Subgroups — C₆₇×#61067 #30740318

Order 17152.

2778 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#575×C₆₇	C₂	1	2	yes	maximal, complemented
2	D₄×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#547×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3284	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3283	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3276	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3272	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3269	C₂	1	4	yes	maximal, complemented
9	C₆₇×#3267	C₂	1	4	yes	maximal, complemented
10	C₆₇×#3152	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3056	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3039	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3036	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3007	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3005	C₂	1	2	yes	maximal, complemented
16	C₄×AGL(1,ℤ/8)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	D₄×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₆₇	C₂²	1	2	yes	—
19	C₂²×#41×C₆₇	C₂²	1	2	yes	complemented
20	#575×C₆₇	—	2	16	no	—
21	C₂×#137×C₆₇	C₂²	1	2	yes	—
22	C₂×#137×C₆₇	C₂²	1	4	yes	complemented
23	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
24	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
25	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	complemented
27	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
28	C₂×#135×C₆₇	C₂²	1	4	yes	complemented
29	C₂×#135×C₆₇	C₂²	1	4	yes	complemented
30	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	complemented
31	#550×C₆₇	C₂²	1	1	yes	characteristic, complemented
32	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	#548×C₆₇	C₂²	1	2	yes	complemented
34	#547×C₆₇	—	2	1	no	—
35	#547×C₆₇	—	2	1	no	—
36	#547×C₆₇	—	2	2	no	—
37	#547×C₆₇	—	2	1	no	—
38	#547×C₆₇	C₂²	1	2	yes	—
39	#547×C₆₇	C₂²	1	4	yes	complemented
40	#547×C₆₇	C₂²	1	1	yes	characteristic, complemented
41	#547×C₆₇	C₂²	1	2	yes	complemented
42	#546×C₆₇	—	2	2	no	—
43	#546×C₆₇	C₂²	1	2	yes	complemented
44	D₄²×C₆₇	—	2	1	no	—
45	D₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	#532×C₆₇	—	2	1	no	—
47	#532×C₆₇	C₂²	1	1	yes	characteristic
48	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#525×C₆₇	—	2	2	no	—
50	#525×C₆₇	C₂²	1	2	yes	—
51	C₂×#123×C₆₇	—	2	2	no	—
52	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
53	C₂×#121×C₆₇	—	2	1	no	—
54	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄×C₆₇	—	2	1	no	—
56	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
57	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
58	C₂²×C₄⋊C₄×C₆₇	—	2	1	no	—
59	#497×C₆₇	C₂²	1	4	yes	complemented
60	#494×C₆₇	C₂²	1	2	yes	complemented
61	#492×C₆₇	C₂²	1	2	yes	complemented
62	#470×C₆₇	C₂²	1	4	yes	complemented
63	#468×C₆₇	C₂²	1	4	yes	complemented
64	#467×C₆₇	C₂²	1	4	yes	complemented
65	#465×C₆₇	C₂²	1	4	yes	complemented
66	#463×C₆₇	C₂²	1	4	yes	complemented
67	#462×C₆₇	C₂²	1	2	yes	complemented
68	#462×C₆₇	C₂²	1	2	yes	complemented
69	#461×C₆₇	C₂²	1	2	yes	complemented
70	#461×C₆₇	C₂²	1	2	yes	complemented
71	#461×C₆₇	C₂²	1	2	yes	complemented
72	#459×C₆₇	C₂²	1	2	yes	complemented
73	#452×C₆₇	C₂²	1	4	yes	complemented
74	#452×C₆₇	C₂²	1	4	yes	complemented
75	#452×C₆₇	C₂²	1	4	yes	complemented
76	#452×C₆₇	C₂²	1	4	yes	complemented
77	#451×C₆₇	C₂²	1	4	yes	complemented
78	#450×C₆₇	C₂²	1	4	yes	complemented
79	#449×C₆₇	C₂²	1	4	yes	complemented
80	#449×C₆₇	C₂²	1	4	yes	complemented
81	#442×C₆₇	C₂²	1	2	yes	complemented
82	#440×C₆₇	C₂²	1	2	yes	complemented
83	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
84	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
85	#436×C₆₇	C₂²	1	2	yes	complemented
86	#435×C₆₇	C₂²	1	4	yes	complemented
87	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
88	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
89	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	#419×C₆₇	C₂²	1	2	yes	complemented
91	#418×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	#417×C₆₇	C₂²	1	1	yes	characteristic
93	#417×C₆₇	C₂²	1	2	yes	complemented
94	#407×C₆₇	C₂²	1	2	yes	complemented
95	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
96	C₂×#41×C₆₇	—	2	2	no	—
97	C₂×#41×C₆₇	—	2	2	no	—
98	C₂×#41×C₆₇	—	2	2	no	—
99	C₂×#41×C₆₇	—	2	2	no	—
100	C₂×#41×C₆₇	—	2	8	no	—
101	C₂×#41×C₆₇	—	2	8	no	—
102	C₂×#41×C₆₇	—	4	4	no	—
103	C₂×#41×C₆₇	—	4	4	no	—
104	C₂×#41×C₆₇	C₂³	1	2	yes	—
105	C₂×#41×C₆₇	C₂³	1	4	yes	—
106	C₂×#41×C₆₇	C₂³	1	4	yes	—
107	C₂×#41×C₆₇	C₂³	1	2	yes	—
108	C₂×#41×C₆₇	C₂³	1	2	yes	—
109	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
110	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
111	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
112	C₂²×D₄×C₆₇	—	2	2	no	—
113	C₂²×D₄×C₆₇	—	2	2	no	—
114	C₂²×D₄×C₆₇	—	2	1	no	—
115	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
116	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
117	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₆₇	—	2	1	no	—
119	C₂³×C₄×C₆₇	—	2	2	no	—
120	C₂³×C₄×C₆₇	—	2	2	no	—
121	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
122	#137×C₆₇	—	2	8	no	—
123	#137×C₆₇	—	2	16	no	—
124	#137×C₆₇	—	2	8	no	—
125	#137×C₆₇	—	4	4	no	—
126	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
127	AGL(1,ℤ/8)×C₆₇	—	2	16	no	—
128	AGL(1,ℤ/8)×C₆₇	D₄	1	8	yes	complemented
129	#135×C₆₇	—	2	16	no	—
130	#135×C₆₇	—	2	16	no	—
131	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
132	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
133	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
134	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
135	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
136	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
137	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
138	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
139	C₂×D₈×C₆₇	C₂³	1	4	yes	—
140	C₂×D₈×C₆₇	C₂³	1	2	yes	—
141	C₂×M₁₆×C₆₇	—	2	8	no	—
142	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
143	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
144	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
146	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
147	C₄⋊Q₈×C₆₇	—	2	1	no	—
148	C₄⋊Q₈×C₆₇	—	2	1	no	—
149	C₄⋊Q₈×C₆₇	—	2	1	no	—
150	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
151	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
152	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
153	#127×C₆₇	—	2	1	no	—
154	#127×C₆₇	C₂³	1	1	yes	characteristic
155	#124×C₆₇	—	2	2	no	—
156	#124×C₆₇	C₂³	1	2	yes	—
157	#123×C₆₇	—	2	2	no	—
158	#123×C₆₇	—	2	2	no	—
159	#123×C₆₇	—	2	4	no	—
160	#123×C₆₇	—	2	4	no	—
161	#123×C₆₇	—	2	4	no	—
162	#123×C₆₇	—	2	4	no	—
163	#123×C₆₇	—	2	2	no	—
164	C₂²⋊Q₈×C₆₇	—	2	2	no	—
165	C₂²⋊Q₈×C₆₇	—	2	2	no	—
166	C₂²⋊Q₈×C₆₇	—	2	2	no	—
167	C₂²⋊Q₈×C₆₇	—	2	2	no	—
168	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
169	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
170	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
171	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
172	#121×C₆₇	—	2	2	no	—
173	#121×C₆₇	—	2	2	no	—
174	#121×C₆₇	—	2	4	no	—
175	#121×C₆₇	—	2	2	no	—
176	#121×C₆₇	—	2	1	no	—
177	#121×C₆₇	—	2	1	no	—
178	#121×C₆₇	—	2	1	no	—
179	#121×C₆₇	—	2	1	no	—
180	#121×C₆₇	—	2	2	no	—
181	#121×C₆₇	—	2	2	no	—
182	#121×C₆₇	C₂³	1	2	yes	—
183	#121×C₆₇	C₂³	1	2	yes	—
184	#120×C₆₇	—	2	2	no	—
185	#120×C₆₇	—	2	2	no	—
186	#120×C₆₇	—	2	2	no	—
187	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
188	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
189	C₄×D₄×C₆₇	—	2	1	no	—
190	C₄×D₄×C₆₇	—	2	2	no	—
191	C₄×D₄×C₆₇	—	2	1	no	—
192	C₄×D₄×C₆₇	—	2	1	no	—
193	C₄×D₄×C₆₇	—	2	2	no	—
194	C₄×D₄×C₆₇	—	2	1	no	—
195	C₄×D₄×C₆₇	—	2	2	no	—
196	C₄×D₄×C₆₇	—	2	1	no	—
197	C₄×D₄×C₆₇	—	2	1	no	—
198	C₄×D₄×C₆₇	—	2	1	no	—
199	C₄×D₄×C₆₇	—	2	1	no	—
200	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
201	C₄×D₄×C₆₇	D₄	1	2	yes	—
202	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
203	C₄×D₄×C₆₇	C₂³	1	2	yes	—
204	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
205	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
206	C₄×D₄×C₆₇	C₂³	1	2	yes	—
207	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
208	C₄×D₄×C₆₇	C₂³	1	2	yes	—
209	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
210	#117×C₆₇	—	2	1	no	—
211	#117×C₆₇	C₂³	1	1	yes	characteristic
212	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
213	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
214	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
215	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
216	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
217	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
218	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
219	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
220	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
222	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
223	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
224	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
225	C₂×C₄²×C₆₇	—	2	1	no	—
226	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
227	#107×C₆₇	C₂³	1	2	yes	—
228	#106×C₆₇	C₂³	1	2	yes	—
229	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
230	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
231	#103×C₆₇	C₂³	1	4	yes	—
232	#103×C₆₇	C₂³	1	4	yes	—
233	#103×C₆₇	C₂³	1	2	yes	—
234	#103×C₆₇	C₂³	1	4	yes	—
235	#102×C₆₇	C₂³	1	2	yes	—
236	#102×C₆₇	C₂³	1	2	yes	—
237	#102×C₆₇	C₂³	1	2	yes	—
238	#102×C₆₇	C₂³	1	4	yes	—
239	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
240	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
241	#97×C₆₇	C₂³	1	2	yes	—
242	C₄×C₈×C₆₇	C₂³	1	2	yes	—
243	C₂⁴×C₆₇	—	2	1	no	—
244	C₂⁴×C₆₇	—	2	2	no	—
245	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
246	#41×C₆₇	—	2	2	no	—
247	#41×C₆₇	—	2	4	no	—
248	#41×C₆₇	—	2	8	no	—
249	#41×C₆₇	—	2	4	no	—
250	#41×C₆₇	—	2	8	no	—
251	#41×C₆₇	—	2	4	no	—
252	#41×C₆₇	—	2	4	no	—
253	#41×C₆₇	—	4	8	no	—
254	#41×C₆₇	—	4	4	no	—
255	#41×C₆₇	—	4	2	no	—
256	#41×C₆₇	—	4	4	no	—
257	#41×C₆₇	—	4	2	no	—
258	#41×C₆₇	—	4	8	no	—
259	#41×C₆₇	—	4	8	no	—
260	#41×C₆₇	—	4	8	no	—
261	#41×C₆₇	C₂×D₄	1	4	yes	—
262	C₂×Q₈×C₆₇	—	2	2	no	—
263	C₂×Q₈×C₆₇	—	2	2	no	—
264	C₂×Q₈×C₆₇	—	2	4	no	—
265	C₂×Q₈×C₆₇	—	2	4	no	—
266	C₂×Q₈×C₆₇	—	2	4	no	—
267	C₂×Q₈×C₆₇	—	4	2	no	—
268	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
269	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
270	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
271	C₂×D₄×C₆₇	—	2	1	no	—
272	C₂×D₄×C₆₇	—	2	4	no	—
273	C₂×D₄×C₆₇	—	2	2	no	—
274	C₂×D₄×C₆₇	—	2	2	no	—
275	C₂×D₄×C₆₇	—	2	2	no	—
276	C₂×D₄×C₆₇	—	2	4	no	—
277	C₂×D₄×C₆₇	—	2	4	no	—
278	C₂×D₄×C₆₇	—	2	2	no	—
279	C₂×D₄×C₆₇	—	2	2	no	—
280	C₂×D₄×C₆₇	—	2	1	no	—
281	C₂×D₄×C₆₇	—	2	1	no	—
282	C₂×D₄×C₆₇	—	2	2	no	—
283	C₂×D₄×C₆₇	—	2	1	no	—
284	C₂×D₄×C₆₇	—	2	2	no	—
285	C₂×D₄×C₆₇	—	4	2	no	—
286	C₂×D₄×C₆₇	—	4	2	no	—
287	C₂×D₄×C₆₇	—	4	8	no	—
288	C₂×D₄×C₆₇	—	4	4	no	—
289	C₂×D₄×C₆₇	—	4	8	no	—
290	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
291	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
292	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
293	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	complemented
294	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
295	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
296	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₆₇	—	2	1	no	—
298	C₂²×C₄×C₆₇	—	2	4	no	—
299	C₂²×C₄×C₆₇	—	2	4	no	—
300	C₂²×C₄×C₆₇	—	2	1	no	—
301	C₂²×C₄×C₆₇	—	2	2	no	—
302	C₂²×C₄×C₆₇	—	2	2	no	—
303	C₂²×C₄×C₆₇	—	2	1	no	—
304	C₂²×C₄×C₆₇	—	2	2	no	—
305	C₂²×C₄×C₆₇	—	2	2	no	—
306	C₂²×C₄×C₆₇	—	2	2	no	—
307	C₂²×C₄×C₆₇	—	2	4	no	—
308	C₂²×C₄×C₆₇	—	2	4	no	—
309	C₂²×C₄×C₆₇	—	2	2	no	—
310	C₂²×C₄×C₆₇	—	2	2	no	—
311	C₂²×C₄×C₆₇	—	2	1	no	—
312	C₂²×C₄×C₆₇	—	4	8	no	—
313	C₂²×C₄×C₆₇	—	4	8	no	—
314	C₂²×C₄×C₆₇	—	4	4	no	—
315	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
316	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
317	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
318	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
319	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
320	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
322	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
323	Q₁₆×C₆₇	—	2	8	no	—
324	Q₁₆×C₆₇	—	2	8	no	—
325	Q₁₆×C₆₇	—	4	4	no	—
326	SD₁₆×C₆₇	—	2	8	no	—
327	SD₁₆×C₆₇	—	2	8	no	—
328	SD₁₆×C₆₇	—	2	8	no	—
329	SD₁₆×C₆₇	—	4	4	no	—
330	SD₁₆×C₆₇	C₂×D₄	1	8	yes	complemented
331	D₈×C₆₇	—	2	8	no	—
332	D₈×C₆₇	C₂×D₄	1	8	yes	complemented
333	M₁₆×C₆₇	—	2	4	no	—
334	M₁₆×C₆₇	—	2	2	no	—
335	M₁₆×C₆₇	—	2	8	no	—
336	M₁₆×C₆₇	C₂×D₄	1	4	yes	complemented
337	C₂×C₈×C₆₇	—	2	8	no	—
338	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
339	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
340	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
341	C₄⋊C₄×C₆₇	—	2	2	no	—
342	C₄⋊C₄×C₆₇	—	2	2	no	—
343	C₄⋊C₄×C₆₇	—	2	4	no	—
344	C₄⋊C₄×C₆₇	—	2	4	no	—
345	C₄⋊C₄×C₆₇	—	2	1	no	—
346	C₄⋊C₄×C₆₇	—	2	2	no	—
347	C₄⋊C₄×C₆₇	—	2	2	no	—
348	C₄⋊C₄×C₆₇	—	2	2	no	—
349	C₄⋊C₄×C₆₇	—	2	1	no	—
350	C₄⋊C₄×C₆₇	—	2	1	no	—
351	C₄⋊C₄×C₆₇	—	2	1	no	—
352	C₄⋊C₄×C₆₇	—	2	1	no	—
353	C₄⋊C₄×C₆₇	—	2	2	no	—
354	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
355	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
356	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
357	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
358	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
359	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
360	C₂²⋊C₄×C₆₇	—	2	2	no	—
361	C₂²⋊C₄×C₆₇	—	2	4	no	—
362	C₂²⋊C₄×C₆₇	—	2	4	no	—
363	C₂²⋊C₄×C₆₇	—	2	1	no	—
364	C₂²⋊C₄×C₆₇	—	2	2	no	—
365	C₂²⋊C₄×C₆₇	—	2	2	no	—
366	C₂²⋊C₄×C₆₇	—	2	2	no	—
367	C₂²⋊C₄×C₆₇	—	2	2	no	—
368	C₂²⋊C₄×C₆₇	—	2	2	no	—
369	C₂²⋊C₄×C₆₇	—	2	1	no	—
370	C₂²⋊C₄×C₆₇	—	2	1	no	—
371	C₂²⋊C₄×C₆₇	—	2	2	no	—
372	C₂²⋊C₄×C₆₇	—	2	2	no	—
373	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
374	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
375	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
376	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
377	C₄²×C₆₇	—	2	1	no	—
378	C₄²×C₆₇	—	2	1	no	—
379	C₄²×C₆₇	—	2	1	no	—
380	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
381	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
382	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
383	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
384	C₂³×C₆₇	—	2	4	no	—
385	C₂³×C₆₇	—	2	2	no	—
386	C₂³×C₆₇	—	2	1	no	—
387	C₂³×C₆₇	—	2	4	no	—
388	C₂³×C₆₇	—	2	2	no	—
389	C₂³×C₆₇	—	4	2	no	—
390	C₂³×C₆₇	—	4	2	no	—
391	C₂³×C₆₇	—	4	4	no	—
392	C₂³×C₆₇	—	4	2	no	—
393	C₂³×C₆₇	—	4	2	no	—
394	C₂³×C₆₇	—	4	4	no	—
395	C₂³×C₆₇	—	8	2	no	—
396	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
397	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
398	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
399	Q₈×C₆₇	—	2	1	no	—
400	Q₈×C₆₇	—	2	2	no	—
401	Q₈×C₆₇	—	2	4	no	—
402	Q₈×C₆₇	—	2	4	no	—
403	Q₈×C₆₇	—	2	2	no	—
404	Q₈×C₆₇	—	4	4	no	—
405	Q₈×C₆₇	—	4	4	no	—
406	Q₈×C₆₇	C₂²×D₄	1	2	yes	—
407	D₄×C₆₇	—	2	4	no	—
408	D₄×C₆₇	—	2	4	no	—
409	D₄×C₆₇	—	2	2	no	—
410	D₄×C₆₇	—	2	2	no	—
411	D₄×C₆₇	—	2	2	no	—
412	D₄×C₆₇	—	2	2	no	—
413	D₄×C₆₇	—	2	1	no	—
414	D₄×C₆₇	—	2	2	no	—
415	D₄×C₆₇	—	4	2	no	—
416	D₄×C₆₇	—	4	4	no	—
417	D₄×C₆₇	—	4	4	no	—
418	D₄×C₆₇	—	4	8	no	—
419	D₄×C₆₇	—	4	4	no	—
420	D₄×C₆₇	—	4	8	no	—
421	D₄×C₆₇	—	4	4	no	—
422	D₄×C₆₇	—	4	4	no	—
423	D₄×C₆₇	—	4	2	no	—
424	D₄×C₆₇	—	8	1	no	—
425	D₄×C₆₇	—	8	2	no	—
426	D₄×C₆₇	C₂²×D₄	1	4	yes	—
427	D₄×C₆₇	C₂²×D₄	1	2	yes	—
428	C₂×C₄×C₆₇	—	2	4	no	—
429	C₂×C₄×C₆₇	—	2	1	no	—
430	C₂×C₄×C₆₇	—	2	4	no	—
431	C₂×C₄×C₆₇	—	2	4	no	—
432	C₂×C₄×C₆₇	—	2	4	no	—
433	C₂×C₄×C₆₇	—	2	2	no	—
434	C₂×C₄×C₆₇	—	2	2	no	—
435	C₂×C₄×C₆₇	—	2	2	no	—
436	C₂×C₄×C₆₇	—	2	2	no	—
437	C₂×C₄×C₆₇	—	2	2	no	—
438	C₂×C₄×C₆₇	—	2	1	no	—
439	C₂×C₄×C₆₇	—	2	1	no	—
440	C₂×C₄×C₆₇	—	2	2	no	—
441	C₂×C₄×C₆₇	—	2	2	no	—
442	C₂×C₄×C₆₇	—	2	4	no	—
443	C₂×C₄×C₆₇	—	4	1	no	—
444	C₂×C₄×C₆₇	—	4	4	no	—
445	C₂×C₄×C₆₇	—	4	4	no	—
446	C₂×C₄×C₆₇	—	4	4	no	—
447	C₂×C₄×C₆₇	—	4	8	no	—
448	C₂×C₄×C₆₇	—	4	8	no	—
449	C₂×C₄×C₆₇	—	4	4	no	—
450	C₂×C₄×C₆₇	—	4	2	no	—
451	C₂×C₄×C₆₇	—	4	4	no	—
452	C₂×C₄×C₆₇	—	4	4	no	—
453	C₂×C₄×C₆₇	—	4	4	no	—
454	C₂×C₄×C₆₇	—	4	2	no	—
455	C₂×C₄×C₆₇	—	8	1	no	—
456	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
460	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
461	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
462	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
463	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
465	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
466	C₈×C₆₇	—	2	4	no	—
467	C₈×C₆₇	—	2	2	no	—
468	C₈×C₆₇	C₂²×D₄	1	4	yes	—
469	C₂²×C₆₇	—	2	1	no	—
470	C₂²×C₆₇	—	2	1	no	—
471	C₂²×C₆₇	—	2	2	no	—
472	C₂²×C₆₇	—	2	2	no	—
473	C₂²×C₆₇	—	2	2	no	—
474	C₂²×C₆₇	—	2	2	no	—
475	C₂²×C₆₇	—	2	2	no	—
476	C₂²×C₆₇	—	2	4	no	—
477	C₂²×C₆₇	—	2	2	no	—
478	C₂²×C₆₇	—	2	2	no	—
479	C₂²×C₆₇	—	4	8	no	—
480	C₂²×C₆₇	—	4	1	no	—
481	C₂²×C₆₇	—	4	2	no	—
482	C₂²×C₆₇	—	4	2	no	—
483	C₂²×C₆₇	—	4	1	no	—
484	C₂²×C₆₇	—	4	2	no	—
485	C₂²×C₆₇	—	4	2	no	—
486	C₂²×C₆₇	—	4	2	no	—
487	C₂²×C₆₇	—	8	4	no	—
488	C₂²×C₆₇	—	8	8	no	—
489	C₂²×C₆₇	D₄²	1	2	yes	—
490	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
491	C₄×C₆₇	—	2	1	no	—
492	C₄×C₆₇	—	2	1	no	—
493	C₄×C₆₇	—	2	2	no	—
494	C₄×C₆₇	—	2	2	no	—
495	C₄×C₆₇	—	2	2	no	—
496	C₄×C₆₇	—	2	1	no	—
497	C₄×C₆₇	—	4	1	no	—
498	C₄×C₆₇	—	4	2	no	—
499	C₄×C₆₇	—	4	4	no	—
500	C₄×C₆₇	—	4	2	no	—
501	C₄×C₆₇	—	4	1	no	—
502	C₄×C₆₇	D₄²	1	2	yes	—
503	C₄×C₆₇	#575	1	2	yes	complemented
504	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
505	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
506	#61067	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
507	C₂×C₆₇	—	2	2	no	—
508	C₂×C₆₇	—	4	2	no	—
509	C₂×C₆₇	—	4	2	no	—
510	C₂×C₆₇	—	4	4	no	—
511	C₂×C₆₇	—	4	2	no	—
512	C₂×C₆₇	—	8	2	no	—
513	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
514	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
515	C₂×C₆₇	#3586	1	1	yes	characteristic
516	C₂×#575	C₂×C₆₇	1	2	yes	complemented
517	D₄×#41	C₂×C₆₇	1	1	yes	characteristic, complemented
518	C₂×#547	C₂×C₆₇	1	1	yes	characteristic, complemented
519	#3284	C₂×C₆₇	1	2	yes	complemented
520	#3283	C₂×C₆₇	1	2	yes	complemented
521	#3276	C₂×C₆₇	1	2	yes	complemented
522	#3272	C₂×C₆₇	1	2	yes	complemented
523	#3269	C₂×C₆₇	1	4	yes	complemented
524	#3267	C₂×C₆₇	1	4	yes	complemented
525	#3152	C₂×C₆₇	1	1	yes	characteristic, complemented
526	#3056	C₂×C₆₇	1	2	yes	complemented
527	#3039	C₂×C₆₇	1	1	yes	characteristic, complemented
528	#3036	C₂×C₆₇	1	1	yes	characteristic, complemented
529	#3007	C₂×C₆₇	1	2	yes	complemented
530	#3005	C₂×C₆₇	1	2	yes	complemented
531	C₄×AGL(1,ℤ/8)	C₂×C₆₇	1	1	yes	characteristic, complemented
532	D₄×M₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
533	C₆₇	#61067	1	1	yes	characteristic, direct product factor, Sylow
534	C₂²×#41	C₂²×C₆₇	1	2	yes	—
535	C₂²×#41	C₂²×C₆₇	1	2	yes	complemented
536	#575	—	2	16	no	—
537	C₂×#137	C₂²×C₆₇	1	2	yes	—
538	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
539	C₂×#137	C₂²×C₆₇	1	4	yes	complemented
540	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
541	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
542	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
543	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
544	C₂×#135	C₂²×C₆₇	1	4	yes	complemented
545	C₂×#135	C₂²×C₆₇	1	4	yes	complemented
546	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	complemented
547	#550	C₂²×C₆₇	1	1	yes	characteristic, complemented
548	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
549	#548	C₂²×C₆₇	1	2	yes	complemented
550	#547	—	2	1	no	—
551	#547	—	2	1	no	—
552	#547	—	2	2	no	—
553	#547	—	2	1	no	—
554	#547	C₂²×C₆₇	1	2	yes	—
555	#547	C₂²×C₆₇	1	4	yes	complemented
556	#547	C₂²×C₆₇	1	2	yes	complemented
557	#547	C₂²×C₆₇	1	1	yes	characteristic, complemented
558	#546	—	2	2	no	—
559	#546	C₂²×C₆₇	1	2	yes	complemented
560	D₄²	—	2	1	no	—
561	D₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
562	#532	—	2	1	no	—
563	#532	C₂²×C₆₇	1	1	yes	characteristic
564	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
565	#525	—	2	2	no	—
566	#525	C₂²×C₆₇	1	2	yes	—
567	C₂×#123	—	2	2	no	—
568	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
569	C₂×#121	—	2	1	no	—
570	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
571	C₂×C₄×D₄	—	2	1	no	—
572	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
573	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
574	C₂²×C₄⋊C₄	—	2	1	no	—
575	#497	C₂²×C₆₇	1	4	yes	complemented
576	#494	C₂²×C₆₇	1	2	yes	complemented
577	#492	C₂²×C₆₇	1	2	yes	complemented
578	#470	C₂²×C₆₇	1	4	yes	complemented
579	#468	C₂²×C₆₇	1	4	yes	complemented
580	#467	C₂²×C₆₇	1	4	yes	complemented
581	#465	C₂²×C₆₇	1	4	yes	complemented
582	#463	C₂²×C₆₇	1	4	yes	complemented
583	#462	C₂²×C₆₇	1	2	yes	complemented
584	#462	C₂²×C₆₇	1	2	yes	complemented
585	#461	C₂²×C₆₇	1	2	yes	complemented
586	#461	C₂²×C₆₇	1	2	yes	complemented
587	#461	C₂²×C₆₇	1	2	yes	complemented
588	#459	C₂²×C₆₇	1	2	yes	complemented
589	#452	C₂²×C₆₇	1	4	yes	complemented
590	#452	C₂²×C₆₇	1	4	yes	complemented
591	#452	C₂²×C₆₇	1	4	yes	complemented
592	#452	C₂²×C₆₇	1	4	yes	complemented
593	#451	C₂²×C₆₇	1	4	yes	complemented
594	#450	C₂²×C₆₇	1	4	yes	complemented
595	#449	C₂²×C₆₇	1	4	yes	complemented
596	#449	C₂²×C₆₇	1	4	yes	complemented
597	#442	C₂²×C₆₇	1	2	yes	complemented
598	#440	C₂²×C₆₇	1	2	yes	complemented
599	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
600	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
601	#436	C₂²×C₆₇	1	2	yes	complemented
602	#435	C₂²×C₆₇	1	4	yes	complemented
603	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
604	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
605	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
606	#419	C₂²×C₆₇	1	2	yes	complemented
607	#418	C₂²×C₆₇	1	1	yes	characteristic, complemented
608	#417	C₂²×C₆₇	1	1	yes	characteristic
609	#417	C₂²×C₆₇	1	2	yes	complemented
610	#407	C₂²×C₆₇	1	2	yes	complemented
611	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
612	C₂×#41	—	2	2	no	—
613	C₂×#41	—	2	2	no	—
614	C₂×#41	—	2	2	no	—
615	C₂×#41	—	2	2	no	—
616	C₂×#41	—	2	8	no	—
617	C₂×#41	—	2	8	no	—
618	C₂×#41	—	4	4	no	—
619	C₂×#41	—	4	4	no	—
620	C₂×#41	C₂³×C₆₇	1	2	yes	—
621	C₂×#41	C₂³×C₆₇	1	2	yes	—
622	C₂×#41	C₂³×C₆₇	1	4	yes	—
623	C₂×#41	C₂³×C₆₇	1	4	yes	—
624	C₂×#41	C₂³×C₆₇	1	2	yes	—
625	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
626	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
627	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
628	C₂²×D₄	—	2	2	no	—
629	C₂²×D₄	—	2	2	no	—
630	C₂²×D₄	—	2	1	no	—
631	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
632	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
633	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
634	C₂³×C₄	—	2	1	no	—
635	C₂³×C₄	—	2	2	no	—
636	C₂³×C₄	—	2	2	no	—
637	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
638	#137	—	2	8	no	—
639	#137	—	2	16	no	—
640	#137	—	2	8	no	—
641	#137	—	4	4	no	—
642	AGL(1,ℤ/8)	—	2	8	no	—
643	AGL(1,ℤ/8)	—	2	16	no	—
644	AGL(1,ℤ/8)	D₄×C₆₇	1	8	yes	complemented
645	#135	—	2	16	no	—
646	#135	—	2	16	no	—
647	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
648	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
649	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
650	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
651	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
652	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
653	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
654	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
655	C₂×D₈	C₂³×C₆₇	1	4	yes	—
656	C₂×D₈	C₂³×C₆₇	1	2	yes	—
657	C₂×M₁₆	—	2	8	no	—
658	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
659	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
660	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
661	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
662	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
663	C₄⋊Q₈	—	2	1	no	—
664	C₄⋊Q₈	—	2	1	no	—
665	C₄⋊Q₈	—	2	1	no	—
666	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
667	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
668	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
669	#127	—	2	1	no	—
670	#127	C₂³×C₆₇	1	1	yes	characteristic
671	#124	—	2	2	no	—
672	#124	C₂³×C₆₇	1	2	yes	—
673	#123	—	2	2	no	—
674	#123	—	2	2	no	—
675	#123	—	2	4	no	—
676	#123	—	2	4	no	—
677	#123	—	2	4	no	—
678	#123	—	2	4	no	—
679	#123	—	2	2	no	—
680	C₂²⋊Q₈	—	2	2	no	—
681	C₂²⋊Q₈	—	2	2	no	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	—	2	2	no	—
684	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
685	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
686	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
687	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
688	#121	—	2	2	no	—
689	#121	—	2	2	no	—
690	#121	—	2	4	no	—
691	#121	—	2	2	no	—
692	#121	—	2	1	no	—
693	#121	—	2	1	no	—
694	#121	—	2	1	no	—
695	#121	—	2	1	no	—
696	#121	—	2	2	no	—
697	#121	—	2	2	no	—
698	#121	C₂³×C₆₇	1	2	yes	—
699	#121	C₂³×C₆₇	1	2	yes	—
700	#120	—	2	2	no	—
701	#120	—	2	2	no	—
702	#120	—	2	2	no	—
703	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
704	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
705	C₄×D₄	—	2	1	no	—
706	C₄×D₄	—	2	2	no	—
707	C₄×D₄	—	2	1	no	—
708	C₄×D₄	—	2	1	no	—
709	C₄×D₄	—	2	2	no	—
710	C₄×D₄	—	2	1	no	—
711	C₄×D₄	—	2	2	no	—
712	C₄×D₄	—	2	1	no	—
713	C₄×D₄	—	2	1	no	—
714	C₄×D₄	—	2	1	no	—
715	C₄×D₄	—	2	1	no	—
716	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
717	C₄×D₄	D₄×C₆₇	1	2	yes	—
718	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
719	C₄×D₄	C₂³×C₆₇	1	2	yes	—
720	C₄×D₄	C₂³×C₆₇	1	2	yes	—
721	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
722	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
723	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
724	C₄×D₄	C₂³×C₆₇	1	2	yes	—
725	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
726	#117	—	2	1	no	—
727	#117	C₂³×C₆₇	1	1	yes	characteristic
728	C₂×C₄⋊C₄	—	2	1	no	—
729	C₂×C₄⋊C₄	—	2	2	no	—
730	C₂×C₄⋊C₄	—	2	1	no	—
731	C₂×C₄⋊C₄	—	2	2	no	—
732	C₂×C₄⋊C₄	—	2	2	no	—
733	C₂×C₄⋊C₄	—	2	4	no	—
734	C₂×C₄⋊C₄	—	2	1	no	—
735	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
736	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
737	C₂×C₂²⋊C₄	—	2	2	no	—
738	C₂×C₂²⋊C₄	—	2	1	no	—
739	C₂×C₂²⋊C₄	—	2	2	no	—
740	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
741	C₂×C₄²	—	2	1	no	—
742	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
743	#107	C₂³×C₆₇	1	2	yes	—
744	#106	C₂³×C₆₇	1	2	yes	—
745	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
746	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
747	#103	C₂³×C₆₇	1	2	yes	—
748	#103	C₂³×C₆₇	1	4	yes	—
749	#103	C₂³×C₆₇	1	4	yes	—
750	#103	C₂³×C₆₇	1	4	yes	—
751	#102	C₂³×C₆₇	1	2	yes	—
752	#102	C₂³×C₆₇	1	4	yes	—
753	#102	C₂³×C₆₇	1	2	yes	—
754	#102	C₂³×C₆₇	1	2	yes	—
755	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
756	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
757	#97	C₂³×C₆₇	1	2	yes	—
758	C₄×C₈	C₂³×C₆₇	1	2	yes	—
759	C₂⁴	—	2	1	no	—
760	C₂⁴	—	2	2	no	—
761	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
762	#41	—	2	2	no	—
763	#41	—	2	4	no	—
764	#41	—	2	8	no	—
765	#41	—	2	4	no	—
766	#41	—	2	8	no	—
767	#41	—	2	4	no	—
768	#41	—	2	4	no	—
769	#41	—	4	8	no	—
770	#41	—	4	4	no	—
771	#41	—	4	2	no	—
772	#41	—	4	4	no	—
773	#41	—	4	2	no	—
774	#41	—	4	8	no	—
775	#41	—	4	8	no	—
776	#41	—	4	8	no	—
777	#41	C₂×D₄×C₆₇	1	4	yes	—
778	C₂×Q₈	—	2	2	no	—
779	C₂×Q₈	—	2	2	no	—
780	C₂×Q₈	—	2	4	no	—
781	C₂×Q₈	—	2	4	no	—
782	C₂×Q₈	—	2	4	no	—
783	C₂×Q₈	—	4	2	no	—
784	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
785	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
786	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
787	C₂×D₄	—	2	1	no	—
788	C₂×D₄	—	2	4	no	—
789	C₂×D₄	—	2	2	no	—
790	C₂×D₄	—	2	2	no	—
791	C₂×D₄	—	2	2	no	—
792	C₂×D₄	—	2	4	no	—
793	C₂×D₄	—	2	4	no	—
794	C₂×D₄	—	2	2	no	—
795	C₂×D₄	—	2	2	no	—
796	C₂×D₄	—	2	1	no	—
797	C₂×D₄	—	2	1	no	—
798	C₂×D₄	—	2	2	no	—
799	C₂×D₄	—	2	1	no	—
800	C₂×D₄	—	2	2	no	—
801	C₂×D₄	—	4	2	no	—
802	C₂×D₄	—	4	2	no	—
803	C₂×D₄	—	4	8	no	—
804	C₂×D₄	—	4	4	no	—
805	C₂×D₄	—	4	8	no	—
806	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
807	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
808	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
809	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	complemented
810	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
811	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
812	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
813	C₂²×C₄	—	2	1	no	—
814	C₂²×C₄	—	2	4	no	—
815	C₂²×C₄	—	2	4	no	—
816	C₂²×C₄	—	2	1	no	—
817	C₂²×C₄	—	2	2	no	—
818	C₂²×C₄	—	2	2	no	—
819	C₂²×C₄	—	2	1	no	—
820	C₂²×C₄	—	2	2	no	—
821	C₂²×C₄	—	2	2	no	—
822	C₂²×C₄	—	2	2	no	—
823	C₂²×C₄	—	2	4	no	—
824	C₂²×C₄	—	2	4	no	—
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	—	2	2	no	—
827	C₂²×C₄	—	2	1	no	—
828	C₂²×C₄	—	4	8	no	—
829	C₂²×C₄	—	4	8	no	—
830	C₂²×C₄	—	4	4	no	—
831	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
832	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
833	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
834	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
835	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
836	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
837	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
838	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
839	Q₁₆	—	2	8	no	—
840	Q₁₆	—	2	8	no	—
841	Q₁₆	—	4	4	no	—
842	SD₁₆	—	2	8	no	—
843	SD₁₆	—	2	8	no	—
844	SD₁₆	—	2	8	no	—
845	SD₁₆	—	4	4	no	—
846	SD₁₆	C₂×D₄×C₆₇	1	8	yes	complemented
847	D₈	—	2	8	no	—
848	D₈	C₂×D₄×C₆₇	1	8	yes	complemented
849	M₁₆	—	2	4	no	—
850	M₁₆	—	2	2	no	—
851	M₁₆	—	2	8	no	—
852	M₁₆	C₂×D₄×C₆₇	1	4	yes	complemented
853	C₂×C₈	—	2	8	no	—
854	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
855	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
856	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	4	no	—
860	C₄⋊C₄	—	2	4	no	—
861	C₄⋊C₄	—	2	1	no	—
862	C₄⋊C₄	—	2	2	no	—
863	C₄⋊C₄	—	2	2	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	1	no	—
866	C₄⋊C₄	—	2	1	no	—
867	C₄⋊C₄	—	2	1	no	—
868	C₄⋊C₄	—	2	1	no	—
869	C₄⋊C₄	—	2	2	no	—
870	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
871	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
872	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
873	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
874	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
875	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	4	no	—
878	C₂²⋊C₄	—	2	4	no	—
879	C₂²⋊C₄	—	2	1	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	1	no	—
886	C₂²⋊C₄	—	2	1	no	—
887	C₂²⋊C₄	—	2	2	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
890	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
891	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
892	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
893	C₄²	—	2	1	no	—
894	C₄²	—	2	1	no	—
895	C₄²	—	2	1	no	—
896	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
897	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
898	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
899	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
900	C₂³	—	2	4	no	—
901	C₂³	—	2	2	no	—
902	C₂³	—	2	1	no	—
903	C₂³	—	2	4	no	—
904	C₂³	—	2	2	no	—
905	C₂³	—	4	2	no	—
906	C₂³	—	4	2	no	—
907	C₂³	—	4	4	no	—
908	C₂³	—	4	2	no	—
909	C₂³	—	4	2	no	—
910	C₂³	—	4	4	no	—
911	C₂³	—	8	2	no	—
912	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
913	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
914	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
915	Q₈	—	2	1	no	—
916	Q₈	—	2	2	no	—
917	Q₈	—	2	4	no	—
918	Q₈	—	2	4	no	—
919	Q₈	—	2	2	no	—
920	Q₈	—	4	4	no	—
921	Q₈	—	4	4	no	—
922	Q₈	C₂²×D₄×C₆₇	1	2	yes	—
923	D₄	—	2	4	no	—
924	D₄	—	2	4	no	—
925	D₄	—	2	2	no	—
926	D₄	—	2	2	no	—
927	D₄	—	2	2	no	—
928	D₄	—	2	2	no	—
929	D₄	—	2	1	no	—
930	D₄	—	2	2	no	—
931	D₄	—	4	2	no	—
932	D₄	—	4	4	no	—
933	D₄	—	4	4	no	—
934	D₄	—	4	8	no	—
935	D₄	—	4	4	no	—
936	D₄	—	4	8	no	—
937	D₄	—	4	4	no	—
938	D₄	—	4	4	no	—
939	D₄	—	4	2	no	—
940	D₄	—	8	1	no	—
941	D₄	—	8	2	no	—
942	D₄	C₂²×D₄×C₆₇	1	4	yes	—
943	D₄	C₂²×D₄×C₆₇	1	2	yes	—
944	C₂×C₄	—	2	4	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	4	no	—
947	C₂×C₄	—	2	4	no	—
948	C₂×C₄	—	2	4	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	4	no	—
959	C₂×C₄	—	4	1	no	—
960	C₂×C₄	—	4	4	no	—
961	C₂×C₄	—	4	4	no	—
962	C₂×C₄	—	4	4	no	—
963	C₂×C₄	—	4	8	no	—
964	C₂×C₄	—	4	8	no	—
965	C₂×C₄	—	4	4	no	—
966	C₂×C₄	—	4	2	no	—
967	C₂×C₄	—	4	4	no	—
968	C₂×C₄	—	4	4	no	—
969	C₂×C₄	—	4	4	no	—
970	C₂×C₄	—	4	2	no	—
971	C₂×C₄	—	8	1	no	—
972	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
973	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
974	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
975	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
976	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
977	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
978	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
979	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
980	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
981	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
982	C₈	—	2	4	no	—
983	C₈	—	2	2	no	—
984	C₈	C₂²×D₄×C₆₇	1	4	yes	—
985	C₂²	—	2	1	no	—
986	C₂²	—	2	1	no	—
987	C₂²	—	2	2	no	—
988	C₂²	—	2	2	no	—
989	C₂²	—	2	2	no	—
990	C₂²	—	2	2	no	—
991	C₂²	—	2	2	no	—
992	C₂²	—	2	2	no	—
993	C₂²	—	2	2	no	—
994	C₂²	—	2	4	no	—
995	C₂²	—	4	8	no	—
996	C₂²	—	4	2	no	—
997	C₂²	—	4	1	no	—
998	C₂²	—	4	1	no	—
999	C₂²	—	4	2	no	—
1000	C₂²	—	4	2	no	—
1001	C₂²	—	4	2	no	—
1002	C₂²	—	4	2	no	—
1003	C₂²	—	8	4	no	—
1004	C₂²	—	8	8	no	—
1005	C₂²	D₄²×C₆₇	1	2	yes	—
1006	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1007	C₄	—	2	1	no	—
1008	C₄	—	2	1	no	—
1009	C₄	—	2	1	no	—
1010	C₄	—	2	2	no	—
1011	C₄	—	2	2	no	—
1012	C₄	—	2	2	no	—
1013	C₄	—	4	2	no	—
1014	C₄	—	4	1	no	—
1015	C₄	—	4	1	no	—
1016	C₄	—	4	2	no	—
1017	C₄	—	4	4	no	—
1018	C₄	D₄²×C₆₇	1	2	yes	—
1019	C₄	#575×C₆₇	1	2	yes	complemented
1020	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
1021	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1022	C₂	—	2	2	no	—
1023	C₂	—	4	2	no	—
1024	C₂	—	4	2	no	—
1025	C₂	—	4	4	no	—
1026	C₂	—	4	2	no	—
1027	C₂	—	8	2	no	—
1028	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
1029	C₂	C₂×#575×C₆₇	1	1	yes	characteristic
1030	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 ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#575×C₆₇	C₂	semidirect
2. D₄×#41×C₆₇	C₂	semidirect
3. C₂×#547×C₆₇	C₂	semidirect
4. C₆₇×#3284	C₂	semidirect
5. C₆₇×#3283	C₂	semidirect
6. C₆₇×#3276	C₂	semidirect
7. C₆₇×#3272	C₂	semidirect
8. C₆₇×#3269	C₂	semidirect
9. C₆₇×#3267	C₂	semidirect
10. C₆₇×#3152	C₂	semidirect
11. C₆₇×#3056	C₂	semidirect
12. C₆₇×#3039	C₂	semidirect
13. C₆₇×#3036	C₂	semidirect
14. C₆₇×#3007	C₂	semidirect
15. C₆₇×#3005	C₂	semidirect
16. C₄×AGL(1,ℤ/8)×C₆₇	C₂	semidirect
17. D₄×M₁₆×C₆₇	C₂	semidirect
19. C₂²×#41×C₆₇	C₂²	semidirect
22. C₂×#137×C₆₇	C₂²	semidirect
23. C₂×#137×C₆₇	C₂²	semidirect
24. C₂×#137×C₆₇	C₂²	semidirect
26. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
27. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
28. C₂×#135×C₆₇	C₂²	semidirect
29. C₂×#135×C₆₇	C₂²	semidirect
30. C₂²×M₁₆×C₆₇	C₂²	semidirect
31. #550×C₆₇	C₂²	semidirect
32. D₄×Q₈×C₆₇	C₂²	semidirect
33. #548×C₆₇	C₂²	semidirect
39. #547×C₆₇	C₂²	semidirect
40. #547×C₆₇	C₂²	semidirect
41. #547×C₆₇	C₂²	semidirect
43. #546×C₆₇	C₂²	semidirect
45. D₄²×C₆₇	C₂²	semidirect
48. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
52. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
57. C₂×C₄×D₄×C₆₇	C₂²	semidirect
59. #497×C₆₇	C₂²	semidirect
60. #494×C₆₇	C₂²	semidirect
61. #492×C₆₇	C₂²	semidirect
62. #470×C₆₇	C₂²	semidirect
63. #468×C₆₇	C₂²	semidirect
64. #467×C₆₇	C₂²	semidirect
65. #465×C₆₇	C₂²	semidirect
66. #463×C₆₇	C₂²	semidirect
67. #462×C₆₇	C₂²	semidirect
68. #462×C₆₇	C₂²	semidirect
69. #461×C₆₇	C₂²	semidirect
70. #461×C₆₇	C₂²	semidirect
71. #461×C₆₇	C₂²	semidirect
72. #459×C₆₇	C₂²	semidirect
73. #452×C₆₇	C₂²	semidirect
74. #452×C₆₇	C₂²	semidirect
75. #452×C₆₇	C₂²	semidirect
76. #452×C₆₇	C₂²	semidirect
77. #451×C₆₇	C₂²	semidirect
78. #450×C₆₇	C₂²	semidirect
79. #449×C₆₇	C₂²	semidirect
80. #449×C₆₇	C₂²	semidirect
81. #442×C₆₇	C₂²	semidirect
82. #440×C₆₇	C₂²	semidirect
83. C₄×SD₁₆×C₆₇	C₂²	semidirect
84. C₄×D₈×C₆₇	C₂²	semidirect
85. #436×C₆₇	C₂²	semidirect
86. #435×C₆₇	C₂²	semidirect
87. C₈×D₄×C₆₇	C₂²	semidirect
88. #428×C₆₇	C₂²	semidirect
89. #423×C₆₇	C₂²	semidirect
90. #419×C₆₇	C₂²	semidirect
91. #418×C₆₇	C₂²	semidirect
93. #417×C₆₇	C₂²	semidirect
94. #407×C₆₇	C₂²	semidirect
95. C₄×M₁₆×C₆₇	C₂²	semidirect
128. AGL(1,ℤ/8)×C₆₇	D₄	semidirect
293. C₂×D₄×C₆₇	C₂×D₄	semidirect
330. SD₁₆×C₆₇	C₂×D₄	semidirect
332. D₈×C₆₇	C₂×D₄	semidirect
336. M₁₆×C₆₇	C₂×D₄	semidirect
503. C₄×C₆₇	#575	semidirect
506. #61067	C₆₇	direct (N × H)
516. C₂×#575	C₂×C₆₇	semidirect
517. D₄×#41	C₂×C₆₇	semidirect
518. C₂×#547	C₂×C₆₇	semidirect
519. #3284	C₂×C₆₇	semidirect
520. #3283	C₂×C₆₇	semidirect
521. #3276	C₂×C₆₇	semidirect
522. #3272	C₂×C₆₇	semidirect
523. #3269	C₂×C₆₇	semidirect
524. #3267	C₂×C₆₇	semidirect
525. #3152	C₂×C₆₇	semidirect
526. #3056	C₂×C₆₇	semidirect
527. #3039	C₂×C₆₇	semidirect
528. #3036	C₂×C₆₇	semidirect
529. #3007	C₂×C₆₇	semidirect
530. #3005	C₂×C₆₇	semidirect
531. C₄×AGL(1,ℤ/8)	C₂×C₆₇	semidirect
532. D₄×M₁₆	C₂×C₆₇	semidirect
533. C₆₇	#61067	direct (N × H)
535. C₂²×#41	C₂²×C₆₇	semidirect
538. C₂×#137	C₂²×C₆₇	semidirect
539. C₂×#137	C₂²×C₆₇	semidirect
540. C₂×#137	C₂²×C₆₇	semidirect
542. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
543. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
544. C₂×#135	C₂²×C₆₇	semidirect
545. C₂×#135	C₂²×C₆₇	semidirect
546. C₂²×M₁₆	C₂²×C₆₇	semidirect
547. #550	C₂²×C₆₇	semidirect
548. D₄×Q₈	C₂²×C₆₇	semidirect
549. #548	C₂²×C₆₇	semidirect
555. #547	C₂²×C₆₇	semidirect
556. #547	C₂²×C₆₇	semidirect
557. #547	C₂²×C₆₇	semidirect
559. #546	C₂²×C₆₇	semidirect
561. D₄²	C₂²×C₆₇	semidirect
564. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
568. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
573. C₂×C₄×D₄	C₂²×C₆₇	semidirect
575. #497	C₂²×C₆₇	semidirect
576. #494	C₂²×C₆₇	semidirect
577. #492	C₂²×C₆₇	semidirect
578. #470	C₂²×C₆₇	semidirect
579. #468	C₂²×C₆₇	semidirect
580. #467	C₂²×C₆₇	semidirect
581. #465	C₂²×C₆₇	semidirect
582. #463	C₂²×C₆₇	semidirect
583. #462	C₂²×C₆₇	semidirect
584. #462	C₂²×C₆₇	semidirect
585. #461	C₂²×C₆₇	semidirect
586. #461	C₂²×C₆₇	semidirect
587. #461	C₂²×C₆₇	semidirect
588. #459	C₂²×C₆₇	semidirect
589. #452	C₂²×C₆₇	semidirect
590. #452	C₂²×C₆₇	semidirect
591. #452	C₂²×C₆₇	semidirect
592. #452	C₂²×C₆₇	semidirect
593. #451	C₂²×C₆₇	semidirect
594. #450	C₂²×C₆₇	semidirect
595. #449	C₂²×C₆₇	semidirect
596. #449	C₂²×C₆₇	semidirect
597. #442	C₂²×C₆₇	semidirect
598. #440	C₂²×C₆₇	semidirect
599. C₄×SD₁₆	C₂²×C₆₇	semidirect
600. C₄×D₈	C₂²×C₆₇	semidirect
601. #436	C₂²×C₆₇	semidirect
602. #435	C₂²×C₆₇	semidirect
603. C₈×D₄	C₂²×C₆₇	semidirect
604. #428	C₂²×C₆₇	semidirect
605. #423	C₂²×C₆₇	semidirect
606. #419	C₂²×C₆₇	semidirect
607. #418	C₂²×C₆₇	semidirect
609. #417	C₂²×C₆₇	semidirect
610. #407	C₂²×C₆₇	semidirect
611. C₄×M₁₆	C₂²×C₆₇	semidirect
644. AGL(1,ℤ/8)	D₄×C₆₇	semidirect
809. C₂×D₄	C₂×D₄×C₆₇	semidirect
846. SD₁₆	C₂×D₄×C₆₇	semidirect
848. D₈	C₂×D₄×C₆₇	semidirect
852. M₁₆	C₂×D₄×C₆₇	semidirect
1019. C₄	#575×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#575×C₆₇	2
D₄×#41×C₆₇	2
C₂×#547×C₆₇	2
C₆₇×#3284	2
C₆₇×#3283	2
C₆₇×#3276	2
C₆₇×#3272	2
C₆₇×#3269	2
C₆₇×#3267	2
C₆₇×#3152	2
C₆₇×#3056	2
C₆₇×#3039	2
C₆₇×#3036	2
C₆₇×#3007	2
C₆₇×#3005	2
C₄×AGL(1,ℤ/8)×C₆₇	2
D₄×M₁₆×C₆₇	2
#61067	67

Subgroups — C67×#61067 #30740318

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61067 #30740318