Subgroups — C₆₇×#22558 #30701809

Order 17152.

1100 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#433×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂²⋊C₈×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#2280	C₂	1	1	yes	maximal, characteristic
4	C₆₇×#1924	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#1924	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#1923	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1923	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#1850	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#1850	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#1818	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#1798	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#1779	C₂	1	1	yes	maximal, characteristic
13	C₆₇×#1752	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×C₂²⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#1750	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
20	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
21	#433×C₆₇	—	2	4	no	—
22	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₂²⋊C₈×C₆₇	—	2	4	no	—
27	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
41	#381×C₆₇	C₄	1	1	yes	characteristic
42	#381×C₆₇	C₄	1	1	yes	characteristic
43	#380×C₆₇	C₄	1	1	yes	characteristic
44	#380×C₆₇	C₄	1	1	yes	characteristic
45	#380×C₆₇	C₄	1	1	yes	characteristic
46	#380×C₆₇	C₄	1	1	yes	characteristic
47	#379×C₆₇	C₄	1	1	yes	characteristic
48	#379×C₆₇	C₄	1	1	yes	characteristic
49	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
50	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
51	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
52	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
53	#336×C₆₇	C₂²	1	1	yes	characteristic, complemented
54	#336×C₆₇	C₂²	1	1	yes	characteristic, complemented
55	#336×C₆₇	C₂²	1	1	yes	characteristic, complemented
56	#336×C₆₇	C₂²	1	1	yes	characteristic, complemented
57	#336×C₆₇	C₂²	1	1	yes	characteristic, complemented
58	#336×C₆₇	C₂²	1	1	yes	characteristic, complemented
59	#336×C₆₇	C₂²	1	1	yes	characteristic, complemented
60	#336×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	C₂⁵×C₆₇	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₄×C₆₇	—	2	2	no	—
63	C₂³×C₄×C₆₇	—	2	2	no	—
64	C₂³×C₄×C₆₇	—	2	2	no	—
65	C₂³×C₄×C₆₇	—	2	2	no	—
66	C₂³×C₄×C₆₇	—	4	1	no	—
67	C₂³×C₄×C₆₇	—	4	1	no	—
68	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
69	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
70	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
71	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₆₇	—	2	2	no	—
75	C₂²×C₈×C₆₇	—	2	2	no	—
76	C₂²×C₈×C₆₇	—	2	2	no	—
77	C₂²×C₈×C₆₇	—	2	2	no	—
78	C₂²×C₈×C₆₇	—	4	1	no	—
79	C₂²×C₈×C₆₇	—	4	1	no	—
80	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
88	#117×C₆₇	—	2	2	no	—
89	#117×C₆₇	—	2	2	no	—
90	#117×C₆₇	—	4	1	no	—
91	#117×C₆₇	—	4	1	no	—
92	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
97	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
98	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
106	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
112	C₄⋊C₈×C₆₇	—	2	2	no	—
113	C₄⋊C₈×C₆₇	—	2	2	no	—
114	C₄⋊C₈×C₆₇	—	4	1	no	—
115	C₄⋊C₈×C₆₇	—	4	1	no	—
116	C₂²⋊C₈×C₆₇	—	2	2	no	—
117	C₂²⋊C₈×C₆₇	—	2	2	no	—
118	C₂²⋊C₈×C₆₇	—	2	2	no	—
119	C₂²⋊C₈×C₆₇	—	2	2	no	—
120	C₂²⋊C₈×C₆₇	—	2	2	no	—
121	C₂²⋊C₈×C₆₇	—	2	2	no	—
122	C₂²⋊C₈×C₆₇	—	2	2	no	—
123	C₂²⋊C₈×C₆₇	—	4	1	no	—
124	C₂²⋊C₈×C₆₇	—	4	1	no	—
125	C₂²⋊C₈×C₆₇	D₄	1	4	yes	—
126	#97×C₆₇	—	2	2	no	—
127	#97×C₆₇	—	4	1	no	—
128	C₄×C₈×C₆₇	—	2	2	no	—
129	C₄×C₈×C₆₇	—	4	1	no	—
130	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
131	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
132	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
133	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
134	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
135	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
136	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
137	#95×C₆₇	C₂×C₄	1	1	yes	characteristic
138	C₂⁴×C₆₇	—	2	2	no	—
139	C₂⁴×C₆₇	—	2	2	no	—
140	C₂⁴×C₆₇	—	2	2	no	—
141	C₂⁴×C₆₇	—	2	2	no	—
142	C₂⁴×C₆₇	—	2	2	no	—
143	C₂⁴×C₆₇	—	4	1	no	—
144	C₂⁴×C₆₇	—	4	1	no	—
145	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
146	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
147	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₆₇	—	2	1	no	—
149	C₂²×C₄×C₆₇	—	2	1	no	—
150	C₂²×C₄×C₆₇	—	2	1	no	—
151	C₂²×C₄×C₆₇	—	2	1	no	—
152	C₂²×C₄×C₆₇	—	2	1	no	—
153	C₂²×C₄×C₆₇	—	2	1	no	—
154	C₂²×C₄×C₆₇	—	2	1	no	—
155	C₂²×C₄×C₆₇	—	2	1	no	—
156	C₂²×C₄×C₆₇	—	2	2	no	—
157	C₂²×C₄×C₆₇	—	2	2	no	—
158	C₂²×C₄×C₆₇	—	2	2	no	—
159	C₂²×C₄×C₆₇	—	2	2	no	—
160	C₂²×C₄×C₆₇	—	2	2	no	—
161	C₂²×C₄×C₆₇	—	2	2	no	—
162	C₂²×C₄×C₆₇	—	2	1	no	—
163	C₂²×C₄×C₆₇	—	2	1	no	—
164	C₂²×C₄×C₆₇	—	2	1	no	—
165	C₂²×C₄×C₆₇	—	2	1	no	—
166	C₂²×C₄×C₆₇	—	2	1	no	—
167	C₂²×C₄×C₆₇	—	2	1	no	—
168	C₂²×C₄×C₆₇	—	4	1	no	—
169	C₂²×C₄×C₆₇	—	4	1	no	—
170	C₂²×C₄×C₆₇	—	4	1	no	—
171	C₂²×C₄×C₆₇	—	4	4	no	—
172	C₂²×C₄×C₆₇	—	4	4	no	—
173	C₂²×C₄×C₆₇	—	4	4	no	—
174	C₂²×C₄×C₆₇	—	4	4	no	—
175	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
183	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
184	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
187	C₂²×C₄×C₆₇	#41	1	2	yes	—
188	C₂²×C₄×C₆₇	#41	1	2	yes	—
189	C₂²×C₄×C₆₇	#41	1	2	yes	—
190	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
191	C₂×C₈×C₆₇	—	2	1	no	—
192	C₂×C₈×C₆₇	—	2	1	no	—
193	C₂×C₈×C₆₇	—	2	1	no	—
194	C₂×C₈×C₆₇	—	2	1	no	—
195	C₂×C₈×C₆₇	—	2	1	no	—
196	C₂×C₈×C₆₇	—	2	1	no	—
197	C₂×C₈×C₆₇	—	2	1	no	—
198	C₂×C₈×C₆₇	—	2	1	no	—
199	C₂×C₈×C₆₇	—	2	1	no	—
200	C₂×C₈×C₆₇	—	2	1	no	—
201	C₂×C₈×C₆₇	—	2	1	no	—
202	C₂×C₈×C₆₇	—	2	1	no	—
203	C₂×C₈×C₆₇	—	2	1	no	—
204	C₂×C₈×C₆₇	—	2	1	no	—
205	C₂×C₈×C₆₇	—	2	1	no	—
206	C₂×C₈×C₆₇	—	2	1	no	—
207	C₂×C₈×C₆₇	—	2	1	no	—
208	C₂×C₈×C₆₇	—	2	1	no	—
209	C₂×C₈×C₆₇	—	2	1	no	—
210	C₂×C₈×C₆₇	—	2	1	no	—
211	C₂×C₈×C₆₇	—	2	1	no	—
212	C₂×C₈×C₆₇	—	2	1	no	—
213	C₂×C₈×C₆₇	—	4	4	no	—
214	C₂×C₈×C₆₇	—	4	4	no	—
215	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
216	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
217	C₄⋊C₄×C₆₇	—	2	2	no	—
218	C₄⋊C₄×C₆₇	—	2	2	no	—
219	C₄⋊C₄×C₆₇	—	4	1	no	—
220	C₄⋊C₄×C₆₇	—	4	1	no	—
221	C₂²⋊C₄×C₆₇	—	2	2	no	—
222	C₂²⋊C₄×C₆₇	—	2	2	no	—
223	C₂²⋊C₄×C₆₇	—	2	2	no	—
224	C₂²⋊C₄×C₆₇	—	2	2	no	—
225	C₂²⋊C₄×C₆₇	—	2	2	no	—
226	C₂²⋊C₄×C₆₇	—	2	2	no	—
227	C₂²⋊C₄×C₆₇	—	2	2	no	—
228	C₂²⋊C₄×C₆₇	—	2	2	no	—
229	C₂²⋊C₄×C₆₇	—	4	1	no	—
230	C₂²⋊C₄×C₆₇	—	4	1	no	—
231	C₂²⋊C₄×C₆₇	—	4	1	no	—
232	C₂²⋊C₄×C₆₇	—	4	1	no	—
233	C₄²×C₆₇	—	2	1	no	—
234	C₄²×C₆₇	—	2	1	no	—
235	C₄²×C₆₇	—	2	1	no	—
236	C₄²×C₆₇	—	2	1	no	—
237	C₄²×C₆₇	—	2	1	no	—
238	C₄²×C₆₇	—	2	1	no	—
239	C₄²×C₆₇	—	2	1	no	—
240	C₄²×C₆₇	—	2	1	no	—
241	C₂³×C₆₇	—	2	1	no	—
242	C₂³×C₆₇	—	2	1	no	—
243	C₂³×C₆₇	—	2	1	no	—
244	C₂³×C₆₇	—	2	1	no	—
245	C₂³×C₆₇	—	2	8	no	—
246	C₂³×C₆₇	—	2	1	no	—
247	C₂³×C₆₇	—	2	1	no	—
248	C₂³×C₆₇	—	2	1	no	—
249	C₂³×C₆₇	—	2	1	no	—
250	C₂³×C₆₇	—	2	1	no	—
251	C₂³×C₆₇	—	2	1	no	—
252	C₂³×C₆₇	—	2	1	no	—
253	C₂³×C₆₇	—	2	1	no	—
254	C₂³×C₆₇	—	2	1	no	—
255	C₂³×C₆₇	—	2	1	no	—
256	C₂³×C₆₇	—	2	1	no	—
257	C₂³×C₆₇	—	2	1	no	—
258	C₂³×C₆₇	—	4	4	no	—
259	C₂³×C₆₇	—	4	4	no	—
260	C₂³×C₆₇	—	4	4	no	—
261	C₂³×C₆₇	—	4	4	no	—
262	C₂³×C₆₇	—	4	4	no	—
263	C₂³×C₆₇	—	4	4	no	—
264	C₂³×C₆₇	#117	1	2	yes	—
265	C₂³×C₆₇	C₄×D₄	1	2	yes	—
266	C₂³×C₆₇	#131	1	2	yes	—
267	C₂³×C₆₇	#131	1	2	yes	—
268	C₂³×C₆₇	#131	1	2	yes	—
269	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
270	C₂×C₄×C₆₇	—	2	1	no	—
271	C₂×C₄×C₆₇	—	2	1	no	—
272	C₂×C₄×C₆₇	—	2	1	no	—
273	C₂×C₄×C₆₇	—	2	1	no	—
274	C₂×C₄×C₆₇	—	2	2	no	—
275	C₂×C₄×C₆₇	—	2	2	no	—
276	C₂×C₄×C₆₇	—	2	2	no	—
277	C₂×C₄×C₆₇	—	2	2	no	—
278	C₂×C₄×C₆₇	—	2	2	no	—
279	C₂×C₄×C₆₇	—	2	2	no	—
280	C₂×C₄×C₆₇	—	2	2	no	—
281	C₂×C₄×C₆₇	—	2	2	no	—
282	C₂×C₄×C₆₇	—	2	1	no	—
283	C₂×C₄×C₆₇	—	2	1	no	—
284	C₂×C₄×C₆₇	—	2	1	no	—
285	C₂×C₄×C₆₇	—	2	1	no	—
286	C₂×C₄×C₆₇	—	2	1	no	—
287	C₂×C₄×C₆₇	—	2	1	no	—
288	C₂×C₄×C₆₇	—	2	1	no	—
289	C₂×C₄×C₆₇	—	2	1	no	—
290	C₂×C₄×C₆₇	—	2	1	no	—
291	C₂×C₄×C₆₇	—	2	1	no	—
292	C₂×C₄×C₆₇	—	2	1	no	—
293	C₂×C₄×C₆₇	—	2	1	no	—
294	C₂×C₄×C₆₇	—	2	1	no	—
295	C₂×C₄×C₆₇	—	2	1	no	—
296	C₂×C₄×C₆₇	—	2	1	no	—
297	C₂×C₄×C₆₇	—	2	1	no	—
298	C₂×C₄×C₆₇	—	2	1	no	—
299	C₂×C₄×C₆₇	—	2	1	no	—
300	C₂×C₄×C₆₇	—	2	1	no	—
301	C₂×C₄×C₆₇	—	2	1	no	—
302	C₂×C₄×C₆₇	—	2	1	no	—
303	C₂×C₄×C₆₇	—	2	1	no	—
304	C₂×C₄×C₆₇	—	2	1	no	—
305	C₂×C₄×C₆₇	—	2	1	no	—
306	C₂×C₄×C₆₇	—	2	1	no	—
307	C₂×C₄×C₆₇	—	2	1	no	—
308	C₂×C₄×C₆₇	—	2	1	no	—
309	C₂×C₄×C₆₇	—	4	4	no	—
310	C₂×C₄×C₆₇	—	4	4	no	—
311	C₂×C₄×C₆₇	—	4	4	no	—
312	C₂×C₄×C₆₇	—	4	1	no	—
313	C₂×C₄×C₆₇	—	4	1	no	—
314	C₂×C₄×C₆₇	—	4	1	no	—
315	C₂×C₄×C₆₇	—	4	1	no	—
316	C₂×C₄×C₆₇	#117	1	2	yes	—
317	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
318	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
320	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
321	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
322	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
323	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
324	C₈×C₆₇	—	2	2	no	—
325	C₈×C₆₇	—	2	2	no	—
326	C₈×C₆₇	—	4	1	no	—
327	C₈×C₆₇	—	4	1	no	—
328	C₈×C₆₇	—	4	1	no	—
329	C₈×C₆₇	—	4	1	no	—
330	C₈×C₆₇	—	4	1	no	—
331	C₈×C₆₇	—	4	1	no	—
332	C₂²×C₆₇	—	2	2	no	—
333	C₂²×C₆₇	—	2	2	no	—
334	C₂²×C₆₇	—	2	2	no	—
335	C₂²×C₆₇	—	2	2	no	—
336	C₂²×C₆₇	—	2	2	no	—
337	C₂²×C₆₇	—	2	2	no	—
338	C₂²×C₆₇	—	2	2	no	—
339	C₂²×C₆₇	—	2	2	no	—
340	C₂²×C₆₇	—	2	2	no	—
341	C₂²×C₆₇	—	2	2	no	—
342	C₂²×C₆₇	—	2	2	no	—
343	C₂²×C₆₇	—	2	2	no	—
344	C₂²×C₆₇	—	4	16	no	—
345	C₂²×C₆₇	—	4	1	no	—
346	C₂²×C₆₇	—	4	1	no	—
347	C₂²×C₆₇	—	4	1	no	—
348	C₂²×C₆₇	—	4	1	no	—
349	C₂²×C₆₇	—	4	1	no	—
350	C₂²×C₆₇	—	4	1	no	—
351	C₂²×C₆₇	—	4	1	no	—
352	C₂²×C₆₇	—	4	1	no	—
353	C₂²×C₆₇	#433	1	4	yes	complemented
354	C₂²×C₆₇	C₂×#117	1	1	yes	characteristic
355	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
356	C₂²×C₆₇	#518	1	1	yes	characteristic
357	C₂²×C₆₇	C₂×#131	1	1	yes	characteristic
358	C₂²×C₆₇	C₂×#131	1	1	yes	characteristic
359	C₂²×C₆₇	C₂×#131	1	1	yes	characteristic
360	C₂²×C₆₇	#568	1	1	yes	characteristic
361	C₄×C₆₇	—	2	2	no	—
362	C₄×C₆₇	—	2	2	no	—
363	C₄×C₆₇	—	4	1	no	—
364	C₄×C₆₇	—	4	1	no	—
365	C₄×C₆₇	—	4	1	no	—
366	C₄×C₆₇	—	4	1	no	—
367	C₄×C₆₇	—	4	1	no	—
368	C₄×C₆₇	—	4	1	no	—
369	C₄×C₆₇	—	4	1	no	—
370	C₄×C₆₇	—	4	1	no	—
371	C₄×C₆₇	—	4	1	no	—
372	C₄×C₆₇	#546	1	1	yes	characteristic
373	C₄×C₆₇	#546	1	1	yes	characteristic
374	C₄×C₆₇	#551	1	1	yes	characteristic
375	C₄×C₆₇	#551	1	1	yes	characteristic
376	#22558	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
377	C₂×C₆₇	—	2	4	no	—
378	C₂×C₆₇	—	4	2	no	—
379	C₂×C₆₇	—	4	2	no	—
380	C₂×C₆₇	#2342	1	1	yes	characteristic
381	C₂×C₆₇	C₂×#433	1	1	yes	characteristic
382	C₂×C₆₇	#2924	1	1	yes	characteristic
383	C₂×C₆₇	#2929	1	1	yes	characteristic
384	C₂×C₆₇	#2933	1	1	yes	characteristic
385	C₂×C₆₇	#2976	1	1	yes	characteristic
386	C₂×C₆₇	#2977	1	1	yes	characteristic
387	C₂×#433	C₂×C₆₇	1	1	yes	characteristic, complemented
388	C₂²×C₂²⋊C₈	C₂×C₆₇	1	1	yes	characteristic
389	#2280	C₂×C₆₇	1	1	yes	characteristic
390	#1924	C₂×C₆₇	1	1	yes	characteristic, complemented
391	#1924	C₂×C₆₇	1	1	yes	characteristic, complemented
392	#1923	C₂×C₆₇	1	1	yes	characteristic, complemented
393	#1923	C₂×C₆₇	1	1	yes	characteristic, complemented
394	#1850	C₂×C₆₇	1	1	yes	characteristic, complemented
395	#1850	C₂×C₆₇	1	1	yes	characteristic, complemented
396	#1818	C₂×C₆₇	1	1	yes	characteristic, complemented
397	#1798	C₂×C₆₇	1	1	yes	characteristic, complemented
398	#1779	C₂×C₆₇	1	1	yes	characteristic
399	#1752	C₂×C₆₇	1	1	yes	characteristic, complemented
400	C₈×C₂²⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
401	#1750	C₂×C₆₇	1	1	yes	characteristic, complemented
402	C₆₇	#22558	1	1	yes	characteristic, direct product factor, Sylow
403	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
404	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
405	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
406	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
407	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
408	#433	—	2	4	no	—
409	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
410	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
411	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
412	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
413	C₂×C₂²⋊C₈	—	2	4	no	—
414	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
415	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
416	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
417	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
418	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
419	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
420	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
421	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
422	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
423	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
424	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic, complemented
425	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic, complemented
426	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
427	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
428	#381	C₄×C₆₇	1	1	yes	characteristic
429	#381	C₄×C₆₇	1	1	yes	characteristic
430	#380	C₄×C₆₇	1	1	yes	characteristic
431	#380	C₄×C₆₇	1	1	yes	characteristic
432	#380	C₄×C₆₇	1	1	yes	characteristic
433	#380	C₄×C₆₇	1	1	yes	characteristic
434	#379	C₄×C₆₇	1	1	yes	characteristic
435	#379	C₄×C₆₇	1	1	yes	characteristic
436	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
437	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
438	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
439	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
440	#336	C₂²×C₆₇	1	1	yes	characteristic, complemented
441	#336	C₂²×C₆₇	1	1	yes	characteristic, complemented
442	#336	C₂²×C₆₇	1	1	yes	characteristic, complemented
443	#336	C₂²×C₆₇	1	1	yes	characteristic, complemented
444	#336	C₂²×C₆₇	1	1	yes	characteristic, complemented
445	#336	C₂²×C₆₇	1	1	yes	characteristic, complemented
446	#336	C₂²×C₆₇	1	1	yes	characteristic, complemented
447	#336	C₂²×C₆₇	1	1	yes	characteristic, complemented
448	C₂⁵	C₂×C₄×C₆₇	1	1	yes	characteristic
449	C₂³×C₄	—	2	2	no	—
450	C₂³×C₄	—	2	2	no	—
451	C₂³×C₄	—	2	2	no	—
452	C₂³×C₄	—	2	2	no	—
453	C₂³×C₄	—	4	1	no	—
454	C₂³×C₄	—	4	1	no	—
455	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
456	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
457	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
458	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
459	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
460	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
461	C₂²×C₈	—	2	2	no	—
462	C₂²×C₈	—	2	2	no	—
463	C₂²×C₈	—	2	2	no	—
464	C₂²×C₈	—	2	2	no	—
465	C₂²×C₈	—	4	1	no	—
466	C₂²×C₈	—	4	1	no	—
467	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
468	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
469	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
470	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
471	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
472	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
473	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
474	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
475	#117	—	2	2	no	—
476	#117	—	2	2	no	—
477	#117	—	4	1	no	—
478	#117	—	4	1	no	—
479	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
480	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
481	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
482	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
483	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
484	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
485	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
486	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
487	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
488	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
489	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
490	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
491	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
492	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
493	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
494	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
495	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
496	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
497	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
498	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
499	C₄⋊C₈	—	2	2	no	—
500	C₄⋊C₈	—	2	2	no	—
501	C₄⋊C₈	—	4	1	no	—
502	C₄⋊C₈	—	4	1	no	—
503	C₂²⋊C₈	—	2	2	no	—
504	C₂²⋊C₈	—	2	2	no	—
505	C₂²⋊C₈	—	2	2	no	—
506	C₂²⋊C₈	—	2	2	no	—
507	C₂²⋊C₈	—	2	2	no	—
508	C₂²⋊C₈	—	2	2	no	—
509	C₂²⋊C₈	—	2	2	no	—
510	C₂²⋊C₈	—	4	1	no	—
511	C₂²⋊C₈	—	4	1	no	—
512	C₂²⋊C₈	D₄×C₆₇	1	4	yes	—
513	#97	—	2	2	no	—
514	#97	—	4	1	no	—
515	C₄×C₈	—	2	2	no	—
516	C₄×C₈	—	4	1	no	—
517	#95	C₂×C₄×C₆₇	1	1	yes	characteristic
518	#95	C₂×C₄×C₆₇	1	1	yes	characteristic
519	#95	C₂×C₄×C₆₇	1	1	yes	characteristic
520	#95	C₂×C₄×C₆₇	1	1	yes	characteristic
521	#95	C₂×C₄×C₆₇	1	1	yes	characteristic
522	#95	C₂×C₄×C₆₇	1	1	yes	characteristic
523	#95	C₂×C₄×C₆₇	1	1	yes	characteristic
524	#95	C₂×C₄×C₆₇	1	1	yes	characteristic
525	C₂⁴	—	2	2	no	—
526	C₂⁴	—	2	2	no	—
527	C₂⁴	—	2	2	no	—
528	C₂⁴	—	2	2	no	—
529	C₂⁴	—	2	2	no	—
530	C₂⁴	—	4	1	no	—
531	C₂⁴	—	4	1	no	—
532	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
533	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
534	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	4	1	no	—
556	C₂²×C₄	—	4	1	no	—
557	C₂²×C₄	—	4	1	no	—
558	C₂²×C₄	—	4	4	no	—
559	C₂²×C₄	—	4	4	no	—
560	C₂²×C₄	—	4	4	no	—
561	C₂²×C₄	—	4	4	no	—
562	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
563	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
564	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
565	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
566	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
567	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
568	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
569	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
570	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
571	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
572	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
573	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
574	C₂²×C₄	#41×C₆₇	1	2	yes	—
575	C₂²×C₄	#41×C₆₇	1	2	yes	—
576	C₂²×C₄	#41×C₆₇	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
578	C₂×C₈	—	2	1	no	—
579	C₂×C₈	—	2	1	no	—
580	C₂×C₈	—	2	1	no	—
581	C₂×C₈	—	2	1	no	—
582	C₂×C₈	—	2	1	no	—
583	C₂×C₈	—	2	1	no	—
584	C₂×C₈	—	2	1	no	—
585	C₂×C₈	—	2	1	no	—
586	C₂×C₈	—	2	1	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	—	2	1	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	—	2	1	no	—
595	C₂×C₈	—	2	1	no	—
596	C₂×C₈	—	2	1	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	2	1	no	—
599	C₂×C₈	—	2	1	no	—
600	C₂×C₈	—	4	4	no	—
601	C₂×C₈	—	4	4	no	—
602	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
603	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	2	2	no	—
606	C₄⋊C₄	—	4	1	no	—
607	C₄⋊C₄	—	4	1	no	—
608	C₂²⋊C₄	—	2	2	no	—
609	C₂²⋊C₄	—	2	2	no	—
610	C₂²⋊C₄	—	2	2	no	—
611	C₂²⋊C₄	—	2	2	no	—
612	C₂²⋊C₄	—	2	2	no	—
613	C₂²⋊C₄	—	2	2	no	—
614	C₂²⋊C₄	—	2	2	no	—
615	C₂²⋊C₄	—	2	2	no	—
616	C₂²⋊C₄	—	4	1	no	—
617	C₂²⋊C₄	—	4	1	no	—
618	C₂²⋊C₄	—	4	1	no	—
619	C₂²⋊C₄	—	4	1	no	—
620	C₄²	—	2	1	no	—
621	C₄²	—	2	1	no	—
622	C₄²	—	2	1	no	—
623	C₄²	—	2	1	no	—
624	C₄²	—	2	1	no	—
625	C₄²	—	2	1	no	—
626	C₄²	—	2	1	no	—
627	C₄²	—	2	1	no	—
628	C₂³	—	2	1	no	—
629	C₂³	—	2	1	no	—
630	C₂³	—	2	1	no	—
631	C₂³	—	2	1	no	—
632	C₂³	—	2	8	no	—
633	C₂³	—	2	1	no	—
634	C₂³	—	2	1	no	—
635	C₂³	—	2	1	no	—
636	C₂³	—	2	1	no	—
637	C₂³	—	2	1	no	—
638	C₂³	—	2	1	no	—
639	C₂³	—	2	1	no	—
640	C₂³	—	2	1	no	—
641	C₂³	—	2	1	no	—
642	C₂³	—	2	1	no	—
643	C₂³	—	2	1	no	—
644	C₂³	—	2	1	no	—
645	C₂³	—	4	4	no	—
646	C₂³	—	4	4	no	—
647	C₂³	—	4	4	no	—
648	C₂³	—	4	4	no	—
649	C₂³	—	4	4	no	—
650	C₂³	—	4	4	no	—
651	C₂³	#117×C₆₇	1	2	yes	—
652	C₂³	C₄×D₄×C₆₇	1	2	yes	—
653	C₂³	#131×C₆₇	1	2	yes	—
654	C₂³	#131×C₆₇	1	2	yes	—
655	C₂³	#131×C₆₇	1	2	yes	—
656	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	4	4	no	—
697	C₂×C₄	—	4	4	no	—
698	C₂×C₄	—	4	4	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	#117×C₆₇	1	2	yes	—
704	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
705	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
706	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
707	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
708	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
709	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
710	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
711	C₈	—	2	2	no	—
712	C₈	—	2	2	no	—
713	C₈	—	4	1	no	—
714	C₈	—	4	1	no	—
715	C₈	—	4	1	no	—
716	C₈	—	4	1	no	—
717	C₈	—	4	1	no	—
718	C₈	—	4	1	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	2	no	—
725	C₂²	—	2	2	no	—
726	C₂²	—	2	2	no	—
727	C₂²	—	2	2	no	—
728	C₂²	—	2	2	no	—
729	C₂²	—	2	2	no	—
730	C₂²	—	2	2	no	—
731	C₂²	—	4	16	no	—
732	C₂²	—	4	1	no	—
733	C₂²	—	4	1	no	—
734	C₂²	—	4	1	no	—
735	C₂²	—	4	1	no	—
736	C₂²	—	4	1	no	—
737	C₂²	—	4	1	no	—
738	C₂²	—	4	1	no	—
739	C₂²	—	4	1	no	—
740	C₂²	#433×C₆₇	1	4	yes	complemented
741	C₂²	C₂×#117×C₆₇	1	1	yes	characteristic
742	C₂²	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
743	C₂²	#518×C₆₇	1	1	yes	characteristic
744	C₂²	C₂×#131×C₆₇	1	1	yes	characteristic
745	C₂²	C₂×#131×C₆₇	1	1	yes	characteristic
746	C₂²	C₂×#131×C₆₇	1	1	yes	characteristic
747	C₂²	#568×C₆₇	1	1	yes	characteristic
748	C₄	—	2	2	no	—
749	C₄	—	2	2	no	—
750	C₄	—	4	1	no	—
751	C₄	—	4	1	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	1	no	—
754	C₄	—	4	1	no	—
755	C₄	—	4	1	no	—
756	C₄	—	4	1	no	—
757	C₄	—	4	1	no	—
758	C₄	—	4	1	no	—
759	C₄	#546×C₆₇	1	1	yes	characteristic
760	C₄	#546×C₆₇	1	1	yes	characteristic
761	C₄	#551×C₆₇	1	1	yes	characteristic
762	C₄	#551×C₆₇	1	1	yes	characteristic
763	C₂	—	2	4	no	—
764	C₂	—	4	2	no	—
765	C₂	—	4	2	no	—
766	C₂	C₆₇×#2342	1	1	yes	characteristic
767	C₂	C₂×#433×C₆₇	1	1	yes	characteristic
768	C₂	C₆₇×#2924	1	1	yes	characteristic
769	C₂	C₆₇×#2929	1	1	yes	characteristic
770	C₂	C₆₇×#2933	1	1	yes	characteristic
771	C₂	C₆₇×#2976	1	1	yes	characteristic
772	C₂	C₆₇×#2977	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
socle	C₂³×C₆₇	C₂³×C₄
prime radical	C₂⁵×C₆₇	C₂×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#433×C₆₇	C₂	semidirect
4. C₆₇×#1924	C₂	semidirect
5. C₆₇×#1924	C₂	semidirect
6. C₆₇×#1923	C₂	semidirect
7. C₆₇×#1923	C₂	semidirect
8. C₆₇×#1850	C₂	semidirect
9. C₆₇×#1850	C₂	semidirect
10. C₆₇×#1818	C₂	semidirect
11. C₆₇×#1798	C₂	semidirect
13. C₆₇×#1752	C₂	semidirect
14. C₈×C₂²⋊C₄×C₆₇	C₂	semidirect
15. C₆₇×#1750	C₂	semidirect
22. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
23. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
24. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
25. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
37. C₂×#97×C₆₇	C₂²	semidirect
38. C₂×#97×C₆₇	C₂²	semidirect
39. C₂×C₄×C₈×C₆₇	C₂²	semidirect
40. C₂×C₄×C₈×C₆₇	C₂²	semidirect
53. #336×C₆₇	C₂²	semidirect
54. #336×C₆₇	C₂²	semidirect
55. #336×C₆₇	C₂²	semidirect
56. #336×C₆₇	C₂²	semidirect
57. #336×C₆₇	C₂²	semidirect
58. #336×C₆₇	C₂²	semidirect
59. #336×C₆₇	C₂²	semidirect
60. #336×C₆₇	C₂²	semidirect
353. C₂²×C₆₇	#433	semidirect
376. #22558	C₆₇	direct (N × H)
387. C₂×#433	C₂×C₆₇	semidirect
390. #1924	C₂×C₆₇	semidirect
391. #1924	C₂×C₆₇	semidirect
392. #1923	C₂×C₆₇	semidirect
393. #1923	C₂×C₆₇	semidirect
394. #1850	C₂×C₆₇	semidirect
395. #1850	C₂×C₆₇	semidirect
396. #1818	C₂×C₆₇	semidirect
397. #1798	C₂×C₆₇	semidirect
399. #1752	C₂×C₆₇	semidirect
400. C₈×C₂²⋊C₄	C₂×C₆₇	semidirect
401. #1750	C₂×C₆₇	semidirect
402. C₆₇	#22558	direct (N × H)
409. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
410. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
411. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
412. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
424. C₂×#97	C₂²×C₆₇	semidirect
425. C₂×#97	C₂²×C₆₇	semidirect
426. C₂×C₄×C₈	C₂²×C₆₇	semidirect
427. C₂×C₄×C₈	C₂²×C₆₇	semidirect
440. #336	C₂²×C₆₇	semidirect
441. #336	C₂²×C₆₇	semidirect
442. #336	C₂²×C₆₇	semidirect
443. #336	C₂²×C₆₇	semidirect
444. #336	C₂²×C₆₇	semidirect
445. #336	C₂²×C₆₇	semidirect
446. #336	C₂²×C₆₇	semidirect
447. #336	C₂²×C₆₇	semidirect
740. C₂²	#433×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#433×C₆₇	2
C₂²×C₂²⋊C₈×C₆₇	2
C₆₇×#2280	2
C₆₇×#1924	2
C₆₇×#1923	2
C₆₇×#1850	2
C₆₇×#1818	2
C₆₇×#1798	2
C₆₇×#1779	2
C₆₇×#1752	2
C₈×C₂²⋊C₄×C₆₇	2
C₆₇×#1750	2
#22558	67

Subgroups — C67×#22558 #30701809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#22558 #30701809