Subgroups — C₆₇×#59803 #30739054

Order 17152.

3136 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#546×C₆₇	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2712	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2693	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2688	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2557	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2543	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2535	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2488	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2483	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2450	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2444	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2424	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2412	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2404	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2403	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2358	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2339	C₂	1	2	yes	maximal, complemented
18	C₄×#120×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#386×C₆₇	C₂	1	2	yes	maximal, complemented
20	C₂²×#41×C₆₇	C₂²	1	2	yes	—
21	C₂³×D₄×C₆₇	C₂²	1	2	yes	—
22	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
23	#546×C₆₇	—	2	16	no	—
24	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
25	C₂×#123×C₆₇	C₂²	1	2	yes	—
26	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
27	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
28	C₂×#121×C₆₇	C₂²	1	2	yes	—
29	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
30	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
31	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
32	C₂×#120×C₆₇	C₂²	1	2	yes	—
33	C₂×#120×C₆₇	C₂²	1	2	yes	—
34	C₂×#120×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×#120×C₆₇	C₂²	1	2	yes	complemented
36	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
38	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
41	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
42	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
43	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
44	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
45	#400×C₆₇	C₂²	1	2	yes	complemented
46	#400×C₆₇	C₂²	1	2	yes	complemented
47	#398×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	#397×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#397×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	#397×C₆₇	C₂²	1	1	yes	characteristic, complemented
51	#397×C₆₇	C₂²	1	2	yes	complemented
52	#397×C₆₇	C₂²	1	2	yes	complemented
53	#397×C₆₇	C₂²	1	2	yes	complemented
54	#396×C₆₇	C₂²	1	2	yes	complemented
55	#394×C₆₇	C₂²	1	1	yes	characteristic, complemented
56	#394×C₆₇	C₂²	1	2	yes	complemented
57	#394×C₆₇	C₂²	1	2	yes	complemented
58	#393×C₆₇	C₂²	1	2	yes	complemented
59	#393×C₆₇	C₂²	1	2	yes	complemented
60	#392×C₆₇	C₂²	1	1	yes	characteristic
61	#392×C₆₇	C₂²	1	1	yes	characteristic
62	#392×C₆₇	C₂²	1	2	yes	—
63	#392×C₆₇	C₂²	1	1	yes	characteristic, complemented
64	#392×C₆₇	C₂²	1	2	yes	complemented
65	#391×C₆₇	C₂²	1	2	yes	complemented
66	#391×C₆₇	C₂²	1	2	yes	complemented
67	#390×C₆₇	C₂²	1	2	yes	complemented
68	#388×C₆₇	C₂²	1	2	yes	complemented
69	#388×C₆₇	C₂²	1	2	yes	complemented
70	#388×C₆₇	C₂²	1	2	yes	complemented
71	#387×C₆₇	C₂²	1	2	yes	complemented
72	#386×C₆₇	C₂²	1	2	yes	—
73	#386×C₆₇	C₂²	1	2	yes	—
74	#386×C₆₇	C₂²	1	2	yes	—
75	#386×C₆₇	C₂²	1	2	yes	—
76	#386×C₆₇	C₂²	1	2	yes	—
77	#386×C₆₇	C₂²	1	2	yes	—
78	#386×C₆₇	C₂²	1	2	yes	complemented
79	#386×C₆₇	C₂²	1	2	yes	complemented
80	#386×C₆₇	C₂²	1	2	yes	complemented
81	#386×C₆₇	C₂²	1	2	yes	complemented
82	#386×C₆₇	C₂²	1	2	yes	complemented
83	#386×C₆₇	C₂²	1	2	yes	complemented
84	#386×C₆₇	C₂²	1	2	yes	complemented
85	#386×C₆₇	C₂²	1	1	yes	characteristic, complemented
86	#386×C₆₇	C₂²	1	2	yes	complemented
87	#386×C₆₇	C₂²	1	2	yes	complemented
88	#386×C₆₇	C₂²	1	2	yes	complemented
89	#386×C₆₇	C₂²	1	2	yes	complemented
90	#385×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	#382×C₆₇	C₂²	1	1	yes	characteristic, complemented
96	#381×C₆₇	C₂²	1	2	yes	complemented
97	#381×C₆₇	C₂²	1	2	yes	complemented
98	#381×C₆₇	C₂²	1	2	yes	complemented
99	#380×C₆₇	C₂²	1	2	yes	complemented
100	#380×C₆₇	C₂²	1	2	yes	complemented
101	#379×C₆₇	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
103	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
104	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
105	C₂×#95×C₆₇	C₂²	1	2	yes	complemented
106	C₂×#95×C₆₇	C₂²	1	2	yes	complemented
107	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic, complemented
108	C₂⁵×C₆₇	C₂³	1	2	yes	—
109	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
110	C₂×#41×C₆₇	—	2	8	no	—
111	C₂×#41×C₆₇	—	2	8	no	—
112	C₂×#41×C₆₇	—	4	4	no	—
113	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
114	C₂²×D₄×C₆₇	—	2	8	no	—
115	C₂²×D₄×C₆₇	—	2	8	no	—
116	C₂²×D₄×C₆₇	—	4	4	no	—
117	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
118	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
119	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
120	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
121	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
122	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
123	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
124	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
125	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
126	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₆₇	—	4	2	no	—
129	C₂³×C₄×C₆₇	—	4	4	no	—
130	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
131	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
132	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
133	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
134	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
135	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
136	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
137	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
138	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
141	#124×C₆₇	—	2	8	no	—
142	#123×C₆₇	—	2	8	no	—
143	#123×C₆₇	—	2	8	no	—
144	C₂²⋊Q₈×C₆₇	—	2	8	no	—
145	#121×C₆₇	—	2	8	no	—
146	#121×C₆₇	—	2	8	no	—
147	#121×C₆₇	—	2	8	no	—
148	#121×C₆₇	—	4	2	no	—
149	#120×C₆₇	—	2	8	no	—
150	#120×C₆₇	—	2	8	no	—
151	#120×C₆₇	—	4	4	no	—
152	#120×C₆₇	D₄	1	8	yes	complemented
153	C₄×D₄×C₆₇	—	2	8	no	—
154	C₄×D₄×C₆₇	—	2	8	no	—
155	C₄×D₄×C₆₇	—	4	2	no	—
156	C₄×D₄×C₆₇	—	4	2	no	—
157	C₄×D₄×C₆₇	—	4	4	no	—
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	2	yes	—
164	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
168	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
169	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
170	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
171	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₆₇	C₂³	1	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	2	yes	—
187	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
201	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
203	#95×C₆₇	C₂³	1	2	yes	—
204	#95×C₆₇	C₂³	1	1	yes	characteristic
205	#95×C₆₇	C₂³	1	2	yes	—
206	#95×C₆₇	C₂³	1	2	yes	—
207	#95×C₆₇	C₂³	1	2	yes	—
208	#95×C₆₇	C₂³	1	2	yes	—
209	#95×C₆₇	C₂³	1	1	yes	characteristic
210	#95×C₆₇	C₂³	1	2	yes	—
211	#95×C₆₇	C₂³	1	2	yes	—
212	#95×C₆₇	C₂³	1	2	yes	—
213	#95×C₆₇	C₂³	1	2	yes	—
214	#95×C₆₇	C₂³	1	2	yes	—
215	#95×C₆₇	C₂³	1	2	yes	—
216	#95×C₆₇	C₂³	1	2	yes	—
217	#95×C₆₇	C₂³	1	2	yes	—
218	#95×C₆₇	C₂³	1	1	yes	characteristic
219	#95×C₆₇	C₂³	1	2	yes	—
220	#95×C₆₇	C₂³	1	2	yes	—
221	#95×C₆₇	C₂³	1	2	yes	—
222	#95×C₆₇	C₂³	1	2	yes	—
223	#95×C₆₇	C₂³	1	1	yes	characteristic
224	C₂⁴×C₆₇	—	2	4	no	—
225	C₂⁴×C₆₇	—	2	4	no	—
226	C₂⁴×C₆₇	—	2	4	no	—
227	C₂⁴×C₆₇	—	2	4	no	—
228	C₂⁴×C₆₇	—	2	4	no	—
229	C₂⁴×C₆₇	—	2	4	no	—
230	C₂⁴×C₆₇	—	4	1	no	—
231	C₂⁴×C₆₇	—	4	1	no	—
232	C₂⁴×C₆₇	—	4	2	no	—
233	C₂⁴×C₆₇	—	4	2	no	—
234	C₂⁴×C₆₇	—	4	2	no	—
235	C₂⁴×C₆₇	C₂×D₄	1	4	yes	—
236	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
237	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
238	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
239	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
240	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
241	#41×C₆₇	—	4	32	no	—
242	C₂×Q₈×C₆₇	—	2	4	no	—
243	C₂×Q₈×C₆₇	—	2	4	no	—
244	C₂×Q₈×C₆₇	—	4	2	no	—
245	C₂×D₄×C₆₇	—	2	4	no	—
246	C₂×D₄×C₆₇	—	2	4	no	—
247	C₂×D₄×C₆₇	—	2	4	no	—
248	C₂×D₄×C₆₇	—	2	4	no	—
249	C₂×D₄×C₆₇	—	2	4	no	—
250	C₂×D₄×C₆₇	—	2	4	no	—
251	C₂×D₄×C₆₇	—	2	4	no	—
252	C₂×D₄×C₆₇	—	2	4	no	—
253	C₂×D₄×C₆₇	—	2	4	no	—
254	C₂×D₄×C₆₇	—	2	4	no	—
255	C₂×D₄×C₆₇	—	2	4	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	4	no	—
260	C₂×D₄×C₆₇	—	2	4	no	—
261	C₂×D₄×C₆₇	—	4	1	no	—
262	C₂×D₄×C₆₇	—	4	1	no	—
263	C₂×D₄×C₆₇	—	4	2	no	—
264	C₂×D₄×C₆₇	—	4	2	no	—
265	C₂×D₄×C₆₇	—	4	1	no	—
266	C₂×D₄×C₆₇	—	4	2	no	—
267	C₂×D₄×C₆₇	—	4	2	no	—
268	C₂×D₄×C₆₇	—	4	2	no	—
269	C₂×D₄×C₆₇	—	4	2	no	—
270	C₂×D₄×C₆₇	—	4	1	no	—
271	C₂×D₄×C₆₇	—	4	2	no	—
272	C₂×D₄×C₆₇	—	4	2	no	—
273	C₂×D₄×C₆₇	—	4	32	no	—
274	C₂×D₄×C₆₇	C₂×D₄	1	8	yes	—
275	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
276	C₂×D₄×C₆₇	#41	1	8	yes	complemented
277	C₂²×C₄×C₆₇	—	2	4	no	—
278	C₂²×C₄×C₆₇	—	2	4	no	—
279	C₂²×C₄×C₆₇	—	2	4	no	—
280	C₂²×C₄×C₆₇	—	2	4	no	—
281	C₂²×C₄×C₆₇	—	2	4	no	—
282	C₂²×C₄×C₆₇	—	2	4	no	—
283	C₂²×C₄×C₆₇	—	2	4	no	—
284	C₂²×C₄×C₆₇	—	2	4	no	—
285	C₂²×C₄×C₆₇	—	2	4	no	—
286	C₂²×C₄×C₆₇	—	2	4	no	—
287	C₂²×C₄×C₆₇	—	2	4	no	—
288	C₂²×C₄×C₆₇	—	2	4	no	—
289	C₂²×C₄×C₆₇	—	2	4	no	—
290	C₂²×C₄×C₆₇	—	2	2	no	—
291	C₂²×C₄×C₆₇	—	2	4	no	—
292	C₂²×C₄×C₆₇	—	2	2	no	—
293	C₂²×C₄×C₆₇	—	4	2	no	—
294	C₂²×C₄×C₆₇	—	4	2	no	—
295	C₂²×C₄×C₆₇	—	4	1	no	—
296	C₂²×C₄×C₆₇	—	4	2	no	—
297	C₂²×C₄×C₆₇	—	4	2	no	—
298	C₂²×C₄×C₆₇	—	4	2	no	—
299	C₂²×C₄×C₆₇	—	4	2	no	—
300	C₂²×C₄×C₆₇	—	4	2	no	—
301	C₂²×C₄×C₆₇	—	4	2	no	—
302	C₂²×C₄×C₆₇	—	4	2	no	—
303	C₂²×C₄×C₆₇	—	4	2	no	—
304	C₂²×C₄×C₆₇	—	4	2	no	—
305	C₂²×C₄×C₆₇	—	4	2	no	—
306	C₂²×C₄×C₆₇	—	4	2	no	—
307	C₂²×C₄×C₆₇	—	4	16	no	—
308	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
311	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
319	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
322	C₄⋊C₄×C₆₇	—	2	4	no	—
323	C₄⋊C₄×C₆₇	—	2	4	no	—
324	C₄⋊C₄×C₆₇	—	2	4	no	—
325	C₄⋊C₄×C₆₇	—	2	4	no	—
326	C₄⋊C₄×C₆₇	—	4	2	no	—
327	C₄⋊C₄×C₆₇	—	4	1	no	—
328	C₄⋊C₄×C₆₇	—	4	2	no	—
329	C₄⋊C₄×C₆₇	—	4	1	no	—
330	C₄⋊C₄×C₆₇	—	4	1	no	—
331	C₂²⋊C₄×C₆₇	—	2	4	no	—
332	C₂²⋊C₄×C₆₇	—	2	4	no	—
333	C₂²⋊C₄×C₆₇	—	2	4	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	4	no	—
340	C₂²⋊C₄×C₆₇	—	2	4	no	—
341	C₂²⋊C₄×C₆₇	—	2	4	no	—
342	C₂²⋊C₄×C₆₇	—	2	4	no	—
343	C₂²⋊C₄×C₆₇	—	2	4	no	—
344	C₂²⋊C₄×C₆₇	—	2	4	no	—
345	C₂²⋊C₄×C₆₇	—	2	4	no	—
346	C₂²⋊C₄×C₆₇	—	4	2	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	2	no	—
352	C₂²⋊C₄×C₆₇	—	4	1	no	—
353	C₂²⋊C₄×C₆₇	—	4	1	no	—
354	C₂²⋊C₄×C₆₇	—	4	1	no	—
355	C₂²⋊C₄×C₆₇	—	4	2	no	—
356	C₂²⋊C₄×C₆₇	—	4	2	no	—
357	C₂²⋊C₄×C₆₇	—	4	2	no	—
358	C₂²⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
359	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
360	C₄²×C₆₇	—	2	4	no	—
361	C₄²×C₆₇	—	2	2	no	—
362	C₄²×C₆₇	—	4	2	no	—
363	C₂³×C₆₇	—	2	2	no	—
364	C₂³×C₆₇	—	2	2	no	—
365	C₂³×C₆₇	—	2	2	no	—
366	C₂³×C₆₇	—	2	2	no	—
367	C₂³×C₆₇	—	2	16	no	—
368	C₂³×C₆₇	—	2	2	no	—
369	C₂³×C₆₇	—	2	2	no	—
370	C₂³×C₆₇	—	2	2	no	—
371	C₂³×C₆₇	—	2	2	no	—
372	C₂³×C₆₇	—	2	2	no	—
373	C₂³×C₆₇	—	2	2	no	—
374	C₂³×C₆₇	—	2	1	no	—
375	C₂³×C₆₇	—	2	1	no	—
376	C₂³×C₆₇	—	2	2	no	—
377	C₂³×C₆₇	—	2	2	no	—
378	C₂³×C₆₇	—	2	2	no	—
379	C₂³×C₆₇	—	2	1	no	—
380	C₂³×C₆₇	—	2	2	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	2	no	—
386	C₂³×C₆₇	—	2	2	no	—
387	C₂³×C₆₇	—	2	2	no	—
388	C₂³×C₆₇	—	2	2	no	—
389	C₂³×C₆₇	—	4	4	no	—
390	C₂³×C₆₇	—	4	4	no	—
391	C₂³×C₆₇	—	4	4	no	—
392	C₂³×C₆₇	—	4	8	no	—
393	C₂³×C₆₇	—	4	8	no	—
394	C₂³×C₆₇	—	4	8	no	—
395	C₂³×C₆₇	—	4	8	no	—
396	C₂³×C₆₇	—	4	8	no	—
397	C₂³×C₆₇	—	8	4	no	—
398	C₂³×C₆₇	—	8	4	no	—
399	C₂³×C₆₇	—	8	4	no	—
400	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
401	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
402	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
403	C₂³×C₆₇	C₂×#41	1	4	yes	—
404	C₂³×C₆₇	C₂×#41	1	4	yes	—
405	C₂³×C₆₇	H(5,𝔽₂)	1	4	yes	—
406	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
407	Q₈×C₆₇	—	4	8	no	—
408	D₄×C₆₇	—	2	16	no	—
409	D₄×C₆₇	—	2	16	no	—
410	D₄×C₆₇	—	4	4	no	—
411	D₄×C₆₇	—	4	8	no	—
412	D₄×C₆₇	—	4	4	no	—
413	D₄×C₆₇	—	4	8	no	—
414	D₄×C₆₇	—	4	8	no	—
415	D₄×C₆₇	—	4	8	no	—
416	D₄×C₆₇	—	8	4	no	—
417	D₄×C₆₇	—	8	4	no	—
418	D₄×C₆₇	—	8	2	no	—
419	C₂×C₄×C₆₇	—	2	2	no	—
420	C₂×C₄×C₆₇	—	2	2	no	—
421	C₂×C₄×C₆₇	—	2	1	no	—
422	C₂×C₄×C₆₇	—	2	2	no	—
423	C₂×C₄×C₆₇	—	2	2	no	—
424	C₂×C₄×C₆₇	—	2	2	no	—
425	C₂×C₄×C₆₇	—	2	1	no	—
426	C₂×C₄×C₆₇	—	2	2	no	—
427	C₂×C₄×C₆₇	—	2	2	no	—
428	C₂×C₄×C₆₇	—	2	2	no	—
429	C₂×C₄×C₆₇	—	2	2	no	—
430	C₂×C₄×C₆₇	—	2	2	no	—
431	C₂×C₄×C₆₇	—	2	2	no	—
432	C₂×C₄×C₆₇	—	2	2	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	2	no	—
438	C₂×C₄×C₆₇	—	2	2	no	—
439	C₂×C₄×C₆₇	—	2	2	no	—
440	C₂×C₄×C₆₇	—	2	2	no	—
441	C₂×C₄×C₆₇	—	2	2	no	—
442	C₂×C₄×C₆₇	—	2	2	no	—
443	C₂×C₄×C₆₇	—	2	2	no	—
444	C₂×C₄×C₆₇	—	2	2	no	—
445	C₂×C₄×C₆₇	—	2	2	no	—
446	C₂×C₄×C₆₇	—	2	2	no	—
447	C₂×C₄×C₆₇	—	2	1	no	—
448	C₂×C₄×C₆₇	—	2	2	no	—
449	C₂×C₄×C₆₇	—	2	1	no	—
450	C₂×C₄×C₆₇	—	2	2	no	—
451	C₂×C₄×C₆₇	—	2	2	no	—
452	C₂×C₄×C₆₇	—	2	2	no	—
453	C₂×C₄×C₆₇	—	4	8	no	—
454	C₂×C₄×C₆₇	—	4	8	no	—
455	C₂×C₄×C₆₇	—	4	8	no	—
456	C₂×C₄×C₆₇	—	4	8	no	—
457	C₂×C₄×C₆₇	—	4	4	no	—
458	C₂×C₄×C₆₇	—	4	8	no	—
459	C₂×C₄×C₆₇	—	4	4	no	—
460	C₂×C₄×C₆₇	—	4	8	no	—
461	C₂×C₄×C₆₇	—	8	4	no	—
462	C₂×C₄×C₆₇	—	8	2	no	—
463	C₂×C₄×C₆₇	—	8	4	no	—
464	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
465	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
466	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
467	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
468	C₂²×C₆₇	—	2	4	no	—
469	C₂²×C₆₇	—	2	4	no	—
470	C₂²×C₆₇	—	2	4	no	—
471	C₂²×C₆₇	—	2	4	no	—
472	C₂²×C₆₇	—	2	4	no	—
473	C₂²×C₆₇	—	2	4	no	—
474	C₂²×C₆₇	—	2	4	no	—
475	C₂²×C₆₇	—	2	4	no	—
476	C₂²×C₆₇	—	2	4	no	—
477	C₂²×C₆₇	—	2	4	no	—
478	C₂²×C₆₇	—	2	2	no	—
479	C₂²×C₆₇	—	2	2	no	—
480	C₂²×C₆₇	—	2	4	no	—
481	C₂²×C₆₇	—	4	16	no	—
482	C₂²×C₆₇	—	4	2	no	—
483	C₂²×C₆₇	—	4	1	no	—
484	C₂²×C₆₇	—	4	1	no	—
485	C₂²×C₆₇	—	4	2	no	—
486	C₂²×C₆₇	—	4	2	no	—
487	C₂²×C₆₇	—	4	2	no	—
488	C₂²×C₆₇	—	4	2	no	—
489	C₂²×C₆₇	—	4	1	no	—
490	C₂²×C₆₇	—	4	1	no	—
491	C₂²×C₆₇	—	4	2	no	—
492	C₂²×C₆₇	—	4	2	no	—
493	C₂²×C₆₇	—	4	2	no	—
494	C₂²×C₆₇	—	4	2	no	—
495	C₂²×C₆₇	—	4	2	no	—
496	C₂²×C₆₇	—	4	2	no	—
497	C₂²×C₆₇	—	4	2	no	—
498	C₂²×C₆₇	—	4	2	no	—
499	C₂²×C₆₇	—	8	16	no	—
500	C₂²×C₆₇	#546	1	8	yes	—
501	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
502	C₂²×C₆₇	C₂²×#41	1	2	yes	—
503	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
504	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
505	C₂²×C₆₇	#585	1	1	yes	characteristic
506	C₄×C₆₇	—	2	4	no	—
507	C₄×C₆₇	—	2	4	no	—
508	C₄×C₆₇	—	2	2	no	—
509	C₄×C₆₇	—	2	2	no	—
510	C₄×C₆₇	—	4	2	no	—
511	C₄×C₆₇	—	4	2	no	—
512	C₄×C₆₇	—	4	2	no	—
513	C₄×C₆₇	—	4	1	no	—
514	C₄×C₆₇	—	4	2	no	—
515	C₄×C₆₇	—	4	2	no	—
516	C₄×C₆₇	—	4	2	no	—
517	C₄×C₆₇	—	4	2	no	—
518	C₄×C₆₇	—	4	1	no	—
519	C₄×C₆₇	—	4	1	no	—
520	#59803	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
521	C₂×C₆₇	—	2	8	no	—
522	C₂×C₆₇	—	4	2	no	—
523	C₂×C₆₇	—	4	2	no	—
524	C₂×C₆₇	—	4	4	no	—
525	C₂×C₆₇	—	8	2	no	—
526	C₂×C₆₇	C₂×#546	1	2	yes	—
527	C₂×C₆₇	#3481	1	1	yes	characteristic
528	C₂×C₆₇	#3496	1	1	yes	characteristic
529	C₂×C₆₇	#3513	1	2	yes	—
530	C₂×C₆₇	#3532	1	1	yes	characteristic
531	C₂×#546	C₂×C₆₇	1	2	yes	complemented
532	#2712	C₂×C₆₇	1	1	yes	characteristic, complemented
533	#2693	C₂×C₆₇	1	1	yes	characteristic, complemented
534	#2688	C₂×C₆₇	1	2	yes	complemented
535	#2557	C₂×C₆₇	1	2	yes	complemented
536	#2543	C₂×C₆₇	1	1	yes	characteristic, complemented
537	#2535	C₂×C₆₇	1	1	yes	characteristic, complemented
538	#2488	C₂×C₆₇	1	2	yes	complemented
539	#2483	C₂×C₆₇	1	1	yes	characteristic, complemented
540	#2450	C₂×C₆₇	1	2	yes	complemented
541	#2444	C₂×C₆₇	1	2	yes	complemented
542	#2424	C₂×C₆₇	1	2	yes	complemented
543	#2412	C₂×C₆₇	1	2	yes	complemented
544	#2404	C₂×C₆₇	1	2	yes	complemented
545	#2403	C₂×C₆₇	1	1	yes	characteristic, complemented
546	#2358	C₂×C₆₇	1	2	yes	complemented
547	#2339	C₂×C₆₇	1	2	yes	complemented
548	C₄×#120	C₂×C₆₇	1	1	yes	characteristic, complemented
549	C₂×#386	C₂×C₆₇	1	2	yes	complemented
550	C₆₇	#59803	1	1	yes	characteristic, direct product factor, Sylow
551	C₂²×#41	C₂²×C₆₇	1	2	yes	—
552	C₂³×D₄	C₂²×C₆₇	1	2	yes	—
553	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
554	#546	—	2	16	no	—
555	C₂×#124	C₂²×C₆₇	1	2	yes	complemented
556	C₂×#123	C₂²×C₆₇	1	2	yes	—
557	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
558	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
559	C₂×#121	C₂²×C₆₇	1	2	yes	—
560	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
561	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
562	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
563	C₂×#120	C₂²×C₆₇	1	2	yes	—
564	C₂×#120	C₂²×C₆₇	1	2	yes	—
565	C₂×#120	C₂²×C₆₇	1	1	yes	characteristic
566	C₂×#120	C₂²×C₆₇	1	2	yes	complemented
567	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
568	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
569	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
570	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
571	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
572	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
573	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
574	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
575	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
576	#400	C₂²×C₆₇	1	2	yes	complemented
577	#400	C₂²×C₆₇	1	2	yes	complemented
578	#398	C₂²×C₆₇	1	1	yes	characteristic, complemented
579	#397	C₂²×C₆₇	1	2	yes	complemented
580	#397	C₂²×C₆₇	1	2	yes	complemented
581	#397	C₂²×C₆₇	1	2	yes	complemented
582	#397	C₂²×C₆₇	1	1	yes	characteristic, complemented
583	#397	C₂²×C₆₇	1	1	yes	characteristic, complemented
584	#397	C₂²×C₆₇	1	1	yes	characteristic, complemented
585	#396	C₂²×C₆₇	1	2	yes	complemented
586	#394	C₂²×C₆₇	1	1	yes	characteristic, complemented
587	#394	C₂²×C₆₇	1	2	yes	complemented
588	#394	C₂²×C₆₇	1	2	yes	complemented
589	#393	C₂²×C₆₇	1	2	yes	complemented
590	#393	C₂²×C₆₇	1	2	yes	complemented
591	#392	C₂²×C₆₇	1	2	yes	—
592	#392	C₂²×C₆₇	1	1	yes	characteristic
593	#392	C₂²×C₆₇	1	1	yes	characteristic
594	#392	C₂²×C₆₇	1	1	yes	characteristic, complemented
595	#392	C₂²×C₆₇	1	2	yes	complemented
596	#391	C₂²×C₆₇	1	2	yes	complemented
597	#391	C₂²×C₆₇	1	2	yes	complemented
598	#390	C₂²×C₆₇	1	2	yes	complemented
599	#388	C₂²×C₆₇	1	2	yes	complemented
600	#388	C₂²×C₆₇	1	2	yes	complemented
601	#388	C₂²×C₆₇	1	2	yes	complemented
602	#387	C₂²×C₆₇	1	2	yes	complemented
603	#386	C₂²×C₆₇	1	2	yes	—
604	#386	C₂²×C₆₇	1	2	yes	—
605	#386	C₂²×C₆₇	1	2	yes	—
606	#386	C₂²×C₆₇	1	2	yes	—
607	#386	C₂²×C₆₇	1	2	yes	—
608	#386	C₂²×C₆₇	1	2	yes	—
609	#386	C₂²×C₆₇	1	2	yes	complemented
610	#386	C₂²×C₆₇	1	2	yes	complemented
611	#386	C₂²×C₆₇	1	2	yes	complemented
612	#386	C₂²×C₆₇	1	2	yes	complemented
613	#386	C₂²×C₆₇	1	2	yes	complemented
614	#386	C₂²×C₆₇	1	2	yes	complemented
615	#386	C₂²×C₆₇	1	2	yes	complemented
616	#386	C₂²×C₆₇	1	1	yes	characteristic, complemented
617	#386	C₂²×C₆₇	1	2	yes	complemented
618	#386	C₂²×C₆₇	1	2	yes	complemented
619	#386	C₂²×C₆₇	1	2	yes	complemented
620	#386	C₂²×C₆₇	1	2	yes	complemented
621	#385	C₂²×C₆₇	1	2	yes	complemented
622	#385	C₂²×C₆₇	1	2	yes	complemented
623	#385	C₂²×C₆₇	1	2	yes	complemented
624	#385	C₂²×C₆₇	1	2	yes	complemented
625	#385	C₂²×C₆₇	1	1	yes	characteristic, complemented
626	#382	C₂²×C₆₇	1	1	yes	characteristic, complemented
627	#381	C₂²×C₆₇	1	2	yes	complemented
628	#381	C₂²×C₆₇	1	2	yes	complemented
629	#381	C₂²×C₆₇	1	2	yes	complemented
630	#380	C₂²×C₆₇	1	2	yes	complemented
631	#380	C₂²×C₆₇	1	2	yes	complemented
632	#379	C₂²×C₆₇	1	1	yes	characteristic
633	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
634	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
635	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
636	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic, complemented
637	C₂×#95	C₂²×C₆₇	1	2	yes	complemented
638	C₂×#95	C₂²×C₆₇	1	2	yes	complemented
639	C₂⁵	C₂³×C₆₇	1	2	yes	—
640	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
641	C₂×#41	—	2	8	no	—
642	C₂×#41	—	2	8	no	—
643	C₂×#41	—	4	4	no	—
644	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
645	C₂²×D₄	—	2	8	no	—
646	C₂²×D₄	—	2	8	no	—
647	C₂²×D₄	—	4	4	no	—
648	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
649	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
650	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
651	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
652	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
653	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
654	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
655	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
656	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
657	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
658	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
659	C₂³×C₄	—	4	2	no	—
660	C₂³×C₄	—	4	4	no	—
661	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
662	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
663	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
664	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
665	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
666	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
667	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
668	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
669	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
670	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
671	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
672	#124	—	2	8	no	—
673	#123	—	2	8	no	—
674	#123	—	2	8	no	—
675	C₂²⋊Q₈	—	2	8	no	—
676	#121	—	2	8	no	—
677	#121	—	2	8	no	—
678	#121	—	2	8	no	—
679	#121	—	4	2	no	—
680	#120	—	2	8	no	—
681	#120	—	2	8	no	—
682	#120	—	4	4	no	—
683	#120	D₄×C₆₇	1	8	yes	complemented
684	C₄×D₄	—	2	8	no	—
685	C₄×D₄	—	2	8	no	—
686	C₄×D₄	—	4	2	no	—
687	C₄×D₄	—	4	2	no	—
688	C₄×D₄	—	4	4	no	—
689	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
690	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
691	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
692	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
693	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
694	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
695	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
696	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
697	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
698	C₂×C₂²⋊C₄	—	2	8	no	—
699	C₂×C₂²⋊C₄	—	2	8	no	—
700	C₂×C₂²⋊C₄	—	4	4	no	—
701	C₂×C₂²⋊C₄	—	4	4	no	—
702	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
703	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
704	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
705	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
706	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
707	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
708	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
709	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
710	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
711	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
712	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
713	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
714	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
715	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
716	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
717	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
718	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
719	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
720	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
721	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
722	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
723	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
724	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
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	1	yes	characteristic
729	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
730	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
731	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
732	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
733	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
734	#95	C₂³×C₆₇	1	2	yes	—
735	#95	C₂³×C₆₇	1	1	yes	characteristic
736	#95	C₂³×C₆₇	1	2	yes	—
737	#95	C₂³×C₆₇	1	2	yes	—
738	#95	C₂³×C₆₇	1	2	yes	—
739	#95	C₂³×C₆₇	1	2	yes	—
740	#95	C₂³×C₆₇	1	1	yes	characteristic
741	#95	C₂³×C₆₇	1	2	yes	—
742	#95	C₂³×C₆₇	1	2	yes	—
743	#95	C₂³×C₆₇	1	2	yes	—
744	#95	C₂³×C₆₇	1	2	yes	—
745	#95	C₂³×C₆₇	1	2	yes	—
746	#95	C₂³×C₆₇	1	2	yes	—
747	#95	C₂³×C₆₇	1	2	yes	—
748	#95	C₂³×C₆₇	1	2	yes	—
749	#95	C₂³×C₆₇	1	1	yes	characteristic
750	#95	C₂³×C₆₇	1	2	yes	—
751	#95	C₂³×C₆₇	1	2	yes	—
752	#95	C₂³×C₆₇	1	2	yes	—
753	#95	C₂³×C₆₇	1	2	yes	—
754	#95	C₂³×C₆₇	1	1	yes	characteristic
755	C₂⁴	—	2	4	no	—
756	C₂⁴	—	2	4	no	—
757	C₂⁴	—	2	4	no	—
758	C₂⁴	—	2	4	no	—
759	C₂⁴	—	2	4	no	—
760	C₂⁴	—	2	4	no	—
761	C₂⁴	—	4	1	no	—
762	C₂⁴	—	4	1	no	—
763	C₂⁴	—	4	2	no	—
764	C₂⁴	—	4	2	no	—
765	C₂⁴	—	4	2	no	—
766	C₂⁴	C₂×D₄×C₆₇	1	4	yes	—
767	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
768	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
769	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
770	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
771	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
772	#41	—	4	32	no	—
773	C₂×Q₈	—	2	4	no	—
774	C₂×Q₈	—	2	4	no	—
775	C₂×Q₈	—	4	2	no	—
776	C₂×D₄	—	2	4	no	—
777	C₂×D₄	—	2	4	no	—
778	C₂×D₄	—	2	4	no	—
779	C₂×D₄	—	2	4	no	—
780	C₂×D₄	—	2	4	no	—
781	C₂×D₄	—	2	4	no	—
782	C₂×D₄	—	2	4	no	—
783	C₂×D₄	—	2	4	no	—
784	C₂×D₄	—	2	4	no	—
785	C₂×D₄	—	2	4	no	—
786	C₂×D₄	—	2	4	no	—
787	C₂×D₄	—	2	4	no	—
788	C₂×D₄	—	2	4	no	—
789	C₂×D₄	—	2	4	no	—
790	C₂×D₄	—	2	4	no	—
791	C₂×D₄	—	2	4	no	—
792	C₂×D₄	—	4	1	no	—
793	C₂×D₄	—	4	1	no	—
794	C₂×D₄	—	4	2	no	—
795	C₂×D₄	—	4	2	no	—
796	C₂×D₄	—	4	2	no	—
797	C₂×D₄	—	4	1	no	—
798	C₂×D₄	—	4	2	no	—
799	C₂×D₄	—	4	2	no	—
800	C₂×D₄	—	4	2	no	—
801	C₂×D₄	—	4	1	no	—
802	C₂×D₄	—	4	2	no	—
803	C₂×D₄	—	4	2	no	—
804	C₂×D₄	—	4	32	no	—
805	C₂×D₄	C₂×D₄×C₆₇	1	8	yes	—
806	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
807	C₂×D₄	#41×C₆₇	1	8	yes	complemented
808	C₂²×C₄	—	2	4	no	—
809	C₂²×C₄	—	2	4	no	—
810	C₂²×C₄	—	2	4	no	—
811	C₂²×C₄	—	2	4	no	—
812	C₂²×C₄	—	2	4	no	—
813	C₂²×C₄	—	2	4	no	—
814	C₂²×C₄	—	2	4	no	—
815	C₂²×C₄	—	2	4	no	—
816	C₂²×C₄	—	2	4	no	—
817	C₂²×C₄	—	2	4	no	—
818	C₂²×C₄	—	2	4	no	—
819	C₂²×C₄	—	2	4	no	—
820	C₂²×C₄	—	2	4	no	—
821	C₂²×C₄	—	2	2	no	—
822	C₂²×C₄	—	2	4	no	—
823	C₂²×C₄	—	2	2	no	—
824	C₂²×C₄	—	4	2	no	—
825	C₂²×C₄	—	4	2	no	—
826	C₂²×C₄	—	4	1	no	—
827	C₂²×C₄	—	4	2	no	—
828	C₂²×C₄	—	4	2	no	—
829	C₂²×C₄	—	4	2	no	—
830	C₂²×C₄	—	4	2	no	—
831	C₂²×C₄	—	4	2	no	—
832	C₂²×C₄	—	4	2	no	—
833	C₂²×C₄	—	4	2	no	—
834	C₂²×C₄	—	4	2	no	—
835	C₂²×C₄	—	4	2	no	—
836	C₂²×C₄	—	4	2	no	—
837	C₂²×C₄	—	4	2	no	—
838	C₂²×C₄	—	4	16	no	—
839	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
840	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
841	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
842	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
843	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
844	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
845	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
846	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
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	2	yes	—
852	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
853	C₄⋊C₄	—	2	4	no	—
854	C₄⋊C₄	—	2	4	no	—
855	C₄⋊C₄	—	2	4	no	—
856	C₄⋊C₄	—	2	4	no	—
857	C₄⋊C₄	—	4	1	no	—
858	C₄⋊C₄	—	4	2	no	—
859	C₄⋊C₄	—	4	1	no	—
860	C₄⋊C₄	—	4	1	no	—
861	C₄⋊C₄	—	4	2	no	—
862	C₂²⋊C₄	—	2	4	no	—
863	C₂²⋊C₄	—	2	4	no	—
864	C₂²⋊C₄	—	2	4	no	—
865	C₂²⋊C₄	—	2	4	no	—
866	C₂²⋊C₄	—	2	4	no	—
867	C₂²⋊C₄	—	2	4	no	—
868	C₂²⋊C₄	—	2	4	no	—
869	C₂²⋊C₄	—	2	4	no	—
870	C₂²⋊C₄	—	2	4	no	—
871	C₂²⋊C₄	—	2	4	no	—
872	C₂²⋊C₄	—	2	4	no	—
873	C₂²⋊C₄	—	2	4	no	—
874	C₂²⋊C₄	—	2	4	no	—
875	C₂²⋊C₄	—	2	4	no	—
876	C₂²⋊C₄	—	2	4	no	—
877	C₂²⋊C₄	—	4	2	no	—
878	C₂²⋊C₄	—	4	2	no	—
879	C₂²⋊C₄	—	4	2	no	—
880	C₂²⋊C₄	—	4	2	no	—
881	C₂²⋊C₄	—	4	2	no	—
882	C₂²⋊C₄	—	4	2	no	—
883	C₂²⋊C₄	—	4	1	no	—
884	C₂²⋊C₄	—	4	1	no	—
885	C₂²⋊C₄	—	4	2	no	—
886	C₂²⋊C₄	—	4	2	no	—
887	C₂²⋊C₄	—	4	2	no	—
888	C₂²⋊C₄	—	4	1	no	—
889	C₂²⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
890	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
891	C₄²	—	2	4	no	—
892	C₄²	—	2	2	no	—
893	C₄²	—	4	2	no	—
894	C₂³	—	2	2	no	—
895	C₂³	—	2	2	no	—
896	C₂³	—	2	2	no	—
897	C₂³	—	2	2	no	—
898	C₂³	—	2	16	no	—
899	C₂³	—	2	2	no	—
900	C₂³	—	2	2	no	—
901	C₂³	—	2	2	no	—
902	C₂³	—	2	2	no	—
903	C₂³	—	2	2	no	—
904	C₂³	—	2	2	no	—
905	C₂³	—	2	1	no	—
906	C₂³	—	2	1	no	—
907	C₂³	—	2	2	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	2	2	no	—
910	C₂³	—	2	1	no	—
911	C₂³	—	2	2	no	—
912	C₂³	—	2	1	no	—
913	C₂³	—	2	2	no	—
914	C₂³	—	2	2	no	—
915	C₂³	—	2	2	no	—
916	C₂³	—	2	2	no	—
917	C₂³	—	2	2	no	—
918	C₂³	—	2	2	no	—
919	C₂³	—	2	2	no	—
920	C₂³	—	4	4	no	—
921	C₂³	—	4	4	no	—
922	C₂³	—	4	4	no	—
923	C₂³	—	4	8	no	—
924	C₂³	—	4	8	no	—
925	C₂³	—	4	8	no	—
926	C₂³	—	4	8	no	—
927	C₂³	—	4	8	no	—
928	C₂³	—	8	4	no	—
929	C₂³	—	8	4	no	—
930	C₂³	—	8	4	no	—
931	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
932	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
933	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
934	C₂³	C₂×#41×C₆₇	1	4	yes	—
935	C₂³	C₂×#41×C₆₇	1	4	yes	—
936	C₂³	H(5,𝔽₂)×C₆₇	1	4	yes	—
937	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
938	Q₈	—	4	8	no	—
939	D₄	—	2	16	no	—
940	D₄	—	2	16	no	—
941	D₄	—	4	4	no	—
942	D₄	—	4	8	no	—
943	D₄	—	4	8	no	—
944	D₄	—	4	8	no	—
945	D₄	—	4	4	no	—
946	D₄	—	4	8	no	—
947	D₄	—	8	4	no	—
948	D₄	—	8	4	no	—
949	D₄	—	8	2	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	2	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	4	8	no	—
985	C₂×C₄	—	4	8	no	—
986	C₂×C₄	—	4	8	no	—
987	C₂×C₄	—	4	8	no	—
988	C₂×C₄	—	4	4	no	—
989	C₂×C₄	—	4	8	no	—
990	C₂×C₄	—	4	4	no	—
991	C₂×C₄	—	4	8	no	—
992	C₂×C₄	—	8	2	no	—
993	C₂×C₄	—	8	4	no	—
994	C₂×C₄	—	8	4	no	—
995	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
996	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
997	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
998	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
999	C₂²	—	2	4	no	—
1000	C₂²	—	2	4	no	—
1001	C₂²	—	2	4	no	—
1002	C₂²	—	2	4	no	—
1003	C₂²	—	2	4	no	—
1004	C₂²	—	2	4	no	—
1005	C₂²	—	2	4	no	—
1006	C₂²	—	2	4	no	—
1007	C₂²	—	2	4	no	—
1008	C₂²	—	2	4	no	—
1009	C₂²	—	2	2	no	—
1010	C₂²	—	2	2	no	—
1011	C₂²	—	2	4	no	—
1012	C₂²	—	4	16	no	—
1013	C₂²	—	4	1	no	—
1014	C₂²	—	4	1	no	—
1015	C₂²	—	4	2	no	—
1016	C₂²	—	4	2	no	—
1017	C₂²	—	4	1	no	—
1018	C₂²	—	4	1	no	—
1019	C₂²	—	4	2	no	—
1020	C₂²	—	4	2	no	—
1021	C₂²	—	4	2	no	—
1022	C₂²	—	4	2	no	—
1023	C₂²	—	4	2	no	—
1024	C₂²	—	4	2	no	—
1025	C₂²	—	4	2	no	—
1026	C₂²	—	4	2	no	—
1027	C₂²	—	4	2	no	—
1028	C₂²	—	4	2	no	—
1029	C₂²	—	4	2	no	—
1030	C₂²	—	8	16	no	—
1031	C₂²	#546×C₆₇	1	8	yes	—
1032	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1033	C₂²	C₂²×#41×C₆₇	1	2	yes	—
1034	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
1035	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1036	C₂²	#585×C₆₇	1	1	yes	characteristic
1037	C₄	—	2	2	no	—
1038	C₄	—	2	4	no	—
1039	C₄	—	2	4	no	—
1040	C₄	—	2	2	no	—
1041	C₄	—	4	2	no	—
1042	C₄	—	4	1	no	—
1043	C₄	—	4	1	no	—
1044	C₄	—	4	2	no	—
1045	C₄	—	4	2	no	—
1046	C₄	—	4	2	no	—
1047	C₄	—	4	1	no	—
1048	C₄	—	4	2	no	—
1049	C₄	—	4	2	no	—
1050	C₄	—	4	2	no	—
1051	C₂	—	2	8	no	—
1052	C₂	—	4	2	no	—
1053	C₂	—	4	4	no	—
1054	C₂	—	4	2	no	—
1055	C₂	—	8	2	no	—
1056	C₂	C₂×#546×C₆₇	1	2	yes	—
1057	C₂	C₆₇×#3481	1	1	yes	characteristic
1058	C₂	C₆₇×#3496	1	1	yes	characteristic
1059	C₂	C₆₇×#3513	1	2	yes	—
1060	C₂	C₆₇×#3532	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×#546×C₆₇	C₂	semidirect
2. C₆₇×#2712	C₂	semidirect
3. C₆₇×#2693	C₂	semidirect
4. C₆₇×#2688	C₂	semidirect
5. C₆₇×#2557	C₂	semidirect
6. C₆₇×#2543	C₂	semidirect
7. C₆₇×#2535	C₂	semidirect
8. C₆₇×#2488	C₂	semidirect
9. C₆₇×#2483	C₂	semidirect
10. C₆₇×#2450	C₂	semidirect
11. C₆₇×#2444	C₂	semidirect
12. C₆₇×#2424	C₂	semidirect
13. C₆₇×#2412	C₂	semidirect
14. C₆₇×#2404	C₂	semidirect
15. C₆₇×#2403	C₂	semidirect
16. C₆₇×#2358	C₂	semidirect
17. C₆₇×#2339	C₂	semidirect
18. C₄×#120×C₆₇	C₂	semidirect
19. C₂×#386×C₆₇	C₂	semidirect
24. C₂×#124×C₆₇	C₂²	semidirect
26. C₂×#123×C₆₇	C₂²	semidirect
27. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
29. C₂×#121×C₆₇	C₂²	semidirect
30. C₂×#121×C₆₇	C₂²	semidirect
31. C₂×#121×C₆₇	C₂²	semidirect
35. C₂×#120×C₆₇	C₂²	semidirect
37. C₂×C₄×D₄×C₆₇	C₂²	semidirect
38. C₂×C₄×D₄×C₆₇	C₂²	semidirect
39. C₂×C₄×D₄×C₆₇	C₂²	semidirect
40. C₂×C₄×D₄×C₆₇	C₂²	semidirect
42. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
43. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
44. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
45. #400×C₆₇	C₂²	semidirect
46. #400×C₆₇	C₂²	semidirect
47. #398×C₆₇	C₂²	semidirect
48. #397×C₆₇	C₂²	semidirect
49. #397×C₆₇	C₂²	semidirect
50. #397×C₆₇	C₂²	semidirect
51. #397×C₆₇	C₂²	semidirect
52. #397×C₆₇	C₂²	semidirect
53. #397×C₆₇	C₂²	semidirect
54. #396×C₆₇	C₂²	semidirect
55. #394×C₆₇	C₂²	semidirect
56. #394×C₆₇	C₂²	semidirect
57. #394×C₆₇	C₂²	semidirect
58. #393×C₆₇	C₂²	semidirect
59. #393×C₆₇	C₂²	semidirect
63. #392×C₆₇	C₂²	semidirect
64. #392×C₆₇	C₂²	semidirect
65. #391×C₆₇	C₂²	semidirect
66. #391×C₆₇	C₂²	semidirect
67. #390×C₆₇	C₂²	semidirect
68. #388×C₆₇	C₂²	semidirect
69. #388×C₆₇	C₂²	semidirect
70. #388×C₆₇	C₂²	semidirect
71. #387×C₆₇	C₂²	semidirect
78. #386×C₆₇	C₂²	semidirect
79. #386×C₆₇	C₂²	semidirect
80. #386×C₆₇	C₂²	semidirect
81. #386×C₆₇	C₂²	semidirect
82. #386×C₆₇	C₂²	semidirect
83. #386×C₆₇	C₂²	semidirect
84. #386×C₆₇	C₂²	semidirect
85. #386×C₆₇	C₂²	semidirect
86. #386×C₆₇	C₂²	semidirect
87. #386×C₆₇	C₂²	semidirect
88. #386×C₆₇	C₂²	semidirect
89. #386×C₆₇	C₂²	semidirect
90. #385×C₆₇	C₂²	semidirect
91. #385×C₆₇	C₂²	semidirect
92. #385×C₆₇	C₂²	semidirect
93. #385×C₆₇	C₂²	semidirect
94. #385×C₆₇	C₂²	semidirect
95. #382×C₆₇	C₂²	semidirect
96. #381×C₆₇	C₂²	semidirect
97. #381×C₆₇	C₂²	semidirect
98. #381×C₆₇	C₂²	semidirect
99. #380×C₆₇	C₂²	semidirect
100. #380×C₆₇	C₂²	semidirect
102. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
103. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
105. C₂×#95×C₆₇	C₂²	semidirect
106. C₂×#95×C₆₇	C₂²	semidirect
107. C₂×#95×C₆₇	C₂²	semidirect
152. #120×C₆₇	D₄	semidirect
276. C₂×D₄×C₆₇	#41	semidirect
520. #59803	C₆₇	direct (N × H)
531. C₂×#546	C₂×C₆₇	semidirect
532. #2712	C₂×C₆₇	semidirect
533. #2693	C₂×C₆₇	semidirect
534. #2688	C₂×C₆₇	semidirect
535. #2557	C₂×C₆₇	semidirect
536. #2543	C₂×C₆₇	semidirect
537. #2535	C₂×C₆₇	semidirect
538. #2488	C₂×C₆₇	semidirect
539. #2483	C₂×C₆₇	semidirect
540. #2450	C₂×C₆₇	semidirect
541. #2444	C₂×C₆₇	semidirect
542. #2424	C₂×C₆₇	semidirect
543. #2412	C₂×C₆₇	semidirect
544. #2404	C₂×C₆₇	semidirect
545. #2403	C₂×C₆₇	semidirect
546. #2358	C₂×C₆₇	semidirect
547. #2339	C₂×C₆₇	semidirect
548. C₄×#120	C₂×C₆₇	semidirect
549. C₂×#386	C₂×C₆₇	semidirect
550. C₆₇	#59803	direct (N × H)
555. C₂×#124	C₂²×C₆₇	semidirect
557. C₂×#123	C₂²×C₆₇	semidirect
558. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
560. C₂×#121	C₂²×C₆₇	semidirect
561. C₂×#121	C₂²×C₆₇	semidirect
562. C₂×#121	C₂²×C₆₇	semidirect
566. C₂×#120	C₂²×C₆₇	semidirect
568. C₂×C₄×D₄	C₂²×C₆₇	semidirect
569. C₂×C₄×D₄	C₂²×C₆₇	semidirect
570. C₂×C₄×D₄	C₂²×C₆₇	semidirect
571. C₂×C₄×D₄	C₂²×C₆₇	semidirect
573. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
574. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
575. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
576. #400	C₂²×C₆₇	semidirect
577. #400	C₂²×C₆₇	semidirect
578. #398	C₂²×C₆₇	semidirect
579. #397	C₂²×C₆₇	semidirect
580. #397	C₂²×C₆₇	semidirect
581. #397	C₂²×C₆₇	semidirect
582. #397	C₂²×C₆₇	semidirect
583. #397	C₂²×C₆₇	semidirect
584. #397	C₂²×C₆₇	semidirect
585. #396	C₂²×C₆₇	semidirect
586. #394	C₂²×C₆₇	semidirect
587. #394	C₂²×C₆₇	semidirect
588. #394	C₂²×C₆₇	semidirect
589. #393	C₂²×C₆₇	semidirect
590. #393	C₂²×C₆₇	semidirect
594. #392	C₂²×C₆₇	semidirect
595. #392	C₂²×C₆₇	semidirect
596. #391	C₂²×C₆₇	semidirect
597. #391	C₂²×C₆₇	semidirect
598. #390	C₂²×C₆₇	semidirect
599. #388	C₂²×C₆₇	semidirect
600. #388	C₂²×C₆₇	semidirect
601. #388	C₂²×C₆₇	semidirect
602. #387	C₂²×C₆₇	semidirect
609. #386	C₂²×C₆₇	semidirect
610. #386	C₂²×C₆₇	semidirect
611. #386	C₂²×C₆₇	semidirect
612. #386	C₂²×C₆₇	semidirect
613. #386	C₂²×C₆₇	semidirect
614. #386	C₂²×C₆₇	semidirect
615. #386	C₂²×C₆₇	semidirect
616. #386	C₂²×C₆₇	semidirect
617. #386	C₂²×C₆₇	semidirect
618. #386	C₂²×C₆₇	semidirect
619. #386	C₂²×C₆₇	semidirect
620. #386	C₂²×C₆₇	semidirect
621. #385	C₂²×C₆₇	semidirect
622. #385	C₂²×C₆₇	semidirect
623. #385	C₂²×C₆₇	semidirect
624. #385	C₂²×C₆₇	semidirect
625. #385	C₂²×C₆₇	semidirect
626. #382	C₂²×C₆₇	semidirect
627. #381	C₂²×C₆₇	semidirect
628. #381	C₂²×C₆₇	semidirect
629. #381	C₂²×C₆₇	semidirect
630. #380	C₂²×C₆₇	semidirect
631. #380	C₂²×C₆₇	semidirect
633. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
634. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
635. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
636. C₂×#95	C₂²×C₆₇	semidirect
637. C₂×#95	C₂²×C₆₇	semidirect
638. C₂×#95	C₂²×C₆₇	semidirect
683. #120	D₄×C₆₇	semidirect
807. C₂×D₄	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#546×C₆₇	2
C₆₇×#2712	2
C₆₇×#2693	2
C₆₇×#2688	2
C₆₇×#2557	2
C₆₇×#2543	2
C₆₇×#2535	2
C₆₇×#2488	2
C₆₇×#2483	2
C₆₇×#2450	2
C₆₇×#2444	2
C₆₇×#2424	2
C₆₇×#2412	2
C₆₇×#2404	2
C₆₇×#2403	2
C₆₇×#2358	2
C₆₇×#2339	2
C₄×#120×C₆₇	2
C₂×#386×C₆₇	2
#59803	67

Subgroups — C67×#59803 #30739054

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59803 #30739054