Subgroups — #61336

Order 256.

896 conjugacy classes of subgroups.

The subgroup lattice has 565 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	#3377	C₂	1	2	yes	maximal, complemented
4	#3376	C₂	1	2	yes	maximal, complemented
5	#3375	C₂	1	2	yes	maximal, complemented
6	#3373	C₂	1	2	yes	maximal, complemented
7	#3371	C₂	1	2	yes	maximal, complemented
8	#3370	C₂	1	2	yes	maximal, complemented
9	#3369	C₂	1	2	yes	maximal, complemented
10	#3367	C₂	1	2	yes	maximal, complemented
11	#3137	C₂	1	1	yes	maximal, characteristic, complemented
12	#3136	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#489	C₂	1	1	yes	maximal, characteristic, complemented
14	#3082	C₂	1	1	yes	maximal, characteristic, complemented
15	#3081	C₂	1	1	yes	maximal, characteristic, complemented
16	#3079	C₂	1	1	yes	maximal, characteristic, complemented
17	#3046	C₂	1	1	yes	maximal, characteristic, complemented
18	#3045	C₂	1	1	yes	maximal, characteristic
19	#3040	C₂	1	1	yes	maximal, characteristic, complemented
20	#2961	C₂	1	1	yes	maximal, characteristic, complemented
21	#2947	C₂	1	1	yes	maximal, characteristic, complemented
22	#2946	C₂	1	1	yes	maximal, characteristic, complemented
23	#2943	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137	C₂²	1	1	yes	characteristic
25	C₂×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
26	C₂×#135	C₂²	1	1	yes	characteristic
27	#559	C₂²	1	2	yes	—
28	#559	C₂²	1	2	yes	—
29	Q₈²	C₂²	1	2	yes	complemented
30	#557	C₂²	1	2	yes	complemented
31	#556	C₂²	1	2	yes	—
32	#556	C₂²	1	2	yes	—
33	#554	—	2	2	no	—
34	#554	C₂²	1	2	yes	complemented
35	#551	—	2	2	no	—
36	#551	—	2	2	no	—
37	D₄×Q₈	—	2	2	no	—
38	D₄×Q₈	C₂²	1	2	yes	complemented
39	#544	—	2	1	no	—
40	#544	—	2	1	no	—
41	#544	C₂²	1	1	yes	characteristic
42	#544	C₂²	1	1	yes	characteristic
43	#542	—	2	1	no	—
44	#542	—	2	1	no	—
45	#536	C₂²	1	1	yes	characteristic
46	#535	C₂²	1	1	yes	characteristic
47	#533	—	2	1	no	—
48	#533	C₂²	1	1	yes	characteristic
49	C₂×C₄⋊Q₈	—	2	1	no	—
50	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic
51	#529	—	2	1	no	—
52	#529	—	2	1	no	—
53	C₂×#124	C₂²	1	1	yes	characteristic
54	#520	C₂²	1	1	yes	characteristic
55	#520	C₂²	1	1	yes	characteristic
56	#519	C₂²	1	1	yes	characteristic
57	#518	C₂²	1	1	yes	characteristic
58	C₄×#41	C₂²	1	1	yes	characteristic
59	C₄×#41	C₂²	1	1	yes	characteristic
60	#491	C₂²	1	2	yes	complemented
61	#490	C₂²	1	2	yes	—
62	#489	C₂²	1	2	yes	—
63	#489	C₂²	1	2	yes	—
64	#489	C₂²	1	2	yes	—
65	#489	C₂²	1	2	yes	—
66	#489	C₂²	1	2	yes	—
67	#489	C₂²	1	2	yes	complemented
68	#488	C₂²	1	2	yes	—
69	#488	C₂²	1	2	yes	complemented
70	#487	C₂²	1	2	yes	complemented
71	#486	C₂²	1	2	yes	—
72	#479	C₂²	1	2	yes	complemented
73	#479	C₂²	1	2	yes	complemented
74	#478	C₂²	1	2	yes	—
75	#478	C₂²	1	2	yes	—
76	#477	C₂²	1	2	yes	complemented
77	#477	C₂²	1	2	yes	complemented
78	#476	C₂²	1	2	yes	—
79	#476	C₂²	1	2	yes	complemented
80	#475	C₂²	1	2	yes	complemented
81	#475	C₂²	1	2	yes	complemented
82	#474	C₂²	1	2	yes	—
83	#474	C₂²	1	2	yes	complemented
84	#464	C₂²	1	2	yes	—
85	#464	C₂²	1	2	yes	—
86	#464	C₂²	1	2	yes	—
87	#464	C₂²	1	2	yes	complemented
88	#463	C₂²	1	2	yes	—
89	#463	C₂²	1	2	yes	—
90	#463	C₂²	1	2	yes	—
91	#463	C₂²	1	2	yes	complemented
92	#462	C₂²	1	2	yes	complemented
93	#461	C₂²	1	2	yes	complemented
94	#460	C₂²	1	2	yes	—
95	#459	C₂²	1	2	yes	—
96	#446	C₂²	1	2	yes	complemented
97	#446	C₂²	1	2	yes	complemented
98	#446	C₂²	1	2	yes	complemented
99	#446	C₂²	1	2	yes	complemented
100	#442	C₂²	1	2	yes	—
101	#442	C₂²	1	1	yes	characteristic, complemented
102	#442	C₂²	1	1	yes	characteristic, complemented
103	#441	C₂²	1	1	yes	characteristic, complemented
104	#441	C₂²	1	2	yes	complemented
105	#441	C₂²	1	1	yes	characteristic, complemented
106	#440	C₂²	1	2	yes	—
107	#440	C₂²	1	1	yes	characteristic, complemented
108	#440	C₂²	1	2	yes	complemented
109	#440	C₂²	1	1	yes	characteristic, complemented
110	#440	C₂²	1	1	yes	characteristic, complemented
111	#440	C₂²	1	1	yes	characteristic, complemented
112	C₄×Q₁₆	C₂²	1	2	yes	complemented
113	C₄×SD₁₆	C₂²	1	2	yes	—
114	C₄×SD₁₆	C₂²	1	2	yes	complemented
115	C₄×D₈	C₂²	1	2	yes	—
116	#428	C₂²	1	1	yes	characteristic
117	#428	C₂²	1	1	yes	characteristic
118	#427	C₂²	1	1	yes	characteristic
119	#424	C₂²	1	1	yes	characteristic
120	#424	C₂²	1	1	yes	characteristic
121	#423	C₂²	1	1	yes	characteristic
122	#419	C₂²	1	1	yes	characteristic
123	#418	C₂²	1	1	yes	characteristic
124	#417	C₂²	1	1	yes	characteristic
125	#417	C₂²	1	1	yes	characteristic
126	#416	C₂²	1	1	yes	characteristic
127	#416	C₂²	1	1	yes	characteristic
128	C₂×#103	C₂²	1	1	yes	characteristic
129	C₂×#103	C₂²	1	1	yes	characteristic
130	C₂×#102	C₂²	1	1	yes	characteristic
131	C₂×#102	C₂²	1	1	yes	characteristic
132	#405	C₂²	1	1	yes	characteristic
133	#405	C₂²	1	1	yes	characteristic
134	C₂×#97	C₂²	1	1	yes	characteristic
135	C₂×#41	C₂³	1	1	yes	characteristic
136	C₂×#41	C₂³	1	1	yes	characteristic
137	C₂²×Q₈	—	2	2	no	—
138	C₂²×Q₈	—	2	1	no	—
139	C₂²×Q₈	C₂³	1	1	yes	characteristic
140	C₂²×D₄	C₂³	1	1	yes	characteristic
141	#137	—	2	4	no	—
142	AGL(1,ℤ/8)	—	2	4	no	—
143	#135	—	2	4	no	—
144	C₂×Q₁₆	C₂³	1	1	yes	characteristic
145	C₂×Q₁₆	C₂³	1	2	yes	—
146	C₂×SD₁₆	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆	C₂³	1	2	yes	—
149	C₂×SD₁₆	C₂³	1	2	yes	—
150	C₂×D₈	C₂³	1	1	yes	characteristic
151	C₂×D₈	C₂³	1	2	yes	—
152	C₂×M₁₆	C₂³	1	1	yes	characteristic
153	C₂×M₁₆	C₂³	1	1	yes	characteristic
154	C₂²×C₈	C₂³	1	1	yes	characteristic
155	C₂²×C₈	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈	—	2	2	no	—
157	C₄⋊Q₈	—	2	1	no	—
158	C₄⋊Q₈	—	2	1	no	—
159	C₄⋊Q₈	—	2	2	no	—
160	C₄⋊Q₈	—	2	2	no	—
161	C₄⋊Q₈	—	2	2	no	—
162	C₄⋊Q₈	—	2	1	no	—
163	C₄⋊Q₈	—	2	1	no	—
164	C₄⋊Q₈	D₄	1	1	yes	characteristic
165	C₄⋊Q₈	D₄	1	1	yes	characteristic
166	C₄⋊Q₈	C₂³	1	2	yes	—
167	C₄⋊Q₈	C₂³	1	2	yes	—
168	C₄⋊Q₈	C₂³	1	2	yes	—
169	C₄⋊Q₈	C₂³	1	2	yes	—
170	C₄⋊Q₈	C₂³	1	2	yes	—
171	#127	C₂³	1	2	yes	—
172	#126	—	2	2	no	—
173	#126	—	2	2	no	—
174	#126	—	2	2	no	—
175	#126	—	2	2	no	—
176	#125	—	2	1	no	—
177	#125	—	2	1	no	—
178	#125	—	2	2	no	—
179	#125	—	2	2	no	—
180	#125	D₄	1	1	yes	characteristic
181	#125	D₄	1	1	yes	characteristic
182	#125	C₂³	1	2	yes	—
183	#125	C₂³	1	2	yes	—
184	#124	—	2	2	no	—
185	#124	—	2	2	no	—
186	#124	—	2	1	no	—
187	#124	—	2	1	no	—
188	#124	C₂³	1	2	yes	—
189	#124	C₂³	1	2	yes	—
190	#124	C₂³	1	2	yes	—
191	#124	C₂³	1	2	yes	—
192	#123	—	2	2	no	—
193	#123	—	2	2	no	—
194	#123	—	2	2	no	—
195	#123	—	2	2	no	—
196	#123	—	2	2	no	—
197	C₂²⋊Q₈	—	2	2	no	—
198	C₂²⋊Q₈	—	2	2	no	—
199	C₂²⋊Q₈	—	2	2	no	—
200	C₂²⋊Q₈	—	2	1	no	—
201	C₂²⋊Q₈	—	2	1	no	—
202	C₂²⋊Q₈	—	2	2	no	—
203	C₂²⋊Q₈	—	2	2	no	—
204	C₂²⋊Q₈	—	2	2	no	—
205	C₂²⋊Q₈	—	2	2	no	—
206	C₂²⋊Q₈	—	2	2	no	—
207	C₂²⋊Q₈	—	2	2	no	—
208	C₂²⋊Q₈	—	2	2	no	—
209	C₂²⋊Q₈	D₄	1	2	yes	—
210	C₂²⋊Q₈	D₄	1	2	yes	—
211	#121	—	2	1	no	—
212	#121	—	2	1	no	—
213	#120	—	2	2	no	—
214	C₄×Q₈	—	2	2	no	—
215	C₄×Q₈	—	2	1	no	—
216	C₄×Q₈	—	2	1	no	—
217	C₄×Q₈	—	2	2	no	—
218	C₄×Q₈	C₂³	1	1	yes	characteristic
219	C₄×Q₈	C₂³	1	1	yes	characteristic
220	C₄×Q₈	C₂³	1	1	yes	characteristic
221	C₄×Q₈	C₂³	1	1	yes	characteristic
222	C₄×Q₈	C₂³	1	2	yes	—
223	C₄×Q₈	C₂³	1	2	yes	—
224	C₄×Q₈	C₂³	1	2	yes	—
225	C₄×Q₈	C₂³	1	2	yes	—
226	C₄×Q₈	C₂³	1	2	yes	—
227	C₄×Q₈	C₂³	1	2	yes	—
228	C₄×D₄	—	2	1	no	—
229	C₄×D₄	—	2	1	no	—
230	C₄×D₄	—	2	1	no	—
231	C₄×D₄	—	2	1	no	—
232	C₄×D₄	—	2	1	no	—
233	C₄×D₄	—	2	1	no	—
234	C₄×D₄	—	2	2	no	—
235	C₄×D₄	—	2	2	no	—
236	C₄×D₄	—	2	2	no	—
237	C₄×D₄	—	2	2	no	—
238	C₄×D₄	C₂³	1	1	yes	characteristic
239	C₄×D₄	C₂³	1	1	yes	characteristic
240	C₄×D₄	C₂³	1	1	yes	characteristic
241	C₄×D₄	C₂³	1	1	yes	characteristic
242	C₄×D₄	C₂³	1	2	yes	—
243	C₄×D₄	C₂³	1	2	yes	—
244	C₄×D₄	C₂³	1	2	yes	—
245	C₄×D₄	C₂³	1	2	yes	—
246	#117	—	2	1	no	—
247	#117	—	2	1	no	—
248	#117	—	2	2	no	—
249	#117	—	2	2	no	—
250	#117	—	2	2	no	—
251	#117	—	2	1	no	—
252	#117	—	2	1	no	—
253	#117	C₂³	1	1	yes	characteristic
254	#117	C₂³	1	1	yes	characteristic
255	#117	C₂³	1	1	yes	characteristic
256	#117	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₄²	—	2	1	no	—
267	C₂×C₄²	—	2	1	no	—
268	C₂×C₄²	C₂³	1	1	yes	characteristic
269	#107	C₂³	1	1	yes	characteristic
270	#107	C₂³	1	1	yes	characteristic
271	#107	C₂³	1	2	yes	—
272	#107	C₂³	1	2	yes	—
273	#106	C₂³	1	1	yes	characteristic
274	#106	C₂³	1	1	yes	characteristic
275	#106	C₂³	1	2	yes	—
276	#106	C₂³	1	2	yes	—
277	C₄⋊C₈	C₂³	1	2	yes	—
278	C₄⋊C₈	C₂³	1	2	yes	—
279	C₄⋊C₈	C₂³	1	2	yes	—
280	C₄⋊C₈	C₂³	1	2	yes	—
281	C₄⋊C₈	C₂³	1	2	yes	—
282	C₄⋊C₈	C₂³	1	2	yes	—
283	#103	C₂³	1	2	yes	—
284	#103	C₂³	1	2	yes	—
285	#103	C₂³	1	2	yes	—
286	#103	C₂³	1	2	yes	—
287	#103	C₂³	1	1	yes	characteristic
288	#103	C₂³	1	1	yes	characteristic
289	#103	C₂³	1	1	yes	characteristic
290	#103	C₂³	1	1	yes	characteristic
291	#103	C₂³	1	2	yes	—
292	#103	C₂³	1	2	yes	—
293	#103	C₂³	1	2	yes	—
294	#103	C₂³	1	2	yes	—
295	#102	C₂³	1	2	yes	—
296	#102	C₂³	1	2	yes	—
297	#102	C₂³	1	2	yes	—
298	#102	C₂³	1	2	yes	—
299	#102	C₂³	1	1	yes	characteristic
300	#102	C₂³	1	1	yes	characteristic
301	#102	C₂³	1	1	yes	characteristic
302	#102	C₂³	1	1	yes	characteristic
303	#102	C₂³	1	2	yes	—
304	#102	C₂³	1	2	yes	—
305	#102	C₂³	1	2	yes	—
306	#102	C₂³	1	2	yes	—
307	#97	C₂³	1	1	yes	characteristic
308	#97	C₂³	1	1	yes	characteristic
309	#97	C₂³	1	1	yes	characteristic
310	#97	C₂³	1	1	yes	characteristic
311	#97	C₂³	1	2	yes	—
312	#97	C₂³	1	2	yes	—
313	C₄×C₈	C₂³	1	2	yes	—
314	C₄×C₈	C₂³	1	2	yes	—
315	C₂⁴	—	2	1	no	—
316	#41	—	2	2	no	—
317	#41	—	2	2	no	—
318	#41	—	2	2	no	—
319	#41	#41	1	4	yes	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	8	2	no	—
328	C₂×Q₈	—	8	4	no	—
329	C₂×Q₈	C₂×D₄	1	2	yes	—
330	C₂×Q₈	C₂×D₄	1	2	yes	—
331	C₂×Q₈	C₂⁴	1	2	yes	—
332	C₂×Q₈	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈	C₂⁴	1	1	yes	characteristic
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	C₂⁴	1	2	yes	—
342	C₂×D₄	C₂⁴	1	1	yes	characteristic
343	C₂×D₄	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
359	C₂²×C₄	C₂⁴	1	1	yes	characteristic
360	Q₁₆	—	2	2	no	—
361	Q₁₆	—	2	4	no	—
362	SD₁₆	—	2	2	no	—
363	SD₁₆	—	2	4	no	—
364	SD₁₆	—	2	2	no	—
365	SD₁₆	—	2	4	no	—
366	D₈	—	2	2	no	—
367	D₈	—	2	4	no	—
368	M₁₆	—	2	2	no	—
369	M₁₆	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	C₂⁴	1	1	yes	characteristic
373	C₂×C₈	C₂⁴	1	1	yes	characteristic
374	C₂×C₈	C₂⁴	1	2	yes	—
375	C₂×C₈	C₂⁴	1	2	yes	—
376	C₂×C₈	C₂⁴	1	1	yes	characteristic
377	C₂×C₈	C₂⁴	1	1	yes	characteristic
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄	C₂×D₄	1	2	yes	—
401	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
402	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
403	C₄⋊C₄	C₂×D₄	1	2	yes	—
404	C₄⋊C₄	C₂×D₄	1	2	yes	—
405	C₄⋊C₄	C₂×D₄	1	2	yes	—
406	C₄⋊C₄	C₂×D₄	1	2	yes	—
407	C₄⋊C₄	C₂×D₄	1	2	yes	—
408	C₄⋊C₄	C₂⁴	1	2	yes	—
409	C₄⋊C₄	C₂⁴	1	2	yes	—
410	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
414	C₂²⋊C₄	—	2	1	no	—
415	C₂²⋊C₄	—	2	1	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	1	no	—
423	C₂²⋊C₄	—	2	1	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	2	1	no	—
427	C₂²⋊C₄	—	2	1	no	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄	C₂×D₄	1	2	yes	—
434	C₄²	—	2	1	no	—
435	C₄²	—	2	1	no	—
436	C₄²	—	2	1	no	—
437	C₄²	—	2	1	no	—
438	C₄²	—	2	1	no	—
439	C₄²	—	2	1	no	—
440	C₄²	—	2	2	no	—
441	C₄²	—	2	2	no	—
442	C₄²	—	2	2	no	—
443	C₄²	—	2	2	no	—
444	C₄²	C₂×D₄	1	1	yes	characteristic
445	C₄²	C₂×D₄	1	1	yes	characteristic
446	C₄²	C₂⁴	1	2	yes	—
447	C₄²	C₂⁴	1	2	yes	—
448	C₄²	C₂⁴	1	1	yes	characteristic
449	C₄²	C₂⁴	1	1	yes	characteristic
450	C₂³	—	2	1	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	2	1	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	8	1	no	—
455	C₂³	—	8	1	no	—
456	C₂³	C₂²×D₄	1	1	yes	characteristic
457	Q₈	—	2	1	no	—
458	Q₈	—	2	2	no	—
459	Q₈	—	2	1	no	—
460	Q₈	—	2	2	no	—
461	Q₈	—	2	1	no	—
462	Q₈	—	4	2	no	—
463	Q₈	—	4	2	no	—
464	Q₈	—	4	4	no	—
465	Q₈	—	4	2	no	—
466	Q₈	—	8	2	no	—
467	Q₈	—	8	2	no	—
468	Q₈	—	8	2	no	—
469	Q₈	C₂×#41	1	2	yes	—
470	D₄	—	2	4	no	—
471	D₄	—	2	2	no	—
472	D₄	—	2	1	no	—
473	D₄	—	2	1	no	—
474	D₄	—	2	2	no	—
475	D₄	—	2	1	no	—
476	D₄	—	4	2	no	—
477	D₄	—	4	2	no	—
478	D₄	—	8	2	no	—
479	D₄	—	8	2	no	—
480	D₄	C₂×#41	1	2	yes	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	8	1	no	—
498	C₂×C₄	—	8	2	no	—
499	C₂×C₄	—	8	1	no	—
500	C₂×C₄	—	8	2	no	—
501	C₂×C₄	—	8	2	no	—
502	C₂×C₄	—	8	2	no	—
503	C₂×C₄	—	8	1	no	—
504	C₂×C₄	—	8	1	no	—
505	C₂×C₄	C₂²×D₄	1	2	yes	—
506	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄	C₂²×D₄	1	2	yes	—
511	C₂×C₄	C₂²×D₄	1	2	yes	—
512	C₂×C₄	C₂²×D₄	1	2	yes	—
513	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄	C₂×#41	1	2	yes	—
515	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
516	C₂×C₄	C₂⁵	1	1	yes	characteristic
517	C₈	—	2	1	no	—
518	C₈	—	2	1	no	—
519	C₈	—	2	2	no	—
520	C₈	—	2	2	no	—
521	C₈	—	2	1	no	—
522	C₈	—	2	1	no	—
523	C₂²	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	2	no	—
526	C₂²	—	4	1	no	—
527	C₂²	—	4	1	no	—
528	C₂²	—	4	1	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	1	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	16	2	no	—
535	C₂²	#548	1	2	yes	—
536	C₂²	C₂³×D₄	1	1	yes	characteristic
537	C₄	—	2	1	no	—
538	C₄	—	2	1	no	—
539	C₄	—	2	2	no	—
540	C₄	—	2	2	no	—
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	2	no	—
544	C₄	—	2	2	no	—
545	C₄	—	2	2	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	1	no	—
548	C₄	—	4	2	no	—
549	C₄	—	4	2	no	—
550	C₄	—	4	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	2	no	—
554	C₄	#548	1	2	yes	—
555	C₄	C₂²×#41	1	1	yes	characteristic
556	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
557	C₂	—	2	2	no	—
558	C₂	—	4	2	no	—
559	C₂	—	8	1	no	—
560	C₂	—	8	2	no	—
561	C₂	C₂×#548	1	1	yes	characteristic
562	C₂	#3585	1	1	yes	characteristic
563	C₂	#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
prime radical	#3045	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ #533 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3510	C₂	semidirect
2. #3503	C₂	semidirect
3. #3377	C₂	semidirect
4. #3376	C₂	semidirect
5. #3375	C₂	semidirect
6. #3373	C₂	semidirect
7. #3371	C₂	semidirect
8. #3370	C₂	semidirect
9. #3369	C₂	semidirect
10. #3367	C₂	semidirect
11. #3137	C₂	semidirect
12. #3136	C₂	semidirect
13. C₂×#489	C₂	semidirect
14. #3082	C₂	semidirect
15. #3081	C₂	semidirect
16. #3079	C₂	semidirect
17. #3046	C₂	semidirect
19. #3040	C₂	semidirect
20. #2961	C₂	semidirect
21. #2947	C₂	semidirect
22. #2946	C₂	semidirect
23. #2943	C₂	semidirect
29. Q₈²	C₂²	semidirect
30. #557	C₂²	semidirect
34. #554	C₂²	semidirect
38. D₄×Q₈	C₂²	semidirect
60. #491	C₂²	semidirect
67. #489	C₂²	semidirect
69. #488	C₂²	semidirect
70. #487	C₂²	semidirect
72. #479	C₂²	semidirect
73. #479	C₂²	semidirect
76. #477	C₂²	semidirect
77. #477	C₂²	semidirect
79. #476	C₂²	semidirect
80. #475	C₂²	semidirect
81. #475	C₂²	semidirect
83. #474	C₂²	semidirect
87. #464	C₂²	semidirect
91. #463	C₂²	semidirect
92. #462	C₂²	semidirect
93. #461	C₂²	semidirect
96. #446	C₂²	semidirect
97. #446	C₂²	semidirect
98. #446	C₂²	semidirect
99. #446	C₂²	semidirect
101. #442	C₂²	semidirect
102. #442	C₂²	semidirect
103. #441	C₂²	semidirect
104. #441	C₂²	semidirect
105. #441	C₂²	semidirect
107. #440	C₂²	semidirect
108. #440	C₂²	semidirect
109. #440	C₂²	semidirect
110. #440	C₂²	semidirect
111. #440	C₂²	semidirect
112. C₄×Q₁₆	C₂²	semidirect
114. C₄×SD₁₆	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3510	2
#3503	2
#3377	2
#3376	2
#3375	2
#3373	2
#3371	2
#3370	2
#3369	2
#3367	2
#3137	2
#3136	2
C₂×#489	2
#3082	2
#3081	2
#3079	2
#3046	2
#3045	2
#3040	2
#2961	2
#2947	2
#2946	2
#2943	2