Subgroups — C₆₇×#61346 #30740597

Order 17152.

1782 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3376	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3374	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3373	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3369	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3365	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3359	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3141	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3137	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3084	C₂	1	2	yes	maximal, complemented
12	C₂×#475×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3046	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3035	C₂	1	1	yes	maximal, characteristic
15	C₆₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2952	C₂	1	2	yes	maximal, complemented
17	C₄×#137×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×#135×C₆₇	C₂²	1	2	yes	—
20	#559×C₆₇	C₂²	1	2	yes	—
21	Q₈²×C₆₇	C₂²	1	2	yes	—
22	#557×C₆₇	C₂²	1	2	yes	—
23	#557×C₆₇	C₂²	1	2	yes	—
24	#556×C₆₇	—	2	1	no	—
25	#556×C₆₇	C₂²	1	4	yes	—
26	#554×C₆₇	—	2	1	no	—
27	#554×C₆₇	—	2	2	no	—
28	#554×C₆₇	C₂²	1	2	yes	—
29	#552×C₆₇	—	2	2	no	—
30	D₄×Q₈×C₆₇	—	2	2	no	—
31	D₄×Q₈×C₆₇	C₂²	1	2	yes	—
32	#544×C₆₇	—	2	2	no	—
33	#544×C₆₇	C₂²	1	2	yes	—
34	#539×C₆₇	—	2	2	no	—
35	#536×C₆₇	C₂²	1	2	yes	—
36	#533×C₆₇	—	2	1	no	—
37	#533×C₆₇	C₂²	1	1	yes	characteristic
38	#532×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊Q₈×C₆₇	—	2	1	no	—
40	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
41	#529×C₆₇	—	2	2	no	—
42	#520×C₆₇	C₂²	1	2	yes	—
43	#520×C₆₇	C₂²	1	2	yes	—
44	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
46	#491×C₆₇	C₂²	1	4	yes	—
47	#489×C₆₇	C₂²	1	4	yes	—
48	#489×C₆₇	C₂²	1	4	yes	—
49	#488×C₆₇	C₂²	1	4	yes	—
50	#487×C₆₇	C₂²	1	4	yes	—
51	#487×C₆₇	C₂²	1	2	yes	—
52	#486×C₆₇	C₂²	1	2	yes	—
53	#479×C₆₇	C₂²	1	4	yes	—
54	#478×C₆₇	C₂²	1	4	yes	—
55	#476×C₆₇	C₂²	1	4	yes	—
56	#475×C₆₇	C₂²	1	2	yes	—
57	#475×C₆₇	C₂²	1	4	yes	—
58	#475×C₆₇	C₂²	1	2	yes	—
59	#475×C₆₇	C₂²	1	4	yes	—
60	#464×C₆₇	C₂²	1	2	yes	—
61	#464×C₆₇	C₂²	1	4	yes	—
62	#463×C₆₇	C₂²	1	2	yes	—
63	#463×C₆₇	C₂²	1	4	yes	—
64	#462×C₆₇	C₂²	1	1	yes	characteristic
65	#462×C₆₇	C₂²	1	4	yes	—
66	#461×C₆₇	C₂²	1	1	yes	characteristic
67	#461×C₆₇	C₂²	1	4	yes	—
68	#460×C₆₇	C₂²	1	1	yes	characteristic
69	#459×C₆₇	C₂²	1	1	yes	characteristic
70	#446×C₆₇	C₂²	1	4	yes	—
71	#446×C₆₇	C₂²	1	2	yes	—
72	C₈×Q₈×C₆₇	C₂²	1	2	yes	—
73	#442×C₆₇	C₂²	1	4	yes	—
74	#441×C₆₇	C₂²	1	2	yes	—
75	#441×C₆₇	C₂²	1	4	yes	—
76	#440×C₆₇	C₂²	1	2	yes	—
77	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
78	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
79	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	—
80	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	—
81	#428×C₆₇	C₂²	1	1	yes	characteristic
82	C₂×#106×C₆₇	C₂²	1	2	yes	—
83	#424×C₆₇	C₂²	1	2	yes	—
84	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
85	#419×C₆₇	C₂²	1	1	yes	characteristic
86	#417×C₆₇	C₂²	1	2	yes	—
87	#417×C₆₇	C₂²	1	2	yes	—
88	#417×C₆₇	C₂²	1	1	yes	characteristic
89	#416×C₆₇	C₂²	1	2	yes	—
90	C₂×#103×C₆₇	C₂²	1	2	yes	—
91	#405×C₆₇	C₂²	1	2	yes	—
92	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
93	C₂×#41×C₆₇	C₂³	1	2	yes	—
94	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
95	C₂²×Q₈×C₆₇	—	2	2	no	—
96	C₂²×Q₈×C₆₇	—	2	1	no	—
97	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
98	#137×C₆₇	—	2	4	no	—
99	#135×C₆₇	—	2	8	no	—
100	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
101	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
102	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
105	C₂×D₈×C₆₇	C₂³	1	2	yes	—
106	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
107	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
109	C₄⋊Q₈×C₆₇	—	2	2	no	—
110	C₄⋊Q₈×C₆₇	—	2	2	no	—
111	C₄⋊Q₈×C₆₇	—	2	2	no	—
112	C₄⋊Q₈×C₆₇	—	2	4	no	—
113	C₄⋊Q₈×C₆₇	—	2	1	no	—
114	C₄⋊Q₈×C₆₇	—	2	1	no	—
115	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
116	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
117	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
118	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
119	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
120	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
121	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
122	#127×C₆₇	C₂³	1	1	yes	characteristic
123	#126×C₆₇	—	2	4	no	—
124	#126×C₆₇	—	2	4	no	—
125	#125×C₆₇	—	2	2	no	—
126	#125×C₆₇	—	2	2	no	—
127	#125×C₆₇	—	2	4	no	—
128	#125×C₆₇	—	2	4	no	—
129	#125×C₆₇	D₄	1	2	yes	—
130	#125×C₆₇	C₂³	1	4	yes	—
131	#124×C₆₇	—	2	2	no	—
132	#124×C₆₇	C₂³	1	4	yes	—
133	#124×C₆₇	C₂³	1	2	yes	—
134	#123×C₆₇	—	2	4	no	—
135	#123×C₆₇	—	2	4	no	—
136	C₂²⋊Q₈×C₆₇	—	2	2	no	—
137	C₂²⋊Q₈×C₆₇	—	2	4	no	—
138	C₂²⋊Q₈×C₆₇	—	2	2	no	—
139	C₂²⋊Q₈×C₆₇	—	2	2	no	—
140	C₂²⋊Q₈×C₆₇	—	2	2	no	—
141	C₂²⋊Q₈×C₆₇	—	2	4	no	—
142	C₂²⋊Q₈×C₆₇	—	2	4	no	—
143	C₂²⋊Q₈×C₆₇	—	2	4	no	—
144	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
145	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
146	#121×C₆₇	—	2	1	no	—
147	#121×C₆₇	—	2	1	no	—
148	C₄×Q₈×C₆₇	—	2	2	no	—
149	C₄×Q₈×C₆₇	—	2	2	no	—
150	C₄×Q₈×C₆₇	—	2	2	no	—
151	C₄×Q₈×C₆₇	—	2	1	no	—
152	C₄×Q₈×C₆₇	—	2	1	no	—
153	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
154	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
155	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
156	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
157	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
158	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
159	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
160	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
161	C₄×D₄×C₆₇	—	2	1	no	—
162	C₄×D₄×C₆₇	—	2	1	no	—
163	C₄×D₄×C₆₇	—	2	2	no	—
164	C₄×D₄×C₆₇	—	2	4	no	—
165	C₄×D₄×C₆₇	—	2	4	no	—
166	C₄×D₄×C₆₇	—	2	1	no	—
167	C₄×D₄×C₆₇	—	2	1	no	—
168	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
169	C₄×D₄×C₆₇	C₂³	1	4	yes	—
170	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
171	C₄×D₄×C₆₇	C₂³	1	4	yes	—
172	#117×C₆₇	—	2	2	no	—
173	#117×C₆₇	—	2	2	no	—
174	#117×C₆₇	—	2	4	no	—
175	#117×C₆₇	—	2	1	no	—
176	#117×C₆₇	C₂³	1	1	yes	characteristic
177	#117×C₆₇	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
179	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
180	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
181	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
182	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
183	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
185	C₂×C₄²×C₆₇	—	2	1	no	—
186	C₂×C₄²×C₆₇	—	2	1	no	—
187	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
188	#107×C₆₇	C₂³	1	2	yes	—
189	#106×C₆₇	C₂³	1	4	yes	—
190	#106×C₆₇	C₂³	1	2	yes	—
191	#106×C₆₇	C₂³	1	4	yes	—
192	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
193	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
194	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
195	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
196	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
197	#103×C₆₇	C₂³	1	4	yes	—
198	#103×C₆₇	C₂³	1	2	yes	—
199	#103×C₆₇	C₂³	1	4	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	4	yes	—
204	#103×C₆₇	C₂³	1	2	yes	—
205	#103×C₆₇	C₂³	1	2	yes	—
206	#102×C₆₇	C₂³	1	2	yes	—
207	#102×C₆₇	C₂³	1	2	yes	—
208	#102×C₆₇	C₂³	1	4	yes	—
209	#102×C₆₇	C₂³	1	4	yes	—
210	#102×C₆₇	C₂³	1	2	yes	—
211	#97×C₆₇	C₂³	1	2	yes	—
212	#97×C₆₇	C₂³	1	4	yes	—
213	C₄×C₈×C₆₇	C₂³	1	2	yes	—
214	C₄×C₈×C₆₇	C₂³	1	4	yes	—
215	#41×C₆₇	—	2	2	no	—
216	#41×C₆₇	—	2	4	no	—
217	#41×C₆₇	—	2	4	no	—
218	#41×C₆₇	#41	1	4	yes	—
219	C₂×Q₈×C₆₇	—	2	1	no	—
220	C₂×Q₈×C₆₇	—	2	2	no	—
221	C₂×Q₈×C₆₇	—	2	4	no	—
222	C₂×Q₈×C₆₇	—	2	2	no	—
223	C₂×Q₈×C₆₇	—	2	2	no	—
224	C₂×Q₈×C₆₇	—	2	2	no	—
225	C₂×Q₈×C₆₇	—	8	2	no	—
226	C₂×Q₈×C₆₇	—	8	4	no	—
227	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
228	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
229	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
230	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
231	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
232	C₂×D₄×C₆₇	—	2	1	no	—
233	C₂×D₄×C₆₇	—	2	2	no	—
234	C₂×D₄×C₆₇	—	2	1	no	—
235	C₂×D₄×C₆₇	—	2	1	no	—
236	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
237	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₆₇	—	2	1	no	—
239	C₂²×C₄×C₆₇	—	2	1	no	—
240	C₂²×C₄×C₆₇	—	2	1	no	—
241	C₂²×C₄×C₆₇	—	2	2	no	—
242	C₂²×C₄×C₆₇	—	2	1	no	—
243	C₂²×C₄×C₆₇	—	2	1	no	—
244	C₂²×C₄×C₆₇	—	2	2	no	—
245	C₂²×C₄×C₆₇	—	2	4	no	—
246	C₂²×C₄×C₆₇	—	2	4	no	—
247	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
250	Q₁₆×C₆₇	—	2	4	no	—
251	Q₁₆×C₆₇	—	2	4	no	—
252	SD₁₆×C₆₇	—	2	4	no	—
253	SD₁₆×C₆₇	—	2	4	no	—
254	SD₁₆×C₆₇	—	2	4	no	—
255	D₈×C₆₇	—	2	4	no	—
256	M₁₆×C₆₇	—	2	2	no	—
257	M₁₆×C₆₇	—	2	2	no	—
258	C₂×C₈×C₆₇	—	2	4	no	—
259	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
260	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
261	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
262	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
263	C₄⋊C₄×C₆₇	—	2	1	no	—
264	C₄⋊C₄×C₆₇	—	2	2	no	—
265	C₄⋊C₄×C₆₇	—	2	2	no	—
266	C₄⋊C₄×C₆₇	—	2	4	no	—
267	C₄⋊C₄×C₆₇	—	2	4	no	—
268	C₄⋊C₄×C₆₇	—	2	2	no	—
269	C₄⋊C₄×C₆₇	—	2	2	no	—
270	C₄⋊C₄×C₆₇	—	2	2	no	—
271	C₄⋊C₄×C₆₇	—	2	4	no	—
272	C₄⋊C₄×C₆₇	—	2	1	no	—
273	C₄⋊C₄×C₆₇	—	2	1	no	—
274	C₄⋊C₄×C₆₇	—	2	4	no	—
275	C₄⋊C₄×C₆₇	—	2	1	no	—
276	C₄⋊C₄×C₆₇	—	2	1	no	—
277	C₄⋊C₄×C₆₇	—	2	4	no	—
278	C₄⋊C₄×C₆₇	—	2	4	no	—
279	C₄⋊C₄×C₆₇	—	2	4	no	—
280	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
281	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
282	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
283	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
284	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
285	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
286	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
287	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
288	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
289	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
290	C₂²⋊C₄×C₆₇	—	2	1	no	—
291	C₂²⋊C₄×C₆₇	—	2	2	no	—
292	C₂²⋊C₄×C₆₇	—	2	1	no	—
293	C₂²⋊C₄×C₆₇	—	2	1	no	—
294	C₂²⋊C₄×C₆₇	—	2	4	no	—
295	C₂²⋊C₄×C₆₇	—	2	4	no	—
296	C₂²⋊C₄×C₆₇	—	2	4	no	—
297	C₂²⋊C₄×C₆₇	—	2	2	no	—
298	C₂²⋊C₄×C₆₇	—	2	4	no	—
299	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
300	C₄²×C₆₇	—	2	2	no	—
301	C₄²×C₆₇	—	2	1	no	—
302	C₄²×C₆₇	—	2	2	no	—
303	C₄²×C₆₇	—	2	1	no	—
304	C₄²×C₆₇	—	2	1	no	—
305	C₄²×C₆₇	—	2	4	no	—
306	C₄²×C₆₇	—	2	4	no	—
307	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
310	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
311	C₄²×C₆₇	C₂⁴	1	4	yes	—
312	C₂³×C₆₇	—	2	1	no	—
313	C₂³×C₆₇	—	2	2	no	—
314	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
315	Q₈×C₆₇	—	2	4	no	—
316	Q₈×C₆₇	—	2	1	no	—
317	Q₈×C₆₇	—	2	2	no	—
318	Q₈×C₆₇	—	2	2	no	—
319	Q₈×C₆₇	—	2	2	no	—
320	Q₈×C₆₇	—	2	2	no	—
321	Q₈×C₆₇	—	4	2	no	—
322	Q₈×C₆₇	—	4	2	no	—
323	Q₈×C₆₇	—	4	4	no	—
324	Q₈×C₆₇	—	8	2	no	—
325	Q₈×C₆₇	—	8	4	no	—
326	Q₈×C₆₇	C₂×#41	1	2	yes	—
327	D₄×C₆₇	—	2	4	no	—
328	D₄×C₆₇	—	2	2	no	—
329	D₄×C₆₇	—	2	1	no	—
330	D₄×C₆₇	—	2	2	no	—
331	D₄×C₆₇	—	4	4	no	—
332	D₄×C₆₇	—	4	2	no	—
333	D₄×C₆₇	—	8	1	no	—
334	D₄×C₆₇	C₂×#41	1	2	yes	—
335	C₂×C₄×C₆₇	—	2	1	no	—
336	C₂×C₄×C₆₇	—	2	4	no	—
337	C₂×C₄×C₆₇	—	2	2	no	—
338	C₂×C₄×C₆₇	—	2	2	no	—
339	C₂×C₄×C₆₇	—	2	2	no	—
340	C₂×C₄×C₆₇	—	2	1	no	—
341	C₂×C₄×C₆₇	—	2	2	no	—
342	C₂×C₄×C₆₇	—	2	1	no	—
343	C₂×C₄×C₆₇	—	2	4	no	—
344	C₂×C₄×C₆₇	—	4	1	no	—
345	C₂×C₄×C₆₇	—	4	2	no	—
346	C₂×C₄×C₆₇	—	4	2	no	—
347	C₂×C₄×C₆₇	—	4	4	no	—
348	C₂×C₄×C₆₇	—	4	2	no	—
349	C₂×C₄×C₆₇	—	8	4	no	—
350	C₂×C₄×C₆₇	—	8	4	no	—
351	C₂×C₄×C₆₇	—	8	1	no	—
352	C₂×C₄×C₆₇	—	8	2	no	—
353	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
356	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
357	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
361	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
362	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
363	C₈×C₆₇	—	2	2	no	—
364	C₈×C₆₇	—	2	2	no	—
365	C₈×C₆₇	—	2	2	no	—
366	C₈×C₆₇	—	2	2	no	—
367	C₂²×C₆₇	—	2	1	no	—
368	C₂²×C₆₇	—	2	1	no	—
369	C₂²×C₆₇	—	2	2	no	—
370	C₂²×C₆₇	—	4	1	no	—
371	C₂²×C₆₇	—	4	1	no	—
372	C₂²×C₆₇	—	4	2	no	—
373	C₂²×C₆₇	—	4	2	no	—
374	C₂²×C₆₇	—	4	2	no	—
375	C₂²×C₆₇	#548	1	2	yes	—
376	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
377	C₄×C₆₇	—	2	1	no	—
378	C₄×C₆₇	—	2	1	no	—
379	C₄×C₆₇	—	2	4	no	—
380	C₄×C₆₇	—	2	2	no	—
381	C₄×C₆₇	—	2	1	no	—
382	C₄×C₆₇	—	2	4	no	—
383	C₄×C₆₇	—	4	1	no	—
384	C₄×C₆₇	—	4	2	no	—
385	C₄×C₆₇	—	4	2	no	—
386	C₄×C₆₇	—	4	2	no	—
387	C₄×C₆₇	—	4	1	no	—
388	C₄×C₆₇	—	4	4	no	—
389	C₄×C₆₇	#548	1	2	yes	—
390	C₄×C₆₇	#577	1	2	yes	—
391	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
392	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
393	#61346	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
394	C₂×C₆₇	—	2	2	no	—
395	C₂×C₆₇	—	4	2	no	—
396	C₂×C₆₇	—	8	2	no	—
397	C₂×C₆₇	C₂×#548	1	1	yes	characteristic
398	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
399	C₂×C₆₇	#3586	1	1	yes	characteristic
400	#3507	C₂×C₆₇	1	1	yes	characteristic, complemented
401	#3503	C₂×C₆₇	1	1	yes	characteristic, complemented
402	#3376	C₂×C₆₇	1	4	yes	complemented
403	#3374	C₂×C₆₇	1	2	yes	complemented
404	#3373	C₂×C₆₇	1	2	yes	complemented
405	#3369	C₂×C₆₇	1	4	yes	complemented
406	#3365	C₂×C₆₇	1	2	yes	complemented
407	#3359	C₂×C₆₇	1	2	yes	complemented
408	#3141	C₂×C₆₇	1	1	yes	characteristic, complemented
409	#3137	C₂×C₆₇	1	2	yes	complemented
410	#3084	C₂×C₆₇	1	2	yes	complemented
411	C₂×#475	C₂×C₆₇	1	1	yes	characteristic, complemented
412	#3046	C₂×C₆₇	1	2	yes	complemented
413	#3035	C₂×C₆₇	1	1	yes	characteristic
414	#2962	C₂×C₆₇	1	1	yes	characteristic, complemented
415	#2952	C₂×C₆₇	1	2	yes	complemented
416	C₄×#137	C₂×C₆₇	1	1	yes	characteristic, complemented
417	C₆₇	#61346	1	1	yes	characteristic, direct product factor, Sylow
418	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
419	C₂×#135	C₂²×C₆₇	1	2	yes	—
420	#559	C₂²×C₆₇	1	2	yes	—
421	Q₈²	C₂²×C₆₇	1	2	yes	—
422	#557	C₂²×C₆₇	1	2	yes	—
423	#557	C₂²×C₆₇	1	2	yes	—
424	#556	—	2	1	no	—
425	#556	C₂²×C₆₇	1	4	yes	—
426	#554	—	2	1	no	—
427	#554	—	2	2	no	—
428	#554	C₂²×C₆₇	1	2	yes	—
429	#552	—	2	2	no	—
430	D₄×Q₈	—	2	2	no	—
431	D₄×Q₈	C₂²×C₆₇	1	2	yes	—
432	#544	—	2	2	no	—
433	#544	C₂²×C₆₇	1	2	yes	—
434	#539	—	2	2	no	—
435	#536	C₂²×C₆₇	1	2	yes	—
436	#533	—	2	1	no	—
437	#533	C₂²×C₆₇	1	1	yes	characteristic
438	#532	C₂²×C₆₇	1	1	yes	characteristic
439	C₂×C₄⋊Q₈	—	2	1	no	—
440	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
441	#529	—	2	2	no	—
442	#520	C₂²×C₆₇	1	2	yes	—
443	#520	C₂²×C₆₇	1	2	yes	—
444	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
445	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
446	#491	C₂²×C₆₇	1	4	yes	—
447	#489	C₂²×C₆₇	1	4	yes	—
448	#489	C₂²×C₆₇	1	4	yes	—
449	#488	C₂²×C₆₇	1	4	yes	—
450	#487	C₂²×C₆₇	1	4	yes	—
451	#487	C₂²×C₆₇	1	2	yes	—
452	#486	C₂²×C₆₇	1	2	yes	—
453	#479	C₂²×C₆₇	1	4	yes	—
454	#478	C₂²×C₆₇	1	4	yes	—
455	#476	C₂²×C₆₇	1	4	yes	—
456	#475	C₂²×C₆₇	1	2	yes	—
457	#475	C₂²×C₆₇	1	4	yes	—
458	#475	C₂²×C₆₇	1	2	yes	—
459	#475	C₂²×C₆₇	1	4	yes	—
460	#464	C₂²×C₆₇	1	4	yes	—
461	#464	C₂²×C₆₇	1	2	yes	—
462	#463	C₂²×C₆₇	1	4	yes	—
463	#463	C₂²×C₆₇	1	2	yes	—
464	#462	C₂²×C₆₇	1	4	yes	—
465	#462	C₂²×C₆₇	1	1	yes	characteristic
466	#461	C₂²×C₆₇	1	1	yes	characteristic
467	#461	C₂²×C₆₇	1	4	yes	—
468	#460	C₂²×C₆₇	1	1	yes	characteristic
469	#459	C₂²×C₆₇	1	1	yes	characteristic
470	#446	C₂²×C₆₇	1	4	yes	—
471	#446	C₂²×C₆₇	1	2	yes	—
472	C₈×Q₈	C₂²×C₆₇	1	2	yes	—
473	#442	C₂²×C₆₇	1	4	yes	—
474	#441	C₂²×C₆₇	1	2	yes	—
475	#441	C₂²×C₆₇	1	4	yes	—
476	#440	C₂²×C₆₇	1	2	yes	—
477	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
478	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
479	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	—
480	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	—
481	#428	C₂²×C₆₇	1	1	yes	characteristic
482	C₂×#106	C₂²×C₆₇	1	2	yes	—
483	#424	C₂²×C₆₇	1	2	yes	—
484	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
485	#419	C₂²×C₆₇	1	1	yes	characteristic
486	#417	C₂²×C₆₇	1	2	yes	—
487	#417	C₂²×C₆₇	1	2	yes	—
488	#417	C₂²×C₆₇	1	1	yes	characteristic
489	#416	C₂²×C₆₇	1	2	yes	—
490	C₂×#103	C₂²×C₆₇	1	2	yes	—
491	#405	C₂²×C₆₇	1	2	yes	—
492	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
493	C₂×#41	C₂³×C₆₇	1	2	yes	—
494	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
495	C₂²×Q₈	—	2	2	no	—
496	C₂²×Q₈	—	2	1	no	—
497	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
498	#137	—	2	4	no	—
499	#135	—	2	8	no	—
500	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
501	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
502	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
503	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
504	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
505	C₂×D₈	C₂³×C₆₇	1	2	yes	—
506	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
507	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
508	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
509	C₄⋊Q₈	—	2	2	no	—
510	C₄⋊Q₈	—	2	2	no	—
511	C₄⋊Q₈	—	2	2	no	—
512	C₄⋊Q₈	—	2	4	no	—
513	C₄⋊Q₈	—	2	1	no	—
514	C₄⋊Q₈	—	2	1	no	—
515	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
516	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
517	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
518	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
519	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
520	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
521	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
522	#127	C₂³×C₆₇	1	1	yes	characteristic
523	#126	—	2	4	no	—
524	#126	—	2	4	no	—
525	#125	—	2	2	no	—
526	#125	—	2	2	no	—
527	#125	—	2	4	no	—
528	#125	—	2	4	no	—
529	#125	D₄×C₆₇	1	2	yes	—
530	#125	C₂³×C₆₇	1	4	yes	—
531	#124	—	2	2	no	—
532	#124	C₂³×C₆₇	1	2	yes	—
533	#124	C₂³×C₆₇	1	4	yes	—
534	#123	—	2	4	no	—
535	#123	—	2	4	no	—
536	C₂²⋊Q₈	—	2	2	no	—
537	C₂²⋊Q₈	—	2	4	no	—
538	C₂²⋊Q₈	—	2	2	no	—
539	C₂²⋊Q₈	—	2	2	no	—
540	C₂²⋊Q₈	—	2	2	no	—
541	C₂²⋊Q₈	—	2	4	no	—
542	C₂²⋊Q₈	—	2	4	no	—
543	C₂²⋊Q₈	—	2	4	no	—
544	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
545	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
546	#121	—	2	1	no	—
547	#121	—	2	1	no	—
548	C₄×Q₈	—	2	2	no	—
549	C₄×Q₈	—	2	2	no	—
550	C₄×Q₈	—	2	2	no	—
551	C₄×Q₈	—	2	1	no	—
552	C₄×Q₈	—	2	1	no	—
553	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
554	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
555	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
556	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
557	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
558	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
559	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
560	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
561	C₄×D₄	—	2	1	no	—
562	C₄×D₄	—	2	1	no	—
563	C₄×D₄	—	2	2	no	—
564	C₄×D₄	—	2	4	no	—
565	C₄×D₄	—	2	4	no	—
566	C₄×D₄	—	2	1	no	—
567	C₄×D₄	—	2	1	no	—
568	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
569	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
570	C₄×D₄	C₂³×C₆₇	1	4	yes	—
571	C₄×D₄	C₂³×C₆₇	1	4	yes	—
572	#117	—	2	2	no	—
573	#117	—	2	2	no	—
574	#117	—	2	4	no	—
575	#117	—	2	1	no	—
576	#117	C₂³×C₆₇	1	1	yes	characteristic
577	#117	C₂³×C₆₇	1	2	yes	—
578	C₂×C₄⋊C₄	—	2	1	no	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	—	2	2	no	—
581	C₂×C₄⋊C₄	—	2	2	no	—
582	C₂×C₄⋊C₄	—	2	2	no	—
583	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
585	C₂×C₄²	—	2	1	no	—
586	C₂×C₄²	—	2	1	no	—
587	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
588	#107	C₂³×C₆₇	1	2	yes	—
589	#106	C₂³×C₆₇	1	4	yes	—
590	#106	C₂³×C₆₇	1	4	yes	—
591	#106	C₂³×C₆₇	1	2	yes	—
592	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
593	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
594	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
595	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
596	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
597	#103	C₂³×C₆₇	1	4	yes	—
598	#103	C₂³×C₆₇	1	4	yes	—
599	#103	C₂³×C₆₇	1	2	yes	—
600	#103	C₂³×C₆₇	1	2	yes	—
601	#103	C₂³×C₆₇	1	2	yes	—
602	#103	C₂³×C₆₇	1	4	yes	—
603	#103	C₂³×C₆₇	1	4	yes	—
604	#103	C₂³×C₆₇	1	2	yes	—
605	#103	C₂³×C₆₇	1	2	yes	—
606	#102	C₂³×C₆₇	1	2	yes	—
607	#102	C₂³×C₆₇	1	2	yes	—
608	#102	C₂³×C₆₇	1	2	yes	—
609	#102	C₂³×C₆₇	1	4	yes	—
610	#102	C₂³×C₆₇	1	4	yes	—
611	#97	C₂³×C₆₇	1	2	yes	—
612	#97	C₂³×C₆₇	1	4	yes	—
613	C₄×C₈	C₂³×C₆₇	1	2	yes	—
614	C₄×C₈	C₂³×C₆₇	1	4	yes	—
615	#41	—	2	2	no	—
616	#41	—	2	4	no	—
617	#41	—	2	4	no	—
618	#41	#41×C₆₇	1	4	yes	—
619	C₂×Q₈	—	2	1	no	—
620	C₂×Q₈	—	2	2	no	—
621	C₂×Q₈	—	2	4	no	—
622	C₂×Q₈	—	2	2	no	—
623	C₂×Q₈	—	2	2	no	—
624	C₂×Q₈	—	2	2	no	—
625	C₂×Q₈	—	8	2	no	—
626	C₂×Q₈	—	8	4	no	—
627	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
628	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
629	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
630	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
631	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	—	2	2	no	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	—	2	1	no	—
636	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
637	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	2	4	no	—
646	C₂²×C₄	—	2	4	no	—
647	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
648	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
649	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
650	Q₁₆	—	2	4	no	—
651	Q₁₆	—	2	4	no	—
652	SD₁₆	—	2	4	no	—
653	SD₁₆	—	2	4	no	—
654	SD₁₆	—	2	4	no	—
655	D₈	—	2	4	no	—
656	M₁₆	—	2	2	no	—
657	M₁₆	—	2	2	no	—
658	C₂×C₈	—	2	4	no	—
659	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
660	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
661	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
662	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	4	no	—
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	2	2	no	—
669	C₄⋊C₄	—	2	2	no	—
670	C₄⋊C₄	—	2	2	no	—
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	1	no	—
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	4	no	—
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
681	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
682	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
683	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
684	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
685	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
686	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
687	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
688	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
689	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
690	C₂²⋊C₄	—	2	1	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	1	no	—
693	C₂²⋊C₄	—	2	1	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	2	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
700	C₄²	—	2	2	no	—
701	C₄²	—	2	1	no	—
702	C₄²	—	2	2	no	—
703	C₄²	—	2	1	no	—
704	C₄²	—	2	1	no	—
705	C₄²	—	2	4	no	—
706	C₄²	—	2	4	no	—
707	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
708	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
709	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
710	C₄²	C₂⁴×C₆₇	1	4	yes	—
711	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
712	C₂³	—	2	1	no	—
713	C₂³	—	2	2	no	—
714	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
715	Q₈	—	2	4	no	—
716	Q₈	—	2	1	no	—
717	Q₈	—	2	2	no	—
718	Q₈	—	2	2	no	—
719	Q₈	—	2	2	no	—
720	Q₈	—	2	2	no	—
721	Q₈	—	4	2	no	—
722	Q₈	—	4	2	no	—
723	Q₈	—	4	4	no	—
724	Q₈	—	8	2	no	—
725	Q₈	—	8	4	no	—
726	Q₈	C₂×#41×C₆₇	1	2	yes	—
727	D₄	—	2	4	no	—
728	D₄	—	2	2	no	—
729	D₄	—	2	1	no	—
730	D₄	—	2	2	no	—
731	D₄	—	4	4	no	—
732	D₄	—	4	2	no	—
733	D₄	—	8	1	no	—
734	D₄	C₂×#41×C₆₇	1	2	yes	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	4	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	4	no	—
744	C₂×C₄	—	4	1	no	—
745	C₂×C₄	—	4	2	no	—
746	C₂×C₄	—	4	2	no	—
747	C₂×C₄	—	4	4	no	—
748	C₂×C₄	—	4	2	no	—
749	C₂×C₄	—	8	4	no	—
750	C₂×C₄	—	8	4	no	—
751	C₂×C₄	—	8	2	no	—
752	C₂×C₄	—	8	1	no	—
753	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
754	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
755	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
756	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
757	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
758	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
759	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
760	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
761	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
762	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
763	C₈	—	2	2	no	—
764	C₈	—	2	2	no	—
765	C₈	—	2	2	no	—
766	C₈	—	2	2	no	—
767	C₂²	—	2	1	no	—
768	C₂²	—	2	1	no	—
769	C₂²	—	2	2	no	—
770	C₂²	—	4	1	no	—
771	C₂²	—	4	1	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	#548×C₆₇	1	2	yes	—
776	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
777	C₄	—	2	1	no	—
778	C₄	—	2	4	no	—
779	C₄	—	2	1	no	—
780	C₄	—	2	1	no	—
781	C₄	—	2	4	no	—
782	C₄	—	2	2	no	—
783	C₄	—	4	1	no	—
784	C₄	—	4	4	no	—
785	C₄	—	4	1	no	—
786	C₄	—	4	2	no	—
787	C₄	—	4	2	no	—
788	C₄	—	4	2	no	—
789	C₄	#548×C₆₇	1	2	yes	—
790	C₄	#577×C₆₇	1	2	yes	—
791	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
792	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
793	C₂	—	2	2	no	—
794	C₂	—	4	2	no	—
795	C₂	—	8	2	no	—
796	C₂	C₂×#548×C₆₇	1	1	yes	characteristic
797	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
798	C₂	C₆₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₆₇×#3035	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #533×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3507	C₂	semidirect
2. C₆₇×#3503	C₂	semidirect
3. C₆₇×#3376	C₂	semidirect
4. C₆₇×#3374	C₂	semidirect
5. C₆₇×#3373	C₂	semidirect
6. C₆₇×#3369	C₂	semidirect
7. C₆₇×#3365	C₂	semidirect
8. C₆₇×#3359	C₂	semidirect
9. C₆₇×#3141	C₂	semidirect
10. C₆₇×#3137	C₂	semidirect
11. C₆₇×#3084	C₂	semidirect
12. C₂×#475×C₆₇	C₂	semidirect
13. C₆₇×#3046	C₂	semidirect
15. C₆₇×#2962	C₂	semidirect
16. C₆₇×#2952	C₂	semidirect
17. C₄×#137×C₆₇	C₂	semidirect
393. #61346	C₆₇	direct (N × H)
400. #3507	C₂×C₆₇	semidirect
401. #3503	C₂×C₆₇	semidirect
402. #3376	C₂×C₆₇	semidirect
403. #3374	C₂×C₆₇	semidirect
404. #3373	C₂×C₆₇	semidirect
405. #3369	C₂×C₆₇	semidirect
406. #3365	C₂×C₆₇	semidirect
407. #3359	C₂×C₆₇	semidirect
408. #3141	C₂×C₆₇	semidirect
409. #3137	C₂×C₆₇	semidirect
410. #3084	C₂×C₆₇	semidirect
411. C₂×#475	C₂×C₆₇	semidirect
412. #3046	C₂×C₆₇	semidirect
414. #2962	C₂×C₆₇	semidirect
415. #2952	C₂×C₆₇	semidirect
416. C₄×#137	C₂×C₆₇	semidirect
417. C₆₇	#61346	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#3507	2
C₆₇×#3503	2
C₆₇×#3376	2
C₆₇×#3374	2
C₆₇×#3373	2
C₆₇×#3369	2
C₆₇×#3365	2
C₆₇×#3359	2
C₆₇×#3141	2
C₆₇×#3137	2
C₆₇×#3084	2
C₂×#475×C₆₇	2
C₆₇×#3046	2
C₆₇×#3035	2
C₆₇×#2962	2
C₆₇×#2952	2
C₄×#137×C₆₇	2
#61346	67

Subgroups — C67×#61346 #30740597

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61346 #30740597