Subgroups — #61451

Order 256.

1089 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3481	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	#3373	C₂	1	1	yes	maximal, characteristic, complemented
6	#3366	C₂	1	1	yes	maximal, characteristic, complemented
7	#3345	C₂	1	2	yes	maximal, complemented
8	#3335	C₂	1	1	yes	maximal, characteristic, complemented
9	#3318	C₂	1	2	yes	maximal, complemented
10	#3306	C₂	1	2	yes	maximal, complemented
11	#3295	C₂	1	1	yes	maximal, characteristic, complemented
12	#3294	C₂	1	1	yes	maximal, characteristic, complemented
13	D₄×D₈	C₂	1	1	yes	maximal, characteristic, complemented
14	#3264	C₂	1	2	yes	maximal, complemented
15	#3184	C₂	1	1	yes	maximal, characteristic, complemented
16	#3180	C₂	1	2	yes	maximal, complemented
17	#3115	C₂	1	1	yes	maximal, characteristic, complemented
18	#3114	C₂	1	2	yes	maximal, complemented
19	#3109	C₂	1	1	yes	maximal, characteristic, complemented
20	#3109	C₂	1	2	yes	maximal, complemented
21	#2970	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#442	C₂	1	2	yes	maximal, complemented
24	C₂²×#41	—	2	1	no	—
25	C₂×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
26	C₂²×D₈	C₂²	1	2	yes	—
27	#559	C₂²	1	1	yes	characteristic, complemented
28	#554	C₂²	1	1	yes	characteristic, complemented
29	#554	C₂²	1	1	yes	characteristic, complemented
30	#553	—	2	1	no	—
31	#553	C₂²	1	2	yes	complemented
32	#551	—	2	2	no	—
33	#550	C₂²	1	1	yes	characteristic, complemented
34	D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
35	#548	—	2	1	no	—
36	#547	C₂²	1	1	yes	characteristic
37	#547	C₂²	1	2	yes	complemented
38	#546	—	2	1	no	—
39	#546	—	2	1	no	—
40	#546	—	2	2	no	—
41	#546	C₂²	1	2	yes	complemented
42	D₄²	C₂²	1	1	yes	characteristic
43	D₄²	C₂²	1	2	yes	complemented
44	D₄²	C₂²	1	1	yes	characteristic, complemented
45	#532	C₂²	1	2	yes	complemented
46	#532	C₂²	1	1	yes	characteristic, complemented
47	#532	C₂²	1	1	yes	characteristic, complemented
48	#529	—	2	1	no	—
49	#529	C₂²	1	2	yes	complemented
50	#525	—	2	2	no	—
51	#525	—	2	2	no	—
52	#525	—	2	1	no	—
53	C₄×#41	C₂²	1	1	yes	characteristic
54	C₄×#41	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₄×D₄	—	2	1	no	—
56	C₂×C₄×D₄	C₂²	1	2	yes	complemented
57	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×D₄	C₂²	1	2	yes	complemented
59	#501	C₂²	1	2	yes	complemented
60	#498	C₂²	1	1	yes	characteristic, complemented
61	#496	C₂²	1	2	yes	complemented
62	#493	C₂²	1	1	yes	characteristic, complemented
63	#490	C₂²	1	2	yes	complemented
64	#489	C₂²	1	2	yes	complemented
65	#486	C₂²	1	1	yes	characteristic, complemented
66	#486	C₂²	1	1	yes	characteristic, complemented
67	#483	C₂²	1	2	yes	complemented
68	#482	C₂²	1	2	yes	complemented
69	#481	C₂²	1	2	yes	complemented
70	#481	C₂²	1	2	yes	complemented
71	#481	C₂²	1	2	yes	complemented
72	#480	C₂²	1	2	yes	complemented
73	#478	C₂²	1	2	yes	complemented
74	#478	C₂²	1	2	yes	complemented
75	#476	C₂²	1	1	yes	characteristic, complemented
76	#476	C₂²	1	2	yes	complemented
77	#476	C₂²	1	1	yes	characteristic, complemented
78	#476	C₂²	1	2	yes	complemented
79	#475	C₂²	1	1	yes	characteristic, complemented
80	#474	C₂²	1	1	yes	characteristic, complemented
81	#469	C₂²	1	2	yes	complemented
82	#469	C₂²	1	2	yes	complemented
83	#466	C₂²	1	2	yes	complemented
84	#466	C₂²	1	2	yes	complemented
85	#465	C₂²	1	2	yes	complemented
86	#465	C₂²	1	2	yes	complemented
87	#463	C₂²	1	2	yes	complemented
88	#463	C₂²	1	2	yes	complemented
89	#460	C₂²	1	1	yes	characteristic, complemented
90	#459	C₂²	1	1	yes	characteristic
91	#459	C₂²	1	2	yes	complemented
92	#459	C₂²	1	1	yes	characteristic, complemented
93	#459	C₂²	1	2	yes	complemented
94	#459	C₂²	1	1	yes	characteristic, complemented
95	#450	C₂²	1	2	yes	complemented
96	#449	C₂²	1	2	yes	complemented
97	#447	C₂²	1	2	yes	—
98	#447	C₂²	1	2	yes	complemented
99	#447	C₂²	1	2	yes	complemented
100	#447	C₂²	1	2	yes	complemented
101	#446	C₂²	1	1	yes	characteristic, complemented
102	#446	C₂²	1	1	yes	characteristic, complemented
103	#442	C₂²	1	2	yes	—
104	#442	C₂²	1	1	yes	characteristic
105	#442	C₂²	1	2	yes	complemented
106	#442	C₂²	1	2	yes	complemented
107	#442	C₂²	1	1	yes	characteristic, complemented
108	#442	C₂²	1	2	yes	complemented
109	#442	C₂²	1	2	yes	complemented
110	#442	C₂²	1	2	yes	complemented
111	#442	C₂²	1	2	yes	complemented
112	#442	C₂²	1	2	yes	complemented
113	#442	C₂²	1	2	yes	complemented
114	#440	C₂²	1	1	yes	characteristic, complemented
115	#440	C₂²	1	2	yes	complemented
116	#440	C₂²	1	1	yes	characteristic, complemented
117	C₄×SD₁₆	C₂²	1	1	yes	characteristic, 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, complemented
121	#435	C₂²	1	2	yes	complemented
122	#435	C₂²	1	2	yes	complemented
123	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
124	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
125	#432	C₂²	1	2	yes	complemented
126	#432	C₂²	1	1	yes	characteristic, complemented
127	#428	C₂²	1	1	yes	characteristic, complemented
128	C₂×#106	C₂²	1	2	yes	complemented
129	#418	C₂²	1	1	yes	characteristic, complemented
130	#417	C₂²	1	1	yes	characteristic, complemented
131	C₂×#102	C₂²	1	2	yes	complemented
132	C₂×#102	C₂²	1	2	yes	complemented
133	C₄×M₁₆	C₂²	1	1	yes	characteristic, complemented
134	C₂×#97	C₂²	1	2	yes	complemented
135	C₂×#41	—	2	1	no	—
136	C₂×#41	—	2	1	no	—
137	C₂×#41	—	2	2	no	—
138	C₂×#41	—	2	2	no	—
139	C₂×#41	—	2	1	no	—
140	C₂×#41	—	2	1	no	—
141	C₂×#41	—	4	8	no	—
142	C₂×#41	D₄	1	1	yes	characteristic
143	C₂×#41	C₂³	1	1	yes	characteristic
144	C₂²×Q₈	—	2	1	no	—
145	C₂²×D₄	—	2	1	no	—
146	C₂²×D₄	—	2	1	no	—
147	C₂²×D₄	—	2	2	no	—
148	C₂²×D₄	C₂³	1	2	yes	—
149	C₂²×D₄	C₂³	1	1	yes	characteristic
150	C₂²×D₄	C₂³	1	2	yes	—
151	C₂³×C₄	—	2	2	no	—
152	C₂³×C₄	—	2	1	no	—
153	C₂³×C₄	—	2	2	no	—
154	AGL(1,ℤ/8)	—	2	4	no	—
155	C₂×SD₁₆	C₂³	1	1	yes	characteristic
156	C₂×SD₁₆	C₂³	1	1	yes	characteristic
157	C₂×SD₁₆	C₂³	1	2	yes	—
158	C₂×D₈	—	2	8	no	—
159	C₂×D₈	C₂³	1	2	yes	—
160	C₂×D₈	C₂³	1	2	yes	—
161	C₂×D₈	C₂³	1	2	yes	—
162	C₂×D₈	C₂³	1	1	yes	characteristic
163	C₂×D₈	C₂³	1	2	yes	—
164	C₂×D₈	C₂³	1	2	yes	—
165	C₂×D₈	C₂³	1	1	yes	characteristic
166	C₂×M₁₆	C₂³	1	1	yes	characteristic
167	C₂×M₁₆	C₂³	1	1	yes	characteristic
168	C₂²×C₈	C₂³	1	2	yes	—
169	C₂²×C₈	C₂³	1	2	yes	—
170	C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₄⋊Q₈	C₂³	1	2	yes	—
172	C₄⋊Q₈	C₂³	1	1	yes	characteristic
173	#127	C₂³	1	1	yes	characteristic
174	#127	C₂³	1	2	yes	—
175	#127	C₂³	1	1	yes	characteristic
176	#126	—	2	2	no	—
177	#126	—	2	2	no	—
178	#125	—	2	1	no	—
179	#125	C₂³	1	2	yes	—
180	#124	—	2	1	no	—
181	#124	—	2	1	no	—
182	#124	—	2	2	no	—
183	#124	—	2	1	no	—
184	#124	C₂³	1	2	yes	—
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	C₂²⋊Q₈	—	2	1	no	—
193	C₂²⋊Q₈	—	2	1	no	—
194	C₂²⋊Q₈	—	2	2	no	—
195	C₂²⋊Q₈	—	2	1	no	—
196	C₂²⋊Q₈	—	2	2	no	—
197	C₂²⋊Q₈	—	2	2	no	—
198	C₂²⋊Q₈	—	2	2	no	—
199	C₂²⋊Q₈	C₂³	1	2	yes	—
200	#121	—	2	2	no	—
201	#121	—	2	2	no	—
202	#121	—	2	1	no	—
203	#121	—	2	1	no	—
204	#121	—	2	1	no	—
205	#121	—	2	2	no	—
206	#121	—	2	1	no	—
207	#121	—	2	2	no	—
208	#121	—	2	1	no	—
209	#121	—	2	2	no	—
210	#121	C₂³	1	2	yes	—
211	#121	C₂³	1	2	yes	—
212	#121	C₂³	1	2	yes	—
213	#121	C₂³	1	2	yes	—
214	#121	C₂³	1	2	yes	—
215	#120	—	2	2	no	—
216	#120	—	2	2	no	—
217	#120	—	2	2	no	—
218	#120	—	2	2	no	—
219	#120	—	2	2	no	—
220	C₄×Q₈	D₄	1	1	yes	characteristic
221	C₄×Q₈	C₂³	1	1	yes	characteristic
222	C₄×Q₈	C₂³	1	1	yes	characteristic
223	C₄×Q₈	C₂³	1	1	yes	characteristic
224	C₄×D₄	—	2	1	no	—
225	C₄×D₄	—	2	2	no	—
226	C₄×D₄	—	2	1	no	—
227	C₄×D₄	—	2	1	no	—
228	C₄×D₄	—	2	1	no	—
229	C₄×D₄	—	2	2	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	2	no	—
236	C₄×D₄	—	2	2	no	—
237	C₄×D₄	—	2	1	no	—
238	C₄×D₄	—	2	2	no	—
239	C₄×D₄	D₄	1	1	yes	characteristic
240	C₄×D₄	D₄	1	2	yes	—
241	C₄×D₄	C₂³	1	1	yes	characteristic
242	C₄×D₄	C₂³	1	1	yes	characteristic
243	C₄×D₄	C₂³	1	2	yes	—
244	C₄×D₄	C₂³	1	1	yes	characteristic
245	C₄×D₄	C₂³	1	2	yes	—
246	C₄×D₄	C₂³	1	1	yes	characteristic
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	C₄×D₄	C₂³	1	2	yes	—
252	C₄×D₄	C₂³	1	1	yes	characteristic
253	C₄×D₄	C₂³	1	1	yes	characteristic
254	C₄×D₄	C₂³	1	2	yes	—
255	#117	—	2	1	no	—
256	#117	—	2	2	no	—
257	#117	D₄	1	2	yes	—
258	#117	D₄	1	1	yes	characteristic
259	#117	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂³	1	2	yes	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₂²⋊C₄	—	2	1	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₄²	—	2	1	no	—
269	C₂×C₄²	C₂³	1	2	yes	—
270	C₂×C₄²	C₂³	1	1	yes	characteristic
271	#107	C₂³	1	1	yes	characteristic
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	2	yes	—
277	#106	C₂³	1	2	yes	—
278	#106	C₂³	1	1	yes	characteristic
279	#106	C₂³	1	2	yes	—
280	#106	C₂³	1	2	yes	—
281	C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₄⋊C₈	C₂³	1	1	yes	characteristic
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	2	yes	—
288	#102	C₂³	1	1	yes	characteristic
289	#102	C₂³	1	1	yes	characteristic
290	#102	C₂³	1	2	yes	—
291	#102	C₂³	1	2	yes	—
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	1	yes	characteristic
298	#102	C₂³	1	1	yes	characteristic
299	#102	C₂³	1	1	yes	characteristic
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	#102	C₂³	1	2	yes	—
305	C₂²⋊C₈	C₂³	1	2	yes	—
306	C₂²⋊C₈	C₂³	1	2	yes	—
307	C₂²⋊C₈	C₂³	1	2	yes	—
308	#97	C₂³	1	1	yes	characteristic
309	#97	C₂³	1	2	yes	—
310	#97	C₂³	1	2	yes	—
311	#97	C₂³	1	2	yes	—
312	#97	C₂³	1	1	yes	characteristic
313	C₄×C₈	C₂³	1	1	yes	characteristic
314	C₄×C₈	C₂³	1	1	yes	characteristic
315	C₂⁴	—	2	2	no	—
316	C₂⁴	—	2	1	no	—
317	C₂⁴	—	2	2	no	—
318	#41	—	2	4	no	—
319	#41	—	2	2	no	—
320	#41	—	4	1	no	—
321	#41	—	4	8	no	—
322	#41	—	4	4	no	—
323	#41	—	4	8	no	—
324	#41	—	4	4	no	—
325	#41	—	4	4	no	—
326	#41	—	8	2	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	4	4	no	—
331	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
332	C₂×Q₈	C₂⁴	1	1	yes	characteristic
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	4	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	2	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	—	2	1	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	4	2	no	—
352	C₂×D₄	—	4	2	no	—
353	C₂×D₄	—	4	1	no	—
354	C₂×D₄	—	4	8	no	—
355	C₂×D₄	—	4	4	no	—
356	C₂×D₄	—	4	4	no	—
357	C₂×D₄	C₂×D₄	1	2	yes	—
358	C₂×D₄	C₂×D₄	1	1	yes	characteristic
359	C₂×D₄	C₂⁴	1	2	yes	—
360	C₂×D₄	C₂⁴	1	2	yes	—
361	C₂×D₄	C₂⁴	1	1	yes	characteristic
362	C₂×D₄	C₂⁴	1	1	yes	characteristic
363	C₂×D₄	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	4	8	no	—
381	C₂²×C₄	—	4	4	no	—
382	C₂²×C₄	—	8	4	no	—
383	C₂²×C₄	C₂×D₄	1	2	yes	—
384	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
385	C₂²×C₄	C₂×D₄	1	2	yes	—
386	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄	C₂⁴	1	2	yes	—
388	C₂²×C₄	C₂⁴	1	1	yes	characteristic
389	SD₁₆	—	2	2	no	—
390	SD₁₆	—	2	2	no	—
391	SD₁₆	—	4	2	no	—
392	D₈	—	2	4	no	—
393	D₈	—	2	4	no	—
394	D₈	—	2	2	no	—
395	D₈	—	2	4	no	—
396	D₈	—	4	2	no	—
397	D₈	—	4	2	no	—
398	D₈	#41	1	4	yes	complemented
399	M₁₆	—	2	2	no	—
400	M₁₆	—	4	1	no	—
401	C₂×C₈	—	2	4	no	—
402	C₂×C₈	—	4	2	no	—
403	C₂×C₈	C₂⁴	1	1	yes	characteristic
404	C₂×C₈	C₂⁴	1	1	yes	characteristic
405	C₂×C₈	C₂⁴	1	1	yes	characteristic
406	C₂×C₈	C₂⁴	1	2	yes	—
407	C₂×C₈	C₂⁴	1	2	yes	—
408	C₂×C₈	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
421	C₄⋊C₄	C₂×D₄	1	2	yes	—
422	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
423	C₄⋊C₄	C₂×D₄	1	2	yes	—
424	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
425	C₄⋊C₄	C₂⁴	1	2	yes	—
426	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
427	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
428	C₄⋊C₄	C₂⁴	1	2	yes	—
429	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	2	1	no	—
432	C₂²⋊C₄	—	2	1	no	—
433	C₂²⋊C₄	—	2	1	no	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	2	no	—
437	C₂²⋊C₄	—	2	1	no	—
438	C₂²⋊C₄	—	2	2	no	—
439	C₂²⋊C₄	—	2	2	no	—
440	C₂²⋊C₄	—	2	1	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	1	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	2	1	no	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	—	2	2	no	—
450	C₂²⋊C₄	—	2	2	no	—
451	C₂²⋊C₄	C₂×D₄	1	2	yes	—
452	C₂²⋊C₄	C₂×D₄	1	2	yes	—
453	C₂²⋊C₄	C₂×D₄	1	2	yes	—
454	C₄²	—	2	1	no	—
455	C₄²	—	2	1	no	—
456	C₄²	—	2	1	no	—
457	C₄²	C₂×D₄	1	1	yes	characteristic
458	C₄²	C₂×D₄	1	1	yes	characteristic
459	C₄²	C₂×D₄	1	2	yes	—
460	C₄²	C₂×D₄	1	2	yes	—
461	C₄²	C₂⁴	1	1	yes	characteristic
462	C₄²	C₂⁴	1	1	yes	characteristic
463	C₄²	C₂⁴	1	2	yes	—
464	C₂³	—	2	1	no	—
465	C₂³	—	2	1	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	2	1	no	—
469	C₂³	—	4	4	no	—
470	C₂³	—	4	4	no	—
471	C₂³	—	4	2	no	—
472	C₂³	—	4	2	no	—
473	C₂³	—	4	4	no	—
474	C₂³	—	4	4	no	—
475	C₂³	—	8	2	no	—
476	C₂³	—	8	2	no	—
477	C₂³	—	8	1	no	—
478	C₂³	C₂²×D₄	1	1	yes	characteristic
479	C₂³	C₂²×D₄	1	2	yes	—
480	Q₈	—	2	2	no	—
481	Q₈	—	2	1	no	—
482	Q₈	—	2	1	no	—
483	Q₈	—	4	4	no	—
484	Q₈	—	4	2	no	—
485	Q₈	—	8	1	no	—
486	D₄	—	2	4	no	—
487	D₄	—	2	2	no	—
488	D₄	—	2	2	no	—
489	D₄	—	2	1	no	—
490	D₄	—	2	1	no	—
491	D₄	—	2	1	no	—
492	D₄	—	2	2	no	—
493	D₄	—	2	1	no	—
494	D₄	—	2	2	no	—
495	D₄	—	4	2	no	—
496	D₄	—	4	4	no	—
497	D₄	—	4	4	no	—
498	D₄	—	4	4	no	—
499	D₄	—	4	2	no	—
500	D₄	—	4	4	no	—
501	D₄	—	4	4	no	—
502	D₄	—	4	4	no	—
503	D₄	—	4	4	no	—
504	D₄	—	4	2	no	—
505	D₄	—	4	2	no	—
506	D₄	—	8	2	no	—
507	D₄	—	8	1	no	—
508	D₄	—	8	1	no	—
509	D₄	—	8	2	no	—
510	D₄	AGL(1,ℤ/8)	1	4	yes	complemented
511	D₄	C₂×#41	1	2	yes	—
512	D₄	C₂×#41	1	2	yes	complemented
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	4	no	—
531	C₂×C₄	—	4	4	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	4	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	4	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	4	4	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	8	2	no	—
542	C₂×C₄	—	8	2	no	—
543	C₂×C₄	—	8	2	no	—
544	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
547	C₂×C₄	C₂²×D₄	1	2	yes	—
548	C₂×C₄	C₂²×D₄	1	2	yes	—
549	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
550	C₂×C₄	C₂²×D₄	1	2	yes	—
551	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄	C₂⁵	1	1	yes	characteristic
553	C₈	—	2	2	no	—
554	C₈	—	2	1	no	—
555	C₈	—	2	1	no	—
556	C₈	—	2	2	no	—
557	C₈	—	2	1	no	—
558	C₈	C₂×#41	1	2	yes	complemented
559	C₂²	—	2	2	no	—
560	C₂²	—	2	2	no	—
561	C₂²	—	2	1	no	—
562	C₂²	—	2	1	no	—
563	C₂²	—	2	2	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	1	no	—
570	C₂²	—	4	2	no	—
571	C₂²	—	4	2	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	2	no	—
574	C₂²	—	4	2	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	2	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	2	no	—
579	C₂²	—	8	8	no	—
580	C₂²	—	8	8	no	—
581	C₂²	—	8	4	no	—
582	C₂²	C₂×AGL(1,ℤ/8)	1	4	yes	—
583	C₂²	C₂³×D₄	1	1	yes	characteristic
584	C₄	—	2	1	no	—
585	C₄	—	2	2	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	2	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	2	no	—
591	C₄	—	4	1	no	—
592	C₄	—	4	2	no	—
593	C₄	—	4	1	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	2	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	C₂×AGL(1,ℤ/8)	1	2	yes	—
599	C₄	C₂²×#41	1	1	yes	characteristic
600	C₄	#585	1	1	yes	characteristic
601	C₂	—	2	4	no	—
602	C₂	—	4	1	no	—
603	C₂	—	4	2	no	—
604	C₂	—	4	2	no	—
605	C₂	—	8	2	no	—
606	C₂	—	8	2	no	—
607	C₂	—	8	1	no	—
608	C₂	D₄×#41	1	1	yes	characteristic
609	C₂	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
610	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 ◁ C₄×#41 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3481	C₂	semidirect
2. D₄×#41	C₂	semidirect
3. #3399	C₂	semidirect
4. #3384	C₂	semidirect
5. #3373	C₂	semidirect
6. #3366	C₂	semidirect
7. #3345	C₂	semidirect
8. #3335	C₂	semidirect
9. #3318	C₂	semidirect
10. #3306	C₂	semidirect
11. #3295	C₂	semidirect
12. #3294	C₂	semidirect
13. D₄×D₈	C₂	semidirect
14. #3264	C₂	semidirect
15. #3184	C₂	semidirect
16. #3180	C₂	semidirect
17. #3115	C₂	semidirect
18. #3114	C₂	semidirect
19. #3109	C₂	semidirect
20. #3109	C₂	semidirect
21. #2970	C₂	semidirect
22. C₄×AGL(1,ℤ/8)	C₂	semidirect
23. C₂×#442	C₂	semidirect
27. #559	C₂²	semidirect
28. #554	C₂²	semidirect
29. #554	C₂²	semidirect
31. #553	C₂²	semidirect
33. #550	C₂²	semidirect
34. D₄×Q₈	C₂²	semidirect
37. #547	C₂²	semidirect
41. #546	C₂²	semidirect
43. D₄²	C₂²	semidirect
44. D₄²	C₂²	semidirect
45. #532	C₂²	semidirect
46. #532	C₂²	semidirect
47. #532	C₂²	semidirect
49. #529	C₂²	semidirect
54. C₄×#41	C₂²	semidirect
56. C₂×C₄×D₄	C₂²	semidirect
57. C₂×C₄×D₄	C₂²	semidirect
58. C₂×C₄×D₄	C₂²	semidirect
59. #501	C₂²	semidirect
60. #498	C₂²	semidirect
61. #496	C₂²	semidirect
62. #493	C₂²	semidirect
63. #490	C₂²	semidirect
64. #489	C₂²	semidirect
65. #486	C₂²	semidirect
66. #486	C₂²	semidirect
67. #483	C₂²	semidirect
68. #482	C₂²	semidirect
69. #481	C₂²	semidirect
70. #481	C₂²	semidirect
71. #481	C₂²	semidirect
72. #480	C₂²	semidirect
73. #478	C₂²	semidirect
74. #478	C₂²	semidirect
75. #476	C₂²	semidirect
76. #476	C₂²	semidirect
77. #476	C₂²	semidirect
78. #476	C₂²	semidirect
79. #475	C₂²	semidirect
80. #474	C₂²	semidirect
81. #469	C₂²	semidirect
82. #469	C₂²	semidirect
83. #466	C₂²	semidirect
84. #466	C₂²	semidirect
85. #465	C₂²	semidirect
86. #465	C₂²	semidirect
87. #463	C₂²	semidirect
88. #463	C₂²	semidirect
89. #460	C₂²	semidirect
91. #459	C₂²	semidirect
92. #459	C₂²	semidirect
93. #459	C₂²	semidirect
94. #459	C₂²	semidirect
95. #450	C₂²	semidirect
96. #449	C₂²	semidirect
98. #447	C₂²	semidirect
99. #447	C₂²	semidirect
100. #447	C₂²	semidirect
101. #446	C₂²	semidirect
102. #446	C₂²	semidirect
105. #442	C₂²	semidirect
106. #442	C₂²	semidirect
107. #442	C₂²	semidirect
108. #442	C₂²	semidirect
109. #442	C₂²	semidirect
110. #442	C₂²	semidirect
111. #442	C₂²	semidirect
112. #442	C₂²	semidirect
113. #442	C₂²	semidirect
114. #440	C₂²	semidirect
115. #440	C₂²	semidirect
116. #440	C₂²	semidirect
117. C₄×SD₁₆	C₂²	semidirect
118. C₄×SD₁₆	C₂²	semidirect
120. C₄×D₈	C₂²	semidirect
121. #435	C₂²	semidirect
122. #435	C₂²	semidirect
123. C₈×D₄	C₂²	semidirect
124. C₈×D₄	C₂²	semidirect
125. #432	C₂²	semidirect
126. #432	C₂²	semidirect
127. #428	C₂²	semidirect
128. C₂×#106	C₂²	semidirect
129. #418	C₂²	semidirect
130. #417	C₂²	semidirect
131. C₂×#102	C₂²	semidirect
132. C₂×#102	C₂²	semidirect
133. C₄×M₁₆	C₂²	semidirect
134. C₂×#97	C₂²	semidirect
398. D₈	#41	semidirect
510. D₄	AGL(1,ℤ/8)	semidirect
512. D₄	C₂×#41	semidirect
558. C₈	C₂×#41	semidirect

Maximal subgroups

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

subgroup	index
#3481	2
D₄×#41	2
#3399	2
#3384	2
#3373	2
#3366	2
#3345	2
#3335	2
#3318	2
#3306	2
#3295	2
#3294	2
D₄×D₈	2
#3264	2
#3184	2
#3180	2
#3115	2
#3114	2
#3109	2
#2970	2
C₄×AGL(1,ℤ/8)	2
C₂×#442	2