Subgroups — #62103

Order 256.

902 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	#3515	C₂	1	1	yes	maximal, characteristic, complemented
2	#3481	C₂	1	1	yes	maximal, characteristic, complemented
3	#3381	C₂	1	1	yes	maximal, characteristic, complemented
4	#3380	C₂	1	1	yes	maximal, characteristic, complemented
5	#3365	C₂	1	1	yes	maximal, characteristic, complemented
6	#3361	C₂	1	1	yes	maximal, characteristic, complemented
7	#3339	C₂	1	2	yes	maximal, complemented
8	#3338	C₂	1	1	yes	maximal, characteristic, complemented
9	#3337	C₂	1	2	yes	maximal, complemented
10	#3335	C₂	1	1	yes	maximal, characteristic, complemented
11	#3297	C₂	1	2	yes	maximal, complemented
12	#3296	C₂	1	2	yes	maximal, complemented
13	#3295	C₂	1	1	yes	maximal, characteristic, complemented
14	#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	#3250	C₂	1	2	yes	maximal, complemented
16	#3247	C₂	1	1	yes	maximal, characteristic, complemented
17	#3232	C₂	1	2	yes	maximal, complemented
18	#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	#3105	C₂	1	2	yes	maximal, complemented
20	#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	#3076	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#478	C₂	1	2	yes	maximal, complemented
23	#2988	C₂	1	1	yes	maximal, characteristic, complemented
24	#559	C₂²	1	1	yes	characteristic
25	#557	C₂²	1	1	yes	characteristic, complemented
26	#554	C₂²	1	1	yes	characteristic
27	#554	C₂²	1	1	yes	characteristic
28	#554	C₂²	1	1	yes	characteristic
29	#554	C₂²	1	1	yes	characteristic, complemented
30	#553	—	2	1	no	—
31	#553	C₂²	1	2	yes	—
32	#553	C₂²	1	2	yes	complemented
33	#552	—	2	2	no	—
34	#552	—	2	1	no	—
35	#552	C₂²	1	2	yes	complemented
36	#551	—	2	2	no	—
37	#547	—	2	1	no	—
38	#547	C₂²	1	1	yes	characteristic
39	#546	—	2	1	no	—
40	#546	C₂²	1	2	yes	—
41	D₄²	C₂²	1	1	yes	characteristic
42	#541	—	2	1	no	—
43	#539	—	2	2	no	—
44	#533	C₂²	1	1	yes	characteristic, complemented
45	#532	C₂²	1	1	yes	characteristic
46	#529	—	2	1	no	—
47	#529	C₂²	1	2	yes	—
48	#529	C₂²	1	1	yes	characteristic, complemented
49	#529	C₂²	1	2	yes	complemented
50	C₂×#125	C₂²	1	2	yes	complemented
51	#525	—	2	2	no	—
52	#520	—	2	1	no	—
53	C₄×#41	C₂²	1	1	yes	characteristic
54	C₄×#41	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄	—	2	1	no	—
56	C₂×C₄×D₄	C₂²	1	2	yes	—
57	#500	C₂²	1	1	yes	characteristic, complemented
58	#499	C₂²	1	2	yes	complemented
59	#499	C₂²	1	2	yes	complemented
60	#498	C₂²	1	1	yes	characteristic, complemented
61	#488	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	1	yes	characteristic, complemented
66	#484	C₂²	1	2	yes	complemented
67	#484	C₂²	1	2	yes	complemented
68	#483	C₂²	1	2	yes	complemented
69	#482	C₂²	1	2	yes	complemented
70	#482	C₂²	1	1	yes	characteristic, complemented
71	#482	C₂²	1	2	yes	complemented
72	#481	C₂²	1	2	yes	—
73	#481	C₂²	1	2	yes	complemented
74	#480	C₂²	1	2	yes	—
75	#479	C₂²	1	2	yes	complemented
76	#479	C₂²	1	2	yes	complemented
77	#479	C₂²	1	1	yes	characteristic, complemented
78	#478	C₂²	1	1	yes	characteristic
79	#478	C₂²	1	2	yes	—
80	#478	C₂²	1	2	yes	—
81	#478	C₂²	1	2	yes	—
82	#478	C₂²	1	2	yes	complemented
83	#478	C₂²	1	2	yes	complemented
84	#478	C₂²	1	2	yes	complemented
85	#478	C₂²	1	2	yes	complemented
86	#478	C₂²	1	2	yes	complemented
87	#478	C₂²	1	2	yes	complemented
88	#477	C₂²	1	1	yes	characteristic, complemented
89	#477	C₂²	1	1	yes	characteristic, complemented
90	#476	C₂²	1	1	yes	characteristic
91	#476	C₂²	1	1	yes	characteristic, complemented
92	#475	C₂²	1	1	yes	characteristic, complemented
93	#474	C₂²	1	1	yes	characteristic
94	#467	C₂²	1	2	yes	complemented
95	#466	C₂²	1	2	yes	—
96	#466	C₂²	1	2	yes	complemented
97	#465	C₂²	1	2	yes	—
98	#465	C₂²	1	2	yes	complemented
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	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
113	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
114	C₄×SD₁₆	C₂²	1	1	yes	characteristic
115	C₄×SD₁₆	C₂²	1	2	yes	—
116	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
117	C₄×SD₁₆	C₂²	1	2	yes	complemented
118	C₄×D₈	C₂²	1	1	yes	characteristic
119	C₄×D₈	C₂²	1	2	yes	—
120	C₄×D₈	C₂²	1	2	yes	complemented
121	C₈×D₄	C₂²	1	1	yes	characteristic
122	C₈×D₄	C₂²	1	1	yes	characteristic
123	C₈×D₄	C₂²	1	2	yes	complemented
124	C₈×D₄	C₂²	1	2	yes	complemented
125	#431	C₂²	1	1	yes	characteristic, complemented
126	#431	C₂²	1	2	yes	complemented
127	#427	C₂²	1	2	yes	complemented
128	C₂×#107	C₂²	1	2	yes	complemented
129	C₂×#106	C₂²	1	2	yes	complemented
130	C₂×C₄⋊C₈	C₂²	1	2	yes	complemented
131	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
132	#416	C₂²	1	2	yes	—
133	C₂×#102	C₂²	1	2	yes	—
134	C₂×#102	C₂²	1	2	yes	—
135	C₂×#41	—	2	1	no	—
136	C₂×#41	—	2	1	no	—
137	C₂×#41	D₄	1	1	yes	characteristic
138	C₂×#41	C₂³	1	1	yes	characteristic
139	C₂²×D₄	—	2	1	no	—
140	C₂²×D₄	C₂³	1	2	yes	—
141	C₂³×C₄	—	2	2	no	—
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	C₂²×C₈	C₂³	1	2	yes	—
149	C₂²×C₈	C₂³	1	2	yes	—
150	C₂²×C₈	C₂³	1	2	yes	—
151	C₄⋊Q₈	—	2	1	no	—
152	C₄⋊Q₈	C₂³	1	1	yes	characteristic
153	C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	#127	C₂³	1	1	yes	characteristic
156	#126	—	2	2	no	—
157	#126	—	2	2	no	—
158	#126	—	2	2	no	—
159	#126	—	2	2	no	—
160	#126	—	2	2	no	—
161	#126	—	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	—	2	2	no	—
167	#125	—	2	2	no	—
168	#125	C₂³	1	1	yes	characteristic
169	#125	C₂³	1	2	yes	—
170	#125	C₂³	1	2	yes	—
171	#125	C₂³	1	2	yes	—
172	#125	C₂³	1	2	yes	—
173	#124	—	2	1	no	—
174	#124	—	2	1	no	—
175	#124	C₂³	1	2	yes	—
176	#124	C₂³	1	1	yes	characteristic
177	#123	—	2	2	no	—
178	#123	—	2	2	no	—
179	#123	—	2	1	no	—
180	#123	—	2	2	no	—
181	#123	—	2	2	no	—
182	#123	—	2	2	no	—
183	#123	—	2	2	no	—
184	#123	—	2	2	no	—
185	#123	—	2	2	no	—
186	C₂²⋊Q₈	—	2	1	no	—
187	C₂²⋊Q₈	—	2	1	no	—
188	C₂²⋊Q₈	—	2	1	no	—
189	C₂²⋊Q₈	—	2	1	no	—
190	C₂²⋊Q₈	—	2	2	no	—
191	C₂²⋊Q₈	—	2	2	no	—
192	C₂²⋊Q₈	—	2	1	no	—
193	C₂²⋊Q₈	—	2	2	no	—
194	C₂²⋊Q₈	—	2	2	no	—
195	C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
197	C₂²⋊Q₈	C₂³	1	2	yes	—
198	#121	—	2	2	no	—
199	#121	—	2	2	no	—
200	#121	—	2	1	no	—
201	#121	—	2	1	no	—
202	#121	—	2	2	no	—
203	#121	C₂³	1	2	yes	—
204	#121	C₂³	1	2	yes	—
205	#121	C₂³	1	1	yes	characteristic
206	#121	C₂³	1	2	yes	—
207	#120	—	2	2	no	—
208	#120	—	2	2	no	—
209	C₄×Q₈	—	2	1	no	—
210	C₄×Q₈	—	2	1	no	—
211	C₄×Q₈	—	2	1	no	—
212	C₄×Q₈	D₄	1	1	yes	characteristic
213	C₄×Q₈	C₂³	1	1	yes	characteristic
214	C₄×Q₈	C₂³	1	1	yes	characteristic
215	C₄×Q₈	C₂³	1	2	yes	—
216	C₄×Q₈	C₂³	1	1	yes	characteristic
217	C₄×Q₈	C₂³	1	1	yes	characteristic
218	C₄×D₄	—	2	1	no	—
219	C₄×D₄	—	2	1	no	—
220	C₄×D₄	—	2	2	no	—
221	C₄×D₄	—	2	1	no	—
222	C₄×D₄	—	2	1	no	—
223	C₄×D₄	—	2	2	no	—
224	C₄×D₄	—	2	1	no	—
225	C₄×D₄	—	2	1	no	—
226	C₄×D₄	—	2	2	no	—
227	C₄×D₄	—	2	2	no	—
228	C₄×D₄	—	2	1	no	—
229	C₄×D₄	—	2	2	no	—
230	C₄×D₄	—	2	2	no	—
231	C₄×D₄	D₄	1	1	yes	characteristic
232	C₄×D₄	D₄	1	2	yes	—
233	C₄×D₄	C₂³	1	1	yes	characteristic
234	C₄×D₄	C₂³	1	2	yes	—
235	C₄×D₄	C₂³	1	2	yes	—
236	C₄×D₄	C₂³	1	2	yes	—
237	C₄×D₄	C₂³	1	1	yes	characteristic
238	C₄×D₄	C₂³	1	1	yes	characteristic
239	C₄×D₄	C₂³	1	2	yes	—
240	C₄×D₄	C₂³	1	1	yes	characteristic
241	C₄×D₄	C₂³	1	2	yes	—
242	#117	—	2	2	no	—
243	#117	—	2	1	no	—
244	#117	—	2	1	no	—
245	#117	—	2	2	no	—
246	#117	—	2	2	no	—
247	#117	D₄	1	2	yes	—
248	#117	D₄	1	1	yes	characteristic
249	#117	C₂³	1	1	yes	characteristic
250	#117	C₂³	1	2	yes	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	C₂³	1	2	yes	—
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×C₄²	—	2	1	no	—
261	C₂×C₄²	C₂³	1	2	yes	—
262	C₂×C₄²	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	#107	C₂³	1	2	yes	—
269	#107	C₂³	1	1	yes	characteristic
270	#106	C₂³	1	1	yes	characteristic
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	2	yes	—
276	#106	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
293	#102	C₂³	1	2	yes	—
294	#102	C₂³	1	2	yes	—
295	#102	C₂³	1	2	yes	—
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	1	yes	characteristic
301	#102	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
307	C₂²⋊C₈	C₂³	1	1	yes	characteristic
308	C₄×C₈	C₂³	1	1	yes	characteristic
309	C₄×C₈	C₂³	1	1	yes	characteristic
310	C₄×C₈	C₂³	1	2	yes	—
311	C₄×C₈	C₂³	1	2	yes	—
312	C₂⁴	—	2	2	no	—
313	#41	—	2	4	no	—
314	#41	—	2	2	no	—
315	#41	—	4	1	no	—
316	#41	—	4	4	no	—
317	#41	—	8	2	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
322	C₂×Q₈	C₂⁴	1	1	yes	characteristic
323	C₂×Q₈	C₂⁴	1	1	yes	characteristic
324	C₂×D₄	—	2	4	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	2	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	1	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	4	2	no	—
334	C₂×D₄	—	4	4	no	—
335	C₂×D₄	C₂×D₄	1	2	yes	—
336	C₂×D₄	C₂×D₄	1	1	yes	characteristic
337	C₂×D₄	C₂⁴	1	2	yes	—
338	C₂×D₄	C₂⁴	1	1	yes	characteristic
339	C₂×D₄	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	8	4	no	—
352	C₂²×C₄	C₂×D₄	1	2	yes	—
353	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄	1	2	yes	—
355	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄	C₂⁴	1	2	yes	—
357	C₂²×C₄	C₂⁴	1	1	yes	characteristic
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	C₂×C₈	—	4	2	no	—
365	C₂×C₈	—	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	2	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	1	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	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	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	1	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
397	C₄⋊C₄	C₂×D₄	1	2	yes	—
398	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄	C₂×D₄	1	2	yes	—
400	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄	C₂⁴	1	2	yes	—
402	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄	C₂⁴	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	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	2	2	no	—
409	C₂²⋊C₄	—	2	1	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	1	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	1	no	—
420	C₂²⋊C₄	—	2	1	no	—
421	C₂²⋊C₄	—	2	1	no	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	2	1	no	—
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	C₄²	—	2	1	no	—
431	C₄²	—	2	1	no	—
432	C₄²	—	2	1	no	—
433	C₄²	—	2	2	no	—
434	C₄²	—	2	2	no	—
435	C₄²	—	2	1	no	—
436	C₄²	C₂×D₄	1	1	yes	characteristic
437	C₄²	C₂×D₄	1	2	yes	—
438	C₄²	C₂×D₄	1	1	yes	characteristic
439	C₄²	C₂×D₄	1	2	yes	—
440	C₄²	C₂⁴	1	2	yes	—
441	C₄²	C₂⁴	1	1	yes	characteristic
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	—	4	4	no	—
448	C₂³	—	8	2	no	—
449	C₂³	C₂²×D₄	1	1	yes	characteristic
450	C₂³	C₂²×D₄	1	2	yes	—
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	1	no	—
458	Q₈	—	8	1	no	—
459	D₄	—	2	4	no	—
460	D₄	—	2	1	no	—
461	D₄	—	2	2	no	—
462	D₄	—	2	1	no	—
463	D₄	—	2	1	no	—
464	D₄	—	2	2	no	—
465	D₄	—	4	4	no	—
466	D₄	—	4	2	no	—
467	D₄	—	4	4	no	—
468	D₄	—	4	4	no	—
469	D₄	—	4	2	no	—
470	D₄	—	8	1	no	—
471	D₄	—	8	1	no	—
472	D₄	—	8	2	no	—
473	D₄	#135	1	4	yes	—
474	D₄	2₋¹⁺⁴	1	2	yes	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	4	no	—
495	C₂×C₄	—	4	4	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	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	1	yes	characteristic
504	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄	C₂²×D₄	1	2	yes	—
506	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄	C₂²×D₄	1	2	yes	—
508	C₂×C₄	C₂²×D₄	1	2	yes	—
509	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
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	2	no	—
515	C₈	—	2	2	no	—
516	C₈	—	2	1	no	—
517	C₈	—	2	1	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	2	1	no	—
521	C₂²	—	2	1	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	1	no	—
524	C₂²	—	4	1	no	—
525	C₂²	—	4	1	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	1	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	1	no	—
530	C₂²	—	4	1	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	8	8	no	—
533	C₂²	C₂×#135	1	4	yes	—
534	C₂²	C₂³×D₄	1	1	yes	characteristic
535	C₄	—	2	1	no	—
536	C₄	—	2	2	no	—
537	C₄	—	2	1	no	—
538	C₄	—	2	1	no	—
539	C₄	—	2	2	no	—
540	C₄	—	2	1	no	—
541	C₄	—	2	2	no	—
542	C₄	—	4	1	no	—
543	C₄	—	4	2	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	2	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	C₂×#135	1	2	yes	—
552	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
553	C₄	#585	1	1	yes	characteristic
554	C₂	—	2	4	no	—
555	C₂	—	4	1	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	C₂²×#135	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 ◁ 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. #3515	C₂	semidirect
2. #3481	C₂	semidirect
3. #3381	C₂	semidirect
4. #3380	C₂	semidirect
5. #3365	C₂	semidirect
6. #3361	C₂	semidirect
7. #3339	C₂	semidirect
8. #3338	C₂	semidirect
9. #3337	C₂	semidirect
10. #3335	C₂	semidirect
11. #3297	C₂	semidirect
12. #3296	C₂	semidirect
13. #3295	C₂	semidirect
14. #3294	C₂	semidirect
15. #3250	C₂	semidirect
16. #3247	C₂	semidirect
17. #3232	C₂	semidirect
18. #3228	C₂	semidirect
19. #3105	C₂	semidirect
20. #3102	C₂	semidirect
21. #3076	C₂	semidirect
22. C₂×#478	C₂	semidirect
23. #2988	C₂	semidirect
25. #557	C₂²	semidirect
29. #554	C₂²	semidirect
32. #553	C₂²	semidirect
35. #552	C₂²	semidirect
44. #533	C₂²	semidirect
48. #529	C₂²	semidirect
49. #529	C₂²	semidirect
50. C₂×#125	C₂²	semidirect
57. #500	C₂²	semidirect
58. #499	C₂²	semidirect
59. #499	C₂²	semidirect
60. #498	C₂²	semidirect
61. #488	C₂²	semidirect
62. #488	C₂²	semidirect
65. #485	C₂²	semidirect
66. #484	C₂²	semidirect
67. #484	C₂²	semidirect
68. #483	C₂²	semidirect
69. #482	C₂²	semidirect
70. #482	C₂²	semidirect
71. #482	C₂²	semidirect
73. #481	C₂²	semidirect
75. #479	C₂²	semidirect
76. #479	C₂²	semidirect
77. #479	C₂²	semidirect
82. #478	C₂²	semidirect
83. #478	C₂²	semidirect
84. #478	C₂²	semidirect
85. #478	C₂²	semidirect
86. #478	C₂²	semidirect
87. #478	C₂²	semidirect
88. #477	C₂²	semidirect
89. #477	C₂²	semidirect
91. #476	C₂²	semidirect
92. #475	C₂²	semidirect
94. #467	C₂²	semidirect
96. #466	C₂²	semidirect
98. #465	C₂²	semidirect
99. #465	C₂²	semidirect
100. #464	C₂²	semidirect
101. #464	C₂²	semidirect
103. #463	C₂²	semidirect
104. #463	C₂²	semidirect
111. C₈×Q₈	C₂²	semidirect
112. C₈×Q₈	C₂²	semidirect
113. C₄×Q₁₆	C₂²	semidirect
116. C₄×SD₁₆	C₂²	semidirect
117. C₄×SD₁₆	C₂²	semidirect
120. C₄×D₈	C₂²	semidirect
123. C₈×D₄	C₂²	semidirect
124. C₈×D₄	C₂²	semidirect
125. #431	C₂²	semidirect
126. #431	C₂²	semidirect
127. #427	C₂²	semidirect
128. C₂×#107	C₂²	semidirect
129. C₂×#106	C₂²	semidirect
130. C₂×C₄⋊C₈	C₂²	semidirect
131. C₂×C₄⋊C₈	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3515	2
#3481	2
#3381	2
#3380	2
#3365	2
#3361	2
#3339	2
#3338	2
#3337	2
#3335	2
#3297	2
#3296	2
#3295	2
#3294	2
#3250	2
#3247	2
#3232	2
#3228	2
#3105	2
#3102	2
#3076	2
C₂×#478	2
#2988	2