Subgroups — C₆₇×#61558 #30740809

Order 17152.

1810 conjugacy classes of subgroups.

The subgroup lattice has 1130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3522	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3394	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×Q₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#3369	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#3357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3353	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3313	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3308	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3305	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3299	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3278	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3277	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3182	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3175	C₂	1	2	yes	maximal, complemented
17	C₆₇×#3124	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3121	C₂	1	2	yes	maximal, complemented
19	C₆₇×#3106	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3104	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2969	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2947	C₂	1	2	yes	maximal, complemented
23	C₄×#137×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#137×C₆₇	C₂²	1	2	yes	—
26	#559×C₆₇	—	2	1	no	—
27	#559×C₆₇	C₂²	1	1	yes	characteristic
28	Q₈²×C₆₇	C₂²	1	1	yes	characteristic
29	Q₈²×C₆₇	C₂²	1	1	yes	characteristic
30	#556×C₆₇	—	2	2	no	—
31	#556×C₆₇	—	2	1	no	—
32	#556×C₆₇	C₂²	1	1	yes	characteristic
33	#556×C₆₇	C₂²	1	2	yes	—
34	#555×C₆₇	—	2	1	no	—
35	#555×C₆₇	C₂²	1	1	yes	characteristic
36	#554×C₆₇	—	2	1	no	—
37	#554×C₆₇	C₂²	1	1	yes	characteristic
38	#550×C₆₇	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
40	#548×C₆₇	C₂²	1	2	yes	—
41	#548×C₆₇	C₂²	1	2	yes	—
42	#547×C₆₇	—	2	2	no	—
43	#547×C₆₇	C₂²	1	2	yes	—
44	#542×C₆₇	—	2	2	no	—
45	#542×C₆₇	—	2	2	no	—
46	#542×C₆₇	C₂²	1	2	yes	—
47	#542×C₆₇	C₂²	1	2	yes	—
48	#533×C₆₇	—	2	1	no	—
49	#533×C₆₇	C₂²	1	1	yes	characteristic
50	#532×C₆₇	—	2	1	no	—
51	#532×C₆₇	C₂²	1	1	yes	characteristic
52	#529×C₆₇	—	2	1	no	—
53	#529×C₆₇	—	2	1	no	—
54	#529×C₆₇	C₂²	1	1	yes	characteristic
55	#520×C₆₇	C₂²	1	2	yes	—
56	#519×C₆₇	C₂²	1	2	yes	—
57	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
58	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
59	#500×C₆₇	C₂²	1	2	yes	—
60	#500×C₆₇	C₂²	1	1	yes	characteristic
61	#495×C₆₇	C₂²	1	2	yes	—
62	#492×C₆₇	C₂²	1	1	yes	characteristic
63	#489×C₆₇	C₂²	1	2	yes	—
64	#489×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	#484×C₆₇	C₂²	1	2	yes	—
70	#482×C₆₇	C₂²	1	2	yes	—
71	#482×C₆₇	C₂²	1	2	yes	—
72	#480×C₆₇	C₂²	1	2	yes	—
73	#477×C₆₇	C₂²	1	1	yes	characteristic
74	#477×C₆₇	C₂²	1	1	yes	characteristic
75	#477×C₆₇	C₂²	1	2	yes	—
76	#477×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	2	yes	—
80	#474×C₆₇	C₂²	1	2	yes	—
81	#468×C₆₇	C₂²	1	2	yes	—
82	#468×C₆₇	C₂²	1	2	yes	—
83	#468×C₆₇	C₂²	1	2	yes	—
84	#468×C₆₇	C₂²	1	2	yes	—
85	#467×C₆₇	C₂²	1	2	yes	—
86	#466×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	#462×C₆₇	C₂²	1	1	yes	characteristic
92	#462×C₆₇	C₂²	1	1	yes	characteristic
93	#460×C₆₇	C₂²	1	1	yes	characteristic
94	#459×C₆₇	C₂²	1	1	yes	characteristic
95	#452×C₆₇	C₂²	1	2	yes	—
96	#451×C₆₇	C₂²	1	2	yes	—
97	#451×C₆₇	C₂²	1	2	yes	—
98	#449×C₆₇	C₂²	1	2	yes	—
99	#449×C₆₇	C₂²	1	2	yes	—
100	#448×C₆₇	C₂²	1	2	yes	—
101	#446×C₆₇	C₂²	1	1	yes	characteristic
102	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic
103	#441×C₆₇	C₂²	1	2	yes	—
104	#441×C₆₇	C₂²	1	1	yes	characteristic
105	#441×C₆₇	C₂²	1	1	yes	characteristic
106	#440×C₆₇	C₂²	1	2	yes	—
107	#440×C₆₇	C₂²	1	2	yes	—
108	#440×C₆₇	C₂²	1	1	yes	characteristic
109	#440×C₆₇	C₂²	1	1	yes	characteristic
110	#440×C₆₇	C₂²	1	2	yes	—
111	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
112	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
113	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
114	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
115	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
116	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
118	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
120	C₄×D₈×C₆₇	C₂²	1	2	yes	—
121	#436×C₆₇	C₂²	1	2	yes	—
122	#436×C₆₇	C₂²	1	1	yes	characteristic
123	#435×C₆₇	C₂²	1	2	yes	—
124	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
125	#433×C₆₇	C₂²	1	2	yes	—
126	#431×C₆₇	C₂²	1	1	yes	characteristic
127	#428×C₆₇	C₂²	1	1	yes	characteristic
128	#428×C₆₇	C₂²	1	2	yes	—
129	#419×C₆₇	C₂²	1	1	yes	characteristic
130	#417×C₆₇	C₂²	1	1	yes	characteristic
131	#416×C₆₇	C₂²	1	2	yes	—
132	C₂×#103×C₆₇	C₂²	1	2	yes	—
133	#405×C₆₇	C₂²	1	2	yes	—
134	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
135	C₂×#41×C₆₇	—	2	2	no	—
136	C₂×#41×C₆₇	—	2	1	no	—
137	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
138	C₂×#41×C₆₇	C₂³	1	2	yes	—
139	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
140	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
141	#137×C₆₇	—	2	4	no	—
142	#137×C₆₇	—	2	8	no	—
143	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
144	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
145	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
152	C₂×D₈×C₆₇	C₂³	1	2	yes	—
153	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
154	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
155	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
156	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
157	C₄⋊Q₈×C₆₇	—	2	1	no	—
158	C₄⋊Q₈×C₆₇	—	2	1	no	—
159	C₄⋊Q₈×C₆₇	—	2	1	no	—
160	C₄⋊Q₈×C₆₇	—	2	2	no	—
161	C₄⋊Q₈×C₆₇	—	2	2	no	—
162	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
164	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
165	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
166	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
167	#127×C₆₇	—	2	1	no	—
168	#127×C₆₇	C₂³	1	1	yes	characteristic
169	#126×C₆₇	—	2	2	no	—
170	#126×C₆₇	—	2	2	no	—
171	#126×C₆₇	—	2	2	no	—
172	#126×C₆₇	—	2	2	no	—
173	#126×C₆₇	—	2	2	no	—
174	#126×C₆₇	D₄	1	2	yes	—
175	#125×C₆₇	—	2	1	no	—
176	#125×C₆₇	—	2	1	no	—
177	#125×C₆₇	D₄	1	1	yes	characteristic
178	#124×C₆₇	—	2	1	no	—
179	#124×C₆₇	—	2	2	no	—
180	#124×C₆₇	—	2	2	no	—
181	#124×C₆₇	—	2	2	no	—
182	#124×C₆₇	—	2	2	no	—
183	#124×C₆₇	—	2	2	no	—
184	#124×C₆₇	—	2	2	no	—
185	#124×C₆₇	—	2	1	no	—
186	#124×C₆₇	D₄	1	1	yes	characteristic
187	#124×C₆₇	C₂³	1	2	yes	—
188	#124×C₆₇	C₂³	1	2	yes	—
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	—	2	2	no	—
194	#123×C₆₇	D₄	1	2	yes	—
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	—	2	2	no	—
200	C₂²⋊Q₈×C₆₇	—	2	2	no	—
201	C₂²⋊Q₈×C₆₇	—	2	2	no	—
202	C₂²⋊Q₈×C₆₇	—	2	2	no	—
203	C₂²⋊Q₈×C₆₇	—	2	2	no	—
204	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
205	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
206	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
207	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
208	#121×C₆₇	—	2	1	no	—
209	#121×C₆₇	—	2	2	no	—
210	#121×C₆₇	—	2	2	no	—
211	#121×C₆₇	—	2	1	no	—
212	#121×C₆₇	—	2	2	no	—
213	#121×C₆₇	D₄	1	1	yes	characteristic
214	#121×C₆₇	C₂³	1	2	yes	—
215	#121×C₆₇	C₂³	1	2	yes	—
216	#121×C₆₇	C₂³	1	2	yes	—
217	C₄×Q₈×C₆₇	—	2	1	no	—
218	C₄×Q₈×C₆₇	—	2	1	no	—
219	C₄×Q₈×C₆₇	—	2	2	no	—
220	C₄×Q₈×C₆₇	—	2	2	no	—
221	C₄×Q₈×C₆₇	—	2	2	no	—
222	C₄×Q₈×C₆₇	—	2	1	no	—
223	C₄×Q₈×C₆₇	—	2	1	no	—
224	C₄×Q₈×C₆₇	—	2	1	no	—
225	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
229	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
230	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
231	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
234	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
235	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
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	1	no	—
241	C₄×D₄×C₆₇	—	2	1	no	—
242	C₄×D₄×C₆₇	—	2	2	no	—
243	C₄×D₄×C₆₇	—	2	2	no	—
244	C₄×D₄×C₆₇	—	2	2	no	—
245	C₄×D₄×C₆₇	—	2	2	no	—
246	C₄×D₄×C₆₇	—	2	1	no	—
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	C₄×D₄×C₆₇	C₂³	1	2	yes	—
252	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
253	#117×C₆₇	—	2	1	no	—
254	#117×C₆₇	—	2	2	no	—
255	#117×C₆₇	—	2	1	no	—
256	#117×C₆₇	—	2	1	no	—
257	#117×C₆₇	—	2	2	no	—
258	#117×C₆₇	—	2	2	no	—
259	#117×C₆₇	—	2	1	no	—
260	#117×C₆₇	C₂³	1	1	yes	characteristic
261	#117×C₆₇	C₂³	1	2	yes	—
262	#117×C₆₇	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
264	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
265	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
266	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
274	#107×C₆₇	C₂³	1	2	yes	—
275	#107×C₆₇	C₂³	1	1	yes	characteristic
276	#107×C₆₇	C₂³	1	2	yes	—
277	#106×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
282	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
283	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
284	#103×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
292	#103×C₆₇	C₂³	1	1	yes	characteristic
293	#103×C₆₇	C₂³	1	1	yes	characteristic
294	#103×C₆₇	C₂³	1	2	yes	—
295	#103×C₆₇	C₂³	1	1	yes	characteristic
296	#103×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
302	#102×C₆₇	C₂³	1	1	yes	characteristic
303	#102×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	#97×C₆₇	C₂³	1	2	yes	—
308	#97×C₆₇	C₂³	1	1	yes	characteristic
309	#97×C₆₇	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₆₇	C₂³	1	2	yes	—
313	C₄×C₈×C₆₇	C₂³	1	2	yes	—
314	#41×C₆₇	—	2	2	no	—
315	#41×C₆₇	—	2	4	no	—
316	#41×C₆₇	—	4	2	no	—
317	#41×C₆₇	—	4	1	no	—
318	#41×C₆₇	—	8	2	no	—
319	#41×C₆₇	—	8	4	no	—
320	C₂×Q₈×C₆₇	—	2	1	no	—
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	2	no	—
325	C₂×Q₈×C₆₇	—	2	1	no	—
326	C₂×Q₈×C₆₇	—	2	4	no	—
327	C₂×Q₈×C₆₇	—	2	2	no	—
328	C₂×Q₈×C₆₇	—	4	2	no	—
329	C₂×Q₈×C₆₇	—	4	1	no	—
330	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
333	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
334	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
335	C₂×D₄×C₆₇	—	2	1	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	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	C₂²×C₄×C₆₇	—	2	1	no	—
347	C₂²×C₄×C₆₇	—	2	1	no	—
348	C₂²×C₄×C₆₇	—	2	2	no	—
349	C₂²×C₄×C₆₇	—	2	2	no	—
350	C₂²×C₄×C₆₇	—	2	1	no	—
351	C₂²×C₄×C₆₇	—	2	1	no	—
352	C₂²×C₄×C₆₇	—	2	2	no	—
353	C₂²×C₄×C₆₇	—	2	1	no	—
354	C₂²×C₄×C₆₇	—	2	2	no	—
355	C₂²×C₄×C₆₇	—	2	2	no	—
356	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
357	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
358	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
360	Q₁₆×C₆₇	—	2	2	no	—
361	Q₁₆×C₆₇	—	2	4	no	—
362	Q₁₆×C₆₇	—	4	2	no	—
363	Q₁₆×C₆₇	#41	1	4	yes	complemented
364	SD₁₆×C₆₇	—	2	4	no	—
365	SD₁₆×C₆₇	—	2	2	no	—
366	SD₁₆×C₆₇	—	2	4	no	—
367	SD₁₆×C₆₇	—	2	2	no	—
368	SD₁₆×C₆₇	—	4	2	no	—
369	D₈×C₆₇	—	4	2	no	—
370	M₁₆×C₆₇	—	2	2	no	—
371	M₁₆×C₆₇	—	2	4	no	—
372	M₁₆×C₆₇	—	4	1	no	—
373	C₂×C₈×C₆₇	—	4	2	no	—
374	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
377	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
378	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
380	C₄⋊C₄×C₆₇	—	2	1	no	—
381	C₄⋊C₄×C₆₇	—	2	2	no	—
382	C₄⋊C₄×C₆₇	—	2	2	no	—
383	C₄⋊C₄×C₆₇	—	2	1	no	—
384	C₄⋊C₄×C₆₇	—	2	1	no	—
385	C₄⋊C₄×C₆₇	—	2	1	no	—
386	C₄⋊C₄×C₆₇	—	2	1	no	—
387	C₄⋊C₄×C₆₇	—	2	1	no	—
388	C₄⋊C₄×C₆₇	—	2	1	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	2	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	1	no	—
398	C₄⋊C₄×C₆₇	—	2	2	no	—
399	C₄⋊C₄×C₆₇	—	2	2	no	—
400	C₄⋊C₄×C₆₇	—	2	2	no	—
401	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
404	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
406	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
410	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
412	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
413	C₂²⋊C₄×C₆₇	—	2	2	no	—
414	C₂²⋊C₄×C₆₇	—	2	2	no	—
415	C₂²⋊C₄×C₆₇	—	2	1	no	—
416	C₂²⋊C₄×C₆₇	—	2	2	no	—
417	C₂²⋊C₄×C₆₇	—	2	2	no	—
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	2	no	—
424	C₂²⋊C₄×C₆₇	—	2	2	no	—
425	C₂²⋊C₄×C₆₇	—	2	2	no	—
426	C₂²⋊C₄×C₆₇	—	2	2	no	—
427	C₂²⋊C₄×C₆₇	—	2	2	no	—
428	C₂²⋊C₄×C₆₇	—	2	2	no	—
429	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
434	C₄²×C₆₇	—	2	1	no	—
435	C₄²×C₆₇	—	2	1	no	—
436	C₄²×C₆₇	—	2	1	no	—
437	C₄²×C₆₇	—	2	1	no	—
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	2	no	—
444	C₄²×C₆₇	—	2	2	no	—
445	C₄²×C₆₇	—	2	2	no	—
446	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
447	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
448	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
449	C₄²×C₆₇	C₂⁴	1	2	yes	—
450	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
451	C₂³×C₆₇	—	2	1	no	—
452	C₂³×C₆₇	—	2	2	no	—
453	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
454	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
455	Q₈×C₆₇	—	2	2	no	—
456	Q₈×C₆₇	—	2	1	no	—
457	Q₈×C₆₇	—	2	1	no	—
458	Q₈×C₆₇	—	2	1	no	—
459	Q₈×C₆₇	—	2	2	no	—
460	Q₈×C₆₇	—	2	2	no	—
461	Q₈×C₆₇	—	2	1	no	—
462	Q₈×C₆₇	—	4	2	no	—
463	Q₈×C₆₇	—	4	4	no	—
464	Q₈×C₆₇	—	8	1	no	—
465	Q₈×C₆₇	—	8	2	no	—
466	Q₈×C₆₇	—	8	1	no	—
467	Q₈×C₆₇	—	8	2	no	—
468	Q₈×C₆₇	C₂×#41	1	2	yes	—
469	Q₈×C₆₇	C₂×#41	1	2	yes	—
470	D₄×C₆₇	—	2	2	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	4	no	—
477	D₄×C₆₇	—	4	2	no	—
478	D₄×C₆₇	—	4	4	no	—
479	D₄×C₆₇	—	4	2	no	—
480	D₄×C₆₇	—	8	1	no	—
481	D₄×C₆₇	—	8	2	no	—
482	D₄×C₆₇	—	8	2	no	—
483	C₂×C₄×C₆₇	—	2	1	no	—
484	C₂×C₄×C₆₇	—	2	1	no	—
485	C₂×C₄×C₆₇	—	2	2	no	—
486	C₂×C₄×C₆₇	—	2	1	no	—
487	C₂×C₄×C₆₇	—	2	2	no	—
488	C₂×C₄×C₆₇	—	2	2	no	—
489	C₂×C₄×C₆₇	—	2	1	no	—
490	C₂×C₄×C₆₇	—	2	1	no	—
491	C₂×C₄×C₆₇	—	2	2	no	—
492	C₂×C₄×C₆₇	—	2	1	no	—
493	C₂×C₄×C₆₇	—	2	2	no	—
494	C₂×C₄×C₆₇	—	2	1	no	—
495	C₂×C₄×C₆₇	—	2	1	no	—
496	C₂×C₄×C₆₇	—	2	1	no	—
497	C₂×C₄×C₆₇	—	2	2	no	—
498	C₂×C₄×C₆₇	—	4	1	no	—
499	C₂×C₄×C₆₇	—	4	4	no	—
500	C₂×C₄×C₆₇	—	4	2	no	—
501	C₂×C₄×C₆₇	—	4	2	no	—
502	C₂×C₄×C₆₇	—	4	4	no	—
503	C₂×C₄×C₆₇	—	4	2	no	—
504	C₂×C₄×C₆₇	—	4	2	no	—
505	C₂×C₄×C₆₇	—	8	1	no	—
506	C₂×C₄×C₆₇	—	8	2	no	—
507	C₂×C₄×C₆₇	—	8	2	no	—
508	C₂×C₄×C₆₇	—	8	2	no	—
509	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
511	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
514	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
515	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
518	C₈×C₆₇	—	2	1	no	—
519	C₈×C₆₇	—	2	2	no	—
520	C₈×C₆₇	—	2	1	no	—
521	C₈×C₆₇	—	2	2	no	—
522	C₈×C₆₇	—	2	1	no	—
523	C₈×C₆₇	C₂×#41	1	2	yes	—
524	C₂²×C₆₇	—	2	1	no	—
525	C₂²×C₆₇	—	2	2	no	—
526	C₂²×C₆₇	—	2	2	no	—
527	C₂²×C₆₇	—	2	1	no	—
528	C₂²×C₆₇	—	2	1	no	—
529	C₂²×C₆₇	—	2	2	no	—
530	C₂²×C₆₇	—	4	2	no	—
531	C₂²×C₆₇	—	4	1	no	—
532	C₂²×C₆₇	—	4	1	no	—
533	C₂²×C₆₇	—	4	2	no	—
534	C₂²×C₆₇	—	4	1	no	—
535	C₂²×C₆₇	—	4	2	no	—
536	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
537	C₄×C₆₇	—	2	1	no	—
538	C₄×C₆₇	—	2	1	no	—
539	C₄×C₆₇	—	2	2	no	—
540	C₄×C₆₇	—	2	2	no	—
541	C₄×C₆₇	—	2	1	no	—
542	C₄×C₆₇	—	2	2	no	—
543	C₄×C₆₇	—	2	2	no	—
544	C₄×C₆₇	—	2	1	no	—
545	C₄×C₆₇	—	2	2	no	—
546	C₄×C₆₇	—	4	1	no	—
547	C₄×C₆₇	—	4	1	no	—
548	C₄×C₆₇	—	4	2	no	—
549	C₄×C₆₇	—	4	1	no	—
550	C₄×C₆₇	—	4	2	no	—
551	C₄×C₆₇	—	4	1	no	—
552	C₄×C₆₇	—	4	2	no	—
553	C₄×C₆₇	—	4	1	no	—
554	C₄×C₆₇	#578	1	2	yes	—
555	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
556	C₄×C₆₇	#585	1	1	yes	characteristic
557	#61558	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
558	C₂×C₆₇	—	4	1	no	—
559	C₂×C₆₇	—	4	2	no	—
560	C₂×C₆₇	—	8	2	no	—
561	C₂×C₆₇	—	8	1	no	—
562	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
563	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
564	C₂×C₆₇	#3585	1	1	yes	characteristic
565	#3522	C₂×C₆₇	1	1	yes	characteristic, complemented
566	#3518	C₂×C₆₇	1	1	yes	characteristic, complemented
567	#3394	C₂×C₆₇	1	1	yes	characteristic, complemented
568	Q₈×Q₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
569	#3375	C₂×C₆₇	1	1	yes	characteristic, complemented
570	#3369	C₂×C₆₇	1	1	yes	characteristic, complemented
571	#3357	C₂×C₆₇	1	1	yes	characteristic, complemented
572	#3353	C₂×C₆₇	1	2	yes	complemented
573	#3313	C₂×C₆₇	1	2	yes	complemented
574	#3308	C₂×C₆₇	1	2	yes	complemented
575	#3305	C₂×C₆₇	1	1	yes	characteristic, complemented
576	#3299	C₂×C₆₇	1	1	yes	characteristic, complemented
577	#3278	C₂×C₆₇	1	1	yes	characteristic, complemented
578	#3277	C₂×C₆₇	1	2	yes	complemented
579	#3182	C₂×C₆₇	1	1	yes	characteristic, complemented
580	#3175	C₂×C₆₇	1	2	yes	complemented
581	#3124	C₂×C₆₇	1	2	yes	complemented
582	#3121	C₂×C₆₇	1	2	yes	complemented
583	#3106	C₂×C₆₇	1	1	yes	characteristic, complemented
584	#3104	C₂×C₆₇	1	1	yes	characteristic, complemented
585	#2969	C₂×C₆₇	1	1	yes	characteristic, complemented
586	#2947	C₂×C₆₇	1	2	yes	complemented
587	C₄×#137	C₂×C₆₇	1	1	yes	characteristic, complemented
588	C₆₇	#61558	1	1	yes	characteristic, direct product factor, Sylow
589	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
590	C₂×#137	C₂²×C₆₇	1	2	yes	—
591	#559	—	2	1	no	—
592	#559	C₂²×C₆₇	1	1	yes	characteristic
593	Q₈²	C₂²×C₆₇	1	1	yes	characteristic
594	Q₈²	C₂²×C₆₇	1	1	yes	characteristic
595	#556	—	2	2	no	—
596	#556	—	2	1	no	—
597	#556	C₂²×C₆₇	1	1	yes	characteristic
598	#556	C₂²×C₆₇	1	2	yes	—
599	#555	—	2	1	no	—
600	#555	C₂²×C₆₇	1	1	yes	characteristic
601	#554	—	2	1	no	—
602	#554	C₂²×C₆₇	1	1	yes	characteristic
603	#550	C₂²×C₆₇	1	1	yes	characteristic
604	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
605	#548	C₂²×C₆₇	1	2	yes	—
606	#548	C₂²×C₆₇	1	2	yes	—
607	#547	—	2	2	no	—
608	#547	C₂²×C₆₇	1	2	yes	—
609	#542	—	2	2	no	—
610	#542	—	2	2	no	—
611	#542	C₂²×C₆₇	1	2	yes	—
612	#542	C₂²×C₆₇	1	2	yes	—
613	#533	—	2	1	no	—
614	#533	C₂²×C₆₇	1	1	yes	characteristic
615	#532	—	2	1	no	—
616	#532	C₂²×C₆₇	1	1	yes	characteristic
617	#529	—	2	1	no	—
618	#529	—	2	1	no	—
619	#529	C₂²×C₆₇	1	1	yes	characteristic
620	#520	C₂²×C₆₇	1	2	yes	—
621	#519	C₂²×C₆₇	1	2	yes	—
622	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
623	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
624	#500	C₂²×C₆₇	1	2	yes	—
625	#500	C₂²×C₆₇	1	1	yes	characteristic
626	#495	C₂²×C₆₇	1	2	yes	—
627	#492	C₂²×C₆₇	1	1	yes	characteristic
628	#489	C₂²×C₆₇	1	2	yes	—
629	#489	C₂²×C₆₇	1	2	yes	—
630	#487	C₂²×C₆₇	1	1	yes	characteristic
631	#486	C₂²×C₆₇	1	1	yes	characteristic
632	#485	C₂²×C₆₇	1	2	yes	—
633	#484	C₂²×C₆₇	1	2	yes	—
634	#484	C₂²×C₆₇	1	2	yes	—
635	#482	C₂²×C₆₇	1	2	yes	—
636	#482	C₂²×C₆₇	1	2	yes	—
637	#480	C₂²×C₆₇	1	2	yes	—
638	#477	C₂²×C₆₇	1	1	yes	characteristic
639	#477	C₂²×C₆₇	1	1	yes	characteristic
640	#477	C₂²×C₆₇	1	1	yes	characteristic
641	#477	C₂²×C₆₇	1	2	yes	—
642	#477	C₂²×C₆₇	1	2	yes	—
643	#476	C₂²×C₆₇	1	1	yes	characteristic
644	#475	C₂²×C₆₇	1	2	yes	—
645	#474	C₂²×C₆₇	1	2	yes	—
646	#468	C₂²×C₆₇	1	2	yes	—
647	#468	C₂²×C₆₇	1	2	yes	—
648	#468	C₂²×C₆₇	1	2	yes	—
649	#468	C₂²×C₆₇	1	2	yes	—
650	#467	C₂²×C₆₇	1	2	yes	—
651	#466	C₂²×C₆₇	1	2	yes	—
652	#464	C₂²×C₆₇	1	2	yes	—
653	#464	C₂²×C₆₇	1	2	yes	—
654	#464	C₂²×C₆₇	1	2	yes	—
655	#463	C₂²×C₆₇	1	2	yes	—
656	#462	C₂²×C₆₇	1	1	yes	characteristic
657	#462	C₂²×C₆₇	1	1	yes	characteristic
658	#460	C₂²×C₆₇	1	1	yes	characteristic
659	#459	C₂²×C₆₇	1	1	yes	characteristic
660	#452	C₂²×C₆₇	1	2	yes	—
661	#451	C₂²×C₆₇	1	2	yes	—
662	#451	C₂²×C₆₇	1	2	yes	—
663	#449	C₂²×C₆₇	1	2	yes	—
664	#449	C₂²×C₆₇	1	2	yes	—
665	#448	C₂²×C₆₇	1	2	yes	—
666	#446	C₂²×C₆₇	1	1	yes	characteristic
667	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic
668	#441	C₂²×C₆₇	1	2	yes	—
669	#441	C₂²×C₆₇	1	1	yes	characteristic
670	#441	C₂²×C₆₇	1	1	yes	characteristic
671	#440	C₂²×C₆₇	1	2	yes	—
672	#440	C₂²×C₆₇	1	2	yes	—
673	#440	C₂²×C₆₇	1	1	yes	characteristic
674	#440	C₂²×C₆₇	1	1	yes	characteristic
675	#440	C₂²×C₆₇	1	2	yes	—
676	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
677	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
678	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
679	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
680	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
681	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
682	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
683	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
684	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
685	C₄×D₈	C₂²×C₆₇	1	2	yes	—
686	#436	C₂²×C₆₇	1	2	yes	—
687	#436	C₂²×C₆₇	1	1	yes	characteristic
688	#435	C₂²×C₆₇	1	2	yes	—
689	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
690	#433	C₂²×C₆₇	1	2	yes	—
691	#431	C₂²×C₆₇	1	1	yes	characteristic
692	#428	C₂²×C₆₇	1	1	yes	characteristic
693	#428	C₂²×C₆₇	1	2	yes	—
694	#419	C₂²×C₆₇	1	1	yes	characteristic
695	#417	C₂²×C₆₇	1	1	yes	characteristic
696	#416	C₂²×C₆₇	1	2	yes	—
697	C₂×#103	C₂²×C₆₇	1	2	yes	—
698	#405	C₂²×C₆₇	1	2	yes	—
699	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
700	C₂×#41	—	2	2	no	—
701	C₂×#41	—	2	1	no	—
702	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
703	C₂×#41	C₂³×C₆₇	1	2	yes	—
704	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
705	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
706	#137	—	2	4	no	—
707	#137	—	2	8	no	—
708	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
709	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
710	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
711	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
712	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
713	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
714	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
715	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
716	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
717	C₂×D₈	C₂³×C₆₇	1	2	yes	—
718	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
719	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
720	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
721	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
722	C₄⋊Q₈	—	2	1	no	—
723	C₄⋊Q₈	—	2	1	no	—
724	C₄⋊Q₈	—	2	1	no	—
725	C₄⋊Q₈	—	2	2	no	—
726	C₄⋊Q₈	—	2	2	no	—
727	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
728	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
729	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
730	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
731	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
732	#127	—	2	1	no	—
733	#127	C₂³×C₆₇	1	1	yes	characteristic
734	#126	—	2	2	no	—
735	#126	—	2	2	no	—
736	#126	—	2	2	no	—
737	#126	—	2	2	no	—
738	#126	—	2	2	no	—
739	#126	D₄×C₆₇	1	2	yes	—
740	#125	—	2	1	no	—
741	#125	—	2	1	no	—
742	#125	D₄×C₆₇	1	1	yes	characteristic
743	#124	—	2	1	no	—
744	#124	—	2	2	no	—
745	#124	—	2	2	no	—
746	#124	—	2	2	no	—
747	#124	—	2	2	no	—
748	#124	—	2	2	no	—
749	#124	—	2	2	no	—
750	#124	—	2	1	no	—
751	#124	D₄×C₆₇	1	1	yes	characteristic
752	#124	C₂³×C₆₇	1	2	yes	—
753	#124	C₂³×C₆₇	1	2	yes	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	#123	—	2	2	no	—
758	#123	—	2	2	no	—
759	#123	D₄×C₆₇	1	2	yes	—
760	C₂²⋊Q₈	—	2	1	no	—
761	C₂²⋊Q₈	—	2	1	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	—	2	2	no	—
765	C₂²⋊Q₈	—	2	2	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
770	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
771	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
772	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
773	#121	—	2	1	no	—
774	#121	—	2	2	no	—
775	#121	—	2	2	no	—
776	#121	—	2	1	no	—
777	#121	—	2	2	no	—
778	#121	D₄×C₆₇	1	1	yes	characteristic
779	#121	C₂³×C₆₇	1	2	yes	—
780	#121	C₂³×C₆₇	1	2	yes	—
781	#121	C₂³×C₆₇	1	2	yes	—
782	C₄×Q₈	—	2	1	no	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	—	2	2	no	—
785	C₄×Q₈	—	2	2	no	—
786	C₄×Q₈	—	2	2	no	—
787	C₄×Q₈	—	2	1	no	—
788	C₄×Q₈	—	2	1	no	—
789	C₄×Q₈	—	2	1	no	—
790	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
791	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
792	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
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	2	yes	—
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	1	no	—
812	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
813	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
814	C₄×D₄	C₂³×C₆₇	1	2	yes	—
815	C₄×D₄	C₂³×C₆₇	1	2	yes	—
816	C₄×D₄	C₂³×C₆₇	1	2	yes	—
817	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
818	#117	—	2	1	no	—
819	#117	—	2	2	no	—
820	#117	—	2	1	no	—
821	#117	—	2	1	no	—
822	#117	—	2	2	no	—
823	#117	—	2	2	no	—
824	#117	—	2	1	no	—
825	#117	C₂³×C₆₇	1	1	yes	characteristic
826	#117	C₂³×C₆₇	1	2	yes	—
827	#117	C₂³×C₆₇	1	2	yes	—
828	C₂×C₄⋊C₄	—	2	1	no	—
829	C₂×C₄⋊C₄	—	2	2	no	—
830	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
831	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
832	C₂×C₄²	—	2	1	no	—
833	C₂×C₄²	—	2	1	no	—
834	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
835	#107	C₂³×C₆₇	1	1	yes	characteristic
836	#107	C₂³×C₆₇	1	2	yes	—
837	#107	C₂³×C₆₇	1	1	yes	characteristic
838	#107	C₂³×C₆₇	1	2	yes	—
839	#107	C₂³×C₆₇	1	2	yes	—
840	#107	C₂³×C₆₇	1	2	yes	—
841	#107	C₂³×C₆₇	1	2	yes	—
842	#106	C₂³×C₆₇	1	1	yes	characteristic
843	#106	C₂³×C₆₇	1	1	yes	characteristic
844	#106	C₂³×C₆₇	1	2	yes	—
845	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
846	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
847	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
848	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
849	#103	C₂³×C₆₇	1	1	yes	characteristic
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	1	yes	characteristic
854	#103	C₂³×C₆₇	1	2	yes	—
855	#103	C₂³×C₆₇	1	1	yes	characteristic
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	2	yes	—
860	#103	C₂³×C₆₇	1	2	yes	—
861	#103	C₂³×C₆₇	1	2	yes	—
862	#102	C₂³×C₆₇	1	2	yes	—
863	#102	C₂³×C₆₇	1	2	yes	—
864	#102	C₂³×C₆₇	1	1	yes	characteristic
865	#102	C₂³×C₆₇	1	1	yes	characteristic
866	#102	C₂³×C₆₇	1	2	yes	—
867	#102	C₂³×C₆₇	1	2	yes	—
868	#102	C₂³×C₆₇	1	2	yes	—
869	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
870	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
871	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
872	#97	C₂³×C₆₇	1	1	yes	characteristic
873	#97	C₂³×C₆₇	1	1	yes	characteristic
874	#97	C₂³×C₆₇	1	2	yes	—
875	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
876	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
877	C₄×C₈	C₂³×C₆₇	1	2	yes	—
878	C₄×C₈	C₂³×C₆₇	1	2	yes	—
879	#41	—	2	2	no	—
880	#41	—	2	4	no	—
881	#41	—	4	2	no	—
882	#41	—	4	1	no	—
883	#41	—	8	2	no	—
884	#41	—	8	4	no	—
885	C₂×Q₈	—	2	1	no	—
886	C₂×Q₈	—	2	2	no	—
887	C₂×Q₈	—	2	1	no	—
888	C₂×Q₈	—	2	2	no	—
889	C₂×Q₈	—	2	2	no	—
890	C₂×Q₈	—	2	1	no	—
891	C₂×Q₈	—	2	4	no	—
892	C₂×Q₈	—	2	2	no	—
893	C₂×Q₈	—	4	2	no	—
894	C₂×Q₈	—	4	1	no	—
895	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
896	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
897	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
898	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
899	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
900	C₂×D₄	—	2	1	no	—
901	C₂×D₄	—	2	2	no	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
908	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
909	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
910	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	—	2	1	no	—
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	2	no	—
918	C₂²×C₄	—	2	1	no	—
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
922	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
923	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
924	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
925	Q₁₆	—	2	2	no	—
926	Q₁₆	—	2	4	no	—
927	Q₁₆	—	4	2	no	—
928	Q₁₆	#41×C₆₇	1	4	yes	complemented
929	SD₁₆	—	2	4	no	—
930	SD₁₆	—	2	2	no	—
931	SD₁₆	—	2	4	no	—
932	SD₁₆	—	2	2	no	—
933	SD₁₆	—	4	2	no	—
934	D₈	—	4	2	no	—
935	M₁₆	—	2	2	no	—
936	M₁₆	—	2	4	no	—
937	M₁₆	—	4	1	no	—
938	C₂×C₈	—	4	2	no	—
939	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
940	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
941	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
942	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
943	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
944	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
967	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
968	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
969	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
970	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
971	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
972	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
973	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
974	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
975	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
976	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
977	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	1	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
995	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
996	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
997	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
998	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	2	1	no	—
1001	C₄²	—	2	1	no	—
1002	C₄²	—	2	1	no	—
1003	C₄²	—	2	1	no	—
1004	C₄²	—	2	1	no	—
1005	C₄²	—	2	1	no	—
1006	C₄²	—	2	2	no	—
1007	C₄²	—	2	2	no	—
1008	C₄²	—	2	2	no	—
1009	C₄²	—	2	2	no	—
1010	C₄²	—	2	2	no	—
1011	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1012	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1013	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1014	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1015	C₄²	C₂⁴×C₆₇	1	2	yes	—
1016	C₂³	—	2	1	no	—
1017	C₂³	—	2	2	no	—
1018	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1019	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1020	Q₈	—	2	2	no	—
1021	Q₈	—	2	1	no	—
1022	Q₈	—	2	1	no	—
1023	Q₈	—	2	1	no	—
1024	Q₈	—	2	2	no	—
1025	Q₈	—	2	2	no	—
1026	Q₈	—	2	1	no	—
1027	Q₈	—	4	2	no	—
1028	Q₈	—	4	4	no	—
1029	Q₈	—	8	1	no	—
1030	Q₈	—	8	2	no	—
1031	Q₈	—	8	1	no	—
1032	Q₈	—	8	2	no	—
1033	Q₈	C₂×#41×C₆₇	1	2	yes	—
1034	Q₈	C₂×#41×C₆₇	1	2	yes	—
1035	D₄	—	2	2	no	—
1036	D₄	—	2	1	no	—
1037	D₄	—	2	2	no	—
1038	D₄	—	2	1	no	—
1039	D₄	—	2	2	no	—
1040	D₄	—	4	2	no	—
1041	D₄	—	4	4	no	—
1042	D₄	—	4	2	no	—
1043	D₄	—	4	4	no	—
1044	D₄	—	4	2	no	—
1045	D₄	—	8	1	no	—
1046	D₄	—	8	2	no	—
1047	D₄	—	8	2	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	4	1	no	—
1064	C₂×C₄	—	4	4	no	—
1065	C₂×C₄	—	4	2	no	—
1066	C₂×C₄	—	4	2	no	—
1067	C₂×C₄	—	4	4	no	—
1068	C₂×C₄	—	4	2	no	—
1069	C₂×C₄	—	4	2	no	—
1070	C₂×C₄	—	8	2	no	—
1071	C₂×C₄	—	8	2	no	—
1072	C₂×C₄	—	8	1	no	—
1073	C₂×C₄	—	8	2	no	—
1074	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1075	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1076	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1077	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1078	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1079	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1080	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1081	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1082	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1083	C₈	—	2	1	no	—
1084	C₈	—	2	2	no	—
1085	C₈	—	2	1	no	—
1086	C₈	—	2	2	no	—
1087	C₈	—	2	1	no	—
1088	C₈	C₂×#41×C₆₇	1	2	yes	—
1089	C₂²	—	2	1	no	—
1090	C₂²	—	2	2	no	—
1091	C₂²	—	2	1	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	—	2	2	no	—
1094	C₂²	—	2	1	no	—
1095	C₂²	—	4	1	no	—
1096	C₂²	—	4	2	no	—
1097	C₂²	—	4	2	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	1	no	—
1100	C₂²	—	4	2	no	—
1101	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1102	C₄	—	2	1	no	—
1103	C₄	—	2	2	no	—
1104	C₄	—	2	1	no	—
1105	C₄	—	2	1	no	—
1106	C₄	—	2	2	no	—
1107	C₄	—	2	2	no	—
1108	C₄	—	2	1	no	—
1109	C₄	—	2	2	no	—
1110	C₄	—	2	2	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	1	no	—
1113	C₄	—	4	1	no	—
1114	C₄	—	4	2	no	—
1115	C₄	—	4	1	no	—
1116	C₄	—	4	2	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	2	no	—
1119	C₄	#578×C₆₇	1	2	yes	—
1120	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1121	C₄	#585×C₆₇	1	1	yes	characteristic
1122	C₂	—	4	1	no	—
1123	C₂	—	4	2	no	—
1124	C₂	—	8	1	no	—
1125	C₂	—	8	2	no	—
1126	C₂	D₄×#41×C₆₇	1	1	yes	characteristic
1127	C₂	C₂×#578×C₆₇	1	1	yes	characteristic
1128	C₂	C₆₇×#3585	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×#3522	C₂	semidirect
2. C₆₇×#3518	C₂	semidirect
3. C₆₇×#3394	C₂	semidirect
4. Q₈×Q₁₆×C₆₇	C₂	semidirect
5. C₆₇×#3375	C₂	semidirect
6. C₆₇×#3369	C₂	semidirect
7. C₆₇×#3357	C₂	semidirect
8. C₆₇×#3353	C₂	semidirect
9. C₆₇×#3313	C₂	semidirect
10. C₆₇×#3308	C₂	semidirect
11. C₆₇×#3305	C₂	semidirect
12. C₆₇×#3299	C₂	semidirect
13. C₆₇×#3278	C₂	semidirect
14. C₆₇×#3277	C₂	semidirect
15. C₆₇×#3182	C₂	semidirect
16. C₆₇×#3175	C₂	semidirect
17. C₆₇×#3124	C₂	semidirect
18. C₆₇×#3121	C₂	semidirect
19. C₆₇×#3106	C₂	semidirect
20. C₆₇×#3104	C₂	semidirect
21. C₆₇×#2969	C₂	semidirect
22. C₆₇×#2947	C₂	semidirect
23. C₄×#137×C₆₇	C₂	semidirect
363. Q₁₆×C₆₇	#41	semidirect
557. #61558	C₆₇	direct (N × H)
565. #3522	C₂×C₆₇	semidirect
566. #3518	C₂×C₆₇	semidirect
567. #3394	C₂×C₆₇	semidirect
568. Q₈×Q₁₆	C₂×C₆₇	semidirect
569. #3375	C₂×C₆₇	semidirect
570. #3369	C₂×C₆₇	semidirect
571. #3357	C₂×C₆₇	semidirect
572. #3353	C₂×C₆₇	semidirect
573. #3313	C₂×C₆₇	semidirect
574. #3308	C₂×C₆₇	semidirect
575. #3305	C₂×C₆₇	semidirect
576. #3299	C₂×C₆₇	semidirect
577. #3278	C₂×C₆₇	semidirect
578. #3277	C₂×C₆₇	semidirect
579. #3182	C₂×C₆₇	semidirect
580. #3175	C₂×C₆₇	semidirect
581. #3124	C₂×C₆₇	semidirect
582. #3121	C₂×C₆₇	semidirect
583. #3106	C₂×C₆₇	semidirect
584. #3104	C₂×C₆₇	semidirect
585. #2969	C₂×C₆₇	semidirect
586. #2947	C₂×C₆₇	semidirect
587. C₄×#137	C₂×C₆₇	semidirect
588. C₆₇	#61558	direct (N × H)
928. Q₁₆	#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×#3522	2
C₆₇×#3518	2
C₆₇×#3394	2
Q₈×Q₁₆×C₆₇	2
C₆₇×#3375	2
C₆₇×#3369	2
C₆₇×#3357	2
C₆₇×#3353	2
C₆₇×#3313	2
C₆₇×#3308	2
C₆₇×#3305	2
C₆₇×#3299	2
C₆₇×#3278	2
C₆₇×#3277	2
C₆₇×#3182	2
C₆₇×#3175	2
C₆₇×#3124	2
C₆₇×#3121	2
C₆₇×#3106	2
C₆₇×#3104	2
C₆₇×#2969	2
C₆₇×#2947	2
C₄×#137×C₆₇	2
#61558	67

Subgroups — C67×#61558 #30740809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61558 #30740809