Subgroups — #62189

Order 256.

846 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	#3520	C₂	1	1	yes	maximal, characteristic
3	#3386	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	#3369	C₂	1	1	yes	maximal, characteristic, complemented
6	#3364	C₂	1	1	yes	maximal, characteristic, complemented
7	#3356	C₂	1	2	yes	maximal, complemented
8	#3353	C₂	1	1	yes	maximal, characteristic, complemented
9	#3344	C₂	1	2	yes	maximal, complemented
10	#3335	C₂	1	1	yes	maximal, characteristic, complemented
11	#3331	C₂	1	1	yes	maximal, characteristic, complemented
12	#3323	C₂	1	2	yes	maximal, complemented
13	#3311	C₂	1	2	yes	maximal, complemented
14	#3302	C₂	1	1	yes	maximal, characteristic, complemented
15	#3258	C₂	1	2	yes	maximal, complemented
16	#3255	C₂	1	1	yes	maximal, characteristic, complemented
17	#3244	C₂	1	2	yes	maximal, complemented
18	#3231	C₂	1	1	yes	maximal, characteristic, complemented
19	#3120	C₂	1	2	yes	maximal, complemented
20	#3101	C₂	1	1	yes	maximal, characteristic, complemented
21	#3084	C₂	1	2	yes	maximal, complemented
22	#3077	C₂	1	1	yes	maximal, characteristic, complemented
23	#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	#563	—	2	2	no	—
25	Q₈²	C₂²	1	1	yes	characteristic, complemented
26	#557	—	2	1	no	—
27	#557	C₂²	1	1	yes	characteristic, complemented
28	#556	—	2	1	no	—
29	#556	C₂²	1	1	yes	characteristic
30	#556	C₂²	1	2	yes	—
31	#556	C₂²	1	1	yes	characteristic, complemented
32	#554	C₂²	1	2	yes	—
33	#554	C₂²	1	1	yes	characteristic, complemented
34	#552	—	2	1	no	—
35	#552	C₂²	1	2	yes	—
36	#551	—	2	2	no	—
37	D₄×Q₈	C₂²	1	1	yes	characteristic
38	#548	—	2	1	no	—
39	#547	C₂²	1	1	yes	characteristic
40	#547	C₂²	1	1	yes	characteristic
41	#546	C₂²	1	2	yes	—
42	#544	C₂²	1	2	yes	complemented
43	#542	—	2	1	no	—
44	#542	C₂²	1	2	yes	—
45	#541	—	2	2	no	—
46	#541	—	2	1	no	—
47	#541	C₂²	1	2	yes	complemented
48	#539	—	2	2	no	—
49	#533	C₂²	1	1	yes	characteristic
50	#533	C₂²	1	1	yes	characteristic
51	#533	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	#498	C₂²	1	1	yes	characteristic, complemented
60	#498	C₂²	1	2	yes	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	—
66	#485	C₂²	1	2	yes	—
67	#485	C₂²	1	2	yes	complemented
68	#484	C₂²	1	2	yes	complemented
69	#483	C₂²	1	1	yes	characteristic
70	#483	C₂²	1	1	yes	characteristic
71	#483	C₂²	1	2	yes	complemented
72	#483	C₂²	1	2	yes	complemented
73	#482	C₂²	1	2	yes	—
74	#481	C₂²	1	2	yes	—
75	#479	C₂²	1	2	yes	complemented
76	#479	C₂²	1	2	yes	complemented
77	#479	C₂²	1	2	yes	complemented
78	#478	C₂²	1	2	yes	—
79	#478	C₂²	1	2	yes	—
80	#478	C₂²	1	2	yes	—
81	#477	C₂²	1	2	yes	complemented
82	#476	C₂²	1	1	yes	characteristic
83	#476	C₂²	1	1	yes	characteristic
84	#476	C₂²	1	1	yes	characteristic
85	#476	C₂²	1	2	yes	—
86	#476	C₂²	1	1	yes	characteristic
87	#475	C₂²	1	1	yes	characteristic, complemented
88	#475	C₂²	1	2	yes	complemented
89	#475	C₂²	1	2	yes	complemented
90	#475	C₂²	1	2	yes	complemented
91	#475	C₂²	1	1	yes	characteristic, complemented
92	#474	C₂²	1	1	yes	characteristic
93	#474	C₂²	1	1	yes	characteristic
94	#470	C₂²	1	2	yes	—
95	#470	C₂²	1	2	yes	—
96	#470	C₂²	1	2	yes	complemented
97	#468	C₂²	1	2	yes	—
98	#467	C₂²	1	2	yes	complemented
99	#465	C₂²	1	2	yes	—
100	#464	C₂²	1	2	yes	—
101	#464	C₂²	1	2	yes	—
102	#462	C₂²	1	1	yes	characteristic, complemented
103	#462	C₂²	1	1	yes	characteristic, complemented
104	#462	C₂²	1	2	yes	complemented
105	#461	C₂²	1	1	yes	characteristic
106	#461	C₂²	1	1	yes	characteristic
107	#452	C₂²	1	2	yes	—
108	#452	C₂²	1	2	yes	—
109	#450	C₂²	1	1	yes	characteristic
110	#450	C₂²	1	1	yes	characteristic
111	#446	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
113	#441	C₂²	1	2	yes	complemented
114	#440	C₂²	1	2	yes	—
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×SD₁₆	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆	C₂²	1	2	yes	—
121	#436	C₂²	1	2	yes	—
122	#436	C₂²	1	1	yes	characteristic, complemented
123	#435	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	—
128	#428	C₂²	1	2	yes	complemented
129	C₂×#106	C₂²	1	2	yes	complemented
130	#424	C₂²	1	2	yes	complemented
131	#423	C₂²	1	1	yes	characteristic
132	#418	C₂²	1	2	yes	—
133	#417	C₂²	1	2	yes	—
134	#416	C₂²	1	2	yes	—
135	C₂×#41	—	2	1	no	—
136	C₂×#41	C₂³	1	2	yes	—
137	C₂²×Q₈	—	2	1	no	—
138	C₂²×D₄	C₂³	1	1	yes	characteristic
139	C₂³×C₄	—	2	1	no	—
140	C₂×Q₁₆	C₂³	1	2	yes	—
141	C₂×Q₁₆	C₂³	1	2	yes	—
142	C₂×SD₁₆	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆	C₂³	1	1	yes	characteristic
146	C₂×M₁₆	C₂³	1	2	yes	—
147	C₂×M₁₆	C₂³	1	2	yes	—
148	C₂²×C₈	C₂³	1	2	yes	—
149	C₄⋊Q₈	—	2	1	no	—
150	C₄⋊Q₈	—	2	2	no	—
151	C₄⋊Q₈	—	2	1	no	—
152	C₄⋊Q₈	—	2	2	no	—
153	C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₄⋊Q₈	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈	C₂³	1	2	yes	—
160	C₄⋊Q₈	C₂³	1	2	yes	—
161	#126	—	2	2	no	—
162	#126	—	2	2	no	—
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	2	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	—	2	2	no	—
176	#125	—	2	2	no	—
177	#125	—	2	1	no	—
178	#125	—	2	1	no	—
179	#125	D₄	1	1	yes	characteristic
180	#125	C₂³	1	2	yes	—
181	#125	C₂³	1	2	yes	—
182	#124	—	2	1	no	—
183	#124	—	2	2	no	—
184	#124	—	2	2	no	—
185	#124	D₄	1	1	yes	characteristic
186	#124	C₂³	1	2	yes	—
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	1	no	—
196	C₂²⋊Q₈	—	2	1	no	—
197	C₂²⋊Q₈	—	2	1	no	—
198	C₂²⋊Q₈	—	2	2	no	—
199	C₂²⋊Q₈	—	2	1	no	—
200	C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
206	C₂²⋊Q₈	—	2	2	no	—
207	C₂²⋊Q₈	D₄	1	1	yes	characteristic
208	C₂²⋊Q₈	C₂³	1	2	yes	—
209	C₂²⋊Q₈	C₂³	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	D₄	1	1	yes	characteristic
217	#121	C₂³	1	2	yes	—
218	#120	—	2	2	no	—
219	C₄×Q₈	—	2	1	no	—
220	C₄×Q₈	—	2	2	no	—
221	C₄×Q₈	—	2	1	no	—
222	C₄×Q₈	—	2	1	no	—
223	C₄×Q₈	—	2	1	no	—
224	C₄×Q₈	—	2	1	no	—
225	C₄×Q₈	—	2	1	no	—
226	C₄×Q₈	—	2	1	no	—
227	C₄×Q₈	C₂³	1	2	yes	—
228	C₄×Q₈	C₂³	1	2	yes	—
229	C₄×Q₈	C₂³	1	1	yes	characteristic
230	C₄×Q₈	C₂³	1	1	yes	characteristic
231	C₄×Q₈	C₂³	1	2	yes	—
232	C₄×Q₈	C₂³	1	2	yes	—
233	C₄×Q₈	C₂³	1	1	yes	characteristic
234	C₄×D₄	—	2	2	no	—
235	C₄×D₄	—	2	1	no	—
236	C₄×D₄	—	2	2	no	—
237	C₄×D₄	—	2	2	no	—
238	C₄×D₄	—	2	1	no	—
239	C₄×D₄	—	2	1	no	—
240	C₄×D₄	C₂³	1	1	yes	characteristic
241	C₄×D₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
247	#117	—	2	1	no	—
248	#117	—	2	1	no	—
249	#117	—	2	2	no	—
250	#117	—	2	1	no	—
251	#117	—	2	2	no	—
252	#117	C₂³	1	2	yes	—
253	#117	C₂³	1	2	yes	—
254	#117	C₂³	1	2	yes	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	#106	C₂³	1	1	yes	characteristic
268	#106	C₂³	1	2	yes	—
269	#106	C₂³	1	2	yes	—
270	#106	C₂³	1	2	yes	—
271	#106	C₂³	1	2	yes	—
272	#106	C₂³	1	1	yes	characteristic
273	#106	C₂³	1	2	yes	—
274	#106	C₂³	1	1	yes	characteristic
275	#106	C₂³	1	1	yes	characteristic
276	#106	C₂³	1	2	yes	—
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	1	yes	characteristic
291	#103	C₂³	1	1	yes	characteristic
292	#103	C₂³	1	2	yes	—
293	#103	C₂³	1	2	yes	—
294	#103	C₂³	1	2	yes	—
295	#103	C₂³	1	2	yes	—
296	#102	C₂³	1	1	yes	characteristic
297	#102	C₂³	1	2	yes	—
298	#102	C₂³	1	1	yes	characteristic
299	#102	C₂³	1	2	yes	—
300	#102	C₂³	1	2	yes	—
301	#102	C₂³	1	2	yes	—
302	#102	C₂³	1	1	yes	characteristic
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	C₂×Q₈	—	2	1	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	—	8	2	no	—
323	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈	C₂⁴	1	2	yes	—
325	C₂×Q₈	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈	C₂⁴	1	1	yes	characteristic
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	4	1	no	—
332	C₂×D₄	C₂×D₄	1	1	yes	characteristic
333	C₂×D₄	C₂×D₄	1	2	yes	—
334	C₂×D₄	C₂⁴	1	1	yes	characteristic
335	C₂×D₄	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	8	2	no	—
346	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄	C₂⁴	1	2	yes	—
350	Q₁₆	—	4	2	no	—
351	Q₁₆	—	4	2	no	—
352	SD₁₆	—	2	2	no	—
353	SD₁₆	—	2	2	no	—
354	SD₁₆	—	4	1	no	—
355	SD₁₆	—	4	1	no	—
356	M₁₆	—	4	2	no	—
357	M₁₆	—	4	2	no	—
358	C₂×C₈	—	4	2	no	—
359	C₂×C₈	C₂⁴	1	1	yes	characteristic
360	C₂×C₈	C₂⁴	1	1	yes	characteristic
361	C₂×C₈	C₂⁴	1	2	yes	—
362	C₂×C₈	C₂⁴	1	1	yes	characteristic
363	C₂×C₈	C₂⁴	1	1	yes	characteristic
364	C₂×C₈	C₂⁴	1	2	yes	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	2	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	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	C₂×D₄	1	2	yes	—
395	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
396	C₄⋊C₄	C₂×D₄	1	2	yes	—
397	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
398	C₄⋊C₄	C₂×D₄	1	2	yes	—
399	C₄⋊C₄	C₂×D₄	1	2	yes	—
400	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄	C₂⁴	1	2	yes	—
402	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄	C₂⁴	1	2	yes	—
404	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄	C₂⁴	1	2	yes	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	2	1	no	—
409	C₂²⋊C₄	—	2	1	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	2	2	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	C₂×D₄	1	2	yes	—
424	C₂²⋊C₄	C₂×D₄	1	2	yes	—
425	C₂²⋊C₄	C₂×D₄	1	2	yes	—
426	C₂²⋊C₄	C₂×D₄	1	2	yes	—
427	C₂²⋊C₄	C₂×D₄	1	2	yes	—
428	C₄²	—	2	2	no	—
429	C₄²	—	2	2	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	2	1	no	—
432	C₄²	—	2	1	no	—
433	C₄²	—	2	2	no	—
434	C₄²	—	2	2	no	—
435	C₄²	—	2	2	no	—
436	C₄²	C₂×D₄	1	1	yes	characteristic
437	C₄²	C₂×D₄	1	1	yes	characteristic
438	C₄²	C₂⁴	1	1	yes	characteristic
439	C₄²	C₂⁴	1	2	yes	—
440	C₄²	C₂⁴	1	1	yes	characteristic
441	C₂³	—	2	1	no	—
442	C₂³	—	2	1	no	—
443	C₂³	—	4	2	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	8	1	no	—
446	C₂³	C₂²×D₄	1	1	yes	characteristic
447	C₂³	C₂²×D₄	1	2	yes	—
448	Q₈	—	2	2	no	—
449	Q₈	—	2	1	no	—
450	Q₈	—	2	1	no	—
451	Q₈	—	2	2	no	—
452	Q₈	—	2	1	no	—
453	Q₈	—	2	1	no	—
454	Q₈	—	2	2	no	—
455	Q₈	—	4	2	no	—
456	Q₈	—	4	2	no	—
457	Q₈	—	8	1	no	—
458	Q₈	—	8	1	no	—
459	Q₈	—	8	2	no	—
460	Q₈	—	8	2	no	—
461	D₄	—	2	2	no	—
462	D₄	—	2	1	no	—
463	D₄	—	2	1	no	—
464	D₄	—	2	1	no	—
465	D₄	—	4	2	no	—
466	D₄	—	4	2	no	—
467	D₄	—	4	4	no	—
468	D₄	—	8	2	no	—
469	D₄	2₋¹⁺⁴	1	2	yes	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	4	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	8	1	no	—
490	C₂×C₄	—	8	1	no	—
491	C₂×C₄	—	8	2	no	—
492	C₂×C₄	—	8	2	no	—
493	C₂×C₄	—	8	1	no	—
494	C₂×C₄	—	8	2	no	—
495	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄	C₂²×D₄	1	2	yes	—
498	C₂×C₄	C₂²×D₄	1	2	yes	—
499	C₂×C₄	C₂²×D₄	1	2	yes	—
500	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄	C₂⁵	1	1	yes	characteristic
504	C₈	—	2	1	no	—
505	C₈	—	2	1	no	—
506	C₈	—	2	1	no	—
507	C₈	—	2	2	no	—
508	C₈	—	2	1	no	—
509	C₈	—	2	2	no	—
510	C₂²	—	2	1	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	2	2	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	2	2	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	4	1	no	—
518	C₂²	—	4	1	no	—
519	C₂²	—	4	1	no	—
520	C₂²	—	4	1	no	—
521	C₂²	—	4	1	no	—
522	C₂²	—	8	4	no	—
523	C₂²	C₂³×D₄	1	1	yes	characteristic
524	C₄	—	2	1	no	—
525	C₄	—	2	1	no	—
526	C₄	—	2	2	no	—
527	C₄	—	2	2	no	—
528	C₄	—	2	1	no	—
529	C₄	—	2	1	no	—
530	C₄	—	2	2	no	—
531	C₄	—	4	1	no	—
532	C₄	—	4	2	no	—
533	C₄	—	4	1	no	—
534	C₄	—	4	2	no	—
535	C₄	—	4	1	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	1	no	—
538	C₄	—	4	1	no	—
539	C₄	—	4	2	no	—
540	C₄	—	4	2	no	—
541	C₄	#577	1	2	yes	—
542	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
543	C₄	#585	1	1	yes	characteristic
544	C₂	—	4	2	no	—
545	C₂	—	4	1	no	—
546	C₂	—	4	2	no	—
547	C₂	—	8	1	no	—
548	C₂	#3489	1	1	yes	characteristic
549	C₂	C₂×#577	1	1	yes	characteristic
550	C₂	#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
prime radical	#3520	C₂
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. #3555	C₂	semidirect
3. #3386	C₂	semidirect
4. Q₈×SD₁₆	C₂	semidirect
5. #3369	C₂	semidirect
6. #3364	C₂	semidirect
7. #3356	C₂	semidirect
8. #3353	C₂	semidirect
9. #3344	C₂	semidirect
10. #3335	C₂	semidirect
11. #3331	C₂	semidirect
12. #3323	C₂	semidirect
13. #3311	C₂	semidirect
14. #3302	C₂	semidirect
15. #3258	C₂	semidirect
16. #3255	C₂	semidirect
17. #3244	C₂	semidirect
18. #3231	C₂	semidirect
19. #3120	C₂	semidirect
20. #3101	C₂	semidirect
21. #3084	C₂	semidirect
22. #3077	C₂	semidirect
23. #2993	C₂	semidirect
25. Q₈²	C₂²	semidirect
27. #557	C₂²	semidirect
31. #556	C₂²	semidirect
33. #554	C₂²	semidirect
42. #544	C₂²	semidirect
47. #541	C₂²	semidirect
57. #501	C₂²	semidirect
58. #500	C₂²	semidirect
59. #498	C₂²	semidirect
60. #498	C₂²	semidirect
63. #487	C₂²	semidirect
64. #487	C₂²	semidirect
67. #485	C₂²	semidirect
68. #484	C₂²	semidirect
71. #483	C₂²	semidirect
72. #483	C₂²	semidirect
75. #479	C₂²	semidirect
76. #479	C₂²	semidirect
77. #479	C₂²	semidirect
81. #477	C₂²	semidirect
87. #475	C₂²	semidirect
88. #475	C₂²	semidirect
89. #475	C₂²	semidirect
90. #475	C₂²	semidirect
91. #475	C₂²	semidirect
96. #470	C₂²	semidirect
98. #467	C₂²	semidirect
102. #462	C₂²	semidirect
103. #462	C₂²	semidirect
104. #462	C₂²	semidirect
111. #446	C₂²	semidirect
112. C₈×Q₈	C₂²	semidirect
113. #441	C₂²	semidirect
115. C₄×Q₁₆	C₂²	semidirect
122. #436	C₂²	semidirect
124. C₈×D₄	C₂²	semidirect
125. #433	C₂²	semidirect
128. #428	C₂²	semidirect
129. C₂×#106	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
#3555	2
#3520	2
#3386	2
Q₈×SD₁₆	2
#3369	2
#3364	2
#3356	2
#3353	2
#3344	2
#3335	2
#3331	2
#3323	2
#3311	2
#3302	2
#3258	2
#3255	2
#3244	2
#3231	2
#3120	2
#3101	2
#3084	2
#3077	2
#2993	2