Subgroups — #61438

Order 256.

918 conjugacy classes of subgroups.

The subgroup lattice has 567 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	#3475	C₂	1	1	yes	maximal, characteristic
3	#3398	C₂	1	1	yes	maximal, characteristic, complemented
4	#3385	C₂	1	1	yes	maximal, characteristic, complemented
5	#3372	C₂	1	1	yes	maximal, characteristic, complemented
6	#3369	C₂	1	1	yes	maximal, characteristic, complemented
7	#3357	C₂	1	1	yes	maximal, characteristic, complemented
8	#3344	C₂	1	2	yes	maximal, complemented
9	#3331	C₂	1	1	yes	maximal, characteristic, complemented
10	#3329	C₂	1	1	yes	maximal, characteristic, complemented
11	#3314	C₂	1	2	yes	maximal, complemented
12	#3312	C₂	1	2	yes	maximal, complemented
13	#3276	C₂	1	1	yes	maximal, characteristic, complemented
14	#3266	C₂	1	2	yes	maximal, complemented
15	#3172	C₂	1	2	yes	maximal, complemented
16	#3170	C₂	1	1	yes	maximal, characteristic, complemented
17	#3108	C₂	1	2	yes	maximal, complemented
18	#3107	C₂	1	2	yes	maximal, complemented
19	#3104	C₂	1	1	yes	maximal, characteristic, complemented
20	#3101	C₂	1	1	yes	maximal, characteristic, complemented
21	#2965	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#137	C₂	1	2	yes	maximal, complemented
23	C₂×C₄×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137	C₂²	1	2	yes	—
25	C₂²×SD₁₆	C₂²	1	1	yes	characteristic
26	Q₈²	C₂²	1	1	yes	characteristic, complemented
27	#557	—	2	1	no	—
28	#557	C₂²	1	1	yes	characteristic, complemented
29	#556	C₂²	1	1	yes	characteristic
30	#555	C₂²	1	1	yes	characteristic
31	#554	—	2	2	no	—
32	#554	—	2	1	no	—
33	#554	C₂²	1	1	yes	characteristic
34	#554	C₂²	1	2	yes	—
35	#554	C₂²	1	1	yes	characteristic, complemented
36	#553	—	2	1	no	—
37	#552	—	2	1	no	—
38	#552	C₂²	1	2	yes	—
39	#551	—	2	2	no	—
40	D₄×Q₈	C₂²	1	2	yes	—
41	D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
42	#547	C₂²	1	1	yes	characteristic
43	#546	C₂²	1	2	yes	—
44	#533	—	2	1	no	—
45	#533	—	2	2	no	—
46	#533	C₂²	1	1	yes	characteristic
47	#533	C₂²	1	1	yes	characteristic
48	#533	C₂²	1	2	yes	complemented
49	#529	—	2	2	no	—
50	#529	C₂²	1	2	yes	—
51	#525	—	2	1	no	—
52	C₄×#41	—	2	1	no	—
53	C₄×#41	C₂²	1	2	yes	—
54	C₄×#41	C₂²	1	1	yes	characteristic
55	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic
56	C₂×C₄×Q₈	C₂²	1	2	yes	complemented
57	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
58	C₂×#117	—	2	1	no	—
59	#501	C₂²	1	2	yes	complemented
60	#500	C₂²	1	1	yes	characteristic, complemented
61	#497	C₂²	1	2	yes	—
62	#494	C₂²	1	1	yes	characteristic, complemented
63	#491	C₂²	1	2	yes	complemented
64	#489	C₂²	1	2	yes	—
65	#487	C₂²	1	1	yes	characteristic, complemented
66	#487	C₂²	1	1	yes	characteristic, complemented
67	#485	C₂²	1	2	yes	complemented
68	#485	C₂²	1	2	yes	complemented
69	#484	C₂²	1	2	yes	—
70	#483	C₂²	1	2	yes	—
71	#483	C₂²	1	2	yes	complemented
72	#480	C₂²	1	2	yes	—
73	#479	C₂²	1	2	yes	complemented
74	#479	C₂²	1	2	yes	complemented
75	#477	C₂²	1	1	yes	characteristic, complemented
76	#477	C₂²	1	1	yes	characteristic, complemented
77	#476	C₂²	1	1	yes	characteristic
78	#476	C₂²	1	1	yes	characteristic
79	#475	C₂²	1	2	yes	complemented
80	#474	C₂²	1	2	yes	—
81	#470	C₂²	1	2	yes	complemented
82	#470	C₂²	1	2	yes	complemented
83	#468	C₂²	1	2	yes	—
84	#468	C₂²	1	2	yes	—
85	#467	C₂²	1	2	yes	—
86	#467	C₂²	1	2	yes	—
87	#464	C₂²	1	2	yes	—
88	#464	C₂²	1	2	yes	—
89	#462	C₂²	1	1	yes	characteristic, complemented
90	#462	C₂²	1	1	yes	characteristic, complemented
91	#462	C₂²	1	2	yes	complemented
92	#461	C₂²	1	1	yes	characteristic
93	#461	C₂²	1	1	yes	characteristic
94	#461	C₂²	1	2	yes	—
95	#452	C₂²	1	2	yes	—
96	#452	C₂²	1	2	yes	—
97	#451	C₂²	1	2	yes	—
98	#451	C₂²	1	2	yes	complemented
99	#450	C₂²	1	2	yes	—
100	#448	C₂²	1	2	yes	—
101	#446	C₂²	1	1	yes	characteristic, complemented
102	#446	C₂²	1	1	yes	characteristic, complemented
103	#441	C₂²	1	2	yes	complemented
104	#441	C₂²	1	2	yes	complemented
105	#440	C₂²	1	2	yes	—
106	#440	C₂²	1	2	yes	—
107	C₄×Q₁₆	C₂²	1	2	yes	complemented
108	C₄×Q₁₆	C₂²	1	2	yes	complemented
109	C₄×Q₁₆	C₂²	1	2	yes	complemented
110	C₄×Q₁₆	C₂²	1	2	yes	complemented
111	C₄×SD₁₆	C₂²	1	1	yes	characteristic
112	C₄×SD₁₆	C₂²	1	1	yes	characteristic
113	C₄×SD₁₆	C₂²	1	2	yes	—
114	C₄×SD₁₆	C₂²	1	2	yes	—
115	C₄×SD₁₆	C₂²	1	1	yes	characteristic
116	C₄×SD₁₆	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆	C₂²	1	1	yes	characteristic
121	#436	C₂²	1	1	yes	characteristic, complemented
122	#436	C₂²	1	1	yes	characteristic, complemented
123	#435	C₂²	1	2	yes	—
124	#435	C₂²	1	2	yes	—
125	#431	C₂²	1	1	yes	characteristic
126	#431	C₂²	1	2	yes	complemented
127	#428	C₂²	1	2	yes	complemented
128	C₂×#106	C₂²	1	1	yes	characteristic
129	#419	C₂²	1	2	yes	complemented
130	#417	C₂²	1	2	yes	—
131	C₂×#103	C₂²	1	1	yes	characteristic
132	C₂×#102	C₂²	1	1	yes	characteristic
133	C₄×M₁₆	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
135	C₂×#41	D₄	1	1	yes	characteristic
136	C₂×#41	C₂³	1	2	yes	—
137	C₂²×Q₈	C₂³	1	1	yes	characteristic
138	C₂²×Q₈	C₂³	1	2	yes	—
139	C₂²×D₄	C₂³	1	1	yes	characteristic
140	C₂³×C₄	—	2	1	no	—
141	#137	—	2	8	no	—
142	C₂×Q₁₆	C₂³	1	2	yes	—
143	C₂×Q₁₆	C₂³	1	2	yes	—
144	C₂×Q₁₆	C₂³	1	2	yes	—
145	C₂×Q₁₆	C₂³	1	2	yes	—
146	C₂×SD₁₆	—	2	4	no	—
147	C₂×SD₁₆	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆	C₂³	1	2	yes	—
151	C₂×SD₁₆	C₂³	1	2	yes	—
152	C₂×SD₁₆	C₂³	1	1	yes	characteristic
153	C₂×M₁₆	C₂³	1	2	yes	—
154	C₂×M₁₆	C₂³	1	2	yes	—
155	C₂²×C₈	C₂³	1	1	yes	characteristic
156	C₂²×C₈	C₂³	1	1	yes	characteristic
157	C₄⋊Q₈	—	2	2	no	—
158	C₄⋊Q₈	—	2	1	no	—
159	C₄⋊Q₈	—	2	1	no	—
160	C₄⋊Q₈	—	2	2	no	—
161	C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈	C₂³	1	2	yes	—
164	C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₄⋊Q₈	C₂³	1	2	yes	—
167	#126	—	2	2	no	—
168	#126	—	2	2	no	—
169	#126	—	2	2	no	—
170	#125	—	2	2	no	—
171	#125	—	2	1	no	—
172	#125	—	2	2	no	—
173	#125	—	2	2	no	—
174	#125	—	2	1	no	—
175	#125	—	2	1	no	—
176	#125	—	2	1	no	—
177	#125	—	2	2	no	—
178	#125	C₂³	1	2	yes	—
179	#124	—	2	2	no	—
180	#124	C₂³	1	2	yes	—
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	2	no	—
190	C₂²⋊Q₈	—	2	2	no	—
191	C₂²⋊Q₈	—	2	2	no	—
192	C₂²⋊Q₈	—	2	2	no	—
193	C₂²⋊Q₈	—	2	2	no	—
194	C₂²⋊Q₈	—	2	2	no	—
195	C₂²⋊Q₈	—	2	2	no	—
196	C₂²⋊Q₈	—	2	2	no	—
197	C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₂²⋊Q₈	C₂³	1	2	yes	—
202	#121	—	2	1	no	—
203	#121	—	2	1	no	—
204	#121	—	2	2	no	—
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	—	2	2	no	—
212	C₄×Q₈	—	2	2	no	—
213	C₄×Q₈	—	2	1	no	—
214	C₄×Q₈	—	2	1	no	—
215	C₄×Q₈	—	2	2	no	—
216	C₄×Q₈	D₄	1	1	yes	characteristic
217	C₄×Q₈	C₂³	1	1	yes	characteristic
218	C₄×Q₈	C₂³	1	1	yes	characteristic
219	C₄×Q₈	C₂³	1	1	yes	characteristic
220	C₄×Q₈	C₂³	1	1	yes	characteristic
221	C₄×Q₈	C₂³	1	2	yes	—
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×D₄	—	2	2	no	—
228	C₄×D₄	—	2	1	no	—
229	C₄×D₄	—	2	2	no	—
230	C₄×D₄	—	2	1	no	—
231	C₄×D₄	—	2	2	no	—
232	C₄×D₄	—	2	2	no	—
233	C₄×D₄	—	2	2	no	—
234	C₄×D₄	—	2	1	no	—
235	C₄×D₄	—	2	1	no	—
236	C₄×D₄	D₄	1	2	yes	—
237	C₄×D₄	D₄	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	1	yes	characteristic
245	#117	—	2	1	no	—
246	#117	—	2	1	no	—
247	#117	—	2	2	no	—
248	#117	—	2	1	no	—
249	#117	—	2	1	no	—
250	#117	—	2	2	no	—
251	#117	—	2	2	no	—
252	#117	—	2	2	no	—
253	#117	D₄	1	1	yes	characteristic
254	#117	D₄	1	2	yes	—
255	#117	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂³	1	2	yes	—
263	C₂×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₄²	—	2	1	no	—
266	C₂×C₄²	—	2	2	no	—
267	C₂×C₄²	—	2	2	no	—
268	C₂×C₄²	C₂³	1	1	yes	characteristic
269	C₂×C₄²	C₂³	1	2	yes	—
270	#107	C₂³	1	2	yes	—
271	#107	C₂³	1	2	yes	—
272	#107	C₂³	1	2	yes	—
273	#107	C₂³	1	2	yes	—
274	#106	C₂³	1	1	yes	characteristic
275	#106	C₂³	1	1	yes	characteristic
276	#106	C₂³	1	1	yes	characteristic
277	#106	C₂³	1	1	yes	characteristic
278	#106	C₂³	1	2	yes	—
279	#106	C₂³	1	2	yes	—
280	C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₄⋊C₈	C₂³	1	2	yes	—
283	C₄⋊C₈	C₂³	1	2	yes	—
284	#103	C₂³	1	1	yes	characteristic
285	#103	C₂³	1	1	yes	characteristic
286	#103	C₂³	1	1	yes	characteristic
287	#103	C₂³	1	1	yes	characteristic
288	#103	C₂³	1	2	yes	—
289	#103	C₂³	1	2	yes	—
290	#103	C₂³	1	2	yes	—
291	#103	C₂³	1	2	yes	—
292	#103	C₂³	1	2	yes	—
293	#103	C₂³	1	2	yes	—
294	#103	C₂³	1	2	yes	—
295	#103	C₂³	1	2	yes	—
296	#103	C₂³	1	2	yes	—
297	#103	C₂³	1	2	yes	—
298	#102	C₂³	1	1	yes	characteristic
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	2	yes	—
304	C₂²⋊C₈	C₂³	1	2	yes	—
305	C₂²⋊C₈	C₂³	1	2	yes	—
306	C₂²⋊C₈	C₂³	1	2	yes	—
307	#97	C₂³	1	2	yes	—
308	#97	C₂³	1	2	yes	—
309	C₄×C₈	C₂³	1	1	yes	characteristic
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	2	yes	—
314	C₂⁴	—	2	1	no	—
315	#41	—	2	4	no	—
316	#41	—	2	4	no	—
317	#41	—	4	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	4	no	—
325	C₂×Q₈	—	4	1	no	—
326	C₂×Q₈	—	4	2	no	—
327	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈	C₂⁴	1	2	yes	—
329	C₂×Q₈	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈	C₂⁴	1	2	yes	—
331	C₂×Q₈	C₂⁴	1	1	yes	characteristic
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	4	1	no	—
337	C₂×D₄	C₂×D₄	1	2	yes	—
338	C₂×D₄	C₂×D₄	1	1	yes	characteristic
339	C₂×D₄	C₂⁴	1	1	yes	characteristic
340	C₂×D₄	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	4	4	no	—
353	C₂²×C₄	C₂×D₄	1	2	yes	—
354	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄	1	2	yes	—
356	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
357	C₂²×C₄	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄	C₂⁴	1	2	yes	—
359	Q₁₆	—	2	4	no	—
360	Q₁₆	—	2	4	no	—
361	Q₁₆	—	4	2	no	—
362	Q₁₆	—	4	2	no	—
363	SD₁₆	—	2	2	no	—
364	SD₁₆	—	2	2	no	—
365	SD₁₆	—	2	4	no	—
366	SD₁₆	—	2	2	no	—
367	SD₁₆	—	4	2	no	—
368	SD₁₆	#41	1	4	yes	complemented
369	M₁₆	—	2	4	no	—
370	M₁₆	—	4	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	4	1	no	—
373	C₂×C₈	C₂⁴	1	1	yes	characteristic
374	C₂×C₈	C₂⁴	1	1	yes	characteristic
375	C₂×C₈	C₂⁴	1	1	yes	characteristic
376	C₂×C₈	C₂⁴	1	2	yes	—
377	C₂×C₈	C₂⁴	1	2	yes	—
378	C₂×C₈	C₂⁴	1	1	yes	characteristic
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄	C₂×D₄	1	2	yes	—
410	C₄⋊C₄	C₂×D₄	1	2	yes	—
411	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄	C₂⁴	1	2	yes	—
414	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄	C₂⁴	1	2	yes	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	1	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	2	1	no	—
427	C₂²⋊C₄	—	2	1	no	—
428	C₂²⋊C₄	—	2	1	no	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄	C₂×D₄	1	2	yes	—
434	C₄²	—	2	2	no	—
435	C₄²	—	2	2	no	—
436	C₄²	—	2	2	no	—
437	C₄²	—	2	1	no	—
438	C₄²	—	2	2	no	—
439	C₄²	—	2	1	no	—
440	C₄²	—	2	1	no	—
441	C₄²	—	2	2	no	—
442	C₄²	—	2	1	no	—
443	C₄²	—	2	2	no	—
444	C₄²	C₂×D₄	1	2	yes	—
445	C₄²	C₂×D₄	1	1	yes	characteristic
446	C₄²	C₂×D₄	1	2	yes	—
447	C₄²	C₂×D₄	1	1	yes	characteristic
448	C₄²	C₂⁴	1	1	yes	characteristic
449	C₄²	C₂⁴	1	2	yes	—
450	C₄²	C₂⁴	1	1	yes	characteristic
451	C₂³	—	2	1	no	—
452	C₂³	—	2	1	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	8	1	no	—
456	C₂³	C₂²×D₄	1	2	yes	—
457	C₂³	C₂²×D₄	1	1	yes	characteristic
458	Q₈	—	2	2	no	—
459	Q₈	—	2	1	no	—
460	Q₈	—	2	1	no	—
461	Q₈	—	2	2	no	—
462	Q₈	—	2	2	no	—
463	Q₈	—	2	2	no	—
464	Q₈	—	2	1	no	—
465	Q₈	—	2	2	no	—
466	Q₈	—	4	4	no	—
467	Q₈	—	4	2	no	—
468	Q₈	—	8	2	no	—
469	Q₈	—	8	1	no	—
470	Q₈	—	8	1	no	—
471	Q₈	C₂×#41	1	2	yes	—
472	D₄	—	2	4	no	—
473	D₄	—	2	2	no	—
474	D₄	—	2	1	no	—
475	D₄	—	2	1	no	—
476	D₄	—	2	1	no	—
477	D₄	—	4	2	no	—
478	D₄	—	4	4	no	—
479	D₄	—	8	2	no	—
480	D₄	C₂×#41	1	2	yes	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	4	no	—
500	C₂×C₄	—	4	4	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	8	2	no	—
507	C₂×C₄	—	8	1	no	—
508	C₂×C₄	—	8	2	no	—
509	C₂×C₄	#137	1	4	yes	complemented
510	C₂×C₄	C₂²×D₄	1	2	yes	—
511	C₂×C₄	C₂²×D₄	1	2	yes	—
512	C₂×C₄	C₂²×D₄	1	2	yes	—
513	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄	C₂⁵	1	1	yes	characteristic
519	C₈	—	2	1	no	—
520	C₈	—	2	2	no	—
521	C₈	—	2	1	no	—
522	C₈	—	2	1	no	—
523	C₈	—	2	2	no	—
524	C₈	C₂×#41	1	2	yes	—
525	C₂²	—	2	1	no	—
526	C₂²	—	2	1	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	4	1	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	1	no	—
535	C₂²	—	4	1	no	—
536	C₂²	—	8	4	no	—
537	C₂²	C₂×#137	1	2	yes	—
538	C₂²	C₂³×D₄	1	1	yes	characteristic
539	C₄	—	2	1	no	—
540	C₄	—	2	2	no	—
541	C₄	—	2	1	no	—
542	C₄	—	2	2	no	—
543	C₄	—	2	1	no	—
544	C₄	—	2	2	no	—
545	C₄	—	2	2	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	2	no	—
548	C₄	—	4	1	no	—
549	C₄	—	4	2	no	—
550	C₄	—	4	2	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	1	no	—
554	C₄	—	4	1	no	—
555	C₄	C₂×#137	1	2	yes	—
556	C₄	C₂×#137	1	2	yes	—
557	C₄	C₂²×#41	1	1	yes	characteristic
558	C₄	#585	1	1	yes	characteristic
559	C₂	—	2	2	no	—
560	C₂	—	4	2	no	—
561	C₂	—	4	2	no	—
562	C₂	—	8	1	no	—
563	C₂	D₄×#41	1	1	yes	characteristic
564	C₂	C₂²×#137	1	1	yes	characteristic
565	C₂	#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
socle	C₂²	C₂³×D₄
prime radical	#3475	C₂
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. Q₈×#41	C₂	semidirect
3. #3398	C₂	semidirect
4. #3385	C₂	semidirect
5. #3372	C₂	semidirect
6. #3369	C₂	semidirect
7. #3357	C₂	semidirect
8. #3344	C₂	semidirect
9. #3331	C₂	semidirect
10. #3329	C₂	semidirect
11. #3314	C₂	semidirect
12. #3312	C₂	semidirect
13. #3276	C₂	semidirect
14. #3266	C₂	semidirect
15. #3172	C₂	semidirect
16. #3170	C₂	semidirect
17. #3108	C₂	semidirect
18. #3107	C₂	semidirect
19. #3104	C₂	semidirect
20. #3101	C₂	semidirect
21. #2965	C₂	semidirect
22. C₄×#137	C₂	semidirect
23. C₂×C₄×SD₁₆	C₂	semidirect
26. Q₈²	C₂²	semidirect
28. #557	C₂²	semidirect
35. #554	C₂²	semidirect
41. D₄×Q₈	C₂²	semidirect
48. #533	C₂²	semidirect
56. C₂×C₄×Q₈	C₂²	semidirect
59. #501	C₂²	semidirect
60. #500	C₂²	semidirect
62. #494	C₂²	semidirect
63. #491	C₂²	semidirect
65. #487	C₂²	semidirect
66. #487	C₂²	semidirect
67. #485	C₂²	semidirect
68. #485	C₂²	semidirect
71. #483	C₂²	semidirect
73. #479	C₂²	semidirect
74. #479	C₂²	semidirect
75. #477	C₂²	semidirect
76. #477	C₂²	semidirect
79. #475	C₂²	semidirect
81. #470	C₂²	semidirect
82. #470	C₂²	semidirect
89. #462	C₂²	semidirect
90. #462	C₂²	semidirect
91. #462	C₂²	semidirect
98. #451	C₂²	semidirect
101. #446	C₂²	semidirect
102. #446	C₂²	semidirect
103. #441	C₂²	semidirect
104. #441	C₂²	semidirect
107. C₄×Q₁₆	C₂²	semidirect
108. C₄×Q₁₆	C₂²	semidirect
109. C₄×Q₁₆	C₂²	semidirect
110. C₄×Q₁₆	C₂²	semidirect
121. #436	C₂²	semidirect
122. #436	C₂²	semidirect
126. #431	C₂²	semidirect
127. #428	C₂²	semidirect
129. #419	C₂²	semidirect
133. C₄×M₁₆	C₂²	semidirect
368. SD₁₆	#41	semidirect
509. C₂×C₄	#137	semidirect

Maximal subgroups

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

subgroup	index
Q₈×#41	2
#3475	2
#3398	2
#3385	2
#3372	2
#3369	2
#3357	2
#3344	2
#3331	2
#3329	2
#3314	2
#3312	2
#3276	2
#3266	2
#3172	2
#3170	2
#3108	2
#3107	2
#3104	2
#3101	2
#2965	2
C₄×#137	2
C₂×C₄×SD₁₆	2