Subgroups — C₆₇×#61316 #30740567

Order 17152.

1820 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3480	C₂	1	1	yes	maximal, characteristic, complemented
2	Q₈×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3377	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3376	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#3374	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#3373	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3372	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3371	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3370	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3369	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3368	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3367	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3366	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3135	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3131	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3076	C₂	1	2	yes	maximal, complemented
19	C₆₇×#3035	C₂	1	2	yes	maximal, complemented
20	C₆₇×#3035	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#446×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2943	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	#559×C₆₇	C₂²	1	2	yes	—
27	#559×C₆₇	C₂²	1	1	yes	characteristic
28	Q₈²×C₆₇	C₂²	1	1	yes	characteristic
29	#557×C₆₇	C₂²	1	1	yes	characteristic
30	#557×C₆₇	C₂²	1	1	yes	characteristic
31	#557×C₆₇	C₂²	1	2	yes	—
32	#556×C₆₇	C₂²	1	1	yes	characteristic
33	#556×C₆₇	C₂²	1	2	yes	—
34	#554×C₆₇	—	2	1	no	—
35	#554×C₆₇	—	2	2	no	—
36	#554×C₆₇	C₂²	1	1	yes	characteristic
37	#554×C₆₇	C₂²	1	2	yes	—
38	#553×C₆₇	—	2	1	no	—
39	#553×C₆₇	—	2	2	no	—
40	#550×C₆₇	C₂²	1	1	yes	characteristic
41	D₄×Q₈×C₆₇	—	2	1	no	—
42	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
43	#548×C₆₇	—	2	1	no	—
44	#533×C₆₇	—	2	1	no	—
45	#533×C₆₇	—	2	2	no	—
46	#533×C₆₇	C₂²	1	1	yes	characteristic
47	#533×C₆₇	C₂²	1	2	yes	—
48	#532×C₆₇	C₂²	1	1	yes	characteristic
49	#532×C₆₇	C₂²	1	2	yes	—
50	#529×C₆₇	—	2	1	no	—
51	#529×C₆₇	—	2	2	no	—
52	C₄×#41×C₆₇	—	2	1	no	—
53	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
54	C₄×#41×C₆₇	C₂²	1	2	yes	—
55	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
56	C₄×#41×C₆₇	C₂²	1	2	yes	—
57	C₂×C₄×Q₈×C₆₇	—	2	1	no	—
58	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
59	#491×C₆₇	C₂²	1	2	yes	—
60	#491×C₆₇	C₂²	1	2	yes	—
61	#490×C₆₇	C₂²	1	2	yes	—
62	#490×C₆₇	C₂²	1	2	yes	—
63	#489×C₆₇	C₂²	1	2	yes	—
64	#489×C₆₇	C₂²	1	2	yes	—
65	#489×C₆₇	C₂²	1	2	yes	—
66	#489×C₆₇	C₂²	1	2	yes	—
67	#488×C₆₇	C₂²	1	2	yes	—
68	#488×C₆₇	C₂²	1	2	yes	—
69	#487×C₆₇	C₂²	1	1	yes	characteristic
70	#487×C₆₇	C₂²	1	1	yes	characteristic
71	#486×C₆₇	C₂²	1	1	yes	characteristic
72	#486×C₆₇	C₂²	1	1	yes	characteristic
73	#479×C₆₇	C₂²	1	2	yes	—
74	#479×C₆₇	C₂²	1	2	yes	—
75	#479×C₆₇	C₂²	1	2	yes	—
76	#478×C₆₇	C₂²	1	2	yes	—
77	#478×C₆₇	C₂²	1	2	yes	—
78	#478×C₆₇	C₂²	1	2	yes	—
79	#477×C₆₇	C₂²	1	2	yes	—
80	#477×C₆₇	C₂²	1	1	yes	characteristic
81	#476×C₆₇	C₂²	1	1	yes	characteristic
82	#476×C₆₇	C₂²	1	2	yes	—
83	#475×C₆₇	C₂²	1	2	yes	—
84	#475×C₆₇	C₂²	1	1	yes	characteristic
85	#474×C₆₇	C₂²	1	1	yes	characteristic
86	#474×C₆₇	C₂²	1	2	yes	—
87	#464×C₆₇	C₂²	1	2	yes	—
88	#464×C₆₇	C₂²	1	2	yes	—
89	#464×C₆₇	C₂²	1	2	yes	—
90	#463×C₆₇	C₂²	1	2	yes	—
91	#463×C₆₇	C₂²	1	2	yes	—
92	#463×C₆₇	C₂²	1	2	yes	—
93	#462×C₆₇	C₂²	1	1	yes	characteristic
94	#462×C₆₇	C₂²	1	2	yes	—
95	#461×C₆₇	C₂²	1	1	yes	characteristic
96	#461×C₆₇	C₂²	1	2	yes	—
97	#460×C₆₇	C₂²	1	2	yes	—
98	#460×C₆₇	C₂²	1	1	yes	characteristic
99	#459×C₆₇	C₂²	1	2	yes	—
100	#459×C₆₇	C₂²	1	1	yes	characteristic
101	#446×C₆₇	C₂²	1	1	yes	characteristic
102	#446×C₆₇	C₂²	1	1	yes	characteristic
103	#446×C₆₇	C₂²	1	1	yes	characteristic
104	#446×C₆₇	C₂²	1	1	yes	characteristic
105	#446×C₆₇	C₂²	1	2	yes	—
106	#446×C₆₇	C₂²	1	2	yes	—
107	#442×C₆₇	C₂²	1	2	yes	—
108	#442×C₆₇	C₂²	1	2	yes	—
109	#441×C₆₇	C₂²	1	2	yes	—
110	#441×C₆₇	C₂²	1	2	yes	—
111	#440×C₆₇	C₂²	1	2	yes	—
112	#440×C₆₇	C₂²	1	2	yes	—
113	#440×C₆₇	C₂²	1	2	yes	—
114	#440×C₆₇	C₂²	1	2	yes	—
115	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
116	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
121	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
122	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
123	#427×C₆₇	C₂²	1	1	yes	characteristic
124	#427×C₆₇	C₂²	1	2	yes	—
125	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
126	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	—
127	#416×C₆₇	C₂²	1	2	yes	—
128	#416×C₆₇	C₂²	1	2	yes	—
129	#416×C₆₇	C₂²	1	2	yes	—
130	#416×C₆₇	C₂²	1	2	yes	—
131	#416×C₆₇	C₂²	1	1	yes	characteristic
132	#416×C₆₇	C₂²	1	1	yes	characteristic
133	C₂×#97×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	C₂³	1	1	yes	characteristic
137	C₂×#41×C₆₇	C₂³	1	2	yes	—
138	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
139	C₂²×Q₈×C₆₇	—	2	1	no	—
140	C₂²×Q₈×C₆₇	D₄	1	1	yes	characteristic
141	#135×C₆₇	—	2	4	no	—
142	#135×C₆₇	—	2	8	no	—
143	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
144	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
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	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
153	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
154	C₄⋊Q₈×C₆₇	—	2	1	no	—
155	C₄⋊Q₈×C₆₇	—	2	2	no	—
156	C₄⋊Q₈×C₆₇	—	2	1	no	—
157	C₄⋊Q₈×C₆₇	—	2	2	no	—
158	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
160	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
162	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
164	#127×C₆₇	C₂³	1	1	yes	characteristic
165	#127×C₆₇	C₂³	1	2	yes	—
166	#126×C₆₇	—	2	2	no	—
167	#126×C₆₇	—	2	2	no	—
168	#126×C₆₇	—	2	2	no	—
169	#125×C₆₇	—	2	1	no	—
170	#125×C₆₇	—	2	2	no	—
171	#125×C₆₇	—	2	2	no	—
172	#125×C₆₇	—	2	2	no	—
173	#125×C₆₇	—	2	2	no	—
174	#125×C₆₇	C₂³	1	2	yes	—
175	#125×C₆₇	C₂³	1	2	yes	—
176	#125×C₆₇	C₂³	1	2	yes	—
177	#124×C₆₇	—	2	1	no	—
178	#124×C₆₇	—	2	2	no	—
179	#124×C₆₇	C₂³	1	2	yes	—
180	#124×C₆₇	C₂³	1	2	yes	—
181	#124×C₆₇	C₂³	1	2	yes	—
182	#123×C₆₇	—	2	2	no	—
183	#123×C₆₇	—	2	2	no	—
184	#123×C₆₇	—	2	2	no	—
185	C₂²⋊Q₈×C₆₇	—	2	1	no	—
186	C₂²⋊Q₈×C₆₇	—	2	2	no	—
187	C₂²⋊Q₈×C₆₇	—	2	1	no	—
188	C₂²⋊Q₈×C₆₇	—	2	2	no	—
189	C₂²⋊Q₈×C₆₇	—	2	1	no	—
190	C₂²⋊Q₈×C₆₇	—	2	2	no	—
191	C₂²⋊Q₈×C₆₇	—	2	1	no	—
192	C₂²⋊Q₈×C₆₇	—	2	2	no	—
193	C₂²⋊Q₈×C₆₇	—	2	1	no	—
194	C₂²⋊Q₈×C₆₇	—	2	2	no	—
195	C₂²⋊Q₈×C₆₇	—	2	2	no	—
196	C₂²⋊Q₈×C₆₇	—	2	2	no	—
197	C₂²⋊Q₈×C₆₇	—	2	2	no	—
198	#121×C₆₇	—	2	1	no	—
199	#121×C₆₇	—	2	2	no	—
200	#121×C₆₇	—	2	1	no	—
201	#121×C₆₇	—	2	2	no	—
202	#121×C₆₇	—	2	1	no	—
203	#121×C₆₇	—	2	2	no	—
204	C₄×Q₈×C₆₇	—	2	1	no	—
205	C₄×Q₈×C₆₇	—	2	1	no	—
206	C₄×Q₈×C₆₇	—	2	1	no	—
207	C₄×Q₈×C₆₇	—	2	2	no	—
208	C₄×Q₈×C₆₇	—	2	1	no	—
209	C₄×Q₈×C₆₇	—	2	2	no	—
210	C₄×Q₈×C₆₇	—	2	2	no	—
211	C₄×Q₈×C₆₇	—	2	1	no	—
212	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
213	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
214	C₄×Q₈×C₆₇	D₄	1	2	yes	—
215	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
216	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
219	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
220	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
225	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
226	C₄×D₄×C₆₇	—	2	1	no	—
227	C₄×D₄×C₆₇	—	2	2	no	—
228	C₄×D₄×C₆₇	—	2	1	no	—
229	C₄×D₄×C₆₇	—	2	2	no	—
230	C₄×D₄×C₆₇	—	2	1	no	—
231	C₄×D₄×C₆₇	—	2	2	no	—
232	C₄×D₄×C₆₇	—	2	1	no	—
233	C₄×D₄×C₆₇	—	2	2	no	—
234	C₄×D₄×C₆₇	—	2	2	no	—
235	C₄×D₄×C₆₇	—	2	1	no	—
236	C₄×D₄×C₆₇	—	2	1	no	—
237	C₄×D₄×C₆₇	—	2	2	no	—
238	C₄×D₄×C₆₇	—	2	2	no	—
239	C₄×D₄×C₆₇	—	2	1	no	—
240	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₆₇	C₂³	1	2	yes	—
242	C₄×D₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
247	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
248	#117×C₆₇	—	2	2	no	—
249	#117×C₆₇	—	2	1	no	—
250	#117×C₆₇	—	2	2	no	—
251	#117×C₆₇	—	2	1	no	—
252	#117×C₆₇	—	2	2	no	—
253	#117×C₆₇	—	2	1	no	—
254	#117×C₆₇	C₂³	1	1	yes	characteristic
255	#117×C₆₇	C₂³	1	1	yes	characteristic
256	#117×C₆₇	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
258	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
259	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₆₇	D₄	1	2	yes	—
261	C₂×C₄²×C₆₇	—	2	1	no	—
262	C₂×C₄²×C₆₇	—	2	2	no	—
263	C₂×C₄²×C₆₇	—	2	1	no	—
264	C₂×C₄²×C₆₇	—	2	2	no	—
265	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
266	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
267	#107×C₆₇	C₂³	1	1	yes	characteristic
268	#107×C₆₇	C₂³	1	2	yes	—
269	#107×C₆₇	C₂³	1	2	yes	—
270	#107×C₆₇	C₂³	1	1	yes	characteristic
271	#106×C₆₇	C₂³	1	1	yes	characteristic
272	#106×C₆₇	C₂³	1	2	yes	—
273	#106×C₆₇	C₂³	1	2	yes	—
274	#106×C₆₇	C₂³	1	1	yes	characteristic
275	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
276	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
277	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
278	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
279	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
280	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
281	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
282	#103×C₆₇	C₂³	1	2	yes	—
283	#103×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	2	yes	—
289	#103×C₆₇	C₂³	1	2	yes	—
290	#103×C₆₇	C₂³	1	1	yes	characteristic
291	#103×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
301	#102×C₆₇	C₂³	1	2	yes	—
302	#102×C₆₇	C₂³	1	1	yes	characteristic
303	#102×C₆₇	C₂³	1	1	yes	characteristic
304	#102×C₆₇	C₂³	1	1	yes	characteristic
305	#102×C₆₇	C₂³	1	1	yes	characteristic
306	#97×C₆₇	C₂³	1	2	yes	—
307	#97×C₆₇	C₂³	1	2	yes	—
308	#97×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	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	2	no	—
316	#41×C₆₇	—	2	4	no	—
317	#41×C₆₇	—	2	2	no	—
318	#41×C₆₇	—	2	4	no	—
319	#41×C₆₇	—	4	4	no	—
320	#41×C₆₇	#41	1	4	yes	complemented
321	C₂×Q₈×C₆₇	—	2	2	no	—
322	C₂×Q₈×C₆₇	—	2	1	no	—
323	C₂×Q₈×C₆₇	—	2	2	no	—
324	C₂×Q₈×C₆₇	—	2	1	no	—
325	C₂×Q₈×C₆₇	—	4	2	no	—
326	C₂×Q₈×C₆₇	—	4	4	no	—
327	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
329	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
330	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
331	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
333	C₂×D₄×C₆₇	—	2	1	no	—
334	C₂×D₄×C₆₇	—	2	1	no	—
335	C₂×D₄×C₆₇	—	2	2	no	—
336	C₂×D₄×C₆₇	—	2	2	no	—
337	C₂×D₄×C₆₇	—	2	1	no	—
338	C₂×D₄×C₆₇	—	2	2	no	—
339	C₂×D₄×C₆₇	—	2	1	no	—
340	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
341	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
342	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₆₇	—	2	1	no	—
344	C₂²×C₄×C₆₇	—	2	2	no	—
345	C₂²×C₄×C₆₇	—	2	1	no	—
346	C₂²×C₄×C₆₇	—	2	2	no	—
347	C₂²×C₄×C₆₇	—	2	1	no	—
348	C₂²×C₄×C₆₇	—	2	1	no	—
349	C₂²×C₄×C₆₇	—	2	2	no	—
350	C₂²×C₄×C₆₇	—	2	1	no	—
351	C₂²×C₄×C₆₇	—	2	2	no	—
352	C₂²×C₄×C₆₇	—	2	1	no	—
353	C₂²×C₄×C₆₇	—	2	2	no	—
354	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
357	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
358	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
359	Q₁₆×C₆₇	—	2	2	no	—
360	Q₁₆×C₆₇	—	2	4	no	—
361	SD₁₆×C₆₇	—	2	2	no	—
362	SD₁₆×C₆₇	—	2	4	no	—
363	SD₁₆×C₆₇	—	2	2	no	—
364	SD₁₆×C₆₇	—	2	4	no	—
365	D₈×C₆₇	—	2	2	no	—
366	D₈×C₆₇	—	2	4	no	—
367	C₂×C₈×C₆₇	—	2	2	no	—
368	C₂×C₈×C₆₇	—	2	4	no	—
369	C₂×C₈×C₆₇	—	2	2	no	—
370	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
373	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
376	C₄⋊C₄×C₆₇	—	2	2	no	—
377	C₄⋊C₄×C₆₇	—	2	2	no	—
378	C₄⋊C₄×C₆₇	—	2	2	no	—
379	C₄⋊C₄×C₆₇	—	2	2	no	—
380	C₄⋊C₄×C₆₇	—	2	1	no	—
381	C₄⋊C₄×C₆₇	—	2	2	no	—
382	C₄⋊C₄×C₆₇	—	2	1	no	—
383	C₄⋊C₄×C₆₇	—	2	2	no	—
384	C₄⋊C₄×C₆₇	—	2	1	no	—
385	C₄⋊C₄×C₆₇	—	2	2	no	—
386	C₄⋊C₄×C₆₇	—	2	1	no	—
387	C₄⋊C₄×C₆₇	—	2	2	no	—
388	C₄⋊C₄×C₆₇	—	2	2	no	—
389	C₄⋊C₄×C₆₇	—	2	1	no	—
390	C₄⋊C₄×C₆₇	—	2	1	no	—
391	C₄⋊C₄×C₆₇	—	2	2	no	—
392	C₄⋊C₄×C₆₇	—	2	1	no	—
393	C₄⋊C₄×C₆₇	—	2	2	no	—
394	C₄⋊C₄×C₆₇	—	2	1	no	—
395	C₄⋊C₄×C₆₇	—	2	2	no	—
396	C₄⋊C₄×C₆₇	—	2	2	no	—
397	C₄⋊C₄×C₆₇	—	2	2	no	—
398	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
402	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
405	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
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	1	yes	characteristic
410	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
411	C₂²⋊C₄×C₆₇	—	2	1	no	—
412	C₂²⋊C₄×C₆₇	—	2	1	no	—
413	C₂²⋊C₄×C₆₇	—	2	2	no	—
414	C₂²⋊C₄×C₆₇	—	2	2	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	1	no	—
423	C₂²⋊C₄×C₆₇	—	2	2	no	—
424	C₂²⋊C₄×C₆₇	—	2	1	no	—
425	C₂²⋊C₄×C₆₇	—	2	2	no	—
426	C₂²⋊C₄×C₆₇	—	2	2	no	—
427	C₂²⋊C₄×C₆₇	—	2	2	no	—
428	C₄²×C₆₇	—	2	1	no	—
429	C₄²×C₆₇	—	2	2	no	—
430	C₄²×C₆₇	—	2	2	no	—
431	C₄²×C₆₇	—	2	1	no	—
432	C₄²×C₆₇	—	2	1	no	—
433	C₄²×C₆₇	—	2	2	no	—
434	C₄²×C₆₇	—	2	2	no	—
435	C₄²×C₆₇	—	2	1	no	—
436	C₄²×C₆₇	—	2	1	no	—
437	C₄²×C₆₇	—	2	1	no	—
438	C₄²×C₆₇	—	2	2	no	—
439	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
440	C₄²×C₆₇	C₂×D₄	1	2	yes	—
441	C₄²×C₆₇	C₂×D₄	1	2	yes	—
442	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
443	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
444	C₄²×C₆₇	C₂⁴	1	2	yes	—
445	C₄²×C₆₇	C₂⁴	1	2	yes	—
446	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
447	C₂³×C₆₇	—	2	1	no	—
448	C₂³×C₆₇	—	2	2	no	—
449	C₂³×C₆₇	—	2	1	no	—
450	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
451	Q₈×C₆₇	—	2	2	no	—
452	Q₈×C₆₇	—	2	2	no	—
453	Q₈×C₆₇	—	2	1	no	—
454	Q₈×C₆₇	—	2	1	no	—
455	Q₈×C₆₇	—	2	2	no	—
456	Q₈×C₆₇	—	2	2	no	—
457	Q₈×C₆₇	—	2	1	no	—
458	Q₈×C₆₇	—	4	2	no	—
459	Q₈×C₆₇	—	4	4	no	—
460	Q₈×C₆₇	—	4	2	no	—
461	Q₈×C₆₇	—	8	2	no	—
462	Q₈×C₆₇	—	8	1	no	—
463	Q₈×C₆₇	C₂×#41	1	2	yes	—
464	D₄×C₆₇	—	2	4	no	—
465	D₄×C₆₇	—	2	1	no	—
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	—	4	4	no	—
471	D₄×C₆₇	—	4	2	no	—
472	D₄×C₆₇	—	4	4	no	—
473	D₄×C₆₇	—	4	2	no	—
474	D₄×C₆₇	—	8	2	no	—
475	D₄×C₆₇	—	8	1	no	—
476	D₄×C₆₇	C₂×#41	1	2	yes	—
477	C₂×C₄×C₆₇	—	2	1	no	—
478	C₂×C₄×C₆₇	—	2	4	no	—
479	C₂×C₄×C₆₇	—	2	2	no	—
480	C₂×C₄×C₆₇	—	2	1	no	—
481	C₂×C₄×C₆₇	—	2	1	no	—
482	C₂×C₄×C₆₇	—	2	1	no	—
483	C₂×C₄×C₆₇	—	2	2	no	—
484	C₂×C₄×C₆₇	—	2	2	no	—
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	—	4	1	no	—
489	C₂×C₄×C₆₇	—	4	2	no	—
490	C₂×C₄×C₆₇	—	4	2	no	—
491	C₂×C₄×C₆₇	—	4	4	no	—
492	C₂×C₄×C₆₇	—	4	4	no	—
493	C₂×C₄×C₆₇	—	4	2	no	—
494	C₂×C₄×C₆₇	—	4	4	no	—
495	C₂×C₄×C₆₇	—	4	2	no	—
496	C₂×C₄×C₆₇	—	4	2	no	—
497	C₂×C₄×C₆₇	—	8	1	no	—
498	C₂×C₄×C₆₇	—	8	1	no	—
499	C₂×C₄×C₆₇	—	8	2	no	—
500	C₂×C₄×C₆₇	—	8	2	no	—
501	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
503	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
504	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
505	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
506	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
511	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
512	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
513	C₈×C₆₇	—	2	2	no	—
514	C₈×C₆₇	—	2	1	no	—
515	C₈×C₆₇	—	2	1	no	—
516	C₈×C₆₇	—	2	2	no	—
517	C₈×C₆₇	—	2	1	no	—
518	C₈×C₆₇	—	2	1	no	—
519	C₂²×C₆₇	—	2	1	no	—
520	C₂²×C₆₇	—	2	1	no	—
521	C₂²×C₆₇	—	2	2	no	—
522	C₂²×C₆₇	—	4	1	no	—
523	C₂²×C₆₇	—	4	1	no	—
524	C₂²×C₆₇	—	4	1	no	—
525	C₂²×C₆₇	—	4	2	no	—
526	C₂²×C₆₇	—	4	2	no	—
527	C₂²×C₆₇	—	4	1	no	—
528	C₂²×C₆₇	—	4	2	no	—
529	C₂²×C₆₇	—	4	1	no	—
530	C₂²×C₆₇	#548	1	2	yes	—
531	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
532	C₄×C₆₇	—	2	1	no	—
533	C₄×C₆₇	—	2	2	no	—
534	C₄×C₆₇	—	2	2	no	—
535	C₄×C₆₇	—	2	1	no	—
536	C₄×C₆₇	—	2	2	no	—
537	C₄×C₆₇	—	2	1	no	—
538	C₄×C₆₇	—	2	2	no	—
539	C₄×C₆₇	—	2	2	no	—
540	C₄×C₆₇	—	4	1	no	—
541	C₄×C₆₇	—	4	1	no	—
542	C₄×C₆₇	—	4	2	no	—
543	C₄×C₆₇	—	4	1	no	—
544	C₄×C₆₇	—	4	2	no	—
545	C₄×C₆₇	—	4	1	no	—
546	C₄×C₆₇	—	4	2	no	—
547	C₄×C₆₇	—	4	1	no	—
548	C₄×C₆₇	#548	1	2	yes	—
549	C₄×C₆₇	#575	1	2	yes	—
550	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
551	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
552	#61316	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
553	C₂×C₆₇	—	2	2	no	—
554	C₂×C₆₇	—	4	2	no	—
555	C₂×C₆₇	—	8	2	no	—
556	C₂×C₆₇	—	8	1	no	—
557	C₂×C₆₇	C₂×#548	1	1	yes	characteristic
558	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
559	C₂×C₆₇	#3584	1	1	yes	characteristic
560	#3480	C₂×C₆₇	1	1	yes	characteristic, complemented
561	Q₈×#41	C₂×C₆₇	1	1	yes	characteristic, complemented
562	#3377	C₂×C₆₇	1	2	yes	complemented
563	#3376	C₂×C₆₇	1	2	yes	complemented
564	#3375	C₂×C₆₇	1	1	yes	characteristic, complemented
565	#3374	C₂×C₆₇	1	1	yes	characteristic, complemented
566	#3373	C₂×C₆₇	1	1	yes	characteristic, complemented
567	#3372	C₂×C₆₇	1	1	yes	characteristic, complemented
568	#3371	C₂×C₆₇	1	2	yes	complemented
569	#3370	C₂×C₆₇	1	2	yes	complemented
570	#3369	C₂×C₆₇	1	1	yes	characteristic, complemented
571	#3368	C₂×C₆₇	1	1	yes	characteristic, complemented
572	#3367	C₂×C₆₇	1	1	yes	characteristic, complemented
573	#3366	C₂×C₆₇	1	1	yes	characteristic, complemented
574	#3135	C₂×C₆₇	1	2	yes	complemented
575	#3131	C₂×C₆₇	1	1	yes	characteristic, complemented
576	#3076	C₂×C₆₇	1	1	yes	characteristic, complemented
577	#3076	C₂×C₆₇	1	2	yes	complemented
578	#3035	C₂×C₆₇	1	1	yes	characteristic, complemented
579	#3035	C₂×C₆₇	1	2	yes	complemented
580	C₂×#446	C₂×C₆₇	1	1	yes	characteristic, complemented
581	#2943	C₂×C₆₇	1	2	yes	complemented
582	C₄×#135	C₂×C₆₇	1	1	yes	characteristic, complemented
583	C₆₇	#61316	1	1	yes	characteristic, direct product factor, Sylow
584	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
585	C₂×#135	C₂²×C₆₇	1	2	yes	—
586	#559	C₂²×C₆₇	1	2	yes	—
587	#559	C₂²×C₆₇	1	1	yes	characteristic
588	Q₈²	C₂²×C₆₇	1	1	yes	characteristic
589	#557	C₂²×C₆₇	1	1	yes	characteristic
590	#557	C₂²×C₆₇	1	1	yes	characteristic
591	#557	C₂²×C₆₇	1	2	yes	—
592	#556	C₂²×C₆₇	1	1	yes	characteristic
593	#556	C₂²×C₆₇	1	2	yes	—
594	#554	—	2	1	no	—
595	#554	—	2	2	no	—
596	#554	C₂²×C₆₇	1	1	yes	characteristic
597	#554	C₂²×C₆₇	1	2	yes	—
598	#553	—	2	1	no	—
599	#553	—	2	2	no	—
600	#550	C₂²×C₆₇	1	1	yes	characteristic
601	D₄×Q₈	—	2	1	no	—
602	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
603	#548	—	2	1	no	—
604	#533	—	2	1	no	—
605	#533	—	2	2	no	—
606	#533	C₂²×C₆₇	1	1	yes	characteristic
607	#533	C₂²×C₆₇	1	2	yes	—
608	#532	C₂²×C₆₇	1	1	yes	characteristic
609	#532	C₂²×C₆₇	1	2	yes	—
610	#529	—	2	1	no	—
611	#529	—	2	2	no	—
612	C₄×#41	—	2	1	no	—
613	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
614	C₄×#41	C₂²×C₆₇	1	2	yes	—
615	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
616	C₄×#41	C₂²×C₆₇	1	2	yes	—
617	C₂×C₄×Q₈	—	2	1	no	—
618	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
619	#491	C₂²×C₆₇	1	2	yes	—
620	#491	C₂²×C₆₇	1	2	yes	—
621	#490	C₂²×C₆₇	1	2	yes	—
622	#490	C₂²×C₆₇	1	2	yes	—
623	#489	C₂²×C₆₇	1	2	yes	—
624	#489	C₂²×C₆₇	1	2	yes	—
625	#489	C₂²×C₆₇	1	2	yes	—
626	#489	C₂²×C₆₇	1	2	yes	—
627	#488	C₂²×C₆₇	1	2	yes	—
628	#488	C₂²×C₆₇	1	2	yes	—
629	#487	C₂²×C₆₇	1	1	yes	characteristic
630	#487	C₂²×C₆₇	1	1	yes	characteristic
631	#486	C₂²×C₆₇	1	1	yes	characteristic
632	#486	C₂²×C₆₇	1	1	yes	characteristic
633	#479	C₂²×C₆₇	1	2	yes	—
634	#479	C₂²×C₆₇	1	2	yes	—
635	#479	C₂²×C₆₇	1	2	yes	—
636	#478	C₂²×C₆₇	1	2	yes	—
637	#478	C₂²×C₆₇	1	2	yes	—
638	#478	C₂²×C₆₇	1	2	yes	—
639	#477	C₂²×C₆₇	1	2	yes	—
640	#477	C₂²×C₆₇	1	1	yes	characteristic
641	#476	C₂²×C₆₇	1	1	yes	characteristic
642	#476	C₂²×C₆₇	1	2	yes	—
643	#475	C₂²×C₆₇	1	2	yes	—
644	#475	C₂²×C₆₇	1	1	yes	characteristic
645	#474	C₂²×C₆₇	1	1	yes	characteristic
646	#474	C₂²×C₆₇	1	2	yes	—
647	#464	C₂²×C₆₇	1	2	yes	—
648	#464	C₂²×C₆₇	1	2	yes	—
649	#464	C₂²×C₆₇	1	2	yes	—
650	#463	C₂²×C₆₇	1	2	yes	—
651	#463	C₂²×C₆₇	1	2	yes	—
652	#463	C₂²×C₆₇	1	2	yes	—
653	#462	C₂²×C₆₇	1	1	yes	characteristic
654	#462	C₂²×C₆₇	1	2	yes	—
655	#461	C₂²×C₆₇	1	1	yes	characteristic
656	#461	C₂²×C₆₇	1	2	yes	—
657	#460	C₂²×C₆₇	1	2	yes	—
658	#460	C₂²×C₆₇	1	1	yes	characteristic
659	#459	C₂²×C₆₇	1	2	yes	—
660	#459	C₂²×C₆₇	1	1	yes	characteristic
661	#446	C₂²×C₆₇	1	1	yes	characteristic
662	#446	C₂²×C₆₇	1	1	yes	characteristic
663	#446	C₂²×C₆₇	1	1	yes	characteristic
664	#446	C₂²×C₆₇	1	1	yes	characteristic
665	#446	C₂²×C₆₇	1	2	yes	—
666	#446	C₂²×C₆₇	1	2	yes	—
667	#442	C₂²×C₆₇	1	2	yes	—
668	#442	C₂²×C₆₇	1	2	yes	—
669	#441	C₂²×C₆₇	1	2	yes	—
670	#441	C₂²×C₆₇	1	2	yes	—
671	#440	C₂²×C₆₇	1	2	yes	—
672	#440	C₂²×C₆₇	1	2	yes	—
673	#440	C₂²×C₆₇	1	2	yes	—
674	#440	C₂²×C₆₇	1	2	yes	—
675	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
676	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
677	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
678	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
679	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
680	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
681	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
682	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
683	#427	C₂²×C₆₇	1	1	yes	characteristic
684	#427	C₂²×C₆₇	1	2	yes	—
685	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
686	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	—
687	#416	C₂²×C₆₇	1	2	yes	—
688	#416	C₂²×C₆₇	1	2	yes	—
689	#416	C₂²×C₆₇	1	2	yes	—
690	#416	C₂²×C₆₇	1	2	yes	—
691	#416	C₂²×C₆₇	1	1	yes	characteristic
692	#416	C₂²×C₆₇	1	1	yes	characteristic
693	C₂×#97	C₂²×C₆₇	1	2	yes	—
694	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
695	C₂×#41	—	2	1	no	—
696	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
697	C₂×#41	C₂³×C₆₇	1	2	yes	—
698	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
699	C₂²×Q₈	—	2	1	no	—
700	C₂²×Q₈	D₄×C₆₇	1	1	yes	characteristic
701	#135	—	2	4	no	—
702	#135	—	2	8	no	—
703	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
704	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
705	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
706	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
707	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
708	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
709	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
710	C₂×D₈	C₂³×C₆₇	1	2	yes	—
711	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
712	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
713	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
714	C₄⋊Q₈	—	2	1	no	—
715	C₄⋊Q₈	—	2	2	no	—
716	C₄⋊Q₈	—	2	1	no	—
717	C₄⋊Q₈	—	2	2	no	—
718	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
719	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
720	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
721	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
722	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
723	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
724	#127	C₂³×C₆₇	1	1	yes	characteristic
725	#127	C₂³×C₆₇	1	2	yes	—
726	#126	—	2	2	no	—
727	#126	—	2	2	no	—
728	#126	—	2	2	no	—
729	#125	—	2	1	no	—
730	#125	—	2	2	no	—
731	#125	—	2	2	no	—
732	#125	—	2	2	no	—
733	#125	—	2	2	no	—
734	#125	C₂³×C₆₇	1	2	yes	—
735	#125	C₂³×C₆₇	1	2	yes	—
736	#125	C₂³×C₆₇	1	2	yes	—
737	#124	—	2	1	no	—
738	#124	—	2	2	no	—
739	#124	C₂³×C₆₇	1	2	yes	—
740	#124	C₂³×C₆₇	1	2	yes	—
741	#124	C₂³×C₆₇	1	2	yes	—
742	#123	—	2	2	no	—
743	#123	—	2	2	no	—
744	#123	—	2	2	no	—
745	C₂²⋊Q₈	—	2	1	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	—	2	1	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	1	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	1	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	#121	—	2	1	no	—
759	#121	—	2	2	no	—
760	#121	—	2	1	no	—
761	#121	—	2	2	no	—
762	#121	—	2	1	no	—
763	#121	—	2	2	no	—
764	C₄×Q₈	—	2	1	no	—
765	C₄×Q₈	—	2	1	no	—
766	C₄×Q₈	—	2	1	no	—
767	C₄×Q₈	—	2	2	no	—
768	C₄×Q₈	—	2	1	no	—
769	C₄×Q₈	—	2	2	no	—
770	C₄×Q₈	—	2	2	no	—
771	C₄×Q₈	—	2	1	no	—
772	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
773	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
774	C₄×Q₈	D₄×C₆₇	1	2	yes	—
775	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
776	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
777	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
778	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
779	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
780	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
781	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
782	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
783	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
784	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
785	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
786	C₄×D₄	—	2	1	no	—
787	C₄×D₄	—	2	2	no	—
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	—	2	2	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	2	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	2	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
801	C₄×D₄	C₂³×C₆₇	1	2	yes	—
802	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
803	C₄×D₄	C₂³×C₆₇	1	2	yes	—
804	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
805	C₄×D₄	C₂³×C₆₇	1	2	yes	—
806	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
807	C₄×D₄	C₂³×C₆₇	1	2	yes	—
808	#117	—	2	2	no	—
809	#117	—	2	1	no	—
810	#117	—	2	2	no	—
811	#117	—	2	1	no	—
812	#117	—	2	2	no	—
813	#117	—	2	1	no	—
814	#117	C₂³×C₆₇	1	1	yes	characteristic
815	#117	C₂³×C₆₇	1	1	yes	characteristic
816	#117	C₂³×C₆₇	1	2	yes	—
817	C₂×C₄⋊C₄	—	2	1	no	—
818	C₂×C₄⋊C₄	—	2	2	no	—
819	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
820	C₂×C₄⋊C₄	D₄×C₆₇	1	2	yes	—
821	C₂×C₄²	—	2	1	no	—
822	C₂×C₄²	—	2	2	no	—
823	C₂×C₄²	—	2	1	no	—
824	C₂×C₄²	—	2	2	no	—
825	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
826	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
827	#107	C₂³×C₆₇	1	1	yes	characteristic
828	#107	C₂³×C₆₇	1	1	yes	characteristic
829	#107	C₂³×C₆₇	1	2	yes	—
830	#107	C₂³×C₆₇	1	2	yes	—
831	#106	C₂³×C₆₇	1	1	yes	characteristic
832	#106	C₂³×C₆₇	1	1	yes	characteristic
833	#106	C₂³×C₆₇	1	2	yes	—
834	#106	C₂³×C₆₇	1	2	yes	—
835	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
836	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
837	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
838	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
839	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
840	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
841	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
842	#103	C₂³×C₆₇	1	1	yes	characteristic
843	#103	C₂³×C₆₇	1	1	yes	characteristic
844	#103	C₂³×C₆₇	1	1	yes	characteristic
845	#103	C₂³×C₆₇	1	1	yes	characteristic
846	#103	C₂³×C₆₇	1	2	yes	—
847	#103	C₂³×C₆₇	1	2	yes	—
848	#103	C₂³×C₆₇	1	2	yes	—
849	#103	C₂³×C₆₇	1	2	yes	—
850	#103	C₂³×C₆₇	1	2	yes	—
851	#103	C₂³×C₆₇	1	2	yes	—
852	#103	C₂³×C₆₇	1	2	yes	—
853	#103	C₂³×C₆₇	1	2	yes	—
854	#102	C₂³×C₆₇	1	1	yes	characteristic
855	#102	C₂³×C₆₇	1	1	yes	characteristic
856	#102	C₂³×C₆₇	1	1	yes	characteristic
857	#102	C₂³×C₆₇	1	1	yes	characteristic
858	#102	C₂³×C₆₇	1	2	yes	—
859	#102	C₂³×C₆₇	1	2	yes	—
860	#102	C₂³×C₆₇	1	2	yes	—
861	#102	C₂³×C₆₇	1	2	yes	—
862	#102	C₂³×C₆₇	1	2	yes	—
863	#102	C₂³×C₆₇	1	2	yes	—
864	#102	C₂³×C₆₇	1	2	yes	—
865	#102	C₂³×C₆₇	1	2	yes	—
866	#97	C₂³×C₆₇	1	2	yes	—
867	#97	C₂³×C₆₇	1	2	yes	—
868	#97	C₂³×C₆₇	1	2	yes	—
869	#97	C₂³×C₆₇	1	2	yes	—
870	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
871	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
872	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
873	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
874	#41	—	2	2	no	—
875	#41	—	2	2	no	—
876	#41	—	2	4	no	—
877	#41	—	2	2	no	—
878	#41	—	2	4	no	—
879	#41	—	4	4	no	—
880	#41	#41×C₆₇	1	4	yes	complemented
881	C₂×Q₈	—	2	2	no	—
882	C₂×Q₈	—	2	1	no	—
883	C₂×Q₈	—	2	2	no	—
884	C₂×Q₈	—	2	1	no	—
885	C₂×Q₈	—	4	2	no	—
886	C₂×Q₈	—	4	4	no	—
887	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
888	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
889	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
890	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
891	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
892	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
893	C₂×D₄	—	2	1	no	—
894	C₂×D₄	—	2	1	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	—	2	1	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	2	1	no	—
900	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
901	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
902	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
903	C₂²×C₄	—	2	1	no	—
904	C₂²×C₄	—	2	2	no	—
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
915	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
916	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
917	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
918	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
919	Q₁₆	—	2	2	no	—
920	Q₁₆	—	2	4	no	—
921	SD₁₆	—	2	2	no	—
922	SD₁₆	—	2	4	no	—
923	SD₁₆	—	2	2	no	—
924	SD₁₆	—	2	4	no	—
925	D₈	—	2	2	no	—
926	D₈	—	2	4	no	—
927	C₂×C₈	—	2	2	no	—
928	C₂×C₈	—	2	4	no	—
929	C₂×C₈	—	2	2	no	—
930	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
931	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
932	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
933	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
934	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
935	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
959	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
960	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
961	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
962	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
963	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
964	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
965	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
966	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
967	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
968	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
969	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
970	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
971	C₂²⋊C₄	—	2	1	no	—
972	C₂²⋊C₄	—	2	1	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₄²	—	2	1	no	—
989	C₄²	—	2	1	no	—
990	C₄²	—	2	2	no	—
991	C₄²	—	2	1	no	—
992	C₄²	—	2	2	no	—
993	C₄²	—	2	2	no	—
994	C₄²	—	2	1	no	—
995	C₄²	—	2	1	no	—
996	C₄²	—	2	2	no	—
997	C₄²	—	2	2	no	—
998	C₄²	—	2	1	no	—
999	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1000	C₄²	C₂×D₄×C₆₇	1	2	yes	—
1001	C₄²	C₂×D₄×C₆₇	1	2	yes	—
1002	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1003	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1004	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1005	C₄²	C₂⁴×C₆₇	1	2	yes	—
1006	C₄²	C₂⁴×C₆₇	1	2	yes	—
1007	C₂³	—	2	1	no	—
1008	C₂³	—	2	2	no	—
1009	C₂³	—	2	1	no	—
1010	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1011	Q₈	—	2	2	no	—
1012	Q₈	—	2	2	no	—
1013	Q₈	—	2	1	no	—
1014	Q₈	—	2	1	no	—
1015	Q₈	—	2	2	no	—
1016	Q₈	—	2	1	no	—
1017	Q₈	—	2	2	no	—
1018	Q₈	—	4	2	no	—
1019	Q₈	—	4	4	no	—
1020	Q₈	—	4	2	no	—
1021	Q₈	—	8	2	no	—
1022	Q₈	—	8	1	no	—
1023	Q₈	C₂×#41×C₆₇	1	2	yes	—
1024	D₄	—	2	4	no	—
1025	D₄	—	2	1	no	—
1026	D₄	—	2	2	no	—
1027	D₄	—	2	1	no	—
1028	D₄	—	2	1	no	—
1029	D₄	—	2	2	no	—
1030	D₄	—	4	4	no	—
1031	D₄	—	4	2	no	—
1032	D₄	—	4	4	no	—
1033	D₄	—	4	2	no	—
1034	D₄	—	8	2	no	—
1035	D₄	—	8	1	no	—
1036	D₄	C₂×#41×C₆₇	1	2	yes	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	4	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	4	2	no	—
1049	C₂×C₄	—	4	1	no	—
1050	C₂×C₄	—	4	2	no	—
1051	C₂×C₄	—	4	4	no	—
1052	C₂×C₄	—	4	4	no	—
1053	C₂×C₄	—	4	2	no	—
1054	C₂×C₄	—	4	4	no	—
1055	C₂×C₄	—	4	2	no	—
1056	C₂×C₄	—	4	2	no	—
1057	C₂×C₄	—	8	1	no	—
1058	C₂×C₄	—	8	1	no	—
1059	C₂×C₄	—	8	2	no	—
1060	C₂×C₄	—	8	2	no	—
1061	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1062	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1063	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1064	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1065	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1066	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1067	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1068	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1069	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1070	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1071	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
1072	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1073	C₈	—	2	1	no	—
1074	C₈	—	2	2	no	—
1075	C₈	—	2	1	no	—
1076	C₈	—	2	2	no	—
1077	C₈	—	2	1	no	—
1078	C₈	—	2	1	no	—
1079	C₂²	—	2	1	no	—
1080	C₂²	—	2	1	no	—
1081	C₂²	—	2	2	no	—
1082	C₂²	—	4	1	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	—	4	2	no	—
1085	C₂²	—	4	1	no	—
1086	C₂²	—	4	1	no	—
1087	C₂²	—	4	2	no	—
1088	C₂²	—	4	2	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	#548×C₆₇	1	2	yes	—
1091	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1092	C₄	—	2	1	no	—
1093	C₄	—	2	2	no	—
1094	C₄	—	2	2	no	—
1095	C₄	—	2	1	no	—
1096	C₄	—	2	2	no	—
1097	C₄	—	2	2	no	—
1098	C₄	—	2	1	no	—
1099	C₄	—	2	2	no	—
1100	C₄	—	4	1	no	—
1101	C₄	—	4	2	no	—
1102	C₄	—	4	1	no	—
1103	C₄	—	4	1	no	—
1104	C₄	—	4	1	no	—
1105	C₄	—	4	2	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	2	no	—
1108	C₄	#548×C₆₇	1	2	yes	—
1109	C₄	#575×C₆₇	1	2	yes	—
1110	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1111	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
1112	C₂	—	2	2	no	—
1113	C₂	—	4	2	no	—
1114	C₂	—	8	2	no	—
1115	C₂	—	8	1	no	—
1116	C₂	C₂×#548×C₆₇	1	1	yes	characteristic
1117	C₂	C₂×#575×C₆₇	1	1	yes	characteristic
1118	C₂	C₆₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂²×C₆₇	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ C₂×C₄×Q₈×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3480	C₂	semidirect
2. Q₈×#41×C₆₇	C₂	semidirect
3. C₆₇×#3377	C₂	semidirect
4. C₆₇×#3376	C₂	semidirect
5. C₆₇×#3375	C₂	semidirect
6. C₆₇×#3374	C₂	semidirect
7. C₆₇×#3373	C₂	semidirect
8. C₆₇×#3372	C₂	semidirect
9. C₆₇×#3371	C₂	semidirect
10. C₆₇×#3370	C₂	semidirect
11. C₆₇×#3369	C₂	semidirect
12. C₆₇×#3368	C₂	semidirect
13. C₆₇×#3367	C₂	semidirect
14. C₆₇×#3366	C₂	semidirect
15. C₆₇×#3135	C₂	semidirect
16. C₆₇×#3131	C₂	semidirect
17. C₆₇×#3076	C₂	semidirect
18. C₆₇×#3076	C₂	semidirect
19. C₆₇×#3035	C₂	semidirect
20. C₆₇×#3035	C₂	semidirect
21. C₂×#446×C₆₇	C₂	semidirect
22. C₆₇×#2943	C₂	semidirect
23. C₄×#135×C₆₇	C₂	semidirect
320. #41×C₆₇	#41	semidirect
552. #61316	C₆₇	direct (N × H)
560. #3480	C₂×C₆₇	semidirect
561. Q₈×#41	C₂×C₆₇	semidirect
562. #3377	C₂×C₆₇	semidirect
563. #3376	C₂×C₆₇	semidirect
564. #3375	C₂×C₆₇	semidirect
565. #3374	C₂×C₆₇	semidirect
566. #3373	C₂×C₆₇	semidirect
567. #3372	C₂×C₆₇	semidirect
568. #3371	C₂×C₆₇	semidirect
569. #3370	C₂×C₆₇	semidirect
570. #3369	C₂×C₆₇	semidirect
571. #3368	C₂×C₆₇	semidirect
572. #3367	C₂×C₆₇	semidirect
573. #3366	C₂×C₆₇	semidirect
574. #3135	C₂×C₆₇	semidirect
575. #3131	C₂×C₆₇	semidirect
576. #3076	C₂×C₆₇	semidirect
577. #3076	C₂×C₆₇	semidirect
578. #3035	C₂×C₆₇	semidirect
579. #3035	C₂×C₆₇	semidirect
580. C₂×#446	C₂×C₆₇	semidirect
581. #2943	C₂×C₆₇	semidirect
582. C₄×#135	C₂×C₆₇	semidirect
583. C₆₇	#61316	direct (N × H)
880. #41	#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×#3480	2
Q₈×#41×C₆₇	2
C₆₇×#3377	2
C₆₇×#3376	2
C₆₇×#3375	2
C₆₇×#3374	2
C₆₇×#3373	2
C₆₇×#3372	2
C₆₇×#3371	2
C₆₇×#3370	2
C₆₇×#3369	2
C₆₇×#3368	2
C₆₇×#3367	2
C₆₇×#3366	2
C₆₇×#3135	2
C₆₇×#3131	2
C₆₇×#3076	2
C₆₇×#3035	2
C₂×#446×C₆₇	2
C₆₇×#2943	2
C₄×#135×C₆₇	2
#61316	67

Subgroups — C67×#61316 #30740567

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61316 #30740567