Subgroups — C₆₇×#34882 #30714133

Order 17152.

1750 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2586	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2585	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2574	C₂	1	2	yes	maximal
4	C₆₇×#2556	C₂	1	2	yes	maximal
5	C₆₇×#2522	C₂	1	2	yes	maximal
6	C₆₇×#2520	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2465	C₂	1	2	yes	maximal
8	C₆₇×#2462	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2399	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2399	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2396	C₂	1	1	yes	maximal, characteristic
12	C₆₇×#2396	C₂	1	1	yes	maximal, characteristic
13	C₄×#125×C₆₇	C₂	1	2	yes	maximal, complemented
14	C₄×C₂²⋊Q₈×C₆₇	C₂	1	2	yes	maximal
15	C₆₇×#2298	C₂	1	2	yes	maximal
16	C₆₇×#2295	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2295	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄²×Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#117×C₆₇	C₂	1	1	yes	maximal, characteristic
20	C₂×#125×C₆₇	C₂²	1	2	yes	—
21	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
29	#400×C₆₇	C₂²	1	1	yes	characteristic
30	#400×C₆₇	C₂²	1	1	yes	characteristic
31	#399×C₆₇	C₂²	1	1	yes	characteristic
32	#399×C₆₇	C₂²	1	1	yes	characteristic
33	#398×C₆₇	C₂²	1	2	yes	—
34	#398×C₆₇	C₂²	1	2	yes	—
35	#398×C₆₇	C₂²	1	2	yes	—
36	#398×C₆₇	C₂²	1	2	yes	—
37	#398×C₆₇	C₂²	1	2	yes	—
38	#398×C₆₇	C₂²	1	2	yes	—
39	#396×C₆₇	C₂²	1	2	yes	—
40	#396×C₆₇	C₂²	1	2	yes	—
41	#395×C₆₇	C₂²	1	2	yes	—
42	#395×C₆₇	C₂²	1	2	yes	—
43	#395×C₆₇	C₂²	1	2	yes	—
44	#395×C₆₇	C₂²	1	1	yes	characteristic
45	#395×C₆₇	C₂²	1	1	yes	characteristic
46	#395×C₆₇	C₂²	1	2	yes	—
47	#393×C₆₇	C₂²	1	1	yes	characteristic
48	#393×C₆₇	C₂²	1	1	yes	characteristic
49	#391×C₆₇	C₂²	1	2	yes	—
50	#391×C₆₇	C₂²	1	2	yes	—
51	#391×C₆₇	C₂²	1	2	yes	—
52	#391×C₆₇	C₂²	1	2	yes	—
53	#389×C₆₇	C₂²	1	2	yes	—
54	#389×C₆₇	C₂²	1	2	yes	—
55	#389×C₆₇	C₂²	1	2	yes	—
56	#389×C₆₇	C₂²	1	2	yes	—
57	#389×C₆₇	C₂²	1	2	yes	—
58	#389×C₆₇	C₂²	1	2	yes	—
59	#388×C₆₇	C₂²	1	2	yes	—
60	#388×C₆₇	C₂²	1	2	yes	—
61	#388×C₆₇	C₂²	1	2	yes	—
62	#388×C₆₇	C₂²	1	2	yes	—
63	#387×C₆₇	C₂²	1	2	yes	—
64	#387×C₆₇	C₂²	1	2	yes	—
65	#387×C₆₇	C₂²	1	2	yes	—
66	#387×C₆₇	C₂²	1	2	yes	—
67	#387×C₆₇	C₂²	1	2	yes	—
68	#387×C₆₇	C₂²	1	2	yes	—
69	#387×C₆₇	C₂²	1	2	yes	—
70	#387×C₆₇	C₂²	1	2	yes	—
71	#387×C₆₇	C₂²	1	2	yes	—
72	#387×C₆₇	C₂²	1	2	yes	—
73	#387×C₆₇	C₂²	1	2	yes	—
74	#387×C₆₇	C₂²	1	2	yes	—
75	#387×C₆₇	C₂²	1	2	yes	—
76	#387×C₆₇	C₂²	1	2	yes	—
77	#387×C₆₇	C₂²	1	2	yes	—
78	#387×C₆₇	C₂²	1	2	yes	—
79	#385×C₆₇	C₂²	1	2	yes	—
80	#385×C₆₇	C₂²	1	2	yes	—
81	#382×C₆₇	C₂²	1	2	yes	—
82	#380×C₆₇	C₂²	1	2	yes	—
83	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
84	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
85	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
86	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
87	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
88	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
89	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
90	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
95	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
101	#376×C₆₇	C₂²	1	1	yes	characteristic
102	#376×C₆₇	C₂²	1	1	yes	characteristic
103	#376×C₆₇	C₂²	1	2	yes	—
104	C₄³×C₆₇	C₂²	1	1	yes	characteristic
105	C₄³×C₆₇	C₂²	1	1	yes	characteristic
106	C₄³×C₆₇	C₂²	1	2	yes	—
107	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
109	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
111	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
112	#125×C₆₇	—	2	8	no	—
113	C₂²⋊Q₈×C₆₇	—	2	8	no	—
114	C₄×Q₈×C₆₇	—	2	8	no	—
115	C₄×Q₈×C₆₇	—	2	8	no	—
116	C₄×Q₈×C₆₇	—	2	4	no	—
117	C₄×Q₈×C₆₇	—	2	4	no	—
118	#117×C₆₇	—	2	4	no	—
119	#117×C₆₇	Q₈	1	8	yes	complemented
120	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
153	C₂×C₄²×C₆₇	—	2	4	no	—
154	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
155	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
156	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
157	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
158	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
159	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
162	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
163	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
164	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
165	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
166	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
167	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
168	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
169	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
173	#95×C₆₇	C₂³	1	2	yes	—
174	#95×C₆₇	C₂³	1	2	yes	—
175	#95×C₆₇	C₂³	1	2	yes	—
176	#95×C₆₇	C₂³	1	2	yes	—
177	#95×C₆₇	C₂³	1	2	yes	—
178	#95×C₆₇	C₂³	1	2	yes	—
179	#95×C₆₇	C₂³	1	2	yes	—
180	#95×C₆₇	C₂³	1	2	yes	—
181	#95×C₆₇	C₂³	1	2	yes	—
182	#95×C₆₇	C₂³	1	2	yes	—
183	#95×C₆₇	C₂³	1	2	yes	—
184	#95×C₆₇	C₂³	1	2	yes	—
185	#95×C₆₇	C₂³	1	2	yes	—
186	#95×C₆₇	C₂³	1	2	yes	—
187	#95×C₆₇	C₂³	1	1	yes	characteristic
188	#95×C₆₇	C₂³	1	1	yes	characteristic
189	#95×C₆₇	C₂³	1	2	yes	—
190	#95×C₆₇	C₂³	1	2	yes	—
191	#95×C₆₇	C₂³	1	2	yes	—
192	#95×C₆₇	C₂³	1	2	yes	—
193	#95×C₆₇	C₂³	1	2	yes	—
194	#95×C₆₇	C₂³	1	2	yes	—
195	#95×C₆₇	C₂³	1	2	yes	—
196	#95×C₆₇	C₂³	1	2	yes	—
197	#95×C₆₇	C₂³	1	2	yes	—
198	#95×C₆₇	C₂³	1	2	yes	—
199	#95×C₆₇	C₂³	1	2	yes	—
200	#95×C₆₇	C₂³	1	2	yes	—
201	#95×C₆₇	C₂³	1	1	yes	characteristic
202	#95×C₆₇	C₂³	1	1	yes	characteristic
203	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
204	C₂×Q₈×C₆₇	—	2	4	no	—
205	C₂×Q₈×C₆₇	—	2	2	no	—
206	C₂×Q₈×C₆₇	—	2	4	no	—
207	C₂×Q₈×C₆₇	—	2	2	no	—
208	C₂×Q₈×C₆₇	—	2	4	no	—
209	C₂×Q₈×C₆₇	—	4	2	no	—
210	C₂×Q₈×C₆₇	—	4	2	no	—
211	C₂²×C₄×C₆₇	—	2	2	no	—
212	C₂²×C₄×C₆₇	—	2	2	no	—
213	C₂²×C₄×C₆₇	—	2	4	no	—
214	C₂²×C₄×C₆₇	—	2	4	no	—
215	C₂²×C₄×C₆₇	—	4	2	no	—
216	C₂²×C₄×C₆₇	C₂×Q₈	1	4	yes	—
217	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
218	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
235	C₄⋊C₄×C₆₇	—	2	2	no	—
236	C₄⋊C₄×C₆₇	—	2	2	no	—
237	C₄⋊C₄×C₆₇	—	2	4	no	—
238	C₄⋊C₄×C₆₇	—	2	4	no	—
239	C₄⋊C₄×C₆₇	—	2	4	no	—
240	C₄⋊C₄×C₆₇	—	2	4	no	—
241	C₄⋊C₄×C₆₇	—	2	4	no	—
242	C₄⋊C₄×C₆₇	—	2	2	no	—
243	C₄⋊C₄×C₆₇	—	2	2	no	—
244	C₄⋊C₄×C₆₇	—	2	4	no	—
245	C₄⋊C₄×C₆₇	—	2	4	no	—
246	C₄⋊C₄×C₆₇	—	2	4	no	—
247	C₄⋊C₄×C₆₇	—	2	4	no	—
248	C₄⋊C₄×C₆₇	—	2	4	no	—
249	C₄⋊C₄×C₆₇	—	2	4	no	—
250	C₄⋊C₄×C₆₇	—	2	4	no	—
251	C₄⋊C₄×C₆₇	—	2	4	no	—
252	C₄⋊C₄×C₆₇	—	2	4	no	—
253	C₄⋊C₄×C₆₇	—	4	2	no	—
254	C₄⋊C₄×C₆₇	—	4	2	no	—
255	C₄⋊C₄×C₆₇	—	4	2	no	—
256	C₄⋊C₄×C₆₇	—	4	2	no	—
257	C₄⋊C₄×C₆₇	—	4	2	no	—
258	C₄⋊C₄×C₆₇	—	4	2	no	—
259	C₄⋊C₄×C₆₇	C₂×Q₈	1	8	yes	—
260	C₄⋊C₄×C₆₇	#41	1	8	yes	—
261	C₂²⋊C₄×C₆₇	—	2	2	no	—
262	C₂²⋊C₄×C₆₇	—	2	2	no	—
263	C₂²⋊C₄×C₆₇	—	2	4	no	—
264	C₂²⋊C₄×C₆₇	—	2	4	no	—
265	C₂²⋊C₄×C₆₇	—	4	2	no	—
266	C₂²⋊C₄×C₆₇	—	4	2	no	—
267	C₂²⋊C₄×C₆₇	C₂×Q₈	1	8	yes	—
268	C₄²×C₆₇	—	2	4	no	—
269	C₄²×C₆₇	—	2	2	no	—
270	C₄²×C₆₇	—	2	2	no	—
271	C₄²×C₆₇	—	2	4	no	—
272	C₄²×C₆₇	—	2	4	no	—
273	C₄²×C₆₇	—	2	4	no	—
274	C₄²×C₆₇	—	2	4	no	—
275	C₄²×C₆₇	—	2	4	no	—
276	C₄²×C₆₇	—	2	4	no	—
277	C₄²×C₆₇	—	2	4	no	—
278	C₄²×C₆₇	—	2	4	no	—
279	C₄²×C₆₇	—	4	2	no	—
280	C₄²×C₆₇	—	4	2	no	—
281	C₄²×C₆₇	—	4	2	no	—
282	C₄²×C₆₇	—	4	2	no	—
283	C₄²×C₆₇	C₂×Q₈	1	4	yes	—
284	C₄²×C₆₇	C₂×Q₈	1	4	yes	—
285	C₄²×C₆₇	#41	1	4	yes	—
286	C₄²×C₆₇	#41	1	4	yes	—
287	C₂³×C₆₇	—	2	1	no	—
288	C₂³×C₆₇	—	2	2	no	—
289	C₂³×C₆₇	—	2	1	no	—
290	C₂³×C₆₇	—	2	2	no	—
291	C₂³×C₆₇	C₂²×Q₈	1	2	yes	—
292	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
293	Q₈×C₆₇	—	2	8	no	—
294	Q₈×C₆₇	—	4	8	no	—
295	Q₈×C₆₇	—	4	4	no	—
296	C₂×C₄×C₆₇	—	2	2	no	—
297	C₂×C₄×C₆₇	—	2	1	no	—
298	C₂×C₄×C₆₇	—	2	2	no	—
299	C₂×C₄×C₆₇	—	2	2	no	—
300	C₂×C₄×C₆₇	—	2	2	no	—
301	C₂×C₄×C₆₇	—	2	2	no	—
302	C₂×C₄×C₆₇	—	2	2	no	—
303	C₂×C₄×C₆₇	—	2	2	no	—
304	C₂×C₄×C₆₇	—	2	1	no	—
305	C₂×C₄×C₆₇	—	2	2	no	—
306	C₂×C₄×C₆₇	—	2	2	no	—
307	C₂×C₄×C₆₇	—	2	2	no	—
308	C₂×C₄×C₆₇	—	2	2	no	—
309	C₂×C₄×C₆₇	—	2	2	no	—
310	C₂×C₄×C₆₇	—	2	2	no	—
311	C₂×C₄×C₆₇	—	2	2	no	—
312	C₂×C₄×C₆₇	—	2	8	no	—
313	C₂×C₄×C₆₇	—	2	1	no	—
314	C₂×C₄×C₆₇	—	2	1	no	—
315	C₂×C₄×C₆₇	—	2	2	no	—
316	C₂×C₄×C₆₇	—	2	2	no	—
317	C₂×C₄×C₆₇	—	2	2	no	—
318	C₂×C₄×C₆₇	—	2	2	no	—
319	C₂×C₄×C₆₇	—	2	2	no	—
320	C₂×C₄×C₆₇	—	2	2	no	—
321	C₂×C₄×C₆₇	—	2	2	no	—
322	C₂×C₄×C₆₇	—	2	2	no	—
323	C₂×C₄×C₆₇	—	2	2	no	—
324	C₂×C₄×C₆₇	—	2	2	no	—
325	C₂×C₄×C₆₇	—	2	2	no	—
326	C₂×C₄×C₆₇	—	2	2	no	—
327	C₂×C₄×C₆₇	—	2	2	no	—
328	C₂×C₄×C₆₇	—	2	2	no	—
329	C₂×C₄×C₆₇	—	2	2	no	—
330	C₂×C₄×C₆₇	—	2	2	no	—
331	C₂×C₄×C₆₇	—	2	2	no	—
332	C₂×C₄×C₆₇	—	2	2	no	—
333	C₂×C₄×C₆₇	—	2	2	no	—
334	C₂×C₄×C₆₇	—	2	2	no	—
335	C₂×C₄×C₆₇	—	4	8	no	—
336	C₂×C₄×C₆₇	C₂²×Q₈	1	4	yes	—
337	C₂×C₄×C₆₇	C₂²×Q₈	1	4	yes	—
338	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
339	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
340	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
341	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
342	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
343	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
344	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
345	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
346	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
347	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
348	C₂²×C₆₇	—	2	2	no	—
349	C₂²×C₆₇	—	2	4	no	—
350	C₂²×C₆₇	—	4	1	no	—
351	C₂²×C₆₇	—	4	1	no	—
352	C₂²×C₆₇	—	4	2	no	—
353	C₂²×C₆₇	C₂³×Q₈	1	1	yes	characteristic
354	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
355	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
356	C₂²×C₆₇	C₂²×#41	1	2	yes	—
357	C₂²×C₆₇	#585	1	2	yes	—
358	C₄×C₆₇	—	2	2	no	—
359	C₄×C₆₇	—	2	4	no	—
360	C₄×C₆₇	—	2	2	no	—
361	C₄×C₆₇	—	2	2	no	—
362	C₄×C₆₇	—	2	4	no	—
363	C₄×C₆₇	—	2	4	no	—
364	C₄×C₆₇	—	2	4	no	—
365	C₄×C₆₇	—	2	4	no	—
366	C₄×C₆₇	—	2	4	no	—
367	C₄×C₆₇	—	4	1	no	—
368	C₄×C₆₇	—	4	2	no	—
369	C₄×C₆₇	—	4	1	no	—
370	C₄×C₆₇	—	4	2	no	—
371	C₄×C₆₇	—	4	2	no	—
372	C₄×C₆₇	—	4	2	no	—
373	C₄×C₆₇	—	4	2	no	—
374	C₄×C₆₇	—	4	2	no	—
375	C₄×C₆₇	#533	1	4	yes	—
376	#34882	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
377	C₂×C₆₇	—	4	2	no	—
378	C₂×C₆₇	C₂×#533	1	1	yes	characteristic
379	C₂×C₆₇	#3444	1	1	yes	characteristic
380	C₂×C₆₇	#3455	1	1	yes	characteristic
381	C₂×C₆₇	#3475	1	2	yes	—
382	C₂×C₆₇	Q₈×#41	1	2	yes	—
383	#2586	C₂×C₆₇	1	2	yes	complemented
384	#2585	C₂×C₆₇	1	2	yes	complemented
385	#2574	C₂×C₆₇	1	2	yes	—
386	#2556	C₂×C₆₇	1	2	yes	—
387	#2522	C₂×C₆₇	1	2	yes	—
388	#2520	C₂×C₆₇	1	2	yes	complemented
389	#2465	C₂×C₆₇	1	2	yes	—
390	#2462	C₂×C₆₇	1	2	yes	complemented
391	#2399	C₂×C₆₇	1	1	yes	characteristic, complemented
392	#2399	C₂×C₆₇	1	1	yes	characteristic, complemented
393	#2396	C₂×C₆₇	1	1	yes	characteristic
394	#2396	C₂×C₆₇	1	1	yes	characteristic
395	C₄×#125	C₂×C₆₇	1	2	yes	complemented
396	C₄×C₂²⋊Q₈	C₂×C₆₇	1	2	yes	—
397	#2298	C₂×C₆₇	1	2	yes	—
398	#2295	C₂×C₆₇	1	1	yes	characteristic, complemented
399	#2295	C₂×C₆₇	1	2	yes	complemented
400	C₄²×Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
401	C₄×#117	C₂×C₆₇	1	1	yes	characteristic
402	C₆₇	#34882	1	1	yes	characteristic, direct product factor, Sylow
403	C₂×#125	C₂²×C₆₇	1	2	yes	—
404	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
405	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
406	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
407	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
408	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
409	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
410	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
411	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
412	#400	C₂²×C₆₇	1	1	yes	characteristic
413	#400	C₂²×C₆₇	1	1	yes	characteristic
414	#399	C₂²×C₆₇	1	1	yes	characteristic
415	#399	C₂²×C₆₇	1	1	yes	characteristic
416	#398	C₂²×C₆₇	1	2	yes	—
417	#398	C₂²×C₆₇	1	2	yes	—
418	#398	C₂²×C₆₇	1	2	yes	—
419	#398	C₂²×C₆₇	1	2	yes	—
420	#398	C₂²×C₆₇	1	2	yes	—
421	#398	C₂²×C₆₇	1	2	yes	—
422	#396	C₂²×C₆₇	1	2	yes	—
423	#396	C₂²×C₆₇	1	2	yes	—
424	#395	C₂²×C₆₇	1	2	yes	—
425	#395	C₂²×C₆₇	1	1	yes	characteristic
426	#395	C₂²×C₆₇	1	2	yes	—
427	#395	C₂²×C₆₇	1	1	yes	characteristic
428	#395	C₂²×C₆₇	1	2	yes	—
429	#395	C₂²×C₆₇	1	2	yes	—
430	#393	C₂²×C₆₇	1	1	yes	characteristic
431	#393	C₂²×C₆₇	1	1	yes	characteristic
432	#391	C₂²×C₆₇	1	2	yes	—
433	#391	C₂²×C₆₇	1	2	yes	—
434	#391	C₂²×C₆₇	1	2	yes	—
435	#391	C₂²×C₆₇	1	2	yes	—
436	#389	C₂²×C₆₇	1	2	yes	—
437	#389	C₂²×C₆₇	1	2	yes	—
438	#389	C₂²×C₆₇	1	2	yes	—
439	#389	C₂²×C₆₇	1	2	yes	—
440	#389	C₂²×C₆₇	1	2	yes	—
441	#389	C₂²×C₆₇	1	2	yes	—
442	#388	C₂²×C₆₇	1	2	yes	—
443	#388	C₂²×C₆₇	1	2	yes	—
444	#388	C₂²×C₆₇	1	2	yes	—
445	#388	C₂²×C₆₇	1	2	yes	—
446	#387	C₂²×C₆₇	1	2	yes	—
447	#387	C₂²×C₆₇	1	2	yes	—
448	#387	C₂²×C₆₇	1	2	yes	—
449	#387	C₂²×C₆₇	1	2	yes	—
450	#387	C₂²×C₆₇	1	2	yes	—
451	#387	C₂²×C₆₇	1	2	yes	—
452	#387	C₂²×C₆₇	1	2	yes	—
453	#387	C₂²×C₆₇	1	2	yes	—
454	#387	C₂²×C₆₇	1	2	yes	—
455	#387	C₂²×C₆₇	1	2	yes	—
456	#387	C₂²×C₆₇	1	2	yes	—
457	#387	C₂²×C₆₇	1	2	yes	—
458	#387	C₂²×C₆₇	1	2	yes	—
459	#387	C₂²×C₆₇	1	2	yes	—
460	#387	C₂²×C₆₇	1	2	yes	—
461	#387	C₂²×C₆₇	1	2	yes	—
462	#385	C₂²×C₆₇	1	2	yes	—
463	#385	C₂²×C₆₇	1	2	yes	—
464	#382	C₂²×C₆₇	1	2	yes	—
465	#380	C₂²×C₆₇	1	2	yes	—
466	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
467	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
468	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
469	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
470	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
471	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
472	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
473	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
474	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
475	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
476	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
477	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
478	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
479	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
480	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
481	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
482	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
483	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
484	#376	C₂²×C₆₇	1	1	yes	characteristic
485	#376	C₂²×C₆₇	1	1	yes	characteristic
486	#376	C₂²×C₆₇	1	2	yes	—
487	C₄³	C₂²×C₆₇	1	1	yes	characteristic
488	C₄³	C₂²×C₆₇	1	1	yes	characteristic
489	C₄³	C₂²×C₆₇	1	2	yes	—
490	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
491	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
492	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
493	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
494	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
495	#125	—	2	8	no	—
496	C₂²⋊Q₈	—	2	8	no	—
497	C₄×Q₈	—	2	8	no	—
498	C₄×Q₈	—	2	8	no	—
499	C₄×Q₈	—	2	4	no	—
500	C₄×Q₈	—	2	4	no	—
501	#117	—	2	4	no	—
502	#117	Q₈×C₆₇	1	8	yes	complemented
503	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
530	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
531	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
536	C₂×C₄²	—	2	4	no	—
537	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
538	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
539	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
540	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
541	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
542	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
543	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
544	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
545	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
546	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
547	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
548	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
549	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
550	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
551	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
552	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
553	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
554	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
555	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
556	#95	C₂³×C₆₇	1	2	yes	—
557	#95	C₂³×C₆₇	1	2	yes	—
558	#95	C₂³×C₆₇	1	2	yes	—
559	#95	C₂³×C₆₇	1	2	yes	—
560	#95	C₂³×C₆₇	1	2	yes	—
561	#95	C₂³×C₆₇	1	2	yes	—
562	#95	C₂³×C₆₇	1	2	yes	—
563	#95	C₂³×C₆₇	1	2	yes	—
564	#95	C₂³×C₆₇	1	2	yes	—
565	#95	C₂³×C₆₇	1	2	yes	—
566	#95	C₂³×C₆₇	1	2	yes	—
567	#95	C₂³×C₆₇	1	2	yes	—
568	#95	C₂³×C₆₇	1	2	yes	—
569	#95	C₂³×C₆₇	1	2	yes	—
570	#95	C₂³×C₆₇	1	1	yes	characteristic
571	#95	C₂³×C₆₇	1	1	yes	characteristic
572	#95	C₂³×C₆₇	1	2	yes	—
573	#95	C₂³×C₆₇	1	2	yes	—
574	#95	C₂³×C₆₇	1	2	yes	—
575	#95	C₂³×C₆₇	1	2	yes	—
576	#95	C₂³×C₆₇	1	2	yes	—
577	#95	C₂³×C₆₇	1	2	yes	—
578	#95	C₂³×C₆₇	1	2	yes	—
579	#95	C₂³×C₆₇	1	2	yes	—
580	#95	C₂³×C₆₇	1	2	yes	—
581	#95	C₂³×C₆₇	1	2	yes	—
582	#95	C₂³×C₆₇	1	2	yes	—
583	#95	C₂³×C₆₇	1	2	yes	—
584	#95	C₂³×C₆₇	1	1	yes	characteristic
585	#95	C₂³×C₆₇	1	1	yes	characteristic
586	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
587	C₂×Q₈	—	2	4	no	—
588	C₂×Q₈	—	2	2	no	—
589	C₂×Q₈	—	2	4	no	—
590	C₂×Q₈	—	2	2	no	—
591	C₂×Q₈	—	2	4	no	—
592	C₂×Q₈	—	4	2	no	—
593	C₂×Q₈	—	4	2	no	—
594	C₂²×C₄	—	2	2	no	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	2	4	no	—
597	C₂²×C₄	—	2	4	no	—
598	C₂²×C₄	—	4	2	no	—
599	C₂²×C₄	C₂×Q₈×C₆₇	1	4	yes	—
600	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
603	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
604	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
607	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
608	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
613	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
615	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
617	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	2	no	—
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	4	2	no	—
637	C₄⋊C₄	—	4	2	no	—
638	C₄⋊C₄	—	4	2	no	—
639	C₄⋊C₄	—	4	2	no	—
640	C₄⋊C₄	—	4	2	no	—
641	C₄⋊C₄	—	4	2	no	—
642	C₄⋊C₄	C₂×Q₈×C₆₇	1	8	yes	—
643	C₄⋊C₄	#41×C₆₇	1	8	yes	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	4	2	no	—
649	C₂²⋊C₄	—	4	2	no	—
650	C₂²⋊C₄	C₂×Q₈×C₆₇	1	8	yes	—
651	C₄²	—	2	4	no	—
652	C₄²	—	2	2	no	—
653	C₄²	—	2	2	no	—
654	C₄²	—	2	4	no	—
655	C₄²	—	2	4	no	—
656	C₄²	—	2	4	no	—
657	C₄²	—	2	4	no	—
658	C₄²	—	2	4	no	—
659	C₄²	—	2	4	no	—
660	C₄²	—	2	4	no	—
661	C₄²	—	2	4	no	—
662	C₄²	—	4	2	no	—
663	C₄²	—	4	2	no	—
664	C₄²	—	4	2	no	—
665	C₄²	—	4	2	no	—
666	C₄²	C₂×Q₈×C₆₇	1	4	yes	—
667	C₄²	C₂×Q₈×C₆₇	1	4	yes	—
668	C₄²	#41×C₆₇	1	4	yes	—
669	C₄²	#41×C₆₇	1	4	yes	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	2	no	—
674	C₂³	C₂²×Q₈×C₆₇	1	2	yes	—
675	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
676	Q₈	—	2	8	no	—
677	Q₈	—	4	8	no	—
678	Q₈	—	4	4	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	8	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	4	8	no	—
719	C₂×C₄	C₂²×Q₈×C₆₇	1	4	yes	—
720	C₂×C₄	C₂²×Q₈×C₆₇	1	4	yes	—
721	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
722	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
723	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
724	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
725	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
726	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
727	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
728	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
729	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
730	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
731	C₂²	—	2	2	no	—
732	C₂²	—	2	4	no	—
733	C₂²	—	4	1	no	—
734	C₂²	—	4	1	no	—
735	C₂²	—	4	2	no	—
736	C₂²	C₂³×Q₈×C₆₇	1	1	yes	characteristic
737	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
738	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
739	C₂²	C₂²×#41×C₆₇	1	2	yes	—
740	C₂²	#585×C₆₇	1	2	yes	—
741	C₄	—	2	2	no	—
742	C₄	—	2	4	no	—
743	C₄	—	2	2	no	—
744	C₄	—	2	2	no	—
745	C₄	—	2	4	no	—
746	C₄	—	2	4	no	—
747	C₄	—	2	4	no	—
748	C₄	—	2	4	no	—
749	C₄	—	2	4	no	—
750	C₄	—	4	1	no	—
751	C₄	—	4	2	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	1	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	2	no	—
758	C₄	#533×C₆₇	1	4	yes	—
759	C₂	—	4	2	no	—
760	C₂	C₂×#533×C₆₇	1	1	yes	characteristic
761	C₂	C₆₇×#3444	1	1	yes	characteristic
762	C₂	C₆₇×#3455	1	1	yes	characteristic
763	C₂	C₆₇×#3475	1	2	yes	—
764	C₂	Q₈×#41×C₆₇	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
socle	C₂³×C₆₇	C₂⁵
prime radical	C₂⁴×C₆₇	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#2586	C₂	semidirect
2. C₆₇×#2585	C₂	semidirect
6. C₆₇×#2520	C₂	semidirect
8. C₆₇×#2462	C₂	semidirect
9. C₆₇×#2399	C₂	semidirect
10. C₆₇×#2399	C₂	semidirect
13. C₄×#125×C₆₇	C₂	semidirect
16. C₆₇×#2295	C₂	semidirect
17. C₆₇×#2295	C₂	semidirect
18. C₄²×Q₈×C₆₇	C₂	semidirect
119. #117×C₆₇	Q₈	semidirect
376. #34882	C₆₇	direct (N × H)
383. #2586	C₂×C₆₇	semidirect
384. #2585	C₂×C₆₇	semidirect
388. #2520	C₂×C₆₇	semidirect
390. #2462	C₂×C₆₇	semidirect
391. #2399	C₂×C₆₇	semidirect
392. #2399	C₂×C₆₇	semidirect
395. C₄×#125	C₂×C₆₇	semidirect
398. #2295	C₂×C₆₇	semidirect
399. #2295	C₂×C₆₇	semidirect
400. C₄²×Q₈	C₂×C₆₇	semidirect
402. C₆₇	#34882	direct (N × H)
502. #117	Q₈×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#2586	2
C₆₇×#2585	2
C₆₇×#2574	2
C₆₇×#2556	2
C₆₇×#2522	2
C₆₇×#2520	2
C₆₇×#2465	2
C₆₇×#2462	2
C₆₇×#2399	2
C₆₇×#2396	2
C₄×#125×C₆₇	2
C₄×C₂²⋊Q₈×C₆₇	2
C₆₇×#2298	2
C₆₇×#2295	2
C₄²×Q₈×C₆₇	2
C₄×#117×C₆₇	2
#34882	67

Subgroups — C67×#34882 #30714133

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34882 #30714133