Subgroups — C₆₇×#61199 #30740450

Order 17152.

2152 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3496	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3330	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3324	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3319	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3314	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3302	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3294	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3141	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3098	C₂	1	2	yes	maximal, complemented
11	C₂×#474×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3061	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3035	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3012	C₂	1	2	yes	maximal, complemented
15	C₄×AGL(1,ℤ/8)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2935	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2897	C₂	1	2	yes	maximal, complemented
18	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	2	yes	—
19	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
20	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
21	C₂×#131×C₆₇	C₂²	1	2	yes	complemented
22	#556×C₆₇	C₂²	1	2	yes	complemented
23	#555×C₆₇	C₂²	1	2	yes	complemented
24	#554×C₆₇	C₂²	1	2	yes	complemented
25	#553×C₆₇	—	2	2	no	—
26	#548×C₆₇	—	2	2	no	—
27	#547×C₆₇	—	2	1	no	—
28	#547×C₆₇	C₂²	1	2	yes	—
29	#547×C₆₇	C₂²	1	2	yes	complemented
30	#546×C₆₇	—	2	2	no	—
31	#546×C₆₇	C₂²	1	4	yes	—
32	D₄²×C₆₇	—	2	1	no	—
33	D₄²×C₆₇	C₂²	1	2	yes	—
34	#542×C₆₇	—	2	2	no	—
35	#537×C₆₇	C₂²	1	2	yes	—
36	#537×C₆₇	C₂²	1	2	yes	complemented
37	#534×C₆₇	—	2	2	no	—
38	#533×C₆₇	—	2	1	no	—
39	#532×C₆₇	—	2	1	no	—
40	#532×C₆₇	C₂²	1	1	yes	characteristic
41	#532×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	C₂×#121×C₆₇	—	2	2	no	—
44	#520×C₆₇	C₂²	1	2	yes	complemented
45	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
47	#489×C₆₇	C₂²	1	4	yes	complemented
48	#487×C₆₇	C₂²	1	2	yes	complemented
49	#486×C₆₇	C₂²	1	2	yes	complemented
50	#485×C₆₇	C₂²	1	4	yes	complemented
51	#484×C₆₇	C₂²	1	4	yes	complemented
52	#482×C₆₇	C₂²	1	4	yes	complemented
53	#480×C₆₇	C₂²	1	4	yes	complemented
54	#474×C₆₇	C₂²	1	2	yes	complemented
55	#474×C₆₇	C₂²	1	4	yes	complemented
56	#474×C₆₇	C₂²	1	2	yes	complemented
57	#468×C₆₇	C₂²	1	4	yes	complemented
58	#468×C₆₇	C₂²	1	4	yes	complemented
59	#467×C₆₇	C₂²	1	4	yes	complemented
60	#466×C₆₇	C₂²	1	4	yes	complemented
61	#464×C₆₇	C₂²	1	2	yes	complemented
62	#463×C₆₇	C₂²	1	2	yes	complemented
63	#462×C₆₇	C₂²	1	1	yes	characteristic, complemented
64	#461×C₆₇	C₂²	1	1	yes	characteristic, complemented
65	#460×C₆₇	C₂²	1	1	yes	characteristic, complemented
66	#459×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	#452×C₆₇	C₂²	1	4	yes	complemented
68	#450×C₆₇	C₂²	1	4	yes	complemented
69	#449×C₆₇	C₂²	1	4	yes	complemented
70	#447×C₆₇	C₂²	1	4	yes	complemented
71	#442×C₆₇	C₂²	1	2	yes	complemented
72	#440×C₆₇	C₂²	1	2	yes	complemented
73	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
74	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
75	#436×C₆₇	C₂²	1	2	yes	complemented
76	#435×C₆₇	C₂²	1	4	yes	complemented
77	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
78	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
79	C₂×#107×C₆₇	C₂²	1	2	yes	complemented
80	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
81	#418×C₆₇	C₂²	1	1	yes	characteristic
82	#418×C₆₇	C₂²	1	4	yes	complemented
83	#417×C₆₇	C₂²	1	2	yes	complemented
84	#417×C₆₇	C₂²	1	4	yes	complemented
85	#417×C₆₇	C₂²	1	1	yes	characteristic, complemented
86	#417×C₆₇	C₂²	1	2	yes	complemented
87	#416×C₆₇	C₂²	1	2	yes	complemented
88	#416×C₆₇	C₂²	1	4	yes	complemented
89	C₂×#102×C₆₇	C₂²	1	2	yes	—
90	C₂×#102×C₆₇	C₂²	1	4	yes	complemented
91	#408×C₆₇	C₂²	1	2	yes	complemented
92	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
93	H(5,𝔽₂)×C₆₇	—	2	8	no	—
94	H(5,𝔽₂)×C₆₇	—	4	4	no	—
95	C₂×#41×C₆₇	—	2	2	no	—
96	C₂×#41×C₆₇	—	2	2	no	—
97	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
98	C₂×#41×C₆₇	C₂³	1	2	yes	—
99	C₂×#41×C₆₇	C₂³	1	4	yes	—
100	C₂×#41×C₆₇	C₂³	1	2	yes	—
101	C₂²×Q₈×C₆₇	—	2	1	no	—
102	C₂²×D₄×C₆₇	—	2	4	no	—
103	C₂²×D₄×C₆₇	—	2	2	no	—
104	C₂²×D₄×C₆₇	—	2	2	no	—
105	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
106	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₆₇	—	2	1	no	—
108	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
109	#135×C₆₇	—	4	4	no	—
110	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
111	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
112	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
113	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
114	C₂×D₈×C₆₇	C₂³	1	2	yes	—
115	C₂×D₈×C₆₇	C₂³	1	2	yes	—
116	#131×C₆₇	—	4	4	no	—
117	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
118	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
119	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
120	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
121	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
122	C₄⋊Q₈×C₆₇	—	2	1	no	—
123	C₄⋊Q₈×C₆₇	—	2	1	no	—
124	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
125	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
126	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
127	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
128	#127×C₆₇	D₄	1	1	yes	characteristic
129	#127×C₆₇	C₂³	1	1	yes	characteristic
130	#126×C₆₇	—	2	4	no	—
131	#125×C₆₇	—	2	2	no	—
132	#124×C₆₇	—	2	2	no	—
133	#124×C₆₇	—	2	4	no	—
134	#124×C₆₇	D₄	1	2	yes	—
135	#124×C₆₇	C₂³	1	2	yes	—
136	#123×C₆₇	—	2	4	no	—
137	#123×C₆₇	—	2	4	no	—
138	#123×C₆₇	—	2	4	no	—
139	C₂²⋊Q₈×C₆₇	—	2	2	no	—
140	C₂²⋊Q₈×C₆₇	—	2	2	no	—
141	C₂²⋊Q₈×C₆₇	—	2	2	no	—
142	C₂²⋊Q₈×C₆₇	—	2	4	no	—
143	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
144	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
145	#121×C₆₇	—	2	4	no	—
146	#121×C₆₇	—	2	2	no	—
147	#121×C₆₇	—	2	2	no	—
148	#121×C₆₇	—	2	2	no	—
149	#121×C₆₇	—	2	2	no	—
150	#121×C₆₇	—	2	4	no	—
151	#121×C₆₇	—	2	1	no	—
152	#121×C₆₇	—	2	1	no	—
153	#121×C₆₇	—	2	2	no	—
154	#121×C₆₇	—	2	4	no	—
155	#121×C₆₇	D₄	1	2	yes	—
156	#121×C₆₇	D₄	1	2	yes	—
157	#121×C₆₇	C₂³	1	4	yes	—
158	#121×C₆₇	C₂³	1	4	yes	—
159	#120×C₆₇	—	2	4	no	—
160	#120×C₆₇	—	2	4	no	—
161	C₄×Q₈×C₆₇	—	2	2	no	—
162	C₄×Q₈×C₆₇	—	2	2	no	—
163	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
164	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
165	C₄×D₄×C₆₇	—	2	2	no	—
166	C₄×D₄×C₆₇	—	2	4	no	—
167	C₄×D₄×C₆₇	—	2	2	no	—
168	C₄×D₄×C₆₇	—	2	1	no	—
169	C₄×D₄×C₆₇	—	2	1	no	—
170	C₄×D₄×C₆₇	—	2	1	no	—
171	C₄×D₄×C₆₇	—	2	1	no	—
172	C₄×D₄×C₆₇	—	2	1	no	—
173	C₄×D₄×C₆₇	—	2	1	no	—
174	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
175	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₆₇	C₂³	1	2	yes	—
177	C₄×D₄×C₆₇	C₂³	1	2	yes	—
178	C₄×D₄×C₆₇	C₂³	1	2	yes	—
179	C₄×D₄×C₆₇	C₂³	1	2	yes	—
180	#117×C₆₇	—	2	2	no	—
181	#117×C₆₇	—	2	1	no	—
182	#117×C₆₇	C₂³	1	4	yes	—
183	#117×C₆₇	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
185	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
186	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
187	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
190	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
191	C₂×C₄²×C₆₇	—	2	1	no	—
192	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
193	#107×C₆₇	C₂³	1	4	yes	—
194	#107×C₆₇	C₂³	1	4	yes	—
195	#107×C₆₇	C₂³	1	2	yes	—
196	#106×C₆₇	C₂³	1	2	yes	—
197	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
198	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
199	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
200	#103×C₆₇	C₂³	1	4	yes	—
201	#103×C₆₇	C₂³	1	2	yes	—
202	#103×C₆₇	C₂³	1	2	yes	—
203	#103×C₆₇	C₂³	1	2	yes	—
204	#103×C₆₇	C₂³	1	4	yes	—
205	#102×C₆₇	C₂³	1	4	yes	—
206	#102×C₆₇	C₂³	1	4	yes	—
207	#102×C₆₇	C₂³	1	4	yes	—
208	#102×C₆₇	C₂³	1	2	yes	—
209	#102×C₆₇	C₂³	1	2	yes	—
210	#102×C₆₇	C₂³	1	2	yes	—
211	#102×C₆₇	C₂³	1	4	yes	—
212	#102×C₆₇	C₂³	1	2	yes	—
213	#102×C₆₇	C₂³	1	2	yes	—
214	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
215	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
216	#97×C₆₇	C₂³	1	2	yes	—
217	C₄×C₈×C₆₇	C₂³	1	2	yes	—
218	C₂⁴×C₆₇	—	2	1	no	—
219	C₂⁴×C₆₇	—	2	4	no	—
220	#41×C₆₇	—	2	4	no	—
221	#41×C₆₇	—	2	4	no	—
222	#41×C₆₇	—	2	8	no	—
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	—	4	4	no	—
228	#41×C₆₇	—	4	8	no	—
229	#41×C₆₇	—	8	4	no	—
230	C₂×Q₈×C₆₇	—	2	2	no	—
231	C₂×Q₈×C₆₇	—	2	2	no	—
232	C₂×Q₈×C₆₇	—	8	2	no	—
233	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
234	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
235	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
236	C₂×D₄×C₆₇	—	2	8	no	—
237	C₂×D₄×C₆₇	—	2	1	no	—
238	C₂×D₄×C₆₇	—	2	4	no	—
239	C₂×D₄×C₆₇	—	2	2	no	—
240	C₂×D₄×C₆₇	—	2	4	no	—
241	C₂×D₄×C₆₇	—	2	4	no	—
242	C₂×D₄×C₆₇	—	2	1	no	—
243	C₂×D₄×C₆₇	—	2	1	no	—
244	C₂×D₄×C₆₇	—	2	4	no	—
245	C₂×D₄×C₆₇	—	2	1	no	—
246	C₂×D₄×C₆₇	—	2	2	no	—
247	C₂×D₄×C₆₇	—	4	4	no	—
248	C₂×D₄×C₆₇	—	4	8	no	—
249	C₂×D₄×C₆₇	—	4	16	no	—
250	C₂×D₄×C₆₇	—	8	4	no	—
251	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
252	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
253	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
254	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
255	C₂×D₄×C₆₇	#41	1	4	yes	complemented
256	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
257	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
258	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₆₇	—	2	1	no	—
260	C₂²×C₄×C₆₇	—	2	2	no	—
261	C₂²×C₄×C₆₇	—	2	4	no	—
262	C₂²×C₄×C₆₇	—	2	1	no	—
263	C₂²×C₄×C₆₇	—	2	1	no	—
264	C₂²×C₄×C₆₇	—	2	1	no	—
265	C₂²×C₄×C₆₇	—	2	4	no	—
266	C₂²×C₄×C₆₇	—	2	2	no	—
267	C₂²×C₄×C₆₇	—	2	2	no	—
268	C₂²×C₄×C₆₇	—	2	2	no	—
269	C₂²×C₄×C₆₇	—	8	2	no	—
270	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
273	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
274	Q₁₆×C₆₇	—	4	2	no	—
275	SD₁₆×C₆₇	—	2	4	no	—
276	SD₁₆×C₆₇	—	4	2	no	—
277	SD₁₆×C₆₇	—	4	2	no	—
278	D₈×C₆₇	—	2	4	no	—
279	D₈×C₆₇	—	4	2	no	—
280	M₁₆×C₆₇	—	2	2	no	—
281	M₁₆×C₆₇	—	2	2	no	—
282	M₁₆×C₆₇	—	4	4	no	—
283	C₂×C₈×C₆₇	—	2	4	no	—
284	C₂×C₈×C₆₇	—	4	4	no	—
285	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
286	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
287	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
288	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
289	C₄⋊C₄×C₆₇	—	2	1	no	—
290	C₄⋊C₄×C₆₇	—	2	2	no	—
291	C₄⋊C₄×C₆₇	—	2	4	no	—
292	C₄⋊C₄×C₆₇	—	2	2	no	—
293	C₄⋊C₄×C₆₇	—	2	1	no	—
294	C₄⋊C₄×C₆₇	—	2	2	no	—
295	C₄⋊C₄×C₆₇	—	2	4	no	—
296	C₄⋊C₄×C₆₇	—	2	1	no	—
297	C₄⋊C₄×C₆₇	—	2	1	no	—
298	C₄⋊C₄×C₆₇	—	2	1	no	—
299	C₄⋊C₄×C₆₇	—	2	4	no	—
300	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
301	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
302	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
303	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
304	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
305	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
306	C₂²⋊C₄×C₆₇	—	2	4	no	—
307	C₂²⋊C₄×C₆₇	—	2	1	no	—
308	C₂²⋊C₄×C₆₇	—	2	4	no	—
309	C₂²⋊C₄×C₆₇	—	2	4	no	—
310	C₂²⋊C₄×C₆₇	—	2	2	no	—
311	C₂²⋊C₄×C₆₇	—	2	2	no	—
312	C₂²⋊C₄×C₆₇	—	2	2	no	—
313	C₂²⋊C₄×C₆₇	—	2	4	no	—
314	C₂²⋊C₄×C₆₇	—	2	1	no	—
315	C₂²⋊C₄×C₆₇	—	2	1	no	—
316	C₂²⋊C₄×C₆₇	—	2	4	no	—
317	C₂²⋊C₄×C₆₇	—	2	2	no	—
318	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
319	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
320	C₄²×C₆₇	—	2	1	no	—
321	C₄²×C₆₇	—	2	1	no	—
322	C₄²×C₆₇	—	2	1	no	—
323	C₄²×C₆₇	—	2	4	no	—
324	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
325	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
326	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
327	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
328	C₂³×C₆₇	—	2	2	no	—
329	C₂³×C₆₇	—	2	4	no	—
330	C₂³×C₆₇	—	2	1	no	—
331	C₂³×C₆₇	—	2	2	no	—
332	C₂³×C₆₇	—	4	8	no	—
333	C₂³×C₆₇	—	8	1	no	—
334	C₂³×C₆₇	—	8	1	no	—
335	C₂³×C₆₇	—	8	4	no	—
336	C₂³×C₆₇	—	8	4	no	—
337	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
338	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
339	Q₈×C₆₇	—	2	4	no	—
340	Q₈×C₆₇	—	2	1	no	—
341	Q₈×C₆₇	—	2	2	no	—
342	Q₈×C₆₇	—	2	1	no	—
343	Q₈×C₆₇	—	2	2	no	—
344	Q₈×C₆₇	—	4	4	no	—
345	Q₈×C₆₇	—	8	2	no	—
346	D₄×C₆₇	—	2	8	no	—
347	D₄×C₆₇	—	2	4	no	—
348	D₄×C₆₇	—	2	4	no	—
349	D₄×C₆₇	—	2	4	no	—
350	D₄×C₆₇	—	2	1	no	—
351	D₄×C₆₇	—	2	2	no	—
352	D₄×C₆₇	—	2	2	no	—
353	D₄×C₆₇	—	2	1	no	—
354	D₄×C₆₇	—	2	2	no	—
355	D₄×C₆₇	—	4	2	no	—
356	D₄×C₆₇	—	4	8	no	—
357	D₄×C₆₇	—	4	8	no	—
358	D₄×C₆₇	—	4	4	no	—
359	D₄×C₆₇	—	4	2	no	—
360	D₄×C₆₇	—	4	2	no	—
361	D₄×C₆₇	—	8	1	no	—
362	D₄×C₆₇	—	8	4	no	—
363	D₄×C₆₇	—	8	4	no	—
364	D₄×C₆₇	C₂×#41	1	4	yes	—
365	C₂×C₄×C₆₇	—	2	2	no	—
366	C₂×C₄×C₆₇	—	2	4	no	—
367	C₂×C₄×C₆₇	—	2	4	no	—
368	C₂×C₄×C₆₇	—	2	1	no	—
369	C₂×C₄×C₆₇	—	2	1	no	—
370	C₂×C₄×C₆₇	—	2	1	no	—
371	C₂×C₄×C₆₇	—	2	4	no	—
372	C₂×C₄×C₆₇	—	2	2	no	—
373	C₂×C₄×C₆₇	—	2	2	no	—
374	C₂×C₄×C₆₇	—	4	1	no	—
375	C₂×C₄×C₆₇	—	4	8	no	—
376	C₂×C₄×C₆₇	—	4	2	no	—
377	C₂×C₄×C₆₇	—	4	4	no	—
378	C₂×C₄×C₆₇	—	4	2	no	—
379	C₂×C₄×C₆₇	—	4	4	no	—
380	C₂×C₄×C₆₇	—	4	2	no	—
381	C₂×C₄×C₆₇	—	8	2	no	—
382	C₂×C₄×C₆₇	—	8	1	no	—
383	C₂×C₄×C₆₇	—	8	2	no	—
384	C₂×C₄×C₆₇	—	8	4	no	—
385	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
387	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
392	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
393	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
394	C₈×C₆₇	—	2	2	no	—
395	C₈×C₆₇	—	2	2	no	—
396	C₈×C₆₇	—	2	2	no	—
397	C₈×C₆₇	—	2	2	no	—
398	C₂²×C₆₇	—	2	1	no	—
399	C₂²×C₆₇	—	2	1	no	—
400	C₂²×C₆₇	—	2	4	no	—
401	C₂²×C₆₇	—	2	4	no	—
402	C₂²×C₆₇	—	2	4	no	—
403	C₂²×C₆₇	—	2	4	no	—
404	C₂²×C₆₇	—	4	2	no	—
405	C₂²×C₆₇	—	4	2	no	—
406	C₂²×C₆₇	—	4	1	no	—
407	C₂²×C₆₇	—	4	2	no	—
408	C₂²×C₆₇	—	4	2	no	—
409	C₂²×C₆₇	—	4	1	no	—
410	C₂²×C₆₇	—	4	1	no	—
411	C₂²×C₆₇	—	4	2	no	—
412	C₂²×C₆₇	—	8	4	no	—
413	C₂²×C₆₇	—	16	8	no	—
414	C₂²×C₆₇	#546	1	2	yes	—
415	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
416	C₄×C₆₇	—	2	1	no	—
417	C₄×C₆₇	—	2	1	no	—
418	C₄×C₆₇	—	2	4	no	—
419	C₄×C₆₇	—	2	1	no	—
420	C₄×C₆₇	—	4	1	no	—
421	C₄×C₆₇	—	4	2	no	—
422	C₄×C₆₇	—	4	1	no	—
423	C₄×C₆₇	—	4	1	no	—
424	C₄×C₆₇	—	4	2	no	—
425	C₄×C₆₇	—	4	4	no	—
426	C₄×C₆₇	#546	1	2	yes	—
427	C₄×C₆₇	#576	1	2	yes	—
428	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
429	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
430	#61199	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
431	C₂×C₆₇	—	2	2	no	—
432	C₂×C₆₇	—	4	4	no	—
433	C₂×C₆₇	—	4	4	no	—
434	C₂×C₆₇	—	8	1	no	—
435	C₂×C₆₇	—	8	2	no	—
436	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
437	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
438	C₂×C₆₇	#3586	1	1	yes	characteristic
439	#3511	C₂×C₆₇	1	1	yes	characteristic, complemented
440	#3496	C₂×C₆₇	1	1	yes	characteristic, complemented
441	#3330	C₂×C₆₇	1	2	yes	complemented
442	#3324	C₂×C₆₇	1	2	yes	complemented
443	#3319	C₂×C₆₇	1	4	yes	complemented
444	#3314	C₂×C₆₇	1	4	yes	complemented
445	#3302	C₂×C₆₇	1	2	yes	complemented
446	#3294	C₂×C₆₇	1	2	yes	complemented
447	#3141	C₂×C₆₇	1	1	yes	characteristic, complemented
448	#3098	C₂×C₆₇	1	2	yes	complemented
449	C₂×#474	C₂×C₆₇	1	1	yes	characteristic, complemented
450	#3061	C₂×C₆₇	1	2	yes	complemented
451	#3035	C₂×C₆₇	1	1	yes	characteristic, complemented
452	#3012	C₂×C₆₇	1	2	yes	complemented
453	C₄×AGL(1,ℤ/8)	C₂×C₆₇	1	1	yes	characteristic, complemented
454	#2935	C₂×C₆₇	1	1	yes	characteristic, complemented
455	#2897	C₂×C₆₇	1	2	yes	complemented
456	C₆₇	#61199	1	1	yes	characteristic, direct product factor, Sylow
457	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	—
458	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
459	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
460	C₂×#131	C₂²×C₆₇	1	2	yes	complemented
461	#556	C₂²×C₆₇	1	2	yes	complemented
462	#555	C₂²×C₆₇	1	2	yes	complemented
463	#554	C₂²×C₆₇	1	2	yes	complemented
464	#553	—	2	2	no	—
465	#548	—	2	2	no	—
466	#547	—	2	1	no	—
467	#547	C₂²×C₆₇	1	2	yes	—
468	#547	C₂²×C₆₇	1	2	yes	complemented
469	#546	—	2	2	no	—
470	#546	C₂²×C₆₇	1	4	yes	—
471	D₄²	—	2	1	no	—
472	D₄²	C₂²×C₆₇	1	2	yes	—
473	#542	—	2	2	no	—
474	#537	C₂²×C₆₇	1	2	yes	—
475	#537	C₂²×C₆₇	1	2	yes	complemented
476	#534	—	2	2	no	—
477	#533	—	2	1	no	—
478	#532	—	2	1	no	—
479	#532	C₂²×C₆₇	1	1	yes	characteristic
480	#532	C₂²×C₆₇	1	1	yes	characteristic
481	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
482	C₂×#121	—	2	2	no	—
483	#520	C₂²×C₆₇	1	2	yes	complemented
484	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
485	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
486	#489	C₂²×C₆₇	1	4	yes	complemented
487	#487	C₂²×C₆₇	1	2	yes	complemented
488	#486	C₂²×C₆₇	1	2	yes	complemented
489	#485	C₂²×C₆₇	1	4	yes	complemented
490	#484	C₂²×C₆₇	1	4	yes	complemented
491	#482	C₂²×C₆₇	1	4	yes	complemented
492	#480	C₂²×C₆₇	1	4	yes	complemented
493	#474	C₂²×C₆₇	1	2	yes	complemented
494	#474	C₂²×C₆₇	1	2	yes	complemented
495	#474	C₂²×C₆₇	1	4	yes	complemented
496	#468	C₂²×C₆₇	1	4	yes	complemented
497	#468	C₂²×C₆₇	1	4	yes	complemented
498	#467	C₂²×C₆₇	1	4	yes	complemented
499	#466	C₂²×C₆₇	1	4	yes	complemented
500	#464	C₂²×C₆₇	1	2	yes	complemented
501	#463	C₂²×C₆₇	1	2	yes	complemented
502	#462	C₂²×C₆₇	1	1	yes	characteristic, complemented
503	#461	C₂²×C₆₇	1	1	yes	characteristic, complemented
504	#460	C₂²×C₆₇	1	1	yes	characteristic, complemented
505	#459	C₂²×C₆₇	1	1	yes	characteristic, complemented
506	#452	C₂²×C₆₇	1	4	yes	complemented
507	#450	C₂²×C₆₇	1	4	yes	complemented
508	#449	C₂²×C₆₇	1	4	yes	complemented
509	#447	C₂²×C₆₇	1	4	yes	complemented
510	#442	C₂²×C₆₇	1	2	yes	complemented
511	#440	C₂²×C₆₇	1	2	yes	complemented
512	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
513	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
514	#436	C₂²×C₆₇	1	2	yes	complemented
515	#435	C₂²×C₆₇	1	4	yes	complemented
516	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
517	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
518	C₂×#107	C₂²×C₆₇	1	2	yes	complemented
519	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
520	#418	C₂²×C₆₇	1	1	yes	characteristic
521	#418	C₂²×C₆₇	1	4	yes	complemented
522	#417	C₂²×C₆₇	1	4	yes	complemented
523	#417	C₂²×C₆₇	1	2	yes	complemented
524	#417	C₂²×C₆₇	1	2	yes	complemented
525	#417	C₂²×C₆₇	1	1	yes	characteristic, complemented
526	#416	C₂²×C₆₇	1	2	yes	complemented
527	#416	C₂²×C₆₇	1	4	yes	complemented
528	C₂×#102	C₂²×C₆₇	1	2	yes	—
529	C₂×#102	C₂²×C₆₇	1	4	yes	complemented
530	#408	C₂²×C₆₇	1	2	yes	complemented
531	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
532	H(5,𝔽₂)	—	2	8	no	—
533	H(5,𝔽₂)	—	4	4	no	—
534	C₂×#41	—	2	2	no	—
535	C₂×#41	—	2	2	no	—
536	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
537	C₂×#41	C₂³×C₆₇	1	2	yes	—
538	C₂×#41	C₂³×C₆₇	1	4	yes	—
539	C₂×#41	C₂³×C₆₇	1	2	yes	—
540	C₂²×Q₈	—	2	1	no	—
541	C₂²×D₄	—	2	4	no	—
542	C₂²×D₄	—	2	2	no	—
543	C₂²×D₄	—	2	2	no	—
544	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
545	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
546	C₂³×C₄	—	2	1	no	—
547	AGL(1,ℤ/8)	—	2	4	no	—
548	#135	—	4	4	no	—
549	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
550	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
551	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
552	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
553	C₂×D₈	C₂³×C₆₇	1	2	yes	—
554	C₂×D₈	C₂³×C₆₇	1	2	yes	—
555	#131	—	4	4	no	—
556	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
557	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
558	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
559	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
560	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
561	C₄⋊Q₈	—	2	1	no	—
562	C₄⋊Q₈	—	2	1	no	—
563	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
564	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
565	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
566	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
567	#127	D₄×C₆₇	1	1	yes	characteristic
568	#127	C₂³×C₆₇	1	1	yes	characteristic
569	#126	—	2	4	no	—
570	#125	—	2	2	no	—
571	#124	—	2	2	no	—
572	#124	—	2	4	no	—
573	#124	D₄×C₆₇	1	2	yes	—
574	#124	C₂³×C₆₇	1	2	yes	—
575	#123	—	2	4	no	—
576	#123	—	2	4	no	—
577	#123	—	2	4	no	—
578	C₂²⋊Q₈	—	2	2	no	—
579	C₂²⋊Q₈	—	2	2	no	—
580	C₂²⋊Q₈	—	2	2	no	—
581	C₂²⋊Q₈	—	2	4	no	—
582	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
583	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
584	#121	—	2	4	no	—
585	#121	—	2	2	no	—
586	#121	—	2	2	no	—
587	#121	—	2	2	no	—
588	#121	—	2	2	no	—
589	#121	—	2	4	no	—
590	#121	—	2	1	no	—
591	#121	—	2	1	no	—
592	#121	—	2	2	no	—
593	#121	—	2	4	no	—
594	#121	D₄×C₆₇	1	2	yes	—
595	#121	D₄×C₆₇	1	2	yes	—
596	#121	C₂³×C₆₇	1	4	yes	—
597	#121	C₂³×C₆₇	1	4	yes	—
598	#120	—	2	4	no	—
599	#120	—	2	4	no	—
600	C₄×Q₈	—	2	2	no	—
601	C₄×Q₈	—	2	2	no	—
602	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
603	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	—	2	4	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	—	2	1	no	—
613	C₄×D₄	C₂³×C₆₇	1	2	yes	—
614	C₄×D₄	C₂³×C₆₇	1	2	yes	—
615	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
616	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
617	C₄×D₄	C₂³×C₆₇	1	2	yes	—
618	C₄×D₄	C₂³×C₆₇	1	2	yes	—
619	#117	—	2	2	no	—
620	#117	—	2	1	no	—
621	#117	C₂³×C₆₇	1	1	yes	characteristic
622	#117	C₂³×C₆₇	1	4	yes	—
623	C₂×C₄⋊C₄	—	2	1	no	—
624	C₂×C₄⋊C₄	—	2	2	no	—
625	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
627	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
628	C₂×C₂²⋊C₄	—	2	1	no	—
629	C₂×C₂²⋊C₄	—	2	4	no	—
630	C₂×C₄²	—	2	1	no	—
631	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
632	#107	C₂³×C₆₇	1	4	yes	—
633	#107	C₂³×C₆₇	1	4	yes	—
634	#107	C₂³×C₆₇	1	2	yes	—
635	#106	C₂³×C₆₇	1	2	yes	—
636	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
637	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
638	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
639	#103	C₂³×C₆₇	1	2	yes	—
640	#103	C₂³×C₆₇	1	2	yes	—
641	#103	C₂³×C₆₇	1	4	yes	—
642	#103	C₂³×C₆₇	1	2	yes	—
643	#103	C₂³×C₆₇	1	4	yes	—
644	#102	C₂³×C₆₇	1	4	yes	—
645	#102	C₂³×C₆₇	1	4	yes	—
646	#102	C₂³×C₆₇	1	2	yes	—
647	#102	C₂³×C₆₇	1	2	yes	—
648	#102	C₂³×C₆₇	1	4	yes	—
649	#102	C₂³×C₆₇	1	2	yes	—
650	#102	C₂³×C₆₇	1	2	yes	—
651	#102	C₂³×C₆₇	1	2	yes	—
652	#102	C₂³×C₆₇	1	4	yes	—
653	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
654	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
655	#97	C₂³×C₆₇	1	2	yes	—
656	C₄×C₈	C₂³×C₆₇	1	2	yes	—
657	C₂⁴	—	2	1	no	—
658	C₂⁴	—	2	4	no	—
659	#41	—	2	4	no	—
660	#41	—	2	4	no	—
661	#41	—	2	8	no	—
662	#41	—	2	2	no	—
663	#41	—	2	4	no	—
664	#41	—	2	2	no	—
665	#41	—	2	4	no	—
666	#41	—	4	4	no	—
667	#41	—	4	8	no	—
668	#41	—	8	4	no	—
669	C₂×Q₈	—	2	2	no	—
670	C₂×Q₈	—	2	2	no	—
671	C₂×Q₈	—	8	2	no	—
672	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
673	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
674	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
675	C₂×D₄	—	2	8	no	—
676	C₂×D₄	—	2	1	no	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	2	4	no	—
680	C₂×D₄	—	2	4	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	1	no	—
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	1	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	4	4	no	—
687	C₂×D₄	—	4	8	no	—
688	C₂×D₄	—	4	16	no	—
689	C₂×D₄	—	8	4	no	—
690	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
691	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
692	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
693	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
694	C₂×D₄	#41×C₆₇	1	4	yes	complemented
695	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
696	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
697	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
698	C₂²×C₄	—	2	1	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	4	no	—
701	C₂²×C₄	—	2	1	no	—
702	C₂²×C₄	—	2	1	no	—
703	C₂²×C₄	—	2	1	no	—
704	C₂²×C₄	—	2	4	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	8	2	no	—
709	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
710	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
712	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
713	Q₁₆	—	4	2	no	—
714	SD₁₆	—	2	4	no	—
715	SD₁₆	—	4	2	no	—
716	SD₁₆	—	4	2	no	—
717	D₈	—	2	4	no	—
718	D₈	—	4	2	no	—
719	M₁₆	—	2	2	no	—
720	M₁₆	—	2	2	no	—
721	M₁₆	—	4	4	no	—
722	C₂×C₈	—	2	4	no	—
723	C₂×C₈	—	4	4	no	—
724	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
725	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
726	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
727	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	4	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	4	no	—
735	C₄⋊C₄	—	2	1	no	—
736	C₄⋊C₄	—	2	1	no	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
740	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
741	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
742	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
743	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
744	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	1	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	1	no	—
754	C₂²⋊C₄	—	2	1	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
758	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
759	C₄²	—	2	1	no	—
760	C₄²	—	2	1	no	—
761	C₄²	—	2	1	no	—
762	C₄²	—	2	4	no	—
763	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
764	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
765	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
766	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
767	C₂³	—	2	2	no	—
768	C₂³	—	2	4	no	—
769	C₂³	—	2	1	no	—
770	C₂³	—	2	2	no	—
771	C₂³	—	4	8	no	—
772	C₂³	—	8	1	no	—
773	C₂³	—	8	1	no	—
774	C₂³	—	8	4	no	—
775	C₂³	—	8	4	no	—
776	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
777	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
778	Q₈	—	2	4	no	—
779	Q₈	—	2	1	no	—
780	Q₈	—	2	2	no	—
781	Q₈	—	2	1	no	—
782	Q₈	—	2	2	no	—
783	Q₈	—	4	4	no	—
784	Q₈	—	8	2	no	—
785	D₄	—	2	8	no	—
786	D₄	—	2	4	no	—
787	D₄	—	2	4	no	—
788	D₄	—	2	4	no	—
789	D₄	—	2	1	no	—
790	D₄	—	2	2	no	—
791	D₄	—	2	2	no	—
792	D₄	—	2	1	no	—
793	D₄	—	2	2	no	—
794	D₄	—	4	2	no	—
795	D₄	—	4	8	no	—
796	D₄	—	4	8	no	—
797	D₄	—	4	4	no	—
798	D₄	—	4	2	no	—
799	D₄	—	4	2	no	—
800	D₄	—	8	1	no	—
801	D₄	—	8	4	no	—
802	D₄	—	8	4	no	—
803	D₄	C₂×#41×C₆₇	1	4	yes	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	4	no	—
806	C₂×C₄	—	2	4	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	4	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	4	1	no	—
814	C₂×C₄	—	4	8	no	—
815	C₂×C₄	—	4	2	no	—
816	C₂×C₄	—	4	4	no	—
817	C₂×C₄	—	4	2	no	—
818	C₂×C₄	—	4	4	no	—
819	C₂×C₄	—	4	2	no	—
820	C₂×C₄	—	8	2	no	—
821	C₂×C₄	—	8	1	no	—
822	C₂×C₄	—	8	2	no	—
823	C₂×C₄	—	8	4	no	—
824	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
825	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
826	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
827	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
828	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
829	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
830	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
831	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
832	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
833	C₈	—	2	2	no	—
834	C₈	—	2	2	no	—
835	C₈	—	2	2	no	—
836	C₈	—	2	2	no	—
837	C₂²	—	2	1	no	—
838	C₂²	—	2	1	no	—
839	C₂²	—	2	4	no	—
840	C₂²	—	2	4	no	—
841	C₂²	—	2	4	no	—
842	C₂²	—	2	4	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	4	1	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	4	1	no	—
851	C₂²	—	8	4	no	—
852	C₂²	—	16	8	no	—
853	C₂²	#546×C₆₇	1	2	yes	—
854	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
855	C₄	—	2	1	no	—
856	C₄	—	2	1	no	—
857	C₄	—	2	1	no	—
858	C₄	—	2	4	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	2	no	—
861	C₄	—	4	4	no	—
862	C₄	—	4	1	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	1	no	—
865	C₄	#546×C₆₇	1	2	yes	—
866	C₄	#576×C₆₇	1	2	yes	—
867	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
868	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
869	C₂	—	2	2	no	—
870	C₂	—	4	4	no	—
871	C₂	—	4	4	no	—
872	C₂	—	8	2	no	—
873	C₂	—	8	1	no	—
874	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
875	C₂	C₂×#576×C₆₇	1	1	yes	characteristic
876	C₂	C₆₇×#3586	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. C₆₇×#3511	C₂	semidirect
2. C₆₇×#3496	C₂	semidirect
3. C₆₇×#3330	C₂	semidirect
4. C₆₇×#3324	C₂	semidirect
5. C₆₇×#3319	C₂	semidirect
6. C₆₇×#3314	C₂	semidirect
7. C₆₇×#3302	C₂	semidirect
8. C₆₇×#3294	C₂	semidirect
9. C₆₇×#3141	C₂	semidirect
10. C₆₇×#3098	C₂	semidirect
11. C₂×#474×C₆₇	C₂	semidirect
12. C₆₇×#3061	C₂	semidirect
13. C₆₇×#3035	C₂	semidirect
14. C₆₇×#3012	C₂	semidirect
15. C₄×AGL(1,ℤ/8)×C₆₇	C₂	semidirect
16. C₆₇×#2935	C₂	semidirect
17. C₆₇×#2897	C₂	semidirect
20. C₂×#135×C₆₇	C₂²	semidirect
21. C₂×#131×C₆₇	C₂²	semidirect
22. #556×C₆₇	C₂²	semidirect
23. #555×C₆₇	C₂²	semidirect
24. #554×C₆₇	C₂²	semidirect
29. #547×C₆₇	C₂²	semidirect
36. #537×C₆₇	C₂²	semidirect
42. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
44. #520×C₆₇	C₂²	semidirect
45. C₄×#41×C₆₇	C₂²	semidirect
47. #489×C₆₇	C₂²	semidirect
48. #487×C₆₇	C₂²	semidirect
49. #486×C₆₇	C₂²	semidirect
50. #485×C₆₇	C₂²	semidirect
51. #484×C₆₇	C₂²	semidirect
52. #482×C₆₇	C₂²	semidirect
53. #480×C₆₇	C₂²	semidirect
54. #474×C₆₇	C₂²	semidirect
55. #474×C₆₇	C₂²	semidirect
56. #474×C₆₇	C₂²	semidirect
57. #468×C₆₇	C₂²	semidirect
58. #468×C₆₇	C₂²	semidirect
59. #467×C₆₇	C₂²	semidirect
60. #466×C₆₇	C₂²	semidirect
61. #464×C₆₇	C₂²	semidirect
62. #463×C₆₇	C₂²	semidirect
63. #462×C₆₇	C₂²	semidirect
64. #461×C₆₇	C₂²	semidirect
65. #460×C₆₇	C₂²	semidirect
66. #459×C₆₇	C₂²	semidirect
67. #452×C₆₇	C₂²	semidirect
68. #450×C₆₇	C₂²	semidirect
69. #449×C₆₇	C₂²	semidirect
70. #447×C₆₇	C₂²	semidirect
71. #442×C₆₇	C₂²	semidirect
72. #440×C₆₇	C₂²	semidirect
73. C₄×SD₁₆×C₆₇	C₂²	semidirect
74. C₄×D₈×C₆₇	C₂²	semidirect
75. #436×C₆₇	C₂²	semidirect
76. #435×C₆₇	C₂²	semidirect
77. C₈×D₄×C₆₇	C₂²	semidirect
78. #428×C₆₇	C₂²	semidirect
79. C₂×#107×C₆₇	C₂²	semidirect
80. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
82. #418×C₆₇	C₂²	semidirect
83. #417×C₆₇	C₂²	semidirect
84. #417×C₆₇	C₂²	semidirect
85. #417×C₆₇	C₂²	semidirect
86. #417×C₆₇	C₂²	semidirect
87. #416×C₆₇	C₂²	semidirect
88. #416×C₆₇	C₂²	semidirect
90. C₂×#102×C₆₇	C₂²	semidirect
91. #408×C₆₇	C₂²	semidirect
92. C₄×M₁₆×C₆₇	C₂²	semidirect
255. C₂×D₄×C₆₇	#41	semidirect
430. #61199	C₆₇	direct (N × H)
439. #3511	C₂×C₆₇	semidirect
440. #3496	C₂×C₆₇	semidirect
441. #3330	C₂×C₆₇	semidirect
442. #3324	C₂×C₆₇	semidirect
443. #3319	C₂×C₆₇	semidirect
444. #3314	C₂×C₆₇	semidirect
445. #3302	C₂×C₆₇	semidirect
446. #3294	C₂×C₆₇	semidirect
447. #3141	C₂×C₆₇	semidirect
448. #3098	C₂×C₆₇	semidirect
449. C₂×#474	C₂×C₆₇	semidirect
450. #3061	C₂×C₆₇	semidirect
451. #3035	C₂×C₆₇	semidirect
452. #3012	C₂×C₆₇	semidirect
453. C₄×AGL(1,ℤ/8)	C₂×C₆₇	semidirect
454. #2935	C₂×C₆₇	semidirect
455. #2897	C₂×C₆₇	semidirect
456. C₆₇	#61199	direct (N × H)
459. C₂×#135	C₂²×C₆₇	semidirect
460. C₂×#131	C₂²×C₆₇	semidirect
461. #556	C₂²×C₆₇	semidirect
462. #555	C₂²×C₆₇	semidirect
463. #554	C₂²×C₆₇	semidirect
468. #547	C₂²×C₆₇	semidirect
475. #537	C₂²×C₆₇	semidirect
481. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
483. #520	C₂²×C₆₇	semidirect
484. C₄×#41	C₂²×C₆₇	semidirect
486. #489	C₂²×C₆₇	semidirect
487. #487	C₂²×C₆₇	semidirect
488. #486	C₂²×C₆₇	semidirect
489. #485	C₂²×C₆₇	semidirect
490. #484	C₂²×C₆₇	semidirect
491. #482	C₂²×C₆₇	semidirect
492. #480	C₂²×C₆₇	semidirect
493. #474	C₂²×C₆₇	semidirect
494. #474	C₂²×C₆₇	semidirect
495. #474	C₂²×C₆₇	semidirect
496. #468	C₂²×C₆₇	semidirect
497. #468	C₂²×C₆₇	semidirect
498. #467	C₂²×C₆₇	semidirect
499. #466	C₂²×C₆₇	semidirect
500. #464	C₂²×C₆₇	semidirect
501. #463	C₂²×C₆₇	semidirect
502. #462	C₂²×C₆₇	semidirect
503. #461	C₂²×C₆₇	semidirect
504. #460	C₂²×C₆₇	semidirect
505. #459	C₂²×C₆₇	semidirect
506. #452	C₂²×C₆₇	semidirect
507. #450	C₂²×C₆₇	semidirect
508. #449	C₂²×C₆₇	semidirect
509. #447	C₂²×C₆₇	semidirect
510. #442	C₂²×C₆₇	semidirect
511. #440	C₂²×C₆₇	semidirect
512. C₄×SD₁₆	C₂²×C₆₇	semidirect
513. C₄×D₈	C₂²×C₆₇	semidirect
514. #436	C₂²×C₆₇	semidirect
515. #435	C₂²×C₆₇	semidirect
516. C₈×D₄	C₂²×C₆₇	semidirect
517. #428	C₂²×C₆₇	semidirect
518. C₂×#107	C₂²×C₆₇	semidirect
519. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
521. #418	C₂²×C₆₇	semidirect
522. #417	C₂²×C₆₇	semidirect
523. #417	C₂²×C₆₇	semidirect
524. #417	C₂²×C₆₇	semidirect
525. #417	C₂²×C₆₇	semidirect
526. #416	C₂²×C₆₇	semidirect
527. #416	C₂²×C₆₇	semidirect
529. C₂×#102	C₂²×C₆₇	semidirect
530. #408	C₂²×C₆₇	semidirect
531. C₄×M₁₆	C₂²×C₆₇	semidirect
694. C₂×D₄	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3511	2
C₆₇×#3496	2
C₆₇×#3330	2
C₆₇×#3324	2
C₆₇×#3319	2
C₆₇×#3314	2
C₆₇×#3302	2
C₆₇×#3294	2
C₆₇×#3141	2
C₆₇×#3098	2
C₂×#474×C₆₇	2
C₆₇×#3061	2
C₆₇×#3035	2
C₆₇×#3012	2
C₄×AGL(1,ℤ/8)×C₆₇	2
C₆₇×#2935	2
C₆₇×#2897	2
#61199	67

Subgroups — C67×#61199 #30740450

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61199 #30740450