Subgroups — #61349

Order 256.

905 conjugacy classes of subgroups.

The subgroup lattice has 575 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	#3504	C₂	1	1	yes	maximal, characteristic, complemented
3	#3377	C₂	1	2	yes	maximal, complemented
4	#3376	C₂	1	2	yes	maximal, complemented
5	#3371	C₂	1	2	yes	maximal, complemented
6	#3370	C₂	1	2	yes	maximal, complemented
7	#3368	C₂	1	2	yes	maximal, complemented
8	#3366	C₂	1	2	yes	maximal, complemented
9	#3365	C₂	1	2	yes	maximal, complemented
10	#3361	C₂	1	2	yes	maximal, complemented
11	#3142	C₂	1	1	yes	maximal, characteristic, complemented
12	#3136	C₂	1	1	yes	maximal, characteristic, complemented
13	#3136	C₂	1	1	yes	maximal, characteristic, complemented
14	#3084	C₂	1	1	yes	maximal, characteristic, complemented
15	#3083	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#478	C₂	1	1	yes	maximal, characteristic, complemented
17	#3045	C₂	1	1	yes	maximal, characteristic, complemented
18	#3045	C₂	1	1	yes	maximal, characteristic, complemented
19	#3035	C₂	1	1	yes	maximal, characteristic, complemented
20	#2962	C₂	1	1	yes	maximal, characteristic, complemented
21	#2952	C₂	1	1	yes	maximal, characteristic, complemented
22	#2951	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
25	C₂×#135	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	#557	C₂²	1	2	yes	complemented
30	#557	C₂²	1	2	yes	complemented
31	#556	C₂²	1	2	yes	—
32	#555	—	2	1	no	—
33	#554	—	2	2	no	—
34	#554	—	2	2	no	—
35	#554	C₂²	1	2	yes	complemented
36	#554	C₂²	1	2	yes	complemented
37	#553	—	2	1	no	—
38	#553	—	2	1	no	—
39	#550	C₂²	1	2	yes	—
40	#547	—	2	1	no	—
41	#544	—	2	1	no	—
42	#544	—	2	1	no	—
43	#544	C₂²	1	1	yes	characteristic
44	#544	C₂²	1	1	yes	characteristic
45	#538	—	2	2	no	—
46	#535	C₂²	1	1	yes	characteristic
47	#535	C₂²	1	1	yes	characteristic
48	#533	—	2	1	no	—
49	#533	C₂²	1	1	yes	characteristic
50	#532	C₂²	1	1	yes	characteristic
51	C₂×#125	—	2	1	no	—
52	C₂×#125	C₂²	1	1	yes	characteristic
53	#525	—	2	2	no	—
54	#520	C₂²	1	1	yes	characteristic
55	#520	C₂²	1	1	yes	characteristic
56	#520	C₂²	1	1	yes	characteristic
57	#520	C₂²	1	1	yes	characteristic
58	C₄×#41	C₂²	1	1	yes	characteristic
59	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
60	#491	C₂²	1	2	yes	complemented
61	#490	C₂²	1	2	yes	—
62	#490	C₂²	1	2	yes	—
63	#490	C₂²	1	2	yes	complemented
64	#489	C₂²	1	2	yes	—
65	#489	C₂²	1	2	yes	—
66	#488	C₂²	1	2	yes	—
67	#488	C₂²	1	2	yes	—
68	#488	C₂²	1	2	yes	complemented
69	#488	C₂²	1	2	yes	complemented
70	#486	C₂²	1	2	yes	—
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	#478	C₂²	1	2	yes	—
77	#478	C₂²	1	2	yes	—
78	#478	C₂²	1	2	yes	complemented
79	#478	C₂²	1	2	yes	complemented
80	#477	C₂²	1	2	yes	complemented
81	#476	C₂²	1	2	yes	complemented
82	#475	C₂²	1	2	yes	complemented
83	#474	C₂²	1	2	yes	complemented
84	#464	C₂²	1	2	yes	—
85	#464	C₂²	1	2	yes	—
86	#464	C₂²	1	1	yes	characteristic, complemented
87	#464	C₂²	1	1	yes	characteristic, complemented
88	#463	C₂²	1	2	yes	—
89	#463	C₂²	1	2	yes	—
90	#463	C₂²	1	1	yes	characteristic, complemented
91	#463	C₂²	1	1	yes	characteristic, complemented
92	#462	C₂²	1	1	yes	characteristic, complemented
93	#461	C₂²	1	1	yes	characteristic, complemented
94	#460	C₂²	1	2	yes	—
95	#460	C₂²	1	2	yes	—
96	#460	C₂²	1	1	yes	characteristic, complemented
97	#459	C₂²	1	2	yes	—
98	#459	C₂²	1	2	yes	—
99	#459	C₂²	1	1	yes	characteristic, complemented
100	#446	C₂²	1	2	yes	complemented
101	#446	C₂²	1	2	yes	complemented
102	#446	C₂²	1	2	yes	complemented
103	C₈×Q₈	C₂²	1	2	yes	complemented
104	#442	C₂²	1	2	yes	—
105	#442	C₂²	1	2	yes	complemented
106	#441	C₂²	1	2	yes	complemented
107	#440	C₂²	1	2	yes	—
108	#440	C₂²	1	2	yes	complemented
109	#440	C₂²	1	2	yes	complemented
110	C₄×Q₁₆	C₂²	1	2	yes	complemented
111	C₄×SD₁₆	C₂²	1	2	yes	—
112	C₄×SD₁₆	C₂²	1	2	yes	complemented
113	C₄×SD₁₆	C₂²	1	2	yes	complemented
114	C₄×D₈	C₂²	1	2	yes	—
115	C₄×D₈	C₂²	1	2	yes	complemented
116	#428	C₂²	1	1	yes	characteristic
117	C₂×#107	C₂²	1	1	yes	characteristic
118	C₂×#106	C₂²	1	1	yes	characteristic
119	#424	C₂²	1	1	yes	characteristic
120	#424	C₂²	1	1	yes	characteristic
121	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic
122	#418	C₂²	1	1	yes	characteristic
123	#417	C₂²	1	1	yes	characteristic
124	#417	C₂²	1	1	yes	characteristic
125	#417	C₂²	1	1	yes	characteristic
126	#417	C₂²	1	1	yes	characteristic
127	#417	C₂²	1	1	yes	characteristic
128	#416	C₂²	1	1	yes	characteristic
129	#416	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	C₄×M₁₆	C₂²	1	1	yes	characteristic
135	C₂×#41	—	2	2	no	—
136	C₂×#41	C₂³	1	1	yes	characteristic
137	C₂×#41	C₂³	1	1	yes	characteristic
138	C₂×#41	C₂³	1	1	yes	characteristic
139	C₂²×D₄	C₂³	1	1	yes	characteristic
140	C₂³×C₄	—	2	1	no	—
141	AGL(1,ℤ/8)	—	2	4	no	—
142	#135	—	2	4	no	—
143	#135	—	2	4	no	—
144	C₂×Q₁₆	C₂³	1	1	yes	characteristic
145	C₂×Q₁₆	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆	C₂³	1	2	yes	—
151	C₂×D₈	C₂³	1	1	yes	characteristic
152	C₂×D₈	C₂³	1	1	yes	characteristic
153	C₂×D₈	C₂³	1	2	yes	—
154	C₂×M₁₆	C₂³	1	1	yes	characteristic
155	C₂×M₁₆	C₂³	1	1	yes	characteristic
156	C₂²×C₈	C₂³	1	1	yes	characteristic
157	C₂²×C₈	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈	—	2	2	no	—
159	C₄⋊Q₈	—	2	2	no	—
160	C₄⋊Q₈	—	2	1	no	—
161	C₄⋊Q₈	—	2	1	no	—
162	C₄⋊Q₈	D₄	1	1	yes	characteristic
163	C₄⋊Q₈	D₄	1	1	yes	characteristic
164	C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈	C₂³	1	2	yes	—
166	C₄⋊Q₈	C₂³	1	2	yes	—
167	#127	C₂³	1	1	yes	characteristic
168	#127	C₂³	1	2	yes	—
169	#127	C₂³	1	2	yes	—
170	#126	—	2	2	no	—
171	#126	—	2	2	no	—
172	#125	—	2	1	no	—
173	#125	—	2	1	no	—
174	#125	—	2	2	no	—
175	#125	—	2	2	no	—
176	#125	—	2	2	no	—
177	#125	—	2	2	no	—
178	#125	—	2	1	no	—
179	#125	—	2	1	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	#125	C₂³	1	2	yes	—
185	#125	C₂³	1	2	yes	—
186	#124	—	2	2	no	—
187	#124	—	2	2	no	—
188	#124	C₂³	1	1	yes	characteristic
189	#124	C₂³	1	1	yes	characteristic
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	C₂²⋊Q₈	—	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	2	no	—
201	C₂²⋊Q₈	—	2	2	no	—
202	C₂²⋊Q₈	—	2	2	no	—
203	C₂²⋊Q₈	—	2	2	no	—
204	C₂²⋊Q₈	—	2	2	no	—
205	C₂²⋊Q₈	D₄	1	2	yes	—
206	C₂²⋊Q₈	D₄	1	2	yes	—
207	#121	—	2	1	no	—
208	#121	—	2	1	no	—
209	#121	—	2	2	no	—
210	#121	—	2	1	no	—
211	#121	—	2	1	no	—
212	#121	—	2	1	no	—
213	#121	—	2	1	no	—
214	#121	—	2	2	no	—
215	#121	—	2	2	no	—
216	#120	—	2	2	no	—
217	#120	—	2	2	no	—
218	C₄×Q₈	—	2	2	no	—
219	C₄×Q₈	—	2	2	no	—
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	2	no	—
231	C₄×D₄	—	2	2	no	—
232	C₄×D₄	—	2	2	no	—
233	C₄×D₄	—	2	2	no	—
234	C₄×D₄	—	2	2	no	—
235	C₄×D₄	—	2	2	no	—
236	C₄×D₄	—	2	1	no	—
237	C₄×D₄	—	2	1	no	—
238	C₄×D₄	—	2	1	no	—
239	C₄×D₄	—	2	1	no	—
240	C₄×D₄	C₂³	1	2	yes	—
241	C₄×D₄	C₂³	1	2	yes	—
242	C₄×D₄	C₂³	1	1	yes	characteristic
243	C₄×D₄	C₂³	1	1	yes	characteristic
244	C₄×D₄	C₂³	1	2	yes	—
245	C₄×D₄	C₂³	1	2	yes	—
246	C₄×D₄	C₂³	1	2	yes	—
247	C₄×D₄	C₂³	1	2	yes	—
248	#117	—	2	1	no	—
249	#117	—	2	1	no	—
250	#117	—	2	1	no	—
251	#117	—	2	1	no	—
252	#117	—	2	2	no	—
253	#117	—	2	1	no	—
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	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
268	C₂×C₂²⋊C₄	—	2	1	no	—
269	C₂×C₄²	—	2	1	no	—
270	C₂×C₄²	C₂³	1	1	yes	characteristic
271	#107	C₂³	1	2	yes	—
272	#107	C₂³	1	2	yes	—
273	#107	C₂³	1	2	yes	—
274	#106	C₂³	1	2	yes	—
275	#106	C₂³	1	2	yes	—
276	#106	C₂³	1	2	yes	—
277	C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₄⋊C₈	C₂³	1	2	yes	—
282	C₄⋊C₈	C₂³	1	2	yes	—
283	C₄⋊C₈	C₂³	1	2	yes	—
284	C₄⋊C₈	C₂³	1	2	yes	—
285	#103	C₂³	1	1	yes	characteristic
286	#103	C₂³	1	1	yes	characteristic
287	#103	C₂³	1	1	yes	characteristic
288	#103	C₂³	1	1	yes	characteristic
289	#103	C₂³	1	2	yes	—
290	#103	C₂³	1	2	yes	—
291	#103	C₂³	1	2	yes	—
292	#103	C₂³	1	2	yes	—
293	#103	C₂³	1	2	yes	—
294	#102	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	1	yes	characteristic
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	2	yes	—
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	#102	C₂³	1	2	yes	—
308	#102	C₂³	1	2	yes	—
309	#97	C₂³	1	2	yes	—
310	#97	C₂³	1	2	yes	—
311	#97	C₂³	1	2	yes	—
312	C₄×C₈	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	—	2	2	no	—
320	#41	—	2	2	no	—
321	#41	—	8	4	no	—
322	#41	#41	1	4	yes	complemented
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	C₂×D₄	1	2	yes	—
326	C₂×Q₈	C₂×D₄	1	2	yes	—
327	C₂×Q₈	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈	C₂⁴	1	1	yes	characteristic
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	C₂⁴	1	2	yes	—
343	C₂×D₄	C₂⁴	1	1	yes	characteristic
344	C₂×D₄	C₂⁴	1	1	yes	characteristic
345	C₂×D₄	C₂⁴	1	1	yes	characteristic
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	2	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	8	2	no	—
361	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄	C₂⁴	1	1	yes	characteristic
364	Q₁₆	—	2	2	no	—
365	Q₁₆	—	2	2	no	—
366	SD₁₆	—	2	2	no	—
367	SD₁₆	—	2	2	no	—
368	SD₁₆	—	2	4	no	—
369	SD₁₆	—	2	2	no	—
370	SD₁₆	—	2	2	no	—
371	D₈	—	2	2	no	—
372	D₈	—	2	2	no	—
373	D₈	—	2	4	no	—
374	M₁₆	—	2	2	no	—
375	M₁₆	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	C₂⁴	1	2	yes	—
379	C₂×C₈	C₂⁴	1	1	yes	characteristic
380	C₂×C₈	C₂⁴	1	1	yes	characteristic
381	C₂×C₈	C₂⁴	1	2	yes	—
382	C₂×C₈	C₂⁴	1	1	yes	characteristic
383	C₂×C₈	C₂⁴	1	1	yes	characteristic
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	2	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	—	2	2	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
406	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
407	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄	C₂×D₄	1	2	yes	—
409	C₄⋊C₄	C₂×D₄	1	2	yes	—
410	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
411	C₄⋊C₄	C₂×D₄	1	2	yes	—
412	C₄⋊C₄	C₂×D₄	1	2	yes	—
413	C₄⋊C₄	C₂×D₄	1	2	yes	—
414	C₄⋊C₄	C₂×D₄	1	2	yes	—
415	C₄⋊C₄	C₂⁴	1	2	yes	—
416	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄	C₂⁴	1	2	yes	—
418	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄	C₂⁴	1	2	yes	—
420	C₂²⋊C₄	—	2	1	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	2	1	no	—
426	C₂²⋊C₄	—	2	1	no	—
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	2	1	no	—
432	C₂²⋊C₄	—	2	1	no	—
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	1	no	—
436	C₂²⋊C₄	—	2	1	no	—
437	C₂²⋊C₄	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄	C₂×D₄	1	2	yes	—
439	C₄²	—	2	1	no	—
440	C₄²	—	2	1	no	—
441	C₄²	—	2	1	no	—
442	C₄²	—	2	2	no	—
443	C₄²	—	2	2	no	—
444	C₄²	—	2	2	no	—
445	C₄²	—	2	2	no	—
446	C₄²	C₂×D₄	1	1	yes	characteristic
447	C₄²	C₂×D₄	1	1	yes	characteristic
448	C₄²	C₂⁴	1	1	yes	characteristic
449	C₄²	C₂⁴	1	2	yes	—
450	C₄²	C₂⁴	1	2	yes	—
451	C₄²	C₂⁴	1	1	yes	characteristic
452	C₂³	—	2	1	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	2	1	no	—
455	C₂³	—	2	1	no	—
456	C₂³	—	4	2	no	—
457	C₂³	—	8	1	no	—
458	C₂³	—	8	1	no	—
459	C₂³	C₂²×D₄	1	1	yes	characteristic
460	Q₈	—	2	1	no	—
461	Q₈	—	2	1	no	—
462	Q₈	—	2	1	no	—
463	Q₈	—	2	1	no	—
464	Q₈	—	2	1	no	—
465	Q₈	—	4	2	no	—
466	Q₈	—	4	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	1	no	—
475	D₄	—	2	2	no	—
476	D₄	—	2	1	no	—
477	D₄	—	2	1	no	—
478	D₄	—	4	2	no	—
479	D₄	—	4	2	no	—
480	D₄	—	4	2	no	—
481	D₄	—	4	2	no	—
482	D₄	—	8	1	no	—
483	D₄	—	8	2	no	—
484	D₄	—	8	2	no	—
485	D₄	—	8	2	no	—
486	D₄	—	8	2	no	—
487	D₄	C₂×#41	1	2	yes	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	4	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	8	1	no	—
503	C₂×C₄	—	8	2	no	—
504	C₂×C₄	—	8	1	no	—
505	C₂×C₄	—	8	2	no	—
506	C₂×C₄	—	8	2	no	—
507	C₂×C₄	—	8	2	no	—
508	C₂×C₄	—	8	2	no	—
509	C₂×C₄	—	8	1	no	—
510	C₂×C₄	—	8	1	no	—
511	C₂×C₄	—	8	1	no	—
512	C₂×C₄	C₂²×D₄	1	2	yes	—
513	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄	C₂²×D₄	1	2	yes	—
516	C₂×C₄	C₂²×D₄	1	2	yes	—
517	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄	C₂²×D₄	1	2	yes	—
520	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄	C₂×#41	1	2	yes	—
522	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
523	C₂×C₄	C₂⁵	1	1	yes	characteristic
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	2	1	no	—
527	C₈	—	2	1	no	—
528	C₈	—	2	2	no	—
529	C₈	—	2	2	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	1	no	—
535	C₂²	—	4	1	no	—
536	C₂²	—	4	1	no	—
537	C₂²	—	4	2	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	4	1	no	—
540	C₂²	—	4	1	no	—
541	C₂²	—	4	1	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	8	4	no	—
545	C₂²	#548	1	2	yes	—
546	C₂²	C₂³×D₄	1	1	yes	characteristic
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	2	no	—
550	C₄	—	2	2	no	—
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	2	2	no	—
554	C₄	—	2	2	no	—
555	C₄	—	2	2	no	—
556	C₄	—	4	2	no	—
557	C₄	—	4	1	no	—
558	C₄	—	4	2	no	—
559	C₄	—	4	2	no	—
560	C₄	—	4	1	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	1	no	—
563	C₄	#548	1	2	yes	—
564	C₄	C₂²×#41	1	1	yes	characteristic
565	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
566	C₂	—	2	2	no	—
567	C₂	—	4	2	no	—
568	C₂	—	8	1	no	—
569	C₂	—	8	1	no	—
570	C₂	—	8	2	no	—
571	C₂	C₂×#548	1	1	yes	characteristic
572	C₂	#3584	1	1	yes	characteristic
573	C₂	#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
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. #3506	C₂	semidirect
2. #3504	C₂	semidirect
3. #3377	C₂	semidirect
4. #3376	C₂	semidirect
5. #3371	C₂	semidirect
6. #3370	C₂	semidirect
7. #3368	C₂	semidirect
8. #3366	C₂	semidirect
9. #3365	C₂	semidirect
10. #3361	C₂	semidirect
11. #3142	C₂	semidirect
12. #3136	C₂	semidirect
13. #3136	C₂	semidirect
14. #3084	C₂	semidirect
15. #3083	C₂	semidirect
16. C₂×#478	C₂	semidirect
17. #3045	C₂	semidirect
18. #3045	C₂	semidirect
19. #3035	C₂	semidirect
20. #2962	C₂	semidirect
21. #2952	C₂	semidirect
22. #2951	C₂	semidirect
23. C₄×AGL(1,ℤ/8)	C₂	semidirect
29. #557	C₂²	semidirect
30. #557	C₂²	semidirect
35. #554	C₂²	semidirect
36. #554	C₂²	semidirect
60. #491	C₂²	semidirect
63. #490	C₂²	semidirect
68. #488	C₂²	semidirect
69. #488	C₂²	semidirect
72. #479	C₂²	semidirect
73. #479	C₂²	semidirect
78. #478	C₂²	semidirect
79. #478	C₂²	semidirect
80. #477	C₂²	semidirect
81. #476	C₂²	semidirect
82. #475	C₂²	semidirect
83. #474	C₂²	semidirect
86. #464	C₂²	semidirect
87. #464	C₂²	semidirect
90. #463	C₂²	semidirect
91. #463	C₂²	semidirect
92. #462	C₂²	semidirect
93. #461	C₂²	semidirect
96. #460	C₂²	semidirect
99. #459	C₂²	semidirect
100. #446	C₂²	semidirect
101. #446	C₂²	semidirect
102. #446	C₂²	semidirect
103. C₈×Q₈	C₂²	semidirect
105. #442	C₂²	semidirect
106. #441	C₂²	semidirect
108. #440	C₂²	semidirect
109. #440	C₂²	semidirect
110. C₄×Q₁₆	C₂²	semidirect
112. C₄×SD₁₆	C₂²	semidirect
113. C₄×SD₁₆	C₂²	semidirect
115. C₄×D₈	C₂²	semidirect
322. #41	#41	semidirect

Maximal subgroups

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

subgroup	index
#3506	2
#3504	2
#3377	2
#3376	2
#3371	2
#3370	2
#3368	2
#3366	2
#3365	2
#3361	2
#3142	2
#3136	2
#3084	2
#3083	2
C₂×#478	2
#3045	2
#3035	2
#2962	2
#2952	2
#2951	2
C₄×AGL(1,ℤ/8)	2