Subgroups — C₆₇×#61217 #30740468

Order 17152.

2064 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3331	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3330	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3329	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3328	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3303	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3302	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3299	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3298	C₂	1	2	yes	maximal, complemented
11	C₂×#487×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3097	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3079	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3063	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3039	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3013	C₂	1	2	yes	maximal, complemented
17	C₄×#135×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2898	C₂	1	2	yes	maximal, complemented
20	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	2	yes	—
21	C₂×#137×C₆₇	C₂²	1	2	yes	—
22	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×#131×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	#553×C₆₇	—	2	2	no	—
28	D₄×Q₈×C₆₇	C₂²	1	2	yes	—
29	D₄×Q₈×C₆₇	C₂²	1	2	yes	—
30	#548×C₆₇	—	2	2	no	—
31	#547×C₆₇	—	2	2	no	—
32	#547×C₆₇	—	2	2	no	—
33	#547×C₆₇	C₂²	1	2	yes	—
34	#547×C₆₇	C₂²	1	2	yes	—
35	#547×C₆₇	C₂²	1	2	yes	—
36	#542×C₆₇	—	2	2	no	—
37	#537×C₆₇	C₂²	1	2	yes	—
38	#536×C₆₇	—	2	2	no	—
39	#536×C₆₇	C₂²	1	2	yes	—
40	#533×C₆₇	—	2	1	no	—
41	#532×C₆₇	—	2	1	no	—
42	#532×C₆₇	—	2	1	no	—
43	#532×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊Q₈×C₆₇	—	2	1	no	—
45	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
47	#520×C₆₇	C₂²	1	2	yes	—
48	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
49	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
50	#487×C₆₇	C₂²	1	2	yes	—
51	#487×C₆₇	C₂²	1	2	yes	—
52	#487×C₆₇	C₂²	1	2	yes	—
53	#487×C₆₇	C₂²	1	2	yes	—
54	#485×C₆₇	C₂²	1	4	yes	—
55	#485×C₆₇	C₂²	1	4	yes	—
56	#484×C₆₇	C₂²	1	4	yes	—
57	#483×C₆₇	C₂²	1	4	yes	—
58	#477×C₆₇	C₂²	1	2	yes	—
59	#476×C₆₇	C₂²	1	2	yes	—
60	#475×C₆₇	C₂²	1	2	yes	—
61	#474×C₆₇	C₂²	1	2	yes	—
62	#470×C₆₇	C₂²	1	4	yes	—
63	#468×C₆₇	C₂²	1	4	yes	—
64	#467×C₆₇	C₂²	1	4	yes	—
65	#465×C₆₇	C₂²	1	4	yes	—
66	#462×C₆₇	C₂²	1	2	yes	—
67	#462×C₆₇	C₂²	1	2	yes	—
68	#461×C₆₇	C₂²	1	2	yes	—
69	#461×C₆₇	C₂²	1	2	yes	—
70	#452×C₆₇	C₂²	1	4	yes	—
71	#451×C₆₇	C₂²	1	4	yes	—
72	#449×C₆₇	C₂²	1	4	yes	—
73	#448×C₆₇	C₂²	1	4	yes	—
74	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
75	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
76	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
77	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
78	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
79	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
80	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
81	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
82	#436×C₆₇	C₂²	1	2	yes	—
83	#436×C₆₇	C₂²	1	2	yes	—
84	C₈×D₄×C₆₇	C₂²	1	2	yes	—
85	C₈×D₄×C₆₇	C₂²	1	2	yes	—
86	#428×C₆₇	C₂²	1	2	yes	—
87	#427×C₆₇	C₂²	1	1	yes	characteristic
88	#423×C₆₇	C₂²	1	1	yes	characteristic
89	#419×C₆₇	C₂²	1	2	yes	—
90	#419×C₆₇	C₂²	1	4	yes	—
91	#417×C₆₇	C₂²	1	2	yes	—
92	#417×C₆₇	C₂²	1	4	yes	—
93	#416×C₆₇	C₂²	1	4	yes	—
94	#416×C₆₇	C₂²	1	1	yes	characteristic
95	#416×C₆₇	C₂²	1	1	yes	characteristic
96	C₂×#103×C₆₇	C₂²	1	2	yes	—
97	C₂×#103×C₆₇	C₂²	1	4	yes	—
98	C₂×#103×C₆₇	C₂²	1	2	yes	—
99	#408×C₆₇	C₂²	1	2	yes	—
100	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
101	2₋¹⁺⁴×C₆₇	—	2	8	no	—
102	2₋¹⁺⁴×C₆₇	—	4	4	no	—
103	C₂×#41×C₆₇	—	2	2	no	—
104	C₂×#41×C₆₇	—	2	4	no	—
105	C₂×#41×C₆₇	—	2	2	no	—
106	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
107	C₂×#41×C₆₇	C₂³	1	4	yes	—
108	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
109	C₂×#41×C₆₇	C₂³	1	2	yes	—
110	C₂²×Q₈×C₆₇	—	2	2	no	—
111	C₂²×Q₈×C₆₇	—	2	1	no	—
112	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
113	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
114	#137×C₆₇	—	4	4	no	—
115	#135×C₆₇	—	2	4	no	—
116	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
117	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
118	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
119	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
120	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
121	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
122	#131×C₆₇	—	4	4	no	—
123	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
124	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
125	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
126	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
127	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
128	C₄⋊Q₈×C₆₇	—	2	2	no	—
129	C₄⋊Q₈×C₆₇	—	2	2	no	—
130	C₄⋊Q₈×C₆₇	—	2	2	no	—
131	C₄⋊Q₈×C₆₇	—	2	1	no	—
132	C₄⋊Q₈×C₆₇	—	2	1	no	—
133	C₄⋊Q₈×C₆₇	—	2	1	no	—
134	C₄⋊Q₈×C₆₇	—	2	1	no	—
135	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
136	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
137	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
138	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
139	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
140	#127×C₆₇	D₄	1	1	yes	characteristic
141	#126×C₆₇	—	2	4	no	—
142	#125×C₆₇	—	2	2	no	—
143	#124×C₆₇	—	2	2	no	—
144	#124×C₆₇	—	2	2	no	—
145	#124×C₆₇	—	2	4	no	—
146	#124×C₆₇	D₄	1	2	yes	—
147	#123×C₆₇	—	2	4	no	—
148	#123×C₆₇	—	2	4	no	—
149	#123×C₆₇	—	2	4	no	—
150	#123×C₆₇	—	2	4	no	—
151	C₂²⋊Q₈×C₆₇	—	2	2	no	—
152	C₂²⋊Q₈×C₆₇	—	2	2	no	—
153	C₂²⋊Q₈×C₆₇	—	2	4	no	—
154	C₂²⋊Q₈×C₆₇	—	2	4	no	—
155	C₂²⋊Q₈×C₆₇	—	2	4	no	—
156	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
157	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
158	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
159	#121×C₆₇	—	2	2	no	—
160	#121×C₆₇	—	2	2	no	—
161	#121×C₆₇	—	2	2	no	—
162	#121×C₆₇	—	2	2	no	—
163	#121×C₆₇	—	2	4	no	—
164	#121×C₆₇	D₄	1	2	yes	—
165	#121×C₆₇	D₄	1	2	yes	—
166	#121×C₆₇	C₂³	1	4	yes	—
167	C₄×Q₈×C₆₇	—	2	2	no	—
168	C₄×Q₈×C₆₇	—	2	2	no	—
169	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
170	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
172	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
173	C₄×D₄×C₆₇	—	2	2	no	—
174	C₄×D₄×C₆₇	—	2	4	no	—
175	C₄×D₄×C₆₇	—	2	2	no	—
176	C₄×D₄×C₆₇	—	2	2	no	—
177	C₄×D₄×C₆₇	—	2	2	no	—
178	C₄×D₄×C₆₇	—	2	1	no	—
179	C₄×D₄×C₆₇	—	2	1	no	—
180	C₄×D₄×C₆₇	—	2	1	no	—
181	C₄×D₄×C₆₇	—	2	1	no	—
182	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
183	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
185	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₆₇	C₂³	1	2	yes	—
187	C₄×D₄×C₆₇	C₂³	1	2	yes	—
188	#117×C₆₇	—	2	2	no	—
189	#117×C₆₇	—	2	1	no	—
190	#117×C₆₇	—	2	1	no	—
191	#117×C₆₇	C₂³	1	4	yes	—
192	#117×C₆₇	C₂³	1	1	yes	characteristic
193	#117×C₆₇	C₂³	1	1	yes	characteristic
194	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
195	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
196	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
197	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
198	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
199	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
200	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
201	C₂×C₄²×C₆₇	—	2	1	no	—
202	C₂×C₄²×C₆₇	—	2	1	no	—
203	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
204	#107×C₆₇	C₂³	1	4	yes	—
205	#107×C₆₇	C₂³	1	1	yes	characteristic
206	#107×C₆₇	C₂³	1	1	yes	characteristic
207	#106×C₆₇	C₂³	1	4	yes	—
208	#106×C₆₇	C₂³	1	1	yes	characteristic
209	#106×C₆₇	C₂³	1	1	yes	characteristic
210	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
211	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
212	#103×C₆₇	C₂³	1	4	yes	—
213	#103×C₆₇	C₂³	1	4	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	1	yes	characteristic
219	#103×C₆₇	C₂³	1	4	yes	—
220	#103×C₆₇	C₂³	1	1	yes	characteristic
221	#103×C₆₇	C₂³	1	1	yes	characteristic
222	#103×C₆₇	C₂³	1	1	yes	characteristic
223	#102×C₆₇	C₂³	1	4	yes	—
224	#102×C₆₇	C₂³	1	1	yes	characteristic
225	#102×C₆₇	C₂³	1	1	yes	characteristic
226	#102×C₆₇	C₂³	1	1	yes	characteristic
227	#102×C₆₇	C₂³	1	1	yes	characteristic
228	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
229	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
230	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
231	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
232	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
233	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
234	#41×C₆₇	—	2	4	no	—
235	#41×C₆₇	—	2	4	no	—
236	#41×C₆₇	—	2	2	no	—
237	#41×C₆₇	—	2	8	no	—
238	#41×C₆₇	—	2	2	no	—
239	#41×C₆₇	—	2	2	no	—
240	#41×C₆₇	—	4	4	no	—
241	#41×C₆₇	—	4	8	no	—
242	#41×C₆₇	—	4	16	no	—
243	#41×C₆₇	—	8	4	no	—
244	#41×C₆₇	#41	1	4	yes	complemented
245	C₂×Q₈×C₆₇	—	2	2	no	—
246	C₂×Q₈×C₆₇	—	2	4	no	—
247	C₂×Q₈×C₆₇	—	2	2	no	—
248	C₂×Q₈×C₆₇	—	2	2	no	—
249	C₂×Q₈×C₆₇	—	2	8	no	—
250	C₂×Q₈×C₆₇	—	2	4	no	—
251	C₂×Q₈×C₆₇	—	2	4	no	—
252	C₂×Q₈×C₆₇	—	4	4	no	—
253	C₂×Q₈×C₆₇	—	4	8	no	—
254	C₂×Q₈×C₆₇	—	8	2	no	—
255	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
256	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
257	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
258	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
259	C₂×D₄×C₆₇	—	2	1	no	—
260	C₂×D₄×C₆₇	—	2	1	no	—
261	C₂×D₄×C₆₇	—	2	4	no	—
262	C₂×D₄×C₆₇	—	2	4	no	—
263	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
264	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
265	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
266	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
267	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
268	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₆₇	—	2	1	no	—
270	C₂²×C₄×C₆₇	—	2	2	no	—
271	C₂²×C₄×C₆₇	—	2	4	no	—
272	C₂²×C₄×C₆₇	—	2	2	no	—
273	C₂²×C₄×C₆₇	—	2	4	no	—
274	C₂²×C₄×C₆₇	—	2	1	no	—
275	C₂²×C₄×C₆₇	—	2	1	no	—
276	C₂²×C₄×C₆₇	—	2	1	no	—
277	C₂²×C₄×C₆₇	—	2	1	no	—
278	C₂²×C₄×C₆₇	—	2	1	no	—
279	C₂²×C₄×C₆₇	—	2	4	no	—
280	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
283	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
284	Q₁₆×C₆₇	—	2	2	no	—
285	Q₁₆×C₆₇	—	4	4	no	—
286	SD₁₆×C₆₇	—	2	2	no	—
287	SD₁₆×C₆₇	—	2	2	no	—
288	SD₁₆×C₆₇	—	4	4	no	—
289	D₈×C₆₇	—	2	2	no	—
290	M₁₆×C₆₇	—	2	4	no	—
291	M₁₆×C₆₇	—	4	4	no	—
292	C₂×C₈×C₆₇	—	2	2	no	—
293	C₂×C₈×C₆₇	—	2	2	no	—
294	C₂×C₈×C₆₇	—	4	4	no	—
295	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
296	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
297	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
298	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
299	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
300	C₄⋊C₄×C₆₇	—	2	2	no	—
301	C₄⋊C₄×C₆₇	—	2	2	no	—
302	C₄⋊C₄×C₆₇	—	2	2	no	—
303	C₄⋊C₄×C₆₇	—	2	2	no	—
304	C₄⋊C₄×C₆₇	—	2	2	no	—
305	C₄⋊C₄×C₆₇	—	2	4	no	—
306	C₄⋊C₄×C₆₇	—	2	4	no	—
307	C₄⋊C₄×C₆₇	—	2	2	no	—
308	C₄⋊C₄×C₆₇	—	2	2	no	—
309	C₄⋊C₄×C₆₇	—	2	4	no	—
310	C₄⋊C₄×C₆₇	—	2	1	no	—
311	C₄⋊C₄×C₆₇	—	2	1	no	—
312	C₄⋊C₄×C₆₇	—	2	1	no	—
313	C₄⋊C₄×C₆₇	—	2	1	no	—
314	C₄⋊C₄×C₆₇	—	2	4	no	—
315	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
316	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
317	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
318	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
319	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
320	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
321	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
322	C₂²⋊C₄×C₆₇	—	2	1	no	—
323	C₂²⋊C₄×C₆₇	—	2	4	no	—
324	C₂²⋊C₄×C₆₇	—	2	1	no	—
325	C₂²⋊C₄×C₆₇	—	2	4	no	—
326	C₂²⋊C₄×C₆₇	—	2	4	no	—
327	C₂²⋊C₄×C₆₇	—	2	4	no	—
328	C₂²⋊C₄×C₆₇	—	2	1	no	—
329	C₂²⋊C₄×C₆₇	—	2	1	no	—
330	C₂²⋊C₄×C₆₇	—	2	1	no	—
331	C₂²⋊C₄×C₆₇	—	2	1	no	—
332	C₂²⋊C₄×C₆₇	—	2	4	no	—
333	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
334	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
335	C₄²×C₆₇	—	2	1	no	—
336	C₄²×C₆₇	—	2	1	no	—
337	C₄²×C₆₇	—	2	1	no	—
338	C₄²×C₆₇	—	2	1	no	—
339	C₄²×C₆₇	—	2	1	no	—
340	C₄²×C₆₇	—	2	1	no	—
341	C₄²×C₆₇	—	2	4	no	—
342	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
343	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
344	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
345	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
346	C₂³×C₆₇	—	2	1	no	—
347	C₂³×C₆₇	—	2	1	no	—
348	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
349	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
350	Q₈×C₆₇	—	2	4	no	—
351	Q₈×C₆₇	—	2	1	no	—
352	Q₈×C₆₇	—	2	1	no	—
353	Q₈×C₆₇	—	2	4	no	—
354	Q₈×C₆₇	—	2	4	no	—
355	Q₈×C₆₇	—	2	1	no	—
356	Q₈×C₆₇	—	4	8	no	—
357	Q₈×C₆₇	—	4	4	no	—
358	Q₈×C₆₇	—	4	4	no	—
359	Q₈×C₆₇	—	8	2	no	—
360	Q₈×C₆₇	C₂×#41	1	2	yes	—
361	D₄×C₆₇	—	2	4	no	—
362	D₄×C₆₇	—	2	8	no	—
363	D₄×C₆₇	—	2	4	no	—
364	D₄×C₆₇	—	2	4	no	—
365	D₄×C₆₇	—	2	4	no	—
366	D₄×C₆₇	—	2	1	no	—
367	D₄×C₆₇	—	2	1	no	—
368	D₄×C₆₇	—	2	1	no	—
369	D₄×C₆₇	—	4	8	no	—
370	D₄×C₆₇	—	4	2	no	—
371	D₄×C₆₇	—	8	4	no	—
372	D₄×C₆₇	C₂×#41	1	2	yes	—
373	C₂×C₄×C₆₇	—	2	1	no	—
374	C₂×C₄×C₆₇	—	2	4	no	—
375	C₂×C₄×C₆₇	—	2	2	no	—
376	C₂×C₄×C₆₇	—	2	2	no	—
377	C₂×C₄×C₆₇	—	2	4	no	—
378	C₂×C₄×C₆₇	—	2	4	no	—
379	C₂×C₄×C₆₇	—	2	1	no	—
380	C₂×C₄×C₆₇	—	2	1	no	—
381	C₂×C₄×C₆₇	—	2	1	no	—
382	C₂×C₄×C₆₇	—	2	1	no	—
383	C₂×C₄×C₆₇	—	2	1	no	—
384	C₂×C₄×C₆₇	—	2	4	no	—
385	C₂×C₄×C₆₇	—	2	4	no	—
386	C₂×C₄×C₆₇	—	4	8	no	—
387	C₂×C₄×C₆₇	—	4	8	no	—
388	C₂×C₄×C₆₇	—	4	4	no	—
389	C₂×C₄×C₆₇	—	4	2	no	—
390	C₂×C₄×C₆₇	—	4	2	no	—
391	C₂×C₄×C₆₇	—	4	2	no	—
392	C₂×C₄×C₆₇	—	4	2	no	—
393	C₂×C₄×C₆₇	—	4	2	no	—
394	C₂×C₄×C₆₇	—	8	2	no	—
395	C₂×C₄×C₆₇	—	8	4	no	—
396	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
397	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
403	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
404	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
405	C₈×C₆₇	—	2	1	no	—
406	C₈×C₆₇	—	2	1	no	—
407	C₈×C₆₇	—	2	1	no	—
408	C₈×C₆₇	—	2	1	no	—
409	C₈×C₆₇	—	2	4	no	—
410	C₂²×C₆₇	—	2	1	no	—
411	C₂²×C₆₇	—	2	1	no	—
412	C₂²×C₆₇	—	2	2	no	—
413	C₂²×C₆₇	—	2	4	no	—
414	C₂²×C₆₇	—	2	4	no	—
415	C₂²×C₆₇	—	2	4	no	—
416	C₂²×C₆₇	—	4	1	no	—
417	C₂²×C₆₇	—	4	1	no	—
418	C₂²×C₆₇	—	4	1	no	—
419	C₂²×C₆₇	—	4	1	no	—
420	C₂²×C₆₇	—	4	1	no	—
421	C₂²×C₆₇	#546	1	2	yes	—
422	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
423	C₄×C₆₇	—	2	2	no	—
424	C₄×C₆₇	—	2	4	no	—
425	C₄×C₆₇	—	2	1	no	—
426	C₄×C₆₇	—	2	1	no	—
427	C₄×C₆₇	—	4	4	no	—
428	C₄×C₆₇	—	4	1	no	—
429	C₄×C₆₇	—	4	1	no	—
430	C₄×C₆₇	—	4	1	no	—
431	C₄×C₆₇	—	4	4	no	—
432	C₄×C₆₇	—	4	1	no	—
433	C₄×C₆₇	—	4	1	no	—
434	C₄×C₆₇	#546	1	2	yes	—
435	C₄×C₆₇	#577	1	2	yes	—
436	C₄×C₆₇	#578	1	2	yes	—
437	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
438	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
439	#61217	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
440	C₂×C₆₇	—	2	2	no	—
441	C₂×C₆₇	—	4	4	no	—
442	C₂×C₆₇	—	4	2	no	—
443	C₂×C₆₇	—	8	1	no	—
444	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
445	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
446	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
447	#3511	C₂×C₆₇	1	1	yes	characteristic, complemented
448	#3499	C₂×C₆₇	1	1	yes	characteristic, complemented
449	#3331	C₂×C₆₇	1	2	yes	complemented
450	#3330	C₂×C₆₇	1	2	yes	complemented
451	#3329	C₂×C₆₇	1	2	yes	complemented
452	#3328	C₂×C₆₇	1	2	yes	complemented
453	#3303	C₂×C₆₇	1	2	yes	complemented
454	#3302	C₂×C₆₇	1	2	yes	complemented
455	#3299	C₂×C₆₇	1	2	yes	complemented
456	#3298	C₂×C₆₇	1	2	yes	complemented
457	C₂×#487	C₂×C₆₇	1	1	yes	characteristic, complemented
458	#3097	C₂×C₆₇	1	2	yes	complemented
459	#3079	C₂×C₆₇	1	1	yes	characteristic, complemented
460	#3063	C₂×C₆₇	1	2	yes	complemented
461	#3039	C₂×C₆₇	1	1	yes	characteristic, complemented
462	#3013	C₂×C₆₇	1	2	yes	complemented
463	C₄×#135	C₂×C₆₇	1	1	yes	characteristic, complemented
464	#2931	C₂×C₆₇	1	1	yes	characteristic, complemented
465	#2898	C₂×C₆₇	1	2	yes	complemented
466	C₆₇	#61217	1	1	yes	characteristic, direct product factor, Sylow
467	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	2	yes	—
468	C₂×#137	C₂²×C₆₇	1	2	yes	—
469	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
470	C₂×#131	C₂²×C₆₇	1	2	yes	—
471	#556	C₂²×C₆₇	1	2	yes	—
472	#555	C₂²×C₆₇	1	2	yes	—
473	#554	C₂²×C₆₇	1	2	yes	—
474	#553	—	2	2	no	—
475	D₄×Q₈	C₂²×C₆₇	1	2	yes	—
476	D₄×Q₈	C₂²×C₆₇	1	2	yes	—
477	#548	—	2	2	no	—
478	#547	—	2	2	no	—
479	#547	—	2	2	no	—
480	#547	C₂²×C₆₇	1	2	yes	—
481	#547	C₂²×C₆₇	1	2	yes	—
482	#547	C₂²×C₆₇	1	2	yes	—
483	#542	—	2	2	no	—
484	#537	C₂²×C₆₇	1	2	yes	—
485	#536	—	2	2	no	—
486	#536	C₂²×C₆₇	1	2	yes	—
487	#533	—	2	1	no	—
488	#532	—	2	1	no	—
489	#532	—	2	1	no	—
490	#532	C₂²×C₆₇	1	1	yes	characteristic
491	C₂×C₄⋊Q₈	—	2	1	no	—
492	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
493	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
494	#520	C₂²×C₆₇	1	2	yes	—
495	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
496	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
497	#487	C₂²×C₆₇	1	2	yes	—
498	#487	C₂²×C₆₇	1	2	yes	—
499	#487	C₂²×C₆₇	1	2	yes	—
500	#487	C₂²×C₆₇	1	2	yes	—
501	#485	C₂²×C₆₇	1	4	yes	—
502	#485	C₂²×C₆₇	1	4	yes	—
503	#484	C₂²×C₆₇	1	4	yes	—
504	#483	C₂²×C₆₇	1	4	yes	—
505	#477	C₂²×C₆₇	1	2	yes	—
506	#476	C₂²×C₆₇	1	2	yes	—
507	#475	C₂²×C₆₇	1	2	yes	—
508	#474	C₂²×C₆₇	1	2	yes	—
509	#470	C₂²×C₆₇	1	4	yes	—
510	#468	C₂²×C₆₇	1	4	yes	—
511	#467	C₂²×C₆₇	1	4	yes	—
512	#465	C₂²×C₆₇	1	4	yes	—
513	#462	C₂²×C₆₇	1	2	yes	—
514	#462	C₂²×C₆₇	1	2	yes	—
515	#461	C₂²×C₆₇	1	2	yes	—
516	#461	C₂²×C₆₇	1	2	yes	—
517	#452	C₂²×C₆₇	1	4	yes	—
518	#451	C₂²×C₆₇	1	4	yes	—
519	#449	C₂²×C₆₇	1	4	yes	—
520	#448	C₂²×C₆₇	1	4	yes	—
521	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
522	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
523	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
524	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
525	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
526	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
527	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
528	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
529	#436	C₂²×C₆₇	1	2	yes	—
530	#436	C₂²×C₆₇	1	2	yes	—
531	C₈×D₄	C₂²×C₆₇	1	2	yes	—
532	C₈×D₄	C₂²×C₆₇	1	2	yes	—
533	#428	C₂²×C₆₇	1	2	yes	—
534	#427	C₂²×C₆₇	1	1	yes	characteristic
535	#423	C₂²×C₆₇	1	1	yes	characteristic
536	#419	C₂²×C₆₇	1	4	yes	—
537	#419	C₂²×C₆₇	1	2	yes	—
538	#417	C₂²×C₆₇	1	4	yes	—
539	#417	C₂²×C₆₇	1	2	yes	—
540	#416	C₂²×C₆₇	1	1	yes	characteristic
541	#416	C₂²×C₆₇	1	4	yes	—
542	#416	C₂²×C₆₇	1	1	yes	characteristic
543	C₂×#103	C₂²×C₆₇	1	2	yes	—
544	C₂×#103	C₂²×C₆₇	1	2	yes	—
545	C₂×#103	C₂²×C₆₇	1	4	yes	—
546	#408	C₂²×C₆₇	1	2	yes	—
547	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
548	2₋¹⁺⁴	—	2	8	no	—
549	2₋¹⁺⁴	—	4	4	no	—
550	C₂×#41	—	2	2	no	—
551	C₂×#41	—	2	4	no	—
552	C₂×#41	—	2	2	no	—
553	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
554	C₂×#41	C₂³×C₆₇	1	4	yes	—
555	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
556	C₂×#41	C₂³×C₆₇	1	2	yes	—
557	C₂²×Q₈	—	2	2	no	—
558	C₂²×Q₈	—	2	1	no	—
559	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
560	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
561	#137	—	4	4	no	—
562	#135	—	2	4	no	—
563	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
564	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
565	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
566	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
567	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
568	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
569	#131	—	4	4	no	—
570	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
571	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
572	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
573	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
574	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
575	C₄⋊Q₈	—	2	2	no	—
576	C₄⋊Q₈	—	2	2	no	—
577	C₄⋊Q₈	—	2	2	no	—
578	C₄⋊Q₈	—	2	1	no	—
579	C₄⋊Q₈	—	2	1	no	—
580	C₄⋊Q₈	—	2	1	no	—
581	C₄⋊Q₈	—	2	1	no	—
582	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
583	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
584	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
585	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
586	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
587	#127	D₄×C₆₇	1	1	yes	characteristic
588	#126	—	2	4	no	—
589	#125	—	2	2	no	—
590	#124	—	2	2	no	—
591	#124	—	2	2	no	—
592	#124	—	2	4	no	—
593	#124	D₄×C₆₇	1	2	yes	—
594	#123	—	2	4	no	—
595	#123	—	2	4	no	—
596	#123	—	2	4	no	—
597	#123	—	2	4	no	—
598	C₂²⋊Q₈	—	2	2	no	—
599	C₂²⋊Q₈	—	2	2	no	—
600	C₂²⋊Q₈	—	2	4	no	—
601	C₂²⋊Q₈	—	2	4	no	—
602	C₂²⋊Q₈	—	2	4	no	—
603	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
604	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
605	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
606	#121	—	2	2	no	—
607	#121	—	2	2	no	—
608	#121	—	2	2	no	—
609	#121	—	2	2	no	—
610	#121	—	2	4	no	—
611	#121	D₄×C₆₇	1	2	yes	—
612	#121	D₄×C₆₇	1	2	yes	—
613	#121	C₂³×C₆₇	1	4	yes	—
614	C₄×Q₈	—	2	2	no	—
615	C₄×Q₈	—	2	2	no	—
616	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
617	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
618	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
619	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
620	C₄×D₄	—	2	2	no	—
621	C₄×D₄	—	2	4	no	—
622	C₄×D₄	—	2	2	no	—
623	C₄×D₄	—	2	2	no	—
624	C₄×D₄	—	2	2	no	—
625	C₄×D₄	—	2	1	no	—
626	C₄×D₄	—	2	1	no	—
627	C₄×D₄	—	2	1	no	—
628	C₄×D₄	—	2	1	no	—
629	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
630	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
631	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
632	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
633	C₄×D₄	C₂³×C₆₇	1	2	yes	—
634	C₄×D₄	C₂³×C₆₇	1	2	yes	—
635	#117	—	2	2	no	—
636	#117	—	2	1	no	—
637	#117	—	2	1	no	—
638	#117	C₂³×C₆₇	1	1	yes	characteristic
639	#117	C₂³×C₆₇	1	1	yes	characteristic
640	#117	C₂³×C₆₇	1	4	yes	—
641	C₂×C₄⋊C₄	—	2	1	no	—
642	C₂×C₄⋊C₄	—	2	1	no	—
643	C₂×C₄⋊C₄	—	2	1	no	—
644	C₂×C₄⋊C₄	—	2	2	no	—
645	C₂×C₄⋊C₄	—	2	2	no	—
646	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
648	C₂×C₄²	—	2	1	no	—
649	C₂×C₄²	—	2	1	no	—
650	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
651	#107	C₂³×C₆₇	1	1	yes	characteristic
652	#107	C₂³×C₆₇	1	1	yes	characteristic
653	#107	C₂³×C₆₇	1	4	yes	—
654	#106	C₂³×C₆₇	1	1	yes	characteristic
655	#106	C₂³×C₆₇	1	1	yes	characteristic
656	#106	C₂³×C₆₇	1	4	yes	—
657	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
658	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
659	#103	C₂³×C₆₇	1	1	yes	characteristic
660	#103	C₂³×C₆₇	1	4	yes	—
661	#103	C₂³×C₆₇	1	4	yes	—
662	#103	C₂³×C₆₇	1	4	yes	—
663	#103	C₂³×C₆₇	1	4	yes	—
664	#103	C₂³×C₆₇	1	4	yes	—
665	#103	C₂³×C₆₇	1	4	yes	—
666	#103	C₂³×C₆₇	1	1	yes	characteristic
667	#103	C₂³×C₆₇	1	4	yes	—
668	#103	C₂³×C₆₇	1	1	yes	characteristic
669	#103	C₂³×C₆₇	1	1	yes	characteristic
670	#102	C₂³×C₆₇	1	1	yes	characteristic
671	#102	C₂³×C₆₇	1	1	yes	characteristic
672	#102	C₂³×C₆₇	1	4	yes	—
673	#102	C₂³×C₆₇	1	1	yes	characteristic
674	#102	C₂³×C₆₇	1	1	yes	characteristic
675	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
676	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
677	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
678	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
679	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
680	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
681	#41	—	2	4	no	—
682	#41	—	2	4	no	—
683	#41	—	2	2	no	—
684	#41	—	2	8	no	—
685	#41	—	2	2	no	—
686	#41	—	2	2	no	—
687	#41	—	4	4	no	—
688	#41	—	4	8	no	—
689	#41	—	4	16	no	—
690	#41	—	8	4	no	—
691	#41	#41×C₆₇	1	4	yes	complemented
692	C₂×Q₈	—	2	2	no	—
693	C₂×Q₈	—	2	4	no	—
694	C₂×Q₈	—	2	2	no	—
695	C₂×Q₈	—	2	2	no	—
696	C₂×Q₈	—	2	8	no	—
697	C₂×Q₈	—	2	4	no	—
698	C₂×Q₈	—	2	4	no	—
699	C₂×Q₈	—	4	4	no	—
700	C₂×Q₈	—	4	8	no	—
701	C₂×Q₈	—	8	2	no	—
702	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
703	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
704	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
705	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
706	C₂×D₄	—	2	1	no	—
707	C₂×D₄	—	2	1	no	—
708	C₂×D₄	—	2	4	no	—
709	C₂×D₄	—	2	4	no	—
710	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
711	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
712	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
713	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
714	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
715	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	4	no	—
721	C₂²×C₄	—	2	1	no	—
722	C₂²×C₄	—	2	1	no	—
723	C₂²×C₄	—	2	1	no	—
724	C₂²×C₄	—	2	1	no	—
725	C₂²×C₄	—	2	1	no	—
726	C₂²×C₄	—	2	4	no	—
727	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
728	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
730	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
731	Q₁₆	—	2	2	no	—
732	Q₁₆	—	4	4	no	—
733	SD₁₆	—	2	2	no	—
734	SD₁₆	—	2	2	no	—
735	SD₁₆	—	4	4	no	—
736	D₈	—	2	2	no	—
737	M₁₆	—	2	4	no	—
738	M₁₆	—	4	4	no	—
739	C₂×C₈	—	2	2	no	—
740	C₂×C₈	—	2	2	no	—
741	C₂×C₈	—	4	4	no	—
742	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
743	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
744	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
745	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
746	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	4	no	—
757	C₄⋊C₄	—	2	1	no	—
758	C₄⋊C₄	—	2	1	no	—
759	C₄⋊C₄	—	2	1	no	—
760	C₄⋊C₄	—	2	1	no	—
761	C₄⋊C₄	—	2	4	no	—
762	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
763	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
764	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
765	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
766	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
767	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
768	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
769	C₂²⋊C₄	—	2	1	no	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	—	2	1	no	—
772	C₂²⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	2	4	no	—
774	C₂²⋊C₄	—	2	4	no	—
775	C₂²⋊C₄	—	2	1	no	—
776	C₂²⋊C₄	—	2	1	no	—
777	C₂²⋊C₄	—	2	1	no	—
778	C₂²⋊C₄	—	2	1	no	—
779	C₂²⋊C₄	—	2	4	no	—
780	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
781	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
782	C₄²	—	2	1	no	—
783	C₄²	—	2	1	no	—
784	C₄²	—	2	1	no	—
785	C₄²	—	2	1	no	—
786	C₄²	—	2	1	no	—
787	C₄²	—	2	1	no	—
788	C₄²	—	2	4	no	—
789	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
790	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
791	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
792	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
793	C₂³	—	2	1	no	—
794	C₂³	—	2	1	no	—
795	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
796	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
797	Q₈	—	2	4	no	—
798	Q₈	—	2	1	no	—
799	Q₈	—	2	1	no	—
800	Q₈	—	2	4	no	—
801	Q₈	—	2	4	no	—
802	Q₈	—	2	1	no	—
803	Q₈	—	4	8	no	—
804	Q₈	—	4	4	no	—
805	Q₈	—	4	4	no	—
806	Q₈	—	8	2	no	—
807	Q₈	C₂×#41×C₆₇	1	2	yes	—
808	D₄	—	2	4	no	—
809	D₄	—	2	8	no	—
810	D₄	—	2	4	no	—
811	D₄	—	2	4	no	—
812	D₄	—	2	4	no	—
813	D₄	—	2	1	no	—
814	D₄	—	2	1	no	—
815	D₄	—	2	1	no	—
816	D₄	—	4	8	no	—
817	D₄	—	4	2	no	—
818	D₄	—	8	4	no	—
819	D₄	C₂×#41×C₆₇	1	2	yes	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	4	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	4	no	—
825	C₂×C₄	—	2	4	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	4	no	—
832	C₂×C₄	—	2	4	no	—
833	C₂×C₄	—	4	8	no	—
834	C₂×C₄	—	4	8	no	—
835	C₂×C₄	—	4	4	no	—
836	C₂×C₄	—	4	2	no	—
837	C₂×C₄	—	4	2	no	—
838	C₂×C₄	—	4	2	no	—
839	C₂×C₄	—	4	2	no	—
840	C₂×C₄	—	4	2	no	—
841	C₂×C₄	—	8	2	no	—
842	C₂×C₄	—	8	4	no	—
843	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
844	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
845	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
846	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
847	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
848	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
849	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
850	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
851	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
852	C₈	—	2	1	no	—
853	C₈	—	2	1	no	—
854	C₈	—	2	1	no	—
855	C₈	—	2	1	no	—
856	C₈	—	2	4	no	—
857	C₂²	—	2	1	no	—
858	C₂²	—	2	1	no	—
859	C₂²	—	2	4	no	—
860	C₂²	—	2	4	no	—
861	C₂²	—	2	2	no	—
862	C₂²	—	2	4	no	—
863	C₂²	—	4	1	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	4	1	no	—
866	C₂²	—	4	1	no	—
867	C₂²	—	4	1	no	—
868	C₂²	#546×C₆₇	1	2	yes	—
869	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
870	C₄	—	2	1	no	—
871	C₄	—	2	1	no	—
872	C₄	—	2	2	no	—
873	C₄	—	2	4	no	—
874	C₄	—	4	1	no	—
875	C₄	—	4	1	no	—
876	C₄	—	4	4	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	1	no	—
879	C₄	—	4	4	no	—
880	C₄	—	4	1	no	—
881	C₄	#546×C₆₇	1	2	yes	—
882	C₄	#577×C₆₇	1	2	yes	—
883	C₄	#578×C₆₇	1	2	yes	—
884	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
885	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
886	C₂	—	2	2	no	—
887	C₂	—	4	4	no	—
888	C₂	—	4	2	no	—
889	C₂	—	8	1	no	—
890	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
891	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
892	C₂	C₂×#578×C₆₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3511	C₂	semidirect
2. C₆₇×#3499	C₂	semidirect
3. C₆₇×#3331	C₂	semidirect
4. C₆₇×#3330	C₂	semidirect
5. C₆₇×#3329	C₂	semidirect
6. C₆₇×#3328	C₂	semidirect
7. C₆₇×#3303	C₂	semidirect
8. C₆₇×#3302	C₂	semidirect
9. C₆₇×#3299	C₂	semidirect
10. C₆₇×#3298	C₂	semidirect
11. C₂×#487×C₆₇	C₂	semidirect
12. C₆₇×#3097	C₂	semidirect
13. C₆₇×#3079	C₂	semidirect
14. C₆₇×#3063	C₂	semidirect
15. C₆₇×#3039	C₂	semidirect
16. C₆₇×#3013	C₂	semidirect
17. C₄×#135×C₆₇	C₂	semidirect
18. C₆₇×#2931	C₂	semidirect
19. C₆₇×#2898	C₂	semidirect
244. #41×C₆₇	#41	semidirect
439. #61217	C₆₇	direct (N × H)
447. #3511	C₂×C₆₇	semidirect
448. #3499	C₂×C₆₇	semidirect
449. #3331	C₂×C₆₇	semidirect
450. #3330	C₂×C₆₇	semidirect
451. #3329	C₂×C₆₇	semidirect
452. #3328	C₂×C₆₇	semidirect
453. #3303	C₂×C₆₇	semidirect
454. #3302	C₂×C₆₇	semidirect
455. #3299	C₂×C₆₇	semidirect
456. #3298	C₂×C₆₇	semidirect
457. C₂×#487	C₂×C₆₇	semidirect
458. #3097	C₂×C₆₇	semidirect
459. #3079	C₂×C₆₇	semidirect
460. #3063	C₂×C₆₇	semidirect
461. #3039	C₂×C₆₇	semidirect
462. #3013	C₂×C₆₇	semidirect
463. C₄×#135	C₂×C₆₇	semidirect
464. #2931	C₂×C₆₇	semidirect
465. #2898	C₂×C₆₇	semidirect
466. C₆₇	#61217	direct (N × H)
691. #41	#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×#3499	2
C₆₇×#3331	2
C₆₇×#3330	2
C₆₇×#3329	2
C₆₇×#3328	2
C₆₇×#3303	2
C₆₇×#3302	2
C₆₇×#3299	2
C₆₇×#3298	2
C₂×#487×C₆₇	2
C₆₇×#3097	2
C₆₇×#3079	2
C₆₇×#3063	2
C₆₇×#3039	2
C₆₇×#3013	2
C₄×#135×C₆₇	2
C₆₇×#2931	2
C₆₇×#2898	2
#61217	67

Subgroups — C67×#61217 #30740468

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61217 #30740468