Subgroups — C₆₇×#59382 #30738633

Order 17152.

2212 conjugacy classes of subgroups.

The subgroup lattice has 1098 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2743	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2735	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2598	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2578	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2562	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2534	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2497	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2495	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2457	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2454	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2454	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2422	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2420	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2418	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2408	C₂	1	1	yes	maximal, characteristic
16	C₆₇×#2357	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2354	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2342	C₂	1	2	yes	maximal, complemented
19	D₄×C₂²⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	D₄×C₂²⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#123×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
26	C₂×#123×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
28	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#120×C₆₇	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
37	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
38	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
39	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
40	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
41	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	#400×C₆₇	C₂²	1	2	yes	complemented
43	#400×C₆₇	C₂²	1	2	yes	complemented
44	#400×C₆₇	C₂²	1	2	yes	complemented
45	#399×C₆₇	C₂²	1	2	yes	complemented
46	#399×C₆₇	C₂²	1	2	yes	complemented
47	#397×C₆₇	C₂²	1	2	yes	—
48	#397×C₆₇	C₂²	1	2	yes	complemented
49	#397×C₆₇	C₂²	1	2	yes	complemented
50	#396×C₆₇	C₂²	1	2	yes	—
51	#396×C₆₇	C₂²	1	2	yes	complemented
52	#396×C₆₇	C₂²	1	2	yes	complemented
53	#394×C₆₇	C₂²	1	2	yes	—
54	#394×C₆₇	C₂²	1	2	yes	—
55	#394×C₆₇	C₂²	1	2	yes	complemented
56	#394×C₆₇	C₂²	1	2	yes	complemented
57	#392×C₆₇	C₂²	1	2	yes	—
58	#390×C₆₇	C₂²	1	1	yes	characteristic
59	#390×C₆₇	C₂²	1	1	yes	characteristic
60	#390×C₆₇	C₂²	1	1	yes	characteristic
61	#390×C₆₇	C₂²	1	1	yes	characteristic
62	#390×C₆₇	C₂²	1	1	yes	characteristic
63	#390×C₆₇	C₂²	1	1	yes	characteristic
64	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
65	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
66	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	#388×C₆₇	C₂²	1	2	yes	—
69	#388×C₆₇	C₂²	1	2	yes	—
70	#388×C₆₇	C₂²	1	1	yes	characteristic
71	#388×C₆₇	C₂²	1	1	yes	characteristic
72	#388×C₆₇	C₂²	1	2	yes	—
73	#388×C₆₇	C₂²	1	2	yes	complemented
74	#388×C₆₇	C₂²	1	2	yes	complemented
75	#388×C₆₇	C₂²	1	2	yes	complemented
76	#388×C₆₇	C₂²	1	2	yes	complemented
77	#388×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	1	yes	characteristic, complemented
82	#387×C₆₇	C₂²	1	1	yes	characteristic, complemented
83	#386×C₆₇	C₂²	1	1	yes	characteristic
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	complemented
89	#386×C₆₇	C₂²	1	2	yes	complemented
90	#386×C₆₇	C₂²	1	2	yes	complemented
91	#385×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	#385×C₆₇	C₂²	1	2	yes	complemented
93	#385×C₆₇	C₂²	1	2	yes	complemented
94	#385×C₆₇	C₂²	1	2	yes	complemented
95	#384×C₆₇	C₂²	1	1	yes	characteristic, complemented
96	#383×C₆₇	C₂²	1	2	yes	complemented
97	#382×C₆₇	C₂²	1	1	yes	characteristic, complemented
98	#381×C₆₇	C₂²	1	2	yes	complemented
99	#381×C₆₇	C₂²	1	1	yes	characteristic, complemented
100	#381×C₆₇	C₂²	1	2	yes	complemented
101	#380×C₆₇	C₂²	1	1	yes	characteristic
102	#380×C₆₇	C₂²	1	1	yes	characteristic
103	#380×C₆₇	C₂²	1	1	yes	characteristic
104	#380×C₆₇	C₂²	1	2	yes	complemented
105	#380×C₆₇	C₂²	1	1	yes	characteristic, complemented
106	#380×C₆₇	C₂²	1	1	yes	characteristic, complemented
107	#380×C₆₇	C₂²	1	2	yes	complemented
108	#380×C₆₇	C₂²	1	2	yes	complemented
109	#379×C₆₇	C₂²	1	2	yes	—
110	#379×C₆₇	C₂²	1	2	yes	—
111	#379×C₆₇	C₂²	1	2	yes	—
112	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
114	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
115	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
116	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
117	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
120	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
121	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
122	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
123	C₂⁵×C₆₇	C₂³	1	2	yes	—
124	C₂²×D₄×C₆₇	—	2	4	no	—
125	C₂²×D₄×C₆₇	—	2	4	no	—
126	C₂²×D₄×C₆₇	—	4	2	no	—
127	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
129	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
130	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
131	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
132	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
137	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
139	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
140	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
141	#125×C₆₇	—	4	2	no	—
142	#123×C₆₇	—	2	4	no	—
143	#123×C₆₇	—	4	4	no	—
144	#121×C₆₇	—	2	4	no	—
145	#121×C₆₇	—	2	4	no	—
146	#120×C₆₇	—	4	4	no	—
147	C₄×D₄×C₆₇	—	2	4	no	—
148	C₄×D₄×C₆₇	—	2	4	no	—
149	C₄×D₄×C₆₇	—	4	2	no	—
150	C₄×D₄×C₆₇	—	4	2	no	—
151	C₄×D₄×C₆₇	—	4	2	no	—
152	C₄×D₄×C₆₇	—	4	4	no	—
153	C₄×D₄×C₆₇	—	4	4	no	—
154	#117×C₆₇	—	4	4	no	—
155	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
166	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
175	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
176	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	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	1	yes	characteristic
188	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
199	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₆₇	—	4	2	no	—
208	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
211	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
217	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
218	#95×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
228	#95×C₆₇	C₂³	1	1	yes	characteristic
229	#95×C₆₇	C₂³	1	1	yes	characteristic
230	#95×C₆₇	C₂³	1	1	yes	characteristic
231	#95×C₆₇	C₂³	1	2	yes	—
232	#95×C₆₇	C₂³	1	2	yes	—
233	#95×C₆₇	C₂³	1	1	yes	characteristic
234	#95×C₆₇	C₂³	1	2	yes	—
235	#95×C₆₇	C₂³	1	1	yes	characteristic
236	#95×C₆₇	C₂³	1	2	yes	—
237	#95×C₆₇	C₂³	1	2	yes	—
238	#95×C₆₇	C₂³	1	2	yes	—
239	#95×C₆₇	C₂³	1	2	yes	—
240	#95×C₆₇	C₂³	1	2	yes	—
241	#95×C₆₇	C₂³	1	2	yes	—
242	C₂⁴×C₆₇	—	2	4	no	—
243	C₂⁴×C₆₇	—	2	4	no	—
244	C₂⁴×C₆₇	—	2	4	no	—
245	C₂⁴×C₆₇	—	4	2	no	—
246	C₂⁴×C₆₇	—	4	2	no	—
247	C₂⁴×C₆₇	—	4	2	no	—
248	C₂⁴×C₆₇	—	4	2	no	—
249	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
250	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
251	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
252	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
253	C₂×D₄×C₆₇	—	2	4	no	—
254	C₂×D₄×C₆₇	—	2	4	no	—
255	C₂×D₄×C₆₇	—	2	2	no	—
256	C₂×D₄×C₆₇	—	2	4	no	—
257	C₂×D₄×C₆₇	—	2	4	no	—
258	C₂×D₄×C₆₇	—	2	4	no	—
259	C₂×D₄×C₆₇	—	2	2	no	—
260	C₂×D₄×C₆₇	—	2	4	no	—
261	C₂×D₄×C₆₇	—	2	2	no	—
262	C₂×D₄×C₆₇	—	2	2	no	—
263	C₂×D₄×C₆₇	—	2	2	no	—
264	C₂×D₄×C₆₇	—	2	2	no	—
265	C₂×D₄×C₆₇	—	4	2	no	—
266	C₂×D₄×C₆₇	—	4	1	no	—
267	C₂×D₄×C₆₇	—	4	2	no	—
268	C₂×D₄×C₆₇	—	4	2	no	—
269	C₂×D₄×C₆₇	—	4	16	no	—
270	C₂×D₄×C₆₇	#41	1	4	yes	—
271	C₂×D₄×C₆₇	#41	1	4	yes	—
272	C₂²×C₄×C₆₇	—	2	4	no	—
273	C₂²×C₄×C₆₇	—	2	2	no	—
274	C₂²×C₄×C₆₇	—	2	4	no	—
275	C₂²×C₄×C₆₇	—	2	4	no	—
276	C₂²×C₄×C₆₇	—	2	2	no	—
277	C₂²×C₄×C₆₇	—	2	2	no	—
278	C₂²×C₄×C₆₇	—	2	2	no	—
279	C₂²×C₄×C₆₇	—	2	2	no	—
280	C₂²×C₄×C₆₇	—	2	2	no	—
281	C₂²×C₄×C₆₇	—	2	2	no	—
282	C₂²×C₄×C₆₇	—	2	2	no	—
283	C₂²×C₄×C₆₇	—	2	2	no	—
284	C₂²×C₄×C₆₇	—	2	4	no	—
285	C₂²×C₄×C₆₇	—	2	4	no	—
286	C₂²×C₄×C₆₇	—	4	1	no	—
287	C₂²×C₄×C₆₇	—	4	1	no	—
288	C₂²×C₄×C₆₇	—	4	2	no	—
289	C₂²×C₄×C₆₇	—	4	1	no	—
290	C₂²×C₄×C₆₇	—	4	2	no	—
291	C₂²×C₄×C₆₇	—	4	2	no	—
292	C₂²×C₄×C₆₇	—	4	2	no	—
293	C₂²×C₄×C₆₇	—	4	2	no	—
294	C₂²×C₄×C₆₇	—	4	2	no	—
295	C₂²×C₄×C₆₇	—	4	2	no	—
296	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
315	C₄⋊C₄×C₆₇	—	2	2	no	—
316	C₄⋊C₄×C₆₇	—	2	2	no	—
317	C₄⋊C₄×C₆₇	—	2	2	no	—
318	C₄⋊C₄×C₆₇	—	2	2	no	—
319	C₄⋊C₄×C₆₇	—	2	2	no	—
320	C₄⋊C₄×C₆₇	—	2	2	no	—
321	C₄⋊C₄×C₆₇	—	2	2	no	—
322	C₄⋊C₄×C₆₇	—	2	2	no	—
323	C₄⋊C₄×C₆₇	—	2	2	no	—
324	C₄⋊C₄×C₆₇	—	4	1	no	—
325	C₄⋊C₄×C₆₇	—	4	2	no	—
326	C₄⋊C₄×C₆₇	—	4	2	no	—
327	C₄⋊C₄×C₆₇	—	4	2	no	—
328	C₄⋊C₄×C₆₇	—	4	1	no	—
329	C₄⋊C₄×C₆₇	—	4	2	no	—
330	C₄⋊C₄×C₆₇	—	4	2	no	—
331	C₄⋊C₄×C₆₇	—	4	2	no	—
332	C₄⋊C₄×C₆₇	—	4	2	no	—
333	C₄⋊C₄×C₆₇	—	4	2	no	—
334	C₂²⋊C₄×C₆₇	—	2	4	no	—
335	C₂²⋊C₄×C₆₇	—	2	4	no	—
336	C₂²⋊C₄×C₆₇	—	2	4	no	—
337	C₂²⋊C₄×C₆₇	—	2	4	no	—
338	C₂²⋊C₄×C₆₇	—	2	4	no	—
339	C₂²⋊C₄×C₆₇	—	2	2	no	—
340	C₂²⋊C₄×C₆₇	—	2	4	no	—
341	C₂²⋊C₄×C₆₇	—	2	2	no	—
342	C₂²⋊C₄×C₆₇	—	2	4	no	—
343	C₂²⋊C₄×C₆₇	—	2	4	no	—
344	C₂²⋊C₄×C₆₇	—	2	2	no	—
345	C₂²⋊C₄×C₆₇	—	2	2	no	—
346	C₂²⋊C₄×C₆₇	—	2	4	no	—
347	C₂²⋊C₄×C₆₇	—	4	2	no	—
348	C₂²⋊C₄×C₆₇	—	4	2	no	—
349	C₂²⋊C₄×C₆₇	—	4	2	no	—
350	C₂²⋊C₄×C₆₇	—	4	2	no	—
351	C₂²⋊C₄×C₆₇	—	4	1	no	—
352	C₂²⋊C₄×C₆₇	—	4	2	no	—
353	C₂²⋊C₄×C₆₇	—	4	2	no	—
354	C₂²⋊C₄×C₆₇	—	4	2	no	—
355	C₂²⋊C₄×C₆₇	—	4	2	no	—
356	C₂²⋊C₄×C₆₇	—	4	2	no	—
357	C₂²⋊C₄×C₆₇	—	4	1	no	—
358	C₂²⋊C₄×C₆₇	—	4	1	no	—
359	C₂²⋊C₄×C₆₇	—	4	2	no	—
360	C₂²⋊C₄×C₆₇	—	4	2	no	—
361	C₂²⋊C₄×C₆₇	—	4	2	no	—
362	C₂²⋊C₄×C₆₇	—	4	2	no	—
363	C₂²⋊C₄×C₆₇	—	4	2	no	—
364	C₂²⋊C₄×C₆₇	#41	1	4	yes	—
365	C₄²×C₆₇	—	2	2	no	—
366	C₄²×C₆₇	—	2	2	no	—
367	C₄²×C₆₇	—	2	2	no	—
368	C₄²×C₆₇	—	2	2	no	—
369	C₄²×C₆₇	—	2	4	no	—
370	C₄²×C₆₇	—	2	2	no	—
371	C₄²×C₆₇	—	4	1	no	—
372	C₄²×C₆₇	—	4	1	no	—
373	C₄²×C₆₇	—	4	2	no	—
374	C₄²×C₆₇	—	4	2	no	—
375	C₂³×C₆₇	—	2	2	no	—
376	C₂³×C₆₇	—	2	1	no	—
377	C₂³×C₆₇	—	2	2	no	—
378	C₂³×C₆₇	—	2	1	no	—
379	C₂³×C₆₇	—	2	1	no	—
380	C₂³×C₆₇	—	2	1	no	—
381	C₂³×C₆₇	—	2	1	no	—
382	C₂³×C₆₇	—	2	2	no	—
383	C₂³×C₆₇	—	2	2	no	—
384	C₂³×C₆₇	—	2	2	no	—
385	C₂³×C₆₇	—	2	1	no	—
386	C₂³×C₆₇	—	2	1	no	—
387	C₂³×C₆₇	—	2	2	no	—
388	C₂³×C₆₇	—	2	2	no	—
389	C₂³×C₆₇	—	2	1	no	—
390	C₂³×C₆₇	—	2	1	no	—
391	C₂³×C₆₇	—	2	2	no	—
392	C₂³×C₆₇	—	2	1	no	—
393	C₂³×C₆₇	—	2	2	no	—
394	C₂³×C₆₇	—	2	2	no	—
395	C₂³×C₆₇	—	2	2	no	—
396	C₂³×C₆₇	—	2	2	no	—
397	C₂³×C₆₇	—	2	1	no	—
398	C₂³×C₆₇	—	2	1	no	—
399	C₂³×C₆₇	—	4	8	no	—
400	C₂³×C₆₇	—	4	8	no	—
401	C₂³×C₆₇	—	4	8	no	—
402	C₂³×C₆₇	—	8	4	no	—
403	C₂³×C₆₇	—	8	4	no	—
404	C₂³×C₆₇	—	8	4	no	—
405	C₂³×C₆₇	—	8	4	no	—
406	C₂³×C₆₇	C₂×#41	1	2	yes	—
407	C₂³×C₆₇	C₂×#41	1	4	yes	—
408	C₂³×C₆₇	C₂×#41	1	4	yes	—
409	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
410	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
411	D₄×C₆₇	—	2	8	no	—
412	D₄×C₆₇	—	2	8	no	—
413	D₄×C₆₇	—	4	8	no	—
414	D₄×C₆₇	—	4	4	no	—
415	D₄×C₆₇	—	4	8	no	—
416	D₄×C₆₇	—	4	8	no	—
417	C₂×C₄×C₆₇	—	2	1	no	—
418	C₂×C₄×C₆₇	—	2	1	no	—
419	C₂×C₄×C₆₇	—	2	1	no	—
420	C₂×C₄×C₆₇	—	2	1	no	—
421	C₂×C₄×C₆₇	—	2	1	no	—
422	C₂×C₄×C₆₇	—	2	1	no	—
423	C₂×C₄×C₆₇	—	2	1	no	—
424	C₂×C₄×C₆₇	—	2	1	no	—
425	C₂×C₄×C₆₇	—	2	1	no	—
426	C₂×C₄×C₆₇	—	2	1	no	—
427	C₂×C₄×C₆₇	—	2	1	no	—
428	C₂×C₄×C₆₇	—	2	1	no	—
429	C₂×C₄×C₆₇	—	2	2	no	—
430	C₂×C₄×C₆₇	—	2	2	no	—
431	C₂×C₄×C₆₇	—	2	2	no	—
432	C₂×C₄×C₆₇	—	2	1	no	—
433	C₂×C₄×C₆₇	—	2	2	no	—
434	C₂×C₄×C₆₇	—	2	2	no	—
435	C₂×C₄×C₆₇	—	2	2	no	—
436	C₂×C₄×C₆₇	—	2	1	no	—
437	C₂×C₄×C₆₇	—	2	1	no	—
438	C₂×C₄×C₆₇	—	2	1	no	—
439	C₂×C₄×C₆₇	—	2	2	no	—
440	C₂×C₄×C₆₇	—	2	1	no	—
441	C₂×C₄×C₆₇	—	2	1	no	—
442	C₂×C₄×C₆₇	—	2	1	no	—
443	C₂×C₄×C₆₇	—	2	2	no	—
444	C₂×C₄×C₆₇	—	2	1	no	—
445	C₂×C₄×C₆₇	—	2	1	no	—
446	C₂×C₄×C₆₇	—	2	1	no	—
447	C₂×C₄×C₆₇	—	2	2	no	—
448	C₂×C₄×C₆₇	—	2	2	no	—
449	C₂×C₄×C₆₇	—	2	2	no	—
450	C₂×C₄×C₆₇	—	2	1	no	—
451	C₂×C₄×C₆₇	—	2	1	no	—
452	C₂×C₄×C₆₇	—	2	2	no	—
453	C₂×C₄×C₆₇	—	2	1	no	—
454	C₂×C₄×C₆₇	—	2	1	no	—
455	C₂×C₄×C₆₇	—	2	2	no	—
456	C₂×C₄×C₆₇	—	2	1	no	—
457	C₂×C₄×C₆₇	—	2	1	no	—
458	C₂×C₄×C₆₇	—	2	2	no	—
459	C₂×C₄×C₆₇	—	2	2	no	—
460	C₂×C₄×C₆₇	—	2	2	no	—
461	C₂×C₄×C₆₇	—	2	1	no	—
462	C₂×C₄×C₆₇	—	2	1	no	—
463	C₂×C₄×C₆₇	—	2	1	no	—
464	C₂×C₄×C₆₇	—	2	1	no	—
465	C₂×C₄×C₆₇	—	2	1	no	—
466	C₂×C₄×C₆₇	—	2	2	no	—
467	C₂×C₄×C₆₇	—	2	2	no	—
468	C₂×C₄×C₆₇	—	4	8	no	—
469	C₂×C₄×C₆₇	—	4	4	no	—
470	C₂×C₄×C₆₇	—	4	4	no	—
471	C₂×C₄×C₆₇	—	4	4	no	—
472	C₂×C₄×C₆₇	—	4	4	no	—
473	C₂×C₄×C₆₇	—	8	4	no	—
474	C₂×C₄×C₆₇	—	8	4	no	—
475	C₂×C₄×C₆₇	—	8	4	no	—
476	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
477	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
478	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
479	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
480	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
481	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
482	C₂²×C₆₇	—	2	4	no	—
483	C₂²×C₆₇	—	2	4	no	—
484	C₂²×C₆₇	—	2	2	no	—
485	C₂²×C₆₇	—	2	4	no	—
486	C₂²×C₆₇	—	2	4	no	—
487	C₂²×C₆₇	—	2	2	no	—
488	C₂²×C₆₇	—	2	2	no	—
489	C₂²×C₆₇	—	2	4	no	—
490	C₂²×C₆₇	—	2	2	no	—
491	C₂²×C₆₇	—	2	4	no	—
492	C₂²×C₆₇	—	2	2	no	—
493	C₂²×C₆₇	—	2	2	no	—
494	C₂²×C₆₇	—	4	1	no	—
495	C₂²×C₆₇	—	4	1	no	—
496	C₂²×C₆₇	—	4	1	no	—
497	C₂²×C₆₇	—	4	2	no	—
498	C₂²×C₆₇	—	4	1	no	—
499	C₂²×C₆₇	—	4	2	no	—
500	C₂²×C₆₇	—	4	2	no	—
501	C₂²×C₆₇	—	4	1	no	—
502	C₂²×C₆₇	—	4	2	no	—
503	C₂²×C₆₇	—	4	2	no	—
504	C₂²×C₆₇	—	4	2	no	—
505	C₂²×C₆₇	—	4	1	no	—
506	C₂²×C₆₇	—	4	1	no	—
507	C₂²×C₆₇	—	4	2	no	—
508	C₂²×C₆₇	—	4	2	no	—
509	C₂²×C₆₇	—	4	1	no	—
510	C₂²×C₆₇	—	8	16	no	—
511	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
512	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
513	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
514	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
515	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
516	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
517	C₂²×C₆₇	#585	1	1	yes	characteristic
518	C₄×C₆₇	—	2	2	no	—
519	C₄×C₆₇	—	2	2	no	—
520	C₄×C₆₇	—	2	2	no	—
521	C₄×C₆₇	—	4	1	no	—
522	C₄×C₆₇	—	4	1	no	—
523	C₄×C₆₇	—	4	1	no	—
524	C₄×C₆₇	—	4	2	no	—
525	C₄×C₆₇	—	4	1	no	—
526	C₄×C₆₇	—	4	2	no	—
527	C₄×C₆₇	—	4	1	no	—
528	C₄×C₆₇	—	4	2	no	—
529	C₄×C₆₇	—	4	2	no	—
530	C₄×C₆₇	—	4	1	no	—
531	C₄×C₆₇	—	4	1	no	—
532	C₄×C₆₇	—	4	2	no	—
533	C₄×C₆₇	—	4	1	no	—
534	C₄×C₆₇	—	4	1	no	—
535	C₄×C₆₇	—	4	2	no	—
536	C₄×C₆₇	#551	1	4	yes	—
537	#59382	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
538	C₂×C₆₇	—	4	2	no	—
539	C₂×C₆₇	—	4	4	no	—
540	C₂×C₆₇	—	4	4	no	—
541	C₂×C₆₇	—	4	2	no	—
542	C₂×C₆₇	C₂×#551	1	1	yes	characteristic
543	C₂×C₆₇	#3475	1	1	yes	characteristic
544	C₂×C₆₇	#3481	1	1	yes	characteristic
545	C₂×C₆₇	#3513	1	1	yes	characteristic
546	C₂×C₆₇	#3519	1	1	yes	characteristic
547	C₂×C₆₇	#3519	1	1	yes	characteristic
548	C₂×C₆₇	#3542	1	1	yes	characteristic
549	#2743	C₂×C₆₇	1	2	yes	complemented
550	#2735	C₂×C₆₇	1	2	yes	complemented
551	#2598	C₂×C₆₇	1	2	yes	complemented
552	#2578	C₂×C₆₇	1	2	yes	complemented
553	#2562	C₂×C₆₇	1	1	yes	characteristic, complemented
554	#2534	C₂×C₆₇	1	2	yes	complemented
555	#2497	C₂×C₆₇	1	1	yes	characteristic, complemented
556	#2495	C₂×C₆₇	1	1	yes	characteristic, complemented
557	#2457	C₂×C₆₇	1	2	yes	complemented
558	#2454	C₂×C₆₇	1	1	yes	characteristic, complemented
559	#2454	C₂×C₆₇	1	1	yes	characteristic, complemented
560	#2422	C₂×C₆₇	1	1	yes	characteristic, complemented
561	#2420	C₂×C₆₇	1	1	yes	characteristic, complemented
562	#2418	C₂×C₆₇	1	2	yes	complemented
563	#2408	C₂×C₆₇	1	1	yes	characteristic
564	#2357	C₂×C₆₇	1	1	yes	characteristic, complemented
565	#2354	C₂×C₆₇	1	1	yes	characteristic, complemented
566	#2342	C₂×C₆₇	1	2	yes	complemented
567	D₄×C₂²⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
568	D₄×C₂²⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
569	C₄×#123	C₂×C₆₇	1	1	yes	characteristic, complemented
570	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
571	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
572	C₆₇	#59382	1	1	yes	characteristic, direct product factor, Sylow
573	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
574	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic, complemented
575	C₂×#123	C₂²×C₆₇	1	1	yes	characteristic
576	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
577	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
578	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
579	C₂×#120	C₂²×C₆₇	1	2	yes	—
580	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
581	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
582	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
583	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
584	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
585	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
586	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
587	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
588	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
589	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
590	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
591	#400	C₂²×C₆₇	1	2	yes	complemented
592	#400	C₂²×C₆₇	1	2	yes	complemented
593	#400	C₂²×C₆₇	1	2	yes	complemented
594	#399	C₂²×C₆₇	1	2	yes	complemented
595	#399	C₂²×C₆₇	1	2	yes	complemented
596	#397	C₂²×C₆₇	1	2	yes	—
597	#397	C₂²×C₆₇	1	2	yes	complemented
598	#397	C₂²×C₆₇	1	2	yes	complemented
599	#396	C₂²×C₆₇	1	2	yes	—
600	#396	C₂²×C₆₇	1	2	yes	complemented
601	#396	C₂²×C₆₇	1	2	yes	complemented
602	#394	C₂²×C₆₇	1	2	yes	—
603	#394	C₂²×C₆₇	1	2	yes	—
604	#394	C₂²×C₆₇	1	2	yes	complemented
605	#394	C₂²×C₆₇	1	2	yes	complemented
606	#392	C₂²×C₆₇	1	2	yes	—
607	#390	C₂²×C₆₇	1	1	yes	characteristic
608	#390	C₂²×C₆₇	1	1	yes	characteristic
609	#390	C₂²×C₆₇	1	1	yes	characteristic
610	#390	C₂²×C₆₇	1	1	yes	characteristic
611	#390	C₂²×C₆₇	1	1	yes	characteristic
612	#390	C₂²×C₆₇	1	1	yes	characteristic
613	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
614	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
615	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
616	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
617	#388	C₂²×C₆₇	1	2	yes	—
618	#388	C₂²×C₆₇	1	1	yes	characteristic
619	#388	C₂²×C₆₇	1	2	yes	—
620	#388	C₂²×C₆₇	1	2	yes	—
621	#388	C₂²×C₆₇	1	1	yes	characteristic
622	#388	C₂²×C₆₇	1	2	yes	complemented
623	#388	C₂²×C₆₇	1	2	yes	complemented
624	#388	C₂²×C₆₇	1	2	yes	complemented
625	#388	C₂²×C₆₇	1	2	yes	complemented
626	#388	C₂²×C₆₇	1	2	yes	complemented
627	#388	C₂²×C₆₇	1	2	yes	complemented
628	#388	C₂²×C₆₇	1	2	yes	complemented
629	#387	C₂²×C₆₇	1	1	yes	characteristic, complemented
630	#387	C₂²×C₆₇	1	2	yes	complemented
631	#387	C₂²×C₆₇	1	1	yes	characteristic, complemented
632	#386	C₂²×C₆₇	1	2	yes	—
633	#386	C₂²×C₆₇	1	2	yes	—
634	#386	C₂²×C₆₇	1	2	yes	—
635	#386	C₂²×C₆₇	1	2	yes	—
636	#386	C₂²×C₆₇	1	1	yes	characteristic
637	#386	C₂²×C₆₇	1	2	yes	complemented
638	#386	C₂²×C₆₇	1	2	yes	complemented
639	#386	C₂²×C₆₇	1	2	yes	complemented
640	#385	C₂²×C₆₇	1	2	yes	complemented
641	#385	C₂²×C₆₇	1	2	yes	complemented
642	#385	C₂²×C₆₇	1	2	yes	complemented
643	#385	C₂²×C₆₇	1	1	yes	characteristic, complemented
644	#384	C₂²×C₆₇	1	1	yes	characteristic, complemented
645	#383	C₂²×C₆₇	1	2	yes	complemented
646	#382	C₂²×C₆₇	1	1	yes	characteristic, complemented
647	#381	C₂²×C₆₇	1	2	yes	complemented
648	#381	C₂²×C₆₇	1	2	yes	complemented
649	#381	C₂²×C₆₇	1	1	yes	characteristic, complemented
650	#380	C₂²×C₆₇	1	1	yes	characteristic
651	#380	C₂²×C₆₇	1	1	yes	characteristic
652	#380	C₂²×C₆₇	1	1	yes	characteristic
653	#380	C₂²×C₆₇	1	1	yes	characteristic, complemented
654	#380	C₂²×C₆₇	1	1	yes	characteristic, complemented
655	#380	C₂²×C₆₇	1	2	yes	complemented
656	#380	C₂²×C₆₇	1	2	yes	complemented
657	#380	C₂²×C₆₇	1	2	yes	complemented
658	#379	C₂²×C₆₇	1	2	yes	—
659	#379	C₂²×C₆₇	1	2	yes	—
660	#379	C₂²×C₆₇	1	2	yes	—
661	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
662	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
663	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
664	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
665	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
666	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
667	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
668	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
669	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
670	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
671	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
672	C₂⁵	C₂³×C₆₇	1	2	yes	—
673	C₂²×D₄	—	2	4	no	—
674	C₂²×D₄	—	2	4	no	—
675	C₂²×D₄	—	4	2	no	—
676	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
677	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
678	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
679	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
680	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
681	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
682	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
683	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
684	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
685	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
686	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
687	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
688	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
689	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
690	#125	—	4	2	no	—
691	#123	—	2	4	no	—
692	#123	—	4	4	no	—
693	#121	—	2	4	no	—
694	#121	—	2	4	no	—
695	#120	—	4	4	no	—
696	C₄×D₄	—	2	4	no	—
697	C₄×D₄	—	2	4	no	—
698	C₄×D₄	—	4	2	no	—
699	C₄×D₄	—	4	2	no	—
700	C₄×D₄	—	4	2	no	—
701	C₄×D₄	—	4	4	no	—
702	C₄×D₄	—	4	4	no	—
703	#117	—	4	4	no	—
704	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
705	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
706	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
707	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
708	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
709	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
710	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
711	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
712	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
713	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
714	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
715	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
716	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
717	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
718	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
719	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
720	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
721	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
722	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
723	C₂×C₂²⋊C₄	—	2	8	no	—
724	C₂×C₂²⋊C₄	—	4	4	no	—
725	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
726	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
727	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
728	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
729	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
730	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
731	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
732	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
733	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
734	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
735	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
736	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
737	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
738	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
739	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
740	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
741	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
742	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
743	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
744	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
745	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
746	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
747	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
748	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
749	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
750	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
751	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
752	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
753	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
755	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
756	C₂×C₄²	—	4	2	no	—
757	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
758	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
759	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
760	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
761	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
762	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
763	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
764	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
765	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
766	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
767	#95	C₂³×C₆₇	1	1	yes	characteristic
768	#95	C₂³×C₆₇	1	1	yes	characteristic
769	#95	C₂³×C₆₇	1	1	yes	characteristic
770	#95	C₂³×C₆₇	1	1	yes	characteristic
771	#95	C₂³×C₆₇	1	1	yes	characteristic
772	#95	C₂³×C₆₇	1	2	yes	—
773	#95	C₂³×C₆₇	1	2	yes	—
774	#95	C₂³×C₆₇	1	2	yes	—
775	#95	C₂³×C₆₇	1	2	yes	—
776	#95	C₂³×C₆₇	1	2	yes	—
777	#95	C₂³×C₆₇	1	1	yes	characteristic
778	#95	C₂³×C₆₇	1	1	yes	characteristic
779	#95	C₂³×C₆₇	1	1	yes	characteristic
780	#95	C₂³×C₆₇	1	2	yes	—
781	#95	C₂³×C₆₇	1	2	yes	—
782	#95	C₂³×C₆₇	1	1	yes	characteristic
783	#95	C₂³×C₆₇	1	2	yes	—
784	#95	C₂³×C₆₇	1	1	yes	characteristic
785	#95	C₂³×C₆₇	1	2	yes	—
786	#95	C₂³×C₆₇	1	2	yes	—
787	#95	C₂³×C₆₇	1	2	yes	—
788	#95	C₂³×C₆₇	1	2	yes	—
789	#95	C₂³×C₆₇	1	2	yes	—
790	#95	C₂³×C₆₇	1	2	yes	—
791	C₂⁴	—	2	4	no	—
792	C₂⁴	—	2	4	no	—
793	C₂⁴	—	2	4	no	—
794	C₂⁴	—	4	2	no	—
795	C₂⁴	—	4	2	no	—
796	C₂⁴	—	4	2	no	—
797	C₂⁴	—	4	2	no	—
798	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
799	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
800	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
801	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
802	C₂×D₄	—	2	4	no	—
803	C₂×D₄	—	2	4	no	—
804	C₂×D₄	—	2	2	no	—
805	C₂×D₄	—	2	4	no	—
806	C₂×D₄	—	2	4	no	—
807	C₂×D₄	—	2	4	no	—
808	C₂×D₄	—	2	2	no	—
809	C₂×D₄	—	2	4	no	—
810	C₂×D₄	—	2	2	no	—
811	C₂×D₄	—	2	2	no	—
812	C₂×D₄	—	2	2	no	—
813	C₂×D₄	—	2	2	no	—
814	C₂×D₄	—	4	2	no	—
815	C₂×D₄	—	4	1	no	—
816	C₂×D₄	—	4	2	no	—
817	C₂×D₄	—	4	2	no	—
818	C₂×D₄	—	4	16	no	—
819	C₂×D₄	#41×C₆₇	1	4	yes	—
820	C₂×D₄	#41×C₆₇	1	4	yes	—
821	C₂²×C₄	—	2	4	no	—
822	C₂²×C₄	—	2	2	no	—
823	C₂²×C₄	—	2	4	no	—
824	C₂²×C₄	—	2	4	no	—
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	—	2	2	no	—
827	C₂²×C₄	—	2	2	no	—
828	C₂²×C₄	—	2	2	no	—
829	C₂²×C₄	—	2	2	no	—
830	C₂²×C₄	—	2	2	no	—
831	C₂²×C₄	—	2	2	no	—
832	C₂²×C₄	—	2	2	no	—
833	C₂²×C₄	—	2	4	no	—
834	C₂²×C₄	—	2	4	no	—
835	C₂²×C₄	—	4	1	no	—
836	C₂²×C₄	—	4	1	no	—
837	C₂²×C₄	—	4	2	no	—
838	C₂²×C₄	—	4	1	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	—	4	2	no	—
845	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
846	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
847	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
848	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
849	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
850	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
851	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
852	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
853	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
854	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
855	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
856	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
857	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
858	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
859	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
860	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
861	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
862	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
863	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	—	2	2	no	—
868	C₄⋊C₄	—	2	2	no	—
869	C₄⋊C₄	—	2	2	no	—
870	C₄⋊C₄	—	2	2	no	—
871	C₄⋊C₄	—	2	2	no	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	4	2	no	—
874	C₄⋊C₄	—	4	2	no	—
875	C₄⋊C₄	—	4	1	no	—
876	C₄⋊C₄	—	4	2	no	—
877	C₄⋊C₄	—	4	2	no	—
878	C₄⋊C₄	—	4	2	no	—
879	C₄⋊C₄	—	4	2	no	—
880	C₄⋊C₄	—	4	2	no	—
881	C₄⋊C₄	—	4	1	no	—
882	C₄⋊C₄	—	4	2	no	—
883	C₂²⋊C₄	—	2	4	no	—
884	C₂²⋊C₄	—	2	4	no	—
885	C₂²⋊C₄	—	2	4	no	—
886	C₂²⋊C₄	—	2	4	no	—
887	C₂²⋊C₄	—	2	4	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	4	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	4	no	—
892	C₂²⋊C₄	—	2	4	no	—
893	C₂²⋊C₄	—	2	2	no	—
894	C₂²⋊C₄	—	2	2	no	—
895	C₂²⋊C₄	—	2	4	no	—
896	C₂²⋊C₄	—	4	2	no	—
897	C₂²⋊C₄	—	4	2	no	—
898	C₂²⋊C₄	—	4	2	no	—
899	C₂²⋊C₄	—	4	2	no	—
900	C₂²⋊C₄	—	4	2	no	—
901	C₂²⋊C₄	—	4	2	no	—
902	C₂²⋊C₄	—	4	2	no	—
903	C₂²⋊C₄	—	4	1	no	—
904	C₂²⋊C₄	—	4	1	no	—
905	C₂²⋊C₄	—	4	2	no	—
906	C₂²⋊C₄	—	4	2	no	—
907	C₂²⋊C₄	—	4	2	no	—
908	C₂²⋊C₄	—	4	2	no	—
909	C₂²⋊C₄	—	4	2	no	—
910	C₂²⋊C₄	—	4	2	no	—
911	C₂²⋊C₄	—	4	2	no	—
912	C₂²⋊C₄	—	4	1	no	—
913	C₂²⋊C₄	#41×C₆₇	1	4	yes	—
914	C₄²	—	2	2	no	—
915	C₄²	—	2	2	no	—
916	C₄²	—	2	2	no	—
917	C₄²	—	2	2	no	—
918	C₄²	—	2	4	no	—
919	C₄²	—	2	2	no	—
920	C₄²	—	4	1	no	—
921	C₄²	—	4	1	no	—
922	C₄²	—	4	2	no	—
923	C₄²	—	4	2	no	—
924	C₂³	—	2	2	no	—
925	C₂³	—	2	1	no	—
926	C₂³	—	2	2	no	—
927	C₂³	—	2	1	no	—
928	C₂³	—	2	1	no	—
929	C₂³	—	2	1	no	—
930	C₂³	—	2	1	no	—
931	C₂³	—	2	2	no	—
932	C₂³	—	2	2	no	—
933	C₂³	—	2	2	no	—
934	C₂³	—	2	1	no	—
935	C₂³	—	2	1	no	—
936	C₂³	—	2	2	no	—
937	C₂³	—	2	2	no	—
938	C₂³	—	2	1	no	—
939	C₂³	—	2	1	no	—
940	C₂³	—	2	2	no	—
941	C₂³	—	2	1	no	—
942	C₂³	—	2	2	no	—
943	C₂³	—	2	2	no	—
944	C₂³	—	2	2	no	—
945	C₂³	—	2	2	no	—
946	C₂³	—	2	1	no	—
947	C₂³	—	2	1	no	—
948	C₂³	—	4	8	no	—
949	C₂³	—	4	8	no	—
950	C₂³	—	4	8	no	—
951	C₂³	—	8	4	no	—
952	C₂³	—	8	4	no	—
953	C₂³	—	8	4	no	—
954	C₂³	—	8	4	no	—
955	C₂³	C₂×#41×C₆₇	1	2	yes	—
956	C₂³	C₂×#41×C₆₇	1	4	yes	—
957	C₂³	C₂×#41×C₆₇	1	4	yes	—
958	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
959	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
960	D₄	—	2	8	no	—
961	D₄	—	2	8	no	—
962	D₄	—	4	8	no	—
963	D₄	—	4	8	no	—
964	D₄	—	4	4	no	—
965	D₄	—	4	8	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	1	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	4	8	no	—
1018	C₂×C₄	—	4	4	no	—
1019	C₂×C₄	—	4	4	no	—
1020	C₂×C₄	—	4	4	no	—
1021	C₂×C₄	—	4	4	no	—
1022	C₂×C₄	—	8	4	no	—
1023	C₂×C₄	—	8	4	no	—
1024	C₂×C₄	—	8	4	no	—
1025	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1026	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1027	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1028	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1029	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1030	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1031	C₂²	—	2	4	no	—
1032	C₂²	—	2	4	no	—
1033	C₂²	—	2	2	no	—
1034	C₂²	—	2	4	no	—
1035	C₂²	—	2	4	no	—
1036	C₂²	—	2	2	no	—
1037	C₂²	—	2	2	no	—
1038	C₂²	—	2	4	no	—
1039	C₂²	—	2	2	no	—
1040	C₂²	—	2	4	no	—
1041	C₂²	—	2	2	no	—
1042	C₂²	—	2	2	no	—
1043	C₂²	—	4	1	no	—
1044	C₂²	—	4	2	no	—
1045	C₂²	—	4	1	no	—
1046	C₂²	—	4	2	no	—
1047	C₂²	—	4	1	no	—
1048	C₂²	—	4	1	no	—
1049	C₂²	—	4	2	no	—
1050	C₂²	—	4	1	no	—
1051	C₂²	—	4	2	no	—
1052	C₂²	—	4	1	no	—
1053	C₂²	—	4	1	no	—
1054	C₂²	—	4	2	no	—
1055	C₂²	—	4	2	no	—
1056	C₂²	—	4	1	no	—
1057	C₂²	—	4	2	no	—
1058	C₂²	—	4	2	no	—
1059	C₂²	—	8	16	no	—
1060	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1061	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1062	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1063	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1064	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1065	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1066	C₂²	#585×C₆₇	1	1	yes	characteristic
1067	C₄	—	2	2	no	—
1068	C₄	—	2	2	no	—
1069	C₄	—	2	2	no	—
1070	C₄	—	4	1	no	—
1071	C₄	—	4	2	no	—
1072	C₄	—	4	1	no	—
1073	C₄	—	4	1	no	—
1074	C₄	—	4	1	no	—
1075	C₄	—	4	1	no	—
1076	C₄	—	4	2	no	—
1077	C₄	—	4	2	no	—
1078	C₄	—	4	1	no	—
1079	C₄	—	4	1	no	—
1080	C₄	—	4	1	no	—
1081	C₄	—	4	2	no	—
1082	C₄	—	4	2	no	—
1083	C₄	—	4	1	no	—
1084	C₄	—	4	2	no	—
1085	C₄	#551×C₆₇	1	4	yes	—
1086	C₂	—	4	2	no	—
1087	C₂	—	4	4	no	—
1088	C₂	—	4	4	no	—
1089	C₂	—	4	2	no	—
1090	C₂	C₂×#551×C₆₇	1	1	yes	characteristic
1091	C₂	C₆₇×#3475	1	1	yes	characteristic
1092	C₂	C₆₇×#3481	1	1	yes	characteristic
1093	C₂	C₆₇×#3513	1	1	yes	characteristic
1094	C₂	C₆₇×#3519	1	1	yes	characteristic
1095	C₂	C₆₇×#3519	1	1	yes	characteristic
1096	C₂	C₆₇×#3542	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₆₇×#2408	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×#2743	C₂	semidirect
2. C₆₇×#2735	C₂	semidirect
3. C₆₇×#2598	C₂	semidirect
4. C₆₇×#2578	C₂	semidirect
5. C₆₇×#2562	C₂	semidirect
6. C₆₇×#2534	C₂	semidirect
7. C₆₇×#2497	C₂	semidirect
8. C₆₇×#2495	C₂	semidirect
9. C₆₇×#2457	C₂	semidirect
10. C₆₇×#2454	C₂	semidirect
11. C₆₇×#2454	C₂	semidirect
12. C₆₇×#2422	C₂	semidirect
13. C₆₇×#2420	C₂	semidirect
14. C₆₇×#2418	C₂	semidirect
16. C₆₇×#2357	C₂	semidirect
17. C₆₇×#2354	C₂	semidirect
18. C₆₇×#2342	C₂	semidirect
19. D₄×C₂²⋊C₄×C₆₇	C₂	semidirect
20. D₄×C₂²⋊C₄×C₆₇	C₂	semidirect
21. C₄×#123×C₆₇	C₂	semidirect
22. C₄×#121×C₆₇	C₂	semidirect
23. C₄×#121×C₆₇	C₂	semidirect
25. C₂×#125×C₆₇	C₂²	semidirect
27. C₂×#123×C₆₇	C₂²	semidirect
36. C₂×C₄×D₄×C₆₇	C₂²	semidirect
37. C₂×C₄×D₄×C₆₇	C₂²	semidirect
38. C₂×#117×C₆₇	C₂²	semidirect
41. C₂²×C₄²×C₆₇	C₂²	semidirect
42. #400×C₆₇	C₂²	semidirect
43. #400×C₆₇	C₂²	semidirect
44. #400×C₆₇	C₂²	semidirect
45. #399×C₆₇	C₂²	semidirect
46. #399×C₆₇	C₂²	semidirect
48. #397×C₆₇	C₂²	semidirect
49. #397×C₆₇	C₂²	semidirect
51. #396×C₆₇	C₂²	semidirect
52. #396×C₆₇	C₂²	semidirect
55. #394×C₆₇	C₂²	semidirect
56. #394×C₆₇	C₂²	semidirect
64. #389×C₆₇	C₂²	semidirect
65. #389×C₆₇	C₂²	semidirect
66. #389×C₆₇	C₂²	semidirect
67. #389×C₆₇	C₂²	semidirect
73. #388×C₆₇	C₂²	semidirect
74. #388×C₆₇	C₂²	semidirect
75. #388×C₆₇	C₂²	semidirect
76. #388×C₆₇	C₂²	semidirect
77. #388×C₆₇	C₂²	semidirect
78. #388×C₆₇	C₂²	semidirect
79. #388×C₆₇	C₂²	semidirect
80. #387×C₆₇	C₂²	semidirect
81. #387×C₆₇	C₂²	semidirect
82. #387×C₆₇	C₂²	semidirect
88. #386×C₆₇	C₂²	semidirect
89. #386×C₆₇	C₂²	semidirect
90. #386×C₆₇	C₂²	semidirect
91. #385×C₆₇	C₂²	semidirect
92. #385×C₆₇	C₂²	semidirect
93. #385×C₆₇	C₂²	semidirect
94. #385×C₆₇	C₂²	semidirect
95. #384×C₆₇	C₂²	semidirect
96. #383×C₆₇	C₂²	semidirect
97. #382×C₆₇	C₂²	semidirect
98. #381×C₆₇	C₂²	semidirect
99. #381×C₆₇	C₂²	semidirect
100. #381×C₆₇	C₂²	semidirect
104. #380×C₆₇	C₂²	semidirect
105. #380×C₆₇	C₂²	semidirect
106. #380×C₆₇	C₂²	semidirect
107. #380×C₆₇	C₂²	semidirect
108. #380×C₆₇	C₂²	semidirect
112. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
113. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
114. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
115. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
116. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
119. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
120. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
121. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
122. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
537. #59382	C₆₇	direct (N × H)
549. #2743	C₂×C₆₇	semidirect
550. #2735	C₂×C₆₇	semidirect
551. #2598	C₂×C₆₇	semidirect
552. #2578	C₂×C₆₇	semidirect
553. #2562	C₂×C₆₇	semidirect
554. #2534	C₂×C₆₇	semidirect
555. #2497	C₂×C₆₇	semidirect
556. #2495	C₂×C₆₇	semidirect
557. #2457	C₂×C₆₇	semidirect
558. #2454	C₂×C₆₇	semidirect
559. #2454	C₂×C₆₇	semidirect
560. #2422	C₂×C₆₇	semidirect
561. #2420	C₂×C₆₇	semidirect
562. #2418	C₂×C₆₇	semidirect
564. #2357	C₂×C₆₇	semidirect
565. #2354	C₂×C₆₇	semidirect
566. #2342	C₂×C₆₇	semidirect
567. D₄×C₂²⋊C₄	C₂×C₆₇	semidirect
568. D₄×C₂²⋊C₄	C₂×C₆₇	semidirect
569. C₄×#123	C₂×C₆₇	semidirect
570. C₄×#121	C₂×C₆₇	semidirect
571. C₄×#121	C₂×C₆₇	semidirect
572. C₆₇	#59382	direct (N × H)
574. C₂×#125	C₂²×C₆₇	semidirect
576. C₂×#123	C₂²×C₆₇	semidirect
585. C₂×C₄×D₄	C₂²×C₆₇	semidirect
586. C₂×C₄×D₄	C₂²×C₆₇	semidirect
587. C₂×#117	C₂²×C₆₇	semidirect
590. C₂²×C₄²	C₂²×C₆₇	semidirect
591. #400	C₂²×C₆₇	semidirect
592. #400	C₂²×C₆₇	semidirect
593. #400	C₂²×C₆₇	semidirect
594. #399	C₂²×C₆₇	semidirect
595. #399	C₂²×C₆₇	semidirect
597. #397	C₂²×C₆₇	semidirect
598. #397	C₂²×C₆₇	semidirect
600. #396	C₂²×C₆₇	semidirect
601. #396	C₂²×C₆₇	semidirect
604. #394	C₂²×C₆₇	semidirect
605. #394	C₂²×C₆₇	semidirect
613. #389	C₂²×C₆₇	semidirect
614. #389	C₂²×C₆₇	semidirect
615. #389	C₂²×C₆₇	semidirect
616. #389	C₂²×C₆₇	semidirect
622. #388	C₂²×C₆₇	semidirect
623. #388	C₂²×C₆₇	semidirect
624. #388	C₂²×C₆₇	semidirect
625. #388	C₂²×C₆₇	semidirect
626. #388	C₂²×C₆₇	semidirect
627. #388	C₂²×C₆₇	semidirect
628. #388	C₂²×C₆₇	semidirect
629. #387	C₂²×C₆₇	semidirect
630. #387	C₂²×C₆₇	semidirect
631. #387	C₂²×C₆₇	semidirect
637. #386	C₂²×C₆₇	semidirect
638. #386	C₂²×C₆₇	semidirect
639. #386	C₂²×C₆₇	semidirect
640. #385	C₂²×C₆₇	semidirect
641. #385	C₂²×C₆₇	semidirect
642. #385	C₂²×C₆₇	semidirect
643. #385	C₂²×C₆₇	semidirect
644. #384	C₂²×C₆₇	semidirect
645. #383	C₂²×C₆₇	semidirect
646. #382	C₂²×C₆₇	semidirect
647. #381	C₂²×C₆₇	semidirect
648. #381	C₂²×C₆₇	semidirect
649. #381	C₂²×C₆₇	semidirect
653. #380	C₂²×C₆₇	semidirect
654. #380	C₂²×C₆₇	semidirect
655. #380	C₂²×C₆₇	semidirect
656. #380	C₂²×C₆₇	semidirect
657. #380	C₂²×C₆₇	semidirect
661. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
662. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
663. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
664. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
665. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
668. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
669. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
670. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
671. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#2743	2
C₆₇×#2735	2
C₆₇×#2598	2
C₆₇×#2578	2
C₆₇×#2562	2
C₆₇×#2534	2
C₆₇×#2497	2
C₆₇×#2495	2
C₆₇×#2457	2
C₆₇×#2454	2
C₆₇×#2422	2
C₆₇×#2420	2
C₆₇×#2418	2
C₆₇×#2408	2
C₆₇×#2357	2
C₆₇×#2354	2
C₆₇×#2342	2
D₄×C₂²⋊C₄×C₆₇	2
C₄×#123×C₆₇	2
C₄×#121×C₆₇	2
#59382	67

Subgroups — C67×#59382 #30738633

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59382 #30738633