Subgroups — C₆₇×#61476 #30740727

Order 17152.

1826 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3517	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3515	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3392	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3381	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#3366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#3337	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3335	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3333	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3330	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3317	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3307	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3284	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3284	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3174	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3120	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3119	C₂	1	2	yes	maximal, complemented
19	C₆₇×#3116	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3115	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2952	C₂	1	2	yes	maximal, complemented
23	C₄×#135×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#135×C₆₇	C₂²	1	2	yes	—
26	#557×C₆₇	C₂²	1	1	yes	characteristic
27	#557×C₆₇	C₂²	1	1	yes	characteristic
28	#554×C₆₇	C₂²	1	1	yes	characteristic
29	#554×C₆₇	C₂²	1	1	yes	characteristic
30	#553×C₆₇	—	2	2	no	—
31	#553×C₆₇	—	2	1	no	—
32	#553×C₆₇	C₂²	1	2	yes	—
33	#552×C₆₇	—	2	2	no	—
34	#552×C₆₇	—	2	1	no	—
35	#552×C₆₇	C₂²	1	2	yes	—
36	#550×C₆₇	—	2	1	no	—
37	#550×C₆₇	C₂²	1	2	yes	—
38	#550×C₆₇	C₂²	1	1	yes	characteristic
39	#550×C₆₇	C₂²	1	1	yes	characteristic
40	#547×C₆₇	—	2	1	no	—
41	#547×C₆₇	C₂²	1	2	yes	—
42	#547×C₆₇	C₂²	1	1	yes	characteristic
43	#547×C₆₇	C₂²	1	1	yes	characteristic
44	#541×C₆₇	C₂²	1	2	yes	—
45	#540×C₆₇	—	2	2	no	—
46	#540×C₆₇	C₂²	1	2	yes	—
47	#539×C₆₇	—	2	2	no	—
48	#533×C₆₇	C₂²	1	1	yes	characteristic
49	#532×C₆₇	—	2	1	no	—
50	#532×C₆₇	C₂²	1	1	yes	characteristic
51	#529×C₆₇	—	2	1	no	—
52	#529×C₆₇	—	2	1	no	—
53	#529×C₆₇	C₂²	1	1	yes	characteristic
54	C₂×#125×C₆₇	—	2	1	no	—
55	#520×C₆₇	C₂²	1	2	yes	—
56	#520×C₆₇	C₂²	1	2	yes	—
57	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
58	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
59	#499×C₆₇	C₂²	1	2	yes	—
60	#498×C₆₇	C₂²	1	1	yes	characteristic
61	#492×C₆₇	C₂²	1	1	yes	characteristic
62	#492×C₆₇	C₂²	1	2	yes	—
63	#491×C₆₇	C₂²	1	2	yes	—
64	#490×C₆₇	C₂²	1	2	yes	—
65	#487×C₆₇	C₂²	1	1	yes	characteristic
66	#486×C₆₇	C₂²	1	1	yes	characteristic
67	#485×C₆₇	C₂²	1	2	yes	—
68	#484×C₆₇	C₂²	1	2	yes	—
69	#483×C₆₇	C₂²	1	2	yes	—
70	#482×C₆₇	C₂²	1	2	yes	—
71	#481×C₆₇	C₂²	1	2	yes	—
72	#480×C₆₇	C₂²	1	2	yes	—
73	#479×C₆₇	C₂²	1	2	yes	—
74	#479×C₆₇	C₂²	1	2	yes	—
75	#478×C₆₇	C₂²	1	2	yes	—
76	#478×C₆₇	C₂²	1	2	yes	—
77	#477×C₆₇	C₂²	1	1	yes	characteristic
78	#476×C₆₇	C₂²	1	1	yes	characteristic
79	#475×C₆₇	C₂²	1	1	yes	characteristic
80	#474×C₆₇	C₂²	1	1	yes	characteristic
81	#468×C₆₇	C₂²	1	2	yes	—
82	#468×C₆₇	C₂²	1	2	yes	—
83	#465×C₆₇	C₂²	1	2	yes	—
84	#465×C₆₇	C₂²	1	2	yes	—
85	#465×C₆₇	C₂²	1	2	yes	—
86	#465×C₆₇	C₂²	1	2	yes	—
87	#462×C₆₇	C₂²	1	1	yes	characteristic
88	#462×C₆₇	C₂²	1	2	yes	—
89	#461×C₆₇	C₂²	1	2	yes	—
90	#461×C₆₇	C₂²	1	1	yes	characteristic
91	#460×C₆₇	C₂²	1	2	yes	—
92	#460×C₆₇	C₂²	1	1	yes	characteristic
93	#459×C₆₇	C₂²	1	1	yes	characteristic
94	#459×C₆₇	C₂²	1	2	yes	—
95	#452×C₆₇	C₂²	1	2	yes	—
96	#452×C₆₇	C₂²	1	2	yes	—
97	#452×C₆₇	C₂²	1	2	yes	—
98	#449×C₆₇	C₂²	1	2	yes	—
99	#449×C₆₇	C₂²	1	2	yes	—
100	#449×C₆₇	C₂²	1	2	yes	—
101	#446×C₆₇	C₂²	1	1	yes	characteristic
102	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic
103	#442×C₆₇	C₂²	1	2	yes	—
104	#442×C₆₇	C₂²	1	2	yes	—
105	#441×C₆₇	C₂²	1	2	yes	—
106	#441×C₆₇	C₂²	1	2	yes	—
107	#440×C₆₇	C₂²	1	2	yes	—
108	#440×C₆₇	C₂²	1	2	yes	—
109	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
110	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
111	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
112	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
113	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
114	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
115	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
116	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
117	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
119	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
121	#436×C₆₇	C₂²	1	1	yes	characteristic
122	#435×C₆₇	C₂²	1	2	yes	—
123	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₆₇	C₂²	1	2	yes	—
125	#433×C₆₇	C₂²	1	2	yes	—
126	#432×C₆₇	C₂²	1	1	yes	characteristic
127	#427×C₆₇	C₂²	1	1	yes	characteristic
128	C₂×#106×C₆₇	C₂²	1	2	yes	—
129	#417×C₆₇	C₂²	1	2	yes	—
130	#417×C₆₇	C₂²	1	2	yes	—
131	#416×C₆₇	C₂²	1	1	yes	characteristic
132	#416×C₆₇	C₂²	1	1	yes	characteristic
133	#405×C₆₇	C₂²	1	2	yes	—
134	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
135	C₂×#41×C₆₇	—	2	1	no	—
136	C₂×#41×C₆₇	—	2	1	no	—
137	C₂×#41×C₆₇	—	2	1	no	—
138	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
139	C₂×#41×C₆₇	C₂³	1	2	yes	—
140	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×#41×C₆₇	C₂³	1	2	yes	—
142	#135×C₆₇	—	2	4	no	—
143	#135×C₆₇	—	2	8	no	—
144	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
152	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
153	C₂×D₈×C₆₇	C₂³	1	2	yes	—
154	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
155	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
156	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
157	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈×C₆₇	—	2	1	no	—
159	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
161	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
163	#127×C₆₇	—	2	1	no	—
164	#127×C₆₇	—	2	2	no	—
165	#127×C₆₇	C₂³	1	1	yes	characteristic
166	#127×C₆₇	C₂³	1	2	yes	—
167	#126×C₆₇	—	2	2	no	—
168	#126×C₆₇	—	2	2	no	—
169	#126×C₆₇	—	2	2	no	—
170	#126×C₆₇	—	2	2	no	—
171	#126×C₆₇	D₄	1	2	yes	—
172	#125×C₆₇	—	2	2	no	—
173	#125×C₆₇	—	2	2	no	—
174	#125×C₆₇	—	2	1	no	—
175	#125×C₆₇	—	2	1	no	—
176	#125×C₆₇	—	2	2	no	—
177	#125×C₆₇	—	2	2	no	—
178	#125×C₆₇	—	2	2	no	—
179	#125×C₆₇	—	2	1	no	—
180	#125×C₆₇	D₄	1	1	yes	characteristic
181	#125×C₆₇	C₂³	1	2	yes	—
182	#125×C₆₇	C₂³	1	2	yes	—
183	#124×C₆₇	—	2	1	no	—
184	#124×C₆₇	D₄	1	1	yes	characteristic
185	#123×C₆₇	—	2	2	no	—
186	#123×C₆₇	—	2	2	no	—
187	#123×C₆₇	—	2	2	no	—
188	#123×C₆₇	—	2	2	no	—
189	#123×C₆₇	—	2	2	no	—
190	#123×C₆₇	—	2	2	no	—
191	#123×C₆₇	—	2	2	no	—
192	#123×C₆₇	—	2	2	no	—
193	#123×C₆₇	D₄	1	2	yes	—
194	C₂²⋊Q₈×C₆₇	—	2	1	no	—
195	C₂²⋊Q₈×C₆₇	—	2	1	no	—
196	C₂²⋊Q₈×C₆₇	—	2	1	no	—
197	C₂²⋊Q₈×C₆₇	—	2	2	no	—
198	C₂²⋊Q₈×C₆₇	—	2	2	no	—
199	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
200	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
201	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
202	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
203	#121×C₆₇	—	2	1	no	—
204	#121×C₆₇	—	2	2	no	—
205	#121×C₆₇	—	2	2	no	—
206	#121×C₆₇	—	2	1	no	—
207	#121×C₆₇	—	2	1	no	—
208	#121×C₆₇	—	2	2	no	—
209	#121×C₆₇	—	2	2	no	—
210	#121×C₆₇	—	2	2	no	—
211	#121×C₆₇	—	2	2	no	—
212	#121×C₆₇	—	2	2	no	—
213	#121×C₆₇	—	2	2	no	—
214	#121×C₆₇	D₄	1	1	yes	characteristic
215	#121×C₆₇	C₂³	1	2	yes	—
216	#121×C₆₇	C₂³	1	2	yes	—
217	#121×C₆₇	C₂³	1	2	yes	—
218	C₄×Q₈×C₆₇	—	2	1	no	—
219	C₄×Q₈×C₆₇	—	2	1	no	—
220	C₄×Q₈×C₆₇	—	2	1	no	—
221	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
223	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
225	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
228	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
229	C₄×D₄×C₆₇	—	2	1	no	—
230	C₄×D₄×C₆₇	—	2	1	no	—
231	C₄×D₄×C₆₇	—	2	1	no	—
232	C₄×D₄×C₆₇	—	2	1	no	—
233	C₄×D₄×C₆₇	—	2	1	no	—
234	C₄×D₄×C₆₇	—	2	1	no	—
235	C₄×D₄×C₆₇	—	2	2	no	—
236	C₄×D₄×C₆₇	—	2	2	no	—
237	C₄×D₄×C₆₇	—	2	2	no	—
238	C₄×D₄×C₆₇	—	2	2	no	—
239	C₄×D₄×C₆₇	—	2	2	no	—
240	C₄×D₄×C₆₇	—	2	2	no	—
241	C₄×D₄×C₆₇	—	2	1	no	—
242	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₆₇	C₂³	1	2	yes	—
244	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₆₇	C₂³	1	2	yes	—
246	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₆₇	C₂³	1	2	yes	—
249	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₆₇	C₂³	1	2	yes	—
251	#117×C₆₇	—	2	1	no	—
252	#117×C₆₇	—	2	2	no	—
253	#117×C₆₇	—	2	2	no	—
254	#117×C₆₇	—	2	2	no	—
255	#117×C₆₇	—	2	1	no	—
256	#117×C₆₇	—	2	1	no	—
257	#117×C₆₇	C₂³	1	1	yes	characteristic
258	#117×C₆₇	C₂³	1	1	yes	characteristic
259	#117×C₆₇	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
261	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
262	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
263	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
264	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
265	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
266	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
267	C₂×C₄²×C₆₇	—	2	1	no	—
268	C₂×C₄²×C₆₇	—	2	1	no	—
269	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
270	#107×C₆₇	C₂³	1	2	yes	—
271	#107×C₆₇	C₂³	1	2	yes	—
272	#107×C₆₇	C₂³	1	1	yes	characteristic
273	#107×C₆₇	C₂³	1	1	yes	characteristic
274	#106×C₆₇	C₂³	1	2	yes	—
275	#106×C₆₇	C₂³	1	1	yes	characteristic
276	#106×C₆₇	C₂³	1	2	yes	—
277	#106×C₆₇	C₂³	1	2	yes	—
278	#106×C₆₇	C₂³	1	2	yes	—
279	#106×C₆₇	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
282	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
284	#103×C₆₇	C₂³	1	2	yes	—
285	#103×C₆₇	C₂³	1	2	yes	—
286	#103×C₆₇	C₂³	1	2	yes	—
287	#103×C₆₇	C₂³	1	2	yes	—
288	#103×C₆₇	C₂³	1	1	yes	characteristic
289	#103×C₆₇	C₂³	1	1	yes	characteristic
290	#103×C₆₇	C₂³	1	2	yes	—
291	#103×C₆₇	C₂³	1	2	yes	—
292	#103×C₆₇	C₂³	1	1	yes	characteristic
293	#103×C₆₇	C₂³	1	1	yes	characteristic
294	#102×C₆₇	C₂³	1	2	yes	—
295	#102×C₆₇	C₂³	1	1	yes	characteristic
296	#102×C₆₇	C₂³	1	2	yes	—
297	#102×C₆₇	C₂³	1	2	yes	—
298	#102×C₆₇	C₂³	1	2	yes	—
299	#102×C₆₇	C₂³	1	2	yes	—
300	#102×C₆₇	C₂³	1	1	yes	characteristic
301	#102×C₆₇	C₂³	1	2	yes	—
302	#102×C₆₇	C₂³	1	1	yes	characteristic
303	#102×C₆₇	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
307	#97×C₆₇	C₂³	1	2	yes	—
308	#97×C₆₇	C₂³	1	2	yes	—
309	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₆₇	C₂³	1	2	yes	—
312	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
314	#41×C₆₇	—	2	2	no	—
315	#41×C₆₇	—	2	4	no	—
316	#41×C₆₇	—	2	2	no	—
317	#41×C₆₇	—	2	4	no	—
318	#41×C₆₇	—	4	1	no	—
319	#41×C₆₇	—	4	1	no	—
320	#41×C₆₇	—	4	2	no	—
321	#41×C₆₇	—	4	2	no	—
322	#41×C₆₇	—	8	2	no	—
323	#41×C₆₇	—	8	2	no	—
324	#41×C₆₇	—	8	2	no	—
325	C₂×Q₈×C₆₇	—	2	1	no	—
326	C₂×Q₈×C₆₇	—	2	1	no	—
327	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
330	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₆₇	—	2	1	no	—
332	C₂×D₄×C₆₇	—	2	2	no	—
333	C₂×D₄×C₆₇	—	2	1	no	—
334	C₂×D₄×C₆₇	—	2	2	no	—
335	C₂×D₄×C₆₇	—	2	2	no	—
336	C₂×D₄×C₆₇	—	2	2	no	—
337	C₂×D₄×C₆₇	—	2	2	no	—
338	C₂×D₄×C₆₇	—	2	1	no	—
339	C₂×D₄×C₆₇	—	2	1	no	—
340	C₂×D₄×C₆₇	—	2	2	no	—
341	C₂×D₄×C₆₇	—	2	2	no	—
342	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
343	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
344	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
345	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
346	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₆₇	—	2	2	no	—
348	C₂²×C₄×C₆₇	—	2	2	no	—
349	C₂²×C₄×C₆₇	—	2	1	no	—
350	C₂²×C₄×C₆₇	—	2	1	no	—
351	C₂²×C₄×C₆₇	—	2	1	no	—
352	C₂²×C₄×C₆₇	—	2	1	no	—
353	C₂²×C₄×C₆₇	—	2	2	no	—
354	C₂²×C₄×C₆₇	—	2	2	no	—
355	C₂²×C₄×C₆₇	—	2	1	no	—
356	C₂²×C₄×C₆₇	—	2	1	no	—
357	C₂²×C₄×C₆₇	—	2	2	no	—
358	C₂²×C₄×C₆₇	—	2	2	no	—
359	C₂²×C₄×C₆₇	—	2	2	no	—
360	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
362	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
364	Q₁₆×C₆₇	—	2	2	no	—
365	Q₁₆×C₆₇	—	2	4	no	—
366	SD₁₆×C₆₇	—	2	2	no	—
367	SD₁₆×C₆₇	—	2	4	no	—
368	SD₁₆×C₆₇	—	4	2	no	—
369	SD₁₆×C₆₇	—	4	2	no	—
370	SD₁₆×C₆₇	—	4	2	no	—
371	SD₁₆×C₆₇	#41	1	4	yes	complemented
372	D₈×C₆₇	—	2	2	no	—
373	D₈×C₆₇	—	2	4	no	—
374	M₁₆×C₆₇	—	4	2	no	—
375	C₂×C₈×C₆₇	—	2	2	no	—
376	C₂×C₈×C₆₇	—	2	4	no	—
377	C₂×C₈×C₆₇	—	4	1	no	—
378	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
380	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
381	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
382	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
383	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
384	C₄⋊C₄×C₆₇	—	2	1	no	—
385	C₄⋊C₄×C₆₇	—	2	2	no	—
386	C₄⋊C₄×C₆₇	—	2	2	no	—
387	C₄⋊C₄×C₆₇	—	2	1	no	—
388	C₄⋊C₄×C₆₇	—	2	1	no	—
389	C₄⋊C₄×C₆₇	—	2	2	no	—
390	C₄⋊C₄×C₆₇	—	2	2	no	—
391	C₄⋊C₄×C₆₇	—	2	2	no	—
392	C₄⋊C₄×C₆₇	—	2	2	no	—
393	C₄⋊C₄×C₆₇	—	2	2	no	—
394	C₄⋊C₄×C₆₇	—	2	2	no	—
395	C₄⋊C₄×C₆₇	—	2	2	no	—
396	C₄⋊C₄×C₆₇	—	2	2	no	—
397	C₄⋊C₄×C₆₇	—	2	1	no	—
398	C₄⋊C₄×C₆₇	—	2	1	no	—
399	C₄⋊C₄×C₆₇	—	2	1	no	—
400	C₄⋊C₄×C₆₇	—	2	2	no	—
401	C₄⋊C₄×C₆₇	—	2	1	no	—
402	C₄⋊C₄×C₆₇	—	2	2	no	—
403	C₄⋊C₄×C₆₇	—	2	2	no	—
404	C₄⋊C₄×C₆₇	—	2	1	no	—
405	C₄⋊C₄×C₆₇	—	2	2	no	—
406	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
408	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
411	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
414	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
417	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
418	C₂²⋊C₄×C₆₇	—	2	2	no	—
419	C₂²⋊C₄×C₆₇	—	2	2	no	—
420	C₂²⋊C₄×C₆₇	—	2	1	no	—
421	C₂²⋊C₄×C₆₇	—	2	1	no	—
422	C₂²⋊C₄×C₆₇	—	2	2	no	—
423	C₂²⋊C₄×C₆₇	—	2	1	no	—
424	C₂²⋊C₄×C₆₇	—	2	2	no	—
425	C₂²⋊C₄×C₆₇	—	2	1	no	—
426	C₂²⋊C₄×C₆₇	—	2	1	no	—
427	C₂²⋊C₄×C₆₇	—	2	2	no	—
428	C₂²⋊C₄×C₆₇	—	2	1	no	—
429	C₂²⋊C₄×C₆₇	—	2	2	no	—
430	C₂²⋊C₄×C₆₇	—	2	2	no	—
431	C₂²⋊C₄×C₆₇	—	2	2	no	—
432	C₂²⋊C₄×C₆₇	—	2	2	no	—
433	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
438	C₄²×C₆₇	—	2	1	no	—
439	C₄²×C₆₇	—	2	1	no	—
440	C₄²×C₆₇	—	2	1	no	—
441	C₄²×C₆₇	—	2	1	no	—
442	C₄²×C₆₇	—	2	1	no	—
443	C₄²×C₆₇	—	2	1	no	—
444	C₄²×C₆₇	—	2	2	no	—
445	C₄²×C₆₇	—	2	2	no	—
446	C₄²×C₆₇	—	2	2	no	—
447	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
448	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
449	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
450	C₄²×C₆₇	C₂⁴	1	2	yes	—
451	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
452	C₂³×C₆₇	—	2	1	no	—
453	C₂³×C₆₇	—	2	1	no	—
454	C₂³×C₆₇	—	2	2	no	—
455	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
456	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
457	Q₈×C₆₇	—	2	2	no	—
458	Q₈×C₆₇	—	2	1	no	—
459	Q₈×C₆₇	—	2	1	no	—
460	Q₈×C₆₇	—	2	2	no	—
461	Q₈×C₆₇	—	2	2	no	—
462	Q₈×C₆₇	—	2	1	no	—
463	Q₈×C₆₇	—	4	2	no	—
464	Q₈×C₆₇	—	8	1	no	—
465	Q₈×C₆₇	C₂×#41	1	2	yes	—
466	D₄×C₆₇	—	2	2	no	—
467	D₄×C₆₇	—	2	1	no	—
468	D₄×C₆₇	—	2	2	no	—
469	D₄×C₆₇	—	2	1	no	—
470	D₄×C₆₇	—	2	2	no	—
471	D₄×C₆₇	—	2	1	no	—
472	D₄×C₆₇	—	4	2	no	—
473	D₄×C₆₇	—	4	2	no	—
474	D₄×C₆₇	—	4	4	no	—
475	D₄×C₆₇	—	4	2	no	—
476	D₄×C₆₇	—	4	4	no	—
477	D₄×C₆₇	—	4	2	no	—
478	D₄×C₆₇	—	8	1	no	—
479	D₄×C₆₇	—	8	2	no	—
480	D₄×C₆₇	—	8	2	no	—
481	D₄×C₆₇	—	8	2	no	—
482	D₄×C₆₇	—	8	2	no	—
483	D₄×C₆₇	—	8	2	no	—
484	D₄×C₆₇	C₂×#41	1	2	yes	—
485	C₂×C₄×C₆₇	—	2	1	no	—
486	C₂×C₄×C₆₇	—	2	2	no	—
487	C₂×C₄×C₆₇	—	2	1	no	—
488	C₂×C₄×C₆₇	—	2	2	no	—
489	C₂×C₄×C₆₇	—	2	1	no	—
490	C₂×C₄×C₆₇	—	2	2	no	—
491	C₂×C₄×C₆₇	—	2	1	no	—
492	C₂×C₄×C₆₇	—	2	1	no	—
493	C₂×C₄×C₆₇	—	2	1	no	—
494	C₂×C₄×C₆₇	—	2	1	no	—
495	C₂×C₄×C₆₇	—	2	1	no	—
496	C₂×C₄×C₆₇	—	2	2	no	—
497	C₂×C₄×C₆₇	—	2	2	no	—
498	C₂×C₄×C₆₇	—	2	2	no	—
499	C₂×C₄×C₆₇	—	4	1	no	—
500	C₂×C₄×C₆₇	—	4	2	no	—
501	C₂×C₄×C₆₇	—	4	4	no	—
502	C₂×C₄×C₆₇	—	4	2	no	—
503	C₂×C₄×C₆₇	—	4	4	no	—
504	C₂×C₄×C₆₇	—	4	2	no	—
505	C₂×C₄×C₆₇	—	4	2	no	—
506	C₂×C₄×C₆₇	—	8	1	no	—
507	C₂×C₄×C₆₇	—	8	1	no	—
508	C₂×C₄×C₆₇	—	8	2	no	—
509	C₂×C₄×C₆₇	—	8	2	no	—
510	C₂×C₄×C₆₇	—	8	2	no	—
511	C₂×C₄×C₆₇	—	8	2	no	—
512	C₂×C₄×C₆₇	—	8	2	no	—
513	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
518	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
520	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
522	C₈×C₆₇	—	2	2	no	—
523	C₈×C₆₇	—	2	1	no	—
524	C₈×C₆₇	—	2	1	no	—
525	C₈×C₆₇	—	2	1	no	—
526	C₈×C₆₇	—	2	2	no	—
527	C₈×C₆₇	C₂×#41	1	2	yes	—
528	C₂²×C₆₇	—	2	1	no	—
529	C₂²×C₆₇	—	2	2	no	—
530	C₂²×C₆₇	—	2	1	no	—
531	C₂²×C₆₇	—	2	2	no	—
532	C₂²×C₆₇	—	2	2	no	—
533	C₂²×C₆₇	—	2	1	no	—
534	C₂²×C₆₇	—	2	2	no	—
535	C₂²×C₆₇	—	4	1	no	—
536	C₂²×C₆₇	—	4	1	no	—
537	C₂²×C₆₇	—	4	1	no	—
538	C₂²×C₆₇	—	4	2	no	—
539	C₂²×C₆₇	—	4	1	no	—
540	C₂²×C₆₇	—	4	2	no	—
541	C₂²×C₆₇	—	4	1	no	—
542	C₂²×C₆₇	—	4	2	no	—
543	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
544	C₄×C₆₇	—	2	1	no	—
545	C₄×C₆₇	—	2	1	no	—
546	C₄×C₆₇	—	2	2	no	—
547	C₄×C₆₇	—	2	1	no	—
548	C₄×C₆₇	—	2	2	no	—
549	C₄×C₆₇	—	2	2	no	—
550	C₄×C₆₇	—	2	1	no	—
551	C₄×C₆₇	—	2	2	no	—
552	C₄×C₆₇	—	4	1	no	—
553	C₄×C₆₇	—	4	2	no	—
554	C₄×C₆₇	—	4	1	no	—
555	C₄×C₆₇	—	4	1	no	—
556	C₄×C₆₇	—	4	2	no	—
557	C₄×C₆₇	—	4	1	no	—
558	C₄×C₆₇	—	4	1	no	—
559	C₄×C₆₇	—	4	2	no	—
560	C₄×C₆₇	#577	1	2	yes	—
561	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
562	C₄×C₆₇	#585	1	1	yes	characteristic
563	#61476	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
564	C₂×C₆₇	—	4	1	no	—
565	C₂×C₆₇	—	4	2	no	—
566	C₂×C₆₇	—	4	2	no	—
567	C₂×C₆₇	—	8	1	no	—
568	C₂×C₆₇	—	8	2	no	—
569	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
570	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
571	C₂×C₆₇	#3584	1	1	yes	characteristic
572	#3517	C₂×C₆₇	1	1	yes	characteristic, complemented
573	#3515	C₂×C₆₇	1	1	yes	characteristic, complemented
574	#3392	C₂×C₆₇	1	1	yes	characteristic, complemented
575	#3381	C₂×C₆₇	1	1	yes	characteristic, complemented
576	#3374	C₂×C₆₇	1	1	yes	characteristic, complemented
577	#3366	C₂×C₆₇	1	1	yes	characteristic, complemented
578	#3337	C₂×C₆₇	1	2	yes	complemented
579	#3335	C₂×C₆₇	1	1	yes	characteristic, complemented
580	#3333	C₂×C₆₇	1	1	yes	characteristic, complemented
581	#3330	C₂×C₆₇	1	1	yes	characteristic, complemented
582	#3317	C₂×C₆₇	1	2	yes	complemented
583	#3307	C₂×C₆₇	1	2	yes	complemented
584	#3284	C₂×C₆₇	1	1	yes	characteristic, complemented
585	#3284	C₂×C₆₇	1	2	yes	complemented
586	#3174	C₂×C₆₇	1	2	yes	complemented
587	#3167	C₂×C₆₇	1	1	yes	characteristic, complemented
588	#3120	C₂×C₆₇	1	2	yes	complemented
589	#3119	C₂×C₆₇	1	2	yes	complemented
590	#3116	C₂×C₆₇	1	1	yes	characteristic, complemented
591	#3115	C₂×C₆₇	1	1	yes	characteristic, complemented
592	#2966	C₂×C₆₇	1	1	yes	characteristic, complemented
593	#2952	C₂×C₆₇	1	2	yes	complemented
594	C₄×#135	C₂×C₆₇	1	1	yes	characteristic, complemented
595	C₆₇	#61476	1	1	yes	characteristic, direct product factor, Sylow
596	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
597	C₂×#135	C₂²×C₆₇	1	2	yes	—
598	#557	C₂²×C₆₇	1	1	yes	characteristic
599	#557	C₂²×C₆₇	1	1	yes	characteristic
600	#554	C₂²×C₆₇	1	1	yes	characteristic
601	#554	C₂²×C₆₇	1	1	yes	characteristic
602	#553	—	2	2	no	—
603	#553	—	2	1	no	—
604	#553	C₂²×C₆₇	1	2	yes	—
605	#552	—	2	2	no	—
606	#552	—	2	1	no	—
607	#552	C₂²×C₆₇	1	2	yes	—
608	#550	—	2	1	no	—
609	#550	C₂²×C₆₇	1	1	yes	characteristic
610	#550	C₂²×C₆₇	1	2	yes	—
611	#550	C₂²×C₆₇	1	1	yes	characteristic
612	#547	—	2	1	no	—
613	#547	C₂²×C₆₇	1	1	yes	characteristic
614	#547	C₂²×C₆₇	1	2	yes	—
615	#547	C₂²×C₆₇	1	1	yes	characteristic
616	#541	C₂²×C₆₇	1	2	yes	—
617	#540	—	2	2	no	—
618	#540	C₂²×C₆₇	1	2	yes	—
619	#539	—	2	2	no	—
620	#533	C₂²×C₆₇	1	1	yes	characteristic
621	#532	—	2	1	no	—
622	#532	C₂²×C₆₇	1	1	yes	characteristic
623	#529	—	2	1	no	—
624	#529	—	2	1	no	—
625	#529	C₂²×C₆₇	1	1	yes	characteristic
626	C₂×#125	—	2	1	no	—
627	#520	C₂²×C₆₇	1	2	yes	—
628	#520	C₂²×C₆₇	1	2	yes	—
629	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
630	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
631	#499	C₂²×C₆₇	1	2	yes	—
632	#498	C₂²×C₆₇	1	1	yes	characteristic
633	#492	C₂²×C₆₇	1	1	yes	characteristic
634	#492	C₂²×C₆₇	1	2	yes	—
635	#491	C₂²×C₆₇	1	2	yes	—
636	#490	C₂²×C₆₇	1	2	yes	—
637	#487	C₂²×C₆₇	1	1	yes	characteristic
638	#486	C₂²×C₆₇	1	1	yes	characteristic
639	#485	C₂²×C₆₇	1	2	yes	—
640	#484	C₂²×C₆₇	1	2	yes	—
641	#483	C₂²×C₆₇	1	2	yes	—
642	#482	C₂²×C₆₇	1	2	yes	—
643	#481	C₂²×C₆₇	1	2	yes	—
644	#480	C₂²×C₆₇	1	2	yes	—
645	#479	C₂²×C₆₇	1	2	yes	—
646	#479	C₂²×C₆₇	1	2	yes	—
647	#478	C₂²×C₆₇	1	2	yes	—
648	#478	C₂²×C₆₇	1	2	yes	—
649	#477	C₂²×C₆₇	1	1	yes	characteristic
650	#476	C₂²×C₆₇	1	1	yes	characteristic
651	#475	C₂²×C₆₇	1	1	yes	characteristic
652	#474	C₂²×C₆₇	1	1	yes	characteristic
653	#468	C₂²×C₆₇	1	2	yes	—
654	#468	C₂²×C₆₇	1	2	yes	—
655	#465	C₂²×C₆₇	1	2	yes	—
656	#465	C₂²×C₆₇	1	2	yes	—
657	#465	C₂²×C₆₇	1	2	yes	—
658	#465	C₂²×C₆₇	1	2	yes	—
659	#462	C₂²×C₆₇	1	1	yes	characteristic
660	#462	C₂²×C₆₇	1	2	yes	—
661	#461	C₂²×C₆₇	1	1	yes	characteristic
662	#461	C₂²×C₆₇	1	2	yes	—
663	#460	C₂²×C₆₇	1	1	yes	characteristic
664	#460	C₂²×C₆₇	1	2	yes	—
665	#459	C₂²×C₆₇	1	1	yes	characteristic
666	#459	C₂²×C₆₇	1	2	yes	—
667	#452	C₂²×C₆₇	1	2	yes	—
668	#452	C₂²×C₆₇	1	2	yes	—
669	#452	C₂²×C₆₇	1	2	yes	—
670	#449	C₂²×C₆₇	1	2	yes	—
671	#449	C₂²×C₆₇	1	2	yes	—
672	#449	C₂²×C₆₇	1	2	yes	—
673	#446	C₂²×C₆₇	1	1	yes	characteristic
674	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic
675	#442	C₂²×C₆₇	1	2	yes	—
676	#442	C₂²×C₆₇	1	2	yes	—
677	#441	C₂²×C₆₇	1	2	yes	—
678	#441	C₂²×C₆₇	1	2	yes	—
679	#440	C₂²×C₆₇	1	2	yes	—
680	#440	C₂²×C₆₇	1	2	yes	—
681	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
682	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
683	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
684	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
685	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
686	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
687	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
688	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
689	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
690	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
691	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
692	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
693	#436	C₂²×C₆₇	1	1	yes	characteristic
694	#435	C₂²×C₆₇	1	2	yes	—
695	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
696	C₈×D₄	C₂²×C₆₇	1	2	yes	—
697	#433	C₂²×C₆₇	1	2	yes	—
698	#432	C₂²×C₆₇	1	1	yes	characteristic
699	#427	C₂²×C₆₇	1	1	yes	characteristic
700	C₂×#106	C₂²×C₆₇	1	2	yes	—
701	#417	C₂²×C₆₇	1	2	yes	—
702	#417	C₂²×C₆₇	1	2	yes	—
703	#416	C₂²×C₆₇	1	1	yes	characteristic
704	#416	C₂²×C₆₇	1	1	yes	characteristic
705	#405	C₂²×C₆₇	1	2	yes	—
706	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
707	C₂×#41	—	2	1	no	—
708	C₂×#41	—	2	1	no	—
709	C₂×#41	—	2	1	no	—
710	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
711	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
712	C₂×#41	C₂³×C₆₇	1	2	yes	—
713	C₂×#41	C₂³×C₆₇	1	2	yes	—
714	#135	—	2	4	no	—
715	#135	—	2	8	no	—
716	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
717	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
718	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
719	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
720	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
721	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
722	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
723	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
724	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
725	C₂×D₈	C₂³×C₆₇	1	2	yes	—
726	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
727	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
728	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
729	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
730	C₄⋊Q₈	—	2	1	no	—
731	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
732	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
733	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
734	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
735	#127	—	2	1	no	—
736	#127	—	2	2	no	—
737	#127	C₂³×C₆₇	1	1	yes	characteristic
738	#127	C₂³×C₆₇	1	2	yes	—
739	#126	—	2	2	no	—
740	#126	—	2	2	no	—
741	#126	—	2	2	no	—
742	#126	—	2	2	no	—
743	#126	D₄×C₆₇	1	2	yes	—
744	#125	—	2	2	no	—
745	#125	—	2	2	no	—
746	#125	—	2	1	no	—
747	#125	—	2	1	no	—
748	#125	—	2	2	no	—
749	#125	—	2	2	no	—
750	#125	—	2	2	no	—
751	#125	—	2	1	no	—
752	#125	D₄×C₆₇	1	1	yes	characteristic
753	#125	C₂³×C₆₇	1	2	yes	—
754	#125	C₂³×C₆₇	1	2	yes	—
755	#124	—	2	1	no	—
756	#124	D₄×C₆₇	1	1	yes	characteristic
757	#123	—	2	2	no	—
758	#123	—	2	2	no	—
759	#123	—	2	2	no	—
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	#123	—	2	2	no	—
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	#123	D₄×C₆₇	1	2	yes	—
766	C₂²⋊Q₈	—	2	1	no	—
767	C₂²⋊Q₈	—	2	1	no	—
768	C₂²⋊Q₈	—	2	1	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
772	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
773	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
774	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
775	#121	—	2	1	no	—
776	#121	—	2	2	no	—
777	#121	—	2	2	no	—
778	#121	—	2	1	no	—
779	#121	—	2	1	no	—
780	#121	—	2	2	no	—
781	#121	—	2	2	no	—
782	#121	—	2	2	no	—
783	#121	—	2	2	no	—
784	#121	—	2	2	no	—
785	#121	—	2	2	no	—
786	#121	D₄×C₆₇	1	1	yes	characteristic
787	#121	C₂³×C₆₇	1	2	yes	—
788	#121	C₂³×C₆₇	1	2	yes	—
789	#121	C₂³×C₆₇	1	2	yes	—
790	C₄×Q₈	—	2	1	no	—
791	C₄×Q₈	—	2	1	no	—
792	C₄×Q₈	—	2	1	no	—
793	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
794	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
795	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
796	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
797	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
798	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
799	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
800	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	2	no	—
812	C₄×D₄	—	2	2	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
815	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
816	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
817	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
818	C₄×D₄	C₂³×C₆₇	1	2	yes	—
819	C₄×D₄	C₂³×C₆₇	1	2	yes	—
820	C₄×D₄	C₂³×C₆₇	1	2	yes	—
821	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
822	C₄×D₄	C₂³×C₆₇	1	2	yes	—
823	#117	—	2	1	no	—
824	#117	—	2	2	no	—
825	#117	—	2	2	no	—
826	#117	—	2	2	no	—
827	#117	—	2	1	no	—
828	#117	—	2	1	no	—
829	#117	C₂³×C₆₇	1	1	yes	characteristic
830	#117	C₂³×C₆₇	1	1	yes	characteristic
831	#117	C₂³×C₆₇	1	2	yes	—
832	C₂×C₄⋊C₄	—	2	2	no	—
833	C₂×C₄⋊C₄	—	2	2	no	—
834	C₂×C₄⋊C₄	—	2	1	no	—
835	C₂×C₄⋊C₄	—	2	2	no	—
836	C₂×C₄⋊C₄	—	2	1	no	—
837	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
838	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
839	C₂×C₄²	—	2	1	no	—
840	C₂×C₄²	—	2	1	no	—
841	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
842	#107	C₂³×C₆₇	1	1	yes	characteristic
843	#107	C₂³×C₆₇	1	1	yes	characteristic
844	#107	C₂³×C₆₇	1	2	yes	—
845	#107	C₂³×C₆₇	1	2	yes	—
846	#106	C₂³×C₆₇	1	1	yes	characteristic
847	#106	C₂³×C₆₇	1	2	yes	—
848	#106	C₂³×C₆₇	1	2	yes	—
849	#106	C₂³×C₆₇	1	2	yes	—
850	#106	C₂³×C₆₇	1	1	yes	characteristic
851	#106	C₂³×C₆₇	1	2	yes	—
852	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
853	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
854	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
855	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
856	#103	C₂³×C₆₇	1	1	yes	characteristic
857	#103	C₂³×C₆₇	1	1	yes	characteristic
858	#103	C₂³×C₆₇	1	1	yes	characteristic
859	#103	C₂³×C₆₇	1	1	yes	characteristic
860	#103	C₂³×C₆₇	1	2	yes	—
861	#103	C₂³×C₆₇	1	2	yes	—
862	#103	C₂³×C₆₇	1	2	yes	—
863	#103	C₂³×C₆₇	1	2	yes	—
864	#103	C₂³×C₆₇	1	2	yes	—
865	#103	C₂³×C₆₇	1	2	yes	—
866	#102	C₂³×C₆₇	1	1	yes	characteristic
867	#102	C₂³×C₆₇	1	1	yes	characteristic
868	#102	C₂³×C₆₇	1	1	yes	characteristic
869	#102	C₂³×C₆₇	1	1	yes	characteristic
870	#102	C₂³×C₆₇	1	2	yes	—
871	#102	C₂³×C₆₇	1	2	yes	—
872	#102	C₂³×C₆₇	1	2	yes	—
873	#102	C₂³×C₆₇	1	2	yes	—
874	#102	C₂³×C₆₇	1	2	yes	—
875	#102	C₂³×C₆₇	1	2	yes	—
876	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
877	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
878	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
879	#97	C₂³×C₆₇	1	2	yes	—
880	#97	C₂³×C₆₇	1	2	yes	—
881	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
882	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
883	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
884	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
885	C₄×C₈	C₂³×C₆₇	1	2	yes	—
886	#41	—	2	2	no	—
887	#41	—	2	4	no	—
888	#41	—	2	2	no	—
889	#41	—	2	4	no	—
890	#41	—	4	1	no	—
891	#41	—	4	1	no	—
892	#41	—	4	2	no	—
893	#41	—	4	2	no	—
894	#41	—	8	2	no	—
895	#41	—	8	2	no	—
896	#41	—	8	2	no	—
897	C₂×Q₈	—	2	1	no	—
898	C₂×Q₈	—	2	1	no	—
899	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
900	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
901	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
902	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
903	C₂×D₄	—	2	1	no	—
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	2	2	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	2	no	—
910	C₂×D₄	—	2	1	no	—
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
915	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
916	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
917	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
918	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	—	2	1	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	—	2	1	no	—
928	C₂²×C₄	—	2	1	no	—
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
933	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
934	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
935	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
936	Q₁₆	—	2	2	no	—
937	Q₁₆	—	2	4	no	—
938	SD₁₆	—	2	2	no	—
939	SD₁₆	—	2	4	no	—
940	SD₁₆	—	4	2	no	—
941	SD₁₆	—	4	2	no	—
942	SD₁₆	—	4	2	no	—
943	SD₁₆	#41×C₆₇	1	4	yes	complemented
944	D₈	—	2	2	no	—
945	D₈	—	2	4	no	—
946	M₁₆	—	4	2	no	—
947	C₂×C₈	—	2	2	no	—
948	C₂×C₈	—	2	4	no	—
949	C₂×C₈	—	4	1	no	—
950	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
951	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
952	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
953	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
954	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
955	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
979	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
980	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
981	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
982	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
983	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
984	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
985	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
986	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
987	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
988	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
989	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	1	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1006	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1007	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1008	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1009	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1010	C₄²	—	2	1	no	—
1011	C₄²	—	2	1	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	2	1	no	—
1014	C₄²	—	2	1	no	—
1015	C₄²	—	2	1	no	—
1016	C₄²	—	2	2	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	2	no	—
1019	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1020	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1021	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1022	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1023	C₄²	C₂⁴×C₆₇	1	2	yes	—
1024	C₂³	—	2	1	no	—
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	2	no	—
1027	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1028	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1029	Q₈	—	2	2	no	—
1030	Q₈	—	2	1	no	—
1031	Q₈	—	2	1	no	—
1032	Q₈	—	2	2	no	—
1033	Q₈	—	2	2	no	—
1034	Q₈	—	2	1	no	—
1035	Q₈	—	4	2	no	—
1036	Q₈	—	8	1	no	—
1037	Q₈	C₂×#41×C₆₇	1	2	yes	—
1038	D₄	—	2	2	no	—
1039	D₄	—	2	1	no	—
1040	D₄	—	2	2	no	—
1041	D₄	—	2	1	no	—
1042	D₄	—	2	2	no	—
1043	D₄	—	2	1	no	—
1044	D₄	—	4	2	no	—
1045	D₄	—	4	2	no	—
1046	D₄	—	4	4	no	—
1047	D₄	—	4	2	no	—
1048	D₄	—	4	4	no	—
1049	D₄	—	4	2	no	—
1050	D₄	—	8	2	no	—
1051	D₄	—	8	1	no	—
1052	D₄	—	8	2	no	—
1053	D₄	—	8	2	no	—
1054	D₄	—	8	2	no	—
1055	D₄	—	8	2	no	—
1056	D₄	C₂×#41×C₆₇	1	2	yes	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	4	1	no	—
1072	C₂×C₄	—	4	2	no	—
1073	C₂×C₄	—	4	4	no	—
1074	C₂×C₄	—	4	2	no	—
1075	C₂×C₄	—	4	4	no	—
1076	C₂×C₄	—	4	2	no	—
1077	C₂×C₄	—	4	2	no	—
1078	C₂×C₄	—	8	2	no	—
1079	C₂×C₄	—	8	2	no	—
1080	C₂×C₄	—	8	1	no	—
1081	C₂×C₄	—	8	1	no	—
1082	C₂×C₄	—	8	2	no	—
1083	C₂×C₄	—	8	2	no	—
1084	C₂×C₄	—	8	2	no	—
1085	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1086	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1087	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1088	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1089	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1090	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1091	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1092	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1093	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1094	C₈	—	2	1	no	—
1095	C₈	—	2	2	no	—
1096	C₈	—	2	1	no	—
1097	C₈	—	2	1	no	—
1098	C₈	—	2	2	no	—
1099	C₈	C₂×#41×C₆₇	1	2	yes	—
1100	C₂²	—	2	1	no	—
1101	C₂²	—	2	2	no	—
1102	C₂²	—	2	1	no	—
1103	C₂²	—	2	2	no	—
1104	C₂²	—	2	1	no	—
1105	C₂²	—	2	2	no	—
1106	C₂²	—	2	2	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	4	1	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	2	no	—
1111	C₂²	—	4	1	no	—
1112	C₂²	—	4	2	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	4	2	no	—
1115	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1116	C₄	—	2	1	no	—
1117	C₄	—	2	2	no	—
1118	C₄	—	2	1	no	—
1119	C₄	—	2	1	no	—
1120	C₄	—	2	2	no	—
1121	C₄	—	2	1	no	—
1122	C₄	—	2	2	no	—
1123	C₄	—	2	2	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	2	no	—
1127	C₄	—	4	1	no	—
1128	C₄	—	4	2	no	—
1129	C₄	—	4	1	no	—
1130	C₄	—	4	1	no	—
1131	C₄	—	4	2	no	—
1132	C₄	#577×C₆₇	1	2	yes	—
1133	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1134	C₄	#585×C₆₇	1	1	yes	characteristic
1135	C₂	—	4	1	no	—
1136	C₂	—	4	2	no	—
1137	C₂	—	4	2	no	—
1138	C₂	—	8	1	no	—
1139	C₂	—	8	2	no	—
1140	C₂	D₄×#41×C₆₇	1	1	yes	characteristic
1141	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
1142	C₂	C₆₇×#3584	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 ◁ #529×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3517	C₂	semidirect
2. C₆₇×#3515	C₂	semidirect
3. C₆₇×#3392	C₂	semidirect
4. C₆₇×#3381	C₂	semidirect
5. C₆₇×#3374	C₂	semidirect
6. C₆₇×#3366	C₂	semidirect
7. C₆₇×#3337	C₂	semidirect
8. C₆₇×#3335	C₂	semidirect
9. C₆₇×#3333	C₂	semidirect
10. C₆₇×#3330	C₂	semidirect
11. C₆₇×#3317	C₂	semidirect
12. C₆₇×#3307	C₂	semidirect
13. C₆₇×#3284	C₂	semidirect
14. C₆₇×#3284	C₂	semidirect
15. C₆₇×#3174	C₂	semidirect
16. C₆₇×#3167	C₂	semidirect
17. C₆₇×#3120	C₂	semidirect
18. C₆₇×#3119	C₂	semidirect
19. C₆₇×#3116	C₂	semidirect
20. C₆₇×#3115	C₂	semidirect
21. C₆₇×#2966	C₂	semidirect
22. C₆₇×#2952	C₂	semidirect
23. C₄×#135×C₆₇	C₂	semidirect
371. SD₁₆×C₆₇	#41	semidirect
563. #61476	C₆₇	direct (N × H)
572. #3517	C₂×C₆₇	semidirect
573. #3515	C₂×C₆₇	semidirect
574. #3392	C₂×C₆₇	semidirect
575. #3381	C₂×C₆₇	semidirect
576. #3374	C₂×C₆₇	semidirect
577. #3366	C₂×C₆₇	semidirect
578. #3337	C₂×C₆₇	semidirect
579. #3335	C₂×C₆₇	semidirect
580. #3333	C₂×C₆₇	semidirect
581. #3330	C₂×C₆₇	semidirect
582. #3317	C₂×C₆₇	semidirect
583. #3307	C₂×C₆₇	semidirect
584. #3284	C₂×C₆₇	semidirect
585. #3284	C₂×C₆₇	semidirect
586. #3174	C₂×C₆₇	semidirect
587. #3167	C₂×C₆₇	semidirect
588. #3120	C₂×C₆₇	semidirect
589. #3119	C₂×C₆₇	semidirect
590. #3116	C₂×C₆₇	semidirect
591. #3115	C₂×C₆₇	semidirect
592. #2966	C₂×C₆₇	semidirect
593. #2952	C₂×C₆₇	semidirect
594. C₄×#135	C₂×C₆₇	semidirect
595. C₆₇	#61476	direct (N × H)
943. SD₁₆	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3517	2
C₆₇×#3515	2
C₆₇×#3392	2
C₆₇×#3381	2
C₆₇×#3374	2
C₆₇×#3366	2
C₆₇×#3337	2
C₆₇×#3335	2
C₆₇×#3333	2
C₆₇×#3330	2
C₆₇×#3317	2
C₆₇×#3307	2
C₆₇×#3284	2
C₆₇×#3174	2
C₆₇×#3167	2
C₆₇×#3120	2
C₆₇×#3119	2
C₆₇×#3116	2
C₆₇×#3115	2
C₆₇×#2966	2
C₆₇×#2952	2
C₄×#135×C₆₇	2
#61476	67

Subgroups — C67×#61476 #30740727

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61476 #30740727