Subgroups — D₄×AGL(1,ℤ/8)×C₆₇ #30740316

Order 17152.

3230 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×AGL(1,ℤ/8)×C₆₇	C₂	1	2	yes	maximal, complemented
2	D₄×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄²×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×SD₁₆×C₆₇	C₂	1	2	yes	maximal, complemented
5	D₄×D₈×C₆₇	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3274	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3272	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3265	C₂	1	4	yes	maximal, complemented
9	C₆₇×#3264	C₂	1	4	yes	maximal, complemented
10	C₆₇×#3151	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3055	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3038	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3036	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3006	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3003	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	complemented
19	C₂³×D₄×C₆₇	—	2	1	no	—
20	C₂³×D₄×C₆₇	C₂²	1	2	yes	complemented
21	C₂×AGL(1,ℤ/8)×C₆₇	—	2	16	no	—
22	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
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×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
26	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
27	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	complemented
28	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	complemented
29	C₂²×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
30	C₂²×D₈×C₆₇	C₂²	1	4	yes	complemented
31	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	complemented
32	#550×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
34	#548×C₆₇	C₂²	1	2	yes	complemented
35	#547×C₆₇	—	2	1	no	—
36	#547×C₆₇	C₂²	1	1	yes	characteristic, complemented
37	#546×C₆₇	—	2	2	no	—
38	#546×C₆₇	C₂²	1	2	yes	complemented
39	D₄²×C₆₇	—	2	1	no	—
40	D₄²×C₆₇	—	2	1	no	—
41	D₄²×C₆₇	—	2	2	no	—
42	D₄²×C₆₇	—	2	1	no	—
43	D₄²×C₆₇	C₂²	1	2	yes	—
44	D₄²×C₆₇	C₂²	1	4	yes	complemented
45	D₄²×C₆₇	C₂²	1	2	yes	complemented
46	D₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
47	#532×C₆₇	—	2	1	no	—
48	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	#525×C₆₇	—	2	2	no	—
51	#525×C₆₇	C₂²	1	2	yes	complemented
52	C₂×#121×C₆₇	—	2	1	no	—
53	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
54	C₂×#120×C₆₇	—	2	2	no	—
55	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄×D₄×C₆₇	—	2	1	no	—
57	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
59	#496×C₆₇	C₂²	1	4	yes	complemented
60	#493×C₆₇	C₂²	1	2	yes	complemented
61	#492×C₆₇	C₂²	1	2	yes	complemented
62	#469×C₆₇	C₂²	1	4	yes	complemented
63	#468×C₆₇	C₂²	1	4	yes	complemented
64	#466×C₆₇	C₂²	1	4	yes	complemented
65	#465×C₆₇	C₂²	1	4	yes	complemented
66	#463×C₆₇	C₂²	1	4	yes	complemented
67	#461×C₆₇	C₂²	1	2	yes	complemented
68	#460×C₆₇	C₂²	1	2	yes	complemented
69	#460×C₆₇	C₂²	1	2	yes	complemented
70	#459×C₆₇	C₂²	1	2	yes	complemented
71	#459×C₆₇	C₂²	1	2	yes	complemented
72	#459×C₆₇	C₂²	1	2	yes	complemented
73	#450×C₆₇	C₂²	1	4	yes	complemented
74	#450×C₆₇	C₂²	1	4	yes	complemented
75	#449×C₆₇	C₂²	1	4	yes	complemented
76	#449×C₆₇	C₂²	1	4	yes	complemented
77	#448×C₆₇	C₂²	1	4	yes	complemented
78	#447×C₆₇	C₂²	1	4	yes	complemented
79	#447×C₆₇	C₂²	1	4	yes	complemented
80	#447×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	#418×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	#418×C₆₇	C₂²	1	2	yes	complemented
92	#417×C₆₇	C₂²	1	2	yes	complemented
93	#417×C₆₇	C₂²	1	1	yes	characteristic, complemented
94	#407×C₆₇	C₂²	1	2	yes	complemented
95	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
96	C₂⁵×C₆₇	—	2	2	no	—
97	C₂×#41×C₆₇	—	2	2	no	—
98	C₂×#41×C₆₇	—	2	2	no	—
99	C₂×#41×C₆₇	—	2	8	no	—
100	C₂×#41×C₆₇	—	4	4	no	—
101	C₂×#41×C₆₇	C₂³	1	2	yes	—
102	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
103	C₂×#41×C₆₇	C₂³	1	2	yes	complemented
104	C₂×#41×C₆₇	C₂³	1	2	yes	complemented
105	C₂²×Q₈×C₆₇	C₂³	1	2	yes	complemented
106	C₂²×D₄×C₆₇	—	2	8	no	—
107	C₂²×D₄×C₆₇	—	2	2	no	—
108	C₂²×D₄×C₆₇	—	2	2	no	—
109	C₂²×D₄×C₆₇	—	2	1	no	—
110	C₂²×D₄×C₆₇	—	2	2	no	—
111	C₂²×D₄×C₆₇	—	2	4	no	—
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	—	2	2	no	—
116	C₂²×D₄×C₆₇	—	2	2	no	—
117	C₂²×D₄×C₆₇	—	2	1	no	—
118	C₂²×D₄×C₆₇	—	4	4	no	—
119	C₂²×D₄×C₆₇	—	4	8	no	—
120	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
121	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
122	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
123	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
124	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₆₇	C₂³	1	2	yes	complemented
126	C₂³×C₄×C₆₇	—	2	2	no	—
127	C₂³×C₄×C₆₇	—	2	1	no	—
128	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
129	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
130	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
131	AGL(1,ℤ/8)×C₆₇	—	2	16	no	—
132	AGL(1,ℤ/8)×C₆₇	—	2	16	no	—
133	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
134	AGL(1,ℤ/8)×C₆₇	—	4	4	no	—
135	AGL(1,ℤ/8)×C₆₇	D₄	1	8	yes	direct product factor
136	C₂×SD₁₆×C₆₇	—	2	16	no	—
137	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
138	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
139	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	complemented
140	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	complemented
141	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	complemented
142	C₂×D₈×C₆₇	—	2	16	no	—
143	C₂×D₈×C₆₇	C₂³	1	4	yes	—
144	C₂×D₈×C₆₇	C₂³	1	2	yes	—
145	C₂×D₈×C₆₇	C₂³	1	4	yes	complemented
146	C₂×D₈×C₆₇	C₂³	1	4	yes	complemented
147	C₂×D₈×C₆₇	C₂³	1	4	yes	complemented
148	C₂×M₁₆×C₆₇	—	2	8	no	—
149	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
150	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
151	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
152	C₂×M₁₆×C₆₇	C₂³	1	4	yes	complemented
153	C₂²×C₈×C₆₇	C₂³	1	4	yes	complemented
154	C₄⋊Q₈×C₆₇	—	2	1	no	—
155	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
156	#127×C₆₇	—	2	1	no	—
157	#127×C₆₇	—	2	1	no	—
158	#127×C₆₇	—	2	1	no	—
159	#127×C₆₇	C₂³	1	2	yes	—
160	#127×C₆₇	C₂³	1	2	yes	—
161	#127×C₆₇	C₂³	1	1	yes	characteristic, complemented
162	#124×C₆₇	—	2	2	no	—
163	#124×C₆₇	C₂³	1	2	yes	complemented
164	#123×C₆₇	—	2	2	no	—
165	#123×C₆₇	—	2	2	no	—
166	#123×C₆₇	—	2	2	no	—
167	C₂²⋊Q₈×C₆₇	—	2	2	no	—
168	C₂²⋊Q₈×C₆₇	—	2	2	no	—
169	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	complemented
170	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	complemented
171	#121×C₆₇	—	2	2	no	—
172	#121×C₆₇	—	2	1	no	—
173	#121×C₆₇	—	2	2	no	—
174	#121×C₆₇	—	2	2	no	—
175	#121×C₆₇	—	2	1	no	—
176	#121×C₆₇	—	2	1	no	—
177	#121×C₆₇	—	2	2	no	—
178	#121×C₆₇	—	2	2	no	—
179	#121×C₆₇	—	2	4	no	—
180	#121×C₆₇	—	2	1	no	—
181	#121×C₆₇	—	2	2	no	—
182	#121×C₆₇	—	2	2	no	—
183	#121×C₆₇	C₂³	1	4	yes	—
184	#121×C₆₇	C₂³	1	4	yes	—
185	#121×C₆₇	C₂³	1	2	yes	complemented
186	#121×C₆₇	C₂³	1	2	yes	complemented
187	#120×C₆₇	—	2	2	no	—
188	#120×C₆₇	—	2	2	no	—
189	#120×C₆₇	—	2	4	no	—
190	#120×C₆₇	—	2	4	no	—
191	#120×C₆₇	—	2	4	no	—
192	#120×C₆₇	—	2	4	no	—
193	#120×C₆₇	—	2	2	no	—
194	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
195	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
196	C₄×D₄×C₆₇	—	2	1	no	—
197	C₄×D₄×C₆₇	—	2	2	no	—
198	C₄×D₄×C₆₇	—	2	1	no	—
199	C₄×D₄×C₆₇	—	2	1	no	—
200	C₄×D₄×C₆₇	—	2	2	no	—
201	C₄×D₄×C₆₇	—	2	1	no	—
202	C₄×D₄×C₆₇	—	2	2	no	—
203	C₄×D₄×C₆₇	—	2	1	no	—
204	C₄×D₄×C₆₇	—	2	1	no	—
205	C₄×D₄×C₆₇	—	2	1	no	—
206	C₄×D₄×C₆₇	—	2	1	no	—
207	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
208	C₄×D₄×C₆₇	D₄	1	2	yes	—
209	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
210	C₄×D₄×C₆₇	C₂³	1	2	yes	—
211	C₄×D₄×C₆₇	C₂³	1	2	yes	—
212	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
213	C₄×D₄×C₆₇	C₂³	1	2	yes	—
214	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
215	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic, complemented
216	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic, complemented
217	#117×C₆₇	—	2	1	no	—
218	#117×C₆₇	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
220	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
221	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
222	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
223	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
224	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
225	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
226	C₂×C₄²×C₆₇	—	2	1	no	—
227	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
228	#107×C₆₇	C₂³	1	2	yes	complemented
229	#106×C₆₇	C₂³	1	2	yes	complemented
230	C₄⋊C₈×C₆₇	C₂³	1	2	yes	complemented
231	C₄⋊C₈×C₆₇	C₂³	1	2	yes	complemented
232	#103×C₆₇	C₂³	1	2	yes	complemented
233	#103×C₆₇	C₂³	1	4	yes	complemented
234	#102×C₆₇	C₂³	1	2	yes	—
235	#102×C₆₇	C₂³	1	2	yes	—
236	#102×C₆₇	C₂³	1	2	yes	complemented
237	#102×C₆₇	C₂³	1	4	yes	complemented
238	#102×C₆₇	C₂³	1	4	yes	complemented
239	#102×C₆₇	C₂³	1	4	yes	complemented
240	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	complemented
241	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	complemented
242	#97×C₆₇	C₂³	1	2	yes	complemented
243	C₄×C₈×C₆₇	C₂³	1	2	yes	complemented
244	C₂⁴×C₆₇	—	2	1	no	—
245	C₂⁴×C₆₇	—	2	2	no	—
246	C₂⁴×C₆₇	—	2	2	no	—
247	C₂⁴×C₆₇	—	2	4	no	—
248	C₂⁴×C₆₇	—	2	4	no	—
249	C₂⁴×C₆₇	—	4	8	no	—
250	C₂⁴×C₆₇	—	4	8	no	—
251	C₂⁴×C₆₇	—	8	4	no	—
252	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
253	#41×C₆₇	—	2	2	no	—
254	#41×C₆₇	—	2	4	no	—
255	#41×C₆₇	—	2	4	no	—
256	#41×C₆₇	—	2	4	no	—
257	#41×C₆₇	—	2	4	no	—
258	#41×C₆₇	—	4	8	no	—
259	#41×C₆₇	—	4	2	no	—
260	#41×C₆₇	—	4	2	no	—
261	#41×C₆₇	—	4	8	no	—
262	#41×C₆₇	C₂×D₄	1	4	yes	complemented
263	C₂×Q₈×C₆₇	—	2	2	no	—
264	C₂×Q₈×C₆₇	—	2	4	no	—
265	C₂×Q₈×C₆₇	—	4	2	no	—
266	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
267	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
268	C₂×D₄×C₆₇	—	2	1	no	—
269	C₂×D₄×C₆₇	—	2	4	no	—
270	C₂×D₄×C₆₇	—	2	8	no	—
271	C₂×D₄×C₆₇	—	2	8	no	—
272	C₂×D₄×C₆₇	—	2	4	no	—
273	C₂×D₄×C₆₇	—	2	2	no	—
274	C₂×D₄×C₆₇	—	2	4	no	—
275	C₂×D₄×C₆₇	—	2	4	no	—
276	C₂×D₄×C₆₇	—	2	2	no	—
277	C₂×D₄×C₆₇	—	2	2	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	4	no	—
282	C₂×D₄×C₆₇	—	2	1	no	—
283	C₂×D₄×C₆₇	—	2	4	no	—
284	C₂×D₄×C₆₇	—	2	4	no	—
285	C₂×D₄×C₆₇	—	2	2	no	—
286	C₂×D₄×C₆₇	—	2	2	no	—
287	C₂×D₄×C₆₇	—	2	2	no	—
288	C₂×D₄×C₆₇	—	2	2	no	—
289	C₂×D₄×C₆₇	—	2	1	no	—
290	C₂×D₄×C₆₇	—	2	2	no	—
291	C₂×D₄×C₆₇	—	2	2	no	—
292	C₂×D₄×C₆₇	—	2	2	no	—
293	C₂×D₄×C₆₇	—	2	4	no	—
294	C₂×D₄×C₆₇	—	4	4	no	—
295	C₂×D₄×C₆₇	—	4	4	no	—
296	C₂×D₄×C₆₇	—	4	2	no	—
297	C₂×D₄×C₆₇	—	4	8	no	—
298	C₂×D₄×C₆₇	—	4	8	no	—
299	C₂×D₄×C₆₇	—	4	8	no	—
300	C₂×D₄×C₆₇	—	4	4	no	—
301	C₂×D₄×C₆₇	—	4	8	no	—
302	C₂×D₄×C₆₇	—	4	16	no	—
303	C₂×D₄×C₆₇	—	4	8	no	—
304	C₂×D₄×C₆₇	—	4	8	no	—
305	C₂×D₄×C₆₇	—	4	4	no	—
306	C₂×D₄×C₆₇	—	4	8	no	—
307	C₂×D₄×C₆₇	—	8	2	no	—
308	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
309	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
310	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
311	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	complemented
312	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
313	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
314	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
315	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₆₇	—	2	1	no	—
317	C₂²×C₄×C₆₇	—	2	4	no	—
318	C₂²×C₄×C₆₇	—	2	4	no	—
319	C₂²×C₄×C₆₇	—	2	1	no	—
320	C₂²×C₄×C₆₇	—	2	2	no	—
321	C₂²×C₄×C₆₇	—	2	1	no	—
322	C₂²×C₄×C₆₇	—	2	2	no	—
323	C₂²×C₄×C₆₇	—	2	2	no	—
324	C₂²×C₄×C₆₇	—	2	2	no	—
325	C₂²×C₄×C₆₇	—	2	2	no	—
326	C₂²×C₄×C₆₇	—	2	2	no	—
327	C₂²×C₄×C₆₇	—	2	1	no	—
328	C₂²×C₄×C₆₇	—	4	8	no	—
329	C₂²×C₄×C₆₇	—	4	4	no	—
330	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
331	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
332	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
333	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
334	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
335	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
336	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
337	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
338	SD₁₆×C₆₇	—	2	8	no	—
339	SD₁₆×C₆₇	—	2	8	no	—
340	SD₁₆×C₆₇	—	2	8	no	—
341	SD₁₆×C₆₇	—	4	4	no	—
342	SD₁₆×C₆₇	C₂×D₄	1	8	yes	complemented
343	D₈×C₆₇	—	2	8	no	—
344	D₈×C₆₇	—	2	8	no	—
345	D₈×C₆₇	—	2	8	no	—
346	D₈×C₆₇	—	4	4	no	—
347	D₈×C₆₇	C₂×D₄	1	8	yes	complemented
348	M₁₆×C₆₇	—	2	4	no	—
349	M₁₆×C₆₇	—	2	2	no	—
350	M₁₆×C₆₇	—	2	8	no	—
351	M₁₆×C₆₇	C₂×D₄	1	4	yes	complemented
352	C₂×C₈×C₆₇	—	2	8	no	—
353	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
354	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
355	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
356	C₄⋊C₄×C₆₇	—	2	1	no	—
357	C₄⋊C₄×C₆₇	—	2	2	no	—
358	C₄⋊C₄×C₆₇	—	2	1	no	—
359	C₄⋊C₄×C₆₇	—	2	1	no	—
360	C₄⋊C₄×C₆₇	—	2	1	no	—
361	C₄⋊C₄×C₆₇	—	2	1	no	—
362	C₄⋊C₄×C₆₇	—	2	2	no	—
363	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
364	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
365	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
366	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
367	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
368	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
369	C₂²⋊C₄×C₆₇	—	2	2	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	—	2	2	no	—
374	C₂²⋊C₄×C₆₇	—	2	2	no	—
375	C₂²⋊C₄×C₆₇	—	2	2	no	—
376	C₂²⋊C₄×C₆₇	—	2	4	no	—
377	C₂²⋊C₄×C₆₇	—	2	4	no	—
378	C₂²⋊C₄×C₆₇	—	2	1	no	—
379	C₂²⋊C₄×C₆₇	—	2	1	no	—
380	C₂²⋊C₄×C₆₇	—	2	2	no	—
381	C₂²⋊C₄×C₆₇	—	2	2	no	—
382	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
383	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
384	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
385	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
386	C₄²×C₆₇	—	2	1	no	—
387	C₄²×C₆₇	—	2	1	no	—
388	C₄²×C₆₇	—	2	1	no	—
389	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
390	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
391	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
392	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
393	C₂³×C₆₇	—	2	4	no	—
394	C₂³×C₆₇	—	2	4	no	—
395	C₂³×C₆₇	—	2	4	no	—
396	C₂³×C₆₇	—	2	1	no	—
397	C₂³×C₆₇	—	2	2	no	—
398	C₂³×C₆₇	—	2	2	no	—
399	C₂³×C₆₇	—	2	4	no	—
400	C₂³×C₆₇	—	4	2	no	—
401	C₂³×C₆₇	—	4	4	no	—
402	C₂³×C₆₇	—	4	8	no	—
403	C₂³×C₆₇	—	4	8	no	—
404	C₂³×C₆₇	—	4	2	no	—
405	C₂³×C₆₇	—	4	2	no	—
406	C₂³×C₆₇	—	4	4	no	—
407	C₂³×C₆₇	—	4	8	no	—
408	C₂³×C₆₇	—	4	4	no	—
409	C₂³×C₆₇	—	4	4	no	—
410	C₂³×C₆₇	—	4	8	no	—
411	C₂³×C₆₇	—	4	4	no	—
412	C₂³×C₆₇	—	8	2	no	—
413	C₂³×C₆₇	—	8	4	no	—
414	C₂³×C₆₇	—	8	4	no	—
415	C₂³×C₆₇	—	8	32	no	—
416	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
417	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
418	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
419	Q₈×C₆₇	—	2	1	no	—
420	Q₈×C₆₇	—	2	2	no	—
421	Q₈×C₆₇	—	2	2	no	—
422	Q₈×C₆₇	—	4	4	no	—
423	Q₈×C₆₇	C₂²×D₄	1	2	yes	complemented
424	D₄×C₆₇	—	2	4	no	—
425	D₄×C₆₇	—	2	4	no	—
426	D₄×C₆₇	—	2	4	no	—
427	D₄×C₆₇	—	2	2	no	—
428	D₄×C₆₇	—	2	2	no	—
429	D₄×C₆₇	—	2	4	no	—
430	D₄×C₆₇	—	2	2	no	—
431	D₄×C₆₇	—	2	1	no	—
432	D₄×C₆₇	—	2	2	no	—
433	D₄×C₆₇	—	2	4	no	—
434	D₄×C₆₇	—	4	8	no	—
435	D₄×C₆₇	—	4	8	no	—
436	D₄×C₆₇	—	4	4	no	—
437	D₄×C₆₇	—	4	4	no	—
438	D₄×C₆₇	—	4	4	no	—
439	D₄×C₆₇	—	4	4	no	—
440	D₄×C₆₇	—	4	8	no	—
441	D₄×C₆₇	—	4	4	no	—
442	D₄×C₆₇	—	4	4	no	—
443	D₄×C₆₇	—	4	8	no	—
444	D₄×C₆₇	—	4	4	no	—
445	D₄×C₆₇	—	4	2	no	—
446	D₄×C₆₇	—	4	4	no	—
447	D₄×C₆₇	—	8	1	no	—
448	D₄×C₆₇	—	8	2	no	—
449	D₄×C₆₇	—	8	2	no	—
450	D₄×C₆₇	—	8	2	no	—
451	D₄×C₆₇	AGL(1,ℤ/8)	1	4	yes	direct product factor
452	D₄×C₆₇	C₂²×D₄	1	4	yes	—
453	D₄×C₆₇	C₂²×D₄	1	2	yes	complemented
454	C₂×C₄×C₆₇	—	2	4	no	—
455	C₂×C₄×C₆₇	—	2	1	no	—
456	C₂×C₄×C₆₇	—	2	4	no	—
457	C₂×C₄×C₆₇	—	2	4	no	—
458	C₂×C₄×C₆₇	—	2	4	no	—
459	C₂×C₄×C₆₇	—	2	2	no	—
460	C₂×C₄×C₆₇	—	2	2	no	—
461	C₂×C₄×C₆₇	—	2	2	no	—
462	C₂×C₄×C₆₇	—	2	2	no	—
463	C₂×C₄×C₆₇	—	2	2	no	—
464	C₂×C₄×C₆₇	—	2	1	no	—
465	C₂×C₄×C₆₇	—	2	1	no	—
466	C₂×C₄×C₆₇	—	2	2	no	—
467	C₂×C₄×C₆₇	—	2	2	no	—
468	C₂×C₄×C₆₇	—	4	1	no	—
469	C₂×C₄×C₆₇	—	4	4	no	—
470	C₂×C₄×C₆₇	—	4	4	no	—
471	C₂×C₄×C₆₇	—	4	4	no	—
472	C₂×C₄×C₆₇	—	4	4	no	—
473	C₂×C₄×C₆₇	—	4	2	no	—
474	C₂×C₄×C₆₇	—	4	4	no	—
475	C₂×C₄×C₆₇	—	4	4	no	—
476	C₂×C₄×C₆₇	—	4	2	no	—
477	C₂×C₄×C₆₇	—	8	1	no	—
478	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
480	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
481	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
482	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
483	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
485	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
487	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
488	C₈×C₆₇	—	2	4	no	—
489	C₈×C₆₇	—	2	2	no	—
490	C₈×C₆₇	C₂²×D₄	1	4	yes	complemented
491	C₂²×C₆₇	—	2	1	no	—
492	C₂²×C₆₇	—	2	2	no	—
493	C₂²×C₆₇	—	2	2	no	—
494	C₂²×C₆₇	—	2	1	no	—
495	C₂²×C₆₇	—	2	2	no	—
496	C₂²×C₆₇	—	2	2	no	—
497	C₂²×C₆₇	—	2	2	no	—
498	C₂²×C₆₇	—	2	4	no	—
499	C₂²×C₆₇	—	2	2	no	—
500	C₂²×C₆₇	—	4	8	no	—
501	C₂²×C₆₇	—	4	8	no	—
502	C₂²×C₆₇	—	4	1	no	—
503	C₂²×C₆₇	—	4	2	no	—
504	C₂²×C₆₇	—	4	2	no	—
505	C₂²×C₆₇	—	4	1	no	—
506	C₂²×C₆₇	—	4	4	no	—
507	C₂²×C₆₇	—	4	2	no	—
508	C₂²×C₆₇	—	4	2	no	—
509	C₂²×C₆₇	—	4	4	no	—
510	C₂²×C₆₇	—	4	4	no	—
511	C₂²×C₆₇	—	4	2	no	—
512	C₂²×C₆₇	—	8	8	no	—
513	C₂²×C₆₇	—	8	16	no	—
514	C₂²×C₆₇	—	8	8	no	—
515	C₂²×C₆₇	—	8	16	no	—
516	C₂²×C₆₇	D₄²	1	2	yes	—
517	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	4	yes	complemented
518	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
519	C₄×C₆₇	—	2	1	no	—
520	C₄×C₆₇	—	2	1	no	—
521	C₄×C₆₇	—	2	2	no	—
522	C₄×C₆₇	—	2	2	no	—
523	C₄×C₆₇	—	2	2	no	—
524	C₄×C₆₇	—	2	1	no	—
525	C₄×C₆₇	—	4	1	no	—
526	C₄×C₆₇	—	4	2	no	—
527	C₄×C₆₇	—	4	2	no	—
528	C₄×C₆₇	—	4	1	no	—
529	C₄×C₆₇	D₄²	1	2	yes	—
530	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	2	yes	complemented
531	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
532	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
533	D₄×AGL(1,ℤ/8)	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
534	C₂×C₆₇	—	2	2	no	—
535	C₂×C₆₇	—	2	4	no	—
536	C₂×C₆₇	—	4	2	no	—
537	C₂×C₆₇	—	4	4	no	—
538	C₂×C₆₇	—	4	2	no	—
539	C₂×C₆₇	—	8	2	no	—
540	C₂×C₆₇	—	8	4	no	—
541	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
542	C₂×C₆₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
543	C₂×C₆₇	#3585	1	1	yes	characteristic
544	C₂²×AGL(1,ℤ/8)	C₂×C₆₇	1	2	yes	complemented
545	D₄×#41	C₂×C₆₇	1	1	yes	characteristic, complemented
546	C₂×D₄²	C₂×C₆₇	1	1	yes	characteristic, complemented
547	D₄×SD₁₆	C₂×C₆₇	1	2	yes	complemented
548	D₄×D₈	C₂×C₆₇	1	2	yes	complemented
549	#3274	C₂×C₆₇	1	2	yes	complemented
550	#3272	C₂×C₆₇	1	2	yes	complemented
551	#3265	C₂×C₆₇	1	4	yes	complemented
552	#3264	C₂×C₆₇	1	4	yes	complemented
553	#3151	C₂×C₆₇	1	1	yes	characteristic, complemented
554	#3055	C₂×C₆₇	1	2	yes	complemented
555	#3038	C₂×C₆₇	1	1	yes	characteristic, complemented
556	#3036	C₂×C₆₇	1	1	yes	characteristic, complemented
557	#3006	C₂×C₆₇	1	2	yes	complemented
558	#3003	C₂×C₆₇	1	2	yes	complemented
559	C₄×AGL(1,ℤ/8)	C₂×C₆₇	1	1	yes	characteristic, complemented
560	D₄×M₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
561	C₆₇	D₄×AGL(1,ℤ/8)	1	1	yes	characteristic, direct product factor, Sylow
562	C₂²×#41	C₂²×C₆₇	1	2	yes	complemented
563	C₂³×D₄	—	2	1	no	—
564	C₂³×D₄	C₂²×C₆₇	1	2	yes	complemented
565	C₂×AGL(1,ℤ/8)	—	2	16	no	—
566	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
567	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
568	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
569	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
570	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
571	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
572	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
573	C₂²×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
574	C₂²×D₈	C₂²×C₆₇	1	4	yes	complemented
575	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	complemented
576	#550	C₂²×C₆₇	1	1	yes	characteristic, complemented
577	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
578	#548	C₂²×C₆₇	1	2	yes	complemented
579	#547	—	2	1	no	—
580	#547	C₂²×C₆₇	1	1	yes	characteristic, complemented
581	#546	—	2	2	no	—
582	#546	C₂²×C₆₇	1	2	yes	complemented
583	D₄²	—	2	1	no	—
584	D₄²	—	2	1	no	—
585	D₄²	—	2	2	no	—
586	D₄²	—	2	1	no	—
587	D₄²	C₂²×C₆₇	1	2	yes	—
588	D₄²	C₂²×C₆₇	1	4	yes	complemented
589	D₄²	C₂²×C₆₇	1	2	yes	complemented
590	D₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
591	#532	—	2	1	no	—
592	#532	C₂²×C₆₇	1	1	yes	characteristic, complemented
593	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic, complemented
594	#525	—	2	2	no	—
595	#525	C₂²×C₆₇	1	2	yes	complemented
596	C₂×#121	—	2	1	no	—
597	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
598	C₂×#120	—	2	2	no	—
599	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
600	C₂×C₄×D₄	—	2	1	no	—
601	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
602	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
603	#496	C₂²×C₆₇	1	4	yes	complemented
604	#493	C₂²×C₆₇	1	2	yes	complemented
605	#492	C₂²×C₆₇	1	2	yes	complemented
606	#469	C₂²×C₆₇	1	4	yes	complemented
607	#468	C₂²×C₆₇	1	4	yes	complemented
608	#466	C₂²×C₆₇	1	4	yes	complemented
609	#465	C₂²×C₆₇	1	4	yes	complemented
610	#463	C₂²×C₆₇	1	4	yes	complemented
611	#461	C₂²×C₆₇	1	2	yes	complemented
612	#460	C₂²×C₆₇	1	2	yes	complemented
613	#460	C₂²×C₆₇	1	2	yes	complemented
614	#459	C₂²×C₆₇	1	2	yes	complemented
615	#459	C₂²×C₆₇	1	2	yes	complemented
616	#459	C₂²×C₆₇	1	2	yes	complemented
617	#450	C₂²×C₆₇	1	4	yes	complemented
618	#450	C₂²×C₆₇	1	4	yes	complemented
619	#449	C₂²×C₆₇	1	4	yes	complemented
620	#449	C₂²×C₆₇	1	4	yes	complemented
621	#448	C₂²×C₆₇	1	4	yes	complemented
622	#447	C₂²×C₆₇	1	4	yes	complemented
623	#447	C₂²×C₆₇	1	4	yes	complemented
624	#447	C₂²×C₆₇	1	4	yes	complemented
625	#442	C₂²×C₆₇	1	2	yes	complemented
626	#440	C₂²×C₆₇	1	2	yes	complemented
627	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
628	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
629	#436	C₂²×C₆₇	1	2	yes	complemented
630	#435	C₂²×C₆₇	1	4	yes	complemented
631	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
632	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
633	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
634	#418	C₂²×C₆₇	1	1	yes	characteristic, complemented
635	#418	C₂²×C₆₇	1	2	yes	complemented
636	#417	C₂²×C₆₇	1	1	yes	characteristic, complemented
637	#417	C₂²×C₆₇	1	2	yes	complemented
638	#407	C₂²×C₆₇	1	2	yes	complemented
639	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
640	C₂⁵	—	2	2	no	—
641	C₂×#41	—	2	2	no	—
642	C₂×#41	—	2	2	no	—
643	C₂×#41	—	2	8	no	—
644	C₂×#41	—	4	4	no	—
645	C₂×#41	C₂³×C₆₇	1	2	yes	—
646	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
647	C₂×#41	C₂³×C₆₇	1	2	yes	complemented
648	C₂×#41	C₂³×C₆₇	1	2	yes	complemented
649	C₂²×Q₈	C₂³×C₆₇	1	2	yes	complemented
650	C₂²×D₄	—	2	8	no	—
651	C₂²×D₄	—	2	2	no	—
652	C₂²×D₄	—	2	2	no	—
653	C₂²×D₄	—	2	1	no	—
654	C₂²×D₄	—	2	2	no	—
655	C₂²×D₄	—	2	4	no	—
656	C₂²×D₄	—	2	2	no	—
657	C₂²×D₄	—	2	2	no	—
658	C₂²×D₄	—	2	1	no	—
659	C₂²×D₄	—	2	2	no	—
660	C₂²×D₄	—	2	2	no	—
661	C₂²×D₄	—	2	1	no	—
662	C₂²×D₄	—	4	4	no	—
663	C₂²×D₄	—	4	8	no	—
664	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
665	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
666	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
667	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
668	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
669	C₂²×D₄	C₂³×C₆₇	1	2	yes	complemented
670	C₂³×C₄	—	2	2	no	—
671	C₂³×C₄	—	2	1	no	—
672	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
673	AGL(1,ℤ/8)	—	2	8	no	—
674	AGL(1,ℤ/8)	—	2	8	no	—
675	AGL(1,ℤ/8)	—	2	16	no	—
676	AGL(1,ℤ/8)	—	2	16	no	—
677	AGL(1,ℤ/8)	—	2	8	no	—
678	AGL(1,ℤ/8)	—	4	4	no	—
679	AGL(1,ℤ/8)	D₄×C₆₇	1	8	yes	direct product factor
680	C₂×SD₁₆	—	2	16	no	—
681	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
682	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
683	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	complemented
684	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	complemented
685	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	complemented
686	C₂×D₈	—	2	16	no	—
687	C₂×D₈	C₂³×C₆₇	1	4	yes	—
688	C₂×D₈	C₂³×C₆₇	1	2	yes	—
689	C₂×D₈	C₂³×C₆₇	1	4	yes	complemented
690	C₂×D₈	C₂³×C₆₇	1	4	yes	complemented
691	C₂×D₈	C₂³×C₆₇	1	4	yes	complemented
692	C₂×M₁₆	—	2	8	no	—
693	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
694	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
695	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
696	C₂×M₁₆	C₂³×C₆₇	1	4	yes	complemented
697	C₂²×C₈	C₂³×C₆₇	1	4	yes	complemented
698	C₄⋊Q₈	—	2	1	no	—
699	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
700	#127	—	2	1	no	—
701	#127	—	2	1	no	—
702	#127	—	2	1	no	—
703	#127	C₂³×C₆₇	1	2	yes	—
704	#127	C₂³×C₆₇	1	2	yes	—
705	#127	C₂³×C₆₇	1	1	yes	characteristic, complemented
706	#124	—	2	2	no	—
707	#124	C₂³×C₆₇	1	2	yes	complemented
708	#123	—	2	2	no	—
709	#123	—	2	2	no	—
710	#123	—	2	2	no	—
711	C₂²⋊Q₈	—	2	2	no	—
712	C₂²⋊Q₈	—	2	2	no	—
713	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	complemented
714	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	complemented
715	#121	—	2	2	no	—
716	#121	—	2	1	no	—
717	#121	—	2	2	no	—
718	#121	—	2	2	no	—
719	#121	—	2	1	no	—
720	#121	—	2	1	no	—
721	#121	—	2	2	no	—
722	#121	—	2	2	no	—
723	#121	—	2	4	no	—
724	#121	—	2	1	no	—
725	#121	—	2	2	no	—
726	#121	—	2	2	no	—
727	#121	C₂³×C₆₇	1	4	yes	—
728	#121	C₂³×C₆₇	1	4	yes	—
729	#121	C₂³×C₆₇	1	2	yes	complemented
730	#121	C₂³×C₆₇	1	2	yes	complemented
731	#120	—	2	2	no	—
732	#120	—	2	2	no	—
733	#120	—	2	4	no	—
734	#120	—	2	4	no	—
735	#120	—	2	4	no	—
736	#120	—	2	4	no	—
737	#120	—	2	2	no	—
738	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
739	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
740	C₄×D₄	—	2	1	no	—
741	C₄×D₄	—	2	2	no	—
742	C₄×D₄	—	2	1	no	—
743	C₄×D₄	—	2	1	no	—
744	C₄×D₄	—	2	2	no	—
745	C₄×D₄	—	2	1	no	—
746	C₄×D₄	—	2	2	no	—
747	C₄×D₄	—	2	1	no	—
748	C₄×D₄	—	2	1	no	—
749	C₄×D₄	—	2	1	no	—
750	C₄×D₄	—	2	1	no	—
751	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
752	C₄×D₄	D₄×C₆₇	1	2	yes	—
753	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
754	C₄×D₄	C₂³×C₆₇	1	2	yes	—
755	C₄×D₄	C₂³×C₆₇	1	2	yes	—
756	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
757	C₄×D₄	C₂³×C₆₇	1	2	yes	—
758	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
759	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic, complemented
760	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic, complemented
761	#117	—	2	1	no	—
762	#117	C₂³×C₆₇	1	1	yes	characteristic
763	C₂×C₄⋊C₄	—	2	1	no	—
764	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
765	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
766	C₂×C₂²⋊C₄	—	2	1	no	—
767	C₂×C₂²⋊C₄	—	2	2	no	—
768	C₂×C₂²⋊C₄	—	2	2	no	—
769	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
770	C₂×C₄²	—	2	1	no	—
771	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
772	#107	C₂³×C₆₇	1	2	yes	complemented
773	#106	C₂³×C₆₇	1	2	yes	complemented
774	C₄⋊C₈	C₂³×C₆₇	1	2	yes	complemented
775	C₄⋊C₈	C₂³×C₆₇	1	2	yes	complemented
776	#103	C₂³×C₆₇	1	2	yes	complemented
777	#103	C₂³×C₆₇	1	4	yes	complemented
778	#102	C₂³×C₆₇	1	2	yes	—
779	#102	C₂³×C₆₇	1	2	yes	—
780	#102	C₂³×C₆₇	1	2	yes	complemented
781	#102	C₂³×C₆₇	1	4	yes	complemented
782	#102	C₂³×C₆₇	1	4	yes	complemented
783	#102	C₂³×C₆₇	1	4	yes	complemented
784	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	complemented
785	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	complemented
786	#97	C₂³×C₆₇	1	2	yes	complemented
787	C₄×C₈	C₂³×C₆₇	1	2	yes	complemented
788	C₂⁴	—	2	1	no	—
789	C₂⁴	—	2	2	no	—
790	C₂⁴	—	2	2	no	—
791	C₂⁴	—	2	4	no	—
792	C₂⁴	—	2	4	no	—
793	C₂⁴	—	4	8	no	—
794	C₂⁴	—	4	8	no	—
795	C₂⁴	—	8	4	no	—
796	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
797	#41	—	2	2	no	—
798	#41	—	2	4	no	—
799	#41	—	2	4	no	—
800	#41	—	2	4	no	—
801	#41	—	2	4	no	—
802	#41	—	4	8	no	—
803	#41	—	4	2	no	—
804	#41	—	4	2	no	—
805	#41	—	4	8	no	—
806	#41	C₂×D₄×C₆₇	1	4	yes	complemented
807	C₂×Q₈	—	2	2	no	—
808	C₂×Q₈	—	2	4	no	—
809	C₂×Q₈	—	4	2	no	—
810	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
811	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
812	C₂×D₄	—	2	1	no	—
813	C₂×D₄	—	2	4	no	—
814	C₂×D₄	—	2	8	no	—
815	C₂×D₄	—	2	8	no	—
816	C₂×D₄	—	2	4	no	—
817	C₂×D₄	—	2	2	no	—
818	C₂×D₄	—	2	4	no	—
819	C₂×D₄	—	2	4	no	—
820	C₂×D₄	—	2	2	no	—
821	C₂×D₄	—	2	2	no	—
822	C₂×D₄	—	2	2	no	—
823	C₂×D₄	—	2	2	no	—
824	C₂×D₄	—	2	1	no	—
825	C₂×D₄	—	2	4	no	—
826	C₂×D₄	—	2	1	no	—
827	C₂×D₄	—	2	4	no	—
828	C₂×D₄	—	2	4	no	—
829	C₂×D₄	—	2	2	no	—
830	C₂×D₄	—	2	2	no	—
831	C₂×D₄	—	2	2	no	—
832	C₂×D₄	—	2	2	no	—
833	C₂×D₄	—	2	1	no	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	2	2	no	—
836	C₂×D₄	—	2	2	no	—
837	C₂×D₄	—	2	4	no	—
838	C₂×D₄	—	4	4	no	—
839	C₂×D₄	—	4	4	no	—
840	C₂×D₄	—	4	2	no	—
841	C₂×D₄	—	4	8	no	—
842	C₂×D₄	—	4	8	no	—
843	C₂×D₄	—	4	8	no	—
844	C₂×D₄	—	4	4	no	—
845	C₂×D₄	—	4	8	no	—
846	C₂×D₄	—	4	16	no	—
847	C₂×D₄	—	4	8	no	—
848	C₂×D₄	—	4	8	no	—
849	C₂×D₄	—	4	8	no	—
850	C₂×D₄	—	4	4	no	—
851	C₂×D₄	—	8	2	no	—
852	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
853	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
854	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
855	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	complemented
856	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
857	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
858	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
859	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
860	C₂²×C₄	—	2	1	no	—
861	C₂²×C₄	—	2	4	no	—
862	C₂²×C₄	—	2	4	no	—
863	C₂²×C₄	—	2	1	no	—
864	C₂²×C₄	—	2	2	no	—
865	C₂²×C₄	—	2	1	no	—
866	C₂²×C₄	—	2	2	no	—
867	C₂²×C₄	—	2	2	no	—
868	C₂²×C₄	—	2	2	no	—
869	C₂²×C₄	—	2	2	no	—
870	C₂²×C₄	—	2	2	no	—
871	C₂²×C₄	—	2	1	no	—
872	C₂²×C₄	—	4	8	no	—
873	C₂²×C₄	—	4	4	no	—
874	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
875	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
876	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
877	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
878	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
879	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
880	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
881	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
882	SD₁₆	—	2	8	no	—
883	SD₁₆	—	2	8	no	—
884	SD₁₆	—	2	8	no	—
885	SD₁₆	—	4	4	no	—
886	SD₁₆	C₂×D₄×C₆₇	1	8	yes	complemented
887	D₈	—	2	8	no	—
888	D₈	—	2	8	no	—
889	D₈	—	2	8	no	—
890	D₈	—	4	4	no	—
891	D₈	C₂×D₄×C₆₇	1	8	yes	complemented
892	M₁₆	—	2	4	no	—
893	M₁₆	—	2	2	no	—
894	M₁₆	—	2	8	no	—
895	M₁₆	C₂×D₄×C₆₇	1	4	yes	complemented
896	C₂×C₈	—	2	8	no	—
897	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
898	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
899	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
900	C₄⋊C₄	—	2	1	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	1	no	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
908	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
909	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
910	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
911	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
912	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
913	C₂²⋊C₄	—	2	2	no	—
914	C₂²⋊C₄	—	2	1	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	—	2	2	no	—
917	C₂²⋊C₄	—	2	2	no	—
918	C₂²⋊C₄	—	2	2	no	—
919	C₂²⋊C₄	—	2	2	no	—
920	C₂²⋊C₄	—	2	4	no	—
921	C₂²⋊C₄	—	2	4	no	—
922	C₂²⋊C₄	—	2	1	no	—
923	C₂²⋊C₄	—	2	1	no	—
924	C₂²⋊C₄	—	2	2	no	—
925	C₂²⋊C₄	—	2	2	no	—
926	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
927	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
928	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
929	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
930	C₄²	—	2	1	no	—
931	C₄²	—	2	1	no	—
932	C₄²	—	2	1	no	—
933	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
934	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
935	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
936	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
937	C₂³	—	2	4	no	—
938	C₂³	—	2	4	no	—
939	C₂³	—	2	4	no	—
940	C₂³	—	2	1	no	—
941	C₂³	—	2	2	no	—
942	C₂³	—	2	2	no	—
943	C₂³	—	2	4	no	—
944	C₂³	—	4	2	no	—
945	C₂³	—	4	4	no	—
946	C₂³	—	4	8	no	—
947	C₂³	—	4	8	no	—
948	C₂³	—	4	2	no	—
949	C₂³	—	4	2	no	—
950	C₂³	—	4	4	no	—
951	C₂³	—	4	8	no	—
952	C₂³	—	4	4	no	—
953	C₂³	—	4	4	no	—
954	C₂³	—	4	8	no	—
955	C₂³	—	4	4	no	—
956	C₂³	—	8	4	no	—
957	C₂³	—	8	4	no	—
958	C₂³	—	8	2	no	—
959	C₂³	—	8	32	no	—
960	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
961	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
962	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
963	Q₈	—	2	1	no	—
964	Q₈	—	2	2	no	—
965	Q₈	—	2	2	no	—
966	Q₈	—	4	4	no	—
967	Q₈	C₂²×D₄×C₆₇	1	2	yes	complemented
968	D₄	—	2	4	no	—
969	D₄	—	2	4	no	—
970	D₄	—	2	4	no	—
971	D₄	—	2	2	no	—
972	D₄	—	2	2	no	—
973	D₄	—	2	4	no	—
974	D₄	—	2	2	no	—
975	D₄	—	2	1	no	—
976	D₄	—	2	2	no	—
977	D₄	—	2	4	no	—
978	D₄	—	4	8	no	—
979	D₄	—	4	8	no	—
980	D₄	—	4	4	no	—
981	D₄	—	4	4	no	—
982	D₄	—	4	4	no	—
983	D₄	—	4	4	no	—
984	D₄	—	4	8	no	—
985	D₄	—	4	4	no	—
986	D₄	—	4	8	no	—
987	D₄	—	4	4	no	—
988	D₄	—	4	4	no	—
989	D₄	—	4	4	no	—
990	D₄	—	4	2	no	—
991	D₄	—	8	2	no	—
992	D₄	—	8	2	no	—
993	D₄	—	8	1	no	—
994	D₄	—	8	2	no	—
995	D₄	AGL(1,ℤ/8)×C₆₇	1	4	yes	direct product factor
996	D₄	C₂²×D₄×C₆₇	1	4	yes	—
997	D₄	C₂²×D₄×C₆₇	1	2	yes	complemented
998	C₂×C₄	—	2	4	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	4	no	—
1001	C₂×C₄	—	2	4	no	—
1002	C₂×C₄	—	2	4	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	4	1	no	—
1013	C₂×C₄	—	4	4	no	—
1014	C₂×C₄	—	4	4	no	—
1015	C₂×C₄	—	4	4	no	—
1016	C₂×C₄	—	4	4	no	—
1017	C₂×C₄	—	4	2	no	—
1018	C₂×C₄	—	4	4	no	—
1019	C₂×C₄	—	4	4	no	—
1020	C₂×C₄	—	4	2	no	—
1021	C₂×C₄	—	8	1	no	—
1022	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1023	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1024	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1025	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1026	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1027	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1028	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1029	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1030	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1031	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1032	C₈	—	2	4	no	—
1033	C₈	—	2	2	no	—
1034	C₈	C₂²×D₄×C₆₇	1	4	yes	complemented
1035	C₂²	—	2	1	no	—
1036	C₂²	—	2	1	no	—
1037	C₂²	—	2	2	no	—
1038	C₂²	—	2	2	no	—
1039	C₂²	—	2	2	no	—
1040	C₂²	—	2	2	no	—
1041	C₂²	—	2	2	no	—
1042	C₂²	—	2	2	no	—
1043	C₂²	—	2	4	no	—
1044	C₂²	—	4	8	no	—
1045	C₂²	—	4	8	no	—
1046	C₂²	—	4	2	no	—
1047	C₂²	—	4	1	no	—
1048	C₂²	—	4	1	no	—
1049	C₂²	—	4	2	no	—
1050	C₂²	—	4	4	no	—
1051	C₂²	—	4	2	no	—
1052	C₂²	—	4	4	no	—
1053	C₂²	—	4	2	no	—
1054	C₂²	—	4	2	no	—
1055	C₂²	—	4	4	no	—
1056	C₂²	—	8	16	no	—
1057	C₂²	—	8	8	no	—
1058	C₂²	—	8	8	no	—
1059	C₂²	—	8	16	no	—
1060	C₂²	D₄²×C₆₇	1	2	yes	—
1061	C₂²	C₂×AGL(1,ℤ/8)×C₆₇	1	4	yes	complemented
1062	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1063	C₄	—	2	1	no	—
1064	C₄	—	2	1	no	—
1065	C₄	—	2	1	no	—
1066	C₄	—	2	2	no	—
1067	C₄	—	2	2	no	—
1068	C₄	—	2	2	no	—
1069	C₄	—	4	2	no	—
1070	C₄	—	4	1	no	—
1071	C₄	—	4	1	no	—
1072	C₄	—	4	2	no	—
1073	C₄	D₄²×C₆₇	1	2	yes	—
1074	C₄	C₂×AGL(1,ℤ/8)×C₆₇	1	2	yes	complemented
1075	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
1076	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1077	C₂	—	2	2	no	—
1078	C₂	—	2	4	no	—
1079	C₂	—	4	2	no	—
1080	C₂	—	4	4	no	—
1081	C₂	—	4	2	no	—
1082	C₂	—	8	4	no	—
1083	C₂	—	8	2	no	—
1084	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
1085	C₂	C₂²×AGL(1,ℤ/8)×C₆₇	1	1	yes	characteristic
1086	C₂	C₆₇×#3585	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. C₂²×AGL(1,ℤ/8)×C₆₇	C₂	semidirect
2. D₄×#41×C₆₇	C₂	semidirect
3. C₂×D₄²×C₆₇	C₂	semidirect
4. D₄×SD₁₆×C₆₇	C₂	semidirect
5. D₄×D₈×C₆₇	C₂	semidirect
6. C₆₇×#3274	C₂	semidirect
7. C₆₇×#3272	C₂	semidirect
8. C₆₇×#3265	C₂	semidirect
9. C₆₇×#3264	C₂	semidirect
10. C₆₇×#3151	C₂	semidirect
11. C₆₇×#3055	C₂	semidirect
12. C₆₇×#3038	C₂	semidirect
13. C₆₇×#3036	C₂	semidirect
14. C₆₇×#3006	C₂	semidirect
15. C₆₇×#3003	C₂	semidirect
16. C₄×AGL(1,ℤ/8)×C₆₇	C₂	semidirect
17. D₄×M₁₆×C₆₇	C₂	semidirect
18. C₂²×#41×C₆₇	C₂²	semidirect
20. C₂³×D₄×C₆₇	C₂²	semidirect
23. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
24. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
25. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
26. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
27. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
28. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
29. C₂²×SD₁₆×C₆₇	C₂²	semidirect
30. C₂²×D₈×C₆₇	C₂²	semidirect
31. C₂²×M₁₆×C₆₇	C₂²	semidirect
32. #550×C₆₇	C₂²	semidirect
33. D₄×Q₈×C₆₇	C₂²	semidirect
34. #548×C₆₇	C₂²	semidirect
36. #547×C₆₇	C₂²	semidirect
38. #546×C₆₇	C₂²	semidirect
44. D₄²×C₆₇	C₂²	semidirect
45. D₄²×C₆₇	C₂²	semidirect
46. D₄²×C₆₇	C₂²	semidirect
48. #532×C₆₇	C₂²	semidirect
49. C₂×#127×C₆₇	C₂²	semidirect
51. #525×C₆₇	C₂²	semidirect
53. C₂×#121×C₆₇	C₂²	semidirect
55. C₄×#41×C₆₇	C₂²	semidirect
58. C₂×C₄×D₄×C₆₇	C₂²	semidirect
59. #496×C₆₇	C₂²	semidirect
60. #493×C₆₇	C₂²	semidirect
61. #492×C₆₇	C₂²	semidirect
62. #469×C₆₇	C₂²	semidirect
63. #468×C₆₇	C₂²	semidirect
64. #466×C₆₇	C₂²	semidirect
65. #465×C₆₇	C₂²	semidirect
66. #463×C₆₇	C₂²	semidirect
67. #461×C₆₇	C₂²	semidirect
68. #460×C₆₇	C₂²	semidirect
69. #460×C₆₇	C₂²	semidirect
70. #459×C₆₇	C₂²	semidirect
71. #459×C₆₇	C₂²	semidirect
72. #459×C₆₇	C₂²	semidirect
73. #450×C₆₇	C₂²	semidirect
74. #450×C₆₇	C₂²	semidirect
75. #449×C₆₇	C₂²	semidirect
76. #449×C₆₇	C₂²	semidirect
77. #448×C₆₇	C₂²	semidirect
78. #447×C₆₇	C₂²	semidirect
79. #447×C₆₇	C₂²	semidirect
80. #447×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. #418×C₆₇	C₂²	semidirect
91. #418×C₆₇	C₂²	semidirect
92. #417×C₆₇	C₂²	semidirect
93. #417×C₆₇	C₂²	semidirect
94. #407×C₆₇	C₂²	semidirect
95. C₄×M₁₆×C₆₇	C₂²	semidirect
103. C₂×#41×C₆₇	C₂³	semidirect
104. C₂×#41×C₆₇	C₂³	semidirect
105. C₂²×Q₈×C₆₇	C₂³	semidirect
125. C₂²×D₄×C₆₇	C₂³	semidirect
135. AGL(1,ℤ/8)×C₆₇	D₄	direct (N × H)
139. C₂×SD₁₆×C₆₇	C₂³	semidirect
140. C₂×SD₁₆×C₆₇	C₂³	semidirect
141. C₂×SD₁₆×C₆₇	C₂³	semidirect
145. C₂×D₈×C₆₇	C₂³	semidirect
146. C₂×D₈×C₆₇	C₂³	semidirect
147. C₂×D₈×C₆₇	C₂³	semidirect
152. C₂×M₁₆×C₆₇	C₂³	semidirect
153. C₂²×C₈×C₆₇	C₂³	semidirect
155. C₄⋊Q₈×C₆₇	C₂³	semidirect
161. #127×C₆₇	C₂³	semidirect
163. #124×C₆₇	C₂³	semidirect
169. C₂²⋊Q₈×C₆₇	C₂³	semidirect
170. C₂²⋊Q₈×C₆₇	C₂³	semidirect
185. #121×C₆₇	C₂³	semidirect
186. #121×C₆₇	C₂³	semidirect
194. C₄×Q₈×C₆₇	C₂³	semidirect
195. C₄×Q₈×C₆₇	C₂³	semidirect
215. C₄×D₄×C₆₇	C₂³	semidirect
216. C₄×D₄×C₆₇	C₂³	semidirect
228. #107×C₆₇	C₂³	semidirect
229. #106×C₆₇	C₂³	semidirect
230. C₄⋊C₈×C₆₇	C₂³	semidirect
231. C₄⋊C₈×C₆₇	C₂³	semidirect
232. #103×C₆₇	C₂³	semidirect
233. #103×C₆₇	C₂³	semidirect
236. #102×C₆₇	C₂³	semidirect
237. #102×C₆₇	C₂³	semidirect
238. #102×C₆₇	C₂³	semidirect
239. #102×C₆₇	C₂³	semidirect
240. C₂²⋊C₈×C₆₇	C₂³	semidirect
241. C₂²⋊C₈×C₆₇	C₂³	semidirect
242. #97×C₆₇	C₂³	semidirect
243. C₄×C₈×C₆₇	C₂³	semidirect
262. #41×C₆₇	C₂×D₄	semidirect
311. C₂×D₄×C₆₇	C₂×D₄	semidirect
342. SD₁₆×C₆₇	C₂×D₄	semidirect
347. D₈×C₆₇	C₂×D₄	semidirect
351. M₁₆×C₆₇	C₂×D₄	semidirect
423. Q₈×C₆₇	C₂²×D₄	semidirect
451. D₄×C₆₇	AGL(1,ℤ/8)	direct (N × H)
453. D₄×C₆₇	C₂²×D₄	semidirect
490. C₈×C₆₇	C₂²×D₄	semidirect
517. C₂²×C₆₇	C₂×AGL(1,ℤ/8)	semidirect
530. C₄×C₆₇	C₂×AGL(1,ℤ/8)	semidirect
533. D₄×AGL(1,ℤ/8)	C₆₇	direct (N × H)
544. C₂²×AGL(1,ℤ/8)	C₂×C₆₇	semidirect
545. D₄×#41	C₂×C₆₇	semidirect
546. C₂×D₄²	C₂×C₆₇	semidirect
547. D₄×SD₁₆	C₂×C₆₇	semidirect
548. D₄×D₈	C₂×C₆₇	semidirect
549. #3274	C₂×C₆₇	semidirect
550. #3272	C₂×C₆₇	semidirect
551. #3265	C₂×C₆₇	semidirect
552. #3264	C₂×C₆₇	semidirect
553. #3151	C₂×C₆₇	semidirect
554. #3055	C₂×C₆₇	semidirect
555. #3038	C₂×C₆₇	semidirect
556. #3036	C₂×C₆₇	semidirect
557. #3006	C₂×C₆₇	semidirect
558. #3003	C₂×C₆₇	semidirect
559. C₄×AGL(1,ℤ/8)	C₂×C₆₇	semidirect
560. D₄×M₁₆	C₂×C₆₇	semidirect
561. C₆₇	D₄×AGL(1,ℤ/8)	direct (N × H)
562. C₂²×#41	C₂²×C₆₇	semidirect
564. C₂³×D₄	C₂²×C₆₇	semidirect
567. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
568. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
569. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
570. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
571. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
572. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
573. C₂²×SD₁₆	C₂²×C₆₇	semidirect
574. C₂²×D₈	C₂²×C₆₇	semidirect
575. C₂²×M₁₆	C₂²×C₆₇	semidirect
576. #550	C₂²×C₆₇	semidirect
577. D₄×Q₈	C₂²×C₆₇	semidirect
578. #548	C₂²×C₆₇	semidirect
580. #547	C₂²×C₆₇	semidirect
582. #546	C₂²×C₆₇	semidirect
588. D₄²	C₂²×C₆₇	semidirect
589. D₄²	C₂²×C₆₇	semidirect
590. D₄²	C₂²×C₆₇	semidirect
592. #532	C₂²×C₆₇	semidirect
593. C₂×#127	C₂²×C₆₇	semidirect
595. #525	C₂²×C₆₇	semidirect
597. C₂×#121	C₂²×C₆₇	semidirect
599. C₄×#41	C₂²×C₆₇	semidirect
602. C₂×C₄×D₄	C₂²×C₆₇	semidirect
603. #496	C₂²×C₆₇	semidirect
604. #493	C₂²×C₆₇	semidirect
605. #492	C₂²×C₆₇	semidirect
606. #469	C₂²×C₆₇	semidirect
607. #468	C₂²×C₆₇	semidirect
608. #466	C₂²×C₆₇	semidirect
609. #465	C₂²×C₆₇	semidirect
610. #463	C₂²×C₆₇	semidirect
611. #461	C₂²×C₆₇	semidirect
612. #460	C₂²×C₆₇	semidirect
613. #460	C₂²×C₆₇	semidirect
614. #459	C₂²×C₆₇	semidirect
615. #459	C₂²×C₆₇	semidirect
616. #459	C₂²×C₆₇	semidirect
617. #450	C₂²×C₆₇	semidirect
618. #450	C₂²×C₆₇	semidirect
619. #449	C₂²×C₆₇	semidirect
620. #449	C₂²×C₆₇	semidirect
621. #448	C₂²×C₆₇	semidirect
622. #447	C₂²×C₆₇	semidirect
623. #447	C₂²×C₆₇	semidirect
624. #447	C₂²×C₆₇	semidirect
625. #442	C₂²×C₆₇	semidirect
626. #440	C₂²×C₆₇	semidirect
627. C₄×SD₁₆	C₂²×C₆₇	semidirect
628. C₄×D₈	C₂²×C₆₇	semidirect
629. #436	C₂²×C₆₇	semidirect
630. #435	C₂²×C₆₇	semidirect
631. C₈×D₄	C₂²×C₆₇	semidirect
632. #428	C₂²×C₆₇	semidirect
633. #423	C₂²×C₆₇	semidirect
634. #418	C₂²×C₆₇	semidirect
635. #418	C₂²×C₆₇	semidirect
636. #417	C₂²×C₆₇	semidirect
637. #417	C₂²×C₆₇	semidirect
638. #407	C₂²×C₆₇	semidirect
639. C₄×M₁₆	C₂²×C₆₇	semidirect
647. C₂×#41	C₂³×C₆₇	semidirect
648. C₂×#41	C₂³×C₆₇	semidirect
649. C₂²×Q₈	C₂³×C₆₇	semidirect
669. C₂²×D₄	C₂³×C₆₇	semidirect
679. AGL(1,ℤ/8)	D₄×C₆₇	direct (N × H)
683. C₂×SD₁₆	C₂³×C₆₇	semidirect
684. C₂×SD₁₆	C₂³×C₆₇	semidirect
685. C₂×SD₁₆	C₂³×C₆₇	semidirect
689. C₂×D₈	C₂³×C₆₇	semidirect
690. C₂×D₈	C₂³×C₆₇	semidirect
691. C₂×D₈	C₂³×C₆₇	semidirect
696. C₂×M₁₆	C₂³×C₆₇	semidirect
697. C₂²×C₈	C₂³×C₆₇	semidirect
699. C₄⋊Q₈	C₂³×C₆₇	semidirect
705. #127	C₂³×C₆₇	semidirect
707. #124	C₂³×C₆₇	semidirect
713. C₂²⋊Q₈	C₂³×C₆₇	semidirect
714. C₂²⋊Q₈	C₂³×C₆₇	semidirect
729. #121	C₂³×C₆₇	semidirect
730. #121	C₂³×C₆₇	semidirect
738. C₄×Q₈	C₂³×C₆₇	semidirect
739. C₄×Q₈	C₂³×C₆₇	semidirect
759. C₄×D₄	C₂³×C₆₇	semidirect
760. C₄×D₄	C₂³×C₆₇	semidirect
772. #107	C₂³×C₆₇	semidirect
773. #106	C₂³×C₆₇	semidirect
774. C₄⋊C₈	C₂³×C₆₇	semidirect
775. C₄⋊C₈	C₂³×C₆₇	semidirect
776. #103	C₂³×C₆₇	semidirect
777. #103	C₂³×C₆₇	semidirect
780. #102	C₂³×C₆₇	semidirect
781. #102	C₂³×C₆₇	semidirect
782. #102	C₂³×C₆₇	semidirect
783. #102	C₂³×C₆₇	semidirect
784. C₂²⋊C₈	C₂³×C₆₇	semidirect
785. C₂²⋊C₈	C₂³×C₆₇	semidirect
786. #97	C₂³×C₆₇	semidirect
787. C₄×C₈	C₂³×C₆₇	semidirect
806. #41	C₂×D₄×C₆₇	semidirect
855. C₂×D₄	C₂×D₄×C₆₇	semidirect
886. SD₁₆	C₂×D₄×C₆₇	semidirect
891. D₈	C₂×D₄×C₆₇	semidirect
895. M₁₆	C₂×D₄×C₆₇	semidirect
967. Q₈	C₂²×D₄×C₆₇	semidirect
995. D₄	AGL(1,ℤ/8)×C₆₇	direct (N × H)
997. D₄	C₂²×D₄×C₆₇	semidirect
1034. C₈	C₂²×D₄×C₆₇	semidirect
1061. C₂²	C₂×AGL(1,ℤ/8)×C₆₇	semidirect
1074. C₄	C₂×AGL(1,ℤ/8)×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×AGL(1,ℤ/8)×C₆₇	2
D₄×#41×C₆₇	2
C₂×D₄²×C₆₇	2
D₄×SD₁₆×C₆₇	2
D₄×D₈×C₆₇	2
C₆₇×#3274	2
C₆₇×#3272	2
C₆₇×#3265	2
C₆₇×#3264	2
C₆₇×#3151	2
C₆₇×#3055	2
C₆₇×#3038	2
C₆₇×#3036	2
C₆₇×#3006	2
C₆₇×#3003	2
C₄×AGL(1,ℤ/8)×C₆₇	2
D₄×M₁₆×C₆₇	2
D₄×AGL(1,ℤ/8)	67

Subgroups — D4×AGL(1,ℤ/8)×C67 #30740316

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×AGL(1,ℤ/8)×C₆₇ #30740316