Subgroups — #62201

Order 256.

872 conjugacy classes of subgroups.

The subgroup lattice has 563 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	#3520	C₂	1	1	yes	maximal, characteristic, complemented
3	#3386	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×D₈	C₂	1	1	yes	maximal, characteristic, complemented
5	#3367	C₂	1	1	yes	maximal, characteristic, complemented
6	#3364	C₂	1	1	yes	maximal, characteristic, complemented
7	#3353	C₂	1	1	yes	maximal, characteristic, complemented
8	#3346	C₂	1	2	yes	maximal, complemented
9	#3338	C₂	1	2	yes	maximal, complemented
10	#3334	C₂	1	1	yes	maximal, characteristic, complemented
11	#3330	C₂	1	1	yes	maximal, characteristic, complemented
12	#3314	C₂	1	2	yes	maximal, complemented
13	#3302	C₂	1	1	yes	maximal, characteristic, complemented
14	#3297	C₂	1	2	yes	maximal, complemented
15	#3262	C₂	1	2	yes	maximal, complemented
16	#3248	C₂	1	1	yes	maximal, characteristic, complemented
17	#3243	C₂	1	2	yes	maximal, complemented
18	#3230	C₂	1	1	yes	maximal, characteristic, complemented
19	#3124	C₂	1	2	yes	maximal, complemented
20	#3105	C₂	1	1	yes	maximal, characteristic, complemented
21	#3083	C₂	1	2	yes	maximal, complemented
22	C₂×#474	C₂	1	1	yes	maximal, characteristic, complemented
23	#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	#563	—	2	2	no	—
25	#557	C₂²	1	1	yes	characteristic, complemented
26	#556	C₂²	1	1	yes	characteristic
27	#556	C₂²	1	1	yes	characteristic, complemented
28	#554	C₂²	1	2	yes	—
29	#554	C₂²	1	2	yes	—
30	#553	C₂²	1	2	yes	—
31	#552	—	2	1	no	—
32	#551	—	2	2	no	—
33	D₄×Q₈	—	2	1	no	—
34	D₄×Q₈	C₂²	1	1	yes	characteristic
35	D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
36	#548	—	2	1	no	—
37	#548	—	2	1	no	—
38	#547	C₂²	1	1	yes	characteristic
39	#547	C₂²	1	1	yes	characteristic
40	#547	C₂²	1	1	yes	characteristic, complemented
41	#546	C₂²	1	2	yes	—
42	#544	C₂²	1	2	yes	complemented
43	#542	C₂²	1	2	yes	—
44	#542	C₂²	1	2	yes	complemented
45	#541	—	2	1	no	—
46	#539	—	2	2	no	—
47	#539	—	2	2	no	—
48	#536	—	2	1	no	—
49	#533	C₂²	1	1	yes	characteristic
50	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic
51	#529	C₂²	1	1	yes	characteristic
52	#529	C₂²	1	1	yes	characteristic
53	#525	—	2	1	no	—
54	C₂×C₂²⋊Q₈	—	2	1	no	—
55	#520	C₂²	1	2	yes	—
56	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
57	#501	C₂²	1	2	yes	complemented
58	#500	C₂²	1	1	yes	characteristic, complemented
59	#500	C₂²	1	2	yes	complemented
60	#500	C₂²	1	1	yes	characteristic, complemented
61	#489	C₂²	1	2	yes	—
62	#488	C₂²	1	2	yes	—
63	#487	C₂²	1	1	yes	characteristic, complemented
64	#487	C₂²	1	1	yes	characteristic, complemented
65	#485	C₂²	1	2	yes	complemented
66	#484	C₂²	1	1	yes	characteristic
67	#484	C₂²	1	2	yes	—
68	#484	C₂²	1	2	yes	—
69	#484	C₂²	1	2	yes	complemented
70	#484	C₂²	1	2	yes	complemented
71	#482	C₂²	1	2	yes	—
72	#481	C₂²	1	1	yes	characteristic
73	#480	C₂²	1	2	yes	—
74	#480	C₂²	1	2	yes	complemented
75	#479	C₂²	1	2	yes	complemented
76	#479	C₂²	1	2	yes	complemented
77	#478	C₂²	1	1	yes	characteristic
78	#478	C₂²	1	2	yes	—
79	#478	C₂²	1	1	yes	characteristic
80	#477	C₂²	1	2	yes	complemented
81	#477	C₂²	1	2	yes	complemented
82	#477	C₂²	1	2	yes	complemented
83	#477	C₂²	1	2	yes	complemented
84	#475	C₂²	1	1	yes	characteristic, complemented
85	#474	C₂²	1	1	yes	characteristic
86	#474	C₂²	1	1	yes	characteristic
87	#474	C₂²	1	2	yes	—
88	#474	C₂²	1	2	yes	—
89	#474	C₂²	1	1	yes	characteristic
90	#474	C₂²	1	1	yes	characteristic
91	#474	C₂²	1	2	yes	—
92	#474	C₂²	1	1	yes	characteristic, complemented
93	#474	C₂²	1	2	yes	complemented
94	#468	C₂²	1	2	yes	—
95	#468	C₂²	1	2	yes	complemented
96	#467	C₂²	1	2	yes	—
97	#467	C₂²	1	2	yes	complemented
98	#466	C₂²	1	2	yes	—
99	#465	C₂²	1	2	yes	—
100	#464	C₂²	1	2	yes	—
101	#464	C₂²	1	2	yes	complemented
102	#463	C₂²	1	1	yes	characteristic
103	#463	C₂²	1	1	yes	characteristic
104	#463	C₂²	1	2	yes	—
105	#462	C₂²	1	1	yes	characteristic, complemented
106	#461	C₂²	1	1	yes	characteristic, complemented
107	#452	C₂²	1	2	yes	—
108	#450	C₂²	1	1	yes	characteristic
109	#449	C₂²	1	2	yes	—
110	#447	C₂²	1	1	yes	characteristic
111	#446	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
113	#440	C₂²	1	2	yes	—
114	#440	C₂²	1	2	yes	complemented
115	C₄×Q₁₆	C₂²	1	2	yes	complemented
116	C₄×SD₁₆	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆	C₂²	1	1	yes	characteristic
118	C₄×D₈	C₂²	1	1	yes	characteristic
119	C₄×D₈	C₂²	1	1	yes	characteristic
120	C₄×D₈	C₂²	1	2	yes	—
121	#436	C₂²	1	1	yes	characteristic, complemented
122	#435	C₂²	1	2	yes	—
123	C₈×D₄	C₂²	1	2	yes	—
124	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
125	#433	C₂²	1	2	yes	complemented
126	#431	C₂²	1	1	yes	characteristic
127	#428	C₂²	1	2	yes	complemented
128	C₂×#107	C₂²	1	2	yes	—
129	C₂×#107	C₂²	1	2	yes	complemented
130	#424	C₂²	1	2	yes	complemented
131	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic
132	#417	C₂²	1	2	yes	—
133	#416	C₂²	1	2	yes	—
134	C₂×#102	C₂²	1	2	yes	—
135	C₂×#41	—	2	1	no	—
136	C₂×#41	—	2	1	no	—
137	C₂×#41	C₂³	1	2	yes	—
138	C₂²×Q₈	—	2	1	no	—
139	C₂²×Q₈	—	2	1	no	—
140	C₂²×Q₈	—	2	1	no	—
141	C₂²×D₄	C₂³	1	1	yes	characteristic
142	C₂³×C₄	—	2	1	no	—
143	C₂×Q₁₆	C₂³	1	2	yes	—
144	C₂×SD₁₆	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆	C₂³	1	2	yes	—
147	C₂×D₈	C₂³	1	1	yes	characteristic
148	C₂×D₈	C₂³	1	1	yes	characteristic
149	C₂×M₁₆	C₂³	1	2	yes	—
150	C₂²×C₈	C₂³	1	2	yes	—
151	C₂²×C₈	C₂³	1	2	yes	—
152	C₄⋊Q₈	—	2	1	no	—
153	C₄⋊Q₈	—	2	2	no	—
154	C₄⋊Q₈	—	2	1	no	—
155	C₄⋊Q₈	—	2	1	no	—
156	C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₄⋊Q₈	C₂³	1	2	yes	—
158	C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈	C₂³	1	2	yes	—
162	C₄⋊Q₈	C₂³	1	2	yes	—
163	#126	—	2	2	no	—
164	#126	—	2	2	no	—
165	#126	—	2	2	no	—
166	#126	—	2	2	no	—
167	#126	—	2	2	no	—
168	#126	—	2	1	no	—
169	#126	D₄	1	2	yes	—
170	#125	—	2	2	no	—
171	#125	—	2	2	no	—
172	#125	—	2	2	no	—
173	#125	—	2	2	no	—
174	#125	—	2	1	no	—
175	#125	D₄	1	1	yes	characteristic
176	#125	C₂³	1	1	yes	characteristic
177	#125	C₂³	1	2	yes	—
178	#124	—	2	1	no	—
179	#124	—	2	2	no	—
180	#124	—	2	2	no	—
181	#124	D₄	1	1	yes	characteristic
182	#124	C₂³	1	1	yes	characteristic
183	#124	C₂³	1	2	yes	—
184	#123	—	2	1	no	—
185	#123	—	2	2	no	—
186	#123	—	2	2	no	—
187	#123	—	2	2	no	—
188	#123	—	2	2	no	—
189	#123	—	2	2	no	—
190	#123	—	2	2	no	—
191	#123	—	2	2	no	—
192	#123	D₄	1	2	yes	—
193	C₂²⋊Q₈	—	2	1	no	—
194	C₂²⋊Q₈	—	2	1	no	—
195	C₂²⋊Q₈	—	2	2	no	—
196	C₂²⋊Q₈	—	2	1	no	—
197	C₂²⋊Q₈	—	2	1	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	1	yes	characteristic
210	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
211	C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₂²⋊Q₈	C₂³	1	2	yes	—
214	#121	—	2	1	no	—
215	#121	—	2	2	no	—
216	#121	—	2	2	no	—
217	#121	D₄	1	1	yes	characteristic
218	#121	C₂³	1	1	yes	characteristic
219	#121	C₂³	1	2	yes	—
220	#121	C₂³	1	2	yes	—
221	#120	—	2	2	no	—
222	C₄×Q₈	—	2	1	no	—
223	C₄×Q₈	—	2	1	no	—
224	C₄×Q₈	—	2	1	no	—
225	C₄×Q₈	C₂³	1	2	yes	—
226	C₄×Q₈	C₂³	1	2	yes	—
227	C₄×Q₈	C₂³	1	1	yes	characteristic
228	C₄×Q₈	C₂³	1	2	yes	—
229	C₄×Q₈	C₂³	1	1	yes	characteristic
230	C₄×D₄	—	2	2	no	—
231	C₄×D₄	—	2	2	no	—
232	C₄×D₄	—	2	1	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	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	1	yes	characteristic
244	C₄×D₄	C₂³	1	2	yes	—
245	C₄×D₄	C₂³	1	2	yes	—
246	C₄×D₄	C₂³	1	1	yes	characteristic
247	#117	—	2	1	no	—
248	#117	—	2	2	no	—
249	#117	—	2	1	no	—
250	#117	—	2	1	no	—
251	#117	C₂³	1	2	yes	—
252	#117	C₂³	1	2	yes	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄	C₂³	1	2	yes	—
260	C₂×C₂²⋊C₄	—	2	1	no	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₄²	C₂³	1	1	yes	characteristic
263	#107	C₂³	1	2	yes	—
264	#107	C₂³	1	2	yes	—
265	#107	C₂³	1	2	yes	—
266	#107	C₂³	1	2	yes	—
267	#107	C₂³	1	1	yes	characteristic
268	#107	C₂³	1	2	yes	—
269	#107	C₂³	1	2	yes	—
270	#107	C₂³	1	2	yes	—
271	#107	C₂³	1	2	yes	—
272	#107	C₂³	1	1	yes	characteristic
273	#107	C₂³	1	2	yes	—
274	#106	C₂³	1	1	yes	characteristic
275	#106	C₂³	1	2	yes	—
276	#106	C₂³	1	1	yes	characteristic
277	C₄⋊C₈	C₂³	1	2	yes	—
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	1	yes	characteristic
284	#103	C₂³	1	2	yes	—
285	#103	C₂³	1	2	yes	—
286	#103	C₂³	1	2	yes	—
287	#103	C₂³	1	2	yes	—
288	#103	C₂³	1	1	yes	characteristic
289	#103	C₂³	1	1	yes	characteristic
290	#103	C₂³	1	2	yes	—
291	#103	C₂³	1	2	yes	—
292	#103	C₂³	1	2	yes	—
293	#102	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	1	yes	characteristic
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	1	yes	characteristic
304	C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₂²⋊C₈	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈	C₂³	1	2	yes	—
307	C₂²⋊C₈	C₂³	1	2	yes	—
308	#97	C₂³	1	2	yes	—
309	C₄×C₈	C₂³	1	1	yes	characteristic
310	C₄×C₈	C₂³	1	1	yes	characteristic
311	C₄×C₈	C₂³	1	2	yes	—
312	C₂⁴	—	2	1	no	—
313	#41	—	2	4	no	—
314	#41	—	4	2	no	—
315	#41	—	8	2	no	—
316	#41	—	8	2	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	8	2	no	—
324	C₂×Q₈	—	8	2	no	—
325	C₂×Q₈	—	8	2	no	—
326	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈	C₂⁴	1	2	yes	—
328	C₂×Q₈	C₂⁴	1	1	yes	characteristic
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	4	1	no	—
336	C₂×D₄	C₂×D₄	1	2	yes	—
337	C₂×D₄	C₂×D₄	1	1	yes	characteristic
338	C₂×D₄	C₂⁴	1	1	yes	characteristic
339	C₂×D₄	C₂⁴	1	1	yes	characteristic
340	C₂×D₄	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	8	2	no	—
354	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄	C₂⁴	1	2	yes	—
358	Q₁₆	—	4	2	no	—
359	SD₁₆	—	2	2	no	—
360	SD₁₆	—	4	2	no	—
361	SD₁₆	—	4	1	no	—
362	D₈	—	2	2	no	—
363	D₈	—	4	1	no	—
364	M₁₆	—	4	2	no	—
365	C₂×C₈	—	4	2	no	—
366	C₂×C₈	—	4	2	no	—
367	C₂×C₈	C₂⁴	1	1	yes	characteristic
368	C₂×C₈	C₂⁴	1	1	yes	characteristic
369	C₂×C₈	C₂⁴	1	2	yes	—
370	C₂×C₈	C₂⁴	1	1	yes	characteristic
371	C₂×C₈	C₂⁴	1	1	yes	characteristic
372	C₂×C₈	C₂⁴	1	2	yes	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	1	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	1	no	—
397	C₄⋊C₄	C₂×D₄	1	2	yes	—
398	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄	C₂×D₄	1	2	yes	—
400	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄	C₂×D₄	1	2	yes	—
402	C₄⋊C₄	C₂×D₄	1	2	yes	—
403	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄	C₂⁴	1	2	yes	—
406	C₄⋊C₄	C₂⁴	1	2	yes	—
407	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄	C₂⁴	1	2	yes	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	2	1	no	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	—	2	1	no	—
416	C₂²⋊C₄	—	2	1	no	—
417	C₂²⋊C₄	—	2	1	no	—
418	C₂²⋊C₄	—	2	1	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	1	no	—
424	C₂²⋊C₄	—	2	1	no	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	2	1	no	—
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	2	1	no	—
429	C₂²⋊C₄	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄	C₂×D₄	1	2	yes	—
434	C₄²	—	2	2	no	—
435	C₄²	—	2	2	no	—
436	C₄²	—	2	1	no	—
437	C₄²	—	2	2	no	—
438	C₄²	—	2	2	no	—
439	C₄²	C₂×D₄	1	1	yes	characteristic
440	C₄²	C₂×D₄	1	1	yes	characteristic
441	C₄²	C₂⁴	1	1	yes	characteristic
442	C₄²	C₂⁴	1	2	yes	—
443	C₄²	C₂⁴	1	1	yes	characteristic
444	C₂³	—	2	1	no	—
445	C₂³	—	2	1	no	—
446	C₂³	—	2	1	no	—
447	C₂³	—	4	2	no	—
448	C₂³	—	4	2	no	—
449	C₂³	—	8	1	no	—
450	C₂³	C₂²×D₄	1	2	yes	—
451	C₂³	C₂²×D₄	1	1	yes	characteristic
452	Q₈	—	2	2	no	—
453	Q₈	—	2	1	no	—
454	Q₈	—	2	2	no	—
455	Q₈	—	2	1	no	—
456	Q₈	—	2	2	no	—
457	Q₈	—	4	2	no	—
458	Q₈	—	4	2	no	—
459	Q₈	—	4	2	no	—
460	Q₈	—	8	2	no	—
461	Q₈	—	8	2	no	—
462	Q₈	—	8	2	no	—
463	D₄	—	2	4	no	—
464	D₄	—	2	2	no	—
465	D₄	—	2	1	no	—
466	D₄	—	2	1	no	—
467	D₄	—	2	1	no	—
468	D₄	—	2	1	no	—
469	D₄	—	2	1	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	4	no	—
472	D₄	—	4	2	no	—
473	D₄	—	8	2	no	—
474	D₄	—	8	2	no	—
475	D₄	2₋¹⁺⁴	1	2	yes	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	4	4	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	8	1	no	—
496	C₂×C₄	—	8	1	no	—
497	C₂×C₄	—	8	2	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	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄	C₂²×D₄	1	2	yes	—
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	2	yes	—
510	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄	C₂⁵	1	1	yes	characteristic
512	C₈	—	2	1	no	—
513	C₈	—	2	1	no	—
514	C₈	—	2	1	no	—
515	C₈	—	2	2	no	—
516	C₈	—	2	2	no	—
517	C₈	—	2	1	no	—
518	C₂²	—	2	1	no	—
519	C₂²	—	2	1	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	2	no	—
524	C₂²	—	4	1	no	—
525	C₂²	—	4	1	no	—
526	C₂²	—	4	1	no	—
527	C₂²	—	4	1	no	—
528	C₂²	—	4	1	no	—
529	C₂²	—	4	1	no	—
530	C₂²	—	4	1	no	—
531	C₂²	—	4	1	no	—
532	C₂²	—	8	4	no	—
533	C₂²	#578	1	2	yes	—
534	C₂²	C₂³×D₄	1	1	yes	characteristic
535	C₄	—	2	2	no	—
536	C₄	—	2	1	no	—
537	C₄	—	2	1	no	—
538	C₄	—	2	2	no	—
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	2	2	no	—
542	C₄	—	4	2	no	—
543	C₄	—	4	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	2	no	—
548	C₄	—	4	2	no	—
549	C₄	—	4	2	no	—
550	C₄	—	4	1	no	—
551	C₄	#576	1	2	yes	—
552	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
553	C₄	#585	1	1	yes	characteristic
554	C₂	—	2	2	no	—
555	C₂	—	4	2	no	—
556	C₂	—	4	2	no	—
557	C₂	—	8	1	no	—
558	C₂	—	8	1	no	—
559	C₂	#3489	1	1	yes	characteristic
560	C₂	C₂×#576	1	1	yes	characteristic
561	C₂	C₂×#578	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 ◁ #529 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3552	C₂	semidirect
2. #3520	C₂	semidirect
3. #3386	C₂	semidirect
4. Q₈×D₈	C₂	semidirect
5. #3367	C₂	semidirect
6. #3364	C₂	semidirect
7. #3353	C₂	semidirect
8. #3346	C₂	semidirect
9. #3338	C₂	semidirect
10. #3334	C₂	semidirect
11. #3330	C₂	semidirect
12. #3314	C₂	semidirect
13. #3302	C₂	semidirect
14. #3297	C₂	semidirect
15. #3262	C₂	semidirect
16. #3248	C₂	semidirect
17. #3243	C₂	semidirect
18. #3230	C₂	semidirect
19. #3124	C₂	semidirect
20. #3105	C₂	semidirect
21. #3083	C₂	semidirect
22. C₂×#474	C₂	semidirect
23. #2994	C₂	semidirect
25. #557	C₂²	semidirect
27. #556	C₂²	semidirect
35. D₄×Q₈	C₂²	semidirect
40. #547	C₂²	semidirect
42. #544	C₂²	semidirect
44. #542	C₂²	semidirect
57. #501	C₂²	semidirect
58. #500	C₂²	semidirect
59. #500	C₂²	semidirect
60. #500	C₂²	semidirect
63. #487	C₂²	semidirect
64. #487	C₂²	semidirect
65. #485	C₂²	semidirect
69. #484	C₂²	semidirect
70. #484	C₂²	semidirect
74. #480	C₂²	semidirect
75. #479	C₂²	semidirect
76. #479	C₂²	semidirect
80. #477	C₂²	semidirect
81. #477	C₂²	semidirect
82. #477	C₂²	semidirect
83. #477	C₂²	semidirect
84. #475	C₂²	semidirect
92. #474	C₂²	semidirect
93. #474	C₂²	semidirect
95. #468	C₂²	semidirect
97. #467	C₂²	semidirect
101. #464	C₂²	semidirect
105. #462	C₂²	semidirect
106. #461	C₂²	semidirect
111. #446	C₂²	semidirect
112. C₈×Q₈	C₂²	semidirect
114. #440	C₂²	semidirect
115. C₄×Q₁₆	C₂²	semidirect
121. #436	C₂²	semidirect
124. C₈×D₄	C₂²	semidirect
125. #433	C₂²	semidirect
127. #428	C₂²	semidirect
129. C₂×#107	C₂²	semidirect
130. #424	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3552	2
#3520	2
#3386	2
Q₈×D₈	2
#3367	2
#3364	2
#3353	2
#3346	2
#3338	2
#3334	2
#3330	2
#3314	2
#3302	2
#3297	2
#3262	2
#3248	2
#3243	2
#3230	2
#3124	2
#3105	2
#3083	2
C₂×#474	2
#2994	2