Subgroups — C₆₇×#61811 #30741062

Order 17152.

1788 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3546	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3511	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3353	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3353	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3347	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3346	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3342	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3334	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3332	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3324	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3319	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3314	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3304	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3239	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3226	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3203	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3198	C₂	1	2	yes	maximal, complemented
19	C₆₇×#3115	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#3098	C₂	1	2	yes	maximal, complemented
22	C₆₇×#3096	C₂	1	2	yes	maximal, complemented
23	C₆₇×#2981	C₂	1	1	yes	maximal, characteristic, complemented
24	#560×C₆₇	—	2	2	no	—
25	#556×C₆₇	C₂²	1	1	yes	characteristic
26	#556×C₆₇	C₂²	1	1	yes	characteristic
27	#556×C₆₇	C₂²	1	1	yes	characteristic, complemented
28	#555×C₆₇	C₂²	1	2	yes	complemented
29	#554×C₆₇	C₂²	1	2	yes	complemented
30	#553×C₆₇	—	2	2	no	—
31	#553×C₆₇	C₂²	1	2	yes	—
32	#550×C₆₇	—	2	1	no	—
33	#550×C₆₇	C₂²	1	1	yes	characteristic
34	#548×C₆₇	—	2	1	no	—
35	#548×C₆₇	—	2	1	no	—
36	#547×C₆₇	C₂²	1	1	yes	characteristic
37	#547×C₆₇	C₂²	1	1	yes	characteristic
38	#547×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	#546×C₆₇	—	2	1	no	—
40	#546×C₆₇	C₂²	1	2	yes	—
41	D₄²×C₆₇	C₂²	1	1	yes	characteristic
42	#542×C₆₇	—	2	1	no	—
43	#542×C₆₇	—	2	2	no	—
44	#538×C₆₇	—	2	2	no	—
45	#537×C₆₇	C₂²	1	2	yes	—
46	#537×C₆₇	C₂²	1	2	yes	complemented
47	#535×C₆₇	—	2	1	no	—
48	#535×C₆₇	C₂²	1	2	yes	—
49	#533×C₆₇	—	2	1	no	—
50	#532×C₆₇	—	2	1	no	—
51	#532×C₆₇	C₂²	1	1	yes	characteristic
52	#532×C₆₇	C₂²	1	1	yes	characteristic
53	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
54	#529×C₆₇	C₂²	1	1	yes	characteristic
55	#520×C₆₇	C₂²	1	2	yes	complemented
56	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
57	#501×C₆₇	C₂²	1	2	yes	complemented
58	#500×C₆₇	C₂²	1	1	yes	characteristic, complemented
59	#500×C₆₇	C₂²	1	1	yes	characteristic, complemented
60	#489×C₆₇	C₂²	1	2	yes	—
61	#486×C₆₇	C₂²	1	1	yes	characteristic
62	#486×C₆₇	C₂²	1	1	yes	characteristic
63	#485×C₆₇	C₂²	1	2	yes	complemented
64	#485×C₆₇	C₂²	1	2	yes	complemented
65	#485×C₆₇	C₂²	1	1	yes	characteristic, complemented
66	#484×C₆₇	C₂²	1	2	yes	complemented
67	#484×C₆₇	C₂²	1	2	yes	complemented
68	#484×C₆₇	C₂²	1	2	yes	complemented
69	#482×C₆₇	C₂²	1	2	yes	—
70	#482×C₆₇	C₂²	1	2	yes	—
71	#482×C₆₇	C₂²	1	1	yes	characteristic
72	#482×C₆₇	C₂²	1	2	yes	complemented
73	#482×C₆₇	C₂²	1	2	yes	complemented
74	#482×C₆₇	C₂²	1	2	yes	complemented
75	#481×C₆₇	C₂²	1	2	yes	—
76	#481×C₆₇	C₂²	1	2	yes	complemented
77	#480×C₆₇	C₂²	1	2	yes	—
78	#480×C₆₇	C₂²	1	2	yes	—
79	#480×C₆₇	C₂²	1	2	yes	complemented
80	#480×C₆₇	C₂²	1	2	yes	complemented
81	#480×C₆₇	C₂²	1	2	yes	complemented
82	#479×C₆₇	C₂²	1	1	yes	characteristic, complemented
83	#478×C₆₇	C₂²	1	1	yes	characteristic, complemented
84	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
85	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
86	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
87	#474×C₆₇	C₂²	1	1	yes	characteristic
88	#474×C₆₇	C₂²	1	1	yes	characteristic
89	#474×C₆₇	C₂²	1	2	yes	complemented
90	#474×C₆₇	C₂²	1	2	yes	complemented
91	#474×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	#469×C₆₇	C₂²	1	2	yes	complemented
93	#468×C₆₇	C₂²	1	2	yes	—
94	#468×C₆₇	C₂²	1	2	yes	—
95	#468×C₆₇	C₂²	1	2	yes	complemented
96	#467×C₆₇	C₂²	1	2	yes	complemented
97	#466×C₆₇	C₂²	1	2	yes	—
98	#466×C₆₇	C₂²	1	2	yes	—
99	#465×C₆₇	C₂²	1	2	yes	complemented
100	#464×C₆₇	C₂²	1	1	yes	characteristic
101	#463×C₆₇	C₂²	1	1	yes	characteristic
102	#460×C₆₇	C₂²	1	1	yes	characteristic
103	#459×C₆₇	C₂²	1	1	yes	characteristic
104	#452×C₆₇	C₂²	1	2	yes	complemented
105	#452×C₆₇	C₂²	1	1	yes	characteristic, complemented
106	#450×C₆₇	C₂²	1	2	yes	—
107	#449×C₆₇	C₂²	1	1	yes	characteristic
108	#449×C₆₇	C₂²	1	2	yes	complemented
109	#449×C₆₇	C₂²	1	2	yes	complemented
110	#447×C₆₇	C₂²	1	2	yes	—
111	#442×C₆₇	C₂²	1	2	yes	complemented
112	#440×C₆₇	C₂²	1	2	yes	complemented
113	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
114	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
115	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
117	#436×C₆₇	C₂²	1	1	yes	characteristic
118	#436×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	#435×C₆₇	C₂²	1	2	yes	complemented
120	#435×C₆₇	C₂²	1	2	yes	complemented
121	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
122	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
124	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
125	#428×C₆₇	C₂²	1	2	yes	complemented
126	#428×C₆₇	C₂²	1	2	yes	complemented
127	#427×C₆₇	C₂²	1	2	yes	complemented
128	C₂×#107×C₆₇	C₂²	1	2	yes	complemented
129	#418×C₆₇	C₂²	1	2	yes	—
130	#417×C₆₇	C₂²	1	2	yes	complemented
131	#416×C₆₇	C₂²	1	2	yes	complemented
132	C₂×#102×C₆₇	C₂²	1	2	yes	—
133	#408×C₆₇	C₂²	1	2	yes	complemented
134	#408×C₆₇	C₂²	1	2	yes	complemented
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	—	2	1	no	—
139	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
140	C₂×#41×C₆₇	C₂³	1	2	yes	—
141	C₂×#41×C₆₇	C₂³	1	2	yes	—
142	C₂²×Q₈×C₆₇	—	2	1	no	—
143	C₂²×D₄×C₆₇	—	2	1	no	—
144	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
145	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
149	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
150	C₂×D₈×C₆₇	C₂³	1	2	yes	—
151	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
152	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
153	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
154	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
155	C₄⋊Q₈×C₆₇	—	2	1	no	—
156	C₄⋊Q₈×C₆₇	—	2	1	no	—
157	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
158	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
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	#127×C₆₇	—	2	1	no	—
163	#127×C₆₇	—	2	2	no	—
164	#127×C₆₇	D₄	1	1	yes	characteristic
165	#127×C₆₇	C₂³	1	1	yes	characteristic
166	#126×C₆₇	—	2	2	no	—
167	#126×C₆₇	—	2	2	no	—
168	#126×C₆₇	—	2	2	no	—
169	#126×C₆₇	—	2	2	no	—
170	#126×C₆₇	—	2	1	no	—
171	#125×C₆₇	—	2	2	no	—
172	#125×C₆₇	C₂³	1	1	yes	characteristic
173	#124×C₆₇	—	2	2	no	—
174	#124×C₆₇	—	2	1	no	—
175	#124×C₆₇	—	2	1	no	—
176	#124×C₆₇	—	2	1	no	—
177	#124×C₆₇	—	2	2	no	—
178	#124×C₆₇	—	2	2	no	—
179	#124×C₆₇	—	2	1	no	—
180	#124×C₆₇	D₄	1	2	yes	—
181	#124×C₆₇	C₂³	1	1	yes	characteristic
182	#123×C₆₇	—	2	1	no	—
183	#123×C₆₇	—	2	2	no	—
184	#123×C₆₇	—	2	2	no	—
185	#123×C₆₇	—	2	2	no	—
186	#123×C₆₇	—	2	2	no	—
187	#123×C₆₇	—	2	2	no	—
188	C₂²⋊Q₈×C₆₇	—	2	2	no	—
189	C₂²⋊Q₈×C₆₇	—	2	2	no	—
190	C₂²⋊Q₈×C₆₇	—	2	1	no	—
191	C₂²⋊Q₈×C₆₇	—	2	1	no	—
192	C₂²⋊Q₈×C₆₇	—	2	1	no	—
193	C₂²⋊Q₈×C₆₇	—	2	2	no	—
194	C₂²⋊Q₈×C₆₇	—	2	2	no	—
195	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
196	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
197	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
198	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
199	#121×C₆₇	—	2	2	no	—
200	#121×C₆₇	—	2	2	no	—
201	#121×C₆₇	—	2	2	no	—
202	#121×C₆₇	—	2	2	no	—
203	#121×C₆₇	—	2	2	no	—
204	#121×C₆₇	—	2	2	no	—
205	#121×C₆₇	—	2	2	no	—
206	#121×C₆₇	—	2	2	no	—
207	#121×C₆₇	—	2	1	no	—
208	#121×C₆₇	—	2	1	no	—
209	#121×C₆₇	—	2	2	no	—
210	#121×C₆₇	—	2	2	no	—
211	#121×C₆₇	D₄	1	1	yes	characteristic
212	#121×C₆₇	D₄	1	1	yes	characteristic
213	#121×C₆₇	D₄	1	2	yes	—
214	#121×C₆₇	C₂³	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	#121×C₆₇	C₂³	1	2	yes	—
219	#121×C₆₇	C₂³	1	2	yes	—
220	#121×C₆₇	C₂³	1	2	yes	—
221	#120×C₆₇	—	2	2	no	—
222	#120×C₆₇	—	2	2	no	—
223	#120×C₆₇	—	2	2	no	—
224	#120×C₆₇	—	2	2	no	—
225	C₄×Q₈×C₆₇	—	2	2	no	—
226	C₄×Q₈×C₆₇	—	2	1	no	—
227	C₄×Q₈×C₆₇	—	2	1	no	—
228	C₄×Q₈×C₆₇	—	2	1	no	—
229	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
232	C₄×D₄×C₆₇	—	2	2	no	—
233	C₄×D₄×C₆₇	—	2	2	no	—
234	C₄×D₄×C₆₇	—	2	2	no	—
235	C₄×D₄×C₆₇	—	2	2	no	—
236	C₄×D₄×C₆₇	—	2	1	no	—
237	C₄×D₄×C₆₇	—	2	1	no	—
238	C₄×D₄×C₆₇	—	2	1	no	—
239	C₄×D₄×C₆₇	—	2	1	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	1	yes	characteristic
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	2	yes	—
248	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
249	#117×C₆₇	—	2	2	no	—
250	#117×C₆₇	—	2	1	no	—
251	#117×C₆₇	—	2	1	no	—
252	#117×C₆₇	C₂³	1	1	yes	characteristic
253	#117×C₆₇	C₂³	1	2	yes	—
254	#117×C₆₇	C₂³	1	2	yes	—
255	#117×C₆₇	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
257	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
261	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
262	C₂×C₄²×C₆₇	—	2	1	no	—
263	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
264	#107×C₆₇	C₂³	1	2	yes	—
265	#107×C₆₇	C₂³	1	2	yes	—
266	#107×C₆₇	C₂³	1	2	yes	—
267	#107×C₆₇	C₂³	1	2	yes	—
268	#107×C₆₇	C₂³	1	2	yes	—
269	#107×C₆₇	C₂³	1	2	yes	—
270	#107×C₆₇	C₂³	1	2	yes	—
271	#107×C₆₇	C₂³	1	1	yes	characteristic
272	#107×C₆₇	C₂³	1	1	yes	characteristic
273	#106×C₆₇	C₂³	1	2	yes	—
274	#106×C₆₇	C₂³	1	2	yes	—
275	#106×C₆₇	C₂³	1	2	yes	—
276	#106×C₆₇	C₂³	1	1	yes	characteristic
277	#106×C₆₇	C₂³	1	1	yes	characteristic
278	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
279	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
282	#103×C₆₇	C₂³	1	1	yes	characteristic
283	#103×C₆₇	C₂³	1	2	yes	—
284	#103×C₆₇	C₂³	1	2	yes	—
285	#103×C₆₇	C₂³	1	1	yes	characteristic
286	#103×C₆₇	C₂³	1	2	yes	—
287	#103×C₆₇	C₂³	1	1	yes	characteristic
288	#103×C₆₇	C₂³	1	1	yes	characteristic
289	#102×C₆₇	C₂³	1	1	yes	characteristic
290	#102×C₆₇	C₂³	1	2	yes	—
291	#102×C₆₇	C₂³	1	2	yes	—
292	#102×C₆₇	C₂³	1	2	yes	—
293	#102×C₆₇	C₂³	1	2	yes	—
294	#102×C₆₇	C₂³	1	1	yes	characteristic
295	#102×C₆₇	C₂³	1	2	yes	—
296	#102×C₆₇	C₂³	1	2	yes	—
297	#102×C₆₇	C₂³	1	2	yes	—
298	#102×C₆₇	C₂³	1	1	yes	characteristic
299	#102×C₆₇	C₂³	1	1	yes	characteristic
300	#102×C₆₇	C₂³	1	2	yes	—
301	#102×C₆₇	C₂³	1	2	yes	—
302	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
303	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
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	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
309	#97×C₆₇	C₂³	1	2	yes	—
310	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
312	C₂⁴×C₆₇	—	2	2	no	—
313	#41×C₆₇	—	4	2	no	—
314	#41×C₆₇	—	4	2	no	—
315	#41×C₆₇	—	4	1	no	—
316	#41×C₆₇	—	4	1	no	—
317	#41×C₆₇	—	4	2	no	—
318	#41×C₆₇	—	4	2	no	—
319	#41×C₆₇	—	8	2	no	—
320	#41×C₆₇	—	8	2	no	—
321	#41×C₆₇	—	8	2	no	—
322	#41×C₆₇	—	8	2	no	—
323	C₂×Q₈×C₆₇	—	2	1	no	—
324	C₂×Q₈×C₆₇	—	2	1	no	—
325	C₂×Q₈×C₆₇	—	2	1	no	—
326	C₂×Q₈×C₆₇	—	2	2	no	—
327	C₂×Q₈×C₆₇	—	8	2	no	—
328	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
329	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₆₇	—	2	1	no	—
332	C₂×D₄×C₆₇	—	2	1	no	—
333	C₂×D₄×C₆₇	—	2	2	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	2	no	—
339	C₂×D₄×C₆₇	—	2	2	no	—
340	C₂×D₄×C₆₇	—	2	1	no	—
341	C₂×D₄×C₆₇	—	2	1	no	—
342	C₂×D₄×C₆₇	—	2	2	no	—
343	C₂×D₄×C₆₇	—	4	2	no	—
344	C₂×D₄×C₆₇	—	4	2	no	—
345	C₂×D₄×C₆₇	—	8	2	no	—
346	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
347	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
348	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
349	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
350	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
351	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
352	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
353	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
354	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₆₇	—	2	2	no	—
356	C₂²×C₄×C₆₇	—	2	2	no	—
357	C₂²×C₄×C₆₇	—	2	2	no	—
358	C₂²×C₄×C₆₇	—	2	2	no	—
359	C₂²×C₄×C₆₇	—	2	1	no	—
360	C₂²×C₄×C₆₇	—	2	1	no	—
361	C₂²×C₄×C₆₇	—	2	1	no	—
362	C₂²×C₄×C₆₇	—	2	1	no	—
363	C₂²×C₄×C₆₇	—	2	2	no	—
364	C₂²×C₄×C₆₇	—	2	2	no	—
365	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
369	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
370	Q₁₆×C₆₇	—	4	1	no	—
371	SD₁₆×C₆₇	—	4	2	no	—
372	SD₁₆×C₆₇	—	4	1	no	—
373	SD₁₆×C₆₇	—	4	1	no	—
374	D₈×C₆₇	—	4	1	no	—
375	D₈×C₆₇	—	4	2	no	—
376	M₁₆×C₆₇	—	4	2	no	—
377	M₁₆×C₆₇	—	4	2	no	—
378	C₂×C₈×C₆₇	—	4	2	no	—
379	C₂×C₈×C₆₇	—	4	2	no	—
380	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
381	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
382	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
385	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
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	1	no	—
394	C₄⋊C₄×C₆₇	—	2	1	no	—
395	C₄⋊C₄×C₆₇	—	2	1	no	—
396	C₄⋊C₄×C₆₇	—	2	1	no	—
397	C₄⋊C₄×C₆₇	—	2	1	no	—
398	C₄⋊C₄×C₆₇	—	2	1	no	—
399	C₄⋊C₄×C₆₇	—	2	2	no	—
400	C₄⋊C₄×C₆₇	—	2	2	no	—
401	C₄⋊C₄×C₆₇	—	2	2	no	—
402	C₄⋊C₄×C₆₇	—	2	1	no	—
403	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
406	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
409	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
410	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
413	C₂²⋊C₄×C₆₇	—	2	2	no	—
414	C₂²⋊C₄×C₆₇	—	2	1	no	—
415	C₂²⋊C₄×C₆₇	—	2	2	no	—
416	C₂²⋊C₄×C₆₇	—	2	2	no	—
417	C₂²⋊C₄×C₆₇	—	2	2	no	—
418	C₂²⋊C₄×C₆₇	—	2	1	no	—
419	C₂²⋊C₄×C₆₇	—	2	2	no	—
420	C₂²⋊C₄×C₆₇	—	2	2	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	1	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	2	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	1	no	—
433	C₂²⋊C₄×C₆₇	—	2	2	no	—
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	2	no	—
442	C₄²×C₆₇	—	2	2	no	—
443	C₄²×C₆₇	—	2	1	no	—
444	C₄²×C₆₇	—	2	2	no	—
445	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
446	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
447	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
448	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
449	C₂³×C₆₇	—	2	1	no	—
450	C₂³×C₆₇	—	2	1	no	—
451	C₂³×C₆₇	—	2	2	no	—
452	C₂³×C₆₇	—	8	2	no	—
453	C₂³×C₆₇	—	8	2	no	—
454	C₂³×C₆₇	—	8	2	no	—
455	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
456	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
457	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
458	Q₈×C₆₇	—	2	1	no	—
459	Q₈×C₆₇	—	2	1	no	—
460	Q₈×C₆₇	—	2	1	no	—
461	Q₈×C₆₇	—	2	1	no	—
462	Q₈×C₆₇	—	4	2	no	—
463	Q₈×C₆₇	—	4	2	no	—
464	Q₈×C₆₇	—	4	2	no	—
465	Q₈×C₆₇	—	4	2	no	—
466	Q₈×C₆₇	—	8	2	no	—
467	D₄×C₆₇	—	2	2	no	—
468	D₄×C₆₇	—	2	2	no	—
469	D₄×C₆₇	—	2	1	no	—
470	D₄×C₆₇	—	2	1	no	—
471	D₄×C₆₇	—	2	1	no	—
472	D₄×C₆₇	—	2	2	no	—
473	D₄×C₆₇	—	2	1	no	—
474	D₄×C₆₇	—	2	2	no	—
475	D₄×C₆₇	—	4	2	no	—
476	D₄×C₆₇	—	4	2	no	—
477	D₄×C₆₇	—	4	2	no	—
478	D₄×C₆₇	—	4	2	no	—
479	D₄×C₆₇	—	4	2	no	—
480	D₄×C₆₇	—	4	2	no	—
481	D₄×C₆₇	—	8	1	no	—
482	D₄×C₆₇	—	8	2	no	—
483	D₄×C₆₇	—	8	1	no	—
484	D₄×C₆₇	—	8	2	no	—
485	D₄×C₆₇	—	8	2	no	—
486	D₄×C₆₇	—	8	2	no	—
487	D₄×C₆₇	—	8	2	no	—
488	D₄×C₆₇	—	8	2	no	—
489	D₄×C₆₇	—	8	2	no	—
490	D₄×C₆₇	—	8	2	no	—
491	C₂×C₄×C₆₇	—	2	2	no	—
492	C₂×C₄×C₆₇	—	2	2	no	—
493	C₂×C₄×C₆₇	—	2	2	no	—
494	C₂×C₄×C₆₇	—	2	2	no	—
495	C₂×C₄×C₆₇	—	2	2	no	—
496	C₂×C₄×C₆₇	—	2	1	no	—
497	C₂×C₄×C₆₇	—	2	1	no	—
498	C₂×C₄×C₆₇	—	2	1	no	—
499	C₂×C₄×C₆₇	—	2	1	no	—
500	C₂×C₄×C₆₇	—	2	1	no	—
501	C₂×C₄×C₆₇	—	2	1	no	—
502	C₂×C₄×C₆₇	—	2	1	no	—
503	C₂×C₄×C₆₇	—	2	2	no	—
504	C₂×C₄×C₆₇	—	2	2	no	—
505	C₂×C₄×C₆₇	—	2	2	no	—
506	C₂×C₄×C₆₇	—	2	1	no	—
507	C₂×C₄×C₆₇	—	4	1	no	—
508	C₂×C₄×C₆₇	—	4	2	no	—
509	C₂×C₄×C₆₇	—	4	2	no	—
510	C₂×C₄×C₆₇	—	4	2	no	—
511	C₂×C₄×C₆₇	—	4	2	no	—
512	C₂×C₄×C₆₇	—	8	2	no	—
513	C₂×C₄×C₆₇	—	8	2	no	—
514	C₂×C₄×C₆₇	—	8	2	no	—
515	C₂×C₄×C₆₇	—	8	2	no	—
516	C₂×C₄×C₆₇	—	8	2	no	—
517	C₂×C₄×C₆₇	—	8	2	no	—
518	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
519	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
522	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
526	C₈×C₆₇	—	2	1	no	—
527	C₈×C₆₇	—	2	1	no	—
528	C₈×C₆₇	—	2	2	no	—
529	C₈×C₆₇	—	2	2	no	—
530	C₈×C₆₇	—	2	1	no	—
531	C₈×C₆₇	—	2	1	no	—
532	C₂²×C₆₇	—	2	1	no	—
533	C₂²×C₆₇	—	2	2	no	—
534	C₂²×C₆₇	—	2	2	no	—
535	C₂²×C₆₇	—	2	1	no	—
536	C₂²×C₆₇	—	2	2	no	—
537	C₂²×C₆₇	—	2	2	no	—
538	C₂²×C₆₇	—	2	1	no	—
539	C₂²×C₆₇	—	2	2	no	—
540	C₂²×C₆₇	—	2	2	no	—
541	C₂²×C₆₇	—	4	1	no	—
542	C₂²×C₆₇	—	4	2	no	—
543	C₂²×C₆₇	—	4	1	no	—
544	C₂²×C₆₇	—	4	1	no	—
545	C₂²×C₆₇	—	4	2	no	—
546	C₂²×C₆₇	—	4	1	no	—
547	C₂²×C₆₇	—	4	1	no	—
548	C₂²×C₆₇	—	4	1	no	—
549	C₂²×C₆₇	—	4	2	no	—
550	C₂²×C₆₇	—	16	4	no	—
551	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
552	C₄×C₆₇	—	2	1	no	—
553	C₄×C₆₇	—	2	1	no	—
554	C₄×C₆₇	—	2	1	no	—
555	C₄×C₆₇	—	2	2	no	—
556	C₄×C₆₇	—	2	2	no	—
557	C₄×C₆₇	—	2	1	no	—
558	C₄×C₆₇	—	4	1	no	—
559	C₄×C₆₇	—	4	1	no	—
560	C₄×C₆₇	—	4	1	no	—
561	C₄×C₆₇	—	4	1	no	—
562	C₄×C₆₇	—	4	1	no	—
563	C₄×C₆₇	—	4	1	no	—
564	C₄×C₆₇	—	4	2	no	—
565	C₄×C₆₇	—	4	2	no	—
566	C₄×C₆₇	—	4	2	no	—
567	C₄×C₆₇	#576	1	2	yes	—
568	C₄×C₆₇	#585	1	1	yes	characteristic
569	C₄×C₆₇	#585	1	1	yes	characteristic
570	#61811	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
571	C₂×C₆₇	—	4	1	no	—
572	C₂×C₆₇	—	4	2	no	—
573	C₂×C₆₇	—	4	2	no	—
574	C₂×C₆₇	—	8	1	no	—
575	C₂×C₆₇	—	8	2	no	—
576	C₂×C₆₇	—	8	1	no	—
577	C₂×C₆₇	#3485	1	1	yes	characteristic
578	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
579	C₂×C₆₇	#3586	1	1	yes	characteristic
580	#3546	C₂×C₆₇	1	1	yes	characteristic, complemented
581	#3511	C₂×C₆₇	1	1	yes	characteristic, complemented
582	#3353	C₂×C₆₇	1	1	yes	characteristic, complemented
583	#3353	C₂×C₆₇	1	1	yes	characteristic, complemented
584	#3347	C₂×C₆₇	1	2	yes	complemented
585	#3346	C₂×C₆₇	1	2	yes	complemented
586	#3342	C₂×C₆₇	1	1	yes	characteristic, complemented
587	#3334	C₂×C₆₇	1	1	yes	characteristic, complemented
588	#3332	C₂×C₆₇	1	1	yes	characteristic, complemented
589	#3324	C₂×C₆₇	1	1	yes	characteristic, complemented
590	#3319	C₂×C₆₇	1	2	yes	complemented
591	#3314	C₂×C₆₇	1	2	yes	complemented
592	#3304	C₂×C₆₇	1	1	yes	characteristic, complemented
593	#3294	C₂×C₆₇	1	1	yes	characteristic, complemented
594	#3239	C₂×C₆₇	1	1	yes	characteristic, complemented
595	#3226	C₂×C₆₇	1	1	yes	characteristic, complemented
596	#3203	C₂×C₆₇	1	2	yes	complemented
597	#3198	C₂×C₆₇	1	2	yes	complemented
598	#3115	C₂×C₆₇	1	1	yes	characteristic, complemented
599	#3102	C₂×C₆₇	1	1	yes	characteristic, complemented
600	#3098	C₂×C₆₇	1	2	yes	complemented
601	#3096	C₂×C₆₇	1	2	yes	complemented
602	#2981	C₂×C₆₇	1	1	yes	characteristic, complemented
603	C₆₇	#61811	1	1	yes	characteristic, direct product factor, Sylow
604	#560	—	2	2	no	—
605	#556	C₂²×C₆₇	1	1	yes	characteristic
606	#556	C₂²×C₆₇	1	1	yes	characteristic
607	#556	C₂²×C₆₇	1	1	yes	characteristic, complemented
608	#555	C₂²×C₆₇	1	2	yes	complemented
609	#554	C₂²×C₆₇	1	2	yes	complemented
610	#553	—	2	2	no	—
611	#553	C₂²×C₆₇	1	2	yes	—
612	#550	—	2	1	no	—
613	#550	C₂²×C₆₇	1	1	yes	characteristic
614	#548	—	2	1	no	—
615	#548	—	2	1	no	—
616	#547	C₂²×C₆₇	1	1	yes	characteristic
617	#547	C₂²×C₆₇	1	1	yes	characteristic
618	#547	C₂²×C₆₇	1	1	yes	characteristic, complemented
619	#546	—	2	1	no	—
620	#546	C₂²×C₆₇	1	2	yes	—
621	D₄²	C₂²×C₆₇	1	1	yes	characteristic
622	#542	—	2	1	no	—
623	#542	—	2	2	no	—
624	#538	—	2	2	no	—
625	#537	C₂²×C₆₇	1	2	yes	—
626	#537	C₂²×C₆₇	1	2	yes	complemented
627	#535	—	2	1	no	—
628	#535	C₂²×C₆₇	1	2	yes	—
629	#533	—	2	1	no	—
630	#532	—	2	1	no	—
631	#532	C₂²×C₆₇	1	1	yes	characteristic
632	#532	C₂²×C₆₇	1	1	yes	characteristic
633	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
634	#529	C₂²×C₆₇	1	1	yes	characteristic
635	#520	C₂²×C₆₇	1	2	yes	complemented
636	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
637	#501	C₂²×C₆₇	1	2	yes	complemented
638	#500	C₂²×C₆₇	1	1	yes	characteristic, complemented
639	#500	C₂²×C₆₇	1	1	yes	characteristic, complemented
640	#489	C₂²×C₆₇	1	2	yes	—
641	#486	C₂²×C₆₇	1	1	yes	characteristic
642	#486	C₂²×C₆₇	1	1	yes	characteristic
643	#485	C₂²×C₆₇	1	2	yes	complemented
644	#485	C₂²×C₆₇	1	2	yes	complemented
645	#485	C₂²×C₆₇	1	1	yes	characteristic, complemented
646	#484	C₂²×C₆₇	1	2	yes	complemented
647	#484	C₂²×C₆₇	1	2	yes	complemented
648	#484	C₂²×C₆₇	1	2	yes	complemented
649	#482	C₂²×C₆₇	1	2	yes	—
650	#482	C₂²×C₆₇	1	1	yes	characteristic
651	#482	C₂²×C₆₇	1	2	yes	—
652	#482	C₂²×C₆₇	1	2	yes	complemented
653	#482	C₂²×C₆₇	1	2	yes	complemented
654	#482	C₂²×C₆₇	1	2	yes	complemented
655	#481	C₂²×C₆₇	1	2	yes	—
656	#481	C₂²×C₆₇	1	2	yes	complemented
657	#480	C₂²×C₆₇	1	2	yes	—
658	#480	C₂²×C₆₇	1	2	yes	—
659	#480	C₂²×C₆₇	1	2	yes	complemented
660	#480	C₂²×C₆₇	1	2	yes	complemented
661	#480	C₂²×C₆₇	1	2	yes	complemented
662	#479	C₂²×C₆₇	1	1	yes	characteristic, complemented
663	#478	C₂²×C₆₇	1	1	yes	characteristic, complemented
664	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
665	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
666	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
667	#474	C₂²×C₆₇	1	1	yes	characteristic
668	#474	C₂²×C₆₇	1	1	yes	characteristic
669	#474	C₂²×C₆₇	1	1	yes	characteristic, complemented
670	#474	C₂²×C₆₇	1	2	yes	complemented
671	#474	C₂²×C₆₇	1	2	yes	complemented
672	#469	C₂²×C₆₇	1	2	yes	complemented
673	#468	C₂²×C₆₇	1	2	yes	—
674	#468	C₂²×C₆₇	1	2	yes	—
675	#468	C₂²×C₆₇	1	2	yes	complemented
676	#467	C₂²×C₆₇	1	2	yes	complemented
677	#466	C₂²×C₆₇	1	2	yes	—
678	#466	C₂²×C₆₇	1	2	yes	—
679	#465	C₂²×C₆₇	1	2	yes	complemented
680	#464	C₂²×C₆₇	1	1	yes	characteristic
681	#463	C₂²×C₆₇	1	1	yes	characteristic
682	#460	C₂²×C₆₇	1	1	yes	characteristic
683	#459	C₂²×C₆₇	1	1	yes	characteristic
684	#452	C₂²×C₆₇	1	1	yes	characteristic, complemented
685	#452	C₂²×C₆₇	1	2	yes	complemented
686	#450	C₂²×C₆₇	1	2	yes	—
687	#449	C₂²×C₆₇	1	1	yes	characteristic
688	#449	C₂²×C₆₇	1	2	yes	complemented
689	#449	C₂²×C₆₇	1	2	yes	complemented
690	#447	C₂²×C₆₇	1	2	yes	—
691	#442	C₂²×C₆₇	1	2	yes	complemented
692	#440	C₂²×C₆₇	1	2	yes	complemented
693	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
694	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
695	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
696	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
697	#436	C₂²×C₆₇	1	1	yes	characteristic
698	#436	C₂²×C₆₇	1	1	yes	characteristic, complemented
699	#435	C₂²×C₆₇	1	2	yes	complemented
700	#435	C₂²×C₆₇	1	2	yes	complemented
701	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
702	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
703	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
704	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
705	#428	C₂²×C₆₇	1	2	yes	complemented
706	#428	C₂²×C₆₇	1	2	yes	complemented
707	#427	C₂²×C₆₇	1	2	yes	complemented
708	C₂×#107	C₂²×C₆₇	1	2	yes	complemented
709	#418	C₂²×C₆₇	1	2	yes	—
710	#417	C₂²×C₆₇	1	2	yes	complemented
711	#416	C₂²×C₆₇	1	2	yes	complemented
712	C₂×#102	C₂²×C₆₇	1	2	yes	—
713	#408	C₂²×C₆₇	1	2	yes	complemented
714	#408	C₂²×C₆₇	1	2	yes	complemented
715	C₂×#41	—	2	1	no	—
716	C₂×#41	—	2	1	no	—
717	C₂×#41	—	2	1	no	—
718	C₂×#41	—	2	1	no	—
719	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
720	C₂×#41	C₂³×C₆₇	1	2	yes	—
721	C₂×#41	C₂³×C₆₇	1	2	yes	—
722	C₂²×Q₈	—	2	1	no	—
723	C₂²×D₄	—	2	1	no	—
724	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
725	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
726	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
727	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
728	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
729	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
730	C₂×D₈	C₂³×C₆₇	1	2	yes	—
731	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
732	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
733	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
734	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
735	C₄⋊Q₈	—	2	1	no	—
736	C₄⋊Q₈	—	2	1	no	—
737	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
738	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
739	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
740	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
741	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
742	#127	—	2	1	no	—
743	#127	—	2	2	no	—
744	#127	D₄×C₆₇	1	1	yes	characteristic
745	#127	C₂³×C₆₇	1	1	yes	characteristic
746	#126	—	2	2	no	—
747	#126	—	2	2	no	—
748	#126	—	2	2	no	—
749	#126	—	2	2	no	—
750	#126	—	2	1	no	—
751	#125	—	2	2	no	—
752	#125	C₂³×C₆₇	1	1	yes	characteristic
753	#124	—	2	2	no	—
754	#124	—	2	1	no	—
755	#124	—	2	1	no	—
756	#124	—	2	1	no	—
757	#124	—	2	2	no	—
758	#124	—	2	2	no	—
759	#124	—	2	1	no	—
760	#124	D₄×C₆₇	1	2	yes	—
761	#124	C₂³×C₆₇	1	1	yes	characteristic
762	#123	—	2	1	no	—
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	#123	—	2	2	no	—
766	#123	—	2	2	no	—
767	#123	—	2	2	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	1	no	—
771	C₂²⋊Q₈	—	2	1	no	—
772	C₂²⋊Q₈	—	2	1	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	—	2	2	no	—
775	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
776	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
777	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
778	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
779	#121	—	2	2	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	—	2	2	no	—
787	#121	—	2	1	no	—
788	#121	—	2	1	no	—
789	#121	—	2	2	no	—
790	#121	—	2	2	no	—
791	#121	D₄×C₆₇	1	1	yes	characteristic
792	#121	D₄×C₆₇	1	1	yes	characteristic
793	#121	D₄×C₆₇	1	2	yes	—
794	#121	C₂³×C₆₇	1	1	yes	characteristic
795	#121	C₂³×C₆₇	1	2	yes	—
796	#121	C₂³×C₆₇	1	2	yes	—
797	#121	C₂³×C₆₇	1	2	yes	—
798	#121	C₂³×C₆₇	1	2	yes	—
799	#121	C₂³×C₆₇	1	2	yes	—
800	#121	C₂³×C₆₇	1	2	yes	—
801	#120	—	2	2	no	—
802	#120	—	2	2	no	—
803	#120	—	2	2	no	—
804	#120	—	2	2	no	—
805	C₄×Q₈	—	2	2	no	—
806	C₄×Q₈	—	2	1	no	—
807	C₄×Q₈	—	2	1	no	—
808	C₄×Q₈	—	2	1	no	—
809	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
810	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
811	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
812	C₄×D₄	—	2	2	no	—
813	C₄×D₄	—	2	2	no	—
814	C₄×D₄	—	2	2	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	1	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
823	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
824	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
825	C₄×D₄	C₂³×C₆₇	1	2	yes	—
826	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
827	C₄×D₄	C₂³×C₆₇	1	2	yes	—
828	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
829	#117	—	2	2	no	—
830	#117	—	2	1	no	—
831	#117	—	2	1	no	—
832	#117	C₂³×C₆₇	1	1	yes	characteristic
833	#117	C₂³×C₆₇	1	2	yes	—
834	#117	C₂³×C₆₇	1	2	yes	—
835	#117	C₂³×C₆₇	1	2	yes	—
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×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
840	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
841	C₂×C₂²⋊C₄	—	2	2	no	—
842	C₂×C₄²	—	2	1	no	—
843	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
844	#107	C₂³×C₆₇	1	1	yes	characteristic
845	#107	C₂³×C₆₇	1	2	yes	—
846	#107	C₂³×C₆₇	1	2	yes	—
847	#107	C₂³×C₆₇	1	2	yes	—
848	#107	C₂³×C₆₇	1	1	yes	characteristic
849	#107	C₂³×C₆₇	1	2	yes	—
850	#107	C₂³×C₆₇	1	2	yes	—
851	#107	C₂³×C₆₇	1	2	yes	—
852	#107	C₂³×C₆₇	1	2	yes	—
853	#106	C₂³×C₆₇	1	2	yes	—
854	#106	C₂³×C₆₇	1	2	yes	—
855	#106	C₂³×C₆₇	1	1	yes	characteristic
856	#106	C₂³×C₆₇	1	1	yes	characteristic
857	#106	C₂³×C₆₇	1	2	yes	—
858	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
859	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
860	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
861	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
862	#103	C₂³×C₆₇	1	1	yes	characteristic
863	#103	C₂³×C₆₇	1	2	yes	—
864	#103	C₂³×C₆₇	1	1	yes	characteristic
865	#103	C₂³×C₆₇	1	2	yes	—
866	#103	C₂³×C₆₇	1	1	yes	characteristic
867	#103	C₂³×C₆₇	1	1	yes	characteristic
868	#103	C₂³×C₆₇	1	2	yes	—
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	#102	C₂³×C₆₇	1	1	yes	characteristic
877	#102	C₂³×C₆₇	1	2	yes	—
878	#102	C₂³×C₆₇	1	2	yes	—
879	#102	C₂³×C₆₇	1	1	yes	characteristic
880	#102	C₂³×C₆₇	1	1	yes	characteristic
881	#102	C₂³×C₆₇	1	2	yes	—
882	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
883	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
884	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
885	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
886	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
887	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
888	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
889	#97	C₂³×C₆₇	1	2	yes	—
890	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
891	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
892	C₂⁴	—	2	2	no	—
893	#41	—	4	2	no	—
894	#41	—	4	2	no	—
895	#41	—	4	1	no	—
896	#41	—	4	1	no	—
897	#41	—	4	2	no	—
898	#41	—	4	2	no	—
899	#41	—	8	2	no	—
900	#41	—	8	2	no	—
901	#41	—	8	2	no	—
902	#41	—	8	2	no	—
903	C₂×Q₈	—	2	1	no	—
904	C₂×Q₈	—	2	1	no	—
905	C₂×Q₈	—	2	1	no	—
906	C₂×Q₈	—	2	2	no	—
907	C₂×Q₈	—	8	2	no	—
908	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
909	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
910	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	2	1	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	4	2	no	—
924	C₂×D₄	—	4	2	no	—
925	C₂×D₄	—	8	2	no	—
926	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
927	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
928	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
929	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
930	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
931	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
932	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
933	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
934	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
935	C₂²×C₄	—	2	2	no	—
936	C₂²×C₄	—	2	2	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	1	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
946	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
947	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
948	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
949	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
950	Q₁₆	—	4	1	no	—
951	SD₁₆	—	4	2	no	—
952	SD₁₆	—	4	1	no	—
953	SD₁₆	—	4	1	no	—
954	D₈	—	4	1	no	—
955	D₈	—	4	2	no	—
956	M₁₆	—	4	2	no	—
957	M₁₆	—	4	2	no	—
958	C₂×C₈	—	4	2	no	—
959	C₂×C₈	—	4	2	no	—
960	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
961	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
962	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
963	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
964	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
965	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
984	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
985	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
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	2	yes	—
990	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
991	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
992	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1015	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1016	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1017	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	1	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	2	no	—
1022	C₄²	—	2	2	no	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	2	2	no	—
1025	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1026	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1027	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1028	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1029	C₂³	—	2	1	no	—
1030	C₂³	—	2	1	no	—
1031	C₂³	—	2	2	no	—
1032	C₂³	—	8	2	no	—
1033	C₂³	—	8	2	no	—
1034	C₂³	—	8	2	no	—
1035	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1036	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1037	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1038	Q₈	—	2	1	no	—
1039	Q₈	—	2	1	no	—
1040	Q₈	—	2	1	no	—
1041	Q₈	—	2	1	no	—
1042	Q₈	—	4	2	no	—
1043	Q₈	—	4	2	no	—
1044	Q₈	—	4	2	no	—
1045	Q₈	—	4	2	no	—
1046	Q₈	—	8	2	no	—
1047	D₄	—	2	2	no	—
1048	D₄	—	2	2	no	—
1049	D₄	—	2	1	no	—
1050	D₄	—	2	1	no	—
1051	D₄	—	2	1	no	—
1052	D₄	—	2	2	no	—
1053	D₄	—	2	1	no	—
1054	D₄	—	2	2	no	—
1055	D₄	—	4	2	no	—
1056	D₄	—	4	2	no	—
1057	D₄	—	4	2	no	—
1058	D₄	—	4	2	no	—
1059	D₄	—	4	2	no	—
1060	D₄	—	4	2	no	—
1061	D₄	—	8	2	no	—
1062	D₄	—	8	1	no	—
1063	D₄	—	8	2	no	—
1064	D₄	—	8	2	no	—
1065	D₄	—	8	2	no	—
1066	D₄	—	8	2	no	—
1067	D₄	—	8	2	no	—
1068	D₄	—	8	2	no	—
1069	D₄	—	8	1	no	—
1070	D₄	—	8	2	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	4	1	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	8	2	no	—
1093	C₂×C₄	—	8	2	no	—
1094	C₂×C₄	—	8	2	no	—
1095	C₂×C₄	—	8	2	no	—
1096	C₂×C₄	—	8	2	no	—
1097	C₂×C₄	—	8	2	no	—
1098	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1099	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1100	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1101	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1102	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1103	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1104	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1105	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1106	C₈	—	2	1	no	—
1107	C₈	—	2	1	no	—
1108	C₈	—	2	2	no	—
1109	C₈	—	2	2	no	—
1110	C₈	—	2	1	no	—
1111	C₈	—	2	1	no	—
1112	C₂²	—	2	1	no	—
1113	C₂²	—	2	2	no	—
1114	C₂²	—	2	2	no	—
1115	C₂²	—	2	1	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	2	no	—
1118	C₂²	—	2	1	no	—
1119	C₂²	—	2	2	no	—
1120	C₂²	—	2	2	no	—
1121	C₂²	—	4	1	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	2	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	2	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	4	1	no	—
1128	C₂²	—	4	2	no	—
1129	C₂²	—	4	1	no	—
1130	C₂²	—	16	4	no	—
1131	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1132	C₄	—	2	1	no	—
1133	C₄	—	2	1	no	—
1134	C₄	—	2	1	no	—
1135	C₄	—	2	1	no	—
1136	C₄	—	2	2	no	—
1137	C₄	—	2	2	no	—
1138	C₄	—	4	1	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	2	no	—
1141	C₄	—	4	2	no	—
1142	C₄	—	4	2	no	—
1143	C₄	—	4	1	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	1	no	—
1146	C₄	—	4	1	no	—
1147	C₄	#576×C₆₇	1	2	yes	—
1148	C₄	#585×C₆₇	1	1	yes	characteristic
1149	C₄	#585×C₆₇	1	1	yes	characteristic
1150	C₂	—	4	2	no	—
1151	C₂	—	4	1	no	—
1152	C₂	—	4	2	no	—
1153	C₂	—	8	1	no	—
1154	C₂	—	8	2	no	—
1155	C₂	—	8	1	no	—
1156	C₂	C₆₇×#3485	1	1	yes	characteristic
1157	C₂	C₂×#576×C₆₇	1	1	yes	characteristic
1158	C₂	C₆₇×#3586	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 ◁ #532×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3546	C₂	semidirect
2. C₆₇×#3511	C₂	semidirect
3. C₆₇×#3353	C₂	semidirect
4. C₆₇×#3353	C₂	semidirect
5. C₆₇×#3347	C₂	semidirect
6. C₆₇×#3346	C₂	semidirect
7. C₆₇×#3342	C₂	semidirect
8. C₆₇×#3334	C₂	semidirect
9. C₆₇×#3332	C₂	semidirect
10. C₆₇×#3324	C₂	semidirect
11. C₆₇×#3319	C₂	semidirect
12. C₆₇×#3314	C₂	semidirect
13. C₆₇×#3304	C₂	semidirect
14. C₆₇×#3294	C₂	semidirect
15. C₆₇×#3239	C₂	semidirect
16. C₆₇×#3226	C₂	semidirect
17. C₆₇×#3203	C₂	semidirect
18. C₆₇×#3198	C₂	semidirect
19. C₆₇×#3115	C₂	semidirect
20. C₆₇×#3102	C₂	semidirect
21. C₆₇×#3098	C₂	semidirect
22. C₆₇×#3096	C₂	semidirect
23. C₆₇×#2981	C₂	semidirect
27. #556×C₆₇	C₂²	semidirect
28. #555×C₆₇	C₂²	semidirect
29. #554×C₆₇	C₂²	semidirect
38. #547×C₆₇	C₂²	semidirect
46. #537×C₆₇	C₂²	semidirect
53. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
55. #520×C₆₇	C₂²	semidirect
56. C₄×#41×C₆₇	C₂²	semidirect
57. #501×C₆₇	C₂²	semidirect
58. #500×C₆₇	C₂²	semidirect
59. #500×C₆₇	C₂²	semidirect
63. #485×C₆₇	C₂²	semidirect
64. #485×C₆₇	C₂²	semidirect
65. #485×C₆₇	C₂²	semidirect
66. #484×C₆₇	C₂²	semidirect
67. #484×C₆₇	C₂²	semidirect
68. #484×C₆₇	C₂²	semidirect
72. #482×C₆₇	C₂²	semidirect
73. #482×C₆₇	C₂²	semidirect
74. #482×C₆₇	C₂²	semidirect
76. #481×C₆₇	C₂²	semidirect
79. #480×C₆₇	C₂²	semidirect
80. #480×C₆₇	C₂²	semidirect
81. #480×C₆₇	C₂²	semidirect
82. #479×C₆₇	C₂²	semidirect
83. #478×C₆₇	C₂²	semidirect
84. #475×C₆₇	C₂²	semidirect
85. #475×C₆₇	C₂²	semidirect
86. #475×C₆₇	C₂²	semidirect
89. #474×C₆₇	C₂²	semidirect
90. #474×C₆₇	C₂²	semidirect
91. #474×C₆₇	C₂²	semidirect
92. #469×C₆₇	C₂²	semidirect
95. #468×C₆₇	C₂²	semidirect
96. #467×C₆₇	C₂²	semidirect
99. #465×C₆₇	C₂²	semidirect
104. #452×C₆₇	C₂²	semidirect
105. #452×C₆₇	C₂²	semidirect
108. #449×C₆₇	C₂²	semidirect
109. #449×C₆₇	C₂²	semidirect
111. #442×C₆₇	C₂²	semidirect
112. #440×C₆₇	C₂²	semidirect
113. C₄×Q₁₆×C₆₇	C₂²	semidirect
115. C₄×SD₁₆×C₆₇	C₂²	semidirect
118. #436×C₆₇	C₂²	semidirect
119. #435×C₆₇	C₂²	semidirect
120. #435×C₆₇	C₂²	semidirect
122. C₈×D₄×C₆₇	C₂²	semidirect
123. #432×C₆₇	C₂²	semidirect
124. #431×C₆₇	C₂²	semidirect
125. #428×C₆₇	C₂²	semidirect
126. #428×C₆₇	C₂²	semidirect
127. #427×C₆₇	C₂²	semidirect
128. C₂×#107×C₆₇	C₂²	semidirect
130. #417×C₆₇	C₂²	semidirect
131. #416×C₆₇	C₂²	semidirect
133. #408×C₆₇	C₂²	semidirect
134. #408×C₆₇	C₂²	semidirect
570. #61811	C₆₇	direct (N × H)
580. #3546	C₂×C₆₇	semidirect
581. #3511	C₂×C₆₇	semidirect
582. #3353	C₂×C₆₇	semidirect
583. #3353	C₂×C₆₇	semidirect
584. #3347	C₂×C₆₇	semidirect
585. #3346	C₂×C₆₇	semidirect
586. #3342	C₂×C₆₇	semidirect
587. #3334	C₂×C₆₇	semidirect
588. #3332	C₂×C₆₇	semidirect
589. #3324	C₂×C₆₇	semidirect
590. #3319	C₂×C₆₇	semidirect
591. #3314	C₂×C₆₇	semidirect
592. #3304	C₂×C₆₇	semidirect
593. #3294	C₂×C₆₇	semidirect
594. #3239	C₂×C₆₇	semidirect
595. #3226	C₂×C₆₇	semidirect
596. #3203	C₂×C₆₇	semidirect
597. #3198	C₂×C₆₇	semidirect
598. #3115	C₂×C₆₇	semidirect
599. #3102	C₂×C₆₇	semidirect
600. #3098	C₂×C₆₇	semidirect
601. #3096	C₂×C₆₇	semidirect
602. #2981	C₂×C₆₇	semidirect
603. C₆₇	#61811	direct (N × H)
607. #556	C₂²×C₆₇	semidirect
608. #555	C₂²×C₆₇	semidirect
609. #554	C₂²×C₆₇	semidirect
618. #547	C₂²×C₆₇	semidirect
626. #537	C₂²×C₆₇	semidirect
633. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
635. #520	C₂²×C₆₇	semidirect
636. C₄×#41	C₂²×C₆₇	semidirect
637. #501	C₂²×C₆₇	semidirect
638. #500	C₂²×C₆₇	semidirect
639. #500	C₂²×C₆₇	semidirect
643. #485	C₂²×C₆₇	semidirect
644. #485	C₂²×C₆₇	semidirect
645. #485	C₂²×C₆₇	semidirect
646. #484	C₂²×C₆₇	semidirect
647. #484	C₂²×C₆₇	semidirect
648. #484	C₂²×C₆₇	semidirect
652. #482	C₂²×C₆₇	semidirect
653. #482	C₂²×C₆₇	semidirect
654. #482	C₂²×C₆₇	semidirect
656. #481	C₂²×C₆₇	semidirect
659. #480	C₂²×C₆₇	semidirect
660. #480	C₂²×C₆₇	semidirect
661. #480	C₂²×C₆₇	semidirect
662. #479	C₂²×C₆₇	semidirect
663. #478	C₂²×C₆₇	semidirect
664. #475	C₂²×C₆₇	semidirect
665. #475	C₂²×C₆₇	semidirect
666. #475	C₂²×C₆₇	semidirect
669. #474	C₂²×C₆₇	semidirect
670. #474	C₂²×C₆₇	semidirect
671. #474	C₂²×C₆₇	semidirect
672. #469	C₂²×C₆₇	semidirect
675. #468	C₂²×C₆₇	semidirect
676. #467	C₂²×C₆₇	semidirect
679. #465	C₂²×C₆₇	semidirect
684. #452	C₂²×C₆₇	semidirect
685. #452	C₂²×C₆₇	semidirect
688. #449	C₂²×C₆₇	semidirect
689. #449	C₂²×C₆₇	semidirect
691. #442	C₂²×C₆₇	semidirect
692. #440	C₂²×C₆₇	semidirect
693. C₄×Q₁₆	C₂²×C₆₇	semidirect
695. C₄×SD₁₆	C₂²×C₆₇	semidirect
698. #436	C₂²×C₆₇	semidirect
699. #435	C₂²×C₆₇	semidirect
700. #435	C₂²×C₆₇	semidirect
702. C₈×D₄	C₂²×C₆₇	semidirect
703. #432	C₂²×C₆₇	semidirect
704. #431	C₂²×C₆₇	semidirect
705. #428	C₂²×C₆₇	semidirect
706. #428	C₂²×C₆₇	semidirect
707. #427	C₂²×C₆₇	semidirect
708. C₂×#107	C₂²×C₆₇	semidirect
710. #417	C₂²×C₆₇	semidirect
711. #416	C₂²×C₆₇	semidirect
713. #408	C₂²×C₆₇	semidirect
714. #408	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×#3546	2
C₆₇×#3511	2
C₆₇×#3353	2
C₆₇×#3347	2
C₆₇×#3346	2
C₆₇×#3342	2
C₆₇×#3334	2
C₆₇×#3332	2
C₆₇×#3324	2
C₆₇×#3319	2
C₆₇×#3314	2
C₆₇×#3304	2
C₆₇×#3294	2
C₆₇×#3239	2
C₆₇×#3226	2
C₆₇×#3203	2
C₆₇×#3198	2
C₆₇×#3115	2
C₆₇×#3102	2
C₆₇×#3098	2
C₆₇×#3096	2
C₆₇×#2981	2
#61811	67

Subgroups — C67×#61811 #30741062

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61811 #30741062