Subgroups — C₆₇×#61569 #30740820

Order 17152.

2514 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3496	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#546×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3306	C₂	1	8	yes	maximal, complemented
4	C₆₇×#3264	C₂	1	8	yes	maximal, complemented
5	C₆₇×#3213	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3192	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3187	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3109	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3006	C₂	1	2	yes	maximal, complemented
10	C₂×#447×C₆₇	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2973	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×H(5,𝔽₂)×C₆₇	—	2	1	no	—
13	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
14	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
15	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	complemented
16	C₂²×D₈×C₆₇	C₂²	1	4	yes	complemented
17	#547×C₆₇	C₂²	1	4	yes	complemented
18	#546×C₆₇	—	2	4	no	—
19	#546×C₆₇	—	2	4	no	—
20	#546×C₆₇	C₂²	1	8	yes	complemented
21	D₄²×C₆₇	C₂²	1	4	yes	complemented
22	#537×C₆₇	—	2	1	no	—
23	#534×C₆₇	—	2	1	no	—
24	#534×C₆₇	—	2	1	no	—
25	#532×C₆₇	C₂²	1	2	yes	complemented
26	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×#123×C₆₇	—	2	1	no	—
28	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
29	C₂×#121×C₆₇	—	2	1	no	—
30	C₂×#121×C₆₇	C₂²	1	2	yes	—
31	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
32	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
33	C₂×#120×C₆₇	—	2	1	no	—
34	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	C₂²×C₂²⋊C₄×C₆₇	—	2	1	no	—
37	#496×C₆₇	C₂²	1	4	yes	complemented
38	#489×C₆₇	C₂²	1	4	yes	complemented
39	#483×C₆₇	C₂²	1	4	yes	complemented
40	#481×C₆₇	C₂²	1	4	yes	complemented
41	#481×C₆₇	C₂²	1	4	yes	complemented
42	#476×C₆₇	C₂²	1	4	yes	complemented
43	#469×C₆₇	C₂²	1	8	yes	complemented
44	#465×C₆₇	C₂²	1	8	yes	complemented
45	#463×C₆₇	C₂²	1	8	yes	complemented
46	#459×C₆₇	C₂²	1	4	yes	complemented
47	#450×C₆₇	C₂²	1	4	yes	complemented
48	#449×C₆₇	C₂²	1	8	yes	complemented
49	#448×C₆₇	C₂²	1	4	yes	complemented
50	#447×C₆₇	C₂²	1	8	yes	complemented
51	#447×C₆₇	C₂²	1	4	yes	complemented
52	#447×C₆₇	C₂²	1	4	yes	complemented
53	#447×C₆₇	C₂²	1	4	yes	complemented
54	#442×C₆₇	C₂²	1	8	yes	complemented
55	#435×C₆₇	C₂²	1	8	yes	complemented
56	#432×C₆₇	C₂²	1	2	yes	complemented
57	#417×C₆₇	C₂²	1	4	yes	complemented
58	C₂×#102×C₆₇	C₂²	1	4	yes	complemented
59	#407×C₆₇	C₂²	1	2	yes	complemented
60	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
61	C₂⁵×C₆₇	—	2	1	no	—
62	H(5,𝔽₂)×C₆₇	—	4	8	no	—
63	C₂×#41×C₆₇	—	2	4	no	—
64	C₂×#41×C₆₇	—	2	2	no	—
65	C₂×#41×C₆₇	—	2	2	no	—
66	C₂×#41×C₆₇	—	4	4	no	—
67	C₂×#41×C₆₇	C₂³	1	4	yes	—
68	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₆₇	—	2	1	no	—
70	C₂²×D₄×C₆₇	—	2	2	no	—
71	C₂²×D₄×C₆₇	—	2	2	no	—
72	C₂²×D₄×C₆₇	—	2	1	no	—
73	C₂²×D₄×C₆₇	—	2	4	no	—
74	C₂²×D₄×C₆₇	—	2	1	no	—
75	C₂²×D₄×C₆₇	—	2	2	no	—
76	C₂²×D₄×C₆₇	—	4	4	no	—
77	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
78	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
79	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
80	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
81	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₆₇	C₂³	1	2	yes	complemented
83	C₂³×C₄×C₆₇	—	2	1	no	—
84	C₂³×C₄×C₆₇	—	2	1	no	—
85	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
87	AGL(1,ℤ/8)×C₆₇	—	4	8	no	—
88	C₂×SD₁₆×C₆₇	C₂³	1	8	yes	complemented
89	C₂×D₈×C₆₇	—	4	8	no	—
90	C₂×D₈×C₆₇	C₂³	1	8	yes	—
91	C₂×D₈×C₆₇	C₂³	1	8	yes	—
92	C₂×M₁₆×C₆₇	C₂³	1	4	yes	complemented
93	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
94	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	complemented
95	#127×C₆₇	C₂³	1	2	yes	complemented
96	#124×C₆₇	—	2	2	no	—
97	#124×C₆₇	—	2	2	no	—
98	#124×C₆₇	C₂³	1	4	yes	—
99	#123×C₆₇	—	2	8	no	—
100	#123×C₆₇	—	2	4	no	—
101	#123×C₆₇	—	2	4	no	—
102	C₂²⋊Q₈×C₆₇	—	2	2	no	—
103	C₂²⋊Q₈×C₆₇	—	2	4	no	—
104	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
105	#121×C₆₇	—	2	2	no	—
106	#121×C₆₇	—	2	2	no	—
107	#121×C₆₇	—	2	2	no	—
108	#121×C₆₇	—	2	2	no	—
109	#121×C₆₇	—	2	2	no	—
110	#121×C₆₇	—	2	2	no	—
111	#121×C₆₇	—	2	4	no	—
112	#121×C₆₇	—	2	8	no	—
113	#121×C₆₇	C₂³	1	4	yes	—
114	#121×C₆₇	C₂³	1	4	yes	—
115	#121×C₆₇	C₂³	1	4	yes	—
116	#121×C₆₇	C₂³	1	4	yes	complemented
117	#120×C₆₇	—	2	8	no	—
118	#120×C₆₇	—	2	4	no	—
119	#120×C₆₇	—	2	4	no	—
120	C₄×D₄×C₆₇	—	2	2	no	—
121	C₄×D₄×C₆₇	—	2	2	no	—
122	C₄×D₄×C₆₇	D₄	1	4	yes	—
123	C₄×D₄×C₆₇	C₂³	1	4	yes	—
124	C₄×D₄×C₆₇	C₂³	1	4	yes	—
125	C₄×D₄×C₆₇	C₂³	1	4	yes	complemented
126	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
127	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	complemented
131	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
132	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
133	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
134	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
135	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
136	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
137	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
138	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
139	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
140	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
141	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
142	#106×C₆₇	C₂³	1	8	yes	complemented
143	C₄⋊C₈×C₆₇	C₂³	1	4	yes	complemented
144	#103×C₆₇	C₂³	1	8	yes	complemented
145	#102×C₆₇	C₂³	1	8	yes	—
146	#102×C₆₇	C₂³	1	8	yes	—
147	#102×C₆₇	C₂³	1	8	yes	complemented
148	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
149	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
150	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	complemented
151	#97×C₆₇	C₂³	1	4	yes	complemented
152	C₂⁴×C₆₇	—	2	1	no	—
153	C₂⁴×C₆₇	—	2	1	no	—
154	C₂⁴×C₆₇	—	2	4	no	—
155	C₂⁴×C₆₇	—	2	2	no	—
156	C₂⁴×C₆₇	—	2	2	no	—
157	C₂⁴×C₆₇	—	4	4	no	—
158	C₂⁴×C₆₇	—	4	4	no	—
159	C₂⁴×C₆₇	—	8	2	no	—
160	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
161	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
162	#41×C₆₇	—	2	8	no	—
163	#41×C₆₇	—	4	4	no	—
164	#41×C₆₇	—	4	8	no	—
165	#41×C₆₇	—	4	8	no	—
166	#41×C₆₇	—	4	16	no	—
167	C₂×Q₈×C₆₇	—	2	1	no	—
168	C₂×Q₈×C₆₇	—	2	2	no	—
169	C₂×Q₈×C₆₇	—	4	2	no	—
170	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
171	C₂×D₄×C₆₇	—	2	4	no	—
172	C₂×D₄×C₆₇	—	2	4	no	—
173	C₂×D₄×C₆₇	—	2	8	no	—
174	C₂×D₄×C₆₇	—	2	4	no	—
175	C₂×D₄×C₆₇	—	2	4	no	—
176	C₂×D₄×C₆₇	—	2	4	no	—
177	C₂×D₄×C₆₇	—	2	4	no	—
178	C₂×D₄×C₆₇	—	2	4	no	—
179	C₂×D₄×C₆₇	—	2	1	no	—
180	C₂×D₄×C₆₇	—	2	4	no	—
181	C₂×D₄×C₆₇	—	2	1	no	—
182	C₂×D₄×C₆₇	—	2	2	no	—
183	C₂×D₄×C₆₇	—	2	2	no	—
184	C₂×D₄×C₆₇	—	2	2	no	—
185	C₂×D₄×C₆₇	—	2	2	no	—
186	C₂×D₄×C₆₇	—	4	4	no	—
187	C₂×D₄×C₆₇	—	4	2	no	—
188	C₂×D₄×C₆₇	—	4	4	no	—
189	C₂×D₄×C₆₇	—	4	4	no	—
190	C₂×D₄×C₆₇	—	4	8	no	—
191	C₂×D₄×C₆₇	—	4	16	no	—
192	C₂×D₄×C₆₇	—	4	4	no	—
193	C₂×D₄×C₆₇	—	4	4	no	—
194	C₂×D₄×C₆₇	—	4	8	no	—
195	C₂×D₄×C₆₇	—	4	8	no	—
196	C₂×D₄×C₆₇	—	8	2	no	—
197	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
198	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
199	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
200	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₆₇	—	2	1	no	—
202	C₂²×C₄×C₆₇	—	2	1	no	—
203	C₂²×C₄×C₆₇	—	2	2	no	—
204	C₂²×C₄×C₆₇	—	2	2	no	—
205	C₂²×C₄×C₆₇	—	2	4	no	—
206	C₂²×C₄×C₆₇	—	2	4	no	—
207	C₂²×C₄×C₆₇	—	2	4	no	—
208	C₂²×C₄×C₆₇	—	4	2	no	—
209	C₂²×C₄×C₆₇	—	4	2	no	—
210	C₂²×C₄×C₆₇	—	4	4	no	—
211	C₂²×C₄×C₆₇	—	8	2	no	—
212	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
216	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
217	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
221	SD₁₆×C₆₇	—	4	8	no	—
222	D₈×C₆₇	—	2	16	no	—
223	D₈×C₆₇	—	4	8	no	—
224	M₁₆×C₆₇	—	4	4	no	—
225	C₂×C₈×C₆₇	—	4	4	no	—
226	C₂×C₈×C₆₇	C₂⁴	1	8	yes	—
227	C₄⋊C₄×C₆₇	—	2	4	no	—
228	C₄⋊C₄×C₆₇	—	2	1	no	—
229	C₄⋊C₄×C₆₇	—	2	2	no	—
230	C₄⋊C₄×C₆₇	—	2	2	no	—
231	C₄⋊C₄×C₆₇	—	2	2	no	—
232	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
233	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
234	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
235	C₂²⋊C₄×C₆₇	—	2	4	no	—
236	C₂²⋊C₄×C₆₇	—	2	4	no	—
237	C₂²⋊C₄×C₆₇	—	2	4	no	—
238	C₂²⋊C₄×C₆₇	—	2	4	no	—
239	C₂²⋊C₄×C₆₇	—	2	4	no	—
240	C₂²⋊C₄×C₆₇	—	2	4	no	—
241	C₂²⋊C₄×C₆₇	—	2	4	no	—
242	C₂²⋊C₄×C₆₇	—	2	4	no	—
243	C₂²⋊C₄×C₆₇	—	2	4	no	—
244	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
245	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
246	C₄²×C₆₇	C₂×D₄	1	2	yes	—
247	C₄²×C₆₇	C₂⁴	1	2	yes	—
248	C₂³×C₆₇	—	2	4	no	—
249	C₂³×C₆₇	—	2	2	no	—
250	C₂³×C₆₇	—	2	2	no	—
251	C₂³×C₆₇	—	2	2	no	—
252	C₂³×C₆₇	—	2	4	no	—
253	C₂³×C₆₇	—	4	1	no	—
254	C₂³×C₆₇	—	4	1	no	—
255	C₂³×C₆₇	—	4	1	no	—
256	C₂³×C₆₇	—	4	1	no	—
257	C₂³×C₆₇	—	4	8	no	—
258	C₂³×C₆₇	—	4	2	no	—
259	C₂³×C₆₇	—	4	2	no	—
260	C₂³×C₆₇	—	4	2	no	—
261	C₂³×C₆₇	—	4	4	no	—
262	C₂³×C₆₇	—	4	2	no	—
263	C₂³×C₆₇	—	4	8	no	—
264	C₂³×C₆₇	—	4	2	no	—
265	C₂³×C₆₇	—	4	4	no	—
266	C₂³×C₆₇	—	8	4	no	—
267	C₂³×C₆₇	—	8	2	no	—
268	C₂³×C₆₇	—	8	2	no	—
269	C₂³×C₆₇	—	8	2	no	—
270	C₂³×C₆₇	—	8	2	no	—
271	C₂³×C₆₇	—	8	16	no	—
272	C₂³×C₆₇	AGL(1,ℤ/8)	1	4	yes	complemented
273	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
274	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
275	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
276	Q₈×C₆₇	—	2	4	no	—
277	Q₈×C₆₇	—	4	2	no	—
278	Q₈×C₆₇	—	4	4	no	—
279	D₄×C₆₇	—	2	4	no	—
280	D₄×C₆₇	—	2	8	no	—
281	D₄×C₆₇	—	2	2	no	—
282	D₄×C₆₇	—	2	8	no	—
283	D₄×C₆₇	—	2	4	no	—
284	D₄×C₆₇	—	4	8	no	—
285	D₄×C₆₇	—	4	2	no	—
286	D₄×C₆₇	—	4	4	no	—
287	D₄×C₆₇	—	4	8	no	—
288	D₄×C₆₇	—	4	8	no	—
289	D₄×C₆₇	—	4	8	no	—
290	D₄×C₆₇	—	4	8	no	—
291	D₄×C₆₇	—	8	2	no	—
292	D₄×C₆₇	—	8	2	no	—
293	D₄×C₆₇	—	8	2	no	—
294	D₄×C₆₇	—	8	4	no	—
295	D₄×C₆₇	H(5,𝔽₂)	1	4	yes	complemented
296	C₂×C₄×C₆₇	—	2	2	no	—
297	C₂×C₄×C₆₇	—	2	4	no	—
298	C₂×C₄×C₆₇	—	2	4	no	—
299	C₂×C₄×C₆₇	—	2	2	no	—
300	C₂×C₄×C₆₇	—	2	2	no	—
301	C₂×C₄×C₆₇	—	2	2	no	—
302	C₂×C₄×C₆₇	—	2	4	no	—
303	C₂×C₄×C₆₇	—	4	1	no	—
304	C₂×C₄×C₆₇	—	4	2	no	—
305	C₂×C₄×C₆₇	—	4	1	no	—
306	C₂×C₄×C₆₇	—	4	2	no	—
307	C₂×C₄×C₆₇	—	4	1	no	—
308	C₂×C₄×C₆₇	—	4	8	no	—
309	C₂×C₄×C₆₇	—	4	8	no	—
310	C₂×C₄×C₆₇	—	4	2	no	—
311	C₂×C₄×C₆₇	—	4	2	no	—
312	C₂×C₄×C₆₇	—	4	4	no	—
313	C₂×C₄×C₆₇	—	4	4	no	—
314	C₂×C₄×C₆₇	—	8	4	no	—
315	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
316	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
317	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
318	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
319	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
320	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
321	C₈×C₆₇	—	2	8	no	—
322	C₂²×C₆₇	—	2	1	no	—
323	C₂²×C₆₇	—	2	2	no	—
324	C₂²×C₆₇	—	2	1	no	—
325	C₂²×C₆₇	—	2	2	no	—
326	C₂²×C₆₇	—	2	2	no	—
327	C₂²×C₆₇	—	2	2	no	—
328	C₂²×C₆₇	—	2	4	no	—
329	C₂²×C₆₇	—	2	2	no	—
330	C₂²×C₆₇	—	4	4	no	—
331	C₂²×C₆₇	—	4	8	no	—
332	C₂²×C₆₇	—	4	2	no	—
333	C₂²×C₆₇	—	4	2	no	—
334	C₂²×C₆₇	—	4	2	no	—
335	C₂²×C₆₇	—	4	4	no	—
336	C₂²×C₆₇	—	4	2	no	—
337	C₂²×C₆₇	—	4	4	no	—
338	C₂²×C₆₇	—	4	4	no	—
339	C₂²×C₆₇	—	4	2	no	—
340	C₂²×C₆₇	—	8	2	no	—
341	C₂²×C₆₇	—	8	16	no	—
342	C₂²×C₆₇	—	8	4	no	—
343	C₂²×C₆₇	—	16	4	no	—
344	C₂²×C₆₇	—	16	4	no	—
345	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
346	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	4	yes	—
347	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
348	C₄×C₆₇	—	2	2	no	—
349	C₄×C₆₇	—	2	2	no	—
350	C₄×C₆₇	—	2	1	no	—
351	C₄×C₆₇	—	2	2	no	—
352	C₄×C₆₇	—	2	2	no	—
353	C₄×C₆₇	—	4	2	no	—
354	C₄×C₆₇	—	4	2	no	—
355	C₄×C₆₇	—	4	4	no	—
356	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
357	#61569	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
358	C₂×C₆₇	—	2	2	no	—
359	C₂×C₆₇	—	2	4	no	—
360	C₂×C₆₇	—	4	2	no	—
361	C₂×C₆₇	—	4	4	no	—
362	C₂×C₆₇	—	8	2	no	—
363	C₂×C₆₇	—	8	4	no	—
364	C₂×C₆₇	#3484	1	1	yes	characteristic
365	C₂×C₆₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
366	C₂×C₆₇	#3585	1	1	yes	characteristic
367	#3496	C₂×C₆₇	1	1	yes	characteristic, complemented
368	C₂×#546	C₂×C₆₇	1	1	yes	characteristic, complemented
369	#3306	C₂×C₆₇	1	8	yes	complemented
370	#3264	C₂×C₆₇	1	8	yes	complemented
371	#3213	C₂×C₆₇	1	2	yes	complemented
372	#3192	C₂×C₆₇	1	2	yes	complemented
373	#3187	C₂×C₆₇	1	2	yes	complemented
374	#3109	C₂×C₆₇	1	2	yes	complemented
375	#3006	C₂×C₆₇	1	2	yes	complemented
376	C₂×#447	C₂×C₆₇	1	2	yes	complemented
377	#2973	C₂×C₆₇	1	1	yes	characteristic, complemented
378	C₆₇	#61569	1	1	yes	characteristic, direct product factor, Sylow
379	C₂×H(5,𝔽₂)	—	2	1	no	—
380	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
381	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
382	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
383	C₂²×D₈	C₂²×C₆₇	1	4	yes	complemented
384	#547	C₂²×C₆₇	1	4	yes	complemented
385	#546	—	2	4	no	—
386	#546	—	2	4	no	—
387	#546	C₂²×C₆₇	1	8	yes	complemented
388	D₄²	C₂²×C₆₇	1	4	yes	complemented
389	#537	—	2	1	no	—
390	#534	—	2	1	no	—
391	#534	—	2	1	no	—
392	#532	C₂²×C₆₇	1	2	yes	complemented
393	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
394	C₂×#123	—	2	1	no	—
395	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
396	C₂×#121	—	2	1	no	—
397	C₂×#121	C₂²×C₆₇	1	2	yes	—
398	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
399	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
400	C₂×#120	—	2	1	no	—
401	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
402	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
403	C₂²×C₂²⋊C₄	—	2	1	no	—
404	#496	C₂²×C₆₇	1	4	yes	complemented
405	#489	C₂²×C₆₇	1	4	yes	complemented
406	#483	C₂²×C₆₇	1	4	yes	complemented
407	#481	C₂²×C₆₇	1	4	yes	complemented
408	#481	C₂²×C₆₇	1	4	yes	complemented
409	#476	C₂²×C₆₇	1	4	yes	complemented
410	#469	C₂²×C₆₇	1	8	yes	complemented
411	#465	C₂²×C₆₇	1	8	yes	complemented
412	#463	C₂²×C₆₇	1	8	yes	complemented
413	#459	C₂²×C₆₇	1	4	yes	complemented
414	#450	C₂²×C₆₇	1	4	yes	complemented
415	#449	C₂²×C₆₇	1	8	yes	complemented
416	#448	C₂²×C₆₇	1	4	yes	complemented
417	#447	C₂²×C₆₇	1	4	yes	complemented
418	#447	C₂²×C₆₇	1	4	yes	complemented
419	#447	C₂²×C₆₇	1	8	yes	complemented
420	#447	C₂²×C₆₇	1	4	yes	complemented
421	#442	C₂²×C₆₇	1	8	yes	complemented
422	#435	C₂²×C₆₇	1	8	yes	complemented
423	#432	C₂²×C₆₇	1	2	yes	complemented
424	#417	C₂²×C₆₇	1	4	yes	complemented
425	C₂×#102	C₂²×C₆₇	1	4	yes	complemented
426	#407	C₂²×C₆₇	1	2	yes	complemented
427	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
428	C₂⁵	—	2	1	no	—
429	H(5,𝔽₂)	—	4	8	no	—
430	C₂×#41	—	2	4	no	—
431	C₂×#41	—	2	2	no	—
432	C₂×#41	—	2	2	no	—
433	C₂×#41	—	4	4	no	—
434	C₂×#41	C₂³×C₆₇	1	4	yes	—
435	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
436	C₂²×D₄	—	2	1	no	—
437	C₂²×D₄	—	2	2	no	—
438	C₂²×D₄	—	2	2	no	—
439	C₂²×D₄	—	2	1	no	—
440	C₂²×D₄	—	2	4	no	—
441	C₂²×D₄	—	2	1	no	—
442	C₂²×D₄	—	2	2	no	—
443	C₂²×D₄	—	4	4	no	—
444	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
445	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
446	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
447	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
448	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
449	C₂²×D₄	C₂³×C₆₇	1	2	yes	complemented
450	C₂³×C₄	—	2	1	no	—
451	C₂³×C₄	—	2	1	no	—
452	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
453	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
454	AGL(1,ℤ/8)	—	4	8	no	—
455	C₂×SD₁₆	C₂³×C₆₇	1	8	yes	complemented
456	C₂×D₈	—	4	8	no	—
457	C₂×D₈	C₂³×C₆₇	1	8	yes	—
458	C₂×D₈	C₂³×C₆₇	1	8	yes	—
459	C₂×M₁₆	C₂³×C₆₇	1	4	yes	complemented
460	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
461	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	complemented
462	#127	C₂³×C₆₇	1	2	yes	complemented
463	#124	—	2	2	no	—
464	#124	—	2	2	no	—
465	#124	C₂³×C₆₇	1	4	yes	—
466	#123	—	2	8	no	—
467	#123	—	2	4	no	—
468	#123	—	2	4	no	—
469	C₂²⋊Q₈	—	2	2	no	—
470	C₂²⋊Q₈	—	2	4	no	—
471	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
472	#121	—	2	2	no	—
473	#121	—	2	2	no	—
474	#121	—	2	2	no	—
475	#121	—	2	2	no	—
476	#121	—	2	2	no	—
477	#121	—	2	2	no	—
478	#121	—	2	4	no	—
479	#121	—	2	8	no	—
480	#121	C₂³×C₆₇	1	4	yes	—
481	#121	C₂³×C₆₇	1	4	yes	—
482	#121	C₂³×C₆₇	1	4	yes	—
483	#121	C₂³×C₆₇	1	4	yes	complemented
484	#120	—	2	8	no	—
485	#120	—	2	4	no	—
486	#120	—	2	4	no	—
487	C₄×D₄	—	2	2	no	—
488	C₄×D₄	—	2	2	no	—
489	C₄×D₄	D₄×C₆₇	1	4	yes	—
490	C₄×D₄	C₂³×C₆₇	1	4	yes	—
491	C₄×D₄	C₂³×C₆₇	1	4	yes	—
492	C₄×D₄	C₂³×C₆₇	1	4	yes	complemented
493	C₂×C₄⋊C₄	—	2	1	no	—
494	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
495	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	complemented
498	C₂×C₂²⋊C₄	—	2	1	no	—
499	C₂×C₂²⋊C₄	—	2	1	no	—
500	C₂×C₂²⋊C₄	—	2	1	no	—
501	C₂×C₂²⋊C₄	—	2	1	no	—
502	C₂×C₂²⋊C₄	—	2	1	no	—
503	C₂×C₂²⋊C₄	—	2	2	no	—
504	C₂×C₂²⋊C₄	—	2	2	no	—
505	C₂×C₂²⋊C₄	—	2	8	no	—
506	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
507	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
508	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
509	#106	C₂³×C₆₇	1	8	yes	complemented
510	C₄⋊C₈	C₂³×C₆₇	1	4	yes	complemented
511	#103	C₂³×C₆₇	1	8	yes	complemented
512	#102	C₂³×C₆₇	1	8	yes	—
513	#102	C₂³×C₆₇	1	8	yes	—
514	#102	C₂³×C₆₇	1	8	yes	complemented
515	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
516	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
517	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	complemented
518	#97	C₂³×C₆₇	1	4	yes	complemented
519	C₂⁴	—	2	1	no	—
520	C₂⁴	—	2	1	no	—
521	C₂⁴	—	2	4	no	—
522	C₂⁴	—	2	2	no	—
523	C₂⁴	—	2	2	no	—
524	C₂⁴	—	4	4	no	—
525	C₂⁴	—	4	4	no	—
526	C₂⁴	—	8	2	no	—
527	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
528	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
529	#41	—	2	8	no	—
530	#41	—	4	4	no	—
531	#41	—	4	8	no	—
532	#41	—	4	8	no	—
533	#41	—	4	16	no	—
534	C₂×Q₈	—	2	1	no	—
535	C₂×Q₈	—	2	2	no	—
536	C₂×Q₈	—	4	2	no	—
537	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
538	C₂×D₄	—	2	4	no	—
539	C₂×D₄	—	2	4	no	—
540	C₂×D₄	—	2	8	no	—
541	C₂×D₄	—	2	4	no	—
542	C₂×D₄	—	2	4	no	—
543	C₂×D₄	—	2	4	no	—
544	C₂×D₄	—	2	4	no	—
545	C₂×D₄	—	2	4	no	—
546	C₂×D₄	—	2	1	no	—
547	C₂×D₄	—	2	4	no	—
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	—	2	2	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	4	4	no	—
554	C₂×D₄	—	4	2	no	—
555	C₂×D₄	—	4	4	no	—
556	C₂×D₄	—	4	4	no	—
557	C₂×D₄	—	4	8	no	—
558	C₂×D₄	—	4	16	no	—
559	C₂×D₄	—	4	4	no	—
560	C₂×D₄	—	4	4	no	—
561	C₂×D₄	—	4	8	no	—
562	C₂×D₄	—	4	8	no	—
563	C₂×D₄	—	8	2	no	—
564	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
565	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
566	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
567	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	4	no	—
573	C₂²×C₄	—	2	4	no	—
574	C₂²×C₄	—	2	4	no	—
575	C₂²×C₄	—	4	2	no	—
576	C₂²×C₄	—	4	2	no	—
577	C₂²×C₄	—	4	4	no	—
578	C₂²×C₄	—	8	2	no	—
579	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
580	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
581	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
582	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
583	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
584	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
585	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
586	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
587	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
588	SD₁₆	—	4	8	no	—
589	D₈	—	2	16	no	—
590	D₈	—	4	8	no	—
591	M₁₆	—	4	4	no	—
592	C₂×C₈	—	4	4	no	—
593	C₂×C₈	C₂⁴×C₆₇	1	8	yes	—
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
600	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
601	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
602	C₂²⋊C₄	—	2	4	no	—
603	C₂²⋊C₄	—	2	4	no	—
604	C₂²⋊C₄	—	2	4	no	—
605	C₂²⋊C₄	—	2	4	no	—
606	C₂²⋊C₄	—	2	4	no	—
607	C₂²⋊C₄	—	2	4	no	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
612	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
613	C₄²	C₂×D₄×C₆₇	1	2	yes	—
614	C₄²	C₂⁴×C₆₇	1	2	yes	—
615	C₂³	—	2	4	no	—
616	C₂³	—	2	2	no	—
617	C₂³	—	2	2	no	—
618	C₂³	—	2	2	no	—
619	C₂³	—	2	4	no	—
620	C₂³	—	4	1	no	—
621	C₂³	—	4	1	no	—
622	C₂³	—	4	1	no	—
623	C₂³	—	4	1	no	—
624	C₂³	—	4	8	no	—
625	C₂³	—	4	2	no	—
626	C₂³	—	4	2	no	—
627	C₂³	—	4	2	no	—
628	C₂³	—	4	4	no	—
629	C₂³	—	4	2	no	—
630	C₂³	—	4	8	no	—
631	C₂³	—	4	2	no	—
632	C₂³	—	4	4	no	—
633	C₂³	—	8	4	no	—
634	C₂³	—	8	2	no	—
635	C₂³	—	8	2	no	—
636	C₂³	—	8	2	no	—
637	C₂³	—	8	2	no	—
638	C₂³	—	8	16	no	—
639	C₂³	AGL(1,ℤ/8)×C₆₇	1	4	yes	complemented
640	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
641	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
642	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
643	Q₈	—	2	4	no	—
644	Q₈	—	4	2	no	—
645	Q₈	—	4	4	no	—
646	D₄	—	2	4	no	—
647	D₄	—	2	8	no	—
648	D₄	—	2	2	no	—
649	D₄	—	2	8	no	—
650	D₄	—	2	4	no	—
651	D₄	—	4	8	no	—
652	D₄	—	4	2	no	—
653	D₄	—	4	4	no	—
654	D₄	—	4	8	no	—
655	D₄	—	4	8	no	—
656	D₄	—	4	8	no	—
657	D₄	—	4	8	no	—
658	D₄	—	8	2	no	—
659	D₄	—	8	2	no	—
660	D₄	—	8	2	no	—
661	D₄	—	8	4	no	—
662	D₄	H(5,𝔽₂)×C₆₇	1	4	yes	complemented
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	4	no	—
665	C₂×C₄	—	2	4	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	4	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	2	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	2	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	8	no	—
676	C₂×C₄	—	4	8	no	—
677	C₂×C₄	—	4	2	no	—
678	C₂×C₄	—	4	2	no	—
679	C₂×C₄	—	4	4	no	—
680	C₂×C₄	—	4	4	no	—
681	C₂×C₄	—	8	4	no	—
682	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
683	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
684	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
685	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
686	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
687	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
688	C₈	—	2	8	no	—
689	C₂²	—	2	1	no	—
690	C₂²	—	2	2	no	—
691	C₂²	—	2	1	no	—
692	C₂²	—	2	2	no	—
693	C₂²	—	2	2	no	—
694	C₂²	—	2	2	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	2	4	no	—
697	C₂²	—	4	4	no	—
698	C₂²	—	4	8	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	4	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	4	4	no	—
705	C₂²	—	4	2	no	—
706	C₂²	—	4	4	no	—
707	C₂²	—	8	2	no	—
708	C₂²	—	8	16	no	—
709	C₂²	—	8	4	no	—
710	C₂²	—	16	4	no	—
711	C₂²	—	16	4	no	—
712	C₂²	C₂×AGL(1,ℤ/8)×C₆₇	1	2	yes	—
713	C₂²	C₂×AGL(1,ℤ/8)×C₆₇	1	4	yes	—
714	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
715	C₄	—	2	2	no	—
716	C₄	—	2	2	no	—
717	C₄	—	2	2	no	—
718	C₄	—	2	1	no	—
719	C₄	—	2	2	no	—
720	C₄	—	4	4	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	2	no	—
723	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
724	C₂	—	2	2	no	—
725	C₂	—	2	4	no	—
726	C₂	—	4	2	no	—
727	C₂	—	4	4	no	—
728	C₂	—	8	2	no	—
729	C₂	—	8	4	no	—
730	C₂	C₆₇×#3484	1	1	yes	characteristic
731	C₂	C₂²×AGL(1,ℤ/8)×C₆₇	1	1	yes	characteristic
732	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. C₆₇×#3496	C₂	semidirect
2. C₂×#546×C₆₇	C₂	semidirect
3. C₆₇×#3306	C₂	semidirect
4. C₆₇×#3264	C₂	semidirect
5. C₆₇×#3213	C₂	semidirect
6. C₆₇×#3192	C₂	semidirect
7. C₆₇×#3187	C₂	semidirect
8. C₆₇×#3109	C₂	semidirect
9. C₆₇×#3006	C₂	semidirect
10. C₂×#447×C₆₇	C₂	semidirect
11. C₆₇×#2973	C₂	semidirect
13. C₂²×#41×C₆₇	C₂²	semidirect
14. C₂³×D₄×C₆₇	C₂²	semidirect
15. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
16. C₂²×D₈×C₆₇	C₂²	semidirect
17. #547×C₆₇	C₂²	semidirect
20. #546×C₆₇	C₂²	semidirect
21. D₄²×C₆₇	C₂²	semidirect
25. #532×C₆₇	C₂²	semidirect
26. C₂×#124×C₆₇	C₂²	semidirect
28. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
31. C₂×#121×C₆₇	C₂²	semidirect
32. C₂×#121×C₆₇	C₂²	semidirect
35. C₂×C₄×D₄×C₆₇	C₂²	semidirect
37. #496×C₆₇	C₂²	semidirect
38. #489×C₆₇	C₂²	semidirect
39. #483×C₆₇	C₂²	semidirect
40. #481×C₆₇	C₂²	semidirect
41. #481×C₆₇	C₂²	semidirect
42. #476×C₆₇	C₂²	semidirect
43. #469×C₆₇	C₂²	semidirect
44. #465×C₆₇	C₂²	semidirect
45. #463×C₆₇	C₂²	semidirect
46. #459×C₆₇	C₂²	semidirect
47. #450×C₆₇	C₂²	semidirect
48. #449×C₆₇	C₂²	semidirect
49. #448×C₆₇	C₂²	semidirect
50. #447×C₆₇	C₂²	semidirect
51. #447×C₆₇	C₂²	semidirect
52. #447×C₆₇	C₂²	semidirect
53. #447×C₆₇	C₂²	semidirect
54. #442×C₆₇	C₂²	semidirect
55. #435×C₆₇	C₂²	semidirect
56. #432×C₆₇	C₂²	semidirect
57. #417×C₆₇	C₂²	semidirect
58. C₂×#102×C₆₇	C₂²	semidirect
59. #407×C₆₇	C₂²	semidirect
60. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
82. C₂²×D₄×C₆₇	C₂³	semidirect
88. C₂×SD₁₆×C₆₇	C₂³	semidirect
92. C₂×M₁₆×C₆₇	C₂³	semidirect
94. C₄⋊Q₈×C₆₇	C₂³	semidirect
95. #127×C₆₇	C₂³	semidirect
116. #121×C₆₇	C₂³	semidirect
125. C₄×D₄×C₆₇	C₂³	semidirect
130. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
142. #106×C₆₇	C₂³	semidirect
143. C₄⋊C₈×C₆₇	C₂³	semidirect
144. #103×C₆₇	C₂³	semidirect
147. #102×C₆₇	C₂³	semidirect
150. C₂²⋊C₈×C₆₇	C₂³	semidirect
151. #97×C₆₇	C₂³	semidirect
272. C₂³×C₆₇	AGL(1,ℤ/8)	semidirect
295. D₄×C₆₇	H(5,𝔽₂)	semidirect
357. #61569	C₆₇	direct (N × H)
367. #3496	C₂×C₆₇	semidirect
368. C₂×#546	C₂×C₆₇	semidirect
369. #3306	C₂×C₆₇	semidirect
370. #3264	C₂×C₆₇	semidirect
371. #3213	C₂×C₆₇	semidirect
372. #3192	C₂×C₆₇	semidirect
373. #3187	C₂×C₆₇	semidirect
374. #3109	C₂×C₆₇	semidirect
375. #3006	C₂×C₆₇	semidirect
376. C₂×#447	C₂×C₆₇	semidirect
377. #2973	C₂×C₆₇	semidirect
378. C₆₇	#61569	direct (N × H)
380. C₂²×#41	C₂²×C₆₇	semidirect
381. C₂³×D₄	C₂²×C₆₇	semidirect
382. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
383. C₂²×D₈	C₂²×C₆₇	semidirect
384. #547	C₂²×C₆₇	semidirect
387. #546	C₂²×C₆₇	semidirect
388. D₄²	C₂²×C₆₇	semidirect
392. #532	C₂²×C₆₇	semidirect
393. C₂×#124	C₂²×C₆₇	semidirect
395. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
398. C₂×#121	C₂²×C₆₇	semidirect
399. C₂×#121	C₂²×C₆₇	semidirect
402. C₂×C₄×D₄	C₂²×C₆₇	semidirect
404. #496	C₂²×C₆₇	semidirect
405. #489	C₂²×C₆₇	semidirect
406. #483	C₂²×C₆₇	semidirect
407. #481	C₂²×C₆₇	semidirect
408. #481	C₂²×C₆₇	semidirect
409. #476	C₂²×C₆₇	semidirect
410. #469	C₂²×C₆₇	semidirect
411. #465	C₂²×C₆₇	semidirect
412. #463	C₂²×C₆₇	semidirect
413. #459	C₂²×C₆₇	semidirect
414. #450	C₂²×C₆₇	semidirect
415. #449	C₂²×C₆₇	semidirect
416. #448	C₂²×C₆₇	semidirect
417. #447	C₂²×C₆₇	semidirect
418. #447	C₂²×C₆₇	semidirect
419. #447	C₂²×C₆₇	semidirect
420. #447	C₂²×C₆₇	semidirect
421. #442	C₂²×C₆₇	semidirect
422. #435	C₂²×C₆₇	semidirect
423. #432	C₂²×C₆₇	semidirect
424. #417	C₂²×C₆₇	semidirect
425. C₂×#102	C₂²×C₆₇	semidirect
426. #407	C₂²×C₆₇	semidirect
427. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
449. C₂²×D₄	C₂³×C₆₇	semidirect
455. C₂×SD₁₆	C₂³×C₆₇	semidirect
459. C₂×M₁₆	C₂³×C₆₇	semidirect
461. C₄⋊Q₈	C₂³×C₆₇	semidirect
462. #127	C₂³×C₆₇	semidirect
483. #121	C₂³×C₆₇	semidirect
492. C₄×D₄	C₂³×C₆₇	semidirect
497. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
509. #106	C₂³×C₆₇	semidirect
510. C₄⋊C₈	C₂³×C₆₇	semidirect
511. #103	C₂³×C₆₇	semidirect
514. #102	C₂³×C₆₇	semidirect
517. C₂²⋊C₈	C₂³×C₆₇	semidirect
518. #97	C₂³×C₆₇	semidirect
639. C₂³	AGL(1,ℤ/8)×C₆₇	semidirect
662. D₄	H(5,𝔽₂)×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3496	2
C₂×#546×C₆₇	2
C₆₇×#3306	2
C₆₇×#3264	2
C₆₇×#3213	2
C₆₇×#3192	2
C₆₇×#3187	2
C₆₇×#3109	2
C₆₇×#3006	2
C₂×#447×C₆₇	2
C₆₇×#2973	2
#61569	67

Subgroups — C67×#61569 #30740820

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61569 #30740820