Subgroups — C₆₇×#34919 #30714170

Order 17152.

2392 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#529×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2560	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2558	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2550	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2545	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2540	C₂	1	1	yes	maximal, characteristic
8	C₆₇×#2536	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2519	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2491	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2489	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2461	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2429	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2426	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2396	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2392	C₂	1	2	yes	maximal, complemented
17	C₄×#124×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#124×C₆₇	C₂	1	2	yes	maximal, complemented
19	C₄×C₂²⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2293	C₂	1	2	yes	maximal, complemented
22	C₄²×Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	#533×C₆₇	—	2	8	no	—
25	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
27	#529×C₆₇	—	2	8	no	—
28	C₂×#126×C₆₇	C₂²	1	2	yes	—
29	C₂×#125×C₆₇	C₂²	1	2	yes	—
30	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×#124×C₆₇	C₂²	1	2	yes	—
34	C₂×#123×C₆₇	C₂²	1	2	yes	—
35	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
40	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
46	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
51	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
52	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
53	C₂×#117×C₆₇	C₂²	1	2	yes	—
54	C₂×#117×C₆₇	C₂²	1	2	yes	—
55	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
56	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
57	#400×C₆₇	C₂²	1	2	yes	—
58	#399×C₆₇	C₂²	1	2	yes	—
59	#398×C₆₇	C₂²	1	2	yes	—
60	#398×C₆₇	C₂²	1	2	yes	—
61	#398×C₆₇	C₂²	1	2	yes	—
62	#397×C₆₇	C₂²	1	2	yes	—
63	#396×C₆₇	C₂²	1	2	yes	—
64	#396×C₆₇	C₂²	1	2	yes	—
65	#396×C₆₇	C₂²	1	2	yes	—
66	#396×C₆₇	C₂²	1	2	yes	—
67	#395×C₆₇	C₂²	1	2	yes	—
68	#394×C₆₇	C₂²	1	2	yes	—
69	#394×C₆₇	C₂²	1	2	yes	—
70	#394×C₆₇	C₂²	1	2	yes	—
71	#393×C₆₇	C₂²	1	2	yes	—
72	#392×C₆₇	C₂²	1	2	yes	—
73	#391×C₆₇	C₂²	1	1	yes	characteristic
74	#391×C₆₇	C₂²	1	2	yes	—
75	#391×C₆₇	C₂²	1	1	yes	characteristic
76	#390×C₆₇	C₂²	1	2	yes	—
77	#390×C₆₇	C₂²	1	2	yes	—
78	#390×C₆₇	C₂²	1	1	yes	characteristic
79	#390×C₆₇	C₂²	1	2	yes	—
80	#390×C₆₇	C₂²	1	1	yes	characteristic
81	#389×C₆₇	C₂²	1	2	yes	—
82	#389×C₆₇	C₂²	1	2	yes	—
83	#389×C₆₇	C₂²	1	1	yes	characteristic
84	#389×C₆₇	C₂²	1	1	yes	characteristic
85	#388×C₆₇	C₂²	1	2	yes	—
86	#388×C₆₇	C₂²	1	2	yes	—
87	#388×C₆₇	C₂²	1	2	yes	—
88	#388×C₆₇	C₂²	1	2	yes	—
89	#388×C₆₇	C₂²	1	2	yes	—
90	#388×C₆₇	C₂²	1	2	yes	—
91	#388×C₆₇	C₂²	1	2	yes	—
92	#388×C₆₇	C₂²	1	2	yes	—
93	#388×C₆₇	C₂²	1	2	yes	—
94	#388×C₆₇	C₂²	1	2	yes	—
95	#388×C₆₇	C₂²	1	2	yes	—
96	#387×C₆₇	C₂²	1	2	yes	—
97	#386×C₆₇	C₂²	1	2	yes	—
98	#385×C₆₇	C₂²	1	2	yes	—
99	#382×C₆₇	C₂²	1	2	yes	—
100	#382×C₆₇	C₂²	1	1	yes	characteristic
101	#380×C₆₇	C₂²	1	1	yes	characteristic
102	#380×C₆₇	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
104	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
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	1	yes	characteristic
109	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
110	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
111	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
113	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
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	—
120	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
122	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
123	C₄³×C₆₇	C₂²	1	1	yes	characteristic
124	C₄³×C₆₇	C₂²	1	2	yes	—
125	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
126	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
127	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
131	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
132	C₂³×C₄×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	2	yes	—
136	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
139	C₄⋊Q₈×C₆₇	—	2	4	no	—
140	C₄⋊Q₈×C₆₇	—	2	4	no	—
141	#126×C₆₇	—	2	8	no	—
142	#125×C₆₇	—	2	4	no	—
143	#125×C₆₇	—	2	8	no	—
144	#124×C₆₇	—	2	4	no	—
145	#124×C₆₇	—	2	8	no	—
146	#124×C₆₇	—	2	4	no	—
147	#123×C₆₇	—	2	8	no	—
148	C₂²⋊Q₈×C₆₇	—	2	4	no	—
149	C₂²⋊Q₈×C₆₇	—	2	4	no	—
150	C₂²⋊Q₈×C₆₇	—	2	4	no	—
151	C₂²⋊Q₈×C₆₇	—	2	8	no	—
152	C₂²⋊Q₈×C₆₇	—	2	4	no	—
153	#121×C₆₇	—	2	4	no	—
154	#121×C₆₇	—	2	4	no	—
155	C₄×Q₈×C₆₇	—	2	4	no	—
156	C₄×Q₈×C₆₇	—	2	8	no	—
157	C₄×Q₈×C₆₇	—	2	4	no	—
158	C₄×Q₈×C₆₇	—	2	4	no	—
159	C₄×Q₈×C₆₇	D₄	1	8	yes	complemented
160	C₄×D₄×C₆₇	—	2	4	no	—
161	C₄×D₄×C₆₇	—	2	8	no	—
162	C₄×D₄×C₆₇	—	2	4	no	—
163	C₄×D₄×C₆₇	—	2	4	no	—
164	C₄×D₄×C₆₇	—	2	8	no	—
165	C₄×D₄×C₆₇	—	2	4	no	—
166	#117×C₆₇	—	2	8	no	—
167	#117×C₆₇	—	2	8	no	—
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×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
191	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
207	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₆₇	—	2	4	no	—
215	C₂×C₄²×C₆₇	—	2	4	no	—
216	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
223	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
224	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
225	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
228	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
230	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
233	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
235	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
236	#95×C₆₇	C₂³	1	1	yes	characteristic
237	#95×C₆₇	C₂³	1	1	yes	characteristic
238	#95×C₆₇	C₂³	1	1	yes	characteristic
239	#95×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
244	#95×C₆₇	C₂³	1	2	yes	—
245	#95×C₆₇	C₂³	1	2	yes	—
246	#95×C₆₇	C₂³	1	2	yes	—
247	#95×C₆₇	C₂³	1	2	yes	—
248	#95×C₆₇	C₂³	1	2	yes	—
249	#95×C₆₇	C₂³	1	2	yes	—
250	#95×C₆₇	C₂³	1	2	yes	—
251	#95×C₆₇	C₂³	1	2	yes	—
252	#95×C₆₇	C₂³	1	2	yes	—
253	#95×C₆₇	C₂³	1	2	yes	—
254	#95×C₆₇	C₂³	1	2	yes	—
255	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
256	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
257	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
258	C₂×Q₈×C₆₇	—	2	4	no	—
259	C₂×Q₈×C₆₇	—	2	2	no	—
260	C₂×Q₈×C₆₇	—	2	2	no	—
261	C₂×Q₈×C₆₇	—	2	2	no	—
262	C₂×Q₈×C₆₇	—	2	2	no	—
263	C₂×Q₈×C₆₇	—	2	4	no	—
264	C₂×Q₈×C₆₇	—	2	2	no	—
265	C₂×Q₈×C₆₇	—	4	2	no	—
266	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	—
267	C₂×D₄×C₆₇	—	2	2	no	—
268	C₂×D₄×C₆₇	—	2	2	no	—
269	C₂×D₄×C₆₇	—	2	4	no	—
270	C₂×D₄×C₆₇	—	2	4	no	—
271	C₂×D₄×C₆₇	—	2	4	no	—
272	C₂×D₄×C₆₇	—	2	2	no	—
273	C₂×D₄×C₆₇	—	2	2	no	—
274	C₂×D₄×C₆₇	—	2	4	no	—
275	C₂×D₄×C₆₇	—	2	2	no	—
276	C₂×D₄×C₆₇	—	2	2	no	—
277	C₂×D₄×C₆₇	—	4	2	no	—
278	C₂×D₄×C₆₇	—	4	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	2	no	—
285	C₂²×C₄×C₆₇	—	2	2	no	—
286	C₂²×C₄×C₆₇	—	2	2	no	—
287	C₂²×C₄×C₆₇	—	2	4	no	—
288	C₂²×C₄×C₆₇	—	2	2	no	—
289	C₂²×C₄×C₆₇	—	2	2	no	—
290	C₂²×C₄×C₆₇	—	2	2	no	—
291	C₂²×C₄×C₆₇	—	2	2	no	—
292	C₂²×C₄×C₆₇	—	2	4	no	—
293	C₂²×C₄×C₆₇	—	2	2	no	—
294	C₂²×C₄×C₆₇	—	2	2	no	—
295	C₂²×C₄×C₆₇	—	2	2	no	—
296	C₂²×C₄×C₆₇	—	2	4	no	—
297	C₂²×C₄×C₆₇	—	4	1	no	—
298	C₂²×C₄×C₆₇	—	4	1	no	—
299	C₂²×C₄×C₆₇	#41	1	4	yes	—
300	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
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	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	1	yes	characteristic
314	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
320	C₄⋊C₄×C₆₇	—	2	4	no	—
321	C₄⋊C₄×C₆₇	—	2	4	no	—
322	C₄⋊C₄×C₆₇	—	2	4	no	—
323	C₄⋊C₄×C₆₇	—	2	4	no	—
324	C₄⋊C₄×C₆₇	—	2	2	no	—
325	C₄⋊C₄×C₆₇	—	2	4	no	—
326	C₄⋊C₄×C₆₇	—	2	4	no	—
327	C₄⋊C₄×C₆₇	—	2	4	no	—
328	C₄⋊C₄×C₆₇	—	2	4	no	—
329	C₄⋊C₄×C₆₇	—	2	4	no	—
330	C₄⋊C₄×C₆₇	—	2	2	no	—
331	C₄⋊C₄×C₆₇	—	2	2	no	—
332	C₄⋊C₄×C₆₇	—	2	4	no	—
333	C₄⋊C₄×C₆₇	—	2	2	no	—
334	C₄⋊C₄×C₆₇	—	2	2	no	—
335	C₄⋊C₄×C₆₇	—	2	4	no	—
336	C₄⋊C₄×C₆₇	—	2	4	no	—
337	C₄⋊C₄×C₆₇	—	2	2	no	—
338	C₄⋊C₄×C₆₇	—	2	4	no	—
339	C₄⋊C₄×C₆₇	—	4	2	no	—
340	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
341	C₄⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
342	C₄⋊C₄×C₆₇	#41	1	4	yes	—
343	C₂²⋊C₄×C₆₇	—	2	2	no	—
344	C₂²⋊C₄×C₆₇	—	2	4	no	—
345	C₂²⋊C₄×C₆₇	—	2	4	no	—
346	C₂²⋊C₄×C₆₇	—	2	4	no	—
347	C₂²⋊C₄×C₆₇	—	2	4	no	—
348	C₂²⋊C₄×C₆₇	—	2	4	no	—
349	C₂²⋊C₄×C₆₇	—	2	4	no	—
350	C₂²⋊C₄×C₆₇	—	2	4	no	—
351	C₂²⋊C₄×C₆₇	—	2	4	no	—
352	C₂²⋊C₄×C₆₇	—	2	4	no	—
353	C₂²⋊C₄×C₆₇	—	2	2	no	—
354	C₂²⋊C₄×C₆₇	—	2	4	no	—
355	C₂²⋊C₄×C₆₇	—	2	2	no	—
356	C₂²⋊C₄×C₆₇	—	2	2	no	—
357	C₂²⋊C₄×C₆₇	—	2	2	no	—
358	C₂²⋊C₄×C₆₇	—	2	4	no	—
359	C₂²⋊C₄×C₆₇	—	2	4	no	—
360	C₂²⋊C₄×C₆₇	—	2	4	no	—
361	C₂²⋊C₄×C₆₇	—	2	4	no	—
362	C₂²⋊C₄×C₆₇	—	2	4	no	—
363	C₂²⋊C₄×C₆₇	—	2	4	no	—
364	C₂²⋊C₄×C₆₇	—	4	2	no	—
365	C₂²⋊C₄×C₆₇	#41	1	4	yes	—
366	C₄²×C₆₇	—	2	2	no	—
367	C₄²×C₆₇	—	2	2	no	—
368	C₄²×C₆₇	—	2	2	no	—
369	C₄²×C₆₇	—	2	2	no	—
370	C₄²×C₆₇	—	2	2	no	—
371	C₄²×C₆₇	—	2	2	no	—
372	C₄²×C₆₇	—	2	4	no	—
373	C₄²×C₆₇	—	2	2	no	—
374	C₄²×C₆₇	—	2	2	no	—
375	C₄²×C₆₇	—	2	4	no	—
376	C₄²×C₆₇	—	2	4	no	—
377	C₄²×C₆₇	—	2	2	no	—
378	C₄²×C₆₇	—	2	4	no	—
379	C₄²×C₆₇	—	2	4	no	—
380	C₄²×C₆₇	—	2	2	no	—
381	C₄²×C₆₇	—	4	2	no	—
382	C₄²×C₆₇	—	4	1	no	—
383	C₄²×C₆₇	C₂×D₄	1	4	yes	—
384	C₄²×C₆₇	C₂×D₄	1	8	yes	—
385	C₄²×C₆₇	#41	1	4	yes	—
386	C₂³×C₆₇	—	2	1	no	—
387	C₂³×C₆₇	—	2	1	no	—
388	C₂³×C₆₇	—	2	1	no	—
389	C₂³×C₆₇	—	2	1	no	—
390	C₂³×C₆₇	—	2	1	no	—
391	C₂³×C₆₇	—	2	1	no	—
392	C₂³×C₆₇	—	2	1	no	—
393	C₂³×C₆₇	—	2	1	no	—
394	C₂³×C₆₇	—	2	1	no	—
395	C₂³×C₆₇	—	2	1	no	—
396	C₂³×C₆₇	—	2	1	no	—
397	C₂³×C₆₇	—	2	1	no	—
398	C₂³×C₆₇	—	2	2	no	—
399	C₂³×C₆₇	—	2	2	no	—
400	C₂³×C₆₇	—	2	2	no	—
401	C₂³×C₆₇	—	2	2	no	—
402	C₂³×C₆₇	—	2	2	no	—
403	C₂³×C₆₇	—	2	2	no	—
404	C₂³×C₆₇	—	2	2	no	—
405	C₂³×C₆₇	C₂×#41	1	2	yes	—
406	C₂³×C₆₇	C₂×#41	1	2	yes	—
407	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
408	Q₈×C₆₇	—	2	8	no	—
409	Q₈×C₆₇	—	4	8	no	—
410	Q₈×C₆₇	—	4	4	no	—
411	D₄×C₆₇	—	2	8	no	—
412	D₄×C₆₇	—	4	8	no	—
413	D₄×C₆₇	—	4	8	no	—
414	D₄×C₆₇	—	4	4	no	—
415	C₂×C₄×C₆₇	—	2	1	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	2	no	—
421	C₂×C₄×C₆₇	—	2	2	no	—
422	C₂×C₄×C₆₇	—	2	2	no	—
423	C₂×C₄×C₆₇	—	2	1	no	—
424	C₂×C₄×C₆₇	—	2	2	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	1	no	—
433	C₂×C₄×C₆₇	—	2	8	no	—
434	C₂×C₄×C₆₇	—	2	1	no	—
435	C₂×C₄×C₆₇	—	2	1	no	—
436	C₂×C₄×C₆₇	—	2	1	no	—
437	C₂×C₄×C₆₇	—	2	1	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	1	no	—
444	C₂×C₄×C₆₇	—	2	2	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	1	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	2	no	—
455	C₂×C₄×C₆₇	—	2	1	no	—
456	C₂×C₄×C₆₇	—	2	1	no	—
457	C₂×C₄×C₆₇	—	2	2	no	—
458	C₂×C₄×C₆₇	—	2	1	no	—
459	C₂×C₄×C₆₇	—	2	2	no	—
460	C₂×C₄×C₆₇	—	2	1	no	—
461	C₂×C₄×C₆₇	—	4	4	no	—
462	C₂×C₄×C₆₇	—	4	4	no	—
463	C₂×C₄×C₆₇	—	4	4	no	—
464	C₂×C₄×C₆₇	—	4	4	no	—
465	C₂×C₄×C₆₇	—	4	4	no	—
466	C₂×C₄×C₆₇	—	4	8	no	—
467	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
468	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
469	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
470	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
471	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
472	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
473	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
474	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
475	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
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	C₂×#41	1	2	yes	—
481	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
482	C₂²×C₆₇	—	2	2	no	—
483	C₂²×C₆₇	—	2	2	no	—
484	C₂²×C₆₇	—	2	2	no	—
485	C₂²×C₆₇	—	2	2	no	—
486	C₂²×C₆₇	—	2	2	no	—
487	C₂²×C₆₇	—	2	2	no	—
488	C₂²×C₆₇	—	4	1	no	—
489	C₂²×C₆₇	—	4	1	no	—
490	C₂²×C₆₇	—	4	1	no	—
491	C₂²×C₆₇	—	4	1	no	—
492	C₂²×C₆₇	—	4	1	no	—
493	C₂²×C₆₇	—	4	1	no	—
494	C₂²×C₆₇	—	4	1	no	—
495	C₂²×C₆₇	—	4	1	no	—
496	C₂²×C₆₇	—	4	2	no	—
497	C₂²×C₆₇	—	4	2	no	—
498	C₂²×C₆₇	—	4	2	no	—
499	C₂²×C₆₇	—	4	2	no	—
500	C₂²×C₆₇	—	4	2	no	—
501	C₂²×C₆₇	—	4	2	no	—
502	C₂²×C₆₇	—	4	2	no	—
503	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
504	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
505	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
506	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
507	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
508	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
509	C₂²×C₆₇	#585	1	1	yes	characteristic
510	C₄×C₆₇	—	2	4	no	—
511	C₄×C₆₇	—	2	2	no	—
512	C₄×C₆₇	—	2	2	no	—
513	C₄×C₆₇	—	2	2	no	—
514	C₄×C₆₇	—	2	2	no	—
515	C₄×C₆₇	—	2	2	no	—
516	C₄×C₆₇	—	2	4	no	—
517	C₄×C₆₇	—	2	4	no	—
518	C₄×C₆₇	—	2	2	no	—
519	C₄×C₆₇	—	4	1	no	—
520	C₄×C₆₇	—	4	1	no	—
521	C₄×C₆₇	—	4	2	no	—
522	C₄×C₆₇	—	4	2	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	#532	1	4	yes	—
529	C₄×C₆₇	#548	1	4	yes	—
530	#34919	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
531	C₂×C₆₇	—	4	2	no	—
532	C₂×C₆₇	—	4	2	no	—
533	C₂×C₆₇	—	8	2	no	—
534	C₂×C₆₇	C₂×#532	1	1	yes	characteristic
535	C₂×C₆₇	#3444	1	1	yes	characteristic
536	C₂×C₆₇	#3461	1	1	yes	characteristic
537	C₂×C₆₇	C₂×#548	1	1	yes	characteristic
538	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
539	C₂×C₆₇	#3475	1	1	yes	characteristic
540	C₂×C₆₇	#3482	1	1	yes	characteristic
541	C₂×#533	C₂×C₆₇	1	1	yes	characteristic, complemented
542	C₂×#529	C₂×C₆₇	1	1	yes	characteristic, complemented
543	#2560	C₂×C₆₇	1	2	yes	complemented
544	#2558	C₂×C₆₇	1	2	yes	complemented
545	#2550	C₂×C₆₇	1	1	yes	characteristic, complemented
546	#2545	C₂×C₆₇	1	1	yes	characteristic, complemented
547	#2540	C₂×C₆₇	1	1	yes	characteristic
548	#2536	C₂×C₆₇	1	1	yes	characteristic, complemented
549	#2519	C₂×C₆₇	1	2	yes	complemented
550	#2491	C₂×C₆₇	1	1	yes	characteristic, complemented
551	#2489	C₂×C₆₇	1	1	yes	characteristic, complemented
552	#2461	C₂×C₆₇	1	2	yes	complemented
553	#2429	C₂×C₆₇	1	1	yes	characteristic, complemented
554	#2426	C₂×C₆₇	1	1	yes	characteristic, complemented
555	#2396	C₂×C₆₇	1	2	yes	complemented
556	#2392	C₂×C₆₇	1	2	yes	complemented
557	C₄×#124	C₂×C₆₇	1	2	yes	complemented
558	C₄×#124	C₂×C₆₇	1	1	yes	characteristic, complemented
559	C₄×C₂²⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
560	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
561	#2293	C₂×C₆₇	1	2	yes	complemented
562	C₄²×Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
563	C₄²×D₄	C₂×C₆₇	1	1	yes	characteristic, complemented
564	C₆₇	#34919	1	1	yes	characteristic, direct product factor, Sylow
565	#533	—	2	8	no	—
566	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
567	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
568	#529	—	2	8	no	—
569	C₂×#126	C₂²×C₆₇	1	2	yes	—
570	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
571	C₂×#125	C₂²×C₆₇	1	2	yes	—
572	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
573	C₂×#124	C₂²×C₆₇	1	2	yes	—
574	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
575	C₂×#123	C₂²×C₆₇	1	2	yes	—
576	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
577	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
578	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
579	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
580	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
581	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
582	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
583	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
584	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
585	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
586	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
587	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
588	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
589	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
590	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
591	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
592	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
593	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
594	C₂×#117	C₂²×C₆₇	1	2	yes	—
595	C₂×#117	C₂²×C₆₇	1	2	yes	—
596	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
597	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
598	#400	C₂²×C₆₇	1	2	yes	—
599	#399	C₂²×C₆₇	1	2	yes	—
600	#398	C₂²×C₆₇	1	2	yes	—
601	#398	C₂²×C₆₇	1	2	yes	—
602	#398	C₂²×C₆₇	1	2	yes	—
603	#397	C₂²×C₆₇	1	2	yes	—
604	#396	C₂²×C₆₇	1	2	yes	—
605	#396	C₂²×C₆₇	1	2	yes	—
606	#396	C₂²×C₆₇	1	2	yes	—
607	#396	C₂²×C₆₇	1	2	yes	—
608	#395	C₂²×C₆₇	1	2	yes	—
609	#394	C₂²×C₆₇	1	2	yes	—
610	#394	C₂²×C₆₇	1	2	yes	—
611	#394	C₂²×C₆₇	1	2	yes	—
612	#393	C₂²×C₆₇	1	2	yes	—
613	#392	C₂²×C₆₇	1	2	yes	—
614	#391	C₂²×C₆₇	1	2	yes	—
615	#391	C₂²×C₆₇	1	1	yes	characteristic
616	#391	C₂²×C₆₇	1	1	yes	characteristic
617	#390	C₂²×C₆₇	1	2	yes	—
618	#390	C₂²×C₆₇	1	2	yes	—
619	#390	C₂²×C₆₇	1	1	yes	characteristic
620	#390	C₂²×C₆₇	1	1	yes	characteristic
621	#390	C₂²×C₆₇	1	2	yes	—
622	#389	C₂²×C₆₇	1	1	yes	characteristic
623	#389	C₂²×C₆₇	1	2	yes	—
624	#389	C₂²×C₆₇	1	1	yes	characteristic
625	#389	C₂²×C₆₇	1	2	yes	—
626	#388	C₂²×C₆₇	1	2	yes	—
627	#388	C₂²×C₆₇	1	2	yes	—
628	#388	C₂²×C₆₇	1	2	yes	—
629	#388	C₂²×C₆₇	1	2	yes	—
630	#388	C₂²×C₆₇	1	2	yes	—
631	#388	C₂²×C₆₇	1	2	yes	—
632	#388	C₂²×C₆₇	1	2	yes	—
633	#388	C₂²×C₆₇	1	2	yes	—
634	#388	C₂²×C₆₇	1	2	yes	—
635	#388	C₂²×C₆₇	1	2	yes	—
636	#388	C₂²×C₆₇	1	2	yes	—
637	#387	C₂²×C₆₇	1	2	yes	—
638	#386	C₂²×C₆₇	1	2	yes	—
639	#385	C₂²×C₆₇	1	2	yes	—
640	#382	C₂²×C₆₇	1	2	yes	—
641	#382	C₂²×C₆₇	1	1	yes	characteristic
642	#380	C₂²×C₆₇	1	1	yes	characteristic
643	#380	C₂²×C₆₇	1	1	yes	characteristic
644	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
645	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
646	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
647	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
648	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
649	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
650	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
651	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
652	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
653	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
654	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
655	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
656	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
657	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
658	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
659	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
660	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
661	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
662	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
663	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
664	C₄³	C₂²×C₆₇	1	1	yes	characteristic
665	C₄³	C₂²×C₆₇	1	2	yes	—
666	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
667	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
668	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
669	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
670	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
671	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
672	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
673	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
674	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
675	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
676	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
677	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
678	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
679	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
680	C₄⋊Q₈	—	2	4	no	—
681	C₄⋊Q₈	—	2	4	no	—
682	#126	—	2	8	no	—
683	#125	—	2	4	no	—
684	#125	—	2	8	no	—
685	#124	—	2	4	no	—
686	#124	—	2	8	no	—
687	#124	—	2	4	no	—
688	#123	—	2	8	no	—
689	C₂²⋊Q₈	—	2	4	no	—
690	C₂²⋊Q₈	—	2	4	no	—
691	C₂²⋊Q₈	—	2	4	no	—
692	C₂²⋊Q₈	—	2	8	no	—
693	C₂²⋊Q₈	—	2	4	no	—
694	#121	—	2	4	no	—
695	#121	—	2	4	no	—
696	C₄×Q₈	—	2	4	no	—
697	C₄×Q₈	—	2	8	no	—
698	C₄×Q₈	—	2	4	no	—
699	C₄×Q₈	—	2	4	no	—
700	C₄×Q₈	D₄×C₆₇	1	8	yes	complemented
701	C₄×D₄	—	2	4	no	—
702	C₄×D₄	—	2	8	no	—
703	C₄×D₄	—	2	4	no	—
704	C₄×D₄	—	2	4	no	—
705	C₄×D₄	—	2	8	no	—
706	C₄×D₄	—	2	4	no	—
707	#117	—	2	8	no	—
708	#117	—	2	8	no	—
709	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
710	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
711	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
712	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
713	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
714	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
715	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
716	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
717	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
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	2	yes	—
722	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
723	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
724	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
725	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
726	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
727	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
728	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
729	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
730	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
731	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
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	2	yes	—
736	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
737	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
738	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
739	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
740	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
741	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
742	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
743	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
744	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
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	2	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
755	C₂×C₄²	—	2	4	no	—
756	C₂×C₄²	—	2	4	no	—
757	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
758	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
759	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
760	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
761	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
762	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
763	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
764	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
765	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
766	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
767	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
768	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
769	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
770	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
771	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
772	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
773	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
774	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
775	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
776	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
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	1	yes	characteristic
781	#95	C₂³×C₆₇	1	1	yes	characteristic
782	#95	C₂³×C₆₇	1	1	yes	characteristic
783	#95	C₂³×C₆₇	1	2	yes	—
784	#95	C₂³×C₆₇	1	2	yes	—
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	#95	C₂³×C₆₇	1	2	yes	—
792	#95	C₂³×C₆₇	1	2	yes	—
793	#95	C₂³×C₆₇	1	2	yes	—
794	#95	C₂³×C₆₇	1	2	yes	—
795	#95	C₂³×C₆₇	1	2	yes	—
796	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
797	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
798	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
799	C₂×Q₈	—	2	4	no	—
800	C₂×Q₈	—	2	2	no	—
801	C₂×Q₈	—	2	2	no	—
802	C₂×Q₈	—	2	2	no	—
803	C₂×Q₈	—	2	2	no	—
804	C₂×Q₈	—	2	4	no	—
805	C₂×Q₈	—	2	2	no	—
806	C₂×Q₈	—	4	2	no	—
807	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	—
808	C₂×D₄	—	2	2	no	—
809	C₂×D₄	—	2	2	no	—
810	C₂×D₄	—	2	4	no	—
811	C₂×D₄	—	2	4	no	—
812	C₂×D₄	—	2	4	no	—
813	C₂×D₄	—	2	2	no	—
814	C₂×D₄	—	2	2	no	—
815	C₂×D₄	—	2	4	no	—
816	C₂×D₄	—	2	2	no	—
817	C₂×D₄	—	2	2	no	—
818	C₂×D₄	—	4	2	no	—
819	C₂×D₄	—	4	2	no	—
820	C₂²×C₄	—	2	2	no	—
821	C₂²×C₄	—	2	2	no	—
822	C₂²×C₄	—	2	2	no	—
823	C₂²×C₄	—	2	2	no	—
824	C₂²×C₄	—	2	2	no	—
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	—	2	2	no	—
827	C₂²×C₄	—	2	2	no	—
828	C₂²×C₄	—	2	4	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	2	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	4	no	—
838	C₂²×C₄	—	4	1	no	—
839	C₂²×C₄	—	4	1	no	—
840	C₂²×C₄	#41×C₆₇	1	4	yes	—
841	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
842	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
843	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
844	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
845	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
846	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
847	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
848	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
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	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	1	yes	characteristic
856	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
857	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
858	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
859	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
860	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
861	C₄⋊C₄	—	2	4	no	—
862	C₄⋊C₄	—	2	4	no	—
863	C₄⋊C₄	—	2	4	no	—
864	C₄⋊C₄	—	2	4	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	4	no	—
867	C₄⋊C₄	—	2	4	no	—
868	C₄⋊C₄	—	2	4	no	—
869	C₄⋊C₄	—	2	4	no	—
870	C₄⋊C₄	—	2	4	no	—
871	C₄⋊C₄	—	2	2	no	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	2	4	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	—	2	4	no	—
877	C₄⋊C₄	—	2	4	no	—
878	C₄⋊C₄	—	2	2	no	—
879	C₄⋊C₄	—	2	4	no	—
880	C₄⋊C₄	—	4	2	no	—
881	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
882	C₄⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
883	C₄⋊C₄	#41×C₆₇	1	4	yes	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	4	no	—
886	C₂²⋊C₄	—	2	4	no	—
887	C₂²⋊C₄	—	2	4	no	—
888	C₂²⋊C₄	—	2	4	no	—
889	C₂²⋊C₄	—	2	4	no	—
890	C₂²⋊C₄	—	2	4	no	—
891	C₂²⋊C₄	—	2	4	no	—
892	C₂²⋊C₄	—	2	4	no	—
893	C₂²⋊C₄	—	2	4	no	—
894	C₂²⋊C₄	—	2	2	no	—
895	C₂²⋊C₄	—	2	4	no	—
896	C₂²⋊C₄	—	2	2	no	—
897	C₂²⋊C₄	—	2	2	no	—
898	C₂²⋊C₄	—	2	2	no	—
899	C₂²⋊C₄	—	2	4	no	—
900	C₂²⋊C₄	—	2	4	no	—
901	C₂²⋊C₄	—	2	4	no	—
902	C₂²⋊C₄	—	2	4	no	—
903	C₂²⋊C₄	—	2	4	no	—
904	C₂²⋊C₄	—	2	4	no	—
905	C₂²⋊C₄	—	4	2	no	—
906	C₂²⋊C₄	#41×C₆₇	1	4	yes	—
907	C₄²	—	2	2	no	—
908	C₄²	—	2	2	no	—
909	C₄²	—	2	2	no	—
910	C₄²	—	2	2	no	—
911	C₄²	—	2	2	no	—
912	C₄²	—	2	2	no	—
913	C₄²	—	2	4	no	—
914	C₄²	—	2	2	no	—
915	C₄²	—	2	2	no	—
916	C₄²	—	2	4	no	—
917	C₄²	—	2	4	no	—
918	C₄²	—	2	2	no	—
919	C₄²	—	2	4	no	—
920	C₄²	—	2	4	no	—
921	C₄²	—	2	2	no	—
922	C₄²	—	4	2	no	—
923	C₄²	—	4	1	no	—
924	C₄²	C₂×D₄×C₆₇	1	4	yes	—
925	C₄²	C₂×D₄×C₆₇	1	8	yes	—
926	C₄²	#41×C₆₇	1	4	yes	—
927	C₂³	—	2	1	no	—
928	C₂³	—	2	1	no	—
929	C₂³	—	2	1	no	—
930	C₂³	—	2	1	no	—
931	C₂³	—	2	1	no	—
932	C₂³	—	2	1	no	—
933	C₂³	—	2	1	no	—
934	C₂³	—	2	1	no	—
935	C₂³	—	2	1	no	—
936	C₂³	—	2	1	no	—
937	C₂³	—	2	1	no	—
938	C₂³	—	2	1	no	—
939	C₂³	—	2	2	no	—
940	C₂³	—	2	2	no	—
941	C₂³	—	2	2	no	—
942	C₂³	—	2	2	no	—
943	C₂³	—	2	2	no	—
944	C₂³	—	2	2	no	—
945	C₂³	—	2	2	no	—
946	C₂³	C₂×#41×C₆₇	1	2	yes	—
947	C₂³	C₂×#41×C₆₇	1	2	yes	—
948	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
949	Q₈	—	2	8	no	—
950	Q₈	—	4	8	no	—
951	Q₈	—	4	4	no	—
952	D₄	—	2	8	no	—
953	D₄	—	4	8	no	—
954	D₄	—	4	8	no	—
955	D₄	—	4	4	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	2	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	2	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	8	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	2	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	4	4	no	—
1003	C₂×C₄	—	4	4	no	—
1004	C₂×C₄	—	4	4	no	—
1005	C₂×C₄	—	4	4	no	—
1006	C₂×C₄	—	4	4	no	—
1007	C₂×C₄	—	4	8	no	—
1008	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1009	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
1010	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
1011	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1012	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1013	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1014	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1015	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
1016	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1017	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1018	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1019	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1020	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1021	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1022	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
1023	C₂²	—	2	2	no	—
1024	C₂²	—	2	2	no	—
1025	C₂²	—	2	2	no	—
1026	C₂²	—	2	2	no	—
1027	C₂²	—	2	2	no	—
1028	C₂²	—	2	2	no	—
1029	C₂²	—	4	1	no	—
1030	C₂²	—	4	1	no	—
1031	C₂²	—	4	1	no	—
1032	C₂²	—	4	1	no	—
1033	C₂²	—	4	1	no	—
1034	C₂²	—	4	1	no	—
1035	C₂²	—	4	1	no	—
1036	C₂²	—	4	1	no	—
1037	C₂²	—	4	2	no	—
1038	C₂²	—	4	2	no	—
1039	C₂²	—	4	2	no	—
1040	C₂²	—	4	2	no	—
1041	C₂²	—	4	2	no	—
1042	C₂²	—	4	2	no	—
1043	C₂²	—	4	2	no	—
1044	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1045	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1046	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1047	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1048	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1049	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
1050	C₂²	#585×C₆₇	1	1	yes	characteristic
1051	C₄	—	2	4	no	—
1052	C₄	—	2	2	no	—
1053	C₄	—	2	2	no	—
1054	C₄	—	2	2	no	—
1055	C₄	—	2	2	no	—
1056	C₄	—	2	2	no	—
1057	C₄	—	2	4	no	—
1058	C₄	—	2	4	no	—
1059	C₄	—	2	2	no	—
1060	C₄	—	4	1	no	—
1061	C₄	—	4	1	no	—
1062	C₄	—	4	2	no	—
1063	C₄	—	4	2	no	—
1064	C₄	—	4	1	no	—
1065	C₄	—	4	2	no	—
1066	C₄	—	4	1	no	—
1067	C₄	—	4	2	no	—
1068	C₄	—	4	1	no	—
1069	C₄	#532×C₆₇	1	4	yes	—
1070	C₄	#548×C₆₇	1	4	yes	—
1071	C₂	—	4	2	no	—
1072	C₂	—	4	2	no	—
1073	C₂	—	8	2	no	—
1074	C₂	C₂×#532×C₆₇	1	1	yes	characteristic
1075	C₂	C₆₇×#3444	1	1	yes	characteristic
1076	C₂	C₆₇×#3461	1	1	yes	characteristic
1077	C₂	C₂×#548×C₆₇	1	1	yes	characteristic
1078	C₂	D₄×#41×C₆₇	1	1	yes	characteristic
1079	C₂	C₆₇×#3475	1	1	yes	characteristic
1080	C₂	C₆₇×#3482	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
socle	C₂³×C₆₇	C₂⁵
prime radical	C₆₇×#2540	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#533×C₆₇	C₂	semidirect
2. C₂×#529×C₆₇	C₂	semidirect
3. C₆₇×#2560	C₂	semidirect
4. C₆₇×#2558	C₂	semidirect
5. C₆₇×#2550	C₂	semidirect
6. C₆₇×#2545	C₂	semidirect
8. C₆₇×#2536	C₂	semidirect
9. C₆₇×#2519	C₂	semidirect
10. C₆₇×#2491	C₂	semidirect
11. C₆₇×#2489	C₂	semidirect
12. C₆₇×#2461	C₂	semidirect
13. C₆₇×#2429	C₂	semidirect
14. C₆₇×#2426	C₂	semidirect
15. C₆₇×#2396	C₂	semidirect
16. C₆₇×#2392	C₂	semidirect
17. C₄×#124×C₆₇	C₂	semidirect
18. C₄×#124×C₆₇	C₂	semidirect
19. C₄×C₂²⋊Q₈×C₆₇	C₂	semidirect
20. C₄×#121×C₆₇	C₂	semidirect
21. C₆₇×#2293	C₂	semidirect
22. C₄²×Q₈×C₆₇	C₂	semidirect
23. C₄²×D₄×C₆₇	C₂	semidirect
159. C₄×Q₈×C₆₇	D₄	semidirect
530. #34919	C₆₇	direct (N × H)
541. C₂×#533	C₂×C₆₇	semidirect
542. C₂×#529	C₂×C₆₇	semidirect
543. #2560	C₂×C₆₇	semidirect
544. #2558	C₂×C₆₇	semidirect
545. #2550	C₂×C₆₇	semidirect
546. #2545	C₂×C₆₇	semidirect
548. #2536	C₂×C₆₇	semidirect
549. #2519	C₂×C₆₇	semidirect
550. #2491	C₂×C₆₇	semidirect
551. #2489	C₂×C₆₇	semidirect
552. #2461	C₂×C₆₇	semidirect
553. #2429	C₂×C₆₇	semidirect
554. #2426	C₂×C₆₇	semidirect
555. #2396	C₂×C₆₇	semidirect
556. #2392	C₂×C₆₇	semidirect
557. C₄×#124	C₂×C₆₇	semidirect
558. C₄×#124	C₂×C₆₇	semidirect
559. C₄×C₂²⋊Q₈	C₂×C₆₇	semidirect
560. C₄×#121	C₂×C₆₇	semidirect
561. #2293	C₂×C₆₇	semidirect
562. C₄²×Q₈	C₂×C₆₇	semidirect
563. C₄²×D₄	C₂×C₆₇	semidirect
564. C₆₇	#34919	direct (N × H)
700. C₄×Q₈	D₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#533×C₆₇	2
C₂×#529×C₆₇	2
C₆₇×#2560	2
C₆₇×#2558	2
C₆₇×#2550	2
C₆₇×#2545	2
C₆₇×#2540	2
C₆₇×#2536	2
C₆₇×#2519	2
C₆₇×#2491	2
C₆₇×#2489	2
C₆₇×#2461	2
C₆₇×#2429	2
C₆₇×#2426	2
C₆₇×#2396	2
C₆₇×#2392	2
C₄×#124×C₆₇	2
C₄×C₂²⋊Q₈×C₆₇	2
C₄×#121×C₆₇	2
C₆₇×#2293	2
C₄²×Q₈×C₆₇	2
C₄²×D₄×C₆₇	2
#34919	67

Subgroups — C67×#34919 #30714170

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34919 #30714170