Subgroups — C₆₇×#34298 #30713549

Order 17152.

2584 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#547×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2374	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2369	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2368	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2363	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2359	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2357	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2352	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2345	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2344	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2339	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2335	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2332	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2331	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2324	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#123×C₆₇	C₂	1	2	yes	maximal, complemented
18	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2297	C₂	1	2	yes	maximal, complemented
20	C₆₇×#2290	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2275	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2274	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₆₇	C₂²	1	2	yes	—
25	#547×C₆₇	C₄	1	16	yes	complemented
26	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#123×C₆₇	C₂²	1	2	yes	—
28	C₂×#123×C₆₇	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
30	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#121×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	2	yes	—
35	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×#117×C₆₇	C₂²	1	2	yes	—
41	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
42	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
43	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
45	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
46	#391×C₆₇	C₂²	1	2	yes	—
47	#391×C₆₇	C₂²	1	2	yes	—
48	#391×C₆₇	C₂²	1	2	yes	—
49	#391×C₆₇	C₂²	1	2	yes	—
50	#390×C₆₇	C₂²	1	2	yes	—
51	#390×C₆₇	C₂²	1	2	yes	—
52	#390×C₆₇	C₂²	1	1	yes	characteristic
53	#390×C₆₇	C₂²	1	1	yes	characteristic
54	#389×C₆₇	C₂²	1	1	yes	characteristic
55	#389×C₆₇	C₂²	1	1	yes	characteristic
56	#389×C₆₇	C₂²	1	1	yes	characteristic
57	#389×C₆₇	C₂²	1	1	yes	characteristic
58	#389×C₆₇	C₂²	1	2	yes	—
59	#388×C₆₇	C₂²	1	1	yes	characteristic
60	#388×C₆₇	C₂²	1	1	yes	characteristic
61	#388×C₆₇	C₂²	1	2	yes	—
62	#388×C₆₇	C₂²	1	2	yes	—
63	#388×C₆₇	C₂²	1	2	yes	—
64	#388×C₆₇	C₂²	1	2	yes	—
65	#388×C₆₇	C₂²	1	2	yes	—
66	#388×C₆₇	C₂²	1	2	yes	—
67	#388×C₆₇	C₂²	1	2	yes	—
68	#387×C₆₇	C₂²	1	1	yes	characteristic
69	#387×C₆₇	C₂²	1	1	yes	characteristic
70	#387×C₆₇	C₂²	1	2	yes	—
71	#387×C₆₇	C₂²	1	2	yes	—
72	#387×C₆₇	C₂²	1	2	yes	—
73	#387×C₆₇	C₂²	1	2	yes	—
74	#387×C₆₇	C₂²	1	2	yes	—
75	#387×C₆₇	C₂²	1	2	yes	—
76	#387×C₆₇	C₂²	1	2	yes	—
77	#386×C₆₇	C₂²	1	1	yes	characteristic
78	#386×C₆₇	C₂²	1	1	yes	characteristic
79	#386×C₆₇	C₂²	1	2	yes	—
80	#386×C₆₇	C₂²	1	2	yes	—
81	#386×C₆₇	C₂²	1	2	yes	—
82	#386×C₆₇	C₂²	1	2	yes	—
83	#386×C₆₇	C₂²	1	2	yes	—
84	#385×C₆₇	C₂²	1	1	yes	characteristic
85	#385×C₆₇	C₂²	1	1	yes	characteristic
86	#385×C₆₇	C₂²	1	2	yes	—
87	#385×C₆₇	C₂²	1	2	yes	—
88	#382×C₆₇	C₂²	1	1	yes	characteristic
89	#381×C₆₇	C₂²	1	2	yes	—
90	#381×C₆₇	C₂²	1	2	yes	—
91	#380×C₆₇	C₂²	1	1	yes	characteristic
92	#380×C₆₇	C₂²	1	1	yes	characteristic
93	#380×C₆₇	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
95	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
96	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
97	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
98	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
99	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
100	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
101	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
102	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
104	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
109	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
110	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
111	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
112	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
113	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
114	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
121	#376×C₆₇	C₂²	1	1	yes	characteristic
122	C₂×#95×C₆₇	C₂²	1	2	yes	—
123	C₂×#95×C₆₇	C₂²	1	2	yes	—
124	C₂×#41×C₆₇	—	4	4	no	—
125	C₂×#41×C₆₇	—	4	4	no	—
126	C₂×#41×C₆₇	C₂×C₄	1	16	yes	complemented
127	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
128	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
130	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
131	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
132	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
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	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
142	C₄⋊Q₈×C₆₇	C₂×C₄	1	8	yes	complemented
143	#123×C₆₇	C₂×C₄	1	16	yes	complemented
144	#123×C₆₇	C₂×C₄	1	16	yes	complemented
145	C₂²⋊Q₈×C₆₇	C₂×C₄	1	16	yes	complemented
146	#121×C₆₇	C₂×C₄	1	8	yes	—
147	#121×C₆₇	C₂×C₄	1	8	yes	complemented
148	C₄×D₄×C₆₇	—	2	4	no	—
149	C₄×D₄×C₆₇	—	2	4	no	—
150	C₄×D₄×C₆₇	—	4	4	no	—
151	C₄×D₄×C₆₇	—	4	4	no	—
152	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	complemented
153	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	complemented
154	#117×C₆₇	—	2	4	no	—
155	#117×C₆₇	—	2	4	no	—
156	#117×C₆₇	—	4	4	no	—
157	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
158	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	8	yes	complemented
159	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	8	yes	complemented
160	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₆₇	C₂³	1	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	1	yes	characteristic
172	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
183	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	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	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
200	C₂×C₄²×C₆₇	—	2	4	no	—
201	C₂×C₄²×C₆₇	—	4	4	no	—
202	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
206	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
209	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
210	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
211	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
212	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
213	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
214	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
215	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
216	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
217	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
219	#95×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
224	#95×C₆₇	C₂³	1	2	yes	—
225	#95×C₆₇	C₂³	1	2	yes	—
226	#95×C₆₇	C₂³	1	1	yes	characteristic
227	#95×C₆₇	C₂³	1	1	yes	characteristic
228	#95×C₆₇	C₂³	1	1	yes	characteristic
229	#95×C₆₇	C₂³	1	1	yes	characteristic
230	#95×C₆₇	C₂³	1	2	yes	—
231	#95×C₆₇	C₂³	1	1	yes	characteristic
232	#95×C₆₇	C₂³	1	2	yes	—
233	#95×C₆₇	C₂³	1	2	yes	—
234	#95×C₆₇	C₂³	1	2	yes	—
235	#95×C₆₇	C₂³	1	2	yes	—
236	#95×C₆₇	C₂³	1	2	yes	—
237	#95×C₆₇	C₂³	1	2	yes	—
238	#95×C₆₇	C₂³	1	2	yes	—
239	#95×C₆₇	C₂³	1	2	yes	—
240	#95×C₆₇	C₂³	1	1	yes	characteristic
241	#95×C₆₇	C₂³	1	1	yes	characteristic
242	#95×C₆₇	C₂³	1	2	yes	—
243	#95×C₆₇	C₂³	1	1	yes	characteristic
244	#95×C₆₇	C₂³	1	1	yes	characteristic
245	#95×C₆₇	C₂³	1	2	yes	—
246	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
247	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
248	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
249	#41×C₆₇	—	4	32	no	—
250	C₂×Q₈×C₆₇	—	4	2	no	—
251	C₂×Q₈×C₆₇	—	4	2	no	—
252	C₂×Q₈×C₆₇	C₂²×C₄	1	8	yes	—
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	2	no	—
257	C₂×D₄×C₆₇	—	2	2	no	—
258	C₂×D₄×C₆₇	—	2	2	no	—
259	C₂×D₄×C₆₇	—	4	2	no	—
260	C₂×D₄×C₆₇	—	4	2	no	—
261	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
262	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
263	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
264	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
265	C₂²×C₄×C₆₇	—	2	2	no	—
266	C₂²×C₄×C₆₇	—	2	4	no	—
267	C₂²×C₄×C₆₇	—	2	4	no	—
268	C₂²×C₄×C₆₇	—	2	2	no	—
269	C₂²×C₄×C₆₇	—	2	2	no	—
270	C₂²×C₄×C₆₇	—	2	2	no	—
271	C₂²×C₄×C₆₇	—	2	2	no	—
272	C₂²×C₄×C₆₇	—	2	2	no	—
273	C₂²×C₄×C₆₇	—	2	2	no	—
274	C₂²×C₄×C₆₇	—	2	4	no	—
275	C₂²×C₄×C₆₇	—	2	2	no	—
276	C₂²×C₄×C₆₇	—	2	2	no	—
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	—	4	2	no	—
281	C₂²×C₄×C₆₇	—	4	1	no	—
282	C₂²×C₄×C₆₇	—	4	2	no	—
283	C₂²×C₄×C₆₇	—	4	2	no	—
284	C₂²×C₄×C₆₇	—	4	2	no	—
285	C₂²×C₄×C₆₇	—	4	2	no	—
286	C₂²×C₄×C₆₇	—	4	2	no	—
287	C₂²×C₄×C₆₇	—	4	2	no	—
288	C₂²×C₄×C₆₇	—	4	2	no	—
289	C₂²×C₄×C₆₇	—	4	2	no	—
290	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
291	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
292	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
293	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
294	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
295	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	2	yes	—
301	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
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	4	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	—	4	1	no	—
323	C₄⋊C₄×C₆₇	—	4	2	no	—
324	C₄⋊C₄×C₆₇	—	4	2	no	—
325	C₄⋊C₄×C₆₇	—	4	2	no	—
326	C₄⋊C₄×C₆₇	—	4	2	no	—
327	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
328	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
329	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
330	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
331	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
332	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
333	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
334	C₄⋊C₄×C₆₇	#41	1	4	yes	complemented
335	C₂²⋊C₄×C₆₇	—	2	2	no	—
336	C₂²⋊C₄×C₆₇	—	2	4	no	—
337	C₂²⋊C₄×C₆₇	—	2	2	no	—
338	C₂²⋊C₄×C₆₇	—	2	2	no	—
339	C₂²⋊C₄×C₆₇	—	2	2	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	2	no	—
344	C₂²⋊C₄×C₆₇	—	2	4	no	—
345	C₂²⋊C₄×C₆₇	—	4	2	no	—
346	C₂²⋊C₄×C₆₇	—	4	2	no	—
347	C₂²⋊C₄×C₆₇	—	4	1	no	—
348	C₂²⋊C₄×C₆₇	—	4	2	no	—
349	C₂²⋊C₄×C₆₇	—	4	2	no	—
350	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
351	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
352	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
353	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
354	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
355	C₄²×C₆₇	—	2	2	no	—
356	C₄²×C₆₇	—	2	2	no	—
357	C₄²×C₆₇	—	2	2	no	—
358	C₄²×C₆₇	—	2	4	no	—
359	C₄²×C₆₇	—	2	2	no	—
360	C₄²×C₆₇	—	2	2	no	—
361	C₄²×C₆₇	—	4	2	no	—
362	C₄²×C₆₇	—	4	2	no	—
363	C₄²×C₆₇	—	4	2	no	—
364	C₄²×C₆₇	—	4	2	no	—
365	C₄²×C₆₇	—	4	2	no	—
366	C₄²×C₆₇	—	4	2	no	—
367	C₄²×C₆₇	—	4	2	no	—
368	C₄²×C₆₇	—	4	2	no	—
369	C₄²×C₆₇	—	4	2	no	—
370	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
371	C₄²×C₆₇	#41	1	4	yes	complemented
372	C₂³×C₆₇	—	2	1	no	—
373	C₂³×C₆₇	—	2	1	no	—
374	C₂³×C₆₇	—	2	1	no	—
375	C₂³×C₆₇	—	2	1	no	—
376	C₂³×C₆₇	—	2	1	no	—
377	C₂³×C₆₇	—	2	1	no	—
378	C₂³×C₆₇	—	2	2	no	—
379	C₂³×C₆₇	—	2	2	no	—
380	C₂³×C₆₇	—	2	2	no	—
381	C₂³×C₆₇	—	2	2	no	—
382	C₂³×C₆₇	—	2	1	no	—
383	C₂³×C₆₇	—	2	1	no	—
384	C₂³×C₆₇	—	2	1	no	—
385	C₂³×C₆₇	—	2	2	no	—
386	C₂³×C₆₇	—	2	1	no	—
387	C₂³×C₆₇	—	2	2	no	—
388	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
389	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
390	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
391	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
392	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
393	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
394	Q₈×C₆₇	—	4	8	no	—
395	D₄×C₆₇	—	2	16	no	—
396	D₄×C₆₇	—	2	8	no	—
397	D₄×C₆₇	—	2	8	no	—
398	D₄×C₆₇	—	4	8	no	—
399	C₂×C₄×C₆₇	—	2	8	no	—
400	C₂×C₄×C₆₇	—	2	16	no	—
401	C₂×C₄×C₆₇	—	2	1	no	—
402	C₂×C₄×C₆₇	—	2	1	no	—
403	C₂×C₄×C₆₇	—	2	1	no	—
404	C₂×C₄×C₆₇	—	2	1	no	—
405	C₂×C₄×C₆₇	—	2	1	no	—
406	C₂×C₄×C₆₇	—	2	1	no	—
407	C₂×C₄×C₆₇	—	2	1	no	—
408	C₂×C₄×C₆₇	—	2	2	no	—
409	C₂×C₄×C₆₇	—	2	2	no	—
410	C₂×C₄×C₆₇	—	2	2	no	—
411	C₂×C₄×C₆₇	—	2	1	no	—
412	C₂×C₄×C₆₇	—	2	2	no	—
413	C₂×C₄×C₆₇	—	2	2	no	—
414	C₂×C₄×C₆₇	—	2	2	no	—
415	C₂×C₄×C₆₇	—	2	2	no	—
416	C₂×C₄×C₆₇	—	2	1	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	2	no	—
422	C₂×C₄×C₆₇	—	2	1	no	—
423	C₂×C₄×C₆₇	—	2	8	no	—
424	C₂×C₄×C₆₇	—	2	8	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	1	no	—
431	C₂×C₄×C₆₇	—	2	2	no	—
432	C₂×C₄×C₆₇	—	2	2	no	—
433	C₂×C₄×C₆₇	—	2	1	no	—
434	C₂×C₄×C₆₇	—	2	2	no	—
435	C₂×C₄×C₆₇	—	2	1	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	1	no	—
440	C₂×C₄×C₆₇	—	2	1	no	—
441	C₂×C₄×C₆₇	—	2	1	no	—
442	C₂×C₄×C₆₇	—	2	2	no	—
443	C₂×C₄×C₆₇	—	2	1	no	—
444	C₂×C₄×C₆₇	—	2	2	no	—
445	C₂×C₄×C₆₇	—	2	1	no	—
446	C₂×C₄×C₆₇	—	2	2	no	—
447	C₂×C₄×C₆₇	—	2	1	no	—
448	C₂×C₄×C₆₇	—	2	1	no	—
449	C₂×C₄×C₆₇	—	4	8	no	—
450	C₂×C₄×C₆₇	—	4	8	no	—
451	C₂×C₄×C₆₇	—	4	4	no	—
452	C₂×C₄×C₆₇	—	4	8	no	—
453	C₂×C₄×C₆₇	—	8	4	no	—
454	C₂×C₄×C₆₇	—	8	4	no	—
455	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
456	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
457	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
458	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
459	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
460	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
461	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
462	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
463	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
464	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
465	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
466	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
467	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
468	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
469	C₂²×C₆₇	—	2	2	no	—
470	C₂²×C₆₇	—	2	2	no	—
471	C₂²×C₆₇	—	2	2	no	—
472	C₂²×C₆₇	—	2	2	no	—
473	C₂²×C₆₇	—	2	2	no	—
474	C₂²×C₆₇	—	2	2	no	—
475	C₂²×C₆₇	—	2	2	no	—
476	C₂²×C₆₇	—	2	4	no	—
477	C₂²×C₆₇	—	2	2	no	—
478	C₂²×C₆₇	—	2	4	no	—
479	C₂²×C₆₇	—	2	2	no	—
480	C₂²×C₆₇	—	2	4	no	—
481	C₂²×C₆₇	—	4	1	no	—
482	C₂²×C₆₇	—	4	2	no	—
483	C₂²×C₆₇	—	4	2	no	—
484	C₂²×C₆₇	—	4	1	no	—
485	C₂²×C₆₇	—	4	2	no	—
486	C₂²×C₆₇	—	4	1	no	—
487	C₂²×C₆₇	—	4	1	no	—
488	C₂²×C₆₇	—	4	2	no	—
489	C₂²×C₆₇	#518	1	4	yes	—
490	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
491	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
492	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
493	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
494	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
495	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
496	C₂²×C₆₇	#585	1	1	yes	characteristic
497	C₄×C₆₇	—	2	2	no	—
498	C₄×C₆₇	—	2	2	no	—
499	C₄×C₆₇	—	2	4	no	—
500	C₄×C₆₇	—	2	4	no	—
501	C₄×C₆₇	—	2	2	no	—
502	C₄×C₆₇	—	2	4	no	—
503	C₄×C₆₇	—	2	2	no	—
504	C₄×C₆₇	—	2	2	no	—
505	C₄×C₆₇	—	2	2	no	—
506	C₄×C₆₇	—	2	2	no	—
507	C₄×C₆₇	—	2	4	no	—
508	C₄×C₆₇	—	4	1	no	—
509	C₄×C₆₇	—	4	1	no	—
510	C₄×C₆₇	—	4	1	no	—
511	C₄×C₆₇	—	4	2	no	—
512	C₄×C₆₇	—	4	2	no	—
513	C₄×C₆₇	—	4	1	no	—
514	C₄×C₆₇	—	4	1	no	—
515	C₄×C₆₇	—	4	2	no	—
516	C₄×C₆₇	C₄×#41	1	4	yes	—
517	#34298	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
518	C₂×C₆₇	—	2	4	no	—
519	C₂×C₆₇	—	4	2	no	—
520	C₂×C₆₇	—	4	4	no	—
521	C₂×C₆₇	C₂×C₄×#41	1	1	yes	characteristic
522	C₂×C₆₇	C₂×#518	1	1	yes	characteristic
523	C₂×C₆₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
524	C₂×C₆₇	#3492	1	1	yes	characteristic
525	C₂×C₆₇	#3494	1	1	yes	characteristic
526	C₂×C₆₇	#3513	1	1	yes	characteristic
527	C₂×C₆₇	#3522	1	1	yes	characteristic
528	C₂×#547	C₂×C₆₇	1	1	yes	characteristic
529	#2374	C₂×C₆₇	1	2	yes	complemented
530	#2369	C₂×C₆₇	1	1	yes	characteristic, complemented
531	#2368	C₂×C₆₇	1	2	yes	complemented
532	#2363	C₂×C₆₇	1	1	yes	characteristic, complemented
533	#2361	C₂×C₆₇	1	1	yes	characteristic, complemented
534	#2359	C₂×C₆₇	1	2	yes	complemented
535	#2357	C₂×C₆₇	1	1	yes	characteristic, complemented
536	#2352	C₂×C₆₇	1	1	yes	characteristic, complemented
537	#2345	C₂×C₆₇	1	1	yes	characteristic, complemented
538	#2344	C₂×C₆₇	1	1	yes	characteristic, complemented
539	#2339	C₂×C₆₇	1	2	yes	complemented
540	#2335	C₂×C₆₇	1	2	yes	complemented
541	#2332	C₂×C₆₇	1	2	yes	complemented
542	#2331	C₂×C₆₇	1	1	yes	characteristic, complemented
543	#2324	C₂×C₆₇	1	1	yes	characteristic, complemented
544	C₄×#123	C₂×C₆₇	1	2	yes	complemented
545	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
546	#2297	C₂×C₆₇	1	2	yes	complemented
547	#2290	C₂×C₆₇	1	1	yes	characteristic, complemented
548	#2275	C₂×C₆₇	1	1	yes	characteristic, complemented
549	#2274	C₂×C₆₇	1	1	yes	characteristic, complemented
550	C₂×C₄×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
551	C₆₇	#34298	1	1	yes	characteristic, direct product factor, Sylow
552	C₂²×#41	C₂²×C₆₇	1	2	yes	—
553	#547	C₄×C₆₇	1	16	yes	complemented
554	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
555	C₂×#123	C₂²×C₆₇	1	2	yes	—
556	C₂×#123	C₂²×C₆₇	1	2	yes	—
557	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
558	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
559	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
560	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
561	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
562	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
563	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
564	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
565	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
566	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
567	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
568	C₂×#117	C₂²×C₆₇	1	2	yes	—
569	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
570	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
571	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
572	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
573	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
574	#391	C₂²×C₆₇	1	2	yes	—
575	#391	C₂²×C₆₇	1	2	yes	—
576	#391	C₂²×C₆₇	1	2	yes	—
577	#391	C₂²×C₆₇	1	2	yes	—
578	#390	C₂²×C₆₇	1	2	yes	—
579	#390	C₂²×C₆₇	1	1	yes	characteristic
580	#390	C₂²×C₆₇	1	1	yes	characteristic
581	#390	C₂²×C₆₇	1	2	yes	—
582	#389	C₂²×C₆₇	1	1	yes	characteristic
583	#389	C₂²×C₆₇	1	1	yes	characteristic
584	#389	C₂²×C₆₇	1	1	yes	characteristic
585	#389	C₂²×C₆₇	1	2	yes	—
586	#389	C₂²×C₆₇	1	1	yes	characteristic
587	#388	C₂²×C₆₇	1	2	yes	—
588	#388	C₂²×C₆₇	1	2	yes	—
589	#388	C₂²×C₆₇	1	2	yes	—
590	#388	C₂²×C₆₇	1	2	yes	—
591	#388	C₂²×C₆₇	1	1	yes	characteristic
592	#388	C₂²×C₆₇	1	2	yes	—
593	#388	C₂²×C₆₇	1	2	yes	—
594	#388	C₂²×C₆₇	1	2	yes	—
595	#388	C₂²×C₆₇	1	1	yes	characteristic
596	#387	C₂²×C₆₇	1	2	yes	—
597	#387	C₂²×C₆₇	1	2	yes	—
598	#387	C₂²×C₆₇	1	1	yes	characteristic
599	#387	C₂²×C₆₇	1	2	yes	—
600	#387	C₂²×C₆₇	1	2	yes	—
601	#387	C₂²×C₆₇	1	2	yes	—
602	#387	C₂²×C₆₇	1	2	yes	—
603	#387	C₂²×C₆₇	1	2	yes	—
604	#387	C₂²×C₆₇	1	1	yes	characteristic
605	#386	C₂²×C₆₇	1	2	yes	—
606	#386	C₂²×C₆₇	1	2	yes	—
607	#386	C₂²×C₆₇	1	1	yes	characteristic
608	#386	C₂²×C₆₇	1	2	yes	—
609	#386	C₂²×C₆₇	1	2	yes	—
610	#386	C₂²×C₆₇	1	1	yes	characteristic
611	#386	C₂²×C₆₇	1	2	yes	—
612	#385	C₂²×C₆₇	1	2	yes	—
613	#385	C₂²×C₆₇	1	2	yes	—
614	#385	C₂²×C₆₇	1	1	yes	characteristic
615	#385	C₂²×C₆₇	1	1	yes	characteristic
616	#382	C₂²×C₆₇	1	1	yes	characteristic
617	#381	C₂²×C₆₇	1	2	yes	—
618	#381	C₂²×C₆₇	1	2	yes	—
619	#380	C₂²×C₆₇	1	1	yes	characteristic
620	#380	C₂²×C₆₇	1	2	yes	—
621	#380	C₂²×C₆₇	1	1	yes	characteristic
622	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
623	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
624	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
625	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
626	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
627	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
628	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
629	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
630	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
631	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
632	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
633	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
634	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
635	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
636	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
637	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
638	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
639	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
640	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
641	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
642	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
643	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
644	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
645	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
646	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
647	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
648	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
649	#376	C₂²×C₆₇	1	1	yes	characteristic
650	C₂×#95	C₂²×C₆₇	1	2	yes	—
651	C₂×#95	C₂²×C₆₇	1	2	yes	—
652	C₂×#41	—	4	4	no	—
653	C₂×#41	—	4	4	no	—
654	C₂×#41	C₂×C₄×C₆₇	1	16	yes	complemented
655	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
656	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
657	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
658	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
659	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
660	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
661	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
662	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
663	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
664	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
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	2	yes	—
670	C₄⋊Q₈	C₂×C₄×C₆₇	1	8	yes	complemented
671	#123	C₂×C₄×C₆₇	1	16	yes	complemented
672	#123	C₂×C₄×C₆₇	1	16	yes	complemented
673	C₂²⋊Q₈	C₂×C₄×C₆₇	1	16	yes	complemented
674	#121	C₂×C₄×C₆₇	1	8	yes	—
675	#121	C₂×C₄×C₆₇	1	8	yes	complemented
676	C₄×D₄	—	2	4	no	—
677	C₄×D₄	—	2	4	no	—
678	C₄×D₄	—	4	4	no	—
679	C₄×D₄	—	4	4	no	—
680	C₄×D₄	C₂×C₄×C₆₇	1	8	yes	complemented
681	C₄×D₄	C₂×C₄×C₆₇	1	8	yes	complemented
682	#117	—	2	4	no	—
683	#117	—	2	4	no	—
684	#117	—	4	4	no	—
685	C₂×C₄⋊C₄	—	2	4	no	—
686	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	8	yes	complemented
687	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	8	yes	complemented
688	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
689	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
690	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
691	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
692	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
693	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
694	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
695	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
696	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
697	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
698	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
699	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
700	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
701	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
702	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
703	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
704	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
705	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
706	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
707	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
708	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
709	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
710	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
711	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
712	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
713	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
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×C₄²	—	2	4	no	—
729	C₂×C₄²	—	4	4	no	—
730	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
731	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
732	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
733	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
734	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
735	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
736	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
737	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
738	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
739	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
740	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
741	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
742	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
743	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
744	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
745	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
746	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
747	#95	C₂³×C₆₇	1	1	yes	characteristic
748	#95	C₂³×C₆₇	1	2	yes	—
749	#95	C₂³×C₆₇	1	2	yes	—
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	#95	C₂³×C₆₇	1	1	yes	characteristic
756	#95	C₂³×C₆₇	1	1	yes	characteristic
757	#95	C₂³×C₆₇	1	1	yes	characteristic
758	#95	C₂³×C₆₇	1	2	yes	—
759	#95	C₂³×C₆₇	1	1	yes	characteristic
760	#95	C₂³×C₆₇	1	2	yes	—
761	#95	C₂³×C₆₇	1	2	yes	—
762	#95	C₂³×C₆₇	1	2	yes	—
763	#95	C₂³×C₆₇	1	2	yes	—
764	#95	C₂³×C₆₇	1	2	yes	—
765	#95	C₂³×C₆₇	1	2	yes	—
766	#95	C₂³×C₆₇	1	2	yes	—
767	#95	C₂³×C₆₇	1	2	yes	—
768	#95	C₂³×C₆₇	1	1	yes	characteristic
769	#95	C₂³×C₆₇	1	1	yes	characteristic
770	#95	C₂³×C₆₇	1	2	yes	—
771	#95	C₂³×C₆₇	1	1	yes	characteristic
772	#95	C₂³×C₆₇	1	1	yes	characteristic
773	#95	C₂³×C₆₇	1	2	yes	—
774	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
775	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
776	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
777	#41	—	4	32	no	—
778	C₂×Q₈	—	4	2	no	—
779	C₂×Q₈	—	4	2	no	—
780	C₂×Q₈	C₂²×C₄×C₆₇	1	8	yes	—
781	C₂×D₄	—	2	4	no	—
782	C₂×D₄	—	2	4	no	—
783	C₂×D₄	—	2	2	no	—
784	C₂×D₄	—	2	2	no	—
785	C₂×D₄	—	2	2	no	—
786	C₂×D₄	—	2	2	no	—
787	C₂×D₄	—	4	2	no	—
788	C₂×D₄	—	4	2	no	—
789	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
790	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
791	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
792	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	2	4	no	—
795	C₂²×C₄	—	2	4	no	—
796	C₂²×C₄	—	2	2	no	—
797	C₂²×C₄	—	2	2	no	—
798	C₂²×C₄	—	2	2	no	—
799	C₂²×C₄	—	2	2	no	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	2	no	—
802	C₂²×C₄	—	2	4	no	—
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	2	2	no	—
805	C₂²×C₄	—	2	4	no	—
806	C₂²×C₄	—	2	4	no	—
807	C₂²×C₄	—	2	4	no	—
808	C₂²×C₄	—	4	2	no	—
809	C₂²×C₄	—	4	2	no	—
810	C₂²×C₄	—	4	2	no	—
811	C₂²×C₄	—	4	2	no	—
812	C₂²×C₄	—	4	2	no	—
813	C₂²×C₄	—	4	1	no	—
814	C₂²×C₄	—	4	2	no	—
815	C₂²×C₄	—	4	2	no	—
816	C₂²×C₄	—	4	2	no	—
817	C₂²×C₄	—	4	2	no	—
818	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
819	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
820	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
821	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
822	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
823	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
824	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
825	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
826	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
827	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
828	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
829	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
830	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
831	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
832	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
833	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
834	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
835	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
836	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
837	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
838	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
839	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
840	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
841	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
842	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
843	C₄⋊C₄	—	2	4	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	4	2	no	—
851	C₄⋊C₄	—	4	2	no	—
852	C₄⋊C₄	—	4	2	no	—
853	C₄⋊C₄	—	4	2	no	—
854	C₄⋊C₄	—	4	1	no	—
855	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
856	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
857	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
858	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
859	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
860	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
861	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
862	C₄⋊C₄	#41×C₆₇	1	4	yes	complemented
863	C₂²⋊C₄	—	2	2	no	—
864	C₂²⋊C₄	—	2	4	no	—
865	C₂²⋊C₄	—	2	2	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	2	no	—
868	C₂²⋊C₄	—	2	4	no	—
869	C₂²⋊C₄	—	2	4	no	—
870	C₂²⋊C₄	—	2	4	no	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	—	2	4	no	—
873	C₂²⋊C₄	—	4	2	no	—
874	C₂²⋊C₄	—	4	2	no	—
875	C₂²⋊C₄	—	4	2	no	—
876	C₂²⋊C₄	—	4	2	no	—
877	C₂²⋊C₄	—	4	1	no	—
878	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
879	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
880	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
881	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
882	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
883	C₄²	—	2	2	no	—
884	C₄²	—	2	2	no	—
885	C₄²	—	2	2	no	—
886	C₄²	—	2	4	no	—
887	C₄²	—	2	2	no	—
888	C₄²	—	2	2	no	—
889	C₄²	—	4	2	no	—
890	C₄²	—	4	2	no	—
891	C₄²	—	4	2	no	—
892	C₄²	—	4	2	no	—
893	C₄²	—	4	2	no	—
894	C₄²	—	4	2	no	—
895	C₄²	—	4	2	no	—
896	C₄²	—	4	2	no	—
897	C₄²	—	4	2	no	—
898	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
899	C₄²	#41×C₆₇	1	4	yes	complemented
900	C₂³	—	2	1	no	—
901	C₂³	—	2	1	no	—
902	C₂³	—	2	1	no	—
903	C₂³	—	2	1	no	—
904	C₂³	—	2	1	no	—
905	C₂³	—	2	1	no	—
906	C₂³	—	2	2	no	—
907	C₂³	—	2	2	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	2	2	no	—
910	C₂³	—	2	1	no	—
911	C₂³	—	2	1	no	—
912	C₂³	—	2	1	no	—
913	C₂³	—	2	2	no	—
914	C₂³	—	2	1	no	—
915	C₂³	—	2	2	no	—
916	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
917	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
918	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
919	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
920	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
921	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
922	Q₈	—	4	8	no	—
923	D₄	—	2	8	no	—
924	D₄	—	2	16	no	—
925	D₄	—	2	8	no	—
926	D₄	—	4	8	no	—
927	C₂×C₄	—	2	8	no	—
928	C₂×C₄	—	2	16	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	8	no	—
952	C₂×C₄	—	2	8	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	4	8	no	—
978	C₂×C₄	—	4	8	no	—
979	C₂×C₄	—	4	4	no	—
980	C₂×C₄	—	4	8	no	—
981	C₂×C₄	—	8	4	no	—
982	C₂×C₄	—	8	4	no	—
983	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
984	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
985	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
986	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
987	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
988	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
989	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
990	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
991	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
992	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
993	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
994	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
995	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
996	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
997	C₂²	—	2	2	no	—
998	C₂²	—	2	2	no	—
999	C₂²	—	2	2	no	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	2	2	no	—
1002	C₂²	—	2	2	no	—
1003	C₂²	—	2	2	no	—
1004	C₂²	—	2	4	no	—
1005	C₂²	—	2	2	no	—
1006	C₂²	—	2	4	no	—
1007	C₂²	—	2	2	no	—
1008	C₂²	—	2	4	no	—
1009	C₂²	—	4	1	no	—
1010	C₂²	—	4	2	no	—
1011	C₂²	—	4	1	no	—
1012	C₂²	—	4	2	no	—
1013	C₂²	—	4	2	no	—
1014	C₂²	—	4	1	no	—
1015	C₂²	—	4	2	no	—
1016	C₂²	—	4	1	no	—
1017	C₂²	#518×C₆₇	1	4	yes	—
1018	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
1019	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1020	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1021	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1022	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1023	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
1024	C₂²	#585×C₆₇	1	1	yes	characteristic
1025	C₄	—	2	2	no	—
1026	C₄	—	2	2	no	—
1027	C₄	—	2	4	no	—
1028	C₄	—	2	4	no	—
1029	C₄	—	2	2	no	—
1030	C₄	—	2	4	no	—
1031	C₄	—	2	2	no	—
1032	C₄	—	2	2	no	—
1033	C₄	—	2	2	no	—
1034	C₄	—	2	2	no	—
1035	C₄	—	2	4	no	—
1036	C₄	—	4	1	no	—
1037	C₄	—	4	2	no	—
1038	C₄	—	4	1	no	—
1039	C₄	—	4	1	no	—
1040	C₄	—	4	2	no	—
1041	C₄	—	4	1	no	—
1042	C₄	—	4	2	no	—
1043	C₄	—	4	1	no	—
1044	C₄	C₄×#41×C₆₇	1	4	yes	—
1045	C₂	—	2	4	no	—
1046	C₂	—	4	2	no	—
1047	C₂	—	4	4	no	—
1048	C₂	C₂×C₄×#41×C₆₇	1	1	yes	characteristic
1049	C₂	C₂×#518×C₆₇	1	1	yes	characteristic
1050	C₂	C₄×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
1051	C₂	C₆₇×#3492	1	1	yes	characteristic
1052	C₂	C₆₇×#3494	1	1	yes	characteristic
1053	C₂	C₆₇×#3513	1	1	yes	characteristic
1054	C₂	C₆₇×#3522	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂×#547×C₆₇	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#2374	C₂	semidirect
3. C₆₇×#2369	C₂	semidirect
4. C₆₇×#2368	C₂	semidirect
5. C₆₇×#2363	C₂	semidirect
6. C₆₇×#2361	C₂	semidirect
7. C₆₇×#2359	C₂	semidirect
8. C₆₇×#2357	C₂	semidirect
9. C₆₇×#2352	C₂	semidirect
10. C₆₇×#2345	C₂	semidirect
11. C₆₇×#2344	C₂	semidirect
12. C₆₇×#2339	C₂	semidirect
13. C₆₇×#2335	C₂	semidirect
14. C₆₇×#2332	C₂	semidirect
15. C₆₇×#2331	C₂	semidirect
16. C₆₇×#2324	C₂	semidirect
17. C₄×#123×C₆₇	C₂	semidirect
18. C₄×#121×C₆₇	C₂	semidirect
19. C₆₇×#2297	C₂	semidirect
20. C₆₇×#2290	C₂	semidirect
21. C₆₇×#2275	C₂	semidirect
22. C₆₇×#2274	C₂	semidirect
23. C₂×C₄×C₄⋊C₄×C₆₇	C₂	semidirect
25. #547×C₆₇	C₄	semidirect
126. C₂×#41×C₆₇	C₂×C₄	semidirect
142. C₄⋊Q₈×C₆₇	C₂×C₄	semidirect
143. #123×C₆₇	C₂×C₄	semidirect
144. #123×C₆₇	C₂×C₄	semidirect
145. C₂²⋊Q₈×C₆₇	C₂×C₄	semidirect
147. #121×C₆₇	C₂×C₄	semidirect
152. C₄×D₄×C₆₇	C₂×C₄	semidirect
153. C₄×D₄×C₆₇	C₂×C₄	semidirect
158. C₂×C₄⋊C₄×C₆₇	C₂×C₄	semidirect
159. C₂×C₄⋊C₄×C₆₇	C₂×C₄	semidirect
334. C₄⋊C₄×C₆₇	#41	semidirect
371. C₄²×C₆₇	#41	semidirect
517. #34298	C₆₇	direct (N × H)
529. #2374	C₂×C₆₇	semidirect
530. #2369	C₂×C₆₇	semidirect
531. #2368	C₂×C₆₇	semidirect
532. #2363	C₂×C₆₇	semidirect
533. #2361	C₂×C₆₇	semidirect
534. #2359	C₂×C₆₇	semidirect
535. #2357	C₂×C₆₇	semidirect
536. #2352	C₂×C₆₇	semidirect
537. #2345	C₂×C₆₇	semidirect
538. #2344	C₂×C₆₇	semidirect
539. #2339	C₂×C₆₇	semidirect
540. #2335	C₂×C₆₇	semidirect
541. #2332	C₂×C₆₇	semidirect
542. #2331	C₂×C₆₇	semidirect
543. #2324	C₂×C₆₇	semidirect
544. C₄×#123	C₂×C₆₇	semidirect
545. C₄×#121	C₂×C₆₇	semidirect
546. #2297	C₂×C₆₇	semidirect
547. #2290	C₂×C₆₇	semidirect
548. #2275	C₂×C₆₇	semidirect
549. #2274	C₂×C₆₇	semidirect
550. C₂×C₄×C₄⋊C₄	C₂×C₆₇	semidirect
551. C₆₇	#34298	direct (N × H)
553. #547	C₄×C₆₇	semidirect
654. C₂×#41	C₂×C₄×C₆₇	semidirect
670. C₄⋊Q₈	C₂×C₄×C₆₇	semidirect
671. #123	C₂×C₄×C₆₇	semidirect
672. #123	C₂×C₄×C₆₇	semidirect
673. C₂²⋊Q₈	C₂×C₄×C₆₇	semidirect
675. #121	C₂×C₄×C₆₇	semidirect
680. C₄×D₄	C₂×C₄×C₆₇	semidirect
681. C₄×D₄	C₂×C₄×C₆₇	semidirect
686. C₂×C₄⋊C₄	C₂×C₄×C₆₇	semidirect
687. C₂×C₄⋊C₄	C₂×C₄×C₆₇	semidirect
862. C₄⋊C₄	#41×C₆₇	semidirect
899. C₄²	#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×#547×C₆₇	2
C₆₇×#2374	2
C₆₇×#2369	2
C₆₇×#2368	2
C₆₇×#2363	2
C₆₇×#2361	2
C₆₇×#2359	2
C₆₇×#2357	2
C₆₇×#2352	2
C₆₇×#2345	2
C₆₇×#2344	2
C₆₇×#2339	2
C₆₇×#2335	2
C₆₇×#2332	2
C₆₇×#2331	2
C₆₇×#2324	2
C₄×#123×C₆₇	2
C₄×#121×C₆₇	2
C₆₇×#2297	2
C₆₇×#2290	2
C₆₇×#2275	2
C₆₇×#2274	2
C₂×C₄×C₄⋊C₄×C₆₇	2
#34298	67

Subgroups — C67×#34298 #30713549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34298 #30713549