Subgroups — #62179

Order 256.

874 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	#3544	C₂	1	1	yes	maximal, characteristic, complemented
2	#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	#3384	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	#3361	C₂	1	1	yes	maximal, characteristic, complemented
7	#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	#3354	C₂	1	2	yes	maximal, complemented
9	#3348	C₂	1	2	yes	maximal, complemented
10	#3340	C₂	1	1	yes	maximal, characteristic, complemented
11	#3325	C₂	1	1	yes	maximal, characteristic, complemented
12	#3323	C₂	1	2	yes	maximal, complemented
13	#3306	C₂	1	2	yes	maximal, complemented
14	#3295	C₂	1	1	yes	maximal, characteristic, complemented
15	#3263	C₂	1	2	yes	maximal, complemented
16	#3251	C₂	1	1	yes	maximal, characteristic, complemented
17	#3244	C₂	1	2	yes	maximal, complemented
18	#3227	C₂	1	1	yes	maximal, characteristic, complemented
19	#3118	C₂	1	2	yes	maximal, complemented
20	#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	#3081	C₂	1	2	yes	maximal, complemented
22	#3079	C₂	1	1	yes	maximal, characteristic, complemented
23	#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	#563	—	2	2	no	—
25	#559	C₂²	1	1	yes	characteristic
26	Q₈²	C₂²	1	1	yes	characteristic, complemented
27	#556	C₂²	1	1	yes	characteristic
28	#555	C₂²	1	1	yes	characteristic
29	#555	C₂²	1	2	yes	—
30	#554	C₂²	1	1	yes	characteristic
31	#554	C₂²	1	1	yes	characteristic, complemented
32	#552	—	2	1	no	—
33	#552	C₂²	1	2	yes	complemented
34	#551	—	2	2	no	—
35	D₄×Q₈	C₂²	1	1	yes	characteristic
36	#548	—	2	1	no	—
37	#547	—	2	1	no	—
38	#547	C₂²	1	2	yes	complemented
39	#546	—	2	1	no	—
40	#546	C₂²	1	2	yes	—
41	D₄²	C₂²	1	1	yes	characteristic
42	#544	—	2	1	no	—
43	#544	C₂²	1	2	yes	complemented
44	#542	—	2	1	no	—
45	#542	C₂²	1	2	yes	—
46	#542	C₂²	1	2	yes	complemented
47	#538	—	2	2	no	—
48	#536	—	2	2	no	—
49	#532	C₂²	1	1	yes	characteristic
50	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
51	#529	—	2	1	no	—
52	#529	C₂²	1	1	yes	characteristic
53	#529	C₂²	1	1	yes	characteristic, complemented
54	C₂×#124	—	2	1	no	—
55	#518	C₂²	1	2	yes	—
56	C₄×#41	C₂²	1	1	yes	characteristic
57	#501	C₂²	1	2	yes	complemented
58	#498	C₂²	1	1	yes	characteristic, complemented
59	#498	C₂²	1	2	yes	complemented
60	#498	C₂²	1	1	yes	characteristic, complemented
61	#489	C₂²	1	2	yes	complemented
62	#488	C₂²	1	2	yes	complemented
63	#486	C₂²	1	1	yes	characteristic
64	#486	C₂²	1	1	yes	characteristic
65	#485	C₂²	1	2	yes	complemented
66	#485	C₂²	1	1	yes	characteristic, complemented
67	#485	C₂²	1	2	yes	complemented
68	#483	C₂²	1	2	yes	complemented
69	#482	C₂²	1	2	yes	—
70	#482	C₂²	1	2	yes	complemented
71	#482	C₂²	1	1	yes	characteristic, complemented
72	#481	C₂²	1	2	yes	—
73	#481	C₂²	1	2	yes	complemented
74	#481	C₂²	1	2	yes	complemented
75	#479	C₂²	1	1	yes	characteristic, complemented
76	#478	C₂²	1	1	yes	characteristic
77	#478	C₂²	1	2	yes	—
78	#478	C₂²	1	2	yes	complemented
79	#478	C₂²	1	2	yes	complemented
80	#477	C₂²	1	1	yes	characteristic, complemented
81	#477	C₂²	1	1	yes	characteristic, complemented
82	#476	C₂²	1	1	yes	characteristic
83	#476	C₂²	1	1	yes	characteristic
84	#476	C₂²	1	2	yes	—
85	#476	C₂²	1	2	yes	complemented
86	#476	C₂²	1	2	yes	complemented
87	#476	C₂²	1	2	yes	complemented
88	#475	C₂²	1	2	yes	complemented
89	#475	C₂²	1	2	yes	complemented
90	#475	C₂²	1	1	yes	characteristic, complemented
91	#474	C₂²	1	2	yes	—
92	#474	C₂²	1	2	yes	complemented
93	#474	C₂²	1	1	yes	characteristic, complemented
94	#470	C₂²	1	2	yes	complemented
95	#469	C₂²	1	2	yes	—
96	#469	C₂²	1	2	yes	complemented
97	#468	C₂²	1	2	yes	complemented
98	#465	C₂²	1	2	yes	—
99	#465	C₂²	1	2	yes	complemented
100	#464	C₂²	1	1	yes	characteristic, complemented
101	#464	C₂²	1	2	yes	complemented
102	#463	C₂²	1	1	yes	characteristic
103	#463	C₂²	1	2	yes	complemented
104	#463	C₂²	1	2	yes	complemented
105	#460	C₂²	1	1	yes	characteristic
106	#459	C₂²	1	1	yes	characteristic
107	#452	C₂²	1	1	yes	characteristic
108	#450	C₂²	1	2	yes	—
109	#449	C₂²	1	1	yes	characteristic
110	#447	C₂²	1	2	yes	—
111	#446	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
113	#442	C₂²	1	2	yes	—
114	#440	C₂²	1	2	yes	complemented
115	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
116	C₄×SD₁₆	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆	C₂²	1	2	yes	—
118	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₈	C₂²	1	1	yes	characteristic
120	C₄×D₈	C₂²	1	2	yes	complemented
121	#436	C₂²	1	1	yes	characteristic
122	#436	C₂²	1	2	yes	complemented
123	#435	C₂²	1	2	yes	complemented
124	C₈×D₄	C₂²	1	1	yes	characteristic
125	#433	C₂²	1	2	yes	complemented
126	#431	C₂²	1	1	yes	characteristic, complemented
127	#428	C₂²	1	2	yes	complemented
128	#428	C₂²	1	2	yes	complemented
129	#427	C₂²	1	2	yes	complemented
130	#424	C₂²	1	2	yes	complemented
131	#423	C₂²	1	1	yes	characteristic, complemented
132	#418	C₂²	1	2	yes	—
133	#417	C₂²	1	2	yes	—
134	C₂×#102	C₂²	1	2	yes	—
135	C₂×#41	—	2	2	no	—
136	C₂×#41	—	2	1	no	—
137	C₂×#41	C₂³	1	1	yes	characteristic
138	C₂²×Q₈	—	2	1	no	—
139	C₂²×Q₈	—	2	1	no	—
140	C₂²×D₄	—	2	1	no	—
141	C₂²×D₄	C₂³	1	2	yes	—
142	C₂×Q₁₆	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	2	yes	—
146	C₂×D₈	C₂³	1	1	yes	characteristic
147	C₂×D₈	C₂³	1	2	yes	—
148	C₂×M₁₆	C₂³	1	2	yes	—
149	C₂×M₁₆	C₂³	1	2	yes	—
150	C₂²×C₈	C₂³	1	2	yes	—
151	C₄⋊Q₈	—	2	2	no	—
152	C₄⋊Q₈	—	2	2	no	—
153	C₄⋊Q₈	—	2	1	no	—
154	C₄⋊Q₈	—	2	1	no	—
155	C₄⋊Q₈	—	2	1	no	—
156	C₄⋊Q₈	C₂³	1	2	yes	—
157	C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈	C₂³	1	2	yes	—
161	C₄⋊Q₈	C₂³	1	2	yes	—
162	#127	C₂³	1	1	yes	characteristic
163	#126	—	2	2	no	—
164	#126	—	2	2	no	—
165	#126	—	2	2	no	—
166	#126	—	2	2	no	—
167	#126	—	2	1	no	—
168	#126	D₄	1	2	yes	—
169	#125	—	2	1	no	—
170	#125	—	2	2	no	—
171	#125	—	2	2	no	—
172	#125	D₄	1	1	yes	characteristic
173	#125	C₂³	1	1	yes	characteristic
174	#125	C₂³	1	2	yes	—
175	#124	—	2	1	no	—
176	#124	—	2	1	no	—
177	#124	—	2	2	no	—
178	#124	—	2	2	no	—
179	#124	—	2	2	no	—
180	#124	—	2	2	no	—
181	#124	—	2	2	no	—
182	#124	—	2	1	no	—
183	#124	D₄	1	1	yes	characteristic
184	#124	C₂³	1	1	yes	characteristic
185	#124	C₂³	1	2	yes	—
186	#123	—	2	2	no	—
187	#123	—	2	1	no	—
188	#123	—	2	2	no	—
189	#123	—	2	2	no	—
190	#123	—	2	2	no	—
191	#123	—	2	2	no	—
192	#123	—	2	2	no	—
193	#123	—	2	2	no	—
194	#123	D₄	1	2	yes	—
195	C₂²⋊Q₈	—	2	1	no	—
196	C₂²⋊Q₈	—	2	1	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	1	yes	characteristic
206	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
207	C₂²⋊Q₈	C₂³	1	2	yes	—
208	C₂²⋊Q₈	C₂³	1	2	yes	—
209	#121	—	2	2	no	—
210	#121	—	2	1	no	—
211	#121	—	2	1	no	—
212	#121	—	2	1	no	—
213	#121	—	2	2	no	—
214	#121	D₄	1	1	yes	characteristic
215	#121	C₂³	1	1	yes	characteristic
216	#121	C₂³	1	2	yes	—
217	#121	C₂³	1	2	yes	—
218	#121	C₂³	1	2	yes	—
219	#120	—	2	2	no	—
220	#120	—	2	2	no	—
221	C₄×Q₈	—	2	1	no	—
222	C₄×Q₈	—	2	1	no	—
223	C₄×Q₈	C₂³	1	1	yes	characteristic
224	C₄×Q₈	C₂³	1	1	yes	characteristic
225	C₄×Q₈	C₂³	1	1	yes	characteristic
226	C₄×Q₈	C₂³	1	2	yes	—
227	C₄×Q₈	C₂³	1	1	yes	characteristic
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	2	no	—
233	C₄×D₄	—	2	2	no	—
234	C₄×D₄	—	2	1	no	—
235	C₄×D₄	—	2	1	no	—
236	C₄×D₄	C₂³	1	1	yes	characteristic
237	C₄×D₄	C₂³	1	1	yes	characteristic
238	C₄×D₄	C₂³	1	2	yes	—
239	C₄×D₄	C₂³	1	2	yes	—
240	C₄×D₄	C₂³	1	2	yes	—
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	#117	—	2	2	no	—
246	#117	—	2	1	no	—
247	#117	—	2	2	no	—
248	#117	—	2	1	no	—
249	#117	—	2	1	no	—
250	#117	C₂³	1	1	yes	characteristic
251	#117	C₂³	1	2	yes	—
252	#117	C₂³	1	2	yes	—
253	#117	C₂³	1	2	yes	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄	C₂³	1	2	yes	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₄²	—	2	1	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	1	yes	characteristic
267	#107	C₂³	1	1	yes	characteristic
268	#106	C₂³	1	1	yes	characteristic
269	#106	C₂³	1	2	yes	—
270	#106	C₂³	1	2	yes	—
271	#106	C₂³	1	2	yes	—
272	#106	C₂³	1	2	yes	—
273	#106	C₂³	1	2	yes	—
274	#106	C₂³	1	2	yes	—
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	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	#102	C₂³	1	1	yes	characteristic
292	#102	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	1	yes	characteristic
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	2	yes	—
302	#102	C₂³	1	2	yes	—
303	#102	C₂³	1	2	yes	—
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	2	no	—
313	#41	—	2	2	no	—
314	#41	—	4	1	no	—
315	#41	—	8	2	no	—
316	#41	—	8	4	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	8	2	no	—
324	C₂×Q₈	—	8	2	no	—
325	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈	C₂⁴	1	1	yes	characteristic
328	C₂×D₄	—	2	4	no	—
329	C₂×D₄	—	2	1	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	2	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	4	2	no	—
338	C₂×D₄	—	8	2	no	—
339	C₂×D₄	C₂×D₄	1	1	yes	characteristic
340	C₂×D₄	C₂×D₄	1	2	yes	—
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	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	1	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	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	1	no	—
359	SD₁₆	—	2	2	no	—
360	SD₁₆	—	4	1	no	—
361	SD₁₆	—	4	2	no	—
362	D₈	—	2	2	no	—
363	D₈	—	4	2	no	—
364	M₁₆	—	4	2	no	—
365	M₁₆	—	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	1	yes	characteristic
370	C₂×C₈	C₂⁴	1	1	yes	characteristic
371	C₂×C₈	C₂⁴	1	2	yes	—
372	C₂×C₈	C₂⁴	1	2	yes	—
373	C₄⋊C₄	—	2	1	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	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	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	C₂×D₄	1	1	yes	characteristic
393	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
394	C₄⋊C₄	C₂×D₄	1	2	yes	—
395	C₄⋊C₄	C₂×D₄	1	2	yes	—
396	C₄⋊C₄	C₂×D₄	1	2	yes	—
397	C₄⋊C₄	C₂×D₄	1	2	yes	—
398	C₄⋊C₄	C₂⁴	1	2	yes	—
399	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄	C₂⁴	1	2	yes	—
401	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄	C₂⁴	1	2	yes	—
403	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	2	1	no	—
408	C₂²⋊C₄	—	2	1	no	—
409	C₂²⋊C₄	—	2	2	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	1	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	1	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	1	no	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	1	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	2	1	no	—
426	C₂²⋊C₄	C₂×D₄	1	2	yes	—
427	C₂²⋊C₄	C₂×D₄	1	2	yes	—
428	C₂²⋊C₄	C₂×D₄	1	2	yes	—
429	C₂²⋊C₄	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄	C₂×D₄	1	2	yes	—
431	C₄²	—	2	1	no	—
432	C₄²	—	2	1	no	—
433	C₄²	—	2	1	no	—
434	C₄²	—	2	2	no	—
435	C₄²	—	2	2	no	—
436	C₄²	—	2	1	no	—
437	C₄²	—	2	2	no	—
438	C₄²	C₂×D₄	1	1	yes	characteristic
439	C₄²	C₂×D₄	1	1	yes	characteristic
440	C₄²	C₂⁴	1	1	yes	characteristic
441	C₄²	C₂⁴	1	2	yes	—
442	C₄²	C₂⁴	1	1	yes	characteristic
443	C₂³	—	2	1	no	—
444	C₂³	—	2	1	no	—
445	C₂³	—	2	2	no	—
446	C₂³	—	4	4	no	—
447	C₂³	—	8	2	no	—
448	C₂³	—	8	2	no	—
449	C₂³	C₂²×D₄	1	2	yes	—
450	C₂³	C₂²×D₄	1	1	yes	characteristic
451	Q₈	—	2	2	no	—
452	Q₈	—	2	1	no	—
453	Q₈	—	2	1	no	—
454	Q₈	—	2	1	no	—
455	Q₈	—	2	1	no	—
456	Q₈	—	4	2	no	—
457	Q₈	—	8	2	no	—
458	Q₈	—	8	1	no	—
459	Q₈	—	8	1	no	—
460	Q₈	—	8	2	no	—
461	Q₈	—	8	2	no	—
462	D₄	—	2	2	no	—
463	D₄	—	2	1	no	—
464	D₄	—	2	2	no	—
465	D₄	—	2	1	no	—
466	D₄	—	2	1	no	—
467	D₄	—	2	2	no	—
468	D₄	—	4	2	no	—
469	D₄	—	4	4	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	2	no	—
472	D₄	—	4	2	no	—
473	D₄	—	8	1	no	—
474	D₄	—	8	2	no	—
475	D₄	—	8	2	no	—
476	D₄	—	8	2	no	—
477	D₄	2₋¹⁺⁴	1	2	yes	—
478	C₂×C₄	—	2	2	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	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	4	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	2	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	2	yes	—
504	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄	C₂²×D₄	1	2	yes	—
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	2	no	—
520	C₂²	—	2	1	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	1	no	—
524	C₂²	—	2	2	no	—
525	C₂²	—	4	1	no	—
526	C₂²	—	4	1	no	—
527	C₂²	—	4	1	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	1	no	—
531	C₂²	—	4	1	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	16	4	no	—
534	C₂²	C₂³×D₄	1	1	yes	characteristic
535	C₄	—	2	1	no	—
536	C₄	—	2	1	no	—
537	C₄	—	2	2	no	—
538	C₄	—	2	1	no	—
539	C₄	—	2	2	no	—
540	C₄	—	2	1	no	—
541	C₄	—	2	2	no	—
542	C₄	—	4	2	no	—
543	C₄	—	4	2	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	1	no	—
548	C₄	—	4	1	no	—
549	C₄	—	4	1	no	—
550	C₄	—	4	2	no	—
551	C₄	#577	1	2	yes	—
552	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
553	C₄	#585	1	1	yes	characteristic
554	C₂	—	4	1	no	—
555	C₂	—	4	2	no	—
556	C₂	—	4	2	no	—
557	C₂	—	8	1	no	—
558	C₂	—	8	2	no	—
559	C₂	#3489	1	1	yes	characteristic
560	C₂	C₂×#577	1	1	yes	characteristic
561	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 ◁ #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. #3544	C₂	semidirect
2. #3514	C₂	semidirect
3. #3384	C₂	semidirect
4. Q₈×SD₁₆	C₂	semidirect
5. #3375	C₂	semidirect
6. #3361	C₂	semidirect
7. #3356	C₂	semidirect
8. #3354	C₂	semidirect
9. #3348	C₂	semidirect
10. #3340	C₂	semidirect
11. #3325	C₂	semidirect
12. #3323	C₂	semidirect
13. #3306	C₂	semidirect
14. #3295	C₂	semidirect
15. #3263	C₂	semidirect
16. #3251	C₂	semidirect
17. #3244	C₂	semidirect
18. #3227	C₂	semidirect
19. #3118	C₂	semidirect
20. #3102	C₂	semidirect
21. #3081	C₂	semidirect
22. #3079	C₂	semidirect
23. #2993	C₂	semidirect
26. Q₈²	C₂²	semidirect
31. #554	C₂²	semidirect
33. #552	C₂²	semidirect
38. #547	C₂²	semidirect
43. #544	C₂²	semidirect
46. #542	C₂²	semidirect
50. C₂×C₄⋊Q₈	C₂²	semidirect
53. #529	C₂²	semidirect
57. #501	C₂²	semidirect
58. #498	C₂²	semidirect
59. #498	C₂²	semidirect
60. #498	C₂²	semidirect
61. #489	C₂²	semidirect
62. #488	C₂²	semidirect
65. #485	C₂²	semidirect
66. #485	C₂²	semidirect
67. #485	C₂²	semidirect
68. #483	C₂²	semidirect
70. #482	C₂²	semidirect
71. #482	C₂²	semidirect
73. #481	C₂²	semidirect
74. #481	C₂²	semidirect
75. #479	C₂²	semidirect
78. #478	C₂²	semidirect
79. #478	C₂²	semidirect
80. #477	C₂²	semidirect
81. #477	C₂²	semidirect
85. #476	C₂²	semidirect
86. #476	C₂²	semidirect
87. #476	C₂²	semidirect
88. #475	C₂²	semidirect
89. #475	C₂²	semidirect
90. #475	C₂²	semidirect
92. #474	C₂²	semidirect
93. #474	C₂²	semidirect
94. #470	C₂²	semidirect
96. #469	C₂²	semidirect
97. #468	C₂²	semidirect
99. #465	C₂²	semidirect
100. #464	C₂²	semidirect
101. #464	C₂²	semidirect
103. #463	C₂²	semidirect
104. #463	C₂²	semidirect
111. #446	C₂²	semidirect
112. C₈×Q₈	C₂²	semidirect
114. #440	C₂²	semidirect
115. C₄×Q₁₆	C₂²	semidirect
118. C₄×SD₁₆	C₂²	semidirect
120. C₄×D₈	C₂²	semidirect
122. #436	C₂²	semidirect
123. #435	C₂²	semidirect
125. #433	C₂²	semidirect
126. #431	C₂²	semidirect
127. #428	C₂²	semidirect
128. #428	C₂²	semidirect
129. #427	C₂²	semidirect
130. #424	C₂²	semidirect
131. #423	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3544	2
#3514	2
#3384	2
Q₈×SD₁₆	2
#3375	2
#3361	2
#3356	2
#3354	2
#3348	2
#3340	2
#3325	2
#3323	2
#3306	2
#3295	2
#3263	2
#3251	2
#3244	2
#3227	2
#3118	2
#3102	2
#3081	2
#3079	2
#2993	2