Subgroups — C₆₇×#61670 #30740921

Order 17152.

2102 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3496	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3319	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3315	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3314	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3310	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3269	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3267	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3266	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3265	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3219	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3216	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3203	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3201	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3114	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3110	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3012	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3009	C₂	1	2	yes	maximal, complemented
19	C₆₇×#2980	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	2	yes	—
21	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
22	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
23	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
24	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
25	#562×C₆₇	—	2	2	no	—
26	#555×C₆₇	—	2	1	no	—
27	#555×C₆₇	C₂²	1	1	yes	characteristic, complemented
28	#554×C₆₇	C₂²	1	1	yes	characteristic, complemented
29	#553×C₆₇	—	2	1	no	—
30	#552×C₆₇	C₂²	1	2	yes	complemented
31	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
32	#548×C₆₇	C₂²	1	2	yes	complemented
33	#547×C₆₇	—	2	1	no	—
34	#547×C₆₇	C₂²	1	2	yes	—
35	#547×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	#546×C₆₇	—	2	2	no	—
37	#546×C₆₇	C₂²	1	2	yes	—
38	#546×C₆₇	C₂²	1	2	yes	—
39	D₄²×C₆₇	—	2	1	no	—
40	D₄²×C₆₇	C₂²	1	2	yes	—
41	#544×C₆₇	—	2	1	no	—
42	#542×C₆₇	—	2	2	no	—
43	#540×C₆₇	—	2	1	no	—
44	#537×C₆₇	C₂²	1	2	yes	—
45	#537×C₆₇	C₂²	1	2	yes	complemented
46	#536×C₆₇	C₂²	1	2	yes	complemented
47	#534×C₆₇	—	2	1	no	—
48	#534×C₆₇	—	2	1	no	—
49	#533×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	#532×C₆₇	C₂²	1	1	yes	characteristic
51	#532×C₆₇	C₂²	1	1	yes	characteristic
52	#529×C₆₇	C₂²	1	1	yes	characteristic, complemented
53	C₂×#121×C₆₇	—	2	2	no	—
54	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
55	#497×C₆₇	C₂²	1	2	yes	complemented
56	#497×C₆₇	C₂²	1	1	yes	characteristic, complemented
57	#496×C₆₇	C₂²	1	1	yes	characteristic, complemented
58	#491×C₆₇	C₂²	1	1	yes	characteristic, complemented
59	#490×C₆₇	C₂²	1	1	yes	characteristic, complemented
60	#489×C₆₇	C₂²	1	2	yes	complemented
61	#485×C₆₇	C₂²	1	2	yes	complemented
62	#484×C₆₇	C₂²	1	2	yes	complemented
63	#484×C₆₇	C₂²	1	2	yes	complemented
64	#483×C₆₇	C₂²	1	1	yes	characteristic, complemented
65	#482×C₆₇	C₂²	1	2	yes	complemented
66	#480×C₆₇	C₂²	1	2	yes	complemented
67	#480×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	#478×C₆₇	C₂²	1	2	yes	complemented
69	#474×C₆₇	C₂²	1	2	yes	complemented
70	#470×C₆₇	C₂²	1	2	yes	complemented
71	#468×C₆₇	C₂²	1	2	yes	complemented
72	#468×C₆₇	C₂²	1	2	yes	complemented
73	#468×C₆₇	C₂²	1	2	yes	complemented
74	#467×C₆₇	C₂²	1	2	yes	complemented
75	#467×C₆₇	C₂²	1	2	yes	complemented
76	#466×C₆₇	C₂²	1	2	yes	complemented
77	#465×C₆₇	C₂²	1	2	yes	complemented
78	#464×C₆₇	C₂²	1	2	yes	complemented
79	#463×C₆₇	C₂²	1	2	yes	complemented
80	#463×C₆₇	C₂²	1	2	yes	complemented
81	#462×C₆₇	C₂²	1	2	yes	complemented
82	#461×C₆₇	C₂²	1	2	yes	complemented
83	#460×C₆₇	C₂²	1	2	yes	complemented
84	#452×C₆₇	C₂²	1	2	yes	complemented
85	#452×C₆₇	C₂²	1	2	yes	complemented
86	#452×C₆₇	C₂²	1	2	yes	complemented
87	#452×C₆₇	C₂²	1	2	yes	complemented
88	#452×C₆₇	C₂²	1	2	yes	complemented
89	#452×C₆₇	C₂²	1	2	yes	complemented
90	#452×C₆₇	C₂²	1	2	yes	complemented
91	#451×C₆₇	C₂²	1	2	yes	complemented
92	#450×C₆₇	C₂²	1	1	yes	characteristic
93	#450×C₆₇	C₂²	1	2	yes	—
94	#450×C₆₇	C₂²	1	2	yes	complemented
95	#450×C₆₇	C₂²	1	2	yes	complemented
96	#450×C₆₇	C₂²	1	2	yes	complemented
97	#449×C₆₇	C₂²	1	2	yes	complemented
98	#449×C₆₇	C₂²	1	2	yes	complemented
99	#449×C₆₇	C₂²	1	2	yes	complemented
100	#448×C₆₇	C₂²	1	2	yes	complemented
101	#447×C₆₇	C₂²	1	1	yes	characteristic
102	#447×C₆₇	C₂²	1	2	yes	complemented
103	#442×C₆₇	C₂²	1	2	yes	complemented
104	#440×C₆₇	C₂²	1	2	yes	complemented
105	#440×C₆₇	C₂²	1	2	yes	complemented
106	#440×C₆₇	C₂²	1	2	yes	complemented
107	#435×C₆₇	C₂²	1	2	yes	complemented
108	#435×C₆₇	C₂²	1	2	yes	complemented
109	#435×C₆₇	C₂²	1	2	yes	complemented
110	#435×C₆₇	C₂²	1	2	yes	complemented
111	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
112	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	#418×C₆₇	C₂²	1	2	yes	complemented
114	#417×C₆₇	C₂²	1	2	yes	complemented
115	#416×C₆₇	C₂²	1	2	yes	complemented
116	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
117	#408×C₆₇	C₂²	1	2	yes	complemented
118	#408×C₆₇	C₂²	1	2	yes	complemented
119	H(5,𝔽₂)×C₆₇	—	4	4	no	—
120	H(5,𝔽₂)×C₆₇	—	4	4	no	—
121	C₂×#41×C₆₇	—	2	2	no	—
122	C₂×#41×C₆₇	C₂³	1	2	yes	—
123	C₂×#41×C₆₇	C₂³	1	2	yes	—
124	C₂×#41×C₆₇	C₂³	1	2	yes	—
125	C₂×#41×C₆₇	C₂³	1	2	yes	—
126	C₂×#41×C₆₇	C₂³	1	2	yes	—
127	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
128	C₂²×D₄×C₆₇	—	2	2	no	—
129	C₂²×D₄×C₆₇	—	2	2	no	—
130	C₂²×D₄×C₆₇	—	2	2	no	—
131	C₂²×D₄×C₆₇	—	2	2	no	—
132	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
134	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
135	C₂³×C₄×C₆₇	—	2	1	no	—
136	#137×C₆₇	—	4	4	no	—
137	AGL(1,ℤ/8)×C₆₇	—	4	4	no	—
138	#135×C₆₇	—	4	4	no	—
139	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
140	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
141	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
142	C₂×SD₁₆×C₆₇	—	4	4	no	—
143	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
150	C₂×D₈×C₆₇	C₂³	1	2	yes	—
151	C₂×D₈×C₆₇	C₂³	1	2	yes	—
152	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
153	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
154	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
155	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
156	C₄⋊Q₈×C₆₇	—	2	2	no	—
157	C₄⋊Q₈×C₆₇	—	2	1	no	—
158	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
159	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
162	#127×C₆₇	D₄	1	1	yes	characteristic
163	#127×C₆₇	C₂³	1	1	yes	characteristic
164	#126×C₆₇	—	2	2	no	—
165	#126×C₆₇	—	2	1	no	—
166	#125×C₆₇	—	2	2	no	—
167	#125×C₆₇	—	2	1	no	—
168	#125×C₆₇	—	2	1	no	—
169	#125×C₆₇	C₂³	1	1	yes	characteristic
170	#124×C₆₇	—	2	2	no	—
171	#124×C₆₇	—	2	2	no	—
172	#124×C₆₇	—	2	2	no	—
173	#124×C₆₇	D₄	1	2	yes	—
174	#124×C₆₇	C₂³	1	1	yes	characteristic
175	#124×C₆₇	C₂³	1	2	yes	—
176	#123×C₆₇	—	2	2	no	—
177	#123×C₆₇	—	2	2	no	—
178	#123×C₆₇	—	2	2	no	—
179	#123×C₆₇	—	2	1	no	—
180	#123×C₆₇	—	2	2	no	—
181	#123×C₆₇	—	2	2	no	—
182	#123×C₆₇	—	2	2	no	—
183	#123×C₆₇	—	2	2	no	—
184	#123×C₆₇	—	2	2	no	—
185	C₂²⋊Q₈×C₆₇	—	2	2	no	—
186	C₂²⋊Q₈×C₆₇	—	2	2	no	—
187	C₂²⋊Q₈×C₆₇	—	2	1	no	—
188	C₂²⋊Q₈×C₆₇	—	2	2	no	—
189	C₂²⋊Q₈×C₆₇	—	2	2	no	—
190	C₂²⋊Q₈×C₆₇	—	2	2	no	—
191	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
192	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
193	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
194	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
195	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
196	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
197	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
198	#121×C₆₇	—	2	2	no	—
199	#121×C₆₇	—	2	2	no	—
200	#121×C₆₇	—	2	2	no	—
201	#121×C₆₇	—	2	2	no	—
202	#121×C₆₇	—	2	2	no	—
203	#121×C₆₇	—	2	2	no	—
204	#121×C₆₇	—	2	2	no	—
205	#121×C₆₇	—	2	1	no	—
206	#121×C₆₇	—	2	2	no	—
207	#121×C₆₇	—	2	1	no	—
208	#121×C₆₇	—	2	1	no	—
209	#121×C₆₇	—	2	1	no	—
210	#121×C₆₇	—	2	2	no	—
211	#121×C₆₇	—	2	2	no	—
212	#121×C₆₇	—	2	2	no	—
213	#121×C₆₇	D₄	1	2	yes	—
214	#121×C₆₇	D₄	1	1	yes	characteristic
215	#121×C₆₇	D₄	1	1	yes	characteristic
216	#121×C₆₇	C₂³	1	2	yes	—
217	#121×C₆₇	C₂³	1	1	yes	characteristic
218	#121×C₆₇	C₂³	1	2	yes	—
219	#121×C₆₇	C₂³	1	2	yes	—
220	#120×C₆₇	—	2	2	no	—
221	#120×C₆₇	—	2	2	no	—
222	#120×C₆₇	—	2	2	no	—
223	#120×C₆₇	—	2	2	no	—
224	C₄×Q₈×C₆₇	—	2	1	no	—
225	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
226	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
227	C₄×D₄×C₆₇	—	2	1	no	—
228	C₄×D₄×C₆₇	—	2	1	no	—
229	C₄×D₄×C₆₇	—	2	1	no	—
230	C₄×D₄×C₆₇	—	2	2	no	—
231	C₄×D₄×C₆₇	—	2	1	no	—
232	C₄×D₄×C₆₇	—	2	1	no	—
233	C₄×D₄×C₆₇	—	2	1	no	—
234	C₄×D₄×C₆₇	—	2	1	no	—
235	C₄×D₄×C₆₇	C₂³	1	2	yes	—
236	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₆₇	C₂³	1	2	yes	—
238	C₄×D₄×C₆₇	C₂³	1	2	yes	—
239	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
241	#117×C₆₇	—	2	1	no	—
242	#117×C₆₇	—	2	1	no	—
243	#117×C₆₇	—	2	2	no	—
244	#117×C₆₇	—	2	1	no	—
245	#117×C₆₇	C₂³	1	2	yes	—
246	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
247	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
248	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
249	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
250	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
251	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
252	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
253	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
254	#107×C₆₇	C₂³	1	2	yes	—
255	#107×C₆₇	C₂³	1	2	yes	—
256	#107×C₆₇	C₂³	1	2	yes	—
257	#106×C₆₇	C₂³	1	2	yes	—
258	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
259	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
260	#103×C₆₇	C₂³	1	2	yes	—
261	#103×C₆₇	C₂³	1	2	yes	—
262	#103×C₆₇	C₂³	1	2	yes	—
263	#103×C₆₇	C₂³	1	2	yes	—
264	#103×C₆₇	C₂³	1	2	yes	—
265	#103×C₆₇	C₂³	1	2	yes	—
266	#103×C₆₇	C₂³	1	2	yes	—
267	#102×C₆₇	C₂³	1	2	yes	—
268	#102×C₆₇	C₂³	1	2	yes	—
269	#102×C₆₇	C₂³	1	2	yes	—
270	#102×C₆₇	C₂³	1	2	yes	—
271	#102×C₆₇	C₂³	1	2	yes	—
272	#102×C₆₇	C₂³	1	2	yes	—
273	#102×C₆₇	C₂³	1	2	yes	—
274	#102×C₆₇	C₂³	1	2	yes	—
275	#102×C₆₇	C₂³	1	2	yes	—
276	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
277	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
278	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
279	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
280	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
281	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
282	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
283	#97×C₆₇	C₂³	1	2	yes	—
284	#97×C₆₇	C₂³	1	1	yes	characteristic
285	#97×C₆₇	C₂³	1	1	yes	characteristic
286	C₂⁴×C₆₇	—	2	1	no	—
287	C₂⁴×C₆₇	—	2	2	no	—
288	C₂⁴×C₆₇	—	2	2	no	—
289	#41×C₆₇	—	2	4	no	—
290	#41×C₆₇	—	2	4	no	—
291	#41×C₆₇	—	4	2	no	—
292	#41×C₆₇	—	4	2	no	—
293	#41×C₆₇	—	4	2	no	—
294	#41×C₆₇	—	4	2	no	—
295	#41×C₆₇	—	4	2	no	—
296	#41×C₆₇	—	4	2	no	—
297	#41×C₆₇	—	4	2	no	—
298	#41×C₆₇	—	4	2	no	—
299	#41×C₆₇	—	4	8	no	—
300	C₂×Q₈×C₆₇	—	2	1	no	—
301	C₂×Q₈×C₆₇	—	2	2	no	—
302	C₂×Q₈×C₆₇	—	4	2	no	—
303	C₂×Q₈×C₆₇	—	4	2	no	—
304	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
305	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
306	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
307	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
308	C₂×D₄×C₆₇	—	2	4	no	—
309	C₂×D₄×C₆₇	—	2	4	no	—
310	C₂×D₄×C₆₇	—	2	4	no	—
311	C₂×D₄×C₆₇	—	2	2	no	—
312	C₂×D₄×C₆₇	—	2	2	no	—
313	C₂×D₄×C₆₇	—	2	2	no	—
314	C₂×D₄×C₆₇	—	2	1	no	—
315	C₂×D₄×C₆₇	—	2	2	no	—
316	C₂×D₄×C₆₇	—	2	2	no	—
317	C₂×D₄×C₆₇	—	2	2	no	—
318	C₂×D₄×C₆₇	—	2	2	no	—
319	C₂×D₄×C₆₇	—	2	1	no	—
320	C₂×D₄×C₆₇	—	2	1	no	—
321	C₂×D₄×C₆₇	—	2	2	no	—
322	C₂×D₄×C₆₇	—	2	2	no	—
323	C₂×D₄×C₆₇	—	2	1	no	—
324	C₂×D₄×C₆₇	—	4	2	no	—
325	C₂×D₄×C₆₇	—	4	2	no	—
326	C₂×D₄×C₆₇	—	4	8	no	—
327	C₂×D₄×C₆₇	—	4	8	no	—
328	C₂×D₄×C₆₇	—	4	8	no	—
329	C₂×D₄×C₆₇	—	8	4	no	—
330	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
331	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
332	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
333	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
334	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
335	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
336	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
337	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
338	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
339	C₂²×C₄×C₆₇	—	2	1	no	—
340	C₂²×C₄×C₆₇	—	2	2	no	—
341	C₂²×C₄×C₆₇	—	2	2	no	—
342	C₂²×C₄×C₆₇	—	2	2	no	—
343	C₂²×C₄×C₆₇	—	2	2	no	—
344	C₂²×C₄×C₆₇	—	2	1	no	—
345	C₂²×C₄×C₆₇	—	2	2	no	—
346	C₂²×C₄×C₆₇	—	2	2	no	—
347	C₂²×C₄×C₆₇	—	2	2	no	—
348	C₂²×C₄×C₆₇	—	2	2	no	—
349	C₂²×C₄×C₆₇	—	8	2	no	—
350	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
351	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
352	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
353	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
354	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
355	Q₁₆×C₆₇	—	4	2	no	—
356	Q₁₆×C₆₇	—	4	2	no	—
357	Q₁₆×C₆₇	—	4	2	no	—
358	SD₁₆×C₆₇	—	2	4	no	—
359	SD₁₆×C₆₇	—	2	4	no	—
360	SD₁₆×C₆₇	—	2	4	no	—
361	SD₁₆×C₆₇	—	4	2	no	—
362	SD₁₆×C₆₇	—	4	2	no	—
363	SD₁₆×C₆₇	—	4	2	no	—
364	SD₁₆×C₆₇	—	4	2	no	—
365	D₈×C₆₇	—	2	4	no	—
366	D₈×C₆₇	—	4	2	no	—
367	M₁₆×C₆₇	—	4	2	no	—
368	M₁₆×C₆₇	—	4	2	no	—
369	C₂×C₈×C₆₇	—	4	2	no	—
370	C₂×C₈×C₆₇	—	4	2	no	—
371	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
372	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
373	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
374	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
375	C₄⋊C₄×C₆₇	—	2	1	no	—
376	C₄⋊C₄×C₆₇	—	2	1	no	—
377	C₄⋊C₄×C₆₇	—	2	2	no	—
378	C₄⋊C₄×C₆₇	—	2	2	no	—
379	C₄⋊C₄×C₆₇	—	2	2	no	—
380	C₄⋊C₄×C₆₇	—	2	1	no	—
381	C₄⋊C₄×C₆₇	—	2	2	no	—
382	C₄⋊C₄×C₆₇	—	2	1	no	—
383	C₄⋊C₄×C₆₇	—	2	1	no	—
384	C₄⋊C₄×C₆₇	—	2	2	no	—
385	C₄⋊C₄×C₆₇	—	2	1	no	—
386	C₄⋊C₄×C₆₇	—	2	1	no	—
387	C₄⋊C₄×C₆₇	—	2	1	no	—
388	C₄⋊C₄×C₆₇	—	2	2	no	—
389	C₄⋊C₄×C₆₇	—	2	2	no	—
390	C₄⋊C₄×C₆₇	—	2	1	no	—
391	C₄⋊C₄×C₆₇	—	2	2	no	—
392	C₄⋊C₄×C₆₇	—	2	1	no	—
393	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
394	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
395	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
396	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
397	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
398	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
399	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
400	C₂²⋊C₄×C₆₇	—	2	2	no	—
401	C₂²⋊C₄×C₆₇	—	2	2	no	—
402	C₂²⋊C₄×C₆₇	—	2	2	no	—
403	C₂²⋊C₄×C₆₇	—	2	2	no	—
404	C₂²⋊C₄×C₆₇	—	2	2	no	—
405	C₂²⋊C₄×C₆₇	—	2	2	no	—
406	C₂²⋊C₄×C₆₇	—	2	2	no	—
407	C₂²⋊C₄×C₆₇	—	2	1	no	—
408	C₂²⋊C₄×C₆₇	—	2	2	no	—
409	C₂²⋊C₄×C₆₇	—	2	2	no	—
410	C₂²⋊C₄×C₆₇	—	2	2	no	—
411	C₂²⋊C₄×C₆₇	—	2	2	no	—
412	C₂²⋊C₄×C₆₇	—	2	2	no	—
413	C₂²⋊C₄×C₆₇	—	2	1	no	—
414	C₂²⋊C₄×C₆₇	—	2	1	no	—
415	C₂²⋊C₄×C₆₇	—	2	2	no	—
416	C₂²⋊C₄×C₆₇	—	2	1	no	—
417	C₂²⋊C₄×C₆₇	—	2	2	no	—
418	C₂²⋊C₄×C₆₇	—	2	1	no	—
419	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
420	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
421	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
422	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
423	C₄²×C₆₇	—	2	2	no	—
424	C₄²×C₆₇	—	2	2	no	—
425	C₄²×C₆₇	—	2	1	no	—
426	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
427	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
428	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
429	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
430	C₂³×C₆₇	—	2	4	no	—
431	C₂³×C₆₇	—	2	2	no	—
432	C₂³×C₆₇	—	2	1	no	—
433	C₂³×C₆₇	—	2	2	no	—
434	C₂³×C₆₇	—	4	4	no	—
435	C₂³×C₆₇	—	4	4	no	—
436	C₂³×C₆₇	—	8	1	no	—
437	C₂³×C₆₇	—	8	1	no	—
438	C₂³×C₆₇	—	8	2	no	—
439	C₂³×C₆₇	—	8	2	no	—
440	C₂³×C₆₇	—	8	2	no	—
441	C₂³×C₆₇	—	8	2	no	—
442	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
443	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
444	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
445	Q₈×C₆₇	—	2	2	no	—
446	Q₈×C₆₇	—	2	2	no	—
447	Q₈×C₆₇	—	2	2	no	—
448	Q₈×C₆₇	—	2	2	no	—
449	Q₈×C₆₇	—	2	2	no	—
450	Q₈×C₆₇	—	4	2	no	—
451	Q₈×C₆₇	—	8	1	no	—
452	Q₈×C₆₇	—	8	2	no	—
453	D₄×C₆₇	—	2	4	no	—
454	D₄×C₆₇	—	2	2	no	—
455	D₄×C₆₇	—	2	2	no	—
456	D₄×C₆₇	—	2	2	no	—
457	D₄×C₆₇	—	2	2	no	—
458	D₄×C₆₇	—	4	2	no	—
459	D₄×C₆₇	—	4	2	no	—
460	D₄×C₆₇	—	4	2	no	—
461	D₄×C₆₇	—	4	2	no	—
462	D₄×C₆₇	—	4	1	no	—
463	D₄×C₆₇	—	4	1	no	—
464	D₄×C₆₇	—	4	4	no	—
465	D₄×C₆₇	—	4	4	no	—
466	D₄×C₆₇	—	4	2	no	—
467	D₄×C₆₇	—	4	4	no	—
468	D₄×C₆₇	—	4	4	no	—
469	D₄×C₆₇	—	4	4	no	—
470	D₄×C₆₇	—	8	1	no	—
471	D₄×C₆₇	—	8	1	no	—
472	D₄×C₆₇	—	8	2	no	—
473	D₄×C₆₇	—	8	2	no	—
474	D₄×C₆₇	—	8	2	no	—
475	D₄×C₆₇	—	8	2	no	—
476	D₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
477	C₂×C₄×C₆₇	—	2	2	no	—
478	C₂×C₄×C₆₇	—	2	2	no	—
479	C₂×C₄×C₆₇	—	2	2	no	—
480	C₂×C₄×C₆₇	—	2	2	no	—
481	C₂×C₄×C₆₇	—	2	2	no	—
482	C₂×C₄×C₆₇	—	2	1	no	—
483	C₂×C₄×C₆₇	—	2	2	no	—
484	C₂×C₄×C₆₇	—	2	1	no	—
485	C₂×C₄×C₆₇	—	2	1	no	—
486	C₂×C₄×C₆₇	—	2	2	no	—
487	C₂×C₄×C₆₇	—	2	2	no	—
488	C₂×C₄×C₆₇	—	2	2	no	—
489	C₂×C₄×C₆₇	—	4	1	no	—
490	C₂×C₄×C₆₇	—	4	1	no	—
491	C₂×C₄×C₆₇	—	4	4	no	—
492	C₂×C₄×C₆₇	—	4	4	no	—
493	C₂×C₄×C₆₇	—	4	2	no	—
494	C₂×C₄×C₆₇	—	4	4	no	—
495	C₂×C₄×C₆₇	—	4	4	no	—
496	C₂×C₄×C₆₇	—	8	2	no	—
497	C₂×C₄×C₆₇	—	8	2	no	—
498	C₂×C₄×C₆₇	—	8	2	no	—
499	C₂×C₄×C₆₇	—	8	1	no	—
500	C₂×C₄×C₆₇	—	8	2	no	—
501	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
504	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
508	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
509	C₈×C₆₇	—	2	2	no	—
510	C₈×C₆₇	—	2	2	no	—
511	C₈×C₆₇	—	2	2	no	—
512	C₈×C₆₇	—	2	2	no	—
513	C₂²×C₆₇	—	2	1	no	—
514	C₂²×C₆₇	—	2	2	no	—
515	C₂²×C₆₇	—	2	2	no	—
516	C₂²×C₆₇	—	2	1	no	—
517	C₂²×C₆₇	—	2	2	no	—
518	C₂²×C₆₇	—	2	2	no	—
519	C₂²×C₆₇	—	2	2	no	—
520	C₂²×C₆₇	—	2	1	no	—
521	C₂²×C₆₇	—	2	2	no	—
522	C₂²×C₆₇	—	2	4	no	—
523	C₂²×C₆₇	—	4	2	no	—
524	C₂²×C₆₇	—	4	2	no	—
525	C₂²×C₆₇	—	4	2	no	—
526	C₂²×C₆₇	—	4	1	no	—
527	C₂²×C₆₇	—	4	1	no	—
528	C₂²×C₆₇	—	4	2	no	—
529	C₂²×C₆₇	—	4	2	no	—
530	C₂²×C₆₇	—	4	1	no	—
531	C₂²×C₆₇	—	8	4	no	—
532	C₂²×C₆₇	—	16	4	no	—
533	C₂²×C₆₇	—	16	4	no	—
534	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
535	C₄×C₆₇	—	2	1	no	—
536	C₄×C₆₇	—	2	1	no	—
537	C₄×C₆₇	—	2	1	no	—
538	C₄×C₆₇	—	2	1	no	—
539	C₄×C₆₇	—	2	1	no	—
540	C₄×C₆₇	—	2	2	no	—
541	C₄×C₆₇	—	2	2	no	—
542	C₄×C₆₇	—	4	2	no	—
543	C₄×C₆₇	—	4	1	no	—
544	C₄×C₆₇	—	4	2	no	—
545	C₄×C₆₇	—	4	1	no	—
546	C₄×C₆₇	—	4	2	no	—
547	C₄×C₆₇	—	4	2	no	—
548	C₄×C₆₇	—	4	1	no	—
549	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
550	#61670	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
551	C₂×C₆₇	—	4	1	no	—
552	C₂×C₆₇	—	4	2	no	—
553	C₂×C₆₇	—	4	2	no	—
554	C₂×C₆₇	—	4	4	no	—
555	C₂×C₆₇	—	8	1	no	—
556	C₂×C₆₇	—	8	2	no	—
557	C₂×C₆₇	#3484	1	1	yes	characteristic
558	C₂×C₆₇	#3585	1	1	yes	characteristic
559	C₂×C₆₇	#3586	1	1	yes	characteristic
560	#3547	C₂×C₆₇	1	1	yes	characteristic, complemented
561	#3496	C₂×C₆₇	1	1	yes	characteristic, complemented
562	#3319	C₂×C₆₇	1	2	yes	complemented
563	#3315	C₂×C₆₇	1	2	yes	complemented
564	#3314	C₂×C₆₇	1	2	yes	complemented
565	#3310	C₂×C₆₇	1	2	yes	complemented
566	#3269	C₂×C₆₇	1	2	yes	complemented
567	#3267	C₂×C₆₇	1	2	yes	complemented
568	#3266	C₂×C₆₇	1	2	yes	complemented
569	#3265	C₂×C₆₇	1	2	yes	complemented
570	#3219	C₂×C₆₇	1	1	yes	characteristic, complemented
571	#3216	C₂×C₆₇	1	1	yes	characteristic, complemented
572	#3203	C₂×C₆₇	1	2	yes	complemented
573	#3201	C₂×C₆₇	1	2	yes	complemented
574	#3114	C₂×C₆₇	1	1	yes	characteristic, complemented
575	#3110	C₂×C₆₇	1	1	yes	characteristic, complemented
576	#3012	C₂×C₆₇	1	2	yes	complemented
577	#3009	C₂×C₆₇	1	2	yes	complemented
578	#2980	C₂×C₆₇	1	1	yes	characteristic, complemented
579	C₆₇	#61670	1	1	yes	characteristic, direct product factor, Sylow
580	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	—
581	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
582	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
583	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
584	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
585	#562	—	2	2	no	—
586	#555	—	2	1	no	—
587	#555	C₂²×C₆₇	1	1	yes	characteristic, complemented
588	#554	C₂²×C₆₇	1	1	yes	characteristic, complemented
589	#553	—	2	1	no	—
590	#552	C₂²×C₆₇	1	2	yes	complemented
591	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
592	#548	C₂²×C₆₇	1	2	yes	complemented
593	#547	—	2	1	no	—
594	#547	C₂²×C₆₇	1	2	yes	—
595	#547	C₂²×C₆₇	1	1	yes	characteristic, complemented
596	#546	—	2	2	no	—
597	#546	C₂²×C₆₇	1	2	yes	—
598	#546	C₂²×C₆₇	1	2	yes	—
599	D₄²	—	2	1	no	—
600	D₄²	C₂²×C₆₇	1	2	yes	—
601	#544	—	2	1	no	—
602	#542	—	2	2	no	—
603	#540	—	2	1	no	—
604	#537	C₂²×C₆₇	1	2	yes	—
605	#537	C₂²×C₆₇	1	2	yes	complemented
606	#536	C₂²×C₆₇	1	2	yes	complemented
607	#534	—	2	1	no	—
608	#534	—	2	1	no	—
609	#533	C₂²×C₆₇	1	1	yes	characteristic, complemented
610	#532	C₂²×C₆₇	1	1	yes	characteristic
611	#532	C₂²×C₆₇	1	1	yes	characteristic
612	#529	C₂²×C₆₇	1	1	yes	characteristic, complemented
613	C₂×#121	—	2	2	no	—
614	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
615	#497	C₂²×C₆₇	1	2	yes	complemented
616	#497	C₂²×C₆₇	1	1	yes	characteristic, complemented
617	#496	C₂²×C₆₇	1	1	yes	characteristic, complemented
618	#491	C₂²×C₆₇	1	1	yes	characteristic, complemented
619	#490	C₂²×C₆₇	1	1	yes	characteristic, complemented
620	#489	C₂²×C₆₇	1	2	yes	complemented
621	#485	C₂²×C₆₇	1	2	yes	complemented
622	#484	C₂²×C₆₇	1	2	yes	complemented
623	#484	C₂²×C₆₇	1	2	yes	complemented
624	#483	C₂²×C₆₇	1	1	yes	characteristic, complemented
625	#482	C₂²×C₆₇	1	2	yes	complemented
626	#480	C₂²×C₆₇	1	1	yes	characteristic, complemented
627	#480	C₂²×C₆₇	1	2	yes	complemented
628	#478	C₂²×C₆₇	1	2	yes	complemented
629	#474	C₂²×C₆₇	1	2	yes	complemented
630	#470	C₂²×C₆₇	1	2	yes	complemented
631	#468	C₂²×C₆₇	1	2	yes	complemented
632	#468	C₂²×C₆₇	1	2	yes	complemented
633	#468	C₂²×C₆₇	1	2	yes	complemented
634	#467	C₂²×C₆₇	1	2	yes	complemented
635	#467	C₂²×C₆₇	1	2	yes	complemented
636	#466	C₂²×C₆₇	1	2	yes	complemented
637	#465	C₂²×C₆₇	1	2	yes	complemented
638	#464	C₂²×C₆₇	1	2	yes	complemented
639	#463	C₂²×C₆₇	1	2	yes	complemented
640	#463	C₂²×C₆₇	1	2	yes	complemented
641	#462	C₂²×C₆₇	1	2	yes	complemented
642	#461	C₂²×C₆₇	1	2	yes	complemented
643	#460	C₂²×C₆₇	1	2	yes	complemented
644	#452	C₂²×C₆₇	1	2	yes	complemented
645	#452	C₂²×C₆₇	1	2	yes	complemented
646	#452	C₂²×C₆₇	1	2	yes	complemented
647	#452	C₂²×C₆₇	1	2	yes	complemented
648	#452	C₂²×C₆₇	1	2	yes	complemented
649	#452	C₂²×C₆₇	1	2	yes	complemented
650	#452	C₂²×C₆₇	1	2	yes	complemented
651	#451	C₂²×C₆₇	1	2	yes	complemented
652	#450	C₂²×C₆₇	1	2	yes	—
653	#450	C₂²×C₆₇	1	1	yes	characteristic
654	#450	C₂²×C₆₇	1	2	yes	complemented
655	#450	C₂²×C₆₇	1	2	yes	complemented
656	#450	C₂²×C₆₇	1	2	yes	complemented
657	#449	C₂²×C₆₇	1	2	yes	complemented
658	#449	C₂²×C₆₇	1	2	yes	complemented
659	#449	C₂²×C₆₇	1	2	yes	complemented
660	#448	C₂²×C₆₇	1	2	yes	complemented
661	#447	C₂²×C₆₇	1	1	yes	characteristic
662	#447	C₂²×C₆₇	1	2	yes	complemented
663	#442	C₂²×C₆₇	1	2	yes	complemented
664	#440	C₂²×C₆₇	1	2	yes	complemented
665	#440	C₂²×C₆₇	1	2	yes	complemented
666	#440	C₂²×C₆₇	1	2	yes	complemented
667	#435	C₂²×C₆₇	1	2	yes	complemented
668	#435	C₂²×C₆₇	1	2	yes	complemented
669	#435	C₂²×C₆₇	1	2	yes	complemented
670	#435	C₂²×C₆₇	1	2	yes	complemented
671	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
672	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
673	#418	C₂²×C₆₇	1	2	yes	complemented
674	#417	C₂²×C₆₇	1	2	yes	complemented
675	#416	C₂²×C₆₇	1	2	yes	complemented
676	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
677	#408	C₂²×C₆₇	1	2	yes	complemented
678	#408	C₂²×C₆₇	1	2	yes	complemented
679	H(5,𝔽₂)	—	4	4	no	—
680	H(5,𝔽₂)	—	4	4	no	—
681	C₂×#41	—	2	2	no	—
682	C₂×#41	C₂³×C₆₇	1	2	yes	—
683	C₂×#41	C₂³×C₆₇	1	2	yes	—
684	C₂×#41	C₂³×C₆₇	1	2	yes	—
685	C₂×#41	C₂³×C₆₇	1	2	yes	—
686	C₂×#41	C₂³×C₆₇	1	2	yes	—
687	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
688	C₂²×D₄	—	2	2	no	—
689	C₂²×D₄	—	2	2	no	—
690	C₂²×D₄	—	2	2	no	—
691	C₂²×D₄	—	2	2	no	—
692	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
693	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
694	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
695	C₂³×C₄	—	2	1	no	—
696	#137	—	4	4	no	—
697	AGL(1,ℤ/8)	—	4	4	no	—
698	#135	—	4	4	no	—
699	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
700	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
701	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
702	C₂×SD₁₆	—	4	4	no	—
703	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
704	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
705	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
706	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
707	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
708	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
709	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
710	C₂×D₈	C₂³×C₆₇	1	2	yes	—
711	C₂×D₈	C₂³×C₆₇	1	2	yes	—
712	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
713	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
714	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
715	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
716	C₄⋊Q₈	—	2	2	no	—
717	C₄⋊Q₈	—	2	1	no	—
718	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
719	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
720	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
721	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
722	#127	D₄×C₆₇	1	1	yes	characteristic
723	#127	C₂³×C₆₇	1	1	yes	characteristic
724	#126	—	2	2	no	—
725	#126	—	2	1	no	—
726	#125	—	2	2	no	—
727	#125	—	2	1	no	—
728	#125	—	2	1	no	—
729	#125	C₂³×C₆₇	1	1	yes	characteristic
730	#124	—	2	2	no	—
731	#124	—	2	2	no	—
732	#124	—	2	2	no	—
733	#124	D₄×C₆₇	1	2	yes	—
734	#124	C₂³×C₆₇	1	1	yes	characteristic
735	#124	C₂³×C₆₇	1	2	yes	—
736	#123	—	2	2	no	—
737	#123	—	2	2	no	—
738	#123	—	2	2	no	—
739	#123	—	2	1	no	—
740	#123	—	2	2	no	—
741	#123	—	2	2	no	—
742	#123	—	2	2	no	—
743	#123	—	2	2	no	—
744	#123	—	2	2	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	—	2	1	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
752	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
753	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
754	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
755	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
756	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
757	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
758	#121	—	2	2	no	—
759	#121	—	2	2	no	—
760	#121	—	2	2	no	—
761	#121	—	2	2	no	—
762	#121	—	2	2	no	—
763	#121	—	2	2	no	—
764	#121	—	2	2	no	—
765	#121	—	2	1	no	—
766	#121	—	2	2	no	—
767	#121	—	2	1	no	—
768	#121	—	2	1	no	—
769	#121	—	2	1	no	—
770	#121	—	2	2	no	—
771	#121	—	2	2	no	—
772	#121	—	2	2	no	—
773	#121	D₄×C₆₇	1	2	yes	—
774	#121	D₄×C₆₇	1	1	yes	characteristic
775	#121	D₄×C₆₇	1	1	yes	characteristic
776	#121	C₂³×C₆₇	1	1	yes	characteristic
777	#121	C₂³×C₆₇	1	2	yes	—
778	#121	C₂³×C₆₇	1	2	yes	—
779	#121	C₂³×C₆₇	1	2	yes	—
780	#120	—	2	2	no	—
781	#120	—	2	2	no	—
782	#120	—	2	2	no	—
783	#120	—	2	2	no	—
784	C₄×Q₈	—	2	1	no	—
785	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
786	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	2	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	C₂³×C₆₇	1	2	yes	—
796	C₄×D₄	C₂³×C₆₇	1	2	yes	—
797	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
798	C₄×D₄	C₂³×C₆₇	1	2	yes	—
799	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
800	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
801	#117	—	2	1	no	—
802	#117	—	2	1	no	—
803	#117	—	2	2	no	—
804	#117	—	2	1	no	—
805	#117	C₂³×C₆₇	1	2	yes	—
806	C₂×C₄⋊C₄	—	2	2	no	—
807	C₂×C₄⋊C₄	—	2	1	no	—
808	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
809	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
810	C₂×C₂²⋊C₄	—	2	1	no	—
811	C₂×C₂²⋊C₄	—	2	2	no	—
812	C₂×C₂²⋊C₄	—	2	2	no	—
813	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
814	#107	C₂³×C₆₇	1	2	yes	—
815	#107	C₂³×C₆₇	1	2	yes	—
816	#107	C₂³×C₆₇	1	2	yes	—
817	#106	C₂³×C₆₇	1	2	yes	—
818	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
819	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
820	#103	C₂³×C₆₇	1	2	yes	—
821	#103	C₂³×C₆₇	1	2	yes	—
822	#103	C₂³×C₆₇	1	2	yes	—
823	#103	C₂³×C₆₇	1	2	yes	—
824	#103	C₂³×C₆₇	1	2	yes	—
825	#103	C₂³×C₆₇	1	2	yes	—
826	#103	C₂³×C₆₇	1	2	yes	—
827	#102	C₂³×C₆₇	1	2	yes	—
828	#102	C₂³×C₆₇	1	2	yes	—
829	#102	C₂³×C₆₇	1	2	yes	—
830	#102	C₂³×C₆₇	1	2	yes	—
831	#102	C₂³×C₆₇	1	2	yes	—
832	#102	C₂³×C₆₇	1	2	yes	—
833	#102	C₂³×C₆₇	1	2	yes	—
834	#102	C₂³×C₆₇	1	2	yes	—
835	#102	C₂³×C₆₇	1	2	yes	—
836	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
837	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
838	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
839	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
840	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
841	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
842	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
843	#97	C₂³×C₆₇	1	1	yes	characteristic
844	#97	C₂³×C₆₇	1	1	yes	characteristic
845	#97	C₂³×C₆₇	1	2	yes	—
846	C₂⁴	—	2	1	no	—
847	C₂⁴	—	2	2	no	—
848	C₂⁴	—	2	2	no	—
849	#41	—	2	4	no	—
850	#41	—	2	4	no	—
851	#41	—	4	2	no	—
852	#41	—	4	2	no	—
853	#41	—	4	2	no	—
854	#41	—	4	2	no	—
855	#41	—	4	2	no	—
856	#41	—	4	2	no	—
857	#41	—	4	2	no	—
858	#41	—	4	2	no	—
859	#41	—	4	8	no	—
860	C₂×Q₈	—	2	1	no	—
861	C₂×Q₈	—	2	2	no	—
862	C₂×Q₈	—	4	2	no	—
863	C₂×Q₈	—	4	2	no	—
864	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
865	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
866	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
867	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
868	C₂×D₄	—	2	4	no	—
869	C₂×D₄	—	2	4	no	—
870	C₂×D₄	—	2	4	no	—
871	C₂×D₄	—	2	2	no	—
872	C₂×D₄	—	2	2	no	—
873	C₂×D₄	—	2	2	no	—
874	C₂×D₄	—	2	1	no	—
875	C₂×D₄	—	2	2	no	—
876	C₂×D₄	—	2	2	no	—
877	C₂×D₄	—	2	2	no	—
878	C₂×D₄	—	2	2	no	—
879	C₂×D₄	—	2	1	no	—
880	C₂×D₄	—	2	1	no	—
881	C₂×D₄	—	2	2	no	—
882	C₂×D₄	—	2	2	no	—
883	C₂×D₄	—	2	1	no	—
884	C₂×D₄	—	4	2	no	—
885	C₂×D₄	—	4	2	no	—
886	C₂×D₄	—	4	8	no	—
887	C₂×D₄	—	4	8	no	—
888	C₂×D₄	—	4	8	no	—
889	C₂×D₄	—	8	4	no	—
890	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
891	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
892	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
893	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
894	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
895	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
896	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
897	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
898	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
899	C₂²×C₄	—	2	1	no	—
900	C₂²×C₄	—	2	2	no	—
901	C₂²×C₄	—	2	2	no	—
902	C₂²×C₄	—	2	2	no	—
903	C₂²×C₄	—	2	2	no	—
904	C₂²×C₄	—	2	1	no	—
905	C₂²×C₄	—	2	2	no	—
906	C₂²×C₄	—	2	2	no	—
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	8	2	no	—
910	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
911	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
912	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
913	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
914	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
915	Q₁₆	—	4	2	no	—
916	Q₁₆	—	4	2	no	—
917	Q₁₆	—	4	2	no	—
918	SD₁₆	—	2	4	no	—
919	SD₁₆	—	2	4	no	—
920	SD₁₆	—	2	4	no	—
921	SD₁₆	—	4	2	no	—
922	SD₁₆	—	4	2	no	—
923	SD₁₆	—	4	2	no	—
924	SD₁₆	—	4	2	no	—
925	D₈	—	2	4	no	—
926	D₈	—	4	2	no	—
927	M₁₆	—	4	2	no	—
928	M₁₆	—	4	2	no	—
929	C₂×C₈	—	4	2	no	—
930	C₂×C₈	—	4	2	no	—
931	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
932	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
933	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
934	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
954	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
955	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
956	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
957	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
958	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
959	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	1	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
980	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
981	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
982	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
983	C₄²	—	2	2	no	—
984	C₄²	—	2	2	no	—
985	C₄²	—	2	1	no	—
986	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
987	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
988	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
989	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
990	C₂³	—	2	4	no	—
991	C₂³	—	2	2	no	—
992	C₂³	—	2	1	no	—
993	C₂³	—	2	2	no	—
994	C₂³	—	4	4	no	—
995	C₂³	—	4	4	no	—
996	C₂³	—	8	1	no	—
997	C₂³	—	8	1	no	—
998	C₂³	—	8	2	no	—
999	C₂³	—	8	2	no	—
1000	C₂³	—	8	2	no	—
1001	C₂³	—	8	2	no	—
1002	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1003	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1004	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1005	Q₈	—	2	2	no	—
1006	Q₈	—	2	2	no	—
1007	Q₈	—	2	2	no	—
1008	Q₈	—	2	2	no	—
1009	Q₈	—	2	2	no	—
1010	Q₈	—	4	2	no	—
1011	Q₈	—	8	2	no	—
1012	Q₈	—	8	1	no	—
1013	D₄	—	2	4	no	—
1014	D₄	—	2	2	no	—
1015	D₄	—	2	2	no	—
1016	D₄	—	2	2	no	—
1017	D₄	—	2	2	no	—
1018	D₄	—	4	2	no	—
1019	D₄	—	4	2	no	—
1020	D₄	—	4	2	no	—
1021	D₄	—	4	2	no	—
1022	D₄	—	4	1	no	—
1023	D₄	—	4	1	no	—
1024	D₄	—	4	4	no	—
1025	D₄	—	4	4	no	—
1026	D₄	—	4	2	no	—
1027	D₄	—	4	4	no	—
1028	D₄	—	4	4	no	—
1029	D₄	—	4	4	no	—
1030	D₄	—	8	1	no	—
1031	D₄	—	8	2	no	—
1032	D₄	—	8	2	no	—
1033	D₄	—	8	2	no	—
1034	D₄	—	8	1	no	—
1035	D₄	—	8	2	no	—
1036	D₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
1037	C₂×C₄	—	2	2	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	4	1	no	—
1050	C₂×C₄	—	4	1	no	—
1051	C₂×C₄	—	4	4	no	—
1052	C₂×C₄	—	4	4	no	—
1053	C₂×C₄	—	4	4	no	—
1054	C₂×C₄	—	4	4	no	—
1055	C₂×C₄	—	4	2	no	—
1056	C₂×C₄	—	8	2	no	—
1057	C₂×C₄	—	8	2	no	—
1058	C₂×C₄	—	8	1	no	—
1059	C₂×C₄	—	8	2	no	—
1060	C₂×C₄	—	8	2	no	—
1061	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1062	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1063	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1064	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1065	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1066	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1067	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1068	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1069	C₈	—	2	2	no	—
1070	C₈	—	2	2	no	—
1071	C₈	—	2	2	no	—
1072	C₈	—	2	2	no	—
1073	C₂²	—	2	1	no	—
1074	C₂²	—	2	2	no	—
1075	C₂²	—	2	2	no	—
1076	C₂²	—	2	1	no	—
1077	C₂²	—	2	2	no	—
1078	C₂²	—	2	2	no	—
1079	C₂²	—	2	2	no	—
1080	C₂²	—	2	1	no	—
1081	C₂²	—	2	2	no	—
1082	C₂²	—	2	4	no	—
1083	C₂²	—	4	2	no	—
1084	C₂²	—	4	2	no	—
1085	C₂²	—	4	2	no	—
1086	C₂²	—	4	1	no	—
1087	C₂²	—	4	1	no	—
1088	C₂²	—	4	2	no	—
1089	C₂²	—	4	2	no	—
1090	C₂²	—	4	1	no	—
1091	C₂²	—	8	4	no	—
1092	C₂²	—	16	4	no	—
1093	C₂²	—	16	4	no	—
1094	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1095	C₄	—	2	1	no	—
1096	C₄	—	2	1	no	—
1097	C₄	—	2	1	no	—
1098	C₄	—	2	1	no	—
1099	C₄	—	2	1	no	—
1100	C₄	—	2	2	no	—
1101	C₄	—	2	2	no	—
1102	C₄	—	4	2	no	—
1103	C₄	—	4	1	no	—
1104	C₄	—	4	2	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	2	no	—
1107	C₄	—	4	2	no	—
1108	C₄	—	4	1	no	—
1109	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
1110	C₂	—	4	1	no	—
1111	C₂	—	4	2	no	—
1112	C₂	—	4	2	no	—
1113	C₂	—	4	4	no	—
1114	C₂	—	8	2	no	—
1115	C₂	—	8	1	no	—
1116	C₂	C₆₇×#3484	1	1	yes	characteristic
1117	C₂	C₆₇×#3585	1	1	yes	characteristic
1118	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 ◁ #532×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3547	C₂	semidirect
2. C₆₇×#3496	C₂	semidirect
3. C₆₇×#3319	C₂	semidirect
4. C₆₇×#3315	C₂	semidirect
5. C₆₇×#3314	C₂	semidirect
6. C₆₇×#3310	C₂	semidirect
7. C₆₇×#3269	C₂	semidirect
8. C₆₇×#3267	C₂	semidirect
9. C₆₇×#3266	C₂	semidirect
10. C₆₇×#3265	C₂	semidirect
11. C₆₇×#3219	C₂	semidirect
12. C₆₇×#3216	C₂	semidirect
13. C₆₇×#3203	C₂	semidirect
14. C₆₇×#3201	C₂	semidirect
15. C₆₇×#3114	C₂	semidirect
16. C₆₇×#3110	C₂	semidirect
17. C₆₇×#3012	C₂	semidirect
18. C₆₇×#3009	C₂	semidirect
19. C₆₇×#2980	C₂	semidirect
21. C₂×#137×C₆₇	C₂²	semidirect
22. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
23. C₂×#135×C₆₇	C₂²	semidirect
24. C₂²×SD₁₆×C₆₇	C₂²	semidirect
27. #555×C₆₇	C₂²	semidirect
28. #554×C₆₇	C₂²	semidirect
30. #552×C₆₇	C₂²	semidirect
31. D₄×Q₈×C₆₇	C₂²	semidirect
32. #548×C₆₇	C₂²	semidirect
35. #547×C₆₇	C₂²	semidirect
45. #537×C₆₇	C₂²	semidirect
46. #536×C₆₇	C₂²	semidirect
49. #533×C₆₇	C₂²	semidirect
52. #529×C₆₇	C₂²	semidirect
55. #497×C₆₇	C₂²	semidirect
56. #497×C₆₇	C₂²	semidirect
57. #496×C₆₇	C₂²	semidirect
58. #491×C₆₇	C₂²	semidirect
59. #490×C₆₇	C₂²	semidirect
60. #489×C₆₇	C₂²	semidirect
61. #485×C₆₇	C₂²	semidirect
62. #484×C₆₇	C₂²	semidirect
63. #484×C₆₇	C₂²	semidirect
64. #483×C₆₇	C₂²	semidirect
65. #482×C₆₇	C₂²	semidirect
66. #480×C₆₇	C₂²	semidirect
67. #480×C₆₇	C₂²	semidirect
68. #478×C₆₇	C₂²	semidirect
69. #474×C₆₇	C₂²	semidirect
70. #470×C₆₇	C₂²	semidirect
71. #468×C₆₇	C₂²	semidirect
72. #468×C₆₇	C₂²	semidirect
73. #468×C₆₇	C₂²	semidirect
74. #467×C₆₇	C₂²	semidirect
75. #467×C₆₇	C₂²	semidirect
76. #466×C₆₇	C₂²	semidirect
77. #465×C₆₇	C₂²	semidirect
78. #464×C₆₇	C₂²	semidirect
79. #463×C₆₇	C₂²	semidirect
80. #463×C₆₇	C₂²	semidirect
81. #462×C₆₇	C₂²	semidirect
82. #461×C₆₇	C₂²	semidirect
83. #460×C₆₇	C₂²	semidirect
84. #452×C₆₇	C₂²	semidirect
85. #452×C₆₇	C₂²	semidirect
86. #452×C₆₇	C₂²	semidirect
87. #452×C₆₇	C₂²	semidirect
88. #452×C₆₇	C₂²	semidirect
89. #452×C₆₇	C₂²	semidirect
90. #452×C₆₇	C₂²	semidirect
91. #451×C₆₇	C₂²	semidirect
94. #450×C₆₇	C₂²	semidirect
95. #450×C₆₇	C₂²	semidirect
96. #450×C₆₇	C₂²	semidirect
97. #449×C₆₇	C₂²	semidirect
98. #449×C₆₇	C₂²	semidirect
99. #449×C₆₇	C₂²	semidirect
100. #448×C₆₇	C₂²	semidirect
102. #447×C₆₇	C₂²	semidirect
103. #442×C₆₇	C₂²	semidirect
104. #440×C₆₇	C₂²	semidirect
105. #440×C₆₇	C₂²	semidirect
106. #440×C₆₇	C₂²	semidirect
107. #435×C₆₇	C₂²	semidirect
108. #435×C₆₇	C₂²	semidirect
109. #435×C₆₇	C₂²	semidirect
110. #435×C₆₇	C₂²	semidirect
111. #432×C₆₇	C₂²	semidirect
112. #432×C₆₇	C₂²	semidirect
113. #418×C₆₇	C₂²	semidirect
114. #417×C₆₇	C₂²	semidirect
115. #416×C₆₇	C₂²	semidirect
116. C₂×#102×C₆₇	C₂²	semidirect
117. #408×C₆₇	C₂²	semidirect
118. #408×C₆₇	C₂²	semidirect
550. #61670	C₆₇	direct (N × H)
560. #3547	C₂×C₆₇	semidirect
561. #3496	C₂×C₆₇	semidirect
562. #3319	C₂×C₆₇	semidirect
563. #3315	C₂×C₆₇	semidirect
564. #3314	C₂×C₆₇	semidirect
565. #3310	C₂×C₆₇	semidirect
566. #3269	C₂×C₆₇	semidirect
567. #3267	C₂×C₆₇	semidirect
568. #3266	C₂×C₆₇	semidirect
569. #3265	C₂×C₆₇	semidirect
570. #3219	C₂×C₆₇	semidirect
571. #3216	C₂×C₆₇	semidirect
572. #3203	C₂×C₆₇	semidirect
573. #3201	C₂×C₆₇	semidirect
574. #3114	C₂×C₆₇	semidirect
575. #3110	C₂×C₆₇	semidirect
576. #3012	C₂×C₆₇	semidirect
577. #3009	C₂×C₆₇	semidirect
578. #2980	C₂×C₆₇	semidirect
579. C₆₇	#61670	direct (N × H)
581. C₂×#137	C₂²×C₆₇	semidirect
582. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
583. C₂×#135	C₂²×C₆₇	semidirect
584. C₂²×SD₁₆	C₂²×C₆₇	semidirect
587. #555	C₂²×C₆₇	semidirect
588. #554	C₂²×C₆₇	semidirect
590. #552	C₂²×C₆₇	semidirect
591. D₄×Q₈	C₂²×C₆₇	semidirect
592. #548	C₂²×C₆₇	semidirect
595. #547	C₂²×C₆₇	semidirect
605. #537	C₂²×C₆₇	semidirect
606. #536	C₂²×C₆₇	semidirect
609. #533	C₂²×C₆₇	semidirect
612. #529	C₂²×C₆₇	semidirect
615. #497	C₂²×C₆₇	semidirect
616. #497	C₂²×C₆₇	semidirect
617. #496	C₂²×C₆₇	semidirect
618. #491	C₂²×C₆₇	semidirect
619. #490	C₂²×C₆₇	semidirect
620. #489	C₂²×C₆₇	semidirect
621. #485	C₂²×C₆₇	semidirect
622. #484	C₂²×C₆₇	semidirect
623. #484	C₂²×C₆₇	semidirect
624. #483	C₂²×C₆₇	semidirect
625. #482	C₂²×C₆₇	semidirect
626. #480	C₂²×C₆₇	semidirect
627. #480	C₂²×C₆₇	semidirect
628. #478	C₂²×C₆₇	semidirect
629. #474	C₂²×C₆₇	semidirect
630. #470	C₂²×C₆₇	semidirect
631. #468	C₂²×C₆₇	semidirect
632. #468	C₂²×C₆₇	semidirect
633. #468	C₂²×C₆₇	semidirect
634. #467	C₂²×C₆₇	semidirect
635. #467	C₂²×C₆₇	semidirect
636. #466	C₂²×C₆₇	semidirect
637. #465	C₂²×C₆₇	semidirect
638. #464	C₂²×C₆₇	semidirect
639. #463	C₂²×C₆₇	semidirect
640. #463	C₂²×C₆₇	semidirect
641. #462	C₂²×C₆₇	semidirect
642. #461	C₂²×C₆₇	semidirect
643. #460	C₂²×C₆₇	semidirect
644. #452	C₂²×C₆₇	semidirect
645. #452	C₂²×C₆₇	semidirect
646. #452	C₂²×C₆₇	semidirect
647. #452	C₂²×C₆₇	semidirect
648. #452	C₂²×C₆₇	semidirect
649. #452	C₂²×C₆₇	semidirect
650. #452	C₂²×C₆₇	semidirect
651. #451	C₂²×C₆₇	semidirect
654. #450	C₂²×C₆₇	semidirect
655. #450	C₂²×C₆₇	semidirect
656. #450	C₂²×C₆₇	semidirect
657. #449	C₂²×C₆₇	semidirect
658. #449	C₂²×C₆₇	semidirect
659. #449	C₂²×C₆₇	semidirect
660. #448	C₂²×C₆₇	semidirect
662. #447	C₂²×C₆₇	semidirect
663. #442	C₂²×C₆₇	semidirect
664. #440	C₂²×C₆₇	semidirect
665. #440	C₂²×C₆₇	semidirect
666. #440	C₂²×C₆₇	semidirect
667. #435	C₂²×C₆₇	semidirect
668. #435	C₂²×C₆₇	semidirect
669. #435	C₂²×C₆₇	semidirect
670. #435	C₂²×C₆₇	semidirect
671. #432	C₂²×C₆₇	semidirect
672. #432	C₂²×C₆₇	semidirect
673. #418	C₂²×C₆₇	semidirect
674. #417	C₂²×C₆₇	semidirect
675. #416	C₂²×C₆₇	semidirect
676. C₂×#102	C₂²×C₆₇	semidirect
677. #408	C₂²×C₆₇	semidirect
678. #408	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3547	2
C₆₇×#3496	2
C₆₇×#3319	2
C₆₇×#3315	2
C₆₇×#3314	2
C₆₇×#3310	2
C₆₇×#3269	2
C₆₇×#3267	2
C₆₇×#3266	2
C₆₇×#3265	2
C₆₇×#3219	2
C₆₇×#3216	2
C₆₇×#3203	2
C₆₇×#3201	2
C₆₇×#3114	2
C₆₇×#3110	2
C₆₇×#3012	2
C₆₇×#3009	2
C₆₇×#2980	2
#61670	67

Subgroups — C67×#61670 #30740921

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61670 #30740921