Subgroups — C₆₇×#61673 #30740924

Order 17152.

2160 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3549	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3321	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3319	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3265	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3264	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3213	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3200	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3199	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3115	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3010	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3008	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2980	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic, complemented
15	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic, complemented
16	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
17	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
18	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
19	C₂²×D₈×C₆₇	C₂²	1	2	yes	complemented
20	H(3,𝔽₄)×C₆₇	—	2	1	no	—
21	H(3,𝔽₄)×C₆₇	—	2	1	no	—
22	#555×C₆₇	—	2	1	no	—
23	#555×C₆₇	C₂²	1	4	yes	complemented
24	#548×C₆₇	C₂²	1	4	yes	complemented
25	#546×C₆₇	—	2	4	no	—
26	#546×C₆₇	C₂²	1	4	yes	complemented
27	D₄²×C₆₇	—	2	1	no	—
28	D₄²×C₆₇	C₂²	1	4	yes	complemented
29	#536×C₆₇	—	2	1	no	—
30	#536×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	#535×C₆₇	—	2	1	no	—
32	#535×C₆₇	—	2	4	no	—
33	#535×C₆₇	C₂²	1	2	yes	—
34	#535×C₆₇	C₂²	1	2	yes	complemented
35	#535×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	#532×C₆₇	—	2	1	no	—
37	#532×C₆₇	C₂²	1	1	yes	characteristic
38	#532×C₆₇	C₂²	1	2	yes	complemented
39	C₂×#124×C₆₇	—	2	1	no	—
40	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
41	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	#496×C₆₇	C₂²	1	4	yes	complemented
43	#489×C₆₇	C₂²	1	4	yes	complemented
44	#485×C₆₇	C₂²	1	4	yes	complemented
45	#482×C₆₇	C₂²	1	4	yes	complemented
46	#482×C₆₇	C₂²	1	4	yes	complemented
47	#475×C₆₇	C₂²	1	2	yes	complemented
48	#474×C₆₇	C₂²	1	2	yes	complemented
49	#469×C₆₇	C₂²	1	4	yes	complemented
50	#468×C₆₇	C₂²	1	4	yes	complemented
51	#466×C₆₇	C₂²	1	4	yes	complemented
52	#465×C₆₇	C₂²	1	4	yes	complemented
53	#463×C₆₇	C₂²	1	4	yes	complemented
54	#463×C₆₇	C₂²	1	4	yes	complemented
55	#460×C₆₇	C₂²	1	2	yes	complemented
56	#459×C₆₇	C₂²	1	2	yes	complemented
57	#450×C₆₇	C₂²	1	4	yes	complemented
58	#449×C₆₇	C₂²	1	4	yes	complemented
59	#449×C₆₇	C₂²	1	4	yes	complemented
60	#449×C₆₇	C₂²	1	4	yes	complemented
61	#448×C₆₇	C₂²	1	4	yes	complemented
62	#448×C₆₇	C₂²	1	4	yes	complemented
63	#447×C₆₇	C₂²	1	4	yes	complemented
64	#447×C₆₇	C₂²	1	4	yes	complemented
65	#447×C₆₇	C₂²	1	4	yes	complemented
66	#442×C₆₇	C₂²	1	4	yes	complemented
67	#440×C₆₇	C₂²	1	4	yes	complemented
68	#435×C₆₇	C₂²	1	4	yes	complemented
69	#435×C₆₇	C₂²	1	4	yes	complemented
70	#432×C₆₇	C₂²	1	2	yes	complemented
71	#419×C₆₇	C₂²	1	2	yes	complemented
72	#418×C₆₇	C₂²	1	2	yes	complemented
73	#416×C₆₇	C₂²	1	2	yes	complemented
74	#416×C₆₇	C₂²	1	2	yes	complemented
75	#408×C₆₇	C₂²	1	2	yes	complemented
76	#408×C₆₇	C₂²	1	2	yes	complemented
77	2₋¹⁺⁴×C₆₇	—	4	2	no	—
78	2₋¹⁺⁴×C₆₇	—	4	2	no	—
79	H(5,𝔽₂)×C₆₇	—	4	2	no	—
80	H(5,𝔽₂)×C₆₇	—	4	2	no	—
81	C₂×#41×C₆₇	—	2	1	no	—
82	C₂×#41×C₆₇	—	2	1	no	—
83	C₂×#41×C₆₇	—	2	2	no	—
84	C₂×#41×C₆₇	—	2	2	no	—
85	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
86	C₂×#41×C₆₇	C₂³	1	2	yes	—
87	C₂×#41×C₆₇	C₂³	1	2	yes	—
88	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
89	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
90	C₂²×Q₈×C₆₇	—	2	1	no	—
91	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
92	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₆₇	—	2	1	no	—
94	C₂²×D₄×C₆₇	—	2	2	no	—
95	C₂²×D₄×C₆₇	—	2	4	no	—
96	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
97	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
98	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
100	AGL(1,ℤ/8)×C₆₇	—	4	4	no	—
101	AGL(1,ℤ/8)×C₆₇	—	4	4	no	—
102	C₂×SD₁₆×C₆₇	—	4	4	no	—
103	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
104	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
105	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
106	C₂×D₈×C₆₇	—	4	4	no	—
107	C₂×D₈×C₆₇	C₂³	1	4	yes	—
108	C₂×D₈×C₆₇	C₂³	1	4	yes	—
109	C₂×D₈×C₆₇	C₂³	1	4	yes	—
110	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
111	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
112	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
113	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
114	C₄⋊Q₈×C₆₇	—	2	1	no	—
115	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
116	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
117	#127×C₆₇	—	2	1	no	—
118	#127×C₆₇	—	2	2	no	—
119	#127×C₆₇	—	2	2	no	—
120	#127×C₆₇	D₄	1	1	yes	characteristic
121	#127×C₆₇	C₂³	1	2	yes	—
122	#124×C₆₇	—	2	1	no	—
123	#124×C₆₇	—	2	2	no	—
124	#124×C₆₇	—	2	2	no	—
125	#124×C₆₇	—	2	1	no	—
126	#124×C₆₇	—	2	4	no	—
127	#124×C₆₇	—	2	4	no	—
128	#124×C₆₇	—	2	4	no	—
129	#124×C₆₇	—	2	1	no	—
130	#124×C₆₇	—	2	1	no	—
131	#124×C₆₇	—	2	2	no	—
132	#124×C₆₇	D₄	1	1	yes	characteristic
133	#124×C₆₇	D₄	1	1	yes	characteristic
134	#124×C₆₇	C₂³	1	4	yes	—
135	#123×C₆₇	—	2	2	no	—
136	#123×C₆₇	—	2	4	no	—
137	C₂²⋊Q₈×C₆₇	—	2	4	no	—
138	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
139	#121×C₆₇	—	2	4	no	—
140	#121×C₆₇	—	2	4	no	—
141	#121×C₆₇	—	2	2	no	—
142	#121×C₆₇	—	2	4	no	—
143	#121×C₆₇	—	2	4	no	—
144	#121×C₆₇	D₄	1	4	yes	—
145	#121×C₆₇	C₂³	1	4	yes	—
146	#121×C₆₇	C₂³	1	4	yes	—
147	#121×C₆₇	C₂³	1	4	yes	—
148	#121×C₆₇	C₂³	1	4	yes	—
149	#120×C₆₇	—	2	2	no	—
150	#120×C₆₇	—	2	2	no	—
151	#120×C₆₇	—	2	4	no	—
152	#120×C₆₇	—	2	2	no	—
153	#120×C₆₇	—	2	2	no	—
154	#120×C₆₇	—	2	2	no	—
155	#120×C₆₇	—	2	4	no	—
156	#120×C₆₇	—	2	4	no	—
157	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
158	C₄×D₄×C₆₇	—	2	2	no	—
159	C₄×D₄×C₆₇	—	2	4	no	—
160	C₄×D₄×C₆₇	—	2	2	no	—
161	C₄×D₄×C₆₇	C₂³	1	2	yes	—
162	C₄×D₄×C₆₇	C₂³	1	4	yes	—
163	C₄×D₄×C₆₇	C₂³	1	4	yes	—
164	#117×C₆₇	—	2	4	no	—
165	#117×C₆₇	—	2	1	no	—
166	#117×C₆₇	C₂³	1	1	yes	characteristic
167	#117×C₆₇	C₂³	1	2	yes	—
168	#117×C₆₇	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
170	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
171	C₂×C₄²×C₆₇	—	2	1	no	—
172	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
173	#107×C₆₇	C₂³	1	4	yes	—
174	#106×C₆₇	C₂³	1	4	yes	—
175	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
176	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
177	#103×C₆₇	C₂³	1	4	yes	—
178	#103×C₆₇	C₂³	1	4	yes	—
179	#103×C₆₇	C₂³	1	4	yes	—
180	#102×C₆₇	C₂³	1	4	yes	—
181	#102×C₆₇	C₂³	1	4	yes	—
182	#102×C₆₇	C₂³	1	4	yes	—
183	#102×C₆₇	C₂³	1	4	yes	—
184	#102×C₆₇	C₂³	1	4	yes	—
185	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
186	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
187	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
188	#97×C₆₇	C₂³	1	4	yes	—
189	C₂⁴×C₆₇	—	2	2	no	—
190	C₂⁴×C₆₇	—	2	1	no	—
191	C₂⁴×C₆₇	—	2	2	no	—
192	C₂⁴×C₆₇	—	2	2	no	—
193	#41×C₆₇	—	2	2	no	—
194	#41×C₆₇	—	2	2	no	—
195	#41×C₆₇	—	2	4	no	—
196	#41×C₆₇	—	2	4	no	—
197	#41×C₆₇	—	4	1	no	—
198	#41×C₆₇	—	4	1	no	—
199	#41×C₆₇	—	4	1	no	—
200	#41×C₆₇	—	4	1	no	—
201	#41×C₆₇	—	4	2	no	—
202	#41×C₆₇	—	4	2	no	—
203	#41×C₆₇	—	4	4	no	—
204	#41×C₆₇	—	4	4	no	—
205	#41×C₆₇	—	4	8	no	—
206	#41×C₆₇	—	8	4	no	—
207	C₂×Q₈×C₆₇	—	2	2	no	—
208	C₂×Q₈×C₆₇	—	2	1	no	—
209	C₂×Q₈×C₆₇	—	2	2	no	—
210	C₂×Q₈×C₆₇	—	2	4	no	—
211	C₂×Q₈×C₆₇	—	4	2	no	—
212	C₂×Q₈×C₆₇	—	4	1	no	—
213	C₂×Q₈×C₆₇	—	4	1	no	—
214	C₂×Q₈×C₆₇	—	4	4	no	—
215	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
216	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
217	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
218	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
219	C₂×D₄×C₆₇	—	2	1	no	—
220	C₂×D₄×C₆₇	—	2	4	no	—
221	C₂×D₄×C₆₇	—	2	2	no	—
222	C₂×D₄×C₆₇	—	2	2	no	—
223	C₂×D₄×C₆₇	—	2	4	no	—
224	C₂×D₄×C₆₇	—	2	4	no	—
225	C₂×D₄×C₆₇	—	2	4	no	—
226	C₂×D₄×C₆₇	—	2	4	no	—
227	C₂×D₄×C₆₇	—	2	2	no	—
228	C₂×D₄×C₆₇	—	2	2	no	—
229	C₂×D₄×C₆₇	—	2	1	no	—
230	C₂×D₄×C₆₇	—	2	2	no	—
231	C₂×D₄×C₆₇	—	2	2	no	—
232	C₂×D₄×C₆₇	—	2	2	no	—
233	C₂×D₄×C₆₇	—	4	2	no	—
234	C₂×D₄×C₆₇	—	4	1	no	—
235	C₂×D₄×C₆₇	—	4	1	no	—
236	C₂×D₄×C₆₇	—	4	2	no	—
237	C₂×D₄×C₆₇	—	4	2	no	—
238	C₂×D₄×C₆₇	—	4	2	no	—
239	C₂×D₄×C₆₇	—	4	2	no	—
240	C₂×D₄×C₆₇	—	4	4	no	—
241	C₂×D₄×C₆₇	—	4	8	no	—
242	C₂×D₄×C₆₇	—	8	8	no	—
243	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
244	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
245	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
246	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
247	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
248	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
249	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
250	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₆₇	—	2	1	no	—
252	C₂²×C₄×C₆₇	—	2	1	no	—
253	C₂²×C₄×C₆₇	—	2	2	no	—
254	C₂²×C₄×C₆₇	—	2	2	no	—
255	C₂²×C₄×C₆₇	—	2	4	no	—
256	C₂²×C₄×C₆₇	—	2	2	no	—
257	C₂²×C₄×C₆₇	—	2	2	no	—
258	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
259	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
262	SD₁₆×C₆₇	—	2	8	no	—
263	SD₁₆×C₆₇	—	4	4	no	—
264	SD₁₆×C₆₇	—	4	4	no	—
265	D₈×C₆₇	—	2	8	no	—
266	D₈×C₆₇	—	4	4	no	—
267	D₈×C₆₇	—	4	4	no	—
268	M₁₆×C₆₇	—	4	2	no	—
269	M₁₆×C₆₇	—	4	2	no	—
270	C₂×C₈×C₆₇	—	4	2	no	—
271	C₂×C₈×C₆₇	—	4	2	no	—
272	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
273	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
274	C₄⋊C₄×C₆₇	—	2	2	no	—
275	C₄⋊C₄×C₆₇	—	2	2	no	—
276	C₄⋊C₄×C₆₇	—	2	4	no	—
277	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
278	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
279	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
280	C₂²⋊C₄×C₆₇	—	2	4	no	—
281	C₂²⋊C₄×C₆₇	—	2	1	no	—
282	C₂²⋊C₄×C₆₇	—	2	2	no	—
283	C₂²⋊C₄×C₆₇	—	2	2	no	—
284	C₂²⋊C₄×C₆₇	—	2	4	no	—
285	C₂²⋊C₄×C₆₇	—	2	4	no	—
286	C₂²⋊C₄×C₆₇	—	2	4	no	—
287	C₂²⋊C₄×C₆₇	—	2	2	no	—
288	C₂²⋊C₄×C₆₇	—	2	4	no	—
289	C₂²⋊C₄×C₆₇	—	2	4	no	—
290	C₂²⋊C₄×C₆₇	—	2	4	no	—
291	C₂²⋊C₄×C₆₇	—	2	4	no	—
292	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
293	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
294	C₄²×C₆₇	—	2	1	no	—
295	C₄²×C₆₇	—	2	2	no	—
296	C₄²×C₆₇	—	2	2	no	—
297	C₄²×C₆₇	—	2	2	no	—
298	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
299	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
300	C₄²×C₆₇	C₂⁴	1	2	yes	—
301	C₂³×C₆₇	—	2	1	no	—
302	C₂³×C₆₇	—	2	2	no	—
303	C₂³×C₆₇	—	2	4	no	—
304	C₂³×C₆₇	—	4	4	no	—
305	C₂³×C₆₇	—	4	2	no	—
306	C₂³×C₆₇	—	8	2	no	—
307	C₂³×C₆₇	—	8	2	no	—
308	C₂³×C₆₇	—	8	4	no	—
309	C₂³×C₆₇	—	8	4	no	—
310	C₂³×C₆₇	—	8	2	no	—
311	C₂³×C₆₇	—	8	4	no	—
312	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
313	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
314	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
315	Q₈×C₆₇	—	2	1	no	—
316	Q₈×C₆₇	—	2	2	no	—
317	Q₈×C₆₇	—	2	2	no	—
318	Q₈×C₆₇	—	4	1	no	—
319	Q₈×C₆₇	—	4	1	no	—
320	Q₈×C₆₇	—	4	4	no	—
321	Q₈×C₆₇	—	4	2	no	—
322	Q₈×C₆₇	—	8	2	no	—
323	Q₈×C₆₇	H(5,𝔽₂)	1	2	yes	—
324	D₄×C₆₇	—	2	4	no	—
325	D₄×C₆₇	—	2	1	no	—
326	D₄×C₆₇	—	2	4	no	—
327	D₄×C₆₇	—	2	2	no	—
328	D₄×C₆₇	—	2	2	no	—
329	D₄×C₆₇	—	2	4	no	—
330	D₄×C₆₇	—	4	1	no	—
331	D₄×C₆₇	—	4	2	no	—
332	D₄×C₆₇	—	4	4	no	—
333	D₄×C₆₇	—	4	1	no	—
334	D₄×C₆₇	—	4	2	no	—
335	D₄×C₆₇	—	4	4	no	—
336	D₄×C₆₇	—	4	4	no	—
337	D₄×C₆₇	—	4	2	no	—
338	D₄×C₆₇	—	4	4	no	—
339	D₄×C₆₇	—	4	4	no	—
340	D₄×C₆₇	—	8	2	no	—
341	D₄×C₆₇	—	8	2	no	—
342	D₄×C₆₇	—	8	2	no	—
343	D₄×C₆₇	—	8	4	no	—
344	D₄×C₆₇	—	8	4	no	—
345	D₄×C₆₇	—	8	4	no	—
346	D₄×C₆₇	—	8	4	no	—
347	D₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
348	C₂×C₄×C₆₇	—	2	4	no	—
349	C₂×C₄×C₆₇	—	2	1	no	—
350	C₂×C₄×C₆₇	—	2	2	no	—
351	C₂×C₄×C₆₇	—	2	2	no	—
352	C₂×C₄×C₆₇	—	2	2	no	—
353	C₂×C₄×C₆₇	—	2	2	no	—
354	C₂×C₄×C₆₇	—	2	1	no	—
355	C₂×C₄×C₆₇	—	2	1	no	—
356	C₂×C₄×C₆₇	—	2	2	no	—
357	C₂×C₄×C₆₇	—	2	4	no	—
358	C₂×C₄×C₆₇	—	2	2	no	—
359	C₂×C₄×C₆₇	—	4	2	no	—
360	C₂×C₄×C₆₇	—	4	4	no	—
361	C₂×C₄×C₆₇	—	4	4	no	—
362	C₂×C₄×C₆₇	—	4	4	no	—
363	C₂×C₄×C₆₇	—	4	8	no	—
364	C₂×C₄×C₆₇	—	4	2	no	—
365	C₂×C₄×C₆₇	—	8	2	no	—
366	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
368	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
369	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
370	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
371	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
372	C₈×C₆₇	—	2	4	no	—
373	C₈×C₆₇	—	2	4	no	—
374	C₂²×C₆₇	—	2	2	no	—
375	C₂²×C₆₇	—	2	4	no	—
376	C₂²×C₆₇	—	2	4	no	—
377	C₂²×C₆₇	—	2	1	no	—
378	C₂²×C₆₇	—	2	2	no	—
379	C₂²×C₆₇	—	2	2	no	—
380	C₂²×C₆₇	—	2	2	no	—
381	C₂²×C₆₇	—	4	2	no	—
382	C₂²×C₆₇	—	4	4	no	—
383	C₂²×C₆₇	—	4	4	no	—
384	C₂²×C₆₇	—	4	4	no	—
385	C₂²×C₆₇	—	4	2	no	—
386	C₂²×C₆₇	—	4	4	no	—
387	C₂²×C₆₇	—	16	4	no	—
388	C₂²×C₆₇	—	16	2	no	—
389	C₂²×C₆₇	—	16	4	no	—
390	C₂²×C₆₇	—	16	4	no	—
391	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
392	C₄×C₆₇	—	2	2	no	—
393	C₄×C₆₇	—	2	2	no	—
394	C₄×C₆₇	—	2	1	no	—
395	C₄×C₆₇	—	2	2	no	—
396	C₄×C₆₇	—	2	2	no	—
397	C₄×C₆₇	—	2	2	no	—
398	C₄×C₆₇	—	4	4	no	—
399	C₄×C₆₇	—	4	2	no	—
400	C₄×C₆₇	—	4	2	no	—
401	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
402	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
403	#61673	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
404	C₂×C₆₇	—	4	1	no	—
405	C₂×C₆₇	—	4	2	no	—
406	C₂×C₆₇	—	4	2	no	—
407	C₂×C₆₇	—	4	2	no	—
408	C₂×C₆₇	—	8	4	no	—
409	C₂×C₆₇	—	8	2	no	—
410	C₂×C₆₇	#3484	1	1	yes	characteristic
411	C₂×C₆₇	#3585	1	2	yes	—
412	#3549	C₂×C₆₇	1	1	yes	characteristic, complemented
413	#3500	C₂×C₆₇	1	1	yes	characteristic, complemented
414	#3321	C₂×C₆₇	1	4	yes	complemented
415	#3319	C₂×C₆₇	1	4	yes	complemented
416	#3265	C₂×C₆₇	1	4	yes	complemented
417	#3264	C₂×C₆₇	1	4	yes	complemented
418	#3213	C₂×C₆₇	1	2	yes	complemented
419	#3200	C₂×C₆₇	1	2	yes	complemented
420	#3199	C₂×C₆₇	1	2	yes	complemented
421	#3115	C₂×C₆₇	1	2	yes	complemented
422	#3010	C₂×C₆₇	1	2	yes	complemented
423	#3008	C₂×C₆₇	1	2	yes	complemented
424	#2980	C₂×C₆₇	1	1	yes	characteristic, complemented
425	C₆₇	#61673	1	1	yes	characteristic, direct product factor, Sylow
426	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic, complemented
427	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic, complemented
428	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
429	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
430	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
431	C₂²×D₈	C₂²×C₆₇	1	2	yes	complemented
432	H(3,𝔽₄)	—	2	1	no	—
433	H(3,𝔽₄)	—	2	1	no	—
434	#555	—	2	1	no	—
435	#555	C₂²×C₆₇	1	4	yes	complemented
436	#548	C₂²×C₆₇	1	4	yes	complemented
437	#546	—	2	4	no	—
438	#546	C₂²×C₆₇	1	4	yes	complemented
439	D₄²	—	2	1	no	—
440	D₄²	C₂²×C₆₇	1	4	yes	complemented
441	#536	—	2	1	no	—
442	#536	C₂²×C₆₇	1	1	yes	characteristic, complemented
443	#535	—	2	1	no	—
444	#535	—	2	4	no	—
445	#535	C₂²×C₆₇	1	2	yes	—
446	#535	C₂²×C₆₇	1	1	yes	characteristic, complemented
447	#535	C₂²×C₆₇	1	2	yes	complemented
448	#532	—	2	1	no	—
449	#532	C₂²×C₆₇	1	1	yes	characteristic
450	#532	C₂²×C₆₇	1	2	yes	complemented
451	C₂×#124	—	2	1	no	—
452	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
453	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
454	#496	C₂²×C₆₇	1	4	yes	complemented
455	#489	C₂²×C₆₇	1	4	yes	complemented
456	#485	C₂²×C₆₇	1	4	yes	complemented
457	#482	C₂²×C₆₇	1	4	yes	complemented
458	#482	C₂²×C₆₇	1	4	yes	complemented
459	#475	C₂²×C₆₇	1	2	yes	complemented
460	#474	C₂²×C₆₇	1	2	yes	complemented
461	#469	C₂²×C₆₇	1	4	yes	complemented
462	#468	C₂²×C₆₇	1	4	yes	complemented
463	#466	C₂²×C₆₇	1	4	yes	complemented
464	#465	C₂²×C₆₇	1	4	yes	complemented
465	#463	C₂²×C₆₇	1	4	yes	complemented
466	#463	C₂²×C₆₇	1	4	yes	complemented
467	#460	C₂²×C₆₇	1	2	yes	complemented
468	#459	C₂²×C₆₇	1	2	yes	complemented
469	#450	C₂²×C₆₇	1	4	yes	complemented
470	#449	C₂²×C₆₇	1	4	yes	complemented
471	#449	C₂²×C₆₇	1	4	yes	complemented
472	#449	C₂²×C₆₇	1	4	yes	complemented
473	#448	C₂²×C₆₇	1	4	yes	complemented
474	#448	C₂²×C₆₇	1	4	yes	complemented
475	#447	C₂²×C₆₇	1	4	yes	complemented
476	#447	C₂²×C₆₇	1	4	yes	complemented
477	#447	C₂²×C₆₇	1	4	yes	complemented
478	#442	C₂²×C₆₇	1	4	yes	complemented
479	#440	C₂²×C₆₇	1	4	yes	complemented
480	#435	C₂²×C₆₇	1	4	yes	complemented
481	#435	C₂²×C₆₇	1	4	yes	complemented
482	#432	C₂²×C₆₇	1	2	yes	complemented
483	#419	C₂²×C₆₇	1	2	yes	complemented
484	#418	C₂²×C₆₇	1	2	yes	complemented
485	#416	C₂²×C₆₇	1	2	yes	complemented
486	#416	C₂²×C₆₇	1	2	yes	complemented
487	#408	C₂²×C₆₇	1	2	yes	complemented
488	#408	C₂²×C₆₇	1	2	yes	complemented
489	2₋¹⁺⁴	—	4	2	no	—
490	2₋¹⁺⁴	—	4	2	no	—
491	H(5,𝔽₂)	—	4	2	no	—
492	H(5,𝔽₂)	—	4	2	no	—
493	C₂×#41	—	2	1	no	—
494	C₂×#41	—	2	1	no	—
495	C₂×#41	—	2	2	no	—
496	C₂×#41	—	2	2	no	—
497	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
498	C₂×#41	C₂³×C₆₇	1	2	yes	—
499	C₂×#41	C₂³×C₆₇	1	2	yes	—
500	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
501	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
502	C₂²×Q₈	—	2	1	no	—
503	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
504	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
505	C₂²×D₄	—	2	1	no	—
506	C₂²×D₄	—	2	2	no	—
507	C₂²×D₄	—	2	4	no	—
508	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
509	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
510	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
511	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
512	AGL(1,ℤ/8)	—	4	4	no	—
513	AGL(1,ℤ/8)	—	4	4	no	—
514	C₂×SD₁₆	—	4	4	no	—
515	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
516	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
517	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
518	C₂×D₈	—	4	4	no	—
519	C₂×D₈	C₂³×C₆₇	1	4	yes	—
520	C₂×D₈	C₂³×C₆₇	1	4	yes	—
521	C₂×D₈	C₂³×C₆₇	1	4	yes	—
522	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
523	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
524	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
525	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
526	C₄⋊Q₈	—	2	1	no	—
527	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
528	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
529	#127	—	2	1	no	—
530	#127	—	2	2	no	—
531	#127	—	2	2	no	—
532	#127	D₄×C₆₇	1	1	yes	characteristic
533	#127	C₂³×C₆₇	1	2	yes	—
534	#124	—	2	1	no	—
535	#124	—	2	2	no	—
536	#124	—	2	2	no	—
537	#124	—	2	1	no	—
538	#124	—	2	4	no	—
539	#124	—	2	4	no	—
540	#124	—	2	4	no	—
541	#124	—	2	1	no	—
542	#124	—	2	1	no	—
543	#124	—	2	2	no	—
544	#124	D₄×C₆₇	1	1	yes	characteristic
545	#124	D₄×C₆₇	1	1	yes	characteristic
546	#124	C₂³×C₆₇	1	4	yes	—
547	#123	—	2	2	no	—
548	#123	—	2	4	no	—
549	C₂²⋊Q₈	—	2	4	no	—
550	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
551	#121	—	2	4	no	—
552	#121	—	2	4	no	—
553	#121	—	2	2	no	—
554	#121	—	2	4	no	—
555	#121	—	2	4	no	—
556	#121	D₄×C₆₇	1	4	yes	—
557	#121	C₂³×C₆₇	1	4	yes	—
558	#121	C₂³×C₆₇	1	4	yes	—
559	#121	C₂³×C₆₇	1	4	yes	—
560	#121	C₂³×C₆₇	1	4	yes	—
561	#120	—	2	2	no	—
562	#120	—	2	2	no	—
563	#120	—	2	4	no	—
564	#120	—	2	2	no	—
565	#120	—	2	2	no	—
566	#120	—	2	2	no	—
567	#120	—	2	4	no	—
568	#120	—	2	4	no	—
569	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
570	C₄×D₄	—	2	2	no	—
571	C₄×D₄	—	2	4	no	—
572	C₄×D₄	—	2	2	no	—
573	C₄×D₄	C₂³×C₆₇	1	2	yes	—
574	C₄×D₄	C₂³×C₆₇	1	4	yes	—
575	C₄×D₄	C₂³×C₆₇	1	4	yes	—
576	#117	—	2	4	no	—
577	#117	—	2	1	no	—
578	#117	C₂³×C₆₇	1	1	yes	characteristic
579	#117	C₂³×C₆₇	1	2	yes	—
580	#117	C₂³×C₆₇	1	2	yes	—
581	C₂×C₂²⋊C₄	—	2	2	no	—
582	C₂×C₂²⋊C₄	—	2	4	no	—
583	C₂×C₄²	—	2	1	no	—
584	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
585	#107	C₂³×C₆₇	1	4	yes	—
586	#106	C₂³×C₆₇	1	4	yes	—
587	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
588	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
589	#103	C₂³×C₆₇	1	4	yes	—
590	#103	C₂³×C₆₇	1	4	yes	—
591	#103	C₂³×C₆₇	1	4	yes	—
592	#102	C₂³×C₆₇	1	4	yes	—
593	#102	C₂³×C₆₇	1	4	yes	—
594	#102	C₂³×C₆₇	1	4	yes	—
595	#102	C₂³×C₆₇	1	4	yes	—
596	#102	C₂³×C₆₇	1	4	yes	—
597	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
598	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
599	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
600	#97	C₂³×C₆₇	1	4	yes	—
601	C₂⁴	—	2	2	no	—
602	C₂⁴	—	2	1	no	—
603	C₂⁴	—	2	2	no	—
604	C₂⁴	—	2	2	no	—
605	#41	—	2	2	no	—
606	#41	—	2	2	no	—
607	#41	—	2	4	no	—
608	#41	—	2	4	no	—
609	#41	—	4	1	no	—
610	#41	—	4	1	no	—
611	#41	—	4	1	no	—
612	#41	—	4	1	no	—
613	#41	—	4	2	no	—
614	#41	—	4	2	no	—
615	#41	—	4	4	no	—
616	#41	—	4	4	no	—
617	#41	—	4	8	no	—
618	#41	—	8	4	no	—
619	C₂×Q₈	—	2	2	no	—
620	C₂×Q₈	—	2	1	no	—
621	C₂×Q₈	—	2	2	no	—
622	C₂×Q₈	—	2	4	no	—
623	C₂×Q₈	—	4	2	no	—
624	C₂×Q₈	—	4	1	no	—
625	C₂×Q₈	—	4	1	no	—
626	C₂×Q₈	—	4	4	no	—
627	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
628	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
629	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
630	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	4	no	—
633	C₂×D₄	—	2	2	no	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	2	4	no	—
636	C₂×D₄	—	2	4	no	—
637	C₂×D₄	—	2	4	no	—
638	C₂×D₄	—	2	4	no	—
639	C₂×D₄	—	2	2	no	—
640	C₂×D₄	—	2	2	no	—
641	C₂×D₄	—	2	1	no	—
642	C₂×D₄	—	2	2	no	—
643	C₂×D₄	—	2	2	no	—
644	C₂×D₄	—	2	2	no	—
645	C₂×D₄	—	4	2	no	—
646	C₂×D₄	—	4	1	no	—
647	C₂×D₄	—	4	1	no	—
648	C₂×D₄	—	4	2	no	—
649	C₂×D₄	—	4	2	no	—
650	C₂×D₄	—	4	2	no	—
651	C₂×D₄	—	4	2	no	—
652	C₂×D₄	—	4	4	no	—
653	C₂×D₄	—	4	8	no	—
654	C₂×D₄	—	8	8	no	—
655	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
656	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
657	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
658	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
659	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
660	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
661	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
662	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	4	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
672	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
674	SD₁₆	—	2	8	no	—
675	SD₁₆	—	4	4	no	—
676	SD₁₆	—	4	4	no	—
677	D₈	—	2	8	no	—
678	D₈	—	4	4	no	—
679	D₈	—	4	4	no	—
680	M₁₆	—	4	2	no	—
681	M₁₆	—	4	2	no	—
682	C₂×C₈	—	4	2	no	—
683	C₂×C₈	—	4	2	no	—
684	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
685	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
690	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
691	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	1	no	—
694	C₂²⋊C₄	—	2	2	no	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	2	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
705	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
706	C₄²	—	2	1	no	—
707	C₄²	—	2	2	no	—
708	C₄²	—	2	2	no	—
709	C₄²	—	2	2	no	—
710	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
711	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
712	C₄²	C₂⁴×C₆₇	1	2	yes	—
713	C₂³	—	2	1	no	—
714	C₂³	—	2	2	no	—
715	C₂³	—	2	4	no	—
716	C₂³	—	4	4	no	—
717	C₂³	—	4	2	no	—
718	C₂³	—	8	2	no	—
719	C₂³	—	8	2	no	—
720	C₂³	—	8	4	no	—
721	C₂³	—	8	4	no	—
722	C₂³	—	8	2	no	—
723	C₂³	—	8	4	no	—
724	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
725	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
726	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
727	Q₈	—	2	1	no	—
728	Q₈	—	2	2	no	—
729	Q₈	—	2	2	no	—
730	Q₈	—	4	1	no	—
731	Q₈	—	4	1	no	—
732	Q₈	—	4	4	no	—
733	Q₈	—	4	2	no	—
734	Q₈	—	8	2	no	—
735	Q₈	H(5,𝔽₂)×C₆₇	1	2	yes	—
736	D₄	—	2	4	no	—
737	D₄	—	2	1	no	—
738	D₄	—	2	4	no	—
739	D₄	—	2	2	no	—
740	D₄	—	2	2	no	—
741	D₄	—	2	4	no	—
742	D₄	—	4	1	no	—
743	D₄	—	4	2	no	—
744	D₄	—	4	4	no	—
745	D₄	—	4	1	no	—
746	D₄	—	4	2	no	—
747	D₄	—	4	4	no	—
748	D₄	—	4	4	no	—
749	D₄	—	4	2	no	—
750	D₄	—	4	4	no	—
751	D₄	—	4	4	no	—
752	D₄	—	8	2	no	—
753	D₄	—	8	2	no	—
754	D₄	—	8	2	no	—
755	D₄	—	8	4	no	—
756	D₄	—	8	4	no	—
757	D₄	—	8	4	no	—
758	D₄	—	8	4	no	—
759	D₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
760	C₂×C₄	—	2	4	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	4	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	4	2	no	—
772	C₂×C₄	—	4	4	no	—
773	C₂×C₄	—	4	4	no	—
774	C₂×C₄	—	4	4	no	—
775	C₂×C₄	—	4	8	no	—
776	C₂×C₄	—	4	2	no	—
777	C₂×C₄	—	8	2	no	—
778	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
779	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
780	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
781	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
782	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
783	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
784	C₈	—	2	4	no	—
785	C₈	—	2	4	no	—
786	C₂²	—	2	2	no	—
787	C₂²	—	2	4	no	—
788	C₂²	—	2	4	no	—
789	C₂²	—	2	1	no	—
790	C₂²	—	2	2	no	—
791	C₂²	—	2	2	no	—
792	C₂²	—	2	2	no	—
793	C₂²	—	4	2	no	—
794	C₂²	—	4	4	no	—
795	C₂²	—	4	4	no	—
796	C₂²	—	4	4	no	—
797	C₂²	—	4	2	no	—
798	C₂²	—	4	4	no	—
799	C₂²	—	16	4	no	—
800	C₂²	—	16	2	no	—
801	C₂²	—	16	4	no	—
802	C₂²	—	16	4	no	—
803	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
804	C₄	—	2	2	no	—
805	C₄	—	2	2	no	—
806	C₄	—	2	1	no	—
807	C₄	—	2	2	no	—
808	C₄	—	2	2	no	—
809	C₄	—	2	2	no	—
810	C₄	—	4	4	no	—
811	C₄	—	4	2	no	—
812	C₄	—	4	2	no	—
813	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
814	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
815	C₂	—	4	2	no	—
816	C₂	—	4	1	no	—
817	C₂	—	4	2	no	—
818	C₂	—	4	2	no	—
819	C₂	—	8	4	no	—
820	C₂	—	8	2	no	—
821	C₂	C₆₇×#3484	1	1	yes	characteristic
822	C₂	C₆₇×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #532×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3549	C₂	semidirect
2. C₆₇×#3500	C₂	semidirect
3. C₆₇×#3321	C₂	semidirect
4. C₆₇×#3319	C₂	semidirect
5. C₆₇×#3265	C₂	semidirect
6. C₆₇×#3264	C₂	semidirect
7. C₆₇×#3213	C₂	semidirect
8. C₆₇×#3200	C₂	semidirect
9. C₆₇×#3199	C₂	semidirect
10. C₆₇×#3115	C₂	semidirect
11. C₆₇×#3010	C₂	semidirect
12. C₆₇×#3008	C₂	semidirect
13. C₆₇×#2980	C₂	semidirect
14. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
15. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
16. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
17. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
18. C₂²×SD₁₆×C₆₇	C₂²	semidirect
19. C₂²×D₈×C₆₇	C₂²	semidirect
23. #555×C₆₇	C₂²	semidirect
24. #548×C₆₇	C₂²	semidirect
26. #546×C₆₇	C₂²	semidirect
28. D₄²×C₆₇	C₂²	semidirect
30. #536×C₆₇	C₂²	semidirect
34. #535×C₆₇	C₂²	semidirect
35. #535×C₆₇	C₂²	semidirect
38. #532×C₆₇	C₂²	semidirect
40. C₂×#124×C₆₇	C₂²	semidirect
41. C₄×#41×C₆₇	C₂²	semidirect
42. #496×C₆₇	C₂²	semidirect
43. #489×C₆₇	C₂²	semidirect
44. #485×C₆₇	C₂²	semidirect
45. #482×C₆₇	C₂²	semidirect
46. #482×C₆₇	C₂²	semidirect
47. #475×C₆₇	C₂²	semidirect
48. #474×C₆₇	C₂²	semidirect
49. #469×C₆₇	C₂²	semidirect
50. #468×C₆₇	C₂²	semidirect
51. #466×C₆₇	C₂²	semidirect
52. #465×C₆₇	C₂²	semidirect
53. #463×C₆₇	C₂²	semidirect
54. #463×C₆₇	C₂²	semidirect
55. #460×C₆₇	C₂²	semidirect
56. #459×C₆₇	C₂²	semidirect
57. #450×C₆₇	C₂²	semidirect
58. #449×C₆₇	C₂²	semidirect
59. #449×C₆₇	C₂²	semidirect
60. #449×C₆₇	C₂²	semidirect
61. #448×C₆₇	C₂²	semidirect
62. #448×C₆₇	C₂²	semidirect
63. #447×C₆₇	C₂²	semidirect
64. #447×C₆₇	C₂²	semidirect
65. #447×C₆₇	C₂²	semidirect
66. #442×C₆₇	C₂²	semidirect
67. #440×C₆₇	C₂²	semidirect
68. #435×C₆₇	C₂²	semidirect
69. #435×C₆₇	C₂²	semidirect
70. #432×C₆₇	C₂²	semidirect
71. #419×C₆₇	C₂²	semidirect
72. #418×C₆₇	C₂²	semidirect
73. #416×C₆₇	C₂²	semidirect
74. #416×C₆₇	C₂²	semidirect
75. #408×C₆₇	C₂²	semidirect
76. #408×C₆₇	C₂²	semidirect
403. #61673	C₆₇	direct (N × H)
412. #3549	C₂×C₆₇	semidirect
413. #3500	C₂×C₆₇	semidirect
414. #3321	C₂×C₆₇	semidirect
415. #3319	C₂×C₆₇	semidirect
416. #3265	C₂×C₆₇	semidirect
417. #3264	C₂×C₆₇	semidirect
418. #3213	C₂×C₆₇	semidirect
419. #3200	C₂×C₆₇	semidirect
420. #3199	C₂×C₆₇	semidirect
421. #3115	C₂×C₆₇	semidirect
422. #3010	C₂×C₆₇	semidirect
423. #3008	C₂×C₆₇	semidirect
424. #2980	C₂×C₆₇	semidirect
425. C₆₇	#61673	direct (N × H)
426. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
427. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
428. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
429. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
430. C₂²×SD₁₆	C₂²×C₆₇	semidirect
431. C₂²×D₈	C₂²×C₆₇	semidirect
435. #555	C₂²×C₆₇	semidirect
436. #548	C₂²×C₆₇	semidirect
438. #546	C₂²×C₆₇	semidirect
440. D₄²	C₂²×C₆₇	semidirect
442. #536	C₂²×C₆₇	semidirect
446. #535	C₂²×C₆₇	semidirect
447. #535	C₂²×C₆₇	semidirect
450. #532	C₂²×C₆₇	semidirect
452. C₂×#124	C₂²×C₆₇	semidirect
453. C₄×#41	C₂²×C₆₇	semidirect
454. #496	C₂²×C₆₇	semidirect
455. #489	C₂²×C₆₇	semidirect
456. #485	C₂²×C₆₇	semidirect
457. #482	C₂²×C₆₇	semidirect
458. #482	C₂²×C₆₇	semidirect
459. #475	C₂²×C₆₇	semidirect
460. #474	C₂²×C₆₇	semidirect
461. #469	C₂²×C₆₇	semidirect
462. #468	C₂²×C₆₇	semidirect
463. #466	C₂²×C₆₇	semidirect
464. #465	C₂²×C₆₇	semidirect
465. #463	C₂²×C₆₇	semidirect
466. #463	C₂²×C₆₇	semidirect
467. #460	C₂²×C₆₇	semidirect
468. #459	C₂²×C₆₇	semidirect
469. #450	C₂²×C₆₇	semidirect
470. #449	C₂²×C₆₇	semidirect
471. #449	C₂²×C₆₇	semidirect
472. #449	C₂²×C₆₇	semidirect
473. #448	C₂²×C₆₇	semidirect
474. #448	C₂²×C₆₇	semidirect
475. #447	C₂²×C₆₇	semidirect
476. #447	C₂²×C₆₇	semidirect
477. #447	C₂²×C₆₇	semidirect
478. #442	C₂²×C₆₇	semidirect
479. #440	C₂²×C₆₇	semidirect
480. #435	C₂²×C₆₇	semidirect
481. #435	C₂²×C₆₇	semidirect
482. #432	C₂²×C₆₇	semidirect
483. #419	C₂²×C₆₇	semidirect
484. #418	C₂²×C₆₇	semidirect
485. #416	C₂²×C₆₇	semidirect
486. #416	C₂²×C₆₇	semidirect
487. #408	C₂²×C₆₇	semidirect
488. #408	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3549	2
C₆₇×#3500	2
C₆₇×#3321	2
C₆₇×#3319	2
C₆₇×#3265	2
C₆₇×#3264	2
C₆₇×#3213	2
C₆₇×#3200	2
C₆₇×#3199	2
C₆₇×#3115	2
C₆₇×#3010	2
C₆₇×#3008	2
C₆₇×#2980	2
#61673	67

Subgroups — C67×#61673 #30740924

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61673 #30740924