Subgroups — C₆₇×#61211 #30740462

Order 17152.

2174 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3506	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×#3325	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3322	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3303	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3297	C₂	1	4	yes	maximal, complemented
8	C₆₇×#3294	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3131	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3098	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3077	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3062	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3036	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3008	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×D₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2931	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	2	yes	complemented
20	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×#131×C₆₇	C₂²	1	2	yes	complemented
22	#559×C₆₇	—	2	2	no	—
23	#556×C₆₇	—	2	1	no	—
24	#555×C₆₇	C₂²	1	2	yes	complemented
25	#553×C₆₇	C₂²	1	4	yes	complemented
26	#550×C₆₇	—	2	1	no	—
27	#547×C₆₇	—	2	1	no	—
28	#547×C₆₇	C₂²	1	2	yes	complemented
29	#547×C₆₇	C₂²	1	2	yes	complemented
30	#546×C₆₇	—	2	2	no	—
31	#546×C₆₇	C₂²	1	4	yes	complemented
32	D₄²×C₆₇	—	2	1	no	—
33	D₄²×C₆₇	C₂²	1	2	yes	complemented
34	#538×C₆₇	—	2	2	no	—
35	#537×C₆₇	C₂²	1	2	yes	—
36	#535×C₆₇	C₂²	1	2	yes	complemented
37	#534×C₆₇	—	2	2	no	—
38	#533×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	#532×C₆₇	C₂²	1	1	yes	characteristic
40	#532×C₆₇	C₂²	1	1	yes	characteristic
41	#525×C₆₇	—	2	2	no	—
42	C₂×#121×C₆₇	—	2	2	no	—
43	#520×C₆₇	C₂²	1	2	yes	complemented
44	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	#488×C₆₇	C₂²	1	2	yes	complemented
47	#488×C₆₇	C₂²	1	2	yes	complemented
48	#487×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#487×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	#486×C₆₇	C₂²	1	1	yes	characteristic, complemented
51	#486×C₆₇	C₂²	1	1	yes	characteristic, complemented
52	#485×C₆₇	C₂²	1	4	yes	complemented
53	#484×C₆₇	C₂²	1	4	yes	complemented
54	#482×C₆₇	C₂²	1	4	yes	complemented
55	#480×C₆₇	C₂²	1	4	yes	complemented
56	#478×C₆₇	C₂²	1	4	yes	complemented
57	#476×C₆₇	C₂²	1	2	yes	complemented
58	#474×C₆₇	C₂²	1	2	yes	complemented
59	#469×C₆₇	C₂²	1	4	yes	complemented
60	#468×C₆₇	C₂²	1	4	yes	complemented
61	#466×C₆₇	C₂²	1	4	yes	complemented
62	#465×C₆₇	C₂²	1	4	yes	complemented
63	#463×C₆₇	C₂²	1	4	yes	complemented
64	#461×C₆₇	C₂²	1	2	yes	complemented
65	#459×C₆₇	C₂²	1	2	yes	complemented
66	#449×C₆₇	C₂²	1	4	yes	complemented
67	#449×C₆₇	C₂²	1	4	yes	complemented
68	#447×C₆₇	C₂²	1	4	yes	complemented
69	#447×C₆₇	C₂²	1	4	yes	complemented
70	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
71	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
72	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
73	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
74	#436×C₆₇	C₂²	1	2	yes	complemented
75	#436×C₆₇	C₂²	1	2	yes	complemented
76	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
77	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
78	#428×C₆₇	C₂²	1	2	yes	complemented
79	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic, complemented
80	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
81	#418×C₆₇	C₂²	1	2	yes	—
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	#416×C₆₇	C₂²	1	4	yes	complemented
86	#416×C₆₇	C₂²	1	2	yes	complemented
87	#416×C₆₇	C₂²	1	2	yes	complemented
88	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
89	C₂×#102×C₆₇	C₂²	1	4	yes	complemented
90	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	#408×C₆₇	C₂²	1	2	yes	complemented
92	C₂×C₄×C₈×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	2	yes	—
98	C₂×#41×C₆₇	C₂³	1	4	yes	—
99	C₂×#41×C₆₇	C₂³	1	2	yes	—
100	C₂²×D₄×C₆₇	—	2	4	no	—
101	C₂²×D₄×C₆₇	—	2	2	no	—
102	C₂²×D₄×C₆₇	—	2	2	no	—
103	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
104	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
105	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₆₇	—	2	1	no	—
107	C₂³×C₄×C₆₇	—	2	1	no	—
108	AGL(1,ℤ/8)×C₆₇	—	4	4	no	—
109	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
110	C₂×D₈×C₆₇	—	2	4	no	—
111	C₂×D₈×C₆₇	C₂³	1	2	yes	—
112	C₂×D₈×C₆₇	C₂³	1	2	yes	—
113	C₂×D₈×C₆₇	C₂³	1	4	yes	—
114	#131×C₆₇	—	4	4	no	—
115	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
116	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
117	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
118	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
120	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
121	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
122	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
123	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
124	#127×C₆₇	—	2	2	no	—
125	#127×C₆₇	D₄	1	1	yes	characteristic
126	#127×C₆₇	C₂³	1	1	yes	characteristic
127	#126×C₆₇	—	2	4	no	—
128	#125×C₆₇	C₂³	1	2	yes	—
129	#124×C₆₇	—	2	2	no	—
130	#124×C₆₇	—	2	4	no	—
131	#124×C₆₇	D₄	1	2	yes	—
132	#124×C₆₇	C₂³	1	2	yes	—
133	#123×C₆₇	—	2	4	no	—
134	#123×C₆₇	—	2	4	no	—
135	#123×C₆₇	—	2	4	no	—
136	#123×C₆₇	—	2	4	no	—
137	C₂²⋊Q₈×C₆₇	—	2	2	no	—
138	C₂²⋊Q₈×C₆₇	—	2	1	no	—
139	C₂²⋊Q₈×C₆₇	—	2	1	no	—
140	C₂²⋊Q₈×C₆₇	—	2	2	no	—
141	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
142	#121×C₆₇	—	2	4	no	—
143	#121×C₆₇	—	2	2	no	—
144	#121×C₆₇	—	2	2	no	—
145	#121×C₆₇	—	2	2	no	—
146	#121×C₆₇	—	2	4	no	—
147	#121×C₆₇	—	2	1	no	—
148	#121×C₆₇	—	2	1	no	—
149	#121×C₆₇	—	2	2	no	—
150	#121×C₆₇	—	2	4	no	—
151	#121×C₆₇	D₄	1	2	yes	—
152	#121×C₆₇	D₄	1	2	yes	—
153	#121×C₆₇	C₂³	1	4	yes	—
154	#121×C₆₇	C₂³	1	4	yes	—
155	#121×C₆₇	C₂³	1	4	yes	—
156	#120×C₆₇	—	2	4	no	—
157	#120×C₆₇	—	2	4	no	—
158	#120×C₆₇	—	2	4	no	—
159	C₄×Q₈×C₆₇	—	2	2	no	—
160	C₄×Q₈×C₆₇	—	2	1	no	—
161	C₄×Q₈×C₆₇	—	2	1	no	—
162	C₄×D₄×C₆₇	—	2	4	no	—
163	C₄×D₄×C₆₇	—	2	2	no	—
164	C₄×D₄×C₆₇	—	2	4	no	—
165	C₄×D₄×C₆₇	—	2	1	no	—
166	C₄×D₄×C₆₇	—	2	1	no	—
167	C₄×D₄×C₆₇	—	2	1	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	C₂³	1	2	yes	—
172	C₄×D₄×C₆₇	C₂³	1	2	yes	—
173	C₄×D₄×C₆₇	C₂³	1	2	yes	—
174	C₄×D₄×C₆₇	C₂³	1	2	yes	—
175	C₄×D₄×C₆₇	C₂³	1	2	yes	—
176	C₄×D₄×C₆₇	C₂³	1	2	yes	—
177	#117×C₆₇	—	2	2	no	—
178	#117×C₆₇	C₂³	1	4	yes	—
179	#117×C₆₇	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
181	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
182	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
185	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
186	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
187	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
188	#107×C₆₇	C₂³	1	4	yes	—
189	#107×C₆₇	C₂³	1	2	yes	—
190	#107×C₆₇	C₂³	1	2	yes	—
191	#106×C₆₇	C₂³	1	4	yes	—
192	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
193	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
194	#103×C₆₇	C₂³	1	2	yes	—
195	#103×C₆₇	C₂³	1	2	yes	—
196	#103×C₆₇	C₂³	1	4	yes	—
197	#103×C₆₇	C₂³	1	2	yes	—
198	#103×C₆₇	C₂³	1	2	yes	—
199	#102×C₆₇	C₂³	1	4	yes	—
200	#102×C₆₇	C₂³	1	4	yes	—
201	#102×C₆₇	C₂³	1	4	yes	—
202	#102×C₆₇	C₂³	1	2	yes	—
203	#102×C₆₇	C₂³	1	2	yes	—
204	#102×C₆₇	C₂³	1	2	yes	—
205	#102×C₆₇	C₂³	1	2	yes	—
206	#102×C₆₇	C₂³	1	2	yes	—
207	#102×C₆₇	C₂³	1	2	yes	—
208	#102×C₆₇	C₂³	1	2	yes	—
209	#102×C₆₇	C₂³	1	2	yes	—
210	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
211	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
212	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
213	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
214	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
215	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
216	C₂⁴×C₆₇	—	2	1	no	—
217	C₂⁴×C₆₇	—	2	1	no	—
218	C₂⁴×C₆₇	—	2	4	no	—
219	#41×C₆₇	—	2	4	no	—
220	#41×C₆₇	—	2	4	no	—
221	#41×C₆₇	—	2	8	no	—
222	#41×C₆₇	—	2	4	no	—
223	#41×C₆₇	—	2	4	no	—
224	#41×C₆₇	—	4	4	no	—
225	#41×C₆₇	—	4	8	no	—
226	#41×C₆₇	—	8	4	no	—
227	C₂×Q₈×C₆₇	—	2	1	no	—
228	C₂×Q₈×C₆₇	—	2	1	no	—
229	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
230	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
231	C₂×D₄×C₆₇	—	2	8	no	—
232	C₂×D₄×C₆₇	—	2	4	no	—
233	C₂×D₄×C₆₇	—	2	2	no	—
234	C₂×D₄×C₆₇	—	2	4	no	—
235	C₂×D₄×C₆₇	—	2	4	no	—
236	C₂×D₄×C₆₇	—	2	4	no	—
237	C₂×D₄×C₆₇	—	2	1	no	—
238	C₂×D₄×C₆₇	—	2	1	no	—
239	C₂×D₄×C₆₇	—	2	1	no	—
240	C₂×D₄×C₆₇	—	2	4	no	—
241	C₂×D₄×C₆₇	—	2	1	no	—
242	C₂×D₄×C₆₇	—	2	2	no	—
243	C₂×D₄×C₆₇	—	2	2	no	—
244	C₂×D₄×C₆₇	—	2	2	no	—
245	C₂×D₄×C₆₇	—	4	4	no	—
246	C₂×D₄×C₆₇	—	4	8	no	—
247	C₂×D₄×C₆₇	—	4	16	no	—
248	C₂×D₄×C₆₇	—	8	4	no	—
249	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
250	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
251	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
252	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
253	C₂×D₄×C₆₇	#41	1	4	yes	complemented
254	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
255	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
256	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₆₇	—	2	1	no	—
258	C₂²×C₄×C₆₇	—	2	1	no	—
259	C₂²×C₄×C₆₇	—	2	4	no	—
260	C₂²×C₄×C₆₇	—	2	4	no	—
261	C₂²×C₄×C₆₇	—	2	2	no	—
262	C₂²×C₄×C₆₇	—	2	2	no	—
263	C₂²×C₄×C₆₇	—	2	2	no	—
264	C₂²×C₄×C₆₇	—	2	2	no	—
265	C₂²×C₄×C₆₇	—	2	2	no	—
266	C₂²×C₄×C₆₇	—	8	2	no	—
267	C₂²×C₄×C₆₇	—	8	2	no	—
268	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
271	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
272	SD₁₆×C₆₇	—	4	4	no	—
273	D₈×C₆₇	—	2	4	no	—
274	D₈×C₆₇	—	2	4	no	—
275	D₈×C₆₇	—	4	4	no	—
276	M₁₆×C₆₇	—	2	4	no	—
277	M₁₆×C₆₇	—	4	4	no	—
278	C₂×C₈×C₆₇	—	2	2	no	—
279	C₂×C₈×C₆₇	—	2	2	no	—
280	C₂×C₈×C₆₇	—	4	4	no	—
281	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
282	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
283	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
284	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
285	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
286	C₄⋊C₄×C₆₇	—	2	1	no	—
287	C₄⋊C₄×C₆₇	—	2	4	no	—
288	C₄⋊C₄×C₆₇	—	2	1	no	—
289	C₄⋊C₄×C₆₇	—	2	1	no	—
290	C₄⋊C₄×C₆₇	—	2	4	no	—
291	C₄⋊C₄×C₆₇	—	2	1	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	1	no	—
296	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
297	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
298	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
299	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
300	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
301	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
302	C₂²⋊C₄×C₆₇	—	2	4	no	—
303	C₂²⋊C₄×C₆₇	—	2	2	no	—
304	C₂²⋊C₄×C₆₇	—	2	4	no	—
305	C₂²⋊C₄×C₆₇	—	2	2	no	—
306	C₂²⋊C₄×C₆₇	—	2	2	no	—
307	C₂²⋊C₄×C₆₇	—	2	2	no	—
308	C₂²⋊C₄×C₆₇	—	2	2	no	—
309	C₂²⋊C₄×C₆₇	—	2	2	no	—
310	C₂²⋊C₄×C₆₇	—	2	4	no	—
311	C₂²⋊C₄×C₆₇	—	2	4	no	—
312	C₂²⋊C₄×C₆₇	—	2	2	no	—
313	C₂²⋊C₄×C₆₇	—	2	4	no	—
314	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
315	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
316	C₄²×C₆₇	—	2	4	no	—
317	C₄²×C₆₇	—	2	2	no	—
318	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
320	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
321	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
322	C₂³×C₆₇	—	2	2	no	—
323	C₂³×C₆₇	—	2	4	no	—
324	C₂³×C₆₇	—	2	2	no	—
325	C₂³×C₆₇	—	2	2	no	—
326	C₂³×C₆₇	—	4	8	no	—
327	C₂³×C₆₇	—	4	2	no	—
328	C₂³×C₆₇	—	8	1	no	—
329	C₂³×C₆₇	—	8	1	no	—
330	C₂³×C₆₇	—	8	1	no	—
331	C₂³×C₆₇	—	8	1	no	—
332	C₂³×C₆₇	—	8	4	no	—
333	C₂³×C₆₇	—	8	4	no	—
334	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
335	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
336	Q₈×C₆₇	—	2	4	no	—
337	Q₈×C₆₇	—	2	2	no	—
338	Q₈×C₆₇	—	2	2	no	—
339	Q₈×C₆₇	—	4	2	no	—
340	Q₈×C₆₇	—	8	1	no	—
341	D₄×C₆₇	—	2	8	no	—
342	D₄×C₆₇	—	2	4	no	—
343	D₄×C₆₇	—	2	4	no	—
344	D₄×C₆₇	—	2	4	no	—
345	D₄×C₆₇	—	2	2	no	—
346	D₄×C₆₇	—	2	2	no	—
347	D₄×C₆₇	—	2	2	no	—
348	D₄×C₆₇	—	2	2	no	—
349	D₄×C₆₇	—	2	2	no	—
350	D₄×C₆₇	—	4	2	no	—
351	D₄×C₆₇	—	4	8	no	—
352	D₄×C₆₇	—	4	8	no	—
353	D₄×C₆₇	—	4	4	no	—
354	D₄×C₆₇	—	4	2	no	—
355	D₄×C₆₇	—	4	2	no	—
356	D₄×C₆₇	—	8	1	no	—
357	D₄×C₆₇	—	8	4	no	—
358	D₄×C₆₇	—	8	4	no	—
359	D₄×C₆₇	—	8	4	no	—
360	D₄×C₆₇	C₂×#41	1	4	yes	—
361	C₂×C₄×C₆₇	—	2	2	no	—
362	C₂×C₄×C₆₇	—	2	4	no	—
363	C₂×C₄×C₆₇	—	2	4	no	—
364	C₂×C₄×C₆₇	—	2	2	no	—
365	C₂×C₄×C₆₇	—	2	2	no	—
366	C₂×C₄×C₆₇	—	2	2	no	—
367	C₂×C₄×C₆₇	—	2	2	no	—
368	C₂×C₄×C₆₇	—	2	2	no	—
369	C₂×C₄×C₆₇	—	4	1	no	—
370	C₂×C₄×C₆₇	—	4	8	no	—
371	C₂×C₄×C₆₇	—	4	4	no	—
372	C₂×C₄×C₆₇	—	4	4	no	—
373	C₂×C₄×C₆₇	—	4	4	no	—
374	C₂×C₄×C₆₇	—	8	2	no	—
375	C₂×C₄×C₆₇	—	8	2	no	—
376	C₂×C₄×C₆₇	—	8	1	no	—
377	C₂×C₄×C₆₇	—	8	1	no	—
378	C₂×C₄×C₆₇	—	8	4	no	—
379	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
380	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
386	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
387	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
388	C₈×C₆₇	—	2	1	no	—
389	C₈×C₆₇	—	2	1	no	—
390	C₈×C₆₇	—	2	1	no	—
391	C₈×C₆₇	—	2	1	no	—
392	C₈×C₆₇	—	2	4	no	—
393	C₂²×C₆₇	—	2	1	no	—
394	C₂²×C₆₇	—	2	1	no	—
395	C₂²×C₆₇	—	2	4	no	—
396	C₂²×C₆₇	—	2	4	no	—
397	C₂²×C₆₇	—	2	4	no	—
398	C₂²×C₆₇	—	2	4	no	—
399	C₂²×C₆₇	—	4	2	no	—
400	C₂²×C₆₇	—	4	2	no	—
401	C₂²×C₆₇	—	4	2	no	—
402	C₂²×C₆₇	—	4	2	no	—
403	C₂²×C₆₇	—	4	2	no	—
404	C₂²×C₆₇	—	4	2	no	—
405	C₂²×C₆₇	—	4	2	no	—
406	C₂²×C₆₇	—	4	2	no	—
407	C₂²×C₆₇	—	8	4	no	—
408	C₂²×C₆₇	—	8	4	no	—
409	C₂²×C₆₇	—	16	8	no	—
410	C₂²×C₆₇	#546	1	2	yes	—
411	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
412	C₄×C₆₇	—	2	1	no	—
413	C₄×C₆₇	—	2	1	no	—
414	C₄×C₆₇	—	2	4	no	—
415	C₄×C₆₇	—	2	1	no	—
416	C₄×C₆₇	—	4	2	no	—
417	C₄×C₆₇	—	4	2	no	—
418	C₄×C₆₇	—	4	2	no	—
419	C₄×C₆₇	—	4	2	no	—
420	C₄×C₆₇	—	4	2	no	—
421	C₄×C₆₇	#546	1	2	yes	—
422	C₄×C₆₇	#576	1	2	yes	—
423	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
424	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
425	#61211	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
426	C₂×C₆₇	—	2	2	no	—
427	C₂×C₆₇	—	4	4	no	—
428	C₂×C₆₇	—	4	4	no	—
429	C₂×C₆₇	—	8	2	no	—
430	C₂×C₆₇	—	8	2	no	—
431	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
432	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
433	C₂×C₆₇	#3584	1	1	yes	characteristic
434	#3506	C₂×C₆₇	1	1	yes	characteristic, complemented
435	#3496	C₂×C₆₇	1	1	yes	characteristic, complemented
436	#3330	C₂×C₆₇	1	2	yes	complemented
437	#3325	C₂×C₆₇	1	2	yes	complemented
438	#3322	C₂×C₆₇	1	4	yes	complemented
439	#3303	C₂×C₆₇	1	2	yes	complemented
440	#3297	C₂×C₆₇	1	4	yes	complemented
441	#3294	C₂×C₆₇	1	2	yes	complemented
442	#3131	C₂×C₆₇	1	1	yes	characteristic, complemented
443	#3098	C₂×C₆₇	1	2	yes	complemented
444	#3077	C₂×C₆₇	1	1	yes	characteristic, complemented
445	#3062	C₂×C₆₇	1	2	yes	complemented
446	#3036	C₂×C₆₇	1	1	yes	characteristic, complemented
447	#3008	C₂×C₆₇	1	2	yes	complemented
448	C₂×C₄×D₈	C₂×C₆₇	1	1	yes	characteristic, complemented
449	#2931	C₂×C₆₇	1	1	yes	characteristic, complemented
450	#2897	C₂×C₆₇	1	2	yes	complemented
451	C₆₇	#61211	1	1	yes	characteristic, direct product factor, Sylow
452	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	—
453	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
454	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
455	C₂×#131	C₂²×C₆₇	1	2	yes	complemented
456	#559	—	2	2	no	—
457	#556	—	2	1	no	—
458	#555	C₂²×C₆₇	1	2	yes	complemented
459	#553	C₂²×C₆₇	1	4	yes	complemented
460	#550	—	2	1	no	—
461	#547	—	2	1	no	—
462	#547	C₂²×C₆₇	1	2	yes	complemented
463	#547	C₂²×C₆₇	1	2	yes	complemented
464	#546	—	2	2	no	—
465	#546	C₂²×C₆₇	1	4	yes	complemented
466	D₄²	—	2	1	no	—
467	D₄²	C₂²×C₆₇	1	2	yes	complemented
468	#538	—	2	2	no	—
469	#537	C₂²×C₆₇	1	2	yes	—
470	#535	C₂²×C₆₇	1	2	yes	complemented
471	#534	—	2	2	no	—
472	#533	C₂²×C₆₇	1	1	yes	characteristic, complemented
473	#532	C₂²×C₆₇	1	1	yes	characteristic
474	#532	C₂²×C₆₇	1	1	yes	characteristic
475	#525	—	2	2	no	—
476	C₂×#121	—	2	2	no	—
477	#520	C₂²×C₆₇	1	2	yes	complemented
478	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
479	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
480	#488	C₂²×C₆₇	1	2	yes	complemented
481	#488	C₂²×C₆₇	1	2	yes	complemented
482	#487	C₂²×C₆₇	1	1	yes	characteristic, complemented
483	#487	C₂²×C₆₇	1	1	yes	characteristic, complemented
484	#486	C₂²×C₆₇	1	1	yes	characteristic, complemented
485	#486	C₂²×C₆₇	1	1	yes	characteristic, complemented
486	#485	C₂²×C₆₇	1	4	yes	complemented
487	#484	C₂²×C₆₇	1	4	yes	complemented
488	#482	C₂²×C₆₇	1	4	yes	complemented
489	#480	C₂²×C₆₇	1	4	yes	complemented
490	#478	C₂²×C₆₇	1	4	yes	complemented
491	#476	C₂²×C₆₇	1	2	yes	complemented
492	#474	C₂²×C₆₇	1	2	yes	complemented
493	#469	C₂²×C₆₇	1	4	yes	complemented
494	#468	C₂²×C₆₇	1	4	yes	complemented
495	#466	C₂²×C₆₇	1	4	yes	complemented
496	#465	C₂²×C₆₇	1	4	yes	complemented
497	#463	C₂²×C₆₇	1	4	yes	complemented
498	#461	C₂²×C₆₇	1	2	yes	complemented
499	#459	C₂²×C₆₇	1	2	yes	complemented
500	#449	C₂²×C₆₇	1	4	yes	complemented
501	#449	C₂²×C₆₇	1	4	yes	complemented
502	#447	C₂²×C₆₇	1	4	yes	complemented
503	#447	C₂²×C₆₇	1	4	yes	complemented
504	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
505	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
506	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
507	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
508	#436	C₂²×C₆₇	1	2	yes	complemented
509	#436	C₂²×C₆₇	1	2	yes	complemented
510	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
511	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
512	#428	C₂²×C₆₇	1	2	yes	complemented
513	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic, complemented
514	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
515	#418	C₂²×C₆₇	1	2	yes	—
516	#418	C₂²×C₆₇	1	4	yes	complemented
517	#417	C₂²×C₆₇	1	4	yes	complemented
518	#417	C₂²×C₆₇	1	2	yes	complemented
519	#416	C₂²×C₆₇	1	2	yes	complemented
520	#416	C₂²×C₆₇	1	2	yes	complemented
521	#416	C₂²×C₆₇	1	4	yes	complemented
522	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
523	C₂×#102	C₂²×C₆₇	1	4	yes	complemented
524	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic, complemented
525	#408	C₂²×C₆₇	1	2	yes	complemented
526	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
527	H(5,𝔽₂)	—	2	8	no	—
528	H(5,𝔽₂)	—	4	4	no	—
529	C₂×#41	—	2	2	no	—
530	C₂×#41	—	2	2	no	—
531	C₂×#41	C₂³×C₆₇	1	2	yes	—
532	C₂×#41	C₂³×C₆₇	1	4	yes	—
533	C₂×#41	C₂³×C₆₇	1	2	yes	—
534	C₂²×D₄	—	2	4	no	—
535	C₂²×D₄	—	2	2	no	—
536	C₂²×D₄	—	2	2	no	—
537	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
538	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
539	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
540	C₂³×C₄	—	2	1	no	—
541	C₂³×C₄	—	2	1	no	—
542	AGL(1,ℤ/8)	—	4	4	no	—
543	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
544	C₂×D₈	—	2	4	no	—
545	C₂×D₈	C₂³×C₆₇	1	2	yes	—
546	C₂×D₈	C₂³×C₆₇	1	2	yes	—
547	C₂×D₈	C₂³×C₆₇	1	4	yes	—
548	#131	—	4	4	no	—
549	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
550	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
551	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
552	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
553	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
554	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
555	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
556	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
557	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
558	#127	—	2	2	no	—
559	#127	D₄×C₆₇	1	1	yes	characteristic
560	#127	C₂³×C₆₇	1	1	yes	characteristic
561	#126	—	2	4	no	—
562	#125	C₂³×C₆₇	1	2	yes	—
563	#124	—	2	2	no	—
564	#124	—	2	4	no	—
565	#124	D₄×C₆₇	1	2	yes	—
566	#124	C₂³×C₆₇	1	2	yes	—
567	#123	—	2	4	no	—
568	#123	—	2	4	no	—
569	#123	—	2	4	no	—
570	#123	—	2	4	no	—
571	C₂²⋊Q₈	—	2	2	no	—
572	C₂²⋊Q₈	—	2	1	no	—
573	C₂²⋊Q₈	—	2	1	no	—
574	C₂²⋊Q₈	—	2	2	no	—
575	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
576	#121	—	2	4	no	—
577	#121	—	2	2	no	—
578	#121	—	2	2	no	—
579	#121	—	2	2	no	—
580	#121	—	2	4	no	—
581	#121	—	2	1	no	—
582	#121	—	2	1	no	—
583	#121	—	2	2	no	—
584	#121	—	2	4	no	—
585	#121	D₄×C₆₇	1	2	yes	—
586	#121	D₄×C₆₇	1	2	yes	—
587	#121	C₂³×C₆₇	1	4	yes	—
588	#121	C₂³×C₆₇	1	4	yes	—
589	#121	C₂³×C₆₇	1	4	yes	—
590	#120	—	2	4	no	—
591	#120	—	2	4	no	—
592	#120	—	2	4	no	—
593	C₄×Q₈	—	2	2	no	—
594	C₄×Q₈	—	2	1	no	—
595	C₄×Q₈	—	2	1	no	—
596	C₄×D₄	—	2	4	no	—
597	C₄×D₄	—	2	2	no	—
598	C₄×D₄	—	2	4	no	—
599	C₄×D₄	—	2	1	no	—
600	C₄×D₄	—	2	1	no	—
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	—	2	1	no	—
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	—	2	1	no	—
605	C₄×D₄	C₂³×C₆₇	1	2	yes	—
606	C₄×D₄	C₂³×C₆₇	1	2	yes	—
607	C₄×D₄	C₂³×C₆₇	1	2	yes	—
608	C₄×D₄	C₂³×C₆₇	1	2	yes	—
609	C₄×D₄	C₂³×C₆₇	1	2	yes	—
610	C₄×D₄	C₂³×C₆₇	1	2	yes	—
611	#117	—	2	2	no	—
612	#117	C₂³×C₆₇	1	2	yes	—
613	#117	C₂³×C₆₇	1	4	yes	—
614	C₂×C₄⋊C₄	—	2	2	no	—
615	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
618	C₂×C₂²⋊C₄	—	2	1	no	—
619	C₂×C₂²⋊C₄	—	2	1	no	—
620	C₂×C₂²⋊C₄	—	2	4	no	—
621	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
622	#107	C₂³×C₆₇	1	2	yes	—
623	#107	C₂³×C₆₇	1	2	yes	—
624	#107	C₂³×C₆₇	1	4	yes	—
625	#106	C₂³×C₆₇	1	4	yes	—
626	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
627	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
628	#103	C₂³×C₆₇	1	2	yes	—
629	#103	C₂³×C₆₇	1	4	yes	—
630	#103	C₂³×C₆₇	1	2	yes	—
631	#103	C₂³×C₆₇	1	2	yes	—
632	#103	C₂³×C₆₇	1	2	yes	—
633	#102	C₂³×C₆₇	1	2	yes	—
634	#102	C₂³×C₆₇	1	2	yes	—
635	#102	C₂³×C₆₇	1	2	yes	—
636	#102	C₂³×C₆₇	1	4	yes	—
637	#102	C₂³×C₆₇	1	4	yes	—
638	#102	C₂³×C₆₇	1	2	yes	—
639	#102	C₂³×C₆₇	1	2	yes	—
640	#102	C₂³×C₆₇	1	4	yes	—
641	#102	C₂³×C₆₇	1	2	yes	—
642	#102	C₂³×C₆₇	1	2	yes	—
643	#102	C₂³×C₆₇	1	2	yes	—
644	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
645	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
646	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
647	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
648	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
649	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
650	C₂⁴	—	2	1	no	—
651	C₂⁴	—	2	1	no	—
652	C₂⁴	—	2	4	no	—
653	#41	—	2	4	no	—
654	#41	—	2	4	no	—
655	#41	—	2	8	no	—
656	#41	—	2	4	no	—
657	#41	—	2	4	no	—
658	#41	—	4	4	no	—
659	#41	—	4	8	no	—
660	#41	—	8	4	no	—
661	C₂×Q₈	—	2	1	no	—
662	C₂×Q₈	—	2	1	no	—
663	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
664	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
665	C₂×D₄	—	2	8	no	—
666	C₂×D₄	—	2	4	no	—
667	C₂×D₄	—	2	2	no	—
668	C₂×D₄	—	2	4	no	—
669	C₂×D₄	—	2	4	no	—
670	C₂×D₄	—	2	4	no	—
671	C₂×D₄	—	2	1	no	—
672	C₂×D₄	—	2	1	no	—
673	C₂×D₄	—	2	1	no	—
674	C₂×D₄	—	2	4	no	—
675	C₂×D₄	—	2	1	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	4	4	no	—
680	C₂×D₄	—	4	8	no	—
681	C₂×D₄	—	4	16	no	—
682	C₂×D₄	—	8	4	no	—
683	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
684	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
685	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
686	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
687	C₂×D₄	#41×C₆₇	1	4	yes	complemented
688	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
689	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
690	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
691	C₂²×C₄	—	2	1	no	—
692	C₂²×C₄	—	2	1	no	—
693	C₂²×C₄	—	2	4	no	—
694	C₂²×C₄	—	2	4	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	8	2	no	—
701	C₂²×C₄	—	8	2	no	—
702	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
703	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
704	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
705	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
706	SD₁₆	—	4	4	no	—
707	D₈	—	2	4	no	—
708	D₈	—	2	4	no	—
709	D₈	—	4	4	no	—
710	M₁₆	—	2	4	no	—
711	M₁₆	—	4	4	no	—
712	C₂×C₈	—	2	2	no	—
713	C₂×C₈	—	2	2	no	—
714	C₂×C₈	—	4	4	no	—
715	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
716	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
717	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
718	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
719	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	4	no	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	1	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
731	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
732	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
733	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
734	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
735	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
736	C₂²⋊C₄	—	2	4	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
749	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
750	C₄²	—	2	4	no	—
751	C₄²	—	2	2	no	—
752	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
753	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
754	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
755	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
756	C₂³	—	2	2	no	—
757	C₂³	—	2	4	no	—
758	C₂³	—	2	2	no	—
759	C₂³	—	2	2	no	—
760	C₂³	—	4	8	no	—
761	C₂³	—	4	2	no	—
762	C₂³	—	8	1	no	—
763	C₂³	—	8	1	no	—
764	C₂³	—	8	1	no	—
765	C₂³	—	8	1	no	—
766	C₂³	—	8	4	no	—
767	C₂³	—	8	4	no	—
768	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
769	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
770	Q₈	—	2	4	no	—
771	Q₈	—	2	2	no	—
772	Q₈	—	2	2	no	—
773	Q₈	—	4	2	no	—
774	Q₈	—	8	1	no	—
775	D₄	—	2	8	no	—
776	D₄	—	2	4	no	—
777	D₄	—	2	4	no	—
778	D₄	—	2	4	no	—
779	D₄	—	2	2	no	—
780	D₄	—	2	2	no	—
781	D₄	—	2	2	no	—
782	D₄	—	2	2	no	—
783	D₄	—	2	2	no	—
784	D₄	—	4	2	no	—
785	D₄	—	4	8	no	—
786	D₄	—	4	8	no	—
787	D₄	—	4	4	no	—
788	D₄	—	4	2	no	—
789	D₄	—	4	2	no	—
790	D₄	—	8	1	no	—
791	D₄	—	8	4	no	—
792	D₄	—	8	4	no	—
793	D₄	—	8	4	no	—
794	D₄	C₂×#41×C₆₇	1	4	yes	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	4	no	—
797	C₂×C₄	—	2	4	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	4	1	no	—
804	C₂×C₄	—	4	8	no	—
805	C₂×C₄	—	4	4	no	—
806	C₂×C₄	—	4	4	no	—
807	C₂×C₄	—	4	4	no	—
808	C₂×C₄	—	8	2	no	—
809	C₂×C₄	—	8	2	no	—
810	C₂×C₄	—	8	1	no	—
811	C₂×C₄	—	8	1	no	—
812	C₂×C₄	—	8	4	no	—
813	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
814	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
815	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
816	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
817	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
818	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
819	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
820	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
821	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
822	C₈	—	2	1	no	—
823	C₈	—	2	1	no	—
824	C₈	—	2	1	no	—
825	C₈	—	2	1	no	—
826	C₈	—	2	4	no	—
827	C₂²	—	2	1	no	—
828	C₂²	—	2	1	no	—
829	C₂²	—	2	4	no	—
830	C₂²	—	2	4	no	—
831	C₂²	—	2	4	no	—
832	C₂²	—	2	4	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	8	4	no	—
842	C₂²	—	8	4	no	—
843	C₂²	—	16	8	no	—
844	C₂²	#546×C₆₇	1	2	yes	—
845	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
846	C₄	—	2	1	no	—
847	C₄	—	2	1	no	—
848	C₄	—	2	1	no	—
849	C₄	—	2	4	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	2	no	—
854	C₄	—	4	2	no	—
855	C₄	#546×C₆₇	1	2	yes	—
856	C₄	#576×C₆₇	1	2	yes	—
857	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
858	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
859	C₂	—	2	2	no	—
860	C₂	—	4	4	no	—
861	C₂	—	4	4	no	—
862	C₂	—	8	2	no	—
863	C₂	—	8	2	no	—
864	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
865	C₂	C₂×#576×C₆₇	1	1	yes	characteristic
866	C₂	C₆₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #532×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3506	C₂	semidirect
2. C₆₇×#3496	C₂	semidirect
3. C₆₇×#3330	C₂	semidirect
4. C₆₇×#3325	C₂	semidirect
5. C₆₇×#3322	C₂	semidirect
6. C₆₇×#3303	C₂	semidirect
7. C₆₇×#3297	C₂	semidirect
8. C₆₇×#3294	C₂	semidirect
9. C₆₇×#3131	C₂	semidirect
10. C₆₇×#3098	C₂	semidirect
11. C₆₇×#3077	C₂	semidirect
12. C₆₇×#3062	C₂	semidirect
13. C₆₇×#3036	C₂	semidirect
14. C₆₇×#3008	C₂	semidirect
15. C₂×C₄×D₈×C₆₇	C₂	semidirect
16. C₆₇×#2931	C₂	semidirect
17. C₆₇×#2897	C₂	semidirect
19. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
21. C₂×#131×C₆₇	C₂²	semidirect
24. #555×C₆₇	C₂²	semidirect
25. #553×C₆₇	C₂²	semidirect
28. #547×C₆₇	C₂²	semidirect
29. #547×C₆₇	C₂²	semidirect
31. #546×C₆₇	C₂²	semidirect
33. D₄²×C₆₇	C₂²	semidirect
36. #535×C₆₇	C₂²	semidirect
38. #533×C₆₇	C₂²	semidirect
43. #520×C₆₇	C₂²	semidirect
45. C₂×C₄×D₄×C₆₇	C₂²	semidirect
46. #488×C₆₇	C₂²	semidirect
47. #488×C₆₇	C₂²	semidirect
48. #487×C₆₇	C₂²	semidirect
49. #487×C₆₇	C₂²	semidirect
50. #486×C₆₇	C₂²	semidirect
51. #486×C₆₇	C₂²	semidirect
52. #485×C₆₇	C₂²	semidirect
53. #484×C₆₇	C₂²	semidirect
54. #482×C₆₇	C₂²	semidirect
55. #480×C₆₇	C₂²	semidirect
56. #478×C₆₇	C₂²	semidirect
57. #476×C₆₇	C₂²	semidirect
58. #474×C₆₇	C₂²	semidirect
59. #469×C₆₇	C₂²	semidirect
60. #468×C₆₇	C₂²	semidirect
61. #466×C₆₇	C₂²	semidirect
62. #465×C₆₇	C₂²	semidirect
63. #463×C₆₇	C₂²	semidirect
64. #461×C₆₇	C₂²	semidirect
65. #459×C₆₇	C₂²	semidirect
66. #449×C₆₇	C₂²	semidirect
67. #449×C₆₇	C₂²	semidirect
68. #447×C₆₇	C₂²	semidirect
69. #447×C₆₇	C₂²	semidirect
70. C₄×D₈×C₆₇	C₂²	semidirect
71. C₄×D₈×C₆₇	C₂²	semidirect
72. C₄×D₈×C₆₇	C₂²	semidirect
73. C₄×D₈×C₆₇	C₂²	semidirect
74. #436×C₆₇	C₂²	semidirect
75. #436×C₆₇	C₂²	semidirect
76. C₈×D₄×C₆₇	C₂²	semidirect
77. C₈×D₄×C₆₇	C₂²	semidirect
78. #428×C₆₇	C₂²	semidirect
79. C₂×#107×C₆₇	C₂²	semidirect
80. #423×C₆₇	C₂²	semidirect
82. #418×C₆₇	C₂²	semidirect
83. #417×C₆₇	C₂²	semidirect
84. #417×C₆₇	C₂²	semidirect
85. #416×C₆₇	C₂²	semidirect
86. #416×C₆₇	C₂²	semidirect
87. #416×C₆₇	C₂²	semidirect
89. C₂×#102×C₆₇	C₂²	semidirect
90. C₂×#102×C₆₇	C₂²	semidirect
91. #408×C₆₇	C₂²	semidirect
92. C₂×C₄×C₈×C₆₇	C₂²	semidirect
253. C₂×D₄×C₆₇	#41	semidirect
425. #61211	C₆₇	direct (N × H)
434. #3506	C₂×C₆₇	semidirect
435. #3496	C₂×C₆₇	semidirect
436. #3330	C₂×C₆₇	semidirect
437. #3325	C₂×C₆₇	semidirect
438. #3322	C₂×C₆₇	semidirect
439. #3303	C₂×C₆₇	semidirect
440. #3297	C₂×C₆₇	semidirect
441. #3294	C₂×C₆₇	semidirect
442. #3131	C₂×C₆₇	semidirect
443. #3098	C₂×C₆₇	semidirect
444. #3077	C₂×C₆₇	semidirect
445. #3062	C₂×C₆₇	semidirect
446. #3036	C₂×C₆₇	semidirect
447. #3008	C₂×C₆₇	semidirect
448. C₂×C₄×D₈	C₂×C₆₇	semidirect
449. #2931	C₂×C₆₇	semidirect
450. #2897	C₂×C₆₇	semidirect
451. C₆₇	#61211	direct (N × H)
453. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
455. C₂×#131	C₂²×C₆₇	semidirect
458. #555	C₂²×C₆₇	semidirect
459. #553	C₂²×C₆₇	semidirect
462. #547	C₂²×C₆₇	semidirect
463. #547	C₂²×C₆₇	semidirect
465. #546	C₂²×C₆₇	semidirect
467. D₄²	C₂²×C₆₇	semidirect
470. #535	C₂²×C₆₇	semidirect
472. #533	C₂²×C₆₇	semidirect
477. #520	C₂²×C₆₇	semidirect
479. C₂×C₄×D₄	C₂²×C₆₇	semidirect
480. #488	C₂²×C₆₇	semidirect
481. #488	C₂²×C₆₇	semidirect
482. #487	C₂²×C₆₇	semidirect
483. #487	C₂²×C₆₇	semidirect
484. #486	C₂²×C₆₇	semidirect
485. #486	C₂²×C₆₇	semidirect
486. #485	C₂²×C₆₇	semidirect
487. #484	C₂²×C₆₇	semidirect
488. #482	C₂²×C₆₇	semidirect
489. #480	C₂²×C₆₇	semidirect
490. #478	C₂²×C₆₇	semidirect
491. #476	C₂²×C₆₇	semidirect
492. #474	C₂²×C₆₇	semidirect
493. #469	C₂²×C₆₇	semidirect
494. #468	C₂²×C₆₇	semidirect
495. #466	C₂²×C₆₇	semidirect
496. #465	C₂²×C₆₇	semidirect
497. #463	C₂²×C₆₇	semidirect
498. #461	C₂²×C₆₇	semidirect
499. #459	C₂²×C₆₇	semidirect
500. #449	C₂²×C₆₇	semidirect
501. #449	C₂²×C₆₇	semidirect
502. #447	C₂²×C₆₇	semidirect
503. #447	C₂²×C₆₇	semidirect
504. C₄×D₈	C₂²×C₆₇	semidirect
505. C₄×D₈	C₂²×C₆₇	semidirect
506. C₄×D₈	C₂²×C₆₇	semidirect
507. C₄×D₈	C₂²×C₆₇	semidirect
508. #436	C₂²×C₆₇	semidirect
509. #436	C₂²×C₆₇	semidirect
510. C₈×D₄	C₂²×C₆₇	semidirect
511. C₈×D₄	C₂²×C₆₇	semidirect
512. #428	C₂²×C₆₇	semidirect
513. C₂×#107	C₂²×C₆₇	semidirect
514. #423	C₂²×C₆₇	semidirect
516. #418	C₂²×C₆₇	semidirect
517. #417	C₂²×C₆₇	semidirect
518. #417	C₂²×C₆₇	semidirect
519. #416	C₂²×C₆₇	semidirect
520. #416	C₂²×C₆₇	semidirect
521. #416	C₂²×C₆₇	semidirect
523. C₂×#102	C₂²×C₆₇	semidirect
524. C₂×#102	C₂²×C₆₇	semidirect
525. #408	C₂²×C₆₇	semidirect
526. C₂×C₄×C₈	C₂²×C₆₇	semidirect
687. 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×#3506	2
C₆₇×#3496	2
C₆₇×#3330	2
C₆₇×#3325	2
C₆₇×#3322	2
C₆₇×#3303	2
C₆₇×#3297	2
C₆₇×#3294	2
C₆₇×#3131	2
C₆₇×#3098	2
C₆₇×#3077	2
C₆₇×#3062	2
C₆₇×#3036	2
C₆₇×#3008	2
C₂×C₄×D₈×C₆₇	2
C₆₇×#2931	2
C₆₇×#2897	2
#61211	67

Subgroups — C67×#61211 #30740462

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61211 #30740462