Subgroups — #31732137

Order 17152.

2684 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574985	C₂	1	4	yes	maximal, complemented
2	#22572008	C₂	1	4	yes	maximal, complemented
3	#22572002	C₂	1	4	yes	maximal, complemented
4	#22571975	C₂	1	8	yes	maximal, complemented
5	#22569933	C₂	1	4	yes	maximal, complemented
6	#22569557	C₂	1	2	yes	maximal, complemented
7	C₂×#16863563	C₂	1	2	yes	maximal, complemented
8	#22569120	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3151	C₂	1	1	yes	maximal, characteristic, complemented
10	#16864232	C₂²	1	2	yes	complemented
11	C₂×#14524088	C₂²	1	2	yes	complemented
12	#16864206	—	2	8	no	—
13	#16864202	C₂²	1	16	yes	complemented
14	#16864200	—	2	8	no	—
15	#16864197	C₂²	1	16	yes	complemented
16	#16864196	C₂²	1	2	yes	—
17	#16864194	C₂²	1	4	yes	complemented
18	#16864192	—	2	8	no	—
19	C₂×#14524069	C₂²	1	4	yes	complemented
20	AGL(1,ℤ/8)×D₆₇	—	2	8	no	—
21	#16864162	C₂²	1	4	yes	complemented
22	#16863663	C₂²	1	16	yes	complemented
23	#16863656	C₂²	1	16	yes	complemented
24	#16863578	C₂²	1	4	yes	complemented
25	#16863573	C₂²	1	4	yes	complemented
26	#16863568	C₂²	1	4	yes	complemented
27	#16863563	C₂²	1	8	yes	complemented
28	#16863563	C₂²	1	8	yes	complemented
29	#16863563	C₂²	1	4	yes	complemented
30	#16863519	C₂²	1	8	yes	complemented
31	#16863514	C₂²	1	8	yes	complemented
32	#16863445	C₂²	1	2	yes	complemented
33	C₂×#14523971	C₂²	1	4	yes	complemented
34	#16863380	C₂²	1	2	yes	complemented
35	C₂×#14523960	C₂²	1	2	yes	complemented
36	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	complemented
37	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	#496×C₆₇	C₂²	1	4	yes	complemented
40	#493×C₆₇	C₂²	1	2	yes	complemented
41	#492×C₆₇	C₂²	1	2	yes	complemented
42	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	#14524091	C₂³	1	4	yes	—
44	#14524090	—	2	4	no	—
45	#14524089	—	2	4	no	—
46	#14524088	—	2	8	no	—
47	#14524088	—	4	2	no	—
48	#14524088	—	4	2	no	—
49	#14524088	C₂³	1	4	yes	—
50	#14524088	C₂³	1	8	yes	complemented
51	C₂×#11761628	—	4	2	no	—
52	C₂×#11761628	C₂³	1	4	yes	—
53	C₂×#11761627	—	2	4	no	—
54	#41×D₆₇	—	2	8	no	—
55	C₂²×C₂²⋊D₆₇	—	4	2	no	—
56	C₂×D₄×D₆₇	—	2	4	no	—
57	#14524076	D₄	1	8	yes	complemented
58	#14524074	C₂³	1	8	yes	complemented
59	#14524073	—	2	4	no	—
60	#14524072	—	2	16	no	—
61	#14524071	D₄	1	8	yes	complemented
62	#14524070	—	2	16	no	—
63	#14524069	—	2	8	no	—
64	#14524069	C₂³	1	16	yes	—
65	#14524069	C₂³	1	8	yes	complemented
66	#14524068	—	2	4	no	—
67	#14524067	—	2	16	no	—
68	#14524067	—	2	16	no	—
69	#14524065	C₂³	1	8	yes	—
70	#14524064	—	2	16	no	—
71	#14524063	—	2	8	no	—
72	#14524062	—	2	16	no	—
73	C₂×#11761616	—	2	4	no	—
74	SD₁₆×D₆₇	—	2	16	no	—
75	C₂×#11761613	—	2	4	no	—
76	D₈×D₆₇	—	2	16	no	—
77	#14524051	—	2	8	no	—
78	#14524049	C₂³	1	16	yes	complemented
79	C₂×#11761612	C₂³	1	4	yes	—
80	M₁₆×D₆₇	—	2	8	no	—
81	#14523979	C₂³	1	8	yes	complemented
82	#14523971	C₂³	1	8	yes	complemented
83	#14523971	C₂³	1	8	yes	complemented
84	#14523962	C₂³	1	4	yes	complemented
85	#14523960	C₂³	1	8	yes	complemented
86	#14523960	C₂³	1	4	yes	complemented
87	C₂×#41×C₆₇	C₂³	1	2	yes	—
88	C₂²×D₄×C₆₇	—	4	1	no	—
89	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
90	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
91	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
92	C₂×SD₁₆×C₆₇	C₂³	1	8	yes	complemented
93	C₂×D₈×C₆₇	C₂³	1	8	yes	complemented
94	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
95	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
96	#127×C₆₇	—	4	1	no	—
97	#127×C₆₇	C₂³	1	2	yes	—
98	#127×C₆₇	C₂³	1	2	yes	—
99	#127×C₆₇	C₂³	1	1	yes	characteristic, complemented
100	#124×C₆₇	C₂³	1	2	yes	complemented
101	#121×C₆₇	—	4	1	no	—
102	C₄×D₄×C₆₇	—	4	1	no	—
103	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
104	#97×C₆₇	C₂³	1	2	yes	complemented
105	C₄×C₈×C₆₇	C₂³	1	2	yes	complemented
106	C₂³×D₆₇	—	4	2	no	—
107	#11761629	—	2	8	no	—
108	#11761628	—	2	4	no	—
109	#11761628	—	2	4	no	—
110	#11761628	—	4	4	no	—
111	#11761628	—	4	4	no	—
112	#11761628	—	4	4	no	—
113	#11761628	C₂×D₄	1	8	yes	—
114	#11761628	C₂⁴	1	8	yes	—
115	#11761627	—	2	8	no	—
116	#11761627	—	2	16	no	—
117	#11761627	—	4	8	no	—
118	#11761627	—	4	8	no	—
119	C₂×Dic₁₃₄	—	4	2	no	—
120	C₂×Dic₁₃₄	C₂×D₄	1	4	yes	—
121	Q₈×D₆₇	—	2	8	no	—
122	C₂×D₂₆₈	—	4	2	no	—
123	C₂×D₂₆₈	C₂×D₄	1	4	yes	—
124	C₂×C₂²⋊D₆₇	—	2	4	no	—
125	C₂×C₂²⋊D₆₇	—	4	4	no	—
126	C₂×C₂²⋊D₆₇	—	4	8	no	—
127	C₂×C₂²⋊D₆₇	—	4	4	no	—
128	C₂×C₂²⋊D₆₇	—	4	8	no	—
129	D₄×D₆₇	—	2	8	no	—
130	D₄×D₆₇	—	2	16	no	—
131	D₄×D₆₇	—	4	8	no	—
132	D₄×D₆₇	—	4	8	no	—
133	C₂²×Dic₆₇	—	4	2	no	—
134	C₂×C₄×D₆₇	—	2	4	no	—
135	C₂×C₄×D₆₇	—	4	4	no	—
136	Dic₂₆₈	C₂×D₄	1	8	yes	complemented
137	#11761618	—	2	8	no	—
138	#11761617	C₂×D₄	1	16	yes	complemented
139	#11761616	—	2	16	no	—
140	#11761616	—	2	8	no	—
141	#11761615	—	2	8	no	—
142	D₅₃₆	C₂×D₄	1	8	yes	complemented
143	#11761613	—	2	8	no	—
144	#11761613	—	2	16	no	—
145	#11761612	—	2	4	no	—
146	#11761612	C₂⁴	1	8	yes	—
147	#11761611	—	2	16	no	—
148	C₂×C₆₇⋊C₈	—	2	4	no	—
149	C₈×D₆₇	—	2	16	no	—
150	C₂⁴×C₆₇	—	2	2	no	—
151	#41×C₆₇	—	2	4	no	—
152	#41×C₆₇	—	2	4	no	—
153	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
154	C₂×D₄×C₆₇	—	2	2	no	—
155	C₂×D₄×C₆₇	—	2	4	no	—
156	C₂×D₄×C₆₇	—	2	4	no	—
157	C₂×D₄×C₆₇	—	2	2	no	—
158	C₂×D₄×C₆₇	—	4	1	no	—
159	C₂×D₄×C₆₇	—	4	2	no	—
160	C₂×D₄×C₆₇	—	4	2	no	—
161	C₂×D₄×C₆₇	—	8	4	no	—
162	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
163	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
164	C₂²×C₄×C₆₇	—	2	1	no	—
165	C₂²×C₄×C₆₇	—	2	2	no	—
166	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
167	SD₁₆×C₆₇	—	2	16	no	—
168	D₈×C₆₇	—	2	16	no	—
169	M₁₆×C₆₇	C₂×D₄	1	8	yes	—
170	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
171	C₄⋊C₄×C₆₇	—	4	1	no	—
172	C₂²⋊C₄×C₆₇	—	4	2	no	—
173	C₄²×C₆₇	—	2	1	no	—
174	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
175	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
176	C₂³×C₆₇	—	2	2	no	—
177	C₂³×C₆₇	—	2	4	no	—
178	C₂³×C₆₇	—	4	2	no	—
179	C₂³×C₆₇	—	4	2	no	—
180	C₂³×C₆₇	—	8	4	no	—
181	C₂³×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
182	C₂²×D₆₇	—	2	4	no	—
183	C₂²×D₆₇	—	4	4	no	—
184	C₂²×D₆₇	—	4	8	no	—
185	C₂²×D₆₇	—	16	4	no	—
186	Q₈×C₆₇	—	2	4	no	—
187	D₄×C₆₇	—	2	4	no	—
188	D₄×C₆₇	—	2	8	no	—
189	D₄×C₆₇	—	4	4	no	—
190	D₄×C₆₇	—	4	4	no	—
191	D₄×C₆₇	—	8	2	no	—
192	D₄×C₆₇	—	8	4	no	—
193	D₄×C₆₇	—	8	4	no	—
194	C₂×C₄×C₆₇	—	2	1	no	—
195	C₂×C₄×C₆₇	—	2	1	no	—
196	C₂×C₄×C₆₇	—	2	2	no	—
197	C₂×C₄×C₆₇	—	4	2	no	—
198	C₂×C₄×C₆₇	—	4	2	no	—
199	C₂×C₄×C₆₇	—	4	2	no	—
200	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
201	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
202	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
203	C₂²⋊D₆₇	—	2	8	no	—
204	C₂²⋊D₆₇	—	2	8	no	—
205	C₂²⋊D₆₇	—	4	16	no	—
206	C₂²⋊D₆₇	—	4	8	no	—
207	C₂×Dic₆₇	—	2	4	no	—
208	C₂×Dic₆₇	—	4	4	no	—
209	C₂×Dic₆₇	—	4	8	no	—
210	D₂₆₈	—	2	4	no	—
211	D₂₆₈	—	4	4	no	—
212	D₂₆₈	C₂²×D₄	1	8	yes	—
213	C₄×D₆₇	—	2	8	no	—
214	C₄×D₆₇	—	2	8	no	—
215	C₄×D₆₇	—	4	8	no	—
216	Dic₁₃₄	—	2	4	no	—
217	Dic₁₃₄	—	4	4	no	—
218	Dic₁₃₄	C₂²×D₄	1	8	yes	—
219	C₈×C₆₇	C₂²×D₄	1	8	yes	—
220	C₆₇⋊C₈	—	2	8	no	—
221	C₂²×C₆₇	—	4	1	no	—
222	C₂²×C₆₇	—	4	2	no	—
223	C₂²×C₆₇	—	4	4	no	—
224	C₂²×C₆₇	—	8	4	no	—
225	C₂²×C₆₇	—	8	2	no	—
226	C₂²×C₆₇	—	8	4	no	—
227	C₂²×C₆₇	—	16	2	no	—
228	C₂²×C₆₇	D₄²	1	2	yes	—
229	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
230	C₂×D₆₇	—	2	8	no	—
231	C₂×D₆₇	—	8	4	no	—
232	C₂×D₆₇	—	16	4	no	—
233	C₂×D₆₇	—	16	8	no	—
234	C₄×C₆₇	—	2	2	no	—
235	C₄×C₆₇	—	4	1	no	—
236	C₄×C₆₇	—	4	2	no	—
237	C₄×C₆₇	D₄²	1	2	yes	—
238	C₄×C₆₇	C₂³×D₄	1	2	yes	—
239	Dic₆₇	—	2	8	no	—
240	#61110	—	67	1	no	maximal, Sylow
241	C₂×C₆₇	—	2	1	no	—
242	C₂×C₆₇	—	2	2	no	—
243	C₂×C₆₇	—	8	2	no	—
244	C₂×C₆₇	—	8	4	no	—
245	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
246	D₆₇	—	4	8	no	—
247	#3585	—	67	4	no	—
248	#3292	—	67	4	no	—
249	#3291	—	67	4	no	—
250	#3288	—	67	8	no	—
251	#3151	D₆₇	1	1	yes	characteristic, complemented
252	#3068	—	67	4	no	—
253	#3018	—	67	2	no	—
254	C₂×#453	—	67	2	no	—
255	#2956	—	67	2	no	—
256	C₆₇	#61110	1	1	yes	characteristic, complemented, Sylow
257	#585	—	67	2	no	—
258	C₂×H(5,𝔽₂)	—	67	2	no	—
259	#577	—	67	16	no	—
260	#577	—	134	8	no	—
261	#576	—	67	16	no	—
262	#576	—	134	8	no	—
263	#575	—	67	4	no	—
264	#575	—	67	2	no	—
265	#575	—	134	8	no	—
266	C₂×AGL(1,ℤ/8)	—	67	4	no	—
267	C₂×AGL(1,ℤ/8)	—	134	8	no	—
268	C₂×AGL(1,ℤ/8)	C₂×D₆₇	1	4	yes	complemented
269	#568	—	67	4	no	—
270	#532	C₂×D₆₇	1	1	yes	characteristic, complemented
271	C₂×#127	C₂×D₆₇	1	1	yes	characteristic, complemented
272	#496	C₂×D₆₇	1	4	yes	complemented
273	#493	C₂×D₆₇	1	2	yes	complemented
274	#492	C₂×D₆₇	1	2	yes	complemented
275	#472	—	67	16	no	—
276	#471	—	67	16	no	—
277	#456	—	67	4	no	—
278	#455	—	67	4	no	—
279	#454	—	67	4	no	—
280	#453	—	67	8	no	—
281	#453	—	67	8	no	—
282	#453	—	67	4	no	—
283	#444	—	67	8	no	—
284	#443	—	67	8	no	—
285	#430	—	67	2	no	—
286	C₂×#104	—	67	4	no	—
287	#413	—	67	2	no	—
288	C₂×#100	—	67	2	no	—
289	C₄×M₁₆	C₂×D₆₇	1	1	yes	characteristic, complemented
290	2₋¹⁺⁴	—	67	4	no	—
291	2₋¹⁺⁴	—	134	4	no	—
292	H(5,𝔽₂)	—	268	2	no	—
293	H(5,𝔽₂)	—	268	2	no	—
294	H(5,𝔽₂)	—	67	4	no	—
295	H(5,𝔽₂)	—	67	8	no	—
296	H(5,𝔽₂)	—	134	8	no	—
297	H(5,𝔽₂)	—	134	4	no	—
298	C₂×#41	—	268	2	no	—
299	C₂×#41	—	67	4	no	—
300	C₂×#41	—	134	4	no	—
301	C₂×#41	—	134	8	no	—
302	C₂×#41	C₂²×D₆₇	1	2	yes	—
303	C₂²×D₄	—	4	1	no	—
304	C₂²×D₄	—	268	2	no	—
305	C₂²×D₄	—	134	4	no	—
306	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
307	#137	—	67	8	no	—
308	#137	—	67	8	no	—
309	#137	—	134	16	no	—
310	#137	—	134	4	no	—
311	AGL(1,ℤ/8)	—	2	8	no	—
312	AGL(1,ℤ/8)	—	2	8	no	—
313	AGL(1,ℤ/8)	—	67	16	no	—
314	AGL(1,ℤ/8)	—	67	8	no	—
315	AGL(1,ℤ/8)	—	67	8	no	—
316	AGL(1,ℤ/8)	—	134	16	no	—
317	AGL(1,ℤ/8)	—	134	16	no	—
318	AGL(1,ℤ/8)	—	134	16	no	—
319	AGL(1,ℤ/8)	—	134	8	no	—
320	AGL(1,ℤ/8)	—	134	4	no	—
321	#135	—	67	8	no	—
322	#135	—	134	16	no	—
323	#135	—	134	16	no	—
324	#135	—	134	8	no	—
325	C₂×SD₁₆	—	134	16	no	—
326	C₂×SD₁₆	—	134	4	no	—
327	C₂×SD₁₆	C₂²×D₆₇	1	8	yes	complemented
328	C₂×D₈	—	134	16	no	—
329	C₂×D₈	—	134	4	no	—
330	C₂×D₈	C₂²×D₆₇	1	8	yes	complemented
331	#131	—	67	16	no	—
332	#131	—	134	8	no	—
333	C₂×M₁₆	—	67	4	no	—
334	C₂×M₁₆	—	134	8	no	—
335	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
336	C₄⋊Q₈	C₂²×D₆₇	1	1	yes	characteristic, complemented
337	#127	—	4	1	no	—
338	#127	C₂²×D₆₇	1	2	yes	—
339	#127	C₂²×D₆₇	1	2	yes	—
340	#127	C₂²×D₆₇	1	1	yes	characteristic, complemented
341	#124	C₂²×D₆₇	1	2	yes	complemented
342	#121	—	4	1	no	—
343	C₄×D₄	—	4	1	no	—
344	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
345	#108	—	67	8	no	—
346	#104	—	67	8	no	—
347	#104	—	67	8	no	—
348	#101	—	67	4	no	—
349	#100	—	67	8	no	—
350	#100	—	67	4	no	—
351	#97	C₂²×D₆₇	1	2	yes	complemented
352	C₄×C₈	C₂²×D₆₇	1	2	yes	complemented
353	C₂⁴	—	2	2	no	—
354	C₂⁴	—	268	2	no	—
355	#41	—	2	4	no	—
356	#41	—	2	4	no	—
357	#41	—	268	4	no	—
358	#41	—	268	4	no	—
359	#41	—	268	4	no	—
360	#41	—	268	8	no	—
361	#41	—	268	8	no	—
362	#41	—	67	8	no	—
363	#41	—	67	8	no	—
364	#41	—	134	8	no	—
365	#41	—	134	16	no	—
366	#41	—	134	8	no	—
367	#41	—	134	4	no	—
368	#41	—	134	4	no	—
369	C₂×Q₈	—	268	2	no	—
370	C₂×Q₈	—	67	4	no	—
371	C₂×Q₈	—	134	8	no	—
372	C₂×Q₈	C₂³×D₆₇	1	2	yes	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	4	no	—
375	C₂×D₄	—	2	4	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	4	1	no	—
378	C₂×D₄	—	4	2	no	—
379	C₂×D₄	—	4	2	no	—
380	C₂×D₄	—	8	4	no	—
381	C₂×D₄	—	268	2	no	—
382	C₂×D₄	—	268	8	no	—
383	C₂×D₄	—	268	8	no	—
384	C₂×D₄	—	268	4	no	—
385	C₂×D₄	—	268	8	no	—
386	C₂×D₄	—	268	8	no	—
387	C₂×D₄	—	268	4	no	—
388	C₂×D₄	—	67	4	no	—
389	C₂×D₄	—	134	8	no	—
390	C₂×D₄	—	134	16	no	—
391	C₂×D₄	—	134	4	no	—
392	C₂×D₄	C₂³×D₆₇	1	2	yes	—
393	C₂×D₄	C₂³×D₆₇	1	4	yes	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	268	4	no	—
397	C₂²×C₄	—	268	2	no	—
398	C₂²×C₄	—	134	4	no	—
399	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
400	Q₁₆	—	67	8	no	—
401	Q₁₆	—	134	8	no	—
402	SD₁₆	—	2	16	no	—
403	SD₁₆	—	67	16	no	—
404	SD₁₆	—	134	16	no	—
405	SD₁₆	—	134	8	no	—
406	SD₁₆	—	134	8	no	—
407	D₈	—	2	16	no	—
408	D₈	—	67	8	no	—
409	D₈	—	134	8	no	—
410	D₈	—	134	16	no	—
411	M₁₆	—	67	8	no	—
412	M₁₆	—	134	4	no	—
413	M₁₆	—	134	16	no	—
414	M₁₆	D₄×D₆₇	1	8	yes	—
415	C₂×C₈	—	134	4	no	—
416	C₂×C₈	—	134	16	no	—
417	C₂×C₈	C₂³×D₆₇	1	4	yes	—
418	C₄⋊C₄	—	4	1	no	—
419	C₂²⋊C₄	—	4	2	no	—
420	C₄²	—	2	1	no	—
421	C₄²	C₂³×D₆₇	1	1	yes	characteristic
422	C₄²	C₂³×D₆₇	1	1	yes	characteristic
423	C₂³	—	2	2	no	—
424	C₂³	—	2	4	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	8	4	no	—
428	C₂³	—	268	4	no	—
429	C₂³	—	268	8	no	—
430	C₂³	—	1072	4	no	—
431	C₂³	—	134	4	no	—
432	C₂³	#14524088	1	1	yes	characteristic
433	Q₈	—	2	4	no	—
434	Q₈	—	268	4	no	—
435	Q₈	—	67	8	no	—
436	Q₈	—	134	4	no	—
437	D₄	—	2	4	no	—
438	D₄	—	2	8	no	—
439	D₄	—	4	4	no	—
440	D₄	—	4	4	no	—
441	D₄	—	8	4	no	—
442	D₄	—	8	2	no	—
443	D₄	—	8	4	no	—
444	D₄	—	268	4	no	—
445	D₄	—	268	16	no	—
446	D₄	—	268	8	no	—
447	D₄	—	67	8	no	—
448	D₄	—	134	8	no	—
449	D₄	—	134	8	no	—
450	D₄	—	134	4	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	268	8	no	—
458	C₂×C₄	—	268	8	no	—
459	C₂×C₄	—	268	4	no	—
460	C₂×C₄	—	134	4	no	—
461	C₂×C₄	—	134	8	no	—
462	C₂×C₄	—	134	8	no	—
463	C₂×C₄	C₂×D₄×D₆₇	1	4	yes	—
464	C₂×C₄	#14524088	1	1	yes	characteristic
465	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
466	C₈	—	134	8	no	—
467	C₈	C₂×D₄×D₆₇	1	8	yes	—
468	C₂²	—	4	1	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	4	no	—
471	C₂²	—	8	4	no	—
472	C₂²	—	8	2	no	—
473	C₂²	—	8	4	no	—
474	C₂²	—	16	2	no	—
475	C₂²	—	536	4	no	—
476	C₂²	—	1072	8	no	—
477	C₂²	—	1072	4	no	—
478	C₂²	—	134	8	no	—
479	C₂²	#16864031	1	2	yes	—
480	C₂²	C₂×#14524088	1	1	yes	characteristic
481	C₄	—	2	2	no	—
482	C₄	—	4	1	no	—
483	C₄	—	4	2	no	—
484	C₄	—	134	8	no	—
485	C₄	#16864031	1	2	yes	—
486	C₄	C₂²×D₄×D₆₇	1	2	yes	—
487	C₂	—	2	1	no	—
488	C₂	—	2	2	no	—
489	C₂	—	8	4	no	—
490	C₂	—	8	2	no	—
491	C₂	—	268	8	no	—
492	C₂	C₂×#16864031	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×#16864031
commutator, cosocle	C₂×C₄×C₆₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₆₇
Fitting	C₆₇×#3151	C₂
socle	C₂×C₆₇	C₂×D₄²
hypercenter	#3151	D₆₇
hypocenter	C₆₇	#61110
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #3151

Complements

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

N	H ≅ G/N	type
1. #22574985	C₂	semidirect
2. #22572008	C₂	semidirect
3. #22572002	C₂	semidirect
4. #22571975	C₂	semidirect
5. #22569933	C₂	semidirect
6. #22569557	C₂	semidirect
7. C₂×#16863563	C₂	semidirect
8. #22569120	C₂	semidirect
9. C₆₇×#3151	C₂	semidirect
10. #16864232	C₂²	semidirect
11. C₂×#14524088	C₂²	semidirect
13. #16864202	C₂²	semidirect
15. #16864197	C₂²	semidirect
17. #16864194	C₂²	semidirect
19. C₂×#14524069	C₂²	semidirect
21. #16864162	C₂²	semidirect
22. #16863663	C₂²	semidirect
23. #16863656	C₂²	semidirect
24. #16863578	C₂²	semidirect
25. #16863573	C₂²	semidirect
26. #16863568	C₂²	semidirect
27. #16863563	C₂²	semidirect
28. #16863563	C₂²	semidirect
29. #16863563	C₂²	semidirect
30. #16863519	C₂²	semidirect
31. #16863514	C₂²	semidirect
32. #16863445	C₂²	semidirect
33. C₂×#14523971	C₂²	semidirect
34. #16863380	C₂²	semidirect
35. C₂×#14523960	C₂²	semidirect
36. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
37. #532×C₆₇	C₂²	semidirect
38. C₂×#127×C₆₇	C₂²	semidirect
39. #496×C₆₇	C₂²	semidirect
40. #493×C₆₇	C₂²	semidirect
41. #492×C₆₇	C₂²	semidirect
42. C₄×M₁₆×C₆₇	C₂²	semidirect
50. #14524088	C₂³	semidirect
57. #14524076	D₄	semidirect
58. #14524074	C₂³	semidirect
61. #14524071	D₄	semidirect
65. #14524069	C₂³	semidirect
78. #14524049	C₂³	semidirect
81. #14523979	C₂³	semidirect
82. #14523971	C₂³	semidirect
83. #14523971	C₂³	semidirect
84. #14523962	C₂³	semidirect
85. #14523960	C₂³	semidirect
86. #14523960	C₂³	semidirect
92. C₂×SD₁₆×C₆₇	C₂³	semidirect
93. C₂×D₈×C₆₇	C₂³	semidirect
95. C₄⋊Q₈×C₆₇	C₂³	semidirect
99. #127×C₆₇	C₂³	semidirect
100. #124×C₆₇	C₂³	semidirect
104. #97×C₆₇	C₂³	semidirect
105. C₄×C₈×C₆₇	C₂³	semidirect
136. Dic₂₆₈	C₂×D₄	semidirect
138. #11761617	C₂×D₄	semidirect
142. D₅₃₆	C₂×D₄	semidirect
251. #3151	D₆₇	semidirect
256. C₆₇	#61110	semidirect
268. C₂×AGL(1,ℤ/8)	C₂×D₆₇	semidirect
270. #532	C₂×D₆₇	semidirect
271. C₂×#127	C₂×D₆₇	semidirect
272. #496	C₂×D₆₇	semidirect
273. #493	C₂×D₆₇	semidirect
274. #492	C₂×D₆₇	semidirect
289. C₄×M₁₆	C₂×D₆₇	semidirect
327. C₂×SD₁₆	C₂²×D₆₇	semidirect
330. C₂×D₈	C₂²×D₆₇	semidirect
336. C₄⋊Q₈	C₂²×D₆₇	semidirect
340. #127	C₂²×D₆₇	semidirect
341. #124	C₂²×D₆₇	semidirect
351. #97	C₂²×D₆₇	semidirect
352. C₄×C₈	C₂²×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22574985	2
#22572008	2
#22572002	2
#22571975	2
#22569933	2
#22569557	2
C₂×#16863563	2
#22569120	2
C₆₇×#3151	2
#61110	67