Subgroups — C₆₇×#61005 #30740256

Order 17152.

1672 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3495	C₂	1	2	yes	maximal, complemented
2	C₆₇×#3256	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3255	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3252	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3244	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3242	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3225	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3223	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3197	C₂	1	1	yes	maximal, characteristic
10	C₆₇×#3196	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3195	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3185	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3183	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3172	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3127	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3125	C₂	1	2	yes	maximal, complemented
17	C₆₇×#3121	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3120	C₂	1	2	yes	maximal, complemented
19	C₆₇×#2921	C₂	1	1	yes	maximal, characteristic, complemented
20	#556×C₆₇	—	2	2	no	—
21	#554×C₆₇	—	2	2	no	—
22	#552×C₆₇	—	2	2	no	—
23	#552×C₆₇	—	2	2	no	—
24	#552×C₆₇	—	2	2	no	—
25	#552×C₆₇	—	2	2	no	—
26	#551×C₆₇	—	2	2	no	—
27	#551×C₆₇	—	2	2	no	—
28	#544×C₆₇	C₂²	1	2	yes	—
29	#542×C₆₇	C₂²	1	2	yes	—
30	#542×C₆₇	C₂²	1	2	yes	—
31	#541×C₆₇	C₂²	1	2	yes	—
32	#541×C₆₇	C₂²	1	2	yes	—
33	#536×C₆₇	C₂²	1	2	yes	—
34	#533×C₆₇	C₂²	1	2	yes	—
35	#533×C₆₇	C₂²	1	2	yes	—
36	#529×C₆₇	C₂²	1	2	yes	—
37	#529×C₆₇	C₂²	1	2	yes	—
38	#525×C₆₇	C₂²	1	2	yes	—
39	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
40	#520×C₆₇	C₂²	1	2	yes	—
41	#519×C₆₇	C₂²	1	2	yes	—
42	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
43	#501×C₆₇	C₂²	1	2	yes	complemented
44	#499×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	#498×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	#497×C₆₇	C₂²	1	2	yes	complemented
47	#495×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	#494×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#491×C₆₇	C₂²	1	2	yes	complemented
50	#489×C₆₇	C₂²	1	2	yes	complemented
51	#488×C₆₇	C₂²	1	2	yes	complemented
52	#487×C₆₇	C₂²	1	2	yes	complemented
53	#485×C₆₇	C₂²	1	2	yes	—
54	#485×C₆₇	C₂²	1	2	yes	—
55	#485×C₆₇	C₂²	1	2	yes	—
56	#484×C₆₇	C₂²	1	2	yes	—
57	#483×C₆₇	C₂²	1	2	yes	—
58	#483×C₆₇	C₂²	1	2	yes	—
59	#482×C₆₇	C₂²	1	2	yes	—
60	#481×C₆₇	C₂²	1	2	yes	—
61	#479×C₆₇	C₂²	1	2	yes	complemented
62	#479×C₆₇	C₂²	1	2	yes	complemented
63	#479×C₆₇	C₂²	1	2	yes	complemented
64	#478×C₆₇	C₂²	1	2	yes	complemented
65	#477×C₆₇	C₂²	1	2	yes	complemented
66	#476×C₆₇	C₂²	1	2	yes	complemented
67	#475×C₆₇	C₂²	1	2	yes	complemented
68	#475×C₆₇	C₂²	1	2	yes	complemented
69	#470×C₆₇	C₂²	1	2	yes	—
70	#470×C₆₇	C₂²	1	2	yes	—
71	#470×C₆₇	C₂²	1	1	yes	characteristic
72	#470×C₆₇	C₂²	1	1	yes	characteristic
73	#470×C₆₇	C₂²	1	2	yes	—
74	#470×C₆₇	C₂²	1	1	yes	characteristic
75	#469×C₆₇	C₂²	1	1	yes	characteristic
76	#468×C₆₇	C₂²	1	2	yes	—
77	#468×C₆₇	C₂²	1	2	yes	—
78	#468×C₆₇	C₂²	1	2	yes	—
79	#464×C₆₇	C₂²	1	2	yes	complemented
80	#464×C₆₇	C₂²	1	2	yes	complemented
81	#464×C₆₇	C₂²	1	2	yes	complemented
82	#463×C₆₇	C₂²	1	2	yes	complemented
83	#462×C₆₇	C₂²	1	2	yes	complemented
84	#462×C₆₇	C₂²	1	2	yes	complemented
85	#462×C₆₇	C₂²	1	2	yes	complemented
86	#461×C₆₇	C₂²	1	2	yes	complemented
87	#452×C₆₇	C₂²	1	2	yes	—
88	#452×C₆₇	C₂²	1	2	yes	—
89	#452×C₆₇	C₂²	1	2	yes	—
90	#451×C₆₇	C₂²	1	2	yes	—
91	#451×C₆₇	C₂²	1	2	yes	—
92	#451×C₆₇	C₂²	1	2	yes	—
93	#449×C₆₇	C₂²	1	2	yes	—
94	#448×C₆₇	C₂²	1	2	yes	—
95	#442×C₆₇	C₂²	1	1	yes	characteristic, complemented
96	#441×C₆₇	C₂²	1	1	yes	characteristic, complemented
97	#441×C₆₇	C₂²	1	1	yes	characteristic, complemented
98	#441×C₆₇	C₂²	1	2	yes	complemented
99	#441×C₆₇	C₂²	1	1	yes	characteristic, complemented
100	#440×C₆₇	C₂²	1	2	yes	complemented
101	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
102	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
103	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
104	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
105	#433×C₆₇	C₂²	1	2	yes	—
106	#433×C₆₇	C₂²	1	2	yes	—
107	#433×C₆₇	C₂²	1	2	yes	—
108	#433×C₆₇	C₂²	1	2	yes	—
109	#423×C₆₇	C₂²	1	1	yes	characteristic
110	#423×C₆₇	C₂²	1	1	yes	characteristic
111	#407×C₆₇	C₂²	1	1	yes	characteristic
112	#407×C₆₇	C₂²	1	1	yes	characteristic
113	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
114	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
115	C₂×#41×C₆₇	C₂³	1	2	yes	—
116	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
117	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
118	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
119	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
120	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
121	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
122	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
123	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
124	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
125	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
127	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
128	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
129	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
130	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
131	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
132	C₄⋊Q₈×C₆₇	—	2	2	no	—
133	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
134	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
135	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
136	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
137	#126×C₆₇	—	2	2	no	—
138	#126×C₆₇	—	2	2	no	—
139	#126×C₆₇	—	2	2	no	—
140	#126×C₆₇	—	2	2	no	—
141	#126×C₆₇	—	2	2	no	—
142	#126×C₆₇	—	2	2	no	—
143	#126×C₆₇	—	2	2	no	—
144	#126×C₆₇	—	2	2	no	—
145	#125×C₆₇	—	2	2	no	—
146	#125×C₆₇	—	2	2	no	—
147	#125×C₆₇	—	2	2	no	—
148	#125×C₆₇	—	2	2	no	—
149	#125×C₆₇	—	2	2	no	—
150	#125×C₆₇	—	2	2	no	—
151	#125×C₆₇	—	2	2	no	—
152	#125×C₆₇	C₂³	1	2	yes	—
153	#125×C₆₇	C₂³	1	2	yes	—
154	#124×C₆₇	—	2	2	no	—
155	#124×C₆₇	—	2	2	no	—
156	#124×C₆₇	C₂³	1	2	yes	—
157	#124×C₆₇	C₂³	1	2	yes	—
158	#123×C₆₇	—	2	2	no	—
159	#123×C₆₇	—	2	2	no	—
160	#123×C₆₇	—	2	2	no	—
161	#123×C₆₇	—	2	2	no	—
162	#123×C₆₇	—	2	2	no	—
163	#123×C₆₇	—	2	2	no	—
164	#123×C₆₇	—	2	2	no	—
165	C₂²⋊Q₈×C₆₇	—	2	2	no	—
166	C₂²⋊Q₈×C₆₇	—	2	2	no	—
167	C₂²⋊Q₈×C₆₇	—	2	2	no	—
168	C₂²⋊Q₈×C₆₇	—	2	2	no	—
169	C₂²⋊Q₈×C₆₇	—	2	2	no	—
170	C₂²⋊Q₈×C₆₇	—	2	2	no	—
171	C₂²⋊Q₈×C₆₇	—	2	2	no	—
172	C₂²⋊Q₈×C₆₇	—	2	2	no	—
173	C₂²⋊Q₈×C₆₇	—	2	2	no	—
174	C₂²⋊Q₈×C₆₇	—	2	2	no	—
175	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
176	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
177	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
178	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
179	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
180	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
181	#121×C₆₇	C₂³	1	2	yes	—
182	#121×C₆₇	C₂³	1	2	yes	—
183	#120×C₆₇	—	2	2	no	—
184	C₄×Q₈×C₆₇	—	2	2	no	—
185	C₄×Q₈×C₆₇	—	2	2	no	—
186	C₄×Q₈×C₆₇	—	2	2	no	—
187	C₄×Q₈×C₆₇	—	2	2	no	—
188	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
189	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
190	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
191	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
192	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
193	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
194	C₄×D₄×C₆₇	—	2	2	no	—
195	C₄×D₄×C₆₇	—	2	2	no	—
196	C₄×D₄×C₆₇	—	2	2	no	—
197	C₄×D₄×C₆₇	—	2	2	no	—
198	C₄×D₄×C₆₇	—	2	2	no	—
199	C₄×D₄×C₆₇	—	2	2	no	—
200	C₄×D₄×C₆₇	C₂³	1	2	yes	—
201	C₄×D₄×C₆₇	C₂³	1	2	yes	—
202	#117×C₆₇	—	2	2	no	—
203	#117×C₆₇	—	2	2	no	—
204	#117×C₆₇	—	2	2	no	—
205	#117×C₆₇	—	2	2	no	—
206	#117×C₆₇	—	2	2	no	—
207	#117×C₆₇	—	2	2	no	—
208	#117×C₆₇	—	2	2	no	—
209	#117×C₆₇	D₄	1	2	yes	—
210	#117×C₆₇	D₄	1	2	yes	—
211	#117×C₆₇	C₂³	1	2	yes	—
212	#117×C₆₇	C₂³	1	2	yes	—
213	#117×C₆₇	C₂³	1	2	yes	—
214	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
215	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
216	C₂×C₄⋊C₄×C₆₇	D₄	1	2	yes	—
217	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
219	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
220	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
222	#107×C₆₇	C₂³	1	2	yes	—
223	#107×C₆₇	C₂³	1	2	yes	—
224	#107×C₆₇	C₂³	1	2	yes	—
225	#106×C₆₇	C₂³	1	1	yes	characteristic
226	#106×C₆₇	C₂³	1	2	yes	—
227	#106×C₆₇	C₂³	1	1	yes	characteristic
228	#106×C₆₇	C₂³	1	1	yes	characteristic
229	#106×C₆₇	C₂³	1	2	yes	—
230	#106×C₆₇	C₂³	1	2	yes	—
231	#106×C₆₇	C₂³	1	1	yes	characteristic
232	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
233	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
234	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
235	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
236	#103×C₆₇	C₂³	1	2	yes	—
237	#103×C₆₇	C₂³	1	2	yes	—
238	#103×C₆₇	C₂³	1	2	yes	—
239	#103×C₆₇	C₂³	1	2	yes	—
240	#103×C₆₇	C₂³	1	2	yes	—
241	#103×C₆₇	C₂³	1	2	yes	—
242	#103×C₆₇	C₂³	1	2	yes	—
243	#103×C₆₇	C₂³	1	2	yes	—
244	#103×C₆₇	C₂³	1	2	yes	—
245	#103×C₆₇	C₂³	1	2	yes	—
246	#103×C₆₇	C₂³	1	2	yes	—
247	#103×C₆₇	C₂³	1	2	yes	—
248	#102×C₆₇	C₂³	1	2	yes	—
249	#102×C₆₇	C₂³	1	2	yes	—
250	#102×C₆₇	C₂³	1	2	yes	—
251	#102×C₆₇	C₂³	1	2	yes	—
252	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
253	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
254	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
255	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
256	#97×C₆₇	C₂³	1	2	yes	—
257	#97×C₆₇	C₂³	1	1	yes	characteristic
258	#97×C₆₇	C₂³	1	1	yes	characteristic
259	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
260	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
261	C₄×C₈×C₆₇	C₂³	1	2	yes	—
262	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
263	#41×C₆₇	—	4	2	no	—
264	#41×C₆₇	—	4	2	no	—
265	C₂×Q₈×C₆₇	—	2	2	no	—
266	C₂×Q₈×C₆₇	—	2	2	no	—
267	C₂×Q₈×C₆₇	—	2	2	no	—
268	C₂×Q₈×C₆₇	—	4	2	no	—
269	C₂×Q₈×C₆₇	—	4	2	no	—
270	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
271	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
272	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
273	C₂×D₄×C₆₇	—	2	2	no	—
274	C₂×D₄×C₆₇	—	2	2	no	—
275	C₂×D₄×C₆₇	—	2	2	no	—
276	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₆₇	—	2	2	no	—
278	C₂²×C₄×C₆₇	—	2	2	no	—
279	C₂²×C₄×C₆₇	—	2	2	no	—
280	C₂²×C₄×C₆₇	—	2	2	no	—
281	C₂²×C₄×C₆₇	—	2	2	no	—
282	C₂²×C₄×C₆₇	—	4	1	no	—
283	C₂²×C₄×C₆₇	—	4	1	no	—
284	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
285	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
286	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
287	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
290	Q₁₆×C₆₇	—	4	1	no	—
291	Q₁₆×C₆₇	—	4	2	no	—
292	Q₁₆×C₆₇	—	4	2	no	—
293	Q₁₆×C₆₇	—	4	1	no	—
294	Q₁₆×C₆₇	—	4	2	no	—
295	Q₁₆×C₆₇	—	4	1	no	—
296	SD₁₆×C₆₇	—	4	2	no	—
297	SD₁₆×C₆₇	—	4	2	no	—
298	SD₁₆×C₆₇	—	4	2	no	—
299	D₈×C₆₇	—	4	1	no	—
300	M₁₆×C₆₇	—	4	1	no	—
301	M₁₆×C₆₇	—	4	1	no	—
302	M₁₆×C₆₇	—	4	1	no	—
303	M₁₆×C₆₇	—	4	1	no	—
304	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
305	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
306	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
307	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
308	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
309	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
310	C₄⋊C₄×C₆₇	—	2	2	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	2	no	—
315	C₄⋊C₄×C₆₇	—	2	2	no	—
316	C₄⋊C₄×C₆₇	—	2	2	no	—
317	C₄⋊C₄×C₆₇	—	2	2	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	2	no	—
322	C₄⋊C₄×C₆₇	—	2	2	no	—
323	C₄⋊C₄×C₆₇	—	2	2	no	—
324	C₄⋊C₄×C₆₇	—	2	2	no	—
325	C₄⋊C₄×C₆₇	—	2	2	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	—	2	2	no	—
330	C₄⋊C₄×C₆₇	—	2	2	no	—
331	C₄⋊C₄×C₆₇	—	2	2	no	—
332	C₄⋊C₄×C₆₇	—	2	2	no	—
333	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
334	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
335	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
336	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
337	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
338	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
339	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
340	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
341	C₂²⋊C₄×C₆₇	—	2	2	no	—
342	C₂²⋊C₄×C₆₇	—	2	2	no	—
343	C₂²⋊C₄×C₆₇	—	2	2	no	—
344	C₂²⋊C₄×C₆₇	—	2	2	no	—
345	C₂²⋊C₄×C₆₇	—	2	2	no	—
346	C₂²⋊C₄×C₆₇	—	2	2	no	—
347	C₂²⋊C₄×C₆₇	—	2	2	no	—
348	C₂²⋊C₄×C₆₇	—	2	2	no	—
349	C₂²⋊C₄×C₆₇	—	2	2	no	—
350	C₂²⋊C₄×C₆₇	—	2	2	no	—
351	C₂²⋊C₄×C₆₇	—	2	2	no	—
352	C₂²⋊C₄×C₆₇	—	2	2	no	—
353	C₂²⋊C₄×C₆₇	—	2	2	no	—
354	C₂²⋊C₄×C₆₇	—	2	2	no	—
355	C₂²⋊C₄×C₆₇	—	2	2	no	—
356	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
357	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
358	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
359	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
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	2	no	—
365	C₄²×C₆₇	—	2	2	no	—
366	C₄²×C₆₇	—	2	2	no	—
367	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
368	C₄²×C₆₇	C₂×D₄	1	2	yes	—
369	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
370	C₄²×C₆₇	C₂⁴	1	2	yes	—
371	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
372	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
373	C₂³×C₆₇	—	2	2	no	—
374	C₂³×C₆₇	—	4	1	no	—
375	C₂³×C₆₇	—	4	2	no	—
376	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
377	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
378	Q₈×C₆₇	—	2	2	no	—
379	Q₈×C₆₇	—	2	2	no	—
380	Q₈×C₆₇	—	2	2	no	—
381	Q₈×C₆₇	—	2	2	no	—
382	Q₈×C₆₇	—	2	2	no	—
383	Q₈×C₆₇	—	2	2	no	—
384	Q₈×C₆₇	—	4	4	no	—
385	Q₈×C₆₇	—	8	2	no	—
386	Q₈×C₆₇	—	8	2	no	—
387	D₄×C₆₇	—	2	2	no	—
388	D₄×C₆₇	—	2	2	no	—
389	D₄×C₆₇	—	4	4	no	—
390	D₄×C₆₇	—	4	4	no	—
391	D₄×C₆₇	—	8	2	no	—
392	C₂×C₄×C₆₇	—	2	1	no	—
393	C₂×C₄×C₆₇	—	2	1	no	—
394	C₂×C₄×C₆₇	—	2	2	no	—
395	C₂×C₄×C₆₇	—	2	2	no	—
396	C₂×C₄×C₆₇	—	2	2	no	—
397	C₂×C₄×C₆₇	—	2	2	no	—
398	C₂×C₄×C₆₇	—	2	2	no	—
399	C₂×C₄×C₆₇	—	2	2	no	—
400	C₂×C₄×C₆₇	—	2	2	no	—
401	C₂×C₄×C₆₇	—	2	2	no	—
402	C₂×C₄×C₆₇	—	2	2	no	—
403	C₂×C₄×C₆₇	—	4	1	no	—
404	C₂×C₄×C₆₇	—	4	2	no	—
405	C₂×C₄×C₆₇	—	4	2	no	—
406	C₂×C₄×C₆₇	—	4	2	no	—
407	C₂×C₄×C₆₇	—	4	4	no	—
408	C₂×C₄×C₆₇	—	4	4	no	—
409	C₂×C₄×C₆₇	—	8	2	no	—
410	C₂×C₄×C₆₇	—	8	2	no	—
411	C₂×C₄×C₆₇	—	8	2	no	—
412	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
413	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
414	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
415	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
416	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
418	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
419	C₈×C₆₇	—	2	1	no	—
420	C₈×C₆₇	—	2	1	no	—
421	C₈×C₆₇	—	2	2	no	—
422	C₈×C₆₇	—	2	2	no	—
423	C₈×C₆₇	—	2	1	no	—
424	C₈×C₆₇	—	2	1	no	—
425	C₂²×C₆₇	—	2	2	no	—
426	C₂²×C₆₇	—	2	2	no	—
427	C₂²×C₆₇	—	2	2	no	—
428	C₂²×C₆₇	—	2	2	no	—
429	C₂²×C₆₇	—	2	1	no	—
430	C₂²×C₆₇	—	4	2	no	—
431	C₂²×C₆₇	—	4	2	no	—
432	C₂²×C₆₇	—	4	2	no	—
433	C₂²×C₆₇	—	8	2	no	—
434	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
435	C₄×C₆₇	—	2	2	no	—
436	C₄×C₆₇	—	2	2	no	—
437	C₄×C₆₇	—	2	2	no	—
438	C₄×C₆₇	—	2	2	no	—
439	C₄×C₆₇	—	2	2	no	—
440	C₄×C₆₇	—	2	1	no	—
441	C₄×C₆₇	—	4	2	no	—
442	C₄×C₆₇	—	4	2	no	—
443	C₄×C₆₇	—	4	2	no	—
444	C₄×C₆₇	—	4	2	no	—
445	C₄×C₆₇	—	4	2	no	—
446	C₄×C₆₇	—	4	2	no	—
447	C₄×C₆₇	—	4	2	no	—
448	C₄×C₆₇	#585	1	1	yes	characteristic
449	C₄×C₆₇	#585	1	1	yes	characteristic
450	#61005	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
451	C₂×C₆₇	—	4	1	no	—
452	C₂×C₆₇	—	4	2	no	—
453	C₂×C₆₇	—	8	2	no	—
454	C₂×C₆₇	#3449	1	1	yes	characteristic
455	C₂×C₆₇	#3586	1	2	yes	—
456	#3495	C₂×C₆₇	1	2	yes	complemented
457	#3256	C₂×C₆₇	1	1	yes	characteristic, complemented
458	#3255	C₂×C₆₇	1	1	yes	characteristic, complemented
459	#3252	C₂×C₆₇	1	2	yes	complemented
460	#3244	C₂×C₆₇	1	2	yes	complemented
461	#3242	C₂×C₆₇	1	2	yes	complemented
462	#3225	C₂×C₆₇	1	2	yes	complemented
463	#3223	C₂×C₆₇	1	2	yes	complemented
464	#3197	C₂×C₆₇	1	1	yes	characteristic
465	#3196	C₂×C₆₇	1	2	yes	complemented
466	#3195	C₂×C₆₇	1	1	yes	characteristic, complemented
467	#3185	C₂×C₆₇	1	1	yes	characteristic, complemented
468	#3183	C₂×C₆₇	1	1	yes	characteristic, complemented
469	#3172	C₂×C₆₇	1	2	yes	complemented
470	#3127	C₂×C₆₇	1	2	yes	complemented
471	#3125	C₂×C₆₇	1	2	yes	complemented
472	#3121	C₂×C₆₇	1	2	yes	complemented
473	#3120	C₂×C₆₇	1	2	yes	complemented
474	#2921	C₂×C₆₇	1	1	yes	characteristic, complemented
475	C₆₇	#61005	1	1	yes	characteristic, direct product factor, Sylow
476	#556	—	2	2	no	—
477	#554	—	2	2	no	—
478	#552	—	2	2	no	—
479	#552	—	2	2	no	—
480	#552	—	2	2	no	—
481	#552	—	2	2	no	—
482	#551	—	2	2	no	—
483	#551	—	2	2	no	—
484	#544	C₂²×C₆₇	1	2	yes	—
485	#542	C₂²×C₆₇	1	2	yes	—
486	#542	C₂²×C₆₇	1	2	yes	—
487	#541	C₂²×C₆₇	1	2	yes	—
488	#541	C₂²×C₆₇	1	2	yes	—
489	#536	C₂²×C₆₇	1	2	yes	—
490	#533	C₂²×C₆₇	1	2	yes	—
491	#533	C₂²×C₆₇	1	2	yes	—
492	#529	C₂²×C₆₇	1	2	yes	—
493	#529	C₂²×C₆₇	1	2	yes	—
494	#525	C₂²×C₆₇	1	2	yes	—
495	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
496	#520	C₂²×C₆₇	1	2	yes	—
497	#519	C₂²×C₆₇	1	2	yes	—
498	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
499	#501	C₂²×C₆₇	1	2	yes	complemented
500	#499	C₂²×C₆₇	1	1	yes	characteristic, complemented
501	#498	C₂²×C₆₇	1	1	yes	characteristic, complemented
502	#497	C₂²×C₆₇	1	2	yes	complemented
503	#495	C₂²×C₆₇	1	1	yes	characteristic, complemented
504	#494	C₂²×C₆₇	1	1	yes	characteristic, complemented
505	#491	C₂²×C₆₇	1	2	yes	complemented
506	#489	C₂²×C₆₇	1	2	yes	complemented
507	#488	C₂²×C₆₇	1	2	yes	complemented
508	#487	C₂²×C₆₇	1	2	yes	complemented
509	#485	C₂²×C₆₇	1	2	yes	—
510	#485	C₂²×C₆₇	1	2	yes	—
511	#485	C₂²×C₆₇	1	2	yes	—
512	#484	C₂²×C₆₇	1	2	yes	—
513	#483	C₂²×C₆₇	1	2	yes	—
514	#483	C₂²×C₆₇	1	2	yes	—
515	#482	C₂²×C₆₇	1	2	yes	—
516	#481	C₂²×C₆₇	1	2	yes	—
517	#479	C₂²×C₆₇	1	2	yes	complemented
518	#479	C₂²×C₆₇	1	2	yes	complemented
519	#479	C₂²×C₆₇	1	2	yes	complemented
520	#478	C₂²×C₆₇	1	2	yes	complemented
521	#477	C₂²×C₆₇	1	2	yes	complemented
522	#476	C₂²×C₆₇	1	2	yes	complemented
523	#475	C₂²×C₆₇	1	2	yes	complemented
524	#475	C₂²×C₆₇	1	2	yes	complemented
525	#470	C₂²×C₆₇	1	2	yes	—
526	#470	C₂²×C₆₇	1	2	yes	—
527	#470	C₂²×C₆₇	1	1	yes	characteristic
528	#470	C₂²×C₆₇	1	1	yes	characteristic
529	#470	C₂²×C₆₇	1	2	yes	—
530	#470	C₂²×C₆₇	1	1	yes	characteristic
531	#469	C₂²×C₆₇	1	1	yes	characteristic
532	#468	C₂²×C₆₇	1	2	yes	—
533	#468	C₂²×C₆₇	1	2	yes	—
534	#468	C₂²×C₆₇	1	2	yes	—
535	#464	C₂²×C₆₇	1	2	yes	complemented
536	#464	C₂²×C₆₇	1	2	yes	complemented
537	#464	C₂²×C₆₇	1	2	yes	complemented
538	#463	C₂²×C₆₇	1	2	yes	complemented
539	#462	C₂²×C₆₇	1	2	yes	complemented
540	#462	C₂²×C₆₇	1	2	yes	complemented
541	#462	C₂²×C₆₇	1	2	yes	complemented
542	#461	C₂²×C₆₇	1	2	yes	complemented
543	#452	C₂²×C₆₇	1	2	yes	—
544	#452	C₂²×C₆₇	1	2	yes	—
545	#452	C₂²×C₆₇	1	2	yes	—
546	#451	C₂²×C₆₇	1	2	yes	—
547	#451	C₂²×C₆₇	1	2	yes	—
548	#451	C₂²×C₆₇	1	2	yes	—
549	#449	C₂²×C₆₇	1	2	yes	—
550	#448	C₂²×C₆₇	1	2	yes	—
551	#442	C₂²×C₆₇	1	1	yes	characteristic, complemented
552	#441	C₂²×C₆₇	1	1	yes	characteristic, complemented
553	#441	C₂²×C₆₇	1	1	yes	characteristic, complemented
554	#441	C₂²×C₆₇	1	2	yes	complemented
555	#441	C₂²×C₆₇	1	1	yes	characteristic, complemented
556	#440	C₂²×C₆₇	1	2	yes	complemented
557	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
558	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
559	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
560	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
561	#433	C₂²×C₆₇	1	2	yes	—
562	#433	C₂²×C₆₇	1	2	yes	—
563	#433	C₂²×C₆₇	1	2	yes	—
564	#433	C₂²×C₆₇	1	2	yes	—
565	#423	C₂²×C₆₇	1	1	yes	characteristic
566	#423	C₂²×C₆₇	1	1	yes	characteristic
567	#407	C₂²×C₆₇	1	1	yes	characteristic
568	#407	C₂²×C₆₇	1	1	yes	characteristic
569	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
570	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
571	C₂×#41	C₂³×C₆₇	1	2	yes	—
572	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
573	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
574	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
575	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
576	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
577	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
578	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
579	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
580	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
581	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
582	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
583	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
584	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
585	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
586	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
587	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
588	C₄⋊Q₈	—	2	2	no	—
589	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
590	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
591	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
592	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
593	#126	—	2	2	no	—
594	#126	—	2	2	no	—
595	#126	—	2	2	no	—
596	#126	—	2	2	no	—
597	#126	—	2	2	no	—
598	#126	—	2	2	no	—
599	#126	—	2	2	no	—
600	#126	—	2	2	no	—
601	#125	—	2	2	no	—
602	#125	—	2	2	no	—
603	#125	—	2	2	no	—
604	#125	—	2	2	no	—
605	#125	—	2	2	no	—
606	#125	—	2	2	no	—
607	#125	—	2	2	no	—
608	#125	C₂³×C₆₇	1	2	yes	—
609	#125	C₂³×C₆₇	1	2	yes	—
610	#124	—	2	2	no	—
611	#124	—	2	2	no	—
612	#124	C₂³×C₆₇	1	2	yes	—
613	#124	C₂³×C₆₇	1	2	yes	—
614	#123	—	2	2	no	—
615	#123	—	2	2	no	—
616	#123	—	2	2	no	—
617	#123	—	2	2	no	—
618	#123	—	2	2	no	—
619	#123	—	2	2	no	—
620	#123	—	2	2	no	—
621	C₂²⋊Q₈	—	2	2	no	—
622	C₂²⋊Q₈	—	2	2	no	—
623	C₂²⋊Q₈	—	2	2	no	—
624	C₂²⋊Q₈	—	2	2	no	—
625	C₂²⋊Q₈	—	2	2	no	—
626	C₂²⋊Q₈	—	2	2	no	—
627	C₂²⋊Q₈	—	2	2	no	—
628	C₂²⋊Q₈	—	2	2	no	—
629	C₂²⋊Q₈	—	2	2	no	—
630	C₂²⋊Q₈	—	2	2	no	—
631	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
632	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
633	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
634	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
635	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
636	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
637	#121	C₂³×C₆₇	1	2	yes	—
638	#121	C₂³×C₆₇	1	2	yes	—
639	#120	—	2	2	no	—
640	C₄×Q₈	—	2	2	no	—
641	C₄×Q₈	—	2	2	no	—
642	C₄×Q₈	—	2	2	no	—
643	C₄×Q₈	—	2	2	no	—
644	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
645	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
646	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
647	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
648	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
649	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
650	C₄×D₄	—	2	2	no	—
651	C₄×D₄	—	2	2	no	—
652	C₄×D₄	—	2	2	no	—
653	C₄×D₄	—	2	2	no	—
654	C₄×D₄	—	2	2	no	—
655	C₄×D₄	—	2	2	no	—
656	C₄×D₄	C₂³×C₆₇	1	2	yes	—
657	C₄×D₄	C₂³×C₆₇	1	2	yes	—
658	#117	—	2	2	no	—
659	#117	—	2	2	no	—
660	#117	—	2	2	no	—
661	#117	—	2	2	no	—
662	#117	—	2	2	no	—
663	#117	—	2	2	no	—
664	#117	—	2	2	no	—
665	#117	D₄×C₆₇	1	2	yes	—
666	#117	D₄×C₆₇	1	2	yes	—
667	#117	C₂³×C₆₇	1	2	yes	—
668	#117	C₂³×C₆₇	1	2	yes	—
669	#117	C₂³×C₆₇	1	2	yes	—
670	C₂×C₄⋊C₄	—	2	2	no	—
671	C₂×C₄⋊C₄	—	2	2	no	—
672	C₂×C₄⋊C₄	D₄×C₆₇	1	2	yes	—
673	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
674	C₂×C₂²⋊C₄	—	2	2	no	—
675	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
676	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
677	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
678	#107	C₂³×C₆₇	1	2	yes	—
679	#107	C₂³×C₆₇	1	2	yes	—
680	#107	C₂³×C₆₇	1	2	yes	—
681	#106	C₂³×C₆₇	1	2	yes	—
682	#106	C₂³×C₆₇	1	2	yes	—
683	#106	C₂³×C₆₇	1	1	yes	characteristic
684	#106	C₂³×C₆₇	1	1	yes	characteristic
685	#106	C₂³×C₆₇	1	2	yes	—
686	#106	C₂³×C₆₇	1	1	yes	characteristic
687	#106	C₂³×C₆₇	1	1	yes	characteristic
688	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
689	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
690	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
691	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
692	#103	C₂³×C₆₇	1	2	yes	—
693	#103	C₂³×C₆₇	1	2	yes	—
694	#103	C₂³×C₆₇	1	2	yes	—
695	#103	C₂³×C₆₇	1	2	yes	—
696	#103	C₂³×C₆₇	1	2	yes	—
697	#103	C₂³×C₆₇	1	2	yes	—
698	#103	C₂³×C₆₇	1	2	yes	—
699	#103	C₂³×C₆₇	1	2	yes	—
700	#103	C₂³×C₆₇	1	2	yes	—
701	#103	C₂³×C₆₇	1	2	yes	—
702	#103	C₂³×C₆₇	1	2	yes	—
703	#103	C₂³×C₆₇	1	2	yes	—
704	#102	C₂³×C₆₇	1	2	yes	—
705	#102	C₂³×C₆₇	1	2	yes	—
706	#102	C₂³×C₆₇	1	2	yes	—
707	#102	C₂³×C₆₇	1	2	yes	—
708	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
709	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
710	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
711	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
712	#97	C₂³×C₆₇	1	1	yes	characteristic
713	#97	C₂³×C₆₇	1	1	yes	characteristic
714	#97	C₂³×C₆₇	1	2	yes	—
715	C₄×C₈	C₂³×C₆₇	1	2	yes	—
716	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
717	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
718	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
719	#41	—	4	2	no	—
720	#41	—	4	2	no	—
721	C₂×Q₈	—	2	2	no	—
722	C₂×Q₈	—	2	2	no	—
723	C₂×Q₈	—	2	2	no	—
724	C₂×Q₈	—	4	2	no	—
725	C₂×Q₈	—	4	2	no	—
726	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
727	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
728	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
729	C₂×D₄	—	2	2	no	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	4	1	no	—
739	C₂²×C₄	—	4	1	no	—
740	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
741	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
742	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
743	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
745	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
746	Q₁₆	—	4	1	no	—
747	Q₁₆	—	4	2	no	—
748	Q₁₆	—	4	2	no	—
749	Q₁₆	—	4	1	no	—
750	Q₁₆	—	4	2	no	—
751	Q₁₆	—	4	1	no	—
752	SD₁₆	—	4	2	no	—
753	SD₁₆	—	4	2	no	—
754	SD₁₆	—	4	2	no	—
755	D₈	—	4	1	no	—
756	M₁₆	—	4	1	no	—
757	M₁₆	—	4	1	no	—
758	M₁₆	—	4	1	no	—
759	M₁₆	—	4	1	no	—
760	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
761	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
762	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
763	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
764	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
765	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
790	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
791	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
792	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
793	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
794	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
795	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
796	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	—	2	2	no	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	—	2	2	no	—
812	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
813	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
814	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
815	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
816	C₄²	—	2	2	no	—
817	C₄²	—	2	2	no	—
818	C₄²	—	2	2	no	—
819	C₄²	—	2	2	no	—
820	C₄²	—	2	2	no	—
821	C₄²	—	2	2	no	—
822	C₄²	—	2	2	no	—
823	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
824	C₄²	C₂×D₄×C₆₇	1	2	yes	—
825	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
826	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
827	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
828	C₄²	C₂⁴×C₆₇	1	2	yes	—
829	C₂³	—	2	2	no	—
830	C₂³	—	4	1	no	—
831	C₂³	—	4	2	no	—
832	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
833	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
834	Q₈	—	2	2	no	—
835	Q₈	—	2	2	no	—
836	Q₈	—	2	2	no	—
837	Q₈	—	2	2	no	—
838	Q₈	—	2	2	no	—
839	Q₈	—	2	2	no	—
840	Q₈	—	4	4	no	—
841	Q₈	—	8	2	no	—
842	Q₈	—	8	2	no	—
843	D₄	—	2	2	no	—
844	D₄	—	2	2	no	—
845	D₄	—	4	4	no	—
846	D₄	—	4	4	no	—
847	D₄	—	8	2	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	4	1	no	—
860	C₂×C₄	—	4	2	no	—
861	C₂×C₄	—	4	2	no	—
862	C₂×C₄	—	4	2	no	—
863	C₂×C₄	—	4	4	no	—
864	C₂×C₄	—	4	4	no	—
865	C₂×C₄	—	8	2	no	—
866	C₂×C₄	—	8	2	no	—
867	C₂×C₄	—	8	2	no	—
868	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
869	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
870	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
871	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
872	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
873	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
874	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
875	C₈	—	2	1	no	—
876	C₈	—	2	1	no	—
877	C₈	—	2	2	no	—
878	C₈	—	2	2	no	—
879	C₈	—	2	1	no	—
880	C₈	—	2	1	no	—
881	C₂²	—	2	2	no	—
882	C₂²	—	2	2	no	—
883	C₂²	—	2	2	no	—
884	C₂²	—	2	2	no	—
885	C₂²	—	2	1	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	4	2	no	—
889	C₂²	—	8	2	no	—
890	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
891	C₄	—	2	2	no	—
892	C₄	—	2	2	no	—
893	C₄	—	2	2	no	—
894	C₄	—	2	2	no	—
895	C₄	—	2	2	no	—
896	C₄	—	2	1	no	—
897	C₄	—	4	2	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	2	no	—
904	C₄	#585×C₆₇	1	1	yes	characteristic
905	C₄	#585×C₆₇	1	1	yes	characteristic
906	C₂	—	4	1	no	—
907	C₂	—	4	2	no	—
908	C₂	—	8	2	no	—
909	C₂	C₆₇×#3449	1	1	yes	characteristic
910	C₂	C₆₇×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₆₇×#3197	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂×#117×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3495	C₂	semidirect
2. C₆₇×#3256	C₂	semidirect
3. C₆₇×#3255	C₂	semidirect
4. C₆₇×#3252	C₂	semidirect
5. C₆₇×#3244	C₂	semidirect
6. C₆₇×#3242	C₂	semidirect
7. C₆₇×#3225	C₂	semidirect
8. C₆₇×#3223	C₂	semidirect
10. C₆₇×#3196	C₂	semidirect
11. C₆₇×#3195	C₂	semidirect
12. C₆₇×#3185	C₂	semidirect
13. C₆₇×#3183	C₂	semidirect
14. C₆₇×#3172	C₂	semidirect
15. C₆₇×#3127	C₂	semidirect
16. C₆₇×#3125	C₂	semidirect
17. C₆₇×#3121	C₂	semidirect
18. C₆₇×#3120	C₂	semidirect
19. C₆₇×#2921	C₂	semidirect
43. #501×C₆₇	C₂²	semidirect
44. #499×C₆₇	C₂²	semidirect
45. #498×C₆₇	C₂²	semidirect
46. #497×C₆₇	C₂²	semidirect
47. #495×C₆₇	C₂²	semidirect
48. #494×C₆₇	C₂²	semidirect
49. #491×C₆₇	C₂²	semidirect
50. #489×C₆₇	C₂²	semidirect
51. #488×C₆₇	C₂²	semidirect
52. #487×C₆₇	C₂²	semidirect
61. #479×C₆₇	C₂²	semidirect
62. #479×C₆₇	C₂²	semidirect
63. #479×C₆₇	C₂²	semidirect
64. #478×C₆₇	C₂²	semidirect
65. #477×C₆₇	C₂²	semidirect
66. #476×C₆₇	C₂²	semidirect
67. #475×C₆₇	C₂²	semidirect
68. #475×C₆₇	C₂²	semidirect
79. #464×C₆₇	C₂²	semidirect
80. #464×C₆₇	C₂²	semidirect
81. #464×C₆₇	C₂²	semidirect
82. #463×C₆₇	C₂²	semidirect
83. #462×C₆₇	C₂²	semidirect
84. #462×C₆₇	C₂²	semidirect
85. #462×C₆₇	C₂²	semidirect
86. #461×C₆₇	C₂²	semidirect
95. #442×C₆₇	C₂²	semidirect
96. #441×C₆₇	C₂²	semidirect
97. #441×C₆₇	C₂²	semidirect
98. #441×C₆₇	C₂²	semidirect
99. #441×C₆₇	C₂²	semidirect
100. #440×C₆₇	C₂²	semidirect
101. C₄×Q₁₆×C₆₇	C₂²	semidirect
102. C₄×Q₁₆×C₆₇	C₂²	semidirect
103. C₄×SD₁₆×C₆₇	C₂²	semidirect
104. C₄×SD₁₆×C₆₇	C₂²	semidirect
450. #61005	C₆₇	direct (N × H)
456. #3495	C₂×C₆₇	semidirect
457. #3256	C₂×C₆₇	semidirect
458. #3255	C₂×C₆₇	semidirect
459. #3252	C₂×C₆₇	semidirect
460. #3244	C₂×C₆₇	semidirect
461. #3242	C₂×C₆₇	semidirect
462. #3225	C₂×C₆₇	semidirect
463. #3223	C₂×C₆₇	semidirect
465. #3196	C₂×C₆₇	semidirect
466. #3195	C₂×C₆₇	semidirect
467. #3185	C₂×C₆₇	semidirect
468. #3183	C₂×C₆₇	semidirect
469. #3172	C₂×C₆₇	semidirect
470. #3127	C₂×C₆₇	semidirect
471. #3125	C₂×C₆₇	semidirect
472. #3121	C₂×C₆₇	semidirect
473. #3120	C₂×C₆₇	semidirect
474. #2921	C₂×C₆₇	semidirect
475. C₆₇	#61005	direct (N × H)
499. #501	C₂²×C₆₇	semidirect
500. #499	C₂²×C₆₇	semidirect
501. #498	C₂²×C₆₇	semidirect
502. #497	C₂²×C₆₇	semidirect
503. #495	C₂²×C₆₇	semidirect
504. #494	C₂²×C₆₇	semidirect
505. #491	C₂²×C₆₇	semidirect
506. #489	C₂²×C₆₇	semidirect
507. #488	C₂²×C₆₇	semidirect
508. #487	C₂²×C₆₇	semidirect
517. #479	C₂²×C₆₇	semidirect
518. #479	C₂²×C₆₇	semidirect
519. #479	C₂²×C₆₇	semidirect
520. #478	C₂²×C₆₇	semidirect
521. #477	C₂²×C₆₇	semidirect
522. #476	C₂²×C₆₇	semidirect
523. #475	C₂²×C₆₇	semidirect
524. #475	C₂²×C₆₇	semidirect
535. #464	C₂²×C₆₇	semidirect
536. #464	C₂²×C₆₇	semidirect
537. #464	C₂²×C₆₇	semidirect
538. #463	C₂²×C₆₇	semidirect
539. #462	C₂²×C₆₇	semidirect
540. #462	C₂²×C₆₇	semidirect
541. #462	C₂²×C₆₇	semidirect
542. #461	C₂²×C₆₇	semidirect
551. #442	C₂²×C₆₇	semidirect
552. #441	C₂²×C₆₇	semidirect
553. #441	C₂²×C₆₇	semidirect
554. #441	C₂²×C₆₇	semidirect
555. #441	C₂²×C₆₇	semidirect
556. #440	C₂²×C₆₇	semidirect
557. C₄×Q₁₆	C₂²×C₆₇	semidirect
558. C₄×Q₁₆	C₂²×C₆₇	semidirect
559. C₄×SD₁₆	C₂²×C₆₇	semidirect
560. C₄×SD₁₆	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×#3495	2
C₆₇×#3256	2
C₆₇×#3255	2
C₆₇×#3252	2
C₆₇×#3244	2
C₆₇×#3242	2
C₆₇×#3225	2
C₆₇×#3223	2
C₆₇×#3197	2
C₆₇×#3196	2
C₆₇×#3195	2
C₆₇×#3185	2
C₆₇×#3183	2
C₆₇×#3172	2
C₆₇×#3127	2
C₆₇×#3125	2
C₆₇×#3121	2
C₆₇×#3120	2
C₆₇×#2921	2
#61005	67

Subgroups — C67×#61005 #30740256

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61005 #30740256