Subgroups — C₆₇×#61085 #30740336

Order 17152.

2750 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#577×C₆₇	C₂	1	2	yes	maximal, complemented
2	C₆₇×#3497	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	C₆₇×#3282	C₂	1	4	yes	maximal, complemented
6	D₄×SD₁₆×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3276	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3275	C₂	1	4	yes	maximal, complemented
9	C₆₇×#3274	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3147	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3060	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3037	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3036	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3013	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3012	C₂	1	2	yes	maximal, complemented
16	C₂×C₄×SD₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	2	yes	complemented
19	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	2	yes	—
20	#577×C₆₇	—	2	16	no	—
21	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
22	C₂×#137×C₆₇	C₂²	1	4	yes	complemented
23	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	—
24	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	complemented
25	C₂×#135×C₆₇	C₂²	1	4	yes	complemented
26	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
27	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
28	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
29	C₂²×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
30	C₂×#131×C₆₇	C₂²	1	2	yes	complemented
31	#550×C₆₇	—	2	1	no	—
32	#550×C₆₇	C₂²	1	2	yes	complemented
33	D₄×Q₈×C₆₇	—	2	1	no	—
34	D₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
35	#548×C₆₇	—	2	2	no	—
36	#548×C₆₇	C₂²	1	4	yes	complemented
37	#547×C₆₇	—	2	1	no	—
38	#547×C₆₇	C₂²	1	2	yes	—
39	#546×C₆₇	—	2	2	no	—
40	#546×C₆₇	C₂²	1	4	yes	—
41	D₄²×C₆₇	—	2	1	no	—
42	D₄²×C₆₇	C₂²	1	2	yes	—
43	#537×C₆₇	—	2	2	no	—
44	#537×C₆₇	C₂²	1	2	yes	—
45	#537×C₆₇	C₂²	1	2	yes	complemented
46	#534×C₆₇	—	2	2	no	—
47	#532×C₆₇	—	2	2	no	—
48	#532×C₆₇	C₂²	1	1	yes	characteristic
49	#532×C₆₇	C₂²	1	1	yes	characteristic
50	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
51	C₂×#121×C₆₇	—	2	2	no	—
52	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
54	#495×C₆₇	C₂²	1	2	yes	complemented
55	#495×C₆₇	C₂²	1	2	yes	complemented
56	#494×C₆₇	C₂²	1	1	yes	characteristic, complemented
57	#493×C₆₇	C₂²	1	1	yes	characteristic, complemented
58	#492×C₆₇	C₂²	1	1	yes	characteristic, complemented
59	#492×C₆₇	C₂²	1	1	yes	characteristic, complemented
60	#470×C₆₇	C₂²	1	4	yes	complemented
61	#469×C₆₇	C₂²	1	4	yes	complemented
62	#465×C₆₇	C₂²	1	4	yes	complemented
63	#465×C₆₇	C₂²	1	4	yes	complemented
64	#464×C₆₇	C₂²	1	4	yes	complemented
65	#463×C₆₇	C₂²	1	4	yes	complemented
66	#462×C₆₇	C₂²	1	2	yes	complemented
67	#461×C₆₇	C₂²	1	2	yes	complemented
68	#460×C₆₇	C₂²	1	2	yes	complemented
69	#459×C₆₇	C₂²	1	2	yes	complemented
70	#452×C₆₇	C₂²	1	4	yes	complemented
71	#452×C₆₇	C₂²	1	4	yes	complemented
72	#451×C₆₇	C₂²	1	4	yes	complemented
73	#450×C₆₇	C₂²	1	4	yes	complemented
74	#449×C₆₇	C₂²	1	4	yes	complemented
75	#449×C₆₇	C₂²	1	4	yes	complemented
76	#448×C₆₇	C₂²	1	4	yes	complemented
77	#447×C₆₇	C₂²	1	4	yes	complemented
78	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
79	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
80	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
81	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
82	#436×C₆₇	C₂²	1	2	yes	complemented
83	#436×C₆₇	C₂²	1	2	yes	complemented
84	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
85	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
86	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic, complemented
87	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
88	#417×C₆₇	C₂²	1	2	yes	complemented
89	#417×C₆₇	C₂²	1	2	yes	complemented
90	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
92	#408×C₆₇	C₂²	1	2	yes	complemented
93	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
94	2₋¹⁺⁴×C₆₇	—	2	8	no	—
95	2₋¹⁺⁴×C₆₇	—	4	4	no	—
96	H(5,𝔽₂)×C₆₇	—	2	8	no	—
97	H(5,𝔽₂)×C₆₇	—	4	4	no	—
98	C₂×#41×C₆₇	—	2	2	no	—
99	C₂×#41×C₆₇	—	2	4	no	—
100	C₂×#41×C₆₇	—	2	2	no	—
101	C₂×#41×C₆₇	C₂³	1	2	yes	—
102	C₂×#41×C₆₇	C₂³	1	2	yes	—
103	C₂×#41×C₆₇	C₂³	1	4	yes	—
104	C₂×#41×C₆₇	C₂³	1	4	yes	—
105	C₂×#41×C₆₇	C₂³	1	2	yes	—
106	C₂²×Q₈×C₆₇	—	2	2	no	—
107	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
108	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₆₇	—	2	4	no	—
110	C₂²×D₄×C₆₇	—	2	2	no	—
111	C₂²×D₄×C₆₇	—	2	2	no	—
112	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
113	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₆₇	—	2	1	no	—
115	#137×C₆₇	—	2	8	no	—
116	#137×C₆₇	—	2	16	no	—
117	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
118	AGL(1,ℤ/8)×C₆₇	—	2	16	no	—
119	#135×C₆₇	—	2	16	no	—
120	#135×C₆₇	—	2	8	no	—
121	#135×C₆₇	—	4	4	no	—
122	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
123	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
124	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
125	C₂×SD₁₆×C₆₇	—	2	16	no	—
126	C₂×SD₁₆×C₆₇	D₄	1	8	yes	complemented
127	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
128	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
129	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
130	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
131	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
132	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
133	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
134	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
135	C₂×D₈×C₆₇	C₂³	1	4	yes	—
136	C₂×D₈×C₆₇	C₂³	1	2	yes	—
137	C₂×D₈×C₆₇	C₂³	1	2	yes	—
138	#131×C₆₇	—	2	8	no	—
139	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
140	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
141	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
142	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
144	C₄⋊Q₈×C₆₇	—	2	2	no	—
145	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
146	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
147	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
148	#127×C₆₇	—	2	2	no	—
149	#127×C₆₇	D₄	1	1	yes	characteristic
150	#127×C₆₇	C₂³	1	1	yes	characteristic
151	#127×C₆₇	C₂³	1	1	yes	characteristic
152	#124×C₆₇	—	2	4	no	—
153	#124×C₆₇	D₄	1	2	yes	—
154	#124×C₆₇	C₂³	1	2	yes	—
155	#124×C₆₇	C₂³	1	2	yes	—
156	#123×C₆₇	—	2	4	no	—
157	#123×C₆₇	—	2	4	no	—
158	C₂²⋊Q₈×C₆₇	—	2	2	no	—
159	C₂²⋊Q₈×C₆₇	—	2	2	no	—
160	C₂²⋊Q₈×C₆₇	—	2	4	no	—
161	C₂²⋊Q₈×C₆₇	—	2	4	no	—
162	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
163	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
164	#121×C₆₇	—	2	4	no	—
165	#121×C₆₇	—	2	2	no	—
166	#121×C₆₇	—	2	4	no	—
167	#121×C₆₇	—	2	4	no	—
168	#121×C₆₇	—	2	2	no	—
169	#121×C₆₇	—	2	2	no	—
170	#121×C₆₇	—	2	1	no	—
171	#121×C₆₇	—	2	1	no	—
172	#121×C₆₇	—	2	1	no	—
173	#121×C₆₇	—	2	1	no	—
174	#121×C₆₇	—	2	2	no	—
175	#121×C₆₇	—	2	4	no	—
176	#121×C₆₇	—	2	4	no	—
177	#121×C₆₇	D₄	1	2	yes	—
178	#121×C₆₇	D₄	1	2	yes	—
179	#121×C₆₇	C₂³	1	4	yes	—
180	#121×C₆₇	C₂³	1	4	yes	—
181	#120×C₆₇	—	2	4	no	—
182	#120×C₆₇	—	2	4	no	—
183	C₄×Q₈×C₆₇	—	2	1	no	—
184	C₄×Q₈×C₆₇	—	2	1	no	—
185	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
186	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
187	C₄×D₄×C₆₇	—	2	2	no	—
188	C₄×D₄×C₆₇	—	2	2	no	—
189	C₄×D₄×C₆₇	—	2	4	no	—
190	C₄×D₄×C₆₇	—	2	1	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	—	2	1	no	—
196	C₄×D₄×C₆₇	C₂³	1	2	yes	—
197	C₄×D₄×C₆₇	C₂³	1	2	yes	—
198	C₄×D₄×C₆₇	C₂³	1	2	yes	—
199	C₄×D₄×C₆₇	C₂³	1	2	yes	—
200	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
201	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
202	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
205	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
206	C₂×C₄²×C₆₇	—	2	1	no	—
207	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
208	#106×C₆₇	C₂³	1	2	yes	—
209	#106×C₆₇	C₂³	1	2	yes	—
210	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
211	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
212	#103×C₆₇	C₂³	1	2	yes	—
213	#103×C₆₇	C₂³	1	4	yes	—
214	#103×C₆₇	C₂³	1	2	yes	—
215	#103×C₆₇	C₂³	1	4	yes	—
216	#102×C₆₇	C₂³	1	2	yes	—
217	#102×C₆₇	C₂³	1	4	yes	—
218	#102×C₆₇	C₂³	1	4	yes	—
219	#102×C₆₇	C₂³	1	2	yes	—
220	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
221	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
222	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
223	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
224	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
225	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
226	C₂⁴×C₆₇	—	2	1	no	—
227	C₂⁴×C₆₇	—	2	4	no	—
228	#41×C₆₇	—	2	4	no	—
229	#41×C₆₇	—	2	4	no	—
230	#41×C₆₇	—	2	8	no	—
231	#41×C₆₇	—	2	8	no	—
232	#41×C₆₇	—	2	4	no	—
233	#41×C₆₇	—	2	4	no	—
234	#41×C₆₇	—	2	4	no	—
235	#41×C₆₇	—	2	4	no	—
236	#41×C₆₇	—	4	4	no	—
237	#41×C₆₇	—	4	4	no	—
238	#41×C₆₇	—	4	16	no	—
239	#41×C₆₇	—	4	8	no	—
240	#41×C₆₇	—	4	8	no	—
241	C₂×Q₈×C₆₇	—	2	1	no	—
242	C₂×Q₈×C₆₇	—	2	4	no	—
243	C₂×Q₈×C₆₇	—	2	2	no	—
244	C₂×Q₈×C₆₇	—	2	8	no	—
245	C₂×Q₈×C₆₇	—	4	4	no	—
246	C₂×Q₈×C₆₇	—	4	8	no	—
247	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
248	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	complemented
249	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
250	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
251	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
252	C₂×D₄×C₆₇	—	2	8	no	—
253	C₂×D₄×C₆₇	—	2	4	no	—
254	C₂×D₄×C₆₇	—	2	2	no	—
255	C₂×D₄×C₆₇	—	2	2	no	—
256	C₂×D₄×C₆₇	—	2	4	no	—
257	C₂×D₄×C₆₇	—	2	4	no	—
258	C₂×D₄×C₆₇	—	2	4	no	—
259	C₂×D₄×C₆₇	—	2	1	no	—
260	C₂×D₄×C₆₇	—	2	1	no	—
261	C₂×D₄×C₆₇	—	2	1	no	—
262	C₂×D₄×C₆₇	—	2	4	no	—
263	C₂×D₄×C₆₇	—	2	1	no	—
264	C₂×D₄×C₆₇	—	2	1	no	—
265	C₂×D₄×C₆₇	—	2	2	no	—
266	C₂×D₄×C₆₇	—	4	4	no	—
267	C₂×D₄×C₆₇	—	4	8	no	—
268	C₂×D₄×C₆₇	—	4	16	no	—
269	C₂×D₄×C₆₇	—	8	4	no	—
270	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
271	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
272	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
273	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
274	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
275	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
276	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
277	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₆₇	—	2	1	no	—
279	C₂²×C₄×C₆₇	—	2	4	no	—
280	C₂²×C₄×C₆₇	—	2	1	no	—
281	C₂²×C₄×C₆₇	—	2	1	no	—
282	C₂²×C₄×C₆₇	—	2	4	no	—
283	C₂²×C₄×C₆₇	—	2	2	no	—
284	C₂²×C₄×C₆₇	—	2	2	no	—
285	C₂²×C₄×C₆₇	—	2	4	no	—
286	C₂²×C₄×C₆₇	—	2	2	no	—
287	C₂²×C₄×C₆₇	—	2	2	no	—
288	C₂²×C₄×C₆₇	—	8	2	no	—
289	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
290	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
291	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
292	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
293	Q₁₆×C₆₇	—	2	8	no	—
294	Q₁₆×C₆₇	—	2	4	no	—
295	Q₁₆×C₆₇	—	4	2	no	—
296	SD₁₆×C₆₇	—	2	8	no	—
297	SD₁₆×C₆₇	—	2	8	no	—
298	SD₁₆×C₆₇	—	2	4	no	—
299	SD₁₆×C₆₇	—	2	4	no	—
300	SD₁₆×C₆₇	—	4	2	no	—
301	SD₁₆×C₆₇	—	4	2	no	—
302	SD₁₆×C₆₇	C₂×D₄	1	8	yes	complemented
303	SD₁₆×C₆₇	C₂×D₄	1	8	yes	complemented
304	D₈×C₆₇	—	2	8	no	—
305	D₈×C₆₇	—	2	4	no	—
306	D₈×C₆₇	—	4	2	no	—
307	M₁₆×C₆₇	—	2	4	no	—
308	M₁₆×C₆₇	—	2	8	no	—
309	C₂×C₈×C₆₇	—	2	2	no	—
310	C₂×C₈×C₆₇	—	2	8	no	—
311	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	complemented
312	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
313	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
314	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
315	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
316	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
317	C₄⋊C₄×C₆₇	—	2	1	no	—
318	C₄⋊C₄×C₆₇	—	2	2	no	—
319	C₄⋊C₄×C₆₇	—	2	2	no	—
320	C₄⋊C₄×C₆₇	—	2	4	no	—
321	C₄⋊C₄×C₆₇	—	2	1	no	—
322	C₄⋊C₄×C₆₇	—	2	1	no	—
323	C₄⋊C₄×C₆₇	—	2	1	no	—
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	C₂×D₄	1	2	yes	—
328	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
329	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
330	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
331	C₂²⋊C₄×C₆₇	—	2	4	no	—
332	C₂²⋊C₄×C₆₇	—	2	4	no	—
333	C₂²⋊C₄×C₆₇	—	2	2	no	—
334	C₂²⋊C₄×C₆₇	—	2	2	no	—
335	C₂²⋊C₄×C₆₇	—	2	2	no	—
336	C₂²⋊C₄×C₆₇	—	2	4	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	C₂×D₄	1	4	yes	—
342	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
343	C₄²×C₆₇	—	2	2	no	—
344	C₄²×C₆₇	—	2	2	no	—
345	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
346	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
347	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
348	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
349	C₂³×C₆₇	—	2	2	no	—
350	C₂³×C₆₇	—	2	4	no	—
351	C₂³×C₆₇	—	2	2	no	—
352	C₂³×C₆₇	—	2	2	no	—
353	C₂³×C₆₇	—	4	8	no	—
354	C₂³×C₆₇	—	8	1	no	—
355	C₂³×C₆₇	—	8	1	no	—
356	C₂³×C₆₇	—	8	4	no	—
357	C₂³×C₆₇	—	8	4	no	—
358	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
359	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
360	Q₈×C₆₇	—	2	4	no	—
361	Q₈×C₆₇	—	2	4	no	—
362	Q₈×C₆₇	—	2	2	no	—
363	Q₈×C₆₇	—	2	2	no	—
364	Q₈×C₆₇	—	2	2	no	—
365	Q₈×C₆₇	—	2	2	no	—
366	Q₈×C₆₇	—	2	2	no	—
367	Q₈×C₆₇	—	4	8	no	—
368	Q₈×C₆₇	C₂²×D₄	1	4	yes	—
369	D₄×C₆₇	—	2	8	no	—
370	D₄×C₆₇	—	2	4	no	—
371	D₄×C₆₇	—	2	4	no	—
372	D₄×C₆₇	—	2	4	no	—
373	D₄×C₆₇	—	2	2	no	—
374	D₄×C₆₇	—	2	2	no	—
375	D₄×C₆₇	—	2	2	no	—
376	D₄×C₆₇	—	2	2	no	—
377	D₄×C₆₇	—	2	2	no	—
378	D₄×C₆₇	—	4	2	no	—
379	D₄×C₆₇	—	4	8	no	—
380	D₄×C₆₇	—	4	8	no	—
381	D₄×C₆₇	—	4	8	no	—
382	D₄×C₆₇	—	4	4	no	—
383	D₄×C₆₇	—	4	4	no	—
384	D₄×C₆₇	—	4	2	no	—
385	D₄×C₆₇	—	4	2	no	—
386	D₄×C₆₇	—	8	1	no	—
387	D₄×C₆₇	—	8	1	no	—
388	D₄×C₆₇	—	8	4	no	—
389	D₄×C₆₇	—	8	4	no	—
390	D₄×C₆₇	C₂²×D₄	1	4	yes	—
391	C₂×C₄×C₆₇	—	2	4	no	—
392	C₂×C₄×C₆₇	—	2	2	no	—
393	C₂×C₄×C₆₇	—	2	2	no	—
394	C₂×C₄×C₆₇	—	2	4	no	—
395	C₂×C₄×C₆₇	—	2	4	no	—
396	C₂×C₄×C₆₇	—	2	2	no	—
397	C₂×C₄×C₆₇	—	2	2	no	—
398	C₂×C₄×C₆₇	—	2	2	no	—
399	C₂×C₄×C₆₇	—	2	2	no	—
400	C₂×C₄×C₆₇	—	4	1	no	—
401	C₂×C₄×C₆₇	—	4	8	no	—
402	C₂×C₄×C₆₇	—	4	8	no	—
403	C₂×C₄×C₆₇	—	4	8	no	—
404	C₂×C₄×C₆₇	—	4	4	no	—
405	C₂×C₄×C₆₇	—	4	4	no	—
406	C₂×C₄×C₆₇	—	4	4	no	—
407	C₂×C₄×C₆₇	—	8	2	no	—
408	C₂×C₄×C₆₇	—	8	1	no	—
409	C₂×C₄×C₆₇	—	8	1	no	—
410	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
414	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
416	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
418	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
419	C₈×C₆₇	—	2	4	no	—
420	C₈×C₆₇	—	2	1	no	—
421	C₈×C₆₇	—	2	1	no	—
422	C₈×C₆₇	C₂²×D₄	1	2	yes	—
423	C₈×C₆₇	C₂²×D₄	1	2	yes	—
424	C₂²×C₆₇	—	2	1	no	—
425	C₂²×C₆₇	—	2	1	no	—
426	C₂²×C₆₇	—	2	4	no	—
427	C₂²×C₆₇	—	2	4	no	—
428	C₂²×C₆₇	—	2	4	no	—
429	C₂²×C₆₇	—	2	4	no	—
430	C₂²×C₆₇	—	4	2	no	—
431	C₂²×C₆₇	—	4	2	no	—
432	C₂²×C₆₇	—	4	2	no	—
433	C₂²×C₆₇	—	4	2	no	—
434	C₂²×C₆₇	—	4	2	no	—
435	C₂²×C₆₇	—	4	2	no	—
436	C₂²×C₆₇	—	4	2	no	—
437	C₂²×C₆₇	—	4	2	no	—
438	C₂²×C₆₇	—	8	4	no	—
439	C₂²×C₆₇	—	16	8	no	—
440	C₂²×C₆₇	D₄²	1	2	yes	—
441	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
442	C₄×C₆₇	—	2	1	no	—
443	C₄×C₆₇	—	2	1	no	—
444	C₄×C₆₇	—	2	4	no	—
445	C₄×C₆₇	—	2	4	no	—
446	C₄×C₆₇	—	2	1	no	—
447	C₄×C₆₇	—	4	2	no	—
448	C₄×C₆₇	—	4	2	no	—
449	C₄×C₆₇	—	4	2	no	—
450	C₄×C₆₇	—	4	2	no	—
451	C₄×C₆₇	D₄²	1	2	yes	—
452	C₄×C₆₇	#577	1	2	yes	complemented
453	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
454	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
455	#61085	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
456	C₂×C₆₇	—	2	2	no	—
457	C₂×C₆₇	—	4	4	no	—
458	C₂×C₆₇	—	4	4	no	—
459	C₂×C₆₇	—	8	2	no	—
460	C₂×C₆₇	—	8	2	no	—
461	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
462	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
463	C₂×C₆₇	#3584	1	1	yes	characteristic
464	C₂×#577	C₂×C₆₇	1	2	yes	complemented
465	#3497	C₂×C₆₇	1	1	yes	characteristic, complemented
466	#3496	C₂×C₆₇	1	1	yes	characteristic, complemented
467	#3284	C₂×C₆₇	1	2	yes	complemented
468	#3282	C₂×C₆₇	1	4	yes	complemented
469	D₄×SD₁₆	C₂×C₆₇	1	2	yes	complemented
470	#3276	C₂×C₆₇	1	2	yes	complemented
471	#3275	C₂×C₆₇	1	4	yes	complemented
472	#3274	C₂×C₆₇	1	2	yes	complemented
473	#3147	C₂×C₆₇	1	1	yes	characteristic, complemented
474	#3060	C₂×C₆₇	1	2	yes	complemented
475	#3037	C₂×C₆₇	1	1	yes	characteristic, complemented
476	#3036	C₂×C₆₇	1	1	yes	characteristic, complemented
477	#3013	C₂×C₆₇	1	2	yes	complemented
478	#3012	C₂×C₆₇	1	2	yes	complemented
479	C₂×C₄×SD₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
480	#2931	C₂×C₆₇	1	1	yes	characteristic, complemented
481	C₆₇	#61085	1	1	yes	characteristic, direct product factor, Sylow
482	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	2	yes	complemented
483	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	—
484	#577	—	2	16	no	—
485	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
486	C₂×#137	C₂²×C₆₇	1	4	yes	complemented
487	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	—
488	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
489	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
490	C₂×#135	C₂²×C₆₇	1	4	yes	complemented
491	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
492	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
493	C₂²×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
494	C₂×#131	C₂²×C₆₇	1	2	yes	complemented
495	#550	—	2	1	no	—
496	#550	C₂²×C₆₇	1	2	yes	complemented
497	D₄×Q₈	—	2	1	no	—
498	D₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
499	#548	—	2	2	no	—
500	#548	C₂²×C₆₇	1	4	yes	complemented
501	#547	—	2	1	no	—
502	#547	C₂²×C₆₇	1	2	yes	—
503	#546	—	2	2	no	—
504	#546	C₂²×C₆₇	1	4	yes	—
505	D₄²	—	2	1	no	—
506	D₄²	C₂²×C₆₇	1	2	yes	—
507	#537	—	2	2	no	—
508	#537	C₂²×C₆₇	1	2	yes	—
509	#537	C₂²×C₆₇	1	2	yes	complemented
510	#534	—	2	2	no	—
511	#532	—	2	2	no	—
512	#532	C₂²×C₆₇	1	1	yes	characteristic
513	#532	C₂²×C₆₇	1	1	yes	characteristic
514	#532	C₂²×C₆₇	1	1	yes	characteristic, complemented
515	C₂×#121	—	2	2	no	—
516	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
517	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
518	#495	C₂²×C₆₇	1	2	yes	complemented
519	#495	C₂²×C₆₇	1	2	yes	complemented
520	#494	C₂²×C₆₇	1	1	yes	characteristic, complemented
521	#493	C₂²×C₆₇	1	1	yes	characteristic, complemented
522	#492	C₂²×C₆₇	1	1	yes	characteristic, complemented
523	#492	C₂²×C₆₇	1	1	yes	characteristic, complemented
524	#470	C₂²×C₆₇	1	4	yes	complemented
525	#469	C₂²×C₆₇	1	4	yes	complemented
526	#465	C₂²×C₆₇	1	4	yes	complemented
527	#465	C₂²×C₆₇	1	4	yes	complemented
528	#464	C₂²×C₆₇	1	4	yes	complemented
529	#463	C₂²×C₆₇	1	4	yes	complemented
530	#462	C₂²×C₆₇	1	2	yes	complemented
531	#461	C₂²×C₆₇	1	2	yes	complemented
532	#460	C₂²×C₆₇	1	2	yes	complemented
533	#459	C₂²×C₆₇	1	2	yes	complemented
534	#452	C₂²×C₆₇	1	4	yes	complemented
535	#452	C₂²×C₆₇	1	4	yes	complemented
536	#451	C₂²×C₆₇	1	4	yes	complemented
537	#450	C₂²×C₆₇	1	4	yes	complemented
538	#449	C₂²×C₆₇	1	4	yes	complemented
539	#449	C₂²×C₆₇	1	4	yes	complemented
540	#448	C₂²×C₆₇	1	4	yes	complemented
541	#447	C₂²×C₆₇	1	4	yes	complemented
542	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
543	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
544	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
545	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
546	#436	C₂²×C₆₇	1	2	yes	complemented
547	#436	C₂²×C₆₇	1	2	yes	complemented
548	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
549	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
550	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic, complemented
551	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
552	#417	C₂²×C₆₇	1	2	yes	complemented
553	#417	C₂²×C₆₇	1	2	yes	complemented
554	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic, complemented
555	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
556	#408	C₂²×C₆₇	1	2	yes	complemented
557	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
558	2₋¹⁺⁴	—	2	8	no	—
559	2₋¹⁺⁴	—	4	4	no	—
560	H(5,𝔽₂)	—	2	8	no	—
561	H(5,𝔽₂)	—	4	4	no	—
562	C₂×#41	—	2	2	no	—
563	C₂×#41	—	2	4	no	—
564	C₂×#41	—	2	2	no	—
565	C₂×#41	C₂³×C₆₇	1	2	yes	—
566	C₂×#41	C₂³×C₆₇	1	2	yes	—
567	C₂×#41	C₂³×C₆₇	1	4	yes	—
568	C₂×#41	C₂³×C₆₇	1	4	yes	—
569	C₂×#41	C₂³×C₆₇	1	2	yes	—
570	C₂²×Q₈	—	2	2	no	—
571	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
572	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
573	C₂²×D₄	—	2	4	no	—
574	C₂²×D₄	—	2	2	no	—
575	C₂²×D₄	—	2	2	no	—
576	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
577	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
578	C₂³×C₄	—	2	1	no	—
579	#137	—	2	8	no	—
580	#137	—	2	16	no	—
581	AGL(1,ℤ/8)	—	2	8	no	—
582	AGL(1,ℤ/8)	—	2	16	no	—
583	#135	—	2	16	no	—
584	#135	—	2	8	no	—
585	#135	—	4	4	no	—
586	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
587	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
588	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
589	C₂×SD₁₆	—	2	16	no	—
590	C₂×SD₁₆	D₄×C₆₇	1	8	yes	complemented
591	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
592	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
593	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
594	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
595	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
596	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
597	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
598	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
599	C₂×D₈	C₂³×C₆₇	1	4	yes	—
600	C₂×D₈	C₂³×C₆₇	1	2	yes	—
601	C₂×D₈	C₂³×C₆₇	1	2	yes	—
602	#131	—	2	8	no	—
603	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
604	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
605	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
606	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
607	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
608	C₄⋊Q₈	—	2	2	no	—
609	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
610	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
611	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
612	#127	—	2	2	no	—
613	#127	D₄×C₆₇	1	1	yes	characteristic
614	#127	C₂³×C₆₇	1	1	yes	characteristic
615	#127	C₂³×C₆₇	1	1	yes	characteristic
616	#124	—	2	4	no	—
617	#124	D₄×C₆₇	1	2	yes	—
618	#124	C₂³×C₆₇	1	2	yes	—
619	#124	C₂³×C₆₇	1	2	yes	—
620	#123	—	2	4	no	—
621	#123	—	2	4	no	—
622	C₂²⋊Q₈	—	2	2	no	—
623	C₂²⋊Q₈	—	2	2	no	—
624	C₂²⋊Q₈	—	2	4	no	—
625	C₂²⋊Q₈	—	2	4	no	—
626	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
627	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
628	#121	—	2	4	no	—
629	#121	—	2	2	no	—
630	#121	—	2	4	no	—
631	#121	—	2	4	no	—
632	#121	—	2	2	no	—
633	#121	—	2	2	no	—
634	#121	—	2	1	no	—
635	#121	—	2	1	no	—
636	#121	—	2	1	no	—
637	#121	—	2	1	no	—
638	#121	—	2	2	no	—
639	#121	—	2	4	no	—
640	#121	—	2	4	no	—
641	#121	D₄×C₆₇	1	2	yes	—
642	#121	D₄×C₆₇	1	2	yes	—
643	#121	C₂³×C₆₇	1	4	yes	—
644	#121	C₂³×C₆₇	1	4	yes	—
645	#120	—	2	4	no	—
646	#120	—	2	4	no	—
647	C₄×Q₈	—	2	1	no	—
648	C₄×Q₈	—	2	1	no	—
649	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
650	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
651	C₄×D₄	—	2	2	no	—
652	C₄×D₄	—	2	2	no	—
653	C₄×D₄	—	2	4	no	—
654	C₄×D₄	—	2	1	no	—
655	C₄×D₄	—	2	1	no	—
656	C₄×D₄	—	2	1	no	—
657	C₄×D₄	—	2	1	no	—
658	C₄×D₄	—	2	1	no	—
659	C₄×D₄	—	2	1	no	—
660	C₄×D₄	C₂³×C₆₇	1	2	yes	—
661	C₄×D₄	C₂³×C₆₇	1	2	yes	—
662	C₄×D₄	C₂³×C₆₇	1	2	yes	—
663	C₄×D₄	C₂³×C₆₇	1	2	yes	—
664	C₂×C₄⋊C₄	—	2	1	no	—
665	C₂×C₄⋊C₄	—	2	2	no	—
666	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
667	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
668	C₂×C₂²⋊C₄	—	2	1	no	—
669	C₂×C₂²⋊C₄	—	2	4	no	—
670	C₂×C₄²	—	2	1	no	—
671	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
672	#106	C₂³×C₆₇	1	2	yes	—
673	#106	C₂³×C₆₇	1	2	yes	—
674	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
675	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
676	#103	C₂³×C₆₇	1	2	yes	—
677	#103	C₂³×C₆₇	1	2	yes	—
678	#103	C₂³×C₆₇	1	4	yes	—
679	#103	C₂³×C₆₇	1	4	yes	—
680	#102	C₂³×C₆₇	1	2	yes	—
681	#102	C₂³×C₆₇	1	2	yes	—
682	#102	C₂³×C₆₇	1	4	yes	—
683	#102	C₂³×C₆₇	1	4	yes	—
684	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
685	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
686	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
687	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
688	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
689	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
690	C₂⁴	—	2	1	no	—
691	C₂⁴	—	2	4	no	—
692	#41	—	2	4	no	—
693	#41	—	2	4	no	—
694	#41	—	2	8	no	—
695	#41	—	2	8	no	—
696	#41	—	2	4	no	—
697	#41	—	2	4	no	—
698	#41	—	2	4	no	—
699	#41	—	2	4	no	—
700	#41	—	4	4	no	—
701	#41	—	4	4	no	—
702	#41	—	4	16	no	—
703	#41	—	4	8	no	—
704	#41	—	4	8	no	—
705	C₂×Q₈	—	2	1	no	—
706	C₂×Q₈	—	2	4	no	—
707	C₂×Q₈	—	2	2	no	—
708	C₂×Q₈	—	2	8	no	—
709	C₂×Q₈	—	4	4	no	—
710	C₂×Q₈	—	4	8	no	—
711	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
712	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	complemented
713	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
714	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
715	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
716	C₂×D₄	—	2	8	no	—
717	C₂×D₄	—	2	4	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	4	no	—
721	C₂×D₄	—	2	4	no	—
722	C₂×D₄	—	2	4	no	—
723	C₂×D₄	—	2	1	no	—
724	C₂×D₄	—	2	1	no	—
725	C₂×D₄	—	2	1	no	—
726	C₂×D₄	—	2	4	no	—
727	C₂×D₄	—	2	1	no	—
728	C₂×D₄	—	2	1	no	—
729	C₂×D₄	—	2	2	no	—
730	C₂×D₄	—	4	4	no	—
731	C₂×D₄	—	4	8	no	—
732	C₂×D₄	—	4	16	no	—
733	C₂×D₄	—	8	4	no	—
734	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
735	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
736	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
737	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
738	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
739	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
740	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
741	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
742	C₂²×C₄	—	2	1	no	—
743	C₂²×C₄	—	2	4	no	—
744	C₂²×C₄	—	2	1	no	—
745	C₂²×C₄	—	2	1	no	—
746	C₂²×C₄	—	2	4	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	4	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	8	2	no	—
753	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
754	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
755	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
756	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
757	Q₁₆	—	2	8	no	—
758	Q₁₆	—	2	4	no	—
759	Q₁₆	—	4	2	no	—
760	SD₁₆	—	2	8	no	—
761	SD₁₆	—	2	8	no	—
762	SD₁₆	—	2	4	no	—
763	SD₁₆	—	2	4	no	—
764	SD₁₆	—	4	2	no	—
765	SD₁₆	—	4	2	no	—
766	SD₁₆	C₂×D₄×C₆₇	1	8	yes	complemented
767	SD₁₆	C₂×D₄×C₆₇	1	8	yes	complemented
768	D₈	—	2	8	no	—
769	D₈	—	2	4	no	—
770	D₈	—	4	2	no	—
771	M₁₆	—	2	4	no	—
772	M₁₆	—	2	8	no	—
773	C₂×C₈	—	2	2	no	—
774	C₂×C₈	—	2	8	no	—
775	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	complemented
776	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
777	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
778	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
779	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
780	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
781	C₄⋊C₄	—	2	1	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	4	no	—
785	C₄⋊C₄	—	2	1	no	—
786	C₄⋊C₄	—	2	1	no	—
787	C₄⋊C₄	—	2	1	no	—
788	C₄⋊C₄	—	2	1	no	—
789	C₄⋊C₄	—	2	4	no	—
790	C₄⋊C₄	—	2	1	no	—
791	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
792	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
793	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
794	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	4	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	4	no	—
805	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
806	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
807	C₄²	—	2	2	no	—
808	C₄²	—	2	2	no	—
809	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
810	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
811	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
812	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
813	C₂³	—	2	2	no	—
814	C₂³	—	2	4	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	4	8	no	—
818	C₂³	—	8	1	no	—
819	C₂³	—	8	1	no	—
820	C₂³	—	8	4	no	—
821	C₂³	—	8	4	no	—
822	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
823	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
824	Q₈	—	2	4	no	—
825	Q₈	—	2	4	no	—
826	Q₈	—	2	2	no	—
827	Q₈	—	2	2	no	—
828	Q₈	—	2	2	no	—
829	Q₈	—	2	2	no	—
830	Q₈	—	2	2	no	—
831	Q₈	—	4	8	no	—
832	Q₈	C₂²×D₄×C₆₇	1	4	yes	—
833	D₄	—	2	8	no	—
834	D₄	—	2	4	no	—
835	D₄	—	2	4	no	—
836	D₄	—	2	4	no	—
837	D₄	—	2	2	no	—
838	D₄	—	2	2	no	—
839	D₄	—	2	2	no	—
840	D₄	—	2	2	no	—
841	D₄	—	2	2	no	—
842	D₄	—	4	2	no	—
843	D₄	—	4	8	no	—
844	D₄	—	4	8	no	—
845	D₄	—	4	8	no	—
846	D₄	—	4	4	no	—
847	D₄	—	4	4	no	—
848	D₄	—	4	2	no	—
849	D₄	—	4	2	no	—
850	D₄	—	8	1	no	—
851	D₄	—	8	1	no	—
852	D₄	—	8	4	no	—
853	D₄	—	8	4	no	—
854	D₄	C₂²×D₄×C₆₇	1	4	yes	—
855	C₂×C₄	—	2	4	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	4	no	—
859	C₂×C₄	—	2	4	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	4	1	no	—
865	C₂×C₄	—	4	8	no	—
866	C₂×C₄	—	4	8	no	—
867	C₂×C₄	—	4	8	no	—
868	C₂×C₄	—	4	4	no	—
869	C₂×C₄	—	4	4	no	—
870	C₂×C₄	—	4	4	no	—
871	C₂×C₄	—	8	2	no	—
872	C₂×C₄	—	8	1	no	—
873	C₂×C₄	—	8	1	no	—
874	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
875	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
876	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
877	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
878	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
879	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
880	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
881	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
882	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
883	C₈	—	2	4	no	—
884	C₈	—	2	1	no	—
885	C₈	—	2	1	no	—
886	C₈	C₂²×D₄×C₆₇	1	2	yes	—
887	C₈	C₂²×D₄×C₆₇	1	2	yes	—
888	C₂²	—	2	1	no	—
889	C₂²	—	2	1	no	—
890	C₂²	—	2	4	no	—
891	C₂²	—	2	4	no	—
892	C₂²	—	2	4	no	—
893	C₂²	—	2	4	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	2	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	4	2	no	—
898	C₂²	—	4	2	no	—
899	C₂²	—	4	2	no	—
900	C₂²	—	4	2	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	8	4	no	—
903	C₂²	—	16	8	no	—
904	C₂²	D₄²×C₆₇	1	2	yes	—
905	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
906	C₄	—	2	1	no	—
907	C₄	—	2	1	no	—
908	C₄	—	2	1	no	—
909	C₄	—	2	4	no	—
910	C₄	—	2	4	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	2	no	—
913	C₄	—	4	2	no	—
914	C₄	—	4	2	no	—
915	C₄	D₄²×C₆₇	1	2	yes	—
916	C₄	#577×C₆₇	1	2	yes	complemented
917	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
918	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
919	C₂	—	2	2	no	—
920	C₂	—	4	4	no	—
921	C₂	—	4	4	no	—
922	C₂	—	8	2	no	—
923	C₂	—	8	2	no	—
924	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
925	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
926	C₂	C₆₇×#3584	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×#577×C₆₇	C₂	semidirect
2. C₆₇×#3497	C₂	semidirect
3. C₆₇×#3496	C₂	semidirect
4. C₆₇×#3284	C₂	semidirect
5. C₆₇×#3282	C₂	semidirect
6. D₄×SD₁₆×C₆₇	C₂	semidirect
7. C₆₇×#3276	C₂	semidirect
8. C₆₇×#3275	C₂	semidirect
9. C₆₇×#3274	C₂	semidirect
10. C₆₇×#3147	C₂	semidirect
11. C₆₇×#3060	C₂	semidirect
12. C₆₇×#3037	C₂	semidirect
13. C₆₇×#3036	C₂	semidirect
14. C₆₇×#3013	C₂	semidirect
15. C₆₇×#3012	C₂	semidirect
16. C₂×C₄×SD₁₆×C₆₇	C₂	semidirect
17. C₆₇×#2931	C₂	semidirect
18. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
21. C₂×#137×C₆₇	C₂²	semidirect
22. C₂×#137×C₆₇	C₂²	semidirect
24. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
25. C₂×#135×C₆₇	C₂²	semidirect
26. C₂×#135×C₆₇	C₂²	semidirect
27. C₂×#135×C₆₇	C₂²	semidirect
29. C₂²×SD₁₆×C₆₇	C₂²	semidirect
30. C₂×#131×C₆₇	C₂²	semidirect
32. #550×C₆₇	C₂²	semidirect
34. D₄×Q₈×C₆₇	C₂²	semidirect
36. #548×C₆₇	C₂²	semidirect
45. #537×C₆₇	C₂²	semidirect
50. #532×C₆₇	C₂²	semidirect
52. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
54. #495×C₆₇	C₂²	semidirect
55. #495×C₆₇	C₂²	semidirect
56. #494×C₆₇	C₂²	semidirect
57. #493×C₆₇	C₂²	semidirect
58. #492×C₆₇	C₂²	semidirect
59. #492×C₆₇	C₂²	semidirect
60. #470×C₆₇	C₂²	semidirect
61. #469×C₆₇	C₂²	semidirect
62. #465×C₆₇	C₂²	semidirect
63. #465×C₆₇	C₂²	semidirect
64. #464×C₆₇	C₂²	semidirect
65. #463×C₆₇	C₂²	semidirect
66. #462×C₆₇	C₂²	semidirect
67. #461×C₆₇	C₂²	semidirect
68. #460×C₆₇	C₂²	semidirect
69. #459×C₆₇	C₂²	semidirect
70. #452×C₆₇	C₂²	semidirect
71. #452×C₆₇	C₂²	semidirect
72. #451×C₆₇	C₂²	semidirect
73. #450×C₆₇	C₂²	semidirect
74. #449×C₆₇	C₂²	semidirect
75. #449×C₆₇	C₂²	semidirect
76. #448×C₆₇	C₂²	semidirect
77. #447×C₆₇	C₂²	semidirect
78. C₄×SD₁₆×C₆₇	C₂²	semidirect
79. C₄×SD₁₆×C₆₇	C₂²	semidirect
80. C₄×SD₁₆×C₆₇	C₂²	semidirect
81. C₄×SD₁₆×C₆₇	C₂²	semidirect
82. #436×C₆₇	C₂²	semidirect
83. #436×C₆₇	C₂²	semidirect
84. C₈×D₄×C₆₇	C₂²	semidirect
85. C₈×D₄×C₆₇	C₂²	semidirect
86. C₂×#106×C₆₇	C₂²	semidirect
87. #423×C₆₇	C₂²	semidirect
88. #417×C₆₇	C₂²	semidirect
89. #417×C₆₇	C₂²	semidirect
90. C₂×#103×C₆₇	C₂²	semidirect
92. #408×C₆₇	C₂²	semidirect
93. C₂×C₄×C₈×C₆₇	C₂²	semidirect
126. C₂×SD₁₆×C₆₇	D₄	semidirect
248. C₂×Q₈×C₆₇	C₂×D₄	semidirect
302. SD₁₆×C₆₇	C₂×D₄	semidirect
303. SD₁₆×C₆₇	C₂×D₄	semidirect
311. C₂×C₈×C₆₇	C₂×D₄	semidirect
452. C₄×C₆₇	#577	semidirect
455. #61085	C₆₇	direct (N × H)
464. C₂×#577	C₂×C₆₇	semidirect
465. #3497	C₂×C₆₇	semidirect
466. #3496	C₂×C₆₇	semidirect
467. #3284	C₂×C₆₇	semidirect
468. #3282	C₂×C₆₇	semidirect
469. D₄×SD₁₆	C₂×C₆₇	semidirect
470. #3276	C₂×C₆₇	semidirect
471. #3275	C₂×C₆₇	semidirect
472. #3274	C₂×C₆₇	semidirect
473. #3147	C₂×C₆₇	semidirect
474. #3060	C₂×C₆₇	semidirect
475. #3037	C₂×C₆₇	semidirect
476. #3036	C₂×C₆₇	semidirect
477. #3013	C₂×C₆₇	semidirect
478. #3012	C₂×C₆₇	semidirect
479. C₂×C₄×SD₁₆	C₂×C₆₇	semidirect
480. #2931	C₂×C₆₇	semidirect
481. C₆₇	#61085	direct (N × H)
482. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
485. C₂×#137	C₂²×C₆₇	semidirect
486. C₂×#137	C₂²×C₆₇	semidirect
488. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
489. C₂×#135	C₂²×C₆₇	semidirect
490. C₂×#135	C₂²×C₆₇	semidirect
491. C₂×#135	C₂²×C₆₇	semidirect
493. C₂²×SD₁₆	C₂²×C₆₇	semidirect
494. C₂×#131	C₂²×C₆₇	semidirect
496. #550	C₂²×C₆₇	semidirect
498. D₄×Q₈	C₂²×C₆₇	semidirect
500. #548	C₂²×C₆₇	semidirect
509. #537	C₂²×C₆₇	semidirect
514. #532	C₂²×C₆₇	semidirect
516. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
518. #495	C₂²×C₆₇	semidirect
519. #495	C₂²×C₆₇	semidirect
520. #494	C₂²×C₆₇	semidirect
521. #493	C₂²×C₆₇	semidirect
522. #492	C₂²×C₆₇	semidirect
523. #492	C₂²×C₆₇	semidirect
524. #470	C₂²×C₆₇	semidirect
525. #469	C₂²×C₆₇	semidirect
526. #465	C₂²×C₆₇	semidirect
527. #465	C₂²×C₆₇	semidirect
528. #464	C₂²×C₆₇	semidirect
529. #463	C₂²×C₆₇	semidirect
530. #462	C₂²×C₆₇	semidirect
531. #461	C₂²×C₆₇	semidirect
532. #460	C₂²×C₆₇	semidirect
533. #459	C₂²×C₆₇	semidirect
534. #452	C₂²×C₆₇	semidirect
535. #452	C₂²×C₆₇	semidirect
536. #451	C₂²×C₆₇	semidirect
537. #450	C₂²×C₆₇	semidirect
538. #449	C₂²×C₆₇	semidirect
539. #449	C₂²×C₆₇	semidirect
540. #448	C₂²×C₆₇	semidirect
541. #447	C₂²×C₆₇	semidirect
542. C₄×SD₁₆	C₂²×C₆₇	semidirect
543. C₄×SD₁₆	C₂²×C₆₇	semidirect
544. C₄×SD₁₆	C₂²×C₆₇	semidirect
545. C₄×SD₁₆	C₂²×C₆₇	semidirect
546. #436	C₂²×C₆₇	semidirect
547. #436	C₂²×C₆₇	semidirect
548. C₈×D₄	C₂²×C₆₇	semidirect
549. C₈×D₄	C₂²×C₆₇	semidirect
550. C₂×#106	C₂²×C₆₇	semidirect
551. #423	C₂²×C₆₇	semidirect
552. #417	C₂²×C₆₇	semidirect
553. #417	C₂²×C₆₇	semidirect
554. C₂×#103	C₂²×C₆₇	semidirect
556. #408	C₂²×C₆₇	semidirect
557. C₂×C₄×C₈	C₂²×C₆₇	semidirect
590. C₂×SD₁₆	D₄×C₆₇	semidirect
712. C₂×Q₈	C₂×D₄×C₆₇	semidirect
766. SD₁₆	C₂×D₄×C₆₇	semidirect
767. SD₁₆	C₂×D₄×C₆₇	semidirect
775. C₂×C₈	C₂×D₄×C₆₇	semidirect
916. C₄	#577×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#577×C₆₇	2
C₆₇×#3497	2
C₆₇×#3496	2
C₆₇×#3284	2
C₆₇×#3282	2
D₄×SD₁₆×C₆₇	2
C₆₇×#3276	2
C₆₇×#3275	2
C₆₇×#3274	2
C₆₇×#3147	2
C₆₇×#3060	2
C₆₇×#3037	2
C₆₇×#3036	2
C₆₇×#3013	2
C₆₇×#3012	2
C₂×C₄×SD₁₆×C₆₇	2
C₆₇×#2931	2
#61085	67

Subgroups — C67×#61085 #30740336

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61085 #30740336