Subgroups — C₆₇×#61083 #30740334

Order 17152.

2674 conjugacy classes of subgroups.

The subgroup lattice has 1074 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#578×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#577×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3499	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3270	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3269	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3267	C₂	1	4	yes	maximal, complemented
8	C₆₇×#3266	C₂	1	4	yes	maximal, complemented
9	C₂×#497×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3059	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3057	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3040	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3039	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3011	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3011	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3010	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3009	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2943	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2932	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic, complemented
23	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic
24	#578×C₆₇	—	2	8	no	—
25	#577×C₆₇	—	2	8	no	—
26	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#137×C₆₇	C₂²	1	2	yes	—
29	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
30	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
32	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	—
34	C₂×#135×C₆₇	C₂²	1	2	yes	—
35	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
37	C₂²×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
38	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	—
41	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
42	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	D₄×Q₈×C₆₇	C₂²	1	4	yes	complemented
46	#548×C₆₇	C₂²	1	4	yes	—
47	#547×C₆₇	—	2	4	no	—
48	#547×C₆₇	C₂²	1	4	yes	complemented
49	#546×C₆₇	—	2	4	no	—
50	#546×C₆₇	C₂²	1	4	yes	—
51	#536×C₆₇	—	2	1	no	—
52	#536×C₆₇	—	2	1	no	—
53	#536×C₆₇	—	2	1	no	—
54	#536×C₆₇	C₂²	1	1	yes	characteristic
55	#536×C₆₇	C₂²	1	1	yes	characteristic
56	#536×C₆₇	C₂²	1	1	yes	characteristic, complemented
57	#535×C₆₇	—	2	1	no	—
58	#535×C₆₇	C₂²	1	1	yes	characteristic
59	#532×C₆₇	—	2	1	no	—
60	#532×C₆₇	—	2	1	no	—
61	#532×C₆₇	C₂²	1	1	yes	characteristic
62	C₂×C₄⋊Q₈×C₆₇	—	2	1	no	—
63	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
64	C₂×#124×C₆₇	—	2	1	no	—
65	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
66	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
67	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	#497×C₆₇	C₂²	1	4	yes	complemented
69	#497×C₆₇	C₂²	1	4	yes	complemented
70	#470×C₆₇	C₂²	1	4	yes	complemented
71	#468×C₆₇	C₂²	1	4	yes	complemented
72	#467×C₆₇	C₂²	1	4	yes	complemented
73	#465×C₆₇	C₂²	1	4	yes	complemented
74	#464×C₆₇	C₂²	1	4	yes	complemented
75	#463×C₆₇	C₂²	1	4	yes	complemented
76	#462×C₆₇	C₂²	1	4	yes	complemented
77	#461×C₆₇	C₂²	1	4	yes	complemented
78	#452×C₆₇	C₂²	1	4	yes	—
79	#452×C₆₇	C₂²	1	4	yes	complemented
80	#452×C₆₇	C₂²	1	4	yes	complemented
81	#451×C₆₇	C₂²	1	4	yes	complemented
82	#451×C₆₇	C₂²	1	4	yes	complemented
83	#450×C₆₇	C₂²	1	4	yes	—
84	#449×C₆₇	C₂²	1	4	yes	complemented
85	#448×C₆₇	C₂²	1	4	yes	complemented
86	#442×C₆₇	C₂²	1	2	yes	complemented
87	#441×C₆₇	C₂²	1	2	yes	complemented
88	#440×C₆₇	C₂²	1	2	yes	complemented
89	#440×C₆₇	C₂²	1	2	yes	complemented
90	#435×C₆₇	C₂²	1	4	yes	complemented
91	#435×C₆₇	C₂²	1	4	yes	complemented
92	#427×C₆₇	C₂²	1	1	yes	characteristic, complemented
93	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
94	#419×C₆₇	C₂²	1	1	yes	characteristic, complemented
95	#419×C₆₇	C₂²	1	1	yes	characteristic, complemented
96	#419×C₆₇	C₂²	1	1	yes	characteristic, complemented
97	#418×C₆₇	C₂²	1	1	yes	characteristic
98	#416×C₆₇	C₂²	1	1	yes	characteristic
99	#416×C₆₇	C₂²	1	1	yes	characteristic, complemented
100	#408×C₆₇	C₂²	1	1	yes	characteristic
101	#408×C₆₇	C₂²	1	1	yes	characteristic, complemented
102	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic, complemented
103	2₋¹⁺⁴×C₆₇	—	2	4	no	—
104	2₋¹⁺⁴×C₆₇	—	2	4	no	—
105	2₋¹⁺⁴×C₆₇	—	2	4	no	—
106	2₋¹⁺⁴×C₆₇	—	4	2	no	—
107	2₋¹⁺⁴×C₆₇	—	4	2	no	—
108	2₋¹⁺⁴×C₆₇	—	4	2	no	—
109	H(5,𝔽₂)×C₆₇	—	2	4	no	—
110	H(5,𝔽₂)×C₆₇	—	4	2	no	—
111	C₂×#41×C₆₇	—	2	1	no	—
112	C₂×#41×C₆₇	—	2	1	no	—
113	C₂×#41×C₆₇	—	2	1	no	—
114	C₂×#41×C₆₇	—	2	1	no	—
115	C₂×#41×C₆₇	—	2	2	no	—
116	C₂×#41×C₆₇	—	2	2	no	—
117	C₂×#41×C₆₇	—	2	2	no	—
118	C₂×#41×C₆₇	C₂³	1	2	yes	—
119	C₂×#41×C₆₇	C₂³	1	2	yes	—
120	C₂×#41×C₆₇	C₂³	1	2	yes	—
121	C₂×#41×C₆₇	C₂³	1	2	yes	—
122	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
123	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
124	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
125	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
126	C₂²×Q₈×C₆₇	—	2	1	no	—
127	C₂²×Q₈×C₆₇	—	2	1	no	—
128	C₂²×Q₈×C₆₇	—	2	1	no	—
129	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
130	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
131	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
132	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
133	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
134	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
135	C₂²×D₄×C₆₇	—	2	1	no	—
136	C₂²×D₄×C₆₇	—	2	2	no	—
137	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
139	#137×C₆₇	—	2	4	no	—
140	#137×C₆₇	—	2	4	no	—
141	#137×C₆₇	—	2	4	no	—
142	#137×C₆₇	—	2	8	no	—
143	#137×C₆₇	—	2	8	no	—
144	#137×C₆₇	—	2	8	no	—
145	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
146	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
147	#135×C₆₇	—	2	8	no	—
148	#135×C₆₇	—	2	8	no	—
149	#135×C₆₇	D₄	1	8	yes	complemented
150	C₂×Q₁₆×C₆₇	—	2	8	no	—
151	C₂×Q₁₆×C₆₇	—	2	4	no	—
152	C₂×Q₁₆×C₆₇	—	4	2	no	—
153	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
154	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
155	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
156	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
157	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
158	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
159	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
160	C₂×SD₁₆×C₆₇	—	2	8	no	—
161	C₂×SD₁₆×C₆₇	—	2	4	no	—
162	C₂×SD₁₆×C₆₇	—	4	2	no	—
163	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
164	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
165	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
166	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
167	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
168	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
169	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
170	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
171	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
172	C₂×D₈×C₆₇	C₂³	1	2	yes	—
173	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
174	#131×C₆₇	—	2	4	no	—
175	#131×C₆₇	—	2	4	no	—
176	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
177	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
178	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
179	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
180	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
181	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
182	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
183	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
184	C₄⋊Q₈×C₆₇	—	2	1	no	—
185	C₄⋊Q₈×C₆₇	—	2	1	no	—
186	C₄⋊Q₈×C₆₇	—	2	1	no	—
187	C₄⋊Q₈×C₆₇	—	2	4	no	—
188	C₄⋊Q₈×C₆₇	—	2	1	no	—
189	C₄⋊Q₈×C₆₇	—	2	1	no	—
190	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
191	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
192	#127×C₆₇	—	2	1	no	—
193	#127×C₆₇	D₄	1	1	yes	characteristic
194	#124×C₆₇	—	2	1	no	—
195	#124×C₆₇	—	2	1	no	—
196	#124×C₆₇	—	2	1	no	—
197	#124×C₆₇	—	2	1	no	—
198	#124×C₆₇	—	2	4	no	—
199	#124×C₆₇	—	2	1	no	—
200	#124×C₆₇	—	2	1	no	—
201	#124×C₆₇	D₄	1	1	yes	characteristic
202	#124×C₆₇	D₄	1	1	yes	characteristic
203	#124×C₆₇	C₂³	1	4	yes	—
204	#123×C₆₇	—	2	2	no	—
205	#123×C₆₇	—	2	2	no	—
206	#123×C₆₇	—	2	2	no	—
207	#123×C₆₇	—	2	4	no	—
208	#123×C₆₇	—	2	4	no	—
209	#123×C₆₇	—	2	4	no	—
210	C₂²⋊Q₈×C₆₇	—	2	4	no	—
211	C₂²⋊Q₈×C₆₇	—	2	4	no	—
212	C₂²⋊Q₈×C₆₇	—	2	4	no	—
213	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
214	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
215	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
216	#121×C₆₇	—	2	4	no	—
217	#121×C₆₇	—	2	4	no	—
218	#121×C₆₇	—	2	4	no	—
219	#121×C₆₇	D₄	1	4	yes	—
220	#121×C₆₇	C₂³	1	4	yes	—
221	#120×C₆₇	—	2	4	no	—
222	#120×C₆₇	—	2	2	no	—
223	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
224	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
225	C₄×D₄×C₆₇	—	2	4	no	—
226	C₄×D₄×C₆₇	—	2	2	no	—
227	C₄×D₄×C₆₇	—	2	2	no	—
228	C₄×D₄×C₆₇	—	2	4	no	—
229	C₄×D₄×C₆₇	C₂³	1	2	yes	—
230	C₄×D₄×C₆₇	C₂³	1	2	yes	—
231	C₄×D₄×C₆₇	C₂³	1	4	yes	—
232	#117×C₆₇	—	2	1	no	—
233	#117×C₆₇	—	2	1	no	—
234	#117×C₆₇	C₂³	1	1	yes	characteristic
235	#117×C₆₇	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
237	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
238	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
239	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
240	C₂×C₄²×C₆₇	—	2	1	no	—
241	C₂×C₄²×C₆₇	—	2	1	no	—
242	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
243	#107×C₆₇	C₂³	1	2	yes	—
244	#106×C₆₇	C₂³	1	2	yes	—
245	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
246	#103×C₆₇	C₂³	1	2	yes	—
247	#103×C₆₇	C₂³	1	4	yes	—
248	#103×C₆₇	C₂³	1	2	yes	—
249	#103×C₆₇	C₂³	1	4	yes	—
250	#103×C₆₇	C₂³	1	4	yes	—
251	#102×C₆₇	C₂³	1	2	yes	—
252	#102×C₆₇	C₂³	1	2	yes	—
253	#102×C₆₇	C₂³	1	4	yes	—
254	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
255	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
256	#97×C₆₇	C₂³	1	2	yes	—
257	#97×C₆₇	C₂³	1	2	yes	—
258	C₂⁴×C₆₇	—	2	2	no	—
259	C₂⁴×C₆₇	—	2	1	no	—
260	#41×C₆₇	—	2	2	no	—
261	#41×C₆₇	—	2	2	no	—
262	#41×C₆₇	—	2	2	no	—
263	#41×C₆₇	—	2	2	no	—
264	#41×C₆₇	—	2	2	no	—
265	#41×C₆₇	—	2	2	no	—
266	#41×C₆₇	—	2	4	no	—
267	#41×C₆₇	—	2	4	no	—
268	#41×C₆₇	—	2	4	no	—
269	#41×C₆₇	—	2	4	no	—
270	#41×C₆₇	—	4	2	no	—
271	#41×C₆₇	—	4	2	no	—
272	#41×C₆₇	—	4	2	no	—
273	#41×C₆₇	—	4	2	no	—
274	#41×C₆₇	—	4	4	no	—
275	#41×C₆₇	—	4	4	no	—
276	#41×C₆₇	—	4	4	no	—
277	#41×C₆₇	—	4	4	no	—
278	#41×C₆₇	—	4	8	no	—
279	#41×C₆₇	—	4	8	no	—
280	#41×C₆₇	—	4	8	no	—
281	#41×C₆₇	C₂×D₄	1	4	yes	—
282	#41×C₆₇	C₂×D₄	1	4	yes	—
283	C₂×Q₈×C₆₇	—	2	2	no	—
284	C₂×Q₈×C₆₇	—	2	2	no	—
285	C₂×Q₈×C₆₇	—	2	2	no	—
286	C₂×Q₈×C₆₇	—	2	1	no	—
287	C₂×Q₈×C₆₇	—	2	1	no	—
288	C₂×Q₈×C₆₇	—	2	1	no	—
289	C₂×Q₈×C₆₇	—	2	4	no	—
290	C₂×Q₈×C₆₇	—	2	4	no	—
291	C₂×Q₈×C₆₇	—	2	4	no	—
292	C₂×Q₈×C₆₇	—	2	2	no	—
293	C₂×Q₈×C₆₇	—	2	2	no	—
294	C₂×Q₈×C₆₇	—	2	2	no	—
295	C₂×Q₈×C₆₇	—	2	2	no	—
296	C₂×Q₈×C₆₇	—	2	2	no	—
297	C₂×Q₈×C₆₇	—	2	2	no	—
298	C₂×Q₈×C₆₇	—	4	2	no	—
299	C₂×Q₈×C₆₇	—	4	2	no	—
300	C₂×Q₈×C₆₇	—	4	2	no	—
301	C₂×Q₈×C₆₇	—	4	4	no	—
302	C₂×Q₈×C₆₇	—	4	4	no	—
303	C₂×Q₈×C₆₇	—	4	4	no	—
304	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
305	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
306	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
307	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
308	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
309	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
310	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
311	C₂×D₄×C₆₇	—	2	1	no	—
312	C₂×D₄×C₆₇	—	2	1	no	—
313	C₂×D₄×C₆₇	—	2	4	no	—
314	C₂×D₄×C₆₇	—	2	2	no	—
315	C₂×D₄×C₆₇	—	2	2	no	—
316	C₂×D₄×C₆₇	—	2	2	no	—
317	C₂×D₄×C₆₇	—	2	2	no	—
318	C₂×D₄×C₆₇	—	2	4	no	—
319	C₂×D₄×C₆₇	—	2	2	no	—
320	C₂×D₄×C₆₇	—	2	2	no	—
321	C₂×D₄×C₆₇	—	2	1	no	—
322	C₂×D₄×C₆₇	—	2	2	no	—
323	C₂×D₄×C₆₇	—	4	2	no	—
324	C₂×D₄×C₆₇	—	4	4	no	—
325	C₂×D₄×C₆₇	—	4	8	no	—
326	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
327	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
328	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
329	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
330	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
331	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
332	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
333	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₆₇	—	2	1	no	—
335	C₂²×C₄×C₆₇	—	2	1	no	—
336	C₂²×C₄×C₆₇	—	2	1	no	—
337	C₂²×C₄×C₆₇	—	2	1	no	—
338	C₂²×C₄×C₆₇	—	2	1	no	—
339	C₂²×C₄×C₆₇	—	2	2	no	—
340	C₂²×C₄×C₆₇	—	2	2	no	—
341	C₂²×C₄×C₆₇	—	2	2	no	—
342	C₂²×C₄×C₆₇	—	2	2	no	—
343	C₂²×C₄×C₆₇	—	2	2	no	—
344	C₂²×C₄×C₆₇	—	2	2	no	—
345	C₂²×C₄×C₆₇	—	2	2	no	—
346	C₂²×C₄×C₆₇	—	2	2	no	—
347	C₂²×C₄×C₆₇	—	2	2	no	—
348	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
349	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
350	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
351	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
352	Q₁₆×C₆₇	—	2	4	no	—
353	Q₁₆×C₆₇	—	2	4	no	—
354	Q₁₆×C₆₇	—	2	4	no	—
355	Q₁₆×C₆₇	—	2	4	no	—
356	Q₁₆×C₆₇	—	2	4	no	—
357	Q₁₆×C₆₇	—	4	4	no	—
358	Q₁₆×C₆₇	C₂×D₄	1	4	yes	—
359	SD₁₆×C₆₇	—	2	4	no	—
360	SD₁₆×C₆₇	—	2	4	no	—
361	SD₁₆×C₆₇	—	2	4	no	—
362	SD₁₆×C₆₇	—	2	4	no	—
363	SD₁₆×C₆₇	—	2	4	no	—
364	SD₁₆×C₆₇	—	2	4	no	—
365	SD₁₆×C₆₇	—	4	4	no	—
366	SD₁₆×C₆₇	C₂×D₄	1	4	yes	—
367	SD₁₆×C₆₇	C₂×D₄	1	4	yes	—
368	D₈×C₆₇	—	2	4	no	—
369	D₈×C₆₇	C₂×D₄	1	4	yes	—
370	M₁₆×C₆₇	—	2	2	no	—
371	M₁₆×C₆₇	—	2	2	no	—
372	M₁₆×C₆₇	—	2	4	no	—
373	M₁₆×C₆₇	—	2	4	no	—
374	C₂×C₈×C₆₇	—	2	2	no	—
375	C₂×C₈×C₆₇	—	2	4	no	—
376	C₂×C₈×C₆₇	—	2	4	no	—
377	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	—
378	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
379	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
380	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
381	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
382	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
383	C₄⋊C₄×C₆₇	—	2	4	no	—
384	C₄⋊C₄×C₆₇	—	2	4	no	—
385	C₄⋊C₄×C₆₇	—	2	4	no	—
386	C₄⋊C₄×C₆₇	—	2	4	no	—
387	C₄⋊C₄×C₆₇	—	2	2	no	—
388	C₄⋊C₄×C₆₇	—	2	2	no	—
389	C₄⋊C₄×C₆₇	—	2	4	no	—
390	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
391	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
392	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
393	C₂²⋊C₄×C₆₇	—	2	4	no	—
394	C₂²⋊C₄×C₆₇	—	2	1	no	—
395	C₂²⋊C₄×C₆₇	—	2	1	no	—
396	C₂²⋊C₄×C₆₇	—	2	4	no	—
397	C₂²⋊C₄×C₆₇	—	2	4	no	—
398	C₂²⋊C₄×C₆₇	—	2	4	no	—
399	C₂²⋊C₄×C₆₇	—	2	4	no	—
400	C₂²⋊C₄×C₆₇	—	2	4	no	—
401	C₂²⋊C₄×C₆₇	—	2	2	no	—
402	C₂²⋊C₄×C₆₇	—	2	2	no	—
403	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
404	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
405	C₄²×C₆₇	—	2	1	no	—
406	C₄²×C₆₇	—	2	1	no	—
407	C₄²×C₆₇	—	2	2	no	—
408	C₄²×C₆₇	—	2	2	no	—
409	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
410	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
411	C₄²×C₆₇	C₂⁴	1	2	yes	—
412	C₂³×C₆₇	—	2	1	no	—
413	C₂³×C₆₇	—	2	1	no	—
414	C₂³×C₆₇	—	2	2	no	—
415	C₂³×C₆₇	—	4	4	no	—
416	C₂³×C₆₇	—	4	2	no	—
417	C₂³×C₆₇	—	8	2	no	—
418	C₂³×C₆₇	—	8	4	no	—
419	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
420	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
421	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
422	Q₈×C₆₇	—	2	2	no	—
423	Q₈×C₆₇	—	2	2	no	—
424	Q₈×C₆₇	—	2	1	no	—
425	Q₈×C₆₇	—	2	1	no	—
426	Q₈×C₆₇	—	2	2	no	—
427	Q₈×C₆₇	—	2	2	no	—
428	Q₈×C₆₇	—	2	2	no	—
429	Q₈×C₆₇	—	2	2	no	—
430	Q₈×C₆₇	—	2	2	no	—
431	Q₈×C₆₇	—	2	2	no	—
432	Q₈×C₆₇	—	4	4	no	—
433	Q₈×C₆₇	—	4	4	no	—
434	Q₈×C₆₇	—	4	4	no	—
435	Q₈×C₆₇	—	4	2	no	—
436	Q₈×C₆₇	—	4	2	no	—
437	Q₈×C₆₇	—	4	2	no	—
438	Q₈×C₆₇	C₂²×D₄	1	2	yes	—
439	Q₈×C₆₇	C₂²×D₄	1	2	yes	—
440	D₄×C₆₇	—	2	4	no	—
441	D₄×C₆₇	—	2	4	no	—
442	D₄×C₆₇	—	2	4	no	—
443	D₄×C₆₇	—	2	4	no	—
444	D₄×C₆₇	—	2	2	no	—
445	D₄×C₆₇	—	2	2	no	—
446	D₄×C₆₇	—	2	2	no	—
447	D₄×C₆₇	—	2	1	no	—
448	D₄×C₆₇	—	2	1	no	—
449	D₄×C₆₇	—	2	2	no	—
450	D₄×C₆₇	—	4	4	no	—
451	D₄×C₆₇	—	4	4	no	—
452	D₄×C₆₇	—	4	4	no	—
453	D₄×C₆₇	—	4	4	no	—
454	D₄×C₆₇	—	4	4	no	—
455	D₄×C₆₇	—	4	4	no	—
456	D₄×C₆₇	—	4	2	no	—
457	D₄×C₆₇	—	8	4	no	—
458	D₄×C₆₇	C₂²×D₄	1	2	yes	—
459	D₄×C₆₇	C₂²×D₄	1	2	yes	—
460	C₂×C₄×C₆₇	—	2	1	no	—
461	C₂×C₄×C₆₇	—	2	1	no	—
462	C₂×C₄×C₆₇	—	2	4	no	—
463	C₂×C₄×C₆₇	—	2	4	no	—
464	C₂×C₄×C₆₇	—	2	2	no	—
465	C₂×C₄×C₆₇	—	2	2	no	—
466	C₂×C₄×C₆₇	—	2	2	no	—
467	C₂×C₄×C₆₇	—	2	2	no	—
468	C₂×C₄×C₆₇	—	2	2	no	—
469	C₂×C₄×C₆₇	—	2	2	no	—
470	C₂×C₄×C₆₇	—	2	2	no	—
471	C₂×C₄×C₆₇	—	2	2	no	—
472	C₂×C₄×C₆₇	—	2	2	no	—
473	C₂×C₄×C₆₇	—	4	2	no	—
474	C₂×C₄×C₆₇	—	4	4	no	—
475	C₂×C₄×C₆₇	—	4	4	no	—
476	C₂×C₄×C₆₇	—	4	4	no	—
477	C₂×C₄×C₆₇	—	4	4	no	—
478	C₂×C₄×C₆₇	—	4	4	no	—
479	C₂×C₄×C₆₇	—	4	4	no	—
480	C₂×C₄×C₆₇	—	4	4	no	—
481	C₂×C₄×C₆₇	—	4	4	no	—
482	C₂×C₄×C₆₇	—	4	2	no	—
483	C₂×C₄×C₆₇	—	4	2	no	—
484	C₂×C₄×C₆₇	—	4	2	no	—
485	C₂×C₄×C₆₇	—	8	2	no	—
486	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
487	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
488	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
489	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
490	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
492	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
493	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
494	C₈×C₆₇	—	2	2	no	—
495	C₈×C₆₇	—	2	2	no	—
496	C₈×C₆₇	—	2	2	no	—
497	C₈×C₆₇	C₂²×D₄	1	2	yes	—
498	C₈×C₆₇	C₂²×D₄	1	2	yes	—
499	C₂²×C₆₇	—	2	2	no	—
500	C₂²×C₆₇	—	2	4	no	—
501	C₂²×C₆₇	—	2	4	no	—
502	C₂²×C₆₇	—	2	2	no	—
503	C₂²×C₆₇	—	2	2	no	—
504	C₂²×C₆₇	—	2	2	no	—
505	C₂²×C₆₇	—	2	2	no	—
506	C₂²×C₆₇	—	4	2	no	—
507	C₂²×C₆₇	—	4	2	no	—
508	C₂²×C₆₇	—	4	4	no	—
509	C₂²×C₆₇	—	4	2	no	—
510	C₂²×C₆₇	—	16	2	no	—
511	C₂²×C₆₇	—	16	4	no	—
512	C₂²×C₆₇	D₄²	1	2	yes	—
513	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
514	C₄×C₆₇	—	2	2	no	—
515	C₄×C₆₇	—	2	2	no	—
516	C₄×C₆₇	—	2	2	no	—
517	C₄×C₆₇	—	2	2	no	—
518	C₄×C₆₇	—	2	2	no	—
519	C₄×C₆₇	—	2	2	no	—
520	C₄×C₆₇	—	4	2	no	—
521	C₄×C₆₇	—	4	2	no	—
522	C₄×C₆₇	—	4	2	no	—
523	C₄×C₆₇	—	4	2	no	—
524	C₄×C₆₇	—	4	2	no	—
525	C₄×C₆₇	D₄²	1	2	yes	—
526	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
527	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
528	#61083	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
529	C₂×C₆₇	—	2	2	no	—
530	C₂×C₆₇	—	4	2	no	—
531	C₂×C₆₇	—	4	2	no	—
532	C₂×C₆₇	—	4	2	no	—
533	C₂×C₆₇	—	4	2	no	—
534	C₂×C₆₇	—	8	2	no	—
535	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
536	C₂×C₆₇	#3586	1	2	yes	—
537	C₂×#578	C₂×C₆₇	1	1	yes	characteristic, complemented
538	C₂×#577	C₂×C₆₇	1	1	yes	characteristic, complemented
539	#3500	C₂×C₆₇	1	1	yes	characteristic, complemented
540	#3499	C₂×C₆₇	1	1	yes	characteristic, complemented
541	#3270	C₂×C₆₇	1	4	yes	complemented
542	#3269	C₂×C₆₇	1	4	yes	complemented
543	#3267	C₂×C₆₇	1	4	yes	complemented
544	#3266	C₂×C₆₇	1	4	yes	complemented
545	C₂×#497	C₂×C₆₇	1	1	yes	characteristic, complemented
546	#3059	C₂×C₆₇	1	1	yes	characteristic, complemented
547	#3057	C₂×C₆₇	1	1	yes	characteristic, complemented
548	#3040	C₂×C₆₇	1	1	yes	characteristic, complemented
549	#3039	C₂×C₆₇	1	1	yes	characteristic, complemented
550	#3011	C₂×C₆₇	1	1	yes	characteristic, complemented
551	#3011	C₂×C₆₇	1	1	yes	characteristic, complemented
552	#3010	C₂×C₆₇	1	1	yes	characteristic, complemented
553	#3009	C₂×C₆₇	1	1	yes	characteristic, complemented
554	#2943	C₂×C₆₇	1	1	yes	characteristic, complemented
555	#2932	C₂×C₆₇	1	1	yes	characteristic, complemented
556	C₆₇	#61083	1	1	yes	characteristic, direct product factor, Sylow
557	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic
558	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic
559	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic, complemented
560	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic
561	#578	—	2	8	no	—
562	#577	—	2	8	no	—
563	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
564	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
565	C₂×#137	C₂²×C₆₇	1	2	yes	—
566	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
567	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic, complemented
568	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
569	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
570	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	—
571	C₂×#135	C₂²×C₆₇	1	2	yes	—
572	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
573	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
574	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
575	C₂²×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
576	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
577	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
578	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	—
579	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
580	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic
581	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
582	D₄×Q₈	C₂²×C₆₇	1	4	yes	complemented
583	#548	C₂²×C₆₇	1	4	yes	—
584	#547	—	2	4	no	—
585	#547	C₂²×C₆₇	1	4	yes	complemented
586	#546	—	2	4	no	—
587	#546	C₂²×C₆₇	1	4	yes	—
588	#536	—	2	1	no	—
589	#536	—	2	1	no	—
590	#536	—	2	1	no	—
591	#536	C₂²×C₆₇	1	1	yes	characteristic
592	#536	C₂²×C₆₇	1	1	yes	characteristic
593	#536	C₂²×C₆₇	1	1	yes	characteristic, complemented
594	#535	—	2	1	no	—
595	#535	C₂²×C₆₇	1	1	yes	characteristic
596	#532	—	2	1	no	—
597	#532	—	2	1	no	—
598	#532	C₂²×C₆₇	1	1	yes	characteristic
599	C₂×C₄⋊Q₈	—	2	1	no	—
600	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
601	C₂×#124	—	2	1	no	—
602	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
603	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
604	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
605	#497	C₂²×C₆₇	1	4	yes	complemented
606	#497	C₂²×C₆₇	1	4	yes	complemented
607	#470	C₂²×C₆₇	1	4	yes	complemented
608	#468	C₂²×C₆₇	1	4	yes	complemented
609	#467	C₂²×C₆₇	1	4	yes	complemented
610	#465	C₂²×C₆₇	1	4	yes	complemented
611	#464	C₂²×C₆₇	1	4	yes	complemented
612	#463	C₂²×C₆₇	1	4	yes	complemented
613	#462	C₂²×C₆₇	1	4	yes	complemented
614	#461	C₂²×C₆₇	1	4	yes	complemented
615	#452	C₂²×C₆₇	1	4	yes	—
616	#452	C₂²×C₆₇	1	4	yes	complemented
617	#452	C₂²×C₆₇	1	4	yes	complemented
618	#451	C₂²×C₆₇	1	4	yes	complemented
619	#451	C₂²×C₆₇	1	4	yes	complemented
620	#450	C₂²×C₆₇	1	4	yes	—
621	#449	C₂²×C₆₇	1	4	yes	complemented
622	#448	C₂²×C₆₇	1	4	yes	complemented
623	#442	C₂²×C₆₇	1	2	yes	complemented
624	#441	C₂²×C₆₇	1	2	yes	complemented
625	#440	C₂²×C₆₇	1	2	yes	complemented
626	#440	C₂²×C₆₇	1	2	yes	complemented
627	#435	C₂²×C₆₇	1	4	yes	complemented
628	#435	C₂²×C₆₇	1	4	yes	complemented
629	#427	C₂²×C₆₇	1	1	yes	characteristic, complemented
630	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
631	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
632	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
633	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
634	#418	C₂²×C₆₇	1	1	yes	characteristic
635	#416	C₂²×C₆₇	1	1	yes	characteristic
636	#416	C₂²×C₆₇	1	1	yes	characteristic, complemented
637	#408	C₂²×C₆₇	1	1	yes	characteristic
638	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
639	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic, complemented
640	2₋¹⁺⁴	—	2	4	no	—
641	2₋¹⁺⁴	—	2	4	no	—
642	2₋¹⁺⁴	—	2	4	no	—
643	2₋¹⁺⁴	—	4	2	no	—
644	2₋¹⁺⁴	—	4	2	no	—
645	2₋¹⁺⁴	—	4	2	no	—
646	H(5,𝔽₂)	—	2	4	no	—
647	H(5,𝔽₂)	—	4	2	no	—
648	C₂×#41	—	2	1	no	—
649	C₂×#41	—	2	1	no	—
650	C₂×#41	—	2	1	no	—
651	C₂×#41	—	2	1	no	—
652	C₂×#41	—	2	2	no	—
653	C₂×#41	—	2	2	no	—
654	C₂×#41	—	2	2	no	—
655	C₂×#41	C₂³×C₆₇	1	2	yes	—
656	C₂×#41	C₂³×C₆₇	1	2	yes	—
657	C₂×#41	C₂³×C₆₇	1	2	yes	—
658	C₂×#41	C₂³×C₆₇	1	2	yes	—
659	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
660	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
661	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
662	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
663	C₂²×Q₈	—	2	1	no	—
664	C₂²×Q₈	—	2	1	no	—
665	C₂²×Q₈	—	2	1	no	—
666	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
667	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
668	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
669	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
670	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
671	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
672	C₂²×D₄	—	2	1	no	—
673	C₂²×D₄	—	2	2	no	—
674	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
675	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
676	#137	—	2	4	no	—
677	#137	—	2	4	no	—
678	#137	—	2	4	no	—
679	#137	—	2	8	no	—
680	#137	—	2	8	no	—
681	#137	—	2	8	no	—
682	AGL(1,ℤ/8)	—	2	4	no	—
683	AGL(1,ℤ/8)	—	2	8	no	—
684	#135	—	2	8	no	—
685	#135	—	2	8	no	—
686	#135	D₄×C₆₇	1	8	yes	complemented
687	C₂×Q₁₆	—	2	8	no	—
688	C₂×Q₁₆	—	2	4	no	—
689	C₂×Q₁₆	—	4	2	no	—
690	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
691	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
692	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
693	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
694	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
695	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
696	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
697	C₂×SD₁₆	—	2	8	no	—
698	C₂×SD₁₆	—	2	4	no	—
699	C₂×SD₁₆	—	4	2	no	—
700	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
701	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
702	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
703	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
704	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
705	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
706	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
707	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
708	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
709	C₂×D₈	C₂³×C₆₇	1	2	yes	—
710	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
711	#131	—	2	4	no	—
712	#131	—	2	4	no	—
713	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
714	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
715	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
716	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
717	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
718	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
719	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
720	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
721	C₄⋊Q₈	—	2	1	no	—
722	C₄⋊Q₈	—	2	1	no	—
723	C₄⋊Q₈	—	2	1	no	—
724	C₄⋊Q₈	—	2	4	no	—
725	C₄⋊Q₈	—	2	1	no	—
726	C₄⋊Q₈	—	2	1	no	—
727	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
728	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
729	#127	—	2	1	no	—
730	#127	D₄×C₆₇	1	1	yes	characteristic
731	#124	—	2	1	no	—
732	#124	—	2	1	no	—
733	#124	—	2	1	no	—
734	#124	—	2	1	no	—
735	#124	—	2	4	no	—
736	#124	—	2	1	no	—
737	#124	—	2	1	no	—
738	#124	D₄×C₆₇	1	1	yes	characteristic
739	#124	D₄×C₆₇	1	1	yes	characteristic
740	#124	C₂³×C₆₇	1	4	yes	—
741	#123	—	2	2	no	—
742	#123	—	2	2	no	—
743	#123	—	2	2	no	—
744	#123	—	2	4	no	—
745	#123	—	2	4	no	—
746	#123	—	2	4	no	—
747	C₂²⋊Q₈	—	2	4	no	—
748	C₂²⋊Q₈	—	2	4	no	—
749	C₂²⋊Q₈	—	2	4	no	—
750	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
751	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
752	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
753	#121	—	2	4	no	—
754	#121	—	2	4	no	—
755	#121	—	2	4	no	—
756	#121	D₄×C₆₇	1	4	yes	—
757	#121	C₂³×C₆₇	1	4	yes	—
758	#120	—	2	4	no	—
759	#120	—	2	2	no	—
760	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
761	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
762	C₄×D₄	—	2	4	no	—
763	C₄×D₄	—	2	2	no	—
764	C₄×D₄	—	2	2	no	—
765	C₄×D₄	—	2	4	no	—
766	C₄×D₄	C₂³×C₆₇	1	2	yes	—
767	C₄×D₄	C₂³×C₆₇	1	2	yes	—
768	C₄×D₄	C₂³×C₆₇	1	4	yes	—
769	#117	—	2	1	no	—
770	#117	—	2	1	no	—
771	#117	C₂³×C₆₇	1	1	yes	characteristic
772	#117	C₂³×C₆₇	1	1	yes	characteristic
773	C₂×C₄⋊C₄	—	2	2	no	—
774	C₂×C₄⋊C₄	—	2	4	no	—
775	C₂×C₂²⋊C₄	—	2	2	no	—
776	C₂×C₂²⋊C₄	—	2	4	no	—
777	C₂×C₄²	—	2	1	no	—
778	C₂×C₄²	—	2	1	no	—
779	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
780	#107	C₂³×C₆₇	1	2	yes	—
781	#106	C₂³×C₆₇	1	2	yes	—
782	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
783	#103	C₂³×C₆₇	1	2	yes	—
784	#103	C₂³×C₆₇	1	2	yes	—
785	#103	C₂³×C₆₇	1	4	yes	—
786	#103	C₂³×C₆₇	1	4	yes	—
787	#103	C₂³×C₆₇	1	4	yes	—
788	#102	C₂³×C₆₇	1	2	yes	—
789	#102	C₂³×C₆₇	1	2	yes	—
790	#102	C₂³×C₆₇	1	4	yes	—
791	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
792	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
793	#97	C₂³×C₆₇	1	2	yes	—
794	#97	C₂³×C₆₇	1	2	yes	—
795	C₂⁴	—	2	2	no	—
796	C₂⁴	—	2	1	no	—
797	#41	—	2	2	no	—
798	#41	—	2	2	no	—
799	#41	—	2	2	no	—
800	#41	—	2	2	no	—
801	#41	—	2	2	no	—
802	#41	—	2	2	no	—
803	#41	—	2	4	no	—
804	#41	—	2	4	no	—
805	#41	—	2	4	no	—
806	#41	—	2	4	no	—
807	#41	—	4	2	no	—
808	#41	—	4	2	no	—
809	#41	—	4	2	no	—
810	#41	—	4	2	no	—
811	#41	—	4	4	no	—
812	#41	—	4	4	no	—
813	#41	—	4	4	no	—
814	#41	—	4	4	no	—
815	#41	—	4	8	no	—
816	#41	—	4	8	no	—
817	#41	—	4	8	no	—
818	#41	C₂×D₄×C₆₇	1	4	yes	—
819	#41	C₂×D₄×C₆₇	1	4	yes	—
820	C₂×Q₈	—	2	2	no	—
821	C₂×Q₈	—	2	2	no	—
822	C₂×Q₈	—	2	2	no	—
823	C₂×Q₈	—	2	1	no	—
824	C₂×Q₈	—	2	1	no	—
825	C₂×Q₈	—	2	1	no	—
826	C₂×Q₈	—	2	4	no	—
827	C₂×Q₈	—	2	4	no	—
828	C₂×Q₈	—	2	4	no	—
829	C₂×Q₈	—	2	2	no	—
830	C₂×Q₈	—	2	2	no	—
831	C₂×Q₈	—	2	2	no	—
832	C₂×Q₈	—	2	2	no	—
833	C₂×Q₈	—	2	2	no	—
834	C₂×Q₈	—	2	2	no	—
835	C₂×Q₈	—	4	2	no	—
836	C₂×Q₈	—	4	2	no	—
837	C₂×Q₈	—	4	2	no	—
838	C₂×Q₈	—	4	4	no	—
839	C₂×Q₈	—	4	4	no	—
840	C₂×Q₈	—	4	4	no	—
841	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
842	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
843	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
844	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
845	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
846	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
847	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
848	C₂×D₄	—	2	1	no	—
849	C₂×D₄	—	2	1	no	—
850	C₂×D₄	—	2	4	no	—
851	C₂×D₄	—	2	2	no	—
852	C₂×D₄	—	2	2	no	—
853	C₂×D₄	—	2	2	no	—
854	C₂×D₄	—	2	2	no	—
855	C₂×D₄	—	2	4	no	—
856	C₂×D₄	—	2	2	no	—
857	C₂×D₄	—	2	2	no	—
858	C₂×D₄	—	2	1	no	—
859	C₂×D₄	—	2	2	no	—
860	C₂×D₄	—	4	2	no	—
861	C₂×D₄	—	4	4	no	—
862	C₂×D₄	—	4	8	no	—
863	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
864	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
865	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
866	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
867	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
868	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
869	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
870	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
871	C₂²×C₄	—	2	1	no	—
872	C₂²×C₄	—	2	1	no	—
873	C₂²×C₄	—	2	1	no	—
874	C₂²×C₄	—	2	1	no	—
875	C₂²×C₄	—	2	1	no	—
876	C₂²×C₄	—	2	2	no	—
877	C₂²×C₄	—	2	2	no	—
878	C₂²×C₄	—	2	2	no	—
879	C₂²×C₄	—	2	2	no	—
880	C₂²×C₄	—	2	2	no	—
881	C₂²×C₄	—	2	2	no	—
882	C₂²×C₄	—	2	2	no	—
883	C₂²×C₄	—	2	2	no	—
884	C₂²×C₄	—	2	2	no	—
885	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
886	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
887	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
888	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
889	Q₁₆	—	2	4	no	—
890	Q₁₆	—	2	4	no	—
891	Q₁₆	—	2	4	no	—
892	Q₁₆	—	2	4	no	—
893	Q₁₆	—	2	4	no	—
894	Q₁₆	—	4	4	no	—
895	Q₁₆	C₂×D₄×C₆₇	1	4	yes	—
896	SD₁₆	—	2	4	no	—
897	SD₁₆	—	2	4	no	—
898	SD₁₆	—	2	4	no	—
899	SD₁₆	—	2	4	no	—
900	SD₁₆	—	2	4	no	—
901	SD₁₆	—	2	4	no	—
902	SD₁₆	—	4	4	no	—
903	SD₁₆	C₂×D₄×C₆₇	1	4	yes	—
904	SD₁₆	C₂×D₄×C₆₇	1	4	yes	—
905	D₈	—	2	4	no	—
906	D₈	C₂×D₄×C₆₇	1	4	yes	—
907	M₁₆	—	2	2	no	—
908	M₁₆	—	2	2	no	—
909	M₁₆	—	2	4	no	—
910	M₁₆	—	2	4	no	—
911	C₂×C₈	—	2	2	no	—
912	C₂×C₈	—	2	4	no	—
913	C₂×C₈	—	2	4	no	—
914	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	—
915	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
916	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
917	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
918	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
919	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
920	C₄⋊C₄	—	2	4	no	—
921	C₄⋊C₄	—	2	4	no	—
922	C₄⋊C₄	—	2	4	no	—
923	C₄⋊C₄	—	2	4	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	4	no	—
927	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
928	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
929	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
930	C₂²⋊C₄	—	2	4	no	—
931	C₂²⋊C₄	—	2	1	no	—
932	C₂²⋊C₄	—	2	1	no	—
933	C₂²⋊C₄	—	2	4	no	—
934	C₂²⋊C₄	—	2	4	no	—
935	C₂²⋊C₄	—	2	4	no	—
936	C₂²⋊C₄	—	2	4	no	—
937	C₂²⋊C₄	—	2	4	no	—
938	C₂²⋊C₄	—	2	2	no	—
939	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
941	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
942	C₄²	—	2	1	no	—
943	C₄²	—	2	1	no	—
944	C₄²	—	2	2	no	—
945	C₄²	—	2	2	no	—
946	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
947	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
948	C₄²	C₂⁴×C₆₇	1	2	yes	—
949	C₂³	—	2	1	no	—
950	C₂³	—	2	1	no	—
951	C₂³	—	2	2	no	—
952	C₂³	—	4	4	no	—
953	C₂³	—	4	2	no	—
954	C₂³	—	8	2	no	—
955	C₂³	—	8	4	no	—
956	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
957	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
958	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
959	Q₈	—	2	2	no	—
960	Q₈	—	2	2	no	—
961	Q₈	—	2	1	no	—
962	Q₈	—	2	1	no	—
963	Q₈	—	2	2	no	—
964	Q₈	—	2	2	no	—
965	Q₈	—	2	2	no	—
966	Q₈	—	2	2	no	—
967	Q₈	—	2	2	no	—
968	Q₈	—	2	2	no	—
969	Q₈	—	4	4	no	—
970	Q₈	—	4	4	no	—
971	Q₈	—	4	4	no	—
972	Q₈	—	4	2	no	—
973	Q₈	—	4	2	no	—
974	Q₈	—	4	2	no	—
975	Q₈	C₂²×D₄×C₆₇	1	2	yes	—
976	Q₈	C₂²×D₄×C₆₇	1	2	yes	—
977	D₄	—	2	4	no	—
978	D₄	—	2	4	no	—
979	D₄	—	2	4	no	—
980	D₄	—	2	4	no	—
981	D₄	—	2	2	no	—
982	D₄	—	2	2	no	—
983	D₄	—	2	2	no	—
984	D₄	—	2	1	no	—
985	D₄	—	2	1	no	—
986	D₄	—	2	2	no	—
987	D₄	—	4	4	no	—
988	D₄	—	4	4	no	—
989	D₄	—	4	4	no	—
990	D₄	—	4	4	no	—
991	D₄	—	4	4	no	—
992	D₄	—	4	4	no	—
993	D₄	—	4	2	no	—
994	D₄	—	8	4	no	—
995	D₄	C₂²×D₄×C₆₇	1	2	yes	—
996	D₄	C₂²×D₄×C₆₇	1	2	yes	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	4	no	—
1000	C₂×C₄	—	2	4	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	4	2	no	—
1011	C₂×C₄	—	4	4	no	—
1012	C₂×C₄	—	4	4	no	—
1013	C₂×C₄	—	4	4	no	—
1014	C₂×C₄	—	4	4	no	—
1015	C₂×C₄	—	4	4	no	—
1016	C₂×C₄	—	4	4	no	—
1017	C₂×C₄	—	4	4	no	—
1018	C₂×C₄	—	4	4	no	—
1019	C₂×C₄	—	4	2	no	—
1020	C₂×C₄	—	4	2	no	—
1021	C₂×C₄	—	4	2	no	—
1022	C₂×C₄	—	8	2	no	—
1023	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1024	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1025	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1026	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1027	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1028	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1029	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1030	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1031	C₈	—	2	2	no	—
1032	C₈	—	2	2	no	—
1033	C₈	—	2	2	no	—
1034	C₈	C₂²×D₄×C₆₇	1	2	yes	—
1035	C₈	C₂²×D₄×C₆₇	1	2	yes	—
1036	C₂²	—	2	2	no	—
1037	C₂²	—	2	4	no	—
1038	C₂²	—	2	4	no	—
1039	C₂²	—	2	2	no	—
1040	C₂²	—	2	2	no	—
1041	C₂²	—	2	2	no	—
1042	C₂²	—	2	2	no	—
1043	C₂²	—	4	2	no	—
1044	C₂²	—	4	2	no	—
1045	C₂²	—	4	4	no	—
1046	C₂²	—	4	2	no	—
1047	C₂²	—	16	2	no	—
1048	C₂²	—	16	4	no	—
1049	C₂²	D₄²×C₆₇	1	2	yes	—
1050	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1051	C₄	—	2	2	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	—	4	2	no	—
1058	C₄	—	4	2	no	—
1059	C₄	—	4	2	no	—
1060	C₄	—	4	2	no	—
1061	C₄	—	4	2	no	—
1062	C₄	D₄²×C₆₇	1	2	yes	—
1063	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
1064	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1065	C₂	—	2	2	no	—
1066	C₂	—	4	2	no	—
1067	C₂	—	4	2	no	—
1068	C₂	—	4	2	no	—
1069	C₂	—	4	2	no	—
1070	C₂	—	8	2	no	—
1071	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
1072	C₂	C₆₇×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #532×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#578×C₆₇	C₂	semidirect
2. C₂×#577×C₆₇	C₂	semidirect
3. C₆₇×#3500	C₂	semidirect
4. C₆₇×#3499	C₂	semidirect
5. C₆₇×#3270	C₂	semidirect
6. C₆₇×#3269	C₂	semidirect
7. C₆₇×#3267	C₂	semidirect
8. C₆₇×#3266	C₂	semidirect
9. C₂×#497×C₆₇	C₂	semidirect
10. C₆₇×#3059	C₂	semidirect
11. C₆₇×#3057	C₂	semidirect
12. C₆₇×#3040	C₂	semidirect
13. C₆₇×#3039	C₂	semidirect
14. C₆₇×#3011	C₂	semidirect
15. C₆₇×#3011	C₂	semidirect
16. C₆₇×#3010	C₂	semidirect
17. C₆₇×#3009	C₂	semidirect
18. C₆₇×#2943	C₂	semidirect
19. C₆₇×#2932	C₂	semidirect
22. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
29. C₂×#137×C₆₇	C₂²	semidirect
30. C₂×#137×C₆₇	C₂²	semidirect
31. C₂×#137×C₆₇	C₂²	semidirect
36. C₂×#135×C₆₇	C₂²	semidirect
37. C₂²×Q₁₆×C₆₇	C₂²	semidirect
38. C₂²×Q₁₆×C₆₇	C₂²	semidirect
39. C₂²×Q₁₆×C₆₇	C₂²	semidirect
44. C₂×#131×C₆₇	C₂²	semidirect
45. D₄×Q₈×C₆₇	C₂²	semidirect
48. #547×C₆₇	C₂²	semidirect
56. #536×C₆₇	C₂²	semidirect
63. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
67. C₄×#41×C₆₇	C₂²	semidirect
68. #497×C₆₇	C₂²	semidirect
69. #497×C₆₇	C₂²	semidirect
70. #470×C₆₇	C₂²	semidirect
71. #468×C₆₇	C₂²	semidirect
72. #467×C₆₇	C₂²	semidirect
73. #465×C₆₇	C₂²	semidirect
74. #464×C₆₇	C₂²	semidirect
75. #463×C₆₇	C₂²	semidirect
76. #462×C₆₇	C₂²	semidirect
77. #461×C₆₇	C₂²	semidirect
79. #452×C₆₇	C₂²	semidirect
80. #452×C₆₇	C₂²	semidirect
81. #451×C₆₇	C₂²	semidirect
82. #451×C₆₇	C₂²	semidirect
84. #449×C₆₇	C₂²	semidirect
85. #448×C₆₇	C₂²	semidirect
86. #442×C₆₇	C₂²	semidirect
87. #441×C₆₇	C₂²	semidirect
88. #440×C₆₇	C₂²	semidirect
89. #440×C₆₇	C₂²	semidirect
90. #435×C₆₇	C₂²	semidirect
91. #435×C₆₇	C₂²	semidirect
92. #427×C₆₇	C₂²	semidirect
93. #423×C₆₇	C₂²	semidirect
94. #419×C₆₇	C₂²	semidirect
95. #419×C₆₇	C₂²	semidirect
96. #419×C₆₇	C₂²	semidirect
99. #416×C₆₇	C₂²	semidirect
101. #408×C₆₇	C₂²	semidirect
102. C₂×#97×C₆₇	C₂²	semidirect
149. #135×C₆₇	D₄	semidirect
528. #61083	C₆₇	direct (N × H)
537. C₂×#578	C₂×C₆₇	semidirect
538. C₂×#577	C₂×C₆₇	semidirect
539. #3500	C₂×C₆₇	semidirect
540. #3499	C₂×C₆₇	semidirect
541. #3270	C₂×C₆₇	semidirect
542. #3269	C₂×C₆₇	semidirect
543. #3267	C₂×C₆₇	semidirect
544. #3266	C₂×C₆₇	semidirect
545. C₂×#497	C₂×C₆₇	semidirect
546. #3059	C₂×C₆₇	semidirect
547. #3057	C₂×C₆₇	semidirect
548. #3040	C₂×C₆₇	semidirect
549. #3039	C₂×C₆₇	semidirect
550. #3011	C₂×C₆₇	semidirect
551. #3011	C₂×C₆₇	semidirect
552. #3010	C₂×C₆₇	semidirect
553. #3009	C₂×C₆₇	semidirect
554. #2943	C₂×C₆₇	semidirect
555. #2932	C₂×C₆₇	semidirect
556. C₆₇	#61083	direct (N × H)
559. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
566. C₂×#137	C₂²×C₆₇	semidirect
567. C₂×#137	C₂²×C₆₇	semidirect
568. C₂×#137	C₂²×C₆₇	semidirect
573. C₂×#135	C₂²×C₆₇	semidirect
574. C₂²×Q₁₆	C₂²×C₆₇	semidirect
575. C₂²×Q₁₆	C₂²×C₆₇	semidirect
576. C₂²×Q₁₆	C₂²×C₆₇	semidirect
581. C₂×#131	C₂²×C₆₇	semidirect
582. D₄×Q₈	C₂²×C₆₇	semidirect
585. #547	C₂²×C₆₇	semidirect
593. #536	C₂²×C₆₇	semidirect
600. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
604. C₄×#41	C₂²×C₆₇	semidirect
605. #497	C₂²×C₆₇	semidirect
606. #497	C₂²×C₆₇	semidirect
607. #470	C₂²×C₆₇	semidirect
608. #468	C₂²×C₆₇	semidirect
609. #467	C₂²×C₆₇	semidirect
610. #465	C₂²×C₆₇	semidirect
611. #464	C₂²×C₆₇	semidirect
612. #463	C₂²×C₆₇	semidirect
613. #462	C₂²×C₆₇	semidirect
614. #461	C₂²×C₆₇	semidirect
616. #452	C₂²×C₆₇	semidirect
617. #452	C₂²×C₆₇	semidirect
618. #451	C₂²×C₆₇	semidirect
619. #451	C₂²×C₆₇	semidirect
621. #449	C₂²×C₆₇	semidirect
622. #448	C₂²×C₆₇	semidirect
623. #442	C₂²×C₆₇	semidirect
624. #441	C₂²×C₆₇	semidirect
625. #440	C₂²×C₆₇	semidirect
626. #440	C₂²×C₆₇	semidirect
627. #435	C₂²×C₆₇	semidirect
628. #435	C₂²×C₆₇	semidirect
629. #427	C₂²×C₆₇	semidirect
630. #423	C₂²×C₆₇	semidirect
631. #419	C₂²×C₆₇	semidirect
632. #419	C₂²×C₆₇	semidirect
633. #419	C₂²×C₆₇	semidirect
636. #416	C₂²×C₆₇	semidirect
638. #408	C₂²×C₆₇	semidirect
639. C₂×#97	C₂²×C₆₇	semidirect
686. #135	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×#578×C₆₇	2
C₂×#577×C₆₇	2
C₆₇×#3500	2
C₆₇×#3499	2
C₆₇×#3270	2
C₆₇×#3269	2
C₆₇×#3267	2
C₆₇×#3266	2
C₂×#497×C₆₇	2
C₆₇×#3059	2
C₆₇×#3057	2
C₆₇×#3040	2
C₆₇×#3039	2
C₆₇×#3011	2
C₆₇×#3010	2
C₆₇×#3009	2
C₆₇×#2943	2
C₆₇×#2932	2
#61083	67

Subgroups — C67×#61083 #30740334

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61083 #30740334