Subgroups — C₆₇×#61329 #30740580

Order 17152.

1896 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3375	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3373	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3368	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3366	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3365	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3362	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3361	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3358	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3136	C₂	1	2	yes	maximal, complemented
12	C₂×#486×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3081	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3079	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3045	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3038	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2946	C₂	1	2	yes	maximal, complemented
19	C₄×#135×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	—
21	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
22	#559×C₆₇	C₂²	1	2	yes	—
23	#559×C₆₇	C₂²	1	2	yes	—
24	Q₈²×C₆₇	C₂²	1	2	yes	complemented
25	#557×C₆₇	C₂²	1	2	yes	complemented
26	#554×C₆₇	—	2	2	no	—
27	#554×C₆₇	C₂²	1	2	yes	complemented
28	#550×C₆₇	C₂²	1	2	yes	—
29	#550×C₆₇	C₂²	1	2	yes	—
30	D₄×Q₈×C₆₇	—	2	2	no	—
31	D₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
32	#546×C₆₇	—	2	2	no	—
33	#546×C₆₇	—	2	2	no	—
34	#544×C₆₇	—	2	2	no	—
35	#544×C₆₇	C₂²	1	2	yes	—
36	#540×C₆₇	—	2	2	no	—
37	#535×C₆₇	C₂²	1	2	yes	—
38	#533×C₆₇	—	2	1	no	—
39	#533×C₆₇	C₂²	1	1	yes	characteristic
40	#532×C₆₇	—	2	1	no	—
41	#532×C₆₇	—	2	1	no	—
42	C₂×C₄⋊Q₈×C₆₇	—	2	1	no	—
43	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
45	#520×C₆₇	C₂²	1	2	yes	—
46	#518×C₆₇	C₂²	1	2	yes	—
47	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
48	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
49	#490×C₆₇	C₂²	1	4	yes	complemented
50	#489×C₆₇	C₂²	1	4	yes	complemented
51	#488×C₆₇	C₂²	1	4	yes	complemented
52	#486×C₆₇	C₂²	1	2	yes	—
53	#486×C₆₇	C₂²	1	2	yes	—
54	#486×C₆₇	C₂²	1	2	yes	—
55	#486×C₆₇	C₂²	1	2	yes	—
56	#486×C₆₇	C₂²	1	4	yes	complemented
57	#478×C₆₇	C₂²	1	4	yes	complemented
58	#478×C₆₇	C₂²	1	4	yes	complemented
59	#477×C₆₇	C₂²	1	2	yes	complemented
60	#476×C₆₇	C₂²	1	2	yes	complemented
61	#476×C₆₇	C₂²	1	4	yes	complemented
62	#475×C₆₇	C₂²	1	2	yes	complemented
63	#474×C₆₇	C₂²	1	2	yes	complemented
64	#474×C₆₇	C₂²	1	4	yes	complemented
65	#464×C₆₇	C₂²	1	4	yes	complemented
66	#463×C₆₇	C₂²	1	4	yes	complemented
67	#460×C₆₇	C₂²	1	2	yes	—
68	#460×C₆₇	C₂²	1	2	yes	—
69	#460×C₆₇	C₂²	1	4	yes	complemented
70	#459×C₆₇	C₂²	1	2	yes	—
71	#459×C₆₇	C₂²	1	2	yes	—
72	#459×C₆₇	C₂²	1	4	yes	complemented
73	#446×C₆₇	C₂²	1	2	yes	complemented
74	#446×C₆₇	C₂²	1	2	yes	complemented
75	C₈×Q₈×C₆₇	C₂²	1	2	yes	complemented
76	C₈×Q₈×C₆₇	C₂²	1	2	yes	complemented
77	#442×C₆₇	C₂²	1	4	yes	complemented
78	#440×C₆₇	C₂²	1	4	yes	complemented
79	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
80	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
81	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
82	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
83	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
84	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
85	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
86	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
87	C₄×D₈×C₆₇	C₂²	1	4	yes	complemented
88	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
89	#428×C₆₇	C₂²	1	2	yes	—
90	#427×C₆₇	C₂²	1	1	yes	characteristic
91	#424×C₆₇	C₂²	1	2	yes	—
92	#423×C₆₇	C₂²	1	1	yes	characteristic
93	#418×C₆₇	C₂²	1	2	yes	—
94	#417×C₆₇	C₂²	1	2	yes	—
95	#416×C₆₇	C₂²	1	1	yes	characteristic
96	#416×C₆₇	C₂²	1	1	yes	characteristic
97	C₂×#102×C₆₇	C₂²	1	2	yes	—
98	C₂×#102×C₆₇	C₂²	1	2	yes	—
99	#405×C₆₇	C₂²	1	2	yes	—
100	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
101	C₂×#41×C₆₇	—	2	2	no	—
102	C₂×#41×C₆₇	—	2	2	no	—
103	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
104	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
105	C₂²×Q₈×C₆₇	—	2	2	no	—
106	C₂²×Q₈×C₆₇	—	2	1	no	—
107	C₂²×D₄×C₆₇	—	2	1	no	—
108	C₂²×D₄×C₆₇	—	2	1	no	—
109	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
110	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
111	#135×C₆₇	—	2	4	no	—
112	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
113	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
114	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
115	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
116	C₂×D₈×C₆₇	C₂³	1	4	yes	—
117	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
118	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
119	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
121	C₄⋊Q₈×C₆₇	—	2	2	no	—
122	C₄⋊Q₈×C₆₇	—	2	2	no	—
123	C₄⋊Q₈×C₆₇	—	2	2	no	—
124	C₄⋊Q₈×C₆₇	—	2	4	no	—
125	C₄⋊Q₈×C₆₇	—	2	1	no	—
126	C₄⋊Q₈×C₆₇	—	2	1	no	—
127	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
128	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
129	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
130	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
131	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
132	#127×C₆₇	—	2	1	no	—
133	#127×C₆₇	—	2	1	no	—
134	#127×C₆₇	C₂³	1	2	yes	—
135	#127×C₆₇	C₂³	1	2	yes	—
136	#127×C₆₇	C₂³	1	4	yes	—
137	#125×C₆₇	—	2	2	no	—
138	#125×C₆₇	—	2	4	no	—
139	#125×C₆₇	D₄	1	2	yes	—
140	#125×C₆₇	C₂³	1	4	yes	—
141	#124×C₆₇	—	2	2	no	—
142	#124×C₆₇	—	2	2	no	—
143	#124×C₆₇	C₂³	1	4	yes	—
144	#123×C₆₇	—	2	4	no	—
145	#123×C₆₇	—	2	4	no	—
146	C₂²⋊Q₈×C₆₇	—	2	2	no	—
147	C₂²⋊Q₈×C₆₇	—	2	2	no	—
148	C₂²⋊Q₈×C₆₇	—	2	4	no	—
149	C₂²⋊Q₈×C₆₇	—	2	4	no	—
150	C₂²⋊Q₈×C₆₇	—	2	4	no	—
151	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
152	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
153	#121×C₆₇	—	2	2	no	—
154	#121×C₆₇	—	2	2	no	—
155	#121×C₆₇	—	2	2	no	—
156	#121×C₆₇	—	2	2	no	—
157	#121×C₆₇	—	2	4	no	—
158	#121×C₆₇	—	2	4	no	—
159	#120×C₆₇	—	2	4	no	—
160	C₄×Q₈×C₆₇	—	2	2	no	—
161	C₄×Q₈×C₆₇	—	2	2	no	—
162	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
163	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
164	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
165	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
167	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
168	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
169	C₄×D₄×C₆₇	—	2	1	no	—
170	C₄×D₄×C₆₇	—	2	1	no	—
171	C₄×D₄×C₆₇	—	2	1	no	—
172	C₄×D₄×C₆₇	—	2	1	no	—
173	C₄×D₄×C₆₇	—	2	2	no	—
174	C₄×D₄×C₆₇	—	2	2	no	—
175	C₄×D₄×C₆₇	—	2	2	no	—
176	C₄×D₄×C₆₇	—	2	2	no	—
177	C₄×D₄×C₆₇	—	2	4	no	—
178	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₆₇	C₂³	1	4	yes	—
181	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
182	C₄×D₄×C₆₇	C₂³	1	4	yes	—
183	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₆₇	C₂³	1	4	yes	—
185	#117×C₆₇	—	2	2	no	—
186	#117×C₆₇	—	2	1	no	—
187	#117×C₆₇	—	2	1	no	—
188	#117×C₆₇	C₂³	1	1	yes	characteristic
189	#117×C₆₇	C₂³	1	1	yes	characteristic
190	#117×C₆₇	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
192	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
193	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
194	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
196	C₂×C₄²×C₆₇	—	2	1	no	—
197	C₂×C₄²×C₆₇	—	2	1	no	—
198	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
199	#107×C₆₇	C₂³	1	1	yes	characteristic
200	#107×C₆₇	C₂³	1	4	yes	—
201	#107×C₆₇	C₂³	1	1	yes	characteristic
202	#106×C₆₇	C₂³	1	4	yes	—
203	#106×C₆₇	C₂³	1	1	yes	characteristic
204	#106×C₆₇	C₂³	1	1	yes	characteristic
205	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
206	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
207	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
208	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
209	#103×C₆₇	C₂³	1	4	yes	—
210	#103×C₆₇	C₂³	1	1	yes	characteristic
211	#103×C₆₇	C₂³	1	1	yes	characteristic
212	#103×C₆₇	C₂³	1	1	yes	characteristic
213	#103×C₆₇	C₂³	1	1	yes	characteristic
214	#102×C₆₇	C₂³	1	4	yes	—
215	#102×C₆₇	C₂³	1	4	yes	—
216	#102×C₆₇	C₂³	1	4	yes	—
217	#102×C₆₇	C₂³	1	4	yes	—
218	#102×C₆₇	C₂³	1	4	yes	—
219	#102×C₆₇	C₂³	1	4	yes	—
220	#102×C₆₇	C₂³	1	4	yes	—
221	#102×C₆₇	C₂³	1	1	yes	characteristic
222	#102×C₆₇	C₂³	1	1	yes	characteristic
223	#102×C₆₇	C₂³	1	1	yes	characteristic
224	#102×C₆₇	C₂³	1	1	yes	characteristic
225	#97×C₆₇	C₂³	1	4	yes	—
226	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
227	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
228	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
229	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
230	C₄×C₈×C₆₇	C₂³	1	4	yes	—
231	C₂⁴×C₆₇	—	2	2	no	—
232	#41×C₆₇	—	2	2	no	—
233	#41×C₆₇	—	2	2	no	—
234	#41×C₆₇	—	2	2	no	—
235	#41×C₆₇	—	8	4	no	—
236	#41×C₆₇	—	8	4	no	—
237	#41×C₆₇	#41	1	4	yes	complemented
238	C₂×Q₈×C₆₇	—	2	2	no	—
239	C₂×Q₈×C₆₇	—	2	4	no	—
240	C₂×Q₈×C₆₇	—	2	2	no	—
241	C₂×Q₈×C₆₇	—	8	2	no	—
242	C₂×Q₈×C₆₇	—	8	4	no	—
243	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
244	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
245	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
246	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
247	C₂×D₄×C₆₇	—	2	1	no	—
248	C₂×D₄×C₆₇	—	2	1	no	—
249	C₂×D₄×C₆₇	—	2	2	no	—
250	C₂×D₄×C₆₇	—	2	2	no	—
251	C₂×D₄×C₆₇	—	2	2	no	—
252	C₂×D₄×C₆₇	—	2	4	no	—
253	C₂×D₄×C₆₇	—	2	4	no	—
254	C₂×D₄×C₆₇	—	2	2	no	—
255	C₂×D₄×C₆₇	—	2	2	no	—
256	C₂×D₄×C₆₇	—	2	4	no	—
257	C₂×D₄×C₆₇	—	2	4	no	—
258	C₂×D₄×C₆₇	—	8	2	no	—
259	C₂×D₄×C₆₇	—	8	2	no	—
260	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
261	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
262	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₆₇	—	2	1	no	—
264	C₂²×C₄×C₆₇	—	2	2	no	—
265	C₂²×C₄×C₆₇	—	2	1	no	—
266	C₂²×C₄×C₆₇	—	2	1	no	—
267	C₂²×C₄×C₆₇	—	2	1	no	—
268	C₂²×C₄×C₆₇	—	2	1	no	—
269	C₂²×C₄×C₆₇	—	2	1	no	—
270	C₂²×C₄×C₆₇	—	2	4	no	—
271	C₂²×C₄×C₆₇	—	2	4	no	—
272	C₂²×C₄×C₆₇	—	2	4	no	—
273	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
276	Q₁₆×C₆₇	—	2	2	no	—
277	SD₁₆×C₆₇	—	2	2	no	—
278	SD₁₆×C₆₇	—	2	8	no	—
279	SD₁₆×C₆₇	—	2	2	no	—
280	D₈×C₆₇	—	2	2	no	—
281	D₈×C₆₇	—	2	8	no	—
282	M₁₆×C₆₇	—	2	4	no	—
283	C₂×C₈×C₆₇	—	2	2	no	—
284	C₂×C₈×C₆₇	—	2	2	no	—
285	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
286	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
287	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
288	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
289	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
290	C₄⋊C₄×C₆₇	—	2	2	no	—
291	C₄⋊C₄×C₆₇	—	2	2	no	—
292	C₄⋊C₄×C₆₇	—	2	4	no	—
293	C₄⋊C₄×C₆₇	—	2	2	no	—
294	C₄⋊C₄×C₆₇	—	2	4	no	—
295	C₄⋊C₄×C₆₇	—	2	1	no	—
296	C₄⋊C₄×C₆₇	—	2	1	no	—
297	C₄⋊C₄×C₆₇	—	2	1	no	—
298	C₄⋊C₄×C₆₇	—	2	1	no	—
299	C₄⋊C₄×C₆₇	—	2	4	no	—
300	C₄⋊C₄×C₆₇	—	2	4	no	—
301	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
302	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
303	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
304	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
305	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
306	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
307	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
308	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
309	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
310	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
311	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
312	C₂²⋊C₄×C₆₇	—	2	1	no	—
313	C₂²⋊C₄×C₆₇	—	2	1	no	—
314	C₂²⋊C₄×C₆₇	—	2	4	no	—
315	C₂²⋊C₄×C₆₇	—	2	4	no	—
316	C₂²⋊C₄×C₆₇	—	2	1	no	—
317	C₂²⋊C₄×C₆₇	—	2	1	no	—
318	C₂²⋊C₄×C₆₇	—	2	1	no	—
319	C₂²⋊C₄×C₆₇	—	2	1	no	—
320	C₂²⋊C₄×C₆₇	—	2	4	no	—
321	C₂²⋊C₄×C₆₇	—	2	4	no	—
322	C₂²⋊C₄×C₆₇	—	2	4	no	—
323	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
324	C₄²×C₆₇	—	2	1	no	—
325	C₄²×C₆₇	—	2	1	no	—
326	C₄²×C₆₇	—	2	1	no	—
327	C₄²×C₆₇	—	2	1	no	—
328	C₄²×C₆₇	—	2	1	no	—
329	C₄²×C₆₇	—	2	1	no	—
330	C₄²×C₆₇	—	2	4	no	—
331	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
333	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
334	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
335	C₄²×C₆₇	C₂⁴	1	4	yes	—
336	C₂³×C₆₇	—	2	1	no	—
337	C₂³×C₆₇	—	2	4	no	—
338	C₂³×C₆₇	—	2	1	no	—
339	C₂³×C₆₇	—	4	4	no	—
340	C₂³×C₆₇	—	8	2	no	—
341	C₂³×C₆₇	—	8	2	no	—
342	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
343	Q₈×C₆₇	—	2	4	no	—
344	Q₈×C₆₇	—	2	4	no	—
345	Q₈×C₆₇	—	2	1	no	—
346	Q₈×C₆₇	—	2	1	no	—
347	Q₈×C₆₇	—	2	1	no	—
348	Q₈×C₆₇	—	4	4	no	—
349	Q₈×C₆₇	—	8	2	no	—
350	Q₈×C₆₇	—	8	4	no	—
351	Q₈×C₆₇	C₂×#41	1	2	yes	—
352	D₄×C₆₇	—	2	4	no	—
353	D₄×C₆₇	—	2	4	no	—
354	D₄×C₆₇	—	2	1	no	—
355	D₄×C₆₇	—	2	1	no	—
356	D₄×C₆₇	—	2	4	no	—
357	D₄×C₆₇	—	2	1	no	—
358	D₄×C₆₇	—	4	2	no	—
359	D₄×C₆₇	—	4	4	no	—
360	D₄×C₆₇	—	4	4	no	—
361	D₄×C₆₇	—	4	4	no	—
362	D₄×C₆₇	—	8	2	no	—
363	D₄×C₆₇	—	8	2	no	—
364	D₄×C₆₇	—	8	4	no	—
365	D₄×C₆₇	—	8	4	no	—
366	D₄×C₆₇	C₂×#41	1	2	yes	—
367	C₂×C₄×C₆₇	—	2	1	no	—
368	C₂×C₄×C₆₇	—	2	4	no	—
369	C₂×C₄×C₆₇	—	2	2	no	—
370	C₂×C₄×C₆₇	—	2	2	no	—
371	C₂×C₄×C₆₇	—	2	1	no	—
372	C₂×C₄×C₆₇	—	2	1	no	—
373	C₂×C₄×C₆₇	—	2	1	no	—
374	C₂×C₄×C₆₇	—	2	1	no	—
375	C₂×C₄×C₆₇	—	2	1	no	—
376	C₂×C₄×C₆₇	—	2	4	no	—
377	C₂×C₄×C₆₇	—	4	2	no	—
378	C₂×C₄×C₆₇	—	4	2	no	—
379	C₂×C₄×C₆₇	—	4	2	no	—
380	C₂×C₄×C₆₇	—	4	2	no	—
381	C₂×C₄×C₆₇	—	4	2	no	—
382	C₂×C₄×C₆₇	—	8	4	no	—
383	C₂×C₄×C₆₇	—	8	4	no	—
384	C₂×C₄×C₆₇	—	8	4	no	—
385	C₂×C₄×C₆₇	—	8	2	no	—
386	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
387	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
390	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
394	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
395	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
396	C₈×C₆₇	—	2	1	no	—
397	C₈×C₆₇	—	2	1	no	—
398	C₈×C₆₇	—	2	4	no	—
399	C₈×C₆₇	—	2	1	no	—
400	C₈×C₆₇	—	2	1	no	—
401	C₂²×C₆₇	—	2	1	no	—
402	C₂²×C₆₇	—	2	1	no	—
403	C₂²×C₆₇	—	2	2	no	—
404	C₂²×C₆₇	—	4	1	no	—
405	C₂²×C₆₇	—	4	1	no	—
406	C₂²×C₆₇	—	4	1	no	—
407	C₂²×C₆₇	—	4	4	no	—
408	C₂²×C₆₇	—	4	1	no	—
409	C₂²×C₆₇	—	4	4	no	—
410	C₂²×C₆₇	—	4	1	no	—
411	C₂²×C₆₇	—	4	4	no	—
412	C₂²×C₆₇	—	16	4	no	—
413	C₂²×C₆₇	#548	1	2	yes	—
414	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
415	C₄×C₆₇	—	2	2	no	—
416	C₄×C₆₇	—	2	1	no	—
417	C₄×C₆₇	—	2	4	no	—
418	C₄×C₆₇	—	2	1	no	—
419	C₄×C₆₇	—	2	4	no	—
420	C₄×C₆₇	—	4	1	no	—
421	C₄×C₆₇	—	4	1	no	—
422	C₄×C₆₇	—	4	1	no	—
423	C₄×C₆₇	—	4	4	no	—
424	C₄×C₆₇	—	4	1	no	—
425	C₄×C₆₇	—	4	1	no	—
426	C₄×C₆₇	#548	1	2	yes	—
427	C₄×C₆₇	#576	1	2	yes	—
428	C₄×C₆₇	#577	1	2	yes	—
429	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
430	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
431	#61329	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
432	C₂×C₆₇	—	2	2	no	—
433	C₂×C₆₇	—	4	2	no	—
434	C₂×C₆₇	—	8	1	no	—
435	C₂×C₆₇	—	8	4	no	—
436	C₂×C₆₇	C₂×#548	1	1	yes	characteristic
437	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
438	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
439	#3508	C₂×C₆₇	1	1	yes	characteristic, complemented
440	#3503	C₂×C₆₇	1	1	yes	characteristic, complemented
441	#3375	C₂×C₆₇	1	2	yes	complemented
442	#3373	C₂×C₆₇	1	2	yes	complemented
443	#3368	C₂×C₆₇	1	2	yes	complemented
444	#3366	C₂×C₆₇	1	2	yes	complemented
445	#3365	C₂×C₆₇	1	2	yes	complemented
446	#3362	C₂×C₆₇	1	2	yes	complemented
447	#3361	C₂×C₆₇	1	2	yes	complemented
448	#3358	C₂×C₆₇	1	2	yes	complemented
449	#3136	C₂×C₆₇	1	2	yes	complemented
450	C₂×#486	C₂×C₆₇	1	1	yes	characteristic, complemented
451	#3081	C₂×C₆₇	1	2	yes	complemented
452	#3079	C₂×C₆₇	1	1	yes	characteristic, complemented
453	#3045	C₂×C₆₇	1	2	yes	complemented
454	#3038	C₂×C₆₇	1	1	yes	characteristic, complemented
455	#2960	C₂×C₆₇	1	1	yes	characteristic, complemented
456	#2946	C₂×C₆₇	1	2	yes	complemented
457	C₄×#135	C₂×C₆₇	1	1	yes	characteristic, complemented
458	C₆₇	#61329	1	1	yes	characteristic, direct product factor, Sylow
459	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	—
460	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
461	#559	C₂²×C₆₇	1	2	yes	—
462	#559	C₂²×C₆₇	1	2	yes	—
463	Q₈²	C₂²×C₆₇	1	2	yes	complemented
464	#557	C₂²×C₆₇	1	2	yes	complemented
465	#554	—	2	2	no	—
466	#554	C₂²×C₆₇	1	2	yes	complemented
467	#550	C₂²×C₆₇	1	2	yes	—
468	#550	C₂²×C₆₇	1	2	yes	—
469	D₄×Q₈	—	2	2	no	—
470	D₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
471	#546	—	2	2	no	—
472	#546	—	2	2	no	—
473	#544	—	2	2	no	—
474	#544	C₂²×C₆₇	1	2	yes	—
475	#540	—	2	2	no	—
476	#535	C₂²×C₆₇	1	2	yes	—
477	#533	—	2	1	no	—
478	#533	C₂²×C₆₇	1	1	yes	characteristic
479	#532	—	2	1	no	—
480	#532	—	2	1	no	—
481	C₂×C₄⋊Q₈	—	2	1	no	—
482	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
483	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
484	#520	C₂²×C₆₇	1	2	yes	—
485	#518	C₂²×C₆₇	1	2	yes	—
486	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
487	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
488	#490	C₂²×C₆₇	1	4	yes	complemented
489	#489	C₂²×C₆₇	1	4	yes	complemented
490	#488	C₂²×C₆₇	1	4	yes	complemented
491	#486	C₂²×C₆₇	1	2	yes	—
492	#486	C₂²×C₆₇	1	2	yes	—
493	#486	C₂²×C₆₇	1	2	yes	—
494	#486	C₂²×C₆₇	1	2	yes	—
495	#486	C₂²×C₆₇	1	4	yes	complemented
496	#478	C₂²×C₆₇	1	4	yes	complemented
497	#478	C₂²×C₆₇	1	4	yes	complemented
498	#477	C₂²×C₆₇	1	2	yes	complemented
499	#476	C₂²×C₆₇	1	2	yes	complemented
500	#476	C₂²×C₆₇	1	4	yes	complemented
501	#475	C₂²×C₆₇	1	2	yes	complemented
502	#474	C₂²×C₆₇	1	2	yes	complemented
503	#474	C₂²×C₆₇	1	4	yes	complemented
504	#464	C₂²×C₆₇	1	4	yes	complemented
505	#463	C₂²×C₆₇	1	4	yes	complemented
506	#460	C₂²×C₆₇	1	2	yes	—
507	#460	C₂²×C₆₇	1	2	yes	—
508	#460	C₂²×C₆₇	1	4	yes	complemented
509	#459	C₂²×C₆₇	1	2	yes	—
510	#459	C₂²×C₆₇	1	2	yes	—
511	#459	C₂²×C₆₇	1	4	yes	complemented
512	#446	C₂²×C₆₇	1	2	yes	complemented
513	#446	C₂²×C₆₇	1	2	yes	complemented
514	C₈×Q₈	C₂²×C₆₇	1	2	yes	complemented
515	C₈×Q₈	C₂²×C₆₇	1	2	yes	complemented
516	#442	C₂²×C₆₇	1	4	yes	complemented
517	#440	C₂²×C₆₇	1	4	yes	complemented
518	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
519	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
520	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
521	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
522	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
523	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
524	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
525	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
526	C₄×D₈	C₂²×C₆₇	1	4	yes	complemented
527	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
528	#428	C₂²×C₆₇	1	2	yes	—
529	#427	C₂²×C₆₇	1	1	yes	characteristic
530	#424	C₂²×C₆₇	1	2	yes	—
531	#423	C₂²×C₆₇	1	1	yes	characteristic
532	#418	C₂²×C₆₇	1	2	yes	—
533	#417	C₂²×C₆₇	1	2	yes	—
534	#416	C₂²×C₆₇	1	1	yes	characteristic
535	#416	C₂²×C₆₇	1	1	yes	characteristic
536	C₂×#102	C₂²×C₆₇	1	2	yes	—
537	C₂×#102	C₂²×C₆₇	1	2	yes	—
538	#405	C₂²×C₆₇	1	2	yes	—
539	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
540	C₂×#41	—	2	2	no	—
541	C₂×#41	—	2	2	no	—
542	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
543	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
544	C₂²×Q₈	—	2	2	no	—
545	C₂²×Q₈	—	2	1	no	—
546	C₂²×D₄	—	2	1	no	—
547	C₂²×D₄	—	2	1	no	—
548	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
549	AGL(1,ℤ/8)	—	2	8	no	—
550	#135	—	2	4	no	—
551	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
552	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
553	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
554	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
555	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
556	C₂×D₈	C₂³×C₆₇	1	4	yes	—
557	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
558	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
559	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
560	C₄⋊Q₈	—	2	2	no	—
561	C₄⋊Q₈	—	2	2	no	—
562	C₄⋊Q₈	—	2	2	no	—
563	C₄⋊Q₈	—	2	4	no	—
564	C₄⋊Q₈	—	2	1	no	—
565	C₄⋊Q₈	—	2	1	no	—
566	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
567	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
568	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
569	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
570	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
571	#127	—	2	1	no	—
572	#127	—	2	1	no	—
573	#127	C₂³×C₆₇	1	2	yes	—
574	#127	C₂³×C₆₇	1	2	yes	—
575	#127	C₂³×C₆₇	1	4	yes	—
576	#125	—	2	2	no	—
577	#125	—	2	4	no	—
578	#125	D₄×C₆₇	1	2	yes	—
579	#125	C₂³×C₆₇	1	4	yes	—
580	#124	—	2	2	no	—
581	#124	—	2	2	no	—
582	#124	C₂³×C₆₇	1	4	yes	—
583	#123	—	2	4	no	—
584	#123	—	2	4	no	—
585	C₂²⋊Q₈	—	2	2	no	—
586	C₂²⋊Q₈	—	2	2	no	—
587	C₂²⋊Q₈	—	2	4	no	—
588	C₂²⋊Q₈	—	2	4	no	—
589	C₂²⋊Q₈	—	2	4	no	—
590	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
591	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
592	#121	—	2	2	no	—
593	#121	—	2	2	no	—
594	#121	—	2	2	no	—
595	#121	—	2	2	no	—
596	#121	—	2	4	no	—
597	#121	—	2	4	no	—
598	#120	—	2	4	no	—
599	C₄×Q₈	—	2	2	no	—
600	C₄×Q₈	—	2	2	no	—
601	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
602	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
603	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
604	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
605	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
606	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
607	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	2	no	—
616	C₄×D₄	—	2	4	no	—
617	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
618	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
619	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
620	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
621	C₄×D₄	C₂³×C₆₇	1	4	yes	—
622	C₄×D₄	C₂³×C₆₇	1	4	yes	—
623	C₄×D₄	C₂³×C₆₇	1	4	yes	—
624	#117	—	2	2	no	—
625	#117	—	2	1	no	—
626	#117	—	2	1	no	—
627	#117	C₂³×C₆₇	1	1	yes	characteristic
628	#117	C₂³×C₆₇	1	1	yes	characteristic
629	#117	C₂³×C₆₇	1	2	yes	—
630	C₂×C₄⋊C₄	—	2	1	no	—
631	C₂×C₄⋊C₄	—	2	2	no	—
632	C₂×C₄⋊C₄	—	2	2	no	—
633	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
634	C₂×C₂²⋊C₄	—	2	4	no	—
635	C₂×C₄²	—	2	1	no	—
636	C₂×C₄²	—	2	1	no	—
637	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
638	#107	C₂³×C₆₇	1	1	yes	characteristic
639	#107	C₂³×C₆₇	1	1	yes	characteristic
640	#107	C₂³×C₆₇	1	4	yes	—
641	#106	C₂³×C₆₇	1	1	yes	characteristic
642	#106	C₂³×C₆₇	1	1	yes	characteristic
643	#106	C₂³×C₆₇	1	4	yes	—
644	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
645	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
646	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
647	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
648	#103	C₂³×C₆₇	1	1	yes	characteristic
649	#103	C₂³×C₆₇	1	1	yes	characteristic
650	#103	C₂³×C₆₇	1	1	yes	characteristic
651	#103	C₂³×C₆₇	1	1	yes	characteristic
652	#103	C₂³×C₆₇	1	4	yes	—
653	#102	C₂³×C₆₇	1	4	yes	—
654	#102	C₂³×C₆₇	1	4	yes	—
655	#102	C₂³×C₆₇	1	4	yes	—
656	#102	C₂³×C₆₇	1	4	yes	—
657	#102	C₂³×C₆₇	1	1	yes	characteristic
658	#102	C₂³×C₆₇	1	1	yes	characteristic
659	#102	C₂³×C₆₇	1	1	yes	characteristic
660	#102	C₂³×C₆₇	1	1	yes	characteristic
661	#102	C₂³×C₆₇	1	4	yes	—
662	#102	C₂³×C₆₇	1	4	yes	—
663	#102	C₂³×C₆₇	1	4	yes	—
664	#97	C₂³×C₆₇	1	4	yes	—
665	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
666	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
667	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
668	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
669	C₄×C₈	C₂³×C₆₇	1	4	yes	—
670	C₂⁴	—	2	2	no	—
671	#41	—	2	2	no	—
672	#41	—	2	2	no	—
673	#41	—	2	2	no	—
674	#41	—	8	4	no	—
675	#41	—	8	4	no	—
676	#41	#41×C₆₇	1	4	yes	complemented
677	C₂×Q₈	—	2	2	no	—
678	C₂×Q₈	—	2	4	no	—
679	C₂×Q₈	—	2	2	no	—
680	C₂×Q₈	—	8	2	no	—
681	C₂×Q₈	—	8	4	no	—
682	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
683	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
684	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
685	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	2	2	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	2	2	no	—
691	C₂×D₄	—	2	4	no	—
692	C₂×D₄	—	2	4	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	2	4	no	—
697	C₂×D₄	—	8	2	no	—
698	C₂×D₄	—	8	2	no	—
699	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
700	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
701	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
702	C₂²×C₄	—	2	1	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	1	no	—
707	C₂²×C₄	—	2	1	no	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	4	no	—
710	C₂²×C₄	—	2	4	no	—
711	C₂²×C₄	—	2	4	no	—
712	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
713	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
714	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
715	Q₁₆	—	2	2	no	—
716	SD₁₆	—	2	2	no	—
717	SD₁₆	—	2	8	no	—
718	SD₁₆	—	2	2	no	—
719	D₈	—	2	2	no	—
720	D₈	—	2	8	no	—
721	M₁₆	—	2	4	no	—
722	C₂×C₈	—	2	2	no	—
723	C₂×C₈	—	2	2	no	—
724	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
725	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
726	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
727	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
728	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	4	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	4	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	1	no	—
736	C₄⋊C₄	—	2	1	no	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	2	4	no	—
740	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
741	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
742	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
743	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
744	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
745	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
746	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
747	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
748	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
749	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
750	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
751	C₂²⋊C₄	—	2	1	no	—
752	C₂²⋊C₄	—	2	1	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	2	1	no	—
756	C₂²⋊C₄	—	2	1	no	—
757	C₂²⋊C₄	—	2	1	no	—
758	C₂²⋊C₄	—	2	1	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	4	no	—
761	C₂²⋊C₄	—	2	4	no	—
762	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
763	C₄²	—	2	1	no	—
764	C₄²	—	2	1	no	—
765	C₄²	—	2	1	no	—
766	C₄²	—	2	1	no	—
767	C₄²	—	2	1	no	—
768	C₄²	—	2	1	no	—
769	C₄²	—	2	4	no	—
770	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
771	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
772	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
773	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
774	C₄²	C₂⁴×C₆₇	1	4	yes	—
775	C₂³	—	2	1	no	—
776	C₂³	—	2	4	no	—
777	C₂³	—	2	1	no	—
778	C₂³	—	4	4	no	—
779	C₂³	—	8	2	no	—
780	C₂³	—	8	2	no	—
781	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
782	Q₈	—	2	4	no	—
783	Q₈	—	2	4	no	—
784	Q₈	—	2	1	no	—
785	Q₈	—	2	1	no	—
786	Q₈	—	2	1	no	—
787	Q₈	—	4	4	no	—
788	Q₈	—	8	2	no	—
789	Q₈	—	8	4	no	—
790	Q₈	C₂×#41×C₆₇	1	2	yes	—
791	D₄	—	2	4	no	—
792	D₄	—	2	4	no	—
793	D₄	—	2	1	no	—
794	D₄	—	2	1	no	—
795	D₄	—	2	4	no	—
796	D₄	—	2	1	no	—
797	D₄	—	4	2	no	—
798	D₄	—	4	4	no	—
799	D₄	—	4	4	no	—
800	D₄	—	4	4	no	—
801	D₄	—	8	2	no	—
802	D₄	—	8	2	no	—
803	D₄	—	8	4	no	—
804	D₄	—	8	4	no	—
805	D₄	C₂×#41×C₆₇	1	2	yes	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	4	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	4	no	—
816	C₂×C₄	—	4	2	no	—
817	C₂×C₄	—	4	2	no	—
818	C₂×C₄	—	4	2	no	—
819	C₂×C₄	—	4	2	no	—
820	C₂×C₄	—	4	2	no	—
821	C₂×C₄	—	8	4	no	—
822	C₂×C₄	—	8	4	no	—
823	C₂×C₄	—	8	4	no	—
824	C₂×C₄	—	8	2	no	—
825	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
826	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
827	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
828	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
829	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
830	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
831	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
832	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
833	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
834	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
835	C₈	—	2	1	no	—
836	C₈	—	2	1	no	—
837	C₈	—	2	4	no	—
838	C₈	—	2	1	no	—
839	C₈	—	2	1	no	—
840	C₂²	—	2	1	no	—
841	C₂²	—	2	1	no	—
842	C₂²	—	2	2	no	—
843	C₂²	—	4	1	no	—
844	C₂²	—	4	1	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	4	no	—
847	C₂²	—	4	1	no	—
848	C₂²	—	4	4	no	—
849	C₂²	—	4	1	no	—
850	C₂²	—	4	4	no	—
851	C₂²	—	16	4	no	—
852	C₂²	#548×C₆₇	1	2	yes	—
853	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
854	C₄	—	2	1	no	—
855	C₄	—	2	4	no	—
856	C₄	—	2	1	no	—
857	C₄	—	2	4	no	—
858	C₄	—	2	2	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	4	no	—
862	C₄	—	4	1	no	—
863	C₄	—	4	1	no	—
864	C₄	—	4	1	no	—
865	C₄	#548×C₆₇	1	2	yes	—
866	C₄	#576×C₆₇	1	2	yes	—
867	C₄	#577×C₆₇	1	2	yes	—
868	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
869	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
870	C₂	—	2	2	no	—
871	C₂	—	4	2	no	—
872	C₂	—	8	4	no	—
873	C₂	—	8	1	no	—
874	C₂	C₂×#548×C₆₇	1	1	yes	characteristic
875	C₂	C₂×#576×C₆₇	1	1	yes	characteristic
876	C₂	C₂×#577×C₆₇	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 ◁ #533×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3508	C₂	semidirect
2. C₆₇×#3503	C₂	semidirect
3. C₆₇×#3375	C₂	semidirect
4. C₆₇×#3373	C₂	semidirect
5. C₆₇×#3368	C₂	semidirect
6. C₆₇×#3366	C₂	semidirect
7. C₆₇×#3365	C₂	semidirect
8. C₆₇×#3362	C₂	semidirect
9. C₆₇×#3361	C₂	semidirect
10. C₆₇×#3358	C₂	semidirect
11. C₆₇×#3136	C₂	semidirect
12. C₂×#486×C₆₇	C₂	semidirect
13. C₆₇×#3081	C₂	semidirect
14. C₆₇×#3079	C₂	semidirect
15. C₆₇×#3045	C₂	semidirect
16. C₆₇×#3038	C₂	semidirect
17. C₆₇×#2960	C₂	semidirect
18. C₆₇×#2946	C₂	semidirect
19. C₄×#135×C₆₇	C₂	semidirect
24. Q₈²×C₆₇	C₂²	semidirect
25. #557×C₆₇	C₂²	semidirect
27. #554×C₆₇	C₂²	semidirect
31. D₄×Q₈×C₆₇	C₂²	semidirect
49. #490×C₆₇	C₂²	semidirect
50. #489×C₆₇	C₂²	semidirect
51. #488×C₆₇	C₂²	semidirect
56. #486×C₆₇	C₂²	semidirect
57. #478×C₆₇	C₂²	semidirect
58. #478×C₆₇	C₂²	semidirect
59. #477×C₆₇	C₂²	semidirect
60. #476×C₆₇	C₂²	semidirect
61. #476×C₆₇	C₂²	semidirect
62. #475×C₆₇	C₂²	semidirect
63. #474×C₆₇	C₂²	semidirect
64. #474×C₆₇	C₂²	semidirect
65. #464×C₆₇	C₂²	semidirect
66. #463×C₆₇	C₂²	semidirect
69. #460×C₆₇	C₂²	semidirect
72. #459×C₆₇	C₂²	semidirect
73. #446×C₆₇	C₂²	semidirect
74. #446×C₆₇	C₂²	semidirect
75. C₈×Q₈×C₆₇	C₂²	semidirect
76. C₈×Q₈×C₆₇	C₂²	semidirect
77. #442×C₆₇	C₂²	semidirect
78. #440×C₆₇	C₂²	semidirect
79. C₄×Q₁₆×C₆₇	C₂²	semidirect
80. C₄×Q₁₆×C₆₇	C₂²	semidirect
81. C₄×SD₁₆×C₆₇	C₂²	semidirect
82. C₄×SD₁₆×C₆₇	C₂²	semidirect
83. C₄×SD₁₆×C₆₇	C₂²	semidirect
84. C₄×SD₁₆×C₆₇	C₂²	semidirect
85. C₄×SD₁₆×C₆₇	C₂²	semidirect
86. C₄×D₈×C₆₇	C₂²	semidirect
87. C₄×D₈×C₆₇	C₂²	semidirect
88. C₄×D₈×C₆₇	C₂²	semidirect
237. #41×C₆₇	#41	semidirect
431. #61329	C₆₇	direct (N × H)
439. #3508	C₂×C₆₇	semidirect
440. #3503	C₂×C₆₇	semidirect
441. #3375	C₂×C₆₇	semidirect
442. #3373	C₂×C₆₇	semidirect
443. #3368	C₂×C₆₇	semidirect
444. #3366	C₂×C₆₇	semidirect
445. #3365	C₂×C₆₇	semidirect
446. #3362	C₂×C₆₇	semidirect
447. #3361	C₂×C₆₇	semidirect
448. #3358	C₂×C₆₇	semidirect
449. #3136	C₂×C₆₇	semidirect
450. C₂×#486	C₂×C₆₇	semidirect
451. #3081	C₂×C₆₇	semidirect
452. #3079	C₂×C₆₇	semidirect
453. #3045	C₂×C₆₇	semidirect
454. #3038	C₂×C₆₇	semidirect
455. #2960	C₂×C₆₇	semidirect
456. #2946	C₂×C₆₇	semidirect
457. C₄×#135	C₂×C₆₇	semidirect
458. C₆₇	#61329	direct (N × H)
463. Q₈²	C₂²×C₆₇	semidirect
464. #557	C₂²×C₆₇	semidirect
466. #554	C₂²×C₆₇	semidirect
470. D₄×Q₈	C₂²×C₆₇	semidirect
488. #490	C₂²×C₆₇	semidirect
489. #489	C₂²×C₆₇	semidirect
490. #488	C₂²×C₆₇	semidirect
495. #486	C₂²×C₆₇	semidirect
496. #478	C₂²×C₆₇	semidirect
497. #478	C₂²×C₆₇	semidirect
498. #477	C₂²×C₆₇	semidirect
499. #476	C₂²×C₆₇	semidirect
500. #476	C₂²×C₆₇	semidirect
501. #475	C₂²×C₆₇	semidirect
502. #474	C₂²×C₆₇	semidirect
503. #474	C₂²×C₆₇	semidirect
504. #464	C₂²×C₆₇	semidirect
505. #463	C₂²×C₆₇	semidirect
508. #460	C₂²×C₆₇	semidirect
511. #459	C₂²×C₆₇	semidirect
512. #446	C₂²×C₆₇	semidirect
513. #446	C₂²×C₆₇	semidirect
514. C₈×Q₈	C₂²×C₆₇	semidirect
515. C₈×Q₈	C₂²×C₆₇	semidirect
516. #442	C₂²×C₆₇	semidirect
517. #440	C₂²×C₆₇	semidirect
518. C₄×Q₁₆	C₂²×C₆₇	semidirect
519. C₄×Q₁₆	C₂²×C₆₇	semidirect
520. C₄×SD₁₆	C₂²×C₆₇	semidirect
521. C₄×SD₁₆	C₂²×C₆₇	semidirect
522. C₄×SD₁₆	C₂²×C₆₇	semidirect
523. C₄×SD₁₆	C₂²×C₆₇	semidirect
524. C₄×SD₁₆	C₂²×C₆₇	semidirect
525. C₄×D₈	C₂²×C₆₇	semidirect
526. C₄×D₈	C₂²×C₆₇	semidirect
527. C₄×D₈	C₂²×C₆₇	semidirect
676. #41	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3508	2
C₆₇×#3503	2
C₆₇×#3375	2
C₆₇×#3373	2
C₆₇×#3368	2
C₆₇×#3366	2
C₆₇×#3365	2
C₆₇×#3362	2
C₆₇×#3361	2
C₆₇×#3358	2
C₆₇×#3136	2
C₂×#486×C₆₇	2
C₆₇×#3081	2
C₆₇×#3079	2
C₆₇×#3045	2
C₆₇×#3038	2
C₆₇×#2960	2
C₆₇×#2946	2
C₄×#135×C₆₇	2
#61329	67

Subgroups — C67×#61329 #30740580

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61329 #30740580