Subgroups — C₆₇×#61605 #30740856

Order 17152.

2232 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3519	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#550×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3333	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3309	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3305	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3287	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3274	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3268	C₂	1	4	yes	maximal, complemented
9	C₆₇×#3217	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3205	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3194	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3186	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3112	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3108	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3006	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3002	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2974	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₆₇	C₂²	1	2	yes	complemented
19	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	complemented
20	C₂×#135×C₆₇	C₂²	1	4	yes	complemented
21	#555×C₆₇	C₂²	1	1	yes	characteristic, complemented
22	#554×C₆₇	C₂²	1	1	yes	characteristic, complemented
23	#553×C₆₇	—	2	1	no	—
24	#553×C₆₇	C₂²	1	2	yes	complemented
25	#550×C₆₇	—	2	1	no	—
26	#550×C₆₇	—	2	1	no	—
27	#550×C₆₇	—	2	2	no	—
28	#550×C₆₇	C₂²	1	2	yes	—
29	#550×C₆₇	C₂²	1	4	yes	complemented
30	#550×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	#550×C₆₇	C₂²	1	2	yes	complemented
32	#546×C₆₇	—	2	2	no	—
33	#546×C₆₇	C₂²	1	2	yes	complemented
34	D₄²×C₆₇	—	2	1	no	—
35	D₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	#540×C₆₇	—	2	1	no	—
37	#538×C₆₇	—	2	2	no	—
38	#532×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×#127×C₆₇	—	2	1	no	—
40	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic, complemented
41	#529×C₆₇	C₂²	1	1	yes	characteristic
42	#525×C₆₇	C₂²	1	2	yes	—
43	C₂×#121×C₆₇	—	2	2	no	—
44	C₂×#121×C₆₇	C₂²	1	2	yes	—
45	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
46	#518×C₆₇	—	2	1	no	—
47	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₄×D₄×C₆₇	—	2	1	no	—
49	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
50	#496×C₆₇	C₂²	1	2	yes	complemented
51	#493×C₆₇	C₂²	1	2	yes	complemented
52	#490×C₆₇	C₂²	1	2	yes	complemented
53	#486×C₆₇	C₂²	1	2	yes	complemented
54	#483×C₆₇	C₂²	1	1	yes	characteristic, complemented
55	#482×C₆₇	C₂²	1	4	yes	complemented
56	#480×C₆₇	C₂²	1	1	yes	characteristic
57	#480×C₆₇	C₂²	1	4	yes	complemented
58	#480×C₆₇	C₂²	1	2	yes	complemented
59	#479×C₆₇	C₂²	1	2	yes	complemented
60	#477×C₆₇	C₂²	1	2	yes	complemented
61	#469×C₆₇	C₂²	1	4	yes	complemented
62	#468×C₆₇	C₂²	1	4	yes	complemented
63	#466×C₆₇	C₂²	1	4	yes	complemented
64	#466×C₆₇	C₂²	1	4	yes	complemented
65	#464×C₆₇	C₂²	1	2	yes	complemented
66	#460×C₆₇	C₂²	1	2	yes	complemented
67	#460×C₆₇	C₂²	1	2	yes	complemented
68	#459×C₆₇	C₂²	1	4	yes	complemented
69	#459×C₆₇	C₂²	1	2	yes	complemented
70	#452×C₆₇	C₂²	1	4	yes	complemented
71	#451×C₆₇	C₂²	1	1	yes	characteristic, complemented
72	#450×C₆₇	C₂²	1	2	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	#449×C₆₇	C₂²	1	4	yes	complemented
77	#448×C₆₇	C₂²	1	1	yes	characteristic
78	#448×C₆₇	C₂²	1	2	yes	complemented
79	#447×C₆₇	C₂²	1	2	yes	—
80	#447×C₆₇	C₂²	1	4	yes	complemented
81	#447×C₆₇	C₂²	1	2	yes	complemented
82	#447×C₆₇	C₂²	1	2	yes	complemented
83	#440×C₆₇	C₂²	1	4	yes	complemented
84	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
85	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
86	#436×C₆₇	C₂²	1	2	yes	complemented
87	#435×C₆₇	C₂²	1	4	yes	complemented
88	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
89	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	#417×C₆₇	C₂²	1	4	yes	complemented
92	#416×C₆₇	C₂²	1	4	yes	complemented
93	#407×C₆₇	C₂²	1	2	yes	complemented
94	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
95	C₂×#41×C₆₇	—	2	2	no	—
96	C₂×#41×C₆₇	—	2	2	no	—
97	C₂×#41×C₆₇	—	2	1	no	—
98	C₂×#41×C₆₇	—	4	8	no	—
99	C₂×#41×C₆₇	C₂³	1	4	yes	—
100	C₂×#41×C₆₇	C₂³	1	4	yes	—
101	C₂×#41×C₆₇	C₂³	1	2	yes	—
102	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₆₇	—	2	2	no	—
104	C₂²×D₄×C₆₇	—	2	2	no	—
105	C₂²×D₄×C₆₇	—	2	2	no	—
106	C₂²×D₄×C₆₇	—	2	1	no	—
107	C₂²×D₄×C₆₇	—	2	1	no	—
108	C₂²×D₄×C₆₇	—	2	1	no	—
109	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
110	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
111	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
112	C₂³×C₄×C₆₇	—	2	2	no	—
113	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
114	AGL(1,ℤ/8)×C₆₇	—	4	8	no	—
115	#135×C₆₇	—	4	8	no	—
116	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
117	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
118	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
119	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
120	C₂×D₈×C₆₇	C₂³	1	4	yes	—
121	C₂×D₈×C₆₇	C₂³	1	4	yes	—
122	C₂×D₈×C₆₇	C₂³	1	4	yes	—
123	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
124	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
125	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
126	#127×C₆₇	—	2	2	no	—
127	#127×C₆₇	—	2	2	no	—
128	#127×C₆₇	—	2	4	no	—
129	#127×C₆₇	—	2	1	no	—
130	#127×C₆₇	—	2	1	no	—
131	#127×C₆₇	—	2	1	no	—
132	#127×C₆₇	C₂³	1	2	yes	—
133	#127×C₆₇	C₂³	1	2	yes	—
134	#127×C₆₇	C₂³	1	1	yes	characteristic
135	#126×C₆₇	—	2	2	no	—
136	#126×C₆₇	—	2	1	no	—
137	#125×C₆₇	—	2	1	no	—
138	#125×C₆₇	C₂³	1	1	yes	characteristic
139	#124×C₆₇	—	2	2	no	—
140	#124×C₆₇	—	2	1	no	—
141	#124×C₆₇	C₂³	1	1	yes	characteristic
142	#123×C₆₇	—	2	2	no	—
143	#123×C₆₇	—	2	1	no	—
144	#123×C₆₇	—	2	2	no	—
145	#123×C₆₇	—	2	2	no	—
146	C₂²⋊Q₈×C₆₇	—	2	2	no	—
147	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
148	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
149	#121×C₆₇	—	2	2	no	—
150	#121×C₆₇	—	2	1	no	—
151	#121×C₆₇	—	2	2	no	—
152	#121×C₆₇	—	2	2	no	—
153	#121×C₆₇	—	2	2	no	—
154	#121×C₆₇	—	2	2	no	—
155	#121×C₆₇	—	2	1	no	—
156	#121×C₆₇	—	2	1	no	—
157	#121×C₆₇	—	2	4	no	—
158	#121×C₆₇	—	2	4	no	—
159	#121×C₆₇	—	2	4	no	—
160	#121×C₆₇	—	2	4	no	—
161	#121×C₆₇	—	2	2	no	—
162	#121×C₆₇	—	2	2	no	—
163	#121×C₆₇	C₂³	1	1	yes	characteristic
164	#121×C₆₇	C₂³	1	2	yes	—
165	#121×C₆₇	C₂³	1	2	yes	—
166	#121×C₆₇	C₂³	1	2	yes	—
167	#121×C₆₇	C₂³	1	2	yes	—
168	#121×C₆₇	C₂³	1	4	yes	—
169	#121×C₆₇	C₂³	1	4	yes	—
170	#120×C₆₇	—	2	2	no	—
171	#120×C₆₇	—	2	2	no	—
172	#120×C₆₇	—	2	2	no	—
173	C₄×Q₈×C₆₇	—	2	1	no	—
174	C₄×Q₈×C₆₇	—	2	1	no	—
175	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
176	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
177	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
178	C₄×D₄×C₆₇	—	2	1	no	—
179	C₄×D₄×C₆₇	—	2	2	no	—
180	C₄×D₄×C₆₇	—	2	2	no	—
181	C₄×D₄×C₆₇	—	2	1	no	—
182	C₄×D₄×C₆₇	—	2	2	no	—
183	C₄×D₄×C₆₇	—	2	2	no	—
184	C₄×D₄×C₆₇	—	2	4	no	—
185	C₄×D₄×C₆₇	—	2	1	no	—
186	C₄×D₄×C₆₇	—	2	2	no	—
187	C₄×D₄×C₆₇	—	2	1	no	—
188	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
189	C₄×D₄×C₆₇	D₄	1	2	yes	—
190	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
191	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
192	C₄×D₄×C₆₇	C₂³	1	2	yes	—
193	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
194	C₄×D₄×C₆₇	C₂³	1	2	yes	—
195	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
196	#117×C₆₇	—	2	1	no	—
197	#117×C₆₇	—	2	1	no	—
198	#117×C₆₇	C₂³	1	2	yes	—
199	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
200	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
201	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
204	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
205	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
206	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
207	C₂×C₄²×C₆₇	—	2	1	no	—
208	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
209	#107×C₆₇	C₂³	1	2	yes	—
210	#107×C₆₇	C₂³	1	4	yes	—
211	#106×C₆₇	C₂³	1	2	yes	—
212	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
213	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
214	#103×C₆₇	C₂³	1	2	yes	—
215	#103×C₆₇	C₂³	1	4	yes	—
216	#103×C₆₇	C₂³	1	2	yes	—
217	#103×C₆₇	C₂³	1	2	yes	—
218	#102×C₆₇	C₂³	1	4	yes	—
219	#102×C₆₇	C₂³	1	4	yes	—
220	#102×C₆₇	C₂³	1	4	yes	—
221	#102×C₆₇	C₂³	1	4	yes	—
222	#102×C₆₇	C₂³	1	4	yes	—
223	#102×C₆₇	C₂³	1	2	yes	—
224	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
225	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
226	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
227	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
228	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
229	#97×C₆₇	C₂³	1	2	yes	—
230	C₄×C₈×C₆₇	C₂³	1	2	yes	—
231	C₂⁴×C₆₇	—	2	2	no	—
232	C₂⁴×C₆₇	—	2	2	no	—
233	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
234	#41×C₆₇	—	2	8	no	—
235	#41×C₆₇	—	2	8	no	—
236	#41×C₆₇	—	4	4	no	—
237	#41×C₆₇	—	4	4	no	—
238	#41×C₆₇	—	4	4	no	—
239	#41×C₆₇	—	4	8	no	—
240	#41×C₆₇	—	4	8	no	—
241	#41×C₆₇	—	8	2	no	—
242	C₂×Q₈×C₆₇	—	2	4	no	—
243	C₂×Q₈×C₆₇	—	2	1	no	—
244	C₂×Q₈×C₆₇	—	2	1	no	—
245	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
246	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
247	C₂×D₄×C₆₇	—	2	2	no	—
248	C₂×D₄×C₆₇	—	2	2	no	—
249	C₂×D₄×C₆₇	—	2	1	no	—
250	C₂×D₄×C₆₇	—	2	4	no	—
251	C₂×D₄×C₆₇	—	2	4	no	—
252	C₂×D₄×C₆₇	—	2	2	no	—
253	C₂×D₄×C₆₇	—	2	2	no	—
254	C₂×D₄×C₆₇	—	2	2	no	—
255	C₂×D₄×C₆₇	—	2	4	no	—
256	C₂×D₄×C₆₇	—	2	4	no	—
257	C₂×D₄×C₆₇	—	2	1	no	—
258	C₂×D₄×C₆₇	—	2	2	no	—
259	C₂×D₄×C₆₇	—	2	2	no	—
260	C₂×D₄×C₆₇	—	2	2	no	—
261	C₂×D₄×C₆₇	—	2	1	no	—
262	C₂×D₄×C₆₇	—	2	2	no	—
263	C₂×D₄×C₆₇	—	2	2	no	—
264	C₂×D₄×C₆₇	—	2	2	no	—
265	C₂×D₄×C₆₇	—	4	2	no	—
266	C₂×D₄×C₆₇	—	4	4	no	—
267	C₂×D₄×C₆₇	—	4	4	no	—
268	C₂×D₄×C₆₇	—	4	4	no	—
269	C₂×D₄×C₆₇	—	4	8	no	—
270	C₂×D₄×C₆₇	—	4	4	no	—
271	C₂×D₄×C₆₇	—	8	2	no	—
272	C₂×D₄×C₆₇	—	8	4	no	—
273	C₂×D₄×C₆₇	—	8	4	no	—
274	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
275	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
276	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
277	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
278	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
279	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₆₇	—	2	1	no	—
281	C₂²×C₄×C₆₇	—	2	1	no	—
282	C₂²×C₄×C₆₇	—	2	2	no	—
283	C₂²×C₄×C₆₇	—	2	1	no	—
284	C₂²×C₄×C₆₇	—	2	4	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	—	4	4	no	—
289	C₂²×C₄×C₆₇	—	4	8	no	—
290	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
291	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
292	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
293	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
294	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
295	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
298	Q₁₆×C₆₇	—	2	4	no	—
299	SD₁₆×C₆₇	—	2	8	no	—
300	SD₁₆×C₆₇	—	2	4	no	—
301	SD₁₆×C₆₇	—	4	4	no	—
302	D₈×C₆₇	—	4	4	no	—
303	D₈×C₆₇	—	4	4	no	—
304	D₈×C₆₇	—	4	4	no	—
305	M₁₆×C₆₇	—	4	4	no	—
306	C₂×C₈×C₆₇	—	4	4	no	—
307	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
308	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
309	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
310	C₄⋊C₄×C₆₇	—	2	2	no	—
311	C₄⋊C₄×C₆₇	—	2	2	no	—
312	C₄⋊C₄×C₆₇	—	2	1	no	—
313	C₄⋊C₄×C₆₇	—	2	2	no	—
314	C₄⋊C₄×C₆₇	—	2	1	no	—
315	C₄⋊C₄×C₆₇	—	2	1	no	—
316	C₄⋊C₄×C₆₇	—	2	1	no	—
317	C₄⋊C₄×C₆₇	—	2	1	no	—
318	C₄⋊C₄×C₆₇	—	2	2	no	—
319	C₄⋊C₄×C₆₇	—	2	1	no	—
320	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
321	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
322	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
323	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
324	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
325	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
326	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
327	C₂²⋊C₄×C₆₇	—	2	2	no	—
328	C₂²⋊C₄×C₆₇	—	2	2	no	—
329	C₂²⋊C₄×C₆₇	—	2	1	no	—
330	C₂²⋊C₄×C₆₇	—	2	1	no	—
331	C₂²⋊C₄×C₆₇	—	2	1	no	—
332	C₂²⋊C₄×C₆₇	—	2	2	no	—
333	C₂²⋊C₄×C₆₇	—	2	4	no	—
334	C₂²⋊C₄×C₆₇	—	2	4	no	—
335	C₂²⋊C₄×C₆₇	—	2	2	no	—
336	C₂²⋊C₄×C₆₇	—	2	2	no	—
337	C₂²⋊C₄×C₆₇	—	2	1	no	—
338	C₂²⋊C₄×C₆₇	—	2	2	no	—
339	C₂²⋊C₄×C₆₇	—	2	1	no	—
340	C₂²⋊C₄×C₆₇	—	2	2	no	—
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	2	no	—
346	C₄²×C₆₇	—	2	2	no	—
347	C₄²×C₆₇	—	2	2	no	—
348	C₄²×C₆₇	—	2	1	no	—
349	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
350	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
351	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
352	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
353	C₂³×C₆₇	—	2	4	no	—
354	C₂³×C₆₇	—	2	1	no	—
355	C₂³×C₆₇	—	2	2	no	—
356	C₂³×C₆₇	—	2	4	no	—
357	C₂³×C₆₇	—	4	2	no	—
358	C₂³×C₆₇	—	4	2	no	—
359	C₂³×C₆₇	—	4	4	no	—
360	C₂³×C₆₇	—	4	4	no	—
361	C₂³×C₆₇	—	4	4	no	—
362	C₂³×C₆₇	—	4	4	no	—
363	C₂³×C₆₇	—	8	2	no	—
364	C₂³×C₆₇	—	8	2	no	—
365	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
366	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
367	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
368	Q₈×C₆₇	—	2	4	no	—
369	Q₈×C₆₇	—	2	2	no	—
370	Q₈×C₆₇	—	2	2	no	—
371	Q₈×C₆₇	—	8	1	no	—
372	Q₈×C₆₇	H(5,𝔽₂)	1	4	yes	—
373	D₄×C₆₇	—	2	2	no	—
374	D₄×C₆₇	—	2	2	no	—
375	D₄×C₆₇	—	2	2	no	—
376	D₄×C₆₇	—	2	4	no	—
377	D₄×C₆₇	—	2	4	no	—
378	D₄×C₆₇	—	2	4	no	—
379	D₄×C₆₇	—	4	2	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	4	no	—
385	D₄×C₆₇	—	4	2	no	—
386	D₄×C₆₇	—	4	4	no	—
387	D₄×C₆₇	—	4	2	no	—
388	D₄×C₆₇	—	4	4	no	—
389	D₄×C₆₇	—	8	2	no	—
390	D₄×C₆₇	—	8	2	no	—
391	D₄×C₆₇	—	8	2	no	—
392	D₄×C₆₇	—	8	1	no	—
393	D₄×C₆₇	—	8	4	no	—
394	D₄×C₆₇	—	8	4	no	—
395	D₄×C₆₇	—	8	2	no	—
396	D₄×C₆₇	—	8	2	no	—
397	D₄×C₆₇	—	8	2	no	—
398	C₂×C₄×C₆₇	—	2	4	no	—
399	C₂×C₄×C₆₇	—	2	2	no	—
400	C₂×C₄×C₆₇	—	2	2	no	—
401	C₂×C₄×C₆₇	—	2	2	no	—
402	C₂×C₄×C₆₇	—	2	4	no	—
403	C₂×C₄×C₆₇	—	2	4	no	—
404	C₂×C₄×C₆₇	—	2	2	no	—
405	C₂×C₄×C₆₇	—	2	1	no	—
406	C₂×C₄×C₆₇	—	2	2	no	—
407	C₂×C₄×C₆₇	—	2	1	no	—
408	C₂×C₄×C₆₇	—	2	2	no	—
409	C₂×C₄×C₆₇	—	2	1	no	—
410	C₂×C₄×C₆₇	—	4	2	no	—
411	C₂×C₄×C₆₇	—	4	2	no	—
412	C₂×C₄×C₆₇	—	4	2	no	—
413	C₂×C₄×C₆₇	—	4	8	no	—
414	C₂×C₄×C₆₇	—	4	8	no	—
415	C₂×C₄×C₆₇	—	4	2	no	—
416	C₂×C₄×C₆₇	—	4	2	no	—
417	C₂×C₄×C₆₇	—	8	2	no	—
418	C₂×C₄×C₆₇	—	8	2	no	—
419	C₂×C₄×C₆₇	—	8	2	no	—
420	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
421	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
422	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
424	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
426	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
428	C₈×C₆₇	—	2	2	no	—
429	C₈×C₆₇	—	2	4	no	—
430	C₈×C₆₇	—	2	2	no	—
431	C₂²×C₆₇	—	2	1	no	—
432	C₂²×C₆₇	—	2	1	no	—
433	C₂²×C₆₇	—	2	2	no	—
434	C₂²×C₆₇	—	2	2	no	—
435	C₂²×C₆₇	—	2	2	no	—
436	C₂²×C₆₇	—	2	2	no	—
437	C₂²×C₆₇	—	2	2	no	—
438	C₂²×C₆₇	—	2	2	no	—
439	C₂²×C₆₇	—	4	4	no	—
440	C₂²×C₆₇	—	4	2	no	—
441	C₂²×C₆₇	—	4	1	no	—
442	C₂²×C₆₇	—	4	1	no	—
443	C₂²×C₆₇	—	4	4	no	—
444	C₂²×C₆₇	—	4	2	no	—
445	C₂²×C₆₇	—	4	2	no	—
446	C₂²×C₆₇	—	4	1	no	—
447	C₂²×C₆₇	—	4	4	no	—
448	C₂²×C₆₇	—	8	4	no	—
449	C₂²×C₆₇	—	8	8	no	—
450	C₂²×C₆₇	—	16	4	no	—
451	C₂²×C₆₇	#576	1	2	yes	—
452	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
453	C₄×C₆₇	—	2	4	no	—
454	C₄×C₆₇	—	2	2	no	—
455	C₄×C₆₇	—	2	2	no	—
456	C₄×C₆₇	—	2	1	no	—
457	C₄×C₆₇	—	2	1	no	—
458	C₄×C₆₇	—	2	1	no	—
459	C₄×C₆₇	—	2	1	no	—
460	C₄×C₆₇	—	4	1	no	—
461	C₄×C₆₇	—	4	1	no	—
462	C₄×C₆₇	—	4	2	no	—
463	C₄×C₆₇	—	4	1	no	—
464	C₄×C₆₇	—	4	2	no	—
465	C₄×C₆₇	#575	1	2	yes	—
466	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
467	#61605	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
468	C₂×C₆₇	—	2	2	no	—
469	C₂×C₆₇	—	4	2	no	—
470	C₂×C₆₇	—	4	2	no	—
471	C₂×C₆₇	—	8	4	no	—
472	C₂×C₆₇	—	8	2	no	—
473	C₂×C₆₇	—	8	1	no	—
474	C₂×C₆₇	#3484	1	1	yes	characteristic
475	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
476	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
477	#3519	C₂×C₆₇	1	1	yes	characteristic, complemented
478	C₂×#550	C₂×C₆₇	1	1	yes	characteristic, complemented
479	#3333	C₂×C₆₇	1	2	yes	complemented
480	#3309	C₂×C₆₇	1	4	yes	complemented
481	#3305	C₂×C₆₇	1	2	yes	complemented
482	#3287	C₂×C₆₇	1	2	yes	complemented
483	#3274	C₂×C₆₇	1	2	yes	complemented
484	#3268	C₂×C₆₇	1	4	yes	complemented
485	#3217	C₂×C₆₇	1	1	yes	characteristic, complemented
486	#3205	C₂×C₆₇	1	1	yes	characteristic, complemented
487	#3194	C₂×C₆₇	1	2	yes	complemented
488	#3186	C₂×C₆₇	1	2	yes	complemented
489	#3112	C₂×C₆₇	1	1	yes	characteristic, complemented
490	#3108	C₂×C₆₇	1	1	yes	characteristic, complemented
491	#3006	C₂×C₆₇	1	2	yes	complemented
492	#3002	C₂×C₆₇	1	2	yes	complemented
493	#2974	C₂×C₆₇	1	1	yes	characteristic, complemented
494	C₆₇	#61605	1	1	yes	characteristic, direct product factor, Sylow
495	C₂²×#41	C₂²×C₆₇	1	2	yes	complemented
496	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
497	C₂×#135	C₂²×C₆₇	1	4	yes	complemented
498	#555	C₂²×C₆₇	1	1	yes	characteristic, complemented
499	#554	C₂²×C₆₇	1	1	yes	characteristic, complemented
500	#553	—	2	1	no	—
501	#553	C₂²×C₆₇	1	2	yes	complemented
502	#550	—	2	1	no	—
503	#550	—	2	1	no	—
504	#550	—	2	2	no	—
505	#550	C₂²×C₆₇	1	2	yes	—
506	#550	C₂²×C₆₇	1	4	yes	complemented
507	#550	C₂²×C₆₇	1	2	yes	complemented
508	#550	C₂²×C₆₇	1	1	yes	characteristic, complemented
509	#546	—	2	2	no	—
510	#546	C₂²×C₆₇	1	2	yes	complemented
511	D₄²	—	2	1	no	—
512	D₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
513	#540	—	2	1	no	—
514	#538	—	2	2	no	—
515	#532	C₂²×C₆₇	1	1	yes	characteristic
516	C₂×#127	—	2	1	no	—
517	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic, complemented
518	#529	C₂²×C₆₇	1	1	yes	characteristic
519	#525	C₂²×C₆₇	1	2	yes	—
520	C₂×#121	—	2	2	no	—
521	C₂×#121	C₂²×C₆₇	1	2	yes	—
522	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
523	#518	—	2	1	no	—
524	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
525	C₂×C₄×D₄	—	2	1	no	—
526	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
527	#496	C₂²×C₆₇	1	2	yes	complemented
528	#493	C₂²×C₆₇	1	2	yes	complemented
529	#490	C₂²×C₆₇	1	2	yes	complemented
530	#486	C₂²×C₆₇	1	2	yes	complemented
531	#483	C₂²×C₆₇	1	1	yes	characteristic, complemented
532	#482	C₂²×C₆₇	1	4	yes	complemented
533	#480	C₂²×C₆₇	1	1	yes	characteristic
534	#480	C₂²×C₆₇	1	4	yes	complemented
535	#480	C₂²×C₆₇	1	2	yes	complemented
536	#479	C₂²×C₆₇	1	2	yes	complemented
537	#477	C₂²×C₆₇	1	2	yes	complemented
538	#469	C₂²×C₆₇	1	4	yes	complemented
539	#468	C₂²×C₆₇	1	4	yes	complemented
540	#466	C₂²×C₆₇	1	4	yes	complemented
541	#466	C₂²×C₆₇	1	4	yes	complemented
542	#464	C₂²×C₆₇	1	2	yes	complemented
543	#460	C₂²×C₆₇	1	2	yes	complemented
544	#460	C₂²×C₆₇	1	2	yes	complemented
545	#459	C₂²×C₆₇	1	4	yes	complemented
546	#459	C₂²×C₆₇	1	2	yes	complemented
547	#452	C₂²×C₆₇	1	4	yes	complemented
548	#451	C₂²×C₆₇	1	1	yes	characteristic, complemented
549	#450	C₂²×C₆₇	1	2	yes	complemented
550	#449	C₂²×C₆₇	1	4	yes	complemented
551	#449	C₂²×C₆₇	1	4	yes	complemented
552	#449	C₂²×C₆₇	1	4	yes	complemented
553	#449	C₂²×C₆₇	1	4	yes	complemented
554	#448	C₂²×C₆₇	1	1	yes	characteristic
555	#448	C₂²×C₆₇	1	2	yes	complemented
556	#447	C₂²×C₆₇	1	2	yes	—
557	#447	C₂²×C₆₇	1	2	yes	complemented
558	#447	C₂²×C₆₇	1	4	yes	complemented
559	#447	C₂²×C₆₇	1	2	yes	complemented
560	#440	C₂²×C₆₇	1	4	yes	complemented
561	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
562	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
563	#436	C₂²×C₆₇	1	2	yes	complemented
564	#435	C₂²×C₆₇	1	4	yes	complemented
565	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
566	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
567	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
568	#417	C₂²×C₆₇	1	4	yes	complemented
569	#416	C₂²×C₆₇	1	4	yes	complemented
570	#407	C₂²×C₆₇	1	2	yes	complemented
571	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
572	C₂×#41	—	2	2	no	—
573	C₂×#41	—	2	2	no	—
574	C₂×#41	—	2	1	no	—
575	C₂×#41	—	4	8	no	—
576	C₂×#41	C₂³×C₆₇	1	4	yes	—
577	C₂×#41	C₂³×C₆₇	1	4	yes	—
578	C₂×#41	C₂³×C₆₇	1	2	yes	—
579	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
580	C₂²×D₄	—	2	2	no	—
581	C₂²×D₄	—	2	2	no	—
582	C₂²×D₄	—	2	2	no	—
583	C₂²×D₄	—	2	1	no	—
584	C₂²×D₄	—	2	1	no	—
585	C₂²×D₄	—	2	1	no	—
586	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
587	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
588	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
589	C₂³×C₄	—	2	2	no	—
590	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
591	AGL(1,ℤ/8)	—	4	8	no	—
592	#135	—	4	8	no	—
593	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
594	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
595	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
596	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
597	C₂×D₈	C₂³×C₆₇	1	4	yes	—
598	C₂×D₈	C₂³×C₆₇	1	4	yes	—
599	C₂×D₈	C₂³×C₆₇	1	4	yes	—
600	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
601	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
602	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
603	#127	—	2	2	no	—
604	#127	—	2	2	no	—
605	#127	—	2	4	no	—
606	#127	—	2	1	no	—
607	#127	—	2	1	no	—
608	#127	—	2	1	no	—
609	#127	C₂³×C₆₇	1	2	yes	—
610	#127	C₂³×C₆₇	1	2	yes	—
611	#127	C₂³×C₆₇	1	1	yes	characteristic
612	#126	—	2	2	no	—
613	#126	—	2	1	no	—
614	#125	—	2	1	no	—
615	#125	C₂³×C₆₇	1	1	yes	characteristic
616	#124	—	2	2	no	—
617	#124	—	2	1	no	—
618	#124	C₂³×C₆₇	1	1	yes	characteristic
619	#123	—	2	2	no	—
620	#123	—	2	1	no	—
621	#123	—	2	2	no	—
622	#123	—	2	2	no	—
623	C₂²⋊Q₈	—	2	2	no	—
624	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
625	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
626	#121	—	2	2	no	—
627	#121	—	2	1	no	—
628	#121	—	2	2	no	—
629	#121	—	2	2	no	—
630	#121	—	2	2	no	—
631	#121	—	2	2	no	—
632	#121	—	2	1	no	—
633	#121	—	2	1	no	—
634	#121	—	2	4	no	—
635	#121	—	2	4	no	—
636	#121	—	2	4	no	—
637	#121	—	2	4	no	—
638	#121	—	2	2	no	—
639	#121	—	2	2	no	—
640	#121	C₂³×C₆₇	1	1	yes	characteristic
641	#121	C₂³×C₆₇	1	2	yes	—
642	#121	C₂³×C₆₇	1	2	yes	—
643	#121	C₂³×C₆₇	1	2	yes	—
644	#121	C₂³×C₆₇	1	4	yes	—
645	#121	C₂³×C₆₇	1	4	yes	—
646	#121	C₂³×C₆₇	1	2	yes	—
647	#120	—	2	2	no	—
648	#120	—	2	2	no	—
649	#120	—	2	2	no	—
650	C₄×Q₈	—	2	1	no	—
651	C₄×Q₈	—	2	1	no	—
652	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
653	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
654	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
655	C₄×D₄	—	2	1	no	—
656	C₄×D₄	—	2	2	no	—
657	C₄×D₄	—	2	2	no	—
658	C₄×D₄	—	2	1	no	—
659	C₄×D₄	—	2	2	no	—
660	C₄×D₄	—	2	2	no	—
661	C₄×D₄	—	2	4	no	—
662	C₄×D₄	—	2	1	no	—
663	C₄×D₄	—	2	2	no	—
664	C₄×D₄	—	2	1	no	—
665	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
666	C₄×D₄	D₄×C₆₇	1	2	yes	—
667	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
668	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
669	C₄×D₄	C₂³×C₆₇	1	2	yes	—
670	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
671	C₄×D₄	C₂³×C₆₇	1	2	yes	—
672	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
673	#117	—	2	1	no	—
674	#117	—	2	1	no	—
675	#117	C₂³×C₆₇	1	2	yes	—
676	C₂×C₄⋊C₄	—	2	1	no	—
677	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
678	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
679	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
680	C₂×C₂²⋊C₄	—	2	2	no	—
681	C₂×C₂²⋊C₄	—	2	2	no	—
682	C₂×C₂²⋊C₄	—	2	2	no	—
683	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
684	C₂×C₄²	—	2	1	no	—
685	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
686	#107	C₂³×C₆₇	1	2	yes	—
687	#107	C₂³×C₆₇	1	4	yes	—
688	#106	C₂³×C₆₇	1	2	yes	—
689	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
690	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
691	#103	C₂³×C₆₇	1	2	yes	—
692	#103	C₂³×C₆₇	1	4	yes	—
693	#103	C₂³×C₆₇	1	2	yes	—
694	#103	C₂³×C₆₇	1	2	yes	—
695	#102	C₂³×C₆₇	1	4	yes	—
696	#102	C₂³×C₆₇	1	4	yes	—
697	#102	C₂³×C₆₇	1	4	yes	—
698	#102	C₂³×C₆₇	1	4	yes	—
699	#102	C₂³×C₆₇	1	2	yes	—
700	#102	C₂³×C₆₇	1	4	yes	—
701	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
702	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
703	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
704	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
705	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
706	#97	C₂³×C₆₇	1	2	yes	—
707	C₄×C₈	C₂³×C₆₇	1	2	yes	—
708	C₂⁴	—	2	2	no	—
709	C₂⁴	—	2	2	no	—
710	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
711	#41	—	2	8	no	—
712	#41	—	2	8	no	—
713	#41	—	4	4	no	—
714	#41	—	4	4	no	—
715	#41	—	4	4	no	—
716	#41	—	4	8	no	—
717	#41	—	4	8	no	—
718	#41	—	8	2	no	—
719	C₂×Q₈	—	2	4	no	—
720	C₂×Q₈	—	2	1	no	—
721	C₂×Q₈	—	2	1	no	—
722	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
723	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
724	C₂×D₄	—	2	2	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	2	1	no	—
727	C₂×D₄	—	2	4	no	—
728	C₂×D₄	—	2	4	no	—
729	C₂×D₄	—	2	2	no	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	—	2	4	no	—
733	C₂×D₄	—	2	4	no	—
734	C₂×D₄	—	2	1	no	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	2	2	no	—
737	C₂×D₄	—	2	2	no	—
738	C₂×D₄	—	2	1	no	—
739	C₂×D₄	—	2	2	no	—
740	C₂×D₄	—	2	2	no	—
741	C₂×D₄	—	2	2	no	—
742	C₂×D₄	—	4	2	no	—
743	C₂×D₄	—	4	4	no	—
744	C₂×D₄	—	4	4	no	—
745	C₂×D₄	—	4	8	no	—
746	C₂×D₄	—	4	4	no	—
747	C₂×D₄	—	4	4	no	—
748	C₂×D₄	—	8	2	no	—
749	C₂×D₄	—	8	4	no	—
750	C₂×D₄	—	8	4	no	—
751	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
752	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
753	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
754	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
755	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
756	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
757	C₂²×C₄	—	2	1	no	—
758	C₂²×C₄	—	2	1	no	—
759	C₂²×C₄	—	2	2	no	—
760	C₂²×C₄	—	2	1	no	—
761	C₂²×C₄	—	2	4	no	—
762	C₂²×C₄	—	2	4	no	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	4	4	no	—
766	C₂²×C₄	—	4	8	no	—
767	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
768	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
769	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
770	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
771	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
772	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
773	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
774	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
775	Q₁₆	—	2	4	no	—
776	SD₁₆	—	2	8	no	—
777	SD₁₆	—	2	4	no	—
778	SD₁₆	—	4	4	no	—
779	D₈	—	4	4	no	—
780	D₈	—	4	4	no	—
781	D₈	—	4	4	no	—
782	M₁₆	—	4	4	no	—
783	C₂×C₈	—	4	4	no	—
784	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
785	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
786	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	1	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	1	no	—
792	C₄⋊C₄	—	2	1	no	—
793	C₄⋊C₄	—	2	1	no	—
794	C₄⋊C₄	—	2	1	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	2	1	no	—
797	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
798	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
799	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
800	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
801	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
802	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
803	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	1	no	—
807	C₂²⋊C₄	—	2	1	no	—
808	C₂²⋊C₄	—	2	1	no	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	2	4	no	—
811	C₂²⋊C₄	—	2	4	no	—
812	C₂²⋊C₄	—	2	2	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	1	no	—
815	C₂²⋊C₄	—	2	2	no	—
816	C₂²⋊C₄	—	2	1	no	—
817	C₂²⋊C₄	—	2	2	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	C₄²	—	2	2	no	—
823	C₄²	—	2	2	no	—
824	C₄²	—	2	2	no	—
825	C₄²	—	2	1	no	—
826	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
827	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
828	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
829	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
830	C₂³	—	2	4	no	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	2	no	—
833	C₂³	—	2	4	no	—
834	C₂³	—	4	2	no	—
835	C₂³	—	4	2	no	—
836	C₂³	—	4	4	no	—
837	C₂³	—	4	4	no	—
838	C₂³	—	4	4	no	—
839	C₂³	—	4	4	no	—
840	C₂³	—	8	2	no	—
841	C₂³	—	8	2	no	—
842	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
843	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
844	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
845	Q₈	—	2	4	no	—
846	Q₈	—	2	2	no	—
847	Q₈	—	2	2	no	—
848	Q₈	—	8	1	no	—
849	Q₈	H(5,𝔽₂)×C₆₇	1	4	yes	—
850	D₄	—	2	2	no	—
851	D₄	—	2	2	no	—
852	D₄	—	2	2	no	—
853	D₄	—	2	4	no	—
854	D₄	—	2	4	no	—
855	D₄	—	2	4	no	—
856	D₄	—	4	2	no	—
857	D₄	—	4	8	no	—
858	D₄	—	4	8	no	—
859	D₄	—	4	4	no	—
860	D₄	—	4	4	no	—
861	D₄	—	4	4	no	—
862	D₄	—	4	2	no	—
863	D₄	—	4	4	no	—
864	D₄	—	4	2	no	—
865	D₄	—	4	4	no	—
866	D₄	—	8	2	no	—
867	D₄	—	8	2	no	—
868	D₄	—	8	2	no	—
869	D₄	—	8	1	no	—
870	D₄	—	8	4	no	—
871	D₄	—	8	4	no	—
872	D₄	—	8	2	no	—
873	D₄	—	8	2	no	—
874	D₄	—	8	2	no	—
875	C₂×C₄	—	2	4	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	4	no	—
880	C₂×C₄	—	2	4	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	4	2	no	—
888	C₂×C₄	—	4	2	no	—
889	C₂×C₄	—	4	2	no	—
890	C₂×C₄	—	4	8	no	—
891	C₂×C₄	—	4	8	no	—
892	C₂×C₄	—	4	2	no	—
893	C₂×C₄	—	4	2	no	—
894	C₂×C₄	—	8	2	no	—
895	C₂×C₄	—	8	2	no	—
896	C₂×C₄	—	8	2	no	—
897	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
898	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
899	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
900	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
901	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
902	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
903	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
904	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
905	C₈	—	2	2	no	—
906	C₈	—	2	4	no	—
907	C₈	—	2	2	no	—
908	C₂²	—	2	1	no	—
909	C₂²	—	2	1	no	—
910	C₂²	—	2	2	no	—
911	C₂²	—	2	2	no	—
912	C₂²	—	2	2	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	4	1	no	—
917	C₂²	—	4	4	no	—
918	C₂²	—	4	2	no	—
919	C₂²	—	4	2	no	—
920	C₂²	—	4	1	no	—
921	C₂²	—	4	4	no	—
922	C₂²	—	4	4	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	1	no	—
925	C₂²	—	8	4	no	—
926	C₂²	—	8	8	no	—
927	C₂²	—	16	4	no	—
928	C₂²	#576×C₆₇	1	2	yes	—
929	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
930	C₄	—	2	1	no	—
931	C₄	—	2	1	no	—
932	C₄	—	2	1	no	—
933	C₄	—	2	4	no	—
934	C₄	—	2	2	no	—
935	C₄	—	2	2	no	—
936	C₄	—	2	1	no	—
937	C₄	—	4	1	no	—
938	C₄	—	4	2	no	—
939	C₄	—	4	1	no	—
940	C₄	—	4	2	no	—
941	C₄	—	4	1	no	—
942	C₄	#575×C₆₇	1	2	yes	—
943	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
944	C₂	—	2	2	no	—
945	C₂	—	4	2	no	—
946	C₂	—	4	2	no	—
947	C₂	—	8	4	no	—
948	C₂	—	8	1	no	—
949	C₂	—	8	2	no	—
950	C₂	C₆₇×#3484	1	1	yes	characteristic
951	C₂	C₂×#575×C₆₇	1	1	yes	characteristic
952	C₂	C₂×#576×C₆₇	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 ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3519	C₂	semidirect
2. C₂×#550×C₆₇	C₂	semidirect
3. C₆₇×#3333	C₂	semidirect
4. C₆₇×#3309	C₂	semidirect
5. C₆₇×#3305	C₂	semidirect
6. C₆₇×#3287	C₂	semidirect
7. C₆₇×#3274	C₂	semidirect
8. C₆₇×#3268	C₂	semidirect
9. C₆₇×#3217	C₂	semidirect
10. C₆₇×#3205	C₂	semidirect
11. C₆₇×#3194	C₂	semidirect
12. C₆₇×#3186	C₂	semidirect
13. C₆₇×#3112	C₂	semidirect
14. C₆₇×#3108	C₂	semidirect
15. C₆₇×#3006	C₂	semidirect
16. C₆₇×#3002	C₂	semidirect
17. C₆₇×#2974	C₂	semidirect
18. C₂²×#41×C₆₇	C₂²	semidirect
19. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
20. C₂×#135×C₆₇	C₂²	semidirect
21. #555×C₆₇	C₂²	semidirect
22. #554×C₆₇	C₂²	semidirect
24. #553×C₆₇	C₂²	semidirect
29. #550×C₆₇	C₂²	semidirect
30. #550×C₆₇	C₂²	semidirect
31. #550×C₆₇	C₂²	semidirect
33. #546×C₆₇	C₂²	semidirect
35. D₄²×C₆₇	C₂²	semidirect
40. C₂×#127×C₆₇	C₂²	semidirect
45. C₂×#121×C₆₇	C₂²	semidirect
47. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
50. #496×C₆₇	C₂²	semidirect
51. #493×C₆₇	C₂²	semidirect
52. #490×C₆₇	C₂²	semidirect
53. #486×C₆₇	C₂²	semidirect
54. #483×C₆₇	C₂²	semidirect
55. #482×C₆₇	C₂²	semidirect
57. #480×C₆₇	C₂²	semidirect
58. #480×C₆₇	C₂²	semidirect
59. #479×C₆₇	C₂²	semidirect
60. #477×C₆₇	C₂²	semidirect
61. #469×C₆₇	C₂²	semidirect
62. #468×C₆₇	C₂²	semidirect
63. #466×C₆₇	C₂²	semidirect
64. #466×C₆₇	C₂²	semidirect
65. #464×C₆₇	C₂²	semidirect
66. #460×C₆₇	C₂²	semidirect
67. #460×C₆₇	C₂²	semidirect
68. #459×C₆₇	C₂²	semidirect
69. #459×C₆₇	C₂²	semidirect
70. #452×C₆₇	C₂²	semidirect
71. #451×C₆₇	C₂²	semidirect
72. #450×C₆₇	C₂²	semidirect
73. #449×C₆₇	C₂²	semidirect
74. #449×C₆₇	C₂²	semidirect
75. #449×C₆₇	C₂²	semidirect
76. #449×C₆₇	C₂²	semidirect
78. #448×C₆₇	C₂²	semidirect
80. #447×C₆₇	C₂²	semidirect
81. #447×C₆₇	C₂²	semidirect
82. #447×C₆₇	C₂²	semidirect
83. #440×C₆₇	C₂²	semidirect
84. C₄×Q₁₆×C₆₇	C₂²	semidirect
85. C₄×SD₁₆×C₆₇	C₂²	semidirect
86. #436×C₆₇	C₂²	semidirect
87. #435×C₆₇	C₂²	semidirect
88. C₈×D₄×C₆₇	C₂²	semidirect
89. #432×C₆₇	C₂²	semidirect
90. #431×C₆₇	C₂²	semidirect
91. #417×C₆₇	C₂²	semidirect
92. #416×C₆₇	C₂²	semidirect
93. #407×C₆₇	C₂²	semidirect
94. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
467. #61605	C₆₇	direct (N × H)
477. #3519	C₂×C₆₇	semidirect
478. C₂×#550	C₂×C₆₇	semidirect
479. #3333	C₂×C₆₇	semidirect
480. #3309	C₂×C₆₇	semidirect
481. #3305	C₂×C₆₇	semidirect
482. #3287	C₂×C₆₇	semidirect
483. #3274	C₂×C₆₇	semidirect
484. #3268	C₂×C₆₇	semidirect
485. #3217	C₂×C₆₇	semidirect
486. #3205	C₂×C₆₇	semidirect
487. #3194	C₂×C₆₇	semidirect
488. #3186	C₂×C₆₇	semidirect
489. #3112	C₂×C₆₇	semidirect
490. #3108	C₂×C₆₇	semidirect
491. #3006	C₂×C₆₇	semidirect
492. #3002	C₂×C₆₇	semidirect
493. #2974	C₂×C₆₇	semidirect
494. C₆₇	#61605	direct (N × H)
495. C₂²×#41	C₂²×C₆₇	semidirect
496. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
497. C₂×#135	C₂²×C₆₇	semidirect
498. #555	C₂²×C₆₇	semidirect
499. #554	C₂²×C₆₇	semidirect
501. #553	C₂²×C₆₇	semidirect
506. #550	C₂²×C₆₇	semidirect
507. #550	C₂²×C₆₇	semidirect
508. #550	C₂²×C₆₇	semidirect
510. #546	C₂²×C₆₇	semidirect
512. D₄²	C₂²×C₆₇	semidirect
517. C₂×#127	C₂²×C₆₇	semidirect
522. C₂×#121	C₂²×C₆₇	semidirect
524. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
527. #496	C₂²×C₆₇	semidirect
528. #493	C₂²×C₆₇	semidirect
529. #490	C₂²×C₆₇	semidirect
530. #486	C₂²×C₆₇	semidirect
531. #483	C₂²×C₆₇	semidirect
532. #482	C₂²×C₆₇	semidirect
534. #480	C₂²×C₆₇	semidirect
535. #480	C₂²×C₆₇	semidirect
536. #479	C₂²×C₆₇	semidirect
537. #477	C₂²×C₆₇	semidirect
538. #469	C₂²×C₆₇	semidirect
539. #468	C₂²×C₆₇	semidirect
540. #466	C₂²×C₆₇	semidirect
541. #466	C₂²×C₆₇	semidirect
542. #464	C₂²×C₆₇	semidirect
543. #460	C₂²×C₆₇	semidirect
544. #460	C₂²×C₆₇	semidirect
545. #459	C₂²×C₆₇	semidirect
546. #459	C₂²×C₆₇	semidirect
547. #452	C₂²×C₆₇	semidirect
548. #451	C₂²×C₆₇	semidirect
549. #450	C₂²×C₆₇	semidirect
550. #449	C₂²×C₆₇	semidirect
551. #449	C₂²×C₆₇	semidirect
552. #449	C₂²×C₆₇	semidirect
553. #449	C₂²×C₆₇	semidirect
555. #448	C₂²×C₆₇	semidirect
557. #447	C₂²×C₆₇	semidirect
558. #447	C₂²×C₆₇	semidirect
559. #447	C₂²×C₆₇	semidirect
560. #440	C₂²×C₆₇	semidirect
561. C₄×Q₁₆	C₂²×C₆₇	semidirect
562. C₄×SD₁₆	C₂²×C₆₇	semidirect
563. #436	C₂²×C₆₇	semidirect
564. #435	C₂²×C₆₇	semidirect
565. C₈×D₄	C₂²×C₆₇	semidirect
566. #432	C₂²×C₆₇	semidirect
567. #431	C₂²×C₆₇	semidirect
568. #417	C₂²×C₆₇	semidirect
569. #416	C₂²×C₆₇	semidirect
570. #407	C₂²×C₆₇	semidirect
571. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3519	2
C₂×#550×C₆₇	2
C₆₇×#3333	2
C₆₇×#3309	2
C₆₇×#3305	2
C₆₇×#3287	2
C₆₇×#3274	2
C₆₇×#3268	2
C₆₇×#3217	2
C₆₇×#3205	2
C₆₇×#3194	2
C₆₇×#3186	2
C₆₇×#3112	2
C₆₇×#3108	2
C₆₇×#3006	2
C₆₇×#3002	2
C₆₇×#2974	2
#61605	67

Subgroups — C67×#61605 #30740856

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61605 #30740856