Subgroups — C₂×#443×D₆₇ #31720118

Order 17152.

2750 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#135×D₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#131×D₆₇	C₂	1	2	yes	maximal, complemented
3	C₂×#16863514	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16863513	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16863512	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16863511	C₂	1	2	yes	maximal, complemented
7	C₂×#16863510	C₂	1	2	yes	maximal, complemented
8	#443×D₆₇	C₂	1	16	yes	maximal, direct product factor
9	C₂×#108×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#104×D₆₇	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×C₈×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#443×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#41×D₆₇	C₂²	1	2	yes	—
14	C₂×#14524066	C₄	1	1	yes	characteristic, complemented
15	C₂×#14524065	C₂²	1	1	yes	characteristic
16	C₂×#14524064	C₄	1	2	yes	complemented
17	C₂×#14524063	C₂²	1	2	yes	—
18	C₂×#14524062	C₄	1	1	yes	characteristic, complemented
19	#135×D₆₇	C₄	1	8	yes	complemented
20	#135×D₆₇	C₂²	1	8	yes	—
21	C₂×Q₁₆×D₆₇	C₄	1	1	yes	characteristic, complemented
22	C₂×SD₁₆×D₆₇	C₄	1	2	yes	complemented
23	C₂×D₈×D₆₇	C₄	1	1	yes	characteristic, complemented
24	C₂×#14524051	—	2	2	no	—
25	C₂×#14524051	C₂²	1	2	yes	complemented
26	C₂×#14524050	C₂²	1	2	yes	complemented
27	C₂×#14524049	—	2	2	no	—
28	C₂×#14524049	C₂²	1	2	yes	complemented
29	#131×D₆₇	—	2	8	no	—
30	#131×D₆₇	C₂²	1	16	yes	complemented
31	C₂×M₁₆×D₆₇	—	2	2	no	—
32	C₂×M₁₆×D₆₇	C₂²	1	2	yes	—
33	C₂²×C₈×D₆₇	—	2	2	no	—
34	C₂²×C₈×D₆₇	C₂²	1	1	yes	characteristic
35	C₂²×C₈×D₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₄²×D₆₇	C₂²	1	1	yes	characteristic
37	#16863514	C₂²	1	8	yes	complemented
38	#16863513	C₂²	1	8	yes	complemented
39	#16863512	C₂²	1	8	yes	complemented
40	#16863511	C₂²	1	16	yes	complemented
41	#16863510	C₂²	1	16	yes	complemented
42	C₂×#14523979	C₂²	1	1	yes	characteristic, complemented
43	C₂×#14523978	C₂²	1	2	yes	complemented
44	#108×D₆₇	C₂²	1	8	yes	complemented
45	C₂×#14523971	C₂²	1	2	yes	complemented
46	C₂×#14523970	C₂²	1	2	yes	complemented
47	C₂×#14523969	C₂²	1	2	yes	complemented
48	#104×D₆₇	C₂²	1	16	yes	complemented
49	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
52	C₄×C₈×D₆₇	C₂²	1	8	yes	complemented
53	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
54	C₂×#131×C₆₇	C₂²	1	2	yes	complemented
55	#443×C₆₇	C₂²	1	8	yes	complemented
56	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic, complemented
57	C₂×#104×C₆₇	C₂²	1	2	yes	complemented
58	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
59	C₂×#11761629	C₂×C₄	1	2	yes	—
60	C₂×#11761628	—	2	2	no	—
61	C₂×#11761628	C₂³	1	2	yes	—
62	C₂×#11761627	—	2	2	no	—
63	C₂×#11761627	C₂×C₄	1	2	yes	—
64	#41×D₆₇	—	2	4	no	—
65	#41×D₆₇	—	2	4	no	—
66	#41×D₆₇	C₂×C₄	1	8	yes	—
67	#41×D₆₇	C₂³	1	8	yes	—
68	C₂×Q₈×D₆₇	C₂×C₄	1	2	yes	—
69	C₂×D₄×D₆₇	—	2	2	no	—
70	C₂×D₄×D₆₇	C₂×C₄	1	2	yes	—
71	C₂²×C₄×D₆₇	—	2	1	no	—
72	C₂²×C₄×D₆₇	—	2	2	no	—
73	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
74	#14524066	C₂×C₄	1	8	yes	complemented
75	#14524065	C₂×C₄	1	4	yes	complemented
76	#14524065	C₂³	1	4	yes	—
77	#14524064	C₂×C₄	1	16	yes	complemented
78	#14524063	C₂×C₄	1	8	yes	complemented
79	#14524063	C₂³	1	8	yes	—
80	#14524062	C₂×C₄	1	8	yes	complemented
81	C₂×Dic₂₆₈	C₂×C₄	1	1	yes	characteristic, complemented
82	C₂×#11761618	C₂×C₄	1	2	yes	complemented
83	Q₁₆×D₆₇	C₂×C₄	1	8	yes	complemented
84	C₂×#11761617	C₂×C₄	1	2	yes	complemented
85	C₂×#11761616	C₂×C₄	1	2	yes	complemented
86	C₂×#11761615	C₂×C₄	1	2	yes	complemented
87	SD₁₆×D₆₇	C₂×C₄	1	16	yes	complemented
88	C₂×D₅₃₆	C₂×C₄	1	1	yes	characteristic, complemented
89	C₂×#11761613	C₂×C₄	1	2	yes	complemented
90	D₈×D₆₇	C₂×C₄	1	8	yes	complemented
91	#14524051	—	2	4	no	—
92	#14524051	—	2	16	no	—
93	#14524051	C₂³	1	8	yes	complemented
94	#14524050	—	2	4	no	—
95	#14524050	C₂³	1	8	yes	complemented
96	#14524049	—	2	16	no	—
97	#14524049	—	2	4	no	—
98	#14524049	C₂³	1	8	yes	complemented
99	C₂×#11761612	—	2	2	no	—
100	C₂×#11761612	C₂³	1	2	yes	—
101	C₂×#11761611	—	2	2	no	—
102	C₂×#11761611	—	2	2	no	—
103	C₂×#11761611	—	2	2	no	—
104	M₁₆×D₆₇	—	2	4	no	—
105	M₁₆×D₆₇	—	2	16	no	—
106	M₁₆×D₆₇	C₂³	1	8	yes	—
107	C₂²×C₆₇⋊C₈	—	2	2	no	—
108	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
109	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
110	C₂×C₈×D₆₇	—	2	2	no	—
111	C₂×C₈×D₆₇	—	2	2	no	—
112	C₂×C₈×D₆₇	—	2	16	no	—
113	C₂×C₈×D₆₇	—	2	2	no	—
114	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
115	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
116	C₂×C₈×D₆₇	C₂×C₄	1	4	yes	—
117	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
118	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
119	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
120	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
121	C₂×C₈×D₆₇	D₄	1	4	yes	—
122	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
123	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
124	C₂×C₈×D₆₇	C₂³	1	4	yes	—
125	C₂×C₈×D₆₇	C₂³	1	4	yes	—
126	C₂×C₄×Dic₆₇	—	2	1	no	—
127	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
128	C₄²×D₆₇	—	2	2	no	—
129	C₄²×D₆₇	C₂³	1	4	yes	—
130	#14523979	C₂³	1	4	yes	complemented
131	#14523978	C₂³	1	8	yes	complemented
132	#14523971	C₂³	1	8	yes	complemented
133	#14523970	C₂³	1	8	yes	complemented
134	#14523969	C₂³	1	8	yes	complemented
135	C₄×C₆₇⋊C₈	C₂³	1	4	yes	complemented
136	C₈×Dic₆₇	C₂³	1	4	yes	complemented
137	C₈×Dic₆₇	C₂³	1	4	yes	complemented
138	C₂×#41×C₆₇	C₂³	1	2	yes	—
139	#135×C₆₇	C₂×C₄	1	4	yes	complemented
140	#135×C₆₇	C₂³	1	4	yes	—
141	C₂×Q₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
142	C₂×SD₁₆×C₆₇	C₂×C₄	1	2	yes	complemented
143	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
144	#131×C₆₇	—	2	4	no	—
145	#131×C₆₇	C₂³	1	8	yes	complemented
146	C₂×M₁₆×C₆₇	—	2	2	no	—
147	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
148	C₂²×C₈×C₆₇	—	2	2	no	—
149	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
152	#108×C₆₇	C₂³	1	4	yes	complemented
153	#104×C₆₇	C₂³	1	8	yes	complemented
154	C₄×C₈×C₆₇	C₂³	1	4	yes	complemented
155	C₂³×D₆₇	—	2	2	no	—
156	C₂³×D₆₇	#41	1	1	yes	characteristic
157	#11761629	—	2	4	no	—
158	#11761629	C₂²×C₄	1	8	yes	—
159	#11761628	—	2	2	no	—
160	#11761628	—	2	2	no	—
161	#11761628	—	2	8	no	—
162	#11761628	—	2	8	no	—
163	#11761628	C₂²×C₄	1	4	yes	—
164	#11761628	C₂⁴	1	4	yes	—
165	#11761627	—	2	8	no	—
166	#11761627	—	2	8	no	—
167	#11761627	—	2	4	no	—
168	#11761627	C₂²×C₄	1	8	yes	—
169	C₂×Dic₁₃₄	—	2	2	no	—
170	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
171	Q₈×D₆₇	—	2	4	no	—
172	Q₈×D₆₇	C₂²×C₄	1	8	yes	—
173	C₂×D₂₆₈	—	2	2	no	—
174	C₂×D₂₆₈	C₂²×C₄	1	2	yes	—
175	C₂×C₂²⋊D₆₇	—	2	2	no	—
176	C₂×C₂²⋊D₆₇	—	2	2	no	—
177	C₂×C₂²⋊D₆₇	—	2	2	no	—
178	D₄×D₆₇	—	2	8	no	—
179	D₄×D₆₇	—	2	8	no	—
180	D₄×D₆₇	—	2	4	no	—
181	D₄×D₆₇	C₂²×C₄	1	8	yes	—
182	C₂²×Dic₆₇	—	2	1	no	—
183	C₂²×Dic₆₇	—	2	2	no	—
184	C₂²×Dic₆₇	#41	1	1	yes	characteristic
185	C₂×C₄×D₆₇	—	2	8	no	—
186	C₂×C₄×D₆₇	—	2	2	no	—
187	C₂×C₄×D₆₇	—	2	4	no	—
188	C₂×C₄×D₆₇	—	2	2	no	—
189	C₂×C₄×D₆₇	—	2	2	no	—
190	C₂×C₄×D₆₇	—	2	8	no	—
191	C₂×C₄×D₆₇	—	2	8	no	—
192	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₄×D₆₇	C₂²×C₄	1	2	yes	—
194	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
195	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
196	C₂×C₄×D₆₇	C₂×D₄	1	2	yes	—
197	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
198	C₂×C₄×D₆₇	#41	1	2	yes	—
199	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
200	Dic₂₆₈	C₂²×C₄	1	4	yes	complemented
201	#11761618	C₂²×C₄	1	8	yes	complemented
202	#11761617	C₂²×C₄	1	8	yes	complemented
203	#11761616	C₂²×C₄	1	8	yes	complemented
204	#11761615	C₂²×C₄	1	8	yes	complemented
205	D₅₃₆	C₂²×C₄	1	4	yes	complemented
206	#11761613	C₂²×C₄	1	8	yes	complemented
207	#11761612	—	2	2	no	—
208	#11761612	—	2	8	no	—
209	#11761612	C₂⁴	1	4	yes	—
210	#11761611	—	2	8	no	—
211	#11761611	—	2	8	no	—
212	#11761611	—	2	8	no	—
213	C₂×C₆₇⋊C₈	—	2	2	no	—
214	C₂×C₆₇⋊C₈	—	2	8	no	—
215	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
216	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
217	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
218	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
219	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
220	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
221	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
222	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
223	C₈×D₆₇	—	2	8	no	—
224	C₈×D₆₇	—	2	8	no	—
225	C₈×D₆₇	—	2	8	no	—
226	C₈×D₆₇	C₂²×C₄	1	4	yes	—
227	C₈×D₆₇	C₂²×C₄	1	4	yes	—
228	C₈×D₆₇	C₂²×C₄	1	4	yes	—
229	C₈×D₆₇	C₂²×C₄	1	4	yes	—
230	C₈×D₆₇	C₂×D₄	1	4	yes	—
231	C₈×D₆₇	C₂×D₄	1	4	yes	—
232	C₈×D₆₇	C₂×D₄	1	4	yes	—
233	C₈×D₆₇	C₂×D₄	1	4	yes	—
234	C₄×Dic₆₇	—	2	1	no	—
235	C₄×Dic₆₇	—	2	4	no	—
236	C₄×Dic₆₇	C₂⁴	1	2	yes	—
237	#41×C₆₇	—	2	2	no	—
238	#41×C₆₇	—	2	2	no	—
239	#41×C₆₇	C₂²×C₄	1	4	yes	—
240	#41×C₆₇	C₂⁴	1	4	yes	—
241	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
242	C₂×D₄×C₆₇	—	2	2	no	—
243	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
244	C₂²×C₄×C₆₇	—	2	1	no	—
245	C₂²×C₄×C₆₇	—	2	2	no	—
246	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
247	Q₁₆×C₆₇	C₂²×C₄	1	4	yes	complemented
248	SD₁₆×C₆₇	C₂²×C₄	1	8	yes	complemented
249	D₈×C₆₇	C₂²×C₄	1	4	yes	complemented
250	M₁₆×C₆₇	—	2	2	no	—
251	M₁₆×C₆₇	—	2	8	no	—
252	M₁₆×C₆₇	C₂⁴	1	4	yes	—
253	C₂×C₈×C₆₇	—	2	2	no	—
254	C₂×C₈×C₆₇	—	2	8	no	—
255	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
256	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
257	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
258	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
259	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
260	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
261	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
262	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
263	C₄²×C₆₇	—	2	1	no	—
264	C₄²×C₆₇	C₂⁴	1	2	yes	—
265	C₂³×C₆₇	—	2	2	no	—
266	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
267	C₂²×D₆₇	—	2	4	no	—
268	C₂²×D₆₇	—	2	2	no	—
269	C₂²×D₆₇	—	2	8	no	—
270	C₂²×D₆₇	—	4	8	no	—
271	C₂²×D₆₇	C₄×D₄	1	2	yes	—
272	C₂²×D₆₇	C₄×D₄	1	1	yes	characteristic
273	C₂²×D₆₇	C₄×D₄	1	1	yes	characteristic
274	C₂²×D₆₇	C₂×#41	1	2	yes	—
275	Q₈×C₆₇	—	2	2	no	—
276	Q₈×C₆₇	C₂³×C₄	1	4	yes	—
277	D₄×C₆₇	—	2	4	no	—
278	D₄×C₆₇	—	2	4	no	—
279	D₄×C₆₇	—	2	2	no	—
280	D₄×C₆₇	C₂³×C₄	1	4	yes	—
281	C₂×C₄×C₆₇	—	2	4	no	—
282	C₂×C₄×C₆₇	—	2	2	no	—
283	C₂×C₄×C₆₇	—	2	2	no	—
284	C₂×C₄×C₆₇	—	2	4	no	—
285	C₂×C₄×C₆₇	—	2	4	no	—
286	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
287	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
288	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
289	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
290	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
291	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
292	C₂²⋊D₆₇	—	2	4	no	—
293	C₂²⋊D₆₇	—	2	4	no	—
294	C₂²⋊D₆₇	—	2	8	no	—
295	C₂²⋊D₆₇	—	2	8	no	—
296	C₂×Dic₆₇	—	2	4	no	—
297	C₂×Dic₆₇	—	2	2	no	—
298	C₂×Dic₆₇	—	2	2	no	—
299	C₂×Dic₆₇	—	2	8	no	—
300	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
301	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
302	C₂×Dic₆₇	C₄×D₄	1	2	yes	—
303	C₂×Dic₆₇	C₂×#41	1	2	yes	—
304	D₂₆₈	—	2	8	no	—
305	D₂₆₈	—	2	2	no	—
306	D₂₆₈	C₂³×C₄	1	4	yes	—
307	C₄×D₆₇	—	2	16	no	—
308	C₄×D₆₇	—	2	8	no	—
309	C₄×D₆₇	—	2	4	no	—
310	C₄×D₆₇	—	2	4	no	—
311	C₄×D₆₇	—	2	8	no	—
312	C₄×D₆₇	C₄×D₄	1	2	yes	—
313	C₄×D₆₇	C₄×D₄	1	2	yes	—
314	C₄×D₆₇	C₄×D₄	1	2	yes	—
315	C₄×D₆₇	C₄×D₄	1	2	yes	—
316	C₄×D₆₇	C₂³×C₄	1	2	yes	—
317	C₄×D₆₇	C₂³×C₄	1	2	yes	—
318	C₄×D₆₇	C₂²×D₄	1	2	yes	—
319	C₄×D₆₇	C₂²×D₄	1	2	yes	—
320	Dic₁₃₄	—	2	2	no	—
321	Dic₁₃₄	—	2	8	no	—
322	Dic₁₃₄	C₂³×C₄	1	4	yes	—
323	C₈×C₆₇	—	2	4	no	—
324	C₈×C₆₇	C₂³×C₄	1	2	yes	—
325	C₈×C₆₇	C₂³×C₄	1	2	yes	—
326	C₈×C₆₇	C₂²×D₄	1	2	yes	—
327	C₈×C₆₇	C₂²×D₄	1	2	yes	—
328	C₆₇⋊C₈	—	2	4	no	—
329	C₆₇⋊C₈	C₂³×C₄	1	2	yes	—
330	C₆₇⋊C₈	C₂³×C₄	1	2	yes	—
331	C₆₇⋊C₈	C₂²×D₄	1	2	yes	—
332	C₆₇⋊C₈	C₂²×D₄	1	2	yes	—
333	C₂²×C₆₇	—	2	2	no	—
334	C₂²×C₆₇	—	2	4	no	—
335	C₂²×C₆₇	—	4	4	no	—
336	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
337	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
338	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
339	C₂×D₆₇	—	2	2	no	—
340	C₂×D₆₇	—	2	4	no	—
341	C₂×D₆₇	—	2	4	no	—
342	C₂×D₆₇	—	2	4	no	—
343	C₂×D₆₇	—	4	4	no	—
344	C₂×D₆₇	—	4	16	no	—
345	C₂×D₆₇	#443	1	4	yes	direct product factor
346	C₂×D₆₇	C₂×C₄×D₄	1	2	yes	—
347	C₂×D₆₇	C₂×C₄×D₄	1	2	yes	—
348	C₄×C₆₇	—	2	4	no	—
349	C₄×C₆₇	—	2	4	no	—
350	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
351	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
352	C₄×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
353	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
354	Dic₆₇	—	2	4	no	—
355	Dic₆₇	—	2	4	no	—
356	Dic₆₇	C₂×C₄×D₄	1	2	yes	—
357	Dic₆₇	C₂×C₄×D₄	1	2	yes	—
358	C₂²×#443	—	67	1	no	maximal, Sylow
359	C₂×C₆₇	—	2	1	no	—
360	C₂×C₆₇	—	2	1	no	—
361	C₂×C₆₇	—	4	4	no	—
362	C₂×C₆₇	C₂×#443	1	2	yes	complemented
363	C₂×C₆₇	C₂²×C₄×D₄	1	1	yes	characteristic
364	D₆₇	—	2	2	no	—
365	D₆₇	—	4	4	no	—
366	D₆₇	C₂×#443	1	4	yes	direct product factor
367	C₂²×#135	—	67	1	no	—
368	C₂²×#131	—	67	2	no	—
369	C₂×#443	—	67	16	no	—
370	C₂×#443	—	67	1	no	—
371	C₂×#443	—	67	2	no	—
372	C₂×#443	—	67	1	no	—
373	C₂×#443	—	67	1	no	—
374	C₂×#443	—	67	2	no	—
375	C₂×#443	D₆₇	1	1	yes	characteristic, direct product factor
376	C₂²×#108	—	67	1	no	—
377	C₂²×#104	—	67	2	no	—
378	C₂²×C₄×C₈	—	67	1	no	—
379	C₆₇	C₂²×#443	1	1	yes	characteristic, complemented, Sylow
380	C₂²×#41	—	67	2	no	—
381	C₂×#135	—	67	2	no	—
382	C₂×#135	—	67	8	no	—
383	C₂×#135	—	67	8	no	—
384	C₂×#135	—	67	1	no	—
385	C₂×#135	—	67	2	no	—
386	C₂×#135	—	67	1	no	—
387	C₂×#135	—	67	1	no	—
388	C₂×#135	C₂×D₆₇	1	1	yes	characteristic
389	C₂²×Q₁₆	—	67	1	no	—
390	C₂²×SD₁₆	—	67	2	no	—
391	C₂²×D₈	—	67	1	no	—
392	C₂×#131	—	67	2	no	—
393	C₂×#131	—	67	16	no	—
394	C₂×#131	—	67	2	no	—
395	C₂×#131	—	67	2	no	—
396	C₂×#131	—	134	2	no	—
397	C₂×#131	—	134	2	no	—
398	C₂×#131	—	134	8	no	—
399	C₂×#131	C₂×D₆₇	1	2	yes	complemented
400	C₂²×M₁₆	—	67	2	no	—
401	C₂²×M₁₆	—	134	2	no	—
402	C₂³×C₈	—	67	1	no	—
403	C₂³×C₈	—	67	1	no	—
404	C₂³×C₈	—	134	2	no	—
405	C₂²×C₄²	—	67	1	no	—
406	#443	—	67	8	no	—
407	#443	—	67	16	no	—
408	#443	—	67	8	no	—
409	#443	—	67	16	no	—
410	#443	—	67	8	no	—
411	#443	C₂×D₆₇	1	8	yes	direct product factor
412	C₂×#108	—	67	2	no	—
413	C₂×#108	—	67	1	no	—
414	C₂×#108	—	67	8	no	—
415	C₂×#108	C₂×D₆₇	1	1	yes	characteristic, complemented
416	C₂×#104	—	67	2	no	—
417	C₂×#104	—	67	2	no	—
418	C₂×#104	—	67	2	no	—
419	C₂×#104	—	67	16	no	—
420	C₂×#104	C₂×D₆₇	1	2	yes	complemented
421	C₂×C₄×C₈	—	67	1	no	—
422	C₂×C₄×C₈	—	67	1	no	—
423	C₂×C₄×C₈	—	67	1	no	—
424	C₂×C₄×C₈	—	67	8	no	—
425	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic, complemented
426	C₂×#41	—	67	8	no	—
427	C₂×#41	—	67	8	no	—
428	C₂×#41	—	67	2	no	—
429	C₂×#41	—	67	2	no	—
430	C₂×#41	—	67	2	no	—
431	C₂×#41	—	134	2	no	—
432	C₂×#41	—	134	2	no	—
433	C₂×#41	—	134	4	no	—
434	C₂×#41	—	134	4	no	—
435	C₂×#41	C₂²×D₆₇	1	2	yes	—
436	C₂²×Q₈	—	67	2	no	—
437	C₂²×D₄	—	67	2	no	—
438	C₂²×D₄	—	134	2	no	—
439	C₂³×C₄	—	67	1	no	—
440	C₂³×C₄	—	134	2	no	—
441	C₂³×C₄	—	134	1	no	—
442	#135	—	67	8	no	—
443	#135	—	67	8	no	—
444	#135	—	67	8	no	—
445	#135	—	67	16	no	—
446	#135	—	67	8	no	—
447	#135	—	67	4	no	—
448	#135	—	67	4	no	—
449	#135	C₄×D₆₇	1	4	yes	complemented
450	#135	C₂²×D₆₇	1	4	yes	—
451	C₂×Q₁₆	—	67	2	no	—
452	C₂×Q₁₆	—	67	8	no	—
453	C₂×Q₁₆	—	67	1	no	—
454	C₂×Q₁₆	C₄×D₆₇	1	1	yes	characteristic, complemented
455	C₂×SD₁₆	—	67	2	no	—
456	C₂×SD₁₆	—	67	2	no	—
457	C₂×SD₁₆	—	67	16	no	—
458	C₂×SD₁₆	—	67	2	no	—
459	C₂×SD₁₆	C₄×D₆₇	1	2	yes	complemented
460	C₂×D₈	—	67	2	no	—
461	C₂×D₈	—	67	8	no	—
462	C₂×D₈	—	67	1	no	—
463	C₂×D₈	C₄×D₆₇	1	1	yes	characteristic, complemented
464	#131	—	2	4	no	—
465	#131	—	67	8	no	—
466	#131	—	67	8	no	—
467	#131	—	67	8	no	—
468	#131	—	134	16	no	—
469	#131	—	134	4	no	—
470	#131	—	134	16	no	—
471	#131	—	134	4	no	—
472	#131	—	134	4	no	—
473	#131	C₂²×D₆₇	1	8	yes	complemented
474	C₂×M₁₆	—	2	2	no	—
475	C₂×M₁₆	—	67	2	no	—
476	C₂×M₁₆	—	67	8	no	—
477	C₂×M₁₆	—	134	2	no	—
478	C₂×M₁₆	—	134	2	no	—
479	C₂×M₁₆	—	134	16	no	—
480	C₂×M₁₆	—	134	2	no	—
481	C₂×M₁₆	—	134	4	no	—
482	C₂×M₁₆	—	134	2	no	—
483	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
484	C₂²×C₈	—	2	2	no	—
485	C₂²×C₈	—	67	1	no	—
486	C₂²×C₈	—	67	1	no	—
487	C₂²×C₈	—	67	1	no	—
488	C₂²×C₈	—	67	1	no	—
489	C₂²×C₈	—	67	1	no	—
490	C₂²×C₈	—	67	1	no	—
491	C₂²×C₈	—	67	4	no	—
492	C₂²×C₈	—	67	1	no	—
493	C₂²×C₈	—	67	1	no	—
494	C₂²×C₈	—	67	4	no	—
495	C₂²×C₈	—	67	1	no	—
496	C₂²×C₈	—	67	1	no	—
497	C₂²×C₈	—	67	4	no	—
498	C₂²×C₈	—	67	4	no	—
499	C₂²×C₈	—	134	2	no	—
500	C₂²×C₈	—	134	16	no	—
501	C₂²×C₈	—	134	2	no	—
502	C₂²×C₈	—	134	2	no	—
503	C₂²×C₈	—	134	2	no	—
504	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
505	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
506	C₂×C₄²	—	67	1	no	—
507	C₂×C₄²	—	67	4	no	—
508	C₂×C₄²	—	134	2	no	—
509	C₂×C₄²	—	134	1	no	—
510	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
511	#108	—	67	8	no	—
512	#108	—	67	4	no	—
513	#108	C₂²×D₆₇	1	4	yes	complemented
514	#104	—	67	8	no	—
515	#104	—	67	8	no	—
516	#104	—	67	8	no	—
517	#104	C₂²×D₆₇	1	8	yes	complemented
518	C₄×C₈	—	67	4	no	—
519	C₄×C₈	—	67	4	no	—
520	C₄×C₈	—	67	4	no	—
521	C₄×C₈	C₂²×D₆₇	1	4	yes	complemented
522	C₂⁴	—	67	1	no	—
523	C₂⁴	—	134	2	no	—
524	#41	—	2	2	no	—
525	#41	—	2	2	no	—
526	#41	—	67	8	no	—
527	#41	—	67	8	no	—
528	#41	—	67	4	no	—
529	#41	—	67	4	no	—
530	#41	—	134	8	no	—
531	#41	—	134	8	no	—
532	#41	—	134	8	no	—
533	#41	—	134	8	no	—
534	#41	—	134	4	no	—
535	#41	—	134	4	no	—
536	#41	—	134	2	no	—
537	#41	—	134	2	no	—
538	#41	C₂×C₄×D₆₇	1	4	yes	—
539	#41	C₂³×D₆₇	1	4	yes	—
540	C₂×Q₈	—	67	8	no	—
541	C₂×Q₈	—	67	2	no	—
542	C₂×Q₈	—	134	2	no	—
543	C₂×Q₈	—	134	4	no	—
544	C₂×Q₈	C₂×C₄×D₆₇	1	2	yes	—
545	C₂×D₄	—	2	2	no	—
546	C₂×D₄	—	67	8	no	—
547	C₂×D₄	—	67	2	no	—
548	C₂×D₄	—	134	2	no	—
549	C₂×D₄	—	134	4	no	—
550	C₂×D₄	—	134	2	no	—
551	C₂×D₄	—	134	8	no	—
552	C₂×D₄	—	134	8	no	—
553	C₂×D₄	—	134	2	no	—
554	C₂×D₄	—	134	2	no	—
555	C₂×D₄	C₂×C₄×D₆₇	1	2	yes	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	2	no	—
558	C₂²×C₄	—	67	1	no	—
559	C₂²×C₄	—	67	1	no	—
560	C₂²×C₄	—	67	1	no	—
561	C₂²×C₄	—	67	2	no	—
562	C₂²×C₄	—	67	1	no	—
563	C₂²×C₄	—	67	1	no	—
564	C₂²×C₄	—	67	2	no	—
565	C₂²×C₄	—	67	2	no	—
566	C₂²×C₄	—	67	2	no	—
567	C₂²×C₄	—	134	8	no	—
568	C₂²×C₄	—	134	2	no	—
569	C₂²×C₄	—	134	8	no	—
570	C₂²×C₄	—	134	4	no	—
571	C₂²×C₄	—	134	2	no	—
572	C₂²×C₄	—	134	8	no	—
573	C₂²×C₄	—	134	2	no	—
574	C₂²×C₄	—	134	1	no	—
575	C₂²×C₄	—	134	2	no	—
576	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
577	Q₁₆	—	67	8	no	—
578	Q₁₆	—	67	4	no	—
579	Q₁₆	C₂×C₄×D₆₇	1	4	yes	complemented
580	SD₁₆	—	67	8	no	—
581	SD₁₆	—	67	8	no	—
582	SD₁₆	—	67	8	no	—
583	SD₁₆	C₂×C₄×D₆₇	1	8	yes	complemented
584	D₈	—	67	8	no	—
585	D₈	—	67	4	no	—
586	D₈	C₂×C₄×D₆₇	1	4	yes	complemented
587	M₁₆	—	2	2	no	—
588	M₁₆	—	2	8	no	—
589	M₁₆	—	67	4	no	—
590	M₁₆	—	134	8	no	—
591	M₁₆	—	134	8	no	—
592	M₁₆	—	134	8	no	—
593	M₁₆	—	134	2	no	—
594	M₁₆	—	134	8	no	—
595	M₁₆	C₂³×D₆₇	1	4	yes	—
596	C₂×C₈	—	2	2	no	—
597	C₂×C₈	—	2	8	no	—
598	C₂×C₈	—	67	1	no	—
599	C₂×C₈	—	67	1	no	—
600	C₂×C₈	—	67	2	no	—
601	C₂×C₈	—	67	1	no	—
602	C₂×C₈	—	67	1	no	—
603	C₂×C₈	—	67	2	no	—
604	C₂×C₈	—	67	2	no	—
605	C₂×C₈	—	67	2	no	—
606	C₂×C₈	—	67	4	no	—
607	C₂×C₈	—	67	4	no	—
608	C₂×C₈	—	67	4	no	—
609	C₂×C₈	—	67	4	no	—
610	C₂×C₈	—	67	4	no	—
611	C₂×C₈	—	67	4	no	—
612	C₂×C₈	—	67	4	no	—
613	C₂×C₈	—	67	4	no	—
614	C₂×C₈	—	134	8	no	—
615	C₂×C₈	—	134	8	no	—
616	C₂×C₈	—	134	8	no	—
617	C₂×C₈	—	134	2	no	—
618	C₂×C₈	—	134	8	no	—
619	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
620	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
621	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
622	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
623	C₂×C₈	D₄×D₆₇	1	2	yes	—
624	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
625	C₂×C₈	C₂³×D₆₇	1	2	yes	—
626	C₂×C₈	C₂³×D₆₇	1	2	yes	—
627	C₄²	—	2	1	no	—
628	C₄²	—	67	2	no	—
629	C₄²	—	134	4	no	—
630	C₄²	—	134	1	no	—
631	C₄²	C₂³×D₆₇	1	2	yes	—
632	C₂³	—	2	2	no	—
633	C₂³	—	268	8	no	—
634	C₂³	—	67	1	no	—
635	C₂³	—	67	2	no	—
636	C₂³	—	67	1	no	—
637	C₂³	—	67	2	no	—
638	C₂³	—	134	8	no	—
639	C₂³	—	134	4	no	—
640	C₂³	—	134	2	no	—
641	C₂³	#41×D₆₇	1	1	yes	characteristic
642	Q₈	—	2	2	no	—
643	Q₈	—	67	4	no	—
644	Q₈	—	134	8	no	—
645	Q₈	—	134	2	no	—
646	Q₈	C₂²×C₄×D₆₇	1	4	yes	—
647	D₄	—	2	4	no	—
648	D₄	—	2	4	no	—
649	D₄	—	2	2	no	—
650	D₄	—	67	4	no	—
651	D₄	—	134	8	no	—
652	D₄	—	134	8	no	—
653	D₄	—	134	8	no	—
654	D₄	—	134	4	no	—
655	D₄	—	134	4	no	—
656	D₄	—	134	2	no	—
657	D₄	C₂²×C₄×D₆₇	1	4	yes	—
658	C₂×C₄	—	2	4	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	4	no	—
662	C₂×C₄	—	2	4	no	—
663	C₂×C₄	—	67	1	no	—
664	C₂×C₄	—	67	1	no	—
665	C₂×C₄	—	67	2	no	—
666	C₂×C₄	—	67	2	no	—
667	C₂×C₄	—	67	2	no	—
668	C₂×C₄	—	67	2	no	—
669	C₂×C₄	—	67	2	no	—
670	C₂×C₄	—	67	2	no	—
671	C₂×C₄	—	67	2	no	—
672	C₂×C₄	—	67	2	no	—
673	C₂×C₄	—	67	2	no	—
674	C₂×C₄	—	67	2	no	—
675	C₂×C₄	—	134	8	no	—
676	C₂×C₄	—	134	8	no	—
677	C₂×C₄	—	134	16	no	—
678	C₂×C₄	—	134	8	no	—
679	C₂×C₄	—	134	4	no	—
680	C₂×C₄	—	134	2	no	—
681	C₂×C₄	—	134	2	no	—
682	C₂×C₄	—	134	4	no	—
683	C₂×C₄	—	134	4	no	—
684	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
685	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
686	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
687	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
688	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
689	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
690	C₈	—	2	4	no	—
691	C₈	—	67	2	no	—
692	C₈	—	67	2	no	—
693	C₈	—	67	2	no	—
694	C₈	—	67	2	no	—
695	C₈	—	134	4	no	—
696	C₈	C₂²×C₄×D₆₇	1	2	yes	—
697	C₈	C₂²×C₄×D₆₇	1	2	yes	—
698	C₈	C₂×D₄×D₆₇	1	2	yes	—
699	C₈	C₂×D₄×D₆₇	1	2	yes	—
700	C₂²	—	2	2	no	—
701	C₂²	—	2	4	no	—
702	C₂²	—	4	4	no	—
703	C₂²	—	268	16	no	—
704	C₂²	—	268	4	no	—
705	C₂²	—	67	2	no	—
706	C₂²	—	67	4	no	—
707	C₂²	—	67	2	no	—
708	C₂²	—	134	4	no	—
709	C₂²	—	134	4	no	—
710	C₂²	—	134	4	no	—
711	C₂²	—	134	2	no	—
712	C₂²	C₄×D₄×D₆₇	1	1	yes	characteristic
713	C₂²	C₄×D₄×D₆₇	1	1	yes	characteristic
714	C₂²	C₂×#41×D₆₇	1	1	yes	characteristic
715	C₄	—	2	4	no	—
716	C₄	—	2	4	no	—
717	C₄	—	67	2	no	—
718	C₄	—	67	2	no	—
719	C₄	—	134	4	no	—
720	C₄	—	134	4	no	—
721	C₄	C₄×D₄×D₆₇	1	1	yes	characteristic
722	C₄	C₄×D₄×D₆₇	1	1	yes	characteristic
723	C₄	C₂³×C₄×D₆₇	1	1	yes	characteristic
724	C₄	C₂²×D₄×D₆₇	1	1	yes	characteristic
725	C₂	—	2	1	no	—
726	C₂	—	2	1	no	—
727	C₂	—	4	4	no	—
728	C₂	—	268	4	no	—
729	C₂	—	67	4	no	—
730	C₂	—	134	2	no	—
731	C₂	#443×D₆₇	1	2	yes	direct product factor
732	C₂	C₂×C₄×D₄×D₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₄×D₆₇
commutator	C₄×C₆₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₆₇
Fitting	C₂×#443×C₆₇	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂×#135×D₆₇	C₂
cosocle	C₂×C₄×C₆₇	C₂⁵
hypercenter	C₂×#443	D₆₇
hypocenter	C₆₇	C₂²×#443
LCS	G ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×#443

Complements

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

N	H ≅ G/N	type
2. C₂×#131×D₆₇	C₂	semidirect
3. C₂×#16863514	C₂	semidirect
4. C₂×#16863513	C₂	semidirect
5. C₂×#16863512	C₂	semidirect
6. C₂×#16863511	C₂	semidirect
7. C₂×#16863510	C₂	semidirect
8. #443×D₆₇	C₂	direct (N × H)
9. C₂×#108×D₆₇	C₂	semidirect
10. C₂×#104×D₆₇	C₂	semidirect
11. C₂×C₄×C₈×D₆₇	C₂	semidirect
12. C₂×#443×C₆₇	C₂	semidirect
14. C₂×#14524066	C₄	semidirect
16. C₂×#14524064	C₄	semidirect
18. C₂×#14524062	C₄	semidirect
19. #135×D₆₇	C₄	semidirect
21. C₂×Q₁₆×D₆₇	C₄	semidirect
22. C₂×SD₁₆×D₆₇	C₄	semidirect
23. C₂×D₈×D₆₇	C₄	semidirect
25. C₂×#14524051	C₂²	semidirect
26. C₂×#14524050	C₂²	semidirect
28. C₂×#14524049	C₂²	semidirect
30. #131×D₆₇	C₂²	semidirect
37. #16863514	C₂²	semidirect
38. #16863513	C₂²	semidirect
39. #16863512	C₂²	semidirect
40. #16863511	C₂²	semidirect
41. #16863510	C₂²	semidirect
42. C₂×#14523979	C₂²	semidirect
43. C₂×#14523978	C₂²	semidirect
44. #108×D₆₇	C₂²	semidirect
45. C₂×#14523971	C₂²	semidirect
46. C₂×#14523970	C₂²	semidirect
47. C₂×#14523969	C₂²	semidirect
48. #104×D₆₇	C₂²	semidirect
49. C₂×C₄×C₆₇⋊C₈	C₂²	semidirect
50. C₂×C₈×Dic₆₇	C₂²	semidirect
51. C₂×C₈×Dic₆₇	C₂²	semidirect
52. C₄×C₈×D₆₇	C₂²	semidirect
54. C₂×#131×C₆₇	C₂²	semidirect
55. #443×C₆₇	C₂²	semidirect
56. C₂×#108×C₆₇	C₂²	semidirect
57. C₂×#104×C₆₇	C₂²	semidirect
58. C₂×C₄×C₈×C₆₇	C₂²	semidirect
74. #14524066	C₂×C₄	semidirect
75. #14524065	C₂×C₄	semidirect
77. #14524064	C₂×C₄	semidirect
78. #14524063	C₂×C₄	semidirect
80. #14524062	C₂×C₄	semidirect
81. C₂×Dic₂₆₈	C₂×C₄	semidirect
82. C₂×#11761618	C₂×C₄	semidirect
83. Q₁₆×D₆₇	C₂×C₄	semidirect
84. C₂×#11761617	C₂×C₄	semidirect
85. C₂×#11761616	C₂×C₄	semidirect
86. C₂×#11761615	C₂×C₄	semidirect
87. SD₁₆×D₆₇	C₂×C₄	semidirect
88. C₂×D₅₃₆	C₂×C₄	semidirect
89. C₂×#11761613	C₂×C₄	semidirect
90. D₈×D₆₇	C₂×C₄	semidirect
93. #14524051	C₂³	semidirect
95. #14524050	C₂³	semidirect
98. #14524049	C₂³	semidirect
130. #14523979	C₂³	semidirect
131. #14523978	C₂³	semidirect
132. #14523971	C₂³	semidirect
133. #14523970	C₂³	semidirect
134. #14523969	C₂³	semidirect
135. C₄×C₆₇⋊C₈	C₂³	semidirect
136. C₈×Dic₆₇	C₂³	semidirect
137. C₈×Dic₆₇	C₂³	semidirect
139. #135×C₆₇	C₂×C₄	semidirect
141. C₂×Q₁₆×C₆₇	C₂×C₄	semidirect
142. C₂×SD₁₆×C₆₇	C₂×C₄	semidirect
143. C₂×D₈×C₆₇	C₂×C₄	semidirect
145. #131×C₆₇	C₂³	semidirect
152. #108×C₆₇	C₂³	semidirect
153. #104×C₆₇	C₂³	semidirect
154. C₄×C₈×C₆₇	C₂³	semidirect
200. Dic₂₆₈	C₂²×C₄	semidirect
201. #11761618	C₂²×C₄	semidirect
202. #11761617	C₂²×C₄	semidirect
203. #11761616	C₂²×C₄	semidirect
204. #11761615	C₂²×C₄	semidirect
205. D₅₃₆	C₂²×C₄	semidirect
206. #11761613	C₂²×C₄	semidirect
247. Q₁₆×C₆₇	C₂²×C₄	semidirect
248. SD₁₆×C₆₇	C₂²×C₄	semidirect
249. D₈×C₆₇	C₂²×C₄	semidirect
345. C₂×D₆₇	#443	direct (N × H)
362. C₂×C₆₇	C₂×#443	semidirect
366. D₆₇	C₂×#443	direct (N × H)
375. C₂×#443	D₆₇	direct (N × H)
379. C₆₇	C₂²×#443	semidirect
399. C₂×#131	C₂×D₆₇	semidirect
411. #443	C₂×D₆₇	direct (N × H)
415. C₂×#108	C₂×D₆₇	semidirect
420. C₂×#104	C₂×D₆₇	semidirect
425. C₂×C₄×C₈	C₂×D₆₇	semidirect
449. #135	C₄×D₆₇	semidirect
454. C₂×Q₁₆	C₄×D₆₇	semidirect
459. C₂×SD₁₆	C₄×D₆₇	semidirect
463. C₂×D₈	C₄×D₆₇	semidirect
473. #131	C₂²×D₆₇	semidirect
513. #108	C₂²×D₆₇	semidirect
517. #104	C₂²×D₆₇	semidirect
521. C₄×C₈	C₂²×D₆₇	semidirect
579. Q₁₆	C₂×C₄×D₆₇	semidirect
583. SD₁₆	C₂×C₄×D₆₇	semidirect
586. D₈	C₂×C₄×D₆₇	semidirect
731. C₂	#443×D₆₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#135×D₆₇	2
C₂×#131×D₆₇	2
C₂×#16863514	2
C₂×#16863513	2
C₂×#16863512	2
C₂×#16863511	2
C₂×#16863510	2
#443×D₆₇	2
C₂×#108×D₆₇	2
C₂×#104×D₆₇	2
C₂×C₄×C₈×D₆₇	2
C₂×#443×C₆₇	2
C₂²×#443	67

Subgroups — C2×#443×D67 #31720118

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#443×D₆₇ #31720118