Subgroups — C₂×#22574732 #31763161

Order 17152.

8122 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574732	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16864140	C₂	1	2	yes	maximal, complemented
3	C₂×#16864138	C₂	1	2	yes	maximal, complemented
4	C₂×#16864129	C₂	1	2	yes	maximal, complemented
5	C₂×#16864052	C₂	1	2	yes	maximal, complemented
6	C₂×#16864041	C₂	1	2	yes	maximal, complemented
7	C₂×#16864034	C₂	1	4	yes	maximal, complemented
8	C₂×#16864030	C₂	1	2	yes	maximal, complemented
9	C₂×#16864020	C₂	1	2	yes	maximal, complemented
10	C₂×#16863983	C₂	1	2	yes	maximal, complemented
11	C₂×#16863979	C₂	1	4	yes	maximal, complemented
12	C₂×#16863959	C₂	1	2	yes	maximal, complemented
13	C₂×#16863954	C₂	1	2	yes	maximal, complemented
14	C₂×#16863930	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#14524031	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#532×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#11761627	C₂²	1	2	yes	complemented
18	C₂³×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
19	C₂³×D₂₆₈	C₂²	1	1	yes	characteristic
20	C₂²×D₄×D₆₇	C₂²	1	4	yes	complemented
21	C₂²×D₄×D₆₇	C₂²	1	2	yes	complemented
22	#16864140	C₂²	1	32	yes	complemented
23	#16864138	C₂²	1	32	yes	complemented
24	#16864129	C₂²	1	32	yes	complemented
25	#16864052	C₂²	1	32	yes	complemented
26	#16864041	C₂²	1	32	yes	complemented
27	#16864034	C₂²	1	64	yes	complemented
28	#16864030	C₂²	1	32	yes	complemented
29	#16864020	C₂²	1	32	yes	complemented
30	#16863983	C₂²	1	32	yes	complemented
31	#16863979	C₂²	1	64	yes	complemented
32	#16863959	C₂²	1	32	yes	complemented
33	#16863954	C₂²	1	32	yes	complemented
34	C₂×#14524039	C₂²	1	2	yes	—
35	#16863930	C₂²	1	16	yes	complemented
36	C₂×#14524038	C₂²	1	4	yes	complemented
37	C₂×#14524037	C₂²	1	2	yes	complemented
38	C₂×#14524035	C₂²	1	1	yes	characteristic, complemented
39	C₂×#14524032	C₂²	1	4	yes	complemented
40	C₂×#14524031	C₂²	1	2	yes	complemented
41	C₂×#14524031	C₂²	1	2	yes	complemented
42	C₂×#14524031	C₂²	1	2	yes	complemented
43	C₂×#14524031	C₂²	1	2	yes	complemented
44	C₂×#14524031	C₂²	1	1	yes	characteristic, complemented
45	C₂×#14524031	C₂²	1	16	yes	complemented
46	C₂×#14524030	C₂²	1	2	yes	complemented
47	C₂×#14524029	C₂²	1	4	yes	complemented
48	C₂×#14524029	C₂²	1	4	yes	complemented
49	C₂×#14524028	C₂²	1	4	yes	complemented
50	C₂×#14524027	C₂²	1	4	yes	complemented
51	C₂×#14524026	C₂²	1	2	yes	complemented
52	C₂×#14524026	C₂²	1	4	yes	complemented
53	C₂×#14524025	C₂²	1	4	yes	complemented
54	C₂×#14524023	C₂²	1	2	yes	complemented
55	C₂×#14524022	C₂²	1	1	yes	characteristic, complemented
56	C₂×#14524020	C₂²	1	4	yes	complemented
57	C₂×#14524019	C₂²	1	4	yes	complemented
58	C₂×#14524018	C₂²	1	2	yes	—
59	C₂×#14524017	C₂²	1	1	yes	characteristic
60	C₂×#14524017	C₂²	1	4	yes	complemented
61	C₂×#14524016	C₂²	1	4	yes	complemented
62	C₂×#14524015	C₂²	1	4	yes	complemented
63	C₂×#14524015	C₂²	1	4	yes	complemented
64	C₂×#14524015	C₂²	1	4	yes	complemented
65	C₂×#14524013	C₂²	1	4	yes	complemented
66	C₂×#14524013	C₂²	1	4	yes	complemented
67	C₂×#14524011	C₂²	1	4	yes	complemented
68	C₂×#14524011	C₂²	1	4	yes	complemented
69	C₂×#14524011	C₂²	1	4	yes	complemented
70	C₂×C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
71	C₂×#14524008	C₂²	1	2	yes	complemented
72	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
73	C₂×D₄×Dic₆₇	C₂²	1	4	yes	complemented
74	C₂×#14524005	C₂²	1	2	yes	complemented
75	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
76	C₂×C₄×C₂²⋊D₆₇	C₂²	1	4	yes	complemented
77	C₂×#14524000	C₂²	1	2	yes	complemented
78	C₂²×(C₂×D₆₇)⋊C₄	C₂²	1	2	yes	complemented
79	C₂²×(C₂×D₆₇)⋊C₄	C₂²	1	4	yes	complemented
80	C₂²×(C₂×D₆₇)⋊C₄	C₂²	1	2	yes	complemented
81	C₂²×#41×C₆₇	C₂²	1	2	yes	complemented
82	#532×C₆₇	C₂²	1	16	yes	complemented
83	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
84	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic, complemented
85	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
86	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
87	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
88	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
89	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
90	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	C₂⁴×D₆₇	C₂³	1	2	yes	—
92	C₂⁴×D₆₇	C₂³	1	4	yes	—
93	C₂×#11761627	—	4	8	no	—
94	C₂×#11761627	C₂³	1	16	yes	complemented
95	C₂²×Dic₁₃₄	—	4	4	no	—
96	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
97	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
98	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
99	C₂²×Dic₁₃₄	C₂³	1	8	yes	complemented
100	C₂²×D₂₆₈	—	4	4	no	—
101	C₂²×D₂₆₈	C₂³	1	2	yes	—
102	C₂²×D₂₆₈	C₂³	1	8	yes	—
103	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
104	C₂²×D₂₆₈	C₂³	1	2	yes	—
105	C₂²×D₂₆₈	C₂³	1	4	yes	—
106	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
107	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
108	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
109	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
110	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
111	C₂×D₄×D₆₇	—	4	8	no	—
112	C₂×D₄×D₆₇	—	4	16	no	—
113	C₂×D₄×D₆₇	C₂³	1	32	yes	complemented
114	C₂×D₄×D₆₇	C₂³	1	16	yes	complemented
115	C₂³×Dic₆₇	C₂³	1	2	yes	—
116	C₂³×Dic₆₇	C₂³	1	4	yes	—
117	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
118	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
119	#14524039	C₂³	1	16	yes	—
120	#14524038	C₂³	1	32	yes	complemented
121	#14524037	C₂³	1	16	yes	complemented
122	#14524035	C₂³	1	8	yes	complemented
123	#14524032	C₂³	1	32	yes	complemented
124	#14524031	C₂³	1	16	yes	complemented
125	#14524031	C₂³	1	16	yes	complemented
126	#14524031	C₂³	1	8	yes	complemented
127	#14524031	C₂³	1	16	yes	complemented
128	#14524031	C₂³	1	16	yes	complemented
129	#14524030	C₂³	1	16	yes	complemented
130	#14524029	C₂³	1	32	yes	complemented
131	#14524029	C₂³	1	32	yes	complemented
132	#14524028	C₂³	1	32	yes	complemented
133	#14524027	C₂³	1	32	yes	complemented
134	#14524026	C₂³	1	16	yes	complemented
135	#14524026	C₂³	1	32	yes	complemented
136	#14524025	C₂³	1	32	yes	complemented
137	#14524023	C₂³	1	16	yes	complemented
138	#14524022	C₂³	1	8	yes	complemented
139	#14524020	C₂³	1	32	yes	complemented
140	#14524019	C₂³	1	32	yes	complemented
141	#14524018	C₂³	1	16	yes	—
142	#14524017	C₂³	1	8	yes	—
143	#14524017	C₂³	1	32	yes	complemented
144	#14524016	C₂³	1	32	yes	complemented
145	#14524015	C₂³	1	32	yes	complemented
146	#14524015	C₂³	1	32	yes	complemented
147	#14524015	C₂³	1	32	yes	complemented
148	#14524013	C₂³	1	32	yes	complemented
149	#14524013	C₂³	1	32	yes	complemented
150	#14524011	C₂³	1	32	yes	complemented
151	#14524011	C₂³	1	32	yes	complemented
152	#14524011	C₂³	1	32	yes	complemented
153	C₄×Dic₁₃₄	C₂³	1	8	yes	complemented
154	#14524008	C₂³	1	16	yes	complemented
155	C₄×D₂₆₈	C₂³	1	8	yes	complemented
156	D₄×Dic₆₇	C₂³	1	32	yes	complemented
157	#14524005	C₂³	1	16	yes	complemented
158	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
159	C₄×C₂²⋊D₆₇	C₂³	1	32	yes	complemented
160	#14524000	C₂³	1	16	yes	complemented
161	C₂×C₄⋊Dic₆₇	C₂³	1	4	yes	—
162	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
164	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
165	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
166	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
167	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
168	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	—
169	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
170	C₂×C₂²⋊Dic₆₇	C₂³	1	4	yes	—
171	C₂×C₂²⋊Dic₆₇	C₂³	1	4	yes	—
172	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
173	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
174	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
175	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
176	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
177	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
178	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
179	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
180	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
181	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
182	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
183	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	16	yes	complemented
184	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	32	yes	complemented
185	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	16	yes	complemented
186	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
187	C₂×C₄×Dic₆₇	C₂³	1	4	yes	—
188	C₂×#41×C₆₇	—	4	8	no	—
189	C₂×#41×C₆₇	C₂³	1	16	yes	complemented
190	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
191	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
192	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
193	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
194	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
195	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
196	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
197	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
198	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
199	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
200	#127×C₆₇	C₂³	1	8	yes	complemented
201	#124×C₆₇	C₂³	1	16	yes	complemented
202	#121×C₆₇	C₂³	1	16	yes	complemented
203	#121×C₆₇	C₂³	1	16	yes	complemented
204	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
205	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
206	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
207	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
209	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
210	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₆₇	C₂³	1	8	yes	complemented
215	C₂³×D₆₇	—	2	8	no	—
216	C₂³×D₆₇	—	4	8	no	—
217	C₂³×D₆₇	—	4	8	no	—
218	C₂³×D₆₇	—	4	4	no	—
219	C₂³×D₆₇	—	4	4	no	—
220	C₂³×D₆₇	—	4	8	no	—
221	C₂³×D₆₇	C₂⁴	1	2	yes	—
222	C₂³×D₆₇	C₂⁴	1	4	yes	—
223	C₂³×D₆₇	C₂⁴	1	8	yes	—
224	C₂³×D₆₇	C₂⁴	1	16	yes	—
225	#11761627	—	4	32	no	—
226	C₂×Dic₁₃₄	—	2	8	no	—
227	C₂×Dic₁₃₄	—	4	16	no	—
228	C₂×Dic₁₃₄	—	4	4	no	—
229	C₂×Dic₁₃₄	—	4	2	no	—
230	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
231	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
232	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
233	C₂×D₂₆₈	—	2	8	no	—
234	C₂×D₂₆₈	—	4	16	no	—
235	C₂×D₂₆₈	—	4	8	no	—
236	C₂×D₂₆₈	—	4	4	no	—
237	C₂×D₂₆₈	—	4	2	no	—
238	C₂×D₂₆₈	C₂⁴	1	8	yes	—
239	C₂×D₂₆₈	C₂⁴	1	4	yes	—
240	C₂×D₂₆₈	C₂⁴	1	8	yes	—
241	C₂×D₂₆₈	C₂⁴	1	16	yes	—
242	C₂×C₂²⋊D₆₇	—	2	8	no	—
243	C₂×C₂²⋊D₆₇	—	4	8	no	—
244	C₂×C₂²⋊D₆₇	—	4	8	no	—
245	C₂×C₂²⋊D₆₇	—	4	8	no	—
246	C₂×C₂²⋊D₆₇	—	4	8	no	—
247	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
248	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
249	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
250	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
251	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
252	D₄×D₆₇	—	4	32	no	—
253	D₄×D₆₇	—	4	64	no	—
254	C₂²×Dic₆₇	—	4	4	no	—
255	C₂²×Dic₆₇	—	4	8	no	—
256	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
257	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
258	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
259	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
260	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
261	C₂²×Dic₆₇	C₂⁴	1	16	yes	—
262	C₂×C₄×D₆₇	—	2	8	no	—
263	C₂×C₄×D₆₇	—	4	8	no	—
264	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
265	C₂×C₄×D₆₇	C₂⁴	1	16	yes	—
266	C₄⋊Dic₆₇	C₂⁴	1	16	yes	—
267	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
268	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
269	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
270	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
271	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
272	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
273	Dic₆₇⋊C₄	C₂⁴	1	16	yes	—
274	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
275	C₂²⋊Dic₆₇	C₂⁴	1	16	yes	—
276	C₂²⋊Dic₆₇	C₂⁴	1	16	yes	—
277	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
278	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
279	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
280	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
281	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
282	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
283	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
284	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
285	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
286	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
287	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
288	C₄×Dic₆₇	C₂⁴	1	8	yes	—
289	C₄×Dic₆₇	C₂⁴	1	16	yes	—
290	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
291	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
292	#41×C₆₇	—	4	32	no	—
293	C₂×Q₈×C₆₇	—	4	4	no	—
294	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
295	C₂×D₄×C₆₇	—	2	16	no	—
296	C₂×D₄×C₆₇	—	2	8	no	—
297	C₂×D₄×C₆₇	—	4	4	no	—
298	C₂×D₄×C₆₇	—	4	4	no	—
299	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
300	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
301	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
302	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
303	C₂²×C₄×C₆₇	—	2	4	no	—
304	C₂²×C₄×C₆₇	—	2	4	no	—
305	C₂²×C₄×C₆₇	—	4	2	no	—
306	C₂²×C₄×C₆₇	—	4	8	no	—
307	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
313	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
314	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
315	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
316	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
317	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
318	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
319	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
320	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
321	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
322	C₄²×C₆₇	C₂⁴	1	4	yes	—
323	C₄²×C₆₇	C₂⁴	1	4	yes	—
324	C₄²×C₆₇	C₂⁴	1	4	yes	—
325	C₄²×C₆₇	C₂⁴	1	4	yes	—
326	C₂³×C₆₇	—	2	2	no	—
327	C₂³×C₆₇	—	2	2	no	—
328	C₂³×C₆₇	—	2	8	no	—
329	C₂³×C₆₇	—	2	8	no	—
330	C₂³×C₆₇	—	2	8	no	—
331	C₂³×C₆₇	H(5,𝔽₂)	1	4	yes	—
332	C₂³×C₆₇	C₂⁵	1	8	yes	—
333	C₂³×C₆₇	C₂⁵	1	2	yes	—
334	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
335	C₂²×D₆₇	—	2	4	no	—
336	C₂²×D₆₇	—	2	8	no	—
337	C₂²×D₆₇	—	2	4	no	—
338	C₂²×D₆₇	—	2	8	no	—
339	C₂²×D₆₇	—	2	8	no	—
340	C₂²×D₆₇	—	2	4	no	—
341	C₂²×D₆₇	—	2	16	no	—
342	C₂²×D₆₇	—	4	16	no	—
343	C₂²×D₆₇	—	4	16	no	—
344	C₂²×D₆₇	—	4	8	no	—
345	C₂²×D₆₇	—	4	16	no	—
346	C₂²×D₆₇	—	4	8	no	—
347	C₂²×D₆₇	—	8	16	no	—
348	C₂²×D₆₇	—	8	32	no	—
349	C₂²×D₆₇	C₂⁵	1	4	yes	—
350	C₂²×D₆₇	C₂⁵	1	8	yes	—
351	Q₈×C₆₇	—	4	8	no	—
352	D₄×C₆₇	—	2	32	no	—
353	D₄×C₆₇	—	2	16	no	—
354	D₄×C₆₇	—	4	8	no	—
355	D₄×C₆₇	—	4	8	no	—
356	C₂×C₄×C₆₇	—	2	2	no	—
357	C₂×C₄×C₆₇	—	2	2	no	—
358	C₂×C₄×C₆₇	—	2	8	no	—
359	C₂×C₄×C₆₇	—	2	2	no	—
360	C₂×C₄×C₆₇	—	2	8	no	—
361	C₂×C₄×C₆₇	—	2	2	no	—
362	C₂×C₄×C₆₇	—	2	2	no	—
363	C₂×C₄×C₆₇	—	2	8	no	—
364	C₂×C₄×C₆₇	—	4	4	no	—
365	C₂×C₄×C₆₇	—	4	16	no	—
366	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
367	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
368	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
369	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
370	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
371	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
372	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
373	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
374	C₂²⋊D₆₇	—	2	16	no	—
375	C₂²⋊D₆₇	—	4	16	no	—
376	C₂²⋊D₆₇	—	4	16	no	—
377	C₂²⋊D₆₇	—	4	16	no	—
378	C₂²⋊D₆₇	—	4	16	no	—
379	C₂×Dic₆₇	—	2	4	no	—
380	C₂×Dic₆₇	—	2	4	no	—
381	C₂×Dic₆₇	—	2	8	no	—
382	C₂×Dic₆₇	—	2	4	no	—
383	C₂×Dic₆₇	—	4	8	no	—
384	C₂×Dic₆₇	—	4	16	no	—
385	C₂×Dic₆₇	C₂⁵	1	4	yes	—
386	C₂×Dic₆₇	C₂⁵	1	8	yes	—
387	C₂×Dic₆₇	C₂⁵	1	4	yes	—
388	C₂×Dic₆₇	C₂⁵	1	4	yes	—
389	D₂₆₈	—	2	16	no	—
390	D₂₆₈	—	4	16	no	—
391	D₂₆₈	—	4	8	no	—
392	D₂₆₈	—	4	4	no	—
393	C₄×D₆₇	—	2	16	no	—
394	C₄×D₆₇	—	4	16	no	—
395	Dic₁₃₄	—	2	16	no	—
396	Dic₁₃₄	—	4	8	no	—
397	Dic₁₃₄	—	4	4	no	—
398	C₂²×C₆₇	—	2	2	no	—
399	C₂²×C₆₇	—	2	2	no	—
400	C₂²×C₆₇	—	2	8	no	—
401	C₂²×C₆₇	—	2	8	no	—
402	C₂²×C₆₇	—	2	8	no	—
403	C₂²×C₆₇	—	2	8	no	—
404	C₂²×C₆₇	—	4	16	no	—
405	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
406	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
407	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
408	C₂²×C₆₇	#585	1	2	yes	—
409	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
410	C₂×D₆₇	—	2	4	no	—
411	C₂×D₆₇	—	2	8	no	—
412	C₂×D₆₇	—	2	8	no	—
413	C₂×D₆₇	—	2	4	no	—
414	C₂×D₆₇	—	2	4	no	—
415	C₂×D₆₇	—	2	8	no	—
416	C₂×D₆₇	—	4	8	no	—
417	C₂×D₆₇	—	4	16	no	—
418	C₂×D₆₇	—	8	16	no	—
419	C₂×D₆₇	—	8	32	no	—
420	C₄×C₆₇	—	2	2	no	—
421	C₄×C₆₇	—	2	8	no	—
422	C₄×C₆₇	—	2	2	no	—
423	C₄×C₆₇	—	2	2	no	—
424	C₄×C₆₇	—	2	2	no	—
425	C₄×C₆₇	—	2	2	no	—
426	C₄×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
427	Dic₆₇	—	2	8	no	—
428	Dic₆₇	—	2	4	no	—
429	Dic₆₇	—	2	4	no	—
430	Dic₆₇	—	2	4	no	—
431	C₂×#3558	—	67	1	no	maximal, Sylow
432	C₂×C₆₇	—	2	4	no	—
433	C₂×C₆₇	—	4	8	no	—
434	C₂×C₆₇	#3558	1	4	yes	complemented
435	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
436	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
437	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
438	D₆₇	—	4	4	no	—
439	D₆₇	—	4	8	no	—
440	#3558	—	67	32	no	—
441	C₂×#562	—	67	2	no	—
442	C₂×H(3,𝔽₄)	—	67	2	no	—
443	C₂×#559	—	67	2	no	—
444	C₂×#548	—	67	2	no	—
445	C₂×#546	—	67	4	no	—
446	C₂×#546	—	67	2	no	—
447	C₂×D₄²	—	67	2	no	—
448	C₂×#542	—	67	2	no	—
449	C₂×#538	—	67	2	no	—
450	C₂×#538	—	67	4	no	—
451	C₂×#535	—	67	2	no	—
452	C₂×#534	—	67	2	no	—
453	C₂×#532	D₆₇	1	1	yes	characteristic, complemented
454	C₂×#529	—	67	1	no	—
455	C₂²×#124	—	67	1	no	—
456	C₆₇	C₂×#3558	1	1	yes	characteristic, complemented, Sylow
457	C₂²×#41	—	67	2	no	—
458	C₂²×#41	C₂×D₆₇	1	2	yes	complemented
459	C₂³×Q₈	—	67	1	no	—
460	C₂³×D₄	—	67	4	no	—
461	C₂³×D₄	—	67	2	no	—
462	C₂³×D₄	—	67	1	no	—
463	#562	—	67	32	no	—
464	H(3,𝔽₄)	—	67	32	no	—
465	#559	—	67	32	no	—
466	#548	—	67	32	no	—
467	#546	—	67	64	no	—
468	#546	—	67	32	no	—
469	D₄²	—	67	32	no	—
470	#542	—	67	32	no	—
471	#538	—	67	32	no	—
472	#538	—	67	64	no	—
473	#535	—	67	32	no	—
474	#534	—	67	32	no	—
475	#532	C₂×D₆₇	1	16	yes	complemented
476	C₂×C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
477	C₂×#127	—	67	2	no	—
478	C₂×#127	C₂×D₆₇	1	1	yes	characteristic, complemented
479	#529	—	67	16	no	—
480	C₂×#126	—	67	4	no	—
481	C₂×#126	—	67	2	no	—
482	C₂×#125	—	67	1	no	—
483	C₂×#124	—	67	4	no	—
484	C₂×#124	—	67	2	no	—
485	C₂×#124	—	67	4	no	—
486	C₂×#124	—	67	4	no	—
487	C₂×#124	—	67	2	no	—
488	C₂×#124	—	67	2	no	—
489	C₂×#124	—	67	2	no	—
490	C₂×#124	—	67	2	no	—
491	C₂×#124	—	67	1	no	—
492	C₂×#124	—	67	16	no	—
493	C₂×#124	C₂×D₆₇	1	2	yes	complemented
494	C₂×#123	—	67	2	no	—
495	C₂×#123	—	67	4	no	—
496	C₂×#123	—	67	4	no	—
497	C₂×#123	—	67	4	no	—
498	C₂×#123	—	67	4	no	—
499	C₂×C₂²⋊Q₈	—	67	4	no	—
500	C₂×C₂²⋊Q₈	—	67	1	no	—
501	C₂×C₂²⋊Q₈	—	67	2	no	—
502	C₂×C₂²⋊Q₈	—	67	4	no	—
503	C₂×#121	—	67	4	no	—
504	C₂×#121	—	67	4	no	—
505	C₂×#121	—	67	4	no	—
506	C₂×#121	—	67	1	no	—
507	C₂×#121	—	67	4	no	—
508	C₂×#121	—	67	2	no	—
509	C₂×#121	—	67	4	no	—
510	C₂×#121	C₂×D₆₇	1	2	yes	complemented
511	C₂×#121	C₂×D₆₇	1	2	yes	complemented
512	C₂×#120	—	67	4	no	—
513	C₂×#120	—	67	4	no	—
514	C₂×#120	—	67	4	no	—
515	C₂×#120	—	67	4	no	—
516	C₂×#120	—	67	4	no	—
517	C₂×C₄×Q₈	—	67	2	no	—
518	C₂×C₄×Q₈	—	67	1	no	—
519	C₂×C₄×D₄	—	67	4	no	—
520	C₂×C₄×D₄	—	67	2	no	—
521	C₂×C₄×D₄	—	67	4	no	—
522	C₂×C₄×D₄	—	67	2	no	—
523	C₂×C₄×D₄	—	67	1	no	—
524	C₂×C₄×D₄	C₂×D₆₇	1	2	yes	complemented
525	C₂×C₄×D₄	C₂×D₆₇	1	2	yes	complemented
526	C₂×#117	—	67	2	no	—
527	C₂²×C₂²⋊C₄	—	67	2	no	—
528	C₂²×C₂²⋊C₄	—	67	2	no	—
529	C₂²×C₂²⋊C₄	—	67	4	no	—
530	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic, complemented
531	C₂⁵	—	67	4	no	—
532	C₂⁵	—	67	2	no	—
533	C₂×#41	—	4	8	no	—
534	C₂×#41	—	268	8	no	—
535	C₂×#41	—	67	16	no	—
536	C₂×#41	C₂²×D₆₇	1	16	yes	complemented
537	C₂²×Q₈	—	268	4	no	—
538	C₂²×Q₈	—	67	1	no	—
539	C₂²×Q₈	—	67	2	no	—
540	C₂²×Q₈	—	67	8	no	—
541	C₂²×Q₈	—	67	2	no	—
542	C₂²×Q₈	C₂²×D₆₇	1	2	yes	—
543	C₂²×D₄	—	268	4	no	—
544	C₂²×D₄	—	268	16	no	—
545	C₂²×D₄	—	268	8	no	—
546	C₂²×D₄	—	67	4	no	—
547	C₂²×D₄	—	67	4	no	—
548	C₂²×D₄	—	67	4	no	—
549	C₂²×D₄	—	67	4	no	—
550	C₂²×D₄	—	67	32	no	—
551	C₂²×D₄	—	67	16	no	—
552	C₂²×D₄	—	67	2	no	—
553	C₂²×D₄	—	67	1	no	—
554	C₂²×D₄	—	67	4	no	—
555	C₂²×D₄	—	67	2	no	—
556	C₂²×D₄	—	67	8	no	—
557	C₂²×D₄	—	67	2	no	—
558	C₂²×D₄	C₂²×D₆₇	1	4	yes	—
559	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
560	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
561	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
562	C₂³×C₄	—	67	2	no	—
563	C₂³×C₄	—	67	4	no	—
564	C₂³×C₄	—	67	4	no	—
565	C₂³×C₄	—	67	2	no	—
566	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
567	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
568	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
569	C₂³×C₄	C₂²×D₆₇	1	4	yes	—
570	C₄⋊Q₈	C₂²×D₆₇	1	8	yes	complemented
571	#127	—	67	16	no	—
572	#127	C₂²×D₆₇	1	8	yes	complemented
573	#126	—	67	32	no	—
574	#126	—	67	16	no	—
575	#125	—	67	8	no	—
576	#124	—	67	32	no	—
577	#124	—	67	16	no	—
578	#124	—	67	32	no	—
579	#124	—	67	32	no	—
580	#124	—	67	16	no	—
581	#124	—	67	16	no	—
582	#124	—	67	16	no	—
583	#124	—	67	16	no	—
584	#124	—	67	8	no	—
585	#124	C₂²×D₆₇	1	16	yes	complemented
586	#123	—	67	16	no	—
587	#123	—	67	32	no	—
588	#123	—	67	32	no	—
589	#123	—	67	32	no	—
590	#123	—	67	32	no	—
591	C₂²⋊Q₈	—	67	32	no	—
592	C₂²⋊Q₈	—	67	8	no	—
593	C₂²⋊Q₈	—	67	16	no	—
594	C₂²⋊Q₈	—	67	32	no	—
595	#121	—	67	32	no	—
596	#121	—	67	32	no	—
597	#121	—	67	32	no	—
598	#121	—	67	8	no	—
599	#121	—	67	32	no	—
600	#121	—	67	16	no	—
601	#121	—	67	32	no	—
602	#121	C₂²×D₆₇	1	16	yes	complemented
603	#121	C₂²×D₆₇	1	16	yes	complemented
604	#120	—	67	32	no	—
605	#120	—	67	32	no	—
606	#120	—	67	32	no	—
607	#120	—	67	32	no	—
608	#120	—	67	32	no	—
609	C₄×Q₈	—	67	16	no	—
610	C₄×Q₈	—	67	8	no	—
611	C₄×D₄	—	67	32	no	—
612	C₄×D₄	—	67	16	no	—
613	C₄×D₄	—	67	32	no	—
614	C₄×D₄	—	67	16	no	—
615	C₄×D₄	—	67	8	no	—
616	C₄×D₄	C₂²×D₆₇	1	16	yes	complemented
617	C₄×D₄	C₂²×D₆₇	1	16	yes	complemented
618	#117	—	67	16	no	—
619	C₂×C₄⋊C₄	—	67	2	no	—
620	C₂×C₄⋊C₄	—	67	2	no	—
621	C₂×C₄⋊C₄	—	67	2	no	—
622	C₂×C₄⋊C₄	—	67	2	no	—
623	C₂×C₄⋊C₄	—	67	4	no	—
624	C₂×C₄⋊C₄	—	67	1	no	—
625	C₂×C₄⋊C₄	—	67	4	no	—
626	C₂×C₄⋊C₄	—	67	1	no	—
627	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
628	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
629	C₂×C₂²⋊C₄	—	67	2	no	—
630	C₂×C₂²⋊C₄	—	67	4	no	—
631	C₂×C₂²⋊C₄	—	67	4	no	—
632	C₂×C₂²⋊C₄	—	67	2	no	—
633	C₂×C₂²⋊C₄	—	67	4	no	—
634	C₂×C₂²⋊C₄	—	67	4	no	—
635	C₂×C₂²⋊C₄	—	67	4	no	—
636	C₂×C₂²⋊C₄	—	67	4	no	—
637	C₂×C₂²⋊C₄	—	67	4	no	—
638	C₂×C₂²⋊C₄	—	67	4	no	—
639	C₂×C₂²⋊C₄	—	67	16	no	—
640	C₂×C₂²⋊C₄	—	67	16	no	—
641	C₂×C₂²⋊C₄	—	67	32	no	—
642	C₂×C₂²⋊C₄	—	67	2	no	—
643	C₂×C₂²⋊C₄	—	67	2	no	—
644	C₂×C₂²⋊C₄	—	67	4	no	—
645	C₂×C₂²⋊C₄	—	67	2	no	—
646	C₂×C₂²⋊C₄	C₂²×D₆₇	1	4	yes	—
647	C₂×C₂²⋊C₄	C₂²×D₆₇	1	4	yes	—
648	C₂×C₄²	—	67	2	no	—
649	C₂×C₄²	—	67	4	no	—
650	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
651	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
652	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
653	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
654	C₂×C₄²	C₂²×D₆₇	1	8	yes	complemented
655	C₂⁴	—	268	4	no	—
656	C₂⁴	—	268	8	no	—
657	C₂⁴	—	268	8	no	—
658	C₂⁴	—	268	4	no	—
659	C₂⁴	—	268	8	no	—
660	C₂⁴	—	67	16	no	—
661	C₂⁴	—	67	8	no	—
662	C₂⁴	—	67	4	no	—
663	C₂⁴	—	67	2	no	—
664	C₂⁴	—	134	8	no	—
665	C₂⁴	C₂³×D₆₇	1	4	yes	—
666	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
667	#41	—	4	32	no	—
668	#41	—	268	32	no	—
669	C₂×Q₈	—	4	4	no	—
670	C₂×Q₈	—	268	16	no	—
671	C₂×Q₈	—	268	4	no	—
672	C₂×Q₈	—	268	2	no	—
673	C₂×Q₈	—	67	4	no	—
674	C₂×Q₈	—	67	8	no	—
675	C₂×Q₈	—	67	8	no	—
676	C₂×Q₈	—	134	8	no	—
677	C₂×Q₈	C₂³×D₆₇	1	8	yes	—
678	C₂×D₄	—	2	16	no	—
679	C₂×D₄	—	2	8	no	—
680	C₂×D₄	—	4	4	no	—
681	C₂×D₄	—	4	4	no	—
682	C₂×D₄	—	268	8	no	—
683	C₂×D₄	—	268	4	no	—
684	C₂×D₄	—	268	2	no	—
685	C₂×D₄	—	268	16	no	—
686	C₂×D₄	—	268	64	no	—
687	C₂×D₄	—	268	32	no	—
688	C₂×D₄	—	268	8	no	—
689	C₂×D₄	—	268	8	no	—
690	C₂×D₄	—	268	8	no	—
691	C₂×D₄	—	268	8	no	—
692	C₂×D₄	—	67	16	no	—
693	C₂×D₄	—	67	16	no	—
694	C₂×D₄	—	67	16	no	—
695	C₂×D₄	—	67	16	no	—
696	C₂×D₄	—	67	8	no	—
697	C₂×D₄	—	67	4	no	—
698	C₂×D₄	—	67	16	no	—
699	C₂×D₄	—	67	8	no	—
700	C₂×D₄	—	67	8	no	—
701	C₂×D₄	—	134	8	no	—
702	C₂×D₄	—	134	8	no	—
703	C₂×D₄	C₂³×D₆₇	1	16	yes	—
704	C₂×D₄	C₂³×D₆₇	1	8	yes	—
705	C₂×D₄	C₂³×D₆₇	1	8	yes	—
706	C₂×D₄	C₂³×D₆₇	1	8	yes	—
707	C₂²×C₄	—	2	4	no	—
708	C₂²×C₄	—	2	4	no	—
709	C₂²×C₄	—	4	8	no	—
710	C₂²×C₄	—	4	2	no	—
711	C₂²×C₄	—	268	8	no	—
712	C₂²×C₄	—	268	4	no	—
713	C₂²×C₄	—	268	8	no	—
714	C₂²×C₄	—	67	8	no	—
715	C₂²×C₄	—	67	16	no	—
716	C₂²×C₄	—	67	16	no	—
717	C₂²×C₄	—	67	2	no	—
718	C₂²×C₄	—	67	4	no	—
719	C₂²×C₄	—	67	2	no	—
720	C₂²×C₄	—	67	2	no	—
721	C₂²×C₄	—	67	8	no	—
722	C₂²×C₄	—	134	8	no	—
723	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
724	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
725	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
726	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
727	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
728	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
729	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
730	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
731	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
732	C₂²×C₄	C₂³×D₆₇	1	16	yes	—
733	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
734	C₄⋊C₄	—	67	8	no	—
735	C₄⋊C₄	—	67	8	no	—
736	C₄⋊C₄	—	67	8	no	—
737	C₄⋊C₄	—	67	8	no	—
738	C₄⋊C₄	—	67	16	no	—
739	C₄⋊C₄	—	67	4	no	—
740	C₄⋊C₄	—	67	16	no	—
741	C₄⋊C₄	—	67	4	no	—
742	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
743	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
744	C₂²⋊C₄	—	67	8	no	—
745	C₂²⋊C₄	—	67	16	no	—
746	C₂²⋊C₄	—	67	16	no	—
747	C₂²⋊C₄	—	67	8	no	—
748	C₂²⋊C₄	—	67	16	no	—
749	C₂²⋊C₄	—	67	16	no	—
750	C₂²⋊C₄	—	67	16	no	—
751	C₂²⋊C₄	—	67	16	no	—
752	C₂²⋊C₄	—	67	16	no	—
753	C₂²⋊C₄	—	67	16	no	—
754	C₂²⋊C₄	—	67	8	no	—
755	C₂²⋊C₄	—	67	8	no	—
756	C₂²⋊C₄	—	67	16	no	—
757	C₂²⋊C₄	—	67	8	no	—
758	C₂²⋊C₄	C₂³×D₆₇	1	16	yes	—
759	C₂²⋊C₄	C₂³×D₆₇	1	16	yes	—
760	C₄²	—	67	8	no	—
761	C₄²	—	67	16	no	—
762	C₄²	C₂³×D₆₇	1	4	yes	—
763	C₄²	C₂³×D₆₇	1	4	yes	—
764	C₄²	C₂³×D₆₇	1	4	yes	—
765	C₄²	C₂³×D₆₇	1	4	yes	—
766	C₂³	—	2	2	no	—
767	C₂³	—	2	2	no	—
768	C₂³	—	2	8	no	—
769	C₂³	—	2	8	no	—
770	C₂³	—	2	8	no	—
771	C₂³	—	268	8	no	—
772	C₂³	—	268	16	no	—
773	C₂³	—	268	16	no	—
774	C₂³	—	268	8	no	—
775	C₂³	—	268	16	no	—
776	C₂³	—	536	16	no	—
777	C₂³	—	536	32	no	—
778	C₂³	—	67	8	no	—
779	C₂³	—	67	4	no	—
780	C₂³	—	134	8	no	—
781	C₂³	—	134	4	no	—
782	C₂³	—	134	4	no	—
783	C₂³	—	134	8	no	—
784	C₂³	—	134	4	no	—
785	C₂³	—	134	8	no	—
786	C₂³	—	134	16	no	—
787	C₂³	#14524088	1	4	yes	—
788	C₂³	C₂⁴×D₆₇	1	8	yes	—
789	C₂³	C₂⁴×D₆₇	1	2	yes	—
790	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
791	Q₈	—	4	8	no	—
792	Q₈	—	268	8	no	—
793	Q₈	—	268	4	no	—
794	Q₈	—	134	16	no	—
795	D₄	—	2	32	no	—
796	D₄	—	2	16	no	—
797	D₄	—	4	8	no	—
798	D₄	—	4	8	no	—
799	D₄	—	268	16	no	—
800	D₄	—	268	8	no	—
801	D₄	—	268	4	no	—
802	D₄	—	268	16	no	—
803	D₄	—	268	16	no	—
804	D₄	—	268	16	no	—
805	D₄	—	268	16	no	—
806	D₄	—	134	16	no	—
807	D₄	—	134	16	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	8	no	—
811	C₂×C₄	—	2	8	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	8	no	—
816	C₂×C₄	—	4	16	no	—
817	C₂×C₄	—	4	4	no	—
818	C₂×C₄	—	268	16	no	—
819	C₂×C₄	—	268	8	no	—
820	C₂×C₄	—	268	16	no	—
821	C₂×C₄	—	67	4	no	—
822	C₂×C₄	—	67	8	no	—
823	C₂×C₄	—	67	4	no	—
824	C₂×C₄	—	67	4	no	—
825	C₂×C₄	—	134	4	no	—
826	C₂×C₄	—	134	4	no	—
827	C₂×C₄	—	134	8	no	—
828	C₂×C₄	—	134	4	no	—
829	C₂×C₄	—	134	16	no	—
830	C₂×C₄	#14524089	1	4	yes	—
831	C₂×C₄	C₂⁴×D₆₇	1	8	yes	—
832	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
833	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
834	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
835	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
836	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
837	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
838	C₂²	—	2	8	no	—
839	C₂²	—	2	2	no	—
840	C₂²	—	2	2	no	—
841	C₂²	—	2	8	no	—
842	C₂²	—	2	8	no	—
843	C₂²	—	2	8	no	—
844	C₂²	—	4	16	no	—
845	C₂²	—	268	16	no	—
846	C₂²	—	268	8	no	—
847	C₂²	—	536	16	no	—
848	C₂²	—	536	32	no	—
849	C₂²	—	134	8	no	—
850	C₂²	—	134	4	no	—
851	C₂²	—	134	4	no	—
852	C₂²	—	134	8	no	—
853	C₂²	—	134	4	no	—
854	C₂²	—	134	8	no	—
855	C₂²	C₂×#14524088	1	4	yes	—
856	C₂²	C₂×#14524088	1	2	yes	—
857	C₂²	C₂×#14524089	1	2	yes	—
858	C₂²	#16864232	1	2	yes	—
859	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
860	C₄	—	2	2	no	—
861	C₄	—	2	2	no	—
862	C₄	—	2	8	no	—
863	C₄	—	2	2	no	—
864	C₄	—	2	2	no	—
865	C₄	—	2	2	no	—
866	C₄	—	134	4	no	—
867	C₄	—	134	4	no	—
868	C₄	—	134	8	no	—
869	C₄	—	134	4	no	—
870	C₄	C₂×#14524089	1	4	yes	—
871	C₂	—	2	4	no	—
872	C₂	—	4	8	no	—
873	C₂	—	268	8	no	—
874	C₂	—	268	4	no	—
875	C₂	#22574732	1	4	yes	direct product factor
876	C₂	C₂²×#14524088	1	1	yes	characteristic
877	C₂	C₂²×#14524089	1	1	yes	characteristic
878	C₂	C₂×#16864232	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₆₇
commutator, cosocle	C₂²×C₆₇	C₂⁶
Frattini	C₂²	C₂⁵×D₆₇
Fitting	C₂×#532×C₆₇	C₂
socle	C₂³×C₆₇	C₂⁵
hypercenter	C₂×#532	D₆₇
hypocenter	C₆₇	C₂×#3558
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. #22574732	C₂	direct (N × H)
2. C₂×#16864140	C₂	semidirect
3. C₂×#16864138	C₂	semidirect
4. C₂×#16864129	C₂	semidirect
5. C₂×#16864052	C₂	semidirect
6. C₂×#16864041	C₂	semidirect
7. C₂×#16864034	C₂	semidirect
8. C₂×#16864030	C₂	semidirect
9. C₂×#16864020	C₂	semidirect
10. C₂×#16863983	C₂	semidirect
11. C₂×#16863979	C₂	semidirect
12. C₂×#16863959	C₂	semidirect
13. C₂×#16863954	C₂	semidirect
14. C₂×#16863930	C₂	semidirect
15. C₂²×#14524031	C₂	semidirect
16. C₂×#532×C₆₇	C₂	semidirect
17. C₂²×#11761627	C₂²	semidirect
18. C₂³×Dic₁₃₄	C₂²	semidirect
20. C₂²×D₄×D₆₇	C₂²	semidirect
21. C₂²×D₄×D₆₇	C₂²	semidirect
22. #16864140	C₂²	semidirect
23. #16864138	C₂²	semidirect
24. #16864129	C₂²	semidirect
25. #16864052	C₂²	semidirect
26. #16864041	C₂²	semidirect
27. #16864034	C₂²	semidirect
28. #16864030	C₂²	semidirect
29. #16864020	C₂²	semidirect
30. #16863983	C₂²	semidirect
31. #16863979	C₂²	semidirect
32. #16863959	C₂²	semidirect
33. #16863954	C₂²	semidirect
35. #16863930	C₂²	semidirect
36. C₂×#14524038	C₂²	semidirect
37. C₂×#14524037	C₂²	semidirect
38. C₂×#14524035	C₂²	semidirect
39. C₂×#14524032	C₂²	semidirect
40. C₂×#14524031	C₂²	semidirect
41. C₂×#14524031	C₂²	semidirect
42. C₂×#14524031	C₂²	semidirect
43. C₂×#14524031	C₂²	semidirect
44. C₂×#14524031	C₂²	semidirect
45. C₂×#14524031	C₂²	semidirect
46. C₂×#14524030	C₂²	semidirect
47. C₂×#14524029	C₂²	semidirect
48. C₂×#14524029	C₂²	semidirect
49. C₂×#14524028	C₂²	semidirect
50. C₂×#14524027	C₂²	semidirect
51. C₂×#14524026	C₂²	semidirect
52. C₂×#14524026	C₂²	semidirect
53. C₂×#14524025	C₂²	semidirect
54. C₂×#14524023	C₂²	semidirect
55. C₂×#14524022	C₂²	semidirect
56. C₂×#14524020	C₂²	semidirect
57. C₂×#14524019	C₂²	semidirect
60. C₂×#14524017	C₂²	semidirect
61. C₂×#14524016	C₂²	semidirect
62. C₂×#14524015	C₂²	semidirect
63. C₂×#14524015	C₂²	semidirect
64. C₂×#14524015	C₂²	semidirect
65. C₂×#14524013	C₂²	semidirect
66. C₂×#14524013	C₂²	semidirect
67. C₂×#14524011	C₂²	semidirect
68. C₂×#14524011	C₂²	semidirect
69. C₂×#14524011	C₂²	semidirect
70. C₂×C₄×Dic₁₃₄	C₂²	semidirect
71. C₂×#14524008	C₂²	semidirect
72. C₂×C₄×D₂₆₈	C₂²	semidirect
73. C₂×D₄×Dic₆₇	C₂²	semidirect
74. C₂×#14524005	C₂²	semidirect
75. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
76. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
77. C₂×#14524000	C₂²	semidirect
78. C₂²×(C₂×D₆₇)⋊C₄	C₂²	semidirect
79. C₂²×(C₂×D₆₇)⋊C₄	C₂²	semidirect
80. C₂²×(C₂×D₆₇)⋊C₄	C₂²	semidirect
81. C₂²×#41×C₆₇	C₂²	semidirect
82. #532×C₆₇	C₂²	semidirect
83. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
84. C₂×#127×C₆₇	C₂²	semidirect
85. C₂×#124×C₆₇	C₂²	semidirect
86. C₂×#121×C₆₇	C₂²	semidirect
87. C₂×#121×C₆₇	C₂²	semidirect
88. C₂×C₄×D₄×C₆₇	C₂²	semidirect
89. C₂×C₄×D₄×C₆₇	C₂²	semidirect
90. C₂²×C₄²×C₆₇	C₂²	semidirect
94. C₂×#11761627	C₂³	semidirect
99. C₂²×Dic₁₃₄	C₂³	semidirect
113. C₂×D₄×D₆₇	C₂³	semidirect
114. C₂×D₄×D₆₇	C₂³	semidirect
120. #14524038	C₂³	semidirect
121. #14524037	C₂³	semidirect
122. #14524035	C₂³	semidirect
123. #14524032	C₂³	semidirect
124. #14524031	C₂³	semidirect
125. #14524031	C₂³	semidirect
126. #14524031	C₂³	semidirect
127. #14524031	C₂³	semidirect
128. #14524031	C₂³	semidirect
129. #14524030	C₂³	semidirect
130. #14524029	C₂³	semidirect
131. #14524029	C₂³	semidirect
132. #14524028	C₂³	semidirect
133. #14524027	C₂³	semidirect
134. #14524026	C₂³	semidirect
135. #14524026	C₂³	semidirect
136. #14524025	C₂³	semidirect
137. #14524023	C₂³	semidirect
138. #14524022	C₂³	semidirect
139. #14524020	C₂³	semidirect
140. #14524019	C₂³	semidirect
143. #14524017	C₂³	semidirect
144. #14524016	C₂³	semidirect
145. #14524015	C₂³	semidirect
146. #14524015	C₂³	semidirect
147. #14524015	C₂³	semidirect
148. #14524013	C₂³	semidirect
149. #14524013	C₂³	semidirect
150. #14524011	C₂³	semidirect
151. #14524011	C₂³	semidirect
152. #14524011	C₂³	semidirect
153. C₄×Dic₁₃₄	C₂³	semidirect
154. #14524008	C₂³	semidirect
155. C₄×D₂₆₈	C₂³	semidirect
156. D₄×Dic₆₇	C₂³	semidirect
157. #14524005	C₂³	semidirect
158. C₄×C₂²⋊D₆₇	C₂³	semidirect
159. C₄×C₂²⋊D₆₇	C₂³	semidirect
160. #14524000	C₂³	semidirect
183. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
184. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
185. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
189. C₂×#41×C₆₇	C₂³	semidirect
199. C₄⋊Q₈×C₆₇	C₂³	semidirect
200. #127×C₆₇	C₂³	semidirect
201. #124×C₆₇	C₂³	semidirect
202. #121×C₆₇	C₂³	semidirect
203. #121×C₆₇	C₂³	semidirect
204. C₄×D₄×C₆₇	C₂³	semidirect
205. C₄×D₄×C₆₇	C₂³	semidirect
214. C₂×C₄²×C₆₇	C₂³	semidirect
434. C₂×C₆₇	#3558	semidirect
453. C₂×#532	D₆₇	semidirect
456. C₆₇	C₂×#3558	semidirect
458. C₂²×#41	C₂×D₆₇	semidirect
475. #532	C₂×D₆₇	semidirect
476. C₂×C₄⋊Q₈	C₂×D₆₇	semidirect
478. C₂×#127	C₂×D₆₇	semidirect
493. C₂×#124	C₂×D₆₇	semidirect
510. C₂×#121	C₂×D₆₇	semidirect
511. C₂×#121	C₂×D₆₇	semidirect
524. C₂×C₄×D₄	C₂×D₆₇	semidirect
525. C₂×C₄×D₄	C₂×D₆₇	semidirect
530. C₂²×C₄²	C₂×D₆₇	semidirect
536. C₂×#41	C₂²×D₆₇	semidirect
570. C₄⋊Q₈	C₂²×D₆₇	semidirect
572. #127	C₂²×D₆₇	semidirect
585. #124	C₂²×D₆₇	semidirect
602. #121	C₂²×D₆₇	semidirect
603. #121	C₂²×D₆₇	semidirect
616. C₄×D₄	C₂²×D₆₇	semidirect
617. C₄×D₄	C₂²×D₆₇	semidirect
654. C₂×C₄²	C₂²×D₆₇	semidirect
875. C₂	#22574732	direct (N × H)

Maximal subgroups

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

subgroup	index
#22574732	2
C₂×#16864140	2
C₂×#16864138	2
C₂×#16864129	2
C₂×#16864052	2
C₂×#16864041	2
C₂×#16864034	2
C₂×#16864030	2
C₂×#16864020	2
C₂×#16863983	2
C₂×#16863979	2
C₂×#16863959	2
C₂×#16863954	2
C₂×#16863930	2
C₂²×#14524031	2
C₂×#532×C₆₇	2
C₂×#3558	67

Subgroups — C2×#22574732 #31763161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22574732 #31763161