Subgroups — C₆₇×#35156 #30714407

Order 17152.

2494 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#540×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2854	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2853	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2635	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2630	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2476	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2470	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2456	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2455	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2453	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2445	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2441	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2431	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2426	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2422	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2414	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2407	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2326	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2323	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2319	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2290	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
25	#540×C₆₇	—	2	8	no	—
26	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×#123×C₆₇	C₂²	1	2	yes	—
30	C₂×#123×C₆₇	C₂²	1	2	yes	—
31	C₂×#123×C₆₇	C₂²	1	2	yes	—
32	C₂×#123×C₆₇	C₂²	1	2	yes	—
33	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×#121×C₆₇	C₂²	1	2	yes	—
36	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#121×C₆₇	C₂²	1	2	yes	—
39	C₄×#41×C₆₇	—	2	8	no	—
40	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
45	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
47	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
48	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
49	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
50	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
51	C₂×#117×C₆₇	C₂²	1	2	yes	—
52	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
53	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
54	#400×C₆₇	C₂²	1	2	yes	—
55	#399×C₆₇	C₂²	1	2	yes	—
56	#398×C₆₇	C₂²	1	2	yes	—
57	#397×C₆₇	C₂²	1	2	yes	—
58	#396×C₆₇	C₂²	1	2	yes	—
59	#396×C₆₇	C₂²	1	2	yes	—
60	#394×C₆₇	C₂²	1	2	yes	—
61	#394×C₆₇	C₂²	1	2	yes	—
62	#394×C₆₇	C₂²	1	2	yes	—
63	#394×C₆₇	C₂²	1	2	yes	—
64	#394×C₆₇	C₂²	1	2	yes	—
65	#394×C₆₇	C₂²	1	2	yes	—
66	#392×C₆₇	C₂²	1	2	yes	—
67	#392×C₆₇	C₂²	1	2	yes	—
68	#392×C₆₇	C₂²	1	2	yes	—
69	#392×C₆₇	C₂²	1	2	yes	—
70	#391×C₆₇	C₂²	1	1	yes	characteristic
71	#391×C₆₇	C₂²	1	1	yes	characteristic
72	#390×C₆₇	C₂²	1	1	yes	characteristic
73	#390×C₆₇	C₂²	1	1	yes	characteristic
74	#390×C₆₇	C₂²	1	1	yes	characteristic
75	#390×C₆₇	C₂²	1	1	yes	characteristic
76	#390×C₆₇	C₂²	1	2	yes	—
77	#390×C₆₇	C₂²	1	2	yes	—
78	#389×C₆₇	C₂²	1	1	yes	characteristic
79	#389×C₆₇	C₂²	1	1	yes	characteristic
80	#389×C₆₇	C₂²	1	1	yes	characteristic
81	#389×C₆₇	C₂²	1	1	yes	characteristic
82	#389×C₆₇	C₂²	1	2	yes	—
83	#389×C₆₇	C₂²	1	2	yes	—
84	#389×C₆₇	C₂²	1	2	yes	—
85	#388×C₆₇	C₂²	1	1	yes	characteristic
86	#388×C₆₇	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
97	#387×C₆₇	C₂²	1	1	yes	characteristic
98	#387×C₆₇	C₂²	1	2	yes	—
99	#387×C₆₇	C₂²	1	2	yes	—
100	#387×C₆₇	C₂²	1	2	yes	—
101	#386×C₆₇	C₂²	1	1	yes	characteristic
102	#386×C₆₇	C₂²	1	1	yes	characteristic
103	#386×C₆₇	C₂²	1	2	yes	—
104	#386×C₆₇	C₂²	1	2	yes	—
105	#386×C₆₇	C₂²	1	2	yes	—
106	#386×C₆₇	C₂²	1	2	yes	—
107	#386×C₆₇	C₂²	1	2	yes	—
108	#385×C₆₇	C₂²	1	1	yes	characteristic
109	#385×C₆₇	C₂²	1	1	yes	characteristic
110	#385×C₆₇	C₂²	1	2	yes	—
111	#385×C₆₇	C₂²	1	2	yes	—
112	#385×C₆₇	C₂²	1	2	yes	—
113	#385×C₆₇	C₂²	1	2	yes	—
114	#384×C₆₇	C₂²	1	1	yes	characteristic
115	#381×C₆₇	C₂²	1	2	yes	—
116	#380×C₆₇	C₂²	1	1	yes	characteristic
117	#380×C₆₇	C₂²	1	2	yes	—
118	#380×C₆₇	C₂²	1	1	yes	characteristic
119	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
120	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
122	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
123	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
124	#376×C₆₇	C₂²	1	1	yes	characteristic
125	C₂×#41×C₆₇	—	2	4	no	—
126	C₂×#41×C₆₇	—	2	4	no	—
127	C₂×#41×C₆₇	—	2	4	no	—
128	C₂²×Q₈×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	1	yes	characteristic
132	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
133	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
135	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
136	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
137	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
138	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
139	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
142	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
145	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
146	#127×C₆₇	—	2	4	no	—
147	#125×C₆₇	—	2	4	no	—
148	#124×C₆₇	—	2	4	no	—
149	#123×C₆₇	—	2	8	no	—
150	#123×C₆₇	—	2	8	no	—
151	#123×C₆₇	—	4	4	no	—
152	#123×C₆₇	—	4	4	no	—
153	C₂²⋊Q₈×C₆₇	—	2	4	no	—
154	#121×C₆₇	—	2	4	no	—
155	#121×C₆₇	—	2	8	no	—
156	#121×C₆₇	—	2	4	no	—
157	#121×C₆₇	—	2	4	no	—
158	#121×C₆₇	—	2	8	no	—
159	C₄×Q₈×C₆₇	—	2	4	no	—
160	C₄×Q₈×C₆₇	—	2	4	no	—
161	C₄×D₄×C₆₇	—	2	4	no	—
162	C₄×D₄×C₆₇	—	2	8	no	—
163	C₄×D₄×C₆₇	—	2	4	no	—
164	C₄×D₄×C₆₇	—	2	8	no	—
165	C₄×D₄×C₆₇	—	2	4	no	—
166	C₄×D₄×C₆₇	—	4	4	no	—
167	C₄×D₄×C₆₇	D₄	1	8	yes	complemented
168	#117×C₆₇	—	2	4	no	—
169	#117×C₆₇	—	2	8	no	—
170	#117×C₆₇	—	2	4	no	—
171	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
183	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
184	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
188	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
213	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
220	C₂×C₄²×C₆₇	—	2	8	no	—
221	C₂×C₄²×C₆₇	—	2	4	no	—
222	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
225	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
227	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
228	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
232	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
233	#95×C₆₇	C₂³	1	1	yes	characteristic
234	#95×C₆₇	C₂³	1	1	yes	characteristic
235	#95×C₆₇	C₂³	1	1	yes	characteristic
236	#95×C₆₇	C₂³	1	1	yes	characteristic
237	#95×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
245	#95×C₆₇	C₂³	1	1	yes	characteristic
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	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
255	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
256	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
257	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
258	#41×C₆₇	—	2	32	no	—
259	C₂×Q₈×C₆₇	—	2	2	no	—
260	C₂×Q₈×C₆₇	—	2	2	no	—
261	C₂×Q₈×C₆₇	#41	1	4	yes	—
262	C₂×D₄×C₆₇	—	2	4	no	—
263	C₂×D₄×C₆₇	—	2	4	no	—
264	C₂×D₄×C₆₇	—	2	2	no	—
265	C₂×D₄×C₆₇	—	2	4	no	—
266	C₂×D₄×C₆₇	—	2	4	no	—
267	C₂×D₄×C₆₇	—	2	4	no	—
268	C₂×D₄×C₆₇	—	2	4	no	—
269	C₂×D₄×C₆₇	—	2	2	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	2	no	—
275	C₂×D₄×C₆₇	—	2	2	no	—
276	C₂×D₄×C₆₇	—	4	2	no	—
277	C₂×D₄×C₆₇	—	4	1	no	—
278	C₂×D₄×C₆₇	—	4	1	no	—
279	C₂×D₄×C₆₇	—	4	2	no	—
280	C₂×D₄×C₆₇	—	4	2	no	—
281	C₂×D₄×C₆₇	—	4	2	no	—
282	C₂×D₄×C₆₇	—	4	2	no	—
283	C₂×D₄×C₆₇	—	4	2	no	—
284	C₂×D₄×C₆₇	—	4	2	no	—
285	C₂×D₄×C₆₇	—	4	2	no	—
286	C₂×D₄×C₆₇	—	4	2	no	—
287	C₂×D₄×C₆₇	—	4	2	no	—
288	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
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	4	no	—
293	C₂²×C₄×C₆₇	—	2	2	no	—
294	C₂²×C₄×C₆₇	—	2	4	no	—
295	C₂²×C₄×C₆₇	—	2	2	no	—
296	C₂²×C₄×C₆₇	—	2	2	no	—
297	C₂²×C₄×C₆₇	—	2	2	no	—
298	C₂²×C₄×C₆₇	—	2	2	no	—
299	C₂²×C₄×C₆₇	—	2	2	no	—
300	C₂²×C₄×C₆₇	—	2	2	no	—
301	C₂²×C₄×C₆₇	—	2	4	no	—
302	C₂²×C₄×C₆₇	—	2	4	no	—
303	C₂²×C₄×C₆₇	—	4	2	no	—
304	C₂²×C₄×C₆₇	—	4	2	no	—
305	C₂²×C₄×C₆₇	—	4	1	no	—
306	C₂²×C₄×C₆₇	—	4	1	no	—
307	C₂²×C₄×C₆₇	—	4	2	no	—
308	C₂²×C₄×C₆₇	—	4	1	no	—
309	C₂²×C₄×C₆₇	—	4	2	no	—
310	C₂²×C₄×C₆₇	—	4	2	no	—
311	C₂²×C₄×C₆₇	C₂×D₄	1	8	yes	—
312	C₂²×C₄×C₆₇	#41	1	4	yes	—
313	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
328	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
330	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
332	C₄⋊C₄×C₆₇	—	2	4	no	—
333	C₄⋊C₄×C₆₇	—	2	4	no	—
334	C₄⋊C₄×C₆₇	—	2	2	no	—
335	C₄⋊C₄×C₆₇	—	2	2	no	—
336	C₄⋊C₄×C₆₇	—	2	2	no	—
337	C₄⋊C₄×C₆₇	—	2	2	no	—
338	C₄⋊C₄×C₆₇	—	2	4	no	—
339	C₄⋊C₄×C₆₇	—	2	4	no	—
340	C₄⋊C₄×C₆₇	—	2	2	no	—
341	C₄⋊C₄×C₆₇	—	2	2	no	—
342	C₄⋊C₄×C₆₇	—	2	2	no	—
343	C₄⋊C₄×C₆₇	—	2	4	no	—
344	C₄⋊C₄×C₆₇	—	2	4	no	—
345	C₄⋊C₄×C₆₇	—	2	2	no	—
346	C₄⋊C₄×C₆₇	—	4	2	no	—
347	C₄⋊C₄×C₆₇	—	4	2	no	—
348	C₄⋊C₄×C₆₇	—	4	2	no	—
349	C₄⋊C₄×C₆₇	—	4	1	no	—
350	C₄⋊C₄×C₆₇	—	4	2	no	—
351	C₄⋊C₄×C₆₇	—	4	2	no	—
352	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
353	C₂²⋊C₄×C₆₇	—	2	4	no	—
354	C₂²⋊C₄×C₆₇	—	2	4	no	—
355	C₂²⋊C₄×C₆₇	—	2	2	no	—
356	C₂²⋊C₄×C₆₇	—	2	4	no	—
357	C₂²⋊C₄×C₆₇	—	2	2	no	—
358	C₂²⋊C₄×C₆₇	—	2	2	no	—
359	C₂²⋊C₄×C₆₇	—	2	4	no	—
360	C₂²⋊C₄×C₆₇	—	2	4	no	—
361	C₂²⋊C₄×C₆₇	—	2	2	no	—
362	C₂²⋊C₄×C₆₇	—	2	4	no	—
363	C₂²⋊C₄×C₆₇	—	2	4	no	—
364	C₂²⋊C₄×C₆₇	—	2	4	no	—
365	C₂²⋊C₄×C₆₇	—	2	4	no	—
366	C₂²⋊C₄×C₆₇	—	2	4	no	—
367	C₂²⋊C₄×C₆₇	—	2	2	no	—
368	C₂²⋊C₄×C₆₇	—	4	1	no	—
369	C₂²⋊C₄×C₆₇	—	4	2	no	—
370	C₂²⋊C₄×C₆₇	—	4	2	no	—
371	C₂²⋊C₄×C₆₇	—	4	2	no	—
372	C₂²⋊C₄×C₆₇	—	4	2	no	—
373	C₂²⋊C₄×C₆₇	—	4	1	no	—
374	C₂²⋊C₄×C₆₇	—	4	1	no	—
375	C₂²⋊C₄×C₆₇	—	4	2	no	—
376	C₂²⋊C₄×C₆₇	—	4	2	no	—
377	C₂²⋊C₄×C₆₇	—	4	2	no	—
378	C₂²⋊C₄×C₆₇	—	4	2	no	—
379	C₂²⋊C₄×C₆₇	—	4	2	no	—
380	C₂²⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
381	C₄²×C₆₇	—	2	2	no	—
382	C₄²×C₆₇	—	2	4	no	—
383	C₄²×C₆₇	—	2	2	no	—
384	C₄²×C₆₇	—	2	4	no	—
385	C₄²×C₆₇	—	2	2	no	—
386	C₄²×C₆₇	—	2	4	no	—
387	C₄²×C₆₇	—	2	2	no	—
388	C₄²×C₆₇	—	2	2	no	—
389	C₄²×C₆₇	—	2	2	no	—
390	C₄²×C₆₇	—	4	2	no	—
391	C₄²×C₆₇	C₂×D₄	1	4	yes	—
392	C₂³×C₆₇	—	2	1	no	—
393	C₂³×C₆₇	—	2	2	no	—
394	C₂³×C₆₇	—	2	2	no	—
395	C₂³×C₆₇	—	2	1	no	—
396	C₂³×C₆₇	—	2	1	no	—
397	C₂³×C₆₇	—	2	2	no	—
398	C₂³×C₆₇	—	2	1	no	—
399	C₂³×C₆₇	—	2	1	no	—
400	C₂³×C₆₇	—	2	2	no	—
401	C₂³×C₆₇	—	2	2	no	—
402	C₂³×C₆₇	—	2	1	no	—
403	C₂³×C₆₇	—	2	2	no	—
404	C₂³×C₆₇	—	2	1	no	—
405	C₂³×C₆₇	—	2	2	no	—
406	C₂³×C₆₇	—	2	1	no	—
407	C₂³×C₆₇	—	2	2	no	—
408	C₂³×C₆₇	—	2	1	no	—
409	C₂³×C₆₇	—	2	2	no	—
410	C₂³×C₆₇	—	2	1	no	—
411	C₂³×C₆₇	—	2	2	no	—
412	C₂³×C₆₇	—	2	2	no	—
413	C₂³×C₆₇	—	2	2	no	—
414	C₂³×C₆₇	—	2	1	no	—
415	C₂³×C₆₇	—	2	1	no	—
416	C₂³×C₆₇	—	2	1	no	—
417	C₂³×C₆₇	—	2	2	no	—
418	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
419	C₂³×C₆₇	C₂×#41	1	2	yes	—
420	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
421	Q₈×C₆₇	—	2	8	no	—
422	D₄×C₆₇	—	2	16	no	—
423	D₄×C₆₇	—	2	8	no	—
424	D₄×C₆₇	—	4	4	no	—
425	D₄×C₆₇	—	4	8	no	—
426	D₄×C₆₇	—	4	4	no	—
427	D₄×C₆₇	—	8	4	no	—
428	D₄×C₆₇	—	8	4	no	—
429	D₄×C₆₇	—	8	4	no	—
430	D₄×C₆₇	—	8	4	no	—
431	C₂×C₄×C₆₇	—	2	16	no	—
432	C₂×C₄×C₆₇	—	2	1	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	2	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	1	no	—
441	C₂×C₄×C₆₇	—	2	1	no	—
442	C₂×C₄×C₆₇	—	2	1	no	—
443	C₂×C₄×C₆₇	—	2	1	no	—
444	C₂×C₄×C₆₇	—	2	8	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	—	2	1	no	—
450	C₂×C₄×C₆₇	—	2	2	no	—
451	C₂×C₄×C₆₇	—	2	1	no	—
452	C₂×C₄×C₆₇	—	2	1	no	—
453	C₂×C₄×C₆₇	—	2	1	no	—
454	C₂×C₄×C₆₇	—	2	1	no	—
455	C₂×C₄×C₆₇	—	2	2	no	—
456	C₂×C₄×C₆₇	—	2	1	no	—
457	C₂×C₄×C₆₇	—	2	2	no	—
458	C₂×C₄×C₆₇	—	2	1	no	—
459	C₂×C₄×C₆₇	—	2	2	no	—
460	C₂×C₄×C₆₇	—	2	2	no	—
461	C₂×C₄×C₆₇	—	2	1	no	—
462	C₂×C₄×C₆₇	—	2	1	no	—
463	C₂×C₄×C₆₇	—	2	2	no	—
464	C₂×C₄×C₆₇	—	2	2	no	—
465	C₂×C₄×C₆₇	—	2	1	no	—
466	C₂×C₄×C₆₇	—	2	1	no	—
467	C₂×C₄×C₆₇	—	2	2	no	—
468	C₂×C₄×C₆₇	—	2	1	no	—
469	C₂×C₄×C₆₇	—	2	1	no	—
470	C₂×C₄×C₆₇	—	2	1	no	—
471	C₂×C₄×C₆₇	—	2	1	no	—
472	C₂×C₄×C₆₇	—	2	1	no	—
473	C₂×C₄×C₆₇	—	2	1	no	—
474	C₂×C₄×C₆₇	—	2	2	no	—
475	C₂×C₄×C₆₇	—	2	2	no	—
476	C₂×C₄×C₆₇	—	2	1	no	—
477	C₂×C₄×C₆₇	—	2	1	no	—
478	C₂×C₄×C₆₇	—	2	1	no	—
479	C₂×C₄×C₆₇	—	2	2	no	—
480	C₂×C₄×C₆₇	—	2	1	no	—
481	C₂×C₄×C₆₇	—	4	8	no	—
482	C₂×C₄×C₆₇	—	4	4	no	—
483	C₂×C₄×C₆₇	—	4	8	no	—
484	C₂×C₄×C₆₇	—	4	4	no	—
485	C₂×C₄×C₆₇	—	4	4	no	—
486	C₂×C₄×C₆₇	—	8	4	no	—
487	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
488	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
489	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
490	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
491	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
492	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
493	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
494	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
495	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
496	C₂²×C₆₇	—	2	4	no	—
497	C₂²×C₆₇	—	2	2	no	—
498	C₂²×C₆₇	—	2	2	no	—
499	C₂²×C₆₇	—	2	2	no	—
500	C₂²×C₆₇	—	2	4	no	—
501	C₂²×C₆₇	—	2	4	no	—
502	C₂²×C₆₇	—	4	2	no	—
503	C₂²×C₆₇	—	4	2	no	—
504	C₂²×C₆₇	—	4	1	no	—
505	C₂²×C₆₇	—	4	1	no	—
506	C₂²×C₆₇	—	4	2	no	—
507	C₂²×C₆₇	—	4	1	no	—
508	C₂²×C₆₇	—	4	2	no	—
509	C₂²×C₆₇	—	4	1	no	—
510	C₂²×C₆₇	—	4	1	no	—
511	C₂²×C₆₇	—	4	2	no	—
512	C₂²×C₆₇	—	4	1	no	—
513	C₂²×C₆₇	—	4	2	no	—
514	C₂²×C₆₇	—	4	2	no	—
515	C₂²×C₆₇	—	4	1	no	—
516	C₂²×C₆₇	—	4	1	no	—
517	C₂²×C₆₇	—	4	2	no	—
518	C₂²×C₆₇	—	4	2	no	—
519	C₂²×C₆₇	—	4	1	no	—
520	C₂²×C₆₇	—	4	1	no	—
521	C₂²×C₆₇	—	4	2	no	—
522	C₂²×C₆₇	—	4	1	no	—
523	C₂²×C₆₇	—	4	2	no	—
524	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
525	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
526	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
527	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
528	C₂²×C₆₇	#585	1	1	yes	characteristic
529	C₂²×C₆₇	#585	1	1	yes	characteristic
530	C₂²×C₆₇	#585	1	1	yes	characteristic
531	C₄×C₆₇	—	2	2	no	—
532	C₄×C₆₇	—	2	4	no	—
533	C₄×C₆₇	—	2	2	no	—
534	C₄×C₆₇	—	2	4	no	—
535	C₄×C₆₇	—	2	2	no	—
536	C₄×C₆₇	—	2	2	no	—
537	C₄×C₆₇	—	4	1	no	—
538	C₄×C₆₇	—	4	1	no	—
539	C₄×C₆₇	—	4	1	no	—
540	C₄×C₆₇	—	4	2	no	—
541	C₄×C₆₇	—	4	1	no	—
542	C₄×C₆₇	—	4	1	no	—
543	C₄×C₆₇	—	4	2	no	—
544	C₄×C₆₇	—	4	2	no	—
545	C₄×C₆₇	—	4	1	no	—
546	C₄×C₆₇	—	4	1	no	—
547	C₄×C₆₇	—	4	2	no	—
548	C₄×C₆₇	—	4	1	no	—
549	C₄×C₆₇	#525	1	4	yes	—
550	#35156	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
551	C₂×C₆₇	—	4	4	no	—
552	C₂×C₆₇	—	4	2	no	—
553	C₂×C₆₇	—	8	1	no	—
554	C₂×C₆₇	—	8	2	no	—
555	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
556	C₂×C₆₇	#3455	1	1	yes	characteristic
557	C₂×C₆₇	#3460	1	1	yes	characteristic
558	C₂×C₆₇	#3485	1	1	yes	characteristic
559	C₂×C₆₇	#3488	1	1	yes	characteristic
560	C₂×C₆₇	#3517	1	1	yes	characteristic
561	C₂×C₆₇	#3524	1	1	yes	characteristic
562	C₂×#540	C₂×C₆₇	1	1	yes	characteristic, complemented
563	C₂×C₄×#41	C₂×C₆₇	1	1	yes	characteristic, complemented
564	#2854	C₂×C₆₇	1	2	yes	complemented
565	#2853	C₂×C₆₇	1	2	yes	complemented
566	#2635	C₂×C₆₇	1	2	yes	complemented
567	#2630	C₂×C₆₇	1	2	yes	complemented
568	#2476	C₂×C₆₇	1	2	yes	complemented
569	#2470	C₂×C₆₇	1	2	yes	complemented
570	#2456	C₂×C₆₇	1	2	yes	complemented
571	#2455	C₂×C₆₇	1	2	yes	complemented
572	#2453	C₂×C₆₇	1	1	yes	characteristic, complemented
573	#2445	C₂×C₆₇	1	1	yes	characteristic, complemented
574	#2441	C₂×C₆₇	1	1	yes	characteristic, complemented
575	#2431	C₂×C₆₇	1	1	yes	characteristic, complemented
576	#2426	C₂×C₆₇	1	1	yes	characteristic, complemented
577	#2422	C₂×C₆₇	1	1	yes	characteristic, complemented
578	#2414	C₂×C₆₇	1	1	yes	characteristic, complemented
579	#2407	C₂×C₆₇	1	1	yes	characteristic, complemented
580	#2326	C₂×C₆₇	1	1	yes	characteristic, complemented
581	#2323	C₂×C₆₇	1	1	yes	characteristic, complemented
582	#2319	C₂×C₆₇	1	1	yes	characteristic, complemented
583	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
584	#2290	C₂×C₆₇	1	1	yes	characteristic, complemented
585	C₆₇	#35156	1	1	yes	characteristic, direct product factor, Sylow
586	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
587	#540	—	2	8	no	—
588	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
589	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
590	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
591	C₂×#123	C₂²×C₆₇	1	2	yes	—
592	C₂×#123	C₂²×C₆₇	1	2	yes	—
593	C₂×#123	C₂²×C₆₇	1	2	yes	—
594	C₂×#123	C₂²×C₆₇	1	2	yes	—
595	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
596	C₂×#121	C₂²×C₆₇	1	2	yes	—
597	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
598	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
599	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
600	C₂×#121	C₂²×C₆₇	1	2	yes	—
601	C₄×#41	—	2	8	no	—
602	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
603	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
604	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
605	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
606	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
607	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
608	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
609	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
610	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
611	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
612	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
613	C₂×#117	C₂²×C₆₇	1	2	yes	—
614	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
615	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
616	#400	C₂²×C₆₇	1	2	yes	—
617	#399	C₂²×C₆₇	1	2	yes	—
618	#398	C₂²×C₆₇	1	2	yes	—
619	#397	C₂²×C₆₇	1	2	yes	—
620	#396	C₂²×C₆₇	1	2	yes	—
621	#396	C₂²×C₆₇	1	2	yes	—
622	#394	C₂²×C₆₇	1	2	yes	—
623	#394	C₂²×C₆₇	1	2	yes	—
624	#394	C₂²×C₆₇	1	2	yes	—
625	#394	C₂²×C₆₇	1	2	yes	—
626	#394	C₂²×C₆₇	1	2	yes	—
627	#394	C₂²×C₆₇	1	2	yes	—
628	#392	C₂²×C₆₇	1	2	yes	—
629	#392	C₂²×C₆₇	1	2	yes	—
630	#392	C₂²×C₆₇	1	2	yes	—
631	#392	C₂²×C₆₇	1	2	yes	—
632	#391	C₂²×C₆₇	1	1	yes	characteristic
633	#391	C₂²×C₆₇	1	1	yes	characteristic
634	#390	C₂²×C₆₇	1	1	yes	characteristic
635	#390	C₂²×C₆₇	1	1	yes	characteristic
636	#390	C₂²×C₆₇	1	1	yes	characteristic
637	#390	C₂²×C₆₇	1	2	yes	—
638	#390	C₂²×C₆₇	1	2	yes	—
639	#390	C₂²×C₆₇	1	1	yes	characteristic
640	#389	C₂²×C₆₇	1	1	yes	characteristic
641	#389	C₂²×C₆₇	1	1	yes	characteristic
642	#389	C₂²×C₆₇	1	1	yes	characteristic
643	#389	C₂²×C₆₇	1	2	yes	—
644	#389	C₂²×C₆₇	1	2	yes	—
645	#389	C₂²×C₆₇	1	2	yes	—
646	#389	C₂²×C₆₇	1	1	yes	characteristic
647	#388	C₂²×C₆₇	1	2	yes	—
648	#388	C₂²×C₆₇	1	2	yes	—
649	#388	C₂²×C₆₇	1	2	yes	—
650	#388	C₂²×C₆₇	1	2	yes	—
651	#388	C₂²×C₆₇	1	2	yes	—
652	#388	C₂²×C₆₇	1	2	yes	—
653	#388	C₂²×C₆₇	1	2	yes	—
654	#388	C₂²×C₆₇	1	2	yes	—
655	#388	C₂²×C₆₇	1	2	yes	—
656	#388	C₂²×C₆₇	1	1	yes	characteristic
657	#388	C₂²×C₆₇	1	1	yes	characteristic
658	#387	C₂²×C₆₇	1	2	yes	—
659	#387	C₂²×C₆₇	1	1	yes	characteristic
660	#387	C₂²×C₆₇	1	2	yes	—
661	#387	C₂²×C₆₇	1	2	yes	—
662	#387	C₂²×C₆₇	1	1	yes	characteristic
663	#386	C₂²×C₆₇	1	2	yes	—
664	#386	C₂²×C₆₇	1	2	yes	—
665	#386	C₂²×C₆₇	1	2	yes	—
666	#386	C₂²×C₆₇	1	2	yes	—
667	#386	C₂²×C₆₇	1	2	yes	—
668	#386	C₂²×C₆₇	1	1	yes	characteristic
669	#386	C₂²×C₆₇	1	1	yes	characteristic
670	#385	C₂²×C₆₇	1	2	yes	—
671	#385	C₂²×C₆₇	1	2	yes	—
672	#385	C₂²×C₆₇	1	2	yes	—
673	#385	C₂²×C₆₇	1	2	yes	—
674	#385	C₂²×C₆₇	1	1	yes	characteristic
675	#385	C₂²×C₆₇	1	1	yes	characteristic
676	#384	C₂²×C₆₇	1	1	yes	characteristic
677	#381	C₂²×C₆₇	1	2	yes	—
678	#380	C₂²×C₆₇	1	2	yes	—
679	#380	C₂²×C₆₇	1	1	yes	characteristic
680	#380	C₂²×C₆₇	1	1	yes	characteristic
681	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
682	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
683	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
684	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
685	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
686	#376	C₂²×C₆₇	1	1	yes	characteristic
687	C₂×#41	—	2	4	no	—
688	C₂×#41	—	2	4	no	—
689	C₂×#41	—	2	4	no	—
690	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
691	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
692	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
693	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
694	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
695	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
696	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
697	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
698	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
699	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
700	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
701	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
702	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
703	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
704	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
705	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
706	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
707	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
708	#127	—	2	4	no	—
709	#125	—	2	4	no	—
710	#124	—	2	4	no	—
711	#123	—	2	8	no	—
712	#123	—	2	8	no	—
713	#123	—	4	4	no	—
714	#123	—	4	4	no	—
715	C₂²⋊Q₈	—	2	4	no	—
716	#121	—	2	4	no	—
717	#121	—	2	8	no	—
718	#121	—	2	4	no	—
719	#121	—	2	4	no	—
720	#121	—	2	8	no	—
721	C₄×Q₈	—	2	4	no	—
722	C₄×Q₈	—	2	4	no	—
723	C₄×D₄	—	2	4	no	—
724	C₄×D₄	—	2	8	no	—
725	C₄×D₄	—	2	4	no	—
726	C₄×D₄	—	2	8	no	—
727	C₄×D₄	—	2	4	no	—
728	C₄×D₄	—	4	4	no	—
729	C₄×D₄	D₄×C₆₇	1	8	yes	complemented
730	#117	—	2	4	no	—
731	#117	—	2	8	no	—
732	#117	—	2	4	no	—
733	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
734	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
735	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
736	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
737	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
738	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
739	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
740	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
741	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
742	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
743	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
744	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
745	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
746	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
747	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
748	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
749	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
750	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
751	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
752	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
753	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
754	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
755	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
756	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
757	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
758	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
759	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
760	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
761	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
762	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
763	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
764	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
765	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
766	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
767	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
768	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
769	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
770	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
771	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
772	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
773	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
774	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
775	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
776	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
777	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
778	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
779	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
780	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
781	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
782	C₂×C₄²	—	2	8	no	—
783	C₂×C₄²	—	2	4	no	—
784	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
785	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
786	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
787	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
788	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
789	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
790	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
791	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
792	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
793	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
794	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
795	#95	C₂³×C₆₇	1	1	yes	characteristic
796	#95	C₂³×C₆₇	1	1	yes	characteristic
797	#95	C₂³×C₆₇	1	1	yes	characteristic
798	#95	C₂³×C₆₇	1	1	yes	characteristic
799	#95	C₂³×C₆₇	1	2	yes	—
800	#95	C₂³×C₆₇	1	1	yes	characteristic
801	#95	C₂³×C₆₇	1	1	yes	characteristic
802	#95	C₂³×C₆₇	1	1	yes	characteristic
803	#95	C₂³×C₆₇	1	1	yes	characteristic
804	#95	C₂³×C₆₇	1	2	yes	—
805	#95	C₂³×C₆₇	1	2	yes	—
806	#95	C₂³×C₆₇	1	1	yes	characteristic
807	#95	C₂³×C₆₇	1	1	yes	characteristic
808	#95	C₂³×C₆₇	1	2	yes	—
809	#95	C₂³×C₆₇	1	2	yes	—
810	#95	C₂³×C₆₇	1	2	yes	—
811	#95	C₂³×C₆₇	1	2	yes	—
812	#95	C₂³×C₆₇	1	2	yes	—
813	#95	C₂³×C₆₇	1	2	yes	—
814	#95	C₂³×C₆₇	1	2	yes	—
815	#95	C₂³×C₆₇	1	2	yes	—
816	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
817	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
818	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
819	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
820	#41	—	2	32	no	—
821	C₂×Q₈	—	2	2	no	—
822	C₂×Q₈	—	2	2	no	—
823	C₂×Q₈	#41×C₆₇	1	4	yes	—
824	C₂×D₄	—	2	4	no	—
825	C₂×D₄	—	2	4	no	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	2	4	no	—
828	C₂×D₄	—	2	4	no	—
829	C₂×D₄	—	2	4	no	—
830	C₂×D₄	—	2	4	no	—
831	C₂×D₄	—	2	2	no	—
832	C₂×D₄	—	2	4	no	—
833	C₂×D₄	—	2	4	no	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	2	2	no	—
836	C₂×D₄	—	2	2	no	—
837	C₂×D₄	—	2	2	no	—
838	C₂×D₄	—	4	2	no	—
839	C₂×D₄	—	4	1	no	—
840	C₂×D₄	—	4	1	no	—
841	C₂×D₄	—	4	2	no	—
842	C₂×D₄	—	4	2	no	—
843	C₂×D₄	—	4	2	no	—
844	C₂×D₄	—	4	2	no	—
845	C₂×D₄	—	4	2	no	—
846	C₂×D₄	—	4	2	no	—
847	C₂×D₄	—	4	2	no	—
848	C₂×D₄	—	4	2	no	—
849	C₂×D₄	—	4	2	no	—
850	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
851	C₂²×C₄	—	2	4	no	—
852	C₂²×C₄	—	2	2	no	—
853	C₂²×C₄	—	2	4	no	—
854	C₂²×C₄	—	2	4	no	—
855	C₂²×C₄	—	2	2	no	—
856	C₂²×C₄	—	2	4	no	—
857	C₂²×C₄	—	2	2	no	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	—	2	2	no	—
860	C₂²×C₄	—	2	2	no	—
861	C₂²×C₄	—	2	2	no	—
862	C₂²×C₄	—	2	2	no	—
863	C₂²×C₄	—	2	4	no	—
864	C₂²×C₄	—	2	4	no	—
865	C₂²×C₄	—	4	2	no	—
866	C₂²×C₄	—	4	2	no	—
867	C₂²×C₄	—	4	1	no	—
868	C₂²×C₄	—	4	1	no	—
869	C₂²×C₄	—	4	2	no	—
870	C₂²×C₄	—	4	1	no	—
871	C₂²×C₄	—	4	2	no	—
872	C₂²×C₄	—	4	2	no	—
873	C₂²×C₄	C₂×D₄×C₆₇	1	8	yes	—
874	C₂²×C₄	#41×C₆₇	1	4	yes	—
875	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
876	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
877	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
878	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
879	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
880	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
881	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
882	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
883	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
884	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
885	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
886	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
887	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
888	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
889	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
890	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
891	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
892	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
893	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
894	C₄⋊C₄	—	2	4	no	—
895	C₄⋊C₄	—	2	4	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	4	no	—
901	C₄⋊C₄	—	2	4	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	4	no	—
906	C₄⋊C₄	—	2	4	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	4	2	no	—
909	C₄⋊C₄	—	4	2	no	—
910	C₄⋊C₄	—	4	2	no	—
911	C₄⋊C₄	—	4	2	no	—
912	C₄⋊C₄	—	4	2	no	—
913	C₄⋊C₄	—	4	1	no	—
914	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
915	C₂²⋊C₄	—	2	4	no	—
916	C₂²⋊C₄	—	2	4	no	—
917	C₂²⋊C₄	—	2	2	no	—
918	C₂²⋊C₄	—	2	4	no	—
919	C₂²⋊C₄	—	2	2	no	—
920	C₂²⋊C₄	—	2	2	no	—
921	C₂²⋊C₄	—	2	4	no	—
922	C₂²⋊C₄	—	2	4	no	—
923	C₂²⋊C₄	—	2	2	no	—
924	C₂²⋊C₄	—	2	4	no	—
925	C₂²⋊C₄	—	2	4	no	—
926	C₂²⋊C₄	—	2	4	no	—
927	C₂²⋊C₄	—	2	4	no	—
928	C₂²⋊C₄	—	2	4	no	—
929	C₂²⋊C₄	—	2	2	no	—
930	C₂²⋊C₄	—	4	2	no	—
931	C₂²⋊C₄	—	4	2	no	—
932	C₂²⋊C₄	—	4	2	no	—
933	C₂²⋊C₄	—	4	2	no	—
934	C₂²⋊C₄	—	4	2	no	—
935	C₂²⋊C₄	—	4	1	no	—
936	C₂²⋊C₄	—	4	2	no	—
937	C₂²⋊C₄	—	4	2	no	—
938	C₂²⋊C₄	—	4	2	no	—
939	C₂²⋊C₄	—	4	2	no	—
940	C₂²⋊C₄	—	4	1	no	—
941	C₂²⋊C₄	—	4	1	no	—
942	C₂²⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
943	C₄²	—	2	2	no	—
944	C₄²	—	2	4	no	—
945	C₄²	—	2	2	no	—
946	C₄²	—	2	4	no	—
947	C₄²	—	2	2	no	—
948	C₄²	—	2	4	no	—
949	C₄²	—	2	2	no	—
950	C₄²	—	2	2	no	—
951	C₄²	—	2	2	no	—
952	C₄²	—	4	2	no	—
953	C₄²	C₂×D₄×C₆₇	1	4	yes	—
954	C₂³	—	2	1	no	—
955	C₂³	—	2	2	no	—
956	C₂³	—	2	2	no	—
957	C₂³	—	2	1	no	—
958	C₂³	—	2	1	no	—
959	C₂³	—	2	2	no	—
960	C₂³	—	2	1	no	—
961	C₂³	—	2	1	no	—
962	C₂³	—	2	2	no	—
963	C₂³	—	2	2	no	—
964	C₂³	—	2	1	no	—
965	C₂³	—	2	2	no	—
966	C₂³	—	2	1	no	—
967	C₂³	—	2	2	no	—
968	C₂³	—	2	1	no	—
969	C₂³	—	2	2	no	—
970	C₂³	—	2	1	no	—
971	C₂³	—	2	2	no	—
972	C₂³	—	2	1	no	—
973	C₂³	—	2	2	no	—
974	C₂³	—	2	2	no	—
975	C₂³	—	2	1	no	—
976	C₂³	—	2	2	no	—
977	C₂³	—	2	1	no	—
978	C₂³	—	2	2	no	—
979	C₂³	—	2	1	no	—
980	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
981	C₂³	C₂×#41×C₆₇	1	2	yes	—
982	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
983	Q₈	—	2	8	no	—
984	D₄	—	2	16	no	—
985	D₄	—	2	8	no	—
986	D₄	—	4	4	no	—
987	D₄	—	4	8	no	—
988	D₄	—	4	4	no	—
989	D₄	—	8	4	no	—
990	D₄	—	8	4	no	—
991	D₄	—	8	4	no	—
992	D₄	—	8	4	no	—
993	C₂×C₄	—	2	16	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	2	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	2	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	8	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	2	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	4	8	no	—
1044	C₂×C₄	—	4	4	no	—
1045	C₂×C₄	—	4	8	no	—
1046	C₂×C₄	—	4	4	no	—
1047	C₂×C₄	—	4	4	no	—
1048	C₂×C₄	—	8	4	no	—
1049	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1050	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
1051	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1052	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1053	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1054	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
1055	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1056	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1057	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1058	C₂²	—	2	4	no	—
1059	C₂²	—	2	2	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	—	2	2	no	—
1062	C₂²	—	2	4	no	—
1063	C₂²	—	2	4	no	—
1064	C₂²	—	4	2	no	—
1065	C₂²	—	4	1	no	—
1066	C₂²	—	4	2	no	—
1067	C₂²	—	4	2	no	—
1068	C₂²	—	4	1	no	—
1069	C₂²	—	4	1	no	—
1070	C₂²	—	4	2	no	—
1071	C₂²	—	4	1	no	—
1072	C₂²	—	4	1	no	—
1073	C₂²	—	4	2	no	—
1074	C₂²	—	4	1	no	—
1075	C₂²	—	4	2	no	—
1076	C₂²	—	4	1	no	—
1077	C₂²	—	4	2	no	—
1078	C₂²	—	4	2	no	—
1079	C₂²	—	4	1	no	—
1080	C₂²	—	4	1	no	—
1081	C₂²	—	4	2	no	—
1082	C₂²	—	4	2	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	—	4	1	no	—
1085	C₂²	—	4	2	no	—
1086	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1087	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1088	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1089	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1090	C₂²	#585×C₆₇	1	1	yes	characteristic
1091	C₂²	#585×C₆₇	1	1	yes	characteristic
1092	C₂²	#585×C₆₇	1	1	yes	characteristic
1093	C₄	—	2	2	no	—
1094	C₄	—	2	4	no	—
1095	C₄	—	2	2	no	—
1096	C₄	—	2	4	no	—
1097	C₄	—	2	2	no	—
1098	C₄	—	2	2	no	—
1099	C₄	—	4	1	no	—
1100	C₄	—	4	1	no	—
1101	C₄	—	4	1	no	—
1102	C₄	—	4	2	no	—
1103	C₄	—	4	1	no	—
1104	C₄	—	4	1	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	2	no	—
1107	C₄	—	4	2	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	2	no	—
1111	C₄	#525×C₆₇	1	4	yes	—
1112	C₂	—	4	4	no	—
1113	C₂	—	4	2	no	—
1114	C₂	—	8	1	no	—
1115	C₂	—	8	2	no	—
1116	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
1117	C₂	C₆₇×#3455	1	1	yes	characteristic
1118	C₂	C₆₇×#3460	1	1	yes	characteristic
1119	C₂	C₆₇×#3485	1	1	yes	characteristic
1120	C₂	C₆₇×#3488	1	1	yes	characteristic
1121	C₂	C₆₇×#3517	1	1	yes	characteristic
1122	C₂	C₆₇×#3524	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×#540×C₆₇	C₂	semidirect
2. C₂×C₄×#41×C₆₇	C₂	semidirect
3. C₆₇×#2854	C₂	semidirect
4. C₆₇×#2853	C₂	semidirect
5. C₆₇×#2635	C₂	semidirect
6. C₆₇×#2630	C₂	semidirect
7. C₆₇×#2476	C₂	semidirect
8. C₆₇×#2470	C₂	semidirect
9. C₆₇×#2456	C₂	semidirect
10. C₆₇×#2455	C₂	semidirect
11. C₆₇×#2453	C₂	semidirect
12. C₆₇×#2445	C₂	semidirect
13. C₆₇×#2441	C₂	semidirect
14. C₆₇×#2431	C₂	semidirect
15. C₆₇×#2426	C₂	semidirect
16. C₆₇×#2422	C₂	semidirect
17. C₆₇×#2414	C₂	semidirect
18. C₆₇×#2407	C₂	semidirect
19. C₆₇×#2326	C₂	semidirect
20. C₆₇×#2323	C₂	semidirect
21. C₆₇×#2319	C₂	semidirect
22. C₄×#121×C₆₇	C₂	semidirect
23. C₆₇×#2290	C₂	semidirect
167. C₄×D₄×C₆₇	D₄	semidirect
550. #35156	C₆₇	direct (N × H)
562. C₂×#540	C₂×C₆₇	semidirect
563. C₂×C₄×#41	C₂×C₆₇	semidirect
564. #2854	C₂×C₆₇	semidirect
565. #2853	C₂×C₆₇	semidirect
566. #2635	C₂×C₆₇	semidirect
567. #2630	C₂×C₆₇	semidirect
568. #2476	C₂×C₆₇	semidirect
569. #2470	C₂×C₆₇	semidirect
570. #2456	C₂×C₆₇	semidirect
571. #2455	C₂×C₆₇	semidirect
572. #2453	C₂×C₆₇	semidirect
573. #2445	C₂×C₆₇	semidirect
574. #2441	C₂×C₆₇	semidirect
575. #2431	C₂×C₆₇	semidirect
576. #2426	C₂×C₆₇	semidirect
577. #2422	C₂×C₆₇	semidirect
578. #2414	C₂×C₆₇	semidirect
579. #2407	C₂×C₆₇	semidirect
580. #2326	C₂×C₆₇	semidirect
581. #2323	C₂×C₆₇	semidirect
582. #2319	C₂×C₆₇	semidirect
583. C₄×#121	C₂×C₆₇	semidirect
584. #2290	C₂×C₆₇	semidirect
585. C₆₇	#35156	direct (N × H)
729. C₄×D₄	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×#540×C₆₇	2
C₂×C₄×#41×C₆₇	2
C₆₇×#2854	2
C₆₇×#2853	2
C₆₇×#2635	2
C₆₇×#2630	2
C₆₇×#2476	2
C₆₇×#2470	2
C₆₇×#2456	2
C₆₇×#2455	2
C₆₇×#2453	2
C₆₇×#2445	2
C₆₇×#2441	2
C₆₇×#2431	2
C₆₇×#2426	2
C₆₇×#2422	2
C₆₇×#2414	2
C₆₇×#2407	2
C₆₇×#2326	2
C₆₇×#2323	2
C₆₇×#2319	2
C₄×#121×C₆₇	2
C₆₇×#2290	2
#35156	67

Subgroups — C67×#35156 #30714407

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#35156 #30714407