Subgroups — C₆₇×#61735 #30740986

Order 17152.

1796 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3520	C₂	1	1	yes	maximal, characteristic
2	C₂×#554×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3356	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3344	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3335	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3331	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3316	C₂	1	4	yes	maximal, complemented
8	C₆₇×#3299	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3238	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3229	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3195	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3190	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3113	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3108	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3092	C₂	1	2	yes	maximal, complemented
16	C₂×#483×C₆₇	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2974	C₂	1	1	yes	maximal, characteristic, complemented
18	#556×C₆₇	C₂²	1	1	yes	characteristic
19	#554×C₆₇	—	2	1	no	—
20	#554×C₆₇	—	2	2	no	—
21	#554×C₆₇	—	2	1	no	—
22	#554×C₆₇	—	2	1	no	—
23	#554×C₆₇	C₂²	1	2	yes	—
24	#554×C₆₇	C₂²	1	4	yes	—
25	#554×C₆₇	C₂²	1	2	yes	—
26	#552×C₆₇	C₂²	1	2	yes	—
27	#551×C₆₇	—	2	2	no	—
28	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
29	#548×C₆₇	C₂²	1	2	yes	—
30	#547×C₆₇	C₂²	1	1	yes	characteristic
31	#547×C₆₇	C₂²	1	1	yes	characteristic
32	#546×C₆₇	—	2	1	no	—
33	#542×C₆₇	—	2	1	no	—
34	#539×C₆₇	—	2	2	no	—
35	#533×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
37	#529×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#125×C₆₇	—	2	1	no	—
39	#525×C₆₇	C₂²	1	2	yes	—
40	C₂×C₂²⋊Q₈×C₆₇	—	2	2	no	—
41	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
42	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
43	#520×C₆₇	—	2	1	no	—
44	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₆₇	—	2	1	no	—
46	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
47	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
48	#501×C₆₇	C₂²	1	2	yes	complemented
49	#498×C₆₇	C₂²	1	2	yes	complemented
50	#489×C₆₇	C₂²	1	2	yes	complemented
51	#487×C₆₇	C₂²	1	2	yes	complemented
52	#485×C₆₇	C₂²	1	4	yes	complemented
53	#484×C₆₇	C₂²	1	4	yes	complemented
54	#483×C₆₇	C₂²	1	1	yes	characteristic
55	#483×C₆₇	C₂²	1	2	yes	—
56	#483×C₆₇	C₂²	1	2	yes	—
57	#483×C₆₇	C₂²	1	2	yes	—
58	#483×C₆₇	C₂²	1	2	yes	—
59	#483×C₆₇	C₂²	1	4	yes	complemented
60	#483×C₆₇	C₂²	1	4	yes	complemented
61	#483×C₆₇	C₂²	1	4	yes	complemented
62	#481×C₆₇	C₂²	1	4	yes	complemented
63	#480×C₆₇	C₂²	1	1	yes	characteristic
64	#480×C₆₇	C₂²	1	2	yes	—
65	#479×C₆₇	C₂²	1	2	yes	complemented
66	#477×C₆₇	C₂²	1	2	yes	complemented
67	#476×C₆₇	C₂²	1	2	yes	complemented
68	#475×C₆₇	C₂²	1	4	yes	complemented
69	#475×C₆₇	C₂²	1	2	yes	complemented
70	#470×C₆₇	C₂²	1	4	yes	complemented
71	#470×C₆₇	C₂²	1	4	yes	complemented
72	#467×C₆₇	C₂²	1	4	yes	complemented
73	#465×C₆₇	C₂²	1	4	yes	complemented
74	#464×C₆₇	C₂²	1	2	yes	complemented
75	#462×C₆₇	C₂²	1	2	yes	complemented
76	#452×C₆₇	C₂²	1	4	yes	complemented
77	#451×C₆₇	C₂²	1	1	yes	characteristic
78	#451×C₆₇	C₂²	1	2	yes	—
79	#451×C₆₇	C₂²	1	4	yes	complemented
80	#448×C₆₇	C₂²	1	1	yes	characteristic
81	#441×C₆₇	C₂²	1	4	yes	complemented
82	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
83	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
84	#436×C₆₇	C₂²	1	2	yes	—
85	#435×C₆₇	C₂²	1	4	yes	—
86	C₈×D₄×C₆₇	C₂²	1	2	yes	—
87	#432×C₆₇	C₂²	1	1	yes	characteristic
88	#431×C₆₇	C₂²	1	1	yes	characteristic
89	#428×C₆₇	C₂²	1	4	yes	complemented
90	C₂×#106×C₆₇	C₂²	1	4	yes	complemented
91	#417×C₆₇	C₂²	1	4	yes	complemented
92	C₂×#103×C₆₇	C₂²	1	4	yes	complemented
93	#407×C₆₇	C₂²	1	2	yes	—
94	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	—
95	C₂×#41×C₆₇	—	2	1	no	—
96	C₂×#41×C₆₇	C₂³	1	2	yes	—
97	C₂²×Q₈×C₆₇	—	2	1	no	—
98	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
99	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
100	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
101	C₂³×C₄×C₆₇	—	2	2	no	—
102	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
103	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
104	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
105	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
106	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
107	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
108	C₄⋊Q₈×C₆₇	—	2	1	no	—
109	C₄⋊Q₈×C₆₇	—	2	1	no	—
110	C₄⋊Q₈×C₆₇	—	2	1	no	—
111	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
113	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
114	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
115	#126×C₆₇	—	2	2	no	—
116	#126×C₆₇	—	2	2	no	—
117	#126×C₆₇	—	2	1	no	—
118	#125×C₆₇	—	2	2	no	—
119	#125×C₆₇	—	2	4	no	—
120	#125×C₆₇	—	2	2	no	—
121	#125×C₆₇	—	2	2	no	—
122	#125×C₆₇	—	2	1	no	—
123	#125×C₆₇	C₂³	1	1	yes	characteristic
124	#124×C₆₇	—	2	1	no	—
125	#124×C₆₇	—	2	2	no	—
126	#124×C₆₇	C₂³	1	1	yes	characteristic
127	#123×C₆₇	—	2	2	no	—
128	#123×C₆₇	—	2	2	no	—
129	#123×C₆₇	—	2	1	no	—
130	#123×C₆₇	—	2	2	no	—
131	#123×C₆₇	—	2	2	no	—
132	C₂²⋊Q₈×C₆₇	—	2	2	no	—
133	C₂²⋊Q₈×C₆₇	—	2	2	no	—
134	C₂²⋊Q₈×C₆₇	—	2	2	no	—
135	C₂²⋊Q₈×C₆₇	—	2	2	no	—
136	C₂²⋊Q₈×C₆₇	—	2	1	no	—
137	C₂²⋊Q₈×C₆₇	—	2	2	no	—
138	C₂²⋊Q₈×C₆₇	—	2	1	no	—
139	C₂²⋊Q₈×C₆₇	—	2	4	no	—
140	C₂²⋊Q₈×C₆₇	—	2	4	no	—
141	C₂²⋊Q₈×C₆₇	—	2	4	no	—
142	C₂²⋊Q₈×C₆₇	—	2	4	no	—
143	C₂²⋊Q₈×C₆₇	—	2	2	no	—
144	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
145	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
146	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
147	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
148	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
149	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
150	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
151	#121×C₆₇	—	2	2	no	—
152	#121×C₆₇	—	2	1	no	—
153	#121×C₆₇	C₂³	1	1	yes	characteristic
154	#121×C₆₇	C₂³	1	2	yes	—
155	#120×C₆₇	—	2	2	no	—
156	C₄×Q₈×C₆₇	—	2	1	no	—
157	C₄×Q₈×C₆₇	—	2	1	no	—
158	C₄×Q₈×C₆₇	—	2	1	no	—
159	C₄×Q₈×C₆₇	—	2	1	no	—
160	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
161	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
162	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
163	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
164	C₄×D₄×C₆₇	—	2	4	no	—
165	C₄×D₄×C₆₇	—	2	2	no	—
166	C₄×D₄×C₆₇	—	2	2	no	—
167	C₄×D₄×C₆₇	—	2	1	no	—
168	C₄×D₄×C₆₇	—	2	2	no	—
169	C₄×D₄×C₆₇	—	2	2	no	—
170	C₄×D₄×C₆₇	—	2	1	no	—
171	C₄×D₄×C₆₇	—	2	2	no	—
172	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
173	C₄×D₄×C₆₇	D₄	1	2	yes	—
174	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
175	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
177	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₆₇	C₂³	1	2	yes	—
179	#117×C₆₇	—	2	1	no	—
180	#117×C₆₇	—	2	2	no	—
181	#117×C₆₇	—	2	1	no	—
182	#117×C₆₇	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
184	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
185	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
186	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
187	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
188	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
189	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
190	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
191	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
193	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
195	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
196	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
198	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
200	C₂×C₄²×C₆₇	—	2	1	no	—
201	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
202	#107×C₆₇	C₂³	1	4	yes	—
203	#107×C₆₇	C₂³	1	2	yes	—
204	#106×C₆₇	C₂³	1	4	yes	—
205	#106×C₆₇	C₂³	1	4	yes	—
206	#106×C₆₇	C₂³	1	4	yes	—
207	#106×C₆₇	C₂³	1	4	yes	—
208	#106×C₆₇	C₂³	1	2	yes	—
209	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
210	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
211	#103×C₆₇	C₂³	1	2	yes	—
212	#103×C₆₇	C₂³	1	4	yes	—
213	#103×C₆₇	C₂³	1	2	yes	—
214	#103×C₆₇	C₂³	1	4	yes	—
215	#103×C₆₇	C₂³	1	4	yes	—
216	#103×C₆₇	C₂³	1	4	yes	—
217	#103×C₆₇	C₂³	1	4	yes	—
218	#103×C₆₇	C₂³	1	2	yes	—
219	#102×C₆₇	C₂³	1	4	yes	—
220	#102×C₆₇	C₂³	1	2	yes	—
221	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
222	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
223	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
224	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
225	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
226	#97×C₆₇	C₂³	1	2	yes	—
227	C₄×C₈×C₆₇	C₂³	1	2	yes	—
228	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
229	#41×C₆₇	—	4	4	no	—
230	#41×C₆₇	—	4	4	no	—
231	C₂×Q₈×C₆₇	—	2	1	no	—
232	C₂×Q₈×C₆₇	—	2	1	no	—
233	C₂×Q₈×C₆₇	—	2	2	no	—
234	C₂×Q₈×C₆₇	—	2	2	no	—
235	C₂×Q₈×C₆₇	—	2	2	no	—
236	C₂×Q₈×C₆₇	—	4	2	no	—
237	C₂×Q₈×C₆₇	—	4	4	no	—
238	C₂×Q₈×C₆₇	—	8	2	no	—
239	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
240	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
241	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
242	C₂×D₄×C₆₇	—	2	4	no	—
243	C₂×D₄×C₆₇	—	2	1	no	—
244	C₂×D₄×C₆₇	—	2	2	no	—
245	C₂×D₄×C₆₇	—	2	2	no	—
246	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
247	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
248	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
249	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₆₇	—	2	1	no	—
251	C₂²×C₄×C₆₇	—	2	1	no	—
252	C₂²×C₄×C₆₇	—	2	2	no	—
253	C₂²×C₄×C₆₇	—	2	2	no	—
254	C₂²×C₄×C₆₇	—	2	2	no	—
255	C₂²×C₄×C₆₇	—	2	4	no	—
256	C₂²×C₄×C₆₇	—	2	4	no	—
257	C₂²×C₄×C₆₇	—	2	1	no	—
258	C₂²×C₄×C₆₇	—	2	2	no	—
259	C₂²×C₄×C₆₇	—	4	4	no	—
260	C₂²×C₄×C₆₇	—	8	4	no	—
261	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
264	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
265	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
266	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
269	Q₁₆×C₆₇	—	4	4	no	—
270	Q₁₆×C₆₇	—	4	2	no	—
271	SD₁₆×C₆₇	—	4	2	no	—
272	M₁₆×C₆₇	—	4	4	no	—
273	C₂×C₈×C₆₇	—	4	4	no	—
274	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
275	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
276	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
277	C₄⋊C₄×C₆₇	—	2	1	no	—
278	C₄⋊C₄×C₆₇	—	2	4	no	—
279	C₄⋊C₄×C₆₇	—	2	4	no	—
280	C₄⋊C₄×C₆₇	—	2	2	no	—
281	C₄⋊C₄×C₆₇	—	2	1	no	—
282	C₄⋊C₄×C₆₇	—	2	2	no	—
283	C₄⋊C₄×C₆₇	—	2	2	no	—
284	C₄⋊C₄×C₆₇	—	2	2	no	—
285	C₄⋊C₄×C₆₇	—	2	1	no	—
286	C₄⋊C₄×C₆₇	—	2	2	no	—
287	C₄⋊C₄×C₆₇	—	2	2	no	—
288	C₄⋊C₄×C₆₇	—	2	2	no	—
289	C₄⋊C₄×C₆₇	—	2	2	no	—
290	C₄⋊C₄×C₆₇	—	2	4	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	1	no	—
295	C₄⋊C₄×C₆₇	—	2	1	no	—
296	C₄⋊C₄×C₆₇	—	2	2	no	—
297	C₄⋊C₄×C₆₇	—	2	1	no	—
298	C₄⋊C₄×C₆₇	—	2	2	no	—
299	C₄⋊C₄×C₆₇	—	2	1	no	—
300	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
301	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
302	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
303	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
304	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
305	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
306	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
307	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
308	C₂²⋊C₄×C₆₇	—	2	1	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	2	no	—
314	C₂²⋊C₄×C₆₇	—	2	2	no	—
315	C₂²⋊C₄×C₆₇	—	2	2	no	—
316	C₂²⋊C₄×C₆₇	—	2	1	no	—
317	C₂²⋊C₄×C₆₇	—	2	1	no	—
318	C₂²⋊C₄×C₆₇	—	2	1	no	—
319	C₂²⋊C₄×C₆₇	—	2	2	no	—
320	C₂²⋊C₄×C₆₇	—	2	1	no	—
321	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
322	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
323	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
324	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
325	C₄²×C₆₇	—	2	2	no	—
326	C₄²×C₆₇	—	2	2	no	—
327	C₄²×C₆₇	—	2	2	no	—
328	C₄²×C₆₇	—	2	2	no	—
329	C₄²×C₆₇	—	2	1	no	—
330	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
333	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
334	C₂³×C₆₇	—	2	4	no	—
335	C₂³×C₆₇	—	2	4	no	—
336	C₂³×C₆₇	—	2	1	no	—
337	C₂³×C₆₇	—	4	2	no	—
338	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
339	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
340	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
341	Q₈×C₆₇	—	2	2	no	—
342	Q₈×C₆₇	—	2	2	no	—
343	Q₈×C₆₇	—	2	2	no	—
344	Q₈×C₆₇	—	2	4	no	—
345	Q₈×C₆₇	—	4	2	no	—
346	Q₈×C₆₇	—	4	2	no	—
347	Q₈×C₆₇	—	8	2	no	—
348	Q₈×C₆₇	—	8	2	no	—
349	Q₈×C₆₇	—	8	2	no	—
350	D₄×C₆₇	—	2	4	no	—
351	D₄×C₆₇	—	2	2	no	—
352	D₄×C₆₇	—	2	2	no	—
353	D₄×C₆₇	—	4	4	no	—
354	D₄×C₆₇	—	4	2	no	—
355	D₄×C₆₇	—	8	2	no	—
356	D₄×C₆₇	#137	1	4	yes	—
357	C₂×C₄×C₆₇	—	2	2	no	—
358	C₂×C₄×C₆₇	—	2	2	no	—
359	C₂×C₄×C₆₇	—	2	4	no	—
360	C₂×C₄×C₆₇	—	2	4	no	—
361	C₂×C₄×C₆₇	—	2	2	no	—
362	C₂×C₄×C₆₇	—	2	1	no	—
363	C₂×C₄×C₆₇	—	2	2	no	—
364	C₂×C₄×C₆₇	—	2	2	no	—
365	C₂×C₄×C₆₇	—	2	2	no	—
366	C₂×C₄×C₆₇	—	2	1	no	—
367	C₂×C₄×C₆₇	—	2	2	no	—
368	C₂×C₄×C₆₇	—	2	1	no	—
369	C₂×C₄×C₆₇	—	2	4	no	—
370	C₂×C₄×C₆₇	—	4	2	no	—
371	C₂×C₄×C₆₇	—	4	2	no	—
372	C₂×C₄×C₆₇	—	4	2	no	—
373	C₂×C₄×C₆₇	—	4	2	no	—
374	C₂×C₄×C₆₇	—	4	4	no	—
375	C₂×C₄×C₆₇	—	4	2	no	—
376	C₂×C₄×C₆₇	—	4	4	no	—
377	C₂×C₄×C₆₇	—	4	2	no	—
378	C₂×C₄×C₆₇	—	8	2	no	—
379	C₂×C₄×C₆₇	—	8	4	no	—
380	C₂×C₄×C₆₇	—	8	4	no	—
381	C₂×C₄×C₆₇	—	8	2	no	—
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	2	yes	—
385	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
388	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
390	C₈×C₆₇	—	2	2	no	—
391	C₈×C₆₇	—	2	4	no	—
392	C₈×C₆₇	—	2	2	no	—
393	C₂²×C₆₇	—	2	1	no	—
394	C₂²×C₆₇	—	2	2	no	—
395	C₂²×C₆₇	—	2	1	no	—
396	C₂²×C₆₇	—	2	2	no	—
397	C₂²×C₆₇	—	2	2	no	—
398	C₂²×C₆₇	—	2	2	no	—
399	C₂²×C₆₇	—	2	2	no	—
400	C₂²×C₆₇	—	4	8	no	—
401	C₂²×C₆₇	—	4	1	no	—
402	C₂²×C₆₇	—	4	1	no	—
403	C₂²×C₆₇	—	4	1	no	—
404	C₂²×C₆₇	C₂×#137	1	4	yes	—
405	C₂²×C₆₇	#577	1	2	yes	—
406	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
407	C₄×C₆₇	—	2	1	no	—
408	C₄×C₆₇	—	2	2	no	—
409	C₄×C₆₇	—	2	2	no	—
410	C₄×C₆₇	—	2	1	no	—
411	C₄×C₆₇	—	2	1	no	—
412	C₄×C₆₇	—	2	1	no	—
413	C₄×C₆₇	—	4	2	no	—
414	C₄×C₆₇	—	4	2	no	—
415	C₄×C₆₇	—	4	1	no	—
416	C₄×C₆₇	—	4	1	no	—
417	C₄×C₆₇	—	4	2	no	—
418	C₄×C₆₇	—	4	2	no	—
419	C₄×C₆₇	—	4	4	no	—
420	C₄×C₆₇	—	4	1	no	—
421	C₄×C₆₇	C₂×#137	1	2	yes	—
422	C₄×C₆₇	#585	1	2	yes	—
423	#61735	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
424	C₂×C₆₇	—	2	2	no	—
425	C₂×C₆₇	—	2	4	no	—
426	C₂×C₆₇	—	4	2	no	—
427	C₂×C₆₇	—	8	1	no	—
428	C₂×C₆₇	#3485	1	1	yes	characteristic
429	C₂×C₆₇	C₂²×#137	1	1	yes	characteristic
430	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
431	#3520	C₂×C₆₇	1	1	yes	characteristic
432	C₂×#554	C₂×C₆₇	1	1	yes	characteristic, complemented
433	#3356	C₂×C₆₇	1	2	yes	complemented
434	#3344	C₂×C₆₇	1	4	yes	complemented
435	#3335	C₂×C₆₇	1	2	yes	complemented
436	#3331	C₂×C₆₇	1	2	yes	complemented
437	#3316	C₂×C₆₇	1	4	yes	complemented
438	#3299	C₂×C₆₇	1	2	yes	complemented
439	#3238	C₂×C₆₇	1	1	yes	characteristic, complemented
440	#3229	C₂×C₆₇	1	1	yes	characteristic, complemented
441	#3195	C₂×C₆₇	1	2	yes	complemented
442	#3190	C₂×C₆₇	1	2	yes	complemented
443	#3113	C₂×C₆₇	1	1	yes	characteristic, complemented
444	#3108	C₂×C₆₇	1	1	yes	characteristic, complemented
445	#3092	C₂×C₆₇	1	2	yes	complemented
446	C₂×#483	C₂×C₆₇	1	2	yes	complemented
447	#2974	C₂×C₆₇	1	1	yes	characteristic, complemented
448	C₆₇	#61735	1	1	yes	characteristic, direct product factor, Sylow
449	#556	C₂²×C₆₇	1	1	yes	characteristic
450	#554	—	2	1	no	—
451	#554	—	2	2	no	—
452	#554	—	2	1	no	—
453	#554	—	2	1	no	—
454	#554	C₂²×C₆₇	1	2	yes	—
455	#554	C₂²×C₆₇	1	2	yes	—
456	#554	C₂²×C₆₇	1	4	yes	—
457	#552	C₂²×C₆₇	1	2	yes	—
458	#551	—	2	2	no	—
459	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
460	#548	C₂²×C₆₇	1	2	yes	—
461	#547	C₂²×C₆₇	1	1	yes	characteristic
462	#547	C₂²×C₆₇	1	1	yes	characteristic
463	#546	—	2	1	no	—
464	#542	—	2	1	no	—
465	#539	—	2	2	no	—
466	#533	C₂²×C₆₇	1	1	yes	characteristic
467	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
468	#529	C₂²×C₆₇	1	1	yes	characteristic
469	C₂×#125	—	2	1	no	—
470	#525	C₂²×C₆₇	1	2	yes	—
471	C₂×C₂²⋊Q₈	—	2	2	no	—
472	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
473	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
474	#520	—	2	1	no	—
475	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
476	C₂×C₄×D₄	—	2	1	no	—
477	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
478	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
479	#501	C₂²×C₆₇	1	2	yes	complemented
480	#498	C₂²×C₆₇	1	2	yes	complemented
481	#489	C₂²×C₆₇	1	2	yes	complemented
482	#487	C₂²×C₆₇	1	2	yes	complemented
483	#485	C₂²×C₆₇	1	4	yes	complemented
484	#484	C₂²×C₆₇	1	4	yes	complemented
485	#483	C₂²×C₆₇	1	1	yes	characteristic
486	#483	C₂²×C₆₇	1	2	yes	—
487	#483	C₂²×C₆₇	1	2	yes	—
488	#483	C₂²×C₆₇	1	2	yes	—
489	#483	C₂²×C₆₇	1	2	yes	—
490	#483	C₂²×C₆₇	1	4	yes	complemented
491	#483	C₂²×C₆₇	1	4	yes	complemented
492	#483	C₂²×C₆₇	1	4	yes	complemented
493	#481	C₂²×C₆₇	1	4	yes	complemented
494	#480	C₂²×C₆₇	1	1	yes	characteristic
495	#480	C₂²×C₆₇	1	2	yes	—
496	#479	C₂²×C₆₇	1	2	yes	complemented
497	#477	C₂²×C₆₇	1	2	yes	complemented
498	#476	C₂²×C₆₇	1	2	yes	complemented
499	#475	C₂²×C₆₇	1	2	yes	complemented
500	#475	C₂²×C₆₇	1	4	yes	complemented
501	#470	C₂²×C₆₇	1	4	yes	complemented
502	#470	C₂²×C₆₇	1	4	yes	complemented
503	#467	C₂²×C₆₇	1	4	yes	complemented
504	#465	C₂²×C₆₇	1	4	yes	complemented
505	#464	C₂²×C₆₇	1	2	yes	complemented
506	#462	C₂²×C₆₇	1	2	yes	complemented
507	#452	C₂²×C₆₇	1	4	yes	complemented
508	#451	C₂²×C₆₇	1	1	yes	characteristic
509	#451	C₂²×C₆₇	1	2	yes	—
510	#451	C₂²×C₆₇	1	4	yes	complemented
511	#448	C₂²×C₆₇	1	1	yes	characteristic
512	#441	C₂²×C₆₇	1	4	yes	complemented
513	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
514	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
515	#436	C₂²×C₆₇	1	2	yes	—
516	#435	C₂²×C₆₇	1	4	yes	—
517	C₈×D₄	C₂²×C₆₇	1	2	yes	—
518	#432	C₂²×C₆₇	1	1	yes	characteristic
519	#431	C₂²×C₆₇	1	1	yes	characteristic
520	#428	C₂²×C₆₇	1	4	yes	complemented
521	C₂×#106	C₂²×C₆₇	1	4	yes	complemented
522	#417	C₂²×C₆₇	1	4	yes	complemented
523	C₂×#103	C₂²×C₆₇	1	4	yes	complemented
524	#407	C₂²×C₆₇	1	2	yes	—
525	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	—
526	C₂×#41	—	2	1	no	—
527	C₂×#41	C₂³×C₆₇	1	2	yes	—
528	C₂²×Q₈	—	2	1	no	—
529	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
530	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
531	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
532	C₂³×C₄	—	2	2	no	—
533	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
534	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
535	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
536	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
537	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
538	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
539	C₄⋊Q₈	—	2	1	no	—
540	C₄⋊Q₈	—	2	1	no	—
541	C₄⋊Q₈	—	2	1	no	—
542	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
543	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
544	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
545	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
546	#126	—	2	2	no	—
547	#126	—	2	2	no	—
548	#126	—	2	1	no	—
549	#125	—	2	2	no	—
550	#125	—	2	4	no	—
551	#125	—	2	2	no	—
552	#125	—	2	2	no	—
553	#125	—	2	1	no	—
554	#125	C₂³×C₆₇	1	1	yes	characteristic
555	#124	—	2	1	no	—
556	#124	—	2	2	no	—
557	#124	C₂³×C₆₇	1	1	yes	characteristic
558	#123	—	2	2	no	—
559	#123	—	2	2	no	—
560	#123	—	2	1	no	—
561	#123	—	2	2	no	—
562	#123	—	2	2	no	—
563	C₂²⋊Q₈	—	2	2	no	—
564	C₂²⋊Q₈	—	2	2	no	—
565	C₂²⋊Q₈	—	2	2	no	—
566	C₂²⋊Q₈	—	2	2	no	—
567	C₂²⋊Q₈	—	2	1	no	—
568	C₂²⋊Q₈	—	2	2	no	—
569	C₂²⋊Q₈	—	2	1	no	—
570	C₂²⋊Q₈	—	2	4	no	—
571	C₂²⋊Q₈	—	2	4	no	—
572	C₂²⋊Q₈	—	2	4	no	—
573	C₂²⋊Q₈	—	2	4	no	—
574	C₂²⋊Q₈	—	2	2	no	—
575	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
576	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
577	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
578	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
579	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
580	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
581	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
582	#121	—	2	2	no	—
583	#121	—	2	1	no	—
584	#121	C₂³×C₆₇	1	1	yes	characteristic
585	#121	C₂³×C₆₇	1	2	yes	—
586	#120	—	2	2	no	—
587	C₄×Q₈	—	2	1	no	—
588	C₄×Q₈	—	2	1	no	—
589	C₄×Q₈	—	2	1	no	—
590	C₄×Q₈	—	2	1	no	—
591	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
592	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
593	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
594	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
595	C₄×D₄	—	2	4	no	—
596	C₄×D₄	—	2	2	no	—
597	C₄×D₄	—	2	2	no	—
598	C₄×D₄	—	2	1	no	—
599	C₄×D₄	—	2	2	no	—
600	C₄×D₄	—	2	2	no	—
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
604	C₄×D₄	D₄×C₆₇	1	2	yes	—
605	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
606	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
607	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
608	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
609	C₄×D₄	C₂³×C₆₇	1	2	yes	—
610	#117	—	2	1	no	—
611	#117	—	2	2	no	—
612	#117	—	2	1	no	—
613	#117	C₂³×C₆₇	1	2	yes	—
614	C₂×C₄⋊C₄	—	2	2	no	—
615	C₂×C₄⋊C₄	—	2	2	no	—
616	C₂×C₄⋊C₄	—	2	2	no	—
617	C₂×C₄⋊C₄	—	2	1	no	—
618	C₂×C₄⋊C₄	—	2	1	no	—
619	C₂×C₄⋊C₄	—	2	2	no	—
620	C₂×C₄⋊C₄	—	2	2	no	—
621	C₂×C₄⋊C₄	—	2	1	no	—
622	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
626	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
627	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
628	C₂×C₂²⋊C₄	—	2	2	no	—
629	C₂×C₂²⋊C₄	—	2	2	no	—
630	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
631	C₂×C₄²	—	2	1	no	—
632	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
633	#107	C₂³×C₆₇	1	2	yes	—
634	#107	C₂³×C₆₇	1	4	yes	—
635	#106	C₂³×C₆₇	1	2	yes	—
636	#106	C₂³×C₆₇	1	4	yes	—
637	#106	C₂³×C₆₇	1	4	yes	—
638	#106	C₂³×C₆₇	1	4	yes	—
639	#106	C₂³×C₆₇	1	4	yes	—
640	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
641	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
642	#103	C₂³×C₆₇	1	2	yes	—
643	#103	C₂³×C₆₇	1	4	yes	—
644	#103	C₂³×C₆₇	1	4	yes	—
645	#103	C₂³×C₆₇	1	4	yes	—
646	#103	C₂³×C₆₇	1	4	yes	—
647	#103	C₂³×C₆₇	1	2	yes	—
648	#103	C₂³×C₆₇	1	2	yes	—
649	#103	C₂³×C₆₇	1	4	yes	—
650	#102	C₂³×C₆₇	1	2	yes	—
651	#102	C₂³×C₆₇	1	4	yes	—
652	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
653	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
654	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
655	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
656	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
657	#97	C₂³×C₆₇	1	2	yes	—
658	C₄×C₈	C₂³×C₆₇	1	2	yes	—
659	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
660	#41	—	4	4	no	—
661	#41	—	4	4	no	—
662	C₂×Q₈	—	2	1	no	—
663	C₂×Q₈	—	2	1	no	—
664	C₂×Q₈	—	2	2	no	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	2	2	no	—
667	C₂×Q₈	—	4	2	no	—
668	C₂×Q₈	—	4	4	no	—
669	C₂×Q₈	—	8	2	no	—
670	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
671	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
672	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
673	C₂×D₄	—	2	4	no	—
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
678	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
679	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
680	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
681	C₂²×C₄	—	2	1	no	—
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	2	2	no	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	4	no	—
687	C₂²×C₄	—	2	4	no	—
688	C₂²×C₄	—	2	1	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	4	4	no	—
691	C₂²×C₄	—	8	4	no	—
692	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
693	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
694	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
695	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
696	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
700	Q₁₆	—	4	4	no	—
701	Q₁₆	—	4	2	no	—
702	SD₁₆	—	4	2	no	—
703	M₁₆	—	4	4	no	—
704	C₂×C₈	—	4	4	no	—
705	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
706	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
707	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	—	2	1	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
732	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
733	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
734	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
735	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
736	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
737	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
738	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
739	C₂²⋊C₄	—	2	1	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	1	no	—
748	C₂²⋊C₄	—	2	1	no	—
749	C₂²⋊C₄	—	2	1	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	1	no	—
752	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
753	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
754	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
755	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
756	C₄²	—	2	2	no	—
757	C₄²	—	2	2	no	—
758	C₄²	—	2	2	no	—
759	C₄²	—	2	2	no	—
760	C₄²	—	2	1	no	—
761	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
762	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
763	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
764	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
765	C₂³	—	2	4	no	—
766	C₂³	—	2	4	no	—
767	C₂³	—	2	1	no	—
768	C₂³	—	4	2	no	—
769	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
770	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
771	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
772	Q₈	—	2	2	no	—
773	Q₈	—	2	2	no	—
774	Q₈	—	2	2	no	—
775	Q₈	—	2	4	no	—
776	Q₈	—	4	2	no	—
777	Q₈	—	4	2	no	—
778	Q₈	—	8	2	no	—
779	Q₈	—	8	2	no	—
780	Q₈	—	8	2	no	—
781	D₄	—	2	4	no	—
782	D₄	—	2	2	no	—
783	D₄	—	2	2	no	—
784	D₄	—	4	4	no	—
785	D₄	—	4	2	no	—
786	D₄	—	8	2	no	—
787	D₄	#137×C₆₇	1	4	yes	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	4	no	—
791	C₂×C₄	—	2	4	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	4	2	no	—
802	C₂×C₄	—	4	2	no	—
803	C₂×C₄	—	4	2	no	—
804	C₂×C₄	—	4	2	no	—
805	C₂×C₄	—	4	4	no	—
806	C₂×C₄	—	4	2	no	—
807	C₂×C₄	—	4	4	no	—
808	C₂×C₄	—	4	2	no	—
809	C₂×C₄	—	8	2	no	—
810	C₂×C₄	—	8	4	no	—
811	C₂×C₄	—	8	4	no	—
812	C₂×C₄	—	8	2	no	—
813	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
814	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
815	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
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	2	yes	—
819	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
820	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
821	C₈	—	2	2	no	—
822	C₈	—	2	4	no	—
823	C₈	—	2	2	no	—
824	C₂²	—	2	1	no	—
825	C₂²	—	2	2	no	—
826	C₂²	—	2	1	no	—
827	C₂²	—	2	2	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	4	8	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	1	no	—
835	C₂²	C₂×#137×C₆₇	1	4	yes	—
836	C₂²	#577×C₆₇	1	2	yes	—
837	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
838	C₄	—	2	1	no	—
839	C₄	—	2	1	no	—
840	C₄	—	2	1	no	—
841	C₄	—	2	1	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	2	no	—
844	C₄	—	4	1	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	2	no	—
847	C₄	—	4	4	no	—
848	C₄	—	4	1	no	—
849	C₄	—	4	2	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	1	no	—
852	C₄	C₂×#137×C₆₇	1	2	yes	—
853	C₄	#585×C₆₇	1	2	yes	—
854	C₂	—	2	2	no	—
855	C₂	—	2	4	no	—
856	C₂	—	4	2	no	—
857	C₂	—	8	1	no	—
858	C₂	C₆₇×#3485	1	1	yes	characteristic
859	C₂	C₂²×#137×C₆₇	1	1	yes	characteristic
860	C₂	C₂×#577×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₆₇×#3520	C₂
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
2. C₂×#554×C₆₇	C₂	semidirect
3. C₆₇×#3356	C₂	semidirect
4. C₆₇×#3344	C₂	semidirect
5. C₆₇×#3335	C₂	semidirect
6. C₆₇×#3331	C₂	semidirect
7. C₆₇×#3316	C₂	semidirect
8. C₆₇×#3299	C₂	semidirect
9. C₆₇×#3238	C₂	semidirect
10. C₆₇×#3229	C₂	semidirect
11. C₆₇×#3195	C₂	semidirect
12. C₆₇×#3190	C₂	semidirect
13. C₆₇×#3113	C₂	semidirect
14. C₆₇×#3108	C₂	semidirect
15. C₆₇×#3092	C₂	semidirect
16. C₂×#483×C₆₇	C₂	semidirect
17. C₆₇×#2974	C₂	semidirect
48. #501×C₆₇	C₂²	semidirect
49. #498×C₆₇	C₂²	semidirect
50. #489×C₆₇	C₂²	semidirect
51. #487×C₆₇	C₂²	semidirect
52. #485×C₆₇	C₂²	semidirect
53. #484×C₆₇	C₂²	semidirect
59. #483×C₆₇	C₂²	semidirect
60. #483×C₆₇	C₂²	semidirect
61. #483×C₆₇	C₂²	semidirect
62. #481×C₆₇	C₂²	semidirect
65. #479×C₆₇	C₂²	semidirect
66. #477×C₆₇	C₂²	semidirect
67. #476×C₆₇	C₂²	semidirect
68. #475×C₆₇	C₂²	semidirect
69. #475×C₆₇	C₂²	semidirect
70. #470×C₆₇	C₂²	semidirect
71. #470×C₆₇	C₂²	semidirect
72. #467×C₆₇	C₂²	semidirect
73. #465×C₆₇	C₂²	semidirect
74. #464×C₆₇	C₂²	semidirect
75. #462×C₆₇	C₂²	semidirect
76. #452×C₆₇	C₂²	semidirect
79. #451×C₆₇	C₂²	semidirect
81. #441×C₆₇	C₂²	semidirect
82. C₄×Q₁₆×C₆₇	C₂²	semidirect
83. C₄×SD₁₆×C₆₇	C₂²	semidirect
89. #428×C₆₇	C₂²	semidirect
90. C₂×#106×C₆₇	C₂²	semidirect
91. #417×C₆₇	C₂²	semidirect
92. C₂×#103×C₆₇	C₂²	semidirect
423. #61735	C₆₇	direct (N × H)
432. C₂×#554	C₂×C₆₇	semidirect
433. #3356	C₂×C₆₇	semidirect
434. #3344	C₂×C₆₇	semidirect
435. #3335	C₂×C₆₇	semidirect
436. #3331	C₂×C₆₇	semidirect
437. #3316	C₂×C₆₇	semidirect
438. #3299	C₂×C₆₇	semidirect
439. #3238	C₂×C₆₇	semidirect
440. #3229	C₂×C₆₇	semidirect
441. #3195	C₂×C₆₇	semidirect
442. #3190	C₂×C₆₇	semidirect
443. #3113	C₂×C₆₇	semidirect
444. #3108	C₂×C₆₇	semidirect
445. #3092	C₂×C₆₇	semidirect
446. C₂×#483	C₂×C₆₇	semidirect
447. #2974	C₂×C₆₇	semidirect
448. C₆₇	#61735	direct (N × H)
479. #501	C₂²×C₆₇	semidirect
480. #498	C₂²×C₆₇	semidirect
481. #489	C₂²×C₆₇	semidirect
482. #487	C₂²×C₆₇	semidirect
483. #485	C₂²×C₆₇	semidirect
484. #484	C₂²×C₆₇	semidirect
490. #483	C₂²×C₆₇	semidirect
491. #483	C₂²×C₆₇	semidirect
492. #483	C₂²×C₆₇	semidirect
493. #481	C₂²×C₆₇	semidirect
496. #479	C₂²×C₆₇	semidirect
497. #477	C₂²×C₆₇	semidirect
498. #476	C₂²×C₆₇	semidirect
499. #475	C₂²×C₆₇	semidirect
500. #475	C₂²×C₆₇	semidirect
501. #470	C₂²×C₆₇	semidirect
502. #470	C₂²×C₆₇	semidirect
503. #467	C₂²×C₆₇	semidirect
504. #465	C₂²×C₆₇	semidirect
505. #464	C₂²×C₆₇	semidirect
506. #462	C₂²×C₆₇	semidirect
507. #452	C₂²×C₆₇	semidirect
510. #451	C₂²×C₆₇	semidirect
512. #441	C₂²×C₆₇	semidirect
513. C₄×Q₁₆	C₂²×C₆₇	semidirect
514. C₄×SD₁₆	C₂²×C₆₇	semidirect
520. #428	C₂²×C₆₇	semidirect
521. C₂×#106	C₂²×C₆₇	semidirect
522. #417	C₂²×C₆₇	semidirect
523. C₂×#103	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×#3520	2
C₂×#554×C₆₇	2
C₆₇×#3356	2
C₆₇×#3344	2
C₆₇×#3335	2
C₆₇×#3331	2
C₆₇×#3316	2
C₆₇×#3299	2
C₆₇×#3238	2
C₆₇×#3229	2
C₆₇×#3195	2
C₆₇×#3190	2
C₆₇×#3113	2
C₆₇×#3108	2
C₆₇×#3092	2
C₂×#483×C₆₇	2
C₆₇×#2974	2
#61735	67

Subgroups — C67×#61735 #30740986

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61735 #30740986