Subgroups — C₆₇×#59371 #30738622

Order 17152.

2246 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2763	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#2746	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2693	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2598	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2589	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2576	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2564	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2561	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2523	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2493	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2463	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2449	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2418	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2404	C₂	1	1	yes	maximal, characteristic
15	C₆₇×#2359	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2352	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2339	C₂	1	2	yes	maximal, complemented
18	C₄×#120×C₆₇	C₂	1	2	yes	maximal, complemented
19	C₂×#385×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#123×C₆₇	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
25	C₂×#120×C₆₇	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
30	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
31	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
32	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
34	#401×C₆₇	C₂²	1	2	yes	complemented
35	#400×C₆₇	C₂²	1	2	yes	complemented
36	#400×C₆₇	C₂²	1	2	yes	complemented
37	#400×C₆₇	C₂²	1	2	yes	complemented
38	#399×C₆₇	C₂²	1	2	yes	—
39	#399×C₆₇	C₂²	1	2	yes	complemented
40	#398×C₆₇	C₂²	1	2	yes	complemented
41	#397×C₆₇	C₂²	1	1	yes	characteristic
42	#397×C₆₇	C₂²	1	2	yes	—
43	#397×C₆₇	C₂²	1	1	yes	characteristic
44	#396×C₆₇	C₂²	1	2	yes	complemented
45	#395×C₆₇	C₂²	1	2	yes	complemented
46	#394×C₆₇	C₂²	1	2	yes	—
47	#394×C₆₇	C₂²	1	2	yes	—
48	#393×C₆₇	C₂²	1	1	yes	characteristic
49	#393×C₆₇	C₂²	1	1	yes	characteristic
50	#393×C₆₇	C₂²	1	1	yes	characteristic
51	#393×C₆₇	C₂²	1	1	yes	characteristic
52	#392×C₆₇	C₂²	1	1	yes	characteristic
53	#392×C₆₇	C₂²	1	1	yes	characteristic
54	#391×C₆₇	C₂²	1	2	yes	complemented
55	#391×C₆₇	C₂²	1	2	yes	complemented
56	#389×C₆₇	C₂²	1	2	yes	complemented
57	#388×C₆₇	C₂²	1	2	yes	—
58	#388×C₆₇	C₂²	1	2	yes	—
59	#388×C₆₇	C₂²	1	2	yes	—
60	#388×C₆₇	C₂²	1	2	yes	—
61	#388×C₆₇	C₂²	1	2	yes	complemented
62	#388×C₆₇	C₂²	1	2	yes	complemented
63	#387×C₆₇	C₂²	1	2	yes	complemented
64	#387×C₆₇	C₂²	1	2	yes	complemented
65	#387×C₆₇	C₂²	1	2	yes	complemented
66	#387×C₆₇	C₂²	1	2	yes	complemented
67	#387×C₆₇	C₂²	1	2	yes	complemented
68	#387×C₆₇	C₂²	1	2	yes	complemented
69	#386×C₆₇	C₂²	1	2	yes	—
70	#386×C₆₇	C₂²	1	2	yes	—
71	#386×C₆₇	C₂²	1	2	yes	—
72	#386×C₆₇	C₂²	1	2	yes	—
73	#386×C₆₇	C₂²	1	2	yes	—
74	#386×C₆₇	C₂²	1	2	yes	—
75	#386×C₆₇	C₂²	1	2	yes	—
76	#386×C₆₇	C₂²	1	2	yes	—
77	#386×C₆₇	C₂²	1	2	yes	complemented
78	#386×C₆₇	C₂²	1	2	yes	complemented
79	#385×C₆₇	C₂²	1	1	yes	characteristic
80	#385×C₆₇	C₂²	1	2	yes	—
81	#385×C₆₇	C₂²	1	1	yes	characteristic
82	#385×C₆₇	C₂²	1	2	yes	—
83	#385×C₆₇	C₂²	1	2	yes	—
84	#385×C₆₇	C₂²	1	1	yes	characteristic
85	#385×C₆₇	C₂²	1	1	yes	characteristic
86	#385×C₆₇	C₂²	1	2	yes	—
87	#385×C₆₇	C₂²	1	2	yes	—
88	#385×C₆₇	C₂²	1	2	yes	—
89	#385×C₆₇	C₂²	1	2	yes	complemented
90	#383×C₆₇	C₂²	1	2	yes	complemented
91	#382×C₆₇	C₂²	1	2	yes	complemented
92	#381×C₆₇	C₂²	1	2	yes	—
93	#381×C₆₇	C₂²	1	1	yes	characteristic
94	#381×C₆₇	C₂²	1	2	yes	complemented
95	#380×C₆₇	C₂²	1	2	yes	—
96	#380×C₆₇	C₂²	1	2	yes	complemented
97	#380×C₆₇	C₂²	1	2	yes	complemented
98	#379×C₆₇	C₂²	1	2	yes	—
99	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
100	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
104	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
105	C₂×#95×C₆₇	C₂²	1	2	yes	—
106	C₂×#95×C₆₇	C₂²	1	2	yes	complemented
107	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
108	C₂×#41×C₆₇	—	2	8	no	—
109	C₂×#41×C₆₇	—	4	2	no	—
110	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
111	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
113	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
114	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
115	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
116	C₂³×C₄×C₆₇	—	4	4	no	—
117	C₂³×C₄×C₆₇	—	4	2	no	—
118	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
120	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
121	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
122	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
124	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
126	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
127	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
128	#123×C₆₇	—	2	8	no	—
129	C₂²⋊Q₈×C₆₇	—	4	2	no	—
130	C₂²⋊Q₈×C₆₇	—	4	4	no	—
131	#120×C₆₇	—	2	8	no	—
132	C₄×D₄×C₆₇	—	2	8	no	—
133	C₄×D₄×C₆₇	—	4	4	no	—
134	C₄×D₄×C₆₇	—	4	4	no	—
135	C₄×D₄×C₆₇	—	4	4	no	—
136	#117×C₆₇	—	4	4	no	—
137	C₂×C₄⋊C₄×C₆₇	—	4	4	no	—
138	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
153	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
154	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
167	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
168	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
178	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
179	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
180	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
181	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
182	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
183	#95×C₆₇	C₂³	1	2	yes	—
184	#95×C₆₇	C₂³	1	2	yes	—
185	#95×C₆₇	C₂³	1	2	yes	—
186	#95×C₆₇	C₂³	1	2	yes	—
187	#95×C₆₇	C₂³	1	2	yes	—
188	#95×C₆₇	C₂³	1	2	yes	—
189	#95×C₆₇	C₂³	1	2	yes	—
190	#95×C₆₇	C₂³	1	1	yes	characteristic
191	#95×C₆₇	C₂³	1	2	yes	—
192	#95×C₆₇	C₂³	1	2	yes	—
193	#95×C₆₇	C₂³	1	1	yes	characteristic
194	#95×C₆₇	C₂³	1	2	yes	—
195	#95×C₆₇	C₂³	1	2	yes	—
196	#95×C₆₇	C₂³	1	2	yes	—
197	#95×C₆₇	C₂³	1	2	yes	—
198	#95×C₆₇	C₂³	1	2	yes	—
199	#95×C₆₇	C₂³	1	2	yes	—
200	#95×C₆₇	C₂³	1	2	yes	—
201	#95×C₆₇	C₂³	1	1	yes	characteristic
202	#95×C₆₇	C₂³	1	2	yes	—
203	#95×C₆₇	C₂³	1	2	yes	—
204	#95×C₆₇	C₂³	1	2	yes	—
205	#95×C₆₇	C₂³	1	1	yes	characteristic
206	#95×C₆₇	C₂³	1	2	yes	—
207	#95×C₆₇	C₂³	1	2	yes	—
208	#95×C₆₇	C₂³	1	2	yes	—
209	#95×C₆₇	C₂³	1	2	yes	—
210	C₂⁴×C₆₇	—	2	2	no	—
211	C₂⁴×C₆₇	—	2	2	no	—
212	C₂⁴×C₆₇	—	2	2	no	—
213	C₂⁴×C₆₇	—	2	4	no	—
214	C₂⁴×C₆₇	—	4	2	no	—
215	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
216	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
217	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
218	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
219	#41×C₆₇	—	4	16	no	—
220	C₂×Q₈×C₆₇	—	2	4	no	—
221	C₂×Q₈×C₆₇	—	4	1	no	—
222	C₂×Q₈×C₆₇	—	4	1	no	—
223	C₂×Q₈×C₆₇	—	4	2	no	—
224	C₂×D₄×C₆₇	—	2	4	no	—
225	C₂×D₄×C₆₇	—	2	4	no	—
226	C₂×D₄×C₆₇	—	2	4	no	—
227	C₂×D₄×C₆₇	—	2	4	no	—
228	C₂×D₄×C₆₇	—	2	4	no	—
229	C₂×D₄×C₆₇	—	2	4	no	—
230	C₂×D₄×C₆₇	—	2	4	no	—
231	C₂×D₄×C₆₇	—	4	2	no	—
232	C₂×D₄×C₆₇	—	4	2	no	—
233	C₂×D₄×C₆₇	—	4	1	no	—
234	C₂×D₄×C₆₇	#41	1	8	yes	—
235	C₂²×C₄×C₆₇	—	2	4	no	—
236	C₂²×C₄×C₆₇	—	2	4	no	—
237	C₂²×C₄×C₆₇	—	2	4	no	—
238	C₂²×C₄×C₆₇	—	2	4	no	—
239	C₂²×C₄×C₆₇	—	2	2	no	—
240	C₂²×C₄×C₆₇	—	2	4	no	—
241	C₂²×C₄×C₆₇	—	2	2	no	—
242	C₂²×C₄×C₆₇	—	2	4	no	—
243	C₂²×C₄×C₆₇	—	2	4	no	—
244	C₂²×C₄×C₆₇	—	2	4	no	—
245	C₂²×C₄×C₆₇	—	2	4	no	—
246	C₂²×C₄×C₆₇	—	2	4	no	—
247	C₂²×C₄×C₆₇	—	2	4	no	—
248	C₂²×C₄×C₆₇	—	2	4	no	—
249	C₂²×C₄×C₆₇	—	4	2	no	—
250	C₂²×C₄×C₆₇	—	4	2	no	—
251	C₂²×C₄×C₆₇	—	4	1	no	—
252	C₂²×C₄×C₆₇	—	4	2	no	—
253	C₂²×C₄×C₆₇	—	4	2	no	—
254	C₂²×C₄×C₆₇	—	4	2	no	—
255	C₂²×C₄×C₆₇	—	4	1	no	—
256	C₂²×C₄×C₆₇	—	4	2	no	—
257	C₂²×C₄×C₆₇	—	4	2	no	—
258	C₂²×C₄×C₆₇	—	4	2	no	—
259	C₂²×C₄×C₆₇	—	4	2	no	—
260	C₂²×C₄×C₆₇	—	4	2	no	—
261	C₂²×C₄×C₆₇	—	4	16	no	—
262	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
277	C₄⋊C₄×C₆₇	—	2	4	no	—
278	C₄⋊C₄×C₆₇	—	2	4	no	—
279	C₄⋊C₄×C₆₇	—	2	4	no	—
280	C₄⋊C₄×C₆₇	—	2	4	no	—
281	C₄⋊C₄×C₆₇	—	2	4	no	—
282	C₄⋊C₄×C₆₇	—	2	4	no	—
283	C₄⋊C₄×C₆₇	—	4	2	no	—
284	C₄⋊C₄×C₆₇	—	4	2	no	—
285	C₄⋊C₄×C₆₇	—	4	2	no	—
286	C₄⋊C₄×C₆₇	—	4	2	no	—
287	C₄⋊C₄×C₆₇	—	4	2	no	—
288	C₄⋊C₄×C₆₇	—	4	1	no	—
289	C₄⋊C₄×C₆₇	—	4	2	no	—
290	C₄⋊C₄×C₆₇	—	4	2	no	—
291	C₂²⋊C₄×C₆₇	—	2	2	no	—
292	C₂²⋊C₄×C₆₇	—	2	4	no	—
293	C₂²⋊C₄×C₆₇	—	2	4	no	—
294	C₂²⋊C₄×C₆₇	—	2	4	no	—
295	C₂²⋊C₄×C₆₇	—	2	4	no	—
296	C₂²⋊C₄×C₆₇	—	2	4	no	—
297	C₂²⋊C₄×C₆₇	—	2	4	no	—
298	C₂²⋊C₄×C₆₇	—	2	4	no	—
299	C₂²⋊C₄×C₆₇	—	2	4	no	—
300	C₂²⋊C₄×C₆₇	—	2	4	no	—
301	C₂²⋊C₄×C₆₇	—	2	4	no	—
302	C₂²⋊C₄×C₆₇	—	2	4	no	—
303	C₂²⋊C₄×C₆₇	—	4	1	no	—
304	C₂²⋊C₄×C₆₇	—	4	1	no	—
305	C₂²⋊C₄×C₆₇	—	4	1	no	—
306	C₂²⋊C₄×C₆₇	—	4	1	no	—
307	C₂²⋊C₄×C₆₇	—	4	2	no	—
308	C₂²⋊C₄×C₆₇	—	4	2	no	—
309	C₂²⋊C₄×C₆₇	—	4	2	no	—
310	C₂²⋊C₄×C₆₇	—	4	2	no	—
311	C₂²⋊C₄×C₆₇	—	4	2	no	—
312	C₂²⋊C₄×C₆₇	—	4	2	no	—
313	C₂²⋊C₄×C₆₇	—	4	2	no	—
314	C₂²⋊C₄×C₆₇	#41	1	4	yes	complemented
315	C₄²×C₆₇	—	2	4	no	—
316	C₄²×C₆₇	—	2	4	no	—
317	C₄²×C₆₇	—	4	2	no	—
318	C₄²×C₆₇	—	4	2	no	—
319	C₄²×C₆₇	—	4	2	no	—
320	C₂³×C₆₇	—	2	1	no	—
321	C₂³×C₆₇	—	2	2	no	—
322	C₂³×C₆₇	—	2	1	no	—
323	C₂³×C₆₇	—	2	8	no	—
324	C₂³×C₆₇	—	2	1	no	—
325	C₂³×C₆₇	—	2	2	no	—
326	C₂³×C₆₇	—	2	2	no	—
327	C₂³×C₆₇	—	2	2	no	—
328	C₂³×C₆₇	—	2	2	no	—
329	C₂³×C₆₇	—	2	2	no	—
330	C₂³×C₆₇	—	2	2	no	—
331	C₂³×C₆₇	—	2	1	no	—
332	C₂³×C₆₇	—	2	1	no	—
333	C₂³×C₆₇	—	2	2	no	—
334	C₂³×C₆₇	—	2	2	no	—
335	C₂³×C₆₇	—	2	2	no	—
336	C₂³×C₆₇	—	2	2	no	—
337	C₂³×C₆₇	—	2	1	no	—
338	C₂³×C₆₇	—	4	8	no	—
339	C₂³×C₆₇	—	4	8	no	—
340	C₂³×C₆₇	—	4	4	no	—
341	C₂³×C₆₇	—	4	4	no	—
342	C₂³×C₆₇	C₂×#41	1	2	yes	—
343	C₂³×C₆₇	C₂×#41	1	4	yes	—
344	C₂³×C₆₇	C₂×#41	1	4	yes	—
345	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
346	C₂³×C₆₇	2₋¹⁺⁴	1	2	yes	—
347	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
348	Q₈×C₆₇	—	4	4	no	—
349	Q₈×C₆₇	—	8	2	no	—
350	D₄×C₆₇	—	2	16	no	—
351	D₄×C₆₇	—	4	8	no	—
352	D₄×C₆₇	—	4	8	no	—
353	D₄×C₆₇	—	4	4	no	—
354	C₂×C₄×C₆₇	—	2	2	no	—
355	C₂×C₄×C₆₇	—	2	2	no	—
356	C₂×C₄×C₆₇	—	2	2	no	—
357	C₂×C₄×C₆₇	—	2	2	no	—
358	C₂×C₄×C₆₇	—	2	2	no	—
359	C₂×C₄×C₆₇	—	2	2	no	—
360	C₂×C₄×C₆₇	—	2	2	no	—
361	C₂×C₄×C₆₇	—	2	2	no	—
362	C₂×C₄×C₆₇	—	2	2	no	—
363	C₂×C₄×C₆₇	—	2	2	no	—
364	C₂×C₄×C₆₇	—	2	2	no	—
365	C₂×C₄×C₆₇	—	2	2	no	—
366	C₂×C₄×C₆₇	—	2	2	no	—
367	C₂×C₄×C₆₇	—	2	2	no	—
368	C₂×C₄×C₆₇	—	2	2	no	—
369	C₂×C₄×C₆₇	—	2	2	no	—
370	C₂×C₄×C₆₇	—	2	2	no	—
371	C₂×C₄×C₆₇	—	2	2	no	—
372	C₂×C₄×C₆₇	—	2	2	no	—
373	C₂×C₄×C₆₇	—	2	2	no	—
374	C₂×C₄×C₆₇	—	2	2	no	—
375	C₂×C₄×C₆₇	—	2	2	no	—
376	C₂×C₄×C₆₇	—	2	2	no	—
377	C₂×C₄×C₆₇	—	2	2	no	—
378	C₂×C₄×C₆₇	—	2	2	no	—
379	C₂×C₄×C₆₇	—	2	1	no	—
380	C₂×C₄×C₆₇	—	2	1	no	—
381	C₂×C₄×C₆₇	—	2	1	no	—
382	C₂×C₄×C₆₇	—	2	1	no	—
383	C₂×C₄×C₆₇	—	2	2	no	—
384	C₂×C₄×C₆₇	—	2	2	no	—
385	C₂×C₄×C₆₇	—	2	2	no	—
386	C₂×C₄×C₆₇	—	2	2	no	—
387	C₂×C₄×C₆₇	—	2	2	no	—
388	C₂×C₄×C₆₇	—	2	2	no	—
389	C₂×C₄×C₆₇	—	2	2	no	—
390	C₂×C₄×C₆₇	—	2	2	no	—
391	C₂×C₄×C₆₇	—	2	2	no	—
392	C₂×C₄×C₆₇	—	4	4	no	—
393	C₂×C₄×C₆₇	—	4	8	no	—
394	C₂×C₄×C₆₇	—	4	8	no	—
395	C₂×C₄×C₆₇	—	4	8	no	—
396	C₂×C₄×C₆₇	—	4	8	no	—
397	C₂×C₄×C₆₇	—	4	8	no	—
398	C₂×C₄×C₆₇	—	4	4	no	—
399	C₂×C₄×C₆₇	—	4	4	no	—
400	C₂×C₄×C₆₇	—	8	4	no	—
401	C₂×C₄×C₆₇	—	8	2	no	—
402	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
403	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
404	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
405	C₂²×C₆₇	—	2	4	no	—
406	C₂²×C₆₇	—	2	2	no	—
407	C₂²×C₆₇	—	2	4	no	—
408	C₂²×C₆₇	—	2	2	no	—
409	C₂²×C₆₇	—	2	4	no	—
410	C₂²×C₆₇	—	2	4	no	—
411	C₂²×C₆₇	—	2	4	no	—
412	C₂²×C₆₇	—	2	2	no	—
413	C₂²×C₆₇	—	2	2	no	—
414	C₂²×C₆₇	—	2	4	no	—
415	C₂²×C₆₇	—	2	4	no	—
416	C₂²×C₆₇	—	4	16	no	—
417	C₂²×C₆₇	—	4	1	no	—
418	C₂²×C₆₇	—	4	1	no	—
419	C₂²×C₆₇	—	4	2	no	—
420	C₂²×C₆₇	—	4	2	no	—
421	C₂²×C₆₇	—	4	2	no	—
422	C₂²×C₆₇	—	4	2	no	—
423	C₂²×C₆₇	—	4	2	no	—
424	C₂²×C₆₇	—	4	1	no	—
425	C₂²×C₆₇	—	4	1	no	—
426	C₂²×C₆₇	—	4	2	no	—
427	C₂²×C₆₇	#551	1	4	yes	—
428	C₂²×C₆₇	C₂²×#41	1	2	yes	—
429	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
430	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
431	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
432	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
433	C₄×C₆₇	—	2	4	no	—
434	C₄×C₆₇	—	2	4	no	—
435	C₄×C₆₇	—	2	4	no	—
436	C₄×C₆₇	—	4	1	no	—
437	C₄×C₆₇	—	4	1	no	—
438	C₄×C₆₇	—	4	2	no	—
439	C₄×C₆₇	—	4	2	no	—
440	C₄×C₆₇	—	4	2	no	—
441	C₄×C₆₇	—	4	2	no	—
442	C₄×C₆₇	—	4	2	no	—
443	C₄×C₆₇	—	4	2	no	—
444	C₄×C₆₇	—	4	2	no	—
445	C₄×C₆₇	—	4	1	no	—
446	C₄×C₆₇	—	4	2	no	—
447	C₄×C₆₇	—	4	1	no	—
448	#59371	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
449	C₂×C₆₇	—	2	4	no	—
450	C₂×C₆₇	—	4	4	no	—
451	C₂×C₆₇	—	4	2	no	—
452	C₂×C₆₇	—	4	2	no	—
453	C₂×C₆₇	C₂×#551	1	1	yes	characteristic
454	C₂×C₆₇	#3481	1	2	yes	—
455	C₂×C₆₇	#3492	1	1	yes	characteristic
456	C₂×C₆₇	#3520	1	2	yes	—
457	C₂×C₆₇	#3532	1	1	yes	characteristic
458	#2763	C₂×C₆₇	1	1	yes	characteristic, complemented
459	#2746	C₂×C₆₇	1	2	yes	complemented
460	#2693	C₂×C₆₇	1	1	yes	characteristic, complemented
461	#2598	C₂×C₆₇	1	2	yes	complemented
462	#2589	C₂×C₆₇	1	2	yes	complemented
463	#2576	C₂×C₆₇	1	2	yes	complemented
464	#2564	C₂×C₆₇	1	2	yes	complemented
465	#2561	C₂×C₆₇	1	1	yes	characteristic, complemented
466	#2523	C₂×C₆₇	1	1	yes	characteristic, complemented
467	#2493	C₂×C₆₇	1	2	yes	complemented
468	#2463	C₂×C₆₇	1	1	yes	characteristic, complemented
469	#2449	C₂×C₆₇	1	2	yes	complemented
470	#2418	C₂×C₆₇	1	2	yes	complemented
471	#2404	C₂×C₆₇	1	1	yes	characteristic
472	#2359	C₂×C₆₇	1	2	yes	complemented
473	#2352	C₂×C₆₇	1	2	yes	complemented
474	#2339	C₂×C₆₇	1	2	yes	complemented
475	C₄×#120	C₂×C₆₇	1	2	yes	complemented
476	C₂×#385	C₂×C₆₇	1	1	yes	characteristic, complemented
477	C₆₇	#59371	1	1	yes	characteristic, direct product factor, Sylow
478	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
479	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
480	C₂×#123	C₂²×C₆₇	1	2	yes	—
481	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
482	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
483	C₂×#120	C₂²×C₆₇	1	2	yes	—
484	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
485	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
486	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
487	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
488	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
489	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
490	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
491	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
492	#401	C₂²×C₆₇	1	2	yes	complemented
493	#400	C₂²×C₆₇	1	2	yes	complemented
494	#400	C₂²×C₆₇	1	2	yes	complemented
495	#400	C₂²×C₆₇	1	2	yes	complemented
496	#399	C₂²×C₆₇	1	2	yes	—
497	#399	C₂²×C₆₇	1	2	yes	complemented
498	#398	C₂²×C₆₇	1	2	yes	complemented
499	#397	C₂²×C₆₇	1	1	yes	characteristic
500	#397	C₂²×C₆₇	1	1	yes	characteristic
501	#397	C₂²×C₆₇	1	2	yes	—
502	#396	C₂²×C₆₇	1	2	yes	complemented
503	#395	C₂²×C₆₇	1	2	yes	complemented
504	#394	C₂²×C₆₇	1	2	yes	—
505	#394	C₂²×C₆₇	1	2	yes	—
506	#393	C₂²×C₆₇	1	1	yes	characteristic
507	#393	C₂²×C₆₇	1	1	yes	characteristic
508	#393	C₂²×C₆₇	1	1	yes	characteristic
509	#393	C₂²×C₆₇	1	1	yes	characteristic
510	#392	C₂²×C₆₇	1	1	yes	characteristic
511	#392	C₂²×C₆₇	1	1	yes	characteristic
512	#391	C₂²×C₆₇	1	2	yes	complemented
513	#391	C₂²×C₆₇	1	2	yes	complemented
514	#389	C₂²×C₆₇	1	2	yes	complemented
515	#388	C₂²×C₆₇	1	2	yes	—
516	#388	C₂²×C₆₇	1	2	yes	—
517	#388	C₂²×C₆₇	1	2	yes	—
518	#388	C₂²×C₆₇	1	2	yes	—
519	#388	C₂²×C₆₇	1	2	yes	complemented
520	#388	C₂²×C₆₇	1	2	yes	complemented
521	#387	C₂²×C₆₇	1	2	yes	complemented
522	#387	C₂²×C₆₇	1	2	yes	complemented
523	#387	C₂²×C₆₇	1	2	yes	complemented
524	#387	C₂²×C₆₇	1	2	yes	complemented
525	#387	C₂²×C₆₇	1	2	yes	complemented
526	#387	C₂²×C₆₇	1	2	yes	complemented
527	#386	C₂²×C₆₇	1	2	yes	—
528	#386	C₂²×C₆₇	1	2	yes	—
529	#386	C₂²×C₆₇	1	2	yes	—
530	#386	C₂²×C₆₇	1	2	yes	—
531	#386	C₂²×C₆₇	1	2	yes	—
532	#386	C₂²×C₆₇	1	2	yes	—
533	#386	C₂²×C₆₇	1	2	yes	—
534	#386	C₂²×C₆₇	1	2	yes	—
535	#386	C₂²×C₆₇	1	2	yes	complemented
536	#386	C₂²×C₆₇	1	2	yes	complemented
537	#385	C₂²×C₆₇	1	2	yes	—
538	#385	C₂²×C₆₇	1	2	yes	—
539	#385	C₂²×C₆₇	1	2	yes	—
540	#385	C₂²×C₆₇	1	1	yes	characteristic
541	#385	C₂²×C₆₇	1	2	yes	—
542	#385	C₂²×C₆₇	1	1	yes	characteristic
543	#385	C₂²×C₆₇	1	2	yes	—
544	#385	C₂²×C₆₇	1	1	yes	characteristic
545	#385	C₂²×C₆₇	1	1	yes	characteristic
546	#385	C₂²×C₆₇	1	2	yes	—
547	#385	C₂²×C₆₇	1	2	yes	complemented
548	#383	C₂²×C₆₇	1	2	yes	complemented
549	#382	C₂²×C₆₇	1	2	yes	complemented
550	#381	C₂²×C₆₇	1	2	yes	—
551	#381	C₂²×C₆₇	1	1	yes	characteristic
552	#381	C₂²×C₆₇	1	2	yes	complemented
553	#380	C₂²×C₆₇	1	2	yes	—
554	#380	C₂²×C₆₇	1	2	yes	complemented
555	#380	C₂²×C₆₇	1	2	yes	complemented
556	#379	C₂²×C₆₇	1	2	yes	—
557	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
558	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
559	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
560	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
561	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
562	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
563	C₂×#95	C₂²×C₆₇	1	2	yes	—
564	C₂×#95	C₂²×C₆₇	1	2	yes	complemented
565	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
566	C₂×#41	—	2	8	no	—
567	C₂×#41	—	4	2	no	—
568	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
569	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
570	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
571	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
572	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
573	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
574	C₂³×C₄	—	4	4	no	—
575	C₂³×C₄	—	4	2	no	—
576	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
577	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
578	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
579	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
580	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
581	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
582	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
583	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
584	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
585	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
586	#123	—	2	8	no	—
587	C₂²⋊Q₈	—	4	2	no	—
588	C₂²⋊Q₈	—	4	4	no	—
589	#120	—	2	8	no	—
590	C₄×D₄	—	2	8	no	—
591	C₄×D₄	—	4	4	no	—
592	C₄×D₄	—	4	4	no	—
593	C₄×D₄	—	4	4	no	—
594	#117	—	4	4	no	—
595	C₂×C₄⋊C₄	—	4	4	no	—
596	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
610	C₂×C₂²⋊C₄	—	2	4	no	—
611	C₂×C₂²⋊C₄	—	4	2	no	—
612	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
614	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
625	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
626	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
627	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
628	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
636	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
637	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
638	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
639	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
640	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
641	#95	C₂³×C₆₇	1	2	yes	—
642	#95	C₂³×C₆₇	1	2	yes	—
643	#95	C₂³×C₆₇	1	2	yes	—
644	#95	C₂³×C₆₇	1	2	yes	—
645	#95	C₂³×C₆₇	1	2	yes	—
646	#95	C₂³×C₆₇	1	2	yes	—
647	#95	C₂³×C₆₇	1	2	yes	—
648	#95	C₂³×C₆₇	1	1	yes	characteristic
649	#95	C₂³×C₆₇	1	2	yes	—
650	#95	C₂³×C₆₇	1	2	yes	—
651	#95	C₂³×C₆₇	1	1	yes	characteristic
652	#95	C₂³×C₆₇	1	2	yes	—
653	#95	C₂³×C₆₇	1	2	yes	—
654	#95	C₂³×C₆₇	1	2	yes	—
655	#95	C₂³×C₆₇	1	2	yes	—
656	#95	C₂³×C₆₇	1	2	yes	—
657	#95	C₂³×C₆₇	1	2	yes	—
658	#95	C₂³×C₆₇	1	2	yes	—
659	#95	C₂³×C₆₇	1	1	yes	characteristic
660	#95	C₂³×C₆₇	1	2	yes	—
661	#95	C₂³×C₆₇	1	2	yes	—
662	#95	C₂³×C₆₇	1	2	yes	—
663	#95	C₂³×C₆₇	1	1	yes	characteristic
664	#95	C₂³×C₆₇	1	2	yes	—
665	#95	C₂³×C₆₇	1	2	yes	—
666	#95	C₂³×C₆₇	1	2	yes	—
667	#95	C₂³×C₆₇	1	2	yes	—
668	C₂⁴	—	2	2	no	—
669	C₂⁴	—	2	2	no	—
670	C₂⁴	—	2	2	no	—
671	C₂⁴	—	2	4	no	—
672	C₂⁴	—	4	2	no	—
673	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
674	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
675	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
676	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
677	#41	—	4	16	no	—
678	C₂×Q₈	—	2	4	no	—
679	C₂×Q₈	—	4	1	no	—
680	C₂×Q₈	—	4	1	no	—
681	C₂×Q₈	—	4	2	no	—
682	C₂×D₄	—	2	4	no	—
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	2	4	no	—
686	C₂×D₄	—	2	4	no	—
687	C₂×D₄	—	2	4	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	4	2	no	—
690	C₂×D₄	—	4	2	no	—
691	C₂×D₄	—	4	1	no	—
692	C₂×D₄	#41×C₆₇	1	8	yes	—
693	C₂²×C₄	—	2	4	no	—
694	C₂²×C₄	—	2	4	no	—
695	C₂²×C₄	—	2	4	no	—
696	C₂²×C₄	—	2	4	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	4	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	4	no	—
701	C₂²×C₄	—	2	4	no	—
702	C₂²×C₄	—	2	4	no	—
703	C₂²×C₄	—	2	4	no	—
704	C₂²×C₄	—	2	4	no	—
705	C₂²×C₄	—	2	4	no	—
706	C₂²×C₄	—	2	4	no	—
707	C₂²×C₄	—	4	2	no	—
708	C₂²×C₄	—	4	2	no	—
709	C₂²×C₄	—	4	1	no	—
710	C₂²×C₄	—	4	2	no	—
711	C₂²×C₄	—	4	2	no	—
712	C₂²×C₄	—	4	2	no	—
713	C₂²×C₄	—	4	1	no	—
714	C₂²×C₄	—	4	2	no	—
715	C₂²×C₄	—	4	2	no	—
716	C₂²×C₄	—	4	2	no	—
717	C₂²×C₄	—	4	2	no	—
718	C₂²×C₄	—	4	2	no	—
719	C₂²×C₄	—	4	16	no	—
720	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	2	4	no	—
740	C₄⋊C₄	—	2	4	no	—
741	C₄⋊C₄	—	4	2	no	—
742	C₄⋊C₄	—	4	2	no	—
743	C₄⋊C₄	—	4	2	no	—
744	C₄⋊C₄	—	4	2	no	—
745	C₄⋊C₄	—	4	2	no	—
746	C₄⋊C₄	—	4	1	no	—
747	C₄⋊C₄	—	4	2	no	—
748	C₄⋊C₄	—	4	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	4	no	—
761	C₂²⋊C₄	—	4	1	no	—
762	C₂²⋊C₄	—	4	1	no	—
763	C₂²⋊C₄	—	4	1	no	—
764	C₂²⋊C₄	—	4	1	no	—
765	C₂²⋊C₄	—	4	2	no	—
766	C₂²⋊C₄	—	4	2	no	—
767	C₂²⋊C₄	—	4	2	no	—
768	C₂²⋊C₄	—	4	2	no	—
769	C₂²⋊C₄	—	4	2	no	—
770	C₂²⋊C₄	—	4	2	no	—
771	C₂²⋊C₄	—	4	2	no	—
772	C₂²⋊C₄	#41×C₆₇	1	4	yes	complemented
773	C₄²	—	2	4	no	—
774	C₄²	—	2	4	no	—
775	C₄²	—	4	2	no	—
776	C₄²	—	4	2	no	—
777	C₄²	—	4	2	no	—
778	C₂³	—	2	1	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	1	no	—
781	C₂³	—	2	8	no	—
782	C₂³	—	2	1	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	1	no	—
790	C₂³	—	2	1	no	—
791	C₂³	—	2	2	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	1	no	—
796	C₂³	—	4	8	no	—
797	C₂³	—	4	8	no	—
798	C₂³	—	4	4	no	—
799	C₂³	—	4	4	no	—
800	C₂³	C₂×#41×C₆₇	1	2	yes	—
801	C₂³	C₂×#41×C₆₇	1	4	yes	—
802	C₂³	C₂×#41×C₆₇	1	4	yes	—
803	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
804	C₂³	2₋¹⁺⁴×C₆₇	1	2	yes	—
805	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
806	Q₈	—	4	4	no	—
807	Q₈	—	8	2	no	—
808	D₄	—	2	16	no	—
809	D₄	—	4	4	no	—
810	D₄	—	4	8	no	—
811	D₄	—	4	8	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	4	4	no	—
851	C₂×C₄	—	4	8	no	—
852	C₂×C₄	—	4	8	no	—
853	C₂×C₄	—	4	8	no	—
854	C₂×C₄	—	4	8	no	—
855	C₂×C₄	—	4	8	no	—
856	C₂×C₄	—	4	4	no	—
857	C₂×C₄	—	4	4	no	—
858	C₂×C₄	—	8	4	no	—
859	C₂×C₄	—	8	2	no	—
860	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
861	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
862	C₂×C₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
863	C₂²	—	2	2	no	—
864	C₂²	—	2	4	no	—
865	C₂²	—	2	2	no	—
866	C₂²	—	2	4	no	—
867	C₂²	—	2	4	no	—
868	C₂²	—	2	4	no	—
869	C₂²	—	2	4	no	—
870	C₂²	—	2	2	no	—
871	C₂²	—	2	2	no	—
872	C₂²	—	2	4	no	—
873	C₂²	—	2	4	no	—
874	C₂²	—	4	16	no	—
875	C₂²	—	4	1	no	—
876	C₂²	—	4	1	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	1	no	—
879	C₂²	—	4	1	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	2	no	—
882	C₂²	—	4	2	no	—
883	C₂²	—	4	2	no	—
884	C₂²	—	4	2	no	—
885	C₂²	#551×C₆₇	1	4	yes	—
886	C₂²	C₂²×#41×C₆₇	1	2	yes	—
887	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
888	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
889	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
890	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
891	C₄	—	2	4	no	—
892	C₄	—	2	4	no	—
893	C₄	—	2	4	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	2	no	—
896	C₄	—	4	1	no	—
897	C₄	—	4	1	no	—
898	C₄	—	4	1	no	—
899	C₄	—	4	1	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	2	no	—
904	C₄	—	4	2	no	—
905	C₄	—	4	2	no	—
906	C₂	—	2	4	no	—
907	C₂	—	4	2	no	—
908	C₂	—	4	2	no	—
909	C₂	—	4	4	no	—
910	C₂	C₂×#551×C₆₇	1	1	yes	characteristic
911	C₂	C₆₇×#3481	1	2	yes	—
912	C₂	C₆₇×#3492	1	1	yes	characteristic
913	C₂	C₆₇×#3520	1	2	yes	—
914	C₂	C₆₇×#3532	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₆₇×#2404	C₂
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. C₆₇×#2763	C₂	semidirect
2. C₆₇×#2746	C₂	semidirect
3. C₆₇×#2693	C₂	semidirect
4. C₆₇×#2598	C₂	semidirect
5. C₆₇×#2589	C₂	semidirect
6. C₆₇×#2576	C₂	semidirect
7. C₆₇×#2564	C₂	semidirect
8. C₆₇×#2561	C₂	semidirect
9. C₆₇×#2523	C₂	semidirect
10. C₆₇×#2493	C₂	semidirect
11. C₆₇×#2463	C₂	semidirect
12. C₆₇×#2449	C₂	semidirect
13. C₆₇×#2418	C₂	semidirect
15. C₆₇×#2359	C₂	semidirect
16. C₆₇×#2352	C₂	semidirect
17. C₆₇×#2339	C₂	semidirect
18. C₄×#120×C₆₇	C₂	semidirect
19. C₂×#385×C₆₇	C₂	semidirect
24. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
30. C₂×#117×C₆₇	C₂²	semidirect
34. #401×C₆₇	C₂²	semidirect
35. #400×C₆₇	C₂²	semidirect
36. #400×C₆₇	C₂²	semidirect
37. #400×C₆₇	C₂²	semidirect
39. #399×C₆₇	C₂²	semidirect
40. #398×C₆₇	C₂²	semidirect
44. #396×C₆₇	C₂²	semidirect
45. #395×C₆₇	C₂²	semidirect
54. #391×C₆₇	C₂²	semidirect
55. #391×C₆₇	C₂²	semidirect
56. #389×C₆₇	C₂²	semidirect
61. #388×C₆₇	C₂²	semidirect
62. #388×C₆₇	C₂²	semidirect
63. #387×C₆₇	C₂²	semidirect
64. #387×C₆₇	C₂²	semidirect
65. #387×C₆₇	C₂²	semidirect
66. #387×C₆₇	C₂²	semidirect
67. #387×C₆₇	C₂²	semidirect
68. #387×C₆₇	C₂²	semidirect
77. #386×C₆₇	C₂²	semidirect
78. #386×C₆₇	C₂²	semidirect
89. #385×C₆₇	C₂²	semidirect
90. #383×C₆₇	C₂²	semidirect
91. #382×C₆₇	C₂²	semidirect
94. #381×C₆₇	C₂²	semidirect
96. #380×C₆₇	C₂²	semidirect
97. #380×C₆₇	C₂²	semidirect
99. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
106. C₂×#95×C₆₇	C₂²	semidirect
314. C₂²⋊C₄×C₆₇	#41	semidirect
448. #59371	C₆₇	direct (N × H)
458. #2763	C₂×C₆₇	semidirect
459. #2746	C₂×C₆₇	semidirect
460. #2693	C₂×C₆₇	semidirect
461. #2598	C₂×C₆₇	semidirect
462. #2589	C₂×C₆₇	semidirect
463. #2576	C₂×C₆₇	semidirect
464. #2564	C₂×C₆₇	semidirect
465. #2561	C₂×C₆₇	semidirect
466. #2523	C₂×C₆₇	semidirect
467. #2493	C₂×C₆₇	semidirect
468. #2463	C₂×C₆₇	semidirect
469. #2449	C₂×C₆₇	semidirect
470. #2418	C₂×C₆₇	semidirect
472. #2359	C₂×C₆₇	semidirect
473. #2352	C₂×C₆₇	semidirect
474. #2339	C₂×C₆₇	semidirect
475. C₄×#120	C₂×C₆₇	semidirect
476. C₂×#385	C₂×C₆₇	semidirect
477. C₆₇	#59371	direct (N × H)
482. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
488. C₂×#117	C₂²×C₆₇	semidirect
492. #401	C₂²×C₆₇	semidirect
493. #400	C₂²×C₆₇	semidirect
494. #400	C₂²×C₆₇	semidirect
495. #400	C₂²×C₆₇	semidirect
497. #399	C₂²×C₆₇	semidirect
498. #398	C₂²×C₆₇	semidirect
502. #396	C₂²×C₆₇	semidirect
503. #395	C₂²×C₆₇	semidirect
512. #391	C₂²×C₆₇	semidirect
513. #391	C₂²×C₆₇	semidirect
514. #389	C₂²×C₆₇	semidirect
519. #388	C₂²×C₆₇	semidirect
520. #388	C₂²×C₆₇	semidirect
521. #387	C₂²×C₆₇	semidirect
522. #387	C₂²×C₆₇	semidirect
523. #387	C₂²×C₆₇	semidirect
524. #387	C₂²×C₆₇	semidirect
525. #387	C₂²×C₆₇	semidirect
526. #387	C₂²×C₆₇	semidirect
535. #386	C₂²×C₆₇	semidirect
536. #386	C₂²×C₆₇	semidirect
547. #385	C₂²×C₆₇	semidirect
548. #383	C₂²×C₆₇	semidirect
549. #382	C₂²×C₆₇	semidirect
552. #381	C₂²×C₆₇	semidirect
554. #380	C₂²×C₆₇	semidirect
555. #380	C₂²×C₆₇	semidirect
557. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
562. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
564. C₂×#95	C₂²×C₆₇	semidirect
772. C₂²⋊C₄	#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×#2763	2
C₆₇×#2746	2
C₆₇×#2693	2
C₆₇×#2598	2
C₆₇×#2589	2
C₆₇×#2576	2
C₆₇×#2564	2
C₆₇×#2561	2
C₆₇×#2523	2
C₆₇×#2493	2
C₆₇×#2463	2
C₆₇×#2449	2
C₆₇×#2418	2
C₆₇×#2404	2
C₆₇×#2359	2
C₆₇×#2352	2
C₆₇×#2339	2
C₄×#120×C₆₇	2
C₂×#385×C₆₇	2
#59371	67

Subgroups — C67×#59371 #30738622

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59371 #30738622