Subgroups — C₂×#22574728 #31763166

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	#22574728	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×#16864128	C₂	1	2	yes	maximal, complemented
5	C₂×#16864057	C₂	1	2	yes	maximal, complemented
6	C₂×#16864039	C₂	1	2	yes	maximal, complemented
7	C₂×#16864036	C₂	1	4	yes	maximal, complemented
8	C₂×D₄×C₂²⋊D₆₇	C₂	1	2	yes	maximal, complemented
9	C₂×#16864015	C₂	1	2	yes	maximal, complemented
10	C₂×#16863984	C₂	1	2	yes	maximal, complemented
11	C₂×#16863980	C₂	1	4	yes	maximal, complemented
12	C₂×#16863964	C₂	1	2	yes	maximal, complemented
13	C₂×#16863958	C₂	1	2	yes	maximal, complemented
14	C₂×#16863946	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#16863930	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#124×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#11761629	C₂²	1	2	yes	complemented
18	C₂²×#11761628	C₂²	1	2	yes	complemented
19	C₂³×C₂²⋊D₆₇	C₂²	1	4	yes	complemented
20	C₂²×D₄×D₆₇	C₂²	1	2	yes	complemented
21	#16864140	C₂²	1	32	yes	complemented
22	#16864138	C₂²	1	32	yes	complemented
23	#16864128	C₂²	1	32	yes	complemented
24	#16864057	C₂²	1	32	yes	complemented
25	#16864039	C₂²	1	32	yes	complemented
26	#16864036	C₂²	1	64	yes	complemented
27	D₄×C₂²⋊D₆₇	C₂²	1	32	yes	complemented
28	#16864015	C₂²	1	32	yes	complemented
29	#16863984	C₂²	1	32	yes	complemented
30	#16863980	C₂²	1	64	yes	complemented
31	#16863964	C₂²	1	32	yes	complemented
32	#16863958	C₂²	1	32	yes	complemented
33	#16863946	C₂²	1	16	yes	complemented
34	C₂×#14524043	C₂²	1	1	yes	characteristic, complemented
35	C₂×#14524040	C₂²	1	1	yes	characteristic, complemented
36	C₂×#14524039	C₂²	1	2	yes	—
37	#16863930	C₂²	1	16	yes	complemented
38	C₂×#14524037	C₂²	1	2	yes	complemented
39	C₂×#14524036	C₂²	1	4	yes	complemented
40	C₂×#14524035	C₂²	1	1	yes	characteristic, complemented
41	C₂×#14524032	C₂²	1	2	yes	complemented
42	C₂×#14524032	C₂²	1	4	yes	complemented
43	C₂×#14524031	C₂²	1	1	yes	characteristic, complemented
44	C₂×#14524031	C₂²	1	2	yes	complemented
45	C₂×#14524029	C₂²	1	4	yes	complemented
46	C₂×#14524029	C₂²	1	4	yes	complemented
47	C₂×#14524027	C₂²	1	4	yes	complemented
48	C₂×#14524027	C₂²	1	4	yes	complemented
49	C₂×#14524026	C₂²	1	2	yes	complemented
50	C₂×#14524025	C₂²	1	4	yes	complemented
51	C₂×#14524025	C₂²	1	4	yes	complemented
52	C₂×#14524022	C₂²	1	1	yes	characteristic, complemented
53	C₂×#14524020	C₂²	1	4	yes	complemented
54	C₂×#14524019	C₂²	1	2	yes	complemented
55	C₂×#14524019	C₂²	1	4	yes	complemented
56	C₂×#14524017	C₂²	1	1	yes	characteristic
57	C₂×#14524017	C₂²	1	2	yes	complemented
58	C₂×#14524017	C₂²	1	4	yes	complemented
59	C₂×#14524017	C₂²	1	2	yes	complemented
60	C₂×#14524016	C₂²	1	4	yes	complemented
61	C₂×#14524016	C₂²	1	4	yes	complemented
62	C₂×#14524016	C₂²	1	4	yes	complemented
63	C₂×#14524015	C₂²	1	4	yes	complemented
64	C₂×#14524014	C₂²	1	2	yes	—
65	C₂×#14524013	C₂²	1	4	yes	complemented
66	C₂×#14524013	C₂²	1	4	yes	complemented
67	C₂×#14524013	C₂²	1	4	yes	complemented
68	C₂×#14524012	C₂²	1	4	yes	complemented
69	C₂×#14524011	C₂²	1	4	yes	complemented
70	C₂×Q₈×Dic₆₇	C₂²	1	2	yes	complemented
71	C₂×C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
73	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
74	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
75	C₂×D₄×Dic₆₇	C₂²	1	2	yes	complemented
76	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
77	C₂×C₄×C₂²⋊D₆₇	C₂²	1	4	yes	complemented
78	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	4	yes	complemented
79	C₂×#14524000	C₂²	1	2	yes	complemented
80	C₂×C₂²⋊C₄×D₆₇	C₂²	1	4	yes	complemented
81	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
82	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
83	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
84	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
85	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
86	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
87	C₂×#124×C₆₇	C₂²	1	16	yes	complemented
88	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
89	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
90	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	C₂⁴×D₆₇	C₂³	1	4	yes	—
92	C₂×#11761629	—	4	8	no	—
93	C₂×#11761629	C₂³	1	16	yes	complemented
94	C₂×#11761628	—	4	8	no	—
95	C₂×#11761628	C₂³	1	16	yes	complemented
96	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
97	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
98	C₂²×D₂₆₈	C₂³	1	2	yes	—
99	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
100	C₂²×D₂₆₈	C₂³	1	2	yes	—
101	C₂²×D₂₆₈	C₂³	1	4	yes	—
102	C₂²×D₂₆₈	C₂³	1	2	yes	—
103	C₂²×C₂²⋊D₆₇	—	4	16	no	—
104	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
105	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
106	C₂²×C₂²⋊D₆₇	C₂³	1	4	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	32	yes	complemented
111	C₂×D₄×D₆₇	—	4	8	no	—
112	C₂×D₄×D₆₇	C₂³	1	16	yes	complemented
113	C₂³×Dic₆₇	C₂³	1	4	yes	—
114	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
115	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
116	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
117	#14524043	C₂³	1	8	yes	complemented
118	#14524040	C₂³	1	8	yes	complemented
119	#14524039	C₂³	1	16	yes	—
120	#14524037	C₂³	1	16	yes	complemented
121	#14524036	C₂³	1	32	yes	complemented
122	#14524035	C₂³	1	8	yes	complemented
123	#14524032	C₂³	1	16	yes	complemented
124	#14524032	C₂³	1	32	yes	complemented
125	#14524031	C₂³	1	8	yes	complemented
126	#14524031	C₂³	1	16	yes	complemented
127	#14524029	C₂³	1	32	yes	complemented
128	#14524029	C₂³	1	32	yes	complemented
129	#14524027	C₂³	1	32	yes	complemented
130	#14524027	C₂³	1	32	yes	complemented
131	#14524026	C₂³	1	16	yes	complemented
132	#14524025	C₂³	1	32	yes	complemented
133	#14524025	C₂³	1	32	yes	complemented
134	#14524022	C₂³	1	8	yes	complemented
135	#14524020	C₂³	1	32	yes	complemented
136	#14524019	C₂³	1	16	yes	complemented
137	#14524019	C₂³	1	32	yes	complemented
138	#14524017	C₂³	1	8	yes	—
139	#14524017	C₂³	1	16	yes	complemented
140	#14524017	C₂³	1	32	yes	complemented
141	#14524017	C₂³	1	16	yes	complemented
142	#14524016	C₂³	1	32	yes	complemented
143	#14524016	C₂³	1	32	yes	complemented
144	#14524016	C₂³	1	32	yes	complemented
145	#14524015	C₂³	1	32	yes	complemented
146	#14524014	C₂³	1	16	yes	—
147	#14524013	C₂³	1	32	yes	complemented
148	#14524013	C₂³	1	32	yes	complemented
149	#14524013	C₂³	1	32	yes	complemented
150	#14524012	C₂³	1	32	yes	complemented
151	#14524011	C₂³	1	32	yes	complemented
152	Q₈×Dic₆₇	C₂³	1	16	yes	complemented
153	C₄×Dic₁₃₄	C₂³	1	8	yes	complemented
154	C₄×D₂₆₈	C₂³	1	8	yes	complemented
155	C₄×D₂₆₈	C₂³	1	16	yes	complemented
156	C₄×D₂₆₈	C₂³	1	16	yes	complemented
157	D₄×Dic₆₇	C₂³	1	16	yes	complemented
158	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
159	C₄×C₂²⋊D₆₇	C₂³	1	32	yes	complemented
160	(C₂²⋊D₆₇)⋊C₄	C₂³	1	32	yes	complemented
161	#14524000	C₂³	1	16	yes	complemented
162	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
163	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
164	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊Dic₆₇	C₂³	1	4	yes	—
167	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
168	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
169	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
170	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
171	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	—
172	C₂×C₂²⋊Dic₆₇	C₂³	1	4	yes	—
173	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
174	C₂×C₂²⋊Dic₆₇	C₂³	1	4	yes	—
175	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
176	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
177	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
178	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
179	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
180	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
181	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
182	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
183	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
184	C₂²⋊C₄×D₆₇	C₂³	1	32	yes	complemented
185	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
186	C₂×C₄×Dic₆₇	C₂³	1	4	yes	—
187	C₂⁵×C₆₇	C₂³	1	2	yes	—
188	C₂²×Q₈×C₆₇	—	4	4	no	—
189	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
190	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
191	C₂²×Q₈×C₆₇	C₂³	1	8	yes	complemented
192	C₂²×D₄×C₆₇	—	4	4	no	—
193	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
194	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
195	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
196	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
197	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
198	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
199	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
200	#124×C₆₇	C₂³	1	16	yes	complemented
201	#124×C₆₇	C₂³	1	16	yes	complemented
202	#124×C₆₇	C₂³	1	16	yes	complemented
203	#124×C₆₇	C₂³	1	16	yes	complemented
204	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
205	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
206	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
207	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
208	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	complemented
209	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	complemented
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	—	4	8	no	—
216	C₂³×D₆₇	—	4	8	no	—
217	C₂³×D₆₇	—	4	8	no	—
218	C₂³×D₆₇	C₂⁴	1	2	yes	—
219	C₂³×D₆₇	C₂⁴	1	4	yes	—
220	C₂³×D₆₇	C₂⁴	1	16	yes	—
221	#11761629	—	4	32	no	—
222	#11761628	—	4	32	no	—
223	C₂×Dic₁₃₄	—	4	2	no	—
224	C₂×Dic₁₃₄	—	4	4	no	—
225	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
226	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
227	C₂×D₂₆₈	—	2	8	no	—
228	C₂×D₂₆₈	—	4	4	no	—
229	C₂×D₂₆₈	—	4	2	no	—
230	C₂×D₂₆₈	—	4	4	no	—
231	C₂×D₂₆₈	—	4	8	no	—
232	C₂×D₂₆₈	C₂⁴	1	8	yes	—
233	C₂×D₂₆₈	C₂⁴	1	4	yes	—
234	C₂×D₂₆₈	C₂⁴	1	8	yes	—
235	C₂×D₂₆₈	C₂⁴	1	16	yes	—
236	C₂×D₂₆₈	C₂⁴	1	8	yes	—
237	C₂×C₂²⋊D₆₇	—	2	8	no	—
238	C₂×C₂²⋊D₆₇	—	2	16	no	—
239	C₂×C₂²⋊D₆₇	—	4	8	no	—
240	C₂×C₂²⋊D₆₇	—	4	8	no	—
241	C₂×C₂²⋊D₆₇	—	4	8	no	—
242	C₂×C₂²⋊D₆₇	—	4	8	no	—
243	C₂×C₂²⋊D₆₇	—	4	64	no	—
244	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
245	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
246	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
247	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
248	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
249	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
250	D₄×D₆₇	—	4	32	no	—
251	C₂²×Dic₆₇	—	4	8	no	—
252	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
253	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
254	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
255	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
256	C₂²×Dic₆₇	C₂⁴	1	16	yes	—
257	C₂×C₄×D₆₇	—	2	8	no	—
258	C₂×C₄×D₆₇	—	4	8	no	—
259	C₂×C₄×D₆₇	—	4	8	no	—
260	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
261	C₂×C₄×D₆₇	C₂⁴	1	16	yes	—
262	C₂×C₄×D₆₇	C₂⁴	1	16	yes	—
263	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
264	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
265	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
266	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
267	C₄⋊Dic₆₇	C₂⁴	1	16	yes	—
268	Dic₆₇⋊C₄	C₂⁴	1	8	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	16	yes	—
273	C₂²⋊Dic₆₇	C₂⁴	1	16	yes	—
274	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
275	C₂²⋊Dic₆₇	C₂⁴	1	16	yes	—
276	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
277	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
278	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
279	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
280	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
281	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
282	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
283	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
284	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
285	C₄×Dic₆₇	C₂⁴	1	8	yes	—
286	C₄×Dic₆₇	C₂⁴	1	16	yes	—
287	C₂⁴×C₆₇	—	2	8	no	—
288	C₂⁴×C₆₇	—	4	4	no	—
289	C₂⁴×C₆₇	—	4	4	no	—
290	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
291	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
292	C₂⁴×C₆₇	C₂⁴	1	8	yes	—
293	C₂×Q₈×C₆₇	—	2	8	no	—
294	C₂×Q₈×C₆₇	—	4	4	no	—
295	C₂×Q₈×C₆₇	—	4	16	no	—
296	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
297	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
298	C₂×D₄×C₆₇	—	2	8	no	—
299	C₂×D₄×C₆₇	—	4	16	no	—
300	C₂×D₄×C₆₇	—	4	4	no	—
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	4	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	8	yes	—
317	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
318	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
319	C₂²⋊C₄×C₆₇	C₂⁴	1	16	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	—	2	16	no	—
332	C₂³×C₆₇	—	4	8	no	—
333	C₂³×C₆₇	—	4	8	no	—
334	C₂³×C₆₇	—	8	16	no	—
335	C₂³×C₆₇	H(5,𝔽₂)	1	4	yes	—
336	C₂³×C₆₇	C₂⁵	1	8	yes	—
337	C₂³×C₆₇	C₂⁵	1	2	yes	—
338	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
339	C₂²×D₆₇	—	2	4	no	—
340	C₂²×D₆₇	—	2	8	no	—
341	C₂²×D₆₇	—	2	8	no	—
342	C₂²×D₆₇	—	2	4	no	—
343	C₂²×D₆₇	—	2	8	no	—
344	C₂²×D₆₇	—	2	4	no	—
345	C₂²×D₆₇	—	4	16	no	—
346	C₂²×D₆₇	—	4	16	no	—
347	C₂²×D₆₇	—	4	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	—	2	16	no	—
352	Q₈×C₆₇	—	4	8	no	—
353	D₄×C₆₇	—	2	16	no	—
354	D₄×C₆₇	—	4	8	no	—
355	C₂×C₄×C₆₇	—	2	2	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	8	no	—
360	C₂×C₄×C₆₇	—	2	2	no	—
361	C₂×C₄×C₆₇	—	2	2	no	—
362	C₂×C₄×C₆₇	—	2	8	no	—
363	C₂×C₄×C₆₇	—	4	4	no	—
364	C₂×C₄×C₆₇	—	4	8	no	—
365	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
366	C₂×C₄×C₆₇	C₂⁵	1	2	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	8	yes	—
372	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
373	C₂²⋊D₆₇	—	2	16	no	—
374	C₂²⋊D₆₇	—	2	32	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	8	no	—
381	C₂×Dic₆₇	—	2	4	no	—
382	C₂×Dic₆₇	—	2	4	no	—
383	C₂×Dic₆₇	—	4	16	no	—
384	C₂×Dic₆₇	C₂⁵	1	4	yes	—
385	C₂×Dic₆₇	C₂⁵	1	8	yes	—
386	C₂×Dic₆₇	C₂⁵	1	4	yes	—
387	C₂×Dic₆₇	C₂⁵	1	4	yes	—
388	D₂₆₈	—	2	16	no	—
389	D₂₆₈	—	4	4	no	—
390	D₂₆₈	—	4	8	no	—
391	D₂₆₈	—	4	8	no	—
392	D₂₆₈	—	4	16	no	—
393	C₄×D₆₇	—	2	16	no	—
394	C₄×D₆₇	—	4	16	no	—
395	C₄×D₆₇	—	4	16	no	—
396	Dic₁₃₄	—	4	4	no	—
397	Dic₁₃₄	—	4	8	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	—	8	16	no	—
406	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
407	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
408	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
409	C₂²×C₆₇	#585	1	2	yes	—
410	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
411	C₂×D₆₇	—	2	4	no	—
412	C₂×D₆₇	—	2	8	no	—
413	C₂×D₆₇	—	2	8	no	—
414	C₂×D₆₇	—	2	4	no	—
415	C₂×D₆₇	—	2	8	no	—
416	C₂×D₆₇	—	2	4	no	—
417	C₂×D₆₇	—	4	16	no	—
418	C₂×D₆₇	—	4	8	no	—
419	C₂×D₆₇	—	8	32	no	—
420	C₄×C₆₇	—	2	2	no	—
421	C₄×C₆₇	—	2	2	no	—
422	C₄×C₆₇	—	2	8	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	8	no	—
439	D₆₇	—	4	4	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	2	no	—
446	C₂×#546	—	67	4	no	—
447	C₂×D₄²	—	67	2	no	—
448	C₂×#542	—	67	2	no	—
449	C₂×#538	—	67	4	no	—
450	C₂×#538	—	67	2	no	—
451	C₂×#535	—	67	2	no	—
452	C₂×#534	—	67	2	no	—
453	C₂×#532	—	67	1	no	—
454	C₂×#529	—	67	1	no	—
455	C₂²×#124	D₆₇	1	1	yes	characteristic, complemented
456	C₆₇	C₂×#3558	1	1	yes	characteristic, complemented, Sylow
457	C₂²×#41	—	67	2	no	—
458	C₂²×#41	—	67	2	no	—
459	C₂³×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
460	C₂³×D₄	—	67	4	no	—
461	C₂³×D₄	—	67	2	no	—
462	C₂³×D₄	C₂×D₆₇	1	1	yes	characteristic
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	32	no	—
468	#546	—	67	64	no	—
469	D₄²	—	67	32	no	—
470	#542	—	67	32	no	—
471	#538	—	67	64	no	—
472	#538	—	67	32	no	—
473	#535	—	67	32	no	—
474	#534	—	67	32	no	—
475	#532	—	67	16	no	—
476	C₂×C₄⋊Q₈	—	67	1	no	—
477	C₂×#127	—	67	2	no	—
478	C₂×#127	—	67	1	no	—
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	2	no	—
484	C₂×#124	—	67	4	no	—
485	C₂×#124	—	67	4	no	—
486	C₂×#124	—	67	4	no	—
487	C₂×#124	—	67	1	no	—
488	C₂×#124	—	67	2	no	—
489	C₂×#124	C₂×D₆₇	1	2	yes	complemented
490	C₂×#124	C₂×D₆₇	1	2	yes	complemented
491	C₂×#124	C₂×D₆₇	1	2	yes	complemented
492	C₂×#124	C₂×D₆₇	1	2	yes	complemented
493	C₂×#124	C₂×D₆₇	1	16	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	2	no	—
501	C₂×C₂²⋊Q₈	—	67	1	no	—
502	C₂×C₂²⋊Q₈	—	67	4	no	—
503	C₂×#121	—	67	4	no	—
504	C₂×#121	—	67	2	no	—
505	C₂×#121	—	67	1	no	—
506	C₂×#121	—	67	2	no	—
507	C₂×#121	—	67	2	no	—
508	C₂×#121	—	67	4	no	—
509	C₂×#121	—	67	4	no	—
510	C₂×#121	—	67	4	no	—
511	C₂×#121	—	67	4	no	—
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	2	no	—
520	C₂×C₄×D₄	—	67	2	no	—
521	C₂×C₄×D₄	—	67	4	no	—
522	C₂×C₄×D₄	—	67	4	no	—
523	C₂×C₄×D₄	—	67	1	no	—
524	C₂×C₄×D₄	—	67	2	no	—
525	C₂×C₄×D₄	—	67	2	no	—
526	C₂×#117	—	67	2	no	—
527	C₂²×C₂²⋊C₄	—	67	4	no	—
528	C₂²×C₂²⋊C₄	C₂×D₆₇	1	2	yes	complemented
529	C₂²×C₂²⋊C₄	C₂×D₆₇	1	2	yes	complemented
530	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic, complemented
531	C₂⁵	—	67	4	no	—
532	C₂⁵	C₂²×D₆₇	1	2	yes	—
533	C₂×#41	—	268	8	no	—
534	C₂×#41	—	268	8	no	—
535	C₂×#41	—	67	16	no	—
536	C₂×#41	—	67	16	no	—
537	C₂²×Q₈	—	4	4	no	—
538	C₂²×Q₈	—	67	1	no	—
539	C₂²×Q₈	—	67	2	no	—
540	C₂²×Q₈	C₂²×D₆₇	1	2	yes	—
541	C₂²×Q₈	C₂²×D₆₇	1	2	yes	—
542	C₂²×Q₈	C₂²×D₆₇	1	8	yes	complemented
543	C₂²×D₄	—	4	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	4	no	—
553	C₂²×D₄	—	67	2	no	—
554	C₂²×D₄	—	67	1	no	—
555	C₂²×D₄	—	67	2	no	—
556	C₂²×D₄	—	67	4	no	—
557	C₂²×D₄	—	67	2	no	—
558	C₂²×D₄	—	67	2	no	—
559	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
560	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
561	C₂²×D₄	C₂²×D₆₇	1	8	yes	—
562	C₂³×C₄	—	67	4	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	2	yes	—
569	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
570	C₄⋊Q₈	—	67	8	no	—
571	#127	—	67	16	no	—
572	#127	—	67	8	no	—
573	#126	—	67	32	no	—
574	#126	—	67	16	no	—
575	#125	—	67	8	no	—
576	#124	—	67	16	no	—
577	#124	—	67	32	no	—
578	#124	—	67	32	no	—
579	#124	—	67	32	no	—
580	#124	—	67	8	no	—
581	#124	—	67	16	no	—
582	#124	C₂²×D₆₇	1	16	yes	complemented
583	#124	C₂²×D₆₇	1	16	yes	complemented
584	#124	C₂²×D₆₇	1	16	yes	complemented
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	16	no	—
593	C₂²⋊Q₈	—	67	8	no	—
594	C₂²⋊Q₈	—	67	32	no	—
595	#121	—	67	32	no	—
596	#121	—	67	16	no	—
597	#121	—	67	8	no	—
598	#121	—	67	16	no	—
599	#121	—	67	16	no	—
600	#121	—	67	32	no	—
601	#121	—	67	32	no	—
602	#121	—	67	32	no	—
603	#121	—	67	32	no	—
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	16	no	—
612	C₄×D₄	—	67	16	no	—
613	C₄×D₄	—	67	32	no	—
614	C₄×D₄	—	67	32	no	—
615	C₄×D₄	—	67	8	no	—
616	C₄×D₄	—	67	16	no	—
617	C₄×D₄	—	67	16	no	—
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	2	no	—
624	C₂×C₄⋊C₄	—	67	4	no	—
625	C₂×C₄⋊C₄	—	67	2	no	—
626	C₂×C₄⋊C₄	—	67	1	no	—
627	C₂×C₄⋊C₄	—	67	4	no	—
628	C₂×C₄⋊C₄	—	67	1	no	—
629	C₂×C₂²⋊C₄	—	67	4	no	—
630	C₂×C₂²⋊C₄	—	67	2	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	2	no	—
635	C₂×C₂²⋊C₄	—	67	2	no	—
636	C₂×C₂²⋊C₄	—	67	2	no	—
637	C₂×C₂²⋊C₄	—	67	4	no	—
638	C₂×C₂²⋊C₄	—	67	4	no	—
639	C₂×C₂²⋊C₄	—	67	4	no	—
640	C₂×C₂²⋊C₄	—	67	4	no	—
641	C₂×C₂²⋊C₄	—	67	32	no	—
642	C₂×C₂²⋊C₄	C₂²×D₆₇	1	4	yes	—
643	C₂×C₂²⋊C₄	C₂²×D₆₇	1	4	yes	—
644	C₂×C₂²⋊C₄	C₂²×D₆₇	1	4	yes	—
645	C₂×C₂²⋊C₄	C₂²×D₆₇	1	4	yes	—
646	C₂×C₂²⋊C₄	C₂²×D₆₇	1	16	yes	complemented
647	C₂×C₂²⋊C₄	C₂²×D₆₇	1	16	yes	complemented
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	—	2	8	no	—
656	C₂⁴	—	4	4	no	—
657	C₂⁴	—	4	4	no	—
658	C₂⁴	—	268	8	no	—
659	C₂⁴	—	268	8	no	—
660	C₂⁴	—	268	8	no	—
661	C₂⁴	—	67	16	no	—
662	C₂⁴	—	67	2	no	—
663	C₂⁴	—	67	4	no	—
664	C₂⁴	C₂³×D₆₇	1	4	yes	—
665	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
666	C₂⁴	C₂³×D₆₇	1	8	yes	—
667	#41	—	268	32	no	—
668	#41	—	268	32	no	—
669	C₂×Q₈	—	2	8	no	—
670	C₂×Q₈	—	4	4	no	—
671	C₂×Q₈	—	4	16	no	—
672	C₂×Q₈	—	268	4	no	—
673	C₂×Q₈	—	268	2	no	—
674	C₂×Q₈	—	67	4	no	—
675	C₂×Q₈	—	67	8	no	—
676	C₂×Q₈	C₂³×D₆₇	1	8	yes	—
677	C₂×Q₈	C₂³×D₆₇	1	8	yes	—
678	C₂×D₄	—	2	8	no	—
679	C₂×D₄	—	4	16	no	—
680	C₂×D₄	—	4	4	no	—
681	C₂×D₄	—	268	8	no	—
682	C₂×D₄	—	268	4	no	—
683	C₂×D₄	—	268	4	no	—
684	C₂×D₄	—	268	2	no	—
685	C₂×D₄	—	268	64	no	—
686	C₂×D₄	—	268	32	no	—
687	C₂×D₄	—	268	8	no	—
688	C₂×D₄	—	268	8	no	—
689	C₂×D₄	—	268	8	no	—
690	C₂×D₄	—	268	8	no	—
691	C₂×D₄	—	67	16	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	8	no	—
699	C₂×D₄	—	67	16	no	—
700	C₂×D₄	—	67	8	no	—
701	C₂×D₄	—	67	8	no	—
702	C₂×D₄	—	134	8	no	—
703	C₂×D₄	—	134	16	no	—
704	C₂×D₄	—	134	8	no	—
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	4	no	—
710	C₂²×C₄	—	4	2	no	—
711	C₂²×C₄	—	268	8	no	—
712	C₂²×C₄	—	268	8	no	—
713	C₂²×C₄	—	268	8	no	—
714	C₂²×C₄	—	67	16	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	8	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	8	no	—
739	C₄⋊C₄	—	67	16	no	—
740	C₄⋊C₄	—	67	8	no	—
741	C₄⋊C₄	—	67	4	no	—
742	C₄⋊C₄	—	67	16	no	—
743	C₄⋊C₄	—	67	4	no	—
744	C₂²⋊C₄	—	67	16	no	—
745	C₂²⋊C₄	—	67	8	no	—
746	C₂²⋊C₄	—	67	16	no	—
747	C₂²⋊C₄	—	67	8	no	—
748	C₂²⋊C₄	—	67	16	no	—
749	C₂²⋊C₄	—	67	8	no	—
750	C₂²⋊C₄	—	67	8	no	—
751	C₂²⋊C₄	—	67	8	no	—
752	C₂²⋊C₄	—	67	16	no	—
753	C₂²⋊C₄	—	67	16	no	—
754	C₂²⋊C₄	—	67	16	no	—
755	C₂²⋊C₄	—	67	16	no	—
756	C₂²⋊C₄	C₂³×D₆₇	1	16	yes	—
757	C₂²⋊C₄	C₂³×D₆₇	1	16	yes	—
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	—	2	16	no	—
772	C₂³	—	4	8	no	—
773	C₂³	—	4	8	no	—
774	C₂³	—	8	16	no	—
775	C₂³	—	268	16	no	—
776	C₂³	—	268	16	no	—
777	C₂³	—	268	16	no	—
778	C₂³	—	536	32	no	—
779	C₂³	—	67	4	no	—
780	C₂³	—	67	8	no	—
781	C₂³	—	134	8	no	—
782	C₂³	—	134	4	no	—
783	C₂³	—	134	8	no	—
784	C₂³	—	134	4	no	—
785	C₂³	—	134	8	no	—
786	C₂³	—	134	4	no	—
787	C₂³	#14524089	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	—	2	16	no	—
792	Q₈	—	4	8	no	—
793	Q₈	—	268	8	no	—
794	Q₈	—	268	4	no	—
795	D₄	—	2	16	no	—
796	D₄	—	4	8	no	—
797	D₄	—	268	16	no	—
798	D₄	—	268	8	no	—
799	D₄	—	268	8	no	—
800	D₄	—	268	4	no	—
801	D₄	—	268	16	no	—
802	D₄	—	268	16	no	—
803	D₄	—	268	16	no	—
804	D₄	—	268	16	no	—
805	D₄	—	134	16	no	—
806	D₄	—	134	32	no	—
807	D₄	—	134	16	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	8	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	8	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	8	no	—
816	C₂×C₄	—	4	8	no	—
817	C₂×C₄	—	4	4	no	—
818	C₂×C₄	—	268	16	no	—
819	C₂×C₄	—	268	16	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	#14524088	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	—	8	16	no	—
846	C₂²	—	268	8	no	—
847	C₂²	—	268	16	no	—
848	C₂²	—	536	32	no	—
849	C₂²	—	134	8	no	—
850	C₂²	—	134	4	no	—
851	C₂²	—	134	8	no	—
852	C₂²	—	134	4	no	—
853	C₂²	—	134	8	no	—
854	C₂²	—	134	4	no	—
855	C₂²	C₂×#14524088	1	2	yes	—
856	C₂²	C₂×#14524089	1	4	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	8	no	—
862	C₄	—	2	2	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×#14524088	1	4	yes	—
871	C₂	—	2	4	no	—
872	C₂	—	4	8	no	—
873	C₂	—	268	4	no	—
874	C₂	—	268	8	no	—
875	C₂	#22574728	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	C₂²×#124×C₆₇	C₂
socle	C₂³×C₆₇	C₂⁵
hypercenter	C₂²×#124	D₆₇
hypocenter	C₆₇	C₂×#3558
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂²×#124

Complements

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

N	H ≅ G/N	type
1. #22574728	C₂	direct (N × H)
2. C₂×#16864140	C₂	semidirect
3. C₂×#16864138	C₂	semidirect
4. C₂×#16864128	C₂	semidirect
5. C₂×#16864057	C₂	semidirect
6. C₂×#16864039	C₂	semidirect
7. C₂×#16864036	C₂	semidirect
8. C₂×D₄×C₂²⋊D₆₇	C₂	semidirect
9. C₂×#16864015	C₂	semidirect
10. C₂×#16863984	C₂	semidirect
11. C₂×#16863980	C₂	semidirect
12. C₂×#16863964	C₂	semidirect
13. C₂×#16863958	C₂	semidirect
14. C₂×#16863946	C₂	semidirect
15. C₂×#16863930	C₂	semidirect
16. C₂²×#124×C₆₇	C₂	semidirect
17. C₂²×#11761629	C₂²	semidirect
18. C₂²×#11761628	C₂²	semidirect
19. C₂³×C₂²⋊D₆₇	C₂²	semidirect
20. C₂²×D₄×D₆₇	C₂²	semidirect
21. #16864140	C₂²	semidirect
22. #16864138	C₂²	semidirect
23. #16864128	C₂²	semidirect
24. #16864057	C₂²	semidirect
25. #16864039	C₂²	semidirect
26. #16864036	C₂²	semidirect
27. D₄×C₂²⋊D₆₇	C₂²	semidirect
28. #16864015	C₂²	semidirect
29. #16863984	C₂²	semidirect
30. #16863980	C₂²	semidirect
31. #16863964	C₂²	semidirect
32. #16863958	C₂²	semidirect
33. #16863946	C₂²	semidirect
34. C₂×#14524043	C₂²	semidirect
35. C₂×#14524040	C₂²	semidirect
37. #16863930	C₂²	semidirect
38. C₂×#14524037	C₂²	semidirect
39. C₂×#14524036	C₂²	semidirect
40. C₂×#14524035	C₂²	semidirect
41. C₂×#14524032	C₂²	semidirect
42. C₂×#14524032	C₂²	semidirect
43. C₂×#14524031	C₂²	semidirect
44. C₂×#14524031	C₂²	semidirect
45. C₂×#14524029	C₂²	semidirect
46. C₂×#14524029	C₂²	semidirect
47. C₂×#14524027	C₂²	semidirect
48. C₂×#14524027	C₂²	semidirect
49. C₂×#14524026	C₂²	semidirect
50. C₂×#14524025	C₂²	semidirect
51. C₂×#14524025	C₂²	semidirect
52. C₂×#14524022	C₂²	semidirect
53. C₂×#14524020	C₂²	semidirect
54. C₂×#14524019	C₂²	semidirect
55. C₂×#14524019	C₂²	semidirect
57. C₂×#14524017	C₂²	semidirect
58. C₂×#14524017	C₂²	semidirect
59. C₂×#14524017	C₂²	semidirect
60. C₂×#14524016	C₂²	semidirect
61. C₂×#14524016	C₂²	semidirect
62. C₂×#14524016	C₂²	semidirect
63. C₂×#14524015	C₂²	semidirect
65. C₂×#14524013	C₂²	semidirect
66. C₂×#14524013	C₂²	semidirect
67. C₂×#14524013	C₂²	semidirect
68. C₂×#14524012	C₂²	semidirect
69. C₂×#14524011	C₂²	semidirect
70. C₂×Q₈×Dic₆₇	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×D₄×Dic₆₇	C₂²	semidirect
76. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
77. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
78. C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
79. C₂×#14524000	C₂²	semidirect
80. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
81. C₂³×Q₈×C₆₇	C₂²	semidirect
83. C₂×#124×C₆₇	C₂²	semidirect
84. C₂×#124×C₆₇	C₂²	semidirect
85. C₂×#124×C₆₇	C₂²	semidirect
86. C₂×#124×C₆₇	C₂²	semidirect
87. C₂×#124×C₆₇	C₂²	semidirect
88. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
89. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
90. C₂²×C₄²×C₆₇	C₂²	semidirect
93. C₂×#11761629	C₂³	semidirect
95. C₂×#11761628	C₂³	semidirect
110. C₂²×C₂²⋊D₆₇	C₂³	semidirect
112. C₂×D₄×D₆₇	C₂³	semidirect
117. #14524043	C₂³	semidirect
118. #14524040	C₂³	semidirect
120. #14524037	C₂³	semidirect
121. #14524036	C₂³	semidirect
122. #14524035	C₂³	semidirect
123. #14524032	C₂³	semidirect
124. #14524032	C₂³	semidirect
125. #14524031	C₂³	semidirect
126. #14524031	C₂³	semidirect
127. #14524029	C₂³	semidirect
128. #14524029	C₂³	semidirect
129. #14524027	C₂³	semidirect
130. #14524027	C₂³	semidirect
131. #14524026	C₂³	semidirect
132. #14524025	C₂³	semidirect
133. #14524025	C₂³	semidirect
134. #14524022	C₂³	semidirect
135. #14524020	C₂³	semidirect
136. #14524019	C₂³	semidirect
137. #14524019	C₂³	semidirect
139. #14524017	C₂³	semidirect
140. #14524017	C₂³	semidirect
141. #14524017	C₂³	semidirect
142. #14524016	C₂³	semidirect
143. #14524016	C₂³	semidirect
144. #14524016	C₂³	semidirect
145. #14524015	C₂³	semidirect
147. #14524013	C₂³	semidirect
148. #14524013	C₂³	semidirect
149. #14524013	C₂³	semidirect
150. #14524012	C₂³	semidirect
151. #14524011	C₂³	semidirect
152. Q₈×Dic₆₇	C₂³	semidirect
153. C₄×Dic₁₃₄	C₂³	semidirect
154. C₄×D₂₆₈	C₂³	semidirect
155. C₄×D₂₆₈	C₂³	semidirect
156. C₄×D₂₆₈	C₂³	semidirect
157. D₄×Dic₆₇	C₂³	semidirect
158. C₄×C₂²⋊D₆₇	C₂³	semidirect
159. C₄×C₂²⋊D₆₇	C₂³	semidirect
160. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
161. #14524000	C₂³	semidirect
184. C₂²⋊C₄×D₆₇	C₂³	semidirect
191. C₂²×Q₈×C₆₇	C₂³	semidirect
200. #124×C₆₇	C₂³	semidirect
201. #124×C₆₇	C₂³	semidirect
202. #124×C₆₇	C₂³	semidirect
203. #124×C₆₇	C₂³	semidirect
208. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
209. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
214. C₂×C₄²×C₆₇	C₂³	semidirect
434. C₂×C₆₇	#3558	semidirect
455. C₂²×#124	D₆₇	semidirect
456. C₆₇	C₂×#3558	semidirect
459. C₂³×Q₈	C₂×D₆₇	semidirect
489. C₂×#124	C₂×D₆₇	semidirect
490. C₂×#124	C₂×D₆₇	semidirect
491. C₂×#124	C₂×D₆₇	semidirect
492. C₂×#124	C₂×D₆₇	semidirect
493. C₂×#124	C₂×D₆₇	semidirect
528. C₂²×C₂²⋊C₄	C₂×D₆₇	semidirect
529. C₂²×C₂²⋊C₄	C₂×D₆₇	semidirect
530. C₂²×C₄²	C₂×D₆₇	semidirect
542. C₂²×Q₈	C₂²×D₆₇	semidirect
582. #124	C₂²×D₆₇	semidirect
583. #124	C₂²×D₆₇	semidirect
584. #124	C₂²×D₆₇	semidirect
585. #124	C₂²×D₆₇	semidirect
646. C₂×C₂²⋊C₄	C₂²×D₆₇	semidirect
647. C₂×C₂²⋊C₄	C₂²×D₆₇	semidirect
654. C₂×C₄²	C₂²×D₆₇	semidirect
875. C₂	#22574728	direct (N × H)

Maximal subgroups

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

subgroup	index
#22574728	2
C₂×#16864140	2
C₂×#16864138	2
C₂×#16864128	2
C₂×#16864057	2
C₂×#16864039	2
C₂×#16864036	2
C₂×D₄×C₂²⋊D₆₇	2
C₂×#16864015	2
C₂×#16863984	2
C₂×#16863980	2
C₂×#16863964	2
C₂×#16863958	2
C₂×#16863946	2
C₂×#16863930	2
C₂²×#124×C₆₇	2
C₂×#3558	67

Subgroups — C2×#22574728 #31763166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22574728 #31763166