂×D₂₄₄	—	2	2	no	—
92	C₂×D₂₄₄	—	2	8	no	—
93	C₂×D₂₄₄	D₄	1	1	yes	characteristic
94	C₂×D₂₄₄	C₂³	1	2	yes	—
95	C₂×D₂₄₄	C₂³	1	4	yes	—
96	C₂×C₄×D₆₁	—	2	2	no	—
97	C₂×C₄×D₆₁	—	2	2	no	—
98	C₂×C₄×D₆₁	C₂³	1	2	yes	—
99	C₂×Dic₁₂₂	—	2	1	no	—
100	C₂×Dic₁₂₂	—	2	2	no	—
101	C₂×Dic₁₂₂	—	2	2	no	—
102	C₂×Dic₁₂₂	—	2	8	no	—
103	C₂×Dic₁₂₂	D₄	1	1	yes	characteristic
104	C₂×Dic₁₂₂	C₂³	1	2	yes	—
105	C₂×Dic₁₂₂	C₂³	1	4	yes	complemented
106	Q₁₆×C₆₁	C₂³	1	4	yes	complemented
107	SD₁₆×C₆₁	C₂³	1	4	yes	complemented
108	SD₁₆×C₆₁	C₂³	1	4	yes	complemented
109	D₈×C₆₁	C₂³	1	4	yes	complemented
110	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
111	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
112	C₂×C₈×C₆₁	C₂³	1	4	yes	complemented
113	#11758202	C₂³	1	8	yes	complemented
114	#11758201	C₂³	1	8	yes	complemented
115	#11758200	C₂³	1	8	yes	complemented
116	#11758199	C₂³	1	8	yes	complemented
117	#11758194	C₂³	1	4	yes	complemented
118	C₂×#92418	C₂³	1	2	yes	—
119	#11758190	C₂³	1	8	yes	complemented
120	#11758190	C₂³	1	8	yes	complemented
121	#11758189	C₂³	1	8	yes	complemented
122	C₈×D₆₁	C₂³	1	8	yes	complemented
123	C₂³×C₆₁	—	2	1	no	—
124	C₂³×C₆₁	—	2	1	no	—
125	C₂³×C₆₁	C₂×D₄	1	1	yes	characteristic
126	C₂²×D₆₁	—	2	2	no	—
127	C₂²×D₆₁	—	2	4	no	—
128	C₂²×D₆₁	—	2	8	no	—
129	C₂²×D₆₁	—	8	4	no	—
130	C₂²×D₆₁	—	8	2	no	—
131	C₂²×D₆₁	C₂×D₄	1	2	yes	—
132	Q₈×C₆₁	—	2	1	no	—
133	Q₈×C₆₁	—	2	1	no	—
134	Q₈×C₆₁	C₂⁴	1	2	yes	—
135	Q₈×C₆₁	C₂⁴	1	2	yes	—
136	D₄×C₆₁	—	2	4	no	—
137	D₄×C₆₁	—	2	4	no	—
138	D₄×C₆₁	—	2	1	no	—
139	D₄×C₆₁	—	2	1	no	—
140	D₄×C₆₁	C₂⁴	1	2	yes	—
141	D₄×C₆₁	C₂⁴	1	2	yes	—
142	C₂×C₄×C₆₁	—	2	1	no	—
143	C₂×C₄×C₆₁	—	2	1	no	—
144	C₂×C₄×C₆₁	—	2	4	no	—
145	C₂×C₄×C₆₁	—	2	4	no	—
146	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
147	C₂×C₄×C₆₁	C₂×D₄	1	2	yes	—
148	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
149	C₂×C₄×C₆₁	C₂⁴	1	2	yes	—
150	C₂²⋊D₆₁	—	2	8	no	—
151	C₂²⋊D₆₁	—	2	8	no	—
152	C₂²⋊D₆₁	C₂×D₄	1	8	yes	—
153	C₂×Dic₆₁	—	2	2	no	—
154	C₂×Dic₆₁	—	2	4	no	—
155	C₂×Dic₆₁	—	2	8	no	—
156	C₂×Dic₆₁	C₂×D₄	1	2	yes	—
157	D₂₄₄	—	2	8	no	—
158	D₂₄₄	—	2	4	no	—
159	D₂₄₄	—	2	2	no	—
160	D₂₄₄	C₂×D₄	1	4	yes	—
161	D₂₄₄	C₂⁴	1	4	yes	—
162	C₄×D₆₁	—	2	8	no	—
163	C₄×D₆₁	—	2	8	no	—
164	C₄×D₆₁	C₂×D₄	1	4	yes	—
165	C₄×D₆₁	C₂⁴	1	4	yes	—
166	Dic₁₂₂	—	2	4	no	—
167	Dic₁₂₂	—	2	2	no	—
168	Dic₁₂₂	—	2	8	no	—
169	Dic₁₂₂	C₂×D₄	1	4	yes	—
170	Dic₁₂₂	C₂⁴	1	4	yes	—
171	C₈×C₆₁	C₂⁴	1	2	yes	—
172	C₈×C₆₁	C₂⁴	1	2	yes	—
173	#92418	C₂⁴	1	4	yes	—
174	C₂²×C₆₁	—	2	2	no	—
175	C₂²×C₆₁	—	2	2	no	—
176	C₂²×C₆₁	—	2	2	no	—
177	C₂²×C₆₁	—	4	2	no	—
178	C₂²×C₆₁	—	4	2	no	—
179	C₂²×C₆₁	C₂²×D₄	1	2	yes	—
180	C₂²×C₆₁	C₂²×D₄	1	1	yes	characteristic
181	C₂×D₆₁	—	2	4	no	—
182	C₂×D₆₁	—	2	4	no	—
183	C₂×D₆₁	—	4	4	no	—
184	C₂×D₆₁	—	8	8	no	—
185	C₂×D₆₁	—	8	4	no	—
186	C₂×D₆₁	C₂²×D₄	1	4	yes	—
187	C₄×C₆₁	—	2	2	no	—
188	C₄×C₆₁	—	2	2	no	—
189	C₄×C₆₁	C₂²×D₄	1	2	yes	—
190	C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
191	C₄×C₆₁	C₂⁵	1	1	yes	characteristic
192	Dic₆₁	—	2	4	no	—
193	Dic₆₁	C₂²×D₄	1	4	yes	—
194	C₂×#577	—	61	1	no	maximal, Sylow
195	C₂×C₆₁	—	2	2	no	—
196	C₂×C₆₁	—	4	2	no	—
197	C₂×C₆₁	—	4	2	no	—
198	C₂×C₆₁	#577	1	2	yes	complemented
199	C₂×C₆₁	C₂³×D₄	1	1	yes	characteristic
200	D₆₁	—	2	4	no	—
201	D₆₁	—	4	4	no	—
202	C₂×2₋¹⁺⁴	—	61	1	no	—
203	C₂×H(5,𝔽₂)	—	61	1	no	—
204	#577	—	61	16	no	—
205	C₂×#137	—	61	1	no	—
206	C₂×#137	—	61	2	no	—
207	C₂×AGL(1,ℤ/8)	—	61	1	no	—
208	C₂×AGL(1,ℤ/8)	—	61	2	no	—
209	C₂×#135	—	61	2	no	—
210	C₂×#135	D₆₁	1	1	yes	characteristic, complemented
211	C₂²×SD₁₆	—	61	2	no	—
212	C₂²×SD₁₆	—	61	1	no	—
213	C₂×#131	—	61	1	no	—
214	C₆₁	C₂×#577	1	1	yes	characteristic, complemented, Sylow
215	2₋¹⁺⁴	—	61	8	no	—
216	2₋¹⁺⁴	—	122	4	no	—
217	H(5,𝔽₂)	—	61	8	no	—
218	H(5,𝔽₂)	—	122	4	no	—
219	C₂×#41	—	61	1	no	—
220	C₂×#41	—	61	2	no	—
221	C₂×#41	—	61	2	no	—
222	C₂×#41	—	122	1	no	—
223	C₂×#41	—	122	1	no	—
224	C₂×#41	—	122	2	no	—
225	C₂×#41	C₂×D₆₁	1	1	yes	characteristic
226	C₂×#41	C₂×D₆₁	1	1	yes	characteristic, complemented
227	C₂²×Q₈	—	61	2	no	—
228	C₂²×Q₈	—	61	1	no	—
229	C₂²×Q₈	—	122	1	no	—
230	C₂²×D₄	—	61	2	no	—
231	C₂²×D₄	—	61	1	no	—
232	C₂²×D₄	—	122	1	no	—
233	C₂²×D₄	—	122	2	no	—
234	#137	—	61	8	no	—
235	#137	—	61	16	no	—
236	AGL(1,ℤ/8)	—	61	8	no	—
237	AGL(1,ℤ/8)	—	61	16	no	—
238	#135	—	61	16	no	—
239	#135	C₂×D₆₁	1	8	yes	complemented
240	C₂×Q₁₆	—	61	2	no	—
241	C₂×Q₁₆	C₂×D₆₁	1	1	yes	characteristic, complemented
242	C₂×SD₁₆	—	61	2	no	—
243	C₂×SD₁₆	—	61	2	no	—
244	C₂×SD₁₆	—	61	16	no	—
245	C₂×SD₁₆	—	61	2	no	—
246	C₂×SD₁₆	—	61	2	no	—
247	C₂×SD₁₆	—	61	8	no	—
248	C₂×SD₁₆	C₂×D₆₁	1	1	yes	characteristic, complemented
249	C₂×SD₁₆	C₂×D₆₁	1	1	yes	characteristic, complemented
250	C₂×D₈	—	61	2	no	—
251	C₂×D₈	C₂×D₆₁	1	1	yes	characteristic, complemented
252	#131	—	61	8	no	—
253	C₂×M₁₆	—	61	1	no	—
254	C₂×M₁₆	—	61	2	no	—
255	C₂²×C₈	—	61	2	no	—
256	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic, complemented
257	C₂⁴	—	122	2	no	—
258	C₂⁴	—	122	1	no	—
259	#41	—	2	2	no	—
260	#41	—	2	2	no	—
261	#41	—	61	4	no	—
262	#41	—	61	4	no	—
263	#41	—	61	8	no	—
264	#41	—	61	8	no	—
265	#41	—	122	8	no	—
266	#41	—	122	8	no	—
267	#41	—	122	4	no	—
268	#41	—	122	4	no	—
269	#41	—	122	16	no	—
270	#41	C₂²×D₆₁	1	4	yes	—
271	#41	C₂²×D₆₁	1	4	yes	complemented
272	C₂×Q₈	—	61	1	no	—
273	C₂×Q₈	—	61	8	no	—
274	C₂×Q₈	—	61	2	no	—
275	C₂×Q₈	—	61	4	no	—
276	C₂×Q₈	—	122	2	no	—
277	C₂×Q₈	—	122	8	no	—
278	C₂×Q₈	—	122	4	no	—
279	C₂×Q₈	—	122	1	no	—
280	C₂×Q₈	—	122	2	no	—
281	C₂×Q₈	C₂²×D₆₁	1	1	yes	characteristic
282	C₂×Q₈	C₂²×D₆₁	1	1	yes	characteristic
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	—	61	2	no	—
286	C₂×D₄	—	61	8	no	—
287	C₂×D₄	—	61	1	no	—
288	C₂×D₄	—	61	2	no	—
289	C₂×D₄	—	61	4	no	—
290	C₂×D₄	—	122	8	no	—
291	C₂×D₄	—	122	2	no	—
292	C₂×D₄	—	122	4	no	—
293	C₂×D₄	—	122	2	no	—
294	C₂×D₄	—	122	16	no	—
295	C₂×D₄	—	122	2	no	—
296	C₂×D₄	—	122	1	no	—
297	C₂×D₄	—	122	2	no	—
298	C₂×D₄	C₂²×D₆₁	1	1	yes	characteristic
299	C₂×D₄	C₂²×D₆₁	1	1	yes	characteristic
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	61	2	no	—
303	C₂²×C₄	—	122	2	no	—
304	C₂²×C₄	—	122	2	no	—
305	C₂²×C₄	—	122	2	no	—
306	C₂²×C₄	—	122	1	no	—
307	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
308	Q₁₆	—	61	8	no	—
309	Q₁₆	C₂²×D₆₁	1	4	yes	complemented
310	SD₁₆	—	61	8	no	—
311	SD₁₆	—	61	8	no	—
312	SD₁₆	—	61	8	no	—
313	SD₁₆	—	61	8	no	—
314	SD₁₆	C₂²×D₆₁	1	4	yes	complemented
315	SD₁₆	C₂²×D₆₁	1	4	yes	complemented
316	D₈	—	61	8	no	—
317	D₈	C₂²×D₆₁	1	4	yes	complemented
318	M₁₆	—	61	4	no	—
319	M₁₆	—	61	8	no	—
320	C₂×C₈	—	61	2	no	—
321	C₂×C₈	—	61	8	no	—
322	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
323	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
324	C₂×C₈	C₂²×D₆₁	1	4	yes	complemented
325	C₂³	—	2	1	no	—
326	C₂³	—	2	1	no	—
327	C₂³	—	61	2	no	—
328	C₂³	—	122	8	no	—
329	C₂³	—	122	4	no	—
330	C₂³	—	122	2	no	—
331	C₂³	—	488	2	no	—
332	C₂³	—	488	4	no	—
333	C₂³	D₄×D₆₁	1	1	yes	characteristic
334	Q₈	—	2	1	no	—
335	Q₈	—	2	1	no	—
336	Q₈	—	61	4	no	—
337	Q₈	—	61	4	no	—
338	Q₈	—	122	8	no	—
339	Q₈	—	122	4	no	—
340	Q₈	—	122	2	no	—
341	Q₈	C₂³×D₆₁	1	2	yes	—
342	Q₈	C₂³×D₆₁	1	2	yes	—
343	D₄	—	2	4	no	—
344	D₄	—	2	4	no	—
345	D₄	—	2	1	no	—
346	D₄	—	2	1	no	—
347	D₄	—	61	8	no	—
348	D₄	—	61	4	no	—
349	D₄	—	61	4	no	—
350	D₄	—	122	8	no	—
351	D₄	—	122	8	no	—
352	D₄	—	122	8	no	—
353	D₄	—	122	4	no	—
354	D₄	—	122	2	no	—
355	D₄	C₂³×D₆₁	1	2	yes	—
356	D₄	C₂³×D₆₁	1	2	yes	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	61	2	no	—
362	C₂×C₄	—	61	4	no	—
363	C₂×C₄	—	61	4	no	—
364	C₂×C₄	—	122	8	no	—
365	C₂×C₄	—	122	8	no	—
366	C₂×C₄	—	122	8	no	—
367	C₂×C₄	—	122	4	no	—
368	C₂×C₄	—	122	2	no	—
369	C₂×C₄	D₄×D₆₁	1	2	yes	—
370	C₂×C₄	D₄×D₆₁	1	1	yes	characteristic
371	C₂×C₄	C₂³×D₆₁	1	2	yes	—
372	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
373	C₈	—	61	4	no	—
374	C₈	C₂³×D₆₁	1	2	yes	—
375	C₈	C₂³×D₆₁	1	2	yes	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	61	4	no	—
382	C₂²	—	122	4	no	—
383	C₂²	—	122	4	no	—
384	C₂²	—	488	4	no	—
385	C₂²	—	488	8	no	—
386	C₂²	—	244	4	no	—
387	C₂²	C₂×D₄×D₆₁	1	2	yes	—
388	C₂²	C₂×D₄×D₆₁	1	1	yes	characteristic
389	C₄	—	2	2	no	—
390	C₄	—	2	2	no	—
391	C₄	—	61	4	no	—
392	C₄	—	122	4	no	—
393	C₄	C₂×D₄×D₆₁	1	2	yes	—
394	C₄	C₂×D₄×D₆₁	1	1	yes	characteristic
395	C₄	C₂⁴×D₆₁	1	1	yes	characteristic
396	C₂	—	2	2	no	—
397	C₂	—	4	2	no	—
398	C₂	—	4	2	no	—
399	C₂	—	122	4	no	—
400	C₂	—	244	4	no	—
401	C₂	#16840569	1	2	yes	direct product factor
402	C₂	C₂²×D₄×D₆₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₆₁
commutator	C₄×C₆₁	C₂⁵
Frattini	C₄	C₂⁴×D₆₁
Fitting	C₂×#135×C₆₁	C₂
socle	C₂²×C₆₁	C₂²×D₄
hypercenter	C₂×#135	D₆₁
hypocenter	C₆₁	C₂×#577
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#135

Complements

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

N	H ≅ G/N	type
1. C₂×#14519824	C₂	semidirect
2. C₂×#14519823	C₂	semidirect
3. #16840569	C₂	direct (N × H)
4. C₂×#14519809	C₂	semidirect
5. C₂×#14519807	C₂	semidirect
6. C₂×#14519802	C₂	semidirect
7. C₂×#14519801	C₂	semidirect
8. C₂×#14519798	C₂	semidirect
9. C₂²×#11758190	C₂	semidirect
10. C₂×SD₁₆×D₆₁	C₂	semidirect
11. C₂×#14519783	C₂	semidirect
12. C₂×#135×C₆₁	C₂	semidirect
14. #14519824	C₂²	semidirect
16. #14519823	C₂²	semidirect
22. C₂×#11758224	C₂²	semidirect
24. C₂²×Dic₁₂₂	C₂²	semidirect
25. C₂×Q₈×D₆₁	C₂²	semidirect
30. #14519809	C₂²	semidirect
31. #14519807	C₂²	semidirect
32. #14519802	C₂²	semidirect
33. #14519801	C₂²	semidirect
34. #14519798	C₂²	semidirect
35. C₂×#11758202	C₂²	semidirect
36. C₂×#11758190	C₂²	semidirect
37. C₂×#11758190	C₂²	semidirect
38. C₂×#11758190	C₂²	semidirect
39. C₂×#11758200	C₂²	semidirect
40. C₂×#11758201	C₂²	semidirect
41. SD₁₆×D₆₁	C₂²	semidirect
42. C₂×#11758199	C₂²	semidirect
43. #14519783	C₂²	semidirect
44. C₂×#11758194	C₂²	semidirect
45. C₂×#11758189	C₂²	semidirect
46. C₂×C₈×D₆₁	C₂²	semidirect
48. C₂×#41×C₆₁	C₂²	semidirect
49. #135×C₆₁	C₂²	semidirect
50. C₂×Q₁₆×C₆₁	C₂²	semidirect
51. C₂×SD₁₆×C₆₁	C₂²	semidirect
52. C₂×SD₁₆×C₆₁	C₂²	semidirect
53. C₂×D₈×C₆₁	C₂²	semidirect
54. C₂²×C₈×C₆₁	C₂²	semidirect
60. #41×C₆₁	C₂³	semidirect
78. Q₈×D₆₁	C₂³	semidirect
81. #11758224	C₂³	semidirect
105. C₂×Dic₁₂₂	C₂³	semidirect
106. Q₁₆×C₆₁	C₂³	semidirect
107. SD₁₆×C₆₁	C₂³	semidirect
108. SD₁₆×C₆₁	C₂³	semidirect
109. D₈×C₆₁	C₂³	semidirect
112. C₂×C₈×C₆₁	C₂³	semidirect
113. #11758202	C₂³	semidirect
114. #11758201	C₂³	semidirect
115. #11758200	C₂³	semidirect
116. #11758199	C₂³	semidirect
117. #11758194	C₂³	semidirect
119. #11758190	C₂³	semidirect
120. #11758190	C₂³	semidirect
121. #11758189	C₂³	semidirect
122. C₈×D₆₁	C₂³	semidirect
198. C₂×C₆₁	#577	semidirect
210. C₂×#135	D₆₁	semidirect
214. C₆₁	C₂×#577	semidirect
226. C₂×#41	C₂×D₆₁	semidirect
239. #135	C₂×D₆₁	semidirect
241. C₂×Q₁₆	C₂×D₆₁	semidirect
248. C₂×SD₁₆	C₂×D₆₁	semidirect
249. C₂×SD₁₆	C₂×D₆₁	semidirect
251. C₂×D₈	C₂×D₆₁	semidirect
256. C₂²×C₈	C₂×D₆₁	semidirect
271. #41	C₂²×D₆₁	semidirect
309. Q₁₆	C₂²×D₆₁	semidirect
314. SD₁₆	C₂²×D₆₁	semidirect
315. SD₁₆	C₂²×D₆₁	semidirect
317. D₈	C₂²×D₆₁	semidirect
324. C₂×C₈	C₂²×D₆₁	semidirect
401. C₂	#16840569	direct (N × H)

Subgroups — C2×#16840569 #21460575

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16840569 #21460575