Subgroups — #62389

Order 256.

828 conjugacy classes of subgroups.

The subgroup lattice has 815 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3557	C₂	1	1	yes	maximal, characteristic, complemented
2	#3550	C₂	1	1	yes	maximal, characteristic, complemented
3	#3403	C₂	1	1	yes	maximal, characteristic, complemented
4	#3402	C₂	1	1	yes	maximal, characteristic, complemented
5	#3401	C₂	1	1	yes	maximal, characteristic, complemented
6	#3401	C₂	1	1	yes	maximal, characteristic, complemented
7	#3387	C₂	1	1	yes	maximal, characteristic, complemented
8	#3386	C₂	1	1	yes	maximal, characteristic, complemented
9	#3385	C₂	1	1	yes	maximal, characteristic, complemented
10	#3384	C₂	1	1	yes	maximal, characteristic, complemented
11	#3377	C₂	1	1	yes	maximal, characteristic, complemented
12	#3376	C₂	1	1	yes	maximal, characteristic, complemented
13	#3375	C₂	1	1	yes	maximal, characteristic, complemented
14	#3373	C₂	1	1	yes	maximal, characteristic, complemented
15	#3371	C₂	1	1	yes	maximal, characteristic, complemented
16	#3370	C₂	1	1	yes	maximal, characteristic, complemented
17	#3369	C₂	1	1	yes	maximal, characteristic, complemented
18	#3367	C₂	1	1	yes	maximal, characteristic, complemented
19	#3263	C₂	1	1	yes	maximal, characteristic, complemented
20	#3262	C₂	1	1	yes	maximal, characteristic, complemented
21	#3258	C₂	1	1	yes	maximal, characteristic, complemented
22	#3257	C₂	1	1	yes	maximal, characteristic, complemented
23	#3252	C₂	1	1	yes	maximal, characteristic, complemented
24	#3251	C₂	1	1	yes	maximal, characteristic, complemented
25	#3181	C₂	1	1	yes	maximal, characteristic, complemented
26	#3180	C₂	1	1	yes	maximal, characteristic, complemented
27	#3179	C₂	1	1	yes	maximal, characteristic, complemented
28	#3178	C₂	1	1	yes	maximal, characteristic, complemented
29	#3175	C₂	1	1	yes	maximal, characteristic, complemented
30	#3173	C₂	1	1	yes	maximal, characteristic, complemented
31	#2961	C₂	1	1	yes	maximal, characteristic, complemented
32	#563	—	2	1	no	—
33	#563	—	2	1	no	—
34	#563	—	2	1	no	—
35	#563	—	2	1	no	—
36	#559	C₂²	1	1	yes	characteristic
37	#559	C₂²	1	1	yes	characteristic
38	#559	C₂²	1	1	yes	characteristic
39	#559	C₂²	1	1	yes	characteristic
40	Q₈²	C₂²	1	1	yes	characteristic
41	Q₈²	C₂²	1	1	yes	characteristic
42	#557	C₂²	1	1	yes	characteristic
43	#557	C₂²	1	1	yes	characteristic
44	#556	—	2	1	no	—
45	#556	C₂²	1	1	yes	characteristic
46	#556	C₂²	1	1	yes	characteristic
47	#556	C₂²	1	1	yes	characteristic
48	#556	C₂²	1	1	yes	characteristic
49	#554	C₂²	1	1	yes	characteristic
50	#554	C₂²	1	1	yes	characteristic
51	#552	—	2	1	no	—
52	#552	—	2	1	no	—
53	D₄×Q₈	—	2	1	no	—
54	D₄×Q₈	C₂²	1	1	yes	characteristic
55	D₄×Q₈	C₂²	1	1	yes	characteristic
56	#542	—	2	1	no	—
57	#542	—	2	1	no	—
58	#542	—	2	1	no	—
59	#542	—	2	1	no	—
60	#542	C₂²	1	1	yes	characteristic
61	#542	C₂²	1	1	yes	characteristic
62	#542	C₂²	1	1	yes	characteristic
63	#542	C₂²	1	1	yes	characteristic
64	#542	C₂²	1	1	yes	characteristic
65	#542	C₂²	1	1	yes	characteristic
66	#541	C₂²	1	1	yes	characteristic
67	#540	C₂²	1	1	yes	characteristic
68	#539	—	2	1	no	—
69	#539	—	2	1	no	—
70	#536	—	2	1	no	—
71	#536	—	2	1	no	—
72	#533	C₂²	1	1	yes	characteristic
73	#533	C₂²	1	1	yes	characteristic
74	#532	C₂²	1	1	yes	characteristic
75	#529	C₂²	1	1	yes	characteristic
76	#529	C₂²	1	1	yes	characteristic
77	#501	C₂²	1	1	yes	characteristic
78	#501	C₂²	1	1	yes	characteristic
79	#501	C₂²	1	1	yes	characteristic
80	#501	C₂²	1	1	yes	characteristic
81	#500	C₂²	1	1	yes	characteristic
82	#498	C₂²	1	1	yes	characteristic
83	#497	C₂²	1	1	yes	characteristic
84	#497	C₂²	1	1	yes	characteristic
85	#496	C₂²	1	1	yes	characteristic
86	#496	C₂²	1	1	yes	characteristic
87	#495	C₂²	1	1	yes	characteristic
88	#495	C₂²	1	1	yes	characteristic
89	#491	C₂²	1	1	yes	characteristic
90	#490	C₂²	1	1	yes	characteristic
91	#489	C₂²	1	1	yes	characteristic
92	#489	C₂²	1	1	yes	characteristic
93	#489	C₂²	1	1	yes	characteristic
94	#489	C₂²	1	1	yes	characteristic
95	#489	C₂²	1	1	yes	characteristic
96	#489	C₂²	1	1	yes	characteristic
97	#488	C₂²	1	1	yes	characteristic
98	#488	C₂²	1	1	yes	characteristic
99	#487	C₂²	1	1	yes	characteristic
100	#486	C₂²	1	1	yes	characteristic
101	#479	C₂²	1	1	yes	characteristic
102	#479	C₂²	1	1	yes	characteristic
103	#479	C₂²	1	1	yes	characteristic
104	#479	C₂²	1	1	yes	characteristic
105	#478	C₂²	1	1	yes	characteristic
106	#478	C₂²	1	1	yes	characteristic
107	#478	C₂²	1	1	yes	characteristic
108	#478	C₂²	1	1	yes	characteristic
109	#477	C₂²	1	1	yes	characteristic
110	#477	C₂²	1	1	yes	characteristic
111	#477	C₂²	1	1	yes	characteristic
112	#477	C₂²	1	1	yes	characteristic
113	#476	C₂²	1	1	yes	characteristic
114	#476	C₂²	1	1	yes	characteristic
115	#476	C₂²	1	1	yes	characteristic
116	#476	C₂²	1	1	yes	characteristic
117	#475	C₂²	1	1	yes	characteristic
118	#475	C₂²	1	1	yes	characteristic
119	#475	C₂²	1	1	yes	characteristic
120	#475	C₂²	1	1	yes	characteristic
121	#474	C₂²	1	1	yes	characteristic
122	#474	C₂²	1	1	yes	characteristic
123	#474	C₂²	1	1	yes	characteristic
124	#474	C₂²	1	1	yes	characteristic
125	#470	C₂²	1	1	yes	characteristic
126	#470	C₂²	1	1	yes	characteristic
127	#469	C₂²	1	1	yes	characteristic
128	#469	C₂²	1	1	yes	characteristic
129	#468	C₂²	1	1	yes	characteristic
130	#468	C₂²	1	1	yes	characteristic
131	#468	C₂²	1	1	yes	characteristic
132	#468	C₂²	1	1	yes	characteristic
133	#467	C₂²	1	1	yes	characteristic
134	#467	C₂²	1	1	yes	characteristic
135	#466	C₂²	1	1	yes	characteristic
136	#466	C₂²	1	1	yes	characteristic
137	#465	C₂²	1	1	yes	characteristic
138	#465	C₂²	1	1	yes	characteristic
139	#465	C₂²	1	1	yes	characteristic
140	#465	C₂²	1	1	yes	characteristic
141	#464	C₂²	1	1	yes	characteristic
142	#464	C₂²	1	1	yes	characteristic
143	#464	C₂²	1	1	yes	characteristic
144	#464	C₂²	1	1	yes	characteristic
145	#464	C₂²	1	1	yes	characteristic
146	#464	C₂²	1	1	yes	characteristic
147	#464	C₂²	1	1	yes	characteristic
148	#464	C₂²	1	1	yes	characteristic
149	#463	C₂²	1	1	yes	characteristic
150	#463	C₂²	1	1	yes	characteristic
151	#463	C₂²	1	1	yes	characteristic
152	#463	C₂²	1	1	yes	characteristic
153	#463	C₂²	1	1	yes	characteristic
154	#463	C₂²	1	1	yes	characteristic
155	#463	C₂²	1	1	yes	characteristic
156	#463	C₂²	1	1	yes	characteristic
157	#462	C₂²	1	1	yes	characteristic
158	#462	C₂²	1	1	yes	characteristic
159	#461	C₂²	1	1	yes	characteristic
160	#461	C₂²	1	1	yes	characteristic
161	#460	C₂²	1	1	yes	characteristic
162	#460	C₂²	1	1	yes	characteristic
163	#459	C₂²	1	1	yes	characteristic
164	#459	C₂²	1	1	yes	characteristic
165	#446	C₂²	1	1	yes	characteristic
166	#446	C₂²	1	1	yes	characteristic
167	#446	C₂²	1	1	yes	characteristic
168	#446	C₂²	1	1	yes	characteristic
169	#446	C₂²	1	1	yes	characteristic
170	#446	C₂²	1	1	yes	characteristic
171	#446	C₂²	1	1	yes	characteristic
172	#446	C₂²	1	1	yes	characteristic
173	#442	C₂²	1	1	yes	characteristic
174	#442	C₂²	1	1	yes	characteristic
175	#442	C₂²	1	1	yes	characteristic
176	#442	C₂²	1	1	yes	characteristic
177	#441	C₂²	1	1	yes	characteristic
178	#441	C₂²	1	1	yes	characteristic
179	#441	C₂²	1	1	yes	characteristic
180	#441	C₂²	1	1	yes	characteristic
181	#440	C₂²	1	1	yes	characteristic
182	#440	C₂²	1	1	yes	characteristic
183	#440	C₂²	1	1	yes	characteristic
184	#440	C₂²	1	1	yes	characteristic
185	#440	C₂²	1	1	yes	characteristic
186	#440	C₂²	1	1	yes	characteristic
187	#440	C₂²	1	1	yes	characteristic
188	#440	C₂²	1	1	yes	characteristic
189	C₄×Q₁₆	C₂²	1	1	yes	characteristic
190	C₄×Q₁₆	C₂²	1	1	yes	characteristic
191	C₄×SD₁₆	C₂²	1	1	yes	characteristic
192	C₄×SD₁₆	C₂²	1	1	yes	characteristic
193	C₄×SD₁₆	C₂²	1	1	yes	characteristic
194	C₄×SD₁₆	C₂²	1	1	yes	characteristic
195	C₄×D₈	C₂²	1	1	yes	characteristic
196	C₄×D₈	C₂²	1	1	yes	characteristic
197	#424	C₂²	1	1	yes	characteristic
198	#424	C₂²	1	1	yes	characteristic
199	#423	C₂²	1	1	yes	characteristic
200	#405	C₂²	1	1	yes	characteristic
201	#405	C₂²	1	1	yes	characteristic
202	C₂×#97	C₂²	1	1	yes	characteristic
203	C₂×#41	—	2	1	no	—
204	C₂²×Q₈	—	2	1	no	—
205	C₂²×Q₈	—	2	1	no	—
206	C₂×Q₁₆	C₂³	1	1	yes	characteristic
207	C₂×Q₁₆	C₂³	1	1	yes	characteristic
208	C₂×Q₁₆	C₂³	1	1	yes	characteristic
209	C₂×Q₁₆	C₂³	1	1	yes	characteristic
210	C₂×SD₁₆	C₂³	1	1	yes	characteristic
211	C₂×SD₁₆	C₂³	1	1	yes	characteristic
212	C₂×SD₁₆	C₂³	1	1	yes	characteristic
213	C₂×SD₁₆	C₂³	1	1	yes	characteristic
214	C₂×SD₁₆	C₂³	1	1	yes	characteristic
215	C₂×SD₁₆	C₂³	1	1	yes	characteristic
216	C₂×SD₁₆	C₂³	1	1	yes	characteristic
217	C₂×SD₁₆	C₂³	1	1	yes	characteristic
218	C₂×D₈	C₂³	1	1	yes	characteristic
219	C₂×D₈	C₂³	1	1	yes	characteristic
220	C₂×D₈	C₂³	1	1	yes	characteristic
221	C₂×D₈	C₂³	1	1	yes	characteristic
222	C₂×M₁₆	C₂³	1	1	yes	characteristic
223	C₂×M₁₆	C₂³	1	1	yes	characteristic
224	C₂²×C₈	C₂³	1	1	yes	characteristic
225	C₂²×C₈	C₂³	1	1	yes	characteristic
226	C₄⋊Q₈	—	2	1	no	—
227	C₄⋊Q₈	—	2	1	no	—
228	C₄⋊Q₈	—	2	1	no	—
229	C₄⋊Q₈	—	2	1	no	—
230	C₄⋊Q₈	—	2	1	no	—
231	C₄⋊Q₈	—	2	1	no	—
232	C₄⋊Q₈	—	2	1	no	—
233	C₄⋊Q₈	—	2	1	no	—
234	C₄⋊Q₈	D₄	1	1	yes	characteristic
235	C₄⋊Q₈	D₄	1	1	yes	characteristic
236	C₄⋊Q₈	C₂³	1	1	yes	characteristic
237	C₄⋊Q₈	C₂³	1	1	yes	characteristic
238	C₄⋊Q₈	C₂³	1	1	yes	characteristic
239	C₄⋊Q₈	C₂³	1	1	yes	characteristic
240	C₄⋊Q₈	C₂³	1	1	yes	characteristic
241	C₄⋊Q₈	C₂³	1	1	yes	characteristic
242	C₄⋊Q₈	C₂³	1	1	yes	characteristic
243	C₄⋊Q₈	C₂³	1	1	yes	characteristic
244	C₄⋊Q₈	C₂³	1	1	yes	characteristic
245	C₄⋊Q₈	C₂³	1	1	yes	characteristic
246	#127	C₂³	1	1	yes	characteristic
247	#127	C₂³	1	1	yes	characteristic
248	#126	—	2	1	no	—
249	#126	—	2	1	no	—
250	#126	—	2	1	no	—
251	#126	—	2	1	no	—
252	#126	—	2	1	no	—
253	#126	—	2	1	no	—
254	#126	—	2	1	no	—
255	#126	—	2	1	no	—
256	#126	—	2	1	no	—
257	#126	—	2	1	no	—
258	#126	—	2	1	no	—
259	#126	—	2	1	no	—
260	#126	—	2	1	no	—
261	#126	—	2	1	no	—
262	#126	—	2	1	no	—
263	#126	—	2	1	no	—
264	#126	—	2	1	no	—
265	#126	—	2	1	no	—
266	#125	—	2	1	no	—
267	#125	—	2	1	no	—
268	#125	—	2	1	no	—
269	#125	—	2	1	no	—
270	#125	—	2	1	no	—
271	#125	—	2	1	no	—
272	#125	—	2	1	no	—
273	#125	D₄	1	1	yes	characteristic
274	#125	D₄	1	1	yes	characteristic
275	#125	C₂³	1	1	yes	characteristic
276	#125	C₂³	1	1	yes	characteristic
277	#125	C₂³	1	1	yes	characteristic
278	#125	C₂³	1	1	yes	characteristic
279	#124	—	2	1	no	—
280	#124	—	2	1	no	—
281	#124	—	2	1	no	—
282	#124	—	2	1	no	—
283	#124	—	2	1	no	—
284	#124	—	2	1	no	—
285	#124	—	2	1	no	—
286	#124	—	2	1	no	—
287	#124	—	2	1	no	—
288	#124	—	2	1	no	—
289	#124	—	2	1	no	—
290	#124	C₂³	1	1	yes	characteristic
291	#124	C₂³	1	1	yes	characteristic
292	#124	C₂³	1	1	yes	characteristic
293	#124	C₂³	1	1	yes	characteristic
294	#124	C₂³	1	1	yes	characteristic
295	#124	C₂³	1	1	yes	characteristic
296	#124	C₂³	1	1	yes	characteristic
297	#124	C₂³	1	1	yes	characteristic
298	#123	—	2	1	no	—
299	#123	—	2	1	no	—
300	#123	—	2	1	no	—
301	#123	—	2	1	no	—
302	#123	—	2	1	no	—
303	#123	—	2	1	no	—
304	#123	—	2	1	no	—
305	#123	—	2	1	no	—
306	#123	—	2	1	no	—
307	#123	—	2	1	no	—
308	#123	—	2	1	no	—
309	#123	—	2	1	no	—
310	#123	—	2	1	no	—
311	#123	—	2	1	no	—
312	#123	—	2	1	no	—
313	#123	—	2	1	no	—
314	#123	—	2	1	no	—
315	#123	—	2	1	no	—
316	C₂²⋊Q₈	—	2	1	no	—
317	C₂²⋊Q₈	—	2	1	no	—
318	C₂²⋊Q₈	—	2	1	no	—
319	C₂²⋊Q₈	—	2	1	no	—
320	C₂²⋊Q₈	—	2	1	no	—
321	C₂²⋊Q₈	—	2	1	no	—
322	C₂²⋊Q₈	—	2	1	no	—
323	C₂²⋊Q₈	—	2	1	no	—
324	C₂²⋊Q₈	—	2	1	no	—
325	C₂²⋊Q₈	—	2	1	no	—
326	C₂²⋊Q₈	—	2	1	no	—
327	C₂²⋊Q₈	—	2	1	no	—
328	C₂²⋊Q₈	—	2	1	no	—
329	C₂²⋊Q₈	—	2	1	no	—
330	C₂²⋊Q₈	—	2	1	no	—
331	C₂²⋊Q₈	—	2	1	no	—
332	C₂²⋊Q₈	—	2	1	no	—
333	C₂²⋊Q₈	—	2	1	no	—
334	C₂²⋊Q₈	—	2	1	no	—
335	C₂²⋊Q₈	—	2	1	no	—
336	C₂²⋊Q₈	—	2	1	no	—
337	C₂²⋊Q₈	—	2	1	no	—
338	C₂²⋊Q₈	—	2	1	no	—
339	C₂²⋊Q₈	D₄	1	1	yes	characteristic
340	C₂²⋊Q₈	D₄	1	1	yes	characteristic
341	C₂²⋊Q₈	D₄	1	1	yes	characteristic
342	C₂²⋊Q₈	D₄	1	1	yes	characteristic
343	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
344	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
345	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
346	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
347	#121	—	2	1	no	—
348	#121	—	2	1	no	—
349	#121	—	2	1	no	—
350	#121	C₂³	1	1	yes	characteristic
351	#121	C₂³	1	1	yes	characteristic
352	#121	C₂³	1	1	yes	characteristic
353	#121	C₂³	1	1	yes	characteristic
354	C₄×Q₈	—	2	1	no	—
355	C₄×Q₈	—	2	1	no	—
356	C₄×Q₈	—	2	1	no	—
357	C₄×Q₈	—	2	1	no	—
358	C₄×Q₈	—	2	1	no	—
359	C₄×Q₈	C₂³	1	1	yes	characteristic
360	C₄×Q₈	C₂³	1	1	yes	characteristic
361	C₄×Q₈	C₂³	1	1	yes	characteristic
362	C₄×Q₈	C₂³	1	1	yes	characteristic
363	C₄×Q₈	C₂³	1	1	yes	characteristic
364	C₄×Q₈	C₂³	1	1	yes	characteristic
365	C₄×Q₈	C₂³	1	1	yes	characteristic
366	C₄×Q₈	C₂³	1	1	yes	characteristic
367	C₄×Q₈	C₂³	1	1	yes	characteristic
368	C₄×Q₈	C₂³	1	1	yes	characteristic
369	C₄×Q₈	C₂³	1	1	yes	characteristic
370	C₄×Q₈	C₂³	1	1	yes	characteristic
371	C₄×Q₈	C₂³	1	1	yes	characteristic
372	C₄×Q₈	C₂³	1	1	yes	characteristic
373	C₄×Q₈	C₂³	1	1	yes	characteristic
374	C₄×Q₈	C₂³	1	1	yes	characteristic
375	C₄×D₄	—	2	1	no	—
376	C₄×D₄	—	2	1	no	—
377	C₄×D₄	—	2	1	no	—
378	C₄×D₄	—	2	1	no	—
379	C₄×D₄	—	2	1	no	—
380	C₄×D₄	—	2	1	no	—
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	C₂³	1	1	yes	characteristic
383	C₄×D₄	C₂³	1	1	yes	characteristic
384	C₄×D₄	C₂³	1	1	yes	characteristic
385	C₄×D₄	C₂³	1	1	yes	characteristic
386	C₄×D₄	C₂³	1	1	yes	characteristic
387	C₄×D₄	C₂³	1	1	yes	characteristic
388	C₄×D₄	C₂³	1	1	yes	characteristic
389	C₄×D₄	C₂³	1	1	yes	characteristic
390	C₄×D₄	C₂³	1	1	yes	characteristic
391	C₄×D₄	C₂³	1	1	yes	characteristic
392	C₄×D₄	C₂³	1	1	yes	characteristic
393	C₄×D₄	C₂³	1	1	yes	characteristic
394	#117	—	2	1	no	—
395	#117	—	2	1	no	—
396	#117	—	2	1	no	—
397	#117	—	2	1	no	—
398	#117	—	2	1	no	—
399	#117	—	2	1	no	—
400	#117	—	2	1	no	—
401	#117	C₂³	1	1	yes	characteristic
402	#117	C₂³	1	1	yes	characteristic
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄²	C₂³	1	1	yes	characteristic
406	#107	C₂³	1	1	yes	characteristic
407	#107	C₂³	1	1	yes	characteristic
408	#107	C₂³	1	1	yes	characteristic
409	#107	C₂³	1	1	yes	characteristic
410	#107	C₂³	1	1	yes	characteristic
411	#107	C₂³	1	1	yes	characteristic
412	#107	C₂³	1	1	yes	characteristic
413	#107	C₂³	1	1	yes	characteristic
414	#106	C₂³	1	1	yes	characteristic
415	#106	C₂³	1	1	yes	characteristic
416	#106	C₂³	1	1	yes	characteristic
417	#106	C₂³	1	1	yes	characteristic
418	#106	C₂³	1	1	yes	characteristic
419	#106	C₂³	1	1	yes	characteristic
420	#106	C₂³	1	1	yes	characteristic
421	#106	C₂³	1	1	yes	characteristic
422	C₄⋊C₈	C₂³	1	1	yes	characteristic
423	C₄⋊C₈	C₂³	1	1	yes	characteristic
424	C₄⋊C₈	C₂³	1	1	yes	characteristic
425	C₄⋊C₈	C₂³	1	1	yes	characteristic
426	C₄⋊C₈	C₂³	1	1	yes	characteristic
427	C₄⋊C₈	C₂³	1	1	yes	characteristic
428	C₄⋊C₈	C₂³	1	1	yes	characteristic
429	C₄⋊C₈	C₂³	1	1	yes	characteristic
430	C₄⋊C₈	C₂³	1	1	yes	characteristic
431	C₄⋊C₈	C₂³	1	1	yes	characteristic
432	C₄⋊C₈	C₂³	1	1	yes	characteristic
433	C₄⋊C₈	C₂³	1	1	yes	characteristic
434	#103	C₂³	1	1	yes	characteristic
435	#103	C₂³	1	1	yes	characteristic
436	#103	C₂³	1	1	yes	characteristic
437	#103	C₂³	1	1	yes	characteristic
438	#103	C₂³	1	1	yes	characteristic
439	#103	C₂³	1	1	yes	characteristic
440	#103	C₂³	1	1	yes	characteristic
441	#103	C₂³	1	1	yes	characteristic
442	#103	C₂³	1	1	yes	characteristic
443	#103	C₂³	1	1	yes	characteristic
444	#103	C₂³	1	1	yes	characteristic
445	#103	C₂³	1	1	yes	characteristic
446	#103	C₂³	1	1	yes	characteristic
447	#103	C₂³	1	1	yes	characteristic
448	#103	C₂³	1	1	yes	characteristic
449	#103	C₂³	1	1	yes	characteristic
450	#102	C₂³	1	1	yes	characteristic
451	#102	C₂³	1	1	yes	characteristic
452	#102	C₂³	1	1	yes	characteristic
453	#102	C₂³	1	1	yes	characteristic
454	#102	C₂³	1	1	yes	characteristic
455	#102	C₂³	1	1	yes	characteristic
456	#102	C₂³	1	1	yes	characteristic
457	#102	C₂³	1	1	yes	characteristic
458	#102	C₂³	1	1	yes	characteristic
459	#102	C₂³	1	1	yes	characteristic
460	#102	C₂³	1	1	yes	characteristic
461	#102	C₂³	1	1	yes	characteristic
462	#102	C₂³	1	1	yes	characteristic
463	#102	C₂³	1	1	yes	characteristic
464	#102	C₂³	1	1	yes	characteristic
465	#102	C₂³	1	1	yes	characteristic
466	#97	C₂³	1	1	yes	characteristic
467	#97	C₂³	1	1	yes	characteristic
468	#97	C₂³	1	1	yes	characteristic
469	#97	C₂³	1	1	yes	characteristic
470	#97	C₂³	1	1	yes	characteristic
471	#97	C₂³	1	1	yes	characteristic
472	#97	C₂³	1	1	yes	characteristic
473	#97	C₂³	1	1	yes	characteristic
474	C₄×C₈	C₂³	1	1	yes	characteristic
475	C₄×C₈	C₂³	1	1	yes	characteristic
476	C₄×C₈	C₂³	1	1	yes	characteristic
477	C₄×C₈	C₂³	1	1	yes	characteristic
478	#41	—	8	2	no	—
479	C₂×Q₈	—	2	1	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	—	2	1	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	8	2	no	—
488	C₂×Q₈	—	8	2	no	—
489	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
490	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
491	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
492	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
493	C₂×Q₈	C₂⁴	1	1	yes	characteristic
494	C₂×Q₈	C₂⁴	1	1	yes	characteristic
495	C₂×Q₈	C₂⁴	1	1	yes	characteristic
496	C₂×Q₈	C₂⁴	1	1	yes	characteristic
497	C₂×D₄	—	2	1	no	—
498	C₂×D₄	—	2	1	no	—
499	C₂×D₄	—	2	1	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	C₂⁴	1	1	yes	characteristic
506	C₂×D₄	C₂⁴	1	1	yes	characteristic
507	C₂×D₄	C₂⁴	1	1	yes	characteristic
508	C₂×D₄	C₂⁴	1	1	yes	characteristic
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
522	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
523	C₂²×C₄	C₂⁴	1	1	yes	characteristic
524	Q₁₆	—	2	2	no	—
525	Q₁₆	—	4	1	no	—
526	Q₁₆	—	4	1	no	—
527	Q₁₆	—	4	1	no	—
528	SD₁₆	—	2	2	no	—
529	SD₁₆	—	2	2	no	—
530	SD₁₆	—	4	1	no	—
531	SD₁₆	—	4	1	no	—
532	SD₁₆	—	4	1	no	—
533	SD₁₆	—	4	1	no	—
534	SD₁₆	—	4	1	no	—
535	SD₁₆	—	4	1	no	—
536	D₈	—	2	2	no	—
537	D₈	—	4	1	no	—
538	D₈	—	4	1	no	—
539	D₈	—	4	1	no	—
540	M₁₆	—	4	1	no	—
541	M₁₆	—	4	1	no	—
542	C₂×C₈	—	2	2	no	—
543	C₂×C₈	—	4	1	no	—
544	C₂×C₈	C₂⁴	1	1	yes	characteristic
545	C₂×C₈	C₂⁴	1	1	yes	characteristic
546	C₂×C₈	C₂⁴	1	1	yes	characteristic
547	C₂×C₈	C₂⁴	1	1	yes	characteristic
548	C₂×C₈	C₂⁴	1	1	yes	characteristic
549	C₂×C₈	C₂⁴	1	1	yes	characteristic
550	C₂×C₈	C₂⁴	1	1	yes	characteristic
551	C₂×C₈	C₂⁴	1	1	yes	characteristic
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	—	2	1	no	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	—	2	1	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	2	1	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
589	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
590	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
591	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
592	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
593	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
594	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
595	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
596	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
597	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
598	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
599	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
600	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
601	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
602	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
603	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
604	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
605	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
606	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
607	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
608	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
609	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
610	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
611	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
612	C₂²⋊C₄	—	2	1	no	—
613	C₂²⋊C₄	—	2	1	no	—
614	C₂²⋊C₄	—	2	1	no	—
615	C₂²⋊C₄	—	2	1	no	—
616	C₂²⋊C₄	—	2	1	no	—
617	C₂²⋊C₄	—	2	1	no	—
618	C₂²⋊C₄	—	2	1	no	—
619	C₂²⋊C₄	—	2	1	no	—
620	C₂²⋊C₄	—	2	1	no	—
621	C₂²⋊C₄	—	2	1	no	—
622	C₂²⋊C₄	—	2	1	no	—
623	C₂²⋊C₄	—	2	1	no	—
624	C₂²⋊C₄	—	2	1	no	—
625	C₂²⋊C₄	—	2	1	no	—
626	C₂²⋊C₄	—	2	1	no	—
627	C₂²⋊C₄	—	2	1	no	—
628	C₂²⋊C₄	—	2	1	no	—
629	C₂²⋊C₄	—	2	1	no	—
630	C₂²⋊C₄	—	2	1	no	—
631	C₂²⋊C₄	—	2	1	no	—
632	C₂²⋊C₄	—	2	1	no	—
633	C₂²⋊C₄	—	2	1	no	—
634	C₂²⋊C₄	—	2	1	no	—
635	C₂²⋊C₄	—	2	1	no	—
636	C₂²⋊C₄	—	2	1	no	—
637	C₂²⋊C₄	—	2	1	no	—
638	C₂²⋊C₄	—	2	1	no	—
639	C₂²⋊C₄	—	2	1	no	—
640	C₂²⋊C₄	—	2	1	no	—
641	C₂²⋊C₄	—	2	1	no	—
642	C₂²⋊C₄	—	2	1	no	—
643	C₂²⋊C₄	—	2	1	no	—
644	C₂²⋊C₄	—	2	1	no	—
645	C₂²⋊C₄	—	2	1	no	—
646	C₂²⋊C₄	—	2	1	no	—
647	C₂²⋊C₄	—	2	1	no	—
648	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
649	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
650	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
651	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
652	C₄²	—	2	1	no	—
653	C₄²	—	2	1	no	—
654	C₄²	—	2	1	no	—
655	C₄²	—	2	1	no	—
656	C₄²	—	2	1	no	—
657	C₄²	—	2	1	no	—
658	C₄²	—	2	1	no	—
659	C₄²	—	2	1	no	—
660	C₄²	—	2	1	no	—
661	C₄²	—	2	1	no	—
662	C₄²	—	2	1	no	—
663	C₄²	—	2	1	no	—
664	C₄²	C₂×D₄	1	1	yes	characteristic
665	C₄²	C₂×D₄	1	1	yes	characteristic
666	C₄²	C₂⁴	1	1	yes	characteristic
667	C₄²	C₂⁴	1	1	yes	characteristic
668	C₄²	C₂⁴	1	1	yes	characteristic
669	C₄²	C₂⁴	1	1	yes	characteristic
670	C₄²	C₂⁴	1	1	yes	characteristic
671	C₄²	C₂⁴	1	1	yes	characteristic
672	C₂³	—	2	1	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	1	no	—
675	C₂³	—	2	1	no	—
676	C₂³	C₂²×D₄	1	1	yes	characteristic
677	Q₈	—	2	1	no	—
678	Q₈	—	2	1	no	—
679	Q₈	—	2	1	no	—
680	Q₈	—	2	1	no	—
681	Q₈	—	2	1	no	—
682	Q₈	—	2	1	no	—
683	Q₈	—	2	1	no	—
684	Q₈	—	2	1	no	—
685	Q₈	—	4	1	no	—
686	Q₈	—	4	1	no	—
687	Q₈	—	4	1	no	—
688	Q₈	—	4	1	no	—
689	Q₈	—	4	2	no	—
690	Q₈	—	8	1	no	—
691	Q₈	—	8	1	no	—
692	Q₈	—	8	1	no	—
693	Q₈	—	8	1	no	—
694	Q₈	—	8	1	no	—
695	Q₈	—	8	1	no	—
696	Q₈	—	8	1	no	—
697	D₄	—	2	1	no	—
698	D₄	—	2	1	no	—
699	D₄	—	2	1	no	—
700	D₄	—	2	1	no	—
701	D₄	—	2	1	no	—
702	D₄	—	2	1	no	—
703	D₄	—	2	1	no	—
704	D₄	—	2	1	no	—
705	D₄	—	4	2	no	—
706	D₄	—	8	1	no	—
707	D₄	—	8	1	no	—
708	D₄	—	8	1	no	—
709	D₄	—	8	1	no	—
710	D₄	—	8	1	no	—
711	D₄	—	8	1	no	—
712	D₄	—	8	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	2	no	—
730	C₂×C₄	—	4	2	no	—
731	C₂×C₄	—	8	1	no	—
732	C₂×C₄	—	8	1	no	—
733	C₂×C₄	—	8	1	no	—
734	C₂×C₄	—	8	1	no	—
735	C₂×C₄	—	8	1	no	—
736	C₂×C₄	—	8	1	no	—
737	C₂×C₄	—	8	1	no	—
738	C₂×C₄	—	8	1	no	—
739	C₂×C₄	—	8	1	no	—
740	C₂×C₄	—	8	1	no	—
741	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
742	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
743	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
744	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
745	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
746	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
747	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
748	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
749	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
750	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
751	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
752	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
753	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
754	C₂×C₄	C₂⁵	1	1	yes	characteristic
755	C₈	—	2	1	no	—
756	C₈	—	2	1	no	—
757	C₈	—	2	1	no	—
758	C₈	—	2	1	no	—
759	C₈	—	2	1	no	—
760	C₈	—	2	1	no	—
761	C₈	—	2	1	no	—
762	C₈	2₋¹⁺⁴	1	2	yes	—
763	C₂²	—	2	1	no	—
764	C₂²	—	2	1	no	—
765	C₂²	—	2	1	no	—
766	C₂²	—	4	1	no	—
767	C₂²	—	4	1	no	—
768	C₂²	—	4	1	no	—
769	C₂²	—	4	1	no	—
770	C₂²	—	4	1	no	—
771	C₂²	—	4	1	no	—
772	C₂²	—	4	1	no	—
773	C₂²	—	4	1	no	—
774	C₂²	—	4	1	no	—
775	C₂²	—	4	1	no	—
776	C₂²	—	4	1	no	—
777	C₂²	—	4	1	no	—
778	C₂²	C₂³×D₄	1	1	yes	characteristic
779	C₄	—	2	1	no	—
780	C₄	—	2	1	no	—
781	C₄	—	2	1	no	—
782	C₄	—	2	1	no	—
783	C₄	—	2	1	no	—
784	C₄	—	2	1	no	—
785	C₄	—	2	1	no	—
786	C₄	—	2	1	no	—
787	C₄	—	2	1	no	—
788	C₄	—	2	1	no	—
789	C₄	—	2	1	no	—
790	C₄	—	2	1	no	—
791	C₄	—	2	1	no	—
792	C₄	—	4	1	no	—
793	C₄	—	4	1	no	—
794	C₄	—	4	1	no	—
795	C₄	—	4	1	no	—
796	C₄	—	4	1	no	—
797	C₄	—	4	1	no	—
798	C₄	—	4	1	no	—
799	C₄	—	4	1	no	—
800	C₄	—	4	1	no	—
801	C₄	—	4	1	no	—
802	C₄	—	4	1	no	—
803	C₄	—	4	1	no	—
804	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
805	C₄	#585	1	1	yes	characteristic
806	C₂	—	4	1	no	—
807	C₂	—	8	1	no	—
808	C₂	—	8	1	no	—
809	C₂	—	8	1	no	—
810	C₂	—	8	1	no	—
811	C₂	#3497	1	1	yes	characteristic
812	C₂	#3585	1	1	yes	characteristic
813	C₂	#3586	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 ◁ #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. #3557	C₂	semidirect
2. #3550	C₂	semidirect
3. #3403	C₂	semidirect
4. #3402	C₂	semidirect
5. #3401	C₂	semidirect
6. #3401	C₂	semidirect
7. #3387	C₂	semidirect
8. #3386	C₂	semidirect
9. #3385	C₂	semidirect
10. #3384	C₂	semidirect
11. #3377	C₂	semidirect
12. #3376	C₂	semidirect
13. #3375	C₂	semidirect
14. #3373	C₂	semidirect
15. #3371	C₂	semidirect
16. #3370	C₂	semidirect
17. #3369	C₂	semidirect
18. #3367	C₂	semidirect
19. #3263	C₂	semidirect
20. #3262	C₂	semidirect
21. #3258	C₂	semidirect
22. #3257	C₂	semidirect
23. #3252	C₂	semidirect
24. #3251	C₂	semidirect
25. #3181	C₂	semidirect
26. #3180	C₂	semidirect
27. #3179	C₂	semidirect
28. #3178	C₂	semidirect
29. #3175	C₂	semidirect
30. #3173	C₂	semidirect
31. #2961	C₂	semidirect

Maximal subgroups

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

subgroup	index
#3557	2
#3550	2
#3403	2
#3402	2
#3401	2
#3387	2
#3386	2
#3385	2
#3384	2
#3377	2
#3376	2
#3375	2
#3373	2
#3371	2
#3370	2
#3369	2
#3367	2
#3263	2
#3262	2
#3258	2
#3257	2
#3252	2
#3251	2
#3181	2
#3180	2
#3179	2
#3178	2
#3175	2
#3173	2
#2961	2