Subgroups — C₆₇×#61056 #30740307

Order 17152.

2832 conjugacy classes of subgroups.

The subgroup lattice has 956 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	C₂²×#135×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3488	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3287	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3285	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3280	C₂	1	2	yes	maximal, complemented
7	D₄×D₈×C₆₇	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3268	C₂	1	4	yes	maximal, complemented
9	C₆₇×#3265	C₂	1	4	yes	maximal, complemented
10	C₆₇×#3155	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3061	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#466×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3045	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3012	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3006	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2951	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2929	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	2	yes	complemented
19	C₂²×#41×C₆₇	C₂²	1	2	yes	complemented
20	#576×C₆₇	—	2	8	no	—
21	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	complemented
22	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
23	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
24	C₂×#135×C₆₇	—	2	8	no	—
25	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
27	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
28	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic, complemented
29	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
30	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic, complemented
32	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
34	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	C₂²×D₈×C₆₇	C₂²	1	2	yes	complemented
36	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
37	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	#550×C₆₇	C₂²	1	4	yes	complemented
40	#548×C₆₇	C₂²	1	4	yes	complemented
41	#546×C₆₇	—	2	4	no	—
42	#546×C₆₇	C₂²	1	4	yes	complemented
43	D₄²×C₆₇	—	2	4	no	—
44	D₄²×C₆₇	C₂²	1	4	yes	complemented
45	#537×C₆₇	—	2	2	no	—
46	#537×C₆₇	C₂²	1	2	yes	complemented
47	#535×C₆₇	—	2	2	no	—
48	#535×C₆₇	C₂²	1	2	yes	complemented
49	#525×C₆₇	—	2	2	no	—
50	#525×C₆₇	C₂²	1	1	yes	characteristic
51	C₂×#121×C₆₇	—	2	2	no	—
52	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
53	#520×C₆₇	C₂²	1	2	yes	complemented
54	#496×C₆₇	C₂²	1	4	yes	complemented
55	#495×C₆₇	C₂²	1	2	yes	complemented
56	#493×C₆₇	C₂²	1	2	yes	complemented
57	#468×C₆₇	C₂²	1	4	yes	complemented
58	#467×C₆₇	C₂²	1	2	yes	complemented
59	#466×C₆₇	C₂²	1	2	yes	complemented
60	#466×C₆₇	C₂²	1	2	yes	complemented
61	#466×C₆₇	C₂²	1	2	yes	complemented
62	#466×C₆₇	C₂²	1	2	yes	complemented
63	#466×C₆₇	C₂²	1	2	yes	complemented
64	#464×C₆₇	C₂²	1	4	yes	complemented
65	#463×C₆₇	C₂²	1	4	yes	complemented
66	#460×C₆₇	C₂²	1	4	yes	complemented
67	#459×C₆₇	C₂²	1	4	yes	complemented
68	#452×C₆₇	C₂²	1	4	yes	complemented
69	#450×C₆₇	C₂²	1	4	yes	complemented
70	#449×C₆₇	C₂²	1	4	yes	complemented
71	#449×C₆₇	C₂²	1	4	yes	complemented
72	#449×C₆₇	C₂²	1	4	yes	complemented
73	#448×C₆₇	C₂²	1	4	yes	complemented
74	#447×C₆₇	C₂²	1	4	yes	complemented
75	#447×C₆₇	C₂²	1	4	yes	complemented
76	#440×C₆₇	C₂²	1	4	yes	complemented
77	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
78	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
79	#435×C₆₇	C₂²	1	2	yes	complemented
80	#435×C₆₇	C₂²	1	2	yes	complemented
81	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
82	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
83	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic, complemented
84	#424×C₆₇	C₂²	1	1	yes	characteristic, complemented
85	#417×C₆₇	C₂²	1	2	yes	complemented
86	#417×C₆₇	C₂²	1	2	yes	complemented
87	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
88	#408×C₆₇	C₂²	1	1	yes	characteristic, complemented
89	#407×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	#405×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	H(5,𝔽₂)×C₆₇	—	2	8	no	—
92	H(5,𝔽₂)×C₆₇	—	4	4	no	—
93	C₂×#41×C₆₇	—	2	2	no	—
94	C₂×#41×C₆₇	—	2	2	no	—
95	C₂×#41×C₆₇	—	2	2	no	—
96	C₂×#41×C₆₇	—	2	8	no	—
97	C₂×#41×C₆₇	—	4	4	no	—
98	C₂×#41×C₆₇	C₂³	1	2	yes	—
99	C₂×#41×C₆₇	C₂³	1	2	yes	—
100	C₂×#41×C₆₇	C₂³	1	2	yes	—
101	C₂×#41×C₆₇	C₂³	1	4	yes	—
102	C₂×#41×C₆₇	C₂³	1	2	yes	—
103	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
104	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
105	C₂²×D₄×C₆₇	—	2	2	no	—
106	C₂²×D₄×C₆₇	—	2	2	no	—
107	C₂²×D₄×C₆₇	—	2	2	no	—
108	C₂²×D₄×C₆₇	—	2	4	no	—
109	C₂²×D₄×C₆₇	—	2	4	no	—
110	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
111	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
112	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
113	C₂³×C₄×C₆₇	—	2	2	no	—
114	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
115	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
116	AGL(1,ℤ/8)×C₆₇	—	2	16	no	—
117	AGL(1,ℤ/8)×C₆₇	—	4	4	no	—
118	#135×C₆₇	—	2	8	no	—
119	#135×C₆₇	—	2	4	no	—
120	#135×C₆₇	—	2	8	no	—
121	#135×C₆₇	—	2	8	no	—
122	#135×C₆₇	—	2	4	no	—
123	#135×C₆₇	—	2	4	no	—
124	#135×C₆₇	D₄	1	8	yes	complemented
125	C₂×Q₁₆×C₆₇	—	2	4	no	—
126	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
127	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
128	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
129	C₂×SD₁₆×C₆₇	—	2	8	no	—
130	C₂×SD₁₆×C₆₇	C₂³	1	4	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	4	yes	—
135	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
136	C₂×D₈×C₆₇	—	2	4	no	—
137	C₂×D₈×C₆₇	—	2	8	no	—
138	C₂×D₈×C₆₇	—	2	4	no	—
139	C₂×D₈×C₆₇	C₂³	1	4	yes	—
140	C₂×D₈×C₆₇	C₂³	1	2	yes	—
141	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×D₈×C₆₇	C₂³	1	2	yes	—
143	C₂×D₈×C₆₇	C₂³	1	2	yes	—
144	C₂×D₈×C₆₇	C₂³	1	4	yes	—
145	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
146	#131×C₆₇	—	2	4	no	—
147	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
148	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₆₇	—	2	4	no	—
151	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
153	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
154	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
155	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
156	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
157	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
158	#127×C₆₇	—	2	4	no	—
159	#127×C₆₇	C₂³	1	4	yes	—
160	#124×C₆₇	—	2	4	no	—
161	#124×C₆₇	C₂³	1	4	yes	—
162	#123×C₆₇	—	2	4	no	—
163	#123×C₆₇	D₄	1	2	yes	—
164	C₂²⋊Q₈×C₆₇	—	2	2	no	—
165	C₂²⋊Q₈×C₆₇	—	2	4	no	—
166	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
167	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
168	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
169	#121×C₆₇	—	2	2	no	—
170	#121×C₆₇	—	2	4	no	—
171	#121×C₆₇	—	2	4	no	—
172	#121×C₆₇	—	2	2	no	—
173	#121×C₆₇	—	2	2	no	—
174	#121×C₆₇	—	2	2	no	—
175	#121×C₆₇	—	2	2	no	—
176	#121×C₆₇	—	2	4	no	—
177	#121×C₆₇	—	2	4	no	—
178	#121×C₆₇	—	2	4	no	—
179	#121×C₆₇	—	2	4	no	—
180	#121×C₆₇	D₄	1	1	yes	characteristic
181	#121×C₆₇	D₄	1	1	yes	characteristic
182	#121×C₆₇	C₂³	1	4	yes	—
183	#121×C₆₇	C₂³	1	4	yes	—
184	#121×C₆₇	C₂³	1	4	yes	—
185	#120×C₆₇	—	2	4	no	—
186	#120×C₆₇	—	2	4	no	—
187	#120×C₆₇	—	2	4	no	—
188	#120×C₆₇	—	2	4	no	—
189	#120×C₆₇	D₄	1	2	yes	—
190	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
191	C₄×D₄×C₆₇	—	2	4	no	—
192	C₄×D₄×C₆₇	—	2	4	no	—
193	C₄×D₄×C₆₇	—	2	4	no	—
194	C₄×D₄×C₆₇	C₂³	1	4	yes	—
195	C₄×D₄×C₆₇	C₂³	1	2	yes	—
196	C₄×D₄×C₆₇	C₂³	1	2	yes	—
197	#117×C₆₇	—	2	2	no	—
198	#117×C₆₇	C₂³	1	1	yes	characteristic
199	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
200	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
202	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
203	#107×C₆₇	C₂³	1	2	yes	—
204	#107×C₆₇	C₂³	1	2	yes	—
205	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
206	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
207	#103×C₆₇	C₂³	1	4	yes	—
208	#103×C₆₇	C₂³	1	4	yes	—
209	#102×C₆₇	C₂³	1	4	yes	—
210	#102×C₆₇	C₂³	1	4	yes	—
211	#102×C₆₇	C₂³	1	4	yes	—
212	#102×C₆₇	C₂³	1	4	yes	—
213	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
214	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
215	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
216	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
217	#97×C₆₇	C₂³	1	2	yes	—
218	C₄×C₈×C₆₇	C₂³	1	2	yes	—
219	C₂⁴×C₆₇	—	2	2	no	—
220	C₂⁴×C₆₇	—	2	4	no	—
221	C₂⁴×C₆₇	—	2	2	no	—
222	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
223	#41×C₆₇	—	2	2	no	—
224	#41×C₆₇	—	2	4	no	—
225	#41×C₆₇	—	2	2	no	—
226	#41×C₆₇	—	2	4	no	—
227	#41×C₆₇	—	2	8	no	—
228	#41×C₆₇	—	2	4	no	—
229	#41×C₆₇	—	2	4	no	—
230	#41×C₆₇	—	2	4	no	—
231	#41×C₆₇	—	4	8	no	—
232	#41×C₆₇	—	4	2	no	—
233	#41×C₆₇	—	4	2	no	—
234	#41×C₆₇	—	4	4	no	—
235	#41×C₆₇	—	4	8	no	—
236	#41×C₆₇	—	4	8	no	—
237	#41×C₆₇	C₂×D₄	1	8	yes	complemented
238	C₂×Q₈×C₆₇	—	2	2	no	—
239	C₂×Q₈×C₆₇	—	2	4	no	—
240	C₂×Q₈×C₆₇	—	4	2	no	—
241	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
242	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
243	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
244	C₂×D₄×C₆₇	—	2	2	no	—
245	C₂×D₄×C₆₇	—	2	4	no	—
246	C₂×D₄×C₆₇	—	2	8	no	—
247	C₂×D₄×C₆₇	—	2	4	no	—
248	C₂×D₄×C₆₇	—	2	2	no	—
249	C₂×D₄×C₆₇	—	2	2	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	2	no	—
256	C₂×D₄×C₆₇	—	2	4	no	—
257	C₂×D₄×C₆₇	—	2	2	no	—
258	C₂×D₄×C₆₇	—	2	4	no	—
259	C₂×D₄×C₆₇	—	2	4	no	—
260	C₂×D₄×C₆₇	—	2	4	no	—
261	C₂×D₄×C₆₇	—	4	2	no	—
262	C₂×D₄×C₆₇	—	4	4	no	—
263	C₂×D₄×C₆₇	—	4	8	no	—
264	C₂×D₄×C₆₇	—	4	16	no	—
265	C₂×D₄×C₆₇	—	4	8	no	—
266	C₂×D₄×C₆₇	—	8	8	no	—
267	C₂×D₄×C₆₇	—	8	4	no	—
268	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
269	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
270	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
271	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
272	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
273	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
274	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₆₇	—	2	2	no	—
276	C₂²×C₄×C₆₇	—	2	2	no	—
277	C₂²×C₄×C₆₇	—	2	2	no	—
278	C₂²×C₄×C₆₇	—	2	2	no	—
279	C₂²×C₄×C₆₇	—	2	2	no	—
280	C₂²×C₄×C₆₇	—	2	2	no	—
281	C₂²×C₄×C₆₇	—	2	2	no	—
282	C₂²×C₄×C₆₇	—	2	4	no	—
283	C₂²×C₄×C₆₇	—	2	2	no	—
284	C₂²×C₄×C₆₇	—	2	4	no	—
285	C₂²×C₄×C₆₇	—	4	8	no	—
286	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
289	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
293	Q₁₆×C₆₇	—	2	4	no	—
294	Q₁₆×C₆₇	—	2	2	no	—
295	Q₁₆×C₆₇	C₂×D₄	1	4	yes	complemented
296	SD₁₆×C₆₇	—	2	4	no	—
297	SD₁₆×C₆₇	—	2	8	no	—
298	SD₁₆×C₆₇	—	2	4	no	—
299	SD₁₆×C₆₇	—	2	4	no	—
300	SD₁₆×C₆₇	—	4	4	no	—
301	SD₁₆×C₆₇	C₂×D₄	1	8	yes	complemented
302	D₈×C₆₇	—	2	4	no	—
303	D₈×C₆₇	—	2	8	no	—
304	D₈×C₆₇	—	2	4	no	—
305	D₈×C₆₇	—	2	2	no	—
306	D₈×C₆₇	—	2	4	no	—
307	D₈×C₆₇	—	4	4	no	—
308	D₈×C₆₇	C₂×D₄	1	4	yes	complemented
309	M₁₆×C₆₇	—	2	2	no	—
310	M₁₆×C₆₇	—	2	2	no	—
311	M₁₆×C₆₇	—	2	4	no	—
312	C₂×C₈×C₆₇	—	2	2	no	—
313	C₂×C₈×C₆₇	—	2	2	no	—
314	C₂×C₈×C₆₇	—	2	2	no	—
315	C₂×C₈×C₆₇	—	2	2	no	—
316	C₂×C₈×C₆₇	—	2	2	no	—
317	C₂×C₈×C₆₇	—	2	4	no	—
318	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	complemented
319	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
320	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
321	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
322	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
323	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
324	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
325	C₄⋊C₄×C₆₇	—	2	2	no	—
326	C₄⋊C₄×C₆₇	—	2	4	no	—
327	C₄⋊C₄×C₆₇	—	2	4	no	—
328	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
329	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
330	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
331	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
332	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
333	C₂²⋊C₄×C₆₇	—	2	4	no	—
334	C₂²⋊C₄×C₆₇	—	2	4	no	—
335	C₂²⋊C₄×C₆₇	—	2	4	no	—
336	C₂²⋊C₄×C₆₇	—	2	4	no	—
337	C₂²⋊C₄×C₆₇	—	2	4	no	—
338	C₂²⋊C₄×C₆₇	—	2	4	no	—
339	C₂²⋊C₄×C₆₇	—	2	4	no	—
340	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
341	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
342	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
343	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
344	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
345	C₄²×C₆₇	—	2	4	no	—
346	C₄²×C₆₇	C₂⁴	1	2	yes	—
347	C₂³×C₆₇	—	2	2	no	—
348	C₂³×C₆₇	—	2	2	no	—
349	C₂³×C₆₇	—	2	2	no	—
350	C₂³×C₆₇	—	2	4	no	—
351	C₂³×C₆₇	—	2	2	no	—
352	C₂³×C₆₇	—	4	1	no	—
353	C₂³×C₆₇	—	4	4	no	—
354	C₂³×C₆₇	—	4	8	no	—
355	C₂³×C₆₇	—	4	4	no	—
356	C₂³×C₆₇	—	4	4	no	—
357	C₂³×C₆₇	—	8	2	no	—
358	C₂³×C₆₇	—	8	2	no	—
359	C₂³×C₆₇	—	8	4	no	—
360	C₂³×C₆₇	—	8	2	no	—
361	C₂³×C₆₇	—	8	4	no	—
362	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
363	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
364	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
365	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
366	Q₈×C₆₇	—	2	2	no	—
367	Q₈×C₆₇	—	2	2	no	—
368	Q₈×C₆₇	—	2	2	no	—
369	Q₈×C₆₇	—	2	2	no	—
370	Q₈×C₆₇	—	4	4	no	—
371	Q₈×C₆₇	C₂²×D₄	1	4	yes	—
372	D₄×C₆₇	—	2	8	no	—
373	D₄×C₆₇	—	2	4	no	—
374	D₄×C₆₇	—	2	4	no	—
375	D₄×C₆₇	—	2	2	no	—
376	D₄×C₆₇	—	2	4	no	—
377	D₄×C₆₇	—	2	2	no	—
378	D₄×C₆₇	—	2	2	no	—
379	D₄×C₆₇	—	2	2	no	—
380	D₄×C₆₇	—	2	4	no	—
381	D₄×C₆₇	—	4	2	no	—
382	D₄×C₆₇	—	4	8	no	—
383	D₄×C₆₇	—	4	4	no	—
384	D₄×C₆₇	—	4	8	no	—
385	D₄×C₆₇	—	4	4	no	—
386	D₄×C₆₇	—	4	4	no	—
387	D₄×C₆₇	—	4	4	no	—
388	D₄×C₆₇	—	4	8	no	—
389	D₄×C₆₇	—	4	4	no	—
390	D₄×C₆₇	—	8	4	no	—
391	D₄×C₆₇	—	8	4	no	—
392	D₄×C₆₇	—	8	4	no	—
393	D₄×C₆₇	—	8	4	no	—
394	D₄×C₆₇	C₂²×D₄	1	4	yes	—
395	C₂×C₄×C₆₇	—	2	2	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	8	no	—
400	C₂×C₄×C₆₇	—	2	1	no	—
401	C₂×C₄×C₆₇	—	2	1	no	—
402	C₂×C₄×C₆₇	—	2	2	no	—
403	C₂×C₄×C₆₇	—	2	1	no	—
404	C₂×C₄×C₆₇	—	2	1	no	—
405	C₂×C₄×C₆₇	—	2	2	no	—
406	C₂×C₄×C₆₇	—	2	4	no	—
407	C₂×C₄×C₆₇	—	2	2	no	—
408	C₂×C₄×C₆₇	—	4	4	no	—
409	C₂×C₄×C₆₇	—	4	8	no	—
410	C₂×C₄×C₆₇	—	4	4	no	—
411	C₂×C₄×C₆₇	—	4	4	no	—
412	C₂×C₄×C₆₇	—	4	4	no	—
413	C₂×C₄×C₆₇	—	8	4	no	—
414	C₂×C₄×C₆₇	—	8	2	no	—
415	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
416	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
417	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
419	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
420	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
421	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
422	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
423	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
424	C₈×C₆₇	—	2	1	no	—
425	C₈×C₆₇	—	2	1	no	—
426	C₈×C₆₇	—	2	2	no	—
427	C₈×C₆₇	—	2	2	no	—
428	C₈×C₆₇	C₂²×D₄	1	2	yes	—
429	C₈×C₆₇	C₂²×D₄	1	2	yes	—
430	C₂²×C₆₇	—	2	1	no	—
431	C₂²×C₆₇	—	2	1	no	—
432	C₂²×C₆₇	—	2	1	no	—
433	C₂²×C₆₇	—	2	1	no	—
434	C₂²×C₆₇	—	2	1	no	—
435	C₂²×C₆₇	—	2	2	no	—
436	C₂²×C₆₇	—	2	1	no	—
437	C₂²×C₆₇	—	2	4	no	—
438	C₂²×C₆₇	—	2	2	no	—
439	C₂²×C₆₇	—	2	2	no	—
440	C₂²×C₆₇	—	2	1	no	—
441	C₂²×C₆₇	—	4	4	no	—
442	C₂²×C₆₇	—	4	2	no	—
443	C₂²×C₆₇	—	4	2	no	—
444	C₂²×C₆₇	—	4	2	no	—
445	C₂²×C₆₇	—	4	4	no	—
446	C₂²×C₆₇	—	4	2	no	—
447	C₂²×C₆₇	—	4	4	no	—
448	C₂²×C₆₇	—	4	4	no	—
449	C₂²×C₆₇	—	4	2	no	—
450	C₂²×C₆₇	—	8	8	no	—
451	C₂²×C₆₇	—	16	4	no	—
452	C₂²×C₆₇	—	16	8	no	—
453	C₂²×C₆₇	D₄²	1	2	yes	—
454	C₂²×C₆₇	#576	1	2	yes	complemented
455	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
456	C₄×C₆₇	—	2	2	no	—
457	C₄×C₆₇	—	2	1	no	—
458	C₄×C₆₇	—	2	1	no	—
459	C₄×C₆₇	—	2	4	no	—
460	C₄×C₆₇	—	2	2	no	—
461	C₄×C₆₇	—	2	2	no	—
462	C₄×C₆₇	—	4	2	no	—
463	C₄×C₆₇	—	4	4	no	—
464	C₄×C₆₇	D₄²	1	2	yes	—
465	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
466	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
467	#61056	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
468	C₂×C₆₇	—	2	2	no	—
469	C₂×C₆₇	—	2	2	no	—
470	C₂×C₆₇	—	4	1	no	—
471	C₂×C₆₇	—	4	2	no	—
472	C₂×C₆₇	—	4	4	no	—
473	C₂×C₆₇	—	8	2	no	—
474	C₂×C₆₇	—	8	4	no	—
475	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
476	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
477	C₂×C₆₇	#3584	1	1	yes	characteristic
478	C₂×#576	C₂×C₆₇	1	1	yes	characteristic, complemented
479	C₂²×#135	C₂×C₆₇	1	1	yes	characteristic, complemented
480	#3488	C₂×C₆₇	1	2	yes	complemented
481	#3287	C₂×C₆₇	1	2	yes	complemented
482	#3285	C₂×C₆₇	1	2	yes	complemented
483	#3280	C₂×C₆₇	1	2	yes	complemented
484	D₄×D₈	C₂×C₆₇	1	2	yes	complemented
485	#3268	C₂×C₆₇	1	4	yes	complemented
486	#3265	C₂×C₆₇	1	4	yes	complemented
487	#3155	C₂×C₆₇	1	1	yes	characteristic, complemented
488	#3061	C₂×C₆₇	1	1	yes	characteristic, complemented
489	C₂×#466	C₂×C₆₇	1	1	yes	characteristic, complemented
490	#3045	C₂×C₆₇	1	2	yes	complemented
491	#3012	C₂×C₆₇	1	2	yes	complemented
492	#3006	C₂×C₆₇	1	2	yes	complemented
493	#2951	C₂×C₆₇	1	1	yes	characteristic, complemented
494	#2929	C₂×C₆₇	1	1	yes	characteristic, complemented
495	C₆₇	#61056	1	1	yes	characteristic, direct product factor, Sylow
496	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	complemented
497	C₂²×#41	C₂²×C₆₇	1	2	yes	complemented
498	#576	—	2	8	no	—
499	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
500	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
501	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
502	C₂×#135	—	2	8	no	—
503	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
504	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic, complemented
505	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
506	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
507	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic, complemented
508	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
509	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic, complemented
510	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
511	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
512	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
513	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
514	C₂²×D₈	C₂²×C₆₇	1	2	yes	complemented
515	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
516	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
517	#550	C₂²×C₆₇	1	4	yes	complemented
518	#548	C₂²×C₆₇	1	4	yes	complemented
519	#546	—	2	4	no	—
520	#546	C₂²×C₆₇	1	4	yes	complemented
521	D₄²	—	2	4	no	—
522	D₄²	C₂²×C₆₇	1	4	yes	complemented
523	#537	—	2	2	no	—
524	#537	C₂²×C₆₇	1	2	yes	complemented
525	#535	—	2	2	no	—
526	#535	C₂²×C₆₇	1	2	yes	complemented
527	#525	—	2	2	no	—
528	#525	C₂²×C₆₇	1	1	yes	characteristic
529	C₂×#121	—	2	2	no	—
530	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
531	#520	C₂²×C₆₇	1	2	yes	complemented
532	#496	C₂²×C₆₇	1	4	yes	complemented
533	#495	C₂²×C₆₇	1	2	yes	complemented
534	#493	C₂²×C₆₇	1	2	yes	complemented
535	#468	C₂²×C₆₇	1	4	yes	complemented
536	#467	C₂²×C₆₇	1	2	yes	complemented
537	#466	C₂²×C₆₇	1	2	yes	complemented
538	#466	C₂²×C₆₇	1	2	yes	complemented
539	#466	C₂²×C₆₇	1	2	yes	complemented
540	#466	C₂²×C₆₇	1	2	yes	complemented
541	#466	C₂²×C₆₇	1	2	yes	complemented
542	#464	C₂²×C₆₇	1	4	yes	complemented
543	#463	C₂²×C₆₇	1	4	yes	complemented
544	#460	C₂²×C₆₇	1	4	yes	complemented
545	#459	C₂²×C₆₇	1	4	yes	complemented
546	#452	C₂²×C₆₇	1	4	yes	complemented
547	#450	C₂²×C₆₇	1	4	yes	complemented
548	#449	C₂²×C₆₇	1	4	yes	complemented
549	#449	C₂²×C₆₇	1	4	yes	complemented
550	#449	C₂²×C₆₇	1	4	yes	complemented
551	#448	C₂²×C₆₇	1	4	yes	complemented
552	#447	C₂²×C₆₇	1	4	yes	complemented
553	#447	C₂²×C₆₇	1	4	yes	complemented
554	#440	C₂²×C₆₇	1	4	yes	complemented
555	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
556	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
557	#435	C₂²×C₆₇	1	2	yes	complemented
558	#435	C₂²×C₆₇	1	2	yes	complemented
559	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
560	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
561	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic, complemented
562	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
563	#417	C₂²×C₆₇	1	2	yes	complemented
564	#417	C₂²×C₆₇	1	2	yes	complemented
565	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
566	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
567	#407	C₂²×C₆₇	1	1	yes	characteristic, complemented
568	#405	C₂²×C₆₇	1	1	yes	characteristic, complemented
569	H(5,𝔽₂)	—	2	8	no	—
570	H(5,𝔽₂)	—	4	4	no	—
571	C₂×#41	—	2	2	no	—
572	C₂×#41	—	2	2	no	—
573	C₂×#41	—	2	2	no	—
574	C₂×#41	—	2	8	no	—
575	C₂×#41	—	4	4	no	—
576	C₂×#41	C₂³×C₆₇	1	2	yes	—
577	C₂×#41	C₂³×C₆₇	1	2	yes	—
578	C₂×#41	C₂³×C₆₇	1	4	yes	—
579	C₂×#41	C₂³×C₆₇	1	2	yes	—
580	C₂×#41	C₂³×C₆₇	1	2	yes	—
581	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
582	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
583	C₂²×D₄	—	2	2	no	—
584	C₂²×D₄	—	2	2	no	—
585	C₂²×D₄	—	2	2	no	—
586	C₂²×D₄	—	2	4	no	—
587	C₂²×D₄	—	2	4	no	—
588	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
589	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
590	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
591	C₂³×C₄	—	2	2	no	—
592	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
593	AGL(1,ℤ/8)	—	2	8	no	—
594	AGL(1,ℤ/8)	—	2	16	no	—
595	AGL(1,ℤ/8)	—	4	4	no	—
596	#135	—	2	8	no	—
597	#135	—	2	4	no	—
598	#135	—	2	8	no	—
599	#135	—	2	8	no	—
600	#135	—	2	4	no	—
601	#135	—	2	4	no	—
602	#135	D₄×C₆₇	1	8	yes	complemented
603	C₂×Q₁₆	—	2	4	no	—
604	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
605	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
606	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
607	C₂×SD₁₆	—	2	8	no	—
608	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
609	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
610	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
611	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
612	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
613	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
614	C₂×D₈	—	2	4	no	—
615	C₂×D₈	—	2	8	no	—
616	C₂×D₈	—	2	4	no	—
617	C₂×D₈	C₂³×C₆₇	1	2	yes	—
618	C₂×D₈	C₂³×C₆₇	1	2	yes	—
619	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
620	C₂×D₈	C₂³×C₆₇	1	4	yes	—
621	C₂×D₈	C₂³×C₆₇	1	2	yes	—
622	C₂×D₈	C₂³×C₆₇	1	4	yes	—
623	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
624	#131	—	2	4	no	—
625	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
626	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
627	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
628	C₂²×C₈	—	2	4	no	—
629	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
630	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
631	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
632	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
633	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
634	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
635	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
636	#127	—	2	4	no	—
637	#127	C₂³×C₆₇	1	4	yes	—
638	#124	—	2	4	no	—
639	#124	C₂³×C₆₇	1	4	yes	—
640	#123	—	2	4	no	—
641	#123	D₄×C₆₇	1	2	yes	—
642	C₂²⋊Q₈	—	2	2	no	—
643	C₂²⋊Q₈	—	2	4	no	—
644	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
645	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
646	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
647	#121	—	2	2	no	—
648	#121	—	2	4	no	—
649	#121	—	2	4	no	—
650	#121	—	2	2	no	—
651	#121	—	2	2	no	—
652	#121	—	2	2	no	—
653	#121	—	2	2	no	—
654	#121	—	2	4	no	—
655	#121	—	2	4	no	—
656	#121	—	2	4	no	—
657	#121	—	2	4	no	—
658	#121	D₄×C₆₇	1	1	yes	characteristic
659	#121	D₄×C₆₇	1	1	yes	characteristic
660	#121	C₂³×C₆₇	1	4	yes	—
661	#121	C₂³×C₆₇	1	4	yes	—
662	#121	C₂³×C₆₇	1	4	yes	—
663	#120	—	2	4	no	—
664	#120	—	2	4	no	—
665	#120	—	2	4	no	—
666	#120	—	2	4	no	—
667	#120	D₄×C₆₇	1	2	yes	—
668	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
669	C₄×D₄	—	2	4	no	—
670	C₄×D₄	—	2	4	no	—
671	C₄×D₄	—	2	4	no	—
672	C₄×D₄	C₂³×C₆₇	1	4	yes	—
673	C₄×D₄	C₂³×C₆₇	1	2	yes	—
674	C₄×D₄	C₂³×C₆₇	1	2	yes	—
675	#117	—	2	2	no	—
676	#117	C₂³×C₆₇	1	1	yes	characteristic
677	C₂×C₄⋊C₄	—	2	2	no	—
678	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
679	C₂×C₂²⋊C₄	—	2	2	no	—
680	C₂×C₂²⋊C₄	—	2	4	no	—
681	#107	C₂³×C₆₇	1	2	yes	—
682	#107	C₂³×C₆₇	1	2	yes	—
683	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
684	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
685	#103	C₂³×C₆₇	1	4	yes	—
686	#103	C₂³×C₆₇	1	4	yes	—
687	#102	C₂³×C₆₇	1	4	yes	—
688	#102	C₂³×C₆₇	1	4	yes	—
689	#102	C₂³×C₆₇	1	4	yes	—
690	#102	C₂³×C₆₇	1	4	yes	—
691	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
692	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
693	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
694	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
695	#97	C₂³×C₆₇	1	2	yes	—
696	C₄×C₈	C₂³×C₆₇	1	2	yes	—
697	C₂⁴	—	2	2	no	—
698	C₂⁴	—	2	4	no	—
699	C₂⁴	—	2	2	no	—
700	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
701	#41	—	2	2	no	—
702	#41	—	2	4	no	—
703	#41	—	2	2	no	—
704	#41	—	2	4	no	—
705	#41	—	2	8	no	—
706	#41	—	2	4	no	—
707	#41	—	2	4	no	—
708	#41	—	2	4	no	—
709	#41	—	4	8	no	—
710	#41	—	4	2	no	—
711	#41	—	4	2	no	—
712	#41	—	4	4	no	—
713	#41	—	4	8	no	—
714	#41	—	4	8	no	—
715	#41	C₂×D₄×C₆₇	1	8	yes	complemented
716	C₂×Q₈	—	2	2	no	—
717	C₂×Q₈	—	2	4	no	—
718	C₂×Q₈	—	4	2	no	—
719	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
720	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
721	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	2	4	no	—
724	C₂×D₄	—	2	8	no	—
725	C₂×D₄	—	2	4	no	—
726	C₂×D₄	—	2	2	no	—
727	C₂×D₄	—	2	2	no	—
728	C₂×D₄	—	2	4	no	—
729	C₂×D₄	—	2	2	no	—
730	C₂×D₄	—	2	4	no	—
731	C₂×D₄	—	2	4	no	—
732	C₂×D₄	—	2	4	no	—
733	C₂×D₄	—	2	2	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	—	4	2	no	—
740	C₂×D₄	—	4	4	no	—
741	C₂×D₄	—	4	8	no	—
742	C₂×D₄	—	4	16	no	—
743	C₂×D₄	—	4	8	no	—
744	C₂×D₄	—	8	8	no	—
745	C₂×D₄	—	8	4	no	—
746	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
747	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
748	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
749	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
750	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
751	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
752	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	—	2	2	no	—
760	C₂²×C₄	—	2	4	no	—
761	C₂²×C₄	—	2	2	no	—
762	C₂²×C₄	—	2	4	no	—
763	C₂²×C₄	—	4	8	no	—
764	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
765	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
766	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
769	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
770	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
771	Q₁₆	—	2	4	no	—
772	Q₁₆	—	2	2	no	—
773	Q₁₆	C₂×D₄×C₆₇	1	4	yes	complemented
774	SD₁₆	—	2	4	no	—
775	SD₁₆	—	2	8	no	—
776	SD₁₆	—	2	4	no	—
777	SD₁₆	—	2	4	no	—
778	SD₁₆	—	4	4	no	—
779	SD₁₆	C₂×D₄×C₆₇	1	8	yes	complemented
780	D₈	—	2	4	no	—
781	D₈	—	2	8	no	—
782	D₈	—	2	4	no	—
783	D₈	—	2	2	no	—
784	D₈	—	2	4	no	—
785	D₈	—	4	4	no	—
786	D₈	C₂×D₄×C₆₇	1	4	yes	complemented
787	M₁₆	—	2	2	no	—
788	M₁₆	—	2	2	no	—
789	M₁₆	—	2	4	no	—
790	C₂×C₈	—	2	2	no	—
791	C₂×C₈	—	2	2	no	—
792	C₂×C₈	—	2	2	no	—
793	C₂×C₈	—	2	2	no	—
794	C₂×C₈	—	2	2	no	—
795	C₂×C₈	—	2	4	no	—
796	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	complemented
797	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
798	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
799	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
800	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
801	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
802	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	4	no	—
805	C₄⋊C₄	—	2	4	no	—
806	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
807	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
808	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
809	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
810	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
811	C₂²⋊C₄	—	2	4	no	—
812	C₂²⋊C₄	—	2	4	no	—
813	C₂²⋊C₄	—	2	4	no	—
814	C₂²⋊C₄	—	2	4	no	—
815	C₂²⋊C₄	—	2	4	no	—
816	C₂²⋊C₄	—	2	4	no	—
817	C₂²⋊C₄	—	2	4	no	—
818	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
819	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
820	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
821	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
822	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
823	C₄²	—	2	4	no	—
824	C₄²	C₂⁴×C₆₇	1	2	yes	—
825	C₂³	—	2	2	no	—
826	C₂³	—	2	2	no	—
827	C₂³	—	2	2	no	—
828	C₂³	—	2	4	no	—
829	C₂³	—	2	2	no	—
830	C₂³	—	4	1	no	—
831	C₂³	—	4	4	no	—
832	C₂³	—	4	8	no	—
833	C₂³	—	4	4	no	—
834	C₂³	—	4	4	no	—
835	C₂³	—	8	2	no	—
836	C₂³	—	8	2	no	—
837	C₂³	—	8	4	no	—
838	C₂³	—	8	2	no	—
839	C₂³	—	8	4	no	—
840	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
841	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
842	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
843	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
844	Q₈	—	2	2	no	—
845	Q₈	—	2	2	no	—
846	Q₈	—	2	2	no	—
847	Q₈	—	2	2	no	—
848	Q₈	—	4	4	no	—
849	Q₈	C₂²×D₄×C₆₇	1	4	yes	—
850	D₄	—	2	8	no	—
851	D₄	—	2	4	no	—
852	D₄	—	2	4	no	—
853	D₄	—	2	2	no	—
854	D₄	—	2	4	no	—
855	D₄	—	2	2	no	—
856	D₄	—	2	2	no	—
857	D₄	—	2	2	no	—
858	D₄	—	2	4	no	—
859	D₄	—	4	2	no	—
860	D₄	—	4	8	no	—
861	D₄	—	4	4	no	—
862	D₄	—	4	8	no	—
863	D₄	—	4	4	no	—
864	D₄	—	4	4	no	—
865	D₄	—	4	4	no	—
866	D₄	—	4	8	no	—
867	D₄	—	4	4	no	—
868	D₄	—	8	4	no	—
869	D₄	—	8	4	no	—
870	D₄	—	8	4	no	—
871	D₄	—	8	4	no	—
872	D₄	C₂²×D₄×C₆₇	1	4	yes	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	8	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	4	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	4	4	no	—
887	C₂×C₄	—	4	8	no	—
888	C₂×C₄	—	4	4	no	—
889	C₂×C₄	—	4	4	no	—
890	C₂×C₄	—	4	4	no	—
891	C₂×C₄	—	8	4	no	—
892	C₂×C₄	—	8	2	no	—
893	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
894	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
895	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
896	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
897	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
898	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
899	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
900	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
901	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
902	C₈	—	2	1	no	—
903	C₈	—	2	1	no	—
904	C₈	—	2	2	no	—
905	C₈	—	2	2	no	—
906	C₈	C₂²×D₄×C₆₇	1	2	yes	—
907	C₈	C₂²×D₄×C₆₇	1	2	yes	—
908	C₂²	—	2	1	no	—
909	C₂²	—	2	1	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	2	no	—
913	C₂²	—	2	1	no	—
914	C₂²	—	2	1	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	1	no	—
917	C₂²	—	2	4	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	4	4	no	—
920	C₂²	—	4	2	no	—
921	C₂²	—	4	2	no	—
922	C₂²	—	4	4	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	4	4	no	—
926	C₂²	—	4	2	no	—
927	C₂²	—	4	4	no	—
928	C₂²	—	8	8	no	—
929	C₂²	—	16	4	no	—
930	C₂²	—	16	8	no	—
931	C₂²	D₄²×C₆₇	1	2	yes	—
932	C₂²	#576×C₆₇	1	2	yes	complemented
933	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
934	C₄	—	2	2	no	—
935	C₄	—	2	2	no	—
936	C₄	—	2	1	no	—
937	C₄	—	2	1	no	—
938	C₄	—	2	4	no	—
939	C₄	—	2	2	no	—
940	C₄	—	4	4	no	—
941	C₄	—	4	2	no	—
942	C₄	D₄²×C₆₇	1	2	yes	—
943	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
944	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
945	C₂	—	2	2	no	—
946	C₂	—	2	2	no	—
947	C₂	—	4	1	no	—
948	C₂	—	4	2	no	—
949	C₂	—	4	4	no	—
950	C₂	—	8	2	no	—
951	C₂	—	8	4	no	—
952	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
953	C₂	C₂×#576×C₆₇	1	1	yes	characteristic
954	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 ◁ #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. C₂²×#135×C₆₇	C₂	semidirect
3. C₆₇×#3488	C₂	semidirect
4. C₆₇×#3287	C₂	semidirect
5. C₆₇×#3285	C₂	semidirect
6. C₆₇×#3280	C₂	semidirect
7. D₄×D₈×C₆₇	C₂	semidirect
8. C₆₇×#3268	C₂	semidirect
9. C₆₇×#3265	C₂	semidirect
10. C₆₇×#3155	C₂	semidirect
11. C₆₇×#3061	C₂	semidirect
12. C₂×#466×C₆₇	C₂	semidirect
13. C₆₇×#3045	C₂	semidirect
14. C₆₇×#3012	C₂	semidirect
15. C₆₇×#3006	C₂	semidirect
16. C₆₇×#2951	C₂	semidirect
17. C₆₇×#2929	C₂	semidirect
18. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
19. C₂²×#41×C₆₇	C₂²	semidirect
21. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
22. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
23. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
26. C₂×#135×C₆₇	C₂²	semidirect
27. C₂×#135×C₆₇	C₂²	semidirect
28. C₂×#135×C₆₇	C₂²	semidirect
29. C₂×#135×C₆₇	C₂²	semidirect
30. C₂×#135×C₆₇	C₂²	semidirect
31. C₂×#135×C₆₇	C₂²	semidirect
32. C₂²×Q₁₆×C₆₇	C₂²	semidirect
33. C₂²×SD₁₆×C₆₇	C₂²	semidirect
34. C₂²×D₈×C₆₇	C₂²	semidirect
35. C₂²×D₈×C₆₇	C₂²	semidirect
36. C₂²×D₈×C₆₇	C₂²	semidirect
37. C₂×#131×C₆₇	C₂²	semidirect
38. C₂³×C₈×C₆₇	C₂²	semidirect
39. #550×C₆₇	C₂²	semidirect
40. #548×C₆₇	C₂²	semidirect
42. #546×C₆₇	C₂²	semidirect
44. D₄²×C₆₇	C₂²	semidirect
46. #537×C₆₇	C₂²	semidirect
48. #535×C₆₇	C₂²	semidirect
52. C₂×#121×C₆₇	C₂²	semidirect
53. #520×C₆₇	C₂²	semidirect
54. #496×C₆₇	C₂²	semidirect
55. #495×C₆₇	C₂²	semidirect
56. #493×C₆₇	C₂²	semidirect
57. #468×C₆₇	C₂²	semidirect
58. #467×C₆₇	C₂²	semidirect
59. #466×C₆₇	C₂²	semidirect
60. #466×C₆₇	C₂²	semidirect
61. #466×C₆₇	C₂²	semidirect
62. #466×C₆₇	C₂²	semidirect
63. #466×C₆₇	C₂²	semidirect
64. #464×C₆₇	C₂²	semidirect
65. #463×C₆₇	C₂²	semidirect
66. #460×C₆₇	C₂²	semidirect
67. #459×C₆₇	C₂²	semidirect
68. #452×C₆₇	C₂²	semidirect
69. #450×C₆₇	C₂²	semidirect
70. #449×C₆₇	C₂²	semidirect
71. #449×C₆₇	C₂²	semidirect
72. #449×C₆₇	C₂²	semidirect
73. #448×C₆₇	C₂²	semidirect
74. #447×C₆₇	C₂²	semidirect
75. #447×C₆₇	C₂²	semidirect
76. #440×C₆₇	C₂²	semidirect
77. C₄×Q₁₆×C₆₇	C₂²	semidirect
78. C₄×D₈×C₆₇	C₂²	semidirect
79. #435×C₆₇	C₂²	semidirect
80. #435×C₆₇	C₂²	semidirect
81. C₈×D₄×C₆₇	C₂²	semidirect
82. C₈×D₄×C₆₇	C₂²	semidirect
83. C₂×#107×C₆₇	C₂²	semidirect
84. #424×C₆₇	C₂²	semidirect
85. #417×C₆₇	C₂²	semidirect
86. #417×C₆₇	C₂²	semidirect
87. C₂×#102×C₆₇	C₂²	semidirect
88. #408×C₆₇	C₂²	semidirect
89. #407×C₆₇	C₂²	semidirect
90. #405×C₆₇	C₂²	semidirect
124. #135×C₆₇	D₄	semidirect
237. #41×C₆₇	C₂×D₄	semidirect
295. Q₁₆×C₆₇	C₂×D₄	semidirect
301. SD₁₆×C₆₇	C₂×D₄	semidirect
308. D₈×C₆₇	C₂×D₄	semidirect
318. C₂×C₈×C₆₇	C₂×D₄	semidirect
454. C₂²×C₆₇	#576	semidirect
467. #61056	C₆₇	direct (N × H)
478. C₂×#576	C₂×C₆₇	semidirect
479. C₂²×#135	C₂×C₆₇	semidirect
480. #3488	C₂×C₆₇	semidirect
481. #3287	C₂×C₆₇	semidirect
482. #3285	C₂×C₆₇	semidirect
483. #3280	C₂×C₆₇	semidirect
484. D₄×D₈	C₂×C₆₇	semidirect
485. #3268	C₂×C₆₇	semidirect
486. #3265	C₂×C₆₇	semidirect
487. #3155	C₂×C₆₇	semidirect
488. #3061	C₂×C₆₇	semidirect
489. C₂×#466	C₂×C₆₇	semidirect
490. #3045	C₂×C₆₇	semidirect
491. #3012	C₂×C₆₇	semidirect
492. #3006	C₂×C₆₇	semidirect
493. #2951	C₂×C₆₇	semidirect
494. #2929	C₂×C₆₇	semidirect
495. C₆₇	#61056	direct (N × H)
496. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
497. C₂²×#41	C₂²×C₆₇	semidirect
499. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
500. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
501. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
504. C₂×#135	C₂²×C₆₇	semidirect
505. C₂×#135	C₂²×C₆₇	semidirect
506. C₂×#135	C₂²×C₆₇	semidirect
507. C₂×#135	C₂²×C₆₇	semidirect
508. C₂×#135	C₂²×C₆₇	semidirect
509. C₂×#135	C₂²×C₆₇	semidirect
510. C₂²×Q₁₆	C₂²×C₆₇	semidirect
511. C₂²×SD₁₆	C₂²×C₆₇	semidirect
512. C₂²×D₈	C₂²×C₆₇	semidirect
513. C₂²×D₈	C₂²×C₆₇	semidirect
514. C₂²×D₈	C₂²×C₆₇	semidirect
515. C₂×#131	C₂²×C₆₇	semidirect
516. C₂³×C₈	C₂²×C₆₇	semidirect
517. #550	C₂²×C₆₇	semidirect
518. #548	C₂²×C₆₇	semidirect
520. #546	C₂²×C₆₇	semidirect
522. D₄²	C₂²×C₆₇	semidirect
524. #537	C₂²×C₆₇	semidirect
526. #535	C₂²×C₆₇	semidirect
530. C₂×#121	C₂²×C₆₇	semidirect
531. #520	C₂²×C₆₇	semidirect
532. #496	C₂²×C₆₇	semidirect
533. #495	C₂²×C₆₇	semidirect
534. #493	C₂²×C₆₇	semidirect
535. #468	C₂²×C₆₇	semidirect
536. #467	C₂²×C₆₇	semidirect
537. #466	C₂²×C₆₇	semidirect
538. #466	C₂²×C₆₇	semidirect
539. #466	C₂²×C₆₇	semidirect
540. #466	C₂²×C₆₇	semidirect
541. #466	C₂²×C₆₇	semidirect
542. #464	C₂²×C₆₇	semidirect
543. #463	C₂²×C₆₇	semidirect
544. #460	C₂²×C₆₇	semidirect
545. #459	C₂²×C₆₇	semidirect
546. #452	C₂²×C₆₇	semidirect
547. #450	C₂²×C₆₇	semidirect
548. #449	C₂²×C₆₇	semidirect
549. #449	C₂²×C₆₇	semidirect
550. #449	C₂²×C₆₇	semidirect
551. #448	C₂²×C₆₇	semidirect
552. #447	C₂²×C₆₇	semidirect
553. #447	C₂²×C₆₇	semidirect
554. #440	C₂²×C₆₇	semidirect
555. C₄×Q₁₆	C₂²×C₆₇	semidirect
556. C₄×D₈	C₂²×C₆₇	semidirect
557. #435	C₂²×C₆₇	semidirect
558. #435	C₂²×C₆₇	semidirect
559. C₈×D₄	C₂²×C₆₇	semidirect
560. C₈×D₄	C₂²×C₆₇	semidirect
561. C₂×#107	C₂²×C₆₇	semidirect
562. #424	C₂²×C₆₇	semidirect
563. #417	C₂²×C₆₇	semidirect
564. #417	C₂²×C₆₇	semidirect
565. C₂×#102	C₂²×C₆₇	semidirect
566. #408	C₂²×C₆₇	semidirect
567. #407	C₂²×C₆₇	semidirect
568. #405	C₂²×C₆₇	semidirect
602. #135	D₄×C₆₇	semidirect
715. #41	C₂×D₄×C₆₇	semidirect
773. Q₁₆	C₂×D₄×C₆₇	semidirect
779. SD₁₆	C₂×D₄×C₆₇	semidirect
786. D₈	C₂×D₄×C₆₇	semidirect
796. C₂×C₈	C₂×D₄×C₆₇	semidirect
932. C₂²	#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
C₂²×#135×C₆₇	2
C₆₇×#3488	2
C₆₇×#3287	2
C₆₇×#3285	2
C₆₇×#3280	2
D₄×D₈×C₆₇	2
C₆₇×#3268	2
C₆₇×#3265	2
C₆₇×#3155	2
C₆₇×#3061	2
C₂×#466×C₆₇	2
C₆₇×#3045	2
C₆₇×#3012	2
C₆₇×#3006	2
C₆₇×#2951	2
C₆₇×#2929	2
#61056	67

Subgroups — C67×#61056 #30740307

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61056 #30740307