Subgroups — #61864

Order 256.

837 conjugacy classes of subgroups.

The subgroup lattice has 546 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	#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	#3388	C₂	1	2	yes	maximal, complemented
4	#3385	C₂	1	1	yes	maximal, characteristic, complemented
5	#3384	C₂	1	1	yes	maximal, characteristic, complemented
6	#3381	C₂	1	2	yes	maximal, complemented
7	#3380	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	#3376	C₂	1	2	yes	maximal, complemented
10	#3372	C₂	1	1	yes	maximal, characteristic, complemented
11	#3367	C₂	1	1	yes	maximal, characteristic, complemented
12	#3360	C₂	1	1	yes	maximal, characteristic, complemented
13	#3360	C₂	1	2	yes	maximal, complemented
14	#3359	C₂	1	1	yes	maximal, characteristic, complemented
15	#3244	C₂	1	2	yes	maximal, complemented
16	#3242	C₂	1	2	yes	maximal, complemented
17	#3233	C₂	1	1	yes	maximal, characteristic, complemented
18	#3231	C₂	1	1	yes	maximal, characteristic, complemented
19	#3123	C₂	1	2	yes	maximal, complemented
20	#3118	C₂	1	2	yes	maximal
21	#3105	C₂	1	1	yes	maximal, characteristic
22	#3101	C₂	1	1	yes	maximal, characteristic, complemented
23	#2986	C₂	1	1	yes	maximal, characteristic, complemented
24	#563	—	2	2	no	—
25	Q₈²	C₂²	1	1	yes	characteristic, complemented
26	#557	C₂²	1	1	yes	characteristic, complemented
27	#557	C₂²	1	2	yes	complemented
28	#556	—	2	1	no	—
29	#556	C₂²	1	1	yes	characteristic, complemented
30	#556	C₂²	1	2	yes	complemented
31	#554	—	2	1	no	—
32	#554	—	2	2	no	—
33	#554	C₂²	1	1	yes	characteristic
34	#554	C₂²	1	2	yes	—
35	#554	C₂²	1	1	yes	characteristic
36	#554	C₂²	1	2	yes	—
37	#554	C₂²	1	1	yes	characteristic, complemented
38	#552	—	2	1	no	—
39	D₄×Q₈	—	2	1	no	—
40	D₄×Q₈	C₂²	1	1	yes	characteristic
41	D₄×Q₈	C₂²	1	1	yes	characteristic
42	#544	—	2	1	no	—
43	#544	C₂²	1	2	yes	—
44	#543	—	2	2	no	—
45	#542	C₂²	1	2	yes	—
46	#541	—	2	1	no	—
47	#541	—	2	2	no	—
48	#541	C₂²	1	2	yes	—
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	C₂×C₂²⋊Q₈	—	2	1	no	—
54	C₂×C₂²⋊Q₈	—	2	1	no	—
55	#518	C₂²	1	2	yes	—
56	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
57	#501	C₂²	1	2	yes	complemented
58	#501	C₂²	1	2	yes	complemented
59	#500	C₂²	1	1	yes	characteristic, complemented
60	#499	C₂²	1	2	yes	complemented
61	#499	C₂²	1	2	yes	complemented
62	#498	C₂²	1	2	yes	complemented
63	#498	C₂²	1	1	yes	characteristic, complemented
64	#491	C₂²	1	2	yes	complemented
65	#489	C₂²	1	2	yes	complemented
66	#488	C₂²	1	2	yes	complemented
67	#488	C₂²	1	2	yes	complemented
68	#487	C₂²	1	2	yes	complemented
69	#487	C₂²	1	1	yes	characteristic, complemented
70	#487	C₂²	1	1	yes	characteristic, complemented
71	#485	C₂²	1	2	yes	—
72	#485	C₂²	1	2	yes	—
73	#485	C₂²	1	2	yes	—
74	#484	C₂²	1	1	yes	characteristic
75	#483	C₂²	1	2	yes	—
76	#482	C₂²	1	2	yes	—
77	#481	C₂²	1	1	yes	characteristic
78	#479	C₂²	1	2	yes	complemented
79	#479	C₂²	1	2	yes	complemented
80	#479	C₂²	1	2	yes	complemented
81	#479	C₂²	1	2	yes	complemented
82	#479	C₂²	1	2	yes	complemented
83	#478	C₂²	1	1	yes	characteristic
84	#478	C₂²	1	1	yes	characteristic
85	#478	C₂²	1	2	yes	—
86	#478	C₂²	1	2	yes	—
87	#478	C₂²	1	2	yes	complemented
88	#477	C₂²	1	2	yes	complemented
89	#477	C₂²	1	1	yes	characteristic, complemented
90	#476	C₂²	1	1	yes	characteristic
91	#476	C₂²	1	1	yes	characteristic
92	#476	C₂²	1	2	yes	—
93	#476	C₂²	1	1	yes	characteristic, complemented
94	#476	C₂²	1	2	yes	complemented
95	#475	C₂²	1	1	yes	characteristic, complemented
96	#475	C₂²	1	2	yes	complemented
97	#475	C₂²	1	2	yes	complemented
98	#474	C₂²	1	2	yes	—
99	#474	C₂²	1	1	yes	characteristic, complemented
100	#463	C₂²	1	1	yes	characteristic
101	#463	C₂²	1	2	yes	—
102	#463	C₂²	1	2	yes	—
103	#463	C₂²	1	1	yes	characteristic
104	#461	C₂²	1	1	yes	characteristic
105	#461	C₂²	1	1	yes	characteristic
106	#461	C₂²	1	2	yes	—
107	#461	C₂²	1	2	yes	—
108	#450	C₂²	1	2	yes	—
109	#450	C₂²	1	1	yes	characteristic
110	#447	C₂²	1	1	yes	characteristic
111	#446	C₂²	1	1	yes	characteristic, complemented
112	#446	C₂²	1	1	yes	characteristic, complemented
113	#446	C₂²	1	2	yes	complemented
114	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
116	C₈×Q₈	C₂²	1	2	yes	complemented
117	#442	C₂²	1	2	yes	—
118	#440	C₂²	1	2	yes	—
119	#440	C₂²	1	2	yes	—
120	#440	C₂²	1	2	yes	—
121	C₄×SD₁₆	C₂²	1	2	yes	—
122	C₄×SD₁₆	C₂²	1	2	yes	—
123	C₄×SD₁₆	C₂²	1	1	yes	characteristic
124	C₄×SD₁₆	C₂²	1	2	yes	—
125	C₄×SD₁₆	C₂²	1	2	yes	—
126	C₄×SD₁₆	C₂²	1	2	yes	—
127	C₄×SD₁₆	C₂²	1	1	yes	characteristic
128	C₄×D₈	C₂²	1	1	yes	characteristic
129	C₄×D₈	C₂²	1	2	yes	—
130	C₄×D₈	C₂²	1	1	yes	characteristic
131	#433	C₂²	1	2	yes	—
132	#433	C₂²	1	2	yes	—
133	#431	C₂²	1	1	yes	characteristic
134	#431	C₂²	1	1	yes	characteristic
135	C₂²×Q₈	—	2	1	no	—
136	C₂²×Q₈	—	2	1	no	—
137	C₂²×D₄	C₂³	1	1	yes	characteristic
138	C₂³×C₄	—	2	1	no	—
139	C₂×SD₁₆	C₂³	1	2	yes	—
140	C₂×SD₁₆	C₂³	1	1	yes	characteristic
141	C₂×SD₁₆	C₂³	1	2	yes	—
142	C₂×SD₁₆	C₂³	1	1	yes	characteristic
143	C₂×D₈	C₂³	1	1	yes	characteristic
144	C₂×D₈	C₂³	1	1	yes	characteristic
145	C₄⋊Q₈	—	2	2	no	—
146	C₄⋊Q₈	—	2	2	no	—
147	C₄⋊Q₈	—	2	1	no	—
148	C₄⋊Q₈	—	2	2	no	—
149	C₄⋊Q₈	D₄	1	1	yes	characteristic
150	C₄⋊Q₈	D₄	1	1	yes	characteristic
151	C₄⋊Q₈	C₂³	1	1	yes	characteristic
152	C₄⋊Q₈	C₂³	1	2	yes	—
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	2	yes	—
157	C₄⋊Q₈	C₂³	1	2	yes	—
158	C₄⋊Q₈	C₂³	1	2	yes	—
159	#126	—	2	2	no	—
160	#126	—	2	2	no	—
161	#126	—	2	2	no	—
162	#126	—	2	2	no	—
163	#126	—	2	2	no	—
164	#126	—	2	2	no	—
165	#126	—	2	1	no	—
166	#125	—	2	2	no	—
167	#125	—	2	2	no	—
168	#125	—	2	2	no	—
169	#125	—	2	2	no	—
170	#125	—	2	2	no	—
171	#125	—	2	1	no	—
172	#125	—	2	2	no	—
173	#125	—	2	1	no	—
174	#125	D₄	1	2	yes	—
175	#125	C₂³	1	1	yes	characteristic
176	#125	C₂³	1	2	yes	—
177	#125	C₂³	1	2	yes	—
178	#125	C₂³	1	2	yes	—
179	#125	C₂³	1	2	yes	—
180	#124	—	2	2	no	—
181	#124	C₂³	1	1	yes	characteristic
182	#124	C₂³	1	2	yes	—
183	#123	—	2	1	no	—
184	#123	—	2	2	no	—
185	C₂²⋊Q₈	—	2	1	no	—
186	C₂²⋊Q₈	—	2	1	no	—
187	C₂²⋊Q₈	—	2	1	no	—
188	C₂²⋊Q₈	—	2	1	no	—
189	C₂²⋊Q₈	—	2	2	no	—
190	C₂²⋊Q₈	—	2	2	no	—
191	C₂²⋊Q₈	—	2	2	no	—
192	C₂²⋊Q₈	—	2	1	no	—
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	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	—	2	2	no	—
206	C₂²⋊Q₈	—	2	2	no	—
207	C₂²⋊Q₈	—	2	2	no	—
208	C₂²⋊Q₈	—	2	2	no	—
209	C₂²⋊Q₈	D₄	1	1	yes	characteristic
210	C₂²⋊Q₈	D₄	1	1	yes	characteristic
211	C₂²⋊Q₈	D₄	1	2	yes	—
212	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
213	C₂²⋊Q₈	C₂³	1	2	yes	—
214	#121	C₂³	1	1	yes	characteristic
215	C₄×Q₈	—	2	1	no	—
216	C₄×Q₈	—	2	1	no	—
217	C₄×Q₈	—	2	2	no	—
218	C₄×Q₈	—	2	1	no	—
219	C₄×Q₈	—	2	1	no	—
220	C₄×Q₈	—	2	1	no	—
221	C₄×Q₈	C₂³	1	1	yes	characteristic
222	C₄×Q₈	C₂³	1	2	yes	—
223	C₄×Q₈	C₂³	1	2	yes	—
224	C₄×Q₈	C₂³	1	2	yes	—
225	C₄×Q₈	C₂³	1	2	yes	—
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×D₄	—	2	1	no	—
230	C₄×D₄	—	2	2	no	—
231	C₄×D₄	—	2	2	no	—
232	C₄×D₄	—	2	1	no	—
233	C₄×D₄	—	2	1	no	—
234	C₄×D₄	C₂³	1	1	yes	characteristic
235	C₄×D₄	C₂³	1	1	yes	characteristic
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	2	yes	—
242	C₄×D₄	C₂³	1	1	yes	characteristic
243	C₄×D₄	C₂³	1	2	yes	—
244	#117	—	2	1	no	—
245	#117	—	2	2	no	—
246	#117	—	2	1	no	—
247	#117	—	2	1	no	—
248	#117	C₂³	1	2	yes	—
249	#117	C₂³	1	2	yes	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊C₄	—	2	1	no	—
257	C₂×C₂²⋊C₄	—	2	2	no	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₄²	C₂³	1	1	yes	characteristic
260	#107	C₂³	1	2	yes	—
261	#107	C₂³	1	1	yes	characteristic
262	#107	C₂³	1	1	yes	characteristic
263	#107	C₂³	1	2	yes	—
264	#107	C₂³	1	2	yes	—
265	#107	C₂³	1	2	yes	—
266	#106	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	C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₄⋊C₈	C₂³	1	1	yes	characteristic
277	C₄⋊C₈	C₂³	1	1	yes	characteristic
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	2	yes	—
283	#103	C₂³	1	2	yes	—
284	#103	C₂³	1	2	yes	—
285	#103	C₂³	1	2	yes	—
286	#103	C₂³	1	1	yes	characteristic
287	#103	C₂³	1	2	yes	—
288	#103	C₂³	1	1	yes	characteristic
289	#103	C₂³	1	2	yes	—
290	#103	C₂³	1	2	yes	—
291	#103	C₂³	1	2	yes	—
292	#102	C₂³	1	2	yes	—
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	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	C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₂²⋊C₈	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈	C₂³	1	2	yes	—
305	#97	C₂³	1	2	yes	—
306	#97	C₂³	1	2	yes	—
307	C₄×C₈	C₂³	1	1	yes	characteristic
308	C₄×C₈	C₂³	1	1	yes	characteristic
309	C₄×C₈	C₂³	1	2	yes	—
310	C₄×C₈	C₂³	1	2	yes	—
311	C₄×C₈	C₂³	1	2	yes	—
312	C₂⁴	—	2	1	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	8	2	no	—
320	C₂×Q₈	—	8	2	no	—
321	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
322	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
323	C₂×Q₈	C₂×D₄	1	2	yes	—
324	C₂×Q₈	C₂⁴	1	1	yes	characteristic
325	C₂×Q₈	C₂⁴	1	2	yes	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	C₂⁴	1	1	yes	characteristic
331	C₂×D₄	C₂⁴	1	1	yes	characteristic
332	C₂×D₄	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
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	2	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	8	2	no	—
345	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
347	C₂²×C₄	C₂⁴	1	1	yes	characteristic
348	SD₁₆	—	2	4	no	—
349	SD₁₆	—	2	2	no	—
350	SD₁₆	—	2	4	no	—
351	SD₁₆	—	2	2	no	—
352	D₈	—	2	2	no	—
353	D₈	—	2	2	no	—
354	C₂×C₈	C₂⁴	1	1	yes	characteristic
355	C₂×C₈	C₂⁴	1	2	yes	—
356	C₂×C₈	C₂⁴	1	1	yes	characteristic
357	C₂×C₈	C₂⁴	1	1	yes	characteristic
358	C₂×C₈	C₂⁴	1	2	yes	—
359	C₂×C₈	C₂⁴	1	1	yes	characteristic
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	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	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	2	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	2	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
389	C₄⋊C₄	C₂×D₄	1	2	yes	—
390	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
391	C₄⋊C₄	C₂×D₄	1	2	yes	—
392	C₄⋊C₄	C₂×D₄	1	2	yes	—
393	C₄⋊C₄	C₂×D₄	1	2	yes	—
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	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	1	yes	characteristic
401	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄	C₂⁴	1	2	yes	—
403	C₄⋊C₄	C₂⁴	1	2	yes	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	1	no	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	2	2	no	—
409	C₂²⋊C₄	—	2	2	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	1	no	—
413	C₂²⋊C₄	—	2	1	no	—
414	C₂²⋊C₄	—	2	1	no	—
415	C₂²⋊C₄	—	2	1	no	—
416	C₂²⋊C₄	—	2	1	no	—
417	C₂²⋊C₄	—	2	1	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	1	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	C₂×D₄	1	2	yes	—
423	C₂²⋊C₄	C₂×D₄	1	2	yes	—
424	C₄²	—	2	2	no	—
425	C₄²	—	2	1	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	2	no	—
428	C₄²	—	2	2	no	—
429	C₄²	—	2	2	no	—
430	C₄²	C₂×D₄	1	1	yes	characteristic
431	C₄²	C₂×D₄	1	1	yes	characteristic
432	C₄²	C₂⁴	1	1	yes	characteristic
433	C₄²	C₂⁴	1	1	yes	characteristic
434	C₄²	C₂⁴	1	2	yes	—
435	C₄²	C₂⁴	1	2	yes	—
436	C₂³	—	2	4	no	—
437	C₂³	—	2	1	no	—
438	C₂³	—	2	1	no	—
439	C₂³	—	2	1	no	—
440	C₂³	—	8	1	no	—
441	C₂³	—	8	1	no	—
442	C₂³	C₂²×D₄	1	1	yes	characteristic
443	Q₈	—	2	2	no	—
444	Q₈	—	2	2	no	—
445	Q₈	—	2	1	no	—
446	Q₈	—	2	2	no	—
447	Q₈	—	2	1	no	—
448	Q₈	—	2	2	no	—
449	Q₈	—	4	2	no	—
450	Q₈	—	4	2	no	—
451	Q₈	—	8	1	no	—
452	Q₈	—	8	1	no	—
453	Q₈	—	8	2	no	—
454	Q₈	—	8	2	no	—
455	Q₈	—	8	2	no	—
456	D₄	—	2	4	no	—
457	D₄	—	2	1	no	—
458	D₄	—	2	1	no	—
459	D₄	—	2	1	no	—
460	D₄	—	2	1	no	—
461	D₄	—	8	1	no	—
462	D₄	2₋¹⁺⁴	1	2	yes	—
463	D₄	2₋¹⁺⁴	1	2	yes	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	2	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	—	4	1	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	8	2	no	—
481	C₂×C₄	—	8	2	no	—
482	C₂×C₄	—	8	2	no	—
483	C₂×C₄	—	8	1	no	—
484	C₂×C₄	—	8	1	no	—
485	C₂×C₄	—	8	2	no	—
486	C₂×C₄	—	8	2	no	—
487	C₂×C₄	—	8	1	no	—
488	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄	C₂²×D₄	1	2	yes	—
491	C₂×C₄	C₂²×D₄	1	2	yes	—
492	C₂×C₄	C₂²×D₄	1	2	yes	—
493	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄	C₂²×D₄	1	2	yes	—
496	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄	C₂⁵	1	1	yes	characteristic
498	C₈	—	2	1	no	—
499	C₈	—	2	1	no	—
500	C₈	—	2	1	no	—
501	C₈	—	2	2	no	—
502	C₈	—	2	1	no	—
503	C₈	—	2	2	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	2	1	no	—
509	C₂²	—	4	1	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	1	no	—
512	C₂²	—	4	1	no	—
513	C₂²	—	4	1	no	—
514	C₂²	—	4	1	no	—
515	C₂²	—	4	1	no	—
516	C₂²	—	8	4	no	—
517	C₂²	C₂³×D₄	1	1	yes	characteristic
518	C₄	—	2	1	no	—
519	C₄	—	2	1	no	—
520	C₄	—	2	2	no	—
521	C₄	—	2	2	no	—
522	C₄	—	2	1	no	—
523	C₄	—	2	1	no	—
524	C₄	—	2	2	no	—
525	C₄	—	2	2	no	—
526	C₄	—	4	2	no	—
527	C₄	—	4	2	no	—
528	C₄	—	4	1	no	—
529	C₄	—	4	2	no	—
530	C₄	—	4	1	no	—
531	C₄	—	4	1	no	—
532	C₄	—	4	1	no	—
533	C₄	—	4	1	no	—
534	C₄	—	4	2	no	—
535	C₄	#577	1	2	yes	—
536	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
537	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
538	C₂	—	4	1	no	—
539	C₂	—	4	2	no	—
540	C₂	—	4	2	no	—
541	C₂	—	8	1	no	—
542	C₂	#3486	1	1	yes	characteristic
543	C₂	C₂×#577	1	1	yes	characteristic
544	C₂	#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
prime radical	#447	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ #533 ◁ 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
2. #3501	C₂	semidirect
3. #3388	C₂	semidirect
4. #3385	C₂	semidirect
5. #3384	C₂	semidirect
6. #3381	C₂	semidirect
7. #3380	C₂	semidirect
8. Q₈×SD₁₆	C₂	semidirect
9. #3376	C₂	semidirect
10. #3372	C₂	semidirect
11. #3367	C₂	semidirect
12. #3360	C₂	semidirect
13. #3360	C₂	semidirect
14. #3359	C₂	semidirect
15. #3244	C₂	semidirect
16. #3242	C₂	semidirect
17. #3233	C₂	semidirect
18. #3231	C₂	semidirect
19. #3123	C₂	semidirect
22. #3101	C₂	semidirect
23. #2986	C₂	semidirect
25. Q₈²	C₂²	semidirect
26. #557	C₂²	semidirect
27. #557	C₂²	semidirect
29. #556	C₂²	semidirect
30. #556	C₂²	semidirect
37. #554	C₂²	semidirect
57. #501	C₂²	semidirect
58. #501	C₂²	semidirect
59. #500	C₂²	semidirect
60. #499	C₂²	semidirect
61. #499	C₂²	semidirect
62. #498	C₂²	semidirect
63. #498	C₂²	semidirect
64. #491	C₂²	semidirect
65. #489	C₂²	semidirect
66. #488	C₂²	semidirect
67. #488	C₂²	semidirect
68. #487	C₂²	semidirect
69. #487	C₂²	semidirect
70. #487	C₂²	semidirect
78. #479	C₂²	semidirect
79. #479	C₂²	semidirect
80. #479	C₂²	semidirect
81. #479	C₂²	semidirect
82. #479	C₂²	semidirect
87. #478	C₂²	semidirect
88. #477	C₂²	semidirect
89. #477	C₂²	semidirect
93. #476	C₂²	semidirect
94. #476	C₂²	semidirect
95. #475	C₂²	semidirect
96. #475	C₂²	semidirect
97. #475	C₂²	semidirect
99. #474	C₂²	semidirect
111. #446	C₂²	semidirect
112. #446	C₂²	semidirect
113. #446	C₂²	semidirect
114. C₈×Q₈	C₂²	semidirect
115. C₈×Q₈	C₂²	semidirect
116. C₈×Q₈	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
#3501	2
#3388	2
#3385	2
#3384	2
#3381	2
#3380	2
Q₈×SD₁₆	2
#3376	2
#3372	2
#3367	2
#3360	2
#3359	2
#3244	2
#3242	2
#3233	2
#3231	2
#3123	2
#3118	2
#3105	2
#3101	2
#2986	2