Subgroups — #60875

Order 256.

850 conjugacy classes of subgroups.

The subgroup lattice has 557 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3494	C₂	1	1	yes	maximal, characteristic
2	#3458	C₂	1	1	yes	maximal, characteristic, complemented
3	#3244	C₂	1	2	yes	maximal, complemented
4	#3243	C₂	1	2	yes	maximal, complemented
5	#3241	C₂	1	2	yes	maximal, complemented
6	#3241	C₂	1	2	yes	maximal, complemented
7	#3240	C₂	1	2	yes	maximal, complemented
8	#3235	C₂	1	2	yes	maximal, complemented
9	#3233	C₂	1	2	yes	maximal, complemented
10	#3228	C₂	1	2	yes	maximal, complemented
11	#3164	C₂	1	1	yes	maximal, characteristic, complemented
12	#3163	C₂	1	1	yes	maximal, characteristic, complemented
13	#3136	C₂	1	1	yes	maximal, characteristic, complemented
14	#3136	C₂	1	1	yes	maximal, characteristic, complemented
15	#3094	C₂	1	1	yes	maximal, characteristic, complemented
16	#3093	C₂	1	1	yes	maximal, characteristic, complemented
17	#3091	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#482	C₂	1	1	yes	maximal, characteristic, complemented
19	#3084	C₂	1	1	yes	maximal, characteristic, complemented
20	#3083	C₂	1	1	yes	maximal, characteristic, complemented
21	#3081	C₂	1	1	yes	maximal, characteristic, complemented
22	#3081	C₂	1	1	yes	maximal, characteristic, complemented
23	#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	#555	—	2	1	no	—
25	#553	—	2	1	no	—
26	#553	—	2	1	no	—
27	#551	—	2	2	no	—
28	#547	—	2	1	no	—
29	#546	—	2	2	no	—
30	#544	—	2	1	no	—
31	#544	—	2	1	no	—
32	#544	C₂²	1	1	yes	characteristic
33	#544	C₂²	1	1	yes	characteristic
34	#544	C₂²	1	1	yes	characteristic
35	#544	C₂²	1	1	yes	characteristic
36	#544	C₂²	1	1	yes	characteristic
37	#544	C₂²	1	2	yes	complemented
38	#544	C₂²	1	2	yes	complemented
39	#543	—	2	2	no	—
40	#542	C₂²	1	2	yes	—
41	#540	C₂²	1	2	yes	—
42	#535	C₂²	1	1	yes	characteristic
43	#533	—	2	2	no	—
44	#533	—	2	1	no	—
45	#533	—	2	1	no	—
46	#533	C₂²	1	2	yes	complemented
47	#533	C₂²	1	2	yes	complemented
48	#532	C₂²	1	2	yes	—
49	#529	C₂²	1	2	yes	—
50	#525	C₂²	1	1	yes	characteristic
51	C₂×#121	C₂²	1	1	yes	characteristic
52	#520	C₂²	1	1	yes	characteristic
53	#518	C₂²	1	1	yes	characteristic
54	C₂×#117	C₂²	1	1	yes	characteristic
55	C₂×#117	C₂²	1	1	yes	characteristic
56	C₂×#117	C₂²	1	1	yes	characteristic
57	#501	C₂²	1	2	yes	complemented
58	#501	C₂²	1	2	yes	complemented
59	#501	C₂²	1	2	yes	complemented
60	#501	C₂²	1	2	yes	complemented
61	#500	C₂²	1	2	yes	complemented
62	#499	C₂²	1	2	yes	complemented
63	#499	C₂²	1	2	yes	complemented
64	#498	C₂²	1	2	yes	complemented
65	#490	C₂²	1	2	yes	complemented
66	#490	C₂²	1	2	yes	complemented
67	#489	C₂²	1	2	yes	complemented
68	#489	C₂²	1	2	yes	complemented
69	#488	C₂²	1	2	yes	complemented
70	#488	C₂²	1	2	yes	complemented
71	#486	C₂²	1	2	yes	complemented
72	#486	C₂²	1	2	yes	complemented
73	#485	C₂²	1	1	yes	characteristic, complemented
74	#485	C₂²	1	1	yes	characteristic, complemented
75	#485	C₂²	1	2	yes	complemented
76	#485	C₂²	1	2	yes	complemented
77	#484	C₂²	1	1	yes	characteristic, complemented
78	#483	C₂²	1	1	yes	characteristic, complemented
79	#482	C₂²	1	2	yes	—
80	#482	C₂²	1	2	yes	—
81	#482	C₂²	1	2	yes	—
82	#482	C₂²	1	2	yes	—
83	#482	C₂²	1	2	yes	—
84	#482	C₂²	1	2	yes	—
85	#482	C₂²	1	1	yes	characteristic, complemented
86	#482	C₂²	1	1	yes	characteristic, complemented
87	#482	C₂²	1	2	yes	complemented
88	#482	C₂²	1	2	yes	complemented
89	#481	C₂²	1	2	yes	—
90	#481	C₂²	1	1	yes	characteristic, complemented
91	#480	C₂²	1	2	yes	—
92	#480	C₂²	1	1	yes	characteristic, complemented
93	#479	C₂²	1	2	yes	complemented
94	#479	C₂²	1	2	yes	complemented
95	#478	C₂²	1	2	yes	complemented
96	#478	C₂²	1	2	yes	complemented
97	#478	C₂²	1	2	yes	complemented
98	#478	C₂²	1	2	yes	complemented
99	#478	C₂²	1	2	yes	complemented
100	#478	C₂²	1	2	yes	complemented
101	#477	C₂²	1	2	yes	complemented
102	#476	C₂²	1	2	yes	complemented
103	#476	C₂²	1	2	yes	complemented
104	#476	C₂²	1	2	yes	complemented
105	#475	C₂²	1	2	yes	complemented
106	#474	C₂²	1	2	yes	complemented
107	#474	C₂²	1	2	yes	complemented
108	#474	C₂²	1	2	yes	complemented
109	#433	C₂²	1	2	yes	complemented
110	#433	C₂²	1	2	yes	complemented
111	#432	C₂²	1	2	yes	complemented
112	#431	C₂²	1	2	yes	complemented
113	#428	C₂²	1	1	yes	characteristic
114	#428	C₂²	1	1	yes	characteristic
115	#428	C₂²	1	1	yes	characteristic
116	#428	C₂²	1	1	yes	characteristic
117	#427	C₂²	1	1	yes	characteristic
118	#427	C₂²	1	1	yes	characteristic
119	C₂×#107	C₂²	1	1	yes	characteristic
120	C₂×#106	C₂²	1	1	yes	characteristic
121	#424	C₂²	1	1	yes	characteristic
122	#424	C₂²	1	1	yes	characteristic
123	#418	C₂²	1	1	yes	characteristic
124	#418	C₂²	1	1	yes	characteristic
125	#417	C₂²	1	1	yes	characteristic
126	#417	C₂²	1	1	yes	characteristic
127	#416	C₂²	1	1	yes	characteristic
128	#416	C₂²	1	1	yes	characteristic
129	C₂×#102	C₂²	1	1	yes	characteristic
130	C₂×#102	C₂²	1	1	yes	characteristic
131	#407	C₂²	1	1	yes	characteristic
132	C₂×C₂²⋊C₈	C₂²	1	1	yes	characteristic
133	#405	C₂²	1	1	yes	characteristic
134	#405	C₂²	1	1	yes	characteristic
135	C₂×#41	—	2	2	no	—
136	C₂×#41	C₂³	1	1	yes	characteristic
137	C₂²×D₄	—	2	1	no	—
138	C₂²×D₄	C₂³	1	1	yes	characteristic
139	C₂³×C₄	C₂³	1	1	yes	characteristic
140	C₂×M₁₆	C₂³	1	1	yes	characteristic
141	C₂×M₁₆	C₂³	1	1	yes	characteristic
142	C₂²×C₈	C₂³	1	1	yes	characteristic
143	C₂²×C₈	C₂³	1	1	yes	characteristic
144	C₄⋊Q₈	—	2	1	no	—
145	C₄⋊Q₈	—	2	1	no	—
146	C₄⋊Q₈	—	2	1	no	—
147	C₄⋊Q₈	—	2	1	no	—
148	C₄⋊Q₈	—	2	2	no	—
149	C₄⋊Q₈	—	2	2	no	—
150	C₄⋊Q₈	—	2	1	no	—
151	C₄⋊Q₈	C₂³	1	2	yes	—
152	C₄⋊Q₈	C₂³	1	2	yes	—
153	C₄⋊Q₈	C₂³	1	2	yes	—
154	C₄⋊Q₈	C₂³	1	2	yes	—
155	C₄⋊Q₈	C₂³	1	2	yes	—
156	#127	C₂³	1	2	yes	—
157	#126	—	2	2	no	—
158	#126	—	2	2	no	—
159	#125	—	2	1	no	—
160	#125	—	2	1	no	—
161	#125	—	2	1	no	—
162	#125	—	2	1	no	—
163	#125	—	2	2	no	—
164	#125	—	2	2	no	—
165	#125	—	2	1	no	—
166	#125	C₂³	1	2	yes	—
167	#125	C₂³	1	2	yes	—
168	#125	C₂³	1	2	yes	—
169	#125	C₂³	1	2	yes	—
170	#125	C₂³	1	2	yes	—
171	#124	—	2	2	no	—
172	#124	—	2	2	no	—
173	#124	C₂³	1	2	yes	—
174	#123	—	2	1	no	—
175	#123	—	2	2	no	—
176	#123	—	2	2	no	—
177	#123	—	2	2	no	—
178	#123	—	2	2	no	—
179	C₂²⋊Q₈	—	2	2	no	—
180	C₂²⋊Q₈	—	2	2	no	—
181	C₂²⋊Q₈	—	2	2	no	—
182	C₂²⋊Q₈	—	2	2	no	—
183	C₂²⋊Q₈	—	2	2	no	—
184	C₂²⋊Q₈	—	2	2	no	—
185	C₂²⋊Q₈	—	2	2	no	—
186	C₂²⋊Q₈	—	2	2	no	—
187	C₂²⋊Q₈	—	2	2	no	—
188	C₂²⋊Q₈	—	2	2	no	—
189	C₂²⋊Q₈	—	2	2	no	—
190	C₂²⋊Q₈	—	2	2	no	—
191	C₂²⋊Q₈	—	2	2	no	—
192	C₂²⋊Q₈	—	2	2	no	—
193	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
194	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
195	#121	—	2	1	no	—
196	#121	—	2	1	no	—
197	#121	—	2	2	no	—
198	#121	—	2	1	no	—
199	#121	—	2	1	no	—
200	#121	—	2	2	no	—
201	#121	—	2	2	no	—
202	#121	C₂³	1	2	yes	—
203	#121	C₂³	1	2	yes	—
204	#121	C₂³	1	1	yes	characteristic
205	#121	C₂³	1	1	yes	characteristic
206	#120	—	2	1	no	—
207	#120	—	2	2	no	—
208	C₄×Q₈	—	2	2	no	—
209	C₄×Q₈	—	2	2	no	—
210	C₄×Q₈	—	2	2	no	—
211	C₄×Q₈	—	2	2	no	—
212	C₄×Q₈	C₂³	1	2	yes	—
213	C₄×D₄	—	2	1	no	—
214	C₄×D₄	—	2	1	no	—
215	C₄×D₄	—	2	2	no	—
216	C₄×D₄	—	2	1	no	—
217	C₄×D₄	—	2	1	no	—
218	C₄×D₄	—	2	2	no	—
219	C₄×D₄	—	2	2	no	—
220	C₄×D₄	C₂³	1	2	yes	—
221	C₄×D₄	C₂³	1	2	yes	—
222	C₄×D₄	C₂³	1	2	yes	—
223	#117	—	2	1	no	—
224	#117	—	2	1	no	—
225	#117	—	2	1	no	—
226	#117	—	2	1	no	—
227	#117	—	2	1	no	—
228	#117	—	2	2	no	—
229	#117	D₄	1	2	yes	—
230	#117	D₄	1	1	yes	characteristic
231	#117	D₄	1	1	yes	characteristic
232	#117	C₂³	1	2	yes	—
233	#117	C₂³	1	1	yes	characteristic
234	#117	C₂³	1	1	yes	characteristic
235	#117	C₂³	1	1	yes	characteristic
236	#117	C₂³	1	1	yes	characteristic
237	#117	C₂³	1	2	yes	—
238	#117	C₂³	1	1	yes	characteristic
239	#117	C₂³	1	1	yes	characteristic
240	#117	C₂³	1	1	yes	characteristic
241	#117	C₂³	1	2	yes	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
244	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
245	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
249	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
250	C₂×C₂²⋊C₄	—	2	1	no	—
251	C₂×C₂²⋊C₄	—	2	1	no	—
252	C₂×C₂²⋊C₄	—	2	1	no	—
253	C₂×C₂²⋊C₄	—	2	2	no	—
254	C₂×C₂²⋊C₄	D₄	1	2	yes	—
255	C₂×C₄²	—	2	1	no	—
256	C₂×C₄²	—	2	1	no	—
257	C₂×C₄²	C₂³	1	2	yes	—
258	#107	C₂³	1	2	yes	—
259	#107	C₂³	1	2	yes	—
260	#107	C₂³	1	1	yes	characteristic
261	#107	C₂³	1	1	yes	characteristic
262	#107	C₂³	1	1	yes	characteristic
263	#107	C₂³	1	1	yes	characteristic
264	#107	C₂³	1	2	yes	—
265	#107	C₂³	1	2	yes	—
266	#107	C₂³	1	2	yes	—
267	#107	C₂³	1	2	yes	—
268	#106	C₂³	1	2	yes	—
269	#106	C₂³	1	2	yes	—
270	#106	C₂³	1	1	yes	characteristic
271	#106	C₂³	1	1	yes	characteristic
272	#106	C₂³	1	1	yes	characteristic
273	#106	C₂³	1	1	yes	characteristic
274	#106	C₂³	1	2	yes	—
275	#106	C₂³	1	2	yes	—
276	#106	C₂³	1	2	yes	—
277	#106	C₂³	1	2	yes	—
278	C₄⋊C₈	C₂³	1	2	yes	—
279	C₄⋊C₈	C₂³	1	2	yes	—
280	C₄⋊C₈	C₂³	1	2	yes	—
281	C₄⋊C₈	C₂³	1	2	yes	—
282	#103	C₂³	1	1	yes	characteristic
283	#103	C₂³	1	1	yes	characteristic
284	#103	C₂³	1	1	yes	characteristic
285	#103	C₂³	1	1	yes	characteristic
286	#103	C₂³	1	2	yes	—
287	#103	C₂³	1	2	yes	—
288	#102	C₂³	1	2	yes	—
289	#102	C₂³	1	2	yes	—
290	#102	C₂³	1	2	yes	—
291	#102	C₂³	1	2	yes	—
292	#102	C₂³	1	1	yes	characteristic
293	#102	C₂³	1	1	yes	characteristic
294	#102	C₂³	1	1	yes	characteristic
295	#102	C₂³	1	1	yes	characteristic
296	#102	C₂³	1	2	yes	—
297	#102	C₂³	1	2	yes	—
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	C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₂²⋊C₈	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	#97	C₂³	1	2	yes	—
310	C₄×C₈	C₂³	1	2	yes	—
311	C₄×C₈	C₂³	1	2	yes	—
312	C₂⁴	—	2	1	no	—
313	C₂⁴	C₂×D₄	1	1	yes	characteristic
314	#41	—	2	2	no	—
315	#41	—	2	2	no	—
316	#41	—	8	4	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	C₂⁴	1	1	yes	characteristic
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	8	2	no	—
334	C₂×D₄	C₂⁴	1	2	yes	—
335	C₂×D₄	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄	1	2	yes	—
351	C₂²×C₄	C₂×D₄	1	2	yes	—
352	C₂²×C₄	C₂⁴	1	1	yes	characteristic
353	C₂²×C₄	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄	C₂⁴	1	1	yes	characteristic
355	M₁₆	—	2	2	no	—
356	M₁₆	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	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	2	yes	—
363	C₂×C₈	C₂⁴	1	1	yes	characteristic
364	C₂×C₈	C₂⁴	1	1	yes	characteristic
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	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	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
389	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
390	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
391	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
392	C₄⋊C₄	C₂×D₄	1	2	yes	—
393	C₄⋊C₄	C₂×D₄	1	2	yes	—
394	C₄⋊C₄	C₂⁴	1	2	yes	—
395	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
396	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
397	C₄⋊C₄	C₂⁴	1	2	yes	—
398	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
403	C₂²⋊C₄	—	2	1	no	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	2	1	no	—
406	C₂²⋊C₄	—	2	1	no	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	2	1	no	—
409	C₂²⋊C₄	—	2	1	no	—
410	C₂²⋊C₄	—	2	1	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	2	no	—
418	C₂²⋊C₄	—	2	1	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	1	no	—
421	C₂²⋊C₄	C₂×D₄	1	2	yes	—
422	C₂²⋊C₄	C₂×D₄	1	2	yes	—
423	C₂²⋊C₄	C₂×D₄	1	2	yes	—
424	C₂²⋊C₄	C₂×D₄	1	2	yes	—
425	C₄²	—	2	2	no	—
426	C₄²	—	2	1	no	—
427	C₄²	—	2	1	no	—
428	C₄²	—	2	2	no	—
429	C₄²	—	2	1	no	—
430	C₄²	—	2	1	no	—
431	C₄²	—	2	2	no	—
432	C₄²	—	2	1	no	—
433	C₄²	C₂×D₄	1	2	yes	—
434	C₄²	C₂×D₄	1	2	yes	—
435	C₄²	C₂⁴	1	2	yes	—
436	C₄²	C₂⁴	1	2	yes	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	1	no	—
440	C₂³	—	4	1	no	—
441	C₂³	—	4	1	no	—
442	C₂³	—	4	2	no	—
443	C₂³	—	8	1	no	—
444	C₂³	—	8	1	no	—
445	C₂³	C₂²×D₄	1	1	yes	characteristic
446	C₂³	C₂²×D₄	1	1	yes	characteristic
447	C₂³	C₂²×D₄	1	1	yes	characteristic
448	Q₈	—	2	1	no	—
449	Q₈	—	2	1	no	—
450	Q₈	—	8	2	no	—
451	Q₈	—	8	2	no	—
452	Q₈	—	8	2	no	—
453	Q₈	—	8	2	no	—
454	Q₈	—	8	2	no	—
455	D₄	—	2	2	no	—
456	D₄	—	2	2	no	—
457	D₄	—	2	1	no	—
458	D₄	—	2	1	no	—
459	D₄	—	4	4	no	—
460	D₄	—	4	2	no	—
461	D₄	—	4	2	no	—
462	D₄	—	4	2	no	—
463	D₄	—	8	2	no	—
464	D₄	—	8	2	no	—
465	D₄	—	8	1	no	—
466	D₄	—	8	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	8	2	no	—
488	C₂×C₄	—	8	2	no	—
489	C₂×C₄	—	8	2	no	—
490	C₂×C₄	—	8	1	no	—
491	C₂×C₄	—	8	1	no	—
492	C₂×C₄	—	8	1	no	—
493	C₂×C₄	—	8	1	no	—
494	C₂×C₄	—	8	1	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	2	yes	—
501	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
503	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
504	C₂×C₄	C₂⁵	1	1	yes	characteristic
505	C₈	—	2	1	no	—
506	C₈	—	2	1	no	—
507	C₈	—	2	1	no	—
508	C₈	—	2	1	no	—
509	C₈	—	2	2	no	—
510	C₈	—	2	2	no	—
511	C₂²	—	2	1	no	—
512	C₂²	—	2	1	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	2	1	no	—
517	C₂²	—	2	1	no	—
518	C₂²	—	2	1	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	1	no	—
521	C₂²	—	4	1	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	4	1	no	—
524	C₂²	—	4	2	no	—
525	C₂²	—	8	2	no	—
526	C₂²	—	16	2	no	—
527	C₂²	#536	1	2	yes	—
528	C₂²	C₂³×D₄	1	1	yes	characteristic
529	C₄	—	2	2	no	—
530	C₄	—	2	2	no	—
531	C₄	—	2	2	no	—
532	C₄	—	2	2	no	—
533	C₄	—	2	1	no	—
534	C₄	—	2	1	no	—
535	C₄	—	4	1	no	—
536	C₄	—	4	2	no	—
537	C₄	—	4	1	no	—
538	C₄	—	4	1	no	—
539	C₄	—	4	2	no	—
540	C₄	—	4	1	no	—
541	C₄	—	4	2	no	—
542	C₄	—	4	1	no	—
543	C₄	—	4	1	no	—
544	C₄	—	4	1	no	—
545	C₄	#536	1	2	yes	—
546	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
547	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
548	C₂	—	2	2	no	—
549	C₂	—	4	1	no	—
550	C₂	—	4	1	no	—
551	C₂	—	8	1	no	—
552	C₂	—	8	2	no	—
553	C₂	C₂×#536	1	1	yes	characteristic
554	C₂	#3584	1	1	yes	characteristic
555	C₂	#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
prime radical	#3494	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂×#117 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #3458	C₂	semidirect
3. #3244	C₂	semidirect
4. #3243	C₂	semidirect
5. #3241	C₂	semidirect
6. #3241	C₂	semidirect
7. #3240	C₂	semidirect
8. #3235	C₂	semidirect
9. #3233	C₂	semidirect
10. #3228	C₂	semidirect
11. #3164	C₂	semidirect
12. #3163	C₂	semidirect
13. #3136	C₂	semidirect
14. #3136	C₂	semidirect
15. #3094	C₂	semidirect
16. #3093	C₂	semidirect
17. #3091	C₂	semidirect
18. C₂×#482	C₂	semidirect
19. #3084	C₂	semidirect
20. #3083	C₂	semidirect
21. #3081	C₂	semidirect
22. #3081	C₂	semidirect
23. #2924	C₂	semidirect
37. #544	C₂²	semidirect
38. #544	C₂²	semidirect
46. #533	C₂²	semidirect
47. #533	C₂²	semidirect
57. #501	C₂²	semidirect
58. #501	C₂²	semidirect
59. #501	C₂²	semidirect
60. #501	C₂²	semidirect
61. #500	C₂²	semidirect
62. #499	C₂²	semidirect
63. #499	C₂²	semidirect
64. #498	C₂²	semidirect
65. #490	C₂²	semidirect
66. #490	C₂²	semidirect
67. #489	C₂²	semidirect
68. #489	C₂²	semidirect
69. #488	C₂²	semidirect
70. #488	C₂²	semidirect
71. #486	C₂²	semidirect
72. #486	C₂²	semidirect
73. #485	C₂²	semidirect
74. #485	C₂²	semidirect
75. #485	C₂²	semidirect
76. #485	C₂²	semidirect
77. #484	C₂²	semidirect
78. #483	C₂²	semidirect
85. #482	C₂²	semidirect
86. #482	C₂²	semidirect
87. #482	C₂²	semidirect
88. #482	C₂²	semidirect
90. #481	C₂²	semidirect
92. #480	C₂²	semidirect
93. #479	C₂²	semidirect
94. #479	C₂²	semidirect
95. #478	C₂²	semidirect
96. #478	C₂²	semidirect
97. #478	C₂²	semidirect
98. #478	C₂²	semidirect
99. #478	C₂²	semidirect
100. #478	C₂²	semidirect
101. #477	C₂²	semidirect
102. #476	C₂²	semidirect
103. #476	C₂²	semidirect
104. #476	C₂²	semidirect
105. #475	C₂²	semidirect
106. #474	C₂²	semidirect
107. #474	C₂²	semidirect
108. #474	C₂²	semidirect
109. #433	C₂²	semidirect
110. #433	C₂²	semidirect
111. #432	C₂²	semidirect
112. #431	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3494	2
#3458	2
#3244	2
#3243	2
#3241	2
#3240	2
#3235	2
#3233	2
#3228	2
#3164	2
#3163	2
#3136	2
#3094	2
#3093	2
#3091	2
C₂×#482	2
#3084	2
#3083	2
#3081	2
#2924	2