Subgroups — #30862733

Order 17152.

938 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863666	C₂	1	1	yes	maximal, characteristic
2	C₄×#14524068	C₂	1	2	yes	maximal, complemented
3	C₂×#16863509	C₂	1	1	yes	maximal, characteristic, complemented
4	#22561119	C₂	1	1	yes	maximal, characteristic, complemented
5	#22560989	C₂	1	1	yes	maximal, characteristic, complemented
6	#22560871	C₂	1	2	yes	maximal, complemented
7	#22560717	C₂	1	2	yes	maximal, complemented
8	#22560268	C₂	1	1	yes	maximal, characteristic, complemented
9	#22560115	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#14523959	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2875	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14524068	C₂²	1	2	yes	—
13	C₂²×D₅₃₆	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₂₆₈	C₂²	1	2	yes	—
15	#16863666	C₄	1	8	yes	complemented
16	#16863509	—	2	1	no	—
17	#16863509	—	2	1	no	—
18	#16863509	—	2	1	no	—
19	#16863509	—	2	1	no	—
20	#16863506	—	2	2	no	—
21	#16863494	—	2	2	no	—
22	C₄×#11761615	—	2	2	no	—
23	C₄×#11761613	—	2	2	no	—
24	C₂×#14523979	C₂²	1	1	yes	characteristic
25	C₂×#14523979	C₂²	1	1	yes	characteristic
26	#16863439	C₂²	1	2	yes	—
27	C₂×#14523975	C₂²	1	1	yes	characteristic
28	#16863400	C₂²	1	2	yes	—
29	#16863397	C₂²	1	2	yes	—
30	C₂×#14523965	C₂²	1	2	yes	—
31	C₂×#14523959	C₂²	1	2	yes	—
32	C₂×#14523959	C₂²	1	2	yes	—
33	C₄×#11761612	C₂²	1	2	yes	—
34	#16863164	C₂²	1	2	yes	—
35	#16863164	C₂²	1	2	yes	—
36	#16863161	C₂²	1	2	yes	—
37	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
39	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
40	#405×C₆₇	—	2	1	no	—
41	#405×C₆₇	—	2	1	no	—
42	#405×C₆₇	C₂²	1	1	yes	characteristic
43	#405×C₆₇	C₂²	1	1	yes	characteristic
44	C₄×M₁₆×C₆₇	—	2	1	no	—
45	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
46	C₂×#97×C₆₇	—	2	1	no	—
47	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
48	C₂²×D₂₆₈	C₂³	1	2	yes	—
49	C₂²×C₄×D₆₇	—	2	2	no	—
50	#14524068	—	2	4	no	—
51	#14524068	C₂×C₄	1	8	yes	complemented
52	C₂×#11761615	—	2	2	no	—
53	C₂×D₅₃₆	—	2	1	no	—
54	C₂×D₅₃₆	—	2	1	no	—
55	C₂×D₅₃₆	—	2	2	no	—
56	C₂×D₅₃₆	C₂×C₄	1	4	yes	complemented
57	C₂×#11761613	—	2	2	no	—
58	C₂×#11761612	C₂³	1	2	yes	—
59	C₂×#11761612	C₂³	1	2	yes	—
60	C₄×D₂₆₈	—	2	2	no	—
61	C₄×D₂₆₈	—	2	2	no	—
62	C₄×D₂₆₈	—	2	2	no	—
63	C₄×D₂₆₈	—	2	2	no	—
64	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
65	C₂×(C₂×D₆₇)⋊C₄	—	2	2	no	—
66	#14523979	—	2	2	no	—
67	#14523979	C₂×C₄	1	4	yes	complemented
68	#14523976	—	2	2	no	—
69	#14523975	—	2	1	no	—
70	#14523975	—	2	1	no	—
71	#14523974	—	2	2	no	—
72	#14523967	—	2	2	no	—
73	#14523965	—	2	2	no	—
74	#14523965	—	2	2	no	—
75	#14523964	—	2	2	no	—
76	#14523963	—	2	2	no	—
77	#14523963	—	2	2	no	—
78	#14523959	—	2	4	no	—
79	#14523959	C₂×C₄	1	8	yes	complemented
80	#14523954	—	2	2	no	—
81	C₄×C₆₇⋊C₈	—	2	2	no	—
82	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
83	#131×C₆₇	—	2	2	no	—
84	#131×C₆₇	—	2	2	no	—
85	#131×C₆₇	—	2	2	no	—
86	#131×C₆₇	C₂×C₄	1	4	yes	complemented
87	C₂×M₁₆×C₆₇	—	2	1	no	—
88	C₂×M₁₆×C₆₇	—	2	1	no	—
89	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
90	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₆₇	—	2	1	no	—
92	C₂²×C₈×C₆₇	—	2	1	no	—
93	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
95	C₄×Q₈×C₆₇	D₄	1	2	yes	—
96	C₄×D₄×C₆₇	—	2	2	no	—
97	C₄×D₄×C₆₇	D₄	1	2	yes	—
98	#117×C₆₇	—	2	1	no	—
99	#117×C₆₇	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₆₇	—	2	1	no	—
101	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
102	#97×C₆₇	—	2	1	no	—
103	#97×C₆₇	—	2	1	no	—
104	#97×C₆₇	—	2	1	no	—
105	#97×C₆₇	D₄	1	1	yes	characteristic
106	#97×C₆₇	D₄	1	1	yes	characteristic
107	#97×C₆₇	D₄	1	1	yes	characteristic
108	#97×C₆₇	D₄	1	1	yes	characteristic
109	C₄×C₈×C₆₇	—	2	1	no	—
110	C₄×C₈×C₆₇	—	2	1	no	—
111	C₄×C₈×C₆₇	—	2	1	no	—
112	C₂³×D₆₇	—	2	2	no	—
113	C₂×D₂₆₈	—	2	2	no	—
114	C₂×D₂₆₈	—	2	2	no	—
115	C₂×D₂₆₈	—	2	2	no	—
116	C₂×D₂₆₈	—	2	2	no	—
117	C₂×D₂₆₈	—	2	2	no	—
118	C₂×D₂₆₈	C₂²×C₄	1	4	yes	—
119	C₂²×Dic₆₇	—	2	2	no	—
120	C₂×C₄×D₆₇	—	4	2	no	—
121	C₂×C₄×D₆₇	—	4	2	no	—
122	C₂×C₄×D₆₇	—	8	4	no	—
123	#11761615	—	2	8	no	—
124	D₅₃₆	—	2	4	no	—
125	D₅₃₆	—	2	4	no	—
126	#11761613	—	2	8	no	—
127	#11761612	—	2	2	no	—
128	#11761612	—	2	2	no	—
129	#11761612	—	2	2	no	—
130	#11761612	C₂²×C₄	1	4	yes	—
131	C₂×C₆₇⋊C₈	—	2	2	no	—
132	C₂×C₆₇⋊C₈	—	2	2	no	—
133	C₄⋊Dic₆₇	—	2	2	no	—
134	C₄⋊Dic₆₇	—	2	2	no	—
135	(C₂×D₆₇)⋊C₄	—	4	2	no	—
136	(C₂×D₆₇)⋊C₄	—	4	2	no	—
137	#41×C₆₇	—	2	1	no	—
138	#41×C₆₇	—	2	1	no	—
139	#41×C₆₇	C₂²×C₄	1	2	yes	—
140	#41×C₆₇	#41	1	2	yes	—
141	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
142	C₂×D₄×C₆₇	—	2	1	no	—
143	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₆₇	—	2	1	no	—
145	C₂²×C₄×C₆₇	—	2	2	no	—
146	C₂²×C₄×C₆₇	#41	1	2	yes	—
147	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
148	M₁₆×C₆₇	—	2	4	no	—
149	M₁₆×C₆₇	—	2	1	no	—
150	M₁₆×C₆₇	—	2	1	no	—
151	M₁₆×C₆₇	—	2	4	no	—
152	M₁₆×C₆₇	C₂²×C₄	1	2	yes	—
153	M₁₆×C₆₇	#41	1	2	yes	—
154	C₂×C₈×C₆₇	—	2	4	no	—
155	C₂×C₈×C₆₇	—	2	1	no	—
156	C₂×C₈×C₆₇	—	2	1	no	—
157	C₂×C₈×C₆₇	—	2	1	no	—
158	C₂×C₈×C₆₇	—	2	1	no	—
159	C₂×C₈×C₆₇	—	2	4	no	—
160	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
161	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
162	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
163	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
164	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
165	C₂×C₈×C₆₇	#41	1	2	yes	—
166	C₄⋊C₄×C₆₇	—	2	2	no	—
167	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
168	C₂²⋊C₄×C₆₇	—	2	1	no	—
169	C₂²⋊C₄×C₆₇	—	2	2	no	—
170	C₄²×C₆₇	—	2	2	no	—
171	C₄²×C₆₇	—	2	1	no	—
172	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₆₇	C₂×D₄	1	2	yes	—
175	C₂³×C₆₇	—	2	1	no	—
176	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
177	C₂²×D₆₇	—	2	4	no	—
178	C₂²×D₆₇	—	4	2	no	—
179	C₂²×D₆₇	—	4	2	no	—
180	C₂²×D₆₇	—	8	2	no	—
181	C₂²×D₆₇	—	8	2	no	—
182	Q₈×C₆₇	—	2	1	no	—
183	Q₈×C₆₇	C₄×D₄	1	2	yes	—
184	D₄×C₆₇	—	2	2	no	—
185	D₄×C₆₇	—	2	2	no	—
186	D₄×C₆₇	—	2	1	no	—
187	D₄×C₆₇	C₄×D₄	1	2	yes	—
188	C₂×C₄×C₆₇	—	2	1	no	—
189	C₂×C₄×C₆₇	—	2	2	no	—
190	C₂×C₄×C₆₇	—	2	2	no	—
191	C₂×C₄×C₆₇	—	2	2	no	—
192	C₂×C₄×C₆₇	—	4	2	no	—
193	C₂×C₄×C₆₇	—	8	2	no	—
194	C₂×C₄×C₆₇	#121	1	2	yes	—
195	C₂×C₄×C₆₇	#121	1	2	yes	—
196	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
197	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
202	C₂×Dic₆₇	—	4	2	no	—
203	C₂×Dic₆₇	—	8	2	no	—
204	D₂₆₈	—	2	4	no	—
205	D₂₆₈	—	2	4	no	—
206	D₂₆₈	—	4	2	no	—
207	D₂₆₈	—	4	2	no	—
208	C₄×D₆₇	—	8	4	no	—
209	C₄×D₆₇	—	8	4	no	—
210	C₈×C₆₇	—	2	2	no	—
211	C₈×C₆₇	—	2	1	no	—
212	C₈×C₆₇	—	2	2	no	—
213	C₈×C₆₇	—	2	1	no	—
214	C₈×C₆₇	C₄×D₄	1	2	yes	—
215	C₈×C₆₇	C₄×D₄	1	2	yes	—
216	C₆₇⋊C₈	—	2	4	no	—
217	C₆₇⋊C₈	—	4	2	no	—
218	C₂²×C₆₇	—	2	2	no	—
219	C₂²×C₆₇	—	2	2	no	—
220	C₂²×C₆₇	—	4	2	no	—
221	C₂²×C₆₇	C₄×#41	1	1	yes	characteristic
222	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
223	C₂²×C₆₇	#529	1	1	yes	characteristic
224	C₂×D₆₇	—	4	4	no	—
225	C₂×D₆₇	—	8	4	no	—
226	C₂×D₆₇	—	8	2	no	—
227	C₂×D₆₇	—	8	2	no	—
228	C₂×D₆₇	—	8	4	no	—
229	C₄×C₆₇	—	2	2	no	—
230	C₄×C₆₇	—	2	2	no	—
231	C₄×C₆₇	—	2	2	no	—
232	C₄×C₆₇	—	4	2	no	—
233	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
234	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
235	C₄×C₆₇	#525	1	1	yes	characteristic
236	C₄×C₆₇	#532	1	1	yes	characteristic
237	Dic₆₇	—	8	2	no	—
238	#21555	—	67	1	no	maximal, Sylow
239	C₂×C₆₇	—	2	1	no	—
240	C₂×C₆₇	—	2	1	no	—
241	C₂×C₆₇	—	4	2	no	—
242	C₂×C₆₇	C₄×#121	1	1	yes	characteristic
243	C₂×C₆₇	#3068	1	2	yes	—
244	D₆₇	—	8	4	no	—
245	C₂×#472	—	67	1	no	—
246	C₄×AGL(1,ℤ/8)	—	67	2	no	—
247	C₂×#442	—	67	1	no	—
248	#2875	D₆₇	1	1	yes	characteristic, complemented
249	#1978	—	67	1	no	—
250	#1951	—	67	1	no	—
251	#1931	—	67	2	no	—
252	#1907	—	67	2	no	—
253	#1815	—	67	1	no	—
254	#1778	—	67	1	no	—
255	C₄×#100	—	67	2	no	—
256	C₆₇	#21555	1	1	yes	characteristic, complemented, Sylow
257	C₂×AGL(1,ℤ/8)	—	67	2	no	—
258	C₂²×D₈	—	67	1	no	—
259	C₂×#131	C₂×D₆₇	1	1	yes	characteristic
260	C₂×#131	C₂×D₆₇	1	1	yes	characteristic
261	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
262	C₂×C₄×D₄	—	67	2	no	—
263	#472	—	67	8	no	—
264	#442	—	134	2	no	—
265	#442	—	134	1	no	—
266	#442	—	134	1	no	—
267	#442	—	134	1	no	—
268	#442	—	134	1	no	—
269	#440	—	134	2	no	—
270	C₄×SD₁₆	—	134	2	no	—
271	C₄×D₈	—	134	2	no	—
272	C₂×#108	—	67	1	no	—
273	C₂×#108	—	67	1	no	—
274	#428	—	67	2	no	—
275	C₂×#106	—	67	1	no	—
276	#418	—	67	2	no	—
277	#417	—	67	2	no	—
278	C₂×#102	—	67	2	no	—
279	C₂×#100	—	67	2	no	—
280	C₂×#100	—	67	2	no	—
281	#405	—	2	1	no	—
282	#405	—	2	1	no	—
283	#405	C₂×D₆₇	1	1	yes	characteristic
284	#405	C₂×D₆₇	1	1	yes	characteristic
285	C₄×M₁₆	—	2	1	no	—
286	C₄×M₁₆	—	67	2	no	—
287	C₄×M₁₆	C₂×D₆₇	1	1	yes	characteristic
288	C₂×#97	—	2	1	no	—
289	C₂×#97	C₂×D₆₇	1	1	yes	characteristic
290	#343	—	67	2	no	—
291	#343	—	67	2	no	—
292	#341	—	67	2	no	—
293	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
294	C₂²×D₄	—	67	2	no	—
295	C₂³×C₄	—	134	2	no	—
296	AGL(1,ℤ/8)	—	67	8	no	—
297	AGL(1,ℤ/8)	—	134	4	no	—
298	C₂×SD₁₆	—	134	2	no	—
299	C₂×D₈	—	67	4	no	—
300	C₂×D₈	—	134	2	no	—
301	C₂×D₈	—	134	1	no	—
302	C₂×D₈	—	134	1	no	—
303	C₂×D₈	—	134	2	no	—
304	#131	—	2	2	no	—
305	#131	—	2	2	no	—
306	#131	—	2	2	no	—
307	#131	C₄×D₆₇	1	4	yes	complemented
308	C₂×M₁₆	—	2	1	no	—
309	C₂×M₁₆	—	2	1	no	—
310	C₂×M₁₆	—	67	2	no	—
311	C₂×M₁₆	—	67	2	no	—
312	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
313	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
314	C₂²×C₈	—	2	1	no	—
315	C₂²×C₈	—	2	1	no	—
316	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
317	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
318	C₄×Q₈	D₂₆₈	1	2	yes	—
319	C₄×D₄	—	2	2	no	—
320	C₄×D₄	—	134	2	no	—
321	C₄×D₄	—	134	2	no	—
322	C₄×D₄	—	134	2	no	—
323	C₄×D₄	—	134	2	no	—
324	C₄×D₄	D₂₆₈	1	2	yes	—
325	#117	—	2	1	no	—
326	#117	C₂²×D₆₇	1	1	yes	characteristic
327	C₂×C₄⋊C₄	—	67	2	no	—
328	C₂×C₂²⋊C₄	—	134	2	no	—
329	C₂×C₄²	—	2	1	no	—
330	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
331	#108	—	67	4	no	—
332	#108	—	134	2	no	—
333	#107	—	134	2	no	—
334	#106	—	134	1	no	—
335	#106	—	134	1	no	—
336	#106	—	134	2	no	—
337	#103	—	134	2	no	—
338	#102	—	134	2	no	—
339	#102	—	134	2	no	—
340	#102	—	134	2	no	—
341	#102	—	134	2	no	—
342	#102	—	134	2	no	—
343	#100	—	67	8	no	—
344	#100	—	134	4	no	—
345	#97	—	2	1	no	—
346	#97	—	2	1	no	—
347	#97	—	2	1	no	—
348	#97	—	134	2	no	—
349	#97	C₂²⋊D₆₇	1	1	yes	characteristic
350	#97	C₂²⋊D₆₇	1	1	yes	characteristic
351	#97	C₂²⋊D₆₇	1	1	yes	characteristic
352	#97	C₂²⋊D₆₇	1	1	yes	characteristic
353	C₄×C₈	—	2	1	no	—
354	C₄×C₈	—	2	1	no	—
355	C₄×C₈	—	2	1	no	—
356	C₄×C₈	—	134	2	no	—
357	C₂⁴	—	134	2	no	—
358	#41	—	2	1	no	—
359	#41	—	2	1	no	—
360	#41	C₂×C₄×D₆₇	1	2	yes	—
361	#41	#11761628	1	2	yes	—
362	C₂×Q₈	C₂×D₂₆₈	1	1	yes	characteristic
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	67	4	no	—
365	C₂×D₄	—	134	2	no	—
366	C₂×D₄	—	134	2	no	—
367	C₂×D₄	—	134	2	no	—
368	C₂×D₄	—	134	2	no	—
369	C₂×D₄	—	134	2	no	—
370	C₂×D₄	C₂×D₂₆₈	1	1	yes	characteristic
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	268	2	no	—
374	C₂²×C₄	—	268	2	no	—
375	C₂²×C₄	—	536	4	no	—
376	C₂²×C₄	—	134	2	no	—
377	C₂²×C₄	#11761628	1	2	yes	—
378	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
379	SD₁₆	—	134	8	no	—
380	D₈	—	134	8	no	—
381	D₈	—	134	4	no	—
382	D₈	—	134	4	no	—
383	M₁₆	—	2	4	no	—
384	M₁₆	—	2	1	no	—
385	M₁₆	—	2	1	no	—
386	M₁₆	—	2	4	no	—
387	M₁₆	—	67	4	no	—
388	M₁₆	—	134	2	no	—
389	M₁₆	—	134	2	no	—
390	M₁₆	—	134	2	no	—
391	M₁₆	C₂×C₄×D₆₇	1	2	yes	—
392	M₁₆	#11761628	1	2	yes	—
393	C₂×C₈	—	2	4	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	4	no	—
399	C₂×C₈	—	134	2	no	—
400	C₂×C₈	—	134	2	no	—
401	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
402	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
403	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
404	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
405	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
406	C₂×C₈	#11761628	1	2	yes	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	134	2	no	—
409	C₄⋊C₄	—	134	2	no	—
410	C₄⋊C₄	C₂×D₂₆₈	1	2	yes	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	268	2	no	—
414	C₂²⋊C₄	—	268	2	no	—
415	C₄²	—	2	2	no	—
416	C₄²	—	2	1	no	—
417	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
418	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
419	C₄²	C₂×D₂₆₈	1	2	yes	—
420	C₂³	—	2	1	no	—
421	C₂³	—	268	2	no	—
422	C₂³	—	268	2	no	—
423	C₂³	—	536	2	no	—
424	C₂³	—	536	2	no	—
425	C₂³	—	134	4	no	—
426	C₂³	C₂×#11761628	1	1	yes	characteristic
427	Q₈	—	2	1	no	—
428	Q₈	C₄×D₂₆₈	1	2	yes	—
429	D₄	—	2	2	no	—
430	D₄	—	2	2	no	—
431	D₄	—	2	1	no	—
432	D₄	—	268	2	no	—
433	D₄	—	268	2	no	—
434	D₄	—	134	4	no	—
435	D₄	—	134	4	no	—
436	D₄	C₄×D₂₆₈	1	2	yes	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	8	2	no	—
443	C₂×C₄	—	268	2	no	—
444	C₂×C₄	—	536	4	no	—
445	C₂×C₄	—	536	4	no	—
446	C₂×C₄	—	536	2	no	—
447	C₂×C₄	#14524017	1	2	yes	—
448	C₂×C₄	#14524017	1	2	yes	—
449	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
450	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
451	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
452	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
453	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
454	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
455	C₈	—	2	2	no	—
456	C₈	—	2	1	no	—
457	C₈	—	2	2	no	—
458	C₈	—	2	1	no	—
459	C₈	—	268	2	no	—
460	C₈	—	134	4	no	—
461	C₈	C₄×C₂²⋊D₆₇	1	2	yes	—
462	C₈	C₄×C₂²⋊D₆₇	1	2	yes	—
463	C₂²	—	2	2	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	268	4	no	—
467	C₂²	—	536	4	no	—
468	C₂²	—	536	4	no	—
469	C₂²	—	536	2	no	—
470	C₂²	—	536	2	no	—
471	C₂²	C₄×#11761628	1	1	yes	characteristic
472	C₂²	C₂×#14524017	1	1	yes	characteristic
473	C₂²	#16863930	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	4	2	no	—
478	C₄	—	536	2	no	—
479	C₄	C₂×C₄×C₂²⋊D₆₇	1	1	yes	characteristic
480	C₄	C₂×C₄×D₂₆₈	1	1	yes	characteristic
481	C₄	#16863907	1	1	yes	characteristic
482	C₄	#16863946	1	1	yes	characteristic
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	4	2	no	—
486	C₂	—	536	4	no	—
487	C₂	C₄×#14524017	1	1	yes	characteristic
488	C₂	#22569937	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#14524017
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₆₇×#2875	C₂
socle	C₂²×C₆₇	C₂×#121
prime radical	C₂×#16863666	C₂
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#2875	D₆₇
hypocenter	C₆₇	#21555
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2875

Complements

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

N	H ≅ G/N	type
2. C₄×#14524068	C₂	semidirect
3. C₂×#16863509	C₂	semidirect
4. #22561119	C₂	semidirect
5. #22560989	C₂	semidirect
6. #22560871	C₂	semidirect
7. #22560717	C₂	semidirect
8. #22560268	C₂	semidirect
9. #22560115	C₂	semidirect
10. C₄×#14523959	C₂	semidirect
11. C₆₇×#2875	C₂	semidirect
15. #16863666	C₄	semidirect
51. #14524068	C₂×C₄	semidirect
56. C₂×D₅₃₆	C₂×C₄	semidirect
67. #14523979	C₂×C₄	semidirect
79. #14523959	C₂×C₄	semidirect
86. #131×C₆₇	C₂×C₄	semidirect
248. #2875	D₆₇	semidirect
256. C₆₇	#21555	semidirect
307. #131	C₄×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863666	2
C₄×#14524068	2
C₂×#16863509	2
#22561119	2
#22560989	2
#22560871	2
#22560717	2
#22560268	2
#22560115	2
C₄×#14523959	2
C₆₇×#2875	2
#21555	67