Subgroups — C₂×#12841 #493823

Order 512.

944 conjugacy classes of subgroups.

The subgroup lattice has 451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#504	C₂	1	1	yes	maximal, characteristic
2	C₂²×#368	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#2158	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#1814	C₂	1	2	yes	maximal
5	#12841	C₂	1	8	yes	maximal, direct product factor
6	C₂×#1389	C₂	1	2	yes	maximal, complemented
7	C₂²×#131	C₂²	1	1	yes	characteristic
8	C₂×#504	—	2	1	no	—
9	C₂×#504	—	2	1	no	—
10	C₂×#504	—	2	2	no	—
11	C₂×#504	—	2	2	no	—
12	C₂×#504	C₄	1	2	yes	complemented
13	C₂×#504	C₄	1	2	yes	complemented
14	C₂×#504	C₄	1	4	yes	complemented
15	C₂×#504	C₂²	1	4	yes	—
16	C₂²×M₃₂	—	2	1	no	—
17	C₂²×M₃₂	C₂²	1	1	yes	characteristic
18	C₂³×C₁₆	—	2	1	no	—
19	C₂³×C₁₆	C₂²	1	1	yes	characteristic
20	C₂²×#108	C₂²	1	2	yes	—
21	C₂×#427	C₂²	1	2	yes	—
22	C₂×#421	—	2	2	no	—
23	C₂×#368	—	2	1	no	—
24	C₂×#368	—	2	1	no	—
25	C₂×#368	—	2	2	no	—
26	C₂×#368	C₂²	1	4	yes	complemented
27	#2158	—	2	2	no	—
28	#2158	C₂²	1	4	yes	complemented
29	C₂×#367	—	2	1	no	—
30	C₂×#366	—	2	1	no	—
31	#1814	—	2	4	no	—
32	#1814	C₂²	1	8	yes	—
33	C₂×#344	—	2	2	no	—
34	#1389	C₂²	1	8	yes	complemented
35	C₂²×#41	D₄	1	1	yes	characteristic
36	C₂×#131	—	2	1	no	—
37	C₂×#131	—	2	1	no	—
38	C₂×#131	—	2	1	no	—
39	C₂×#131	—	2	1	no	—
40	C₂×#131	—	2	1	no	—
41	C₂×#131	—	2	1	no	—
42	C₂×#131	C₂×C₄	1	2	yes	—
43	C₂×#131	C₂×C₄	1	2	yes	—
44	C₂×#131	D₄	1	2	yes	—
45	C₂×#131	Q₈	1	2	yes	—
46	C₂×#131	Q₈	1	2	yes	—
47	C₂×#131	C₂³	1	2	yes	—
48	C₂²×M₁₆	—	2	1	no	—
49	C₂²×M₁₆	—	2	2	no	—
50	C₂²×M₁₆	D₄	1	1	yes	characteristic
51	C₂³×C₈	—	2	1	no	—
52	C₂³×C₈	C₂³	1	1	yes	characteristic
53	C₂×#117	—	2	2	no	—
54	#504	—	2	4	no	—
55	#504	—	2	4	no	—
56	#504	—	2	4	no	—
57	#504	—	2	4	no	—
58	#504	—	2	4	no	—
59	#504	—	2	4	no	—
60	#504	C₂×C₄	1	8	yes	complemented
61	#504	C₂×C₄	1	8	yes	complemented
62	C₂×M₃₂	—	2	1	no	—
63	C₂×M₃₂	—	2	1	no	—
64	C₂×M₃₂	—	2	1	no	—
65	C₂×M₃₂	—	2	2	no	—
66	C₂×M₃₂	—	2	2	no	—
67	C₂×M₃₂	—	2	4	no	—
68	C₂×M₃₂	—	2	4	no	—
69	C₂×M₃₂	C₂×C₄	1	2	yes	—
70	C₂×M₃₂	C₂×C₄	1	2	yes	—
71	C₂×M₃₂	C₂³	1	2	yes	—
72	C₂²×C₁₆	—	2	1	no	—
73	C₂²×C₁₆	—	2	2	no	—
74	C₂²×C₁₆	—	2	2	no	—
75	C₂²×C₁₆	—	2	4	no	—
76	C₂²×C₁₆	—	2	4	no	—
77	C₂²×C₁₆	C₂×C₄	1	1	yes	characteristic
78	C₂²×C₁₆	C₂×C₄	1	1	yes	characteristic
79	C₂²×C₁₆	C₂×C₄	1	2	yes	—
80	C₂²×C₁₆	D₄	1	1	yes	characteristic
81	C₂²×C₁₆	D₄	1	1	yes	characteristic
82	C₂²×C₁₆	D₄	1	1	yes	characteristic
83	C₂²×C₁₆	D₄	1	1	yes	characteristic
84	C₂²×C₁₆	D₄	1	2	yes	—
85	C₂²×C₁₆	D₄	1	2	yes	—
86	C₂²×C₁₆	C₂³	1	2	yes	—
87	C₂×#108	—	2	2	no	—
88	C₂×#108	—	2	2	no	—
89	C₂×#108	—	2	2	no	—
90	C₂×#108	—	2	2	no	—
91	C₂×#108	—	2	2	no	—
92	C₂×#108	C₂³	1	4	yes	—
93	#427	—	2	2	no	—
94	#427	—	2	2	no	—
95	#427	—	2	2	no	—
96	#427	C₂³	1	4	yes	—
97	C₂×#107	—	2	2	no	—
98	C₂×#106	—	2	2	no	—
99	#421	—	2	8	no	—
100	#421	—	4	4	no	—
101	C₂×#104	—	4	4	no	—
102	#368	—	2	4	no	—
103	#368	—	2	4	no	—
104	#367	—	2	4	no	—
105	#366	—	2	4	no	—
106	#344	—	2	8	no	—
107	C₂×#41	—	2	1	no	—
108	C₂×#41	—	2	1	no	—
109	C₂×#41	—	2	1	no	—
110	C₂×#41	—	2	1	no	—
111	C₂×#41	—	2	1	no	—
112	C₂×#41	—	2	1	no	—
113	C₂×#41	C₄⋊C₄	1	2	yes	—
114	C₂×#41	C₄⋊C₄	1	2	yes	—
115	C₂×#41	D₈	1	2	yes	—
116	C₂×#41	D₈	1	2	yes	—
117	C₂×#41	Q₁₆	1	2	yes	—
118	C₂×#41	C₂×D₄	1	2	yes	—
119	C₂²×Q₈	Q₁₆	1	1	yes	characteristic
120	C₂²×D₄	—	2	1	no	—
121	C₂²×D₄	Q₁₆	1	1	yes	characteristic
122	C₂³×C₄	—	2	1	no	—
123	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
124	#131	—	2	2	no	—
125	#131	—	2	2	no	—
126	#131	—	2	2	no	—
127	#131	—	2	2	no	—
128	#131	—	2	2	no	—
129	#131	—	2	2	no	—
130	#131	—	2	2	no	—
131	#131	—	2	2	no	—
132	#131	—	2	2	no	—
133	#131	—	2	2	no	—
134	#131	—	2	2	no	—
135	#131	—	2	2	no	—
136	#131	C₄⋊C₄	1	4	yes	—
137	#131	C₄⋊C₄	1	4	yes	—
138	#131	C₂²×C₄	1	4	yes	—
139	#131	C₂×Q₈	1	4	yes	—
140	C₂×M₁₆	—	2	1	no	—
141	C₂×M₁₆	—	2	1	no	—
142	C₂×M₁₆	—	2	1	no	—
143	C₂×M₁₆	—	2	2	no	—
144	C₂×M₁₆	—	2	2	no	—
145	C₂×M₁₆	—	2	2	no	—
146	C₂×M₁₆	—	2	2	no	—
147	C₂×M₁₆	—	2	2	no	—
148	C₂×M₁₆	—	2	2	no	—
149	C₂×M₁₆	—	2	4	no	—
150	C₂×M₁₆	—	4	2	no	—
151	C₂×M₁₆	—	4	2	no	—
152	C₂×M₁₆	—	4	2	no	—
153	C₂×M₁₆	—	4	2	no	—
154	C₂×M₁₆	—	4	2	no	—
155	C₂×M₁₆	C₄⋊C₄	1	2	yes	—
156	C₂×M₁₆	C₄⋊C₄	1	2	yes	—
157	C₂×M₁₆	C₂×D₄	1	2	yes	—
158	C₂²×C₈	—	2	1	no	—
159	C₂²×C₈	—	2	2	no	—
160	C₂²×C₈	—	2	2	no	—
161	C₂²×C₈	—	2	2	no	—
162	C₂²×C₈	—	2	2	no	—
163	C₂²×C₈	—	2	2	no	—
164	C₂²×C₈	—	2	2	no	—
165	C₂²×C₈	—	4	2	no	—
166	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₈	C₂×Q₈	1	1	yes	characteristic
174	C₂²×C₈	C₂×Q₈	1	1	yes	characteristic
175	C₂²×C₈	#41	1	1	yes	characteristic
176	C₂²×C₈	#41	1	1	yes	characteristic
177	C₂²×C₈	#41	1	1	yes	characteristic
178	C₂²×C₈	#41	1	1	yes	characteristic
179	C₂²×C₈	C₂⁴	1	1	yes	characteristic
180	#117	—	2	4	no	—
181	#117	—	4	2	no	—
182	#117	—	4	2	no	—
183	#117	—	4	2	no	—
184	C₂×C₄⋊C₄	—	4	2	no	—
185	C₂×C₂²⋊C₄	—	4	2	no	—
186	C₂×C₄²	—	4	2	no	—
187	M₃₂	—	2	2	no	—
188	M₃₂	—	2	2	no	—
189	M₃₂	—	2	2	no	—
190	M₃₂	—	2	8	no	—
191	M₃₂	—	2	8	no	—
192	M₃₂	C₂²×C₄	1	4	yes	—
193	C₂×C₁₆	—	2	2	no	—
194	C₂×C₁₆	—	2	2	no	—
195	C₂×C₁₆	—	2	2	no	—
196	C₂×C₁₆	—	2	8	no	—
197	C₂×C₁₆	—	2	8	no	—
198	C₂×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
199	C₂×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
200	C₂×C₁₆	C₂²⋊C₄	1	2	yes	—
201	C₂×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
202	C₂×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
203	C₂×C₁₆	C₂²⋊C₄	1	2	yes	—
204	C₂×C₁₆	C₂²⋊C₄	1	2	yes	—
205	C₂×C₁₆	C₂²⋊C₄	1	2	yes	—
206	C₂×C₁₆	C₂²⋊C₄	1	2	yes	—
207	C₂×C₁₆	C₂²⋊C₄	1	2	yes	—
208	C₂×C₁₆	C₂²×C₄	1	2	yes	—
209	C₂×C₁₆	C₂²×C₄	1	2	yes	—
210	C₂×C₁₆	C₂×D₄	1	2	yes	—
211	C₂×C₁₆	C₂×D₄	1	2	yes	—
212	C₂×C₁₆	C₂×D₄	1	2	yes	—
213	C₂×C₁₆	C₂×D₄	1	2	yes	—
214	#108	—	2	4	no	—
215	#108	—	2	4	no	—
216	#108	—	4	2	no	—
217	#108	—	4	2	no	—
218	#107	—	2	4	no	—
219	#107	—	4	2	no	—
220	#106	—	2	4	no	—
221	#106	—	4	2	no	—
222	#104	—	4	16	no	—
223	C₂⁴	—	2	1	no	—
224	C₂⁴	#135	1	1	yes	characteristic
225	#41	—	2	2	no	—
226	#41	—	2	2	no	—
227	#41	—	2	2	no	—
228	#41	—	2	2	no	—
229	#41	—	2	2	no	—
230	#41	—	2	2	no	—
231	#41	—	2	2	no	—
232	#41	—	2	2	no	—
233	#41	—	2	2	no	—
234	#41	—	2	2	no	—
235	#41	—	2	2	no	—
236	#41	—	2	2	no	—
237	#41	#107	1	4	yes	—
238	#41	#107	1	4	yes	—
239	#41	C₂×C₄⋊C₄	1	4	yes	—
240	#41	C₂×D₈	1	4	yes	—
241	C₂×Q₈	—	2	1	no	—
242	C₂×Q₈	—	2	1	no	—
243	C₂×Q₈	—	2	1	no	—
244	C₂×Q₈	#107	1	2	yes	—
245	C₂×Q₈	#107	1	2	yes	—
246	C₂×Q₈	C₂×Q₁₆	1	2	yes	—
247	C₂×D₄	—	2	2	no	—
248	C₂×D₄	—	2	2	no	—
249	C₂×D₄	—	2	2	no	—
250	C₂×D₄	—	2	2	no	—
251	C₂×D₄	—	2	2	no	—
252	C₂×D₄	—	2	2	no	—
253	C₂×D₄	—	2	1	no	—
254	C₂×D₄	—	2	1	no	—
255	C₂×D₄	—	2	1	no	—
256	C₂×D₄	#107	1	2	yes	—
257	C₂×D₄	#107	1	2	yes	—
258	C₂×D₄	C₂×Q₁₆	1	2	yes	—
259	C₂²×C₄	—	2	1	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	8	2	no	—
267	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
268	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
269	C₂²×C₄	#121	1	1	yes	characteristic
270	C₂²×C₄	#121	1	1	yes	characteristic
271	C₂²×C₄	#121	1	1	yes	characteristic
272	C₂²×C₄	#121	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₈	1	1	yes	characteristic
274	C₂²×C₄	C₂×D₈	1	1	yes	characteristic
275	C₂²×C₄	C₂×Q₁₆	1	1	yes	characteristic
276	C₂²×C₄	C₂×Q₁₆	1	1	yes	characteristic
277	C₂²×C₄	#135	1	1	yes	characteristic
278	C₂²×C₄	#135	1	1	yes	characteristic
279	C₂²×C₄	#135	1	1	yes	characteristic
280	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
281	M₁₆	—	2	2	no	—
282	M₁₆	—	2	2	no	—
283	M₁₆	—	2	2	no	—
284	M₁₆	—	2	4	no	—
285	M₁₆	—	2	4	no	—
286	M₁₆	—	2	4	no	—
287	M₁₆	—	2	4	no	—
288	M₁₆	—	4	4	no	—
289	M₁₆	—	4	4	no	—
290	M₁₆	—	8	2	no	—
291	M₁₆	—	8	2	no	—
292	M₁₆	C₂×C₄⋊C₄	1	4	yes	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	4	no	—
297	C₂×C₈	—	2	4	no	—
298	C₂×C₈	—	2	4	no	—
299	C₂×C₈	—	2	4	no	—
300	C₂×C₈	—	4	4	no	—
301	C₂×C₈	—	8	2	no	—
302	C₂×C₈	—	8	2	no	—
303	C₂×C₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
304	C₂×C₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
305	C₂×C₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
306	C₂×C₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
307	C₂×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
308	C₂×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
309	C₂×C₈	#117	1	1	yes	characteristic
310	C₂×C₈	#117	1	1	yes	characteristic
311	C₂×C₈	#117	1	1	yes	characteristic
312	C₂×C₈	#117	1	1	yes	characteristic
313	C₂×C₈	#121	1	1	yes	characteristic
314	C₂×C₈	#121	1	1	yes	characteristic
315	C₂×C₈	#121	1	1	yes	characteristic
316	C₂×C₈	#121	1	1	yes	characteristic
317	C₂×C₈	C₂²⋊Q₈	1	1	yes	characteristic
318	C₂×C₈	C₂²⋊Q₈	1	1	yes	characteristic
319	C₂×C₈	C₂²⋊Q₈	1	1	yes	characteristic
320	C₂×C₈	C₂²⋊Q₈	1	1	yes	characteristic
321	C₂×C₈	C₂²⋊Q₈	1	1	yes	characteristic
322	C₂×C₈	C₂²⋊Q₈	1	1	yes	characteristic
323	C₂×C₈	C₂²⋊Q₈	1	1	yes	characteristic
324	C₂×C₈	C₂²⋊Q₈	1	1	yes	characteristic
325	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
326	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₈	C₂²×Q₈	1	1	yes	characteristic
329	C₂×C₈	C₂×#41	1	1	yes	characteristic
330	C₂×C₈	C₂×#41	1	1	yes	characteristic
331	C₄⋊C₄	—	4	4	no	—
332	C₄⋊C₄	—	8	2	no	—
333	C₂²⋊C₄	—	4	4	no	—
334	C₂²⋊C₄	—	8	2	no	—
335	C₄²	—	4	4	no	—
336	C₄²	—	8	2	no	—
337	C₁₆	—	2	4	no	—
338	C₁₆	C₂×C₂²⋊C₄	1	2	yes	—
339	C₁₆	C₂×C₂²⋊C₄	1	2	yes	—
340	C₁₆	C₂×C₂²⋊C₄	1	2	yes	—
341	C₁₆	C₂×C₂²⋊C₄	1	2	yes	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	4	no	—
347	C₂³	#427	1	1	yes	characteristic
348	C₂³	#427	1	1	yes	characteristic
349	C₂³	#466	1	1	yes	characteristic
350	C₂³	#466	1	1	yes	characteristic
351	C₂³	#467	1	1	yes	characteristic
352	C₂³	#467	1	1	yes	characteristic
353	C₂³	C₂×#135	1	1	yes	characteristic
354	Q₈	—	2	2	no	—
355	Q₈	—	2	2	no	—
356	Q₈	—	2	2	no	—
357	Q₈	C₂×#107	1	4	yes	—
358	D₄	—	2	4	no	—
359	D₄	—	2	4	no	—
360	D₄	—	2	4	no	—
361	D₄	—	2	4	no	—
362	D₄	—	2	2	no	—
363	D₄	—	2	2	no	—
364	D₄	—	2	2	no	—
365	D₄	C₂×#107	1	4	yes	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	8	4	no	—
374	C₂×C₄	—	16	4	no	—
375	C₂×C₄	#380	1	1	yes	characteristic
376	C₂×C₄	#380	1	1	yes	characteristic
377	C₂×C₄	#380	1	1	yes	characteristic
378	C₂×C₄	#380	1	1	yes	characteristic
379	C₂×C₄	C₂×#107	1	1	yes	characteristic
380	C₂×C₄	C₂×#107	1	1	yes	characteristic
381	C₂×C₄	C₂×#107	1	1	yes	characteristic
382	C₂×C₄	C₂×#107	1	1	yes	characteristic
383	C₂×C₄	#427	1	1	yes	characteristic
384	C₂×C₄	#427	1	1	yes	characteristic
385	C₂×C₄	#466	1	1	yes	characteristic
386	C₂×C₄	#466	1	1	yes	characteristic
387	C₂×C₄	#466	1	1	yes	characteristic
388	C₂×C₄	#466	1	1	yes	characteristic
389	C₂×C₄	#466	1	1	yes	characteristic
390	C₂×C₄	#466	1	1	yes	characteristic
391	C₂×C₄	#467	1	1	yes	characteristic
392	C₂×C₄	#467	1	1	yes	characteristic
393	C₂×C₄	#467	1	1	yes	characteristic
394	C₂×C₄	#467	1	1	yes	characteristic
395	C₂×C₄	#467	1	1	yes	characteristic
396	C₂×C₄	#467	1	1	yes	characteristic
397	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
398	C₂×C₄	C₂×#121	1	1	yes	characteristic
399	C₂×C₄	C₂×#121	1	1	yes	characteristic
400	C₂×C₄	C₂²×D₈	1	1	yes	characteristic
401	C₂×C₄	C₂²×Q₁₆	1	1	yes	characteristic
402	C₂×C₄	C₂×#135	1	1	yes	characteristic
403	C₈	—	2	4	no	—
404	C₈	—	8	4	no	—
405	C₈	#380	1	1	yes	characteristic
406	C₈	#380	1	1	yes	characteristic
407	C₈	#380	1	1	yes	characteristic
408	C₈	#380	1	1	yes	characteristic
409	C₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
410	C₈	C₂×#117	1	1	yes	characteristic
411	C₈	C₂×C₂²⋊Q₈	1	1	yes	characteristic
412	C₈	C₂×C₂²⋊Q₈	1	1	yes	characteristic
413	C₂²	—	2	2	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	4	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	4	1	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	1	no	—
421	C₂²	—	4	4	no	—
422	C₂²	—	4	4	no	—
423	C₂²	—	4	4	no	—
424	C₂²	#1808	1	1	yes	characteristic
425	C₂²	#1808	1	1	yes	characteristic
426	C₂²	#1808	1	1	yes	characteristic
427	C₂²	#1808	1	1	yes	characteristic
428	C₂²	C₂×#427	1	1	yes	characteristic
429	C₂²	C₂×#466	1	1	yes	characteristic
430	C₂²	C₂×#467	1	1	yes	characteristic
431	C₄	—	2	4	no	—
432	C₄	—	16	4	no	—
433	C₄	#1808	1	1	yes	characteristic
434	C₄	#1808	1	1	yes	characteristic
435	C₄	#1808	1	1	yes	characteristic
436	C₄	#1808	1	1	yes	characteristic
437	C₄	C₂×#380	1	1	yes	characteristic
438	C₄	C₂²×#107	1	1	yes	characteristic
439	C₄	C₂×#466	1	1	yes	characteristic
440	C₄	C₂×#467	1	1	yes	characteristic
441	C₂	—	2	1	no	—
442	C₂	—	2	1	no	—
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	—	2	1	no	—
446	C₂	—	2	1	no	—
447	C₂	—	4	4	no	—
448	C₂	#12841	1	2	yes	direct product factor
449	C₂	C₂×#1808	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#466
commutator	C₂×C₈	C₂³×C₄
Frattini, cosocle	C₂²×C₈	C₂⁴
socle	C₂²	#1808
prime radical	C₂²×#41	D₄
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#131 ◁ G
LECS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. C₂²×#368	C₂	semidirect
3. C₂×#2158	C₂	semidirect
5. #12841	C₂	direct (N × H)
6. C₂×#1389	C₂	semidirect
12. C₂×#504	C₄	semidirect
13. C₂×#504	C₄	semidirect
14. C₂×#504	C₄	semidirect
26. C₂×#368	C₂²	semidirect
28. #2158	C₂²	semidirect
34. #1389	C₂²	semidirect
60. #504	C₂×C₄	semidirect
61. #504	C₂×C₄	semidirect
448. C₂	#12841	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×#504	2
C₂²×#368	2
C₂×#2158	2
C₂×#1814	2
#12841	2
C₂×#1389	2

Subgroups — C2×#12841 #493823

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#12841 #493823