Subgroups — #2221×D₆₇ #31010384

Order 17152.

678 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₆×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#504×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#472×D₆₇	C₂	1	2	yes	maximal, complemented
4	#22562330	C₂	1	1	yes	maximal, characteristic, complemented
5	#22562329	C₂	1	1	yes	maximal, characteristic, complemented
6	#22562328	C₂	1	2	yes	maximal, complemented
7	#22562327	C₂	1	2	yes	maximal, complemented
8	#22562326	C₂	1	1	yes	maximal, characteristic, complemented
9	#368×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#361×D₆₇	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2221	C₂	1	1	yes	maximal, characteristic, complemented
12	AGL(1,ℤ/8)×D₆₇	—	2	2	no	—
13	C₂×D₈×D₆₇	C₂²	1	2	yes	—
14	#131×D₆₇	C₂²	1	1	yes	characteristic
15	C₂×D₁₀₇₂	C₂²	1	1	yes	characteristic, complemented
16	C₂×#14523984	C₂²	1	2	yes	complemented
17	D₁₆×D₆₇	—	2	1	no	—
18	D₁₆×D₆₇	—	2	1	no	—
19	D₁₆×D₆₇	—	2	1	no	—
20	D₁₆×D₆₇	—	2	1	no	—
21	#16863814	—	2	1	no	—
22	#16863814	C₂²	1	1	yes	characteristic, complemented
23	#16863813	C₂²	1	1	yes	characteristic, complemented
24	#16863812	—	2	1	no	—
25	#16863812	C₂²	1	1	yes	characteristic, complemented
26	M₃₂×D₆₇	—	2	1	no	—
27	M₃₂×D₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₁₆×D₆₇	—	2	1	no	—
29	C₂×C₁₆×D₆₇	C₂²	1	1	yes	characteristic
30	#16863667	C₂²	1	2	yes	complemented
31	#16863666	C₂²	1	2	yes	complemented
32	#16863665	—	2	2	no	—
33	#16863664	—	2	2	no	—
34	#16863663	C₂²	1	2	yes	complemented
35	#108×D₆₇	C₂²	1	2	yes	—
36	#100×D₆₇	—	2	2	no	—
37	#16863226	C₂²	1	1	yes	characteristic, complemented
38	#16863225	C₂²	1	2	yes	complemented
39	#16863210	C₂²	1	2	yes	complemented
40	#16863209	C₂²	1	2	yes	complemented
41	#16863208	C₂²	1	2	yes	complemented
42	C₂×D₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	#504×C₆₇	C₂²	1	1	yes	characteristic, complemented
44	#472×C₆₇	C₂²	1	2	yes	complemented
45	#368×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	#361×C₆₇	C₂²	1	2	yes	complemented
47	#41×D₆₇	D₄	1	1	yes	characteristic
48	C₂×D₄×D₆₇	—	2	2	no	—
49	#14524071	—	2	2	no	—
50	#14524070	—	4	2	no	—
51	#14524069	—	2	2	no	—
52	#14524068	—	2	2	no	—
53	#14524067	—	4	2	no	—
54	SD₁₆×D₆₇	—	4	2	no	—
55	C₂×D₅₃₆	C₂³	1	2	yes	—
56	C₂×#11761613	—	2	2	no	—
57	D₈×D₆₇	—	2	2	no	—
58	D₈×D₆₇	—	2	2	no	—
59	D₈×D₆₇	—	2	2	no	—
60	D₈×D₆₇	—	2	2	no	—
61	D₈×D₆₇	—	4	2	no	—
62	#14524051	—	2	1	no	—
63	#14524051	D₄	1	1	yes	characteristic
64	#14524050	D₄	1	1	yes	characteristic
65	#14524049	—	2	1	no	—
66	#14524049	C₂³	1	1	yes	characteristic
67	M₁₆×D₆₇	—	2	1	no	—
68	M₁₆×D₆₇	—	2	2	no	—
69	M₁₆×D₆₇	D₄	1	1	yes	characteristic
70	C₂×C₈×D₆₇	—	2	1	no	—
71	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
72	D₁₀₇₂	—	2	1	no	—
73	D₁₀₇₂	—	2	1	no	—
74	#14523984	—	2	2	no	—
75	#14523984	—	2	2	no	—
76	#14523983	—	2	1	no	—
77	#14523983	C₂³	1	1	yes	characteristic
78	#14523982	—	2	1	no	—
79	#14523982	—	2	1	no	—
80	#14523982	—	2	1	no	—
81	C₂×C₆₇⋊C₁₆	—	2	1	no	—
82	C₂×C₆₇⋊C₁₆	C₂³	1	1	yes	characteristic
83	C₁₆×D₆₇	—	2	1	no	—
84	C₁₆×D₆₇	—	2	1	no	—
85	C₁₆×D₆₇	—	2	1	no	—
86	C₁₆×D₆₇	D₄	1	1	yes	characteristic
87	C₁₆×D₆₇	D₄	1	1	yes	characteristic
88	C₁₆×D₆₇	D₄	1	1	yes	characteristic
89	C₁₆×D₆₇	D₄	1	1	yes	characteristic
90	#14523979	C₂³	1	2	yes	—
91	#14523978	—	2	2	no	—
92	#14523960	—	2	2	no	—
93	#14523959	—	2	2	no	—
94	#14523959	—	2	2	no	—
95	AGL(1,ℤ/8)×C₆₇	—	2	2	no	—
96	C₂×D₈×C₆₇	C₂³	1	2	yes	—
97	#131×C₆₇	C₂³	1	1	yes	characteristic
98	D₁₆×C₆₇	—	2	1	no	—
99	D₁₆×C₆₇	—	2	1	no	—
100	M₃₂×C₆₇	—	2	1	no	—
101	M₃₂×C₆₇	C₂³	1	1	yes	characteristic
102	C₂×C₁₆×C₆₇	—	2	1	no	—
103	C₂×C₁₆×C₆₇	C₂³	1	1	yes	characteristic
104	#108×C₆₇	C₂³	1	2	yes	—
105	#100×C₆₇	—	2	2	no	—
106	C₂³×D₆₇	—	4	2	no	—
107	#11761629	D₈	1	1	yes	characteristic
108	#11761628	—	2	1	no	—
109	#11761628	C₂×D₄	1	1	yes	characteristic
110	#11761627	—	2	1	no	—
111	#11761627	D₈	1	1	yes	characteristic
112	Q₈×D₆₇	D₈	1	1	yes	characteristic
113	C₂×D₂₆₈	—	2	2	no	—
114	C₂×C₂²⋊D₆₇	—	4	2	no	—
115	D₄×D₆₇	—	2	1	no	—
116	D₄×D₆₇	—	4	2	no	—
117	D₄×D₆₇	—	4	2	no	—
118	D₄×D₆₇	—	4	2	no	—
119	D₄×D₆₇	—	4	2	no	—
120	D₄×D₆₇	D₈	1	1	yes	characteristic
121	C₂×C₄×D₆₇	—	2	1	no	—
122	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
123	#11761617	—	4	2	no	—
124	#11761616	—	4	2	no	—
125	#11761615	—	4	2	no	—
126	D₅₃₆	—	2	2	no	—
127	D₅₃₆	—	2	2	no	—
128	D₅₃₆	—	4	2	no	—
129	#11761613	—	4	2	no	—
130	#11761613	—	4	2	no	—
131	#11761613	—	4	2	no	—
132	#11761613	—	4	2	no	—
133	#11761612	—	2	1	no	—
134	#11761612	—	2	2	no	—
135	#11761612	C₂×D₄	1	1	yes	characteristic
136	#11761611	—	2	1	no	—
137	#11761611	—	2	1	no	—
138	#11761611	—	2	1	no	—
139	#11761611	—	4	2	no	—
140	C₂×C₆₇⋊C₈	—	2	1	no	—
141	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
142	C₈×D₆₇	—	2	1	no	—
143	C₈×D₆₇	—	2	1	no	—
144	C₈×D₆₇	—	2	1	no	—
145	C₈×D₆₇	—	4	2	no	—
146	C₈×D₆₇	C₂×D₄	1	1	yes	characteristic
147	C₈×D₆₇	C₂×D₄	1	1	yes	characteristic
148	C₈×D₆₇	#41	1	1	yes	characteristic
149	C₈×D₆₇	#41	1	1	yes	characteristic
150	C₆₇⋊C₁₆	—	2	1	no	—
151	C₆₇⋊C₁₆	C₂×D₄	1	1	yes	characteristic
152	C₆₇⋊C₁₆	C₂×D₄	1	1	yes	characteristic
153	#41×C₆₇	C₂×D₄	1	1	yes	characteristic
154	C₂×D₄×C₆₇	—	2	2	no	—
155	SD₁₆×C₆₇	—	4	2	no	—
156	D₈×C₆₇	—	2	2	no	—
157	D₈×C₆₇	—	2	2	no	—
158	D₈×C₆₇	—	4	2	no	—
159	M₁₆×C₆₇	—	2	1	no	—
160	M₁₆×C₆₇	—	2	2	no	—
161	M₁₆×C₆₇	C₂×D₄	1	1	yes	characteristic
162	C₂×C₈×C₆₇	—	2	1	no	—
163	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
164	C₁₆×C₆₇	—	2	1	no	—
165	C₁₆×C₆₇	C₂×D₄	1	1	yes	characteristic
166	C₁₆×C₆₇	C₂×D₄	1	1	yes	characteristic
167	C₂³×C₆₇	—	4	2	no	—
168	C₂²×D₆₇	—	2	1	no	—
169	C₂²×D₆₇	—	4	2	no	—
170	C₂²×D₆₇	—	8	2	no	—
171	C₂²×D₆₇	—	8	2	no	—
172	C₂²×D₆₇	—	16	4	no	—
173	C₂²×D₆₇	#135	1	1	yes	characteristic
174	Q₈×C₆₇	C₂×D₈	1	1	yes	characteristic
175	D₄×C₆₇	—	2	1	no	—
176	D₄×C₆₇	—	4	2	no	—
177	D₄×C₆₇	—	4	2	no	—
178	D₄×C₆₇	C₂×D₈	1	1	yes	characteristic
179	C₂×C₄×C₆₇	—	2	1	no	—
180	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
181	C₂²⋊D₆₇	—	2	1	no	—
182	C₂²⋊D₆₇	—	2	1	no	—
183	C₂²⋊D₆₇	—	2	1	no	—
184	C₂²⋊D₆₇	—	8	2	no	—
185	C₂²⋊D₆₇	—	8	2	no	—
186	C₂×Dic₆₇	—	2	1	no	—
187	C₂×Dic₆₇	#135	1	1	yes	characteristic
188	D₂₆₈	—	2	1	no	—
189	D₂₆₈	—	4	2	no	—
190	D₂₆₈	—	4	2	no	—
191	D₂₆₈	C₂×D₈	1	1	yes	characteristic
192	C₄×D₆₇	—	2	1	no	—
193	C₄×D₆₇	—	2	1	no	—
194	C₄×D₆₇	—	2	1	no	—
195	C₄×D₆₇	#121	1	1	yes	characteristic
196	C₄×D₆₇	#121	1	1	yes	characteristic
197	C₄×D₆₇	C₂×D₈	1	1	yes	characteristic
198	C₄×D₆₇	C₂×D₈	1	1	yes	characteristic
199	Dic₁₃₄	—	2	1	no	—
200	Dic₁₃₄	C₂×D₈	1	1	yes	characteristic
201	C₈×C₆₇	—	2	1	no	—
202	C₈×C₆₇	—	4	2	no	—
203	C₈×C₆₇	C₂²×D₄	1	1	yes	characteristic
204	C₈×C₆₇	C₂×#41	1	1	yes	characteristic
205	C₆₇⋊C₈	—	2	1	no	—
206	C₆₇⋊C₈	—	4	2	no	—
207	C₆₇⋊C₈	#121	1	1	yes	characteristic
208	C₆₇⋊C₈	#121	1	1	yes	characteristic
209	C₂²×C₆₇	—	2	1	no	—
210	C₂²×C₆₇	—	8	2	no	—
211	C₂²×C₆₇	—	16	2	no	—
212	C₂²×C₆₇	C₂×#135	1	1	yes	characteristic
213	C₂×D₆₇	—	2	2	no	—
214	C₂×D₆₇	—	2	1	no	—
215	C₂×D₆₇	—	4	2	no	—
216	C₂×D₆₇	—	8	2	no	—
217	C₂×D₆₇	—	16	4	no	—
218	C₂×D₆₇	—	16	4	no	—
219	C₂×D₆₇	—	16	2	no	—
220	C₂×D₆₇	#466	1	1	yes	characteristic
221	C₂×D₆₇	#466	1	1	yes	characteristic
222	C₄×C₆₇	—	2	1	no	—
223	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
224	C₄×C₆₇	C₂²×D₈	1	1	yes	characteristic
225	Dic₆₇	—	2	1	no	—
226	Dic₆₇	#466	1	1	yes	characteristic
227	Dic₆₇	#466	1	1	yes	characteristic
228	C₂×#2221	—	67	1	no	maximal, Sylow
229	C₂×C₆₇	—	2	1	no	—
230	C₂×C₆₇	—	4	1	no	—
231	C₂×C₆₇	—	16	2	no	—
232	C₂×C₆₇	C₂×#466	1	1	yes	characteristic
233	D₆₇	—	2	1	no	—
234	D₆₇	—	4	1	no	—
235	D₆₇	—	16	2	no	—
236	D₆₇	#2221	1	2	yes	direct product factor
237	C₂²×D₁₆	—	67	1	no	—
238	C₂×#504	—	67	1	no	—
239	C₂×#472	—	67	2	no	—
240	#2221	—	67	1	no	—
241	#2221	—	67	1	no	—
242	#2221	—	67	2	no	—
243	#2221	—	67	1	no	—
244	#2221	—	67	2	no	—
245	#2221	D₆₇	1	1	yes	characteristic, direct product factor
246	C₂×#368	—	67	1	no	—
247	C₂×#361	—	67	2	no	—
248	C₆₇	C₂×#2221	1	1	yes	characteristic, complemented, Sylow
249	C₂×AGL(1,ℤ/8)	—	134	2	no	—
250	C₂²×D₈	—	67	2	no	—
251	C₂×#131	—	67	1	no	—
252	C₂×D₁₆	—	67	2	no	—
253	C₂×D₁₆	—	67	1	no	—
254	C₂×D₁₆	—	134	1	no	—
255	C₂×D₁₆	—	134	1	no	—
256	C₂×D₁₆	—	134	1	no	—
257	C₂×D₁₆	—	134	1	no	—
258	C₂×D₁₆	C₂×D₆₇	1	1	yes	characteristic, complemented
259	#504	—	67	1	no	—
260	#504	—	67	1	no	—
261	#504	—	67	1	no	—
262	#504	—	134	1	no	—
263	#504	—	134	1	no	—
264	#504	C₂×D₆₇	1	1	yes	characteristic, complemented
265	C₂×M₃₂	—	67	1	no	—
266	C₂×M₃₂	—	134	1	no	—
267	C₂²×C₁₆	—	67	1	no	—
268	C₂²×C₁₆	—	134	1	no	—
269	#472	—	67	2	no	—
270	#472	—	67	2	no	—
271	#472	—	67	2	no	—
272	#472	—	134	2	no	—
273	#472	—	134	2	no	—
274	#472	C₂×D₆₇	1	2	yes	complemented
275	C₂×#108	—	67	2	no	—
276	C₂×#100	—	134	2	no	—
277	#368	—	67	1	no	—
278	#368	—	67	2	no	—
279	#368	C₂×D₆₇	1	1	yes	characteristic, complemented
280	#361	—	67	2	no	—
281	#361	—	67	2	no	—
282	#361	—	67	2	no	—
283	#361	C₂×D₆₇	1	2	yes	complemented
284	C₂×#41	—	67	1	no	—
285	C₂²×D₄	—	134	2	no	—
286	AGL(1,ℤ/8)	—	2	2	no	—
287	AGL(1,ℤ/8)	—	268	2	no	—
288	AGL(1,ℤ/8)	—	268	2	no	—
289	AGL(1,ℤ/8)	—	134	2	no	—
290	AGL(1,ℤ/8)	—	134	2	no	—
291	AGL(1,ℤ/8)	—	134	2	no	—
292	C₂×SD₁₆	—	268	2	no	—
293	C₂×D₈	—	268	2	no	—
294	C₂×D₈	—	67	2	no	—
295	C₂×D₈	—	134	2	no	—
296	C₂×D₈	—	134	2	no	—
297	C₂×D₈	—	134	2	no	—
298	C₂×D₈	—	134	2	no	—
299	C₂×D₈	—	134	2	no	—
300	C₂×D₈	C₂²×D₆₇	1	2	yes	—
301	#131	—	67	1	no	—
302	#131	—	67	1	no	—
303	#131	—	67	1	no	—
304	#131	—	134	1	no	—
305	#131	—	134	1	no	—
306	#131	C₂²×D₆₇	1	1	yes	characteristic
307	C₂×M₁₆	—	67	1	no	—
308	C₂×M₁₆	—	134	2	no	—
309	C₂×M₁₆	—	134	1	no	—
310	C₂²×C₈	—	67	1	no	—
311	C₂²×C₈	—	134	1	no	—
312	D₁₆	—	2	1	no	—
313	D₁₆	—	2	1	no	—
314	D₁₆	—	134	2	no	—
315	D₁₆	—	134	2	no	—
316	D₁₆	—	134	1	no	—
317	D₁₆	—	134	1	no	—
318	M₃₂	—	2	1	no	—
319	M₃₂	—	67	1	no	—
320	M₃₂	—	134	1	no	—
321	M₃₂	—	134	1	no	—
322	M₃₂	—	134	1	no	—
323	M₃₂	—	134	1	no	—
324	M₃₂	C₂²×D₆₇	1	1	yes	characteristic
325	C₂×C₁₆	—	2	1	no	—
326	C₂×C₁₆	—	67	1	no	—
327	C₂×C₁₆	—	67	1	no	—
328	C₂×C₁₆	—	67	1	no	—
329	C₂×C₁₆	—	67	1	no	—
330	C₂×C₁₆	—	67	1	no	—
331	C₂×C₁₆	—	134	1	no	—
332	C₂×C₁₆	—	134	1	no	—
333	C₂×C₁₆	—	134	1	no	—
334	C₂×C₁₆	—	134	1	no	—
335	C₂×C₁₆	C₂²×D₆₇	1	1	yes	characteristic
336	#108	—	67	2	no	—
337	#108	—	134	2	no	—
338	#108	C₂²×D₆₇	1	2	yes	—
339	#100	—	2	2	no	—
340	#100	—	134	2	no	—
341	#100	—	134	2	no	—
342	#100	—	134	2	no	—
343	C₂⁴	—	268	2	no	—
344	#41	—	67	1	no	—
345	#41	—	67	1	no	—
346	#41	—	67	1	no	—
347	#41	—	134	1	no	—
348	#41	—	134	1	no	—
349	#41	D₄×D₆₇	1	1	yes	characteristic
350	C₂×Q₈	—	67	1	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	268	2	no	—
353	C₂×D₄	—	268	2	no	—
354	C₂×D₄	—	268	2	no	—
355	C₂×D₄	—	268	2	no	—
356	C₂×D₄	—	268	2	no	—
357	C₂×D₄	—	67	1	no	—
358	C₂×D₄	—	134	1	no	—
359	C₂×D₄	—	134	2	no	—
360	C₂²×C₄	—	67	1	no	—
361	C₂²×C₄	—	134	1	no	—
362	SD₁₆	—	4	2	no	—
363	SD₁₆	—	268	2	no	—
364	SD₁₆	—	268	2	no	—
365	SD₁₆	—	268	2	no	—
366	D₈	—	2	2	no	—
367	D₈	—	2	2	no	—
368	D₈	—	4	2	no	—
369	D₈	—	268	2	no	—
370	D₈	—	268	2	no	—
371	D₈	—	268	2	no	—
372	D₈	—	268	2	no	—
373	D₈	—	268	2	no	—
374	D₈	—	134	2	no	—
375	D₈	—	134	2	no	—
376	M₁₆	—	2	1	no	—
377	M₁₆	—	2	2	no	—
378	M₁₆	—	268	2	no	—
379	M₁₆	—	67	1	no	—
380	M₁₆	—	134	1	no	—
381	M₁₆	—	134	1	no	—
382	M₁₆	—	134	2	no	—
383	M₁₆	—	134	1	no	—
384	M₁₆	—	134	1	no	—
385	M₁₆	D₄×D₆₇	1	1	yes	characteristic
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	268	2	no	—
388	C₂×C₈	—	67	1	no	—
389	C₂×C₈	—	67	1	no	—
390	C₂×C₈	—	67	1	no	—
391	C₂×C₈	—	67	1	no	—
392	C₂×C₈	—	67	1	no	—
393	C₂×C₈	—	134	1	no	—
394	C₂×C₈	—	134	1	no	—
395	C₂×C₈	—	134	1	no	—
396	C₂×C₈	—	134	1	no	—
397	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
398	C₁₆	—	2	1	no	—
399	C₁₆	—	67	1	no	—
400	C₁₆	—	67	1	no	—
401	C₁₆	—	134	1	no	—
402	C₁₆	D₄×D₆₇	1	1	yes	characteristic
403	C₁₆	D₄×D₆₇	1	1	yes	characteristic
404	C₂³	—	4	2	no	—
405	C₂³	—	268	2	no	—
406	C₂³	—	536	2	no	—
407	C₂³	—	536	2	no	—
408	C₂³	—	1072	4	no	—
409	C₂³	—	67	1	no	—
410	C₂³	—	134	1	no	—
411	Q₈	—	67	1	no	—
412	Q₈	—	134	1	no	—
413	Q₈	D₈×D₆₇	1	1	yes	characteristic
414	D₄	—	2	1	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	2	no	—
417	D₄	—	268	2	no	—
418	D₄	—	268	2	no	—
419	D₄	—	536	2	no	—
420	D₄	—	536	2	no	—
421	D₄	—	67	1	no	—
422	D₄	—	134	1	no	—
423	D₄	—	134	1	no	—
424	D₄	—	134	1	no	—
425	D₄	—	134	1	no	—
426	D₄	D₈×D₆₇	1	1	yes	characteristic
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	67	1	no	—
429	C₂×C₄	—	67	1	no	—
430	C₂×C₄	—	67	1	no	—
431	C₂×C₄	—	67	1	no	—
432	C₂×C₄	—	67	1	no	—
433	C₂×C₄	—	134	1	no	—
434	C₂×C₄	—	134	1	no	—
435	C₂×C₄	—	134	1	no	—
436	C₂×C₄	—	134	1	no	—
437	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
438	C₈	—	2	1	no	—
439	C₈	—	4	2	no	—
440	C₈	—	268	2	no	—
441	C₈	—	67	1	no	—
442	C₈	—	67	1	no	—
443	C₈	—	134	1	no	—
444	C₈	C₂×D₄×D₆₇	1	1	yes	characteristic
445	C₈	#41×D₆₇	1	1	yes	characteristic
446	C₂²	—	2	1	no	—
447	C₂²	—	8	2	no	—
448	C₂²	—	268	2	no	—
449	C₂²	—	16	2	no	—
450	C₂²	—	536	2	no	—
451	C₂²	—	1072	2	no	—
452	C₂²	—	1072	4	no	—
453	C₂²	—	1072	4	no	—
454	C₂²	—	67	1	no	—
455	C₂²	—	67	1	no	—
456	C₂²	—	134	2	no	—
457	C₂²	—	134	1	no	—
458	C₂²	#135×D₆₇	1	1	yes	characteristic
459	C₄	—	2	1	no	—
460	C₄	—	67	1	no	—
461	C₄	—	67	1	no	—
462	C₄	—	134	1	no	—
463	C₄	#121×D₆₇	1	1	yes	characteristic
464	C₄	C₂×D₈×D₆₇	1	1	yes	characteristic
465	C₂	—	2	1	no	—
466	C₂	—	4	1	no	—
467	C₂	—	268	1	no	—
468	C₂	—	16	2	no	—
469	C₂	—	1072	2	no	—
470	C₂	—	67	2	no	—
471	C₂	—	134	1	no	—
472	C₂	#466×D₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#466×D₆₇
commutator, cosocle	C₂×C₈×C₆₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₆₇
Fitting	C₆₇×#2221	C₂
socle	C₂×C₆₇	C₂×#466
hypercenter	#2221	D₆₇
hypocenter	C₆₇	C₂×#2221
LCS	G ▷ C₂×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131 ◁ #2221

Complements

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

N	H ≅ G/N	type
1. C₂×D₁₆×D₆₇	C₂	semidirect
2. #504×D₆₇	C₂	semidirect
3. #472×D₆₇	C₂	semidirect
4. #22562330	C₂	semidirect
5. #22562329	C₂	semidirect
6. #22562328	C₂	semidirect
7. #22562327	C₂	semidirect
8. #22562326	C₂	semidirect
9. #368×D₆₇	C₂	semidirect
10. #361×D₆₇	C₂	semidirect
11. C₆₇×#2221	C₂	semidirect
15. C₂×D₁₀₇₂	C₂²	semidirect
16. C₂×#14523984	C₂²	semidirect
22. #16863814	C₂²	semidirect
23. #16863813	C₂²	semidirect
25. #16863812	C₂²	semidirect
30. #16863667	C₂²	semidirect
31. #16863666	C₂²	semidirect
34. #16863663	C₂²	semidirect
37. #16863226	C₂²	semidirect
38. #16863225	C₂²	semidirect
39. #16863210	C₂²	semidirect
40. #16863209	C₂²	semidirect
41. #16863208	C₂²	semidirect
42. C₂×D₁₆×C₆₇	C₂²	semidirect
43. #504×C₆₇	C₂²	semidirect
44. #472×C₆₇	C₂²	semidirect
45. #368×C₆₇	C₂²	semidirect
46. #361×C₆₇	C₂²	semidirect
236. D₆₇	#2221	direct (N × H)
245. #2221	D₆₇	direct (N × H)
248. C₆₇	C₂×#2221	semidirect
258. C₂×D₁₆	C₂×D₆₇	semidirect
264. #504	C₂×D₆₇	semidirect
274. #472	C₂×D₆₇	semidirect
279. #368	C₂×D₆₇	semidirect
283. #361	C₂×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₆×D₆₇	2
#504×D₆₇	2
#472×D₆₇	2
#22562330	2
#22562329	2
#22562328	2
#22562327	2
#22562326	2
#368×D₆₇	2
#361×D₆₇	2
C₆₇×#2221	2
C₂×#2221	67

Subgroups — #2221×D67 #31010384

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2221×D₆₇ #31010384