Subgroups — #61991

Order 256.

924 conjugacy classes of subgroups.

The subgroup lattice has 575 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3514	C₂	1	1	yes	maximal, characteristic
2	Q₈×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	#3398	C₂	1	1	yes	maximal, characteristic, complemented
5	#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	#3369	C₂	1	1	yes	maximal, characteristic, complemented
7	#3316	C₂	1	2	yes	maximal, complemented
8	#3314	C₂	1	2	yes	maximal, complemented
9	#3299	C₂	1	1	yes	maximal, characteristic, complemented
10	#3295	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
13	#3270	C₂	1	2	yes	maximal, complemented
14	#3266	C₂	1	2	yes	maximal, complemented
15	#3252	C₂	1	1	yes	maximal, characteristic, complemented
16	#3248	C₂	1	2	yes	maximal, complemented
17	#3215	C₂	1	2	yes	maximal, complemented
18	#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	#3117	C₂	1	2	yes	maximal, complemented
20	#3108	C₂	1	1	yes	maximal, characteristic, complemented
21	#3037	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#464	C₂	1	2	yes	maximal, complemented
23	#2990	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137	C₂²	1	2	yes	complemented
25	C₂²×Q₁₆	C₂²	1	2	yes	complemented
26	C₂²×SD₁₆	C₂²	1	2	yes	—
27	#559	C₂²	1	1	yes	characteristic
28	Q₈²	C₂²	1	1	yes	characteristic, complemented
29	#557	—	2	1	no	—
30	#557	C₂²	1	1	yes	characteristic, complemented
31	#556	C₂²	1	1	yes	characteristic
32	#555	—	2	1	no	—
33	#554	—	2	1	no	—
34	#554	—	2	2	no	—
35	#554	C₂²	1	1	yes	characteristic
36	#554	C₂²	1	2	yes	complemented
37	#551	—	2	2	no	—
38	D₄×Q₈	C₂²	1	1	yes	characteristic
39	D₄×Q₈	C₂²	1	1	yes	characteristic
40	D₄×Q₈	C₂²	1	2	yes	complemented
41	#548	C₂²	1	2	yes	—
42	#546	—	2	1	no	—
43	#546	C₂²	1	2	yes	—
44	D₄²	C₂²	1	1	yes	characteristic
45	#542	—	2	1	no	—
46	#538	—	2	2	no	—
47	#533	—	2	2	no	—
48	#533	—	2	1	no	—
49	#533	C₂²	1	1	yes	characteristic, complemented
50	#533	C₂²	1	2	yes	complemented
51	#532	C₂²	1	1	yes	characteristic
52	#529	C₂²	1	1	yes	characteristic
53	#529	C₂²	1	2	yes	—
54	C₂×#124	C₂²	1	2	yes	—
55	#518	—	2	1	no	—
56	C₄×#41	—	2	1	no	—
57	C₄×#41	C₂²	1	1	yes	characteristic
58	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₄×Q₈	C₂²	1	2	yes	complemented
60	#497	C₂²	1	2	yes	—
61	#497	C₂²	1	2	yes	complemented
62	#494	C₂²	1	1	yes	characteristic, complemented
63	#492	C₂²	1	1	yes	characteristic
64	#489	C₂²	1	2	yes	—
65	#489	C₂²	1	2	yes	complemented
66	#487	C₂²	1	1	yes	characteristic, complemented
67	#486	C₂²	1	1	yes	characteristic
68	#484	C₂²	1	2	yes	complemented
69	#483	C₂²	1	1	yes	characteristic, complemented
70	#481	C₂²	1	2	yes	—
71	#480	C₂²	1	1	yes	characteristic
72	#479	C₂²	1	1	yes	characteristic, complemented
73	#479	C₂²	1	1	yes	characteristic, complemented
74	#479	C₂²	1	2	yes	complemented
75	#477	C₂²	1	1	yes	characteristic, complemented
76	#476	C₂²	1	1	yes	characteristic
77	#475	C₂²	1	2	yes	complemented
78	#474	C₂²	1	2	yes	complemented
79	#470	C₂²	1	2	yes	complemented
80	#468	C₂²	1	2	yes	—
81	#467	C₂²	1	2	yes	complemented
82	#467	C₂²	1	2	yes	complemented
83	#465	C₂²	1	2	yes	—
84	#465	C₂²	1	2	yes	—
85	#464	C₂²	1	1	yes	characteristic
86	#464	C₂²	1	1	yes	characteristic
87	#464	C₂²	1	2	yes	—
88	#464	C₂²	1	2	yes	—
89	#464	C₂²	1	2	yes	—
90	#464	C₂²	1	2	yes	complemented
91	#464	C₂²	1	2	yes	complemented
92	#464	C₂²	1	2	yes	complemented
93	#464	C₂²	1	2	yes	complemented
94	#464	C₂²	1	2	yes	complemented
95	#464	C₂²	1	2	yes	complemented
96	#462	C₂²	1	1	yes	characteristic, complemented
97	#462	C₂²	1	2	yes	complemented
98	#462	C₂²	1	1	yes	characteristic, complemented
99	#462	C₂²	1	1	yes	characteristic, complemented
100	#461	C₂²	1	1	yes	characteristic
101	#461	C₂²	1	2	yes	complemented
102	#460	C₂²	1	1	yes	characteristic
103	#460	C₂²	1	1	yes	characteristic
104	#452	C₂²	1	2	yes	complemented
105	#452	C₂²	1	2	yes	complemented
106	#451	C₂²	1	1	yes	characteristic, complemented
107	#451	C₂²	1	2	yes	complemented
108	#451	C₂²	1	2	yes	complemented
109	#451	C₂²	1	2	yes	complemented
110	#450	C₂²	1	2	yes	—
111	#450	C₂²	1	2	yes	—
112	#448	C₂²	1	1	yes	characteristic
113	#448	C₂²	1	2	yes	—
114	#446	C₂²	1	1	yes	characteristic, complemented
115	#446	C₂²	1	1	yes	characteristic, complemented
116	#441	C₂²	1	2	yes	complemented
117	#441	C₂²	1	2	yes	complemented
118	#440	C₂²	1	2	yes	complemented
119	#440	C₂²	1	2	yes	complemented
120	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
121	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
122	C₄×SD₁₆	C₂²	1	1	yes	characteristic
123	C₄×SD₁₆	C₂²	1	1	yes	characteristic
124	#435	C₂²	1	2	yes	complemented
125	#435	C₂²	1	2	yes	complemented
126	C₈×D₄	C₂²	1	1	yes	characteristic
127	C₈×D₄	C₂²	1	1	yes	characteristic
128	#432	C₂²	1	2	yes	complemented
129	#431	C₂²	1	1	yes	characteristic, complemented
130	#423	C₂²	1	1	yes	characteristic, complemented
131	C₂×C₄⋊C₈	C₂²	1	2	yes	complemented
132	#417	C₂²	1	2	yes	complemented
133	C₂×#103	C₂²	1	2	yes	complemented
134	C₂×#102	C₂²	1	2	yes	—
135	C₂×#41	D₄	1	1	yes	characteristic
136	C₂×#41	C₂³	1	2	yes	—
137	C₂²×Q₈	C₂³	1	2	yes	—
138	C₂²×Q₈	C₂³	1	1	yes	characteristic
139	C₂²×Q₈	C₂³	1	2	yes	—
140	C₂²×D₄	—	2	1	no	—
141	C₂²×D₄	C₂³	1	2	yes	—
142	#137	—	4	4	no	—
143	C₂×Q₁₆	—	4	4	no	—
144	C₂×Q₁₆	C₂³	1	1	yes	characteristic
145	C₂×Q₁₆	C₂³	1	2	yes	—
146	C₂×Q₁₆	C₂³	1	2	yes	—
147	C₂×Q₁₆	C₂³	1	2	yes	—
148	C₂×Q₁₆	C₂³	1	2	yes	—
149	C₂×Q₁₆	C₂³	1	1	yes	characteristic
150	C₂×Q₁₆	C₂³	1	2	yes	—
151	C₂×SD₁₆	—	4	4	no	—
152	C₂×SD₁₆	C₂³	1	1	yes	characteristic
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×SD₁₆	C₂³	1	1	yes	characteristic
158	C₂×SD₁₆	C₂³	1	2	yes	—
159	C₂×M₁₆	C₂³	1	2	yes	—
160	C₂²×C₈	C₂³	1	2	yes	—
161	C₂²×C₈	C₂³	1	2	yes	—
162	C₄⋊Q₈	—	2	1	no	—
163	C₄⋊Q₈	—	2	2	no	—
164	C₄⋊Q₈	—	2	1	no	—
165	C₄⋊Q₈	—	2	2	no	—
166	C₄⋊Q₈	—	2	1	no	—
167	C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	C₄⋊Q₈	C₂³	1	2	yes	—
170	C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₄⋊Q₈	C₂³	1	2	yes	—
172	#127	C₂³	1	1	yes	characteristic
173	#126	—	2	2	no	—
174	#126	—	2	2	no	—
175	#126	—	2	1	no	—
176	#125	—	2	1	no	—
177	#125	—	2	2	no	—
178	#125	—	2	1	no	—
179	#125	—	2	2	no	—
180	#125	—	2	1	no	—
181	#125	—	2	2	no	—
182	#125	C₂³	1	1	yes	characteristic
183	#124	—	2	1	no	—
184	#124	—	2	2	no	—
185	#124	—	2	2	no	—
186	#124	—	2	2	no	—
187	#124	C₂³	1	1	yes	characteristic
188	#124	C₂³	1	2	yes	—
189	#124	C₂³	1	2	yes	—
190	#124	C₂³	1	2	yes	—
191	#123	—	2	1	no	—
192	#123	—	2	2	no	—
193	#123	—	2	2	no	—
194	#123	—	2	2	no	—
195	C₂²⋊Q₈	—	2	1	no	—
196	C₂²⋊Q₈	—	2	2	no	—
197	C₂²⋊Q₈	—	2	1	no	—
198	C₂²⋊Q₈	—	2	2	no	—
199	C₂²⋊Q₈	—	2	2	no	—
200	C₂²⋊Q₈	—	2	2	no	—
201	C₂²⋊Q₈	—	2	2	no	—
202	C₂²⋊Q₈	—	2	2	no	—
203	C₂²⋊Q₈	—	2	2	no	—
204	C₂²⋊Q₈	—	2	2	no	—
205	C₂²⋊Q₈	—	2	2	no	—
206	C₂²⋊Q₈	C₂³	1	2	yes	—
207	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
208	C₂²⋊Q₈	C₂³	1	2	yes	—
209	C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₂²⋊Q₈	C₂³	1	2	yes	—
211	#121	—	2	2	no	—
212	#121	—	2	1	no	—
213	#121	—	2	1	no	—
214	#121	—	2	1	no	—
215	#121	—	2	2	no	—
216	#121	C₂³	1	2	yes	—
217	#121	C₂³	1	1	yes	characteristic
218	#120	—	2	2	no	—
219	#120	—	2	2	no	—
220	C₄×Q₈	—	2	1	no	—
221	C₄×Q₈	—	2	1	no	—
222	C₄×Q₈	—	2	2	no	—
223	C₄×Q₈	—	2	1	no	—
224	C₄×Q₈	—	2	1	no	—
225	C₄×Q₈	—	2	2	no	—
226	C₄×Q₈	—	2	2	no	—
227	C₄×Q₈	—	2	1	no	—
228	C₄×Q₈	D₄	1	1	yes	characteristic
229	C₄×Q₈	C₂³	1	1	yes	characteristic
230	C₄×Q₈	C₂³	1	1	yes	characteristic
231	C₄×Q₈	C₂³	1	2	yes	—
232	C₄×Q₈	C₂³	1	1	yes	characteristic
233	C₄×Q₈	C₂³	1	2	yes	—
234	C₄×Q₈	C₂³	1	1	yes	characteristic
235	C₄×Q₈	C₂³	1	2	yes	—
236	C₄×Q₈	C₂³	1	2	yes	—
237	C₄×Q₈	C₂³	1	1	yes	characteristic
238	C₄×Q₈	C₂³	1	1	yes	characteristic
239	C₄×D₄	—	2	1	no	—
240	C₄×D₄	—	2	2	no	—
241	C₄×D₄	—	2	1	no	—
242	C₄×D₄	—	2	2	no	—
243	C₄×D₄	—	2	1	no	—
244	C₄×D₄	—	2	2	no	—
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	—	2	2	no	—
248	C₄×D₄	—	2	1	no	—
249	C₄×D₄	—	2	1	no	—
250	C₄×D₄	D₄	1	1	yes	characteristic
251	C₄×D₄	D₄	1	2	yes	—
252	C₄×D₄	C₂³	1	1	yes	characteristic
253	C₄×D₄	C₂³	1	2	yes	—
254	C₄×D₄	C₂³	1	1	yes	characteristic
255	C₄×D₄	C₂³	1	2	yes	—
256	#117	—	2	2	no	—
257	#117	—	2	1	no	—
258	#117	—	2	1	no	—
259	#117	—	2	1	no	—
260	#117	—	2	2	no	—
261	#117	D₄	1	2	yes	—
262	#117	D₄	1	1	yes	characteristic
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	C₂³	1	2	yes	—
266	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₄²	—	2	2	no	—
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	C₂³	1	2	yes	—
273	C₂×C₄²	C₂³	1	1	yes	characteristic
274	#107	C₂³	1	1	yes	characteristic
275	#107	C₂³	1	1	yes	characteristic
276	#107	C₂³	1	2	yes	—
277	#106	C₂³	1	1	yes	characteristic
278	#106	C₂³	1	1	yes	characteristic
279	#106	C₂³	1	2	yes	—
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	2	yes	—
284	C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₄⋊C₈	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	1	yes	characteristic
293	#103	C₂³	1	1	yes	characteristic
294	#103	C₂³	1	1	yes	characteristic
295	#103	C₂³	1	1	yes	characteristic
296	#103	C₂³	1	1	yes	characteristic
297	#103	C₂³	1	2	yes	—
298	#103	C₂³	1	2	yes	—
299	#103	C₂³	1	2	yes	—
300	#102	C₂³	1	1	yes	characteristic
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	#102	C₂³	1	1	yes	characteristic
306	#102	C₂³	1	2	yes	—
307	C₂²⋊C₈	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈	C₂³	1	2	yes	—
310	C₂²⋊C₈	C₂³	1	2	yes	—
311	#97	C₂³	1	2	yes	—
312	#97	C₂³	1	2	yes	—
313	C₄×C₈	C₂³	1	1	yes	characteristic
314	C₄×C₈	C₂³	1	1	yes	characteristic
315	C₂⁴	—	2	2	no	—
316	#41	—	2	4	no	—
317	#41	—	4	2	no	—
318	#41	—	4	2	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	2	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	—	2	2	no	—
326	C₂×Q₈	—	4	2	no	—
327	C₂×Q₈	—	4	1	no	—
328	C₂×Q₈	—	4	2	no	—
329	C₂×Q₈	—	4	2	no	—
330	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈	C₂⁴	1	2	yes	—
333	C₂×Q₈	C₂⁴	1	1	yes	characteristic
334	C₂×Q₈	C₂⁴	1	2	yes	—
335	C₂×Q₈	C₂⁴	1	1	yes	characteristic
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	4	2	no	—
343	C₂×D₄	—	4	2	no	—
344	C₂×D₄	—	4	4	no	—
345	C₂×D₄	C₂×D₄	1	2	yes	—
346	C₂×D₄	C₂×D₄	1	1	yes	characteristic
347	C₂×D₄	C₂⁴	1	1	yes	characteristic
348	C₂×D₄	C₂⁴	1	2	yes	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	C₂×D₄	1	2	yes	—
358	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄	1	2	yes	—
360	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄	C₂⁴	1	2	yes	—
362	C₂²×C₄	C₂⁴	1	1	yes	characteristic
363	Q₁₆	—	2	2	no	—
364	Q₁₆	—	2	4	no	—
365	Q₁₆	—	4	2	no	—
366	Q₁₆	—	4	2	no	—
367	Q₁₆	—	4	1	no	—
368	Q₁₆	—	4	2	no	—
369	Q₁₆	—	4	2	no	—
370	SD₁₆	—	2	2	no	—
371	SD₁₆	—	2	4	no	—
372	SD₁₆	—	4	2	no	—
373	SD₁₆	—	4	2	no	—
374	SD₁₆	—	4	2	no	—
375	SD₁₆	—	4	1	no	—
376	SD₁₆	—	4	2	no	—
377	M₁₆	—	4	2	no	—
378	C₂×C₈	—	4	2	no	—
379	C₂×C₈	—	4	2	no	—
380	C₂×C₈	C₂⁴	1	1	yes	characteristic
381	C₂×C₈	C₂⁴	1	1	yes	characteristic
382	C₂×C₈	C₂⁴	1	1	yes	characteristic
383	C₂×C₈	C₂⁴	1	1	yes	characteristic
384	C₂×C₈	C₂⁴	1	2	yes	—
385	C₂×C₈	C₂⁴	1	2	yes	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
413	C₄⋊C₄	C₂×D₄	1	2	yes	—
414	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
415	C₄⋊C₄	C₂×D₄	1	2	yes	—
416	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄	C₂⁴	1	2	yes	—
418	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	2	1	no	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	2	1	no	—
428	C₂²⋊C₄	—	2	1	no	—
429	C₂²⋊C₄	—	2	1	no	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	—	2	2	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	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄	C₂×D₄	1	2	yes	—
441	C₄²	—	2	1	no	—
442	C₄²	—	2	2	no	—
443	C₄²	—	2	1	no	—
444	C₄²	—	2	2	no	—
445	C₄²	—	2	1	no	—
446	C₄²	—	2	2	no	—
447	C₄²	—	2	1	no	—
448	C₄²	—	2	2	no	—
449	C₄²	—	2	1	no	—
450	C₄²	C₂×D₄	1	2	yes	—
451	C₄²	C₂×D₄	1	1	yes	characteristic
452	C₄²	C₂×D₄	1	1	yes	characteristic
453	C₄²	C₂×D₄	1	2	yes	—
454	C₄²	C₂⁴	1	1	yes	characteristic
455	C₄²	C₂⁴	1	2	yes	—
456	C₄²	C₂⁴	1	1	yes	characteristic
457	C₂³	—	2	1	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	4	4	no	—
460	C₂³	—	8	2	no	—
461	C₂³	—	8	2	no	—
462	C₂³	C₂²×D₄	1	1	yes	characteristic
463	C₂³	C₂²×D₄	1	2	yes	—
464	Q₈	—	2	2	no	—
465	Q₈	—	2	1	no	—
466	Q₈	—	2	2	no	—
467	Q₈	—	2	1	no	—
468	Q₈	—	2	1	no	—
469	Q₈	—	2	2	no	—
470	Q₈	—	2	2	no	—
471	Q₈	—	2	1	no	—
472	Q₈	—	2	1	no	—
473	Q₈	—	2	2	no	—
474	Q₈	—	4	2	no	—
475	Q₈	—	4	4	no	—
476	Q₈	—	8	2	no	—
477	Q₈	—	8	1	no	—
478	Q₈	—	8	2	no	—
479	Q₈	H(5,𝔽₂)	1	2	yes	—
480	D₄	—	2	4	no	—
481	D₄	—	2	1	no	—
482	D₄	—	2	2	no	—
483	D₄	—	2	1	no	—
484	D₄	—	2	2	no	—
485	D₄	—	4	4	no	—
486	D₄	—	4	2	no	—
487	D₄	—	8	1	no	—
488	D₄	—	8	2	no	—
489	D₄	—	8	1	no	—
490	D₄	—	8	2	no	—
491	D₄	#137	1	4	yes	complemented
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	4	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	8	2	no	—
514	C₂×C₄	—	8	2	no	—
515	C₂×C₄	—	8	2	no	—
516	C₂×C₄	—	8	1	no	—
517	C₂×C₄	—	8	2	no	—
518	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄	C₂²×D₄	1	2	yes	—
520	C₂×C₄	C₂²×D₄	1	2	yes	—
521	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄	C₂²×D₄	1	2	yes	—
524	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄	C₂⁵	1	1	yes	characteristic
527	C₈	—	2	1	no	—
528	C₈	—	2	1	no	—
529	C₈	—	2	2	no	—
530	C₈	—	2	2	no	—
531	C₈	—	2	1	no	—
532	C₈	—	2	1	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	2	2	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	4	1	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	1	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	16	4	no	—
545	C₂²	C₂×#137	1	4	yes	—
546	C₂²	C₂³×D₄	1	1	yes	characteristic
547	C₄	—	2	1	no	—
548	C₄	—	2	2	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	2	no	—
552	C₄	—	2	2	no	—
553	C₄	—	2	1	no	—
554	C₄	—	2	2	no	—
555	C₄	—	4	1	no	—
556	C₄	—	4	1	no	—
557	C₄	—	4	2	no	—
558	C₄	—	4	1	no	—
559	C₄	—	4	2	no	—
560	C₄	—	4	1	no	—
561	C₄	—	4	2	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	1	no	—
564	C₄	C₂×#137	1	2	yes	—
565	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
566	C₄	#585	1	1	yes	characteristic
567	C₂	—	2	4	no	—
568	C₂	—	4	1	no	—
569	C₂	—	8	2	no	—
570	C₂	—	8	1	no	—
571	C₂	#3488	1	1	yes	characteristic
572	C₂	C₂²×#137	1	1	yes	characteristic
573	C₂	#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
prime radical	#3514	C₂
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
2. Q₈×#41	C₂	semidirect
3. #3400	C₂	semidirect
4. #3398	C₂	semidirect
5. #3375	C₂	semidirect
6. #3369	C₂	semidirect
7. #3316	C₂	semidirect
8. #3314	C₂	semidirect
9. #3299	C₂	semidirect
10. #3295	C₂	semidirect
11. D₄×Q₁₆	C₂	semidirect
12. D₄×SD₁₆	C₂	semidirect
13. #3270	C₂	semidirect
14. #3266	C₂	semidirect
15. #3252	C₂	semidirect
16. #3248	C₂	semidirect
17. #3215	C₂	semidirect
18. #3210	C₂	semidirect
19. #3117	C₂	semidirect
20. #3108	C₂	semidirect
21. #3037	C₂	semidirect
22. C₂×#464	C₂	semidirect
23. #2990	C₂	semidirect
24. C₂×#137	C₂²	semidirect
25. C₂²×Q₁₆	C₂²	semidirect
28. Q₈²	C₂²	semidirect
30. #557	C₂²	semidirect
36. #554	C₂²	semidirect
40. D₄×Q₈	C₂²	semidirect
49. #533	C₂²	semidirect
50. #533	C₂²	semidirect
58. C₂×C₄×Q₈	C₂²	semidirect
59. C₂×C₄×Q₈	C₂²	semidirect
61. #497	C₂²	semidirect
62. #494	C₂²	semidirect
65. #489	C₂²	semidirect
66. #487	C₂²	semidirect
68. #484	C₂²	semidirect
69. #483	C₂²	semidirect
72. #479	C₂²	semidirect
73. #479	C₂²	semidirect
74. #479	C₂²	semidirect
75. #477	C₂²	semidirect
77. #475	C₂²	semidirect
78. #474	C₂²	semidirect
79. #470	C₂²	semidirect
81. #467	C₂²	semidirect
82. #467	C₂²	semidirect
90. #464	C₂²	semidirect
91. #464	C₂²	semidirect
92. #464	C₂²	semidirect
93. #464	C₂²	semidirect
94. #464	C₂²	semidirect
95. #464	C₂²	semidirect
96. #462	C₂²	semidirect
97. #462	C₂²	semidirect
98. #462	C₂²	semidirect
99. #462	C₂²	semidirect
101. #461	C₂²	semidirect
104. #452	C₂²	semidirect
105. #452	C₂²	semidirect
106. #451	C₂²	semidirect
107. #451	C₂²	semidirect
108. #451	C₂²	semidirect
109. #451	C₂²	semidirect
114. #446	C₂²	semidirect
115. #446	C₂²	semidirect
116. #441	C₂²	semidirect
117. #441	C₂²	semidirect
118. #440	C₂²	semidirect
119. #440	C₂²	semidirect
120. C₄×Q₁₆	C₂²	semidirect
121. C₄×Q₁₆	C₂²	semidirect
124. #435	C₂²	semidirect
125. #435	C₂²	semidirect
128. #432	C₂²	semidirect
129. #431	C₂²	semidirect
130. #423	C₂²	semidirect
131. C₂×C₄⋊C₈	C₂²	semidirect
132. #417	C₂²	semidirect
133. C₂×#103	C₂²	semidirect
491. D₄	#137	semidirect

Maximal subgroups

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

subgroup	index
#3514	2
Q₈×#41	2
#3400	2
#3398	2
#3375	2
#3369	2
#3316	2
#3314	2
#3299	2
#3295	2
D₄×Q₁₆	2
D₄×SD₁₆	2
#3270	2
#3266	2
#3252	2
#3248	2
#3215	2
#3210	2
#3117	2
#3108	2
#3037	2
C₂×#464	2
#2990	2