Subgroups — C₆₇×#36738 #30715989

Order 17152.

2522 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#538×C₆₇	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2847	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2722	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2715	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2712	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2695	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2693	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2691	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2676	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2675	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2672	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2671	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2617	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2617	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2564	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2543	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2417	C₂	1	2	yes	maximal, complemented
18	C₆₇×#2416	C₂	1	2	yes	maximal, complemented
19	C₂×#385×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
21	#538×C₆₇	—	2	16	no	—
22	C₂×#126×C₆₇	C₂²	1	2	yes	—
23	C₂×#126×C₆₇	C₂²	1	2	yes	—
24	C₂×#124×C₆₇	C₂²	1	2	yes	—
25	C₂×#124×C₆₇	C₂²	1	2	yes	—
26	C₂×#123×C₆₇	C₂²	1	2	yes	—
27	C₂×#123×C₆₇	C₂²	1	2	yes	—
28	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
30	C₂×#121×C₆₇	C₂²	1	2	yes	—
31	C₂×#121×C₆₇	C₂²	1	2	yes	—
32	C₂×#121×C₆₇	C₂²	1	2	yes	—
33	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×#121×C₆₇	C₂²	1	2	yes	—
35	C₂×#121×C₆₇	C₂²	1	2	yes	—
36	C₂×#121×C₆₇	C₂²	1	2	yes	—
37	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
39	C₂×#120×C₆₇	C₂²	1	2	yes	—
40	C₂×#120×C₆₇	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
42	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
43	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
44	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
45	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
46	#400×C₆₇	C₂²	1	2	yes	complemented
47	#399×C₆₇	C₂²	1	2	yes	complemented
48	#398×C₆₇	C₂²	1	2	yes	complemented
49	#398×C₆₇	C₂²	1	2	yes	complemented
50	#398×C₆₇	C₂²	1	2	yes	complemented
51	#397×C₆₇	C₂²	1	1	yes	characteristic
52	#397×C₆₇	C₂²	1	1	yes	characteristic
53	#397×C₆₇	C₂²	1	1	yes	characteristic
54	#397×C₆₇	C₂²	1	1	yes	characteristic
55	#397×C₆₇	C₂²	1	2	yes	complemented
56	#396×C₆₇	C₂²	1	2	yes	complemented
57	#396×C₆₇	C₂²	1	2	yes	complemented
58	#396×C₆₇	C₂²	1	2	yes	complemented
59	#396×C₆₇	C₂²	1	2	yes	complemented
60	#395×C₆₇	C₂²	1	2	yes	complemented
61	#394×C₆₇	C₂²	1	2	yes	—
62	#394×C₆₇	C₂²	1	2	yes	—
63	#394×C₆₇	C₂²	1	2	yes	—
64	#394×C₆₇	C₂²	1	2	yes	—
65	#394×C₆₇	C₂²	1	2	yes	complemented
66	#394×C₆₇	C₂²	1	2	yes	complemented
67	#394×C₆₇	C₂²	1	2	yes	complemented
68	#393×C₆₇	C₂²	1	2	yes	complemented
69	#392×C₆₇	C₂²	1	1	yes	characteristic
70	#392×C₆₇	C₂²	1	1	yes	characteristic
71	#392×C₆₇	C₂²	1	1	yes	characteristic
72	#392×C₆₇	C₂²	1	1	yes	characteristic
73	#392×C₆₇	C₂²	1	2	yes	complemented
74	#391×C₆₇	C₂²	1	2	yes	complemented
75	#390×C₆₇	C₂²	1	2	yes	complemented
76	#389×C₆₇	C₂²	1	2	yes	complemented
77	#389×C₆₇	C₂²	1	2	yes	complemented
78	#388×C₆₇	C₂²	1	2	yes	complemented
79	#388×C₆₇	C₂²	1	2	yes	complemented
80	#387×C₆₇	C₂²	1	2	yes	complemented
81	#387×C₆₇	C₂²	1	2	yes	complemented
82	#386×C₆₇	C₂²	1	2	yes	—
83	#386×C₆₇	C₂²	1	2	yes	—
84	#386×C₆₇	C₂²	1	2	yes	—
85	#386×C₆₇	C₂²	1	2	yes	—
86	#386×C₆₇	C₂²	1	2	yes	—
87	#386×C₆₇	C₂²	1	2	yes	—
88	#386×C₆₇	C₂²	1	2	yes	—
89	#386×C₆₇	C₂²	1	2	yes	—
90	#386×C₆₇	C₂²	1	2	yes	complemented
91	#386×C₆₇	C₂²	1	2	yes	complemented
92	#385×C₆₇	C₂²	1	2	yes	—
93	#385×C₆₇	C₂²	1	1	yes	characteristic
94	#385×C₆₇	C₂²	1	1	yes	characteristic
95	#385×C₆₇	C₂²	1	2	yes	—
96	#385×C₆₇	C₂²	1	1	yes	characteristic
97	#385×C₆₇	C₂²	1	1	yes	characteristic
98	#385×C₆₇	C₂²	1	2	yes	complemented
99	#385×C₆₇	C₂²	1	2	yes	complemented
100	#380×C₆₇	C₂²	1	1	yes	characteristic
101	#380×C₆₇	C₂²	1	2	yes	—
102	#380×C₆₇	C₂²	1	2	yes	—
103	#380×C₆₇	C₂²	1	2	yes	—
104	#380×C₆₇	C₂²	1	1	yes	characteristic
105	#380×C₆₇	C₂²	1	2	yes	complemented
106	#380×C₆₇	C₂²	1	2	yes	complemented
107	C₂×#95×C₆₇	C₂²	1	2	yes	—
108	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
110	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
111	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
112	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
113	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
114	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
115	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
116	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
117	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
118	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
119	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₆₇	—	4	4	no	—
121	C₂³×C₄×C₆₇	—	4	2	no	—
122	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
123	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
127	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
128	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
129	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
131	#126×C₆₇	—	2	8	no	—
132	#126×C₆₇	—	2	8	no	—
133	#124×C₆₇	—	2	8	no	—
134	#124×C₆₇	—	2	8	no	—
135	#123×C₆₇	—	2	8	no	—
136	#123×C₆₇	—	2	8	no	—
137	C₂²⋊Q₈×C₆₇	—	2	8	no	—
138	C₂²⋊Q₈×C₆₇	—	4	4	no	—
139	#121×C₆₇	—	2	8	no	—
140	#121×C₆₇	—	2	8	no	—
141	#121×C₆₇	—	2	8	no	—
142	#121×C₆₇	—	4	4	no	—
143	#121×C₆₇	—	4	4	no	—
144	#121×C₆₇	—	4	4	no	—
145	#121×C₆₇	—	4	4	no	—
146	#121×C₆₇	—	4	2	no	—
147	#121×C₆₇	—	4	2	no	—
148	#120×C₆₇	—	2	8	no	—
149	#120×C₆₇	—	2	8	no	—
150	C₄×D₄×C₆₇	—	2	8	no	—
151	C₄×D₄×C₆₇	—	2	8	no	—
152	C₂×C₄⋊C₄×C₆₇	—	4	4	no	—
153	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
171	C₂×C₂²⋊C₄×C₆₇	D₄	1	8	yes	complemented
172	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
187	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
188	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
202	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
203	#95×C₆₇	C₂³	1	2	yes	—
204	#95×C₆₇	C₂³	1	2	yes	—
205	#95×C₆₇	C₂³	1	2	yes	—
206	#95×C₆₇	C₂³	1	2	yes	—
207	#95×C₆₇	C₂³	1	1	yes	characteristic
208	#95×C₆₇	C₂³	1	2	yes	—
209	#95×C₆₇	C₂³	1	2	yes	—
210	#95×C₆₇	C₂³	1	1	yes	characteristic
211	#95×C₆₇	C₂³	1	2	yes	—
212	#95×C₆₇	C₂³	1	2	yes	—
213	#95×C₆₇	C₂³	1	2	yes	—
214	#95×C₆₇	C₂³	1	2	yes	—
215	#95×C₆₇	C₂³	1	1	yes	characteristic
216	#95×C₆₇	C₂³	1	1	yes	characteristic
217	#95×C₆₇	C₂³	1	2	yes	—
218	#95×C₆₇	C₂³	1	2	yes	—
219	#95×C₆₇	C₂³	1	2	yes	—
220	#95×C₆₇	C₂³	1	2	yes	—
221	C₂⁴×C₆₇	—	2	2	no	—
222	C₂⁴×C₆₇	—	2	2	no	—
223	C₂⁴×C₆₇	—	4	2	no	—
224	C₂⁴×C₆₇	—	4	2	no	—
225	C₂⁴×C₆₇	C₂×D₄	1	4	yes	—
226	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
227	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
228	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
229	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
230	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
231	C₂×Q₈×C₆₇	—	2	4	no	—
232	C₂×Q₈×C₆₇	—	4	2	no	—
233	C₂×Q₈×C₆₇	—	4	2	no	—
234	C₂×D₄×C₆₇	—	2	4	no	—
235	C₂×D₄×C₆₇	—	2	4	no	—
236	C₂×D₄×C₆₇	—	2	4	no	—
237	C₂×D₄×C₆₇	—	2	4	no	—
238	C₂×D₄×C₆₇	—	2	4	no	—
239	C₂×D₄×C₆₇	—	2	4	no	—
240	C₂×D₄×C₆₇	—	2	4	no	—
241	C₂×D₄×C₆₇	—	2	4	no	—
242	C₂×D₄×C₆₇	—	2	4	no	—
243	C₂×D₄×C₆₇	—	2	4	no	—
244	C₂×D₄×C₆₇	—	2	4	no	—
245	C₂×D₄×C₆₇	—	2	4	no	—
246	C₂×D₄×C₆₇	—	4	2	no	—
247	C₂×D₄×C₆₇	—	4	2	no	—
248	C₂×D₄×C₆₇	—	4	2	no	—
249	C₂×D₄×C₆₇	—	4	2	no	—
250	C₂×D₄×C₆₇	—	4	2	no	—
251	C₂×D₄×C₆₇	—	4	2	no	—
252	C₂×D₄×C₆₇	—	4	1	no	—
253	C₂×D₄×C₆₇	—	4	1	no	—
254	C₂×D₄×C₆₇	—	4	2	no	—
255	C₂×D₄×C₆₇	—	4	2	no	—
256	C₂×D₄×C₆₇	—	4	2	no	—
257	C₂×D₄×C₆₇	—	4	2	no	—
258	C₂×D₄×C₆₇	—	4	2	no	—
259	C₂×D₄×C₆₇	—	4	2	no	—
260	C₂×D₄×C₆₇	—	4	2	no	—
261	C₂×D₄×C₆₇	—	4	2	no	—
262	C₂²×C₄×C₆₇	—	2	4	no	—
263	C₂²×C₄×C₆₇	—	2	2	no	—
264	C₂²×C₄×C₆₇	—	2	2	no	—
265	C₂²×C₄×C₆₇	—	2	4	no	—
266	C₂²×C₄×C₆₇	—	2	4	no	—
267	C₂²×C₄×C₆₇	—	2	4	no	—
268	C₂²×C₄×C₆₇	—	2	4	no	—
269	C₂²×C₄×C₆₇	—	2	4	no	—
270	C₂²×C₄×C₆₇	—	4	2	no	—
271	C₂²×C₄×C₆₇	—	4	1	no	—
272	C₂²×C₄×C₆₇	—	4	2	no	—
273	C₂²×C₄×C₆₇	—	4	2	no	—
274	C₂²×C₄×C₆₇	—	4	2	no	—
275	C₂²×C₄×C₆₇	—	4	1	no	—
276	C₂²×C₄×C₆₇	—	4	2	no	—
277	C₂²×C₄×C₆₇	—	4	2	no	—
278	C₂²×C₄×C₆₇	—	4	2	no	—
279	C₂²×C₄×C₆₇	—	4	2	no	—
280	C₂²×C₄×C₆₇	—	4	2	no	—
281	C₂²×C₄×C₆₇	—	4	2	no	—
282	C₂²×C₄×C₆₇	—	4	2	no	—
283	C₂²×C₄×C₆₇	—	4	2	no	—
284	C₂²×C₄×C₆₇	—	4	16	no	—
285	C₂²×C₄×C₆₇	C₂×D₄	1	8	yes	—
286	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
300	C₄⋊C₄×C₆₇	—	2	4	no	—
301	C₄⋊C₄×C₆₇	—	2	4	no	—
302	C₄⋊C₄×C₆₇	—	2	4	no	—
303	C₄⋊C₄×C₆₇	—	2	4	no	—
304	C₄⋊C₄×C₆₇	—	2	4	no	—
305	C₄⋊C₄×C₆₇	—	2	4	no	—
306	C₄⋊C₄×C₆₇	—	2	4	no	—
307	C₄⋊C₄×C₆₇	—	2	4	no	—
308	C₄⋊C₄×C₆₇	—	2	4	no	—
309	C₄⋊C₄×C₆₇	—	4	2	no	—
310	C₄⋊C₄×C₆₇	—	4	2	no	—
311	C₄⋊C₄×C₆₇	—	4	2	no	—
312	C₄⋊C₄×C₆₇	—	4	2	no	—
313	C₄⋊C₄×C₆₇	—	4	2	no	—
314	C₄⋊C₄×C₆₇	—	4	1	no	—
315	C₄⋊C₄×C₆₇	—	4	1	no	—
316	C₄⋊C₄×C₆₇	—	4	2	no	—
317	C₂²⋊C₄×C₆₇	—	2	4	no	—
318	C₂²⋊C₄×C₆₇	—	2	4	no	—
319	C₂²⋊C₄×C₆₇	—	2	4	no	—
320	C₂²⋊C₄×C₆₇	—	2	4	no	—
321	C₂²⋊C₄×C₆₇	—	2	4	no	—
322	C₂²⋊C₄×C₆₇	—	2	4	no	—
323	C₂²⋊C₄×C₆₇	—	2	4	no	—
324	C₂²⋊C₄×C₆₇	—	2	4	no	—
325	C₂²⋊C₄×C₆₇	—	2	4	no	—
326	C₂²⋊C₄×C₆₇	—	2	4	no	—
327	C₂²⋊C₄×C₆₇	—	2	4	no	—
328	C₂²⋊C₄×C₆₇	—	2	4	no	—
329	C₂²⋊C₄×C₆₇	—	4	1	no	—
330	C₂²⋊C₄×C₆₇	—	4	1	no	—
331	C₂²⋊C₄×C₆₇	—	4	1	no	—
332	C₂²⋊C₄×C₆₇	—	4	1	no	—
333	C₂²⋊C₄×C₆₇	—	4	2	no	—
334	C₂²⋊C₄×C₆₇	—	4	2	no	—
335	C₂²⋊C₄×C₆₇	—	4	2	no	—
336	C₂²⋊C₄×C₆₇	—	4	2	no	—
337	C₂²⋊C₄×C₆₇	—	4	2	no	—
338	C₂²⋊C₄×C₆₇	—	4	2	no	—
339	C₂²⋊C₄×C₆₇	—	4	2	no	—
340	C₂²⋊C₄×C₆₇	—	4	2	no	—
341	C₂²⋊C₄×C₆₇	—	4	2	no	—
342	C₂²⋊C₄×C₆₇	—	4	2	no	—
343	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
344	C₂²⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
345	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
346	C₄²×C₆₇	—	2	4	no	—
347	C₄²×C₆₇	—	2	4	no	—
348	C₂³×C₆₇	—	2	2	no	—
349	C₂³×C₆₇	—	2	2	no	—
350	C₂³×C₆₇	—	2	8	no	—
351	C₂³×C₆₇	—	2	1	no	—
352	C₂³×C₆₇	—	2	1	no	—
353	C₂³×C₆₇	—	2	2	no	—
354	C₂³×C₆₇	—	2	2	no	—
355	C₂³×C₆₇	—	2	1	no	—
356	C₂³×C₆₇	—	2	1	no	—
357	C₂³×C₆₇	—	2	2	no	—
358	C₂³×C₆₇	—	2	2	no	—
359	C₂³×C₆₇	—	2	2	no	—
360	C₂³×C₆₇	—	2	2	no	—
361	C₂³×C₆₇	—	2	2	no	—
362	C₂³×C₆₇	—	2	2	no	—
363	C₂³×C₆₇	—	2	2	no	—
364	C₂³×C₆₇	—	2	2	no	—
365	C₂³×C₆₇	—	2	2	no	—
366	C₂³×C₆₇	—	2	2	no	—
367	C₂³×C₆₇	—	2	2	no	—
368	C₂³×C₆₇	—	2	2	no	—
369	C₂³×C₆₇	—	2	2	no	—
370	C₂³×C₆₇	—	2	2	no	—
371	C₂³×C₆₇	—	2	2	no	—
372	C₂³×C₆₇	—	2	2	no	—
373	C₂³×C₆₇	—	4	8	no	—
374	C₂³×C₆₇	—	4	4	no	—
375	C₂³×C₆₇	—	4	4	no	—
376	C₂³×C₆₇	—	4	8	no	—
377	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
378	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
379	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
380	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
381	C₂³×C₆₇	2₋¹⁺⁴	1	2	yes	—
382	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
383	Q₈×C₆₇	—	8	4	no	—
384	D₄×C₆₇	—	4	8	no	—
385	D₄×C₆₇	—	4	8	no	—
386	D₄×C₆₇	—	8	4	no	—
387	D₄×C₆₇	—	8	4	no	—
388	D₄×C₆₇	—	8	4	no	—
389	D₄×C₆₇	—	8	4	no	—
390	D₄×C₆₇	—	8	4	no	—
391	D₄×C₆₇	—	8	4	no	—
392	D₄×C₆₇	—	8	2	no	—
393	D₄×C₆₇	—	8	2	no	—
394	C₂×C₄×C₆₇	—	2	2	no	—
395	C₂×C₄×C₆₇	—	2	2	no	—
396	C₂×C₄×C₆₇	—	2	2	no	—
397	C₂×C₄×C₆₇	—	2	2	no	—
398	C₂×C₄×C₆₇	—	2	2	no	—
399	C₂×C₄×C₆₇	—	2	2	no	—
400	C₂×C₄×C₆₇	—	2	2	no	—
401	C₂×C₄×C₆₇	—	2	2	no	—
402	C₂×C₄×C₆₇	—	2	2	no	—
403	C₂×C₄×C₆₇	—	2	2	no	—
404	C₂×C₄×C₆₇	—	2	2	no	—
405	C₂×C₄×C₆₇	—	2	2	no	—
406	C₂×C₄×C₆₇	—	2	2	no	—
407	C₂×C₄×C₆₇	—	2	2	no	—
408	C₂×C₄×C₆₇	—	2	1	no	—
409	C₂×C₄×C₆₇	—	2	1	no	—
410	C₂×C₄×C₆₇	—	2	2	no	—
411	C₂×C₄×C₆₇	—	2	2	no	—
412	C₂×C₄×C₆₇	—	2	2	no	—
413	C₂×C₄×C₆₇	—	2	1	no	—
414	C₂×C₄×C₆₇	—	2	1	no	—
415	C₂×C₄×C₆₇	—	2	2	no	—
416	C₂×C₄×C₆₇	—	2	2	no	—
417	C₂×C₄×C₆₇	—	2	2	no	—
418	C₂×C₄×C₆₇	—	2	2	no	—
419	C₂×C₄×C₆₇	—	2	2	no	—
420	C₂×C₄×C₆₇	—	2	2	no	—
421	C₂×C₄×C₆₇	—	2	2	no	—
422	C₂×C₄×C₆₇	—	2	2	no	—
423	C₂×C₄×C₆₇	—	2	2	no	—
424	C₂×C₄×C₆₇	—	2	2	no	—
425	C₂×C₄×C₆₇	—	2	2	no	—
426	C₂×C₄×C₆₇	—	2	2	no	—
427	C₂×C₄×C₆₇	—	2	2	no	—
428	C₂×C₄×C₆₇	—	2	2	no	—
429	C₂×C₄×C₆₇	—	4	8	no	—
430	C₂×C₄×C₆₇	—	4	4	no	—
431	C₂×C₄×C₆₇	—	4	8	no	—
432	C₂×C₄×C₆₇	—	4	8	no	—
433	C₂×C₄×C₆₇	—	4	4	no	—
434	C₂×C₄×C₆₇	—	8	4	no	—
435	C₂×C₄×C₆₇	—	8	4	no	—
436	C₂×C₄×C₆₇	—	8	2	no	—
437	C₂×C₄×C₆₇	—	8	2	no	—
438	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
439	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
440	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
441	C₂²×C₆₇	—	2	4	no	—
442	C₂²×C₆₇	—	2	2	no	—
443	C₂²×C₆₇	—	2	2	no	—
444	C₂²×C₆₇	—	2	4	no	—
445	C₂²×C₆₇	—	2	2	no	—
446	C₂²×C₆₇	—	2	2	no	—
447	C₂²×C₆₇	—	2	4	no	—
448	C₂²×C₆₇	—	2	4	no	—
449	C₂²×C₆₇	—	4	16	no	—
450	C₂²×C₆₇	—	4	1	no	—
451	C₂²×C₆₇	—	4	1	no	—
452	C₂²×C₆₇	—	4	1	no	—
453	C₂²×C₆₇	—	4	1	no	—
454	C₂²×C₆₇	—	4	2	no	—
455	C₂²×C₆₇	—	4	2	no	—
456	C₂²×C₆₇	—	4	2	no	—
457	C₂²×C₆₇	—	4	2	no	—
458	C₂²×C₆₇	—	4	2	no	—
459	C₂²×C₆₇	—	4	2	no	—
460	C₂²×C₆₇	—	4	2	no	—
461	C₂²×C₆₇	—	4	2	no	—
462	C₂²×C₆₇	—	4	2	no	—
463	C₂²×C₆₇	—	4	2	no	—
464	C₂²×C₆₇	—	4	2	no	—
465	C₂²×C₆₇	—	4	2	no	—
466	C₂²×C₆₇	—	4	2	no	—
467	C₂²×C₆₇	—	4	2	no	—
468	C₂²×C₆₇	—	4	2	no	—
469	C₂²×C₆₇	—	4	2	no	—
470	C₂²×C₆₇	#537	1	4	yes	—
471	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
472	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
473	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
474	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
475	C₂²×C₆₇	#585	1	2	yes	—
476	C₄×C₆₇	—	2	4	no	—
477	C₄×C₆₇	—	2	4	no	—
478	C₄×C₆₇	—	2	4	no	—
479	C₄×C₆₇	—	4	2	no	—
480	C₄×C₆₇	—	4	2	no	—
481	C₄×C₆₇	—	4	2	no	—
482	C₄×C₆₇	—	4	2	no	—
483	C₄×C₆₇	—	4	2	no	—
484	C₄×C₆₇	—	4	2	no	—
485	C₄×C₆₇	—	4	2	no	—
486	C₄×C₆₇	—	4	1	no	—
487	C₄×C₆₇	—	4	1	no	—
488	C₄×C₆₇	—	4	1	no	—
489	C₄×C₆₇	—	4	1	no	—
490	#36738	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
491	C₂×C₆₇	—	2	4	no	—
492	C₂×C₆₇	—	4	2	no	—
493	C₂×C₆₇	—	4	2	no	—
494	C₂×C₆₇	—	8	2	no	—
495	C₂×C₆₇	—	8	2	no	—
496	C₂×C₆₇	C₂×#537	1	1	yes	characteristic
497	C₂×C₆₇	#3496	1	2	yes	—
498	C₂×C₆₇	#3532	1	1	yes	characteristic
499	C₂×C₆₇	#3533	1	1	yes	characteristic
500	C₂×C₆₇	#3541	1	2	yes	—
501	C₂×#538	C₂×C₆₇	1	2	yes	complemented
502	#2847	C₂×C₆₇	1	2	yes	complemented
503	#2722	C₂×C₆₇	1	1	yes	characteristic, complemented
504	#2715	C₂×C₆₇	1	2	yes	complemented
505	#2712	C₂×C₆₇	1	1	yes	characteristic, complemented
506	#2695	C₂×C₆₇	1	2	yes	complemented
507	#2693	C₂×C₆₇	1	1	yes	characteristic, complemented
508	#2691	C₂×C₆₇	1	2	yes	complemented
509	#2676	C₂×C₆₇	1	2	yes	complemented
510	#2675	C₂×C₆₇	1	1	yes	characteristic, complemented
511	#2672	C₂×C₆₇	1	2	yes	complemented
512	#2671	C₂×C₆₇	1	2	yes	complemented
513	#2617	C₂×C₆₇	1	1	yes	characteristic, complemented
514	#2617	C₂×C₆₇	1	1	yes	characteristic, complemented
515	#2564	C₂×C₆₇	1	2	yes	complemented
516	#2543	C₂×C₆₇	1	2	yes	complemented
517	#2417	C₂×C₆₇	1	2	yes	complemented
518	#2416	C₂×C₆₇	1	2	yes	complemented
519	C₂×#385	C₂×C₆₇	1	1	yes	characteristic, complemented
520	C₆₇	#36738	1	1	yes	characteristic, direct product factor, Sylow
521	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
522	#538	—	2	16	no	—
523	C₂×#126	C₂²×C₆₇	1	2	yes	—
524	C₂×#126	C₂²×C₆₇	1	2	yes	—
525	C₂×#124	C₂²×C₆₇	1	2	yes	—
526	C₂×#124	C₂²×C₆₇	1	2	yes	—
527	C₂×#123	C₂²×C₆₇	1	2	yes	—
528	C₂×#123	C₂²×C₆₇	1	2	yes	—
529	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
530	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
531	C₂×#121	C₂²×C₆₇	1	2	yes	—
532	C₂×#121	C₂²×C₆₇	1	2	yes	—
533	C₂×#121	C₂²×C₆₇	1	2	yes	—
534	C₂×#121	C₂²×C₆₇	1	2	yes	—
535	C₂×#121	C₂²×C₆₇	1	2	yes	—
536	C₂×#121	C₂²×C₆₇	1	2	yes	—
537	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
538	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
539	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
540	C₂×#120	C₂²×C₆₇	1	2	yes	—
541	C₂×#120	C₂²×C₆₇	1	2	yes	—
542	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
543	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
544	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
545	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
546	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
547	#400	C₂²×C₆₇	1	2	yes	complemented
548	#399	C₂²×C₆₇	1	2	yes	complemented
549	#398	C₂²×C₆₇	1	2	yes	complemented
550	#398	C₂²×C₆₇	1	2	yes	complemented
551	#398	C₂²×C₆₇	1	2	yes	complemented
552	#397	C₂²×C₆₇	1	1	yes	characteristic
553	#397	C₂²×C₆₇	1	1	yes	characteristic
554	#397	C₂²×C₆₇	1	1	yes	characteristic
555	#397	C₂²×C₆₇	1	1	yes	characteristic
556	#397	C₂²×C₆₇	1	2	yes	complemented
557	#396	C₂²×C₆₇	1	2	yes	complemented
558	#396	C₂²×C₆₇	1	2	yes	complemented
559	#396	C₂²×C₆₇	1	2	yes	complemented
560	#396	C₂²×C₆₇	1	2	yes	complemented
561	#395	C₂²×C₆₇	1	2	yes	complemented
562	#394	C₂²×C₆₇	1	2	yes	—
563	#394	C₂²×C₆₇	1	2	yes	—
564	#394	C₂²×C₆₇	1	2	yes	—
565	#394	C₂²×C₆₇	1	2	yes	—
566	#394	C₂²×C₆₇	1	2	yes	complemented
567	#394	C₂²×C₆₇	1	2	yes	complemented
568	#394	C₂²×C₆₇	1	2	yes	complemented
569	#393	C₂²×C₆₇	1	2	yes	complemented
570	#392	C₂²×C₆₇	1	1	yes	characteristic
571	#392	C₂²×C₆₇	1	1	yes	characteristic
572	#392	C₂²×C₆₇	1	1	yes	characteristic
573	#392	C₂²×C₆₇	1	1	yes	characteristic
574	#392	C₂²×C₆₇	1	2	yes	complemented
575	#391	C₂²×C₆₇	1	2	yes	complemented
576	#390	C₂²×C₆₇	1	2	yes	complemented
577	#389	C₂²×C₆₇	1	2	yes	complemented
578	#389	C₂²×C₆₇	1	2	yes	complemented
579	#388	C₂²×C₆₇	1	2	yes	complemented
580	#388	C₂²×C₆₇	1	2	yes	complemented
581	#387	C₂²×C₆₇	1	2	yes	complemented
582	#387	C₂²×C₆₇	1	2	yes	complemented
583	#386	C₂²×C₆₇	1	2	yes	—
584	#386	C₂²×C₆₇	1	2	yes	—
585	#386	C₂²×C₆₇	1	2	yes	—
586	#386	C₂²×C₆₇	1	2	yes	—
587	#386	C₂²×C₆₇	1	2	yes	—
588	#386	C₂²×C₆₇	1	2	yes	—
589	#386	C₂²×C₆₇	1	2	yes	—
590	#386	C₂²×C₆₇	1	2	yes	—
591	#386	C₂²×C₆₇	1	2	yes	complemented
592	#386	C₂²×C₆₇	1	2	yes	complemented
593	#385	C₂²×C₆₇	1	2	yes	—
594	#385	C₂²×C₆₇	1	1	yes	characteristic
595	#385	C₂²×C₆₇	1	1	yes	characteristic
596	#385	C₂²×C₆₇	1	2	yes	—
597	#385	C₂²×C₆₇	1	1	yes	characteristic
598	#385	C₂²×C₆₇	1	1	yes	characteristic
599	#385	C₂²×C₆₇	1	2	yes	complemented
600	#385	C₂²×C₆₇	1	2	yes	complemented
601	#380	C₂²×C₆₇	1	1	yes	characteristic
602	#380	C₂²×C₆₇	1	2	yes	—
603	#380	C₂²×C₆₇	1	2	yes	—
604	#380	C₂²×C₆₇	1	2	yes	—
605	#380	C₂²×C₆₇	1	1	yes	characteristic
606	#380	C₂²×C₆₇	1	2	yes	complemented
607	#380	C₂²×C₆₇	1	2	yes	complemented
608	C₂×#95	C₂²×C₆₇	1	2	yes	—
609	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
610	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
611	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
612	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
613	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
614	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
615	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
616	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
617	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
618	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
619	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
620	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
621	C₂³×C₄	—	4	4	no	—
622	C₂³×C₄	—	4	2	no	—
623	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
624	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
625	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
626	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
627	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
628	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
629	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
630	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
631	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
632	#126	—	2	8	no	—
633	#126	—	2	8	no	—
634	#124	—	2	8	no	—
635	#124	—	2	8	no	—
636	#123	—	2	8	no	—
637	#123	—	2	8	no	—
638	C₂²⋊Q₈	—	2	8	no	—
639	C₂²⋊Q₈	—	4	4	no	—
640	#121	—	2	8	no	—
641	#121	—	2	8	no	—
642	#121	—	2	8	no	—
643	#121	—	4	4	no	—
644	#121	—	4	4	no	—
645	#121	—	4	4	no	—
646	#121	—	4	4	no	—
647	#121	—	4	2	no	—
648	#121	—	4	2	no	—
649	#120	—	2	8	no	—
650	#120	—	2	8	no	—
651	C₄×D₄	—	2	8	no	—
652	C₄×D₄	—	2	8	no	—
653	C₂×C₄⋊C₄	—	4	4	no	—
654	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
663	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
664	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
665	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
666	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
667	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
668	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
669	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
670	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
671	C₂×C₂²⋊C₄	—	4	2	no	—
672	C₂×C₂²⋊C₄	D₄×C₆₇	1	8	yes	complemented
673	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
684	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
686	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
687	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
688	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
689	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
690	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
691	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
692	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
693	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
694	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
695	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
697	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
698	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
699	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
700	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
701	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
702	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
703	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
704	#95	C₂³×C₆₇	1	2	yes	—
705	#95	C₂³×C₆₇	1	2	yes	—
706	#95	C₂³×C₆₇	1	2	yes	—
707	#95	C₂³×C₆₇	1	2	yes	—
708	#95	C₂³×C₆₇	1	1	yes	characteristic
709	#95	C₂³×C₆₇	1	2	yes	—
710	#95	C₂³×C₆₇	1	2	yes	—
711	#95	C₂³×C₆₇	1	1	yes	characteristic
712	#95	C₂³×C₆₇	1	2	yes	—
713	#95	C₂³×C₆₇	1	2	yes	—
714	#95	C₂³×C₆₇	1	2	yes	—
715	#95	C₂³×C₆₇	1	2	yes	—
716	#95	C₂³×C₆₇	1	1	yes	characteristic
717	#95	C₂³×C₆₇	1	1	yes	characteristic
718	#95	C₂³×C₆₇	1	2	yes	—
719	#95	C₂³×C₆₇	1	2	yes	—
720	#95	C₂³×C₆₇	1	2	yes	—
721	#95	C₂³×C₆₇	1	2	yes	—
722	C₂⁴	—	2	2	no	—
723	C₂⁴	—	2	2	no	—
724	C₂⁴	—	4	2	no	—
725	C₂⁴	—	4	2	no	—
726	C₂⁴	C₂×D₄×C₆₇	1	4	yes	—
727	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
728	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
729	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
730	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
731	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
732	C₂×Q₈	—	2	4	no	—
733	C₂×Q₈	—	4	2	no	—
734	C₂×Q₈	—	4	2	no	—
735	C₂×D₄	—	2	4	no	—
736	C₂×D₄	—	2	4	no	—
737	C₂×D₄	—	2	4	no	—
738	C₂×D₄	—	2	4	no	—
739	C₂×D₄	—	2	4	no	—
740	C₂×D₄	—	2	4	no	—
741	C₂×D₄	—	2	4	no	—
742	C₂×D₄	—	2	4	no	—
743	C₂×D₄	—	2	4	no	—
744	C₂×D₄	—	2	4	no	—
745	C₂×D₄	—	2	4	no	—
746	C₂×D₄	—	2	4	no	—
747	C₂×D₄	—	4	2	no	—
748	C₂×D₄	—	4	2	no	—
749	C₂×D₄	—	4	2	no	—
750	C₂×D₄	—	4	2	no	—
751	C₂×D₄	—	4	2	no	—
752	C₂×D₄	—	4	2	no	—
753	C₂×D₄	—	4	1	no	—
754	C₂×D₄	—	4	1	no	—
755	C₂×D₄	—	4	2	no	—
756	C₂×D₄	—	4	2	no	—
757	C₂×D₄	—	4	2	no	—
758	C₂×D₄	—	4	2	no	—
759	C₂×D₄	—	4	2	no	—
760	C₂×D₄	—	4	2	no	—
761	C₂×D₄	—	4	2	no	—
762	C₂×D₄	—	4	2	no	—
763	C₂²×C₄	—	2	4	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	4	no	—
767	C₂²×C₄	—	2	4	no	—
768	C₂²×C₄	—	2	4	no	—
769	C₂²×C₄	—	2	4	no	—
770	C₂²×C₄	—	2	4	no	—
771	C₂²×C₄	—	4	2	no	—
772	C₂²×C₄	—	4	1	no	—
773	C₂²×C₄	—	4	2	no	—
774	C₂²×C₄	—	4	2	no	—
775	C₂²×C₄	—	4	2	no	—
776	C₂²×C₄	—	4	1	no	—
777	C₂²×C₄	—	4	2	no	—
778	C₂²×C₄	—	4	2	no	—
779	C₂²×C₄	—	4	2	no	—
780	C₂²×C₄	—	4	2	no	—
781	C₂²×C₄	—	4	2	no	—
782	C₂²×C₄	—	4	2	no	—
783	C₂²×C₄	—	4	2	no	—
784	C₂²×C₄	—	4	2	no	—
785	C₂²×C₄	—	4	16	no	—
786	C₂²×C₄	C₂×D₄×C₆₇	1	8	yes	—
787	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
788	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
789	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
790	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
791	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
792	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
793	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
794	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
795	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
796	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
798	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
799	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
800	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
801	C₄⋊C₄	—	2	4	no	—
802	C₄⋊C₄	—	2	4	no	—
803	C₄⋊C₄	—	2	4	no	—
804	C₄⋊C₄	—	2	4	no	—
805	C₄⋊C₄	—	2	4	no	—
806	C₄⋊C₄	—	2	4	no	—
807	C₄⋊C₄	—	2	4	no	—
808	C₄⋊C₄	—	2	4	no	—
809	C₄⋊C₄	—	2	4	no	—
810	C₄⋊C₄	—	4	2	no	—
811	C₄⋊C₄	—	4	2	no	—
812	C₄⋊C₄	—	4	2	no	—
813	C₄⋊C₄	—	4	2	no	—
814	C₄⋊C₄	—	4	1	no	—
815	C₄⋊C₄	—	4	1	no	—
816	C₄⋊C₄	—	4	2	no	—
817	C₄⋊C₄	—	4	2	no	—
818	C₂²⋊C₄	—	2	4	no	—
819	C₂²⋊C₄	—	2	4	no	—
820	C₂²⋊C₄	—	2	4	no	—
821	C₂²⋊C₄	—	2	4	no	—
822	C₂²⋊C₄	—	2	4	no	—
823	C₂²⋊C₄	—	2	4	no	—
824	C₂²⋊C₄	—	2	4	no	—
825	C₂²⋊C₄	—	2	4	no	—
826	C₂²⋊C₄	—	2	4	no	—
827	C₂²⋊C₄	—	2	4	no	—
828	C₂²⋊C₄	—	2	4	no	—
829	C₂²⋊C₄	—	2	4	no	—
830	C₂²⋊C₄	—	4	1	no	—
831	C₂²⋊C₄	—	4	1	no	—
832	C₂²⋊C₄	—	4	1	no	—
833	C₂²⋊C₄	—	4	1	no	—
834	C₂²⋊C₄	—	4	2	no	—
835	C₂²⋊C₄	—	4	2	no	—
836	C₂²⋊C₄	—	4	2	no	—
837	C₂²⋊C₄	—	4	2	no	—
838	C₂²⋊C₄	—	4	2	no	—
839	C₂²⋊C₄	—	4	2	no	—
840	C₂²⋊C₄	—	4	2	no	—
841	C₂²⋊C₄	—	4	2	no	—
842	C₂²⋊C₄	—	4	2	no	—
843	C₂²⋊C₄	—	4	2	no	—
844	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
845	C₂²⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
846	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
847	C₄²	—	2	4	no	—
848	C₄²	—	2	4	no	—
849	C₂³	—	2	2	no	—
850	C₂³	—	2	2	no	—
851	C₂³	—	2	8	no	—
852	C₂³	—	2	1	no	—
853	C₂³	—	2	1	no	—
854	C₂³	—	2	2	no	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	1	no	—
857	C₂³	—	2	1	no	—
858	C₂³	—	2	2	no	—
859	C₂³	—	2	2	no	—
860	C₂³	—	2	2	no	—
861	C₂³	—	2	2	no	—
862	C₂³	—	2	2	no	—
863	C₂³	—	2	2	no	—
864	C₂³	—	2	2	no	—
865	C₂³	—	2	2	no	—
866	C₂³	—	2	2	no	—
867	C₂³	—	2	2	no	—
868	C₂³	—	2	2	no	—
869	C₂³	—	2	2	no	—
870	C₂³	—	2	2	no	—
871	C₂³	—	2	2	no	—
872	C₂³	—	2	2	no	—
873	C₂³	—	2	2	no	—
874	C₂³	—	4	8	no	—
875	C₂³	—	4	4	no	—
876	C₂³	—	4	4	no	—
877	C₂³	—	4	8	no	—
878	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
879	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
880	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
881	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
882	C₂³	2₋¹⁺⁴×C₆₇	1	2	yes	—
883	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
884	Q₈	—	8	4	no	—
885	D₄	—	4	8	no	—
886	D₄	—	4	8	no	—
887	D₄	—	8	4	no	—
888	D₄	—	8	4	no	—
889	D₄	—	8	4	no	—
890	D₄	—	8	4	no	—
891	D₄	—	8	4	no	—
892	D₄	—	8	4	no	—
893	D₄	—	8	2	no	—
894	D₄	—	8	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	4	8	no	—
931	C₂×C₄	—	4	4	no	—
932	C₂×C₄	—	4	8	no	—
933	C₂×C₄	—	4	8	no	—
934	C₂×C₄	—	4	4	no	—
935	C₂×C₄	—	8	4	no	—
936	C₂×C₄	—	8	4	no	—
937	C₂×C₄	—	8	2	no	—
938	C₂×C₄	—	8	2	no	—
939	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
940	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
941	C₂×C₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
942	C₂²	—	2	2	no	—
943	C₂²	—	2	2	no	—
944	C₂²	—	2	4	no	—
945	C₂²	—	2	4	no	—
946	C₂²	—	2	2	no	—
947	C₂²	—	2	2	no	—
948	C₂²	—	2	4	no	—
949	C₂²	—	2	4	no	—
950	C₂²	—	4	16	no	—
951	C₂²	—	4	1	no	—
952	C₂²	—	4	1	no	—
953	C₂²	—	4	1	no	—
954	C₂²	—	4	1	no	—
955	C₂²	—	4	2	no	—
956	C₂²	—	4	2	no	—
957	C₂²	—	4	2	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	2	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	4	2	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	4	2	no	—
964	C₂²	—	4	2	no	—
965	C₂²	—	4	2	no	—
966	C₂²	—	4	2	no	—
967	C₂²	—	4	2	no	—
968	C₂²	—	4	2	no	—
969	C₂²	—	4	2	no	—
970	C₂²	—	4	2	no	—
971	C₂²	#537×C₆₇	1	4	yes	—
972	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
973	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
974	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
975	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
976	C₂²	#585×C₆₇	1	2	yes	—
977	C₄	—	2	4	no	—
978	C₄	—	2	4	no	—
979	C₄	—	2	4	no	—
980	C₄	—	4	2	no	—
981	C₄	—	4	1	no	—
982	C₄	—	4	1	no	—
983	C₄	—	4	1	no	—
984	C₄	—	4	1	no	—
985	C₄	—	4	2	no	—
986	C₄	—	4	2	no	—
987	C₄	—	4	2	no	—
988	C₄	—	4	2	no	—
989	C₄	—	4	2	no	—
990	C₄	—	4	2	no	—
991	C₂	—	2	4	no	—
992	C₂	—	4	2	no	—
993	C₂	—	4	2	no	—
994	C₂	—	8	2	no	—
995	C₂	—	8	2	no	—
996	C₂	C₂×#537×C₆₇	1	1	yes	characteristic
997	C₂	C₆₇×#3496	1	2	yes	—
998	C₂	C₆₇×#3532	1	1	yes	characteristic
999	C₂	C₆₇×#3533	1	1	yes	characteristic
1000	C₂	C₆₇×#3541	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#538×C₆₇	C₂	semidirect
2. C₆₇×#2847	C₂	semidirect
3. C₆₇×#2722	C₂	semidirect
4. C₆₇×#2715	C₂	semidirect
5. C₆₇×#2712	C₂	semidirect
6. C₆₇×#2695	C₂	semidirect
7. C₆₇×#2693	C₂	semidirect
8. C₆₇×#2691	C₂	semidirect
9. C₆₇×#2676	C₂	semidirect
10. C₆₇×#2675	C₂	semidirect
11. C₆₇×#2672	C₂	semidirect
12. C₆₇×#2671	C₂	semidirect
13. C₆₇×#2617	C₂	semidirect
14. C₆₇×#2617	C₂	semidirect
15. C₆₇×#2564	C₂	semidirect
16. C₆₇×#2543	C₂	semidirect
17. C₆₇×#2417	C₂	semidirect
18. C₆₇×#2416	C₂	semidirect
19. C₂×#385×C₆₇	C₂	semidirect
29. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
38. C₂×#121×C₆₇	C₂²	semidirect
46. #400×C₆₇	C₂²	semidirect
47. #399×C₆₇	C₂²	semidirect
48. #398×C₆₇	C₂²	semidirect
49. #398×C₆₇	C₂²	semidirect
50. #398×C₆₇	C₂²	semidirect
55. #397×C₆₇	C₂²	semidirect
56. #396×C₆₇	C₂²	semidirect
57. #396×C₆₇	C₂²	semidirect
58. #396×C₆₇	C₂²	semidirect
59. #396×C₆₇	C₂²	semidirect
60. #395×C₆₇	C₂²	semidirect
65. #394×C₆₇	C₂²	semidirect
66. #394×C₆₇	C₂²	semidirect
67. #394×C₆₇	C₂²	semidirect
68. #393×C₆₇	C₂²	semidirect
73. #392×C₆₇	C₂²	semidirect
74. #391×C₆₇	C₂²	semidirect
75. #390×C₆₇	C₂²	semidirect
76. #389×C₆₇	C₂²	semidirect
77. #389×C₆₇	C₂²	semidirect
78. #388×C₆₇	C₂²	semidirect
79. #388×C₆₇	C₂²	semidirect
80. #387×C₆₇	C₂²	semidirect
81. #387×C₆₇	C₂²	semidirect
90. #386×C₆₇	C₂²	semidirect
91. #386×C₆₇	C₂²	semidirect
98. #385×C₆₇	C₂²	semidirect
99. #385×C₆₇	C₂²	semidirect
105. #380×C₆₇	C₂²	semidirect
106. #380×C₆₇	C₂²	semidirect
171. C₂×C₂²⋊C₄×C₆₇	D₄	semidirect
490. #36738	C₆₇	direct (N × H)
501. C₂×#538	C₂×C₆₇	semidirect
502. #2847	C₂×C₆₇	semidirect
503. #2722	C₂×C₆₇	semidirect
504. #2715	C₂×C₆₇	semidirect
505. #2712	C₂×C₆₇	semidirect
506. #2695	C₂×C₆₇	semidirect
507. #2693	C₂×C₆₇	semidirect
508. #2691	C₂×C₆₇	semidirect
509. #2676	C₂×C₆₇	semidirect
510. #2675	C₂×C₆₇	semidirect
511. #2672	C₂×C₆₇	semidirect
512. #2671	C₂×C₆₇	semidirect
513. #2617	C₂×C₆₇	semidirect
514. #2617	C₂×C₆₇	semidirect
515. #2564	C₂×C₆₇	semidirect
516. #2543	C₂×C₆₇	semidirect
517. #2417	C₂×C₆₇	semidirect
518. #2416	C₂×C₆₇	semidirect
519. C₂×#385	C₂×C₆₇	semidirect
520. C₆₇	#36738	direct (N × H)
530. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
539. C₂×#121	C₂²×C₆₇	semidirect
547. #400	C₂²×C₆₇	semidirect
548. #399	C₂²×C₆₇	semidirect
549. #398	C₂²×C₆₇	semidirect
550. #398	C₂²×C₆₇	semidirect
551. #398	C₂²×C₆₇	semidirect
556. #397	C₂²×C₆₇	semidirect
557. #396	C₂²×C₆₇	semidirect
558. #396	C₂²×C₆₇	semidirect
559. #396	C₂²×C₆₇	semidirect
560. #396	C₂²×C₆₇	semidirect
561. #395	C₂²×C₆₇	semidirect
566. #394	C₂²×C₆₇	semidirect
567. #394	C₂²×C₆₇	semidirect
568. #394	C₂²×C₆₇	semidirect
569. #393	C₂²×C₆₇	semidirect
574. #392	C₂²×C₆₇	semidirect
575. #391	C₂²×C₆₇	semidirect
576. #390	C₂²×C₆₇	semidirect
577. #389	C₂²×C₆₇	semidirect
578. #389	C₂²×C₆₇	semidirect
579. #388	C₂²×C₆₇	semidirect
580. #388	C₂²×C₆₇	semidirect
581. #387	C₂²×C₆₇	semidirect
582. #387	C₂²×C₆₇	semidirect
591. #386	C₂²×C₆₇	semidirect
592. #386	C₂²×C₆₇	semidirect
599. #385	C₂²×C₆₇	semidirect
600. #385	C₂²×C₆₇	semidirect
606. #380	C₂²×C₆₇	semidirect
607. #380	C₂²×C₆₇	semidirect
672. C₂×C₂²⋊C₄	D₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#538×C₆₇	2
C₆₇×#2847	2
C₆₇×#2722	2
C₆₇×#2715	2
C₆₇×#2712	2
C₆₇×#2695	2
C₆₇×#2693	2
C₆₇×#2691	2
C₆₇×#2676	2
C₆₇×#2675	2
C₆₇×#2672	2
C₆₇×#2671	2
C₆₇×#2617	2
C₆₇×#2564	2
C₆₇×#2543	2
C₆₇×#2417	2
C₆₇×#2416	2
C₂×#385×C₆₇	2
#36738	67

Subgroups — C67×#36738 #30715989

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#36738 #30715989