Subgroups — #30821530

Order 17152.

734 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22569171	C₂	1	1	yes	maximal, characteristic
2	C₈×#11761628	C₂	1	1	yes	maximal, characteristic
3	#22568848	C₂	1	1	yes	maximal, characteristic
4	#22558509	C₂	1	1	yes	maximal, characteristic, complemented
5	#22558508	C₂	1	1	yes	maximal, characteristic, complemented
6	#22558506	C₂	1	1	yes	maximal, characteristic, complemented
7	#22558503	C₂	1	1	yes	maximal, characteristic, complemented
8	#22558501	C₂	1	1	yes	maximal, characteristic, complemented
9	#22558500	C₂	1	1	yes	maximal, characteristic, complemented
10	#22558497	C₂	1	1	yes	maximal, characteristic, complemented
11	#22558491	C₂	1	1	yes	maximal, characteristic, complemented
12	#22558488	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈×#11761611	C₂	1	1	yes	maximal, characteristic, complemented
14	#322×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#11761628	C₂²	1	1	yes	characteristic
17	#16863524	C₄	1	2	yes	—
18	C₈×Dic₁₃₄	C₄	1	2	yes	—
19	#16863472	C₄	1	2	yes	—
20	#16863469	C₄	1	2	yes	—
21	#16863465	C₄	1	2	yes	—
22	C₈×D₂₆₈	C₄	1	2	yes	—
23	C₈×C₂²⋊D₆₇	C₄	1	2	yes	—
24	C₈×C₂²⋊D₆₇	C₄	1	2	yes	—
25	#16863456	C₄	1	2	yes	—
26	#16863454	C₄	1	2	yes	—
27	#16863449	C₂²	1	1	yes	characteristic
28	#16863449	C₂²	1	1	yes	characteristic
29	#16863449	C₂²	1	1	yes	characteristic
30	#16863447	C₂²	1	1	yes	characteristic
31	#16863447	C₂²	1	1	yes	characteristic
32	#16863447	C₂²	1	1	yes	characteristic
33	#16863447	C₂²	1	1	yes	characteristic
34	#16863447	C₂²	1	1	yes	characteristic
35	#16863447	C₂²	1	1	yes	characteristic
36	#16863421	C₄	1	2	yes	—
37	#16863361	C₄	1	2	yes	—
38	C₄×#11761611	C₂²	1	1	yes	characteristic
39	C₄×#11761611	C₂²	1	1	yes	characteristic
40	C₄×C₈×D₆₇	C₂²	1	1	yes	characteristic
41	C₄×C₈×D₆₇	C₂²	1	1	yes	characteristic
42	C₄×C₈×D₆₇	C₂²	1	1	yes	characteristic
43	C₄×C₈×D₆₇	C₂²	1	1	yes	characteristic
44	#16863118	C₂²	1	1	yes	characteristic
45	#16863118	C₂²	1	1	yes	characteristic
46	#16863118	C₂²	1	1	yes	characteristic
47	#16863118	C₂²	1	1	yes	characteristic
48	#16863118	C₂²	1	1	yes	characteristic
49	#16863118	C₂²	1	1	yes	characteristic
50	#16863118	C₂²	1	1	yes	characteristic
51	#16863118	C₂²	1	1	yes	characteristic
52	#16863117	C₂²	1	1	yes	characteristic
53	#16863117	C₂²	1	1	yes	characteristic
54	C₈×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
55	C₈×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
56	#431×C₆₇	C₂²	1	1	yes	characteristic
57	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
58	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
59	#322×C₆₇	C₂²	1	1	yes	characteristic
60	#322×C₆₇	C₂²	1	1	yes	characteristic
61	C₈²×C₆₇	C₂²	1	1	yes	characteristic
62	C₈²×C₆₇	C₂²	1	1	yes	characteristic
63	C₂×#11761628	C₂×C₄	1	1	yes	characteristic
64	C₂×#11761611	C₂×C₄	1	2	yes	—
65	C₂×#11761611	C₂×C₄	1	2	yes	—
66	C₂×C₈×D₆₇	C₂×C₄	1	2	yes	—
67	C₂×C₈×D₆₇	C₂×C₄	1	2	yes	—
68	C₂×C₈×D₆₇	C₂×C₄	1	2	yes	—
69	C₂×C₈×D₆₇	C₂×C₄	1	2	yes	—
70	C₄×Dic₁₃₄	C₂×C₄	1	1	yes	characteristic
71	C₄×Dic₁₃₄	C₂×C₄	1	1	yes	characteristic
72	C₄×D₂₆₈	C₂×C₄	1	1	yes	characteristic
73	C₄×D₂₆₈	C₂×C₄	1	1	yes	characteristic
74	C₄×C₂²⋊D₆₇	C₂×C₄	1	1	yes	characteristic
75	C₄×C₂²⋊D₆₇	C₂×C₄	1	1	yes	characteristic
76	C₄×C₂²⋊D₆₇	C₂×C₄	1	1	yes	characteristic
77	C₄×C₂²⋊D₆₇	C₂×C₄	1	1	yes	characteristic
78	#14524002	C₂×C₄	1	1	yes	characteristic
79	#14524000	C₂×C₄	1	1	yes	characteristic
80	#14524000	C₂×C₄	1	1	yes	characteristic
81	C₄²×D₆₇	C₂³	1	1	yes	characteristic
82	C₄²×D₆₇	C₂³	1	1	yes	characteristic
83	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	2	yes	—
84	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	2	yes	—
85	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	2	yes	—
86	Dic₆₇⋊C₈	C₂×C₄	1	2	yes	—
87	Dic₆₇⋊C₈	C₂×C₄	1	2	yes	—
88	Dic₆₇⋊C₈	C₂×C₄	1	2	yes	—
89	Dic₆₇⋊C₈	C₂×C₄	1	2	yes	—
90	Dic₆₇⋊C₈	C₂×C₄	1	2	yes	—
91	Dic₆₇⋊C₈	C₂×C₄	1	2	yes	—
92	C₂²⋊(C₆₇⋊C₈)	C₂×C₄	1	2	yes	—
93	C₂²⋊(C₆₇⋊C₈)	C₂×C₄	1	2	yes	—
94	C₂²⋊(C₆₇⋊C₈)	C₂×C₄	1	2	yes	—
95	(C₂×D₆₇)⋊C₈	C₂×C₄	1	2	yes	—
96	(C₂×D₆₇)⋊C₈	C₂×C₄	1	2	yes	—
97	(C₂×D₆₇)⋊C₈	C₂×C₄	1	2	yes	—
98	(C₂×D₆₇)⋊C₈	C₂×C₄	1	2	yes	—
99	(C₂×D₆₇)⋊C₈	C₂×C₄	1	2	yes	—
100	(C₂×D₆₇)⋊C₈	C₂×C₄	1	2	yes	—
101	#14523953	C₂×C₄	1	2	yes	—
102	#14523953	C₂×C₄	1	2	yes	—
103	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
104	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
105	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
106	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
107	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
108	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
109	C₈×Dic₆₇	C₂×C₄	1	2	yes	—
110	C₈×Dic₆₇	C₂×C₄	1	2	yes	—
111	C₈×Dic₆₇	C₂×C₄	1	2	yes	—
112	C₈×Dic₆₇	C₂×C₄	1	2	yes	—
113	C₂×M₁₆×C₆₇	C₂×C₄	1	2	yes	—
114	C₂²×C₈×C₆₇	C₂×C₄	1	2	yes	—
115	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
116	C₄⋊C₈×C₆₇	C₂×C₄	1	2	yes	—
117	C₂²⋊C₈×C₆₇	C₂×C₄	1	2	yes	—
118	#97×C₆₇	C₂×C₄	1	2	yes	—
119	C₄×C₈×C₆₇	C₂×C₄	1	2	yes	—
120	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
121	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
122	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
123	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
124	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
125	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
126	#11761628	—	2	4	no	—
127	C₂×Dic₁₃₄	C₄²	1	1	yes	characteristic
128	C₂×D₂₆₈	C₄²	1	1	yes	characteristic
129	C₂×C₂²⋊D₆₇	C₄²	1	1	yes	characteristic
130	C₂×C₂²⋊D₆₇	C₄²	1	1	yes	characteristic
131	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
137	#11761611	—	2	4	no	—
138	#11761611	—	2	4	no	—
139	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
140	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
141	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
142	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
143	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
144	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
145	C₈×D₆₇	—	2	4	no	—
146	C₈×D₆₇	—	2	4	no	—
147	C₈×D₆₇	—	4	2	no	—
148	C₈×D₆₇	—	4	2	no	—
149	C₄⋊Dic₆₇	C₄²	1	1	yes	characteristic
150	C₄⋊Dic₆₇	C₄²	1	1	yes	characteristic
151	Dic₆₇⋊C₄	C₄²	1	1	yes	characteristic
152	Dic₆₇⋊C₄	C₄²	1	1	yes	characteristic
153	Dic₆₇⋊C₄	C₄²	1	1	yes	characteristic
154	Dic₆₇⋊C₄	C₄²	1	1	yes	characteristic
155	C₂²⋊Dic₆₇	C₄²	1	1	yes	characteristic
156	C₂²⋊Dic₆₇	C₄²	1	1	yes	characteristic
157	(C₂×D₆₇)⋊C₄	C₄²	1	1	yes	characteristic
158	(C₂×D₆₇)⋊C₄	C₄²	1	1	yes	characteristic
159	(C₂×D₆₇)⋊C₄	C₄²	1	1	yes	characteristic
160	(C₂×D₆₇)⋊C₄	C₄²	1	1	yes	characteristic
161	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
162	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
163	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
164	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
165	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
166	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
170	M₁₆×C₆₇	—	2	4	no	—
171	C₂×C₈×C₆₇	—	4	2	no	—
172	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
173	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
174	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
175	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
176	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
177	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
178	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
179	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
180	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
181	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
182	C₂³×C₆₇	C₂×C₄²	1	1	yes	characteristic
183	C₂²×D₆₇	C₂×C₄²	1	1	yes	characteristic
184	C₂²×D₆₇	C₂×C₄²	1	1	yes	characteristic
185	C₂×C₄×C₆₇	—	2	2	no	—
186	C₂×C₄×C₆₇	—	2	2	no	—
187	C₂×C₄×C₆₇	—	2	2	no	—
188	C₂×C₄×C₆₇	C₂×C₄²	1	1	yes	characteristic
189	C₂×C₄×C₆₇	C₂×C₄²	1	1	yes	characteristic
190	C₂×C₄×C₆₇	C₂×C₄²	1	1	yes	characteristic
191	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
192	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
193	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
194	C₂²⋊D₆₇	—	2	2	no	—
195	C₂²⋊D₆₇	—	2	2	no	—
196	C₂×Dic₆₇	C₂×C₄²	1	1	yes	characteristic
197	C₂×Dic₆₇	C₂×C₄²	1	1	yes	characteristic
198	C₂×Dic₆₇	C₂×C₄²	1	1	yes	characteristic
199	C₂×Dic₆₇	C₂×C₄²	1	1	yes	characteristic
200	C₂×Dic₆₇	C₂×C₄²	1	1	yes	characteristic
201	C₂×Dic₆₇	C₂×C₄²	1	1	yes	characteristic
202	D₂₆₈	—	2	2	no	—
203	C₄×D₆₇	—	2	2	no	—
204	C₄×D₆₇	—	2	2	no	—
205	C₄×D₆₇	—	2	2	no	—
206	C₄×D₆₇	—	2	2	no	—
207	C₄×D₆₇	—	2	2	no	—
208	C₄×D₆₇	#131	1	4	yes	—
209	Dic₁₃₄	—	2	2	no	—
210	C₈×C₆₇	—	2	2	no	—
211	C₈×C₆₇	—	2	2	no	—
212	C₈×C₆₇	—	2	2	no	—
213	C₈×C₆₇	—	2	2	no	—
214	C₈×C₆₇	—	2	2	no	—
215	C₈×C₆₇	#131	1	4	yes	—
216	C₆₇⋊C₈	—	2	2	no	—
217	C₆₇⋊C₈	—	2	2	no	—
218	C₆₇⋊C₈	—	2	2	no	—
219	C₆₇⋊C₈	—	2	2	no	—
220	C₆₇⋊C₈	—	2	2	no	—
221	C₆₇⋊C₈	—	2	2	no	—
222	C₂²×C₆₇	—	2	1	no	—
223	C₂²×C₆₇	—	2	1	no	—
224	C₂²×C₆₇	—	2	1	no	—
225	C₂²×C₆₇	C₂²×C₄²	1	1	yes	characteristic
226	C₂×D₆₇	—	2	1	no	—
227	C₂×D₆₇	—	2	1	no	—
228	C₂×D₆₇	—	2	1	no	—
229	C₂×D₆₇	—	2	1	no	—
230	C₂×D₆₇	—	2	1	no	—
231	C₂×D₆₇	#405	1	2	yes	—
232	C₄×C₆₇	—	2	1	no	—
233	C₄×C₆₇	—	2	1	no	—
234	C₄×C₆₇	—	2	1	no	—
235	C₄×C₆₇	C₂×#131	1	2	yes	—
236	C₄×C₆₇	C₂×#131	1	2	yes	—
237	C₄×C₆₇	#568	1	2	yes	—
238	Dic₆₇	—	2	1	no	—
239	Dic₆₇	—	2	1	no	—
240	Dic₆₇	—	2	1	no	—
241	Dic₆₇	—	2	1	no	—
242	Dic₆₇	—	2	1	no	—
243	Dic₆₇	#405	1	2	yes	—
244	#17331	—	67	1	no	maximal, Sylow
245	C₂×C₆₇	—	4	1	no	—
246	C₂×C₆₇	C₂×#405	1	1	yes	characteristic
247	C₂×C₆₇	C₄×#131	1	1	yes	characteristic
248	C₂×C₆₇	#2875	1	1	yes	characteristic
249	D₆₇	—	2	2	no	—
250	D₆₇	—	4	1	no	—
251	#2965	—	67	1	no	—
252	C₈×#41	—	67	1	no	—
253	#2922	—	67	1	no	—
254	#1454	—	67	1	no	—
255	#1454	—	67	1	no	—
256	#1453	—	67	1	no	—
257	#1453	—	67	1	no	—
258	#1452	—	67	1	no	—
259	#1452	—	67	1	no	—
260	#1451	—	67	1	no	—
261	#1450	—	67	1	no	—
262	C₈×M₁₆	—	67	1	no	—
263	C₈×M₁₆	—	67	1	no	—
264	C₈×M₁₆	D₆₇	1	1	yes	characteristic, complemented
265	C₂×#322	—	67	1	no	—
266	C₆₇	#17331	1	1	yes	characteristic, complemented, Sylow
267	C₄×#41	—	67	1	no	—
268	#446	—	67	2	no	—
269	C₈×Q₈	—	67	2	no	—
270	#436	—	67	2	no	—
271	#435	—	67	2	no	—
272	#435	—	67	2	no	—
273	C₈×D₄	—	67	2	no	—
274	C₈×D₄	—	67	2	no	—
275	C₈×D₄	—	67	2	no	—
276	#433	—	67	2	no	—
277	#433	—	67	2	no	—
278	#431	—	67	1	no	—
279	#431	—	67	1	no	—
280	#431	—	67	1	no	—
281	#431	—	67	1	no	—
282	#431	—	67	1	no	—
283	#431	—	67	1	no	—
284	#431	—	67	1	no	—
285	#431	—	67	1	no	—
286	#431	—	67	1	no	—
287	#431	C₂×D₆₇	1	1	yes	characteristic
288	#424	—	67	2	no	—
289	#408	—	67	2	no	—
290	C₄×M₁₆	—	67	1	no	—
291	C₄×M₁₆	—	67	1	no	—
292	C₄×M₁₆	C₂×D₆₇	1	1	yes	characteristic
293	C₂×C₄×C₈	—	67	1	no	—
294	C₂×C₄×C₈	—	67	1	no	—
295	C₂×C₄×C₈	—	67	1	no	—
296	C₂×C₄×C₈	—	67	1	no	—
297	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
298	#322	—	67	1	no	—
299	#322	—	67	1	no	—
300	#322	—	67	1	no	—
301	#322	—	67	1	no	—
302	#322	—	67	1	no	—
303	#322	—	67	1	no	—
304	#322	—	67	1	no	—
305	#322	—	67	1	no	—
306	#322	—	67	1	no	—
307	#322	—	67	1	no	—
308	#322	C₂×D₆₇	1	1	yes	characteristic
309	#322	C₂×D₆₇	1	1	yes	characteristic
310	C₈²	—	67	1	no	—
311	C₈²	—	67	1	no	—
312	C₈²	C₂×D₆₇	1	1	yes	characteristic
313	C₈²	C₂×D₆₇	1	1	yes	characteristic
314	C₂×#41	—	67	1	no	—
315	C₂×M₁₆	—	67	2	no	—
316	C₂×M₁₆	—	67	2	no	—
317	C₂×M₁₆	C₄×D₆₇	1	2	yes	—
318	C₂²×C₈	—	67	2	no	—
319	C₂²×C₈	—	67	2	no	—
320	C₂²×C₈	—	67	2	no	—
321	C₂²×C₈	—	67	2	no	—
322	C₂²×C₈	C₄×D₆₇	1	2	yes	—
323	C₄×Q₈	—	67	1	no	—
324	C₄×Q₈	—	67	1	no	—
325	C₄×D₄	—	67	1	no	—
326	C₄×D₄	—	67	1	no	—
327	C₄×D₄	—	67	1	no	—
328	C₄×D₄	—	67	1	no	—
329	C₄×D₄	—	67	1	no	—
330	C₄×D₄	—	67	1	no	—
331	#117	—	67	1	no	—
332	#117	—	67	1	no	—
333	#117	—	67	1	no	—
334	C₂×C₄²	—	67	1	no	—
335	C₂×C₄²	—	67	1	no	—
336	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
337	C₄⋊C₈	—	67	2	no	—
338	C₄⋊C₈	—	67	2	no	—
339	C₄⋊C₈	—	67	2	no	—
340	C₄⋊C₈	—	67	2	no	—
341	C₄⋊C₈	—	67	2	no	—
342	C₄⋊C₈	—	67	2	no	—
343	C₄⋊C₈	—	67	2	no	—
344	C₄⋊C₈	—	67	2	no	—
345	C₄⋊C₈	—	67	2	no	—
346	C₄⋊C₈	C₄×D₆₇	1	2	yes	—
347	C₂²⋊C₈	—	67	2	no	—
348	C₂²⋊C₈	—	67	2	no	—
349	C₂²⋊C₈	—	67	2	no	—
350	C₂²⋊C₈	—	67	2	no	—
351	C₂²⋊C₈	—	67	2	no	—
352	C₂²⋊C₈	—	67	2	no	—
353	C₂²⋊C₈	—	67	2	no	—
354	C₂²⋊C₈	—	67	2	no	—
355	C₂²⋊C₈	—	67	2	no	—
356	C₂²⋊C₈	C₄×D₆₇	1	2	yes	—
357	#97	—	67	2	no	—
358	#97	—	67	2	no	—
359	#97	C₄×D₆₇	1	2	yes	—
360	C₄×C₈	—	67	2	no	—
361	C₄×C₈	—	67	2	no	—
362	C₄×C₈	—	67	2	no	—
363	C₄×C₈	—	67	2	no	—
364	C₄×C₈	—	67	1	no	—
365	C₄×C₈	—	67	1	no	—
366	C₄×C₈	—	67	1	no	—
367	C₄×C₈	—	67	1	no	—
368	C₄×C₈	—	67	1	no	—
369	C₄×C₈	—	67	1	no	—
370	C₄×C₈	C₄×D₆₇	1	2	yes	—
371	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
372	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
373	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
374	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
375	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
376	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
377	#41	—	134	4	no	—
378	C₂×Q₈	—	67	1	no	—
379	C₂×D₄	—	67	1	no	—
380	C₂×D₄	—	67	1	no	—
381	C₂×D₄	—	67	1	no	—
382	C₂²×C₄	—	67	1	no	—
383	C₂²×C₄	—	67	1	no	—
384	C₂²×C₄	—	67	1	no	—
385	C₂²×C₄	—	67	1	no	—
386	C₂²×C₄	—	67	1	no	—
387	C₂²×C₄	—	67	1	no	—
388	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
390	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
391	M₁₆	—	2	4	no	—
392	M₁₆	—	134	4	no	—
393	M₁₆	—	134	4	no	—
394	C₂×C₈	—	4	2	no	—
395	C₂×C₈	—	268	2	no	—
396	C₂×C₈	—	268	2	no	—
397	C₂×C₈	—	67	2	no	—
398	C₂×C₈	—	67	2	no	—
399	C₂×C₈	—	67	2	no	—
400	C₂×C₈	—	67	2	no	—
401	C₂×C₈	—	67	2	no	—
402	C₂×C₈	—	67	2	no	—
403	C₂×C₈	—	134	4	no	—
404	C₂×C₈	—	134	4	no	—
405	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
406	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
407	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
408	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
409	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
410	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
411	C₄⋊C₄	—	67	1	no	—
412	C₄⋊C₄	—	67	1	no	—
413	C₄⋊C₄	—	67	1	no	—
414	C₄⋊C₄	—	67	1	no	—
415	C₄⋊C₄	—	67	1	no	—
416	C₄⋊C₄	—	67	1	no	—
417	C₂²⋊C₄	—	67	1	no	—
418	C₂²⋊C₄	—	67	1	no	—
419	C₂²⋊C₄	—	67	1	no	—
420	C₂²⋊C₄	—	67	1	no	—
421	C₂²⋊C₄	—	67	1	no	—
422	C₂²⋊C₄	—	67	1	no	—
423	C₄²	—	67	1	no	—
424	C₄²	—	67	1	no	—
425	C₄²	—	67	1	no	—
426	C₄²	—	67	1	no	—
427	C₄²	—	67	1	no	—
428	C₄²	—	67	1	no	—
429	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
430	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
431	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
432	C₄²	C₂³×D₆₇	1	1	yes	characteristic
433	C₂³	—	67	1	no	—
434	C₂³	—	67	1	no	—
435	C₂³	C₄²×D₆₇	1	1	yes	characteristic
436	Q₈	—	134	2	no	—
437	D₄	—	134	2	no	—
438	D₄	—	134	2	no	—
439	D₄	—	134	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	67	1	no	—
444	C₂×C₄	—	67	4	no	—
445	C₂×C₄	—	67	1	no	—
446	C₂×C₄	—	67	1	no	—
447	C₂×C₄	—	67	1	no	—
448	C₂×C₄	—	67	1	no	—
449	C₂×C₄	—	67	1	no	—
450	C₂×C₄	—	134	2	no	—
451	C₂×C₄	—	134	2	no	—
452	C₂×C₄	—	134	2	no	—
453	C₂×C₄	—	134	2	no	—
454	C₂×C₄	—	134	2	no	—
455	C₂×C₄	C₄²×D₆₇	1	1	yes	characteristic
456	C₂×C₄	C₄²×D₆₇	1	1	yes	characteristic
457	C₂×C₄	C₄²×D₆₇	1	1	yes	characteristic
458	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
459	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
460	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
461	C₈	—	2	2	no	—
462	C₈	—	2	2	no	—
463	C₈	—	2	2	no	—
464	C₈	—	2	2	no	—
465	C₈	—	2	2	no	—
466	C₈	—	134	2	no	—
467	C₈	—	134	2	no	—
468	C₈	—	134	2	no	—
469	C₈	—	134	2	no	—
470	C₈	—	134	2	no	—
471	C₈	—	134	2	no	—
472	C₈	#14524049	1	4	yes	—
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	67	2	no	—
477	C₂²	—	134	1	no	—
478	C₂²	—	134	1	no	—
479	C₂²	—	134	1	no	—
480	C₂²	—	134	1	no	—
481	C₂²	—	134	1	no	—
482	C₂²	C₂×C₄²×D₆₇	1	1	yes	characteristic
483	C₄	—	2	1	no	—
484	C₄	—	2	1	no	—
485	C₄	—	2	1	no	—
486	C₄	—	67	2	no	—
487	C₄	—	134	1	no	—
488	C₄	—	134	1	no	—
489	C₄	—	134	1	no	—
490	C₄	—	134	1	no	—
491	C₄	—	134	1	no	—
492	C₄	#131×D₆₇	1	2	yes	—
493	C₄	C₂×#14524049	1	2	yes	—
494	C₄	#16864162	1	2	yes	—
495	C₂	—	4	1	no	—
496	C₂	—	268	1	no	—
497	C₂	—	134	2	no	—
498	C₂	#405×D₆₇	1	1	yes	characteristic
499	C₂	C₄×#14524049	1	1	yes	characteristic
500	C₂	#22568638	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₆₇
commutator, socle	C₂²×C₆₇	C₂²×C₄²
Fitting	C₈×M₁₆×C₆₇	C₂
prime radical	C₂×#11761628	C₂×C₄
cosocle	C₄²×C₆₇	C₂⁴
hypercenter	C₈×M₁₆	D₆₇
hypocenter	C₆₇	#17331
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₄² ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
4. #22558509	C₂	semidirect
5. #22558508	C₂	semidirect
6. #22558506	C₂	semidirect
7. #22558503	C₂	semidirect
8. #22558501	C₂	semidirect
9. #22558500	C₂	semidirect
10. #22558497	C₂	semidirect
11. #22558491	C₂	semidirect
12. #22558488	C₂	semidirect
13. C₈×#11761611	C₂	semidirect
14. #322×D₆₇	C₂	semidirect
15. C₈×M₁₆×C₆₇	C₂	semidirect
264. C₈×M₁₆	D₆₇	semidirect
266. C₆₇	#17331	semidirect

Maximal subgroups

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

subgroup	index
#22569171	2
C₈×#11761628	2
#22568848	2
#22558509	2
#22558508	2
#22558506	2
#22558503	2
#22558501	2
#22558500	2
#22558497	2
#22558491	2
#22558488	2
C₈×#11761611	2
#322×D₆₇	2
C₈×M₁₆×C₆₇	2
#17331	67