Subgroups — C₆₇×#61070 #30740321

Order 17152.

2830 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#575×C₆₇	C₂	1	2	yes	maximal, complemented
2	D₄×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#550×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3287	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3284	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3278	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3274	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3271	C₂	1	4	yes	maximal, complemented
9	C₆₇×#3268	C₂	1	4	yes	maximal, complemented
10	C₆₇×#3151	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3055	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3038	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3037	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3006	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3005	C₂	1	2	yes	maximal, complemented
16	C₄×#137×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	D₄×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₆₇	C₂²	1	2	yes	—
19	C₂²×#41×C₆₇	C₂²	1	2	yes	complemented
20	#575×C₆₇	—	2	16	no	—
21	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#137×C₆₇	C₂²	1	4	yes	complemented
23	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
24	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	—
25	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	complemented
26	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
27	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
28	C₂×#135×C₆₇	C₂²	1	4	yes	complemented
29	C₂×#135×C₆₇	C₂²	1	4	yes	complemented
30	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	complemented
31	#550×C₆₇	—	2	1	no	—
32	#550×C₆₇	—	2	1	no	—
33	#550×C₆₇	—	2	2	no	—
34	#550×C₆₇	C₂²	1	2	yes	—
35	#550×C₆₇	C₂²	1	4	yes	complemented
36	#550×C₆₇	C₂²	1	2	yes	complemented
37	#550×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	#548×C₆₇	C₂²	1	2	yes	complemented
40	#547×C₆₇	—	2	1	no	—
41	#547×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	#546×C₆₇	—	2	2	no	—
43	#546×C₆₇	C₂²	1	2	yes	complemented
44	D₄²×C₆₇	—	2	1	no	—
45	D₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	#532×C₆₇	—	2	1	no	—
47	#532×C₆₇	C₂²	1	1	yes	characteristic
48	C₂×#127×C₆₇	—	2	1	no	—
49	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	#525×C₆₇	—	2	2	no	—
51	#525×C₆₇	C₂²	1	2	yes	—
52	C₂×#121×C₆₇	—	2	2	no	—
53	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
54	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
55	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄×D₄×C₆₇	—	2	1	no	—
57	C₂×C₄×D₄×C₆₇	—	2	1	no	—
58	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
59	#496×C₆₇	C₂²	1	4	yes	complemented
60	#493×C₆₇	C₂²	1	2	yes	complemented
61	#492×C₆₇	C₂²	1	2	yes	complemented
62	#469×C₆₇	C₂²	1	4	yes	complemented
63	#468×C₆₇	C₂²	1	4	yes	complemented
64	#466×C₆₇	C₂²	1	4	yes	complemented
65	#465×C₆₇	C₂²	1	4	yes	complemented
66	#464×C₆₇	C₂²	1	4	yes	complemented
67	#462×C₆₇	C₂²	1	2	yes	complemented
68	#460×C₆₇	C₂²	1	2	yes	complemented
69	#460×C₆₇	C₂²	1	2	yes	complemented
70	#460×C₆₇	C₂²	1	2	yes	complemented
71	#459×C₆₇	C₂²	1	2	yes	complemented
72	#459×C₆₇	C₂²	1	2	yes	complemented
73	#452×C₆₇	C₂²	1	4	yes	complemented
74	#452×C₆₇	C₂²	1	4	yes	complemented
75	#449×C₆₇	C₂²	1	4	yes	complemented
76	#449×C₆₇	C₂²	1	4	yes	complemented
77	#449×C₆₇	C₂²	1	4	yes	complemented
78	#449×C₆₇	C₂²	1	4	yes	complemented
79	#448×C₆₇	C₂²	1	4	yes	complemented
80	#447×C₆₇	C₂²	1	4	yes	complemented
81	#441×C₆₇	C₂²	1	2	yes	complemented
82	#440×C₆₇	C₂²	1	2	yes	complemented
83	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
84	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
85	#436×C₆₇	C₂²	1	2	yes	complemented
86	#435×C₆₇	C₂²	1	4	yes	complemented
87	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
88	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
89	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	#419×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	#418×C₆₇	C₂²	1	2	yes	complemented
92	#417×C₆₇	C₂²	1	1	yes	characteristic
93	#417×C₆₇	C₂²	1	2	yes	complemented
94	#407×C₆₇	C₂²	1	2	yes	complemented
95	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
96	C₂×#41×C₆₇	—	2	2	no	—
97	C₂×#41×C₆₇	—	2	2	no	—
98	C₂×#41×C₆₇	—	2	2	no	—
99	C₂×#41×C₆₇	—	2	2	no	—
100	C₂×#41×C₆₇	—	2	8	no	—
101	C₂×#41×C₆₇	—	2	8	no	—
102	C₂×#41×C₆₇	—	4	4	no	—
103	C₂×#41×C₆₇	—	4	4	no	—
104	C₂×#41×C₆₇	C₂³	1	2	yes	—
105	C₂×#41×C₆₇	C₂³	1	2	yes	—
106	C₂×#41×C₆₇	C₂³	1	2	yes	—
107	C₂×#41×C₆₇	C₂³	1	4	yes	—
108	C₂×#41×C₆₇	C₂³	1	4	yes	—
109	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
110	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
111	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₆₇	—	2	2	no	—
113	C₂²×D₄×C₆₇	—	2	2	no	—
114	C₂²×D₄×C₆₇	—	2	2	no	—
115	C₂²×D₄×C₆₇	—	2	1	no	—
116	C₂²×D₄×C₆₇	—	2	1	no	—
117	C₂²×D₄×C₆₇	—	2	1	no	—
118	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
119	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
120	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
121	C₂³×C₄×C₆₇	—	2	2	no	—
122	C₂³×C₄×C₆₇	—	2	2	no	—
123	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
124	#137×C₆₇	—	2	8	no	—
125	#137×C₆₇	—	2	16	no	—
126	#137×C₆₇	D₄	1	8	yes	complemented
127	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
128	AGL(1,ℤ/8)×C₆₇	—	2	16	no	—
129	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
130	AGL(1,ℤ/8)×C₆₇	—	4	4	no	—
131	#135×C₆₇	—	2	16	no	—
132	#135×C₆₇	—	2	16	no	—
133	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
134	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
135	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
136	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
137	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
138	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
139	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
140	C₂×D₈×C₆₇	C₂³	1	4	yes	—
141	C₂×D₈×C₆₇	C₂³	1	4	yes	—
142	C₂×D₈×C₆₇	C₂³	1	4	yes	—
143	C₂×M₁₆×C₆₇	—	2	8	no	—
144	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
145	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
146	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
148	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
149	C₄⋊Q₈×C₆₇	—	2	1	no	—
150	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
151	#127×C₆₇	—	2	2	no	—
152	#127×C₆₇	—	2	2	no	—
153	#127×C₆₇	—	2	4	no	—
154	#127×C₆₇	—	2	1	no	—
155	#127×C₆₇	—	2	1	no	—
156	#127×C₆₇	—	2	1	no	—
157	#127×C₆₇	C₂³	1	2	yes	—
158	#127×C₆₇	C₂³	1	2	yes	—
159	#127×C₆₇	C₂³	1	1	yes	characteristic
160	#124×C₆₇	—	2	2	no	—
161	#124×C₆₇	C₂³	1	2	yes	—
162	#123×C₆₇	—	2	2	no	—
163	#123×C₆₇	—	2	2	no	—
164	#123×C₆₇	—	2	2	no	—
165	C₂²⋊Q₈×C₆₇	—	2	2	no	—
166	C₂²⋊Q₈×C₆₇	—	2	2	no	—
167	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
168	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
169	#121×C₆₇	—	2	2	no	—
170	#121×C₆₇	—	2	1	no	—
171	#121×C₆₇	—	2	2	no	—
172	#121×C₆₇	—	2	2	no	—
173	#121×C₆₇	—	2	1	no	—
174	#121×C₆₇	—	2	1	no	—
175	#121×C₆₇	—	2	1	no	—
176	#121×C₆₇	—	2	4	no	—
177	#121×C₆₇	—	2	4	no	—
178	#121×C₆₇	—	2	4	no	—
179	#121×C₆₇	—	2	4	no	—
180	#121×C₆₇	—	2	2	no	—
181	#121×C₆₇	—	2	2	no	—
182	#121×C₆₇	C₂³	1	4	yes	—
183	#121×C₆₇	C₂³	1	4	yes	—
184	#121×C₆₇	C₂³	1	2	yes	—
185	#121×C₆₇	C₂³	1	2	yes	—
186	#120×C₆₇	—	2	2	no	—
187	#120×C₆₇	—	2	2	no	—
188	#120×C₆₇	—	2	2	no	—
189	C₄×Q₈×C₆₇	—	2	1	no	—
190	C₄×Q₈×C₆₇	—	2	1	no	—
191	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
192	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
193	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
194	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
195	C₄×D₄×C₆₇	—	2	1	no	—
196	C₄×D₄×C₆₇	—	2	2	no	—
197	C₄×D₄×C₆₇	—	2	1	no	—
198	C₄×D₄×C₆₇	—	2	1	no	—
199	C₄×D₄×C₆₇	—	2	2	no	—
200	C₄×D₄×C₆₇	—	2	1	no	—
201	C₄×D₄×C₆₇	—	2	2	no	—
202	C₄×D₄×C₆₇	—	2	2	no	—
203	C₄×D₄×C₆₇	—	2	4	no	—
204	C₄×D₄×C₆₇	—	2	2	no	—
205	C₄×D₄×C₆₇	—	2	1	no	—
206	C₄×D₄×C₆₇	—	2	1	no	—
207	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
208	C₄×D₄×C₆₇	D₄	1	2	yes	—
209	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
210	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
211	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
212	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
213	C₄×D₄×C₆₇	C₂³	1	2	yes	—
214	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
215	#117×C₆₇	—	2	1	no	—
216	#117×C₆₇	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
218	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
219	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
220	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
222	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
223	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
224	C₂×C₄²×C₆₇	—	2	1	no	—
225	C₂×C₄²×C₆₇	—	2	1	no	—
226	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
227	#107×C₆₇	C₂³	1	2	yes	—
228	#106×C₆₇	C₂³	1	2	yes	—
229	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
230	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
231	#103×C₆₇	C₂³	1	2	yes	—
232	#103×C₆₇	C₂³	1	4	yes	—
233	#103×C₆₇	C₂³	1	2	yes	—
234	#103×C₆₇	C₂³	1	2	yes	—
235	#102×C₆₇	C₂³	1	2	yes	—
236	#102×C₆₇	C₂³	1	4	yes	—
237	#102×C₆₇	C₂³	1	4	yes	—
238	#102×C₆₇	C₂³	1	4	yes	—
239	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
240	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
241	#97×C₆₇	C₂³	1	2	yes	—
242	C₄×C₈×C₆₇	C₂³	1	2	yes	—
243	C₂⁴×C₆₇	—	2	2	no	—
244	C₂⁴×C₆₇	—	2	2	no	—
245	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
246	#41×C₆₇	—	2	2	no	—
247	#41×C₆₇	—	2	4	no	—
248	#41×C₆₇	—	2	8	no	—
249	#41×C₆₇	—	2	8	no	—
250	#41×C₆₇	—	2	4	no	—
251	#41×C₆₇	—	2	4	no	—
252	#41×C₆₇	—	2	4	no	—
253	#41×C₆₇	—	4	8	no	—
254	#41×C₆₇	—	4	4	no	—
255	#41×C₆₇	—	4	2	no	—
256	#41×C₆₇	—	4	4	no	—
257	#41×C₆₇	—	4	2	no	—
258	#41×C₆₇	—	4	8	no	—
259	#41×C₆₇	—	4	8	no	—
260	#41×C₆₇	—	4	8	no	—
261	#41×C₆₇	C₂×D₄	1	4	yes	—
262	C₂×Q₈×C₆₇	—	2	1	no	—
263	C₂×Q₈×C₆₇	—	2	2	no	—
264	C₂×Q₈×C₆₇	—	2	2	no	—
265	C₂×Q₈×C₆₇	—	2	4	no	—
266	C₂×Q₈×C₆₇	—	4	2	no	—
267	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	complemented
268	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
269	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
270	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
271	C₂×D₄×C₆₇	—	2	1	no	—
272	C₂×D₄×C₆₇	—	2	4	no	—
273	C₂×D₄×C₆₇	—	2	2	no	—
274	C₂×D₄×C₆₇	—	2	2	no	—
275	C₂×D₄×C₆₇	—	2	2	no	—
276	C₂×D₄×C₆₇	—	2	2	no	—
277	C₂×D₄×C₆₇	—	2	4	no	—
278	C₂×D₄×C₆₇	—	2	4	no	—
279	C₂×D₄×C₆₇	—	2	2	no	—
280	C₂×D₄×C₆₇	—	2	4	no	—
281	C₂×D₄×C₆₇	—	2	4	no	—
282	C₂×D₄×C₆₇	—	2	4	no	—
283	C₂×D₄×C₆₇	—	2	1	no	—
284	C₂×D₄×C₆₇	—	2	2	no	—
285	C₂×D₄×C₆₇	—	2	2	no	—
286	C₂×D₄×C₆₇	—	2	2	no	—
287	C₂×D₄×C₆₇	—	2	2	no	—
288	C₂×D₄×C₆₇	—	2	1	no	—
289	C₂×D₄×C₆₇	—	2	2	no	—
290	C₂×D₄×C₆₇	—	2	2	no	—
291	C₂×D₄×C₆₇	—	2	4	no	—
292	C₂×D₄×C₆₇	—	4	2	no	—
293	C₂×D₄×C₆₇	—	4	2	no	—
294	C₂×D₄×C₆₇	—	4	8	no	—
295	C₂×D₄×C₆₇	—	4	4	no	—
296	C₂×D₄×C₆₇	—	4	8	no	—
297	C₂×D₄×C₆₇	—	4	4	no	—
298	C₂×D₄×C₆₇	—	8	2	no	—
299	C₂×D₄×C₆₇	—	8	4	no	—
300	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
301	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
302	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
303	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
304	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
305	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₆₇	—	2	1	no	—
307	C₂²×C₄×C₆₇	—	2	1	no	—
308	C₂²×C₄×C₆₇	—	2	4	no	—
309	C₂²×C₄×C₆₇	—	2	4	no	—
310	C₂²×C₄×C₆₇	—	2	1	no	—
311	C₂²×C₄×C₆₇	—	2	2	no	—
312	C₂²×C₄×C₆₇	—	2	1	no	—
313	C₂²×C₄×C₆₇	—	2	2	no	—
314	C₂²×C₄×C₆₇	—	2	2	no	—
315	C₂²×C₄×C₆₇	—	2	4	no	—
316	C₂²×C₄×C₆₇	—	2	4	no	—
317	C₂²×C₄×C₆₇	—	2	2	no	—
318	C₂²×C₄×C₆₇	—	2	1	no	—
319	C₂²×C₄×C₆₇	—	4	8	no	—
320	C₂²×C₄×C₆₇	—	4	8	no	—
321	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
322	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
323	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
324	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
325	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
326	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
327	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
328	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
329	Q₁₆×C₆₇	—	2	8	no	—
330	Q₁₆×C₆₇	C₂×D₄	1	8	yes	complemented
331	SD₁₆×C₆₇	—	2	8	no	—
332	SD₁₆×C₆₇	—	2	8	no	—
333	SD₁₆×C₆₇	—	2	8	no	—
334	SD₁₆×C₆₇	—	4	4	no	—
335	SD₁₆×C₆₇	C₂×D₄	1	8	yes	complemented
336	D₈×C₆₇	—	2	8	no	—
337	D₈×C₆₇	—	2	8	no	—
338	D₈×C₆₇	—	4	4	no	—
339	M₁₆×C₆₇	—	2	4	no	—
340	M₁₆×C₆₇	—	2	2	no	—
341	M₁₆×C₆₇	—	2	8	no	—
342	M₁₆×C₆₇	C₂×D₄	1	4	yes	complemented
343	C₂×C₈×C₆₇	—	2	8	no	—
344	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
345	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
346	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
347	C₄⋊C₄×C₆₇	—	2	1	no	—
348	C₄⋊C₄×C₆₇	—	2	2	no	—
349	C₄⋊C₄×C₆₇	—	2	2	no	—
350	C₄⋊C₄×C₆₇	—	2	2	no	—
351	C₄⋊C₄×C₆₇	—	2	1	no	—
352	C₄⋊C₄×C₆₇	—	2	1	no	—
353	C₄⋊C₄×C₆₇	—	2	1	no	—
354	C₄⋊C₄×C₆₇	—	2	1	no	—
355	C₄⋊C₄×C₆₇	—	2	2	no	—
356	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
357	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
358	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
359	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
360	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
361	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
362	C₂²⋊C₄×C₆₇	—	2	2	no	—
363	C₂²⋊C₄×C₆₇	—	2	1	no	—
364	C₂²⋊C₄×C₆₇	—	2	2	no	—
365	C₂²⋊C₄×C₆₇	—	2	4	no	—
366	C₂²⋊C₄×C₆₇	—	2	4	no	—
367	C₂²⋊C₄×C₆₇	—	2	2	no	—
368	C₂²⋊C₄×C₆₇	—	2	2	no	—
369	C₂²⋊C₄×C₆₇	—	2	1	no	—
370	C₂²⋊C₄×C₆₇	—	2	1	no	—
371	C₂²⋊C₄×C₆₇	—	2	2	no	—
372	C₂²⋊C₄×C₆₇	—	2	2	no	—
373	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
374	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
375	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
376	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
377	C₄²×C₆₇	—	2	1	no	—
378	C₄²×C₆₇	—	2	1	no	—
379	C₄²×C₆₇	—	2	1	no	—
380	C₄²×C₆₇	—	2	2	no	—
381	C₄²×C₆₇	—	2	2	no	—
382	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
383	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
384	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
385	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
386	C₂³×C₆₇	—	2	1	no	—
387	C₂³×C₆₇	—	2	4	no	—
388	C₂³×C₆₇	—	2	2	no	—
389	C₂³×C₆₇	—	2	4	no	—
390	C₂³×C₆₇	—	4	2	no	—
391	C₂³×C₆₇	—	4	2	no	—
392	C₂³×C₆₇	—	4	4	no	—
393	C₂³×C₆₇	—	4	4	no	—
394	C₂³×C₆₇	—	4	4	no	—
395	C₂³×C₆₇	—	4	4	no	—
396	C₂³×C₆₇	—	4	4	no	—
397	C₂³×C₆₇	—	8	2	no	—
398	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
399	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
400	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
401	Q₈×C₆₇	—	2	4	no	—
402	Q₈×C₆₇	—	2	2	no	—
403	Q₈×C₆₇	—	2	1	no	—
404	Q₈×C₆₇	—	2	2	no	—
405	Q₈×C₆₇	—	2	2	no	—
406	Q₈×C₆₇	—	4	4	no	—
407	Q₈×C₆₇	C₂²×D₄	1	2	yes	—
408	Q₈×C₆₇	C₂²×D₄	1	4	yes	—
409	D₄×C₆₇	—	2	4	no	—
410	D₄×C₆₇	—	2	2	no	—
411	D₄×C₆₇	—	2	2	no	—
412	D₄×C₆₇	—	2	4	no	—
413	D₄×C₆₇	—	2	2	no	—
414	D₄×C₆₇	—	2	1	no	—
415	D₄×C₆₇	—	2	2	no	—
416	D₄×C₆₇	—	2	4	no	—
417	D₄×C₆₇	—	4	2	no	—
418	D₄×C₆₇	—	4	4	no	—
419	D₄×C₆₇	—	4	4	no	—
420	D₄×C₆₇	—	4	8	no	—
421	D₄×C₆₇	—	4	8	no	—
422	D₄×C₆₇	—	4	4	no	—
423	D₄×C₆₇	—	4	4	no	—
424	D₄×C₆₇	—	4	4	no	—
425	D₄×C₆₇	—	4	4	no	—
426	D₄×C₆₇	—	4	4	no	—
427	D₄×C₆₇	—	4	2	no	—
428	D₄×C₆₇	—	4	4	no	—
429	D₄×C₆₇	—	8	1	no	—
430	D₄×C₆₇	—	8	2	no	—
431	D₄×C₆₇	—	8	2	no	—
432	D₄×C₆₇	—	8	2	no	—
433	D₄×C₆₇	—	8	4	no	—
434	D₄×C₆₇	—	8	4	no	—
435	D₄×C₆₇	C₂²×D₄	1	2	yes	—
436	C₂×C₄×C₆₇	—	2	4	no	—
437	C₂×C₄×C₆₇	—	2	4	no	—
438	C₂×C₄×C₆₇	—	2	2	no	—
439	C₂×C₄×C₆₇	—	2	1	no	—
440	C₂×C₄×C₆₇	—	2	4	no	—
441	C₂×C₄×C₆₇	—	2	4	no	—
442	C₂×C₄×C₆₇	—	2	4	no	—
443	C₂×C₄×C₆₇	—	2	2	no	—
444	C₂×C₄×C₆₇	—	2	2	no	—
445	C₂×C₄×C₆₇	—	2	2	no	—
446	C₂×C₄×C₆₇	—	2	2	no	—
447	C₂×C₄×C₆₇	—	2	2	no	—
448	C₂×C₄×C₆₇	—	2	1	no	—
449	C₂×C₄×C₆₇	—	2	1	no	—
450	C₂×C₄×C₆₇	—	2	2	no	—
451	C₂×C₄×C₆₇	—	2	2	no	—
452	C₂×C₄×C₆₇	—	4	1	no	—
453	C₂×C₄×C₆₇	—	4	4	no	—
454	C₂×C₄×C₆₇	—	4	8	no	—
455	C₂×C₄×C₆₇	—	4	8	no	—
456	C₂×C₄×C₆₇	—	4	4	no	—
457	C₂×C₄×C₆₇	—	4	4	no	—
458	C₂×C₄×C₆₇	—	4	2	no	—
459	C₂×C₄×C₆₇	—	4	4	no	—
460	C₂×C₄×C₆₇	—	4	2	no	—
461	C₂×C₄×C₆₇	—	8	1	no	—
462	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
466	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
467	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
469	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
470	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
471	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
472	C₈×C₆₇	—	2	4	no	—
473	C₈×C₆₇	—	2	2	no	—
474	C₈×C₆₇	C₂²×D₄	1	4	yes	—
475	C₂²×C₆₇	—	2	1	no	—
476	C₂²×C₆₇	—	2	1	no	—
477	C₂²×C₆₇	—	2	2	no	—
478	C₂²×C₆₇	—	2	2	no	—
479	C₂²×C₆₇	—	2	2	no	—
480	C₂²×C₆₇	—	2	2	no	—
481	C₂²×C₆₇	—	2	2	no	—
482	C₂²×C₆₇	—	2	2	no	—
483	C₂²×C₆₇	—	2	2	no	—
484	C₂²×C₆₇	—	4	1	no	—
485	C₂²×C₆₇	—	4	1	no	—
486	C₂²×C₆₇	—	4	4	no	—
487	C₂²×C₆₇	—	4	2	no	—
488	C₂²×C₆₇	—	4	4	no	—
489	C₂²×C₆₇	—	4	2	no	—
490	C₂²×C₆₇	—	4	4	no	—
491	C₂²×C₆₇	—	4	2	no	—
492	C₂²×C₆₇	—	8	4	no	—
493	C₂²×C₆₇	—	8	8	no	—
494	C₂²×C₆₇	—	8	8	no	—
495	C₂²×C₆₇	D₄²	1	2	yes	—
496	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
497	C₄×C₆₇	—	2	1	no	—
498	C₄×C₆₇	—	2	1	no	—
499	C₄×C₆₇	—	2	2	no	—
500	C₄×C₆₇	—	2	2	no	—
501	C₄×C₆₇	—	2	2	no	—
502	C₄×C₆₇	—	2	4	no	—
503	C₄×C₆₇	—	2	1	no	—
504	C₄×C₆₇	—	4	2	no	—
505	C₄×C₆₇	—	4	1	no	—
506	C₄×C₆₇	—	4	2	no	—
507	C₄×C₆₇	—	4	1	no	—
508	C₄×C₆₇	D₄²	1	2	yes	—
509	C₄×C₆₇	#575	1	2	yes	complemented
510	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
511	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
512	#61070	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
513	C₂×C₆₇	—	2	2	no	—
514	C₂×C₆₇	—	4	2	no	—
515	C₂×C₆₇	—	4	2	no	—
516	C₂×C₆₇	—	4	2	no	—
517	C₂×C₆₇	—	8	4	no	—
518	C₂×C₆₇	—	8	2	no	—
519	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
520	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
521	C₂×C₆₇	#3585	1	1	yes	characteristic
522	C₂×#575	C₂×C₆₇	1	2	yes	complemented
523	D₄×#41	C₂×C₆₇	1	1	yes	characteristic, complemented
524	C₂×#550	C₂×C₆₇	1	1	yes	characteristic, complemented
525	#3287	C₂×C₆₇	1	2	yes	complemented
526	#3284	C₂×C₆₇	1	2	yes	complemented
527	#3278	C₂×C₆₇	1	2	yes	complemented
528	#3274	C₂×C₆₇	1	2	yes	complemented
529	#3271	C₂×C₆₇	1	4	yes	complemented
530	#3268	C₂×C₆₇	1	4	yes	complemented
531	#3151	C₂×C₆₇	1	1	yes	characteristic, complemented
532	#3055	C₂×C₆₇	1	2	yes	complemented
533	#3038	C₂×C₆₇	1	1	yes	characteristic, complemented
534	#3037	C₂×C₆₇	1	1	yes	characteristic, complemented
535	#3006	C₂×C₆₇	1	2	yes	complemented
536	#3005	C₂×C₆₇	1	2	yes	complemented
537	C₄×#137	C₂×C₆₇	1	1	yes	characteristic, complemented
538	D₄×M₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
539	C₆₇	#61070	1	1	yes	characteristic, direct product factor, Sylow
540	C₂²×#41	C₂²×C₆₇	1	2	yes	—
541	C₂²×#41	C₂²×C₆₇	1	2	yes	complemented
542	#575	—	2	16	no	—
543	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
544	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
545	C₂×#137	C₂²×C₆₇	1	4	yes	complemented
546	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	—
547	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
548	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
549	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
550	C₂×#135	C₂²×C₆₇	1	4	yes	complemented
551	C₂×#135	C₂²×C₆₇	1	4	yes	complemented
552	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	complemented
553	#550	—	2	1	no	—
554	#550	—	2	1	no	—
555	#550	—	2	2	no	—
556	#550	C₂²×C₆₇	1	2	yes	—
557	#550	C₂²×C₆₇	1	4	yes	complemented
558	#550	C₂²×C₆₇	1	2	yes	complemented
559	#550	C₂²×C₆₇	1	1	yes	characteristic, complemented
560	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
561	#548	C₂²×C₆₇	1	2	yes	complemented
562	#547	—	2	1	no	—
563	#547	C₂²×C₆₇	1	1	yes	characteristic, complemented
564	#546	—	2	2	no	—
565	#546	C₂²×C₆₇	1	2	yes	complemented
566	D₄²	—	2	1	no	—
567	D₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
568	#532	—	2	1	no	—
569	#532	C₂²×C₆₇	1	1	yes	characteristic
570	C₂×#127	—	2	1	no	—
571	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic, complemented
572	#525	—	2	2	no	—
573	#525	C₂²×C₆₇	1	2	yes	—
574	C₂×#121	—	2	2	no	—
575	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
576	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
577	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
578	C₂×C₄×D₄	—	2	1	no	—
579	C₂×C₄×D₄	—	2	1	no	—
580	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
581	#496	C₂²×C₆₇	1	4	yes	complemented
582	#493	C₂²×C₆₇	1	2	yes	complemented
583	#492	C₂²×C₆₇	1	2	yes	complemented
584	#469	C₂²×C₆₇	1	4	yes	complemented
585	#468	C₂²×C₆₇	1	4	yes	complemented
586	#466	C₂²×C₆₇	1	4	yes	complemented
587	#465	C₂²×C₆₇	1	4	yes	complemented
588	#464	C₂²×C₆₇	1	4	yes	complemented
589	#462	C₂²×C₆₇	1	2	yes	complemented
590	#460	C₂²×C₆₇	1	2	yes	complemented
591	#460	C₂²×C₆₇	1	2	yes	complemented
592	#460	C₂²×C₆₇	1	2	yes	complemented
593	#459	C₂²×C₆₇	1	2	yes	complemented
594	#459	C₂²×C₆₇	1	2	yes	complemented
595	#452	C₂²×C₆₇	1	4	yes	complemented
596	#452	C₂²×C₆₇	1	4	yes	complemented
597	#449	C₂²×C₆₇	1	4	yes	complemented
598	#449	C₂²×C₆₇	1	4	yes	complemented
599	#449	C₂²×C₆₇	1	4	yes	complemented
600	#449	C₂²×C₆₇	1	4	yes	complemented
601	#448	C₂²×C₆₇	1	4	yes	complemented
602	#447	C₂²×C₆₇	1	4	yes	complemented
603	#441	C₂²×C₆₇	1	2	yes	complemented
604	#440	C₂²×C₆₇	1	2	yes	complemented
605	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
606	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
607	#436	C₂²×C₆₇	1	2	yes	complemented
608	#435	C₂²×C₆₇	1	4	yes	complemented
609	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
610	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
611	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
612	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
613	#418	C₂²×C₆₇	1	2	yes	complemented
614	#417	C₂²×C₆₇	1	1	yes	characteristic
615	#417	C₂²×C₆₇	1	2	yes	complemented
616	#407	C₂²×C₆₇	1	2	yes	complemented
617	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
618	C₂×#41	—	2	2	no	—
619	C₂×#41	—	2	2	no	—
620	C₂×#41	—	2	2	no	—
621	C₂×#41	—	2	2	no	—
622	C₂×#41	—	2	8	no	—
623	C₂×#41	—	2	8	no	—
624	C₂×#41	—	4	4	no	—
625	C₂×#41	—	4	4	no	—
626	C₂×#41	C₂³×C₆₇	1	2	yes	—
627	C₂×#41	C₂³×C₆₇	1	2	yes	—
628	C₂×#41	C₂³×C₆₇	1	2	yes	—
629	C₂×#41	C₂³×C₆₇	1	4	yes	—
630	C₂×#41	C₂³×C₆₇	1	4	yes	—
631	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
632	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
633	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
634	C₂²×D₄	—	2	2	no	—
635	C₂²×D₄	—	2	2	no	—
636	C₂²×D₄	—	2	2	no	—
637	C₂²×D₄	—	2	1	no	—
638	C₂²×D₄	—	2	1	no	—
639	C₂²×D₄	—	2	1	no	—
640	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
641	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
642	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
643	C₂³×C₄	—	2	2	no	—
644	C₂³×C₄	—	2	2	no	—
645	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
646	#137	—	2	8	no	—
647	#137	—	2	16	no	—
648	#137	D₄×C₆₇	1	8	yes	complemented
649	AGL(1,ℤ/8)	—	2	8	no	—
650	AGL(1,ℤ/8)	—	2	16	no	—
651	AGL(1,ℤ/8)	—	2	8	no	—
652	AGL(1,ℤ/8)	—	4	4	no	—
653	#135	—	2	16	no	—
654	#135	—	2	16	no	—
655	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
656	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
657	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
658	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
659	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
660	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
661	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
662	C₂×D₈	C₂³×C₆₇	1	4	yes	—
663	C₂×D₈	C₂³×C₆₇	1	4	yes	—
664	C₂×D₈	C₂³×C₆₇	1	4	yes	—
665	C₂×M₁₆	—	2	8	no	—
666	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
667	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
668	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
669	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
670	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
671	C₄⋊Q₈	—	2	1	no	—
672	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
673	#127	—	2	2	no	—
674	#127	—	2	2	no	—
675	#127	—	2	4	no	—
676	#127	—	2	1	no	—
677	#127	—	2	1	no	—
678	#127	—	2	1	no	—
679	#127	C₂³×C₆₇	1	2	yes	—
680	#127	C₂³×C₆₇	1	2	yes	—
681	#127	C₂³×C₆₇	1	1	yes	characteristic
682	#124	—	2	2	no	—
683	#124	C₂³×C₆₇	1	2	yes	—
684	#123	—	2	2	no	—
685	#123	—	2	2	no	—
686	#123	—	2	2	no	—
687	C₂²⋊Q₈	—	2	2	no	—
688	C₂²⋊Q₈	—	2	2	no	—
689	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
690	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
691	#121	—	2	2	no	—
692	#121	—	2	1	no	—
693	#121	—	2	2	no	—
694	#121	—	2	2	no	—
695	#121	—	2	1	no	—
696	#121	—	2	1	no	—
697	#121	—	2	1	no	—
698	#121	—	2	4	no	—
699	#121	—	2	4	no	—
700	#121	—	2	4	no	—
701	#121	—	2	4	no	—
702	#121	—	2	2	no	—
703	#121	—	2	2	no	—
704	#121	C₂³×C₆₇	1	4	yes	—
705	#121	C₂³×C₆₇	1	4	yes	—
706	#121	C₂³×C₆₇	1	2	yes	—
707	#121	C₂³×C₆₇	1	2	yes	—
708	#120	—	2	2	no	—
709	#120	—	2	2	no	—
710	#120	—	2	2	no	—
711	C₄×Q₈	—	2	1	no	—
712	C₄×Q₈	—	2	1	no	—
713	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
714	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
715	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
716	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
717	C₄×D₄	—	2	1	no	—
718	C₄×D₄	—	2	2	no	—
719	C₄×D₄	—	2	1	no	—
720	C₄×D₄	—	2	1	no	—
721	C₄×D₄	—	2	2	no	—
722	C₄×D₄	—	2	1	no	—
723	C₄×D₄	—	2	2	no	—
724	C₄×D₄	—	2	2	no	—
725	C₄×D₄	—	2	4	no	—
726	C₄×D₄	—	2	2	no	—
727	C₄×D₄	—	2	1	no	—
728	C₄×D₄	—	2	1	no	—
729	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
730	C₄×D₄	D₄×C₆₇	1	2	yes	—
731	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
732	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
733	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
734	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
735	C₄×D₄	C₂³×C₆₇	1	2	yes	—
736	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
737	#117	—	2	1	no	—
738	#117	C₂³×C₆₇	1	1	yes	characteristic
739	C₂×C₄⋊C₄	—	2	1	no	—
740	C₂×C₄⋊C₄	—	2	1	no	—
741	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
742	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
743	C₂×C₂²⋊C₄	—	2	2	no	—
744	C₂×C₂²⋊C₄	—	2	2	no	—
745	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
746	C₂×C₄²	—	2	1	no	—
747	C₂×C₄²	—	2	1	no	—
748	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
749	#107	C₂³×C₆₇	1	2	yes	—
750	#106	C₂³×C₆₇	1	2	yes	—
751	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
752	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
753	#103	C₂³×C₆₇	1	2	yes	—
754	#103	C₂³×C₆₇	1	4	yes	—
755	#103	C₂³×C₆₇	1	2	yes	—
756	#103	C₂³×C₆₇	1	2	yes	—
757	#102	C₂³×C₆₇	1	2	yes	—
758	#102	C₂³×C₆₇	1	4	yes	—
759	#102	C₂³×C₆₇	1	4	yes	—
760	#102	C₂³×C₆₇	1	4	yes	—
761	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
762	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
763	#97	C₂³×C₆₇	1	2	yes	—
764	C₄×C₈	C₂³×C₆₇	1	2	yes	—
765	C₂⁴	—	2	2	no	—
766	C₂⁴	—	2	2	no	—
767	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
768	#41	—	2	2	no	—
769	#41	—	2	4	no	—
770	#41	—	2	8	no	—
771	#41	—	2	8	no	—
772	#41	—	2	4	no	—
773	#41	—	2	4	no	—
774	#41	—	2	4	no	—
775	#41	—	4	8	no	—
776	#41	—	4	4	no	—
777	#41	—	4	2	no	—
778	#41	—	4	4	no	—
779	#41	—	4	2	no	—
780	#41	—	4	8	no	—
781	#41	—	4	8	no	—
782	#41	—	4	8	no	—
783	#41	C₂×D₄×C₆₇	1	4	yes	—
784	C₂×Q₈	—	2	1	no	—
785	C₂×Q₈	—	2	2	no	—
786	C₂×Q₈	—	2	2	no	—
787	C₂×Q₈	—	2	4	no	—
788	C₂×Q₈	—	4	2	no	—
789	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	complemented
790	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
791	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
792	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
793	C₂×D₄	—	2	1	no	—
794	C₂×D₄	—	2	4	no	—
795	C₂×D₄	—	2	2	no	—
796	C₂×D₄	—	2	2	no	—
797	C₂×D₄	—	2	2	no	—
798	C₂×D₄	—	2	2	no	—
799	C₂×D₄	—	2	4	no	—
800	C₂×D₄	—	2	4	no	—
801	C₂×D₄	—	2	2	no	—
802	C₂×D₄	—	2	4	no	—
803	C₂×D₄	—	2	4	no	—
804	C₂×D₄	—	2	4	no	—
805	C₂×D₄	—	2	1	no	—
806	C₂×D₄	—	2	2	no	—
807	C₂×D₄	—	2	2	no	—
808	C₂×D₄	—	2	2	no	—
809	C₂×D₄	—	2	2	no	—
810	C₂×D₄	—	2	1	no	—
811	C₂×D₄	—	2	2	no	—
812	C₂×D₄	—	2	2	no	—
813	C₂×D₄	—	2	4	no	—
814	C₂×D₄	—	4	2	no	—
815	C₂×D₄	—	4	2	no	—
816	C₂×D₄	—	4	8	no	—
817	C₂×D₄	—	4	4	no	—
818	C₂×D₄	—	4	8	no	—
819	C₂×D₄	—	4	4	no	—
820	C₂×D₄	—	8	2	no	—
821	C₂×D₄	—	8	4	no	—
822	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
823	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
824	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
825	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
826	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
827	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
828	C₂²×C₄	—	2	1	no	—
829	C₂²×C₄	—	2	1	no	—
830	C₂²×C₄	—	2	4	no	—
831	C₂²×C₄	—	2	4	no	—
832	C₂²×C₄	—	2	1	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	1	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	4	no	—
838	C₂²×C₄	—	2	4	no	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	—	2	1	no	—
841	C₂²×C₄	—	4	8	no	—
842	C₂²×C₄	—	4	8	no	—
843	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
844	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
845	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
846	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
847	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
848	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
849	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
850	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
851	Q₁₆	—	2	8	no	—
852	Q₁₆	C₂×D₄×C₆₇	1	8	yes	complemented
853	SD₁₆	—	2	8	no	—
854	SD₁₆	—	2	8	no	—
855	SD₁₆	—	2	8	no	—
856	SD₁₆	—	4	4	no	—
857	SD₁₆	C₂×D₄×C₆₇	1	8	yes	complemented
858	D₈	—	2	8	no	—
859	D₈	—	2	8	no	—
860	D₈	—	4	4	no	—
861	M₁₆	—	2	4	no	—
862	M₁₆	—	2	2	no	—
863	M₁₆	—	2	8	no	—
864	M₁₆	C₂×D₄×C₆₇	1	4	yes	complemented
865	C₂×C₈	—	2	8	no	—
866	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
867	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
868	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
869	C₄⋊C₄	—	2	1	no	—
870	C₄⋊C₄	—	2	2	no	—
871	C₄⋊C₄	—	2	2	no	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	2	1	no	—
874	C₄⋊C₄	—	2	1	no	—
875	C₄⋊C₄	—	2	1	no	—
876	C₄⋊C₄	—	2	1	no	—
877	C₄⋊C₄	—	2	2	no	—
878	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
879	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
880	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
881	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
882	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
883	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	1	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	4	no	—
888	C₂²⋊C₄	—	2	4	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	1	no	—
892	C₂²⋊C₄	—	2	1	no	—
893	C₂²⋊C₄	—	2	2	no	—
894	C₂²⋊C₄	—	2	2	no	—
895	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
896	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
897	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
898	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
899	C₄²	—	2	1	no	—
900	C₄²	—	2	1	no	—
901	C₄²	—	2	1	no	—
902	C₄²	—	2	2	no	—
903	C₄²	—	2	2	no	—
904	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
905	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
906	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
907	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
908	C₂³	—	2	1	no	—
909	C₂³	—	2	4	no	—
910	C₂³	—	2	2	no	—
911	C₂³	—	2	4	no	—
912	C₂³	—	4	2	no	—
913	C₂³	—	4	2	no	—
914	C₂³	—	4	4	no	—
915	C₂³	—	4	4	no	—
916	C₂³	—	4	4	no	—
917	C₂³	—	4	4	no	—
918	C₂³	—	4	4	no	—
919	C₂³	—	8	2	no	—
920	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
921	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
922	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
923	Q₈	—	2	4	no	—
924	Q₈	—	2	2	no	—
925	Q₈	—	2	1	no	—
926	Q₈	—	2	2	no	—
927	Q₈	—	2	2	no	—
928	Q₈	—	4	4	no	—
929	Q₈	C₂²×D₄×C₆₇	1	2	yes	—
930	Q₈	C₂²×D₄×C₆₇	1	4	yes	—
931	D₄	—	2	4	no	—
932	D₄	—	2	2	no	—
933	D₄	—	2	2	no	—
934	D₄	—	2	4	no	—
935	D₄	—	2	2	no	—
936	D₄	—	2	1	no	—
937	D₄	—	2	2	no	—
938	D₄	—	2	4	no	—
939	D₄	—	4	2	no	—
940	D₄	—	4	4	no	—
941	D₄	—	4	4	no	—
942	D₄	—	4	8	no	—
943	D₄	—	4	8	no	—
944	D₄	—	4	4	no	—
945	D₄	—	4	4	no	—
946	D₄	—	4	4	no	—
947	D₄	—	4	4	no	—
948	D₄	—	4	4	no	—
949	D₄	—	4	2	no	—
950	D₄	—	4	4	no	—
951	D₄	—	8	2	no	—
952	D₄	—	8	2	no	—
953	D₄	—	8	1	no	—
954	D₄	—	8	4	no	—
955	D₄	—	8	4	no	—
956	D₄	—	8	2	no	—
957	D₄	C₂²×D₄×C₆₇	1	2	yes	—
958	C₂×C₄	—	2	4	no	—
959	C₂×C₄	—	2	4	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	4	no	—
963	C₂×C₄	—	2	4	no	—
964	C₂×C₄	—	2	4	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	4	1	no	—
975	C₂×C₄	—	4	4	no	—
976	C₂×C₄	—	4	8	no	—
977	C₂×C₄	—	4	8	no	—
978	C₂×C₄	—	4	4	no	—
979	C₂×C₄	—	4	4	no	—
980	C₂×C₄	—	4	2	no	—
981	C₂×C₄	—	4	4	no	—
982	C₂×C₄	—	4	2	no	—
983	C₂×C₄	—	8	1	no	—
984	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
985	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
986	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
987	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
988	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
989	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
990	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
991	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
992	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
993	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
994	C₈	—	2	4	no	—
995	C₈	—	2	2	no	—
996	C₈	C₂²×D₄×C₆₇	1	4	yes	—
997	C₂²	—	2	1	no	—
998	C₂²	—	2	1	no	—
999	C₂²	—	2	2	no	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	2	2	no	—
1002	C₂²	—	2	2	no	—
1003	C₂²	—	2	2	no	—
1004	C₂²	—	2	2	no	—
1005	C₂²	—	2	2	no	—
1006	C₂²	—	4	1	no	—
1007	C₂²	—	4	1	no	—
1008	C₂²	—	4	4	no	—
1009	C₂²	—	4	2	no	—
1010	C₂²	—	4	4	no	—
1011	C₂²	—	4	2	no	—
1012	C₂²	—	4	4	no	—
1013	C₂²	—	4	2	no	—
1014	C₂²	—	8	4	no	—
1015	C₂²	—	8	8	no	—
1016	C₂²	—	8	8	no	—
1017	C₂²	D₄²×C₆₇	1	2	yes	—
1018	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1019	C₄	—	2	1	no	—
1020	C₄	—	2	1	no	—
1021	C₄	—	2	1	no	—
1022	C₄	—	2	2	no	—
1023	C₄	—	2	2	no	—
1024	C₄	—	2	2	no	—
1025	C₄	—	2	4	no	—
1026	C₄	—	4	1	no	—
1027	C₄	—	4	2	no	—
1028	C₄	—	4	1	no	—
1029	C₄	—	4	2	no	—
1030	C₄	D₄²×C₆₇	1	2	yes	—
1031	C₄	#575×C₆₇	1	2	yes	complemented
1032	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
1033	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1034	C₂	—	2	2	no	—
1035	C₂	—	4	2	no	—
1036	C₂	—	4	2	no	—
1037	C₂	—	4	2	no	—
1038	C₂	—	8	4	no	—
1039	C₂	—	8	2	no	—
1040	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
1041	C₂	C₂×#575×C₆₇	1	1	yes	characteristic
1042	C₂	C₆₇×#3585	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 ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#575×C₆₇	C₂	semidirect
2. D₄×#41×C₆₇	C₂	semidirect
3. C₂×#550×C₆₇	C₂	semidirect
4. C₆₇×#3287	C₂	semidirect
5. C₆₇×#3284	C₂	semidirect
6. C₆₇×#3278	C₂	semidirect
7. C₆₇×#3274	C₂	semidirect
8. C₆₇×#3271	C₂	semidirect
9. C₆₇×#3268	C₂	semidirect
10. C₆₇×#3151	C₂	semidirect
11. C₆₇×#3055	C₂	semidirect
12. C₆₇×#3038	C₂	semidirect
13. C₆₇×#3037	C₂	semidirect
14. C₆₇×#3006	C₂	semidirect
15. C₆₇×#3005	C₂	semidirect
16. C₄×#137×C₆₇	C₂	semidirect
17. D₄×M₁₆×C₆₇	C₂	semidirect
19. C₂²×#41×C₆₇	C₂²	semidirect
22. C₂×#137×C₆₇	C₂²	semidirect
23. C₂×#137×C₆₇	C₂²	semidirect
25. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
26. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
27. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
28. C₂×#135×C₆₇	C₂²	semidirect
29. C₂×#135×C₆₇	C₂²	semidirect
30. C₂²×M₁₆×C₆₇	C₂²	semidirect
35. #550×C₆₇	C₂²	semidirect
36. #550×C₆₇	C₂²	semidirect
37. #550×C₆₇	C₂²	semidirect
38. D₄×Q₈×C₆₇	C₂²	semidirect
39. #548×C₆₇	C₂²	semidirect
41. #547×C₆₇	C₂²	semidirect
43. #546×C₆₇	C₂²	semidirect
45. D₄²×C₆₇	C₂²	semidirect
49. C₂×#127×C₆₇	C₂²	semidirect
53. C₂×#121×C₆₇	C₂²	semidirect
55. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
59. #496×C₆₇	C₂²	semidirect
60. #493×C₆₇	C₂²	semidirect
61. #492×C₆₇	C₂²	semidirect
62. #469×C₆₇	C₂²	semidirect
63. #468×C₆₇	C₂²	semidirect
64. #466×C₆₇	C₂²	semidirect
65. #465×C₆₇	C₂²	semidirect
66. #464×C₆₇	C₂²	semidirect
67. #462×C₆₇	C₂²	semidirect
68. #460×C₆₇	C₂²	semidirect
69. #460×C₆₇	C₂²	semidirect
70. #460×C₆₇	C₂²	semidirect
71. #459×C₆₇	C₂²	semidirect
72. #459×C₆₇	C₂²	semidirect
73. #452×C₆₇	C₂²	semidirect
74. #452×C₆₇	C₂²	semidirect
75. #449×C₆₇	C₂²	semidirect
76. #449×C₆₇	C₂²	semidirect
77. #449×C₆₇	C₂²	semidirect
78. #449×C₆₇	C₂²	semidirect
79. #448×C₆₇	C₂²	semidirect
80. #447×C₆₇	C₂²	semidirect
81. #441×C₆₇	C₂²	semidirect
82. #440×C₆₇	C₂²	semidirect
83. C₄×Q₁₆×C₆₇	C₂²	semidirect
84. C₄×SD₁₆×C₆₇	C₂²	semidirect
85. #436×C₆₇	C₂²	semidirect
86. #435×C₆₇	C₂²	semidirect
87. C₈×D₄×C₆₇	C₂²	semidirect
88. #428×C₆₇	C₂²	semidirect
89. #423×C₆₇	C₂²	semidirect
90. #419×C₆₇	C₂²	semidirect
91. #418×C₆₇	C₂²	semidirect
93. #417×C₆₇	C₂²	semidirect
94. #407×C₆₇	C₂²	semidirect
95. C₄×M₁₆×C₆₇	C₂²	semidirect
126. #137×C₆₇	D₄	semidirect
267. C₂×Q₈×C₆₇	C₂×D₄	semidirect
330. Q₁₆×C₆₇	C₂×D₄	semidirect
335. SD₁₆×C₆₇	C₂×D₄	semidirect
342. M₁₆×C₆₇	C₂×D₄	semidirect
509. C₄×C₆₇	#575	semidirect
512. #61070	C₆₇	direct (N × H)
522. C₂×#575	C₂×C₆₇	semidirect
523. D₄×#41	C₂×C₆₇	semidirect
524. C₂×#550	C₂×C₆₇	semidirect
525. #3287	C₂×C₆₇	semidirect
526. #3284	C₂×C₆₇	semidirect
527. #3278	C₂×C₆₇	semidirect
528. #3274	C₂×C₆₇	semidirect
529. #3271	C₂×C₆₇	semidirect
530. #3268	C₂×C₆₇	semidirect
531. #3151	C₂×C₆₇	semidirect
532. #3055	C₂×C₆₇	semidirect
533. #3038	C₂×C₆₇	semidirect
534. #3037	C₂×C₆₇	semidirect
535. #3006	C₂×C₆₇	semidirect
536. #3005	C₂×C₆₇	semidirect
537. C₄×#137	C₂×C₆₇	semidirect
538. D₄×M₁₆	C₂×C₆₇	semidirect
539. C₆₇	#61070	direct (N × H)
541. C₂²×#41	C₂²×C₆₇	semidirect
544. C₂×#137	C₂²×C₆₇	semidirect
545. C₂×#137	C₂²×C₆₇	semidirect
547. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
548. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
549. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
550. C₂×#135	C₂²×C₆₇	semidirect
551. C₂×#135	C₂²×C₆₇	semidirect
552. C₂²×M₁₆	C₂²×C₆₇	semidirect
557. #550	C₂²×C₆₇	semidirect
558. #550	C₂²×C₆₇	semidirect
559. #550	C₂²×C₆₇	semidirect
560. D₄×Q₈	C₂²×C₆₇	semidirect
561. #548	C₂²×C₆₇	semidirect
563. #547	C₂²×C₆₇	semidirect
565. #546	C₂²×C₆₇	semidirect
567. D₄²	C₂²×C₆₇	semidirect
571. C₂×#127	C₂²×C₆₇	semidirect
575. C₂×#121	C₂²×C₆₇	semidirect
577. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
581. #496	C₂²×C₆₇	semidirect
582. #493	C₂²×C₆₇	semidirect
583. #492	C₂²×C₆₇	semidirect
584. #469	C₂²×C₆₇	semidirect
585. #468	C₂²×C₆₇	semidirect
586. #466	C₂²×C₆₇	semidirect
587. #465	C₂²×C₆₇	semidirect
588. #464	C₂²×C₆₇	semidirect
589. #462	C₂²×C₆₇	semidirect
590. #460	C₂²×C₆₇	semidirect
591. #460	C₂²×C₆₇	semidirect
592. #460	C₂²×C₆₇	semidirect
593. #459	C₂²×C₆₇	semidirect
594. #459	C₂²×C₆₇	semidirect
595. #452	C₂²×C₆₇	semidirect
596. #452	C₂²×C₆₇	semidirect
597. #449	C₂²×C₆₇	semidirect
598. #449	C₂²×C₆₇	semidirect
599. #449	C₂²×C₆₇	semidirect
600. #449	C₂²×C₆₇	semidirect
601. #448	C₂²×C₆₇	semidirect
602. #447	C₂²×C₆₇	semidirect
603. #441	C₂²×C₆₇	semidirect
604. #440	C₂²×C₆₇	semidirect
605. C₄×Q₁₆	C₂²×C₆₇	semidirect
606. C₄×SD₁₆	C₂²×C₆₇	semidirect
607. #436	C₂²×C₆₇	semidirect
608. #435	C₂²×C₆₇	semidirect
609. C₈×D₄	C₂²×C₆₇	semidirect
610. #428	C₂²×C₆₇	semidirect
611. #423	C₂²×C₆₇	semidirect
612. #419	C₂²×C₆₇	semidirect
613. #418	C₂²×C₆₇	semidirect
615. #417	C₂²×C₆₇	semidirect
616. #407	C₂²×C₆₇	semidirect
617. C₄×M₁₆	C₂²×C₆₇	semidirect
648. #137	D₄×C₆₇	semidirect
789. C₂×Q₈	C₂×D₄×C₆₇	semidirect
852. Q₁₆	C₂×D₄×C₆₇	semidirect
857. SD₁₆	C₂×D₄×C₆₇	semidirect
864. M₁₆	C₂×D₄×C₆₇	semidirect
1031. C₄	#575×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#575×C₆₇	2
D₄×#41×C₆₇	2
C₂×#550×C₆₇	2
C₆₇×#3287	2
C₆₇×#3284	2
C₆₇×#3278	2
C₆₇×#3274	2
C₆₇×#3271	2
C₆₇×#3268	2
C₆₇×#3151	2
C₆₇×#3055	2
C₆₇×#3038	2
C₆₇×#3037	2
C₆₇×#3006	2
C₆₇×#3005	2
C₄×#137×C₆₇	2
D₄×M₁₆×C₆₇	2
#61070	67

Subgroups — C67×#61070 #30740321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61070 #30740321