Subgroups — C₆₇×#61063 #30740314

Order 17152.

2818 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#576×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#575×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3488	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3275	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3274	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3271	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3264	C₂	1	4	yes	maximal, complemented
8	C₆₇×#3155	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3060	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#469×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3045	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3012	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3006	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2952	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2930	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	2	yes	complemented
17	C₂²×#41×C₆₇	C₂²	1	2	yes	complemented
18	#576×C₆₇	—	2	8	no	—
19	#575×C₆₇	—	2	8	no	—
20	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
21	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
22	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
23	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	complemented
24	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
25	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
26	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
27	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
29	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
30	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
32	C₂²×D₈×C₆₇	C₂²	1	2	yes	complemented
33	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
34	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	#550×C₆₇	C₂²	1	4	yes	complemented
36	#548×C₆₇	C₂²	1	4	yes	complemented
37	#546×C₆₇	—	2	4	no	—
38	#546×C₆₇	C₂²	1	4	yes	complemented
39	D₄²×C₆₇	—	2	4	no	—
40	D₄²×C₆₇	C₂²	1	4	yes	complemented
41	#537×C₆₇	—	2	2	no	—
42	#537×C₆₇	C₂²	1	2	yes	complemented
43	#535×C₆₇	—	2	2	no	—
44	#535×C₆₇	C₂²	1	2	yes	complemented
45	#525×C₆₇	—	2	2	no	—
46	#525×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×#121×C₆₇	—	2	2	no	—
48	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
49	#520×C₆₇	C₂²	1	2	yes	complemented
50	#496×C₆₇	C₂²	1	4	yes	complemented
51	#495×C₆₇	C₂²	1	2	yes	complemented
52	#493×C₆₇	C₂²	1	2	yes	complemented
53	#470×C₆₇	C₂²	1	2	yes	complemented
54	#469×C₆₇	C₂²	1	4	yes	complemented
55	#469×C₆₇	C₂²	1	2	yes	complemented
56	#469×C₆₇	C₂²	1	4	yes	complemented
57	#465×C₆₇	C₂²	1	4	yes	complemented
58	#464×C₆₇	C₂²	1	4	yes	complemented
59	#463×C₆₇	C₂²	1	4	yes	complemented
60	#460×C₆₇	C₂²	1	4	yes	complemented
61	#459×C₆₇	C₂²	1	4	yes	complemented
62	#452×C₆₇	C₂²	1	4	yes	complemented
63	#450×C₆₇	C₂²	1	4	yes	complemented
64	#449×C₆₇	C₂²	1	4	yes	complemented
65	#449×C₆₇	C₂²	1	4	yes	complemented
66	#449×C₆₇	C₂²	1	4	yes	complemented
67	#448×C₆₇	C₂²	1	4	yes	complemented
68	#447×C₆₇	C₂²	1	4	yes	complemented
69	#447×C₆₇	C₂²	1	4	yes	complemented
70	#442×C₆₇	C₂²	1	2	yes	complemented
71	#441×C₆₇	C₂²	1	2	yes	complemented
72	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
73	#436×C₆₇	C₂²	1	4	yes	complemented
74	#435×C₆₇	C₂²	1	4	yes	complemented
75	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic, complemented
76	#424×C₆₇	C₂²	1	1	yes	characteristic, complemented
77	#417×C₆₇	C₂²	1	2	yes	complemented
78	#417×C₆₇	C₂²	1	2	yes	complemented
79	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
80	#408×C₆₇	C₂²	1	1	yes	characteristic, complemented
81	#407×C₆₇	C₂²	1	1	yes	characteristic, complemented
82	#405×C₆₇	C₂²	1	1	yes	characteristic, complemented
83	H(5,𝔽₂)×C₆₇	—	2	8	no	—
84	H(5,𝔽₂)×C₆₇	—	4	4	no	—
85	C₂×#41×C₆₇	—	2	2	no	—
86	C₂×#41×C₆₇	—	2	2	no	—
87	C₂×#41×C₆₇	—	2	2	no	—
88	C₂×#41×C₆₇	—	2	8	no	—
89	C₂×#41×C₆₇	—	4	4	no	—
90	C₂×#41×C₆₇	C₂³	1	2	yes	—
91	C₂×#41×C₆₇	C₂³	1	2	yes	—
92	C₂×#41×C₆₇	C₂³	1	2	yes	—
93	C₂×#41×C₆₇	C₂³	1	4	yes	—
94	C₂×#41×C₆₇	C₂³	1	2	yes	—
95	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
97	C₂²×D₄×C₆₇	—	2	2	no	—
98	C₂²×D₄×C₆₇	—	2	2	no	—
99	C₂²×D₄×C₆₇	—	2	2	no	—
100	C₂²×D₄×C₆₇	—	2	4	no	—
101	C₂²×D₄×C₆₇	—	2	4	no	—
102	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
103	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
104	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
105	C₂³×C₄×C₆₇	—	2	2	no	—
106	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
107	#137×C₆₇	—	2	8	no	—
108	#137×C₆₇	—	2	8	no	—
109	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
110	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
111	AGL(1,ℤ/8)×C₆₇	—	2	16	no	—
112	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
113	AGL(1,ℤ/8)×C₆₇	—	4	4	no	—
114	#135×C₆₇	—	2	8	no	—
115	#135×C₆₇	—	2	8	no	—
116	#135×C₆₇	—	2	4	no	—
117	#135×C₆₇	D₄	1	8	yes	complemented
118	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
119	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
120	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
121	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
122	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
123	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
124	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
125	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
126	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
127	C₂×D₈×C₆₇	—	2	8	no	—
128	C₂×D₈×C₆₇	—	2	4	no	—
129	C₂×D₈×C₆₇	C₂³	1	4	yes	—
130	C₂×D₈×C₆₇	C₂³	1	2	yes	—
131	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
132	C₂×D₈×C₆₇	C₂³	1	2	yes	—
133	C₂×D₈×C₆₇	C₂³	1	2	yes	—
134	C₂×D₈×C₆₇	C₂³	1	4	yes	—
135	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
136	#131×C₆₇	—	2	4	no	—
137	C₂×M₁₆×C₆₇	—	2	4	no	—
138	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
139	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
140	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
141	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
144	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
145	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
146	#127×C₆₇	—	2	4	no	—
147	#127×C₆₇	C₂³	1	4	yes	—
148	#124×C₆₇	—	2	4	no	—
149	#124×C₆₇	C₂³	1	4	yes	—
150	#123×C₆₇	—	2	4	no	—
151	#123×C₆₇	D₄	1	2	yes	—
152	C₂²⋊Q₈×C₆₇	—	2	2	no	—
153	C₂²⋊Q₈×C₆₇	—	2	4	no	—
154	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
155	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
156	#121×C₆₇	—	2	2	no	—
157	#121×C₆₇	—	2	4	no	—
158	#121×C₆₇	—	2	4	no	—
159	#121×C₆₇	—	2	2	no	—
160	#121×C₆₇	—	2	2	no	—
161	#121×C₆₇	—	2	2	no	—
162	#121×C₆₇	—	2	2	no	—
163	#121×C₆₇	—	2	4	no	—
164	#121×C₆₇	—	2	4	no	—
165	#121×C₆₇	—	2	4	no	—
166	#121×C₆₇	—	2	4	no	—
167	#121×C₆₇	D₄	1	2	yes	—
168	#121×C₆₇	C₂³	1	4	yes	—
169	#121×C₆₇	C₂³	1	4	yes	—
170	#121×C₆₇	C₂³	1	4	yes	—
171	#120×C₆₇	—	2	4	no	—
172	#120×C₆₇	—	2	4	no	—
173	#120×C₆₇	—	2	4	no	—
174	#120×C₆₇	—	2	4	no	—
175	#120×C₆₇	D₄	1	2	yes	—
176	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
177	C₄×D₄×C₆₇	—	2	4	no	—
178	C₄×D₄×C₆₇	—	2	4	no	—
179	C₄×D₄×C₆₇	—	2	4	no	—
180	C₄×D₄×C₆₇	C₂³	1	4	yes	—
181	C₄×D₄×C₆₇	C₂³	1	4	yes	—
182	#117×C₆₇	—	2	2	no	—
183	#117×C₆₇	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
185	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
187	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
188	#106×C₆₇	C₂³	1	2	yes	—
189	#106×C₆₇	C₂³	1	2	yes	—
190	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
191	#103×C₆₇	C₂³	1	4	yes	—
192	#103×C₆₇	C₂³	1	4	yes	—
193	#102×C₆₇	C₂³	1	4	yes	—
194	#102×C₆₇	C₂³	1	4	yes	—
195	#102×C₆₇	C₂³	1	4	yes	—
196	#102×C₆₇	C₂³	1	4	yes	—
197	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
198	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
199	#97×C₆₇	C₂³	1	2	yes	—
200	C₄×C₈×C₆₇	C₂³	1	2	yes	—
201	C₂⁴×C₆₇	—	2	2	no	—
202	C₂⁴×C₆₇	—	2	4	no	—
203	C₂⁴×C₆₇	—	2	2	no	—
204	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
205	#41×C₆₇	—	2	2	no	—
206	#41×C₆₇	—	2	4	no	—
207	#41×C₆₇	—	2	2	no	—
208	#41×C₆₇	—	2	8	no	—
209	#41×C₆₇	—	2	4	no	—
210	#41×C₆₇	—	2	4	no	—
211	#41×C₆₇	—	2	4	no	—
212	#41×C₆₇	—	2	4	no	—
213	#41×C₆₇	—	4	8	no	—
214	#41×C₆₇	—	4	2	no	—
215	#41×C₆₇	—	4	2	no	—
216	#41×C₆₇	—	4	4	no	—
217	#41×C₆₇	—	4	8	no	—
218	#41×C₆₇	—	4	8	no	—
219	#41×C₆₇	C₂×D₄	1	8	yes	complemented
220	C₂×Q₈×C₆₇	—	2	2	no	—
221	C₂×Q₈×C₆₇	—	2	4	no	—
222	C₂×Q₈×C₆₇	—	4	2	no	—
223	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
224	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
225	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
226	C₂×D₄×C₆₇	—	2	2	no	—
227	C₂×D₄×C₆₇	—	2	8	no	—
228	C₂×D₄×C₆₇	—	2	4	no	—
229	C₂×D₄×C₆₇	—	2	4	no	—
230	C₂×D₄×C₆₇	—	2	2	no	—
231	C₂×D₄×C₆₇	—	2	2	no	—
232	C₂×D₄×C₆₇	—	2	4	no	—
233	C₂×D₄×C₆₇	—	2	2	no	—
234	C₂×D₄×C₆₇	—	2	4	no	—
235	C₂×D₄×C₆₇	—	2	4	no	—
236	C₂×D₄×C₆₇	—	2	4	no	—
237	C₂×D₄×C₆₇	—	2	2	no	—
238	C₂×D₄×C₆₇	—	2	4	no	—
239	C₂×D₄×C₆₇	—	2	2	no	—
240	C₂×D₄×C₆₇	—	2	4	no	—
241	C₂×D₄×C₆₇	—	2	4	no	—
242	C₂×D₄×C₆₇	—	2	4	no	—
243	C₂×D₄×C₆₇	—	4	2	no	—
244	C₂×D₄×C₆₇	—	4	4	no	—
245	C₂×D₄×C₆₇	—	4	8	no	—
246	C₂×D₄×C₆₇	—	4	16	no	—
247	C₂×D₄×C₆₇	—	4	8	no	—
248	C₂×D₄×C₆₇	—	8	8	no	—
249	C₂×D₄×C₆₇	—	8	4	no	—
250	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
251	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
252	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
253	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
254	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
255	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₆₇	—	2	2	no	—
257	C₂²×C₄×C₆₇	—	2	2	no	—
258	C₂²×C₄×C₆₇	—	2	2	no	—
259	C₂²×C₄×C₆₇	—	2	2	no	—
260	C₂²×C₄×C₆₇	—	2	2	no	—
261	C₂²×C₄×C₆₇	—	2	2	no	—
262	C₂²×C₄×C₆₇	—	2	2	no	—
263	C₂²×C₄×C₆₇	—	2	4	no	—
264	C₂²×C₄×C₆₇	—	2	2	no	—
265	C₂²×C₄×C₆₇	—	2	4	no	—
266	C₂²×C₄×C₆₇	—	4	8	no	—
267	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
269	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
272	Q₁₆×C₆₇	—	2	4	no	—
273	Q₁₆×C₆₇	—	2	2	no	—
274	Q₁₆×C₆₇	C₂×D₄	1	4	yes	complemented
275	SD₁₆×C₆₇	—	2	8	no	—
276	SD₁₆×C₆₇	—	2	4	no	—
277	SD₁₆×C₆₇	—	2	4	no	—
278	SD₁₆×C₆₇	—	2	4	no	—
279	SD₁₆×C₆₇	—	4	4	no	—
280	SD₁₆×C₆₇	C₂×D₄	1	8	yes	complemented
281	D₈×C₆₇	—	2	8	no	—
282	D₈×C₆₇	—	2	4	no	—
283	D₈×C₆₇	—	2	4	no	—
284	D₈×C₆₇	—	2	4	no	—
285	D₈×C₆₇	—	2	2	no	—
286	D₈×C₆₇	—	4	4	no	—
287	D₈×C₆₇	C₂×D₄	1	4	yes	complemented
288	M₁₆×C₆₇	—	2	2	no	—
289	M₁₆×C₆₇	—	2	2	no	—
290	M₁₆×C₆₇	—	2	4	no	—
291	M₁₆×C₆₇	—	2	4	no	—
292	M₁₆×C₆₇	—	2	4	no	—
293	C₂×C₈×C₆₇	—	2	2	no	—
294	C₂×C₈×C₆₇	—	2	4	no	—
295	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	complemented
296	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
297	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
298	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
299	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
300	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
301	C₄⋊C₄×C₆₇	—	2	2	no	—
302	C₄⋊C₄×C₆₇	—	2	4	no	—
303	C₄⋊C₄×C₆₇	—	2	4	no	—
304	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
305	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
306	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
307	C₂²⋊C₄×C₆₇	—	2	4	no	—
308	C₂²⋊C₄×C₆₇	—	2	4	no	—
309	C₂²⋊C₄×C₆₇	—	2	4	no	—
310	C₂²⋊C₄×C₆₇	—	2	4	no	—
311	C₂²⋊C₄×C₆₇	—	2	4	no	—
312	C₂²⋊C₄×C₆₇	—	2	4	no	—
313	C₂²⋊C₄×C₆₇	—	2	4	no	—
314	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
315	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
316	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
317	C₄²×C₆₇	—	2	4	no	—
318	C₄²×C₆₇	C₂⁴	1	2	yes	—
319	C₂³×C₆₇	—	2	2	no	—
320	C₂³×C₆₇	—	2	2	no	—
321	C₂³×C₆₇	—	2	4	no	—
322	C₂³×C₆₇	—	2	2	no	—
323	C₂³×C₆₇	—	4	2	no	—
324	C₂³×C₆₇	—	4	4	no	—
325	C₂³×C₆₇	—	4	8	no	—
326	C₂³×C₆₇	—	4	4	no	—
327	C₂³×C₆₇	—	4	4	no	—
328	C₂³×C₆₇	—	8	2	no	—
329	C₂³×C₆₇	—	8	2	no	—
330	C₂³×C₆₇	—	8	4	no	—
331	C₂³×C₆₇	—	8	2	no	—
332	C₂³×C₆₇	—	8	4	no	—
333	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
334	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
335	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
336	Q₈×C₆₇	—	2	2	no	—
337	Q₈×C₆₇	—	2	2	no	—
338	Q₈×C₆₇	—	2	2	no	—
339	Q₈×C₆₇	—	2	2	no	—
340	Q₈×C₆₇	—	4	4	no	—
341	Q₈×C₆₇	C₂²×D₄	1	4	yes	—
342	D₄×C₆₇	—	2	8	no	—
343	D₄×C₆₇	—	2	4	no	—
344	D₄×C₆₇	—	2	2	no	—
345	D₄×C₆₇	—	2	4	no	—
346	D₄×C₆₇	—	2	2	no	—
347	D₄×C₆₇	—	2	2	no	—
348	D₄×C₆₇	—	2	2	no	—
349	D₄×C₆₇	—	2	4	no	—
350	D₄×C₆₇	—	4	4	no	—
351	D₄×C₆₇	—	4	8	no	—
352	D₄×C₆₇	—	4	4	no	—
353	D₄×C₆₇	—	4	8	no	—
354	D₄×C₆₇	—	4	4	no	—
355	D₄×C₆₇	—	4	4	no	—
356	D₄×C₆₇	—	4	8	no	—
357	D₄×C₆₇	—	4	4	no	—
358	D₄×C₆₇	—	4	4	no	—
359	D₄×C₆₇	—	8	4	no	—
360	D₄×C₆₇	—	8	4	no	—
361	D₄×C₆₇	—	8	4	no	—
362	D₄×C₆₇	—	8	4	no	—
363	D₄×C₆₇	C₂²×D₄	1	4	yes	—
364	C₂×C₄×C₆₇	—	2	2	no	—
365	C₂×C₄×C₆₇	—	2	2	no	—
366	C₂×C₄×C₆₇	—	2	4	no	—
367	C₂×C₄×C₆₇	—	2	8	no	—
368	C₂×C₄×C₆₇	—	2	2	no	—
369	C₂×C₄×C₆₇	—	2	2	no	—
370	C₂×C₄×C₆₇	—	2	2	no	—
371	C₂×C₄×C₆₇	—	2	2	no	—
372	C₂×C₄×C₆₇	—	2	4	no	—
373	C₂×C₄×C₆₇	—	2	2	no	—
374	C₂×C₄×C₆₇	—	4	4	no	—
375	C₂×C₄×C₆₇	—	4	8	no	—
376	C₂×C₄×C₆₇	—	4	4	no	—
377	C₂×C₄×C₆₇	—	4	4	no	—
378	C₂×C₄×C₆₇	—	4	4	no	—
379	C₂×C₄×C₆₇	—	8	4	no	—
380	C₂×C₄×C₆₇	—	8	2	no	—
381	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
382	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
383	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
384	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
386	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
387	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
388	C₈×C₆₇	—	2	2	no	—
389	C₈×C₆₇	—	2	2	no	—
390	C₈×C₆₇	—	2	2	no	—
391	C₈×C₆₇	C₂²×D₄	1	2	yes	—
392	C₈×C₆₇	C₂²×D₄	1	2	yes	—
393	C₂²×C₆₇	—	2	2	no	—
394	C₂²×C₆₇	—	2	2	no	—
395	C₂²×C₆₇	—	2	4	no	—
396	C₂²×C₆₇	—	2	2	no	—
397	C₂²×C₆₇	—	2	2	no	—
398	C₂²×C₆₇	—	2	4	no	—
399	C₂²×C₆₇	—	2	2	no	—
400	C₂²×C₆₇	—	4	2	no	—
401	C₂²×C₆₇	—	4	2	no	—
402	C₂²×C₆₇	—	4	4	no	—
403	C₂²×C₆₇	—	4	2	no	—
404	C₂²×C₆₇	—	4	2	no	—
405	C₂²×C₆₇	—	4	4	no	—
406	C₂²×C₆₇	—	4	2	no	—
407	C₂²×C₆₇	—	4	4	no	—
408	C₂²×C₆₇	—	8	2	no	—
409	C₂²×C₆₇	—	8	8	no	—
410	C₂²×C₆₇	—	16	4	no	—
411	C₂²×C₆₇	—	16	8	no	—
412	C₂²×C₆₇	D₄²	1	2	yes	—
413	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
414	C₄×C₆₇	—	2	4	no	—
415	C₄×C₆₇	—	2	2	no	—
416	C₄×C₆₇	—	2	4	no	—
417	C₄×C₆₇	—	2	2	no	—
418	C₄×C₆₇	—	4	4	no	—
419	C₄×C₆₇	—	4	2	no	—
420	C₄×C₆₇	D₄²	1	2	yes	—
421	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
422	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
423	#61063	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
424	C₂×C₆₇	—	2	2	no	—
425	C₂×C₆₇	—	4	2	no	—
426	C₂×C₆₇	—	4	2	no	—
427	C₂×C₆₇	—	4	4	no	—
428	C₂×C₆₇	—	8	2	no	—
429	C₂×C₆₇	—	8	4	no	—
430	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
431	C₂×C₆₇	#3585	1	2	yes	—
432	C₂×#576	C₂×C₆₇	1	1	yes	characteristic, complemented
433	C₂×#575	C₂×C₆₇	1	1	yes	characteristic, complemented
434	#3488	C₂×C₆₇	1	2	yes	complemented
435	#3275	C₂×C₆₇	1	4	yes	complemented
436	#3274	C₂×C₆₇	1	4	yes	complemented
437	#3271	C₂×C₆₇	1	4	yes	complemented
438	#3264	C₂×C₆₇	1	4	yes	complemented
439	#3155	C₂×C₆₇	1	1	yes	characteristic, complemented
440	#3060	C₂×C₆₇	1	1	yes	characteristic, complemented
441	C₂×#469	C₂×C₆₇	1	1	yes	characteristic, complemented
442	#3045	C₂×C₆₇	1	2	yes	complemented
443	#3012	C₂×C₆₇	1	2	yes	complemented
444	#3006	C₂×C₆₇	1	2	yes	complemented
445	#2952	C₂×C₆₇	1	1	yes	characteristic, complemented
446	#2930	C₂×C₆₇	1	1	yes	characteristic, complemented
447	C₆₇	#61063	1	1	yes	characteristic, direct product factor, Sylow
448	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	complemented
449	C₂²×#41	C₂²×C₆₇	1	2	yes	complemented
450	#576	—	2	8	no	—
451	#575	—	2	8	no	—
452	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
453	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
454	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
455	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
456	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
457	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
458	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
459	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
460	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic, complemented
461	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
462	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
463	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
464	C₂²×D₈	C₂²×C₆₇	1	2	yes	complemented
465	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
466	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
467	#550	C₂²×C₆₇	1	4	yes	complemented
468	#548	C₂²×C₆₇	1	4	yes	complemented
469	#546	—	2	4	no	—
470	#546	C₂²×C₆₇	1	4	yes	complemented
471	D₄²	—	2	4	no	—
472	D₄²	C₂²×C₆₇	1	4	yes	complemented
473	#537	—	2	2	no	—
474	#537	C₂²×C₆₇	1	2	yes	complemented
475	#535	—	2	2	no	—
476	#535	C₂²×C₆₇	1	2	yes	complemented
477	#525	—	2	2	no	—
478	#525	C₂²×C₆₇	1	1	yes	characteristic
479	C₂×#121	—	2	2	no	—
480	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
481	#520	C₂²×C₆₇	1	2	yes	complemented
482	#496	C₂²×C₆₇	1	4	yes	complemented
483	#495	C₂²×C₆₇	1	2	yes	complemented
484	#493	C₂²×C₆₇	1	2	yes	complemented
485	#470	C₂²×C₆₇	1	2	yes	complemented
486	#469	C₂²×C₆₇	1	4	yes	complemented
487	#469	C₂²×C₆₇	1	2	yes	complemented
488	#469	C₂²×C₆₇	1	4	yes	complemented
489	#465	C₂²×C₆₇	1	4	yes	complemented
490	#464	C₂²×C₆₇	1	4	yes	complemented
491	#463	C₂²×C₆₇	1	4	yes	complemented
492	#460	C₂²×C₆₇	1	4	yes	complemented
493	#459	C₂²×C₆₇	1	4	yes	complemented
494	#452	C₂²×C₆₇	1	4	yes	complemented
495	#450	C₂²×C₆₇	1	4	yes	complemented
496	#449	C₂²×C₆₇	1	4	yes	complemented
497	#449	C₂²×C₆₇	1	4	yes	complemented
498	#449	C₂²×C₆₇	1	4	yes	complemented
499	#448	C₂²×C₆₇	1	4	yes	complemented
500	#447	C₂²×C₆₇	1	4	yes	complemented
501	#447	C₂²×C₆₇	1	4	yes	complemented
502	#442	C₂²×C₆₇	1	2	yes	complemented
503	#441	C₂²×C₆₇	1	2	yes	complemented
504	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
505	#436	C₂²×C₆₇	1	4	yes	complemented
506	#435	C₂²×C₆₇	1	4	yes	complemented
507	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic, complemented
508	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
509	#417	C₂²×C₆₇	1	2	yes	complemented
510	#417	C₂²×C₆₇	1	2	yes	complemented
511	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
512	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
513	#407	C₂²×C₆₇	1	1	yes	characteristic, complemented
514	#405	C₂²×C₆₇	1	1	yes	characteristic, complemented
515	H(5,𝔽₂)	—	2	8	no	—
516	H(5,𝔽₂)	—	4	4	no	—
517	C₂×#41	—	2	2	no	—
518	C₂×#41	—	2	2	no	—
519	C₂×#41	—	2	2	no	—
520	C₂×#41	—	2	8	no	—
521	C₂×#41	—	4	4	no	—
522	C₂×#41	C₂³×C₆₇	1	2	yes	—
523	C₂×#41	C₂³×C₆₇	1	2	yes	—
524	C₂×#41	C₂³×C₆₇	1	4	yes	—
525	C₂×#41	C₂³×C₆₇	1	2	yes	—
526	C₂×#41	C₂³×C₆₇	1	2	yes	—
527	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
528	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
529	C₂²×D₄	—	2	2	no	—
530	C₂²×D₄	—	2	2	no	—
531	C₂²×D₄	—	2	2	no	—
532	C₂²×D₄	—	2	4	no	—
533	C₂²×D₄	—	2	4	no	—
534	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
535	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
536	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
537	C₂³×C₄	—	2	2	no	—
538	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
539	#137	—	2	8	no	—
540	#137	—	2	8	no	—
541	AGL(1,ℤ/8)	—	2	8	no	—
542	AGL(1,ℤ/8)	—	2	8	no	—
543	AGL(1,ℤ/8)	—	2	16	no	—
544	AGL(1,ℤ/8)	—	2	8	no	—
545	AGL(1,ℤ/8)	—	4	4	no	—
546	#135	—	2	8	no	—
547	#135	—	2	8	no	—
548	#135	—	2	4	no	—
549	#135	D₄×C₆₇	1	8	yes	complemented
550	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
551	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
552	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
553	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
554	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
555	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
556	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
557	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
558	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
559	C₂×D₈	—	2	8	no	—
560	C₂×D₈	—	2	4	no	—
561	C₂×D₈	C₂³×C₆₇	1	2	yes	—
562	C₂×D₈	C₂³×C₆₇	1	4	yes	—
563	C₂×D₈	C₂³×C₆₇	1	2	yes	—
564	C₂×D₈	C₂³×C₆₇	1	2	yes	—
565	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
566	C₂×D₈	C₂³×C₆₇	1	4	yes	—
567	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
568	#131	—	2	4	no	—
569	C₂×M₁₆	—	2	4	no	—
570	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
571	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
572	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
573	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
574	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
575	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
576	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
577	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
578	#127	—	2	4	no	—
579	#127	C₂³×C₆₇	1	4	yes	—
580	#124	—	2	4	no	—
581	#124	C₂³×C₆₇	1	4	yes	—
582	#123	—	2	4	no	—
583	#123	D₄×C₆₇	1	2	yes	—
584	C₂²⋊Q₈	—	2	2	no	—
585	C₂²⋊Q₈	—	2	4	no	—
586	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
587	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
588	#121	—	2	2	no	—
589	#121	—	2	4	no	—
590	#121	—	2	4	no	—
591	#121	—	2	2	no	—
592	#121	—	2	2	no	—
593	#121	—	2	2	no	—
594	#121	—	2	2	no	—
595	#121	—	2	4	no	—
596	#121	—	2	4	no	—
597	#121	—	2	4	no	—
598	#121	—	2	4	no	—
599	#121	D₄×C₆₇	1	2	yes	—
600	#121	C₂³×C₆₇	1	4	yes	—
601	#121	C₂³×C₆₇	1	4	yes	—
602	#121	C₂³×C₆₇	1	4	yes	—
603	#120	—	2	4	no	—
604	#120	—	2	4	no	—
605	#120	—	2	4	no	—
606	#120	—	2	4	no	—
607	#120	D₄×C₆₇	1	2	yes	—
608	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
609	C₄×D₄	—	2	4	no	—
610	C₄×D₄	—	2	4	no	—
611	C₄×D₄	—	2	4	no	—
612	C₄×D₄	C₂³×C₆₇	1	4	yes	—
613	C₄×D₄	C₂³×C₆₇	1	4	yes	—
614	#117	—	2	2	no	—
615	#117	C₂³×C₆₇	1	1	yes	characteristic
616	C₂×C₄⋊C₄	—	2	2	no	—
617	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
618	C₂×C₂²⋊C₄	—	2	2	no	—
619	C₂×C₂²⋊C₄	—	2	4	no	—
620	#106	C₂³×C₆₇	1	2	yes	—
621	#106	C₂³×C₆₇	1	2	yes	—
622	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
623	#103	C₂³×C₆₇	1	4	yes	—
624	#103	C₂³×C₆₇	1	4	yes	—
625	#102	C₂³×C₆₇	1	4	yes	—
626	#102	C₂³×C₆₇	1	4	yes	—
627	#102	C₂³×C₆₇	1	4	yes	—
628	#102	C₂³×C₆₇	1	4	yes	—
629	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
630	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
631	#97	C₂³×C₆₇	1	2	yes	—
632	C₄×C₈	C₂³×C₆₇	1	2	yes	—
633	C₂⁴	—	2	2	no	—
634	C₂⁴	—	2	4	no	—
635	C₂⁴	—	2	2	no	—
636	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
637	#41	—	2	2	no	—
638	#41	—	2	4	no	—
639	#41	—	2	2	no	—
640	#41	—	2	8	no	—
641	#41	—	2	4	no	—
642	#41	—	2	4	no	—
643	#41	—	2	4	no	—
644	#41	—	2	4	no	—
645	#41	—	4	8	no	—
646	#41	—	4	2	no	—
647	#41	—	4	2	no	—
648	#41	—	4	4	no	—
649	#41	—	4	8	no	—
650	#41	—	4	8	no	—
651	#41	C₂×D₄×C₆₇	1	8	yes	complemented
652	C₂×Q₈	—	2	2	no	—
653	C₂×Q₈	—	2	4	no	—
654	C₂×Q₈	—	4	2	no	—
655	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
656	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
657	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
658	C₂×D₄	—	2	2	no	—
659	C₂×D₄	—	2	8	no	—
660	C₂×D₄	—	2	4	no	—
661	C₂×D₄	—	2	4	no	—
662	C₂×D₄	—	2	2	no	—
663	C₂×D₄	—	2	2	no	—
664	C₂×D₄	—	2	4	no	—
665	C₂×D₄	—	2	2	no	—
666	C₂×D₄	—	2	4	no	—
667	C₂×D₄	—	2	4	no	—
668	C₂×D₄	—	2	4	no	—
669	C₂×D₄	—	2	2	no	—
670	C₂×D₄	—	2	4	no	—
671	C₂×D₄	—	2	2	no	—
672	C₂×D₄	—	2	4	no	—
673	C₂×D₄	—	2	4	no	—
674	C₂×D₄	—	2	4	no	—
675	C₂×D₄	—	4	2	no	—
676	C₂×D₄	—	4	4	no	—
677	C₂×D₄	—	4	8	no	—
678	C₂×D₄	—	4	16	no	—
679	C₂×D₄	—	4	8	no	—
680	C₂×D₄	—	8	8	no	—
681	C₂×D₄	—	8	4	no	—
682	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
683	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
684	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
685	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
686	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
687	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	2	2	no	—
695	C₂²×C₄	—	2	4	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	4	no	—
698	C₂²×C₄	—	4	8	no	—
699	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
700	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
701	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
704	Q₁₆	—	2	4	no	—
705	Q₁₆	—	2	2	no	—
706	Q₁₆	C₂×D₄×C₆₇	1	4	yes	complemented
707	SD₁₆	—	2	8	no	—
708	SD₁₆	—	2	4	no	—
709	SD₁₆	—	2	4	no	—
710	SD₁₆	—	2	4	no	—
711	SD₁₆	—	4	4	no	—
712	SD₁₆	C₂×D₄×C₆₇	1	8	yes	complemented
713	D₈	—	2	8	no	—
714	D₈	—	2	4	no	—
715	D₈	—	2	4	no	—
716	D₈	—	2	4	no	—
717	D₈	—	2	2	no	—
718	D₈	—	4	4	no	—
719	D₈	C₂×D₄×C₆₇	1	4	yes	complemented
720	M₁₆	—	2	2	no	—
721	M₁₆	—	2	2	no	—
722	M₁₆	—	2	4	no	—
723	M₁₆	—	2	4	no	—
724	M₁₆	—	2	4	no	—
725	C₂×C₈	—	2	2	no	—
726	C₂×C₈	—	2	4	no	—
727	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	complemented
728	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
729	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
730	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
731	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
732	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	4	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
737	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
738	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	4	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
747	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
748	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
749	C₄²	—	2	4	no	—
750	C₄²	C₂⁴×C₆₇	1	2	yes	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	4	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	4	2	no	—
756	C₂³	—	4	4	no	—
757	C₂³	—	4	8	no	—
758	C₂³	—	4	4	no	—
759	C₂³	—	4	4	no	—
760	C₂³	—	8	2	no	—
761	C₂³	—	8	2	no	—
762	C₂³	—	8	4	no	—
763	C₂³	—	8	2	no	—
764	C₂³	—	8	4	no	—
765	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
766	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
767	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
768	Q₈	—	2	2	no	—
769	Q₈	—	2	2	no	—
770	Q₈	—	2	2	no	—
771	Q₈	—	2	2	no	—
772	Q₈	—	4	4	no	—
773	Q₈	C₂²×D₄×C₆₇	1	4	yes	—
774	D₄	—	2	8	no	—
775	D₄	—	2	4	no	—
776	D₄	—	2	2	no	—
777	D₄	—	2	4	no	—
778	D₄	—	2	2	no	—
779	D₄	—	2	2	no	—
780	D₄	—	2	2	no	—
781	D₄	—	2	4	no	—
782	D₄	—	4	4	no	—
783	D₄	—	4	8	no	—
784	D₄	—	4	4	no	—
785	D₄	—	4	8	no	—
786	D₄	—	4	4	no	—
787	D₄	—	4	4	no	—
788	D₄	—	4	8	no	—
789	D₄	—	4	4	no	—
790	D₄	—	4	4	no	—
791	D₄	—	8	4	no	—
792	D₄	—	8	4	no	—
793	D₄	—	8	4	no	—
794	D₄	—	8	4	no	—
795	D₄	C₂²×D₄×C₆₇	1	4	yes	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	4	no	—
799	C₂×C₄	—	2	8	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	4	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	4	4	no	—
807	C₂×C₄	—	4	8	no	—
808	C₂×C₄	—	4	4	no	—
809	C₂×C₄	—	4	4	no	—
810	C₂×C₄	—	4	4	no	—
811	C₂×C₄	—	8	4	no	—
812	C₂×C₄	—	8	2	no	—
813	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
814	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
815	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
816	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
817	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
818	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
819	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
820	C₈	—	2	2	no	—
821	C₈	—	2	2	no	—
822	C₈	—	2	2	no	—
823	C₈	C₂²×D₄×C₆₇	1	2	yes	—
824	C₈	C₂²×D₄×C₆₇	1	2	yes	—
825	C₂²	—	2	2	no	—
826	C₂²	—	2	2	no	—
827	C₂²	—	2	4	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	4	no	—
831	C₂²	—	2	2	no	—
832	C₂²	—	4	2	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	4	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	4	4	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	4	no	—
840	C₂²	—	8	2	no	—
841	C₂²	—	8	8	no	—
842	C₂²	—	16	4	no	—
843	C₂²	—	16	8	no	—
844	C₂²	D₄²×C₆₇	1	2	yes	—
845	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
846	C₄	—	2	4	no	—
847	C₄	—	2	2	no	—
848	C₄	—	2	4	no	—
849	C₄	—	2	2	no	—
850	C₄	—	4	4	no	—
851	C₄	—	4	2	no	—
852	C₄	D₄²×C₆₇	1	2	yes	—
853	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
854	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
855	C₂	—	2	2	no	—
856	C₂	—	4	2	no	—
857	C₂	—	4	2	no	—
858	C₂	—	4	4	no	—
859	C₂	—	8	2	no	—
860	C₂	—	8	4	no	—
861	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
862	C₂	C₆₇×#3585	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 ◁ #525×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#576×C₆₇	C₂	semidirect
2. C₂×#575×C₆₇	C₂	semidirect
3. C₆₇×#3488	C₂	semidirect
4. C₆₇×#3275	C₂	semidirect
5. C₆₇×#3274	C₂	semidirect
6. C₆₇×#3271	C₂	semidirect
7. C₆₇×#3264	C₂	semidirect
8. C₆₇×#3155	C₂	semidirect
9. C₆₇×#3060	C₂	semidirect
10. C₂×#469×C₆₇	C₂	semidirect
11. C₆₇×#3045	C₂	semidirect
12. C₆₇×#3012	C₂	semidirect
13. C₆₇×#3006	C₂	semidirect
14. C₆₇×#2952	C₂	semidirect
15. C₆₇×#2930	C₂	semidirect
16. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
17. C₂²×#41×C₆₇	C₂²	semidirect
20. C₂×#137×C₆₇	C₂²	semidirect
21. C₂×#137×C₆₇	C₂²	semidirect
22. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
23. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
24. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
25. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
26. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
28. C₂×#135×C₆₇	C₂²	semidirect
29. C₂×#135×C₆₇	C₂²	semidirect
30. C₂×#135×C₆₇	C₂²	semidirect
31. C₂²×D₈×C₆₇	C₂²	semidirect
32. C₂²×D₈×C₆₇	C₂²	semidirect
33. C₂×#131×C₆₇	C₂²	semidirect
34. C₂²×M₁₆×C₆₇	C₂²	semidirect
35. #550×C₆₇	C₂²	semidirect
36. #548×C₆₇	C₂²	semidirect
38. #546×C₆₇	C₂²	semidirect
40. D₄²×C₆₇	C₂²	semidirect
42. #537×C₆₇	C₂²	semidirect
44. #535×C₆₇	C₂²	semidirect
48. C₂×#121×C₆₇	C₂²	semidirect
49. #520×C₆₇	C₂²	semidirect
50. #496×C₆₇	C₂²	semidirect
51. #495×C₆₇	C₂²	semidirect
52. #493×C₆₇	C₂²	semidirect
53. #470×C₆₇	C₂²	semidirect
54. #469×C₆₇	C₂²	semidirect
55. #469×C₆₇	C₂²	semidirect
56. #469×C₆₇	C₂²	semidirect
57. #465×C₆₇	C₂²	semidirect
58. #464×C₆₇	C₂²	semidirect
59. #463×C₆₇	C₂²	semidirect
60. #460×C₆₇	C₂²	semidirect
61. #459×C₆₇	C₂²	semidirect
62. #452×C₆₇	C₂²	semidirect
63. #450×C₆₇	C₂²	semidirect
64. #449×C₆₇	C₂²	semidirect
65. #449×C₆₇	C₂²	semidirect
66. #449×C₆₇	C₂²	semidirect
67. #448×C₆₇	C₂²	semidirect
68. #447×C₆₇	C₂²	semidirect
69. #447×C₆₇	C₂²	semidirect
70. #442×C₆₇	C₂²	semidirect
71. #441×C₆₇	C₂²	semidirect
72. C₄×SD₁₆×C₆₇	C₂²	semidirect
73. #436×C₆₇	C₂²	semidirect
74. #435×C₆₇	C₂²	semidirect
75. C₂×#106×C₆₇	C₂²	semidirect
76. #424×C₆₇	C₂²	semidirect
77. #417×C₆₇	C₂²	semidirect
78. #417×C₆₇	C₂²	semidirect
79. C₂×#102×C₆₇	C₂²	semidirect
80. #408×C₆₇	C₂²	semidirect
81. #407×C₆₇	C₂²	semidirect
82. #405×C₆₇	C₂²	semidirect
117. #135×C₆₇	D₄	semidirect
219. #41×C₆₇	C₂×D₄	semidirect
274. Q₁₆×C₆₇	C₂×D₄	semidirect
280. SD₁₆×C₆₇	C₂×D₄	semidirect
287. D₈×C₆₇	C₂×D₄	semidirect
295. C₂×C₈×C₆₇	C₂×D₄	semidirect
423. #61063	C₆₇	direct (N × H)
432. C₂×#576	C₂×C₆₇	semidirect
433. C₂×#575	C₂×C₆₇	semidirect
434. #3488	C₂×C₆₇	semidirect
435. #3275	C₂×C₆₇	semidirect
436. #3274	C₂×C₆₇	semidirect
437. #3271	C₂×C₆₇	semidirect
438. #3264	C₂×C₆₇	semidirect
439. #3155	C₂×C₆₇	semidirect
440. #3060	C₂×C₆₇	semidirect
441. C₂×#469	C₂×C₆₇	semidirect
442. #3045	C₂×C₆₇	semidirect
443. #3012	C₂×C₆₇	semidirect
444. #3006	C₂×C₆₇	semidirect
445. #2952	C₂×C₆₇	semidirect
446. #2930	C₂×C₆₇	semidirect
447. C₆₇	#61063	direct (N × H)
448. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
449. C₂²×#41	C₂²×C₆₇	semidirect
452. C₂×#137	C₂²×C₆₇	semidirect
453. C₂×#137	C₂²×C₆₇	semidirect
454. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
455. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
456. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
457. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
458. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
460. C₂×#135	C₂²×C₆₇	semidirect
461. C₂×#135	C₂²×C₆₇	semidirect
462. C₂×#135	C₂²×C₆₇	semidirect
463. C₂²×D₈	C₂²×C₆₇	semidirect
464. C₂²×D₈	C₂²×C₆₇	semidirect
465. C₂×#131	C₂²×C₆₇	semidirect
466. C₂²×M₁₆	C₂²×C₆₇	semidirect
467. #550	C₂²×C₆₇	semidirect
468. #548	C₂²×C₆₇	semidirect
470. #546	C₂²×C₆₇	semidirect
472. D₄²	C₂²×C₆₇	semidirect
474. #537	C₂²×C₆₇	semidirect
476. #535	C₂²×C₆₇	semidirect
480. C₂×#121	C₂²×C₆₇	semidirect
481. #520	C₂²×C₆₇	semidirect
482. #496	C₂²×C₆₇	semidirect
483. #495	C₂²×C₆₇	semidirect
484. #493	C₂²×C₆₇	semidirect
485. #470	C₂²×C₆₇	semidirect
486. #469	C₂²×C₆₇	semidirect
487. #469	C₂²×C₆₇	semidirect
488. #469	C₂²×C₆₇	semidirect
489. #465	C₂²×C₆₇	semidirect
490. #464	C₂²×C₆₇	semidirect
491. #463	C₂²×C₆₇	semidirect
492. #460	C₂²×C₆₇	semidirect
493. #459	C₂²×C₆₇	semidirect
494. #452	C₂²×C₆₇	semidirect
495. #450	C₂²×C₆₇	semidirect
496. #449	C₂²×C₆₇	semidirect
497. #449	C₂²×C₆₇	semidirect
498. #449	C₂²×C₆₇	semidirect
499. #448	C₂²×C₆₇	semidirect
500. #447	C₂²×C₆₇	semidirect
501. #447	C₂²×C₆₇	semidirect
502. #442	C₂²×C₆₇	semidirect
503. #441	C₂²×C₆₇	semidirect
504. C₄×SD₁₆	C₂²×C₆₇	semidirect
505. #436	C₂²×C₆₇	semidirect
506. #435	C₂²×C₆₇	semidirect
507. C₂×#106	C₂²×C₆₇	semidirect
508. #424	C₂²×C₆₇	semidirect
509. #417	C₂²×C₆₇	semidirect
510. #417	C₂²×C₆₇	semidirect
511. C₂×#102	C₂²×C₆₇	semidirect
512. #408	C₂²×C₆₇	semidirect
513. #407	C₂²×C₆₇	semidirect
514. #405	C₂²×C₆₇	semidirect
549. #135	D₄×C₆₇	semidirect
651. #41	C₂×D₄×C₆₇	semidirect
706. Q₁₆	C₂×D₄×C₆₇	semidirect
712. SD₁₆	C₂×D₄×C₆₇	semidirect
719. D₈	C₂×D₄×C₆₇	semidirect
727. C₂×C₈	C₂×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×#576×C₆₇	2
C₂×#575×C₆₇	2
C₆₇×#3488	2
C₆₇×#3275	2
C₆₇×#3274	2
C₆₇×#3271	2
C₆₇×#3264	2
C₆₇×#3155	2
C₆₇×#3060	2
C₂×#469×C₆₇	2
C₆₇×#3045	2
C₆₇×#3012	2
C₆₇×#3006	2
C₆₇×#2952	2
C₆₇×#2930	2
#61063	67

Subgroups — C67×#61063 #30740314

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61063 #30740314