Subgroups — C₂×#22574169 #31763926

Order 17152.

8006 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574169	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16864119	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16864111	C₂	1	2	yes	maximal, complemented
4	C₂×#16864069	C₂	1	4	yes	maximal, complemented
5	C₂×Q₈×D₂₆₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16864054	C₂	1	2	yes	maximal, complemented
7	C₂×#16864041	C₂	1	2	yes	maximal, complemented
8	C₂×#16864039	C₂	1	2	yes	maximal, complemented
9	C₂×#16864031	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16864015	C₂	1	2	yes	maximal, complemented
11	C₂×#16863982	C₂	1	4	yes	maximal, complemented
12	C₂×#16863944	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#16863933	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#16863928	C₂	1	2	yes	maximal, complemented
15	C₂×#124×D₆₇	C₂	1	2	yes	maximal, complemented
16	C₂×#16863868	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×#11761629	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#559×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#11761629	C₂²	1	1	yes	characteristic
20	C₂²×#11761627	C₂²	1	2	yes	complemented
21	C₂²×Q₈×D₆₇	C₂²	1	2	yes	complemented
22	C₂²×D₄×D₆₇	C₂²	1	2	yes	—
23	C₂²×D₄×D₆₇	C₂²	1	2	yes	—
24	#16864119	C₂²	1	16	yes	complemented
25	#16864111	C₂²	1	32	yes	complemented
26	#16864069	C₂²	1	64	yes	complemented
27	Q₈×D₂₆₈	C₂²	1	16	yes	complemented
28	#16864054	C₂²	1	32	yes	complemented
29	#16864041	C₂²	1	32	yes	complemented
30	#16864039	C₂²	1	32	yes	complemented
31	#16864031	C₂²	1	16	yes	complemented
32	#16864015	C₂²	1	32	yes	complemented
33	#16863982	C₂²	1	64	yes	complemented
34	#16863944	C₂²	1	16	yes	complemented
35	C₂×#14524043	C₂²	1	2	yes	complemented
36	C₂×#14524043	C₂²	1	1	yes	characteristic, complemented
37	#16863933	C₂²	1	16	yes	complemented
38	#16863928	C₂²	1	32	yes	complemented
39	C₂×#14524038	C₂²	1	2	yes	complemented
40	C₂×#14524038	C₂²	1	4	yes	complemented
41	C₂×#14524036	C₂²	1	4	yes	complemented
42	C₂×#14524034	C₂²	1	1	yes	characteristic, complemented
43	C₂×#14524032	C₂²	1	1	yes	characteristic
44	C₂×#14524031	C₂²	1	2	yes	—
45	C₂×#14524030	C₂²	1	2	yes	complemented
46	C₂×#14524029	C₂²	1	4	yes	complemented
47	C₂×#14524029	C₂²	1	4	yes	complemented
48	C₂×#14524029	C₂²	1	4	yes	complemented
49	#124×D₆₇	C₂²	1	32	yes	complemented
50	C₂×#14524028	C₂²	1	2	yes	complemented
51	C₂×#14524027	C₂²	1	4	yes	complemented
52	C₂×#14524025	C₂²	1	4	yes	complemented
53	C₂×#14524023	C₂²	1	2	yes	complemented
54	C₂×#14524023	C₂²	1	4	yes	complemented
55	C₂×#14524020	C₂²	1	4	yes	complemented
56	C₂×#14524019	C₂²	1	2	yes	complemented
57	C₂×#14524019	C₂²	1	1	yes	characteristic, complemented
58	C₂×#14524018	C₂²	1	1	yes	characteristic
59	C₂×#14524017	C₂²	1	4	yes	complemented
60	C₂×#14524016	C₂²	1	4	yes	complemented
61	C₂×#14524014	C₂²	1	2	yes	—
62	C₂×#14524014	C₂²	1	2	yes	—
63	C₂×#14524014	C₂²	1	2	yes	complemented
64	C₂×#14524014	C₂²	1	2	yes	complemented
65	C₂×#14524013	C₂²	1	4	yes	complemented
66	C₂×#14524011	C₂²	1	4	yes	—
67	#16863868	C₂²	1	32	yes	complemented
68	C₄×#11761629	C₂²	1	16	yes	complemented
69	C₂×Q₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
70	C₂×C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
71	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
72	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
73	C₂×C₄×D₂₆₈	C₂²	1	2	yes	—
74	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
75	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
76	C₂×D₄×Dic₆₇	C₂²	1	2	yes	complemented
77	C₂×D₄×Dic₆₇	C₂²	1	2	yes	complemented
78	C₂×#14524005	C₂²	1	1	yes	characteristic
79	C₂×#14524005	C₂²	1	2	yes	complemented
80	C₂×C₄×C₂²⋊D₆₇	C₂²	1	4	yes	complemented
81	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	4	yes	complemented
82	C₂×#14524002	C₂²	1	4	yes	complemented
83	C₂×#14524001	C₂²	1	2	yes	complemented
84	C₂×#14524001	C₂²	1	1	yes	characteristic, complemented
85	C₂×#14524001	C₂²	1	2	yes	complemented
86	C₂×#14524000	C₂²	1	2	yes	complemented
87	C₂²×(C₂×D₆₇)⋊C₄	C₂²	1	4	yes	complemented
88	C₂×C₂²⋊C₄×D₆₇	C₂²	1	4	yes	complemented
89	C₂×C₂²⋊C₄×D₆₇	C₂²	1	4	yes	complemented
90	C₂×C₄²×D₆₇	C₂²	1	2	yes	complemented
91	C₂×C₄²×D₆₇	C₂²	1	1	yes	characteristic, complemented
92	#559×C₆₇	C₂²	1	16	yes	complemented
93	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
94	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
95	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
96	C₂×#123×C₆₇	C₂²	1	4	yes	complemented
97	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
98	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
99	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
100	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
101	C₂⁴×D₆₇	C₂³	1	4	yes	—
102	C₂×#11761629	—	2	8	no	—
103	C₂×#11761629	C₂³	1	8	yes	—
104	C₂×#11761627	—	4	8	no	—
105	C₂×#11761627	C₂³	1	16	yes	complemented
106	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
107	C₂²×Dic₁₃₄	C₂³	1	4	yes	—
108	C₂×Q₈×D₆₇	—	4	8	no	—
109	C₂×Q₈×D₆₇	C₂³	1	16	yes	complemented
110	C₂²×D₂₆₈	C₂³	1	2	yes	—
111	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
112	C₂²×D₂₆₈	C₂³	1	2	yes	—
113	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
114	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
115	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
116	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
117	C₂×D₄×D₆₇	—	2	16	no	—
118	C₂×D₄×D₆₇	—	4	8	no	—
119	C₂×D₄×D₆₇	C₂³	1	16	yes	—
120	C₂×D₄×D₆₇	C₂³	1	16	yes	—
121	C₂³×Dic₆₇	C₂³	1	4	yes	—
122	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
123	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
124	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
125	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
126	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
127	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
128	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
129	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
130	#14524043	C₂³	1	16	yes	complemented
131	#14524043	C₂³	1	8	yes	complemented
132	#14524038	C₂³	1	16	yes	complemented
133	#14524038	C₂³	1	32	yes	complemented
134	#14524036	C₂³	1	32	yes	complemented
135	#14524034	C₂³	1	8	yes	complemented
136	#14524032	C₂³	1	8	yes	—
137	#14524031	C₂³	1	16	yes	—
138	#14524030	C₂³	1	16	yes	complemented
139	#14524029	C₂³	1	32	yes	complemented
140	#14524029	C₂³	1	32	yes	complemented
141	#14524029	C₂³	1	32	yes	complemented
142	#14524028	C₂³	1	16	yes	complemented
143	#14524027	C₂³	1	32	yes	complemented
144	#14524025	C₂³	1	32	yes	complemented
145	#14524023	C₂³	1	16	yes	complemented
146	#14524023	C₂³	1	32	yes	complemented
147	#14524020	C₂³	1	32	yes	complemented
148	#14524019	C₂³	1	16	yes	complemented
149	#14524019	C₂³	1	8	yes	complemented
150	#14524018	C₂³	1	8	yes	—
151	#14524017	C₂³	1	32	yes	complemented
152	#14524016	C₂³	1	32	yes	complemented
153	#14524014	C₂³	1	16	yes	—
154	#14524014	C₂³	1	16	yes	—
155	#14524014	C₂³	1	16	yes	complemented
156	#14524014	C₂³	1	16	yes	complemented
157	#14524013	C₂³	1	32	yes	complemented
158	#14524011	C₂³	1	32	yes	—
159	Q₈×Dic₆₇	C₂³	1	8	yes	complemented
160	C₄×Dic₁₃₄	C₂³	1	16	yes	complemented
161	C₄×D₂₆₈	C₂³	1	8	yes	—
162	C₄×D₂₆₈	C₂³	1	8	yes	—
163	C₄×D₂₆₈	C₂³	1	16	yes	—
164	C₄×D₂₆₈	C₂³	1	16	yes	complemented
165	C₄×D₂₆₈	C₂³	1	16	yes	complemented
166	D₄×Dic₆₇	C₂³	1	16	yes	complemented
167	D₄×Dic₆₇	C₂³	1	16	yes	complemented
168	#14524005	C₂³	1	8	yes	—
169	#14524005	C₂³	1	16	yes	complemented
170	C₄×C₂²⋊D₆₇	C₂³	1	32	yes	complemented
171	(C₂²⋊D₆₇)⋊C₄	C₂³	1	32	yes	complemented
172	#14524002	C₂³	1	32	yes	complemented
173	#14524001	C₂³	1	16	yes	complemented
174	#14524001	C₂³	1	8	yes	complemented
175	#14524001	C₂³	1	16	yes	complemented
176	#14524000	C₂³	1	16	yes	complemented
177	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
178	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
180	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
181	C₂×C₄⋊Dic₆₇	C₂³	1	4	yes	—
182	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
183	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
184	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
185	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
186	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	—
187	C₂×C₂²⋊Dic₆₇	C₂³	1	4	yes	—
188	C₂×C₂²⋊Dic₆₇	C₂³	1	4	yes	—
189	C₂×C₂²⋊Dic₆₇	C₂³	1	4	yes	—
190	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
191	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
192	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
193	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
194	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
195	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
196	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
197	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
198	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
199	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
200	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
201	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	32	yes	complemented
202	C₂²⋊C₄×D₆₇	C₂³	1	32	yes	complemented
203	C₂²⋊C₄×D₆₇	C₂³	1	32	yes	complemented
204	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
205	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
206	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
207	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
208	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
209	C₂×C₄×Dic₆₇	C₂³	1	4	yes	—
210	C₄²×D₆₇	C₂³	1	16	yes	complemented
211	C₄²×D₆₇	C₂³	1	8	yes	complemented
212	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
213	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
214	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
215	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
216	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
217	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
218	#127×C₆₇	C₂³	1	8	yes	—
219	#124×C₆₇	C₂³	1	16	yes	complemented
220	#124×C₆₇	C₂³	1	16	yes	complemented
221	#123×C₆₇	C₂³	1	32	yes	complemented
222	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
223	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
224	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
225	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
226	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
229	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
230	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
231	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
232	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
233	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
234	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
235	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
236	C₂³×D₆₇	—	2	16	no	—
237	C₂³×D₆₇	—	4	8	no	—
238	C₂³×D₆₇	—	4	8	no	—
239	C₂³×D₆₇	C₂⁴	1	2	yes	—
240	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
241	C₂³×D₆₇	C₂⁴	1	2	yes	—
242	C₂³×D₆₇	C₂⁴	1	16	yes	—
243	#11761629	—	2	32	no	—
244	#11761627	—	4	32	no	—
245	C₂×Dic₁₃₄	—	2	8	no	—
246	C₂×Dic₁₃₄	—	4	8	no	—
247	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
248	C₂×Dic₁₃₄	C₂⁴	1	16	yes	—
249	Q₈×D₆₇	—	4	32	no	—
250	C₂×D₂₆₈	—	2	8	no	—
251	C₂×D₂₆₈	—	2	4	no	—
252	C₂×D₂₆₈	—	4	4	no	—
253	C₂×D₂₆₈	#41	1	8	yes	complemented
254	C₂×D₂₆₈	C₂⁴	1	8	yes	—
255	C₂×D₂₆₈	C₂⁴	1	4	yes	—
256	C₂×D₂₆₈	C₂⁴	1	8	yes	—
257	C₂×D₂₆₈	C₂⁴	1	4	yes	—
258	C₂×C₂²⋊D₆₇	—	2	16	no	—
259	C₂×C₂²⋊D₆₇	—	4	8	no	—
260	C₂×C₂²⋊D₆₇	—	4	8	no	—
261	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
262	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
263	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
264	D₄×D₆₇	—	2	64	no	—
265	D₄×D₆₇	—	4	32	no	—
266	C₂²×Dic₆₇	—	4	8	no	—
267	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
268	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
269	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
270	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
271	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
272	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
273	C₂²×Dic₆₇	C₂⁴	1	16	yes	—
274	C₂×C₄×D₆₇	—	2	8	no	—
275	C₂×C₄×D₆₇	—	2	8	no	—
276	C₂×C₄×D₆₇	—	2	4	no	—
277	C₂×C₄×D₆₇	—	2	8	no	—
278	C₂×C₄×D₆₇	—	2	4	no	—
279	C₂×C₄×D₆₇	—	4	4	no	—
280	C₂×C₄×D₆₇	—	4	2	no	—
281	C₂×C₄×D₆₇	—	4	8	no	—
282	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
283	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
284	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
285	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
286	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
287	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
288	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
289	C₂×C₄×D₆₇	C₂⁴	1	16	yes	—
290	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
291	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
292	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
293	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
294	C₄⋊Dic₆₇	C₂⁴	1	16	yes	—
295	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
296	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
297	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
298	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
299	Dic₆₇⋊C₄	C₂⁴	1	16	yes	—
300	C₂²⋊Dic₆₇	C₂⁴	1	16	yes	—
301	C₂²⋊Dic₆₇	C₂⁴	1	16	yes	—
302	C₂²⋊Dic₆₇	C₂⁴	1	16	yes	—
303	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
304	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
305	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
306	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
307	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
308	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
309	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
310	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
311	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
312	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
313	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
314	C₄×Dic₆₇	C₂⁴	1	4	yes	—
315	C₄×Dic₆₇	C₂⁴	1	4	yes	—
316	C₄×Dic₆₇	C₂⁴	1	8	yes	—
317	C₄×Dic₆₇	C₂⁴	1	4	yes	—
318	C₄×Dic₆₇	C₂⁴	1	8	yes	—
319	C₄×Dic₆₇	C₂⁴	1	16	yes	—
320	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
321	C₂×Q₈×C₆₇	—	2	4	no	—
322	C₂×Q₈×C₆₇	—	2	4	no	—
323	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
324	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
325	C₂×D₄×C₆₇	—	2	8	no	—
326	C₂×D₄×C₆₇	—	2	8	no	—
327	C₂×D₄×C₆₇	—	4	4	no	—
328	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
329	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
330	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
331	C₂²×C₄×C₆₇	—	4	8	no	—
332	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
333	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
334	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
335	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
336	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
338	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
340	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
341	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
342	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
343	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
344	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
345	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
346	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
347	C₄²×C₆₇	C₂⁴	1	8	yes	—
348	C₄²×C₆₇	C₂⁴	1	8	yes	—
349	C₄²×C₆₇	C₂⁴	1	4	yes	—
350	C₂³×C₆₇	—	2	8	no	—
351	C₂³×C₆₇	—	2	8	no	—
352	C₂³×C₆₇	—	2	8	no	—
353	C₂³×C₆₇	C₂⁵	1	8	yes	—
354	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
355	C₂²×D₆₇	—	2	4	no	—
356	C₂²×D₆₇	—	2	4	no	—
357	C₂²×D₆₇	—	2	2	no	—
358	C₂²×D₆₇	—	2	4	no	—
359	C₂²×D₆₇	—	2	2	no	—
360	C₂²×D₆₇	—	2	4	no	—
361	C₂²×D₆₇	—	2	2	no	—
362	C₂²×D₆₇	—	2	4	no	—
363	C₂²×D₆₇	—	2	32	no	—
364	C₂²×D₆₇	—	4	16	no	—
365	C₂²×D₆₇	—	4	16	no	—
366	C₂²×D₆₇	—	8	32	no	—
367	C₂²×D₆₇	C₂×#41	1	8	yes	—
368	C₂²×D₆₇	C₂⁵	1	4	yes	—
369	C₂²×D₆₇	C₂⁵	1	2	yes	—
370	C₂²×D₆₇	C₂⁵	1	4	yes	—
371	Q₈×C₆₇	—	2	8	no	—
372	Q₈×C₆₇	—	2	8	no	—
373	D₄×C₆₇	—	2	16	no	—
374	D₄×C₆₇	—	2	16	no	—
375	D₄×C₆₇	—	4	8	no	—
376	C₂×C₄×C₆₇	—	2	4	no	—
377	C₂×C₄×C₆₇	—	2	4	no	—
378	C₂×C₄×C₆₇	—	2	4	no	—
379	C₂×C₄×C₆₇	—	2	4	no	—
380	C₂×C₄×C₆₇	—	2	2	no	—
381	C₂×C₄×C₆₇	—	4	16	no	—
382	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
383	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
384	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
385	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
386	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
387	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
388	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
389	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
390	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
391	C₂²⋊D₆₇	—	2	32	no	—
392	C₂²⋊D₆₇	—	4	16	no	—
393	C₂²⋊D₆₇	—	4	16	no	—
394	C₂×Dic₆₇	—	2	2	no	—
395	C₂×Dic₆₇	—	2	4	no	—
396	C₂×Dic₆₇	—	2	2	no	—
397	C₂×Dic₆₇	—	2	4	no	—
398	C₂×Dic₆₇	—	2	8	no	—
399	C₂×Dic₆₇	—	2	2	no	—
400	C₂×Dic₆₇	—	4	16	no	—
401	C₂×Dic₆₇	C₂⁵	1	2	yes	—
402	C₂×Dic₆₇	C₂⁵	1	2	yes	—
403	C₂×Dic₆₇	C₂⁵	1	2	yes	—
404	C₂×Dic₆₇	C₂⁵	1	4	yes	—
405	C₂×Dic₆₇	C₂⁵	1	4	yes	—
406	C₂×Dic₆₇	C₂⁵	1	8	yes	—
407	D₂₆₈	—	2	16	no	—
408	D₂₆₈	—	2	8	no	—
409	D₂₆₈	—	4	8	no	—
410	D₂₆₈	C₂×#41	1	16	yes	complemented
411	C₄×D₆₇	—	2	16	no	—
412	C₄×D₆₇	—	2	16	no	—
413	C₄×D₆₇	—	2	8	no	—
414	C₄×D₆₇	—	2	16	no	—
415	C₄×D₆₇	—	2	8	no	—
416	C₄×D₆₇	—	4	8	no	—
417	C₄×D₆₇	—	4	4	no	—
418	C₄×D₆₇	—	4	16	no	—
419	Dic₁₃₄	—	2	16	no	—
420	Dic₁₃₄	—	4	16	no	—
421	C₂²×C₆₇	—	2	8	no	—
422	C₂²×C₆₇	—	2	8	no	—
423	C₂²×C₆₇	—	2	8	no	—
424	C₂²×C₆₇	—	4	16	no	—
425	C₂²×C₆₇	C₂²×#41	1	2	yes	—
426	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
427	C₂²×C₆₇	#585	1	2	yes	—
428	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
429	C₂×D₆₇	—	2	4	no	—
430	C₂×D₆₇	—	2	4	no	—
431	C₂×D₆₇	—	2	16	no	—
432	C₂×D₆₇	—	2	2	no	—
433	C₂×D₆₇	—	2	4	no	—
434	C₂×D₆₇	—	2	2	no	—
435	C₂×D₆₇	—	2	4	no	—
436	C₂×D₆₇	—	2	2	no	—
437	C₂×D₆₇	—	2	4	no	—
438	C₂×D₆₇	—	4	4	no	—
439	C₂×D₆₇	—	4	8	no	—
440	C₂×D₆₇	—	8	32	no	—
441	C₂×D₆₇	C₂²×#41	1	8	yes	—
442	C₄×C₆₇	—	2	4	no	—
443	C₄×C₆₇	—	2	4	no	—
444	C₄×C₆₇	—	2	4	no	—
445	C₄×C₆₇	—	2	2	no	—
446	C₄×C₆₇	—	2	4	no	—
447	C₄×C₆₇	C₂²×#41	1	4	yes	—
448	C₄×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
449	Dic₆₇	—	2	2	no	—
450	Dic₆₇	—	2	4	no	—
451	Dic₆₇	—	2	8	no	—
452	Dic₆₇	—	2	4	no	—
453	Dic₆₇	—	2	2	no	—
454	Dic₆₇	—	2	2	no	—
455	C₂×#3514	—	67	1	no	maximal, Sylow
456	C₂×C₆₇	—	4	8	no	—
457	C₂×C₆₇	#3514	1	4	yes	complemented
458	C₂×C₆₇	C₂³×#41	1	1	yes	characteristic
459	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
460	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
461	D₆₇	—	2	8	no	—
462	D₆₇	—	4	2	no	—
463	D₆₇	—	4	4	no	—
464	#3514	—	67	32	no	—
465	C₂×#559	D₆₇	1	1	yes	characteristic, complemented
466	C₂×#556	—	67	1	no	—
467	C₂×#555	—	67	2	no	—
468	C₂×#551	—	67	4	no	—
469	C₂×D₄×Q₈	—	67	1	no	—
470	C₂×#548	—	67	2	no	—
471	C₂×#546	—	67	2	no	—
472	C₂×#546	—	67	2	no	—
473	C₂×D₄²	—	67	1	no	—
474	C₂×#542	—	67	2	no	—
475	C₂×#538	—	67	4	no	—
476	C₂×#532	—	67	1	no	—
477	C₂×#529	—	67	1	no	—
478	C₂×#529	—	67	2	no	—
479	C₂²×#124	—	67	2	no	—
480	C₂×#518	—	67	2	no	—
481	C₂×C₄×#41	—	67	1	no	—
482	C₆₇	C₂×#3514	1	1	yes	characteristic, complemented, Sylow
483	C₂²×#41	—	67	1	no	—
484	C₂²×#41	—	67	2	no	—
485	C₂³×Q₈	—	67	2	no	—
486	C₂³×D₄	—	67	2	no	—
487	C₂³×D₄	—	67	2	no	—
488	#559	C₂×D₆₇	1	16	yes	complemented
489	#556	—	67	16	no	—
490	#555	—	67	32	no	—
491	#551	—	67	64	no	—
492	D₄×Q₈	—	67	16	no	—
493	#548	—	67	32	no	—
494	#546	—	67	32	no	—
495	#546	—	67	32	no	—
496	D₄²	—	67	16	no	—
497	#542	—	67	32	no	—
498	#538	—	67	64	no	—
499	#532	—	67	16	no	—
500	C₂×C₄⋊Q₈	—	67	1	no	—
501	C₂×C₄⋊Q₈	—	67	2	no	—
502	C₂×#127	C₂×D₆₇	1	1	yes	characteristic
503	#529	—	67	16	no	—
504	#529	—	67	32	no	—
505	C₂×#126	—	67	2	no	—
506	C₂×#126	—	67	4	no	—
507	C₂×#126	—	67	4	no	—
508	C₂×#125	—	67	1	no	—
509	C₂×#124	—	67	1	no	—
510	C₂×#124	—	67	2	no	—
511	C₂×#124	—	67	32	no	—
512	C₂×#124	—	67	4	no	—
513	C₂×#124	—	67	4	no	—
514	C₂×#124	—	67	4	no	—
515	C₂×#124	—	67	2	no	—
516	C₂×#124	C₂×D₆₇	1	2	yes	complemented
517	C₂×#124	C₂×D₆₇	1	2	yes	complemented
518	C₂×#123	—	67	2	no	—
519	C₂×#123	—	67	4	no	—
520	C₂×#123	—	67	4	no	—
521	C₂×#123	C₂×D₆₇	1	4	yes	complemented
522	C₂×C₂²⋊Q₈	—	67	1	no	—
523	C₂×C₂²⋊Q₈	—	67	2	no	—
524	C₂×C₂²⋊Q₈	—	67	2	no	—
525	C₂×C₂²⋊Q₈	—	67	4	no	—
526	C₂×C₂²⋊Q₈	—	67	4	no	—
527	C₂×#121	—	67	2	no	—
528	C₂×#121	—	67	2	no	—
529	C₂×#121	—	67	2	no	—
530	C₂×#121	—	67	2	no	—
531	C₂×#121	—	67	4	no	—
532	C₂×#121	—	67	1	no	—
533	C₂×#121	—	67	4	no	—
534	C₂×#120	—	67	4	no	—
535	C₂×#120	—	67	4	no	—
536	#518	—	67	32	no	—
537	C₄×#41	—	67	16	no	—
538	C₂×C₄×Q₈	—	67	1	no	—
539	C₂×C₄×Q₈	—	67	2	no	—
540	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
541	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
542	C₂×C₄×D₄	—	67	2	no	—
543	C₂×C₄×D₄	—	67	2	no	—
544	C₂×C₄×D₄	—	67	4	no	—
545	C₂×C₄×D₄	—	67	1	no	—
546	C₂×C₄×D₄	—	67	2	no	—
547	C₂×C₄×D₄	—	67	4	no	—
548	C₂×C₄×D₄	—	67	1	no	—
549	C₂×C₄×D₄	—	67	2	no	—
550	C₂×C₄×D₄	—	67	2	no	—
551	C₂×C₄×D₄	—	67	1	no	—
552	C₂×C₄×D₄	—	67	2	no	—
553	C₂×C₄×D₄	C₂×D₆₇	1	2	yes	complemented
554	C₂×C₄×D₄	C₂×D₆₇	1	2	yes	complemented
555	C₂×#117	—	67	4	no	—
556	C₂×#117	—	67	2	no	—
557	C₂×#117	—	67	1	no	—
558	C₂×#117	—	67	2	no	—
559	C₂×#117	—	67	2	no	—
560	C₂²×C₂²⋊C₄	—	67	4	no	—
561	C₂²×C₂²⋊C₄	—	67	4	no	—
562	C₂²×C₂²⋊C₄	—	67	4	no	—
563	C₂²×C₄²	—	67	2	no	—
564	C₂²×C₄²	—	67	1	no	—
565	C₂⁵	—	67	4	no	—
566	C₂×#41	—	268	8	no	—
567	C₂×#41	—	67	8	no	—
568	C₂×#41	—	67	16	no	—
569	C₂×#41	—	134	8	no	—
570	C₂²×Q₈	—	268	8	no	—
571	C₂²×Q₈	—	67	16	no	—
572	C₂²×Q₈	—	67	4	no	—
573	C₂²×Q₈	—	67	2	no	—
574	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
575	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
576	C₂²×D₄	—	268	8	no	—
577	C₂²×D₄	—	67	4	no	—
578	C₂²×D₄	—	67	4	no	—
579	C₂²×D₄	—	67	16	no	—
580	C₂²×D₄	—	67	4	no	—
581	C₂²×D₄	—	67	16	no	—
582	C₂²×D₄	—	67	2	no	—
583	C₂²×D₄	—	67	1	no	—
584	C₂²×D₄	—	67	2	no	—
585	C₂²×D₄	—	67	1	no	—
586	C₂²×D₄	—	134	16	no	—
587	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
588	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
589	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
590	C₂³×C₄	—	67	4	no	—
591	C₂³×C₄	—	67	2	no	—
592	C₂³×C₄	—	67	4	no	—
593	C₂³×C₄	—	67	1	no	—
594	C₂³×C₄	—	67	2	no	—
595	C₂³×C₄	—	67	2	no	—
596	C₂³×C₄	—	67	1	no	—
597	C₂³×C₄	—	67	2	no	—
598	C₂³×C₄	—	67	1	no	—
599	C₂³×C₄	C₂²×D₆₇	1	4	yes	—
600	C₄⋊Q₈	—	67	8	no	—
601	C₄⋊Q₈	—	67	16	no	—
602	#127	C₂²×D₆₇	1	8	yes	—
603	#126	—	67	16	no	—
604	#126	—	67	32	no	—
605	#126	—	67	32	no	—
606	#125	—	67	8	no	—
607	#124	—	67	8	no	—
608	#124	—	67	16	no	—
609	#124	—	67	32	no	—
610	#124	—	67	32	no	—
611	#124	—	67	32	no	—
612	#124	—	67	16	no	—
613	#124	C₂²×D₆₇	1	16	yes	complemented
614	#124	C₂²×D₆₇	1	16	yes	complemented
615	#123	—	67	16	no	—
616	#123	—	67	32	no	—
617	#123	—	67	32	no	—
618	#123	C₂²×D₆₇	1	32	yes	complemented
619	C₂²⋊Q₈	—	67	8	no	—
620	C₂²⋊Q₈	—	67	16	no	—
621	C₂²⋊Q₈	—	67	16	no	—
622	C₂²⋊Q₈	—	67	32	no	—
623	C₂²⋊Q₈	—	67	32	no	—
624	#121	—	67	16	no	—
625	#121	—	67	16	no	—
626	#121	—	67	16	no	—
627	#121	—	67	16	no	—
628	#121	—	67	32	no	—
629	#121	—	67	8	no	—
630	#121	—	67	32	no	—
631	#120	—	67	32	no	—
632	#120	—	67	32	no	—
633	C₄×Q₈	—	67	8	no	—
634	C₄×Q₈	—	67	16	no	—
635	C₄×Q₈	C₂²×D₆₇	1	8	yes	complemented
636	C₄×Q₈	C₂²×D₆₇	1	8	yes	complemented
637	C₄×D₄	—	67	16	no	—
638	C₄×D₄	—	67	16	no	—
639	C₄×D₄	—	67	32	no	—
640	C₄×D₄	—	67	8	no	—
641	C₄×D₄	—	67	16	no	—
642	C₄×D₄	—	67	32	no	—
643	C₄×D₄	—	67	8	no	—
644	C₄×D₄	—	67	16	no	—
645	C₄×D₄	—	67	16	no	—
646	C₄×D₄	—	67	8	no	—
647	C₄×D₄	—	67	16	no	—
648	C₄×D₄	C₂²×D₆₇	1	16	yes	complemented
649	C₄×D₄	C₂²×D₆₇	1	16	yes	complemented
650	#117	—	67	32	no	—
651	#117	—	67	16	no	—
652	#117	—	67	8	no	—
653	#117	—	67	16	no	—
654	#117	—	67	16	no	—
655	C₂×C₄⋊C₄	—	67	2	no	—
656	C₂×C₄⋊C₄	—	67	2	no	—
657	C₂×C₄⋊C₄	—	67	2	no	—
658	C₂×C₄⋊C₄	—	67	2	no	—
659	C₂×C₄⋊C₄	—	67	1	no	—
660	C₂×C₄⋊C₄	—	67	2	no	—
661	C₂×C₄⋊C₄	—	67	4	no	—
662	C₂×C₄⋊C₄	—	67	1	no	—
663	C₂×C₄⋊C₄	—	67	2	no	—
664	C₂×C₄⋊C₄	—	67	4	no	—
665	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
667	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
668	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
669	C₂×C₂²⋊C₄	—	67	4	no	—
670	C₂×C₂²⋊C₄	—	67	4	no	—
671	C₂×C₂²⋊C₄	—	67	4	no	—
672	C₂×C₂²⋊C₄	—	67	2	no	—
673	C₂×C₂²⋊C₄	—	67	2	no	—
674	C₂×C₂²⋊C₄	—	67	4	no	—
675	C₂×C₂²⋊C₄	—	67	2	no	—
676	C₂×C₂²⋊C₄	—	67	2	no	—
677	C₂×C₂²⋊C₄	—	67	4	no	—
678	C₂×C₂²⋊C₄	—	67	32	no	—
679	C₂×C₂²⋊C₄	—	67	4	no	—
680	C₂×C₂²⋊C₄	—	67	2	no	—
681	C₂×C₂²⋊C₄	—	67	2	no	—
682	C₂×C₂²⋊C₄	—	67	2	no	—
683	C₂×C₂²⋊C₄	—	67	2	no	—
684	C₂×C₂²⋊C₄	—	67	32	no	—
685	C₂×C₂²⋊C₄	—	67	32	no	—
686	C₂×C₂²⋊C₄	C₂²×D₆₇	1	4	yes	—
687	C₂×C₂²⋊C₄	C₂²×D₆₇	1	4	yes	—
688	C₂×C₂²⋊C₄	C₂²×D₆₇	1	4	yes	—
689	C₂×C₄²	—	67	2	no	—
690	C₂×C₄²	—	67	1	no	—
691	C₂×C₄²	—	67	4	no	—
692	C₂×C₄²	—	67	1	no	—
693	C₂×C₄²	—	67	2	no	—
694	C₂×C₄²	—	67	1	no	—
695	C₂×C₄²	—	67	16	no	—
696	C₂×C₄²	—	67	8	no	—
697	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
698	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
699	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
700	C₂⁴	—	268	8	no	—
701	C₂⁴	—	268	8	no	—
702	C₂⁴	—	67	16	no	—
703	C₂⁴	—	67	2	no	—
704	C₂⁴	—	67	2	no	—
705	C₂⁴	—	67	1	no	—
706	C₂⁴	—	134	16	no	—
707	C₂⁴	C₂³×D₆₇	1	4	yes	—
708	#41	—	268	32	no	—
709	#41	—	134	32	no	—
710	C₂×Q₈	—	2	4	no	—
711	C₂×Q₈	—	2	4	no	—
712	C₂×Q₈	—	268	8	no	—
713	C₂×Q₈	—	268	32	no	—
714	C₂×Q₈	—	67	16	no	—
715	C₂×Q₈	—	67	8	no	—
716	C₂×Q₈	—	134	8	no	—
717	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
718	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
719	C₂×D₄	—	2	8	no	—
720	C₂×D₄	—	2	8	no	—
721	C₂×D₄	—	4	4	no	—
722	C₂×D₄	—	268	4	no	—
723	C₂×D₄	—	268	32	no	—
724	C₂×D₄	—	268	8	no	—
725	C₂×D₄	—	268	8	no	—
726	C₂×D₄	—	67	16	no	—
727	C₂×D₄	—	67	16	no	—
728	C₂×D₄	—	67	16	no	—
729	C₂×D₄	—	67	8	no	—
730	C₂×D₄	—	67	8	no	—
731	C₂×D₄	—	67	4	no	—
732	C₂×D₄	—	67	8	no	—
733	C₂×D₄	—	67	4	no	—
734	C₂×D₄	—	134	8	no	—
735	C₂×D₄	—	134	64	no	—
736	C₂×D₄	—	134	16	no	—
737	C₂×D₄	—	134	4	no	—
738	C₂×D₄	C₂³×D₆₇	1	8	yes	—
739	C₂×D₄	C₂³×D₆₇	1	8	yes	—
740	C₂×D₄	C₂³×D₆₇	1	8	yes	—
741	C₂²×C₄	—	4	8	no	—
742	C₂²×C₄	—	268	8	no	—
743	C₂²×C₄	—	268	4	no	—
744	C₂²×C₄	—	268	2	no	—
745	C₂²×C₄	—	268	8	no	—
746	C₂²×C₄	—	67	16	no	—
747	C₂²×C₄	—	67	8	no	—
748	C₂²×C₄	—	67	4	no	—
749	C₂²×C₄	—	67	16	no	—
750	C₂²×C₄	—	67	1	no	—
751	C₂²×C₄	—	67	1	no	—
752	C₂²×C₄	—	67	2	no	—
753	C₂²×C₄	—	67	1	no	—
754	C₂²×C₄	—	67	2	no	—
755	C₂²×C₄	—	67	4	no	—
756	C₂²×C₄	—	67	8	no	—
757	C₂²×C₄	—	67	4	no	—
758	C₂²×C₄	—	67	8	no	—
759	C₂²×C₄	—	67	4	no	—
760	C₂²×C₄	—	67	8	no	—
761	C₂²×C₄	—	134	8	no	—
762	C₂²×C₄	—	134	8	no	—
763	C₂²×C₄	—	134	4	no	—
764	C₂²×C₄	—	134	8	no	—
765	C₂²×C₄	—	134	4	no	—
766	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
767	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
768	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
769	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
770	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
771	C₂²×C₄	C₂³×D₆₇	1	16	yes	—
772	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
773	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
774	C₄⋊C₄	—	67	8	no	—
775	C₄⋊C₄	—	67	8	no	—
776	C₄⋊C₄	—	67	8	no	—
777	C₄⋊C₄	—	67	8	no	—
778	C₄⋊C₄	—	67	4	no	—
779	C₄⋊C₄	—	67	8	no	—
780	C₄⋊C₄	—	67	16	no	—
781	C₄⋊C₄	—	67	4	no	—
782	C₄⋊C₄	—	67	8	no	—
783	C₄⋊C₄	—	67	16	no	—
784	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
785	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
786	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
787	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
788	C₂²⋊C₄	—	67	16	no	—
789	C₂²⋊C₄	—	67	16	no	—
790	C₂²⋊C₄	—	67	16	no	—
791	C₂²⋊C₄	—	67	8	no	—
792	C₂²⋊C₄	—	67	8	no	—
793	C₂²⋊C₄	—	67	16	no	—
794	C₂²⋊C₄	—	67	8	no	—
795	C₂²⋊C₄	—	67	8	no	—
796	C₂²⋊C₄	—	67	16	no	—
797	C₂²⋊C₄	—	67	16	no	—
798	C₂²⋊C₄	—	67	8	no	—
799	C₂²⋊C₄	—	67	8	no	—
800	C₂²⋊C₄	—	67	8	no	—
801	C₂²⋊C₄	—	67	8	no	—
802	C₂²⋊C₄	C₂³×D₆₇	1	16	yes	—
803	C₂²⋊C₄	C₂³×D₆₇	1	16	yes	—
804	C₂²⋊C₄	C₂³×D₆₇	1	16	yes	—
805	C₄²	—	67	4	no	—
806	C₄²	—	67	8	no	—
807	C₄²	—	67	4	no	—
808	C₄²	—	67	4	no	—
809	C₄²	—	67	8	no	—
810	C₄²	—	67	16	no	—
811	C₄²	C₂³×D₆₇	1	4	yes	—
812	C₄²	C₂³×D₆₇	1	8	yes	—
813	C₄²	C₂³×D₆₇	1	8	yes	—
814	C₂³	—	2	8	no	—
815	C₂³	—	2	8	no	—
816	C₂³	—	2	8	no	—
817	C₂³	—	268	16	no	—
818	C₂³	—	268	16	no	—
819	C₂³	—	536	32	no	—
820	C₂³	—	67	8	no	—
821	C₂³	—	67	4	no	—
822	C₂³	—	67	4	no	—
823	C₂³	—	67	2	no	—
824	C₂³	—	134	32	no	—
825	C₂³	—	134	2	no	—
826	C₂³	—	134	4	no	—
827	C₂³	—	134	2	no	—
828	C₂³	—	134	4	no	—
829	C₂³	—	134	2	no	—
830	C₂³	—	134	4	no	—
831	C₂³	—	134	4	no	—
832	C₂³	—	134	4	no	—
833	C₂³	C₂⁴×D₆₇	1	8	yes	—
834	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
835	Q₈	—	2	8	no	—
836	Q₈	—	2	8	no	—
837	Q₈	—	268	16	no	—
838	Q₈	—	134	16	no	—
839	D₄	—	2	16	no	—
840	D₄	—	2	16	no	—
841	D₄	—	4	8	no	—
842	D₄	—	268	8	no	—
843	D₄	—	268	16	no	—
844	D₄	—	268	16	no	—
845	D₄	—	67	16	no	—
846	D₄	—	134	16	no	—
847	D₄	—	134	32	no	—
848	D₄	—	134	8	no	—
849	C₂×C₄	—	2	4	no	—
850	C₂×C₄	—	2	4	no	—
851	C₂×C₄	—	2	4	no	—
852	C₂×C₄	—	2	4	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	4	16	no	—
855	C₂×C₄	—	268	16	no	—
856	C₂×C₄	—	268	8	no	—
857	C₂×C₄	—	268	4	no	—
858	C₂×C₄	—	268	16	no	—
859	C₂×C₄	—	67	2	no	—
860	C₂×C₄	—	67	2	no	—
861	C₂×C₄	—	67	4	no	—
862	C₂×C₄	—	67	2	no	—
863	C₂×C₄	—	67	4	no	—
864	C₂×C₄	—	67	8	no	—
865	C₂×C₄	—	134	16	no	—
866	C₂×C₄	—	134	2	no	—
867	C₂×C₄	—	134	4	no	—
868	C₂×C₄	—	134	2	no	—
869	C₂×C₄	—	134	8	no	—
870	C₂×C₄	—	134	4	no	—
871	C₂×C₄	—	134	2	no	—
872	C₂×C₄	—	134	16	no	—
873	C₂×C₄	—	134	8	no	—
874	C₂×C₄	—	134	16	no	—
875	C₂×C₄	—	134	8	no	—
876	C₂×C₄	#41×D₆₇	1	4	yes	—
877	C₂×C₄	#14524089	1	4	yes	—
878	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
879	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
880	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
881	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
882	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
883	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
884	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
885	C₂²	—	2	8	no	—
886	C₂²	—	2	8	no	—
887	C₂²	—	2	8	no	—
888	C₂²	—	4	16	no	—
889	C₂²	—	268	8	no	—
890	C₂²	—	268	4	no	—
891	C₂²	—	536	32	no	—
892	C₂²	—	67	8	no	—
893	C₂²	—	134	2	no	—
894	C₂²	—	134	4	no	—
895	C₂²	—	134	2	no	—
896	C₂²	—	134	4	no	—
897	C₂²	—	134	2	no	—
898	C₂²	—	134	4	no	—
899	C₂²	—	134	16	no	—
900	C₂²	—	134	4	no	—
901	C₂²	—	134	4	no	—
902	C₂²	C₂×#41×D₆₇	1	2	yes	—
903	C₂²	C₂×#14524089	1	2	yes	—
904	C₂²	#16864231	1	2	yes	—
905	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
906	C₄	—	2	4	no	—
907	C₄	—	2	4	no	—
908	C₄	—	2	4	no	—
909	C₄	—	2	4	no	—
910	C₄	—	2	2	no	—
911	C₄	—	134	2	no	—
912	C₄	—	134	4	no	—
913	C₄	—	134	2	no	—
914	C₄	—	134	8	no	—
915	C₄	—	134	4	no	—
916	C₄	—	134	2	no	—
917	C₄	C₂×#41×D₆₇	1	4	yes	—
918	C₄	C₂×#14524089	1	4	yes	—
919	C₂	—	4	8	no	—
920	C₂	—	268	4	no	—
921	C₂	—	268	2	no	—
922	C₂	—	134	8	no	—
923	C₂	#22574169	1	4	yes	direct product factor
924	C₂	C₂²×#41×D₆₇	1	1	yes	characteristic
925	C₂	C₂²×#14524089	1	1	yes	characteristic
926	C₂	C₂×#16864231	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₆₇
commutator, cosocle	C₂²×C₆₇	C₂⁶
Frattini	C₂²	C₂⁵×D₆₇
Fitting	C₂×#559×C₆₇	C₂
socle	C₂³×C₆₇	C₂⁵
hypercenter	C₂×#559	D₆₇
hypocenter	C₆₇	C₂×#3514
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×#559

Complements

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

N	H ≅ G/N	type
1. #22574169	C₂	direct (N × H)
2. C₂×#16864119	C₂	semidirect
3. C₂×#16864111	C₂	semidirect
4. C₂×#16864069	C₂	semidirect
5. C₂×Q₈×D₂₆₈	C₂	semidirect
6. C₂×#16864054	C₂	semidirect
7. C₂×#16864041	C₂	semidirect
8. C₂×#16864039	C₂	semidirect
9. C₂×#16864031	C₂	semidirect
10. C₂×#16864015	C₂	semidirect
11. C₂×#16863982	C₂	semidirect
12. C₂×#16863944	C₂	semidirect
13. C₂×#16863933	C₂	semidirect
14. C₂×#16863928	C₂	semidirect
15. C₂×#124×D₆₇	C₂	semidirect
16. C₂×#16863868	C₂	semidirect
17. C₂×C₄×#11761629	C₂	semidirect
18. C₂×#559×C₆₇	C₂	semidirect
20. C₂²×#11761627	C₂²	semidirect
21. C₂²×Q₈×D₆₇	C₂²	semidirect
24. #16864119	C₂²	semidirect
25. #16864111	C₂²	semidirect
26. #16864069	C₂²	semidirect
27. Q₈×D₂₆₈	C₂²	semidirect
28. #16864054	C₂²	semidirect
29. #16864041	C₂²	semidirect
30. #16864039	C₂²	semidirect
31. #16864031	C₂²	semidirect
32. #16864015	C₂²	semidirect
33. #16863982	C₂²	semidirect
34. #16863944	C₂²	semidirect
35. C₂×#14524043	C₂²	semidirect
36. C₂×#14524043	C₂²	semidirect
37. #16863933	C₂²	semidirect
38. #16863928	C₂²	semidirect
39. C₂×#14524038	C₂²	semidirect
40. C₂×#14524038	C₂²	semidirect
41. C₂×#14524036	C₂²	semidirect
42. C₂×#14524034	C₂²	semidirect
45. C₂×#14524030	C₂²	semidirect
46. C₂×#14524029	C₂²	semidirect
47. C₂×#14524029	C₂²	semidirect
48. C₂×#14524029	C₂²	semidirect
49. #124×D₆₇	C₂²	semidirect
50. C₂×#14524028	C₂²	semidirect
51. C₂×#14524027	C₂²	semidirect
52. C₂×#14524025	C₂²	semidirect
53. C₂×#14524023	C₂²	semidirect
54. C₂×#14524023	C₂²	semidirect
55. C₂×#14524020	C₂²	semidirect
56. C₂×#14524019	C₂²	semidirect
57. C₂×#14524019	C₂²	semidirect
59. C₂×#14524017	C₂²	semidirect
60. C₂×#14524016	C₂²	semidirect
63. C₂×#14524014	C₂²	semidirect
64. C₂×#14524014	C₂²	semidirect
65. C₂×#14524013	C₂²	semidirect
67. #16863868	C₂²	semidirect
68. C₄×#11761629	C₂²	semidirect
69. C₂×Q₈×Dic₆₇	C₂²	semidirect
70. C₂×C₄×Dic₁₃₄	C₂²	semidirect
74. C₂×C₄×D₂₆₈	C₂²	semidirect
75. C₂×C₄×D₂₆₈	C₂²	semidirect
76. C₂×D₄×Dic₆₇	C₂²	semidirect
77. C₂×D₄×Dic₆₇	C₂²	semidirect
79. C₂×#14524005	C₂²	semidirect
80. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
81. C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
82. C₂×#14524002	C₂²	semidirect
83. C₂×#14524001	C₂²	semidirect
84. C₂×#14524001	C₂²	semidirect
85. C₂×#14524001	C₂²	semidirect
86. C₂×#14524000	C₂²	semidirect
87. C₂²×(C₂×D₆₇)⋊C₄	C₂²	semidirect
88. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
89. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
90. C₂×C₄²×D₆₇	C₂²	semidirect
91. C₂×C₄²×D₆₇	C₂²	semidirect
92. #559×C₆₇	C₂²	semidirect
94. C₂×#124×C₆₇	C₂²	semidirect
95. C₂×#124×C₆₇	C₂²	semidirect
96. C₂×#123×C₆₇	C₂²	semidirect
97. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
98. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
99. C₂×C₄×D₄×C₆₇	C₂²	semidirect
100. C₂×C₄×D₄×C₆₇	C₂²	semidirect
105. C₂×#11761627	C₂³	semidirect
109. C₂×Q₈×D₆₇	C₂³	semidirect
130. #14524043	C₂³	semidirect
131. #14524043	C₂³	semidirect
132. #14524038	C₂³	semidirect
133. #14524038	C₂³	semidirect
134. #14524036	C₂³	semidirect
135. #14524034	C₂³	semidirect
138. #14524030	C₂³	semidirect
139. #14524029	C₂³	semidirect
140. #14524029	C₂³	semidirect
141. #14524029	C₂³	semidirect
142. #14524028	C₂³	semidirect
143. #14524027	C₂³	semidirect
144. #14524025	C₂³	semidirect
145. #14524023	C₂³	semidirect
146. #14524023	C₂³	semidirect
147. #14524020	C₂³	semidirect
148. #14524019	C₂³	semidirect
149. #14524019	C₂³	semidirect
151. #14524017	C₂³	semidirect
152. #14524016	C₂³	semidirect
155. #14524014	C₂³	semidirect
156. #14524014	C₂³	semidirect
157. #14524013	C₂³	semidirect
159. Q₈×Dic₆₇	C₂³	semidirect
160. C₄×Dic₁₃₄	C₂³	semidirect
164. C₄×D₂₆₈	C₂³	semidirect
165. C₄×D₂₆₈	C₂³	semidirect
166. D₄×Dic₆₇	C₂³	semidirect
167. D₄×Dic₆₇	C₂³	semidirect
169. #14524005	C₂³	semidirect
170. C₄×C₂²⋊D₆₇	C₂³	semidirect
171. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
172. #14524002	C₂³	semidirect
173. #14524001	C₂³	semidirect
174. #14524001	C₂³	semidirect
175. #14524001	C₂³	semidirect
176. #14524000	C₂³	semidirect
201. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
202. C₂²⋊C₄×D₆₇	C₂³	semidirect
203. C₂²⋊C₄×D₆₇	C₂³	semidirect
210. C₄²×D₆₇	C₂³	semidirect
211. C₄²×D₆₇	C₂³	semidirect
219. #124×C₆₇	C₂³	semidirect
220. #124×C₆₇	C₂³	semidirect
221. #123×C₆₇	C₂³	semidirect
222. C₄×Q₈×C₆₇	C₂³	semidirect
223. C₄×Q₈×C₆₇	C₂³	semidirect
224. C₄×D₄×C₆₇	C₂³	semidirect
225. C₄×D₄×C₆₇	C₂³	semidirect
253. C₂×D₂₆₈	#41	semidirect
410. D₂₆₈	C₂×#41	semidirect
457. C₂×C₆₇	#3514	semidirect
465. C₂×#559	D₆₇	semidirect
482. C₆₇	C₂×#3514	semidirect
488. #559	C₂×D₆₇	semidirect
516. C₂×#124	C₂×D₆₇	semidirect
517. C₂×#124	C₂×D₆₇	semidirect
521. C₂×#123	C₂×D₆₇	semidirect
540. C₂×C₄×Q₈	C₂×D₆₇	semidirect
541. C₂×C₄×Q₈	C₂×D₆₇	semidirect
553. C₂×C₄×D₄	C₂×D₆₇	semidirect
554. C₂×C₄×D₄	C₂×D₆₇	semidirect
613. #124	C₂²×D₆₇	semidirect
614. #124	C₂²×D₆₇	semidirect
618. #123	C₂²×D₆₇	semidirect
635. C₄×Q₈	C₂²×D₆₇	semidirect
636. C₄×Q₈	C₂²×D₆₇	semidirect
648. C₄×D₄	C₂²×D₆₇	semidirect
649. C₄×D₄	C₂²×D₆₇	semidirect
923. C₂	#22574169	direct (N × H)

Maximal subgroups

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

subgroup	index
#22574169	2
C₂×#16864119	2
C₂×#16864111	2
C₂×#16864069	2
C₂×Q₈×D₂₆₈	2
C₂×#16864054	2
C₂×#16864041	2
C₂×#16864039	2
C₂×#16864031	2
C₂×#16864015	2
C₂×#16863982	2
C₂×#16863944	2
C₂×#16863933	2
C₂×#16863928	2
C₂×#124×D₆₇	2
C₂×#16863868	2
C₂×C₄×#11761629	2
C₂×#559×C₆₇	2
C₂×#3514	67

Subgroups — C2×#22574169 #31763926

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22574169 #31763926