Subgroups — C₆₇×#59829 #30739080

Order 17152.

2180 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#559×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#556×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2718	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2674	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2581	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2580	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2553	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2545	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2544	C₂	1	1	yes	maximal, characteristic
10	C₆₇×#2521	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2488	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2470	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2466	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2448	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2447	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2446	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2445	C₂	1	1	yes	maximal, characteristic
18	C₆₇×#2359	C₂	1	2	yes	maximal, complemented
19	C₆₇×#2351	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2349	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₄⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#124×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#124×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	#559×C₆₇	—	2	8	no	—
25	#556×C₆₇	—	2	8	no	—
26	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×#126×C₆₇	C₂²	1	2	yes	—
30	C₂×#126×C₆₇	C₂²	1	2	yes	—
31	C₂×#124×C₆₇	C₂²	1	2	yes	—
32	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×#123×C₆₇	C₂²	1	2	yes	—
37	C₂×#123×C₆₇	C₂²	1	2	yes	—
38	C₂×#123×C₆₇	C₂²	1	2	yes	—
39	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
51	C₂×#117×C₆₇	C₂²	1	2	yes	—
52	#400×C₆₇	C₂²	1	2	yes	—
53	#400×C₆₇	C₂²	1	2	yes	—
54	#399×C₆₇	C₂²	1	2	yes	—
55	#399×C₆₇	C₂²	1	2	yes	—
56	#398×C₆₇	C₂²	1	2	yes	—
57	#397×C₆₇	C₂²	1	2	yes	—
58	#397×C₆₇	C₂²	1	2	yes	—
59	#397×C₆₇	C₂²	1	2	yes	—
60	#396×C₆₇	C₂²	1	2	yes	—
61	#396×C₆₇	C₂²	1	2	yes	—
62	#395×C₆₇	C₂²	1	2	yes	—
63	#394×C₆₇	C₂²	1	2	yes	—
64	#394×C₆₇	C₂²	1	2	yes	—
65	#394×C₆₇	C₂²	1	2	yes	—
66	#394×C₆₇	C₂²	1	2	yes	—
67	#393×C₆₇	C₂²	1	2	yes	—
68	#391×C₆₇	C₂²	1	1	yes	characteristic
69	#391×C₆₇	C₂²	1	1	yes	characteristic
70	#391×C₆₇	C₂²	1	1	yes	characteristic
71	#391×C₆₇	C₂²	1	1	yes	characteristic
72	#391×C₆₇	C₂²	1	1	yes	characteristic
73	#391×C₆₇	C₂²	1	1	yes	characteristic
74	#390×C₆₇	C₂²	1	1	yes	characteristic
75	#390×C₆₇	C₂²	1	1	yes	characteristic
76	#390×C₆₇	C₂²	1	1	yes	characteristic
77	#390×C₆₇	C₂²	1	1	yes	characteristic
78	#389×C₆₇	C₂²	1	1	yes	characteristic
79	#389×C₆₇	C₂²	1	1	yes	characteristic
80	#389×C₆₇	C₂²	1	1	yes	characteristic
81	#389×C₆₇	C₂²	1	1	yes	characteristic
82	#389×C₆₇	C₂²	1	1	yes	characteristic
83	#389×C₆₇	C₂²	1	1	yes	characteristic
84	#389×C₆₇	C₂²	1	1	yes	characteristic
85	#389×C₆₇	C₂²	1	1	yes	characteristic
86	#389×C₆₇	C₂²	1	2	yes	—
87	#389×C₆₇	C₂²	1	2	yes	—
88	#388×C₆₇	C₂²	1	2	yes	—
89	#388×C₆₇	C₂²	1	2	yes	—
90	#388×C₆₇	C₂²	1	2	yes	—
91	#388×C₆₇	C₂²	1	2	yes	—
92	#388×C₆₇	C₂²	1	2	yes	—
93	#388×C₆₇	C₂²	1	2	yes	—
94	#388×C₆₇	C₂²	1	2	yes	—
95	#388×C₆₇	C₂²	1	2	yes	—
96	#387×C₆₇	C₂²	1	2	yes	—
97	#387×C₆₇	C₂²	1	2	yes	—
98	#387×C₆₇	C₂²	1	2	yes	—
99	#387×C₆₇	C₂²	1	2	yes	—
100	#386×C₆₇	C₂²	1	2	yes	—
101	#386×C₆₇	C₂²	1	2	yes	—
102	#386×C₆₇	C₂²	1	2	yes	—
103	#385×C₆₇	C₂²	1	2	yes	—
104	#385×C₆₇	C₂²	1	2	yes	—
105	#385×C₆₇	C₂²	1	2	yes	—
106	#385×C₆₇	C₂²	1	2	yes	—
107	#385×C₆₇	C₂²	1	2	yes	—
108	#384×C₆₇	C₂²	1	1	yes	characteristic
109	#382×C₆₇	C₂²	1	2	yes	—
110	#382×C₆₇	C₂²	1	1	yes	characteristic
111	#382×C₆₇	C₂²	1	1	yes	characteristic
112	#381×C₆₇	C₂²	1	2	yes	—
113	#380×C₆₇	C₂²	1	2	yes	—
114	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
115	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
117	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
118	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
122	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
123	C₂×#95×C₆₇	C₂²	1	2	yes	—
124	C₄³×C₆₇	C₂²	1	1	yes	characteristic
125	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
126	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
127	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
128	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
131	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
132	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
133	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
134	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
135	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
136	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
137	C₄⋊Q₈×C₆₇	—	2	4	no	—
138	C₄⋊Q₈×C₆₇	—	2	4	no	—
139	#127×C₆₇	—	2	4	no	—
140	#126×C₆₇	—	2	8	no	—
141	#126×C₆₇	—	2	8	no	—
142	#124×C₆₇	—	2	4	no	—
143	#124×C₆₇	—	2	4	no	—
144	#124×C₆₇	—	2	8	no	—
145	#124×C₆₇	—	2	4	no	—
146	#124×C₆₇	D₄	1	8	yes	—
147	#123×C₆₇	—	2	8	no	—
148	#123×C₆₇	—	2	8	no	—
149	#123×C₆₇	—	2	8	no	—
150	C₂²⋊Q₈×C₆₇	—	2	8	no	—
151	C₄×Q₈×C₆₇	—	2	4	no	—
152	C₄×Q₈×C₆₇	—	2	4	no	—
153	C₄×Q₈×C₆₇	—	2	4	no	—
154	C₄×Q₈×C₆₇	—	2	4	no	—
155	C₄×Q₈×C₆₇	—	2	4	no	—
156	C₄×Q₈×C₆₇	—	2	4	no	—
157	C₄×D₄×C₆₇	—	2	4	no	—
158	C₄×D₄×C₆₇	—	2	4	no	—
159	C₄×D₄×C₆₇	—	2	8	no	—
160	C₄×D₄×C₆₇	—	2	4	no	—
161	C₄×D₄×C₆₇	—	2	4	no	—
162	#117×C₆₇	—	2	8	no	—
163	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
191	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
211	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
212	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
213	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
215	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
219	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
226	#95×C₆₇	C₂³	1	1	yes	characteristic
227	#95×C₆₇	C₂³	1	2	yes	—
228	#95×C₆₇	C₂³	1	2	yes	—
229	#95×C₆₇	C₂³	1	2	yes	—
230	#95×C₆₇	C₂³	1	2	yes	—
231	#95×C₆₇	C₂³	1	2	yes	—
232	#95×C₆₇	C₂³	1	2	yes	—
233	#95×C₆₇	C₂³	1	2	yes	—
234	#95×C₆₇	C₂³	1	2	yes	—
235	#95×C₆₇	C₂³	1	2	yes	—
236	#95×C₆₇	C₂³	1	2	yes	—
237	#95×C₆₇	C₂³	1	1	yes	characteristic
238	#95×C₆₇	C₂³	1	1	yes	characteristic
239	#95×C₆₇	C₂³	1	1	yes	characteristic
240	#95×C₆₇	C₂³	1	1	yes	characteristic
241	#95×C₆₇	C₂³	1	1	yes	characteristic
242	#95×C₆₇	C₂³	1	1	yes	characteristic
243	#95×C₆₇	C₂³	1	1	yes	characteristic
244	#95×C₆₇	C₂³	1	2	yes	—
245	#95×C₆₇	C₂³	1	2	yes	—
246	#95×C₆₇	C₂³	1	2	yes	—
247	#95×C₆₇	C₂³	1	2	yes	—
248	#95×C₆₇	C₂³	1	2	yes	—
249	#95×C₆₇	C₂³	1	2	yes	—
250	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
251	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
252	C₂×Q₈×C₆₇	—	2	2	no	—
253	C₂×Q₈×C₆₇	—	2	2	no	—
254	C₂×Q₈×C₆₇	—	2	2	no	—
255	C₂×Q₈×C₆₇	—	2	2	no	—
256	C₂×Q₈×C₆₇	—	2	2	no	—
257	C₂×Q₈×C₆₇	—	2	2	no	—
258	C₂×Q₈×C₆₇	—	2	2	no	—
259	C₂×Q₈×C₆₇	—	2	2	no	—
260	C₂×Q₈×C₆₇	—	2	2	no	—
261	C₂×Q₈×C₆₇	—	4	1	no	—
262	C₂×Q₈×C₆₇	—	4	1	no	—
263	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	—
264	C₂×D₄×C₆₇	—	2	4	no	—
265	C₂×D₄×C₆₇	—	2	4	no	—
266	C₂×D₄×C₆₇	—	2	2	no	—
267	C₂×D₄×C₆₇	—	2	2	no	—
268	C₂×D₄×C₆₇	—	2	4	no	—
269	C₂×D₄×C₆₇	—	2	2	no	—
270	C₂×D₄×C₆₇	—	2	2	no	—
271	C₂×D₄×C₆₇	—	2	2	no	—
272	C₂×D₄×C₆₇	—	4	2	no	—
273	C₂×D₄×C₆₇	—	4	2	no	—
274	C₂×D₄×C₆₇	—	4	2	no	—
275	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
276	C₂²×C₄×C₆₇	—	2	4	no	—
277	C₂²×C₄×C₆₇	—	2	4	no	—
278	C₂²×C₄×C₆₇	—	2	4	no	—
279	C₂²×C₄×C₆₇	—	2	4	no	—
280	C₂²×C₄×C₆₇	—	2	4	no	—
281	C₂²×C₄×C₆₇	—	4	2	no	—
282	C₂²×C₄×C₆₇	—	4	2	no	—
283	C₂²×C₄×C₆₇	—	4	2	no	—
284	C₂²×C₄×C₆₇	—	4	2	no	—
285	C₂²×C₄×C₆₇	—	4	2	no	—
286	C₂²×C₄×C₆₇	—	4	2	no	—
287	C₂²×C₄×C₆₇	—	4	2	no	—
288	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
309	C₄⋊C₄×C₆₇	—	2	2	no	—
310	C₄⋊C₄×C₆₇	—	2	4	no	—
311	C₄⋊C₄×C₆₇	—	2	2	no	—
312	C₄⋊C₄×C₆₇	—	2	2	no	—
313	C₄⋊C₄×C₆₇	—	2	2	no	—
314	C₄⋊C₄×C₆₇	—	2	4	no	—
315	C₄⋊C₄×C₆₇	—	2	4	no	—
316	C₄⋊C₄×C₆₇	—	2	2	no	—
317	C₄⋊C₄×C₆₇	—	2	4	no	—
318	C₄⋊C₄×C₆₇	—	2	2	no	—
319	C₄⋊C₄×C₆₇	—	2	2	no	—
320	C₄⋊C₄×C₆₇	—	2	2	no	—
321	C₄⋊C₄×C₆₇	—	2	4	no	—
322	C₄⋊C₄×C₆₇	—	2	2	no	—
323	C₄⋊C₄×C₆₇	—	2	4	no	—
324	C₄⋊C₄×C₆₇	—	2	2	no	—
325	C₄⋊C₄×C₆₇	—	2	4	no	—
326	C₄⋊C₄×C₆₇	—	2	2	no	—
327	C₄⋊C₄×C₆₇	—	2	2	no	—
328	C₄⋊C₄×C₆₇	—	2	2	no	—
329	C₄⋊C₄×C₆₇	—	4	1	no	—
330	C₄⋊C₄×C₆₇	—	4	1	no	—
331	C₄⋊C₄×C₆₇	—	4	1	no	—
332	C₄⋊C₄×C₆₇	—	4	1	no	—
333	C₄⋊C₄×C₆₇	—	4	2	no	—
334	C₄⋊C₄×C₆₇	—	4	2	no	—
335	C₄⋊C₄×C₆₇	—	4	2	no	—
336	C₄⋊C₄×C₆₇	#41	1	4	yes	—
337	C₂²⋊C₄×C₆₇	—	2	4	no	—
338	C₂²⋊C₄×C₆₇	—	2	4	no	—
339	C₂²⋊C₄×C₆₇	—	2	4	no	—
340	C₂²⋊C₄×C₆₇	—	2	4	no	—
341	C₂²⋊C₄×C₆₇	—	2	4	no	—
342	C₂²⋊C₄×C₆₇	—	2	4	no	—
343	C₂²⋊C₄×C₆₇	—	2	4	no	—
344	C₂²⋊C₄×C₆₇	—	2	4	no	—
345	C₂²⋊C₄×C₆₇	—	2	4	no	—
346	C₂²⋊C₄×C₆₇	—	2	4	no	—
347	C₂²⋊C₄×C₆₇	—	2	4	no	—
348	C₂²⋊C₄×C₆₇	—	2	4	no	—
349	C₂²⋊C₄×C₆₇	—	2	4	no	—
350	C₂²⋊C₄×C₆₇	—	4	2	no	—
351	C₂²⋊C₄×C₆₇	—	4	2	no	—
352	C₂²⋊C₄×C₆₇	—	4	2	no	—
353	C₂²⋊C₄×C₆₇	—	4	2	no	—
354	C₂²⋊C₄×C₆₇	—	4	2	no	—
355	C₂²⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
356	C₂²⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
357	C₄²×C₆₇	—	2	4	no	—
358	C₄²×C₆₇	—	2	4	no	—
359	C₄²×C₆₇	—	2	4	no	—
360	C₄²×C₆₇	—	2	2	no	—
361	C₄²×C₆₇	—	2	2	no	—
362	C₄²×C₆₇	—	2	2	no	—
363	C₄²×C₆₇	—	2	2	no	—
364	C₄²×C₆₇	—	2	4	no	—
365	C₄²×C₆₇	—	2	2	no	—
366	C₄²×C₆₇	—	2	2	no	—
367	C₄²×C₆₇	—	4	1	no	—
368	C₄²×C₆₇	—	4	1	no	—
369	C₄²×C₆₇	—	4	1	no	—
370	C₄²×C₆₇	C₂×D₄	1	4	yes	—
371	C₄²×C₆₇	#41	1	4	yes	—
372	C₂³×C₆₇	—	2	2	no	—
373	C₂³×C₆₇	—	2	2	no	—
374	C₂³×C₆₇	—	2	2	no	—
375	C₂³×C₆₇	—	2	2	no	—
376	C₂³×C₆₇	—	2	2	no	—
377	C₂³×C₆₇	—	2	2	no	—
378	C₂³×C₆₇	—	2	2	no	—
379	C₂³×C₆₇	—	2	2	no	—
380	C₂³×C₆₇	—	2	2	no	—
381	C₂³×C₆₇	—	2	2	no	—
382	C₂³×C₆₇	—	2	2	no	—
383	C₂³×C₆₇	—	2	2	no	—
384	C₂³×C₆₇	—	2	2	no	—
385	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
386	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
387	Q₈×C₆₇	—	2	8	no	—
388	Q₈×C₆₇	—	4	4	no	—
389	Q₈×C₆₇	—	4	4	no	—
390	Q₈×C₆₇	—	4	4	no	—
391	D₄×C₆₇	—	2	8	no	—
392	D₄×C₆₇	—	4	8	no	—
393	D₄×C₆₇	—	4	4	no	—
394	D₄×C₆₇	—	8	4	no	—
395	C₂×C₄×C₆₇	—	2	1	no	—
396	C₂×C₄×C₆₇	—	2	1	no	—
397	C₂×C₄×C₆₇	—	2	1	no	—
398	C₂×C₄×C₆₇	—	2	2	no	—
399	C₂×C₄×C₆₇	—	2	1	no	—
400	C₂×C₄×C₆₇	—	2	1	no	—
401	C₂×C₄×C₆₇	—	2	2	no	—
402	C₂×C₄×C₆₇	—	2	1	no	—
403	C₂×C₄×C₆₇	—	2	1	no	—
404	C₂×C₄×C₆₇	—	2	1	no	—
405	C₂×C₄×C₆₇	—	2	1	no	—
406	C₂×C₄×C₆₇	—	2	1	no	—
407	C₂×C₄×C₆₇	—	2	1	no	—
408	C₂×C₄×C₆₇	—	2	1	no	—
409	C₂×C₄×C₆₇	—	2	1	no	—
410	C₂×C₄×C₆₇	—	2	1	no	—
411	C₂×C₄×C₆₇	—	2	1	no	—
412	C₂×C₄×C₆₇	—	2	2	no	—
413	C₂×C₄×C₆₇	—	2	1	no	—
414	C₂×C₄×C₆₇	—	2	1	no	—
415	C₂×C₄×C₆₇	—	2	2	no	—
416	C₂×C₄×C₆₇	—	2	1	no	—
417	C₂×C₄×C₆₇	—	2	2	no	—
418	C₂×C₄×C₆₇	—	2	1	no	—
419	C₂×C₄×C₆₇	—	2	1	no	—
420	C₂×C₄×C₆₇	—	2	2	no	—
421	C₂×C₄×C₆₇	—	2	2	no	—
422	C₂×C₄×C₆₇	—	2	2	no	—
423	C₂×C₄×C₆₇	—	2	2	no	—
424	C₂×C₄×C₆₇	—	2	2	no	—
425	C₂×C₄×C₆₇	—	2	1	no	—
426	C₂×C₄×C₆₇	—	2	1	no	—
427	C₂×C₄×C₆₇	—	2	1	no	—
428	C₂×C₄×C₆₇	—	2	2	no	—
429	C₂×C₄×C₆₇	—	2	1	no	—
430	C₂×C₄×C₆₇	—	2	1	no	—
431	C₂×C₄×C₆₇	—	2	2	no	—
432	C₂×C₄×C₆₇	—	2	1	no	—
433	C₂×C₄×C₆₇	—	2	1	no	—
434	C₂×C₄×C₆₇	—	2	1	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	1	no	—
441	C₂×C₄×C₆₇	—	2	2	no	—
442	C₂×C₄×C₆₇	—	2	1	no	—
443	C₂×C₄×C₆₇	—	2	2	no	—
444	C₂×C₄×C₆₇	—	2	1	no	—
445	C₂×C₄×C₆₇	—	2	1	no	—
446	C₂×C₄×C₆₇	—	2	1	no	—
447	C₂×C₄×C₆₇	—	4	8	no	—
448	C₂×C₄×C₆₇	—	8	4	no	—
449	C₂×C₄×C₆₇	—	8	4	no	—
450	C₂×C₄×C₆₇	—	8	4	no	—
451	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
452	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
453	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
454	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
455	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
456	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
457	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
458	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
459	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
460	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
461	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
462	C₂²×C₆₇	—	2	4	no	—
463	C₂²×C₆₇	—	2	4	no	—
464	C₂²×C₆₇	—	2	4	no	—
465	C₂²×C₆₇	—	4	2	no	—
466	C₂²×C₆₇	—	4	2	no	—
467	C₂²×C₆₇	—	4	2	no	—
468	C₂²×C₆₇	—	4	2	no	—
469	C₂²×C₆₇	—	4	2	no	—
470	C₂²×C₆₇	—	4	2	no	—
471	C₂²×C₆₇	—	4	2	no	—
472	C₂²×C₆₇	—	4	2	no	—
473	C₂²×C₆₇	—	4	2	no	—
474	C₂²×C₆₇	—	4	2	no	—
475	C₂²×C₆₇	—	4	2	no	—
476	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
477	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
478	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
479	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
480	C₂²×C₆₇	#585	1	1	yes	characteristic
481	C₂²×C₆₇	#585	1	1	yes	characteristic
482	C₂²×C₆₇	#585	1	1	yes	characteristic
483	C₄×C₆₇	—	2	4	no	—
484	C₄×C₆₇	—	2	2	no	—
485	C₄×C₆₇	—	2	2	no	—
486	C₄×C₆₇	—	2	2	no	—
487	C₄×C₆₇	—	2	2	no	—
488	C₄×C₆₇	—	2	2	no	—
489	C₄×C₆₇	—	2	2	no	—
490	C₄×C₆₇	—	2	2	no	—
491	C₄×C₆₇	—	4	2	no	—
492	C₄×C₆₇	—	4	2	no	—
493	C₄×C₆₇	—	4	1	no	—
494	C₄×C₆₇	—	4	1	no	—
495	C₄×C₆₇	—	4	2	no	—
496	C₄×C₆₇	—	4	1	no	—
497	C₄×C₆₇	—	4	1	no	—
498	C₄×C₆₇	—	4	2	no	—
499	C₄×C₆₇	—	4	1	no	—
500	C₄×C₆₇	—	4	1	no	—
501	C₄×C₆₇	—	4	2	no	—
502	C₄×C₆₇	—	4	1	no	—
503	C₄×C₆₇	#547	1	4	yes	—
504	#59829	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
505	C₂×C₆₇	—	4	4	no	—
506	C₂×C₆₇	—	8	2	no	—
507	C₂×C₆₇	C₂×#547	1	1	yes	characteristic
508	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
509	C₂×C₆₇	#3480	1	1	yes	characteristic
510	C₂×C₆₇	#3500	1	1	yes	characteristic
511	C₂×C₆₇	#3507	1	1	yes	characteristic
512	C₂×C₆₇	#3510	1	1	yes	characteristic
513	C₂×C₆₇	#3557	1	1	yes	characteristic
514	C₂×#559	C₂×C₆₇	1	1	yes	characteristic
515	C₂×#556	C₂×C₆₇	1	1	yes	characteristic, complemented
516	#2718	C₂×C₆₇	1	2	yes	complemented
517	#2674	C₂×C₆₇	1	2	yes	complemented
518	#2581	C₂×C₆₇	1	1	yes	characteristic, complemented
519	#2580	C₂×C₆₇	1	1	yes	characteristic, complemented
520	#2553	C₂×C₆₇	1	2	yes	complemented
521	#2545	C₂×C₆₇	1	1	yes	characteristic, complemented
522	#2544	C₂×C₆₇	1	1	yes	characteristic
523	#2521	C₂×C₆₇	1	2	yes	complemented
524	#2488	C₂×C₆₇	1	2	yes	complemented
525	#2470	C₂×C₆₇	1	2	yes	complemented
526	#2466	C₂×C₆₇	1	2	yes	complemented
527	#2448	C₂×C₆₇	1	1	yes	characteristic, complemented
528	#2447	C₂×C₆₇	1	1	yes	characteristic, complemented
529	#2446	C₂×C₆₇	1	1	yes	characteristic, complemented
530	#2445	C₂×C₆₇	1	1	yes	characteristic
531	#2359	C₂×C₆₇	1	2	yes	complemented
532	#2351	C₂×C₆₇	1	1	yes	characteristic, complemented
533	#2349	C₂×C₆₇	1	1	yes	characteristic, complemented
534	C₄×C₄⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
535	C₄×#124	C₂×C₆₇	1	1	yes	characteristic, complemented
536	C₄×#124	C₂×C₆₇	1	1	yes	characteristic, complemented
537	C₆₇	#59829	1	1	yes	characteristic, direct product factor, Sylow
538	#559	—	2	8	no	—
539	#556	—	2	8	no	—
540	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
541	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
542	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
543	C₂×#126	C₂²×C₆₇	1	2	yes	—
544	C₂×#126	C₂²×C₆₇	1	2	yes	—
545	C₂×#124	C₂²×C₆₇	1	2	yes	—
546	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
547	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
548	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
549	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
550	C₂×#123	C₂²×C₆₇	1	2	yes	—
551	C₂×#123	C₂²×C₆₇	1	2	yes	—
552	C₂×#123	C₂²×C₆₇	1	2	yes	—
553	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
554	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
555	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
556	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
557	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
558	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
559	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
560	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
561	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
562	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
563	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
564	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
565	C₂×#117	C₂²×C₆₇	1	2	yes	—
566	#400	C₂²×C₆₇	1	2	yes	—
567	#400	C₂²×C₆₇	1	2	yes	—
568	#399	C₂²×C₆₇	1	2	yes	—
569	#399	C₂²×C₆₇	1	2	yes	—
570	#398	C₂²×C₆₇	1	2	yes	—
571	#397	C₂²×C₆₇	1	2	yes	—
572	#397	C₂²×C₆₇	1	2	yes	—
573	#397	C₂²×C₆₇	1	2	yes	—
574	#396	C₂²×C₆₇	1	2	yes	—
575	#396	C₂²×C₆₇	1	2	yes	—
576	#395	C₂²×C₆₇	1	2	yes	—
577	#394	C₂²×C₆₇	1	2	yes	—
578	#394	C₂²×C₆₇	1	2	yes	—
579	#394	C₂²×C₆₇	1	2	yes	—
580	#394	C₂²×C₆₇	1	2	yes	—
581	#393	C₂²×C₆₇	1	2	yes	—
582	#391	C₂²×C₆₇	1	1	yes	characteristic
583	#391	C₂²×C₆₇	1	1	yes	characteristic
584	#391	C₂²×C₆₇	1	1	yes	characteristic
585	#391	C₂²×C₆₇	1	1	yes	characteristic
586	#391	C₂²×C₆₇	1	1	yes	characteristic
587	#391	C₂²×C₆₇	1	1	yes	characteristic
588	#390	C₂²×C₆₇	1	1	yes	characteristic
589	#390	C₂²×C₆₇	1	1	yes	characteristic
590	#390	C₂²×C₆₇	1	1	yes	characteristic
591	#390	C₂²×C₆₇	1	1	yes	characteristic
592	#389	C₂²×C₆₇	1	1	yes	characteristic
593	#389	C₂²×C₆₇	1	1	yes	characteristic
594	#389	C₂²×C₆₇	1	1	yes	characteristic
595	#389	C₂²×C₆₇	1	1	yes	characteristic
596	#389	C₂²×C₆₇	1	1	yes	characteristic
597	#389	C₂²×C₆₇	1	1	yes	characteristic
598	#389	C₂²×C₆₇	1	1	yes	characteristic
599	#389	C₂²×C₆₇	1	1	yes	characteristic
600	#389	C₂²×C₆₇	1	2	yes	—
601	#389	C₂²×C₆₇	1	2	yes	—
602	#388	C₂²×C₆₇	1	2	yes	—
603	#388	C₂²×C₆₇	1	2	yes	—
604	#388	C₂²×C₆₇	1	2	yes	—
605	#388	C₂²×C₆₇	1	2	yes	—
606	#388	C₂²×C₆₇	1	2	yes	—
607	#388	C₂²×C₆₇	1	2	yes	—
608	#388	C₂²×C₆₇	1	2	yes	—
609	#388	C₂²×C₆₇	1	2	yes	—
610	#387	C₂²×C₆₇	1	2	yes	—
611	#387	C₂²×C₆₇	1	2	yes	—
612	#387	C₂²×C₆₇	1	2	yes	—
613	#387	C₂²×C₆₇	1	2	yes	—
614	#386	C₂²×C₆₇	1	2	yes	—
615	#386	C₂²×C₆₇	1	2	yes	—
616	#386	C₂²×C₆₇	1	2	yes	—
617	#385	C₂²×C₆₇	1	2	yes	—
618	#385	C₂²×C₆₇	1	2	yes	—
619	#385	C₂²×C₆₇	1	2	yes	—
620	#385	C₂²×C₆₇	1	2	yes	—
621	#385	C₂²×C₆₇	1	2	yes	—
622	#384	C₂²×C₆₇	1	1	yes	characteristic
623	#382	C₂²×C₆₇	1	1	yes	characteristic
624	#382	C₂²×C₆₇	1	1	yes	characteristic
625	#382	C₂²×C₆₇	1	2	yes	—
626	#381	C₂²×C₆₇	1	2	yes	—
627	#380	C₂²×C₆₇	1	2	yes	—
628	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
629	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
630	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
631	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
632	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
633	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
634	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
635	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
636	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
637	C₂×#95	C₂²×C₆₇	1	2	yes	—
638	C₄³	C₂²×C₆₇	1	1	yes	characteristic
639	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
640	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
641	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
642	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
643	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
644	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
645	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
646	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
647	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
648	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
649	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
650	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
651	C₄⋊Q₈	—	2	4	no	—
652	C₄⋊Q₈	—	2	4	no	—
653	#127	—	2	4	no	—
654	#126	—	2	8	no	—
655	#126	—	2	8	no	—
656	#124	—	2	4	no	—
657	#124	—	2	4	no	—
658	#124	—	2	8	no	—
659	#124	—	2	4	no	—
660	#124	D₄×C₆₇	1	8	yes	—
661	#123	—	2	8	no	—
662	#123	—	2	8	no	—
663	#123	—	2	8	no	—
664	C₂²⋊Q₈	—	2	8	no	—
665	C₄×Q₈	—	2	4	no	—
666	C₄×Q₈	—	2	4	no	—
667	C₄×Q₈	—	2	4	no	—
668	C₄×Q₈	—	2	4	no	—
669	C₄×Q₈	—	2	4	no	—
670	C₄×Q₈	—	2	4	no	—
671	C₄×D₄	—	2	4	no	—
672	C₄×D₄	—	2	4	no	—
673	C₄×D₄	—	2	8	no	—
674	C₄×D₄	—	2	4	no	—
675	C₄×D₄	—	2	4	no	—
676	#117	—	2	8	no	—
677	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
678	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
679	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
680	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
681	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
682	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
683	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
684	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
685	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
686	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
687	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
688	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
689	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
690	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
691	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
692	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
693	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
694	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
695	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
696	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
697	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
698	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
699	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
700	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
701	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
702	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
703	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
704	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
705	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
706	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
707	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
708	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
709	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
710	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
711	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
712	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
713	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
714	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
715	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
716	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
717	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
718	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
719	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
720	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
721	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
722	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
723	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
724	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
725	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
726	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
727	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
728	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
729	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
730	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
731	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
732	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
733	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
734	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
735	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
736	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
737	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
738	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
739	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
740	#95	C₂³×C₆₇	1	1	yes	characteristic
741	#95	C₂³×C₆₇	1	2	yes	—
742	#95	C₂³×C₆₇	1	2	yes	—
743	#95	C₂³×C₆₇	1	2	yes	—
744	#95	C₂³×C₆₇	1	2	yes	—
745	#95	C₂³×C₆₇	1	2	yes	—
746	#95	C₂³×C₆₇	1	2	yes	—
747	#95	C₂³×C₆₇	1	2	yes	—
748	#95	C₂³×C₆₇	1	2	yes	—
749	#95	C₂³×C₆₇	1	2	yes	—
750	#95	C₂³×C₆₇	1	2	yes	—
751	#95	C₂³×C₆₇	1	1	yes	characteristic
752	#95	C₂³×C₆₇	1	1	yes	characteristic
753	#95	C₂³×C₆₇	1	1	yes	characteristic
754	#95	C₂³×C₆₇	1	1	yes	characteristic
755	#95	C₂³×C₆₇	1	1	yes	characteristic
756	#95	C₂³×C₆₇	1	1	yes	characteristic
757	#95	C₂³×C₆₇	1	1	yes	characteristic
758	#95	C₂³×C₆₇	1	2	yes	—
759	#95	C₂³×C₆₇	1	2	yes	—
760	#95	C₂³×C₆₇	1	2	yes	—
761	#95	C₂³×C₆₇	1	2	yes	—
762	#95	C₂³×C₆₇	1	2	yes	—
763	#95	C₂³×C₆₇	1	2	yes	—
764	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
765	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
766	C₂×Q₈	—	2	2	no	—
767	C₂×Q₈	—	2	2	no	—
768	C₂×Q₈	—	2	2	no	—
769	C₂×Q₈	—	2	2	no	—
770	C₂×Q₈	—	2	2	no	—
771	C₂×Q₈	—	2	2	no	—
772	C₂×Q₈	—	2	2	no	—
773	C₂×Q₈	—	2	2	no	—
774	C₂×Q₈	—	2	2	no	—
775	C₂×Q₈	—	4	1	no	—
776	C₂×Q₈	—	4	1	no	—
777	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	—
778	C₂×D₄	—	2	4	no	—
779	C₂×D₄	—	2	4	no	—
780	C₂×D₄	—	2	2	no	—
781	C₂×D₄	—	2	2	no	—
782	C₂×D₄	—	2	4	no	—
783	C₂×D₄	—	2	2	no	—
784	C₂×D₄	—	2	2	no	—
785	C₂×D₄	—	2	2	no	—
786	C₂×D₄	—	4	2	no	—
787	C₂×D₄	—	4	2	no	—
788	C₂×D₄	—	4	2	no	—
789	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
790	C₂²×C₄	—	2	4	no	—
791	C₂²×C₄	—	2	4	no	—
792	C₂²×C₄	—	2	4	no	—
793	C₂²×C₄	—	2	4	no	—
794	C₂²×C₄	—	2	4	no	—
795	C₂²×C₄	—	4	2	no	—
796	C₂²×C₄	—	4	2	no	—
797	C₂²×C₄	—	4	2	no	—
798	C₂²×C₄	—	4	2	no	—
799	C₂²×C₄	—	4	2	no	—
800	C₂²×C₄	—	4	2	no	—
801	C₂²×C₄	—	4	2	no	—
802	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
803	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
804	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
805	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
806	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
807	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
808	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
809	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
810	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
811	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
812	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
813	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
814	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
815	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
816	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
817	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
818	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
819	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
820	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
821	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
822	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	4	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	4	no	—
829	C₄⋊C₄	—	2	4	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	4	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	2	4	no	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	4	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	4	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	4	1	no	—
844	C₄⋊C₄	—	4	1	no	—
845	C₄⋊C₄	—	4	1	no	—
846	C₄⋊C₄	—	4	1	no	—
847	C₄⋊C₄	—	4	2	no	—
848	C₄⋊C₄	—	4	2	no	—
849	C₄⋊C₄	—	4	2	no	—
850	C₄⋊C₄	#41×C₆₇	1	4	yes	—
851	C₂²⋊C₄	—	2	4	no	—
852	C₂²⋊C₄	—	2	4	no	—
853	C₂²⋊C₄	—	2	4	no	—
854	C₂²⋊C₄	—	2	4	no	—
855	C₂²⋊C₄	—	2	4	no	—
856	C₂²⋊C₄	—	2	4	no	—
857	C₂²⋊C₄	—	2	4	no	—
858	C₂²⋊C₄	—	2	4	no	—
859	C₂²⋊C₄	—	2	4	no	—
860	C₂²⋊C₄	—	2	4	no	—
861	C₂²⋊C₄	—	2	4	no	—
862	C₂²⋊C₄	—	2	4	no	—
863	C₂²⋊C₄	—	2	4	no	—
864	C₂²⋊C₄	—	4	2	no	—
865	C₂²⋊C₄	—	4	2	no	—
866	C₂²⋊C₄	—	4	2	no	—
867	C₂²⋊C₄	—	4	2	no	—
868	C₂²⋊C₄	—	4	2	no	—
869	C₂²⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
870	C₂²⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
871	C₄²	—	2	4	no	—
872	C₄²	—	2	4	no	—
873	C₄²	—	2	4	no	—
874	C₄²	—	2	2	no	—
875	C₄²	—	2	2	no	—
876	C₄²	—	2	2	no	—
877	C₄²	—	2	2	no	—
878	C₄²	—	2	4	no	—
879	C₄²	—	2	2	no	—
880	C₄²	—	2	2	no	—
881	C₄²	—	4	1	no	—
882	C₄²	—	4	1	no	—
883	C₄²	—	4	1	no	—
884	C₄²	C₂×D₄×C₆₇	1	4	yes	—
885	C₄²	#41×C₆₇	1	4	yes	—
886	C₂³	—	2	2	no	—
887	C₂³	—	2	2	no	—
888	C₂³	—	2	2	no	—
889	C₂³	—	2	2	no	—
890	C₂³	—	2	2	no	—
891	C₂³	—	2	2	no	—
892	C₂³	—	2	2	no	—
893	C₂³	—	2	2	no	—
894	C₂³	—	2	2	no	—
895	C₂³	—	2	2	no	—
896	C₂³	—	2	2	no	—
897	C₂³	—	2	2	no	—
898	C₂³	—	2	2	no	—
899	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
900	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
901	Q₈	—	2	8	no	—
902	Q₈	—	4	4	no	—
903	Q₈	—	4	4	no	—
904	Q₈	—	4	4	no	—
905	D₄	—	2	8	no	—
906	D₄	—	4	8	no	—
907	D₄	—	4	4	no	—
908	D₄	—	8	4	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	4	8	no	—
962	C₂×C₄	—	8	4	no	—
963	C₂×C₄	—	8	4	no	—
964	C₂×C₄	—	8	4	no	—
965	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
966	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
967	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
968	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
969	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
970	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
971	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
972	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
973	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
974	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
975	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
976	C₂²	—	2	4	no	—
977	C₂²	—	2	4	no	—
978	C₂²	—	2	4	no	—
979	C₂²	—	4	2	no	—
980	C₂²	—	4	2	no	—
981	C₂²	—	4	2	no	—
982	C₂²	—	4	2	no	—
983	C₂²	—	4	2	no	—
984	C₂²	—	4	2	no	—
985	C₂²	—	4	2	no	—
986	C₂²	—	4	2	no	—
987	C₂²	—	4	2	no	—
988	C₂²	—	4	2	no	—
989	C₂²	—	4	2	no	—
990	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
991	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
992	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
993	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
994	C₂²	#585×C₆₇	1	1	yes	characteristic
995	C₂²	#585×C₆₇	1	1	yes	characteristic
996	C₂²	#585×C₆₇	1	1	yes	characteristic
997	C₄	—	2	4	no	—
998	C₄	—	2	2	no	—
999	C₄	—	2	2	no	—
1000	C₄	—	2	2	no	—
1001	C₄	—	2	2	no	—
1002	C₄	—	2	2	no	—
1003	C₄	—	2	2	no	—
1004	C₄	—	2	2	no	—
1005	C₄	—	4	1	no	—
1006	C₄	—	4	2	no	—
1007	C₄	—	4	2	no	—
1008	C₄	—	4	1	no	—
1009	C₄	—	4	1	no	—
1010	C₄	—	4	2	no	—
1011	C₄	—	4	2	no	—
1012	C₄	—	4	1	no	—
1013	C₄	—	4	1	no	—
1014	C₄	—	4	1	no	—
1015	C₄	—	4	1	no	—
1016	C₄	—	4	2	no	—
1017	C₄	#547×C₆₇	1	4	yes	—
1018	C₂	—	4	4	no	—
1019	C₂	—	8	2	no	—
1020	C₂	C₂×#547×C₆₇	1	1	yes	characteristic
1021	C₂	D₄×#41×C₆₇	1	1	yes	characteristic
1022	C₂	C₆₇×#3480	1	1	yes	characteristic
1023	C₂	C₆₇×#3500	1	1	yes	characteristic
1024	C₂	C₆₇×#3507	1	1	yes	characteristic
1025	C₂	C₆₇×#3510	1	1	yes	characteristic
1026	C₂	C₆₇×#3557	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂×#127×C₆₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#556×C₆₇	C₂	semidirect
3. C₆₇×#2718	C₂	semidirect
4. C₆₇×#2674	C₂	semidirect
5. C₆₇×#2581	C₂	semidirect
6. C₆₇×#2580	C₂	semidirect
7. C₆₇×#2553	C₂	semidirect
8. C₆₇×#2545	C₂	semidirect
10. C₆₇×#2521	C₂	semidirect
11. C₆₇×#2488	C₂	semidirect
12. C₆₇×#2470	C₂	semidirect
13. C₆₇×#2466	C₂	semidirect
14. C₆₇×#2448	C₂	semidirect
15. C₆₇×#2447	C₂	semidirect
16. C₆₇×#2446	C₂	semidirect
18. C₆₇×#2359	C₂	semidirect
19. C₆₇×#2351	C₂	semidirect
20. C₆₇×#2349	C₂	semidirect
21. C₄×C₄⋊Q₈×C₆₇	C₂	semidirect
22. C₄×#124×C₆₇	C₂	semidirect
23. C₄×#124×C₆₇	C₂	semidirect
504. #59829	C₆₇	direct (N × H)
515. C₂×#556	C₂×C₆₇	semidirect
516. #2718	C₂×C₆₇	semidirect
517. #2674	C₂×C₆₇	semidirect
518. #2581	C₂×C₆₇	semidirect
519. #2580	C₂×C₆₇	semidirect
520. #2553	C₂×C₆₇	semidirect
521. #2545	C₂×C₆₇	semidirect
523. #2521	C₂×C₆₇	semidirect
524. #2488	C₂×C₆₇	semidirect
525. #2470	C₂×C₆₇	semidirect
526. #2466	C₂×C₆₇	semidirect
527. #2448	C₂×C₆₇	semidirect
528. #2447	C₂×C₆₇	semidirect
529. #2446	C₂×C₆₇	semidirect
531. #2359	C₂×C₆₇	semidirect
532. #2351	C₂×C₆₇	semidirect
533. #2349	C₂×C₆₇	semidirect
534. C₄×C₄⋊Q₈	C₂×C₆₇	semidirect
535. C₄×#124	C₂×C₆₇	semidirect
536. C₄×#124	C₂×C₆₇	semidirect
537. C₆₇	#59829	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#559×C₆₇	2
C₂×#556×C₆₇	2
C₆₇×#2718	2
C₆₇×#2674	2
C₆₇×#2581	2
C₆₇×#2580	2
C₆₇×#2553	2
C₆₇×#2545	2
C₆₇×#2544	2
C₆₇×#2521	2
C₆₇×#2488	2
C₆₇×#2470	2
C₆₇×#2466	2
C₆₇×#2448	2
C₆₇×#2447	2
C₆₇×#2446	2
C₆₇×#2445	2
C₆₇×#2359	2
C₆₇×#2351	2
C₆₇×#2349	2
C₄×C₄⋊Q₈×C₆₇	2
C₄×#124×C₆₇	2
#59829	67

Subgroups — C67×#59829 #30739080

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59829 #30739080