Subgroups — C₆₇×#61093 #30740344

Order 17152.

2874 conjugacy classes of subgroups.

The subgroup lattice has 968 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	2	yes	maximal, complemented
2	C₆₇×#3498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3496	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3284	C₂	1	2	yes	maximal, complemented
5	D₄×D₈×C₆₇	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3274	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3272	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3268	C₂	1	4	yes	maximal, complemented
9	C₆₇×#3264	C₂	1	4	yes	maximal, complemented
10	C₆₇×#3151	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3062	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3035	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#459×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3012	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3008	C₂	1	2	yes	maximal, complemented
16	C₄×AGL(1,ℤ/8)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2935	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	2	yes	complemented
19	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	2	yes	complemented
20	#576×C₆₇	—	2	16	no	—
21	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	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×#135×C₆₇	C₂²	1	2	yes	complemented
27	C₂×#135×C₆₇	C₂²	1	4	yes	complemented
28	C₂²×D₈×C₆₇	C₂²	1	4	yes	complemented
29	C₂²×D₈×C₆₇	C₂²	1	2	yes	complemented
30	C₂×#131×C₆₇	C₂²	1	2	yes	complemented
31	#550×C₆₇	C₂²	1	2	yes	complemented
32	#550×C₆₇	C₂²	1	2	yes	complemented
33	#547×C₆₇	—	2	1	no	—
34	#547×C₆₇	C₂²	1	2	yes	complemented
35	#546×C₆₇	—	2	2	no	—
36	#546×C₆₇	C₂²	1	4	yes	complemented
37	D₄²×C₆₇	—	2	1	no	—
38	D₄²×C₆₇	—	2	2	no	—
39	D₄²×C₆₇	—	2	2	no	—
40	D₄²×C₆₇	C₂²	1	2	yes	complemented
41	D₄²×C₆₇	C₂²	1	2	yes	complemented
42	D₄²×C₆₇	C₂²	1	2	yes	complemented
43	#537×C₆₇	C₂²	1	2	yes	complemented
44	#535×C₆₇	—	2	2	no	—
45	#535×C₆₇	C₂²	1	2	yes	complemented
46	#534×C₆₇	—	2	2	no	—
47	#532×C₆₇	—	2	1	no	—
48	#532×C₆₇	C₂²	1	1	yes	characteristic
49	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	C₂×#127×C₆₇	—	2	1	no	—
51	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic, complemented
52	C₂×#121×C₆₇	—	2	2	no	—
53	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
55	#496×C₆₇	C₂²	1	4	yes	complemented
56	#493×C₆₇	C₂²	1	2	yes	complemented
57	#492×C₆₇	C₂²	1	2	yes	complemented
58	#469×C₆₇	C₂²	1	4	yes	complemented
59	#468×C₆₇	C₂²	1	4	yes	complemented
60	#466×C₆₇	C₂²	1	4	yes	complemented
61	#465×C₆₇	C₂²	1	4	yes	complemented
62	#464×C₆₇	C₂²	1	2	yes	complemented
63	#463×C₆₇	C₂²	1	2	yes	complemented
64	#462×C₆₇	C₂²	1	1	yes	characteristic, complemented
65	#461×C₆₇	C₂²	1	1	yes	characteristic, complemented
66	#460×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	#459×C₆₇	C₂²	1	4	yes	complemented
68	#459×C₆₇	C₂²	1	2	yes	complemented
69	#459×C₆₇	C₂²	1	1	yes	characteristic, complemented
70	#459×C₆₇	C₂²	1	2	yes	complemented
71	#452×C₆₇	C₂²	1	4	yes	complemented
72	#450×C₆₇	C₂²	1	4	yes	complemented
73	#449×C₆₇	C₂²	1	4	yes	complemented
74	#449×C₆₇	C₂²	1	4	yes	complemented
75	#449×C₆₇	C₂²	1	4	yes	complemented
76	#447×C₆₇	C₂²	1	4	yes	complemented
77	#447×C₆₇	C₂²	1	4	yes	complemented
78	#447×C₆₇	C₂²	1	4	yes	complemented
79	#442×C₆₇	C₂²	1	2	yes	complemented
80	#440×C₆₇	C₂²	1	2	yes	complemented
81	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
82	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
83	#436×C₆₇	C₂²	1	2	yes	complemented
84	#435×C₆₇	C₂²	1	4	yes	complemented
85	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
86	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
87	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
88	#418×C₆₇	C₂²	1	1	yes	characteristic, complemented
89	#417×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	#416×C₆₇	C₂²	1	2	yes	complemented
91	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
92	#408×C₆₇	C₂²	1	2	yes	complemented
93	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
94	H(5,𝔽₂)×C₆₇	—	2	8	no	—
95	H(5,𝔽₂)×C₆₇	—	2	8	no	—
96	H(5,𝔽₂)×C₆₇	—	4	4	no	—
97	H(5,𝔽₂)×C₆₇	—	4	4	no	—
98	C₂×#41×C₆₇	—	2	2	no	—
99	C₂×#41×C₆₇	—	2	2	no	—
100	C₂×#41×C₆₇	C₂³	1	2	yes	—
101	C₂×#41×C₆₇	C₂³	1	4	yes	—
102	C₂×#41×C₆₇	C₂³	1	4	yes	—
103	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
104	C₂×#41×C₆₇	C₂³	1	2	yes	—
105	C₂²×D₄×C₆₇	—	2	4	no	—
106	C₂²×D₄×C₆₇	—	2	2	no	—
107	C₂²×D₄×C₆₇	—	2	4	no	—
108	C₂²×D₄×C₆₇	—	2	2	no	—
109	C₂²×D₄×C₆₇	—	2	2	no	—
110	C₂²×D₄×C₆₇	—	2	2	no	—
111	C₂²×D₄×C₆₇	—	2	2	no	—
112	C₂²×D₄×C₆₇	—	2	1	no	—
113	C₂²×D₄×C₆₇	—	2	1	no	—
114	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
115	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
116	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
117	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₆₇	—	2	1	no	—
119	AGL(1,ℤ/8)×C₆₇	—	2	16	no	—
120	AGL(1,ℤ/8)×C₆₇	—	2	16	no	—
121	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
122	AGL(1,ℤ/8)×C₆₇	—	4	4	no	—
123	AGL(1,ℤ/8)×C₆₇	D₄	1	8	yes	complemented
124	#135×C₆₇	—	2	8	no	—
125	#135×C₆₇	—	2	16	no	—
126	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
130	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
131	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
132	C₂×D₈×C₆₇	—	2	8	no	—
133	C₂×D₈×C₆₇	—	2	16	no	—
134	C₂×D₈×C₆₇	C₂³	1	4	yes	—
135	C₂×D₈×C₆₇	C₂³	1	4	yes	—
136	C₂×D₈×C₆₇	C₂³	1	2	yes	—
137	C₂×D₈×C₆₇	C₂³	1	4	yes	—
138	C₂×D₈×C₆₇	C₂³	1	4	yes	—
139	C₂×D₈×C₆₇	C₂³	1	2	yes	—
140	#131×C₆₇	—	2	8	no	—
141	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
142	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
143	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
144	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
145	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
146	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
147	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
148	#127×C₆₇	—	2	2	no	—
149	#127×C₆₇	—	2	2	no	—
150	#127×C₆₇	—	2	2	no	—
151	#127×C₆₇	—	2	1	no	—
152	#127×C₆₇	—	2	1	no	—
153	#127×C₆₇	D₄	1	1	yes	characteristic
154	#127×C₆₇	C₂³	1	2	yes	—
155	#127×C₆₇	C₂³	1	2	yes	—
156	#127×C₆₇	C₂³	1	1	yes	characteristic
157	#124×C₆₇	—	2	2	no	—
158	#124×C₆₇	D₄	1	2	yes	—
159	#124×C₆₇	C₂³	1	2	yes	—
160	#123×C₆₇	—	2	4	no	—
161	#123×C₆₇	—	2	4	no	—
162	C₂²⋊Q₈×C₆₇	—	2	2	no	—
163	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
164	#121×C₆₇	—	2	4	no	—
165	#121×C₆₇	—	2	2	no	—
166	#121×C₆₇	—	2	2	no	—
167	#121×C₆₇	—	2	1	no	—
168	#121×C₆₇	—	2	1	no	—
169	#121×C₆₇	—	2	2	no	—
170	#121×C₆₇	—	2	2	no	—
171	#121×C₆₇	—	2	2	no	—
172	#121×C₆₇	—	2	4	no	—
173	#121×C₆₇	—	2	4	no	—
174	#121×C₆₇	—	2	4	no	—
175	#121×C₆₇	D₄	1	2	yes	—
176	#121×C₆₇	D₄	1	2	yes	—
177	#121×C₆₇	C₂³	1	4	yes	—
178	#121×C₆₇	C₂³	1	4	yes	—
179	#121×C₆₇	C₂³	1	4	yes	—
180	#120×C₆₇	—	2	4	no	—
181	#120×C₆₇	—	2	4	no	—
182	#120×C₆₇	—	2	4	no	—
183	#120×C₆₇	—	2	4	no	—
184	#120×C₆₇	—	2	4	no	—
185	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
186	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
187	C₄×D₄×C₆₇	—	2	1	no	—
188	C₄×D₄×C₆₇	—	2	1	no	—
189	C₄×D₄×C₆₇	—	2	2	no	—
190	C₄×D₄×C₆₇	—	2	2	no	—
191	C₄×D₄×C₆₇	—	2	1	no	—
192	C₄×D₄×C₆₇	—	2	1	no	—
193	C₄×D₄×C₆₇	—	2	1	no	—
194	C₄×D₄×C₆₇	—	2	1	no	—
195	C₄×D₄×C₆₇	C₂³	1	2	yes	—
196	C₄×D₄×C₆₇	C₂³	1	2	yes	—
197	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
198	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
199	C₄×D₄×C₆₇	C₂³	1	2	yes	—
200	C₄×D₄×C₆₇	C₂³	1	2	yes	—
201	#117×C₆₇	—	2	1	no	—
202	#117×C₆₇	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
204	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
206	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
207	C₂×C₄²×C₆₇	—	2	1	no	—
208	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
209	#107×C₆₇	C₂³	1	2	yes	—
210	#106×C₆₇	C₂³	1	2	yes	—
211	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
212	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
213	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
214	#103×C₆₇	C₂³	1	2	yes	—
215	#103×C₆₇	C₂³	1	2	yes	—
216	#103×C₆₇	C₂³	1	2	yes	—
217	#102×C₆₇	C₂³	1	2	yes	—
218	#102×C₆₇	C₂³	1	2	yes	—
219	#102×C₆₇	C₂³	1	4	yes	—
220	#102×C₆₇	C₂³	1	2	yes	—
221	#102×C₆₇	C₂³	1	4	yes	—
222	#102×C₆₇	C₂³	1	2	yes	—
223	#102×C₆₇	C₂³	1	2	yes	—
224	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
225	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
226	#97×C₆₇	C₂³	1	2	yes	—
227	C₄×C₈×C₆₇	C₂³	1	2	yes	—
228	C₂⁴×C₆₇	—	2	1	no	—
229	C₂⁴×C₆₇	—	2	4	no	—
230	C₂⁴×C₆₇	—	2	4	no	—
231	C₂⁴×C₆₇	—	2	2	no	—
232	#41×C₆₇	—	2	4	no	—
233	#41×C₆₇	—	2	2	no	—
234	#41×C₆₇	—	2	4	no	—
235	#41×C₆₇	—	2	8	no	—
236	#41×C₆₇	—	2	8	no	—
237	#41×C₆₇	—	2	4	no	—
238	#41×C₆₇	—	2	4	no	—
239	#41×C₆₇	—	4	4	no	—
240	#41×C₆₇	—	4	4	no	—
241	#41×C₆₇	—	4	8	no	—
242	#41×C₆₇	—	4	8	no	—
243	#41×C₆₇	C₂×D₄	1	4	yes	complemented
244	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
245	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
246	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
247	C₂×D₄×C₆₇	—	2	1	no	—
248	C₂×D₄×C₆₇	—	2	8	no	—
249	C₂×D₄×C₆₇	—	2	8	no	—
250	C₂×D₄×C₆₇	—	2	4	no	—
251	C₂×D₄×C₆₇	—	2	2	no	—
252	C₂×D₄×C₆₇	—	2	4	no	—
253	C₂×D₄×C₆₇	—	2	4	no	—
254	C₂×D₄×C₆₇	—	2	4	no	—
255	C₂×D₄×C₆₇	—	2	4	no	—
256	C₂×D₄×C₆₇	—	2	1	no	—
257	C₂×D₄×C₆₇	—	2	4	no	—
258	C₂×D₄×C₆₇	—	2	1	no	—
259	C₂×D₄×C₆₇	—	2	2	no	—
260	C₂×D₄×C₆₇	—	2	2	no	—
261	C₂×D₄×C₆₇	—	2	4	no	—
262	C₂×D₄×C₆₇	—	2	4	no	—
263	C₂×D₄×C₆₇	—	2	2	no	—
264	C₂×D₄×C₆₇	—	2	1	no	—
265	C₂×D₄×C₆₇	—	2	2	no	—
266	C₂×D₄×C₆₇	—	2	2	no	—
267	C₂×D₄×C₆₇	—	2	2	no	—
268	C₂×D₄×C₆₇	—	2	4	no	—
269	C₂×D₄×C₆₇	—	4	4	no	—
270	C₂×D₄×C₆₇	—	4	4	no	—
271	C₂×D₄×C₆₇	—	4	8	no	—
272	C₂×D₄×C₆₇	—	4	16	no	—
273	C₂×D₄×C₆₇	—	4	8	no	—
274	C₂×D₄×C₆₇	—	4	16	no	—
275	C₂×D₄×C₆₇	—	8	2	no	—
276	C₂×D₄×C₆₇	—	8	4	no	—
277	C₂×D₄×C₆₇	—	8	4	no	—
278	C₂×D₄×C₆₇	—	8	2	no	—
279	C₂×D₄×C₆₇	—	8	4	no	—
280	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
281	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
282	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
283	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
284	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	complemented
285	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
286	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
287	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
288	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₆₇	—	2	1	no	—
290	C₂²×C₄×C₆₇	—	2	1	no	—
291	C₂²×C₄×C₆₇	—	2	1	no	—
292	C₂²×C₄×C₆₇	—	2	1	no	—
293	C₂²×C₄×C₆₇	—	2	4	no	—
294	C₂²×C₄×C₆₇	—	2	2	no	—
295	C₂²×C₄×C₆₇	—	2	4	no	—
296	C₂²×C₄×C₆₇	—	2	2	no	—
297	C₂²×C₄×C₆₇	—	2	2	no	—
298	C₂²×C₄×C₆₇	—	8	2	no	—
299	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
300	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
302	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
303	Q₁₆×C₆₇	—	2	4	no	—
304	SD₁₆×C₆₇	—	2	4	no	—
305	SD₁₆×C₆₇	—	2	4	no	—
306	SD₁₆×C₆₇	—	2	8	no	—
307	SD₁₆×C₆₇	—	4	4	no	—
308	SD₁₆×C₆₇	C₂×D₄	1	8	yes	complemented
309	D₈×C₆₇	—	2	8	no	—
310	D₈×C₆₇	—	2	4	no	—
311	D₈×C₆₇	—	2	8	no	—
312	D₈×C₆₇	—	2	8	no	—
313	D₈×C₆₇	—	4	4	no	—
314	D₈×C₆₇	C₂×D₄	1	8	yes	complemented
315	M₁₆×C₆₇	—	2	2	no	—
316	M₁₆×C₆₇	—	2	8	no	—
317	M₁₆×C₆₇	C₂×D₄	1	4	yes	complemented
318	C₂×C₈×C₆₇	—	2	4	no	—
319	C₂×C₈×C₆₇	—	2	8	no	—
320	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
321	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
322	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
323	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
324	C₄⋊C₄×C₆₇	—	2	1	no	—
325	C₄⋊C₄×C₆₇	—	2	4	no	—
326	C₄⋊C₄×C₆₇	—	2	1	no	—
327	C₄⋊C₄×C₆₇	—	2	1	no	—
328	C₄⋊C₄×C₆₇	—	2	1	no	—
329	C₄⋊C₄×C₆₇	—	2	1	no	—
330	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
331	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
332	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
333	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
334	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
335	C₂²⋊C₄×C₆₇	—	2	4	no	—
336	C₂²⋊C₄×C₆₇	—	2	1	no	—
337	C₂²⋊C₄×C₆₇	—	2	2	no	—
338	C₂²⋊C₄×C₆₇	—	2	2	no	—
339	C₂²⋊C₄×C₆₇	—	2	2	no	—
340	C₂²⋊C₄×C₆₇	—	2	4	no	—
341	C₂²⋊C₄×C₆₇	—	2	1	no	—
342	C₂²⋊C₄×C₆₇	—	2	1	no	—
343	C₂²⋊C₄×C₆₇	—	2	4	no	—
344	C₂²⋊C₄×C₆₇	—	2	4	no	—
345	C₂²⋊C₄×C₆₇	—	2	2	no	—
346	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
347	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
348	C₄²×C₆₇	—	2	1	no	—
349	C₄²×C₆₇	—	2	1	no	—
350	C₄²×C₆₇	—	2	1	no	—
351	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
352	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
353	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
354	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
355	C₂³×C₆₇	—	2	2	no	—
356	C₂³×C₆₇	—	2	1	no	—
357	C₂³×C₆₇	—	2	4	no	—
358	C₂³×C₆₇	—	2	2	no	—
359	C₂³×C₆₇	—	2	4	no	—
360	C₂³×C₆₇	—	4	8	no	—
361	C₂³×C₆₇	—	4	8	no	—
362	C₂³×C₆₇	—	4	4	no	—
363	C₂³×C₆₇	—	8	1	no	—
364	C₂³×C₆₇	—	8	1	no	—
365	C₂³×C₆₇	—	8	2	no	—
366	C₂³×C₆₇	—	8	2	no	—
367	C₂³×C₆₇	—	8	4	no	—
368	C₂³×C₆₇	—	8	4	no	—
369	C₂³×C₆₇	—	8	4	no	—
370	C₂³×C₆₇	—	8	4	no	—
371	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
372	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
373	Q₈×C₆₇	—	2	4	no	—
374	Q₈×C₆₇	—	2	1	no	—
375	Q₈×C₆₇	—	2	2	no	—
376	Q₈×C₆₇	—	2	2	no	—
377	Q₈×C₆₇	C₂²×D₄	1	2	yes	—
378	D₄×C₆₇	—	2	4	no	—
379	D₄×C₆₇	—	2	8	no	—
380	D₄×C₆₇	—	2	4	no	—
381	D₄×C₆₇	—	2	4	no	—
382	D₄×C₆₇	—	2	4	no	—
383	D₄×C₆₇	—	2	4	no	—
384	D₄×C₆₇	—	2	2	no	—
385	D₄×C₆₇	—	2	2	no	—
386	D₄×C₆₇	—	2	1	no	—
387	D₄×C₆₇	—	2	2	no	—
388	D₄×C₆₇	—	2	4	no	—
389	D₄×C₆₇	—	4	2	no	—
390	D₄×C₆₇	—	4	8	no	—
391	D₄×C₆₇	—	4	8	no	—
392	D₄×C₆₇	—	4	8	no	—
393	D₄×C₆₇	—	4	4	no	—
394	D₄×C₆₇	—	4	8	no	—
395	D₄×C₆₇	—	4	4	no	—
396	D₄×C₆₇	—	4	4	no	—
397	D₄×C₆₇	—	4	2	no	—
398	D₄×C₆₇	—	4	4	no	—
399	D₄×C₆₇	—	8	1	no	—
400	D₄×C₆₇	—	8	2	no	—
401	D₄×C₆₇	—	8	2	no	—
402	D₄×C₆₇	—	8	4	no	—
403	D₄×C₆₇	—	8	4	no	—
404	D₄×C₆₇	—	8	4	no	—
405	D₄×C₆₇	C₂²×D₄	1	4	yes	—
406	D₄×C₆₇	C₂²×D₄	1	2	yes	—
407	C₂×C₄×C₆₇	—	2	1	no	—
408	C₂×C₄×C₆₇	—	2	4	no	—
409	C₂×C₄×C₆₇	—	2	2	no	—
410	C₂×C₄×C₆₇	—	2	4	no	—
411	C₂×C₄×C₆₇	—	2	4	no	—
412	C₂×C₄×C₆₇	—	2	1	no	—
413	C₂×C₄×C₆₇	—	2	1	no	—
414	C₂×C₄×C₆₇	—	2	2	no	—
415	C₂×C₄×C₆₇	—	2	2	no	—
416	C₂×C₄×C₆₇	—	4	1	no	—
417	C₂×C₄×C₆₇	—	4	8	no	—
418	C₂×C₄×C₆₇	—	4	8	no	—
419	C₂×C₄×C₆₇	—	4	2	no	—
420	C₂×C₄×C₆₇	—	4	4	no	—
421	C₂×C₄×C₆₇	—	4	4	no	—
422	C₂×C₄×C₆₇	—	4	2	no	—
423	C₂×C₄×C₆₇	—	8	2	no	—
424	C₂×C₄×C₆₇	—	8	1	no	—
425	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
429	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
430	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
431	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
432	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
433	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
434	C₈×C₆₇	—	2	2	no	—
435	C₈×C₆₇	—	2	2	no	—
436	C₈×C₆₇	—	2	2	no	—
437	C₈×C₆₇	C₂²×D₄	1	4	yes	—
438	C₂²×C₆₇	—	2	1	no	—
439	C₂²×C₆₇	—	2	1	no	—
440	C₂²×C₆₇	—	2	4	no	—
441	C₂²×C₆₇	—	2	4	no	—
442	C₂²×C₆₇	—	2	2	no	—
443	C₂²×C₆₇	—	2	4	no	—
444	C₂²×C₆₇	—	2	4	no	—
445	C₂²×C₆₇	—	4	1	no	—
446	C₂²×C₆₇	—	4	2	no	—
447	C₂²×C₆₇	—	4	2	no	—
448	C₂²×C₆₇	—	4	1	no	—
449	C₂²×C₆₇	—	4	4	no	—
450	C₂²×C₆₇	—	4	2	no	—
451	C₂²×C₆₇	—	4	4	no	—
452	C₂²×C₆₇	—	4	2	no	—
453	C₂²×C₆₇	—	4	4	no	—
454	C₂²×C₆₇	—	4	2	no	—
455	C₂²×C₆₇	—	8	4	no	—
456	C₂²×C₆₇	—	16	4	no	—
457	C₂²×C₆₇	—	16	8	no	—
458	C₂²×C₆₇	—	16	8	no	—
459	C₂²×C₆₇	D₄²	1	2	yes	—
460	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
461	C₄×C₆₇	—	2	1	no	—
462	C₄×C₆₇	—	2	1	no	—
463	C₄×C₆₇	—	2	2	no	—
464	C₄×C₆₇	—	2	4	no	—
465	C₄×C₆₇	—	2	1	no	—
466	C₄×C₆₇	—	4	1	no	—
467	C₄×C₆₇	—	4	2	no	—
468	C₄×C₆₇	—	4	2	no	—
469	C₄×C₆₇	—	4	1	no	—
470	C₄×C₆₇	D₄²	1	2	yes	—
471	C₄×C₆₇	#576	1	2	yes	complemented
472	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
473	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
474	#61093	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
475	C₂×C₆₇	—	2	2	no	—
476	C₂×C₆₇	—	4	4	no	—
477	C₂×C₆₇	—	4	4	no	—
478	C₂×C₆₇	—	4	2	no	—
479	C₂×C₆₇	—	8	4	no	—
480	C₂×C₆₇	—	8	2	no	—
481	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
482	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
483	C₂×C₆₇	#3585	1	1	yes	characteristic
484	C₂×#576	C₂×C₆₇	1	2	yes	complemented
485	#3498	C₂×C₆₇	1	1	yes	characteristic, complemented
486	#3496	C₂×C₆₇	1	1	yes	characteristic, complemented
487	#3284	C₂×C₆₇	1	2	yes	complemented
488	D₄×D₈	C₂×C₆₇	1	2	yes	complemented
489	#3274	C₂×C₆₇	1	2	yes	complemented
490	#3272	C₂×C₆₇	1	2	yes	complemented
491	#3268	C₂×C₆₇	1	4	yes	complemented
492	#3264	C₂×C₆₇	1	4	yes	complemented
493	#3151	C₂×C₆₇	1	1	yes	characteristic, complemented
494	#3062	C₂×C₆₇	1	2	yes	complemented
495	#3035	C₂×C₆₇	1	1	yes	characteristic, complemented
496	C₂×#459	C₂×C₆₇	1	1	yes	characteristic, complemented
497	#3012	C₂×C₆₇	1	2	yes	complemented
498	#3008	C₂×C₆₇	1	2	yes	complemented
499	C₄×AGL(1,ℤ/8)	C₂×C₆₇	1	1	yes	characteristic, complemented
500	#2935	C₂×C₆₇	1	1	yes	characteristic, complemented
501	C₆₇	#61093	1	1	yes	characteristic, direct product factor, Sylow
502	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	complemented
503	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	complemented
504	#576	—	2	16	no	—
505	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
506	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
507	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
508	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
509	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
510	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
511	C₂×#135	C₂²×C₆₇	1	4	yes	complemented
512	C₂²×D₈	C₂²×C₆₇	1	2	yes	complemented
513	C₂²×D₈	C₂²×C₆₇	1	4	yes	complemented
514	C₂×#131	C₂²×C₆₇	1	2	yes	complemented
515	#550	C₂²×C₆₇	1	2	yes	complemented
516	#550	C₂²×C₆₇	1	2	yes	complemented
517	#547	—	2	1	no	—
518	#547	C₂²×C₆₇	1	2	yes	complemented
519	#546	—	2	2	no	—
520	#546	C₂²×C₆₇	1	4	yes	complemented
521	D₄²	—	2	1	no	—
522	D₄²	—	2	2	no	—
523	D₄²	—	2	2	no	—
524	D₄²	C₂²×C₆₇	1	2	yes	complemented
525	D₄²	C₂²×C₆₇	1	2	yes	complemented
526	D₄²	C₂²×C₆₇	1	2	yes	complemented
527	#537	C₂²×C₆₇	1	2	yes	complemented
528	#535	—	2	2	no	—
529	#535	C₂²×C₆₇	1	2	yes	complemented
530	#534	—	2	2	no	—
531	#532	—	2	1	no	—
532	#532	C₂²×C₆₇	1	1	yes	characteristic
533	#532	C₂²×C₆₇	1	1	yes	characteristic, complemented
534	C₂×#127	—	2	1	no	—
535	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic, complemented
536	C₂×#121	—	2	2	no	—
537	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
538	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
539	#496	C₂²×C₆₇	1	4	yes	complemented
540	#493	C₂²×C₆₇	1	2	yes	complemented
541	#492	C₂²×C₆₇	1	2	yes	complemented
542	#469	C₂²×C₆₇	1	4	yes	complemented
543	#468	C₂²×C₆₇	1	4	yes	complemented
544	#466	C₂²×C₆₇	1	4	yes	complemented
545	#465	C₂²×C₆₇	1	4	yes	complemented
546	#464	C₂²×C₆₇	1	2	yes	complemented
547	#463	C₂²×C₆₇	1	2	yes	complemented
548	#462	C₂²×C₆₇	1	1	yes	characteristic, complemented
549	#461	C₂²×C₆₇	1	1	yes	characteristic, complemented
550	#460	C₂²×C₆₇	1	1	yes	characteristic, complemented
551	#459	C₂²×C₆₇	1	4	yes	complemented
552	#459	C₂²×C₆₇	1	2	yes	complemented
553	#459	C₂²×C₆₇	1	1	yes	characteristic, complemented
554	#459	C₂²×C₆₇	1	2	yes	complemented
555	#452	C₂²×C₆₇	1	4	yes	complemented
556	#450	C₂²×C₆₇	1	4	yes	complemented
557	#449	C₂²×C₆₇	1	4	yes	complemented
558	#449	C₂²×C₆₇	1	4	yes	complemented
559	#449	C₂²×C₆₇	1	4	yes	complemented
560	#447	C₂²×C₆₇	1	4	yes	complemented
561	#447	C₂²×C₆₇	1	4	yes	complemented
562	#447	C₂²×C₆₇	1	4	yes	complemented
563	#442	C₂²×C₆₇	1	2	yes	complemented
564	#440	C₂²×C₆₇	1	2	yes	complemented
565	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
566	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
567	#436	C₂²×C₆₇	1	2	yes	complemented
568	#435	C₂²×C₆₇	1	4	yes	complemented
569	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
570	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
571	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
572	#418	C₂²×C₆₇	1	1	yes	characteristic, complemented
573	#417	C₂²×C₆₇	1	1	yes	characteristic, complemented
574	#416	C₂²×C₆₇	1	2	yes	complemented
575	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
576	#408	C₂²×C₆₇	1	2	yes	complemented
577	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
578	H(5,𝔽₂)	—	2	8	no	—
579	H(5,𝔽₂)	—	2	8	no	—
580	H(5,𝔽₂)	—	4	4	no	—
581	H(5,𝔽₂)	—	4	4	no	—
582	C₂×#41	—	2	2	no	—
583	C₂×#41	—	2	2	no	—
584	C₂×#41	C₂³×C₆₇	1	2	yes	—
585	C₂×#41	C₂³×C₆₇	1	4	yes	—
586	C₂×#41	C₂³×C₆₇	1	4	yes	—
587	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
588	C₂×#41	C₂³×C₆₇	1	2	yes	—
589	C₂²×D₄	—	2	4	no	—
590	C₂²×D₄	—	2	2	no	—
591	C₂²×D₄	—	2	4	no	—
592	C₂²×D₄	—	2	2	no	—
593	C₂²×D₄	—	2	2	no	—
594	C₂²×D₄	—	2	2	no	—
595	C₂²×D₄	—	2	2	no	—
596	C₂²×D₄	—	2	1	no	—
597	C₂²×D₄	—	2	1	no	—
598	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
599	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
600	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
601	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
602	C₂³×C₄	—	2	1	no	—
603	AGL(1,ℤ/8)	—	2	16	no	—
604	AGL(1,ℤ/8)	—	2	16	no	—
605	AGL(1,ℤ/8)	—	2	8	no	—
606	AGL(1,ℤ/8)	—	4	4	no	—
607	AGL(1,ℤ/8)	D₄×C₆₇	1	8	yes	complemented
608	#135	—	2	8	no	—
609	#135	—	2	16	no	—
610	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
611	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
612	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
613	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
614	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
615	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
616	C₂×D₈	—	2	8	no	—
617	C₂×D₈	—	2	16	no	—
618	C₂×D₈	C₂³×C₆₇	1	2	yes	—
619	C₂×D₈	C₂³×C₆₇	1	4	yes	—
620	C₂×D₈	C₂³×C₆₇	1	4	yes	—
621	C₂×D₈	C₂³×C₆₇	1	4	yes	—
622	C₂×D₈	C₂³×C₆₇	1	4	yes	—
623	C₂×D₈	C₂³×C₆₇	1	2	yes	—
624	#131	—	2	8	no	—
625	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
626	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
627	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
628	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
629	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
630	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
631	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
632	#127	—	2	2	no	—
633	#127	—	2	2	no	—
634	#127	—	2	2	no	—
635	#127	—	2	1	no	—
636	#127	—	2	1	no	—
637	#127	D₄×C₆₇	1	1	yes	characteristic
638	#127	C₂³×C₆₇	1	2	yes	—
639	#127	C₂³×C₆₇	1	2	yes	—
640	#127	C₂³×C₆₇	1	1	yes	characteristic
641	#124	—	2	2	no	—
642	#124	D₄×C₆₇	1	2	yes	—
643	#124	C₂³×C₆₇	1	2	yes	—
644	#123	—	2	4	no	—
645	#123	—	2	4	no	—
646	C₂²⋊Q₈	—	2	2	no	—
647	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
648	#121	—	2	4	no	—
649	#121	—	2	2	no	—
650	#121	—	2	2	no	—
651	#121	—	2	1	no	—
652	#121	—	2	1	no	—
653	#121	—	2	2	no	—
654	#121	—	2	2	no	—
655	#121	—	2	2	no	—
656	#121	—	2	4	no	—
657	#121	—	2	4	no	—
658	#121	—	2	4	no	—
659	#121	D₄×C₆₇	1	2	yes	—
660	#121	D₄×C₆₇	1	2	yes	—
661	#121	C₂³×C₆₇	1	4	yes	—
662	#121	C₂³×C₆₇	1	4	yes	—
663	#121	C₂³×C₆₇	1	4	yes	—
664	#120	—	2	4	no	—
665	#120	—	2	4	no	—
666	#120	—	2	4	no	—
667	#120	—	2	4	no	—
668	#120	—	2	4	no	—
669	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
670	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
671	C₄×D₄	—	2	1	no	—
672	C₄×D₄	—	2	1	no	—
673	C₄×D₄	—	2	2	no	—
674	C₄×D₄	—	2	2	no	—
675	C₄×D₄	—	2	1	no	—
676	C₄×D₄	—	2	1	no	—
677	C₄×D₄	—	2	1	no	—
678	C₄×D₄	—	2	1	no	—
679	C₄×D₄	C₂³×C₆₇	1	2	yes	—
680	C₄×D₄	C₂³×C₆₇	1	2	yes	—
681	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
682	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
683	C₄×D₄	C₂³×C₆₇	1	2	yes	—
684	C₄×D₄	C₂³×C₆₇	1	2	yes	—
685	#117	—	2	1	no	—
686	#117	C₂³×C₆₇	1	1	yes	characteristic
687	C₂×C₄⋊C₄	—	2	2	no	—
688	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
689	C₂×C₂²⋊C₄	—	2	1	no	—
690	C₂×C₂²⋊C₄	—	2	4	no	—
691	C₂×C₄²	—	2	1	no	—
692	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
693	#107	C₂³×C₆₇	1	2	yes	—
694	#106	C₂³×C₆₇	1	2	yes	—
695	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
696	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
697	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
698	#103	C₂³×C₆₇	1	2	yes	—
699	#103	C₂³×C₆₇	1	2	yes	—
700	#103	C₂³×C₆₇	1	2	yes	—
701	#102	C₂³×C₆₇	1	4	yes	—
702	#102	C₂³×C₆₇	1	4	yes	—
703	#102	C₂³×C₆₇	1	2	yes	—
704	#102	C₂³×C₆₇	1	2	yes	—
705	#102	C₂³×C₆₇	1	2	yes	—
706	#102	C₂³×C₆₇	1	2	yes	—
707	#102	C₂³×C₆₇	1	2	yes	—
708	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
709	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
710	#97	C₂³×C₆₇	1	2	yes	—
711	C₄×C₈	C₂³×C₆₇	1	2	yes	—
712	C₂⁴	—	2	1	no	—
713	C₂⁴	—	2	4	no	—
714	C₂⁴	—	2	4	no	—
715	C₂⁴	—	2	2	no	—
716	#41	—	2	4	no	—
717	#41	—	2	2	no	—
718	#41	—	2	4	no	—
719	#41	—	2	8	no	—
720	#41	—	2	8	no	—
721	#41	—	2	4	no	—
722	#41	—	2	4	no	—
723	#41	—	4	4	no	—
724	#41	—	4	4	no	—
725	#41	—	4	8	no	—
726	#41	—	4	8	no	—
727	#41	C₂×D₄×C₆₇	1	4	yes	complemented
728	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
729	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
730	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
731	C₂×D₄	—	2	1	no	—
732	C₂×D₄	—	2	8	no	—
733	C₂×D₄	—	2	8	no	—
734	C₂×D₄	—	2	4	no	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	2	4	no	—
737	C₂×D₄	—	2	4	no	—
738	C₂×D₄	—	2	4	no	—
739	C₂×D₄	—	2	4	no	—
740	C₂×D₄	—	2	1	no	—
741	C₂×D₄	—	2	4	no	—
742	C₂×D₄	—	2	1	no	—
743	C₂×D₄	—	2	2	no	—
744	C₂×D₄	—	2	2	no	—
745	C₂×D₄	—	2	4	no	—
746	C₂×D₄	—	2	4	no	—
747	C₂×D₄	—	2	2	no	—
748	C₂×D₄	—	2	1	no	—
749	C₂×D₄	—	2	2	no	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	—	2	2	no	—
752	C₂×D₄	—	2	4	no	—
753	C₂×D₄	—	4	4	no	—
754	C₂×D₄	—	4	4	no	—
755	C₂×D₄	—	4	8	no	—
756	C₂×D₄	—	4	16	no	—
757	C₂×D₄	—	4	8	no	—
758	C₂×D₄	—	4	16	no	—
759	C₂×D₄	—	8	2	no	—
760	C₂×D₄	—	8	4	no	—
761	C₂×D₄	—	8	4	no	—
762	C₂×D₄	—	8	2	no	—
763	C₂×D₄	—	8	4	no	—
764	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
765	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
766	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
767	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
768	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	complemented
769	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
770	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
771	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
772	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
773	C₂²×C₄	—	2	1	no	—
774	C₂²×C₄	—	2	1	no	—
775	C₂²×C₄	—	2	1	no	—
776	C₂²×C₄	—	2	1	no	—
777	C₂²×C₄	—	2	4	no	—
778	C₂²×C₄	—	2	2	no	—
779	C₂²×C₄	—	2	4	no	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	2	2	no	—
782	C₂²×C₄	—	8	2	no	—
783	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
784	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
786	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
787	Q₁₆	—	2	4	no	—
788	SD₁₆	—	2	4	no	—
789	SD₁₆	—	2	4	no	—
790	SD₁₆	—	2	8	no	—
791	SD₁₆	—	4	4	no	—
792	SD₁₆	C₂×D₄×C₆₇	1	8	yes	complemented
793	D₈	—	2	8	no	—
794	D₈	—	2	4	no	—
795	D₈	—	2	8	no	—
796	D₈	—	2	8	no	—
797	D₈	—	4	4	no	—
798	D₈	C₂×D₄×C₆₇	1	8	yes	complemented
799	M₁₆	—	2	2	no	—
800	M₁₆	—	2	8	no	—
801	M₁₆	C₂×D₄×C₆₇	1	4	yes	complemented
802	C₂×C₈	—	2	4	no	—
803	C₂×C₈	—	2	8	no	—
804	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
805	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
806	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
807	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
808	C₄⋊C₄	—	2	1	no	—
809	C₄⋊C₄	—	2	4	no	—
810	C₄⋊C₄	—	2	1	no	—
811	C₄⋊C₄	—	2	1	no	—
812	C₄⋊C₄	—	2	1	no	—
813	C₄⋊C₄	—	2	1	no	—
814	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
815	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
816	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
817	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
818	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
819	C₂²⋊C₄	—	2	4	no	—
820	C₂²⋊C₄	—	2	1	no	—
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	4	no	—
825	C₂²⋊C₄	—	2	1	no	—
826	C₂²⋊C₄	—	2	1	no	—
827	C₂²⋊C₄	—	2	4	no	—
828	C₂²⋊C₄	—	2	4	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
831	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
832	C₄²	—	2	1	no	—
833	C₄²	—	2	1	no	—
834	C₄²	—	2	1	no	—
835	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
836	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
837	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
838	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
839	C₂³	—	2	2	no	—
840	C₂³	—	2	1	no	—
841	C₂³	—	2	4	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	4	no	—
844	C₂³	—	4	8	no	—
845	C₂³	—	4	8	no	—
846	C₂³	—	4	4	no	—
847	C₂³	—	8	1	no	—
848	C₂³	—	8	1	no	—
849	C₂³	—	8	2	no	—
850	C₂³	—	8	2	no	—
851	C₂³	—	8	4	no	—
852	C₂³	—	8	4	no	—
853	C₂³	—	8	4	no	—
854	C₂³	—	8	4	no	—
855	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
856	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
857	Q₈	—	2	4	no	—
858	Q₈	—	2	1	no	—
859	Q₈	—	2	2	no	—
860	Q₈	—	2	2	no	—
861	Q₈	C₂²×D₄×C₆₇	1	2	yes	—
862	D₄	—	2	4	no	—
863	D₄	—	2	8	no	—
864	D₄	—	2	4	no	—
865	D₄	—	2	4	no	—
866	D₄	—	2	4	no	—
867	D₄	—	2	4	no	—
868	D₄	—	2	2	no	—
869	D₄	—	2	2	no	—
870	D₄	—	2	1	no	—
871	D₄	—	2	2	no	—
872	D₄	—	2	4	no	—
873	D₄	—	4	2	no	—
874	D₄	—	4	8	no	—
875	D₄	—	4	8	no	—
876	D₄	—	4	8	no	—
877	D₄	—	4	4	no	—
878	D₄	—	4	8	no	—
879	D₄	—	4	4	no	—
880	D₄	—	4	4	no	—
881	D₄	—	4	2	no	—
882	D₄	—	4	4	no	—
883	D₄	—	8	2	no	—
884	D₄	—	8	2	no	—
885	D₄	—	8	1	no	—
886	D₄	—	8	4	no	—
887	D₄	—	8	4	no	—
888	D₄	—	8	4	no	—
889	D₄	C₂²×D₄×C₆₇	1	4	yes	—
890	D₄	C₂²×D₄×C₆₇	1	2	yes	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	4	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	4	no	—
895	C₂×C₄	—	2	4	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	4	1	no	—
901	C₂×C₄	—	4	8	no	—
902	C₂×C₄	—	4	8	no	—
903	C₂×C₄	—	4	2	no	—
904	C₂×C₄	—	4	4	no	—
905	C₂×C₄	—	4	4	no	—
906	C₂×C₄	—	4	2	no	—
907	C₂×C₄	—	8	2	no	—
908	C₂×C₄	—	8	1	no	—
909	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
910	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
911	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
912	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
913	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
914	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
915	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
916	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
917	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
918	C₈	—	2	2	no	—
919	C₈	—	2	2	no	—
920	C₈	—	2	2	no	—
921	C₈	C₂²×D₄×C₆₇	1	4	yes	—
922	C₂²	—	2	1	no	—
923	C₂²	—	2	1	no	—
924	C₂²	—	2	4	no	—
925	C₂²	—	2	4	no	—
926	C₂²	—	2	4	no	—
927	C₂²	—	2	2	no	—
928	C₂²	—	2	4	no	—
929	C₂²	—	4	2	no	—
930	C₂²	—	4	1	no	—
931	C₂²	—	4	1	no	—
932	C₂²	—	4	2	no	—
933	C₂²	—	4	4	no	—
934	C₂²	—	4	2	no	—
935	C₂²	—	4	4	no	—
936	C₂²	—	4	2	no	—
937	C₂²	—	4	4	no	—
938	C₂²	—	4	2	no	—
939	C₂²	—	8	4	no	—
940	C₂²	—	16	4	no	—
941	C₂²	—	16	8	no	—
942	C₂²	—	16	8	no	—
943	C₂²	D₄²×C₆₇	1	2	yes	—
944	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
945	C₄	—	2	1	no	—
946	C₄	—	2	1	no	—
947	C₄	—	2	1	no	—
948	C₄	—	2	2	no	—
949	C₄	—	2	4	no	—
950	C₄	—	4	2	no	—
951	C₄	—	4	1	no	—
952	C₄	—	4	1	no	—
953	C₄	—	4	2	no	—
954	C₄	D₄²×C₆₇	1	2	yes	—
955	C₄	#576×C₆₇	1	2	yes	complemented
956	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
957	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
958	C₂	—	2	2	no	—
959	C₂	—	4	4	no	—
960	C₂	—	4	4	no	—
961	C₂	—	4	2	no	—
962	C₂	—	8	4	no	—
963	C₂	—	8	2	no	—
964	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
965	C₂	C₂×#576×C₆₇	1	1	yes	characteristic
966	C₂	C₆₇×#3585	1	1	yes	characteristic

	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×#576×C₆₇	C₂	semidirect
2. C₆₇×#3498	C₂	semidirect
3. C₆₇×#3496	C₂	semidirect
4. C₆₇×#3284	C₂	semidirect
5. D₄×D₈×C₆₇	C₂	semidirect
6. C₆₇×#3274	C₂	semidirect
7. C₆₇×#3272	C₂	semidirect
8. C₆₇×#3268	C₂	semidirect
9. C₆₇×#3264	C₂	semidirect
10. C₆₇×#3151	C₂	semidirect
11. C₆₇×#3062	C₂	semidirect
12. C₆₇×#3035	C₂	semidirect
13. C₂×#459×C₆₇	C₂	semidirect
14. C₆₇×#3012	C₂	semidirect
15. C₆₇×#3008	C₂	semidirect
16. C₄×AGL(1,ℤ/8)×C₆₇	C₂	semidirect
17. C₆₇×#2935	C₂	semidirect
18. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
19. C₂×H(5,𝔽₂)×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×#135×C₆₇	C₂²	semidirect
27. C₂×#135×C₆₇	C₂²	semidirect
28. C₂²×D₈×C₆₇	C₂²	semidirect
29. C₂²×D₈×C₆₇	C₂²	semidirect
30. C₂×#131×C₆₇	C₂²	semidirect
31. #550×C₆₇	C₂²	semidirect
32. #550×C₆₇	C₂²	semidirect
34. #547×C₆₇	C₂²	semidirect
36. #546×C₆₇	C₂²	semidirect
40. D₄²×C₆₇	C₂²	semidirect
41. D₄²×C₆₇	C₂²	semidirect
42. D₄²×C₆₇	C₂²	semidirect
43. #537×C₆₇	C₂²	semidirect
45. #535×C₆₇	C₂²	semidirect
49. #532×C₆₇	C₂²	semidirect
51. C₂×#127×C₆₇	C₂²	semidirect
53. C₄×#41×C₆₇	C₂²	semidirect
54. C₂×C₄×D₄×C₆₇	C₂²	semidirect
55. #496×C₆₇	C₂²	semidirect
56. #493×C₆₇	C₂²	semidirect
57. #492×C₆₇	C₂²	semidirect
58. #469×C₆₇	C₂²	semidirect
59. #468×C₆₇	C₂²	semidirect
60. #466×C₆₇	C₂²	semidirect
61. #465×C₆₇	C₂²	semidirect
62. #464×C₆₇	C₂²	semidirect
63. #463×C₆₇	C₂²	semidirect
64. #462×C₆₇	C₂²	semidirect
65. #461×C₆₇	C₂²	semidirect
66. #460×C₆₇	C₂²	semidirect
67. #459×C₆₇	C₂²	semidirect
68. #459×C₆₇	C₂²	semidirect
69. #459×C₆₇	C₂²	semidirect
70. #459×C₆₇	C₂²	semidirect
71. #452×C₆₇	C₂²	semidirect
72. #450×C₆₇	C₂²	semidirect
73. #449×C₆₇	C₂²	semidirect
74. #449×C₆₇	C₂²	semidirect
75. #449×C₆₇	C₂²	semidirect
76. #447×C₆₇	C₂²	semidirect
77. #447×C₆₇	C₂²	semidirect
78. #447×C₆₇	C₂²	semidirect
79. #442×C₆₇	C₂²	semidirect
80. #440×C₆₇	C₂²	semidirect
81. C₄×SD₁₆×C₆₇	C₂²	semidirect
82. C₄×D₈×C₆₇	C₂²	semidirect
83. #436×C₆₇	C₂²	semidirect
84. #435×C₆₇	C₂²	semidirect
85. C₈×D₄×C₆₇	C₂²	semidirect
86. #428×C₆₇	C₂²	semidirect
87. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
88. #418×C₆₇	C₂²	semidirect
89. #417×C₆₇	C₂²	semidirect
90. #416×C₆₇	C₂²	semidirect
91. C₂×#102×C₆₇	C₂²	semidirect
92. #408×C₆₇	C₂²	semidirect
93. C₄×M₁₆×C₆₇	C₂²	semidirect
123. AGL(1,ℤ/8)×C₆₇	D₄	semidirect
243. #41×C₆₇	C₂×D₄	semidirect
284. C₂×D₄×C₆₇	C₂×D₄	semidirect
308. SD₁₆×C₆₇	C₂×D₄	semidirect
314. D₈×C₆₇	C₂×D₄	semidirect
317. M₁₆×C₆₇	C₂×D₄	semidirect
471. C₄×C₆₇	#576	semidirect
474. #61093	C₆₇	direct (N × H)
484. C₂×#576	C₂×C₆₇	semidirect
485. #3498	C₂×C₆₇	semidirect
486. #3496	C₂×C₆₇	semidirect
487. #3284	C₂×C₆₇	semidirect
488. D₄×D₈	C₂×C₆₇	semidirect
489. #3274	C₂×C₆₇	semidirect
490. #3272	C₂×C₆₇	semidirect
491. #3268	C₂×C₆₇	semidirect
492. #3264	C₂×C₆₇	semidirect
493. #3151	C₂×C₆₇	semidirect
494. #3062	C₂×C₆₇	semidirect
495. #3035	C₂×C₆₇	semidirect
496. C₂×#459	C₂×C₆₇	semidirect
497. #3012	C₂×C₆₇	semidirect
498. #3008	C₂×C₆₇	semidirect
499. C₄×AGL(1,ℤ/8)	C₂×C₆₇	semidirect
500. #2935	C₂×C₆₇	semidirect
501. C₆₇	#61093	direct (N × H)
502. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
503. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
506. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
507. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
508. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
509. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
510. C₂×#135	C₂²×C₆₇	semidirect
511. C₂×#135	C₂²×C₆₇	semidirect
512. C₂²×D₈	C₂²×C₆₇	semidirect
513. C₂²×D₈	C₂²×C₆₇	semidirect
514. C₂×#131	C₂²×C₆₇	semidirect
515. #550	C₂²×C₆₇	semidirect
516. #550	C₂²×C₆₇	semidirect
518. #547	C₂²×C₆₇	semidirect
520. #546	C₂²×C₆₇	semidirect
524. D₄²	C₂²×C₆₇	semidirect
525. D₄²	C₂²×C₆₇	semidirect
526. D₄²	C₂²×C₆₇	semidirect
527. #537	C₂²×C₆₇	semidirect
529. #535	C₂²×C₆₇	semidirect
533. #532	C₂²×C₆₇	semidirect
535. C₂×#127	C₂²×C₆₇	semidirect
537. C₄×#41	C₂²×C₆₇	semidirect
538. C₂×C₄×D₄	C₂²×C₆₇	semidirect
539. #496	C₂²×C₆₇	semidirect
540. #493	C₂²×C₆₇	semidirect
541. #492	C₂²×C₆₇	semidirect
542. #469	C₂²×C₆₇	semidirect
543. #468	C₂²×C₆₇	semidirect
544. #466	C₂²×C₆₇	semidirect
545. #465	C₂²×C₆₇	semidirect
546. #464	C₂²×C₆₇	semidirect
547. #463	C₂²×C₆₇	semidirect
548. #462	C₂²×C₆₇	semidirect
549. #461	C₂²×C₆₇	semidirect
550. #460	C₂²×C₆₇	semidirect
551. #459	C₂²×C₆₇	semidirect
552. #459	C₂²×C₆₇	semidirect
553. #459	C₂²×C₆₇	semidirect
554. #459	C₂²×C₆₇	semidirect
555. #452	C₂²×C₆₇	semidirect
556. #450	C₂²×C₆₇	semidirect
557. #449	C₂²×C₆₇	semidirect
558. #449	C₂²×C₆₇	semidirect
559. #449	C₂²×C₆₇	semidirect
560. #447	C₂²×C₆₇	semidirect
561. #447	C₂²×C₆₇	semidirect
562. #447	C₂²×C₆₇	semidirect
563. #442	C₂²×C₆₇	semidirect
564. #440	C₂²×C₆₇	semidirect
565. C₄×SD₁₆	C₂²×C₆₇	semidirect
566. C₄×D₈	C₂²×C₆₇	semidirect
567. #436	C₂²×C₆₇	semidirect
568. #435	C₂²×C₆₇	semidirect
569. C₈×D₄	C₂²×C₆₇	semidirect
570. #428	C₂²×C₆₇	semidirect
571. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
572. #418	C₂²×C₆₇	semidirect
573. #417	C₂²×C₆₇	semidirect
574. #416	C₂²×C₆₇	semidirect
575. C₂×#102	C₂²×C₆₇	semidirect
576. #408	C₂²×C₆₇	semidirect
577. C₄×M₁₆	C₂²×C₆₇	semidirect
607. AGL(1,ℤ/8)	D₄×C₆₇	semidirect
727. #41	C₂×D₄×C₆₇	semidirect
768. C₂×D₄	C₂×D₄×C₆₇	semidirect
792. SD₁₆	C₂×D₄×C₆₇	semidirect
798. D₈	C₂×D₄×C₆₇	semidirect
801. M₁₆	C₂×D₄×C₆₇	semidirect
955. C₄	#576×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
C₆₇×#3498	2
C₆₇×#3496	2
C₆₇×#3284	2
D₄×D₈×C₆₇	2
C₆₇×#3274	2
C₆₇×#3272	2
C₆₇×#3268	2
C₆₇×#3264	2
C₆₇×#3151	2
C₆₇×#3062	2
C₆₇×#3035	2
C₂×#459×C₆₇	2
C₆₇×#3012	2
C₆₇×#3008	2
C₄×AGL(1,ℤ/8)×C₆₇	2
C₆₇×#2935	2
#61093	67

Subgroups — C67×#61093 #30740344

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61093 #30740344