Subgroups — C₂×#31771412 #46825641

Order 34432.

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×#22575500	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#22575499	C₂	1	1	yes	maximal, characteristic, complemented
3	#31771412	C₂	1	16	yes	maximal, direct product factor
4	C₂×#22575485	C₂	1	2	yes	maximal, complemented
5	C₂×#22575483	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#22575478	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#22575477	C₂	1	2	yes	maximal, complemented
8	C₂×#22575474	C₂	1	2	yes	maximal, complemented
9	C₂²×#16864391	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×SD₁₆×D₂₆₉	C₂	1	2	yes	maximal, complemented
11	C₂×#22575459	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#22575500	—	2	4	no	—
14	#22575500	C₂²	1	8	yes	complemented
15	#22575499	—	2	4	no	—
16	#22575499	C₂²	1	8	yes	complemented
17	C₂×#16864403	C₂²	1	2	yes	—
18	C₂×#16864402	—	2	1	no	—
19	C₂×#16864402	—	2	1	no	—
20	C₂×#16864402	C₂²	1	1	yes	characteristic
21	C₂×#16864401	—	2	2	no	—
22	C₂×#16864401	C₂²	1	2	yes	complemented
23	C₂²×Dic₅₃₈	—	2	1	no	—
24	C₂²×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
25	C₂×Q₈×D₂₆₉	C₂²	1	2	yes	complemented
26	C₂²×D₁₀₇₆	—	2	1	no	—
27	C₂²×D₁₀₇₆	C₂²	1	1	yes	characteristic
28	C₂×D₄×D₂₆₉	—	2	2	no	—
29	C₂×D₄×D₂₆₉	C₂²	1	2	yes	—
30	#22575485	C₂²	1	16	yes	complemented
31	#22575483	C₂²	1	8	yes	complemented
32	#22575478	C₂²	1	8	yes	complemented
33	#22575477	C₂²	1	16	yes	complemented
34	#22575474	C₂²	1	16	yes	complemented
35	C₂×#16864392	C₂²	1	2	yes	complemented
36	C₂×#16864391	C₂²	1	2	yes	complemented
37	C₂×#16864391	C₂²	1	2	yes	complemented
38	C₂×#16864391	C₂²	1	8	yes	complemented
39	C₂×#16864390	C₂²	1	2	yes	complemented
40	C₂×#16864389	C₂²	1	2	yes	complemented
41	SD₁₆×D₂₆₉	C₂²	1	16	yes	complemented
42	C₂×#16864387	C₂²	1	2	yes	complemented
43	#22575459	C₂²	1	8	yes	complemented
44	C₂×#16864386	C₂²	1	1	yes	characteristic, complemented
45	C₂×#16864385	C₂²	1	2	yes	complemented
46	C₂×C₈×D₂₆₉	C₂²	1	2	yes	complemented
47	C₂×#41×C₂₆₉	C₂²	1	1	yes	characteristic
48	C₂×#41×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
49	#135×C₂₆₉	C₂²	1	8	yes	complemented
50	C₂×Q₁₆×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
51	C₂×SD₁₆×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
52	C₂×SD₁₆×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
53	C₂×D₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
54	C₂²×C₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
55	C₂³×D₂₆₉	—	2	2	no	—
56	C₂³×D₂₆₉	—	2	1	no	—
57	#16864403	—	2	4	no	—
58	#16864403	C₂³	1	8	yes	—
59	#16864402	—	2	8	no	—
60	#16864402	—	2	8	no	—
61	#16864402	D₄	1	4	yes	—
62	#16864402	C₂³	1	4	yes	—
63	#16864401	—	2	16	no	—
64	#16864401	—	2	4	no	—
65	#16864401	C₂³	1	8	yes	complemented
66	C₂×Dic₅₃₈	—	2	8	no	—
67	C₂×Dic₅₃₈	—	2	2	no	—
68	C₂×Dic₅₃₈	—	2	1	no	—
69	C₂×Dic₅₃₈	—	2	2	no	—
70	C₂×Dic₅₃₈	D₄	1	1	yes	characteristic
71	C₂×Dic₅₃₈	C₂³	1	2	yes	—
72	C₂×Dic₅₃₈	C₂³	1	4	yes	complemented
73	Q₈×D₂₆₉	—	2	4	no	—
74	Q₈×D₂₆₉	C₂³	1	8	yes	complemented
75	C₂×D₁₀₇₆	—	2	2	no	—
76	C₂×D₁₀₇₆	—	2	8	no	—
77	C₂×D₁₀₇₆	—	2	1	no	—
78	C₂×D₁₀₇₆	—	2	2	no	—
79	C₂×D₁₀₇₆	D₄	1	1	yes	characteristic
80	C₂×D₁₀₇₆	C₂³	1	2	yes	—
81	C₂×D₁₀₇₆	C₂³	1	4	yes	—
82	C₂×C₂²⋊D₂₆₉	—	2	2	no	—
83	C₂×C₂²⋊D₂₆₉	—	2	2	no	—
84	C₂×C₂²⋊D₂₆₉	D₄	1	2	yes	—
85	D₄×D₂₆₉	—	2	16	no	—
86	D₄×D₂₆₉	—	2	4	no	—
87	D₄×D₂₆₉	C₂³	1	8	yes	—
88	C₂²×Dic₂₆₉	—	2	2	no	—
89	C₂²×Dic₂₆₉	—	2	1	no	—
90	C₂×C₄×D₂₆₉	—	2	2	no	—
91	C₂×C₄×D₂₆₉	—	2	2	no	—
92	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
93	#16864392	C₂³	1	8	yes	complemented
94	#16864391	C₂³	1	8	yes	complemented
95	#16864391	C₂³	1	8	yes	complemented
96	#16864390	C₂³	1	8	yes	complemented
97	#16864389	C₂³	1	8	yes	complemented
98	#16864387	C₂³	1	8	yes	complemented
99	#16864386	C₂³	1	4	yes	complemented
100	#16864385	C₂³	1	8	yes	complemented
101	C₂×#14524130	C₂³	1	2	yes	—
102	C₈×D₂₆₉	C₂³	1	8	yes	complemented
103	#41×C₂₆₉	—	2	2	no	—
104	#41×C₂₆₉	—	2	2	no	—
105	#41×C₂₆₉	C₂³	1	4	yes	—
106	#41×C₂₆₉	C₂³	1	4	yes	complemented
107	C₂×Q₈×C₂₆₉	C₂³	1	1	yes	characteristic
108	C₂×Q₈×C₂₆₉	C₂³	1	1	yes	characteristic
109	C₂×D₄×C₂₆₉	—	2	1	no	—
110	C₂×D₄×C₂₆₉	—	2	1	no	—
111	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
112	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
113	C₂²×C₄×C₂₆₉	—	2	1	no	—
114	C₂²×C₄×C₂₆₉	—	2	1	no	—
115	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
116	Q₁₆×C₂₆₉	C₂³	1	4	yes	complemented
117	SD₁₆×C₂₆₉	C₂³	1	4	yes	complemented
118	SD₁₆×C₂₆₉	C₂³	1	4	yes	complemented
119	D₈×C₂₆₉	C₂³	1	4	yes	complemented
120	C₂×C₈×C₂₆₉	C₂³	1	1	yes	characteristic
121	C₂×C₈×C₂₆₉	C₂³	1	1	yes	characteristic
122	C₂×C₈×C₂₆₉	C₂³	1	4	yes	complemented
123	C₂²×D₂₆₉	—	2	2	no	—
124	C₂²×D₂₆₉	—	2	4	no	—
125	C₂²×D₂₆₉	—	2	8	no	—
126	C₂²×D₂₆₉	—	8	4	no	—
127	C₂²×D₂₆₉	—	8	2	no	—
128	C₂²×D₂₆₉	C₂×D₄	1	2	yes	—
129	Dic₅₃₈	—	2	2	no	—
130	Dic₅₃₈	—	2	4	no	—
131	Dic₅₃₈	—	2	8	no	—
132	Dic₅₃₈	C₂×D₄	1	4	yes	—
133	Dic₅₃₈	C₂⁴	1	4	yes	—
134	D₁₀₇₆	—	2	8	no	—
135	D₁₀₇₆	—	2	2	no	—
136	D₁₀₇₆	—	2	4	no	—
137	D₁₀₇₆	C₂×D₄	1	4	yes	—
138	D₁₀₇₆	C₂⁴	1	4	yes	—
139	C₂²⋊D₂₆₉	—	2	8	no	—
140	C₂²⋊D₂₆₉	—	2	8	no	—
141	C₂²⋊D₂₆₉	C₂×D₄	1	8	yes	—
142	C₂×Dic₂₆₉	—	2	2	no	—
143	C₂×Dic₂₆₉	—	2	4	no	—
144	C₂×Dic₂₆₉	—	2	8	no	—
145	C₂×Dic₂₆₉	C₂×D₄	1	2	yes	—
146	C₄×D₂₆₉	—	2	8	no	—
147	C₄×D₂₆₉	—	2	8	no	—
148	C₄×D₂₆₉	C₂×D₄	1	4	yes	—
149	C₄×D₂₆₉	C₂⁴	1	4	yes	—
150	#14524130	C₂⁴	1	4	yes	—
151	C₂³×C₂₆₉	—	2	1	no	—
152	C₂³×C₂₆₉	—	2	1	no	—
153	C₂³×C₂₆₉	C₂×D₄	1	1	yes	characteristic
154	Q₈×C₂₆₉	—	2	1	no	—
155	Q₈×C₂₆₉	—	2	1	no	—
156	Q₈×C₂₆₉	C₂⁴	1	2	yes	—
157	Q₈×C₂₆₉	C₂⁴	1	2	yes	—
158	D₄×C₂₆₉	—	2	4	no	—
159	D₄×C₂₆₉	—	2	4	no	—
160	D₄×C₂₆₉	—	2	1	no	—
161	D₄×C₂₆₉	—	2	1	no	—
162	D₄×C₂₆₉	C₂⁴	1	2	yes	—
163	D₄×C₂₆₉	C₂⁴	1	2	yes	—
164	C₂×C₄×C₂₆₉	—	2	1	no	—
165	C₂×C₄×C₂₆₉	—	2	1	no	—
166	C₂×C₄×C₂₆₉	—	2	4	no	—
167	C₂×C₄×C₂₆₉	—	2	4	no	—
168	C₂×C₄×C₂₆₉	C₂×D₄	1	1	yes	characteristic
169	C₂×C₄×C₂₆₉	C₂×D₄	1	2	yes	—
170	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
172	C₈×C₂₆₉	C₂⁴	1	2	yes	—
173	C₈×C₂₆₉	C₂⁴	1	2	yes	—
174	C₂²×C₂₆₉	—	2	2	no	—
175	C₂²×C₂₆₉	—	2	2	no	—
176	C₂²×C₂₆₉	—	2	2	no	—
177	C₂²×C₂₆₉	—	4	2	no	—
178	C₂²×C₂₆₉	—	4	2	no	—
179	C₂²×C₂₆₉	C₂²×D₄	1	2	yes	—
180	C₂²×C₂₆₉	C₂²×D₄	1	1	yes	characteristic
181	C₂×D₂₆₉	—	2	4	no	—
182	C₂×D₂₆₉	—	2	4	no	—
183	C₂×D₂₆₉	—	4	4	no	—
184	C₂×D₂₆₉	—	8	8	no	—
185	C₂×D₂₆₉	—	8	4	no	—
186	C₂×D₂₆₉	C₂²×D₄	1	4	yes	—
187	C₄×C₂₆₉	—	2	2	no	—
188	C₄×C₂₆₉	—	2	2	no	—
189	C₄×C₂₆₉	C₂²×D₄	1	2	yes	—
190	C₄×C₂₆₉	C₂²×D₄	1	1	yes	characteristic
191	C₄×C₂₆₉	C₂⁵	1	1	yes	characteristic
192	Dic₂₆₉	—	2	4	no	—
193	Dic₂₆₉	C₂²×D₄	1	4	yes	—
194	C₂×C₂₆₉	—	2	2	no	—
195	C₂×C₂₆₉	—	4	2	no	—
196	C₂×C₂₆₉	—	4	2	no	—
197	C₂×C₂₆₉	#577	1	2	yes	complemented
198	C₂×C₂₆₉	C₂³×D₄	1	1	yes	characteristic
199	D₂₆₉	—	2	4	no	—
200	D₂₆₉	—	4	4	no	—
201	C₂₆₉	C₂×#577	1	1	yes	characteristic, complemented, Sylow
202	C₂×#577	—	269	1	no	maximal, Sylow
203	C₂×2₋¹⁺⁴	—	269	1	no	—
204	C₂×H(5,𝔽₂)	—	269	1	no	—
205	#577	—	269	16	no	—
206	C₂×#137	—	269	1	no	—
207	C₂×#137	—	269	2	no	—
208	C₂×AGL(1,ℤ/8)	—	269	1	no	—
209	C₂×AGL(1,ℤ/8)	—	269	2	no	—
210	C₂×#135	—	269	2	no	—
211	C₂×#135	D₂₆₉	1	1	yes	characteristic, complemented
212	C₂²×SD₁₆	—	269	2	no	—
213	C₂²×SD₁₆	—	269	1	no	—
214	C₂×#131	—	269	1	no	—
215	2₋¹⁺⁴	—	269	8	no	—
216	2₋¹⁺⁴	—	538	4	no	—
217	H(5,𝔽₂)	—	269	8	no	—
218	H(5,𝔽₂)	—	538	4	no	—
219	C₂×#41	—	269	1	no	—
220	C₂×#41	—	269	2	no	—
221	C₂×#41	—	269	2	no	—
222	C₂×#41	—	538	1	no	—
223	C₂×#41	—	538	1	no	—
224	C₂×#41	—	538	2	no	—
225	C₂×#41	C₂×D₂₆₉	1	1	yes	characteristic
226	C₂×#41	C₂×D₂₆₉	1	1	yes	characteristic, complemented
227	C₂²×Q₈	—	269	2	no	—
228	C₂²×Q₈	—	269	1	no	—
229	C₂²×Q₈	—	538	1	no	—
230	C₂²×D₄	—	269	2	no	—
231	C₂²×D₄	—	269	1	no	—
232	C₂²×D₄	—	538	1	no	—
233	C₂²×D₄	—	538	2	no	—
234	#137	—	269	8	no	—
235	#137	—	269	16	no	—
236	AGL(1,ℤ/8)	—	269	8	no	—
237	AGL(1,ℤ/8)	—	269	16	no	—
238	#135	—	269	16	no	—
239	#135	C₂×D₂₆₉	1	8	yes	complemented
240	C₂×Q₁₆	—	269	2	no	—
241	C₂×Q₁₆	C₂×D₂₆₉	1	1	yes	characteristic, complemented
242	C₂×SD₁₆	—	269	2	no	—
243	C₂×SD₁₆	—	269	2	no	—
244	C₂×SD₁₆	—	269	16	no	—
245	C₂×SD₁₆	—	269	2	no	—
246	C₂×SD₁₆	—	269	2	no	—
247	C₂×SD₁₆	—	269	8	no	—
248	C₂×SD₁₆	C₂×D₂₆₉	1	1	yes	characteristic, complemented
249	C₂×SD₁₆	C₂×D₂₆₉	1	1	yes	characteristic, complemented
250	C₂×D₈	—	269	2	no	—
251	C₂×D₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
252	#131	—	269	8	no	—
253	C₂×M₁₆	—	269	1	no	—
254	C₂×M₁₆	—	269	2	no	—
255	C₂²×C₈	—	269	2	no	—
256	C₂²×C₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
257	C₂⁴	—	538	2	no	—
258	C₂⁴	—	538	1	no	—
259	#41	—	2	2	no	—
260	#41	—	2	2	no	—
261	#41	—	269	4	no	—
262	#41	—	269	4	no	—
263	#41	—	269	8	no	—
264	#41	—	269	8	no	—
265	#41	—	538	8	no	—
266	#41	—	538	8	no	—
267	#41	—	538	4	no	—
268	#41	—	538	4	no	—
269	#41	—	538	16	no	—
270	#41	C₂²×D₂₆₉	1	4	yes	—
271	#41	C₂²×D₂₆₉	1	4	yes	complemented
272	C₂×Q₈	—	269	1	no	—
273	C₂×Q₈	—	269	8	no	—
274	C₂×Q₈	—	269	2	no	—
275	C₂×Q₈	—	269	4	no	—
276	C₂×Q₈	—	538	2	no	—
277	C₂×Q₈	—	538	8	no	—
278	C₂×Q₈	—	538	4	no	—
279	C₂×Q₈	—	538	1	no	—
280	C₂×Q₈	—	538	2	no	—
281	C₂×Q₈	C₂²×D₂₆₉	1	1	yes	characteristic
282	C₂×Q₈	C₂²×D₂₆₉	1	1	yes	characteristic
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	—	269	2	no	—
286	C₂×D₄	—	269	8	no	—
287	C₂×D₄	—	269	1	no	—
288	C₂×D₄	—	269	2	no	—
289	C₂×D₄	—	269	4	no	—
290	C₂×D₄	—	538	8	no	—
291	C₂×D₄	—	538	2	no	—
292	C₂×D₄	—	538	4	no	—
293	C₂×D₄	—	538	2	no	—
294	C₂×D₄	—	538	16	no	—
295	C₂×D₄	—	538	2	no	—
296	C₂×D₄	—	538	1	no	—
297	C₂×D₄	—	538	2	no	—
298	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
299	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	269	2	no	—
303	C₂²×C₄	—	538	2	no	—
304	C₂²×C₄	—	538	2	no	—
305	C₂²×C₄	—	538	2	no	—
306	C₂²×C₄	—	538	1	no	—
307	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
308	Q₁₆	—	269	8	no	—
309	Q₁₆	C₂²×D₂₆₉	1	4	yes	complemented
310	SD₁₆	—	269	8	no	—
311	SD₁₆	—	269	8	no	—
312	SD₁₆	—	269	8	no	—
313	SD₁₆	—	269	8	no	—
314	SD₁₆	C₂²×D₂₆₉	1	4	yes	complemented
315	SD₁₆	C₂²×D₂₆₉	1	4	yes	complemented
316	D₈	—	269	8	no	—
317	D₈	C₂²×D₂₆₉	1	4	yes	complemented
318	M₁₆	—	269	4	no	—
319	M₁₆	—	269	8	no	—
320	C₂×C₈	—	269	2	no	—
321	C₂×C₈	—	269	8	no	—
322	C₂×C₈	C₂²×D₂₆₉	1	1	yes	characteristic
323	C₂×C₈	C₂²×D₂₆₉	1	1	yes	characteristic
324	C₂×C₈	C₂²×D₂₆₉	1	4	yes	complemented
325	C₂³	—	2	1	no	—
326	C₂³	—	2	1	no	—
327	C₂³	—	269	2	no	—
328	C₂³	—	538	8	no	—
329	C₂³	—	538	2	no	—
330	C₂³	—	538	4	no	—
331	C₂³	—	2152	2	no	—
332	C₂³	—	2152	4	no	—
333	C₂³	D₄×D₂₆₉	1	1	yes	characteristic
334	Q₈	—	2	1	no	—
335	Q₈	—	2	1	no	—
336	Q₈	—	269	4	no	—
337	Q₈	—	269	4	no	—
338	Q₈	—	538	8	no	—
339	Q₈	—	538	4	no	—
340	Q₈	—	538	2	no	—
341	Q₈	C₂³×D₂₆₉	1	2	yes	—
342	Q₈	C₂³×D₂₆₉	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	—	269	8	no	—
348	D₄	—	269	4	no	—
349	D₄	—	269	4	no	—
350	D₄	—	538	8	no	—
351	D₄	—	538	8	no	—
352	D₄	—	538	8	no	—
353	D₄	—	538	4	no	—
354	D₄	—	538	2	no	—
355	D₄	C₂³×D₂₆₉	1	2	yes	—
356	D₄	C₂³×D₂₆₉	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	—	269	2	no	—
362	C₂×C₄	—	269	4	no	—
363	C₂×C₄	—	269	4	no	—
364	C₂×C₄	—	538	8	no	—
365	C₂×C₄	—	538	8	no	—
366	C₂×C₄	—	538	8	no	—
367	C₂×C₄	—	538	4	no	—
368	C₂×C₄	—	538	2	no	—
369	C₂×C₄	D₄×D₂₆₉	1	2	yes	—
370	C₂×C₄	D₄×D₂₆₉	1	1	yes	characteristic
371	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
372	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
373	C₈	—	269	4	no	—
374	C₈	C₂³×D₂₆₉	1	2	yes	—
375	C₈	C₂³×D₂₆₉	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	—	269	4	no	—
382	C₂²	—	538	4	no	—
383	C₂²	—	538	4	no	—
384	C₂²	—	1076	4	no	—
385	C₂²	—	2152	4	no	—
386	C₂²	—	2152	8	no	—
387	C₂²	C₂×D₄×D₂₆₉	1	2	yes	—
388	C₂²	C₂×D₄×D₂₆₉	1	1	yes	characteristic
389	C₄	—	2	2	no	—
390	C₄	—	2	2	no	—
391	C₄	—	269	4	no	—
392	C₄	—	538	4	no	—
393	C₄	C₂×D₄×D₂₆₉	1	2	yes	—
394	C₄	C₂×D₄×D₂₆₉	1	1	yes	characteristic
395	C₄	C₂⁴×D₂₆₉	1	1	yes	characteristic
396	C₂	—	2	2	no	—
397	C₂	—	4	2	no	—
398	C₂	—	4	2	no	—
399	C₂	—	538	4	no	—
400	C₂	—	1076	4	no	—
401	C₂	#31771412	1	2	yes	direct product factor
402	C₂	C₂²×D₄×D₂₆₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₂₆₉
commutator, cosocle	C₄×C₂₆₉	C₂⁵
Frattini	C₄	C₂⁴×D₂₆₉
Fitting	C₂×#135×C₂₆₉	C₂
socle	C₂²×C₂₆₉	C₂²×D₄
hypercenter	C₂×#135	D₂₆₉
hypocenter	C₂₆₉	C₂×#577
LCS	G ▷ C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉
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×#22575500	C₂	semidirect
2. C₂×#22575499	C₂	semidirect
3. #31771412	C₂	direct (N × H)
4. C₂×#22575485	C₂	semidirect
5. C₂×#22575483	C₂	semidirect
6. C₂×#22575478	C₂	semidirect
7. C₂×#22575477	C₂	semidirect
8. C₂×#22575474	C₂	semidirect
9. C₂²×#16864391	C₂	semidirect
10. C₂×SD₁₆×D₂₆₉	C₂	semidirect
11. C₂×#22575459	C₂	semidirect
12. C₂×#135×C₂₆₉	C₂	semidirect
14. #22575500	C₂²	semidirect
16. #22575499	C₂²	semidirect
22. C₂×#16864401	C₂²	semidirect
24. C₂²×Dic₅₃₈	C₂²	semidirect
25. C₂×Q₈×D₂₆₉	C₂²	semidirect
30. #22575485	C₂²	semidirect
31. #22575483	C₂²	semidirect
32. #22575478	C₂²	semidirect
33. #22575477	C₂²	semidirect
34. #22575474	C₂²	semidirect
35. C₂×#16864392	C₂²	semidirect
36. C₂×#16864391	C₂²	semidirect
37. C₂×#16864391	C₂²	semidirect
38. C₂×#16864391	C₂²	semidirect
39. C₂×#16864390	C₂²	semidirect
40. C₂×#16864389	C₂²	semidirect
41. SD₁₆×D₂₆₉	C₂²	semidirect
42. C₂×#16864387	C₂²	semidirect
43. #22575459	C₂²	semidirect
44. C₂×#16864386	C₂²	semidirect
45. C₂×#16864385	C₂²	semidirect
46. C₂×C₈×D₂₆₉	C₂²	semidirect
48. C₂×#41×C₂₆₉	C₂²	semidirect
49. #135×C₂₆₉	C₂²	semidirect
50. C₂×Q₁₆×C₂₆₉	C₂²	semidirect
51. C₂×SD₁₆×C₂₆₉	C₂²	semidirect
52. C₂×SD₁₆×C₂₆₉	C₂²	semidirect
53. C₂×D₈×C₂₆₉	C₂²	semidirect
54. C₂²×C₈×C₂₆₉	C₂²	semidirect
65. #16864401	C₂³	semidirect
72. C₂×Dic₅₃₈	C₂³	semidirect
74. Q₈×D₂₆₉	C₂³	semidirect
93. #16864392	C₂³	semidirect
94. #16864391	C₂³	semidirect
95. #16864391	C₂³	semidirect
96. #16864390	C₂³	semidirect
97. #16864389	C₂³	semidirect
98. #16864387	C₂³	semidirect
99. #16864386	C₂³	semidirect
100. #16864385	C₂³	semidirect
102. C₈×D₂₆₉	C₂³	semidirect
106. #41×C₂₆₉	C₂³	semidirect
116. Q₁₆×C₂₆₉	C₂³	semidirect
117. SD₁₆×C₂₆₉	C₂³	semidirect
118. SD₁₆×C₂₆₉	C₂³	semidirect
119. D₈×C₂₆₉	C₂³	semidirect
122. C₂×C₈×C₂₆₉	C₂³	semidirect
197. C₂×C₂₆₉	#577	semidirect
201. C₂₆₉	C₂×#577	semidirect
211. C₂×#135	D₂₆₉	semidirect
226. C₂×#41	C₂×D₂₆₉	semidirect
239. #135	C₂×D₂₆₉	semidirect
241. C₂×Q₁₆	C₂×D₂₆₉	semidirect
248. C₂×SD₁₆	C₂×D₂₆₉	semidirect
249. C₂×SD₁₆	C₂×D₂₆₉	semidirect
251. C₂×D₈	C₂×D₂₆₉	semidirect
256. C₂²×C₈	C₂×D₂₆₉	semidirect
271. #41	C₂²×D₂₆₉	semidirect
309. Q₁₆	C₂²×D₂₆₉	semidirect
314. SD₁₆	C₂²×D₂₆₉	semidirect
315. SD₁₆	C₂²×D₂₆₉	semidirect
317. D₈	C₂²×D₂₆₉	semidirect
324. C₂×C₈	C₂²×D₂₆₉	semidirect
401. C₂	#31771412	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#22575500	2
C₂×#22575499	2
#31771412	2
C₂×#22575485	2
C₂×#22575483	2
C₂×#22575478	2
C₂×#22575477	2
C₂×#22575474	2
C₂²×#16864391	2
C₂×SD₁₆×D₂₆₉	2
C₂×#22575459	2
C₂×#135×C₂₆₉	2
C₂×#577	269

Subgroups — C2×#31771412 #46825641

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#31771412 #46825641