Subgroups — C₆₇×#61607 #30740858

Order 17152.

2112 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3501	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#3333	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3331	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3316	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3314	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3299	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3295	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×Q₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×SD₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3278	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3276	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3270	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3266	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3216	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3210	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3196	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3190	C₂	1	2	yes	maximal, complemented
19	C₆₇×#3116	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3107	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#3007	C₂	1	2	yes	maximal, complemented
22	C₂×#452×C₆₇	C₂	1	2	yes	maximal, complemented
23	C₆₇×#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₆₇	C₂²	1	2	yes	—
25	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
26	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
27	C₂²×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
28	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
29	#554×C₆₇	—	2	1	no	—
30	#554×C₆₇	—	2	2	no	—
31	#554×C₆₇	—	2	1	no	—
32	#554×C₆₇	C₂²	1	1	yes	characteristic
33	#554×C₆₇	C₂²	1	2	yes	complemented
34	#554×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	#550×C₆₇	C₂²	1	1	yes	characteristic
36	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
37	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
39	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	#548×C₆₇	C₂²	1	2	yes	—
41	#547×C₆₇	—	2	1	no	—
42	#547×C₆₇	C₂²	1	1	yes	characteristic
43	#546×C₆₇	—	2	2	no	—
44	#546×C₆₇	C₂²	1	2	yes	—
45	D₄²×C₆₇	—	2	1	no	—
46	D₄²×C₆₇	C₂²	1	1	yes	characteristic
47	#544×C₆₇	—	2	1	no	—
48	#543×C₆₇	—	2	2	no	—
49	#533×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	#533×C₆₇	C₂²	1	1	yes	characteristic, complemented
51	#532×C₆₇	—	2	1	no	—
52	#532×C₆₇	C₂²	1	1	yes	characteristic
53	#525×C₆₇	—	2	2	no	—
54	#525×C₆₇	C₂²	1	2	yes	—
55	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
56	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
57	#518×C₆₇	—	2	1	no	—
58	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
59	C₂×C₄×D₄×C₆₇	—	2	1	no	—
60	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
61	#497×C₆₇	C₂²	1	2	yes	complemented
62	#494×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	#492×C₆₇	C₂²	1	1	yes	characteristic, complemented
64	#489×C₆₇	C₂²	1	2	yes	complemented
65	#487×C₆₇	C₂²	1	1	yes	characteristic, complemented
66	#486×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	#485×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	#485×C₆₇	C₂²	1	1	yes	characteristic, complemented
69	#485×C₆₇	C₂²	1	2	yes	complemented
70	#484×C₆₇	C₂²	1	2	yes	complemented
71	#483×C₆₇	C₂²	1	2	yes	complemented
72	#481×C₆₇	C₂²	1	2	yes	complemented
73	#480×C₆₇	C₂²	1	2	yes	complemented
74	#477×C₆₇	C₂²	1	1	yes	characteristic, complemented
75	#476×C₆₇	C₂²	1	1	yes	characteristic, complemented
76	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
77	#474×C₆₇	C₂²	1	1	yes	characteristic, complemented
78	#470×C₆₇	C₂²	1	2	yes	complemented
79	#470×C₆₇	C₂²	1	2	yes	complemented
80	#468×C₆₇	C₂²	1	2	yes	complemented
81	#468×C₆₇	C₂²	1	2	yes	complemented
82	#467×C₆₇	C₂²	1	2	yes	complemented
83	#467×C₆₇	C₂²	1	2	yes	complemented
84	#465×C₆₇	C₂²	1	2	yes	complemented
85	#465×C₆₇	C₂²	1	2	yes	complemented
86	#464×C₆₇	C₂²	1	2	yes	complemented
87	#464×C₆₇	C₂²	1	2	yes	complemented
88	#462×C₆₇	C₂²	1	1	yes	characteristic, complemented
89	#462×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	#462×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	#462×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	#461×C₆₇	C₂²	1	1	yes	characteristic, complemented
93	#461×C₆₇	C₂²	1	1	yes	characteristic, complemented
94	#460×C₆₇	C₂²	1	1	yes	characteristic, complemented
95	#460×C₆₇	C₂²	1	1	yes	characteristic, complemented
96	#452×C₆₇	C₂²	1	1	yes	characteristic
97	#452×C₆₇	C₂²	1	1	yes	characteristic
98	#452×C₆₇	C₂²	1	2	yes	—
99	#452×C₆₇	C₂²	1	2	yes	complemented
100	#452×C₆₇	C₂²	1	2	yes	complemented
101	#452×C₆₇	C₂²	1	2	yes	complemented
102	#452×C₆₇	C₂²	1	2	yes	complemented
103	#452×C₆₇	C₂²	1	2	yes	complemented
104	#452×C₆₇	C₂²	1	2	yes	complemented
105	#452×C₆₇	C₂²	1	2	yes	complemented
106	#452×C₆₇	C₂²	1	2	yes	complemented
107	#451×C₆₇	C₂²	1	2	yes	complemented
108	#451×C₆₇	C₂²	1	2	yes	complemented
109	#451×C₆₇	C₂²	1	2	yes	complemented
110	#451×C₆₇	C₂²	1	2	yes	complemented
111	#450×C₆₇	C₂²	1	2	yes	complemented
112	#450×C₆₇	C₂²	1	2	yes	complemented
113	#448×C₆₇	C₂²	1	2	yes	complemented
114	#448×C₆₇	C₂²	1	2	yes	complemented
115	#441×C₆₇	C₂²	1	2	yes	complemented
116	#440×C₆₇	C₂²	1	2	yes	complemented
117	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
120	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
121	#436×C₆₇	C₂²	1	1	yes	characteristic, complemented
122	#436×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	#435×C₆₇	C₂²	1	2	yes	complemented
124	#435×C₆₇	C₂²	1	2	yes	complemented
125	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
126	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
127	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
128	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
129	#417×C₆₇	C₂²	1	2	yes	complemented
130	#417×C₆₇	C₂²	1	2	yes	complemented
131	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
132	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
133	#407×C₆₇	C₂²	1	2	yes	complemented
134	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
135	C₂×#41×C₆₇	—	2	2	no	—
136	C₂×#41×C₆₇	—	2	2	no	—
137	C₂×#41×C₆₇	—	4	4	no	—
138	C₂×#41×C₆₇	—	4	4	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	C₂×#41×C₆₇	C₂³	1	2	yes	—
143	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
144	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
145	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
146	C₂²×D₄×C₆₇	—	2	2	no	—
147	C₂²×D₄×C₆₇	—	2	1	no	—
148	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
149	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
150	C₂³×C₄×C₆₇	—	2	2	no	—
151	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
152	#137×C₆₇	—	4	4	no	—
153	#137×C₆₇	—	4	4	no	—
154	C₂×Q₁₆×C₆₇	—	4	4	no	—
155	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
157	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
158	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
159	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
160	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
161	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
162	C₂×SD₁₆×C₆₇	—	4	4	no	—
163	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
164	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
165	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
166	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
167	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
168	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
169	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
170	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
171	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
172	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
173	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
174	C₄⋊Q₈×C₆₇	—	2	1	no	—
175	C₄⋊Q₈×C₆₇	—	2	1	no	—
176	C₄⋊Q₈×C₆₇	—	2	1	no	—
177	C₄⋊Q₈×C₆₇	—	2	2	no	—
178	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
179	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
180	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
181	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
182	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
183	#127×C₆₇	—	2	1	no	—
184	#127×C₆₇	C₂³	1	1	yes	characteristic
185	#125×C₆₇	—	2	1	no	—
186	#125×C₆₇	—	2	1	no	—
187	#125×C₆₇	—	2	2	no	—
188	#125×C₆₇	—	2	1	no	—
189	#125×C₆₇	—	2	1	no	—
190	#124×C₆₇	—	2	2	no	—
191	#124×C₆₇	C₂³	1	2	yes	—
192	#123×C₆₇	—	2	2	no	—
193	#123×C₆₇	—	2	2	no	—
194	#123×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	C₂²⋊Q₈×C₆₇	—	2	2	no	—
199	C₂²⋊Q₈×C₆₇	—	2	1	no	—
200	C₂²⋊Q₈×C₆₇	—	2	1	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	—	2	2	no	—
205	C₂²⋊Q₈×C₆₇	—	2	2	no	—
206	C₂²⋊Q₈×C₆₇	—	2	2	no	—
207	C₂²⋊Q₈×C₆₇	—	2	2	no	—
208	C₂²⋊Q₈×C₆₇	—	2	2	no	—
209	C₂²⋊Q₈×C₆₇	—	2	2	no	—
210	C₂²⋊Q₈×C₆₇	—	2	2	no	—
211	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
212	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
213	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
214	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
215	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
216	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
217	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
218	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
219	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
220	#121×C₆₇	—	2	2	no	—
221	#121×C₆₇	—	2	1	no	—
222	#121×C₆₇	—	2	1	no	—
223	#121×C₆₇	—	2	1	no	—
224	#121×C₆₇	—	2	1	no	—
225	#121×C₆₇	—	2	2	no	—
226	#121×C₆₇	—	2	2	no	—
227	#121×C₆₇	C₂³	1	2	yes	—
228	#121×C₆₇	C₂³	1	2	yes	—
229	#120×C₆₇	—	2	2	no	—
230	#120×C₆₇	—	2	2	no	—
231	#120×C₆₇	—	2	2	no	—
232	C₄×Q₈×C₆₇	—	2	1	no	—
233	C₄×Q₈×C₆₇	—	2	1	no	—
234	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
235	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
238	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
239	C₄×D₄×C₆₇	—	2	1	no	—
240	C₄×D₄×C₆₇	—	2	1	no	—
241	C₄×D₄×C₆₇	—	2	2	no	—
242	C₄×D₄×C₆₇	—	2	1	no	—
243	C₄×D₄×C₆₇	—	2	1	no	—
244	C₄×D₄×C₆₇	—	2	2	no	—
245	C₄×D₄×C₆₇	—	2	1	no	—
246	C₄×D₄×C₆₇	—	2	2	no	—
247	C₄×D₄×C₆₇	—	2	1	no	—
248	C₄×D₄×C₆₇	—	2	1	no	—
249	C₄×D₄×C₆₇	—	2	2	no	—
250	C₄×D₄×C₆₇	—	2	1	no	—
251	C₄×D₄×C₆₇	—	2	2	no	—
252	C₄×D₄×C₆₇	—	2	1	no	—
253	C₄×D₄×C₆₇	—	2	1	no	—
254	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
255	C₄×D₄×C₆₇	D₄	1	2	yes	—
256	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
257	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₆₇	C₂³	1	2	yes	—
261	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
262	#117×C₆₇	—	2	1	no	—
263	#117×C₆₇	—	2	1	no	—
264	#117×C₆₇	—	2	1	no	—
265	#117×C₆₇	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
267	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
268	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
269	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
270	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
271	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
272	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
273	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
274	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
275	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
276	C₂×C₄²×C₆₇	—	2	1	no	—
277	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
278	#107×C₆₇	C₂³	1	1	yes	characteristic
279	#107×C₆₇	C₂³	1	2	yes	—
280	#107×C₆₇	C₂³	1	1	yes	characteristic
281	#106×C₆₇	C₂³	1	1	yes	characteristic
282	#106×C₆₇	C₂³	1	2	yes	—
283	#106×C₆₇	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
285	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
286	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
287	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
288	#103×C₆₇	C₂³	1	1	yes	characteristic
289	#103×C₆₇	C₂³	1	1	yes	characteristic
290	#103×C₆₇	C₂³	1	2	yes	—
291	#103×C₆₇	C₂³	1	2	yes	—
292	#103×C₆₇	C₂³	1	1	yes	characteristic
293	#103×C₆₇	C₂³	1	1	yes	characteristic
294	#103×C₆₇	C₂³	1	1	yes	characteristic
295	#103×C₆₇	C₂³	1	2	yes	—
296	#103×C₆₇	C₂³	1	2	yes	—
297	#103×C₆₇	C₂³	1	2	yes	—
298	#103×C₆₇	C₂³	1	1	yes	characteristic
299	#103×C₆₇	C₂³	1	2	yes	—
300	#103×C₆₇	C₂³	1	2	yes	—
301	#102×C₆₇	C₂³	1	1	yes	characteristic
302	#102×C₆₇	C₂³	1	2	yes	—
303	#102×C₆₇	C₂³	1	2	yes	—
304	#102×C₆₇	C₂³	1	2	yes	—
305	#102×C₆₇	C₂³	1	1	yes	characteristic
306	#102×C₆₇	C₂³	1	2	yes	—
307	#102×C₆₇	C₂³	1	2	yes	—
308	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
309	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
311	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
312	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
313	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
314	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
315	#97×C₆₇	C₂³	1	2	yes	—
316	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
317	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
318	C₂⁴×C₆₇	—	2	2	no	—
319	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
320	#41×C₆₇	—	2	2	no	—
321	#41×C₆₇	—	2	2	no	—
322	#41×C₆₇	—	2	4	no	—
323	#41×C₆₇	—	2	4	no	—
324	#41×C₆₇	—	4	2	no	—
325	#41×C₆₇	—	4	2	no	—
326	#41×C₆₇	—	4	2	no	—
327	#41×C₆₇	—	4	2	no	—
328	#41×C₆₇	—	4	8	no	—
329	#41×C₆₇	—	4	8	no	—
330	C₂×Q₈×C₆₇	—	2	2	no	—
331	C₂×Q₈×C₆₇	—	2	1	no	—
332	C₂×Q₈×C₆₇	—	2	1	no	—
333	C₂×Q₈×C₆₇	—	2	2	no	—
334	C₂×Q₈×C₆₇	—	2	2	no	—
335	C₂×Q₈×C₆₇	—	2	4	no	—
336	C₂×Q₈×C₆₇	—	4	2	no	—
337	C₂×Q₈×C₆₇	—	4	2	no	—
338	C₂×Q₈×C₆₇	—	4	2	no	—
339	C₂×Q₈×C₆₇	—	4	2	no	—
340	C₂×Q₈×C₆₇	—	4	2	no	—
341	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
342	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
343	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
344	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
345	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
346	C₂×D₄×C₆₇	—	2	1	no	—
347	C₂×D₄×C₆₇	—	2	4	no	—
348	C₂×D₄×C₆₇	—	2	4	no	—
349	C₂×D₄×C₆₇	—	2	2	no	—
350	C₂×D₄×C₆₇	—	2	2	no	—
351	C₂×D₄×C₆₇	—	2	2	no	—
352	C₂×D₄×C₆₇	—	2	2	no	—
353	C₂×D₄×C₆₇	—	2	2	no	—
354	C₂×D₄×C₆₇	—	2	1	no	—
355	C₂×D₄×C₆₇	—	2	2	no	—
356	C₂×D₄×C₆₇	—	2	1	no	—
357	C₂×D₄×C₆₇	—	4	2	no	—
358	C₂×D₄×C₆₇	—	4	8	no	—
359	C₂×D₄×C₆₇	—	4	4	no	—
360	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
361	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
362	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
363	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
364	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₆₇	—	2	1	no	—
366	C₂²×C₄×C₆₇	—	2	2	no	—
367	C₂²×C₄×C₆₇	—	2	2	no	—
368	C₂²×C₄×C₆₇	—	2	2	no	—
369	C₂²×C₄×C₆₇	—	2	2	no	—
370	C₂²×C₄×C₆₇	—	2	2	no	—
371	C₂²×C₄×C₆₇	—	2	1	no	—
372	C₂²×C₄×C₆₇	—	2	2	no	—
373	C₂²×C₄×C₆₇	—	2	2	no	—
374	C₂²×C₄×C₆₇	—	2	2	no	—
375	C₂²×C₄×C₆₇	—	2	1	no	—
376	C₂²×C₄×C₆₇	—	4	2	no	—
377	C₂²×C₄×C₆₇	—	4	2	no	—
378	C₂²×C₄×C₆₇	—	4	8	no	—
379	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
380	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
381	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
382	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
383	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
384	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
385	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
386	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
387	Q₁₆×C₆₇	—	2	2	no	—
388	Q₁₆×C₆₇	—	2	4	no	—
389	Q₁₆×C₆₇	—	2	2	no	—
390	Q₁₆×C₆₇	—	4	2	no	—
391	Q₁₆×C₆₇	—	4	2	no	—
392	Q₁₆×C₆₇	—	4	2	no	—
393	Q₁₆×C₆₇	—	4	2	no	—
394	SD₁₆×C₆₇	—	2	2	no	—
395	SD₁₆×C₆₇	—	2	4	no	—
396	SD₁₆×C₆₇	—	2	2	no	—
397	SD₁₆×C₆₇	—	4	2	no	—
398	SD₁₆×C₆₇	—	4	2	no	—
399	SD₁₆×C₆₇	—	4	2	no	—
400	SD₁₆×C₆₇	—	4	2	no	—
401	M₁₆×C₆₇	—	4	2	no	—
402	M₁₆×C₆₇	—	4	2	no	—
403	C₂×C₈×C₆₇	—	4	2	no	—
404	C₂×C₈×C₆₇	—	4	2	no	—
405	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
406	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
407	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
408	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
409	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
410	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₆₇	—	2	1	no	—
412	C₄⋊C₄×C₆₇	—	2	2	no	—
413	C₄⋊C₄×C₆₇	—	2	1	no	—
414	C₄⋊C₄×C₆₇	—	2	1	no	—
415	C₄⋊C₄×C₆₇	—	2	2	no	—
416	C₄⋊C₄×C₆₇	—	2	2	no	—
417	C₄⋊C₄×C₆₇	—	2	2	no	—
418	C₄⋊C₄×C₆₇	—	2	2	no	—
419	C₄⋊C₄×C₆₇	—	2	2	no	—
420	C₄⋊C₄×C₆₇	—	2	2	no	—
421	C₄⋊C₄×C₆₇	—	2	2	no	—
422	C₄⋊C₄×C₆₇	—	2	1	no	—
423	C₄⋊C₄×C₆₇	—	2	1	no	—
424	C₄⋊C₄×C₆₇	—	2	1	no	—
425	C₄⋊C₄×C₆₇	—	2	1	no	—
426	C₄⋊C₄×C₆₇	—	2	1	no	—
427	C₄⋊C₄×C₆₇	—	2	1	no	—
428	C₄⋊C₄×C₆₇	—	2	1	no	—
429	C₄⋊C₄×C₆₇	—	2	2	no	—
430	C₄⋊C₄×C₆₇	—	2	1	no	—
431	C₄⋊C₄×C₆₇	—	2	1	no	—
432	C₄⋊C₄×C₆₇	—	2	2	no	—
433	C₄⋊C₄×C₆₇	—	2	1	no	—
434	C₄⋊C₄×C₆₇	—	2	1	no	—
435	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
436	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
437	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
438	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
440	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
441	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
442	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
443	C₂²⋊C₄×C₆₇	—	2	1	no	—
444	C₂²⋊C₄×C₆₇	—	2	2	no	—
445	C₂²⋊C₄×C₆₇	—	2	1	no	—
446	C₂²⋊C₄×C₆₇	—	2	2	no	—
447	C₂²⋊C₄×C₆₇	—	2	2	no	—
448	C₂²⋊C₄×C₆₇	—	2	2	no	—
449	C₂²⋊C₄×C₆₇	—	2	2	no	—
450	C₂²⋊C₄×C₆₇	—	2	2	no	—
451	C₂²⋊C₄×C₆₇	—	2	1	no	—
452	C₂²⋊C₄×C₆₇	—	2	2	no	—
453	C₂²⋊C₄×C₆₇	—	2	2	no	—
454	C₂²⋊C₄×C₆₇	—	2	2	no	—
455	C₂²⋊C₄×C₆₇	—	2	1	no	—
456	C₂²⋊C₄×C₆₇	—	2	1	no	—
457	C₂²⋊C₄×C₆₇	—	2	2	no	—
458	C₂²⋊C₄×C₆₇	—	2	2	no	—
459	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
460	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
461	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
462	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
463	C₄²×C₆₇	—	2	1	no	—
464	C₄²×C₆₇	—	2	1	no	—
465	C₄²×C₆₇	—	2	1	no	—
466	C₄²×C₆₇	—	2	2	no	—
467	C₄²×C₆₇	—	2	1	no	—
468	C₄²×C₆₇	—	2	1	no	—
469	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
470	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
471	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
472	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
473	C₂³×C₆₇	—	2	1	no	—
474	C₂³×C₆₇	—	2	4	no	—
475	C₂³×C₆₇	—	2	2	no	—
476	C₂³×C₆₇	—	4	2	no	—
477	C₂³×C₆₇	—	4	2	no	—
478	C₂³×C₆₇	—	4	4	no	—
479	C₂³×C₆₇	—	4	4	no	—
480	C₂³×C₆₇	—	8	2	no	—
481	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
482	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
483	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
484	Q₈×C₆₇	—	2	1	no	—
485	Q₈×C₆₇	—	2	1	no	—
486	Q₈×C₆₇	—	2	2	no	—
487	Q₈×C₆₇	—	2	1	no	—
488	Q₈×C₆₇	—	2	1	no	—
489	Q₈×C₆₇	—	2	2	no	—
490	Q₈×C₆₇	—	2	1	no	—
491	Q₈×C₆₇	—	2	2	no	—
492	Q₈×C₆₇	—	2	2	no	—
493	Q₈×C₆₇	—	4	4	no	—
494	Q₈×C₆₇	—	8	1	no	—
495	Q₈×C₆₇	—	8	1	no	—
496	Q₈×C₆₇	—	8	2	no	—
497	Q₈×C₆₇	—	8	2	no	—
498	Q₈×C₆₇	H(5,𝔽₂)	1	2	yes	—
499	D₄×C₆₇	—	2	4	no	—
500	D₄×C₆₇	—	2	4	no	—
501	D₄×C₆₇	—	2	2	no	—
502	D₄×C₆₇	—	2	1	no	—
503	D₄×C₆₇	—	2	2	no	—
504	D₄×C₆₇	—	2	2	no	—
505	D₄×C₆₇	—	4	4	no	—
506	D₄×C₆₇	—	4	4	no	—
507	D₄×C₆₇	—	4	4	no	—
508	D₄×C₆₇	—	4	4	no	—
509	D₄×C₆₇	—	4	4	no	—
510	D₄×C₆₇	—	4	2	no	—
511	D₄×C₆₇	—	8	1	no	—
512	D₄×C₆₇	—	8	2	no	—
513	D₄×C₆₇	#137	1	4	yes	complemented
514	D₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
515	C₂×C₄×C₆₇	—	2	4	no	—
516	C₂×C₄×C₆₇	—	2	1	no	—
517	C₂×C₄×C₆₇	—	2	2	no	—
518	C₂×C₄×C₆₇	—	2	2	no	—
519	C₂×C₄×C₆₇	—	2	2	no	—
520	C₂×C₄×C₆₇	—	2	2	no	—
521	C₂×C₄×C₆₇	—	2	2	no	—
522	C₂×C₄×C₆₇	—	2	1	no	—
523	C₂×C₄×C₆₇	—	2	1	no	—
524	C₂×C₄×C₆₇	—	2	1	no	—
525	C₂×C₄×C₆₇	—	2	1	no	—
526	C₂×C₄×C₆₇	—	2	2	no	—
527	C₂×C₄×C₆₇	—	2	1	no	—
528	C₂×C₄×C₆₇	—	2	1	no	—
529	C₂×C₄×C₆₇	—	2	1	no	—
530	C₂×C₄×C₆₇	—	2	2	no	—
531	C₂×C₄×C₆₇	—	2	1	no	—
532	C₂×C₄×C₆₇	—	2	2	no	—
533	C₂×C₄×C₆₇	—	4	2	no	—
534	C₂×C₄×C₆₇	—	4	2	no	—
535	C₂×C₄×C₆₇	—	4	2	no	—
536	C₂×C₄×C₆₇	—	4	1	no	—
537	C₂×C₄×C₆₇	—	4	4	no	—
538	C₂×C₄×C₆₇	—	4	4	no	—
539	C₂×C₄×C₆₇	—	4	4	no	—
540	C₂×C₄×C₆₇	—	4	4	no	—
541	C₂×C₄×C₆₇	—	4	2	no	—
542	C₂×C₄×C₆₇	—	8	1	no	—
543	C₂×C₄×C₆₇	—	8	2	no	—
544	C₂×C₄×C₆₇	—	8	2	no	—
545	C₂×C₄×C₆₇	—	8	2	no	—
546	C₂×C₄×C₆₇	—	8	2	no	—
547	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
548	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
549	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
550	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
552	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
553	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
555	C₈×C₆₇	—	2	1	no	—
556	C₈×C₆₇	—	2	1	no	—
557	C₈×C₆₇	—	2	2	no	—
558	C₈×C₆₇	—	2	2	no	—
559	C₈×C₆₇	—	2	1	no	—
560	C₈×C₆₇	—	2	1	no	—
561	C₂²×C₆₇	—	2	2	no	—
562	C₂²×C₆₇	—	2	2	no	—
563	C₂²×C₆₇	—	2	1	no	—
564	C₂²×C₆₇	—	2	2	no	—
565	C₂²×C₆₇	—	2	1	no	—
566	C₂²×C₆₇	—	2	2	no	—
567	C₂²×C₆₇	—	2	2	no	—
568	C₂²×C₆₇	—	2	1	no	—
569	C₂²×C₆₇	—	2	2	no	—
570	C₂²×C₆₇	—	4	1	no	—
571	C₂²×C₆₇	—	4	1	no	—
572	C₂²×C₆₇	—	4	2	no	—
573	C₂²×C₆₇	—	4	2	no	—
574	C₂²×C₆₇	—	4	2	no	—
575	C₂²×C₆₇	—	8	4	no	—
576	C₂²×C₆₇	—	8	8	no	—
577	C₂²×C₆₇	C₂×#137	1	4	yes	—
578	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
579	C₄×C₆₇	—	2	1	no	—
580	C₄×C₆₇	—	2	1	no	—
581	C₄×C₆₇	—	2	1	no	—
582	C₄×C₆₇	—	2	2	no	—
583	C₄×C₆₇	—	2	2	no	—
584	C₄×C₆₇	—	2	2	no	—
585	C₄×C₆₇	—	2	1	no	—
586	C₄×C₆₇	—	4	1	no	—
587	C₄×C₆₇	—	4	2	no	—
588	C₄×C₆₇	—	4	1	no	—
589	C₄×C₆₇	—	4	1	no	—
590	C₄×C₆₇	—	4	2	no	—
591	C₄×C₆₇	—	4	1	no	—
592	C₄×C₆₇	—	4	2	no	—
593	C₄×C₆₇	—	4	1	no	—
594	C₄×C₆₇	—	4	1	no	—
595	C₄×C₆₇	C₂×#137	1	2	yes	—
596	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
597	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
598	#61607	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
599	C₂×C₆₇	—	2	4	no	—
600	C₂×C₆₇	—	4	2	no	—
601	C₂×C₆₇	—	4	1	no	—
602	C₂×C₆₇	—	4	2	no	—
603	C₂×C₆₇	—	8	2	no	—
604	C₂×C₆₇	#3484	1	1	yes	characteristic
605	C₂×C₆₇	C₂²×#137	1	1	yes	characteristic
606	C₂×C₆₇	#3584	1	1	yes	characteristic
607	#3501	C₂×C₆₇	1	1	yes	characteristic, complemented
608	D₄×#41	C₂×C₆₇	1	1	yes	characteristic
609	#3333	C₂×C₆₇	1	1	yes	characteristic, complemented
610	#3331	C₂×C₆₇	1	1	yes	characteristic, complemented
611	#3316	C₂×C₆₇	1	2	yes	complemented
612	#3314	C₂×C₆₇	1	2	yes	complemented
613	#3299	C₂×C₆₇	1	1	yes	characteristic, complemented
614	#3295	C₂×C₆₇	1	1	yes	characteristic, complemented
615	D₄×Q₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
616	D₄×SD₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
617	#3278	C₂×C₆₇	1	1	yes	characteristic, complemented
618	#3276	C₂×C₆₇	1	1	yes	characteristic, complemented
619	#3270	C₂×C₆₇	1	2	yes	complemented
620	#3266	C₂×C₆₇	1	2	yes	complemented
621	#3216	C₂×C₆₇	1	1	yes	characteristic, complemented
622	#3210	C₂×C₆₇	1	1	yes	characteristic, complemented
623	#3196	C₂×C₆₇	1	2	yes	complemented
624	#3190	C₂×C₆₇	1	2	yes	complemented
625	#3116	C₂×C₆₇	1	1	yes	characteristic, complemented
626	#3107	C₂×C₆₇	1	1	yes	characteristic, complemented
627	#3007	C₂×C₆₇	1	2	yes	complemented
628	C₂×#452	C₂×C₆₇	1	2	yes	complemented
629	#2974	C₂×C₆₇	1	1	yes	characteristic, complemented
630	C₆₇	#61607	1	1	yes	characteristic, direct product factor, Sylow
631	C₂²×#41	C₂²×C₆₇	1	2	yes	—
632	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
633	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
634	C₂²×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
635	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
636	#554	—	2	1	no	—
637	#554	—	2	2	no	—
638	#554	—	2	1	no	—
639	#554	C₂²×C₆₇	1	1	yes	characteristic
640	#554	C₂²×C₆₇	1	1	yes	characteristic, complemented
641	#554	C₂²×C₆₇	1	2	yes	complemented
642	#550	C₂²×C₆₇	1	1	yes	characteristic
643	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
644	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
645	D₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
646	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
647	#548	C₂²×C₆₇	1	2	yes	—
648	#547	—	2	1	no	—
649	#547	C₂²×C₆₇	1	1	yes	characteristic
650	#546	—	2	2	no	—
651	#546	C₂²×C₆₇	1	2	yes	—
652	D₄²	—	2	1	no	—
653	D₄²	C₂²×C₆₇	1	1	yes	characteristic
654	#544	—	2	1	no	—
655	#543	—	2	2	no	—
656	#533	C₂²×C₆₇	1	1	yes	characteristic, complemented
657	#533	C₂²×C₆₇	1	1	yes	characteristic, complemented
658	#532	—	2	1	no	—
659	#532	C₂²×C₆₇	1	1	yes	characteristic
660	#525	—	2	2	no	—
661	#525	C₂²×C₆₇	1	2	yes	—
662	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
663	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
664	#518	—	2	1	no	—
665	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
666	C₂×C₄×D₄	—	2	1	no	—
667	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
668	#497	C₂²×C₆₇	1	2	yes	complemented
669	#494	C₂²×C₆₇	1	1	yes	characteristic, complemented
670	#492	C₂²×C₆₇	1	1	yes	characteristic, complemented
671	#489	C₂²×C₆₇	1	2	yes	complemented
672	#487	C₂²×C₆₇	1	1	yes	characteristic, complemented
673	#486	C₂²×C₆₇	1	1	yes	characteristic, complemented
674	#485	C₂²×C₆₇	1	1	yes	characteristic, complemented
675	#485	C₂²×C₆₇	1	1	yes	characteristic, complemented
676	#485	C₂²×C₆₇	1	2	yes	complemented
677	#484	C₂²×C₆₇	1	2	yes	complemented
678	#483	C₂²×C₆₇	1	2	yes	complemented
679	#481	C₂²×C₆₇	1	2	yes	complemented
680	#480	C₂²×C₆₇	1	2	yes	complemented
681	#477	C₂²×C₆₇	1	1	yes	characteristic, complemented
682	#476	C₂²×C₆₇	1	1	yes	characteristic, complemented
683	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
684	#474	C₂²×C₆₇	1	1	yes	characteristic, complemented
685	#470	C₂²×C₆₇	1	2	yes	complemented
686	#470	C₂²×C₆₇	1	2	yes	complemented
687	#468	C₂²×C₆₇	1	2	yes	complemented
688	#468	C₂²×C₆₇	1	2	yes	complemented
689	#467	C₂²×C₆₇	1	2	yes	complemented
690	#467	C₂²×C₆₇	1	2	yes	complemented
691	#465	C₂²×C₆₇	1	2	yes	complemented
692	#465	C₂²×C₆₇	1	2	yes	complemented
693	#464	C₂²×C₆₇	1	2	yes	complemented
694	#464	C₂²×C₆₇	1	2	yes	complemented
695	#462	C₂²×C₆₇	1	1	yes	characteristic, complemented
696	#462	C₂²×C₆₇	1	1	yes	characteristic, complemented
697	#462	C₂²×C₆₇	1	1	yes	characteristic, complemented
698	#462	C₂²×C₆₇	1	1	yes	characteristic, complemented
699	#461	C₂²×C₆₇	1	1	yes	characteristic, complemented
700	#461	C₂²×C₆₇	1	1	yes	characteristic, complemented
701	#460	C₂²×C₆₇	1	1	yes	characteristic, complemented
702	#460	C₂²×C₆₇	1	1	yes	characteristic, complemented
703	#452	C₂²×C₆₇	1	1	yes	characteristic
704	#452	C₂²×C₆₇	1	1	yes	characteristic
705	#452	C₂²×C₆₇	1	2	yes	—
706	#452	C₂²×C₆₇	1	2	yes	complemented
707	#452	C₂²×C₆₇	1	2	yes	complemented
708	#452	C₂²×C₆₇	1	2	yes	complemented
709	#452	C₂²×C₆₇	1	2	yes	complemented
710	#452	C₂²×C₆₇	1	2	yes	complemented
711	#452	C₂²×C₆₇	1	2	yes	complemented
712	#452	C₂²×C₆₇	1	2	yes	complemented
713	#452	C₂²×C₆₇	1	2	yes	complemented
714	#451	C₂²×C₆₇	1	2	yes	complemented
715	#451	C₂²×C₆₇	1	2	yes	complemented
716	#451	C₂²×C₆₇	1	2	yes	complemented
717	#451	C₂²×C₆₇	1	2	yes	complemented
718	#450	C₂²×C₆₇	1	2	yes	complemented
719	#450	C₂²×C₆₇	1	2	yes	complemented
720	#448	C₂²×C₆₇	1	2	yes	complemented
721	#448	C₂²×C₆₇	1	2	yes	complemented
722	#441	C₂²×C₆₇	1	2	yes	complemented
723	#440	C₂²×C₆₇	1	2	yes	complemented
724	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
725	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
726	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
727	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
728	#436	C₂²×C₆₇	1	1	yes	characteristic, complemented
729	#436	C₂²×C₆₇	1	1	yes	characteristic, complemented
730	#435	C₂²×C₆₇	1	2	yes	complemented
731	#435	C₂²×C₆₇	1	2	yes	complemented
732	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
733	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
734	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
735	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
736	#417	C₂²×C₆₇	1	2	yes	complemented
737	#417	C₂²×C₆₇	1	2	yes	complemented
738	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
739	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
740	#407	C₂²×C₆₇	1	2	yes	complemented
741	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
742	C₂×#41	—	2	2	no	—
743	C₂×#41	—	2	2	no	—
744	C₂×#41	—	4	4	no	—
745	C₂×#41	—	4	4	no	—
746	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
747	C₂×#41	C₂³×C₆₇	1	2	yes	—
748	C₂×#41	C₂³×C₆₇	1	2	yes	—
749	C₂×#41	C₂³×C₆₇	1	2	yes	—
750	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
751	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
752	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
753	C₂²×D₄	—	2	2	no	—
754	C₂²×D₄	—	2	1	no	—
755	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
756	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
757	C₂³×C₄	—	2	2	no	—
758	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
759	#137	—	4	4	no	—
760	#137	—	4	4	no	—
761	C₂×Q₁₆	—	4	4	no	—
762	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
763	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
764	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
765	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
766	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
767	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
768	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
769	C₂×SD₁₆	—	4	4	no	—
770	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
771	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
772	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
773	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
774	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
775	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
776	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
777	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
778	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
779	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
780	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
781	C₄⋊Q₈	—	2	1	no	—
782	C₄⋊Q₈	—	2	1	no	—
783	C₄⋊Q₈	—	2	1	no	—
784	C₄⋊Q₈	—	2	2	no	—
785	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
786	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
787	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
788	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
789	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
790	#127	—	2	1	no	—
791	#127	C₂³×C₆₇	1	1	yes	characteristic
792	#125	—	2	1	no	—
793	#125	—	2	1	no	—
794	#125	—	2	2	no	—
795	#125	—	2	1	no	—
796	#125	—	2	1	no	—
797	#124	—	2	2	no	—
798	#124	C₂³×C₆₇	1	2	yes	—
799	#123	—	2	2	no	—
800	#123	—	2	2	no	—
801	#123	—	2	2	no	—
802	C₂²⋊Q₈	—	2	2	no	—
803	C₂²⋊Q₈	—	2	2	no	—
804	C₂²⋊Q₈	—	2	2	no	—
805	C₂²⋊Q₈	—	2	2	no	—
806	C₂²⋊Q₈	—	2	1	no	—
807	C₂²⋊Q₈	—	2	1	no	—
808	C₂²⋊Q₈	—	2	2	no	—
809	C₂²⋊Q₈	—	2	2	no	—
810	C₂²⋊Q₈	—	2	2	no	—
811	C₂²⋊Q₈	—	2	2	no	—
812	C₂²⋊Q₈	—	2	2	no	—
813	C₂²⋊Q₈	—	2	2	no	—
814	C₂²⋊Q₈	—	2	2	no	—
815	C₂²⋊Q₈	—	2	2	no	—
816	C₂²⋊Q₈	—	2	2	no	—
817	C₂²⋊Q₈	—	2	2	no	—
818	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
819	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
820	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
821	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
822	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
823	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
824	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
825	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
826	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
827	#121	—	2	2	no	—
828	#121	—	2	1	no	—
829	#121	—	2	1	no	—
830	#121	—	2	1	no	—
831	#121	—	2	1	no	—
832	#121	—	2	2	no	—
833	#121	—	2	2	no	—
834	#121	C₂³×C₆₇	1	2	yes	—
835	#121	C₂³×C₆₇	1	2	yes	—
836	#120	—	2	2	no	—
837	#120	—	2	2	no	—
838	#120	—	2	2	no	—
839	C₄×Q₈	—	2	1	no	—
840	C₄×Q₈	—	2	1	no	—
841	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
842	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
843	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
844	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
845	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
846	C₄×D₄	—	2	1	no	—
847	C₄×D₄	—	2	1	no	—
848	C₄×D₄	—	2	2	no	—
849	C₄×D₄	—	2	1	no	—
850	C₄×D₄	—	2	1	no	—
851	C₄×D₄	—	2	2	no	—
852	C₄×D₄	—	2	1	no	—
853	C₄×D₄	—	2	2	no	—
854	C₄×D₄	—	2	1	no	—
855	C₄×D₄	—	2	1	no	—
856	C₄×D₄	—	2	2	no	—
857	C₄×D₄	—	2	1	no	—
858	C₄×D₄	—	2	2	no	—
859	C₄×D₄	—	2	1	no	—
860	C₄×D₄	—	2	1	no	—
861	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
862	C₄×D₄	D₄×C₆₇	1	2	yes	—
863	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
864	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
865	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
866	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
867	C₄×D₄	C₂³×C₆₇	1	2	yes	—
868	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
869	#117	—	2	1	no	—
870	#117	—	2	1	no	—
871	#117	—	2	1	no	—
872	#117	C₂³×C₆₇	1	1	yes	characteristic
873	C₂×C₄⋊C₄	—	2	2	no	—
874	C₂×C₄⋊C₄	—	2	2	no	—
875	C₂×C₄⋊C₄	—	2	1	no	—
876	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
877	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
878	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
879	C₂×C₂²⋊C₄	—	2	2	no	—
880	C₂×C₂²⋊C₄	—	2	2	no	—
881	C₂×C₂²⋊C₄	—	2	2	no	—
882	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
883	C₂×C₄²	—	2	1	no	—
884	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
885	#107	C₂³×C₆₇	1	1	yes	characteristic
886	#107	C₂³×C₆₇	1	1	yes	characteristic
887	#107	C₂³×C₆₇	1	2	yes	—
888	#106	C₂³×C₆₇	1	1	yes	characteristic
889	#106	C₂³×C₆₇	1	1	yes	characteristic
890	#106	C₂³×C₆₇	1	2	yes	—
891	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
892	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
893	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
894	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
895	#103	C₂³×C₆₇	1	1	yes	characteristic
896	#103	C₂³×C₆₇	1	2	yes	—
897	#103	C₂³×C₆₇	1	2	yes	—
898	#103	C₂³×C₆₇	1	2	yes	—
899	#103	C₂³×C₆₇	1	1	yes	characteristic
900	#103	C₂³×C₆₇	1	2	yes	—
901	#103	C₂³×C₆₇	1	2	yes	—
902	#103	C₂³×C₆₇	1	1	yes	characteristic
903	#103	C₂³×C₆₇	1	1	yes	characteristic
904	#103	C₂³×C₆₇	1	1	yes	characteristic
905	#103	C₂³×C₆₇	1	1	yes	characteristic
906	#103	C₂³×C₆₇	1	2	yes	—
907	#103	C₂³×C₆₇	1	2	yes	—
908	#102	C₂³×C₆₇	1	1	yes	characteristic
909	#102	C₂³×C₆₇	1	2	yes	—
910	#102	C₂³×C₆₇	1	2	yes	—
911	#102	C₂³×C₆₇	1	2	yes	—
912	#102	C₂³×C₆₇	1	1	yes	characteristic
913	#102	C₂³×C₆₇	1	2	yes	—
914	#102	C₂³×C₆₇	1	2	yes	—
915	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
916	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
917	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
918	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
919	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
920	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
921	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
922	#97	C₂³×C₆₇	1	2	yes	—
923	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
924	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
925	C₂⁴	—	2	2	no	—
926	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
927	#41	—	2	2	no	—
928	#41	—	2	2	no	—
929	#41	—	2	4	no	—
930	#41	—	2	4	no	—
931	#41	—	4	2	no	—
932	#41	—	4	2	no	—
933	#41	—	4	2	no	—
934	#41	—	4	2	no	—
935	#41	—	4	8	no	—
936	#41	—	4	8	no	—
937	C₂×Q₈	—	2	2	no	—
938	C₂×Q₈	—	2	1	no	—
939	C₂×Q₈	—	2	1	no	—
940	C₂×Q₈	—	2	2	no	—
941	C₂×Q₈	—	2	2	no	—
942	C₂×Q₈	—	2	4	no	—
943	C₂×Q₈	—	4	2	no	—
944	C₂×Q₈	—	4	2	no	—
945	C₂×Q₈	—	4	2	no	—
946	C₂×Q₈	—	4	2	no	—
947	C₂×Q₈	—	4	2	no	—
948	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
949	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
950	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
951	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
952	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
953	C₂×D₄	—	2	1	no	—
954	C₂×D₄	—	2	4	no	—
955	C₂×D₄	—	2	4	no	—
956	C₂×D₄	—	2	2	no	—
957	C₂×D₄	—	2	2	no	—
958	C₂×D₄	—	2	2	no	—
959	C₂×D₄	—	2	2	no	—
960	C₂×D₄	—	2	2	no	—
961	C₂×D₄	—	2	1	no	—
962	C₂×D₄	—	2	2	no	—
963	C₂×D₄	—	2	1	no	—
964	C₂×D₄	—	4	2	no	—
965	C₂×D₄	—	4	8	no	—
966	C₂×D₄	—	4	4	no	—
967	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
968	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
969	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
970	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
971	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
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	2	no	—
982	C₂²×C₄	—	2	1	no	—
983	C₂²×C₄	—	4	2	no	—
984	C₂²×C₄	—	4	2	no	—
985	C₂²×C₄	—	4	8	no	—
986	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
987	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
988	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
989	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
990	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
991	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
992	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
993	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
994	Q₁₆	—	2	2	no	—
995	Q₁₆	—	2	4	no	—
996	Q₁₆	—	2	2	no	—
997	Q₁₆	—	4	2	no	—
998	Q₁₆	—	4	2	no	—
999	Q₁₆	—	4	2	no	—
1000	Q₁₆	—	4	2	no	—
1001	SD₁₆	—	2	2	no	—
1002	SD₁₆	—	2	4	no	—
1003	SD₁₆	—	2	2	no	—
1004	SD₁₆	—	4	2	no	—
1005	SD₁₆	—	4	2	no	—
1006	SD₁₆	—	4	2	no	—
1007	SD₁₆	—	4	2	no	—
1008	M₁₆	—	4	2	no	—
1009	M₁₆	—	4	2	no	—
1010	C₂×C₈	—	4	2	no	—
1011	C₂×C₈	—	4	2	no	—
1012	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1013	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1014	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1015	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1016	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1017	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1018	C₄⋊C₄	—	2	1	no	—
1019	C₄⋊C₄	—	2	2	no	—
1020	C₄⋊C₄	—	2	1	no	—
1021	C₄⋊C₄	—	2	1	no	—
1022	C₄⋊C₄	—	2	2	no	—
1023	C₄⋊C₄	—	2	2	no	—
1024	C₄⋊C₄	—	2	2	no	—
1025	C₄⋊C₄	—	2	2	no	—
1026	C₄⋊C₄	—	2	2	no	—
1027	C₄⋊C₄	—	2	2	no	—
1028	C₄⋊C₄	—	2	2	no	—
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	—	2	1	no	—
1031	C₄⋊C₄	—	2	1	no	—
1032	C₄⋊C₄	—	2	1	no	—
1033	C₄⋊C₄	—	2	1	no	—
1034	C₄⋊C₄	—	2	1	no	—
1035	C₄⋊C₄	—	2	1	no	—
1036	C₄⋊C₄	—	2	2	no	—
1037	C₄⋊C₄	—	2	1	no	—
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	2	no	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1043	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1044	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1045	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1046	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1047	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1048	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1049	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1050	C₂²⋊C₄	—	2	1	no	—
1051	C₂²⋊C₄	—	2	2	no	—
1052	C₂²⋊C₄	—	2	1	no	—
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	2	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	2	no	—
1057	C₂²⋊C₄	—	2	2	no	—
1058	C₂²⋊C₄	—	2	1	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	—	2	1	no	—
1063	C₂²⋊C₄	—	2	1	no	—
1064	C₂²⋊C₄	—	2	2	no	—
1065	C₂²⋊C₄	—	2	2	no	—
1066	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1067	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1068	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1069	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1070	C₄²	—	2	1	no	—
1071	C₄²	—	2	1	no	—
1072	C₄²	—	2	1	no	—
1073	C₄²	—	2	2	no	—
1074	C₄²	—	2	1	no	—
1075	C₄²	—	2	1	no	—
1076	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1077	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1078	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1079	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1080	C₂³	—	2	1	no	—
1081	C₂³	—	2	4	no	—
1082	C₂³	—	2	2	no	—
1083	C₂³	—	4	2	no	—
1084	C₂³	—	4	2	no	—
1085	C₂³	—	4	4	no	—
1086	C₂³	—	4	4	no	—
1087	C₂³	—	8	2	no	—
1088	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1089	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1090	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1091	Q₈	—	2	1	no	—
1092	Q₈	—	2	1	no	—
1093	Q₈	—	2	2	no	—
1094	Q₈	—	2	1	no	—
1095	Q₈	—	2	1	no	—
1096	Q₈	—	2	2	no	—
1097	Q₈	—	2	1	no	—
1098	Q₈	—	2	2	no	—
1099	Q₈	—	2	2	no	—
1100	Q₈	—	4	4	no	—
1101	Q₈	—	8	2	no	—
1102	Q₈	—	8	2	no	—
1103	Q₈	—	8	1	no	—
1104	Q₈	—	8	1	no	—
1105	Q₈	H(5,𝔽₂)×C₆₇	1	2	yes	—
1106	D₄	—	2	4	no	—
1107	D₄	—	2	4	no	—
1108	D₄	—	2	2	no	—
1109	D₄	—	2	1	no	—
1110	D₄	—	2	2	no	—
1111	D₄	—	2	2	no	—
1112	D₄	—	4	4	no	—
1113	D₄	—	4	4	no	—
1114	D₄	—	4	4	no	—
1115	D₄	—	4	4	no	—
1116	D₄	—	4	4	no	—
1117	D₄	—	4	2	no	—
1118	D₄	—	8	1	no	—
1119	D₄	—	8	2	no	—
1120	D₄	#137×C₆₇	1	4	yes	complemented
1121	D₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1122	C₂×C₄	—	2	4	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	2	no	—
1125	C₂×C₄	—	2	2	no	—
1126	C₂×C₄	—	2	2	no	—
1127	C₂×C₄	—	2	2	no	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	2	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	2	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	2	no	—
1140	C₂×C₄	—	4	2	no	—
1141	C₂×C₄	—	4	2	no	—
1142	C₂×C₄	—	4	2	no	—
1143	C₂×C₄	—	4	1	no	—
1144	C₂×C₄	—	4	4	no	—
1145	C₂×C₄	—	4	4	no	—
1146	C₂×C₄	—	4	4	no	—
1147	C₂×C₄	—	4	4	no	—
1148	C₂×C₄	—	4	2	no	—
1149	C₂×C₄	—	8	1	no	—
1150	C₂×C₄	—	8	2	no	—
1151	C₂×C₄	—	8	2	no	—
1152	C₂×C₄	—	8	2	no	—
1153	C₂×C₄	—	8	2	no	—
1154	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1155	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1156	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1157	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1158	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1159	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1160	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1161	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1162	C₈	—	2	1	no	—
1163	C₈	—	2	1	no	—
1164	C₈	—	2	2	no	—
1165	C₈	—	2	2	no	—
1166	C₈	—	2	1	no	—
1167	C₈	—	2	1	no	—
1168	C₂²	—	2	2	no	—
1169	C₂²	—	2	2	no	—
1170	C₂²	—	2	1	no	—
1171	C₂²	—	2	2	no	—
1172	C₂²	—	2	1	no	—
1173	C₂²	—	2	2	no	—
1174	C₂²	—	2	1	no	—
1175	C₂²	—	2	2	no	—
1176	C₂²	—	2	2	no	—
1177	C₂²	—	4	1	no	—
1178	C₂²	—	4	1	no	—
1179	C₂²	—	4	2	no	—
1180	C₂²	—	4	2	no	—
1181	C₂²	—	4	2	no	—
1182	C₂²	—	8	4	no	—
1183	C₂²	—	8	8	no	—
1184	C₂²	C₂×#137×C₆₇	1	4	yes	—
1185	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1186	C₄	—	2	1	no	—
1187	C₄	—	2	1	no	—
1188	C₄	—	2	1	no	—
1189	C₄	—	2	1	no	—
1190	C₄	—	2	2	no	—
1191	C₄	—	2	2	no	—
1192	C₄	—	2	2	no	—
1193	C₄	—	4	1	no	—
1194	C₄	—	4	1	no	—
1195	C₄	—	4	2	no	—
1196	C₄	—	4	1	no	—
1197	C₄	—	4	1	no	—
1198	C₄	—	4	2	no	—
1199	C₄	—	4	1	no	—
1200	C₄	—	4	2	no	—
1201	C₄	—	4	1	no	—
1202	C₄	C₂×#137×C₆₇	1	2	yes	—
1203	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1204	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1205	C₂	—	2	4	no	—
1206	C₂	—	4	1	no	—
1207	C₂	—	4	2	no	—
1208	C₂	—	4	2	no	—
1209	C₂	—	8	2	no	—
1210	C₂	C₆₇×#3484	1	1	yes	characteristic
1211	C₂	C₂²×#137×C₆₇	1	1	yes	characteristic
1212	C₂	C₆₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	D₄×#41×C₆₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3501	C₂	semidirect
3. C₆₇×#3333	C₂	semidirect
4. C₆₇×#3331	C₂	semidirect
5. C₆₇×#3316	C₂	semidirect
6. C₆₇×#3314	C₂	semidirect
7. C₆₇×#3299	C₂	semidirect
8. C₆₇×#3295	C₂	semidirect
9. D₄×Q₁₆×C₆₇	C₂	semidirect
10. D₄×SD₁₆×C₆₇	C₂	semidirect
11. C₆₇×#3278	C₂	semidirect
12. C₆₇×#3276	C₂	semidirect
13. C₆₇×#3270	C₂	semidirect
14. C₆₇×#3266	C₂	semidirect
15. C₆₇×#3216	C₂	semidirect
16. C₆₇×#3210	C₂	semidirect
17. C₆₇×#3196	C₂	semidirect
18. C₆₇×#3190	C₂	semidirect
19. C₆₇×#3116	C₂	semidirect
20. C₆₇×#3107	C₂	semidirect
21. C₆₇×#3007	C₂	semidirect
22. C₂×#452×C₆₇	C₂	semidirect
23. C₆₇×#2974	C₂	semidirect
25. C₂×#137×C₆₇	C₂²	semidirect
26. C₂×#137×C₆₇	C₂²	semidirect
27. C₂²×Q₁₆×C₆₇	C₂²	semidirect
28. C₂²×SD₁₆×C₆₇	C₂²	semidirect
33. #554×C₆₇	C₂²	semidirect
34. #554×C₆₇	C₂²	semidirect
38. D₄×Q₈×C₆₇	C₂²	semidirect
39. D₄×Q₈×C₆₇	C₂²	semidirect
49. #533×C₆₇	C₂²	semidirect
50. #533×C₆₇	C₂²	semidirect
55. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
56. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
61. #497×C₆₇	C₂²	semidirect
62. #494×C₆₇	C₂²	semidirect
63. #492×C₆₇	C₂²	semidirect
64. #489×C₆₇	C₂²	semidirect
65. #487×C₆₇	C₂²	semidirect
66. #486×C₆₇	C₂²	semidirect
67. #485×C₆₇	C₂²	semidirect
68. #485×C₆₇	C₂²	semidirect
69. #485×C₆₇	C₂²	semidirect
70. #484×C₆₇	C₂²	semidirect
71. #483×C₆₇	C₂²	semidirect
72. #481×C₆₇	C₂²	semidirect
73. #480×C₆₇	C₂²	semidirect
74. #477×C₆₇	C₂²	semidirect
75. #476×C₆₇	C₂²	semidirect
76. #475×C₆₇	C₂²	semidirect
77. #474×C₆₇	C₂²	semidirect
78. #470×C₆₇	C₂²	semidirect
79. #470×C₆₇	C₂²	semidirect
80. #468×C₆₇	C₂²	semidirect
81. #468×C₆₇	C₂²	semidirect
82. #467×C₆₇	C₂²	semidirect
83. #467×C₆₇	C₂²	semidirect
84. #465×C₆₇	C₂²	semidirect
85. #465×C₆₇	C₂²	semidirect
86. #464×C₆₇	C₂²	semidirect
87. #464×C₆₇	C₂²	semidirect
88. #462×C₆₇	C₂²	semidirect
89. #462×C₆₇	C₂²	semidirect
90. #462×C₆₇	C₂²	semidirect
91. #462×C₆₇	C₂²	semidirect
92. #461×C₆₇	C₂²	semidirect
93. #461×C₆₇	C₂²	semidirect
94. #460×C₆₇	C₂²	semidirect
95. #460×C₆₇	C₂²	semidirect
99. #452×C₆₇	C₂²	semidirect
100. #452×C₆₇	C₂²	semidirect
101. #452×C₆₇	C₂²	semidirect
102. #452×C₆₇	C₂²	semidirect
103. #452×C₆₇	C₂²	semidirect
104. #452×C₆₇	C₂²	semidirect
105. #452×C₆₇	C₂²	semidirect
106. #452×C₆₇	C₂²	semidirect
107. #451×C₆₇	C₂²	semidirect
108. #451×C₆₇	C₂²	semidirect
109. #451×C₆₇	C₂²	semidirect
110. #451×C₆₇	C₂²	semidirect
111. #450×C₆₇	C₂²	semidirect
112. #450×C₆₇	C₂²	semidirect
113. #448×C₆₇	C₂²	semidirect
114. #448×C₆₇	C₂²	semidirect
115. #441×C₆₇	C₂²	semidirect
116. #440×C₆₇	C₂²	semidirect
117. C₄×Q₁₆×C₆₇	C₂²	semidirect
118. C₄×Q₁₆×C₆₇	C₂²	semidirect
119. C₄×SD₁₆×C₆₇	C₂²	semidirect
120. C₄×SD₁₆×C₆₇	C₂²	semidirect
121. #436×C₆₇	C₂²	semidirect
122. #436×C₆₇	C₂²	semidirect
123. #435×C₆₇	C₂²	semidirect
124. #435×C₆₇	C₂²	semidirect
127. #432×C₆₇	C₂²	semidirect
128. #431×C₆₇	C₂²	semidirect
129. #417×C₆₇	C₂²	semidirect
130. #417×C₆₇	C₂²	semidirect
131. C₂×#103×C₆₇	C₂²	semidirect
132. C₂×#102×C₆₇	C₂²	semidirect
133. #407×C₆₇	C₂²	semidirect
134. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
513. D₄×C₆₇	#137	semidirect
598. #61607	C₆₇	direct (N × H)
607. #3501	C₂×C₆₇	semidirect
609. #3333	C₂×C₆₇	semidirect
610. #3331	C₂×C₆₇	semidirect
611. #3316	C₂×C₆₇	semidirect
612. #3314	C₂×C₆₇	semidirect
613. #3299	C₂×C₆₇	semidirect
614. #3295	C₂×C₆₇	semidirect
615. D₄×Q₁₆	C₂×C₆₇	semidirect
616. D₄×SD₁₆	C₂×C₆₇	semidirect
617. #3278	C₂×C₆₇	semidirect
618. #3276	C₂×C₆₇	semidirect
619. #3270	C₂×C₆₇	semidirect
620. #3266	C₂×C₆₇	semidirect
621. #3216	C₂×C₆₇	semidirect
622. #3210	C₂×C₆₇	semidirect
623. #3196	C₂×C₆₇	semidirect
624. #3190	C₂×C₆₇	semidirect
625. #3116	C₂×C₆₇	semidirect
626. #3107	C₂×C₆₇	semidirect
627. #3007	C₂×C₆₇	semidirect
628. C₂×#452	C₂×C₆₇	semidirect
629. #2974	C₂×C₆₇	semidirect
630. C₆₇	#61607	direct (N × H)
632. C₂×#137	C₂²×C₆₇	semidirect
633. C₂×#137	C₂²×C₆₇	semidirect
634. C₂²×Q₁₆	C₂²×C₆₇	semidirect
635. C₂²×SD₁₆	C₂²×C₆₇	semidirect
640. #554	C₂²×C₆₇	semidirect
641. #554	C₂²×C₆₇	semidirect
645. D₄×Q₈	C₂²×C₆₇	semidirect
646. D₄×Q₈	C₂²×C₆₇	semidirect
656. #533	C₂²×C₆₇	semidirect
657. #533	C₂²×C₆₇	semidirect
662. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
663. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
668. #497	C₂²×C₆₇	semidirect
669. #494	C₂²×C₆₇	semidirect
670. #492	C₂²×C₆₇	semidirect
671. #489	C₂²×C₆₇	semidirect
672. #487	C₂²×C₆₇	semidirect
673. #486	C₂²×C₆₇	semidirect
674. #485	C₂²×C₆₇	semidirect
675. #485	C₂²×C₆₇	semidirect
676. #485	C₂²×C₆₇	semidirect
677. #484	C₂²×C₆₇	semidirect
678. #483	C₂²×C₆₇	semidirect
679. #481	C₂²×C₆₇	semidirect
680. #480	C₂²×C₆₇	semidirect
681. #477	C₂²×C₆₇	semidirect
682. #476	C₂²×C₆₇	semidirect
683. #475	C₂²×C₆₇	semidirect
684. #474	C₂²×C₆₇	semidirect
685. #470	C₂²×C₆₇	semidirect
686. #470	C₂²×C₆₇	semidirect
687. #468	C₂²×C₆₇	semidirect
688. #468	C₂²×C₆₇	semidirect
689. #467	C₂²×C₆₇	semidirect
690. #467	C₂²×C₆₇	semidirect
691. #465	C₂²×C₆₇	semidirect
692. #465	C₂²×C₆₇	semidirect
693. #464	C₂²×C₆₇	semidirect
694. #464	C₂²×C₆₇	semidirect
695. #462	C₂²×C₆₇	semidirect
696. #462	C₂²×C₆₇	semidirect
697. #462	C₂²×C₆₇	semidirect
698. #462	C₂²×C₆₇	semidirect
699. #461	C₂²×C₆₇	semidirect
700. #461	C₂²×C₆₇	semidirect
701. #460	C₂²×C₆₇	semidirect
702. #460	C₂²×C₆₇	semidirect
706. #452	C₂²×C₆₇	semidirect
707. #452	C₂²×C₆₇	semidirect
708. #452	C₂²×C₆₇	semidirect
709. #452	C₂²×C₆₇	semidirect
710. #452	C₂²×C₆₇	semidirect
711. #452	C₂²×C₆₇	semidirect
712. #452	C₂²×C₆₇	semidirect
713. #452	C₂²×C₆₇	semidirect
714. #451	C₂²×C₆₇	semidirect
715. #451	C₂²×C₆₇	semidirect
716. #451	C₂²×C₆₇	semidirect
717. #451	C₂²×C₆₇	semidirect
718. #450	C₂²×C₆₇	semidirect
719. #450	C₂²×C₆₇	semidirect
720. #448	C₂²×C₆₇	semidirect
721. #448	C₂²×C₆₇	semidirect
722. #441	C₂²×C₆₇	semidirect
723. #440	C₂²×C₆₇	semidirect
724. C₄×Q₁₆	C₂²×C₆₇	semidirect
725. C₄×Q₁₆	C₂²×C₆₇	semidirect
726. C₄×SD₁₆	C₂²×C₆₇	semidirect
727. C₄×SD₁₆	C₂²×C₆₇	semidirect
728. #436	C₂²×C₆₇	semidirect
729. #436	C₂²×C₆₇	semidirect
730. #435	C₂²×C₆₇	semidirect
731. #435	C₂²×C₆₇	semidirect
734. #432	C₂²×C₆₇	semidirect
735. #431	C₂²×C₆₇	semidirect
736. #417	C₂²×C₆₇	semidirect
737. #417	C₂²×C₆₇	semidirect
738. C₂×#103	C₂²×C₆₇	semidirect
739. C₂×#102	C₂²×C₆₇	semidirect
740. #407	C₂²×C₆₇	semidirect
741. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
1120. D₄	#137×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3501	2
D₄×#41×C₆₇	2
C₆₇×#3333	2
C₆₇×#3331	2
C₆₇×#3316	2
C₆₇×#3314	2
C₆₇×#3299	2
C₆₇×#3295	2
D₄×Q₁₆×C₆₇	2
D₄×SD₁₆×C₆₇	2
C₆₇×#3278	2
C₆₇×#3276	2
C₆₇×#3270	2
C₆₇×#3266	2
C₆₇×#3216	2
C₆₇×#3210	2
C₆₇×#3196	2
C₆₇×#3190	2
C₆₇×#3116	2
C₆₇×#3107	2
C₆₇×#3007	2
C₂×#452×C₆₇	2
C₆₇×#2974	2
#61607	67

Subgroups — C67×#61607 #30740858

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61607 #30740858