Subgroups — C₆₇×#61281 #30740532

Order 17152.

1796 conjugacy classes of subgroups.

The subgroup lattice has 794 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
2	C₆₇×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3356	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3353	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3348	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3344	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3342	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3335	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3099	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3097	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#475×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3063	C₂	1	2	yes	maximal, complemented
15	C₄×#137×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2935	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2912	C₂	1	2	yes	maximal, complemented
18	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×#131×C₆₇	C₂²	1	2	yes	—
20	#559×C₆₇	—	2	1	no	—
21	#557×C₆₇	—	2	1	no	—
22	#556×C₆₇	—	2	2	no	—
23	#556×C₆₇	C₂²	1	2	yes	—
24	#556×C₆₇	C₂²	1	2	yes	—
25	#555×C₆₇	C₂²	1	2	yes	—
26	#554×C₆₇	C₂²	1	2	yes	—
27	#554×C₆₇	C₂²	1	2	yes	—
28	#553×C₆₇	—	2	2	no	—
29	#552×C₆₇	C₂²	1	4	yes	—
30	#548×C₆₇	—	2	2	no	—
31	#547×C₆₇	C₂²	1	2	yes	—
32	#542×C₆₇	—	2	2	no	—
33	#539×C₆₇	—	2	2	no	—
34	#537×C₆₇	C₂²	1	2	yes	—
35	#536×C₆₇	C₂²	1	2	yes	—
36	#533×C₆₇	—	2	1	no	—
37	#533×C₆₇	C₂²	1	1	yes	characteristic
38	#532×C₆₇	—	2	1	no	—
39	#532×C₆₇	C₂²	1	1	yes	characteristic
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	#501×C₆₇	C₂²	1	4	yes	—
47	#500×C₆₇	C₂²	1	2	yes	—
48	#498×C₆₇	C₂²	1	2	yes	—
49	#485×C₆₇	C₂²	1	4	yes	—
50	#485×C₆₇	C₂²	1	4	yes	—
51	#485×C₆₇	C₂²	1	4	yes	—
52	#484×C₆₇	C₂²	1	4	yes	—
53	#483×C₆₇	C₂²	1	4	yes	—
54	#483×C₆₇	C₂²	1	4	yes	—
55	#482×C₆₇	C₂²	1	4	yes	—
56	#481×C₆₇	C₂²	1	4	yes	—
57	#479×C₆₇	C₂²	1	2	yes	—
58	#478×C₆₇	C₂²	1	2	yes	—
59	#477×C₆₇	C₂²	1	1	yes	characteristic
60	#476×C₆₇	C₂²	1	1	yes	characteristic
61	#475×C₆₇	C₂²	1	2	yes	—
62	#475×C₆₇	C₂²	1	4	yes	—
63	#475×C₆₇	C₂²	1	2	yes	—
64	#475×C₆₇	C₂²	1	1	yes	characteristic
65	#474×C₆₇	C₂²	1	1	yes	characteristic
66	#470×C₆₇	C₂²	1	4	yes	—
67	#468×C₆₇	C₂²	1	4	yes	—
68	#467×C₆₇	C₂²	1	4	yes	—
69	#465×C₆₇	C₂²	1	4	yes	—
70	#441×C₆₇	C₂²	1	2	yes	—
71	#440×C₆₇	C₂²	1	2	yes	—
72	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
73	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
74	#436×C₆₇	C₂²	1	2	yes	—
75	#435×C₆₇	C₂²	1	4	yes	—
76	C₈×D₄×C₆₇	C₂²	1	2	yes	—
77	#428×C₆₇	C₂²	1	2	yes	—
78	#428×C₆₇	C₂²	1	4	yes	—
79	#428×C₆₇	C₂²	1	4	yes	—
80	#428×C₆₇	C₂²	1	2	yes	—
81	#428×C₆₇	C₂²	1	1	yes	characteristic
82	#427×C₆₇	C₂²	1	2	yes	—
83	#427×C₆₇	C₂²	1	4	yes	—
84	C₂×#106×C₆₇	C₂²	1	2	yes	—
85	C₂×#106×C₆₇	C₂²	1	4	yes	—
86	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
87	#419×C₆₇	C₂²	1	1	yes	characteristic
88	#417×C₆₇	C₂²	1	1	yes	characteristic
89	#416×C₆₇	C₂²	1	2	yes	—
90	C₂×#103×C₆₇	C₂²	1	2	yes	—
91	#408×C₆₇	C₂²	1	2	yes	—
92	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
93	C₂×#41×C₆₇	—	2	2	no	—
94	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
95	C₂×#41×C₆₇	C₂³	1	2	yes	—
96	C₂²×Q₈×C₆₇	—	2	1	no	—
97	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
98	#137×C₆₇	—	2	4	no	—
99	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
100	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
101	#131×C₆₇	—	2	8	no	—
102	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
103	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
104	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
106	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
107	C₄⋊Q₈×C₆₇	—	2	2	no	—
108	C₄⋊Q₈×C₆₇	—	2	1	no	—
109	C₄⋊Q₈×C₆₇	—	2	1	no	—
110	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
111	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
113	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
114	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
115	#127×C₆₇	D₄	1	1	yes	characteristic
116	#126×C₆₇	—	2	4	no	—
117	#126×C₆₇	—	2	4	no	—
118	#126×C₆₇	—	2	4	no	—
119	#125×C₆₇	—	2	2	no	—
120	#125×C₆₇	—	2	2	no	—
121	#125×C₆₇	—	2	4	no	—
122	#125×C₆₇	C₂³	1	2	yes	—
123	#124×C₆₇	—	2	2	no	—
124	#124×C₆₇	—	2	2	no	—
125	#124×C₆₇	—	2	2	no	—
126	#124×C₆₇	—	2	4	no	—
127	#124×C₆₇	D₄	1	2	yes	—
128	#123×C₆₇	—	2	4	no	—
129	#123×C₆₇	—	2	4	no	—
130	#123×C₆₇	—	2	4	no	—
131	C₂²⋊Q₈×C₆₇	—	2	2	no	—
132	C₂²⋊Q₈×C₆₇	—	2	1	no	—
133	C₂²⋊Q₈×C₆₇	—	2	1	no	—
134	C₂²⋊Q₈×C₆₇	—	2	2	no	—
135	C₂²⋊Q₈×C₆₇	—	2	4	no	—
136	C₂²⋊Q₈×C₆₇	—	2	4	no	—
137	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
138	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
139	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
140	#121×C₆₇	—	2	2	no	—
141	#121×C₆₇	—	2	2	no	—
142	#121×C₆₇	—	2	4	no	—
143	#121×C₆₇	D₄	1	2	yes	—
144	#121×C₆₇	D₄	1	2	yes	—
145	#121×C₆₇	C₂³	1	4	yes	—
146	C₄×Q₈×C₆₇	—	2	2	no	—
147	C₄×Q₈×C₆₇	—	2	2	no	—
148	C₄×Q₈×C₆₇	—	2	2	no	—
149	C₄×Q₈×C₆₇	—	2	2	no	—
150	C₄×Q₈×C₆₇	—	2	1	no	—
151	C₄×Q₈×C₆₇	—	2	1	no	—
152	C₄×Q₈×C₆₇	—	2	1	no	—
153	C₄×Q₈×C₆₇	—	2	1	no	—
154	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
155	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
156	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
157	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
158	C₄×D₄×C₆₇	—	2	4	no	—
159	C₄×D₄×C₆₇	—	2	2	no	—
160	C₄×D₄×C₆₇	—	2	4	no	—
161	C₄×D₄×C₆₇	—	2	2	no	—
162	C₄×D₄×C₆₇	—	2	2	no	—
163	C₄×D₄×C₆₇	—	2	2	no	—
164	C₄×D₄×C₆₇	—	2	1	no	—
165	C₄×D₄×C₆₇	—	2	1	no	—
166	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
167	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
168	C₄×D₄×C₆₇	C₂³	1	2	yes	—
169	C₄×D₄×C₆₇	C₂³	1	2	yes	—
170	#117×C₆₇	—	2	2	no	—
171	#117×C₆₇	—	2	4	no	—
172	#117×C₆₇	—	2	1	no	—
173	#117×C₆₇	C₂³	1	4	yes	—
174	#117×C₆₇	C₂³	1	4	yes	—
175	#117×C₆₇	C₂³	1	1	yes	characteristic
176	#117×C₆₇	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
178	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
179	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
180	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
181	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
183	C₂×C₄²×C₆₇	—	2	1	no	—
184	C₂×C₄²×C₆₇	—	2	1	no	—
185	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
186	#107×C₆₇	C₂³	1	4	yes	—
187	#107×C₆₇	C₂³	1	2	yes	—
188	#107×C₆₇	C₂³	1	2	yes	—
189	#107×C₆₇	C₂³	1	4	yes	—
190	#107×C₆₇	C₂³	1	2	yes	—
191	#106×C₆₇	C₂³	1	4	yes	—
192	#106×C₆₇	C₂³	1	4	yes	—
193	#106×C₆₇	C₂³	1	4	yes	—
194	#106×C₆₇	C₂³	1	2	yes	—
195	#106×C₆₇	C₂³	1	2	yes	—
196	#106×C₆₇	C₂³	1	4	yes	—
197	#106×C₆₇	C₂³	1	2	yes	—
198	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
199	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
200	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
201	#103×C₆₇	C₂³	1	4	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	#103×C₆₇	C₂³	1	2	yes	—
207	#103×C₆₇	C₂³	1	2	yes	—
208	#102×C₆₇	C₂³	1	2	yes	—
209	#102×C₆₇	C₂³	1	2	yes	—
210	#102×C₆₇	C₂³	1	2	yes	—
211	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
212	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
213	#97×C₆₇	C₂³	1	2	yes	—
214	C₄×C₈×C₆₇	C₂³	1	2	yes	—
215	#41×C₆₇	—	2	4	no	—
216	#41×C₆₇	—	2	4	no	—
217	#41×C₆₇	—	2	2	no	—
218	#41×C₆₇	—	2	2	no	—
219	#41×C₆₇	—	8	4	no	—
220	C₂×Q₈×C₆₇	—	2	1	no	—
221	C₂×Q₈×C₆₇	—	2	1	no	—
222	C₂×Q₈×C₆₇	—	2	2	no	—
223	C₂×Q₈×C₆₇	—	2	1	no	—
224	C₂×Q₈×C₆₇	—	2	2	no	—
225	C₂×Q₈×C₆₇	—	2	2	no	—
226	C₂×Q₈×C₆₇	—	2	2	no	—
227	C₂×Q₈×C₆₇	—	8	2	no	—
228	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
229	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
230	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
231	C₂×D₄×C₆₇	—	2	1	no	—
232	C₂×D₄×C₆₇	—	2	4	no	—
233	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
234	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
235	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
236	C₂×D₄×C₆₇	C₂×D₄	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	2	no	—
241	C₂²×C₄×C₆₇	—	2	4	no	—
242	C₂²×C₄×C₆₇	—	2	4	no	—
243	C₂²×C₄×C₆₇	—	2	1	no	—
244	C₂²×C₄×C₆₇	—	2	1	no	—
245	C₂²×C₄×C₆₇	—	2	1	no	—
246	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
249	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
250	Q₁₆×C₆₇	—	2	4	no	—
251	SD₁₆×C₆₇	—	2	4	no	—
252	M₁₆×C₆₇	—	2	2	no	—
253	M₁₆×C₆₇	—	2	8	no	—
254	M₁₆×C₆₇	#41	1	4	yes	complemented
255	C₂×C₈×C₆₇	—	2	4	no	—
256	C₂×C₈×C₆₇	—	2	8	no	—
257	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
258	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
259	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
260	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₆₇	—	2	2	no	—
262	C₄⋊C₄×C₆₇	—	2	2	no	—
263	C₄⋊C₄×C₆₇	—	2	2	no	—
264	C₄⋊C₄×C₆₇	—	2	2	no	—
265	C₄⋊C₄×C₆₇	—	2	1	no	—
266	C₄⋊C₄×C₆₇	—	2	2	no	—
267	C₄⋊C₄×C₆₇	—	2	4	no	—
268	C₄⋊C₄×C₆₇	—	2	4	no	—
269	C₄⋊C₄×C₆₇	—	2	2	no	—
270	C₄⋊C₄×C₆₇	—	2	1	no	—
271	C₄⋊C₄×C₆₇	—	2	1	no	—
272	C₄⋊C₄×C₆₇	—	2	4	no	—
273	C₄⋊C₄×C₆₇	—	2	1	no	—
274	C₄⋊C₄×C₆₇	—	2	4	no	—
275	C₄⋊C₄×C₆₇	—	2	2	no	—
276	C₄⋊C₄×C₆₇	—	2	1	no	—
277	C₄⋊C₄×C₆₇	—	2	4	no	—
278	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
279	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
280	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
281	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
283	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
284	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
285	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
286	C₂²⋊C₄×C₆₇	—	2	4	no	—
287	C₂²⋊C₄×C₆₇	—	2	1	no	—
288	C₂²⋊C₄×C₆₇	—	2	4	no	—
289	C₂²⋊C₄×C₆₇	—	2	2	no	—
290	C₂²⋊C₄×C₆₇	—	2	4	no	—
291	C₂²⋊C₄×C₆₇	—	2	4	no	—
292	C₂²⋊C₄×C₆₇	—	2	4	no	—
293	C₂²⋊C₄×C₆₇	—	2	1	no	—
294	C₂²⋊C₄×C₆₇	—	2	1	no	—
295	C₂²⋊C₄×C₆₇	—	2	4	no	—
296	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
297	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
298	C₄²×C₆₇	—	2	2	no	—
299	C₄²×C₆₇	—	2	1	no	—
300	C₄²×C₆₇	—	2	1	no	—
301	C₄²×C₆₇	—	2	1	no	—
302	C₄²×C₆₇	—	2	2	no	—
303	C₄²×C₆₇	—	2	4	no	—
304	C₄²×C₆₇	—	2	4	no	—
305	C₄²×C₆₇	—	2	2	no	—
306	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
307	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
309	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
310	C₂³×C₆₇	—	2	1	no	—
311	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
312	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
313	Q₈×C₆₇	—	2	4	no	—
314	Q₈×C₆₇	—	2	2	no	—
315	Q₈×C₆₇	—	2	1	no	—
316	Q₈×C₆₇	—	2	2	no	—
317	Q₈×C₆₇	—	2	1	no	—
318	Q₈×C₆₇	—	4	2	no	—
319	Q₈×C₆₇	—	4	2	no	—
320	Q₈×C₆₇	—	4	4	no	—
321	Q₈×C₆₇	—	8	1	no	—
322	Q₈×C₆₇	—	8	2	no	—
323	D₄×C₆₇	—	2	8	no	—
324	D₄×C₆₇	—	2	4	no	—
325	D₄×C₆₇	—	2	4	no	—
326	D₄×C₆₇	—	2	1	no	—
327	D₄×C₆₇	—	2	1	no	—
328	D₄×C₆₇	—	4	2	no	—
329	D₄×C₆₇	—	4	2	no	—
330	D₄×C₆₇	—	8	4	no	—
331	C₂×C₄×C₆₇	—	2	2	no	—
332	C₂×C₄×C₆₇	—	2	4	no	—
333	C₂×C₄×C₆₇	—	2	4	no	—
334	C₂×C₄×C₆₇	—	2	1	no	—
335	C₂×C₄×C₆₇	—	2	2	no	—
336	C₂×C₄×C₆₇	—	2	2	no	—
337	C₂×C₄×C₆₇	—	2	1	no	—
338	C₂×C₄×C₆₇	—	2	2	no	—
339	C₂×C₄×C₆₇	—	2	1	no	—
340	C₂×C₄×C₆₇	—	2	2	no	—
341	C₂×C₄×C₆₇	—	2	4	no	—
342	C₂×C₄×C₆₇	—	4	1	no	—
343	C₂×C₄×C₆₇	—	4	2	no	—
344	C₂×C₄×C₆₇	—	4	2	no	—
345	C₂×C₄×C₆₇	—	4	2	no	—
346	C₂×C₄×C₆₇	—	4	2	no	—
347	C₂×C₄×C₆₇	—	8	1	no	—
348	C₂×C₄×C₆₇	—	8	4	no	—
349	C₂×C₄×C₆₇	—	8	2	no	—
350	C₂×C₄×C₆₇	—	8	4	no	—
351	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
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	1	yes	characteristic
356	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
358	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
359	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
360	C₈×C₆₇	—	2	2	no	—
361	C₈×C₆₇	—	2	2	no	—
362	C₈×C₆₇	—	2	2	no	—
363	C₈×C₆₇	C₂×#41	1	4	yes	—
364	C₂²×C₆₇	—	2	1	no	—
365	C₂²×C₆₇	—	2	1	no	—
366	C₂²×C₆₇	—	2	4	no	—
367	C₂²×C₆₇	—	2	4	no	—
368	C₂²×C₆₇	—	2	4	no	—
369	C₂²×C₆₇	—	4	1	no	—
370	C₂²×C₆₇	—	4	1	no	—
371	C₂²×C₆₇	—	4	1	no	—
372	C₂²×C₆₇	#547	1	2	yes	—
373	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
374	C₄×C₆₇	—	2	1	no	—
375	C₄×C₆₇	—	2	1	no	—
376	C₄×C₆₇	—	2	4	no	—
377	C₄×C₆₇	—	2	1	no	—
378	C₄×C₆₇	—	4	1	no	—
379	C₄×C₆₇	—	4	2	no	—
380	C₄×C₆₇	—	4	2	no	—
381	C₄×C₆₇	—	4	1	no	—
382	C₄×C₆₇	—	4	2	no	—
383	C₄×C₆₇	—	4	1	no	—
384	C₄×C₆₇	—	4	4	no	—
385	C₄×C₆₇	—	4	2	no	—
386	C₄×C₆₇	#547	1	2	yes	—
387	C₄×C₆₇	#577	1	2	yes	—
388	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
389	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
390	#61281	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
391	C₂×C₆₇	—	2	2	no	—
392	C₂×C₆₇	—	4	4	no	—
393	C₂×C₆₇	—	8	1	no	—
394	C₂×C₆₇	C₂×#547	1	1	yes	characteristic
395	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
396	C₂×C₆₇	#3586	1	1	yes	characteristic
397	#3511	C₂×C₆₇	1	1	yes	characteristic
398	#3507	C₂×C₆₇	1	1	yes	characteristic, complemented
399	#3356	C₂×C₆₇	1	2	yes	complemented
400	#3353	C₂×C₆₇	1	2	yes	complemented
401	#3348	C₂×C₆₇	1	4	yes	complemented
402	#3344	C₂×C₆₇	1	4	yes	complemented
403	#3342	C₂×C₆₇	1	2	yes	complemented
404	#3335	C₂×C₆₇	1	2	yes	complemented
405	#3165	C₂×C₆₇	1	1	yes	characteristic, complemented
406	#3099	C₂×C₆₇	1	2	yes	complemented
407	#3097	C₂×C₆₇	1	2	yes	complemented
408	#3076	C₂×C₆₇	1	1	yes	characteristic, complemented
409	C₂×#475	C₂×C₆₇	1	1	yes	characteristic, complemented
410	#3063	C₂×C₆₇	1	2	yes	complemented
411	C₄×#137	C₂×C₆₇	1	1	yes	characteristic, complemented
412	#2935	C₂×C₆₇	1	1	yes	characteristic, complemented
413	#2912	C₂×C₆₇	1	2	yes	complemented
414	C₆₇	#61281	1	1	yes	characteristic, direct product factor, Sylow
415	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
416	C₂×#131	C₂²×C₆₇	1	2	yes	—
417	#559	—	2	1	no	—
418	#557	—	2	1	no	—
419	#556	—	2	2	no	—
420	#556	C₂²×C₆₇	1	2	yes	—
421	#556	C₂²×C₆₇	1	2	yes	—
422	#555	C₂²×C₆₇	1	2	yes	—
423	#554	C₂²×C₆₇	1	2	yes	—
424	#554	C₂²×C₆₇	1	2	yes	—
425	#553	—	2	2	no	—
426	#552	C₂²×C₆₇	1	4	yes	—
427	#548	—	2	2	no	—
428	#547	C₂²×C₆₇	1	2	yes	—
429	#542	—	2	2	no	—
430	#539	—	2	2	no	—
431	#537	C₂²×C₆₇	1	2	yes	—
432	#536	C₂²×C₆₇	1	2	yes	—
433	#533	—	2	1	no	—
434	#533	C₂²×C₆₇	1	1	yes	characteristic
435	#532	—	2	1	no	—
436	#532	C₂²×C₆₇	1	1	yes	characteristic
437	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
438	#529	—	2	2	no	—
439	#520	C₂²×C₆₇	1	2	yes	—
440	#520	C₂²×C₆₇	1	2	yes	—
441	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
442	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
443	#501	C₂²×C₆₇	1	4	yes	—
444	#500	C₂²×C₆₇	1	2	yes	—
445	#498	C₂²×C₆₇	1	2	yes	—
446	#485	C₂²×C₆₇	1	4	yes	—
447	#485	C₂²×C₆₇	1	4	yes	—
448	#485	C₂²×C₆₇	1	4	yes	—
449	#484	C₂²×C₆₇	1	4	yes	—
450	#483	C₂²×C₆₇	1	4	yes	—
451	#483	C₂²×C₆₇	1	4	yes	—
452	#482	C₂²×C₆₇	1	4	yes	—
453	#481	C₂²×C₆₇	1	4	yes	—
454	#479	C₂²×C₆₇	1	2	yes	—
455	#478	C₂²×C₆₇	1	2	yes	—
456	#477	C₂²×C₆₇	1	1	yes	characteristic
457	#476	C₂²×C₆₇	1	1	yes	characteristic
458	#475	C₂²×C₆₇	1	2	yes	—
459	#475	C₂²×C₆₇	1	4	yes	—
460	#475	C₂²×C₆₇	1	2	yes	—
461	#475	C₂²×C₆₇	1	1	yes	characteristic
462	#474	C₂²×C₆₇	1	1	yes	characteristic
463	#470	C₂²×C₆₇	1	4	yes	—
464	#468	C₂²×C₆₇	1	4	yes	—
465	#467	C₂²×C₆₇	1	4	yes	—
466	#465	C₂²×C₆₇	1	4	yes	—
467	#441	C₂²×C₆₇	1	2	yes	—
468	#440	C₂²×C₆₇	1	2	yes	—
469	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
470	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
471	#436	C₂²×C₆₇	1	2	yes	—
472	#435	C₂²×C₆₇	1	4	yes	—
473	C₈×D₄	C₂²×C₆₇	1	2	yes	—
474	#428	C₂²×C₆₇	1	4	yes	—
475	#428	C₂²×C₆₇	1	4	yes	—
476	#428	C₂²×C₆₇	1	2	yes	—
477	#428	C₂²×C₆₇	1	2	yes	—
478	#428	C₂²×C₆₇	1	1	yes	characteristic
479	#427	C₂²×C₆₇	1	2	yes	—
480	#427	C₂²×C₆₇	1	4	yes	—
481	C₂×#106	C₂²×C₆₇	1	2	yes	—
482	C₂×#106	C₂²×C₆₇	1	4	yes	—
483	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
484	#419	C₂²×C₆₇	1	1	yes	characteristic
485	#417	C₂²×C₆₇	1	1	yes	characteristic
486	#416	C₂²×C₆₇	1	2	yes	—
487	C₂×#103	C₂²×C₆₇	1	2	yes	—
488	#408	C₂²×C₆₇	1	2	yes	—
489	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
490	C₂×#41	—	2	2	no	—
491	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
492	C₂×#41	C₂³×C₆₇	1	2	yes	—
493	C₂²×Q₈	—	2	1	no	—
494	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
495	#137	—	2	4	no	—
496	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
497	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
498	#131	—	2	8	no	—
499	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
500	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
501	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
502	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
503	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
504	C₄⋊Q₈	—	2	2	no	—
505	C₄⋊Q₈	—	2	1	no	—
506	C₄⋊Q₈	—	2	1	no	—
507	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
508	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
509	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
510	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
511	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
512	#127	D₄×C₆₇	1	1	yes	characteristic
513	#126	—	2	4	no	—
514	#126	—	2	4	no	—
515	#126	—	2	4	no	—
516	#125	—	2	2	no	—
517	#125	—	2	2	no	—
518	#125	—	2	4	no	—
519	#125	C₂³×C₆₇	1	2	yes	—
520	#124	—	2	2	no	—
521	#124	—	2	2	no	—
522	#124	—	2	2	no	—
523	#124	—	2	4	no	—
524	#124	D₄×C₆₇	1	2	yes	—
525	#123	—	2	4	no	—
526	#123	—	2	4	no	—
527	#123	—	2	4	no	—
528	C₂²⋊Q₈	—	2	2	no	—
529	C₂²⋊Q₈	—	2	1	no	—
530	C₂²⋊Q₈	—	2	1	no	—
531	C₂²⋊Q₈	—	2	2	no	—
532	C₂²⋊Q₈	—	2	4	no	—
533	C₂²⋊Q₈	—	2	4	no	—
534	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
535	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
536	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
537	#121	—	2	2	no	—
538	#121	—	2	2	no	—
539	#121	—	2	4	no	—
540	#121	D₄×C₆₇	1	2	yes	—
541	#121	D₄×C₆₇	1	2	yes	—
542	#121	C₂³×C₆₇	1	4	yes	—
543	C₄×Q₈	—	2	2	no	—
544	C₄×Q₈	—	2	2	no	—
545	C₄×Q₈	—	2	2	no	—
546	C₄×Q₈	—	2	2	no	—
547	C₄×Q₈	—	2	1	no	—
548	C₄×Q₈	—	2	1	no	—
549	C₄×Q₈	—	2	1	no	—
550	C₄×Q₈	—	2	1	no	—
551	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
552	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
553	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
554	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
555	C₄×D₄	—	2	4	no	—
556	C₄×D₄	—	2	2	no	—
557	C₄×D₄	—	2	4	no	—
558	C₄×D₄	—	2	2	no	—
559	C₄×D₄	—	2	2	no	—
560	C₄×D₄	—	2	2	no	—
561	C₄×D₄	—	2	1	no	—
562	C₄×D₄	—	2	1	no	—
563	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
564	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
565	C₄×D₄	C₂³×C₆₇	1	2	yes	—
566	C₄×D₄	C₂³×C₆₇	1	2	yes	—
567	#117	—	2	2	no	—
568	#117	—	2	4	no	—
569	#117	—	2	1	no	—
570	#117	C₂³×C₆₇	1	1	yes	characteristic
571	#117	C₂³×C₆₇	1	2	yes	—
572	#117	C₂³×C₆₇	1	4	yes	—
573	#117	C₂³×C₆₇	1	4	yes	—
574	C₂×C₄⋊C₄	—	2	1	no	—
575	C₂×C₄⋊C₄	—	2	1	no	—
576	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
579	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
580	C₂×C₄²	—	2	1	no	—
581	C₂×C₄²	—	2	1	no	—
582	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
583	#107	C₂³×C₆₇	1	2	yes	—
584	#107	C₂³×C₆₇	1	4	yes	—
585	#107	C₂³×C₆₇	1	2	yes	—
586	#107	C₂³×C₆₇	1	2	yes	—
587	#107	C₂³×C₆₇	1	4	yes	—
588	#106	C₂³×C₆₇	1	4	yes	—
589	#106	C₂³×C₆₇	1	2	yes	—
590	#106	C₂³×C₆₇	1	2	yes	—
591	#106	C₂³×C₆₇	1	4	yes	—
592	#106	C₂³×C₆₇	1	4	yes	—
593	#106	C₂³×C₆₇	1	2	yes	—
594	#106	C₂³×C₆₇	1	4	yes	—
595	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
596	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
597	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
598	#103	C₂³×C₆₇	1	4	yes	—
599	#103	C₂³×C₆₇	1	4	yes	—
600	#103	C₂³×C₆₇	1	2	yes	—
601	#103	C₂³×C₆₇	1	2	yes	—
602	#103	C₂³×C₆₇	1	2	yes	—
603	#103	C₂³×C₆₇	1	2	yes	—
604	#103	C₂³×C₆₇	1	2	yes	—
605	#102	C₂³×C₆₇	1	2	yes	—
606	#102	C₂³×C₆₇	1	2	yes	—
607	#102	C₂³×C₆₇	1	2	yes	—
608	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
609	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
610	#97	C₂³×C₆₇	1	2	yes	—
611	C₄×C₈	C₂³×C₆₇	1	2	yes	—
612	#41	—	2	4	no	—
613	#41	—	2	4	no	—
614	#41	—	2	2	no	—
615	#41	—	2	2	no	—
616	#41	—	8	4	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	2	1	no	—
619	C₂×Q₈	—	2	2	no	—
620	C₂×Q₈	—	2	1	no	—
621	C₂×Q₈	—	2	2	no	—
622	C₂×Q₈	—	2	2	no	—
623	C₂×Q₈	—	2	2	no	—
624	C₂×Q₈	—	8	2	no	—
625	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
626	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
627	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	2	4	no	—
630	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
631	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
632	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
633	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
634	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
644	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
645	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
646	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
647	Q₁₆	—	2	4	no	—
648	SD₁₆	—	2	4	no	—
649	M₁₆	—	2	2	no	—
650	M₁₆	—	2	8	no	—
651	M₁₆	#41×C₆₇	1	4	yes	complemented
652	C₂×C₈	—	2	4	no	—
653	C₂×C₈	—	2	8	no	—
654	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
655	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
656	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
657	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	2	no	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	2	2	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	—	2	2	no	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
676	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
677	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
678	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
679	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
680	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
681	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
682	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
683	C₂²⋊C₄	—	2	4	no	—
684	C₂²⋊C₄	—	2	1	no	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	2	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	1	no	—
691	C₂²⋊C₄	—	2	1	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
694	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
695	C₄²	—	2	2	no	—
696	C₄²	—	2	1	no	—
697	C₄²	—	2	1	no	—
698	C₄²	—	2	1	no	—
699	C₄²	—	2	2	no	—
700	C₄²	—	2	4	no	—
701	C₄²	—	2	4	no	—
702	C₄²	—	2	2	no	—
703	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
704	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
705	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
706	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
707	C₂³	—	2	1	no	—
708	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
709	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
710	Q₈	—	2	4	no	—
711	Q₈	—	2	2	no	—
712	Q₈	—	2	1	no	—
713	Q₈	—	2	2	no	—
714	Q₈	—	2	1	no	—
715	Q₈	—	4	2	no	—
716	Q₈	—	4	4	no	—
717	Q₈	—	4	2	no	—
718	Q₈	—	8	2	no	—
719	Q₈	—	8	1	no	—
720	D₄	—	2	8	no	—
721	D₄	—	2	4	no	—
722	D₄	—	2	4	no	—
723	D₄	—	2	1	no	—
724	D₄	—	2	1	no	—
725	D₄	—	4	2	no	—
726	D₄	—	4	2	no	—
727	D₄	—	8	4	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	4	no	—
730	C₂×C₄	—	2	4	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	4	no	—
739	C₂×C₄	—	4	1	no	—
740	C₂×C₄	—	4	2	no	—
741	C₂×C₄	—	4	2	no	—
742	C₂×C₄	—	4	2	no	—
743	C₂×C₄	—	4	2	no	—
744	C₂×C₄	—	8	2	no	—
745	C₂×C₄	—	8	4	no	—
746	C₂×C₄	—	8	1	no	—
747	C₂×C₄	—	8	4	no	—
748	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
749	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
750	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
751	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
752	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
753	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
754	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
755	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
756	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
757	C₈	—	2	2	no	—
758	C₈	—	2	2	no	—
759	C₈	—	2	2	no	—
760	C₈	C₂×#41×C₆₇	1	4	yes	—
761	C₂²	—	2	1	no	—
762	C₂²	—	2	1	no	—
763	C₂²	—	2	4	no	—
764	C₂²	—	2	4	no	—
765	C₂²	—	2	4	no	—
766	C₂²	—	4	1	no	—
767	C₂²	—	4	1	no	—
768	C₂²	—	4	1	no	—
769	C₂²	#547×C₆₇	1	2	yes	—
770	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
771	C₄	—	2	1	no	—
772	C₄	—	2	1	no	—
773	C₄	—	2	1	no	—
774	C₄	—	2	4	no	—
775	C₄	—	4	1	no	—
776	C₄	—	4	4	no	—
777	C₄	—	4	2	no	—
778	C₄	—	4	1	no	—
779	C₄	—	4	2	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	1	no	—
782	C₄	—	4	2	no	—
783	C₄	#547×C₆₇	1	2	yes	—
784	C₄	#577×C₆₇	1	2	yes	—
785	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
786	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
787	C₂	—	2	2	no	—
788	C₂	—	4	4	no	—
789	C₂	—	8	1	no	—
790	C₂	C₂×#547×C₆₇	1	1	yes	characteristic
791	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
792	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×#3511	C₂
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
2. C₆₇×#3507	C₂	semidirect
3. C₆₇×#3356	C₂	semidirect
4. C₆₇×#3353	C₂	semidirect
5. C₆₇×#3348	C₂	semidirect
6. C₆₇×#3344	C₂	semidirect
7. C₆₇×#3342	C₂	semidirect
8. C₆₇×#3335	C₂	semidirect
9. C₆₇×#3165	C₂	semidirect
10. C₆₇×#3099	C₂	semidirect
11. C₆₇×#3097	C₂	semidirect
12. C₆₇×#3076	C₂	semidirect
13. C₂×#475×C₆₇	C₂	semidirect
14. C₆₇×#3063	C₂	semidirect
15. C₄×#137×C₆₇	C₂	semidirect
16. C₆₇×#2935	C₂	semidirect
17. C₆₇×#2912	C₂	semidirect
254. M₁₆×C₆₇	#41	semidirect
390. #61281	C₆₇	direct (N × H)
398. #3507	C₂×C₆₇	semidirect
399. #3356	C₂×C₆₇	semidirect
400. #3353	C₂×C₆₇	semidirect
401. #3348	C₂×C₆₇	semidirect
402. #3344	C₂×C₆₇	semidirect
403. #3342	C₂×C₆₇	semidirect
404. #3335	C₂×C₆₇	semidirect
405. #3165	C₂×C₆₇	semidirect
406. #3099	C₂×C₆₇	semidirect
407. #3097	C₂×C₆₇	semidirect
408. #3076	C₂×C₆₇	semidirect
409. C₂×#475	C₂×C₆₇	semidirect
410. #3063	C₂×C₆₇	semidirect
411. C₄×#137	C₂×C₆₇	semidirect
412. #2935	C₂×C₆₇	semidirect
413. #2912	C₂×C₆₇	semidirect
414. C₆₇	#61281	direct (N × H)
651. M₁₆	#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×#3507	2
C₆₇×#3356	2
C₆₇×#3353	2
C₆₇×#3348	2
C₆₇×#3344	2
C₆₇×#3342	2
C₆₇×#3335	2
C₆₇×#3165	2
C₆₇×#3099	2
C₆₇×#3097	2
C₆₇×#3076	2
C₂×#475×C₆₇	2
C₆₇×#3063	2
C₄×#137×C₆₇	2
C₆₇×#2935	2
C₆₇×#2912	2
#61281	67

Subgroups — C67×#61281 #30740532

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61281 #30740532