Subgroups — C₆₇×#61557 #30740808

Order 17152.

1820 conjugacy classes of subgroups.

The subgroup lattice has 1144 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, complemented
2	C₆₇×#3518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3393	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×SD₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3369	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#3367	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#3356	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3354	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3316	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3311	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3303	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3298	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3276	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3275	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3185	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3173	C₂	1	2	yes	maximal, complemented
17	C₆₇×#3125	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3121	C₂	1	2	yes	maximal, complemented
19	C₆₇×#3107	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3101	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2969	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2947	C₂	1	2	yes	maximal, complemented
23	C₄×AGL(1,ℤ/8)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₆₇	C₂²	1	2	yes	—
25	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
26	Q₈²×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	#556×C₆₇	—	2	2	no	—
28	#556×C₆₇	—	2	1	no	—
29	#556×C₆₇	C₂²	1	1	yes	characteristic
30	#556×C₆₇	C₂²	1	2	yes	—
31	#556×C₆₇	C₂²	1	1	yes	characteristic, complemented
32	#555×C₆₇	—	2	1	no	—
33	#555×C₆₇	C₂²	1	1	yes	characteristic, complemented
34	#554×C₆₇	C₂²	1	2	yes	—
35	#552×C₆₇	—	2	1	no	—
36	#551×C₆₇	—	2	2	no	—
37	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	#548×C₆₇	—	2	1	no	—
40	#548×C₆₇	C₂²	1	2	yes	—
41	#547×C₆₇	C₂²	1	1	yes	characteristic
42	#547×C₆₇	C₂²	1	1	yes	characteristic
43	#546×C₆₇	C₂²	1	2	yes	—
44	#542×C₆₇	—	2	2	no	—
45	#542×C₆₇	C₂²	1	2	yes	—
46	#542×C₆₇	C₂²	1	2	yes	complemented
47	#539×C₆₇	—	2	2	no	—
48	#533×C₆₇	—	2	1	no	—
49	#533×C₆₇	C₂²	1	1	yes	characteristic
50	#533×C₆₇	C₂²	1	1	yes	characteristic
51	#529×C₆₇	—	2	1	no	—
52	#529×C₆₇	C₂²	1	1	yes	characteristic
53	#525×C₆₇	—	2	1	no	—
54	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
55	#520×C₆₇	C₂²	1	2	yes	—
56	#519×C₆₇	C₂²	1	2	yes	complemented
57	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
59	#498×C₆₇	C₂²	1	1	yes	characteristic, complemented
60	#498×C₆₇	C₂²	1	2	yes	complemented
61	#495×C₆₇	C₂²	1	2	yes	—
62	#494×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	#489×C₆₇	C₂²	1	2	yes	—
64	#489×C₆₇	C₂²	1	2	yes	complemented
65	#487×C₆₇	C₂²	1	1	yes	characteristic, complemented
66	#487×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	#485×C₆₇	C₂²	1	2	yes	—
68	#485×C₆₇	C₂²	1	2	yes	complemented
69	#483×C₆₇	C₂²	1	2	yes	—
70	#483×C₆₇	C₂²	1	2	yes	complemented
71	#482×C₆₇	C₂²	1	2	yes	—
72	#481×C₆₇	C₂²	1	2	yes	complemented
73	#477×C₆₇	C₂²	1	2	yes	complemented
74	#476×C₆₇	C₂²	1	1	yes	characteristic
75	#476×C₆₇	C₂²	1	2	yes	—
76	#476×C₆₇	C₂²	1	1	yes	characteristic
77	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
78	#475×C₆₇	C₂²	1	2	yes	complemented
79	#475×C₆₇	C₂²	1	2	yes	complemented
80	#474×C₆₇	C₂²	1	1	yes	characteristic, complemented
81	#470×C₆₇	C₂²	1	2	yes	—
82	#470×C₆₇	C₂²	1	2	yes	—
83	#470×C₆₇	C₂²	1	2	yes	complemented
84	#469×C₆₇	C₂²	1	2	yes	—
85	#465×C₆₇	C₂²	1	2	yes	—
86	#465×C₆₇	C₂²	1	2	yes	complemented
87	#464×C₆₇	C₂²	1	2	yes	—
88	#464×C₆₇	C₂²	1	2	yes	—
89	#464×C₆₇	C₂²	1	2	yes	complemented
90	#463×C₆₇	C₂²	1	2	yes	—
91	#462×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	#461×C₆₇	C₂²	1	1	yes	characteristic
93	#461×C₆₇	C₂²	1	1	yes	characteristic
94	#461×C₆₇	C₂²	1	1	yes	characteristic, complemented
95	#452×C₆₇	C₂²	1	2	yes	—
96	#452×C₆₇	C₂²	1	2	yes	—
97	#451×C₆₇	C₂²	1	2	yes	complemented
98	#450×C₆₇	C₂²	1	2	yes	—
99	#449×C₆₇	C₂²	1	2	yes	—
100	#448×C₆₇	C₂²	1	2	yes	—
101	#446×C₆₇	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
103	#442×C₆₇	C₂²	1	1	yes	characteristic
104	#442×C₆₇	C₂²	1	1	yes	characteristic
105	#441×C₆₇	C₂²	1	2	yes	complemented
106	#441×C₆₇	C₂²	1	2	yes	complemented
107	#441×C₆₇	C₂²	1	2	yes	complemented
108	#440×C₆₇	C₂²	1	2	yes	—
109	#440×C₆₇	C₂²	1	1	yes	characteristic
110	#440×C₆₇	C₂²	1	1	yes	characteristic
111	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
112	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
113	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
114	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
115	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
116	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
117	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
118	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
119	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
121	#436×C₆₇	C₂²	1	2	yes	—
122	#436×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	#435×C₆₇	C₂²	1	2	yes	—
124	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
125	#433×C₆₇	C₂²	1	2	yes	complemented
126	#431×C₆₇	C₂²	1	1	yes	characteristic
127	#428×C₆₇	C₂²	1	1	yes	characteristic
128	#428×C₆₇	C₂²	1	2	yes	complemented
129	#418×C₆₇	C₂²	1	1	yes	characteristic
130	#417×C₆₇	C₂²	1	1	yes	characteristic
131	#416×C₆₇	C₂²	1	2	yes	—
132	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
133	#405×C₆₇	C₂²	1	2	yes	complemented
134	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
135	C₂×#41×C₆₇	—	2	1	no	—
136	C₂×#41×C₆₇	C₂³	1	2	yes	—
137	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₆₇	—	2	1	no	—
139	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
140	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₆₇	—	2	1	no	—
142	#137×C₆₇	—	2	8	no	—
143	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
144	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
145	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
152	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
153	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
154	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
155	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
157	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
158	C₄⋊Q₈×C₆₇	—	2	1	no	—
159	C₄⋊Q₈×C₆₇	—	2	1	no	—
160	C₄⋊Q₈×C₆₇	—	2	2	no	—
161	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
165	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
166	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
167	#126×C₆₇	—	2	2	no	—
168	#126×C₆₇	—	2	2	no	—
169	#126×C₆₇	—	2	2	no	—
170	#126×C₆₇	—	2	2	no	—
171	#126×C₆₇	—	2	2	no	—
172	#126×C₆₇	—	2	2	no	—
173	#126×C₆₇	D₄	1	2	yes	—
174	#125×C₆₇	—	2	2	no	—
175	#125×C₆₇	—	2	1	no	—
176	#125×C₆₇	—	2	1	no	—
177	#125×C₆₇	D₄	1	1	yes	characteristic
178	#124×C₆₇	—	2	2	no	—
179	#124×C₆₇	—	2	2	no	—
180	#124×C₆₇	—	2	2	no	—
181	#124×C₆₇	—	2	2	no	—
182	#124×C₆₇	—	2	2	no	—
183	#124×C₆₇	D₄	1	1	yes	characteristic
184	#124×C₆₇	C₂³	1	2	yes	—
185	#124×C₆₇	C₂³	1	2	yes	—
186	#123×C₆₇	—	2	2	no	—
187	#123×C₆₇	—	2	2	no	—
188	#123×C₆₇	—	2	2	no	—
189	#123×C₆₇	—	2	2	no	—
190	#123×C₆₇	—	2	2	no	—
191	#123×C₆₇	D₄	1	2	yes	—
192	C₂²⋊Q₈×C₆₇	—	2	1	no	—
193	C₂²⋊Q₈×C₆₇	—	2	1	no	—
194	C₂²⋊Q₈×C₆₇	—	2	1	no	—
195	C₂²⋊Q₈×C₆₇	—	2	1	no	—
196	C₂²⋊Q₈×C₆₇	—	2	2	no	—
197	C₂²⋊Q₈×C₆₇	—	2	1	no	—
198	C₂²⋊Q₈×C₆₇	—	2	1	no	—
199	C₂²⋊Q₈×C₆₇	—	2	2	no	—
200	C₂²⋊Q₈×C₆₇	—	2	2	no	—
201	C₂²⋊Q₈×C₆₇	—	2	2	no	—
202	C₂²⋊Q₈×C₆₇	—	2	2	no	—
203	C₂²⋊Q₈×C₆₇	—	2	2	no	—
204	C₂²⋊Q₈×C₆₇	—	2	2	no	—
205	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
206	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
207	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
208	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
209	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
210	#121×C₆₇	—	2	1	no	—
211	#121×C₆₇	—	2	1	no	—
212	#121×C₆₇	—	2	2	no	—
213	#121×C₆₇	—	2	2	no	—
214	#121×C₆₇	D₄	1	1	yes	characteristic
215	#121×C₆₇	C₂³	1	2	yes	—
216	#121×C₆₇	C₂³	1	2	yes	—
217	#120×C₆₇	—	2	2	no	—
218	C₄×Q₈×C₆₇	—	2	1	no	—
219	C₄×Q₈×C₆₇	—	2	2	no	—
220	C₄×Q₈×C₆₇	—	2	2	no	—
221	C₄×Q₈×C₆₇	—	2	2	no	—
222	C₄×Q₈×C₆₇	—	2	1	no	—
223	C₄×Q₈×C₆₇	—	2	1	no	—
224	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
226	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
227	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
228	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
230	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
231	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
232	C₄×D₄×C₆₇	—	2	2	no	—
233	C₄×D₄×C₆₇	—	2	1	no	—
234	C₄×D₄×C₆₇	—	2	1	no	—
235	C₄×D₄×C₆₇	—	2	1	no	—
236	C₄×D₄×C₆₇	—	2	2	no	—
237	C₄×D₄×C₆₇	—	2	2	no	—
238	C₄×D₄×C₆₇	—	2	2	no	—
239	C₄×D₄×C₆₇	—	2	1	no	—
240	C₄×D₄×C₆₇	—	2	1	no	—
241	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₆₇	C₂³	1	2	yes	—
245	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₆₇	C₂³	1	2	yes	—
249	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
250	#117×C₆₇	—	2	1	no	—
251	#117×C₆₇	—	2	1	no	—
252	#117×C₆₇	—	2	2	no	—
253	#117×C₆₇	—	2	1	no	—
254	#117×C₆₇	—	2	1	no	—
255	#117×C₆₇	—	2	1	no	—
256	#117×C₆₇	—	2	2	no	—
257	#117×C₆₇	—	2	2	no	—
258	#117×C₆₇	—	2	1	no	—
259	#117×C₆₇	C₂³	1	2	yes	—
260	#117×C₆₇	C₂³	1	1	yes	characteristic
261	#117×C₆₇	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
263	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
264	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
265	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
267	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
268	C₂×C₄²×C₆₇	—	2	1	no	—
269	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
270	#107×C₆₇	C₂³	1	2	yes	—
271	#107×C₆₇	C₂³	1	1	yes	characteristic
272	#107×C₆₇	C₂³	1	1	yes	characteristic
273	#106×C₆₇	C₂³	1	2	yes	—
274	#106×C₆₇	C₂³	1	2	yes	—
275	#106×C₆₇	C₂³	1	2	yes	—
276	#106×C₆₇	C₂³	1	2	yes	—
277	#106×C₆₇	C₂³	1	1	yes	characteristic
278	#106×C₆₇	C₂³	1	1	yes	characteristic
279	#106×C₆₇	C₂³	1	2	yes	—
280	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
283	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
284	#103×C₆₇	C₂³	1	2	yes	—
285	#103×C₆₇	C₂³	1	2	yes	—
286	#103×C₆₇	C₂³	1	2	yes	—
287	#103×C₆₇	C₂³	1	1	yes	characteristic
288	#103×C₆₇	C₂³	1	2	yes	—
289	#103×C₆₇	C₂³	1	2	yes	—
290	#103×C₆₇	C₂³	1	2	yes	—
291	#103×C₆₇	C₂³	1	2	yes	—
292	#103×C₆₇	C₂³	1	2	yes	—
293	#103×C₆₇	C₂³	1	2	yes	—
294	#103×C₆₇	C₂³	1	1	yes	characteristic
295	#102×C₆₇	C₂³	1	2	yes	—
296	#102×C₆₇	C₂³	1	2	yes	—
297	#102×C₆₇	C₂³	1	1	yes	characteristic
298	#102×C₆₇	C₂³	1	2	yes	—
299	#102×C₆₇	C₂³	1	1	yes	characteristic
300	#102×C₆₇	C₂³	1	1	yes	characteristic
301	#102×C₆₇	C₂³	1	1	yes	characteristic
302	#102×C₆₇	C₂³	1	1	yes	characteristic
303	#102×C₆₇	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
307	#97×C₆₇	C₂³	1	2	yes	—
308	#97×C₆₇	C₂³	1	1	yes	characteristic
309	#97×C₆₇	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₆₇	C₂³	1	2	yes	—
313	C₄×C₈×C₆₇	C₂³	1	2	yes	—
314	C₂⁴×C₆₇	—	2	1	no	—
315	#41×C₆₇	—	2	2	no	—
316	#41×C₆₇	—	2	4	no	—
317	#41×C₆₇	—	4	2	no	—
318	#41×C₆₇	—	4	1	no	—
319	#41×C₆₇	—	8	2	no	—
320	C₂×Q₈×C₆₇	—	2	2	no	—
321	C₂×Q₈×C₆₇	—	2	1	no	—
322	C₂×Q₈×C₆₇	—	2	1	no	—
323	C₂×Q₈×C₆₇	—	2	2	no	—
324	C₂×Q₈×C₆₇	—	2	2	no	—
325	C₂×Q₈×C₆₇	—	2	4	no	—
326	C₂×Q₈×C₆₇	—	4	2	no	—
327	C₂×Q₈×C₆₇	—	8	2	no	—
328	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
329	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
330	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
331	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
332	C₂×D₄×C₆₇	—	2	2	no	—
333	C₂×D₄×C₆₇	—	2	2	no	—
334	C₂×D₄×C₆₇	—	2	1	no	—
335	C₂×D₄×C₆₇	—	2	2	no	—
336	C₂×D₄×C₆₇	—	2	2	no	—
337	C₂×D₄×C₆₇	—	2	1	no	—
338	C₂×D₄×C₆₇	—	4	1	no	—
339	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
340	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
341	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
342	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
343	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₆₇	—	2	2	no	—
345	C₂²×C₄×C₆₇	—	2	1	no	—
346	C₂²×C₄×C₆₇	—	2	2	no	—
347	C₂²×C₄×C₆₇	—	2	1	no	—
348	C₂²×C₄×C₆₇	—	2	1	no	—
349	C₂²×C₄×C₆₇	—	2	2	no	—
350	C₂²×C₄×C₆₇	—	2	1	no	—
351	C₂²×C₄×C₆₇	—	2	1	no	—
352	C₂²×C₄×C₆₇	—	2	1	no	—
353	C₂²×C₄×C₆₇	—	2	2	no	—
354	C₂²×C₄×C₆₇	—	2	1	no	—
355	C₂²×C₄×C₆₇	—	2	1	no	—
356	C₂²×C₄×C₆₇	—	8	2	no	—
357	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
358	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
359	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
361	Q₁₆×C₆₇	—	2	4	no	—
362	Q₁₆×C₆₇	—	2	4	no	—
363	Q₁₆×C₆₇	—	4	2	no	—
364	SD₁₆×C₆₇	—	2	2	no	—
365	SD₁₆×C₆₇	—	2	4	no	—
366	SD₁₆×C₆₇	—	4	2	no	—
367	SD₁₆×C₆₇	—	4	2	no	—
368	SD₁₆×C₆₇	#41	1	4	yes	complemented
369	D₈×C₆₇	—	2	2	no	—
370	D₈×C₆₇	—	2	2	no	—
371	M₁₆×C₆₇	—	2	2	no	—
372	M₁₆×C₆₇	—	2	4	no	—
373	M₁₆×C₆₇	—	4	1	no	—
374	C₂×C₈×C₆₇	—	4	2	no	—
375	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
378	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
379	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
380	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
381	C₄⋊C₄×C₆₇	—	2	2	no	—
382	C₄⋊C₄×C₆₇	—	2	1	no	—
383	C₄⋊C₄×C₆₇	—	2	2	no	—
384	C₄⋊C₄×C₆₇	—	2	2	no	—
385	C₄⋊C₄×C₆₇	—	2	2	no	—
386	C₄⋊C₄×C₆₇	—	2	1	no	—
387	C₄⋊C₄×C₆₇	—	2	1	no	—
388	C₄⋊C₄×C₆₇	—	2	1	no	—
389	C₄⋊C₄×C₆₇	—	2	1	no	—
390	C₄⋊C₄×C₆₇	—	2	1	no	—
391	C₄⋊C₄×C₆₇	—	2	2	no	—
392	C₄⋊C₄×C₆₇	—	2	2	no	—
393	C₄⋊C₄×C₆₇	—	2	2	no	—
394	C₄⋊C₄×C₆₇	—	2	1	no	—
395	C₄⋊C₄×C₆₇	—	2	1	no	—
396	C₄⋊C₄×C₆₇	—	2	2	no	—
397	C₄⋊C₄×C₆₇	—	2	2	no	—
398	C₄⋊C₄×C₆₇	—	2	2	no	—
399	C₄⋊C₄×C₆₇	—	2	1	no	—
400	C₄⋊C₄×C₆₇	—	2	2	no	—
401	C₄⋊C₄×C₆₇	—	2	2	no	—
402	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
403	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
406	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
408	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
410	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
414	C₂²⋊C₄×C₆₇	—	2	2	no	—
415	C₂²⋊C₄×C₆₇	—	2	2	no	—
416	C₂²⋊C₄×C₆₇	—	2	2	no	—
417	C₂²⋊C₄×C₆₇	—	2	1	no	—
418	C₂²⋊C₄×C₆₇	—	2	2	no	—
419	C₂²⋊C₄×C₆₇	—	2	2	no	—
420	C₂²⋊C₄×C₆₇	—	2	1	no	—
421	C₂²⋊C₄×C₆₇	—	2	1	no	—
422	C₂²⋊C₄×C₆₇	—	2	1	no	—
423	C₂²⋊C₄×C₆₇	—	2	1	no	—
424	C₂²⋊C₄×C₆₇	—	2	2	no	—
425	C₂²⋊C₄×C₆₇	—	2	2	no	—
426	C₂²⋊C₄×C₆₇	—	2	2	no	—
427	C₂²⋊C₄×C₆₇	—	2	1	no	—
428	C₂²⋊C₄×C₆₇	—	2	1	no	—
429	C₂²⋊C₄×C₆₇	—	2	2	no	—
430	C₂²⋊C₄×C₆₇	—	2	2	no	—
431	C₂²⋊C₄×C₆₇	—	2	2	no	—
432	C₂²⋊C₄×C₆₇	—	2	2	no	—
433	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
438	C₄²×C₆₇	—	2	1	no	—
439	C₄²×C₆₇	—	2	1	no	—
440	C₄²×C₆₇	—	2	1	no	—
441	C₄²×C₆₇	—	2	2	no	—
442	C₄²×C₆₇	—	2	2	no	—
443	C₄²×C₆₇	—	2	2	no	—
444	C₄²×C₆₇	—	2	2	no	—
445	C₄²×C₆₇	—	2	2	no	—
446	C₄²×C₆₇	—	2	2	no	—
447	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
448	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
449	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
450	C₄²×C₆₇	C₂⁴	1	2	yes	—
451	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
452	C₂³×C₆₇	—	2	1	no	—
453	C₂³×C₆₇	—	2	1	no	—
454	C₂³×C₆₇	—	2	1	no	—
455	C₂³×C₆₇	—	4	2	no	—
456	C₂³×C₆₇	—	4	2	no	—
457	C₂³×C₆₇	—	8	1	no	—
458	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
459	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
460	Q₈×C₆₇	—	2	2	no	—
461	Q₈×C₆₇	—	2	1	no	—
462	Q₈×C₆₇	—	2	2	no	—
463	Q₈×C₆₇	—	2	2	no	—
464	Q₈×C₆₇	—	2	2	no	—
465	Q₈×C₆₇	—	2	2	no	—
466	Q₈×C₆₇	—	4	4	no	—
467	Q₈×C₆₇	—	4	2	no	—
468	Q₈×C₆₇	—	8	1	no	—
469	Q₈×C₆₇	—	8	2	no	—
470	Q₈×C₆₇	—	8	2	no	—
471	Q₈×C₆₇	C₂×#41	1	2	yes	—
472	D₄×C₆₇	—	2	2	no	—
473	D₄×C₆₇	—	2	1	no	—
474	D₄×C₆₇	—	2	1	no	—
475	D₄×C₆₇	—	2	1	no	—
476	D₄×C₆₇	—	2	1	no	—
477	D₄×C₆₇	—	2	1	no	—
478	D₄×C₆₇	—	4	2	no	—
479	D₄×C₆₇	—	4	2	no	—
480	D₄×C₆₇	—	4	2	no	—
481	D₄×C₆₇	—	4	4	no	—
482	D₄×C₆₇	—	8	2	no	—
483	D₄×C₆₇	—	8	2	no	—
484	D₄×C₆₇	C₂×#41	1	2	yes	—
485	C₂×C₄×C₆₇	—	2	1	no	—
486	C₂×C₄×C₆₇	—	2	2	no	—
487	C₂×C₄×C₆₇	—	2	1	no	—
488	C₂×C₄×C₆₇	—	2	2	no	—
489	C₂×C₄×C₆₇	—	2	2	no	—
490	C₂×C₄×C₆₇	—	2	1	no	—
491	C₂×C₄×C₆₇	—	2	1	no	—
492	C₂×C₄×C₆₇	—	2	2	no	—
493	C₂×C₄×C₆₇	—	2	2	no	—
494	C₂×C₄×C₆₇	—	2	2	no	—
495	C₂×C₄×C₆₇	—	2	1	no	—
496	C₂×C₄×C₆₇	—	2	1	no	—
497	C₂×C₄×C₆₇	—	2	2	no	—
498	C₂×C₄×C₆₇	—	2	1	no	—
499	C₂×C₄×C₆₇	—	4	1	no	—
500	C₂×C₄×C₆₇	—	4	2	no	—
501	C₂×C₄×C₆₇	—	4	4	no	—
502	C₂×C₄×C₆₇	—	4	4	no	—
503	C₂×C₄×C₆₇	—	4	2	no	—
504	C₂×C₄×C₆₇	—	4	2	no	—
505	C₂×C₄×C₆₇	—	4	2	no	—
506	C₂×C₄×C₆₇	—	8	1	no	—
507	C₂×C₄×C₆₇	—	8	1	no	—
508	C₂×C₄×C₆₇	—	8	1	no	—
509	C₂×C₄×C₆₇	—	8	2	no	—
510	C₂×C₄×C₆₇	—	8	1	no	—
511	C₂×C₄×C₆₇	—	8	2	no	—
512	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
515	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
518	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
521	C₈×C₆₇	—	2	1	no	—
522	C₈×C₆₇	—	2	2	no	—
523	C₈×C₆₇	—	2	1	no	—
524	C₈×C₆₇	—	2	2	no	—
525	C₈×C₆₇	—	2	1	no	—
526	C₈×C₆₇	C₂×#41	1	2	yes	—
527	C₂²×C₆₇	—	2	1	no	—
528	C₂²×C₆₇	—	2	2	no	—
529	C₂²×C₆₇	—	2	2	no	—
530	C₂²×C₆₇	—	2	1	no	—
531	C₂²×C₆₇	—	2	2	no	—
532	C₂²×C₆₇	—	2	1	no	—
533	C₂²×C₆₇	—	2	2	no	—
534	C₂²×C₆₇	—	4	1	no	—
535	C₂²×C₆₇	—	4	1	no	—
536	C₂²×C₆₇	—	4	1	no	—
537	C₂²×C₆₇	—	4	1	no	—
538	C₂²×C₆₇	—	4	1	no	—
539	C₂²×C₆₇	—	4	1	no	—
540	C₂²×C₆₇	—	4	1	no	—
541	C₂²×C₆₇	—	4	1	no	—
542	C₂²×C₆₇	—	8	4	no	—
543	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
544	C₄×C₆₇	—	2	1	no	—
545	C₄×C₆₇	—	2	1	no	—
546	C₄×C₆₇	—	2	2	no	—
547	C₄×C₆₇	—	2	1	no	—
548	C₄×C₆₇	—	2	2	no	—
549	C₄×C₆₇	—	2	2	no	—
550	C₄×C₆₇	—	2	1	no	—
551	C₄×C₆₇	—	2	2	no	—
552	C₄×C₆₇	—	4	1	no	—
553	C₄×C₆₇	—	4	2	no	—
554	C₄×C₆₇	—	4	2	no	—
555	C₄×C₆₇	—	4	2	no	—
556	C₄×C₆₇	—	4	1	no	—
557	C₄×C₆₇	—	4	1	no	—
558	C₄×C₆₇	—	4	1	no	—
559	C₄×C₆₇	—	4	2	no	—
560	C₄×C₆₇	#577	1	2	yes	—
561	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
562	C₄×C₆₇	#585	1	1	yes	characteristic
563	#61557	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
564	C₂×C₆₇	—	4	2	no	—
565	C₂×C₆₇	—	4	1	no	—
566	C₂×C₆₇	—	4	2	no	—
567	C₂×C₆₇	—	8	1	no	—
568	C₂×C₆₇	—	8	1	no	—
569	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
570	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
571	C₂×C₆₇	#3586	1	1	yes	characteristic
572	#3520	C₂×C₆₇	1	1	yes	characteristic, complemented
573	#3518	C₂×C₆₇	1	1	yes	characteristic, complemented
574	#3393	C₂×C₆₇	1	1	yes	characteristic, complemented
575	Q₈×SD₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
576	#3369	C₂×C₆₇	1	1	yes	characteristic, complemented
577	#3367	C₂×C₆₇	1	1	yes	characteristic, complemented
578	#3356	C₂×C₆₇	1	2	yes	complemented
579	#3354	C₂×C₆₇	1	1	yes	characteristic, complemented
580	#3316	C₂×C₆₇	1	2	yes	complemented
581	#3311	C₂×C₆₇	1	2	yes	complemented
582	#3303	C₂×C₆₇	1	1	yes	characteristic, complemented
583	#3298	C₂×C₆₇	1	1	yes	characteristic, complemented
584	#3276	C₂×C₆₇	1	1	yes	characteristic, complemented
585	#3275	C₂×C₆₇	1	2	yes	complemented
586	#3185	C₂×C₆₇	1	1	yes	characteristic, complemented
587	#3173	C₂×C₆₇	1	2	yes	complemented
588	#3125	C₂×C₆₇	1	2	yes	complemented
589	#3121	C₂×C₆₇	1	2	yes	complemented
590	#3107	C₂×C₆₇	1	1	yes	characteristic, complemented
591	#3101	C₂×C₆₇	1	1	yes	characteristic, complemented
592	#2969	C₂×C₆₇	1	1	yes	characteristic, complemented
593	#2947	C₂×C₆₇	1	2	yes	complemented
594	C₄×AGL(1,ℤ/8)	C₂×C₆₇	1	1	yes	characteristic, complemented
595	C₆₇	#61557	1	1	yes	characteristic, direct product factor, Sylow
596	C₂×#137	C₂²×C₆₇	1	2	yes	—
597	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
598	Q₈²	C₂²×C₆₇	1	1	yes	characteristic, complemented
599	#556	—	2	2	no	—
600	#556	—	2	1	no	—
601	#556	C₂²×C₆₇	1	1	yes	characteristic
602	#556	C₂²×C₆₇	1	2	yes	—
603	#556	C₂²×C₆₇	1	1	yes	characteristic, complemented
604	#555	—	2	1	no	—
605	#555	C₂²×C₆₇	1	1	yes	characteristic, complemented
606	#554	C₂²×C₆₇	1	2	yes	—
607	#552	—	2	1	no	—
608	#551	—	2	2	no	—
609	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
610	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
611	#548	—	2	1	no	—
612	#548	C₂²×C₆₇	1	2	yes	—
613	#547	C₂²×C₆₇	1	1	yes	characteristic
614	#547	C₂²×C₆₇	1	1	yes	characteristic
615	#546	C₂²×C₆₇	1	2	yes	—
616	#542	—	2	2	no	—
617	#542	C₂²×C₆₇	1	2	yes	—
618	#542	C₂²×C₆₇	1	2	yes	complemented
619	#539	—	2	2	no	—
620	#533	—	2	1	no	—
621	#533	C₂²×C₆₇	1	1	yes	characteristic
622	#533	C₂²×C₆₇	1	1	yes	characteristic
623	#529	—	2	1	no	—
624	#529	C₂²×C₆₇	1	1	yes	characteristic
625	#525	—	2	1	no	—
626	C₂×C₂²⋊Q₈	—	2	1	no	—
627	#520	C₂²×C₆₇	1	2	yes	—
628	#519	C₂²×C₆₇	1	2	yes	complemented
629	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
630	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
631	#498	C₂²×C₆₇	1	1	yes	characteristic, complemented
632	#498	C₂²×C₆₇	1	2	yes	complemented
633	#495	C₂²×C₆₇	1	2	yes	—
634	#494	C₂²×C₆₇	1	1	yes	characteristic, complemented
635	#489	C₂²×C₆₇	1	2	yes	—
636	#489	C₂²×C₆₇	1	2	yes	complemented
637	#487	C₂²×C₆₇	1	1	yes	characteristic, complemented
638	#487	C₂²×C₆₇	1	1	yes	characteristic, complemented
639	#485	C₂²×C₆₇	1	2	yes	—
640	#485	C₂²×C₆₇	1	2	yes	complemented
641	#483	C₂²×C₆₇	1	2	yes	—
642	#483	C₂²×C₆₇	1	2	yes	complemented
643	#482	C₂²×C₆₇	1	2	yes	—
644	#481	C₂²×C₆₇	1	2	yes	complemented
645	#477	C₂²×C₆₇	1	2	yes	complemented
646	#476	C₂²×C₆₇	1	1	yes	characteristic
647	#476	C₂²×C₆₇	1	1	yes	characteristic
648	#476	C₂²×C₆₇	1	2	yes	—
649	#475	C₂²×C₆₇	1	2	yes	complemented
650	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
651	#475	C₂²×C₆₇	1	2	yes	complemented
652	#474	C₂²×C₆₇	1	1	yes	characteristic, complemented
653	#470	C₂²×C₆₇	1	2	yes	—
654	#470	C₂²×C₆₇	1	2	yes	—
655	#470	C₂²×C₆₇	1	2	yes	complemented
656	#469	C₂²×C₆₇	1	2	yes	—
657	#465	C₂²×C₆₇	1	2	yes	—
658	#465	C₂²×C₆₇	1	2	yes	complemented
659	#464	C₂²×C₆₇	1	2	yes	—
660	#464	C₂²×C₆₇	1	2	yes	—
661	#464	C₂²×C₆₇	1	2	yes	complemented
662	#463	C₂²×C₆₇	1	2	yes	—
663	#462	C₂²×C₆₇	1	1	yes	characteristic, complemented
664	#461	C₂²×C₆₇	1	1	yes	characteristic
665	#461	C₂²×C₆₇	1	1	yes	characteristic
666	#461	C₂²×C₆₇	1	1	yes	characteristic, complemented
667	#452	C₂²×C₆₇	1	2	yes	—
668	#452	C₂²×C₆₇	1	2	yes	—
669	#451	C₂²×C₆₇	1	2	yes	complemented
670	#450	C₂²×C₆₇	1	2	yes	—
671	#449	C₂²×C₆₇	1	2	yes	—
672	#448	C₂²×C₆₇	1	2	yes	—
673	#446	C₂²×C₆₇	1	1	yes	characteristic, complemented
674	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
675	#442	C₂²×C₆₇	1	1	yes	characteristic
676	#442	C₂²×C₆₇	1	1	yes	characteristic
677	#441	C₂²×C₆₇	1	2	yes	complemented
678	#441	C₂²×C₆₇	1	2	yes	complemented
679	#441	C₂²×C₆₇	1	2	yes	complemented
680	#440	C₂²×C₆₇	1	2	yes	—
681	#440	C₂²×C₆₇	1	1	yes	characteristic
682	#440	C₂²×C₆₇	1	1	yes	characteristic
683	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
684	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
685	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
686	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
687	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
688	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
689	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
690	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
691	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
692	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
693	#436	C₂²×C₆₇	1	2	yes	—
694	#436	C₂²×C₆₇	1	1	yes	characteristic, complemented
695	#435	C₂²×C₆₇	1	2	yes	—
696	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
697	#433	C₂²×C₆₇	1	2	yes	complemented
698	#431	C₂²×C₆₇	1	1	yes	characteristic
699	#428	C₂²×C₆₇	1	1	yes	characteristic
700	#428	C₂²×C₆₇	1	2	yes	complemented
701	#418	C₂²×C₆₇	1	1	yes	characteristic
702	#417	C₂²×C₆₇	1	1	yes	characteristic
703	#416	C₂²×C₆₇	1	2	yes	—
704	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
705	#405	C₂²×C₆₇	1	2	yes	complemented
706	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
707	C₂×#41	—	2	1	no	—
708	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
709	C₂×#41	C₂³×C₆₇	1	2	yes	—
710	C₂²×Q₈	—	2	1	no	—
711	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
712	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
713	C₂³×C₄	—	2	1	no	—
714	#137	—	2	8	no	—
715	AGL(1,ℤ/8)	—	2	4	no	—
716	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
717	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
718	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
719	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
720	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
721	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
722	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
723	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
724	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
725	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
726	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
727	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
728	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
729	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
730	C₄⋊Q₈	—	2	1	no	—
731	C₄⋊Q₈	—	2	1	no	—
732	C₄⋊Q₈	—	2	2	no	—
733	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
734	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
735	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
736	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
737	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
738	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
739	#126	—	2	2	no	—
740	#126	—	2	2	no	—
741	#126	—	2	2	no	—
742	#126	—	2	2	no	—
743	#126	—	2	2	no	—
744	#126	—	2	2	no	—
745	#126	D₄×C₆₇	1	2	yes	—
746	#125	—	2	2	no	—
747	#125	—	2	1	no	—
748	#125	—	2	1	no	—
749	#125	D₄×C₆₇	1	1	yes	characteristic
750	#124	—	2	2	no	—
751	#124	—	2	2	no	—
752	#124	—	2	2	no	—
753	#124	—	2	2	no	—
754	#124	—	2	2	no	—
755	#124	D₄×C₆₇	1	1	yes	characteristic
756	#124	C₂³×C₆₇	1	2	yes	—
757	#124	C₂³×C₆₇	1	2	yes	—
758	#123	—	2	2	no	—
759	#123	—	2	2	no	—
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	#123	—	2	2	no	—
763	#123	D₄×C₆₇	1	2	yes	—
764	C₂²⋊Q₈	—	2	1	no	—
765	C₂²⋊Q₈	—	2	1	no	—
766	C₂²⋊Q₈	—	2	1	no	—
767	C₂²⋊Q₈	—	2	1	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	2	1	no	—
770	C₂²⋊Q₈	—	2	1	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	—	2	2	no	—
775	C₂²⋊Q₈	—	2	2	no	—
776	C₂²⋊Q₈	—	2	2	no	—
777	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
778	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
779	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
780	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
781	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
782	#121	—	2	1	no	—
783	#121	—	2	1	no	—
784	#121	—	2	2	no	—
785	#121	—	2	2	no	—
786	#121	D₄×C₆₇	1	1	yes	characteristic
787	#121	C₂³×C₆₇	1	2	yes	—
788	#121	C₂³×C₆₇	1	2	yes	—
789	#120	—	2	2	no	—
790	C₄×Q₈	—	2	1	no	—
791	C₄×Q₈	—	2	2	no	—
792	C₄×Q₈	—	2	2	no	—
793	C₄×Q₈	—	2	2	no	—
794	C₄×Q₈	—	2	1	no	—
795	C₄×Q₈	—	2	1	no	—
796	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
797	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
798	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
799	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
800	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
801	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
802	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
803	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
814	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
815	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
816	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
817	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
818	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
819	C₄×D₄	C₂³×C₆₇	1	2	yes	—
820	C₄×D₄	C₂³×C₆₇	1	2	yes	—
821	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
822	#117	—	2	1	no	—
823	#117	—	2	1	no	—
824	#117	—	2	2	no	—
825	#117	—	2	1	no	—
826	#117	—	2	1	no	—
827	#117	—	2	1	no	—
828	#117	—	2	2	no	—
829	#117	—	2	2	no	—
830	#117	—	2	1	no	—
831	#117	C₂³×C₆₇	1	1	yes	characteristic
832	#117	C₂³×C₆₇	1	2	yes	—
833	#117	C₂³×C₆₇	1	2	yes	—
834	C₂×C₄⋊C₄	—	2	2	no	—
835	C₂×C₄⋊C₄	—	2	1	no	—
836	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
837	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
838	C₂×C₂²⋊C₄	—	2	1	no	—
839	C₂×C₂²⋊C₄	—	2	2	no	—
840	C₂×C₄²	—	2	1	no	—
841	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
842	#107	C₂³×C₆₇	1	1	yes	characteristic
843	#107	C₂³×C₆₇	1	1	yes	characteristic
844	#107	C₂³×C₆₇	1	2	yes	—
845	#106	C₂³×C₆₇	1	1	yes	characteristic
846	#106	C₂³×C₆₇	1	1	yes	characteristic
847	#106	C₂³×C₆₇	1	2	yes	—
848	#106	C₂³×C₆₇	1	2	yes	—
849	#106	C₂³×C₆₇	1	2	yes	—
850	#106	C₂³×C₆₇	1	2	yes	—
851	#106	C₂³×C₆₇	1	2	yes	—
852	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
853	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
854	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
855	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
856	#103	C₂³×C₆₇	1	1	yes	characteristic
857	#103	C₂³×C₆₇	1	2	yes	—
858	#103	C₂³×C₆₇	1	2	yes	—
859	#103	C₂³×C₆₇	1	2	yes	—
860	#103	C₂³×C₆₇	1	2	yes	—
861	#103	C₂³×C₆₇	1	2	yes	—
862	#103	C₂³×C₆₇	1	1	yes	characteristic
863	#103	C₂³×C₆₇	1	2	yes	—
864	#103	C₂³×C₆₇	1	2	yes	—
865	#103	C₂³×C₆₇	1	2	yes	—
866	#103	C₂³×C₆₇	1	2	yes	—
867	#102	C₂³×C₆₇	1	1	yes	characteristic
868	#102	C₂³×C₆₇	1	2	yes	—
869	#102	C₂³×C₆₇	1	1	yes	characteristic
870	#102	C₂³×C₆₇	1	1	yes	characteristic
871	#102	C₂³×C₆₇	1	1	yes	characteristic
872	#102	C₂³×C₆₇	1	1	yes	characteristic
873	#102	C₂³×C₆₇	1	1	yes	characteristic
874	#102	C₂³×C₆₇	1	2	yes	—
875	#102	C₂³×C₆₇	1	2	yes	—
876	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
877	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
878	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
879	#97	C₂³×C₆₇	1	1	yes	characteristic
880	#97	C₂³×C₆₇	1	1	yes	characteristic
881	#97	C₂³×C₆₇	1	2	yes	—
882	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
883	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
884	C₄×C₈	C₂³×C₆₇	1	2	yes	—
885	C₄×C₈	C₂³×C₆₇	1	2	yes	—
886	C₂⁴	—	2	1	no	—
887	#41	—	2	2	no	—
888	#41	—	2	4	no	—
889	#41	—	4	2	no	—
890	#41	—	4	1	no	—
891	#41	—	8	2	no	—
892	C₂×Q₈	—	2	2	no	—
893	C₂×Q₈	—	2	1	no	—
894	C₂×Q₈	—	2	1	no	—
895	C₂×Q₈	—	2	2	no	—
896	C₂×Q₈	—	2	2	no	—
897	C₂×Q₈	—	2	4	no	—
898	C₂×Q₈	—	4	2	no	—
899	C₂×Q₈	—	8	2	no	—
900	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
901	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
902	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
903	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	2	2	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	4	1	no	—
911	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
912	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
913	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
914	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
915	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
916	C₂²×C₄	—	2	2	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	2	1	no	—
920	C₂²×C₄	—	2	1	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	1	no	—
928	C₂²×C₄	—	8	2	no	—
929	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
930	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
931	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
932	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
933	Q₁₆	—	2	4	no	—
934	Q₁₆	—	2	4	no	—
935	Q₁₆	—	4	2	no	—
936	SD₁₆	—	2	2	no	—
937	SD₁₆	—	2	4	no	—
938	SD₁₆	—	4	2	no	—
939	SD₁₆	—	4	2	no	—
940	SD₁₆	#41×C₆₇	1	4	yes	complemented
941	D₈	—	2	2	no	—
942	D₈	—	2	2	no	—
943	M₁₆	—	2	2	no	—
944	M₁₆	—	2	4	no	—
945	M₁₆	—	4	1	no	—
946	C₂×C₈	—	4	2	no	—
947	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
948	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
949	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
950	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
951	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
952	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
975	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
976	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
977	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
978	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
979	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
980	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
981	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
982	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
983	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
984	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
985	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	—	2	1	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1006	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1007	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1008	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1009	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1010	C₄²	—	2	1	no	—
1011	C₄²	—	2	1	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	2	2	no	—
1014	C₄²	—	2	2	no	—
1015	C₄²	—	2	2	no	—
1016	C₄²	—	2	2	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	2	no	—
1019	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1020	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1021	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1022	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1023	C₄²	C₂⁴×C₆₇	1	2	yes	—
1024	C₂³	—	2	1	no	—
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	4	2	no	—
1028	C₂³	—	4	2	no	—
1029	C₂³	—	8	1	no	—
1030	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1031	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1032	Q₈	—	2	2	no	—
1033	Q₈	—	2	1	no	—
1034	Q₈	—	2	2	no	—
1035	Q₈	—	2	2	no	—
1036	Q₈	—	2	2	no	—
1037	Q₈	—	2	2	no	—
1038	Q₈	—	4	4	no	—
1039	Q₈	—	4	2	no	—
1040	Q₈	—	8	2	no	—
1041	Q₈	—	8	1	no	—
1042	Q₈	—	8	2	no	—
1043	Q₈	C₂×#41×C₆₇	1	2	yes	—
1044	D₄	—	2	2	no	—
1045	D₄	—	2	1	no	—
1046	D₄	—	2	1	no	—
1047	D₄	—	2	1	no	—
1048	D₄	—	2	1	no	—
1049	D₄	—	2	1	no	—
1050	D₄	—	4	2	no	—
1051	D₄	—	4	2	no	—
1052	D₄	—	4	2	no	—
1053	D₄	—	4	4	no	—
1054	D₄	—	8	2	no	—
1055	D₄	—	8	2	no	—
1056	D₄	C₂×#41×C₆₇	1	2	yes	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	4	1	no	—
1072	C₂×C₄	—	4	2	no	—
1073	C₂×C₄	—	4	4	no	—
1074	C₂×C₄	—	4	4	no	—
1075	C₂×C₄	—	4	2	no	—
1076	C₂×C₄	—	4	2	no	—
1077	C₂×C₄	—	4	2	no	—
1078	C₂×C₄	—	8	1	no	—
1079	C₂×C₄	—	8	1	no	—
1080	C₂×C₄	—	8	2	no	—
1081	C₂×C₄	—	8	1	no	—
1082	C₂×C₄	—	8	1	no	—
1083	C₂×C₄	—	8	2	no	—
1084	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1085	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1086	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1087	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1088	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1089	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1090	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1091	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1092	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1093	C₈	—	2	1	no	—
1094	C₈	—	2	2	no	—
1095	C₈	—	2	1	no	—
1096	C₈	—	2	2	no	—
1097	C₈	—	2	1	no	—
1098	C₈	C₂×#41×C₆₇	1	2	yes	—
1099	C₂²	—	2	1	no	—
1100	C₂²	—	2	2	no	—
1101	C₂²	—	2	1	no	—
1102	C₂²	—	2	2	no	—
1103	C₂²	—	2	2	no	—
1104	C₂²	—	2	1	no	—
1105	C₂²	—	2	2	no	—
1106	C₂²	—	4	1	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	4	1	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	1	no	—
1111	C₂²	—	4	1	no	—
1112	C₂²	—	4	1	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	8	4	no	—
1115	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1116	C₄	—	2	1	no	—
1117	C₄	—	2	2	no	—
1118	C₄	—	2	1	no	—
1119	C₄	—	2	1	no	—
1120	C₄	—	2	2	no	—
1121	C₄	—	2	1	no	—
1122	C₄	—	2	2	no	—
1123	C₄	—	2	2	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	1	no	—
1127	C₄	—	4	2	no	—
1128	C₄	—	4	1	no	—
1129	C₄	—	4	2	no	—
1130	C₄	—	4	2	no	—
1131	C₄	—	4	2	no	—
1132	C₄	#577×C₆₇	1	2	yes	—
1133	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1134	C₄	#585×C₆₇	1	1	yes	characteristic
1135	C₂	—	4	1	no	—
1136	C₂	—	4	2	no	—
1137	C₂	—	4	2	no	—
1138	C₂	—	8	1	no	—
1139	C₂	—	8	1	no	—
1140	C₂	D₄×#41×C₆₇	1	1	yes	characteristic
1141	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
1142	C₂	C₆₇×#3586	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 ◁ #529×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3520	C₂	semidirect
2. C₆₇×#3518	C₂	semidirect
3. C₆₇×#3393	C₂	semidirect
4. Q₈×SD₁₆×C₆₇	C₂	semidirect
5. C₆₇×#3369	C₂	semidirect
6. C₆₇×#3367	C₂	semidirect
7. C₆₇×#3356	C₂	semidirect
8. C₆₇×#3354	C₂	semidirect
9. C₆₇×#3316	C₂	semidirect
10. C₆₇×#3311	C₂	semidirect
11. C₆₇×#3303	C₂	semidirect
12. C₆₇×#3298	C₂	semidirect
13. C₆₇×#3276	C₂	semidirect
14. C₆₇×#3275	C₂	semidirect
15. C₆₇×#3185	C₂	semidirect
16. C₆₇×#3173	C₂	semidirect
17. C₆₇×#3125	C₂	semidirect
18. C₆₇×#3121	C₂	semidirect
19. C₆₇×#3107	C₂	semidirect
20. C₆₇×#3101	C₂	semidirect
21. C₆₇×#2969	C₂	semidirect
22. C₆₇×#2947	C₂	semidirect
23. C₄×AGL(1,ℤ/8)×C₆₇	C₂	semidirect
26. Q₈²×C₆₇	C₂²	semidirect
31. #556×C₆₇	C₂²	semidirect
33. #555×C₆₇	C₂²	semidirect
38. D₄×Q₈×C₆₇	C₂²	semidirect
46. #542×C₆₇	C₂²	semidirect
56. #519×C₆₇	C₂²	semidirect
59. #498×C₆₇	C₂²	semidirect
60. #498×C₆₇	C₂²	semidirect
62. #494×C₆₇	C₂²	semidirect
64. #489×C₆₇	C₂²	semidirect
65. #487×C₆₇	C₂²	semidirect
66. #487×C₆₇	C₂²	semidirect
68. #485×C₆₇	C₂²	semidirect
70. #483×C₆₇	C₂²	semidirect
72. #481×C₆₇	C₂²	semidirect
73. #477×C₆₇	C₂²	semidirect
77. #475×C₆₇	C₂²	semidirect
78. #475×C₆₇	C₂²	semidirect
79. #475×C₆₇	C₂²	semidirect
80. #474×C₆₇	C₂²	semidirect
83. #470×C₆₇	C₂²	semidirect
86. #465×C₆₇	C₂²	semidirect
89. #464×C₆₇	C₂²	semidirect
91. #462×C₆₇	C₂²	semidirect
94. #461×C₆₇	C₂²	semidirect
97. #451×C₆₇	C₂²	semidirect
101. #446×C₆₇	C₂²	semidirect
102. C₈×Q₈×C₆₇	C₂²	semidirect
105. #441×C₆₇	C₂²	semidirect
106. #441×C₆₇	C₂²	semidirect
107. #441×C₆₇	C₂²	semidirect
111. C₄×Q₁₆×C₆₇	C₂²	semidirect
112. C₄×Q₁₆×C₆₇	C₂²	semidirect
118. C₄×SD₁₆×C₆₇	C₂²	semidirect
122. #436×C₆₇	C₂²	semidirect
124. C₈×D₄×C₆₇	C₂²	semidirect
125. #433×C₆₇	C₂²	semidirect
128. #428×C₆₇	C₂²	semidirect
132. C₂×#103×C₆₇	C₂²	semidirect
133. #405×C₆₇	C₂²	semidirect
368. SD₁₆×C₆₇	#41	semidirect
563. #61557	C₆₇	direct (N × H)
572. #3520	C₂×C₆₇	semidirect
573. #3518	C₂×C₆₇	semidirect
574. #3393	C₂×C₆₇	semidirect
575. Q₈×SD₁₆	C₂×C₆₇	semidirect
576. #3369	C₂×C₆₇	semidirect
577. #3367	C₂×C₆₇	semidirect
578. #3356	C₂×C₆₇	semidirect
579. #3354	C₂×C₆₇	semidirect
580. #3316	C₂×C₆₇	semidirect
581. #3311	C₂×C₆₇	semidirect
582. #3303	C₂×C₆₇	semidirect
583. #3298	C₂×C₆₇	semidirect
584. #3276	C₂×C₆₇	semidirect
585. #3275	C₂×C₆₇	semidirect
586. #3185	C₂×C₆₇	semidirect
587. #3173	C₂×C₆₇	semidirect
588. #3125	C₂×C₆₇	semidirect
589. #3121	C₂×C₆₇	semidirect
590. #3107	C₂×C₆₇	semidirect
591. #3101	C₂×C₆₇	semidirect
592. #2969	C₂×C₆₇	semidirect
593. #2947	C₂×C₆₇	semidirect
594. C₄×AGL(1,ℤ/8)	C₂×C₆₇	semidirect
595. C₆₇	#61557	direct (N × H)
598. Q₈²	C₂²×C₆₇	semidirect
603. #556	C₂²×C₆₇	semidirect
605. #555	C₂²×C₆₇	semidirect
610. D₄×Q₈	C₂²×C₆₇	semidirect
618. #542	C₂²×C₆₇	semidirect
628. #519	C₂²×C₆₇	semidirect
631. #498	C₂²×C₆₇	semidirect
632. #498	C₂²×C₆₇	semidirect
634. #494	C₂²×C₆₇	semidirect
636. #489	C₂²×C₆₇	semidirect
637. #487	C₂²×C₆₇	semidirect
638. #487	C₂²×C₆₇	semidirect
640. #485	C₂²×C₆₇	semidirect
642. #483	C₂²×C₆₇	semidirect
644. #481	C₂²×C₆₇	semidirect
645. #477	C₂²×C₆₇	semidirect
649. #475	C₂²×C₆₇	semidirect
650. #475	C₂²×C₆₇	semidirect
651. #475	C₂²×C₆₇	semidirect
652. #474	C₂²×C₆₇	semidirect
655. #470	C₂²×C₆₇	semidirect
658. #465	C₂²×C₆₇	semidirect
661. #464	C₂²×C₆₇	semidirect
663. #462	C₂²×C₆₇	semidirect
666. #461	C₂²×C₆₇	semidirect
669. #451	C₂²×C₆₇	semidirect
673. #446	C₂²×C₆₇	semidirect
674. C₈×Q₈	C₂²×C₆₇	semidirect
677. #441	C₂²×C₆₇	semidirect
678. #441	C₂²×C₆₇	semidirect
679. #441	C₂²×C₆₇	semidirect
683. C₄×Q₁₆	C₂²×C₆₇	semidirect
684. C₄×Q₁₆	C₂²×C₆₇	semidirect
690. C₄×SD₁₆	C₂²×C₆₇	semidirect
694. #436	C₂²×C₆₇	semidirect
696. C₈×D₄	C₂²×C₆₇	semidirect
697. #433	C₂²×C₆₇	semidirect
700. #428	C₂²×C₆₇	semidirect
704. C₂×#103	C₂²×C₆₇	semidirect
705. #405	C₂²×C₆₇	semidirect
940. SD₁₆	#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×#3520	2
C₆₇×#3518	2
C₆₇×#3393	2
Q₈×SD₁₆×C₆₇	2
C₆₇×#3369	2
C₆₇×#3367	2
C₆₇×#3356	2
C₆₇×#3354	2
C₆₇×#3316	2
C₆₇×#3311	2
C₆₇×#3303	2
C₆₇×#3298	2
C₆₇×#3276	2
C₆₇×#3275	2
C₆₇×#3185	2
C₆₇×#3173	2
C₆₇×#3125	2
C₆₇×#3121	2
C₆₇×#3107	2
C₆₇×#3101	2
C₆₇×#2969	2
C₆₇×#2947	2
C₄×AGL(1,ℤ/8)×C₆₇	2
#61557	67

Subgroups — C67×#61557 #30740808

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61557 #30740808