Subgroups — C₆₇×#61740 #30740991

Order 17152.

1880 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3519	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#555×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3357	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3347	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3341	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3325	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3319	C₂	1	4	yes	maximal, complemented
8	C₆₇×#3305	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3238	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3226	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3194	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3186	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3109	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3105	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3094	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3091	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2974	C₂	1	1	yes	maximal, characteristic, complemented
18	#555×C₆₇	—	2	1	no	—
19	#555×C₆₇	—	2	1	no	—
20	#555×C₆₇	—	2	2	no	—
21	#555×C₆₇	C₂²	1	2	yes	—
22	#555×C₆₇	C₂²	1	2	yes	complemented
23	#555×C₆₇	C₂²	1	4	yes	complemented
24	#555×C₆₇	C₂²	1	1	yes	characteristic, complemented
25	#554×C₆₇	C₂²	1	1	yes	characteristic, complemented
26	#553×C₆₇	—	2	1	no	—
27	#553×C₆₇	C₂²	1	2	yes	complemented
28	#550×C₆₇	C₂²	1	1	yes	characteristic, complemented
29	#546×C₆₇	—	2	2	no	—
30	#546×C₆₇	C₂²	1	2	yes	complemented
31	D₄²×C₆₇	—	2	1	no	—
32	D₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	#540×C₆₇	—	2	1	no	—
34	#538×C₆₇	—	2	2	no	—
35	#532×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
37	#529×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#124×C₆₇	—	2	2	no	—
39	#525×C₆₇	C₂²	1	2	yes	—
40	C₂×#121×C₆₇	—	2	1	no	—
41	C₂×#121×C₆₇	C₂²	1	2	yes	—
42	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
43	#518×C₆₇	—	2	1	no	—
44	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	C₂×#117×C₆₇	—	2	1	no	—
47	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
48	#501×C₆₇	C₂²	1	2	yes	complemented
49	#500×C₆₇	C₂²	1	2	yes	complemented
50	#489×C₆₇	C₂²	1	2	yes	complemented
51	#486×C₆₇	C₂²	1	2	yes	complemented
52	#485×C₆₇	C₂²	1	4	yes	complemented
53	#484×C₆₇	C₂²	1	1	yes	characteristic, complemented
54	#483×C₆₇	C₂²	1	2	yes	complemented
55	#482×C₆₇	C₂²	1	4	yes	complemented
56	#482×C₆₇	C₂²	1	4	yes	complemented
57	#482×C₆₇	C₂²	1	4	yes	complemented
58	#482×C₆₇	C₂²	1	4	yes	complemented
59	#481×C₆₇	C₂²	1	1	yes	characteristic
60	#481×C₆₇	C₂²	1	2	yes	complemented
61	#480×C₆₇	C₂²	1	2	yes	—
62	#480×C₆₇	C₂²	1	2	yes	complemented
63	#480×C₆₇	C₂²	1	4	yes	complemented
64	#480×C₆₇	C₂²	1	2	yes	complemented
65	#478×C₆₇	C₂²	1	2	yes	complemented
66	#477×C₆₇	C₂²	1	2	yes	complemented
67	#476×C₆₇	C₂²	1	2	yes	complemented
68	#476×C₆₇	C₂²	1	2	yes	complemented
69	#474×C₆₇	C₂²	1	4	yes	complemented
70	#469×C₆₇	C₂²	1	4	yes	complemented
71	#468×C₆₇	C₂²	1	4	yes	complemented
72	#466×C₆₇	C₂²	1	4	yes	complemented
73	#466×C₆₇	C₂²	1	4	yes	complemented
74	#463×C₆₇	C₂²	1	2	yes	complemented
75	#459×C₆₇	C₂²	1	2	yes	complemented
76	#450×C₆₇	C₂²	1	1	yes	characteristic, complemented
77	#449×C₆₇	C₂²	1	4	yes	complemented
78	#447×C₆₇	C₂²	1	1	yes	characteristic
79	#447×C₆₇	C₂²	1	4	yes	complemented
80	#447×C₆₇	C₂²	1	2	yes	complemented
81	#442×C₆₇	C₂²	1	4	yes	complemented
82	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
83	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
84	#436×C₆₇	C₂²	1	2	yes	complemented
85	#435×C₆₇	C₂²	1	4	yes	complemented
86	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
87	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
88	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
89	#428×C₆₇	C₂²	1	4	yes	complemented
90	#427×C₆₇	C₂²	1	4	yes	complemented
91	#418×C₆₇	C₂²	1	4	yes	complemented
92	#416×C₆₇	C₂²	1	4	yes	complemented
93	#407×C₆₇	C₂²	1	2	yes	complemented
94	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
95	C₂×#41×C₆₇	—	2	1	no	—
96	C₂×#41×C₆₇	C₂³	1	2	yes	—
97	C₂²×Q₈×C₆₇	—	2	1	no	—
98	C₂²×D₄×C₆₇	—	2	2	no	—
99	C₂²×D₄×C₆₇	—	2	2	no	—
100	C₂²×D₄×C₆₇	—	2	1	no	—
101	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
102	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
104	C₂³×C₄×C₆₇	—	2	1	no	—
105	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
106	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
107	C₂×D₈×C₆₇	C₂³	1	4	yes	—
108	C₂×D₈×C₆₇	C₂³	1	2	yes	—
109	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
110	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
111	C₄⋊Q₈×C₆₇	—	2	1	no	—
112	C₄⋊Q₈×C₆₇	—	2	1	no	—
113	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
114	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
115	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
116	#127×C₆₇	—	2	1	no	—
117	#127×C₆₇	C₂³	1	1	yes	characteristic
118	#126×C₆₇	—	2	2	no	—
119	#126×C₆₇	—	2	1	no	—
120	#125×C₆₇	—	2	1	no	—
121	#125×C₆₇	C₂³	1	1	yes	characteristic
122	#124×C₆₇	—	2	4	no	—
123	#124×C₆₇	—	2	4	no	—
124	#124×C₆₇	—	2	4	no	—
125	#124×C₆₇	—	2	4	no	—
126	#124×C₆₇	—	2	2	no	—
127	#124×C₆₇	—	2	1	no	—
128	#124×C₆₇	C₂³	1	1	yes	characteristic
129	#123×C₆₇	—	2	2	no	—
130	#123×C₆₇	—	2	1	no	—
131	#123×C₆₇	—	2	2	no	—
132	#123×C₆₇	—	2	2	no	—
133	C₂²⋊Q₈×C₆₇	—	2	2	no	—
134	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
135	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
136	#121×C₆₇	—	2	2	no	—
137	#121×C₆₇	—	2	2	no	—
138	#121×C₆₇	—	2	4	no	—
139	#121×C₆₇	—	2	2	no	—
140	#121×C₆₇	—	2	1	no	—
141	#121×C₆₇	—	2	2	no	—
142	#121×C₆₇	—	2	2	no	—
143	#121×C₆₇	—	2	2	no	—
144	#121×C₆₇	—	2	2	no	—
145	#121×C₆₇	—	2	1	no	—
146	#121×C₆₇	—	2	1	no	—
147	#121×C₆₇	—	2	2	no	—
148	#121×C₆₇	—	2	2	no	—
149	#121×C₆₇	C₂³	1	4	yes	—
150	#121×C₆₇	C₂³	1	2	yes	—
151	#121×C₆₇	C₂³	1	2	yes	—
152	#121×C₆₇	C₂³	1	4	yes	—
153	#121×C₆₇	C₂³	1	2	yes	—
154	#121×C₆₇	C₂³	1	1	yes	characteristic
155	#121×C₆₇	C₂³	1	2	yes	—
156	#120×C₆₇	—	2	2	no	—
157	#120×C₆₇	—	2	2	no	—
158	#120×C₆₇	—	2	2	no	—
159	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
160	C₄×D₄×C₆₇	—	2	1	no	—
161	C₄×D₄×C₆₇	—	2	2	no	—
162	C₄×D₄×C₆₇	—	2	2	no	—
163	C₄×D₄×C₆₇	—	2	1	no	—
164	C₄×D₄×C₆₇	—	2	1	no	—
165	C₄×D₄×C₆₇	—	2	2	no	—
166	C₄×D₄×C₆₇	—	2	1	no	—
167	C₄×D₄×C₆₇	—	2	1	no	—
168	C₄×D₄×C₆₇	—	2	1	no	—
169	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
170	C₄×D₄×C₆₇	D₄	1	2	yes	—
171	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
172	C₄×D₄×C₆₇	C₂³	1	2	yes	—
173	C₄×D₄×C₆₇	C₂³	1	2	yes	—
174	C₄×D₄×C₆₇	C₂³	1	2	yes	—
175	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
177	C₄×D₄×C₆₇	C₂³	1	2	yes	—
178	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
179	#117×C₆₇	—	2	2	no	—
180	#117×C₆₇	—	2	2	no	—
181	#117×C₆₇	—	2	2	no	—
182	#117×C₆₇	—	2	2	no	—
183	#117×C₆₇	—	2	4	no	—
184	#117×C₆₇	—	2	1	no	—
185	#117×C₆₇	—	2	1	no	—
186	#117×C₆₇	C₂³	1	4	yes	—
187	#117×C₆₇	C₂³	1	2	yes	—
188	#117×C₆₇	C₂³	1	4	yes	—
189	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
190	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
192	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
194	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
195	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
196	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
197	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
198	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
200	C₂×C₄²×C₆₇	—	2	2	no	—
201	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
202	#107×C₆₇	C₂³	1	4	yes	—
203	#107×C₆₇	C₂³	1	4	yes	—
204	#107×C₆₇	C₂³	1	4	yes	—
205	#107×C₆₇	C₂³	1	2	yes	—
206	#106×C₆₇	C₂³	1	4	yes	—
207	#106×C₆₇	C₂³	1	4	yes	—
208	#106×C₆₇	C₂³	1	2	yes	—
209	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
210	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
211	#103×C₆₇	C₂³	1	4	yes	—
212	#103×C₆₇	C₂³	1	2	yes	—
213	#102×C₆₇	C₂³	1	4	yes	—
214	#102×C₆₇	C₂³	1	2	yes	—
215	#102×C₆₇	C₂³	1	4	yes	—
216	#102×C₆₇	C₂³	1	2	yes	—
217	#102×C₆₇	C₂³	1	2	yes	—
218	#102×C₆₇	C₂³	1	4	yes	—
219	#102×C₆₇	C₂³	1	4	yes	—
220	#102×C₆₇	C₂³	1	4	yes	—
221	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
222	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
223	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
224	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
225	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
226	#97×C₆₇	C₂³	1	2	yes	—
227	C₄×C₈×C₆₇	C₂³	1	2	yes	—
228	C₂⁴×C₆₇	—	2	1	no	—
229	C₂⁴×C₆₇	—	2	2	no	—
230	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
231	#41×C₆₇	—	4	4	no	—
232	#41×C₆₇	—	8	2	no	—
233	C₂×Q₈×C₆₇	—	2	1	no	—
234	C₂×Q₈×C₆₇	—	2	2	no	—
235	C₂×Q₈×C₆₇	—	2	2	no	—
236	C₂×Q₈×C₆₇	—	8	2	no	—
237	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
238	C₂×D₄×C₆₇	—	2	2	no	—
239	C₂×D₄×C₆₇	—	2	2	no	—
240	C₂×D₄×C₆₇	—	2	1	no	—
241	C₂×D₄×C₆₇	—	2	2	no	—
242	C₂×D₄×C₆₇	—	2	2	no	—
243	C₂×D₄×C₆₇	—	2	2	no	—
244	C₂×D₄×C₆₇	—	2	4	no	—
245	C₂×D₄×C₆₇	—	2	4	no	—
246	C₂×D₄×C₆₇	—	2	1	no	—
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	—	4	2	no	—
251	C₂×D₄×C₆₇	—	4	2	no	—
252	C₂×D₄×C₆₇	—	4	4	no	—
253	C₂×D₄×C₆₇	—	4	4	no	—
254	C₂×D₄×C₆₇	—	8	4	no	—
255	C₂×D₄×C₆₇	—	8	4	no	—
256	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
257	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
258	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
259	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
260	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
261	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₆₇	—	2	1	no	—
263	C₂²×C₄×C₆₇	—	2	2	no	—
264	C₂²×C₄×C₆₇	—	2	2	no	—
265	C₂²×C₄×C₆₇	—	2	2	no	—
266	C₂²×C₄×C₆₇	—	2	2	no	—
267	C₂²×C₄×C₆₇	—	2	1	no	—
268	C₂²×C₄×C₆₇	—	2	2	no	—
269	C₂²×C₄×C₆₇	—	2	2	no	—
270	C₂²×C₄×C₆₇	—	4	4	no	—
271	C₂²×C₄×C₆₇	—	4	4	no	—
272	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
275	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
276	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
277	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
280	SD₁₆×C₆₇	—	4	2	no	—
281	D₈×C₆₇	—	4	2	no	—
282	D₈×C₆₇	—	4	4	no	—
283	M₁₆×C₆₇	—	4	4	no	—
284	C₂×C₈×C₆₇	—	4	4	no	—
285	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
286	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
287	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
288	C₄⋊C₄×C₆₇	—	2	2	no	—
289	C₄⋊C₄×C₆₇	—	2	2	no	—
290	C₄⋊C₄×C₆₇	—	2	1	no	—
291	C₄⋊C₄×C₆₇	—	2	2	no	—
292	C₄⋊C₄×C₆₇	—	2	2	no	—
293	C₄⋊C₄×C₆₇	—	2	1	no	—
294	C₄⋊C₄×C₆₇	—	2	1	no	—
295	C₄⋊C₄×C₆₇	—	2	1	no	—
296	C₄⋊C₄×C₆₇	—	2	1	no	—
297	C₄⋊C₄×C₆₇	—	2	2	no	—
298	C₄⋊C₄×C₆₇	—	2	1	no	—
299	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
300	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
301	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
302	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
303	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
304	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
305	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
306	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
307	C₂²⋊C₄×C₆₇	—	2	4	no	—
308	C₂²⋊C₄×C₆₇	—	2	4	no	—
309	C₂²⋊C₄×C₆₇	—	2	2	no	—
310	C₂²⋊C₄×C₆₇	—	2	2	no	—
311	C₂²⋊C₄×C₆₇	—	2	1	no	—
312	C₂²⋊C₄×C₆₇	—	2	1	no	—
313	C₂²⋊C₄×C₆₇	—	2	1	no	—
314	C₂²⋊C₄×C₆₇	—	2	2	no	—
315	C₂²⋊C₄×C₆₇	—	2	4	no	—
316	C₂²⋊C₄×C₆₇	—	2	4	no	—
317	C₂²⋊C₄×C₆₇	—	2	2	no	—
318	C₂²⋊C₄×C₆₇	—	2	2	no	—
319	C₂²⋊C₄×C₆₇	—	2	2	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	1	no	—
324	C₂²⋊C₄×C₆₇	—	2	2	no	—
325	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
326	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
327	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
328	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
329	C₄²×C₆₇	—	2	4	no	—
330	C₄²×C₆₇	—	2	4	no	—
331	C₄²×C₆₇	—	2	2	no	—
332	C₄²×C₆₇	—	2	1	no	—
333	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
334	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
335	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
336	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
337	C₂³×C₆₇	—	2	4	no	—
338	C₂³×C₆₇	—	2	2	no	—
339	C₂³×C₆₇	—	2	1	no	—
340	C₂³×C₆₇	—	2	2	no	—
341	C₂³×C₆₇	—	4	2	no	—
342	C₂³×C₆₇	—	4	2	no	—
343	C₂³×C₆₇	—	4	2	no	—
344	C₂³×C₆₇	—	4	2	no	—
345	C₂³×C₆₇	—	4	4	no	—
346	C₂³×C₆₇	—	4	2	no	—
347	C₂³×C₆₇	—	8	2	no	—
348	C₂³×C₆₇	—	8	2	no	—
349	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
350	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
351	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
352	Q₈×C₆₇	—	2	2	no	—
353	Q₈×C₆₇	—	8	2	no	—
354	Q₈×C₆₇	—	8	2	no	—
355	Q₈×C₆₇	—	8	1	no	—
356	D₄×C₆₇	—	2	2	no	—
357	D₄×C₆₇	—	2	2	no	—
358	D₄×C₆₇	—	2	2	no	—
359	D₄×C₆₇	—	2	2	no	—
360	D₄×C₆₇	—	2	2	no	—
361	D₄×C₆₇	—	2	4	no	—
362	D₄×C₆₇	—	4	2	no	—
363	D₄×C₆₇	—	4	2	no	—
364	D₄×C₆₇	—	4	4	no	—
365	D₄×C₆₇	—	4	2	no	—
366	D₄×C₆₇	—	4	4	no	—
367	D₄×C₆₇	—	4	2	no	—
368	D₄×C₆₇	—	8	2	no	—
369	D₄×C₆₇	—	8	1	no	—
370	D₄×C₆₇	—	8	4	no	—
371	D₄×C₆₇	—	8	4	no	—
372	D₄×C₆₇	—	8	2	no	—
373	D₄×C₆₇	—	8	2	no	—
374	D₄×C₆₇	—	8	2	no	—
375	C₂×C₄×C₆₇	—	2	2	no	—
376	C₂×C₄×C₆₇	—	2	2	no	—
377	C₂×C₄×C₆₇	—	2	4	no	—
378	C₂×C₄×C₆₇	—	2	4	no	—
379	C₂×C₄×C₆₇	—	2	2	no	—
380	C₂×C₄×C₆₇	—	2	2	no	—
381	C₂×C₄×C₆₇	—	2	1	no	—
382	C₂×C₄×C₆₇	—	2	4	no	—
383	C₂×C₄×C₆₇	—	2	1	no	—
384	C₂×C₄×C₆₇	—	2	2	no	—
385	C₂×C₄×C₆₇	—	2	1	no	—
386	C₂×C₄×C₆₇	—	4	2	no	—
387	C₂×C₄×C₆₇	—	4	2	no	—
388	C₂×C₄×C₆₇	—	4	2	no	—
389	C₂×C₄×C₆₇	—	4	4	no	—
390	C₂×C₄×C₆₇	—	4	2	no	—
391	C₂×C₄×C₆₇	—	4	4	no	—
392	C₂×C₄×C₆₇	—	4	4	no	—
393	C₂×C₄×C₆₇	—	4	2	no	—
394	C₂×C₄×C₆₇	—	8	2	no	—
395	C₂×C₄×C₆₇	—	8	2	no	—
396	C₂×C₄×C₆₇	—	8	2	no	—
397	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
398	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
399	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
405	C₈×C₆₇	—	2	2	no	—
406	C₈×C₆₇	—	2	4	no	—
407	C₈×C₆₇	—	2	2	no	—
408	C₂²×C₆₇	—	2	1	no	—
409	C₂²×C₆₇	—	2	1	no	—
410	C₂²×C₆₇	—	2	2	no	—
411	C₂²×C₆₇	—	2	2	no	—
412	C₂²×C₆₇	—	2	2	no	—
413	C₂²×C₆₇	—	2	2	no	—
414	C₂²×C₆₇	—	2	2	no	—
415	C₂²×C₆₇	—	2	2	no	—
416	C₂²×C₆₇	—	4	2	no	—
417	C₂²×C₆₇	—	4	2	no	—
418	C₂²×C₆₇	—	4	1	no	—
419	C₂²×C₆₇	—	4	2	no	—
420	C₂²×C₆₇	—	4	1	no	—
421	C₂²×C₆₇	—	4	2	no	—
422	C₂²×C₆₇	—	4	2	no	—
423	C₂²×C₆₇	—	4	1	no	—
424	C₂²×C₆₇	—	4	2	no	—
425	C₂²×C₆₇	—	8	4	no	—
426	C₂²×C₆₇	—	8	4	no	—
427	C₂²×C₆₇	—	16	4	no	—
428	C₂²×C₆₇	#576	1	2	yes	—
429	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
430	C₄×C₆₇	—	2	1	no	—
431	C₄×C₆₇	—	2	2	no	—
432	C₄×C₆₇	—	2	2	no	—
433	C₄×C₆₇	—	2	1	no	—
434	C₄×C₆₇	—	2	1	no	—
435	C₄×C₆₇	—	2	1	no	—
436	C₄×C₆₇	—	4	1	no	—
437	C₄×C₆₇	—	4	2	no	—
438	C₄×C₆₇	—	4	1	no	—
439	C₄×C₆₇	—	4	4	no	—
440	C₄×C₆₇	—	4	1	no	—
441	C₄×C₆₇	—	4	2	no	—
442	C₄×C₆₇	#575	1	2	yes	—
443	C₄×C₆₇	#585	1	2	yes	—
444	#61740	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
445	C₂×C₆₇	—	2	2	no	—
446	C₂×C₆₇	—	4	2	no	—
447	C₂×C₆₇	—	4	2	no	—
448	C₂×C₆₇	—	8	2	no	—
449	C₂×C₆₇	—	8	2	no	—
450	C₂×C₆₇	—	8	1	no	—
451	C₂×C₆₇	#3485	1	1	yes	characteristic
452	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
453	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
454	#3519	C₂×C₆₇	1	1	yes	characteristic, complemented
455	C₂×#555	C₂×C₆₇	1	1	yes	characteristic, complemented
456	#3357	C₂×C₆₇	1	2	yes	complemented
457	#3347	C₂×C₆₇	1	4	yes	complemented
458	#3341	C₂×C₆₇	1	2	yes	complemented
459	#3325	C₂×C₆₇	1	2	yes	complemented
460	#3319	C₂×C₆₇	1	4	yes	complemented
461	#3305	C₂×C₆₇	1	2	yes	complemented
462	#3238	C₂×C₆₇	1	1	yes	characteristic, complemented
463	#3226	C₂×C₆₇	1	1	yes	characteristic, complemented
464	#3194	C₂×C₆₇	1	2	yes	complemented
465	#3186	C₂×C₆₇	1	2	yes	complemented
466	#3109	C₂×C₆₇	1	1	yes	characteristic, complemented
467	#3105	C₂×C₆₇	1	1	yes	characteristic, complemented
468	#3094	C₂×C₆₇	1	2	yes	complemented
469	#3091	C₂×C₆₇	1	2	yes	complemented
470	#2974	C₂×C₆₇	1	1	yes	characteristic, complemented
471	C₆₇	#61740	1	1	yes	characteristic, direct product factor, Sylow
472	#555	—	2	1	no	—
473	#555	—	2	1	no	—
474	#555	—	2	2	no	—
475	#555	C₂²×C₆₇	1	2	yes	—
476	#555	C₂²×C₆₇	1	1	yes	characteristic, complemented
477	#555	C₂²×C₆₇	1	2	yes	complemented
478	#555	C₂²×C₆₇	1	4	yes	complemented
479	#554	C₂²×C₆₇	1	1	yes	characteristic, complemented
480	#553	—	2	1	no	—
481	#553	C₂²×C₆₇	1	2	yes	complemented
482	#550	C₂²×C₆₇	1	1	yes	characteristic, complemented
483	#546	—	2	2	no	—
484	#546	C₂²×C₆₇	1	2	yes	complemented
485	D₄²	—	2	1	no	—
486	D₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
487	#540	—	2	1	no	—
488	#538	—	2	2	no	—
489	#532	C₂²×C₆₇	1	1	yes	characteristic
490	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
491	#529	C₂²×C₆₇	1	1	yes	characteristic
492	C₂×#124	—	2	2	no	—
493	#525	C₂²×C₆₇	1	2	yes	—
494	C₂×#121	—	2	1	no	—
495	C₂×#121	C₂²×C₆₇	1	2	yes	—
496	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
497	#518	—	2	1	no	—
498	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
499	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
500	C₂×#117	—	2	1	no	—
501	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
502	#501	C₂²×C₆₇	1	2	yes	complemented
503	#500	C₂²×C₆₇	1	2	yes	complemented
504	#489	C₂²×C₆₇	1	2	yes	complemented
505	#486	C₂²×C₆₇	1	2	yes	complemented
506	#485	C₂²×C₆₇	1	4	yes	complemented
507	#484	C₂²×C₆₇	1	1	yes	characteristic, complemented
508	#483	C₂²×C₆₇	1	2	yes	complemented
509	#482	C₂²×C₆₇	1	4	yes	complemented
510	#482	C₂²×C₆₇	1	4	yes	complemented
511	#482	C₂²×C₆₇	1	4	yes	complemented
512	#482	C₂²×C₆₇	1	4	yes	complemented
513	#481	C₂²×C₆₇	1	1	yes	characteristic
514	#481	C₂²×C₆₇	1	2	yes	complemented
515	#480	C₂²×C₆₇	1	2	yes	—
516	#480	C₂²×C₆₇	1	2	yes	complemented
517	#480	C₂²×C₆₇	1	4	yes	complemented
518	#480	C₂²×C₆₇	1	2	yes	complemented
519	#478	C₂²×C₆₇	1	2	yes	complemented
520	#477	C₂²×C₆₇	1	2	yes	complemented
521	#476	C₂²×C₆₇	1	2	yes	complemented
522	#476	C₂²×C₆₇	1	2	yes	complemented
523	#474	C₂²×C₆₇	1	4	yes	complemented
524	#469	C₂²×C₆₇	1	4	yes	complemented
525	#468	C₂²×C₆₇	1	4	yes	complemented
526	#466	C₂²×C₆₇	1	4	yes	complemented
527	#466	C₂²×C₆₇	1	4	yes	complemented
528	#463	C₂²×C₆₇	1	2	yes	complemented
529	#459	C₂²×C₆₇	1	2	yes	complemented
530	#450	C₂²×C₆₇	1	1	yes	characteristic, complemented
531	#449	C₂²×C₆₇	1	4	yes	complemented
532	#447	C₂²×C₆₇	1	1	yes	characteristic
533	#447	C₂²×C₆₇	1	2	yes	complemented
534	#447	C₂²×C₆₇	1	4	yes	complemented
535	#442	C₂²×C₆₇	1	4	yes	complemented
536	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
537	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
538	#436	C₂²×C₆₇	1	2	yes	complemented
539	#435	C₂²×C₆₇	1	4	yes	complemented
540	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
541	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
542	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
543	#428	C₂²×C₆₇	1	4	yes	complemented
544	#427	C₂²×C₆₇	1	4	yes	complemented
545	#418	C₂²×C₆₇	1	4	yes	complemented
546	#416	C₂²×C₆₇	1	4	yes	complemented
547	#407	C₂²×C₆₇	1	2	yes	complemented
548	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
549	C₂×#41	—	2	1	no	—
550	C₂×#41	C₂³×C₆₇	1	2	yes	—
551	C₂²×Q₈	—	2	1	no	—
552	C₂²×D₄	—	2	2	no	—
553	C₂²×D₄	—	2	2	no	—
554	C₂²×D₄	—	2	1	no	—
555	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
556	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
557	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
558	C₂³×C₄	—	2	1	no	—
559	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
560	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
561	C₂×D₈	C₂³×C₆₇	1	2	yes	—
562	C₂×D₈	C₂³×C₆₇	1	4	yes	—
563	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
564	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
565	C₄⋊Q₈	—	2	1	no	—
566	C₄⋊Q₈	—	2	1	no	—
567	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
568	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
569	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
570	#127	—	2	1	no	—
571	#127	C₂³×C₆₇	1	1	yes	characteristic
572	#126	—	2	2	no	—
573	#126	—	2	1	no	—
574	#125	—	2	1	no	—
575	#125	C₂³×C₆₇	1	1	yes	characteristic
576	#124	—	2	4	no	—
577	#124	—	2	4	no	—
578	#124	—	2	4	no	—
579	#124	—	2	4	no	—
580	#124	—	2	2	no	—
581	#124	—	2	1	no	—
582	#124	C₂³×C₆₇	1	1	yes	characteristic
583	#123	—	2	2	no	—
584	#123	—	2	1	no	—
585	#123	—	2	2	no	—
586	#123	—	2	2	no	—
587	C₂²⋊Q₈	—	2	2	no	—
588	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
589	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
590	#121	—	2	2	no	—
591	#121	—	2	2	no	—
592	#121	—	2	4	no	—
593	#121	—	2	2	no	—
594	#121	—	2	1	no	—
595	#121	—	2	2	no	—
596	#121	—	2	2	no	—
597	#121	—	2	2	no	—
598	#121	—	2	2	no	—
599	#121	—	2	1	no	—
600	#121	—	2	1	no	—
601	#121	—	2	2	no	—
602	#121	—	2	2	no	—
603	#121	C₂³×C₆₇	1	1	yes	characteristic
604	#121	C₂³×C₆₇	1	2	yes	—
605	#121	C₂³×C₆₇	1	2	yes	—
606	#121	C₂³×C₆₇	1	2	yes	—
607	#121	C₂³×C₆₇	1	4	yes	—
608	#121	C₂³×C₆₇	1	4	yes	—
609	#121	C₂³×C₆₇	1	2	yes	—
610	#120	—	2	2	no	—
611	#120	—	2	2	no	—
612	#120	—	2	2	no	—
613	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
614	C₄×D₄	—	2	1	no	—
615	C₄×D₄	—	2	2	no	—
616	C₄×D₄	—	2	2	no	—
617	C₄×D₄	—	2	1	no	—
618	C₄×D₄	—	2	1	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	1	no	—
621	C₄×D₄	—	2	1	no	—
622	C₄×D₄	—	2	1	no	—
623	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
624	C₄×D₄	D₄×C₆₇	1	2	yes	—
625	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
626	C₄×D₄	C₂³×C₆₇	1	2	yes	—
627	C₄×D₄	C₂³×C₆₇	1	2	yes	—
628	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
629	C₄×D₄	C₂³×C₆₇	1	2	yes	—
630	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
631	C₄×D₄	C₂³×C₆₇	1	2	yes	—
632	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
633	#117	—	2	2	no	—
634	#117	—	2	2	no	—
635	#117	—	2	2	no	—
636	#117	—	2	2	no	—
637	#117	—	2	4	no	—
638	#117	—	2	1	no	—
639	#117	—	2	1	no	—
640	#117	C₂³×C₆₇	1	4	yes	—
641	#117	C₂³×C₆₇	1	4	yes	—
642	#117	C₂³×C₆₇	1	2	yes	—
643	C₂×C₄⋊C₄	—	2	1	no	—
644	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
648	C₂×C₂²⋊C₄	—	2	2	no	—
649	C₂×C₂²⋊C₄	—	2	2	no	—
650	C₂×C₂²⋊C₄	—	2	1	no	—
651	C₂×C₂²⋊C₄	—	2	2	no	—
652	C₂×C₂²⋊C₄	—	2	2	no	—
653	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
654	C₂×C₄²	—	2	2	no	—
655	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
656	#107	C₂³×C₆₇	1	2	yes	—
657	#107	C₂³×C₆₇	1	4	yes	—
658	#107	C₂³×C₆₇	1	4	yes	—
659	#107	C₂³×C₆₇	1	4	yes	—
660	#106	C₂³×C₆₇	1	4	yes	—
661	#106	C₂³×C₆₇	1	4	yes	—
662	#106	C₂³×C₆₇	1	2	yes	—
663	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
664	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
665	#103	C₂³×C₆₇	1	2	yes	—
666	#103	C₂³×C₆₇	1	4	yes	—
667	#102	C₂³×C₆₇	1	4	yes	—
668	#102	C₂³×C₆₇	1	4	yes	—
669	#102	C₂³×C₆₇	1	2	yes	—
670	#102	C₂³×C₆₇	1	4	yes	—
671	#102	C₂³×C₆₇	1	4	yes	—
672	#102	C₂³×C₆₇	1	2	yes	—
673	#102	C₂³×C₆₇	1	2	yes	—
674	#102	C₂³×C₆₇	1	4	yes	—
675	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
676	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
677	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
678	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
679	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
680	#97	C₂³×C₆₇	1	2	yes	—
681	C₄×C₈	C₂³×C₆₇	1	2	yes	—
682	C₂⁴	—	2	1	no	—
683	C₂⁴	—	2	2	no	—
684	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
685	#41	—	4	4	no	—
686	#41	—	8	2	no	—
687	C₂×Q₈	—	2	1	no	—
688	C₂×Q₈	—	2	2	no	—
689	C₂×Q₈	—	2	2	no	—
690	C₂×Q₈	—	8	2	no	—
691	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	1	no	—
695	C₂×D₄	—	2	2	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	4	no	—
699	C₂×D₄	—	2	4	no	—
700	C₂×D₄	—	2	1	no	—
701	C₂×D₄	—	2	1	no	—
702	C₂×D₄	—	2	1	no	—
703	C₂×D₄	—	2	2	no	—
704	C₂×D₄	—	4	2	no	—
705	C₂×D₄	—	4	2	no	—
706	C₂×D₄	—	4	4	no	—
707	C₂×D₄	—	4	4	no	—
708	C₂×D₄	—	8	4	no	—
709	C₂×D₄	—	8	4	no	—
710	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
711	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
712	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
713	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
714	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
715	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	2	no	—
721	C₂²×C₄	—	2	1	no	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	2	no	—
724	C₂²×C₄	—	4	4	no	—
725	C₂²×C₄	—	4	4	no	—
726	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
727	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
728	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
729	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
730	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
734	SD₁₆	—	4	2	no	—
735	D₈	—	4	2	no	—
736	D₈	—	4	4	no	—
737	M₁₆	—	4	4	no	—
738	C₂×C₈	—	4	4	no	—
739	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
740	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
741	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	1	no	—
748	C₄⋊C₄	—	2	1	no	—
749	C₄⋊C₄	—	2	1	no	—
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	1	no	—
753	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
754	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
755	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
756	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
757	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
758	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
759	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
760	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
761	C₂²⋊C₄	—	2	4	no	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	1	no	—
766	C₂²⋊C₄	—	2	1	no	—
767	C₂²⋊C₄	—	2	1	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	1	no	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	—	2	1	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
780	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
781	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
782	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
783	C₄²	—	2	4	no	—
784	C₄²	—	2	4	no	—
785	C₄²	—	2	2	no	—
786	C₄²	—	2	1	no	—
787	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
788	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
789	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
790	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
791	C₂³	—	2	4	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	1	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	4	2	no	—
796	C₂³	—	4	2	no	—
797	C₂³	—	4	2	no	—
798	C₂³	—	4	2	no	—
799	C₂³	—	4	4	no	—
800	C₂³	—	4	2	no	—
801	C₂³	—	8	2	no	—
802	C₂³	—	8	2	no	—
803	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
804	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
805	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
806	Q₈	—	2	2	no	—
807	Q₈	—	8	2	no	—
808	Q₈	—	8	2	no	—
809	Q₈	—	8	1	no	—
810	D₄	—	2	2	no	—
811	D₄	—	2	2	no	—
812	D₄	—	2	2	no	—
813	D₄	—	2	2	no	—
814	D₄	—	2	2	no	—
815	D₄	—	2	4	no	—
816	D₄	—	4	2	no	—
817	D₄	—	4	2	no	—
818	D₄	—	4	4	no	—
819	D₄	—	4	2	no	—
820	D₄	—	4	4	no	—
821	D₄	—	4	2	no	—
822	D₄	—	8	2	no	—
823	D₄	—	8	1	no	—
824	D₄	—	8	4	no	—
825	D₄	—	8	4	no	—
826	D₄	—	8	2	no	—
827	D₄	—	8	2	no	—
828	D₄	—	8	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	4	no	—
832	C₂×C₄	—	2	4	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	4	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	4	2	no	—
841	C₂×C₄	—	4	2	no	—
842	C₂×C₄	—	4	2	no	—
843	C₂×C₄	—	4	4	no	—
844	C₂×C₄	—	4	2	no	—
845	C₂×C₄	—	4	4	no	—
846	C₂×C₄	—	4	4	no	—
847	C₂×C₄	—	4	2	no	—
848	C₂×C₄	—	8	2	no	—
849	C₂×C₄	—	8	2	no	—
850	C₂×C₄	—	8	2	no	—
851	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
852	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
853	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
854	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
855	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
856	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
857	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
858	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
859	C₈	—	2	2	no	—
860	C₈	—	2	4	no	—
861	C₈	—	2	2	no	—
862	C₂²	—	2	1	no	—
863	C₂²	—	2	1	no	—
864	C₂²	—	2	2	no	—
865	C₂²	—	2	2	no	—
866	C₂²	—	2	2	no	—
867	C₂²	—	2	2	no	—
868	C₂²	—	2	2	no	—
869	C₂²	—	2	2	no	—
870	C₂²	—	4	2	no	—
871	C₂²	—	4	1	no	—
872	C₂²	—	4	2	no	—
873	C₂²	—	4	2	no	—
874	C₂²	—	4	1	no	—
875	C₂²	—	4	2	no	—
876	C₂²	—	4	2	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	1	no	—
879	C₂²	—	8	4	no	—
880	C₂²	—	8	4	no	—
881	C₂²	—	16	4	no	—
882	C₂²	#576×C₆₇	1	2	yes	—
883	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
884	C₄	—	2	1	no	—
885	C₄	—	2	1	no	—
886	C₄	—	2	1	no	—
887	C₄	—	2	1	no	—
888	C₄	—	2	2	no	—
889	C₄	—	2	2	no	—
890	C₄	—	4	2	no	—
891	C₄	—	4	1	no	—
892	C₄	—	4	4	no	—
893	C₄	—	4	1	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	1	no	—
896	C₄	#575×C₆₇	1	2	yes	—
897	C₄	#585×C₆₇	1	2	yes	—
898	C₂	—	2	2	no	—
899	C₂	—	4	2	no	—
900	C₂	—	4	2	no	—
901	C₂	—	8	2	no	—
902	C₂	—	8	1	no	—
903	C₂	—	8	2	no	—
904	C₂	C₆₇×#3485	1	1	yes	characteristic
905	C₂	C₂×#575×C₆₇	1	1	yes	characteristic
906	C₂	C₂×#576×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 ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3519	C₂	semidirect
2. C₂×#555×C₆₇	C₂	semidirect
3. C₆₇×#3357	C₂	semidirect
4. C₆₇×#3347	C₂	semidirect
5. C₆₇×#3341	C₂	semidirect
6. C₆₇×#3325	C₂	semidirect
7. C₆₇×#3319	C₂	semidirect
8. C₆₇×#3305	C₂	semidirect
9. C₆₇×#3238	C₂	semidirect
10. C₆₇×#3226	C₂	semidirect
11. C₆₇×#3194	C₂	semidirect
12. C₆₇×#3186	C₂	semidirect
13. C₆₇×#3109	C₂	semidirect
14. C₆₇×#3105	C₂	semidirect
15. C₆₇×#3094	C₂	semidirect
16. C₆₇×#3091	C₂	semidirect
17. C₆₇×#2974	C₂	semidirect
22. #555×C₆₇	C₂²	semidirect
23. #555×C₆₇	C₂²	semidirect
24. #555×C₆₇	C₂²	semidirect
25. #554×C₆₇	C₂²	semidirect
27. #553×C₆₇	C₂²	semidirect
28. #550×C₆₇	C₂²	semidirect
30. #546×C₆₇	C₂²	semidirect
32. D₄²×C₆₇	C₂²	semidirect
36. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
42. C₂×#121×C₆₇	C₂²	semidirect
45. C₂×C₄×D₄×C₆₇	C₂²	semidirect
47. C₂×#117×C₆₇	C₂²	semidirect
48. #501×C₆₇	C₂²	semidirect
49. #500×C₆₇	C₂²	semidirect
50. #489×C₆₇	C₂²	semidirect
51. #486×C₆₇	C₂²	semidirect
52. #485×C₆₇	C₂²	semidirect
53. #484×C₆₇	C₂²	semidirect
54. #483×C₆₇	C₂²	semidirect
55. #482×C₆₇	C₂²	semidirect
56. #482×C₆₇	C₂²	semidirect
57. #482×C₆₇	C₂²	semidirect
58. #482×C₆₇	C₂²	semidirect
60. #481×C₆₇	C₂²	semidirect
62. #480×C₆₇	C₂²	semidirect
63. #480×C₆₇	C₂²	semidirect
64. #480×C₆₇	C₂²	semidirect
65. #478×C₆₇	C₂²	semidirect
66. #477×C₆₇	C₂²	semidirect
67. #476×C₆₇	C₂²	semidirect
68. #476×C₆₇	C₂²	semidirect
69. #474×C₆₇	C₂²	semidirect
70. #469×C₆₇	C₂²	semidirect
71. #468×C₆₇	C₂²	semidirect
72. #466×C₆₇	C₂²	semidirect
73. #466×C₆₇	C₂²	semidirect
74. #463×C₆₇	C₂²	semidirect
75. #459×C₆₇	C₂²	semidirect
76. #450×C₆₇	C₂²	semidirect
77. #449×C₆₇	C₂²	semidirect
79. #447×C₆₇	C₂²	semidirect
80. #447×C₆₇	C₂²	semidirect
81. #442×C₆₇	C₂²	semidirect
82. C₄×SD₁₆×C₆₇	C₂²	semidirect
83. C₄×D₈×C₆₇	C₂²	semidirect
84. #436×C₆₇	C₂²	semidirect
85. #435×C₆₇	C₂²	semidirect
86. C₈×D₄×C₆₇	C₂²	semidirect
87. #432×C₆₇	C₂²	semidirect
88. #431×C₆₇	C₂²	semidirect
89. #428×C₆₇	C₂²	semidirect
90. #427×C₆₇	C₂²	semidirect
91. #418×C₆₇	C₂²	semidirect
92. #416×C₆₇	C₂²	semidirect
93. #407×C₆₇	C₂²	semidirect
94. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
444. #61740	C₆₇	direct (N × H)
454. #3519	C₂×C₆₇	semidirect
455. C₂×#555	C₂×C₆₇	semidirect
456. #3357	C₂×C₆₇	semidirect
457. #3347	C₂×C₆₇	semidirect
458. #3341	C₂×C₆₇	semidirect
459. #3325	C₂×C₆₇	semidirect
460. #3319	C₂×C₆₇	semidirect
461. #3305	C₂×C₆₇	semidirect
462. #3238	C₂×C₆₇	semidirect
463. #3226	C₂×C₆₇	semidirect
464. #3194	C₂×C₆₇	semidirect
465. #3186	C₂×C₆₇	semidirect
466. #3109	C₂×C₆₇	semidirect
467. #3105	C₂×C₆₇	semidirect
468. #3094	C₂×C₆₇	semidirect
469. #3091	C₂×C₆₇	semidirect
470. #2974	C₂×C₆₇	semidirect
471. C₆₇	#61740	direct (N × H)
476. #555	C₂²×C₆₇	semidirect
477. #555	C₂²×C₆₇	semidirect
478. #555	C₂²×C₆₇	semidirect
479. #554	C₂²×C₆₇	semidirect
481. #553	C₂²×C₆₇	semidirect
482. #550	C₂²×C₆₇	semidirect
484. #546	C₂²×C₆₇	semidirect
486. D₄²	C₂²×C₆₇	semidirect
490. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
496. C₂×#121	C₂²×C₆₇	semidirect
499. C₂×C₄×D₄	C₂²×C₆₇	semidirect
501. C₂×#117	C₂²×C₆₇	semidirect
502. #501	C₂²×C₆₇	semidirect
503. #500	C₂²×C₆₇	semidirect
504. #489	C₂²×C₆₇	semidirect
505. #486	C₂²×C₆₇	semidirect
506. #485	C₂²×C₆₇	semidirect
507. #484	C₂²×C₆₇	semidirect
508. #483	C₂²×C₆₇	semidirect
509. #482	C₂²×C₆₇	semidirect
510. #482	C₂²×C₆₇	semidirect
511. #482	C₂²×C₆₇	semidirect
512. #482	C₂²×C₆₇	semidirect
514. #481	C₂²×C₆₇	semidirect
516. #480	C₂²×C₆₇	semidirect
517. #480	C₂²×C₆₇	semidirect
518. #480	C₂²×C₆₇	semidirect
519. #478	C₂²×C₆₇	semidirect
520. #477	C₂²×C₆₇	semidirect
521. #476	C₂²×C₆₇	semidirect
522. #476	C₂²×C₆₇	semidirect
523. #474	C₂²×C₆₇	semidirect
524. #469	C₂²×C₆₇	semidirect
525. #468	C₂²×C₆₇	semidirect
526. #466	C₂²×C₆₇	semidirect
527. #466	C₂²×C₆₇	semidirect
528. #463	C₂²×C₆₇	semidirect
529. #459	C₂²×C₆₇	semidirect
530. #450	C₂²×C₆₇	semidirect
531. #449	C₂²×C₆₇	semidirect
533. #447	C₂²×C₆₇	semidirect
534. #447	C₂²×C₆₇	semidirect
535. #442	C₂²×C₆₇	semidirect
536. C₄×SD₁₆	C₂²×C₆₇	semidirect
537. C₄×D₈	C₂²×C₆₇	semidirect
538. #436	C₂²×C₆₇	semidirect
539. #435	C₂²×C₆₇	semidirect
540. C₈×D₄	C₂²×C₆₇	semidirect
541. #432	C₂²×C₆₇	semidirect
542. #431	C₂²×C₆₇	semidirect
543. #428	C₂²×C₆₇	semidirect
544. #427	C₂²×C₆₇	semidirect
545. #418	C₂²×C₆₇	semidirect
546. #416	C₂²×C₆₇	semidirect
547. #407	C₂²×C₆₇	semidirect
548. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3519	2
C₂×#555×C₆₇	2
C₆₇×#3357	2
C₆₇×#3347	2
C₆₇×#3341	2
C₆₇×#3325	2
C₆₇×#3319	2
C₆₇×#3305	2
C₆₇×#3238	2
C₆₇×#3226	2
C₆₇×#3194	2
C₆₇×#3186	2
C₆₇×#3109	2
C₆₇×#3105	2
C₆₇×#3094	2
C₆₇×#3091	2
C₆₇×#2974	2
#61740	67

Subgroups — C67×#61740 #30740991

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61740 #30740991