Subgroups — #62152

Order 256.

865 conjugacy classes of subgroups.

The subgroup lattice has 558 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	#3475	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	#3364	C₂	1	1	yes	maximal, characteristic, complemented
6	#3360	C₂	1	1	yes	maximal, characteristic, complemented
7	#3357	C₂	1	1	yes	maximal, characteristic, complemented
8	#3354	C₂	1	1	yes	maximal, characteristic, complemented
9	#3352	C₂	1	2	yes	maximal, complemented
10	#3351	C₂	1	2	yes	maximal, complemented
11	#3331	C₂	1	1	yes	maximal, characteristic, complemented
12	#3330	C₂	1	1	yes	maximal, characteristic, complemented
13	#3323	C₂	1	2	yes	maximal, complemented
14	#3322	C₂	1	2	yes	maximal, complemented
15	#3256	C₂	1	2	yes	maximal, complemented
16	#3252	C₂	1	1	yes	maximal, characteristic, complemented
17	#3232	C₂	1	2	yes	maximal, complemented
18	#3231	C₂	1	1	yes	maximal, characteristic, complemented
19	#3105	C₂	1	1	yes	maximal, characteristic, complemented
20	#3102	C₂	1	2	yes	maximal, complemented
21	#3080	C₂	1	2	yes	maximal, complemented
22	#3077	C₂	1	1	yes	maximal, characteristic, complemented
23	#2991	C₂	1	1	yes	maximal, characteristic, complemented
24	#557	C₂²	1	1	yes	characteristic, complemented
25	#556	C₂²	1	1	yes	characteristic
26	#555	C₂²	1	1	yes	characteristic
27	#554	C₂²	1	1	yes	characteristic
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	—
32	#552	—	2	1	no	—
33	#552	—	2	2	no	—
34	#552	—	2	1	no	—
35	#552	C₂²	1	2	yes	—
36	#552	C₂²	1	2	yes	—
37	#551	—	2	2	no	—
38	#547	—	2	1	no	—
39	#547	C₂²	1	1	yes	characteristic
40	#547	C₂²	1	1	yes	characteristic, complemented
41	#546	C₂²	1	2	yes	—
42	#541	—	2	1	no	—
43	#539	—	2	2	no	—
44	#533	C₂²	1	1	yes	characteristic
45	#533	C₂²	1	1	yes	characteristic
46	#529	—	2	2	no	—
47	#529	C₂²	1	1	yes	characteristic
48	#529	C₂²	1	2	yes	—
49	#529	C₂²	1	2	yes	complemented
50	C₂×#125	C₂²	1	2	yes	complemented
51	#525	—	2	1	no	—
52	#520	—	2	1	no	—
53	C₄×#41	C₂²	1	2	yes	—
54	C₄×#41	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
56	C₂×#117	—	2	1	no	—
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	—
62	#488	C₂²	1	2	yes	—
63	#487	C₂²	1	1	yes	characteristic, complemented
64	#487	C₂²	1	1	yes	characteristic, complemented
65	#485	C₂²	1	2	yes	—
66	#485	C₂²	1	2	yes	—
67	#485	C₂²	1	2	yes	complemented
68	#484	C₂²	1	1	yes	characteristic
69	#484	C₂²	1	2	yes	complemented
70	#483	C₂²	1	2	yes	complemented
71	#482	C₂²	1	2	yes	complemented
72	#481	C₂²	1	1	yes	characteristic
73	#481	C₂²	1	2	yes	—
74	#480	C₂²	1	2	yes	—
75	#479	C₂²	1	2	yes	complemented
76	#479	C₂²	1	2	yes	complemented
77	#479	C₂²	1	2	yes	complemented
78	#479	C₂²	1	2	yes	complemented
79	#479	C₂²	1	2	yes	complemented
80	#479	C₂²	1	2	yes	complemented
81	#478	C₂²	1	2	yes	—
82	#478	C₂²	1	2	yes	—
83	#478	C₂²	1	1	yes	characteristic
84	#478	C₂²	1	2	yes	—
85	#478	C₂²	1	2	yes	—
86	#478	C₂²	1	1	yes	characteristic
87	#478	C₂²	1	2	yes	complemented
88	#477	C₂²	1	1	yes	characteristic, complemented
89	#476	C₂²	1	1	yes	characteristic
90	#476	C₂²	1	1	yes	characteristic
91	#476	C₂²	1	1	yes	characteristic, complemented
92	#474	C₂²	1	1	yes	characteristic
93	#474	C₂²	1	1	yes	characteristic
94	#470	C₂²	1	2	yes	—
95	#470	C₂²	1	2	yes	complemented
96	#469	C₂²	1	2	yes	—
97	#468	C₂²	1	2	yes	—
98	#468	C₂²	1	2	yes	—
99	#468	C₂²	1	2	yes	complemented
100	#464	C₂²	1	2	yes	—
101	#464	C₂²	1	2	yes	complemented
102	#463	C₂²	1	1	yes	characteristic
103	#463	C₂²	1	2	yes	—
104	#463	C₂²	1	1	yes	characteristic
105	#462	C₂²	1	1	yes	characteristic, complemented
106	#461	C₂²	1	1	yes	characteristic, complemented
107	#452	C₂²	1	2	yes	—
108	#450	C₂²	1	1	yes	characteristic
109	#449	C₂²	1	2	yes	—
110	#447	C₂²	1	1	yes	characteristic
111	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
113	C₄×Q₁₆	C₂²	1	2	yes	complemented
114	C₄×SD₁₆	C₂²	1	1	yes	characteristic
115	C₄×SD₁₆	C₂²	1	1	yes	characteristic
116	C₄×SD₁₆	C₂²	1	2	yes	—
117	C₄×SD₁₆	C₂²	1	2	yes	complemented
118	C₄×D₈	C₂²	1	1	yes	characteristic
119	C₄×D₈	C₂²	1	1	yes	characteristic
120	C₄×D₈	C₂²	1	2	yes	—
121	#436	C₂²	1	2	yes	—
122	#436	C₂²	1	2	yes	—
123	#436	C₂²	1	1	yes	characteristic, complemented
124	#436	C₂²	1	1	yes	characteristic, complemented
125	#431	C₂²	1	1	yes	characteristic
126	#431	C₂²	1	2	yes	complemented
127	#428	C₂²	1	2	yes	—
128	#428	C₂²	1	2	yes	complemented
129	#428	C₂²	1	2	yes	complemented
130	#423	C₂²	1	1	yes	characteristic
131	#423	C₂²	1	2	yes	complemented
132	#418	C₂²	1	2	yes	—
133	#417	C₂²	1	2	yes	—
134	#417	C₂²	1	2	yes	—
135	C₂×#41	—	2	1	no	—
136	C₂×#41	D₄	1	1	yes	characteristic
137	C₂×#41	C₂³	1	2	yes	—
138	C₂²×D₄	C₂³	1	1	yes	characteristic
139	C₂³×C₄	—	2	1	no	—
140	C₂×Q₁₆	C₂³	1	2	yes	—
141	C₂×SD₁₆	C₂³	1	1	yes	characteristic
142	C₂×SD₁₆	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆	C₂³	1	2	yes	—
144	C₂×D₈	C₂³	1	1	yes	characteristic
145	C₂×D₈	C₂³	1	1	yes	characteristic
146	C₂×M₁₆	C₂³	1	2	yes	—
147	C₂×M₁₆	C₂³	1	2	yes	—
148	C₂×M₁₆	C₂³	1	2	yes	—
149	C₄⋊Q₈	—	2	1	no	—
150	C₄⋊Q₈	C₂³	1	1	yes	characteristic
151	C₄⋊Q₈	C₂³	1	1	yes	characteristic
152	C₄⋊Q₈	C₂³	1	1	yes	characteristic
153	C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	#126	—	2	2	no	—
155	#126	—	2	2	no	—
156	#126	—	2	2	no	—
157	#126	—	2	2	no	—
158	#126	—	2	2	no	—
159	#126	—	2	1	no	—
160	#126	—	2	2	no	—
161	#125	—	2	2	no	—
162	#125	—	2	2	no	—
163	#125	—	2	2	no	—
164	#125	—	2	1	no	—
165	#125	—	2	2	no	—
166	#125	—	2	2	no	—
167	#125	—	2	1	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	2	no	—
174	#124	C₂³	1	1	yes	characteristic
175	#124	C₂³	1	2	yes	—
176	#123	—	2	2	no	—
177	#123	—	2	2	no	—
178	#123	—	2	1	no	—
179	#123	—	2	2	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	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	1	no	—
190	C₂²⋊Q₈	—	2	1	no	—
191	C₂²⋊Q₈	—	2	2	no	—
192	C₂²⋊Q₈	—	2	2	no	—
193	C₂²⋊Q₈	—	2	1	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	C₂²⋊Q₈	C₂³	1	2	yes	—
199	#121	—	2	1	no	—
200	#121	—	2	1	no	—
201	#121	—	2	2	no	—
202	#121	—	2	2	no	—
203	#121	C₂³	1	2	yes	—
204	#121	C₂³	1	1	yes	characteristic
205	#121	C₂³	1	2	yes	—
206	#120	—	2	2	no	—
207	C₄×Q₈	—	2	1	no	—
208	C₄×Q₈	—	2	1	no	—
209	C₄×Q₈	—	2	1	no	—
210	C₄×Q₈	—	2	1	no	—
211	C₄×Q₈	D₄	1	1	yes	characteristic
212	C₄×Q₈	C₂³	1	2	yes	—
213	C₄×Q₈	C₂³	1	2	yes	—
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×D₄	—	2	1	no	—
218	C₄×D₄	—	2	2	no	—
219	C₄×D₄	—	2	2	no	—
220	C₄×D₄	—	2	2	no	—
221	C₄×D₄	—	2	2	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	D₄	1	1	yes	characteristic
227	C₄×D₄	D₄	1	2	yes	—
228	C₄×D₄	C₂³	1	1	yes	characteristic
229	C₄×D₄	C₂³	1	1	yes	characteristic
230	C₄×D₄	C₂³	1	1	yes	characteristic
231	C₄×D₄	C₂³	1	1	yes	characteristic
232	C₄×D₄	C₂³	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	1	yes	characteristic
237	#117	—	2	1	no	—
238	#117	—	2	1	no	—
239	#117	—	2	1	no	—
240	#117	—	2	2	no	—
241	#117	—	2	2	no	—
242	#117	—	2	2	no	—
243	#117	—	2	2	no	—
244	#117	—	2	1	no	—
245	#117	—	2	2	no	—
246	#117	D₄	1	1	yes	characteristic
247	#117	D₄	1	2	yes	—
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×C₄⋊C₄	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄	C₂³	1	2	yes	—
258	C₂×C₂²⋊C₄	—	2	1	no	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₄²	—	2	2	no	—
261	C₂×C₄²	C₂³	1	1	yes	characteristic
262	C₂×C₄²	C₂³	1	2	yes	—
263	#107	C₂³	1	2	yes	—
264	#107	C₂³	1	2	yes	—
265	#107	C₂³	1	1	yes	characteristic
266	#107	C₂³	1	2	yes	—
267	#107	C₂³	1	2	yes	—
268	#107	C₂³	1	1	yes	characteristic
269	#107	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	#106	C₂³	1	2	yes	—
275	#106	C₂³	1	1	yes	characteristic
276	#106	C₂³	1	2	yes	—
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	2	yes	—
288	#103	C₂³	1	1	yes	characteristic
289	#103	C₂³	1	1	yes	characteristic
290	#103	C₂³	1	2	yes	—
291	#103	C₂³	1	2	yes	—
292	#103	C₂³	1	2	yes	—
293	#102	C₂³	1	1	yes	characteristic
294	#102	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
300	#102	C₂³	1	1	yes	characteristic
301	#102	C₂³	1	1	yes	characteristic
302	#102	C₂³	1	2	yes	—
303	#102	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	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	1	no	—
313	#41	—	2	4	no	—
314	#41	—	4	2	no	—
315	#41	—	4	2	no	—
316	#41	—	4	4	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
321	C₂×Q₈	C₂⁴	1	2	yes	—
322	C₂×Q₈	C₂⁴	1	1	yes	characteristic
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	4	1	no	—
330	C₂×D₄	C₂×D₄	1	1	yes	characteristic
331	C₂×D₄	C₂×D₄	1	2	yes	—
332	C₂×D₄	C₂⁴	1	1	yes	characteristic
333	C₂×D₄	C₂⁴	1	1	yes	characteristic
334	C₂×D₄	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	2	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	—	4	4	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	2	yes	—
350	C₂²×C₄	C₂×D₄	1	2	yes	—
351	C₂²×C₄	C₂⁴	1	2	yes	—
352	C₂²×C₄	C₂⁴	1	1	yes	characteristic
353	Q₁₆	—	4	2	no	—
354	SD₁₆	—	2	2	no	—
355	SD₁₆	—	4	2	no	—
356	SD₁₆	—	4	1	no	—
357	D₈	—	2	2	no	—
358	D₈	—	4	1	no	—
359	M₁₆	—	4	2	no	—
360	M₁₆	—	4	2	no	—
361	M₁₆	—	4	2	no	—
362	C₂×C₈	C₂⁴	1	1	yes	characteristic
363	C₂×C₈	C₂⁴	1	1	yes	characteristic
364	C₂×C₈	C₂⁴	1	2	yes	—
365	C₂×C₈	C₂⁴	1	1	yes	characteristic
366	C₂×C₈	C₂⁴	1	2	yes	—
367	C₂×C₈	C₂⁴	1	1	yes	characteristic
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	1	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	1	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
395	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
396	C₄⋊C₄	C₂×D₄	1	2	yes	—
397	C₄⋊C₄	C₂×D₄	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	2	yes	—
402	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄	C₂⁴	1	2	yes	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	2	2	no	—
409	C₂²⋊C₄	—	2	2	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	1	no	—
415	C₂²⋊C₄	—	2	1	no	—
416	C₂²⋊C₄	—	2	1	no	—
417	C₂²⋊C₄	—	2	1	no	—
418	C₂²⋊C₄	—	2	1	no	—
419	C₂²⋊C₄	—	2	1	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	1	no	—
425	C₂²⋊C₄	C₂×D₄	1	2	yes	—
426	C₂²⋊C₄	C₂×D₄	1	2	yes	—
427	C₂²⋊C₄	C₂×D₄	1	2	yes	—
428	C₄²	—	2	2	no	—
429	C₄²	—	2	2	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	2	2	no	—
432	C₄²	—	2	2	no	—
433	C₄²	—	2	1	no	—
434	C₄²	C₂×D₄	1	2	yes	—
435	C₄²	C₂×D₄	1	1	yes	characteristic
436	C₄²	C₂×D₄	1	2	yes	—
437	C₄²	C₂×D₄	1	1	yes	characteristic
438	C₄²	C₂⁴	1	1	yes	characteristic
439	C₄²	C₂⁴	1	2	yes	—
440	C₄²	C₂⁴	1	1	yes	characteristic
441	C₂³	—	2	1	no	—
442	C₂³	—	2	1	no	—
443	C₂³	—	2	1	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	8	1	no	—
447	C₂³	C₂²×D₄	1	1	yes	characteristic
448	C₂³	C₂²×D₄	1	2	yes	—
449	Q₈	—	2	2	no	—
450	Q₈	—	2	1	no	—
451	Q₈	—	2	2	no	—
452	Q₈	—	2	1	no	—
453	Q₈	—	2	2	no	—
454	Q₈	—	4	2	no	—
455	Q₈	—	8	1	no	—
456	Q₈	—	8	1	no	—
457	D₄	—	2	2	no	—
458	D₄	—	2	1	no	—
459	D₄	—	2	1	no	—
460	D₄	—	2	1	no	—
461	D₄	—	2	1	no	—
462	D₄	—	2	1	no	—
463	D₄	—	4	2	no	—
464	D₄	—	4	2	no	—
465	D₄	—	4	4	no	—
466	D₄	—	4	4	no	—
467	D₄	—	8	1	no	—
468	D₄	—	8	2	no	—
469	D₄	2₋¹⁺⁴	1	2	yes	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	4	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	4	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	8	2	no	—
496	C₂×C₄	—	8	2	no	—
497	C₂×C₄	—	8	2	no	—
498	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄	C₂²×D₄	1	2	yes	—
501	C₂×C₄	C₂²×D₄	1	2	yes	—
502	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄	C₂²×D₄	1	2	yes	—
505	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄	C₂⁵	1	1	yes	characteristic
507	C₈	—	2	1	no	—
508	C₈	—	2	1	no	—
509	C₈	—	2	1	no	—
510	C₈	—	2	1	no	—
511	C₈	—	2	2	no	—
512	C₈	—	2	2	no	—
513	C₂²	—	2	2	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	2	1	no	—
517	C₂²	—	2	2	no	—
518	C₂²	—	2	1	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	4	1	no	—
521	C₂²	—	4	1	no	—
522	C₂²	—	4	1	no	—
523	C₂²	—	4	1	no	—
524	C₂²	—	4	1	no	—
525	C₂²	—	4	1	no	—
526	C₂²	—	4	1	no	—
527	C₂²	—	4	1	no	—
528	C₂²	—	8	4	no	—
529	C₂²	C₂³×D₄	1	1	yes	characteristic
530	C₄	—	2	1	no	—
531	C₄	—	2	2	no	—
532	C₄	—	2	1	no	—
533	C₄	—	2	2	no	—
534	C₄	—	2	1	no	—
535	C₄	—	2	1	no	—
536	C₄	—	2	2	no	—
537	C₄	—	4	1	no	—
538	C₄	—	4	2	no	—
539	C₄	—	4	2	no	—
540	C₄	—	4	2	no	—
541	C₄	—	4	1	no	—
542	C₄	—	4	1	no	—
543	C₄	—	4	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	2	no	—
546	C₄	#575	1	2	yes	—
547	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
548	C₄	#585	1	1	yes	characteristic
549	C₂	—	4	2	no	—
550	C₂	—	4	1	no	—
551	C₂	—	4	2	no	—
552	C₂	—	8	1	no	—
553	C₂	—	8	1	no	—
554	C₂	#3489	1	1	yes	characteristic
555	C₂	C₂×#575	1	1	yes	characteristic
556	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 ◁ 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. #3475	C₂	semidirect
3. #3381	C₂	semidirect
4. #3380	C₂	semidirect
5. #3364	C₂	semidirect
6. #3360	C₂	semidirect
7. #3357	C₂	semidirect
8. #3354	C₂	semidirect
9. #3352	C₂	semidirect
10. #3351	C₂	semidirect
11. #3331	C₂	semidirect
12. #3330	C₂	semidirect
13. #3323	C₂	semidirect
14. #3322	C₂	semidirect
15. #3256	C₂	semidirect
16. #3252	C₂	semidirect
17. #3232	C₂	semidirect
18. #3231	C₂	semidirect
19. #3105	C₂	semidirect
20. #3102	C₂	semidirect
21. #3080	C₂	semidirect
22. #3077	C₂	semidirect
23. #2991	C₂	semidirect
24. #557	C₂²	semidirect
28. #554	C₂²	semidirect
29. #554	C₂²	semidirect
40. #547	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
63. #487	C₂²	semidirect
64. #487	C₂²	semidirect
67. #485	C₂²	semidirect
69. #484	C₂²	semidirect
70. #483	C₂²	semidirect
71. #482	C₂²	semidirect
75. #479	C₂²	semidirect
76. #479	C₂²	semidirect
77. #479	C₂²	semidirect
78. #479	C₂²	semidirect
79. #479	C₂²	semidirect
80. #479	C₂²	semidirect
87. #478	C₂²	semidirect
88. #477	C₂²	semidirect
91. #476	C₂²	semidirect
95. #470	C₂²	semidirect
99. #468	C₂²	semidirect
101. #464	C₂²	semidirect
105. #462	C₂²	semidirect
106. #461	C₂²	semidirect
111. C₈×Q₈	C₂²	semidirect
112. C₈×Q₈	C₂²	semidirect
113. C₄×Q₁₆	C₂²	semidirect
117. C₄×SD₁₆	C₂²	semidirect
123. #436	C₂²	semidirect
124. #436	C₂²	semidirect
126. #431	C₂²	semidirect
128. #428	C₂²	semidirect
129. #428	C₂²	semidirect
131. #423	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
#3475	2
#3381	2
#3380	2
#3364	2
#3360	2
#3357	2
#3354	2
#3352	2
#3351	2
#3331	2
#3330	2
#3323	2
#3322	2
#3256	2
#3252	2
#3232	2
#3231	2
#3105	2
#3102	2
#3080	2
#3077	2
#2991	2