Subgroups — #31720177

Order 17152.

2604 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574978	C₂	1	1	yes	maximal, characteristic
2	#22574922	C₂	1	2	yes	maximal, complemented
3	#22569127	C₂	1	1	yes	maximal, characteristic, complemented
4	#22569123	C₂	1	4	yes	maximal, complemented
5	#22569116	C₂	1	2	yes	maximal, complemented
6	#22569114	C₂	1	4	yes	maximal, complemented
7	#22569108	C₂	1	2	yes	maximal, complemented
8	#22569107	C₂	1	4	yes	maximal, complemented
9	C₂×#16863518	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16863517	C₂	1	1	yes	maximal, characteristic, complemented
11	#444×D₆₇	C₂	1	4	yes	maximal, complemented
12	#22568817	C₂	1	1	yes	maximal, characteristic, complemented
13	#22568755	C₂	1	2	yes	maximal, complemented
14	#22568636	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2957	C₂	1	1	yes	maximal, characteristic, complemented
16	#16864232	C₂²	1	2	yes	—
17	#16864210	C₄	1	2	yes	complemented
18	#16864209	C₄	1	2	yes	complemented
19	#16864203	C₄	1	4	yes	complemented
20	#16864202	C₄	1	4	yes	complemented
21	#16864198	C₄	1	2	yes	complemented
22	#16864197	C₄	1	2	yes	complemented
23	#16864194	C₂²	1	2	yes	—
24	#16864193	C₂²	1	4	yes	—
25	C₂×#14524065	C₂²	1	1	yes	characteristic
26	#135×D₆₇	C₂²	1	4	yes	—
27	#16864162	—	2	4	no	—
28	#16864162	C₂²	1	2	yes	—
29	#16864162	C₂²	1	2	yes	complemented
30	#16864161	—	2	4	no	—
31	#16864161	C₂²	1	8	yes	complemented
32	C₂×#14524051	—	2	4	no	—
33	C₂×#14524051	C₂²	1	1	yes	characteristic
34	C₂×#14524051	C₂²	1	2	yes	complemented
35	C₂×#14524050	C₂²	1	2	yes	complemented
36	C₂×#14524049	C₂²	1	1	yes	characteristic
37	#131×D₆₇	—	2	4	no	—
38	#131×D₆₇	C₂²	1	8	yes	complemented
39	#16863864	C₂²	1	1	yes	characteristic
40	#16863519	C₂²	1	4	yes	complemented
41	#16863518	C₂²	1	2	yes	complemented
42	#16863518	C₂²	1	2	yes	complemented
43	#16863518	C₂²	1	2	yes	complemented
44	#16863518	C₂²	1	2	yes	complemented
45	#16863517	C₂²	1	2	yes	complemented
46	#16863517	C₂²	1	2	yes	complemented
47	#16863517	C₂²	1	2	yes	complemented
48	#16863517	C₂²	1	2	yes	complemented
49	#16863516	C₂²	1	8	yes	complemented
50	#16863515	C₂²	1	8	yes	complemented
51	#16863514	C₂²	1	4	yes	complemented
52	#16863511	C₂²	1	8	yes	complemented
53	#16863510	C₂²	1	8	yes	complemented
54	#16863444	C₂²	1	2	yes	complemented
55	#16863443	C₂²	1	4	yes	complemented
56	C₂×#14523979	C₂²	1	1	yes	characteristic, complemented
57	#108×D₆₇	C₂²	1	4	yes	complemented
58	#16863414	C₂²	1	2	yes	complemented
59	#16863411	C₂²	1	8	yes	complemented
60	C₂×#14523970	C₂²	1	2	yes	complemented
61	C₂×#14523969	C₂²	1	2	yes	complemented
62	#104×D₆₇	C₂²	1	8	yes	complemented
63	#16863353	C₂²	1	2	yes	complemented
64	#16863352	C₂²	1	1	yes	characteristic, complemented
65	#16863350	C₂²	1	2	yes	complemented
66	M₁₆×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
67	C₄×#11761611	C₂²	1	2	yes	complemented
68	C₂×#14523953	C₂²	1	1	yes	characteristic, complemented
69	#97×D₆₇	C₂²	1	2	yes	complemented
70	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
71	#568×C₆₇	C₂²	1	2	yes	complemented
72	#444×C₆₇	C₂²	1	4	yes	complemented
73	#443×C₆₇	C₂²	1	4	yes	complemented
74	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic, complemented
75	#421×C₆₇	C₂²	1	2	yes	complemented
76	#405×C₆₇	C₂²	1	1	yes	characteristic, complemented
77	#14524091	C₂×C₄	1	4	yes	—
78	#14524090	—	2	2	no	—
79	#14524090	C₂×C₄	1	4	yes	—
80	#14524089	—	2	2	no	—
81	#14524089	C₂×C₄	1	4	yes	—
82	#14524088	—	2	4	no	—
83	#14524088	C₂×C₄	1	4	yes	—
84	C₂×#11761628	—	2	4	no	—
85	C₂×#11761628	C₂³	1	2	yes	—
86	C₂×#11761628	C₂³	1	1	yes	characteristic
87	#41×D₆₇	—	2	4	no	—
88	#41×D₆₇	C₂³	1	8	yes	—
89	#14524075	C₂×C₄	1	8	yes	complemented
90	#14524074	C₂×C₄	1	4	yes	complemented
91	#14524073	C₂×C₄	1	4	yes	complemented
92	#14524072	C₂×C₄	1	8	yes	complemented
93	#14524070	C₂×C₄	1	8	yes	complemented
94	#14524069	C₂×C₄	1	4	yes	complemented
95	#14524068	C₂×C₄	1	4	yes	complemented
96	#14524067	C₂×C₄	1	8	yes	complemented
97	#14524066	C₂×C₄	1	4	yes	complemented
98	#14524065	C₂×C₄	1	2	yes	complemented
99	#14524065	C₂×C₄	1	2	yes	complemented
100	#14524065	C₂³	1	2	yes	—
101	#14524065	C₂³	1	2	yes	—
102	#14524064	C₂×C₄	1	8	yes	complemented
103	#14524063	C₂³	1	8	yes	—
104	#14524062	C₂×C₄	1	4	yes	complemented
105	C₂×Dic₂₆₈	C₂×C₄	1	1	yes	characteristic, complemented
106	Q₁₆×D₆₇	C₂×C₄	1	4	yes	complemented
107	C₂×#11761617	C₂×C₄	1	2	yes	complemented
108	SD₁₆×D₆₇	C₂×C₄	1	8	yes	complemented
109	C₂×D₅₃₆	C₂×C₄	1	1	yes	characteristic, complemented
110	D₈×D₆₇	C₂×C₄	1	4	yes	complemented
111	#14524051	—	2	4	no	—
112	#14524051	—	2	8	no	—
113	#14524051	—	2	2	no	—
114	#14524051	—	2	2	no	—
115	#14524051	—	2	8	no	—
116	#14524051	—	2	4	no	—
117	#14524051	D₄	1	4	yes	—
118	#14524051	D₄	1	4	yes	—
119	#14524051	C₂³	1	4	yes	—
120	#14524051	C₂³	1	4	yes	—
121	#14524050	—	2	2	no	—
122	#14524050	—	2	2	no	—
123	#14524050	C₂³	1	4	yes	—
124	#14524050	C₂³	1	4	yes	—
125	#14524049	—	2	4	no	—
126	#14524049	—	2	8	no	—
127	#14524049	—	2	8	no	—
128	#14524049	C₂×C₄	1	2	yes	—
129	#14524049	C₂×C₄	1	2	yes	—
130	#14524049	C₂×C₄	1	2	yes	—
131	#14524049	C₂×C₄	1	2	yes	—
132	#14524049	C₂³	1	8	yes	—
133	C₂×#11761612	—	2	2	no	—
134	C₂×#11761612	C₂³	1	2	yes	—
135	C₂×#11761612	C₂³	1	1	yes	characteristic
136	C₂×#11761611	—	2	8	no	—
137	C₂×#11761611	—	2	2	no	—
138	C₂×#11761611	C₂³	1	2	yes	—
139	C₂×#11761611	C₂³	1	2	yes	—
140	M₁₆×D₆₇	—	2	8	no	—
141	M₁₆×D₆₇	—	2	8	no	—
142	M₁₆×D₆₇	—	2	4	no	—
143	M₁₆×D₆₇	C₂³	1	8	yes	—
144	C₂²×C₆₇⋊C₈	—	2	2	no	—
145	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
146	C₂×C₈×D₆₇	—	2	2	no	—
147	C₂×C₈×D₆₇	—	2	8	no	—
148	C₂×C₈×D₆₇	C₂³	1	2	yes	—
149	C₂×C₈×D₆₇	C₂³	1	2	yes	—
150	#14524008	—	2	1	no	—
151	#14524005	—	2	1	no	—
152	(C₂²⋊D₆₇)⋊C₄	—	2	2	no	—
153	#14524000	C₂³	1	2	yes	—
154	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
155	C₄²×D₆₇	C₂³	1	2	yes	—
156	#14523979	C₂³	1	2	yes	—
157	#14523979	C₂³	1	2	yes	—
158	#14523978	C₂³	1	8	yes	—
159	#14523971	C₂³	1	8	yes	—
160	#14523970	C₂³	1	4	yes	—
161	#14523970	C₂³	1	4	yes	—
162	#14523969	C₂³	1	4	yes	—
163	#14523969	C₂³	1	4	yes	—
164	#14523954	C₂³	1	2	yes	—
165	#14523953	C₂³	1	2	yes	—
166	#14523953	C₂³	1	1	yes	characteristic
167	#14523953	C₂³	1	1	yes	characteristic
168	#14523953	C₂³	1	1	yes	characteristic
169	#14523953	C₂³	1	1	yes	characteristic
170	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
171	C₈×Dic₆₇	C₂³	1	2	yes	—
172	C₂×#41×C₆₇	C₂³	1	2	yes	—
173	#135×C₆₇	C₂×C₄	1	2	yes	complemented
174	#135×C₆₇	C₂×C₄	1	2	yes	complemented
175	#135×C₆₇	C₂³	1	2	yes	—
176	#135×C₆₇	C₂³	1	2	yes	—
177	C₂×Q₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
178	C₂×SD₁₆×C₆₇	C₂×C₄	1	2	yes	complemented
179	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
180	#131×C₆₇	—	2	4	no	—
181	#131×C₆₇	C₂³	1	8	yes	—
182	C₂×M₁₆×C₆₇	—	2	4	no	—
183	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
184	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
185	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
186	#117×C₆₇	C₂³	1	1	yes	characteristic
187	#108×C₆₇	C₂³	1	2	yes	—
188	#108×C₆₇	C₂³	1	2	yes	—
189	#104×C₆₇	C₂³	1	8	yes	—
190	#97×C₆₇	C₂³	1	2	yes	—
191	C₄×C₈×C₆₇	C₂³	1	2	yes	—
192	#11761629	—	2	4	no	—
193	#11761629	C₂²×C₄	1	8	yes	—
194	#11761628	—	2	2	no	—
195	#11761628	—	2	2	no	—
196	#11761628	—	2	8	no	—
197	#11761628	—	2	4	no	—
198	#11761628	—	2	8	no	—
199	#11761628	—	2	4	no	—
200	#11761628	C₂²×C₄	1	2	yes	—
201	#11761628	C₂²×C₄	1	2	yes	—
202	#11761628	C₂²×C₄	1	4	yes	—
203	#11761628	C₂×D₄	1	2	yes	—
204	#11761628	C₂×D₄	1	2	yes	—
205	#11761628	C₂⁴	1	4	yes	—
206	#11761627	—	2	8	no	—
207	#11761627	—	2	8	no	—
208	#11761627	—	2	4	no	—
209	#11761627	C₂²×C₄	1	8	yes	—
210	C₂×Dic₁₃₄	—	2	4	no	—
211	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
212	C₂×Dic₁₃₄	#41	1	1	yes	characteristic
213	Q₈×D₆₇	—	2	4	no	—
214	Q₈×D₆₇	C₂²×C₄	1	8	yes	—
215	C₂×D₂₆₈	—	2	4	no	—
216	C₂×D₂₆₈	C₂²×C₄	1	2	yes	—
217	C₂×D₂₆₈	#41	1	1	yes	characteristic
218	C₂×C₂²⋊D₆₇	—	2	2	no	—
219	C₂×C₂²⋊D₆₇	—	2	8	no	—
220	C₂×C₂²⋊D₆₇	#41	1	2	yes	—
221	D₄×D₆₇	—	2	8	no	—
222	D₄×D₆₇	—	2	8	no	—
223	D₄×D₆₇	—	2	4	no	—
224	D₄×D₆₇	C₂²×C₄	1	8	yes	—
225	C₂²×Dic₆₇	—	2	1	no	—
226	C₂×C₄×D₆₇	—	2	2	no	—
227	C₂×C₄×D₆₇	—	2	8	no	—
228	C₂×C₄×D₆₇	—	2	2	no	—
229	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
230	Dic₂₆₈	C₂²×C₄	1	2	yes	—
231	Dic₂₆₈	C₂²×C₄	1	2	yes	—
232	#11761618	C₂²×C₄	1	8	yes	—
233	#11761617	C₂²×C₄	1	4	yes	—
234	#11761617	C₂²×C₄	1	4	yes	—
235	#11761616	C₂²×C₄	1	8	yes	—
236	#11761615	C₂²×C₄	1	8	yes	—
237	D₅₃₆	C₂²×C₄	1	2	yes	—
238	D₅₃₆	C₂²×C₄	1	2	yes	—
239	#11761613	C₂²×C₄	1	8	yes	—
240	#11761612	—	2	2	no	—
241	#11761612	—	2	4	no	—
242	#11761612	—	2	4	no	—
243	#11761612	C₂²×C₄	1	2	yes	—
244	#11761612	C₂²×C₄	1	2	yes	—
245	#11761612	C₂⁴	1	4	yes	—
246	#11761611	—	2	8	no	—
247	#11761611	—	2	8	no	—
248	#11761611	—	2	4	no	—
249	#11761611	—	2	4	no	—
250	#11761611	C₂²×C₄	1	4	yes	—
251	#11761611	C₂²×C₄	1	4	yes	—
252	#11761611	C₂×D₄	1	8	yes	—
253	C₂×C₆₇⋊C₈	—	2	2	no	—
254	C₂×C₆₇⋊C₈	—	2	4	no	—
255	C₂×C₆₇⋊C₈	—	2	4	no	—
256	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
257	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
258	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
259	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
260	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
261	C₈×D₆₇	—	2	8	no	—
262	C₈×D₆₇	—	2	8	no	—
263	C₈×D₆₇	—	2	4	no	—
264	C₈×D₆₇	—	2	4	no	—
265	C₈×D₆₇	C₂²×C₄	1	4	yes	—
266	C₈×D₆₇	C₂²×C₄	1	4	yes	—
267	C₈×D₆₇	C₂×D₄	1	8	yes	—
268	Dic₆₇⋊C₄	—	2	2	no	—
269	(C₂×D₆₇)⋊C₄	—	2	2	no	—
270	C₄×Dic₆₇	—	2	1	no	—
271	C₄×Dic₆₇	—	2	2	no	—
272	C₄×Dic₆₇	C₂⁴	1	1	yes	characteristic
273	C₄×Dic₆₇	C₂⁴	1	1	yes	characteristic
274	#41×C₆₇	—	2	2	no	—
275	#41×C₆₇	—	2	2	no	—
276	#41×C₆₇	C₂²×C₄	1	4	yes	—
277	#41×C₆₇	C₂⁴	1	4	yes	—
278	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
279	C₂×D₄×C₆₇	—	2	2	no	—
280	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
281	C₂²×C₄×C₆₇	—	2	2	no	—
282	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
283	Q₁₆×C₆₇	C₂²×C₄	1	2	yes	—
284	Q₁₆×C₆₇	C₂²×C₄	1	2	yes	—
285	SD₁₆×C₆₇	C₂²×C₄	1	4	yes	—
286	SD₁₆×C₆₇	C₂²×C₄	1	4	yes	—
287	D₈×C₆₇	C₂²×C₄	1	2	yes	—
288	D₈×C₆₇	C₂²×C₄	1	2	yes	—
289	M₁₆×C₆₇	—	2	2	no	—
290	M₁₆×C₆₇	—	2	8	no	—
291	M₁₆×C₆₇	C₂×D₄	1	2	yes	—
292	M₁₆×C₆₇	C₂×D₄	1	2	yes	—
293	M₁₆×C₆₇	C₂⁴	1	4	yes	—
294	C₂×C₈×C₆₇	—	2	2	no	—
295	C₂×C₈×C₆₇	—	2	8	no	—
296	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
297	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
298	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
299	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
300	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
301	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
302	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
303	C₄⋊C₄×C₆₇	—	2	1	no	—
304	C₂²⋊C₄×C₆₇	—	2	1	no	—
305	C₄²×C₆₇	C₂⁴	1	2	yes	—
306	C₂³×C₆₇	—	2	2	no	—
307	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
308	C₂²×D₆₇	—	2	2	no	—
309	C₂²×D₆₇	—	2	8	no	—
310	C₂²×D₆₇	C₂×#41	1	2	yes	—
311	Q₈×C₆₇	—	2	2	no	—
312	Q₈×C₆₇	C₂³×C₄	1	4	yes	—
313	D₄×C₆₇	—	2	4	no	—
314	D₄×C₆₇	—	2	4	no	—
315	D₄×C₆₇	—	2	2	no	—
316	D₄×C₆₇	C₂³×C₄	1	4	yes	—
317	C₂×C₄×C₆₇	—	2	2	no	—
318	C₂×C₄×C₆₇	—	2	4	no	—
319	C₂×C₄×C₆₇	—	2	4	no	—
320	C₂×C₄×C₆₇	—	2	2	no	—
321	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
322	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
323	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
326	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
327	C₂²⋊D₆₇	—	2	4	no	—
328	C₂²⋊D₆₇	—	2	4	no	—
329	C₂²⋊D₆₇	—	2	8	no	—
330	C₂²⋊D₆₇	—	2	8	no	—
331	C₂²⋊D₆₇	C₄×D₄	1	4	yes	—
332	C₂²⋊D₆₇	C₄×D₄	1	4	yes	—
333	C₂×Dic₆₇	—	2	2	no	—
334	C₂×Dic₆₇	—	2	8	no	—
335	C₂×Dic₆₇	—	2	1	no	—
336	C₂×Dic₆₇	—	2	1	no	—
337	C₂×Dic₆₇	—	8	1	no	—
338	C₂×Dic₆₇	C₂×#41	1	2	yes	—
339	D₂₆₈	—	2	8	no	—
340	D₂₆₈	—	2	2	no	—
341	D₂₆₈	C₄×D₄	1	2	yes	—
342	D₂₆₈	C₄×D₄	1	2	yes	—
343	D₂₆₈	C₂³×C₄	1	4	yes	—
344	C₄×D₆₇	—	2	8	no	—
345	C₄×D₆₇	—	2	4	no	—
346	C₄×D₆₇	—	2	4	no	—
347	C₄×D₆₇	—	2	8	no	—
348	C₄×D₆₇	—	8	2	no	—
349	C₄×D₆₇	C₂³×C₄	1	4	yes	—
350	C₄×D₆₇	C₂²×D₄	1	4	yes	—
351	Dic₁₃₄	—	2	2	no	—
352	Dic₁₃₄	—	2	8	no	—
353	Dic₁₃₄	C₄×D₄	1	2	yes	—
354	Dic₁₃₄	C₄×D₄	1	2	yes	—
355	Dic₁₃₄	C₂³×C₄	1	4	yes	—
356	C₈×C₆₇	—	2	4	no	—
357	C₈×C₆₇	C₂³×C₄	1	1	yes	characteristic
358	C₈×C₆₇	C₂³×C₄	1	1	yes	characteristic
359	C₈×C₆₇	C₂³×C₄	1	1	yes	characteristic
360	C₈×C₆₇	C₂³×C₄	1	1	yes	characteristic
361	C₈×C₆₇	C₂²×D₄	1	4	yes	—
362	C₆₇⋊C₈	—	2	4	no	—
363	C₆₇⋊C₈	C₂³×C₄	1	4	yes	—
364	C₆₇⋊C₈	C₂²×D₄	1	2	yes	—
365	C₆₇⋊C₈	C₂²×D₄	1	2	yes	—
366	C₂²×C₆₇	—	2	4	no	—
367	C₂²×C₆₇	—	4	1	no	—
368	C₂²×C₆₇	—	8	2	no	—
369	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
370	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
371	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
372	C₂×D₆₇	—	2	4	no	—
373	C₂×D₆₇	—	4	2	no	—
374	C₂×D₆₇	—	8	8	no	—
375	C₂×D₆₇	—	8	2	no	—
376	C₂×D₆₇	C₂×C₄×D₄	1	4	yes	—
377	C₄×C₆₇	—	2	4	no	—
378	C₄×C₆₇	—	4	2	no	—
379	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
380	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
381	C₄×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
382	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
383	Dic₆₇	—	2	4	no	—
384	Dic₆₇	—	4	1	no	—
385	Dic₆₇	—	4	1	no	—
386	Dic₆₇	C₂×C₄×D₄	1	4	yes	—
387	#60184	—	67	1	no	maximal, Sylow
388	C₂×C₆₇	—	2	1	no	—
389	C₂×C₆₇	—	2	1	no	—
390	C₂×C₆₇	—	2	1	no	—
391	C₂×C₆₇	—	4	4	no	—
392	C₂×C₆₇	C₂²×C₄×D₄	1	1	yes	characteristic
393	D₆₇	—	2	4	no	—
394	D₆₇	—	4	4	no	—
395	#3584	—	67	1	no	—
396	#3573	—	67	2	no	—
397	#2957	—	67	4	no	—
398	#2957	—	67	1	no	—
399	#2957	D₆₇	1	1	yes	characteristic, complemented
400	#2956	—	67	4	no	—
401	#2956	—	67	2	no	—
402	#2955	—	67	4	no	—
403	#2955	—	67	2	no	—
404	C₂×#444	—	67	4	no	—
405	C₂×#444	—	67	1	no	—
406	C₂×#444	—	67	1	no	—
407	#2916	—	67	1	no	—
408	#2901	—	67	2	no	—
409	#2875	—	67	1	no	—
410	C₆₇	#60184	1	1	yes	characteristic, complemented, Sylow
411	#585	—	67	2	no	—
412	#578	—	67	2	no	—
413	#578	—	67	2	no	—
414	#577	—	67	4	no	—
415	#577	—	67	4	no	—
416	#576	—	67	2	no	—
417	#576	—	67	2	no	—
418	#575	—	67	2	no	—
419	#575	—	67	4	no	—
420	C₂×#135	—	67	4	no	—
421	C₂×#135	—	67	1	no	—
422	C₂×#135	C₂×D₆₇	1	1	yes	characteristic
423	#568	—	67	2	no	—
424	#568	—	67	8	no	—
425	#568	—	67	2	no	—
426	#568	—	134	4	no	—
427	#568	—	134	4	no	—
428	#568	C₂×D₆₇	1	2	yes	complemented
429	C₂×#131	—	67	1	no	—
430	C₂×#131	—	67	1	no	—
431	C₂×#131	—	67	2	no	—
432	C₂×#131	—	67	8	no	—
433	C₂×#131	—	67	2	no	—
434	C₂×#131	—	134	4	no	—
435	C₂×#131	—	134	4	no	—
436	C₄×#41	—	67	1	no	—
437	#444	—	67	2	no	—
438	#444	—	67	2	no	—
439	#444	—	67	2	no	—
440	#444	—	67	2	no	—
441	#444	—	67	8	no	—
442	#444	—	67	2	no	—
443	#444	—	67	2	no	—
444	#444	—	67	2	no	—
445	#444	—	67	2	no	—
446	#444	—	67	8	no	—
447	#444	—	67	4	no	—
448	#444	C₂×D₆₇	1	4	yes	complemented
449	#443	—	67	8	no	—
450	#443	—	67	8	no	—
451	#443	—	67	4	no	—
452	#443	C₂×D₆₇	1	4	yes	complemented
453	#430	—	67	2	no	—
454	#430	—	67	4	no	—
455	C₂×#108	—	67	1	no	—
456	C₂×#108	—	67	4	no	—
457	C₂×#108	C₂×D₆₇	1	1	yes	characteristic, complemented
458	#421	—	67	2	no	—
459	#421	—	67	8	no	—
460	#421	C₂×D₆₇	1	2	yes	complemented
461	C₂×#104	—	67	2	no	—
462	C₂×#104	—	67	2	no	—
463	C₂×#104	—	67	8	no	—
464	#405	—	67	1	no	—
465	#405	—	67	2	no	—
466	#405	—	67	2	no	—
467	#405	C₂×D₆₇	1	1	yes	characteristic, complemented
468	C₄×M₁₆	—	67	1	no	—
469	C₄×M₁₆	—	67	2	no	—
470	C₂×#97	—	67	1	no	—
471	C₂×#97	—	67	2	no	—
472	2₋¹⁺⁴	—	67	4	no	—
473	2₋¹⁺⁴	—	67	4	no	—
474	2₋¹⁺⁴	—	134	2	no	—
475	H(5,𝔽₂)	—	67	4	no	—
476	H(5,𝔽₂)	—	67	4	no	—
477	H(5,𝔽₂)	—	134	4	no	—
478	H(5,𝔽₂)	—	134	2	no	—
479	C₂×#41	—	67	1	no	—
480	C₂×#41	—	67	8	no	—
481	C₂×#41	—	67	2	no	—
482	C₂×#41	—	134	4	no	—
483	C₂×#41	—	134	4	no	—
484	C₂×#41	C₂²×D₆₇	1	2	yes	—
485	#137	—	67	4	no	—
486	#137	—	67	4	no	—
487	#137	—	67	8	no	—
488	#137	—	67	8	no	—
489	AGL(1,ℤ/8)	—	67	4	no	—
490	AGL(1,ℤ/8)	—	67	4	no	—
491	AGL(1,ℤ/8)	—	67	8	no	—
492	AGL(1,ℤ/8)	—	67	8	no	—
493	#135	—	67	8	no	—
494	#135	—	67	4	no	—
495	#135	—	67	8	no	—
496	#135	—	67	4	no	—
497	#135	—	67	2	no	—
498	#135	—	67	2	no	—
499	#135	—	67	2	no	—
500	#135	—	67	2	no	—
501	#135	C₄×D₆₇	1	2	yes	complemented
502	#135	C₄×D₆₇	1	2	yes	complemented
503	#135	C₂²×D₆₇	1	2	yes	—
504	#135	C₂²×D₆₇	1	2	yes	—
505	C₂×Q₁₆	—	67	4	no	—
506	C₂×Q₁₆	—	67	1	no	—
507	C₂×Q₁₆	C₄×D₆₇	1	1	yes	characteristic, complemented
508	C₂×SD₁₆	—	67	8	no	—
509	C₂×SD₁₆	—	67	2	no	—
510	C₂×SD₁₆	C₄×D₆₇	1	2	yes	complemented
511	C₂×D₈	—	67	4	no	—
512	C₂×D₈	—	67	1	no	—
513	C₂×D₈	C₄×D₆₇	1	1	yes	characteristic, complemented
514	#131	—	2	4	no	—
515	#131	—	67	4	no	—
516	#131	—	67	4	no	—
517	#131	—	67	2	no	—
518	#131	—	67	2	no	—
519	#131	—	67	2	no	—
520	#131	—	67	2	no	—
521	#131	—	67	4	no	—
522	#131	—	67	4	no	—
523	#131	—	67	4	no	—
524	#131	—	67	4	no	—
525	#131	—	67	8	no	—
526	#131	—	134	8	no	—
527	#131	—	134	8	no	—
528	#131	—	134	4	no	—
529	#131	—	134	2	no	—
530	#131	—	134	8	no	—
531	#131	—	134	2	no	—
532	#131	—	134	2	no	—
533	#131	—	134	2	no	—
534	#131	—	134	8	no	—
535	#131	—	134	4	no	—
536	#131	—	134	4	no	—
537	#131	C₂²×D₆₇	1	8	yes	—
538	C₂×M₁₆	—	2	4	no	—
539	C₂×M₁₆	—	67	1	no	—
540	C₂×M₁₆	—	67	2	no	—
541	C₂×M₁₆	—	67	2	no	—
542	C₂×M₁₆	—	67	2	no	—
543	C₂×M₁₆	—	67	8	no	—
544	C₂×M₁₆	—	134	2	no	—
545	C₂×M₁₆	—	134	8	no	—
546	C₂×M₁₆	—	134	8	no	—
547	C₂×M₁₆	—	134	2	no	—
548	C₂×M₁₆	—	134	8	no	—
549	C₂×M₁₆	—	134	4	no	—
550	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
551	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
552	C₂²×C₈	—	67	1	no	—
553	C₂²×C₈	—	67	2	no	—
554	C₂²×C₈	—	67	2	no	—
555	C₂²×C₈	—	134	2	no	—
556	C₂²×C₈	—	134	8	no	—
557	C₂²×C₈	—	134	2	no	—
558	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
559	C₄×Q₈	—	134	1	no	—
560	C₄×D₄	—	134	2	no	—
561	C₄×D₄	—	134	1	no	—
562	#117	—	67	2	no	—
563	#117	C₂²×D₆₇	1	1	yes	characteristic
564	C₂×C₄²	—	67	1	no	—
565	C₂×C₄²	—	67	2	no	—
566	#108	—	67	8	no	—
567	#108	—	67	2	no	—
568	#108	—	67	2	no	—
569	#108	C₂²×D₆₇	1	2	yes	—
570	#108	C₂²×D₆₇	1	2	yes	—
571	#104	—	67	4	no	—
572	#104	—	67	4	no	—
573	#104	—	67	4	no	—
574	#104	—	67	4	no	—
575	#104	—	67	8	no	—
576	#104	C₂²×D₆₇	1	8	yes	—
577	#97	—	67	1	no	—
578	#97	—	67	2	no	—
579	#97	—	67	1	no	—
580	#97	—	67	1	no	—
581	#97	—	67	1	no	—
582	#97	—	67	2	no	—
583	#97	C₂²×D₆₇	1	2	yes	—
584	C₄×C₈	—	67	2	no	—
585	C₄×C₈	—	67	2	no	—
586	C₄×C₈	C₂²×D₆₇	1	2	yes	—
587	#41	—	2	2	no	—
588	#41	—	2	2	no	—
589	#41	—	67	2	no	—
590	#41	—	67	2	no	—
591	#41	—	67	2	no	—
592	#41	—	67	2	no	—
593	#41	—	67	8	no	—
594	#41	—	67	8	no	—
595	#41	—	67	4	no	—
596	#41	—	67	4	no	—
597	#41	—	134	8	no	—
598	#41	—	134	8	no	—
599	#41	—	134	4	no	—
600	#41	—	134	4	no	—
601	#41	—	134	8	no	—
602	#41	—	134	8	no	—
603	#41	—	134	4	no	—
604	#41	—	134	4	no	—
605	#41	—	134	2	no	—
606	#41	—	134	2	no	—
607	#41	C₂×C₄×D₆₇	1	4	yes	—
608	#41	C₂³×D₆₇	1	4	yes	—
609	C₂×Q₈	—	67	1	no	—
610	C₂×Q₈	—	67	8	no	—
611	C₂×Q₈	—	67	2	no	—
612	C₂×Q₈	—	134	4	no	—
613	C₂×Q₈	—	134	4	no	—
614	C₂×Q₈	C₂×C₄×D₆₇	1	2	yes	—
615	C₂×D₄	—	2	2	no	—
616	C₂×D₄	—	67	2	no	—
617	C₂×D₄	—	67	8	no	—
618	C₂×D₄	—	67	2	no	—
619	C₂×D₄	—	67	1	no	—
620	C₂×D₄	—	134	4	no	—
621	C₂×D₄	—	134	8	no	—
622	C₂×D₄	—	134	4	no	—
623	C₂×D₄	—	134	8	no	—
624	C₂×D₄	—	134	8	no	—
625	C₂×D₄	—	134	2	no	—
626	C₂×D₄	C₂×C₄×D₆₇	1	2	yes	—
627	C₂²×C₄	—	2	2	no	—
628	C₂²×C₄	—	67	2	no	—
629	C₂²×C₄	—	134	2	no	—
630	C₂²×C₄	—	134	8	no	—
631	C₂²×C₄	—	134	1	no	—
632	C₂²×C₄	—	134	2	no	—
633	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
634	Q₁₆	—	67	8	no	—
635	Q₁₆	—	67	2	no	—
636	Q₁₆	—	67	2	no	—
637	Q₁₆	C₂×C₄×D₆₇	1	2	yes	—
638	Q₁₆	C₂×C₄×D₆₇	1	2	yes	—
639	SD₁₆	—	67	8	no	—
640	SD₁₆	—	67	8	no	—
641	SD₁₆	—	67	4	no	—
642	SD₁₆	—	67	4	no	—
643	SD₁₆	C₂×C₄×D₆₇	1	4	yes	—
644	SD₁₆	C₂×C₄×D₆₇	1	4	yes	—
645	D₈	—	67	8	no	—
646	D₈	—	67	2	no	—
647	D₈	—	67	2	no	—
648	D₈	C₂×C₄×D₆₇	1	2	yes	—
649	D₈	C₂×C₄×D₆₇	1	2	yes	—
650	M₁₆	—	2	2	no	—
651	M₁₆	—	2	8	no	—
652	M₁₆	—	67	2	no	—
653	M₁₆	—	67	2	no	—
654	M₁₆	—	67	4	no	—
655	M₁₆	—	67	4	no	—
656	M₁₆	—	67	8	no	—
657	M₁₆	—	67	4	no	—
658	M₁₆	—	134	4	no	—
659	M₁₆	—	134	4	no	—
660	M₁₆	—	134	8	no	—
661	M₁₆	—	134	4	no	—
662	M₁₆	—	134	4	no	—
663	M₁₆	—	134	2	no	—
664	M₁₆	—	134	8	no	—
665	M₁₆	D₄×D₆₇	1	2	yes	—
666	M₁₆	D₄×D₆₇	1	2	yes	—
667	M₁₆	C₂³×D₆₇	1	4	yes	—
668	C₂×C₈	—	2	2	no	—
669	C₂×C₈	—	2	8	no	—
670	C₂×C₈	—	67	2	no	—
671	C₂×C₈	—	67	2	no	—
672	C₂×C₈	—	67	2	no	—
673	C₂×C₈	—	67	1	no	—
674	C₂×C₈	—	67	1	no	—
675	C₂×C₈	—	67	4	no	—
676	C₂×C₈	—	67	4	no	—
677	C₂×C₈	—	67	8	no	—
678	C₂×C₈	—	134	4	no	—
679	C₂×C₈	—	134	4	no	—
680	C₂×C₈	—	134	8	no	—
681	C₂×C₈	—	134	4	no	—
682	C₂×C₈	—	134	4	no	—
683	C₂×C₈	—	134	2	no	—
684	C₂×C₈	—	134	8	no	—
685	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
686	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
687	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
688	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
689	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
690	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
691	C₂×C₈	C₂³×D₆₇	1	2	yes	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	134	2	no	—
694	C₂²⋊C₄	—	2	1	no	—
695	C₂²⋊C₄	—	134	2	no	—
696	C₄²	—	67	1	no	—
697	C₄²	—	67	1	no	—
698	C₄²	—	134	2	no	—
699	C₄²	—	134	1	no	—
700	C₄²	C₂³×D₆₇	1	2	yes	—
701	C₂³	—	2	2	no	—
702	C₂³	—	67	2	no	—
703	C₂³	—	134	8	no	—
704	C₂³	—	134	2	no	—
705	C₂³	#41×D₆₇	1	1	yes	characteristic
706	Q₈	—	2	2	no	—
707	Q₈	—	67	2	no	—
708	Q₈	—	67	2	no	—
709	Q₈	—	67	4	no	—
710	Q₈	—	134	8	no	—
711	Q₈	—	134	2	no	—
712	Q₈	C₂²×C₄×D₆₇	1	4	yes	—
713	D₄	—	2	4	no	—
714	D₄	—	2	4	no	—
715	D₄	—	2	2	no	—
716	D₄	—	67	4	no	—
717	D₄	—	67	4	no	—
718	D₄	—	67	2	no	—
719	D₄	—	67	2	no	—
720	D₄	—	67	4	no	—
721	D₄	—	134	8	no	—
722	D₄	—	134	8	no	—
723	D₄	—	134	8	no	—
724	D₄	—	134	4	no	—
725	D₄	—	134	4	no	—
726	D₄	—	134	2	no	—
727	D₄	C₂²×C₄×D₆₇	1	4	yes	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	4	no	—
730	C₂×C₄	—	2	4	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	536	2	no	—
733	C₂×C₄	—	536	1	no	—
734	C₂×C₄	—	67	2	no	—
735	C₂×C₄	—	67	4	no	—
736	C₂×C₄	—	67	4	no	—
737	C₂×C₄	—	134	8	no	—
738	C₂×C₄	—	134	8	no	—
739	C₂×C₄	—	134	1	no	—
740	C₂×C₄	—	134	1	no	—
741	C₂×C₄	—	134	8	no	—
742	C₂×C₄	—	134	2	no	—
743	C₂×C₄	—	134	4	no	—
744	C₂×C₄	—	134	4	no	—
745	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
746	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
747	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
748	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
749	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
750	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
751	C₈	—	2	4	no	—
752	C₈	—	67	4	no	—
753	C₈	—	67	2	no	—
754	C₈	—	67	2	no	—
755	C₈	—	134	4	no	—
756	C₈	C₂²×C₄×D₆₇	1	1	yes	characteristic
757	C₈	C₂²×C₄×D₆₇	1	1	yes	characteristic
758	C₈	C₂²×C₄×D₆₇	1	1	yes	characteristic
759	C₈	C₂²×C₄×D₆₇	1	1	yes	characteristic
760	C₈	C₂×D₄×D₆₇	1	4	yes	—
761	C₂²	—	2	4	no	—
762	C₂²	—	4	1	no	—
763	C₂²	—	8	2	no	—
764	C₂²	—	268	2	no	—
765	C₂²	—	536	2	no	—
766	C₂²	—	536	8	no	—
767	C₂²	—	67	4	no	—
768	C₂²	—	134	4	no	—
769	C₂²	C₄×D₄×D₆₇	1	1	yes	characteristic
770	C₂²	C₄×D₄×D₆₇	1	1	yes	characteristic
771	C₂²	C₂×#41×D₆₇	1	1	yes	characteristic
772	C₄	—	2	4	no	—
773	C₄	—	4	2	no	—
774	C₄	—	268	1	no	—
775	C₄	—	268	1	no	—
776	C₄	—	67	4	no	—
777	C₄	—	134	4	no	—
778	C₄	C₄×D₄×D₆₇	1	1	yes	characteristic
779	C₄	C₄×D₄×D₆₇	1	1	yes	characteristic
780	C₄	C₂³×C₄×D₆₇	1	1	yes	characteristic
781	C₄	C₂²×D₄×D₆₇	1	1	yes	characteristic
782	C₂	—	2	1	no	—
783	C₂	—	2	1	no	—
784	C₂	—	2	1	no	—
785	C₂	—	4	4	no	—
786	C₂	—	268	4	no	—
787	C₂	—	134	4	no	—
788	C₂	C₂×C₄×D₄×D₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×D₄×D₆₇
commutator	C₄×C₆₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₆₇
Fitting	C₆₇×#2957	C₂
socle	C₂×C₆₇	C₂²×C₄×D₄
prime radical	#22574978	C₂
cosocle	C₂×C₄×C₆₇	C₂⁵
hypercenter	#2957	D₆₇
hypocenter	C₆₇	#60184
LCS	G ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #2957

Complements

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

N	H ≅ G/N	type
2. #22574922	C₂	semidirect
3. #22569127	C₂	semidirect
4. #22569123	C₂	semidirect
5. #22569116	C₂	semidirect
6. #22569114	C₂	semidirect
7. #22569108	C₂	semidirect
8. #22569107	C₂	semidirect
9. C₂×#16863518	C₂	semidirect
10. C₂×#16863517	C₂	semidirect
11. #444×D₆₇	C₂	semidirect
12. #22568817	C₂	semidirect
13. #22568755	C₂	semidirect
14. #22568636	C₂	semidirect
15. C₆₇×#2957	C₂	semidirect
17. #16864210	C₄	semidirect
18. #16864209	C₄	semidirect
19. #16864203	C₄	semidirect
20. #16864202	C₄	semidirect
21. #16864198	C₄	semidirect
22. #16864197	C₄	semidirect
29. #16864162	C₂²	semidirect
31. #16864161	C₂²	semidirect
34. C₂×#14524051	C₂²	semidirect
35. C₂×#14524050	C₂²	semidirect
38. #131×D₆₇	C₂²	semidirect
40. #16863519	C₂²	semidirect
41. #16863518	C₂²	semidirect
42. #16863518	C₂²	semidirect
43. #16863518	C₂²	semidirect
44. #16863518	C₂²	semidirect
45. #16863517	C₂²	semidirect
46. #16863517	C₂²	semidirect
47. #16863517	C₂²	semidirect
48. #16863517	C₂²	semidirect
49. #16863516	C₂²	semidirect
50. #16863515	C₂²	semidirect
51. #16863514	C₂²	semidirect
52. #16863511	C₂²	semidirect
53. #16863510	C₂²	semidirect
54. #16863444	C₂²	semidirect
55. #16863443	C₂²	semidirect
56. C₂×#14523979	C₂²	semidirect
57. #108×D₆₇	C₂²	semidirect
58. #16863414	C₂²	semidirect
59. #16863411	C₂²	semidirect
60. C₂×#14523970	C₂²	semidirect
61. C₂×#14523969	C₂²	semidirect
62. #104×D₆₇	C₂²	semidirect
63. #16863353	C₂²	semidirect
64. #16863352	C₂²	semidirect
65. #16863350	C₂²	semidirect
66. M₁₆×Dic₆₇	C₂²	semidirect
67. C₄×#11761611	C₂²	semidirect
68. C₂×#14523953	C₂²	semidirect
69. #97×D₆₇	C₂²	semidirect
71. #568×C₆₇	C₂²	semidirect
72. #444×C₆₇	C₂²	semidirect
73. #443×C₆₇	C₂²	semidirect
74. C₂×#108×C₆₇	C₂²	semidirect
75. #421×C₆₇	C₂²	semidirect
76. #405×C₆₇	C₂²	semidirect
89. #14524075	C₂×C₄	semidirect
90. #14524074	C₂×C₄	semidirect
91. #14524073	C₂×C₄	semidirect
92. #14524072	C₂×C₄	semidirect
93. #14524070	C₂×C₄	semidirect
94. #14524069	C₂×C₄	semidirect
95. #14524068	C₂×C₄	semidirect
96. #14524067	C₂×C₄	semidirect
97. #14524066	C₂×C₄	semidirect
98. #14524065	C₂×C₄	semidirect
99. #14524065	C₂×C₄	semidirect
102. #14524064	C₂×C₄	semidirect
104. #14524062	C₂×C₄	semidirect
105. C₂×Dic₂₆₈	C₂×C₄	semidirect
106. Q₁₆×D₆₇	C₂×C₄	semidirect
107. C₂×#11761617	C₂×C₄	semidirect
108. SD₁₆×D₆₇	C₂×C₄	semidirect
109. C₂×D₅₃₆	C₂×C₄	semidirect
110. D₈×D₆₇	C₂×C₄	semidirect
173. #135×C₆₇	C₂×C₄	semidirect
174. #135×C₆₇	C₂×C₄	semidirect
177. C₂×Q₁₆×C₆₇	C₂×C₄	semidirect
178. C₂×SD₁₆×C₆₇	C₂×C₄	semidirect
179. C₂×D₈×C₆₇	C₂×C₄	semidirect
399. #2957	D₆₇	semidirect
410. C₆₇	#60184	semidirect
428. #568	C₂×D₆₇	semidirect
448. #444	C₂×D₆₇	semidirect
452. #443	C₂×D₆₇	semidirect
457. C₂×#108	C₂×D₆₇	semidirect
460. #421	C₂×D₆₇	semidirect
467. #405	C₂×D₆₇	semidirect
501. #135	C₄×D₆₇	semidirect
502. #135	C₄×D₆₇	semidirect
507. C₂×Q₁₆	C₄×D₆₇	semidirect
510. C₂×SD₁₆	C₄×D₆₇	semidirect
513. C₂×D₈	C₄×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22574978	2
#22574922	2
#22569127	2
#22569123	2
#22569116	2
#22569114	2
#22569108	2
#22569107	2
C₂×#16863518	2
C₂×#16863517	2
#444×D₆₇	2
#22568817	2
#22568755	2
#22568636	2
C₆₇×#2957	2
#60184	67