Subgroups — C₆₇×#61647 #30740898

Order 17152.

2102 conjugacy classes of subgroups.

The subgroup lattice has 1146 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3536	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3485	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3331	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3330	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3314	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3306	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3275	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3273	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3269	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3267	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3225	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3201	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3196	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3194	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3118	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3012	C₂	1	2	yes	maximal, complemented
17	C₆₇×#3007	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3006	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2978	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic, complemented
21	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
23	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
24	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
25	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
26	#562×C₆₇	—	2	2	no	—
27	#554×C₆₇	C₂²	1	2	yes	complemented
28	#548×C₆₇	C₂²	1	2	yes	complemented
29	#547×C₆₇	—	2	1	no	—
30	#547×C₆₇	—	2	1	no	—
31	#547×C₆₇	C₂²	1	2	yes	—
32	#547×C₆₇	C₂²	1	2	yes	complemented
33	#547×C₆₇	C₂²	1	2	yes	complemented
34	#546×C₆₇	—	2	1	no	—
35	#546×C₆₇	—	2	1	no	—
36	#546×C₆₇	—	2	2	no	—
37	#546×C₆₇	C₂²	1	2	yes	—
38	#546×C₆₇	C₂²	1	2	yes	complemented
39	#546×C₆₇	C₂²	1	2	yes	complemented
40	#543×C₆₇	—	2	1	no	—
41	#542×C₆₇	C₂²	1	2	yes	complemented
42	#539×C₆₇	—	2	1	no	—
43	#538×C₆₇	—	2	1	no	—
44	#537×C₆₇	—	2	1	no	—
45	#537×C₆₇	C₂²	1	2	yes	—
46	#536×C₆₇	C₂²	1	1	yes	characteristic, complemented
47	#536×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	#534×C₆₇	—	2	2	no	—
49	#525×C₆₇	C₂²	1	1	yes	characteristic
50	#525×C₆₇	C₂²	1	1	yes	characteristic
51	C₂×#123×C₆₇	—	2	2	no	—
52	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
53	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
54	#518×C₆₇	C₂²	1	1	yes	characteristic, complemented
55	#497×C₆₇	C₂²	1	2	yes	complemented
56	#495×C₆₇	C₂²	1	2	yes	complemented
57	#489×C₆₇	C₂²	1	2	yes	complemented
58	#487×C₆₇	C₂²	1	2	yes	complemented
59	#485×C₆₇	C₂²	1	2	yes	complemented
60	#484×C₆₇	C₂²	1	2	yes	complemented
61	#484×C₆₇	C₂²	1	1	yes	characteristic, complemented
62	#483×C₆₇	C₂²	1	2	yes	complemented
63	#483×C₆₇	C₂²	1	1	yes	characteristic, complemented
64	#482×C₆₇	C₂²	1	2	yes	complemented
65	#481×C₆₇	C₂²	1	1	yes	characteristic, complemented
66	#480×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	#476×C₆₇	C₂²	1	2	yes	complemented
68	#474×C₆₇	C₂²	1	2	yes	complemented
69	#470×C₆₇	C₂²	1	2	yes	complemented
70	#470×C₆₇	C₂²	1	2	yes	complemented
71	#469×C₆₇	C₂²	1	2	yes	complemented
72	#468×C₆₇	C₂²	1	2	yes	complemented
73	#468×C₆₇	C₂²	1	2	yes	complemented
74	#468×C₆₇	C₂²	1	2	yes	complemented
75	#467×C₆₇	C₂²	1	2	yes	complemented
76	#465×C₆₇	C₂²	1	2	yes	complemented
77	#464×C₆₇	C₂²	1	2	yes	complemented
78	#463×C₆₇	C₂²	1	2	yes	complemented
79	#463×C₆₇	C₂²	1	2	yes	complemented
80	#463×C₆₇	C₂²	1	2	yes	complemented
81	#462×C₆₇	C₂²	1	2	yes	complemented
82	#461×C₆₇	C₂²	1	2	yes	complemented
83	#452×C₆₇	C₂²	1	2	yes	complemented
84	#452×C₆₇	C₂²	1	2	yes	complemented
85	#452×C₆₇	C₂²	1	2	yes	complemented
86	#452×C₆₇	C₂²	1	2	yes	complemented
87	#452×C₆₇	C₂²	1	2	yes	complemented
88	#452×C₆₇	C₂²	1	2	yes	complemented
89	#451×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	#451×C₆₇	C₂²	1	2	yes	complemented
91	#450×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	#450×C₆₇	C₂²	1	2	yes	complemented
93	#450×C₆₇	C₂²	1	2	yes	complemented
94	#449×C₆₇	C₂²	1	2	yes	—
95	#449×C₆₇	C₂²	1	2	yes	complemented
96	#449×C₆₇	C₂²	1	2	yes	complemented
97	#449×C₆₇	C₂²	1	2	yes	complemented
98	#448×C₆₇	C₂²	1	1	yes	characteristic, complemented
99	#448×C₆₇	C₂²	1	2	yes	complemented
100	#447×C₆₇	C₂²	1	2	yes	—
101	#447×C₆₇	C₂²	1	2	yes	complemented
102	#447×C₆₇	C₂²	1	1	yes	characteristic, complemented
103	#442×C₆₇	C₂²	1	2	yes	complemented
104	#440×C₆₇	C₂²	1	2	yes	complemented
105	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
106	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
107	#436×C₆₇	C₂²	1	2	yes	complemented
108	#436×C₆₇	C₂²	1	2	yes	complemented
109	#435×C₆₇	C₂²	1	2	yes	complemented
110	#435×C₆₇	C₂²	1	2	yes	complemented
111	#433×C₆₇	C₂²	1	2	yes	complemented
112	#417×C₆₇	C₂²	1	2	yes	complemented
113	#417×C₆₇	C₂²	1	2	yes	complemented
114	#417×C₆₇	C₂²	1	2	yes	complemented
115	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
116	#408×C₆₇	C₂²	1	2	yes	complemented
117	#407×C₆₇	C₂²	1	1	yes	characteristic, complemented
118	#407×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	H(5,𝔽₂)×C₆₇	—	4	4	no	—
120	C₂×#41×C₆₇	—	2	1	no	—
121	C₂×#41×C₆₇	—	2	2	no	—
122	C₂×#41×C₆₇	—	2	1	no	—
123	C₂×#41×C₆₇	—	2	1	no	—
124	C₂×#41×C₆₇	—	4	4	no	—
125	C₂×#41×C₆₇	C₂³	1	2	yes	—
126	C₂×#41×C₆₇	C₂³	1	2	yes	—
127	C₂×#41×C₆₇	C₂³	1	2	yes	—
128	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
129	C₂×#41×C₆₇	C₂³	1	2	yes	—
130	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
131	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
132	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₆₇	—	2	1	no	—
134	C₂²×D₄×C₆₇	—	2	1	no	—
135	C₂²×D₄×C₆₇	—	2	2	no	—
136	C₂²×D₄×C₆₇	—	2	1	no	—
137	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
139	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₆₇	—	2	1	no	—
141	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
142	#137×C₆₇	—	4	4	no	—
143	AGL(1,ℤ/8)×C₆₇	—	4	4	no	—
144	AGL(1,ℤ/8)×C₆₇	—	4	4	no	—
145	#135×C₆₇	—	4	4	no	—
146	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
155	C₂×D₈×C₆₇	C₂³	1	2	yes	—
156	C₂×D₈×C₆₇	C₂³	1	2	yes	—
157	C₂×D₈×C₆₇	C₂³	1	2	yes	—
158	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
159	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
160	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
161	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
162	C₄⋊Q₈×C₆₇	—	2	1	no	—
163	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
164	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
165	#126×C₆₇	—	2	2	no	—
166	#125×C₆₇	—	2	2	no	—
167	#124×C₆₇	—	2	1	no	—
168	#124×C₆₇	—	2	2	no	—
169	#124×C₆₇	—	2	2	no	—
170	#124×C₆₇	C₂³	1	2	yes	—
171	#124×C₆₇	C₂³	1	2	yes	—
172	#123×C₆₇	—	2	2	no	—
173	#123×C₆₇	—	2	1	no	—
174	#123×C₆₇	—	2	2	no	—
175	#123×C₆₇	—	2	2	no	—
176	#123×C₆₇	—	2	2	no	—
177	#123×C₆₇	—	2	2	no	—
178	#123×C₆₇	—	2	2	no	—
179	#123×C₆₇	—	2	2	no	—
180	#123×C₆₇	—	2	2	no	—
181	#123×C₆₇	—	2	2	no	—
182	#123×C₆₇	—	2	2	no	—
183	#123×C₆₇	—	2	2	no	—
184	#123×C₆₇	—	2	2	no	—
185	#123×C₆₇	D₄	1	2	yes	—
186	C₂²⋊Q₈×C₆₇	—	2	2	no	—
187	C₂²⋊Q₈×C₆₇	—	2	1	no	—
188	C₂²⋊Q₈×C₆₇	—	2	1	no	—
189	C₂²⋊Q₈×C₆₇	—	2	1	no	—
190	C₂²⋊Q₈×C₆₇	—	2	1	no	—
191	C₂²⋊Q₈×C₆₇	—	2	2	no	—
192	C₂²⋊Q₈×C₆₇	—	2	2	no	—
193	C₂²⋊Q₈×C₆₇	—	2	2	no	—
194	C₂²⋊Q₈×C₆₇	—	2	2	no	—
195	C₂²⋊Q₈×C₆₇	—	2	2	no	—
196	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
197	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
198	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
199	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
200	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
201	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
202	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
203	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
204	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
205	#121×C₆₇	—	2	2	no	—
206	#121×C₆₇	—	2	2	no	—
207	#121×C₆₇	—	2	2	no	—
208	#121×C₆₇	—	2	2	no	—
209	#121×C₆₇	—	2	2	no	—
210	#121×C₆₇	—	2	2	no	—
211	#121×C₆₇	—	2	1	no	—
212	#121×C₆₇	—	2	1	no	—
213	#121×C₆₇	—	2	2	no	—
214	#121×C₆₇	—	2	2	no	—
215	#121×C₆₇	—	2	2	no	—
216	#121×C₆₇	D₄	1	1	yes	characteristic
217	#121×C₆₇	D₄	1	1	yes	characteristic
218	#121×C₆₇	C₂³	1	2	yes	—
219	#121×C₆₇	C₂³	1	1	yes	characteristic
220	#121×C₆₇	C₂³	1	2	yes	—
221	#121×C₆₇	C₂³	1	2	yes	—
222	#121×C₆₇	C₂³	1	1	yes	characteristic
223	#120×C₆₇	—	2	1	no	—
224	#120×C₆₇	—	2	2	no	—
225	#120×C₆₇	—	2	2	no	—
226	#120×C₆₇	—	2	2	no	—
227	#120×C₆₇	D₄	1	2	yes	—
228	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
229	C₄×D₄×C₆₇	—	2	2	no	—
230	C₄×D₄×C₆₇	—	2	1	no	—
231	C₄×D₄×C₆₇	—	2	1	no	—
232	C₄×D₄×C₆₇	—	2	1	no	—
233	C₄×D₄×C₆₇	—	2	1	no	—
234	C₄×D₄×C₆₇	—	2	2	no	—
235	C₄×D₄×C₆₇	C₂³	1	2	yes	—
236	C₄×D₄×C₆₇	C₂³	1	2	yes	—
237	C₄×D₄×C₆₇	C₂³	1	2	yes	—
238	C₄×D₄×C₆₇	C₂³	1	2	yes	—
239	C₄×D₄×C₆₇	C₂³	1	2	yes	—
240	#117×C₆₇	C₂³	1	1	yes	characteristic
241	#117×C₆₇	C₂³	1	1	yes	characteristic
242	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
243	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
244	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
245	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
248	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
249	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
250	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
251	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
252	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
253	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
254	#107×C₆₇	C₂³	1	2	yes	—
255	#107×C₆₇	C₂³	1	2	yes	—
256	#106×C₆₇	C₂³	1	2	yes	—
257	#106×C₆₇	C₂³	1	2	yes	—
258	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
259	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
260	#103×C₆₇	C₂³	1	2	yes	—
261	#103×C₆₇	C₂³	1	2	yes	—
262	#103×C₆₇	C₂³	1	2	yes	—
263	#103×C₆₇	C₂³	1	2	yes	—
264	#103×C₆₇	C₂³	1	2	yes	—
265	#103×C₆₇	C₂³	1	2	yes	—
266	#103×C₆₇	C₂³	1	2	yes	—
267	#103×C₆₇	C₂³	1	2	yes	—
268	#102×C₆₇	C₂³	1	2	yes	—
269	#102×C₆₇	C₂³	1	2	yes	—
270	#102×C₆₇	C₂³	1	2	yes	—
271	#102×C₆₇	C₂³	1	2	yes	—
272	#102×C₆₇	C₂³	1	2	yes	—
273	#102×C₆₇	C₂³	1	2	yes	—
274	#102×C₆₇	C₂³	1	2	yes	—
275	#102×C₆₇	C₂³	1	2	yes	—
276	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
277	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
278	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
279	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
280	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
281	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
282	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
283	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
284	#97×C₆₇	C₂³	1	2	yes	—
285	C₄×C₈×C₆₇	C₂³	1	2	yes	—
286	C₂⁴×C₆₇	—	2	1	no	—
287	C₂⁴×C₆₇	—	2	1	no	—
288	C₂⁴×C₆₇	—	2	2	no	—
289	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
290	#41×C₆₇	—	2	4	no	—
291	#41×C₆₇	—	2	4	no	—
292	#41×C₆₇	—	2	4	no	—
293	#41×C₆₇	—	4	2	no	—
294	#41×C₆₇	—	4	2	no	—
295	#41×C₆₇	—	4	2	no	—
296	#41×C₆₇	—	4	2	no	—
297	#41×C₆₇	—	4	2	no	—
298	#41×C₆₇	—	4	2	no	—
299	#41×C₆₇	—	4	2	no	—
300	#41×C₆₇	—	4	4	no	—
301	#41×C₆₇	—	4	4	no	—
302	#41×C₆₇	—	4	4	no	—
303	#41×C₆₇	—	8	4	no	—
304	C₂×Q₈×C₆₇	—	2	1	no	—
305	C₂×Q₈×C₆₇	—	2	1	no	—
306	C₂×Q₈×C₆₇	—	2	2	no	—
307	C₂×Q₈×C₆₇	—	4	2	no	—
308	C₂×Q₈×C₆₇	—	4	2	no	—
309	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
310	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
311	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
312	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
313	C₂×D₄×C₆₇	—	2	4	no	—
314	C₂×D₄×C₆₇	—	2	4	no	—
315	C₂×D₄×C₆₇	—	2	2	no	—
316	C₂×D₄×C₆₇	—	2	2	no	—
317	C₂×D₄×C₆₇	—	2	2	no	—
318	C₂×D₄×C₆₇	—	2	1	no	—
319	C₂×D₄×C₆₇	—	2	2	no	—
320	C₂×D₄×C₆₇	—	2	1	no	—
321	C₂×D₄×C₆₇	—	2	1	no	—
322	C₂×D₄×C₆₇	—	2	2	no	—
323	C₂×D₄×C₆₇	—	2	2	no	—
324	C₂×D₄×C₆₇	—	2	2	no	—
325	C₂×D₄×C₆₇	—	2	1	no	—
326	C₂×D₄×C₆₇	—	2	2	no	—
327	C₂×D₄×C₆₇	—	2	1	no	—
328	C₂×D₄×C₆₇	—	4	2	no	—
329	C₂×D₄×C₆₇	—	4	2	no	—
330	C₂×D₄×C₆₇	—	4	4	no	—
331	C₂×D₄×C₆₇	—	4	4	no	—
332	C₂×D₄×C₆₇	—	4	8	no	—
333	C₂×D₄×C₆₇	—	8	2	no	—
334	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
335	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
336	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
337	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
338	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
339	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
340	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
341	C₂²×C₄×C₆₇	—	2	1	no	—
342	C₂²×C₄×C₆₇	—	2	1	no	—
343	C₂²×C₄×C₆₇	—	2	1	no	—
344	C₂²×C₄×C₆₇	—	2	1	no	—
345	C₂²×C₄×C₆₇	—	2	2	no	—
346	C₂²×C₄×C₆₇	—	2	2	no	—
347	C₂²×C₄×C₆₇	—	2	2	no	—
348	C₂²×C₄×C₆₇	—	2	2	no	—
349	C₂²×C₄×C₆₇	—	2	1	no	—
350	C₂²×C₄×C₆₇	—	2	2	no	—
351	C₂²×C₄×C₆₇	—	2	2	no	—
352	C₂²×C₄×C₆₇	—	2	2	no	—
353	C₂²×C₄×C₆₇	—	2	2	no	—
354	C₂²×C₄×C₆₇	—	4	2	no	—
355	C₂²×C₄×C₆₇	—	4	4	no	—
356	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
357	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
358	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
359	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
361	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
363	Q₁₆×C₆₇	—	4	2	no	—
364	Q₁₆×C₆₇	—	4	2	no	—
365	Q₁₆×C₆₇	—	4	2	no	—
366	SD₁₆×C₆₇	—	2	4	no	—
367	SD₁₆×C₆₇	—	2	4	no	—
368	SD₁₆×C₆₇	—	4	2	no	—
369	SD₁₆×C₆₇	—	4	2	no	—
370	SD₁₆×C₆₇	—	4	2	no	—
371	SD₁₆×C₆₇	—	4	2	no	—
372	D₈×C₆₇	—	2	4	no	—
373	D₈×C₆₇	—	2	4	no	—
374	D₈×C₆₇	—	4	2	no	—
375	M₁₆×C₆₇	—	4	2	no	—
376	M₁₆×C₆₇	—	4	2	no	—
377	M₁₆×C₆₇	—	4	2	no	—
378	C₂×C₈×C₆₇	—	4	2	no	—
379	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
380	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
381	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
382	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
383	C₄⋊C₄×C₆₇	—	2	1	no	—
384	C₄⋊C₄×C₆₇	—	2	1	no	—
385	C₄⋊C₄×C₆₇	—	2	2	no	—
386	C₄⋊C₄×C₆₇	—	2	2	no	—
387	C₄⋊C₄×C₆₇	—	2	2	no	—
388	C₄⋊C₄×C₆₇	—	2	2	no	—
389	C₄⋊C₄×C₆₇	—	2	2	no	—
390	C₄⋊C₄×C₆₇	—	2	2	no	—
391	C₄⋊C₄×C₆₇	—	2	1	no	—
392	C₄⋊C₄×C₆₇	—	2	2	no	—
393	C₄⋊C₄×C₆₇	—	2	1	no	—
394	C₄⋊C₄×C₆₇	—	2	2	no	—
395	C₄⋊C₄×C₆₇	—	2	2	no	—
396	C₄⋊C₄×C₆₇	—	2	2	no	—
397	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
402	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
403	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
405	C₂²⋊C₄×C₆₇	—	2	1	no	—
406	C₂²⋊C₄×C₆₇	—	2	2	no	—
407	C₂²⋊C₄×C₆₇	—	2	2	no	—
408	C₂²⋊C₄×C₆₇	—	2	2	no	—
409	C₂²⋊C₄×C₆₇	—	2	2	no	—
410	C₂²⋊C₄×C₆₇	—	2	1	no	—
411	C₂²⋊C₄×C₆₇	—	2	1	no	—
412	C₂²⋊C₄×C₆₇	—	2	2	no	—
413	C₂²⋊C₄×C₆₇	—	2	1	no	—
414	C₂²⋊C₄×C₆₇	—	2	1	no	—
415	C₂²⋊C₄×C₆₇	—	2	2	no	—
416	C₂²⋊C₄×C₆₇	—	2	2	no	—
417	C₂²⋊C₄×C₆₇	—	2	2	no	—
418	C₂²⋊C₄×C₆₇	—	2	2	no	—
419	C₂²⋊C₄×C₆₇	—	2	2	no	—
420	C₂²⋊C₄×C₆₇	—	2	2	no	—
421	C₂²⋊C₄×C₆₇	—	2	2	no	—
422	C₂²⋊C₄×C₆₇	—	2	2	no	—
423	C₂²⋊C₄×C₆₇	—	2	2	no	—
424	C₂²⋊C₄×C₆₇	—	2	2	no	—
425	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
426	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
427	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
428	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
429	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
430	C₄²×C₆₇	—	2	1	no	—
431	C₄²×C₆₇	—	2	2	no	—
432	C₄²×C₆₇	C₂⁴	1	2	yes	—
433	C₂³×C₆₇	—	2	4	no	—
434	C₂³×C₆₇	—	2	2	no	—
435	C₂³×C₆₇	—	2	2	no	—
436	C₂³×C₆₇	—	2	1	no	—
437	C₂³×C₆₇	—	4	1	no	—
438	C₂³×C₆₇	—	4	1	no	—
439	C₂³×C₆₇	—	4	1	no	—
440	C₂³×C₆₇	—	4	4	no	—
441	C₂³×C₆₇	—	4	2	no	—
442	C₂³×C₆₇	—	8	1	no	—
443	C₂³×C₆₇	—	8	1	no	—
444	C₂³×C₆₇	—	8	1	no	—
445	C₂³×C₆₇	—	8	1	no	—
446	C₂³×C₆₇	—	8	2	no	—
447	C₂³×C₆₇	—	8	2	no	—
448	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
449	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
450	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
451	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
452	Q₈×C₆₇	—	2	2	no	—
453	Q₈×C₆₇	—	2	2	no	—
454	Q₈×C₆₇	—	2	2	no	—
455	Q₈×C₆₇	—	2	2	no	—
456	Q₈×C₆₇	—	2	2	no	—
457	Q₈×C₆₇	—	4	1	no	—
458	Q₈×C₆₇	—	4	2	no	—
459	Q₈×C₆₇	—	8	1	no	—
460	Q₈×C₆₇	—	8	2	no	—
461	D₄×C₆₇	—	2	4	no	—
462	D₄×C₆₇	—	2	2	no	—
463	D₄×C₆₇	—	2	2	no	—
464	D₄×C₆₇	—	2	2	no	—
465	D₄×C₆₇	—	2	2	no	—
466	D₄×C₆₇	—	4	1	no	—
467	D₄×C₆₇	—	4	2	no	—
468	D₄×C₆₇	—	4	2	no	—
469	D₄×C₆₇	—	4	2	no	—
470	D₄×C₆₇	—	4	4	no	—
471	D₄×C₆₇	—	4	4	no	—
472	D₄×C₆₇	—	4	4	no	—
473	D₄×C₆₇	—	4	4	no	—
474	D₄×C₆₇	—	4	2	no	—
475	D₄×C₆₇	—	4	4	no	—
476	D₄×C₆₇	—	8	1	no	—
477	D₄×C₆₇	—	8	1	no	—
478	D₄×C₆₇	—	8	1	no	—
479	D₄×C₆₇	—	8	2	no	—
480	D₄×C₆₇	—	8	2	no	—
481	D₄×C₆₇	—	8	2	no	—
482	D₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
483	C₂×C₄×C₆₇	—	2	2	no	—
484	C₂×C₄×C₆₇	—	2	2	no	—
485	C₂×C₄×C₆₇	—	2	2	no	—
486	C₂×C₄×C₆₇	—	2	2	no	—
487	C₂×C₄×C₆₇	—	2	2	no	—
488	C₂×C₄×C₆₇	—	2	1	no	—
489	C₂×C₄×C₆₇	—	2	1	no	—
490	C₂×C₄×C₆₇	—	2	2	no	—
491	C₂×C₄×C₆₇	—	2	2	no	—
492	C₂×C₄×C₆₇	—	2	2	no	—
493	C₂×C₄×C₆₇	—	2	2	no	—
494	C₂×C₄×C₆₇	—	2	1	no	—
495	C₂×C₄×C₆₇	—	4	1	no	—
496	C₂×C₄×C₆₇	—	4	1	no	—
497	C₂×C₄×C₆₇	—	4	1	no	—
498	C₂×C₄×C₆₇	—	4	4	no	—
499	C₂×C₄×C₆₇	—	4	4	no	—
500	C₂×C₄×C₆₇	—	4	4	no	—
501	C₂×C₄×C₆₇	—	4	2	no	—
502	C₂×C₄×C₆₇	—	4	2	no	—
503	C₂×C₄×C₆₇	—	4	2	no	—
504	C₂×C₄×C₆₇	—	8	2	no	—
505	C₂×C₄×C₆₇	—	8	2	no	—
506	C₂×C₄×C₆₇	—	8	2	no	—
507	C₂×C₄×C₆₇	—	8	2	no	—
508	C₂×C₄×C₆₇	—	8	1	no	—
509	C₂×C₄×C₆₇	—	8	1	no	—
510	C₂×C₄×C₆₇	—	8	2	no	—
511	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
512	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
514	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
518	C₈×C₆₇	—	2	2	no	—
519	C₈×C₆₇	—	2	2	no	—
520	C₈×C₆₇	—	2	2	no	—
521	C₈×C₆₇	—	2	2	no	—
522	C₂²×C₆₇	—	2	1	no	—
523	C₂²×C₆₇	—	2	2	no	—
524	C₂²×C₆₇	—	2	1	no	—
525	C₂²×C₆₇	—	2	1	no	—
526	C₂²×C₆₇	—	2	1	no	—
527	C₂²×C₆₇	—	2	2	no	—
528	C₂²×C₆₇	—	2	1	no	—
529	C₂²×C₆₇	—	2	1	no	—
530	C₂²×C₆₇	—	2	1	no	—
531	C₂²×C₆₇	—	2	1	no	—
532	C₂²×C₆₇	—	2	1	no	—
533	C₂²×C₆₇	—	2	2	no	—
534	C₂²×C₆₇	—	2	4	no	—
535	C₂²×C₆₇	—	4	2	no	—
536	C₂²×C₆₇	—	4	2	no	—
537	C₂²×C₆₇	—	4	2	no	—
538	C₂²×C₆₇	—	4	1	no	—
539	C₂²×C₆₇	—	4	1	no	—
540	C₂²×C₆₇	—	4	2	no	—
541	C₂²×C₆₇	—	4	1	no	—
542	C₂²×C₆₇	—	4	2	no	—
543	C₂²×C₆₇	—	8	4	no	—
544	C₂²×C₆₇	—	8	2	no	—
545	C₂²×C₆₇	—	16	4	no	—
546	C₂²×C₆₇	—	16	2	no	—
547	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
548	C₄×C₆₇	—	2	2	no	—
549	C₄×C₆₇	—	2	2	no	—
550	C₄×C₆₇	—	2	1	no	—
551	C₄×C₆₇	—	2	1	no	—
552	C₄×C₆₇	—	2	1	no	—
553	C₄×C₆₇	—	2	2	no	—
554	C₄×C₆₇	—	4	2	no	—
555	C₄×C₆₇	—	4	2	no	—
556	C₄×C₆₇	—	4	1	no	—
557	C₄×C₆₇	—	4	1	no	—
558	C₄×C₆₇	—	4	1	no	—
559	C₄×C₆₇	—	4	2	no	—
560	C₄×C₆₇	—	4	2	no	—
561	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
562	#61647	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
563	C₂×C₆₇	—	4	1	no	—
564	C₂×C₆₇	—	4	1	no	—
565	C₂×C₆₇	—	4	1	no	—
566	C₂×C₆₇	—	4	2	no	—
567	C₂×C₆₇	—	4	4	no	—
568	C₂×C₆₇	—	8	2	no	—
569	C₂×C₆₇	—	8	1	no	—
570	C₂×C₆₇	#3484	1	1	yes	characteristic
571	C₂×C₆₇	#3585	1	1	yes	characteristic
572	C₂×C₆₇	#3586	1	1	yes	characteristic
573	#3536	C₂×C₆₇	1	1	yes	characteristic, complemented
574	#3485	C₂×C₆₇	1	1	yes	characteristic, complemented
575	#3331	C₂×C₆₇	1	2	yes	complemented
576	#3330	C₂×C₆₇	1	2	yes	complemented
577	#3314	C₂×C₆₇	1	2	yes	complemented
578	#3306	C₂×C₆₇	1	2	yes	complemented
579	#3275	C₂×C₆₇	1	2	yes	complemented
580	#3273	C₂×C₆₇	1	2	yes	complemented
581	#3269	C₂×C₆₇	1	2	yes	complemented
582	#3267	C₂×C₆₇	1	2	yes	complemented
583	#3225	C₂×C₆₇	1	2	yes	complemented
584	#3201	C₂×C₆₇	1	2	yes	complemented
585	#3196	C₂×C₆₇	1	1	yes	characteristic, complemented
586	#3194	C₂×C₆₇	1	1	yes	characteristic, complemented
587	#3118	C₂×C₆₇	1	2	yes	complemented
588	#3012	C₂×C₆₇	1	2	yes	complemented
589	#3007	C₂×C₆₇	1	1	yes	characteristic, complemented
590	#3006	C₂×C₆₇	1	1	yes	characteristic, complemented
591	#2978	C₂×C₆₇	1	1	yes	characteristic, complemented
592	C₆₇	#61647	1	1	yes	characteristic, direct product factor, Sylow
593	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic, complemented
594	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
595	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
596	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
597	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
598	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
599	#562	—	2	2	no	—
600	#554	C₂²×C₆₇	1	2	yes	complemented
601	#548	C₂²×C₆₇	1	2	yes	complemented
602	#547	—	2	1	no	—
603	#547	—	2	1	no	—
604	#547	C₂²×C₆₇	1	2	yes	—
605	#547	C₂²×C₆₇	1	2	yes	complemented
606	#547	C₂²×C₆₇	1	2	yes	complemented
607	#546	—	2	1	no	—
608	#546	—	2	1	no	—
609	#546	—	2	2	no	—
610	#546	C₂²×C₆₇	1	2	yes	—
611	#546	C₂²×C₆₇	1	2	yes	complemented
612	#546	C₂²×C₆₇	1	2	yes	complemented
613	#543	—	2	1	no	—
614	#542	C₂²×C₆₇	1	2	yes	complemented
615	#539	—	2	1	no	—
616	#538	—	2	1	no	—
617	#537	—	2	1	no	—
618	#537	C₂²×C₆₇	1	2	yes	—
619	#536	C₂²×C₆₇	1	1	yes	characteristic, complemented
620	#536	C₂²×C₆₇	1	1	yes	characteristic, complemented
621	#534	—	2	2	no	—
622	#525	C₂²×C₆₇	1	1	yes	characteristic
623	#525	C₂²×C₆₇	1	1	yes	characteristic
624	C₂×#123	—	2	2	no	—
625	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
626	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
627	#518	C₂²×C₆₇	1	1	yes	characteristic, complemented
628	#497	C₂²×C₆₇	1	2	yes	complemented
629	#495	C₂²×C₆₇	1	2	yes	complemented
630	#489	C₂²×C₆₇	1	2	yes	complemented
631	#487	C₂²×C₆₇	1	2	yes	complemented
632	#485	C₂²×C₆₇	1	2	yes	complemented
633	#484	C₂²×C₆₇	1	1	yes	characteristic, complemented
634	#484	C₂²×C₆₇	1	2	yes	complemented
635	#483	C₂²×C₆₇	1	1	yes	characteristic, complemented
636	#483	C₂²×C₆₇	1	2	yes	complemented
637	#482	C₂²×C₆₇	1	2	yes	complemented
638	#481	C₂²×C₆₇	1	1	yes	characteristic, complemented
639	#480	C₂²×C₆₇	1	1	yes	characteristic, complemented
640	#476	C₂²×C₆₇	1	2	yes	complemented
641	#474	C₂²×C₆₇	1	2	yes	complemented
642	#470	C₂²×C₆₇	1	2	yes	complemented
643	#470	C₂²×C₆₇	1	2	yes	complemented
644	#469	C₂²×C₆₇	1	2	yes	complemented
645	#468	C₂²×C₆₇	1	2	yes	complemented
646	#468	C₂²×C₆₇	1	2	yes	complemented
647	#468	C₂²×C₆₇	1	2	yes	complemented
648	#467	C₂²×C₆₇	1	2	yes	complemented
649	#465	C₂²×C₆₇	1	2	yes	complemented
650	#464	C₂²×C₆₇	1	2	yes	complemented
651	#463	C₂²×C₆₇	1	2	yes	complemented
652	#463	C₂²×C₆₇	1	2	yes	complemented
653	#463	C₂²×C₆₇	1	2	yes	complemented
654	#462	C₂²×C₆₇	1	2	yes	complemented
655	#461	C₂²×C₆₇	1	2	yes	complemented
656	#452	C₂²×C₆₇	1	2	yes	complemented
657	#452	C₂²×C₆₇	1	2	yes	complemented
658	#452	C₂²×C₆₇	1	2	yes	complemented
659	#452	C₂²×C₆₇	1	2	yes	complemented
660	#452	C₂²×C₆₇	1	2	yes	complemented
661	#452	C₂²×C₆₇	1	2	yes	complemented
662	#451	C₂²×C₆₇	1	1	yes	characteristic, complemented
663	#451	C₂²×C₆₇	1	2	yes	complemented
664	#450	C₂²×C₆₇	1	2	yes	complemented
665	#450	C₂²×C₆₇	1	1	yes	characteristic, complemented
666	#450	C₂²×C₆₇	1	2	yes	complemented
667	#449	C₂²×C₆₇	1	2	yes	—
668	#449	C₂²×C₆₇	1	2	yes	complemented
669	#449	C₂²×C₆₇	1	2	yes	complemented
670	#449	C₂²×C₆₇	1	2	yes	complemented
671	#448	C₂²×C₆₇	1	1	yes	characteristic, complemented
672	#448	C₂²×C₆₇	1	2	yes	complemented
673	#447	C₂²×C₆₇	1	2	yes	—
674	#447	C₂²×C₆₇	1	1	yes	characteristic, complemented
675	#447	C₂²×C₆₇	1	2	yes	complemented
676	#442	C₂²×C₆₇	1	2	yes	complemented
677	#440	C₂²×C₆₇	1	2	yes	complemented
678	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
679	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
680	#436	C₂²×C₆₇	1	2	yes	complemented
681	#436	C₂²×C₆₇	1	2	yes	complemented
682	#435	C₂²×C₆₇	1	2	yes	complemented
683	#435	C₂²×C₆₇	1	2	yes	complemented
684	#433	C₂²×C₆₇	1	2	yes	complemented
685	#417	C₂²×C₆₇	1	2	yes	complemented
686	#417	C₂²×C₆₇	1	2	yes	complemented
687	#417	C₂²×C₆₇	1	2	yes	complemented
688	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
689	#408	C₂²×C₆₇	1	2	yes	complemented
690	#407	C₂²×C₆₇	1	1	yes	characteristic, complemented
691	#407	C₂²×C₆₇	1	1	yes	characteristic, complemented
692	H(5,𝔽₂)	—	4	4	no	—
693	C₂×#41	—	2	1	no	—
694	C₂×#41	—	2	2	no	—
695	C₂×#41	—	2	1	no	—
696	C₂×#41	—	2	1	no	—
697	C₂×#41	—	4	4	no	—
698	C₂×#41	C₂³×C₆₇	1	2	yes	—
699	C₂×#41	C₂³×C₆₇	1	2	yes	—
700	C₂×#41	C₂³×C₆₇	1	2	yes	—
701	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
702	C₂×#41	C₂³×C₆₇	1	2	yes	—
703	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
704	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
705	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
706	C₂²×D₄	—	2	1	no	—
707	C₂²×D₄	—	2	1	no	—
708	C₂²×D₄	—	2	2	no	—
709	C₂²×D₄	—	2	1	no	—
710	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
711	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
712	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
713	C₂³×C₄	—	2	1	no	—
714	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
715	#137	—	4	4	no	—
716	AGL(1,ℤ/8)	—	4	4	no	—
717	AGL(1,ℤ/8)	—	4	4	no	—
718	#135	—	4	4	no	—
719	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
720	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
721	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
722	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
723	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
724	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
725	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
726	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
727	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
728	C₂×D₈	C₂³×C₆₇	1	2	yes	—
729	C₂×D₈	C₂³×C₆₇	1	2	yes	—
730	C₂×D₈	C₂³×C₆₇	1	2	yes	—
731	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
732	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
733	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
734	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
735	C₄⋊Q₈	—	2	1	no	—
736	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
737	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
738	#126	—	2	2	no	—
739	#125	—	2	2	no	—
740	#124	—	2	1	no	—
741	#124	—	2	2	no	—
742	#124	—	2	2	no	—
743	#124	C₂³×C₆₇	1	2	yes	—
744	#124	C₂³×C₆₇	1	2	yes	—
745	#123	—	2	2	no	—
746	#123	—	2	1	no	—
747	#123	—	2	2	no	—
748	#123	—	2	2	no	—
749	#123	—	2	2	no	—
750	#123	—	2	2	no	—
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	#123	—	2	2	no	—
758	#123	D₄×C₆₇	1	2	yes	—
759	C₂²⋊Q₈	—	2	2	no	—
760	C₂²⋊Q₈	—	2	1	no	—
761	C₂²⋊Q₈	—	2	1	no	—
762	C₂²⋊Q₈	—	2	1	no	—
763	C₂²⋊Q₈	—	2	1	no	—
764	C₂²⋊Q₈	—	2	2	no	—
765	C₂²⋊Q₈	—	2	2	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
770	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
771	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
772	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
773	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
774	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
775	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
776	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
777	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
778	#121	—	2	2	no	—
779	#121	—	2	2	no	—
780	#121	—	2	2	no	—
781	#121	—	2	2	no	—
782	#121	—	2	2	no	—
783	#121	—	2	2	no	—
784	#121	—	2	1	no	—
785	#121	—	2	1	no	—
786	#121	—	2	2	no	—
787	#121	—	2	2	no	—
788	#121	—	2	2	no	—
789	#121	D₄×C₆₇	1	1	yes	characteristic
790	#121	D₄×C₆₇	1	1	yes	characteristic
791	#121	C₂³×C₆₇	1	2	yes	—
792	#121	C₂³×C₆₇	1	2	yes	—
793	#121	C₂³×C₆₇	1	1	yes	characteristic
794	#121	C₂³×C₆₇	1	1	yes	characteristic
795	#121	C₂³×C₆₇	1	2	yes	—
796	#120	—	2	1	no	—
797	#120	—	2	2	no	—
798	#120	—	2	2	no	—
799	#120	—	2	2	no	—
800	#120	D₄×C₆₇	1	2	yes	—
801	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	C₂³×C₆₇	1	2	yes	—
809	C₄×D₄	C₂³×C₆₇	1	2	yes	—
810	C₄×D₄	C₂³×C₆₇	1	2	yes	—
811	C₄×D₄	C₂³×C₆₇	1	2	yes	—
812	C₄×D₄	C₂³×C₆₇	1	2	yes	—
813	#117	C₂³×C₆₇	1	1	yes	characteristic
814	#117	C₂³×C₆₇	1	1	yes	characteristic
815	C₂×C₄⋊C₄	—	2	1	no	—
816	C₂×C₄⋊C₄	—	2	2	no	—
817	C₂×C₄⋊C₄	—	2	2	no	—
818	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
819	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
820	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
821	C₂×C₂²⋊C₄	—	2	1	no	—
822	C₂×C₂²⋊C₄	—	2	1	no	—
823	C₂×C₂²⋊C₄	—	2	2	no	—
824	C₂×C₂²⋊C₄	—	2	2	no	—
825	C₂×C₂²⋊C₄	—	2	2	no	—
826	C₂×C₂²⋊C₄	—	2	2	no	—
827	#107	C₂³×C₆₇	1	2	yes	—
828	#107	C₂³×C₆₇	1	2	yes	—
829	#106	C₂³×C₆₇	1	2	yes	—
830	#106	C₂³×C₆₇	1	2	yes	—
831	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
832	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
833	#103	C₂³×C₆₇	1	2	yes	—
834	#103	C₂³×C₆₇	1	2	yes	—
835	#103	C₂³×C₆₇	1	2	yes	—
836	#103	C₂³×C₆₇	1	2	yes	—
837	#103	C₂³×C₆₇	1	2	yes	—
838	#103	C₂³×C₆₇	1	2	yes	—
839	#103	C₂³×C₆₇	1	2	yes	—
840	#103	C₂³×C₆₇	1	2	yes	—
841	#102	C₂³×C₆₇	1	2	yes	—
842	#102	C₂³×C₆₇	1	2	yes	—
843	#102	C₂³×C₆₇	1	2	yes	—
844	#102	C₂³×C₆₇	1	2	yes	—
845	#102	C₂³×C₆₇	1	2	yes	—
846	#102	C₂³×C₆₇	1	2	yes	—
847	#102	C₂³×C₆₇	1	2	yes	—
848	#102	C₂³×C₆₇	1	2	yes	—
849	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
850	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
851	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
852	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
853	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
854	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
855	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
856	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
857	#97	C₂³×C₆₇	1	2	yes	—
858	C₄×C₈	C₂³×C₆₇	1	2	yes	—
859	C₂⁴	—	2	1	no	—
860	C₂⁴	—	2	1	no	—
861	C₂⁴	—	2	2	no	—
862	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
863	#41	—	2	4	no	—
864	#41	—	2	4	no	—
865	#41	—	2	4	no	—
866	#41	—	4	2	no	—
867	#41	—	4	2	no	—
868	#41	—	4	2	no	—
869	#41	—	4	2	no	—
870	#41	—	4	2	no	—
871	#41	—	4	2	no	—
872	#41	—	4	2	no	—
873	#41	—	4	4	no	—
874	#41	—	4	4	no	—
875	#41	—	4	4	no	—
876	#41	—	8	4	no	—
877	C₂×Q₈	—	2	1	no	—
878	C₂×Q₈	—	2	1	no	—
879	C₂×Q₈	—	2	2	no	—
880	C₂×Q₈	—	4	2	no	—
881	C₂×Q₈	—	4	2	no	—
882	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
883	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
884	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
885	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
886	C₂×D₄	—	2	4	no	—
887	C₂×D₄	—	2	4	no	—
888	C₂×D₄	—	2	2	no	—
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	—	2	2	no	—
891	C₂×D₄	—	2	1	no	—
892	C₂×D₄	—	2	2	no	—
893	C₂×D₄	—	2	1	no	—
894	C₂×D₄	—	2	1	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	1	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	1	no	—
901	C₂×D₄	—	4	2	no	—
902	C₂×D₄	—	4	2	no	—
903	C₂×D₄	—	4	4	no	—
904	C₂×D₄	—	4	4	no	—
905	C₂×D₄	—	4	8	no	—
906	C₂×D₄	—	8	2	no	—
907	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
908	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
909	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
910	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
911	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
912	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
913	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	2	1	no	—
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	2	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	—	4	2	no	—
928	C₂²×C₄	—	4	4	no	—
929	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
930	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
931	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
932	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
933	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
934	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
935	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
936	Q₁₆	—	4	2	no	—
937	Q₁₆	—	4	2	no	—
938	Q₁₆	—	4	2	no	—
939	SD₁₆	—	2	4	no	—
940	SD₁₆	—	2	4	no	—
941	SD₁₆	—	4	2	no	—
942	SD₁₆	—	4	2	no	—
943	SD₁₆	—	4	2	no	—
944	SD₁₆	—	4	2	no	—
945	D₈	—	2	4	no	—
946	D₈	—	2	4	no	—
947	D₈	—	4	2	no	—
948	M₁₆	—	4	2	no	—
949	M₁₆	—	4	2	no	—
950	M₁₆	—	4	2	no	—
951	C₂×C₈	—	4	2	no	—
952	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
953	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
954	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
955	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
971	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
972	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
973	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
974	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
975	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
976	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
977	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
999	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1000	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1001	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1002	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1003	C₄²	—	2	1	no	—
1004	C₄²	—	2	2	no	—
1005	C₄²	C₂⁴×C₆₇	1	2	yes	—
1006	C₂³	—	2	4	no	—
1007	C₂³	—	2	2	no	—
1008	C₂³	—	2	2	no	—
1009	C₂³	—	2	1	no	—
1010	C₂³	—	4	1	no	—
1011	C₂³	—	4	1	no	—
1012	C₂³	—	4	1	no	—
1013	C₂³	—	4	4	no	—
1014	C₂³	—	4	2	no	—
1015	C₂³	—	8	1	no	—
1016	C₂³	—	8	1	no	—
1017	C₂³	—	8	1	no	—
1018	C₂³	—	8	1	no	—
1019	C₂³	—	8	2	no	—
1020	C₂³	—	8	2	no	—
1021	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1022	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1023	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1024	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1025	Q₈	—	2	2	no	—
1026	Q₈	—	2	2	no	—
1027	Q₈	—	2	2	no	—
1028	Q₈	—	2	2	no	—
1029	Q₈	—	2	2	no	—
1030	Q₈	—	4	1	no	—
1031	Q₈	—	4	2	no	—
1032	Q₈	—	8	1	no	—
1033	Q₈	—	8	2	no	—
1034	D₄	—	2	4	no	—
1035	D₄	—	2	2	no	—
1036	D₄	—	2	2	no	—
1037	D₄	—	2	2	no	—
1038	D₄	—	2	2	no	—
1039	D₄	—	4	1	no	—
1040	D₄	—	4	2	no	—
1041	D₄	—	4	2	no	—
1042	D₄	—	4	2	no	—
1043	D₄	—	4	4	no	—
1044	D₄	—	4	4	no	—
1045	D₄	—	4	4	no	—
1046	D₄	—	4	4	no	—
1047	D₄	—	4	2	no	—
1048	D₄	—	4	4	no	—
1049	D₄	—	8	1	no	—
1050	D₄	—	8	2	no	—
1051	D₄	—	8	2	no	—
1052	D₄	—	8	2	no	—
1053	D₄	—	8	1	no	—
1054	D₄	—	8	1	no	—
1055	D₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	4	1	no	—
1069	C₂×C₄	—	4	1	no	—
1070	C₂×C₄	—	4	1	no	—
1071	C₂×C₄	—	4	4	no	—
1072	C₂×C₄	—	4	4	no	—
1073	C₂×C₄	—	4	4	no	—
1074	C₂×C₄	—	4	2	no	—
1075	C₂×C₄	—	4	2	no	—
1076	C₂×C₄	—	4	2	no	—
1077	C₂×C₄	—	8	2	no	—
1078	C₂×C₄	—	8	2	no	—
1079	C₂×C₄	—	8	2	no	—
1080	C₂×C₄	—	8	2	no	—
1081	C₂×C₄	—	8	1	no	—
1082	C₂×C₄	—	8	1	no	—
1083	C₂×C₄	—	8	2	no	—
1084	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1085	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1086	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1087	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1088	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1089	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1090	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1091	C₈	—	2	2	no	—
1092	C₈	—	2	2	no	—
1093	C₈	—	2	2	no	—
1094	C₈	—	2	2	no	—
1095	C₂²	—	2	1	no	—
1096	C₂²	—	2	2	no	—
1097	C₂²	—	2	1	no	—
1098	C₂²	—	2	1	no	—
1099	C₂²	—	2	1	no	—
1100	C₂²	—	2	2	no	—
1101	C₂²	—	2	1	no	—
1102	C₂²	—	2	1	no	—
1103	C₂²	—	2	1	no	—
1104	C₂²	—	2	1	no	—
1105	C₂²	—	2	1	no	—
1106	C₂²	—	2	2	no	—
1107	C₂²	—	2	4	no	—
1108	C₂²	—	4	2	no	—
1109	C₂²	—	4	2	no	—
1110	C₂²	—	4	2	no	—
1111	C₂²	—	4	1	no	—
1112	C₂²	—	4	1	no	—
1113	C₂²	—	4	2	no	—
1114	C₂²	—	4	1	no	—
1115	C₂²	—	4	2	no	—
1116	C₂²	—	8	4	no	—
1117	C₂²	—	8	2	no	—
1118	C₂²	—	16	4	no	—
1119	C₂²	—	16	2	no	—
1120	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1121	C₄	—	2	2	no	—
1122	C₄	—	2	2	no	—
1123	C₄	—	2	1	no	—
1124	C₄	—	2	1	no	—
1125	C₄	—	2	1	no	—
1126	C₄	—	2	2	no	—
1127	C₄	—	4	2	no	—
1128	C₄	—	4	2	no	—
1129	C₄	—	4	1	no	—
1130	C₄	—	4	1	no	—
1131	C₄	—	4	1	no	—
1132	C₄	—	4	2	no	—
1133	C₄	—	4	2	no	—
1134	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
1135	C₂	—	4	1	no	—
1136	C₂	—	4	1	no	—
1137	C₂	—	4	1	no	—
1138	C₂	—	4	2	no	—
1139	C₂	—	4	4	no	—
1140	C₂	—	8	1	no	—
1141	C₂	—	8	2	no	—
1142	C₂	C₆₇×#3484	1	1	yes	characteristic
1143	C₂	C₆₇×#3585	1	1	yes	characteristic
1144	C₂	C₆₇×#3586	1	1	yes	characteristic

	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 ◁ #525×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3536	C₂	semidirect
2. C₆₇×#3485	C₂	semidirect
3. C₆₇×#3331	C₂	semidirect
4. C₆₇×#3330	C₂	semidirect
5. C₆₇×#3314	C₂	semidirect
6. C₆₇×#3306	C₂	semidirect
7. C₆₇×#3275	C₂	semidirect
8. C₆₇×#3273	C₂	semidirect
9. C₆₇×#3269	C₂	semidirect
10. C₆₇×#3267	C₂	semidirect
11. C₆₇×#3225	C₂	semidirect
12. C₆₇×#3201	C₂	semidirect
13. C₆₇×#3196	C₂	semidirect
14. C₆₇×#3194	C₂	semidirect
15. C₆₇×#3118	C₂	semidirect
16. C₆₇×#3012	C₂	semidirect
17. C₆₇×#3007	C₂	semidirect
18. C₆₇×#3006	C₂	semidirect
19. C₆₇×#2978	C₂	semidirect
20. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
22. C₂×#137×C₆₇	C₂²	semidirect
23. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
24. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
25. C₂×#135×C₆₇	C₂²	semidirect
27. #554×C₆₇	C₂²	semidirect
28. #548×C₆₇	C₂²	semidirect
32. #547×C₆₇	C₂²	semidirect
33. #547×C₆₇	C₂²	semidirect
38. #546×C₆₇	C₂²	semidirect
39. #546×C₆₇	C₂²	semidirect
41. #542×C₆₇	C₂²	semidirect
46. #536×C₆₇	C₂²	semidirect
47. #536×C₆₇	C₂²	semidirect
52. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
53. C₂×#121×C₆₇	C₂²	semidirect
54. #518×C₆₇	C₂²	semidirect
55. #497×C₆₇	C₂²	semidirect
56. #495×C₆₇	C₂²	semidirect
57. #489×C₆₇	C₂²	semidirect
58. #487×C₆₇	C₂²	semidirect
59. #485×C₆₇	C₂²	semidirect
60. #484×C₆₇	C₂²	semidirect
61. #484×C₆₇	C₂²	semidirect
62. #483×C₆₇	C₂²	semidirect
63. #483×C₆₇	C₂²	semidirect
64. #482×C₆₇	C₂²	semidirect
65. #481×C₆₇	C₂²	semidirect
66. #480×C₆₇	C₂²	semidirect
67. #476×C₆₇	C₂²	semidirect
68. #474×C₆₇	C₂²	semidirect
69. #470×C₆₇	C₂²	semidirect
70. #470×C₆₇	C₂²	semidirect
71. #469×C₆₇	C₂²	semidirect
72. #468×C₆₇	C₂²	semidirect
73. #468×C₆₇	C₂²	semidirect
74. #468×C₆₇	C₂²	semidirect
75. #467×C₆₇	C₂²	semidirect
76. #465×C₆₇	C₂²	semidirect
77. #464×C₆₇	C₂²	semidirect
78. #463×C₆₇	C₂²	semidirect
79. #463×C₆₇	C₂²	semidirect
80. #463×C₆₇	C₂²	semidirect
81. #462×C₆₇	C₂²	semidirect
82. #461×C₆₇	C₂²	semidirect
83. #452×C₆₇	C₂²	semidirect
84. #452×C₆₇	C₂²	semidirect
85. #452×C₆₇	C₂²	semidirect
86. #452×C₆₇	C₂²	semidirect
87. #452×C₆₇	C₂²	semidirect
88. #452×C₆₇	C₂²	semidirect
89. #451×C₆₇	C₂²	semidirect
90. #451×C₆₇	C₂²	semidirect
91. #450×C₆₇	C₂²	semidirect
92. #450×C₆₇	C₂²	semidirect
93. #450×C₆₇	C₂²	semidirect
95. #449×C₆₇	C₂²	semidirect
96. #449×C₆₇	C₂²	semidirect
97. #449×C₆₇	C₂²	semidirect
98. #448×C₆₇	C₂²	semidirect
99. #448×C₆₇	C₂²	semidirect
101. #447×C₆₇	C₂²	semidirect
102. #447×C₆₇	C₂²	semidirect
103. #442×C₆₇	C₂²	semidirect
104. #440×C₆₇	C₂²	semidirect
105. C₄×SD₁₆×C₆₇	C₂²	semidirect
106. C₄×D₈×C₆₇	C₂²	semidirect
107. #436×C₆₇	C₂²	semidirect
108. #436×C₆₇	C₂²	semidirect
109. #435×C₆₇	C₂²	semidirect
110. #435×C₆₇	C₂²	semidirect
111. #433×C₆₇	C₂²	semidirect
112. #417×C₆₇	C₂²	semidirect
113. #417×C₆₇	C₂²	semidirect
114. #417×C₆₇	C₂²	semidirect
115. C₂×#102×C₆₇	C₂²	semidirect
116. #408×C₆₇	C₂²	semidirect
117. #407×C₆₇	C₂²	semidirect
118. #407×C₆₇	C₂²	semidirect
562. #61647	C₆₇	direct (N × H)
573. #3536	C₂×C₆₇	semidirect
574. #3485	C₂×C₆₇	semidirect
575. #3331	C₂×C₆₇	semidirect
576. #3330	C₂×C₆₇	semidirect
577. #3314	C₂×C₆₇	semidirect
578. #3306	C₂×C₆₇	semidirect
579. #3275	C₂×C₆₇	semidirect
580. #3273	C₂×C₆₇	semidirect
581. #3269	C₂×C₆₇	semidirect
582. #3267	C₂×C₆₇	semidirect
583. #3225	C₂×C₆₇	semidirect
584. #3201	C₂×C₆₇	semidirect
585. #3196	C₂×C₆₇	semidirect
586. #3194	C₂×C₆₇	semidirect
587. #3118	C₂×C₆₇	semidirect
588. #3012	C₂×C₆₇	semidirect
589. #3007	C₂×C₆₇	semidirect
590. #3006	C₂×C₆₇	semidirect
591. #2978	C₂×C₆₇	semidirect
592. C₆₇	#61647	direct (N × H)
593. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
595. C₂×#137	C₂²×C₆₇	semidirect
596. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
597. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
598. C₂×#135	C₂²×C₆₇	semidirect
600. #554	C₂²×C₆₇	semidirect
601. #548	C₂²×C₆₇	semidirect
605. #547	C₂²×C₆₇	semidirect
606. #547	C₂²×C₆₇	semidirect
611. #546	C₂²×C₆₇	semidirect
612. #546	C₂²×C₆₇	semidirect
614. #542	C₂²×C₆₇	semidirect
619. #536	C₂²×C₆₇	semidirect
620. #536	C₂²×C₆₇	semidirect
625. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
626. C₂×#121	C₂²×C₆₇	semidirect
627. #518	C₂²×C₆₇	semidirect
628. #497	C₂²×C₆₇	semidirect
629. #495	C₂²×C₆₇	semidirect
630. #489	C₂²×C₆₇	semidirect
631. #487	C₂²×C₆₇	semidirect
632. #485	C₂²×C₆₇	semidirect
633. #484	C₂²×C₆₇	semidirect
634. #484	C₂²×C₆₇	semidirect
635. #483	C₂²×C₆₇	semidirect
636. #483	C₂²×C₆₇	semidirect
637. #482	C₂²×C₆₇	semidirect
638. #481	C₂²×C₆₇	semidirect
639. #480	C₂²×C₆₇	semidirect
640. #476	C₂²×C₆₇	semidirect
641. #474	C₂²×C₆₇	semidirect
642. #470	C₂²×C₆₇	semidirect
643. #470	C₂²×C₆₇	semidirect
644. #469	C₂²×C₆₇	semidirect
645. #468	C₂²×C₆₇	semidirect
646. #468	C₂²×C₆₇	semidirect
647. #468	C₂²×C₆₇	semidirect
648. #467	C₂²×C₆₇	semidirect
649. #465	C₂²×C₆₇	semidirect
650. #464	C₂²×C₆₇	semidirect
651. #463	C₂²×C₆₇	semidirect
652. #463	C₂²×C₆₇	semidirect
653. #463	C₂²×C₆₇	semidirect
654. #462	C₂²×C₆₇	semidirect
655. #461	C₂²×C₆₇	semidirect
656. #452	C₂²×C₆₇	semidirect
657. #452	C₂²×C₆₇	semidirect
658. #452	C₂²×C₆₇	semidirect
659. #452	C₂²×C₆₇	semidirect
660. #452	C₂²×C₆₇	semidirect
661. #452	C₂²×C₆₇	semidirect
662. #451	C₂²×C₆₇	semidirect
663. #451	C₂²×C₆₇	semidirect
664. #450	C₂²×C₆₇	semidirect
665. #450	C₂²×C₆₇	semidirect
666. #450	C₂²×C₆₇	semidirect
668. #449	C₂²×C₆₇	semidirect
669. #449	C₂²×C₆₇	semidirect
670. #449	C₂²×C₆₇	semidirect
671. #448	C₂²×C₆₇	semidirect
672. #448	C₂²×C₆₇	semidirect
674. #447	C₂²×C₆₇	semidirect
675. #447	C₂²×C₆₇	semidirect
676. #442	C₂²×C₆₇	semidirect
677. #440	C₂²×C₆₇	semidirect
678. C₄×SD₁₆	C₂²×C₆₇	semidirect
679. C₄×D₈	C₂²×C₆₇	semidirect
680. #436	C₂²×C₆₇	semidirect
681. #436	C₂²×C₆₇	semidirect
682. #435	C₂²×C₆₇	semidirect
683. #435	C₂²×C₆₇	semidirect
684. #433	C₂²×C₆₇	semidirect
685. #417	C₂²×C₆₇	semidirect
686. #417	C₂²×C₆₇	semidirect
687. #417	C₂²×C₆₇	semidirect
688. C₂×#102	C₂²×C₆₇	semidirect
689. #408	C₂²×C₆₇	semidirect
690. #407	C₂²×C₆₇	semidirect
691. #407	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×#3536	2
C₆₇×#3485	2
C₆₇×#3331	2
C₆₇×#3330	2
C₆₇×#3314	2
C₆₇×#3306	2
C₆₇×#3275	2
C₆₇×#3273	2
C₆₇×#3269	2
C₆₇×#3267	2
C₆₇×#3225	2
C₆₇×#3201	2
C₆₇×#3196	2
C₆₇×#3194	2
C₆₇×#3118	2
C₆₇×#3012	2
C₆₇×#3007	2
C₆₇×#3006	2
C₆₇×#2978	2
#61647	67

Subgroups — C67×#61647 #30740898

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61647 #30740898