Subgroups — #61437

Order 256.

1063 conjugacy classes of subgroups.

The subgroup lattice has 607 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3475	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	#3367	C₂	1	1	yes	maximal, characteristic, complemented
6	#3366	C₂	1	1	yes	maximal, characteristic, complemented
7	#3354	C₂	1	1	yes	maximal, characteristic, complemented
8	#3343	C₂	1	2	yes	maximal, complemented
9	#3330	C₂	1	1	yes	maximal, characteristic, complemented
10	#3325	C₂	1	1	yes	maximal, characteristic, complemented
11	#3310	C₂	1	2	yes	maximal, complemented
12	#3306	C₂	1	2	yes	maximal, complemented
13	#3272	C₂	1	1	yes	maximal, characteristic, complemented
14	#3264	C₂	1	2	yes	maximal, complemented
15	#3171	C₂	1	2	yes	maximal, complemented
16	#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	#3106	C₂	1	2	yes	maximal, complemented
18	#3105	C₂	1	2	yes	maximal, complemented
19	#3101	C₂	1	1	yes	maximal, characteristic, complemented
20	#3100	C₂	1	1	yes	maximal, characteristic, complemented
21	#2965	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
23	C₂×C₄×D₈	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41	—	2	1	no	—
25	C₂×AGL(1,ℤ/8)	C₂²	1	2	yes	—
26	C₂²×D₈	C₂²	1	1	yes	characteristic
27	#556	C₂²	1	1	yes	characteristic, complemented
28	#555	C₂²	1	1	yes	characteristic, complemented
29	#554	C₂²	1	1	yes	characteristic, complemented
30	#553	—	2	1	no	—
31	#552	—	2	1	no	—
32	#552	C₂²	1	2	yes	complemented
33	#551	—	2	2	no	—
34	#550	C₂²	1	1	yes	characteristic, complemented
35	D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
36	#548	—	2	1	no	—
37	#547	C₂²	1	2	yes	—
38	#547	C₂²	1	1	yes	characteristic, complemented
39	#547	C₂²	1	1	yes	characteristic, complemented
40	#546	—	2	2	no	—
41	#546	—	2	1	no	—
42	#546	C₂²	1	2	yes	complemented
43	D₄²	C₂²	1	2	yes	—
44	D₄²	C₂²	1	1	yes	characteristic, complemented
45	#533	C₂²	1	1	yes	characteristic, complemented
46	#532	C₂²	1	1	yes	characteristic
47	#532	C₂²	1	2	yes	complemented
48	#529	—	2	2	no	—
49	#529	C₂²	1	2	yes	complemented
50	#525	—	2	1	no	—
51	#525	—	2	1	no	—
52	#525	—	2	2	no	—
53	C₄×#41	C₂²	1	1	yes	characteristic
54	C₄×#41	C₂²	1	2	yes	complemented
55	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
56	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₄×D₄	C₂²	1	2	yes	complemented
58	C₂×#117	—	2	1	no	—
59	#501	C₂²	1	2	yes	complemented
60	#498	C₂²	1	1	yes	characteristic, complemented
61	#496	C₂²	1	2	yes	complemented
62	#492	C₂²	1	1	yes	characteristic, complemented
63	#490	C₂²	1	2	yes	complemented
64	#489	C₂²	1	2	yes	complemented
65	#487	C₂²	1	1	yes	characteristic, complemented
66	#486	C₂²	1	1	yes	characteristic, 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	2	yes	complemented
71	#481	C₂²	1	2	yes	complemented
72	#480	C₂²	1	2	yes	complemented
73	#478	C₂²	1	2	yes	complemented
74	#478	C₂²	1	2	yes	complemented
75	#477	C₂²	1	2	yes	complemented
76	#476	C₂²	1	1	yes	characteristic, complemented
77	#476	C₂²	1	1	yes	characteristic, complemented
78	#476	C₂²	1	2	yes	complemented
79	#474	C₂²	1	1	yes	characteristic, complemented
80	#474	C₂²	1	1	yes	characteristic, complemented
81	#469	C₂²	1	2	yes	complemented
82	#469	C₂²	1	2	yes	complemented
83	#468	C₂²	1	2	yes	complemented
84	#468	C₂²	1	2	yes	complemented
85	#465	C₂²	1	2	yes	complemented
86	#465	C₂²	1	2	yes	complemented
87	#463	C₂²	1	2	yes	—
88	#463	C₂²	1	2	yes	complemented
89	#461	C₂²	1	1	yes	characteristic, complemented
90	#461	C₂²	1	1	yes	characteristic, complemented
91	#460	C₂²	1	2	yes	complemented
92	#459	C₂²	1	1	yes	characteristic, complemented
93	#459	C₂²	1	1	yes	characteristic, complemented
94	#459	C₂²	1	2	yes	complemented
95	#450	C₂²	1	2	yes	—
96	#450	C₂²	1	2	yes	complemented
97	#449	C₂²	1	2	yes	complemented
98	#449	C₂²	1	2	yes	complemented
99	#447	C₂²	1	2	yes	—
100	#447	C₂²	1	2	yes	complemented
101	#446	C₂²	1	1	yes	characteristic, complemented
102	#446	C₂²	1	1	yes	characteristic, complemented
103	#442	C₂²	1	2	yes	—
104	#442	C₂²	1	2	yes	complemented
105	#440	C₂²	1	2	yes	complemented
106	#440	C₂²	1	2	yes	complemented
107	C₄×SD₁₆	C₂²	1	2	yes	complemented
108	C₄×SD₁₆	C₂²	1	2	yes	complemented
109	C₄×SD₁₆	C₂²	1	2	yes	complemented
110	C₄×SD₁₆	C₂²	1	2	yes	complemented
111	C₄×D₈	C₂²	1	1	yes	characteristic
112	C₄×D₈	C₂²	1	1	yes	characteristic
113	C₄×D₈	C₂²	1	1	yes	characteristic
114	C₄×D₈	C₂²	1	1	yes	characteristic
115	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
117	C₄×D₈	C₂²	1	2	yes	complemented
118	C₄×D₈	C₂²	1	2	yes	complemented
119	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
121	#436	C₂²	1	1	yes	characteristic, complemented
122	#436	C₂²	1	1	yes	characteristic, complemented
123	#435	C₂²	1	2	yes	complemented
124	#435	C₂²	1	2	yes	complemented
125	#431	C₂²	1	1	yes	characteristic, complemented
126	#431	C₂²	1	2	yes	complemented
127	#428	C₂²	1	2	yes	complemented
128	C₂×#107	C₂²	1	1	yes	characteristic, complemented
129	#418	C₂²	1	2	yes	complemented
130	#417	C₂²	1	2	yes	complemented
131	C₂×#102	C₂²	1	1	yes	characteristic
132	C₂×#102	C₂²	1	1	yes	characteristic, complemented
133	C₄×M₁₆	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41	—	2	1	no	—
136	C₂×#41	—	2	2	no	—
137	C₂×#41	—	2	1	no	—
138	C₂×#41	—	2	1	no	—
139	C₂×#41	—	2	2	no	—
140	C₂×#41	—	4	8	no	—
141	C₂×#41	D₄	1	1	yes	characteristic
142	C₂×#41	C₂³	1	2	yes	—
143	C₂²×Q₈	—	2	1	no	—
144	C₂²×D₄	—	2	2	no	—
145	C₂²×D₄	—	2	1	no	—
146	C₂²×D₄	C₂³	1	1	yes	characteristic
147	C₂²×D₄	C₂³	1	2	yes	—
148	C₂²×D₄	C₂³	1	1	yes	characteristic
149	C₂³×C₄	—	2	1	no	—
150	C₂³×C₄	—	2	1	no	—
151	C₂³×C₄	—	2	2	no	—
152	AGL(1,ℤ/8)	—	2	8	no	—
153	C₂×SD₁₆	C₂³	1	2	yes	—
154	C₂×SD₁₆	C₂³	1	2	yes	—
155	C₂×SD₁₆	C₂³	1	2	yes	—
156	C₂×SD₁₆	C₂³	1	2	yes	—
157	C₂×D₈	—	2	4	no	—
158	C₂×D₈	C₂³	1	1	yes	characteristic
159	C₂×D₈	C₂³	1	1	yes	characteristic
160	C₂×D₈	C₂³	1	1	yes	characteristic
161	C₂×D₈	C₂³	1	2	yes	—
162	C₂×D₈	C₂³	1	2	yes	—
163	C₂×D₈	C₂³	1	1	yes	characteristic
164	C₂×M₁₆	C₂³	1	2	yes	—
165	C₂×M₁₆	C₂³	1	2	yes	—
166	C₂²×C₈	C₂³	1	1	yes	characteristic
167	C₂²×C₈	C₂³	1	1	yes	characteristic
168	C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₄⋊Q₈	C₂³	1	2	yes	—
171	C₄⋊Q₈	C₂³	1	1	yes	characteristic
172	#127	C₂³	1	1	yes	characteristic
173	#127	C₂³	1	2	yes	—
174	#126	—	2	2	no	—
175	#126	—	2	2	no	—
176	#126	—	2	2	no	—
177	#125	—	2	2	no	—
178	#125	—	2	1	no	—
179	#125	C₂³	1	2	yes	—
180	#124	—	2	2	no	—
181	#124	—	2	1	no	—
182	#124	—	2	2	no	—
183	#124	C₂³	1	2	yes	—
184	#123	—	2	2	no	—
185	#123	—	2	2	no	—
186	#123	—	2	2	no	—
187	#123	—	2	2	no	—
188	#123	—	2	2	no	—
189	#123	—	2	2	no	—
190	#123	—	2	2	no	—
191	C₂²⋊Q₈	—	2	1	no	—
192	C₂²⋊Q₈	—	2	1	no	—
193	C₂²⋊Q₈	—	2	1	no	—
194	C₂²⋊Q₈	—	2	1	no	—
195	C₂²⋊Q₈	—	2	2	no	—
196	C₂²⋊Q₈	—	2	2	no	—
197	C₂²⋊Q₈	—	2	1	no	—
198	C₂²⋊Q₈	—	2	2	no	—
199	C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₂²⋊Q₈	C₂³	1	2	yes	—
201	#121	—	2	1	no	—
202	#121	—	2	1	no	—
203	#121	—	2	1	no	—
204	#121	—	2	2	no	—
205	#121	—	2	2	no	—
206	#121	—	2	1	no	—
207	#121	—	2	1	no	—
208	#121	—	2	2	no	—
209	#121	—	2	2	no	—
210	#121	C₂³	1	2	yes	—
211	#121	C₂³	1	2	yes	—
212	#121	C₂³	1	2	yes	—
213	#121	C₂³	1	2	yes	—
214	#120	—	2	2	no	—
215	#120	—	2	2	no	—
216	#120	—	2	2	no	—
217	#120	—	2	2	no	—
218	C₄×Q₈	—	2	1	no	—
219	C₄×Q₈	D₄	1	1	yes	characteristic
220	C₄×Q₈	C₂³	1	2	yes	—
221	C₄×Q₈	C₂³	1	2	yes	—
222	C₄×Q₈	C₂³	1	1	yes	characteristic
223	C₄×D₄	—	2	2	no	—
224	C₄×D₄	—	2	2	no	—
225	C₄×D₄	—	2	2	no	—
226	C₄×D₄	—	2	1	no	—
227	C₄×D₄	—	2	1	no	—
228	C₄×D₄	—	2	2	no	—
229	C₄×D₄	—	2	1	no	—
230	C₄×D₄	—	2	2	no	—
231	C₄×D₄	—	2	1	no	—
232	C₄×D₄	—	2	1	no	—
233	C₄×D₄	—	2	2	no	—
234	C₄×D₄	D₄	1	2	yes	—
235	C₄×D₄	D₄	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	1	yes	characteristic
239	C₄×D₄	C₂³	1	1	yes	characteristic
240	C₄×D₄	C₂³	1	1	yes	characteristic
241	C₄×D₄	C₂³	1	1	yes	characteristic
242	C₄×D₄	C₂³	1	2	yes	—
243	C₄×D₄	C₂³	1	2	yes	—
244	C₄×D₄	C₂³	1	2	yes	—
245	C₄×D₄	C₂³	1	1	yes	characteristic
246	C₄×D₄	C₂³	1	1	yes	characteristic
247	C₄×D₄	C₂³	1	2	yes	—
248	C₄×D₄	C₂³	1	2	yes	—
249	C₄×D₄	C₂³	1	1	yes	characteristic
250	#117	—	2	1	no	—
251	#117	—	2	1	no	—
252	#117	—	2	1	no	—
253	#117	—	2	2	no	—
254	#117	—	2	2	no	—
255	#117	—	2	2	no	—
256	#117	D₄	1	1	yes	characteristic
257	#117	D₄	1	2	yes	—
258	#117	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	1	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₄²	—	2	2	no	—
269	C₂×C₄²	C₂³	1	1	yes	characteristic
270	C₂×C₄²	C₂³	1	2	yes	—
271	#107	C₂³	1	1	yes	characteristic
272	#107	C₂³	1	1	yes	characteristic
273	#107	C₂³	1	1	yes	characteristic
274	#107	C₂³	1	1	yes	characteristic
275	#107	C₂³	1	2	yes	—
276	#107	C₂³	1	2	yes	—
277	#106	C₂³	1	2	yes	—
278	#106	C₂³	1	2	yes	—
279	#106	C₂³	1	2	yes	—
280	#106	C₂³	1	2	yes	—
281	C₄⋊C₈	C₂³	1	2	yes	—
282	C₄⋊C₈	C₂³	1	2	yes	—
283	C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₄⋊C₈	C₂³	1	1	yes	characteristic
285	#103	C₂³	1	2	yes	—
286	#103	C₂³	1	2	yes	—
287	#103	C₂³	1	2	yes	—
288	#103	C₂³	1	2	yes	—
289	#102	C₂³	1	1	yes	characteristic
290	#102	C₂³	1	1	yes	characteristic
291	#102	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	#102	C₂³	1	2	yes	—
303	#102	C₂³	1	2	yes	—
304	#102	C₂³	1	2	yes	—
305	C₂²⋊C₈	C₂³	1	2	yes	—
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	1	yes	characteristic
311	C₄×C₈	C₂³	1	1	yes	characteristic
312	C₄×C₈	C₂³	1	1	yes	characteristic
313	C₄×C₈	C₂³	1	1	yes	characteristic
314	C₄×C₈	C₂³	1	2	yes	—
315	C₂⁴	—	2	1	no	—
316	C₂⁴	—	2	2	no	—
317	C₂⁴	—	2	1	no	—
318	#41	—	2	4	no	—
319	#41	—	2	4	no	—
320	#41	—	4	2	no	—
321	#41	—	4	8	no	—
322	#41	—	4	8	no	—
323	#41	—	4	4	no	—
324	#41	—	4	4	no	—
325	#41	—	4	4	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	4	4	no	—
330	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈	C₂⁴	1	2	yes	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	4	1	no	—
348	C₂×D₄	—	4	1	no	—
349	C₂×D₄	—	4	2	no	—
350	C₂×D₄	—	4	8	no	—
351	C₂×D₄	—	4	4	no	—
352	C₂×D₄	C₂×D₄	1	2	yes	—
353	C₂×D₄	C₂×D₄	1	1	yes	characteristic
354	C₂×D₄	C₂⁴	1	1	yes	characteristic
355	C₂×D₄	C₂⁴	1	1	yes	characteristic
356	C₂×D₄	C₂⁴	1	2	yes	—
357	C₂×D₄	C₂⁴	1	1	yes	characteristic
358	C₂×D₄	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	4	8	no	—
376	C₂²×C₄	—	4	4	no	—
377	C₂²×C₄	—	4	4	no	—
378	C₂²×C₄	C₂×D₄	1	2	yes	—
379	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₄	1	2	yes	—
381	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
382	C₂²×C₄	C₂⁴	1	1	yes	characteristic
383	C₂²×C₄	C₂⁴	1	2	yes	—
384	SD₁₆	—	2	4	no	—
385	SD₁₆	—	2	4	no	—
386	SD₁₆	—	4	2	no	—
387	SD₁₆	—	4	2	no	—
388	D₈	—	2	2	no	—
389	D₈	—	2	2	no	—
390	D₈	—	2	4	no	—
391	D₈	—	2	2	no	—
392	D₈	—	4	2	no	—
393	D₈	#41	1	4	yes	complemented
394	M₁₆	—	2	4	no	—
395	M₁₆	—	4	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	4	1	no	—
398	C₂×C₈	C₂⁴	1	1	yes	characteristic
399	C₂×C₈	C₂⁴	1	1	yes	characteristic
400	C₂×C₈	C₂⁴	1	1	yes	characteristic
401	C₂×C₈	C₂⁴	1	2	yes	—
402	C₂×C₈	C₂⁴	1	2	yes	—
403	C₂×C₈	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
419	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
420	C₄⋊C₄	C₂×D₄	1	2	yes	—
421	C₄⋊C₄	C₂×D₄	1	2	yes	—
422	C₄⋊C₄	C₂⁴	1	2	yes	—
423	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
425	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
426	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
427	C₄⋊C₄	C₂⁴	1	2	yes	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	2	1	no	—
432	C₂²⋊C₄	—	2	1	no	—
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	1	no	—
437	C₂²⋊C₄	—	2	2	no	—
438	C₂²⋊C₄	—	2	1	no	—
439	C₂²⋊C₄	—	2	1	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	2	1	no	—
442	C₂²⋊C₄	—	2	1	no	—
443	C₂²⋊C₄	—	2	1	no	—
444	C₂²⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	C₂×D₄	1	2	yes	—
450	C₂²⋊C₄	C₂×D₄	1	2	yes	—
451	C₂²⋊C₄	C₂×D₄	1	2	yes	—
452	C₄²	—	2	2	no	—
453	C₄²	—	2	2	no	—
454	C₄²	—	2	2	no	—
455	C₄²	C₂×D₄	1	2	yes	—
456	C₄²	C₂×D₄	1	1	yes	characteristic
457	C₄²	C₂×D₄	1	2	yes	—
458	C₄²	C₂×D₄	1	1	yes	characteristic
459	C₄²	C₂⁴	1	1	yes	characteristic
460	C₄²	C₂⁴	1	2	yes	—
461	C₄²	C₂⁴	1	1	yes	characteristic
462	C₂³	—	2	1	no	—
463	C₂³	—	2	1	no	—
464	C₂³	—	2	1	no	—
465	C₂³	—	2	1	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	4	2	no	—
468	C₂³	—	4	2	no	—
469	C₂³	—	4	4	no	—
470	C₂³	—	4	4	no	—
471	C₂³	—	4	2	no	—
472	C₂³	—	4	2	no	—
473	C₂³	—	8	1	no	—
474	C₂³	—	8	1	no	—
475	C₂³	—	8	2	no	—
476	C₂³	C₂²×D₄	1	2	yes	—
477	C₂³	C₂²×D₄	1	1	yes	characteristic
478	Q₈	—	2	2	no	—
479	Q₈	—	2	2	no	—
480	Q₈	—	2	2	no	—
481	Q₈	—	4	4	no	—
482	Q₈	—	4	2	no	—
483	Q₈	—	8	1	no	—
484	D₄	—	2	4	no	—
485	D₄	—	2	2	no	—
486	D₄	—	2	1	no	—
487	D₄	—	2	1	no	—
488	D₄	—	2	2	no	—
489	D₄	—	2	1	no	—
490	D₄	—	2	1	no	—
491	D₄	—	2	1	no	—
492	D₄	—	2	2	no	—
493	D₄	—	2	1	no	—
494	D₄	—	4	4	no	—
495	D₄	—	4	2	no	—
496	D₄	—	4	2	no	—
497	D₄	—	4	4	no	—
498	D₄	—	4	4	no	—
499	D₄	—	4	4	no	—
500	D₄	—	4	4	no	—
501	D₄	—	4	4	no	—
502	D₄	—	4	2	no	—
503	D₄	—	8	2	no	—
504	D₄	—	8	1	no	—
505	D₄	—	8	2	no	—
506	D₄	C₂×#41	1	2	yes	—
507	D₄	C₂×#41	1	2	yes	complemented
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	4	no	—
523	C₂×C₄	—	4	4	no	—
524	C₂×C₄	—	4	4	no	—
525	C₂×C₄	—	4	4	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	4	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	8	2	no	—
538	C₂×C₄	AGL(1,ℤ/8)	1	4	yes	complemented
539	C₂×C₄	C₂²×D₄	1	2	yes	—
540	C₂×C₄	C₂²×D₄	1	2	yes	—
541	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
543	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
544	C₂×C₄	C₂²×D₄	1	2	yes	—
545	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
547	C₂×C₄	C₂⁵	1	1	yes	characteristic
548	C₈	—	2	1	no	—
549	C₈	—	2	2	no	—
550	C₈	—	2	1	no	—
551	C₈	—	2	1	no	—
552	C₈	—	2	2	no	—
553	C₈	C₂×#41	1	2	yes	complemented
554	C₂²	—	2	1	no	—
555	C₂²	—	2	1	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	2	2	no	—
559	C₂²	—	2	2	no	—
560	C₂²	—	2	2	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	1	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	1	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	4	2	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	1	no	—
570	C₂²	—	4	2	no	—
571	C₂²	—	4	2	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	8	4	no	—
575	C₂²	—	8	4	no	—
576	C₂²	—	8	8	no	—
577	C₂²	C₂×AGL(1,ℤ/8)	1	2	yes	—
578	C₂²	C₂³×D₄	1	1	yes	characteristic
579	C₄	—	2	1	no	—
580	C₄	—	2	2	no	—
581	C₄	—	2	1	no	—
582	C₄	—	2	2	no	—
583	C₄	—	2	1	no	—
584	C₄	—	2	2	no	—
585	C₄	—	4	2	no	—
586	C₄	—	4	2	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	2	no	—
591	C₄	—	4	1	no	—
592	C₄	C₂×AGL(1,ℤ/8)	1	2	yes	—
593	C₄	C₂×AGL(1,ℤ/8)	1	2	yes	—
594	C₄	C₂²×#41	1	1	yes	characteristic
595	C₄	#585	1	1	yes	characteristic
596	C₂	—	2	2	no	—
597	C₂	—	4	2	no	—
598	C₂	—	4	2	no	—
599	C₂	—	4	2	no	—
600	C₂	—	8	1	no	—
601	C₂	—	8	2	no	—
602	C₂	—	8	1	no	—
603	C₂	D₄×#41	1	1	yes	characteristic
604	C₂	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
605	C₂	#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
socle	C₂²	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ 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. #3475	C₂	semidirect
2. D₄×#41	C₂	semidirect
3. #3397	C₂	semidirect
4. #3384	C₂	semidirect
5. #3367	C₂	semidirect
6. #3366	C₂	semidirect
7. #3354	C₂	semidirect
8. #3343	C₂	semidirect
9. #3330	C₂	semidirect
10. #3325	C₂	semidirect
11. #3310	C₂	semidirect
12. #3306	C₂	semidirect
13. #3272	C₂	semidirect
14. #3264	C₂	semidirect
15. #3171	C₂	semidirect
16. #3167	C₂	semidirect
17. #3106	C₂	semidirect
18. #3105	C₂	semidirect
19. #3101	C₂	semidirect
20. #3100	C₂	semidirect
21. #2965	C₂	semidirect
22. C₄×AGL(1,ℤ/8)	C₂	semidirect
23. C₂×C₄×D₈	C₂	semidirect
27. #556	C₂²	semidirect
28. #555	C₂²	semidirect
29. #554	C₂²	semidirect
32. #552	C₂²	semidirect
34. #550	C₂²	semidirect
35. D₄×Q₈	C₂²	semidirect
38. #547	C₂²	semidirect
39. #547	C₂²	semidirect
42. #546	C₂²	semidirect
44. D₄²	C₂²	semidirect
45. #533	C₂²	semidirect
47. #532	C₂²	semidirect
49. #529	C₂²	semidirect
54. C₄×#41	C₂²	semidirect
56. C₂×C₄×D₄	C₂²	semidirect
57. C₂×C₄×D₄	C₂²	semidirect
59. #501	C₂²	semidirect
60. #498	C₂²	semidirect
61. #496	C₂²	semidirect
62. #492	C₂²	semidirect
63. #490	C₂²	semidirect
64. #489	C₂²	semidirect
65. #487	C₂²	semidirect
66. #486	C₂²	semidirect
67. #484	C₂²	semidirect
68. #483	C₂²	semidirect
69. #482	C₂²	semidirect
70. #482	C₂²	semidirect
71. #481	C₂²	semidirect
72. #480	C₂²	semidirect
73. #478	C₂²	semidirect
74. #478	C₂²	semidirect
75. #477	C₂²	semidirect
76. #476	C₂²	semidirect
77. #476	C₂²	semidirect
78. #476	C₂²	semidirect
79. #474	C₂²	semidirect
80. #474	C₂²	semidirect
81. #469	C₂²	semidirect
82. #469	C₂²	semidirect
83. #468	C₂²	semidirect
84. #468	C₂²	semidirect
85. #465	C₂²	semidirect
86. #465	C₂²	semidirect
88. #463	C₂²	semidirect
89. #461	C₂²	semidirect
90. #461	C₂²	semidirect
91. #460	C₂²	semidirect
92. #459	C₂²	semidirect
93. #459	C₂²	semidirect
94. #459	C₂²	semidirect
96. #450	C₂²	semidirect
97. #449	C₂²	semidirect
98. #449	C₂²	semidirect
100. #447	C₂²	semidirect
101. #446	C₂²	semidirect
102. #446	C₂²	semidirect
104. #442	C₂²	semidirect
105. #440	C₂²	semidirect
106. #440	C₂²	semidirect
107. C₄×SD₁₆	C₂²	semidirect
108. C₄×SD₁₆	C₂²	semidirect
109. C₄×SD₁₆	C₂²	semidirect
110. C₄×SD₁₆	C₂²	semidirect
115. C₄×D₈	C₂²	semidirect
116. C₄×D₈	C₂²	semidirect
117. C₄×D₈	C₂²	semidirect
118. C₄×D₈	C₂²	semidirect
119. C₄×D₈	C₂²	semidirect
120. C₄×D₈	C₂²	semidirect
121. #436	C₂²	semidirect
122. #436	C₂²	semidirect
123. #435	C₂²	semidirect
124. #435	C₂²	semidirect
125. #431	C₂²	semidirect
126. #431	C₂²	semidirect
127. #428	C₂²	semidirect
128. C₂×#107	C₂²	semidirect
129. #418	C₂²	semidirect
130. #417	C₂²	semidirect
132. C₂×#102	C₂²	semidirect
133. C₄×M₁₆	C₂²	semidirect
134. C₂×C₄×C₈	C₂²	semidirect
393. D₈	#41	semidirect
507. D₄	C₂×#41	semidirect
538. C₂×C₄	AGL(1,ℤ/8)	semidirect
553. C₈	C₂×#41	semidirect

Maximal subgroups

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

subgroup	index
#3475	2
D₄×#41	2
#3397	2
#3384	2
#3367	2
#3366	2
#3354	2
#3343	2
#3330	2
#3325	2
#3310	2
#3306	2
#3272	2
#3264	2
#3171	2
#3167	2
#3106	2
#3105	2
#3101	2
#3100	2
#2965	2
C₄×AGL(1,ℤ/8)	2
C₂×C₄×D₈	2