Subgroups — C₂×#22573944 #31764178

Order 17152.

8006 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22573944	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16864109	C₂	1	2	yes	maximal, complemented
3	C₂×#16864094	C₂	1	2	yes	maximal, complemented
4	C₂×#16864090	C₂	1	2	yes	maximal, complemented
5	C₂×#16864070	C₂	1	4	yes	maximal, complemented
6	C₂×#16864047	C₂	1	2	yes	maximal, complemented
7	C₂×#16864036	C₂	1	4	yes	maximal, complemented
8	C₂×#16864024	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#16864017	C₂	1	2	yes	maximal, complemented
10	C₂×#16864001	C₂	1	2	yes	maximal, complemented
11	C₂×#16863965	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#16863946	C₂	1	2	yes	maximal, complemented
13	C₂×#16863930	C₂	1	2	yes	maximal, complemented
14	C₂×#16863907	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#14524017	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#16863876	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#16863870	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#117×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#11761628	C₂²	1	1	yes	characteristic
20	C₂²×#11761628	C₂²	1	4	yes	complemented
21	C₂³×D₂₆₈	C₂²	1	1	yes	characteristic
22	C₂³×C₂²⋊D₆₇	C₂²	1	2	yes	—
23	#16864109	C₂²	1	32	yes	complemented
24	#16864094	C₂²	1	32	yes	complemented
25	#16864090	C₂²	1	32	yes	complemented
26	#16864070	C₂²	1	64	yes	complemented
27	#16864047	C₂²	1	32	yes	complemented
28	#16864036	C₂²	1	64	yes	complemented
29	#16864024	C₂²	1	16	yes	complemented
30	#16864017	C₂²	1	32	yes	complemented
31	#16864001	C₂²	1	32	yes	complemented
32	#16863965	C₂²	1	16	yes	complemented
33	#16863946	C₂²	1	32	yes	complemented
34	C₂×#14524043	C₂²	1	2	yes	complemented
35	C₂×#14524042	C₂²	1	2	yes	complemented
36	C₂×#14524040	C₂²	1	2	yes	complemented
37	#16863930	C₂²	1	32	yes	complemented
38	C₂×#14524038	C₂²	1	4	yes	complemented
39	C₂×#14524037	C₂²	1	4	yes	complemented
40	C₂×#14524035	C₂²	1	2	yes	complemented
41	C₂×#14524034	C₂²	1	2	yes	complemented
42	C₂×#14524031	C₂²	1	2	yes	complemented
43	C₂×#14524031	C₂²	1	4	yes	complemented
44	C₂×#14524029	C₂²	1	4	yes	complemented
45	#16863907	C₂²	1	16	yes	complemented
46	C₂×#14524028	C₂²	1	4	yes	complemented
47	C₂×#14524028	C₂²	1	4	yes	complemented
48	C₂×#14524026	C₂²	1	2	yes	—
49	C₂×#14524026	C₂²	1	4	yes	complemented
50	C₂×#14524025	C₂²	1	4	yes	complemented
51	C₂×#14524022	C₂²	1	1	yes	characteristic, complemented
52	C₂×#14524022	C₂²	1	1	yes	characteristic, complemented
53	C₂×#14524021	C₂²	1	4	yes	complemented
54	C₂×#14524020	C₂²	1	4	yes	—
55	C₂×#14524018	C₂²	1	2	yes	complemented
56	C₂×#14524018	C₂²	1	2	yes	complemented
57	C₂×#14524017	C₂²	1	2	yes	—
58	C₂×#14524017	C₂²	1	2	yes	—
59	C₂×#14524017	C₂²	1	2	yes	—
60	C₂×#14524017	C₂²	1	2	yes	—
61	C₂×#14524017	C₂²	1	16	yes	complemented
62	C₂×#14524017	C₂²	1	1	yes	characteristic, complemented
63	C₂×#14524017	C₂²	1	4	yes	complemented
64	C₂×#14524017	C₂²	1	1	yes	characteristic, complemented
65	C₂×#14524016	C₂²	1	4	yes	complemented
66	C₂×#14524016	C₂²	1	4	yes	complemented
67	C₂×#14524013	C₂²	1	4	yes	—
68	C₂×#14524012	C₂²	1	2	yes	—
69	#16863876	C₂²	1	16	yes	complemented
70	#16863870	C₂²	1	16	yes	complemented
71	C₂×C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
72	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
73	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
74	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
75	C₂×C₄×D₂₆₈	C₂²	1	4	yes	complemented
76	C₂×#14524005	C₂²	1	2	yes	complemented
77	C₂×#14524005	C₂²	1	2	yes	complemented
78	C₂×C₄×C₂²⋊D₆₇	C₂²	1	4	yes	complemented
79	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
80	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
81	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	4	yes	—
82	C₂×#14524002	C₂²	1	1	yes	characteristic
83	C₂×#14524001	C₂²	1	2	yes	complemented
84	C₂×#14524000	C₂²	1	4	yes	complemented
85	C₂²×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
86	C₂×C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
87	C₂²×(C₂×D₆₇)⋊C₄	C₂²	1	2	yes	—
88	C₂×C₂²⋊C₄×D₆₇	C₂²	1	4	yes	—
89	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
90	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
91	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
92	C₂×#117×C₆₇	C₂²	1	2	yes	—
93	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
94	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
95	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
96	C₂×#117×C₆₇	C₂²	1	16	yes	complemented
97	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
98	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
99	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
100	C₂²×C₄²×C₆₇	C₂²	1	2	yes	complemented
101	C₂⁴×D₆₇	C₂³	1	2	yes	—
102	C₂×#11761628	—	2	8	no	—
103	C₂×#11761628	—	4	16	no	—
104	C₂×#11761628	C₂³	1	8	yes	—
105	C₂×#11761628	C₂³	1	32	yes	complemented
106	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
107	C₂²×Dic₁₃₄	C₂³	1	4	yes	—
108	C₂²×D₂₆₈	—	2	8	no	—
109	C₂²×D₂₆₈	C₂³	1	2	yes	—
110	C₂²×D₂₆₈	C₂³	1	2	yes	—
111	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
112	C₂²×D₂₆₈	C₂³	1	8	yes	—
113	C₂²×D₂₆₈	C₂³	1	4	yes	—
114	C₂²×D₂₆₈	C₂³	1	4	yes	—
115	C₂²×C₂²⋊D₆₇	—	4	8	no	—
116	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
117	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
118	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
119	C₂²×C₂²⋊D₆₇	C₂³	1	16	yes	—
120	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
121	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
122	C₂³×Dic₆₇	C₂³	1	2	yes	—
123	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
124	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
125	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
126	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
127	#14524043	C₂³	1	16	yes	complemented
128	#14524042	C₂³	1	16	yes	complemented
129	#14524040	C₂³	1	16	yes	complemented
130	#14524038	C₂³	1	32	yes	complemented
131	#14524037	C₂³	1	32	yes	complemented
132	#14524035	C₂³	1	16	yes	complemented
133	#14524034	C₂³	1	16	yes	complemented
134	#14524031	C₂³	1	16	yes	complemented
135	#14524031	C₂³	1	32	yes	complemented
136	#14524029	C₂³	1	32	yes	complemented
137	#14524028	C₂³	1	32	yes	complemented
138	#14524028	C₂³	1	32	yes	complemented
139	#14524026	C₂³	1	16	yes	—
140	#14524026	C₂³	1	32	yes	complemented
141	#14524025	C₂³	1	32	yes	complemented
142	#14524022	C₂³	1	8	yes	complemented
143	#14524022	C₂³	1	8	yes	complemented
144	#14524021	C₂³	1	32	yes	complemented
145	#14524020	C₂³	1	32	yes	—
146	#14524018	C₂³	1	16	yes	complemented
147	#14524018	C₂³	1	16	yes	complemented
148	#14524017	C₂³	1	16	yes	—
149	#14524017	C₂³	1	16	yes	—
150	#14524017	C₂³	1	16	yes	—
151	#14524017	C₂³	1	16	yes	—
152	#14524017	C₂³	1	8	yes	complemented
153	#14524017	C₂³	1	32	yes	complemented
154	#14524017	C₂³	1	8	yes	complemented
155	#14524016	C₂³	1	32	yes	complemented
156	#14524016	C₂³	1	32	yes	complemented
157	#14524013	C₂³	1	32	yes	—
158	#14524012	C₂³	1	16	yes	—
159	C₄×Dic₁₃₄	C₂³	1	16	yes	complemented
160	C₄×D₂₆₈	C₂³	1	16	yes	complemented
161	C₄×D₂₆₈	C₂³	1	16	yes	complemented
162	C₄×D₂₆₈	C₂³	1	16	yes	complemented
163	C₄×D₂₆₈	C₂³	1	32	yes	complemented
164	#14524005	C₂³	1	16	yes	complemented
165	#14524005	C₂³	1	16	yes	complemented
166	C₄×C₂²⋊D₆₇	C₂³	1	32	yes	complemented
167	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
168	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
169	(C₂²⋊D₆₇)⋊C₄	C₂³	1	32	yes	—
170	#14524002	C₂³	1	8	yes	—
171	#14524001	C₂³	1	16	yes	complemented
172	#14524000	C₂³	1	32	yes	complemented
173	C₂×C₄⋊Dic₆₇	C₂³	1	8	yes	—
174	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
175	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
176	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊Dic₆₇	C₂³	1	4	yes	—
179	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	—
180	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
181	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	—
182	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	—
183	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
184	C₄⋊C₄×D₆₇	C₂³	1	16	yes	complemented
185	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
186	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
187	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
188	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	16	yes	—
189	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
190	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
191	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	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	4	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	C₂²⋊C₄×D₆₇	C₂³	1	32	yes	—
199	C₂×C₄×Dic₆₇	C₂³	1	4	yes	—
200	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
201	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
202	C₂³×C₄×C₆₇	—	2	8	no	—
203	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
204	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
205	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
206	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
207	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
208	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
209	C₂³×C₄×C₆₇	C₂³	1	8	yes	—
210	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
211	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
212	#117×C₆₇	C₂³	1	8	yes	—
213	#117×C₆₇	C₂³	1	16	yes	—
214	#117×C₆₇	C₂³	1	8	yes	—
215	#117×C₆₇	C₂³	1	16	yes	complemented
216	#117×C₆₇	C₂³	1	8	yes	complemented
217	#117×C₆₇	C₂³	1	8	yes	complemented
218	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
223	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
224	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	complemented
225	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	complemented
226	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	—
227	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
228	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
229	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
230	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
231	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
232	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
233	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
234	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
235	C₂×C₄²×C₆₇	C₂³	1	16	yes	complemented
236	C₂³×D₆₇	—	2	8	no	—
237	C₂³×D₆₇	—	4	4	no	—
238	C₂³×D₆₇	—	4	4	no	—
239	C₂³×D₆₇	C₂⁴	1	4	yes	—
240	C₂³×D₆₇	C₂⁴	1	2	yes	—
241	C₂³×D₆₇	C₂⁴	1	8	yes	—
242	#11761628	—	2	32	no	—
243	#11761628	—	4	64	no	—
244	C₂×Dic₁₃₄	—	2	4	no	—
245	C₂×Dic₁₃₄	—	4	8	no	—
246	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
247	C₂×Dic₁₃₄	C₂⁴	1	16	yes	—
248	C₂×D₂₆₈	—	2	8	no	—
249	C₂×D₂₆₈	—	2	8	no	—
250	C₂×D₂₆₈	—	2	4	no	—
251	C₂×D₂₆₈	—	2	32	no	—
252	C₂×D₂₆₈	—	4	8	no	—
253	C₂×D₂₆₈	—	4	8	no	—
254	C₂×D₂₆₈	C₂⁴	1	8	yes	—
255	C₂×D₂₆₈	C₂⁴	1	8	yes	—
256	C₂×D₂₆₈	C₂⁴	1	4	yes	—
257	C₂×D₂₆₈	C₂⁴	1	16	yes	—
258	C₂×D₂₆₈	C₂⁴	1	16	yes	—
259	C₂×C₂²⋊D₆₇	—	2	8	no	—
260	C₂×C₂²⋊D₆₇	—	2	16	no	—
261	C₂×C₂²⋊D₆₇	—	2	8	no	—
262	C₂×C₂²⋊D₆₇	—	4	8	no	—
263	C₂×C₂²⋊D₆₇	—	4	4	no	—
264	C₂×C₂²⋊D₆₇	—	4	32	no	—
265	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
266	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
267	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
268	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
269	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
270	C₂²×Dic₆₇	—	4	4	no	—
271	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
272	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
273	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
274	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
275	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
276	C₂×C₄×D₆₇	—	2	8	no	—
277	C₂×C₄×D₆₇	—	4	8	no	—
278	C₂×C₄×D₆₇	—	4	8	no	—
279	C₂×C₄×D₆₇	—	4	8	no	—
280	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
281	C₂×C₄×D₆₇	C₂⁴	1	16	yes	—
282	C₂×C₄×D₆₇	C₂⁴	1	16	yes	—
283	C₂×C₄×D₆₇	C₂⁴	1	16	yes	—
284	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
285	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
286	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
287	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
288	C₄⋊Dic₆₇	C₂⁴	1	16	yes	—
289	Dic₆₇⋊C₄	C₂⁴	1	16	yes	—
290	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
291	Dic₆₇⋊C₄	C₂⁴	1	16	yes	—
292	Dic₆₇⋊C₄	C₂⁴	1	16	yes	—
293	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
294	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
295	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
296	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
297	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
298	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
299	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
300	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
301	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
302	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
303	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
304	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
305	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
306	C₄×Dic₆₇	C₂⁴	1	16	yes	—
307	C₄×Dic₆₇	C₂⁴	1	8	yes	—
308	C₂⁴×C₆₇	—	2	4	no	—
309	C₂⁴×C₆₇	—	2	4	no	—
310	C₂⁴×C₆₇	—	4	2	no	—
311	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
312	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
313	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
314	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₆₇	—	2	4	no	—
316	C₂²×C₄×C₆₇	—	2	8	no	—
317	C₂²×C₄×C₆₇	—	2	4	no	—
318	C₂²×C₄×C₆₇	—	2	4	no	—
319	C₂²×C₄×C₆₇	—	2	4	no	—
320	C₂²×C₄×C₆₇	—	2	4	no	—
321	C₂²×C₄×C₆₇	—	2	32	no	—
322	C₂²×C₄×C₆₇	—	4	4	no	—
323	C₂²×C₄×C₆₇	#41	1	8	yes	complemented
324	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
326	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
327	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
328	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
329	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
330	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
331	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
333	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
334	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
335	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
336	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
337	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
340	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
341	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
342	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
343	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
344	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
345	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
346	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
347	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
348	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
349	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
350	C₄²×C₆₇	C₂⁴	1	8	yes	—
351	C₄²×C₆₇	C₂⁴	1	8	yes	—
352	C₄²×C₆₇	C₂⁴	1	8	yes	—
353	C₄²×C₆₇	C₂⁴	1	8	yes	—
354	C₂³×C₆₇	—	2	2	no	—
355	C₂³×C₆₇	—	2	2	no	—
356	C₂³×C₆₇	—	2	2	no	—
357	C₂³×C₆₇	—	2	2	no	—
358	C₂³×C₆₇	—	2	8	no	—
359	C₂³×C₆₇	—	2	2	no	—
360	C₂³×C₆₇	—	2	8	no	—
361	C₂³×C₆₇	—	2	2	no	—
362	C₂³×C₆₇	—	2	2	no	—
363	C₂³×C₆₇	—	4	4	no	—
364	C₂³×C₆₇	—	4	16	no	—
365	C₂³×C₆₇	C₂×#41	1	4	yes	—
366	C₂³×C₆₇	H(5,𝔽₂)	1	4	yes	—
367	C₂³×C₆₇	C₂⁵	1	2	yes	—
368	C₂³×C₆₇	C₂⁵	1	2	yes	—
369	C₂³×C₆₇	C₂⁵	1	2	yes	—
370	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
371	C₂²×D₆₇	—	2	4	no	—
372	C₂²×D₆₇	—	2	8	no	—
373	C₂²×D₆₇	—	2	4	no	—
374	C₂²×D₆₇	—	2	8	no	—
375	C₂²×D₆₇	—	2	8	no	—
376	C₂²×D₆₇	—	2	4	no	—
377	C₂²×D₆₇	—	2	16	no	—
378	C₂²×D₆₇	—	4	8	no	—
379	C₂²×D₆₇	—	4	8	no	—
380	C₂²×D₆₇	—	8	16	no	—
381	C₂²×D₆₇	C₂⁵	1	8	yes	—
382	C₂²×D₆₇	C₂⁵	1	4	yes	—
383	C₂×C₄×C₆₇	—	2	8	no	—
384	C₂×C₄×C₆₇	—	2	2	no	—
385	C₂×C₄×C₆₇	—	2	2	no	—
386	C₂×C₄×C₆₇	—	2	4	no	—
387	C₂×C₄×C₆₇	—	2	4	no	—
388	C₂×C₄×C₆₇	—	2	16	no	—
389	C₂×C₄×C₆₇	—	2	4	no	—
390	C₂×C₄×C₆₇	—	2	4	no	—
391	C₂×C₄×C₆₇	—	2	8	no	—
392	C₂×C₄×C₆₇	—	2	8	no	—
393	C₂×C₄×C₆₇	—	2	8	no	—
394	C₂×C₄×C₆₇	—	2	8	no	—
395	C₂×C₄×C₆₇	—	4	8	no	—
396	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
397	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
398	C₂×C₄×C₆₇	C₂×#41	1	16	yes	complemented
399	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
400	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
401	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
402	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
403	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
404	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
405	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
406	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
407	C₂²⋊D₆₇	—	2	16	no	—
408	C₂²⋊D₆₇	—	2	32	no	—
409	C₂²⋊D₆₇	—	2	16	no	—
410	C₂²⋊D₆₇	—	4	16	no	—
411	C₂²⋊D₆₇	—	4	8	no	—
412	C₂×Dic₆₇	—	2	4	no	—
413	C₂×Dic₆₇	—	2	4	no	—
414	C₂×Dic₆₇	—	2	8	no	—
415	C₂×Dic₆₇	—	2	4	no	—
416	C₂×Dic₆₇	—	4	8	no	—
417	C₂×Dic₆₇	C₂⁵	1	4	yes	—
418	C₂×Dic₆₇	C₂⁵	1	4	yes	—
419	C₂×Dic₆₇	C₂⁵	1	4	yes	—
420	C₂×Dic₆₇	C₂⁵	1	8	yes	—
421	D₂₆₈	—	2	16	no	—
422	D₂₆₈	—	2	16	no	—
423	D₂₆₈	—	2	8	no	—
424	D₂₆₈	—	4	16	no	—
425	D₂₆₈	—	4	16	no	—
426	C₄×D₆₇	—	2	16	no	—
427	C₄×D₆₇	—	4	16	no	—
428	C₄×D₆₇	—	4	16	no	—
429	C₄×D₆₇	—	4	16	no	—
430	Dic₁₃₄	—	2	8	no	—
431	Dic₁₃₄	—	4	16	no	—
432	C₂²×C₆₇	—	2	2	no	—
433	C₂²×C₆₇	—	2	2	no	—
434	C₂²×C₆₇	—	2	2	no	—
435	C₂²×C₆₇	—	2	2	no	—
436	C₂²×C₆₇	—	2	8	no	—
437	C₂²×C₆₇	—	2	8	no	—
438	C₂²×C₆₇	—	2	2	no	—
439	C₂²×C₆₇	—	2	2	no	—
440	C₂²×C₆₇	—	2	2	no	—
441	C₂²×C₆₇	—	4	16	no	—
442	C₂²×C₆₇	—	4	4	no	—
443	C₂²×C₆₇	C₂²×#41	1	4	yes	—
444	C₂²×C₆₇	C₂²×#41	1	2	yes	—
445	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
446	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
447	C₂²×C₆₇	#585	1	2	yes	—
448	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
449	C₂×D₆₇	—	2	4	no	—
450	C₂×D₆₇	—	2	8	no	—
451	C₂×D₆₇	—	2	4	no	—
452	C₂×D₆₇	—	2	8	no	—
453	C₂×D₆₇	—	2	8	no	—
454	C₂×D₆₇	—	2	4	no	—
455	C₂×D₆₇	—	4	8	no	—
456	C₂×D₆₇	—	4	16	no	—
457	C₂×D₆₇	—	8	16	no	—
458	C₄×C₆₇	—	2	2	no	—
459	C₄×C₆₇	—	2	2	no	—
460	C₄×C₆₇	—	2	4	no	—
461	C₄×C₆₇	—	2	4	no	—
462	C₄×C₆₇	—	2	4	no	—
463	C₄×C₆₇	—	2	4	no	—
464	C₄×C₆₇	C₂²×#41	1	4	yes	—
465	C₄×C₆₇	C₂²×#41	1	4	yes	—
466	Dic₆₇	—	2	4	no	—
467	Dic₆₇	—	2	4	no	—
468	Dic₆₇	—	2	8	no	—
469	Dic₆₇	—	2	4	no	—
470	C₂×#3494	—	67	1	no	maximal, Sylow
471	C₂×C₆₇	—	2	4	no	—
472	C₂×C₆₇	—	2	4	no	—
473	C₂×C₆₇	—	4	2	no	—
474	C₂×C₆₇	#3494	1	4	yes	complemented
475	C₂×C₆₇	C₂³×#41	1	1	yes	characteristic
476	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
477	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
478	D₆₇	—	4	4	no	—
479	D₆₇	—	4	8	no	—
480	#3494	—	67	32	no	—
481	C₂×#555	—	67	2	no	—
482	C₂×#553	—	67	2	no	—
483	C₂×#553	—	67	2	no	—
484	C₂×#551	—	67	4	no	—
485	C₂×#547	—	67	2	no	—
486	C₂×#546	—	67	4	no	—
487	C₂×#544	—	67	1	no	—
488	C₂×#542	—	67	2	no	—
489	C₂×#540	—	67	2	no	—
490	C₂×#535	—	67	1	no	—
491	C₂×#532	—	67	2	no	—
492	C₂×#529	—	67	2	no	—
493	C₂×#525	—	67	1	no	—
494	C₂²×#121	—	67	1	no	—
495	C₂×#520	—	67	1	no	—
496	C₂×#518	—	67	1	no	—
497	C₂²×#117	D₆₇	1	1	yes	characteristic, complemented
498	C₆₇	C₂×#3494	1	1	yes	characteristic, complemented, Sylow
499	C₂²×#41	—	67	4	no	—
500	C₂²×#41	—	67	1	no	—
501	C₂³×D₄	—	67	2	no	—
502	C₂³×D₄	—	67	1	no	—
503	C₂⁴×C₄	C₂×D₆₇	1	1	yes	characteristic
504	#555	—	67	32	no	—
505	#553	—	67	32	no	—
506	#553	—	67	32	no	—
507	#551	—	67	64	no	—
508	#547	—	67	32	no	—
509	#546	—	67	64	no	—
510	#544	—	67	16	no	—
511	#542	—	67	32	no	—
512	#540	—	67	32	no	—
513	#535	—	67	16	no	—
514	#532	—	67	32	no	—
515	C₂×C₄⋊Q₈	—	67	2	no	—
516	C₂×C₄⋊Q₈	—	67	2	no	—
517	C₂×#127	—	67	2	no	—
518	#529	—	67	32	no	—
519	C₂×#126	—	67	4	no	—
520	C₂×#126	—	67	4	no	—
521	C₂×#125	—	67	2	no	—
522	C₂×#125	—	67	2	no	—
523	C₂×#124	—	67	4	no	—
524	C₂×#124	—	67	2	no	—
525	C₂×#124	—	67	4	no	—
526	#525	—	67	16	no	—
527	C₂×#123	—	67	2	no	—
528	C₂×#123	—	67	4	no	—
529	C₂×#123	—	67	4	no	—
530	C₂×#123	—	67	4	no	—
531	C₂×#123	—	67	4	no	—
532	C₂×C₂²⋊Q₈	—	67	1	no	—
533	C₂×C₂²⋊Q₈	—	67	1	no	—
534	C₂×C₂²⋊Q₈	—	67	4	no	—
535	C₂×C₂²⋊Q₈	—	67	4	no	—
536	C₂×#121	—	67	2	no	—
537	C₂×#121	—	67	2	no	—
538	C₂×#121	—	67	2	no	—
539	C₂×#121	—	67	2	no	—
540	C₂×#121	—	67	16	no	—
541	C₂×#121	—	67	1	no	—
542	C₂×#121	—	67	1	no	—
543	C₂×#121	—	67	4	no	—
544	C₂×#121	—	67	2	no	—
545	C₂×#121	—	67	2	no	—
546	C₂×#121	—	67	4	no	—
547	C₂×#121	—	67	4	no	—
548	C₂×#120	—	67	2	no	—
549	C₂×#120	—	67	4	no	—
550	#520	—	67	16	no	—
551	#518	—	67	16	no	—
552	C₂×C₄×Q₈	—	67	2	no	—
553	C₂×C₄×D₄	—	67	2	no	—
554	C₂×C₄×D₄	—	67	2	no	—
555	C₂×C₄×D₄	—	67	4	no	—
556	C₂×C₄×D₄	—	67	2	no	—
557	C₂×C₄×D₄	—	67	2	no	—
558	C₂×C₄×D₄	—	67	4	no	—
559	C₂×C₄×D₄	—	67	2	no	—
560	C₂×C₄×D₄	—	67	2	no	—
561	C₂×C₄×D₄	—	67	2	no	—
562	C₂×C₄×D₄	—	67	4	no	—
563	C₂×#117	—	67	1	no	—
564	C₂×#117	—	67	2	no	—
565	C₂×#117	—	67	4	no	—
566	C₂×#117	C₂×D₆₇	1	1	yes	characteristic
567	C₂×#117	C₂×D₆₇	1	1	yes	characteristic
568	C₂×#117	C₂×D₆₇	1	2	yes	—
569	C₂×#117	C₂×D₆₇	1	2	yes	complemented
570	C₂×#117	C₂×D₆₇	1	1	yes	characteristic, complemented
571	C₂×#117	C₂×D₆₇	1	1	yes	characteristic, complemented
572	C₂×#117	C₂×D₆₇	1	16	yes	complemented
573	C₂²×C₄⋊C₄	—	67	1	no	—
574	C₂²×C₄⋊C₄	—	67	2	no	—
575	C₂²×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic, complemented
576	C₂²×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic, complemented
577	C₂²×C₂²⋊C₄	—	67	2	no	—
578	C₂²×C₂²⋊C₄	—	67	4	no	—
579	C₂²×C₂²⋊C₄	C₂×D₆₇	1	2	yes	—
580	C₂²×C₄²	C₂×D₆₇	1	2	yes	complemented
581	C₂⁵	—	67	2	no	—
582	C₂⁵	C₂²×D₆₇	1	1	yes	characteristic
583	C₂×#41	—	268	16	no	—
584	C₂×#41	—	67	32	no	—
585	C₂×#41	—	67	8	no	—
586	C₂×#41	—	134	8	no	—
587	C₂²×Q₈	—	67	4	no	—
588	C₂²×Q₈	—	67	1	no	—
589	C₂²×D₄	—	268	8	no	—
590	C₂²×D₄	—	67	2	no	—
591	C₂²×D₄	—	67	4	no	—
592	C₂²×D₄	—	67	16	no	—
593	C₂²×D₄	—	67	2	no	—
594	C₂²×D₄	—	67	2	no	—
595	C₂²×D₄	—	67	4	no	—
596	C₂²×D₄	—	67	4	no	—
597	C₂²×D₄	—	67	4	no	—
598	C₂²×D₄	—	67	2	no	—
599	C₂²×D₄	—	67	2	no	—
600	C₂²×D₄	—	67	1	no	—
601	C₂²×D₄	—	67	8	no	—
602	C₂²×D₄	—	134	8	no	—
603	C₂³×C₄	—	2	8	no	—
604	C₂³×C₄	—	67	2	no	—
605	C₂³×C₄	—	67	4	no	—
606	C₂³×C₄	—	67	4	no	—
607	C₂³×C₄	—	67	4	no	—
608	C₂³×C₄	—	67	2	no	—
609	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
610	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
611	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
612	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
613	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
614	C₂³×C₄	C₂²×D₆₇	1	8	yes	—
615	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
616	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
617	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
618	C₄⋊Q₈	—	67	16	no	—
619	C₄⋊Q₈	—	67	16	no	—
620	#127	—	67	16	no	—
621	#126	—	67	32	no	—
622	#126	—	67	32	no	—
623	#125	—	67	16	no	—
624	#125	—	67	16	no	—
625	#124	—	67	32	no	—
626	#124	—	67	16	no	—
627	#124	—	67	32	no	—
628	#123	—	67	16	no	—
629	#123	—	67	32	no	—
630	#123	—	67	32	no	—
631	#123	—	67	32	no	—
632	#123	—	67	32	no	—
633	C₂²⋊Q₈	—	67	8	no	—
634	C₂²⋊Q₈	—	67	8	no	—
635	C₂²⋊Q₈	—	67	32	no	—
636	C₂²⋊Q₈	—	67	32	no	—
637	#121	—	67	16	no	—
638	#121	—	67	16	no	—
639	#121	—	67	16	no	—
640	#121	—	67	16	no	—
641	#121	—	67	8	no	—
642	#121	—	67	8	no	—
643	#121	—	67	32	no	—
644	#121	—	67	16	no	—
645	#121	—	67	16	no	—
646	#121	—	67	32	no	—
647	#121	—	67	32	no	—
648	#120	—	67	16	no	—
649	#120	—	67	32	no	—
650	C₄×Q₈	—	67	16	no	—
651	C₄×D₄	—	67	16	no	—
652	C₄×D₄	—	67	16	no	—
653	C₄×D₄	—	67	32	no	—
654	C₄×D₄	—	67	16	no	—
655	C₄×D₄	—	67	16	no	—
656	C₄×D₄	—	67	32	no	—
657	C₄×D₄	—	67	16	no	—
658	C₄×D₄	—	67	16	no	—
659	C₄×D₄	—	67	16	no	—
660	C₄×D₄	—	67	32	no	—
661	#117	—	67	8	no	—
662	#117	—	67	16	no	—
663	#117	—	67	32	no	—
664	#117	C₂²×D₆₇	1	8	yes	—
665	#117	C₂²×D₆₇	1	8	yes	—
666	#117	C₂²×D₆₇	1	16	yes	—
667	#117	C₂²×D₆₇	1	16	yes	complemented
668	#117	C₂²×D₆₇	1	8	yes	complemented
669	#117	C₂²×D₆₇	1	8	yes	complemented
670	C₂×C₄⋊C₄	—	67	2	no	—
671	C₂×C₄⋊C₄	—	67	2	no	—
672	C₂×C₄⋊C₄	—	67	4	no	—
673	C₂×C₄⋊C₄	—	67	8	no	—
674	C₂×C₄⋊C₄	—	67	2	no	—
675	C₂×C₄⋊C₄	—	67	1	no	—
676	C₂×C₄⋊C₄	—	67	1	no	—
677	C₂×C₄⋊C₄	—	67	4	no	—
678	C₂×C₄⋊C₄	—	67	4	no	—
679	C₂×C₄⋊C₄	—	67	4	no	—
680	C₂×C₄⋊C₄	—	67	2	no	—
681	C₂×C₄⋊C₄	—	67	16	no	—
682	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
683	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
684	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
685	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
686	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
687	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
688	C₂×C₄⋊C₄	C₂²×D₆₇	1	8	yes	complemented
689	C₂×C₄⋊C₄	C₂²×D₆₇	1	8	yes	complemented
690	C₂×C₂²⋊C₄	—	67	2	no	—
691	C₂×C₂²⋊C₄	—	67	2	no	—
692	C₂×C₂²⋊C₄	—	67	2	no	—
693	C₂×C₂²⋊C₄	—	67	4	no	—
694	C₂×C₂²⋊C₄	—	67	4	no	—
695	C₂×C₂²⋊C₄	—	67	4	no	—
696	C₂×C₂²⋊C₄	—	67	4	no	—
697	C₂×C₂²⋊C₄	—	67	16	no	—
698	C₂×C₂²⋊C₄	—	67	4	no	—
699	C₂×C₂²⋊C₄	—	67	4	no	—
700	C₂×C₂²⋊C₄	—	67	2	no	—
701	C₂×C₂²⋊C₄	—	67	4	no	—
702	C₂×C₂²⋊C₄	—	67	2	no	—
703	C₂×C₂²⋊C₄	—	67	32	no	—
704	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
705	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
706	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
707	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
708	C₂×C₂²⋊C₄	C₂²×D₆₇	1	16	yes	—
709	C₂×C₄²	—	67	4	no	—
710	C₂×C₄²	—	67	2	no	—
711	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
712	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
713	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
714	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
715	C₂×C₄²	C₂²×D₆₇	1	16	yes	complemented
716	C₂⁴	—	2	4	no	—
717	C₂⁴	—	2	4	no	—
718	C₂⁴	—	4	2	no	—
719	C₂⁴	—	268	4	no	—
720	C₂⁴	—	268	4	no	—
721	C₂⁴	—	67	8	no	—
722	C₂⁴	—	67	4	no	—
723	C₂⁴	—	67	2	no	—
724	C₂⁴	—	134	8	no	—
725	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
726	C₂⁴	C₂³×D₆₇	1	4	yes	—
727	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
728	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
729	#41	—	268	64	no	—
730	#41	—	134	32	no	—
731	C₂×Q₈	—	268	8	no	—
732	C₂×Q₈	—	67	16	no	—
733	C₂×Q₈	—	67	4	no	—
734	C₂×Q₈	—	134	4	no	—
735	C₂×D₄	—	268	8	no	—
736	C₂×D₄	—	268	8	no	—
737	C₂×D₄	—	268	32	no	—
738	C₂×D₄	—	268	8	no	—
739	C₂×D₄	—	268	4	no	—
740	C₂×D₄	—	67	8	no	—
741	C₂×D₄	—	67	16	no	—
742	C₂×D₄	—	67	8	no	—
743	C₂×D₄	—	67	8	no	—
744	C₂×D₄	—	67	16	no	—
745	C₂×D₄	—	67	16	no	—
746	C₂×D₄	—	67	16	no	—
747	C₂×D₄	—	67	8	no	—
748	C₂×D₄	—	67	8	no	—
749	C₂×D₄	—	67	4	no	—
750	C₂×D₄	—	134	8	no	—
751	C₂×D₄	—	134	16	no	—
752	C₂×D₄	—	134	8	no	—
753	C₂×D₄	—	134	8	no	—
754	C₂×D₄	—	134	8	no	—
755	C₂×D₄	—	134	4	no	—
756	C₂×D₄	—	134	32	no	—
757	C₂²×C₄	—	2	4	no	—
758	C₂²×C₄	—	2	8	no	—
759	C₂²×C₄	—	2	4	no	—
760	C₂²×C₄	—	2	4	no	—
761	C₂²×C₄	—	2	4	no	—
762	C₂²×C₄	—	2	4	no	—
763	C₂²×C₄	—	2	32	no	—
764	C₂²×C₄	—	4	4	no	—
765	C₂²×C₄	—	268	8	no	—
766	C₂²×C₄	—	268	8	no	—
767	C₂²×C₄	—	268	8	no	—
768	C₂²×C₄	—	268	4	no	—
769	C₂²×C₄	—	67	8	no	—
770	C₂²×C₄	—	67	16	no	—
771	C₂²×C₄	—	67	16	no	—
772	C₂²×C₄	—	67	16	no	—
773	C₂²×C₄	—	67	2	no	—
774	C₂²×C₄	—	67	2	no	—
775	C₂²×C₄	—	67	2	no	—
776	C₂²×C₄	—	67	4	no	—
777	C₂²×C₄	—	67	8	no	—
778	C₂²×C₄	—	134	8	no	—
779	C₂²×C₄	#11761628	1	8	yes	complemented
780	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
781	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
782	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
783	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
784	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
785	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
786	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
787	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
788	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
789	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
790	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
791	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
792	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
793	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
794	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
795	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
796	C₄⋊C₄	—	67	8	no	—
797	C₄⋊C₄	—	67	8	no	—
798	C₄⋊C₄	—	67	16	no	—
799	C₄⋊C₄	—	67	8	no	—
800	C₄⋊C₄	—	67	4	no	—
801	C₄⋊C₄	—	67	4	no	—
802	C₄⋊C₄	—	67	16	no	—
803	C₄⋊C₄	—	67	16	no	—
804	C₄⋊C₄	—	67	16	no	—
805	C₄⋊C₄	—	67	8	no	—
806	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
807	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
808	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
809	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
810	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
811	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
812	C₂²⋊C₄	—	67	8	no	—
813	C₂²⋊C₄	—	67	8	no	—
814	C₂²⋊C₄	—	67	8	no	—
815	C₂²⋊C₄	—	67	16	no	—
816	C₂²⋊C₄	—	67	16	no	—
817	C₂²⋊C₄	—	67	16	no	—
818	C₂²⋊C₄	—	67	16	no	—
819	C₂²⋊C₄	—	67	16	no	—
820	C₂²⋊C₄	—	67	16	no	—
821	C₂²⋊C₄	—	67	8	no	—
822	C₂²⋊C₄	—	67	16	no	—
823	C₂²⋊C₄	—	67	8	no	—
824	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
825	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
826	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
827	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
828	C₄²	—	67	16	no	—
829	C₄²	—	67	8	no	—
830	C₄²	C₂³×D₆₇	1	8	yes	—
831	C₄²	C₂³×D₆₇	1	8	yes	—
832	C₄²	C₂³×D₆₇	1	8	yes	—
833	C₄²	C₂³×D₆₇	1	8	yes	—
834	C₂³	—	2	2	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	2	no	—
837	C₂³	—	2	2	no	—
838	C₂³	—	2	8	no	—
839	C₂³	—	2	2	no	—
840	C₂³	—	2	8	no	—
841	C₂³	—	2	2	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	4	4	no	—
844	C₂³	—	4	16	no	—
845	C₂³	—	268	8	no	—
846	C₂³	—	268	8	no	—
847	C₂³	—	536	16	no	—
848	C₂³	—	67	8	no	—
849	C₂³	—	67	4	no	—
850	C₂³	—	134	4	no	—
851	C₂³	—	134	8	no	—
852	C₂³	—	134	4	no	—
853	C₂³	—	134	8	no	—
854	C₂³	—	134	8	no	—
855	C₂³	—	134	4	no	—
856	C₂³	—	134	16	no	—
857	C₂³	C₂×#11761628	1	4	yes	—
858	C₂³	#14524089	1	4	yes	—
859	C₂³	C₂⁴×D₆₇	1	2	yes	—
860	C₂³	C₂⁴×D₆₇	1	2	yes	—
861	C₂³	C₂⁴×D₆₇	1	2	yes	—
862	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
863	Q₈	—	268	16	no	—
864	Q₈	—	134	8	no	—
865	D₄	—	268	16	no	—
866	D₄	—	268	16	no	—
867	D₄	—	268	16	no	—
868	D₄	—	268	8	no	—
869	D₄	—	134	16	no	—
870	D₄	—	134	32	no	—
871	D₄	—	134	16	no	—
872	D₄	—	134	16	no	—
873	D₄	—	134	16	no	—
874	D₄	—	134	8	no	—
875	C₂×C₄	—	2	8	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	4	no	—
879	C₂×C₄	—	2	4	no	—
880	C₂×C₄	—	2	16	no	—
881	C₂×C₄	—	2	4	no	—
882	C₂×C₄	—	2	4	no	—
883	C₂×C₄	—	2	8	no	—
884	C₂×C₄	—	2	8	no	—
885	C₂×C₄	—	2	8	no	—
886	C₂×C₄	—	2	8	no	—
887	C₂×C₄	—	4	8	no	—
888	C₂×C₄	—	268	16	no	—
889	C₂×C₄	—	268	16	no	—
890	C₂×C₄	—	268	16	no	—
891	C₂×C₄	—	268	8	no	—
892	C₂×C₄	—	67	4	no	—
893	C₂×C₄	—	67	4	no	—
894	C₂×C₄	—	67	4	no	—
895	C₂×C₄	—	67	8	no	—
896	C₂×C₄	—	134	4	no	—
897	C₂×C₄	—	134	8	no	—
898	C₂×C₄	—	134	4	no	—
899	C₂×C₄	—	134	4	no	—
900	C₂×C₄	—	134	16	no	—
901	C₂×C₄	C₂×#11761628	1	4	yes	—
902	C₂×C₄	C₂×#11761628	1	4	yes	—
903	C₂×C₄	C₂×#11761628	1	16	yes	complemented
904	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
905	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
906	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
907	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
908	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
909	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
910	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
911	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
912	C₂²	—	2	8	no	—
913	C₂²	—	2	8	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	2	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	2	2	no	—
920	C₂²	—	2	2	no	—
921	C₂²	—	4	16	no	—
922	C₂²	—	4	4	no	—
923	C₂²	—	268	16	no	—
924	C₂²	—	268	8	no	—
925	C₂²	—	536	16	no	—
926	C₂²	—	134	4	no	—
927	C₂²	—	134	8	no	—
928	C₂²	—	134	4	no	—
929	C₂²	—	134	8	no	—
930	C₂²	—	134	8	no	—
931	C₂²	—	134	4	no	—
932	C₂²	C₂²×#11761628	1	4	yes	—
933	C₂²	C₂²×#11761628	1	2	yes	—
934	C₂²	C₂×#14524089	1	4	yes	—
935	C₂²	C₂×#14524089	1	2	yes	—
936	C₂²	#16864232	1	2	yes	—
937	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
938	C₄	—	2	2	no	—
939	C₄	—	2	2	no	—
940	C₄	—	2	4	no	—
941	C₄	—	2	4	no	—
942	C₄	—	2	4	no	—
943	C₄	—	2	4	no	—
944	C₄	—	134	4	no	—
945	C₄	—	134	8	no	—
946	C₄	—	134	4	no	—
947	C₄	—	134	4	no	—
948	C₄	C₂²×#11761628	1	4	yes	—
949	C₄	C₂²×#11761628	1	4	yes	—
950	C₂	—	2	4	no	—
951	C₂	—	2	4	no	—
952	C₂	—	4	2	no	—
953	C₂	—	268	8	no	—
954	C₂	—	268	4	no	—
955	C₂	#22573944	1	4	yes	direct product factor
956	C₂	C₂³×#11761628	1	1	yes	characteristic
957	C₂	C₂²×#14524089	1	1	yes	characteristic
958	C₂	C₂×#16864232	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₆₇
commutator, cosocle	C₂²×C₆₇	C₂⁶
Frattini	C₂²	C₂⁵×D₆₇
Fitting	C₂²×#117×C₆₇	C₂
socle	C₂³×C₆₇	C₂⁵
hypercenter	C₂²×#117	D₆₇
hypocenter	C₆₇	C₂×#3494
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂²×#117

Complements

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

N	H ≅ G/N	type
1. #22573944	C₂	direct (N × H)
2. C₂×#16864109	C₂	semidirect
3. C₂×#16864094	C₂	semidirect
4. C₂×#16864090	C₂	semidirect
5. C₂×#16864070	C₂	semidirect
6. C₂×#16864047	C₂	semidirect
7. C₂×#16864036	C₂	semidirect
8. C₂×#16864024	C₂	semidirect
9. C₂×#16864017	C₂	semidirect
10. C₂×#16864001	C₂	semidirect
11. C₂×#16863965	C₂	semidirect
12. C₂×#16863946	C₂	semidirect
13. C₂×#16863930	C₂	semidirect
14. C₂×#16863907	C₂	semidirect
15. C₂²×#14524017	C₂	semidirect
16. C₂×#16863876	C₂	semidirect
17. C₂×#16863870	C₂	semidirect
18. C₂²×#117×C₆₇	C₂	semidirect
20. C₂²×#11761628	C₂²	semidirect
23. #16864109	C₂²	semidirect
24. #16864094	C₂²	semidirect
25. #16864090	C₂²	semidirect
26. #16864070	C₂²	semidirect
27. #16864047	C₂²	semidirect
28. #16864036	C₂²	semidirect
29. #16864024	C₂²	semidirect
30. #16864017	C₂²	semidirect
31. #16864001	C₂²	semidirect
32. #16863965	C₂²	semidirect
33. #16863946	C₂²	semidirect
34. C₂×#14524043	C₂²	semidirect
35. C₂×#14524042	C₂²	semidirect
36. C₂×#14524040	C₂²	semidirect
37. #16863930	C₂²	semidirect
38. C₂×#14524038	C₂²	semidirect
39. C₂×#14524037	C₂²	semidirect
40. C₂×#14524035	C₂²	semidirect
41. C₂×#14524034	C₂²	semidirect
42. C₂×#14524031	C₂²	semidirect
43. C₂×#14524031	C₂²	semidirect
44. C₂×#14524029	C₂²	semidirect
45. #16863907	C₂²	semidirect
46. C₂×#14524028	C₂²	semidirect
47. C₂×#14524028	C₂²	semidirect
49. C₂×#14524026	C₂²	semidirect
50. C₂×#14524025	C₂²	semidirect
51. C₂×#14524022	C₂²	semidirect
52. C₂×#14524022	C₂²	semidirect
53. C₂×#14524021	C₂²	semidirect
55. C₂×#14524018	C₂²	semidirect
56. C₂×#14524018	C₂²	semidirect
61. C₂×#14524017	C₂²	semidirect
62. C₂×#14524017	C₂²	semidirect
63. C₂×#14524017	C₂²	semidirect
64. C₂×#14524017	C₂²	semidirect
65. C₂×#14524016	C₂²	semidirect
66. C₂×#14524016	C₂²	semidirect
69. #16863876	C₂²	semidirect
70. #16863870	C₂²	semidirect
71. C₂×C₄×Dic₁₃₄	C₂²	semidirect
72. C₂×C₄×D₂₆₈	C₂²	semidirect
73. C₂×C₄×D₂₆₈	C₂²	semidirect
74. C₂×C₄×D₂₆₈	C₂²	semidirect
75. C₂×C₄×D₂₆₈	C₂²	semidirect
76. C₂×#14524005	C₂²	semidirect
77. C₂×#14524005	C₂²	semidirect
78. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
79. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
80. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
83. C₂×#14524001	C₂²	semidirect
84. C₂×#14524000	C₂²	semidirect
86. C₂×C₄⋊C₄×D₆₇	C₂²	semidirect
93. C₂×#117×C₆₇	C₂²	semidirect
94. C₂×#117×C₆₇	C₂²	semidirect
95. C₂×#117×C₆₇	C₂²	semidirect
96. C₂×#117×C₆₇	C₂²	semidirect
97. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
98. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
100. C₂²×C₄²×C₆₇	C₂²	semidirect
105. C₂×#11761628	C₂³	semidirect
127. #14524043	C₂³	semidirect
128. #14524042	C₂³	semidirect
129. #14524040	C₂³	semidirect
130. #14524038	C₂³	semidirect
131. #14524037	C₂³	semidirect
132. #14524035	C₂³	semidirect
133. #14524034	C₂³	semidirect
134. #14524031	C₂³	semidirect
135. #14524031	C₂³	semidirect
136. #14524029	C₂³	semidirect
137. #14524028	C₂³	semidirect
138. #14524028	C₂³	semidirect
140. #14524026	C₂³	semidirect
141. #14524025	C₂³	semidirect
142. #14524022	C₂³	semidirect
143. #14524022	C₂³	semidirect
144. #14524021	C₂³	semidirect
146. #14524018	C₂³	semidirect
147. #14524018	C₂³	semidirect
152. #14524017	C₂³	semidirect
153. #14524017	C₂³	semidirect
154. #14524017	C₂³	semidirect
155. #14524016	C₂³	semidirect
156. #14524016	C₂³	semidirect
159. C₄×Dic₁₃₄	C₂³	semidirect
160. C₄×D₂₆₈	C₂³	semidirect
161. C₄×D₂₆₈	C₂³	semidirect
162. C₄×D₂₆₈	C₂³	semidirect
163. C₄×D₂₆₈	C₂³	semidirect
164. #14524005	C₂³	semidirect
165. #14524005	C₂³	semidirect
166. C₄×C₂²⋊D₆₇	C₂³	semidirect
167. C₄×C₂²⋊D₆₇	C₂³	semidirect
168. C₄×C₂²⋊D₆₇	C₂³	semidirect
171. #14524001	C₂³	semidirect
172. #14524000	C₂³	semidirect
184. C₄⋊C₄×D₆₇	C₂³	semidirect
215. #117×C₆₇	C₂³	semidirect
216. #117×C₆₇	C₂³	semidirect
217. #117×C₆₇	C₂³	semidirect
224. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
225. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
235. C₂×C₄²×C₆₇	C₂³	semidirect
323. C₂²×C₄×C₆₇	#41	semidirect
398. C₂×C₄×C₆₇	C₂×#41	semidirect
474. C₂×C₆₇	#3494	semidirect
497. C₂²×#117	D₆₇	semidirect
498. C₆₇	C₂×#3494	semidirect
569. C₂×#117	C₂×D₆₇	semidirect
570. C₂×#117	C₂×D₆₇	semidirect
571. C₂×#117	C₂×D₆₇	semidirect
572. C₂×#117	C₂×D₆₇	semidirect
575. C₂²×C₄⋊C₄	C₂×D₆₇	semidirect
576. C₂²×C₄⋊C₄	C₂×D₆₇	semidirect
580. C₂²×C₄²	C₂×D₆₇	semidirect
667. #117	C₂²×D₆₇	semidirect
668. #117	C₂²×D₆₇	semidirect
669. #117	C₂²×D₆₇	semidirect
688. C₂×C₄⋊C₄	C₂²×D₆₇	semidirect
689. C₂×C₄⋊C₄	C₂²×D₆₇	semidirect
715. C₂×C₄²	C₂²×D₆₇	semidirect
779. C₂²×C₄	#11761628	semidirect
903. C₂×C₄	C₂×#11761628	semidirect
955. C₂	#22573944	direct (N × H)

Maximal subgroups

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

subgroup	index
#22573944	2
C₂×#16864109	2
C₂×#16864094	2
C₂×#16864090	2
C₂×#16864070	2
C₂×#16864047	2
C₂×#16864036	2
C₂×#16864024	2
C₂×#16864017	2
C₂×#16864001	2
C₂×#16863965	2
C₂×#16863946	2
C₂×#16863930	2
C₂×#16863907	2
C₂²×#14524017	2
C₂×#16863876	2
C₂×#16863870	2
C₂²×#117×C₆₇	2
C₂×#3494	67

Subgroups — C2×#22573944 #31764178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22573944 #31764178