Subgroups — #61474

Order 256.

917 conjugacy classes of subgroups.

The subgroup lattice has 573 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3518	C₂	1	1	yes	maximal, characteristic, complemented
2	#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	#3394	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	#3367	C₂	1	1	yes	maximal, characteristic, complemented
7	#3340	C₂	1	1	yes	maximal, characteristic, complemented
8	#3340	C₂	1	2	yes	maximal, complemented
9	#3328	C₂	1	1	yes	maximal, characteristic, complemented
10	#3325	C₂	1	1	yes	maximal, characteristic, complemented
11	#3321	C₂	1	2	yes	maximal, complemented
12	#3311	C₂	1	2	yes	maximal, complemented
13	#3282	C₂	1	2	yes	maximal, complemented
14	D₄×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
15	#3173	C₂	1	2	yes	maximal, complemented
16	#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	#3121	C₂	1	2	yes	maximal, complemented
18	#3118	C₂	1	2	yes	maximal, complemented
19	#3116	C₂	1	1	yes	maximal, characteristic, complemented
20	#3115	C₂	1	1	yes	maximal, characteristic, complemented
21	#2966	C₂	1	1	yes	maximal, characteristic, complemented
22	#2949	C₂	1	2	yes	maximal, complemented
23	C₄×#135	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#135	C₂²	1	1	yes	characteristic
25	C₂²×SD₁₆	C₂²	1	2	yes	—
26	#559	C₂²	1	1	yes	characteristic
27	Q₈²	C₂²	1	1	yes	characteristic, complemented
28	#556	—	2	2	no	—
29	#556	—	2	1	no	—
30	#556	C₂²	1	1	yes	characteristic
31	#556	C₂²	1	1	yes	characteristic, complemented
32	#556	C₂²	1	2	yes	complemented
33	#555	—	2	1	no	—
34	#555	C₂²	1	2	yes	—
35	#555	C₂²	1	1	yes	characteristic
36	#551	—	2	2	no	—
37	D₄×Q₈	C₂²	1	1	yes	characteristic
38	D₄×Q₈	C₂²	1	1	yes	characteristic
39	#548	—	2	1	no	—
40	#548	C₂²	1	2	yes	complemented
41	#546	—	2	1	no	—
42	#546	C₂²	1	2	yes	—
43	D₄²	C₂²	1	1	yes	characteristic
44	#542	—	2	2	no	—
45	#542	C₂²	1	2	yes	—
46	#542	C₂²	1	2	yes	complemented
47	#538	—	2	2	no	—
48	#533	—	2	1	no	—
49	#533	C₂²	1	1	yes	characteristic, complemented
50	#532	C₂²	1	1	yes	characteristic
51	#529	—	2	1	no	—
52	#529	—	2	1	no	—
53	#529	C₂²	1	1	yes	characteristic
54	C₂×#124	—	2	1	no	—
55	#519	C₂²	1	2	yes	complemented
56	#518	C₂²	1	2	yes	—
57	C₄×#41	C₂²	1	1	yes	characteristic
58	C₄×#41	C₂²	1	1	yes	characteristic, complemented
59	#498	C₂²	1	1	yes	characteristic, complemented
60	#498	C₂²	1	2	yes	complemented
61	#495	C₂²	1	2	yes	complemented
62	#492	C₂²	1	1	yes	characteristic
63	#489	C₂²	1	2	yes	complemented
64	#489	C₂²	1	2	yes	complemented
65	#487	C₂²	1	1	yes	characteristic, complemented
66	#486	C₂²	1	1	yes	characteristic
67	#485	C₂²	1	2	yes	complemented
68	#485	C₂²	1	2	yes	complemented
69	#485	C₂²	1	2	yes	complemented
70	#482	C₂²	1	2	yes	—
71	#482	C₂²	1	2	yes	complemented
72	#482	C₂²	1	2	yes	complemented
73	#477	C₂²	1	2	yes	complemented
74	#477	C₂²	1	1	yes	characteristic, complemented
75	#476	C₂²	1	1	yes	characteristic
76	#476	C₂²	1	2	yes	—
77	#475	C₂²	1	1	yes	characteristic, complemented
78	#475	C₂²	1	2	yes	complemented
79	#474	C₂²	1	1	yes	characteristic, complemented
80	#474	C₂²	1	2	yes	complemented
81	#470	C₂²	1	2	yes	complemented
82	#469	C₂²	1	2	yes	—
83	#465	C₂²	1	2	yes	—
84	#465	C₂²	1	2	yes	complemented
85	#465	C₂²	1	2	yes	complemented
86	#465	C₂²	1	2	yes	complemented
87	#464	C₂²	1	2	yes	complemented
88	#464	C₂²	1	2	yes	complemented
89	#463	C₂²	1	2	yes	—
90	#463	C₂²	1	2	yes	complemented
91	#462	C₂²	1	1	yes	characteristic, complemented
92	#461	C₂²	1	1	yes	characteristic
93	#460	C₂²	1	1	yes	characteristic
94	#459	C₂²	1	1	yes	characteristic
95	#452	C₂²	1	2	yes	—
96	#451	C₂²	1	2	yes	complemented
97	#450	C₂²	1	2	yes	—
98	#449	C₂²	1	2	yes	complemented
99	#448	C₂²	1	2	yes	—
100	#447	C₂²	1	2	yes	—
101	#446	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
103	#442	C₂²	1	2	yes	complemented
104	#441	C₂²	1	2	yes	complemented
105	#440	C₂²	1	2	yes	—
106	#440	C₂²	1	2	yes	—
107	#440	C₂²	1	2	yes	complemented
108	#440	C₂²	1	2	yes	complemented
109	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
110	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
111	C₄×SD₁₆	C₂²	1	1	yes	characteristic
112	C₄×SD₁₆	C₂²	1	2	yes	—
113	C₄×SD₁₆	C₂²	1	1	yes	characteristic
114	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
115	C₄×SD₁₆	C₂²	1	2	yes	complemented
116	C₄×SD₁₆	C₂²	1	2	yes	complemented
117	C₄×SD₁₆	C₂²	1	2	yes	complemented
118	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₈	C₂²	1	1	yes	characteristic
120	C₄×D₈	C₂²	1	1	yes	characteristic
121	#436	C₂²	1	1	yes	characteristic
122	#435	C₂²	1	2	yes	complemented
123	C₈×D₄	C₂²	1	1	yes	characteristic
124	C₈×D₄	C₂²	1	2	yes	complemented
125	#433	C₂²	1	2	yes	complemented
126	#432	C₂²	1	1	yes	characteristic, complemented
127	#427	C₂²	1	1	yes	characteristic, complemented
128	#427	C₂²	1	2	yes	complemented
129	#419	C₂²	1	2	yes	complemented
130	#418	C₂²	1	2	yes	—
131	#416	C₂²	1	1	yes	characteristic
132	#416	C₂²	1	1	yes	characteristic, complemented
133	#405	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41	—	2	1	no	—
136	C₂×#41	C₂³	1	1	yes	characteristic
137	C₂×#41	C₂³	1	1	yes	characteristic
138	C₂²×Q₈	—	2	1	no	—
139	C₂²×Q₈	C₂³	1	2	yes	—
140	C₂²×D₄	—	2	1	no	—
141	C₂²×D₄	C₂³	1	2	yes	—
142	#135	—	2	4	no	—
143	C₂×Q₁₆	C₂³	1	1	yes	characteristic
144	C₂×Q₁₆	C₂³	1	2	yes	—
145	C₂×SD₁₆	—	2	8	no	—
146	C₂×SD₁₆	C₂³	1	2	yes	—
147	C₂×SD₁₆	C₂³	1	2	yes	—
148	C₂×SD₁₆	C₂³	1	2	yes	—
149	C₂×SD₁₆	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆	C₂³	1	2	yes	—
151	C₂×SD₁₆	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	2	yes	—
155	C₂²×C₈	C₂³	1	2	yes	—
156	C₂²×C₈	C₂³	1	1	yes	characteristic
157	C₂²×C₈	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈	—	2	1	no	—
159	C₄⋊Q₈	—	2	1	no	—
160	C₄⋊Q₈	—	2	2	no	—
161	C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈	C₂³	1	2	yes	—
165	C₄⋊Q₈	C₂³	1	2	yes	—
166	#127	C₂³	1	1	yes	characteristic
167	#126	—	2	2	no	—
168	#126	—	2	2	no	—
169	#126	—	2	2	no	—
170	#126	—	2	2	no	—
171	#126	—	2	2	no	—
172	#126	—	2	2	no	—
173	#126	D₄	1	2	yes	—
174	#125	—	2	1	no	—
175	#125	D₄	1	1	yes	characteristic
176	#124	—	2	1	no	—
177	#124	—	2	1	no	—
178	#124	—	2	2	no	—
179	#124	—	2	2	no	—
180	#124	—	2	2	no	—
181	#124	—	2	2	no	—
182	#124	—	2	2	no	—
183	#124	—	2	2	no	—
184	#124	—	2	2	no	—
185	#124	—	2	1	no	—
186	#124	D₄	1	1	yes	characteristic
187	#124	C₂³	1	2	yes	—
188	#124	C₂³	1	2	yes	—
189	#123	—	2	2	no	—
190	#123	—	2	2	no	—
191	#123	—	2	2	no	—
192	#123	—	2	2	no	—
193	#123	D₄	1	2	yes	—
194	C₂²⋊Q₈	—	2	1	no	—
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	D₄	1	1	yes	characteristic
203	C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₂²⋊Q₈	C₂³	1	2	yes	—
205	C₂²⋊Q₈	C₂³	1	2	yes	—
206	#121	—	2	1	no	—
207	#121	—	2	2	no	—
208	#121	—	2	2	no	—
209	#121	—	2	1	no	—
210	#121	—	2	1	no	—
211	#121	—	2	2	no	—
212	#121	D₄	1	1	yes	characteristic
213	#121	C₂³	1	2	yes	—
214	#121	C₂³	1	2	yes	—
215	#121	C₂³	1	2	yes	—
216	#120	—	2	2	no	—
217	#120	—	2	2	no	—
218	C₄×Q₈	—	2	1	no	—
219	C₄×Q₈	—	2	2	no	—
220	C₄×Q₈	—	2	2	no	—
221	C₄×Q₈	—	2	1	no	—
222	C₄×Q₈	—	2	2	no	—
223	C₄×Q₈	—	2	1	no	—
224	C₄×Q₈	C₂³	1	1	yes	characteristic
225	C₄×Q₈	C₂³	1	1	yes	characteristic
226	C₄×Q₈	C₂³	1	1	yes	characteristic
227	C₄×Q₈	C₂³	1	1	yes	characteristic
228	C₄×Q₈	C₂³	1	2	yes	—
229	C₄×Q₈	C₂³	1	2	yes	—
230	C₄×Q₈	C₂³	1	2	yes	—
231	C₄×Q₈	C₂³	1	1	yes	characteristic
232	C₄×D₄	—	2	1	no	—
233	C₄×D₄	—	2	1	no	—
234	C₄×D₄	—	2	1	no	—
235	C₄×D₄	—	2	1	no	—
236	C₄×D₄	—	2	1	no	—
237	C₄×D₄	—	2	2	no	—
238	C₄×D₄	—	2	2	no	—
239	C₄×D₄	—	2	1	no	—
240	C₄×D₄	—	2	2	no	—
241	C₄×D₄	—	2	1	no	—
242	C₄×D₄	C₂³	1	1	yes	characteristic
243	C₄×D₄	C₂³	1	1	yes	characteristic
244	C₄×D₄	C₂³	1	1	yes	characteristic
245	C₄×D₄	C₂³	1	1	yes	characteristic
246	C₄×D₄	C₂³	1	2	yes	—
247	C₄×D₄	C₂³	1	2	yes	—
248	C₄×D₄	C₂³	1	2	yes	—
249	C₄×D₄	C₂³	1	1	yes	characteristic
250	C₄×D₄	C₂³	1	2	yes	—
251	#117	—	2	1	no	—
252	#117	—	2	2	no	—
253	#117	—	2	1	no	—
254	#117	—	2	1	no	—
255	#117	—	2	2	no	—
256	#117	—	2	2	no	—
257	#117	—	2	1	no	—
258	#117	—	2	1	no	—
259	#117	C₂³	1	1	yes	characteristic
260	#117	C₂³	1	1	yes	characteristic
261	#117	C₂³	1	2	yes	—
262	#117	C₂³	1	2	yes	—
263	#117	C₂³	1	2	yes	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₄²	—	2	1	no	—
268	C₂×C₄²	—	2	1	no	—
269	C₂×C₄²	C₂³	1	1	yes	characteristic
270	#107	C₂³	1	1	yes	characteristic
271	#107	C₂³	1	1	yes	characteristic
272	#107	C₂³	1	2	yes	—
273	#107	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	#106	C₂³	1	2	yes	—
278	#106	C₂³	1	2	yes	—
279	#106	C₂³	1	2	yes	—
280	C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₄⋊C₈	C₂³	1	2	yes	—
283	C₄⋊C₈	C₂³	1	2	yes	—
284	#103	C₂³	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
295	#102	C₂³	1	1	yes	characteristic
296	#102	C₂³	1	1	yes	characteristic
297	#102	C₂³	1	1	yes	characteristic
298	#102	C₂³	1	2	yes	—
299	#102	C₂³	1	2	yes	—
300	#102	C₂³	1	2	yes	—
301	#102	C₂³	1	2	yes	—
302	#102	C₂³	1	2	yes	—
303	#102	C₂³	1	2	yes	—
304	C₂²⋊C₈	C₂³	1	2	yes	—
305	C₂²⋊C₈	C₂³	1	2	yes	—
306	C₂²⋊C₈	C₂³	1	2	yes	—
307	#97	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	1	yes	characteristic
312	C₄×C₈	C₂³	1	1	yes	characteristic
313	C₄×C₈	C₂³	1	2	yes	—
314	C₂⁴	—	2	2	no	—
315	#41	—	2	2	no	—
316	#41	—	2	2	no	—
317	#41	—	4	1	no	—
318	#41	—	4	1	no	—
319	#41	—	8	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	4	no	—
326	C₂×Q₈	—	4	2	no	—
327	C₂×Q₈	—	8	2	no	—
328	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
329	C₂×Q₈	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈	C₂⁴	1	2	yes	—
331	C₂×Q₈	C₂⁴	1	1	yes	characteristic
332	C₂×D₄	—	2	4	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	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	4	2	no	—
342	C₂×D₄	—	8	2	no	—
343	C₂×D₄	C₂×D₄	1	1	yes	characteristic
344	C₂×D₄	C₂×D₄	1	2	yes	—
345	C₂×D₄	C₂⁴	1	1	yes	characteristic
346	C₂×D₄	C₂⁴	1	2	yes	—
347	C₂×D₄	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄	—	2	2	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	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	C₂×D₄	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
360	C₂²×C₄	C₂⁴	1	1	yes	characteristic
361	C₂²×C₄	C₂⁴	1	2	yes	—
362	Q₁₆	—	2	2	no	—
363	Q₁₆	—	4	2	no	—
364	SD₁₆	—	2	4	no	—
365	SD₁₆	—	2	4	no	—
366	SD₁₆	—	2	4	no	—
367	SD₁₆	—	2	2	no	—
368	SD₁₆	—	4	2	no	—
369	SD₁₆	#41	1	4	yes	complemented
370	D₈	—	2	2	no	—
371	D₈	—	4	2	no	—
372	M₁₆	—	4	2	no	—
373	C₂×C₈	—	2	4	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	4	1	no	—
376	C₂×C₈	C₂⁴	1	1	yes	characteristic
377	C₂×C₈	C₂⁴	1	1	yes	characteristic
378	C₂×C₈	C₂⁴	1	1	yes	characteristic
379	C₂×C₈	C₂⁴	1	2	yes	—
380	C₂×C₈	C₂⁴	1	2	yes	—
381	C₂×C₈	C₂⁴	1	1	yes	characteristic
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	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	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	1	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	2	yes	—
402	C₄⋊C₄	C₂×D₄	1	2	yes	—
403	C₄⋊C₄	C₂×D₄	1	2	yes	—
404	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄	C₂⁴	1	2	yes	—
406	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄	C₂⁴	1	2	yes	—
408	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	1	no	—
415	C₂²⋊C₄	—	2	1	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	1	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	2	no	—
423	C₂²⋊C₄	—	2	1	no	—
424	C₂²⋊C₄	—	2	1	no	—
425	C₂²⋊C₄	—	2	1	no	—
426	C₂²⋊C₄	—	2	2	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	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄	C₂×D₄	1	2	yes	—
436	C₄²	—	2	1	no	—
437	C₄²	—	2	1	no	—
438	C₄²	—	2	1	no	—
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	—	2	2	no	—
447	C₄²	C₂×D₄	1	1	yes	characteristic
448	C₄²	C₂×D₄	1	1	yes	characteristic
449	C₄²	C₂⁴	1	1	yes	characteristic
450	C₄²	C₂⁴	1	1	yes	characteristic
451	C₄²	C₂⁴	1	2	yes	—
452	C₂³	—	2	1	no	—
453	C₂³	—	2	1	no	—
454	C₂³	—	2	2	no	—
455	C₂³	—	4	4	no	—
456	C₂³	—	8	2	no	—
457	C₂³	—	8	2	no	—
458	C₂³	C₂²×D₄	1	2	yes	—
459	C₂³	C₂²×D₄	1	1	yes	characteristic
460	Q₈	—	2	2	no	—
461	Q₈	—	2	1	no	—
462	Q₈	—	2	2	no	—
463	Q₈	—	2	1	no	—
464	Q₈	—	2	2	no	—
465	Q₈	—	2	1	no	—
466	Q₈	—	4	4	no	—
467	Q₈	—	4	2	no	—
468	Q₈	—	8	1	no	—
469	Q₈	—	8	2	no	—
470	Q₈	—	8	2	no	—
471	Q₈	C₂×#41	1	2	yes	—
472	D₄	—	2	2	no	—
473	D₄	—	2	1	no	—
474	D₄	—	2	2	no	—
475	D₄	—	2	1	no	—
476	D₄	—	2	1	no	—
477	D₄	—	2	2	no	—
478	D₄	—	4	2	no	—
479	D₄	—	4	4	no	—
480	D₄	—	4	2	no	—
481	D₄	—	4	2	no	—
482	D₄	—	4	2	no	—
483	D₄	—	8	1	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	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	4	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	8	1	no	—
509	C₂×C₄	—	8	1	no	—
510	C₂×C₄	—	8	2	no	—
511	C₂×C₄	—	8	2	no	—
512	C₂×C₄	—	8	2	no	—
513	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄	C₂²×D₄	1	2	yes	—
517	C₂×C₄	C₂²×D₄	1	2	yes	—
518	C₂×C₄	C₂²×D₄	1	2	yes	—
519	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄	C₂⁵	1	1	yes	characteristic
522	C₈	—	2	1	no	—
523	C₈	—	2	2	no	—
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	2	2	no	—
527	C₈	C₂×#41	1	2	yes	—
528	C₂²	—	2	1	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	1	no	—
534	C₂²	—	2	2	no	—
535	C₂²	—	4	1	no	—
536	C₂²	—	4	1	no	—
537	C₂²	—	4	1	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	4	1	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	1	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	16	4	no	—
544	C₂²	C₂³×D₄	1	1	yes	characteristic
545	C₄	—	2	1	no	—
546	C₄	—	2	1	no	—
547	C₄	—	2	2	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	2	no	—
550	C₄	—	2	2	no	—
551	C₄	—	2	1	no	—
552	C₄	—	2	2	no	—
553	C₄	—	4	1	no	—
554	C₄	—	4	1	no	—
555	C₄	—	4	2	no	—
556	C₄	—	4	1	no	—
557	C₄	—	4	2	no	—
558	C₄	—	4	1	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	2	no	—
561	C₄	#577	1	2	yes	—
562	C₄	C₂²×#41	1	1	yes	characteristic
563	C₄	#585	1	1	yes	characteristic
564	C₂	—	4	1	no	—
565	C₂	—	4	2	no	—
566	C₂	—	4	2	no	—
567	C₂	—	8	1	no	—
568	C₂	—	8	2	no	—
569	C₂	D₄×#41	1	1	yes	characteristic
570	C₂	C₂×#577	1	1	yes	characteristic
571	C₂	#3584	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. #3518	C₂	semidirect
2. #3514	C₂	semidirect
3. #3394	C₂	semidirect
4. Q₈×SD₁₆	C₂	semidirect
5. #3375	C₂	semidirect
6. #3367	C₂	semidirect
7. #3340	C₂	semidirect
8. #3340	C₂	semidirect
9. #3328	C₂	semidirect
10. #3325	C₂	semidirect
11. #3321	C₂	semidirect
12. #3311	C₂	semidirect
13. #3282	C₂	semidirect
14. D₄×SD₁₆	C₂	semidirect
15. #3173	C₂	semidirect
16. #3167	C₂	semidirect
17. #3121	C₂	semidirect
18. #3118	C₂	semidirect
19. #3116	C₂	semidirect
20. #3115	C₂	semidirect
21. #2966	C₂	semidirect
22. #2949	C₂	semidirect
23. C₄×#135	C₂	semidirect
27. Q₈²	C₂²	semidirect
31. #556	C₂²	semidirect
32. #556	C₂²	semidirect
40. #548	C₂²	semidirect
46. #542	C₂²	semidirect
49. #533	C₂²	semidirect
55. #519	C₂²	semidirect
58. C₄×#41	C₂²	semidirect
59. #498	C₂²	semidirect
60. #498	C₂²	semidirect
61. #495	C₂²	semidirect
63. #489	C₂²	semidirect
64. #489	C₂²	semidirect
65. #487	C₂²	semidirect
67. #485	C₂²	semidirect
68. #485	C₂²	semidirect
69. #485	C₂²	semidirect
71. #482	C₂²	semidirect
72. #482	C₂²	semidirect
73. #477	C₂²	semidirect
74. #477	C₂²	semidirect
77. #475	C₂²	semidirect
78. #475	C₂²	semidirect
79. #474	C₂²	semidirect
80. #474	C₂²	semidirect
81. #470	C₂²	semidirect
84. #465	C₂²	semidirect
85. #465	C₂²	semidirect
86. #465	C₂²	semidirect
87. #464	C₂²	semidirect
88. #464	C₂²	semidirect
90. #463	C₂²	semidirect
91. #462	C₂²	semidirect
96. #451	C₂²	semidirect
98. #449	C₂²	semidirect
101. #446	C₂²	semidirect
102. C₈×Q₈	C₂²	semidirect
103. #442	C₂²	semidirect
104. #441	C₂²	semidirect
107. #440	C₂²	semidirect
108. #440	C₂²	semidirect
109. C₄×Q₁₆	C₂²	semidirect
110. C₄×Q₁₆	C₂²	semidirect
114. C₄×SD₁₆	C₂²	semidirect
115. C₄×SD₁₆	C₂²	semidirect
116. C₄×SD₁₆	C₂²	semidirect
117. C₄×SD₁₆	C₂²	semidirect
118. C₄×SD₁₆	C₂²	semidirect
122. #435	C₂²	semidirect
124. C₈×D₄	C₂²	semidirect
125. #433	C₂²	semidirect
126. #432	C₂²	semidirect
127. #427	C₂²	semidirect
128. #427	C₂²	semidirect
129. #419	C₂²	semidirect
132. #416	C₂²	semidirect
133. #405	C₂²	semidirect
134. C₂×C₄×C₈	C₂²	semidirect
369. SD₁₆	#41	semidirect

Maximal subgroups

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

subgroup	index
#3518	2
#3514	2
#3394	2
Q₈×SD₁₆	2
#3375	2
#3367	2
#3340	2
#3328	2
#3325	2
#3321	2
#3311	2
#3282	2
D₄×SD₁₆	2
#3173	2
#3167	2
#3121	2
#3118	2
#3116	2
#3115	2
#2966	2
#2949	2
C₄×#135	2