Subgroups — C₆₇×#34300 #30713551

Order 17152.

2128 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#552×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2374	C₂	1	2	yes	maximal
3	C₆₇×#2373	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2371	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2370	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2362	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2355	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2354	C₂	1	1	yes	maximal, characteristic
10	C₆₇×#2346	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2346	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2345	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2335	C₂	1	2	yes	maximal
14	C₆₇×#2334	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2330	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2323	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#125×C₆₇	C₂	1	2	yes	maximal, complemented
18	C₄×C₂²⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2298	C₂	1	2	yes	maximal, complemented
20	C₆₇×#2290	C₂	1	1	yes	maximal, characteristic
21	C₆₇×#2276	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2274	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#117×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	#552×C₆₇	C₄	1	16	yes	complemented
25	C₂×#126×C₆₇	C₂²	1	2	yes	—
26	C₂×#125×C₆₇	C₂²	1	2	yes	—
27	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#123×C₆₇	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×#117×C₆₇	C₂²	1	2	yes	—
40	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
41	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
42	#391×C₆₇	C₂²	1	1	yes	characteristic
43	#391×C₆₇	C₂²	1	1	yes	characteristic
44	#390×C₆₇	C₂²	1	2	yes	—
45	#389×C₆₇	C₂²	1	1	yes	characteristic
46	#389×C₆₇	C₂²	1	2	yes	—
47	#389×C₆₇	C₂²	1	2	yes	—
48	#389×C₆₇	C₂²	1	1	yes	characteristic
49	#389×C₆₇	C₂²	1	1	yes	characteristic
50	#389×C₆₇	C₂²	1	1	yes	characteristic
51	#389×C₆₇	C₂²	1	2	yes	—
52	#389×C₆₇	C₂²	1	2	yes	—
53	#388×C₆₇	C₂²	1	1	yes	characteristic
54	#388×C₆₇	C₂²	1	1	yes	characteristic
55	#388×C₆₇	C₂²	1	2	yes	—
56	#388×C₆₇	C₂²	1	2	yes	—
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	—
62	#388×C₆₇	C₂²	1	2	yes	—
63	#388×C₆₇	C₂²	1	2	yes	—
64	#388×C₆₇	C₂²	1	2	yes	—
65	#387×C₆₇	C₂²	1	1	yes	characteristic
66	#387×C₆₇	C₂²	1	1	yes	characteristic
67	#387×C₆₇	C₂²	1	2	yes	—
68	#387×C₆₇	C₂²	1	2	yes	—
69	#387×C₆₇	C₂²	1	2	yes	—
70	#387×C₆₇	C₂²	1	2	yes	—
71	#387×C₆₇	C₂²	1	2	yes	—
72	#387×C₆₇	C₂²	1	2	yes	—
73	#387×C₆₇	C₂²	1	2	yes	—
74	#387×C₆₇	C₂²	1	2	yes	—
75	#387×C₆₇	C₂²	1	2	yes	—
76	#387×C₆₇	C₂²	1	2	yes	—
77	#387×C₆₇	C₂²	1	2	yes	—
78	#387×C₆₇	C₂²	1	2	yes	—
79	#386×C₆₇	C₂²	1	1	yes	characteristic
80	#386×C₆₇	C₂²	1	1	yes	characteristic
81	#385×C₆₇	C₂²	1	1	yes	characteristic
82	#385×C₆₇	C₂²	1	1	yes	characteristic
83	#385×C₆₇	C₂²	1	2	yes	—
84	#384×C₆₇	C₂²	1	1	yes	characteristic
85	#382×C₆₇	C₂²	1	2	yes	—
86	#382×C₆₇	C₂²	1	2	yes	—
87	#380×C₆₇	C₂²	1	1	yes	characteristic
88	#380×C₆₇	C₂²	1	1	yes	characteristic
89	#380×C₆₇	C₂²	1	2	yes	—
90	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
91	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
92	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
93	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
94	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
95	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
97	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
98	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
99	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
100	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
101	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
102	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
104	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
106	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
107	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
108	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
109	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
110	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
111	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
112	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
113	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
114	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
115	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
119	#376×C₆₇	C₂²	1	2	yes	—
120	#376×C₆₇	C₂²	1	1	yes	characteristic
121	#376×C₆₇	C₂²	1	2	yes	—
122	#376×C₆₇	C₂²	1	2	yes	—
123	C₄³×C₆₇	C₂²	1	2	yes	—
124	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
131	#126×C₆₇	C₂×C₄	1	16	yes	—
132	#125×C₆₇	C₂×C₄	1	16	yes	complemented
133	#125×C₆₇	C₂×C₄	1	8	yes	complemented
134	#123×C₆₇	C₂×C₄	1	16	yes	—
135	C₂²⋊Q₈×C₆₇	C₂×C₄	1	8	yes	—
136	C₂²⋊Q₈×C₆₇	C₂×C₄	1	8	yes	complemented
137	C₄×Q₈×C₆₇	—	2	4	no	—
138	C₄×Q₈×C₆₇	—	2	4	no	—
139	C₄×Q₈×C₆₇	C₂×C₄	1	8	yes	complemented
140	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	—
141	#117×C₆₇	—	2	4	no	—
142	#117×C₆₇	—	2	4	no	—
143	#117×C₆₇	—	2	4	no	—
144	#117×C₆₇	C₂×C₄	1	8	yes	—
145	#117×C₆₇	C₂×C₄	1	16	yes	complemented
146	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	8	yes	complemented
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
163	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
168	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
183	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
187	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
188	C₂×C₄²×C₆₇	—	2	4	no	—
189	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
193	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
195	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
197	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
198	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
199	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
200	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
201	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
202	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
203	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
204	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
205	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
206	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
207	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
208	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
209	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
211	#95×C₆₇	C₂³	1	1	yes	characteristic
212	#95×C₆₇	C₂³	1	2	yes	—
213	#95×C₆₇	C₂³	1	1	yes	characteristic
214	#95×C₆₇	C₂³	1	2	yes	—
215	#95×C₆₇	C₂³	1	2	yes	—
216	#95×C₆₇	C₂³	1	2	yes	—
217	#95×C₆₇	C₂³	1	2	yes	—
218	#95×C₆₇	C₂³	1	2	yes	—
219	#95×C₆₇	C₂³	1	1	yes	characteristic
220	#95×C₆₇	C₂³	1	1	yes	characteristic
221	#95×C₆₇	C₂³	1	1	yes	characteristic
222	#95×C₆₇	C₂³	1	2	yes	—
223	#95×C₆₇	C₂³	1	2	yes	—
224	#95×C₆₇	C₂³	1	2	yes	—
225	#95×C₆₇	C₂³	1	2	yes	—
226	#95×C₆₇	C₂³	1	2	yes	—
227	#95×C₆₇	C₂³	1	1	yes	characteristic
228	#95×C₆₇	C₂³	1	1	yes	characteristic
229	#95×C₆₇	C₂³	1	2	yes	—
230	#95×C₆₇	C₂³	1	2	yes	—
231	#95×C₆₇	C₂³	1	2	yes	—
232	#95×C₆₇	C₂³	1	1	yes	characteristic
233	#95×C₆₇	C₂³	1	2	yes	—
234	#95×C₆₇	C₂³	1	1	yes	characteristic
235	#95×C₆₇	C₂³	1	2	yes	—
236	#95×C₆₇	C₂³	1	2	yes	—
237	#95×C₆₇	C₂³	1	2	yes	—
238	#95×C₆₇	C₂³	1	1	yes	characteristic
239	#95×C₆₇	C₂³	1	2	yes	—
240	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
241	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
242	C₂×Q₈×C₆₇	—	2	2	no	—
243	C₂×Q₈×C₆₇	—	2	2	no	—
244	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
245	C₂×D₄×C₆₇	—	4	1	no	—
246	C₂×D₄×C₆₇	—	4	1	no	—
247	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
248	C₂²×C₄×C₆₇	—	2	2	no	—
249	C₂²×C₄×C₆₇	—	2	2	no	—
250	C₂²×C₄×C₆₇	—	2	2	no	—
251	C₂²×C₄×C₆₇	—	2	2	no	—
252	C₂²×C₄×C₆₇	—	2	2	no	—
253	C₂²×C₄×C₆₇	—	2	2	no	—
254	C₂²×C₄×C₆₇	—	2	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	1	no	—
259	C₂²×C₄×C₆₇	—	4	1	no	—
260	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
261	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
262	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
263	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
269	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
284	C₄⋊C₄×C₆₇	—	2	2	no	—
285	C₄⋊C₄×C₆₇	—	2	2	no	—
286	C₄⋊C₄×C₆₇	—	2	2	no	—
287	C₄⋊C₄×C₆₇	—	2	2	no	—
288	C₄⋊C₄×C₆₇	—	2	4	no	—
289	C₄⋊C₄×C₆₇	—	2	4	no	—
290	C₄⋊C₄×C₆₇	—	2	2	no	—
291	C₄⋊C₄×C₆₇	—	2	2	no	—
292	C₄⋊C₄×C₆₇	—	4	2	no	—
293	C₄⋊C₄×C₆₇	—	4	2	no	—
294	C₄⋊C₄×C₆₇	—	4	2	no	—
295	C₄⋊C₄×C₆₇	—	4	2	no	—
296	C₄⋊C₄×C₆₇	—	4	2	no	—
297	C₄⋊C₄×C₆₇	—	4	1	no	—
298	C₄⋊C₄×C₆₇	—	4	2	no	—
299	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
300	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
301	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
302	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
303	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
304	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
305	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
306	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
307	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
308	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
309	C₄⋊C₄×C₆₇	#41	1	4	yes	—
310	C₂²⋊C₄×C₆₇	—	2	2	no	—
311	C₂²⋊C₄×C₆₇	—	2	4	no	—
312	C₂²⋊C₄×C₆₇	—	2	4	no	—
313	C₂²⋊C₄×C₆₇	—	2	2	no	—
314	C₂²⋊C₄×C₆₇	—	2	2	no	—
315	C₂²⋊C₄×C₆₇	—	4	1	no	—
316	C₂²⋊C₄×C₆₇	—	4	1	no	—
317	C₂²⋊C₄×C₆₇	—	4	2	no	—
318	C₂²⋊C₄×C₆₇	—	4	2	no	—
319	C₂²⋊C₄×C₆₇	—	4	1	no	—
320	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
321	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
322	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
323	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
324	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
325	C₄²×C₆₇	—	2	2	no	—
326	C₄²×C₆₇	—	2	2	no	—
327	C₄²×C₆₇	—	2	2	no	—
328	C₄²×C₆₇	—	2	4	no	—
329	C₄²×C₆₇	—	2	4	no	—
330	C₄²×C₆₇	—	2	2	no	—
331	C₄²×C₆₇	—	2	4	no	—
332	C₄²×C₆₇	—	2	4	no	—
333	C₄²×C₆₇	—	2	2	no	—
334	C₄²×C₆₇	—	2	4	no	—
335	C₄²×C₆₇	—	4	2	no	—
336	C₄²×C₆₇	—	4	2	no	—
337	C₄²×C₆₇	—	4	2	no	—
338	C₄²×C₆₇	—	4	2	no	—
339	C₄²×C₆₇	—	4	2	no	—
340	C₄²×C₆₇	—	4	2	no	—
341	C₄²×C₆₇	—	4	2	no	—
342	C₄²×C₆₇	—	4	2	no	—
343	C₄²×C₆₇	C₂²×C₄	1	8	yes	—
344	C₄²×C₆₇	C₂²×C₄	1	8	yes	—
345	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
346	C₄²×C₆₇	#41	1	4	yes	—
347	C₂³×C₆₇	—	2	1	no	—
348	C₂³×C₆₇	—	2	1	no	—
349	C₂³×C₆₇	—	2	1	no	—
350	C₂³×C₆₇	—	2	1	no	—
351	C₂³×C₆₇	—	2	1	no	—
352	C₂³×C₆₇	—	2	1	no	—
353	C₂³×C₆₇	—	2	1	no	—
354	C₂³×C₆₇	—	2	1	no	—
355	C₂³×C₆₇	—	2	1	no	—
356	C₂³×C₆₇	—	2	1	no	—
357	C₂³×C₆₇	—	2	1	no	—
358	C₂³×C₆₇	—	2	1	no	—
359	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
360	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
361	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
362	Q₈×C₆₇	—	2	8	no	—
363	D₄×C₆₇	—	4	4	no	—
364	C₂×C₄×C₆₇	—	2	1	no	—
365	C₂×C₄×C₆₇	—	2	1	no	—
366	C₂×C₄×C₆₇	—	2	1	no	—
367	C₂×C₄×C₆₇	—	2	1	no	—
368	C₂×C₄×C₆₇	—	2	2	no	—
369	C₂×C₄×C₆₇	—	2	2	no	—
370	C₂×C₄×C₆₇	—	2	1	no	—
371	C₂×C₄×C₆₇	—	2	2	no	—
372	C₂×C₄×C₆₇	—	2	2	no	—
373	C₂×C₄×C₆₇	—	2	1	no	—
374	C₂×C₄×C₆₇	—	2	1	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	1	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	1	no	—
387	C₂×C₄×C₆₇	—	2	1	no	—
388	C₂×C₄×C₆₇	—	2	8	no	—
389	C₂×C₄×C₆₇	—	2	8	no	—
390	C₂×C₄×C₆₇	—	2	1	no	—
391	C₂×C₄×C₆₇	—	2	1	no	—
392	C₂×C₄×C₆₇	—	2	1	no	—
393	C₂×C₄×C₆₇	—	2	1	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	1	no	—
398	C₂×C₄×C₆₇	—	2	1	no	—
399	C₂×C₄×C₆₇	—	2	1	no	—
400	C₂×C₄×C₆₇	—	2	1	no	—
401	C₂×C₄×C₆₇	—	2	1	no	—
402	C₂×C₄×C₆₇	—	2	1	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	1	no	—
412	C₂×C₄×C₆₇	—	2	1	no	—
413	C₂×C₄×C₆₇	—	2	1	no	—
414	C₂×C₄×C₆₇	—	4	8	no	—
415	C₂×C₄×C₆₇	—	4	4	no	—
416	C₂×C₄×C₆₇	—	4	4	no	—
417	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
418	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
419	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
420	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
421	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
422	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
423	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
424	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
425	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
426	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
427	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
428	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
429	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
430	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
431	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
432	C₂²×C₆₇	—	2	2	no	—
433	C₂²×C₆₇	—	2	2	no	—
434	C₂²×C₆₇	—	2	2	no	—
435	C₂²×C₆₇	—	2	2	no	—
436	C₂²×C₆₇	—	2	2	no	—
437	C₂²×C₆₇	—	2	2	no	—
438	C₂²×C₆₇	—	4	1	no	—
439	C₂²×C₆₇	—	4	1	no	—
440	C₂²×C₆₇	—	4	1	no	—
441	C₂²×C₆₇	—	4	1	no	—
442	C₂²×C₆₇	—	4	1	no	—
443	C₂²×C₆₇	—	4	1	no	—
444	C₂²×C₆₇	—	4	1	no	—
445	C₂²×C₆₇	—	4	1	no	—
446	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
447	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
448	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
449	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
450	C₂²×C₆₇	#585	1	1	yes	characteristic
451	C₂²×C₆₇	#585	1	1	yes	characteristic
452	C₂²×C₆₇	#585	1	1	yes	characteristic
453	C₄×C₆₇	—	2	2	no	—
454	C₄×C₆₇	—	2	2	no	—
455	C₄×C₆₇	—	2	4	no	—
456	C₄×C₆₇	—	2	4	no	—
457	C₄×C₆₇	—	2	4	no	—
458	C₄×C₆₇	—	2	2	no	—
459	C₄×C₆₇	—	2	4	no	—
460	C₄×C₆₇	—	2	2	no	—
461	C₄×C₆₇	—	2	2	no	—
462	C₄×C₆₇	—	2	2	no	—
463	C₄×C₆₇	—	2	2	no	—
464	C₄×C₆₇	—	2	4	no	—
465	C₄×C₆₇	—	4	1	no	—
466	C₄×C₆₇	—	4	2	no	—
467	C₄×C₆₇	—	4	1	no	—
468	C₄×C₆₇	—	4	1	no	—
469	C₄×C₆₇	—	4	1	no	—
470	C₄×C₆₇	—	4	1	no	—
471	C₄×C₆₇	—	4	2	no	—
472	C₄×C₆₇	—	4	2	no	—
473	C₄×C₆₇	C₄×#41	1	4	yes	—
474	#34300	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
475	C₂×C₆₇	—	4	2	no	—
476	C₂×C₆₇	—	4	2	no	—
477	C₂×C₆₇	C₂×C₄×#41	1	1	yes	characteristic
478	C₂×C₆₇	#3428	1	1	yes	characteristic
479	C₂×C₆₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
480	C₂×C₆₇	#3493	1	1	yes	characteristic
481	C₂×C₆₇	#3495	1	1	yes	characteristic
482	C₂×C₆₇	#3515	1	1	yes	characteristic
483	C₂×C₆₇	#3524	1	1	yes	characteristic
484	C₂×#552	C₂×C₆₇	1	1	yes	characteristic
485	#2374	C₂×C₆₇	1	2	yes	—
486	#2373	C₂×C₆₇	1	2	yes	complemented
487	#2371	C₂×C₆₇	1	2	yes	complemented
488	#2370	C₂×C₆₇	1	1	yes	characteristic, complemented
489	#2362	C₂×C₆₇	1	1	yes	characteristic, complemented
490	#2362	C₂×C₆₇	1	1	yes	characteristic, complemented
491	#2355	C₂×C₆₇	1	1	yes	characteristic, complemented
492	#2354	C₂×C₆₇	1	1	yes	characteristic
493	#2346	C₂×C₆₇	1	1	yes	characteristic, complemented
494	#2346	C₂×C₆₇	1	2	yes	complemented
495	#2345	C₂×C₆₇	1	1	yes	characteristic, complemented
496	#2335	C₂×C₆₇	1	2	yes	—
497	#2334	C₂×C₆₇	1	2	yes	complemented
498	#2330	C₂×C₆₇	1	1	yes	characteristic, complemented
499	#2323	C₂×C₆₇	1	1	yes	characteristic, complemented
500	C₄×#125	C₂×C₆₇	1	2	yes	complemented
501	C₄×C₂²⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
502	#2298	C₂×C₆₇	1	2	yes	complemented
503	#2290	C₂×C₆₇	1	1	yes	characteristic
504	#2276	C₂×C₆₇	1	1	yes	characteristic, complemented
505	#2274	C₂×C₆₇	1	1	yes	characteristic, complemented
506	C₄×#117	C₂×C₆₇	1	1	yes	characteristic, complemented
507	C₆₇	#34300	1	1	yes	characteristic, direct product factor, Sylow
508	#552	C₄×C₆₇	1	16	yes	complemented
509	C₂×#126	C₂²×C₆₇	1	2	yes	—
510	C₂×#125	C₂²×C₆₇	1	2	yes	—
511	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
512	C₂×#123	C₂²×C₆₇	1	2	yes	—
513	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
514	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
515	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
516	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
517	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
518	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
519	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
520	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
521	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
522	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
523	C₂×#117	C₂²×C₆₇	1	2	yes	—
524	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
525	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
526	#391	C₂²×C₆₇	1	1	yes	characteristic
527	#391	C₂²×C₆₇	1	1	yes	characteristic
528	#390	C₂²×C₆₇	1	2	yes	—
529	#389	C₂²×C₆₇	1	2	yes	—
530	#389	C₂²×C₆₇	1	2	yes	—
531	#389	C₂²×C₆₇	1	1	yes	characteristic
532	#389	C₂²×C₆₇	1	1	yes	characteristic
533	#389	C₂²×C₆₇	1	1	yes	characteristic
534	#389	C₂²×C₆₇	1	2	yes	—
535	#389	C₂²×C₆₇	1	2	yes	—
536	#389	C₂²×C₆₇	1	1	yes	characteristic
537	#388	C₂²×C₆₇	1	2	yes	—
538	#388	C₂²×C₆₇	1	2	yes	—
539	#388	C₂²×C₆₇	1	2	yes	—
540	#388	C₂²×C₆₇	1	2	yes	—
541	#388	C₂²×C₆₇	1	2	yes	—
542	#388	C₂²×C₆₇	1	2	yes	—
543	#388	C₂²×C₆₇	1	2	yes	—
544	#388	C₂²×C₆₇	1	2	yes	—
545	#388	C₂²×C₆₇	1	1	yes	characteristic
546	#388	C₂²×C₆₇	1	2	yes	—
547	#388	C₂²×C₆₇	1	2	yes	—
548	#388	C₂²×C₆₇	1	1	yes	characteristic
549	#387	C₂²×C₆₇	1	1	yes	characteristic
550	#387	C₂²×C₆₇	1	2	yes	—
551	#387	C₂²×C₆₇	1	2	yes	—
552	#387	C₂²×C₆₇	1	2	yes	—
553	#387	C₂²×C₆₇	1	2	yes	—
554	#387	C₂²×C₆₇	1	2	yes	—
555	#387	C₂²×C₆₇	1	2	yes	—
556	#387	C₂²×C₆₇	1	2	yes	—
557	#387	C₂²×C₆₇	1	2	yes	—
558	#387	C₂²×C₆₇	1	2	yes	—
559	#387	C₂²×C₆₇	1	2	yes	—
560	#387	C₂²×C₆₇	1	2	yes	—
561	#387	C₂²×C₆₇	1	2	yes	—
562	#387	C₂²×C₆₇	1	1	yes	characteristic
563	#386	C₂²×C₆₇	1	1	yes	characteristic
564	#386	C₂²×C₆₇	1	1	yes	characteristic
565	#385	C₂²×C₆₇	1	1	yes	characteristic
566	#385	C₂²×C₆₇	1	2	yes	—
567	#385	C₂²×C₆₇	1	1	yes	characteristic
568	#384	C₂²×C₆₇	1	1	yes	characteristic
569	#382	C₂²×C₆₇	1	2	yes	—
570	#382	C₂²×C₆₇	1	2	yes	—
571	#380	C₂²×C₆₇	1	1	yes	characteristic
572	#380	C₂²×C₆₇	1	2	yes	—
573	#380	C₂²×C₆₇	1	1	yes	characteristic
574	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
575	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
576	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
577	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
578	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
579	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
580	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
581	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
582	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
583	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
584	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
585	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
586	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
587	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
588	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
589	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
590	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
591	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
592	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
593	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
594	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
595	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
596	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
597	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
598	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
599	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
600	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
601	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
602	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
603	#376	C₂²×C₆₇	1	1	yes	characteristic
604	#376	C₂²×C₆₇	1	2	yes	—
605	#376	C₂²×C₆₇	1	2	yes	—
606	#376	C₂²×C₆₇	1	2	yes	—
607	C₄³	C₂²×C₆₇	1	2	yes	—
608	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
609	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
610	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
611	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
612	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
613	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
614	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
615	#126	C₂×C₄×C₆₇	1	16	yes	—
616	#125	C₂×C₄×C₆₇	1	16	yes	complemented
617	#125	C₂×C₄×C₆₇	1	8	yes	complemented
618	#123	C₂×C₄×C₆₇	1	16	yes	—
619	C₂²⋊Q₈	C₂×C₄×C₆₇	1	8	yes	—
620	C₂²⋊Q₈	C₂×C₄×C₆₇	1	8	yes	complemented
621	C₄×Q₈	—	2	4	no	—
622	C₄×Q₈	—	2	4	no	—
623	C₄×Q₈	C₂×C₄×C₆₇	1	8	yes	complemented
624	C₄×D₄	C₂×C₄×C₆₇	1	8	yes	—
625	#117	—	2	4	no	—
626	#117	—	2	4	no	—
627	#117	—	2	4	no	—
628	#117	C₂×C₄×C₆₇	1	8	yes	—
629	#117	C₂×C₄×C₆₇	1	16	yes	complemented
630	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	8	yes	complemented
631	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
652	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
653	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
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	1	yes	characteristic
657	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
658	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
659	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
662	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
663	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
666	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
667	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
668	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
671	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
672	C₂×C₄²	—	2	4	no	—
673	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
674	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
675	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
676	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
677	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
678	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
679	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
680	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
681	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
682	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
683	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
684	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
685	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
686	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
687	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
688	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
689	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
690	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
691	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
692	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
693	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
694	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
695	#95	C₂³×C₆₇	1	1	yes	characteristic
696	#95	C₂³×C₆₇	1	2	yes	—
697	#95	C₂³×C₆₇	1	1	yes	characteristic
698	#95	C₂³×C₆₇	1	2	yes	—
699	#95	C₂³×C₆₇	1	2	yes	—
700	#95	C₂³×C₆₇	1	2	yes	—
701	#95	C₂³×C₆₇	1	2	yes	—
702	#95	C₂³×C₆₇	1	2	yes	—
703	#95	C₂³×C₆₇	1	1	yes	characteristic
704	#95	C₂³×C₆₇	1	1	yes	characteristic
705	#95	C₂³×C₆₇	1	1	yes	characteristic
706	#95	C₂³×C₆₇	1	2	yes	—
707	#95	C₂³×C₆₇	1	2	yes	—
708	#95	C₂³×C₆₇	1	2	yes	—
709	#95	C₂³×C₆₇	1	2	yes	—
710	#95	C₂³×C₆₇	1	1	yes	characteristic
711	#95	C₂³×C₆₇	1	2	yes	—
712	#95	C₂³×C₆₇	1	1	yes	characteristic
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	2	yes	—
718	#95	C₂³×C₆₇	1	1	yes	characteristic
719	#95	C₂³×C₆₇	1	2	yes	—
720	#95	C₂³×C₆₇	1	2	yes	—
721	#95	C₂³×C₆₇	1	2	yes	—
722	#95	C₂³×C₆₇	1	1	yes	characteristic
723	#95	C₂³×C₆₇	1	2	yes	—
724	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
725	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
726	C₂×Q₈	—	2	2	no	—
727	C₂×Q₈	—	2	2	no	—
728	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
729	C₂×D₄	—	4	1	no	—
730	C₂×D₄	—	4	1	no	—
731	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	4	1	no	—
740	C₂²×C₄	—	4	2	no	—
741	C₂²×C₄	—	4	2	no	—
742	C₂²×C₄	—	4	1	no	—
743	C₂²×C₄	—	4	1	no	—
744	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
745	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
746	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
747	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
750	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
751	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
752	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
753	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
754	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
755	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
756	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
757	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
760	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
761	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
762	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
763	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
764	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
765	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
766	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	4	no	—
773	C₄⋊C₄	—	2	4	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	4	2	no	—
777	C₄⋊C₄	—	4	2	no	—
778	C₄⋊C₄	—	4	2	no	—
779	C₄⋊C₄	—	4	2	no	—
780	C₄⋊C₄	—	4	2	no	—
781	C₄⋊C₄	—	4	1	no	—
782	C₄⋊C₄	—	4	2	no	—
783	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
784	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
785	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
786	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
787	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
788	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
789	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
790	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
791	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
792	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
793	C₄⋊C₄	#41×C₆₇	1	4	yes	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	4	1	no	—
800	C₂²⋊C₄	—	4	1	no	—
801	C₂²⋊C₄	—	4	2	no	—
802	C₂²⋊C₄	—	4	2	no	—
803	C₂²⋊C₄	—	4	1	no	—
804	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
805	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
806	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
807	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
808	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
809	C₄²	—	2	2	no	—
810	C₄²	—	2	2	no	—
811	C₄²	—	2	2	no	—
812	C₄²	—	2	4	no	—
813	C₄²	—	2	4	no	—
814	C₄²	—	2	2	no	—
815	C₄²	—	2	4	no	—
816	C₄²	—	2	4	no	—
817	C₄²	—	2	2	no	—
818	C₄²	—	2	4	no	—
819	C₄²	—	4	2	no	—
820	C₄²	—	4	2	no	—
821	C₄²	—	4	2	no	—
822	C₄²	—	4	2	no	—
823	C₄²	—	4	2	no	—
824	C₄²	—	4	2	no	—
825	C₄²	—	4	2	no	—
826	C₄²	—	4	2	no	—
827	C₄²	C₂²×C₄×C₆₇	1	8	yes	—
828	C₄²	C₂²×C₄×C₆₇	1	8	yes	—
829	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
830	C₄²	#41×C₆₇	1	4	yes	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	1	no	—
833	C₂³	—	2	1	no	—
834	C₂³	—	2	1	no	—
835	C₂³	—	2	1	no	—
836	C₂³	—	2	1	no	—
837	C₂³	—	2	1	no	—
838	C₂³	—	2	1	no	—
839	C₂³	—	2	1	no	—
840	C₂³	—	2	1	no	—
841	C₂³	—	2	1	no	—
842	C₂³	—	2	1	no	—
843	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
844	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
845	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
846	Q₈	—	2	8	no	—
847	D₄	—	4	4	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	8	no	—
873	C₂×C₄	—	2	8	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	4	8	no	—
899	C₂×C₄	—	4	4	no	—
900	C₂×C₄	—	4	4	no	—
901	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
902	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
903	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
904	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
905	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
906	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
907	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
908	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
909	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
910	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
911	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
912	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
913	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
914	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
915	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	2	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	2	2	no	—
920	C₂²	—	2	2	no	—
921	C₂²	—	2	2	no	—
922	C₂²	—	4	1	no	—
923	C₂²	—	4	1	no	—
924	C₂²	—	4	1	no	—
925	C₂²	—	4	1	no	—
926	C₂²	—	4	1	no	—
927	C₂²	—	4	1	no	—
928	C₂²	—	4	1	no	—
929	C₂²	—	4	1	no	—
930	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
931	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
932	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
933	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
934	C₂²	#585×C₆₇	1	1	yes	characteristic
935	C₂²	#585×C₆₇	1	1	yes	characteristic
936	C₂²	#585×C₆₇	1	1	yes	characteristic
937	C₄	—	2	2	no	—
938	C₄	—	2	2	no	—
939	C₄	—	2	4	no	—
940	C₄	—	2	4	no	—
941	C₄	—	2	4	no	—
942	C₄	—	2	2	no	—
943	C₄	—	2	4	no	—
944	C₄	—	2	2	no	—
945	C₄	—	2	2	no	—
946	C₄	—	2	2	no	—
947	C₄	—	2	2	no	—
948	C₄	—	2	4	no	—
949	C₄	—	4	1	no	—
950	C₄	—	4	2	no	—
951	C₄	—	4	2	no	—
952	C₄	—	4	1	no	—
953	C₄	—	4	1	no	—
954	C₄	—	4	2	no	—
955	C₄	—	4	1	no	—
956	C₄	—	4	1	no	—
957	C₄	C₄×#41×C₆₇	1	4	yes	—
958	C₂	—	4	2	no	—
959	C₂	—	4	2	no	—
960	C₂	C₂×C₄×#41×C₆₇	1	1	yes	characteristic
961	C₂	C₆₇×#3428	1	1	yes	characteristic
962	C₂	C₄×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
963	C₂	C₆₇×#3493	1	1	yes	characteristic
964	C₂	C₆₇×#3495	1	1	yes	characteristic
965	C₂	C₆₇×#3515	1	1	yes	characteristic
966	C₂	C₆₇×#3524	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂²×D₄×C₆₇	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₆₇×#2373	C₂	semidirect
4. C₆₇×#2371	C₂	semidirect
5. C₆₇×#2370	C₂	semidirect
6. C₆₇×#2362	C₂	semidirect
7. C₆₇×#2362	C₂	semidirect
8. C₆₇×#2355	C₂	semidirect
10. C₆₇×#2346	C₂	semidirect
11. C₆₇×#2346	C₂	semidirect
12. C₆₇×#2345	C₂	semidirect
14. C₆₇×#2334	C₂	semidirect
15. C₆₇×#2330	C₂	semidirect
16. C₆₇×#2323	C₂	semidirect
17. C₄×#125×C₆₇	C₂	semidirect
18. C₄×C₂²⋊Q₈×C₆₇	C₂	semidirect
19. C₆₇×#2298	C₂	semidirect
21. C₆₇×#2276	C₂	semidirect
22. C₆₇×#2274	C₂	semidirect
23. C₄×#117×C₆₇	C₂	semidirect
24. #552×C₆₇	C₄	semidirect
132. #125×C₆₇	C₂×C₄	semidirect
133. #125×C₆₇	C₂×C₄	semidirect
136. C₂²⋊Q₈×C₆₇	C₂×C₄	semidirect
139. C₄×Q₈×C₆₇	C₂×C₄	semidirect
145. #117×C₆₇	C₂×C₄	semidirect
146. C₂×C₄⋊C₄×C₆₇	C₂×C₄	semidirect
474. #34300	C₆₇	direct (N × H)
486. #2373	C₂×C₆₇	semidirect
487. #2371	C₂×C₆₇	semidirect
488. #2370	C₂×C₆₇	semidirect
489. #2362	C₂×C₆₇	semidirect
490. #2362	C₂×C₆₇	semidirect
491. #2355	C₂×C₆₇	semidirect
493. #2346	C₂×C₆₇	semidirect
494. #2346	C₂×C₆₇	semidirect
495. #2345	C₂×C₆₇	semidirect
497. #2334	C₂×C₆₇	semidirect
498. #2330	C₂×C₆₇	semidirect
499. #2323	C₂×C₆₇	semidirect
500. C₄×#125	C₂×C₆₇	semidirect
501. C₄×C₂²⋊Q₈	C₂×C₆₇	semidirect
502. #2298	C₂×C₆₇	semidirect
504. #2276	C₂×C₆₇	semidirect
505. #2274	C₂×C₆₇	semidirect
506. C₄×#117	C₂×C₆₇	semidirect
507. C₆₇	#34300	direct (N × H)
508. #552	C₄×C₆₇	semidirect
616. #125	C₂×C₄×C₆₇	semidirect
617. #125	C₂×C₄×C₆₇	semidirect
620. C₂²⋊Q₈	C₂×C₄×C₆₇	semidirect
623. C₄×Q₈	C₂×C₄×C₆₇	semidirect
629. #117	C₂×C₄×C₆₇	semidirect
630. C₂×C₄⋊C₄	C₂×C₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#552×C₆₇	2
C₆₇×#2374	2
C₆₇×#2373	2
C₆₇×#2371	2
C₆₇×#2370	2
C₆₇×#2362	2
C₆₇×#2355	2
C₆₇×#2354	2
C₆₇×#2346	2
C₆₇×#2345	2
C₆₇×#2335	2
C₆₇×#2334	2
C₆₇×#2330	2
C₆₇×#2323	2
C₄×#125×C₆₇	2
C₄×C₂²⋊Q₈×C₆₇	2
C₆₇×#2298	2
C₆₇×#2290	2
C₆₇×#2276	2
C₆₇×#2274	2
C₄×#117×C₆₇	2
#34300	67

Subgroups — C67×#34300 #30713551

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34300 #30713551