Subgroups — C₂×#22562187 #31009778

Order 17152.

1078 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863836	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#14523989	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16863671	C₂	1	1	yes	maximal, characteristic, complemented
4	#22562187	C₂	1	8	yes	maximal, direct product factor
5	C₂×#16863212	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16863203	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16863180	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#578×C₆₇	C₂	1	1	yes	maximal, characteristic
9	C₂×#14524073	—	2	1	no	—
10	C₂²×Dic₂₆₈	C₂²	1	1	yes	characteristic
11	#16863836	—	2	2	no	—
12	#16863836	C₂²	1	4	yes	complemented
13	C₂×#14523989	—	2	2	no	—
14	C₂×#14523989	—	2	2	no	—
15	C₂×#14523989	—	2	1	no	—
16	C₂×#14523989	C₂²	1	4	yes	complemented
17	C₂×#14523987	—	2	1	no	—
18	C₂×#14523983	C₂²	1	1	yes	characteristic
19	C₂²×C₆₇⋊C₁₆	C₂²	1	1	yes	characteristic
20	#16863671	—	2	2	no	—
21	#16863671	C₂²	1	4	yes	complemented
22	C₂×#14523979	C₂²	1	1	yes	characteristic
23	C₂×#14523961	—	2	1	no	—
24	#16863212	C₂²	1	4	yes	complemented
25	#16863203	C₂²	1	4	yes	complemented
26	#16863180	C₂²	1	4	yes	complemented
27	C₂×2₋¹⁺⁴×C₆₇	—	2	1	no	—
28	#578×C₆₇	—	2	2	no	—
29	#578×C₆₇	—	2	2	no	—
30	#578×C₆₇	—	2	2	no	—
31	#578×C₆₇	C₂²	1	4	yes	—
32	C₂×#137×C₆₇	—	2	2	no	—
33	C₂×#137×C₆₇	—	2	1	no	—
34	C₂×#135×C₆₇	—	2	1	no	—
35	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
36	C₂²×Q₁₆×C₆₇	—	2	1	no	—
37	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
39	C₂²×Dic₁₃₄	—	2	1	no	—
40	#14524073	—	2	4	no	—
41	#14524073	—	4	2	no	—
42	C₂×Dic₂₆₈	—	2	1	no	—
43	C₂×Dic₂₆₈	—	2	1	no	—
44	C₂×Dic₂₆₈	—	2	1	no	—
45	C₂×Dic₂₆₈	—	2	1	no	—
46	C₂×Dic₂₆₈	—	2	1	no	—
47	C₂×Dic₂₆₈	C₂³	1	2	yes	—
48	C₂×#11761618	—	4	1	no	—
49	C₂×#11761616	—	4	1	no	—
50	C₂×#11761612	—	2	1	no	—
51	#14523989	—	2	8	no	—
52	#14523989	—	2	4	no	—
53	#14523987	—	2	4	no	—
54	#14523983	—	2	1	no	—
55	#14523983	C₂³	1	2	yes	—
56	C₂×C₆₇⋊C₁₆	—	2	1	no	—
57	C₂×C₆₇⋊C₁₆	—	2	1	no	—
58	C₂×C₆₇⋊C₁₆	—	2	1	no	—
59	C₂×C₆₇⋊C₁₆	C₂³	1	2	yes	—
60	#14523979	—	2	1	no	—
61	#14523979	C₂³	1	2	yes	—
62	#14523961	—	2	4	no	—
63	2₋¹⁺⁴×C₆₇	—	2	4	no	—
64	2₋¹⁺⁴×C₆₇	—	2	4	no	—
65	2₋¹⁺⁴×C₆₇	—	4	2	no	—
66	2₋¹⁺⁴×C₆₇	—	4	2	no	—
67	C₂×#41×C₆₇	—	2	2	no	—
68	C₂×#41×C₆₇	—	2	1	no	—
69	C₂×#41×C₆₇	—	4	2	no	—
70	C₂×#41×C₆₇	—	4	1	no	—
71	C₂×#41×C₆₇	D₄	1	1	yes	characteristic
72	C₂²×Q₈×C₆₇	—	2	2	no	—
73	C₂²×Q₈×C₆₇	—	2	1	no	—
74	C₂²×Q₈×C₆₇	—	4	1	no	—
75	#137×C₆₇	—	2	4	no	—
76	#137×C₆₇	—	2	8	no	—
77	#137×C₆₇	—	2	8	no	—
78	#137×C₆₇	—	2	4	no	—
79	#135×C₆₇	—	2	4	no	—
80	#135×C₆₇	—	2	4	no	—
81	#135×C₆₇	—	2	1	no	—
82	#135×C₆₇	—	2	1	no	—
83	#135×C₆₇	D₄	1	2	yes	—
84	#135×C₆₇	C₂³	1	2	yes	—
85	C₂×Q₁₆×C₆₇	—	2	2	no	—
86	C₂×Q₁₆×C₆₇	—	2	4	no	—
87	C₂×Q₁₆×C₆₇	—	2	4	no	—
88	C₂×Q₁₆×C₆₇	—	2	1	no	—
89	C₂×Q₁₆×C₆₇	—	2	1	no	—
90	C₂×Q₁₆×C₆₇	—	2	1	no	—
91	C₂×Q₁₆×C₆₇	D₄	1	1	yes	characteristic
92	C₂×Q₁₆×C₆₇	D₄	1	2	yes	—
93	C₂×Q₁₆×C₆₇	D₄	1	2	yes	—
94	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
95	C₂×SD₁₆×C₆₇	—	2	2	no	—
96	C₂×SD₁₆×C₆₇	—	2	1	no	—
97	C₂×D₈×C₆₇	D₄	1	1	yes	characteristic
98	#131×C₆₇	—	2	1	no	—
99	#131×C₆₇	—	2	1	no	—
100	#131×C₆₇	D₄	1	2	yes	—
101	#131×C₆₇	C₂³	1	2	yes	—
102	C₂×M₁₆×C₆₇	—	2	1	no	—
103	C₂×M₁₆×C₆₇	D₄	1	1	yes	characteristic
104	C₂²×C₈×C₆₇	—	2	1	no	—
105	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
106	C₂×Dic₁₃₄	—	2	2	no	—
107	C₂×Dic₁₃₄	—	4	1	no	—
108	C₂×Dic₁₃₄	—	4	1	no	—
109	C₂×Dic₁₃₄	—	4	1	no	—
110	C₂×Dic₁₃₄	—	4	1	no	—
111	C₂×Dic₁₃₄	—	4	1	no	—
112	C₂²×Dic₆₇	—	4	1	no	—
113	Dic₂₆₈	—	2	2	no	—
114	Dic₂₆₈	—	2	2	no	—
115	Dic₂₆₈	—	4	1	no	—
116	Dic₂₆₈	—	4	1	no	—
117	#11761618	—	4	4	no	—
118	#11761616	—	4	4	no	—
119	#11761612	—	2	2	no	—
120	#11761612	—	4	1	no	—
121	C₂×C₆₇⋊C₈	—	4	1	no	—
122	C₆₇⋊C₁₆	—	2	2	no	—
123	C₆₇⋊C₁₆	—	2	2	no	—
124	#41×C₆₇	—	2	1	no	—
125	#41×C₆₇	—	2	1	no	—
126	#41×C₆₇	—	2	8	no	—
127	#41×C₆₇	—	2	2	no	—
128	#41×C₆₇	—	2	2	no	—
129	#41×C₆₇	—	4	4	no	—
130	#41×C₆₇	—	4	8	no	—
131	#41×C₆₇	—	4	8	no	—
132	#41×C₆₇	—	4	4	no	—
133	#41×C₆₇	—	4	4	no	—
134	#41×C₆₇	—	4	1	no	—
135	#41×C₆₇	—	4	1	no	—
136	#41×C₆₇	D₈	1	2	yes	—
137	#41×C₆₇	C₂×D₄	1	2	yes	—
138	C₂×Q₈×C₆₇	—	2	8	no	—
139	C₂×Q₈×C₆₇	—	2	2	no	—
140	C₂×Q₈×C₆₇	—	2	1	no	—
141	C₂×Q₈×C₆₇	—	2	2	no	—
142	C₂×Q₈×C₆₇	—	2	2	no	—
143	C₂×Q₈×C₆₇	—	4	2	no	—
144	C₂×Q₈×C₆₇	—	4	4	no	—
145	C₂×Q₈×C₆₇	—	4	4	no	—
146	C₂×Q₈×C₆₇	—	4	4	no	—
147	C₂×Q₈×C₆₇	—	4	1	no	—
148	C₂×Q₈×C₆₇	—	4	1	no	—
149	C₂×Q₈×C₆₇	—	4	1	no	—
150	C₂×Q₈×C₆₇	D₈	1	1	yes	characteristic
151	C₂×D₄×C₆₇	—	2	1	no	—
152	C₂×D₄×C₆₇	—	2	1	no	—
153	C₂×D₄×C₆₇	—	4	2	no	—
154	C₂×D₄×C₆₇	—	4	1	no	—
155	C₂×D₄×C₆₇	D₈	1	1	yes	characteristic
156	C₂²×C₄×C₆₇	—	2	1	no	—
157	C₂²×C₄×C₆₇	—	4	2	no	—
158	C₂²×C₄×C₆₇	—	4	2	no	—
159	C₂²×C₄×C₆₇	—	4	1	no	—
160	C₂²×C₄×C₆₇	—	4	1	no	—
161	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
162	Q₁₆×C₆₇	—	2	8	no	—
163	Q₁₆×C₆₇	—	2	1	no	—
164	Q₁₆×C₆₇	—	2	2	no	—
165	Q₁₆×C₆₇	—	2	2	no	—
166	Q₁₆×C₆₇	—	2	2	no	—
167	Q₁₆×C₆₇	C₂×D₄	1	2	yes	—
168	Q₁₆×C₆₇	C₂×D₄	1	4	yes	—
169	SD₁₆×C₆₇	—	2	8	no	—
170	SD₁₆×C₆₇	—	2	2	no	—
171	SD₁₆×C₆₇	—	2	2	no	—
172	D₈×C₆₇	—	2	1	no	—
173	D₈×C₆₇	C₂×D₄	1	2	yes	—
174	M₁₆×C₆₇	—	2	1	no	—
175	M₁₆×C₆₇	—	2	2	no	—
176	M₁₆×C₆₇	—	2	2	no	—
177	M₁₆×C₆₇	C₂×D₄	1	2	yes	—
178	C₂×C₈×C₆₇	—	2	1	no	—
179	C₂×C₈×C₆₇	—	2	2	no	—
180	C₂×C₈×C₆₇	—	2	2	no	—
181	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
185	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
186	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
187	C₂³×C₆₇	—	2	1	no	—
188	C₂³×C₆₇	—	4	1	no	—
189	C₂³×C₆₇	AGL(1,ℤ/8)	1	1	yes	characteristic
190	Q₈×C₆₇	—	2	1	no	—
191	Q₈×C₆₇	—	2	4	no	—
192	Q₈×C₆₇	—	2	2	no	—
193	Q₈×C₆₇	—	4	8	no	—
194	Q₈×C₆₇	—	4	2	no	—
195	Q₈×C₆₇	—	4	1	no	—
196	Q₈×C₆₇	—	4	2	no	—
197	Q₈×C₆₇	—	4	2	no	—
198	Q₈×C₆₇	C₂×D₈	1	2	yes	—
199	D₄×C₆₇	—	2	2	no	—
200	D₄×C₆₇	—	2	2	no	—
201	D₄×C₆₇	—	2	2	no	—
202	D₄×C₆₇	—	2	1	no	—
203	D₄×C₆₇	—	4	8	no	—
204	D₄×C₆₇	—	4	2	no	—
205	D₄×C₆₇	—	4	2	no	—
206	D₄×C₆₇	—	4	1	no	—
207	D₄×C₆₇	C₂×D₈	1	2	yes	—
208	C₂×C₄×C₆₇	—	2	1	no	—
209	C₂×C₄×C₆₇	—	2	2	no	—
210	C₂×C₄×C₆₇	—	2	2	no	—
211	C₂×C₄×C₆₇	—	4	8	no	—
212	C₂×C₄×C₆₇	—	4	8	no	—
213	C₂×C₄×C₆₇	—	4	2	no	—
214	C₂×C₄×C₆₇	—	4	2	no	—
215	C₂×C₄×C₆₇	—	4	1	no	—
216	C₂×C₄×C₆₇	—	4	2	no	—
217	C₂×C₄×C₆₇	—	4	2	no	—
218	C₂×C₄×C₆₇	—	4	2	no	—
219	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
220	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
221	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
222	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
223	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	1	yes	characteristic
224	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
225	C₂×Dic₆₇	—	4	2	no	—
226	C₂×Dic₆₇	—	8	1	no	—
227	C₂×Dic₆₇	—	8	1	no	—
228	Dic₁₃₄	—	4	2	no	—
229	Dic₁₃₄	—	4	2	no	—
230	Dic₁₃₄	—	8	1	no	—
231	Dic₁₃₄	—	8	1	no	—
232	C₈×C₆₇	—	2	2	no	—
233	C₈×C₆₇	#120	1	1	yes	characteristic
234	C₈×C₆₇	#120	1	1	yes	characteristic
235	C₈×C₆₇	C₂²×D₄	1	1	yes	characteristic
236	C₈×C₆₇	C₂²×D₄	1	1	yes	characteristic
237	C₆₇⋊C₈	—	4	2	no	—
238	C₂²×C₆₇	—	2	2	no	—
239	C₂²×C₆₇	—	2	2	no	—
240	C₂²×C₆₇	—	4	2	no	—
241	C₂²×C₆₇	—	4	2	no	—
242	C₂²×C₆₇	—	8	2	no	—
243	C₂²×C₆₇	#447	1	1	yes	characteristic
244	C₂²×C₆₇	#447	1	1	yes	characteristic
245	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
246	C₄×C₆₇	—	2	2	no	—
247	C₄×C₆₇	—	4	4	no	—
248	C₄×C₆₇	—	4	2	no	—
249	C₄×C₆₇	#447	1	1	yes	characteristic
250	C₄×C₆₇	#447	1	1	yes	characteristic
251	C₄×C₆₇	C₂×#120	1	1	yes	characteristic
252	C₄×C₆₇	C₂²×D₈	1	1	yes	characteristic
253	Dic₆₇	—	8	2	no	—
254	C₂×#2195	—	67	1	no	maximal, Sylow
255	C₂×C₆₇	—	2	1	no	—
256	C₂×C₆₇	—	2	1	no	—
257	C₂×C₆₇	—	4	2	no	—
258	C₂×C₆₇	—	8	2	no	—
259	C₂×C₆₇	#2195	1	2	yes	complemented
260	C₂×C₆₇	C₂×#447	1	1	yes	characteristic
261	C₂×#578	D₆₇	1	1	yes	characteristic
262	C₂×#510	—	67	1	no	—
263	C₂²×Q₃₂	—	67	1	no	—
264	C₂×#473	—	67	1	no	—
265	#2195	—	67	8	no	—
266	C₂×#362	—	67	1	no	—
267	C₂×#359	—	67	1	no	—
268	C₂×#350	—	67	1	no	—
269	C₆₇	C₂×#2195	1	1	yes	characteristic, complemented, Sylow
270	C₂×2₋¹⁺⁴	—	2	1	no	—
271	#578	—	2	2	no	—
272	#578	—	2	2	no	—
273	#578	—	2	2	no	—
274	#578	C₂×D₆₇	1	4	yes	—
275	C₂×#137	—	2	2	no	—
276	C₂×#137	—	2	1	no	—
277	C₂×#137	—	134	1	no	—
278	C₂×#135	—	2	1	no	—
279	C₂×#135	C₂×D₆₇	1	1	yes	characteristic
280	C₂²×Q₁₆	—	2	1	no	—
281	C₂²×Q₁₆	—	67	1	no	—
282	C₂²×Q₁₆	C₂×D₆₇	1	1	yes	characteristic
283	C₂×#131	C₂×D₆₇	1	1	yes	characteristic
284	#510	—	67	4	no	—
285	#510	—	134	2	no	—
286	C₂×Q₃₂	—	67	4	no	—
287	C₂×Q₃₂	—	134	2	no	—
288	C₂×Q₃₂	—	134	2	no	—
289	C₂×Q₃₂	—	134	1	no	—
290	C₂×SD₃₂	—	134	1	no	—
291	C₂×M₃₂	—	67	1	no	—
292	C₂²×C₁₆	—	67	1	no	—
293	#473	—	67	4	no	—
294	#473	—	134	2	no	—
295	C₂×#108	—	67	1	no	—
296	C₂×#101	—	134	1	no	—
297	#362	—	67	4	no	—
298	#359	—	67	4	no	—
299	#350	—	67	4	no	—
300	2₋¹⁺⁴	—	2	4	no	—
301	2₋¹⁺⁴	—	2	4	no	—
302	2₋¹⁺⁴	—	4	2	no	—
303	2₋¹⁺⁴	—	4	2	no	—
304	C₂×#41	—	2	2	no	—
305	C₂×#41	—	2	1	no	—
306	C₂×#41	—	4	2	no	—
307	C₂×#41	—	4	1	no	—
308	C₂×#41	C₂²⋊D₆₇	1	1	yes	characteristic
309	C₂²×Q₈	—	2	2	no	—
310	C₂²×Q₈	—	2	1	no	—
311	C₂²×Q₈	—	4	1	no	—
312	C₂²×Q₈	—	134	1	no	—
313	#137	—	2	4	no	—
314	#137	—	2	8	no	—
315	#137	—	2	8	no	—
316	#137	—	2	4	no	—
317	#137	—	268	2	no	—
318	#137	—	134	4	no	—
319	#135	—	2	4	no	—
320	#135	—	2	4	no	—
321	#135	—	2	1	no	—
322	#135	—	2	1	no	—
323	#135	C₂²⋊D₆₇	1	2	yes	—
324	#135	C₂²×D₆₇	1	2	yes	—
325	C₂×Q₁₆	—	2	2	no	—
326	C₂×Q₁₆	—	2	4	no	—
327	C₂×Q₁₆	—	2	4	no	—
328	C₂×Q₁₆	—	2	1	no	—
329	C₂×Q₁₆	—	2	1	no	—
330	C₂×Q₁₆	—	2	1	no	—
331	C₂×Q₁₆	—	268	1	no	—
332	C₂×Q₁₆	—	67	2	no	—
333	C₂×Q₁₆	—	134	1	no	—
334	C₂×Q₁₆	—	134	1	no	—
335	C₂×Q₁₆	—	134	1	no	—
336	C₂×Q₁₆	—	134	1	no	—
337	C₂×Q₁₆	—	134	1	no	—
338	C₂×Q₁₆	C₂²⋊D₆₇	1	1	yes	characteristic
339	C₂×Q₁₆	C₂²⋊D₆₇	1	2	yes	—
340	C₂×Q₁₆	C₂²⋊D₆₇	1	2	yes	—
341	C₂×Q₁₆	C₂²×D₆₇	1	2	yes	—
342	C₂×SD₁₆	—	2	2	no	—
343	C₂×SD₁₆	—	2	1	no	—
344	C₂×SD₁₆	—	268	1	no	—
345	C₂×D₈	C₂²⋊D₆₇	1	1	yes	characteristic
346	#131	—	2	1	no	—
347	#131	—	2	1	no	—
348	#131	C₂²⋊D₆₇	1	2	yes	—
349	#131	C₂²×D₆₇	1	2	yes	—
350	C₂×M₁₆	—	2	1	no	—
351	C₂×M₁₆	—	134	1	no	—
352	C₂×M₁₆	C₂²⋊D₆₇	1	1	yes	characteristic
353	C₂²×C₈	—	2	1	no	—
354	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
355	Q₃₂	—	134	8	no	—
356	Q₃₂	—	134	4	no	—
357	SD₃₂	—	134	4	no	—
358	M₃₂	—	67	2	no	—
359	M₃₂	—	134	1	no	—
360	C₂×C₁₆	—	67	2	no	—
361	C₂×C₁₆	—	134	1	no	—
362	C₂×C₁₆	—	134	1	no	—
363	C₂×C₁₆	—	134	1	no	—
364	#108	—	67	2	no	—
365	#108	—	134	1	no	—
366	#101	—	134	4	no	—
367	#41	—	2	1	no	—
368	#41	—	2	1	no	—
369	#41	—	2	8	no	—
370	#41	—	2	2	no	—
371	#41	—	2	2	no	—
372	#41	—	4	4	no	—
373	#41	—	4	8	no	—
374	#41	—	4	8	no	—
375	#41	—	4	4	no	—
376	#41	—	4	4	no	—
377	#41	—	4	1	no	—
378	#41	—	4	1	no	—
379	#41	#11761613	1	2	yes	—
380	#41	C₂×C₂²⋊D₆₇	1	2	yes	—
381	C₂×Q₈	—	2	8	no	—
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	—	2	1	no	—
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	—	4	2	no	—
387	C₂×Q₈	—	4	4	no	—
388	C₂×Q₈	—	4	4	no	—
389	C₂×Q₈	—	4	4	no	—
390	C₂×Q₈	—	4	1	no	—
391	C₂×Q₈	—	4	1	no	—
392	C₂×Q₈	—	4	1	no	—
393	C₂×Q₈	—	268	1	no	—
394	C₂×Q₈	—	268	1	no	—
395	C₂×Q₈	—	268	1	no	—
396	C₂×Q₈	—	268	1	no	—
397	C₂×Q₈	—	268	1	no	—
398	C₂×Q₈	—	134	2	no	—
399	C₂×Q₈	#11761613	1	1	yes	characteristic
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	—	4	2	no	—
403	C₂×D₄	—	4	1	no	—
404	C₂×D₄	#11761613	1	1	yes	characteristic
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	4	2	no	—
407	C₂²×C₄	—	4	2	no	—
408	C₂²×C₄	—	4	1	no	—
409	C₂²×C₄	—	4	1	no	—
410	C₂²×C₄	—	268	1	no	—
411	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
412	Q₁₆	—	2	8	no	—
413	Q₁₆	—	2	1	no	—
414	Q₁₆	—	2	2	no	—
415	Q₁₆	—	2	2	no	—
416	Q₁₆	—	2	2	no	—
417	Q₁₆	—	268	4	no	—
418	Q₁₆	—	268	1	no	—
419	Q₁₆	—	268	1	no	—
420	Q₁₆	—	134	2	no	—
421	Q₁₆	—	134	2	no	—
422	Q₁₆	C₂×C₂²⋊D₆₇	1	2	yes	—
423	Q₁₆	C₂×C₂²⋊D₆₇	1	4	yes	—
424	SD₁₆	—	2	8	no	—
425	SD₁₆	—	2	2	no	—
426	SD₁₆	—	2	2	no	—
427	SD₁₆	—	268	4	no	—
428	D₈	—	2	1	no	—
429	D₈	C₂×C₂²⋊D₆₇	1	2	yes	—
430	M₁₆	—	2	1	no	—
431	M₁₆	—	2	2	no	—
432	M₁₆	—	2	2	no	—
433	M₁₆	—	268	1	no	—
434	M₁₆	—	134	2	no	—
435	M₁₆	C₂×C₂²⋊D₆₇	1	2	yes	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	268	1	no	—
440	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
441	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
442	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
443	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
444	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
445	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
446	C₁₆	—	134	2	no	—
447	C₁₆	—	134	2	no	—
448	C₂³	—	2	1	no	—
449	C₂³	—	4	1	no	—
450	C₂³	#14524069	1	1	yes	characteristic
451	Q₈	—	2	1	no	—
452	Q₈	—	2	4	no	—
453	Q₈	—	2	2	no	—
454	Q₈	—	4	8	no	—
455	Q₈	—	4	1	no	—
456	Q₈	—	4	2	no	—
457	Q₈	—	4	2	no	—
458	Q₈	—	4	2	no	—
459	Q₈	—	268	2	no	—
460	Q₈	—	268	2	no	—
461	Q₈	—	536	1	no	—
462	Q₈	—	536	1	no	—
463	Q₈	C₂×#11761613	1	2	yes	—
464	D₄	—	2	2	no	—
465	D₄	—	2	2	no	—
466	D₄	—	2	1	no	—
467	D₄	—	2	2	no	—
468	D₄	—	4	8	no	—
469	D₄	—	4	2	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	1	no	—
472	D₄	C₂×#11761613	1	2	yes	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	4	8	no	—
477	C₂×C₄	—	4	8	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	268	2	no	—
485	C₂×C₄	—	536	1	no	—
486	C₂×C₄	—	536	1	no	—
487	C₂×C₄	#14524012	1	1	yes	characteristic
488	C₂×C₄	#14524012	1	1	yes	characteristic
489	C₂×C₄	C₂×#11761613	1	1	yes	characteristic
490	C₂×C₄	C₂×#11761613	1	1	yes	characteristic
491	C₂×C₄	#14524069	1	1	yes	characteristic
492	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
493	C₈	—	2	2	no	—
494	C₈	—	268	2	no	—
495	C₈	#14524012	1	1	yes	characteristic
496	C₈	#14524012	1	1	yes	characteristic
497	C₈	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
498	C₈	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
499	C₂²	—	2	2	no	—
500	C₂²	—	2	2	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	8	2	no	—
504	C₂²	#16863530	1	1	yes	characteristic
505	C₂²	#16863530	1	1	yes	characteristic
506	C₂²	C₂×#14524069	1	1	yes	characteristic
507	C₄	—	2	2	no	—
508	C₄	—	4	4	no	—
509	C₄	—	4	2	no	—
510	C₄	—	536	2	no	—
511	C₄	#16863530	1	1	yes	characteristic
512	C₄	#16863530	1	1	yes	characteristic
513	C₄	C₂×#14524012	1	1	yes	characteristic
514	C₄	C₂²×#11761613	1	1	yes	characteristic
515	C₂	—	2	1	no	—
516	C₂	—	2	1	no	—
517	C₂	—	4	2	no	—
518	C₂	—	8	2	no	—
519	C₂	#22562187	1	2	yes	direct product factor
520	C₂	C₂×#16863530	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16863530
commutator, cosocle	C₂×C₈×C₆₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₆₇
Fitting, prime radical	C₂×#578×C₆₇	C₂
socle	C₂²×C₆₇	#447
hypercenter	C₂×#578	D₆₇
hypocenter	C₆₇	C₂×#2195
LCS	G ▷ C₂×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#131 ◁ C₂×#578

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#16863836	C₂	semidirect
2. C₂²×#14523989	C₂	semidirect
3. C₂×#16863671	C₂	semidirect
4. #22562187	C₂	direct (N × H)
5. C₂×#16863212	C₂	semidirect
6. C₂×#16863203	C₂	semidirect
7. C₂×#16863180	C₂	semidirect
12. #16863836	C₂²	semidirect
16. C₂×#14523989	C₂²	semidirect
21. #16863671	C₂²	semidirect
24. #16863212	C₂²	semidirect
25. #16863203	C₂²	semidirect
26. #16863180	C₂²	semidirect
259. C₂×C₆₇	#2195	semidirect
269. C₆₇	C₂×#2195	semidirect
519. C₂	#22562187	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#16863836	2
C₂²×#14523989	2
C₂×#16863671	2
#22562187	2
C₂×#16863212	2
C₂×#16863203	2
C₂×#16863180	2
C₂×#578×C₆₇	2
C₂×#2195	67

Subgroups — C2×#22562187 #31009778

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22562187 #31009778